LMFDB - Embedded newform 460.2.o.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41287 + 0.0615925i) q^{2} +(2.08651 - 0.612653i) q^{3} +(1.99241 - 0.174045i) q^{4} +(-0.546640 - 2.16822i) q^{5} +(-2.91023 + 0.994114i) q^{6} +(-1.11477 + 0.160279i) q^{7} +(-2.80430 + 0.368620i) q^{8} +(1.45440 - 0.934688i) q^{9} +O(q^{10})$	\(q+(-1.41287 + 0.0615925i) q^{2} +(2.08651 - 0.612653i) q^{3} +(1.99241 - 0.174045i) q^{4} +(-0.546640 - 2.16822i) q^{5} +(-2.91023 + 0.994114i) q^{6} +(-1.11477 + 0.160279i) q^{7} +(-2.80430 + 0.368620i) q^{8} +(1.45440 - 0.934688i) q^{9} +(0.905878 + 3.02975i) q^{10} +(0.704801 - 1.54330i) q^{11} +(4.05055 - 1.58380i) q^{12} +(3.74255 + 0.538097i) q^{13} +(1.56515 - 0.295115i) q^{14} +(-2.46894 - 4.18911i) q^{15} +(3.93942 - 0.693537i) q^{16} +(-4.44059 - 5.12471i) q^{17} +(-1.99732 + 1.41017i) q^{18} +(3.42536 - 3.95308i) q^{19} +(-1.46650 - 4.22485i) q^{20} +(-2.22777 + 1.01739i) q^{21} +(-0.900738 + 2.22389i) q^{22} +(3.30298 - 3.47711i) q^{23} +(-5.62536 + 2.48720i) q^{24} +(-4.40237 + 2.37047i) q^{25} +(-5.32088 - 0.529749i) q^{26} +(-1.81018 + 2.08906i) q^{27} +(-2.19318 + 0.513361i) q^{28} +(3.27507 + 3.77963i) q^{29} +(3.74631 + 5.76660i) q^{30} +(-0.333958 + 1.13736i) q^{31} +(-5.52317 + 1.22252i) q^{32} +(0.525064 - 3.65190i) q^{33} +(6.58962 + 6.96705i) q^{34} +(0.956896 + 2.32944i) q^{35} +(2.73509 - 2.11542i) q^{36} +(-1.25133 + 0.804179i) q^{37} +(-4.59611 + 5.79617i) q^{38} +(8.13851 - 1.17014i) q^{39} +(2.33219 + 5.87885i) q^{40} +(-9.31959 - 5.98934i) q^{41} +(3.08489 - 1.57465i) q^{42} +(-1.35966 - 4.63058i) q^{43} +(1.13565 - 3.19755i) q^{44} +(-2.82165 - 2.64253i) q^{45} +(-4.45252 + 5.11615i) q^{46} +12.8231 q^{47} +(7.79472 - 3.86057i) q^{48} +(-5.49944 + 1.61478i) q^{49} +(6.07398 - 3.62033i) q^{50} +(-12.4050 - 7.97220i) q^{51} +(7.55035 + 0.420741i) q^{52} +(1.27045 + 8.83617i) q^{53} +(2.42889 - 3.06307i) q^{54} +(-3.73149 - 0.684536i) q^{55} +(3.06706 - 0.860397i) q^{56} +(4.72517 - 10.3467i) q^{57} +(-4.86004 - 5.13841i) q^{58} +(1.17321 + 0.168683i) q^{59} +(-5.64823 - 7.91673i) q^{60} +(-1.31880 + 4.49141i) q^{61} +(0.401787 - 1.62751i) q^{62} +(-1.47151 + 1.27507i) q^{63} +(7.72824 - 2.06745i) q^{64} +(-0.879111 - 8.40881i) q^{65} +(-0.516918 + 5.19201i) q^{66} +(8.61940 - 3.93635i) q^{67} +(-9.73941 - 9.43768i) q^{68} +(4.76142 - 9.27860i) q^{69} +(-1.49545 - 3.23227i) q^{70} +(4.41233 - 2.01504i) q^{71} +(-3.73404 + 3.15727i) q^{72} +(9.75980 + 8.45691i) q^{73} +(1.71843 - 1.21327i) q^{74} +(-7.73329 + 7.64313i) q^{75} +(6.13672 - 8.47233i) q^{76} +(-0.538329 + 1.83338i) q^{77} +(-11.4266 + 2.15453i) q^{78} +(-0.567969 + 3.95031i) q^{79} +(-3.65718 - 8.16241i) q^{80} +(-4.65166 + 10.1857i) q^{81} +(13.5363 + 7.88815i) q^{82} +(-0.474664 - 0.738592i) q^{83} +(-4.26157 + 2.41479i) q^{84} +(-8.68411 + 12.4295i) q^{85} +(2.20624 + 6.45867i) q^{86} +(9.14905 + 5.87973i) q^{87} +(-1.40758 + 4.58768i) q^{88} +(0.269426 + 0.917582i) q^{89} +(4.14938 + 3.55976i) q^{90} -4.25831 q^{91} +(5.97573 - 7.50271i) q^{92} +2.57770i q^{93} +(-18.1173 + 0.789804i) q^{94} +(-10.4436 - 5.26603i) q^{95} +(-10.7752 + 5.93458i) q^{96} +(7.31510 + 4.70113i) q^{97} +(7.67054 - 2.62020i) q^{98} +(-0.417438 - 2.90335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−1.41287	+	0.0615925i	−0.999051	+	0.0435525i
$2$	−1.41287	+	0.0615925i	−0.999051	+	0.0435525i
$3$	2.08651	−	0.612653i	1.20464	−	0.353716i	0.383018	−	0.923741i	$-0.374885\pi$
$3$	2.08651	−	0.612653i	1.20464	−	0.353716i	0.821627	+	0.570025i	$0.193067\pi$
$4$	1.99241	−	0.174045i	0.996206	−	0.0870223i
$5$	−0.546640	−	2.16822i	−0.244465	−	0.969658i
$5$	−0.546640	−	2.16822i	−0.244465	−	0.969658i
$6$	−2.91023	+	0.994114i	−1.18810	+	0.405845i
$7$	−1.11477	+	0.160279i	−0.421342	+	0.0605798i	−0.349725	−	0.936852i	$-0.613725\pi$
$7$	−1.11477	+	0.160279i	−0.421342	+	0.0605798i	−0.0716169	+	0.997432i	$0.522816\pi$
$8$	−2.80430	+	0.368620i	−0.991471	+	0.130327i
$9$	1.45440	−	0.934688i	0.484801	−	0.311563i
$10$	0.905878	+	3.02975i	0.286464	+	0.958091i
$11$	0.704801	−	1.54330i	0.212505	−	0.465322i	−0.773122	−	0.634258i	$-0.781306\pi$
$11$	0.704801	−	1.54330i	0.212505	−	0.465322i	0.985627	+	0.168936i	$0.0540330\pi$
$12$	4.05055	−	1.58380i	1.16929	−	0.457205i
$13$	3.74255	+	0.538097i	1.03800	+	0.149241i	0.640181	−	0.768224i	$-0.278860\pi$
$13$	3.74255	+	0.538097i	1.03800	+	0.149241i	0.397815	+	0.917466i	$0.369769\pi$
$14$	1.56515	−	0.295115i	0.418304	−	0.0788728i
$15$	−2.46894	−	4.18911i	−0.637476	−	1.08162i
$16$	3.93942	−	0.693537i	0.984854	−	0.173384i
$17$	−4.44059	−	5.12471i	−1.07700	−	1.24292i	−0.968549	−	0.248823i	$-0.919956\pi$
$17$	−4.44059	−	5.12471i	−1.07700	−	1.24292i	−0.108451	−	0.994102i	$-0.534589\pi$
$18$	−1.99732	+	1.41017i	−0.470772	+	0.332381i
$19$	3.42536	−	3.95308i	0.785832	−	0.906898i	−0.211684	−	0.977338i	$-0.567895\pi$
$19$	3.42536	−	3.95308i	0.785832	−	0.906898i	0.997516	+	0.0704401i	$0.0224404\pi$
$20$	−1.46650	−	4.22485i	−0.327919	−	0.944706i
$21$	−2.22777	+	1.01739i	−0.486139	+	0.222012i
$22$	−0.900738	+	2.22389i	−0.192038	+	0.474136i
$23$	3.30298	−	3.47711i	0.688719	−	0.725028i
$23$	3.30298	−	3.47711i	0.688719	−	0.725028i
$24$	−5.62536	+	2.48720i	−1.14827	+	0.507697i
$25$	−4.40237	+	2.37047i	−0.880474	+	0.474094i
$26$	−5.32088	−	0.529749i	−1.04351	−	0.103892i
$27$	−1.81018	+	2.08906i	−0.348370	+	0.402041i
$28$	−2.19318	+	0.513361i	−0.414472	+	0.0970161i
$29$	3.27507	+	3.77963i	0.608164	+	0.701859i	0.973415	−	0.229050i	$-0.0735620\pi$
$29$	3.27507	+	3.77963i	0.608164	+	0.701859i	−0.365250	+	0.930909i	$0.619017\pi$
$30$	3.74631	+	5.76660i	0.683979	+	1.05283i
$31$	−0.333958	+	1.13736i	−0.0599806	+	0.204275i	−0.984032	−	0.177994i	$-0.943039\pi$
$31$	−0.333958	+	1.13736i	−0.0599806	+	0.204275i	0.924051	+	0.382269i	$0.124857\pi$
$32$	−5.52317	+	1.22252i	−0.976368	+	0.216113i
$33$	0.525064	−	3.65190i	0.0914019	−	0.635714i
$34$	6.58962	+	6.96705i	1.13011	+	1.19484i
$35$	0.956896	+	2.32944i	0.161745	+	0.393748i
$36$	2.73509	−	2.11542i	0.455849	−	0.352569i
$37$	−1.25133	+	0.804179i	−0.205717	+	0.132206i	−0.639443	−	0.768839i	$-0.720835\pi$
$37$	−1.25133	+	0.804179i	−0.205717	+	0.132206i	0.433726	+	0.901045i	$0.357199\pi$
$38$	−4.59611	+	5.79617i	−0.745588	+	0.940262i
$39$	8.13851	−	1.17014i	1.30320	−	0.187373i
$40$	2.33219	+	5.87885i	0.368752	+	0.929528i
$41$	−9.31959	−	5.98934i	−1.45548	−	0.935378i	−0.998957	−	0.0456641i	$-0.985460\pi$
$41$	−9.31959	−	5.98934i	−1.45548	−	0.935378i	−0.456519	−	0.889714i	$-0.650904\pi$
$42$	3.08489	−	1.57465i	0.476009	−	0.242974i
$43$	−1.35966	−	4.63058i	−0.207346	−	0.706157i	−0.995840	−	0.0911145i	$-0.970957\pi$
$43$	−1.35966	−	4.63058i	−0.207346	−	0.706157i	0.788494	−	0.615042i	$-0.210861\pi$
$44$	1.13565	−	3.19755i	0.171206	−	0.482050i
$45$	−2.82165	−	2.64253i	−0.420626	−	0.393925i
$46$	−4.45252	+	5.11615i	−0.656489	+	0.754336i
$47$	12.8231			1.87043			0.935217	−	0.354075i	$-0.115204\pi$
$47$	12.8231			1.87043			0.935217	+	0.354075i	$0.115204\pi$
$48$	7.79472	−	3.86057i	1.12507	−	0.557225i
$49$	−5.49944	+	1.61478i	−0.785634	+	0.230683i
$50$	6.07398	−	3.62033i	0.858991	−	0.511991i
$51$	−12.4050	−	7.97220i	−1.73704	−	1.11633i
$52$	7.55035	+	0.420741i	1.04705	+	0.0583463i
$53$	1.27045	+	8.83617i	0.174510	+	1.21374i	0.869210	+	0.494442i	$0.164628\pi$
$53$	1.27045	+	8.83617i	0.174510	+	1.21374i	−0.694701	+	0.719299i	$0.744463\pi$
$54$	2.42889	−	3.06307i	0.330530	−	0.416831i
$55$	−3.73149	−	0.684536i	−0.503153	−	0.0923029i
$56$	3.06706	−	0.860397i	0.409853	−	0.114975i
$57$	4.72517	−	10.3467i	0.625864	−	1.37045i
$58$	−4.86004	−	5.13841i	−0.638155	−	0.674706i
$59$	1.17321	+	0.168683i	0.152739	+	0.0219606i	0.218260	−	0.975891i	$-0.429962\pi$
$59$	1.17321	+	0.168683i	0.152739	+	0.0219606i	−0.0655209	+	0.997851i	$0.520871\pi$
$60$	−5.64823	−	7.91673i	−0.729183	−	1.02204i
$61$	−1.31880	+	4.49141i	−0.168855	+	0.575066i	0.830970	+	0.556318i	$0.187786\pi$
$61$	−1.31880	+	4.49141i	−0.168855	+	0.575066i	−0.999824	+	0.0187482i	$0.994032\pi$
$62$	0.401787	−	1.62751i	0.0510270	−	0.206694i
$63$	−1.47151	+	1.27507i	−0.185393	+	0.160644i
$64$	7.72824	−	2.06745i	0.966030	−	0.258431i
$65$	−0.879111	−	8.40881i	−0.109040	−	1.04299i
$66$	−0.516918	+	5.19201i	−0.0636283	+	0.639092i
$67$	8.61940	−	3.93635i	1.05303	−	0.480902i	0.187762	−	0.982215i	$-0.439877\pi$
$67$	8.61940	−	3.93635i	1.05303	−	0.480902i	0.865266	+	0.501313i	$0.167149\pi$
$68$	−9.73941	−	9.43768i	−1.18108	−	1.14449i
$69$	4.76142	−	9.27860i	0.573208	−	1.11701i
$70$	−1.49545	−	3.23227i	−0.178740	−	0.386330i
$71$	4.41233	−	2.01504i	0.523647	−	0.239142i	−0.136011	−	0.990707i	$-0.543428\pi$
$71$	4.41233	−	2.01504i	0.523647	−	0.239142i	0.659658	+	0.751566i	$0.270701\pi$
$72$	−3.73404	+	3.15727i	−0.440061	+	0.372088i
$73$	9.75980	+	8.45691i	1.14230	+	0.989807i	1.00000		1.74114e-5i	$-5.54223e-6\pi$
$73$	9.75980	+	8.45691i	1.14230	+	0.989807i	0.142298	+	0.989824i	$0.454551\pi$
$74$	1.71843	−	1.21327i	0.199764	−	0.141040i
$75$	−7.73329	+	7.64313i	−0.892964	+	0.882553i
$76$	6.13672	−	8.47233i	0.703930	−	0.971842i
$77$	−0.538329	+	1.83338i	−0.0613483	+	0.208933i
$78$	−11.4266	+	2.15453i	−1.29381	+	0.243953i
$79$	−0.567969	+	3.95031i	−0.0639015	+	0.444445i	0.932603	+	0.360904i	$0.117532\pi$
