LMFDB - Embedded newform 570.2.bi.a.17.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.16
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(1.16230 - 1.28416i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.22020 - 1.87380i) q^{5} +(-1.71859 - 0.215538i) q^{6} +(-0.489365 + 1.82633i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.298119 - 2.98515i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(1.16230 - 1.28416i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.22020 - 1.87380i) q^{5} +(-1.71859 - 0.215538i) q^{6} +(-0.489365 + 1.82633i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.298119 - 2.98515i) q^{9} +(-2.23480 + 0.0752363i) q^{10} +(0.702340 + 0.405496i) q^{11} +(0.809183 + 1.53141i) q^{12} +(0.272070 - 3.10977i) q^{13} +(1.77673 - 0.646678i) q^{14} +(-0.988011 - 3.74484i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.553666 - 0.790717i) q^{17} +(-2.27430 + 1.95642i) q^{18} +(1.15251 - 4.20377i) q^{19} +(1.34346 + 1.78749i) q^{20} +(1.77651 + 2.75117i) q^{21} +(-0.0706826 - 0.807906i) q^{22} +(0.0535876 + 0.114919i) q^{23} +(0.790331 - 1.54123i) q^{24} +(-2.02223 - 4.57281i) q^{25} +(-2.70343 + 1.56083i) q^{26} +(-4.17991 - 3.08681i) q^{27} +(-1.54882 - 1.08450i) q^{28} +(-0.520730 - 2.95321i) q^{29} +(-2.50089 + 2.95728i) q^{30} +(3.93035 + 6.80757i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(1.33705 - 0.430607i) q^{33} +(-0.330148 + 0.907073i) q^{34} +(2.82506 + 3.14546i) q^{35} +(2.90709 + 0.740842i) q^{36} +(1.78904 + 1.78904i) q^{37} +(-4.10458 + 1.46710i) q^{38} +(-3.67721 - 3.96387i) q^{39} +(0.693648 - 2.12576i) q^{40} +(-0.0602308 + 0.0717803i) q^{41} +(1.23466 - 3.03324i) q^{42} +(-2.39907 + 5.14482i) q^{43} +(-0.621256 + 0.521296i) q^{44} +(-5.95733 - 3.08387i) q^{45} +(0.0633995 - 0.109811i) q^{46} +(-5.98377 - 4.18988i) q^{47} +(-1.71581 + 0.236610i) q^{48} +(2.96616 + 1.71251i) q^{49} +(-2.58593 + 4.27937i) q^{50} +(-1.65893 - 0.208056i) q^{51} +(2.82918 + 1.31927i) q^{52} +(-1.85280 - 3.97334i) q^{53} +(-0.131070 + 5.19450i) q^{54} +(1.61681 - 0.821255i) q^{55} +1.89076i q^{56} +(-4.05874 - 6.36605i) q^{57} +(-2.12045 + 2.12045i) q^{58} +(-1.44123 + 8.17364i) q^{59} +(3.85692 + 0.352385i) q^{60} +(8.78941 + 3.19908i) q^{61} +(3.32208 - 7.12422i) q^{62} +(5.59777 + 0.916363i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-5.49510 - 4.30435i) q^{65} +(-1.11963 - 0.848261i) q^{66} +(3.73999 - 5.34126i) q^{67} +(0.932395 - 0.249835i) q^{68} +(0.209859 + 0.0647553i) q^{69} +(0.956227 - 4.11831i) q^{70} +(3.39736 + 9.33417i) q^{71} +(-1.06057 - 2.80628i) q^{72} +(-11.3017 + 0.988772i) q^{73} +(0.439345 - 2.49165i) q^{74} +(-8.22264 - 2.71812i) q^{75} +(3.55607 + 2.52078i) q^{76} +(-1.08427 + 1.08427i) q^{77} +(-1.13785 + 5.28578i) q^{78} +(3.69564 - 4.40429i) q^{79} +(-2.13918 + 0.651082i) q^{80} +(-8.82225 + 1.77986i) q^{81} +(0.0933459 + 0.00816671i) q^{82} +(2.23908 - 8.35635i) q^{83} +(-3.19286 + 0.728420i) q^{84} +(-2.15722 + 0.0726246i) q^{85} +(5.59044 - 0.985745i) q^{86} +(-4.39763 - 2.76381i) q^{87} +(0.783358 + 0.209900i) q^{88} +(-10.0564 + 8.43831i) q^{89} +(0.890828 + 6.64879i) q^{90} +(5.54634 + 2.01870i) q^{91} +(-0.126316 + 0.0110513i) q^{92} +(13.3102 + 2.86525i) q^{93} +7.30484i q^{94} +(-6.47072 - 7.28902i) q^{95} +(1.17797 + 1.26980i) q^{96} +(6.85792 - 4.80197i) q^{97} +(-0.298510 - 3.41199i) q^{98} +(1.00109 - 2.21748i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$	1.16230	−	1.28416i	0.671054	−	0.741408i
$3$	1.16230	−	1.28416i	0.671054	−	0.741408i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	1.22020	−	1.87380i	0.545690	−	0.837987i
$5$	1.22020	−	1.87380i	0.545690	−	0.837987i
$6$	−1.71859	−	0.215538i	−0.701610	−	0.0879930i
$7$	−0.489365	+	1.82633i	−0.184963	+	0.690290i	0.809676	+	0.586877i	$0.199643\pi$
$7$	−0.489365	+	1.82633i	−0.184963	+	0.690290i	−0.994639	+	0.103412i	$0.967024\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−0.298119	−	2.98515i	−0.0993729	−	0.995050i
$10$	−2.23480	+	0.0752363i	−0.706706	+	0.0237918i
$11$	0.702340	+	0.405496i	0.211763	+	0.122262i	0.602131	−	0.798398i	$-0.294319\pi$
$11$	0.702340	+	0.405496i	0.211763	+	0.122262i	−0.390367	+	0.920659i	$0.627652\pi$
$12$	0.809183	+	1.53141i	0.233591	+	0.442081i
$13$	0.272070	−	3.10977i	0.0754586	−	0.862496i	−0.860285	−	0.509814i	$-0.829714\pi$
$13$	0.272070	−	3.10977i	0.0754586	−	0.862496i	0.935743	−	0.352682i	$-0.114730\pi$
$14$	1.77673	−	0.646678i	0.474852	−	0.172832i
$15$	−0.988011	−	3.74484i	−0.255103	−	0.966914i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−0.553666	−	0.790717i	−0.134284	−	0.191777i	0.746379	−	0.665522i	$-0.231791\pi$
$17$	−0.553666	−	0.790717i	−0.134284	−	0.191777i	−0.880662	+	0.473745i	$0.842902\pi$
$18$	−2.27430	+	1.95642i	−0.536057	+	0.461132i
$19$	1.15251	−	4.20377i	0.264404	−	0.964412i
$19$	1.15251	−	4.20377i	0.264404	−	0.964412i
$20$	1.34346	+	1.78749i	0.300407	+	0.399695i
$21$	1.77651	+	2.75117i	0.387667	+	0.600354i
$22$	−0.0706826	−	0.807906i	−0.0150696	−	0.172246i
$23$	0.0535876	+	0.114919i	0.0111738	+	0.0239622i	0.911815	−	0.410600i	$-0.134681\pi$
$23$	0.0535876	+	0.114919i	0.0111738	+	0.0239622i	−0.900642	+	0.434562i	$0.856903\pi$
$24$	0.790331	−	1.54123i	0.161326	−	0.314601i
$25$	−2.02223	−	4.57281i	−0.404445	−	0.914562i
$26$	−2.70343	+	1.56083i	−0.530186	+	0.306103i
$27$	−4.17991	−	3.08681i	−0.804423	−	0.594057i
$28$	−1.54882	−	1.08450i	−0.292700	−	0.204950i
$29$	−0.520730	−	2.95321i	−0.0966972	−	0.548397i	−0.994214	−	0.107417i	$-0.965742\pi$
$29$	−0.520730	−	2.95321i	−0.0966972	−	0.548397i	0.897517	−	0.440980i	$-0.145369\pi$
$30$	−2.50089	+	2.95728i	−0.456599	+	0.539924i
$31$	3.93035	+	6.80757i	0.705912	+	1.22268i	0.966361	+	0.257188i	$0.0827959\pi$
$31$	3.93035	+	6.80757i	0.705912	+	1.22268i	−0.260449	+	0.965487i	$0.583871\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	1.33705	−	0.430607i	0.232750	−	0.0749590i
$34$	−0.330148	+	0.907073i	−0.0566198	+	0.155562i
$35$	2.82506	+	3.14546i	0.477522	+	0.531680i
$36$	2.90709	+	0.740842i	0.484514	+	0.123474i
$37$	1.78904	+	1.78904i	0.294117	+	0.294117i	0.838704	−	0.544587i	$-0.183314\pi$
$37$	1.78904	+	1.78904i	0.294117	+	0.294117i	−0.544587	+	0.838704i	$0.683314\pi$
$38$	−4.10458	+	1.46710i	−0.665851	+	0.237996i
$39$	−3.67721	−	3.96387i	−0.588825	−	0.634727i
$40$	0.693648	−	2.12576i	0.109675	−	0.336112i
$41$	−0.0602308	+	0.0717803i	−0.00940647	+	0.0112102i	−0.770727	−	0.637165i	$-0.780107\pi$
$41$	−0.0602308	+	0.0717803i	−0.00940647	+	0.0112102i	0.761321	+	0.648375i	$0.224551\pi$
$42$	1.23466	−	3.03324i	0.190512	−	0.468039i
$43$	−2.39907	+	5.14482i	−0.365855	+	0.784578i	0.634081	+	0.773266i	$0.281378\pi$
$43$	−2.39907	+	5.14482i	−0.365855	+	0.784578i	−0.999936	+	0.0113114i	$0.996399\pi$
$44$	−0.621256	+	0.521296i	−0.0936578	+	0.0785883i
$45$	−5.95733	−	3.08387i	−0.888066	−	0.459716i
$46$	0.0633995	−	0.109811i	0.00934774	−	0.0161908i
$47$	−5.98377	−	4.18988i	−0.872823	−	0.611157i	0.0489870	−	0.998799i	$-0.484401\pi$
$47$	−5.98377	−	4.18988i	−0.872823	−	0.611157i	−0.921810	+	0.387642i	$0.873290\pi$
$48$	−1.71581	+	0.236610i	−0.247656	+	0.0341516i
$49$	2.96616	+	1.71251i	0.423737	+	0.244645i
$50$	−2.58593	+	4.27937i	−0.365705	+	0.605194i
$51$	−1.65893	−	0.208056i	−0.232297	−	0.0291337i
$52$	2.82918	+	1.31927i	0.392336	+	0.182949i
$53$	−1.85280	−	3.97334i	−0.254502	−	0.545781i	0.736997	−	0.675896i	$-0.236243\pi$
$53$	−1.85280	−	3.97334i	−0.254502	−	0.545781i	−0.991499	+	0.130115i	$0.958465\pi$
$54$	−0.131070	+	5.19450i	−0.0178364	+	0.706882i
$55$	1.61681	−	0.821255i	0.218011	−	0.110738i
$56$			1.89076i			0.252664i
$57$	−4.05874	−	6.36605i	−0.537593	−	0.843204i
$58$	−2.12045	+	2.12045i	−0.278428	+	0.278428i
$59$	−1.44123	+	8.17364i	−0.187633	+	1.06412i	0.734893	+	0.678183i	$0.237232\pi$
$59$	−1.44123	+	8.17364i	−0.187633	+	1.06412i	−0.922526	+	0.385935i	$0.873879\pi$
$60$	3.85692	+	0.352385i	0.497926	+	0.0454926i
$61$	8.78941	+	3.19908i	1.12537	+	0.409601i	0.836609	−	0.547801i	$-0.184535\pi$
$61$	8.78941	+	3.19908i	1.12537	+	0.409601i	0.288760	+	0.957402i	$0.406757\pi$
$62$	3.32208	−	7.12422i	0.421904	−	0.904776i
$63$	5.59777	+	0.916363i	0.705253	+	0.115451i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−5.49510	−	4.30435i	−0.681583	−	0.533889i
$66$	−1.11963	−	0.848261i	−0.137817	−	0.104414i
$67$	3.73999	−	5.34126i	0.456913	−	0.652539i	−0.522915	−	0.852385i	$-0.675155\pi$
$67$	3.73999	−	5.34126i	0.456913	−	0.652539i	0.979827	+	0.199846i	$0.0640443\pi$
$68$	0.932395	−	0.249835i	0.113070	−	0.0302969i
$69$	0.209859	+	0.0647553i	0.0252640	+	0.00779563i
$70$	0.956227	−	4.11831i	0.114291	−	0.492233i
$71$	3.39736	+	9.33417i	0.403192	+	1.10776i	0.960700	+	0.277590i	$0.0895356\pi$
$71$	3.39736	+	9.33417i	0.403192	+	1.10776i	−0.557507	+	0.830172i	$0.688242\pi$
$72$	−1.06057	−	2.80628i	−0.124990	−	0.330723i
$73$	−11.3017	+	0.988772i	−1.32277	+	0.115727i	−0.726559	−	0.687104i	$-0.758882\pi$
$73$	−11.3017	+	0.988772i	−1.32277	+	0.115727i	−0.596206	+	0.802831i	$0.703326\pi$
$74$	0.439345	−	2.49165i	0.0510728	−	0.289648i
$75$	−8.22264	−	2.71812i	−0.949469	−	0.313862i
$76$	3.55607	+	2.52078i	0.407910	+	0.289154i
$77$	−1.08427	+	1.08427i	−0.123564	+	0.123564i
$78$	−1.13785	+	5.28578i	−0.128836	+	0.598496i
$79$	3.69564	−	4.40429i	0.415792	−	0.495522i	−0.516975	−	0.856000i	$-0.672942\pi$
$79$	3.69564	−	4.40429i	0.415792	−	0.495522i	0.932768	+	0.360479i	$0.117387\pi$
