LMFDB - Embedded newform 552.2.bb.a.85.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.14
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.832989 - 1.14286i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.612258 + 1.90398i) q^{4} +(2.21313 - 1.01070i) q^{5} +(-0.511087 + 1.31863i) q^{6} +(-3.93606 + 1.15573i) q^{7} +(2.68599 - 0.886269i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.832989 - 1.14286i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.612258 + 1.90398i) q^{4} +(2.21313 - 1.01070i) q^{5} +(-0.511087 + 1.31863i) q^{6} +(-3.93606 + 1.15573i) q^{7} +(2.68599 - 0.886269i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-2.99860 - 1.68739i) q^{10} +(-1.69367 + 1.46758i) q^{11} +(1.93274 - 0.514305i) q^{12} +(-0.366797 + 1.24920i) q^{13} +(4.59954 + 3.53566i) q^{14} +(-2.04676 - 1.31537i) q^{15} +(-3.25028 - 2.33146i) q^{16} +(-0.326777 + 2.27279i) q^{17} +(1.38562 - 0.282952i) q^{18} +(-3.05560 + 0.439329i) q^{19} +(0.569349 + 4.83256i) q^{20} +(3.10026 + 2.68639i) q^{21} +(3.08804 + 0.713156i) q^{22} +(-4.34498 + 2.03006i) q^{23} +(-2.19773 - 1.78044i) q^{24} +(0.602107 - 0.694868i) q^{25} +(1.73319 - 0.621369i) q^{26} +(0.989821 - 0.142315i) q^{27} +(0.209396 - 8.20179i) q^{28} +(-6.81354 - 0.979640i) q^{29} +(0.201642 + 3.43485i) q^{30} +(0.892638 + 0.573664i) q^{31} +(0.0429204 + 5.65669i) q^{32} +(2.15027 + 0.631376i) q^{33} +(2.86968 - 1.51975i) q^{34} +(-7.54290 + 6.53596i) q^{35} +(-1.47758 - 1.34787i) q^{36} +(1.62977 + 0.744293i) q^{37} +(3.04738 + 3.12617i) q^{38} +(1.24920 - 0.366797i) q^{39} +(5.04868 - 4.67615i) q^{40} +(4.91248 + 10.7568i) q^{41} +(0.487686 - 5.78090i) q^{42} +(-1.53959 - 2.39564i) q^{43} +(-1.75727 - 4.12325i) q^{44} +2.43299i q^{45} +(5.93939 + 3.27469i) q^{46} +9.60060 q^{47} +(-0.204111 + 3.99479i) q^{48} +(8.26810 - 5.31359i) q^{49} +(-1.29569 - 0.109306i) q^{50} +(2.08866 - 0.953858i) q^{51} +(-2.15387 - 1.46320i) q^{52} +(-2.57267 - 8.76172i) q^{53} +(-0.987156 - 1.01268i) q^{54} +(-2.26503 + 4.95972i) q^{55} +(-9.54793 + 6.59269i) q^{56} +(2.02157 + 2.33302i) q^{57} +(4.55602 + 8.60296i) q^{58} +(-2.65301 + 9.03534i) q^{59} +(3.75759 - 3.09164i) q^{60} +(-3.08448 + 4.79955i) q^{61} +(-0.0879405 - 1.49802i) q^{62} +(0.583809 - 4.06048i) q^{63} +(6.42905 - 4.76101i) q^{64} +(0.450795 + 3.13535i) q^{65} +(-1.06958 - 2.98339i) q^{66} +(3.69443 + 3.20124i) q^{67} +(-4.12727 - 2.01371i) q^{68} +(4.05687 + 2.55770i) q^{69} +(13.7528 + 3.17610i) q^{70} +(-3.08398 + 3.55910i) q^{71} +(-0.309621 + 2.81143i) q^{72} +(-1.00106 - 6.96251i) q^{73} +(-0.506962 - 2.48259i) q^{74} +(-0.910084 - 0.130850i) q^{75} +(1.03434 - 6.08679i) q^{76} +(4.97028 - 7.73390i) q^{77} +(-1.45976 - 1.12212i) q^{78} +(-2.34151 - 0.687529i) q^{79} +(-9.54968 - 1.87474i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.20151 - 14.5746i) q^{82} +(6.16808 + 2.81687i) q^{83} +(-7.01300 + 4.25807i) q^{84} +(1.57391 + 5.36024i) q^{85} +(-1.45543 + 3.75508i) q^{86} +(2.85955 + 6.26155i) q^{87} +(-3.24851 + 5.44294i) q^{88} +(0.684426 - 0.439854i) q^{89} +(2.78057 - 2.02665i) q^{90} -5.34083i q^{91} +(-1.20494 - 9.51568i) q^{92} -1.06108i q^{93} +(-7.99719 - 10.9721i) q^{94} +(-6.31840 + 4.06059i) q^{95} +(4.73551 - 3.09435i) q^{96} +(-3.23759 - 7.08933i) q^{97} +(-12.9599 - 5.02313i) q^{98} +(-0.631376 - 2.15027i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.832989	−	1.14286i	−0.589012	−	0.808124i
$2$	−0.832989	−	1.14286i	−0.589012	−	0.808124i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$4$	−0.612258	+	1.90398i	−0.306129	+	0.951990i
$5$	2.21313	−	1.01070i	0.989740	−	0.451999i	0.146310	−	0.989239i	$-0.453260\pi$
$5$	2.21313	−	1.01070i	0.989740	−	0.451999i	0.843430	+	0.537240i	$0.180533\pi$
$6$	−0.511087	+	1.31863i	−0.208650	+	0.538329i
$7$	−3.93606	+	1.15573i	−1.48769	+	0.436826i	−0.921804	−	0.387656i	$-0.873285\pi$
$7$	−3.93606	+	1.15573i	−1.48769	+	0.436826i	−0.565888	+	0.824482i	$0.691467\pi$
$8$	2.68599	−	0.886269i	0.949640	−	0.313343i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−2.99860	−	1.68739i	−0.948240	−	0.533600i
$11$	−1.69367	+	1.46758i	−0.510661	+	0.442491i	−0.871685	−	0.490066i	$-0.836973\pi$
$11$	−1.69367	+	1.46758i	−0.510661	+	0.442491i	0.361024	+	0.932557i	$0.382427\pi$
$12$	1.93274	−	0.514305i	0.557934	−	0.148467i
$13$	−0.366797	+	1.24920i	−0.101731	+	0.346465i	−0.994591	−	0.103870i	$-0.966877\pi$
$13$	−0.366797	+	1.24920i	−0.101731	+	0.346465i	0.892860	+	0.450335i	$0.148695\pi$
$14$	4.59954	+	3.53566i	1.22928	+	0.944944i
$15$	−2.04676	−	1.31537i	−0.528472	−	0.339628i
$16$	−3.25028	−	2.33146i	−0.812570	−	0.582864i
$17$	−0.326777	+	2.27279i	−0.0792551	+	0.551232i	0.911047	+	0.412302i	$0.135275\pi$
$17$	−0.326777	+	2.27279i	−0.0792551	+	0.551232i	−0.990302	+	0.138929i	$0.955634\pi$
$18$	1.38562	−	0.282952i	0.326593	−	0.0666925i
$19$	−3.05560	+	0.439329i	−0.701003	+	0.100789i	−0.483595	−	0.875292i	$-0.660669\pi$
$19$	−3.05560	+	0.439329i	−0.701003	+	0.100789i	−0.217408	+	0.976081i	$0.569760\pi$
$20$	0.569349	+	4.83256i	0.127310	+	1.08059i
$21$	3.10026	+	2.68639i	0.676532	+	0.586219i
$22$	3.08804	+	0.713156i	0.658373	+	0.152045i
$23$	−4.34498	+	2.03006i	−0.905991	+	0.423296i
$23$	−4.34498	+	2.03006i	−0.905991	+	0.423296i
$24$	−2.19773	−	1.78044i	−0.448610	−	0.363431i
$25$	0.602107	−	0.694868i	0.120421	−	0.138974i
$26$	1.73319	−	0.621369i	0.339907	−	0.121860i
$27$	0.989821	−	0.142315i	0.190491	−	0.0273885i
$28$	0.209396	−	8.20179i	0.0395721	−	1.54999i
$29$	−6.81354	−	0.979640i	−1.26524	−	0.181915i	−0.523167	−	0.852230i	$-0.675250\pi$
$29$	−6.81354	−	0.979640i	−1.26524	−	0.181915i	−0.742076	+	0.670316i	$0.766159\pi$
$30$	0.201642	+	3.43485i	0.0368146	+	0.627116i
$31$	0.892638	+	0.573664i	0.160323	+	0.103033i	0.618342	−	0.785909i	$-0.287805\pi$
$31$	0.892638	+	0.573664i	0.160323	+	0.103033i	−0.458020	+	0.888942i	$0.651441\pi$
$32$	0.0429204	+	5.65669i	0.00758733	+	0.999971i
$33$	2.15027	+	0.631376i	0.374314	+	0.109909i
$34$	2.86968	−	1.51975i	0.492146	−	0.260634i
$35$	−7.54290	+	6.53596i	−1.27498	+	1.10478i
$36$	−1.47758	−	1.34787i	−0.246263	−	0.224645i
$37$	1.62977	+	0.744293i	0.267933	+	0.122361i	0.544852	−	0.838532i	$-0.316586\pi$
$37$	1.62977	+	0.744293i	0.267933	+	0.122361i	−0.276918	+	0.960893i	$0.589313\pi$
$38$	3.04738	+	3.12617i	0.494350	+	0.507132i
$39$	1.24920	−	0.366797i	0.200031	−	0.0587345i
$40$	5.04868	−	4.67615i	0.798266	−	0.739365i
$41$	4.91248	+	10.7568i	0.767200	+	1.67993i	0.732721	+	0.680529i	$0.238250\pi$
$41$	4.91248	+	10.7568i	0.767200	+	1.67993i	0.0344796	+	0.999405i	$0.489023\pi$
$42$	0.487686	−	5.78090i	0.0752516	−	0.892012i
$43$	−1.53959	−	2.39564i	−0.234785	−	0.365332i	0.703790	−	0.710408i	$-0.251490\pi$
$43$	−1.53959	−	2.39564i	−0.234785	−	0.365332i	−0.938575	+	0.345076i	$0.887853\pi$
$44$	−1.75727	−	4.12325i	−0.264918	−	0.621604i
$45$			2.43299i			0.362689i
$46$	5.93939	+	3.27469i	0.875716	+	0.482827i
$47$	9.60060			1.40039			0.700196	−	0.713951i	$-0.253096\pi$
$47$	9.60060			1.40039			0.700196	+	0.713951i	$0.253096\pi$
$48$	−0.204111	+	3.99479i	−0.0294609	+	0.576598i
$49$	8.26810	−	5.31359i	1.18116	−	0.759084i
$50$	−1.29569	−	0.109306i	−0.183238	−	0.0154582i
$51$	2.08866	−	0.953858i	0.292471	−	0.133567i
$52$	−2.15387	−	1.46320i	−0.298688	−	0.202910i
$53$	−2.57267	−	8.76172i	−0.353384	−	1.20351i	−0.924030	−	0.382319i	$-0.875126\pi$
$53$	−2.57267	−	8.76172i	−0.353384	−	1.20351i	0.570647	−	0.821196i	$-0.306693\pi$
$54$	−0.987156	−	1.01268i	−0.134335	−	0.137808i
$55$	−2.26503	+	4.95972i	−0.305417	+	0.668769i
$56$	−9.54793	+	6.59269i	−1.27590	+	0.880986i
$57$	2.02157	+	2.33302i	0.267764	+	0.309016i
$58$	4.55602	+	8.60296i	0.598234	+	1.12962i
$59$	−2.65301	+	9.03534i	−0.345393	+	1.17630i	0.585397	+	0.810747i	$0.300939\pi$
$59$	−2.65301	+	9.03534i	−0.345393	+	1.17630i	−0.930790	+	0.365554i	$0.880880\pi$
$60$	3.75759	−	3.09164i	0.485103	−	0.399130i
$61$	−3.08448	+	4.79955i	−0.394928	+	0.614519i	−0.980598	−	0.196030i	$-0.937195\pi$
$61$	−3.08448	+	4.79955i	−0.394928	+	0.614519i	0.585670	+	0.810549i	$0.300831\pi$
$62$	−0.0879405	−	1.49802i	−0.0111685	−	0.190248i
$63$	0.583809	−	4.06048i	0.0735530	−	0.511572i
$64$	6.42905	−	4.76101i	0.803632	−	0.595127i
