LMFDB - Embedded newform 558.2.bb.b.493.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(7,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 28])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.bb (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [128,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			493.6
Character	$\chi$	$=$	558.493
Dual form			558.2.bb.b.103.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.104528 - 0.994522i) q^{2} +(-0.768131 + 1.55241i) q^{3} +(-0.978148 + 0.207912i) q^{4} +2.90916 q^{5} +(1.62420 + 0.601652i) q^{6} +(1.14867 - 3.53525i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.81995 - 2.38491i) q^{9} +(-0.304090 - 2.89323i) q^{10} +(0.427416 - 0.0908500i) q^{11} +(0.428581 - 1.67819i) q^{12} +(-3.67802 - 2.67224i) q^{13} +(-3.63595 - 0.772845i) q^{14} +(-2.23462 + 4.51621i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.0519686 - 0.0577170i) q^{17} +(-2.18161 + 2.05927i) q^{18} +(4.84680 + 2.15793i) q^{19} +(-2.84559 + 0.604849i) q^{20} +(4.60582 + 4.49874i) q^{21} +(-0.135029 - 0.415578i) q^{22} +(3.11385 - 3.45828i) q^{23} +(-1.71379 - 0.250815i) q^{24} +3.46323 q^{25} +(-2.27314 + 3.93720i) q^{26} +(5.10031 - 0.993389i) q^{27} +(-0.388551 + 3.69682i) q^{28} +(-0.787696 - 7.49443i) q^{29} +(4.72505 + 1.75030i) q^{30} +(1.12610 + 5.45270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.187275 + 0.733309i) q^{33} +(-0.0628330 - 0.0456509i) q^{34} +(3.34167 - 10.2846i) q^{35} +(2.27603 + 1.95440i) q^{36} +(-0.723607 - 1.25332i) q^{37} +(1.63948 - 5.04581i) q^{38} +(6.97361 - 3.65716i) q^{39} +(0.898981 + 2.76678i) q^{40} +(5.36616 - 3.89875i) q^{41} +(3.99266 - 5.05084i) q^{42} +(-0.787435 + 0.572105i) q^{43} +(-0.399187 + 0.177729i) q^{44} +(-5.29453 - 6.93808i) q^{45} +(-3.76482 - 2.73530i) q^{46} +(-3.77257 + 1.67966i) q^{47} +(-0.0703004 + 1.73062i) q^{48} +(-5.51541 - 4.00718i) q^{49} +(-0.362007 - 3.44426i) q^{50} +(0.0496817 + 0.125011i) q^{51} +(4.15323 + 1.84914i) q^{52} +(1.83657 + 0.390376i) q^{53} +(-1.52107 - 4.96853i) q^{54} +(1.24342 - 0.264298i) q^{55} +3.71718 q^{56} +(-7.07297 + 5.86664i) q^{57} +(-7.37104 + 1.56676i) q^{58} +(2.03689 - 0.906882i) q^{59} +(1.24681 - 4.88213i) q^{60} +(-5.25630 + 9.10417i) q^{61} +(5.30512 - 1.68990i) q^{62} +(-10.5218 + 3.69450i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-10.7000 - 7.77398i) q^{65} +(0.748867 + 0.109597i) q^{66} +15.2761 q^{67} +(-0.0388330 + 0.0672606i) q^{68} +(2.97683 + 7.49039i) q^{69} +(-10.5776 - 2.24833i) q^{70} +(10.9387 + 2.32509i) q^{71} +(1.70579 - 2.46785i) q^{72} +(2.20473 + 2.44860i) q^{73} +(-1.17082 + 0.850651i) q^{74} +(-2.66022 + 5.37636i) q^{75} +(-5.18955 - 1.10307i) q^{76} +(0.169783 - 1.61538i) q^{77} +(-4.36607 - 6.55313i) q^{78} +(2.53818 + 7.81172i) q^{79} +(2.65765 - 1.18326i) q^{80} +(-2.37556 + 8.68082i) q^{81} +(-4.43830 - 4.92924i) q^{82} +(-11.1672 - 4.97194i) q^{83} +(-5.44052 - 3.44283i) q^{84} +(0.151185 - 0.167908i) q^{85} +(0.651281 + 0.723321i) q^{86} +(12.2395 + 4.53387i) q^{87} +(0.218482 + 0.378422i) q^{88} +(-2.32530 + 7.15653i) q^{89} +(-6.34665 + 5.99076i) q^{90} +(-13.6719 + 9.93319i) q^{91} +(-2.32679 + 4.03012i) q^{92} +(-9.32981 - 2.44021i) q^{93} +(2.06480 + 3.57633i) q^{94} +(14.1001 + 6.27778i) q^{95} +(1.72849 - 0.110984i) q^{96} +(-11.1919 - 12.4298i) q^{97} +(-3.40871 + 5.90406i) q^{98} +(-0.994545 - 0.854004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	−0.768131	+	1.55241i	−0.443480	+	0.896284i
$3$	−0.768131	+	1.55241i	−0.443480	+	0.896284i
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	2.90916			1.30102			0.650509	−	0.759499i	$-0.274556\pi$
$5$	2.90916			1.30102			0.650509	+	0.759499i	$0.274556\pi$
$6$	1.62420	+	0.601652i	0.663076	+	0.245623i
$7$	1.14867	−	3.53525i	0.434157	−	1.33620i	−0.459791	−	0.888027i	$-0.652076\pi$
$7$	1.14867	−	3.53525i	0.434157	−	1.33620i	0.893948	−	0.448171i	$-0.147924\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−1.81995	−	2.38491i	−0.606650	−	0.794969i
$10$	−0.304090	−	2.89323i	−0.0961618	−	0.914919i
$11$	0.427416	−	0.0908500i	0.128871	−	0.0273923i	−0.143025	−	0.989719i	$-0.545683\pi$
$11$	0.427416	−	0.0908500i	0.128871	−	0.0273923i	0.271895	+	0.962327i	$0.412350\pi$
$12$	0.428581	−	1.67819i	0.123721	−	0.484451i
$13$	−3.67802	−	2.67224i	−1.02010	−	0.741145i	−0.0537958	−	0.998552i	$-0.517132\pi$
$13$	−3.67802	−	2.67224i	−1.02010	−	0.741145i	−0.966303	+	0.257407i	$0.917132\pi$
$14$	−3.63595	−	0.772845i	−0.971749	−	0.206552i
$15$	−2.23462	+	4.51621i	−0.576976	+	1.16608i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	0.0519686	−	0.0577170i	0.0126042	−	0.0139984i	−0.736810	−	0.676100i	$-0.763669\pi$
$17$	0.0519686	−	0.0577170i	0.0126042	−	0.0139984i	0.749414	+	0.662102i	$0.230335\pi$
$18$	−2.18161	+	2.05927i	−0.514209	+	0.485375i
$19$	4.84680	+	2.15793i	1.11193	+	0.495064i	0.878708	−	0.477359i	$-0.158406\pi$
$19$	4.84680	+	2.15793i	1.11193	+	0.495064i	0.233224	+	0.972423i	$0.425073\pi$
$20$	−2.84559	+	0.604849i	−0.636294	+	0.135248i
$21$	4.60582	+	4.49874i	1.00507	+	0.981706i
$22$	−0.135029	−	0.415578i	−0.0287884	−	0.0886015i
$23$	3.11385	−	3.45828i	0.649283	−	0.721102i	−0.325180	−	0.945652i	$-0.605425\pi$
$23$	3.11385	−	3.45828i	0.649283	−	0.721102i	0.974462	+	0.224551i	$0.0720914\pi$
$24$	−1.71379	−	0.250815i	−0.349827	−	0.0511973i
$25$	3.46323			0.692647
$26$	−2.27314	+	3.93720i	−0.445800	+	0.772148i
$27$	5.10031	−	0.993389i	0.981555	−	0.191178i
$28$	−0.388551	+	3.69682i	−0.0734292	+	0.698633i
$29$	−0.787696	−	7.49443i	−0.146272	−	1.39168i	−0.783685	−	0.621159i	$-0.786662\pi$
$29$	−0.787696	−	7.49443i	−0.146272	−	1.39168i	0.637413	−	0.770522i	$-0.280004\pi$
$30$	4.72505	+	1.75030i	0.862673	+	0.319560i
$31$	1.12610	+	5.45270i	0.202254	+	0.979333i
$31$	1.12610	+	5.45270i	0.202254	+	0.979333i
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.187275	+	0.733309i	−0.0326003	+	0.127653i
$34$	−0.0628330	−	0.0456509i	−0.0107758	−	0.00782906i
$35$	3.34167	−	10.2846i	0.564846	−	1.73842i
$36$	2.27603	+	1.95440i	0.379338	+	0.325734i
$37$	−0.723607	−	1.25332i	−0.118960	−	0.206045i	0.800396	−	0.599472i	$-0.204623\pi$
$37$	−0.723607	−	1.25332i	−0.118960	−	0.206045i	−0.919356	+	0.393427i	$0.871289\pi$
$38$	1.63948	−	5.04581i	0.265960	−	0.818539i
$39$	6.97361	−	3.65716i	1.11667	−	0.585615i
$40$	0.898981	+	2.76678i	0.142141	+	0.437466i
$41$	5.36616	−	3.89875i	0.838054	−	0.608882i	−0.0837726	−	0.996485i	$-0.526697\pi$
$41$	5.36616	−	3.89875i	0.838054	−	0.608882i	0.921826	+	0.387603i	$0.126697\pi$
$42$	3.99266	−	5.05084i	0.616080	−	0.779361i
$43$	−0.787435	+	0.572105i	−0.120083	+	0.0872452i	−0.646206	−	0.763163i	$-0.723645\pi$
$43$	−0.787435	+	0.572105i	−0.120083	+	0.0872452i	0.526123	+	0.850409i	$0.323645\pi$
$44$	−0.399187	+	0.177729i	−0.0601797	+	0.0267937i
$45$	−5.29453	−	6.93808i	−0.789263	−	1.03427i
$46$	−3.76482	−	2.73530i	−0.555093	−	0.403299i
$47$	−3.77257	+	1.67966i	−0.550286	+	0.245003i	−0.662993	−	0.748625i	$-0.730714\pi$
$47$	−3.77257	+	1.67966i	−0.550286	+	0.245003i	0.112708	+	0.993628i	$0.464048\pi$
$48$	−0.0703004	+	1.73062i	−0.0101470	+	0.249794i
$49$	−5.51541	−	4.00718i	−0.787916	−	0.572454i
$50$	−0.362007	−	3.44426i	−0.0511955	−	0.487092i
$51$	0.0496817	+	0.125011i	0.00695684	+	0.0175050i
$52$	4.15323	+	1.84914i	0.575950	+	0.256429i
$53$	1.83657	+	0.390376i	0.252273	+	0.0536223i	0.332312	−	0.943169i	$-0.392171\pi$
$53$	1.83657	+	0.390376i	0.252273	+	0.0536223i	−0.0800393	+	0.996792i	$0.525505\pi$
$54$	−1.52107	−	4.96853i	−0.206992	−	0.676132i
$55$	1.24342	−	0.264298i	0.167663	−	0.0356379i
$56$	3.71718			0.496729
$57$	−7.07297	+	5.86664i	−0.936838	+	0.777056i
$58$	−7.37104	+	1.56676i	−0.967865	+	0.205726i
$59$	2.03689	−	0.906882i	0.265181	−	0.118066i	−0.269840	−	0.962905i	$-0.586971\pi$
$59$	2.03689	−	0.906882i	0.265181	−	0.118066i	0.535020	+	0.844839i	$0.320304\pi$
$60$	1.24681	−	4.88213i	0.160963	−	0.630280i
$61$	−5.25630	+	9.10417i	−0.673000	+	1.16567i	0.304049	+	0.952656i	$0.401661\pi$
$61$	−5.25630	+	9.10417i	−0.673000	+	1.16567i	−0.977049	+	0.213014i	$0.931672\pi$
$62$	5.30512	−	1.68990i	0.673750	−	0.214617i
$63$	−10.5218	+	3.69450i	−1.32562	+	0.465464i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−10.7000	−	7.77398i	−1.32717	−	0.964243i
$66$	0.748867	+	0.109597i	0.0921792	+	0.0134905i
$67$	15.2761			1.86627			0.933134	−	0.359530i	$-0.117063\pi$
$67$	15.2761			1.86627			0.933134	+	0.359530i	$0.117063\pi$
$68$	−0.0388330	+	0.0672606i	−0.00470919	+	0.00815655i
$69$	2.97683	+	7.49039i	0.358368	+	0.901736i
$70$	−10.5776	−	2.24833i	−1.26426	−	0.268727i
$71$	10.9387	+	2.32509i	1.29818	+	0.275937i	0.804628	−	0.593779i	$-0.202365\pi$
$71$	10.9387	+	2.32509i	1.29818	+	0.275937i	0.493553	+	0.869716i	$0.335698\pi$
$72$	1.70579	−	2.46785i	0.201029	−	0.290839i
$73$	2.20473	+	2.44860i	0.258044	+	0.286587i	0.858221	−	0.513281i	$-0.171570\pi$
$73$	2.20473	+	2.44860i	0.258044	+	0.286587i	−0.600177	+	0.799867i	$0.704903\pi$
$74$	−1.17082	+	0.850651i	−0.136105	+	0.0988861i
$75$	−2.66022	+	5.37636i	−0.307175	+	0.620808i
$76$	−5.18955	−	1.10307i	−0.595282	−	0.126531i
$77$	0.169783	−	1.61538i	0.0193486	−	0.184089i
$78$	−4.36607	−	6.55313i	−0.494360	−	0.741995i
$79$	2.53818	+	7.81172i	0.285568	+	0.878887i	0.986228	+	0.165392i	$0.0528889\pi$
$79$	2.53818	+	7.81172i	0.285568	+	0.878887i	−0.700660	+	0.713495i	$0.747111\pi$
$80$	2.65765	−	1.18326i	0.297135	−	0.132293i
$81$	−2.37556	+	8.68082i	−0.263951	+	0.964536i