$80$	−2.13918	+	0.651082i	−0.239168	+	0.0727932i
$81$	−8.82225	+	1.77986i	−0.980250	+	0.197762i
$82$	0.0933459	+	0.00816671i	0.0103083	+	0.000901862i
$83$	2.23908	−	8.35635i	0.245771	−	0.917229i	−0.727224	−	0.686401i	$-0.759190\pi$
$83$	2.23908	−	8.35635i	0.245771	−	0.917229i	0.972994	−	0.230828i	$-0.0741436\pi$
$84$	−3.19286	+	0.728420i	−0.348369	+	0.0794771i
$85$	−2.15722	+	0.0726246i	−0.233984	+	0.00787724i
$86$	5.59044	−	0.985745i	0.602833	−	0.106296i
$87$	−4.39763	−	2.76381i	−0.471475	−	0.296312i
$88$	0.783358	+	0.209900i	0.0835063	+	0.0223754i
$89$	−10.0564	+	8.43831i	−1.06597	+	0.894459i	−0.994682	−	0.102997i	$-0.967157\pi$
$89$	−10.0564	+	8.43831i	−1.06597	+	0.894459i	−0.0712926	+	0.997455i	$0.522712\pi$
$90$	0.890828	+	6.64879i	0.0939015	+	0.700844i
$91$	5.54634	+	2.01870i	0.581415	+	0.211618i
$92$	−0.126316	+	0.0110513i	−0.0131694	+	0.00115217i
$93$	13.3102	+	2.86525i	1.38021	+	0.297112i
$94$			7.30484i			0.753436i
$95$	−6.47072	−	7.28902i	−0.663882	−	0.747837i
$96$	1.17797	+	1.26980i	0.120226	+	0.129598i
$97$	6.85792	−	4.80197i	0.696316	−	0.487566i	−0.171034	−	0.985265i	$-0.554711\pi$
$97$	6.85792	−	4.80197i	0.696316	−	0.487566i	0.867350	+	0.497699i	$0.165822\pi$
$98$	−0.298510	−	3.41199i	−0.0301541	−	0.344663i
$99$	1.00109	−	2.21748i	0.100613	−	0.222865i
$100$	4.98868	−	0.336276i	0.498868	−	0.0336276i
$101$	4.83841	+	5.76619i	0.481440	+	0.573758i	0.951019	−	0.309133i	$-0.100039\pi$
$101$	4.83841	+	5.76619i	0.481440	+	0.573758i	−0.469579	+	0.882890i	$0.655594\pi$
$102$	0.781094	+	1.47825i	0.0773398	+	0.146369i
$103$	1.29671	+	4.83939i	0.127769	+	0.476839i	0.999923	−	0.0123914i	$-0.00394440\pi$
$103$	1.29671	+	4.83939i	0.127769	+	0.476839i	−0.872155	+	0.489230i	$0.837278\pi$
$104$	−0.542069	−	3.07423i	−0.0531542	−	0.301453i
$105$	7.32283	+	0.0281552i	0.714635	+	0.00274766i
$106$	−2.19205	+	3.79674i	−0.212911	+	0.368772i
$107$	14.5858	+	3.90825i	1.41006	+	0.377825i	0.881947	−	0.471348i	$-0.156232\pi$
$107$	14.5858	+	3.90825i	1.41006	+	0.377825i	0.528115	+	0.849173i	$0.322899\pi$
$108$	4.33026	−	2.87208i	0.416680	−	0.276366i
$109$	1.55950	+	4.28469i	0.149373	+	0.410398i	0.991701	−	0.128567i	$-0.0410377\pi$
$109$	1.55950	+	4.28469i	0.149373	+	0.410398i	−0.842328	+	0.538965i	$0.818815\pi$
$110$	−1.60010	−	0.853362i	−0.152563	−	0.0813649i
$111$	4.37681	−	0.218008i	0.415429	−	0.0206924i
$112$	1.54882	−	1.08450i	0.146350	−	0.102475i
$113$	4.99598	+	4.99598i	0.469983	+	0.469983i	0.901909	−	0.431926i	$-0.142166\pi$
$113$	4.99598	+	4.99598i	0.469983	+	0.469983i	−0.431926	+	0.901909i	$0.642166\pi$
$114$	−2.88677	+	6.97614i	−0.270370	+	0.653376i
$115$	0.280722	+	0.0398118i	0.0261775	+	0.00371247i
$116$	2.95321	+	0.520730i	0.274199	+	0.0483486i
$117$	−9.36425	+	0.114912i	−0.865725	+	0.0106236i
$118$	7.52211	−	3.50762i	0.692467	−	0.322902i
$119$	1.71506	−	0.624230i	0.157219	−	0.0572231i
$120$	−1.92358	−	3.36152i	−0.175598	−	0.306864i
$121$	−5.17115	−	8.95669i	−0.470104	−	0.814244i
$122$	−2.42086	−	9.03478i	−0.219175	−	0.817971i
$123$	0.0221709	+	0.160776i	0.00199908	+	0.0144967i
$124$	−7.74128	+	1.36500i	−0.695188	+	0.122580i
$125$	−11.0360	−	1.79051i	−0.987093	−	0.160148i
$126$	−2.46011	−	5.11103i	−0.219164	−	0.455327i
$127$	12.0874	+	1.05751i	1.07259	+	0.0938392i	0.609742	−	0.792600i	$-0.291273\pi$
$127$	12.0874	+	1.05751i	1.07259	+	0.0938392i	0.462845	+	0.886439i	$0.346829\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	3.81832	+	9.06060i	0.336184	+	0.797742i
$130$	−0.374055	+	6.97019i	−0.0328068	+	0.611327i
$131$	19.7198	+	3.47713i	1.72293	+	0.303798i	0.945608	−	0.325308i	$-0.105468\pi$
$131$	19.7198	+	3.47713i	1.72293	+	0.303798i	0.777319	+	0.629107i	$0.216579\pi$
$132$	−0.0526601	+	1.40369i	−0.00458348	+	0.122176i
$133$	7.11350	+	4.16205i	0.616819	+	0.360896i
$134$	−6.52048			−0.563283
$135$	−10.8844	+	4.06577i	−0.936777	+	0.349926i
$136$	−0.739453	−	0.620474i	−0.0634075	−	0.0532052i
$137$	−15.3881	+	7.17559i	−1.31469	+	0.613052i	−0.948290	−	0.317404i	$-0.897189\pi$
$137$	−15.3881	+	7.17559i	−1.31469	+	0.613052i	−0.366403	+	0.930456i	$0.619411\pi$
$138$	−0.0673255	−	0.209048i	−0.00573113	−	0.0177954i
$139$	2.79181	+	3.32715i	0.236798	+	0.282205i	0.871336	−	0.490687i	$-0.163254\pi$
$139$	2.79181	+	3.32715i	0.236798	+	0.282205i	−0.634538	+	0.772892i	$0.718810\pi$
$140$	−3.92199	+	1.57887i	−0.331469	+	0.133439i
$141$	−12.3354	+	2.81420i	−1.03883	+	0.236999i
$142$	5.69746	−	8.13681i	0.478120	−	0.682826i
$143$	1.45209	−	2.07379i	0.121430	−	0.173419i
$144$	−1.69045	+	2.47839i	−0.140870	+	0.206532i
$145$	−6.16911	−	2.62776i	−0.512316	−	0.218224i
$146$	7.29235	+	8.69068i	0.603519	+	0.719246i
$147$	5.64670	−	1.81856i	0.465732	−	0.149992i
$148$	−2.29304	+	1.06926i	−0.188487	+	0.0878927i
$149$	10.5409	+	8.84489i	0.863547	+	0.724602i	0.962729	−	0.270467i	$-0.0871782\pi$
$149$	10.5409	+	8.84489i	0.863547	+	0.724602i	−0.0991821	+	0.995069i	$0.531623\pi$
$150$	2.48976	+	8.29464i	0.203288	+	0.677255i
$151$	15.6362			1.27246			0.636229	−	0.771500i	$-0.280493\pi$
$151$	15.6362			1.27246			0.636229	+	0.771500i	$0.280493\pi$
$152$	0.0252247	−	4.35883i	0.00204599	−	0.353547i
$153$	−2.19535	+	1.88850i	−0.177484	+	0.152676i
$154$	1.51010	+	0.266271i	0.121687	+	0.0214567i
$155$	17.5518	+	0.941915i	1.40980	+	0.0756565i
$156$	4.98250	−	2.09972i	0.398919	−	0.168112i
$157$	15.0294	+	7.00832i	1.19948	+	0.559325i	0.916590	−	0.399828i	$-0.130930\pi$
$157$	15.0294	+	7.00832i	1.19948	+	0.559325i	0.282886	+	0.959153i	$0.408708\pi$
$158$	−5.72752	−	0.501093i	−0.455657	−	0.0398648i
$159$	−7.25591	−	2.23893i	−0.575431	−	0.177559i
$160$	1.76032	+	1.37887i	0.139165	+	0.109009i
$161$	−0.236104	+	0.0416315i	−0.0186076	+	0.00328102i
$162$	6.51821	+	6.20588i	0.512119	+	0.487580i
$163$	−0.400865	−	1.49605i	−0.0313982	−	0.117180i	0.948448	−	0.316932i	$-0.102653\pi$
$163$	−0.400865	−	1.49605i	−0.0313982	−	0.117180i	−0.979846	+	0.199753i	$0.935986\pi$
$164$	−0.0468512	−	0.0811487i	−0.00365847	−	0.00633665i
$165$	0.824599	−	3.03078i	0.0641949	−	0.235946i
$166$	−8.12941	+	2.95886i	−0.630964	+	0.229652i
$167$	13.5263	−	6.30742i	1.04670	−	0.488083i	0.178312	−	0.983974i	$-0.442936\pi$
$167$	13.5263	−	6.30742i	1.04670	−	0.488083i	0.868385	+	0.495891i	$0.165158\pi$
$168$	2.42803	+	2.19763i	0.187327	+	0.169551i
$169$	3.20584	+	0.565276i	0.246603	+	0.0434828i
$170$	1.29682	+	1.72544i	0.0994619	+	0.132335i
$171$	−12.8925	−	2.18720i	−0.985913	−	0.167259i
$172$	−4.01402	−	4.01402i	−0.306066	−	0.306066i
$173$	−12.4324	+	8.70527i	−0.945219	+	0.661849i	−0.941095	−	0.338142i	$-0.890202\pi$
$173$	−12.4324	+	8.70527i	−0.945219	+	0.661849i	−0.00412392	+	0.999991i	$0.501313\pi$
$174$	0.258392	+	5.18758i	0.0195887	+	0.393270i
$175$	9.34109	−	1.45549i	0.706120	−	0.110024i
$176$	−0.277376	−	0.762083i	−0.0209080	−	0.0574442i
$177$	8.82109	+	11.3510i	0.663034	+	0.853193i
$178$	12.6804	+	3.39769i	0.950433	+	0.254668i
$179$	−11.0375	+	19.1175i	−0.824981	+	1.42891i	0.0769521	+	0.997035i	$0.475481\pi$
$179$	−11.0375	+	19.1175i	−0.824981	+	1.42891i	−0.901934	+	0.431875i	$0.857852\pi$
$180$	4.93541	−	4.54331i	0.367864	−	0.338639i
$181$	−2.54393	−	14.4273i	−0.189089	−	1.07237i	−0.920589	−	0.390533i	$-0.872291\pi$
$181$	−2.54393	−	14.4273i	−0.189089	−	1.07237i	0.731500	−	0.681841i	$-0.238821\pi$
$182$	−1.52763	−	5.70118i	−0.113235	−	0.422600i
$183$	14.3241	−	7.56869i	1.05886	−	0.559493i
$184$	0.0815048	+	0.0971336i	0.00600861	+	0.00716079i
$185$	5.53529	−	1.16931i	0.406962	−	0.0859695i
$186$	−5.28736	−	12.5465i	−0.387688	−	0.919957i
$187$	−0.0682290	−	0.779861i	−0.00498940	−	0.0570291i
$188$	5.98377	−	4.18988i	0.436411	−	0.305579i
$189$	7.68304	−	6.12333i	0.558859	−	0.445407i
$190$	−2.25936	+	9.48131i	−0.163911	+	0.687847i
$191$		−	0.627614i		−	0.0454125i	−0.999742	−	0.0227063i	$-0.992772\pi$
$191$		−	0.627614i		−	0.0454125i	0.999742	−	0.0227063i	$-0.00722825\pi$
$192$	0.364503	−	1.69326i	0.0263057	−	0.122201i
$193$	7.43320	−	0.650321i	0.535054	−	0.0468111i	0.183573	−	0.983006i	$-0.441234\pi$
$193$	7.43320	−	0.650321i	0.535054	−	0.0468111i	0.351481	+	0.936195i	$0.385678\pi$
$194$	−7.86708	−	2.86338i	−0.564823	−	0.205579i
$195$	−11.9144	+	2.05363i	−0.853209	+	0.147064i
$196$	−2.62372	+	2.20156i	−0.187409	+	0.157254i
$197$	−11.0310	−	2.95576i	−0.785929	−	0.210589i	−0.156532	−	0.987673i	$-0.550031\pi$
$197$	−11.0310	−	2.95576i	−0.785929	−	0.210589i	−0.629397	+	0.777084i	$0.716698\pi$
$198$	−2.39065	+	0.451850i	−0.169896	+	0.0321116i
$199$	−26.0915	+	4.60064i	−1.84958	+	0.326131i	−0.984484	−	0.175477i	$-0.943853\pi$
$199$	−26.0915	+	4.60064i	−1.84958	+	0.326131i	−0.865095	+	0.501608i	$0.832742\pi$
$200$	−3.13685	−	3.89361i	−0.221809	−	0.275320i
$201$	−2.51203	−	11.0109i	−0.177185	−	0.776648i
$202$	1.94819	−	7.27075i	0.137074	−	0.511568i
$203$	5.64837	+	0.494169i	0.396438	+	0.0346838i
$204$	0.762896	−	1.48772i	0.0534134	−	0.104162i
$205$	0.0610080	+	0.200446i	0.00426098	+	0.0139998i
$206$	3.22043	−	3.83796i	0.224378	−	0.267403i
$207$	0.327075	−	0.194226i	0.0227333	−	0.0134997i
$208$	−2.20734	+	2.20734i	−0.153052	+	0.153052i
$209$	2.51407	−	2.48514i	0.173902	−	0.171901i
$210$	−4.17714	−	6.01466i	−0.288250	−	0.415051i
$211$	−1.43988	+	8.16597i	−0.0991255	+	0.562168i	0.894279	+	0.447509i	$0.147689\pi$
$211$	−1.43988	+	8.16597i	−0.0991255	+	0.562168i	−0.993405	+	0.114659i	$0.963422\pi$
$212$	4.36742	−	0.382099i	0.299955	−	0.0262427i
$213$	15.9353	+	6.48636i	1.09187	+	0.444438i
