LMFDB - Embedded newform 429.2.bj.a.112.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(73,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 14, 5]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bj (of order $20$, degree $8$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.1
Character	$\chi$	$=$	429.112
Dual form			429.2.bj.a.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13354 - 2.22470i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.48880 + 3.42554i) q^{4} +(-0.0990937 + 0.194482i) q^{5} +(2.22470 + 1.13354i) q^{6} +(-0.728003 - 4.59643i) q^{7} +(5.50974 + 0.872657i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.13354 - 2.22470i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.48880 + 3.42554i) q^{4} +(-0.0990937 + 0.194482i) q^{5} +(2.22470 + 1.13354i) q^{6} +(-0.728003 - 4.59643i) q^{7} +(5.50974 + 0.872657i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.544991 q^{10} +(-2.15256 + 2.52319i) q^{11} -4.23419i q^{12} +(-3.60547 + 0.0240641i) q^{13} +(-9.40045 + 6.82983i) q^{14} +(-0.0341454 - 0.215585i) q^{15} +(-1.68724 - 5.19278i) q^{16} +(1.04259 + 3.20875i) q^{17} +(-2.46610 + 0.390591i) q^{18} +(0.666492 - 4.20806i) q^{19} +(-0.419582 - 0.823476i) q^{20} +(3.29068 + 3.29068i) q^{21} +(8.05335 + 1.92865i) q^{22} +6.37942i q^{23} +(-4.97041 + 2.53255i) q^{24} +(2.91092 + 4.00654i) q^{25} +(4.14048 + 7.99381i) q^{26} +(0.309017 + 0.951057i) q^{27} +(17.5571 + 8.94578i) q^{28} +(-2.63654 + 3.62888i) q^{29} +(-0.440907 + 0.320338i) q^{30} +(-4.39370 + 2.23870i) q^{31} +(-1.75074 + 1.75074i) q^{32} +(0.258360 - 3.30655i) q^{33} +(5.95669 - 5.95669i) q^{34} +(0.966065 + 0.313894i) q^{35} +(2.48880 + 3.42554i) q^{36} +(-5.90777 + 0.935698i) q^{37} +(-10.1172 + 3.28727i) q^{38} +(2.90274 - 2.13871i) q^{39} +(-0.715697 + 0.985073i) q^{40} +(-0.930149 + 5.87273i) q^{41} +(3.59065 - 11.0509i) q^{42} +8.98558 q^{43} +(-3.28601 - 13.6534i) q^{44} +(0.154342 + 0.154342i) q^{45} +(14.1923 - 7.23133i) q^{46} +(1.20555 - 7.61152i) q^{47} +(4.41724 + 3.20932i) q^{48} +(-13.9398 + 4.52931i) q^{49} +(5.61370 - 11.0175i) q^{50} +(-2.72953 - 1.98312i) q^{51} +(8.89085 - 12.4106i) q^{52} +(-0.440899 + 1.35695i) q^{53} +(1.76553 - 1.76553i) q^{54} +(-0.277412 - 0.668667i) q^{55} -25.9604i q^{56} +(1.93423 + 3.79615i) q^{57} +(11.0618 + 1.75202i) q^{58} +(-10.9635 + 1.73645i) q^{59} +(0.823476 + 0.419582i) q^{60} +(-3.11467 + 1.01202i) q^{61} +(9.96088 + 7.23700i) q^{62} +(-4.59643 - 0.728003i) q^{63} +(-4.50615 - 1.46414i) q^{64} +(0.352600 - 0.703585i) q^{65} +(-7.64893 + 3.17333i) q^{66} +(7.83844 + 7.83844i) q^{67} +(-13.5865 - 4.41451i) q^{68} +(-3.74973 - 5.16106i) q^{69} +(-0.396755 - 2.50501i) q^{70} +(-1.72642 + 3.38830i) q^{71} +(2.53255 - 4.97041i) q^{72} +(-0.666851 - 4.21033i) q^{73} +(8.77834 + 12.0823i) q^{74} +(-4.70997 - 1.53036i) q^{75} +(12.7561 + 12.7561i) q^{76} +(13.1647 + 8.05719i) q^{77} +(-8.04836 - 4.03341i) q^{78} +(-14.6936 - 4.77425i) q^{79} +(1.17710 + 0.186434i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(14.1194 - 4.58767i) q^{82} +(0.689705 + 0.351422i) q^{83} +(-19.4622 + 3.08251i) q^{84} +(-0.727360 - 0.115202i) q^{85} +(-10.1855 - 19.9902i) q^{86} -4.48555i q^{87} +(-14.0619 + 12.0237i) q^{88} +(6.92983 - 6.92983i) q^{89} +(0.168412 - 0.518318i) q^{90} +(2.73540 + 16.5548i) q^{91} +(-21.8529 - 15.8771i) q^{92} +(2.23870 - 4.39370i) q^{93} +(-18.2999 + 5.94599i) q^{94} +(0.752349 + 0.546614i) q^{95} +(0.387320 - 2.44544i) q^{96} +(-0.247468 + 0.126091i) q^{97} +(25.8777 + 25.8777i) q^{98} +(1.73452 + 2.82691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	$ 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) $ 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−1.13354	−	2.22470i	−0.801534	−	1.57310i	−0.819375	−	0.573258i	$-0.805679\pi$
$2$	−1.13354	−	2.22470i	−0.801534	−	1.57310i	0.0178408	−	0.999841i	$-0.494321\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	−2.48880	+	3.42554i	−1.24440	+	1.71277i
$5$	−0.0990937	+	0.194482i	−0.0443161	+	0.0869752i	−0.912103	−	0.409962i	$-0.865542\pi$
$5$	−0.0990937	+	0.194482i	−0.0443161	+	0.0869752i	0.867787	+	0.496937i	$0.165542\pi$
$6$	2.22470	+	1.13354i	0.908229	+	0.462766i
$7$	−0.728003	−	4.59643i	−0.275159	−	1.73729i	−0.607672	−	0.794188i	$-0.707896\pi$
$7$	−0.728003	−	4.59643i	−0.275159	−	1.73729i	0.332512	−	0.943099i	$-0.392104\pi$
$8$	5.50974	+	0.872657i	1.94799	+	0.308531i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	0.544991			0.172341
$11$	−2.15256	+	2.52319i	−0.649020	+	0.760771i
$11$	−2.15256	+	2.52319i	−0.649020	+	0.760771i
$12$		−	4.23419i		−	1.22231i
$13$	−3.60547	+	0.0240641i	−0.999978	+	0.00667419i
$13$	−3.60547	+	0.0240641i	−0.999978	+	0.00667419i
$14$	−9.40045	+	6.82983i	−2.51238	+	1.82535i
$15$	−0.0341454	−	0.215585i	−0.00881630	−	0.0556639i
$16$	−1.68724	−	5.19278i	−0.421809	−	1.29820i
$17$	1.04259	+	3.20875i	0.252864	+	0.778237i	0.994243	+	0.107150i	$0.0341724\pi$
$17$	1.04259	+	3.20875i	0.252864	+	0.778237i	−0.741378	+	0.671087i	$0.765828\pi$
$18$	−2.46610	+	0.390591i	−0.581265	+	0.0920633i
$19$	0.666492	−	4.20806i	0.152904	−	0.965396i	−0.785250	−	0.619178i	$-0.787466\pi$
$19$	0.666492	−	4.20806i	0.152904	−	0.965396i	0.938154	−	0.346218i	$-0.112534\pi$
$20$	−0.419582	−	0.823476i	−0.0938214	−	0.184135i
$21$	3.29068	+	3.29068i	0.718085	+	0.718085i
$22$	8.05335	+	1.92865i	1.71698	+	0.411189i
$23$			6.37942i			1.33020i	0.746754	+	0.665101i	$0.231611\pi$
$23$			6.37942i			1.33020i	−0.746754	+	0.665101i	$0.768389\pi$
$24$	−4.97041	+	2.53255i	−1.01458	+	0.516954i
$25$	2.91092	+	4.00654i	0.582184	+	0.801308i
$26$	4.14048	+	7.99381i	0.812015	+	1.56771i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	17.5571	+	8.94578i	3.31798	+	1.69059i
$29$	−2.63654	+	3.62888i	−0.489593	+	0.673867i	−0.980313	−	0.197451i	$-0.936734\pi$
$29$	−2.63654	+	3.62888i	−0.489593	+	0.673867i	0.490720	+	0.871317i	$0.336734\pi$
$30$	−0.440907	+	0.320338i	−0.0804983	+	0.0584854i
$31$	−4.39370	+	2.23870i	−0.789132	+	0.402083i	−0.801616	−	0.597839i	$-0.796026\pi$
$31$	−4.39370	+	2.23870i	−0.789132	+	0.402083i	0.0124839	+	0.999922i	$0.496026\pi$
$32$	−1.75074	+	1.75074i	−0.309491	+	0.309491i
$33$	0.258360	−	3.30655i	0.0449747	−	0.575596i
$34$	5.95669	−	5.95669i	1.02156	−	1.02156i
$35$	0.966065	+	0.313894i	0.163295	+	0.0530577i
$36$	2.48880	+	3.42554i	0.414800	+	0.570923i
$37$	−5.90777	+	0.935698i	−0.971231	+	0.153828i	−0.621836	−	0.783148i	$-0.713613\pi$
$37$	−5.90777	+	0.935698i	−0.971231	+	0.153828i	−0.349395	+	0.936975i	$0.613613\pi$
$38$	−10.1172	+	3.28727i	−1.64122	+	0.533265i
$39$	2.90274	−	2.13871i	0.464811	−	0.342468i
$40$	−0.715697	+	0.985073i	−0.113162	+	0.155754i
$41$	−0.930149	+	5.87273i	−0.145265	+	0.917166i	0.802142	+	0.597134i	$0.203694\pi$
$41$	−0.930149	+	5.87273i	−0.145265	+	0.917166i	−0.947407	+	0.320032i	$0.896306\pi$
$42$	3.59065	−	11.0509i	0.554050	−	1.70519i
$43$	8.98558			1.37029			0.685144	−	0.728408i	$-0.259739\pi$
$43$	8.98558			1.37029			0.685144	+	0.728408i	$0.259739\pi$
$44$	−3.28601	−	13.6534i	−0.495384	−	2.05832i
$45$	0.154342	+	0.154342i	0.0230080	+	0.0230080i
$46$	14.1923	−	7.23133i	2.09254	−	1.06620i
$47$	1.20555	−	7.61152i	0.175847	−	1.11025i	−0.728999	−	0.684515i	$-0.760014\pi$
$47$	1.20555	−	7.61152i	0.175847	−	1.11025i	0.904846	−	0.425740i	$-0.139986\pi$
$48$	4.41724	+	3.20932i	0.637574	+	0.463225i
$49$	−13.9398	+	4.52931i	−1.99140	+	0.647045i
$50$	5.61370	−	11.0175i	0.793896	−	1.55811i
$51$	−2.72953	−	1.98312i	−0.382210	−	0.277692i
$52$	8.89085	−	12.4106i	1.23294	−	1.72103i
$53$	−0.440899	+	1.35695i	−0.0605621	+	0.186391i	−0.976760	−	0.214334i	$-0.931242\pi$
$53$	−0.440899	+	1.35695i	−0.0605621	+	0.186391i	0.916198	+	0.400725i	$0.131242\pi$
$54$	1.76553	−	1.76553i	0.240258	−	0.240258i
$55$	−0.277412	−	0.668667i	−0.0374062	−	0.0901630i
$56$		−	25.9604i		−	3.46911i
$57$	1.93423	+	3.79615i	0.256196	+	0.502812i
$58$	11.0618	+	1.75202i	1.45248	+	0.230051i
$59$	−10.9635	+	1.73645i	−1.42733	+	0.226067i	−0.821809	−	0.569763i	$-0.807035\pi$
$59$	−10.9635	+	1.73645i	−1.42733	+	0.226067i	−0.605521	+	0.795829i	$0.707035\pi$
$60$	0.823476	+	0.419582i	0.106310	+	0.0541678i
$61$	−3.11467	+	1.01202i	−0.398793	+	0.129576i	−0.501545	−	0.865131i	$-0.667235\pi$
$61$	−3.11467	+	1.01202i	−0.398793	+	0.129576i	0.102753	+	0.994707i	$0.467235\pi$
$62$	9.96088	+	7.23700i	1.26503	+	0.919100i
$63$	−4.59643	−	0.728003i	−0.579096	−	0.0917198i
$64$	−4.50615	−	1.46414i	−0.563269	−	0.183017i
$65$	0.352600	−	0.703585i	0.0437346	−	0.0872690i
$66$	−7.64893	+	3.17333i	−0.941518	+	0.390610i
$67$	7.83844	+	7.83844i	0.957618	+	0.957618i	0.999138	−	0.0415199i	$-0.0132200\pi$
$67$	7.83844	+	7.83844i	0.957618	+	0.957618i	−0.0415199	+	0.999138i	$0.513220\pi$
$68$	−13.5865	−	4.41451i	−1.64760	−	0.535339i
$69$	−3.74973	−	5.16106i	−0.451414	−	0.621319i
$70$	−0.396755	−	2.50501i	−0.0474213	−	0.299407i
$71$	−1.72642	+	3.38830i	−0.204889	+	0.402117i	−0.970470	−	0.241223i	$-0.922452\pi$
$71$	−1.72642	+	3.38830i	−0.204889	+	0.402117i	0.765581	+	0.643339i	$0.222452\pi$
$72$	2.53255	−	4.97041i	0.298464	−	0.585768i
$73$	−0.666851	−	4.21033i	−0.0780490	−	0.492782i	−0.995487	−	0.0949024i	$-0.969746\pi$
$73$	−0.666851	−	4.21033i	−0.0780490	−	0.492782i	0.917438	−	0.397880i	$-0.130254\pi$
$74$	8.77834	+	12.0823i	1.02046	+	1.40454i
$75$	−4.70997	−	1.53036i	−0.543861	−	0.176711i