$79$	−0.567969	+	3.95031i	−0.0639015	+	0.444445i	−0.996504	+	0.0835406i	$0.973377\pi$
$80$	−3.65718	−	8.16241i	−0.408886	−	0.912586i
$81$	−4.65166	+	10.1857i	−0.516851	+	1.13175i
$82$	13.5363	+	7.88815i	1.49483	+	0.871101i
$83$	−0.474664	−	0.738592i	−0.0521012	−	0.0810710i	0.814226	−	0.580548i	$-0.197162\pi$
$83$	−0.474664	−	0.738592i	−0.0521012	−	0.0810710i	−0.866327	+	0.499477i	$0.833525\pi$
$84$	−4.26157	+	2.41479i	−0.464975	+	0.263475i
$85$	−8.68411	+	12.4295i	−0.941924	+	1.34817i
$86$	2.20624	+	6.45867i	0.237905	+	0.696456i
$87$	9.14905	+	5.87973i	0.980881	+	0.630374i
$88$	−1.40758	+	4.58768i	−0.150049	+	0.489049i
$89$	0.269426	+	0.917582i	0.0285591	+	0.0972635i	0.972539	−	0.232739i	$-0.0747687\pi$
$89$	0.269426	+	0.917582i	0.0285591	+	0.0972635i	−0.943980	+	0.330002i	$0.892951\pi$
$90$	4.14938	+	3.55976i	0.437383	+	0.375232i
$91$	−4.25831			−0.446392
$92$	5.97573	−	7.50271i	0.623013	−	0.782212i
$93$			2.57770i			0.267295i
$94$	−18.1173	+	0.789804i	−1.86866	+	0.0814620i
$95$	−10.4436	−	5.26603i	−1.07149	−	0.540283i
$96$	−10.7752	+	5.93458i	−1.09973	+	0.605696i
$97$	7.31510	+	4.70113i	0.742736	+	0.477327i	0.856478	−	0.516183i	$-0.172648\pi$
$97$	7.31510	+	4.70113i	0.742736	+	0.477327i	−0.113742	+	0.993510i	$0.536284\pi$
$98$	7.67054	−	2.62020i	0.774842	−	0.264680i
$99$	−0.417438	−	2.90335i	−0.0419541	−	0.291797i
$100$	−8.35877	+	5.48917i	−0.835877	+	0.548917i
$101$	−5.70557	+	3.66675i	−0.567725	+	0.364855i	−0.792796	−	0.609488i	$-0.791375\pi$
$101$	−5.70557	+	3.66675i	−0.567725	+	0.364855i	0.225070	+	0.974343i	$0.427739\pi$
$102$	18.0177	+	10.4996i	1.78402	+	1.03962i
$103$	9.57611	+	4.37326i	0.943562	+	0.430910i	0.826955	−	0.562268i	$-0.190071\pi$
$103$	9.57611	+	4.37326i	0.943562	+	0.430910i	0.116607	+	0.993178i	$0.462798\pi$
$104$	−10.6936	−	0.129408i	−1.04859	−	0.0126895i
$105$	3.42371	+	4.27415i	0.334120	+	0.417115i
$106$	−2.33922	−	12.4061i	−0.227205	−	1.20499i
$107$	−3.11644	+	10.6136i	−0.301277	+	1.02606i	0.660181	+	0.751106i	$0.270479\pi$
$107$	−3.11644	+	10.6136i	−0.301277	+	1.02606i	−0.961459	+	0.274950i	$0.911339\pi$
$108$	−3.24304	+	4.47733i	−0.312062	+	0.430831i
$109$	2.93881	−	2.54650i	0.281487	−	0.243910i	−0.502661	−	0.864484i	$-0.667646\pi$
$109$	2.93881	−	2.54650i	0.281487	−	0.243910i	0.784148	+	0.620573i	$0.213100\pi$
$110$	5.31427	+	0.737330i	0.506696	+	0.0703017i
$111$	−2.11822	+	2.44456i	−0.201052	+	0.232027i
$112$	−4.28037	+	1.40454i	−0.404457	+	0.132716i
$113$	−1.62406	−	3.55619i	−0.152778	−	0.334538i	0.817731	−	0.575600i	$-0.195231\pi$
$113$	−1.62406	−	3.55619i	−0.152778	−	0.334538i	−0.970510	+	0.241062i	$0.922504\pi$
$114$	−6.03878	+	14.9096i	−0.565584	+	1.39641i
$115$	−9.34469	−	5.26086i	−0.871397	−	0.490578i
$116$	7.18311	+	6.96057i	0.666935	+	0.646273i
$117$	5.94612	−	2.71550i	0.549719	−	0.251048i
$118$	−1.66799	−	0.166066i	−0.153551	−	0.0152876i
$119$	5.77160	+	5.00112i	0.529081	+	0.458452i
$120$	8.46784	+	10.8374i	0.773004	+	0.989317i
$121$	5.31844	+	6.13781i	0.483495	+	0.557983i
$122$	1.58665	−	6.42701i	0.143649	−	0.581874i
$123$	−23.1148	−	6.78711i	−2.08419	−	0.611973i
$124$	−0.467431	+	2.32421i	−0.0419766	+	0.208720i
$125$	7.54622	+	8.24952i	0.674954	+	0.737860i
$126$	2.00052	−	1.89214i	0.178220	−	0.168565i
$127$	−3.93299	+	8.61205i	−0.348997	+	0.764196i	0.650990	+	0.759086i	$0.274354\pi$
$127$	−3.93299	+	8.61205i	−0.348997	+	0.764196i	−0.999987	+	0.00510991i	$0.998373\pi$
$128$	−10.7917	+	3.39704i	−0.953858	+	0.300259i
$129$	−5.67388	−	8.82873i	−0.499558	−	0.777327i
$130$	1.75999	+	11.8264i	0.154361	+	1.03725i
$131$	3.88020	−	0.557889i	0.339015	−	0.0487430i	0.0292950	−	0.999571i	$-0.490674\pi$
$131$	3.88020	−	0.557889i	0.339015	−	0.0487430i	0.309720	+	0.950828i	$0.399765\pi$
$132$	0.410551	−	7.36748i	0.0357339	−	0.641257i
$133$	−3.18488	+	4.95577i	−0.276164	+	0.429720i
$134$	−11.9357	+	6.09245i	−1.03108	+	0.526307i
$135$	5.51907	+	2.78292i	0.475006	+	0.239515i
$136$	14.3418	+	12.7344i	1.22980	+	1.09196i
$137$	−2.71355			−0.231835			−0.115917	−	0.993259i	$-0.536981\pi$
$137$	−2.71355			−0.231835			−0.115917	+	0.993259i	$0.536981\pi$
$138$	−6.15579	+	13.4027i	−0.524015	+	1.14092i
$139$			14.1865i			1.20329i	0.798765	+	0.601644i	$0.205487\pi$
$139$			14.1865i			1.20329i	−0.798765	+	0.601644i	$0.794513\pi$
$140$	2.31196	+	4.47467i	0.195396	+	0.378179i
$141$	26.7554	−	7.85609i	2.25321	−	0.661602i
$142$	−6.10994	+	3.11876i	−0.512735	+	0.261721i
$143$	3.46819	−	5.39662i	0.290025	−	0.451288i
$144$	5.08126	−	4.69081i	0.423438	−	0.390901i
$145$	6.40479	−	9.16716i	0.531889	−	0.761291i
$146$	−14.3102	−	11.3474i	−1.18432	−	0.939117i
$147$	−10.4853	+	6.73850i	−0.864814	+	0.555782i
$148$	−2.35320	+	1.82004i	−0.193432	+	0.149607i
$149$	−0.241424	−	0.110254i	−0.0197782	−	0.00903240i	0.405501	−	0.914094i	$-0.367097\pi$
$149$	−0.241424	−	0.110254i	−0.0197782	−	0.00903240i	−0.425280	+	0.905062i	$0.639824\pi$
$150$	10.4554	−	11.2751i	0.853679	−	0.920606i
$151$	−7.50583	−	1.07917i	−0.610815	−	0.0878220i	−0.170037	−	0.985438i	$-0.554389\pi$
$151$	−7.50583	−	1.07917i	−0.610815	−	0.0878220i	−0.440779	+	0.897616i	$0.645298\pi$
$152$	−8.14857	+	12.3483i	−0.660936	+	1.00158i
$153$	−11.2484	−	3.30283i	−0.909380	−	0.267018i
$154$	0.647668	−	2.62349i	0.0521906	−	0.211407i
$155$	2.64859	+	0.102371i	0.212740	+	0.00822262i
$156$	16.0116	−	3.74787i	1.28196	−	0.300070i
$157$	7.14915	−	8.25056i	0.570565	−	0.658467i	−0.394984	−	0.918688i	$-0.629250\pi$
$157$	7.14915	−	8.25056i	0.570565	−	0.658467i	0.965549	+	0.260221i	$0.0837955\pi$
$158$	0.559158	−	5.61627i	0.0444842	−	0.446806i
$159$	8.06431	+	17.6584i	0.639541	+	1.40040i
$160$	5.66988	+	11.3072i	0.448243	+	0.893912i
$161$	−3.12474	+	4.40557i	−0.246264	+	0.347207i
$162$	5.94484	−	14.6776i	0.467071	−	1.15318i
$163$	4.37696	+	9.58420i	0.342830	+	0.750692i	0.999995	−	0.00305398i	$-0.000972113\pi$
$163$	4.37696	+	9.58420i	0.342830	+	0.750692i	−0.657166	+	0.753746i	$0.728245\pi$
$164$	−19.6109	−	10.3112i	−1.53135	−	0.805170i
$165$	−8.20515	+	0.857819i	−0.638770	+	0.0667811i
$166$	0.716131	+	1.01430i	0.0555826	+	0.0787249i
$167$	−14.1859	−	16.3714i	−1.09774	−	1.26686i	−0.961089	−	0.276237i	$-0.910912\pi$
$167$	−14.1859	−	16.3714i	−1.09774	−	1.26686i	−0.136648	−	0.990620i	$-0.543633\pi$
$168$	5.87231	−	3.67427i	0.453059	−	0.283476i
$169$	1.24369	+	0.365181i	0.0956687	+	0.0280909i
$170$	11.5040	−	18.0962i	0.882314	−	1.38792i
$171$	1.28696	−	8.95101i	0.0984164	−	0.684501i
$172$	−3.51493	−	8.98939i	−0.268011	−	0.685434i
$173$	−3.11026	−	1.42041i	−0.236469	−	0.107992i	0.293656	−	0.955911i	$-0.405128\pi$
$173$	−3.11026	−	1.42041i	−0.236469	−	0.107992i	−0.530125	+	0.847919i	$0.677855\pi$
$174$	−13.2886	−	7.74380i	−1.00740	−	0.587056i
$175$	4.52767	−	3.34813i	0.342260	−	0.253095i
$176$	1.70617	−	6.56850i	0.128607	−	0.495120i
$177$	2.55126	−	0.366816i	0.191765	−	0.0275716i
$178$	−0.437181	−	1.27983i	−0.0327681	−	0.0959274i
$179$	12.3251	−	19.1782i	0.921221	−	1.43345i	0.0201406	−	0.999797i	$-0.493589\pi$
$179$	12.3251	−	19.1782i	0.921221	−	1.43345i	0.901081	−	0.433651i	$-0.142775\pi$
$180$	−6.08180	−	4.77392i	−0.453311	−	0.355827i
$181$	2.89772	+	9.86872i	0.215386	+	0.733536i	0.994320	+	0.106431i	$0.0339422\pi$
$181$	2.89772	+	9.86872i	0.215386	+	0.733536i	−0.778935	+	0.627105i	$0.784240\pi$
$182$	6.01644	−	0.262280i	0.445968	−	0.0194415i
$183$			10.1793i			0.752477i
$184$	−7.98082	+	10.9684i	−0.588354	+	0.808603i
$185$	2.42766	+	2.27356i	0.178485	+	0.167155i
$186$	−0.158767	−	3.64196i	−0.0116414	−	0.267042i
$187$	−11.0387	+	3.24125i	−0.807229	+	0.237024i
$188$	25.5488	−	2.23178i	1.86334	−	0.162769i
$189$	1.68310	−	2.61895i	0.122427	−	0.190501i
$190$	15.0798	+	6.79698i	1.09400	+	0.493105i
$191$	3.49184	+	24.2863i	0.252660	+	1.75729i	0.582102	+	0.813116i	$0.302230\pi$
$191$	3.49184	+	24.2863i	0.252660	+	1.75729i	−0.329442	+	0.944176i	$0.606861\pi$
$192$	14.8584	−	9.04847i	1.07231	−	0.653017i
$193$	−8.41194	−	13.0892i	−0.605505	−	0.942184i	−0.999732	−	0.0231708i	$-0.992624\pi$
$193$	−8.41194	−	13.0892i	−0.605505	−	0.942184i	0.394227	−	0.919013i	$-0.371013\pi$
$194$	−10.6249	−	6.19154i	−0.762820	−	0.444527i
$195$	−6.98596	−	17.0065i	−0.500275	−	1.21786i
$196$	−10.6761	+	4.17446i	−0.762579	+	0.298175i
$197$	−3.43682	−	0.494140i	−0.244863	−	0.0352060i	0.0187903	−	0.999823i	$-0.494019\pi$
$197$	−3.43682	−	0.494140i	−0.244863	−	0.0352060i	−0.263654	+	0.964617i	$0.584928\pi$
$198$	0.768611	+	4.07635i	0.0546228	+	0.289693i
$199$	−11.1284	−	3.26760i	−0.788872	−	0.231634i	−0.137610	−	0.990487i	$-0.543942\pi$
$199$	−11.1284	−	3.26760i	−0.788872	−	0.231634i	−0.651262	+	0.758853i	$0.725760\pi$
$200$	11.4718	−	8.27033i	0.811177	−	0.584800i
$201$	15.5728	−	13.4939i	1.09842	−	0.951788i
$202$	7.83539	−	5.53206i	0.551296	−	0.389235i
$203$	−4.25673	−	3.68847i	−0.298764	−	0.258880i
$204$	−26.1034	−	13.7249i	−1.82760	−	0.960934i
$205$	−7.89176	+	23.4810i	−0.551184	+	1.63998i
$206$	−13.7992	−	5.58904i	−0.961434	−	0.389407i
$207$	1.55385	−	8.14438i	0.108000	−	0.566074i
$208$	15.1166	−	0.475807i	1.04815	−	0.0329913i
$209$	−3.68658	−	8.07249i	−0.255006	−	0.558386i
$210$	−5.10052	−	5.82796i	−0.351969	−	0.402167i
$211$	−4.14050	−	3.58777i	−0.285044	−	0.246992i	0.500589	−	0.865685i	$-0.333117\pi$
$211$	−4.14050	−	3.58777i	−0.285044	−	0.246992i	−0.785633	+	0.618693i	$0.787662\pi$
$212$	4.06915	+	17.3842i	0.279470	+	1.19395i