$214$	−5.16462	−	14.1897i	−0.353046	−	0.969986i
$215$	6.71300	+	10.7731i	0.457823	+	0.734718i
$216$	−4.83640	−	1.89979i	−0.329076	−	0.129264i
$217$	−14.3563	+	3.84675i	−0.974567	+	0.261135i
$218$	2.61532	−	3.73506i	0.177132	−	0.252970i
$219$	−11.8662	+	15.6624i	−0.801846	+	1.05837i
$220$	0.218745	+	1.80019i	0.0147478	+	0.121369i
$221$	−2.60958	+	1.50664i	−0.175540	+	0.101348i
$222$	−2.68902	−	3.46023i	−0.180475	−	0.232235i
$223$	−7.00655	+	15.0256i	−0.469193	+	1.00619i	0.519254	+	0.854620i	$0.326210\pi$
$223$	−7.00655	+	15.0256i	−0.469193	+	1.00619i	−0.988447	+	0.151568i	$0.951568\pi$
$224$	−1.77673	−	0.646678i	−0.118713	−	0.0432080i
$225$	−13.0477	+	7.39989i	−0.869845	+	0.493326i
$226$	1.22689	−	6.95805i	0.0816116	−	0.462843i
$227$	2.98701	−	2.98701i	0.198255	−	0.198255i	−0.600997	−	0.799252i	$-0.705229\pi$
$227$	2.98701	−	2.98701i	0.198255	−	0.198255i	0.799252	+	0.600997i	$0.205229\pi$
$228$	7.37030	−	1.63665i	0.488110	−	0.108390i
$229$		−	29.5837i		−	1.95494i	−0.211064	−	0.977472i	$-0.567693\pi$
$229$		−	29.5837i		−	1.95494i	0.211064	−	0.977472i	$-0.432307\pi$
$230$	−0.128404	−	0.252789i	−0.00846668	−	0.0166684i
$231$	0.132126	+	2.65262i	0.00869328	+	0.174530i
$232$	−1.26733	−	2.71781i	−0.0832045	−	0.178433i
$233$	−6.32787	−	2.95073i	−0.414552	−	0.193309i	0.204141	−	0.978941i	$-0.434560\pi$
$233$	−6.32787	−	2.95073i	−0.414552	−	0.193309i	−0.618693	+	0.785633i	$0.712338\pi$
$234$	5.46524	+	7.60483i	0.357274	+	0.497143i
$235$	−15.1524	+	6.09988i	−0.988433	+	0.397912i
$236$	−7.18778	−	4.14987i	−0.467885	−	0.270133i
$237$	−1.36036	−	9.86489i	−0.0883650	−	0.640794i
$238$	−1.49506	−	1.04685i	−0.0969101	−	0.0678572i
$239$	9.20937	−	15.9511i	0.595704	−	1.03179i	−0.397743	−	0.917497i	$-0.630206\pi$
$239$	9.20937	−	15.9511i	0.595704	−	1.03179i	0.993447	−	0.114293i	$-0.0364603\pi$
$240$	−1.65028	+	3.50380i	−0.106525	+	0.226169i
$241$	−14.0796	+	11.8142i	−0.906949	+	0.761020i	−0.971536	−	0.236892i	$-0.923871\pi$
$241$	−14.0796	+	11.8142i	−0.906949	+	0.761020i	0.0645875	+	0.997912i	$0.479427\pi$
$242$	−4.37084	+	9.37330i	−0.280968	+	0.602539i
$243$	−7.96848	+	13.3979i	−0.511178	+	0.859475i
$244$	−6.01231	+	7.16519i	−0.384899	+	0.458704i
$245$	6.82820	−	3.46837i	0.436238	−	0.221586i
$246$	0.118983	−	0.110379i	0.00758610	−	0.00703749i
$247$	−12.7592	−	4.72777i	−0.811850	−	0.300821i
$248$	5.55836	+	5.55836i	0.352956	+	0.352956i
$249$	−8.12839	−	12.5879i	−0.515116	−	0.797727i
$250$	4.86331	+	10.0672i	0.307583	+	0.636705i
$251$	−7.35246	+	20.2007i	−0.464083	+	1.27506i	0.458306	+	0.888795i	$0.348456\pi$
$251$	−7.35246	+	20.2007i	−0.464083	+	1.27506i	−0.922389	+	0.386263i	$0.873766\pi$
$252$	−2.77565	+	4.94677i	−0.174850	+	0.311617i
$253$	−0.00896248	+	0.102442i	−0.000563466	+	0.00644045i
$254$	−6.06681	−	10.5080i	−0.380665	−	0.659332i
$255$	−2.41408	+	2.85463i	−0.151176	+	0.178764i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−12.5262	−	8.77096i	−0.781364	−	0.547117i	0.113456	−	0.993543i	$-0.463808\pi$
$257$	−12.5262	−	8.77096i	−0.781364	−	0.547117i	−0.894821	+	0.446426i	$0.852697\pi$
$258$	5.23191	−	8.32473i	0.325725	−	0.518275i
$259$	−4.14288	+	2.39189i	−0.257426	+	0.148625i
$260$	5.92420	−	3.69153i	0.367403	−	0.228939i
$261$	−8.66053	+	2.43487i	−0.536074	+	0.150714i
$262$	−8.46251	−	18.1479i	−0.522816	−	1.12118i
$263$	−1.25894	−	14.3897i	−0.0776295	−	0.887309i	−0.930765	−	0.365619i	$-0.880857\pi$
$263$	−1.25894	−	14.3897i	−0.0776295	−	0.887309i	0.853135	−	0.521690i	$-0.174698\pi$
$264$	1.18004	−	0.761988i	0.0726265	−	0.0468971i
$265$	−9.70602	−	1.37650i	−0.596236	−	0.0845578i
$266$	−0.670781	−	8.21429i	−0.0411283	−	0.503651i
$267$	−0.852419	+	22.7218i	−0.0521672	+	1.39055i
$268$	3.73999	+	5.34126i	0.228456	+	0.326269i
$269$	11.9260	+	10.0071i	0.727142	+	0.610145i	0.929351	−	0.369198i	$-0.120367\pi$
$269$	11.9260	+	10.0071i	0.727142	+	0.610145i	−0.202209	+	0.979342i	$0.564812\pi$
$270$	9.57350	+	6.58393i	0.582625	+	0.400685i
$271$	−18.8364	+	6.85589i	−1.14423	+	0.416466i	−0.843439	−	0.537224i	$-0.819473\pi$
$271$	−18.8364	+	6.85589i	−1.14423	+	0.416466i	−0.300791	+	0.953690i	$0.597251\pi$
$272$	−0.0841303	+	0.961614i	−0.00510115	+	0.0583064i
$273$	9.03885	−	4.77604i	0.547056	−	0.289059i
$274$	14.7041	+	8.48944i	0.888310	+	0.512866i
$275$	0.433968	−	4.03167i	0.0261692	−	0.243119i
$276$	−0.132626	+	0.175055i	−0.00798315	+	0.0105371i
$277$	2.81906	−	0.755366i	0.169381	−	0.0453855i	−0.173132	−	0.984899i	$-0.555389\pi$
$277$	2.81906	−	0.755366i	0.169381	−	0.0453855i	0.342513	+	0.939513i	$0.388722\pi$
$278$	1.12412	−	4.19529i	0.0674205	−	0.251617i
$279$	19.1499	−	13.7622i	1.14647	−	0.823919i
$280$	3.54290	+	2.30711i	0.211729	+	0.137876i
$281$	2.11319	−	5.80593i	0.126062	−	0.346353i	−0.860566	−	0.509338i	$-0.829890\pi$
$281$	2.11319	−	5.80593i	0.126062	−	0.346353i	0.986628	+	0.162986i	$0.0521124\pi$
$282$	9.38056	+	8.49041i	0.558604	+	0.505597i
$283$	−16.0433	−	22.9121i	−0.953673	−	1.36199i	−0.932093	−	0.362219i	$-0.882019\pi$
$283$	−16.0433	−	22.9121i	−0.953673	−	1.36199i	−0.0215796	−	0.999767i	$-0.506870\pi$
$284$	−9.93321			−0.589428
$285$	−16.8812	−	0.162601i	−0.999954	−	0.00963165i
$286$	−2.53163			−0.149699
$287$	−0.101620	−	0.145128i	−0.00599844	−	0.00856665i
$288$	2.99977	−	0.0368113i	0.176763	−	0.00216913i
$289$	5.49566	−	15.0992i	0.323274	−	0.888188i
$290$	1.38592	+	6.56066i	0.0813839	+	0.385255i
$291$	1.80448	−	14.3880i	0.105780	−	0.843438i
$292$	2.93627	−	10.9583i	0.171832	−	0.641287i
$293$	−3.62013	+	0.970011i	−0.211490	+	0.0566687i	−0.363009	−	0.931786i	$-0.618250\pi$
$293$	−3.62013	+	0.970011i	−0.211490	+	0.0566687i	0.151518	+	0.988454i	$0.451584\pi$
$294$	−4.72849	−	3.58242i	−0.275771	−	0.208931i
$295$	13.5571	+	12.6741i	0.789328	+	0.737912i
$296$	2.19112	+	1.26504i	0.127356	+	0.0735292i
$297$	−1.68403	−	3.86292i	−0.0977170	−	0.224150i
$298$	1.19928	−	13.7079i	0.0694725	−	0.794075i
$299$	0.371951	−	0.135379i	0.0215105	−	0.00782918i
$300$	5.36651	−	6.79710i	0.309836	−	0.392431i
$301$	−8.22214	−	6.89920i	−0.473916	−	0.397663i
$302$	−8.96857	−	12.8084i	−0.516083	−	0.737043i
$303$	13.0284	+	0.488766i	0.748461	+	0.0280788i
$304$	−3.58501	+	2.47946i	−0.205614	+	0.142207i
$305$	16.7193	−	12.5660i	0.957342	−	0.719529i
$306$	2.80617	+	0.715125i	0.160418	+	0.0408810i
$307$	0.937919	+	10.7205i	0.0535298	+	0.611849i	0.974823	+	0.222980i	$0.0715785\pi$
$307$	0.937919	+	10.7205i	0.0535298	+	0.611849i	−0.921293	+	0.388869i	$0.872866\pi$
$308$	−0.648039	−	1.38972i	−0.0369255	−	0.0791869i
$309$	7.72170	+	3.95964i	0.439272	+	0.225256i
$310$	−9.29573	−	14.9179i	−0.527962	−	0.847278i
$311$	16.5036	−	9.52837i	0.935834	−	0.540304i	0.0471822	−	0.998886i	$-0.484976\pi$
$311$	16.5036	−	9.52837i	0.935834	−	0.540304i	0.888652	+	0.458582i	$0.151643\pi$
$312$	−4.57784	−	2.87707i	−0.259169	−	0.162882i
$313$	−20.7662	−	14.5407i	−1.17378	−	0.821887i	−0.186744	−	0.982409i	$-0.559793\pi$
$313$	−20.7662	−	14.5407i	−1.17378	−	0.821887i	−0.987032	+	0.160522i	$0.948682\pi$
$314$	−2.87963	−	16.3312i	−0.162507	−	0.921621i
$315$	8.54748	−	9.37094i	0.481596	−	0.527993i
$316$	2.87470	+	4.97912i	0.161714	+	0.280098i
$317$	0.0732189	−	0.836895i	0.00411238	−	0.0470047i	−0.993861	−	0.110634i	$-0.964712\pi$
$317$	0.0732189	−	0.836895i	0.00411238	−	0.0470047i	0.997974	+	0.0636291i	$0.0202675\pi$
$318$	2.32779	+	7.22789i	0.130536	+	0.405320i
$319$	0.831785	−	2.28531i	0.0465710	−	0.127953i
$320$	0.119826	−	2.23286i	0.00669847	−	0.124820i
$321$	21.9719	−	14.1879i	1.22635	−	0.791891i
$322$	0.169526	+	0.169526i	0.00944733	+	0.00944733i
$323$	−3.96210	+	1.41618i	−0.220457	+	0.0787981i
$324$	1.34487	−	8.89895i	0.0747148	−	0.494386i
$325$	−14.7706	+	5.04454i	−0.819325	+	0.279820i
$326$	−0.995565	+	1.18647i	−0.0551392	+	0.0657124i
$327$	7.31481	+	2.97745i	0.404510	+	0.164653i
$328$	−0.0396004	+	0.0849233i	−0.00218657	+	0.00468910i
$329$	10.5804	−	8.87799i	0.583315	−	0.489459i
$330$	−2.95564	+	1.06291i	−0.162703	+	0.0585115i
$331$	−8.02075	+	13.8923i	−0.440860	+	0.763592i	−0.997754	−	0.0669918i	$-0.978660\pi$
$331$	−8.02075	+	13.8923i	−0.440860	+	0.763592i	0.556893	+	0.830584i	$0.311993\pi$
$332$	7.08659	+	4.96209i	0.388927	+	0.272330i
$333$	4.80721	−	5.87391i	0.263434	−	0.321888i
$334$	−12.9251	−	7.46231i	−0.707230	−	0.408320i
$335$	−5.44490	−	13.5254i	−0.297487	−	0.738971i
$336$	0.407531	−	3.24944i	0.0222326	−	0.177271i
$337$	−20.6980	−	9.65166i	−1.12749	−	0.525759i	−0.232839	−	0.972515i	$-0.574801\pi$
$337$	−20.6980	−	9.65166i	−1.12749	−	0.525759i	−0.894656	+	0.446756i	$0.852579\pi$
$338$	−1.37575	−	2.95030i	−0.0748307	−	0.160475i
$339$	12.2225	−	0.608797i	0.663833	−	0.0330653i
$340$	0.669570	−	2.05197i	0.0363125	−	0.111284i
$341$			6.37497i			0.345224i
$342$	5.60318	+	11.8154i	0.302985	+	0.638905i
$343$	−13.9379	+	13.9379i	−0.752578	+	0.752578i
$344$	−0.985745	+	5.59044i	−0.0531478	+	0.301416i
$345$	0.377408	−	0.314218i	0.0203190	−	0.0169169i
$346$	14.2619	+	5.19090i	0.766723	+	0.279065i
$347$	11.4741	−	24.6064i	0.615964	−	1.32094i	−0.312641	−	0.949871i	$-0.601214\pi$
$347$	11.4741	−	24.6064i	0.615964	−	1.32094i	0.928606	−	0.371068i	$-0.121008\pi$
$348$	4.10121	−	3.18714i	0.219848	−	0.170849i
$349$	17.8745	−	10.3199i	0.956802	−	0.552410i	0.0616145	−	0.998100i	$-0.480375\pi$
$349$	17.8745	−	10.3199i	0.956802	−	0.552410i	0.895187	+	0.445690i	$0.147042\pi$
$350$	−6.55009	−	6.81694i	−0.350117	−	0.364381i
$351$	−10.7365	+	12.1587i	−0.573072	+	0.648985i
