LMFDB - Embedded newform 570.2.bi.a.47.27

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			47.27
Character	$\chi$	$=$	570.47
Dual form			570.2.bi.a.473.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 + 0.573576i) q^{2} +(-1.06282 - 1.36763i) q^{3} +(0.342020 + 0.939693i) q^{4} +(2.13918 - 0.651082i) q^{5} +(-0.0861662 - 1.72991i) q^{6} +(1.82633 - 0.489365i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.740842 + 2.90709i) q^{9} +O(q^{10})$	\(q+(0.819152 + 0.573576i) q^{2} +(-1.06282 - 1.36763i) q^{3} +(0.342020 + 0.939693i) q^{4} +(2.13918 - 0.651082i) q^{5} +(-0.0861662 - 1.72991i) q^{6} +(1.82633 - 0.489365i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.740842 + 2.90709i) q^{9} +(2.12576 + 0.693648i) q^{10} +(-0.702340 + 0.405496i) q^{11} +(0.921650 - 1.46648i) q^{12} +(3.10977 - 0.272070i) q^{13} +(1.77673 + 0.646678i) q^{14} +(-3.16400 - 2.23363i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(0.790717 + 0.553666i) q^{17} +(-2.27430 + 1.95642i) q^{18} +(-1.15251 - 4.20377i) q^{19} +(1.34346 + 1.78749i) q^{20} +(-2.61033 - 1.97765i) q^{21} +(-0.807906 - 0.0706826i) q^{22} +(0.114919 + 0.0535876i) q^{23} +(1.59611 - 0.672632i) q^{24} +(4.15218 - 2.78556i) q^{25} +(2.70343 + 1.56083i) q^{26} +(4.76321 - 2.07650i) q^{27} +(1.08450 + 1.54882i) q^{28} +(-0.520730 + 2.95321i) q^{29} +(-1.31064 - 3.64448i) q^{30} +(3.93035 - 6.80757i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(1.30103 + 0.529575i) q^{33} +(0.330148 + 0.907073i) q^{34} +(3.58824 - 2.23593i) q^{35} +(-2.98515 + 0.298119i) q^{36} +(1.78904 + 1.78904i) q^{37} +(1.46710 - 4.10458i) q^{38} +(-3.67721 - 3.96387i) q^{39} +(0.0752363 + 2.23480i) q^{40} +(0.0602308 + 0.0717803i) q^{41} +(-1.00392 - 3.11722i) q^{42} +(-5.14482 + 2.39907i) q^{43} +(-0.621256 - 0.521296i) q^{44} +(0.307958 + 6.70113i) q^{45} +(0.0633995 + 0.109811i) q^{46} +(4.18988 + 5.98377i) q^{47} +(1.69326 + 0.364503i) q^{48} +(-2.96616 + 1.71251i) q^{49} +(4.99900 + 0.0997953i) q^{50} +(-0.0831751 - 1.66986i) q^{51} +(1.31927 + 2.82918i) q^{52} +(-3.97334 - 1.85280i) q^{53} +(5.09282 + 1.03109i) q^{54} +(-1.23842 + 1.32471i) q^{55} +1.89076i q^{56} +(-4.52431 + 6.04405i) q^{57} +(-2.12045 + 2.12045i) q^{58} +(-1.44123 - 8.17364i) q^{59} +(1.01678 - 3.73713i) q^{60} +(8.78941 - 3.19908i) q^{61} +(7.12422 - 3.32208i) q^{62} +(0.0696013 + 5.67186i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(6.47522 - 2.60672i) q^{65} +(0.761988 + 1.18004i) q^{66} +(-5.34126 + 3.73999i) q^{67} +(-0.249835 + 0.932395i) q^{68} +(-0.0488496 - 0.214121i) q^{69} +(4.22179 + 0.226562i) q^{70} +(-3.39736 + 9.33417i) q^{71} +(-2.61629 - 1.46801i) q^{72} +(-0.988772 + 11.3017i) 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} +(-0.738612 - 5.35617i) q^{78} +(-3.69564 - 4.40429i) q^{79} +(-1.22020 + 1.87380i) q^{80} +(-7.90231 - 4.30738i) q^{81} +(0.00816671 + 0.0933459i) q^{82} +(-8.35635 + 2.23908i) q^{83} +(0.965598 - 3.12930i) q^{84} +(2.05197 + 0.669570i) q^{85} +(-5.59044 - 0.985745i) q^{86} +(4.59235 - 2.42655i) q^{87} +(-0.209900 - 0.783358i) q^{88} +(-10.0564 - 8.43831i) q^{89} +(-3.59135 + 5.66588i) q^{90} +(5.54634 - 2.01870i) q^{91} +(-0.0110513 + 0.126316i) q^{92} +(-13.4875 + 1.85992i) q^{93} +7.30484i q^{94} +(-5.20243 - 8.24225i) q^{95} +(1.17797 + 1.26980i) q^{96} +(-4.80197 + 6.85792i) q^{97} +(-3.41199 - 0.298510i) q^{98} +(-0.658490 - 2.34217i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$	−1.06282	−	1.36763i	−0.613617	−	0.789603i
$3$	−1.06282	−	1.36763i	−0.613617	−	0.789603i
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	2.13918	−	0.651082i	0.956671	−	0.291173i
$5$	2.13918	−	0.651082i	0.956671	−	0.291173i
$6$	−0.0861662	−	1.72991i	−0.0351772	−	0.706231i
$7$	1.82633	−	0.489365i	0.690290	−	0.184963i	0.103412	−	0.994639i	$-0.467024\pi$
$7$	1.82633	−	0.489365i	0.690290	−	0.184963i	0.586877	+	0.809676i	$0.300357\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	−0.740842	+	2.90709i	−0.246947	+	0.969029i
$10$	2.12576	+	0.693648i	0.672224	+	0.219351i
$11$	−0.702340	+	0.405496i	−0.211763	+	0.122262i	−0.602131	−	0.798398i	$-0.705681\pi$
$11$	−0.702340	+	0.405496i	−0.211763	+	0.122262i	0.390367	+	0.920659i	$0.372348\pi$
$12$	0.921650	−	1.46648i	0.266058	−	0.423336i
$13$	3.10977	−	0.272070i	0.862496	−	0.0754586i	0.352682	−	0.935743i	$-0.385270\pi$
$13$	3.10977	−	0.272070i	0.862496	−	0.0754586i	0.509814	+	0.860285i	$0.329714\pi$
$14$	1.77673	+	0.646678i	0.474852	+	0.172832i
$15$	−3.16400	−	2.23363i	−0.816941	−	0.576722i
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.790717	+	0.553666i	0.191777	+	0.134284i	0.665522	−	0.746379i	$-0.268209\pi$
$17$	0.790717	+	0.553666i	0.191777	+	0.134284i	−0.473745	+	0.880662i	$0.657098\pi$
$18$	−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
$21$	−2.61033	−	1.97765i	−0.569621	−	0.431559i
$22$	−0.807906	−	0.0706826i	−0.172246	−	0.0150696i
$23$	0.114919	+	0.0535876i	0.0239622	+	0.0111738i	0.434562	−	0.900642i	$-0.356903\pi$
$23$	0.114919	+	0.0535876i	0.0239622	+	0.0111738i	−0.410600	+	0.911815i	$0.634681\pi$
$24$	1.59611	−	0.672632i	0.325804	−	0.137301i
$25$	4.15218	−	2.78556i	0.830437	−	0.557113i
$26$	2.70343	+	1.56083i	0.530186	+	0.306103i
$27$	4.76321	−	2.07650i	0.916680	−	0.399623i
$28$	1.08450	+	1.54882i	0.204950	+	0.292700i
$29$	−0.520730	+	2.95321i	−0.0966972	+	0.548397i	0.897517	+	0.440980i	$0.145369\pi$
$29$	−0.520730	+	2.95321i	−0.0966972	+	0.548397i	−0.994214	+	0.107417i	$0.965742\pi$
$30$	−1.31064	−	3.64448i	−0.239288	−	0.665388i
$31$	3.93035	−	6.80757i	0.705912	−	1.22268i	−0.260449	−	0.965487i	$-0.583871\pi$
$31$	3.93035	−	6.80757i	0.705912	−	1.22268i	0.966361	−	0.257188i	$-0.0827959\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$	1.30103	+	0.529575i	0.226480	+	0.0921872i
$34$	0.330148	+	0.907073i	0.0566198	+	0.155562i
$35$	3.58824	−	2.23593i	0.606524	−	0.377942i
$36$	−2.98515	+	0.298119i	−0.497525	+	0.0496865i
$37$	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	$0.683314\pi$
$38$	1.46710	−	4.10458i	0.237996	−	0.665851i
$39$	−3.67721	−	3.96387i	−0.588825	−	0.634727i
$40$	0.0752363	+	2.23480i	0.0118959	+	0.353353i
$41$	0.0602308	+	0.0717803i	0.00940647	+	0.0112102i	0.770727	−	0.637165i	$-0.219893\pi$
$41$	0.0602308	+	0.0717803i	0.00940647	+	0.0112102i	−0.761321	+	0.648375i	$0.775449\pi$
$42$	−1.00392	−	3.11722i	−0.154909	−	0.480998i
$43$	−5.14482	+	2.39907i	−0.784578	+	0.365855i	−0.773266	−	0.634081i	$-0.781378\pi$
$43$	−5.14482	+	2.39907i	−0.784578	+	0.365855i	−0.0113114	+	0.999936i	$0.503601\pi$
$44$	−0.621256	−	0.521296i	−0.0936578	−	0.0785883i
$45$	0.307958	+	6.70113i	0.0459076	+	0.998946i
$46$	0.0633995	+	0.109811i	0.00934774	+	0.0161908i
$47$	4.18988	+	5.98377i	0.611157	+	0.872823i	0.998799	−	0.0489870i	$-0.0155993\pi$
$47$	4.18988	+	5.98377i	0.611157	+	0.872823i	−0.387642	+	0.921810i	$0.626710\pi$
$48$	1.69326	+	0.364503i	0.244401	+	0.0526114i
$49$	−2.96616	+	1.71251i	−0.423737	+	0.244645i
$50$	4.99900	+	0.0997953i	0.706966	+	0.0141132i
$51$	−0.0831751	−	1.66986i	−0.0116468	−	0.233827i
$52$	1.31927	+	2.82918i	0.182949	+	0.392336i
$53$	−3.97334	−	1.85280i	−0.545781	−	0.254502i	0.130115	−	0.991499i	$-0.458465\pi$
$53$	−3.97334	−	1.85280i	−0.545781	−	0.254502i	−0.675896	+	0.736997i	$0.736243\pi$
$54$	5.09282	+	1.03109i	0.693045	+	0.140314i
$55$	−1.23842	+	1.32471i	−0.166989	+	0.178624i
$56$			1.89076i			0.252664i
$57$	−4.52431	+	6.04405i	−0.599260	+	0.800555i
$58$	−2.12045	+	2.12045i	−0.278428	+	0.278428i
$59$	−1.44123	−	8.17364i	−0.187633	−	1.06412i	−0.922526	−	0.385935i	$-0.873879\pi$
$59$	−1.44123	−	8.17364i	−0.187633	−	1.06412i	0.734893	−	0.678183i	$-0.237232\pi$
$60$	1.01678	−	3.73713i	0.131265	−	0.482462i
$61$	8.78941	−	3.19908i	1.12537	−	0.409601i	0.288760	−	0.957402i	$-0.406757\pi$
$61$	8.78941	−	3.19908i	1.12537	−	0.409601i	0.836609	+	0.547801i	$0.184535\pi$
$62$	7.12422	−	3.32208i	0.904776	−	0.421904i
$63$	0.0696013	+	5.67186i	0.00876894	+	0.714587i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	6.47522	−	2.60672i	0.803153	−	0.323324i
$66$	0.761988	+	1.18004i	0.0937942	+	0.145253i
$67$	−5.34126	+	3.73999i	−0.652539	+	0.456913i	−0.852385	−	0.522915i	$-0.824845\pi$
$67$	−5.34126	+	3.73999i	−0.652539	+	0.456913i	0.199846	+	0.979827i	$0.435956\pi$
$68$	−0.249835	+	0.932395i	−0.0302969	+	0.113070i
$69$	−0.0488496	−	0.214121i	−0.00588080	−	0.0257771i
$70$	4.22179	+	0.226562i	0.504601	+	0.0270793i
$71$	−3.39736	+	9.33417i	−0.403192	+	1.10776i	0.557507	+	0.830172i	$0.311758\pi$
$71$	−3.39736	+	9.33417i	−0.403192	+	1.10776i	−0.960700	+	0.277590i	$0.910464\pi$
$72$	−2.61629	−	1.46801i	−0.308332	−	0.173006i
$73$	−0.988772	+	11.3017i	−0.115727	+	1.32277i	0.687104	+	0.726559i	$0.258882\pi$
$73$	−0.988772	+	11.3017i	−0.115727	+	1.32277i	−0.802831	+	0.596206i	$0.796674\pi$
$74$	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
$78$	−0.738612	−	5.35617i	−0.0836314	−	0.606467i
$79$	−3.69564	−	4.40429i	−0.415792	−	0.495522i	0.516975	−	0.856000i	$-0.327058\pi$
$79$	−3.69564	−	4.40429i	−0.415792	−	0.495522i	−0.932768	+	0.360479i	$0.882613\pi$