$76$	12.7561	+	12.7561i	1.46323	+	1.46323i
$77$	13.1647	+	8.05719i	1.50026	+	0.918202i
$78$	−8.04836	−	4.03341i	−0.911297	−	0.456694i
$79$	−14.6936	−	4.77425i	−1.65316	−	0.537145i	−0.673741	−	0.738967i	$-0.735314\pi$
$79$	−14.6936	−	4.77425i	−1.65316	−	0.537145i	−0.979422	+	0.201822i	$0.935314\pi$
$80$	1.17710	+	0.186434i	0.131604	+	0.0208440i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	14.1194	−	4.58767i	1.55923	−	0.506624i
$83$	0.689705	+	0.351422i	0.0757049	+	0.0385736i	0.491433	−	0.870915i	$-0.336473\pi$
$83$	0.689705	+	0.351422i	0.0757049	+	0.0385736i	−0.415728	+	0.909489i	$0.636473\pi$
$84$	−19.4622	+	3.08251i	−2.12350	+	0.336329i
$85$	−0.727360	−	0.115202i	−0.0788932	−	0.0124955i
$86$	−10.1855	−	19.9902i	−1.09833	−	2.15560i
$87$		−	4.48555i		−	0.480901i
$88$	−14.0619	+	12.0237i	−1.49900	+	1.28173i
$89$	6.92983	−	6.92983i	0.734561	−	0.734561i	−0.236959	−	0.971520i	$-0.576151\pi$
$89$	6.92983	−	6.92983i	0.734561	−	0.734561i	0.971520	+	0.236959i	$0.0761507\pi$
$90$	0.168412	−	0.518318i	0.0177521	−	0.0546355i
$91$	2.73540	+	16.5548i	0.286748	+	1.73541i
$92$	−21.8529	−	15.8771i	−2.27833	−	1.65530i
$93$	2.23870	−	4.39370i	0.232143	−	0.455606i
$94$	−18.2999	+	5.94599i	−1.88749	+	0.613282i
$95$	0.752349	+	0.546614i	0.0771894	+	0.0560814i
$96$	0.387320	−	2.44544i	0.0395307	−	0.249587i
$97$	−0.247468	+	0.126091i	−0.0251266	+	0.0128026i	−0.466509	−	0.884517i	$-0.654488\pi$
$97$	−0.247468	+	0.126091i	−0.0251266	+	0.0128026i	0.441382	+	0.897319i	$0.354488\pi$
$98$	25.8777	+	25.8777i	2.61404	+	2.61404i
$99$	1.73452	+	2.82691i	0.174326	+	0.284115i
$100$	−20.9692			−2.09692
$101$	−1.08601	+	3.34240i	−0.108062	+	0.332581i	−0.990437	−	0.137966i	$-0.955944\pi$
$101$	−1.08601	+	3.34240i	−0.108062	+	0.332581i	0.882375	+	0.470547i	$0.155944\pi$
$102$	−1.31781	+	8.32032i	−0.130483	+	0.823834i
$103$	4.42980	−	6.09710i	0.436481	−	0.600765i	−0.532944	−	0.846150i	$-0.678915\pi$
$103$	4.42980	−	6.09710i	0.436481	−	0.600765i	0.969426	+	0.245385i	$0.0789145\pi$
$104$	−19.8862	−	3.01375i	−1.95000	−	0.295523i
$105$	−0.966065	+	0.313894i	−0.0942783	+	0.0306329i
$106$	3.51858	−	0.557288i	0.341754	−	0.0541286i
$107$	−1.19468	−	1.64434i	−0.115494	−	0.158964i	0.747356	−	0.664424i	$-0.231323\pi$
$107$	−1.19468	−	1.64434i	−0.115494	−	0.158964i	−0.862850	+	0.505460i	$0.831323\pi$
$108$	−4.02696	−	1.30844i	−0.387494	−	0.125905i
$109$	−14.5412	+	14.5412i	−1.39279	+	1.39279i	−0.573788	+	0.819004i	$0.694527\pi$
$109$	−14.5412	+	14.5412i	−1.39279	+	1.39279i	−0.819004	+	0.573788i	$0.805473\pi$
$110$	−1.17313	+	1.37512i	−0.111853	+	0.131112i
$111$	4.22949	−	4.22949i	0.401446	−	0.401446i
$112$	−22.6399	+	11.5356i	−2.13927	+	1.09001i
$113$	−3.92304	+	2.85026i	−0.369049	+	0.268130i	−0.756816	−	0.653628i	$-0.773246\pi$
$113$	−3.92304	+	2.85026i	−0.369049	+	0.268130i	0.387768	+	0.921757i	$0.373246\pi$
$114$	6.25275	−	8.60618i	0.585624	−	0.806042i
$115$	−1.24069	−	0.632161i	−0.115695	−	0.0589493i
$116$	−5.86906	−	18.0631i	−0.544929	−	1.67712i
$117$	−1.09127	+	3.43644i	−0.100888	+	0.317699i
$118$	16.2907	+	22.4222i	1.49968	+	2.06413i
$119$	13.9898	−	7.12816i	1.28244	−	0.653437i
$120$		−	1.21762i		−	0.111153i
$121$	−1.73300	−	10.8626i	−0.157545	−	0.987512i
$122$	5.78204	+	5.78204i	0.523481	+	0.523481i
$123$	−2.69940	−	5.29786i	−0.243396	−	0.477692i
$124$	3.26628	−	20.6225i	0.293320	−	1.85195i
$125$	−2.14558	+	0.339827i	−0.191907	+	0.0303950i
$126$	3.59065	+	11.0509i	0.319881	+	0.984492i
$127$	−2.51597	−	7.74337i	−0.223257	−	0.687113i	−0.998464	−	0.0554062i	$-0.982355\pi$
$127$	−2.51597	−	7.74337i	−0.223257	−	0.687113i	0.775207	−	0.631707i	$-0.217645\pi$
$128$	2.62528	+	16.5754i	0.232044	+	1.46507i
$129$	−7.26949	+	5.28159i	−0.640043	+	0.465018i
$130$	−1.96495	+	0.0131147i	−0.172338	+	0.00115024i
$131$		−	2.87142i		−	0.250878i	−0.992101	−	0.125439i	$-0.959966\pi$
$131$		−	2.87142i		−	0.250878i	0.992101	−	0.125439i	$-0.0400339\pi$
$132$	10.6837	+	9.11435i	0.929895	+	0.793302i
$133$	−19.8273			−1.71924
$134$	8.55297	−	26.3233i	0.738864	−	2.27399i
$135$	−0.215585	−	0.0341454i	−0.0185546	−	0.00293877i
$136$	2.94424	+	18.5892i	0.252467	+	1.59401i
$137$	−14.7817	−	7.53168i	−1.26289	−	0.643475i	−0.311144	−	0.950363i	$-0.600712\pi$
$137$	−14.7817	−	7.53168i	−1.26289	−	0.643475i	−0.951746	+	0.306888i	$0.900712\pi$
$138$	−7.23133	+	14.1923i	−0.615572	+	1.20813i
$139$	7.36411	−	10.1358i	0.624616	−	0.859710i	−0.373063	−	0.927806i	$-0.621692\pi$
$139$	7.36411	−	10.1358i	0.624616	−	0.859710i	0.997679	+	0.0680959i	$0.0216924\pi$
$140$	−3.47959	+	2.52807i	−0.294079	+	0.213661i
$141$	3.49863	+	6.86645i	0.294638	+	0.578260i
$142$	9.49491			0.796795
$143$	7.70026	−	9.14910i	0.643928	−	0.765086i
$144$	−5.46001			−0.455001
$145$	−0.444490	−	0.872360i	−0.0369129	−	0.0724456i
$146$	−8.61082	+	6.25613i	−0.712636	+	0.517761i
$147$	8.61526	−	11.8579i	0.710575	−	0.978022i
$148$	11.4980	−	22.5660i	0.945127	−	1.85492i
$149$	−11.3874	−	5.80217i	−0.932892	−	0.475332i	−0.0796356	−	0.996824i	$-0.525376\pi$
$149$	−11.3874	−	5.80217i	−0.932892	−	0.475332i	−0.853256	+	0.521492i	$0.825376\pi$
$150$	1.93435	+	12.2130i	0.157939	+	0.997187i
$151$	7.49936	+	1.18778i	0.610290	+	0.0966604i	0.453926	−	0.891039i	$-0.350023\pi$
$151$	7.49936	+	1.18778i	0.610290	+	0.0966604i	0.156363	+	0.987700i	$0.450023\pi$
$152$	7.34439	−	22.6037i	0.595709	−	1.83340i
$153$	3.37388			0.272762
$154$	3.00204	−	38.4207i	0.241911	−	3.09603i
$155$		−	1.07634i		−	0.0864536i
$156$	0.101892	+	15.2663i	0.00815790	+	1.22228i
$157$	7.77838	−	5.65132i	0.620782	−	0.451025i	−0.232413	−	0.972617i	$-0.574662\pi$
$157$	7.77838	−	5.65132i	0.620782	−	0.451025i	0.853195	+	0.521593i	$0.174662\pi$
$158$	6.03456	+	38.1007i	0.480084	+	3.03113i
$159$	−0.440899	−	1.35695i	−0.0349656	−	0.107613i
$160$	−0.167001	−	0.513976i	−0.0132026	−	0.0406334i
$161$	29.3226	−	4.64424i	2.31094	−	0.366017i
$162$	−0.390591	+	2.46610i	−0.0306878	+	0.193755i
$163$	−1.71594	−	3.36773i	−0.134403	−	0.263781i	0.813989	−	0.580880i	$-0.197291\pi$
$163$	−1.71594	−	3.36773i	−0.134403	−	0.263781i	−0.948393	+	0.317099i	$0.897291\pi$
$164$	−17.8023	−	17.8023i	−1.39012	−	1.39012i
$165$	0.617463	+	0.377905i	0.0480695	+	0.0294198i
$166$		−	1.93274i		−	0.150009i
$167$	−15.4940	+	7.89457i	−1.19896	+	0.610900i	−0.935348	−	0.353729i	$-0.884913\pi$
$167$	−15.4940	+	7.89457i	−1.19896	+	0.610900i	−0.263611	+	0.964629i	$0.584913\pi$
$168$	15.2592	+	21.0024i	1.17727	+	1.62037i
$169$	12.9988	−	0.173525i	0.999911	−	0.0133481i
$170$	0.568201	+	1.74874i	0.0435790	+	0.134122i
$171$	−3.79615	−	1.93423i	−0.290299	−	0.147915i
$172$	−22.3633	+	30.7804i	−1.70518	+	2.34699i
$173$	−8.17085	+	5.93647i	−0.621218	+	0.451341i	−0.853347	−	0.521344i	$-0.825431\pi$
$173$	−8.17085	+	5.93647i	−0.621218	+	0.451341i	0.232129	+	0.972685i	$0.425431\pi$
$174$	−9.97899	+	5.08455i	−0.756505	+	0.385459i
$175$	16.2966	−	16.2966i	1.23191	−	1.23191i
$176$	16.7343	+	6.92054i	1.26139	+	0.521655i
$177$	7.84902	−	7.84902i	0.589969	−	0.589969i
$178$	−23.2720	−	7.56154i	−1.74431	−	0.566761i
$179$	−1.53124	−	2.10757i	−0.114450	−	0.157527i	0.747949	−	0.663757i	$-0.231039\pi$
$179$	−1.53124	−	2.10757i	−0.114450	−	0.157527i	−0.862399	+	0.506229i	$0.831039\pi$
$180$	−0.912831	+	0.144578i	−0.0680384	+	0.0107762i
$181$	−15.2209	+	4.94556i	−1.13136	+	0.367600i	−0.814092	−	0.580736i	$-0.802765\pi$
$181$	−15.2209	+	4.94556i	−1.13136	+	0.367600i	−0.317266	+	0.948337i	$0.602765\pi$
$182$	33.7287	−	24.8510i	2.50014	−	1.84208i
$183$	1.92497	−	2.64950i	0.142298	−	0.195856i
$184$	−5.56705	+	35.1490i	−0.410408	+	2.59122i
$185$	0.403446	−	1.24168i	0.0296619	−	0.0912900i
$186$	−12.3123			−0.902783
$187$	−10.3405	−	4.27638i	−0.756174	−	0.312720i
$188$	23.0732	+	23.0732i	1.68278	+	1.68278i
$189$	4.14650	−	2.11275i	0.301613	−	0.153680i
$190$	0.363232	−	2.29336i	0.0263516	−	0.166378i
$191$	−3.28324	−	2.38541i	−0.237567	−	0.172602i	0.462632	−	0.886551i	$-0.346905\pi$
$191$	−3.28324	−	2.38541i	−0.237567	−	0.172602i	−0.700199	+	0.713948i	$0.746905\pi$
$192$	4.50615	−	1.46414i	0.325203	−	0.105665i
$193$	7.23879	−	14.2069i	0.521059	−	1.02264i	−0.469159	−	0.883114i	$-0.655443\pi$
$193$	7.23879	−	14.2069i	0.521059	−	1.02264i	0.990219	−	0.139523i	$-0.0445570\pi$
$194$	0.561030	+	0.407612i	0.0402796	+	0.0292648i
$195$	0.128298	+	0.776465i	0.00918761	+	0.0556038i
$196$	19.1780	−	59.0238i	1.36986	−	4.21598i
$197$	−16.7094	+	16.7094i	−1.19050	+	1.19050i	−0.213567	+	0.976928i	$0.568508\pi$
$197$	−16.7094	+	16.7094i	−1.19050	+	1.19050i	−0.976928	+	0.213567i	$0.931492\pi$
$198$	4.32288	−	7.06321i	0.307213	−	0.501960i
$199$			0.0685810i			0.00486158i	0.999997	+	0.00243079i	$0.000773745\pi$
$199$			0.0685810i			0.00486158i	−0.999997	+	0.00243079i	$0.999226\pi$
$200$	12.5421	+	24.6152i	0.886860	+	1.74056i
$201$	−10.9487	−	1.73411i	−0.772265	−	0.122315i
$202$	8.66687	−	1.37270i	0.609799	−	0.0965826i
$203$	18.5993	+	9.47683i	1.30542	+	0.665143i
$204$	13.5865	−	4.41451i	0.951244	−	0.309078i
$205$	−1.04997	−	0.762848i	−0.0733331	−	0.0532796i
$206$	−18.5856	−	2.94366i	−1.29492	−	0.205095i
$207$	6.06719	+	1.97135i	0.421699	+	0.137018i
$208$	6.20824	+	18.6818i	0.430464	+	1.29535i
$209$	9.18309	+	10.7398i	0.635208	+	0.742886i
$210$	1.79339	+	1.79339i	0.123756	+	0.123756i
$211$	−3.42357	−	1.11238i	−0.235688	−	0.0765797i	0.188792	−	0.982017i	$-0.439543\pi$
$211$	−3.42357	−	1.11238i	−0.235688	−	0.0765797i	−0.424480	+	0.905437i	$0.639543\pi$