$65$	0.450795	+	3.13535i	0.0559143	+	0.388892i
$66$	−1.06958	−	2.98339i	−0.131656	−	0.367230i
$67$	3.69443	+	3.20124i	0.451346	+	0.391094i	0.850656	−	0.525722i	$-0.176205\pi$
$67$	3.69443	+	3.20124i	0.451346	+	0.391094i	−0.399310	+	0.916816i	$0.630750\pi$
$68$	−4.12727	−	2.01371i	−0.500505	−	0.244198i
$69$	4.05687	+	2.55770i	0.488389	+	0.307911i
$70$	13.7528	+	3.17610i	1.64378	+	0.379616i
$71$	−3.08398	+	3.55910i	−0.366001	+	0.422387i	−0.908641	−	0.417578i	$-0.862879\pi$
$71$	−3.08398	+	3.55910i	−0.366001	+	0.422387i	0.542641	+	0.839965i	$0.317425\pi$
$72$	−0.309621	+	2.81143i	−0.0364892	+	0.331330i
$73$	−1.00106	−	6.96251i	−0.117165	−	0.814900i	−0.960653	−	0.277752i	$-0.910411\pi$
$73$	−1.00106	−	6.96251i	−0.117165	−	0.814900i	0.843488	−	0.537148i	$-0.180498\pi$
$74$	−0.506962	−	2.48259i	−0.0589331	−	0.288595i
$75$	−0.910084	−	0.130850i	−0.105087	−	0.0151093i
$76$	1.03434	−	6.08679i	0.118647	−	0.698203i
$77$	4.97028	−	7.73390i	0.566416	−	0.881360i
$78$	−1.45976	−	1.12212i	−0.165286	−	0.127055i
$79$	−2.34151	−	0.687529i	−0.263440	−	0.0773530i	0.147345	−	0.989085i	$-0.452927\pi$
$79$	−2.34151	−	0.687529i	−0.263440	−	0.0773530i	−0.410785	+	0.911732i	$0.634745\pi$
$80$	−9.54968	−	1.87474i	−1.06769	−	0.209603i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	8.20151	−	14.5746i	0.905705	−	1.60950i
$83$	6.16808	+	2.81687i	0.677035	+	0.309191i	0.724095	−	0.689701i	$-0.242258\pi$
$83$	6.16808	+	2.81687i	0.677035	+	0.309191i	−0.0470598	+	0.998892i	$0.514985\pi$
$84$	−7.01300	+	4.25807i	−0.765181	+	0.464593i
$85$	1.57391	+	5.36024i	0.170714	+	0.581399i
$86$	−1.45543	+	3.75508i	−0.156943	+	0.404921i
$87$	2.85955	+	6.26155i	0.306576	+	0.671309i
$88$	−3.24851	+	5.44294i	−0.346293	+	0.580219i
$89$	0.684426	−	0.439854i	0.0725490	−	0.0466244i	−0.503863	−	0.863783i	$-0.668089\pi$
$89$	0.684426	−	0.439854i	0.0725490	−	0.0466244i	0.576413	+	0.817159i	$0.304452\pi$
$90$	2.78057	−	2.02665i	0.293098	−	0.213628i
$91$		−	5.34083i		−	0.559872i
$92$	−1.20494	−	9.51568i	−0.125624	−	0.992078i
$93$		−	1.06108i		−	0.110029i
$94$	−7.99719	−	10.9721i	−0.824848	−	1.13169i
$95$	−6.31840	+	4.06059i	−0.648255	+	0.416608i
$96$	4.73551	−	3.09435i	0.483316	−	0.315815i
$97$	−3.23759	−	7.08933i	−0.328727	−	0.719812i	0.671039	−	0.741422i	$-0.265848\pi$
$97$	−3.23759	−	7.08933i	−0.328727	−	0.719812i	−0.999766	+	0.0216097i	$0.993121\pi$
$98$	−12.9599	−	5.02313i	−1.30915	−	0.507412i
$99$	−0.631376	−	2.15027i	−0.0634557	−	0.216110i
$100$	0.954370	+	1.57184i	0.0954370	+	0.157184i
$101$	−13.1635	−	6.01159i	−1.30982	−	0.598176i	−0.366612	−	0.930374i	$-0.619482\pi$
$101$	−13.1635	−	6.01159i	−1.30982	−	0.598176i	−0.943210	+	0.332198i	$0.892210\pi$
$102$	−2.82996	−	1.59249i	−0.280207	−	0.157680i
$103$	−12.6318	−	14.5779i	−1.24465	−	1.43640i	−0.857578	−	0.514354i	$-0.828032\pi$
$103$	−12.6318	−	14.5779i	−1.24465	−	1.43640i	−0.387073	−	0.922049i	$-0.626514\pi$
$104$	0.121912	+	3.68041i	0.0119544	+	0.360893i
$105$	9.57640	+	2.81189i	0.934561	+	0.274412i
$106$	−7.87041	+	10.2386i	−0.764442	+	0.994463i
$107$	3.82150	−	5.94636i	0.369438	−	0.574857i	−0.605909	−	0.795534i	$-0.707190\pi$
$107$	3.82150	−	5.94636i	0.369438	−	0.574857i	0.975347	+	0.220677i	$0.0708268\pi$
$108$	−0.335062	+	1.97173i	−0.0322413	+	0.189730i
$109$	−18.5801	−	2.67141i	−1.77965	−	0.255875i	−0.827491	−	0.561480i	$-0.810232\pi$
$109$	−18.5801	−	2.67141i	−1.77965	−	0.255875i	−0.952158	+	0.305605i	$0.901141\pi$
$110$	7.55502	−	1.54278i	0.720342	−	0.147099i
$111$	−0.254983	−	1.77345i	−0.0242020	−	0.168328i
$112$	15.4878	+	5.42030i	1.46346	+	0.512170i
$113$	−5.26304	+	6.07387i	−0.495105	+	0.571382i	−0.947223	−	0.320577i	$-0.896123\pi$
$113$	−5.26304	+	6.07387i	−0.495105	+	0.571382i	0.452118	+	0.891958i	$0.350669\pi$
$114$	0.982366	−	4.25375i	0.0920070	−	0.398400i
$115$	−7.56421	+	8.88425i	−0.705366	+	0.828461i
$116$	6.03686	−	12.3731i	0.560509	−	1.14881i
$117$	−0.983936	−	0.852585i	−0.0909649	−	0.0788215i
$118$	12.5361	−	4.49431i	1.15404	−	0.413735i
$119$	−1.34052	−	9.32350i	−0.122885	−	0.854684i
$120$	−6.66335	−	1.71910i	−0.608278	−	0.156931i
$121$	−0.850715	+	5.91685i	−0.0773378	+	0.537896i
$122$	8.05455	−	0.472840i	0.729225	−	0.0428089i
$123$	6.39333	−	9.94822i	0.576468	−	0.897001i
$124$	−1.63877	+	1.34833i	−0.147166	+	0.121084i
$125$	−2.79703	+	9.52581i	−0.250174	+	0.852014i
$126$	−5.12686	+	2.71512i	−0.456737	+	0.241882i
$127$	−5.09184	−	5.87630i	−0.451828	−	0.521437i	0.483440	−	0.875377i	$-0.339387\pi$
$127$	−5.09184	−	5.87630i	−0.451828	−	0.521437i	−0.935268	+	0.353940i	$0.884842\pi$
$128$	−10.7965	−	3.38164i	−0.954285	−	0.298897i
$129$	−1.18298	+	2.59037i	−0.104156	+	0.228069i
$130$	3.20776	−	3.12691i	0.281339	−	0.274248i
$131$	1.47564	+	5.02557i	0.128927	+	0.439086i	0.998502	−	0.0547154i	$-0.0174251\pi$
$131$	1.47564	+	5.02557i	0.128927	+	0.439086i	−0.869575	+	0.493801i	$0.835607\pi$
$132$	−2.51865	+	3.70751i	−0.219220	+	0.322697i
$133$	11.5193	−	5.26069i	0.998850	−	0.456160i
$134$	0.581151	−	6.88881i	0.0502038	−	0.595103i
$135$	2.04676	−	1.31537i	0.176157	−	0.113209i
$136$	1.13658	+	6.39429i	0.0974610	+	0.548306i
$137$	21.9774			1.87765			0.938827	−	0.344389i	$-0.111914\pi$
$137$	21.9774			1.87765			0.938827	+	0.344389i	$0.111914\pi$
$138$	−0.456234	−	6.76697i	−0.0388373	−	0.576043i
$139$			9.92173i			0.841550i	0.907165	+	0.420775i	$0.138242\pi$
$139$			9.92173i			0.841550i	−0.907165	+	0.420775i	$0.861758\pi$
$140$	−7.82614	−	18.3632i	−0.661429	−	1.55198i
$141$	−5.19048	−	8.07654i	−0.437117	−	0.680167i
$142$	6.63647	+	0.559863i	0.556920	+	0.0469827i
$143$	−1.21205	−	2.65403i	−0.101357	−	0.221941i
$144$	3.47098	−	1.98804i	0.289248	−	0.165670i
$145$	−16.0694	+	4.71839i	−1.33449	+	0.391841i
$146$	−7.12331	+	6.94377i	−0.589529	+	0.574670i
$147$	−8.94015	−	4.08283i	−0.737371	−	0.336746i
$148$	−2.41496	+	2.64736i	−0.198509	+	0.217612i
$149$	1.10129	−	0.954277i	0.0902215	−	0.0781774i	−0.608582	−	0.793491i	$-0.708261\pi$
$149$	1.10129	−	0.954277i	0.0902215	−	0.0781774i	0.698804	+	0.715313i	$0.253716\pi$
$150$	0.608546	+	1.14910i	0.0496876	+	0.0938232i
$151$	−17.2379	−	5.06149i	−1.40280	−	0.411899i	−0.509154	−	0.860676i	$-0.670042\pi$
$151$	−17.2379	−	5.06149i	−1.40280	−	0.411899i	−0.893644	+	0.448777i	$0.851860\pi$
$152$	−7.81795	+	3.88812i	−0.634119	+	0.315368i
$153$	−1.93165	−	1.24140i	−0.156165	−	0.100361i
$154$	−12.9790	+	0.761925i	−1.04587	+	0.0613976i
$155$	2.55532	+	0.367400i	0.205248	+	0.0295103i
$156$	−0.0664564	+	2.60302i	−0.00532077	+	0.208408i
$157$	−5.27901	+	0.759007i	−0.421311	+	0.0605753i	−0.349710	−	0.936858i	$-0.613720\pi$
$157$	−5.27901	+	0.759007i	−0.421311	+	0.0605753i	−0.0716007	+	0.997433i	$0.522811\pi$
$158$	1.16470	+	3.24872i	0.0926586	+	0.258454i
$159$	−5.97993	+	6.90121i	−0.474240	+	0.547302i
$160$	5.81221	+	12.4756i	0.459496	+	0.986282i
$161$	14.7559	−	13.0121i	1.16293	−	1.02550i
$162$	−0.318224	+	1.37795i	−0.0250021	+	0.108262i
$163$	−11.4793	−	9.94691i	−0.899132	−	0.779102i	0.0768301	−	0.997044i	$-0.475520\pi$
$163$	−11.4793	−	9.94691i	−0.899132	−	0.779102i	−0.975962	+	0.217942i	$0.930066\pi$
$164$	−23.4885	+	2.76730i	−1.83414	+	0.216090i
$165$	5.39695	−	0.775965i	0.420152	−	0.0604088i
$166$	−1.91866	−	9.39567i	−0.148917	−	0.729246i
$167$	−0.249174	+	1.73304i	−0.0192817	+	0.134107i	−0.997188	−	0.0749344i	$-0.976125\pi$
$167$	−0.249174	+	1.73304i	−0.0192817	+	0.134107i	0.977907	+	0.209041i	$0.0670343\pi$
$168$	10.7081	+	4.46795i	0.826150	+	0.344710i
$169$	9.51035	+	6.11193i	0.731565	+	0.470148i
$170$	4.81495	−	6.26377i	0.369290	−	0.480410i
$171$	0.869715	−	2.96198i	0.0665088	−	0.226508i
$172$	5.50388	−	1.46459i	0.419667	−	0.111674i
$173$	5.76207	−	4.99286i	0.438082	−	0.379600i	−0.407711	−	0.913111i	$-0.633673\pi$
$173$	5.76207	−	4.99286i	0.438082	−	0.379600i	0.845793	+	0.533511i	$0.179128\pi$
$174$	4.77410	−	8.48388i	0.361924	−	0.643161i
$175$	−1.56685	+	3.43092i	−0.118443	+	0.259353i
$176$	8.92649	−	0.821309i	0.672860	−	0.0619085i
$177$	9.03534	−	2.65301i	0.679138	−	0.199413i
$178$	−1.07281	−	0.415810i	−0.0804106	−	0.0311663i
$179$	−11.4817	+	5.24351i	−0.858181	+	0.391918i	−0.795382	−	0.606108i	$-0.792730\pi$
$179$	−11.4817	+	5.24351i	−0.858181	+	0.391918i	−0.0627989	+	0.998026i	$0.520003\pi$
$180$	−4.63237	−	1.48962i	−0.345276	−	0.111030i