$352$	−0.465166	+	0.664326i	−0.0247934	+	0.0354087i
$353$	−28.7761	+	7.71053i	−1.53160	+	0.410390i	−0.923540	−	0.383503i	$-0.874718\pi$
$353$	−28.7761	+	7.71053i	−1.53160	+	0.410390i	−0.608058	+	0.793893i	$0.708051\pi$
$354$	4.23862	−	13.7365i	0.225280	−	0.730086i
$355$	21.6358	+	5.02359i	1.14831	+	0.266624i
$356$	−4.48993	−	12.3360i	−0.237966	−	0.653806i
$357$	1.19180	−	2.92795i	0.0630768	−	0.154963i
$358$	21.9910	−	1.92396i	1.16226	−	0.101685i
$359$	0.382778	−	2.17084i	0.0202022	−	0.114573i	−0.973039	−	0.230640i	$-0.925918\pi$
$359$	0.382778	−	2.17084i	0.0202022	−	0.114573i	0.993241	+	0.116068i	$0.0370290\pi$
$360$	−6.55250	−	1.43692i	−0.345347	−	0.0757321i
$361$	−16.3434	−	9.68980i	−0.860181	−	0.509990i
$362$	−10.3590	+	10.3590i	−0.544459	+	0.544459i
$363$	−17.5122	−	3.76979i	−0.919153	−	0.197863i
$364$	−3.79392	+	4.52142i	−0.198856	+	0.236987i
$365$	−11.9376	+	22.3836i	−0.624842	+	1.17161i
$366$	−14.4158	−	7.39236i	−0.753528	−	0.386405i
$367$	−13.3898	−	1.17145i	−0.698940	−	0.0611494i	−0.267853	−	0.963460i	$-0.586314\pi$
$367$	−13.3898	−	1.17145i	−0.698940	−	0.0611494i	−0.431087	+	0.902310i	$0.641870\pi$
$368$	0.0328180	−	0.122478i	0.00171076	−	0.00638463i
$369$	0.232231	+	0.158399i	0.0120895	+	0.00824592i
$370$	−4.13275	−	3.86355i	−0.214852	−	0.200857i
$371$	8.16335	−	1.43942i	0.423820	−	0.0747309i
$372$	−7.24482	+	11.5276i	−0.375626	+	0.597676i
$373$	−8.26502	−	2.21460i	−0.427946	−	0.114668i	0.0384156	−	0.999262i	$-0.487769\pi$
$373$	−8.26502	−	2.21460i	−0.427946	−	0.114668i	−0.466362	+	0.884594i	$0.654436\pi$
$374$	−0.599690	+	0.503200i	−0.0310092	+	0.0260198i
$375$	−15.1265	+	12.0909i	−0.781128	+	0.624371i
$376$	−6.86430	−	2.49840i	−0.353999	−	0.128845i
$377$	−9.32548	+	0.815874i	−0.480287	+	0.0420196i
$378$	−9.42275	−	2.78138i	−0.484654	−	0.143059i
$379$			8.49100i			0.436153i	0.975932	+	0.218077i	$0.0699783\pi$
$379$			8.49100i			0.436153i	−0.975932	+	0.218077i	$0.930022\pi$
$380$	9.06255	−	3.58750i	0.464899	−	0.184035i
$381$	15.4072	−	14.2930i	0.789337	−	0.732254i
$382$	−0.514111	+	0.359984i	−0.0263042	+	0.0184184i
$383$	2.33314	+	26.6679i	0.119218	+	1.36267i	0.786375	+	0.617749i	$0.211955\pi$
$383$	2.33314	+	26.6679i	0.119218	+	1.36267i	−0.667157	+	0.744917i	$0.732489\pi$
$384$	−1.59611	+	0.672632i	−0.0814511	+	0.0343251i
$385$	0.708676	+	3.35473i	0.0361175	+	0.170973i
$386$	−4.79622	−	5.71591i	−0.244121	−	0.290932i
$387$	16.0733	+	5.62781i	0.817050	+	0.286078i
$388$	2.16683	+	8.08670i	0.110004	+	0.410540i
$389$	5.41544	+	30.7125i	0.274574	+	1.55719i	0.740312	+	0.672263i	$0.234678\pi$
$389$	5.41544	+	30.7125i	0.274574	+	1.55719i	−0.465738	+	0.884922i	$0.654211\pi$
$390$	8.51606	+	8.58180i	0.431228	+	0.434556i
$391$	0.0611987	−	0.105999i	0.00309495	−	0.00536061i
$392$	3.30832	+	0.886461i	0.167095	+	0.0447731i
$393$	27.3855	−	21.2818i	1.38142	−	1.07353i
$394$	3.90593	+	10.7315i	0.196778	+	0.540643i
$395$	−3.74333	−	12.2990i	−0.188347	−	0.618830i
$396$	1.74135	+	1.69913i	0.0875063	+	0.0853847i
$397$	−7.51244	+	5.26027i	−0.377038	+	0.264005i	−0.746700	−	0.665161i	$-0.768363\pi$
$397$	−7.51244	+	5.26027i	−0.377038	+	0.264005i	0.369661	+	0.929167i	$0.379474\pi$
$398$	18.7341	+	18.7341i	0.939056	+	0.939056i
$399$	13.6127	−	4.29730i	0.681490	−	0.215134i
$400$	−1.39023	+	4.80284i	−0.0695116	+	0.240142i
$401$	−12.6041	−	2.22244i	−0.629417	−	0.110983i	−0.150166	−	0.988661i	$-0.547981\pi$
$401$	−12.6041	−	2.22244i	−0.629417	−	0.110983i	−0.479251	+	0.877678i	$0.659092\pi$
$402$	−7.57875	+	8.37331i	−0.377994	+	0.417623i
$403$	22.2393	−	10.3704i	1.10782	−	0.516585i
$404$	−7.07328	+	2.57446i	−0.351909	+	0.128084i
$405$	−7.42982	+	18.7029i	−0.369190	+	0.929354i
$406$	−2.83497	−	4.91032i	−0.140697	−	0.243695i
$407$	0.531066	+	1.98196i	0.0263239	+	0.0982423i
$408$	−1.65625	+	0.228396i	−0.0819967	+	0.0113073i
$409$	16.3531	−	2.88349i	0.808607	−	0.142579i	0.245964	−	0.969279i	$-0.420896\pi$
$409$	16.3531	−	2.88349i	0.808607	−	0.142579i	0.562643	+	0.826700i	$0.309784\pi$
$410$	0.129203	−	0.164946i	0.00638090	−	0.00814611i
$411$	−8.67100	+	28.1009i	−0.427709	+	1.38612i
$412$	−4.99104	−	0.436659i	−0.245891	−	0.0215127i
$413$	−14.2225	−	6.63207i	−0.699844	−	0.326343i
$414$	−0.346703	−	0.156520i	−0.0170395	−	0.00769255i
$415$	−12.9260	−	14.3920i	−0.634511	−	0.706475i
$416$	3.07423	+	0.542069i	0.150726	+	0.0265771i
$417$	7.51750	+	0.282022i	0.368133	+	0.0138107i
$418$	−3.47772	−	0.633988i	−0.170101	−	0.0310094i
$419$	−7.98682			−0.390182			−0.195091	−	0.980785i	$-0.562500\pi$
$419$	−7.98682			−0.390182			−0.195091	+	0.980785i	$0.562500\pi$
$420$	−2.53101	+	6.87158i	−0.123501	+	0.335299i
$421$	23.2537	+	19.5122i	1.13332	+	0.950965i	0.999200	−	0.0400000i	$-0.0127358\pi$
$421$	23.2537	+	19.5122i	1.13332	+	0.950965i	0.134117	+	0.990966i	$0.457180\pi$
$422$	7.51505	−	3.50433i	0.365827	−	0.170588i
$423$	−10.7236	+	19.1115i	−0.521397	+	0.929235i
$424$	−2.81804	−	3.35841i	−0.136856	−	0.163099i
$425$	−2.49616	+	4.13082i	−0.121082	+	0.200374i
$426$	−3.82679	−	16.7738i	−0.185409	−	0.812695i
$427$	−10.1438	+	14.4869i	−0.490894	+	0.701069i
$428$	−8.66119	+	12.3695i	−0.418655	+	0.597901i
$429$	−0.975318	−	4.27508i	−0.0470888	−	0.206403i
$430$	4.97437	−	11.6781i	0.239885	−	0.563170i
$431$	20.7023	+	24.6720i	0.997194	+	1.18841i	0.982069	+	0.188523i	$0.0603701\pi$
$431$	20.7023	+	24.6720i	0.997194	+	1.18841i	0.0151249	+	0.999886i	$0.495185\pi$
$432$	1.21783	+	5.05142i	0.0585929	+	0.243037i
$433$	−25.8832	+	12.0696i	−1.24387	+	0.580026i	−0.929341	−	0.369222i	$-0.879624\pi$
$433$	−25.8832	+	12.0696i	−1.24387	+	0.580026i	−0.314528	+	0.949248i	$0.601846\pi$
$434$	11.3855	+	9.55357i	0.546521	+	0.458586i
$435$	−10.5448	+	4.86785i	−0.505585	+	0.233396i
$436$	−4.55967			−0.218368
$437$	0.544853	−	0.0928245i	0.0260639	−	0.00444040i
$438$	19.6361	+	0.736657i	0.938249	+	0.0351988i
$439$	6.31942	+	1.11428i	0.301609	+	0.0531819i	0.322405	−	0.946602i	$-0.395509\pi$
$439$	6.31942	+	1.11428i	0.301609	+	0.0531819i	−0.0207955	+	0.999784i	$0.506620\pi$
$440$	1.34916	−	1.21173i	0.0643188	−	0.0577671i
$441$	4.22784	−	9.36496i	0.201326	−	0.445950i
$442$	2.73097	+	1.27347i	0.129899	+	0.0605728i
$443$	−15.1052	−	1.32154i	−0.717671	−	0.0627881i	−0.277530	−	0.960717i	$-0.589516\pi$
$443$	−15.1052	−	1.32154i	−0.717671	−	0.0627881i	−0.440141	+	0.897929i	$0.645071\pi$
$444$	−1.29210	+	4.18742i	−0.0613202	+	0.198726i
$445$	3.54087	+	29.1400i	0.167853	+	1.38137i
$446$	16.3270	−	2.87890i	0.773108	−	0.136320i
$447$	23.6100	−	3.25580i	1.11671	−	0.153994i
$448$	0.489365	+	1.82633i	0.0231203	+	0.0862862i
$449$	2.31054	+	4.00197i	0.109041	+	0.188865i	0.915382	−	0.402586i	$-0.131889\pi$
$449$	2.31054	+	4.00197i	0.109041	+	0.188865i	−0.806341	+	0.591451i	$0.798555\pi$
$450$	13.5455	+	6.44362i	0.638540	+	0.303755i
$451$	−0.0714091	+	0.0259908i	−0.00336252	+	0.00122386i
$452$	−6.40342	+	2.98596i	−0.301191	+	0.140448i
$453$	18.1740	−	20.0794i	0.853888	−	0.943411i
$454$	−4.16010	−	0.733537i	−0.195243	−	0.0344266i
$455$	10.5503	−	7.92950i	0.494605	−	0.371741i
$456$	−5.56810	−	5.09865i	−0.260750	−	0.238766i
$457$	15.4936	+	15.4936i	0.724762	+	0.724762i	0.969571	−	0.244809i	$-0.0787253\pi$
$457$	15.4936	+	15.4936i	0.724762	+	0.724762i	−0.244809	+	0.969571i	$0.578725\pi$
$458$	−24.2335	+	16.9685i	−1.13236	+	0.792886i
$459$	−0.126520	+	5.01418i	−0.00590546	+	0.234042i
$460$	−0.133423	+	0.250176i	−0.00622090	+	0.0116645i
$461$	−2.61369	−	7.18105i	−0.121732	−	0.334455i	0.863827	−	0.503788i	$-0.168061\pi$
$461$	−2.61369	−	7.18105i	−0.121732	−	0.334455i	−0.985559	+	0.169333i	$0.945839\pi$
$462$	2.09712	−	1.62971i	0.0975667	−	0.0758212i
$463$	33.5356	+	8.98584i	1.55853	+	0.417607i	0.932198	−	0.361948i	$-0.117888\pi$
$463$	33.5356	+	8.98584i	1.55853	+	0.417607i	0.626334	+	0.779555i	$0.284555\pi$
$464$	−1.49938	+	2.59701i	−0.0696071	+	0.120563i
$465$	21.6100	−	21.4445i	1.00214	−	0.994465i
$466$	1.21242	+	6.87596i	0.0561641	+	0.318523i
$467$	4.29264	+	16.0203i	0.198640	+	0.741333i	0.991295	+	0.131663i	$0.0420316\pi$
$467$	4.29264	+	16.0203i	0.198640	+	0.741333i	−0.792655	+	0.609671i	$0.791302\pi$
$468$	3.09478	−	8.83882i	0.143056	−	0.408574i
$469$	7.92471	+	9.44430i	0.365929	+	0.436097i
$470$	13.6878	+	8.91336i	0.631370	+	0.411143i
$471$	26.4684	−	11.1543i	1.21960	−	0.513965i
$472$	0.723369	+	8.26815i	0.0332958	+	0.380572i
$473$	−3.77116	+	2.64060i	−0.173398	+	0.121415i
$474$	−7.30057	+	6.77261i	−0.335326	+	0.311076i
$475$	−21.5537	+	3.23076i	−0.988952	+	0.148237i
$476$			1.82513i			0.0836545i
$477$	−11.3087	+	6.71542i	−0.517789	+	0.307478i
$478$	−18.3486	+	1.60530i	−0.839247	+	0.0734246i
$479$	−11.0651	−	4.02738i	−0.505579	−	0.184016i	0.0766227	−	0.997060i	$-0.475586\pi$
$479$	−11.0651	−	4.02738i	−0.505579	−	0.184016i	−0.582202	+	0.813044i	$0.697809\pi$
$480$	3.81670	−	0.657867i	0.174208	−	0.0300274i
$481$	6.05026	−	5.07677i	0.275868	−	0.231481i
$482$	17.7534	+	4.75700i	0.808644	+	0.216676i
$483$	−0.220962	+	0.351583i	−0.0100541	+	0.0159976i
$484$	10.1852	−	1.79592i	0.462962	−	0.0816327i
$485$	−0.629876	−	18.7097i	−0.0286012	−	0.849564i
$486$	15.5454	−	1.15731i	0.705155	−	0.0524968i
$487$	−5.78963	+	21.6072i	−0.262353	+	0.979115i	0.701498	+	0.712672i	$0.252515\pi$
$487$	−5.78963	+	21.6072i	−0.262353	+	0.979115i	−0.963851	+	0.266443i	$0.914152\pi$
$488$	9.31790	+	0.815211i	0.421802	+	0.0369029i
$489$	−2.38709	−	1.22408i	−0.107948	−	0.0553550i
$490$	−6.75762	−	3.60396i	−0.305278	−	0.162810i