$212$	−3.55096	−	4.88748i	−0.243881	−	0.335674i
$213$	−0.594885	−	3.75596i	−0.0407609	−	0.257354i
$214$	−2.30394	+	4.52173i	−0.157494	+	0.309099i
$215$	−0.890415	+	1.74754i	−0.0607258	+	0.119181i
$216$	0.872657	+	5.50974i	0.0593768	+	0.374890i
$217$	13.4887	+	18.5656i	0.915671	+	1.26031i
$218$	48.8327	+	15.8667i	3.30737	+	1.07463i
$219$	3.01427	+	3.01427i	0.203685	+	0.203685i
$220$	2.98096	+	0.713893i	0.200977	+	0.0481307i
$221$	−3.83623	−	11.5440i	−0.258053	−	0.776532i
$222$	−14.2036	−	4.61505i	−0.953286	−	0.309742i
$223$	−1.02617	−	0.162529i	−0.0687174	−	0.0108838i	0.121981	−	0.992532i	$-0.461075\pi$
$223$	−1.02617	−	0.162529i	−0.0687174	−	0.0108838i	−0.190698	+	0.981649i	$0.561075\pi$
$224$	9.32172	+	6.77262i	0.622833	+	0.452515i
$225$	4.70997	−	1.53036i	0.313998	−	0.102024i
$226$	10.7879	+	5.49670i	0.717600	+	0.365635i
$227$	14.1286	−	2.23776i	0.937751	−	0.148525i	0.331192	−	0.943564i	$-0.392549\pi$
$227$	14.1286	−	2.23776i	0.937751	−	0.148525i	0.606559	+	0.795038i	$0.292549\pi$
$228$	−17.8178	−	2.82206i	−1.18001	−	0.186895i
$229$	10.1110	+	19.8439i	0.668153	+	1.31132i	0.937401	+	0.348253i	$0.113225\pi$
$229$	10.1110	+	19.8439i	0.668153	+	1.31132i	−0.269248	+	0.963071i	$0.586775\pi$
$230$			3.47673i			0.229249i
$231$	−15.3864	+	1.21964i	−1.01235	+	0.0802465i
$232$	−17.6934	+	17.6934i	−1.16163	+	1.16163i
$233$	2.80192	−	8.62343i	0.183560	−	0.564939i	−0.816361	−	0.577543i	$-0.804012\pi$
$233$	2.80192	−	8.62343i	0.183560	−	0.564939i	0.999921	+	0.0126030i	$0.00401177\pi$
$234$	8.88204	−	1.46761i	0.580637	−	0.0959407i
$235$	1.36085	+	0.988712i	0.0887718	+	0.0644965i
$236$	21.3377	−	41.8776i	1.38897	−	2.72600i
$237$	14.6936	−	4.77425i	0.954454	−	0.310121i
$238$	−31.7160	−	23.0430i	−2.05584	−	1.49366i
$239$	1.39007	−	8.77654i	0.0899160	−	0.567707i	−0.901063	−	0.433689i	$-0.857212\pi$
$239$	1.39007	−	8.77654i	0.0899160	−	0.567707i	0.990979	−	0.134019i	$-0.0427882\pi$
$240$	−1.06188	+	0.541053i	−0.0685438	+	0.0349248i
$241$	−0.309616	−	0.309616i	−0.0199441	−	0.0199441i	0.697064	−	0.717009i	$-0.254489\pi$
$241$	−0.309616	−	0.309616i	−0.0199441	−	0.0199441i	−0.717009	+	0.697064i	$0.754489\pi$
$242$	−22.2016	+	16.1686i	−1.42718	+	1.03936i
$243$	1.00000			0.0641500
$244$	4.28508	−	13.1881i	0.274324	−	0.844283i
$245$	0.500474	−	3.15987i	0.0319741	−	0.201877i
$246$	−8.72627	+	12.0107i	−0.556367	+	0.765773i
$247$	−2.30175	+	15.1881i	−0.146457	+	0.966395i
$248$	−26.1618	+	8.50048i	−1.66127	+	0.539781i
$249$	−0.764544	+	0.121092i	−0.0484510	+	0.00767388i
$250$	3.18812	+	4.38807i	0.201634	+	0.277526i
$251$	11.1266	+	3.61526i	0.702307	+	0.228193i	0.638335	−	0.769758i	$-0.279623\pi$
$251$	11.1266	+	3.61526i	0.702307	+	0.228193i	0.0639717	+	0.997952i	$0.479623\pi$
$252$	13.9334	−	13.9334i	0.877721	−	0.877721i
$253$	−16.0965	−	13.7321i	−1.01198	−	0.863328i
$254$	−14.3747	+	14.3747i	−0.901949	+	0.901949i
$255$	0.656161	−	0.334331i	0.0410904	−	0.0209366i
$256$	26.2330	−	19.0594i	1.63956	−	1.19121i
$257$	6.84874	−	9.42648i	0.427213	−	0.588008i	−0.540098	−	0.841602i	$-0.681613\pi$
$257$	6.84874	−	9.42648i	0.427213	−	0.588008i	0.967311	+	0.253594i	$0.0816129\pi$
$258$	19.9902	+	10.1855i	1.24454	+	0.634123i
$259$	8.60174	+	26.4734i	0.534486	+	1.64498i
$260$	1.53261	+	2.95892i	0.0950483	+	0.183505i
$261$	2.63654	+	3.62888i	0.163198	+	0.224622i
$262$	−6.38805	+	3.25488i	−0.394655	+	0.201087i
$263$		−	15.1835i		−	0.936253i	−0.883661	−	0.468127i	$-0.844929\pi$
$263$		−	15.1835i		−	0.936253i	0.883661	−	0.468127i	$-0.155071\pi$
$264$	4.30898	−	17.9927i	0.265199	−	1.10738i
$265$	−0.220212	−	0.220212i	−0.0135275	−	0.0135275i
$266$	22.4750	+	44.1097i	1.37803	+	2.70454i
$267$	−1.53310	+	9.67960i	−0.0938241	+	0.592382i
$268$	−46.3591	+	7.34257i	−2.83183	+	0.448519i
$269$	8.92856	+	27.4793i	0.544384	+	1.67544i	0.722451	+	0.691422i	$0.243016\pi$
$269$	8.92856	+	27.4793i	0.544384	+	1.67544i	−0.178067	+	0.984018i	$0.556984\pi$
$270$	0.168412	+	0.518318i	0.0102492	+	0.0315438i
$271$	4.93928	+	31.1854i	0.300040	+	1.89438i	0.429951	+	0.902852i	$0.358531\pi$
$271$	4.93928	+	31.1854i	0.300040	+	1.89438i	−0.129911	+	0.991526i	$0.541469\pi$
$272$	14.9033	−	10.8278i	0.903643	−	0.656535i
$273$	−11.9436	−	11.7853i	−0.722862	−	0.713277i
$274$			41.4224i			2.50242i
$275$	−16.3752	−	1.27949i	−0.987462	−	0.0771563i
$276$	27.0117			1.62591
$277$	−9.12789	+	28.0927i	−0.548442	+	1.68793i	0.164222	+	0.986423i	$0.447489\pi$
$277$	−9.12789	+	28.0927i	−0.548442	+	1.68793i	−0.712663	+	0.701506i	$0.752511\pi$
$278$	−30.8967	−	4.89355i	−1.85306	−	0.293496i
$279$	0.771404	+	4.87046i	0.0461828	+	0.291587i
$280$	5.04885	+	2.57252i	0.301726	+	0.153737i
$281$	−0.628373	+	1.23325i	−0.0374856	+	0.0735696i	−0.908990	−	0.416819i	$-0.863145\pi$
$281$	−0.628373	+	1.23325i	−0.0374856	+	0.0735696i	0.871504	+	0.490388i	$0.163145\pi$
$282$	11.3099	−	15.5668i	0.673498	−	0.926990i
$283$	10.9464	−	7.95306i	0.650698	−	0.472760i	−0.212811	−	0.977093i	$-0.568262\pi$
$283$	10.9464	−	7.95306i	0.650698	−	0.472760i	0.863509	+	0.504333i	$0.168262\pi$
$284$	−7.31001	−	14.3467i	−0.433769	−	0.851321i
$285$	−0.929955			−0.0550858
$286$	−29.0825	−	6.75989i	−1.71969	−	0.399721i
$287$	27.6707			1.63335
$288$	1.12405	+	2.20607i	0.0662351	+	0.129994i
$289$	4.54419	−	3.30154i	0.267305	−	0.194209i
$290$	−1.43689	+	1.97771i	−0.0843771	+	0.116135i
$291$	0.126091	−	0.247468i	0.00739160	−	0.0145068i
$292$	16.0823	+	8.19434i	0.941146	+	0.479538i
$293$	1.22575	+	7.73909i	0.0716091	+	0.452122i	0.997275	+	0.0737792i	$0.0235060\pi$
$293$	1.22575	+	7.73909i	0.0716091	+	0.452122i	−0.925665	+	0.378343i	$0.876494\pi$
$294$	−36.1460	−	5.72496i	−2.10808	−	0.333886i
$295$	0.748708	−	2.30429i	0.0435915	−	0.134161i
$296$	−33.3668			−1.93941
$297$	−3.06487	−	1.26749i	−0.177842	−	0.0735475i
$298$			31.9105i			1.84853i
$299$	−0.153515	−	23.0008i	−0.00887801	−	1.33017i
$300$	16.9645	−	12.3254i	0.979444	−	0.711608i
$301$	−6.54153	−	41.3016i	−0.377048	−	2.38058i
$302$	−5.85837	−	18.0302i	−0.337111	−	1.03752i
$303$	−1.08601	−	3.34240i	−0.0623897	−	0.192016i
$304$	−22.9761	+	3.63905i	−1.31777	+	0.208714i
$305$	0.111825	−	0.706033i	0.00640306	−	0.0404273i
$306$	−3.82443	−	7.50587i	−0.218628	−	0.429082i
$307$	−7.60979	−	7.60979i	−0.434314	−	0.434314i	0.455779	−	0.890093i	$-0.349361\pi$
$307$	−7.60979	−	7.60979i	−0.434314	−	0.434314i	−0.890093	+	0.455779i	$0.849361\pi$
$308$	−60.3646	+	25.0436i	−3.43959	+	1.42699i
$309$			7.53643i			0.428732i
$310$	−2.39453	+	1.22007i	−0.136000	+	0.0692955i
$311$	−4.36452	−	6.00725i	−0.247489	−	0.340640i	0.667141	−	0.744932i	$-0.267518\pi$
$311$	−4.36452	−	6.00725i	−0.247489	−	0.340640i	−0.914630	+	0.404292i	$0.867518\pi$
$312$	17.8597	−	9.25064i	1.01111	−	0.523714i
$313$	−7.03048	−	21.6376i	−0.397386	−	1.22303i	−0.927088	−	0.374844i	$-0.877696\pi$
$313$	−7.03048	−	21.6376i	−0.397386	−	1.22303i	0.529702	−	0.848184i	$-0.322304\pi$
$314$	−21.3896	−	10.8985i	−1.20708	−	0.615040i
$315$	0.597061	−	0.821784i	0.0336406	−	0.0463023i
$316$	52.9239	−	38.4514i	2.97720	−	2.16306i
$317$	−29.4383	+	14.9996i	−1.65342	+	0.842459i	−0.657379	+	0.753561i	$0.728335\pi$
$317$	−29.4383	+	14.9996i	−1.65342	+	0.842459i	−0.996041	+	0.0888986i	$0.971665\pi$
$318$	−2.51902	+	2.51902i	−0.141260	+	0.141260i
$319$	−3.48107	−	14.4639i	−0.194903	−	0.809821i
$320$	0.731280	−	0.731280i	0.0408798	−	0.0408798i
$321$	1.93304	+	0.628081i	0.107892	+	0.0350561i
$322$	−43.5703	−	59.9694i	−2.42808	−	3.34197i
$323$	14.1975	−	2.24866i	0.789970	−	0.125119i
$324$	4.02696	−	1.30844i	0.223720	−	0.0726910i
$325$	−10.5917	−	14.3754i	−0.587520	−	0.797405i
$326$	−5.54709	+	7.63491i	−0.307225	+	0.422859i
$327$	3.21697	−	20.3111i	0.177899	−	1.12321i
$328$	−10.2498	+	31.5455i	−0.565948	+	1.74181i
$329$	−35.8635			−1.97722
$330$	0.140804	−	1.80204i	0.00775101	−	0.0991990i
$331$	3.45816	+	3.45816i	0.190078	+	0.190078i	0.795730	−	0.605652i	$-0.207088\pi$
$331$	3.45816	+	3.45816i	0.190078	+	0.190078i	−0.605652	+	0.795730i	$0.707088\pi$
$332$	−2.92034	+	1.48799i	−0.160275	+	0.0816640i
$333$	−0.935698	+	5.90777i	−0.0512760	+	0.323744i
$334$	35.1261	+	25.5206i	1.92201	+	1.39642i
$335$	−2.30118	+	0.747698i	−0.125727	+	0.0408511i
$336$	11.5356	−	22.6399i	0.629320	−	1.23511i
$337$	14.2331	+	10.3409i	0.775326	+	0.563307i	0.903573	−	0.428435i	$-0.140935\pi$
$337$	14.2331	+	10.3409i	0.775326	+	0.563307i	−0.128247	+	0.991742i	$0.540935\pi$
$338$	−15.1208	−	28.7218i	−0.822460	−	1.56226i
$339$	1.49847	−	4.61181i	0.0813857	−	0.250479i
$340$	2.20488	−	2.20488i	0.119576	−	0.119576i
$341$	3.80902	−	15.9051i	0.206270	−	0.861309i
$342$			10.6378i			0.575227i
$343$	16.1776	+	31.7504i	0.873511	+	1.71436i
$344$	49.5082	+	7.84133i	2.66930	+	0.422776i
$345$	1.37531	−	0.217828i	0.0740442	−	0.0117275i
$346$	22.4688	+	11.4484i	1.20793	+	0.615472i
$347$	−1.03863	+	0.337470i	−0.0557564	+	0.0181164i	−0.336762	−	0.941590i	$-0.609332\pi$
$347$	−1.03863	+	0.337470i	−0.0557564	+	0.0181164i	0.281006	+	0.959706i	$0.409332\pi$
$348$	15.3654	+	11.1636i	0.823672	+	0.598433i
$349$	−11.8685	−	1.87979i	−0.635309	−	0.100623i	−0.169531	−	0.985525i	$-0.554225\pi$
$349$	−11.8685	−	1.87979i	−0.635309	−	0.100623i	−0.465778	+	0.884902i	$0.654225\pi$
$350$	−54.7280	−	17.7822i	−2.92533	−	0.950498i
$351$	−1.13704	−	3.42157i	−0.0606906	−	0.182630i
$352$	−0.648887	−	8.18604i	−0.0345858	−	0.436317i
