LMFDB - Embedded newform 38.10.e.b.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.6
Character	$\chi$	$=$	38.5
Dual form			38.10.e.b.23.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-15.0351 + 5.47232i) q^{2} +(19.6083 - 111.204i) q^{3} +(196.107 - 164.554i) q^{4} +(-757.043 - 635.234i) q^{5} +(313.732 + 1779.26i) q^{6} +(3786.65 + 6558.68i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(6514.11 + 2370.94i) q^{9} +O(q^{10})$	\(q+(-15.0351 + 5.47232i) q^{2} +(19.6083 - 111.204i) q^{3} +(196.107 - 164.554i) q^{4} +(-757.043 - 635.234i) q^{5} +(313.732 + 1779.26i) q^{6} +(3786.65 + 6558.68i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(6514.11 + 2370.94i) q^{9} +(14858.4 + 5408.02i) q^{10} +(-7007.71 + 12137.7i) q^{11} +(-14453.7 - 25034.5i) q^{12} +(-1071.26 - 6075.43i) q^{13} +(-92823.9 - 77888.5i) q^{14} +(-85484.9 + 71730.4i) q^{15} +(11380.2 - 64540.4i) q^{16} +(196340. - 71462.0i) q^{17} -110915. q^{18} +(-450430. + 346122. i) q^{19} -252992. q^{20} +(803601. - 292487. i) q^{21} +(38940.0 - 220840. i) q^{22} +(1.87323e6 - 1.57182e6i) q^{23} +(354310. + 297301. i) q^{24} +(-169566. - 961654. i) q^{25} +(49353.3 + 85482.4i) q^{26} +(1.50269e6 - 2.60273e6i) q^{27} +(1.82185e6 + 663097. i) q^{28} +(6.41787e6 + 2.33591e6i) q^{29} +(892741. - 1.54627e6i) q^{30} +(631296. + 1.09344e6i) q^{31} +(182083. + 1.03265e6i) q^{32} +(1.21235e6 + 1.01729e6i) q^{33} +(-2.56093e6 + 2.14887e6i) q^{34} +(1.29964e6 - 7.37061e6i) q^{35} +(1.66761e6 - 606961. i) q^{36} +8.20215e6 q^{37} +(4.87816e6 - 7.66888e6i) q^{38} -696619. q^{39} +(3.80375e6 - 1.38445e6i) q^{40} +(2.75444e6 - 1.56212e7i) q^{41} +(-1.04816e7 + 8.79513e6i) q^{42} +(-1.56663e7 - 1.31456e7i) q^{43} +(623041. + 3.53344e6i) q^{44} +(-3.42536e6 - 5.93289e6i) q^{45} +(-1.95626e7 + 3.38834e7i) q^{46} +(-7.72823e6 - 2.81284e6i) q^{47} +(-6.95400e6 - 2.53105e6i) q^{48} +(-8.50070e6 + 1.47236e7i) q^{49} +(7.81191e6 + 1.35306e7i) q^{50} +(-4.09697e6 - 2.32351e7i) q^{51} +(-1.20982e6 - 1.01516e6i) q^{52} +(-3.39457e7 + 2.84839e7i) q^{53} +(-8.35004e6 + 4.73554e7i) q^{54} +(1.30154e7 - 4.73723e6i) q^{55} -3.10203e7 q^{56} +(2.96581e7 + 5.68765e7i) q^{57} -1.09276e8 q^{58} +(1.13683e8 - 4.13771e7i) q^{59} +(-4.96073e6 + 2.81337e7i) q^{60} +(-6.22480e6 + 5.22323e6i) q^{61} +(-1.54752e7 - 1.29852e7i) q^{62} +(9.11644e6 + 5.17019e7i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-3.04833e6 + 5.27987e6i) q^{65} +(-2.37948e7 - 8.66058e6i) q^{66} +(-2.21066e7 - 8.04613e6i) q^{67} +(2.67444e7 - 4.63227e7i) q^{68} +(-1.38062e8 - 2.39131e8i) q^{69} +(2.07942e7 + 1.17930e8i) q^{70} +(1.85909e8 + 1.55996e8i) q^{71} +(-2.17512e7 + 1.82514e7i) q^{72} +(2.14334e7 - 1.21555e8i) q^{73} +(-1.23320e8 + 4.48848e7i) q^{74} -1.10265e8 q^{75} +(-3.13769e7 + 1.41997e8i) q^{76} -1.06143e8 q^{77} +(1.04737e7 - 3.81212e6i) q^{78} +(7.39719e7 - 4.19515e8i) q^{79} +(-4.96135e7 + 4.16307e7i) q^{80} +(-1.55445e8 - 1.30434e8i) q^{81} +(4.40710e7 + 2.49939e8i) q^{82} +(3.05119e8 + 5.28482e8i) q^{83} +(1.09462e8 - 1.89594e8i) q^{84} +(-1.94033e8 - 7.06222e7i) q^{85} +(3.07482e8 + 1.11914e8i) q^{86} +(3.85606e8 - 6.67890e8i) q^{87} +(-2.87036e7 - 4.97161e7i) q^{88} +(5.90219e7 + 3.34730e8i) q^{89} +(8.39672e7 + 7.04568e7i) q^{90} +(3.57903e7 - 3.00316e7i) q^{91} +(1.08704e8 - 6.16492e8i) q^{92} +(1.33973e8 - 4.87622e7i) q^{93} +1.31587e8 q^{94} +(5.60863e8 + 2.40990e7i) q^{95} +1.18405e8 q^{96} +(7.12337e8 - 2.59270e8i) q^{97} +(4.72362e7 - 2.67890e8i) q^{98} +(-7.44268e7 + 6.24515e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) $ 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−15.0351	+	5.47232i	−0.664463	+	0.241845i
$2$	−15.0351	+	5.47232i	−0.664463	+	0.241845i
$3$	19.6083	−	111.204i	0.139763	−	0.792638i	−0.831660	−	0.555285i	$-0.812609\pi$
$3$	19.6083	−	111.204i	0.139763	−	0.792638i	0.971423	−	0.237353i	$-0.0762798\pi$
$4$	196.107	−	164.554i	0.383022	−	0.321394i
$5$	−757.043	−	635.234i	−0.541696	−	0.454537i	0.330422	−	0.943833i	$-0.392809\pi$
$5$	−757.043	−	635.234i	−0.541696	−	0.454537i	−0.872117	+	0.489297i	$0.837253\pi$
$6$	313.732	+	1779.26i	0.0988277	+	0.560480i
$7$	3786.65	+	6558.68i	0.596094	+	1.03246i	0.993392	+	0.114775i	$0.0366146\pi$
$7$	3786.65	+	6558.68i	0.596094	+	1.03246i	−0.397298	+	0.917690i	$0.630052\pi$
$8$	−2048.00	+	3547.24i	−0.176777	+	0.306186i
$9$	6514.11	+	2370.94i	0.330951	+	0.120456i
$10$	14858.4	+	5408.02i	0.469864	+	0.171016i
$11$	−7007.71	+	12137.7i	−0.144314	+	0.249960i	−0.929117	−	0.369786i	$-0.879431\pi$
$11$	−7007.71	+	12137.7i	−0.144314	+	0.249960i	0.784803	+	0.619746i	$0.212764\pi$
$12$	−14453.7	−	25034.5i	−0.201216	−	0.348517i
$13$	−1071.26	−	6075.43i	−0.0104028	−	0.0589973i	0.979164	−	0.203069i	$-0.0650915\pi$
$13$	−1071.26	−	6075.43i	−0.0104028	−	0.0589973i	−0.989567	+	0.144072i	$0.953980\pi$
$14$	−92823.9	−	77888.5i	−0.645778	−	0.541872i
$15$	−85484.9	+	71730.4i	−0.435992	+	0.365841i
$16$	11380.2	−	64540.4i	0.0434120	−	0.246202i
$17$	196340.	−	71462.0i	0.570150	−	0.207518i	−0.0408267	−	0.999166i	$-0.512999\pi$
$17$	196340.	−	71462.0i	0.570150	−	0.207518i	0.610977	+	0.791649i	$0.290777\pi$
$18$	−110915.			−0.249037
$19$	−450430.	+	346122.i	−0.792932	+	0.609310i
$19$	−450430.	+	346122.i	−0.792932	+	0.609310i
$20$	−252992.			−0.353567
$21$	803601.	−	292487.i	0.901683	−	0.328186i
$22$	38940.0	−	220840.i	0.0354401	−	0.200991i
$23$	1.87323e6	−	1.57182e6i	1.39577	−	1.17119i	0.432834	−	0.901474i	$-0.357514\pi$
$23$	1.87323e6	−	1.57182e6i	1.39577	−	1.17119i	0.962939	−	0.269719i	$-0.0869307\pi$
$24$	354310.	+	297301.i	0.217988	+	0.182914i
$25$	−169566.	−	961654.i	−0.0868176	−	0.492367i
$26$	49353.3	+	85482.4i	0.0211805	+	0.0366857i
$27$	1.50269e6	−	2.60273e6i	0.544166	−	0.942523i
$28$	1.82185e6	+	663097.i	0.560145	+	0.203876i
$29$	6.41787e6	+	2.33591e6i	1.68500	+	0.613290i	0.993982	−	0.109548i	$-0.0349403\pi$
$29$	6.41787e6	+	2.33591e6i	1.68500	+	0.613290i	0.691018	+	0.722837i	$0.257162\pi$
$30$	892741.	−	1.54627e6i	0.201224	−	0.348530i
$31$	631296.	+	1.09344e6i	0.122774	+	0.212650i	0.920860	−	0.389892i	$-0.127488\pi$
$31$	631296.	+	1.09344e6i	0.122774	+	0.212650i	−0.798087	+	0.602542i	$0.794154\pi$
$32$	182083.	+	1.03265e6i	0.0306970	+	0.174091i
$33$	1.21235e6	+	1.01729e6i	0.177958	+	0.149324i
$34$	−2.56093e6	+	2.14887e6i	−0.328656	+	0.275776i
$35$	1.29964e6	−	7.37061e6i	0.146392	−	0.830228i
$36$	1.66761e6	−	606961.i	0.165476	−	0.0602282i
$37$	8.20215e6			0.719482			0.359741	−	0.933052i	$-0.382865\pi$
$37$	8.20215e6			0.719482			0.359741	+	0.933052i	$0.382865\pi$
$38$	4.87816e6	−	7.66888e6i	0.379515	−	0.596631i
$39$	−696619.			−0.0482175
$40$	3.80375e6	−	1.38445e6i	0.234932	−	0.0855082i
$41$	2.75444e6	−	1.56212e7i	0.152232	−	0.863350i	−0.809041	−	0.587752i	$-0.800013\pi$
$41$	2.75444e6	−	1.56212e7i	0.152232	−	0.863350i	0.961273	−	0.275598i	$-0.0888759\pi$
$42$	−1.04816e7	+	8.79513e6i	−0.519765	+	0.436135i
$43$	−1.56663e7	−	1.31456e7i	−0.698810	−	0.586372i	0.222625	−	0.974904i	$-0.428538\pi$
$43$	−1.56663e7	−	1.31456e7i	−0.698810	−	0.586372i	−0.921435	+	0.388533i	$0.872982\pi$
$44$	623041.	+	3.53344e6i	0.0250599	+	0.142122i
$45$	−3.42536e6	−	5.93289e6i	−0.124523	−	0.215680i
$46$	−1.95626e7	+	3.38834e7i	−0.644193	+	1.11577i
$47$	−7.72823e6	−	2.81284e6i	−0.231015	−	0.0840824i	0.223919	−	0.974608i	$-0.428115\pi$
$47$	−7.72823e6	−	2.81284e6i	−0.231015	−	0.0840824i	−0.454934	+	0.890525i	$0.650337\pi$
$48$	−6.95400e6	−	2.53105e6i	−0.189082	−	0.0688201i
$49$	−8.50070e6	+	1.47236e7i	−0.210655	+	0.364866i
$50$	7.81191e6	+	1.35306e7i	0.176763	+	0.306163i
$51$	−4.09697e6	−	2.32351e7i	−0.0848002	−	0.480926i
$52$	−1.20982e6	−	1.01516e6i	−0.0229459	−	0.0192539i
$53$	−3.39457e7	+	2.84839e7i	−0.590941	+	0.495858i	−0.888519	−	0.458839i	$-0.848265\pi$
$53$	−3.39457e7	+	2.84839e7i	−0.590941	+	0.495858i	0.297579	+	0.954697i	$0.403821\pi$
$54$	−8.35004e6	+	4.73554e7i	−0.133634	+	0.757876i
$55$	1.30154e7	−	4.73723e6i	0.191790	−	0.0698059i
$56$	−3.10203e7			−0.421502
$57$	2.96581e7	+	5.68765e7i	0.372140	+	0.713667i
$58$	−1.09276e8			−1.26794
$59$	1.13683e8	−	4.13771e7i	1.22141	−	0.444556i	0.350760	−	0.936465i	$-0.385923\pi$
$59$	1.13683e8	−	4.13771e7i	1.22141	−	0.444556i	0.870646	+	0.491910i	$0.163701\pi$
$60$	−4.96073e6	+	2.81337e7i	−0.0494157	+	0.280250i
$61$	−6.22480e6	+	5.22323e6i	−0.0575627	+	0.0483008i	−0.671115	−	0.741353i	$-0.734184\pi$
$61$	−6.22480e6	+	5.22323e6i	−0.0575627	+	0.0483008i	0.613552	+	0.789654i	$0.289740\pi$
$62$	−1.54752e7	−	1.29852e7i	−0.133007	−	0.111606i
$63$	9.11644e6	+	5.17019e7i	0.0729110	+	0.413499i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	−3.04833e6	+	5.27987e6i	−0.0211813	+	0.0366870i
$66$	−2.37948e7	−	8.66058e6i	−0.154360	−	0.0561823i
$67$	−2.21066e7	−	8.04613e6i	−0.134025	−	0.0487810i	0.274137	−	0.961691i	$-0.411608\pi$
$67$	−2.21066e7	−	8.04613e6i	−0.134025	−	0.0487810i	−0.408162	+	0.912910i	$0.633830\pi$
$68$	2.67444e7	−	4.63227e7i	0.151685	−	0.262726i
$69$	−1.38062e8	−	2.39131e8i	−0.733254	−	1.27003i
$70$	2.07942e7	+	1.17930e8i	0.103514	+	0.587060i
$71$	1.85909e8	+	1.55996e8i	0.868234	+	0.728535i	0.963726	−	0.266895i	$-0.0859977\pi$
$71$	1.85909e8	+	1.55996e8i	0.868234	+	0.728535i	−0.0954911	+	0.995430i	$0.530442\pi$
$72$	−2.17512e7	+	1.82514e7i	−0.0953865	+	0.0800388i
$73$	2.14334e7	−	1.21555e8i	0.0883359	−	0.500978i	−0.908251	−	0.418426i	$-0.862582\pi$
$73$	2.14334e7	−	1.21555e8i	0.0883359	−	0.500978i	0.996587	−	0.0825518i	$-0.0263070\pi$
$74$	−1.23320e8	+	4.48848e7i	−0.478069	+	0.174003i
$75$	−1.10265e8			−0.402403
$76$	−3.13769e7	+	1.41997e8i	−0.107882	+	0.488223i
$77$	−1.06143e8			−0.344099
$78$	1.04737e7	−	3.81212e6i	0.0320387	−	0.0116611i
$79$	7.39719e7	−	4.19515e8i	0.213671	−	1.21179i	−0.669528	−	0.742787i	$-0.733504\pi$
$79$	7.39719e7	−	4.19515e8i	0.213671	−	1.21179i	0.883199	−	0.468999i	$-0.155385\pi$
$80$	−4.96135e7	+	4.16307e7i	−0.135424	+	0.113634i
$81$	−1.55445e8	−	1.30434e8i	−0.401232	−	0.336673i
$82$	4.40710e7	+	2.49939e8i	0.107644	+	0.610481i
$83$	3.05119e8	+	5.28482e8i	0.705697	+	1.22230i	0.966439	+	0.256895i	$0.0826993\pi$