$80$	−1.22020	+	1.87380i	−0.136422	+	0.209497i
$81$	−7.90231	−	4.30738i	−0.878034	−	0.478598i
$82$	0.00816671	+	0.0933459i	0.000901862	+	0.0103083i
$83$	−8.35635	+	2.23908i	−0.917229	+	0.245771i	−0.686401	−	0.727224i	$-0.740810\pi$
$83$	−8.35635	+	2.23908i	−0.917229	+	0.245771i	−0.230828	+	0.972994i	$0.574144\pi$
$84$	0.965598	−	3.12930i	0.105355	−	0.341435i
$85$	2.05197	+	0.669570i	0.222567	+	0.0726250i
$86$	−5.59044	−	0.985745i	−0.602833	−	0.106296i
$87$	4.59235	−	2.42655i	0.492351	−	0.260154i
$88$	−0.209900	−	0.783358i	−0.0223754	−	0.0835063i
$89$	−10.0564	−	8.43831i	−1.06597	−	0.894459i	−0.0712926	−	0.997455i	$-0.522712\pi$
$89$	−10.0564	−	8.43831i	−1.06597	−	0.894459i	−0.994682	+	0.102997i	$0.967157\pi$
$90$	−3.59135	+	5.66588i	−0.378561	+	0.597236i
$91$	5.54634	−	2.01870i	0.581415	−	0.211618i
$92$	−0.0110513	+	0.126316i	−0.00115217	+	0.0131694i
$93$	−13.4875	+	1.85992i	−1.39859	+	0.192864i
$94$			7.30484i			0.753436i
$95$	−5.20243	−	8.24225i	−0.533758	−	0.845637i
$96$	1.17797	+	1.26980i	0.120226	+	0.129598i
$97$	−4.80197	+	6.85792i	−0.487566	+	0.696316i	−0.985265	−	0.171034i	$-0.945289\pi$
$97$	−4.80197	+	6.85792i	−0.487566	+	0.696316i	0.497699	+	0.867350i	$0.334178\pi$
$98$	−3.41199	−	0.298510i	−0.344663	−	0.0301541i
$99$	−0.658490	−	2.34217i	−0.0661807	−	0.235397i
$100$	4.03770	+	2.94906i	0.403770	+	0.294906i
$101$	−4.83841	+	5.76619i	−0.481440	+	0.573758i	−0.951019	−	0.309133i	$-0.899961\pi$
$101$	−4.83841	+	5.76619i	−0.481440	+	0.573758i	0.469579	+	0.882890i	$0.344406\pi$
$102$	0.889657	−	1.41557i	0.0880892	−	0.140163i
$103$	−4.83939	−	1.29671i	−0.476839	−	0.127769i	0.0123914	−	0.999923i	$-0.496056\pi$
$103$	−4.83939	−	1.29671i	−0.476839	−	0.127769i	−0.489230	+	0.872155i	$0.662722\pi$
$104$	−0.542069	+	3.07423i	−0.0531542	+	0.301453i
$105$	−6.87158	−	2.53101i	−0.670598	−	0.247002i
$106$	−2.19205	−	3.79674i	−0.212911	−	0.368772i
$107$	−3.90825	−	14.5858i	−0.377825	−	1.41006i	−0.849173	−	0.528115i	$-0.822899\pi$
$107$	−3.90825	−	14.5858i	−0.377825	−	1.41006i	0.471348	−	0.881947i	$-0.343768\pi$
$108$	3.58038	+	3.76575i	0.344523	+	0.362359i
$109$	−1.55950	+	4.28469i	−0.149373	+	0.410398i	−0.991701	−	0.128567i	$-0.958962\pi$
$109$	−1.55950	+	4.28469i	−0.149373	+	0.410398i	0.842328	+	0.538965i	$0.181185\pi$
$110$	−1.77428	+	0.374810i	−0.169171	+	0.0357367i
$111$	0.545330	−	4.34818i	0.0517604	−	0.412711i
$112$	−1.08450	+	1.54882i	−0.102475	+	0.146350i
$113$	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	$0.642166\pi$
$114$	−7.17283	+	2.35596i	−0.671797	+	0.220656i
$115$	0.280722	+	0.0398118i	0.0261775	+	0.00371247i
$116$	−2.95321	+	0.520730i	−0.274199	+	0.0483486i
$117$	−1.51292	+	9.24194i	−0.139869	+	0.854418i
$118$	3.50762	−	7.52211i	0.322902	−	0.692467i
$119$	1.71506	+	0.624230i	0.157219	+	0.0572231i
$120$	2.97643	−	2.47808i	0.271709	−	0.226217i
$121$	−5.17115	+	8.95669i	−0.470104	+	0.814244i
$122$	9.03478	+	2.42086i	0.817971	+	0.219175i
$123$	0.0341548	−	0.158663i	0.00307963	−	0.0143062i
$124$	7.74128	+	1.36500i	0.695188	+	0.122580i
$125$	7.06864	−	8.66223i	0.632239	−	0.774774i
$126$	−3.19623	+	4.68603i	−0.284743	+	0.417465i
$127$	1.05751	+	12.0874i	0.0938392	+	1.07259i	0.886439	+	0.462845i	$0.153171\pi$
$127$	1.05751	+	12.0874i	0.0938392	+	1.07259i	−0.792600	+	0.609742i	$0.791273\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$	8.74905	+	4.48646i	0.770311	+	0.395010i
$130$	6.79935	+	1.57873i	0.596342	+	0.138464i
$131$	−19.7198	+	3.47713i	−1.72293	+	0.303798i	−0.945608	−	0.325308i	$-0.894532\pi$
$131$	−19.7198	+	3.47713i	−1.72293	+	0.303798i	−0.777319	+	0.629107i	$0.783421\pi$
$132$	−0.0526601	+	1.40369i	−0.00458348	+	0.122176i
$133$	−4.16205	−	7.11350i	−0.360896	−	0.616819i
$134$	−6.52048			−0.563283
$135$	8.83739	−	7.54325i	0.760601	−	0.649219i
$136$	−0.739453	+	0.620474i	−0.0634075	+	0.0532052i
$137$	−7.17559	+	15.3881i	−0.613052	+	1.31469i	0.317404	+	0.948290i	$0.397189\pi$
$137$	−7.17559	+	15.3881i	−0.613052	+	1.31469i	−0.930456	+	0.366403i	$0.880589\pi$
$138$	0.0827993	−	0.203416i	0.00704835	−	0.0173159i
$139$	−2.79181	+	3.32715i	−0.236798	+	0.282205i	−0.871336	−	0.490687i	$-0.836746\pi$
$139$	−2.79181	+	3.32715i	−0.236798	+	0.282205i	0.634538	+	0.772892i	$0.281190\pi$
$140$	3.32834	+	2.60711i	0.281296	+	0.220341i
$141$	3.73053	−	12.0899i	0.314167	−	1.01815i
$142$	−8.13681	+	5.69746i	−0.682826	+	0.478120i
$143$	−2.07379	+	1.45209i	−0.173419	+	0.121430i
$144$	−1.30112	−	2.70316i	−0.108427	−	0.225263i
$145$	0.808845	+	6.65648i	0.0671709	+	0.552791i
$146$	−7.29235	+	8.69068i	−0.603519	+	0.719246i
$147$	5.49457	+	2.23653i	0.453184	+	0.184466i
$148$	−1.06926	+	2.29304i	−0.0878927	+	0.188487i
$149$	10.5409	−	8.84489i	0.863547	−	0.724602i	−0.0991821	−	0.995069i	$-0.531623\pi$
$149$	10.5409	−	8.84489i	0.863547	−	0.724602i	0.962729	+	0.270467i	$0.0871782\pi$
$150$	−5.17654	−	6.94287i	−0.422663	−	0.566883i
$151$	15.6362			1.27246			0.636229	−	0.771500i	$-0.280493\pi$
$151$	15.6362			1.27246			0.636229	+	0.771500i	$0.280493\pi$
$152$	4.35883	−	0.0252247i	0.353547	−	0.00204599i
$153$	−2.19535	+	1.88850i	−0.177484	+	0.152676i
$154$	−1.51010	+	0.266271i	−0.121687	+	0.0214567i
$155$	3.97545	−	17.1216i	0.319315	−	1.37524i
$156$	2.46714	−	4.81117i	0.197529	−	0.385202i
$157$	7.00832	+	15.0294i	0.559325	+	1.19948i	0.959153	+	0.282886i	$0.0912919\pi$
$157$	7.00832	+	15.0294i	0.559325	+	1.19948i	−0.399828	+	0.916590i	$0.630930\pi$
$158$	−0.501093	−	5.72752i	−0.0398648	−	0.455657i
$159$	1.68898	+	7.40326i	0.133945	+	0.587117i
$160$	−2.07429	+	0.835046i	−0.163987	+	0.0660162i
$161$	0.236104	+	0.0416315i	0.0186076	+	0.00328102i
$162$	−4.00258	−	8.06098i	−0.314472	−	0.633330i
$163$	1.49605	+	0.400865i	0.117180	+	0.0313982i	0.316932	−	0.948448i	$-0.397347\pi$
$163$	1.49605	+	0.400865i	0.117180	+	0.0313982i	−0.199753	+	0.979846i	$0.564014\pi$
$164$	−0.0468512	+	0.0811487i	−0.00365847	+	0.00633665i
$165$	3.12793	+	0.285781i	0.243509	+	0.0222480i
$166$	−8.12941	−	2.95886i	−0.630964	−	0.229652i
$167$	6.30742	−	13.5263i	0.488083	−	1.04670i	−0.495891	−	0.868385i	$-0.665158\pi$
$167$	6.30742	−	13.5263i	0.488083	−	1.04670i	0.983974	−	0.178312i	$-0.0570637\pi$
$168$	2.58587	−	2.00953i	0.199504	−	0.155039i
$169$	−3.20584	+	0.565276i	−0.246603	+	0.0434828i
$170$	1.29682	+	1.72544i	0.0994619	+	0.132335i
$171$	13.0746	−	0.236122i	0.999837	−	0.0180567i
$172$	−4.01402	−	4.01402i	−0.306066	−	0.306066i
$173$	8.70527	−	12.4324i	0.661849	−	0.945219i	−0.338142	−	0.941095i	$-0.609798\pi$
$173$	8.70527	−	12.4324i	0.661849	−	0.945219i	0.999991	−	0.00412392i	$-0.00131269\pi$
$174$	5.15364	+	0.646348i	0.390697	+	0.0489995i
$175$	6.22012	−	7.11930i	0.470197	−	0.538169i
$176$	0.277376	−	0.762083i	0.0209080	−	0.0574442i
$177$	−9.64678	+	10.6582i	−0.725096	+	0.801116i
$178$	−3.39769	−	12.6804i	−0.254668	−	0.950433i
$179$	−11.0375	−	19.1175i	−0.824981	−	1.42891i	−0.901934	−	0.431875i	$-0.857852\pi$
$179$	−11.0375	−	19.1175i	−0.824981	−	1.42891i	0.0769521	−	0.997035i	$-0.475481\pi$
$180$	−6.19168	+	2.58131i	−0.461500	+	0.192399i
$181$	−2.54393	+	14.4273i	−0.189089	+	1.07237i	0.731500	+	0.681841i	$0.238821\pi$
$181$	−2.54393	+	14.4273i	−0.189089	+	1.07237i	−0.920589	+	0.390533i	$0.872291\pi$
$182$	5.70118	+	1.52763i	0.422600	+	0.113235i
$183$	−13.7167	−	8.62065i	−1.01397	−	0.637257i
$184$	−0.0815048	+	0.0971336i	−0.00600861	+	0.00716079i
$185$	4.99189	+	2.66227i	0.367011	+	0.195734i
$186$	−12.1151	−	6.21256i	−0.888324	−	0.455527i
$187$	−0.779861	−	0.0682290i	−0.0570291	−	0.00498940i
$188$	−4.18988	+	5.98377i	−0.305579	+	0.436411i
$189$	7.68304	−	6.12333i	0.558859	−	0.445407i
$190$	0.465977	−	9.73565i	0.0338055	−	0.706298i
$191$		−	0.627614i		−	0.0454125i	−0.999742	−	0.0227063i	$-0.992772\pi$
$191$		−	0.627614i		−	0.0454125i	0.999742	−	0.0227063i	$-0.00722825\pi$
$192$	0.236610	+	1.71581i	0.0170758	+	0.123828i
$193$	0.650321	−	7.43320i	0.0468111	−	0.535054i	−0.936195	−	0.351481i	$-0.885678\pi$
$193$	0.650321	−	7.43320i	0.0468111	−	0.535054i	0.983006	−	0.183573i	$-0.0587663\pi$
$194$	−7.86708	+	2.86338i	−0.564823	+	0.205579i
$195$	−10.4470	−	6.08526i	−0.748126	−	0.435775i
$196$	−2.62372	−	2.20156i	−0.187409	−	0.157254i
$197$	2.95576	+	11.0310i	0.210589	+	0.785929i	0.987673	+	0.156532i	$0.0500315\pi$
$197$	2.95576	+	11.0310i	0.210589	+	0.785929i	−0.777084	+	0.629397i	$0.783302\pi$
$198$	0.804011	−	2.29629i	0.0571386	−	0.163190i
$199$	26.0915	+	4.60064i	1.84958	+	0.326131i	0.984484	−	0.175477i	$-0.0561468\pi$
$199$	26.0915	+	4.60064i	1.84958	+	0.326131i	0.865095	+	0.501608i	$0.167258\pi$
$200$	1.61598	+	4.73166i	0.114267	+	0.334579i
$201$	10.7917	+	3.32996i	0.761189	+	0.234877i
$202$	−7.27075	+	1.94819i	−0.511568	+	0.137074i
$203$	0.494169	+	5.64837i	0.0346838	+	0.396438i
$204$	1.54070	−	0.649283i	0.107871	−	0.0454589i
$205$	0.175579	+	0.114336i	0.0122630	+	0.00798555i
$206$	−3.22043	−	3.83796i	−0.224378	−	0.267403i
$207$	−0.240920	+	0.294379i	−0.0167451	+	0.0204608i
$208$	−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	−0.993405	−	0.114659i	$-0.963422\pi$