$353$	11.0613	+	11.0613i	0.588732	+	0.588732i	0.937288	−	0.348556i	$-0.113328\pi$
$353$	11.0613	+	11.0613i	0.588732	+	0.588732i	−0.348556	+	0.937288i	$0.613328\pi$
$354$	−26.3589	−	8.56452i	−1.40096	−	0.455199i
$355$	−0.487886	−	0.671518i	−0.0258943	−	0.0356405i
$356$	6.49144	+	40.9853i	0.344045	+	2.17222i
$357$	−7.12816	+	13.9898i	−0.377262	+	0.740419i
$358$	−2.95299	+	5.79556i	−0.156070	+	0.306305i
$359$	1.03545	+	6.53755i	0.0546488	+	0.345039i	0.999829	+	0.0184899i	$0.00588584\pi$
$359$	1.03545	+	6.53755i	0.0546488	+	0.345039i	−0.945180	+	0.326549i	$0.894114\pi$
$360$	0.715697	+	0.985073i	0.0377205	+	0.0519179i
$361$	0.806485	+	0.262043i	0.0424466	+	0.0137917i
$362$	28.2558	+	28.2558i	1.48509	+	1.48509i
$363$	7.78692	+	7.76942i	0.408707	+	0.407789i
$364$	−63.5168	−	31.8313i	−3.32919	−	1.66841i
$365$	0.884917	+	0.287527i	0.0463187	+	0.0150498i
$366$	−8.07636	−	1.27917i	−0.422158	−	0.0668633i
$367$	−6.41695	−	4.66218i	−0.334962	−	0.243364i	0.407571	−	0.913173i	$-0.366376\pi$
$367$	−6.41695	−	4.66218i	−0.334962	−	0.243364i	−0.742533	+	0.669809i	$0.766376\pi$
$368$	33.1269	−	10.7636i	1.72686	−	0.561091i
$369$	5.29786	+	2.69940i	0.275796	+	0.140525i
$370$	−3.21968	+	0.509948i	−0.167383	+	0.0265109i
$371$	6.55809	+	1.03870i	0.340479	+	0.0539266i
$372$	9.47910	+	18.6038i	0.491469	+	0.964562i
$373$		−	7.93350i		−	0.410781i	−0.978680	−	0.205390i	$-0.934154\pi$
$373$		−	7.93350i		−	0.410781i	0.978680	−	0.205390i	$-0.0658464\pi$
$374$	2.20776	+	27.8520i	0.114160	+	1.44019i
$375$	1.53607	−	1.53607i	0.0793222	−	0.0793222i
$376$	13.2845	−	40.8855i	0.685096	−	2.10851i
$377$	9.41864	−	13.1473i	0.485084	−	0.677119i
$378$	−9.40045	−	6.82983i	−0.483507	−	0.351288i
$379$	−10.5551	+	20.7156i	−0.542180	+	1.06409i	0.443628	+	0.896211i	$0.353691\pi$
$379$	−10.5551	+	20.7156i	−0.542180	+	1.06409i	−0.985808	+	0.167877i	$0.946309\pi$
$380$	−3.74489	+	1.21679i	−0.192109	+	0.0624199i
$381$	6.58690	+	4.78567i	0.337457	+	0.245177i
$382$	−1.58514	+	10.0082i	−0.0811028	+	0.512063i
$383$	18.6758	−	9.51577i	0.954287	−	0.486233i	0.0937353	−	0.995597i	$-0.470119\pi$
$383$	18.6758	−	9.51577i	0.954287	−	0.486233i	0.860551	+	0.509364i	$0.170119\pi$
$384$	−11.8667	−	11.8667i	−0.605567	−	0.605567i
$385$	−2.87153	+	1.76189i	−0.146346	+	0.0897945i
$386$	−39.8116			−2.02636
$387$	2.77670	−	8.54580i	0.141147	−	0.434407i
$388$	0.183968	−	1.16153i	0.00933954	−	0.0589676i
$389$	2.87793	−	3.96114i	0.145917	−	0.200838i	−0.729802	−	0.683658i	$-0.760388\pi$
$389$	2.87793	−	3.96114i	0.145917	−	0.200838i	0.875719	+	0.482821i	$0.160388\pi$
$390$	1.58197	−	1.16558i	0.0801062	−	0.0590214i
$391$	−20.4700	+	6.65110i	−1.03521	+	0.336361i
$392$	−80.7571	+	12.7907i	−4.07885	+	0.646027i
$393$	1.68778	+	2.32303i	0.0851373	+	0.117181i
$394$	56.1142	+	18.2326i	2.82699	+	0.918545i
$395$	2.38456	−	2.38456i	0.119980	−	0.119980i
$396$	−14.0006	−	1.09395i	−0.703555	−	0.0549729i
$397$	−10.1743	+	10.1743i	−0.510634	+	0.510634i	−0.914721	−	0.404087i	$-0.867589\pi$
$397$	−10.1743	+	10.1743i	−0.510634	+	0.510634i	0.404087	+	0.914721i	$0.367589\pi$
$398$	0.152572	−	0.0777394i	0.00764775	−	0.00389672i
$399$	16.0406	−	11.6542i	0.803035	−	0.583439i
$400$	15.8937	−	21.8758i	0.794684	−	1.09379i
$401$	11.9332	+	6.08026i	0.595914	+	0.303634i	0.725811	−	0.687894i	$-0.241465\pi$
$401$	11.9332	+	6.08026i	0.595914	+	0.303634i	−0.129897	+	0.991528i	$0.541465\pi$
$402$	8.55297	+	26.3233i	0.426584	+	1.31289i
$403$	15.7875	−	8.17731i	0.786431	−	0.407341i
$404$	−8.74665	−	12.0387i	−0.435162	−	0.598949i
$405$	0.194482	−	0.0990937i	0.00966391	−	0.00492401i
$406$		−	52.1202i		−	2.58668i
$407$	10.3559	−	16.9206i	0.513321	−	0.838722i
$408$	−13.3084	−	13.3084i	−0.658864	−	0.658864i
$409$	6.96047	+	13.6607i	0.344173	+	0.675478i	0.996602	−	0.0823727i	$-0.0262498\pi$
$409$	6.96047	+	13.6607i	0.344173	+	0.675478i	−0.652429	+	0.757850i	$0.726250\pi$
$410$	−0.506923	+	3.20059i	−0.0250351	+	0.158066i
$411$	16.3857	−	2.59524i	0.808247	−	0.128014i
$412$	9.86095	+	30.3489i	0.485814	+	1.49518i
$413$	15.9630	+	49.1290i	0.785486	+	2.41748i
$414$	−2.49175	−	15.7323i	−0.122463	−	0.773199i
$415$	−0.136691	+	0.0993117i	−0.00670989	+	0.00487502i
$416$	6.27012	−	6.35438i	0.307418	−	0.311549i
$417$			12.5286i			0.613527i
$418$	13.4834	−	32.6036i	0.659493	−	1.59469i
$419$	3.80574			0.185923			0.0929613	−	0.995670i	$-0.470367\pi$
$419$	3.80574			0.185923			0.0929613	+	0.995670i	$0.470367\pi$
$420$	1.32909	−	4.09051i	0.0648528	−	0.199596i
$421$	−2.76759	−	0.438342i	−0.134884	−	0.0213635i	0.0886274	−	0.996065i	$-0.471752\pi$
$421$	−2.76759	−	0.438342i	−0.134884	−	0.0213635i	−0.223511	+	0.974701i	$0.571752\pi$
$422$	1.40603	+	8.87734i	0.0684446	+	0.432142i
$423$	−6.86645	−	3.49863i	−0.333858	−	0.170109i
$424$	−3.61339	+	7.09167i	−0.175482	+	0.344402i
$425$	−9.82111	+	13.5176i	−0.476394	+	0.655700i
$426$	−7.68154	+	5.58097i	−0.372172	+	0.270399i
$427$	6.91916	+	13.5796i	0.334841	+	0.657163i
$428$	8.60606			0.415990
$429$	−0.851941	+	11.9279i	−0.0411321	+	0.575883i
$430$	4.89706			0.236157
$431$	−16.4729	−	32.3300i	−0.793474	−	1.55728i	−0.829880	−	0.557943i	$-0.811591\pi$
$431$	−16.4729	−	32.3300i	−0.793474	−	1.55728i	0.0364059	−	0.999337i	$-0.488409\pi$
$432$	4.41724	−	3.20932i	0.212525	−	0.154408i
$433$	7.55975	−	10.4051i	0.363299	−	0.500038i	−0.587766	−	0.809031i	$-0.699992\pi$
$433$	7.55975	−	10.4051i	0.363299	−	0.500038i	0.951064	+	0.308994i	$0.0999922\pi$
$434$	26.0128	−	51.0530i	1.24866	−	2.45062i
$435$	0.872360	+	0.444490i	0.0418265	+	0.0213116i
$436$	−13.6213	−	86.0013i	−0.652341	−	4.11872i
$437$	26.8450	+	4.25183i	1.28417	+	0.203393i
$438$	3.28904	−	10.1226i	0.157156	−	0.483678i
$439$	−10.2158			−0.487574			−0.243787	−	0.969829i	$-0.578390\pi$
$439$	−10.2158			−0.487574			−0.243787	+	0.969829i	$0.578390\pi$
$440$	−0.944948	−	3.92627i	−0.0450486	−	0.187177i
$441$			14.6572i			0.697960i
$442$	−21.3333	+	21.6200i	−1.01472	+	1.02836i
$443$	−30.4820	+	22.1464i	−1.44824	+	1.05221i	−0.462003	+	0.886878i	$0.652869\pi$
$443$	−30.4820	+	22.1464i	−1.44824	+	1.05221i	−0.986238	+	0.165330i	$0.947131\pi$
$444$	3.96193	+	25.0146i	0.188025	+	1.18714i
$445$	0.661027	+	2.03443i	0.0313357	+	0.0964414i
$446$	0.801626	+	2.46715i	0.0379581	+	0.116823i
$447$	12.6230	−	1.99929i	0.597049	−	0.0945632i
$448$	−3.44931	+	21.7781i	−0.162965	+	1.02892i
$449$	0.937202	+	1.83936i	0.0442293	+	0.0868049i	0.912063	−	0.410049i	$-0.134488\pi$
$449$	0.937202	+	1.83936i	0.0442293	+	0.0868049i	−0.867834	+	0.496854i	$0.834488\pi$
$450$	−8.74354	−	8.74354i	−0.412174	−	0.412174i
$451$	−12.8158	−	14.9883i	−0.603473	−	0.705773i
$452$		−	20.5322i		−	0.965755i
$453$	−6.76527	+	3.44708i	−0.317860	+	0.161958i
$454$	−20.9937	−	28.8954i	−0.985284	−	1.35613i
$455$	−3.49067	−	1.10849i	−0.163645	−	0.0519667i
$456$	7.34439	+	22.6037i	0.343933	+	1.05852i
$457$	1.44531	+	0.736424i	0.0676089	+	0.0344485i	0.487468	−	0.873141i	$-0.337921\pi$
$457$	1.44531	+	0.736424i	0.0676089	+	0.0344485i	−0.419859	+	0.907589i	$0.637921\pi$
$458$	32.6855	−	44.9878i	1.52730	−	2.10214i
$459$	−2.72953	+	1.98312i	−0.127403	+	0.0925640i
$460$	5.25330	−	2.67669i	0.244937	−	0.124801i
$461$	−2.46033	+	2.46033i	−0.114589	+	0.114589i	−0.762076	−	0.647487i	$-0.775820\pi$
$461$	−2.46033	+	2.46033i	−0.114589	+	0.114589i	0.647487	+	0.762076i	$0.275820\pi$
$462$	20.1544	+	32.8476i	0.937669	+	1.52821i
$463$	−3.63777	+	3.63777i	−0.169062	+	0.169062i	−0.786567	−	0.617505i	$-0.788143\pi$
$463$	−3.63777	+	3.63777i	−0.169062	+	0.169062i	0.617505	+	0.786567i	$0.288143\pi$
$464$	23.2925	+	7.56818i	1.08133	+	0.351344i
$465$	0.632656	+	0.870777i	0.0293387	+	0.0403813i
$466$	−22.3606	+	3.54157i	−1.03584	+	0.164060i
$467$	−30.8085	+	10.0103i	−1.42565	+	0.463221i	−0.917392	−	0.397984i	$-0.869710\pi$
$467$	−30.8085	+	10.0103i	−1.42565	+	0.463221i	−0.508256	+	0.861206i	$0.669710\pi$
$468$	−9.05572	−	12.2908i	−0.418601	−	0.568141i
$469$	30.3224	−	41.7352i	1.40016	−	1.92715i
$470$	0.657013	−	4.14821i	0.0303057	−	0.191343i
$471$	−2.97108	+	9.14403i	−0.136900	+	0.421335i
$472$	−61.9215			−2.85017
$473$	−19.3420	+	22.6723i	−0.889345	+	1.04248i
$474$	−27.2771	−	27.2771i	−1.25288	−	1.25288i
$475$	18.7999	−	9.57902i	0.862598	−	0.439516i
$476$	−10.4000	+	65.6631i	−0.476684	+	3.00966i
$477$	1.15429	+	0.838640i	0.0528512	+	0.0383987i
$478$	−21.1008	+	6.85608i	−0.965130	+	0.313590i
$479$	15.5330	−	30.4853i	0.709722	−	1.39291i	−0.200876	−	0.979617i	$-0.564379\pi$
$479$	15.5330	−	30.4853i	0.709722	−	1.39291i	0.910599	−	0.413292i	$-0.135621\pi$
$480$	0.437215	+	0.317655i	0.0199560	+	0.0144989i
$481$	21.2778	−	3.51580i	0.970183	−	0.160307i
$482$	−0.337840	+	1.03977i	−0.0153882	+	0.0473600i
$483$	−20.9926	+	20.9926i	−0.955198	+	0.955198i
$484$	41.5234	+	21.0984i	1.88743	+	0.959020i
$485$		−	0.0606230i		−	0.00275275i
$486$	−1.13354	−	2.22470i	−0.0514184	−	0.100914i
$487$	1.84856	+	0.292783i	0.0837663	+	0.0132673i	0.198177	−	0.980166i	$-0.436498\pi$
$487$	1.84856	+	0.292783i	0.0837663	+	0.0132673i	−0.114411	+	0.993434i	$0.536498\pi$
$488$	−18.0442	+	2.85791i	−0.816821	+	0.129372i
$489$	3.36773	+	1.71594i	0.152294	+	0.0775976i
$490$	−7.59706	+	2.46844i	−0.343200	+	0.111513i
$491$	−4.78694	−	3.47792i	−0.216032	−	0.156956i	0.474507	−	0.880252i	$-0.342626\pi$
$491$	−4.78694	−	3.47792i	−0.216032	−	0.156956i	−0.690539	+	0.723296i	$0.742626\pi$
$492$	24.8663	+	3.93843i	1.12106	+	0.177558i
$493$	−14.3930	−	4.67657i	−0.648228	−	0.210622i