$181$	5.89498	+	9.17277i	0.438171	+	0.681807i	0.988171	−	0.153358i	$-0.0490087\pi$
$181$	5.89498	+	9.17277i	0.438171	+	0.681807i	−0.550000	+	0.835165i	$0.685372\pi$
$182$	−6.10383	+	4.44886i	−0.452446	+	0.329771i
$183$	5.70523			0.421743
$184$	−9.87139	+	9.30353i	−0.727728	+	0.685865i
$185$	4.35915			0.320491
$186$	−1.21267	+	0.883869i	−0.0889170	+	0.0648084i
$187$	−2.78203	−	4.32892i	−0.203442	−	0.316562i
$188$	−5.87805	+	18.2793i	−0.428701	+	1.33316i
$189$	−3.73152	+	1.70413i	−0.271428	+	0.123957i
$190$	9.90385	+	3.83862i	0.718501	+	0.278483i
$191$	15.5097	−	4.55406i	1.12224	−	0.329520i	0.332588	−	0.943072i	$-0.392078\pi$
$191$	15.5097	−	4.55406i	1.12224	−	0.329520i	0.789654	+	0.613552i	$0.210260\pi$
$192$	−7.48103	−	2.83447i	−0.539897	−	0.204560i
$193$	0.999226	−	2.18800i	0.0719258	−	0.157496i	−0.870254	−	0.492603i	$-0.836045\pi$
$193$	0.999226	−	2.18800i	0.0719258	−	0.157496i	0.942180	+	0.335108i	$0.108773\pi$
$194$	−5.40523	+	9.60544i	−0.388073	+	0.689630i
$195$	2.39391	−	2.07433i	0.171431	−	0.148546i
$196$	5.05475	+	18.9956i	0.361054	+	1.35683i
$197$	0.190526	−	0.648870i	0.0135744	−	0.0462301i	−0.952427	−	0.304766i	$-0.901422\pi$
$197$	0.190526	−	0.648870i	0.0135744	−	0.0462301i	0.966002	+	0.258536i	$0.0832400\pi$
$198$	−1.93153	+	2.51273i	−0.137268	+	0.178572i
$199$	−17.2058	−	11.0575i	−1.21968	−	0.783843i	−0.237431	−	0.971404i	$-0.576305\pi$
$199$	−17.2058	−	11.0575i	−1.21968	−	0.783843i	−0.982253	+	0.187561i	$0.939942\pi$
$200$	1.00141	−	2.40004i	0.0708104	−	0.169708i
$201$	0.695696	−	4.83867i	0.0490706	−	0.341294i
$202$	4.09469	+	20.0517i	0.288101	+	1.41083i
$203$	27.9507	−	4.01871i	1.96176	−	0.282058i
$204$	0.537329	+	4.56077i	0.0376205	+	0.319318i
$205$	21.7439	+	18.8412i	1.51866	+	1.31592i
$206$	−6.13833	+	26.5796i	−0.427678	+	1.85189i
$207$	−0.0416349	−	4.79565i	−0.00289383	−	0.333321i
$208$	4.10464	−	3.20507i	0.284605	−	0.222231i
$209$	4.53044	−	5.22841i	0.313377	−	0.361656i
$210$	−4.76345	−	13.2868i	−0.328709	−	0.916874i
$211$	27.8611	−	4.00582i	1.91804	−	0.275772i	0.923793	−	0.382893i	$-0.125072\pi$
$211$	27.8611	−	4.00582i	1.91804	−	0.275772i	0.994246	+	0.107121i	$0.0341632\pi$
$212$	18.2573	+	0.466118i	1.25391	+	0.0320131i
$213$	4.66143	+	0.670212i	0.319396	+	0.0459222i
$214$	−9.97913	+	0.585821i	−0.682159	+	0.0400459i
$215$	−5.82858	−	3.74580i	−0.397506	−	0.255461i
$216$	2.53252	−	1.25950i	0.172316	−	0.0856984i
$217$	−4.17648	−	1.22633i	−0.283518	−	0.0832484i
$218$	12.4240	+	23.4597i	0.841456	+	1.58889i
$219$	−5.31602	+	4.60636i	−0.359224	+	0.311269i
$220$	−8.05643	−	7.34920i	−0.543164	−	0.495483i
$221$	−2.71929	−	1.24186i	−0.182920	−	0.0835366i
$222$	−1.81441	+	1.76867i	−0.121775	+	0.118706i
$223$	19.7087	−	5.78699i	1.31979	−	0.387525i	0.455373	−	0.890301i	$-0.349506\pi$
$223$	19.7087	−	5.78699i	1.31979	−	0.387525i	0.864417	+	0.502775i	$0.167688\pi$
$224$	−6.70656	−	22.2155i	−0.448101	−	1.48434i
$225$	0.381950	+	0.836354i	0.0254633	+	0.0557569i
$226$	11.3256	+	0.955449i	0.753370	+	0.0635555i
$227$	−10.1761	−	15.8343i	−0.675409	−	1.05096i	−0.994652	−	0.103284i	$-0.967065\pi$
$227$	−10.1761	−	15.8343i	−0.675409	−	1.05096i	0.319243	−	0.947673i	$-0.396571\pi$
$228$	−5.67974	+	2.42062i	−0.376150	+	0.160310i
$229$		−	23.6800i		−	1.56482i	−0.622763	−	0.782411i	$-0.713990\pi$
$229$		−	23.6800i		−	1.56482i	0.622763	−	0.782411i	$-0.286010\pi$
$230$	16.4544	+	1.24435i	1.08497	+	0.0820501i
$231$	−9.19330			−0.604875
$232$	−19.1693	+	3.40733i	−1.25853	+	0.223702i
$233$	−20.1852	+	12.9722i	−1.32238	+	0.849840i	−0.995457	−	0.0952121i	$-0.969647\pi$
$233$	−20.1852	+	12.9722i	−1.32238	+	0.849840i	−0.326920	+	0.945052i	$0.606011\pi$
$234$	−0.154778	+	1.83469i	−0.0101181	+	0.119938i
$235$	21.2473	−	9.70333i	1.38602	−	0.632976i
$236$	−15.5788	−	10.5832i	−1.01409	−	0.688911i
$237$	0.687529	+	2.34151i	0.0446598	+	0.152097i
$238$	−9.53882	+	9.29840i	−0.618310	+	0.602725i
$239$	−5.57717	+	12.2123i	−0.360757	+	0.789948i	0.639027	+	0.769184i	$0.279337\pi$
$239$	−5.57717	+	12.2123i	−0.360757	+	0.789948i	−0.999784	+	0.0207641i	$0.993390\pi$
$240$	3.58581	+	9.04727i	0.231463	+	0.583999i
$241$	8.15906	+	9.41605i	0.525571	+	0.606541i	0.955017	−	0.296551i	$-0.0958366\pi$
$241$	8.15906	+	9.41605i	0.525571	+	0.606541i	−0.429446	+	0.903093i	$0.641291\pi$
$242$	7.47077	−	3.95643i	0.480240	−	0.254329i
$243$	−0.281733	+	0.959493i	−0.0180732	+	0.0615515i
$244$	−7.24974	−	8.81136i	−0.464117	−	0.564089i
$245$	12.9279	−	20.1162i	0.825934	−	1.28518i
$246$	−16.6950	+	0.980074i	−1.06443	+	0.0624873i
$247$	0.571978	−	3.97819i	0.0363941	−	0.253126i
$248$	2.90603	+	0.749736i	0.184533	+	0.0476083i
$249$	−0.965016	−	6.71183i	−0.0611554	−	0.425345i
$250$	13.2166	−	4.73828i	0.835888	−	0.299675i
$251$	14.4208	+	12.4957i	0.910230	+	0.788719i	0.977918	−	0.208987i	$-0.0670168\pi$
$251$	14.4208	+	12.4957i	0.910230	+	0.788719i	−0.0676879	+	0.997707i	$0.521562\pi$
$252$	7.37363	+	3.59762i	0.464495	+	0.226629i
$253$	4.37971	−	9.81484i	0.275350	−	0.617054i
$254$	−2.47434	+	10.7142i	−0.155254	+	0.672266i
$255$	3.65840	−	4.22202i	0.229098	−	0.264393i
$256$	5.12863	+	15.1558i	0.320540	+	0.947235i
$257$	−2.99698	−	20.8444i	−0.186946	−	1.30024i	−0.839858	−	0.542806i	$-0.817362\pi$
$257$	−2.99698	−	20.8444i	−0.186946	−	1.30024i	0.652912	−	0.757434i	$-0.273547\pi$
$258$	3.94584	−	0.805766i	0.245657	−	0.0501648i
$259$	−7.27510	−	1.04600i	−0.452053	−	0.0649954i
$260$	−6.24565	−	1.06134i	−0.387339	−	0.0658214i
$261$	3.72156	−	5.79086i	0.230359	−	0.358445i
$262$	4.51433	−	5.87270i	0.278896	−	0.362816i
$263$	25.9453	+	7.61823i	1.59986	+	0.469760i	0.955506	−	0.294971i	$-0.0953099\pi$
$263$	25.9453	+	7.61823i	1.59986	+	0.469760i	0.644350	+	0.764731i	$0.277128\pi$
$264$	6.33517	−	0.209849i	0.389903	−	0.0129153i
$265$	−14.5491	−	16.7906i	−0.893745	−	1.03144i
$266$	−15.6077	−	8.78285i	−0.956968	−	0.538511i
$267$	−0.740058	−	0.337973i	−0.0452908	−	0.0206836i
$268$	−8.35704	+	5.07413i	−0.510488	+	0.309952i
$269$	4.72890	+	16.1052i	0.288326	+	0.981949i	0.968524	+	0.248920i	$0.0800757\pi$
$269$	4.72890	+	16.1052i	0.288326	+	0.981949i	−0.680198	+	0.733029i	$0.738106\pi$
$270$	−3.20822	−	1.24347i	−0.195246	−	0.0756752i
$271$	7.91541	+	17.3323i	0.480827	+	1.05286i	0.982235	+	0.187653i	$0.0600882\pi$
$271$	7.91541	+	17.3323i	0.480827	+	1.05286i	−0.501408	+	0.865211i	$0.667185\pi$
$272$	6.36102	−	6.62532i	0.385693	−	0.401719i
$273$	−4.49300	+	2.88747i	−0.271928	+	0.174758i
$274$	−18.3069	−	25.1171i	−1.10596	−	1.51738i
$275$			2.06052i			0.124254i
$276$	−7.35366	+	6.15822i	−0.442638	+	0.370681i
$277$			32.0448i			1.92539i	0.270592	+	0.962694i	$0.412781\pi$
$277$			32.0448i			1.92539i	−0.270592	+	0.962694i	$0.587219\pi$
$278$	11.3392	−	8.26470i	0.680077	−	0.495684i
$279$	−0.892638	+	0.573664i	−0.0534408	+	0.0343443i
$280$	−14.4675	+	24.2406i	−0.864600	+	1.44865i
$281$	−3.01755	−	6.60751i	−0.180012	−	0.394171i	0.798019	−	0.602633i	$-0.205882\pi$
$281$	−3.01755	−	6.60751i	−0.180012	−	0.394171i	−0.978031	+	0.208462i	$0.933154\pi$
$282$	−4.90674	+	12.6597i	−0.292192	+	0.753871i
$283$	−2.45945	−	8.37613i	−0.146199	−	0.497909i	0.853533	−	0.521039i	$-0.174455\pi$
$283$	−2.45945	−	8.37613i	−0.146199	−	0.497909i	−0.999732	+	0.0231292i	$0.992637\pi$
$284$	−4.88826	−	8.05092i	−0.290065	−	0.477734i
$285$	6.83197	+	3.12006i	0.404691	+	0.184816i
$286$	−2.02356	+	3.59599i	−0.119655	+	0.212635i
$287$	−31.7679	−	36.6621i	−1.87520	−	2.16409i
$288$	−5.16334	−	2.31083i	−0.304253	−	0.136167i
$289$	11.2526	+	3.30406i	0.661918	+	0.194357i
$290$	18.7781	+	14.4347i	1.10269	+	0.847632i
$291$	−4.21355	+	6.55641i	−0.247003	+	0.384344i
$292$	13.8694	+	2.35686i	0.811645	+	0.137925i
$293$	0.907285	+	0.130448i	0.0530042	+	0.00762085i	0.168766	−	0.985656i	$-0.446022\pi$
$293$	0.907285	+	0.130448i	0.0530042	+	0.00762085i	−0.115762	+	0.993277i	$0.536931\pi$
$294$	2.78094	+	13.6183i	0.162188	+	0.794235i
$295$	3.26057	+	22.6777i	0.189838	+	1.32035i
$296$	5.03720	+	0.554743i	0.292781	+	0.0322438i
$297$	−1.46758	+	1.69367i	−0.0851573	+	0.0982768i
$298$	−2.00797	−	0.463723i	−0.116319	−	0.0268627i
$299$	−0.942214	−	6.17235i	−0.0544896	−	0.356956i
$300$	0.806343	−	1.65267i	0.0465542	−	0.0954168i
$301$	8.82864	+	7.65006i	0.508874	+	0.440942i