$211$	−1.43988	−	8.16597i	−0.0991255	−	0.562168i	0.894279	−	0.447509i	$-0.147689\pi$
$212$	0.382099	−	4.36742i	0.0262427	−	0.299955i
$213$	16.3765	−	5.27417i	1.12210	−	0.361380i
$214$	5.16462	−	14.1897i	0.353046	−	0.969986i
$215$	−9.44371	+	8.48174i	−0.644055	+	0.578450i
$216$	0.772936	+	5.13834i	0.0525917	+	0.349620i
$217$	3.84675	−	14.3563i	0.261135	−	0.974567i
$218$	−3.73506	+	2.61532i	−0.252970	+	0.177132i
$219$	16.5075	−	10.6594i	1.11547	−	0.720293i
$220$	−1.66838	−	0.710657i	−0.112482	−	0.0479125i
$221$	2.60958	+	1.50664i	0.175540	+	0.101348i
$222$	2.94072	−	3.24903i	0.197368	−	0.218061i
$223$	−15.0256	+	7.00655i	−1.00619	+	0.469193i	−0.854620	−	0.519254i	$-0.826210\pi$
$223$	−15.0256	+	7.00655i	−1.00619	+	0.469193i	−0.151568	+	0.988447i	$0.548432\pi$
$224$	−1.77673	+	0.646678i	−0.118713	+	0.0432080i
$225$	5.02176	+	14.1344i	0.334784	+	0.942295i
$226$	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	$0.205229\pi$
$228$	−7.22696	−	2.18427i	−0.478617	−	0.144657i
$229$		−	29.5837i		−	1.95494i	−0.211064	−	0.977472i	$-0.567693\pi$
$229$		−	29.5837i		−	1.95494i	0.211064	−	0.977472i	$-0.432307\pi$
$230$	0.207119	+	0.193628i	0.0136570	+	0.0127674i
$231$	2.63527	+	0.330504i	0.173388	+	0.0217456i
$232$	−2.71781	−	1.26733i	−0.178433	−	0.0832045i
$233$	−2.95073	−	6.32787i	−0.193309	−	0.414552i	0.785633	−	0.618693i	$-0.212338\pi$
$233$	−2.95073	−	6.32787i	−0.193309	−	0.414552i	−0.978941	+	0.204141i	$0.934560\pi$
$234$	−6.54027	+	6.70278i	−0.427551	+	0.438174i
$235$	12.8588	+	10.0724i	0.838818	+	0.657052i
$236$	7.18778	−	4.14987i	0.467885	−	0.270133i
$237$	−2.09567	+	9.73524i	−0.136128	+	0.632372i
$238$	1.04685	+	1.49506i	0.0678572	+	0.0969101i
$239$	9.20937	+	15.9511i	0.595704	+	1.03179i	0.993447	+	0.114293i	$0.0364603\pi$
$239$	9.20937	+	15.9511i	0.595704	+	1.03179i	−0.397743	+	0.917497i	$0.630206\pi$
$240$	3.85951	−	0.322716i	0.249131	−	0.0208312i
$241$	−14.0796	−	11.8142i	−0.906949	−	0.761020i	0.0645875	−	0.997912i	$-0.479427\pi$
$241$	−14.0796	−	11.8142i	−0.906949	−	0.761020i	−0.971536	+	0.236892i	$0.923871\pi$
$242$	−9.37330	+	4.37084i	−0.602539	+	0.280968i
$243$	2.50778	+	15.3854i	0.160874	+	0.986975i
$244$	6.01231	+	7.16519i	0.384899	+	0.458704i
$245$	−5.23016	+	5.59458i	−0.334143	+	0.357425i
$246$	0.118983	−	0.110379i	0.00758610	−	0.00703749i
$247$	−4.72777	−	12.7592i	−0.300821	−	0.811850i
$248$	5.55836	+	5.55836i	0.352956	+	0.352956i
$249$	11.9435	+	9.04870i	0.756889	+	0.573438i
$250$	10.7587	−	3.04128i	0.680443	−	0.192348i
$251$	7.35246	+	20.2007i	0.464083	+	1.27506i	0.922389	+	0.386263i	$0.126234\pi$
$251$	7.35246	+	20.2007i	0.464083	+	1.27506i	−0.458306	+	0.888795i	$0.651544\pi$
$252$	−5.30600	+	2.00529i	−0.334246	+	0.126322i
$253$	−0.102442	+	0.00896248i	−0.00644045	+	0.000563466i
$254$	−6.06681	+	10.5080i	−0.380665	+	0.659332i
$255$	−1.26514	−	3.51797i	−0.0792261	−	0.220304i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	8.77096	+	12.5262i	0.547117	+	0.781364i	0.993543	−	0.113456i	$-0.0361922\pi$
$257$	8.77096	+	12.5262i	0.547117	+	0.781364i	−0.446426	+	0.894821i	$0.647303\pi$
$258$	4.59347	+	8.69334i	0.285977	+	0.541224i
$259$	4.14288	+	2.39189i	0.257426	+	0.148625i
$260$	4.66418	+	5.19317i	0.289260	+	0.322067i
$261$	−8.19945	−	3.70167i	−0.507533	−	0.229128i
$262$	−18.1479	−	8.46251i	−1.12118	−	0.522816i
$263$	−14.3897	−	1.25894i	−0.887309	−	0.0776295i	−0.365619	−	0.930765i	$-0.619143\pi$
$263$	−14.3897	−	1.25894i	−0.887309	−	0.0776295i	−0.521690	+	0.853135i	$0.674698\pi$
$264$	−0.848261	+	1.11963i	−0.0522069	+	0.0689086i
$265$	−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
$268$	−5.34126	−	3.73999i	−0.326269	−	0.228456i
$269$	11.9260	−	10.0071i	0.727142	−	0.610145i	−0.202209	−	0.979342i	$-0.564812\pi$
$269$	11.9260	−	10.0071i	0.727142	−	0.610145i	0.929351	+	0.369198i	$0.120367\pi$
$270$	11.5658	−	1.11015i	0.703872	−	0.0675615i
$271$	−18.8364	−	6.85589i	−1.14423	−	0.416466i	−0.300791	−	0.953690i	$-0.597251\pi$
$271$	−18.8364	−	6.85589i	−1.14423	−	0.416466i	−0.843439	+	0.537224i	$0.819473\pi$
$272$	−0.961614	+	0.0841303i	−0.0583064	+	0.00510115i
$273$	−8.65559	−	5.43985i	−0.523860	−	0.329235i
$274$	−14.7041	+	8.48944i	−0.888310	+	0.512866i
$275$	−1.78671	+	3.64011i	−0.107743	+	0.219507i
$276$	0.184500	−	0.119137i	0.0111056	−	0.00717121i
$277$	−0.755366	+	2.81906i	−0.0453855	+	0.169381i	−0.984899	−	0.173132i	$-0.944611\pi$
$277$	−0.755366	+	2.81906i	−0.0453855	+	0.169381i	0.939513	+	0.342513i	$0.111278\pi$
$278$	−4.19529	+	1.12412i	−0.251617	+	0.0674205i
$279$	16.8784	+	16.4692i	1.01048	+	0.985985i
$280$	1.23104	+	4.04468i	0.0735687	+	0.241716i
$281$	−2.11319	−	5.80593i	−0.126062	−	0.346353i	0.860566	−	0.509338i	$-0.170110\pi$
$281$	−2.11319	−	5.80593i	−0.126062	−	0.346353i	−0.986628	+	0.162986i	$0.947888\pi$
$282$	9.99034	−	7.76370i	0.594916	−	0.462322i
$283$	22.9121	+	16.0433i	1.36199	+	0.953673i	0.999767	+	0.0215796i	$0.00686955\pi$
$283$	22.9121	+	16.0433i	1.36199	+	0.953673i	0.362219	+	0.932093i	$0.382019\pi$
$284$	−9.93321			−0.589428
$285$	−5.74314	+	15.8750i	−0.340194	+	0.940355i
$286$	−2.53163			−0.149699
$287$	0.145128	+	0.101620i	0.00856665	+	0.00599844i
$288$	0.484653	−	2.96059i	0.0285585	−	0.174455i
$289$	−5.49566	−	15.0992i	−0.323274	−	0.888188i
$290$	−3.15544	+	5.91661i	−0.185294	+	0.347435i
$291$	14.4827	−	0.721381i	0.848992	−	0.0422881i
$292$	−10.9583	+	2.93627i	−0.641287	+	0.171832i
$293$	0.970011	−	3.62013i	0.0566687	−	0.211490i	−0.931786	−	0.363009i	$-0.881750\pi$
$293$	0.970011	−	3.62013i	0.0566687	−	0.211490i	0.988454	+	0.151518i	$0.0484162\pi$
$294$	3.21807	+	4.98361i	0.187681	+	0.290650i
$295$	−8.40477	−	16.5465i	−0.489345	−	0.963376i
$296$	−2.19112	+	1.26504i	−0.127356	+	0.0735292i
$297$	−2.50338	+	3.38987i	−0.145261	+	0.196700i
$298$	13.7079	−	1.19928i	0.794075	−	0.0694725i
$299$	0.371951	+	0.135379i	0.0215105	+	0.00782918i
$300$	−0.258108	−	8.65641i	−0.0149019	−	0.499778i
$301$	−8.22214	+	6.89920i	−0.473916	+	0.397663i
$302$	12.8084	+	8.96857i	0.737043	+	0.516083i
$303$	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
$306$	−2.88153	+	0.287770i	−0.164726	+	0.0164507i
$307$	10.7205	+	0.937919i	0.611849	+	0.0535298i	0.388869	−	0.921293i	$-0.372866\pi$
$307$	10.7205	+	0.937919i	0.611849	+	0.0535298i	0.222980	+	0.974823i	$0.428421\pi$
$308$	−1.38972	−	0.648039i	−0.0791869	−	0.0369255i
$309$	3.36996	+	7.99667i	0.191710	+	0.454915i
$310$	13.0770	−	11.7450i	0.742726	−	0.667069i
$311$	−16.5036	−	9.52837i	−0.935834	−	0.540304i	−0.0471822	−	0.998886i	$-0.515024\pi$
$311$	−16.5036	−	9.52837i	−0.935834	−	0.540304i	−0.888652	+	0.458582i	$0.848357\pi$
$312$	4.78053	−	2.52599i	0.270644	−	0.143006i
$313$	14.5407	+	20.7662i	0.821887	+	1.17378i	0.982409	+	0.186744i	$0.0597934\pi$
$313$	14.5407	+	20.7662i	0.821887	+	1.17378i	−0.160522	+	0.987032i	$0.551318\pi$
$314$	−2.87963	+	16.3312i	−0.162507	+	0.921621i
$315$	3.84173	+	12.0878i	0.216457	+	0.681071i
$316$	2.87470	−	4.97912i	0.161714	−	0.280098i
$317$	0.836895	−	0.0732189i	0.0470047	−	0.00411238i	−0.0636291	−	0.997974i	$-0.520267\pi$
$317$	0.836895	−	0.0732189i	0.0470047	−	0.00411238i	0.110634	+	0.993861i	$0.464712\pi$
$318$	−2.86280	+	7.03316i	−0.160538	+	0.394400i
$319$	−0.831785	−	2.28531i	−0.0465710	−	0.127953i
$320$	−2.17813	−	0.505737i	−0.121761	−	0.0282715i
$321$	−15.7943	+	20.8471i	−0.881550	+	1.16357i
$322$	0.169526	+	0.169526i	0.00944733	+	0.00944733i
$323$	1.41618	−	3.96210i	0.0787981	−	0.220457i
$324$	1.34487	−	8.89895i	0.0747148	−	0.494386i
$325$	12.1545	−	9.79215i	0.674209	−	0.543171i
$326$	0.995565	+	1.18647i	0.0551392	+	0.0657124i
$327$	7.51734	−	2.42101i	0.415710	−	0.133882i
$328$	−0.0849233	+	0.0396004i	−0.00468910	+	0.00218657i
$329$	10.5804	+	8.87799i	0.583315	+	0.489459i
$330$	2.39833	+	2.02821i	0.132024	+	0.111649i
$331$	−8.02075	−	13.8923i	−0.440860	−	0.763592i	0.556893	−	0.830584i	$-0.311993\pi$
$331$	−8.02075	−	13.8923i	−0.440860	−	0.763592i	−0.997754	+	0.0669918i	$0.978660\pi$
$332$	−4.96209	−	7.08659i	−0.272330	−	0.388927i
$333$	−6.52630	+	3.87550i	−0.357639	+	0.212376i
$334$	12.9251	−	7.46231i	0.707230	−	0.408320i
$335$	−8.99088	+	11.4781i	−0.491224	+	0.627116i
$336$	3.27084	−	0.162920i	0.178439	−	0.00888799i
$337$	−9.65166	−	20.6980i	−0.525759	−	1.12749i	−0.972515	−	0.232839i	$-0.925199\pi$
$337$	−9.65166	−	20.6980i	−0.525759	−	1.12749i	0.446756	−	0.894656i	$-0.352579\pi$
$338$	−2.95030	−	1.37575i	−0.160475	−	0.0748307i
$339$	1.52286	−	12.1425i	0.0827104	−	0.659490i
$340$	0.0726246	+	2.15722i	0.00393862	+	0.116992i
$341$			6.37497i			0.345224i
$342$	10.8455	+	7.30584i	0.586457	+	0.395055i
$343$	−13.9379	+	13.9379i	−0.752578	+	0.752578i
$344$	−0.985745	−	5.59044i	−0.0531478	−	0.301416i
$345$	−0.243908	−	0.426238i	−0.0131316	−	0.0229479i
$346$	14.2619	−	5.19090i	0.766723	−	0.279065i
$347$	24.6064	−	11.4741i	1.32094	−	0.615964i	0.371068	−	0.928606i	$-0.378992\pi$
$347$	24.6064	−	11.4741i	1.32094	−	0.615964i	0.949871	+	0.312641i	$0.101214\pi$
$348$	3.85089	+	3.48547i	0.206429	+	0.186841i
$349$	−17.8745	−	10.3199i	−0.956802	−	0.552410i	−0.0616145	−	0.998100i	$-0.519625\pi$
