LMFDB - Embedded newform 5.17.c.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,17,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 17, names="a")

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 17 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, degree $2$, 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:	$8.11622719283$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 354217 x^{12} + 47647865256 x^{10} + \cdots + 84\!\cdots\!36 $ x^14 + 354217x^12 + 47647865256x^10 + 3062948254140560x^8 + 97982926395671183360x^6 + 1450505914836224854327296x^4 + 7749363027207208037244731392x^2 + 8484029084015876402584471207936
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{34}\cdot 3^{10}\cdot 5^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.6
Root			$233.161i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.17.c.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(233.161 + 233.161i) q^{2} +(-4708.07 + 4708.07i) q^{3} +43191.7i q^{4} +(-387973. - 45440.9i) q^{5} -2.19547e6 q^{6} +(-216284. - 216284. i) q^{7} +(5.20981e6 - 5.20981e6i) q^{8} -1.28506e6i q^{9} +O(q^{10})$	\(q+(233.161 + 233.161i) q^{2} +(-4708.07 + 4708.07i) q^{3} +43191.7i q^{4} +(-387973. - 45440.9i) q^{5} -2.19547e6 q^{6} +(-216284. - 216284. i) q^{7} +(5.20981e6 - 5.20981e6i) q^{8} -1.28506e6i q^{9} +(-7.98650e7 - 1.01055e8i) q^{10} -2.53185e8 q^{11} +(-2.03349e8 - 2.03349e8i) q^{12} +(-7.01806e8 + 7.01806e8i) q^{13} -1.00858e8i q^{14} +(2.04054e9 - 1.61266e9i) q^{15} +5.26006e9 q^{16} +(1.16211e9 + 1.16211e9i) q^{17} +(2.99625e8 - 2.99625e8i) q^{18} +3.15847e10i q^{19} +(1.96267e9 - 1.67572e10i) q^{20} +2.03656e9 q^{21} +(-5.90327e10 - 5.90327e10i) q^{22} +(2.72162e10 - 2.72162e10i) q^{23} +4.90563e10i q^{24} +(1.48458e11 + 3.52597e10i) q^{25} -3.27267e11 q^{26} +(-1.96617e11 - 1.96617e11i) q^{27} +(9.34167e9 - 9.34167e9i) q^{28} +2.93982e11i q^{29} +(8.51783e11 + 9.97642e10i) q^{30} -2.25922e11 q^{31} +(8.85007e11 + 8.85007e11i) q^{32} +(1.19201e12 - 1.19201e12i) q^{33} +5.41915e11i q^{34} +(7.40841e10 + 9.37404e10i) q^{35} +5.55039e10 q^{36} +(-4.39223e12 - 4.39223e12i) q^{37} +(-7.36430e12 + 7.36430e12i) q^{38} -6.60830e12i q^{39} +(-2.25800e12 + 1.78453e12i) q^{40} +1.29852e13 q^{41} +(4.74845e11 + 4.74845e11i) q^{42} +(-1.86284e12 + 1.86284e12i) q^{43} -1.09355e13i q^{44} +(-5.83943e10 + 4.98568e11i) q^{45} +1.26915e13 q^{46} +(1.81805e13 + 1.81805e13i) q^{47} +(-2.47647e13 + 2.47647e13i) q^{48} -3.31394e13i q^{49} +(2.63934e13 + 4.28358e13i) q^{50} -1.09426e13 q^{51} +(-3.03122e13 - 3.03122e13i) q^{52} +(-1.95823e13 + 1.95823e13i) q^{53} -9.16865e13i q^{54} +(9.82289e13 + 1.15050e13i) q^{55} -2.25360e12 q^{56} +(-1.48703e14 - 1.48703e14i) q^{57} +(-6.85451e13 + 6.85451e13i) q^{58} +1.51945e14i q^{59} +(6.96537e13 + 8.81344e13i) q^{60} -6.79450e13 q^{61} +(-5.26760e13 - 5.26760e13i) q^{62} +(-2.77938e11 + 2.77938e11i) q^{63} +6.79747e13i q^{64} +(3.04173e14 - 2.40391e14i) q^{65} +5.55860e14 q^{66} +(6.76181e13 + 6.76181e13i) q^{67} +(-5.01934e13 + 5.01934e13i) q^{68} +2.56271e14i q^{69} +(-4.58307e12 + 3.91301e13i) q^{70} -2.56703e14 q^{71} +(-6.69492e12 - 6.69492e12i) q^{72} +(-7.68501e14 + 7.68501e14i) q^{73} -2.04819e15i q^{74} +(-8.64956e14 + 5.32946e14i) q^{75} -1.36420e15 q^{76} +(5.47598e13 + 5.47598e13i) q^{77} +(1.54080e15 - 1.54080e15i) q^{78} +1.48596e15i q^{79} +(-2.04076e15 - 2.39022e14i) q^{80} +1.90669e15 q^{81} +(3.02763e15 + 3.02763e15i) q^{82} +(1.97416e15 - 1.97416e15i) q^{83} +8.79624e13i q^{84} +(-3.98059e14 - 5.03673e14i) q^{85} -8.68684e14 q^{86} +(-1.38409e15 - 1.38409e15i) q^{87} +(-1.31905e15 + 1.31905e15i) q^{88} +2.36453e15i q^{89} +(-1.29862e14 + 1.02631e14i) q^{90} +3.03579e14 q^{91} +(1.17551e15 + 1.17551e15i) q^{92} +(1.06365e15 - 1.06365e15i) q^{93} +8.47797e15i q^{94} +(1.43524e15 - 1.22540e16i) q^{95} -8.33335e15 q^{96} +(-3.97508e15 - 3.97508e15i) q^{97} +(7.72679e15 - 7.72679e15i) q^{98} +3.25358e14i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) $ 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	233.161	+	233.161i	0.910783	+	0.910783i	0.996334	−	0.0855504i	$-0.0272649\pi$
$2$	233.161	+	233.161i	0.910783	+	0.910783i	−0.0855504	+	0.996334i	$0.527265\pi$
$3$	−4708.07	+	4708.07i	−0.717584	+	0.717584i	−0.968110	−	0.250526i	$-0.919396\pi$
$3$	−4708.07	+	4708.07i	−0.717584	+	0.717584i	0.250526	+	0.968110i	$0.419396\pi$
$4$			43191.7i			0.659053i
$5$	−387973.	−	45440.9i	−0.993211	−	0.116329i
$5$	−387973.	−	45440.9i	−0.993211	−	0.116329i
$6$	−2.19547e6			−1.30713
$7$	−216284.	−	216284.i	−0.0375180	−	0.0375180i	0.688099	−	0.725617i	$-0.258446\pi$
$7$	−216284.	−	216284.i	−0.0375180	−	0.0375180i	−0.725617	+	0.688099i	$0.758446\pi$
$8$	5.20981e6	−	5.20981e6i	0.310529	−	0.310529i
$9$		−	1.28506e6i		−	0.0298527i
$10$	−7.98650e7	−	1.01055e8i	−0.798650	−	1.01055i
$11$	−2.53185e8			−1.18113			−0.590563	−	0.806991i	$-0.701094\pi$
$11$	−2.53185e8			−1.18113			−0.590563	+	0.806991i	$0.701094\pi$
$12$	−2.03349e8	−	2.03349e8i	−0.472926	−	0.472926i
$13$	−7.01806e8	+	7.01806e8i	−0.860341	+	0.860341i	−0.991378	−	0.131037i	$-0.958169\pi$
$13$	−7.01806e8	+	7.01806e8i	−0.860341	+	0.860341i	0.131037	+	0.991378i	$0.458169\pi$
$14$		−	1.00858e8i		−	0.0683416i
$15$	2.04054e9	−	1.61266e9i	0.796187	−	0.629236i
$16$	5.26006e9			1.22470
$17$	1.16211e9	+	1.16211e9i	0.166592	+	0.166592i	0.785480	−	0.618887i	$-0.212416\pi$
$17$	1.16211e9	+	1.16211e9i	0.166592	+	0.166592i	−0.618887	+	0.785480i	$0.712416\pi$
$18$	2.99625e8	−	2.99625e8i	0.0271893	−	0.0271893i
$19$			3.15847e10i			1.85972i	0.367913	+	0.929860i	$0.380073\pi$
$19$			3.15847e10i			1.85972i	−0.367913	+	0.929860i	$0.619927\pi$
$20$	1.96267e9	−	1.67572e10i	0.0766668	−	0.654579i
$21$	2.03656e9			0.0538446
$22$	−5.90327e10	−	5.90327e10i	−1.07575	−	1.07575i
$23$	2.72162e10	−	2.72162e10i	0.347540	−	0.347540i	−0.511652	−	0.859192i	$-0.670966\pi$
$23$	2.72162e10	−	2.72162e10i	0.347540	−	0.347540i	0.859192	+	0.511652i	$0.170966\pi$
$24$			4.90563e10i			0.445661i
$25$	1.48458e11	+	3.52597e10i	0.972935	+	0.231078i
$26$	−3.27267e11			−1.56717
$27$	−1.96617e11	−	1.96617e11i	−0.696162	−	0.696162i
$28$	9.34167e9	−	9.34167e9i	0.0247264	−	0.0247264i
$29$			2.93982e11i			0.587675i	0.955855	+	0.293838i	$0.0949325\pi$
$29$			2.93982e11i			0.587675i	−0.955855	+	0.293838i	$0.905067\pi$
$30$	8.51783e11	+	9.97642e10i	1.29825	+	0.152056i
$31$	−2.25922e11			−0.264889			−0.132445	−	0.991190i	$-0.542283\pi$
$31$	−2.25922e11			−0.264889			−0.132445	+	0.991190i	$0.542283\pi$
$32$	8.85007e11	+	8.85007e11i	0.804910	+	0.804910i
$33$	1.19201e12	−	1.19201e12i	0.847557	−	0.847557i
$34$			5.41915e11i			0.303459i
$35$	7.40841e10	+	9.37404e10i	0.0328989	+	0.0416277i
$36$	5.55039e10			0.0196745
$37$	−4.39223e12	−	4.39223e12i	−1.25046	−	1.25046i	−0.955513	−	0.294950i	$-0.904697\pi$
$37$	−4.39223e12	−	4.39223e12i	−1.25046	−	1.25046i	−0.294950	−	0.955513i	$-0.595303\pi$
$38$	−7.36430e12	+	7.36430e12i	−1.69380	+	1.69380i
$39$		−	6.60830e12i		−	1.23473i
$40$	−2.25800e12	+	1.78453e12i	−0.344544	+	0.272297i
$41$	1.29852e13			1.62621			0.813106	−	0.582116i	$-0.197775\pi$
$41$	1.29852e13			1.62621			0.813106	+	0.582116i	$0.197775\pi$
$42$	4.74845e11	+	4.74845e11i	0.0490408	+	0.0490408i
$43$	−1.86284e12	+	1.86284e12i	−0.159378	+	0.159378i	−0.782291	−	0.622913i	$-0.785949\pi$
$43$	−1.86284e12	+	1.86284e12i	−0.159378	+	0.159378i	0.622913	+	0.782291i	$0.285949\pi$
$44$		−	1.09355e13i		−	0.778425i
$45$	−5.83943e10	+	4.98568e11i	−0.00347272	+	0.0296500i
$46$	1.26915e13			0.633067
$47$	1.81805e13	+	1.81805e13i	0.763526	+	0.763526i	0.976958	−	0.213432i	$-0.0684640\pi$
$47$	1.81805e13	+	1.81805e13i	0.763526	+	0.763526i	−0.213432	+	0.976958i	$0.568464\pi$
$48$	−2.47647e13	+	2.47647e13i	−0.878826	+	0.878826i
$49$		−	3.31394e13i		−	0.997185i
$50$	2.63934e13	+	4.28358e13i	0.675671	+	1.09660i
$51$	−1.09426e13			−0.239088
$52$	−3.03122e13	−	3.03122e13i	−0.567010	−	0.567010i
$53$	−1.95823e13	+	1.95823e13i	−0.314527	+	0.314527i	−0.846660	−	0.532134i	$-0.821390\pi$
$53$	−1.95823e13	+	1.95823e13i	−0.314527	+	0.314527i	0.532134	+	0.846660i	$0.321390\pi$
$54$		−	9.16865e13i		−	1.26811i
$55$	9.82289e13	+	1.15050e13i	1.17311	+	0.137399i
$56$	−2.25360e12			−0.0233008
$57$	−1.48703e14	−	1.48703e14i	−1.33451	−	1.33451i
$58$	−6.85451e13	+	6.85451e13i	−0.535245	+	0.535245i
$59$			1.51945e14i			1.03483i	0.855734	+	0.517416i	$0.173106\pi$
$59$			1.51945e14i			1.03483i	−0.855734	+	0.517416i	$0.826894\pi$
$60$	6.96537e13	+	8.81344e13i	0.414700	+	0.524730i
$61$	−6.79450e13			−0.354420			−0.177210	−	0.984173i	$-0.556707\pi$
$61$	−6.79450e13			−0.354420			−0.177210	+	0.984173i	$0.556707\pi$
$62$	−5.26760e13	−	5.26760e13i	−0.241257	−	0.241257i
$63$	−2.77938e11	+	2.77938e11i	−0.00112001	+	0.00112001i
$64$			6.79747e13i			0.241494i
$65$	3.04173e14	−	2.40391e14i	0.954582	−	0.754417i
$66$	5.55860e14			1.54388
$67$	6.76181e13	+	6.76181e13i	0.166519	+	0.166519i	0.785448	−	0.618928i	$-0.212433\pi$
$67$	6.76181e13	+	6.76181e13i	0.166519	+	0.166519i	−0.618928	+	0.785448i	$0.712433\pi$
$68$	−5.01934e13	+	5.01934e13i	−0.109793	+	0.109793i
$69$			2.56271e14i			0.498778i
$70$	−4.58307e12	+	3.91301e13i	−0.00795009	+	0.0678776i
$71$	−2.56703e14			−0.397525			−0.198763	−	0.980048i	$-0.563692\pi$
$71$	−2.56703e14			−0.397525			−0.198763	+	0.980048i	$0.563692\pi$
$72$	−6.69492e12	−	6.69492e12i	−0.00927012	−	0.00927012i