$491$	−28.3791	+	33.8209i	−1.28073	+	1.52631i	−0.573920	+	0.818912i	$0.694578\pi$
$491$	−28.3791	+	33.8209i	−1.28073	+	1.52631i	−0.706810	+	0.707403i	$0.749867\pi$
$492$	−0.158663	−	0.0341548i	−0.00715308	−	0.00153982i
$493$	−2.04684	+	2.04684i	−0.0921851	+	0.0921851i
$494$	3.44562	+	13.1635i	0.155026	+	0.592253i
$495$	−2.93357	−	4.58159i	−0.131854	−	0.205927i
$496$	1.36500	−	7.74128i	0.0612902	−	0.347594i
$497$	−18.7099	+	1.63690i	−0.839252	+	0.0734250i
$498$	−5.64916	+	13.8785i	−0.253145	+	0.621911i
$499$	−7.58348	−	20.8355i	−0.339483	−	0.932723i	−0.985541	−	0.169435i	$-0.945806\pi$
$499$	−7.58348	−	20.8355i	−0.339483	−	0.932723i	0.646058	−	0.763288i	$-0.276416\pi$
$500$	5.45707	−	9.75809i	0.244048	−	0.436395i
$501$	7.62190	−	24.7010i	0.340522	−	1.10356i
$502$	20.7646	−	5.56387i	0.926772	−	0.248328i
$503$	21.7162	−	31.0139i	0.968277	−	1.38284i	0.0448811	−	0.998992i	$-0.485709\pi$
$503$	21.7162	−	31.0139i	0.968277	−	1.38284i	0.923395	−	0.383850i	$-0.125402\pi$
$504$	5.64421	−	0.563671i	0.251413	−	0.0251079i
$505$	16.7085	−	2.03029i	0.743518	−	0.0903466i
$506$	0.0890559	−	0.0514165i	0.00395902	−	0.00228574i
$507$	4.45205	−	3.45978i	0.197722	−	0.153654i
$508$	−5.12789	+	10.9968i	−0.227513	+	0.487904i
$509$	−31.6430	−	11.5171i	−1.40255	−	0.510486i	−0.473615	−	0.880732i	$-0.657051\pi$
$509$	−31.6430	−	11.5171i	−1.40255	−	0.510486i	−0.928934	+	0.370246i	$0.879273\pi$
$510$	3.72303	+	0.340152i	0.164859	+	0.0150622i
$511$	3.72483	−	21.1246i	0.164777	−	0.934496i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−17.7936	+	14.0138i	−0.785608	+	0.618724i
$514$			15.2917i			0.674488i
$515$	10.6503	+	3.47525i	0.469307	+	0.153138i
$516$	−9.82012	+	0.489138i	−0.432307	+	0.0215331i
$517$	−2.50366	−	5.36912i	−0.110111	−	0.236133i
$518$	4.33559	+	2.02172i	0.190495	+	0.0888291i
$519$	−3.27126	+	26.0833i	−0.143592	+	1.14493i
$520$	−6.42191	−	2.73544i	−0.281619	−	0.119957i
$521$	−1.88567	−	1.08869i	−0.0826129	−	0.0476966i	0.458125	−	0.888888i	$-0.348521\pi$
$521$	−1.88567	−	1.08869i	−0.0826129	−	0.0476966i	−0.540737	+	0.841191i	$0.681855\pi$
$522$	6.96200	+	5.69771i	0.304719	+	0.249382i
$523$	−32.1392	−	22.5041i	−1.40535	−	0.984035i	−0.997477	−	0.0709962i	$-0.977382\pi$
$523$	−32.1392	−	22.5041i	−1.40535	−	0.984035i	−0.407872	−	0.913039i	$-0.633729\pi$
$524$	−10.0120	+	17.3413i	−0.437376	+	0.757558i
$525$	8.98807	−	13.6871i	0.392272	−	0.597356i
$526$	−11.0653	+	9.28488i	−0.482469	+	0.404840i
$527$	3.20676	−	6.87691i	0.139689	−	0.299563i
$528$	−1.30103	−	0.529575i	−0.0566200	−	0.0230468i
$529$	14.7738	−	17.6067i	0.642338	−	0.765509i
$530$	4.43958	+	8.74024i	0.192843	+	0.379652i
$531$	24.8292	+	1.86558i	1.07750	+	0.0809594i
$532$	−6.34401	+	5.26100i	−0.275048	+	0.228093i
$533$	0.206833	+	0.206833i	0.00895894	+	0.00895894i
$534$	19.1015	−	12.3344i	0.826605	−	0.533763i
$535$	25.1209	−	22.5620i	1.08607	−	0.975439i
$536$	2.23013	−	6.12724i	0.0963271	−	0.264657i
$537$	11.7210	+	36.3942i	0.505799	+	1.57052i
$538$	1.35687	−	15.5091i	0.0584987	−	0.668644i
$539$	1.38883	+	2.40553i	0.0598213	+	0.103614i
$540$	−0.0978990	−	11.6185i	−0.00421290	−	0.499982i
$541$	−5.69603	−	32.3038i	−0.244891	−	1.38885i	−0.820745	−	0.571295i	$-0.806441\pi$
$541$	−5.69603	−	32.3038i	−0.244891	−	1.38885i	0.575854	−	0.817553i	$-0.304670\pi$
$542$	16.4201	+	11.4975i	0.705305	+	0.493860i
$543$	−21.4838	−	13.5021i	−0.921956	−	0.579430i
$544$	0.835963	−	0.482643i	0.0358416	−	0.0206932i
$545$	9.93153	+	2.30599i	0.425420	+	0.0987778i
$546$	−9.09677	−	4.66477i	−0.389306	−	0.199634i
$547$	−3.17496	−	6.80872i	−0.135751	−	0.291120i	0.826667	−	0.562692i	$-0.190234\pi$
$547$	−3.17496	−	6.80872i	−0.135751	−	0.291120i	−0.962418	+	0.271572i	$0.912456\pi$
$548$	−1.47981	−	16.9143i	−0.0632142	−	0.722542i
$549$	6.92946	−	27.1914i	0.295742	−	1.16050i
$550$	−3.55147	+	1.95699i	−0.151435	+	0.0834462i
$551$	−13.0148	−	1.21458i	−0.554448	−	0.0517427i
$552$	0.219468	+	0.00823343i	0.00934117	+	0.000350438i
$553$	6.23520	+	8.90478i	0.265148	+	0.378670i
$554$	−2.23571	−	1.87598i	−0.0949861	−	0.0797028i
$555$	4.93208	−	8.46727i	0.209355	−	0.359416i
$556$	−4.08135	+	1.48549i	−0.173088	+	0.0629988i
$557$	1.04739	−	11.9717i	0.0443794	−	0.507258i	−0.941177	−	0.337913i	$-0.890279\pi$
$557$	1.04739	−	11.9717i	0.0443794	−	0.507258i	0.985557	−	0.169345i	$-0.0541654\pi$
$558$	−22.2572	−	7.79304i	−0.942224	−	0.329906i
$559$	15.3465	+	8.86031i	0.649088	+	0.374751i
$560$	−0.142254	−	4.22548i	−0.00601132	−	0.178559i
$561$	−1.08077	−	0.818815i	−0.0456300	−	0.0345704i
$562$	−5.96801	+	1.59912i	−0.251745	+	0.0674550i
$563$	−2.05076	+	7.65353i	−0.0864291	+	0.322558i	−0.995581	−	0.0939070i	$-0.970064\pi$
$563$	−2.05076	+	7.65353i	−0.0864291	+	0.322558i	0.909152	+	0.416465i	$0.136731\pi$
$564$	1.57447	−	12.5540i	0.0662971	−	0.528619i
$565$	15.4576	−	3.26536i	0.650304	−	0.137375i
$566$	−9.56650	+	26.2837i	−0.402110	+	1.10479i
$567$	1.06668	−	16.9834i	0.0447964	−	0.713235i
$568$	5.69746	+	8.13681i	0.239060	+	0.341413i
$569$	10.3664			0.434582			0.217291	−	0.976107i	$-0.430278\pi$
$569$	10.3664			0.434582			0.217291	+	0.976107i	$0.430278\pi$
$570$	9.54944	+	13.9215i	0.399982	+	0.583107i
$571$	7.43668			0.311215			0.155608	−	0.987819i	$-0.450266\pi$
$571$	7.43668			0.311215			0.155608	+	0.987819i	$0.450266\pi$
$572$	1.45209	+	2.07379i	0.0607148	+	0.0867097i
$573$	−0.805955	−	0.729475i	−0.0336692	−	0.0304743i
$574$	−0.0605954	+	0.166484i	−0.00252920	+	0.00694892i
$575$	0.417136	−	0.477438i	0.0173958	−	0.0199105i
$576$	−1.75075	−	2.43616i	−0.0729481	−	0.101507i
$577$	−8.00504	+	29.8752i	−0.333254	+	1.24372i	0.572495	+	0.819908i	$0.305975\pi$
$577$	−8.00504	+	29.8752i	−0.333254	+	1.24372i	−0.905749	+	0.423814i	$0.860691\pi$
$578$	−15.5207	+	4.15876i	−0.645576	+	0.172982i
$579$	7.80450	−	10.3013i	0.324344	−	0.428106i
$580$	4.57925	−	4.89832i	0.190143	−	0.203391i
$581$	14.1658	+	8.17861i	0.587695	+	0.339306i
$582$	−12.8209	+	6.77446i	−0.531445	+	0.280810i
$583$	0.309880	−	3.54194i	0.0128339	−	0.146692i
$584$	−10.6607	+	3.88018i	−0.441143	+	0.160563i
$585$	−11.2109	+	17.6869i	−0.463515	+	0.731264i
$586$	2.87101	+	2.40906i	0.118600	+	0.0995174i
$587$	14.2331	+	20.3270i	0.587464	+	0.838985i	0.997320	−	0.0731653i	$-0.0233101\pi$
$587$	14.2331	+	20.3270i	0.587464	+	0.838985i	−0.409856	+	0.912150i	$0.634421\pi$
$588$	−0.222397	+	5.92814i	−0.00917150	+	0.244473i
$589$	33.1473	−	8.67650i	1.36581	−	0.357509i
$590$	2.60592	−	18.3749i	0.107284	−	0.756483i
$591$	−16.6170	+	10.7301i	−0.683534	+	0.441378i
$592$	−0.220512	−	2.52046i	−0.00906297	−	0.103590i
$593$	9.96781	+	21.3760i	0.409329	+	0.877808i	0.997606	+	0.0691493i	$0.0220285\pi$
$593$	9.96781	+	21.3760i	0.409329	+	0.877808i	−0.588278	+	0.808659i	$0.700194\pi$
$594$	−2.19840	+	3.59515i	−0.0902016	+	0.147511i
$595$	0.923033	−	3.97535i	0.0378407	−	0.162974i
$596$	−11.9167	+	6.88011i	−0.488127	+	0.281820i
$597$	−24.4182	+	38.8529i	−0.999371	+	1.59014i
$598$	−0.324238	−	0.227034i	−0.0132591	−	0.00928412i
$599$	−6.24630	−	35.4245i	−0.255217	−	1.44741i	−0.795515	−	0.605934i	$-0.792800\pi$
$599$	−6.24630	−	35.4245i	−0.255217	−	1.44741i	0.540298	−	0.841474i	$-0.318311\pi$
$600$	−8.64596	−	0.497329i	−0.352970	−	0.0203034i
$601$	−9.61272	−	16.6497i	−0.392111	−	0.679156i	0.600617	−	0.799537i	$-0.294922\pi$
$601$	−9.61272	−	16.6497i	−0.392111	−	0.679156i	−0.992728	+	0.120381i	$0.961588\pi$
$602$	−0.935464	+	10.6924i	−0.0381267	+	0.435790i
$603$	−17.0594	−	9.57211i	−0.694714	−	0.389806i
$604$	−5.34790	+	14.6932i	−0.217603	+	0.597860i
$605$	−23.0928	−	1.23927i	−0.938857	−	0.0503836i
$606$	−7.07240	−	10.9526i	−0.287297	−	0.444918i
$607$	6.42904	+	6.42904i	0.260947	+	0.260947i	0.825439	−	0.564492i	$-0.190928\pi$
$607$	6.42904	+	6.42904i	0.260947	+	0.260947i	−0.564492	+	0.825439i	$0.690928\pi$
$608$	4.08733	+	1.51451i	0.165763	+	0.0614215i
$609$	7.19969	−	6.67903i	0.291746	−	0.270648i
$610$	−19.8833	−	6.48803i	−0.805050	−	0.262693i
$611$	−14.6576	+	17.4682i	−0.592982	+	0.706689i
$612$	−1.02376	−	2.70886i	−0.0413830	−	0.109499i
$613$	15.5748	−	33.4002i	0.629059	−	1.34902i	−0.290804	−	0.956783i	$-0.593923\pi$
$613$	15.5748	−	33.4002i	0.629059	−	1.34902i	0.919863	−	0.392239i	$-0.128299\pi$
$614$	8.24372	−	6.91730i	0.332689	−	0.279160i
$615$	0.328314	+	0.154635i	0.0132389	+	0.00623549i
$616$	−0.766696	+	1.32796i	−0.0308911	+	0.0535049i
$617$	11.8596	+	8.30416i	0.477448	+	0.334313i	0.787403	−	0.616439i	$-0.211425\pi$
$617$	11.8596	+	8.30416i	0.477448	+	0.334313i	−0.309955	+	0.950751i	$0.600314\pi$
$618$	−1.18544	−	8.59640i	−0.0476853	−	0.345798i
$619$	3.70601	+	2.13967i	0.148957	+	0.0860005i	0.572626	−	0.819817i	$-0.305925\pi$
$619$	3.70601	+	2.13967i	0.148957	+	0.0860005i	−0.423669	+	0.905817i	$0.639258\pi$
$620$	−6.88818	+	16.1712i	−0.276636	+	0.649449i
$621$	0.130742	−	0.645765i	0.00524648	−	0.0259136i
$622$	−17.2713	−	8.05372i	−0.692515	−	0.322925i
$623$	−10.4899	−	22.4957i	−0.420270	−	0.901272i
$624$	0.268981	+	5.40016i	0.0107678	+	0.216180i
$625$	−16.8212	+	18.4945i	−0.672848	+	0.739780i
$626$			25.3509i			1.01322i
$627$	−0.269206	−	6.11693i	−0.0107511	−	0.244287i
$628$	−11.7260	+	11.7260i	−0.467919	+	0.467919i
$629$	0.424094	−	2.40516i	0.0169097	−	0.0958999i
$630$	−12.5789	−	1.62674i	−0.501154	−	0.0648107i
$631$	33.8150	+	12.3076i	1.34615	+	0.489959i	0.911745	−	0.410757i	$-0.134736\pi$
$631$	33.8150	+	12.3076i	1.34615	+	0.489959i	0.434407	+	0.900717i	$0.356958\pi$