$494$	36.3980	−	12.0956i	1.63763	−	0.544207i
$495$	−0.721665	+	0.0572046i	−0.0324364	+	0.00257116i
$496$	19.0383	+	19.0383i	0.854845	+	0.854845i
$497$	16.8309	+	5.46870i	0.754970	+	0.245305i
$498$	1.13603	+	1.56362i	0.0509069	+	0.0700673i
$499$	4.91687	+	31.0439i	0.220109	+	1.38972i	0.811981	+	0.583684i	$0.198389\pi$
$499$	4.91687	+	31.0439i	0.220109	+	1.38972i	−0.591872	+	0.806032i	$0.701611\pi$
$500$	4.17583	−	8.19553i	0.186749	−	0.366515i
$501$	7.89457	−	15.4940i	0.352703	−	0.692219i
$502$	−4.56962	−	28.8515i	−0.203952	−	1.28770i
$503$	11.1862	+	15.3964i	0.498766	+	0.686493i	0.981975	−	0.189013i	$-0.0605287\pi$
$503$	11.1862	+	15.3964i	0.498766	+	0.686493i	−0.483208	+	0.875505i	$0.660529\pi$
$504$	−24.6898	−	8.02221i	−1.09977	−	0.357338i
$505$	−0.542421	−	0.542421i	−0.0241374	−	0.0241374i
$506$	−12.3037	+	51.3757i	−0.546965	+	2.28393i
$507$	−10.4143	+	7.78091i	−0.462515	+	0.345562i
$508$	32.7869	+	10.6531i	1.45469	+	0.472656i
$509$	24.3239	+	3.85253i	1.07814	+	0.170760i	0.670149	−	0.742227i	$-0.266230\pi$
$509$	24.3239	+	3.85253i	1.07814	+	0.170760i	0.407989	+	0.912987i	$0.366230\pi$
$510$	−1.48757	−	1.08078i	−0.0658707	−	0.0478578i
$511$	−18.8670	+	6.13027i	−0.834629	+	0.271187i
$512$	−42.2318	−	21.5182i	−1.86640	−	0.950979i
$513$	4.20806	−	0.666492i	0.185791	−	0.0294263i
$514$	−28.7344	−	4.55108i	−1.26742	−	0.200740i
$515$	0.746813	+	1.46570i	0.0329085	+	0.0645866i
$516$		−	38.0467i		−	1.67491i
$517$	16.6103	+	19.4261i	0.730521	+	0.854357i
$518$	49.1450	−	49.1450i	2.15931	−	2.15931i
$519$	3.12099	−	9.60541i	0.136996	−	0.421631i
$520$	2.55672	−	3.56887i	0.112120	−	0.156505i
$521$	−2.53284	−	1.84022i	−0.110966	−	0.0806213i	0.530918	−	0.847423i	$-0.321847\pi$
$521$	−2.53284	−	1.84022i	−0.110966	−	0.0806213i	−0.641884	+	0.766802i	$0.721847\pi$
$522$	5.08455	−	9.97899i	0.222545	−	0.436768i
$523$	6.77246	−	2.20051i	0.296139	−	0.0962214i	−0.157179	−	0.987570i	$-0.550240\pi$
$523$	6.77246	−	2.20051i	0.296139	−	0.0962214i	0.453318	+	0.891349i	$0.350240\pi$
$524$	9.83617	+	7.14639i	0.429695	+	0.312192i
$525$	−3.60533	+	22.7632i	−0.157350	+	0.993466i
$526$	−33.7786	+	17.2111i	−1.47282	+	0.750439i
$527$	−11.7643	−	11.7643i	−0.512459	−	0.512459i
$528$	−17.6061	+	4.23732i	−0.766207	+	0.184406i
$529$	−17.6970			−0.769436
$530$	−0.240286	+	0.739525i	−0.0104374	+	0.0321229i
$531$	−1.73645	+	10.9635i	−0.0753556	+	0.475777i
$532$	49.3461	−	67.9190i	2.13942	−	2.94466i
$533$	3.21230	−	21.1963i	0.139140	−	0.918115i
$534$	23.2720	−	7.56154i	1.00708	−	0.327220i
$535$	0.438180	−	0.0694010i	0.0189442	−	0.00300047i
$536$	36.3475	+	50.0280i	1.56997	+	2.16088i
$537$	2.47760	+	0.805020i	0.106916	+	0.0347392i
$538$	51.0122	−	51.0122i	2.19929	−	2.19929i
$539$	18.5779	−	44.9224i	0.800205	−	1.93494i
$540$	0.653515	−	0.653515i	0.0281228	−	0.0281228i
$541$	18.9885	−	9.67514i	0.816381	−	0.415967i	0.00464339	−	0.999989i	$-0.498522\pi$
$541$	18.9885	−	9.67514i	0.816381	−	0.415967i	0.811738	+	0.584022i	$0.198522\pi$
$542$	63.7792	−	46.3383i	2.73955	−	1.99040i
$543$	9.40701	−	12.9476i	0.403694	−	0.555636i
$544$	−7.44300	−	3.79240i	−0.319116	−	0.162598i
$545$	−1.38706	−	4.26894i	−0.0594153	−	0.182861i
$546$	−12.6801	+	39.9301i	−0.542657	+	1.70885i
$547$	−0.305351	−	0.420280i	−0.0130559	−	0.0179699i	0.802439	−	0.596734i	$-0.203535\pi$
$547$	−0.305351	−	0.420280i	−0.0130559	−	0.0179699i	−0.815495	+	0.578764i	$0.803535\pi$
$548$	62.5888	−	31.8906i	2.67366	−	1.36230i
$549$			3.27496i			0.139772i
$550$	15.7155	+	37.8802i	0.670110	+	1.61522i
$551$	13.5133	+	13.5133i	0.575688	+	0.575688i
$552$	−16.1562	−	31.7083i	−0.687654	−	1.34960i
$553$	−11.2475	+	71.0140i	−0.478293	+	3.01982i
$554$	72.8447	−	11.5375i	3.09487	−	0.490180i
$555$	0.403446	+	1.24168i	0.0171253	+	0.0527063i
$556$	16.3929	+	50.4521i	0.695213	+	2.13964i
$557$	−6.32248	−	39.9186i	−0.267892	−	1.69140i	−0.644158	−	0.764893i	$-0.722792\pi$
$557$	−6.32248	−	39.9186i	−0.267892	−	1.69140i	0.376266	−	0.926512i	$-0.377208\pi$
$558$	9.96088	−	7.23700i	0.421678	−	0.306367i
$559$	−32.3973	+	0.216230i	−1.37026	+	0.00914556i
$560$		−	5.54618i		−	0.234369i
$561$	10.8793	−	2.61835i	0.459322	−	0.110547i
$562$	3.45590			0.145778
$563$	−3.27254	+	10.0719i	−0.137921	+	0.424478i	−0.996033	−	0.0889851i	$-0.971638\pi$
$563$	−3.27254	+	10.0719i	−0.137921	+	0.424478i	0.858112	+	0.513463i	$0.171638\pi$
$564$	−32.2287	−	5.10452i	−1.35707	−	0.214939i
$565$	−0.165576	−	1.04541i	−0.00696583	−	0.0439805i
$566$	−30.1014	−	15.3374i	−1.26526	−	0.644680i
$567$	−2.11275	+	4.14650i	−0.0887270	+	0.174137i
$568$	−12.4690	+	17.1621i	−0.523186	+	0.720104i
$569$	−35.9209	+	26.0980i	−1.50588	+	1.09409i	−0.537916	+	0.842998i	$0.680788\pi$
$569$	−35.9209	+	26.0980i	−1.50588	+	1.09409i	−0.967964	+	0.251088i	$0.919212\pi$
$570$	1.05414	+	2.06887i	0.0441531	+	0.0866554i
$571$	−14.9845			−0.627082			−0.313541	−	0.949575i	$-0.601515\pi$
$571$	−14.9845			−0.627082			−0.313541	+	0.949575i	$0.601515\pi$
$572$	12.1762	+	49.1478i	0.509111	+	2.05497i
$573$	4.05831			0.169538
$574$	−31.3659	−	61.5590i	−1.30919	−	2.56942i
$575$	−25.5594	+	18.5700i	−1.06590	+	0.774423i
$576$	−2.78495	+	3.83316i	−0.116040	+	0.159715i
$577$	−4.49537	+	8.82266i	−0.187145	+	0.367292i	−0.965448	−	0.260597i	$-0.916081\pi$
$577$	−4.49537	+	8.82266i	−0.187145	+	0.367292i	0.778303	+	0.627889i	$0.216081\pi$
$578$	−12.4960	−	6.36701i	−0.519763	−	0.264833i
$579$	2.49432	+	15.7485i	0.103660	+	0.654485i
$580$	4.09454	+	0.648512i	0.170017	+	0.0269280i
$581$	1.11318	−	3.42602i	0.0461825	−	0.142135i
$582$	−0.693471			−0.0287453
$583$	−2.47478	−	4.03338i	−0.102495	−	0.167046i
$584$		−	23.7798i		−	0.984014i
$585$	−0.560190	−	0.552762i	−0.0231610	−	0.0228539i
$586$	15.8277	−	11.4995i	0.653836	−	0.475040i
$587$	−5.00721	−	31.6143i	−0.206670	−	1.30486i	−0.844862	−	0.534984i	$-0.820318\pi$
$587$	−5.00721	−	31.6143i	−0.206670	−	1.30486i	0.638192	−	0.769877i	$-0.279682\pi$
$588$	19.1780	+	59.0238i	0.790887	+	2.43410i
$589$	6.49224	+	19.9811i	0.267508	+	0.823305i
$590$	−5.97503	+	0.946352i	−0.245988	+	0.0389607i
$591$	3.69665	−	23.3397i	0.152060	−	0.960068i
$592$	14.8267	+	29.0990i	0.609373	+	1.19596i
$593$	−10.9166	−	10.9166i	−0.448292	−	0.448292i	0.446494	−	0.894786i	$-0.352672\pi$
$593$	−10.9166	−	10.9166i	−0.448292	−	0.448292i	−0.894786	+	0.446494i	$0.852672\pi$
$594$	0.654367	+	8.25518i	0.0268490	+	0.338714i
$595$			3.42713i			0.140498i
$596$	48.2164	−	24.5675i	1.97502	−	1.00632i
$597$	−0.0403109	−	0.0554832i	−0.00164982	−	0.00227078i
$598$	−50.9959	+	26.4139i	−2.08538	+	1.08014i
$599$	−4.47324	−	13.7672i	−0.182772	−	0.562513i	0.817131	−	0.576452i	$-0.195563\pi$
$599$	−4.47324	−	13.7672i	−0.182772	−	0.562513i	−0.999903	+	0.0139385i	$0.995563\pi$
$600$	−24.6152	−	12.5421i	−1.00491	−	0.512029i
$601$	−12.2162	+	16.8141i	−0.498307	+	0.685861i	−0.981893	−	0.189436i	$-0.939334\pi$
$601$	−12.2162	+	16.8141i	−0.498307	+	0.685861i	0.483586	+	0.875297i	$0.339334\pi$
$602$	−84.4685	+	61.3700i	−3.44268	+	2.50125i
$603$	9.87701	−	5.03259i	0.402223	−	0.204943i
$604$	−22.7332	+	22.7332i	−0.925000	+	0.925000i
$605$	2.28432	+	0.739381i	0.0928708	+	0.0300601i
$606$	−6.20479	+	6.20479i	−0.252053	+	0.252053i
$607$	30.9414	+	10.0535i	1.25587	+	0.408057i	0.860021	−	0.510258i	$-0.170450\pi$
$607$	30.9414	+	10.0535i	1.25587	+	0.408057i	0.395850	+	0.918315i	$0.370450\pi$
$608$	6.20038	+	8.53410i	0.251459	+	0.346103i
$609$	−20.6175	+	3.26549i	−0.835463	+	0.132324i
$610$	−1.69747	+	0.551541i	−0.0687285	+	0.0223312i
$611$	−4.16340	+	27.4721i	−0.168433	+	1.11140i
$612$	−8.39691	+	11.5573i	−0.339425	+	0.467178i
$613$	−3.29242	+	20.7875i	−0.132980	+	0.839600i	0.827544	+	0.561401i	$0.189738\pi$
$613$	−3.29242	+	20.7875i	−0.132980	+	0.839600i	−0.960523	+	0.278199i	$0.910262\pi$
$614$	−8.30348	+	25.5555i	−0.335101	+	1.03134i
$615$	1.29783			0.0523337
$616$	65.5032	+	55.8813i	2.63920	+	2.25152i
$617$	−34.3303	−	34.3303i	−1.38209	−	1.38209i	−0.840909	−	0.541176i	$-0.817979\pi$
$617$	−34.3303	−	34.3303i	−1.38209	−	1.38209i	−0.541176	−	0.840909i	$-0.682021\pi$
$618$	16.7663	−	8.54284i	0.674438	−	0.343643i
$619$	5.53489	−	34.9459i	0.222466	−	1.40459i	−0.583250	−	0.812293i	$-0.698219\pi$
$619$	5.53489	−	34.9459i	0.222466	−	1.40459i	0.805716	−	0.592302i	$-0.201781\pi$
$620$	3.68704	+	2.67879i	0.148075	+	0.107583i
$621$	−6.06719	+	1.97135i	−0.243468	+	0.0791075i
$622$	−8.41695	+	16.5192i	−0.337489	+	0.662360i
$623$	−36.8974	−	26.8075i	−1.47826	−	1.07402i
$624$	−16.0035	−	11.4648i	−0.640652	−	0.458959i
$625$	−7.50529	+	23.0989i	−0.300212	+	0.923956i
$626$	−40.1678	+	40.1678i	−1.60543	+	1.60543i
$627$	−13.7420	−	3.29098i	−0.548801	−	0.131429i
$628$			40.7101i			1.62451i
$629$	−9.16178	−	17.9810i	−0.365304	−	0.716950i
$630$	−2.50501	−	0.396755i	−0.0998022	−	0.0158071i
$631$	−41.9837	+	6.64957i	−1.67135	+	0.264715i	−0.919059	−	0.394120i	$-0.871049\pi$
$631$	−41.9837	+	6.64957i	−1.67135	+	0.264715i	−0.752287	+	0.658835i	$0.771049\pi$
$632$	−76.7918	−	39.1274i	−3.05462	−	1.55640i
$633$	3.42357	−	1.11238i	0.136075	−	0.0442133i
$634$	66.7390	+	48.4887i	2.65054	+	1.92573i
$635$	1.75527	+	0.278007i	0.0696556	+	0.0110324i
$636$	5.74558	+	1.86685i	0.227827	+	0.0740255i
$637$	50.1505	−	16.6658i	1.98704	−	0.660321i
$638$	−28.2318	+	24.1397i	−1.11771	+	0.955700i
$639$	2.68897	+	2.68897i	0.106374	+	0.106374i
$640$	−3.48377	−	1.13194i	−0.137708	−	0.0447440i
$641$	17.4848	+	24.0657i	0.690607	+	0.950538i	1.00000		0.000395761i	$-0.000125975\pi$