$82$	−4.43830	−	4.92924i	−0.490129	−	0.544343i
$83$	−11.1672	−	4.97194i	−1.22575	−	0.545741i	−0.311254	−	0.950327i	$-0.600749\pi$
$83$	−11.1672	−	4.97194i	−1.22575	−	0.545741i	−0.914500	+	0.404586i	$0.867416\pi$
$84$	−5.44052	−	3.44283i	−0.593609	−	0.375643i
$85$	0.151185	−	0.167908i	0.0163983	−	0.0182122i
$86$	0.651281	+	0.723321i	0.0702294	+	0.0779977i
$87$	12.2395	+	4.53387i	1.31221	+	0.486082i
$88$	0.218482	+	0.378422i	0.0232903	+	0.0403400i
$89$	−2.32530	+	7.15653i	−0.246481	+	0.758591i	0.748908	+	0.662674i	$0.230578\pi$
$89$	−2.32530	+	7.15653i	−0.246481	+	0.758591i	−0.995389	+	0.0959170i	$0.969422\pi$
$90$	−6.34665	+	5.99076i	−0.668995	+	0.631481i
$91$	−13.6719	+	9.93319i	−1.43320	+	1.04128i
$92$	−2.32679	+	4.03012i	−0.242585	+	0.420169i
$93$	−9.32981	−	2.44021i	−0.967456	−	0.253038i
$94$	2.06480	+	3.57633i	0.212967	+	0.368870i
$95$	14.1001	+	6.27778i	1.44664	+	0.644087i
$96$	1.72849	−	0.110984i	0.176413	−	0.0113273i
$97$	−11.1919	−	12.4298i	−1.13636	−	1.26206i	−0.960694	−	0.277610i	$-0.910458\pi$
$97$	−11.1919	−	12.4298i	−1.13636	−	1.26206i	−0.175670	−	0.984449i	$-0.556209\pi$
$98$	−3.40871	+	5.90406i	−0.344332	+	0.596400i
$99$	−0.994545	−	0.854004i	−0.0999555	−	0.0858307i
$100$	−3.38755	+	0.720047i	−0.338755	+	0.0720047i
$101$	−0.199134	−	0.0423271i	−0.0198145	−	0.00421171i	0.197994	−	0.980203i	$-0.436557\pi$
$101$	−0.199134	−	0.0423271i	−0.0198145	−	0.00421171i	−0.217808	+	0.975992i	$0.569891\pi$
$102$	0.119133	−	0.0624768i	0.0117959	−	0.00618612i
$103$	−14.2843	+	10.3782i	−1.40748	+	1.02259i	−0.413792	+	0.910371i	$0.635796\pi$
$103$	−14.2843	+	10.3782i	−1.40748	+	1.02259i	−0.993683	+	0.112220i	$0.964204\pi$
$104$	1.40488	−	4.32377i	0.137760	−	0.423981i
$105$	13.3991	+	13.0876i	1.30762	+	1.27722i
$106$	0.196263	−	1.86732i	0.0190628	−	0.181370i
$107$	7.33900	−	8.15078i	0.709487	−	0.787966i	−0.275369	−	0.961339i	$-0.588800\pi$
$107$	7.33900	−	8.15078i	0.709487	−	0.787966i	0.984856	+	0.173373i	$0.0554666\pi$
$108$	−4.78232	+	2.03210i	−0.460179	+	0.195538i
$109$	−5.93104	−	4.30915i	−0.568091	−	0.412742i	0.266320	−	0.963885i	$-0.414192\pi$
$109$	−5.93104	−	4.30915i	−0.568091	−	0.412742i	−0.834411	+	0.551142i	$0.814192\pi$
$110$	−0.392823	−	1.20898i	−0.0374542	−	0.115272i
$111$	2.50150	−	0.160618i	0.237431	−	0.0152452i
$112$	−0.388551	−	3.69682i	−0.0367146	−	0.349316i
$113$	−3.58911	+	11.0461i	−0.337635	+	1.03913i	0.627775	+	0.778395i	$0.283966\pi$
$113$	−3.58911	+	11.0461i	−0.337635	+	1.03913i	−0.965410	+	0.260738i	$0.916034\pi$
$114$	6.57383	+	6.42100i	0.615696	+	0.601381i
$115$	9.05870	−	10.0607i	0.844728	−	0.938166i
$116$	2.32866	+	7.16689i	0.216211	+	0.665429i
$117$	0.320777	+	13.6351i	0.0296558	+	1.26056i
$118$	−1.11483	−	1.93094i	−0.102628	−	0.177757i
$119$	−0.144349	−	0.250020i	−0.0132325	−	0.0229193i
$120$	−4.98571	−	0.729661i	−0.455131	−	0.0666086i
$121$	−9.87457	+	4.39644i	−0.897688	+	0.399677i
$122$	9.60373	+	4.27586i	0.869481	+	0.387118i
$123$	1.93054	+	11.3252i	0.174071	+	1.02116i
$124$	−2.23518	−	5.09941i	−0.200725	−	0.457941i
$125$	−4.47070			−0.399872
$126$	4.77409	+	10.0779i	0.425309	+	0.897814i
$127$	−1.60811	+	15.3001i	−0.142696	+	1.35766i	0.655467	+	0.755224i	$0.272472\pi$
$127$	−1.60811	+	15.3001i	−0.142696	+	1.35766i	−0.798163	+	0.602441i	$0.794195\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	−0.283289	−	1.66187i	−0.0249422	−	0.146320i
$130$	−6.61294	+	11.4539i	−0.579993	+	1.00458i
$131$	−10.1021	−	11.2195i	−0.882624	−	0.980253i	0.117294	−	0.993097i	$-0.462578\pi$
$131$	−10.1021	−	11.2195i	−0.882624	−	0.980253i	−0.999918	+	0.0128443i	$0.995911\pi$
$132$	0.0307188	−	0.756221i	0.00267373	−	0.0658206i
$133$	13.1962	−	14.6559i	1.14426	−	1.27083i
$134$	−1.59678	−	15.1924i	−0.137941	−	1.31242i
$135$	14.8376	−	2.88993i	1.27702	−	0.248726i
$136$	0.0709513	+	0.0315896i	0.00608403	+	0.00270878i
$137$	−0.0273155	+	0.259889i	−0.00233372	+	0.0222039i	−0.995627	−	0.0934200i	$-0.970220\pi$
$137$	−0.0273155	+	0.259889i	−0.00233372	+	0.0222039i	0.993293	+	0.115624i	$0.0368867\pi$
$138$	7.13819	−	3.74348i	0.607643	−	0.318666i
$139$	−1.13219	+	10.7721i	−0.0960310	+	0.913674i	0.835372	+	0.549685i	$0.185252\pi$
$139$	−1.13219	+	10.7721i	−0.0960310	+	0.913674i	−0.931403	+	0.363989i	$0.881415\pi$
$140$	−1.13036	+	10.7546i	−0.0955327	+	0.908933i
$141$	0.290312	−	7.14677i	0.0244487	−	0.601866i
$142$	1.16895	−	11.1218i	0.0980958	−	0.933319i
$143$	−1.81482	−	0.808008i	−0.151763	−	0.0675691i
$144$	−2.63264	−	1.43848i	−0.219386	−	0.119873i
$145$	−2.29154	−	21.8025i	−0.190302	−	1.81060i
$146$	2.20473	−	2.44860i	0.182464	−	0.202647i
$147$	10.4573	−	5.48414i	0.862507	−	0.452324i
$148$	0.968375	+	1.07549i	0.0795999	+	0.0884046i
$149$	10.7004	−	18.5336i	0.876608	−	1.51833i	0.0215684	−	0.999767i	$-0.493134\pi$
$149$	10.7004	−	18.5336i	0.876608	−	1.51833i	0.855040	−	0.518563i	$-0.173533\pi$
$150$	5.62497	+	2.08366i	0.459277	+	0.170130i
$151$	10.7449	+	11.9334i	0.874404	+	0.971124i	0.999780	−	0.0209856i	$-0.00668040\pi$
$151$	10.7449	+	11.9334i	0.874404	+	0.971124i	−0.125376	+	0.992109i	$0.540014\pi$
$152$	−0.554574	+	5.27642i	−0.0449819	+	0.427974i
$153$	−0.232230	−	0.0188982i	−0.0187747	−	0.00152783i
$154$	−1.62428			−0.130888
$155$	3.27602	+	15.8628i	0.263136	+	1.27413i
$156$	−6.06085	+	5.02714i	−0.485256	+	0.402493i
$157$	7.38064	+	3.28607i	0.589039	+	0.262257i	0.679539	−	0.733639i	$-0.262180\pi$
$157$	7.38064	+	3.28607i	0.589039	+	0.262257i	−0.0904999	+	0.995896i	$0.528846\pi$
$158$	7.50361	−	3.34082i	0.596955	−	0.265782i
$159$	−2.01675	+	2.55126i	−0.159939	+	0.202328i
$160$	−1.45458	−	2.51941i	−0.114995	−	0.199177i
$161$	−8.64909	−	14.9807i	−0.681644	−	1.18064i
$162$	8.88158	+	1.45515i	0.697803	+	0.114328i
$163$	−3.83642	−	11.8073i	−0.300492	−	0.924819i	−0.981321	−	0.192377i	$-0.938380\pi$
$163$	−3.83642	−	11.8073i	−0.300492	−	0.924819i	0.680829	−	0.732442i	$-0.261620\pi$
$164$	−4.43830	+	4.92924i	−0.346573	+	0.384909i
$165$	−0.544813	+	2.13332i	−0.0424136	+	0.166078i
$166$	−3.77741	+	11.6257i	−0.293184	+	0.902328i
$167$	1.86267	+	17.7221i	0.144137	+	1.37138i	0.792420	+	0.609976i	$0.208821\pi$
$167$	1.86267	+	17.7221i	0.144137	+	1.37138i	−0.648282	+	0.761400i	$0.724512\pi$
$168$	−2.85528	+	5.77058i	−0.220290	+	0.445210i
$169$	2.36975	+	7.29334i	0.182289	+	0.561026i
$170$	−0.182792	−	0.132806i	−0.0140195	−	0.0101857i
$171$	−3.67447	−	15.4865i	−0.280993	−	1.18428i
$172$	0.651281	−	0.723321i	0.0496597	−	0.0551527i
$173$	−0.708492	+	6.74085i	−0.0538657	+	0.512497i	0.934010	+	0.357248i	$0.116285\pi$
$173$	−0.708492	+	6.74085i	−0.0538657	+	0.512497i	−0.987875	+	0.155250i	$0.950382\pi$
$174$	3.22966	−	12.6463i	0.244840	−	0.958717i
$175$	3.97812	−	12.2434i	0.300718	−	0.925513i
$176$	0.353512	−	0.256841i	0.0266470	−	0.0193601i
$177$	−0.156746	+	3.85869i	−0.0117817	+	0.290037i
$178$	7.36039	+	1.56450i	0.551684	+	0.117264i
$179$	−16.6978	+	3.54924i	−1.24806	+	0.265282i	−0.784133	−	0.620593i	$-0.786892\pi$
$179$	−16.6978	+	3.54924i	−1.24806	+	0.265282i	−0.463923	+	0.885876i	$0.653558\pi$
$180$	6.62135	+	5.68567i	0.493526	+	0.423785i
$181$	−4.69356	+	8.12948i	−0.348869	+	0.604260i	−0.986049	−	0.166456i	$-0.946768\pi$
$181$	−4.69356	+	8.12948i	−0.348869	+	0.604260i	0.637179	+	0.770715i	$0.280101\pi$
$182$	11.3079	+	12.5587i	0.838195	+	0.930910i
$183$	−10.0959	−	15.1531i	−0.746309	−	1.12015i
$184$	4.25125	+	1.89278i	0.313407	+	0.139538i
$185$	−2.10509	−	3.64612i	−0.154769	−	0.268068i
$186$	−1.45161	+	9.53377i	−0.106437	+	0.699050i
$187$	0.0169686	−	0.0293905i	0.00124087	−	0.00214925i
$188$	3.34091	−	2.42731i	0.243661	−	0.177030i
$189$	2.34671	−	19.1719i	0.170698	−	1.39455i
$190$	4.76953	−	14.6791i	0.346018	−	1.06493i
$191$	7.45102	+	12.9055i	0.539137	+	0.933812i	0.998951	+	0.0457972i	$0.0145828\pi$
$191$	7.45102	+	12.9055i	0.539137	+	0.933812i	−0.459814	+	0.888015i	$0.652084\pi$
$192$	−0.291053	−	1.70742i	−0.0210049	−	0.123223i
$193$	4.40480	+	4.89203i	0.317065	+	0.352136i	0.880519	−	0.474011i	$-0.157194\pi$
$193$	4.40480	+	4.89203i	0.317065	+	0.352136i	−0.563454	+	0.826147i	$0.690528\pi$
$194$	−11.1919	+	12.4298i	−0.803530	+	0.892411i
$195$	20.2874	−	10.6393i	1.45281	−	0.761895i
$196$	6.22803	+	2.77290i	0.444859	+	0.198064i
$197$	−7.36247	−	8.17685i	−0.524554	−	0.582576i	0.421401	−	0.906874i	$-0.361539\pi$
$197$	−7.36247	−	8.17685i	−0.524554	−	0.582576i	−0.945955	+	0.324298i	$0.894872\pi$
$198$	−0.745368	+	1.07836i	−0.0529710	+	0.0766360i
$199$	−20.6469	+	9.19261i	−1.46362	+	0.651647i	−0.975273	−	0.221001i	$-0.929067\pi$
$199$	−20.6469	+	9.19261i	−1.46362	+	0.651647i	−0.488349	+	0.872648i	$0.662401\pi$
$200$	1.07020	+	3.29373i	0.0756744	+	0.232902i
$201$	−11.7340	+	23.7147i	−0.827653	+	1.67271i
$202$	−0.0212801	+	0.202467i	−0.00149727	+	0.0142455i
$203$	−27.3995	−	5.82394i	−1.92307	−	0.408760i
$204$	−0.0745873	−	0.111950i	−0.00522215	−	0.00783804i
$205$	15.6110	−	11.3421i	1.09032	−	0.792166i
$206$	11.8144	+	13.1213i	0.823150	+	0.914201i
$207$	−13.9147	−	1.13234i	−0.967141	−	0.0787032i
$208$	−4.44693	−	0.945225i	−0.308339	−	0.0655396i
$209$	2.26765	+	0.482003i	0.156856	+	0.0333409i
$210$	11.6153	−	14.6937i	0.801531	−	1.01396i
$211$	0.798318	−	1.38273i	0.0549585	−	0.0951909i	−0.837237	−	0.546840i	$-0.815831\pi$
$211$	0.798318	−	1.38273i	0.0549585	−	0.0951909i	0.892196	+	0.451649i	$0.149164\pi$
$212$	−1.87760			−0.128954
$213$	−12.0118	+	15.1953i	−0.823036	+	1.04117i
$214$	−8.87326	−	6.44680i	−0.606564	−	0.440694i
$215$	−2.29078	+	1.66435i	−0.156230	+	0.113508i
