LMFDB - Embedded newform 9.9.d.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,9,Mod(2,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("9.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, 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:	$3.66640749055$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
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} - x^{13} + 427 x^{12} - 1362 x^{11} + 135762 x^{10} - 371244 x^{9} + 18261508 x^{8} + \cdots + 872385888256 $ x^14 - x^13 + 427x^12 - 1362x^11 + 135762x^10 - 371244x^9 + 18261508x^8 - 29352736x^7 + 1757083840x^6 - 1434930432x^5 + 61638378240x^4 + 183604924416x^3 + 1254910111744x^2 + 1078377512960x + 872385888256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{21} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.6
Root			$-5.49482 + 9.51731i$ of defining polynomial
Character	$\chi$	$=$	9.5
Dual form			9.9.d.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.4845 - 9.51731i) q^{2} +(80.5605 - 8.42672i) q^{3} +(53.1583 - 92.0729i) q^{4} +(-46.9888 - 27.1290i) q^{5} +(1247.80 - 905.629i) q^{6} +(-921.012 - 1595.24i) q^{7} +2849.17i q^{8} +(6418.98 - 1357.72i) q^{9} +O(q^{10})$	\(q+(16.4845 - 9.51731i) q^{2} +(80.5605 - 8.42672i) q^{3} +(53.1583 - 92.0729i) q^{4} +(-46.9888 - 27.1290i) q^{5} +(1247.80 - 905.629i) q^{6} +(-921.012 - 1595.24i) q^{7} +2849.17i q^{8} +(6418.98 - 1357.72i) q^{9} -1032.78 q^{10} +(-15872.1 + 9163.77i) q^{11} +(3506.59 - 7865.39i) q^{12} +(-16240.1 + 28128.7i) q^{13} +(-30364.8 - 17531.1i) q^{14} +(-4014.05 - 1789.56i) q^{15} +(40724.9 + 70537.6i) q^{16} -97572.1i q^{17} +(92891.6 - 83472.7i) q^{18} +208951. q^{19} +(-4995.69 + 2884.26i) q^{20} +(-87639.8 - 120752. i) q^{21} +(-174429. + 302119. i) q^{22} +(-273878. - 158124. i) q^{23} +(24009.1 + 229530. i) q^{24} +(-193841. - 335742. i) q^{25} +618248. i q^{26} +(505675. - 163470. i) q^{27} -195838. q^{28} +(96164.1 - 55520.4i) q^{29} +(-83201.2 + 8702.94i) q^{30} +(181257. - 313947. i) q^{31} +(710990. + 410490. i) q^{32} +(-1.20144e6 + 871987. i) q^{33} +(-928623. - 1.60842e6i) q^{34} +99944.5i q^{35} +(216213. - 663188. i) q^{36} +1.91887e6 q^{37} +(3.44445e6 - 1.98865e6i) q^{38} +(-1.07128e6 + 2.40291e6i) q^{39} +(77295.0 - 133879. i) q^{40} +(-1.16149e6 - 670589. i) q^{41} +(-2.59393e6 - 1.15644e6i) q^{42} +(1.49489e6 + 2.58922e6i) q^{43} +1.94852e6i q^{44} +(-338454. - 110343. i) q^{45} -6.01964e6 q^{46} +(-1.67689e6 + 968152. i) q^{47} +(3.87522e6 + 5.33937e6i) q^{48} +(1.18588e6 - 2.05400e6i) q^{49} +(-6.39071e6 - 3.68968e6i) q^{50} +(-822212. - 7.86045e6i) q^{51} +(1.72659e6 + 2.99054e6i) q^{52} +1.03471e7i q^{53} +(6.77999e6 - 7.50737e6i) q^{54} +994415. q^{55} +(4.54510e6 - 2.62411e6i) q^{56} +(1.68332e7 - 1.76077e6i) q^{57} +(1.05681e6 - 1.83045e6i) q^{58} +(-1.10364e7 - 6.37189e6i) q^{59} +(-378150. + 274455. i) q^{60} +(6.41822e6 + 1.11167e7i) q^{61} -6.90032e6i q^{62} +(-8.07784e6 - 8.98933e6i) q^{63} -5.22412e6 q^{64} +(1.52620e6 - 881155. i) q^{65} +(-1.15062e7 + 2.58088e7i) q^{66} +(-7.00252e6 + 1.21287e7i) q^{67} +(-8.98374e6 - 5.18677e6i) q^{68} +(-2.33962e7 - 1.04306e7i) q^{69} +(951202. + 1.64753e6i) q^{70} +1.72828e7i q^{71} +(3.86837e6 + 1.82887e7i) q^{72} +2.32289e7 q^{73} +(3.16315e7 - 1.82624e7i) q^{74} +(-1.84451e7 - 2.54141e7i) q^{75} +(1.11075e7 - 1.92388e7i) q^{76} +(2.92368e7 + 1.68799e7i) q^{77} +(5.20980e6 + 4.98063e7i) q^{78} +(-3.55263e7 - 6.15333e7i) q^{79} -4.41930e6i q^{80} +(3.93599e7 - 1.74304e7i) q^{81} -2.55288e7 q^{82} +(-2.74593e7 + 1.58536e7i) q^{83} +(-1.57768e7 + 1.65027e6i) q^{84} +(-2.64703e6 + 4.58479e6i) q^{85} +(4.92848e7 + 2.84546e7i) q^{86} +(7.27917e6 - 5.28310e6i) q^{87} +(-2.61091e7 - 4.52223e7i) q^{88} -4.71037e6i q^{89} +(-6.62939e6 + 1.40223e6i) q^{90} +5.98292e7 q^{91} +(-2.91178e7 + 1.68112e7i) q^{92} +(1.19566e7 - 2.68191e7i) q^{93} +(-1.84284e7 + 3.19189e7i) q^{94} +(-9.81837e6 - 5.66864e6i) q^{95} +(6.07367e7 + 2.70780e7i) q^{96} +(3.45744e7 + 5.98847e7i) q^{97} -4.51454e7i q^{98} +(-8.94409e7 + 8.03719e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) $ 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	16.4845	−	9.51731i	1.03028	−	0.594832i	0.113214	−	0.993571i	$-0.463885\pi$
$2$	16.4845	−	9.51731i	1.03028	−	0.594832i	0.917065	+	0.398739i	$0.130552\pi$
$3$	80.5605	−	8.42672i	0.994574	−	0.104034i
$3$	80.5605	−	8.42672i	0.994574	−	0.104034i
$4$	53.1583	−	92.0729i	0.207650	−	0.359660i
$5$	−46.9888	−	27.1290i	−0.0751821	−	0.0434064i	0.461938	−	0.886912i	$-0.347154\pi$
$5$	−46.9888	−	27.1290i	−0.0751821	−	0.0434064i	−0.537120	+	0.843506i	$0.680488\pi$
$6$	1247.80	−	905.629i	0.962806	−	0.698788i
$7$	−921.012	−	1595.24i	−0.383595	−	0.664406i	0.607978	−	0.793954i	$-0.291981\pi$
$7$	−921.012	−	1595.24i	−0.383595	−	0.664406i	−0.991573	+	0.129548i	$0.958647\pi$
$8$			2849.17i			0.695597i
$9$	6418.98	−	1357.72i	0.978354	−	0.206938i
$10$	−1032.78			−0.103278
$11$	−15872.1	+	9163.77i	−1.08409	+	0.625897i	−0.931996	−	0.362469i	$-0.881934\pi$
$11$	−15872.1	+	9163.77i	−1.08409	+	0.625897i	−0.152090	+	0.988367i	$0.548601\pi$
$12$	3506.59	−	7865.39i	0.169106	−	0.379311i
$13$	−16240.1	+	28128.7i	−0.568611	+	0.984863i	0.428093	+	0.903735i	$0.359186\pi$
$13$	−16240.1	+	28128.7i	−0.568611	+	0.984863i	−0.996704	+	0.0811279i	$0.974148\pi$
$14$	−30364.8	−	17531.1i	−0.790420	−	0.456349i
$15$	−4014.05	−	1789.56i	−0.0792898	−	0.0353494i
$16$	40724.9	+	70537.6i	0.621413	+	1.07632i
$17$		−	97572.1i		−	1.16823i	−0.811670	−	0.584117i	$-0.801441\pi$
$17$		−	97572.1i		−	1.16823i	0.811670	−	0.584117i	$-0.198559\pi$
$18$	92891.6	−	83472.7i	0.884884	−	0.795160i
$19$	208951.			1.60336			0.801680	−	0.597754i	$-0.203940\pi$
$19$	208951.			1.60336			0.801680	+	0.597754i	$0.203940\pi$
$20$	−4995.69	+	2884.26i	−0.0312231	+	0.0180266i
$21$	−87639.8	−	120752.i	−0.450634	−	0.620894i
$22$	−174429.	+	302119.i	−0.744607	+	1.28970i
$23$	−273878.	−	158124.i	−0.978692	−	0.565048i	−0.0768167	−	0.997045i	$-0.524476\pi$
$23$	−273878.	−	158124.i	−0.978692	−	0.565048i	−0.901875	+	0.431997i	$0.857809\pi$
$24$	24009.1	+	229530.i	0.0723654	+	0.691823i
$25$	−193841.	−	335742.i	−0.496232	−	0.859499i
$26$			618248.i			1.35291i
$27$	505675.	−	163470.i	0.951517	−	0.307597i
$28$	−195838.			−0.318614
$29$	96164.1	−	55520.4i	0.135963	−	0.0784983i	−0.430476	−	0.902602i	$-0.641654\pi$
$29$	96164.1	−	55520.4i	0.135963	−	0.0784983i	0.566439	+	0.824104i	$0.308321\pi$
$30$	−83201.2	+	8702.94i	−0.102718	+	0.0107444i
$31$	181257.	−	313947.i	0.196268	−	0.339945i	−0.751048	−	0.660248i	$-0.770451\pi$
$31$	181257.	−	313947.i	0.196268	−	0.339945i	0.947315	+	0.320303i	$0.103785\pi$
$32$	710990.	+	410490.i	0.678052	+	0.391474i
$33$	−1.20144e6	+	871987.i	−1.01309	+	0.735283i
$34$	−928623.	−	1.60842e6i	−0.694903	−	1.20361i
$35$			99944.5i			0.0666019i
$36$	216213.	−	663188.i	0.128728	−	0.394845i
$37$	1.91887e6			1.02385			0.511927	−	0.859029i	$-0.328932\pi$
$37$	1.91887e6			1.02385			0.511927	+	0.859029i	$0.328932\pi$
$38$	3.44445e6	−	1.98865e6i	1.65191	−	0.953729i
$39$	−1.07128e6	+	2.40291e6i	−0.463067	+	1.03867i
$40$	77295.0	−	133879.i	0.0301934	−	0.0522964i
$41$	−1.16149e6	−	670589.i	−0.411038	−	0.237313i	0.280198	−	0.959942i	$-0.409600\pi$
$41$	−1.16149e6	−	670589.i	−0.411038	−	0.237313i	−0.691235	+	0.722630i	$0.742933\pi$
$42$	−2.59393e6	−	1.15644e6i	−0.833606	−	0.371643i
$43$	1.49489e6	+	2.58922e6i	0.437254	+	0.757346i	0.997477	−	0.0709957i	$-0.0226177\pi$
$43$	1.49489e6	+	2.58922e6i	0.437254	+	0.757346i	−0.560222	+	0.828342i	$0.689284\pi$
$44$			1.94852e6i			0.519870i
$45$	−338454.	−	110343.i	−0.0825371	−	0.0269088i
$46$	−6.01964e6			−1.34443
$47$	−1.67689e6	+	968152.i	−0.343647	+	0.198405i	−0.661884	−	0.749607i	$-0.730243\pi$
$47$	−1.67689e6	+	968152.i	−0.343647	+	0.198405i	0.318237	+	0.948011i	$0.396909\pi$
$48$	3.87522e6	+	5.33937e6i	0.730014	+	1.00583i
$49$	1.18588e6	−	2.05400e6i	0.205710	−	0.356300i
$50$	−6.39071e6	−	3.68968e6i	−1.02251	−	0.590349i
$51$	−822212.	−	7.86045e6i	−0.121535	−	1.16189i
$52$	1.72659e6	+	2.99054e6i	0.236144	+	0.409013i
$53$			1.03471e7i			1.31134i	0.755048	+	0.655669i	$0.227613\pi$
$53$			1.03471e7i			1.31134i	−0.755048	+	0.655669i	$0.772387\pi$
$54$	6.77999e6	−	7.50737e6i	0.797359	−	0.882903i
$55$	994415.			0.108672
$56$	4.54510e6	−	2.62411e6i	0.462159	−	0.266828i
$57$	1.68332e7	−	1.76077e6i	1.59466	−	0.166803i
$58$	1.05681e6	−	1.83045e6i	0.0933866	−	0.161750i
$59$	−1.10364e7	−	6.37189e6i	−0.910796	−	0.525848i	−0.0301085	−	0.999547i	$-0.509585\pi$
$59$	−1.10364e7	−	6.37189e6i	−0.910796	−	0.525848i	−0.880687	+	0.473699i	$0.842919\pi$
$60$	−378150.	+	274455.i	−0.0291783	+	0.0211771i
$61$	6.41822e6	+	1.11167e7i	0.463549	+	0.802890i	0.999135	−	0.0415910i	$-0.0132426\pi$
$61$	6.41822e6	+	1.11167e7i	0.463549	+	0.802890i	−0.535586	+	0.844481i	$0.679909\pi$
$62$		−	6.90032e6i		−	0.466985i
$63$	−8.07784e6	−	8.98933e6i	−0.512783	−	0.570644i
$64$	−5.22412e6			−0.311382
$65$	1.52620e6	−	881155.i	0.0854987	−	0.0493627i
$66$	−1.15062e7	+	2.58088e7i	−0.606395	+	1.36016i
$67$	−7.00252e6	+	1.21287e7i	−0.347500	+	0.601888i	−0.985805	−	0.167896i	$-0.946303\pi$
$67$	−7.00252e6	+	1.21287e7i	−0.347500	+	0.601888i	0.638304	+	0.769784i	$0.279636\pi$
$68$	−8.98374e6	−	5.18677e6i	−0.420167	−	0.242583i
$69$	−2.33962e7	−	1.04306e7i	−1.03216	−	0.460165i
$70$	951202.	+	1.64753e6i	0.0396169	+	0.0686185i
$71$			1.72828e7i			0.680112i	0.940405	+	0.340056i	$0.110446\pi$
$71$			1.72828e7i			0.680112i	−0.940405	+	0.340056i	$0.889554\pi$
$72$	3.86837e6	+	1.82887e7i	0.143946	+	0.680540i
$73$	2.32289e7			0.817970			0.408985	−	0.912541i	$-0.365883\pi$
$73$	2.32289e7			0.817970			0.408985	+	0.912541i	$0.365883\pi$
$74$	3.16315e7	−	1.82624e7i	1.05485	−	0.609020i
$75$	−1.84451e7	−	2.54141e7i	−0.582956	−	0.803210i
$76$	1.11075e7	−	1.92388e7i	0.332937	−	0.576664i
$77$	2.92368e7	+	1.68799e7i	0.831700	+	0.480182i