$73$	−7.68501e14	+	7.68501e14i	−0.952932	+	0.952932i	−0.998941	−	0.0460093i	$-0.985350\pi$
$73$	−7.68501e14	+	7.68501e14i	−0.952932	+	0.952932i	0.0460093	+	0.998941i	$0.485350\pi$
$74$		−	2.04819e15i		−	2.27780i
$75$	−8.64956e14	+	5.32946e14i	−0.863980	+	0.532345i
$76$	−1.36420e15			−1.22565
$77$	5.47598e13	+	5.47598e13i	0.0443135	+	0.0443135i
$78$	1.54080e15	−	1.54080e15i	1.12457	−	1.12457i
$79$			1.48596e15i			0.979468i	0.871872	+	0.489734i	$0.162906\pi$
$79$			1.48596e15i			0.979468i	−0.871872	+	0.489734i	$0.837094\pi$
$80$	−2.04076e15	−	2.39022e14i	−1.21639	−	0.142468i
$81$	1.90669e15			1.02896
$82$	3.02763e15	+	3.02763e15i	1.48113	+	1.48113i
$83$	1.97416e15	−	1.97416e15i	0.876511	−	0.876511i	−0.116661	−	0.993172i	$-0.537219\pi$
$83$	1.97416e15	−	1.97416e15i	0.876511	−	0.876511i	0.993172	+	0.116661i	$0.0372190\pi$
$84$			8.79624e13i			0.0354865i
$85$	−3.98059e14	−	5.03673e14i	−0.146082	−	0.184841i
$86$	−8.68684e14			−0.290318
$87$	−1.38409e15	−	1.38409e15i	−0.421706	−	0.421706i
$88$	−1.31905e15	+	1.31905e15i	−0.366774	+	0.366774i
$89$			2.36453e15i			0.600655i	0.953836	+	0.300328i	$0.0970960\pi$
$89$			2.36453e15i			0.600655i	−0.953836	+	0.300328i	$0.902904\pi$
$90$	−1.29862e14	+	1.02631e14i	−0.0301676	+	0.0238418i
$91$	3.03579e14			0.0645565
$92$	1.17551e15	+	1.17551e15i	0.229047	+	0.229047i
$93$	1.06365e15	−	1.06365e15i	0.190080	−	0.190080i
$94$			8.47797e15i			1.39081i
$95$	1.43524e15	−	1.22540e16i	0.216339	−	1.84709i
$96$	−8.33335e15			−1.15518
$97$	−3.97508e15	−	3.97508e15i	−0.507191	−	0.507191i	0.406472	−	0.913663i	$-0.366759\pi$
$97$	−3.97508e15	−	3.97508e15i	−0.507191	−	0.507191i	−0.913663	+	0.406472i	$0.866759\pi$
$98$	7.72679e15	−	7.72679e15i	0.908219	−	0.908219i
$99$			3.25358e14i			0.0352598i
$100$	−1.52293e15	+	6.41216e15i	−0.152293	+	0.641216i
$101$	−1.13638e15			−0.104943			−0.0524713	−	0.998622i	$-0.516710\pi$
$101$	−1.13638e15			−0.104943			−0.0524713	+	0.998622i	$0.516710\pi$
$102$	−2.55137e15	−	2.55137e15i	−0.217757	−	0.217757i
$103$	−5.35479e15	+	5.35479e15i	−0.422712	+	0.422712i	−0.886137	−	0.463424i	$-0.846621\pi$
$103$	−5.35479e15	+	5.35479e15i	−0.422712	+	0.422712i	0.463424	+	0.886137i	$0.346621\pi$
$104$			7.31256e15i			0.534321i
$105$	−7.90129e14	−	9.25431e13i	−0.0534791	−	0.00626368i
$106$	−9.13165e15			−0.572931
$107$	7.94958e15	+	7.94958e15i	0.462673	+	0.462673i	0.899531	−	0.436858i	$-0.143909\pi$
$107$	7.94958e15	+	7.94958e15i	0.462673	+	0.462673i	−0.436858	+	0.899531i	$0.643909\pi$
$108$	8.49221e15	−	8.49221e15i	0.458808	−	0.458808i
$109$		−	4.06535e15i		−	0.204026i	−0.994783	−	0.102013i	$-0.967472\pi$
$109$		−	4.06535e15i		−	0.204026i	0.994783	−	0.102013i	$-0.0325284\pi$
$110$	2.02206e16	+	2.55856e16i	0.943306	+	1.19359i
$111$	4.13578e16			1.79462
$112$	−1.13766e15	−	1.13766e15i	−0.0459484	−	0.0459484i
$113$	−1.22019e16	+	1.22019e16i	−0.458985	+	0.458985i	−0.898322	−	0.439337i	$-0.855213\pi$
$113$	−1.22019e16	+	1.22019e16i	−0.458985	+	0.458985i	0.439337	+	0.898322i	$0.355213\pi$
$114$		−	6.93433e16i		−	2.43089i
$115$	−1.17959e16	+	9.32242e15i	−0.385609	+	0.304752i
$116$	−1.26976e16			−0.387309
$117$	9.01863e14	+	9.01863e14i	0.0256835	+	0.0256835i
$118$	−3.54275e16	+	3.54275e16i	−0.942507	+	0.942507i
$119$		−	5.02690e14i		−	0.0125004i
$120$	2.22916e15	−	1.90325e16i	0.0518432	−	0.442635i
$121$	1.81529e16			0.395059
$122$	−1.58421e16	−	1.58421e16i	−0.322800	−	0.322800i
$123$	−6.11351e16	+	6.11351e16i	−1.16694	+	1.16694i
$124$		−	9.75794e15i		−	0.174576i
$125$	−5.59955e16	−	2.04259e16i	−0.939449	−	0.342690i
$126$	−1.29608e14			−0.00204018
$127$	−3.10647e16	−	3.10647e16i	−0.459026	−	0.459026i	0.439310	−	0.898336i	$-0.355223\pi$
$127$	−3.10647e16	−	3.10647e16i	−0.459026	−	0.459026i	−0.898336	+	0.439310i	$0.855223\pi$
$128$	4.21508e16	−	4.21508e16i	0.584960	−	0.584960i
$129$		−	1.75408e16i		−	0.228734i
$130$	1.26971e17	+	1.48713e16i	1.55653	+	0.182307i
$131$	9.03912e16			1.04221			0.521106	−	0.853492i	$-0.325520\pi$
$131$	9.03912e16			1.04221			0.521106	+	0.853492i	$0.325520\pi$
$132$	5.14850e16	+	5.14850e16i	0.558585	+	0.558585i
$133$	6.83126e15	−	6.83126e15i	0.0697730	−	0.0697730i
$134$			3.15318e16i			0.303326i
$135$	6.73475e16	+	8.52164e16i	0.610452	+	0.772419i
$136$	1.21087e16			0.103463
$137$	−1.01319e17	−	1.01319e17i	−0.816447	−	0.816447i	0.169145	−	0.985591i	$-0.445900\pi$
$137$	−1.01319e17	−	1.01319e17i	−0.816447	−	0.816447i	−0.985591	+	0.169145i	$0.945900\pi$
$138$	−5.97524e16	+	5.97524e16i	−0.454279	+	0.454279i
$139$			1.49380e17i			1.07195i	0.844235	+	0.535973i	$0.180055\pi$
$139$			1.49380e17i			1.07195i	−0.844235	+	0.535973i	$0.819945\pi$
$140$	−4.04881e15	+	3.19982e15i	−0.0274349	+	0.0216821i
$141$	−1.71190e17			−1.09579
$142$	−5.98531e16	−	5.98531e16i	−0.362059	−	0.362059i
$143$	1.77687e17	−	1.77687e17i	1.01617	−	1.01617i
$144$		−	6.75948e15i		−	0.0365606i
$145$	1.33588e16	−	1.14057e17i	0.0683636	−	0.583685i
$146$	−3.58368e17			−1.73583
$147$	1.56022e17	+	1.56022e17i	0.715564	+	0.715564i
$148$	1.89708e17	−	1.89708e17i	0.824121	−	0.824121i
$149$			6.04361e16i			0.248775i	0.992234	+	0.124387i	$0.0396966\pi$
$149$			6.04361e16i			0.248775i	−0.992234	+	0.124387i	$0.960303\pi$
$150$	−3.25936e17	−	7.74117e16i	−1.27175	−	0.302048i
$151$	4.23349e16			0.156633			0.0783164	−	0.996929i	$-0.475046\pi$
$151$	4.23349e16			0.156633			0.0783164	+	0.996929i	$0.475046\pi$
$152$	1.64550e17	+	1.64550e17i	0.577497	+	0.577497i
$153$	1.49338e15	−	1.49338e15i	0.00497322	−	0.00497322i
$154$			2.55357e16i			0.0807200i
$155$	8.76515e16	+	1.02661e16i	0.263091	+	0.0308142i
$156$	2.85424e17			0.813754
$157$	−1.60279e17	−	1.60279e17i	−0.434190	−	0.434190i	0.455861	−	0.890051i	$-0.349331\pi$
$157$	−1.60279e17	−	1.60279e17i	−0.434190	−	0.434190i	−0.890051	+	0.455861i	$0.849331\pi$
$158$	−3.46467e17	+	3.46467e17i	−0.892083	+	0.892083i
$159$		−	1.84390e17i		−	0.451398i
$160$	−3.03143e17	−	3.83575e17i	−0.705811	−	0.893079i
$161$	−1.17728e16			−0.0260780
$162$	4.44564e17	+	4.44564e17i	0.937161	+	0.937161i
$163$	3.37213e17	−	3.37213e17i	0.676711	−	0.676711i	−0.282544	−	0.959254i	$-0.591178\pi$
$163$	3.37213e17	−	3.37213e17i	0.676711	−	0.676711i	0.959254	+	0.282544i	$0.0911782\pi$
$164$			5.60852e17i			1.07176i
$165$	−5.16634e17	+	4.08302e17i	−0.940398	+	0.743207i
$166$	9.20592e17			1.59662
$167$	2.02119e17	+	2.02119e17i	0.334100	+	0.334100i	0.854141	−	0.520041i	$-0.174083\pi$
$167$	2.02119e17	+	2.02119e17i	0.334100	+	0.334100i	−0.520041	+	0.854141i	$0.674083\pi$
$168$	1.06101e16	−	1.06101e16i	0.0167203	−	0.0167203i
$169$		−	3.19648e17i		−	0.480372i
$170$	2.46251e16	−	2.10248e17i	0.0353010	−	0.301399i
$171$	4.05882e16			0.0555176
$172$	−8.04594e16	−	8.04594e16i	−0.105039	−	0.105039i
$173$	3.85861e17	−	3.85861e17i	0.480908	−	0.480908i	−0.424514	−	0.905422i	$-0.639555\pi$
$173$	3.85861e17	−	3.85861e17i	0.480908	−	0.480908i	0.905422	+	0.424514i	$0.139555\pi$
$174$		−	6.45430e17i		−	0.768166i
$175$	−2.44830e16	−	3.97352e16i	−0.0278330	−	0.0451722i
$176$	−1.33177e18			−1.44653
$177$	−7.15366e17	−	7.15366e17i	−0.742578	−	0.742578i
$178$	−5.51316e17	+	5.51316e17i	−0.547067	+	0.547067i
$179$			6.58055e17i			0.624364i	0.950022	+	0.312182i	$0.101060\pi$
$179$			6.58055e17i			0.624364i	−0.950022	+	0.312182i	$0.898940\pi$
$180$	−2.15340e16	−	2.52215e15i	−0.0195409	−	0.00228871i
$181$	−1.65266e18			−1.43468			−0.717338	−	0.696725i	$-0.754640\pi$
$181$	−1.65266e18			−1.43468			−0.717338	+	0.696725i	$0.754640\pi$
$182$	7.07826e16	+	7.07826e16i	0.0587970	+	0.0587970i
$183$	3.19889e17	−	3.19889e17i	0.254326	−	0.254326i
$184$		−	2.83582e17i		−	0.215842i
$185$	1.50448e18	+	1.90365e18i	1.09651	+	1.38744i
$186$	4.96004e17			0.346244
$187$	−2.94228e17	−	2.94228e17i	−0.196766	−	0.196766i
$188$	−7.85249e17	+	7.85249e17i	−0.503204	+	0.503204i
$189$			8.50500e16i			0.0522372i
$190$	3.19179e18	−	2.52251e18i	1.87934	−	1.48527i
$191$	2.23846e18			1.26381			0.631907	−	0.775044i	$-0.282272\pi$
$191$	2.23846e18			1.26381			0.631907	+	0.775044i	$0.282272\pi$
$192$	−3.20029e17	−	3.20029e17i	−0.173292	−	0.173292i
$193$	−6.67656e17	+	6.67656e17i	−0.346812	+	0.346812i	−0.858921	−	0.512109i	$-0.828864\pi$
$193$	−6.67656e17	+	6.67656e17i	−0.346812	+	0.346812i	0.512109	+	0.858921i	$0.328864\pi$
$194$		−	1.85366e18i		−	0.923883i
$195$	−3.00287e17	+	2.56384e18i	−0.143635	+	1.22635i
$196$	1.43135e18			0.657198
$197$	−1.14144e18	−	1.14144e18i	−0.503181	−	0.503181i	0.409244	−	0.912425i	$-0.365793\pi$
$197$	−1.14144e18	−	1.14144e18i	−0.503181	−	0.503181i	−0.912425	+	0.409244i	$0.865793\pi$
$198$	−7.58606e16	+	7.58606e16i	−0.0321140	+	0.0321140i
$199$			4.07863e18i			1.65840i	0.558950	+	0.829202i	$0.311205\pi$
$199$			4.07863e18i			1.65840i	−0.558950	+	0.829202i	$0.688795\pi$
$200$	9.57135e17	−	5.89742e17i	0.373881	−	0.230368i
$201$	−6.36701e17			−0.238983
$202$	−2.64959e17	−	2.64959e17i	−0.0955800	−	0.0955800i
$203$	6.35837e16	−	6.35837e16i	0.0220484	−	0.0220484i
$204$		−	4.72628e17i		−	0.157572i
$205$	−5.03790e18	−	5.90058e17i	−1.61517	−	0.189175i
$206$	−2.49705e18			−0.769999
$207$	−3.49744e16	−	3.49744e16i	−0.0103750	−	0.0103750i
$208$	−3.69154e18	+	3.69154e18i	−1.05366	+	1.05366i
$209$		−	7.99677e18i		−	2.19656i
$210$	−1.62650e17	−	2.05804e17i	−0.0430030	−	0.0544127i
$211$	7.42252e18			1.88926			0.944630	−	0.328137i	$-0.106421\pi$
$211$	7.42252e18			1.88926			0.944630	+	0.328137i	$0.106421\pi$
$212$	−8.45794e17	−	8.45794e17i	−0.207290	−	0.207290i