$83$	3.05119e8	+	5.28482e8i	0.705697	+	1.22230i	−0.260742	+	0.965408i	$0.583967\pi$
$84$	1.09462e8	−	1.89594e8i	0.239888	−	0.415498i
$85$	−1.94033e8	−	7.06222e7i	−0.403172	−	0.146743i
$86$	3.07482e8	+	1.11914e8i	0.606145	+	0.220619i
$87$	3.85606e8	−	6.67890e8i	0.721618	−	1.24988i
$88$	−2.87036e7	−	4.97161e7i	−0.0510228	−	0.0883741i
$89$	5.90219e7	+	3.34730e8i	0.0997145	+	0.565509i	0.993200	+	0.116418i	$0.0371411\pi$
$89$	5.90219e7	+	3.34730e8i	0.0997145	+	0.565509i	−0.893486	+	0.449091i	$0.851748\pi$
$90$	8.39672e7	+	7.04568e7i	0.134902	+	0.113196i
$91$	3.57903e7	−	3.00316e7i	0.0547116	−	0.0459085i
$92$	1.08704e8	−	6.16492e8i	0.158198	−	0.897185i
$93$	1.33973e8	−	4.87622e7i	0.185714	−	0.0675943i
$94$	1.31587e8			0.173836
$95$	5.60863e8	+	2.40990e7i	0.706481	+	0.0303559i
$96$	1.18405e8			0.142282
$97$	7.12337e8	−	2.59270e8i	0.816983	−	0.297357i	0.100478	−	0.994939i	$-0.467963\pi$
$97$	7.12337e8	−	2.59270e8i	0.816983	−	0.297357i	0.716505	+	0.697582i	$0.245741\pi$
$98$	4.72362e7	−	2.67890e8i	0.0517318	−	0.293386i
$99$	−7.44268e7	+	6.24515e7i	−0.0778702	+	0.0653408i
$100$	−1.91497e8	−	1.60685e8i	−0.191497	−	0.160685i
$101$	4.31546e6	+	2.44742e7i	0.00412649	+	0.0234025i	0.986801	−	0.161935i	$-0.0517734\pi$
$101$	4.31546e6	+	2.44742e7i	0.00412649	+	0.0234025i	−0.982675	+	0.185337i	$0.940662\pi$
$102$	1.88748e8	+	3.26921e8i	0.172656	+	0.299049i
$103$	−6.10555e8	+	1.05751e9i	−0.534512	+	0.925802i	0.464675	+	0.885481i	$0.346171\pi$
$103$	−6.10555e8	+	1.05751e9i	−0.534512	+	0.925802i	−0.999187	+	0.0403206i	$0.987162\pi$
$104$	2.37450e7	+	8.64246e6i	0.0199031	+	0.00724415i
$105$	−7.94158e8	−	2.89050e8i	−0.637610	−	0.232071i
$106$	3.54504e8	−	6.14019e8i	0.272738	−	0.472395i
$107$	3.12889e8	+	5.41940e8i	0.230762	+	0.399691i	0.958032	−	0.286660i	$-0.0925449\pi$
$107$	3.12889e8	+	5.41940e8i	0.230762	+	0.399691i	−0.727271	+	0.686351i	$0.759212\pi$
$108$	−1.33601e8	−	7.57687e8i	−0.0944935	−	0.535899i
$109$	1.75395e8	+	1.47174e8i	0.119014	+	0.0998646i	0.700352	−	0.713797i	$-0.253026\pi$
$109$	1.75395e8	+	1.47174e8i	0.119014	+	0.0998646i	−0.581338	+	0.813662i	$0.697471\pi$
$110$	−1.69764e8	+	1.42449e8i	−0.110555	+	0.0927669i
$111$	1.60830e8	−	9.12112e8i	0.100557	−	0.570289i
$112$	4.66392e8	−	1.69753e8i	0.280072	−	0.101938i
$113$	−4.34227e8			−0.250533			−0.125266	−	0.992123i	$-0.539979\pi$
$113$	−4.34227e8			−0.250533			−0.125266	+	0.992123i	$0.539979\pi$
$114$	−7.57158e8	−	6.92844e8i	−0.419870	−	0.384206i
$115$	−2.41659e9			−1.28843
$116$	1.64297e9	−	5.97994e8i	0.842500	−	0.306645i
$117$	7.42618e6	−	4.21160e7i	0.00366378	−	0.0207783i
$118$	−1.48280e9	+	1.24422e9i	−0.704066	+	0.590782i
$119$	1.21217e9	+	1.01713e9i	0.554117	+	0.464960i
$120$	−7.93717e7	−	4.50139e8i	−0.0349422	−	0.198167i
$121$	1.08076e9	+	1.87193e9i	0.458347	+	0.793880i
$122$	6.50072e7	−	1.12596e8i	0.0265670	−	0.0460154i
$123$	−1.68313e9	−	6.12610e8i	−0.663048	−	0.241330i
$124$	3.03731e8	+	1.10549e8i	0.115369	+	0.0419911i
$125$	−1.44759e9	+	2.50731e9i	−0.530337	+	0.918570i
$126$	−4.19996e8	−	7.27454e8i	−0.148449	−	0.257121i
$127$	7.04655e8	+	3.99630e9i	0.240359	+	1.36314i	0.831029	+	0.556229i	$0.187752\pi$
$127$	7.04655e8	+	3.99630e9i	0.240359	+	1.36314i	−0.590671	+	0.806913i	$0.701137\pi$
$128$	2.05633e8	+	1.72547e8i	0.0677094	+	0.0568149i
$129$	−1.76904e9	+	1.48440e9i	−0.562449	+	0.471950i
$130$	1.69388e7	−	9.60647e7i	0.00520160	−	0.0294998i
$131$	−3.38816e9	+	1.23319e9i	−1.00518	+	0.365854i	−0.791579	−	0.611067i	$-0.790741\pi$
$131$	−3.38816e9	+	1.23319e9i	−1.00518	+	0.365854i	−0.213598	+	0.976922i	$0.568518\pi$
$132$	4.05150e8			0.116154
$133$	−3.97573e9	−	1.64358e9i	−1.10175	−	0.455468i
$134$	3.76405e8			0.100852
$135$	−2.79094e9	+	1.01582e9i	−0.723184	+	0.263217i
$136$	−1.48612e8	+	8.42820e8i	−0.0372502	+	0.211256i
$137$	2.80260e9	−	2.35166e9i	0.679702	−	0.570338i	−0.236217	−	0.971700i	$-0.575908\pi$
$137$	2.80260e9	−	2.35166e9i	0.679702	−	0.570338i	0.915919	+	0.401363i	$0.131463\pi$
$138$	3.38438e9	+	2.83983e9i	0.794371	+	0.666556i
$139$	−2.69390e8	−	1.52778e9i	−0.0612088	−	0.347133i	−0.999997	−	0.00263631i	$-0.999161\pi$
$139$	−2.69390e8	−	1.52778e9i	−0.0612088	−	0.347133i	0.938788	−	0.344496i	$-0.111950\pi$
$140$	−9.57992e8	−	1.65929e9i	−0.210759	−	0.365045i
$141$	−4.64337e8	+	8.04255e8i	−0.0989344	+	0.171359i
$142$	−3.64881e9	−	1.32806e9i	−0.753102	−	0.274107i
$143$	8.12490e7	+	2.95722e7i	0.0162482	+	0.00591387i
$144$	2.27153e8	−	3.93441e8i	0.0440239	−	0.0762516i
$145$	−3.37475e9	−	5.84523e9i	−0.633994	−	1.09811i
$146$	3.42934e8	+	1.94487e9i	0.0624629	+	0.354245i
$147$	1.47064e9	+	1.23402e9i	0.259764	+	0.217968i
$148$	1.60850e9	−	1.34969e9i	0.275577	−	0.231237i
$149$	1.59124e9	−	9.02439e9i	0.264483	−	1.49996i	−0.506019	−	0.862522i	$-0.668884\pi$
$149$	1.59124e9	−	9.02439e9i	0.264483	−	1.49996i	0.770502	−	0.637437i	$-0.220005\pi$
$150$	1.65784e9	−	6.03404e8i	0.267382	−	0.0973190i
$151$	1.57686e9			0.246829			0.123415	−	0.992355i	$-0.460615\pi$
$151$	1.57686e9			0.246829			0.123415	+	0.992355i	$0.460615\pi$
$152$	−3.05299e8	−	2.30664e9i	−0.0463905	−	0.350497i
$153$	1.44841e9			0.213689
$154$	1.59587e9	−	5.80849e8i	0.228641	−	0.0832186i
$155$	2.16670e8	−	1.22880e9i	0.0301513	−	0.170997i
$156$	−1.36612e8	+	1.14631e8i	−0.0184684	+	0.0154968i
$157$	3.16832e9	+	2.65854e9i	0.416180	+	0.349216i	0.826708	−	0.562632i	$-0.190211\pi$
$157$	3.16832e9	+	2.65854e9i	0.416180	+	0.349216i	−0.410528	+	0.911848i	$0.634655\pi$
$158$	1.18355e9	+	6.71225e9i	0.151088	+	0.856862i
$159$	2.50190e9	+	4.33342e9i	0.310444	+	0.537705i
$160$	5.18127e8	−	8.97422e8i	0.0625023	−	0.108257i
$161$	1.74023e10	+	6.33393e9i	2.04123	+	0.742945i
$162$	3.05091e9	+	1.11044e9i	0.348026	+	0.126671i
$163$	−3.82887e9	+	6.63180e9i	−0.424841	+	0.735847i	−0.996406	−	0.0847104i	$-0.973003\pi$
$163$	−3.82887e9	+	6.63180e9i	−0.424841	+	0.735847i	0.571564	+	0.820557i	$0.306337\pi$
$164$	−2.03036e9	−	3.51669e9i	−0.219167	−	0.379609i
$165$	−2.71589e8	−	1.54026e9i	−0.0285256	−	0.161776i
$166$	−7.47952e9	−	6.27606e9i	−0.764517	−	0.641506i
$167$	1.50335e10	−	1.26146e10i	1.49567	−	1.25502i	0.608527	−	0.793534i	$-0.291761\pi$
$167$	1.50335e10	−	1.26146e10i	1.49567	−	1.25502i	0.887147	−	0.461486i	$-0.152684\pi$
$168$	−6.08254e8	+	3.44958e9i	−0.0589106	+	0.334098i
$169$	9.92921e9	−	3.61394e9i	0.936320	−	0.340793i
$170$	3.30377e9			0.303382
$171$	−3.75479e9	+	1.18674e9i	−0.335817	+	0.106138i
$172$	−5.23544e9			−0.456116
$173$	1.14529e10	−	4.16852e9i	0.972095	−	0.353814i	0.193333	−	0.981133i	$-0.438070\pi$
$173$	1.14529e10	−	4.16852e9i	0.972095	−	0.353814i	0.778762	+	0.627319i	$0.215848\pi$
$174$	−2.14271e9	+	1.21519e10i	−0.177212	+	1.00502i
$175$	5.66509e9	−	4.75358e9i	0.456600	−	0.383133i
$176$	7.03623e8	+	5.90410e8i	0.0552756	+	0.0463817i
$177$	−2.37218e9	−	1.34533e10i	−0.181664	−	1.03027i
$178$	−2.71915e9	−	4.70970e9i	−0.203022	−	0.351644i
$179$	−4.70684e9	+	8.15249e9i	−0.342682	+	0.593542i	−0.984930	−	0.172955i	$-0.944669\pi$
$179$	−4.70684e9	+	8.15249e9i	−0.342682	+	0.593542i	0.642248	+	0.766497i	$0.278002\pi$
$180$	−1.64802e9	−	5.99829e8i	−0.117013	−	0.0425894i
$181$	−2.15703e10	−	7.85096e9i	−1.49384	−	0.543712i	−0.539381	−	0.842062i	$-0.681342\pi$
$181$	−2.15703e10	−	7.85096e9i	−1.49384	−	0.543712i	−0.954457	+	0.298350i	$0.903564\pi$
$182$	−3.73768e8	+	6.47384e8i	−0.0252511	+	0.0437362i
$183$	4.58786e8	+	7.94641e8i	0.0302399	+	0.0523771i
$184$	1.73927e9	+	9.86387e9i	0.111863	+	0.634406i
$185$	−6.20937e9	−	5.21028e9i	−0.389740	−	0.327031i
$186$	−1.74745e9	+	1.46629e9i	−0.107053	+	0.0898279i
$187$	−5.08510e8	+	2.88391e9i	−0.0304097	+	0.172462i
$188$	−1.97843e9	+	7.20088e8i	−0.115507	+	0.0420412i
$189$	2.27606e10			1.29750
$190$	−8.56450e9	+	2.70689e9i	−0.476772	+	0.150688i
$191$	−1.09504e10			−0.595361			−0.297680	−	0.954666i	$-0.596213\pi$
$191$	−1.09504e10			−0.595361			−0.297680	+	0.954666i	$0.596213\pi$
$192$	−1.78022e9	+	6.47949e8i	−0.0945408	+	0.0344100i
$193$	−7.14825e8	+	4.05397e9i	−0.0370844	+	0.210316i	−0.997719	−	0.0674972i	$-0.978499\pi$
$193$	−7.14825e8	+	4.05397e9i	−0.0370844	+	0.210316i	0.960635	+	0.277813i	$0.0896097\pi$
$194$	−9.29124e9	+	7.79628e9i	−0.470941	+	0.395166i
$195$	5.27370e8	+	4.42516e8i	0.0261192	+	0.0219166i
$196$	7.55779e8	+	4.28624e9i	0.0365799	+	0.207455i
$197$	−1.38021e10	−	2.39060e10i	−0.652902	−	1.13086i	−0.982415	−	0.186708i	$-0.940218\pi$
$197$	−1.38021e10	−	2.39060e10i	−0.652902	−	1.13086i	0.329514	−	0.944151i	$-0.393115\pi$
$198$	7.77259e8	−	1.34625e9i	0.0359395	−	0.0622491i
$199$	−2.74254e10	−	9.98201e9i	−1.23969	−	0.451211i	−0.362785	−	0.931873i	$-0.618174\pi$
$199$	−2.74254e10	−	9.98201e9i	−1.23969	−	0.451211i	−0.876906	+	0.480662i	$0.840396\pi$
$200$	3.75849e9	+	1.36798e9i	0.166103	+	0.0604567i
$201$	−1.32823e9	+	2.30057e9i	−0.0573974	+	0.0994152i
$202$	−1.98814e8	−	3.44356e8i	−0.00840167	−	0.0145521i
$203$	8.98175e9	+	5.09380e10i	0.371218	+	2.10528i
$204$	−4.62686e9	−	3.88240e9i	−0.187047	−	0.156951i
$205$	−1.20083e10	+	1.00762e10i	−0.474888	+	0.398478i
$206$	3.39270e9	−	1.92409e10i	0.131263	−	0.744430i
$207$	1.59291e10	−	5.79772e9i	0.603010	−	0.219478i
$208$	−4.04302e8			−0.0149769
$209$	−1.04465e9	−	7.89271e9i	−0.0378716	−	0.286133i
$210$	1.35220e10			0.479793
$211$	−3.19857e10	+	1.16418e10i	−1.11092	+	0.404343i	−0.831332	−	0.555776i	$-0.812421\pi$
$211$	−3.19857e10	+	1.16418e10i	−1.11092	+	0.404343i	−0.279591	+	0.960119i	$0.590199\pi$
$212$	−1.96989e9	+	1.11718e10i	−0.0669777	+	0.379849i
$213$	2.09927e10	−	1.76150e10i	0.698812	−	0.586373i
$214$	−7.66999e9	−	6.43588e9i	−0.249996	−	0.209771i
$215$	3.50954e9	+	1.99036e10i	0.112015	+	0.635270i
$216$	6.15501e9	+	1.06608e10i	0.192392	+	0.333232i
$217$	−4.78100e9	+	8.28093e9i	−0.146369	+	0.253519i
$218$	−3.44246e9	−	1.25295e9i	−0.103232	−	0.0375734i
$219$	−1.30971e10	−	4.76695e9i	−0.384748	−	0.140037i
$220$	1.77289e9	−	3.07074e9i	0.0510247	−	0.0883774i
$221$	−6.44495e8	−	1.11630e9i	−0.0181741	−	0.0314785i
$222$	2.57328e9	+	1.45938e10i	0.0711047	+	0.403255i
$223$	3.82531e10	+	3.20982e10i	1.03584	+	0.869177i	0.991535	−	0.129841i	$-0.0414467\pi$