$213$	7.97183	−	6.90763i	0.546221	−	0.473303i
$214$	3.74941	−	15.1876i	0.256304	−	1.03820i
$215$	−9.29688	+	5.47931i	−0.634042	+	0.373686i
$216$	4.30624	−	6.52564i	0.293002	−	0.444014i
$217$	0.189990	−	1.32141i	0.0128974	−	0.0897033i
$218$	−3.99532	+	3.77888i	−0.270597	+	0.255938i
$219$	25.5450	+	11.6660i	1.72617	+	0.788317i
$220$	−7.55380	−	0.714434i	−0.509277	−	0.0481671i
$221$	−13.8615	−	21.5689i	−0.932426	−	1.45088i
$222$	2.84221	−	3.58431i	0.190756	−	0.240563i
$223$	−2.78296	−	19.3559i	−0.186361	−	1.29617i	−0.841334	−	0.540516i	$-0.818229\pi$
$223$	−2.78296	−	19.3559i	−0.186361	−	1.29617i	0.654973	−	0.755652i	$-0.272680\pi$
$224$	5.96110	−	2.24807i	0.398293	−	0.150206i
$225$	−4.18717	+	7.56247i	−0.279145	+	0.504164i
$226$	2.51362	+	4.92441i	0.167203	+	0.327567i
$227$	2.62131	+	8.92735i	0.173982	+	0.592529i	0.999600	+	0.0282984i	$0.00900886\pi$
$227$	2.62131	+	8.92735i	0.173982	+	0.592529i	−0.825617	+	0.564230i	$0.809173\pi$
$228$	7.61370	−	21.4372i	0.504230	−	1.41972i
$229$		−	24.7673i		−	1.63667i	−0.574740	−	0.818336i	$-0.694897\pi$
$229$		−	24.7673i		−	1.63667i	0.574740	−	0.818336i	$-0.305103\pi$
$230$	13.5269	+	6.85736i	0.891936	+	0.452161i
$231$			4.15517i			0.273390i
$232$	−10.5775	−	9.39197i	−0.694449	−	0.616613i
$233$	6.21454	+	21.1648i	0.407128	+	1.38655i	0.866886	+	0.498506i	$0.166118\pi$
$233$	6.21454	+	21.1648i	0.407128	+	1.38655i	−0.459758	+	0.888044i	$0.652064\pi$
$234$	−8.23385	+	4.20289i	−0.538264	+	0.274752i
$235$	−7.00959	−	27.8032i	−0.457255	−	1.81368i
$236$	2.36688	+	0.131894i	0.154071	+	0.00858557i
$237$	1.23510	+	8.59032i	0.0802285	+	0.558001i
$238$	−8.46256	−	6.71045i	−0.548546	−	0.434974i
$239$	10.9082	+	16.9735i	0.705592	+	1.09792i	0.990251	+	0.139294i	$0.0444834\pi$
$239$	10.9082	+	16.9735i	0.705592	+	1.09792i	−0.284659	+	0.958629i	$0.591880\pi$
$240$	−12.6315	−	14.7903i	−0.815358	−	0.954712i
$241$	−13.3543	−	6.09872i	−0.860229	−	0.392853i	−0.0640732	−	0.997945i	$-0.520409\pi$
$241$	−13.3543	−	6.09872i	−0.860229	−	0.392853i	−0.796156	+	0.605092i	$0.793136\pi$
$242$	−7.89232	−	8.34436i	−0.507337	−	0.536396i
$243$	−2.28523	+	15.8941i	−0.146598	+	1.01961i
$244$	−1.84588	+	9.17827i	−0.118170	+	0.587578i
$245$	6.50741	+	11.0413i	0.415743	+	0.705403i
$246$	33.0763	+	8.16562i	2.10886	+	0.520621i
$247$	14.9467	−	12.9514i	0.951036	−	0.824078i
$248$	0.517267	−	3.31260i	0.0328465	−	0.210350i
$249$	−1.44289	−	1.25027i	−0.0914395	−	0.0792328i
$250$	−11.1699	−	11.1907i	−0.706449	−	0.707763i
$251$	3.49983	+	7.66356i	0.220907	+	0.483720i	0.987343	−	0.158602i	$-0.0506986\pi$
$251$	3.49983	+	7.66356i	0.220907	+	0.483720i	−0.766435	+	0.642322i	$0.777971\pi$
$252$	−2.70993	+	2.79657i	−0.170710	+	0.176167i
$253$	−3.03828	−	7.54816i	−0.191015	−	0.474549i
$254$	5.02637	−	12.4100i	0.315383	−	0.778670i
$255$	−10.5044	+	31.2547i	−0.657813	+	1.95724i
$256$	15.0380	−	5.46427i	0.939876	−	0.341517i
$257$	−0.344056	−	0.298127i	−0.0214616	−	0.0185966i	0.644064	−	0.764972i	$-0.277247\pi$
$257$	−0.344056	−	0.298127i	−0.0214616	−	0.0185966i	−0.665526	+	0.746375i	$0.731793\pi$
$258$	8.56025	+	12.1244i	0.532938	+	0.754832i
$259$	1.26604	−	1.09703i	0.0786681	−	0.0681663i
$260$	−3.21506	−	16.6008i	−0.199390	−	1.02954i
$261$	8.29604	+	2.43594i	0.513512	+	0.150781i
$262$	−5.44787	+	1.02722i	−0.336571	+	0.0634617i
$263$	−2.97621	−	0.427914i	−0.183521	−	0.0263863i	0.0499416	−	0.998752i	$-0.484096\pi$
$263$	−2.97621	−	0.427914i	−0.183521	−	0.0263863i	−0.233462	+	0.972366i	$0.575006\pi$
$264$	−0.126274	+	10.4346i	−0.00777163	+	0.642205i
$265$	18.4643	−	7.58482i	1.13425	−	0.465932i
$266$	4.19459	−	7.19803i	0.257187	−	0.441339i
$267$	1.12432	+	1.74948i	0.0688072	+	0.107066i
$268$	16.4883	−	9.34299i	1.00718	−	0.570714i
$269$	0.714378	+	4.96861i	0.0435564	+	0.302941i	0.999941	+	0.0108321i	$0.00344802\pi$
$269$	0.714378	+	4.96861i	0.0435564	+	0.302941i	−0.956385	+	0.292109i	$0.905643\pi$
$270$	−7.96915	−	3.59197i	−0.484987	−	0.218600i
$271$	−2.12854	+	3.31207i	−0.129300	+	0.201194i	−0.899867	−	0.436164i	$-0.856337\pi$
$271$	−2.12854	+	3.31207i	−0.129300	+	0.201194i	0.770567	+	0.637358i	$0.219973\pi$
$272$	−21.0475	−	17.1087i	−1.27619	−	1.03736i
$273$	−8.88499	+	2.60887i	−0.537744	+	0.157896i
$274$	3.83390	−	0.167135i	0.231615	−	0.0100970i
$275$	0.555552	+	8.46488i	0.0335010	+	0.510452i
$276$	7.87183	−	19.3155i	0.473828	−	1.16266i
$277$		−	4.47921i		−	0.269130i	−0.990905	−	0.134565i	$-0.957036\pi$
$277$		−	4.47921i		−	0.269130i	0.990905	−	0.134565i	$-0.0429637\pi$
$278$	−0.873785	−	20.0438i	−0.0524061	−	1.20215i
$279$	0.577364	+	1.96632i	0.0345659	+	0.117721i
$280$	−3.54211	−	6.17974i	−0.211681	−	0.369310i
$281$	9.55022	−	14.8604i	0.569719	−	0.886499i	−0.430149	−	0.902758i	$-0.641539\pi$
$281$	9.55022	−	14.8604i	0.569719	−	0.886499i	0.999868	+	0.0162584i	$0.00517544\pi$
$282$	−37.3180	+	12.7476i	−2.22226	+	0.759107i
$283$	16.0613	−	2.30926i	0.954744	−	0.137272i	0.352702	−	0.935736i	$-0.385263\pi$
$283$	16.0613	−	2.30926i	0.954744	−	0.137272i	0.602042	+	0.798464i	$0.294354\pi$
$284$	8.44047	−	4.78274i	0.500850	−	0.283803i
$285$	−25.0169	−	4.58931i	−1.48187	−	0.271847i
$286$	−4.56772	+	7.83834i	−0.270095	+	0.463491i
$287$	11.3491	+	5.18297i	0.669918	+	0.305941i
$288$	−6.89025	+	6.94048i	−0.406012	+	0.408972i
$289$	−4.12449	+	28.6865i	−0.242617	+	1.68744i
$290$	−8.48452	+	13.3465i	−0.498228	+	0.783734i
$291$	18.1432	+	5.32731i	1.06357	+	0.312293i
$292$	20.9174	+	15.1510i	1.22410	+	0.886646i
$293$	0.316818	+	0.365627i	0.0185087	+	0.0213602i	0.764928	−	0.644115i	$-0.222774\pi$
$293$	0.316818	+	0.365627i	0.0185087	+	0.0213602i	−0.746420	+	0.665475i	$0.768229\pi$
$294$	14.3994	−	10.1665i	0.839787	−	0.592919i
$295$	−0.275584	−	2.63600i	−0.0160451	−	0.153474i
$296$	3.21267	−	2.71643i	0.186732	−	0.157889i
$297$	1.94823	+	4.26603i	0.113048	+	0.247540i
$298$	0.347891	+	0.140906i	0.0201528	+	0.00816244i
$299$	14.2326	−	11.2359i	0.823091	−	0.649791i
$300$	−14.0777	+	16.5742i	−0.812775	+	0.956913i
$301$	2.25789	+	4.94409i	0.130143	+	0.284972i
$302$	10.6712	+	1.06243i	0.614061	+	0.0611362i
$303$	−9.65826	+	11.1462i	−0.554853	+	0.640334i
$304$	10.7523	−	17.9484i	0.616688	−	1.02941i
$305$	10.4593	+	0.404261i	0.598896	+	0.0231479i
$306$	16.0960	+	3.97366i	0.920146	+	0.227159i
$307$	−5.62424	−	1.65143i	−0.320992	−	0.0942518i	0.117267	−	0.993100i	$-0.462587\pi$
$307$	−5.62424	−	1.65143i	−0.320992	−	0.0942518i	−0.438259	+	0.898849i	$0.644405\pi$
$308$	−0.753484	+	3.74655i	−0.0429337	+	0.213479i
$309$	22.6599	+	3.25800i	1.28908	+	0.185341i
$310$	−3.74843	+	0.0184968i	−0.212896	+	0.00105055i
$311$	15.6428	+	7.14382i	0.887021	+	0.405089i	0.806202	−	0.591640i	$-0.201519\pi$
$311$	15.6428	+	7.14382i	0.887021	+	0.405089i	0.0808184	+	0.996729i	$0.474247\pi$
$312$	−22.3915	+	6.28145i	−1.26767	+	0.355617i
$313$	−0.952256	+	0.611978i	−0.0538247	+	0.0345910i	−0.567276	−	0.823527i	$-0.692003\pi$
$313$	−0.952256	+	0.611978i	−0.0538247	+	0.0345910i	0.513452	+	0.858118i	$0.328367\pi$
$314$	−9.59267	+	12.0973i	−0.541345	+	0.682691i
$315$	3.56902	+	2.49355i	0.201091	+	0.140496i
$316$	−0.444098	+	7.96951i	−0.0249825	+	0.448320i
$317$	−15.1498	+	23.5736i	−0.850899	+	1.32402i	0.0936342	+	0.995607i	$0.470152\pi$
$317$	−15.1498	+	23.5736i	−0.850899	+	1.32402i	−0.944533	+	0.328417i	$0.893485\pi$
$318$	−12.4815	−	24.4523i	−0.699925	−	1.37122i
$319$	8.14136	−	2.39052i	0.455829	−	0.133843i
$320$	−8.70724	−	15.6264i	−0.486750	−	0.873541i
$321$			24.0547i			1.34260i
$322$	4.14351	−	6.41696i	0.230909	−	0.357603i
$323$	−35.4690			−1.97355
$324$	−7.49526	+	21.1038i	−0.416403	+	1.17243i
$325$	−17.7516	+	6.50270i	−0.984682	+	0.360705i
$326$	−6.77439	−	13.2717i	−0.375199	−	0.735049i
$327$	4.57173	−	7.11376i	0.252817	−	0.393392i
$328$	28.3428	+	13.3605i	1.56497	+	0.737712i
$329$	−14.2947	+	2.05527i	−0.788092	+	0.113311i
$330$	11.5400	−	1.71736i	0.635256	−	0.0945377i
$331$	−7.45887	−	11.6062i	−0.409977	−	0.637936i	0.573451	−	0.819240i	$-0.305604\pi$
$331$	−7.45887	−	11.6062i	−0.409977	−	0.637936i	−0.983427	+	0.181304i	$0.941968\pi$
$332$	−1.07427	−	1.38897i	−0.0589585	−	0.0762295i
$333$	−1.06828	+	2.33920i	−0.0585413	+	0.128187i
$334$	21.0512	+	22.2569i	1.15187	+	1.21785i
$335$	−13.2466	−	16.5370i	−0.723738	−	0.903513i
$336$	−8.07052	+	5.55296i	−0.440283	+	0.302939i
$337$	−33.5244	−	9.84364i	−1.82619	−	0.536217i	−0.826543	−	0.562873i	$-0.809696\pi$
$337$	−33.5244	−	9.84364i	−1.82619	−	0.536217i	−0.999645	+	0.0266558i	$0.991514\pi$
$338$	−1.77967	−	0.439352i	−0.0968013	−	0.0238976i
$339$	−5.56731	−	6.42502i	−0.302375	−	0.348959i
$340$	−15.1390	+	26.2762i	−0.821029	+	1.42503i
$341$	1.51991	+	1.31701i	0.0823075	+	0.0713199i
$342$	−1.26700	+	12.7259i	−0.0685113	+	0.688138i
$343$	13.0429	−	5.95651i	0.704253	−	0.321622i
$344$	5.51983	+	12.4844i	0.297609	+	0.673111i
$345$	−22.7208	−	5.25177i	−1.22325	−	0.282746i
$346$	4.48189	+	1.81529i	0.240948	+	0.0975905i
$347$	−6.05953	−	13.2685i	−0.325293	−	0.712291i	0.674367	−	0.738397i	$-0.264417\pi$
$347$	−6.05953	−	13.2685i	−0.325293	−	0.712291i	−0.999659	+	0.0261053i	$0.991689\pi$
$348$	19.2520	+	10.1225i	1.03202	+	0.542624i
$349$	13.9538	−	16.1036i	0.746931	−	0.862005i	−0.247336	−	0.968930i	$-0.579555\pi$
$349$	13.9538	−	16.1036i	0.746931	−	0.862005i	0.994267	+	0.106925i	$0.0341005\pi$