$349$	−17.8745	−	10.3199i	−0.956802	−	0.552410i	−0.895187	+	0.445690i	$0.852958\pi$
$350$	9.17869	−	2.26408i	0.490622	−	0.121020i
$351$	14.2475	−	7.75337i	0.760477	−	0.413844i
$352$	0.664326	−	0.465166i	0.0354087	−	0.0247934i
$353$	7.71053	−	28.7761i	0.410390	−	1.53160i	−0.383503	−	0.923540i	$-0.625282\pi$
$353$	7.71053	−	28.7761i	0.410390	−	1.53160i	0.793893	−	0.608058i	$-0.208051\pi$
$354$	−14.0154	+	3.19749i	−0.744913	+	0.169945i
$355$	−1.19026	+	22.1794i	−0.0631722	+	1.17716i
$356$	4.48993	−	12.3360i	0.237966	−	0.653806i
$357$	−0.969074	−	3.00901i	−0.0512888	−	0.159254i
$358$	1.92396	−	21.9910i	0.101685	−	1.16226i
$359$	0.382778	+	2.17084i	0.0202022	+	0.114573i	0.993241	−	0.116068i	$-0.0370290\pi$
$359$	0.382778	+	2.17084i	0.0202022	+	0.114573i	−0.973039	+	0.230640i	$0.925918\pi$
$360$	−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
$363$	17.7454	−	2.44708i	0.931394	−	0.128439i
$364$	3.79392	+	4.52142i	0.198856	+	0.236987i
$365$	5.24318	+	24.8202i	0.274441	+	1.29915i
$366$	−6.29146	−	14.9292i	−0.328860	−	0.780362i
$367$	−1.17145	−	13.3898i	−0.0611494	−	0.698940i	−0.963460	−	0.267853i	$-0.913686\pi$
$367$	−1.17145	−	13.3898i	−0.0611494	−	0.698940i	0.902310	−	0.431087i	$-0.141870\pi$
$368$	−0.122478	+	0.0328180i	−0.00638463	+	0.00171076i
$369$	−0.253293	+	0.121918i	−0.0131859	+	0.00634681i
$370$	2.56211	+	5.04404i	0.133198	+	0.262227i
$371$	−8.16335	−	1.43942i	−0.423820	−	0.0747309i
$372$	−6.36075	−	12.0380i	−0.329789	−	0.624140i
$373$	2.21460	+	8.26502i	0.114668	+	0.427946i	0.999262	−	0.0384156i	$-0.0122311\pi$
$373$	2.21460	+	8.26502i	0.114668	+	0.427946i	−0.884594	+	0.466362i	$0.845564\pi$
$374$	−0.599690	−	0.503200i	−0.0310092	−	0.0260198i
$375$	−19.3594	−	0.460943i	−0.999717	−	0.0238030i
$376$	−6.86430	+	2.49840i	−0.353999	+	0.128845i
$377$	−0.815874	+	9.32548i	−0.0420196	+	0.480287i
$378$	9.80578	−	0.609126i	0.504355	−	0.0313300i
$379$			8.49100i			0.436153i	0.975932	+	0.218077i	$0.0699783\pi$
$379$			8.49100i			0.436153i	−0.975932	+	0.218077i	$0.930022\pi$
$380$	5.96584	−	7.70770i	0.306041	−	0.395397i
$381$	15.4072	−	14.2930i	0.789337	−	0.732254i
$382$	0.359984	−	0.514111i	0.0184184	−	0.0263042i
$383$	26.6679	+	2.33314i	1.36267	+	0.119218i	0.744917	−	0.667157i	$-0.232489\pi$
$383$	26.6679	+	2.33314i	1.36267	+	0.119218i	0.617749	+	0.786375i	$0.288045\pi$
$384$	−0.790331	+	1.54123i	−0.0403314	+	0.0786503i
$385$	−1.61350	+	3.02540i	−0.0822317	+	0.154189i
$386$	4.79622	−	5.71591i	0.244121	−	0.290932i
$387$	−3.16280	−	16.7338i	−0.160774	−	0.850625i
$388$	−8.08670	−	2.16683i	−0.410540	−	0.110004i
$389$	5.41544	−	30.7125i	0.274574	−	1.55719i	−0.465738	−	0.884922i	$-0.654211\pi$
$389$	5.41544	−	30.7125i	0.274574	−	1.55719i	0.740312	−	0.672263i	$-0.234678\pi$
$390$	−5.06733	−	10.9769i	−0.256594	−	0.555838i
$391$	0.0611987	+	0.105999i	0.00309495	+	0.00536061i
$392$	−0.886461	−	3.30832i	−0.0447731	−	0.167095i
$393$	25.7140	+	23.2739i	1.29710	+	1.17401i
$394$	−3.90593	+	10.7315i	−0.196778	+	0.540643i
$395$	−10.7732	−	7.01541i	−0.542058	−	0.352984i
$396$	1.97570	−	1.41985i	0.0992829	−	0.0713500i
$397$	5.26027	−	7.51244i	0.264005	−	0.377038i	−0.665161	−	0.746700i	$-0.731637\pi$
$397$	5.26027	−	7.51244i	0.264005	−	0.377038i	0.929167	+	0.369661i	$0.120526\pi$
$398$	18.7341	+	18.7341i	0.939056	+	0.939056i
$399$	−5.30516	+	13.2525i	−0.265590	+	0.663455i
$400$	−1.39023	+	4.80284i	−0.0695116	+	0.240142i
$401$	12.6041	−	2.22244i	0.629417	−	0.110983i	0.150166	−	0.988661i	$-0.452019\pi$
$401$	12.6041	−	2.22244i	0.629417	−	0.110983i	0.479251	+	0.877678i	$0.340908\pi$
$402$	6.93007	+	8.91762i	0.345640	+	0.444770i
$403$	10.3704	−	22.2393i	0.516585	−	1.10782i
$404$	−7.07328	−	2.57446i	−0.351909	−	0.128084i
$405$	−19.7089	−	4.06922i	−0.979344	−	0.202201i
$406$	−2.83497	+	4.91032i	−0.140697	+	0.243695i
$407$	−1.98196	−	0.531066i	−0.0982423	−	0.0263239i
$408$	1.63448	+	0.351850i	0.0809190	+	0.0174191i
$409$	−16.3531	−	2.88349i	−0.808607	−	0.142579i	−0.245964	−	0.969279i	$-0.579104\pi$
$409$	−16.3531	−	2.88349i	−0.808607	−	0.142579i	−0.562643	+	0.826700i	$0.690216\pi$
$410$	0.0782459	+	0.194367i	0.00386429	+	0.00959908i
$411$	28.6716	−	6.54115i	1.41427	−	0.322651i
$412$	−0.436659	−	4.99104i	−0.0215127	−	0.245891i
$413$	−6.63207	−	14.2225i	−0.326343	−	0.699844i
$414$	−0.366199	+	0.102955i	−0.0179977	+	0.00505997i
$415$	−16.4179	+	10.2305i	−0.805924	+	0.502194i
$416$	−3.07423	+	0.542069i	−0.150726	+	0.0265771i
$417$	7.51750	+	0.282022i	0.368133	+	0.0138107i
$418$	0.633988	+	3.47772i	0.0310094	+	0.170101i
$419$	−7.98682			−0.390182			−0.195091	−	0.980785i	$-0.562500\pi$
$419$	−7.98682			−0.390182			−0.195091	+	0.980785i	$0.562500\pi$
$420$	0.0281552	−	7.32283i	0.00137383	−	0.357318i
$421$	23.2537	−	19.5122i	1.13332	−	0.950965i	0.134117	−	0.990966i	$-0.457180\pi$
$421$	23.2537	−	19.5122i	1.13332	−	0.950965i	0.999200	+	0.0400000i	$0.0127358\pi$
$422$	3.50433	−	7.51505i	0.170588	−	0.365827i
$423$	−20.4994	+	7.74732i	−0.996714	+	0.376688i
$424$	2.81804	−	3.35841i	0.136856	−	0.163099i
$425$	4.82547	+	0.0963311i	0.234070	+	0.00467275i
$426$	16.4400	+	5.07282i	0.796519	+	0.245779i
$427$	14.4869	−	10.1438i	0.701069	−	0.490894i
$428$	12.3695	−	8.66119i	0.597901	−	0.418655i
$429$	4.18998	+	1.29289i	0.202294	+	0.0624212i
$430$	−12.6008	+	1.53115i	−0.607662	+	0.0738385i
$431$	−20.7023	+	24.6720i	−0.997194	+	1.18841i	−0.0151249	+	0.999886i	$0.504815\pi$
$431$	−20.7023	+	24.6720i	−0.997194	+	1.18841i	−0.982069	+	0.188523i	$0.939630\pi$
$432$	−2.31408	+	4.65242i	−0.111336	+	0.223840i
$433$	−12.0696	+	25.8832i	−0.580026	+	1.24387i	0.369222	+	0.929341i	$0.379624\pi$
$433$	−12.0696	+	25.8832i	−0.580026	+	1.24387i	−0.949248	+	0.314528i	$0.898154\pi$
$434$	11.3855	−	9.55357i	0.546521	−	0.458586i
$435$	8.24397	−	8.18082i	0.395268	−	0.392240i
$436$	−4.55967			−0.218368
$437$	0.0928245	−	0.544853i	0.00444040	−	0.0260639i
$438$	19.6361	+	0.736657i	0.938249	+	0.0351988i
$439$	−6.31942	+	1.11428i	−0.301609	+	0.0531819i	−0.322405	−	0.946602i	$-0.604491\pi$
$439$	−6.31942	+	1.11428i	−0.301609	+	0.0531819i	0.0207955	+	0.999784i	$0.493380\pi$
$440$	−0.959045	−	1.53908i	−0.0457207	−	0.0733729i
$441$	−2.78097	−	9.89158i	−0.132427	−	0.471028i
$442$	1.27347	+	2.73097i	0.0605728	+	0.129899i
$443$	−1.32154	−	15.1052i	−0.0627881	−	0.717671i	−0.960717	−	0.277530i	$-0.910484\pi$
$443$	−1.32154	−	15.1052i	−0.0627881	−	0.717671i	0.897929	−	0.440141i	$-0.145071\pi$
$444$	4.27246	−	0.974721i	0.202762	−	0.0462582i
$445$	−27.0064	−	11.5035i	−1.28023	−	0.545320i
$446$	−16.3270	−	2.87890i	−0.773108	−	0.136320i
$447$	−23.2997	−	5.01563i	−1.10204	−	0.237231i
$448$	−1.82633	−	0.489365i	−0.0862862	−	0.0231203i
$449$	2.31054	−	4.00197i	0.109041	−	0.188865i	−0.806341	−	0.591451i	$-0.798555\pi$
$449$	2.31054	−	4.00197i	0.109041	−	0.188865i	0.915382	+	0.402586i	$0.131889\pi$
$450$	−3.99358	+	14.4586i	−0.188259	+	0.681585i
$451$	−0.0714091	−	0.0259908i	−0.00336252	−	0.00122386i
$452$	−2.98596	+	6.40342i	−0.140448	+	0.301191i
$453$	−16.6184	−	21.3846i	−0.780802	−	1.00474i
$454$	4.16010	−	0.733537i	0.195243	−	0.0344266i
$455$	10.5503	−	7.92950i	0.494605	−	0.371741i
$456$	−4.66713	−	5.93447i	−0.218558	−	0.277907i
$457$	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	$0.578725\pi$
$458$	16.9685	−	24.2335i	0.792886	−	1.13236i
$459$	4.91603	+	0.995302i	0.229461	+	0.0464567i
$460$	0.0586017	+	0.277409i	0.00273232	+	0.0129343i
$461$	2.61369	−	7.18105i	0.121732	−	0.334455i	−0.863827	−	0.503788i	$-0.831939\pi$
$461$	2.61369	−	7.18105i	0.121732	−	0.334455i	0.985559	+	0.169333i	$0.0541614\pi$
$462$	1.96912	+	1.78226i	0.0916116	+	0.0829183i
$463$	−8.98584	−	33.5356i	−0.417607	−	1.55853i	−0.779555	−	0.626334i	$-0.784555\pi$
$463$	−8.98584	−	33.5356i	−0.417607	−	1.55853i	0.361948	−	0.932198i	$-0.382112\pi$
$464$	−1.49938	−	2.59701i	−0.0696071	−	0.120563i
$465$	−27.6412	+	12.7602i	−1.28183	+	0.591739i
$466$	1.21242	−	6.87596i	0.0561641	−	0.318523i
$467$	−16.0203	−	4.29264i	−0.741333	−	0.198640i	−0.131663	−	0.991295i	$-0.542032\pi$
$467$	−16.0203	−	4.29264i	−0.741333	−	0.198640i	−0.609671	+	0.792655i	$0.708698\pi$
$468$	−9.20203	+	1.73925i	−0.425364	+	0.0803969i
$469$	−7.92471	+	9.44430i	−0.365929	+	0.436097i
$470$	4.75605	+	15.6264i	0.219380	+	0.720790i
$471$	13.1061	−	25.5583i	0.603899	−	1.17766i
$472$	8.26815	+	0.723369i	0.380572	+	0.0332958i
$473$	2.64060	−	3.77116i	0.121415	−	0.173398i
$474$	−7.30057	+	6.77261i	−0.335326	+	0.311076i
$475$	−16.4953	−	14.2444i	−0.756857	−	0.653580i
$476$			1.82513i			0.0836545i
$477$	8.32987	−	10.1782i	0.381399	−	0.466029i
$478$	−1.60530	+	18.3486i	−0.0734246	+	0.839247i
$479$	−11.0651	+	4.02738i	−0.505579	+	0.184016i	−0.582202	−	0.813044i	$-0.697809\pi$
$479$	−11.0651	+	4.02738i	−0.505579	+	0.184016i	0.0766227	+	0.997060i	$0.475586\pi$
$480$	3.34663	+	1.94937i	0.152752	+	0.0889763i
$481$	6.05026	+	5.07677i	0.275868	+	0.231481i
$482$	−4.75700	−	17.7534i	−0.216676	−	0.808644i
$483$	−0.193999	−	0.367151i	−0.00882725	−	0.0167059i
$484$	−10.1852	−	1.79592i	−0.462962	−	0.0816327i
$485$	−5.80720	+	17.7968i	−0.263692	+	0.808111i
$486$	−6.77046	+	14.0414i	−0.307114	+	0.636931i