$632$	2.42980	−	5.21072i	0.0966522	−	0.207271i
$633$	8.81281	+	11.3403i	0.350278	+	0.450738i
$634$	−0.727541	+	0.420046i	−0.0288943	+	0.0166822i
$635$	16.7307	−	21.3590i	0.663936	−	0.847607i
$636$	4.58557	−	6.05256i	0.181830	−	0.240000i
$637$	6.13252	−	8.75815i	0.242979	−	0.347011i
$638$	−2.34911	+	0.629442i	−0.0930021	+	0.0249198i
$639$	26.8511	−	12.9243i	1.06221	−	0.511278i
$640$	−1.89778	+	1.18256i	−0.0750162	+	0.0467447i
$641$	−12.5281	−	34.4206i	−0.494829	−	1.35953i	−0.896214	−	0.443623i	$-0.853693\pi$
$641$	−12.5281	−	34.4206i	−0.494829	−	1.35953i	0.401384	−	0.915910i	$-0.368529\pi$
$642$	−24.2246	−	9.86047i	−0.956069	−	0.389162i
$643$	−0.232671	+	0.0203561i	−0.00917567	+	0.000802767i	−0.0917427	−	0.995783i	$-0.529244\pi$
$643$	−0.232671	+	0.0203561i	−0.00917567	+	0.000802767i	0.0825670	+	0.996586i	$0.473688\pi$
$644$	0.0416315	−	0.236104i	0.00164051	−	0.00930381i
$645$	21.6368	+	3.90099i	0.851950	+	0.153601i
$646$	3.43263	+	2.43328i	0.135055	+	0.0957361i
$647$	−10.8675	+	10.8675i	−0.427245	+	0.427245i	−0.887689	−	0.460444i	$-0.847690\pi$
$647$	−10.8675	+	10.8675i	−0.427245	+	0.427245i	0.460444	+	0.887689i	$0.347690\pi$
$648$	−8.06098	+	4.00258i	−0.316665	+	0.157236i
$649$	−4.32661	+	5.15626i	−0.169834	+	0.202401i
$650$	12.6043	+	9.20593i	0.494381	+	0.361086i
$651$	−11.7465	+	22.9068i	−0.460380	+	0.897788i
$652$	1.54293	+	0.134989i	0.0604258	+	0.00528657i
$653$	6.79675	−	25.3658i	0.265977	−	0.992641i	−0.695672	−	0.718359i	$-0.744893\pi$
$653$	6.79675	−	25.3658i	0.265977	−	0.992641i	0.961649	−	0.274282i	$-0.0884400\pi$
$654$	−1.75662	−	7.69974i	−0.0686893	−	0.301084i
$655$	30.5775	−	32.7081i	1.19476	−	1.27801i
$656$	0.0922789	−	0.0162713i	0.00360289	−	0.000635286i
$657$	6.32088	+	33.4425i	0.246601	+	1.30472i
$658$	−13.3411	−	3.57473i	−0.520089	−	0.139358i
$659$	−3.71987	+	3.12134i	−0.144906	+	0.121590i	−0.712359	−	0.701815i	$-0.752373\pi$
$659$	−3.71987	+	3.12134i	−0.144906	+	0.121590i	0.567453	+	0.823406i	$0.307929\pi$
$660$	2.56598	+	1.81146i	0.0998805	+	0.0705109i
$661$	12.7225	+	4.63060i	0.494847	+	0.180109i	0.577375	−	0.816479i	$-0.304077\pi$
$661$	12.7225	+	4.63060i	0.494847	+	0.180109i	−0.0825282	+	0.996589i	$0.526299\pi$
$662$	15.9805	−	1.39811i	0.621098	−	0.0543390i
$663$	−1.09835	+	5.10229i	−0.0426564	+	0.198156i
$664$		−	8.65113i		−	0.335729i
$665$	16.4787	−	8.25071i	0.639018	−	0.319949i
$666$	−7.56893	−	0.568704i	−0.293290	−	0.0220368i
$667$	0.311475	−	0.218097i	0.0120603	−	0.00844475i
$668$	1.30077	+	14.8678i	0.0503282	+	0.575254i
$669$	11.1515	+	26.4618i	0.431142	+	1.02307i
$670$	−7.95628	+	12.2180i	−0.307378	+	0.472024i
$671$	4.87593	+	5.81091i	0.188233	+	0.224328i
$672$	−2.89553	+	1.52997i	−0.111698	+	0.0590199i
$673$	9.78477	+	36.5172i	0.377175	+	1.40764i	0.850141	+	0.526555i	$0.176517\pi$
$673$	9.78477	+	36.5172i	0.377175	+	1.40764i	−0.472966	+	0.881081i	$0.656817\pi$
$674$	3.96574	+	22.4908i	0.152754	+	0.866314i
$675$	−5.66268	+	25.3561i	−0.217957	+	0.975958i
$676$	−1.62765	+	2.81917i	−0.0626018	+	0.108429i
$677$	32.7093	+	8.76444i	1.25712	+	0.336845i	0.825083	−	0.565011i	$-0.191128\pi$
$677$	32.7093	+	8.76444i	1.25712	+	0.336845i	0.432038	+	0.901855i	$0.357795\pi$
$678$	−7.50921	−	9.66286i	−0.288390	−	0.371100i
$679$	5.41397	+	14.8748i	0.207769	+	0.570841i
$680$	−2.06492	+	0.628481i	−0.0791862	+	0.0241011i
$681$	−0.363989	−	7.30760i	−0.0139481	−	0.280028i
$682$	5.22207	−	3.65653i	0.199963	−	0.140016i
$683$	−23.5109	−	23.5109i	−0.899618	−	0.899618i	0.0957838	−	0.995402i	$-0.469464\pi$
$683$	−23.5109	−	23.5109i	−0.899618	−	0.899618i	−0.995402	+	0.0957838i	$0.969464\pi$
$684$	6.46478	−	11.3669i	0.247187	−	0.434625i
$685$	−5.33096	+	37.5898i	−0.203686	+	1.43623i
$686$	19.4118	+	3.42282i	0.741145	+	0.130684i
$687$	−37.9901	−	34.3851i	−1.44941	−	1.31187i
$688$	5.14482	−	2.39907i	0.196144	−	0.0914636i
$689$	−12.8603	+	4.68076i	−0.489938	+	0.178323i
$690$	−0.473865	−	0.128926i	−0.0180397	−	0.00490814i
$691$	−14.4273	−	24.9888i	−0.548839	−	0.950617i	−0.998354	−	0.0573445i	$-0.981737\pi$
$691$	−14.4273	−	24.9888i	−0.548839	−	0.950617i	0.449515	−	0.893273i	$-0.351597\pi$
$692$	−3.92814	−	14.6600i	−0.149326	−	0.557291i
$693$	3.55996	+	2.91347i	0.135232	+	0.110674i
$694$	−26.7377	+	4.71457i	−1.01495	+	0.178963i
$695$	9.64096	−	1.17150i	0.365702	−	0.0444373i
$696$	−4.96311	−	1.53145i	−0.188126	−	0.0580494i
$697$	0.0901056	+	0.00788322i	0.00341299	+	0.000298598i
$698$	−18.7059	−	8.72273i	−0.708031	−	0.330160i
$699$	−11.1441	+	4.69634i	−0.421508	+	0.177632i
$700$	−1.82713	+	9.27556i	−0.0690591	+	0.350583i
$701$	−27.5630	−	4.86011i	−1.04104	−	0.183564i	−0.373111	−	0.927787i	$-0.621709\pi$
$701$	−27.5630	−	4.86011i	−1.04104	−	0.183564i	−0.667931	+	0.744223i	$0.732820\pi$
$702$	16.1180	+	1.82086i	0.608337	+	0.0687241i
$703$	9.58262	−	5.45883i	0.361415	−	0.205884i
$704$	0.810992			0.0305654
$705$	−9.77841	+	26.5479i	−0.368276	+	0.999853i
$706$	22.8214	+	19.1494i	0.858895	+	0.720698i
$707$	−12.8987	+	6.01478i	−0.485107	+	0.226209i
$708$	−13.6834	+	4.40685i	−0.514255	+	0.165620i
$709$	−8.02993	−	9.56969i	−0.301570	−	0.359397i	0.593884	−	0.804550i	$-0.297594\pi$
$709$	−8.02993	−	9.56969i	−0.301570	−	0.359397i	−0.895454	+	0.445153i	$0.853149\pi$
$710$	−8.29469	−	20.6044i	−0.311294	−	0.773270i
$711$	−14.2492	−	9.71904i	−0.534387	−	0.364493i
$712$	−7.52972	+	10.7536i	−0.282188	+	0.403007i
$713$	−0.571700	+	0.816473i	−0.0214103	+	0.0305771i
$714$	−3.08202	+	0.703134i	−0.115342	+	0.0263141i
$715$	−2.11403	−	5.25135i	−0.0790603	−	0.196390i
$716$	−14.1895	−	16.9104i	−0.530288	−	0.631972i
$717$	−9.77966	−	30.3662i	−0.365228	−	1.13405i
$718$	−1.99780	+	0.931590i	−0.0745572	+	0.0347666i
$719$	−9.51171	−	7.98127i	−0.354727	−	0.297651i	0.447958	−	0.894055i	$-0.352151\pi$
$719$	−9.51171	−	7.98127i	−0.354727	−	0.297651i	−0.802685	+	0.596403i	$0.796596\pi$
$720$	2.58131	+	6.19168i	0.0961997	+	0.230750i
$721$	−9.47290			−0.352789
$722$	1.43679	+	18.9456i	0.0534716	+	0.705082i
$723$	−1.19345	+	31.8121i	−0.0443847	+	1.18310i
$724$	14.4273	+	2.54393i	0.536187	+	0.0945443i
$725$	−12.4514	+	8.35325i	−0.462435	+	0.310232i
$726$	6.95656	+	16.5074i	0.258182	+	0.612648i
$727$	−19.4273	−	9.05908i	−0.720517	−	0.335983i	0.0275368	−	0.999621i	$-0.491234\pi$
$727$	−19.4273	−	9.05908i	−0.720517	−	0.335983i	−0.748054	+	0.663638i	$0.769011\pi$
$728$	5.87984	+	0.514419i	0.217921	+	0.0190656i
$729$	7.94323	+	25.8051i	0.294194	+	0.955746i
$730$	25.1827	−	3.06001i	0.932053	−	0.113256i
$731$	5.39638	−	0.951527i	0.199592	−	0.0351935i
$732$	2.21313	+	16.0488i	0.0817995	+	0.593183i
$733$	−1.87770	−	7.00768i	−0.0693545	−	0.258834i	0.922540	−	0.385903i	$-0.126110\pi$
$733$	−1.87770	−	7.00768i	−0.0693545	−	0.258834i	−0.991894	+	0.127068i	$0.959443\pi$
$734$	6.72046	+	11.6402i	0.248057	+	0.429647i
$735$	3.48249	−	12.7998i	0.128454	−	0.472127i
$736$	−0.119152	+	0.0433678i	−0.00439200	+	0.00159856i
$737$	4.79260	−	2.23483i	0.176538	−	0.0823209i
$738$	−0.00344931	−	0.281086i	−0.000126971	−	0.0103469i
$739$	−12.0005	−	2.11601i	−0.441445	−	0.0778386i	−0.0514918	−	0.998673i	$-0.516398\pi$
$739$	−12.0005	−	2.11601i	−0.441445	−	0.0778386i	−0.389953	+	0.920835i	$0.627509\pi$
$740$	−0.794387	+	5.60140i	−0.0292022	+	0.205911i
$741$	−20.9012	+	10.8898i	−0.767826	+	0.400045i
$742$	−5.86141	−	5.86141i	−0.215179	−	0.215179i
$743$	−8.01028	+	5.60886i	−0.293869	+	0.205769i	−0.711208	−	0.702982i	$-0.751852\pi$
$743$	−8.01028	+	5.60886i	−0.293869	+	0.205769i	0.417339	+	0.908751i	$0.362963\pi$
$744$	13.5983	−	0.677327i	0.498537	−	0.0248320i
$745$	29.4356	−	8.95903i	1.07844	−	0.328233i
$746$	2.92652	+	8.04055i	0.107148	+	0.294385i
$747$	−25.6125	−	4.19280i	−0.937112	−	0.153407i
$748$	0.756165	+	0.202614i	0.0276481	+	0.00740830i
$749$	−14.2756	+	24.7260i	−0.521617	+	0.903468i
$750$	18.5805	+	5.45583i	0.678463	+	0.199219i
$751$	−7.95328	−	45.1053i	−0.290219	−	1.64592i	−0.686023	−	0.727580i	$-0.740645\pi$
$751$	−7.95328	−	45.1053i	−0.290219	−	1.64592i	0.395803	−	0.918335i	$-0.370466\pi$
$752$	1.89063	+	7.05593i	0.0689442	+	0.257303i
$753$	17.3951	+	32.9210i	0.633914	+	1.19971i
$754$	6.01720	+	7.17102i	0.219134	+	0.261153i
$755$	19.0793	−	29.2991i	0.694367	−	1.06630i
$756$	3.12629	+	9.31400i	0.113702	+	0.338747i
$757$	1.73513	+	19.8326i	0.0630642	+	0.720828i	0.960244	+	0.279162i	$0.0900567\pi$
$757$	1.73513	+	19.8326i	0.0630642	+	0.720828i	−0.897180	+	0.441666i	$0.854388\pi$
$758$	6.95542	−	4.87024i	0.252632	−	0.176895i
$759$	0.121134	+	0.130577i	0.00439689	+	0.00473965i
$760$	−8.13677	−	5.36590i	−0.295152	−	0.194642i
$761$		−	16.1848i		−	0.586697i	−0.956006	−	0.293348i	$-0.905230\pi$
$761$		−	16.1848i		−	0.586697i	0.956006	−	0.293348i	$-0.0947696\pi$
$762$	−20.5454	−	4.42273i	−0.744281	−	0.160219i
$763$	−8.58843	+	0.751390i	−0.310922	+	0.0272022i
$764$	0.589764	+	0.214657i	0.0213369	+	0.00776600i
$765$	0.859904	+	6.41799i	0.0310899	+	0.232043i
$766$	20.5068	−	17.2073i	0.740942	−	0.621724i
$767$	25.0260	+	6.70571i	0.903638	+	0.242129i
$768$	1.46648	+	0.921650i	0.0529170	+	0.0332572i
$769$	−31.0642	+	5.47745i	−1.12020	+	0.197522i	−0.702930	−	0.711259i	$-0.748125\pi$
$769$	−31.0642	+	5.47745i	−1.12020	+	0.197522i	−0.417273	+	0.908781i	$0.637014\pi$
$770$	2.34156	−	2.50471i	0.0843838	−	0.0902634i
$771$	−25.8225	+	5.89116i	−0.929975	+	0.212165i
$772$	−1.93120	+	7.20735i	−0.0695055	+	0.259398i
$773$	−15.9770	−	1.39781i	−0.574654	−	0.0502757i	−0.203875	−	0.978997i	$-0.565354\pi$