$350$	−6.19080	+	5.00935i	−0.330912	+	0.267761i
$351$	−7.89882	+	6.84436i	−0.421608	+	0.365325i
$352$	−2.00603	+	9.38554i	−0.106922	+	0.500251i
$353$	1.54332	−	5.25607i	0.0821426	−	0.279752i	−0.908171	−	0.418599i	$-0.862521\pi$
$353$	1.54332	−	5.25607i	0.0821426	−	0.279752i	0.990314	+	0.138847i	$0.0443395\pi$
$354$	−3.58201	+	0.675403i	−0.190382	+	0.0358973i
$355$	−6.78101	−	8.46540i	−0.359899	−	0.449297i
$356$	0.696509	+	1.78131i	0.0369149	+	0.0944092i
$357$	15.1064	+	6.89887i	0.799517	+	0.365127i
$358$	−16.2326	+	27.8555i	−0.857917	+	1.47221i
$359$	−13.9340	+	8.95482i	−0.735407	+	0.472617i	−0.853965	−	0.520330i	$-0.825809\pi$
$359$	−13.9340	+	8.95482i	−0.735407	+	0.472617i	0.118559	+	0.992947i	$0.462173\pi$
$360$	8.88684	+	6.37034i	0.468378	+	0.335747i
$361$	−1.18974	−	8.27482i	−0.0626178	−	0.435517i
$362$	−4.70194	−	13.7648i	−0.247128	−	0.723459i
$363$	14.8573	+	9.54821i	0.779807	+	0.501151i
$364$	−8.48431	+	0.741135i	−0.444699	+	0.0388461i
$365$	13.0014	−	25.7843i	0.680523	−	1.34961i
$366$	−0.626970	−	14.3821i	−0.0327722	−	0.751763i
$367$			10.6926i			0.558149i	0.960269	+	0.279075i	$0.0900277\pi$
$367$			10.6926i			0.558149i	−0.960269	+	0.279075i	$0.909972\pi$
$368$	10.6003	−	15.9885i	0.552579	−	0.833460i
$369$	−19.1526			−0.997045
$370$	−3.57001	−	3.06272i	−0.185596	−	0.159223i
$371$	−2.83251	−	9.64663i	−0.147056	−	0.500828i
$372$	0.448635	+	5.13584i	0.0232606	+	0.266281i
$373$	−23.5965	−	15.1646i	−1.22178	−	0.785191i	−0.239190	−	0.970973i	$-0.576882\pi$
$373$	−23.5965	−	15.1646i	−1.22178	−	0.785191i	−0.982591	+	0.185782i	$0.940518\pi$
$374$	15.3966	−	5.25937i	0.796140	−	0.271956i
$375$	20.7993	+	12.5895i	1.07407	+	0.650117i
$376$	−35.9597	+	4.72684i	−1.85448	+	0.243768i
$377$	10.2233	+	15.9077i	0.526526	+	0.819290i
$378$	−2.21669	+	3.80391i	−0.114014	+	0.195652i
$379$	8.49918	−	18.6106i	0.436574	−	0.955963i	−0.555641	−	0.831422i	$-0.687527\pi$
$379$	8.49918	−	18.6106i	0.436574	−	0.955963i	0.992215	−	0.124540i	$-0.0397456\pi$
$380$	−21.7245	−	8.67446i	−1.11444	−	0.444990i
$381$	−2.93001	+	20.3787i	−0.150109	+	1.04403i
$382$	−6.42937	−	34.0983i	−0.328955	−	1.74462i
$383$	−7.11785	+	24.2412i	−0.363705	+	1.23867i	0.550987	+	0.834514i	$0.314252\pi$
$383$	−7.11785	+	24.2412i	−0.363705	+	1.23867i	−0.914692	+	0.404152i	$0.867567\pi$
$384$	−20.4357	+	13.6995i	−1.04285	+	0.699099i
$385$	4.26945	+	0.165018i	0.217591	+	0.00841012i
$386$	12.6912	+	17.9753i	0.645965	+	0.914919i
$387$	−6.30564	−	5.46387i	−0.320534	−	0.277744i
$388$	15.3929	+	8.09344i	0.781456	+	0.410882i
$389$	−15.3930	+	7.02976i	−0.780458	+	0.356423i	−0.765476	−	0.643465i	$-0.777496\pi$
$389$	−15.3930	+	7.02976i	−0.780458	+	0.356423i	−0.0149818	+	0.999888i	$0.504769\pi$
$390$	10.9177	+	23.5977i	0.552841	+	1.19491i
$391$	−32.4864	−	1.48639i	−1.64291	−	0.0751699i
$392$	14.8269	−	6.55554i	0.748869	−	0.331105i
$393$	7.75428	−	3.54126i	0.391152	−	0.178633i
$394$	4.88622	+	0.486474i	0.246164	+	0.0245082i
$395$	8.87563	−	0.927914i	0.446581	−	0.0466884i
$396$	−1.33702	−	5.71201i	−0.0671879	−	0.287040i
$397$	−0.827903	+	0.717382i	−0.0415513	+	0.0360044i	−0.675389	−	0.737462i	$-0.736024\pi$
$397$	−0.827903	+	0.717382i	−0.0415513	+	0.0360044i	0.633838	+	0.773466i	$0.281479\pi$
$398$	15.9243	+	3.93127i	0.798212	+	0.197057i
$399$	−3.60910	+	12.2915i	−0.180681	+	0.615343i
$400$	−15.6988	+	12.3915i	−0.784938	+	0.619574i
$401$	32.3163	+	4.64639i	1.61380	+	0.232029i	0.889327	−	0.457273i	$-0.151174\pi$
$401$	32.3163	+	4.64639i	1.61380	+	0.232029i	0.724474	+	0.689302i	$0.242083\pi$
$402$	−21.1713	+	20.0244i	−1.05593	+	0.998724i
$403$	−1.86186	+	4.07691i	−0.0927459	+	0.203085i
$404$	−10.7297	+	8.29870i	−0.533821	+	0.412876i
$405$	24.6277	+	4.51792i	1.22376	+	0.224497i
$406$	6.24139	+	4.94916i	0.309755	+	0.245623i
$407$	0.359152	+	2.49796i	0.0178025	+	0.123819i
$408$	37.7261	+	17.7837i	1.86772	+	0.880426i
$409$	15.7342	+	10.1118i	0.778008	+	0.499996i	0.868372	−	0.495913i	$-0.165167\pi$
$409$	15.7342	+	10.1118i	0.778008	+	0.499996i	−0.0903637	+	0.995909i	$0.528803\pi$
$410$	9.70379	−	33.6617i	0.479236	−	1.66243i
$411$	−5.66185	+	1.66247i	−0.279278	+	0.0820035i
$412$	19.8407	+	7.04667i	0.977482	+	0.347165i
$413$	−1.33490			−0.0656859
$414$	−1.69375	+	11.6027i	−0.0832435	+	0.570240i
$415$	−1.34196	+	1.43292i	−0.0658743	+	0.0703393i
$416$	−21.3286	+	1.60333i	−1.04572	+	0.0786096i
$417$	8.69144	+	29.6003i	0.425622	+	1.44953i
$418$	5.70587	+	11.1783i	0.279083	+	0.546750i
$419$	−24.7767	−	15.9230i	−1.21042	−	0.777890i	−0.229692	−	0.973263i	$-0.573772\pi$
$419$	−24.7767	−	15.9230i	−1.21042	−	0.777890i	−0.980729	+	0.195373i	$0.937408\pi$
$420$	7.56534	+	7.92000i	0.369151	+	0.386457i
$421$	−22.0729	+	3.17361i	−1.07577	+	0.154672i	−0.657353	−	0.753583i	$-0.728324\pi$
$421$	−22.0729	+	3.17361i	−1.07577	+	0.154672i	−0.418417	+	0.908255i	$0.637415\pi$
$422$	6.07098	+	4.81403i	0.295531	+	0.234343i
$423$	18.6499	−	11.9856i	0.906788	−	0.582758i
$424$	−6.81992	−	24.3110i	−0.331204	−	1.18065i
$425$	31.6971	+	12.0346i	1.53753	+	0.583763i
$426$	−10.8377	+	10.2506i	−0.525089	+	0.496643i
$427$	0.750270	−	5.21824i	0.0363081	−	0.252529i
$428$	−4.36199	+	21.6891i	−0.210845	+	1.04838i
$429$	3.93015	−	13.3849i	0.189750	−	0.646228i
$430$	12.7978	−	8.31417i	0.617165	−	0.400945i
$431$	−20.2790	−	23.4032i	−0.976805	−	1.12729i	−0.991851	−	0.127406i	$-0.959335\pi$
$431$	−20.2790	−	23.4032i	−0.976805	−	1.12729i	0.0150456	−	0.999887i	$-0.495211\pi$
$432$	−5.68223	+	9.48513i	−0.273386	+	0.456353i
$433$	26.4351	−	30.5077i	1.27039	−	1.46611i	0.451373	−	0.892335i	$-0.350934\pi$
$433$	26.4351	−	30.5077i	1.27039	−	1.46611i	0.819016	−	0.573771i	$-0.194520\pi$
$434$	−0.187043	+	1.87869i	−0.00897835	+	0.0901799i
$435$	7.74734	−	23.0513i	0.371456	−	1.10522i
$436$	5.41213	−	5.58516i	0.259194	−	0.267480i
$437$	−2.43140	−	24.9673i	−0.116310	−	1.19435i
$438$	−36.8104	−	14.9092i	−1.75887	−	0.712390i
$439$	32.1599	−	14.6870i	1.53491	−	0.700970i	0.544453	−	0.838791i	$-0.316737\pi$
$439$	32.1599	−	14.6870i	1.53491	−	0.700970i	0.990457	+	0.137821i	$0.0440100\pi$
$440$	10.7166	+	0.544146i	0.510892	+	0.0259411i
$441$	−6.48908	+	7.48880i	−0.309004	+	0.356610i
$442$	20.9130	+	29.6204i	0.994731	+	1.40890i
$443$	−15.0686	−	17.3901i	−0.715932	−	0.826230i	0.274880	−	0.961479i	$-0.411362\pi$
$443$	−15.0686	−	17.3901i	−0.715932	−	0.826230i	−0.990812	+	0.135249i	$0.956817\pi$
$444$	−3.79491	+	5.23923i	−0.180098	+	0.248643i
$445$	1.84224	−	1.08576i	0.0873306	−	0.0514701i
$446$	5.12415	+	27.1760i	0.242635	+	1.28682i
$447$	−0.571280	−	0.0821376i	−0.0270206	−	0.00388498i
$448$	−8.28381	+	3.54339i	−0.391373	+	0.167410i
$449$	−2.55555	+	5.59588i	−0.120604	+	0.264086i	−0.960299	−	0.278972i	$-0.910006\pi$
$449$	−2.55555	+	5.59588i	−0.120604	+	0.264086i	0.839695	+	0.543058i	$0.182734\pi$
$450$	5.45014	−	10.9427i	0.256922	−	0.515843i
$451$	−15.8118	+	10.1616i	−0.744549	+	0.478492i
$452$	−3.85472	−	6.80273i	−0.181311	−	0.319974i
$453$	−16.3221	+	2.34677i	−0.766880	+	0.110261i
$454$	−4.25343	−	12.4517i	−0.199623	−	0.584389i
$455$	2.32776	+	9.23296i	0.109127	+	0.432848i
$456$	−9.43681	+	30.7570i	−0.441919	+	1.44033i
$457$	6.48598	−	1.90446i	0.303402	−	0.0890867i	−0.126488	−	0.991968i	$-0.540371\pi$
$457$	6.48598	−	1.90446i	0.303402	−	0.0890867i	0.429890	+	0.902881i	$0.358552\pi$
$458$	1.52548	+	34.9931i	0.0712811	+	1.63512i
$459$	18.7441			0.874901
$460$	−19.5341	−	8.85542i	−0.910783	−	0.412886i
$461$	−7.94891			−0.370217			−0.185109	−	0.982718i	$-0.559264\pi$
$461$	−7.94891			−0.370217			−0.185109	+	0.982718i	$0.559264\pi$
$462$	−0.255927	−	5.87072i	−0.0119068	−	0.273131i
$463$	20.7730	−	6.09949i	0.965401	−	0.283467i	0.239216	−	0.970966i	$-0.423110\pi$
$463$	20.7730	−	6.09949i	0.965401	−	0.283467i	0.726185	+	0.687499i	$0.241291\pi$
$464$	15.5232	+	12.6181i	0.720645	+	0.585783i
$465$	5.58903	−	1.40907i	0.259185	−	0.0653442i
$466$	−10.0839	−	29.5203i	−0.467129	−	1.36750i
$467$	−40.2781	+	5.79111i	−1.86385	+	0.267981i	−0.979883	−	0.199574i	$-0.936044\pi$
$467$	−40.2781	+	5.79111i	−1.86385	+	0.267981i	−0.883964	+	0.467554i	$0.845135\pi$
$468$	11.3745	−	6.44529i	0.525787	−	0.297934i
$469$	−8.97770	+	5.76962i	−0.414552	+	0.266416i
$470$	11.6161	+	38.8506i	0.535812	+	1.79205i
$471$	9.86202	−	21.5948i	0.454418	−	0.995036i
$472$	−3.35223	−	0.0405670i	−0.154299	−	0.00186725i
$473$	−8.10466	−	1.16527i	−0.372653	−	0.0535794i
$474$	−2.27414	−	12.0609i	−0.104455	−	0.553978i
$475$	−5.70905	+	25.5226i	−0.261949	+	1.17106i
$476$	12.3698	+	8.95978i	0.566970	+	0.410671i
$477$	10.1068	+	11.6639i	0.462759	+	0.534052i
$478$	−16.4573	−	23.3095i	−0.752740	−	1.06615i
$479$	3.94462	−	4.55234i	0.180234	−	0.208002i	−0.658442	−	0.752631i	$-0.728784\pi$
$479$	3.94462	−	4.55234i	0.180234	−	0.208002i	0.838677	+	0.544630i	$0.183330\pi$
$480$	18.7576	+	20.1188i	0.856164	+	0.918296i
$481$	−5.11588	+	2.33634i	−0.233264	+	0.106528i
$482$	19.2436	+	7.79419i	0.876522	+	0.355016i
$483$	−3.82070	+	11.1066i	−0.173848	+	0.505369i
$484$	11.6648	+	11.3034i	0.530217	+	0.513791i
$485$	6.19437	−	18.4306i	0.281272	−	0.836890i
$486$	2.24978	−	22.5971i	0.102052	−	1.02503i
$487$	24.5892	−	28.3775i	1.11424	−	1.28591i	0.159920	−	0.987130i	$-0.448876\pi$
$487$	24.5892	−	28.3775i	1.11424	−	1.28591i	0.954323	−	0.298775i	$-0.0965781\pi$
$488$	2.04268	−	13.0814i	0.0924678	−	0.592168i