$78$	5.20980e6	+	4.98063e7i	0.140748	+	1.34557i
$79$	−3.55263e7	−	6.15333e7i	−0.912097	−	1.57980i	−0.811096	−	0.584913i	$-0.801129\pi$
$79$	−3.55263e7	−	6.15333e7i	−0.912097	−	1.57980i	−0.101001	−	0.994886i	$-0.532205\pi$
$80$		−	4.41930e6i		−	0.107893i
$81$	3.93599e7	−	1.74304e7i	0.914353	−	0.404917i
$82$	−2.55288e7			−0.564644
$83$	−2.74593e7	+	1.58536e7i	−0.578597	+	0.334053i	−0.760576	−	0.649249i	$-0.775083\pi$
$83$	−2.74593e7	+	1.58536e7i	−0.578597	+	0.334053i	0.181978	+	0.983303i	$0.441750\pi$
$84$	−1.57768e7	+	1.65027e6i	−0.316885	+	0.0331465i
$85$	−2.64703e6	+	4.58479e6i	−0.0507088	+	0.0878302i
$86$	4.92848e7	+	2.84546e7i	0.900988	+	0.520185i
$87$	7.27917e6	−	5.28310e6i	0.127059	−	0.0922171i
$88$	−2.61091e7	−	4.52223e7i	−0.435372	−	0.754087i
$89$		−	4.71037e6i		−	0.0750749i	−0.999295	−	0.0375375i	$-0.988049\pi$
$89$		−	4.71037e6i		−	0.0750749i	0.999295	−	0.0375375i	$-0.0119514\pi$
$90$	−6.62939e6	+	1.40223e6i	−0.101042	+	0.0213721i
$91$	5.98292e7			0.872465
$92$	−2.91178e7	+	1.68112e7i	−0.406450	+	0.234664i
$93$	1.19566e7	−	2.68191e7i	0.159837	−	0.358519i
$94$	−1.84284e7	+	3.19189e7i	−0.236035	+	0.408824i
$95$	−9.81837e6	−	5.66864e6i	−0.120544	−	0.0695960i
$96$	6.07367e7	+	2.70780e7i	0.715100	+	0.318809i
$97$	3.45744e7	+	5.98847e7i	0.390542	+	0.676439i	0.992521	−	0.122073i	$-0.0389542\pi$
$97$	3.45744e7	+	5.98847e7i	0.390542	+	0.676439i	−0.601979	+	0.798512i	$0.705621\pi$
$98$		−	4.51454e7i		−	0.489451i
$99$	−8.94409e7	+	8.03719e7i	−0.931098	+	0.836688i
$100$	−4.12169e7			−0.412169
$101$	−6.62937e7	+	3.82747e7i	−0.637069	+	0.367812i	−0.783485	−	0.621411i	$-0.786560\pi$
$101$	−6.62937e7	+	3.82747e7i	−0.637069	+	0.367812i	0.146416	+	0.989223i	$0.453226\pi$
$102$	−8.83641e7	−	1.21750e8i	−0.816347	−	1.12478i
$103$	−5.37265e7	+	9.30571e7i	−0.477353	+	0.826800i	−0.999663	−	0.0259558i	$-0.991737\pi$
$103$	−5.37265e7	+	9.30571e7i	−0.477353	+	0.826800i	0.522310	+	0.852756i	$0.325070\pi$
$104$	−8.01432e7	−	4.62707e7i	−0.685067	−	0.395524i
$105$	842204.	+	8.05157e6i	0.00692883	+	0.0662405i
$106$	9.84765e7	+	1.70566e8i	0.780026	+	1.35104i
$107$		−	1.67910e8i		−	1.28098i	−0.767968	−	0.640489i	$-0.778732\pi$
$107$		−	1.67910e8i		−	1.28098i	0.767968	−	0.640489i	$-0.221268\pi$
$108$	1.18297e7	−	5.52487e7i	0.0869520	−	0.406095i
$109$	1.20746e8			0.855395			0.427697	−	0.903922i	$-0.359325\pi$
$109$	1.20746e8			0.855395			0.427697	+	0.903922i	$0.359325\pi$
$110$	1.63924e7	−	9.46415e6i	0.111962	−	0.0646414i
$111$	1.54585e8	−	1.61697e7i	1.01830	−	0.106515i
$112$	7.50162e7	−	1.29932e8i	0.476742	−	0.825741i
$113$	4.56007e7	+	2.63276e7i	0.279678	+	0.161472i	0.633278	−	0.773925i	$-0.281709\pi$
$113$	4.56007e7	+	2.63276e7i	0.279678	+	0.161472i	−0.353600	+	0.935397i	$0.615043\pi$
$114$	2.60729e8	−	1.89232e8i	1.54372	−	1.12041i
$115$	8.57947e6	+	1.48601e7i	0.0490534	+	0.0849629i
$116$		−	1.18055e7i		−	0.0652006i
$117$	−6.60540e7	+	2.02607e8i	−0.352497	+	1.08121i
$118$	−2.42573e8			−1.25116
$119$	−1.55651e8	+	8.98650e7i	−0.776182	+	0.448129i
$120$	5.09876e6	−	1.14367e7i	0.0245889	−	0.0551538i
$121$	6.07697e7	−	1.05256e8i	0.283495	−	0.491028i
$122$	2.11602e8	+	1.22168e8i	0.955169	+	0.551467i
$123$	−9.92214e7	−	4.42354e7i	−0.433496	−	0.193263i
$124$	−1.92707e7	−	3.33777e7i	−0.0815098	−	0.141179i
$125$			4.22293e7i			0.172971i
$126$	−2.18713e8	−	7.13050e7i	−0.867746	−	0.282903i
$127$	−2.60681e8			−1.00206			−0.501032	−	0.865429i	$-0.667046\pi$
$127$	−2.60681e8			−1.00206			−0.501032	+	0.865429i	$0.667046\pi$
$128$	−2.68130e8	+	1.54805e8i	−0.998862	+	0.576693i
$129$	1.42247e8	+	1.95992e8i	0.513671	+	0.707748i
$130$	1.67724e7	−	2.90507e7i	0.0587250	−	0.101715i
$131$	8.71036e7	+	5.02893e7i	0.295768	+	0.170762i	0.640540	−	0.767925i	$-0.278711\pi$
$131$	8.71036e7	+	5.02893e7i	0.295768	+	0.170762i	−0.344772	+	0.938686i	$0.612044\pi$
$132$	1.64196e7	+	1.56974e8i	0.0540839	+	0.517049i
$133$	−1.92447e8	−	3.33327e8i	−0.615041	−	1.06528i
$134$			2.66581e8i			0.826817i
$135$	−2.81958e7	−	6.03722e6i	−0.0848887	−	0.0181761i
$136$	2.77999e8			0.812620
$137$	5.57700e8	−	3.21988e8i	1.58314	−	0.914024i	0.588739	−	0.808323i	$-0.299625\pi$
$137$	5.57700e8	−	3.21988e8i	1.58314	−	0.914024i	0.994398	−	0.105701i	$-0.0337086\pi$
$138$	−4.84945e8	+	5.07258e7i	−1.33714	+	0.139866i
$139$	2.55562e7	−	4.42647e7i	0.0684601	−	0.118576i	−0.829764	−	0.558115i	$-0.811525\pi$
$139$	2.55562e7	−	4.42647e7i	0.0684601	−	0.118576i	0.898224	+	0.439539i	$0.144858\pi$
$140$	9.20218e6	+	5.31288e6i	0.0239540	+	0.0138299i
$141$	−1.26933e8	+	9.21254e7i	−0.321142	+	0.233079i
$142$	1.64486e8	+	2.84897e8i	0.404552	+	0.700705i
$143$		−	5.95281e8i		−	1.42357i
$144$	3.57183e8	+	3.97487e8i	0.830693	+	0.924427i
$145$	−6.02485e6			−0.0136293
$146$	3.82916e8	−	2.21077e8i	0.842737	−	0.486555i
$147$	7.82263e7	−	1.75464e8i	0.167526	−	0.375767i
$148$	1.02004e8	−	1.76676e8i	0.212603	−	0.368239i
$149$	8.81724e7	+	5.09063e7i	0.178891	+	0.103282i	0.586771	−	0.809753i	$-0.300399\pi$
$149$	8.81724e7	+	5.09063e7i	0.178891	+	0.103282i	−0.407881	+	0.913035i	$0.633732\pi$
$150$	−5.45931e8	−	2.43390e8i	−1.07838	−	0.480770i
$151$	−1.38856e8	−	2.40506e8i	−0.267090	−	0.462613i	0.701019	−	0.713142i	$-0.252729\pi$
$151$	−1.38856e8	−	2.40506e8i	−0.267090	−	0.462613i	−0.968109	+	0.250529i	$0.919395\pi$
$152$			5.95337e8i			1.11529i
$153$	−1.32476e8	−	6.26313e8i	−0.241752	−	1.14295i
$154$	6.42604e8			1.14251
$155$	−1.70341e7	+	9.83465e6i	−0.0295116	+	0.0170385i
$156$	1.64296e8	+	2.26370e8i	0.277413	+	0.382227i
$157$	−3.32160e8	+	5.75317e8i	−0.546699	+	0.946910i	0.451799	+	0.892120i	$0.350782\pi$
$157$	−3.32160e8	+	5.75317e8i	−0.546699	+	0.946910i	−0.998498	+	0.0547905i	$0.982551\pi$
$158$	−1.17126e9	−	6.76229e8i	−1.87943	−	1.08509i
$159$	8.71920e7	+	8.33567e8i	0.136423	+	1.30422i
$160$	−2.22724e7	−	3.85769e7i	−0.0339849	−	0.0588636i
$161$			5.82535e8i			0.866998i
$162$	4.82937e8	−	6.61931e8i	0.701181	−	0.961064i
$163$	−3.76238e8			−0.532981			−0.266491	−	0.963838i	$-0.585864\pi$
$163$	−3.76238e8			−0.532981			−0.266491	+	0.963838i	$0.585864\pi$
$164$	−1.23486e8	+	7.12947e7i	−0.170704	+	0.0985558i
$165$	8.01105e7	−	8.37965e6i	0.108082	−	0.0113055i
$166$	−3.01767e8	+	5.22676e8i	−0.397411	+	0.688336i
$167$	4.60947e8	+	2.66128e8i	0.592632	+	0.342156i	0.766137	−	0.642677i	$-0.222176\pi$
$167$	4.60947e8	+	2.66128e8i	0.592632	+	0.342156i	−0.173506	+	0.984833i	$0.555510\pi$
$168$	3.44043e8	−	2.49700e8i	0.431892	−	0.313460i
$169$	−1.19616e8	−	2.07180e8i	−0.146636	−	0.253981i
$170$			1.00770e8i			0.120653i
$171$	1.34126e9	−	2.83698e8i	1.56865	−	0.331796i
$172$	3.17862e8			0.363183
$173$	−9.67319e8	+	5.58482e8i	−1.07990	+	0.623483i	−0.930870	−	0.365349i	$-0.880950\pi$
$173$	−9.67319e8	+	5.58482e8i	−1.07990	+	0.623483i	−0.149033	+	0.988832i	$0.547616\pi$
$174$	6.97124e7	−	1.56367e8i	0.0760524	−	0.170588i
$175$	−3.57059e8	+	6.18444e8i	−0.380704	+	0.659399i
$176$	−1.29278e9	−	7.46387e8i	−1.34733	−	0.777882i
$177$	−9.42795e8	−	4.20322e8i	−0.960559	−	0.428241i
$178$	−4.48300e7	−	7.76479e7i	−0.0446570	−	0.0773481i
$179$			1.48500e8i			0.144648i	0.997381	+	0.0723242i	$0.0230416\pi$
$179$			1.48500e8i			0.144648i	−0.997381	+	0.0723242i	$0.976958\pi$
$180$	−2.81512e7	+	2.52968e7i	−0.0268168	+	0.0240977i
$181$	−3.87611e7			−0.0361146			−0.0180573	−	0.999837i	$-0.505748\pi$
$181$	−3.87611e7			−0.0361146			−0.0180573	+	0.999837i	$0.505748\pi$
$182$	9.86253e8	−	5.69413e8i	0.898882	−	0.518970i
$183$	6.10732e8	+	8.41481e8i	0.544561	+	0.750308i
$184$	4.50520e8	−	7.80324e8i	0.393046	−	0.680775i
$185$	−9.01652e7	−	5.20569e7i	−0.0769754	−	0.0444418i
$186$	−5.81471e7	−	5.55893e8i	−0.0485821	−	0.464451i
$187$	8.94127e8	+	1.54867e9i	0.731195	+	1.26647i
$188$			2.05861e8i			0.164795i
$189$	−7.26506e8	−	6.56115e8i	−0.569366	−	0.514201i
$190$	−2.15801e8			−0.165592
$191$	1.34933e9	−	7.79034e8i	1.01387	−	0.585360i	0.101550	−	0.994830i	$-0.467620\pi$
$191$	1.34933e9	−	7.79034e8i	1.01387	−	0.585360i	0.912323	+	0.409470i	$0.134286\pi$
$192$	−4.20857e8	+	4.40222e7i	−0.309692	+	0.0323941i
$193$	1.07571e9	−	1.86319e9i	0.775295	−	1.34285i	−0.159334	−	0.987225i	$-0.550935\pi$
$193$	1.07571e9	−	1.86319e9i	0.775295	−	1.34285i	0.934629	−	0.355625i	$-0.115732\pi$
$194$	1.13988e9	+	6.58111e8i	0.804735	+	0.464614i
$195$	1.15527e8	−	8.38471e7i	0.0798993	−	0.0579895i
$196$	−1.26078e8	−	2.18374e8i	−0.0854311	−	0.147971i
$197$		−	1.66896e9i		−	1.10810i	−0.832483	−	0.554051i	$-0.813081\pi$
$197$		−	1.66896e9i		−	1.10810i	0.832483	−	0.554051i	$-0.186919\pi$
$198$	−7.09461e8	+	2.17612e9i	−0.461602	+	1.41587i
$199$	4.47037e8			0.285057			0.142528	−	0.989791i	$-0.454477\pi$
$199$	4.47037e8			0.285057			0.142528	+	0.989791i	$0.454477\pi$
$200$	9.56584e8	−	5.52284e8i	0.597865	−	0.345177i
$201$	−4.61921e8	+	1.03610e9i	−0.282998	+	0.634774i
$202$	−7.28544e8	+	1.26187e9i	−0.437572	+	0.757898i
$203$	−1.77137e8	−	1.02270e8i	−0.104310	−	0.0602231i
$204$	−7.67442e8	−	3.42145e8i	−0.443124	−	0.197556i
$205$	3.63848e7	+	6.30203e7i	0.0206018	+	0.0356833i
$206$			2.04533e9i			1.13578i
$207$	−1.97271e9	−	6.43142e8i	−1.07444	−	0.350288i
$208$	−2.64551e9			−1.41337
$209$	−3.31650e9	+	1.91478e9i	−1.73818	+	1.00354i
$210$	9.05126e7	+	1.24710e8i	0.0465406	+	0.0641247i
$211$	7.23373e8	−	1.25292e9i	0.364949	−	0.632111i	−0.623819	−	0.781569i	$-0.714420\pi$
$211$	7.23373e8	−	1.25292e9i	0.364949	−	0.632111i	0.988768	+	0.149458i	$0.0477530\pi$
$212$	9.52687e8	+	5.50034e8i	0.471636	+	0.272299i
$213$	1.45637e8	+	1.39231e9i	0.0707545	+	0.676422i
$214$	−1.59805e9	−	2.76791e9i	−0.761966	−	1.31976i
$215$		−	1.62219e8i		−	0.0759185i
$216$	4.65752e8	+	1.44075e9i	0.213963	+	0.661872i
$217$	−6.67760e8			−0.301149
$218$	1.99043e9	−	1.14918e9i	0.881295	−	0.508816i
$219$	1.87133e9	−	1.95743e8i	0.813532	−	0.0850963i
$220$	5.28614e7	−	9.15587e7i	0.0225657	−	0.0390849i
$221$	2.74457e9	+	1.58458e9i	1.15055	+	0.664270i