$223$	3.82531e10	+	3.20982e10i	1.03584	+	0.869177i	0.0443099	+	0.999018i	$0.485891\pi$
$224$	−6.08330e9	+	5.10450e9i	−0.161445	+	0.135468i
$225$	1.17546e9	−	6.66635e9i	0.0305764	−	0.173407i
$226$	6.52864e9	−	2.37623e9i	0.166470	−	0.0605900i
$227$	5.80198e10			1.45031			0.725153	−	0.688588i	$-0.241769\pi$
$227$	5.80198e10			1.45031			0.725153	+	0.688588i	$0.241769\pi$
$228$	1.51754e10	+	6.27356e9i	0.371906	+	0.153747i
$229$	−7.80892e10			−1.87642			−0.938212	−	0.346060i	$-0.887519\pi$
$229$	−7.80892e10			−1.87642			−0.938212	+	0.346060i	$0.887519\pi$
$230$	3.63336e10	−	1.32243e10i	0.856116	−	0.311601i
$231$	−2.08128e9	+	1.18035e10i	−0.0480925	+	0.272746i
$232$	−2.14298e10	+	1.79818e10i	−0.485650	+	0.407508i
$233$	−3.19808e10	−	2.68351e10i	−0.710866	−	0.596488i	0.213976	−	0.976839i	$-0.431359\pi$
$233$	−3.19808e10	−	2.68351e10i	−0.710866	−	0.596488i	−0.924842	+	0.380351i	$0.875803\pi$
$234$	1.18819e8	+	6.73855e8i	0.00259068	+	0.0146925i
$235$	4.06378e9	+	7.03868e9i	0.0869210	+	0.150552i
$236$	1.54853e10	−	2.68213e10i	0.324948	−	0.562827i
$237$	−4.52013e10	−	1.64519e10i	−0.930644	−	0.338727i
$238$	−2.37911e10	−	8.65926e9i	−0.480638	−	0.174938i
$239$	−1.31934e10	+	2.28517e10i	−0.261557	+	0.453031i	−0.966656	−	0.256079i	$-0.917569\pi$
$239$	−1.31934e10	+	2.28517e10i	−0.261557	+	0.453031i	0.705099	+	0.709109i	$0.250903\pi$
$240$	3.65667e9	+	6.33353e9i	0.0711434	+	0.123224i
$241$	−5.15463e9	−	2.92334e10i	−0.0984285	−	0.558216i	−0.993643	−	0.112580i	$-0.964089\pi$
$241$	−5.15463e9	−	2.92334e10i	−0.0984285	−	0.558216i	0.895214	−	0.445636i	$-0.147023\pi$
$242$	−2.64931e10	−	2.22303e10i	−0.496550	−	0.416655i
$243$	2.77624e10	−	2.32954e10i	0.510773	−	0.428590i
$244$	−3.61228e8	+	2.04863e9i	−0.00652420	+	0.0370006i
$245$	1.57884e10	−	5.74649e9i	0.279956	−	0.101896i
$246$	2.86584e10			0.498935
$247$	2.58537e9	+	2.36577e9i	0.0441964	+	0.0404423i
$248$	−5.17157e9			−0.0868141
$249$	6.47522e10	−	2.35679e10i	1.06747	−	0.388529i
$250$	8.04391e9	−	4.56193e10i	0.130238	−	0.738615i
$251$	−2.29928e10	+	1.92932e10i	−0.365645	+	0.306813i	−0.807036	−	0.590502i	$-0.798930\pi$
$251$	−2.29928e10	+	1.92932e10i	−0.365645	+	0.306813i	0.441391	+	0.897315i	$0.354485\pi$
$252$	1.02955e10	+	8.63898e9i	0.160822	+	0.134946i
$253$	5.95131e9	+	3.37515e10i	0.0913209	+	0.517906i
$254$	−3.24636e10	−	5.62285e10i	−0.489378	−	0.847627i
$255$	−1.16581e10	+	2.01925e10i	−0.172662	+	0.299060i
$256$	−4.03595e9	−	1.46897e9i	−0.0587308	−	0.0213763i
$257$	−4.87624e10	−	1.77481e10i	−0.697246	−	0.253777i	−0.0310112	−	0.999519i	$-0.509873\pi$
$257$	−4.87624e10	−	1.77481e10i	−0.697246	−	0.253777i	−0.666234	+	0.745742i	$0.732095\pi$
$258$	1.84745e10	−	3.19988e10i	0.259588	−	0.449619i
$259$	3.10587e10	+	5.37952e10i	0.428878	+	0.742839i
$260$	2.71021e8	+	1.53703e9i	0.00367809	+	0.0208595i
$261$	3.62684e10	+	3.04328e10i	0.483778	+	0.405938i
$262$	4.41928e10	−	3.70822e10i	0.579423	−	0.486194i
$263$	−1.32342e10	+	7.50547e10i	−0.170567	+	0.967336i	0.772569	+	0.634931i	$0.218971\pi$
$263$	−1.32342e10	+	7.50547e10i	−0.170567	+	0.967336i	−0.943137	+	0.332405i	$0.892140\pi$
$264$	−6.09146e9	+	2.21711e9i	−0.0771798	+	0.0280911i
$265$	4.37923e10			0.545496
$266$	6.87696e10	+	2.95487e9i	0.842227	+	0.0361885i
$267$	3.83806e10			0.462180
$268$	−5.65928e9	+	2.05981e9i	−0.0670123	+	0.0243905i
$269$	3.21254e9	−	1.82192e10i	0.0374079	−	0.212151i	−0.960374	−	0.278713i	$-0.910092\pi$
$269$	3.21254e9	−	1.82192e10i	0.0374079	−	0.212151i	0.997782	+	0.0665625i	$0.0212032\pi$
$270$	3.64031e10	−	3.05459e10i	0.416871	−	0.349796i
$271$	−3.20717e10	−	2.69113e10i	−0.361210	−	0.303091i	0.444063	−	0.895996i	$-0.353537\pi$
$271$	−3.20717e10	−	2.69113e10i	−0.361210	−	0.303091i	−0.805273	+	0.592905i	$0.797981\pi$
$272$	−2.37779e9	−	1.34851e10i	−0.0263399	−	0.149381i
$273$	−2.63785e9	−	4.56890e9i	−0.0287421	−	0.0497828i
$274$	−2.92683e10	+	5.06941e10i	−0.313704	+	0.543351i
$275$	1.28605e10	+	4.68086e9i	0.135601	+	0.0493547i
$276$	−6.64249e10	−	2.41767e10i	−0.689033	−	0.250788i
$277$	5.60954e10	−	9.71601e10i	0.572491	−	0.991583i	−0.423819	−	0.905747i	$-0.639311\pi$
$277$	5.60954e10	−	9.71601e10i	0.572491	−	0.991583i	0.996309	−	0.0858358i	$-0.0273561\pi$
$278$	1.24108e10	+	2.14962e10i	0.124623	+	0.215854i
$279$	1.51986e9	+	8.61953e9i	0.0150170	+	0.0851657i
$280$	2.34837e10	+	1.97051e10i	0.228326	+	0.191588i
$281$	4.37833e10	−	3.67385e10i	0.418919	−	0.351515i	−0.408833	−	0.912609i	$-0.634064\pi$
$281$	4.37833e10	−	3.67385e10i	0.418919	−	0.351515i	0.827752	+	0.561095i	$0.189620\pi$
$282$	2.58020e9	−	1.46330e10i	0.0242959	−	0.137789i
$283$	−9.28637e10	+	3.37996e10i	−0.860611	+	0.313237i	−0.734359	−	0.678761i	$-0.762517\pi$
$283$	−9.28637e10	+	3.37996e10i	−0.860611	+	0.313237i	−0.126252	+	0.991998i	$0.540295\pi$
$284$	6.21277e10			0.566700
$285$	1.36775e10	−	6.18977e10i	0.122802	−	0.555742i
$286$	−1.38341e9			−0.0122266
$287$	1.12885e11	−	4.10866e10i	0.982123	−	0.357464i
$288$	−1.26223e9	+	7.15848e9i	−0.0108112	+	0.0613133i
$289$	−5.74009e10	+	4.81651e10i	−0.484037	+	0.406155i
$290$	8.27266e10	+	6.94159e10i	0.686838	+	0.576325i
$291$	−1.48641e10	−	8.42986e10i	−0.121512	−	0.689131i
$292$	−1.57990e10	−	2.73647e10i	−0.127177	−	0.220276i
$293$	−9.30594e10	+	1.61184e11i	−0.737660	+	1.27766i	0.215887	+	0.976418i	$0.430736\pi$
$293$	−9.30594e10	+	1.61184e11i	−0.737660	+	1.27766i	−0.953547	+	0.301246i	$0.902598\pi$
$294$	−2.88642e10	−	1.05057e10i	−0.225318	−	0.0820092i
$295$	−1.12347e11	−	4.08909e10i	−0.863697	−	0.314360i
$296$	−1.67980e10	+	2.90950e10i	−0.127188	+	0.220295i
$297$	2.10608e10	+	3.64784e10i	0.157062	+	0.272039i
$298$	2.54599e10	+	1.44390e11i	0.187018	+	1.06063i
$299$	−1.15562e10	−	9.69682e9i	−0.0836172	−	0.0701631i
$300$	−2.16237e10	+	1.81445e10i	−0.154129	+	0.129330i
$301$	2.68949e10	−	1.52528e11i	0.188851	−	1.07103i
$302$	−2.37082e10	+	8.62908e9i	−0.164009	+	0.0596943i
$303$	2.80625e9			0.0191264
$304$	1.72129e10	+	3.30098e10i	0.115591	+	0.221673i
$305$	8.03041e9			0.0531359
$306$	−2.17770e10	+	7.92619e9i	−0.141988	+	0.0516795i
$307$	−4.73268e10	+	2.68404e11i	−0.304078	+	1.72451i	0.323737	+	0.946147i	$0.395061\pi$
$307$	−4.73268e10	+	2.68404e11i	−0.304078	+	1.72451i	−0.627814	+	0.778363i	$0.716050\pi$
$308$	−2.08155e10	+	1.74662e10i	−0.131798	+	0.110591i
$309$	1.05628e11	+	8.86322e10i	0.659121	+	0.553068i
$310$	3.46672e9	+	1.96608e10i	0.0213202	+	0.120913i
$311$	−7.06985e10	−	1.22453e11i	−0.428537	−	0.742248i	0.568207	−	0.822886i	$-0.307637\pi$
$311$	−7.06985e10	−	1.22453e11i	−0.428537	−	0.742248i	−0.996743	+	0.0806383i	$0.974304\pi$
$312$	1.42667e9	−	2.47107e9i	0.00852372	−	0.0147635i
$313$	−1.04627e11	−	3.80809e10i	−0.616158	−	0.224263i	0.0150373	−	0.999887i	$-0.495213\pi$
$313$	−1.04627e11	−	3.80809e10i	−0.616158	−	0.224263i	−0.631196	+	0.775624i	$0.717436\pi$
$314$	−6.21844e10	−	2.26333e10i	−0.360992	−	0.131390i
$315$	2.59413e10	−	4.49316e10i	0.148455	−	0.257131i
$316$	−5.45263e10	−	9.44424e10i	−0.307620	−	0.532813i
$317$	−4.97759e10	−	2.82293e11i	−0.276855	−	1.57012i	−0.733006	−	0.680222i	$-0.761883\pi$
$317$	−4.97759e10	−	2.82293e11i	−0.276855	−	1.57012i	0.456151	−	0.889902i	$-0.349228\pi$
$318$	−6.13302e10	−	5.14622e10i	−0.336320	−	0.282206i
$319$	−7.33272e10	+	6.15288e10i	−0.396467	+	0.332675i
$320$	−2.87910e9	+	1.63282e10i	−0.0153491	+	0.0870488i
$321$	6.64012e10	−	2.41680e10i	0.349062	−	0.127048i
$322$	−2.96307e11			−1.53600
$323$	−6.37029e10	+	1.00146e11i	−0.325647	+	0.511945i
$324$	−5.19474e10			−0.261885
$325$	−5.66082e9	+	2.06037e9i	−0.0281452	+	0.0102440i
$326$	2.12761e10	−	1.20663e11i	0.104331	−	0.591689i
$327$	1.98055e10	−	1.66188e10i	0.0957903	−	0.0803776i
$328$	4.97711e10	+	4.17629e10i	0.237435	+	0.199232i
$329$	−1.08156e10	−	6.13382e10i	−0.0508942	−	0.288635i
$330$	1.25121e10	+	2.16717e10i	0.0580790	+	0.100596i
$331$	−1.50375e11	+	2.60458e11i	−0.688574	+	1.19265i	0.283725	+	0.958906i	$0.408430\pi$
$331$	−1.50375e11	+	2.60458e11i	−0.688574	+	1.19265i	−0.972299	+	0.233740i	$0.924904\pi$
$332$	1.46800e11	+	5.34308e10i	0.663138	+	0.241363i
$333$	5.34297e10	+	1.94468e10i	0.238113	+	0.0866662i
$334$	−1.56999e11	+	2.71930e11i	−0.690300	+	1.19564i
$335$	1.16244e10	+	2.01341e10i	0.0504278	+	0.0873435i
$336$	−9.73206e9	−	5.51933e10i	−0.0416561	−	0.236243i
$337$	7.63813e10	+	6.40915e10i	0.322591	+	0.270686i	0.789673	−	0.613528i	$-0.210250\pi$
$337$	7.63813e10	+	6.40915e10i	0.322591	+	0.270686i	−0.467082	+	0.884214i	$0.654695\pi$
$338$	−1.29510e11	+	1.08672e11i	−0.539731	+	0.452888i
$339$	−8.51445e9	+	4.82878e10i	−0.0350153	+	0.198582i
$340$	−4.96724e10	+	1.80793e10i	−0.201586	+	0.0733713i
$341$	−1.76958e10			−0.0708719
$342$	4.99593e10	−	3.83901e10i	0.197469	−	0.151741i
$343$	1.76853e11			0.689906
$344$	7.87153e10	−	2.86500e10i	0.303072	−	0.110309i
$345$	−4.73851e10	+	2.68734e11i	−0.180076	+	1.02126i
$346$	−1.49384e11	+	1.25348e11i	−0.560353	+	0.470192i
$347$	2.10286e11	+	1.76451e11i	0.778625	+	0.653344i	0.942902	−	0.333070i	$-0.108085\pi$
$347$	2.10286e11	+	1.76451e11i	0.778625	+	0.653344i	−0.164277	+	0.986414i	$0.552529\pi$
$348$	−3.42834e10	−	1.94431e11i	−0.125308	−	0.710655i
$349$	−1.07710e11	−	1.86559e11i	−0.388635	−	0.673135i	0.603632	−	0.797263i	$-0.293720\pi$
$349$	−1.07710e11	−	1.86559e11i	−0.388635	−	0.673135i	−0.992266	+	0.124129i	$0.960386\pi$
$350$	−5.91620e10	+	1.02472e11i	−0.210735	+	0.365004i
$351$	−1.74225e10	−	6.34127e9i	−0.0612672	−	0.0222994i
$352$	−1.38099e10	−	5.02641e9i	−0.0479457	−	0.0174508i
$353$	1.12883e11	−	1.95519e11i	0.386939	−	0.670199i	−0.605097	−	0.796152i	$-0.706866\pi$
$353$	1.12883e11	−	1.95519e11i	0.386939	−	0.670199i	0.992036	+	0.125953i	$0.0401989\pi$
$354$	1.09287e11	+	1.89290e11i	0.369873	+	0.640639i
$355$	−4.16469e10	−	2.36191e11i	−0.139173	−	0.789289i
$356$	6.66556e10	+	5.59307e10i	0.219944	+	0.184555i
$357$	1.36878e11	−	1.14854e11i	0.445990	−	0.374230i
$358$	2.61547e10	−	1.48331e11i	0.0841543	−	0.477263i
$359$	5.37314e11	−	1.95566e11i	1.70727	−	0.621396i	0.710652	−	0.703544i	$-0.248400\pi$
$359$	5.37314e11	−	1.95566e11i	1.70727	−	0.621396i	0.996620	+	0.0821472i	$0.0261778\pi$
$360$	2.80605e10			0.0880510