$489$	15.0043	+	17.3159i	0.678520	+	0.783053i
$490$	−9.87420	−	15.1991i	−0.446071	−	0.686627i
$491$	9.65982	−	32.8983i	0.435942	−	1.48468i	−0.389942	−	0.920840i	$-0.627505\pi$
$491$	9.65982	−	32.8983i	0.435942	−	1.48468i	0.825883	−	0.563841i	$-0.190677\pi$
$492$	−47.2354	−	9.49973i	−2.12954	−	0.428281i
$493$	4.82628	−	33.5675i	0.217365	−	1.51180i
$494$	−20.3201	+	19.2193i	−0.914243	+	0.864716i
$495$	−6.06691	+	2.49218i	−0.272687	+	0.112015i
$496$	−0.526800	+	4.71213i	−0.0236540	+	0.211581i
$497$	−4.59574	+	2.95350i	−0.206147	+	0.132483i
$498$	2.11563	+	1.67760i	0.0948035	+	0.0751752i
$499$	−17.9773	+	2.58474i	−0.804773	+	0.115709i	−0.532411	−	0.846486i	$-0.678714\pi$
$499$	−17.9773	+	2.58474i	−0.804773	+	0.115709i	−0.272362	+	0.962195i	$0.587805\pi$
$500$	16.4710	+	15.1231i	0.736604	+	0.676324i
$501$	−39.6290	−	25.4680i	−1.77049	−	1.13783i
$502$	−5.41683	−	10.6121i	−0.241765	−	0.473640i
$503$	7.06139	+	24.0489i	0.314852	+	1.07229i	0.953150	+	0.302498i	$0.0978205\pi$
$503$	7.06139	+	24.0489i	0.314852	+	1.07229i	−0.638298	+	0.769789i	$0.720361\pi$
$504$	3.65654	−	4.11811i	0.162875	−	0.183435i
$505$	11.0692	+	10.3666i	0.492573	+	0.461306i
$506$	4.75761	+	10.4774i	0.211502	+	0.465779i
$507$	2.81870			0.125183
$508$	−6.33726	+	17.8433i	−0.281171	+	0.791667i
$509$	32.6350	−	9.58251i	1.44652	−	0.424737i	0.538132	−	0.842861i	$-0.319130\pi$
$509$	32.6350	−	9.58251i	1.44652	−	0.424737i	0.908390	+	0.418124i	$0.137312\pi$
$510$	12.9164	−	44.8058i	0.571946	−	1.98404i
$511$	−12.2354	−	7.86318i	−0.541260	−	0.347847i
$512$	−20.9102	+	8.64653i	−0.924110	+	0.382126i
$513$	2.05770	+	14.3116i	0.0908495	+	0.631872i
$514$	0.504470	+	0.400023i	0.0222512	+	0.0176443i
$515$	4.24752	−	23.1537i	0.187168	−	1.02028i
$516$	−12.8413	−	16.6030i	−0.565307	−	0.730905i
$517$	9.03770	−	19.7898i	0.397478	−	0.870354i
$518$	−1.72119	+	1.62795i	−0.0756247	+	0.0715278i
$519$	−7.35980	−	1.05818i	−0.323060	−	0.0464490i
$520$	5.56495	+	23.2568i	0.244039	+	1.01988i
$521$	9.98272	−	33.9980i	0.437351	−	1.48948i	−0.386294	−	0.922376i	$-0.626245\pi$
$521$	9.98272	−	33.9980i	0.437351	−	1.48948i	0.823645	−	0.567105i	$-0.191937\pi$
$522$	−11.8713	−	2.93069i	−0.519591	−	0.128273i
$523$	27.7265	−	24.0251i	1.21239	−	1.05055i	0.215133	−	0.976585i	$-0.430981\pi$
$523$	27.7265	−	24.0251i	1.21239	−	1.05055i	0.997261	−	0.0739608i	$-0.0235640\pi$
$524$	7.63387	−	1.78687i	0.333487	−	0.0780600i
$525$	7.39578	−	9.75979i	0.322778	−	0.425952i
$526$	4.23136	+	0.421276i	0.184496	+	0.0183685i
$527$	7.31159	−	3.33909i	0.318498	−	0.145453i
$528$	−0.464283	−	14.7505i	−0.0202053	−	0.641934i
$529$	−1.18065	−	22.9697i	−0.0513324	−	0.998682i
$530$	−25.6205	+	11.8536i	−1.11288	+	0.514889i
$531$	1.86399	−	0.851257i	0.0808904	−	0.0369414i
$532$	−5.48307	+	10.4282i	−0.237721	+	0.452122i
$533$	−31.6562	−	27.4302i	−1.37118	−	1.18813i
$534$	−1.69627	−	2.40253i	−0.0734049	−	0.103968i
$535$	24.7162	+	0.955306i	1.06858	+	0.0413015i
$536$	−22.7204	+	14.2160i	−0.981372	+	0.614038i
$537$	13.9668	−	47.5665i	0.602711	−	2.05265i
$538$	−1.31535	−	6.97600i	−0.0567089	−	0.300757i
$539$	−1.38392	+	9.62537i	−0.0596096	+	0.414594i
$540$	11.4806	+	4.58415i	0.494047	+	0.197270i
$541$	−8.20861	+	17.9743i	−0.352916	+	0.772777i	0.647031	+	0.762464i	$0.276010\pi$
$541$	−8.20861	+	17.9743i	−0.352916	+	0.772777i	−0.999947	+	0.0103139i	$0.996717\pi$
$542$	2.80335	−	4.81063i	0.120414	−	0.206634i
$543$	12.0922	+	18.8158i	0.518926	+	0.807465i
$544$	30.7912	+	22.8760i	1.32016	+	0.980799i
$545$	−7.12784	−	4.97998i	−0.305323	−	0.213319i
$546$	12.3927	−	4.23324i	0.530357	−	0.181166i
$547$	0.521569	+	0.335192i	0.0223007	+	0.0143318i	0.551744	−	0.834014i	$-0.313963\pi$
$547$	0.521569	+	0.335192i	0.0223007	+	0.0143318i	−0.529443	+	0.848346i	$0.677599\pi$
$548$	−5.40652	+	0.472279i	−0.230955	+	0.0201748i
$549$	2.28000	+	7.76498i	0.0973082	+	0.331401i
$550$	−1.30630	−	11.9256i	−0.0557007	−	0.508508i
$551$	26.1594			1.11443
$552$	−9.93219	+	27.7752i	−0.422742	+	1.18219i
$553$		−	4.49471i		−	0.191134i
$554$	0.275886	+	6.32855i	0.0117213	+	0.268874i
$555$	6.45824	+	3.25648i	0.274137	+	0.138230i
$556$	2.46909	+	28.2655i	0.104713	+	1.19872i
$557$	−2.71535	−	1.74505i	−0.115053	−	0.0739402i	0.481849	−	0.876254i	$-0.339965\pi$
$557$	−2.71535	−	1.74505i	−0.115053	−	0.0739402i	−0.596902	+	0.802314i	$0.703602\pi$
$558$	−0.936852	−	2.74260i	−0.0396601	−	0.116103i
$559$	−2.59689	−	18.0618i	−0.109837	−	0.763932i
$560$	5.38517	+	8.51301i	0.227565	+	0.359740i
$561$	−21.0465	+	13.5258i	−0.888585	+	0.571059i
$562$	−12.5779	+	21.5841i	−0.530569	+	0.910471i
$563$	16.6851	+	7.61982i	0.703192	+	0.321137i	0.734725	−	0.678366i	$-0.237311\pi$
$563$	16.6851	+	7.61982i	0.703192	+	0.321137i	−0.0315321	+	0.999503i	$0.510039\pi$
$564$	51.9404	−	20.3092i	2.18709	−	0.855171i
$565$	−6.82283	+	5.46527i	−0.287039	+	0.229925i
$566$	−22.5503	+	4.25195i	−0.947860	+	0.178723i
$567$	3.55296	−	12.1003i	0.149210	−	0.508163i
$568$	−11.6307	+	7.27727i	−0.488014	+	0.305347i
$569$	−24.6176	+	21.3313i	−1.03203	+	0.894255i	−0.994468	−	0.105039i	$-0.966503\pi$
$569$	−24.6176	+	21.3313i	−1.03203	+	0.894255i	−0.0375574	+	0.999294i	$0.511958\pi$
$570$	35.6283	+	4.94326i	1.49230	+	0.207050i
$571$	−18.6016	+	21.4674i	−0.778452	+	0.898382i	−0.996997	−	0.0774450i	$-0.975324\pi$
$571$	−18.6016	+	21.4674i	−0.778452	+	0.898382i	0.218544	+	0.975827i	$0.429869\pi$
$572$	5.97082	−	11.3559i	0.249653	−	0.474814i
$573$	22.1648	+	48.5341i	0.925948	+	2.02754i
$574$	−16.3541	−	6.62386i	−0.682607	−	0.276474i
$575$	−6.29854	+	23.1372i	−0.262667	+	0.964886i
$576$	9.30756	−	10.2304i	0.387815	−	0.426266i
$577$	−36.5563	+	16.6947i	−1.52186	+	0.695009i	−0.988547	−	0.150911i	$-0.951779\pi$
$577$	−36.5563	+	16.6947i	−1.52186	+	0.695009i	−0.533310	+	0.845920i	$0.679052\pi$
$578$	4.06051	−	40.7843i	0.168895	−	1.69640i
$579$	−25.5707	−	22.1572i	−1.06268	−	0.920821i
$580$	11.1655	−	19.3795i	0.463622	−	0.804689i
$581$	0.647520	+	0.747278i	0.0268637	+	0.0310023i
$582$	−25.9621	−	6.40933i	−1.07616	−	0.265675i
$583$	14.5323	+	4.26706i	0.601865	+	0.176723i
$584$	−30.4868	−	20.1181i	−1.26155	−	0.832492i
$585$	−9.13820	−	11.4081i	−0.377818	−	0.471667i
$586$	−0.470143	−	0.497071i	−0.0194214	−	0.0205338i
$587$	−12.2272	+	26.7739i	−0.504672	+	1.10508i	0.470250	+	0.882533i	$0.344164\pi$
$587$	−12.2272	+	26.7739i	−0.504672	+	1.10508i	−0.974922	+	0.222545i	$0.928564\pi$
$588$	−19.7183	+	15.2508i	−0.813168	+	0.628932i
$589$	3.35213	+	5.21602i	0.138122	+	0.214922i
$590$	0.551722	+	3.70735i	0.0227140	+	0.152629i
$591$	−7.47368	+	1.07455i	−0.307426	+	0.0442012i
$592$	−4.37177	+	4.03584i	−0.179679	+	0.165872i
$593$	−6.92902	+	10.7818i	−0.284541	+	0.442754i	−0.953874	−	0.300209i	$-0.902944\pi$
$593$	−6.92902	+	10.7818i	−0.284541	+	0.442754i	0.669333	+	0.742963i	$0.266580\pi$
$594$	−3.01536	−	5.90736i	−0.123722	−	0.242382i
$595$	7.68855	−	15.2479i	0.315200	−	0.625103i
$596$	−0.500205	−	0.177654i	−0.0204892	−	0.00727699i
$597$	−25.2214			−1.03224
$598$	−19.4168	+	16.7516i	−0.794010	+	0.685022i
$599$			42.2588i			1.72665i	0.504651	+	0.863324i	$0.331621\pi$
$599$			42.2588i			1.72665i	−0.504651	+	0.863324i	$0.668379\pi$
$600$	18.8691	−	24.2843i	0.770327	−	0.991403i
$601$	10.6416	−	3.12464i	0.434078	−	0.127457i	−0.0573911	−	0.998352i	$-0.518278\pi$
$601$	10.6416	−	3.12464i	0.434078	−	0.127457i	0.491469	+	0.870895i	$0.336460\pi$
$602$	−3.49463	−	6.84629i	−0.142430	−	0.279034i
$603$	8.85683	−	13.7815i	0.360678	−	0.561226i
$604$	−15.1425	−	0.843813i	−0.616141	−	0.0343343i
$605$	10.4009	−	14.8867i	0.422855	−	0.605232i
$606$	12.9594	−	16.3431i	0.526438	−	0.663892i
$607$	−23.8135	+	15.3040i	−0.966562	+	0.621172i	−0.925807	−	0.377997i	$-0.876613\pi$
$607$	−23.8135	+	15.3040i	−0.966562	+	0.621172i	−0.0407555	+	0.999169i	$0.512976\pi$
$608$	−14.0862	+	26.0211i	−0.571269	+	1.05529i
$609$	−11.1414	−	5.08813i	−0.451474	−	0.206181i
$610$	−14.8025	+	0.0730437i	−0.599336	+	0.00295745i
$611$	47.9909	+	6.90004i	1.94150	+	0.279146i
$612$	−22.9863	−	4.62288i	−0.929167	−	0.186869i
$613$	9.67031	+	2.83946i	0.390580	+	0.114685i	0.471125	−	0.882066i	$-0.343848\pi$
$613$	9.67031	+	2.83946i	0.390580	+	0.114685i	−0.0805452	+	0.996751i	$0.525666\pi$
$614$	8.04804	+	1.98684i	0.324793	+	0.0801824i
$615$	−2.08051	+	53.8281i	−0.0838942	+	2.17056i
$616$	0.833817	−	5.33980i	0.0335955	−	0.215147i
$617$	−21.9569	+	25.3396i	−0.883951	+	1.02013i	0.115689	+	0.993286i	$0.463093\pi$
$617$	−21.9569	+	25.3396i	−0.883951	+	1.02013i	−0.999640	+	0.0268481i	$0.991453\pi$
$618$	−32.2162	−	3.20746i	−1.29593	−	0.129023i
$619$	−1.27497	−	2.79180i	−0.0512454	−	0.112212i	0.882277	−	0.470730i	$-0.156009\pi$
$619$	−1.27497	−	2.79180i	−0.0512454	−	0.112212i	−0.933523	+	0.358518i	$0.883282\pi$
$620$	5.29491	−	0.257009i	0.212649	−	0.0103217i
$621$	1.28491	+	13.1944i	0.0515617	+	0.529471i
$622$	−22.5412	−	9.12982i	−0.903822	−	0.366072i
$623$	−0.447416	−	0.979705i	−0.0179254	−	0.0392511i
$624$	31.2495	−	10.2540i	1.25098	−	0.410490i
$625$	13.7617	−	20.8714i	0.550469	−	0.834856i
$626$	1.30772	−	0.923298i	0.0522671	−	0.0369024i
$627$	−12.6377	−	14.5847i	−0.504702	−	0.582457i
$628$	12.8081	−	17.6828i	0.511099	−	0.705621i
$629$	9.67781	+	2.84166i	0.385880	+	0.113304i
$630$	−5.19615	−	3.30324i	−0.207019	−	0.131604i
$631$	−1.31466	+	9.14366i	−0.0523358	+	0.364003i	0.946777	+	0.321890i	$0.104318\pi$