$213$	1.20858e18	−	1.20858e18i	0.285258	−	0.285258i
$214$			3.70706e18i			0.842789i
$215$	8.07383e17	−	6.38084e17i	0.176836	−	0.139756i
$216$	−2.04867e18			−0.432357
$217$	4.88632e16	+	4.88632e16i	0.00993811	+	0.00993811i
$218$	9.47880e17	−	9.47880e17i	0.185824	−	0.185824i
$219$		−	7.23631e18i		−	1.36762i
$220$	−4.96919e17	+	4.24267e18i	−0.0905532	+	0.773140i
$221$	−1.63115e18			−0.286652
$222$	9.64300e18	+	9.64300e18i	1.63451	+	1.63451i
$223$	−2.04883e18	+	2.04883e18i	−0.335017	+	0.335017i	−0.854488	−	0.519471i	$-0.826129\pi$
$223$	−2.04883e18	+	2.04883e18i	−0.335017	+	0.335017i	0.519471	+	0.854488i	$0.326129\pi$
$224$		−	3.82826e17i		−	0.0603972i
$225$	4.53108e16	−	1.90778e17i	0.00689829	−	0.0290447i
$226$	−5.68998e18			−0.836071
$227$	7.42603e17	+	7.42603e17i	0.105329	+	0.105329i	0.757808	−	0.652478i	$-0.226271\pi$
$227$	7.42603e17	+	7.42603e17i	0.105329	+	0.105329i	−0.652478	+	0.757808i	$0.726271\pi$
$228$	6.42273e18	−	6.42273e18i	0.879510	−	0.879510i
$229$			1.29359e19i			1.71046i	0.518250	+	0.855229i	$0.326584\pi$
$229$			1.29359e19i			1.71046i	−0.518250	+	0.855229i	$0.673416\pi$
$230$	−4.92395e18	−	5.76713e17i	−0.628769	−	0.0736440i
$231$	−5.15626e17			−0.0635973
$232$	1.53159e18	+	1.53159e18i	0.182490	+	0.182490i
$233$	1.05662e19	−	1.05662e19i	1.21638	−	1.21638i	0.247491	−	0.968890i	$-0.420394\pi$
$233$	1.05662e19	−	1.05662e19i	1.21638	−	1.21638i	0.968890	−	0.247491i	$-0.0796062\pi$
$234$			4.20558e17i			0.0467841i
$235$	−6.22742e18	−	7.87970e18i	−0.669523	−	0.847163i
$236$	−6.56275e18			−0.682009
$237$	−6.99600e18	−	6.99600e18i	−0.702850	−	0.702850i
$238$	1.17207e17	−	1.17207e17i	0.0113852	−	0.0113852i
$239$			1.54269e19i			1.44909i	0.689225	+	0.724547i	$0.257951\pi$
$239$			1.54269e19i			1.44909i	−0.689225	+	0.724547i	$0.742049\pi$
$240$	1.07334e19	−	8.48270e18i	0.975092	−	0.770627i
$241$	1.57004e19			1.37966			0.689832	−	0.723969i	$-0.257684\pi$
$241$	1.57004e19			1.37966			0.689832	+	0.723969i	$0.257684\pi$
$242$	4.23253e18	+	4.23253e18i	0.359813	+	0.359813i
$243$	−5.13103e17	+	5.13103e17i	−0.0422041	+	0.0422041i
$244$		−	2.93466e18i		−	0.233582i
$245$	−1.50588e18	+	1.28572e19i	−0.116001	+	0.990415i
$246$	−2.85086e19			−2.12566
$247$	−2.21663e19	−	2.21663e19i	−1.59999	−	1.59999i
$248$	−1.17701e18	+	1.17701e18i	−0.0822557	+	0.0822557i
$249$			1.85889e19i			1.25794i
$250$	−8.29343e18	−	1.78185e19i	−0.543518	−	1.16775i
$251$	1.82588e18			0.115899			0.0579497	−	0.998320i	$-0.481544\pi$
$251$	1.82588e18			0.115899			0.0579497	+	0.998320i	$0.481544\pi$
$252$	−1.20046e16	−	1.20046e16i	−0.000738148	−	0.000738148i
$253$	−6.89073e18	+	6.89073e18i	−0.410489	+	0.410489i
$254$		−	1.44861e19i		−	0.836147i
$255$	4.24542e18	+	4.97240e17i	0.237465	+	0.0278128i
$256$	2.41106e19			1.30704
$257$	1.91179e19	+	1.91179e19i	1.00456	+	1.00456i	0.999990	+	0.00456791i	$0.00145402\pi$
$257$	1.91179e19	+	1.91179e19i	1.00456	+	1.00456i	0.00456791	+	0.999990i	$0.498546\pi$
$258$	4.08982e18	−	4.08982e18i	0.208328	−	0.208328i
$259$			1.89993e18i			0.0938297i
$260$	1.03829e19	+	1.31377e19i	0.497201	+	0.629120i
$261$	3.77785e17			0.0175437
$262$	2.10757e19	+	2.10757e19i	0.949229	+	0.949229i
$263$	−7.11769e16	+	7.11769e16i	−0.00310952	+	0.00310952i	−0.708660	−	0.705550i	$-0.750700\pi$
$263$	−7.11769e16	+	7.11769e16i	−0.00310952	+	0.00310952i	0.705550	+	0.708660i	$0.250700\pi$
$264$		−	1.24203e19i		−	0.526382i
$265$	8.48725e18	−	6.70757e18i	0.348980	−	0.275803i
$266$	3.18556e18			0.127096
$267$	−1.11324e19	−	1.11324e19i	−0.431020	−	0.431020i
$268$	−2.92054e18	+	2.92054e18i	−0.109745	+	0.109745i
$269$		−	2.21772e19i		−	0.808888i	−0.914563	−	0.404444i	$-0.867465\pi$
$269$		−	2.21772e19i		−	0.808888i	0.914563	−	0.404444i	$-0.132535\pi$
$270$	−4.16632e18	+	3.55719e19i	−0.147517	+	1.25950i
$271$	7.78947e18			0.267765			0.133882	−	0.990997i	$-0.457256\pi$
$271$	7.78947e18			0.267765			0.133882	+	0.990997i	$0.457256\pi$
$272$	6.11275e18	+	6.11275e18i	0.204026	+	0.204026i
$273$	−1.42927e18	+	1.42927e18i	−0.0463247	+	0.0463247i
$274$		−	4.72473e19i		−	1.48721i
$275$	−3.75874e19	−	8.92722e18i	−1.14916	−	0.272932i
$276$	−1.10688e19			−0.328721
$277$	−8.30354e18	−	8.30354e18i	−0.239566	−	0.239566i	0.577104	−	0.816670i	$-0.304183\pi$
$277$	−8.30354e18	−	8.30354e18i	−0.239566	−	0.239566i	−0.816670	+	0.577104i	$0.804183\pi$
$278$	−3.48294e19	+	3.48294e19i	−0.976310	+	0.976310i
$279$			2.90323e17i			0.00790765i
$280$	8.74334e17	+	1.02405e17i	0.0231427	+	0.00271056i
$281$	−3.43677e19			−0.884097			−0.442048	−	0.896991i	$-0.645748\pi$
$281$	−3.43677e19			−0.884097			−0.442048	+	0.896991i	$0.645748\pi$
$282$	−3.99149e19	−	3.99149e19i	−0.998026	−	0.998026i
$283$	−3.24041e19	+	3.24041e19i	−0.787606	+	0.787606i	−0.981101	−	0.193495i	$-0.938018\pi$
$283$	−3.24041e19	+	3.24041e19i	−0.787606	+	0.787606i	0.193495	+	0.981101i	$0.438018\pi$
$284$		−	1.10875e19i		−	0.261990i
$285$	5.09355e19	+	6.44499e19i	1.17020	+	1.48069i
$286$	8.28591e19			1.85102
$287$	−2.80848e18	−	2.80848e18i	−0.0610122	−	0.0610122i
$288$	1.13729e18	−	1.13729e18i	0.0240287	−	0.0240287i
$289$		−	4.59602e19i		−	0.944494i
$290$	2.97084e19	−	2.34789e19i	0.593875	−	0.469347i
$291$	3.74299e19			0.727904
$292$	−3.31929e19	−	3.31929e19i	−0.628032	−	0.628032i
$293$	3.48850e19	−	3.48850e19i	0.642240	−	0.642240i	−0.308866	−	0.951106i	$-0.599949\pi$
$293$	3.48850e19	−	3.48850e19i	0.642240	−	0.642240i	0.951106	+	0.308866i	$0.0999494\pi$
$294$			7.27565e19i			1.30345i
$295$	6.90451e18	−	5.89505e19i	0.120381	−	1.02781i
$296$	−4.57653e19			−0.776610
$297$	4.97804e19	+	4.97804e19i	0.822255	+	0.822255i
$298$	−1.40913e19	+	1.40913e19i	−0.226580	+	0.226580i
$299$			3.82010e19i			0.598006i
$300$	−2.30188e19	−	3.73589e19i	−0.350843	−	0.569409i
$301$	8.05806e17			0.0119591
$302$	9.87083e18	+	9.87083e18i	0.142659	+	0.142659i
$303$	5.35014e18	−	5.35014e18i	0.0753051	−	0.0753051i
$304$			1.66137e20i			2.27760i
$305$	2.63608e19	+	3.08748e18i	0.352014	+	0.0412293i
$306$	6.96393e17			0.00905906
$307$	−6.57606e18	−	6.57606e18i	−0.0833410	−	0.0833410i	0.664207	−	0.747548i	$-0.268769\pi$
$307$	−6.57606e18	−	6.57606e18i	−0.0833410	−	0.0833410i	−0.747548	+	0.664207i	$0.768769\pi$
$308$	−2.36517e18	+	2.36517e18i	−0.0292049	+	0.0292049i
$309$		−	5.04214e19i		−	0.606663i
$310$	1.80432e19	+	2.28305e19i	0.211554	+	0.267684i
$311$	−9.49449e19			−1.08490			−0.542449	−	0.840089i	$-0.682503\pi$
$311$	−9.49449e19			−1.08490			−0.542449	+	0.840089i	$0.682503\pi$
$312$	−3.44280e19	−	3.44280e19i	−0.383420	−	0.383420i
$313$	7.84340e19	−	7.84340e19i	0.851432	−	0.851432i	−0.138878	−	0.990310i	$-0.544350\pi$
$313$	7.84340e19	−	7.84340e19i	0.851432	−	0.851432i	0.990310	+	0.138878i	$0.0443496\pi$
$314$		−	7.47416e19i		−	0.790907i
$315$	1.20462e17	−	9.52025e16i	0.00124270	−	0.000982119i
$316$	−6.41811e19			−0.645521
$317$	2.01965e19	+	2.01965e19i	0.198062	+	0.198062i	0.799169	−	0.601106i	$-0.205273\pi$
$317$	2.01965e19	+	2.01965e19i	0.198062	+	0.198062i	−0.601106	+	0.799169i	$0.705273\pi$
$318$	4.29924e19	−	4.29924e19i	0.411126	−	0.411126i
$319$		−	7.44319e19i		−	0.694119i
$320$	3.08883e18	−	2.63723e19i	0.0280928	−	0.239855i
$321$	−7.48543e19			−0.664013
$322$	−2.74496e18	−	2.74496e18i	−0.0237514	−	0.0237514i
$323$	−3.67048e19	+	3.67048e19i	−0.309815	+	0.309815i
$324$			8.23530e19i			0.678140i
$325$	−1.28934e20	+	7.94434e19i	−1.03586	+	0.638250i
$326$	1.57249e20			1.23267
$327$	1.91399e19	+	1.91399e19i	0.146406	+	0.146406i
$328$	6.76503e19	−	6.76503e19i	0.504986	−	0.504986i
$329$		−	7.86432e18i		−	0.0572920i
$330$	−2.15659e20	−	2.52588e19i	−1.53340	−	0.179598i
$331$	−7.85271e19			−0.544999			−0.272499	−	0.962156i	$-0.587850\pi$
$331$	−7.85271e19			−0.544999			−0.272499	+	0.962156i	$0.587850\pi$
$332$	8.52673e19	+	8.52673e19i	0.577667	+	0.577667i
$333$	−5.64427e18	+	5.64427e18i	−0.0373296	+	0.0373296i
$334$			9.42525e19i			0.608585i
$335$	−2.31614e19	−	2.93066e19i	−0.146018	−	0.184760i
$336$	1.07124e19			0.0659436
$337$	1.33989e20	+	1.33989e20i	0.805436	+	0.805436i	0.983939	−	0.178503i	$-0.0571254\pi$
$337$	1.33989e20	+	1.33989e20i	0.805436	+	0.805436i	−0.178503	+	0.983939i	$0.557125\pi$
$338$	7.45292e19	−	7.45292e19i	0.437515	−	0.437515i
$339$		−	1.14894e20i		−	0.658720i
$340$	2.17545e19	−	1.71928e19i	0.121820	−	0.0962756i
$341$	5.71999e19			0.312868
$342$	9.46357e18	+	9.46357e18i	0.0505645	+	0.0505645i
$343$	−1.43553e19	+	1.43553e19i	−0.0749304	+	0.0749304i
$344$			1.94101e19i			0.0989831i
$345$	1.16452e19	−	9.94264e19i	0.0580222	−	0.495392i
$346$	1.79935e20			0.876006
$347$	1.56577e20	+	1.56577e20i	0.744891	+	0.744891i	0.973515	−	0.228624i	$-0.0734226\pi$
$347$	1.56577e20	+	1.56577e20i	0.744891	+	0.744891i	−0.228624	+	0.973515i	$0.573423\pi$
$348$	5.97812e19	−	5.97812e19i	0.277927	−	0.277927i
$349$			1.32225e20i			0.600773i	0.953818	+	0.300386i	$0.0971156\pi$
$349$			1.32225e20i			0.600773i	−0.953818	+	0.300386i	$0.902884\pi$
$350$	3.55621e18	−	1.49731e19i	0.0157922	−	0.0664919i
$351$	2.75974e20			1.19787
$352$	−2.24071e20	−	2.24071e20i	−0.950700	−	0.950700i
$353$	−2.70100e20	+	2.70100e20i	−1.12028	+	1.12028i	−0.128582	+	0.991699i	$0.541043\pi$
$353$	−2.70100e20	+	2.70100e20i	−1.12028	+	1.12028i	−0.991699	+	0.128582i	$0.958957\pi$
$354$		−	3.33590e20i		−	1.35266i
$355$	9.95940e19	+	1.16648e19i	0.394826	+	0.0462436i
$356$	−1.02128e20			−0.395864
$357$	2.36670e18	+	2.36670e18i	0.00897010	+	0.00897010i
$358$	−1.53432e20	+	1.53432e20i	−0.568660	+	0.568660i