$773$	−15.9770	−	1.39781i	−0.574654	−	0.0502757i	−0.370779	+	0.928721i	$0.620909\pi$
$774$	−4.60921	−	16.3944i	−0.165675	−	0.589286i
$775$	23.1817	−	31.7392i	0.832710	−	1.14011i
$776$	5.38140	−	6.41330i	0.193181	−	0.230224i
$777$	−1.74370	+	8.10021i	−0.0625550	+	0.290593i
$778$	22.0520	−	22.0520i	0.790604	−	0.790604i
$779$	0.232331	+	0.335924i	0.00832413	+	0.0120357i
$780$	2.14519	−	11.8983i	0.0768100	−	0.426026i
$781$	−1.39887	+	7.93337i	−0.0500554	+	0.283878i
$782$	−0.121932	+	0.0106676i	−0.00436027	+	0.000381474i
$783$	−6.93939	+	13.9515i	−0.247993	+	0.498587i
$784$	−1.17143	−	3.21847i	−0.0418367	−	0.114945i
$785$	31.4710	−	19.6105i	1.12325	−	0.699928i
$786$	−33.1407	−	10.2261i	−1.18209	−	0.364754i
$787$	−32.9323	+	8.82418i	−1.17391	+	0.314548i	−0.792508	−	0.609861i	$-0.791225\pi$
$787$	−32.9323	+	8.82418i	−1.17391	+	0.314548i	−0.381402	+	0.924409i	$0.624558\pi$
$788$	6.55034	−	9.35486i	0.233346	−	0.333253i
$789$	−19.9420	−	15.1085i	−0.709952	−	0.537877i
$790$	−7.92766	+	10.1208i	−0.282054	+	0.360081i
$791$	−11.5692	+	6.67948i	−0.411353	+	0.237495i
$792$	0.393050	−	2.40102i	0.0139664	−	0.0853164i
$793$	12.3398	−	26.4627i	0.438197	−	0.939718i
$794$	8.61792	+	3.13666i	0.305838	+	0.111316i
$795$	−13.0490	+	10.8641i	−0.462799	+	0.385312i
$796$	4.60064	−	26.0915i	0.163065	−	0.924789i
$797$	18.3186	−	18.3186i	0.648877	−	0.648877i	−0.303845	−	0.952722i	$-0.598270\pi$
$797$	18.3186	−	18.3186i	0.648877	−	0.648877i	0.952722	+	0.303845i	$0.0982704\pi$
$798$	−11.3281	−	8.68608i	−0.401010	−	0.307484i
$799$			7.05126i			0.249456i
$800$	4.73166	−	1.61598i	0.167289	−	0.0571336i
$801$	28.1876	+	27.5042i	0.995960	+	0.971813i
$802$	5.40888	+	11.5994i	0.190994	+	0.409588i
$803$	−8.33858	−	3.88834i	−0.294262	−	0.137217i
$804$	11.2060	+	1.40541i	0.395205	+	0.0495650i
$805$	−0.210085	+	0.493210i	−0.00740453	+	0.0173834i
$806$	−21.2509	−	12.2692i	−0.748529	−	0.432164i
$807$	26.7123	−	3.68361i	0.940318	−	0.129669i
$808$	6.16595	+	4.31744i	0.216917	+	0.151887i
$809$	15.5172	−	26.8766i	0.545556	−	0.944930i	−0.453016	−	0.891502i	$-0.649652\pi$
$809$	15.5172	−	26.8766i	0.545556	−	0.944930i	0.998572	−	0.0534278i	$-0.0170147\pi$
$810$	19.5821	−	4.64139i	0.688044	−	0.163082i
$811$	−4.95639	+	4.15890i	−0.174042	+	0.146039i	−0.725648	−	0.688066i	$-0.758460\pi$
$811$	−4.95639	+	4.15890i	−0.174042	+	0.146039i	0.551606	+	0.834105i	$0.314015\pi$
$812$	−2.39622	+	5.13872i	−0.0840910	+	0.180334i
$813$	−13.0895	+	32.1575i	−0.459069	+	1.12781i
$814$	1.31892	−	1.57183i	0.0462282	−	0.0550927i
$815$	−3.29243	−	1.07434i	−0.115329	−	0.0376324i
$816$	1.13708	+	1.22572i	0.0398057	+	0.0429088i
$817$	18.8627	+	16.0146i	0.659922	+	0.560280i
$818$	−11.7417	−	11.7417i	−0.410540	−	0.410540i
$819$	4.37267	−	17.1585i	0.152793	−	0.599566i
$820$	−0.209224	−	0.0112280i	−0.00730642	−	0.000392098i
$821$	2.09915	−	5.76736i	0.0732608	−	0.201282i	−0.897657	−	0.440694i	$-0.854732\pi$
$821$	2.09915	−	5.76736i	0.0732608	−	0.201282i	0.970918	+	0.239412i	$0.0769546\pi$
$822$	27.9924	−	9.01516i	0.976347	−	0.314440i
$823$	−0.132414	+	1.51350i	−0.00461566	+	0.0527572i	−0.998153	−	0.0607466i	$-0.980652\pi$
$823$	−0.132414	+	1.51350i	−0.00461566	+	0.0527572i	0.993538	+	0.113504i	$0.0362074\pi$
$824$	2.50505	+	4.33888i	0.0872676	+	0.151152i
$825$	−4.67290	−	5.24329i	−0.162689	−	0.182548i
$826$	2.72503	+	15.4544i	0.0948158	+	0.537727i
$827$	−10.9067	−	7.63698i	−0.379265	−	0.265564i	0.368363	−	0.929682i	$-0.379918\pi$
$827$	−10.9067	−	7.63698i	−0.379265	−	0.265564i	−0.747628	+	0.664118i	$0.768807\pi$
$828$	0.0706470	+	0.373779i	0.00245515	+	0.0129897i
$829$	−46.2512	+	26.7031i	−1.60637	+	0.927438i	−0.616197	+	0.787592i	$0.711327\pi$
$829$	−46.2512	+	26.7031i	−1.60637	+	0.927438i	−0.990173	+	0.139846i	$0.955339\pi$
$830$	−4.37520	+	18.8433i	−0.151865	+	0.654059i
$831$	2.30659	−	4.49808i	0.0800147	−	0.156037i
$832$	−1.31927	−	2.82918i	−0.0457373	−	0.0980841i
$833$	−0.288148	−	3.29355i	−0.00998374	−	0.114115i
$834$	−4.08084	−	6.31973i	−0.141308	−	0.218835i
$835$	4.68598	−	33.0419i	0.162165	−	1.14346i
$836$	1.47540	+	3.21242i	0.0510279	+	0.111104i
$837$	4.58516	−	40.5872i	0.158486	−	1.40290i
$838$	4.58105	+	6.54242i	0.158250	+	0.226004i
$839$	−23.1259	−	19.4049i	−0.798394	−	0.669932i	0.149414	−	0.988775i	$-0.452261\pi$
$839$	−23.1259	−	19.4049i	−0.798394	−	0.669932i	−0.947808	+	0.318843i	$0.896706\pi$
$840$	7.08060	−	1.86809i	0.244304	−	0.0644553i
$841$	18.8008	−	6.84293i	0.648304	−	0.235963i
$842$	2.64566	−	30.2401i	0.0911755	−	1.04214i
$843$	−4.99957	−	9.46189i	−0.172194	−	0.325885i
$844$	−7.18103	−	4.14597i	−0.247181	−	0.142710i
$845$	4.97097	−	5.31734i	0.171007	−	0.182922i
$846$	21.8060	−	2.17771i	0.749707	−	0.0748712i
$847$	18.8885	−	5.06115i	0.649016	−	0.173903i
$848$	−1.13469	+	4.23471i	−0.0389654	+	0.145421i
$849$	−48.0699	−	6.02872i	−1.64975	−	0.206905i
$850$	4.81551	−	0.324603i	0.165170	−	0.0111338i
$851$	−0.109724	+	0.301465i	−0.00376130	+	0.0103341i
$852$	−11.5454	+	12.7558i	−0.395538	+	0.437007i
$853$	18.6510	+	26.6365i	0.638600	+	0.912015i	0.999790	−	0.0204771i	$-0.00651851\pi$
$853$	18.6510	+	26.6365i	0.638600	+	0.912015i	−0.361191	+	0.932492i	$0.617630\pi$
$854$	17.6852			0.605176
$855$	−19.8298	+	21.4891i	−0.678164	+	0.734911i
$856$	15.1003			0.516119
$857$	−26.4313	−	37.7478i	−0.902875	−	1.28944i	−0.956756	−	0.290892i	$-0.906048\pi$
$857$	−26.4313	−	37.7478i	−0.902875	−	1.28944i	0.0538808	−	0.998547i	$-0.482841\pi$
$858$	−2.94252	+	3.25102i	−0.100456	+	0.110988i
$859$	−6.35333	+	17.4556i	−0.216773	+	0.595578i	−0.999646	−	0.0266028i	$-0.991531\pi$
$859$	−6.35333	+	17.4556i	−0.216773	+	0.595578i	0.782873	+	0.622181i	$0.213753\pi$
$860$	−12.4194	+	2.62355i	−0.423497	+	0.0894623i
$861$	−0.304480	−	0.0381866i	−0.0103767	−	0.00130140i
$862$	8.33579	−	31.1096i	0.283918	−	1.05960i
$863$	46.3837	−	12.4285i	1.57892	−	0.423070i	0.640329	−	0.768101i	$-0.278798\pi$
$863$	46.3837	−	12.4285i	1.57892	−	0.423070i	0.938591	+	0.345030i	$0.112131\pi$
$864$	3.43937	−	3.89497i	0.117010	−	0.132509i
$865$	1.14187	+	33.9180i	0.0388249	+	1.15325i
$866$	24.7328	+	14.2795i	0.840456	+	0.485237i
$867$	−13.0021	−	24.6071i	−0.441576	−	0.835700i
$868$	1.29537	−	14.8062i	0.0439677	−	0.502554i
$869$	4.38152	−	1.59474i	0.148633	−	0.0540979i
$870$	10.0358	+	5.84571i	0.340244	+	0.198188i
$871$	−15.5926	−	13.0837i	−0.528334	−	0.443325i
$872$	2.61532	+	3.73506i	0.0885658	+	0.126485i
$873$	−16.3791	−	19.0404i	−0.554347	−	0.644419i
$874$	−0.388552	−	0.393076i	−0.0131430	−	0.0132960i
$875$	8.67071	−	19.2793i	0.293124	−	0.651759i
$876$	−10.6594	−	16.5075i	−0.360147	−	0.557736i
$877$	1.49155	+	17.0485i	0.0503659	+	0.575685i	0.978887	+	0.204404i	$0.0655258\pi$
$877$	1.49155	+	17.0485i	0.0503659	+	0.575685i	−0.928521	+	0.371281i	$0.878919\pi$
$878$	−2.71190	−	5.81569i	−0.0915222	−	0.196270i
$879$	−2.96203	+	5.77626i	−0.0999068	+	0.194828i
$880$	−1.76644	−	0.410148i	−0.0595468	−	0.0138261i
$881$	36.8817	−	21.2937i	1.24258	−	0.717402i	0.272958	−	0.962026i	$-0.411998\pi$
$881$	36.8817	−	21.2937i	1.24258	−	0.717402i	0.969618	+	0.244624i	$0.0786646\pi$
$882$	−10.0963	+	1.90828i	−0.339961	+	0.0642550i
$883$	−38.0813	−	26.6648i	−1.28154	−	0.897342i	−0.283439	−	0.958990i	$-0.591475\pi$
$883$	−38.0813	−	26.6648i	−1.28154	−	0.897342i	−0.998098	+	0.0616486i	$0.980364\pi$
$884$	−0.523252	−	2.96751i	−0.0175989	−	0.0998082i
$885$	32.0329	−	2.67846i	1.07678	−	0.0900353i
$886$	7.58146	+	13.1315i	0.254704	+	0.441161i
$887$	1.06820	−	12.2096i	0.0358668	−	0.409959i	−0.956945	−	0.290270i	$-0.906255\pi$
$887$	1.06820	−	12.2096i	0.0358668	−	0.409959i	0.992811	−	0.119689i	$-0.0381897\pi$
$888$	4.17125	−	1.34338i	0.139978	−	0.0450809i
$889$	−7.84654	+	21.5582i	−0.263165	+	0.723039i
$890$	21.8392	−	19.6145i	0.732050	−	0.657481i
$891$	−6.91794	−	2.32732i	−0.231760	−	0.0779682i
$892$	−11.7231	−	11.7231i	−0.392517	−	0.392517i
$893$	−24.5097	+	20.3255i	−0.820185	+	0.680168i
$894$	−16.2091	−	17.4727i	−0.542114	−	0.584374i
$895$	22.3544	+	44.0092i	0.747224	+	1.47107i
$896$	1.21536	−	1.44841i	0.0406022	−	0.0483879i
$897$	0.258471	−	0.634995i	0.00863008	−	0.0212019i
$898$	1.95295	−	4.18812i	0.0651709	−	0.139759i
$899$	18.0575	−	15.1521i	0.602252	−	0.505349i
$900$	−2.49105	−	14.7917i	−0.0830351	−	0.493057i
$901$	−2.11596	+	3.66494i	−0.0704927	+	0.122097i
$902$	0.0622490	+	0.0435872i	0.00207266	+	0.00145129i
$903$	−18.4162	+	2.53959i	−0.612854	+	0.0845122i
$904$	6.11881	+	3.53269i	0.203508	+	0.117496i
$905$	−30.1380	−	12.8374i	−1.00182	−	0.426730i
$906$	−26.8722	−	3.37020i	−0.892770	−	0.111967i
$907$	15.3297	+	7.14835i	0.509014	+	0.237357i	0.660120	−	0.751161i	$-0.270506\pi$
$907$	15.3297	+	7.14835i	0.509014	+	0.237357i	−0.151106	+	0.988518i	$0.548283\pi$
$908$	1.78525	+	3.82849i	0.0592458	+	0.127053i
$909$	15.7705	−	16.1624i	0.523076	−	0.536073i
$910$	−12.5469	−	4.09412i	−0.415924	−	0.135719i
$911$		−	13.2633i		−	0.439434i	−0.975564	−	0.219717i	$-0.929487\pi$
$911$		−	13.2633i		−	0.439434i	0.975564	−	0.219717i	$-0.0705134\pi$
$912$	−0.982843	+	7.48559i	−0.0325452	+	0.247873i
$913$	4.96106	−	4.96106i	0.164187	−	0.164187i
$914$	3.80486	−	21.5784i	0.125854	−	0.713752i
$915$	3.29603	−	36.0757i	0.108963	−	1.19262i
$916$	27.7996	+	10.1182i	0.918524	+	0.334315i
$917$	−16.0006	+	34.3134i	−0.528386	+	1.13313i
$918$	4.17995	−	2.77238i	0.137959	−	0.0915021i
$919$	−37.9864	+	21.9314i	−1.25305	+	0.723452i	−0.971715	−	0.236157i	$-0.924112\pi$