$631$	−1.31466	+	9.14366i	−0.0523358	+	0.364003i	−0.999113	+	0.0421133i	$0.986591\pi$
$632$	0.136592	−	11.2872i	0.00543336	−	0.448982i
$633$	−10.8372	−	4.94920i	−0.430742	−	0.196713i
$634$	19.9528	−	34.2396i	0.792427	−	1.35983i
$635$	20.8228	+	3.81991i	0.826326	+	0.151588i
$636$	19.1408	+	33.7792i	0.758981	+	1.33943i
$637$	−21.4508	+	3.08416i	−0.849912	+	0.122199i
$638$	−11.3555	+	3.87894i	−0.449567	+	0.153569i
$639$	4.53387	−	7.05484i	0.179357	−	0.279085i
$640$	13.2647	+	21.5418i	0.524333	+	0.851513i
$641$	0.710923	+	2.42118i	0.0280798	+	0.0956309i	0.972341	−	0.233567i	$-0.0750398\pi$
$641$	0.710923	+	2.42118i	0.0280798	+	0.0956309i	−0.944261	+	0.329198i	$0.893222\pi$
$642$	−1.48159	−	33.9861i	−0.0584736	−	1.34133i
$643$		−	21.5254i		−	0.848880i	−0.905456	−	0.424440i	$-0.860471\pi$
$643$		−	21.5254i		−	0.848880i	0.905456	−	0.424440i	$-0.139529\pi$
$644$	−5.45901	+	9.32155i	−0.215115	+	0.367321i
$645$	−16.0411	+	17.1284i	−0.631617	+	0.674429i
$646$	50.1131	−	2.18462i	1.97167	−	0.0859528i
$647$	17.4350	−	5.11938i	0.685440	−	0.201263i	0.0795728	−	0.996829i	$-0.474644\pi$
$647$	17.4350	−	5.11938i	0.685440	−	0.201263i	0.605867	+	0.795566i	$0.292826\pi$
$648$	9.29001	−	30.2785i	0.364946	−	1.18945i
$649$	1.08721	−	1.69173i	0.0426767	−	0.0664063i
$650$	24.6802	−	10.2808i	0.968039	−	0.403248i
$651$	−0.413152	−	2.87353i	−0.0161927	−	0.112623i
$652$	10.3888	+	18.3339i	0.406856	+	0.718010i
$653$	19.9346	+	31.0188i	0.780101	+	1.21386i	0.972582	+	0.232560i	$0.0747101\pi$
$653$	19.9346	+	31.0188i	0.780101	+	1.21386i	−0.192482	+	0.981301i	$0.561654\pi$
$654$	−6.02112	+	10.3324i	−0.235444	+	0.404029i
$655$	−3.33070	−	8.10818i	−0.130141	−	0.316813i
$656$	−40.8676	−	17.1310i	−1.59561	−	0.668854i
$657$	22.0993	+	3.17739i	0.862174	+	0.123962i
$658$	20.0700	−	3.78428i	0.782409	−	0.147526i
$659$	−39.1396	−	11.4924i	−1.52466	−	0.447682i	−0.591251	−	0.806487i	$-0.701366\pi$
$659$	−39.1396	−	11.4924i	−1.52466	−	0.447682i	−0.933412	+	0.358806i	$0.883184\pi$
$660$	−16.1988	+	3.13719i	−0.630536	+	0.122115i
$661$	−20.9886	+	18.1867i	−0.816361	+	0.707381i	−0.959312	−	0.282349i	$-0.908886\pi$
$661$	−20.9886	+	18.1867i	−0.816361	+	0.707381i	0.142951	+	0.989730i	$0.454341\pi$
$662$	11.2533	+	15.9387i	0.437371	+	0.619475i
$663$	−42.1364	−	36.5114i	−1.63644	−	1.41799i
$664$	1.60336	+	1.89627i	0.0622225	+	0.0735894i
$665$	12.4862	+	4.19650i	0.484193	+	0.162733i
$666$	1.36526	−	3.37079i	0.0529028	−	0.130615i
$667$	23.9597	+	1.09626i	0.927722	+	0.0424472i
$668$	−31.1135	−	30.1496i	−1.20382	−	1.16652i
$669$	−17.6651	−	38.6813i	−0.682974	−	1.49550i
$670$	19.7343	+	22.5488i	0.762402	+	0.871136i
$671$	6.00210	+	5.20085i	0.231708	+	0.200776i
$672$	11.0606	−	8.34270i	0.426671	−	0.321827i
$673$	−9.87929	+	8.56045i	−0.380819	+	0.329981i	−0.824145	−	0.566379i	$-0.808344\pi$
$673$	−9.87929	+	8.56045i	−0.380819	+	0.329981i	0.443326	+	0.896360i	$0.353798\pi$
$674$	47.9719	+	11.8429i	1.84781	+	0.456173i
$675$	3.01703	−	13.4878i	0.116126	−	0.519147i
$676$	2.54151	+	0.511134i	0.0977503	+	0.0196590i
$677$	1.61140	−	11.2075i	0.0619312	−	0.430741i	−0.935141	−	0.354276i	$-0.884727\pi$
$677$	1.61140	−	11.2075i	0.0619312	−	0.430741i	0.997072	−	0.0764653i	$-0.0243635\pi$
$678$	8.26163	+	8.73483i	0.317286	+	0.335459i
$679$	−8.90812	−	4.06820i	−0.341862	−	0.156123i
$680$	19.7711	−	38.0574i	0.758187	−	1.45943i
$681$	10.9387	+	17.0210i	0.419173	+	0.652247i
$682$	−2.22855	−	1.76715i	−0.0853356	−	0.0676675i
$683$	2.15008	+	14.9541i	0.0822706	+	0.572204i	0.988707	+	0.149862i	$0.0478829\pi$
$683$	2.15008	+	14.9541i	0.0822706	+	0.572204i	−0.906436	+	0.422342i	$0.861208\pi$
$684$	1.00628	−	18.0581i	0.0384762	−	0.690469i
$685$	1.48334	+	5.88359i	0.0566753	+	0.224800i
$686$	−18.0611	+	9.21914i	−0.689577	+	0.351988i
$687$	−15.1738	−	51.6772i	−0.578916	−	1.97161i
$688$	−8.56775	−	17.2988i	−0.326643	−	0.659511i
$689$			33.7534i			1.28590i
$690$	32.4251	+	6.02064i	1.23440	+	0.229202i
$691$		−	20.1826i		−	0.767784i	−0.923378	−	0.383892i	$-0.874583\pi$
$691$		−	20.1826i		−	0.767784i	0.923378	−	0.383892i	$-0.125417\pi$
$692$	−6.44414	−	2.28872i	−0.244970	−	0.0870040i
$693$	0.930692	+	3.16965i	0.0353541	+	0.120405i
$694$	9.37858	+	18.3735i	0.356006	+	0.697448i
$695$	30.7596	−	7.75493i	1.16678	−	0.294161i
$696$	−27.8241	−	13.1160i	−1.05467	−	0.497162i
$697$	10.6908	+	74.3564i	0.404944	+	2.81645i
$698$	−18.7231	+	23.6117i	−0.708680	+	0.893717i
$699$	25.9333	+	40.3531i	0.980889	+	1.52629i
$700$	8.43827	−	7.45887i	0.318937	−	0.281919i
$701$	7.38760	+	3.37381i	0.279026	+	0.127427i	0.550013	−	0.835156i	$-0.314623\pi$
$701$	7.38760	+	3.37381i	0.279026	+	0.127427i	−0.270987	+	0.962583i	$0.587350\pi$
$702$	10.7385	−	10.1567i	0.405297	−	0.383341i
$703$	−1.10726	+	7.70120i	−0.0417613	+	0.290456i
$704$	2.25618	−	13.3841i	0.0850330	−	0.504433i
$705$	−31.6593	−	53.7171i	−1.19236	−	2.02310i
$706$	−1.85678	+	7.52120i	−0.0698808	+	0.283064i
$707$	5.77267	−	5.00205i	0.217104	−	0.188121i
$708$	5.01932	−	1.17488i	0.188638	−	0.0441548i
$709$	−15.6772	−	13.5844i	−0.588771	−	0.510173i	0.308751	−	0.951143i	$-0.400089\pi$
$709$	−15.6772	−	13.5844i	−0.588771	−	0.510173i	−0.897522	+	0.440970i	$0.854635\pi$
$710$	10.1021	+	11.5429i	0.379125	+	0.433196i
$711$	2.86625	+	6.27622i	0.107493	+	0.235377i
$712$	−1.09379	−	2.47386i	−0.0409916	−	0.0927119i
$713$	2.85166	+	4.91787i	0.106796	+	0.184176i
$714$	−21.7684	−	8.81678i	−0.814660	−	0.329960i
$715$	−13.5969	−	4.56981i	−0.508496	−	0.170901i
$716$	21.2188	−	40.3561i	0.792985	−	1.50818i
$717$	33.1589	+	28.7323i	1.23834	+	1.07303i
$718$	19.1354	−	13.5102i	0.714125	−	0.504197i
$719$	14.7353	−	12.7682i	0.549534	−	0.476174i	−0.335280	−	0.942119i	$-0.608831\pi$
$719$	14.7353	−	12.7682i	0.549534	−	0.476174i	0.884814	+	0.465944i	$0.154285\pi$
$720$	−12.9483	−	8.45311i	−0.482556	−	0.315029i
$721$	−11.3761	−	3.34031i	−0.423667	−	0.124400i
$722$	2.19062	+	11.6180i	0.0815263	+	0.432376i
$723$	−31.6003	−	4.54344i	−1.17523	−	0.168972i
$724$	7.49104	+	19.1582i	0.278402	+	0.712010i
$725$	−23.3775	−	8.87587i	−0.868220	−	0.329641i
$726$	−21.5796	−	12.5753i	−0.800893	−	0.466713i
$727$	−14.2205	−	22.1275i	−0.527408	−	0.820663i	0.470691	−	0.882298i	$-0.344005\pi$
$727$	−14.2205	−	22.1275i	−0.527408	−	0.820663i	−0.998099	+	0.0616353i	$0.980368\pi$
$728$	11.9416	−	1.56970i	0.442585	−	0.0581769i
$729$	0.188686	+	1.31234i	0.00698837	+	0.0486052i
$730$	−16.7811	+	37.2307i	−0.621098	+	1.37797i
$731$	−17.6927	+	27.5304i	−0.654388	+	1.01825i
$732$	1.77166	+	20.2814i	0.0654823	+	0.749622i
$733$	14.9196	−	4.38079i	0.551068	−	0.161808i	0.00566768	−	0.999984i	$-0.498196\pi$
$733$	14.9196	−	4.38079i	0.551068	−	0.161808i	0.545400	+	0.838176i	$0.316378\pi$
$734$	−0.658584	−	15.1073i	−0.0243088	−	0.557620i
$735$	20.3422	+	19.0509i	0.750335	+	0.702705i
$736$	−13.9921	+	23.2427i	−0.515756	+	0.856736i
$737$		−	16.0767i		−	0.592191i
$738$	27.0602	−	1.17966i	0.996099	−	0.0434238i
$739$	13.4979	+	45.9697i	0.496529	+	1.69102i	0.701847	+	0.712328i	$0.252359\pi$
$739$	13.4979	+	45.9697i	0.496529	+	1.69102i	−0.205318	+	0.978695i	$0.565823\pi$
$740$	5.23261	+	4.10735i	0.192355	+	0.150989i
$741$	23.2517	−	36.1803i	0.854172	−	1.32912i
$742$	4.59613	+	13.4550i	0.168729	+	0.493948i
$743$	−18.1420	+	2.60843i	−0.665565	+	0.0956938i	−0.466813	−	0.884356i	$-0.654598\pi$
$743$	−18.1420	+	2.60843i	−0.665565	+	0.0956938i	−0.198752	+	0.980050i	$0.563689\pi$
$744$	−0.950193	−	7.22866i	−0.0348358	−	0.265015i
$745$	−0.107084	+	0.583729i	−0.00392327	+	0.0213862i
$746$	34.2729	+	19.9722i	1.25482	+	0.731234i
$747$	−1.38071	−	0.630547i	−0.0505174	−	0.0230705i
$748$	−21.4295	+	8.37913i	−0.783540	+	0.306371i
$749$	1.77296	−	12.3312i	0.0647824	−	0.450572i
$750$	−30.1622	−	16.5062i	−1.10137	−	0.602721i
$751$	37.4780	+	11.0045i	1.36759	+	0.401561i	0.881433	−	0.472310i	$-0.156580\pi$
$751$	37.4780	+	11.0045i	1.36759	+	0.401561i	0.486159	+	0.873871i	$0.338398\pi$
$752$	50.5153	−	8.89326i	1.84211	−	0.324304i
$753$	11.9975	+	13.8459i	0.437214	+	0.504572i
$754$	−15.4240	−	21.8459i	−0.561708	−	0.795581i
$755$	1.76309	+	16.8642i	0.0641655	+	0.613752i
$756$	2.89761	−	5.51097i	0.105385	−	0.200432i
$757$	−10.3147	−	22.5860i	−0.374894	−	0.820903i	−0.999210	−	0.0397313i	$-0.987350\pi$
$757$	−10.3147	−	22.5860i	−0.374894	−	0.820903i	0.624317	−	0.781171i	$-0.285377\pi$
$758$	−10.8620	+	26.8179i	−0.394525	+	0.974070i
$759$	−10.9638	−	13.8879i	−0.397961	−	0.504098i
$760$	31.2281	+	10.9178i	1.13276	+	0.396032i
$761$	−5.40064	−	11.8258i	−0.195773	−	0.428683i	0.786132	−	0.618059i	$-0.212081\pi$
$761$	−5.40064	−	11.8258i	−0.195773	−	0.428683i	−0.981905	+	0.189376i	$0.939354\pi$
$762$	2.88455	−	28.9729i	0.104496	−	1.04958i
$763$	−2.86794	+	3.30978i	−0.103826	+	0.119822i
$764$	11.1841	+	47.7805i	0.404625	+	1.72864i
$765$	−1.01244	+	26.1945i	−0.0366050	+	0.947064i
$766$	8.56354	−	34.6881i	0.309413	−	1.25333i
$767$	4.30004	+	1.26261i	0.155265	+	0.0455900i
$768$	28.0292	−	20.6143i	1.01142	−	0.743855i
$769$	0.846137	+	0.121656i	0.0305125	+	0.00438703i	0.157554	−	0.987510i	$-0.449639\pi$
$769$	0.846137	+	0.121656i	0.0305125	+	0.00438703i	−0.127042	+	0.991897i	$0.540548\pi$
$770$	−6.04235	+	0.0298163i	−0.217751	+	0.00107450i
$771$	−0.900524	−	0.411256i	−0.0324316	−	0.0148110i
$772$	−19.0382	−	24.6151i	−0.685199	−	0.885917i