$361$	8.30863e10	−	3.11808e11i	0.257482	−	0.966283i
$362$	3.67275e11			1.12409
$363$	2.29358e11	−	8.34794e10i	0.693320	−	0.252348i
$364$	2.07693e9	−	1.17789e10i	0.00620105	−	0.0351679i
$365$	−9.34416e10	+	7.84068e10i	−0.275564	+	0.231226i
$366$	−1.12464e10	−	9.43687e9i	−0.0327604	−	0.0274893i
$367$	−8.77091e10	−	4.97423e11i	−0.252375	−	1.43129i	−0.802721	−	0.596355i	$-0.796615\pi$
$367$	−8.77091e10	−	4.97423e11i	−0.252375	−	1.43129i	0.550345	−	0.834937i	$-0.314496\pi$
$368$	−8.01283e10	−	1.38786e11i	−0.227756	−	0.394486i
$369$	5.49797e10	−	9.52277e10i	0.154377	−	0.267390i
$370$	1.21871e11	+	4.43573e10i	0.338058	+	0.123043i
$371$	−3.15357e11	−	1.14781e11i	−0.864212	−	0.314547i
$372$	1.82491e10	−	3.16084e10i	0.0494082	−	0.0855774i
$373$	3.98804e10	+	6.90748e10i	0.106677	+	0.184769i	0.914422	−	0.404762i	$-0.132646\pi$
$373$	3.98804e10	+	6.90748e10i	0.106677	+	0.184769i	−0.807745	+	0.589532i	$0.799312\pi$
$374$	−8.13617e9	−	4.61425e10i	−0.0215029	−	0.121949i
$375$	2.50438e11	+	2.10142e11i	0.653972	+	0.548748i
$376$	2.58052e10	−	2.16532e10i	0.0665829	−	0.0558697i
$377$	7.31646e9	−	4.14937e10i	0.0186537	−	0.105790i
$378$	−3.42208e11	+	1.24553e11i	−0.862138	+	0.313793i
$379$	−1.65453e11			−0.411906			−0.205953	−	0.978562i	$-0.566029\pi$
$379$	−1.65453e11			−0.411906			−0.205953	+	0.978562i	$0.566029\pi$
$380$	1.13955e11	−	8.75661e10i	0.280354	−	0.215432i
$381$	4.58221e11			1.11407
$382$	1.64640e11	−	5.99242e10i	0.395595	−	0.143985i
$383$	−4.48831e10	+	2.54545e11i	−0.106583	+	0.604463i	0.883993	+	0.467500i	$0.154845\pi$
$383$	−4.48831e10	+	2.54545e11i	−0.106583	+	0.604463i	−0.990576	+	0.136963i	$0.956266\pi$
$384$	2.32200e10	−	1.94839e10i	0.0544970	−	0.0457284i
$385$	8.03549e10	+	6.74257e10i	0.186397	+	0.156406i
$386$	−1.14372e10	−	6.48636e10i	−0.0262227	−	0.148716i
$387$	−7.08848e10	−	1.22776e11i	−0.160640	−	0.278237i
$388$	9.70309e10	−	1.68062e11i	0.217354	−	0.376468i
$389$	5.63952e9	+	2.05262e9i	0.0124873	+	0.00454501i	0.348256	−	0.937399i	$-0.386774\pi$
$389$	5.63952e9	+	2.05262e9i	0.0124873	+	0.00454501i	−0.335769	+	0.941944i	$0.608996\pi$
$390$	−1.03506e10	−	3.76732e9i	−0.0226556	−	0.00824598i
$391$	2.55464e11	−	4.42476e11i	0.552757	−	0.957403i
$392$	−3.48189e10	−	6.03080e10i	−0.0744779	−	0.128999i
$393$	7.06996e10	+	4.00957e11i	0.149503	+	0.847875i
$394$	3.38337e11	+	2.83899e11i	0.707321	+	0.593513i
$395$	−3.22490e11	+	2.70601e11i	−0.666545	+	0.559298i
$396$	−4.31903e9	+	2.44944e10i	−0.00882587	+	0.0500540i
$397$	−3.49481e11	+	1.27201e11i	−0.706099	+	0.256999i	−0.670013	−	0.742349i	$-0.733711\pi$
$397$	−3.49481e11	+	1.27201e11i	−0.706099	+	0.256999i	−0.0360866	+	0.999349i	$0.511489\pi$
$398$	4.66967e11			0.932852
$399$	−2.60730e11	+	4.09889e11i	−0.515006	+	0.809634i
$400$	−6.39952e10			−0.124991
$401$	−6.22125e11	+	2.26435e11i	−1.20151	+	0.437314i	−0.863751	−	0.503918i	$-0.831891\pi$
$401$	−6.22125e11	+	2.26435e11i	−1.20151	+	0.437314i	−0.337760	+	0.941232i	$0.609669\pi$
$402$	7.38065e9	−	4.18578e10i	0.0140954	−	0.0799390i
$403$	5.96682e9	−	5.00675e9i	0.0112686	−	0.00945548i
$404$	4.87361e9	+	4.08944e9i	0.00910195	+	0.00763744i
$405$	3.48225e10	+	1.97488e11i	0.0643151	+	0.364749i
$406$	−4.13791e11	−	7.16706e11i	−0.755811	−	1.30910i
$407$	−5.74783e10	+	9.95553e10i	−0.103831	+	0.179841i
$408$	9.08110e10	+	3.30525e10i	0.162244	+	0.0590518i
$409$	−2.84263e11	−	1.03463e11i	−0.502302	−	0.182823i	0.0784272	−	0.996920i	$-0.475010\pi$
$409$	−2.84263e11	−	1.03463e11i	−0.502302	−	0.182823i	−0.580729	+	0.814097i	$0.697232\pi$
$410$	1.25406e11	−	2.17210e11i	0.219175	−	0.379623i
$411$	−2.06560e11	−	3.57772e11i	−0.357074	−	0.618470i
$412$	5.42832e10	+	3.07855e11i	0.0928171	+	0.526392i
$413$	7.01856e11	+	5.88927e11i	1.18706	+	0.996062i
$414$	−2.07768e11	+	1.74338e11i	−0.347598	+	0.291670i
$415$	1.04722e11	−	5.93906e11i	0.173308	−	0.982881i
$416$	6.07871e9	−	2.21247e9i	0.00995157	−	0.00362208i
$417$	−1.75178e11			−0.283705
$418$	5.88979e10	+	1.12951e11i	0.0943640	+	0.180966i
$419$	−1.95242e11			−0.309464			−0.154732	−	0.987956i	$-0.549451\pi$
$419$	−1.95242e11			−0.309464			−0.154732	+	0.987956i	$0.549451\pi$
$420$	−2.03304e11	+	7.39968e10i	−0.318805	+	0.116036i
$421$	−1.31696e11	+	7.46883e11i	−0.204316	+	1.15873i	0.694197	+	0.719785i	$0.255760\pi$
$421$	−1.31696e11	+	7.46883e11i	−0.204316	+	1.15873i	−0.898513	+	0.438947i	$0.855351\pi$
$422$	4.17199e11	−	3.50072e11i	0.640379	−	0.537342i
$423$	−4.36734e10	−	3.66464e10i	−0.0663263	−	0.0556544i
$424$	−3.15182e10	−	1.78749e11i	−0.0473604	−	0.268594i
$425$	−1.02014e11	−	1.76694e11i	−0.151674	−	0.262707i
$426$	−2.19232e11	+	3.79722e11i	−0.322524	+	0.558627i
$427$	−5.78286e10	−	2.10479e10i	−0.0841816	−	0.0306396i
$428$	1.50538e11	+	5.47914e10i	0.216845	+	0.0789252i
$429$	4.88170e9	−	8.45536e9i	0.00695847	−	0.0120524i
$430$	−1.61685e11	−	2.80047e11i	−0.228067	−	0.395023i
$431$	−1.06776e11	−	6.05554e11i	−0.149047	−	0.845289i	−0.964028	−	0.265801i	$-0.914364\pi$
$431$	−1.06776e11	−	6.05554e11i	−0.149047	−	0.845289i	0.814981	−	0.579488i	$-0.196747\pi$
$432$	−1.50880e11	−	1.26604e11i	−0.208428	−	0.174892i
$433$	−1.06908e12	+	8.97062e11i	−1.46155	+	1.22639i	−0.537978	+	0.842959i	$0.680812\pi$
$433$	−1.06908e12	+	8.97062e11i	−1.46155	+	1.22639i	−0.923571	+	0.383427i	$0.874744\pi$
$434$	2.65668e10	−	1.50668e11i	0.0359447	−	0.203853i
$435$	−7.16187e11	+	2.60671e11i	−0.959013	+	0.349052i
$436$	5.86142e10			0.0776809
$437$	−2.99713e11	+	1.35636e12i	−0.393133	+	1.77913i
$438$	2.23002e11			0.289518
$439$	9.37082e11	−	3.41070e11i	1.20417	−	0.438281i	0.339491	−	0.940609i	$-0.389745\pi$
$439$	9.37082e11	−	3.41070e11i	1.20417	−	0.438281i	0.864677	+	0.502328i	$0.167523\pi$
$440$	−9.85151e9	+	5.58707e10i	−0.0125304	+	0.0710635i
$441$	−9.02834e10	+	7.57568e10i	−0.113667	+	0.0953779i
$442$	1.57988e10	+	1.32567e10i	0.0196890	+	0.0165210i
$443$	2.42240e10	+	1.37381e11i	0.0298833	+	0.169476i	0.996097	−	0.0882659i	$-0.0281325\pi$
$443$	2.42240e10	+	1.37381e11i	0.0298833	+	0.169476i	−0.966214	+	0.257742i	$0.917021\pi$
$444$	−1.18551e11	−	2.05337e11i	−0.144772	−	0.250752i
$445$	1.67950e11	−	2.90897e11i	0.203030	−	0.351657i
$446$	−7.50790e11	−	2.73265e11i	−0.898486	−	0.327022i
$447$	−9.72347e11	−	3.53905e11i	−1.15196	−	0.419279i
$448$	6.35295e10	−	1.10036e11i	0.0745117	−	0.129058i
$449$	3.98041e11	+	6.89427e11i	0.462189	+	0.800534i	0.999070	−	0.0431239i	$-0.0137310\pi$
$449$	3.98041e11	+	6.89427e11i	0.462189	+	0.800534i	−0.536881	+	0.843658i	$0.680398\pi$
$450$	1.88073e10	+	1.06662e11i	0.0216208	+	0.122617i
$451$	1.70303e11	+	1.42901e11i	0.193833	+	0.162646i
$452$	−8.51552e10	+	7.14537e10i	−0.0959595	+	0.0805196i
$453$	3.09195e10	−	1.75353e11i	0.0344977	−	0.195646i
$454$	−8.72332e11	+	3.17503e11i	−0.963675	+	0.350749i
$455$	−4.61719e10			−0.0505041
$456$	−2.62494e11	−	1.12788e10i	−0.284301	−	0.0122157i
$457$	1.26698e12			1.35877			0.679386	−	0.733781i	$-0.262246\pi$
$457$	1.26698e12			1.35877			0.679386	+	0.733781i	$0.262246\pi$
$458$	1.17408e12	−	4.27329e11i	1.24681	−	0.453804i
$459$	1.09042e11	−	6.18405e11i	0.114666	−	0.650304i
$460$	−4.73910e11	+	3.97658e11i	−0.493499	+	0.414095i
$461$	−1.33814e12	−	1.12284e12i	−1.37990	−	1.15788i	−0.969248	−	0.246086i	$-0.920855\pi$
$461$	−1.33814e12	−	1.12284e12i	−1.37990	−	1.15788i	−0.410655	−	0.911791i	$-0.634700\pi$
$462$	−3.33005e10	−	1.88857e11i	−0.0340065	−	0.192861i
$463$	3.19658e11	+	5.53664e11i	0.323274	+	0.559927i	0.981162	−	0.193189i	$-0.0618830\pi$
$463$	3.19658e11	+	5.53664e11i	0.323274	+	0.559927i	−0.657887	+	0.753116i	$0.728550\pi$
$464$	2.23797e11	−	3.87628e11i	0.224142	−	0.388226i
$465$	−1.32399e11	−	4.81892e10i	−0.131325	−	0.0477982i
$466$	6.27685e11	+	2.28459e11i	0.616602	+	0.224425i
$467$	−6.57391e11	+	1.13863e12i	−0.639584	+	1.10779i	0.345940	+	0.938257i	$0.387560\pi$
$467$	−6.57391e11	+	1.13863e12i	−0.639584	+	1.10779i	−0.985524	+	0.169536i	$0.945773\pi$
$468$	−5.47401e9	−	9.48126e9i	−0.00527471	−	0.00913607i
$469$	−3.09379e10	−	1.75458e11i	−0.0295266	−	0.167454i
$470$	−9.96172e10	−	8.35887e10i	−0.0941659	−	0.0790146i
$471$	3.57766e11	−	3.00201e11i	0.334969	−	0.281072i
$472$	−8.60476e10	+	4.88000e11i	−0.0797994	+	0.452565i
$473$	2.69343e11	−	9.80328e10i	0.247417	−	0.0900526i
$474$	7.69636e11			0.700298
$475$	4.09227e11	+	3.74467e11i	0.368845	+	0.337515i
$476$	4.05088e11			0.361674
$477$	−2.88660e11	+	1.05064e11i	−0.255302	+	0.0929223i
$478$	7.33124e10	−	4.15775e11i	0.0642321	−	0.364278i
$479$	5.64064e11	−	4.73306e11i	0.489574	−	0.410802i	−0.364299	−	0.931282i	$-0.618691\pi$
$479$	5.64064e11	−	4.73306e11i	0.489574	−	0.410802i	0.853874	+	0.520480i	$0.174247\pi$
$480$	−8.96374e10	−	7.52147e10i	−0.0770733	−	0.0646722i
$481$	−8.78666e9	−	4.98316e10i	−0.00748464	−	0.0424475i
$482$	2.37475e11	+	4.11318e11i	0.200404	+	0.347109i
$483$	1.04559e12	−	1.81101e12i	0.874176	−	1.51412i
$484$	5.19977e11	+	1.89256e11i	0.430705	+	0.156764i
$485$	−7.03967e11	−	2.56223e11i	−0.577716	−	0.210271i
$486$	−2.89930e11	+	5.02173e11i	−0.235738	+	0.408310i
$487$	8.74677e11	+	1.51499e12i	0.704640	+	1.22047i	0.966821	+	0.255454i	$0.0822249\pi$
$487$	8.74677e11	+	1.51499e12i	0.704640	+	1.22047i	−0.262181	+	0.965019i	$0.584442\pi$
$488$	−5.77965e9	−	3.27780e10i	−0.00461331	−	0.0261634i
$489$	6.62406e11	+	5.55825e11i	0.523883	+	0.439590i
$490$	−2.05933e11	+	1.72798e11i	−0.161377	+	0.135412i
$491$	4.19985e11	−	2.38186e12i	0.326112	−	1.84948i	−0.175627	−	0.984457i	$-0.556195\pi$
$491$	4.19985e11	−	2.38186e12i	0.326112	−	1.84948i	0.501739	−	0.865019i	$-0.332694\pi$
$492$	−4.30882e11	+	1.56828e11i	−0.331524	+	0.120665i
$493$	1.42701e12			1.08797
$494$	−5.18175e10	−	2.14215e10i	−0.0391476	−	0.0161838i
$495$	9.60156e10			0.0718817
$496$	7.77550e10	−	2.83005e10i	0.0576847	−	0.0209955i
$497$	−3.19155e11	+	1.81002e12i	−0.234638	+	1.33070i
$498$	−8.44584e11	+	7.08690e11i	−0.615334	+	0.516326i
$499$	5.70383e11	+	4.78609e11i	0.411827	+	0.345564i	0.825044	−	0.565069i	$-0.191150\pi$
$499$	5.70383e11	+	4.78609e11i	0.411827	+	0.345564i	−0.413217	+	0.910633i	$0.635595\pi$
$500$	1.28702e11	+	7.29908e11i	0.0920920	+	0.522280i