$222$	2.39435e9	−	1.73778e9i	0.985772	−	0.715456i
$223$	6.71529e8	+	1.16312e9i	0.271547	+	0.470333i	0.969258	−	0.246046i	$-0.0791314\pi$
$223$	6.71529e8	+	1.16312e9i	0.271547	+	0.470333i	−0.697711	+	0.716379i	$0.745798\pi$
$224$		−	1.51226e9i		−	0.600670i
$225$	−1.70010e9	−	1.89194e9i	−0.663353	−	0.738205i
$226$	1.00227e9			0.384195
$227$	−1.83609e9	+	1.06007e9i	−0.691498	+	0.399237i	−0.804173	−	0.594395i	$-0.797391\pi$
$227$	−1.83609e9	+	1.06007e9i	−0.691498	+	0.399237i	0.112675	+	0.993632i	$0.464058\pi$
$228$	7.32706e8	−	1.64348e9i	0.271138	−	0.608171i
$229$	1.89310e9	−	3.27894e9i	0.688385	−	1.19232i	−0.283976	−	0.958831i	$-0.591654\pi$
$229$	1.89310e9	−	3.27894e9i	0.688385	−	1.19232i	0.972360	−	0.233486i	$-0.0750132\pi$
$230$	2.82856e8	+	1.63307e8i	0.101077	+	0.0583570i
$231$	2.49757e9	+	1.11348e9i	0.877142	+	0.391052i
$232$	1.58187e8	+	2.73988e8i	0.0546032	+	0.0945755i
$233$			7.71302e8i			0.261698i	0.991402	+	0.130849i	$0.0417703\pi$
$233$			7.71302e8i			0.261698i	−0.991402	+	0.130849i	$0.958230\pi$
$234$	8.39408e8	+	3.96852e9i	0.279969	+	1.32363i
$235$	1.05060e8			0.0344481
$236$	−1.17336e9	+	6.77438e8i	−0.378253	+	0.218384i
$237$	−3.38054e9	−	4.65778e9i	−1.07150	−	1.47634i
$238$	−1.71055e9	+	2.96275e9i	−0.533122	+	0.923395i
$239$	−4.44884e9	−	2.56854e9i	−1.36350	−	0.787217i	−0.373411	−	0.927666i	$-0.621812\pi$
$239$	−4.44884e9	−	2.56854e9i	−1.36350	−	0.787217i	−0.990088	+	0.140449i	$0.955145\pi$
$240$	−3.72402e7	−	3.56021e8i	−0.0112245	−	0.107308i
$241$	1.52624e9	+	2.64352e9i	0.452433	+	0.783636i	0.998537	−	0.0540811i	$-0.0172230\pi$
$241$	1.52624e9	+	2.64352e9i	0.452433	+	0.783636i	−0.546104	+	0.837717i	$0.683890\pi$
$242$		−	2.31346e9i		−	0.674528i
$243$	3.02397e9	−	1.73587e9i	0.867267	−	0.497844i
$244$	1.36473e9			0.385023
$245$	−1.11446e8	+	6.43432e7i	−0.0309314	+	0.0178582i
$246$	−2.05661e9	+	2.15124e8i	−0.561580	+	0.0587419i
$247$	−3.39339e9	+	5.87752e9i	−0.911687	+	1.57909i
$248$	8.94486e8	+	5.16432e8i	0.236465	+	0.136523i
$249$	−2.07854e9	+	1.50857e9i	−0.540705	+	0.392434i
$250$	4.01909e8	+	6.96128e8i	0.102889	+	0.178209i
$251$		−	7.81654e9i		−	1.96934i	−0.174440	−	0.984668i	$-0.555811\pi$
$251$		−	7.81654e9i		−	1.96934i	0.174440	−	0.984668i	$-0.444189\pi$
$252$	−1.25708e9	+	2.65893e8i	−0.311717	+	0.0659333i
$253$	5.79603e9			1.41465
$254$	−4.29719e9	+	2.48099e9i	−1.03240	+	0.596059i
$255$	−1.74611e8	+	3.91659e8i	−0.0412964	+	0.0926291i
$256$	−2.27797e9	+	3.94555e9i	−0.530380	+	0.918646i
$257$	4.91857e9	+	2.83974e9i	1.12747	+	0.650947i	0.943298	−	0.331946i	$-0.107705\pi$
$257$	4.91857e9	+	2.83974e9i	1.12747	+	0.650947i	0.184175	+	0.982893i	$0.441039\pi$
$258$	4.21018e9	+	1.87700e9i	0.950215	+	0.423630i
$259$	−1.76730e9	−	3.06105e9i	−0.392745	−	0.680254i
$260$		−	1.87363e8i		−	0.0410006i
$261$	5.41895e8	−	4.86948e8i	0.116776	−	0.104935i
$262$	1.91447e9			0.406298
$263$	−3.56245e9	+	2.05678e9i	−0.744606	+	0.429898i	−0.823742	−	0.566966i	$-0.808117\pi$
$263$	−3.56245e9	+	2.05678e9i	−0.744606	+	0.429898i	0.0791358	+	0.996864i	$0.474784\pi$
$264$	−2.48444e9	−	3.42311e9i	−0.511460	−	0.704702i
$265$	2.80706e8	−	4.86197e8i	0.0569205	−	0.0985892i
$266$	−6.34476e9	−	3.66315e9i	−1.26733	−	0.731691i
$267$	−3.96929e7	−	3.79470e8i	−0.00781031	−	0.0746676i
$268$	7.44484e8	+	1.28948e9i	0.144317	+	0.249964i
$269$			7.56195e9i			1.44419i	0.691793	+	0.722096i	$0.256821\pi$
$269$			7.56195e9i			1.44419i	−0.691793	+	0.722096i	$0.743179\pi$
$270$	−5.22251e8	+	1.68828e8i	−0.0982707	+	0.0317680i
$271$	−6.29007e9			−1.16621			−0.583107	−	0.812395i	$-0.698163\pi$
$271$	−6.29007e9			−1.16621			−0.583107	+	0.812395i	$0.698163\pi$
$272$	6.88250e9	−	3.97361e9i	1.25739	−	0.725956i
$273$	4.81987e9	−	5.04164e8i	0.867731	−	0.0907656i
$274$	6.12892e9	−	1.06156e10i	1.08738	−	1.88340i
$275$	6.15332e9	+	3.55262e9i	1.07592	+	0.621180i
$276$	−2.20408e9	+	1.59968e9i	−0.379832	+	0.275675i
$277$	−1.49367e9	−	2.58711e9i	−0.253708	−	0.439436i	0.710836	−	0.703358i	$-0.248317\pi$
$277$	−1.49367e9	−	2.58711e9i	−0.253708	−	0.439436i	−0.964544	+	0.263923i	$0.914984\pi$
$278$		−	9.72906e8i		−	0.162889i
$279$	7.37234e8	−	2.26131e9i	0.121671	−	0.373202i
$280$	−2.84758e8			−0.0463281
$281$	3.13118e8	−	1.80779e8i	0.0502207	−	0.0289949i	−0.474679	−	0.880159i	$-0.657436\pi$
$281$	3.13118e8	−	1.80779e8i	0.0502207	−	0.0289949i	0.524900	+	0.851164i	$0.324103\pi$
$282$	−1.21563e9	+	2.72669e9i	−0.192223	+	0.431162i
$283$	−2.03882e9	+	3.53133e9i	−0.317858	+	0.550545i	−0.980041	−	0.198797i	$-0.936297\pi$
$283$	−2.03882e9	+	3.53133e9i	−0.317858	+	0.550545i	0.662183	+	0.749342i	$0.269630\pi$
$284$	1.59128e9	+	9.18724e8i	0.244609	+	0.141225i
$285$	−8.38741e8	−	3.73932e8i	−0.127130	−	0.0566778i
$286$	−5.66548e9	−	9.81289e9i	−0.846783	−	1.46667i
$287$			2.47048e9i			0.364128i
$288$	5.12116e9	+	1.66960e9i	0.744386	+	0.242685i
$289$	−2.54455e9			−0.364770
$290$	−9.93164e7	+	5.73403e7i	−0.0140420	+	0.00810715i
$291$	3.28996e9	+	4.53299e9i	0.458795	+	0.632139i
$292$	1.23481e9	−	2.13875e9i	0.169851	−	0.294191i
$293$	1.95369e9	+	1.12796e9i	0.265085	+	0.153047i	0.626652	−	0.779299i	$-0.284425\pi$
$293$	1.95369e9	+	1.12796e9i	0.265085	+	0.153047i	−0.361567	+	0.932346i	$0.617758\pi$
$294$	−3.80427e8	−	3.63693e9i	−0.0509193	−	0.486795i
$295$	3.45726e8	+	5.98815e8i	0.0456503	+	0.0790687i
$296$			5.46717e9i			0.712189i
$297$	−6.52813e9	+	7.22849e9i	−0.839002	+	0.929013i
$298$	1.93797e9			0.245743
$299$	8.89561e9	−	5.13588e9i	1.11299	−	0.642584i
$300$	−3.32046e9	+	3.47324e8i	−0.409933	+	0.0428794i
$301$	2.75361e9	−	4.76940e9i	0.335457	−	0.581029i
$302$	−4.57793e9	−	2.64307e9i	−0.550354	−	0.317747i
$303$	−5.01812e9	+	3.64206e9i	−0.595347	+	0.432093i
$304$	8.50953e9	+	1.47389e10i	0.996348	+	1.72573i
$305$		−	6.96479e8i		−	0.0804839i
$306$	−8.14460e9	−	9.06362e9i	−0.928933	−	1.03375i
$307$	−6.57116e9			−0.739756			−0.369878	−	0.929080i	$-0.620601\pi$
$307$	−6.57116e9			−0.739756			−0.369878	+	0.929080i	$0.620601\pi$
$308$	3.10836e9	−	1.79461e9i	0.345405	−	0.199419i
$309$	−3.54407e9	+	7.94946e9i	−0.388748	+	0.871974i
$310$	−1.87199e8	+	3.24238e8i	−0.0202701	+	0.0351089i
$311$	−1.13691e10	−	6.56393e9i	−1.21530	−	0.701653i	−0.251389	−	0.967886i	$-0.580887\pi$
$311$	−1.13691e10	−	6.56393e9i	−1.21530	−	0.701653i	−0.963909	+	0.266233i	$0.914221\pi$
$312$	−6.84628e9	−	3.05225e9i	−0.722498	−	0.322108i
$313$	−1.29417e9	−	2.24157e9i	−0.134839	−	0.233547i	0.790697	−	0.612207i	$-0.209718\pi$
$313$	−1.29417e9	−	2.24157e9i	−0.134839	−	0.233547i	−0.925536	+	0.378660i	$0.876385\pi$
$314$			1.26451e10i			1.30078i
$315$	1.35697e8	+	6.41542e8i	0.0137825	+	0.0651602i
$316$	−7.55407e9			−0.757587
$317$	4.30655e9	−	2.48639e9i	0.426474	−	0.246225i	−0.271369	−	0.962475i	$-0.587477\pi$
$317$	4.30655e9	−	2.48639e9i	0.426474	−	0.246225i	0.697843	+	0.716250i	$0.254143\pi$
$318$	9.37062e9	+	1.29111e10i	0.916347	+	1.26256i
$319$	−1.01755e9	+	1.76245e9i	−0.0982638	+	0.170198i
$320$	2.45475e8	+	1.41725e8i	0.0234103	+	0.0135160i
$321$	−1.41493e9	−	1.35269e10i	−0.133265	−	1.27403i
$322$	5.54416e9	+	9.60277e9i	0.515718	+	0.893250i
$323$		−	2.03878e10i		−	1.87310i
$324$	4.87442e8	−	4.55055e9i	0.0442327	−	0.412937i
$325$	1.25920e10			1.12865
$326$	−6.20208e9	+	3.58077e9i	−0.549119	+	0.317034i
$327$	9.72735e9	−	1.01749e9i	0.850753	−	0.0889897i
$328$	1.91062e9	−	3.30929e9i	0.165074	−	0.285916i
$329$	3.08887e9	+	1.78336e9i	0.263643	+	0.152214i
$330$	1.24083e9	−	9.00571e8i	0.104630	−	0.0759385i
$331$	1.89585e8	+	3.28371e8i	0.0157940	+	0.0273560i	0.873814	−	0.486260i	$-0.161639\pi$
$331$	1.89585e8	+	3.28371e8i	0.0157940	+	0.0273560i	−0.858020	+	0.513616i	$0.828306\pi$
$332$			3.37100e9i			0.277464i
$333$	1.23172e10	−	2.60528e9i	1.00169	−	0.211874i
$334$	1.01313e10			0.814101
$335$	6.58080e8	−	3.79943e8i	0.0522516	−	0.0301675i
$336$	4.94844e9	−	1.10995e10i	0.388250	−	0.870857i
$337$	7.52936e8	−	1.30412e9i	0.0583766	−	0.101111i	−0.835360	−	0.549703i	$-0.814741\pi$
$337$	7.52936e8	−	1.30412e9i	0.0583766	−	0.101111i	0.893737	+	0.448592i	$0.148074\pi$
$338$	−3.94360e9	−	2.27684e9i	−0.302152	−	0.174448i
$339$	3.89547e9	+	1.73670e9i	0.294959	+	0.131500i
$340$	2.81423e8	+	4.87440e8i	0.0210593	+	0.0364758i
$341$			6.64399e9i			0.491373i
$342$	1.94098e10	−	1.74417e10i	1.41879	−	1.27493i
$343$	−1.49877e10			−1.08283
$344$	−7.37711e9	+	4.25917e9i	−0.526808	+	0.304153i
$345$	8.16387e8	+	1.12484e9i	0.0576262	+	0.0793987i
$346$	−1.06305e10	+	1.84125e10i	−0.741735	+	1.28472i
$347$	−1.78865e10	−	1.03268e10i	−1.23369	−	0.712274i	−0.265897	−	0.964002i	$-0.585668\pi$
$347$	−1.78865e10	−	1.03268e10i	−1.23369	−	0.712274i	−0.967798	+	0.251728i	$0.919001\pi$
$348$	−9.94814e7	−	9.51055e8i	−0.00678305	−	0.0648468i
$349$	−5.62214e9	−	9.73783e9i	−0.378966	−	0.656388i	0.611946	−	0.790899i	$-0.290387\pi$
$349$	−5.62214e9	−	9.73783e9i	−0.378966	−	0.656388i	−0.990912	+	0.134511i	$0.957054\pi$
$350$			1.35930e10i			0.905820i
$351$	−3.61403e9	+	1.68787e10i	−0.238102	+	1.11202i
$352$	−1.50465e10			−0.980090
$353$	−3.62138e9	+	2.09080e9i	−0.233225	+	0.134653i	−0.612059	−	0.790812i	$-0.709658\pi$
$353$	−3.62138e9	+	2.09080e9i	−0.233225	+	0.134653i	0.378834	+	0.925465i	$0.376325\pi$
$354$	−1.95418e10	+	2.04409e9i	−1.24438	+	0.130163i
$355$	4.68865e8	−	8.12097e8i	0.0295212	−	0.0511322i
$356$	−4.33697e8	−	2.50395e8i	−0.0270014	−	0.0155893i
$357$	−1.17820e10	+	8.55119e9i	−0.725349	+	0.526446i
$358$	1.41332e9	+	2.44794e9i	0.0860415	+	0.149028i
$359$			1.61776e10i			0.973950i	0.873416	+	0.486975i	$0.161900\pi$
$359$			1.61776e10i			0.973950i	−0.873416	+	0.486975i	$0.838100\pi$
$360$	3.14385e8	−	9.64311e8i	0.0187177	−	0.0574126i
$361$	2.66771e10			1.57076
$362$	−6.38957e8	+	3.68902e8i	−0.0372081	+	0.0214821i
$363$	4.00867e9	−	8.99159e9i	0.230874	−	0.517857i
$364$	3.18042e9	−	5.50865e9i	0.181167	−	0.313791i
$365$	−1.09150e9	−	6.30177e8i	−0.0614967	−	0.0355051i
$366$	1.80762e10	+	8.05883e9i	1.00736	+	0.449105i