$773$	35.6191	−	22.8910i	1.28113	−	0.823331i	0.290102	−	0.956996i	$-0.406311\pi$
$773$	35.6191	−	22.8910i	1.28113	−	0.823331i	0.991027	+	0.133664i	$0.0426744\pi$
$774$	9.24560	+	7.33137i	0.332326	+	0.263521i
$775$	−1.22586	−	5.79870i	−0.0440343	−	0.208295i
$776$	−22.2467	−	10.4869i	−0.798610	−	0.376458i
$777$	1.96951	−	3.06461i	0.0706557	−	0.109942i
$778$	21.3154	−	10.8802i	0.764194	−	0.390076i
$779$	−55.5993	+	16.3254i	−1.99205	+	0.584919i
$780$	−16.8788	−	32.6680i	−0.604358	−	1.16970i
$781$		−	8.22974i		−	0.294483i
$782$	45.9906	+	0.0991598i	1.64462	+	0.00354595i
$783$	−13.8244			−0.494042
$784$	−20.5447	+	10.1754i	−0.733738	+	0.363406i
$785$	−21.7971	−	10.9909i	−0.777971	−	0.392281i
$786$	−10.7377	+	5.48095i	−0.383001	+	0.195499i
$787$	−22.9420	+	35.6984i	−0.817792	+	1.27251i	0.141456	+	0.989945i	$0.454822\pi$
$787$	−22.9420	+	35.6984i	−0.817792	+	1.27251i	−0.959248	+	0.282565i	$0.908815\pi$
$788$	−6.93357	−	0.386371i	−0.246998	−	0.0137639i
$789$	−6.47204	+	0.930539i	−0.230411	+	0.0331281i
$790$	−12.4830	+	1.85770i	−0.444124	+	0.0660939i
$791$	2.38042	+	3.70401i	0.0846382	+	0.131700i
$792$	2.24086	+	7.98799i	0.0796254	+	0.283841i
$793$	−7.35247	+	16.0997i	−0.261094	+	0.571716i
$794$	1.12554	−	1.06456i	0.0399438	−	0.0377799i
$795$	33.8790	−	27.1380i	1.20156	−	0.962485i
$796$	−22.7411	−	4.57356i	−0.806037	−	0.162106i
$797$	−36.8877	−	10.8312i	−1.30663	−	0.383661i	−0.446980	−	0.894544i	$-0.647501\pi$
$797$	−36.8877	−	10.8312i	−1.30663	−	0.383661i	−0.859651	+	0.510882i	$0.829319\pi$
$798$	4.34213	−	17.5886i	0.153710	−	0.622628i
$799$	−56.9419	−	65.7144i	−2.01446	−	2.32481i
$800$	21.4171	−	18.4745i	0.757209	−	0.653172i
$801$	1.24951	+	1.08270i	0.0441492	+	0.0382555i
$802$	−45.9450	−	4.57430i	−1.62237	−	0.161524i
$803$	19.9303	−	9.10184i	0.703323	−	0.321197i
$804$	28.6789	−	29.5958i	1.01143	−	1.04376i
$805$	11.2604	+	4.36687i	0.396875	+	0.153912i
$806$	2.37946	−	5.87482i	0.0838130	−	0.206932i
$807$	4.53459	+	9.92936i	0.159625	+	0.349530i
$808$	14.6485	−	12.3859i	0.515333	−	0.435733i
$809$	8.59383	−	9.91781i	0.302143	−	0.348692i	−0.584293	−	0.811543i	$-0.698628\pi$
$809$	8.59383	−	9.91781i	0.302143	−	0.348692i	0.886436	+	0.462851i	$0.153174\pi$
$810$	−35.0740	−	4.86636i	−1.23238	−	0.170986i
$811$	26.9082	−	23.3161i	0.944875	−	0.818739i	−0.0386977	−	0.999251i	$-0.512321\pi$
$811$	26.9082	−	23.3161i	0.944875	−	0.818739i	0.983573	+	0.180512i	$0.0577755\pi$
$812$	−9.12311	−	6.60810i	−0.320159	−	0.231899i
$813$	−2.41206	+	8.21471i	−0.0845946	+	0.288103i
$814$	−0.661291	−	3.50717i	−0.0231783	−	0.122926i
$815$	18.3880	−	14.7293i	0.644105	−	0.515945i
$816$	−54.3974	−	22.8025i	−1.90429	−	0.798247i
$817$	−22.9624	−	10.4866i	−0.803352	−	0.366878i
$818$	−22.8533	−	13.3175i	−0.799046	−	0.465637i
$819$	−6.19330	+	3.98019i	−0.216411	+	0.139079i
$820$	−11.6369	+	48.1573i	−0.406378	+	1.68172i
$821$	2.83790	+	19.7381i	0.0990435	+	0.688863i	0.977484	+	0.211011i	$0.0676755\pi$
$821$	2.83790	+	19.7381i	0.0990435	+	0.688863i	−0.878440	+	0.477852i	$0.841415\pi$
$822$	7.89707	−	2.69758i	0.275442	−	0.0940889i
$823$	8.50177	+	5.46376i	0.296353	+	0.190455i	0.680365	−	0.732874i	$-0.261821\pi$
$823$	8.50177	+	5.46376i	0.296353	+	0.190455i	−0.384012	+	0.923328i	$0.625458\pi$
$824$	−28.4664	−	8.73401i	−0.991674	−	0.304264i
$825$	6.34520	+	17.3217i	0.220912	+	0.603063i
$826$	1.88604	−	0.0822195i	0.0656236	−	0.00286078i
$827$			42.2703i			1.46988i	0.678130	+	0.734942i	$0.262791\pi$
$827$			42.2703i			1.46988i	−0.678130	+	0.734942i	$0.737209\pi$
$828$	1.67842	−	16.4974i	0.0583291	−	0.573325i
$829$	−14.2240			−0.494020			−0.247010	−	0.969013i	$-0.579448\pi$
$829$	−14.2240			−0.494020			−0.247010	+	0.969013i	$0.579448\pi$
$830$	1.80776	−	2.10719i	0.0627483	−	0.0731416i
$831$	−2.74421	−	9.34591i	−0.0951954	−	0.324206i
$832$	30.0358	−	3.57897i	1.04130	−	0.124079i
$833$	32.6960	+	21.0124i	1.13285	+	0.728038i
$834$	−14.1030	−	41.2861i	−0.488349	−	1.42962i
$835$	−27.7422	+	39.7074i	−0.960060	+	1.37413i
$836$	−8.75016	−	15.4421i	−0.302631	−	0.534076i
$837$	−1.77148	−	2.75648i	−0.0612315	−	0.0952780i
$838$	35.9870	+	20.9711i	1.24315	+	0.724435i
$839$	−16.1366	+	35.3342i	−0.557097	+	1.21987i	0.396291	+	0.918125i	$0.370297\pi$
$839$	−16.1366	+	35.3342i	−0.557097	+	1.21987i	−0.953388	+	0.301748i	$0.902430\pi$
$840$	−11.1767	−	10.7240i	−0.385632	−	0.370012i
$841$	0.567604	−	3.94777i	0.0195726	−	0.136130i
$842$	30.9908	−	5.84343i	1.06801	−	0.201378i
$843$	10.8223	−	36.8574i	0.372740	−	1.26944i
$844$	−8.87402	−	6.42768i	−0.305456	−	0.221250i
$845$	0.111942	−	2.89622i	0.00385092	−	0.0996331i
$846$	−25.6117	+	18.0827i	−0.880548	+	0.621698i
$847$	−6.91258	−	5.98978i	−0.237519	−	0.205811i
$848$	11.1330	+	33.9283i	0.382310	+	1.16510i
$849$	32.0972	−	14.6583i	1.10157	−	0.503072i
$850$	−45.5252	−	15.0510i	−1.56150	−	0.516246i
$851$	−1.33689	+	7.00720i	−0.0458279	+	0.240204i
$852$	14.6809	−	15.1503i	0.502961	−	0.519041i
$853$	−11.0662	+	5.05376i	−0.378899	+	0.173038i	−0.595755	−	0.803166i	$-0.703147\pi$
$853$	−11.0662	+	5.05376i	−0.378899	+	0.173038i	0.216856	+	0.976204i	$0.430420\pi$
$854$	−0.738631	+	7.41892i	−0.0252754	+	0.253870i
$855$	−20.1113	+	2.10256i	−0.687791	+	0.0719061i
$856$	4.82704	−	30.9126i	0.164985	−	1.05657i
$857$	15.4038	−	13.3475i	0.526185	−	0.455942i	−0.350806	−	0.936448i	$-0.614092\pi$
$857$	15.4038	−	13.3475i	0.526185	−	0.455942i	0.876991	+	0.480506i	$0.159547\pi$
$858$	−4.72839	+	19.1532i	−0.161425	+	0.653879i
$859$	−5.06492	+	17.2495i	−0.172813	+	0.588547i	0.826846	+	0.562428i	$0.190133\pi$
$859$	−5.06492	+	17.2495i	−0.172813	+	0.588547i	−0.999659	+	0.0261181i	$0.991685\pi$
$860$	−17.5696	+	12.5351i	−0.599118	+	0.427444i
$861$	26.8554	+	3.86122i	0.915230	+	0.131590i
$862$	30.0931	+	31.8167i	1.02497	+	1.08368i
$863$	−7.65512	+	16.7624i	−0.260583	+	0.570598i	−0.994025	−	0.109155i	$-0.965186\pi$
$863$	−7.65512	+	16.7624i	−0.260583	+	0.570598i	0.733441	+	0.679753i	$0.237913\pi$
$864$	7.44404	−	13.7512i	0.253252	−	0.467827i
$865$	−1.37957	+	7.52019i	−0.0469068	+	0.255694i
$866$	−35.4703	+	44.7317i	−1.20533	+	1.52004i
$867$	8.96909	+	62.3814i	0.304606	+	2.11858i
$868$	0.148555	−	2.66587i	0.00504227	−	0.0904854i
$869$	5.69621	+	3.66073i	0.193231	+	0.124182i
$870$	−9.52621	+	33.0456i	−0.322969	+	1.12035i
$871$	34.3766	−	10.0939i	1.16481	−	0.342019i
$872$	−7.30264	+	8.22446i	−0.247298	+	0.278515i
$873$	15.0332			0.508797
$874$	4.97306	+	35.1258i	0.168216	+	1.18815i
$875$	−9.73449	−	7.98678i	−0.329086	−	0.270003i
$876$	52.9266	+	18.7976i	1.78823	+	0.635111i
$877$	−3.61290	−	12.3044i	−0.121999	−	0.415491i	0.875733	−	0.482795i	$-0.160378\pi$
$877$	−3.61290	−	12.3044i	−0.121999	−	0.415491i	−0.997732	+	0.0673043i	$0.978560\pi$
$878$	−44.5333	+	22.7316i	−1.50292	+	0.767154i
$879$	0.885046	+	0.568784i	0.0298519	+	0.0191846i
$880$	−15.1746	−	0.108749i	−0.511537	−	0.00366593i
$881$	28.3668	−	4.07853i	0.955701	−	0.137409i	0.353218	−	0.935541i	$-0.385087\pi$
$881$	28.3668	−	4.07853i	0.955701	−	0.137409i	0.602483	+	0.798132i	$0.294178\pi$
$882$	8.70699	−	10.9804i	0.293180	−	0.369729i
$883$	−2.45637	+	1.57861i	−0.0826634	+	0.0531246i	−0.581320	−	0.813675i	$-0.697463\pi$
$883$	−2.45637	+	1.57861i	−0.0826634	+	0.0531246i	0.498656	+	0.866800i	$0.333827\pi$
$884$	−31.3718	−	40.5617i	−1.05515	−	1.36424i
$885$	−2.18996	−	5.33119i	−0.0736147	−	0.179206i
$886$	22.3611	+	23.6419i	0.751237	+	0.794265i
$887$	2.96953	−	20.6535i	0.0997070	−	0.693477i	−0.877249	−	0.480036i	$-0.840624\pi$
$887$	2.96953	−	20.6535i	0.0997070	−	0.693477i	0.976956	−	0.213442i	$-0.0684673\pi$
$888$	5.03902	−	7.63609i	0.169098	−	0.256251i
$889$	3.00403	−	10.2308i	0.100752	−	0.343130i
$890$	−2.53598	+	1.64751i	−0.0850061	+	0.0552247i
$891$	12.4411	+	14.3578i	0.416793	+	0.481005i
$892$	−8.91360	−	38.0806i	−0.298449	−	1.27503i
$893$	43.9236	−	50.6905i	1.46985	−	1.69629i
$894$	0.812204	+	0.0808634i	0.0271642	+	0.00270448i
$895$	−48.3200	−	16.2400i	−1.61516	−	0.542842i
$896$	11.4857	−	5.51658i	0.383711	−	0.184296i
$897$	22.8126	−	32.1635i	0.761691	−	1.07391i
$898$	3.26601	−	8.06367i	0.108988	−	0.269088i
$899$	−5.39252	+	2.46268i	−0.179850	+	0.0821349i
$900$	−7.02636	+	15.7963i	−0.234212	+	0.526544i
$901$	39.6413	−	45.7485i	1.32064	−	1.52410i
$902$	21.7142	−	15.3310i	0.723003	−	0.510465i
$903$	7.74011	+	8.93257i	0.257575	+	0.297257i
$904$	5.86523	+	9.37397i	0.195075	+	0.311774i
$905$	19.8136	−	11.6775i	0.658625	−	0.388174i
$906$	22.9165	−	4.32100i	0.761350	−	0.143556i
$907$	−47.5135	−	6.83141i	−1.57766	−	0.226833i	−0.702864	−	0.711324i	$-0.748096\pi$
$907$	−47.5135	−	6.83141i	−1.57766	−	0.226833i	−0.874796	+	0.484491i	$0.839005\pi$
$908$	6.77648	+	17.3307i	0.224885	+	0.575141i
$909$	−4.87093	+	10.6659i	−0.161559	+	0.353764i
$910$	−3.85751	−	12.9016i	−0.127875	−	0.427684i
$911$	15.0767	−	9.68922i	0.499514	−	0.321018i	−0.266508	−	0.963833i	$-0.585870\pi$
$911$	15.0767	−	9.68922i	0.499514	−	0.321018i	0.766022	+	0.642815i	$0.222233\pi$
$912$	11.4386	−	44.0370i	0.378770	−	1.45821i
$913$	−1.47441	+	0.211988i	−0.0487959	+	0.00701579i
$914$	−9.04656	+	3.09024i	−0.299234	+	0.102216i
$915$	22.0710	−	5.56442i	0.729645	−	0.183954i
$916$	−4.31062	−	49.3468i	−0.142427	−	1.63046i
$917$	−4.23610	+	1.24383i	−0.139888	+	0.0410749i
$918$	−26.4830	+	1.15450i	−0.874071	+	0.0381041i