$501$	−1.10802e12	−	1.91914e12i	−0.785736	−	1.36093i
$502$	2.40120e11	−	4.15900e11i	0.168757	−	0.292295i
$503$	−1.26739e12	−	4.61291e11i	−0.882782	−	0.321306i	−0.139450	−	0.990229i	$-0.544533\pi$
$503$	−1.26739e12	−	4.61291e11i	−0.882782	−	0.321306i	−0.743332	+	0.668923i	$0.766756\pi$
$504$	−2.02070e11	−	7.35473e10i	−0.139497	−	0.0507726i
$505$	1.22798e10	−	2.12693e10i	0.00840198	−	0.0145527i
$506$	−2.74178e11	−	4.74890e11i	−0.185932	−	0.322044i
$507$	−2.07190e11	−	1.17503e12i	−0.139262	−	0.789793i
$508$	7.95793e11	+	6.67750e11i	0.530168	+	0.444864i
$509$	−3.30247e11	+	2.77110e11i	−0.218076	+	0.182988i	−0.745281	−	0.666751i	$-0.767685\pi$
$509$	−3.30247e11	+	2.77110e11i	−0.218076	+	0.182988i	0.527204	+	0.849738i	$0.323240\pi$
$510$	6.47812e10	−	3.67392e11i	0.0424017	−	0.240472i
$511$	8.78398e11	−	3.19711e11i	0.569898	−	0.207426i
$512$	6.87195e10			0.0441942
$513$	2.24008e11	+	1.69246e12i	0.142802	+	1.07892i
$514$	8.30269e11			0.524668
$515$	1.13398e12	−	4.12737e11i	0.710354	−	0.258548i
$516$	−1.02658e11	+	5.82202e11i	−0.0637484	+	0.361535i
$517$	8.82987e10	−	7.40914e10i	0.0543559	−	0.0456100i
$518$	−7.61355e11	−	6.38853e11i	−0.464626	−	0.389867i
$519$	−2.38985e11	−	1.35535e12i	−0.144583	−	0.819970i
$520$	−1.24860e10	−	2.16263e10i	−0.00748871	−	0.0129708i
$521$	−4.95173e11	+	8.57665e11i	−0.294433	+	0.509974i	−0.974853	−	0.222849i	$-0.928464\pi$
$521$	−4.95173e11	+	8.57665e11i	−0.294433	+	0.509974i	0.680419	+	0.732823i	$0.261798\pi$
$522$	−7.11836e11	−	2.59087e11i	−0.419627	−	0.152732i
$523$	−4.47274e11	−	1.62794e11i	−0.261406	−	0.0951441i	0.207992	−	0.978130i	$-0.433307\pi$
$523$	−4.47274e11	−	1.62794e11i	−0.261406	−	0.0951441i	−0.469399	+	0.882986i	$0.655529\pi$
$524$	−4.61517e11	+	7.99370e11i	−0.267422	+	0.463188i
$525$	−4.17534e11	−	7.23191e11i	−0.239870	−	0.415467i
$526$	−2.11747e11	−	1.20088e12i	−0.120609	−	0.684010i
$527$	2.02088e11	+	1.69572e11i	0.114128	+	0.0957648i
$528$	7.94528e10	−	6.66688e10i	0.0444894	−	0.0373310i
$529$	7.25580e11	−	4.11497e12i	0.402842	−	2.28463i
$530$	−6.58421e11	+	2.39646e11i	−0.362462	+	0.131925i
$531$	8.38645e11			0.457776
$532$	−1.05013e12	+	3.31903e11i	−0.568380	+	0.179642i
$533$	−9.78563e10			−0.0525190
$534$	−5.77056e11	+	2.10031e11i	−0.307102	+	0.111776i
$535$	1.07388e11	−	6.09030e11i	0.0566716	−	0.321400i
$536$	7.38158e10	−	6.19388e10i	0.0386285	−	0.0324132i
$537$	8.14297e11	+	6.83276e11i	0.422570	+	0.354578i
$538$	5.14006e10	+	2.91508e11i	0.0264514	+	0.150013i
$539$	−1.19141e11	−	2.06358e11i	−0.0608011	−	0.105311i
$540$	−3.80167e11	+	6.58469e11i	−0.192399	+	0.333245i
$541$	2.34704e12	+	8.54252e11i	1.17797	+	0.428744i	0.855483	−	0.517831i	$-0.173260\pi$
$541$	2.34704e12	+	8.54252e11i	1.17797	+	0.428744i	0.322483	+	0.946575i	$0.395483\pi$
$542$	6.29467e11	+	2.29107e11i	0.313312	+	0.114036i
$543$	−1.29602e12	+	2.24477e12i	−0.639751	+	1.10808i
$544$	1.09545e11	+	1.89738e11i	0.0536288	+	0.0928878i
$545$	−3.92916e10	−	2.22834e11i	−0.0190772	−	0.108192i
$546$	6.46628e10	+	5.42586e10i	0.0311378	+	0.0261277i
$547$	1.02875e12	−	8.63227e11i	0.491325	−	0.412270i	−0.363176	−	0.931720i	$-0.618308\pi$
$547$	1.02875e12	−	8.63227e11i	0.491325	−	0.412270i	0.854501	+	0.519450i	$0.173863\pi$
$548$	1.62636e11	−	9.22356e11i	0.0770380	−	0.436904i
$549$	−5.29330e10	+	1.92660e10i	−0.0248686	+	0.00905142i
$550$	−2.18975e11			−0.102038
$551$	−3.69931e12	+	1.16920e12i	−1.70977	+	0.540391i
$552$	1.13101e12			0.518489
$553$	3.03157e12	−	1.10340e12i	1.37849	−	0.501731i
$554$	−3.11708e11	+	1.76778e12i	−0.140590	+	0.797324i
$555$	−7.01160e11	+	5.88343e11i	−0.313688	+	0.263216i
$556$	−3.04232e11	−	2.55281e11i	−0.135011	−	0.113287i
$557$	−5.39510e9	−	3.05971e10i	−0.00237493	−	0.0134689i	0.983597	−	0.180379i	$-0.0577323\pi$
$557$	−5.39510e9	−	3.05971e10i	−0.00237493	−	0.0134689i	−0.985972	+	0.166910i	$0.946621\pi$
$558$	−7.00200e10	−	1.21278e11i	−0.0305751	−	0.0529577i
$559$	−6.30826e10	+	1.09262e11i	−0.0273247	+	0.0473279i
$560$	−4.60912e11	−	1.67758e11i	−0.198049	−	0.0720838i
$561$	3.10731e11	+	1.13097e11i	0.132450	+	0.0482078i
$562$	−4.57240e11	+	7.91963e11i	−0.193344	+	0.334882i
$563$	4.95096e11	+	8.57532e11i	0.207683	+	0.359718i	0.950984	−	0.309239i	$-0.100074\pi$
$563$	4.95096e11	+	8.57532e11i	0.207683	+	0.359718i	−0.743301	+	0.668957i	$0.766741\pi$
$564$	4.12832e10	+	2.34129e11i	0.0171798	+	0.0974313i
$565$	3.28729e11	+	2.75836e11i	0.135712	+	0.113876i
$566$	1.21125e12	−	1.01636e12i	0.496090	−	0.416269i
$567$	2.66858e11	−	1.51342e12i	0.108432	−	0.614946i
$568$	−9.34096e11	+	3.39983e11i	−0.376551	+	0.137053i
$569$	5.16609e11			0.206612			0.103306	−	0.994650i	$-0.467058\pi$
$569$	5.16609e11			0.206612			0.103306	+	0.994650i	$0.467058\pi$
$570$	1.33082e11	+	1.00548e12i	0.0528061	+	0.398969i
$571$	3.13121e12			1.23268			0.616338	−	0.787481i	$-0.288615\pi$
$571$	3.13121e12			1.23268			0.616338	+	0.787481i	$0.288615\pi$
$572$	2.07997e10	−	7.57049e9i	0.00812411	−	0.00295693i
$573$	−2.14719e11	+	1.21773e12i	−0.0832097	+	0.471906i
$574$	−1.47239e12	+	1.23548e12i	−0.566134	+	0.475043i
$575$	−1.82918e12	−	1.53487e12i	−0.697834	−	0.585552i
$576$	−2.01957e10	−	1.14536e11i	−0.00764466	−	0.0433550i
$577$	1.78466e12	+	3.09113e12i	0.670294	+	1.16098i	0.977821	+	0.209444i	$0.0671654\pi$
$577$	1.78466e12	+	3.09113e12i	0.670294	+	1.16098i	−0.307527	+	0.951540i	$0.599501\pi$
$578$	5.99453e11	−	1.03828e12i	0.223398	−	0.386937i
$579$	4.36802e11	+	1.58983e11i	0.161522	+	0.0587891i
$580$	−1.62367e12	−	5.90967e11i	−0.595760	−	0.216839i
$581$	−2.31076e12	+	4.00236e12i	−0.841323	+	1.45721i
$582$	6.84793e11	+	1.18610e12i	0.247403	+	0.428515i
$583$	−1.07847e11	−	6.11630e11i	−0.0386633	−	0.219271i
$584$	3.87288e11	+	3.24973e11i	0.137777	+	0.115608i
$585$	−3.23754e10	+	2.71662e10i	−0.0114292	+	0.00959020i
$586$	5.17107e11	−	2.93266e12i	0.181151	−	1.02736i
$587$	−4.84022e12	+	1.76170e12i	−1.68265	+	0.612435i	−0.993669	−	0.112344i	$-0.964164\pi$
$587$	−4.84022e12	+	1.76170e12i	−1.68265	+	0.612435i	−0.688981	+	0.724779i	$0.741942\pi$
$588$	4.91466e11			0.169549
$589$	−6.62817e11	−	2.74011e11i	−0.226921	−	0.0938099i
$590$	1.91291e12			0.649921
$591$	−2.92908e12	+	1.06610e12i	−0.987614	+	0.359462i
$592$	9.33421e10	−	5.29369e11i	0.0312342	−	0.177138i
$593$	−4.40347e12	+	3.69495e12i	−1.46234	+	1.22705i	−0.539433	+	0.842028i	$0.681361\pi$
$593$	−4.40347e12	+	3.69495e12i	−1.46234	+	1.22705i	−0.922908	+	0.385021i	$0.874194\pi$
$594$	−5.16272e11	−	4.33204e11i	−0.170153	−	0.142775i
$595$	−2.71547e11	−	1.54002e12i	−0.0888217	−	0.503733i
$596$	−1.17294e12	−	2.03159e12i	−0.380775	−	0.659521i
$597$	−1.64780e12	+	2.85408e12i	−0.530910	+	0.919564i
$598$	2.26813e11	+	8.25531e10i	0.0725291	+	0.0263984i
$599$	−2.94073e12	−	1.07034e12i	−0.933330	−	0.339704i	−0.169801	−	0.985478i	$-0.554313\pi$
$599$	−2.94073e12	−	1.07034e12i	−0.933330	−	0.339704i	−0.763529	+	0.645774i	$0.776535\pi$
$600$	2.25822e11	−	3.91135e11i	0.0711354	−	0.123210i
$601$	−2.01386e12	−	3.48810e12i	−0.629642	−	1.09057i	−0.987624	−	0.156843i	$-0.949868\pi$
$601$	−2.01386e12	−	3.48810e12i	−0.629642	−	1.09057i	0.357982	−	0.933729i	$-0.383465\pi$
$602$	4.30318e11	+	2.44045e12i	0.133538	+	0.757332i
$603$	−1.24928e11	−	1.04827e11i	−0.0384796	−	0.0322882i
$604$	3.09234e11	−	2.59478e11i	0.0945411	−	0.0793294i
$605$	3.70933e11	−	2.10366e12i	0.112563	−	0.638377i
$606$	−4.21922e10	+	1.53567e10i	−0.0127088	+	0.00462563i
$607$	1.85768e12			0.555420			0.277710	−	0.960665i	$-0.410425\pi$
$607$	1.85768e12			0.555420			0.277710	+	0.960665i	$0.410425\pi$
$608$	−4.39438e11	−	4.02111e11i	−0.130416	−	0.119338i
$609$	5.84063e12			1.72061
$610$	−1.20738e11	+	4.39450e10i	−0.0353069	+	0.0128506i
$611$	−8.81029e9	+	4.99656e10i	−0.00255744	+	0.0145039i
$612$	2.84045e11	−	2.38342e11i	0.0818475	−	0.0686782i
$613$	−3.96494e12	−	3.32698e12i	−1.13413	−	0.951652i	−0.134903	−	0.990859i	$-0.543072\pi$
$613$	−3.96494e12	−	3.32698e12i	−1.13413	−	0.951652i	−0.999231	+	0.0392068i	$0.987517\pi$
$614$	−7.57229e11	−	4.29446e12i	−0.215015	−	1.21941i
$615$	8.85051e11	+	1.53295e12i	0.249477	+	0.432107i
$616$	2.17381e11	−	3.76515e11i	0.0608287	−	0.105358i
$617$	1.34402e12	+	4.89185e11i	0.373357	+	0.135891i	0.521882	−	0.853018i	$-0.325230\pi$
$617$	1.34402e12	+	4.89185e11i	0.373357	+	0.135891i	−0.148525	+	0.988909i	$0.547452\pi$
$618$	−2.07315e12	−	7.54564e11i	−0.571718	−	0.208088i
$619$	−1.77033e12	+	3.06631e12i	−0.484671	+	0.839475i	−0.999845	−	0.0176105i	$-0.994394\pi$
$619$	−1.77033e12	+	3.06631e12i	−0.484671	+	0.839475i	0.515174	+	0.857086i	$0.327727\pi$
$620$	−1.59713e11	−	2.76630e11i	−0.0434087	−	0.0751860i
$621$	−1.27616e12	−	7.23746e12i	−0.344344	−	1.95287i
$622$	1.73306e12	+	1.45421e12i	0.464256	+	0.389557i
$623$	−1.97189e12	+	1.65461e12i	−0.524429	+	0.440048i
$624$	−7.92766e9	+	4.49600e10i	−0.00209322	+	0.0118712i
$625$	8.96430e11	−	3.26274e11i	0.234994	−	0.0855307i
$626$	1.78146e12			0.463651
$627$	−8.98186e11	−	3.85929e10i	−0.232093	−	0.00997250i
$628$	1.05880e12			0.271642
$629$	1.61041e12	−	5.86142e11i	0.410212	−	0.149305i
$630$	−1.44149e11	+	8.17510e11i	−0.0364569	+	0.206757i
$631$	−3.12806e12	+	2.62475e12i	−0.785493	+	0.659107i	−0.944626	−	0.328150i	$-0.893575\pi$
$631$	−3.12806e12	+	2.62475e12i	−0.785493	+	0.659107i	0.159132	+	0.987257i	$0.449130\pi$
$632$	1.33663e12	+	1.12156e12i	0.333260	+	0.279639i
$633$	6.67435e11	+	3.78521e12i	0.165231	+	0.937073i
$634$	2.29319e12	+	3.97191e12i	0.563686	+	0.976333i
$635$	2.00513e12	−	3.47299e12i	0.489396	−	0.847659i
$636$	1.20372e12	+	4.38119e11i	0.291722	+	0.106178i
$637$	9.85590e10	+	3.58725e10i	0.0237175	+	0.00863246i
$638$	7.65775e11	−	1.32636e12i	0.182982	−	0.316934i
$639$	8.41173e11	+	1.45695e12i	0.199587	+	0.345694i
$640$	−4.60656e10	−	2.61251e11i	−0.0108534	−	0.0615528i
$641$	1.24160e12	+	1.04183e12i	0.290483	+	0.243744i	0.776370	−	0.630278i	$-0.217059\pi$
$641$	1.24160e12	+	1.04183e12i	0.290483	+	0.243744i	−0.485887	+	0.874022i	$0.661503\pi$
$642$	−8.66092e11	+	7.26737e11i	−0.201213	+	0.168838i
$643$	1.15962e11	−	6.57651e11i	0.0267525	−	0.151721i	−0.968505	−	0.248993i	$-0.919900\pi$