$487$	21.6072	−	5.78963i	0.979115	−	0.262353i	0.266443	−	0.963851i	$-0.414152\pi$
$487$	21.6072	−	5.78963i	0.979115	−	0.262353i	0.712672	+	0.701498i	$0.247485\pi$
$488$	0.815211	+	9.31790i	0.0369029	+	0.421802i
$489$	−1.04179	−	2.47209i	−0.0471113	−	0.111792i
$490$	−7.49322	+	1.58292i	−0.338509	+	0.0715089i
$491$	28.3791	+	33.8209i	1.28073	+	1.52631i	0.706810	+	0.707403i	$0.250133\pi$
$491$	28.3791	+	33.8209i	1.28073	+	1.52631i	0.573920	+	0.818912i	$0.305422\pi$
$492$	0.160776	−	0.0221709i	0.00724834	−	0.000999541i
$493$	−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
$497$	−1.63690	+	18.7099i	−0.0734250	+	0.839252i
$498$	4.59343	+	14.2628i	0.205837	+	0.639130i
$499$	7.58348	−	20.8355i	0.339483	−	0.932723i	−0.646058	−	0.763288i	$-0.723584\pi$
$499$	7.58348	−	20.8355i	0.339483	−	0.932723i	0.985541	−	0.169435i	$-0.0541942\pi$
$500$	10.5575	+	3.67969i	0.472144	+	0.164561i
$501$	−25.2027	+	5.74975i	−1.12597	+	0.256880i
$502$	−5.56387	+	20.7646i	−0.248328	+	0.926772i
$503$	−31.0139	+	21.7162i	−1.38284	+	0.968277i	−0.383850	+	0.923395i	$0.625402\pi$
$503$	−31.0139	+	21.7162i	−1.38284	+	0.968277i	−0.998992	+	0.0448811i	$0.985709\pi$
$504$	−5.49661	−	1.40075i	−0.244838	−	0.0623946i
$505$	−6.59597	+	15.4851i	−0.293517	+	0.689079i
$506$	−0.0890559	−	0.0514165i	−0.00395902	−	0.00228574i
$507$	4.18031	+	3.78363i	0.185654	+	0.168037i
$508$	−10.9968	+	5.12789i	−0.487904	+	0.227513i
$509$	−31.6430	+	11.5171i	−1.40255	+	0.510486i	−0.928934	−	0.370246i	$-0.879273\pi$
$509$	−31.6430	+	11.5171i	−1.40255	+	0.510486i	−0.473615	+	0.880732i	$0.657051\pi$
$510$	0.981482	−	3.60741i	0.0434608	−	0.159739i
$511$	3.72483	+	21.1246i	0.164777	+	0.934496i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−14.2188	−	17.6303i	−0.627775	−	0.778395i
$514$			15.2917i			0.674488i
$515$	−11.1966	+	0.376941i	−0.493381	+	0.0166100i
$516$	−1.22354	+	9.75587i	−0.0538633	+	0.429478i
$517$	−5.36912	−	2.50366i	−0.236133	−	0.110111i
$518$	2.02172	+	4.33559i	0.0888291	+	0.190495i
$519$	−26.2551	+	1.30776i	−1.15247	+	0.0574042i
$520$	0.841990	+	6.92926i	0.0369237	+	0.303868i
$521$	1.88567	−	1.08869i	0.0826129	−	0.0476966i	−0.458125	−	0.888888i	$-0.651479\pi$
$521$	1.88567	−	1.08869i	0.0826129	−	0.0476966i	0.540737	+	0.841191i	$0.318145\pi$
$522$	−4.59341	−	7.73524i	−0.201048	−	0.338562i
$523$	22.5041	+	32.1392i	0.984035	+	1.40535i	0.913039	+	0.407872i	$0.133729\pi$
$523$	22.5041	+	32.1392i	0.984035	+	1.40535i	0.0709962	+	0.997477i	$0.477382\pi$
$524$	−10.0120	−	17.3413i	−0.437376	−	0.757558i
$525$	−16.3474	−	0.940331i	−0.713461	−	0.0410394i
$526$	−11.0653	−	9.28488i	−0.482469	−	0.404840i
$527$	6.87691	−	3.20676i	0.299563	−	0.139689i
$528$	−1.33705	+	0.430607i	−0.0581876	+	0.0187397i
$529$	−14.7738	−	17.6067i	−0.642338	−	0.765509i
$530$	−7.16118	−	6.69471i	−0.311062	−	0.290800i
$531$	24.8292	+	1.86558i	1.07750	+	0.0809594i
$532$	5.26100	−	6.34401i	0.228093	−	0.275048i
$533$	0.206833	+	0.206833i	0.00895894	+	0.00895894i
$534$	−13.7310	+	18.1237i	−0.594197	+	0.784289i
$535$	−17.8570	−	28.6571i	−0.772026	−	1.23895i
$536$	−2.23013	−	6.12724i	−0.0963271	−	0.264657i
$537$	−14.4149	+	35.4137i	−0.622049	+	1.52821i
$538$	15.5091	−	1.35687i	0.668644	−	0.0584987i
$539$	1.38883	−	2.40553i	0.0598213	−	0.103614i
$540$	10.1109	+	5.72449i	0.435104	+	0.246343i
$541$	−5.69603	+	32.3038i	−0.244891	+	1.38885i	0.575854	+	0.817553i	$0.304670\pi$
$541$	−5.69603	+	32.3038i	−0.244891	+	1.38885i	−0.820745	+	0.571295i	$0.806441\pi$
$542$	−11.4975	−	16.4201i	−0.493860	−	0.705305i
$543$	22.4350	−	11.8544i	0.962779	−	0.508723i
$544$	−0.835963	−	0.482643i	−0.0358416	−	0.0206932i
$545$	−0.546366	+	10.1811i	−0.0234037	+	0.436109i
$546$	−3.97008	−	9.42071i	−0.169904	−	0.403169i
$547$	−6.80872	−	3.17496i	−0.291120	−	0.135751i	0.271572	−	0.962418i	$-0.412456\pi$
$547$	−6.80872	−	3.17496i	−0.291120	−	0.135751i	−0.562692	+	0.826667i	$0.690234\pi$
$548$	−16.9143	−	1.47981i	−0.722542	−	0.0632142i
$549$	2.78845	+	27.9216i	0.119008	+	1.19166i
$550$	−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
$553$	−8.90478	−	6.23520i	−0.378670	−	0.265148i
$554$	−2.23571	+	1.87598i	−0.0949861	+	0.0797028i
$555$	−1.66446	−	9.65659i	−0.0706524	−	0.409899i
$556$	−4.08135	−	1.48549i	−0.173088	−	0.0629988i
$557$	11.9717	−	1.04739i	0.507258	−	0.0443794i	0.169345	−	0.985557i	$-0.445835\pi$
$557$	11.9717	−	1.04739i	0.507258	−	0.0443794i	0.337913	+	0.941177i	$0.390279\pi$
$558$	4.37965	+	23.1718i	0.185405	+	0.980943i
$559$	−15.3465	+	8.86031i	−0.649088	+	0.374751i
$560$	−1.31152	+	4.01930i	−0.0554220	+	0.169847i
$561$	0.735537	+	1.13908i	0.0310544	+	0.0480919i
$562$	1.59912	−	5.96801i	0.0674550	−	0.251745i
$563$	7.65353	−	2.05076i	0.322558	−	0.0864291i	−0.0939070	−	0.995581i	$-0.529936\pi$
$563$	7.65353	−	2.05076i	0.322558	−	0.0864291i	0.416465	+	0.909152i	$0.363269\pi$
$564$	12.6367	−	0.629430i	0.532100	−	0.0265038i
$565$	13.9401	+	7.43452i	0.586465	+	0.312772i
$566$	9.56650	+	26.2837i	0.402110	+	1.10479i
$567$	−16.5401	−	3.99961i	−0.694621	−	0.167968i
$568$	−8.13681	−	5.69746i	−0.341413	−	0.239060i
$569$	10.3664			0.434582			0.217291	−	0.976107i	$-0.430278\pi$
$569$	10.3664			0.434582			0.217291	+	0.976107i	$0.430278\pi$
$570$	−13.8100	+	9.70992i	−0.578439	+	0.406704i
$571$	7.43668			0.311215			0.155608	−	0.987819i	$-0.450266\pi$
$571$	7.43668			0.311215			0.155608	+	0.987819i	$0.450266\pi$
$572$	−2.07379	−	1.45209i	−0.0867097	−	0.0607148i
$573$	−0.858345	+	0.667038i	−0.0358579	+	0.0278659i
$574$	0.0605954	+	0.166484i	0.00252920	+	0.00694892i
$575$	0.626436	−	0.0976084i	0.0261242	−	0.00407055i
$576$	2.09513	−	2.14719i	0.0872971	−	0.0894663i
$577$	29.8752	−	8.00504i	1.24372	−	0.333254i	0.423814	−	0.905749i	$-0.360691\pi$
$577$	29.8752	−	8.00504i	1.24372	−	0.333254i	0.819908	+	0.572495i	$0.194025\pi$
$578$	4.15876	−	15.5207i	0.172982	−	0.645576i
$579$	−10.8571	+	7.01073i	−0.451204	+	0.291356i
$580$	−5.97841	+	3.03672i	−0.248240	+	0.126093i
$581$	−14.1658	+	8.17861i	−0.587695	+	0.339306i
$582$	12.2773	+	7.71603i	0.508911	+	0.319840i
$583$	3.54194	−	0.309880i	0.146692	−	0.0128339i
$584$	−10.6607	−	3.88018i	−0.441143	−	0.160563i
$585$	2.78085	+	20.7552i	0.114974	+	0.858122i
$586$	2.87101	−	2.40906i	0.118600	−	0.0995174i
$587$	−20.3270	−	14.2331i	−0.838985	−	0.587464i	0.0731653	−	0.997320i	$-0.476690\pi$
$587$	−20.3270	−	14.2331i	−0.838985	−	0.587464i	−0.912150	+	0.409856i	$0.865579\pi$
$588$	−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
$591$	11.9450	−	15.7664i	0.491351	−	0.648542i
$592$	−2.52046	−	0.220512i	−0.103590	−	0.00906297i
$593$	21.3760	+	9.96781i	0.877808	+	0.409329i	0.808659	−	0.588278i	$-0.200194\pi$
$593$	21.3760	+	9.96781i	0.877808	+	0.409329i	0.0691493	+	0.997606i	$0.477972\pi$
$594$	−3.99500	+	1.34094i	−0.163917	+	0.0550195i
$595$	4.07524	+	0.218697i	0.167069	+	0.00896572i
$596$	11.9167	+	6.88011i	0.488127	+	0.281820i
$597$	−21.4385	−	40.5733i	−0.877420	−	1.66055i
$598$	0.227034	+	0.324238i	0.00928412	+	0.0132591i
$599$	−6.24630	+	35.4245i	−0.255217	+	1.44741i	0.540298	+	0.841474i	$0.318311\pi$
$599$	−6.24630	+	35.4245i	−0.255217	+	1.44741i	−0.795515	+	0.605934i	$0.792800\pi$
$600$	4.75368	−	7.23896i	0.194068	−	0.295529i
$601$	−9.61272	+	16.6497i	−0.392111	+	0.679156i	−0.992728	−	0.120381i	$-0.961588\pi$
$601$	−9.61272	+	16.6497i	−0.392111	+	0.679156i	0.600617	+	0.799537i	$0.294922\pi$
$602$	−10.6924	+	0.935464i	−0.435790	+	0.0381267i
$603$	−6.91545	−	18.2982i	−0.281619	−	0.745162i
$604$	5.34790	+	14.6932i	0.217603	+	0.597860i
$605$	−5.23048	+	22.5268i	−0.212649	+	0.915845i
$606$	10.3919	+	7.87315i	0.422141	+	0.319825i
$607$	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	$0.690928\pi$
$608$	1.51451	+	4.08733i	0.0614215	+	0.165763i
$609$	7.19969	−	6.67903i	0.291746	−	0.270648i
$610$	20.9032	−	0.703722i	0.846346	−	0.0284929i
$611$	14.6576	+	17.4682i	0.592982	+	0.706689i
$612$	−2.52547	−	1.41705i	−0.102086	−	0.0572808i
$613$	33.4002	−	15.5748i	1.34902	−	0.629059i	0.392239	−	0.919863i	$-0.371701\pi$
$613$	33.4002	−	15.5748i	1.34902	−	0.629059i	0.956783	+	0.290804i	$0.0939229\pi$
$614$	8.24372	+	6.91730i	0.332689	+	0.279160i
$615$	−0.0302393	−	0.361646i	−0.00121937	−	0.0145830i
$616$	−0.766696	−	1.32796i	−0.0308911	−	0.0535049i
$617$	−8.30416	−	11.8596i	−0.334313	−	0.477448i	0.616439	−	0.787403i	$-0.288575\pi$
$617$	−8.30416	−	11.8596i	−0.334313	−	0.477448i	−0.950751	+	0.309955i	$0.899686\pi$
$618$	−1.82620	+	8.48342i	−0.0734603	+	0.341253i
$619$	−3.70601	+	2.13967i	−0.148957	+	0.0860005i	−0.572626	−	0.819817i	$-0.694075\pi$
$619$	−3.70601	+	2.13967i	−0.148957	+	0.0860005i	0.423669	+	0.905817i	$0.360742\pi$
$620$	17.4487	−	2.12023i	0.700758	−	0.0851507i
$621$	0.658657	+	0.0166196i	0.0264310	+	0.000666920i
$622$	−8.05372	−	17.2713i	−0.322925	−	0.692515i
$623$	−22.4957	−	10.4899i	−0.901272	−	0.420270i
$624$	5.36483	+	0.672834i	0.214765	+	0.0269349i
$625$	9.48127	−	23.1323i	0.379251	−	0.925294i
$626$			25.3509i			1.01322i
$627$	0.726764	−	6.07957i	0.0290241	−	0.242795i
$628$	−11.7260	+	11.7260i	−0.467919	+	0.467919i