$359$			2.04375e20i			0.740752i	0.928882	+	0.370376i	$0.120771\pi$
$359$			2.04375e20i			0.740752i	−0.928882	+	0.370376i	$0.879229\pi$
$360$	2.29322e18	+	2.90167e18i	0.00812880	+	0.0102856i
$361$	−7.09151e20			−2.45856
$362$	−3.85334e20	−	3.85334e20i	−1.30668	−	1.30668i
$363$	−8.54649e19	+	8.54649e19i	−0.283488	+	0.283488i
$364$			1.31121e19i			0.0425462i
$365$	3.33079e20	−	2.63236e20i	1.05732	−	0.835609i
$366$	1.49171e20			0.463272
$367$	−1.44158e20	−	1.44158e20i	−0.438036	−	0.438036i	0.453314	−	0.891351i	$-0.350241\pi$
$367$	−1.44158e20	−	1.44158e20i	−0.438036	−	0.438036i	−0.891351	+	0.453314i	$0.850241\pi$
$368$	1.43159e20	−	1.43159e20i	0.425633	−	0.425633i
$369$		−	1.66867e19i		−	0.0485467i
$370$	−9.30715e19	+	7.94641e20i	−0.264974	+	2.26234i
$371$	8.47068e18			0.0236008
$372$	4.59410e19	+	4.59410e19i	0.125273	+	0.125273i
$373$	2.02567e20	−	2.02567e20i	0.540628	−	0.540628i	−0.383085	−	0.923713i	$-0.625138\pi$
$373$	2.02567e20	−	2.02567e20i	0.540628	−	0.540628i	0.923713	+	0.383085i	$0.125138\pi$
$374$		−	1.37205e20i		−	0.358423i
$375$	3.59797e20	−	1.67464e20i	0.920041	−	0.428225i
$376$	1.89434e20			0.474194
$377$	−2.06319e20	−	2.06319e20i	−0.505601	−	0.505601i
$378$	−1.98303e19	+	1.98303e19i	−0.0475768	+	0.0475768i
$379$			1.52768e20i			0.358854i	0.983771	+	0.179427i	$0.0574243\pi$
$379$			1.52768e20i			0.358854i	−0.983771	+	0.179427i	$0.942576\pi$
$380$	5.29271e20	+	6.19903e19i	1.21733	+	0.142579i
$381$	2.92509e20			0.658779
$382$	5.21922e20	+	5.21922e20i	1.15106	+	1.15106i
$383$	−1.35683e19	+	1.35683e19i	−0.0293045	+	0.0293045i	−0.721607	−	0.692303i	$-0.756596\pi$
$383$	−1.35683e19	+	1.35683e19i	−0.0293045	+	0.0293045i	0.692303	+	0.721607i	$0.256596\pi$
$384$			3.96898e20i			0.839516i
$385$	−1.87570e19	−	2.37337e19i	−0.0388577	−	0.0491676i
$386$	−3.11342e20			−0.631741
$387$	2.39387e18	+	2.39387e18i	0.00475786	+	0.00475786i
$388$	1.71690e20	−	1.71690e20i	0.334266	−	0.334266i
$389$		−	6.31752e20i		−	1.20490i	−0.798158	−	0.602448i	$-0.794192\pi$
$389$		−	6.31752e20i		−	1.20490i	0.798158	−	0.602448i	$-0.205808\pi$
$390$	−6.67802e20	+	5.27772e20i	−1.24776	+	0.986119i
$391$	6.32563e19			0.115795
$392$	−1.72650e20	−	1.72650e20i	−0.309655	−	0.309655i
$393$	−4.25568e20	+	4.25568e20i	−0.747874	+	0.747874i
$394$		−	5.32279e20i		−	0.916578i
$395$	6.75234e19	−	5.76512e20i	0.113940	−	0.972818i
$396$	−1.40527e19			−0.0232381
$397$	−3.62124e20	−	3.62124e20i	−0.586859	−	0.586859i	0.349921	−	0.936779i	$-0.386209\pi$
$397$	−3.62124e20	−	3.62124e20i	−0.586859	−	0.586859i	−0.936779	+	0.349921i	$0.886209\pi$
$398$	−9.50977e20	+	9.50977e20i	−1.51045	+	1.51045i
$399$			6.43240e19i			0.100136i
$400$	7.80898e20	+	1.85468e20i	1.19156	+	0.283002i
$401$	5.76968e20			0.862971			0.431486	−	0.902120i	$-0.357990\pi$
$401$	5.76968e20			0.862971			0.431486	+	0.902120i	$0.357990\pi$
$402$	−1.48454e20	−	1.48454e20i	−0.217662	−	0.217662i
$403$	1.58553e20	−	1.58553e20i	0.227895	−	0.227895i
$404$		−	4.90821e19i		−	0.0691627i
$405$	−7.39743e20	−	8.66416e19i	−1.02198	−	0.119698i
$406$	2.96504e19			0.0401626
$407$	1.11205e21	+	1.11205e21i	1.47695	+	1.47695i
$408$	−5.70086e19	+	5.70086e19i	−0.0742437	+	0.0742437i
$409$		−	5.62087e20i		−	0.717822i	−0.933372	−	0.358911i	$-0.883148\pi$
$409$		−	5.62087e20i		−	0.717822i	0.933372	−	0.358911i	$-0.116852\pi$
$410$	−1.03706e21	−	1.31222e21i	−1.29877	−	1.64337i
$411$	9.54036e20			1.17174
$412$	−2.31283e20	−	2.31283e20i	−0.278590	−	0.278590i
$413$	3.28632e19	−	3.28632e19i	0.0388248	−	0.0388248i
$414$		−	1.63093e19i		−	0.0188988i
$415$	−8.55628e20	+	6.76213e20i	−0.972524	+	0.768597i
$416$	−1.24221e21			−1.38499
$417$	−7.03289e20	−	7.03289e20i	−0.769210	−	0.769210i
$418$	1.86453e21	−	1.86453e21i	2.00060	−	2.00060i
$419$			1.16901e21i			1.23057i	0.788306	+	0.615283i	$0.210958\pi$
$419$			1.16901e21i			1.23057i	−0.788306	+	0.615283i	$0.789042\pi$
$420$	3.99709e18	−	3.41270e19i	0.00412810	−	0.0352455i
$421$	−6.22667e20			−0.630956			−0.315478	−	0.948933i	$-0.602165\pi$
$421$	−6.22667e20			−0.630956			−0.315478	+	0.948933i	$0.602165\pi$
$422$	1.73064e21	+	1.73064e21i	1.72071	+	1.72071i
$423$	2.33631e19	−	2.33631e19i	0.0227933	−	0.0227933i
$424$			2.04040e20i			0.195339i
$425$	1.31549e20	+	2.13500e20i	0.123588	+	0.200579i
$426$	5.63585e20			0.519616
$427$	1.46954e19	+	1.46954e19i	0.0132971	+	0.0132971i
$428$	−3.43356e20	+	3.43356e20i	−0.304926	+	0.304926i
$429$			1.67312e21i			1.45838i
$430$	3.37026e20	+	3.94738e19i	0.288347	+	0.0337723i
$431$	−4.88546e20			−0.410286			−0.205143	−	0.978732i	$-0.565766\pi$
$431$	−4.88546e20			−0.410286			−0.205143	+	0.978732i	$0.565766\pi$
$432$	−1.03421e21	−	1.03421e21i	−0.852591	−	0.852591i
$433$	−3.75339e20	+	3.75339e20i	−0.303753	+	0.303753i	−0.842480	−	0.538727i	$-0.818905\pi$
$433$	−3.75339e20	+	3.75339e20i	−0.303753	+	0.303753i	0.538727	+	0.842480i	$0.318905\pi$
$434$			2.27859e19i			0.0181029i
$435$	4.74095e20	+	5.99883e20i	0.369787	+	0.467900i
$436$	1.75589e20			0.134464
$437$	8.59615e20	+	8.59615e20i	0.646327	+	0.646327i
$438$	1.68722e21	−	1.68722e21i	1.24560	−	1.24560i
$439$		−	1.74040e21i		−	1.26163i	−0.775931	−	0.630817i	$-0.782720\pi$
$439$		−	1.74040e21i		−	1.26163i	0.775931	−	0.630817i	$-0.217280\pi$
$440$	5.71693e20	−	4.51815e20i	0.406950	−	0.321617i
$441$	−4.25861e19			−0.0297686
$442$	−3.80319e20	−	3.80319e20i	−0.261078	−	0.261078i
$443$	8.67734e20	−	8.67734e20i	0.585001	−	0.585001i	−0.351272	−	0.936273i	$-0.614251\pi$
$443$	8.67734e20	−	8.67734e20i	0.585001	−	0.585001i	0.936273	+	0.351272i	$0.114251\pi$
$444$			1.78631e21i			1.18275i
$445$	1.07447e20	−	9.17374e20i	0.0698735	−	0.596577i
$446$	−9.55413e20			−0.610256
$447$	−2.84537e20	−	2.84537e20i	−0.178517	−	0.178517i
$448$	1.47018e19	−	1.47018e19i	0.00906039	−	0.00906039i
$449$			1.62407e20i			0.0983180i	0.998791	+	0.0491590i	$0.0156541\pi$
$449$			1.62407e20i			0.0983180i	−0.998791	+	0.0491590i	$0.984346\pi$
$450$	5.50465e19	−	3.39171e19i	0.0327363	−	0.0201706i
$451$	−3.28765e21			−1.92076
$452$	−5.27019e20	−	5.27019e20i	−0.302495	−	0.302495i
$453$	−1.99315e20	+	1.99315e20i	−0.112397	+	0.112397i
$454$			3.46291e20i			0.191865i
$455$	−1.17780e20	−	1.37949e19i	−0.0641182	−	0.00750978i
$456$	−1.54943e21			−0.828805
$457$	6.79023e19	+	6.79023e19i	0.0356907	+	0.0356907i	0.724727	−	0.689036i	$-0.241966\pi$
$457$	6.79023e19	+	6.79023e19i	0.0356907	+	0.0356907i	−0.689036	+	0.724727i	$0.741966\pi$
$458$	−3.01614e21	+	3.01614e21i	−1.55786	+	1.55786i
$459$		−	4.56979e20i		−	0.231950i
$460$	−4.02651e20	−	5.09484e20i	−0.200847	−	0.254137i
$461$	1.55877e21			0.764144			0.382072	−	0.924133i	$-0.375211\pi$
$461$	1.55877e21			0.764144			0.382072	+	0.924133i	$0.375211\pi$
$462$	−1.20224e20	−	1.20224e20i	−0.0579234	−	0.0579234i
$463$	1.09934e21	−	1.09934e21i	0.520575	−	0.520575i	−0.397170	−	0.917745i	$-0.630008\pi$
$463$	1.09934e21	−	1.09934e21i	0.520575	−	0.520575i	0.917745	+	0.397170i	$0.130008\pi$
$464$			1.54636e21i			0.719727i
$465$	−4.61002e20	+	3.64335e20i	−0.210901	+	0.166678i
$466$	4.92722e21			2.21572
$467$	−1.12075e21	−	1.12075e21i	−0.495419	−	0.495419i	0.414590	−	0.910008i	$-0.363925\pi$
$467$	−1.12075e21	−	1.12075e21i	−0.495419	−	0.495419i	−0.910008	+	0.414590i	$0.863925\pi$
$468$	−3.89530e19	+	3.89530e19i	−0.0169268	+	0.0169268i
$469$		−	2.92494e19i		−	0.0124949i
$470$	3.85247e20	−	3.28922e21i	0.161792	−	1.38137i
$471$	1.50921e21			0.623136
$472$	7.91603e20	+	7.91603e20i	0.321345	+	0.321345i
$473$	4.71644e20	−	4.71644e20i	0.188246	−	0.188246i
$474$		−	3.26238e21i		−	1.28029i
$475$	−1.11367e21	+	4.68900e21i	−0.429741	+	1.80939i
$476$	2.17120e19			0.00823844
$477$	2.51645e19	+	2.51645e19i	0.00938946	+	0.00938946i
$478$	−3.59696e21	+	3.59696e21i	−1.31981	+	1.31981i
$479$		−	4.21827e21i		−	1.52212i	−0.648679	−	0.761062i	$-0.724678\pi$
$479$		−	4.21827e21i		−	1.52212i	0.648679	−	0.761062i	$-0.275322\pi$
$480$	3.23311e21	+	3.78675e20i	1.14734	+	0.134381i
$481$	6.16498e21			2.15165
$482$	3.66071e21	+	3.66071e21i	1.25658	+	1.25658i
$483$	5.54274e19	−	5.54274e19i	0.0187132	−	0.0187132i
$484$			7.84053e20i			0.260365i
$485$	1.36159e21	+	1.72285e21i	0.444747	+	0.562749i
$486$	−2.39271e20			−0.0768775
$487$	−3.00770e21	−	3.00770e21i	−0.950612	−	0.950612i	0.0482245	−	0.998837i	$-0.484644\pi$
$487$	−3.00770e21	−	3.00770e21i	−0.950612	−	0.950612i	−0.998837	+	0.0482245i	$0.984644\pi$
$488$	−3.53980e20	+	3.53980e20i	−0.110058	+	0.110058i
$489$			3.17524e21i			0.971193i
$490$	−3.34890e21	+	2.64667e21i	−1.00771	+	0.796401i
$491$	−4.69568e21			−1.39010			−0.695051	−	0.718961i	$-0.744618\pi$
$491$	−4.69568e21			−1.39010			−0.695051	+	0.718961i	$0.744618\pi$
$492$	−2.64053e21	−	2.64053e21i	−0.769077	−	0.769077i
$493$	−3.41639e20	+	3.41639e20i	−0.0979022	+	0.0979022i
$494$		−	1.03366e22i		−	2.91449i
$495$	1.47846e19	−	1.26230e20i	0.00410173	−	0.0350204i
$496$	−1.18836e21			−0.324410
$497$	5.55208e19	+	5.55208e19i	0.0149144	+	0.0149144i
$498$	−4.33421e21	+	4.33421e21i	−1.14571	+	1.14571i
$499$			1.82134e21i			0.473790i	0.971535	+	0.236895i	$0.0761297\pi$
$499$			1.82134e21i			0.473790i	−0.971535	+	0.236895i	$0.923870\pi$
$500$	8.82229e20	−	2.41854e21i	0.225851	−	0.619146i
$501$	−1.90318e21			−0.479489
$502$	4.25722e20	+	4.25722e20i	0.105559	+	0.105559i
$503$	2.10799e21	−	2.10799e21i	0.514427	−	0.514427i	−0.401452	−	0.915880i	$-0.631494\pi$
$503$	2.10799e21	−	2.10799e21i	0.514427	−	0.514427i	0.915880	+	0.401452i	$0.131494\pi$