$641$	17.4848	+	24.0657i	0.690607	+	0.950538i	−0.309393	+	0.950934i	$0.600126\pi$
$642$	−0.793882	−	5.01238i	−0.0313320	−	0.197823i
$643$	5.94293	−	11.6637i	0.234366	−	0.459970i	−0.743630	−	0.668591i	$-0.766898\pi$
$643$	5.94293	−	11.6637i	0.234366	−	0.459970i	0.977997	+	0.208621i	$0.0668976\pi$
$644$	−57.0689	+	112.004i	−2.24883	+	4.41358i
$645$	−0.306816	−	1.93716i	−0.0120809	−	0.0762756i
$646$	−21.0960	−	29.0362i	−0.830013	−	1.14241i
$647$	−38.7568	−	12.5928i	−1.52369	−	0.495076i	−0.576866	−	0.816839i	$-0.695724\pi$
$647$	−38.7568	−	12.5928i	−1.52369	−	0.495076i	−0.946820	+	0.321763i	$0.895724\pi$
$648$	−3.94454	−	3.94454i	−0.154956	−	0.154956i
$649$	19.2182	−	31.4009i	0.754381	−	1.23259i
$650$	−19.9749	+	39.8584i	−0.783480	+	1.56337i
$651$	−21.8251	−	7.09141i	−0.855394	−	0.277934i
$652$	15.8069	+	2.50357i	0.619046	+	0.0980473i
$653$	8.62772	+	6.26840i	0.337629	+	0.245302i	0.743661	−	0.668557i	$-0.233088\pi$
$653$	8.62772	+	6.26840i	0.337629	+	0.245302i	−0.406032	+	0.913859i	$0.633088\pi$
$654$	−48.8327	+	15.8667i	−1.90951	+	0.620438i
$655$	0.558442	+	0.284540i	0.0218201	+	0.0111179i
$656$	32.0652	−	5.07862i	1.25193	−	0.198287i
$657$	−4.21033	−	0.666851i	−0.164261	−	0.0260163i
$658$	40.6527	+	79.7854i	1.58481	+	3.11036i
$659$		−	11.7331i		−	0.457057i	−0.973537	−	0.228528i	$-0.926609\pi$
$659$		−	11.7331i		−	0.457057i	0.973537	−	0.228528i	$-0.0733914\pi$
$660$	−2.83127	+	1.17461i	−0.110207	+	0.0457218i
$661$	−8.91923	+	8.91923i	−0.346918	+	0.346918i	−0.858960	−	0.512042i	$-0.828889\pi$
$661$	−8.91923	+	8.91923i	−0.346918	+	0.346918i	0.512042	+	0.858960i	$0.328889\pi$
$662$	3.77340	−	11.6133i	0.146657	−	0.451364i
$663$	9.88895	+	7.08439i	0.384055	+	0.275135i
$664$	3.49342	+	2.53812i	0.135571	+	0.0984982i
$665$	1.96476	−	3.85606i	0.0761901	−	0.149531i
$666$	14.2036	−	4.61505i	0.550380	−	0.178829i
$667$	−23.1502	−	16.8196i	−0.896379	−	0.651257i
$668$	11.5182	−	72.7231i	0.445653	−	2.81374i
$669$	0.925721	−	0.471678i	0.0357904	−	0.0182361i
$670$	4.27188	+	4.27188i	0.165037	+	0.165037i
$671$	4.15099	−	10.0373i	0.160247	−	0.387487i
$672$	−11.5223			−0.444481
$673$	11.9270	−	36.7075i	0.459751	−	1.41497i	−0.405714	−	0.914000i	$-0.632977\pi$
$673$	11.9270	−	36.7075i	0.459751	−	1.41497i	0.865465	−	0.500969i	$-0.167023\pi$
$674$	6.87170	−	43.3862i	0.264688	−	1.67117i
$675$	−2.91092	+	4.00654i	−0.112041	+	0.154212i
$676$	−31.7571	+	44.9599i	−1.22143	+	1.72923i
$677$	27.1124	−	8.80935i	1.04201	−	0.338571i	0.262484	−	0.964936i	$-0.415458\pi$
$677$	27.1124	−	8.80935i	1.04201	−	0.338571i	0.779530	+	0.626365i	$0.215458\pi$
$678$	−11.9585	+	1.89403i	−0.459262	+	0.0727400i
$679$	0.759727	+	1.04567i	0.0291557	+	0.0401293i
$680$	−3.90703	−	1.26947i	−0.149828	−	0.0486820i
$681$	−10.1150	+	10.1150i	−0.387607	+	0.387607i
$682$	−39.7017	+	9.55515i	−1.52026	+	0.365886i
$683$	−13.2039	+	13.2039i	−0.505232	+	0.505232i	−0.913059	−	0.407827i	$-0.866287\pi$
$683$	−13.2039	+	13.2039i	−0.505232	+	0.505232i	0.407827	+	0.913059i	$0.366287\pi$
$684$	16.0736	−	8.18993i	0.614591	−	0.313150i
$685$	2.92956	−	2.12845i	0.111933	−	0.0813238i
$686$	52.2971	−	71.9807i	1.99671	−	2.74824i
$687$	−19.8439	−	10.1110i	−0.757093	−	0.385758i
$688$	−15.1608	−	46.6602i	−0.578000	−	1.77890i
$689$	1.55699	−	4.90304i	0.0593168	−	0.186791i
$690$	−2.04357	−	2.81273i	−0.0777974	−	0.107079i
$691$	0.580945	−	0.296006i	0.0221002	−	0.0112606i	−0.442905	−	0.896568i	$-0.646052\pi$
$691$	0.580945	−	0.296006i	0.0221002	−	0.0112606i	0.465006	+	0.885308i	$0.346052\pi$
$692$		−	42.7642i		−	1.62565i
$693$	11.7310	−	10.0306i	0.445623	−	0.381031i
$694$	1.92810	+	1.92810i	0.0731895	+	0.0731895i
$695$	1.24150	+	2.43659i	0.0470929	+	0.0924251i
$696$	3.91434	−	24.7142i	0.148373	−	0.936789i
$697$	−19.8139	+	3.13821i	−0.750504	+	0.118868i
$698$	9.27151	+	28.5348i	0.350932	+	1.08006i
$699$	2.80192	+	8.62343i	0.105978	+	0.326168i
$700$	15.2657	+	96.3837i	0.576988	+	3.64296i
$701$	2.18067	−	1.58435i	0.0823626	−	0.0598399i	−0.545842	−	0.837888i	$-0.683790\pi$
$701$	2.18067	−	1.58435i	0.0823626	−	0.0598399i	0.628205	+	0.778048i	$0.283790\pi$
$702$	−6.32308	+	6.40805i	−0.238649	+	0.241856i
$703$			25.4839i			0.961143i
$704$	13.3940	−	8.21824i	0.504807	−	0.309737i
$705$	−1.68210			−0.0633515
$706$	12.0696	−	37.1464i	0.454245	−	1.39802i
$707$	16.1537	+	2.55850i	0.607524	+	0.0962223i
$708$	7.35248	+	46.4217i	0.276323	+	1.74464i
$709$	46.0189	+	23.4478i	1.72828	+	0.880601i	0.974785	+	0.223145i	$0.0716322\pi$
$709$	46.0189	+	23.4478i	1.72828	+	0.880601i	0.753492	+	0.657457i	$0.228368\pi$
$710$	−0.940886	+	1.84659i	−0.0353108	+	0.0693014i
$711$	−9.08117	+	12.4992i	−0.340570	+	0.468755i
$712$	44.2289	−	32.1342i	1.65755	−	1.20428i
$713$	−14.2816	−	28.0293i	−0.534851	−	1.04970i
$714$	39.2031			1.46714
$715$	1.01629	+	2.40418i	0.0380071	+	0.0899114i
$716$	11.0305			0.412229
$717$	4.03413	+	7.91743i	0.150657	+	0.295682i
$718$	13.3704	−	9.71414i	0.498978	−	0.362528i
$719$	22.0445	−	30.3416i	0.822121	−	1.13155i	−0.167218	−	0.985920i	$-0.553478\pi$
$719$	22.0445	−	30.3416i	0.822121	−	1.13155i	0.989339	−	0.145632i	$-0.0465216\pi$
$720$	0.541053	−	1.06188i	0.0201639	−	0.0395738i
$721$	−31.2498	−	15.9226i	−1.16380	−	0.592987i
$722$	−0.331217	−	2.09122i	−0.0123266	−	0.0778272i
$723$	0.432473	+	0.0684970i	0.0160838	+	0.00254743i
$724$	20.9405	−	64.4481i	0.778246	−	2.39519i
$725$	−22.2140			−0.825008
$726$	8.45783	−	26.1305i	0.313900	−	0.969793i
$727$			7.05463i			0.261642i	0.991406	+	0.130821i	$0.0417613\pi$
$727$			7.05463i			0.261642i	−0.991406	+	0.130821i	$0.958239\pi$
$728$	0.624715	+	93.5996i	0.0231535	+	3.46903i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−0.363428	−	2.29460i	−0.0134511	−	0.0849268i
$731$	9.36825	+	28.8325i	0.346497	+	1.06641i
$732$	4.28508	+	13.1881i	0.158381	+	0.487447i
$733$	21.9812	−	3.48148i	0.811895	−	0.128591i	0.263337	−	0.964704i	$-0.415177\pi$
$733$	21.9812	−	3.48148i	0.811895	−	0.128591i	0.548558	+	0.836113i	$0.315177\pi$
$734$	−3.09809	+	19.5605i	−0.114352	+	0.721993i
$735$	1.45243	+	2.85056i	0.0535738	+	0.105144i
$736$	−11.1687	−	11.1687i	−0.411685	−	0.411685i
$737$	−36.6506	+	2.90520i	−1.35004	+	0.107014i
$738$		−	14.8460i		−	0.546490i
$739$	−35.0369	+	17.8522i	−1.28885	+	0.656704i	−0.957943	−	0.286958i	$-0.907356\pi$
$739$	−35.0369	+	17.8522i	−1.28885	+	0.656704i	−0.330911	+	0.943662i	$0.607356\pi$
$740$	3.24932	+	4.47230i	0.119447	+	0.164405i
$741$	−7.06518	−	13.6404i	−0.259546	−	0.501091i
$742$	−5.12307	−	15.7672i	−0.188074	−	0.578831i
$743$	24.0970	+	12.2780i	0.884033	+	0.450438i	0.836204	−	0.548418i	$-0.184770\pi$
$743$	24.0970	+	12.2780i	0.884033	+	0.450438i	0.0478291	+	0.998856i	$0.484770\pi$
$744$	16.1689	−	22.2545i	0.592779	−	0.815891i
$745$	2.25684	−	1.63969i	0.0826842	−	0.0600736i
$746$	−17.6496	+	8.99294i	−0.646199	+	0.329255i
$747$	0.547353	−	0.547353i	0.0200266	−	0.0200266i
$748$	40.3843	−	24.7788i	1.47660	−	0.906003i
$749$	−6.68836	+	6.68836i	−0.244387	+	0.244387i
$750$	−5.15848	−	1.67609i	−0.188361	−	0.0612022i
$751$	−5.74957	−	7.91360i	−0.209805	−	0.288771i	0.691126	−	0.722734i	$-0.257115\pi$
$751$	−5.74957	−	7.91360i	−0.209805	−	0.288771i	−0.900931	+	0.433963i	$0.857115\pi$
$752$	−41.5590	+	6.58230i	−1.51550	+	0.240032i
$753$	−11.1266	+	3.61526i	−0.405477	+	0.131748i
$754$	−39.9251	−	6.05065i	−1.45399	−	0.220352i
$755$	−0.974143	+	1.34079i	−0.0354527	+	0.0487964i
$756$	−3.08251	+	19.4622i	−0.112110	+	0.707833i
$757$	4.28858	−	13.1989i	0.155871	−	0.479722i	−0.842377	−	0.538889i	$-0.818844\pi$
$757$	4.28858	−	13.1989i	0.155871	−	0.479722i	0.998248	+	0.0591666i	$0.0188443\pi$
$758$	58.0505			2.10849
$759$	21.0939	+	1.64819i	0.765658	+	0.0598255i
$760$	3.66824	+	3.66824i	0.133061	+	0.133061i
$761$	42.9801	−	21.8995i	1.55803	−	0.793855i	0.558660	−	0.829397i	$-0.311316\pi$
$761$	42.9801	−	21.8995i	1.55803	−	0.793855i	0.999368	+	0.0355417i	$0.0113156\pi$
$762$	3.18014	−	20.0786i	0.115204	−	0.727372i
$763$	77.4235	+	56.2515i	2.80292	+	2.03644i
$764$	16.3426	−	5.31004i	0.591256	−	0.192111i
$765$	−0.334331	+	0.656161i	−0.0120877	+	0.0237235i
$766$	−42.3394	−	30.7614i	−1.52979	−	1.11145i
$767$	39.4869	−	6.52456i	1.42579	−	0.235588i
$768$	−10.0201	+	30.8387i	−0.361570	+	1.11280i
$769$	27.4755	−	27.4755i	0.990793	−	0.990793i	−0.00916539	−	0.999958i	$-0.502917\pi$
$769$	27.4755	−	27.4755i	0.990793	−	0.990793i	0.999958	+	0.00916539i	$0.00291747\pi$
$770$	7.17467	+	4.39110i	0.258557	+	0.158244i
$771$			11.6518i			0.419628i
$772$	30.6504	+	60.1549i	1.10313	+	2.16502i
$773$	21.5902	+	3.41955i	0.776545	+	0.122993i	0.532112	−	0.846674i	$-0.321398\pi$
$773$	21.5902	+	3.41955i	0.776545	+	0.122993i	0.244433	+	0.969666i	$0.421398\pi$
$774$	−22.1593	+	3.50969i	−0.796500	+	0.126153i
$775$	−21.7592	−	11.0869i	−0.781613	−	0.398252i
$776$	−1.47352	+	0.478775i	−0.0528963	+	0.0171870i
$777$	−22.5197	−	16.3615i	−0.807888	−	0.586965i
$778$	−12.0746	−	1.91243i	−0.432895	−	0.0685638i
$779$	24.0929	+	7.82825i	0.863217	+	0.280476i
$780$	−2.97912	−	1.49298i	−0.106669	−	0.0534571i
$781$	−4.83310	−	11.6496i	−0.172942	−	0.416856i
$782$	38.0002	+	38.0002i	1.35889	+	1.35889i
$783$	−4.26601	−	1.38611i	−0.152455	−	0.0495355i
$784$	47.0395	+	64.7443i	1.67998	+	2.31229i
$785$	0.328294	+	2.07277i	0.0117173	+	0.0739803i
$786$	3.25488	−	6.38805i	0.116098	−	0.227854i
$787$	−2.15348	+	4.22645i	−0.0767634	+	0.150657i	−0.926198	−	0.377037i	$-0.876943\pi$