$216$	2.52085	+	4.54371i	0.171522	+	0.309160i
$217$	20.5702	+	2.28230i	1.39639	+	0.154933i
$218$	−3.66559	+	6.34898i	−0.248265	+	0.430007i
$219$	−5.49474	+	1.54180i	−0.371300	+	0.104185i
$220$	−1.16130	+	0.517044i	−0.0782949	+	0.0348591i
$221$	−0.345375	+	0.0734118i	−0.0232324	+	0.00493821i
$222$	−0.421215	−	2.47100i	−0.0282701	−	0.165843i
$223$	15.2387			1.02046			0.510230	−	0.860038i	$-0.329560\pi$
$223$	15.2387			1.02046			0.510230	+	0.860038i	$0.329560\pi$
$224$	−3.63595	+	0.772845i	−0.242937	+	0.0516379i
$225$	−6.30292	−	8.25949i	−0.420194	−	0.550633i
$226$	11.3608	+	2.41481i	0.755708	+	0.160631i
$227$	3.64778	+	1.62410i	0.242112	+	0.107795i	0.524206	−	0.851592i	$-0.324362\pi$
$227$	3.64778	+	1.62410i	0.242112	+	0.107795i	−0.282094	+	0.959387i	$0.591029\pi$
$228$	5.69867	−	7.20900i	0.377404	−	0.477427i
$229$	0.768698	+	7.31368i	0.0507970	+	0.483301i	0.990115	+	0.140255i	$0.0447922\pi$
$229$	0.768698	+	7.31368i	0.0507970	+	0.483301i	−0.939318	+	0.343047i	$0.888541\pi$
$230$	−10.9525	−	7.95745i	−0.722186	−	0.524699i
$231$	2.37731	+	1.50439i	0.156416	+	0.0989819i
$232$	6.88421	−	3.06505i	0.451971	−	0.201230i
$233$	−8.15434	−	5.92448i	−0.534209	−	0.388125i	0.287721	−	0.957714i	$-0.407102\pi$
$233$	−8.15434	−	5.92448i	−0.534209	−	0.388125i	−0.821930	+	0.569589i	$0.807102\pi$
$234$	13.5268	−	1.74427i	0.884278	−	0.114027i
$235$	−10.9750	+	4.88639i	−0.715931	+	0.318753i
$236$	−1.80383	+	1.31056i	−0.117419	+	0.0853101i
$237$	−14.0766	−	2.06012i	−0.914376	−	0.133819i
$238$	−0.233562	+	0.169692i	−0.0151396	+	0.0109995i
$239$	2.39417	+	7.36848i	0.154866	+	0.476628i	0.998147	−	0.0608444i	$-0.0193793\pi$
$239$	2.39417	+	7.36848i	0.154866	+	0.476628i	−0.843282	+	0.537472i	$0.819379\pi$
$240$	−0.204515	+	5.03467i	−0.0132014	+	0.324986i
$241$	4.71930	−	14.5245i	0.303997	−	0.935605i	−0.676053	−	0.736853i	$-0.736311\pi$
$241$	4.71930	−	14.5245i	0.303997	−	0.935605i	0.980050	−	0.198752i	$-0.0636889\pi$
$242$	5.40453	+	9.36092i	0.347416	+	0.601743i
$243$	−11.6515	−	10.3558i	−0.747441	−	0.664328i
$244$	3.24857	−	9.99807i	0.207968	−	0.640061i
$245$	−16.0452	−	11.6575i	−1.02509	−	0.744773i
$246$	11.0614	−	3.10377i	0.705248	−	0.197889i
$247$	−12.0601	−	20.8887i	−0.767366	−	1.32912i
$248$	−4.83784	+	2.75596i	−0.307203	+	0.175004i
$249$	16.2963	−	13.5169i	1.03274	−	0.856598i
$250$	0.467316	+	4.44621i	0.0295556	+	0.281203i
$251$	0.340047	−	3.23533i	0.0214636	−	0.204212i	−0.978535	−	0.206082i	$-0.933929\pi$
$251$	0.340047	−	3.23533i	0.0214636	−	0.204212i	0.999998	+	0.00186987i	$0.000595200\pi$
$252$	9.52371	−	5.80137i	0.599937	−	0.365452i
$253$	1.01672	−	1.76102i	0.0639209	−	0.110714i
$254$	15.3844			0.965302
$255$	0.144532	+	0.363677i	0.00905097	+	0.0227743i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−1.97302	−	6.07234i	−0.123074	−	0.378782i	0.870471	−	0.492219i	$-0.163814\pi$
$257$	−1.97302	−	6.07234i	−0.123074	−	0.378782i	−0.993545	+	0.113437i	$0.963814\pi$
$258$	−1.62316	+	0.455450i	−0.101053	+	0.0283551i
$259$	−5.26199	+	1.11847i	−0.326964	+	0.0694984i
$260$	12.0824	+	5.37945i	0.749321	+	0.333619i
$261$	−16.4399	+	15.5181i	−1.01761	+	0.960545i
$262$	−10.1021	+	11.2195i	−0.624109	+	0.693144i
$263$	23.5968	−	10.5060i	1.45504	−	0.647825i	0.481520	−	0.876435i	$-0.340085\pi$
$263$	23.5968	−	10.5060i	1.45504	−	0.647825i	0.973518	+	0.228610i	$0.0734181\pi$
$264$	−0.755289	+	0.0484961i	−0.0464849	+	0.00298473i
$265$	5.34290	+	1.13567i	0.328212	+	0.0697635i
$266$	−15.9550	−	11.5920i	−0.978262	−	0.710749i
$267$	−9.32373	−	9.10696i	−0.570603	−	0.557337i
$268$	−14.9422	+	3.17607i	−0.912742	+	0.194009i
$269$	2.38503	+	22.6920i	0.145418	+	1.38356i	0.787213	+	0.616681i	$0.211523\pi$
$269$	2.38503	+	22.6920i	0.145418	+	1.38356i	−0.641795	+	0.766876i	$0.721810\pi$
$270$	−4.42506	−	14.4543i	−0.269300	−	0.879659i
$271$	−3.18881	−	9.81416i	−0.193707	−	0.596168i	−0.999989	−	0.00463727i	$-0.998524\pi$
$271$	−3.18881	−	9.81416i	−0.193707	−	0.596168i	0.806283	−	0.591531i	$-0.201476\pi$
$272$	0.0240001	−	0.0738647i	0.00145522	−	0.00447870i
$273$	−4.91860	−	28.8543i	−0.297687	−	1.74634i
$274$	0.261321			0.0157870
$275$	1.48024	−	0.314635i	0.0892619	−	0.0189732i
$276$	−4.46911	−	6.70779i	−0.269009	−	0.403761i
$277$	3.13916	+	29.8671i	0.188614	+	1.79454i	0.523236	+	0.852188i	$0.324724\pi$
$277$	3.13916	+	29.8671i	0.188614	+	1.79454i	−0.334623	+	0.942352i	$0.608609\pi$
$278$	10.8314			0.649624
$279$	10.9547	−	12.6093i	0.655842	−	0.754898i
$280$	10.8139			0.646253
$281$	−2.03212	−	19.3343i	−0.121226	−	1.15339i	−0.870859	−	0.491534i	$-0.836436\pi$
$281$	−2.03212	−	19.3343i	−0.121226	−	1.15339i	0.749633	−	0.661854i	$-0.230230\pi$
$282$	−7.13796	+	0.458319i	−0.425060	+	0.0272925i
$283$	2.30673	−	0.490311i	0.137121	−	0.0291460i	−0.138840	−	0.990315i	$-0.544337\pi$
$283$	2.30673	−	0.490311i	0.137121	−	0.0291460i	0.275961	+	0.961169i	$0.411004\pi$
$284$	−11.1830			−0.663591
$285$	−20.5764	+	17.0670i	−1.21884	+	1.01096i
$286$	−0.613882	+	1.88933i	−0.0362996	+	0.111719i
$287$	−7.61907	−	23.4491i	−0.449740	−	1.38416i
$288$	−1.15541	+	2.76858i	−0.0680834	+	0.163140i
$289$	1.77635	+	16.9009i	0.104491	+	0.994169i
$290$	−21.4436	+	4.55797i	−1.25921	+	0.267653i
$291$	27.8930	−	7.82664i	1.63512	−	0.458806i
$292$	−2.66564	−	1.93670i	−0.155995	−	0.113337i
$293$	12.6953	+	2.69847i	0.741669	+	0.157647i	0.563225	−	0.826304i	$-0.309560\pi$
$293$	12.6953	+	2.69847i	0.741669	+	0.157647i	0.178444	+	0.983950i	$0.442894\pi$
$294$	−6.54719	−	9.82681i	−0.381840	−	0.573111i
$295$	5.92565	−	2.63827i	0.345005	−	0.153606i
$296$	0.968375	−	1.07549i	0.0562856	−	0.0625115i
$297$	2.08970	−	0.887954i	0.121257	−	0.0515243i
$298$	−19.5505	−	8.70446i	−1.13253	−	0.504236i
$299$	−20.6942	+	4.39868i	−1.19677	+	0.254382i
$300$	1.48428	−	5.81196i	0.0856947	−	0.335554i
$301$	1.11803	+	3.44094i	0.0644421	+	0.198333i
$302$	10.7449	−	11.9334i	0.618297	−	0.686688i
$303$	0.218670	−	0.276624i	0.0125622	−	0.0158916i
$304$	5.30548			0.304290
$305$	−15.2914	+	26.4855i	−0.875585	+	1.51656i
$306$	0.00547996	+	0.232933i	0.000313268	+	0.0133159i
$307$	2.91183	−	27.7042i	0.166187	−	1.58116i	−0.520278	−	0.853997i	$-0.674172\pi$
$307$	2.91183	−	27.7042i	0.166187	−	1.58116i	0.686464	−	0.727164i	$-0.259162\pi$
$308$	0.169783	+	1.61538i	0.00967429	+	0.0920447i
$309$	−5.13894	−	30.1469i	−0.292344	−	1.71500i
$310$	15.4334	−	4.91619i	0.876561	−	0.279221i
$311$	14.6571	+	25.3868i	0.831128	+	1.43956i	0.897145	+	0.441737i	$0.145638\pi$
$311$	14.6571	+	25.3868i	0.831128	+	1.43956i	−0.0660167	+	0.997819i	$0.521029\pi$
$312$	5.63313	+	5.50217i	0.318913	+	0.311499i
$313$	−7.13798	−	5.18605i	−0.403463	−	0.293133i	0.367487	−	0.930029i	$-0.380218\pi$
$313$	−7.13798	−	5.18605i	−0.403463	−	0.293133i	−0.770950	+	0.636896i	$0.780218\pi$
$314$	2.49658	−	7.68369i	0.140890	−	0.433616i
$315$	−30.6095	+	10.7479i	−1.72465	+	0.605576i
$316$	−4.10686	−	7.11330i	−0.231029	−	0.400154i
$317$	7.38589	−	22.7314i	0.414833	−	1.27672i	−0.497567	−	0.867425i	$-0.665773\pi$
$317$	7.38589	−	22.7314i	0.414833	−	1.27672i	0.912400	−	0.409299i	$-0.134227\pi$
$318$	2.74809	+	1.73903i	0.154105	+	0.0975197i
$319$	−1.01754	−	3.13168i	−0.0569715	−	0.175340i
$320$	−2.35356	+	1.70996i	−0.131568	+	0.0955899i
$321$	7.01604	+	17.6540i	0.391597	+	0.985350i
$322$	−13.9945	+	10.1676i	−0.779884	+	0.566619i
$323$	0.376431	−	0.167598i	0.0209452	−	0.00932540i
$324$	0.518802	−	8.98503i	0.0288224	−	0.499169i
$325$	−12.7378	−	9.25458i	−0.706568	−	0.513352i
$326$	−11.3416	+	5.04960i	−0.628153	+	0.279672i
$327$	11.2454	−	5.89741i	0.621871	−	0.326128i
$328$	5.36616	+	3.89875i	0.296297	+	0.215272i
$329$	1.60456	+	15.2663i	0.0884621	+	0.841661i
$330$	2.17858	+	0.318836i	0.119927	+	0.0175513i
$331$	−4.23531	−	1.88568i	−0.232794	−	0.103647i	0.287025	−	0.957923i	$-0.407334\pi$
$331$	−4.23531	−	1.88568i	−0.232794	−	0.103647i	−0.519819	+	0.854277i	$0.674000\pi$
$332$	11.9568	+	2.54151i	0.656217	+	0.139483i
$333$	−1.67213	+	4.00672i	−0.0916322	+	0.219567i
$334$	17.4303	−	3.70492i	0.953744	−	0.202724i
$335$	44.4405			2.42805
$336$	6.03743	+	2.23645i	0.329369	+	0.122008i
$337$	10.4937	−	2.23050i	0.571628	−	0.121503i	0.0869760	−	0.996210i	$-0.472280\pi$
$337$	10.4937	−	2.23050i	0.571628	−	0.121503i	0.484652	+	0.874707i	$0.338946\pi$
$338$	7.00568	−	3.11913i	0.381059	−	0.169658i
$339$	−14.3912	−	14.0566i	−0.781624	−	0.763452i
$340$	−0.112971	+	0.195672i	−0.00612674	+	0.0106118i
$341$	0.976692	+	2.22826i	0.0528909	+	0.120667i
$342$	−15.0176	+	5.27312i	−0.812058	+	0.285137i
$343$	0.549054	−	0.398911i	0.0296461	−	0.0215392i
$344$	−0.787435	−	0.572105i	−0.0424557	−	0.0308459i
$345$	8.66007	+	21.7908i	0.466243	+	1.17317i
$346$	6.77798			0.364387
$347$	15.2321	−	26.3827i	0.817699	−	1.41630i	−0.0896741	−	0.995971i	$-0.528583\pi$
$347$	15.2321	−	26.3827i	0.817699	−	1.41630i	0.907373	−	0.420326i	$-0.138084\pi$
$348$	−12.9147	−	1.89007i	−0.692299	−	0.101318i
$349$	8.35820	+	1.77659i	0.447404	+	0.0950987i	0.426104	−	0.904674i	$-0.359886\pi$
$349$	8.35820	+	1.77659i	0.447404	+	0.0950987i	0.0213007	+	0.999773i	$0.493219\pi$
$350$	−12.5921	−	2.67654i	−0.673079	−	0.143067i
$351$	−21.4136	−	9.97554i	−1.14297	−	0.532455i
$352$	−0.292386	−	0.324728i	−0.0155842	−	0.0173081i
$353$	19.4508	−	14.1318i	1.03526	−	0.752160i	0.0659045	−	0.997826i	$-0.479007\pi$
$353$	19.4508	−	14.1318i	1.03526	−	0.752160i	0.969354	+	0.245666i	$0.0790067\pi$
$354$	3.85394	−	0.247456i	0.204835	−	0.0131522i
$355$	31.8224	+	6.76405i	1.68896	+	0.358999i