$504$			2.89600e18i			0.000695592i
$505$	4.40884e20	+	5.16381e19i	0.104230	+	0.0122078i
$506$	−3.21329e21			−0.747733
$507$	1.50492e21	+	1.50492e21i	0.344707	+	0.344707i
$508$	1.34174e21	−	1.34174e21i	0.302523	−	0.302523i
$509$		−	2.90249e21i		−	0.644213i	−0.946704	−	0.322106i	$-0.895609\pi$
$509$		−	2.90249e21i		−	0.644213i	0.946704	−	0.322106i	$-0.104391\pi$
$510$	8.73927e20	+	1.10580e21i	0.190947	+	0.241610i
$511$	3.32429e20			0.0715042
$512$	2.85925e21	+	2.85925e21i	0.605469	+	0.605469i
$513$	6.21008e21	−	6.21008e21i	1.29467	−	1.29467i
$514$			8.91507e21i			1.82987i
$515$	2.32084e21	−	1.83419e21i	0.469016	−	0.370669i
$516$	7.57617e20			0.150748
$517$	−4.60304e21	−	4.60304e21i	−0.901821	−	0.901821i
$518$	−4.42990e20	+	4.42990e20i	−0.0854586	+	0.0854586i
$519$			3.63332e21i			0.690184i
$520$	3.32289e20	−	2.83707e21i	0.0621569	−	0.530694i
$521$	1.23070e21			0.226699			0.113349	−	0.993555i	$-0.463842\pi$
$521$	1.23070e21			0.226699			0.113349	+	0.993555i	$0.463842\pi$
$522$	8.80846e19	+	8.80846e19i	0.0159785	+	0.0159785i
$523$	−4.56777e21	+	4.56777e21i	−0.816001	+	0.816001i	−0.985526	−	0.169524i	$-0.945777\pi$
$523$	−4.56777e21	+	4.56777e21i	−0.816001	+	0.816001i	0.169524	+	0.985526i	$0.445777\pi$
$524$			3.90415e21i			0.686873i
$525$	3.02344e20	+	7.18084e19i	0.0523873	+	0.0124423i
$526$	−3.31913e19			−0.00566419
$527$	−2.62545e20	−	2.62545e20i	−0.0441285	−	0.0441285i
$528$	6.27005e21	−	6.27005e21i	1.03800	−	1.03800i
$529$			4.65117e21i			0.758432i
$530$	3.54283e21	+	4.14951e20i	0.569041	+	0.0666484i
$531$	1.95258e20			0.0308925
$532$	2.95054e20	+	2.95054e20i	0.0459841	+	0.0459841i
$533$	−9.11308e21	+	9.11308e21i	−1.39910	+	1.39910i
$534$		−	5.19126e21i		−	0.785132i
$535$	−2.72299e21	−	3.44546e21i	−0.405709	−	0.513354i
$536$	7.04555e20			0.103418
$537$	−3.09817e21	−	3.09817e21i	−0.448033	−	0.448033i
$538$	5.17085e21	−	5.17085e21i	0.736721	−	0.736721i
$539$			8.39039e21i			1.17780i
$540$	−3.68064e21	+	2.90885e21i	−0.509065	+	0.402320i
$541$	5.06048e21			0.689626			0.344813	−	0.938671i	$-0.387942\pi$
$541$	5.06048e21			0.689626			0.344813	+	0.938671i	$0.387942\pi$
$542$	1.81620e21	+	1.81620e21i	0.243876	+	0.243876i
$543$	7.78081e21	−	7.78081e21i	1.02950	−	1.02950i
$544$			2.05695e21i			0.268183i
$545$	−1.84733e20	+	1.57725e21i	−0.0237341	+	0.202641i
$546$	−6.66498e20			−0.0843836
$547$	3.21459e21	+	3.21459e21i	0.401077	+	0.401077i	0.878612	−	0.477536i	$-0.158470\pi$
$547$	3.21459e21	+	3.21459e21i	0.401077	+	0.401077i	−0.477536	+	0.878612i	$0.658470\pi$
$548$	4.37615e21	−	4.37615e21i	0.538082	−	0.538082i
$549$			8.73133e19i			0.0105804i
$550$	−6.68241e21	−	1.08454e22i	−0.798053	−	1.29522i
$551$	−9.28534e21			−1.09291
$552$	1.33513e21	+	1.33513e21i	0.154885	+	0.154885i
$553$	3.21389e20	−	3.21389e20i	0.0367477	−	0.0367477i
$554$		−	3.87212e21i		−	0.436386i
$555$	−1.60457e22	−	1.87934e21i	−1.78244	−	0.208766i
$556$	−6.45195e21			−0.706469
$557$	1.11074e22	+	1.11074e22i	1.19887	+	1.19887i	0.974505	+	0.224365i	$0.0720309\pi$
$557$	1.11074e22	+	1.11074e22i	1.19887	+	1.19887i	0.224365	+	0.974505i	$0.427969\pi$
$558$	−6.76918e19	+	6.76918e19i	−0.00720215	+	0.00720215i
$559$		−	2.61471e21i		−	0.274239i
$560$	3.89687e20	+	4.93080e20i	0.0402913	+	0.0509815i
$561$	2.77049e21			0.282393
$562$	−8.01319e21	−	8.01319e21i	−0.805221	−	0.805221i
$563$	−4.83661e21	+	4.83661e21i	−0.479153	+	0.479153i	−0.904861	−	0.425708i	$-0.860025\pi$
$563$	−4.83661e21	+	4.83661e21i	−0.479153	+	0.479153i	0.425708	+	0.904861i	$0.360025\pi$
$564$		−	7.39401e21i		−	0.722183i
$565$	5.28845e21	−	4.17953e21i	0.509262	−	0.402475i
$566$	−1.51107e22			−1.43468
$567$	−4.12385e20	−	4.12385e20i	−0.0386046	−	0.0386046i
$568$	−1.33738e21	+	1.33738e21i	−0.123443	+	0.123443i
$569$		−	1.01792e22i		−	0.926434i	−0.886245	−	0.463217i	$-0.846695\pi$
$569$		−	1.01792e22i		−	0.926434i	0.886245	−	0.463217i	$-0.153305\pi$
$570$	−3.15102e21	+	2.69033e22i	−0.282783	+	2.41439i
$571$	1.93161e22			1.70935			0.854673	−	0.519167i	$-0.173758\pi$
$571$	1.93161e22			1.70935			0.854673	+	0.519167i	$0.173758\pi$
$572$	7.67459e21	+	7.67459e21i	0.669711	+	0.669711i
$573$	−1.05388e22	+	1.05388e22i	−0.906893	+	0.906893i
$574$		−	1.30966e21i		−	0.111138i
$575$	5.00010e21	−	3.08083e21i	0.418443	−	0.257825i
$576$	8.73515e19			0.00720925
$577$	6.98679e21	+	6.98679e21i	0.568684	+	0.568684i	0.931760	−	0.363075i	$-0.118273\pi$
$577$	6.98679e21	+	6.98679e21i	0.568684	+	0.568684i	−0.363075	+	0.931760i	$0.618273\pi$
$578$	1.07161e22	−	1.07161e22i	0.860230	−	0.860230i
$579$		−	6.28673e21i		−	0.497733i
$580$	4.92633e21	+	5.76991e20i	0.384680	+	0.0450552i
$581$	−8.53957e20			−0.0657699
$582$	8.72717e21	+	8.72717e21i	0.662963	+	0.662963i
$583$	4.95795e21	−	4.95795e21i	0.371496	−	0.371496i
$584$			8.00749e21i			0.591826i
$585$	−3.08917e20	−	3.90880e20i	−0.0225214	−	0.0284968i
$586$	1.62676e22			1.16988
$587$	−4.04562e21	−	4.04562e21i	−0.286999	−	0.286999i	0.548893	−	0.835892i	$-0.315049\pi$
$587$	−4.04562e21	−	4.04562e21i	−0.286999	−	0.286999i	−0.835892	+	0.548893i	$0.815049\pi$
$588$	−6.73887e21	+	6.73887e21i	−0.471594	+	0.471594i
$589$		−	7.13566e21i		−	0.492620i
$590$	1.53548e22	−	1.21351e22i	1.04575	−	0.826468i
$591$	1.07480e22			0.722149
$592$	−2.31033e22	−	2.31033e22i	−1.53144	−	1.53144i
$593$	−1.12952e20	+	1.12952e20i	−0.00738680	+	0.00738680i	−0.710791	−	0.703404i	$-0.751663\pi$
$593$	−1.12952e20	+	1.12952e20i	−0.00738680	+	0.00738680i	0.703404	+	0.710791i	$0.251663\pi$
$594$			2.32136e22i			1.49779i
$595$	−2.28427e19	+	1.95030e20i	−0.00145416	+	0.0124155i
$596$	−2.61034e21			−0.163956
$597$	−1.92025e22	−	1.92025e22i	−1.19004	−	1.19004i
$598$	−8.90697e21	+	8.90697e21i	−0.544654	+	0.544654i
$599$		−	2.73083e21i		−	0.164771i	−0.996601	−	0.0823853i	$-0.973746\pi$
$599$		−	2.73083e21i		−	0.164771i	0.996601	−	0.0823853i	$-0.0262538\pi$
$600$	−1.72971e21	+	7.28280e21i	−0.102982	+	0.433599i
$601$	−9.87923e21			−0.580400			−0.290200	−	0.956966i	$-0.593722\pi$
$601$	−9.87923e21			−0.580400			−0.290200	+	0.956966i	$0.593722\pi$
$602$	1.87882e20	+	1.87882e20i	0.0108922	+	0.0108922i
$603$	8.68933e19	−	8.68933e19i	0.00497105	−	0.00497105i
$604$			1.82852e21i			0.103229i
$605$	−7.04282e21	−	8.24883e20i	−0.392377	−	0.0459568i
$606$	2.49488e21			0.137173
$607$	3.70519e21	+	3.70519e21i	0.201049	+	0.201049i	0.800449	−	0.599401i	$-0.204594\pi$
$607$	3.70519e21	+	3.70519e21i	0.201049	+	0.201049i	−0.599401	+	0.800449i	$0.704594\pi$
$608$	−2.79527e22	+	2.79527e22i	−1.49691	+	1.49691i
$609$			5.98712e20i			0.0316432i
$610$	5.42642e21	+	6.86618e21i	0.283058	+	0.358160i
$611$	−2.55184e22			−1.31379
$612$	6.45015e19	+	6.45015e19i	0.00327762	+	0.00327762i
$613$	1.12036e22	−	1.12036e22i	0.561921	−	0.561921i	−0.367931	−	0.929853i	$-0.619934\pi$
$613$	1.12036e22	−	1.12036e22i	0.561921	−	0.561921i	0.929853	+	0.367931i	$0.119934\pi$
$614$		−	3.06655e21i		−	0.151811i
$615$	2.64968e22	−	2.09407e22i	1.29477	−	1.02327i
$616$	5.70576e20			0.0275212
$617$	−2.02546e22	−	2.02546e22i	−0.964369	−	0.964369i	0.0350175	−	0.999387i	$-0.488851\pi$
$617$	−2.02546e22	−	2.02546e22i	−0.964369	−	0.964369i	−0.999387	+	0.0350175i	$0.988851\pi$
$618$	1.17563e22	−	1.17563e22i	0.552539	−	0.552539i
$619$			1.84020e22i			0.853769i	0.904306	+	0.426884i	$0.140389\pi$
$619$			1.84020e22i			0.853769i	−0.904306	+	0.426884i	$0.859611\pi$
$620$	−4.43410e20	+	3.78582e21i	−0.0203082	+	0.173391i
$621$	−1.07023e22			−0.483888
$622$	−2.21374e22	−	2.21374e22i	−0.988106	−	0.988106i
$623$	5.11410e20	−	5.11410e20i	0.0225354	−	0.0225354i
$624$		−	3.47600e22i		−	1.51218i
$625$	2.07966e22	+	1.04692e22i	0.893206	+	0.449648i
$626$	3.65754e22			1.55094
$627$	3.76493e22	+	3.76493e22i	1.57622	+	1.57622i
$628$	6.92273e21	−	6.92273e21i	0.286154	−	0.286154i
$629$		−	1.02085e22i		−	0.416635i
$630$	5.02845e19	+	5.88952e18i	0.00202633	+	0.000237331i
$631$	1.64524e22			0.654626			0.327313	−	0.944916i	$-0.393857\pi$
$631$	1.64524e22			0.654626			0.327313	+	0.944916i	$0.393857\pi$
$632$	7.74157e21	+	7.74157e21i	0.304153	+	0.304153i
$633$	−3.49457e22	+	3.49457e22i	−1.35570	+	1.35570i
$634$			9.41806e21i			0.360784i
$635$	1.06407e22	+	1.34639e22i	0.402512	+	0.509308i
$636$	7.96411e21			0.297495
$637$	2.32574e22	+	2.32574e22i	0.857919	+	0.857919i
$638$	1.73546e22	−	1.73546e22i	0.632192	−	0.632192i
$639$			3.29879e20i			0.0118672i
$640$	−1.82688e22	+	1.44380e22i	−0.649037	+	0.512941i
$641$	−4.30493e22			−1.51043			−0.755216	−	0.655475i	$-0.772468\pi$
$641$	−4.30493e22			−1.51043			−0.755216	+	0.655475i	$0.772468\pi$
$642$	−1.74531e22	−	1.74531e22i	−0.604772	−	0.604772i
$643$	−1.35121e22	+	1.35121e22i	−0.462420	+	0.462420i	−0.899448	−	0.437028i	$-0.856031\pi$
$643$	−1.35121e22	+	1.35121e22i	−0.462420	+	0.462420i	0.437028	+	0.899448i	$0.356031\pi$
$644$		−	5.08489e20i		−	0.0171868i
$645$	−7.97070e20	+	6.80535e21i	−0.0266084	+	0.227181i
$646$	−1.71162e22			−0.564349
$647$	1.65926e22	+	1.65926e22i	0.540355	+	0.540355i	0.923633	−	0.383278i	$-0.125205\pi$
$647$	1.65926e22	+	1.65926e22i	0.540355	+	0.540355i	−0.383278	+	0.923633i	$0.625205\pi$
$648$	9.93347e21	−	9.93347e21i	0.319522	−	0.319522i
$649$		−	3.84701e22i		−	1.22227i
$650$	−4.85855e22	−	1.15393e22i	−1.52475	−	0.362138i
$651$	−4.60102e20			−0.0142629
$652$	1.45648e22	+	1.45648e22i	0.445988	+	0.445988i
$653$	4.42771e22	−	4.42771e22i	1.33929	−	1.33929i	0.442538	−	0.896750i	$-0.354078\pi$
$653$	4.42771e22	−	4.42771e22i	1.33929	−	1.33929i	0.896750	−	0.442538i	$-0.145922\pi$