$787$	−2.15348	+	4.22645i	−0.0767634	+	0.150657i	0.849435	+	0.527693i	$0.176943\pi$
$788$	−15.6523	−	98.8250i	−0.557591	−	3.52049i
$789$	8.92462	+	12.2837i	0.317725	+	0.437311i
$790$	−8.00791	−	2.60193i	−0.284909	−	0.0925724i
$791$	15.9570	+	15.9570i	0.567365	+	0.567365i
$792$	7.08984	+	17.0892i	0.251926	+	0.607238i
$793$	11.2055	−	3.72375i	0.397919	−	0.132234i
$794$	34.1677	+	11.1018i	1.21257	+	0.393987i
$795$	0.307593	+	0.0487179i	0.0109092	+	0.00172785i
$796$	−0.234927	−	0.170684i	−0.00832676	−	0.00604974i
$797$	25.5088	−	8.28831i	0.903568	−	0.293587i	0.179859	−	0.983692i	$-0.442436\pi$
$797$	25.5088	−	8.28831i	0.903568	−	0.293587i	0.723709	+	0.690105i	$0.242436\pi$
$798$	−44.1097	−	22.4750i	−1.56147	−	0.795607i
$799$	25.6804	−	4.06737i	0.908507	−	0.143893i
$800$	−12.1107	−	1.91815i	−0.428178	−	0.0678167i
$801$	−4.44923	−	8.73210i	−0.157206	−	0.308533i
$802$		−	33.4399i		−	1.18080i
$803$	12.0589	+	7.38039i	0.425550	+	0.260448i
$804$	33.1895	−	33.1895i	1.17050	−	1.17050i
$805$	−2.00246	+	6.16294i	−0.0705775	+	0.217215i
$806$	−36.0878	−	25.8531i	−1.27114	−	0.910636i
$807$	−23.3753	−	16.9831i	−0.822848	−	0.597834i
$808$	−8.90041	+	17.4680i	−0.313115	+	0.614524i
$809$	−9.27743	+	3.01442i	−0.326177	+	0.105981i	−0.467528	−	0.883978i	$-0.654855\pi$
$809$	−9.27743	+	3.01442i	−0.326177	+	0.105981i	0.141351	+	0.989960i	$0.454855\pi$
$810$	−0.440907	−	0.320338i	−0.0154919	−	0.0112555i
$811$	5.48160	−	34.6095i	0.192485	−	1.21530i	−0.682403	−	0.730977i	$-0.739065\pi$
$811$	5.48160	−	34.6095i	0.192485	−	1.21530i	0.874888	−	0.484326i	$-0.160935\pi$
$812$	−78.7531	+	40.1267i	−2.76369	+	1.40817i
$813$	−22.3263	−	22.3263i	−0.783017	−	0.783017i
$814$	−49.3819	−	3.85851i	−1.73084	−	0.135241i
$815$	0.825003			0.0288986
$816$	−5.69254	+	17.5198i	−0.199279	+	0.613317i
$817$	5.98882	−	37.8119i	0.209522	−	1.32287i
$818$	22.5009	−	30.9699i	0.786727	−	1.08284i
$819$	16.5898	+	2.51418i	0.579695	+	0.0878527i
$820$	5.22633	−	1.69814i	0.182511	−	0.0593015i
$821$	−23.6921	+	3.75247i	−0.826861	+	0.130962i	−0.555501	−	0.831516i	$-0.687473\pi$
$821$	−23.6921	+	3.75247i	−0.826861	+	0.130962i	−0.271360	+	0.962478i	$0.587473\pi$
$822$	−24.3475	−	33.5114i	−0.849215	−	1.16884i
$823$	−7.08583	−	2.30233i	−0.246997	−	0.0802541i	0.182902	−	0.983131i	$-0.441451\pi$
$823$	−7.08583	−	2.30233i	−0.246997	−	0.0802541i	−0.429899	+	0.902877i	$0.641451\pi$
$824$	29.7277	−	29.7277i	1.03561	−	1.03561i
$825$	13.9999	−	8.58997i	0.487413	−	0.299064i
$826$	91.2024	−	91.2024i	3.17334	−	3.17334i
$827$	32.2255	−	16.4197i	1.12059	−	0.570970i	0.207300	−	0.978277i	$-0.433532\pi$
$827$	32.2255	−	16.4197i	1.12059	−	0.570970i	0.913291	+	0.407308i	$0.133532\pi$
$828$	−21.8529	+	15.8771i	−0.759442	+	0.551767i
$829$	−17.8529	+	24.5724i	−0.620056	+	0.853434i	−0.997357	−	0.0726570i	$-0.976852\pi$
$829$	−17.8529	+	24.5724i	−0.620056	+	0.853434i	0.377301	+	0.926091i	$0.376852\pi$
$830$	0.375883	+	0.191522i	0.0130471	+	0.00664783i
$831$	−9.12789	−	28.0927i	−0.316643	−	0.974527i
$832$	16.2820	+	5.17047i	0.564478	+	0.179254i
$833$	−29.0669	−	40.0071i	−1.00711	−	1.38616i
$834$	27.8723	−	14.2016i	0.965139	−	0.491763i
$835$		−	3.79561i		−	0.131352i
$836$	−59.6444	+	4.72786i	−2.06284	+	0.163516i
$837$	−3.48686	−	3.48686i	−0.120524	−	0.120524i
$838$	−4.31396	−	8.46662i	−0.149023	−	0.292475i
$839$	−3.49344	+	22.0567i	−0.120607	+	0.761481i	0.851050	+	0.525085i	$0.175966\pi$
$839$	−3.49344	+	22.0567i	−0.120607	+	0.761481i	−0.971657	+	0.236396i	$0.924034\pi$
$840$	−5.59669	+	0.886429i	−0.193104	+	0.0305847i
$841$	2.74403	+	8.44526i	0.0946217	+	0.291216i
$842$	2.16199	+	6.65392i	0.0745071	+	0.229309i
$843$	−0.216523	−	1.36707i	−0.00745744	−	0.0470844i
$844$	12.3311	−	8.95905i	0.424453	−	0.308383i
$845$	−1.25436	+	2.54524i	−0.0431512	+	0.0875590i
$846$			19.2416i			0.661541i
$847$	−48.6677	+	15.8736i	−1.67224	+	0.545424i
$848$	7.79023			0.267518
$849$	−4.18117	+	12.8683i	−0.143497	+	0.441639i
$850$	41.2052	+	6.52626i	1.41333	+	0.223849i
$851$	−5.96921	−	37.6881i	−0.204622	−	1.29193i
$852$	14.3467	+	7.31001i	0.491510	+	0.250437i
$853$	23.8515	−	46.8113i	0.816661	−	1.60279i	0.0188942	−	0.999821i	$-0.493985\pi$
$853$	23.8515	−	46.8113i	0.816661	−	1.60279i	0.797767	−	0.602966i	$-0.206015\pi$
$854$	22.3674	−	30.7861i	0.765396	−	1.05348i
$855$	0.752349	−	0.546614i	0.0257298	−	0.0186938i
$856$	−5.14744	−	10.1024i	−0.175936	−	0.345294i
$857$	−8.46430			−0.289135			−0.144568	−	0.989495i	$-0.546179\pi$
$857$	−8.46430			−0.289135			−0.144568	+	0.989495i	$0.546179\pi$
$858$	27.5016	−	11.6254i	0.938890	−	0.396885i
$859$	−6.20829			−0.211824			−0.105912	−	0.994376i	$-0.533776\pi$
$859$	−6.20829			−0.211824			−0.105912	+	0.994376i	$0.533776\pi$
$860$	−3.77019	−	7.39941i	−0.128562	−	0.252318i
$861$	−22.3861	+	16.2644i	−0.762916	+	0.554291i
$862$	−53.2517	+	73.2946i	−1.81376	+	2.49643i
$863$	−25.4036	+	49.8573i	−0.864748	+	1.69716i	−0.160710	+	0.987002i	$0.551378\pi$
$863$	−25.4036	+	49.8573i	−0.864748	+	1.69716i	−0.704038	+	0.710162i	$0.748622\pi$
$864$	−2.20607	−	1.12405i	−0.0750519	−	0.0382408i
$865$	−0.344859	−	2.17735i	−0.0117256	−	0.0740322i
$866$	−31.7175	−	5.02356i	−1.07780	−	0.170707i
$867$	−1.73572	+	5.34201i	−0.0589483	+	0.181424i
$868$	−97.1676			−3.29808
$869$	43.6753	−	26.7980i	1.48158	−	0.909061i
$870$		−	2.44458i		−	0.0828792i
$871$	−28.4499	−	28.0726i	−0.963988	−	0.951205i
$872$	−92.8075	+	67.4286i	−3.14286	+	2.28342i
$873$	0.0434481	+	0.274320i	0.00147050	+	0.00928434i
$874$	−20.9709	−	64.5417i	−0.709350	−	2.18315i
$875$	3.12398	+	9.61463i	0.105610	+	0.325034i
$876$	−17.8274	+	2.82358i	−0.602331	+	0.0953999i
$877$	4.07964	−	25.7578i	0.137760	−	0.869780i	−0.817912	−	0.575344i	$-0.804868\pi$
$877$	4.07964	−	25.7578i	0.137760	−	0.869780i	0.955671	−	0.294436i	$-0.0951318\pi$
$878$	11.5800	+	22.7271i	0.390807	+	0.767003i
$879$	−5.54057	−	5.54057i	−0.186879	−	0.186879i
$880$	−3.00418	+	2.56874i	−0.101271	+	0.0865921i
$881$			38.5561i			1.29899i	0.760367	+	0.649493i	$0.225019\pi$
$881$			38.5561i			1.29899i	−0.760367	+	0.649493i	$0.774981\pi$
$882$	32.6078	−	16.6145i	1.09796	−	0.559439i
$883$	−6.62766	−	9.12220i	−0.223039	−	0.306986i	0.682803	−	0.730602i	$-0.260761\pi$
$883$	−6.62766	−	9.12220i	−0.223039	−	0.306986i	−0.905842	+	0.423616i	$0.860761\pi$
$884$	49.0919	+	15.5895i	1.65114	+	0.524330i
$885$	0.748708	+	2.30429i	0.0251675	+	0.0774577i
$886$	83.8216	+	42.7093i	2.81604	+	1.43485i
$887$	−11.4050	+	15.6976i	−0.382942	+	0.527075i	−0.956361	−	0.292188i	$-0.905617\pi$
$887$	−11.4050	+	15.6976i	−0.382942	+	0.527075i	0.573419	+	0.819262i	$0.305617\pi$
$888$	26.9943	−	19.6125i	0.905870	−	0.658153i
$889$	−33.7602	+	17.2017i	−1.13228	+	0.576926i
$890$	3.77670	−	3.77670i	0.126595	−	0.126595i
$891$	3.22455	−	0.776064i	0.108027	−	0.0259991i
$892$	3.11068	−	3.11068i	0.104153	−	0.104153i
$893$	−31.2263	−	10.1460i	−1.04495	−	0.339524i
$894$	−18.7565	−	25.8161i	−0.627312	−	0.863421i
$895$	0.561622	−	0.0889521i	0.0187729	−	0.00297334i
$896$	74.2763	−	24.1338i	2.48140	−	0.806255i
$897$	13.6437	+	18.5178i	0.455551	+	0.618292i
$898$	3.02967	−	4.16998i	0.101101	−	0.139154i
$899$	3.46017	−	21.8467i	0.115403	−	0.728627i
$900$	−6.47985	+	19.9429i	−0.215995	+	0.664764i
$901$	−4.81378			−0.160370
$902$	−18.8172	+	45.5012i	−0.626546	+	1.51502i
$903$	29.5687	+	29.5687i	0.983984	+	0.983984i
$904$	−24.1022	+	12.2807i	−0.801629	+	0.408450i
$905$	0.546468	−	3.45026i	0.0181652	−	0.114691i
$906$	15.3374	+	11.1433i	0.509552	+	0.370211i
$907$	31.7479	−	10.3155i	1.05417	−	0.342521i	0.269868	−	0.962897i	$-0.413020\pi$
$907$	31.7479	−	10.3155i	1.05417	−	0.342521i	0.784304	+	0.620376i	$0.213020\pi$
$908$	−27.4978	+	53.9675i	−0.912547	+	1.79097i
$909$	2.84322	+	2.06572i	0.0943035	+	0.0685155i
$910$	1.49077	+	9.02221i	0.0494186	+	0.299083i
$911$	16.8712	−	51.9243i	0.558969	−	1.72033i	−0.126256	−	0.991998i	$-0.540296\pi$
$911$	16.8712	−	51.9243i	0.558969	−	1.72033i	0.685225	−	0.728332i	$-0.259704\pi$
$912$	16.4491	−	16.4491i	0.544683	−	0.544683i
$913$	−2.37133	+	0.983801i	−0.0784797	+	0.0325591i
$914$		−	4.05015i		−	0.133967i
$915$	0.324528	+	0.636922i	0.0107286	+	0.0210560i
$916$	−93.1403	−	14.7520i	−3.07744	−	0.487419i
$917$	−13.1983	+	2.09041i	−0.435846	+	0.0690313i
$918$	7.50587	+	3.82443i	0.247731	+	0.126225i
$919$	32.5401	−	10.5729i	1.07340	−	0.348769i	0.281589	−	0.959535i	$-0.409139\pi$
$919$	32.5401	−	10.5729i	1.07340	−	0.348769i	0.791811	+	0.610766i	$0.209139\pi$
$920$	−6.28419	−	4.56573i	−0.207184	−	0.150528i
$921$	10.6294	+	1.68353i	0.350250	+	0.0554741i
$922$	8.26237	+	2.68461i	0.272107	+	0.0884128i
$923$	6.14303	−	12.2580i	0.202200	−	0.403475i
$924$	34.1157	−	55.7421i	1.12232	−	1.83378i
$925$	−20.9460	−	20.9460i	−0.688699	−	0.688699i
$926$	12.2165	+	3.96938i	0.401459	+	0.130442i
$927$	−4.42980	−	6.09710i	−0.145494	−	0.200255i
$928$	−1.73734	−	10.9691i	−0.0570310	−	0.360080i
$929$	−8.29188	+	16.2737i	−0.272048	+	0.533924i	−0.986097	−	0.166172i	$-0.946859\pi$
$929$	−8.29188	+	16.2737i	−0.272048	+	0.533924i	0.714049	+	0.700096i	$0.246859\pi$
$930$	1.22007	−	2.39453i	0.0400078	−	0.0785197i
$931$	9.76888	+	61.6783i	0.320162	+	2.02142i
$932$	22.5664	+	31.0600i	0.739188	+	1.01741i
$933$	7.06195	+	2.29457i	0.231198	+	0.0751207i
$934$	57.1926	+	57.1926i	1.87140	+	1.87140i
$935$	1.85636	−	1.58729i	0.0607095	−	0.0519099i
$936$	−9.01142	+	17.9816i	−0.294548	+	0.587747i