$643$	1.15962e11	−	6.57651e11i	0.0267525	−	0.151721i	0.995258	+	0.0972716i	$0.0310116\pi$
$644$	4.45500e12	−	1.62149e12i	1.02061	−	0.371473i
$645$	2.28217e12			0.519195
$646$	4.09745e11	−	1.85431e12i	0.0925693	−	0.418925i
$647$	4.25982e12			0.955700			0.477850	−	0.878441i	$-0.341416\pi$
$647$	4.25982e12			0.955700			0.477850	+	0.878441i	$0.341416\pi$
$648$	7.81033e11	−	2.84273e11i	0.174013	−	0.0633356i
$649$	−2.94432e11	+	1.66981e12i	−0.0651454	+	0.369458i
$650$	7.38359e10	−	6.19556e10i	0.0162240	−	0.0136135i
$651$	8.27126e11	+	6.94041e11i	0.180492	+	0.151450i
$652$	3.40417e11	+	1.93060e12i	0.0737729	+	0.418387i
$653$	−4.13467e12	−	7.16146e12i	−0.889881	−	1.54132i	−0.840015	−	0.542563i	$-0.817454\pi$
$653$	−4.13467e12	−	7.16146e12i	−0.889881	−	1.54132i	−0.0498654	−	0.998756i	$-0.515879\pi$
$654$	−2.06834e11	+	3.58247e11i	−0.0442102	+	0.0765743i
$655$	3.34834e12	+	1.21870e12i	0.710794	+	0.258708i
$656$	−9.76852e11	−	3.55545e11i	−0.205950	−	0.0749596i
$657$	4.27818e11	−	7.41003e11i	0.0895809	−	0.155159i
$658$	4.98276e11	+	8.63039e11i	0.103622	+	0.179479i
$659$	9.11202e11	+	5.16769e12i	0.188205	+	1.06736i	0.921768	+	0.387741i	$0.126745\pi$
$659$	9.11202e11	+	5.16769e12i	0.188205	+	1.06736i	−0.733564	+	0.679621i	$0.762144\pi$
$660$	−3.06715e11	−	2.57365e11i	−0.0629199	−	0.0527961i
$661$	−4.94487e12	+	4.14924e12i	−1.00751	+	0.845400i	−0.988007	−	0.154410i	$-0.950652\pi$
$661$	−4.94487e12	+	4.14924e12i	−1.00751	+	0.845400i	−0.0195016	+	0.999810i	$0.506208\pi$
$662$	8.35597e11	−	4.73891e12i	0.169097	−	0.958997i
$663$	−1.36774e11	+	4.97817e10i	−0.0274912	+	0.0100060i
$664$	−2.49954e12			−0.499003
$665$	1.96574e12	+	3.76978e12i	0.389788	+	0.747512i
$666$	−9.09739e11			−0.179177
$667$	1.56938e13	−	5.71206e12i	3.07016	−	1.11745i
$668$	8.72403e11	−	4.94765e12i	0.169521	−	0.961401i
$669$	4.31952e12	−	3.62451e12i	0.833716	−	0.699571i
$670$	−2.84955e11	−	2.39105e11i	−0.0546310	−	0.0458408i
$671$	−1.97764e10	−	1.12158e11i	−0.00376614	−	0.0213588i
$672$	4.48358e11	+	7.76579e11i	0.0848131	+	0.146901i
$673$	−7.42598e11	+	1.28622e12i	−0.139536	+	0.241683i	−0.927321	−	0.374267i	$-0.877894\pi$
$673$	−7.42598e11	+	1.28622e12i	−0.139536	+	0.241683i	0.787785	+	0.615950i	$0.211228\pi$
$674$	−1.49913e12	−	5.45638e11i	−0.279814	−	0.101844i
$675$	−2.75773e12	−	1.00373e12i	−0.511311	−	0.186102i
$676$	1.35250e12	−	2.34261e12i	0.249103	−	0.431459i
$677$	−2.22528e12	−	3.85429e12i	−0.407132	−	0.705173i	0.587435	−	0.809271i	$-0.300138\pi$
$677$	−2.22528e12	−	3.85429e12i	−0.407132	−	0.705173i	−0.994567	+	0.104098i	$0.966804\pi$
$678$	−1.36231e11	−	7.72605e11i	−0.0247596	−	0.140418i
$679$	4.39784e12	+	3.69023e12i	0.794009	+	0.666253i
$680$	6.47893e11	−	5.43647e11i	0.116202	−	0.0975050i
$681$	1.13767e12	−	6.45203e12i	0.202700	−	1.14957i
$682$	2.66057e11	−	9.68369e10i	0.0470918	−	0.0171400i
$683$	6.82209e12			1.19957			0.599783	−	0.800162i	$-0.295253\pi$
$683$	6.82209e12			1.19957			0.599783	+	0.800162i	$0.295253\pi$
$684$	−5.41060e11	+	8.50592e11i	−0.0945132	+	0.148583i
$685$	−3.61554e12			−0.627431
$686$	−2.65901e12	+	9.67799e11i	−0.458417	+	0.166850i
$687$	−1.53119e12	+	8.68383e12i	−0.262256	+	1.48733i
$688$	−1.02671e12	+	8.61511e11i	−0.174703	+	0.146593i
$689$	2.09417e11	+	1.75721e11i	0.0354018	+	0.0297056i
$690$	−7.58161e11	−	4.29975e12i	−0.127333	−	0.722141i
$691$	−2.77704e12	−	4.80998e12i	−0.463374	−	0.802587i	0.535753	−	0.844375i	$-0.320028\pi$
$691$	−2.77704e12	−	4.80998e12i	−0.463374	−	0.802587i	−0.999127	+	0.0417879i	$0.986695\pi$
$692$	1.56006e12	−	2.70210e12i	0.258621	−	0.447944i
$693$	−6.91428e11	−	2.51659e11i	−0.113880	−	0.0414489i
$694$	−4.12727e12	−	1.50220e12i	−0.675376	−	0.245817i
$695$	−7.66561e11	+	1.32772e12i	−0.124628	+	0.215862i
$696$	1.57944e12	+	2.73568e12i	0.255131	+	0.441899i
$697$	−5.75515e11	−	3.26391e12i	−0.0923654	−	0.523830i
$698$	2.64034e12	+	2.21551e12i	0.421027	+	0.353284i
$699$	−3.61126e12	+	3.03021e12i	−0.572152	+	0.480093i
$700$	3.28748e11	−	1.86442e12i	0.0517514	−	0.293497i
$701$	−5.38663e12	+	1.96057e12i	−0.842531	+	0.306656i	−0.726991	−	0.686647i	$-0.759082\pi$
$701$	−5.38663e12	+	1.96057e12i	−0.842531	+	0.306656i	−0.115540	+	0.993303i	$0.536860\pi$
$702$	2.96650e11			0.0461028
$703$	−3.69449e12	+	2.83895e12i	−0.570500	+	0.438388i
$704$	2.35140e11			0.0360786
$705$	8.62413e11	−	3.13893e11i	0.131481	−	0.0478553i
$706$	−6.27263e11	+	3.55738e12i	−0.0950229	+	0.538902i
$707$	−1.44177e11	+	1.20979e11i	−0.0217025	+	0.0182105i
$708$	−2.67899e12	−	2.24794e12i	−0.400702	−	0.336229i
$709$	−6.35254e11	−	3.60271e12i	−0.0944147	−	0.535452i	−0.994925	−	0.100618i	$-0.967918\pi$
$709$	−6.35254e11	−	3.60271e12i	−0.0944147	−	0.535452i	0.900510	−	0.434834i	$-0.143193\pi$
$710$	1.91868e12	+	3.32325e12i	0.283361	+	0.490795i
$711$	1.47651e12	−	2.55739e12i	0.216682	−	0.375304i
$712$	−1.30824e12	−	4.76162e11i	−0.190778	−	0.0694376i
$713$	2.90125e12	+	1.05597e12i	0.420418	+	0.153020i
$714$	−1.42945e12	+	2.47588e12i	−0.205838	+	0.356522i
$715$	−4.27237e10	−	7.39995e10i	−0.00611352	−	0.0105889i
$716$	4.18475e11	+	2.37329e12i	0.0595061	+	0.337476i
$717$	2.28250e12	+	1.91524e12i	0.322533	+	0.270637i
$718$	−7.00835e12	+	5.88071e12i	−0.984138	+	0.825790i
$719$	−1.33731e12	+	7.58424e12i	−0.186617	+	1.05836i	0.737244	+	0.675627i	$0.236127\pi$
$719$	−1.33731e12	+	7.58424e12i	−0.186617	+	1.05836i	−0.923860	+	0.382730i	$0.874984\pi$
$720$	−4.21892e11	+	1.53556e11i	−0.0585067	+	0.0212947i
$721$	−9.24785e12			−1.27448
$722$	4.57103e11	+	5.14273e12i	0.0626032	+	0.704330i
$723$	−3.35194e12			−0.456220
$724$	−5.52201e12	+	2.00985e12i	−0.746919	+	0.271856i
$725$	1.15809e12	−	6.56786e12i	0.155676	−	0.882882i
$726$	−2.99159e12	+	2.51024e12i	−0.399656	+	0.335351i
$727$	3.22909e12	+	2.70953e12i	0.428722	+	0.359740i	0.831469	−	0.555571i	$-0.187500\pi$
$727$	3.22909e12	+	2.70953e12i	0.428722	+	0.359740i	−0.402747	+	0.915311i	$0.631945\pi$
$728$	3.32309e10	+	1.88462e11i	0.00438481	+	0.0248675i
$729$	−4.04320e12	−	7.00303e12i	−0.530214	−	0.918358i
$730$	9.75835e11	−	1.69020e12i	0.127181	−	0.220285i
$731$	−4.01534e12	−	1.46147e12i	−0.520109	−	0.189304i
$732$	2.20733e11	+	8.03401e10i	0.0284162	+	0.0103427i
$733$	6.78721e12	−	1.17558e13i	0.868408	−	1.50413i	0.00478402	−	0.999989i	$-0.498477\pi$
$733$	6.78721e12	−	1.17558e13i	0.868408	−	1.50413i	0.863623	−	0.504137i	$-0.168189\pi$
$734$	4.04077e12	+	6.99882e12i	0.513845	+	0.890005i
$735$	−3.29451e11	−	1.86841e12i	−0.0416387	−	0.236145i
$736$	1.96422e12	+	1.64818e12i	0.246740	+	0.207040i
$737$	2.52578e11	−	2.11938e11i	0.0315349	−	0.0264610i
$738$	−3.05508e11	+	1.73262e12i	−0.0379113	+	0.215006i
$739$	−9.83748e12	+	3.58055e12i	−1.21334	+	0.441621i	−0.867863	−	0.496804i	$-0.834507\pi$
$739$	−9.83748e12	+	3.58055e12i	−1.21334	+	0.441621i	−0.345482	+	0.938425i	$0.612284\pi$
$740$	−2.07507e12			−0.254385
$741$	3.13778e11	−	2.41115e11i	0.0382332	−	0.0293794i
$742$	5.36954e12			0.650309
$743$	9.71861e12	−	3.53729e12i	1.16992	−	0.425815i	0.317286	−	0.948330i	$-0.397229\pi$
$743$	9.71861e12	−	3.53729e12i	1.16992	−	0.425815i	0.852630	+	0.522515i	$0.175006\pi$
$744$	−1.01406e11	+	5.75100e11i	−0.0121334	+	0.0688122i
$745$	−6.93724e12	+	5.82103e12i	−0.825056	+	0.692304i
$746$	−9.77604e11	−	8.20307e11i	−0.115568	−	0.0969732i
$747$	7.34580e11	+	4.16601e12i	0.0863171	+	0.489528i
$748$	3.74834e11	+	6.49232e11i	0.0437807	+	0.0758303i
$749$	−2.36961e12	+	4.10428e12i	−0.275111	+	0.476507i
$750$	−4.91532e12	−	1.78903e12i	−0.567252	−	0.206463i
$751$	−1.32767e13	−	4.83231e12i	−1.52303	−	0.554339i	−0.561130	−	0.827728i	$-0.689633\pi$
$751$	−1.32767e13	−	4.83231e12i	−1.52303	−	0.554339i	−0.961904	+	0.273389i	$0.911855\pi$
$752$	−2.69491e11	+	4.66772e11i	−0.0307301	+	0.0532261i
$753$	1.69464e12	+	2.93520e12i	0.192088	+	0.332706i
$754$	1.17063e11	+	6.63899e11i	0.0131902	+	0.0748051i
$755$	−1.19375e12	−	1.00167e12i	−0.133706	−	0.112193i
$756$	4.46353e12	−	3.74534e12i	0.496970	−	0.417007i
$757$	−5.92127e11	+	3.35812e12i	−0.0655365	+	0.371676i	0.934346	+	0.356366i	$0.115985\pi$
$757$	−5.92127e11	+	3.35812e12i	−0.0655365	+	0.371676i	−0.999883	+	0.0153096i	$0.995127\pi$
$758$	2.48760e12	−	9.05413e11i	0.273696	−	0.0996174i
$759$	3.87000e12			0.423276
$760$	−1.23413e12	+	1.94016e12i	−0.134184	+	0.210949i
$761$	4.75540e12			0.513991			0.256996	−	0.966413i	$-0.417267\pi$
$761$	4.75540e12			0.513991			0.256996	+	0.966413i	$0.417267\pi$
$762$	−6.88940e12	+	2.50753e12i	−0.740259	+	0.269432i
$763$	−3.01106e11	+	1.70766e12i	−0.0321632	+	0.182406i
$764$	−2.14746e12	+	1.80193e12i	−0.228036	+	0.191345i
$765$	−1.09651e12	−	9.20082e11i	−0.115754	−	0.0971293i
$766$	−7.18130e11	−	4.07271e12i	−0.0753656	−	0.427420i
$767$	−3.73168e11	−	6.46346e11i	−0.0389337	−	0.0674351i
$768$	−2.42493e11	+	4.20010e11i	−0.0251521	+	0.0435646i
$769$	8.62045e12	+	3.13759e12i	0.888917	+	0.323539i	0.745803	−	0.666167i	$-0.232066\pi$
$769$	8.62045e12	+	3.13759e12i	0.888917	+	0.323539i	0.143115	+	0.989706i	$0.454288\pi$
$770$	−1.57712e12	−	5.74024e11i	−0.161680	−	0.0588466i
$771$	−2.92980e12	+	5.07456e12i	−0.298603	+	0.517195i
$772$	5.26913e11	+	9.12641e11i	0.0533902	+	0.0924745i
$773$	−8.28099e11	−	4.69638e12i	−0.0834208	−	0.473103i	−0.997686	−	0.0679872i	$-0.978342\pi$
$773$	−8.28099e11	−	4.69638e12i	−0.0834208	−	0.473103i	0.914265	−	0.405116i	$-0.132769\pi$
$774$	1.73763e12	+	1.45804e12i	0.174029	+	0.146028i
$775$	9.44461e11	−	7.92497e11i	0.0940430	−	0.0789115i
$776$	−5.39175e11	+	3.05782e12i	−0.0533768	+	0.302715i
$777$	6.59126e12	−	2.39902e12i	0.648744	−	0.236124i
$778$	−9.60233e10			−0.00939655
$779$	4.16617e12	+	7.98963e12i	0.405339	+	0.777335i
$780$	1.76239e11			0.0170481
$781$	−3.19623e12	+	1.16333e12i	−0.307403	+	0.111886i
$782$	−1.41955e12	+	8.05065e12i	−0.135744	+	0.769840i
$783$	1.57238e13	−	1.31938e13i	1.49496	−	1.25442i
$784$	8.53530e11	+	7.16196e11i	0.0806856	+	0.0677033i
$785$	−7.09761e11	−	4.02526e12i	−0.0667112	−	0.378338i
$786$	−3.25714e12	−	5.64153e12i	−0.304393	−	0.527225i
$787$	−7.29440e12	+	1.26343e13i	−0.677803	+	1.17399i	0.297838	+	0.954616i	$0.403734\pi$
$787$	−7.29440e12	+	1.26343e13i	−0.677803	+	1.17399i	−0.975641	+	0.219373i	$0.929599\pi$