$356$	0.786558	−	7.48360i	0.0416875	−	0.396630i
$357$	0.499012	−	0.0320409i	0.0264105	−	0.00169578i
$358$	5.27519	+	16.2354i	0.278803	+	0.858066i
$359$	2.12416	−	0.945739i	0.112109	−	0.0499142i	−0.349916	−	0.936781i	$-0.613790\pi$
$359$	2.12416	−	0.945739i	0.112109	−	0.0499142i	0.462025	+	0.886867i	$0.347123\pi$
$360$	4.96241	−	7.17939i	0.261542	−	0.378387i
$361$	6.12131	+	6.79840i	0.322174	+	0.357811i
$362$	8.57556	+	3.81808i	0.450721	+	0.200674i
$363$	0.759881	−	18.7064i	0.0398834	−	0.981832i
$364$	11.3079	−	12.5587i	0.592693	−	0.658253i
$365$	6.41391	+	7.12337i	0.335719	+	0.372854i
$366$	−14.0148	+	11.6245i	−0.732565	+	0.607623i
$367$	−11.4763	−	19.8776i	−0.599059	−	1.03760i	−0.992960	−	0.118448i	$-0.962208\pi$
$367$	−11.4763	−	19.8776i	−0.599059	−	1.03760i	0.393901	−	0.919153i	$-0.371125\pi$
$368$	1.43803	−	4.42582i	0.0749627	−	0.230712i
$369$	−19.0643	−	5.70227i	−0.992447	−	0.296848i
$370$	−3.40611	+	2.47468i	−0.177075	+	0.128653i
$371$	3.48970	−	6.04433i	0.181176	−	0.313806i
$372$	9.63328	+	0.447106i	0.499462	+	0.0231814i
$373$	0.480213	+	0.831754i	0.0248645	+	0.0430666i	0.878190	−	0.478312i	$-0.158751\pi$
$373$	0.480213	+	0.831754i	0.0248645	+	0.0430666i	−0.853325	+	0.521379i	$0.825418\pi$
$374$	−0.0310032	−	0.0138035i	−0.00160314	−	0.000713763i
$375$	3.43408	−	6.94036i	0.177335	−	0.358399i
$376$	−2.76324	−	3.06888i	−0.142503	−	0.158266i
$377$	−17.1297	+	29.6696i	−0.882226	+	1.52806i
$378$	−19.3122	−	0.329838i	−0.993313	−	0.0169650i
$379$	7.45481	−	1.58457i	0.382928	−	0.0813939i	−0.0124257	−	0.999923i	$-0.503955\pi$
$379$	7.45481	−	1.58457i	0.382928	−	0.0813939i	0.395354	+	0.918529i	$0.370622\pi$
$380$	−15.0972	−	3.20902i	−0.774472	−	0.164619i
$381$	−22.5168	−	14.2489i	−1.15357	−	0.729994i
$382$	12.0560	−	8.75920i	0.616839	−	0.448160i
$383$	−2.42227	+	7.45500i	−0.123772	+	0.380932i	−0.993675	−	0.112290i	$-0.964181\pi$
$383$	−2.42227	+	7.45500i	−0.123772	+	0.380932i	0.869903	+	0.493223i	$0.164181\pi$
$384$	−1.66764	+	0.467932i	−0.0851016	+	0.0238791i
$385$	0.493927	−	4.69940i	0.0251728	−	0.239504i
$386$	4.40480	−	4.89203i	0.224199	−	0.248998i
$387$	2.79751	+	0.836756i	0.142206	+	0.0425347i
$388$	13.5316	+	9.83130i	0.686964	+	0.499109i
$389$	4.69017	+	14.4349i	0.237801	+	0.731876i	0.996737	+	0.0807117i	$0.0257193\pi$
$389$	4.69017	+	14.4349i	0.237801	+	0.731876i	−0.758936	+	0.651165i	$0.774281\pi$
$390$	−12.7016	−	19.0641i	−0.643171	−	0.965349i
$391$	−0.0377791	−	0.359444i	−0.00191057	−	0.0181779i
$392$	2.10670	−	6.48376i	0.106404	−	0.327479i
$393$	25.1770	−	7.06453i	1.27001	−	0.356359i
$394$	−7.36247	+	8.17685i	−0.370916	+	0.411944i
$395$	7.38398	+	22.7256i	0.371529	+	1.14345i
$396$	1.15037	+	0.628565i	0.0578082	+	0.0315866i
$397$	11.3187	+	19.6046i	0.568071	+	0.983928i	0.996757	+	0.0804740i	$0.0256434\pi$
$397$	11.3187	+	19.6046i	0.568071	+	0.983928i	−0.428686	+	0.903454i	$0.641023\pi$
$398$	11.3004	+	19.5729i	0.566440	+	0.981103i
$399$	12.6155	+	31.7436i	0.631566	+	1.58917i
$400$	3.16382	−	1.40862i	0.158191	−	0.0704312i
$401$	−18.7011	−	8.32626i	−0.933888	−	0.415794i	−0.117353	−	0.993090i	$-0.537441\pi$
$401$	−18.7011	−	8.32626i	−0.933888	−	0.415794i	−0.816535	+	0.577297i	$0.804108\pi$
$402$	24.8113	+	9.19087i	1.23748	+	0.458399i
$403$	10.4291	−	23.0643i	0.519509	−	1.14892i
$404$	0.203582			0.0101286
$405$	−6.91089	+	25.2539i	−0.343405	+	1.25488i
$406$	−2.92801	+	27.8581i	−0.145315	+	1.38258i
$407$	−0.423145	−	0.469951i	−0.0209745	−	0.0232946i
$408$	−0.103540	+	0.0858806i	−0.00512599	+	0.00425172i
$409$	−2.87124	+	4.97313i	−0.141974	+	0.245905i	−0.928240	−	0.371983i	$-0.878678\pi$
$409$	−2.87124	+	4.97313i	−0.141974	+	0.245905i	0.786266	+	0.617888i	$0.212011\pi$
$410$	−12.9118	−	14.3400i	−0.637666	−	0.708200i
$411$	−0.382473	−	0.242034i	−0.0188660	−	0.0119386i
$412$	11.8144	−	13.1213i	0.582055	−	0.646438i
$413$	−0.866335	−	8.24262i	−0.0426295	−	0.405593i
$414$	0.328348	+	13.9569i	0.0161374	+	0.685943i
$415$	−32.4871	−	14.4642i	−1.59473	−	0.710019i
$416$	−0.475216	+	4.52138i	−0.0232994	+	0.221679i
$417$	−15.8530	−	10.0320i	−0.776323	−	0.491267i
$418$	0.242329	−	2.30561i	0.0118527	−	0.112771i
$419$	−3.94830	+	37.5655i	−0.192887	+	1.83520i	0.287076	+	0.957908i	$0.407317\pi$
$419$	−3.94830	+	37.5655i	−0.192887	+	1.83520i	−0.479963	+	0.877289i	$0.659350\pi$
$420$	−15.8273	−	10.0158i	−0.772296	−	0.488719i
$421$	−2.33198	+	22.1873i	−0.113654	+	1.08134i	0.777887	+	0.628404i	$0.216292\pi$
$421$	−2.33198	+	22.1873i	−0.113654	+	1.08134i	−0.891541	+	0.452940i	$0.850375\pi$
$422$	−1.45860	−	0.649410i	−0.0710035	−	0.0316128i
$423$	10.8717	+	5.94033i	0.528601	+	0.288829i
$424$	0.196263	+	1.86732i	0.00953138	+	0.0906850i
$425$	0.179980	−	0.199888i	0.00873029	−	0.00969597i
$426$	16.3677	+	10.3577i	0.793015	+	0.501830i
$427$	26.1478	+	29.0400i	1.26538	+	1.40535i
$428$	−5.48398	+	9.49853i	−0.265078	+	0.459129i
$429$	2.64838	−	2.19668i	0.127865	−	0.106057i
$430$	1.89468	+	2.10426i	0.0913697	+	0.101476i
$431$	0.659707	−	6.27669i	0.0317769	−	0.302337i	−0.967077	−	0.254483i	$-0.918095\pi$
$431$	0.659707	−	6.27669i	0.0317769	−	0.302337i	0.998854	−	0.0478549i	$-0.0152385\pi$
$432$	4.25532	−	2.98199i	0.204734	−	0.143471i
$433$	39.1849			1.88311			0.941553	−	0.336864i	$-0.109366\pi$
$433$	39.1849			1.88311			0.941553	+	0.336864i	$0.109366\pi$
$434$	0.119630	−	20.6960i	0.00574244	−	0.993441i
$435$	35.6066	+	13.1898i	1.70721	+	0.632402i
$436$	6.69736	+	2.98186i	0.320745	+	0.142805i
$437$	22.5550	−	10.0421i	1.07895	−	0.480380i
$438$	2.10771	+	5.30348i	0.100710	+	0.253410i
$439$	15.3581	+	26.6011i	0.733004	+	1.26960i	0.955594	+	0.294688i	$0.0952156\pi$
$439$	15.3581	+	26.6011i	0.733004	+	1.26960i	−0.222590	+	0.974912i	$0.571451\pi$
$440$	0.635601	+	1.10089i	0.0303011	+	0.0524830i
$441$	0.481025	+	20.4466i	0.0229059	+	0.973648i
$442$	0.109111	+	0.335810i	0.00518989	+	0.0159728i
$443$	−6.32583	+	7.02554i	−0.300549	+	0.333794i	−0.874436	−	0.485141i	$-0.838768\pi$
$443$	−6.32583	+	7.02554i	−0.300549	+	0.333794i	0.573887	+	0.818935i	$0.305435\pi$
$444$	−2.41344	+	0.677198i	−0.114537	+	0.0321384i
$445$	−6.76467	+	20.8195i	−0.320676	+	0.986940i
$446$	−1.59288	−	15.1552i	−0.0754251	−	0.717622i
$447$	20.5524	+	30.8476i	0.972096	+	1.45904i
$448$	1.14867	+	3.53525i	0.0542696	+	0.167025i
$449$	17.6224	+	12.8035i	0.831655	+	0.604232i	0.920027	−	0.391855i	$-0.128167\pi$
$449$	17.6224	+	12.8035i	0.831655	+	0.604232i	−0.0883724	+	0.996088i	$0.528167\pi$
$450$	−7.55541	+	7.13174i	−0.356165	+	0.336193i
$451$	1.93938	−	2.15390i	0.0913219	−	0.101423i
$452$	1.21406	−	11.5510i	0.0571044	−	0.543312i
$453$	−26.7789	+	7.51403i	−1.25818	+	0.353040i
$454$	1.23390	−	3.79756i	0.0579099	−	0.178228i
$455$	−39.7737	+	28.8973i	−1.86462	+	1.35472i
$456$	−7.76518	−	4.91391i	−0.363638	−	0.230115i
$457$	−32.8761	−	6.98803i	−1.53788	−	0.326886i	−0.640435	−	0.768013i	$-0.721246\pi$
$457$	−32.8761	−	6.98803i	−1.53788	−	0.326886i	−0.897445	+	0.441126i	$0.854579\pi$
$458$	7.19326	−	1.52897i	0.336119	−	0.0714443i
$459$	0.207721	−	0.346000i	0.00969558	−	0.0161499i
$460$	−6.76901	+	11.7243i	−0.315607	+	0.546647i
$461$	−2.64460	−	2.93713i	−0.123171	−	0.136796i	0.678405	−	0.734688i	$-0.262672\pi$
$461$	−2.64460	−	2.93713i	−0.123171	−	0.136796i	−0.801576	+	0.597893i	$0.796005\pi$
$462$	1.24766	−	2.52154i	0.0580462	−	0.117313i
$463$	−30.1235	−	13.4118i	−1.39996	−	0.623301i	−0.438620	−	0.898673i	$-0.644532\pi$
$463$	−30.1235	−	13.4118i	−1.39996	−	0.623301i	−0.961338	+	0.275372i	$0.911199\pi$
$464$	−3.76786	−	6.52612i	−0.174918	−	0.302967i
$465$	−27.1420	−	7.09896i	−1.25868	−	0.329207i
$466$	−5.03966	+	8.72895i	−0.233458	+	0.404361i
$467$	4.66980	−	3.39280i	0.216092	−	0.157000i	−0.474474	−	0.880270i	$-0.657362\pi$
$467$	4.66980	−	3.39280i	0.216092	−	0.157000i	0.690566	+	0.723269i	$0.257362\pi$
$468$	−3.14866	−	13.2704i	−0.145547	−	0.613425i
$469$	17.5472	−	54.0046i	0.810253	−	2.49370i
$470$	6.00683	+	10.4041i	0.277074	+	0.479907i
$471$	−10.7706	+	8.93364i	−0.496284	+	0.411640i
$472$	1.49193	+	1.65696i	0.0686717	+	0.0762676i
$473$	−0.284587	+	0.316065i	−0.0130853	+	0.0145327i
$474$	−0.577428	+	14.2149i	−0.0265222	+	0.652911i
$475$	16.7856	+	7.47343i	0.770176	+	0.342905i
$476$	0.193177	+	0.214545i	0.00885424	+	0.00983363i
$477$	−2.41147	−	5.09052i	−0.110413	−	0.233079i
$478$	7.07786	−	3.15127i	0.323734	−	0.144136i
$479$	9.70813	+	29.8786i	0.443576	+	1.36519i	0.884038	+	0.467415i	$0.154815\pi$
$479$	9.70813	+	29.8786i	0.443576	+	1.36519i	−0.440462	+	0.897771i	$0.645185\pi$
$480$	5.02846	−	0.322871i	0.229517	−	0.0147370i
$481$	−0.687739	+	6.54340i	−0.0313582	+	0.298353i
$482$	−14.9382	−	3.17522i	−0.680418	−	0.144627i
$483$	29.8998	−	1.91982i	1.36049	−	0.0873550i
$484$	8.74471	−	6.35341i	0.397487	−	0.288791i
$485$	−32.5590	−	36.1605i	−1.47843	−	1.64196i
$486$	−9.08121	+	12.6701i	−0.411932	+	0.574728i
$487$	−34.0755	−	7.24298i	−1.54411	−	0.328211i	−0.644396	−	0.764692i	$-0.722891\pi$
$487$	−34.0755	−	7.24298i	−1.54411	−	0.328211i	−0.899714	+	0.436481i	$0.856225\pi$
$488$	−10.2829	−	2.18569i	−0.465484	−	0.0989416i
$489$	21.2766	+	3.11385i	0.962163	+	0.140813i
$490$	−9.91650	+	17.1759i	−0.447982	+	0.775927i
$491$	−14.4244			−0.650966			−0.325483	−	0.945548i	$-0.605527\pi$
$491$	−14.4244			−0.650966			−0.325483	+	0.945548i	$0.605527\pi$
$492$	−4.24300	−	10.6764i	−0.191289	−	0.481328i
$493$	−0.473492	−	0.344012i	−0.0213250	−	0.0154935i
$494$	−19.5137	+	14.1775i	−0.877961	+	0.637876i
$495$	−2.89329	−	2.48444i	−0.130044	−	0.111667i