$629$	0.424094	+	2.40516i	0.0169097	+	0.0958999i
$630$	−3.78632	+	12.1053i	−0.150850	+	0.482286i
$631$	33.8150	−	12.3076i	1.34615	−	0.489959i	0.434407	−	0.900717i	$-0.356958\pi$
$631$	33.8150	−	12.3076i	1.34615	−	0.489959i	0.911745	+	0.410757i	$0.134736\pi$
$632$	5.21072	−	2.42980i	0.207271	−	0.0966522i
$633$	−9.63772	+	10.6482i	−0.383065	+	0.423226i
$634$	0.727541	+	0.420046i	0.0288943	+	0.0166822i
$635$	10.1321	+	25.1687i	0.402081	+	0.998789i
$636$	−6.37913	+	4.11919i	−0.252949	+	0.163337i
$637$	−8.75815	+	6.13252i	−0.347011	+	0.242979i
$638$	0.629442	−	2.34911i	0.0249198	−	0.0930021i
$639$	−24.6183	−	16.7916i	−0.973886	−	0.664264i
$640$	−1.49414	−	1.66360i	−0.0590610	−	0.0657594i
$641$	12.5281	−	34.4206i	0.494829	−	1.35953i	−0.401384	−	0.915910i	$-0.631471\pi$
$641$	12.5281	−	34.4206i	0.494829	−	1.35953i	0.896214	−	0.443623i	$-0.146307\pi$
$642$	−24.8953	+	8.01771i	−0.982539	+	0.316434i
$643$	−0.0203561	+	0.232671i	−0.000802767	+	0.00917567i	−0.996586	−	0.0825670i	$-0.973688\pi$
$643$	−0.0203561	+	0.232671i	−0.000802767	+	0.00917567i	0.995783	+	0.0917427i	$0.0292437\pi$
$644$	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	$0.347690\pi$
$648$	6.20588	−	6.51821i	0.243790	−	0.256059i
$649$	4.32661	+	5.15626i	0.169834	+	0.202401i
$650$	15.5729	−	1.04974i	0.610820	−	0.0411741i
$651$	−23.7225	+	9.99714i	−0.929759	+	0.391819i
$652$	0.134989	+	1.54293i	0.00528657	+	0.0604258i
$653$	−25.3658	+	6.79675i	−0.992641	+	0.265977i	−0.718359	−	0.695672i	$-0.755107\pi$
$653$	−25.3658	+	6.79675i	−0.992641	+	0.265977i	−0.274282	+	0.961649i	$0.588440\pi$
$654$	7.54648	+	2.32859i	0.295091	+	0.0910551i
$655$	−39.9203	+	20.2774i	−1.55982	+	0.792304i
$656$	−0.0922789	−	0.0162713i	−0.00360289	−	0.000635286i
$657$	−32.1225	−	11.2472i	−1.25322	−	0.438796i
$658$	3.57473	+	13.3411i	0.139358	+	0.520089i
$659$	−3.71987	−	3.12134i	−0.144906	−	0.121590i	0.567453	−	0.823406i	$-0.307929\pi$
$659$	−3.71987	−	3.12134i	−0.144906	−	0.121590i	−0.712359	+	0.701815i	$0.752373\pi$
$660$	0.801269	+	3.03704i	0.0311894	+	0.118216i
$661$	12.7225	−	4.63060i	0.494847	−	0.180109i	−0.0825282	−	0.996589i	$-0.526299\pi$
$661$	12.7225	−	4.63060i	0.494847	−	0.180109i	0.577375	+	0.816479i	$0.304077\pi$
$662$	1.39811	−	15.9805i	0.0543390	−	0.621098i
$663$	−0.712973	−	5.17024i	−0.0276896	−	0.200796i
$664$		−	8.65113i		−	0.335729i
$665$	−13.5349	−	12.5072i	−0.524859	−	0.485009i
$666$	−7.56893	−	0.568704i	−0.293290	−	0.0220368i
$667$	−0.218097	+	0.311475i	−0.00844475	+	0.0120603i
$668$	14.8678	+	1.30077i	0.575254	+	0.0503282i
$669$	25.5518	+	13.1028i	0.987891	+	0.506584i
$670$	−13.9485	+	4.24536i	−0.538876	+	0.164013i
$671$	−4.87593	+	5.81091i	−0.188233	+	0.224328i
$672$	2.77276	+	1.74262i	0.106962	+	0.0672230i
$673$	−36.5172	−	9.78477i	−1.40764	−	0.377175i	−0.526555	−	0.850141i	$-0.676517\pi$
$673$	−36.5172	−	9.78477i	−1.40764	−	0.377175i	−0.881081	+	0.472966i	$0.843183\pi$
$674$	3.96574	−	22.4908i	0.152754	−	0.866314i
$675$	13.9935	−	21.8902i	0.538610	−	0.842555i
$676$	−1.62765	−	2.81917i	−0.0626018	−	0.108429i
$677$	−8.76444	−	32.7093i	−0.336845	−	1.25712i	−0.901855	−	0.432038i	$-0.857795\pi$
$677$	−8.76444	−	32.7093i	−0.336845	−	1.25712i	0.565011	−	0.825083i	$-0.308872\pi$
$678$	8.21210	−	9.07307i	0.315384	−	0.348449i
$679$	−5.41397	+	14.8748i	−0.207769	+	0.570841i
$680$	−1.17784	+	1.80875i	−0.0451682	+	0.0693624i
$681$	−7.25978	−	0.910491i	−0.278195	−	0.0348901i
$682$	−3.65653	+	5.22207i	−0.140016	+	0.199963i
$683$	−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	$0.969464\pi$
$684$	4.69365	+	12.2053i	0.179466	+	0.466682i
$685$	−5.33096	+	37.5898i	−0.203686	+	1.43623i
$686$	−19.4118	+	3.42282i	−0.741145	+	0.130684i
$687$	−40.4596	+	31.4420i	−1.54363	+	1.19959i
$688$	2.39907	−	5.14482i	0.0914636	−	0.196144i
$689$	−12.8603	−	4.68076i	−0.489938	−	0.178323i
$690$	0.0446820	−	0.489053i	0.00170101	−	0.0186179i
$691$	−14.4273	+	24.9888i	−0.548839	+	0.950617i	0.449515	+	0.893273i	$0.351597\pi$
$691$	−14.4273	+	24.9888i	−0.548839	+	0.950617i	−0.998354	+	0.0573445i	$0.981737\pi$
$692$	14.6600	+	3.92814i	0.557291	+	0.149326i
$693$	−2.34880	−	3.95535i	−0.0892235	−	0.150251i
$694$	26.7377	+	4.71457i	1.01495	+	0.178963i
$695$	−3.80593	+	8.93506i	−0.144367	+	0.338926i
$696$	1.15528	+	5.06390i	0.0437908	+	0.191947i
$697$	0.00788322	+	0.0901056i	0.000298598	+	0.00341299i
$698$	−8.72273	−	18.7059i	−0.330160	−	0.708031i
$699$	−5.51811	+	10.7609i	−0.208714	+	0.407014i
$700$	8.81736	+	3.41006i	0.333265	+	0.128888i
$701$	27.5630	−	4.86011i	1.04104	−	0.183564i	0.373111	−	0.927787i	$-0.378291\pi$
$701$	27.5630	−	4.86011i	1.04104	−	0.183564i	0.667931	+	0.744223i	$0.267180\pi$
$702$	16.1180	+	1.82086i	0.608337	+	0.0687241i
$703$	5.45883	−	9.58262i	0.205884	−	0.361415i
$704$	0.810992			0.0305654
$705$	0.108776	−	28.2913i	0.00409673	−	1.06551i
$706$	22.8214	−	19.1494i	0.858895	−	0.720698i
$707$	−6.01478	+	12.8987i	−0.226209	+	0.485107i
$708$	−13.3148	−	5.41970i	−0.500400	−	0.203685i
$709$	8.02993	−	9.56969i	0.301570	−	0.359397i	−0.593884	−	0.804550i	$-0.702406\pi$
$709$	8.02993	−	9.56969i	0.301570	−	0.359397i	0.895454	+	0.445153i	$0.146851\pi$
$710$	−13.6966	+	17.4856i	−0.514024	+	0.656223i
$711$	15.5415	−	7.48066i	0.582854	−	0.280547i
$712$	10.7536	−	7.52972i	0.403007	−	0.282188i
$713$	0.816473	−	0.571700i	0.0305771	−	0.0214103i
$714$	0.932079	−	3.02068i	0.0348822	−	0.113046i
$715$	−3.49079	+	4.45648i	−0.130548	+	0.166663i
$716$	14.1895	−	16.9104i	0.530288	−	0.631972i
$717$	12.0274	−	29.5481i	0.449171	−	1.10349i
$718$	−0.931590	+	1.99780i	−0.0347666	+	0.0745572i
$719$	−9.51171	+	7.98127i	−0.354727	+	0.297651i	−0.802685	−	0.596403i	$-0.796596\pi$
$719$	−9.51171	+	7.98127i	−0.354727	+	0.297651i	0.447958	+	0.894055i	$0.352151\pi$
$720$	−4.54331	−	4.93541i	−0.169319	−	0.183932i
$721$	−9.47290			−0.352789
$722$	−18.9456	−	1.43679i	−0.705082	−	0.0534716i
$723$	−1.19345	+	31.8121i	−0.0443847	+	1.18310i
$724$	−14.4273	+	2.54393i	−0.536187	+	0.0945443i
$725$	6.06418	+	13.7128i	0.225218	+	0.509280i
$726$	15.9398	+	8.17383i	0.591582	+	0.303359i
$727$	−9.05908	−	19.4273i	−0.335983	−	0.720517i	0.663638	−	0.748054i	$-0.269011\pi$
$727$	−9.05908	−	19.4273i	−0.335983	−	0.720517i	−0.999621	+	0.0275368i	$0.991234\pi$
$728$	0.514419	+	5.87984i	0.0190656	+	0.217921i
$729$	18.3763	−	19.7816i	0.680603	−	0.732652i
$730$	−9.94130	+	23.3389i	−0.367944	+	0.863810i
$731$	−5.39638	−	0.951527i	−0.199592	−	0.0351935i
$732$	3.40937	−	15.8379i	0.126014	−	0.585386i
$733$	7.00768	+	1.87770i	0.258834	+	0.0693545i	0.385903	−	0.922540i	$-0.373890\pi$
$733$	7.00768	+	1.87770i	0.258834	+	0.0693545i	−0.127068	+	0.991894i	$0.540557\pi$
$734$	6.72046	−	11.6402i	0.248057	−	0.429647i
$735$	13.2100	+	1.20693i	0.487260	+	0.0445181i
$736$	−0.119152	−	0.0433678i	−0.00439200	−	0.00159856i
$737$	2.23483	−	4.79260i	0.0823209	−	0.176538i
$738$	−0.277415	−	0.0454132i	−0.0102118	−	0.00167168i
$739$	12.0005	−	2.11601i	0.441445	−	0.0778386i	0.0514918	−	0.998673i	$-0.483602\pi$
$739$	12.0005	−	2.11601i	0.441445	−	0.0778386i	0.389953	+	0.920835i	$0.372491\pi$
$740$	−0.794387	+	5.60140i	−0.0292022	+	0.205911i
$741$	−12.4252	+	20.0266i	−0.456450	+	0.735694i
$742$	−5.86141	−	5.86141i	−0.215179	−	0.215179i
$743$	5.60886	−	8.01028i	0.205769	−	0.293869i	−0.702982	−	0.711208i	$-0.748148\pi$
$743$	5.60886	−	8.01028i	0.205769	−	0.293869i	0.908751	+	0.417339i	$0.137037\pi$
$744$	1.69428	−	13.5093i	0.0621153	−	0.495275i
$745$	16.7902	−	25.7838i	0.615146	−	0.944647i
$746$	−2.92652	+	8.04055i	−0.107148	+	0.294385i
$747$	−0.318459	−	25.9514i	−0.0116518	−	0.949514i
$748$	−0.202614	−	0.756165i	−0.00740830	−	0.0276481i
$749$	−14.2756	−	24.7260i	−0.521617	−	0.903468i
$750$	−15.5939	−	11.4817i	−0.569410	−	0.419252i
$751$	−7.95328	+	45.1053i	−0.290219	+	1.64592i	0.395803	+	0.918335i	$0.370466\pi$
$751$	−7.95328	+	45.1053i	−0.290219	+	1.64592i	−0.686023	+	0.727580i	$0.740645\pi$
$752$	−7.05593	−	1.89063i	−0.257303	−	0.0689442i
$753$	19.8128	−	31.5251i	0.722020	−	1.14884i
$754$	−6.01720	+	7.17102i	−0.219134	+	0.261153i
$755$	33.4487	−	10.1805i	1.21732	−	0.370505i
$756$	8.38181	+	5.12540i	0.304843	+	0.186409i
$757$	19.8326	+	1.73513i	0.720828	+	0.0630642i	0.441666	−	0.897180i	$-0.354388\pi$
$757$	19.8326	+	1.73513i	0.720828	+	0.0630642i	0.279162	+	0.960244i	$0.409943\pi$
$758$	−4.87024	+	6.95542i	−0.176895	+	0.252632i
$759$	0.121134	+	0.130577i	0.00439689	+	0.00473965i
$760$	9.30789	−	2.89191i	0.337633	−	0.104901i
$761$		−	16.1848i		−	0.586697i	−0.956006	−	0.293348i	$-0.905230\pi$
$761$		−	16.1848i		−	0.586697i	0.956006	−	0.293348i	$-0.0947696\pi$
$762$	20.8190	−	2.87093i	0.754193	−	0.104003i
$763$	−0.751390	+	8.58843i	−0.0272022	+	0.310922i
$764$	0.589764	−	0.214657i	0.0213369	−	0.00776600i
$765$	−3.46668	+	5.46920i	−0.125338	+	0.197739i
$766$	20.5068	+	17.2073i	0.740942	+	0.621724i
$767$	−6.70571	−	25.0260i	−0.242129	−	0.903638i
$768$	−1.53141	+	0.809183i	−0.0552601	+	0.0291989i
$769$	31.0642	+	5.47745i	1.12020	+	0.197522i	0.702930	−	0.711259i	$-0.251875\pi$
$769$	31.0642	+	5.47745i	1.12020	+	0.197522i	0.417273	+	0.908781i	$0.362986\pi$