$367$	−4.41622e9	−	7.64912e9i	−0.243437	−	0.421646i	0.718254	−	0.695781i	$-0.244942\pi$
$367$	−4.41622e9	−	7.64912e9i	−0.243437	−	0.421646i	−0.961691	+	0.274136i	$0.911608\pi$
$368$		−	2.57583e10i		−	1.40451i
$369$	−8.36608e9	−	2.72751e9i	−0.451249	−	0.147116i
$370$	−1.98177e9			−0.105742
$371$	1.65061e10	−	9.52979e9i	0.871261	−	0.503023i
$372$	−1.83372e9	−	2.52654e9i	−0.0957548	−	0.131933i
$373$	−1.14224e10	+	1.97841e10i	−0.590094	+	1.02207i	0.404125	+	0.914704i	$0.367576\pi$
$373$	−1.14224e10	+	1.97841e10i	−0.590094	+	1.02207i	−0.994219	+	0.107369i	$0.965757\pi$
$374$	2.94784e10	+	1.70194e10i	1.50667	+	0.869876i
$375$	3.55855e8	+	3.40201e9i	0.0179948	+	0.172033i
$376$	−2.75842e9	−	4.77773e9i	−0.138010	−	0.239040i
$377$			3.60662e9i			0.178540i
$378$	−1.82205e10	−	3.90133e9i	−0.892469	−	0.191093i
$379$	2.47178e10			1.19799			0.598995	−	0.800753i	$-0.295567\pi$
$379$	2.47178e10			1.19799			0.598995	+	0.800753i	$0.295567\pi$
$380$	−1.04386e9	+	6.02671e8i	−0.0500618	+	0.0289032i
$381$	−2.10006e10	+	2.19669e9i	−0.996626	+	0.104248i
$382$	1.48286e10	−	2.56839e10i	0.696382	−	1.20617i
$383$	3.94315e9	+	2.27658e9i	0.183252	+	0.105800i	0.588819	−	0.808265i	$-0.299593\pi$
$383$	3.94315e9	+	2.27658e9i	0.183252	+	0.105800i	−0.405568	+	0.914065i	$0.632926\pi$
$384$	−2.02962e10	+	1.47306e10i	−0.933447	+	0.677479i
$385$	−9.15868e8	−	1.58633e9i	−0.0416860	−	0.0722022i
$386$		−	4.09515e10i		−	1.84468i
$387$	1.31111e10	+	1.45905e10i	0.584513	+	0.650468i
$388$	7.35167e9			0.324384
$389$	6.97457e9	−	4.02677e9i	0.304592	−	0.175856i	−0.339912	−	0.940457i	$-0.610397\pi$
$389$	6.97457e9	−	4.02677e9i	0.304592	−	0.175856i	0.644504	+	0.764601i	$0.277064\pi$
$390$	1.10639e9	−	2.48168e9i	0.0478246	−	0.107272i
$391$	−1.54284e10	+	2.67228e10i	−0.660108	+	1.14334i
$392$	5.85218e9	+	3.37876e9i	0.247841	+	0.143091i
$393$	7.44088e9	+	3.31733e9i	0.311928	+	0.139065i
$394$	−1.58840e10	−	2.75118e10i	−0.659134	−	1.14165i
$395$			3.85517e9i			0.158363i
$396$	2.64555e9	+	1.25075e10i	0.107581	+	0.508617i
$397$	−2.77691e10			−1.11789			−0.558946	−	0.829204i	$-0.688794\pi$
$397$	−2.77691e10			−1.11789			−0.558946	+	0.829204i	$0.688794\pi$
$398$	7.36917e9	−	4.25459e9i	0.293688	−	0.169561i
$399$	−1.83125e10	−	2.52313e10i	−0.722528	−	0.995516i
$400$	1.57883e10	−	2.73461e10i	0.616730	−	1.06821i
$401$	2.11169e10	+	1.21919e10i	0.816682	+	0.471512i	0.849271	−	0.527957i	$-0.177042\pi$
$401$	2.11169e10	+	1.21919e10i	0.816682	+	0.471512i	−0.0325886	+	0.999469i	$0.510375\pi$
$402$	2.24640e9	+	2.14759e10i	0.0860167	+	0.822330i
$403$	5.88726e9	+	1.01970e10i	0.223200	+	0.386593i
$404$			8.13847e9i			0.305504i
$405$	−2.32234e9	−	2.48763e8i	−0.0863190	−	0.00924625i
$406$	−3.89333e9			−0.143291
$407$	−3.04564e10	+	1.75840e10i	−1.10995	+	0.640827i
$408$	2.23957e10	−	2.34262e9i	0.808211	−	0.0845397i
$409$	2.41854e10	−	4.18904e10i	0.864292	−	1.49700i	−0.00345597	−	0.999994i	$-0.501100\pi$
$409$	2.41854e10	−	4.18904e10i	0.864292	−	1.49700i	0.867748	−	0.497004i	$-0.165567\pi$
$410$	1.19957e9	+	6.92571e8i	0.0424511	+	0.0245092i
$411$	4.22153e10	−	3.06391e10i	1.47946	−	1.07376i
$412$	5.71202e9	+	9.89351e9i	0.198244	+	0.343370i
$413$			2.34743e10i			0.806851i
$414$	−3.86400e10	+	8.17299e9i	−1.31533	+	0.278215i
$415$	1.72037e9			0.0580002
$416$	−2.30931e10	+	1.33328e10i	−0.771096	+	0.445192i
$417$	1.68582e9	−	3.78134e9i	0.0557527	−	0.125055i
$418$	−3.64471e10	+	6.31283e10i	−1.19387	+	2.06785i
$419$	2.62485e10	+	1.51546e10i	0.851624	+	0.491685i	0.861198	−	0.508269i	$-0.169714\pi$
$419$	2.62485e10	+	1.51546e10i	0.851624	+	0.491685i	−0.00957454	+	0.999954i	$0.503048\pi$
$420$	7.86102e8	+	3.50464e8i	0.0252628	+	0.0112628i
$421$	−3.37935e8	−	5.85321e8i	−0.0107573	−	0.0186323i	0.860597	−	0.509287i	$-0.170091\pi$
$421$	−3.37935e8	−	5.85321e8i	−0.0107573	−	0.0186323i	−0.871354	+	0.490655i	$0.836758\pi$
$422$		−	2.75383e10i		−	0.868334i
$423$	−9.44943e9	+	8.49129e9i	−0.295151	+	0.265224i
$424$	−2.94806e10			−0.912163
$425$	−3.27590e10	+	1.89134e10i	−1.00410	+	0.579715i
$426$	1.56518e10	+	2.15654e10i	0.475254	+	0.654816i
$427$	1.18225e10	−	2.04772e10i	0.355630	−	0.615969i
$428$	−1.54600e10	−	8.92581e9i	−0.460716	−	0.265995i
$429$	−5.01627e9	−	4.79562e10i	−0.148099	−	1.41584i
$430$	−1.54389e9	−	2.67409e9i	−0.0451587	−	0.0782172i
$431$		−	3.59140e9i		−	0.104077i	−0.998645	−	0.0520384i	$-0.983428\pi$
$431$		−	3.59140e9i		−	0.104077i	0.998645	−	0.0520384i	$-0.0165718\pi$
$432$	3.21243e10	+	2.90118e10i	0.922357	+	0.832991i
$433$	−4.82741e10			−1.37329			−0.686646	−	0.726992i	$-0.740918\pi$
$433$	−4.82741e10			−1.37329			−0.686646	+	0.726992i	$0.740918\pi$
$434$	−1.10077e10	+	6.35528e9i	−0.310267	+	0.179133i
$435$	−4.85365e8	+	5.07697e7i	−0.0135554	+	0.00141791i
$436$	6.41865e9	−	1.11174e10i	0.177622	−	0.307651i
$437$	−5.72272e10	−	3.30401e10i	−1.56919	−	0.905975i
$438$	2.89850e10	−	2.10368e10i	0.787546	−	0.571587i
$439$	3.41050e10	+	5.90716e10i	0.918248	+	1.59045i	0.802075	+	0.597223i	$0.203729\pi$
$439$	3.41050e10	+	5.90716e10i	0.918248	+	1.59045i	0.116173	+	0.993229i	$0.462937\pi$
$440$			2.83325e9i			0.0755918i
$441$	4.82336e9	−	1.47947e10i	0.127525	−	0.391156i
$442$	6.03237e10			1.58052
$443$	3.44012e10	−	1.98615e10i	0.893220	−	0.515701i	0.0182258	−	0.999834i	$-0.494198\pi$
$443$	3.44012e10	−	1.98615e10i	0.893220	−	0.515701i	0.874994	+	0.484133i	$0.160865\pi$
$444$	6.72867e9	−	1.50926e10i	0.173140	−	0.388359i
$445$	−1.27788e8	+	2.21335e8i	−0.00325873	+	0.00564429i
$446$	2.21396e10	+	1.27823e10i	0.559539	+	0.323050i
$447$	7.53218e9	+	3.35803e9i	0.188665	+	0.0841115i
$448$	4.81147e9	+	8.33372e9i	0.119444	+	0.206884i
$449$		−	4.02929e10i		−	0.991386i	−0.868498	−	0.495693i	$-0.834914\pi$
$449$		−	4.02929e10i		−	0.991386i	0.868498	−	0.495693i	$-0.165086\pi$
$450$	−4.60314e10	−	1.50072e10i	−1.12255	−	0.365973i
$451$	2.45805e10			0.594133
$452$	4.84812e9	−	2.79906e9i	0.116150	−	0.0670592i
$453$	−1.32130e10	−	1.82052e10i	−0.313768	−	0.432316i
$454$	−2.01780e10	+	3.49493e10i	−0.474957	+	0.822650i
$455$	−2.81130e9	−	1.62311e9i	−0.0655937	−	0.0378705i
$456$	5.01674e9	+	4.79606e10i	0.116028	+	1.10924i
$457$	2.25809e10	+	3.91113e10i	0.517698	+	0.896680i	0.999789	+	0.0205582i	$0.00654433\pi$
$457$	2.25809e10	+	3.91113e10i	0.517698	+	0.896680i	−0.482090	+	0.876121i	$0.660122\pi$
$458$		−	7.20688e10i		−	1.63789i
$459$	−1.59501e10	−	4.93398e10i	−0.359345	−	1.11159i
$460$	1.82428e9			0.0407437
$461$	4.07475e9	−	2.35256e9i	0.0902190	−	0.0520879i	−0.454212	−	0.890894i	$-0.650079\pi$
$461$	4.07475e9	−	2.35256e9i	0.0902190	−	0.0520879i	0.544431	+	0.838806i	$0.316746\pi$
$462$	5.17685e10	−	5.41504e9i	1.13631	−	0.118859i
$463$	1.74222e10	−	3.01762e10i	0.379122	−	0.656659i	−0.611812	−	0.791003i	$-0.709559\pi$
$463$	1.74222e10	−	3.01762e10i	0.379122	−	0.656659i	0.990935	+	0.134344i	$0.0428926\pi$
$464$	7.83255e9	+	4.52213e9i	0.168978	+	0.0975598i
$465$	−1.28940e9	+	9.35826e8i	−0.0275789	+	0.0200163i
$466$	7.34072e9	+	1.27145e10i	0.155666	+	0.269622i
$467$			9.27082e10i			1.94917i	0.224011	+	0.974587i	$0.428085\pi$
$467$			9.27082e10i			1.94917i	−0.224011	+	0.974587i	$0.571915\pi$
$468$	1.51433e10	+	1.68520e10i	0.315672	+	0.351292i
$469$	2.57976e10			0.533198
$470$	1.73186e9	−	9.99888e8i	0.0354912	−	0.0204908i
$471$	−2.19109e10	+	4.91469e10i	−0.445222	+	0.998647i
$472$	1.81546e10	−	3.14446e10i	0.365778	−	0.633547i
$473$	−4.74540e10	−	2.73976e10i	−0.948043	−	0.547353i
$474$	−1.00056e11	−	4.46074e10i	−1.98212	−	0.883677i
$475$	−4.05033e10	−	7.01537e10i	−0.795638	−	1.37809i
$476$			1.91083e10i			0.372215i
$477$	1.40485e10	+	6.64178e10i	0.271366	+	1.28295i
$478$	−9.77822e10			−1.87305
$479$	2.82374e10	−	1.63029e10i	0.536392	−	0.309686i	−0.207224	−	0.978294i	$-0.566443\pi$
$479$	2.82374e10	−	1.63029e10i	0.536392	−	0.309686i	0.743615	+	0.668608i	$0.233109\pi$
$480$	−2.11935e9	−	2.92009e9i	−0.0399243	−	0.0550086i
$481$	−3.11626e10	+	5.39751e10i	−0.582174	+	1.00835i
$482$	5.03184e10	+	2.90513e10i	0.932264	+	0.538243i
$483$	4.90885e9	+	4.69293e10i	0.0901969	+	0.862294i
$484$	−6.46083e9	−	1.11905e10i	−0.117735	−	0.203924i
$485$		−	3.75188e9i		−	0.0678081i
$486$	3.33277e10	−	5.73950e10i	0.597393	−	1.02880i
$487$	7.98358e8			0.0141932			0.00709662	−	0.999975i	$-0.497741\pi$
$487$	7.98358e8			0.0141932			0.00709662	+	0.999975i	$0.497741\pi$
$488$	−3.16733e10	+	1.82866e10i	−0.558488	+	0.322443i
$489$	−3.03099e10	+	3.17045e9i	−0.530089	+	0.0554479i
$490$	−1.22475e9	+	2.12133e9i	−0.0212453	+	0.0367979i
$491$	−4.32216e10	−	2.49540e10i	−0.743660	−	0.429353i	0.0797382	−	0.996816i	$-0.474592\pi$
$491$	−4.32216e10	−	2.49540e10i	−0.743660	−	0.429353i	−0.823399	+	0.567463i	$0.807925\pi$
$492$	−9.34732e9	+	6.78412e9i	−0.159524	+	0.115780i
$493$	−5.41724e9	−	9.38293e9i	−0.0917044	−	0.158837i
$494$			1.29184e11i			2.16920i
$495$	6.38313e9	−	1.35014e9i	0.106319	−	0.0224883i
$496$	2.95267e10			0.487853
$497$	2.75702e10	−	1.59177e10i	0.451871	−	0.260888i
$498$	−1.99061e10	+	4.46500e10i	−0.323645	+	0.725945i
$499$	2.26906e10	−	3.93012e10i	0.365968	−	0.633875i	−0.622963	−	0.782251i	$-0.714071\pi$
$499$	2.26906e10	−	3.93012e10i	0.365968	−	0.633875i	0.988931	+	0.148376i	$0.0474046\pi$
$500$	3.88818e9	+	2.24484e9i	0.0622108	+	0.0359174i
$501$	3.93767e10	+	1.75551e10i	0.625012	+	0.278646i
$502$	−7.43924e10	−	1.28851e11i	−1.17142	−	2.02896i
$503$		−	2.21128e8i		−	0.00345440i	−0.999999	−	0.00172720i	$-0.999450\pi$
$503$		−	2.21128e8i		−	0.00345440i	0.999999	−	0.00172720i	$-0.000549785\pi$
$504$	2.56121e10	−	2.30151e10i	0.396938	−	0.356690i
$505$	4.15341e9			0.0638616
$506$	9.55444e10	−	5.51626e10i	1.45748	−	0.841478i
$507$	−1.13821e10	−	1.56826e10i	−0.172263	−	0.237348i
$508$	−1.38574e10	+	2.40017e10i	−0.208078	+	0.360402i
$509$	8.78597e10	+	5.07258e10i	1.30894	+	0.755715i	0.981919	−	0.189303i	$-0.0606230\pi$
$509$	8.78597e10	+	5.07258e10i	1.30894	+	0.755715i	0.327018	+	0.945018i	$0.393956\pi$