$654$			8.92536e21i			0.266688i
$655$	−3.50694e22	−	4.10746e21i	−1.03514	−	0.121239i
$656$	6.83027e22			1.99162
$657$	9.87570e20	+	9.87570e20i	0.0284476	+	0.0284476i
$658$	1.83365e21	−	1.83365e21i	0.0521806	−	0.0521806i
$659$			4.15777e22i			1.16890i	0.811430	+	0.584450i	$0.198690\pi$
$659$			4.15777e22i			1.16890i	−0.811430	+	0.584450i	$0.801310\pi$
$660$	−1.76353e22	−	2.23143e22i	−0.489813	−	0.619772i
$661$	−5.19270e22			−1.42489			−0.712445	−	0.701728i	$-0.752412\pi$
$661$	−5.19270e22			−1.42489			−0.712445	+	0.701728i	$0.752412\pi$
$662$	−1.83094e22	−	1.83094e22i	−0.496376	−	0.496376i
$663$	7.67955e21	−	7.67955e21i	0.205697	−	0.205697i
$664$		−	2.05700e22i		−	0.544364i
$665$	−2.96076e21	+	2.33992e21i	−0.0774159	+	0.0611827i
$666$	−2.63204e21			−0.0679985
$667$	8.00109e21	+	8.00109e21i	0.204241	+	0.204241i
$668$	−8.72988e21	+	8.72988e21i	−0.220189	+	0.220189i
$669$		−	1.92921e22i		−	0.480806i
$670$	1.43283e21	−	1.22335e22i	0.0352856	−	0.301267i
$671$	1.72026e22			0.418615
$672$	1.80237e21	+	1.80237e21i	0.0433400	+	0.0433400i
$673$	−2.54775e22	+	2.54775e22i	−0.605391	+	0.605391i	−0.941738	−	0.336347i	$-0.890809\pi$
$673$	−2.54775e22	+	2.54775e22i	−0.605391	+	0.605391i	0.336347	+	0.941738i	$0.390809\pi$
$674$			6.24821e22i			1.46716i
$675$	−2.22567e22	−	3.61220e22i	−0.516453	−	0.838188i
$676$	1.38061e22			0.316591
$677$	1.09772e22	+	1.09772e22i	0.248762	+	0.248762i	0.820462	−	0.571701i	$-0.193716\pi$
$677$	1.09772e22	+	1.09772e22i	0.248762	+	0.248762i	−0.571701	+	0.820462i	$0.693716\pi$
$678$	2.67888e22	−	2.67888e22i	0.599951	−	0.599951i
$679$			1.71949e21i			0.0380576i
$680$	−4.69785e21	−	5.50231e20i	−0.102761	−	0.0120358i
$681$	−6.99245e21			−0.151165
$682$	1.33368e22	+	1.33368e22i	0.284955	+	0.284955i
$683$	−6.97544e21	+	6.97544e21i	−0.147301	+	0.147301i	−0.776911	−	0.629610i	$-0.783215\pi$
$683$	−6.97544e21	+	6.97544e21i	−0.147301	+	0.147301i	0.629610	+	0.776911i	$0.283215\pi$
$684$			1.75307e21i			0.0365891i
$685$	3.47051e22	+	4.39132e22i	0.715927	+	0.905880i
$686$	−6.69416e21			−0.136491
$687$	−6.09031e22	−	6.09031e22i	−1.22740	−	1.22740i
$688$	−9.79867e21	+	9.79867e21i	−0.195191	+	0.195191i
$689$		−	2.74860e22i		−	0.541200i
$690$	2.58975e22	−	2.04671e22i	0.504040	−	0.398349i
$691$	−3.27725e22			−0.630499			−0.315250	−	0.949009i	$-0.602088\pi$
$691$	−3.27725e22			−0.630499			−0.315250	+	0.949009i	$0.602088\pi$
$692$	1.66660e22	+	1.66660e22i	0.316944	+	0.316944i
$693$	7.03696e19	−	7.03696e19i	0.00132288	−	0.00132288i
$694$			7.30153e22i			1.35687i
$695$	6.78794e21	−	5.79552e22i	0.124698	−	1.06467i
$696$	−1.44217e22			−0.261904
$697$	1.50902e22	+	1.50902e22i	0.270914	+	0.270914i
$698$	−3.08297e22	+	3.08297e22i	−0.547174	+	0.547174i
$699$			9.94924e22i			1.74571i
$700$	1.71623e21	−	1.05746e21i	0.0297709	−	0.0183434i
$701$	8.96871e22			1.53811			0.769053	−	0.639186i	$-0.220728\pi$
$701$	8.96871e22			1.53811			0.769053	+	0.639186i	$0.220728\pi$
$702$	6.43462e22	+	6.43462e22i	1.09100	+	1.09100i
$703$	1.38727e23	−	1.38727e23i	2.32551	−	2.32551i
$704$		−	1.72102e22i		−	0.285235i
$705$	6.64173e22	+	7.77905e21i	1.08835	+	0.127472i
$706$	−1.25953e23			−2.04067
$707$	2.45780e20	+	2.45780e20i	0.00393724	+	0.00393724i
$708$	3.08979e22	−	3.08979e22i	0.489398	−	0.489398i
$709$		−	2.92261e22i		−	0.457721i	−0.973459	−	0.228861i	$-0.926500\pi$
$709$		−	2.92261e22i		−	0.457721i	0.973459	−	0.228861i	$-0.0735000\pi$
$710$	2.05016e22	+	2.59412e22i	0.317483	+	0.401719i
$711$	1.90955e21			0.0292397
$712$	1.23188e22	+	1.23188e22i	0.186521	+	0.186521i
$713$	−6.14873e21	+	6.14873e21i	−0.0920596	+	0.0920596i
$714$			1.10364e21i			0.0163396i
$715$	−7.70119e22	+	6.08634e22i	−1.12748	+	0.891062i
$716$	−2.84225e22			−0.411489
$717$	−7.26311e22	−	7.26311e22i	−1.03985	−	1.03985i
$718$	−4.76522e22	+	4.76522e22i	−0.674664	+	0.674664i
$719$		−	1.00662e23i		−	1.40940i	−0.709505	−	0.704701i	$-0.751081\pi$
$719$		−	1.00662e23i		−	1.40940i	0.709505	−	0.704701i	$-0.248919\pi$
$720$	−3.07157e20	+	2.62250e21i	−0.00425305	+	0.0363124i
$721$	2.31631e21			0.0317186
$722$	−1.65346e23	−	1.65346e23i	−2.23922	−	2.23922i
$723$	−7.39184e22	+	7.39184e22i	−0.990025	+	0.990025i
$724$		−	7.13810e22i		−	0.945528i
$725$	−1.03657e22	+	4.36441e22i	−0.135799	+	0.571770i
$726$	−3.98541e22			−0.516393
$727$	7.30126e22	+	7.30126e22i	0.935670	+	0.935670i	0.998052	−	0.0623825i	$-0.0198699\pi$
$727$	7.30126e22	+	7.30126e22i	0.935670	+	0.935670i	−0.0623825	+	0.998052i	$0.519870\pi$
$728$	1.58159e21	−	1.58159e21i	0.0200467	−	0.0200467i
$729$			7.72452e22i			0.968392i
$730$	1.39037e23	+	1.62846e22i	1.72404	+	0.201927i
$731$	−4.32965e21			−0.0531024
$732$	1.38166e22	+	1.38166e22i	0.167615	+	0.167615i
$733$	−1.10661e23	+	1.10661e23i	−1.32789	+	1.32789i	−0.420682	+	0.907208i	$0.638209\pi$
$733$	−1.10661e23	+	1.10661e23i	−1.32789	+	1.32789i	−0.907208	+	0.420682i	$0.861791\pi$
$734$		−	6.72239e22i		−	0.797912i
$735$	−5.34427e22	−	6.76223e22i	−0.627465	−	0.793946i
$736$	4.81731e22			0.559477
$737$	−1.71199e22	−	1.71199e22i	−0.196680	−	0.196680i
$738$	3.89069e21	−	3.89069e21i	0.0442156	−	0.0442156i
$739$		−	5.64915e22i		−	0.635079i	−0.948245	−	0.317539i	$-0.897143\pi$
$739$		−	5.64915e22i		−	0.635079i	0.948245	−	0.317539i	$-0.102857\pi$
$740$	−8.22219e22	+	6.49809e22i	−0.914395	+	0.722657i
$741$	2.08721e23			2.29626
$742$	1.97503e21	+	1.97503e21i	0.0214952	+	0.0214952i
$743$	−1.24330e22	+	1.24330e22i	−0.133865	+	0.133865i	−0.770864	−	0.637000i	$-0.780175\pi$
$743$	−1.24330e22	+	1.24330e22i	−0.133865	+	0.133865i	0.637000	+	0.770864i	$0.280175\pi$
$744$		−	1.10829e22i		−	0.118051i
$745$	2.74627e21	−	2.34476e22i	0.0289397	−	0.247086i
$746$	9.44615e22			0.984791
$747$	−2.53691e21	−	2.53691e21i	−0.0261662	−	0.0261662i
$748$	1.27082e22	−	1.27082e22i	0.129680	−	0.129680i
$749$		−	3.43873e21i		−	0.0347171i
$750$	1.22937e23	+	4.48444e22i	1.22798	+	0.447939i
$751$	−1.45600e22			−0.143894			−0.0719469	−	0.997408i	$-0.522921\pi$
$751$	−1.45600e22			−0.143894			−0.0719469	+	0.997408i	$0.522921\pi$
$752$	9.56307e22	+	9.56307e22i	0.935092	+	0.935092i
$753$	−8.59635e21	+	8.59635e21i	−0.0831676	+	0.0831676i
$754$		−	9.62108e22i		−	0.920986i
$755$	−1.64248e22	−	1.92374e21i	−0.155569	−	0.0182209i
$756$	−3.67345e21			−0.0344271
$757$	4.19612e22	+	4.19612e22i	0.389117	+	0.389117i	0.874372	−	0.485255i	$-0.161273\pi$
$757$	4.19612e22	+	4.19612e22i	0.389117	+	0.389117i	−0.485255	+	0.874372i	$0.661273\pi$
$758$	−3.56194e22	+	3.56194e22i	−0.326838	+	0.326838i
$759$		−	6.48840e22i		−	0.589120i
$760$	−5.63637e22	−	7.13183e22i	−0.506397	−	0.640756i
$761$	1.09655e23			0.974877			0.487438	−	0.873157i	$-0.337931\pi$
$761$	1.09655e23			0.974877			0.487438	+	0.873157i	$0.337931\pi$
$762$	6.82016e22	+	6.82016e22i	0.600005	+	0.600005i
$763$	−8.79270e20	+	8.79270e20i	−0.00765466	+	0.00765466i
$764$			9.66831e22i			0.832921i
$765$	−6.47250e20	+	5.11529e20i	−0.00551799	+	0.00436093i
$766$	−6.32718e21			−0.0533802
$767$	−1.06636e23	−	1.06636e23i	−0.890308	−	0.890308i
$768$	−1.13514e23	+	1.13514e23i	−0.937910	+	0.937910i
$769$		−	7.04566e22i		−	0.576118i	−0.957613	−	0.288059i	$-0.906990\pi$
$769$		−	7.04566e22i		−	0.576118i	0.957613	−	0.288059i	$-0.0930099\pi$
$770$	1.16036e21	−	9.90714e21i	0.00939006	−	0.0801720i
$771$	−1.80017e23			−1.44171
$772$	−2.88372e22	−	2.88372e22i	−0.228567	−	0.228567i
$773$	−2.65096e22	+	2.65096e22i	−0.207954	+	0.207954i	−0.803397	−	0.595444i	$-0.796976\pi$
$773$	−2.65096e22	+	2.65096e22i	−0.207954	+	0.207954i	0.595444	+	0.803397i	$0.296976\pi$
$774$			1.11631e21i			0.00866677i
$775$	−3.35399e22	−	7.96593e21i	−0.257720	−	0.0612101i
$776$	−4.14188e22			−0.314995
$777$	−8.94502e21	−	8.94502e21i	−0.0673307	−	0.0673307i
$778$	1.47300e23	−	1.47300e23i	1.09740	−	1.09740i
$779$			4.10133e23i			3.02430i
$780$	−1.10737e23	−	1.29699e22i	−0.808230	−	0.0946631i
$781$	6.49934e22			0.469528
$782$	1.47489e22	+	1.47489e22i	0.105464	+	0.105464i
$783$	5.78019e22	−	5.78019e22i	0.409117	−	0.409117i
$784$		−	1.74315e23i		−	1.22125i
$785$	5.49008e22	+	6.94673e22i	0.380734	+	0.481751i
$786$	−1.98451e23			−1.36230
$787$	−8.35159e22	−	8.35159e22i	−0.567507	−	0.567507i	0.363922	−	0.931429i	$-0.381437\pi$
$787$	−8.35159e22	−	8.35159e22i	−0.567507	−	0.567507i	−0.931429	+	0.363922i	$0.881437\pi$
$788$	4.93009e22	−	4.93009e22i	0.331623	−	0.331623i
$789$		−	6.70211e20i		−	0.00446268i
$790$	1.50164e23	−	1.18676e23i	0.989802	−	0.782252i
$791$	5.27813e21			0.0344404
$792$	1.69505e21	+	1.69505e21i	0.0109492	+	0.0109492i
$793$	4.76842e22	−	4.76842e22i	0.304922	−	0.304922i
$794$		−	1.68866e23i		−	1.06900i
$795$	−8.37884e21	+	7.15383e22i	−0.0525106	+	0.448334i
$796$	−1.76163e23			−1.09298
$797$	−1.61880e23	−	1.61880e23i	−0.994319	−	0.994319i	0.00566492	−	0.999984i	$-0.498197\pi$
$797$	−1.61880e23	−	1.61880e23i	−0.994319	−	0.994319i	−0.999984	+	0.00566492i	$0.998197\pi$
$798$	−1.49978e22	+	1.49978e22i	−0.0912022	+	0.0912022i
$799$			4.22555e22i			0.254395i
$800$	1.00181e23	+	1.62592e23i	0.597128	+	0.969122i
$801$	3.03856e21			0.0179312
$802$	1.34526e23	+	1.34526e23i	0.785980	+	0.785980i
$803$	1.94573e23	−	1.94573e23i	1.12553	−	1.12553i
$804$		−	2.75002e22i		−	0.157503i
$805$	4.56755e21	+	5.34969e20i	0.0259010	+	0.00303362i
$806$	7.39367e22			0.415126
$807$	1.04412e23	+	1.04412e23i	0.580445	+	0.580445i
$808$	−5.92031e21	+	5.92031e21i	−0.0325877	+	0.0325877i
$809$			2.89188e23i			1.57613i	0.615591	+	0.788066i	$0.288917\pi$