$937$	−20.4343	−	6.63950i	−0.667558	−	0.216903i	−0.0444182	−	0.999013i	$-0.514143\pi$
$937$	−20.4343	−	6.63950i	−0.667558	−	0.216903i	−0.623140	+	0.782110i	$0.714143\pi$
$938$	−127.220	−	20.1497i	−4.15388	−	0.657910i
$939$	18.4060	+	13.3728i	0.600658	+	0.436404i
$940$	−6.77374	+	2.20092i	−0.220935	+	0.0717861i
$941$	−33.8753	−	17.2603i	−1.10430	−	0.562670i	−0.195839	−	0.980636i	$-0.562743\pi$
$941$	−33.8753	−	17.2603i	−1.10430	−	0.562670i	−0.908463	+	0.417966i	$0.862743\pi$
$942$	23.7105	−	3.75538i	0.772531	−	0.122357i
$943$	−37.4646	−	5.93381i	−1.22002	−	0.193231i
$944$	27.5151	+	54.0014i	0.895540	+	1.75760i
$945$			1.01578i			0.0330434i
$946$	72.3640	+	17.3300i	2.35276	+	0.563448i
$947$	20.8164	−	20.8164i	0.676443	−	0.676443i	−0.282751	−	0.959193i	$-0.591247\pi$
$947$	20.8164	−	20.8164i	0.676443	−	0.676443i	0.959193	+	0.282751i	$0.0912469\pi$
$948$	−20.2151	+	62.2157i	−0.656556	+	2.02067i
$949$	2.50563	+	15.1642i	0.0813362	+	0.492250i
$950$	−42.6209	−	30.9659i	−1.38280	−	1.00467i
$951$	14.9996	−	29.4383i	0.486394	−	0.954602i
$952$	83.3006	−	27.0660i	2.69979	−	0.877214i
$953$	21.6949	+	15.7622i	0.702766	+	0.510589i	0.880832	−	0.473429i	$-0.156984\pi$
$953$	21.6949	+	15.7622i	0.702766	+	0.510589i	−0.178066	+	0.984019i	$0.556984\pi$
$954$	0.557288	−	3.51858i	0.0180429	−	0.113918i
$955$	0.789269	−	0.402153i	0.0255402	−	0.0130134i
$956$	26.6047	+	26.6047i	0.860459	+	0.860459i
$957$	11.3179	+	9.65540i	0.365856	+	0.312115i
$958$	−85.4279			−2.76005
$959$	−23.8577	+	73.4264i	−0.770404	+	2.37106i
$960$	−0.161782	+	1.02145i	−0.00522150	+	0.0329673i
$961$	−3.92852	+	5.40714i	−0.126726	+	0.174424i
$962$	−31.9408	−	43.3513i	−1.02981	−	1.39770i
$963$	−1.93304	+	0.628081i	−0.0622912	+	0.0202396i
$964$	1.83117	−	0.290029i	0.0589781	−	0.00934122i
$965$	2.04568	+	2.81563i	0.0658527	+	0.0906385i
$966$	70.4983	+	22.9063i	2.26825	+	0.736998i
$967$	12.8217	−	12.8217i	0.412319	−	0.412319i	−0.470226	−	0.882546i	$-0.655828\pi$
$967$	12.8217	−	12.8217i	0.412319	−	0.412319i	0.882546	+	0.470226i	$0.155828\pi$
$968$	−0.0690081	−	61.3626i	−0.00221801	−	1.97227i
$969$	−10.1643	+	10.1643i	−0.326524	+	0.326524i
$970$	−0.134868	+	0.0687187i	−0.00433035	+	0.00220642i
$971$	−44.3239	+	32.2032i	−1.42242	+	1.03345i	−0.431054	+	0.902326i	$0.641858\pi$
$971$	−44.3239	+	32.2032i	−1.42242	+	1.03345i	−0.991366	+	0.131123i	$0.958142\pi$
$972$	−2.48880	+	3.42554i	−0.0798282	+	0.109874i
$973$	−51.9498	−	26.4697i	−1.66543	−	0.848580i
$974$	−1.44406	−	4.44437i	−0.0462708	−	0.142407i
$975$	17.0185	+	5.40434i	0.545028	+	0.173077i
$976$	10.5104	+	14.4663i	0.336429	+	0.463054i
$977$	−5.28772	+	2.69423i	−0.169169	+	0.0861959i	−0.536525	−	0.843885i	$-0.680263\pi$
$977$	−5.28772	+	2.69423i	−0.169169	+	0.0861959i	0.367356	+	0.930081i	$0.380263\pi$
$978$		−	9.43727i		−	0.301771i
$979$	2.56844	+	32.4021i	0.0820876	+	1.03558i
$980$	9.57867	+	9.57867i	0.305979	+	0.305979i
$981$	9.33601	+	18.3229i	0.298076	+	0.585007i
$982$	−2.31112	+	14.5919i	−0.0737509	+	0.465645i
$983$	−26.6073	+	4.21418i	−0.848640	+	0.134411i	−0.565583	−	0.824692i	$-0.691349\pi$
$983$	−26.6073	+	4.21418i	−0.848640	+	0.134411i	−0.283057	+	0.959103i	$0.591349\pi$
$984$	−10.2498	−	31.5455i	−0.326750	−	1.00563i
$985$	−1.59389	−	4.90548i	−0.0507855	−	0.156302i
$986$	5.91109	+	37.3212i	0.188248	+	1.18855i
$987$	29.0142	−	21.0800i	0.923531	−	0.670985i
$988$	−46.2987	−	45.6848i	−1.47296	−	1.45343i
$989$			57.3228i			1.82276i
$990$	0.945299	+	1.54064i	0.0300436	+	0.0489648i
$991$	51.6750			1.64151			0.820755	−	0.571281i	$-0.193553\pi$
$991$	51.6750			1.64151			0.820755	+	0.571281i	$0.193553\pi$
$992$	3.77285	−	11.6116i	0.119788	−	0.368670i
$993$	−4.83036	−	0.765054i	−0.153287	−	0.0242783i
$994$	−6.91232	−	43.6427i	−0.219246	−	1.38426i
$995$	−0.0133378	−	0.00679595i	−0.000422837	−	0.000215446i
$996$	1.48799	−	2.92034i	0.0471488	−	0.0925346i
$997$	12.1266	−	16.6909i	0.384054	−	0.528606i	−0.572599	−	0.819836i	$-0.694065\pi$
$997$	12.1266	−	16.6909i	0.384054	−	0.528606i	0.956653	+	0.291230i	$0.0940646\pi$
$998$	63.4898	−	46.1281i	2.00974	−	1.46016i
$999$	−2.71550	−	5.32947i	−0.0859147	−	0.168617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bj.a.112.1	✓	112
11.6	odd	10	inner	429.2.bj.a.424.1	yes	112
13.5	odd	4	inner	429.2.bj.a.343.1	yes	112
143.83	even	20	inner	429.2.bj.a.226.1	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bj.a.112.1	✓	112	1.1	even	1	trivial
429.2.bj.a.226.1	yes	112	143.83	even	20	inner
429.2.bj.a.343.1	yes	112	13.5	odd	4	inner
429.2.bj.a.424.1	yes	112	11.6	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13354 - 2.22470i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.48880 + 3.42554i) q^{4} +(-0.0990937 + 0.194482i) q^{5} +(2.22470 + 1.13354i) q^{6} +(-0.728003 - 4.59643i) q^{7} +(5.50974 + 0.872657i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.13354 - 2.22470i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-2.48880 + 3.42554i) q^{4} +(-0.0990937 + 0.194482i) q^{5} +(2.22470 + 1.13354i) q^{6} +(-0.728003 - 4.59643i) q^{7} +(5.50974 + 0.872657i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.544991 q^{10} +(-2.15256 + 2.52319i) q^{11} -4.23419i q^{12} +(-3.60547 + 0.0240641i) q^{13} +(-9.40045 + 6.82983i) q^{14} +(-0.0341454 - 0.215585i) q^{15} +(-1.68724 - 5.19278i) q^{16} +(1.04259 + 3.20875i) q^{17} +(-2.46610 + 0.390591i) q^{18} +(0.666492 - 4.20806i) q^{19} +(-0.419582 - 0.823476i) q^{20} +(3.29068 + 3.29068i) q^{21} +(8.05335 + 1.92865i) q^{22} +6.37942i q^{23} +(-4.97041 + 2.53255i) q^{24} +(2.91092 + 4.00654i) q^{25} +(4.14048 + 7.99381i) q^{26} +(0.309017 + 0.951057i) q^{27} +(17.5571 + 8.94578i) q^{28} +(-2.63654 + 3.62888i) q^{29} +(-0.440907 + 0.320338i) q^{30} +(-4.39370 + 2.23870i) q^{31} +(-1.75074 + 1.75074i) q^{32} +(0.258360 - 3.30655i) q^{33} +(5.95669 - 5.95669i) q^{34} +(0.966065 + 0.313894i) q^{35} +(2.48880 + 3.42554i) q^{36} +(-5.90777 + 0.935698i) q^{37} +(-10.1172 + 3.28727i) q^{38} +(2.90274 - 2.13871i) q^{39} +(-0.715697 + 0.985073i) q^{40} +(-0.930149 + 5.87273i) q^{41} +(3.59065 - 11.0509i) q^{42} +8.98558 q^{43} +(-3.28601 - 13.6534i) q^{44} +(0.154342 + 0.154342i) q^{45} +(14.1923 - 7.23133i) q^{46} +(1.20555 - 7.61152i) q^{47} +(4.41724 + 3.20932i) q^{48} +(-13.9398 + 4.52931i) q^{49} +(5.61370 - 11.0175i) q^{50} +(-2.72953 - 1.98312i) q^{51} +(8.89085 - 12.4106i) q^{52} +(-0.440899 + 1.35695i) q^{53} +(1.76553 - 1.76553i) q^{54} +(-0.277412 - 0.668667i) q^{55} -25.9604i q^{56} +(1.93423 + 3.79615i) q^{57} +(11.0618 + 1.75202i) q^{58} +(-10.9635 + 1.73645i) q^{59} +(0.823476 + 0.419582i) q^{60} +(-3.11467 + 1.01202i) q^{61} +(9.96088 + 7.23700i) q^{62} +(-4.59643 - 0.728003i) q^{63} +(-4.50615 - 1.46414i) q^{64} +(0.352600 - 0.703585i) q^{65} +(-7.64893 + 3.17333i) q^{66} +(7.83844 + 7.83844i) q^{67} +(-13.5865 - 4.41451i) q^{68} +(-3.74973 - 5.16106i) q^{69} +(-0.396755 - 2.50501i) q^{70} +(-1.72642 + 3.38830i) q^{71} +(2.53255 - 4.97041i) q^{72} +(-0.666851 - 4.21033i) q^{73} +(8.77834 + 12.0823i) q^{74} +(-4.70997 - 1.53036i) q^{75} +(12.7561 + 12.7561i) q^{76} +(13.1647 + 8.05719i) q^{77} +(-8.04836 - 4.03341i) q^{78} +(-14.6936 - 4.77425i) q^{79} +(1.17710 + 0.186434i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(14.1194 - 4.58767i) q^{82} +(0.689705 + 0.351422i) q^{83} +(-19.4622 + 3.08251i) q^{84} +(-0.727360 - 0.115202i) q^{85} +(-10.1855 - 19.9902i) q^{86} -4.48555i q^{87} +(-14.0619 + 12.0237i) q^{88} +(6.92983 - 6.92983i) q^{89} +(0.168412 - 0.518318i) q^{90} +(2.73540 + 16.5548i) q^{91} +(-21.8529 - 15.8771i) q^{92} +(2.23870 - 4.39370i) q^{93} +(-18.2999 + 5.94599i) q^{94} +(0.752349 + 0.546614i) q^{95} +(0.387320 - 2.44544i) q^{96} +(-0.247468 + 0.126091i) q^{97} +(25.8777 + 25.8777i) q^{98} +(1.73452 + 2.82691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9	\( 112 q - 28 q^{3} - 6 q^{5} - 28 q^{9} - 10 q^{11} + 10 q^{13} - 60 q^{14} + 4 q^{15} + 80 q^{16} - 74 q^{20} + 8 q^{22} + 30 q^{24} + 38 q^{26} - 28 q^{27} - 20 q^{29} - 8 q^{31} + 20 q^{33} - 48 q^{34} + 20 q^{35} + 12 q^{37} - 10 q^{39} + 40 q^{40} - 110 q^{41} + 20 q^{42} - 36 q^{44} + 4 q^{45} - 20 q^{46} - 30 q^{47} - 20 q^{48} + 90 q^{50} - 10 q^{52} + 52 q^{53} - 64 q^{55} + 30 q^{57} + 24 q^{58} - 36 q^{59} - 74 q^{60} - 60 q^{61} + 48 q^{66} + 60 q^{67} + 60 q^{68} + 116 q^{70} + 20 q^{71} - 30 q^{72} + 70 q^{73} + 120 q^{74} - 52 q^{78} - 120 q^{79} + 8 q^{80} - 28 q^{81} + 30 q^{83} + 30 q^{84} - 40 q^{85} + 62 q^{86} + 48 q^{89} - 4 q^{91} - 144 q^{92} - 8 q^{93} - 20 q^{94} + 82 q^{97} - 10 q^{99}+O(q^{100}) \) 112 * q - 28 * q^3 - 6 * q^5 - 28 * q^9 - 10 * q^11 + 10 * q^13 - 60 * q^14 + 4 * q^15 + 80 * q^16 - 74 * q^20 + 8 * q^22 + 30 * q^24 + 38 * q^26 - 28 * q^27 - 20 * q^29 - 8 * q^31 + 20 * q^33 - 48 * q^34 + 20 * q^35 + 12 * q^37 - 10 * q^39 + 40 * q^40 - 110 * q^41 + 20 * q^42 - 36 * q^44 + 4 * q^45 - 20 * q^46 - 30 * q^47 - 20 * q^48 + 90 * q^50 - 10 * q^52 + 52 * q^53 - 64 * q^55 + 30 * q^57 + 24 * q^58 - 36 * q^59 - 74 * q^60 - 60 * q^61 + 48 * q^66 + 60 * q^67 + 60 * q^68 + 116 * q^70 + 20 * q^71 - 30 * q^72 + 70 * q^73 + 120 * q^74 - 52 * q^78 - 120 * q^79 + 8 * q^80 - 28 * q^81 + 30 * q^83 + 30 * q^84 - 40 * q^85 + 62 * q^86 + 48 * q^89 - 4 * q^91 - 144 * q^92 - 8 * q^93 - 20 * q^94 + 82 * q^97 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more