$496$	3.24656	+	4.52326i	0.145775	+	0.203100i
$497$	20.7847	−	36.0001i	0.932321	−	1.61483i
$498$	−15.1463	−	14.7941i	−0.678721	−	0.662941i
$499$	28.9011	−	12.8676i	1.29379	−	0.576032i	0.359699	−	0.933068i	$-0.382879\pi$
$499$	28.9011	−	12.8676i	1.29379	−	0.576032i	0.934091	+	0.357036i	$0.116213\pi$
$500$	4.37301	−	0.929512i	0.195567	−	0.0415690i
$501$	−28.9427	−	10.7213i	−1.29306	−	0.478990i
$502$	−3.25315			−0.145195
$503$	−28.7307	+	6.10689i	−1.28104	+	0.272293i	−0.797654	−	0.603116i	$-0.793926\pi$
$503$	−28.7307	+	6.10689i	−1.28104	+	0.272293i	−0.483384	+	0.875408i	$0.660592\pi$
$504$	−6.76508	−	8.86513i	−0.301341	−	0.394884i
$505$	−0.579312	−	0.123137i	−0.0257790	−	0.00547951i
$506$	−1.85765	−	0.827078i	−0.0825825	−	0.0367681i
$507$	−13.1425	−	1.92342i	−0.583680	−	0.0854219i
$508$	−1.60811	−	15.3001i	−0.0713481	−	0.678832i
$509$	−20.8513	−	15.1494i	−0.924219	−	0.671484i	0.0203515	−	0.999793i	$-0.493521\pi$
$509$	−20.8513	−	15.1494i	−0.924219	−	0.671484i	−0.944571	+	0.328308i	$0.893521\pi$
$510$	0.346577	−	0.181755i	0.0153467	−	0.00804825i
$511$	11.1889	−	4.98162i	0.494968	−	0.220374i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	26.8639	+	6.19138i	1.18607	+	0.273356i
$514$	−5.83284	+	2.59695i	−0.257275	+	0.114546i
$515$	−41.5554	+	30.1918i	−1.83115	+	1.33041i
$516$	0.622621	+	1.56666i	0.0274094	+	0.0689683i
$517$	−1.45986	+	1.06065i	−0.0642045	+	0.0466473i
$518$	1.66237	+	5.11626i	0.0730405	+	0.224795i
$519$	−9.92035	−	6.27772i	−0.435455	−	0.275562i
$520$	4.08702	−	12.5786i	0.179228	−	0.551606i
$521$	14.7398	+	25.5301i	0.645762	+	1.11849i	0.984125	+	0.177477i	$0.0567935\pi$
$521$	14.7398	+	25.5301i	0.645762	+	1.11849i	−0.338363	+	0.941016i	$0.609873\pi$
$522$	17.1515	+	14.7278i	0.750701	+	0.644619i
$523$	−0.700069	+	2.15459i	−0.0306119	+	0.0942137i	−0.965195	−	0.261531i	$-0.915773\pi$
$523$	−0.700069	+	2.15459i	−0.0306119	+	0.0942137i	0.934583	+	0.355745i	$0.115773\pi$
$524$	12.2140	+	8.87399i	0.533571	+	0.387662i
$525$	15.9510	+	15.5802i	0.696161	+	0.679975i
$526$	−12.9149	−	22.3693i	−0.563118	−	0.975349i
$527$	0.373235	+	0.218374i	0.0162584	+	0.00951251i
$528$	0.127180	+	0.746083i	0.00553479	+	0.0324691i
$529$	0.140509	+	1.33685i	0.00610907	+	0.0581239i
$530$	0.570962	−	5.43234i	0.0248010	−	0.235966i
$531$	−5.86987	−	3.20731i	−0.254731	−	0.139186i
$532$	−9.86072	+	17.0793i	−0.427516	+	0.740480i
$533$	−30.1552			−1.30617
$534$	−8.08248	+	10.2246i	−0.349763	+	0.442461i
$535$	21.3503	−	23.7120i	0.923056	−	1.02516i
$536$	4.72056	+	14.5284i	0.203897	+	0.627531i
$537$	7.31625	−	28.6482i	0.315720	−	1.23626i
$538$	22.3184	−	4.74393i	0.962215	−	0.204525i
$539$	−2.72143	−	1.21166i	−0.117220	−	0.0521898i
$540$	−13.9126	+	5.91170i	−0.598701	+	0.254399i
$541$	−7.95316	+	8.83288i	−0.341933	+	0.379755i	−0.889445	−	0.457043i	$-0.848909\pi$
$541$	−7.95316	+	8.83288i	−0.341933	+	0.379755i	0.547512	+	0.836798i	$0.315575\pi$
$542$	−9.42708	+	4.19720i	−0.404928	+	0.180285i
$543$	−9.01502	−	13.5308i	−0.386871	−	0.580663i
$544$	−0.0759687	−	0.0161476i	−0.00325713	−	0.000692325i
$545$	−17.2544	−	12.5360i	−0.739096	−	0.536985i
$546$	−28.1821	+	7.90775i	−1.20608	+	0.338421i
$547$	−28.4506	+	6.04736i	−1.21646	+	0.258566i	−0.771058	−	0.636765i	$-0.780272\pi$
$547$	−28.4506	+	6.04736i	−1.21646	+	0.258566i	−0.445401	+	0.895331i	$0.646939\pi$
$548$	−0.0273155	−	0.259889i	−0.00116686	−	0.0111019i
$549$	31.2788	−	4.03337i	1.33495	−	0.172140i
$550$	−0.467639	−	1.43924i	−0.0199402	−	0.0613696i
$551$	12.3547	−	38.0238i	0.526327	−	1.61987i
$552$	−6.20389	+	5.14579i	−0.264055	+	0.219019i
$553$	30.5319			1.29835
$554$	29.3753	−	6.24392i	1.24804	−	0.265279i
$555$	7.27726	−	0.467263i	0.308902	−	0.0198342i
$556$	−1.13219	−	10.7721i	−0.0480155	−	0.456837i
$557$	−12.9080			−0.546930			−0.273465	−	0.961882i	$-0.588170\pi$
$557$	−12.9080			−0.546930			−0.273465	+	0.961882i	$0.588170\pi$
$558$	−13.6853	−	9.57667i	−0.579345	−	0.405413i
$559$	4.42500			0.187158
$560$	−1.13036	−	10.7546i	−0.0477664	−	0.454467i
$561$	0.0325920	+	0.0489180i	0.00137604	+	0.00206532i
$562$	−19.0160	+	4.04197i	−0.802141	+	0.170500i
$563$	34.1066			1.43742			0.718712	−	0.695308i	$-0.244732\pi$
$563$	34.1066			1.43742			0.718712	+	0.695308i	$0.244732\pi$
$564$	1.20193	+	7.05095i	0.0506103	+	0.296899i
$565$	−10.4413	+	32.1350i	−0.439269	+	1.35193i
$566$	−0.728744	−	2.24284i	−0.0306314	−	0.0942738i
$567$	27.9601	+	18.3696i	1.17422	+	0.771451i
$568$	1.16895	+	11.1218i	0.0490479	+	0.466660i
$569$	−25.5655	+	5.43412i	−1.07176	+	0.227810i	−0.709815	−	0.704388i	$-0.751221\pi$
$569$	−25.5655	+	5.43412i	−1.07176	+	0.227810i	−0.361948	+	0.932198i	$0.617888\pi$
$570$	19.1244	+	18.6797i	0.801031	+	0.782408i
$571$	−7.00158	−	5.08694i	−0.293007	−	0.212882i	0.431564	−	0.902082i	$-0.357962\pi$
$571$	−7.00158	−	5.08694i	−0.293007	−	0.212882i	−0.724571	+	0.689200i	$0.757962\pi$
$572$	1.94315	+	0.413030i	0.0812473	+	0.0172696i
$573$	−25.7580	+	1.65389i	−1.07606	+	0.0690922i
$574$	−22.5242	+	10.0284i	−0.940143	+	0.418579i
$575$	10.7840	−	11.9768i	0.449724	−	0.499469i
$576$	2.87418	+	0.859690i	0.119758	+	0.0358204i
$577$	−2.65142	−	1.18049i	−0.110380	−	0.0491444i	0.350804	−	0.936449i	$-0.385908\pi$
$577$	−2.65142	−	1.18049i	−0.110380	−	0.0491444i	−0.461184	+	0.887305i	$0.652575\pi$
$578$	16.6226	−	3.53324i	0.691409	−	0.146964i
$579$	−10.9779	+	3.08034i	−0.456226	+	0.128015i
$580$	6.77446	+	20.8496i	0.281294	+	0.865735i
$581$	−30.4044	+	33.7675i	−1.26139	+	1.40091i
$582$	−10.6994	−	26.9221i	−0.443504	−	1.11596i
$583$	0.820447			0.0339794
$584$	−1.64746	+	2.85348i	−0.0681722	+	0.118078i
$585$	0.933193	+	39.6667i	0.0385828	+	1.64001i
$586$	1.35667	−	12.9078i	0.0560435	−	0.533218i
$587$	−2.68188	−	25.5164i	−0.110693	−	1.05317i	−0.899017	−	0.437914i	$-0.855718\pi$
$587$	−2.68188	−	25.5164i	−0.110693	−	1.05317i	0.788324	−	0.615260i	$-0.210949\pi$
$588$	−9.08861	+	7.53850i	−0.374808	+	0.310883i
$589$	−6.30856	+	28.8582i	−0.259940	+	1.18908i
$590$	−3.24322	−	5.61741i	−0.133521	−	0.231265i
$591$	18.3491	−	5.14868i	0.754783	−	0.211788i
$592$	−1.17082	−	0.850651i	−0.0481204	−	0.0349615i
$593$	−9.00629	+	27.7185i	−0.369844	+	1.13826i	0.577048	+	0.816710i	$0.304205\pi$
$593$	−9.00629	+	27.7185i	−0.369844	+	1.13826i	−0.946892	+	0.321552i	$0.895795\pi$
$594$	−1.10152	−	1.98544i	−0.0451960	−	0.0814636i
$595$	−0.419935	−	0.727349i	−0.0172157	−	0.0298184i
$596$	−6.61319	+	20.3533i	−0.270887	+	0.833704i
$597$	1.58885	−	39.1136i	0.0650274	−	1.60081i
$598$	6.53771	+	20.1210i	0.267347	+	0.822809i
$599$	18.7878	−	13.6501i	0.767649	−	0.557730i	−0.133598	−	0.991036i	$-0.542653\pi$
$599$	18.7878	−	13.6501i	0.767649	−	0.557730i	0.901247	+	0.433306i	$0.142653\pi$
$600$	−5.93527	−	0.868630i	−0.242306	−	0.0354617i
$601$	21.5418	−	15.6510i	0.878707	−	0.638418i	−0.0542021	−	0.998530i	$-0.517262\pi$
$601$	21.5418	−	15.6510i	0.878707	−	0.638418i	0.932909	+	0.360112i	$0.117262\pi$
$602$	3.30522	−	1.47158i	0.134711	−	0.0599772i
$603$	−27.8017	−	36.4320i	−1.13217	−	1.48362i
$604$	−12.9911	−	9.43861i	−0.528602	−	0.384052i
$605$	−28.7267	+	12.7900i	−1.16791	+	0.519986i
$606$	−0.297966	−	0.188557i	−0.0121040	−	0.00765959i
$607$	20.7602	+	15.0832i	0.842630	+	0.612206i	0.923104	−	0.384550i	$-0.125644\pi$
$607$	20.7602	+	15.0832i	0.842630	+	0.612206i	−0.0804743	+	0.996757i	$0.525644\pi$
$608$	−0.554574	−	5.27642i	−0.0224909	−	0.213987i
$609$	30.0875	−	38.0617i	1.21921	−	1.54234i
$610$	27.9388	+	12.4392i	1.13121	+	0.503647i
$611$	18.3640	+	3.90339i	0.742929	+	0.157914i
$612$	0.231084	−	0.0297981i	0.00934103	−	0.00120452i
$613$	39.2024	−	8.33272i	1.58337	−	0.336555i	0.669578	−	0.742742i	$-0.266475\pi$
$613$	39.2024	−	8.33272i	1.58337	−	0.336555i	0.913790	+	0.406186i	$0.133142\pi$
$614$	−27.8568			−1.12421
$615$	5.61624	+	32.9469i	0.226469	+	1.32855i
$616$	1.58878	−	0.337706i	0.0640138	−	0.0136066i
$617$	42.7191	−	19.0198i	1.71981	−	0.765707i	0.722578	−	0.691289i	$-0.242957\pi$
$617$	42.7191	−	19.0198i	1.71981	−	0.765707i	0.997227	−	0.0744173i	$-0.0237097\pi$
$618$	−29.4446	+	8.26200i	−1.18443	+	0.332346i
$619$	−6.23887	+	10.8060i	−0.250761	+	0.434331i	−0.963736	−	0.266859i	$-0.914014\pi$
$619$	−6.23887	+	10.8060i	−0.250761	+	0.434331i	0.712974	+	0.701190i	$0.247348\pi$
$620$	−6.50249	−	14.8350i	−0.261146	−	0.595789i
$621$	12.4462	−	20.7316i	0.499449	−	0.831930i
$622$	23.7157	−	17.2305i	0.950912	−	0.690878i
$623$	22.6291	+	16.4410i	0.906616	+	0.658695i
$624$	4.88320	−	6.17741i	0.195485	−	0.247294i
$625$	−30.3222			−1.21289
$626$	−4.41152	+	7.64097i	−0.176320	+	0.305395i
$627$	−2.49012	+	3.15008i	−0.0994457	+	0.125802i
$628$	−7.90257	−	1.67974i	−0.315347	−	0.0670290i
$629$	−0.109943	−	0.0233691i	−0.00438371	−	0.000931787i
$630$	13.8886	+	29.3184i	0.553335	+	1.16807i
$631$	−13.0367	−	14.4787i	−0.518982	−	0.576388i	0.425497	−	0.904960i	$-0.360099\pi$
$631$	−13.0367	−	14.4787i	−0.518982	−	0.576388i	−0.944479	+	0.328572i	$0.893433\pi$
$632$	−6.64504	+	4.82791i	−0.264326	+	0.192044i
$633$	1.53335	+	2.30143i	0.0609451	+	0.0914737i
$634$	−23.3789	−	4.96935i	−0.928496	−	0.197358i
$635$	−4.67824	+	44.5105i	−0.185650	+	1.76635i
$636$	1.44225	−	2.91481i	0.0571888	−	0.115580i
$637$	9.57765	+	29.4770i	0.379480	+	1.16792i
$638$	−3.00816	+	1.33932i	−0.119094	+	0.0530241i
$639$	−14.3627	−	30.3192i	−0.568180	−	1.19941i
$640$	1.94661	+	2.16193i	0.0769465	+	0.0854578i
$641$	35.0522	+	15.6063i	1.38448	+	0.616410i	0.957654	−	0.287923i	$-0.0929647\pi$