$302$	8.57438	+	23.9166i	0.493400	+	1.37625i
$303$	2.05948	+	14.3240i	0.118314	+	0.822892i
$304$	10.9558	+	5.69606i	0.628361	+	0.326691i
$305$	−1.97544	+	13.7395i	−0.113113	+	0.786721i
$306$	0.190301	+	3.24168i	0.0108788	+	0.185314i
$307$	−14.5006	+	22.5634i	−0.827593	+	1.28776i	0.127614	+	0.991824i	$0.459268\pi$
$307$	−14.5006	+	22.5634i	−0.827593	+	1.28776i	−0.955208	+	0.295937i	$0.904368\pi$
$308$	11.6821	+	14.1985i	0.665649	+	0.809032i
$309$	−5.43443	+	18.5080i	−0.309154	+	1.05288i
$310$	−1.70867	−	3.22642i	−0.0970459	−	0.183248i
$311$	14.2318	+	16.4244i	0.807012	+	0.931341i	0.998744	−	0.0501060i	$-0.0159559\pi$
$311$	14.2318	+	16.4244i	0.807012	+	0.931341i	−0.191732	+	0.981447i	$0.561410\pi$
$312$	3.03024	−	2.09234i	0.171554	−	0.118455i
$313$	−11.1768	+	24.4738i	−0.631751	+	1.38334i	0.274905	+	0.961471i	$0.411354\pi$
$313$	−11.1768	+	24.4738i	−0.631751	+	1.38334i	−0.906656	+	0.421871i	$0.861374\pi$
$314$	5.26479	+	5.40092i	0.297109	+	0.304792i
$315$	−2.81189	−	9.57640i	−0.158432	−	0.539569i
$316$	2.74265	−	4.03724i	0.154286	−	0.227112i
$317$	20.7335	−	9.46867i	1.16451	−	0.531814i	0.263094	−	0.964770i	$-0.415257\pi$
$317$	20.7335	−	9.46867i	1.16451	−	0.531814i	0.901415	+	0.432957i	$0.142530\pi$
$318$	12.8683	+	1.08559i	0.721621	+	0.0608771i
$319$	12.9776	−	8.34020i	0.726606	−	0.466961i
$320$	9.41635	−	17.0346i	0.526390	−	0.952262i
$321$	−7.06846			−0.394523
$322$	−27.1625	−	6.02504i	−1.51371	−	0.335762i
$323$		−	7.08830i		−	0.394403i
$324$	1.83988	−	0.784128i	0.102215	−	0.0435627i
$325$	0.647176	+	1.00702i	0.0358988	+	0.0558597i
$326$	−1.80576	+	21.4050i	−0.100012	+	1.18551i
$327$	7.79782	+	17.0748i	0.431220	+	0.944240i
$328$	22.7283	+	24.5389i	1.25496	+	1.35494i
$329$	−37.7886	+	11.0957i	−2.08335	+	0.611727i
$330$	−5.38242	−	5.52159i	−0.296293	−	0.303954i
$331$	−24.0392	−	10.9784i	−1.32132	−	0.603425i	−0.375107	−	0.926982i	$-0.622394\pi$
$331$	−24.0392	−	10.9784i	−1.32132	−	0.603425i	−0.946209	+	0.323557i	$0.895121\pi$
$332$	−9.13972	+	10.0193i	−0.501607	+	0.549878i
$333$	−1.35407	+	1.17330i	−0.0742023	+	0.0642967i
$334$	2.18819	−	1.15884i	0.119732	−	0.0634087i
$335$	11.4117	+	3.35079i	0.623489	+	0.183073i
$336$	−3.81351	−	15.9596i	−0.208044	−	0.870670i
$337$	−7.07045	−	4.54390i	−0.385152	−	0.247522i	0.333709	−	0.942676i	$-0.391700\pi$
$337$	−7.07045	−	4.54390i	−0.385152	−	0.247522i	−0.718861	+	0.695154i	$0.755336\pi$
$338$	−0.936936	−	15.9602i	−0.0509626	−	0.868118i
$339$	7.95508	+	1.14377i	0.432060	+	0.0621209i
$340$	−11.1694	−	0.285161i	−0.605747	−	0.0154650i
$341$	−2.35373	+	0.338415i	−0.127462	+	0.0183262i
$342$	−4.10959	+	1.47333i	−0.222221	+	0.0796687i
$343$	−7.59796	+	8.76851i	−0.410251	+	0.473455i
$344$	−6.25850	−	5.07018i	−0.337436	−	0.273366i
$345$	11.5634	+	1.56023i	0.622554	+	0.0840000i
$346$	−10.5059	−	2.42624i	−0.564800	−	0.130435i
$347$	14.3738	+	12.4549i	0.771624	+	0.668616i	0.948911	−	0.315543i	$-0.102187\pi$
$347$	14.3738	+	12.4549i	0.771624	+	0.668616i	−0.177288	+	0.984159i	$0.556732\pi$
$348$	−13.6727	+	1.61085i	−0.732931	+	0.0863505i
$349$	−4.55198	+	0.654475i	−0.243662	+	0.0350333i	−0.263064	−	0.964779i	$-0.584733\pi$
$349$	−4.55198	+	0.654475i	−0.243662	+	0.0350333i	0.0194019	+	0.999812i	$0.493824\pi$
$350$	5.22623	−	1.06723i	0.279354	−	0.0570458i
$351$	−0.185284	+	1.28868i	−0.00988975	+	0.0687847i
$352$	−8.37431	−	9.51759i	−0.446352	−	0.507289i
$353$	−28.1268	−	18.0760i	−1.49704	−	0.962087i	−0.995276	−	0.0970809i	$-0.969049\pi$
$353$	−28.1268	−	18.0760i	−1.49704	−	0.962087i	−0.501761	−	0.865006i	$-0.667314\pi$
$354$	−10.5584	−	8.11619i	−0.561171	−	0.431371i
$355$	−3.22804	+	10.9937i	−0.171327	+	0.583486i
$356$	0.418428	+	1.57244i	0.0221766	+	0.0833391i
$357$	−7.11869	+	6.16838i	−0.376761	+	0.326465i
$358$	15.5567	+	8.75417i	0.822198	+	0.462672i
$359$	−7.07317	+	15.4881i	−0.373308	+	0.817430i	0.625985	+	0.779835i	$0.284697\pi$
$359$	−7.07317	+	15.4881i	−0.373308	+	0.817430i	−0.999293	+	0.0375952i	$0.988030\pi$
$360$	2.15628	+	6.53498i	0.113646	+	0.344424i
$361$	−9.08667	+	2.66809i	−0.478246	+	0.140426i
$362$	5.57274	−	14.3780i	0.292897	−	0.755689i
$363$	5.43751	−	2.48323i	0.285395	−	0.130336i
$364$	10.1688	+	3.26997i	0.532992	+	0.171393i
$365$	−9.25248	−	14.3971i	−0.484297	−	0.753581i
$366$	−4.75240	−	6.52028i	−0.248412	−	0.340821i
$367$	−1.61286			−0.0841908			−0.0420954	−	0.999114i	$-0.513403\pi$
$367$	−1.61286			−0.0841908			−0.0420954	+	0.999114i	$0.513403\pi$
$368$	18.8554	+	3.53187i	0.982905	+	0.184112i
$369$	−11.8255			−0.615610
$370$	−3.63113	−	4.98190i	−0.188773	−	0.258997i
$371$	20.2524	+	31.5134i	1.05145	+	1.63609i
$372$	2.02028	+	0.649656i	0.104746	+	0.0336831i
$373$	5.73583	−	2.61947i	0.296990	−	0.135631i	−0.261347	−	0.965245i	$-0.584167\pi$
$373$	5.73583	−	2.61947i	0.296990	−	0.135631i	0.558337	+	0.829614i	$0.311439\pi$
$374$	−2.62995	+	6.78542i	−0.135992	+	0.350866i
$375$	9.52581	−	2.79703i	0.491910	−	0.144438i
$376$	25.7871	−	8.50871i	1.32987	−	0.438803i
$377$	3.72295	−	8.15212i	0.191742	−	0.419856i
$378$	5.05590	+	2.84509i	0.260047	+	0.146335i
$379$	10.8649	−	9.41451i	0.558094	−	0.483591i	−0.329539	−	0.944142i	$-0.606893\pi$
$379$	10.8649	−	9.41451i	0.558094	−	0.483591i	0.887633	+	0.460551i	$0.152348\pi$
$380$	−3.86279	−	14.5162i	−0.198157	−	0.744668i
$381$	−2.19060	+	7.46049i	−0.112228	+	0.382213i
$382$	−18.1240	−	13.9319i	−0.927307	−	0.712819i
$383$	13.7064	+	8.80859i	0.700366	+	0.450098i	0.841757	−	0.539856i	$-0.181521\pi$
$383$	13.7064	+	8.80859i	0.700366	+	0.450098i	−0.141391	+	0.989954i	$0.545158\pi$
$384$	2.99222	+	10.9108i	0.152696	+	0.556792i
$385$	3.18319	−	22.1396i	0.162230	−	1.12834i
$386$	−3.33292	+	0.680604i	−0.169641	+	0.0346418i
$387$	2.81872	−	0.405271i	0.143284	−	0.0206011i
$388$	15.4802	−	1.82380i	0.785887	−	0.0925895i
$389$	−18.5954	−	16.1130i	−0.942824	−	0.816961i	0.0404340	−	0.999182i	$-0.487126\pi$
$389$	−18.5954	−	16.1130i	−0.942824	−	0.816961i	−0.983258	+	0.182221i	$0.941671\pi$
$390$	−4.36477	−	1.00800i	−0.221019	−	0.0510423i
$391$	−3.19405	−	10.5386i	−0.161530	−	0.532959i
$392$	17.4988	−	21.6000i	0.883821	−	1.09096i
$393$	3.42999	−	3.95842i	0.173020	−	0.199676i
$394$	−0.900274	+	0.322758i	−0.0453551	+	0.0162603i
$395$	−5.87694	+	0.844976i	−0.295701	+	0.0425153i
$396$	4.48064	+	0.114393i	0.225161	+	0.00574847i
$397$	−21.1958	−	3.04749i	−1.06379	−	0.152949i	−0.411871	−	0.911242i	$-0.635125\pi$
$397$	−21.1958	−	3.04749i	−1.06379	−	0.152949i	−0.651914	+	0.758293i	$0.726034\pi$
$398$	1.69507	+	28.8745i	0.0849661	+	1.44735i
$399$	−10.6534	−	6.84651i	−0.533336	−	0.342754i
$400$	−3.57707	+	0.854731i	−0.178853	+	0.0427366i
$401$	0.535562	+	0.157255i	0.0267447	+	0.00785296i	0.295078	−	0.955473i	$-0.404655\pi$
$401$	0.535562	+	0.157255i	0.0267447	+	0.00785296i	−0.268333	+	0.963326i	$0.586473\pi$
$402$	−6.10943	+	3.23548i	−0.304711	+	0.161371i
$403$	−1.04404	+	0.904662i	−0.0520071	+	0.0450644i
$404$	19.5054	−	21.3825i	0.970432	−	1.06382i
$405$	−2.21313	−	1.01070i	−0.109971	−	0.0502221i
$406$	−27.8755	−	28.5962i	−1.38344	−	1.41921i
$407$	−3.85261	+	1.13123i	−0.190967	+	0.0560729i
$408$	4.76474	−	4.41316i	0.235890	−	0.218484i
$409$	−0.658877	−	1.44274i	−0.0325794	−	0.0713389i	0.892643	−	0.450765i	$-0.148849\pi$
$409$	−0.658877	−	1.44274i	−0.0325794	−	0.0713389i	−0.925222	+	0.379426i	$0.876121\pi$
$410$	3.42042	−	40.5447i	0.168922	−	2.00236i
$411$	−11.8819	−	18.4885i	−0.586089	−	0.911973i
$412$	35.4900	−	15.1253i	1.74847	−	0.745170i
$413$		−	38.6298i		−	1.90085i
$414$	−5.44608	+	4.04231i	−0.267660	+	0.198669i
$415$	16.4978			0.809843
$416$	−7.08206	−	2.02124i	−0.347227	−	0.0990995i
$417$	8.34669	−	5.36409i	0.408739	−	0.262681i
$418$	−9.74914	−	0.822453i	−0.476846	−	0.0402275i
$419$	2.37247	−	1.08347i	0.115903	−	0.0529309i	−0.356620	−	0.934250i	$-0.616071\pi$
$419$	2.37247	−	1.08347i	0.115903	−	0.0529309i	0.472522	+	0.881319i	$0.343344\pi$
$420$	−11.2170	+	16.5117i	−0.547334	+	0.805688i
$421$	0.00305699	+	0.0104111i	0.000148988	+	0.000507408i	0.959567	−	0.281479i	$-0.0908249\pi$
$421$	0.00305699	+	0.0104111i	0.000148988	+	0.000507408i	−0.959418	+	0.281986i	$0.909007\pi$
$422$	−27.7861	−	28.5046i	−1.35261	−	1.38758i
$423$	−3.98823	+	8.73301i	−0.193915	+	0.424614i
$424$	−14.6754	−	21.2538i	−0.712701	−	1.03217i