$510$	8.49164e8	+	8.11812e9i	0.0125519	+	0.119998i
$511$	−2.13941e10	−	3.70557e10i	−0.313769	−	0.543464i
$512$			7.46028e9i			0.108561i
$513$	1.05662e11	−	3.41572e10i	1.52562	−	0.493188i
$514$	1.08107e11			1.54882
$515$	5.04909e9	−	2.91509e9i	0.0717768	−	0.0414404i
$516$	2.56071e10	−	2.67854e9i	0.361212	−	0.0377832i
$517$	1.77438e10	−	3.07332e10i	0.248362	−	0.430176i
$518$	−5.82659e10	−	3.36398e10i	−0.809274	−	0.467234i
$519$	−7.32215e10	+	5.31429e10i	−1.00918	+	0.732446i
$520$	2.51056e9	+	4.34841e9i	0.0343365	+	0.0594726i
$521$		−	4.53217e10i		−	0.615114i	−0.951530	−	0.307557i	$-0.900489\pi$
$521$		−	4.53217e10i		−	0.615114i	0.951530	−	0.307557i	$-0.0995114\pi$
$522$	4.29840e9	−	1.31845e10i	0.0578929	−	0.177574i
$523$	1.59979e10			0.213824			0.106912	−	0.994268i	$-0.465904\pi$
$523$	1.59979e10			0.213824			0.106912	+	0.994268i	$0.465904\pi$
$524$	9.26056e9	−	5.34659e9i	0.122832	−	0.0709172i
$525$	−2.35534e10	+	5.28310e10i	−0.310039	+	0.695427i
$526$	−3.91501e10	+	6.78100e10i	−0.511434	+	0.885830i
$527$	−3.06324e10	−	1.76856e10i	−0.397136	−	0.229286i
$528$	−1.10437e11	−	4.92354e10i	−1.42095	−	0.633493i
$529$	1.08506e10	+	1.87938e10i	0.138558	+	0.239990i
$530$		−	1.06863e10i		−	0.135432i
$531$	−7.94939e10	−	2.59166e10i	−0.999899	−	0.325987i
$532$	−4.09206e10			−0.510852
$533$	3.77255e10	−	2.17808e10i	0.467441	−	0.269877i
$534$	−4.26585e9	−	5.87758e9i	−0.0524614	−	0.0722826i
$535$	−4.55523e9	+	7.88989e9i	−0.0556026	+	0.0963065i
$536$	−3.45567e10	−	1.99513e10i	−0.418672	−	0.241720i
$537$	1.25137e9	+	1.19632e10i	0.0150483	+	0.143864i
$538$	7.19694e10	+	1.24655e11i	0.859051	+	1.48792i
$539$			4.34683e10i			0.515013i
$540$	−2.05471e9	+	2.27514e9i	−0.0241643	+	0.0267568i
$541$	−7.28974e10			−0.850987			−0.425494	−	0.904961i	$-0.639899\pi$
$541$	−7.28974e10			−0.850987			−0.425494	+	0.904961i	$0.639899\pi$
$542$	−1.03688e11	+	5.98646e10i	−1.20153	+	0.693701i
$543$	−3.12262e9	+	3.26629e8i	−0.0359186	+	0.00375713i
$544$	4.00524e10	−	6.93727e10i	0.457333	−	0.792124i
$545$	−5.67371e9	−	3.27572e9i	−0.0643104	−	0.0371296i
$546$	7.46547e10	−	5.41831e10i	0.840014	−	0.609668i
$547$	6.24551e10	+	1.08175e11i	0.697619	+	1.20831i	0.969290	+	0.245922i	$0.0790906\pi$
$547$	6.24551e10	+	1.08175e11i	0.697619	+	1.20831i	−0.271670	+	0.962390i	$0.587576\pi$
$548$		−	6.84654e10i		−	0.759187i
$549$	5.62918e10	+	6.26436e10i	0.619663	+	0.689584i
$550$	1.35245e11			1.47799
$551$	2.00936e10	−	1.16011e10i	0.217998	−	0.125861i
$552$	2.97186e10	−	6.66597e10i	0.320089	−	0.717971i
$553$	−6.54402e10	+	1.13346e11i	−0.699752	+	1.21201i
$554$	−4.92446e10	−	2.84314e10i	−0.522781	−	0.301828i
$555$	−7.70242e9	−	3.43393e9i	−0.0811812	−	0.0361926i
$556$	−2.71705e9	−	4.70607e9i	−0.0284314	−	0.0492447i
$557$		−	9.05278e10i		−	0.940505i	−0.882532	−	0.470253i	$-0.844163\pi$
$557$		−	9.05278e10i		−	0.940505i	0.882532	−	0.470253i	$-0.155837\pi$
$558$	−9.36871e9	−	4.42930e10i	−0.0966369	−	0.456876i
$559$	−9.71083e10			−0.994510
$560$	−7.04985e9	+	4.07023e9i	−0.0716849	+	0.0413873i
$561$	8.50816e10	+	1.17227e11i	0.858982	+	1.18353i
$562$	3.44106e9	−	5.96008e9i	0.0344942	−	0.0597457i
$563$	−3.91457e10	−	2.26008e10i	−0.389628	−	0.224952i	0.292371	−	0.956305i	$-0.405556\pi$
$563$	−3.91457e10	−	2.26008e10i	−0.389628	−	0.224952i	−0.681999	+	0.731353i	$0.738889\pi$
$564$	1.73473e9	+	1.65843e10i	0.0171442	+	0.163900i
$565$	−1.42848e9	−	2.47420e9i	−0.0140178	−	0.0242796i
$566$			7.76162e10i			0.756287i
$567$	−6.40565e10	−	4.67349e10i	−0.619771	−	0.452178i
$568$	−4.92415e10			−0.473084
$569$	−4.31087e10	+	2.48888e10i	−0.411259	+	0.237441i	−0.691331	−	0.722539i	$-0.742975\pi$
$569$	−4.31087e10	+	2.48888e10i	−0.411259	+	0.237441i	0.280071	+	0.959979i	$0.409642\pi$
$570$	−1.73850e10	+	1.81849e9i	−0.164693	+	0.0172271i
$571$	1.32484e10	−	2.29469e10i	0.124629	−	0.215863i	−0.796959	−	0.604033i	$-0.793559\pi$
$571$	1.32484e10	−	2.29469e10i	0.124629	−	0.215863i	0.921588	+	0.388170i	$0.126893\pi$
$572$	−5.48093e10	−	3.16442e10i	−0.512000	−	0.295603i
$573$	1.02138e11	−	7.41298e10i	0.947475	−	0.687661i
$574$	2.35123e10	+	4.07245e10i	0.216595	+	0.375153i
$575$			1.22603e11i			1.12158i
$576$	−3.35335e10	+	7.09289e9i	−0.304642	+	0.0644367i
$577$	−6.02736e10			−0.543780			−0.271890	−	0.962328i	$-0.587649\pi$
$577$	−6.02736e10			−0.543780			−0.271890	+	0.962328i	$0.587649\pi$
$578$	−4.19455e10	+	2.42173e10i	−0.375815	+	0.216977i
$579$	7.09593e10	−	1.59164e11i	0.631386	−	1.41622i
$580$	−3.20271e8	+	5.54725e8i	−0.00283012	+	0.00490192i
$581$	5.05806e10	+	2.92027e10i	0.443894	+	0.256282i
$582$	9.73751e10	+	4.34123e10i	0.848704	+	0.378373i
$583$	−9.48183e10	−	1.64230e11i	−0.820764	−	1.42160i
$584$			6.61830e10i			0.568978i
$585$	8.60032e9	−	7.72827e9i	0.0734329	−	0.0659871i
$586$	4.29406e10			0.364148
$587$	1.04499e10	−	6.03326e9i	0.0880157	−	0.0508159i	−0.455346	−	0.890314i	$-0.650484\pi$
$587$	1.04499e10	−	6.03326e9i	0.0880157	−	0.0508159i	0.543362	+	0.839499i	$0.317151\pi$
$588$	−1.19971e10	−	1.65299e10i	−0.100361	−	0.138280i
$589$	3.78739e10	−	6.55996e10i	0.314687	−	0.545054i
$590$	1.13982e10	+	6.58076e9i	0.0940651	+	0.0543085i
$591$	−1.40638e10	−	1.34452e11i	−0.115280	−	1.10209i
$592$	7.81456e10	+	1.35352e11i	0.636236	+	1.10199i
$593$		−	1.37897e11i		−	1.11515i	−0.830125	−	0.557577i	$-0.811731\pi$
$593$		−	1.37897e11i		−	1.11515i	0.830125	−	0.557577i	$-0.188269\pi$
$594$	−3.88169e10	+	1.81288e11i	−0.311800	+	1.45621i
$595$	9.75179e9			0.0778066
$596$	9.37419e9	−	5.41219e9i	0.0742931	−	0.0428932i
$597$	3.60135e10	−	3.76706e9i	0.283510	−	0.0296555i
$598$	9.77595e10	−	1.69324e11i	0.764459	−	1.32408i
$599$	1.44514e11	+	8.34354e10i	1.12255	+	0.648102i	0.942049	−	0.335474i	$-0.108896\pi$
$599$	1.44514e11	+	8.34354e10i	1.12255	+	0.648102i	0.180496	+	0.983576i	$0.442230\pi$
$600$	7.24089e10	−	5.25531e10i	0.558711	−	0.405502i
$601$	−2.54667e10	−	4.41096e10i	−0.195198	−	0.338093i	0.751768	−	0.659428i	$-0.229202\pi$
$601$	−2.54667e10	−	4.41096e10i	−0.195198	−	0.338093i	−0.946965	+	0.321336i	$0.895868\pi$
$602$		−	1.04828e11i		−	0.798162i
$603$	−2.84816e10	+	8.73615e10i	−0.215425	+	0.660771i
$604$	−2.95254e10			−0.221844
$605$	−5.71099e9	+	3.29724e9i	−0.0426275	+	0.0246110i
$606$	−4.80584e10	+	1.07796e11i	−0.356351	+	0.799307i
$607$	1.98453e10	−	3.43730e10i	0.146185	−	0.253200i	−0.783629	−	0.621228i	$-0.786634\pi$
$607$	1.98453e10	−	3.43730e10i	0.146185	−	0.253200i	0.929814	+	0.368029i	$0.119967\pi$
$608$	1.48562e11	+	8.57725e10i	1.08716	+	0.627673i
$609$	−1.51320e10	−	6.74623e9i	−0.110009	−	0.0490447i
$610$	−6.62861e9	−	1.14811e10i	−0.0478744	−	0.0829208i
$611$		−	6.28915e10i		−	0.451260i
$612$	−6.47087e10	−	2.10963e10i	−0.461272	−	0.150384i
$613$	−2.75904e10			−0.195396			−0.0976982	−	0.995216i	$-0.531148\pi$
$613$	−2.75904e10			−0.195396			−0.0976982	+	0.995216i	$0.531148\pi$
$614$	−1.08322e11	+	6.25398e10i	−0.762155	+	0.440030i
$615$	3.46223e9	+	4.77034e9i	0.0242022	+	0.0333464i
$616$	−4.80935e10	+	8.33005e10i	−0.334013	+	0.578528i
$617$	7.51295e10	+	4.33761e10i	0.518406	+	0.299302i	0.736282	−	0.676675i	$-0.236580\pi$
$617$	7.51295e10	+	4.33761e10i	0.518406	+	0.299302i	−0.217876	+	0.975976i	$0.569913\pi$
$618$	1.72354e10	+	1.64773e11i	0.118159	+	1.12962i
$619$	−1.58249e10	−	2.74096e10i	−0.107790	−	0.186698i	0.807085	−	0.590436i	$-0.201044\pi$
$619$	−1.58249e10	−	2.74096e10i	−0.107790	−	0.186698i	−0.914875	+	0.403738i	$0.867711\pi$
$620$			2.09117e9i			0.0141522i
$621$	−1.64342e11	−	3.51884e10i	−1.10505	−	0.236610i
$622$	−2.49884e11			−1.66946
$623$	−7.51416e9	+	4.33830e9i	−0.0498802	+	0.0287984i
$624$	−2.13123e11	+	2.22929e10i	−1.40570	+	0.147038i
$625$	−7.45733e10	+	1.29165e11i	−0.488724	+	0.846494i
$626$	−4.26674e10	−	2.46341e10i	−0.277843	−	0.160413i
$627$	−2.51043e11	+	1.82203e11i	−1.62435	+	1.17892i
$628$	3.53141e10	+	6.11658e10i	0.227044	+	0.393251i
$629$		−	1.87228e11i		−	1.19610i
$630$	8.34264e9	+	9.28400e9i	0.0529592	+	0.0589350i
$631$	2.47836e11			1.56332			0.781659	−	0.623706i	$-0.214374\pi$
$631$	2.47836e11			1.56332			0.781659	+	0.623706i	$0.214374\pi$
$632$	1.75319e11	−	1.01220e11i	1.09890	−	0.634452i
$633$	4.77173e10	−	1.07031e11i	0.297208	−	0.666648i
$634$	4.73274e10	−	8.19735e10i	0.292925	−	0.507361i
$635$	1.22491e10	+	7.07202e9i	0.0753372	+	0.0434960i
$636$	8.13839e10	+	3.62830e10i	0.497405	+	0.221756i
$637$	3.85175e10	+	6.67142e10i	0.233937	+	0.405192i
$638$			3.87374e10i			0.233802i
$639$	2.34652e10	+	1.10938e11i	0.140741	+	0.665390i
$640$	1.67988e10			0.100129
$641$	−2.33521e11	+	1.34823e11i	−1.38323	+	0.798607i	−0.992540	−	0.121917i	$-0.961096\pi$
$641$	−2.33521e11	+	1.34823e11i	−1.38323	+	0.798607i	−0.390687	+	0.920523i	$0.627763\pi$
$642$	−1.52064e11	−	2.09518e11i	−0.895131	−	1.23333i
$643$	1.49218e10	−	2.58453e10i	0.0872926	−	0.151195i	−0.819073	−	0.573689i	$-0.805512\pi$
$643$	1.49218e10	−	2.58453e10i	0.0872926	−	0.151195i	0.906366	+	0.422494i	$0.138845\pi$
$644$	5.36357e10	+	3.09666e10i	0.311824	+	0.180032i
$645$	−1.36697e9	−	1.30684e10i	−0.00789807	−	0.0755066i
$646$	−1.94037e11	−	3.36082e11i	−1.11418	−	1.92981i
$647$			9.21631e10i			0.525944i	0.964803	+	0.262972i	$0.0847028\pi$
$647$			9.21631e10i			0.525944i	−0.964803	+	0.262972i	$0.915297\pi$
$648$	4.96620e10	+	1.12143e11i	0.281659	+	0.636021i
$649$	2.33562e11			1.31651
$650$	2.07572e11	−	1.19841e11i	1.16282	−	0.671357i
$651$	−5.37951e10	+	5.62702e9i	−0.299515	+	0.0313296i
$652$	−2.00002e10	+	3.46413e10i	−0.110673	+	0.191692i
$653$	1.50685e11	+	8.69982e10i	0.828740	+	0.478473i	0.853421	−	0.521222i	$-0.174524\pi$
$653$	1.50685e11	+	8.69982e10i	0.828740	+	0.478473i	−0.0246814	+	0.999695i	$0.507857\pi$
$654$	1.50666e11	−	1.09351e11i	0.823579	−	0.597739i
$655$	−2.72860e9	−	4.72607e9i	−0.0148243	−	0.0256764i
$656$		−	1.09239e11i		−	0.589876i
$657$	1.49106e11	−	3.15384e10i	0.800264	−	0.169269i
$658$	6.78911e10			0.362167