$641$	35.0522	+	15.6063i	1.38448	+	0.616410i	0.426827	+	0.904333i	$0.359631\pi$
$642$	16.8239	−	8.82295i	0.663987	−	0.348214i
$643$	−30.9660	+	34.3912i	−1.22118	+	1.35626i	−0.306604	+	0.951837i	$0.599193\pi$
$643$	−30.9660	+	34.3912i	−1.22118	+	1.35626i	−0.914574	+	0.404419i	$0.867474\pi$
$644$	11.5747	+	12.8551i	0.456109	+	0.506560i
$645$	−0.824133	−	4.83466i	−0.0324502	−	0.190365i
$646$	−0.206028	−	0.356850i	−0.00810605	−	0.0140401i
$647$	−0.994752	+	3.06153i	−0.0391078	+	0.120361i	−0.968704	−	0.248217i	$-0.920155\pi$
$647$	−0.994752	+	3.06153i	−0.0391078	+	0.120361i	0.929597	+	0.368578i	$0.120155\pi$
$648$	−8.99004	+	0.423232i	−0.353162	+	0.0166261i
$649$	0.788209	−	0.572667i	0.0309399	−	0.0224792i
$650$	−7.87242	+	13.6354i	−0.308782	+	0.534826i
$651$	−19.3436	+	30.1802i	−0.758137	+	1.18286i
$652$	6.20746	+	10.7516i	0.243103	+	0.421067i
$653$	−2.96871	−	1.32176i	−0.116175	−	0.0517243i	0.347826	−	0.937559i	$-0.386920\pi$
$653$	−2.96871	−	1.32176i	−0.116175	−	0.0517243i	−0.464001	+	0.885835i	$0.653587\pi$
$654$	−7.04057	−	10.5673i	−0.275308	−	0.413216i
$655$	−29.3886	−	32.6394i	−1.14831	−	1.27533i
$656$	3.31647	−	5.74430i	0.129486	−	0.224277i
$657$	1.82718	−	9.71439i	0.0712851	−	0.378994i
$658$	15.0150	−	3.19153i	0.585345	−	0.124419i
$659$	31.8044	+	6.76022i	1.23892	+	0.263341i	0.780365	−	0.625324i	$-0.215033\pi$
$659$	31.8044	+	6.76022i	1.23892	+	0.263341i	0.458557	+	0.888665i	$0.348367\pi$
$660$	0.0893660	−	2.19997i	0.00347857	−	0.0856338i
$661$	−24.0071	+	17.4422i	−0.933770	+	0.678423i	−0.946913	−	0.321490i	$-0.895816\pi$
$661$	−24.0071	+	17.4422i	−0.933770	+	0.678423i	0.0131433	+	0.999914i	$0.495816\pi$
$662$	−1.43264	+	4.40922i	−0.0556812	+	0.171369i
$663$	0.151328	−	0.592554i	0.00587710	−	0.0230129i
$664$	1.27775	−	12.1570i	0.0495864	−	0.471783i
$665$	38.3900	−	42.6364i	1.48870	−	1.65337i
$666$	4.15956	+	1.24415i	0.161180	+	0.0482100i
$667$	−28.3706	−	20.6125i	−1.09851	−	0.798118i
$668$	−5.50659	−	16.9475i	−0.213056	−	0.655720i
$669$	−11.7053	+	23.6567i	−0.452554	+	0.914622i
$670$	−4.64530	−	44.1971i	−0.179464	−	1.70748i
$671$	−1.41951	+	4.36880i	−0.0547996	+	0.168656i
$672$	1.59311	−	6.23813i	0.0614557	−	0.240641i
$673$	6.96900	−	7.73986i	0.268635	−	0.298349i	−0.593701	−	0.804686i	$-0.702334\pi$
$673$	6.96900	−	7.73986i	0.268635	−	0.298349i	0.862336	+	0.506336i	$0.169001\pi$
$674$	−3.31517	−	10.2031i	−0.127696	−	0.393007i
$675$	17.6636	−	3.44034i	0.679871	−	0.132419i
$676$	−3.83434	−	6.64127i	−0.147475	−	0.255433i
$677$	−4.09270	−	7.08876i	−0.157295	−	0.272443i	0.776597	−	0.629997i	$-0.216944\pi$
$677$	−4.09270	−	7.08876i	−0.157295	−	0.272443i	−0.933892	+	0.357554i	$0.883611\pi$
$678$	−12.4753	+	15.7817i	−0.479113	+	0.606093i
$679$	−56.7984	+	25.2883i	−2.17972	+	0.970475i
$680$	0.206409	+	0.0918992i	0.00791543	+	0.00352417i
$681$	−5.32323	+	4.41533i	−0.203987	+	0.169196i
$682$	2.11396	−	1.20426i	0.0809478	−	0.0461134i
$683$	−19.4065			−0.742567			−0.371284	−	0.928519i	$-0.621082\pi$
$683$	−19.4065			−0.742567			−0.371284	+	0.928519i	$0.621082\pi$
$684$	6.81399	+	14.3841i	0.260540	+	0.549991i
$685$	−0.0794652	+	0.756061i	−0.00303621	+	0.0288876i
$686$	−0.454118	−	0.504349i	−0.0173383	−	0.0192561i
$687$	−11.9443	−	4.42452i	−0.455703	−	0.168806i
$688$	−0.486662	+	0.842923i	−0.0185538	+	0.0321361i
$689$	−5.71178	−	6.34357i	−0.217601	−	0.241671i
$690$	20.7662	−	10.8904i	0.790554	−	0.414590i
$691$	−12.8164	+	14.2340i	−0.487558	+	0.541488i	−0.935850	−	0.352400i	$-0.885366\pi$
$691$	−12.8164	+	14.2340i	−0.487558	+	0.541488i	0.448292	+	0.893887i	$0.352032\pi$
$692$	−0.708492	−	6.74085i	−0.0269328	−	0.256249i
$693$	−4.16152	+	2.53499i	−0.158083	+	0.0962964i
$694$	−27.8303	−	12.3909i	−1.05643	−	0.470351i
$695$	−3.29372	+	31.3377i	−0.124938	+	1.18871i
$696$	−0.529764	+	13.0415i	−0.0200806	+	0.494336i
$697$	0.0538482	−	0.512331i	0.00203965	−	0.0194059i
$698$	0.893188	−	8.49812i	0.0338077	−	0.321659i
$699$	15.4608	−	8.10811i	0.584782	−	0.306677i
$700$	−1.34564	+	12.8029i	−0.0508605	+	0.483906i
$701$	2.59709	+	1.15630i	0.0980906	+	0.0436728i	0.455195	−	0.890392i	$-0.349569\pi$
$701$	2.59709	+	1.15630i	0.0980906	+	0.0436728i	−0.357105	+	0.934064i	$0.616236\pi$
$702$	−7.68256	+	22.3390i	−0.289960	+	0.843133i
$703$	−0.802587	−	7.63610i	−0.0302701	−	0.288001i
$704$	−0.292386	+	0.324728i	−0.0110197	+	0.0122386i
$705$	0.844565	−	20.7911i	0.0318082	−	0.783039i
$706$	−16.0875	−	17.8670i	−0.605463	−	0.672434i
$707$	−0.378376	+	0.655366i	−0.0142303	+	0.0246476i
$708$	−0.648947	−	3.80696i	−0.0243889	−	0.143074i
$709$	−9.38990	−	10.4285i	−0.352645	−	0.391652i	0.540557	−	0.841307i	$-0.318214\pi$
$709$	−9.38990	−	10.4285i	−0.352645	−	0.391652i	−0.893202	+	0.449655i	$0.851547\pi$
$710$	3.40066	−	32.3551i	0.127624	−	1.21426i
$711$	14.0109	−	20.2703i	0.525448	−	0.760194i
$712$	−7.52482			−0.282005
$713$	22.3635	+	13.0845i	0.837519	+	0.490018i
$714$	−0.0840264	−	0.492929i	−0.00314461	−	0.0184474i
$715$	−5.27960	−	2.35063i	−0.197446	−	0.0879085i
$716$	15.5950	−	6.94335i	0.582813	−	0.259485i
$717$	−13.2779	−	1.94323i	−0.495874	−	0.0725714i
$718$	−1.16259	−	2.01367i	−0.0433876	−	0.0751495i
$719$	−14.1827	−	24.5652i	−0.528925	−	0.916126i	−0.999431	−	0.0337288i	$-0.989262\pi$
$719$	−14.1827	−	24.5652i	−0.528925	−	0.916126i	0.470506	−	0.882397i	$-0.344072\pi$
$720$	−7.65877	−	4.18477i	−0.285426	−	0.155957i
$721$	20.2814	+	62.4197i	0.755319	+	2.32463i
$722$	6.12131	−	6.79840i	0.227812	−	0.253010i
$723$	18.9229	+	18.4830i	0.703751	+	0.687390i
$724$	2.90078	−	8.92768i	0.107807	−	0.331795i
$725$	−2.72798	−	25.9550i	−0.101315	−	0.963943i
$726$	−18.6834	+	1.19963i	−0.693405	+	0.0445226i
$727$	−6.15551	−	18.9447i	−0.228295	−	0.702621i	−0.997940	−	0.0641486i	$-0.979567\pi$
$727$	−6.15551	−	18.9447i	−0.228295	−	0.702621i	0.769645	−	0.638472i	$-0.220433\pi$
$728$	−13.6719	−	9.93319i	−0.506713	−	0.368148i
$729$	25.0264	−	10.1332i	0.926902	−	0.375303i
$730$	6.41391	−	7.12337i	0.237389	−	0.263648i
$731$	−0.00790173	+	0.0751800i	−0.000292256	+	0.00278063i
$732$	13.0258	+	12.7229i	0.481446	+	0.470253i
$733$	1.87581	−	5.77314i	0.0692846	−	0.213236i	−0.910419	−	0.413687i	$-0.864241\pi$
$733$	1.87581	−	5.77314i	0.0692846	−	0.213236i	0.979704	+	0.200451i	$0.0642408\pi$
$734$	−18.5691	+	13.4912i	−0.685397	+	0.497970i
$735$	30.4221	−	15.9543i	1.12214	−	0.588482i
$736$	−4.55189	−	0.967533i	−0.167785	−	0.0356637i
$737$	6.52923	−	1.38783i	0.240507	−	0.0511214i
$738$	−3.67827	+	19.5559i	−0.135399	+	0.719863i
$739$	−8.14783	+	14.1125i	−0.299723	+	0.519135i	−0.976072	−	0.217446i	$-0.930228\pi$
$739$	−8.14783	+	14.1125i	−0.299723	+	0.519135i	0.676350	+	0.736581i	$0.263561\pi$
$740$	2.81716	+	3.12877i	0.103561	+	0.115016i
$741$	41.6916	−	2.67696i	1.53158	−	0.0983406i
$742$	−6.37599	−	2.83878i	−0.234070	−	0.104215i
$743$	23.2645	+	40.2954i	0.853493	+	1.47829i	0.878036	+	0.478595i	$0.158854\pi$
$743$	23.2645	+	40.2954i	0.853493	+	1.47829i	−0.0245422	+	0.999699i	$0.507813\pi$
$744$	−0.562295	−	9.62724i	−0.0206147	−	0.352952i
$745$	31.1291	−	53.9172i	1.14048	−	1.97537i
$746$	0.777001	−	0.564524i	0.0284480	−	0.0206687i
$747$	8.46606	+	35.6813i	0.309757	+	1.30551i
$748$	−0.0104872	+	0.0322762i	−0.000383450	+	0.00118014i
$749$	−20.3849	−	35.3077i	−0.744849	−	1.29012i
$750$	−7.26130	−	2.68981i	−0.265145	−	0.0982179i
$751$	0.926211	+	1.02866i	0.0337979	+	0.0375364i	0.759807	−	0.650149i	$-0.225294\pi$
$751$	0.926211	+	1.02866i	0.0337979	+	0.0375364i	−0.726009	+	0.687685i	$0.758627\pi$
$752$	−2.76324	+	3.06888i	−0.100765	+	0.111911i
$753$	4.76136	+	3.01305i	0.173514	+	0.109802i
$754$	31.2976	+	13.9346i	1.13979	+	0.507467i
$755$	31.2585	+	34.7161i	1.13761	+	1.26345i
$756$	1.69065	+	19.2409i	0.0614882	+	0.699785i
$757$	−31.4494	+	14.0022i	−1.14305	+	0.508918i	−0.888833	−	0.458230i	$-0.848483\pi$
$757$	−31.4494	+	14.0022i	−1.14305	+	0.508918i	−0.254214	+	0.967148i	$0.581817\pi$
$758$	−2.35513	−	7.24834i	−0.0855422	−	0.263272i
$759$	1.95284	+	2.93106i	0.0708838	+	0.106391i
$760$	−1.61335	+	15.3500i	−0.0585222	+	0.556802i
$761$	30.4508	+	6.47252i	1.10384	+	0.234629i	0.723573	−	0.690248i	$-0.242498\pi$
$761$	30.4508	+	6.47252i	1.10384	+	0.234629i	0.380268	+	0.924876i	$0.375832\pi$
$762$	−11.8172	+	23.8829i	−0.428092	+	0.865185i
$763$	−22.0468	+	16.0179i	−0.798146	+	0.579887i
$764$	−9.97141	−	11.0744i	−0.360753	−	0.400657i
$765$	−0.675595	−	0.0549780i	−0.0244262	−	0.00198773i
$766$	7.66735	+	1.62975i	0.277033	+	0.0588851i
$767$	−9.91513	−	2.10753i	−0.358015	−	0.0760983i
$768$	0.639685	+	1.60960i	0.0230827	+	0.0580813i
$769$	20.0037	−	34.6475i	0.721353	−	1.24942i	−0.239105	−	0.970994i	$-0.576854\pi$
$769$	20.0037	−	34.6475i	0.721353	−	1.24942i	0.960458	−	0.278426i	$-0.0898128\pi$
$770$	−4.72528			−0.170287
$771$	10.9423	+	1.60141i	0.394077	+	0.0576734i
$772$	−5.32566	−	3.86932i	−0.191675	−	0.139260i
$773$	10.6976	−	7.77228i	0.384767	−	0.279549i	−0.378541	−	0.925585i	$-0.623574\pi$
$773$	10.6976	−	7.77228i	0.384767	−	0.279549i	0.763308	+	0.646035i	$0.223574\pi$
$774$	0.539753	−	2.86965i	0.0194010	−	0.103147i
$775$	3.89996	+	18.8840i	0.140091	+	0.678332i
$776$	8.36300	−	14.4851i	0.300214	−	0.519986i
$777$	2.30557	−	9.02790i	0.0827120	−	0.323874i
$778$	13.8655	−	6.17333i	0.497103	−	0.221325i
$779$	34.4220	−	7.31661i	1.23329	−	0.262145i
$780$	−17.6320	+	14.6248i	−0.631327	+	0.523651i
$781$	4.88659			0.174856
$782$	−0.353526	+	0.0751443i	−0.0126421	+	0.00268716i
$783$	−11.4624	−	37.4414i	−0.409632	−	1.33805i
$784$	−6.66845	−	1.41742i	−0.238159	−	0.0506222i