$919$	20.0462			0.661263			0.330632	−	0.943760i	$-0.392738\pi$
$919$	20.0462			0.661263			0.330632	+	0.943760i	$0.392738\pi$
$920$	28.1446	+	11.3084i	0.927901	+	0.372827i
$921$	−12.7468			−0.420020
$922$	11.2308	−	0.489593i	0.369866	−	0.0161239i
$923$	17.5976	−	5.16713i	0.579233	−	0.170078i
$924$	0.723185	+	8.27882i	0.0237910	+	0.272353i
$925$	3.60252	−	6.50653i	0.118450	−	0.213933i
$926$	−28.9738	+	9.89725i	−0.952139	+	0.325244i
$927$	18.0152	−	2.59019i	0.591696	−	0.0850730i
$928$	−22.7094	−	16.8717i	−0.745473	−	0.553841i
$929$	−19.1454	+	12.3040i	−0.628141	+	0.403682i	−0.815621	−	0.578586i	$-0.803605\pi$
$929$	−19.1454	+	12.3040i	−0.628141	+	0.403682i	0.187480	+	0.982269i	$0.439968\pi$
$930$	−7.80979	+	2.33508i	−0.256093	+	0.0765704i
$931$	−12.4542	+	27.2709i	−0.408170	+	0.893768i
$932$	16.0655	+	41.0873i	0.526244	+	1.34586i
$933$	37.0154	+	5.32202i	1.21183	+	0.174235i
$934$	56.5511	−	10.6629i	1.85041	−	0.348902i
$935$	13.0619	+	22.1625i	0.427171	+	0.724792i
$936$	−15.6737	+	9.80696i	−0.512312	+	0.320550i
$937$	−12.5419	−	14.4741i	−0.409724	−	0.472847i	0.512955	−	0.858416i	$-0.328551\pi$
$937$	−12.5419	−	14.4741i	−0.409724	−	0.472847i	−0.922679	+	0.385568i	$0.874005\pi$
$938$	12.3290	−	8.70469i	0.402555	−	0.284218i
$939$	−1.61196	+	1.86030i	−0.0526042	+	0.0607085i
$940$	−18.8050	−	54.1755i	−0.613351	−	1.76701i
$941$	−22.5527	+	10.2995i	−0.735197	+	0.335753i	−0.747582	−	0.664170i	$-0.768785\pi$
$941$	−22.5527	+	10.2995i	−0.735197	+	0.335753i	0.0123844	+	0.999923i	$0.496058\pi$
$942$	−12.6037	+	31.1181i	−0.410650	+	1.01388i
$943$	−51.6081	+	12.6226i	−1.68059	+	0.411049i
$944$	4.73877	−	0.149156i	0.154234	−	0.00485462i
$945$	−6.59852	−	2.21771i	−0.214650	−	0.0721420i
$946$	11.5226	+	1.14720i	0.374633	+	0.0372986i
$947$	−14.1835	+	16.3687i	−0.460903	+	0.531911i	−0.937859	−	0.347017i	$-0.887195\pi$
$947$	−14.1835	+	16.3687i	−0.460903	+	0.531911i	0.476956	+	0.878927i	$0.341740\pi$
$948$	3.95593	+	16.9005i	0.128483	+	0.548903i
$949$	31.9758	+	36.9021i	1.03798	+	1.19789i
$950$	6.49415	−	36.4118i	0.210698	−	1.18136i
$951$	−17.1678	+	58.4680i	−0.556703	+	1.89595i
$952$	−18.0288	−	11.8971i	−0.584318	−	0.385588i
$953$	−1.89213	+	13.1601i	−0.0612922	+	0.426297i	0.935953	+	0.352124i	$0.114541\pi$
$953$	−1.89213	+	13.1601i	−0.0612922	+	0.426297i	−0.997245	+	0.0741723i	$0.976369\pi$
$954$	−14.9980	−	15.8571i	−0.485579	−	0.513391i
$955$	50.7492	−	20.8469i	1.64221	−	0.674590i
$956$	24.6878	+	31.9197i	0.798459	+	1.03236i
$957$	15.5224	−	9.97567i	0.501769	−	0.322468i
$958$	−5.29286	+	6.67483i	−0.171004	+	0.215654i
$959$	3.02498	−	0.434926i	0.0976816	−	0.0140445i
$960$	−27.7413	−	27.2700i	−0.895346	−	0.880136i
$961$	24.8968	+	16.0002i	0.803123	+	0.516136i
$962$	7.08418	−	3.61605i	0.228403	−	0.116586i
$963$	5.38786	+	18.3494i	0.173621	+	0.591300i
$964$	−27.6688	−	9.82692i	−0.891153	−	0.316504i
$965$	−23.7821	+	25.3941i	−0.765572	+	0.817464i
$966$	4.71408	−	15.9276i	0.151673	−	0.512461i
$967$	48.0312			1.54458			0.772289	−	0.635271i	$-0.219112\pi$
$967$	48.0312			1.54458			0.772289	+	0.635271i	$0.219112\pi$
$968$	−17.1770	−	15.2518i	−0.552091	−	0.490211i
$969$	−74.0062	+	21.7302i	−2.37742	+	0.698074i
$970$	−7.61666	+	26.4216i	−0.244556	+	0.848346i
$971$	26.4673	+	17.0095i	0.849377	+	0.545862i	0.891381	−	0.453256i	$-0.149738\pi$
$971$	26.4673	+	17.0095i	0.849377	+	0.545862i	−0.0420031	+	0.999117i	$0.513374\pi$
$972$	−1.78684	+	32.0654i	−0.0573128	+	1.02850i
$973$	−2.27381	−	15.8147i	−0.0728949	−	0.506995i
$974$	−32.9936	+	41.6082i	−1.05718	+	1.33321i
$975$	−33.0550	+	24.4435i	−1.05861	+	0.782819i
$976$	−2.08033	+	18.6082i	−0.0665897	+	0.595633i
$977$	8.92176	−	19.5359i	0.285433	−	0.625010i	−0.711550	−	0.702635i	$-0.752007\pi$
$977$	8.92176	−	19.5359i	0.285433	−	0.625010i	0.996983	+	0.0776254i	$0.0247338\pi$
$978$	−22.2657	−	23.5410i	−0.711980	−	0.752759i
$979$	1.60599	+	0.230907i	0.0513278	+	0.00737983i
$980$	14.8871	+	20.8662i	0.475552	+	0.666548i
$981$	1.89404	−	6.45051i	0.0604720	−	0.205949i
$982$	−11.6218	+	47.0761i	−0.370866	+	1.50226i
$983$	−12.9670	+	11.2360i	−0.413585	+	0.358373i	−0.836661	−	0.547721i	$-0.815496\pi$
$983$	−12.9670	+	11.2360i	−0.413585	+	0.358373i	0.423077	+	0.906094i	$0.360950\pi$
$984$	67.3227	+	10.5125i	2.14617	+	0.335128i
$985$	0.807297	+	7.72190i	0.0257226	+	0.246040i
$986$	−4.75141	+	47.7239i	−0.151316	+	1.51984i
$987$	−28.5668	+	13.0460i	−0.909292	+	0.415260i
$988$	27.5259	−	28.4059i	0.875715	−	0.903713i
$989$	−20.5920	−	10.5670i	−0.654787	−	0.336012i
$990$	8.41827	−	3.89481i	0.267550	−	0.123785i
$991$	−14.3718	+	6.56338i	−0.456535	+	0.208493i	−0.630390	−	0.776279i	$-0.717105\pi$
$991$	−14.3718	+	6.56338i	−0.456535	+	0.208493i	0.173855	+	0.984771i	$0.444378\pi$
$992$	0.454069	−	6.69008i	0.0144167	−	0.212410i
$993$	−22.6736	−	19.6468i	−0.719524	−	0.623471i
$994$	6.31128	−	4.45599i	0.200182	−	0.141335i
$995$	−1.00164	+	25.9151i	−0.0317542	+	0.821562i
$996$	−3.09244	−	2.23993i	−0.0979876	−	0.0709749i
$997$	−13.5842	+	46.2635i	−0.430215	+	1.46518i	0.404521	+	0.914529i	$0.367438\pi$
$997$	−13.5842	+	46.2635i	−0.430215	+	1.46518i	−0.834736	+	0.550650i	$0.814380\pi$
$998$	25.2404	−	4.75917i	0.798969	−	0.150649i
$999$	0.585151	−	4.06982i	0.0185134	−	0.128763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.2	✓	640
4.3	odd	2	inner	460.2.o.b.19.18	yes	640
5.4	even	2	inner	460.2.o.b.19.63	yes	640
20.19	odd	2	inner	460.2.o.b.19.47	yes	640
23.17	odd	22	inner	460.2.o.b.339.47	yes	640
92.63	even	22	inner	460.2.o.b.339.63	yes	640
115.109	odd	22	inner	460.2.o.b.339.18	yes	640
460.339	even	22	inner	460.2.o.b.339.2	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.2	✓	640	1.1	even	1	trivial
460.2.o.b.19.18	yes	640	4.3	odd	2	inner
460.2.o.b.19.47	yes	640	20.19	odd	2	inner
460.2.o.b.19.63	yes	640	5.4	even	2	inner
460.2.o.b.339.2	yes	640	460.339	even	22	inner
460.2.o.b.339.18	yes	640	115.109	odd	22	inner
460.2.o.b.339.47	yes	640	23.17	odd	22	inner
460.2.o.b.339.63	yes	640	92.63	even	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41287 + 0.0615925i) q^{2} +(2.08651 - 0.612653i) q^{3} +(1.99241 - 0.174045i) q^{4} +(-0.546640 - 2.16822i) q^{5} +(-2.91023 + 0.994114i) q^{6} +(-1.11477 + 0.160279i) q^{7} +(-2.80430 + 0.368620i) q^{8} +(1.45440 - 0.934688i) q^{9} +O(q^{10})\)	\(q+(-1.41287 + 0.0615925i) q^{2} +(2.08651 - 0.612653i) q^{3} +(1.99241 - 0.174045i) q^{4} +(-0.546640 - 2.16822i) q^{5} +(-2.91023 + 0.994114i) q^{6} +(-1.11477 + 0.160279i) q^{7} +(-2.80430 + 0.368620i) q^{8} +(1.45440 - 0.934688i) q^{9} +(0.905878 + 3.02975i) q^{10} +(0.704801 - 1.54330i) q^{11} +(4.05055 - 1.58380i) q^{12} +(3.74255 + 0.538097i) q^{13} +(1.56515 - 0.295115i) q^{14} +(-2.46894 - 4.18911i) q^{15} +(3.93942 - 0.693537i) q^{16} +(-4.44059 - 5.12471i) q^{17} +(-1.99732 + 1.41017i) q^{18} +(3.42536 - 3.95308i) q^{19} +(-1.46650 - 4.22485i) q^{20} +(-2.22777 + 1.01739i) q^{21} +(-0.900738 + 2.22389i) q^{22} +(3.30298 - 3.47711i) q^{23} +(-5.62536 + 2.48720i) q^{24} +(-4.40237 + 2.37047i) q^{25} +(-5.32088 - 0.529749i) q^{26} +(-1.81018 + 2.08906i) q^{27} +(-2.19318 + 0.513361i) q^{28} +(3.27507 + 3.77963i) q^{29} +(3.74631 + 5.76660i) q^{30} +(-0.333958 + 1.13736i) q^{31} +(-5.52317 + 1.22252i) q^{32} +(0.525064 - 3.65190i) q^{33} +(6.58962 + 6.96705i) q^{34} +(0.956896 + 2.32944i) q^{35} +(2.73509 - 2.11542i) q^{36} +(-1.25133 + 0.804179i) q^{37} +(-4.59611 + 5.79617i) q^{38} +(8.13851 - 1.17014i) q^{39} +(2.33219 + 5.87885i) q^{40} +(-9.31959 - 5.98934i) q^{41} +(3.08489 - 1.57465i) q^{42} +(-1.35966 - 4.63058i) q^{43} +(1.13565 - 3.19755i) q^{44} +(-2.82165 - 2.64253i) q^{45} +(-4.45252 + 5.11615i) q^{46} +12.8231 q^{47} +(7.79472 - 3.86057i) q^{48} +(-5.49944 + 1.61478i) q^{49} +(6.07398 - 3.62033i) q^{50} +(-12.4050 - 7.97220i) q^{51} +(7.55035 + 0.420741i) q^{52} +(1.27045 + 8.83617i) q^{53} +(2.42889 - 3.06307i) q^{54} +(-3.73149 - 0.684536i) q^{55} +(3.06706 - 0.860397i) q^{56} +(4.72517 - 10.3467i) q^{57} +(-4.86004 - 5.13841i) q^{58} +(1.17321 + 0.168683i) q^{59} +(-5.64823 - 7.91673i) q^{60} +(-1.31880 + 4.49141i) q^{61} +(0.401787 - 1.62751i) q^{62} +(-1.47151 + 1.27507i) q^{63} +(7.72824 - 2.06745i) q^{64} +(-0.879111 - 8.40881i) q^{65} +(-0.516918 + 5.19201i) q^{66} +(8.61940 - 3.93635i) q^{67} +(-9.73941 - 9.43768i) q^{68} +(4.76142 - 9.27860i) q^{69} +(-1.49545 - 3.23227i) q^{70} +(4.41233 - 2.01504i) q^{71} +(-3.73404 + 3.15727i) q^{72} +(9.75980 + 8.45691i) q^{73} +(1.71843 - 1.21327i) q^{74} +(-7.73329 + 7.64313i) q^{75} +(6.13672 - 8.47233i) q^{76} +(-0.538329 + 1.83338i) q^{77} +(-11.4266 + 2.15453i) q^{78} +(-0.567969 + 3.95031i) q^{79} +(-3.65718 - 8.16241i) q^{80} +(-4.65166 + 10.1857i) q^{81} +(13.5363 + 7.88815i) q^{82} +(-0.474664 - 0.738592i) q^{83} +(-4.26157 + 2.41479i) q^{84} +(-8.68411 + 12.4295i) q^{85} +(2.20624 + 6.45867i) q^{86} +(9.14905 + 5.87973i) q^{87} +(-1.40758 + 4.58768i) q^{88} +(0.269426 + 0.917582i) q^{89} +(4.14938 + 3.55976i) q^{90} -4.25831 q^{91} +(5.97573 - 7.50271i) q^{92} +2.57770i q^{93} +(-18.1173 + 0.789804i) q^{94} +(-10.4436 - 5.26603i) q^{95} +(-10.7752 + 5.93458i) q^{96} +(7.31510 + 4.70113i) q^{97} +(7.67054 - 2.62020i) q^{98} +(-0.417438 - 2.90335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

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