$809$			2.89188e23i			1.57613i	−0.615591	+	0.788066i	$0.711083\pi$
$810$	−1.52277e23	−	1.92680e23i	−0.821780	−	1.03982i
$811$	4.19800e21			0.0224324			0.0112162	−	0.999937i	$-0.496430\pi$
$811$	4.19800e21			0.0224324			0.0112162	+	0.999937i	$0.496430\pi$
$812$	2.74629e21	+	2.74629e21i	0.0145311	+	0.0145311i
$813$	−3.66733e22	+	3.66733e22i	−0.192144	+	0.192144i
$814$			5.18570e23i			2.69037i
$815$	−1.46153e23	+	1.15506e23i	−0.750838	+	0.593396i
$816$	−5.75585e22			−0.292811
$817$	−5.88374e22	−	5.88374e22i	−0.296399	−	0.296399i
$818$	1.31056e23	−	1.31056e23i	0.653781	−	0.653781i
$819$		−	3.90117e20i		−	0.00192718i
$820$	2.54856e22	−	2.17595e23i	0.124676	−	1.06448i
$821$	−1.67070e23			−0.809381			−0.404690	−	0.914454i	$-0.632621\pi$
$821$	−1.67070e23			−0.809381			−0.404690	+	0.914454i	$0.632621\pi$
$822$	2.22444e23	+	2.22444e23i	1.06720	+	1.06720i
$823$	5.78876e22	−	5.78876e22i	0.275034	−	0.275034i	−0.556089	−	0.831123i	$-0.687699\pi$
$823$	5.78876e22	−	5.78876e22i	0.275034	−	0.275034i	0.831123	+	0.556089i	$0.187699\pi$
$824$			5.57949e22i			0.262529i
$825$	2.18994e23	−	1.34934e23i	1.02047	−	0.628766i
$826$	1.53248e22			0.0707220
$827$	1.43828e23	+	1.43828e23i	0.657354	+	0.657354i	0.954753	−	0.297400i	$-0.0961193\pi$
$827$	1.43828e23	+	1.43828e23i	0.657354	+	0.657354i	−0.297400	+	0.954753i	$0.596119\pi$
$828$	1.51061e21	−	1.51061e21i	0.00683767	−	0.00683767i
$829$		−	1.88006e23i		−	0.842823i	−0.906870	−	0.421412i	$-0.861535\pi$
$829$		−	1.88006e23i		−	0.842823i	0.906870	−	0.421412i	$-0.138465\pi$
$830$	−3.57165e23	−	4.18326e22i	−1.58578	−	0.185733i
$831$	7.81873e22			0.343817
$832$	−4.77050e22	−	4.77050e22i	−0.207768	−	0.207768i
$833$	3.85115e22	−	3.85115e22i	0.166123	−	0.166123i
$834$		−	3.27958e23i		−	1.40117i
$835$	−6.92324e22	−	8.76013e22i	−0.292966	−	0.370697i
$836$	3.45394e23			1.44765
$837$	4.44200e22	+	4.44200e22i	0.184406	+	0.184406i
$838$	−2.72566e23	+	2.72566e23i	−1.12078	+	1.12078i
$839$		−	1.74804e23i		−	0.711960i	−0.934494	−	0.355980i	$-0.884147\pi$
$839$		−	1.74804e23i		−	0.711960i	0.934494	−	0.355980i	$-0.115853\pi$
$840$	−4.59855e21	+	3.63429e21i	−0.0185518	+	0.0146617i
$841$	1.63821e23			0.654638
$842$	−1.45181e23	−	1.45181e23i	−0.574664	−	0.574664i
$843$	1.61805e23	−	1.61805e23i	0.634414	−	0.634414i
$844$			3.20591e23i			1.24512i
$845$	−1.45251e22	+	1.24015e23i	−0.0558811	+	0.477111i
$846$	1.08947e22			0.0415195
$847$	−3.92617e21	−	3.92617e21i	−0.0148218	−	0.0148218i
$848$	−1.03004e23	+	1.03004e23i	−0.385201	+	0.385201i
$849$		−	3.05122e23i		−	1.13035i
$850$	−1.91078e22	+	8.04517e22i	−0.0701227	+	0.295246i
$851$	−2.39079e23			−0.869172
$852$	5.22005e22	+	5.22005e22i	0.188000	+	0.188000i
$853$	−3.58209e23	+	3.58209e23i	−1.27804	+	1.27804i	−0.336278	+	0.941763i	$0.609168\pi$
$853$	−3.58209e23	+	3.58209e23i	−1.27804	+	1.27804i	−0.941763	+	0.336278i	$0.890832\pi$
$854$			6.85278e21i			0.0242216i
$855$	−1.57471e22	−	1.84437e21i	−0.0551407	−	0.00645830i
$856$	8.28316e22			0.287346
$857$	−2.53763e23	−	2.53763e23i	−0.872132	−	0.872132i	0.120573	−	0.992704i	$-0.461527\pi$
$857$	−2.53763e23	−	2.53763e23i	−0.872132	−	0.872132i	−0.992704	+	0.120573i	$0.961527\pi$
$858$	−3.90106e23	+	3.90106e23i	−1.32826	+	1.32826i
$859$		−	1.40644e23i		−	0.474436i	−0.971456	−	0.237218i	$-0.923764\pi$
$859$		−	1.40644e23i		−	0.474436i	0.971456	−	0.237218i	$-0.0762355\pi$
$860$	2.75599e22	+	3.48722e22i	0.0921065	+	0.116545i
$861$	2.64451e22			0.0875627
$862$	−1.13910e23	−	1.13910e23i	−0.373682	−	0.373682i
$863$	4.11847e23	−	4.11847e23i	1.33860	−	1.33860i	0.441178	−	0.897420i	$-0.354561\pi$
$863$	4.11847e23	−	4.11847e23i	1.33860	−	1.33860i	0.897420	−	0.441178i	$-0.145439\pi$
$864$		−	3.48014e23i		−	1.12069i
$865$	−1.67238e23	+	1.32170e23i	−0.533587	+	0.421700i
$866$	−1.75029e23			−0.553307
$867$	2.16384e23	+	2.16384e23i	0.677754	+	0.677754i
$868$	−2.11048e21	+	2.11048e21i	−0.00654974	+	0.00654974i
$869$		−	3.76223e23i		−	1.15688i
$870$	−2.93289e22	+	2.50409e23i	−0.0893598	+	0.762951i
$871$	−9.49097e22			−0.286527
$872$	−2.11797e22	−	2.11797e22i	−0.0633561	−	0.0633561i
$873$	−5.10821e21	+	5.10821e21i	−0.0151410	+	0.0151410i
$874$			4.00857e23i			1.17733i
$875$	7.69313e21	+	1.65287e22i	0.0223892	+	0.0481033i
$876$	3.12549e23			0.901332
$877$	2.82060e21	+	2.82060e21i	0.00806017	+	0.00806017i	0.711125	−	0.703065i	$-0.248186\pi$
$877$	2.82060e21	+	2.82060e21i	0.00806017	+	0.00806017i	−0.703065	+	0.711125i	$0.748186\pi$
$878$	4.05793e23	−	4.05793e23i	1.14908	−	1.14908i
$879$			3.28481e23i			0.921721i
$880$	5.16689e23	+	6.05167e22i	1.43671	+	0.168273i
$881$	1.53034e23			0.421679			0.210839	−	0.977521i	$-0.432380\pi$
$881$	1.53034e23			0.421679			0.210839	+	0.977521i	$0.432380\pi$
$882$	−9.92939e21	−	9.92939e21i	−0.0271128	−	0.0271128i
$883$	−1.28167e23	+	1.28167e23i	−0.346810	+	0.346810i	−0.858920	−	0.512110i	$-0.828864\pi$
$883$	−1.28167e23	+	1.28167e23i	−0.346810	+	0.346810i	0.512110	+	0.858920i	$0.328864\pi$
$884$		−	7.04521e22i		−	0.188919i
$885$	2.45036e23	+	3.10050e23i	0.651153	+	0.823920i
$886$	4.04643e23			1.06562
$887$	4.01762e23	+	4.01762e23i	1.04853	+	1.04853i	0.998761	+	0.0497674i	$0.0158480\pi$
$887$	4.01762e23	+	4.01762e23i	1.04853	+	1.04853i	0.0497674	+	0.998761i	$0.484152\pi$
$888$	2.15466e23	−	2.15466e23i	0.557282	−	0.557282i
$889$			1.34376e22i			0.0344435i
$890$	2.38948e23	−	1.88843e23i	0.606992	−	0.479713i
$891$	−4.82744e23			−1.21533
$892$	−8.84925e22	−	8.84925e22i	−0.220794	−	0.220794i
$893$	−5.74227e23	+	5.74227e23i	−1.41995	+	1.41995i
$894$		−	1.32686e23i		−	0.325180i
$895$	2.99026e22	−	2.55308e23i	0.0726315	−	0.620125i
$896$	−1.82331e22			−0.0438931
$897$	−1.79853e23	−	1.79853e23i	−0.429119	−	0.429119i
$898$	−3.78668e22	+	3.78668e22i	−0.0895464	+	0.0895464i
$899$		−	6.64170e22i		−	0.155669i
$900$	8.24000e21	+	1.95705e21i	0.0191420	+	0.00454634i
$901$	−4.55135e22			−0.104795
$902$	−7.66550e23	−	7.66550e23i	−1.74940	−	1.74940i
$903$	−3.79379e21	+	3.79379e21i	−0.00858166	+	0.00858166i
$904$			1.27139e23i			0.285056i
$905$	6.41186e23	+	7.50982e22i	1.42494	+	0.166894i
$906$	−9.29450e22			−0.204739
$907$	3.52460e23	+	3.52460e23i	0.769577	+	0.769577i	0.978032	−	0.208455i	$-0.0668434\pi$
$907$	3.52460e23	+	3.52460e23i	0.769577	+	0.769577i	−0.208455	+	0.978032i	$0.566843\pi$
$908$	−3.20743e22	+	3.20743e22i	−0.0694177	+	0.0694177i
$909$			1.46031e21i			0.00313282i
$910$	−2.42453e22	−	3.06782e22i	−0.0515580	−	0.0652376i
$911$	−4.10677e23			−0.865672			−0.432836	−	0.901473i	$-0.642487\pi$
$911$	−4.10677e23			−0.865672			−0.432836	+	0.901473i	$0.642487\pi$
$912$	−7.82185e23	−	7.82185e23i	−1.63437	−	1.63437i
$913$	−4.99827e23	+	4.99827e23i	−1.03527	+	1.03527i
$914$			3.16643e22i			0.0650130i
$915$	−1.38645e23	+	1.09572e23i	−0.282185	+	0.223014i
$916$	−5.58723e23			−1.12728
$917$	−1.95502e22	−	1.95502e22i	−0.0391017	−	0.0391017i
$918$	1.06550e23	−	1.06550e23i	0.211257	−	0.211257i
$919$			2.21145e23i			0.434663i	0.976098	+	0.217331i	$0.0697352\pi$
$919$			2.21145e23i			0.434663i	−0.976098	+	0.217331i	$0.930265\pi$
$920$	−1.28863e22	+	1.10022e23i	−0.0251087	+	0.214377i
$921$	6.19210e22			0.119608
$922$	3.63444e23	+	3.63444e23i	0.695969	+	0.695969i
$923$	1.80156e23	−	1.80156e23i	0.342007	−	0.342007i
$924$		−	2.22707e22i		−	0.0419140i
$925$	−4.97193e23	−	8.06930e23i	−0.927665	−	1.50557i
$926$	5.12645e23			0.948262
$927$	6.88123e21	+	6.88123e21i	0.0126191	+	0.0126191i
$928$	−2.60177e23	+	2.60177e23i	−0.473026	+	0.473026i
$929$			9.57115e22i			0.172520i	0.996273	+	0.0862598i	$0.0274915\pi$
$929$			9.57115e22i			0.172520i	−0.996273	+	0.0862598i	$0.972508\pi$
$930$	−1.92436e23	−	2.25389e22i	−0.343893	−	0.0402781i
$931$	1.04670e24			1.85449
$932$	4.56370e23	+	4.56370e23i	0.801660	+	0.801660i
$933$	4.47007e23	−	4.47007e23i	0.778504	−	0.778504i
$934$		−	5.22628e23i		−	0.902438i
$935$	1.00783e23	+	1.27522e23i	0.172541	+	0.218320i
$936$	9.39707e21			0.0159509
$937$	−4.49972e23	−	4.49972e23i	−0.757302	−	0.757302i	0.218528	−	0.975831i	$-0.429874\pi$
$937$	−4.49972e23	−	4.49972e23i	−0.757302	−	0.757302i	−0.975831	+	0.218528i	$0.929874\pi$
$938$	6.81981e21	−	6.81981e21i	0.0113802	−	0.0113802i
$939$			7.38545e23i			1.22195i
$940$	3.40338e23	−	2.68973e23i	0.558325	−	0.441251i
$941$	2.77977e22			0.0452160			0.0226080	−	0.999744i	$-0.492803\pi$
$941$	2.77977e22			0.0452160			0.0226080	+	0.999744i	$0.492803\pi$
$942$	3.51888e23	+	3.51888e23i	0.567542	+	0.567542i
$943$	3.53407e23	−	3.53407e23i	0.565173	−	0.565173i
$944$			7.99238e23i			1.26736i
$945$	3.86475e21	−	3.29971e22i	0.00607669	−	0.0518826i
$946$	2.19938e23			0.342902
$947$	1.35553e23	+	1.35553e23i	0.209561	+	0.209561i	0.804081	−	0.594520i	$-0.202658\pi$
$947$	1.35553e23	+	1.35553e23i	0.209561	+	0.209561i	−0.594520	+	0.804081i	$0.702658\pi$
$948$	3.02169e23	−	3.02169e23i	0.463216	−	0.463216i
$949$		−	1.07868e24i		−	1.63969i
$950$	−1.35295e24	+	8.33627e23i	−2.03936	+	1.25656i
$951$	−1.90173e23			−0.284253
$952$	−2.61892e21	−	2.61892e21i	−0.00388174	−	0.00388174i
$953$	−5.18627e23	+	5.18627e23i	−0.762276	+	0.762276i	−0.976733	−	0.214457i	$-0.931202\pi$
$953$	−5.18627e23	+	5.18627e23i	−0.762276	+	0.762276i	0.214457	+	0.976733i	$0.431202\pi$
$954$			1.17347e22i			0.0171035i
$955$	−8.68464e23	−	1.01718e23i	−1.25523	−	0.147018i
$956$	−6.66316e23			−0.955030
$957$	3.50430e23	+	3.50430e23i	0.498088	+	0.498088i
$958$	9.83534e23	−	9.83534e23i	1.38633	−	1.38633i