$785$	21.4715	+	9.55972i	0.766350	+	0.341201i
$786$	−9.65755	−	24.3006i	−0.344473	−	0.866775i
$787$	−2.85758	−	27.1880i	−0.101862	−	0.969149i	−0.919413	−	0.393293i	$-0.871336\pi$
$787$	−2.85758	−	27.1880i	−0.101862	−	0.969149i	0.817551	−	0.575856i	$-0.195331\pi$
$788$	8.90164	+	6.46742i	0.317108	+	0.230392i
$789$	−1.81585	+	44.7018i	−0.0646460	+	1.59143i
$790$	21.8292	−	9.71900i	0.776649	−	0.345787i
$791$	34.9281	+	25.3768i	1.24190	+	0.902294i
$792$	0.504875	−	1.20977i	0.0179400	−	0.0429873i
$793$	43.6613	−	19.4393i	1.55046	−	0.690308i
$794$	18.3141	−	13.3060i	0.649943	−	0.472211i
$795$	−5.86706	+	7.42202i	−0.208083	+	0.263232i
$796$	18.2845	−	13.2845i	0.648077	−	0.470856i
$797$	−4.84501	−	14.9114i	−0.171619	−	0.528189i	0.827844	−	0.560959i	$-0.189567\pi$
$797$	−4.84501	−	14.9114i	−0.171619	−	0.528189i	−0.999463	+	0.0327694i	$0.989567\pi$
$798$	30.2510	−	15.8645i	1.07087	−	0.561598i
$799$	−0.0991105	+	0.305031i	−0.00350628	+	0.0107912i
$800$	−1.73162	−	2.99925i	−0.0612219	−	0.106039i
$801$	21.2996	−	7.47891i	0.752584	−	0.264254i
$802$	−6.32585	+	19.4690i	−0.223374	+	0.687473i
$803$	1.16479	+	0.846269i	0.0411045	+	0.0298642i
$804$	6.54703	−	25.6361i	0.230896	−	0.904116i
$805$	−25.1616	−	43.5812i	−0.886831	−	1.53604i
$806$	−24.0281	−	7.96105i	−0.846354	−	0.280416i
$807$	−37.0593	−	13.7279i	−1.30455	−	0.483245i
$808$	−0.0212801	−	0.202467i	−0.000748633	−	0.00712277i
$809$	1.82611	−	17.3742i	0.0642025	−	0.610846i	−0.914361	−	0.404900i	$-0.867306\pi$
$809$	1.82611	−	17.3742i	0.0642025	−	0.610846i	0.978563	−	0.205946i	$-0.0660270\pi$
$810$	25.8380	+	4.23328i	0.907854	+	0.148742i
$811$	−8.88547	+	15.3901i	−0.312011	+	0.540419i	−0.978798	−	0.204830i	$-0.934336\pi$
$811$	−8.88547	+	15.3901i	−0.312011	+	0.540419i	0.666787	+	0.745249i	$0.267669\pi$
$812$	28.0116			0.983014
$813$	17.6850	+	2.58821i	0.620241	+	0.0907726i
$814$	−0.423145	+	0.469951i	−0.0148312	+	0.0164718i
$815$	−11.1608	−	34.3494i	−0.390945	−	1.20321i
$816$	0.0962330	+	0.0939957i	0.00336883	+	0.00329051i
$817$	−5.05111	+	1.07365i	−0.176716	+	0.0375621i
$818$	5.24601	+	2.33567i	0.183422	+	0.0816649i
$819$	48.5718	+	14.5282i	1.69724	+	0.507656i
$820$	−12.9118	+	14.3400i	−0.450898	+	0.500773i
$821$	32.7097	−	14.5633i	1.14158	−	0.508262i	0.253216	−	0.967410i	$-0.418512\pi$
$821$	32.7097	−	14.5633i	1.14158	−	0.508262i	0.888360	+	0.459148i	$0.151845\pi$
$822$	−0.200729	+	0.405677i	−0.00700122	+	0.0141496i
$823$	−9.00207	−	1.91345i	−0.313792	−	0.0666986i	0.0483234	−	0.998832i	$-0.484612\pi$
$823$	−9.00207	−	1.91345i	−0.313792	−	0.0666986i	−0.362116	+	0.932133i	$0.617946\pi$
$824$	−14.2843	−	10.3782i	−0.497618	−	0.361540i
$825$	−0.648576	+	2.53962i	−0.0225805	+	0.0884183i
$826$	−8.10691	+	1.72318i	−0.282076	+	0.0599570i
$827$	−1.94510	−	18.5064i	−0.0676377	−	0.643530i	−0.974851	−	0.222858i	$-0.928461\pi$
$827$	−1.94510	−	18.5064i	−0.0676377	−	0.643530i	0.907213	−	0.420671i	$-0.138205\pi$
$828$	13.8461	−	1.78544i	0.481185	−	0.0620483i
$829$	−12.6730	−	39.0035i	−0.440152	−	1.35465i	−0.887714	−	0.460396i	$-0.847708\pi$
$829$	−12.6730	−	39.0035i	−0.440152	−	1.35465i	0.447562	−	0.894253i	$-0.352292\pi$
$830$	−10.9891	+	33.8210i	−0.381438	+	1.17394i
$831$	−48.7772	−	18.0686i	−1.69206	−	0.626792i
$832$	4.54628			0.157614
$833$	−0.517911	+	0.110085i	−0.0179446	+	0.00381423i
$834$	−8.31992	+	16.8148i	−0.288095	+	0.582247i
$835$	5.41880	+	51.5564i	0.187525	+	1.78418i
$836$	−2.31831			−0.0801804
$837$	11.1601	+	26.6918i	0.385751	+	0.922603i
$838$	37.7725			1.30483
$839$	−4.19841	−	39.9452i	−0.144945	−	1.37906i	−0.789146	−	0.614205i	$-0.789477\pi$
$839$	−4.19841	−	39.9452i	−0.144945	−	1.37906i	0.644201	−	0.764856i	$-0.277190\pi$
$840$	−8.30648	+	16.7876i	−0.286601	+	0.579226i
$841$	−27.1797	+	5.77723i	−0.937232	+	0.199215i
$842$	22.3095			0.768838
$843$	31.5757	+	11.6966i	1.08752	+	0.402852i
$844$	−0.493388	+	1.51849i	−0.0169831	+	0.0522686i
$845$	6.89399	+	21.2175i	0.237161	+	0.729905i
$846$	4.77139	−	11.4331i	0.164044	−	0.393078i
$847$	4.19987	+	39.9591i	0.144309	+	1.37301i
$848$	1.83657	−	0.390376i	0.0630682	−	0.0134056i
$849$	−1.01071	+	3.95762i	−0.0346874	+	0.135825i
$850$	−0.217606	−	0.158100i	−0.00746381	−	0.00542277i
$851$	−6.58755	−	1.40023i	−0.225818	−	0.0479992i
$852$	8.59004	−	17.3607i	0.294290	−	0.594766i
$853$	−14.1757	+	6.31142i	−0.485366	+	0.216099i	−0.634805	−	0.772672i	$-0.718920\pi$
$853$	−14.1757	+	6.31142i	−0.485366	+	0.216099i	0.149439	+	0.988771i	$0.452253\pi$
$854$	26.1478	−	29.0400i	0.894758	−	0.993729i
$855$	−10.6896	−	45.0528i	−0.365577	−	1.54077i
$856$	10.0197	+	4.46107i	0.342467	+	0.152476i
$857$	21.3185	−	4.53139i	0.728227	−	0.154789i	0.171144	−	0.985246i	$-0.445254\pi$
$857$	21.3185	−	4.53139i	0.728227	−	0.154789i	0.557083	+	0.830457i	$0.311920\pi$
$858$	−2.46148	−	2.40425i	−0.0840335	−	0.0820798i
$859$	−3.44357	−	10.5982i	−0.117493	−	0.361607i	0.874966	−	0.484185i	$-0.160884\pi$
$859$	−3.44357	−	10.5982i	−0.117493	−	0.361607i	−0.992459	+	0.122578i	$0.960884\pi$
$860$	1.89468	−	2.10426i	0.0646081	−	0.0717546i
$861$	42.2550	+	6.18405i	1.44005	+	0.210752i
$862$	−6.31126			−0.214962
$863$	−3.65273	+	6.32671i	−0.124340	+	0.215364i	−0.921475	−	0.388438i	$-0.873015\pi$
$863$	−3.65273	+	6.32671i	−0.124340	+	0.215364i	0.797135	+	0.603802i	$0.206348\pi$
$864$	−3.41046	−	3.92030i	−0.116026	−	0.133371i
$865$	−2.06112	+	19.6102i	−0.0700802	+	0.666768i
$866$	−4.09594	−	38.9703i	−0.139186	−	1.32426i
$867$	−27.6015	−	10.2245i	−0.937398	−	0.347241i
$868$	−20.5952	+	2.04435i	−0.699045	+	0.0693897i
$869$	1.79455	+	3.10826i	0.0608761	+	0.105440i
$870$	9.39562	−	36.7903i	0.318541	−	1.24731i
$871$	−56.1856	−	40.8212i	−1.90378	−	1.38318i
$872$	2.26546	−	6.97236i	0.0767180	−	0.236114i
$873$	−9.27534	+	49.3133i	−0.313923	+	1.66900i
$874$	−12.3447	−	21.3817i	−0.417567	−	0.723247i
$875$	−5.13537	+	15.8050i	−0.173607	+	0.534308i
$876$	5.05411	−	2.65052i	0.170763	−	0.0895529i
$877$	−3.05605	−	9.40554i	−0.103195	−	0.317603i	0.886107	−	0.463480i	$-0.153399\pi$
$877$	−3.05605	−	9.40554i	−0.103195	−	0.317603i	−0.989303	+	0.145878i	$0.953399\pi$
$878$	24.8500	−	18.0546i	0.838646	−	0.609312i
$879$	−13.9408	+	17.6356i	−0.470212	+	0.594833i
$880$	1.02842	−	0.747193i	0.0346682	−	0.0251879i
$881$	−21.5073	+	9.57568i	−0.724601	+	0.322613i	−0.735683	−	0.677326i	$-0.763139\pi$
$881$	−21.5073	+	9.57568i	−0.724601	+	0.322613i	0.0110828	+	0.999939i	$0.496472\pi$
$882$	20.2843	−	2.61564i	0.683009	−	0.0880733i
$883$	6.50197	+	4.72396i	0.218809	+	0.158974i	0.691790	−	0.722099i	$-0.256822\pi$
$883$	6.50197	+	4.72396i	0.218809	+	0.158974i	−0.472982	+	0.881072i	$0.656822\pi$
$884$	0.322565	−	0.143615i	0.0108490	−	0.00483030i
$885$	−0.455999	+	11.2256i	−0.0153282	+	0.377343i
$886$	7.64829	+	5.55681i	0.256949	+	0.186685i
$887$	0.957365	+	9.10872i	0.0321452	+	0.305841i	0.998767	+	0.0496350i	$0.0158058\pi$
$887$	0.957365	+	9.10872i	0.0321452	+	0.305841i	−0.966622	+	0.256206i	$0.917528\pi$
$888$	0.925761	+	2.32943i	0.0310665	+	0.0781705i
$889$	52.2425	+	23.2598i	1.75216	+	0.780110i
$890$	21.4126	+	4.55138i	0.717751	+	0.152563i
$891$	−0.226698	+	3.92614i	−0.00759468	+	0.131531i
$892$	−14.9057	+	3.16831i	−0.499080	+	0.106083i
$893$	−21.9095			−0.733173
$894$	28.5303	−	23.6643i	0.954195	−	0.791452i
$895$	−48.5767	+	10.3253i	−1.62374	+	0.345137i
$896$	3.39581	−	1.51191i	0.113446	−	0.0505095i
$897$	9.06726	−	35.5046i	0.302747	−	1.18546i
$898$	10.8913	−	18.8642i	0.363446	−	0.629508i
$899$	39.9778	−	12.7346i	1.33333	−	0.424722i
$900$	7.88243	+	6.76855i	0.262748	+	0.225618i
$901$	0.117976	−	0.0857143i	0.00393034	−	0.00285556i
$902$	−2.34482	−	1.70361i	−0.0780741	−	0.0567241i
$903$	−6.20054	−	0.907452i	−0.206341	−	0.0301981i
$904$	−11.6146			−0.386296
$905$	−13.6543	+	23.6500i	−0.453885	+	0.786152i
$906$	10.2720	+	25.8468i	0.341265	+	0.858702i
$907$	−36.0461	−	7.66184i	−1.19689	−	0.254407i	−0.433988	−	0.900919i	$-0.642894\pi$
$907$	−36.0461	−	7.66184i	−1.19689	−	0.254407i	−0.762904	+	0.646511i	$0.776227\pi$
$908$	−3.90574	−	0.830190i	−0.129616	−	0.0275508i
$909$	0.261467	+	0.551948i	0.00867231	+	0.0183070i
$910$	32.8964	+	36.5352i	1.09051	+	1.21113i
$911$	−17.0464	+	12.3849i	−0.564772	+	0.410331i	−0.833202	−	0.552968i	$-0.813495\pi$
$911$	−17.0464	+	12.3849i	−0.564772	+	0.410331i	0.268431	+	0.963299i	$0.413495\pi$
$912$	−4.07530	+	8.23628i	−0.134947	+	0.272731i
$913$	−5.22472	−	1.11055i	−0.172913	−	0.0367538i
$914$	−3.51326	+	33.4265i	−0.116208	+	1.10565i
$915$	−29.3706	−	44.0829i	−0.970961	−	1.45734i
$916$	−2.27250	−	6.99403i	−0.0750855	−	0.231089i
$917$	−51.2677	+	22.8259i	−1.69301	+	0.753776i
$918$	−0.365817	−	0.170416i	−0.0120738	−	0.00562457i
$919$	−16.3180	−	18.1230i	−0.538281	−	0.597822i	0.411239	−	0.911527i	$-0.365096\pi$
$919$	−16.3180	−	18.1230i	−0.538281	−	0.597822i	−0.949520	+	0.313706i	$0.898429\pi$
$920$	12.3676	+	5.50641i	0.407748	+	0.181541i
$921$	40.7716	+	25.8008i	1.34347	+	0.850164i
$922$	−2.64460	+	2.93713i	−0.0870954	+	0.0967292i
$923$	−34.0194	−	37.7824i	−1.11976	−	1.24362i
$924$	−2.63814	−	0.977248i	−0.0867885	−	0.0321491i
$925$	−2.50602	−	4.34055i	−0.0823974	−	0.142716i
$926$	−10.1896	+	31.3604i	−0.334851	+	1.03057i
$927$	50.7477	+	15.1790i	1.66677	+	0.498544i
$928$	−6.09652	+	4.42938i	−0.200128	+	0.145402i
$929$	−12.2034	+	21.1369i	−0.400381	+	0.693480i	−0.993772	−	0.111435i	$-0.964455\pi$
$929$	−12.2034	+	21.1369i	−0.400381	+	0.693480i	0.593391	+	0.804914i	$0.297789\pi$
$930$	−4.22297	+	27.7353i	−0.138477	+	0.909477i