$425$	1.38253	+	1.59553i	0.0670627	+	0.0773944i
$426$	−3.11696	−	5.88564i	−0.151017	−	0.285160i
$427$	6.59372	−	22.4562i	0.319093	−	1.08673i
$428$	8.98202	+	10.9168i	0.434162	+	0.527682i
$429$	−1.57743	+	2.45452i	−0.0761588	+	0.118505i
$430$	0.574217	+	9.78146i	0.0276912	+	0.471704i
$431$	1.19476	−	8.30976i	0.0575497	−	0.400267i	−0.940603	−	0.339509i	$-0.889739\pi$
$431$	1.19476	−	8.30976i	0.0575497	−	0.400267i	0.998153	−	0.0607580i	$-0.0193518\pi$
$432$	−3.54900	−	1.84516i	−0.170751	−	0.0887754i
$433$	3.32399	+	23.1189i	0.159741	+	1.11102i	0.899111	+	0.437722i	$0.144214\pi$
$433$	3.32399	+	23.1189i	0.159741	+	1.11102i	−0.739370	+	0.673299i	$0.764876\pi$
$434$	2.07744	+	5.79465i	0.0997205	+	0.278152i
$435$	12.6571	+	10.9674i	0.606862	+	0.525849i
$436$	16.4621	−	33.7405i	0.788393	−	1.61588i
$437$	12.3847	−	8.11193i	0.592439	−	0.388046i
$438$	9.69262	+	2.23842i	0.463131	+	0.106956i
$439$	21.5360	−	24.8539i	1.02786	−	1.18621i	0.0455439	−	0.998962i	$-0.485498\pi$
$439$	21.5360	−	24.8539i	1.02786	−	1.18621i	0.982313	−	0.187248i	$-0.0599566\pi$
$440$	−1.68819	+	15.3292i	−0.0804814	+	0.730790i
$441$	1.39871	+	9.72828i	0.0666055	+	0.463251i
$442$	0.845870	+	4.14223i	0.0402339	+	0.197026i
$443$	10.3828	+	1.49282i	0.493302	+	0.0709262i	0.384477	−	0.923135i	$-0.374382\pi$
$443$	10.3828	+	1.49282i	0.493302	+	0.0709262i	0.108826	+	0.994061i	$0.465291\pi$
$444$	3.53273	+	0.600325i	0.167656	+	0.0284902i
$445$	1.07016	−	1.66520i	0.0507305	−	0.0789382i
$446$	−23.0308	−	17.7038i	−1.09054	−	0.838297i
$447$	−1.39819	−	0.410547i	−0.0661323	−	0.0194182i
$448$	−19.8027	+	26.1699i	−0.935590	+	1.23641i
$449$	3.93150	+	4.53719i	0.185539	+	0.214123i	0.840897	−	0.541195i	$-0.182028\pi$
$449$	3.93150	+	4.53719i	0.185539	+	0.214123i	−0.655358	+	0.755318i	$0.727482\pi$
$450$	0.637675	−	1.13319i	0.0300603	−	0.0534191i
$451$	−24.1066	−	11.0091i	−1.13513	−	0.518399i
$452$	−8.34219	−	13.7395i	−0.392383	−	0.646251i
$453$	5.06149	+	17.2379i	0.237810	+	0.809906i
$454$	−9.61979	+	24.8196i	−0.451479	+	1.16484i
$455$	−5.39798	−	11.8199i	−0.253061	−	0.554127i
$456$	7.49760	+	4.47480i	0.351107	+	0.209552i
$457$	13.8460	−	8.89831i	0.647691	−	0.416246i	−0.175131	−	0.984545i	$-0.556035\pi$
$457$	13.8460	−	8.89831i	0.647691	−	0.416246i	0.822822	+	0.568300i	$0.192399\pi$
$458$	−27.0630	+	19.7252i	−1.26457	+	0.921699i
$459$			2.29616i			0.107175i
$460$	−12.2842	−	19.8416i	−0.572753	−	0.925118i
$461$		−	7.86717i		−	0.366411i	−0.983075	−	0.183205i	$-0.941353\pi$
$461$		−	7.86717i		−	0.366411i	0.983075	−	0.183205i	$-0.0586473\pi$
$462$	7.65792	+	10.5067i	0.356279	+	0.488814i
$463$	1.90156	−	1.22206i	0.0883729	−	0.0567938i	−0.495708	−	0.868489i	$-0.665091\pi$
$463$	1.90156	−	1.22206i	0.0883729	−	0.0567938i	0.584081	+	0.811695i	$0.301455\pi$
$464$	19.8619	+	19.0696i	0.922067	+	0.885283i
$465$	−1.07244	−	2.34831i	−0.0497330	−	0.108900i
$466$	31.6395	+	12.2631i	1.46567	+	0.568078i
$467$	11.0057	+	37.4819i	0.509282	+	1.73446i	0.665179	+	0.746684i	$0.268355\pi$
$467$	11.0057	+	37.4819i	0.509282	+	1.73446i	−0.155897	+	0.987773i	$0.549827\pi$
$468$	2.22573	−	1.35139i	0.102884	−	0.0624681i
$469$	−18.2413	−	8.33051i	−0.842304	−	0.384667i
$470$	−28.7883	−	16.2000i	−1.32791	−	0.747248i
$471$	3.49256	+	4.03063i	0.160929	+	0.185722i
$472$	0.881776	+	26.6201i	0.0405871	+	1.22529i
$473$	6.12334	+	1.79798i	0.281552	+	0.0826710i
$474$	2.10331	−	2.73620i	0.0966083	−	0.125678i
$475$	−1.53452	+	2.38776i	−0.0704088	+	0.109558i
$476$	18.5725	+	3.15607i	0.851269	+	0.144658i
$477$	9.03866	+	1.29956i	0.413852	+	0.0595029i
$478$	18.6027	−	3.79879i	0.850867	−	0.173753i
$479$	0.325156	+	2.26151i	0.0148568	+	0.103331i	0.995901	−	0.0904553i	$-0.0288322\pi$
$479$	0.325156	+	2.26151i	0.0148568	+	0.103331i	−0.981044	+	0.193786i	$0.937923\pi$
$480$	7.35282	−	11.6344i	0.335609	−	0.531033i
$481$	−1.52756	+	1.76290i	−0.0696509	+	0.0803815i
$482$	3.96483	−	17.1681i	0.180593	−	0.781987i
$483$	−18.9241	−	5.37861i	−0.861077	−	0.244735i
$484$	−10.7447	−	5.24239i	−0.488396	−	0.238290i
$485$	−14.3304	−	12.4173i	−0.650709	−	0.563842i
$486$	1.33125	−	0.477266i	0.0603866	−	0.0216492i
$487$	−0.562600	−	3.91297i	−0.0254938	−	0.177314i	0.973096	−	0.230400i	$-0.0740033\pi$
$487$	−0.562600	−	3.91297i	−0.0254938	−	0.177314i	−0.998590	+	0.0530860i	$0.983094\pi$
$488$	−4.03119	+	15.6252i	−0.182483	+	0.707320i
$489$	−2.16167	+	15.0347i	−0.0977541	+	0.679895i
$490$	−33.7588	+	1.98180i	−1.52507	+	0.0895286i
$491$	−3.70299	+	5.76196i	−0.167113	+	0.260034i	−0.914702	−	0.404128i	$-0.867575\pi$
$491$	−3.70299	+	5.76196i	−0.167113	+	0.260034i	0.747589	+	0.664162i	$0.231211\pi$
$492$	15.0268	+	18.2637i	0.677462	+	0.823390i
$493$	4.45302	−	15.1656i	0.200554	−	0.683025i
$494$	−5.02297	+	2.66010i	−0.225994	+	0.119684i
$495$	−3.57060	−	4.12069i	−0.160486	−	0.185211i
$496$	−1.56385	−	3.94571i	−0.0702190	−	0.177168i
$497$	8.02536	−	17.5731i	0.359987	−	0.788261i
$498$	−6.86684	+	6.69376i	−0.307710	+	0.299955i
$499$	1.33589	+	4.54963i	0.0598027	+	0.203669i	0.983975	−	0.178307i	$-0.0570619\pi$
$499$	1.33589	+	4.54963i	0.0598027	+	0.203669i	−0.924172	+	0.381976i	$0.875244\pi$
$500$	−16.4244	−	11.1577i	−0.734523	−	0.498989i
$501$	1.59264	−	0.727336i	0.0711541	−	0.0324950i
$502$	2.26846	−	26.8897i	0.101246	−	1.20014i
$503$	23.4995	−	15.1022i	1.04779	−	0.673373i	0.100888	−	0.994898i	$-0.467832\pi$
$503$	23.4995	−	15.1022i	1.04779	−	0.673373i	0.946901	+	0.321525i	$0.104195\pi$
$504$	−2.03057	−	11.4238i	−0.0904489	−	0.508857i
$505$	−35.2085			−1.56676
$506$	−14.8652	+	3.17026i	−0.660840	+	0.140935i
$507$		−	11.3050i		−	0.502071i
$508$	14.3059	−	6.09695i	0.634720	−	0.270508i
$509$	18.6903	+	29.0827i	0.828433	+	1.28907i	0.954850	+	0.297089i	$0.0960159\pi$
$509$	18.6903	+	29.0827i	0.828433	+	1.28907i	−0.126417	+	0.991977i	$0.540348\pi$
$510$	−7.87258	−	0.664144i	−0.348604	−	0.0294088i
$511$	11.9870	+	26.2479i	0.530275	+	1.16114i
$512$	13.0488	−	18.4859i	0.576682	−	0.816969i
$513$	−2.96198	+	0.869715i	−0.130775	+	0.0383989i
$514$	−21.3258	+	20.7883i	−0.940642	+	0.916933i
$515$	−42.6897	−	19.4957i	−1.88113	−	0.859085i
$516$	−4.20772	−	3.83834i	−0.185234	−	0.168974i
$517$	−16.2603	+	14.0896i	−0.715126	+	0.619660i
$518$	4.86465	+	9.18573i	0.213740	+	0.403598i
$519$	−7.31547	−	2.14802i	−0.321114	−	0.0942874i
$520$	3.98959	+	8.02198i	0.174955	+	0.351787i
$521$	14.9872	+	9.63170i	0.656602	+	0.421972i	0.826073	−	0.563563i	$-0.190570\pi$
$521$	14.9872	+	9.63170i	0.656602	+	0.421972i	−0.169471	+	0.985535i	$0.554206\pi$
$522$	−9.71816	+	0.570501i	−0.425352	+	0.0249702i
$523$	7.89225	+	1.13473i	0.345104	+	0.0496185i	0.312688	−	0.949856i	$-0.398771\pi$
$523$	7.89225	+	1.13473i	0.345104	+	0.0496185i	0.0324164	+	0.999474i	$0.489680\pi$
$524$	−10.4721	−	0.267357i	−0.457474	−	0.0116795i
$525$	3.73338	−	0.536778i	0.162938	−	0.0234269i
$526$	−12.9056	−	35.9978i	−0.562710	−	1.56958i
$527$	−1.59551	+	1.84132i	−0.0695014	+	0.0802089i
$528$	−5.51696	−	7.06541i	−0.240095	−	0.307483i
$529$	14.7577	−	17.6411i	0.641640	−	0.767006i
$530$	−7.07003	+	30.6140i	−0.307102	+	1.32979i
$531$	−7.11673	−	6.16668i	−0.308840	−	0.267611i
$532$	2.96346	+	25.1534i	0.128482	+	1.09054i
$533$	−15.2393	+	2.19108i	−0.660086	+	0.0949061i
$534$	0.230204	+	1.12731i	0.00996191	+	0.0487835i
$535$	2.44746	−	17.0224i	0.105813	−	0.735944i
$536$	12.7603	+	5.32423i	0.551163	+	0.229972i
$537$	10.6186	+	6.82415i	0.458226	+	0.294484i
$538$	14.4668	−	18.8199i	0.623709	−	0.811383i
$539$	−6.20537	+	21.1335i	−0.267284	+	0.910286i
$540$	1.25130	+	4.70234i	0.0538473	+	0.202357i
$541$	−5.51427	+	4.77814i	−0.237077	+	0.205428i	−0.765294	−	0.643681i	$-0.777406\pi$
$541$	−5.51427	+	4.77814i	−0.237077	+	0.205428i	0.528217	+	0.849110i	$0.322861\pi$
$542$	13.2150	−	23.4839i	0.567632	−	1.00872i
$543$	4.52956	−	9.91835i	0.194382	−	0.425637i
$544$	−12.8705	−	1.75093i	−0.551817	−	0.0750705i
$545$	−43.8201	+	12.8667i	−1.87705	+	0.551150i
$546$	7.04259	+	2.72963i	0.301395	+	0.116817i
$547$	−21.1330	+	9.65112i	−0.903583	+	0.412652i	−0.812345	−	0.583177i	$-0.801809\pi$
$547$	−21.1330	+	9.65112i	−0.903583	+	0.412652i	−0.0912373	+	0.995829i	$0.529082\pi$
$548$	−13.4558	+	41.8445i	−0.574805	+	1.78751i
$549$	−3.08448	−	4.79955i	−0.131643	−	0.204840i
$550$	2.35488	−	1.71639i	0.100412	−	0.0731870i