$659$	−1.25628e11	+	7.25316e10i	−0.666110	+	0.384579i	−0.794601	−	0.607132i	$-0.792320\pi$
$659$	−1.25628e11	+	7.25316e10i	−0.666110	+	0.384579i	0.128491	+	0.991711i	$0.458987\pi$
$660$	3.48700e9	−	7.82146e9i	0.0183771	−	0.0412204i
$661$	−9.24740e10	+	1.60170e11i	−0.484411	+	0.839024i	−0.999840	−	0.0179086i	$-0.994299\pi$
$661$	−9.24740e10	+	1.60170e11i	−0.484411	+	0.839024i	0.515429	+	0.856932i	$0.327633\pi$
$662$	6.25041e9	+	3.60867e9i	0.0325444	+	0.0187895i
$663$	2.34457e11	+	1.04527e11i	1.21341	+	0.540970i
$664$	−4.51696e10	−	7.82360e10i	−0.232366	−	0.402471i
$665$			2.08835e10i			0.106787i
$666$	1.78247e11	−	1.60173e11i	0.905992	−	0.814127i
$667$	−3.51163e10			−0.177421
$668$	4.90063e10	−	2.82938e10i	0.246120	−	0.142097i
$669$	6.39000e10	+	8.80429e10i	0.319004	+	0.439531i
$670$	7.23206e9	−	1.25263e10i	0.0358891	−	0.0621618i
$671$	−2.03741e11	−	1.17630e11i	−1.00505	−	0.580268i
$672$	−1.27434e10	−	1.21829e11i	−0.0624898	−	0.597410i
$673$	1.33590e10	+	2.31384e10i	0.0651198	+	0.112791i	0.896747	−	0.442543i	$-0.145924\pi$
$673$	1.33590e10	+	2.31384e10i	0.0651198	+	0.112791i	−0.831627	+	0.555334i	$0.812590\pi$
$674$		−	2.86637e10i		−	0.138897i
$675$	−1.52904e11	−	1.38089e11i	−0.736552	−	0.665188i
$676$	−2.54343e10			−0.121796
$677$	−4.06009e10	+	2.34409e10i	−0.193277	+	0.111589i	−0.593516	−	0.804822i	$-0.702261\pi$
$677$	−4.06009e10	+	2.34409e10i	−0.193277	+	0.111589i	0.400239	+	0.916411i	$0.368927\pi$
$678$	8.07434e10	−	8.44585e9i	0.382110	−	0.0399691i
$679$	6.36869e10	−	1.10309e11i	0.299620	−	0.518957i
$680$	−1.30628e10	−	7.54183e9i	−0.0610945	−	0.0352729i
$681$	−1.38984e11	+	1.00872e11i	−0.646212	+	0.469009i
$682$	6.32329e10	+	1.09523e11i	0.292284	+	0.506252i
$683$			2.98469e11i			1.37156i	0.727807	+	0.685782i	$0.240540\pi$
$683$			2.98469e11i			1.37156i	−0.727807	+	0.685782i	$0.759460\pi$
$684$	4.51780e10	−	1.38574e11i	0.206397	−	0.633079i
$685$	−3.49409e10			−0.158698
$686$	−2.47064e11	+	1.42643e11i	−1.11561	+	0.644100i
$687$	1.24878e11	−	2.80106e11i	0.560608	−	1.25746i
$688$	−1.21758e11	+	2.10891e11i	−0.543431	+	0.941250i
$689$	−2.91050e11	−	1.68038e11i	−1.29149	−	0.745641i
$690$	2.41631e10	+	1.07725e10i	0.106600	+	0.0475249i
$691$	5.31099e10	+	9.19890e10i	0.232950	+	0.403482i	0.958675	−	0.284503i	$-0.0918287\pi$
$691$	5.31099e10	+	9.19890e10i	0.232950	+	0.403482i	−0.725725	+	0.687985i	$0.758495\pi$
$692$			1.18752e11i			0.517864i
$693$	2.10589e11	+	6.86562e10i	0.913065	+	0.297678i
$694$	−3.93133e11			−1.69473
$695$	−2.40171e9	+	1.38663e9i	−0.0102939	+	0.00594321i
$696$	1.50524e10	+	2.07396e10i	0.0641460	+	0.0883818i
$697$	−6.54307e10	+	1.13329e11i	−0.277237	+	0.480188i
$698$	−1.85356e11	−	1.07015e11i	−0.780881	−	0.450842i
$699$	6.49954e9	+	6.21364e10i	0.0272254	+	0.260278i
$700$	3.79613e10	+	6.57509e10i	0.158106	+	0.273848i
$701$		−	1.76564e11i		−	0.731191i	−0.930774	−	0.365595i	$-0.880865\pi$
$701$		−	1.76564e11i		−	0.731191i	0.930774	−	0.365595i	$-0.119135\pi$
$702$	1.01065e11	+	3.12632e11i	0.416151	+	1.28732i
$703$	4.00950e11			1.64160
$704$	8.29178e10	−	4.78726e10i	0.337565	−	0.194893i
$705$	8.46368e9	−	8.85310e8i	0.0342612	−	0.00358376i
$706$	−3.97977e10	+	6.89316e10i	−0.160191	+	0.277459i
$707$	1.22114e11	+	7.05028e10i	0.488753	+	0.282182i
$708$	−8.88176e10	+	6.44623e10i	−0.353481	+	0.256550i
$709$	−4.90765e10	−	8.50029e10i	−0.194217	−	0.336394i	0.752426	−	0.658676i	$-0.228883\pi$
$709$	−4.90765e10	−	8.50029e10i	−0.194217	−	0.336394i	−0.946644	+	0.322282i	$0.895550\pi$
$710$		−	1.78493e10i		−	0.0702406i
$711$	−3.11587e11	−	3.46746e11i	−1.21927	−	1.35686i
$712$	1.34206e10			0.0522219
$713$	−9.92847e10	+	5.73221e10i	−0.384171	+	0.221801i
$714$	−1.12836e11	+	2.53095e11i	−0.434165	+	0.973847i
$715$	−1.61494e10	+	2.79716e10i	−0.0617919	+	0.107027i
$716$	1.36728e10	+	7.89400e9i	0.0520242	+	0.0300362i
$717$	−3.80045e11	−	1.69433e11i	−1.43800	−	0.641095i
$718$	1.53967e11	+	2.66679e11i	0.579337	+	1.00344i
$719$		−	1.05784e11i		−	0.395825i	−0.980220	−	0.197913i	$-0.936584\pi$
$719$		−	1.05784e11i		−	0.395825i	0.980220	−	0.197913i	$-0.0634162\pi$
$720$	−6.00018e9	−	2.83674e10i	−0.0223272	−	0.105558i
$721$	1.97931e11			0.732441
$722$	4.39758e11	−	2.53894e11i	1.61832	−	0.934339i
$723$	1.45231e11	+	2.00102e11i	0.531502	+	0.732316i
$724$	−2.06048e9	+	3.56885e9i	−0.00749918	+	0.0129890i
$725$	−3.72810e10	−	2.15242e10i	−0.134938	−	0.0779067i
$726$	−1.94949e10	−	1.86373e11i	−0.0701736	−	0.670868i
$727$	1.31053e11	+	2.26990e11i	0.469147	+	0.812587i	0.999378	−	0.0352668i	$-0.0112281\pi$
$727$	1.31053e11	+	2.26990e11i	0.469147	+	0.812587i	−0.530231	+	0.847853i	$0.677895\pi$
$728$			1.70463e11i			0.606884i
$729$	2.28985e11	−	1.65325e11i	0.810768	−	0.585367i
$730$	−2.39904e10			−0.0844783
$731$	2.52635e11	−	1.45859e11i	0.884758	−	0.510815i
$732$	1.09943e11	−	1.15002e10i	0.382934	−	0.0400553i
$733$	2.24638e11	−	3.89084e11i	0.778157	−	1.34781i	−0.154846	−	0.987939i	$-0.549488\pi$
$733$	2.24638e11	−	3.89084e11i	0.778157	−	1.34781i	0.933003	−	0.359869i	$-0.117179\pi$
$734$	−1.45598e11	−	8.40611e10i	−0.501616	−	0.289608i
$735$	−8.43592e9	+	6.12264e9i	−0.0289057	+	0.0209792i
$736$	−1.29816e11	−	2.24848e11i	−0.442403	−	0.766264i
$737$		−	2.56678e11i		−	0.869998i
$738$	−1.63869e11	+	3.46610e10i	−0.552422	+	0.116846i
$739$	−3.69989e11			−1.24054			−0.620270	−	0.784388i	$-0.712977\pi$
$739$	−3.69989e11			−1.24054			−0.620270	+	0.784388i	$0.712977\pi$
$740$	−9.58606e9	+	5.53451e9i	−0.0319678	+	0.0184566i
$741$	−2.23845e11	+	5.02091e11i	−0.742462	+	1.66537i
$742$	1.81396e11	−	3.14187e11i	0.598428	−	1.03651i
$743$	1.31608e11	+	7.59837e10i	0.431843	+	0.249325i	0.700132	−	0.714014i	$-0.253125\pi$
$743$	1.31608e11	+	7.59837e10i	0.431843	+	0.249325i	−0.268288	+	0.963339i	$0.586458\pi$
$744$	7.64120e10	+	3.40664e10i	0.249385	+	0.111182i
$745$	−2.76208e9	−	4.78405e9i	−0.00896624	−	0.0155300i
$746$			4.34841e11i			1.40403i
$747$	−1.54736e11	+	1.39046e11i	−0.496945	+	0.446556i
$748$	1.90121e11			0.607329
$749$	−2.67857e11	+	1.54647e11i	−0.851089	+	0.491377i
$750$	3.82441e10	+	5.26936e10i	0.120870	+	0.166538i
$751$	−1.80268e10	+	3.12234e10i	−0.0566708	+	0.0981567i	−0.892969	−	0.450118i	$-0.851382\pi$
$751$	−1.80268e10	+	3.12234e10i	−0.0566708	+	0.0981567i	0.836298	+	0.548275i	$0.184715\pi$
$752$	−1.36582e11	−	7.88558e10i	−0.427093	−	0.246583i
$753$	−6.58678e10	−	6.29704e11i	−0.204877	−	1.95865i
$754$	3.43254e10	+	5.94533e10i	0.106201	+	0.183946i
$755$			1.50681e10i			0.0463736i
$756$	−9.90302e10	+	3.20135e10i	−0.303166	+	0.0980045i
$757$	−6.49675e11			−1.97839			−0.989197	−	0.146590i	$-0.953170\pi$
$757$	−6.49675e11			−1.97839			−0.989197	+	0.146590i	$0.953170\pi$
$758$	4.07460e11	−	2.35247e11i	1.23426	−	0.712602i
$759$	4.66931e11	−	4.88415e10i	1.40697	−	0.147171i
$760$	1.61509e10	−	2.79742e10i	0.0484108	−	0.0838500i
$761$	4.58208e11	+	2.64546e11i	1.36623	+	0.788794i	0.990444	−	0.137913i	$-0.0440394\pi$
$761$	4.58208e11	+	2.64546e11i	1.36623	+	0.788794i	0.375786	+	0.926706i	$0.377373\pi$
$762$	−3.25277e11	+	2.36081e11i	−0.964792	+	0.700229i
$763$	−1.11208e11	−	1.92619e11i	−0.328125	−	0.568329i
$764$		−	1.65649e11i		−	0.486199i
$765$	−1.07664e10	+	3.30236e10i	−0.0314358	+	0.0964227i
$766$	8.66675e10			0.251734
$767$	3.58465e11	−	2.06960e11i	1.03578	−	0.598006i
$768$	−1.50266e11	+	3.37051e11i	−0.431932	+	0.968838i
$769$	1.38751e11	−	2.40323e11i	0.396761	−	0.687211i	−0.596563	−	0.802566i	$-0.703467\pi$
$769$	1.38751e11	−	2.40323e11i	0.396761	−	0.687211i	0.993324	+	0.115355i	$0.0368007\pi$
$770$	−3.01952e10	−	1.74332e10i	−0.0858963	−	0.0495923i
$771$	4.20172e11	+	1.87323e11i	1.18908	+	0.530120i
$772$	−1.14366e11	−	1.98088e11i	−0.321979	−	0.557685i
$773$			6.48893e11i			1.81742i	0.417430	+	0.908709i	$0.362931\pi$
$773$			6.48893e11i			1.81742i	−0.417430	+	0.908709i	$0.637069\pi$
$774$	3.54991e11	+	1.15734e11i	0.989131	+	0.322477i
$775$	−1.40540e11			−0.389577
$776$	−1.70621e11	+	9.85083e10i	−0.470529	+	0.271660i
$777$	−1.68169e11	−	2.31707e11i	−0.461383	−	0.635704i
$778$	7.66480e10	−	1.32758e11i	0.209210	−	0.362362i
$779$	−2.42696e11	−	1.40120e11i	−0.659041	−	0.380497i
$780$	−1.57885e9	−	1.50940e10i	−0.00426543	−	0.0407781i
$781$	−1.58375e11	−	2.74314e11i	−0.425680	−	0.737300i
$782$			5.87349e11i			1.57061i
$783$	3.95519e10	−	4.37952e10i	0.105225	−	0.116514i
$784$	1.93179e11			0.511323
$785$	3.12156e10	−	1.80223e10i	0.0822039	−	0.0474605i
$786$	1.54231e11	−	1.61327e10i	0.404093	−	0.0422686i
$787$	−2.24484e11	+	3.88818e11i	−0.585177	+	1.01356i	0.409677	+	0.912231i	$0.365641\pi$
$787$	−2.24484e11	+	3.88818e11i	−0.585177	+	1.01356i	−0.994853	+	0.101325i	$0.967692\pi$
$788$	−1.53666e11	−	8.87189e10i	−0.398540	−	0.230097i
$789$	−2.69661e11	+	1.95715e11i	−0.695841	+	0.505030i
$790$	3.66908e10	+	6.35504e10i	0.0941996	+	0.163158i
$791$		−	9.69921e10i		−	0.247759i
$792$	−2.28993e11	−	2.54832e11i	−0.581998	−	0.647669i
$793$	−4.16930e11			−1.05431
$794$	−4.57759e11	+	2.64287e11i	−1.15174	+	0.664957i
$795$	1.85168e10	−	4.15337e10i	0.0463550	−	0.103976i
$796$	2.37637e10	−	4.11600e10i	0.0591919	−	0.102523i
$797$	1.23670e11	+	7.14010e10i	0.306501	+	0.176958i	0.645360	−	0.763879i	$-0.276708\pi$
$797$	1.23670e11	+	7.14010e10i	0.306501	+	0.176958i	−0.338859	+	0.940837i	$0.610041\pi$
$798$	−5.42005e11	−	2.41640e11i	−1.33657	−	0.595877i
$799$	9.44646e10	+	1.63617e11i	0.231783	+	0.401460i
$800$		−	3.18278e11i		−	0.777047i
$801$	−6.39537e9	−	3.02358e10i	−0.0155359	−	0.0734499i
$802$	4.64135e11			1.12188
$803$	−3.68692e11	+	2.12864e11i	−0.886750	+	0.511965i
$804$	7.08421e10	+	9.76080e10i	0.169538	+	0.233594i
$805$	1.58036e10	−	2.73726e10i	0.0376333	−	0.0651827i
$806$	1.94097e11	+	1.12062e11i	0.459916	+	0.265532i
$807$	6.37224e10	+	6.09194e11i	0.150244	+	1.43635i
$808$	−1.09051e11	−	1.88882e11i	−0.255849	−	0.443143i
$809$		−	4.15227e11i		−	0.969374i	−0.874688	−	0.484687i	$-0.838934\pi$
$809$		−	4.15227e11i		−	0.969374i	0.874688	−	0.484687i	$-0.161066\pi$