$931$	−18.0849	−	31.3239i	−0.592707	−	1.02660i
$932$	9.20792	+	4.09963i	0.301615	+	0.134288i
$933$	−50.6693	+	3.25341i	−1.65884	+	0.106512i
$934$	−3.86235	−	4.28957i	−0.126380	−	0.140359i
$935$	0.0493645	−	0.0855018i	0.00161439	−	0.00279621i
$936$	−12.8686	+	4.51855i	−0.420623	+	0.147693i
$937$	−25.3623	+	5.39092i	−0.828550	+	0.176114i	−0.602618	−	0.798029i	$-0.705876\pi$
$937$	−25.3623	+	5.39092i	−0.828550	+	0.176114i	−0.225932	+	0.974143i	$0.572543\pi$
$938$	−55.5430	−	11.8060i	−1.81354	−	0.385480i
$939$	13.5338	−	7.09751i	0.441658	−	0.231618i
$940$	9.71925	−	7.06145i	0.317007	−	0.230319i
$941$	9.81012	−	30.1924i	0.319801	−	0.984246i	−0.653932	−	0.756553i	$-0.726882\pi$
$941$	9.81012	−	30.1924i	0.319801	−	0.984246i	0.973733	−	0.227692i	$-0.0731181\pi$
$942$	10.0105	+	9.77780i	0.326161	+	0.318578i
$943$	3.22647	−	30.6978i	0.105068	−	0.999658i
$944$	1.49193	−	1.65696i	0.0485582	−	0.0539293i
$945$	6.82696	−	55.7743i	0.222081	−	1.81434i
$946$	0.344081	+	0.249990i	0.0111871	+	0.00812787i
$947$	−11.9430	−	36.7568i	−0.388096	−	1.19444i	−0.934209	−	0.356726i	$-0.883893\pi$
$947$	−11.9430	−	36.7568i	−0.388096	−	1.19444i	0.546113	−	0.837711i	$-0.316107\pi$
$948$	14.1974	−	0.911593i	0.461109	−	0.0296072i
$949$	−1.56579	−	14.8975i	−0.0508278	−	0.483594i
$950$	5.67792	−	17.4748i	0.184216	−	0.566959i
$951$	29.6152	+	28.9266i	0.960337	+	0.938010i
$952$	0.193177	−	0.214545i	0.00626089	−	0.00695343i
$953$	−16.8284	−	51.7923i	−0.545124	−	1.67772i	−0.720695	−	0.693252i	$-0.756177\pi$
$953$	−16.8284	−	51.7923i	−0.545124	−	1.67772i	0.175572	−	0.984467i	$-0.443823\pi$
$954$	−4.81057	+	2.93036i	−0.155748	+	0.0948739i
$955$	21.6762	+	37.5443i	0.701427	+	1.21491i
$956$	−3.87384	−	6.70969i	−0.125289	−	0.217007i
$957$	5.64325	+	0.825892i	0.182420	+	0.0266973i
$958$	28.7001	−	12.7781i	0.927258	−	0.412842i
$959$	0.887397	+	0.395095i	0.0286555	+	0.0127583i
$960$	−0.846720	−	4.96717i	−0.0273278	−	0.160315i
$961$	−28.4638	+	12.2806i	−0.918186	+	0.396149i
$962$	6.57944			0.212130
$963$	−32.7955	−	2.66880i	−1.05682	−	0.0860009i
$964$	−1.59635	+	15.1883i	−0.0514151	+	0.489182i
$965$	12.8143	+	14.2317i	0.412507	+	0.458135i
$966$	−5.03468	−	29.5353i	−0.161988	−	0.950282i
$967$	17.3191	−	29.9975i	0.556943	−	0.964654i	−0.440806	−	0.897602i	$-0.645307\pi$
$967$	17.3191	−	29.9975i	0.556943	−	0.964654i	0.997750	−	0.0670516i	$-0.0213592\pi$
$968$	−7.23267	−	8.03270i	−0.232467	−	0.258181i
$969$	−0.0289676	+	0.713112i	−0.000930575	+	0.0229085i
$970$	−32.5590	+	36.1605i	−1.04541	+	1.16104i
$971$	−1.19026	−	11.3245i	−0.0381972	−	0.363422i	−0.996879	−	0.0789420i	$-0.974846\pi$
$971$	−1.19026	−	11.3245i	−0.0381972	−	0.363422i	0.958682	−	0.284480i	$-0.0918209\pi$
$972$	13.5499	+	7.70707i	0.434615	+	0.247205i
$973$	36.7814	+	16.3761i	1.17916	+	0.524994i
$974$	−3.64144	+	34.6460i	−0.116679	+	1.11013i
$975$	24.1512	−	12.6656i	0.773458	−	0.405624i
$976$	−1.09887	+	10.4550i	−0.0351738	+	0.334657i
$977$	1.46208	−	13.9108i	0.0467762	−	0.445045i	−0.945920	−	0.324401i	$-0.894837\pi$
$977$	1.46208	−	13.9108i	0.0467762	−	0.445045i	0.992696	−	0.120644i	$-0.0384961\pi$
$978$	0.872774	−	21.4856i	0.0279082	−	0.687032i
$979$	−0.343698	+	3.27007i	−0.0109846	+	0.104512i
$980$	18.1183	+	8.06681i	0.578769	+	0.257685i
$981$	0.517274	+	21.9874i	0.0165153	+	0.702005i
$982$	1.50777	+	14.3454i	0.0481147	+	0.457781i
$983$	12.1436	−	13.4868i	0.387320	−	0.430163i	−0.517680	−	0.855574i	$-0.673204\pi$
$983$	12.1436	−	13.4868i	0.387320	−	0.430163i	0.905000	+	0.425412i	$0.139871\pi$
$984$	−10.1744	+	5.33574i	−0.324347	+	0.170097i
$985$	−21.4186	−	23.7878i	−0.682454	−	0.757942i
$986$	−0.292634	+	0.506857i	−0.00931936	+	0.0161416i
$987$	−24.9321	−	9.23561i	−0.793598	−	0.293973i
$988$	16.1396	+	17.9248i	0.513468	+	0.570264i
$989$	−0.473455	+	4.50463i	−0.0150550	+	0.143239i
$990$	−2.16840	+	3.13714i	−0.0689162	+	0.0997048i
$991$	26.9286			0.855416			0.427708	−	0.903917i	$-0.359321\pi$
$991$	26.9286			0.855416			0.427708	+	0.903917i	$0.359321\pi$
$992$	4.15912	−	3.70158i	0.132052	−	0.117525i
$993$	6.18063	−	5.12649i	0.196136	−	0.162684i
$994$	−37.9755	−	16.9078i	−1.20451	−	0.536282i
$995$	−60.0653	+	26.7428i	−1.90420	+	0.847804i
$996$	−13.1299	+	16.6097i	−0.416036	+	0.526299i
$997$	−23.7990	−	41.2210i	−0.753721	−	1.30548i	−0.946008	−	0.324144i	$-0.894924\pi$
$997$	−23.7990	−	41.2210i	−0.753721	−	1.30548i	0.192287	−	0.981339i	$-0.438410\pi$
$998$	−15.8181	−	27.3977i	−0.500713	−	0.867260i
$999$	−4.93566	−	5.67352i	−0.156157	−	0.179502i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.bb.b.493.6	yes	128
9.4	even	3		558.2.y.b.121.10	✓	128
31.10	even	15		558.2.y.b.475.10	yes	128
279.103	even	15	inner	558.2.bb.b.103.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.y.b.121.10	✓	128	9.4	even	3
558.2.y.b.475.10	yes	128	31.10	even	15
558.2.bb.b.103.6	yes	128	279.103	even	15	inner
558.2.bb.b.493.6	yes	128	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.bb (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(-0.768131 + 1.55241i) q^{3} +(-0.978148 + 0.207912i) q^{4} +2.90916 q^{5} +(1.62420 + 0.601652i) q^{6} +(1.14867 - 3.53525i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-1.81995 - 2.38491i) q^{9} +(-0.304090 - 2.89323i) q^{10} +(0.427416 - 0.0908500i) q^{11} +(0.428581 - 1.67819i) q^{12} +(-3.67802 - 2.67224i) q^{13} +(-3.63595 - 0.772845i) q^{14} +(-2.23462 + 4.51621i) q^{15} +(0.913545 - 0.406737i) q^{16} +(0.0519686 - 0.0577170i) q^{17} +(-2.18161 + 2.05927i) q^{18} +(4.84680 + 2.15793i) q^{19} +(-2.84559 + 0.604849i) q^{20} +(4.60582 + 4.49874i) q^{21} +(-0.135029 - 0.415578i) q^{22} +(3.11385 - 3.45828i) q^{23} +(-1.71379 - 0.250815i) q^{24} +3.46323 q^{25} +(-2.27314 + 3.93720i) q^{26} +(5.10031 - 0.993389i) q^{27} +(-0.388551 + 3.69682i) q^{28} +(-0.787696 - 7.49443i) q^{29} +(4.72505 + 1.75030i) q^{30} +(1.12610 + 5.45270i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.187275 + 0.733309i) q^{33} +(-0.0628330 - 0.0456509i) q^{34} +(3.34167 - 10.2846i) q^{35} +(2.27603 + 1.95440i) q^{36} +(-0.723607 - 1.25332i) q^{37} +(1.63948 - 5.04581i) q^{38} +(6.97361 - 3.65716i) q^{39} +(0.898981 + 2.76678i) q^{40} +(5.36616 - 3.89875i) q^{41} +(3.99266 - 5.05084i) q^{42} +(-0.787435 + 0.572105i) q^{43} +(-0.399187 + 0.177729i) q^{44} +(-5.29453 - 6.93808i) q^{45} +(-3.76482 - 2.73530i) q^{46} +(-3.77257 + 1.67966i) q^{47} +(-0.0703004 + 1.73062i) q^{48} +(-5.51541 - 4.00718i) q^{49} +(-0.362007 - 3.44426i) q^{50} +(0.0496817 + 0.125011i) q^{51} +(4.15323 + 1.84914i) q^{52} +(1.83657 + 0.390376i) q^{53} +(-1.52107 - 4.96853i) q^{54} +(1.24342 - 0.264298i) q^{55} +3.71718 q^{56} +(-7.07297 + 5.86664i) q^{57} +(-7.37104 + 1.56676i) q^{58} +(2.03689 - 0.906882i) q^{59} +(1.24681 - 4.88213i) q^{60} +(-5.25630 + 9.10417i) q^{61} +(5.30512 - 1.68990i) q^{62} +(-10.5218 + 3.69450i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(-10.7000 - 7.77398i) q^{65} +(0.748867 + 0.109597i) q^{66} +15.2761 q^{67} +(-0.0388330 + 0.0672606i) q^{68} +(2.97683 + 7.49039i) q^{69} +(-10.5776 - 2.24833i) q^{70} +(10.9387 + 2.32509i) q^{71} +(1.70579 - 2.46785i) q^{72} +(2.20473 + 2.44860i) q^{73} +(-1.17082 + 0.850651i) q^{74} +(-2.66022 + 5.37636i) q^{75} +(-5.18955 - 1.10307i) q^{76} +(0.169783 - 1.61538i) q^{77} +(-4.36607 - 6.55313i) q^{78} +(2.53818 + 7.81172i) q^{79} +(2.65765 - 1.18326i) q^{80} +(-2.37556 + 8.68082i) q^{81} +(-4.43830 - 4.92924i) q^{82} +(-11.1672 - 4.97194i) q^{83} +(-5.44052 - 3.44283i) q^{84} +(0.151185 - 0.167908i) q^{85} +(0.651281 + 0.723321i) q^{86} +(12.2395 + 4.53387i) q^{87} +(0.218482 + 0.378422i) q^{88} +(-2.32530 + 7.15653i) q^{89} +(-6.34665 + 5.99076i) q^{90} +(-13.6719 + 9.93319i) q^{91} +(-2.32679 + 4.03012i) q^{92} +(-9.32981 - 2.44021i) q^{93} +(2.06480 + 3.57633i) q^{94} +(14.1001 + 6.27778i) q^{95} +(1.72849 - 0.110984i) q^{96} +(-11.1919 - 12.4298i) q^{97} +(-3.40871 + 5.90406i) q^{98} +(-0.994545 - 0.854004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 2 q^{3} + 16 q^{4} - 2 q^{5} + 2 q^{6} + 2 q^{7} - 32 q^{8} - 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 20 q^{13} - q^{14} - 22 q^{15} + 16 q^{16} + 4 q^{17} - 2 q^{18} - 4 q^{19} + q^{20}+ \cdots + 15 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 2 * q^3 + 16 * q^4 - 2 * q^5 + 2 * q^6 + 2 * q^7 - 32 * q^8 - 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 - 20 * q^13 - q^14 - 22 * q^15 + 16 * q^16 + 4 * q^17 - 2 * q^18 - 4 * q^19 + q^20 + 19 * q^21 - 4 * q^22 - 9 * q^23 - 3 * q^24 + 122 * q^25 - 20 * q^26 - 37 * q^27 + 9 * q^28 - 12 * q^29 - 14 * q^30 + 25 * q^31 - 64 * q^32 + 22 * q^33 - 8 * q^34 + 6 * q^36 - 66 * q^37 - 12 * q^38 + 11 * q^39 - 2 * q^40 + 20 * q^41 + 10 * q^42 - 31 * q^43 + 2 * q^44 + 64 * q^45 + 13 * q^46 + 11 * q^47 - 3 * q^48 - 46 * q^49 + 19 * q^50 + 17 * q^51 + 10 * q^52 + 27 * q^53 - 13 * q^54 - 19 * q^55 + 2 * q^56 + 20 * q^57 + 3 * q^58 - 9 * q^59 + 11 * q^60 - 57 * q^61 + 14 * q^62 - 38 * q^63 - 32 * q^64 - 66 * q^65 - 20 * q^66 - 16 * q^67 - 16 * q^68 - 8 * q^69 - 7 * q^71 + q^72 - 7 * q^73 - 28 * q^74 + 74 * q^75 + 6 * q^76 + 46 * q^77 - 24 * q^78 - 48 * q^79 - 9 * q^80 - 64 * q^81 + 50 * q^82 - 99 * q^83 + q^84 + 27 * q^85 + 33 * q^86 + 81 * q^87 - 8 * q^88 - 52 * q^89 - 45 * q^90 + 11 * q^91 + q^92 + 30 * q^93 + 6 * q^94 + 19 * q^95 - 4 * q^96 + 35 * q^97 - 77 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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