$551$	21.2499			0.905275
$552$	13.1635	+	3.27447i	0.560276	+	0.139371i
$553$	10.0109			0.425708
$554$	36.6228	−	26.6930i	1.55595	−	1.13408i
$555$	−2.35674	−	3.66715i	−0.100038	−	0.155662i
$556$	−18.8908	−	6.07466i	−0.801148	−	0.257623i
$557$	−25.2183	+	11.5168i	−1.06854	+	0.487984i	−0.870478	−	0.492207i	$-0.836190\pi$
$557$	−25.2183	+	11.5168i	−1.06854	+	0.487984i	−0.198057	+	0.980190i	$0.563463\pi$
$558$	1.39917	+	0.542305i	0.0592318	+	0.0229576i
$559$	3.55735	−	1.04453i	0.150460	−	0.0441789i
$560$	39.7549	−	3.65777i	1.67995	−	0.154569i
$561$	−2.13764	+	4.68079i	−0.0902514	+	0.197623i
$562$	−5.03787	+	8.95262i	−0.212510	+	0.377643i
$563$	−19.9744	+	17.3079i	−0.841822	+	0.729443i	−0.964805	−	0.262966i	$-0.915299\pi$
$563$	−19.9744	+	17.3079i	−0.841822	+	0.729443i	0.122983	+	0.992409i	$0.460754\pi$
$564$	18.5555	−	4.93763i	0.781327	−	0.207912i
$565$	−5.50890	+	18.7616i	−0.231761	+	0.789306i
$566$	−7.52405	+	9.78804i	−0.316259	+	0.411422i
$567$	3.45102	+	2.21783i	0.144929	+	0.0931403i
$568$	−5.12920	+	12.2929i	−0.215217	+	0.515800i
$569$	4.01178	−	27.9025i	0.168183	−	1.16974i	−0.714455	−	0.699681i	$-0.753325\pi$
$569$	4.01178	−	27.9025i	0.168183	−	1.16974i	0.882638	−	0.470054i	$-0.155766\pi$
$570$	−2.12517	−	10.4070i	−0.0890136	−	0.435900i
$571$	8.60671	−	1.23746i	0.360180	−	0.0517860i	0.0401503	−	0.999194i	$-0.487216\pi$
$571$	8.60671	−	1.23746i	0.360180	−	0.0517860i	0.320029	+	0.947408i	$0.396307\pi$
$572$	5.79531	−	0.682776i	0.242314	−	0.0285483i
$573$	−12.2163	−	10.5855i	−0.510343	−	0.442214i
$574$	−15.4373	+	66.8453i	−0.644342	+	2.79007i
$575$	−1.20552	+	4.24150i	−0.0502737	+	0.176883i
$576$	1.66005	+	7.82587i	0.0691685	+	0.326078i
$577$	20.8755	−	24.0916i	0.869058	−	1.00295i	−0.130875	−	0.991399i	$-0.541779\pi$
$577$	20.8755	−	24.0916i	0.869058	−	1.00295i	0.999933	−	0.0115476i	$-0.00367579\pi$
$578$	−5.59722	−	15.6124i	−0.232814	−	0.649390i
$579$	−2.38088	+	0.342320i	−0.0989462	+	0.0142263i
$580$	0.854879	−	33.4846i	0.0354969	−	1.39037i
$581$	−27.5335	−	3.95872i	−1.14228	−	0.164235i
$582$	11.0029	−	0.645921i	0.456085	−	0.0267743i
$583$	17.2157	+	11.0639i	0.713003	+	0.458219i
$584$	−8.85949	−	17.8140i	−0.366608	−	0.737149i
$585$	−3.03928	−	0.892414i	−0.125659	−	0.0368968i
$586$	−0.606675	−	1.14556i	−0.0250615	−	0.0473227i
$587$	13.7801	−	11.9405i	0.568764	−	0.492837i	−0.322348	−	0.946621i	$-0.604472\pi$
$587$	13.7801	−	11.9405i	0.568764	−	0.492837i	0.891111	+	0.453785i	$0.149926\pi$
$588$	13.2473	−	14.5221i	0.546310	−	0.598882i
$589$	−2.97957	−	1.36073i	−0.122771	−	0.0560677i
$590$	23.2015	−	22.6167i	0.955189	−	0.931114i
$591$	−0.648870	+	0.190526i	−0.0266910	+	0.00783717i
$592$	−3.56194	−	6.21891i	−0.146395	−	0.255595i
$593$	−1.22548	−	2.68342i	−0.0503243	−	0.110195i	0.882800	−	0.469750i	$-0.155656\pi$
$593$	−1.22548	−	2.68342i	−0.0503243	−	0.110195i	−0.933124	+	0.359555i	$0.882929\pi$
$594$	3.15810	+	0.266423i	0.129579	+	0.0109315i
$595$	−12.3900	−	19.2792i	−0.507940	−	0.790371i
$596$	1.14265	+	2.68111i	0.0468047	+	0.109822i
$597$			20.4525i			0.837066i
$598$	−6.26928	+	6.21832i	−0.256370	+	0.254286i
$599$	28.8565			1.17905			0.589523	−	0.807751i	$-0.299316\pi$
$599$	28.8565			1.17905			0.589523	+	0.807751i	$0.299316\pi$
$600$	−2.56044	+	0.455117i	−0.104530	+	0.0185801i
$601$	−4.36646	+	2.80615i	−0.178112	+	0.114465i	−0.626659	−	0.779294i	$-0.715578\pi$
$601$	−4.36646	+	2.80615i	−0.178112	+	0.114465i	0.448547	+	0.893759i	$0.351942\pi$
$602$	1.38879	−	16.4623i	0.0566027	−	0.670954i
$603$	−4.44667	+	2.03073i	−0.181082	+	0.0826976i
$604$	20.1910	−	29.7216i	0.821561	−	1.20936i
$605$	4.09743	+	13.9546i	0.166584	+	0.567334i
$606$	14.6548	−	14.2854i	0.595310	−	0.580306i
$607$	−17.3865	+	38.0711i	−0.705697	+	1.54526i	0.127228	+	0.991873i	$0.459392\pi$
$607$	−17.3865	+	38.0711i	−0.705697	+	1.54526i	−0.832925	+	0.553386i	$0.813335\pi$
$608$	−2.61630	−	17.2657i	−0.106105	−	0.700219i
$609$	−18.4921	−	21.3410i	−0.749336	−	0.864780i
$610$	17.3478	−	9.18720i	0.702393	−	0.371979i
$611$	−3.52147	+	11.9930i	−0.142463	+	0.485186i
$612$	3.54626	−	2.91777i	0.143349	−	0.117944i
$613$	−25.5732	+	39.7927i	−1.03289	+	1.60721i	−0.267598	+	0.963531i	$0.586230\pi$
$613$	−25.5732	+	39.7927i	−1.03289	+	1.60721i	−0.765294	+	0.643681i	$0.777407\pi$
$614$	37.8656	−	2.22289i	1.52813	−	0.0897085i
$615$	4.09458	−	28.4784i	0.165109	−	1.14836i
$616$	6.49578	−	25.1782i	0.261722	−	1.01446i
$617$	0.823648	+	5.72860i	0.0331588	+	0.230625i	0.999661	−	0.0260334i	$-0.00828763\pi$
$617$	0.823648	+	5.72860i	0.0331588	+	0.230625i	−0.966502	+	0.256658i	$0.917379\pi$
$618$	25.6788	−	9.20615i	1.03295	−	0.370326i
$619$	−24.0942	−	20.8778i	−0.968429	−	0.839149i	0.0185774	−	0.999827i	$-0.494086\pi$
$619$	−24.0942	−	20.8778i	−0.968429	−	0.839149i	−0.987007	+	0.160679i	$0.948632\pi$
$620$	−2.26404	+	4.64034i	−0.0909260	+	0.186361i
$621$	−4.01185	+	2.62775i	−0.160990	+	0.105448i
$622$	6.91583	−	29.9463i	0.277300	−	1.20074i
$623$	−2.18559	+	2.52231i	−0.0875639	+	0.101054i
$624$	−4.91541	−	1.72025i	−0.196774	−	0.0688652i
$625$	4.09181	+	28.4592i	0.163673	+	1.13837i
$626$	37.2803	−	7.61289i	1.49002	−	0.304272i
$627$	−6.84776	−	0.984559i	−0.273473	−	0.0393195i
$628$	1.78698	−	10.5158i	0.0713084	−	0.419627i
$629$	−2.22419	+	3.46091i	−0.0886844	+	0.137996i
$630$	−8.60222	+	11.1906i	−0.342721	+	0.445846i
$631$	11.0818	+	3.25390i	0.441158	+	0.129536i	0.494766	−	0.869027i	$-0.335254\pi$
$631$	11.0818	+	3.25390i	0.441158	+	0.129536i	−0.0536080	+	0.998562i	$0.517072\pi$
$632$	−6.89859	+	0.228512i	−0.274411	+	0.00908973i
$633$	−18.4328	−	21.2726i	−0.732637	−	0.845508i
$634$	−28.0921	−	15.8082i	−1.11568	−	0.627823i
$635$	−17.2081	−	7.85866i	−0.682881	−	0.311861i
$636$	−9.47850	−	15.6110i	−0.375847	−	0.619016i
$637$	3.60500	+	12.2775i	0.142835	+	0.486452i
$638$	−20.3419	−	7.88429i	−0.805343	−	0.312142i
$639$	−1.95634	−	4.28379i	−0.0773916	−	0.169464i
$640$	−27.3118	+	3.42805i	−1.07960	+	0.135506i
$641$	−27.2542	+	17.5152i	−1.07647	+	0.691808i	−0.953740	−	0.300631i	$-0.902803\pi$
$641$	−27.2542	+	17.5152i	−1.07647	+	0.691808i	−0.122734	+	0.992440i	$0.539166\pi$
$642$	5.88795	+	8.07826i	0.232379	+	0.318823i
$643$		−	41.6326i		−	1.64183i	−0.571052	−	0.820914i	$-0.693465\pi$
$643$		−	41.6326i		−	1.64183i	0.571052	−	0.820914i	$-0.306535\pi$
$644$	15.7403	+	36.0617i	0.620254	+	1.42103i
$645$			6.92845i			0.272807i
$646$	−8.10093	+	5.90447i	−0.318727	+	0.232308i
$647$	−3.74006	+	2.40359i	−0.147037	+	0.0944950i	−0.612091	−	0.790787i	$-0.709671\pi$
$647$	−3.74006	+	2.40359i	−0.147037	+	0.0944950i	0.465054	+	0.885282i	$0.346035\pi$
$648$	−2.42874	−	1.44955i	−0.0954101	−	0.0569437i
$649$	−8.76670	−	19.1964i	−0.344123	−	0.753524i
$650$	0.611798	−	1.57847i	0.0239967	−	0.0619128i
$651$	1.22633	+	4.17648i	0.0480635	+	0.163689i
$652$	25.9670	−	15.7664i	1.01695	−	0.617458i
$653$	33.8128	+	15.4418i	1.32320	+	0.604285i	0.946695	−	0.322131i	$-0.104399\pi$
$653$	33.8128	+	15.4418i	1.32320	+	0.604285i	0.376503	+	0.926415i	$0.377126\pi$
$654$	13.0187	−	23.1350i	0.509070	−	0.904649i
$655$	8.34512	+	9.63079i	0.326071	+	0.376306i
$656$	9.11214	−	46.4159i	0.355769	−	1.81224i
$657$	6.74918	+	1.98174i	0.263310	+	0.0773149i
$658$	44.1583	+	33.9444i	1.72147	+	1.32329i
$659$	−9.24320	+	14.3827i	−0.360064	+	0.560271i	−0.973273	−	0.229650i	$-0.926242\pi$
$659$	−9.24320	+	14.3827i	−0.360064	+	0.560271i	0.613209	+	0.789920i	$0.289878\pi$
$660$	−1.82691	+	10.7508i	−0.0711123	+	0.418474i
$661$	14.2935	+	2.05509i	0.555952	+	0.0799338i	0.414564	−	0.910020i	$-0.363934\pi$
$661$	14.2935	+	2.05509i	0.555952	+	0.0799338i	0.141388	+	0.989954i	$0.454843\pi$
$662$	7.47770	+	36.6183i	0.290629	+	1.42321i
$663$	0.425442	+	2.95902i	0.0165228	+	0.114919i
$664$	19.0639	+	2.09949i	0.739822	+	0.0814761i
$665$	20.1767	−	23.2851i	0.782418	−	0.902959i
$666$	2.46884	+	0.570158i	0.0956658	+	0.0220932i
$667$	31.5934	−	9.57537i	1.22330	−	0.370760i
$668$	−3.14712	−	1.53549i	−0.121766	−	0.0594100i
$669$	−15.5236	−	13.4513i	−0.600178	−	0.520057i
$670$	−5.67637	−	15.8332i	−0.219297	−	0.611689i
$671$	−1.81960	−	12.6556i	−0.0702447	−	0.488563i
$672$	−15.0630	+	17.6525i	−0.581069	+	0.680961i
$673$	−1.26448	+	8.79468i	−0.0487423	+	0.339010i	0.950829	+	0.309718i	$0.100235\pi$