$810$	−4.06501e10	+	1.80017e10i	−0.0944326	+	0.0418191i
$811$	1.13963e11			0.263440			0.131720	−	0.991287i	$-0.457950\pi$
$811$	1.13963e11			0.263440			0.131720	+	0.991287i	$0.457950\pi$
$812$	−1.88326e10	+	1.08730e10i	−0.0433197	+	0.0250106i
$813$	−5.06731e11	+	5.30047e10i	−1.15989	+	0.121325i
$814$	−3.34705e11	+	5.79727e11i	−0.762369	+	1.32046i
$815$	1.76790e10	+	1.02069e10i	0.0400706	+	0.0231348i
$816$	5.20973e11	−	3.78113e11i	1.17505	−	0.852827i
$817$	3.12358e11	+	5.41020e11i	0.701076	+	1.21430i
$818$		−	9.20721e11i		−	2.05643i
$819$	3.84043e11	−	8.12314e10i	0.853580	−	0.180546i
$820$	7.73662e9			0.0171118
$821$	6.17284e11	−	3.56389e11i	1.35867	−	0.784426i	0.369221	−	0.929342i	$-0.379624\pi$
$821$	6.17284e11	−	3.56389e11i	1.35867	−	0.784426i	0.989444	+	0.144916i	$0.0462912\pi$
$822$	4.04294e11	−	9.06845e11i	0.885544	−	1.98630i
$823$	1.17917e11	−	2.04238e11i	0.257026	−	0.445182i	−0.708418	−	0.705793i	$-0.750591\pi$
$823$	1.17917e11	−	2.04238e11i	0.257026	−	0.445182i	0.965444	+	0.260611i	$0.0839241\pi$
$824$	−2.65135e11	−	1.53076e11i	−0.575120	−	0.332045i
$825$	5.25651e11	+	2.34348e11i	1.13470	+	0.505878i
$826$	2.23413e11	+	3.86962e11i	0.479941	+	0.831281i
$827$		−	5.38659e9i		−	0.0115157i	−0.999983	−	0.00575787i	$-0.998167\pi$
$827$		−	5.38659e9i		−	0.0115157i	0.999983	−	0.00575787i	$-0.00183280\pi$
$828$	−1.64082e11	+	1.47444e11i	−0.349091	+	0.313694i
$829$	6.01700e11			1.27398			0.636989	−	0.770873i	$-0.280180\pi$
$829$	6.01700e11			1.27398			0.636989	+	0.770873i	$0.280180\pi$
$830$	2.83594e10	−	1.63733e10i	0.0597564	−	0.0345004i
$831$	−1.42131e11	−	1.95832e11i	−0.298048	−	0.410657i
$832$	8.48401e10	−	1.46947e11i	0.177055	−	0.306668i
$833$	−2.00413e11	−	1.15708e11i	−0.416241	−	0.240317i
$834$	−8.19841e9	−	7.83778e10i	−0.0169459	−	0.162005i
$835$	−1.44396e10	−	2.50100e10i	−0.0297035	−	0.0514480i
$836$			4.07146e11i			0.833538i
$837$	4.03365e10	−	1.88385e11i	0.0821857	−	0.383835i
$838$	5.76922e11			1.16988
$839$	5.25649e11	−	3.03483e11i	1.06083	−	0.612473i	0.135172	−	0.990822i	$-0.456841\pi$
$839$	5.25649e11	−	3.03483e11i	1.06083	−	0.612473i	0.925663	+	0.378349i	$0.123508\pi$
$840$	−2.29403e10	+	2.39958e9i	−0.0460767	+	0.00481967i
$841$	−2.43958e11	+	4.22548e11i	−0.487676	+	0.844680i
$842$	−1.11414e10	−	6.43247e9i	−0.0221661	−	0.0127976i
$843$	2.37016e10	−	1.72022e10i	0.0469318	−	0.0340622i
$844$	−7.69066e10	−	1.33206e11i	−0.151563	−	0.262515i
$845$			1.29802e10i			0.0254598i
$846$	−7.49546e10	+	2.29908e11i	−0.146324	+	0.448820i
$847$	−2.23879e11			−0.434990
$848$	−7.29859e11	+	4.21384e11i	−1.41142	+	0.814883i
$849$	−1.34491e11	+	3.01667e11i	−0.258858	+	0.580626i
$850$	−3.60010e11	+	6.23555e11i	−0.689665	+	1.19454i
$851$	−5.25535e11	−	3.03418e11i	−1.00204	−	0.578526i
$852$	1.35936e11	+	6.06036e10i	0.257974	+	0.115011i
$853$	−2.19576e11	−	3.80317e11i	−0.414752	−	0.718372i	0.580650	−	0.814153i	$-0.302798\pi$
$853$	−2.19576e11	−	3.80317e11i	−0.414752	−	0.718372i	−0.995402	+	0.0957811i	$0.969465\pi$
$854$		−	4.50074e11i		−	0.846160i
$855$	−7.07204e10	−	2.30563e10i	−0.132337	−	0.0431445i
$856$	4.78403e11			0.891044
$857$	−8.21446e11	+	4.74262e11i	−1.52285	+	0.879216i	−0.523211	+	0.852203i	$0.675266\pi$
$857$	−8.21446e11	+	4.74262e11i	−1.52285	+	0.879216i	−0.999635	+	0.0270123i	$0.991401\pi$
$858$	−5.39104e11	−	7.42790e11i	−0.994772	−	1.37062i
$859$	−2.63139e11	+	4.55769e11i	−0.483294	+	0.837091i	−0.999816	−	0.0191836i	$-0.993893\pi$
$859$	−2.63139e11	+	4.55769e11i	−0.483294	+	0.837091i	0.516521	+	0.856274i	$0.327227\pi$
$860$	−1.49360e10	−	8.62328e9i	−0.0273048	−	0.0157645i
$861$	2.08180e10	+	1.99023e11i	0.0378815	+	0.362152i
$862$	−3.41804e10	−	5.92022e10i	−0.0619082	−	0.107228i
$863$		−	1.08602e11i		−	0.195792i	−0.995197	−	0.0978961i	$-0.968789\pi$
$863$		−	1.08602e11i		−	0.195792i	0.995197	−	0.0978961i	$-0.0312113\pi$
$864$	4.26632e11	+	9.13494e10i	0.765594	+	0.163927i
$865$	6.06042e10			0.108253
$866$	−7.95773e11	+	4.59440e11i	−1.41487	+	0.816877i
$867$	−2.04990e11	+	2.14422e10i	−0.362791	+	0.0379483i
$868$	−3.54970e10	+	6.14826e10i	−0.0625335	+	0.108311i
$869$	1.12775e12	+	6.51109e11i	1.97758	+	1.14176i
$870$	−7.51778e9	+	5.45628e9i	−0.0131224	+	0.00952400i
$871$	−2.27443e11	−	3.93943e11i	−0.395185	−	0.684480i
$872$			3.44025e11i			0.595010i
$873$	3.03239e11	+	3.37456e11i	0.522070	+	0.580979i
$874$	−1.25781e12			−2.15561
$875$	6.73659e10	−	3.88937e10i	0.114923	−	0.0663509i
$876$	8.14542e10	−	1.82704e11i	0.138324	−	0.310265i
$877$	5.18494e11	−	8.98059e11i	0.876487	−	1.51812i	0.0213175	−	0.999773i	$-0.493214\pi$
$877$	5.18494e11	−	8.98059e11i	0.876487	−	1.51812i	0.855170	−	0.518348i	$-0.173453\pi$
$878$	1.12441e12	+	6.49176e11i	1.89210	+	1.09241i
$879$	1.66895e11	+	7.44060e10i	0.279568	+	0.124639i
$880$	4.04975e10	+	7.01437e10i	0.0675301	+	0.116965i
$881$		−	2.08222e11i		−	0.345640i	−0.984953	−	0.172820i	$-0.944712\pi$
$881$		−	2.08222e11i		−	0.345640i	0.984953	−	0.172820i	$-0.0552878\pi$
$882$	−6.12948e10	−	2.89787e11i	−0.101286	−	0.478856i
$883$	−8.43243e11			−1.38711			−0.693554	−	0.720405i	$-0.743956\pi$
$883$	−8.43243e11			−1.38711			−0.693554	+	0.720405i	$0.743956\pi$
$884$	2.91794e11	−	1.68467e11i	0.477823	−	0.275871i
$885$	3.28979e10	+	4.53275e10i	0.0536284	+	0.0738905i
$886$	3.78057e11	−	6.54813e11i	0.613511	−	1.06263i
$887$	−8.92264e11	−	5.15149e11i	−1.44145	−	0.832221i	−0.443502	−	0.896274i	$-0.646264\pi$
$887$	−8.92264e11	−	5.15149e11i	−1.44145	−	0.832221i	−0.997946	+	0.0640530i	$0.979597\pi$
$888$	4.60703e10	+	4.40438e11i	0.0740916	+	0.708325i
$889$	2.40091e11	+	4.15849e11i	0.384386	+	0.665777i
$890$			4.86478e9i			0.00775359i
$891$	−4.64997e11	+	6.37342e11i	−0.737801	+	1.01126i
$892$	1.42789e11			0.225547
$893$	−3.50388e11	+	2.02297e11i	−0.550990	+	0.318114i
$894$	1.56123e11	−	1.63307e10i	0.244409	−	0.0255655i
$895$	4.02865e9	−	6.97782e9i	0.00627866	−	0.0108750i
$896$	4.93902e11	+	2.85154e11i	0.766317	+	0.442433i
$897$	6.73356e11	−	4.88710e11i	1.04010	−	0.754886i
$898$	−3.83480e11	−	6.64206e11i	−0.589708	−	1.02140i
$899$		−	4.02539e10i		−	0.0616267i
$900$	−2.64571e11	+	5.59611e10i	−0.403248	+	0.0852936i
$901$	1.00959e12			1.53195
$902$	4.05196e11	−	2.33940e11i	0.612123	−	0.353409i
$903$	1.81642e11	−	4.07429e11i	0.273190	−	0.612775i
$904$	−7.50117e10	+	1.29924e11i	−0.112319	+	0.194543i
$905$	1.82134e9	+	1.05155e9i	0.00271517	+	0.00156760i
$906$	−3.91073e11	−	1.74350e11i	−0.580424	−	0.258767i
$907$	1.65733e11	+	2.87057e11i	0.244894	+	0.424170i	0.962102	−	0.272690i	$-0.0879134\pi$
$907$	1.65733e11	+	2.87057e11i	0.244894	+	0.424170i	−0.717208	+	0.696860i	$0.754580\pi$
$908$			2.25406e11i			0.331605i
$909$	−3.73571e11	+	3.35693e11i	−0.547165	+	0.491684i
$910$	−6.17904e10			−0.0901064
$911$	7.58390e11	−	4.37857e11i	1.10108	−	0.635709i	0.164576	−	0.986364i	$-0.447374\pi$
$911$	7.58390e11	−	4.37857e11i	1.10108	−	0.635709i	0.936505	+	0.350655i	$0.114041\pi$
$912$	8.09732e11	+	1.11567e12i	1.17048	+	1.61271i
$913$	2.90557e11	−	5.03260e11i	0.418166	−	0.724285i
$914$	7.44468e11	+	4.29819e11i	1.06675	+	0.615887i
$915$	−5.86903e9	−	5.61087e10i	−0.00837302	−	0.0800472i
$916$	−2.01268e11	−	3.48606e11i	−0.285886	−	0.495169i
$917$		−	1.85268e11i		−	0.262013i
$918$	−7.32510e11	−	6.61538e11i	−1.03144	−	0.931502i
$919$	−8.62524e11			−1.20923			−0.604615	−	0.796518i	$-0.706673\pi$
$919$	−8.62524e11			−1.20923			−0.604615	+	0.796518i	$0.706673\pi$
$920$	−4.23388e10	+	2.44443e10i	−0.0591000	+	0.0341214i
$921$	−5.29376e11	+	5.53733e10i	−0.735742	+	0.0769594i
$922$	4.47801e10	−	7.75614e10i	0.0619671	−	0.107330i
$923$	−4.86142e11	−	2.80674e11i	−0.669817	−	0.386719i
$924$	2.35288e11	−	1.70768e11i	0.322784	−	0.234271i
$925$	−3.71954e11	−	6.44243e11i	−0.508069	−	0.880000i
$926$		−	6.63251e11i		−	0.902056i
$927$	−2.18524e11	+	6.70277e11i	−0.295924	+	0.907686i
$928$	9.11623e10			0.122920
$929$	−8.37182e10	+	4.83347e10i	−0.112398	+	0.0648928i	−0.555145	−	0.831754i	$-0.687337\pi$
$929$	−8.37182e10	+	4.83347e10i	−0.112398	+	0.0648928i	0.442747	+	0.896646i	$0.354004\pi$
$930$	−1.23486e10	+	2.76982e10i	−0.0165076	+	0.0370271i
$931$	2.47790e11	−	4.29186e11i	0.329827	−	0.571276i
$932$	7.10160e10	+	4.10011e10i	0.0941223	+	0.0543415i
$933$	−9.71209e11	−	4.32989e11i	−1.28170	−	0.571414i
$934$	8.82332e11	+	1.52824e12i	1.15943	+	2.00819i
$935$		−	9.70271e10i		−	0.126954i
$936$	−5.77260e11	−	1.88199e11i	−0.752087	−	0.245196i
$937$	9.92329e11			1.28735			0.643676	−	0.765298i	$-0.277409\pi$
$937$	9.92329e11			1.28735			0.643676	+	0.765298i	$0.277409\pi$
$938$	4.25260e11	−	2.45524e11i	0.549342	−	0.317163i
$939$	−1.23148e11	−	1.69676e11i	−0.158404	−	0.218252i
$940$	5.58481e9	−	9.67317e9i	0.00715314	−	0.0123896i
$941$	1.17412e12	+	6.77881e11i	1.49746	+	0.864560i	0.999996	−	0.00292364i	$-0.000930626\pi$
$941$	1.17412e12	+	6.77881e11i	1.49746	+	0.864560i	0.497466	+	0.867484i	$0.334264\pi$
$942$	1.06556e11	+	1.01869e12i	0.135324	+	1.29372i
$943$	2.12072e11	+	3.67319e11i	0.268186	+	0.464512i
$944$		−	1.03798e12i		−	1.30708i
$945$	1.63379e10	+	5.05394e10i	0.0204865	+	0.0633728i
$946$	−1.04300e12			−1.30233
$947$	4.88052e11	−	2.81777e11i	0.606828	−	0.350352i	−0.164895	−	0.986311i	$-0.552728\pi$
$947$	4.88052e11	−	2.81777e11i	0.606828	−	0.350352i	0.771723	+	0.635959i	$0.219395\pi$
$948$	−6.08559e11	+	6.36560e10i	−0.753476	+	0.0788145i
$949$	−3.77240e11	+	6.53398e11i	−0.465106	+	0.805588i
$950$	−1.33535e12	−	7.70964e11i	−1.63946	−	0.946541i
$951$	3.25986e11	−	2.36595e11i	0.398544	−	0.289256i
$952$	−2.56040e11	−	4.43475e11i	−0.311717	−	0.539910i
$953$			1.39576e12i			1.69216i	0.533059	+	0.846078i	$0.321042\pi$
$953$			1.39576e12i			1.69216i	−0.533059	+	0.846078i	$0.678958\pi$
$954$	8.63700e11	+	9.61158e11i	1.04272	+	1.16038i
$955$	−8.45377e10			−0.101633
$956$	−4.72985e11	+	2.73078e11i	−0.566260	+	0.326931i
$957$	−6.71228e10	+	1.50559e11i	−0.0800243	+	0.179497i