$770$	−3.05700	+	1.55280i	−0.110167	+	0.0559589i
$771$	7.80936	−	25.3085i	0.281247	−	0.911464i
$772$	7.20735	−	1.93120i	0.259398	−	0.0695055i
$773$	−1.39781	−	15.9770i	−0.0502757	−	0.574654i	−0.978997	−	0.203875i	$-0.934646\pi$
$773$	−1.39781	−	15.9770i	−0.0502757	−	0.574654i	0.928721	−	0.370779i	$-0.120909\pi$
$774$	7.00728	−	15.5216i	0.251871	−	0.557913i
$775$	−2.64337	−	39.2145i	−0.0949526	−	1.40863i
$776$	−5.38140	−	6.41330i	−0.193181	−	0.230224i
$777$	−1.13189	−	8.20809i	−0.0406063	−	0.294464i
$778$	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
$782$	−0.0106676	+	0.121932i	−0.000381474	+	0.00436027i
$783$	3.65199	+	15.1480i	0.130512	+	0.541347i
$784$	1.17143	−	3.21847i	0.0418367	−	0.114945i
$785$	24.7774	+	27.5876i	0.884345	+	0.984644i
$786$	7.71429	+	33.8138i	0.275160	+	1.20610i
$787$	8.82418	−	32.9323i	0.314548	−	1.17391i	−0.609861	−	0.792508i	$-0.708775\pi$
$787$	8.82418	−	32.9323i	0.314548	−	1.17391i	0.924409	−	0.381402i	$-0.124558\pi$
$788$	−9.35486	+	6.55034i	−0.333253	+	0.233346i
$789$	13.5719	+	21.0179i	0.483172	+	0.748257i
$790$	−4.80101	−	11.9259i	−0.170812	−	0.424306i
$791$	11.5692	+	6.67948i	0.411353	+	0.237495i
$792$	2.43279	−	0.0298537i	0.0864455	−	0.00106080i
$793$	26.4627	−	12.3398i	0.939718	−	0.438197i
$794$	8.61792	−	3.13666i	0.305838	−	0.111316i
$795$	8.43317	+	14.7372i	0.299094	+	0.522676i
$796$	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	$0.0982704\pi$
$798$	−11.9471	+	7.81290i	−0.422921	+	0.276574i
$799$			7.05126i			0.249456i
$800$	−3.89361	+	3.13685i	−0.137660	+	0.110904i
$801$	31.9811	−	22.9833i	1.13000	−	0.812076i
$802$	11.5994	+	5.40888i	0.409588	+	0.190994i
$803$	−3.88834	−	8.33858i	−0.137217	−	0.294262i
$804$	0.561844	+	11.2798i	0.0198147	+	0.397808i
$805$	0.532175	−	0.0646658i	0.0187567	−	0.00227917i
$806$	21.2509	−	12.2692i	0.748529	−	0.432164i
$807$	−26.3612	−	5.67469i	−0.927960	−	0.199759i
$808$	−4.31744	−	6.16595i	−0.151887	−	0.216917i
$809$	15.5172	+	26.8766i	0.545556	+	0.944930i	0.998572	+	0.0534278i	$0.0170147\pi$
$809$	15.5172	+	26.8766i	0.545556	+	0.944930i	−0.453016	+	0.891502i	$0.649652\pi$
$810$	−13.8106	−	14.6379i	−0.485255	−	0.514323i
$811$	−4.95639	−	4.15890i	−0.174042	−	0.146039i	0.551606	−	0.834105i	$-0.314015\pi$
$811$	−4.95639	−	4.15890i	−0.174042	−	0.146039i	−0.725648	+	0.688066i	$0.758460\pi$
$812$	−5.13872	+	2.39622i	−0.180334	+	0.0840910i
$813$	10.6433	+	33.0478i	0.373277	+	1.15904i
$814$	−1.31892	−	1.57183i	−0.0462282	−	0.0550927i
$815$	3.46131	−	0.116528i	0.121245	−	0.00408179i
$816$	1.13708	+	1.22572i	0.0398057	+	0.0429088i
$817$	16.0146	+	18.8627i	0.560280	+	0.659922i
$818$	−11.7417	−	11.7417i	−0.410540	−	0.410540i
$819$	1.75959	+	17.6192i	0.0614849	+	0.615666i
$820$	−0.0473888	+	0.204096i	−0.00165489	+	0.00712733i
$821$	−2.09915	−	5.76736i	−0.0732608	−	0.201282i	0.897657	−	0.440694i	$-0.145268\pi$
$821$	−2.09915	−	5.76736i	−0.0732608	−	0.201282i	−0.970918	+	0.239412i	$0.923045\pi$
$822$	27.2383	+	11.0872i	0.950043	+	0.386709i
$823$	−1.51350	+	0.132414i	−0.0527572	+	0.00461566i	−0.113504	−	0.993538i	$-0.536207\pi$
$823$	−1.51350	+	0.132414i	−0.0527572	+	0.00461566i	0.0607466	+	0.998153i	$0.480652\pi$
$824$	2.50505	−	4.33888i	0.0872676	−	0.151152i
$825$	6.87727	−	1.42520i	0.239436	−	0.0496192i
$826$	2.72503	−	15.4544i	0.0948158	−	0.537727i
$827$	7.63698	+	10.9067i	0.265564	+	0.379265i	0.929682	−	0.368363i	$-0.120082\pi$
$827$	7.63698	+	10.9067i	0.265564	+	0.379265i	−0.664118	+	0.747628i	$0.731193\pi$
$828$	−0.359026	−	0.125707i	−0.0124770	−	0.00436864i
$829$	46.2512	+	26.7031i	1.60637	+	0.927438i	0.990173	+	0.139846i	$0.0446606\pi$
$829$	46.2512	+	26.7031i	1.60637	+	0.927438i	0.616197	+	0.787592i	$0.288673\pi$
$830$	−19.3167	−	1.03663i	−0.670493	−	0.0359819i
$831$	4.65826	−	1.96308i	0.161593	−	0.0680986i
$832$	−2.82918	−	1.31927i	−0.0980841	−	0.0457373i
$833$	−3.29355	−	0.288148i	−0.114115	−	0.00998374i
$834$	5.99621	+	4.54288i	0.207632	+	0.157307i
$835$	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
$838$	−6.54242	−	4.58105i	−0.226004	−	0.158250i
$839$	−23.1259	+	19.4049i	−0.798394	+	0.669932i	−0.947808	−	0.318843i	$-0.896706\pi$
$839$	−23.1259	+	19.4049i	−0.798394	+	0.669932i	0.149414	+	0.988775i	$0.452261\pi$
$840$	4.22327	−	5.98236i	0.145717	−	0.206411i
$841$	18.8008	+	6.84293i	0.648304	+	0.235963i
$842$	30.2401	−	2.64566i	1.04214	−	0.0911755i
$843$	−5.69445	+	9.06070i	−0.196127	+	0.312067i
$844$	7.18103	−	4.14597i	0.247181	−	0.142710i
$845$	−6.48982	+	3.29649i	−0.223257	+	0.113403i
$846$	−21.2358	−	5.41173i	−0.730102	−	0.186059i
$847$	−5.06115	+	18.8885i	−0.173903	+	0.649016i
$848$	4.23471	−	1.13469i	0.145421	−	0.0389654i
$849$	−2.41012	−	48.3865i	−0.0827150	−	1.66062i
$850$	3.89754	+	2.84669i	0.133685	+	0.0976406i
$851$	0.109724	+	0.301465i	0.00376130	+	0.0103341i
$852$	10.5572	+	13.5850i	0.361683	+	0.465414i
$853$	−26.6365	−	18.6510i	−0.912015	−	0.638600i	0.0204771	−	0.999790i	$-0.493481\pi$
$853$	−26.6365	−	18.6510i	−0.912015	−	0.638600i	−0.932492	+	0.361191i	$0.882370\pi$
$854$	17.6852			0.605176
$855$	27.8151	−	9.01772i	0.951257	−	0.308400i
$856$	15.1003			0.516119
$857$	37.7478	+	26.4313i	1.28944	+	0.902875i	0.998547	−	0.0538808i	$-0.0171591\pi$
$857$	37.7478	+	26.4313i	1.28944	+	0.902875i	0.290892	+	0.956756i	$0.406048\pi$
$858$	2.69066	+	3.46235i	0.0918577	+	0.118203i
$859$	6.35333	+	17.4556i	0.216773	+	0.595578i	0.999646	−	0.0266028i	$-0.00846894\pi$
$859$	6.35333	+	17.4556i	0.216773	+	0.595578i	−0.782873	+	0.622181i	$0.786247\pi$
$860$	−11.2002	−	5.97326i	−0.381922	−	0.203686i
$861$	−0.0152660	−	0.306486i	−0.000520263	−	0.0104450i
$862$	−31.1096	+	8.33579i	−1.05960	+	0.283918i
$863$	−12.4285	+	46.3837i	−0.423070	+	1.57892i	0.345030	+	0.938591i	$0.387869\pi$
$863$	−12.4285	+	46.3837i	−0.423070	+	1.57892i	−0.768101	+	0.640329i	$0.778798\pi$
$864$	−4.56410	+	2.48374i	−0.155274	+	0.0844985i
$865$	10.5276	−	32.2630i	0.357950	−	1.09698i
$866$	−24.7328	+	14.2795i	−0.840456	+	0.485237i
$867$	−14.8093	+	23.5637i	−0.502950	+	0.800266i
$868$	14.8062	−	1.29537i	0.502554	−	0.0439677i
$869$	4.38152	+	1.59474i	0.148633	+	0.0540979i
$870$	11.4454	−	1.97279i	0.388035	−	0.0668838i
$871$	−15.5926	+	13.0837i	−0.528334	+	0.443325i
$872$	−3.73506	−	2.61532i	−0.126485	−	0.0885658i
$873$	−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
$876$	15.6624	+	11.8662i	0.529184	+	0.400923i
$877$	17.0485	+	1.49155i	0.575685	+	0.0503659i	0.371281	−	0.928521i	$-0.378919\pi$
$877$	17.0485	+	1.49155i	0.575685	+	0.0503659i	0.204404	+	0.978887i	$0.434474\pi$
$878$	−5.81569	−	2.71190i	−0.196270	−	0.0915222i
$879$	−5.98196	+	2.52092i	−0.201766	+	0.0850284i
$880$	0.0971778	−	1.81083i	0.00327586	−	0.0610430i
$881$	−36.8817	−	21.2937i	−1.24258	−	0.717402i	−0.272958	−	0.962026i	$-0.588002\pi$
$881$	−36.8817	−	21.2937i	−1.24258	−	0.717402i	−0.969618	+	0.244624i	$0.921335\pi$
$882$	3.39554	−	9.69780i	0.114334	−	0.326542i
$883$	26.6648	+	38.0813i	0.897342	+	1.28154i	0.958990	+	0.283439i	$0.0914753\pi$
$883$	26.6648	+	38.0813i	0.897342	+	1.28154i	−0.0616486	+	0.998098i	$0.519636\pi$
$884$	−0.523252	+	2.96751i	−0.0175989	+	0.0998082i
$885$	−13.6969	+	29.0806i	−0.460415	+	0.977533i
$886$	7.58146	−	13.1315i	0.254704	−	0.441161i
$887$	12.2096	−	1.06820i	0.409959	−	0.0358668i	0.119689	−	0.992811i	$-0.461810\pi$
$887$	12.2096	−	1.06820i	0.409959	−	0.0358668i	0.290270	+	0.956945i	$0.406255\pi$
$888$	4.05887	+	1.65214i	0.136207	+	0.0554421i
$889$	7.84654	+	21.5582i	0.263165	+	0.723039i
$890$	−15.5242	−	24.9134i	−0.520373	−	0.835099i
$891$	7.29673	−	0.179108i	0.244450	−	0.00600036i
$892$	−11.7231	−	11.7231i	−0.392517	−	0.392517i
$893$	20.3255	−	24.5097i	0.680168	−	0.820185i
$894$	−16.2091	−	17.4727i	−0.542114	−	0.584374i
$895$	−36.0583	−	33.7095i	−1.20529	−	1.12678i
$896$	−1.21536	−	1.44841i	−0.0406022	−	0.0483879i
$897$	−0.210167	−	0.652576i	−0.00701727	−	0.0217889i
$898$	4.18812	−	1.95295i	0.139759	−	0.0651709i
$899$	18.0575	+	15.1521i	0.602252	+	0.505349i
$900$	−11.5645	+	9.55317i	−0.385482	+	0.318439i
$901$	−2.11596	−	3.66494i	−0.0704927	−	0.122097i
$902$	−0.0435872	−	0.0622490i	−0.00145129	−	0.00207266i
$903$	18.1742	+	3.91229i	0.604800	+	0.130193i
$904$	−6.11881	+	3.53269i	−0.203508	+	0.117496i
$905$	3.95145	+	32.5190i	0.131351	+	1.08097i
$906$	−1.34731	−	27.0492i	−0.0447615	−	0.898649i
$907$	7.14835	+	15.3297i	0.237357	+	0.509014i	0.988518	−	0.151106i	$-0.0482834\pi$
$907$	7.14835	+	15.3297i	0.237357	+	0.509014i	−0.751161	+	0.660120i	$0.770506\pi$
$908$	3.82849	+	1.78525i	0.127053	+	0.0592458i
$909$	−13.1783	−	18.3375i	−0.437098	−	0.608217i
$910$	13.1905	−	0.444067i	0.437260	−	0.0147207i
$911$		−	13.2633i		−	0.439434i	−0.975564	−	0.219717i	$-0.929487\pi$
$911$		−	13.2633i		−	0.439434i	0.975564	−	0.219717i	$-0.0705134\pi$
$912$	−0.419220	−	7.53819i	−0.0138817	−	0.249614i
$913$	4.96106	−	4.96106i	0.164187	−	0.164187i
$914$	3.80486	+	21.5784i	0.125854	+	0.713752i
$915$	−34.9552	−	9.51043i	−1.15558	−	0.314405i
$916$	27.7996	−	10.1182i	0.918524	−	0.334315i
$917$	−34.3134	+	16.0006i	−1.13313	+	0.528386i
$918$	3.45610	+	3.63503i	0.114068	+	0.119974i