$673$	−1.26448	+	8.79468i	−0.0487423	+	0.339010i	−0.999571	+	0.0292925i	$0.990675\pi$
$674$	0.696564	+	11.8656i	0.0268306	+	0.457044i
$675$	0.497088	−	0.773484i	0.0191329	−	0.0297714i
$676$	−17.4598	+	14.3654i	−0.671530	+	0.552516i
$677$	−9.48002	+	32.2860i	−0.364347	+	1.24085i	0.549742	+	0.835335i	$0.314726\pi$
$677$	−9.48002	+	32.2860i	−0.364347	+	1.24085i	−0.914088	+	0.405516i	$0.867092\pi$
$678$	−5.31933	−	10.0443i	−0.204287	−	0.385748i
$679$	20.9367	+	24.1623i	0.803477	+	0.927262i
$680$	8.97811	+	13.0026i	0.344295	+	0.498628i
$681$	−7.81903	+	17.1213i	−0.299626	+	0.656089i
$682$	2.34739	+	2.40809i	0.0898863	+	0.0922105i
$683$	−5.32573	−	18.1378i	−0.203784	−	0.694023i	−0.996436	−	0.0843496i	$-0.973119\pi$
$683$	−5.32573	−	18.1378i	−0.203784	−	0.694023i	0.792653	−	0.609674i	$-0.208699\pi$
$684$	5.10706	+	3.46942i	0.195273	+	0.132656i
$685$	48.6387	−	22.2126i	1.85839	−	0.848698i
$686$	16.3502	+	1.37933i	0.624253	+	0.0526630i
$687$	−19.9209	+	12.8024i	−0.760031	+	0.488442i
$688$	−0.581249	+	11.3760i	−0.0221599	+	0.433706i
$689$	11.8887			0.452925
$690$	−7.84908	−	14.5150i	−0.298810	−	0.552578i
$691$			23.7045i			0.901763i	0.892584	+	0.450882i	$0.148890\pi$
$691$			23.7045i			0.901763i	−0.892584	+	0.450882i	$0.851110\pi$
$692$	5.97843	+	14.0278i	0.227266	+	0.533256i
$693$	4.97028	+	7.73390i	0.188805	+	0.293787i
$694$	2.26106	−	26.8020i	0.0858287	−	1.01739i
$695$	10.0279	+	21.9580i	0.380380	+	0.832916i
$696$	13.2301	+	14.2841i	0.501487	+	0.541438i
$697$	−26.0533	+	7.64993i	−0.986838	+	0.289762i
$698$	4.53972	+	4.65710i	0.171831	+	0.176274i
$699$	21.8259	+	9.96755i	0.825531	+	0.377007i
$700$	−5.57309	−	5.08386i	−0.210643	−	0.192152i
$701$	12.0369	−	10.4300i	0.454627	−	0.393936i	−0.397223	−	0.917722i	$-0.630026\pi$
$701$	12.0369	−	10.4300i	0.454627	−	0.393936i	0.851850	+	0.523786i	$0.175481\pi$
$702$	1.62712	−	0.861704i	0.0614118	−	0.0325229i
$703$	−5.30693	−	1.55826i	−0.200155	−	0.0587708i
$704$	−3.90156	+	17.4987i	−0.147046	+	0.659508i
$705$	−19.6501	−	12.6284i	−0.740067	−	0.475612i
$706$	2.77098	+	47.2021i	0.104287	+	1.77647i
$707$	58.7604	+	8.44846i	2.20991	+	0.317737i
$708$	−0.480674	+	18.8274i	−0.0180648	+	0.707578i
$709$	1.69645	−	0.243912i	0.0637114	−	0.00916031i	−0.110385	−	0.993889i	$-0.535209\pi$
$709$	1.69645	−	0.243912i	0.0637114	−	0.00916031i	0.174097	+	0.984729i	$0.444299\pi$
$710$	15.2532	−	5.46844i	0.572442	−	0.205227i
$711$	1.59810	−	1.84430i	0.0599333	−	0.0691667i
$712$	1.44853	−	1.78803i	0.0542860	−	0.0670092i
$713$	−5.04307	−	0.680451i	−0.188864	−	0.0254831i
$714$	12.9794	+	2.99747i	0.485741	+	0.112178i
$715$	−5.36486	−	4.64868i	−0.200634	−	0.173851i
$716$	−2.95378	−	25.0713i	−0.110388	−	0.936958i
$717$	13.2889	−	1.91065i	0.496283	−	0.0713547i
$718$	23.5926	−	4.81776i	0.880468	−	0.179797i
$719$	0.0922866	−	0.641867i	0.00344171	−	0.0239376i	−0.988028	−	0.154273i	$-0.950696\pi$
$719$	0.0922866	−	0.641867i	0.00344171	−	0.0239376i	0.991470	+	0.130336i	$0.0416055\pi$
$720$	5.67241	−	7.90790i	0.211398	−	0.294710i
$721$	66.5678	+	42.7805i	2.47912	+	1.59323i
$722$	10.6183	+	8.16230i	0.395174	+	0.303769i
$723$	3.51017	−	11.9545i	0.130545	−	0.444594i
$724$	−21.0740	+	5.60782i	−0.783210	+	0.208413i
$725$	−4.78320	+	4.14467i	−0.177644	+	0.153929i
$726$	−7.36736	−	4.14581i	−0.273429	−	0.153865i
$727$	−5.79021	+	12.6788i	−0.214747	+	0.470230i	−0.986095	−	0.166184i	$-0.946856\pi$
$727$	−5.79021	+	12.6788i	−0.214747	+	0.470230i	0.771348	+	0.636414i	$0.219583\pi$
$728$	−4.73342	−	14.3454i	−0.175432	−	0.531676i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−8.74670	+	22.5670i	−0.323730	+	0.835241i
$731$	5.94789	−	2.71631i	0.219991	−	0.100466i
$732$	−3.49308	+	10.8627i	−0.129108	+	0.401495i
$733$	−4.40096	−	6.84804i	−0.162553	−	0.252938i	0.750416	−	0.660966i	$-0.229853\pi$
$733$	−4.40096	−	6.84804i	−0.162553	−	0.252938i	−0.912970	+	0.408028i	$0.866217\pi$
$734$	1.34350	+	1.84328i	0.0495894	+	0.0680366i
$735$	−23.9122			−0.882015
$736$	−11.6699	−	24.4911i	−0.430158	−	0.902754i
$737$	−10.9552			−0.403540
$738$	9.85049	+	13.5149i	0.362602	+	0.497489i
$739$	5.65993	+	8.80703i	0.208204	+	0.323972i	0.929613	−	0.368538i	$-0.120141\pi$
$739$	5.65993	+	8.80703i	0.208204	+	0.323972i	−0.721409	+	0.692509i	$0.756505\pi$
$740$	−2.66893	+	8.29974i	−0.0981118	+	0.305105i
$741$	−3.65590	+	1.66959i	−0.134303	+	0.0613341i
$742$	19.1453	−	49.3959i	0.702847	−	1.81338i
$743$	−37.3111	+	10.9555i	−1.36881	+	0.401919i	−0.881861	−	0.471510i	$-0.843709\pi$
$743$	−37.3111	+	10.9555i	−1.36881	+	0.401919i	−0.486951	+	0.873430i	$0.661891\pi$
$744$	−0.940403	−	2.85005i	−0.0344768	−	0.104488i
$745$	1.47281	−	3.22501i	0.0539597	−	0.118155i
$746$	−7.77157	−	4.37327i	−0.284537	−	0.160117i
$747$	−5.12463	+	4.44051i	−0.187500	+	0.162470i
$748$	9.94551	−	2.64651i	0.363644	−	0.0967660i
$749$	−8.16925	+	27.8219i	−0.298498	+	1.01659i
$750$	−11.1315	−	8.55677i	−0.406465	−	0.312449i
$751$	30.4800	+	19.5883i	1.11223	+	0.714788i	0.961778	−	0.273829i	$-0.0882903\pi$
$751$	30.4800	+	19.5883i	1.11223	+	0.714788i	0.150453	+	0.988617i	$0.451927\pi$
$752$	−31.2046	−	22.3834i	−1.13792	−	0.816237i
$753$	2.71557	−	18.8872i	0.0989608	−	0.688287i
$754$	−12.4179	+	2.53582i	−0.452234	+	0.0923491i
$755$	−43.2652	+	6.22060i	−1.57458	+	0.226391i
$756$	−0.959972	−	8.14811i	−0.0349139	−	0.296344i
$757$	−8.24608	−	7.14527i	−0.299709	−	0.259699i	0.492003	−	0.870593i	$-0.336265\pi$
$757$	−8.24608	−	7.14527i	−0.299709	−	0.259699i	−0.791712	+	0.610894i	$0.790810\pi$
$758$	−19.8098	−	4.57491i	−0.719526	−	0.166168i
$759$	−10.6246	+	1.62185i	−0.385649	+	0.0588696i
$760$	−13.3724	+	16.5065i	−0.485067	+	0.598754i
$761$	−12.2086	+	14.0895i	−0.442562	+	0.510744i	−0.932577	−	0.360970i	$-0.882446\pi$
$761$	−12.2086	+	14.0895i	−0.442562	+	0.510744i	0.490016	+	0.871714i	$0.336991\pi$
$762$	10.3510	−	3.71096i	0.374979	−	0.134434i
$763$	76.2198	−	10.9588i	2.75934	−	0.396734i
$764$	−0.825105	+	32.3184i	−0.0298513	+	1.16924i
$765$	−5.52967	−	0.795046i	−0.199926	−	0.0287450i
$766$	−1.35032	−	23.0020i	−0.0487892	−	0.831096i
$767$	−10.3138	−	6.62827i	−0.372409	−	0.239333i
$768$	9.97709	−	12.5083i	0.360017	−	0.451355i
$769$	−25.3870	−	7.45431i	−0.915480	−	0.268809i	−0.210134	−	0.977673i	$-0.567390\pi$
$769$	−25.3870	−	7.45431i	−0.915480	−	0.268809i	−0.705346	+	0.708863i	$0.749208\pi$
$770$	−27.9540	+	14.8041i	−1.00739	+	0.533502i
$771$	−15.9152	+	13.7906i	−0.573171	+	0.496655i
$772$	3.55412	+	3.24213i	0.127916	+	0.116687i
$773$	−35.4260	−	16.1785i	−1.27419	−	0.581901i	−0.340584	−	0.940214i	$-0.610625\pi$
$773$	−35.4260	−	16.1785i	−1.27419	−	0.581901i	−0.933602	+	0.358313i	$0.883352\pi$
$774$	−2.81113	−	2.88382i	−0.101044	−	0.103657i
$775$	0.936084	−	0.274859i	0.0336251	−	0.00987323i
$776$	−14.9792	−	16.1725i	−0.537721	−	0.580558i
$777$	3.05326	+	6.68571i	0.109535	+	0.239849i
$778$	−2.92514	+	34.6739i	−0.104871	+	1.24312i
$779$	−19.7364	−	30.7104i	−0.707129	−	1.10031i
$780$	2.48380	+	5.82798i	0.0889342	+	0.208675i
$781$		−	10.5539i		−	0.377649i
$782$	−9.38353	+	12.4289i	−0.335554	+	0.444456i
$783$	−6.88361			−0.246000
$784$	−39.2620	−	2.00607i	−1.40222	−	0.0716453i
$785$	−10.9160	+	7.01527i	−0.389608	+	0.250386i
$786$	−7.38106	−	0.622678i	−0.263274	−	0.0222102i
$787$	−17.1701	+	7.84132i	−0.612048	+	0.279513i	−0.697224	−	0.716853i	$-0.745582\pi$
$787$	−17.1701	+	7.84132i	−0.612048	+	0.279513i	0.0851764	+	0.996366i	$0.472855\pi$
$788$	1.11879	+	0.760033i	0.0398551	+	0.0270751i
$789$	−7.61823	−	25.9453i	−0.271216	−	0.923677i
$790$	5.86111	+	6.01266i	0.208529	+	0.213921i
$791$	13.6959	−	29.9898i	0.486969	−	1.06631i
$792$	−3.60159	−	5.21603i	−0.127977	−	0.185344i
$793$	−4.86420	−	5.61358i	−0.172733	−	0.199344i
$794$	14.1730	+	26.7623i	0.502981	+	0.949759i
$795$	−6.25929	+	21.3172i	−0.221994	+	0.756042i
$796$	31.5876	−	25.9894i	1.11959	−	0.921170i
$797$	1.18938	−	1.85071i	0.0421299	−	0.0655555i	−0.819550	−	0.573008i	$-0.805776\pi$
$797$	1.18938	−	1.85071i	0.0421299	−	0.0655555i	0.861680	+	0.507453i	$0.169413\pi$
$798$	1.04954	+	17.8784i	0.0371535	+	0.632888i
$799$	−3.13726	+	21.8201i	−0.110988	+	0.771940i
$800$	3.95650	+	3.37611i	0.139883	+	0.119363i
$801$	0.115784	+	0.805298i	0.00409104	+	0.0284538i
$802$	−0.266397	−	0.743065i	−0.00940680	−	0.0262385i