$958$	3.10319e11	−	5.37488e11i	0.368422	−	0.638126i
$959$	−1.02730e12	−	5.93110e11i	−1.21457	−	0.701230i
$960$	2.09699e10	+	9.34889e9i	0.0246894	+	0.0110072i
$961$	3.60737e11	+	6.24815e11i	0.422958	+	0.732585i
$962$			1.18633e12i			1.38518i
$963$	−2.27975e11	−	1.07781e12i	−0.265083	−	1.25325i
$964$	3.24529e11			0.375790
$965$	−1.01093e11	+	5.83660e10i	−0.116577	+	0.0673055i
$966$	5.27560e11	+	7.26885e11i	0.605848	+	0.834751i
$967$	2.45600e10	−	4.25391e10i	0.0280881	−	0.0486500i	−0.851640	−	0.524128i	$-0.824391\pi$
$967$	2.45600e10	−	4.25391e10i	0.0280881	−	0.0486500i	0.879728	+	0.475478i	$0.157725\pi$
$968$	2.99893e11	+	1.73143e11i	0.341558	+	0.197199i
$969$	−1.71802e11	−	1.64245e12i	−0.194865	−	1.86293i
$970$	−3.57078e10	−	6.18477e10i	−0.0403344	−	0.0698613i
$971$			7.05365e11i			0.793482i	0.917931	+	0.396741i	$0.129859\pi$
$971$			7.05365e11i			0.793482i	−0.917931	+	0.396741i	$0.870141\pi$
$972$	9.22375e8	−	3.70702e11i	0.00103334	−	0.415298i
$973$	−9.41504e10			−0.105044
$974$	1.31605e10	−	7.59822e9i	0.0146230	−	0.00844260i
$975$	1.01441e12	−	1.06109e11i	1.12253	−	0.117418i
$976$	−5.22763e11	+	9.05452e11i	−0.576110	+	0.997852i
$977$	−1.00820e12	−	5.82086e11i	−1.10655	−	0.638864i	−0.168613	−	0.985682i	$-0.553929\pi$
$977$	−1.00820e12	−	5.82086e11i	−1.10655	−	0.638864i	−0.937933	+	0.346818i	$0.887262\pi$
$978$	−4.69468e11	+	3.40732e11i	−0.513157	+	0.372441i
$979$	4.31647e10	+	7.47635e10i	0.0469892	+	0.0813877i
$980$			1.36815e10i			0.0148330i
$981$	7.75066e11	−	1.63939e11i	0.836879	−	0.177014i
$982$	−9.49979e11			−1.02157
$983$	−2.64796e11	+	1.52880e11i	−0.283594	+	0.163733i	−0.635049	−	0.772471i	$-0.719020\pi$
$983$	−2.64796e11	+	1.52880e11i	−0.283594	+	0.163733i	0.351455	+	0.936205i	$0.385687\pi$
$984$	1.26034e11	−	2.82698e11i	0.134433	−	0.301538i
$985$	−4.52771e10	+	7.84222e10i	−0.0480987	+	0.0833094i
$986$	−1.78601e11	−	1.03115e11i	−0.188962	−	0.109097i
$987$	2.63868e11	+	1.17639e11i	0.278047	+	0.123961i
$988$	3.60774e11	+	6.24878e11i	0.378623	+	0.655794i
$989$		−	9.45506e11i		−	0.988278i
$990$	9.23728e10	−	8.30065e10i	0.0961620	−	0.0864115i
$991$	3.71498e11			0.385179			0.192589	−	0.981279i	$-0.438311\pi$
$991$	3.71498e11			0.385179			0.192589	+	0.981279i	$0.438311\pi$
$992$	2.57744e11	−	1.48809e11i	0.266159	−	0.153667i
$993$	1.80401e10	+	2.48561e10i	0.0185542	+	0.0255644i
$994$	3.02986e11	−	5.24788e11i	0.310368	−	0.537574i
$995$	−2.10057e10	−	1.21277e10i	−0.0214312	−	0.0123733i
$996$	2.84065e10	+	2.71570e11i	0.0288656	+	0.275959i
$997$	−5.09939e11	−	8.83241e11i	−0.516105	−	0.893920i	−0.999825	−	0.0186972i	$-0.994048\pi$
$997$	−5.09939e11	−	8.83241e11i	−0.516105	−	0.893920i	0.483720	−	0.875223i	$-0.339285\pi$
$998$		−	8.63812e11i		−	0.870757i
$999$	9.70323e11	−	3.13676e11i	0.974214	−	0.314934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.9.d.a.5.6	yes	14
3.2	odd	2		27.9.d.a.17.2		14
4.3	odd	2		144.9.q.a.113.1		14
9.2	odd	6	inner	9.9.d.a.2.6	✓	14
9.4	even	3		81.9.b.a.80.11		14
9.5	odd	6		81.9.b.a.80.4		14
9.7	even	3		27.9.d.a.8.2		14
12.11	even	2		432.9.q.a.17.5		14
36.7	odd	6		432.9.q.a.305.5		14
36.11	even	6		144.9.q.a.65.1		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.9.d.a.2.6	✓	14	9.2	odd	6	inner
9.9.d.a.5.6	yes	14	1.1	even	1	trivial
27.9.d.a.8.2		14	9.7	even	3
27.9.d.a.17.2		14	3.2	odd	2
81.9.b.a.80.4		14	9.5	odd	6
81.9.b.a.80.11		14	9.4	even	3
144.9.q.a.65.1		14	36.11	even	6
144.9.q.a.113.1		14	4.3	odd	2
432.9.q.a.17.5		14	12.11	even	2
432.9.q.a.305.5		14	36.7	odd	6

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(16.4845 - 9.51731i) q^{2} +(80.5605 - 8.42672i) q^{3} +(53.1583 - 92.0729i) q^{4} +(-46.9888 - 27.1290i) q^{5} +(1247.80 - 905.629i) q^{6} +(-921.012 - 1595.24i) q^{7} +2849.17i q^{8} +(6418.98 - 1357.72i) q^{9} +O(q^{10})\)	\(q+(16.4845 - 9.51731i) q^{2} +(80.5605 - 8.42672i) q^{3} +(53.1583 - 92.0729i) q^{4} +(-46.9888 - 27.1290i) q^{5} +(1247.80 - 905.629i) q^{6} +(-921.012 - 1595.24i) q^{7} +2849.17i q^{8} +(6418.98 - 1357.72i) q^{9} -1032.78 q^{10} +(-15872.1 + 9163.77i) q^{11} +(3506.59 - 7865.39i) q^{12} +(-16240.1 + 28128.7i) q^{13} +(-30364.8 - 17531.1i) q^{14} +(-4014.05 - 1789.56i) q^{15} +(40724.9 + 70537.6i) q^{16} -97572.1i q^{17} +(92891.6 - 83472.7i) q^{18} +208951. q^{19} +(-4995.69 + 2884.26i) q^{20} +(-87639.8 - 120752. i) q^{21} +(-174429. + 302119. i) q^{22} +(-273878. - 158124. i) q^{23} +(24009.1 + 229530. i) q^{24} +(-193841. - 335742. i) q^{25} +618248. i q^{26} +(505675. - 163470. i) q^{27} -195838. q^{28} +(96164.1 - 55520.4i) q^{29} +(-83201.2 + 8702.94i) q^{30} +(181257. - 313947. i) q^{31} +(710990. + 410490. i) q^{32} +(-1.20144e6 + 871987. i) q^{33} +(-928623. - 1.60842e6i) q^{34} +99944.5i q^{35} +(216213. - 663188. i) q^{36} +1.91887e6 q^{37} +(3.44445e6 - 1.98865e6i) q^{38} +(-1.07128e6 + 2.40291e6i) q^{39} +(77295.0 - 133879. i) q^{40} +(-1.16149e6 - 670589. i) q^{41} +(-2.59393e6 - 1.15644e6i) q^{42} +(1.49489e6 + 2.58922e6i) q^{43} +1.94852e6i q^{44} +(-338454. - 110343. i) q^{45} -6.01964e6 q^{46} +(-1.67689e6 + 968152. i) q^{47} +(3.87522e6 + 5.33937e6i) q^{48} +(1.18588e6 - 2.05400e6i) q^{49} +(-6.39071e6 - 3.68968e6i) q^{50} +(-822212. - 7.86045e6i) q^{51} +(1.72659e6 + 2.99054e6i) q^{52} +1.03471e7i q^{53} +(6.77999e6 - 7.50737e6i) q^{54} +994415. q^{55} +(4.54510e6 - 2.62411e6i) q^{56} +(1.68332e7 - 1.76077e6i) q^{57} +(1.05681e6 - 1.83045e6i) q^{58} +(-1.10364e7 - 6.37189e6i) q^{59} +(-378150. + 274455. i) q^{60} +(6.41822e6 + 1.11167e7i) q^{61} -6.90032e6i q^{62} +(-8.07784e6 - 8.98933e6i) q^{63} -5.22412e6 q^{64} +(1.52620e6 - 881155. i) q^{65} +(-1.15062e7 + 2.58088e7i) q^{66} +(-7.00252e6 + 1.21287e7i) q^{67} +(-8.98374e6 - 5.18677e6i) q^{68} +(-2.33962e7 - 1.04306e7i) q^{69} +(951202. + 1.64753e6i) q^{70} +1.72828e7i q^{71} +(3.86837e6 + 1.82887e7i) q^{72} +2.32289e7 q^{73} +(3.16315e7 - 1.82624e7i) q^{74} +(-1.84451e7 - 2.54141e7i) q^{75} +(1.11075e7 - 1.92388e7i) q^{76} +(2.92368e7 + 1.68799e7i) q^{77} +(5.20980e6 + 4.98063e7i) q^{78} +(-3.55263e7 - 6.15333e7i) q^{79} -4.41930e6i q^{80} +(3.93599e7 - 1.74304e7i) q^{81} -2.55288e7 q^{82} +(-2.74593e7 + 1.58536e7i) q^{83} +(-1.57768e7 + 1.65027e6i) q^{84} +(-2.64703e6 + 4.58479e6i) q^{85} +(4.92848e7 + 2.84546e7i) q^{86} +(7.27917e6 - 5.28310e6i) q^{87} +(-2.61091e7 - 4.52223e7i) q^{88} -4.71037e6i q^{89} +(-6.62939e6 + 1.40223e6i) q^{90} +5.98292e7 q^{91} +(-2.91178e7 + 1.68112e7i) q^{92} +(1.19566e7 - 2.68191e7i) q^{93} +(-1.84284e7 + 3.19189e7i) q^{94} +(-9.81837e6 - 5.66864e6i) q^{95} +(6.07367e7 + 2.70780e7i) q^{96} +(3.45744e7 + 5.98847e7i) q^{97} -4.51454e7i q^{98} +(-8.94409e7 + 8.03719e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9}+O(q^{10}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9	\( 14 q - 3 q^{2} - 93 q^{3} + 767 q^{4} + 438 q^{5} - 2259 q^{6} + 922 q^{7} + 17973 q^{9} - 516 q^{10} - 28677 q^{11} - 55110 q^{12} + 1684 q^{13} + 120966 q^{14} - 75276 q^{15} - 65281 q^{16} + 243324 q^{18} - 269630 q^{19} + 539454 q^{20} + 354054 q^{21} + 61311 q^{22} - 1000452 q^{23} - 1125513 q^{24} + 65177 q^{25} - 524826 q^{27} + 1075708 q^{28} + 3797682 q^{29} + 2372562 q^{30} - 164132 q^{31} - 8461881 q^{32} - 5761521 q^{33} + 654993 q^{34} + 12958047 q^{36} - 1671668 q^{37} + 10967691 q^{38} + 3383976 q^{39} + 613326 q^{40} - 10239447 q^{41} - 35844228 q^{42} + 791815 q^{43} + 27631638 q^{45} + 1189536 q^{46} + 31148628 q^{47} + 17088189 q^{48} - 4826637 q^{49} - 63849453 q^{50} - 47946573 q^{51} - 5552720 q^{52} + 36967995 q^{54} + 8107476 q^{55} + 116638674 q^{56} + 37276797 q^{57} + 14211822 q^{58} - 83493795 q^{59} - 109012050 q^{60} - 5255600 q^{61} + 38322432 q^{63} - 26813830 q^{64} + 69232992 q^{65} + 36133866 q^{66} - 8288855 q^{67} - 77746743 q^{68} - 62108640 q^{69} + 27813756 q^{70} + 88821171 q^{72} - 36721682 q^{73} - 10383450 q^{74} + 13792011 q^{75} - 42822959 q^{76} + 56158710 q^{77} + 27355140 q^{78} - 32771822 q^{79} - 16336971 q^{81} + 236099418 q^{82} - 198915996 q^{83} - 187060614 q^{84} + 97486146 q^{85} + 146190669 q^{86} + 114294006 q^{87} + 24955827 q^{88} - 222035850 q^{90} - 201514504 q^{91} - 295365804 q^{92} + 94187784 q^{93} - 36698244 q^{94} + 386813838 q^{95} + 768275928 q^{96} + 127049161 q^{97} - 511060752 q^{99}+O(q^{100}) \) 14 * q - 3 * q^2 - 93 * q^3 + 767 * q^4 + 438 * q^5 - 2259 * q^6 + 922 * q^7 + 17973 * q^9 - 516 * q^10 - 28677 * q^11 - 55110 * q^12 + 1684 * q^13 + 120966 * q^14 - 75276 * q^15 - 65281 * q^16 + 243324 * q^18 - 269630 * q^19 + 539454 * q^20 + 354054 * q^21 + 61311 * q^22 - 1000452 * q^23 - 1125513 * q^24 + 65177 * q^25 - 524826 * q^27 + 1075708 * q^28 + 3797682 * q^29 + 2372562 * q^30 - 164132 * q^31 - 8461881 * q^32 - 5761521 * q^33 + 654993 * q^34 + 12958047 * q^36 - 1671668 * q^37 + 10967691 * q^38 + 3383976 * q^39 + 613326 * q^40 - 10239447 * q^41 - 35844228 * q^42 + 791815 * q^43 + 27631638 * q^45 + 1189536 * q^46 + 31148628 * q^47 + 17088189 * q^48 - 4826637 * q^49 - 63849453 * q^50 - 47946573 * q^51 - 5552720 * q^52 + 36967995 * q^54 + 8107476 * q^55 + 116638674 * q^56 + 37276797 * q^57 + 14211822 * q^58 - 83493795 * q^59 - 109012050 * q^60 - 5255600 * q^61 + 38322432 * q^63 - 26813830 * q^64 + 69232992 * q^65 + 36133866 * q^66 - 8288855 * q^67 - 77746743 * q^68 - 62108640 * q^69 + 27813756 * q^70 + 88821171 * q^72 - 36721682 * q^73 - 10383450 * q^74 + 13792011 * q^75 - 42822959 * q^76 + 56158710 * q^77 + 27355140 * q^78 - 32771822 * q^79 - 16336971 * q^81 + 236099418 * q^82 - 198915996 * q^83 - 187060614 * q^84 + 97486146 * q^85 + 146190669 * q^86 + 114294006 * q^87 + 24955827 * q^88 - 222035850 * q^90 - 201514504 * q^91 - 295365804 * q^92 + 94187784 * q^93 - 36698244 * q^94 + 386813838 * q^95 + 768275928 * q^96 + 127049161 * q^97 - 511060752 * q^99

Introduction

L-functions

Modular forms

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