$959$			4.38275e22i			0.0612629i
$960$	1.09620e23	+	1.38705e23i	0.151957	+	0.192275i
$961$	−6.76383e23			−0.929834
$962$	1.43743e24	+	1.43743e24i	1.95969	+	1.95969i
$963$	1.02157e22	−	1.02157e22i	0.0138120	−	0.0138120i
$964$			6.78126e23i			0.909272i
$965$	2.89371e23	−	2.28693e23i	0.384802	−	0.304113i
$966$	2.58469e22			0.0340873
$967$	2.04202e23	+	2.04202e23i	0.267085	+	0.267085i	0.827924	−	0.560840i	$-0.189522\pi$
$967$	2.04202e23	+	2.04202e23i	0.267085	+	0.267085i	−0.560840	+	0.827924i	$0.689522\pi$
$968$	9.45730e22	−	9.45730e22i	0.122677	−	0.122677i
$969$		−	3.45617e23i		−	0.444636i
$970$	−8.42322e22	+	7.19171e23i	−0.107474	+	0.917610i
$971$	7.61327e23			0.963424			0.481712	−	0.876329i	$-0.340015\pi$
$971$	7.61327e23			0.963424			0.481712	+	0.876329i	$0.340015\pi$
$972$	−2.21618e22	−	2.21618e22i	−0.0278147	−	0.0278147i
$973$	3.23084e22	−	3.23084e22i	0.0402173	−	0.0402173i
$974$		−	1.40256e24i		−	1.73160i
$975$	2.33007e23	−	9.81056e23i	0.285320	−	1.20132i
$976$	−3.57394e23			−0.434059
$977$	−4.60796e23	−	4.60796e23i	−0.555075	−	0.555075i	0.372826	−	0.927901i	$-0.378389\pi$
$977$	−4.60796e23	−	4.60796e23i	−0.555075	−	0.555075i	−0.927901	+	0.372826i	$0.878389\pi$
$978$	−7.40341e23	+	7.40341e23i	−0.884547	+	0.884547i
$979$		−	5.98664e23i		−	0.709450i
$980$	−5.55323e23	−	6.50417e22i	−0.652736	−	0.0764510i
$981$	−5.22422e21			−0.00609073
$982$	−1.09485e24	−	1.09485e24i	−1.26608	−	1.26608i
$983$	−3.38978e23	+	3.38978e23i	−0.388815	+	0.388815i	−0.874265	−	0.485449i	$-0.838656\pi$
$983$	−3.38978e23	+	3.38978e23i	−0.388815	+	0.388815i	0.485449	+	0.874265i	$0.338656\pi$
$984$			6.37004e23i			0.724739i
$985$	3.90981e23	+	4.94717e23i	0.441231	+	0.558299i
$986$	−1.59314e23			−0.178335
$987$	3.70257e22	+	3.70257e22i	0.0411118	+	0.0411118i
$988$	9.57401e23	−	9.57401e23i	1.05448	−	1.05448i
$989$			1.01399e23i			0.110781i
$990$	3.28790e22	−	2.59847e22i	0.0356318	−	0.0281602i
$991$	−5.31293e23			−0.571143			−0.285571	−	0.958357i	$-0.592183\pi$
$991$	−5.31293e23			−0.571143			−0.285571	+	0.958357i	$0.592183\pi$
$992$	−1.99942e23	−	1.99942e23i	−0.213212	−	0.213212i
$993$	3.69711e23	−	3.69711e23i	0.391082	−	0.391082i
$994$			2.58905e22i			0.0271675i
$995$	1.85337e23	−	1.58240e24i	0.192920	−	1.64714i
$996$	−8.02888e23			−0.829049
$997$	1.24395e24	+	1.24395e24i	1.27421	+	1.27421i	0.943855	+	0.330359i	$0.107170\pi$
$997$	1.24395e24	+	1.24395e24i	1.27421	+	1.27421i	0.330359	+	0.943855i	$0.392830\pi$
$998$	−4.24664e23	+	4.24664e23i	−0.431520	+	0.431520i
$999$			1.72717e24i			1.74105i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.17.c.a.2.6	✓	14
3.2	odd	2		45.17.g.a.37.2		14
4.3	odd	2		80.17.p.c.17.6		14
5.2	odd	4		25.17.c.b.18.2		14
5.3	odd	4	inner	5.17.c.a.3.6	yes	14
5.4	even	2		25.17.c.b.7.2		14
15.8	even	4		45.17.g.a.28.2		14
20.3	even	4		80.17.p.c.33.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.17.c.a.2.6	✓	14	1.1	even	1	trivial
5.17.c.a.3.6	yes	14	5.3	odd	4	inner
25.17.c.b.7.2		14	5.4	even	2
25.17.c.b.18.2		14	5.2	odd	4
45.17.g.a.28.2		14	15.8	even	4
45.17.g.a.37.2		14	3.2	odd	2
80.17.p.c.17.6		14	4.3	odd	2
80.17.p.c.33.6		14	20.3	even	4

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(233.161 + 233.161i) q^{2} +(-4708.07 + 4708.07i) q^{3} +43191.7i q^{4} +(-387973. - 45440.9i) q^{5} -2.19547e6 q^{6} +(-216284. - 216284. i) q^{7} +(5.20981e6 - 5.20981e6i) q^{8} -1.28506e6i q^{9} +O(q^{10})\)	\(q+(233.161 + 233.161i) q^{2} +(-4708.07 + 4708.07i) q^{3} +43191.7i q^{4} +(-387973. - 45440.9i) q^{5} -2.19547e6 q^{6} +(-216284. - 216284. i) q^{7} +(5.20981e6 - 5.20981e6i) q^{8} -1.28506e6i q^{9} +(-7.98650e7 - 1.01055e8i) q^{10} -2.53185e8 q^{11} +(-2.03349e8 - 2.03349e8i) q^{12} +(-7.01806e8 + 7.01806e8i) q^{13} -1.00858e8i q^{14} +(2.04054e9 - 1.61266e9i) q^{15} +5.26006e9 q^{16} +(1.16211e9 + 1.16211e9i) q^{17} +(2.99625e8 - 2.99625e8i) q^{18} +3.15847e10i q^{19} +(1.96267e9 - 1.67572e10i) q^{20} +2.03656e9 q^{21} +(-5.90327e10 - 5.90327e10i) q^{22} +(2.72162e10 - 2.72162e10i) q^{23} +4.90563e10i q^{24} +(1.48458e11 + 3.52597e10i) q^{25} -3.27267e11 q^{26} +(-1.96617e11 - 1.96617e11i) q^{27} +(9.34167e9 - 9.34167e9i) q^{28} +2.93982e11i q^{29} +(8.51783e11 + 9.97642e10i) q^{30} -2.25922e11 q^{31} +(8.85007e11 + 8.85007e11i) q^{32} +(1.19201e12 - 1.19201e12i) q^{33} +5.41915e11i q^{34} +(7.40841e10 + 9.37404e10i) q^{35} +5.55039e10 q^{36} +(-4.39223e12 - 4.39223e12i) q^{37} +(-7.36430e12 + 7.36430e12i) q^{38} -6.60830e12i q^{39} +(-2.25800e12 + 1.78453e12i) q^{40} +1.29852e13 q^{41} +(4.74845e11 + 4.74845e11i) q^{42} +(-1.86284e12 + 1.86284e12i) q^{43} -1.09355e13i q^{44} +(-5.83943e10 + 4.98568e11i) q^{45} +1.26915e13 q^{46} +(1.81805e13 + 1.81805e13i) q^{47} +(-2.47647e13 + 2.47647e13i) q^{48} -3.31394e13i q^{49} +(2.63934e13 + 4.28358e13i) q^{50} -1.09426e13 q^{51} +(-3.03122e13 - 3.03122e13i) q^{52} +(-1.95823e13 + 1.95823e13i) q^{53} -9.16865e13i q^{54} +(9.82289e13 + 1.15050e13i) q^{55} -2.25360e12 q^{56} +(-1.48703e14 - 1.48703e14i) q^{57} +(-6.85451e13 + 6.85451e13i) q^{58} +1.51945e14i q^{59} +(6.96537e13 + 8.81344e13i) q^{60} -6.79450e13 q^{61} +(-5.26760e13 - 5.26760e13i) q^{62} +(-2.77938e11 + 2.77938e11i) q^{63} +6.79747e13i q^{64} +(3.04173e14 - 2.40391e14i) q^{65} +5.55860e14 q^{66} +(6.76181e13 + 6.76181e13i) q^{67} +(-5.01934e13 + 5.01934e13i) q^{68} +2.56271e14i q^{69} +(-4.58307e12 + 3.91301e13i) q^{70} -2.56703e14 q^{71} +(-6.69492e12 - 6.69492e12i) q^{72} +(-7.68501e14 + 7.68501e14i) q^{73} -2.04819e15i q^{74} +(-8.64956e14 + 5.32946e14i) q^{75} -1.36420e15 q^{76} +(5.47598e13 + 5.47598e13i) q^{77} +(1.54080e15 - 1.54080e15i) q^{78} +1.48596e15i q^{79} +(-2.04076e15 - 2.39022e14i) q^{80} +1.90669e15 q^{81} +(3.02763e15 + 3.02763e15i) q^{82} +(1.97416e15 - 1.97416e15i) q^{83} +8.79624e13i q^{84} +(-3.98059e14 - 5.03673e14i) q^{85} -8.68684e14 q^{86} +(-1.38409e15 - 1.38409e15i) q^{87} +(-1.31905e15 + 1.31905e15i) q^{88} +2.36453e15i q^{89} +(-1.29862e14 + 1.02631e14i) q^{90} +3.03579e14 q^{91} +(1.17551e15 + 1.17551e15i) q^{92} +(1.06365e15 - 1.06365e15i) q^{93} +8.47797e15i q^{94} +(1.43524e15 - 1.22540e16i) q^{95} -8.33335e15 q^{96} +(-3.97508e15 - 3.97508e15i) q^{97} +(7.72679e15 - 7.72679e15i) q^{98} +3.25358e14i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8}+O(q^{10}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8	\( 14 q - 2 q^{2} + 7908 q^{3} + 192880 q^{5} + 4417368 q^{6} - 386452 q^{7} - 10493340 q^{8} + 398727830 q^{10} - 539141632 q^{11} + 1973309928 q^{12} - 681358582 q^{13} + 3514452060 q^{15} - 22953579016 q^{16} + 13124182498 q^{17} - 11293583022 q^{18} - 20186820060 q^{20} + 133652286048 q^{21} - 244784660624 q^{22} + 236373052228 q^{23} + 13144083650 q^{25} + 223473840788 q^{26} + 608106053880 q^{27} - 1494176423768 q^{28} + 2252131613760 q^{30} - 1105223074952 q^{31} - 2024535639992 q^{32} - 6385551058704 q^{33} + 6956678093980 q^{35} + 12514339524924 q^{36} - 9027827087002 q^{37} - 7824802789560 q^{38} + 31912538913900 q^{40} + 39543901484288 q^{41} - 70814500818384 q^{42} - 63017457929452 q^{43} + 126481294123110 q^{45} + 44357914058008 q^{46} - 2826187575452 q^{47} - 405160526368272 q^{48} + 461109216233650 q^{50} + 208649050954008 q^{51} - 389623094881012 q^{52} - 275142037498442 q^{53} + 330504874256560 q^{55} + 865011118900080 q^{56} - 644237427525840 q^{57} - 991296507673440 q^{58} + 16\!\cdots\!80 q^{60}+ \cdots + 48\!\cdots\!02 q^{98}+O(q^{100}) \) 14 * q - 2 * q^2 + 7908 * q^3 + 192880 * q^5 + 4417368 * q^6 - 386452 * q^7 - 10493340 * q^8 + 398727830 * q^10 - 539141632 * q^11 + 1973309928 * q^12 - 681358582 * q^13 + 3514452060 * q^15 - 22953579016 * q^16 + 13124182498 * q^17 - 11293583022 * q^18 - 20186820060 * q^20 + 133652286048 * q^21 - 244784660624 * q^22 + 236373052228 * q^23 + 13144083650 * q^25 + 223473840788 * q^26 + 608106053880 * q^27 - 1494176423768 * q^28 + 2252131613760 * q^30 - 1105223074952 * q^31 - 2024535639992 * q^32 - 6385551058704 * q^33 + 6956678093980 * q^35 + 12514339524924 * q^36 - 9027827087002 * q^37 - 7824802789560 * q^38 + 31912538913900 * q^40 + 39543901484288 * q^41 - 70814500818384 * q^42 - 63017457929452 * q^43 + 126481294123110 * q^45 + 44357914058008 * q^46 - 2826187575452 * q^47 - 405160526368272 * q^48 + 461109216233650 * q^50 + 208649050954008 * q^51 - 389623094881012 * q^52 - 275142037498442 * q^53 + 330504874256560 * q^55 + 865011118900080 * q^56 - 644237427525840 * q^57 - 991296507673440 * q^58 + 1631207111049480 * q^60 + 683634528395968 * q^61 - 938995013191864 * q^62 - 1361911146729372 * q^63 + 517066464980110 * q^65 - 196778043917184 * q^66 - 181547742064252 * q^67 - 917821658187868 * q^68 + 1066699466039880 * q^70 - 1337544011098792 * q^71 + 2573199832214340 * q^72 + 778038215296478 * q^73 - 1442550824447700 * q^75 - 233750796900240 * q^76 + 1099376123524976 * q^77 + 8472064951325256 * q^78 - 14934736099860320 * q^80 + 809940307363794 * q^81 - 303814693723184 * q^82 + 13357181209550188 * q^83 - 16045734952112470 * q^85 - 20034048539985352 * q^86 + 17327533268211840 * q^87 + 22952328705949920 * q^88 - 21878453293909290 * q^90 - 24534035720748632 * q^91 + 40652972845631848 * q^92 + 15958372062212256 * q^93 - 22489885958711400 * q^95 - 27488119051061472 * q^96 - 3303551663290402 * q^97 + 48233459501789102 * q^98

Introduction

L-functions

Modular forms

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