$788$	−6.64051e12	−	2.41695e12i	−0.613527	−	0.223306i
$789$	8.08689e12	+	2.94339e12i	0.742908	+	0.270396i
$790$	3.36785e12	−	5.83329e12i	0.307631	−	0.532833i
$791$	−1.64427e12	−	2.84796e12i	−0.149341	−	0.258666i
$792$	−6.91044e10	−	3.91911e11i	−0.00624083	−	0.0353935i
$793$	3.84018e10	+	3.22229e10i	0.00344843	+	0.00289358i
$794$	4.55839e12	−	3.82494e12i	0.407023	−	0.341533i
$795$	8.58691e11	−	4.86988e12i	0.0762404	−	0.432381i
$796$	−7.02089e12	+	2.55540e12i	−0.619845	+	0.225605i
$797$	8.27212e12			0.726197			0.363098	−	0.931751i	$-0.381719\pi$
$797$	8.27212e12			0.726197			0.363098	+	0.931751i	$0.381719\pi$
$798$	1.67705e12	−	7.58952e12i	0.146397	−	0.662523i
$799$	−1.71837e12			−0.149162
$800$	9.62173e11	−	3.50202e11i	0.0830516	−	0.0302283i
$801$	−4.09150e11	+	2.32041e12i	−0.0351185	+	0.199167i
$802$	8.11457e12	−	6.80893e12i	0.692598	−	0.581158i
$803$	1.32520e12	+	1.11197e12i	0.112476	+	0.0943787i
$804$	1.18090e11	+	6.69724e11i	0.00996696	+	0.0565254i
$805$	−9.15078e12	−	1.58496e13i	−0.768027	−	1.33026i
$806$	−6.23130e10	+	1.07929e11i	−0.00520081	+	0.00900807i
$807$	−1.96306e12	−	7.14495e11i	−0.162931	−	0.0593019i
$808$	−9.56539e10	−	3.48152e10i	−0.00789499	−	0.00287354i
$809$	2.79548e12	−	4.84191e12i	0.229450	−	0.397418i	−0.728196	−	0.685369i	$-0.759641\pi$
$809$	2.79548e12	−	4.84191e12i	0.229450	−	0.397418i	0.957645	+	0.287951i	$0.0929741\pi$
$810$	−1.60428e12	−	2.77869e12i	−0.130948	−	0.226808i
$811$	−1.07919e12	−	6.12039e12i	−0.0876000	−	0.496804i	−0.996765	−	0.0803686i	$-0.974390\pi$
$811$	−1.07919e12	−	6.12039e12i	−0.0876000	−	0.496804i	0.909165	−	0.416436i	$-0.136721\pi$
$812$	1.01434e13	+	8.51134e12i	0.818809	+	0.687062i
$813$	−3.62152e12	+	3.03881e12i	−0.290725	+	0.243948i
$814$	3.19392e11	−	1.81136e12i	0.0254985	−	0.144609i
$815$	7.11137e12	−	2.58833e12i	0.564604	−	0.205499i
$816$	−1.54622e12			−0.122086
$817$	1.16066e13	+	4.98708e11i	0.911391	+	0.0391604i
$818$	4.84009e12			0.377976
$819$	3.04345e11	−	1.10773e11i	0.0236368	−	0.00860310i
$820$	−6.96850e11	+	3.95203e12i	−0.0538242	+	0.305252i
$821$	1.16674e13	−	9.79013e12i	0.896253	−	0.752045i	−0.0732015	−	0.997317i	$-0.523322\pi$
$821$	1.16674e13	−	9.79013e12i	0.896253	−	0.752045i	0.969454	+	0.245272i	$0.0788772\pi$
$822$	5.06349e12	+	4.24878e12i	0.386836	+	0.324594i
$823$	1.44071e11	+	8.17067e11i	0.0109466	+	0.0620810i	0.989792	−	0.142521i	$-0.0455210\pi$
$823$	1.44071e11	+	8.17067e11i	0.0109466	+	0.0620810i	−0.978845	+	0.204602i	$0.934410\pi$
$824$	−2.50083e12	−	4.33157e12i	−0.188979	−	0.327320i
$825$	7.72703e11	−	1.33836e12i	0.0580724	−	0.100584i
$826$	−1.37753e13	−	5.01379e12i	−1.02965	−	0.374762i
$827$	1.80463e13	+	6.56831e12i	1.34157	+	0.488291i	0.910306	−	0.413936i	$-0.135846\pi$
$827$	1.80463e13	+	6.56831e12i	1.34157	+	0.488291i	0.431262	+	0.902227i	$0.358068\pi$
$828$	2.16978e12	−	3.75817e12i	0.160428	−	0.277869i
$829$	−2.52786e12	−	4.37839e12i	−0.185891	−	0.321973i	0.757985	−	0.652272i	$-0.226184\pi$
$829$	−2.52786e12	−	4.37839e12i	−0.185891	−	0.321973i	−0.943876	+	0.330299i	$0.892850\pi$
$830$	1.67555e12	+	9.50249e12i	0.122548	+	0.695002i
$831$	−9.70466e12	−	8.14318e12i	−0.705953	−	0.592365i
$832$	−7.92866e10	+	6.65293e10i	−0.00573647	+	0.00481347i
$833$	−6.16848e11	+	3.49832e12i	−0.0443890	+	0.251743i
$834$	2.63382e12	−	9.58631e11i	0.188512	−	0.0686126i
$835$	−1.93943e13			−1.38065
$836$	−1.50364e12	−	1.37592e12i	−0.106467	−	0.0974236i
$837$	3.79456e12			0.267237
$838$	2.93548e12	−	1.06843e12i	0.205627	−	0.0748422i
$839$	−1.66103e12	+	9.42017e12i	−0.115731	+	0.656341i	0.870655	+	0.491894i	$0.163695\pi$
$839$	−1.66103e12	+	9.42017e12i	−0.115731	+	0.656341i	−0.986386	+	0.164447i	$0.947416\pi$
$840$	2.65177e12	−	2.22510e12i	0.183772	−	0.154203i
$841$	2.46194e13	+	2.06582e13i	1.69706	+	1.42400i
$842$	−2.10713e12	−	1.19501e13i	−0.144473	−	0.819347i
$843$	−3.22696e12	−	5.58926e12i	−0.220074	−	0.381180i
$844$	−4.35692e12	+	7.54640e12i	−0.295555	+	0.511916i
$845$	−9.81253e12	−	3.57147e12i	−0.662103	−	0.240986i
$846$	8.57174e11	+	3.11986e11i	0.0575311	+	0.0209396i
$847$	−8.18491e12	+	1.41767e13i	−0.546435	+	0.946454i
$848$	1.45205e12	+	2.51502e12i	0.0964273	+	0.167017i
$849$	1.93776e12	+	1.09896e13i	0.128002	+	0.725933i
$850$	2.50072e12	+	2.09835e12i	0.164316	+	0.137877i
$851$	1.53645e13	−	1.28923e13i	1.00423	−	0.842651i
$852$	1.21822e12	−	6.90886e12i	0.0792039	−	0.449188i
$853$	−1.35598e13	+	4.93536e12i	−0.876966	+	0.319189i	−0.740985	−	0.671522i	$-0.765641\pi$
$853$	−1.35598e13	+	4.93536e12i	−0.876966	+	0.319189i	−0.135981	+	0.990711i	$0.543419\pi$
$854$	9.84639e11			0.0633456
$855$	3.59639e12	+	1.48676e12i	0.230154	+	0.0951465i
$856$	−2.56319e12			−0.163173
$857$	−1.42822e13	+	5.19831e12i	−0.904445	+	0.329191i	−0.752033	−	0.659126i	$-0.770926\pi$
$857$	−1.42822e13	+	5.19831e12i	−0.904445	+	0.329191i	−0.152413	+	0.988317i	$0.548704\pi$
$858$	−2.71264e10	+	1.53841e11i	−0.00170883	+	0.00969125i
$859$	−4.48368e12	+	3.76226e12i	−0.280974	+	0.235765i	−0.772373	−	0.635170i	$-0.780930\pi$
$859$	−4.48368e12	+	3.76226e12i	−0.280974	+	0.235765i	0.491399	+	0.870935i	$0.336486\pi$
$860$	3.96345e12	+	3.32573e12i	0.247076	+	0.207321i
$861$	−2.35553e12	−	1.33589e13i	−0.146074	−	0.828429i
$862$	4.91917e12	+	8.52024e12i	0.303465	+	0.525617i
$863$	−2.64878e12	+	4.58782e12i	−0.162554	+	0.281551i	−0.935784	−	0.352574i	$-0.885306\pi$
$863$	−2.64878e12	+	4.58782e12i	−0.162554	+	0.281551i	0.773230	+	0.634126i	$0.218640\pi$
$864$	2.96131e12	+	1.07783e12i	0.180789	+	0.0658019i
$865$	−1.13183e13	−	4.11954e12i	−0.687401	−	0.250194i
$866$	1.11646e13	−	1.93377e13i	0.674551	−	1.16836i
$867$	4.23062e12	+	7.32765e12i	0.254284	+	0.440432i
$868$	4.25068e11	+	2.41068e12i	0.0254167	+	0.144146i
$869$	4.57358e12	+	3.83769e12i	0.272062	+	0.228287i
$870$	9.34145e12	−	7.83841e12i	0.552812	−	0.463865i
$871$	−2.52018e10	+	1.42927e11i	−0.00148371	+	0.00841455i
$872$	−8.81270e11	+	3.20756e11i	−0.0516161	+	0.0187867i
$873$	5.25496e12			0.306200
$874$	−2.91623e12	−	2.20331e13i	−0.169052	−	1.27725i
$875$	−2.19262e13			−1.26452
$876$	−3.35286e12	+	1.22034e12i	−0.192374	+	0.0700184i
$877$	1.61151e12	−	9.13933e12i	0.0919888	−	0.521694i	−0.903640	−	0.428293i	$-0.859115\pi$
$877$	1.61151e12	−	9.13933e12i	0.0919888	−	0.521694i	0.995629	−	0.0934011i	$-0.0297739\pi$
$878$	−1.22227e13	+	1.02560e13i	−0.694129	+	0.582444i
$879$	1.60995e13	+	1.35091e13i	0.909627	+	0.763268i
$880$	−1.57624e11	−	8.93931e11i	−0.00886035	−	0.0502495i
$881$	−7.88789e12	−	1.36622e13i	−0.441133	−	0.764065i	0.556641	−	0.830753i	$-0.312090\pi$
$881$	−7.88789e12	−	1.36622e13i	−0.441133	−	0.764065i	−0.997774	+	0.0666885i	$0.978757\pi$
$882$	9.42853e11	−	1.63307e12i	0.0524609	−	0.0908649i
$883$	4.84031e11	+	1.76173e11i	0.0267948	+	0.00975250i	0.355383	−	0.934721i	$-0.384351\pi$
$883$	4.84031e11	+	1.76173e11i	0.0267948	+	0.00975250i	−0.328588	+	0.944473i	$0.606573\pi$
$884$	−3.10081e11	−	1.12860e11i	−0.0170781	−	0.00621592i
$885$	−6.75016e12	+	1.16916e13i	−0.369887	+	0.640663i
$886$	−1.11600e12	−	1.93297e12i	−0.0608433	−	0.105384i
$887$	−1.63820e12	−	9.29069e12i	−0.0888608	−	0.503955i	−0.996457	−	0.0841095i	$-0.973195\pi$
$887$	−1.63820e12	−	9.29069e12i	−0.0888608	−	0.503955i	0.907596	−	0.419845i	$-0.137916\pi$
$888$	2.90610e12	+	2.43851e12i	0.156838	+	0.131603i
$889$	−2.35421e13	+	1.97542e13i	−1.26412	+	1.06072i
$890$	−9.33253e11	+	5.29274e12i	−0.0498591	+	0.282765i
$891$	2.67249e12	−	9.72706e11i	0.142058	−	0.0517049i
$892$	1.27836e13			0.676100
$893$	4.45461e12	−	1.40792e12i	0.234411	−	0.0740879i
$894$	1.65560e13			0.866835
$895$	8.74202e12	−	3.18183e12i	0.455416	−	0.165758i
$896$	−3.53017e11	+	2.00206e12i	−0.0182983	+	0.103775i
$897$	−1.30492e12	+	1.09496e12i	−0.0673006	+	0.0564719i
$898$	−9.75734e12	−	8.18738e12i	−0.500712	−	0.420147i
$899$	1.49740e12	+	8.49218e12i	0.0764574	+	0.433611i
$900$	−8.66457e11	−	1.50075e12i	−0.0440206	−	0.0762459i
$901$	−4.62940e12	+	8.01836e12i	−0.234026	+	0.405344i
$902$	−3.34253e12	−	1.21658e12i	−0.168130	−	0.0611944i
$903$	−1.64344e13	−	5.98164e12i	−0.822544	−	0.299382i
$904$	8.89297e11	−	1.54031e12i	0.0442883	−	0.0767096i
$905$	1.13425e13	+	1.96457e13i	0.562068	+	0.973530i
$906$	4.94712e11	+	2.80565e12i	0.0243936	+	0.138343i
$907$	−1.76851e13	−	1.48395e13i	−0.867708	−	0.728093i	0.0959064	−	0.995390i	$-0.469425\pi$
$907$	−1.76851e13	−	1.48395e13i	−0.867708	−	0.728093i	−0.963614	+	0.267297i	$0.913870\pi$
$908$	1.13781e13	−	9.54736e12i	0.555499	−	0.466119i
$909$	−2.99155e10	+	1.69659e11i	−0.00145331	+	0.00824214i
$910$	6.94198e11	−	2.52668e11i	0.0335581	−	0.0122142i
$911$	−1.18253e13			−0.568827			−0.284413	−	0.958702i	$-0.591799\pi$
$911$	−1.18253e13			−0.568827			−0.284413	+	0.958702i	$0.591799\pi$
$912$	4.00834e12	−	1.26688e12i	0.191862	−	0.0606397i
$913$	−8.55275e12			−0.407368
$914$	−1.90491e13	+	6.93332e12i	−0.902854	+	0.328612i
$915$	1.57462e11	−	8.93014e11i	0.00742647	−	0.0421176i
$916$	−1.53139e13	+	1.28499e13i	−0.718712	+	0.603071i
$917$	−2.09179e13	−	1.75522e13i	−0.976911	−	0.819726i
$918$	1.74466e12	+	9.89449e12i	0.0810812	+	0.459834i
$919$	7.21176e12	+	1.24911e13i	0.333520	+	0.577673i	0.983199	−	0.182535i	$-0.0584303\pi$
$919$	7.21176e12	+	1.24911e13i	0.333520	+	0.577673i	−0.649680	+	0.760208i	$0.725097\pi$
$920$	4.94917e12	−	8.57221e12i	0.227765	−	0.394501i
$921$	2.89196e13	+	1.05259e13i	1.32441	+	0.482047i
$922$	2.62636e13	+	9.55918e12i	1.19692	+	0.435644i
$923$	7.48586e11	−	1.29659e12i	0.0339495	−	0.0588023i
$924$	1.53416e12	+	2.65725e12i	0.0692384	+	0.119924i
$925$	−1.39080e12	−	7.88763e12i	−0.0624637	−	0.354249i
$926$	−7.83591e12	−	6.57511e12i	−0.350219	−	0.293869i
$927$	−6.48453e12	+	5.44117e12i	−0.288416	+	0.242010i
$928$	−1.24358e12	+	7.05272e12i	−0.0550439	+	0.312169i
$929$	3.75865e13	−	1.36804e13i	1.65562	−	0.602597i	0.665956	−	0.745991i	$-0.268024\pi$
$929$	3.75865e13	−	1.36804e13i	1.65562	−	0.602597i	0.989666	+	0.143394i	$0.0458015\pi$
$930$	2.25433e12			0.0988200
$931$	−1.26721e12	−	9.57425e12i	−0.0552811	−	0.417668i
$932$	−1.06875e13			−0.463985
$933$	−1.50036e13	+	5.46086e12i	−0.648228	+	0.235936i