$919$	37.9864	+	21.9314i	1.25305	+	0.723452i	0.971715	−	0.236157i	$-0.0758878\pi$
$919$	37.9864	+	21.9314i	1.25305	+	0.723452i	0.281340	+	0.959608i	$0.409221\pi$
$920$	−0.111111	+	0.260853i	−0.00366324	+	0.00860006i
$921$	−10.1112	−	15.6585i	−0.333174	−	0.515965i
$922$	6.25989	−	4.38322i	0.206159	−	0.144354i
$923$	−8.02547	+	29.9514i	−0.264161	+	0.985864i
$924$	0.590742	+	2.58938i	0.0194340	+	0.0851844i
$925$	12.4119	+	2.44494i	0.408101	+	0.0803892i
$926$	11.8745	−	32.6248i	0.390219	−	1.07212i
$927$	7.35487	−	13.1079i	0.241566	−	0.430519i
$928$	0.261360	−	2.98736i	0.00857955	−	0.0980647i
$929$	3.54805	+	20.1220i	0.116408	+	0.660180i	0.986044	+	0.166487i	$0.0532424\pi$
$929$	3.54805	+	20.1220i	0.116408	+	0.660180i	−0.869636	+	0.493693i	$0.835647\pi$
$930$	−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
$933$	4.50901	+	32.6978i	0.147618	+	1.07048i
$934$	−10.6609	−	12.7052i	−0.348837	−	0.415727i
$935$	−1.71269	+	0.361799i	−0.0560108	+	0.0118321i
$936$	−8.53546	−	3.85336i	−0.278990	−	0.125951i
$937$	−0.944363	−	10.7941i	−0.0308510	−	0.352629i	−0.995893	−	0.0905344i	$-0.971142\pi$
$937$	−0.944363	−	10.7941i	−0.0308510	−	0.352629i	0.965042	−	0.262094i	$-0.0844131\pi$
$938$	−11.9086	+	3.19089i	−0.388829	+	0.104186i
$939$	12.9465	−	41.9570i	0.422493	−	1.36921i
$940$	−5.06699	+	15.5283i	−0.165267	+	0.506478i
$941$	−22.5506	−	3.97628i	−0.735129	−	0.129623i	−0.206465	−	0.978454i	$-0.566196\pi$
$941$	−22.5506	−	3.97628i	−0.735129	−	0.129623i	−0.528664	+	0.848831i	$0.677307\pi$
$942$	25.3956	−	13.4188i	0.827432	−	0.437207i
$943$	0.00307513	+	0.0114765i	0.000100140	+	0.000373727i
$944$	6.35796	+	5.33497i	0.206934	+	0.173638i
$945$	12.4486	−	18.1012i	0.404954	−	0.588832i
$946$	4.32610	−	1.57457i	0.140654	−	0.0511938i
$947$	−1.77503	+	20.2887i	−0.0576808	+	0.659295i	0.911232	+	0.411893i	$0.135132\pi$
$947$	−1.77503	+	20.2887i	−0.0576808	+	0.659295i	−0.968913	+	0.247402i	$0.920423\pi$
$948$	−9.86489	+	1.36036i	−0.320397	+	0.0441825i
$949$			35.4148i			1.14961i
$950$	−5.34190	−	21.1297i	−0.173314	−	0.685538i
$951$	−0.989603	−	1.06675i	−0.0320901	−	0.0345917i
$952$	−1.04685	+	1.49506i	−0.0339286	+	0.0484550i
$953$	44.1751	+	3.86482i	1.43097	+	0.125194i	0.776131	−	0.630572i	$-0.217180\pi$
$953$	44.1751	+	3.86482i	1.43097	+	0.125194i	0.654842	+	0.755766i	$0.272735\pi$
$954$	12.6614	−	3.55969i	0.409929	−	0.115249i
$955$	−0.408628	−	1.34258i	−0.0132229	−	0.0434448i
$956$	−11.8393	+	14.1096i	−0.382911	+	0.456336i
$957$	−2.24143	+	3.56644i	−0.0724552	+	0.115287i
$958$	−11.3740	−	3.04766i	−0.367478	−	0.0984656i
$959$	−5.57463	+	31.6153i	−0.180014	+	1.02091i
$960$	1.62329	+	3.51638i	0.0523913	+	0.113491i
$961$	−15.3953	−	26.6655i	−0.496623	−	0.860177i
$962$	2.04417	+	7.62893i	0.0659065	+	0.245967i
$963$	45.2976	−	0.555863i	1.45969	−	0.0179124i
$964$	6.28621	−	17.2712i	0.202465	−	0.556269i
$965$	−3.44847	−	16.3244i	−0.111010	−	0.525500i
$966$	0.0516745	−	0.412025i	0.00166260	−	0.0132567i
$967$	−14.7058	+	21.0020i	−0.472905	+	0.675378i	−0.982761	−	0.184881i	$-0.940810\pi$
$967$	−14.7058	+	21.0020i	−0.472905	+	0.675378i	0.509856	+	0.860260i	$0.329699\pi$
$968$	−7.31310	−	7.31310i	−0.235052	−	0.235052i
$969$	−6.92384	+	2.27418i	−0.222426	+	0.0730571i
$970$	−14.9648	+	11.2474i	−0.480491	+	0.361132i
$971$	−8.73218	+	1.53972i	−0.280229	+	0.0494120i	−0.311996	−	0.950083i	$-0.600998\pi$
$971$	−8.73218	+	1.53972i	−0.280229	+	0.0494120i	0.0317671	+	0.999495i	$0.489887\pi$
$972$	−13.5998	+	7.61867i	−0.436215	+	0.244369i
$973$	−3.47059	+	7.44270i	−0.111262	+	0.238602i
$974$	21.0204	+	7.65078i	0.673536	+	0.245147i
$975$	−26.3101	−	6.21561i	−0.842596	−	0.199059i
$976$	−4.67675	+	8.10036i	−0.149699	+	0.259286i
$977$	−31.4066	−	8.41536i	−1.00478	−	0.269231i	−0.281336	−	0.959609i	$-0.590778\pi$
$977$	−31.4066	−	8.41536i	−1.00478	−	0.269231i	−0.723449	+	0.690378i	$0.757444\pi$
$978$	0.564550	−	2.62256i	0.0180523	−	0.0838604i
$979$	10.4847	+	1.84873i	0.335092	+	0.0590858i
$980$	−7.04601	−	3.00128i	−0.225076	−	0.0958725i
$981$	−11.3006	−	7.70787i	−0.360801	−	0.246093i
$982$	3.84793	+	43.9820i	0.122792	+	1.40352i
$983$	18.4699	+	39.6089i	0.589099	+	1.26333i	0.944469	+	0.328601i	$0.106577\pi$
$983$	18.4699	+	39.6089i	0.589099	+	1.26333i	−0.355370	+	0.934726i	$0.615645\pi$
$984$	0.144417	+	0.0740560i	0.00460384	+	0.00236082i
$985$	13.5050	+	21.6730i	0.430306	+	0.690558i
$986$	−2.85069	+	0.502654i	−0.0907846	+	0.0160078i
$987$	0.896835	−	23.9057i	0.0285466	−	0.760928i
$988$	10.3727	−	8.80656i	0.330001	−	0.280174i
$989$	−0.719797			−0.0228882
$990$	0.224853	−	5.43565i	0.00714628	−	0.172756i
$991$	−1.32291	+	1.11005i	−0.0420236	+	0.0352620i	−0.663558	−	0.748125i	$-0.730954\pi$
$991$	−1.32291	+	1.11005i	−0.0420236	+	0.0352620i	0.621534	+	0.783387i	$0.286510\pi$
$992$	−3.32208	+	7.12422i	−0.105476	+	0.226194i
$993$	−10.4750	+	25.7345i	−0.332416	+	0.816658i
$994$	−12.0724	+	14.3873i	−0.382913	+	0.456338i
$995$	58.8099	−	7.14612i	1.86440	−	0.226547i
$996$	−4.41807	+	14.3181i	−0.139992	+	0.453685i
$997$	−1.54433	+	1.08135i	−0.0489093	+	0.0342467i	−0.597775	−	0.801664i	$-0.703949\pi$
$997$	−1.54433	+	1.08135i	−0.0489093	+	0.0342467i	0.548866	+	0.835910i	$0.315060\pi$
$998$	18.1628	−	12.7177i	0.574932	−	0.402572i
$999$	12.2365	+	4.80663i	0.387146	+	0.152075i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.16	✓	480	19.17	even	9	inner
570.2.bi.a.17.37	yes	480	57.17	odd	18	inner
570.2.bi.a.47.15	yes	480	3.2	odd	2	inner
570.2.bi.a.47.27	yes	480	1.1	even	1	trivial
570.2.bi.a.473.15	yes	480	95.93	odd	36	inner
570.2.bi.a.473.27	yes	480	285.188	even	36	inner
570.2.bi.a.503.16	yes	480	15.8	even	4	inner
570.2.bi.a.503.37	yes	480	5.3	odd	4	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)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(-1.06282 - 1.36763i) q^{3} +(0.342020 + 0.939693i) q^{4} +(2.13918 - 0.651082i) q^{5} +(-0.0861662 - 1.72991i) q^{6} +(1.82633 - 0.489365i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.740842 + 2.90709i) q^{9} +O(q^{10})\)	\(q+(0.819152 + 0.573576i) q^{2} +(-1.06282 - 1.36763i) q^{3} +(0.342020 + 0.939693i) q^{4} +(2.13918 - 0.651082i) q^{5} +(-0.0861662 - 1.72991i) q^{6} +(1.82633 - 0.489365i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.740842 + 2.90709i) q^{9} +(2.12576 + 0.693648i) q^{10} +(-0.702340 + 0.405496i) q^{11} +(0.921650 - 1.46648i) q^{12} +(3.10977 - 0.272070i) q^{13} +(1.77673 + 0.646678i) q^{14} +(-3.16400 - 2.23363i) q^{15} +(-0.766044 + 0.642788i) q^{16} +(0.790717 + 0.553666i) q^{17} +(-2.27430 + 1.95642i) q^{18} +(-1.15251 - 4.20377i) q^{19} +(1.34346 + 1.78749i) q^{20} +(-2.61033 - 1.97765i) q^{21} +(-0.807906 - 0.0706826i) q^{22} +(0.114919 + 0.0535876i) q^{23} +(1.59611 - 0.672632i) q^{24} +(4.15218 - 2.78556i) q^{25} +(2.70343 + 1.56083i) q^{26} +(4.76321 - 2.07650i) q^{27} +(1.08450 + 1.54882i) q^{28} +(-0.520730 + 2.95321i) q^{29} +(-1.31064 - 3.64448i) q^{30} +(3.93035 - 6.80757i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(1.30103 + 0.529575i) q^{33} +(0.330148 + 0.907073i) q^{34} +(3.58824 - 2.23593i) q^{35} +(-2.98515 + 0.298119i) q^{36} +(1.78904 + 1.78904i) q^{37} +(1.46710 - 4.10458i) q^{38} +(-3.67721 - 3.96387i) q^{39} +(0.0752363 + 2.23480i) q^{40} +(0.0602308 + 0.0717803i) q^{41} +(-1.00392 - 3.11722i) q^{42} +(-5.14482 + 2.39907i) q^{43} +(-0.621256 - 0.521296i) q^{44} +(0.307958 + 6.70113i) q^{45} +(0.0633995 + 0.109811i) q^{46} +(4.18988 + 5.98377i) q^{47} +(1.69326 + 0.364503i) q^{48} +(-2.96616 + 1.71251i) q^{49} +(4.99900 + 0.0997953i) q^{50} +(-0.0831751 - 1.66986i) q^{51} +(1.31927 + 2.82918i) q^{52} +(-3.97334 - 1.85280i) q^{53} +(5.09282 + 1.03109i) q^{54} +(-1.23842 + 1.32471i) q^{55} +1.89076i q^{56} +(-4.52431 + 6.04405i) q^{57} +(-2.12045 + 2.12045i) q^{58} +(-1.44123 - 8.17364i) q^{59} +(1.01678 - 3.73713i) q^{60} +(8.78941 - 3.19908i) q^{61} +(7.12422 - 3.32208i) q^{62} +(0.0696013 + 5.67186i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(6.47522 - 2.60672i) q^{65} +(0.761988 + 1.18004i) q^{66} +(-5.34126 + 3.73999i) q^{67} +(-0.249835 + 0.932395i) q^{68} +(-0.0488496 - 0.214121i) q^{69} +(4.22179 + 0.226562i) q^{70} +(-3.39736 + 9.33417i) q^{71} +(-2.61629 - 1.46801i) q^{72} +(-0.988772 + 11.3017i) 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} +(-0.738612 - 5.35617i) q^{78} +(-3.69564 - 4.40429i) q^{79} +(-1.22020 + 1.87380i) q^{80} +(-7.90231 - 4.30738i) q^{81} +(0.00816671 + 0.0933459i) q^{82} +(-8.35635 + 2.23908i) q^{83} +(0.965598 - 3.12930i) q^{84} +(2.05197 + 0.669570i) q^{85} +(-5.59044 - 0.985745i) q^{86} +(4.59235 - 2.42655i) q^{87} +(-0.209900 - 0.783358i) q^{88} +(-10.0564 - 8.43831i) q^{89} +(-3.59135 + 5.66588i) q^{90} +(5.54634 - 2.01870i) q^{91} +(-0.0110513 + 0.126316i) q^{92} +(-13.4875 + 1.85992i) q^{93} +7.30484i q^{94} +(-5.20243 - 8.24225i) q^{95} +(1.17797 + 1.26980i) q^{96} +(-4.80197 + 6.85792i) q^{97} +(-3.41199 - 0.298510i) q^{98} +(-0.658490 - 2.34217i) 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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