$919$	−37.9864	+	21.9314i	−1.25305	+	0.723452i	−0.281340	+	0.959608i	$0.590779\pi$
$920$	0.281461	−	0.0342009i	0.00927949	−	0.00112757i
$921$	14.8569	+	11.2560i	0.489551	+	0.370896i
$922$	−4.38322	+	6.25989i	−0.144354	+	0.206159i
$923$	29.9514	−	8.02547i	0.985864	−	0.264161i
$924$	−2.53784	−	0.783093i	−0.0834888	−	0.0257619i
$925$	4.56311	−	11.7988i	0.150034	−	0.387942i
$926$	−11.8745	−	32.6248i	−0.390219	−	1.07212i
$927$	14.0597	−	5.31359i	0.461782	−	0.174521i
$928$	2.98736	−	0.261360i	0.0980647	−	0.00857955i
$929$	3.54805	−	20.1220i	0.116408	−	0.660180i	−0.869636	−	0.493693i	$-0.835647\pi$
$929$	3.54805	−	20.1220i	0.116408	−	0.660180i	0.986044	−	0.166487i	$-0.0532424\pi$
$930$	−29.9613	−	5.40185i	−0.982470	−	0.177133i
$931$	10.6175	−	10.4954i	0.347976	−	0.343972i
$932$	4.93704	−	4.93704i	0.161718	−	0.161718i
$933$	6.94623	−	32.2681i	0.227409	−	1.05641i
$934$	10.6609	−	12.7052i	0.348837	−	0.415727i
$935$	−1.54455	−	0.823739i	−0.0505123	−	0.0269391i
$936$	−9.01543	+	2.53464i	−0.294678	+	0.0828474i
$937$	−10.7941	−	0.944363i	−0.352629	−	0.0308510i	−0.0905344	−	0.995893i	$-0.528858\pi$
$937$	−10.7941	−	0.944363i	−0.352629	−	0.0308510i	−0.262094	+	0.965042i	$0.584413\pi$
$938$	3.19089	−	11.9086i	0.104186	−	0.388829i
$939$	−42.8091	+	9.76648i	−1.39702	+	0.318717i
$940$	−0.549589	−	16.3249i	−0.0179256	−	0.532458i
$941$	22.5506	−	3.97628i	0.735129	−	0.129623i	0.206465	−	0.978454i	$-0.433804\pi$
$941$	22.5506	−	3.97628i	0.735129	−	0.129623i	0.528664	+	0.848831i	$0.322693\pi$
$942$	−24.3188	−	15.2838i	−0.792348	−	0.497974i
$943$	−0.0114765	−	0.00307513i	−0.000373727	−	0.000100140i
$944$	6.35796	−	5.33497i	0.206934	−	0.173638i
$945$	−2.09903	−	21.8681i	−0.0682813	−	0.711371i
$946$	4.32610	+	1.57457i	0.140654	+	0.0511938i
$947$	−20.2887	+	1.77503i	−0.659295	+	0.0576808i	−0.411893	−	0.911232i	$-0.635132\pi$
$947$	−20.2887	+	1.77503i	−0.659295	+	0.0576808i	−0.247402	+	0.968913i	$0.579577\pi$
$948$	9.73524	+	2.09567i	0.316186	+	0.0680642i
$949$			35.4148i			1.14961i
$950$	15.0092	+	15.8027i	0.486962	+	0.512707i
$951$	−0.989603	−	1.06675i	−0.0320901	−	0.0345917i
$952$	1.49506	−	1.04685i	0.0484550	−	0.0339286i
$953$	3.86482	+	44.1751i	0.125194	+	1.43097i	0.755766	+	0.654842i	$0.227265\pi$
$953$	3.86482	+	44.1751i	0.125194	+	1.43097i	−0.630572	+	0.776131i	$0.717180\pi$
$954$	11.9873	+	5.41172i	0.388104	+	0.175211i
$955$	−1.17602	−	0.765814i	−0.0380551	−	0.0247812i
$956$	11.8393	+	14.1096i	0.382911	+	0.456336i
$957$	−1.96791	−	3.72436i	−0.0636136	−	0.120391i
$958$	3.04766	+	11.3740i	0.0984656	+	0.367478i
$959$	−5.57463	−	31.6153i	−0.180014	−	1.02091i
$960$	−2.72806	−	2.74912i	−0.0880479	−	0.0887275i
$961$	−15.3953	+	26.6655i	−0.496623	+	0.860177i
$962$	−7.62893	−	2.04417i	−0.245967	−	0.0659065i
$963$	7.31842	−	44.7059i	0.235833	−	1.44063i
$964$	−6.28621	−	17.2712i	−0.202465	−	0.556269i
$965$	7.85142	−	14.7218i	0.252746	−	0.473912i
$966$	0.414739	−	0.0206580i	0.0133440	−	0.000664661i
$967$	21.0020	−	14.7058i	0.675378	−	0.472905i	−0.184881	−	0.982761i	$-0.559190\pi$
$967$	21.0020	−	14.7058i	0.675378	−	0.472905i	0.860260	+	0.509856i	$0.170301\pi$
$968$	−7.31310	−	7.31310i	−0.235052	−	0.235052i
$969$	−2.78656	+	6.73398i	−0.0895171	+	0.216327i
$970$	−14.9648	+	11.2474i	−0.480491	+	0.361132i
$971$	8.73218	+	1.53972i	0.280229	+	0.0494120i	0.311996	−	0.950083i	$-0.399002\pi$
$971$	8.73218	+	1.53972i	0.280229	+	0.0494120i	−0.0317671	+	0.999495i	$0.510113\pi$
$972$	−9.86451	−	12.0703i	−0.316404	−	0.387154i
$973$	−7.44270	+	3.47059i	−0.238602	+	0.111262i
$974$	21.0204	−	7.65078i	0.673536	−	0.245147i
$975$	−10.6899	+	24.8310i	−0.342350	+	0.795229i
$976$	−4.67675	−	8.10036i	−0.149699	−	0.259286i
$977$	8.41536	+	31.4066i	0.269231	+	1.00478i	0.959609	+	0.281336i	$0.0907776\pi$
$977$	8.41536	+	31.4066i	0.269231	+	1.00478i	−0.690378	+	0.723449i	$0.742556\pi$
$978$	0.366466	+	2.65749i	0.0117183	+	0.0849772i
$979$	−10.4847	+	1.84873i	−0.335092	+	0.0590858i
$980$	0.923817	+	7.60266i	0.0295103	+	0.242858i
$981$	12.3255	−	5.93268i	0.393523	−	0.189416i
$982$	43.9820	+	3.84793i	1.40352	+	0.122792i
$983$	39.6089	+	18.4699i	1.26333	+	0.589099i	0.934726	−	0.355370i	$-0.115645\pi$
$983$	39.6089	+	18.4699i	1.26333	+	0.589099i	0.328601	+	0.944469i	$0.393423\pi$
$984$	0.0630273	+	0.149559i	0.00200924	+	0.00476778i
$985$	−18.9986	+	17.0633i	−0.605345	+	0.543682i
$986$	2.85069	+	0.502654i	0.0907846	+	0.0160078i
$987$	0.896835	−	23.9057i	0.0285466	−	0.760928i
$988$	8.80656	−	10.3727i	0.280174	−	0.330001i
$989$	−0.719797			−0.0228882
$990$	−2.07039	+	5.03094i	−0.0658015	+	0.159894i
$991$	−1.32291	−	1.11005i	−0.0420236	−	0.0352620i	0.621534	−	0.783387i	$-0.286510\pi$
$991$	−1.32291	−	1.11005i	−0.0420236	−	0.0352620i	−0.663558	+	0.748125i	$0.730954\pi$
$992$	−7.12422	+	3.32208i	−0.226194	+	0.105476i
$993$	8.51744	+	26.4470i	0.270293	+	0.839269i
$994$	12.0724	+	14.3873i	0.382913	+	0.456338i
$995$	−23.2162	+	54.5039i	−0.736003	+	1.72789i
$996$	14.6088	−	3.33287i	0.462899	−	0.105606i
$997$	1.08135	−	1.54433i	0.0342467	−	0.0489093i	−0.801664	−	0.597775i	$-0.796051\pi$
$997$	1.08135	−	1.54433i	0.0342467	−	0.0489093i	0.835910	+	0.548866i	$0.184940\pi$
$998$	−12.7177	+	18.1628i	−0.402572	+	0.574932i
$999$	−1.95560	−	13.0005i	−0.0618723	−	0.411316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.16	✓	480
3.2	odd	2	inner	570.2.bi.a.17.37	yes	480
5.3	odd	4	inner	570.2.bi.a.473.15	yes	480
15.8	even	4	inner	570.2.bi.a.473.27	yes	480
19.9	even	9	inner	570.2.bi.a.47.27	yes	480
57.47	odd	18	inner	570.2.bi.a.47.15	yes	480
95.28	odd	36	inner	570.2.bi.a.503.37	yes	480
285.218	even	36	inner	570.2.bi.a.503.16	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.16	✓	480	1.1	even	1	trivial
570.2.bi.a.17.37	yes	480	3.2	odd	2	inner
570.2.bi.a.47.15	yes	480	57.47	odd	18	inner
570.2.bi.a.47.27	yes	480	19.9	even	9	inner
570.2.bi.a.473.15	yes	480	5.3	odd	4	inner
570.2.bi.a.473.27	yes	480	15.8	even	4	inner
570.2.bi.a.503.16	yes	480	285.218	even	36	inner
570.2.bi.a.503.37	yes	480	95.28	odd	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(1.16230 - 1.28416i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.22020 - 1.87380i) q^{5} +(-1.71859 - 0.215538i) q^{6} +(-0.489365 + 1.82633i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.298119 - 2.98515i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(1.16230 - 1.28416i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.22020 - 1.87380i) q^{5} +(-1.71859 - 0.215538i) q^{6} +(-0.489365 + 1.82633i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-0.298119 - 2.98515i) q^{9} +(-2.23480 + 0.0752363i) q^{10} +(0.702340 + 0.405496i) q^{11} +(0.809183 + 1.53141i) q^{12} +(0.272070 - 3.10977i) q^{13} +(1.77673 - 0.646678i) q^{14} +(-0.988011 - 3.74484i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.553666 - 0.790717i) q^{17} +(-2.27430 + 1.95642i) q^{18} +(1.15251 - 4.20377i) q^{19} +(1.34346 + 1.78749i) q^{20} +(1.77651 + 2.75117i) q^{21} +(-0.0706826 - 0.807906i) q^{22} +(0.0535876 + 0.114919i) q^{23} +(0.790331 - 1.54123i) q^{24} +(-2.02223 - 4.57281i) q^{25} +(-2.70343 + 1.56083i) q^{26} +(-4.17991 - 3.08681i) q^{27} +(-1.54882 - 1.08450i) q^{28} +(-0.520730 - 2.95321i) q^{29} +(-2.50089 + 2.95728i) q^{30} +(3.93035 + 6.80757i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(1.33705 - 0.430607i) q^{33} +(-0.330148 + 0.907073i) q^{34} +(2.82506 + 3.14546i) q^{35} +(2.90709 + 0.740842i) q^{36} +(1.78904 + 1.78904i) q^{37} +(-4.10458 + 1.46710i) q^{38} +(-3.67721 - 3.96387i) q^{39} +(0.693648 - 2.12576i) q^{40} +(-0.0602308 + 0.0717803i) q^{41} +(1.23466 - 3.03324i) q^{42} +(-2.39907 + 5.14482i) q^{43} +(-0.621256 + 0.521296i) q^{44} +(-5.95733 - 3.08387i) q^{45} +(0.0633995 - 0.109811i) q^{46} +(-5.98377 - 4.18988i) q^{47} +(-1.71581 + 0.236610i) q^{48} +(2.96616 + 1.71251i) q^{49} +(-2.58593 + 4.27937i) q^{50} +(-1.65893 - 0.208056i) q^{51} +(2.82918 + 1.31927i) q^{52} +(-1.85280 - 3.97334i) q^{53} +(-0.131070 + 5.19450i) q^{54} +(1.61681 - 0.821255i) q^{55} +1.89076i q^{56} +(-4.05874 - 6.36605i) q^{57} +(-2.12045 + 2.12045i) q^{58} +(-1.44123 + 8.17364i) q^{59} +(3.85692 + 0.352385i) q^{60} +(8.78941 + 3.19908i) q^{61} +(3.32208 - 7.12422i) q^{62} +(5.59777 + 0.916363i) q^{63} +(0.866025 - 0.500000i) q^{64} +(-5.49510 - 4.30435i) q^{65} +(-1.11963 - 0.848261i) q^{66} +(3.73999 - 5.34126i) q^{67} +(0.932395 - 0.249835i) q^{68} +(0.209859 + 0.0647553i) q^{69} +(0.956227 - 4.11831i) q^{70} +(3.39736 + 9.33417i) q^{71} +(-1.06057 - 2.80628i) q^{72} +(-11.3017 + 0.988772i) q^{73} +(0.439345 - 2.49165i) q^{74} +(-8.22264 - 2.71812i) q^{75} +(3.55607 + 2.52078i) q^{76} +(-1.08427 + 1.08427i) q^{77} +(-1.13785 + 5.28578i) q^{78} +(3.69564 - 4.40429i) q^{79} +(-2.13918 + 0.651082i) q^{80} +(-8.82225 + 1.77986i) q^{81} +(0.0933459 + 0.00816671i) q^{82} +(2.23908 - 8.35635i) q^{83} +(-3.19286 + 0.728420i) q^{84} +(-2.15722 + 0.0726246i) q^{85} +(5.59044 - 0.985745i) q^{86} +(-4.39763 - 2.76381i) q^{87} +(0.783358 + 0.209900i) q^{88} +(-10.0564 + 8.43831i) q^{89} +(0.890828 + 6.64879i) q^{90} +(5.54634 + 2.01870i) q^{91} +(-0.126316 + 0.0110513i) q^{92} +(13.3102 + 2.86525i) q^{93} +7.30484i q^{94} +(-6.47072 - 7.28902i) q^{95} +(1.17797 + 1.26980i) q^{96} +(6.85792 - 4.80197i) q^{97} +(-0.298510 - 3.41199i) q^{98} +(1.00109 - 2.21748i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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