$934$	3.65295e12	−	2.07169e13i	0.157066	−	0.890767i
$935$	2.21692e12	−	1.86022e12i	0.0948632	−	0.0795996i
$936$	1.34187e11	+	1.12596e11i	0.00571436	+	0.00479492i
$937$	7.16838e12	+	4.06539e13i	0.303804	+	1.72296i	0.629083	+	0.777338i	$0.283430\pi$
$937$	7.16838e12	+	4.06539e13i	0.303804	+	1.72296i	−0.325280	+	0.945618i	$0.605459\pi$
$938$	1.42532e12	+	2.46872e12i	0.0601171	+	0.104126i
$939$	−6.28630e12	+	1.08882e13i	−0.263876	+	0.457047i
$940$	1.95518e12	+	7.11626e11i	0.0816791	+	0.0297287i
$941$	−2.11811e13	−	7.70930e12i	−0.880634	−	0.320525i	−0.138168	−	0.990409i	$-0.544122\pi$
$941$	−2.11811e13	−	7.70930e12i	−0.880634	−	0.320525i	−0.742466	+	0.669884i	$0.766344\pi$
$942$	−3.73624e12	+	6.47136e12i	−0.154599	+	0.267773i
$943$	−1.93941e13	−	3.35915e13i	−0.798668	−	1.38333i
$944$	−1.37676e12	−	7.80800e12i	−0.0564267	−	0.320012i
$945$	−1.72308e13	−	1.44583e13i	−0.702848	−	0.589759i
$946$	−3.51312e12	+	2.94786e12i	−0.142621	+	0.119673i
$947$	−1.24047e12	+	7.03506e12i	−0.0501200	+	0.284245i	−0.999559	−	0.0297080i	$-0.990542\pi$
$947$	−1.24047e12	+	7.03506e12i	−0.0501200	+	0.284245i	0.949439	+	0.313953i	$0.101653\pi$
$948$	−1.15715e13	+	4.21170e12i	−0.465322	+	0.169363i
$949$	−7.61458e11			−0.0304753
$950$	−8.20197e12	−	3.39072e12i	−0.326710	−	0.135063i
$951$	−3.23682e13			−1.28323
$952$	−6.09053e12	+	2.21677e12i	−0.240319	+	0.0874690i
$953$	−5.44203e12	+	3.08633e13i	−0.213719	+	1.21206i	0.669397	+	0.742905i	$0.266553\pi$
$953$	−5.44203e12	+	3.08633e13i	−0.213719	+	1.21206i	−0.883116	+	0.469155i	$0.844559\pi$
$954$	3.76509e12	−	3.15928e12i	0.147166	−	0.123487i
$955$	8.28993e12	+	6.95608e12i	0.322504	+	0.270613i
$956$	1.17300e12	+	6.65241e12i	0.0454190	+	0.257584i
$957$	5.40444e12	+	9.36076e12i	0.208280	+	0.360751i
$958$	−5.89067e12	+	1.02029e13i	−0.225954	+	0.391364i
$959$	2.60363e13	+	9.47642e12i	0.994019	+	0.361793i
$960$	1.75931e12	+	6.40335e11i	0.0668530	+	0.0243325i
$961$	1.24227e13	−	2.15168e13i	0.469853	−	0.813810i
$962$	4.04803e11	+	7.01139e11i	0.0152390	+	0.0263947i
$963$	7.53287e11	+	4.27210e12i	0.0282255	+	0.160075i
$964$	−5.82132e12	−	4.88467e12i	−0.217107	−	0.182175i
$965$	3.11637e12	−	2.61495e12i	0.115685	−	0.0970711i
$966$	−5.81007e12	+	3.29505e13i	−0.214676	+	1.21749i
$967$	3.26820e13	−	1.18953e13i	1.20196	−	0.437477i	0.338051	−	0.941128i	$-0.390232\pi$
$967$	3.26820e13	−	1.18953e13i	1.20196	−	0.437477i	0.863908	+	0.503650i	$0.168010\pi$
$968$	−8.85357e12			−0.324100
$969$	9.88758e12	+	9.04771e12i	0.360274	+	0.329672i
$970$	1.19863e13			0.434724
$971$	4.80194e13	−	1.74776e13i	1.73352	−	0.630951i	0.734652	−	0.678444i	$-0.237345\pi$
$971$	4.80194e13	−	1.74776e13i	1.73352	−	0.630951i	0.998872	+	0.0474926i	$0.0151230\pi$
$972$	1.61106e12	−	9.13680e12i	0.0578915	−	0.328319i
$973$	9.00016e12	−	7.55203e12i	0.321916	−	0.270119i
$974$	−2.14413e13	−	1.79914e13i	−0.763372	−	0.640545i
$975$	1.18123e11	+	6.69906e11i	0.00418612	+	0.0237407i
$976$	2.66269e11	+	4.61192e11i	0.00939284	+	0.0162689i
$977$	−1.07484e13	+	1.86168e13i	−0.377414	+	0.653700i	−0.990685	−	0.136172i	$-0.956520\pi$
$977$	−1.07484e13	+	1.86168e13i	−0.377414	+	0.653700i	0.613271	+	0.789872i	$0.289853\pi$
$978$	−1.30010e13	−	4.73197e12i	−0.454414	−	0.165393i
$979$	−4.47646e12	−	1.62930e12i	−0.155745	−	0.0566864i
$980$	2.15061e12	−	3.72496e12i	0.0744807	−	0.129004i
$981$	7.93602e11	+	1.37456e12i	0.0273585	+	0.0473863i
$982$	6.71977e12	+	3.81097e13i	0.230596	+	1.30778i
$983$	−1.53179e12	−	1.28533e12i	−0.0523250	−	0.0439059i	0.616250	−	0.787551i	$-0.288651\pi$
$983$	−1.53179e12	−	1.28533e12i	−0.0523250	−	0.0439059i	−0.668575	+	0.743645i	$0.733095\pi$
$984$	5.62013e12	−	4.71585e12i	0.191103	−	0.160355i
$985$	−4.73710e12	+	2.68654e13i	−0.160343	+	0.909349i
$986$	−2.14553e13	+	7.80908e12i	−0.722916	+	0.263120i
$987$	−7.03313e12			−0.235897
$988$	8.96306e11	+	3.85122e10i	0.0299261	+	0.00128586i
$989$	−5.00091e13			−1.66213
$990$	−1.44360e12	+	5.25428e11i	−0.0477628	+	0.0173842i
$991$	9.69341e12	−	5.49741e13i	0.319261	−	1.81062i	−0.228008	−	0.973659i	$-0.573221\pi$
$991$	9.69341e12	−	5.49741e13i	0.319261	−	1.81062i	0.547269	−	0.836957i	$-0.315668\pi$
$992$	−1.01418e12	+	8.51001e11i	−0.0332517	+	0.0279015i
$993$	2.60154e13	+	2.18295e13i	0.849099	+	0.712479i
$994$	−5.10648e12	−	2.89603e13i	−0.165914	−	0.940945i
$995$	1.44212e13	+	2.49783e13i	0.466443	+	0.807904i
$996$	8.82021e12	−	1.52770e13i	0.283996	−	0.491895i
$997$	1.37311e12	+	4.99772e11i	0.0440127	+	0.0160193i	0.363933	−	0.931425i	$-0.381434\pi$
$997$	1.37311e12	+	4.99772e11i	0.0440127	+	0.0160193i	−0.319920	+	0.947445i	$0.603656\pi$
$998$	−1.11949e13	−	4.07460e12i	−0.357216	−	0.130016i
$999$	1.23253e13	−	2.13480e13i	0.391518	−	0.678128i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.b.5.6	✓	48
19.4	even	9	inner	38.10.e.b.23.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.b.5.6	✓	48	1.1	even	1	trivial
38.10.e.b.23.6	yes	48	19.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-15.0351 + 5.47232i) q^{2} +(19.6083 - 111.204i) q^{3} +(196.107 - 164.554i) q^{4} +(-757.043 - 635.234i) q^{5} +(313.732 + 1779.26i) q^{6} +(3786.65 + 6558.68i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(6514.11 + 2370.94i) q^{9} +O(q^{10})\)	\(q+(-15.0351 + 5.47232i) q^{2} +(19.6083 - 111.204i) q^{3} +(196.107 - 164.554i) q^{4} +(-757.043 - 635.234i) q^{5} +(313.732 + 1779.26i) q^{6} +(3786.65 + 6558.68i) q^{7} +(-2048.00 + 3547.24i) q^{8} +(6514.11 + 2370.94i) q^{9} +(14858.4 + 5408.02i) q^{10} +(-7007.71 + 12137.7i) q^{11} +(-14453.7 - 25034.5i) q^{12} +(-1071.26 - 6075.43i) q^{13} +(-92823.9 - 77888.5i) q^{14} +(-85484.9 + 71730.4i) q^{15} +(11380.2 - 64540.4i) q^{16} +(196340. - 71462.0i) q^{17} -110915. q^{18} +(-450430. + 346122. i) q^{19} -252992. q^{20} +(803601. - 292487. i) q^{21} +(38940.0 - 220840. i) q^{22} +(1.87323e6 - 1.57182e6i) q^{23} +(354310. + 297301. i) q^{24} +(-169566. - 961654. i) q^{25} +(49353.3 + 85482.4i) q^{26} +(1.50269e6 - 2.60273e6i) q^{27} +(1.82185e6 + 663097. i) q^{28} +(6.41787e6 + 2.33591e6i) q^{29} +(892741. - 1.54627e6i) q^{30} +(631296. + 1.09344e6i) q^{31} +(182083. + 1.03265e6i) q^{32} +(1.21235e6 + 1.01729e6i) q^{33} +(-2.56093e6 + 2.14887e6i) q^{34} +(1.29964e6 - 7.37061e6i) q^{35} +(1.66761e6 - 606961. i) q^{36} +8.20215e6 q^{37} +(4.87816e6 - 7.66888e6i) q^{38} -696619. q^{39} +(3.80375e6 - 1.38445e6i) q^{40} +(2.75444e6 - 1.56212e7i) q^{41} +(-1.04816e7 + 8.79513e6i) q^{42} +(-1.56663e7 - 1.31456e7i) q^{43} +(623041. + 3.53344e6i) q^{44} +(-3.42536e6 - 5.93289e6i) q^{45} +(-1.95626e7 + 3.38834e7i) q^{46} +(-7.72823e6 - 2.81284e6i) q^{47} +(-6.95400e6 - 2.53105e6i) q^{48} +(-8.50070e6 + 1.47236e7i) q^{49} +(7.81191e6 + 1.35306e7i) q^{50} +(-4.09697e6 - 2.32351e7i) q^{51} +(-1.20982e6 - 1.01516e6i) q^{52} +(-3.39457e7 + 2.84839e7i) q^{53} +(-8.35004e6 + 4.73554e7i) q^{54} +(1.30154e7 - 4.73723e6i) q^{55} -3.10203e7 q^{56} +(2.96581e7 + 5.68765e7i) q^{57} -1.09276e8 q^{58} +(1.13683e8 - 4.13771e7i) q^{59} +(-4.96073e6 + 2.81337e7i) q^{60} +(-6.22480e6 + 5.22323e6i) q^{61} +(-1.54752e7 - 1.29852e7i) q^{62} +(9.11644e6 + 5.17019e7i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-3.04833e6 + 5.27987e6i) q^{65} +(-2.37948e7 - 8.66058e6i) q^{66} +(-2.21066e7 - 8.04613e6i) q^{67} +(2.67444e7 - 4.63227e7i) q^{68} +(-1.38062e8 - 2.39131e8i) q^{69} +(2.07942e7 + 1.17930e8i) q^{70} +(1.85909e8 + 1.55996e8i) q^{71} +(-2.17512e7 + 1.82514e7i) q^{72} +(2.14334e7 - 1.21555e8i) q^{73} +(-1.23320e8 + 4.48848e7i) q^{74} -1.10265e8 q^{75} +(-3.13769e7 + 1.41997e8i) q^{76} -1.06143e8 q^{77} +(1.04737e7 - 3.81212e6i) q^{78} +(7.39719e7 - 4.19515e8i) q^{79} +(-4.96135e7 + 4.16307e7i) q^{80} +(-1.55445e8 - 1.30434e8i) q^{81} +(4.40710e7 + 2.49939e8i) q^{82} +(3.05119e8 + 5.28482e8i) q^{83} +(1.09462e8 - 1.89594e8i) q^{84} +(-1.94033e8 - 7.06222e7i) q^{85} +(3.07482e8 + 1.11914e8i) q^{86} +(3.85606e8 - 6.67890e8i) q^{87} +(-2.87036e7 - 4.97161e7i) q^{88} +(5.90219e7 + 3.34730e8i) q^{89} +(8.39672e7 + 7.04568e7i) q^{90} +(3.57903e7 - 3.00316e7i) q^{91} +(1.08704e8 - 6.16492e8i) q^{92} +(1.33973e8 - 4.87622e7i) q^{93} +1.31587e8 q^{94} +(5.60863e8 + 2.40990e7i) q^{95} +1.18405e8 q^{96} +(7.12337e8 - 2.59270e8i) q^{97} +(4.72362e7 - 2.67890e8i) q^{98} +(-7.44268e7 + 6.24515e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9	\( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) 48 * q + 33 * q^3 + 528 * q^6 - 25809 * q^7 - 98304 * q^8 + 7953 * q^9 - 55221 * q^11 - 62208 * q^12 + 21777 * q^13 + 28464 * q^14 - 280011 * q^15 + 1055055 * q^17 + 6083232 * q^18 + 2408220 * q^19 + 523776 * q^20 - 5105673 * q^21 - 2513280 * q^22 - 456708 * q^23 + 135168 * q^24 + 19417530 * q^25 - 1077120 * q^26 - 11729661 * q^27 - 30720 * q^28 + 4679889 * q^29 + 4879158 * q^31 - 12360834 * q^33 + 9206400 * q^34 - 47475759 * q^35 + 2035968 * q^36 + 119843604 * q^37 - 39471312 * q^38 + 16552668 * q^39 + 60082911 * q^41 + 59187024 * q^42 + 109939059 * q^43 - 40212480 * q^44 + 3067236 * q^45 - 4919424 * q^46 + 198627789 * q^47 - 4325376 * q^48 - 182954115 * q^49 - 229688016 * q^50 - 228228021 * q^51 - 49495296 * q^52 - 370799859 * q^53 + 111760416 * q^54 - 60369543 * q^55 + 211427328 * q^56 + 128158266 * q^57 + 166196064 * q^58 - 382689396 * q^59 - 36777216 * q^60 - 850085550 * q^61 + 42954480 * q^62 - 803298357 * q^63 - 402653184 * q^64 + 261122181 * q^65 + 516819888 * q^66 + 1146400764 * q^67 + 125611008 * q^68 - 178115667 * q^69 - 759612144 * q^70 + 363378456 * q^71 - 65150976 * q^72 + 1407478230 * q^73 - 12153360 * q^74 + 1715917770 * q^75 - 128288256 * q^76 - 193134048 * q^77 - 1199414208 * q^78 - 2098405449 * q^79 + 3082805319 * q^81 + 961326576 * q^82 + 358330707 * q^83 + 502249728 * q^84 - 1961566422 * q^85 - 588638592 * q^86 - 1222269090 * q^87 - 226185216 * q^88 - 368108670 * q^89 + 1740707616 * q^90 - 3296437032 * q^91 - 819648768 * q^92 + 6597152658 * q^93 + 2953278144 * q^94 - 881990403 * q^95 + 509607936 * q^96 - 3752161206 * q^97 - 458055696 * q^98 + 6061589742 * q^99

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