$803$	11.9135	+	10.3231i	0.420417	+	0.364294i
$804$	8.78679	+	4.28711i	0.309886	+	0.151195i
$805$	19.5054	−	43.7112i	0.687475	−	1.54062i
$806$	1.90357	+	0.439613i	0.0670504	+	0.0154847i
$807$	10.9919	−	12.6853i	0.386933	−	0.446544i
$808$	−40.6850	−	4.48061i	−1.43129	−	0.157627i
$809$	−1.92635	−	13.3980i	−0.0677267	−	0.471050i	−0.995255	−	0.0972975i	$-0.968980\pi$
$809$	−1.92635	−	13.3980i	−0.0677267	−	0.471050i	0.927529	−	0.373752i	$-0.121929\pi$
$810$	0.688420	+	3.37120i	0.0241886	+	0.118452i
$811$	49.8506	+	7.16744i	1.75049	+	0.251683i	0.941710	−	0.336425i	$-0.109218\pi$
$811$	49.8506	+	7.16744i	1.75049	+	0.251683i	0.808783	+	0.588108i	$0.200127\pi$
$812$	−9.46153	+	55.6781i	−0.332035	+	1.95392i
$813$	10.3015	−	16.0294i	0.361289	−	0.562177i
$814$	4.50202	+	3.46069i	0.157796	+	0.121297i
$815$	−35.4586	−	10.4116i	−1.24206	−	0.364702i
$816$	−9.01260	−	1.76931i	−0.315504	−	0.0619381i
$817$	5.75684	+	6.64375i	0.201407	+	0.232435i
$818$	−1.10001	+	1.95479i	−0.0384610	+	0.0683477i
$819$	4.85819	+	2.21866i	0.169759	+	0.0775263i
$820$	−49.1861	+	29.8642i	−1.71765	+	1.04290i
$821$	11.9765	+	40.7882i	0.417983	+	1.42352i	0.852439	+	0.522826i	$0.175122\pi$
$821$	11.9765	+	40.7882i	0.417983	+	1.42352i	−0.434456	+	0.900693i	$0.643059\pi$
$822$	−11.2324	+	28.9801i	−0.391773	+	1.01080i
$823$	13.4981	+	29.5567i	0.470514	+	1.03028i	0.984964	+	0.172761i	$0.0552688\pi$
$823$	13.4981	+	29.5567i	0.470514	+	1.03028i	−0.514450	+	0.857520i	$0.672004\pi$
$824$	−46.8489	−	27.9609i	−1.63206	−	0.974063i
$825$	1.73342	−	1.11400i	0.0603498	−	0.0387845i
$826$	−44.1485	+	32.1782i	−1.53612	+	1.11962i
$827$		−	44.5254i		−	1.54830i	−0.633003	−	0.774149i	$-0.718178\pi$
$827$		−	44.5254i		−	1.54830i	0.633003	−	0.774149i	$-0.281822\pi$
$828$	9.15631	+	2.85690i	0.318204	+	0.0992843i
$829$		−	39.7674i		−	1.38118i	−0.723247	−	0.690590i	$-0.757351\pi$
$829$		−	39.7674i		−	1.38118i	0.723247	−	0.690590i	$-0.242649\pi$
$830$	−13.7424	−	18.8546i	−0.477007	−	0.654453i
$831$	26.9578	−	17.3248i	0.935157	−	0.600989i
$832$	3.58928	+	9.77747i	0.124436	+	0.338973i
$833$	9.37482	+	20.5280i	0.324818	+	0.711253i
$834$	−13.0831	−	5.07087i	−0.453031	−	0.175590i
$835$	1.20014	+	4.08729i	0.0415324	+	0.141446i
$836$	7.18098	+	11.8270i	0.248359	+	0.409045i
$837$	0.965193	+	0.440789i	0.0333620	+	0.0152359i
$838$	−3.21449	−	1.80888i	−0.111043	−	0.0624867i
$839$	−26.6451	−	30.7501i	−0.919892	−	1.06161i	−0.997907	−	0.0646599i	$-0.979404\pi$
$839$	−26.6451	−	30.7501i	−0.919892	−	1.06161i	0.0780152	−	0.996952i	$-0.475142\pi$
$840$	28.2142	−	0.934580i	0.973482	−	0.0322461i
$841$	17.6394	+	5.17939i	0.608255	+	0.178600i
$842$	0.00935204	−	0.0121661i	0.000322292	−	0.000419270i
$843$	−3.92718	+	6.11081i	−0.135259	+	0.210467i
$844$	−9.43119	+	55.4996i	−0.324635	+	1.91038i
$845$	27.2249	+	3.91435i	0.936566	+	0.134658i
$846$	13.3028	−	2.71651i	0.457358	−	0.0933956i
$847$	−3.48983	−	24.2723i	−0.119912	−	0.834007i
$848$	−12.0656	+	34.4761i	−0.414336	+	1.18391i
$849$	−5.71677	+	6.59751i	−0.196199	+	0.226426i
$850$	0.671830	−	2.90910i	0.0230436	−	0.0997812i
$851$	−8.59230	+	0.0745967i	−0.294540	+	0.00255714i
$852$	−4.13007	+	8.46492i	−0.141494	+	0.290003i
$853$	13.6091	+	11.7923i	0.465965	+	0.403761i	0.855949	−	0.517061i	$-0.172974\pi$
$853$	13.6091	+	11.7923i	0.465965	+	0.403761i	−0.389983	+	0.920822i	$0.627519\pi$
$854$	−31.1568	+	11.1700i	−1.06616	+	0.382231i
$855$	−1.06888	−	7.43425i	−0.0365551	−	0.254246i
$856$	4.99441	−	19.3587i	0.170705	−	0.661668i
$857$	−3.95440	+	27.5034i	−0.135080	+	0.939500i	0.803713	+	0.595017i	$0.202855\pi$
$857$	−3.95440	+	27.5034i	−0.135080	+	0.939500i	−0.938793	+	0.344483i	$0.888054\pi$
$858$	4.11915	−	0.241813i	0.140626	−	0.00825538i
$859$	−26.5789	+	41.3576i	−0.906861	+	1.41110i	0.00472231	+	0.999989i	$0.498497\pi$
$859$	−26.5789	+	41.3576i	−0.906861	+	1.41110i	−0.911584	+	0.411115i	$0.865140\pi$
$860$	10.7005	−	8.80410i	0.364885	−	0.300217i
$861$	−13.6671	+	46.5458i	−0.465773	+	1.58628i
$862$	−10.4921	+	5.55649i	−0.357363	+	0.189255i
$863$	20.1888	+	23.2991i	0.687233	+	0.793109i	0.986969	−	0.160913i	$-0.0514438\pi$
$863$	20.1888	+	23.2991i	0.687233	+	0.793109i	−0.299735	+	0.954022i	$0.596898\pi$
$864$	0.847515	+	5.59301i	0.0288330	+	0.190278i
$865$	7.70589	−	16.8736i	0.262008	−	0.573718i
$866$	23.6528	−	23.0566i	0.803754	−	0.783495i
$867$	−3.30406	−	11.2526i	−0.112212	−	0.382159i
$868$	4.89198	−	7.20111i	0.166045	−	0.244422i
$869$	4.97474	−	2.27189i	0.168757	−	0.0770686i
$870$	1.99102	−	23.6011i	0.0675020	−	0.800151i
$871$	−5.35408	+	3.44086i	−0.181416	+	0.116589i
$872$	−52.2734	+	9.29157i	−1.77020	+	0.314652i
$873$	7.79362			0.263774
$874$	−19.5871	−	7.39680i	−0.662544	−	0.250201i
$875$		−	40.7268i		−	1.37682i
$876$	−5.51564	−	12.9419i	−0.186356	−	0.437266i
$877$	10.5598	+	16.4314i	0.356580	+	0.554850i	0.972483	−	0.232972i	$-0.0748450\pi$
$877$	10.5598	+	16.4314i	0.356580	+	0.554850i	−0.615903	+	0.787822i	$0.711209\pi$
$878$	−46.3437	−	3.90963i	−1.56402	−	0.131944i
$879$	−0.380776	−	0.833783i	−0.0128432	−	0.0281228i
$880$	18.9254	−	10.8397i	0.637974	−	0.365405i
$881$	−12.2562	+	3.59874i	−0.412921	+	0.121245i	−0.481594	−	0.876395i	$-0.659942\pi$
$881$	−12.2562	+	3.59874i	−0.412921	+	0.121245i	0.0686724	+	0.997639i	$0.478124\pi$
$882$	9.95294	−	9.70208i	0.335133	−	0.326686i
$883$	43.8564	+	20.0285i	1.47588	+	0.674014i	0.980833	−	0.194850i	$-0.0624219\pi$
$883$	43.8564	+	20.0285i	1.47588	+	0.674014i	0.495052	+	0.868864i	$0.335149\pi$
$884$	4.02939	−	4.41714i	0.135523	−	0.148565i
$885$	17.3149	−	15.0035i	0.582035	−	0.504336i
$886$	−6.94268	−	13.1096i	−0.233244	−	0.440426i
$887$	7.79143	+	2.28777i	0.261611	+	0.0768158i	0.409908	−	0.912127i	$-0.365561\pi$
$887$	7.79143	+	2.28777i	0.261611	+	0.0768158i	−0.148297	+	0.988943i	$0.547379\pi$
$888$	−2.25663	−	4.53748i	−0.0757277	−	0.152268i
$889$	26.8332	+	17.2447i	0.899958	+	0.578368i
$890$	−2.79453	+	0.164052i	−0.0936727	+	0.00549902i
$891$	2.21824	+	0.318935i	0.0743138	+	0.0106847i
$892$	−1.04849	+	41.0680i	−0.0351060	+	1.37506i
$893$	−29.3356	+	4.21783i	−0.981679	+	0.141144i
$894$	0.695482	+	1.93992i	0.0232604	+	0.0648806i
$895$	−20.1108	+	23.2091i	−0.672230	+	0.775794i
$896$	46.4040	+	0.832465i	1.55025	+	0.0278107i
$897$	−4.68311	+	4.12967i	−0.156365	+	0.137886i
$898$	1.91048	−	8.27259i	0.0637536	−	0.276060i
$899$	−5.52004	−	4.78315i	−0.184104	−	0.159527i
$900$	−1.82625	+	0.215161i	−0.0608751	+	0.00717202i
$901$	20.7542	−	2.98400i	0.691423	−	0.0994116i
$902$	7.49865	+	36.7209i	0.249678	+	1.22267i
$903$	1.66252	−	11.5631i	0.0553251	−	0.384794i
$904$	−8.75337	+	20.9788i	−0.291133	+	0.697745i
$905$	22.3173	+	14.3424i	0.741851	+	0.476759i
$906$	15.4843	−	20.1435i	0.514431	−	0.669224i
$907$	−12.6031	+	42.9223i	−0.418480	+	1.42521i	0.433269	+	0.901264i	$0.357360\pi$
$907$	−12.6031	+	42.9223i	−0.418480	+	1.42521i	−0.851750	+	0.523949i	$0.824458\pi$
$908$	36.3785	−	9.68036i	1.20726	−	0.321254i
$909$	10.9367	−	9.47668i	0.362747	−	0.314322i
$910$	−9.01207	+	16.0150i	−0.298747	+	0.530893i
$911$	−6.68346	+	14.6347i	−0.221433	+	0.484870i	−0.987446	−	0.157954i	$-0.949510\pi$
$911$	−6.68346	+	14.6347i	−0.221433	+	0.484870i	0.766014	+	0.642824i	$0.222237\pi$
$912$	−1.13135	−	12.2962i	−0.0374626	−	0.407167i
$913$	−14.5807	+	4.28127i	−0.482550	+	0.141689i
$914$	−21.7031	−	8.41190i	−0.717876	−	0.278241i
$915$	12.6264	−	5.76628i	0.417416	−	0.190627i
$916$	45.0863	+	14.4983i	1.48969	+	0.479037i
$917$	−11.6164	−	18.0755i	−0.383608	−	0.596906i
$918$	2.62419	−	1.91267i	0.0866111	−	0.0631277i
$919$	−30.0467			−0.991150			−0.495575	−	0.868565i	$-0.665043\pi$
$919$	−30.0467			−0.991150			−0.495575	+	0.868565i	$0.665043\pi$
$920$	−12.4435	+	30.5669i	−0.410251	+	1.00776i
$921$	26.8211			0.883787
$922$	−8.99108	+	6.55327i	−0.296105	+	0.215820i
$923$	−3.31482	−	5.15796i	−0.109109	−	0.169776i
$924$	5.62868	−	17.5039i	0.185170	−	0.575835i
$925$	1.49848	−	0.684335i	0.0492698	−	0.0225008i
$926$	−2.98062	−	1.15526i	−0.0979492	−	0.0379640i
$927$	18.5080	−	5.43443i	0.607882	−	0.178490i
$928$	5.24908	−	38.5842i	0.172309	−	1.26659i
$929$	−6.97208	+	15.2667i	−0.228746	+	0.500885i	−0.988850	−	0.148918i	$-0.952421\pi$
$929$	−6.97208	+	15.2667i	−0.228746	+	0.500885i	0.760103	+	0.649802i	$0.225148\pi$
$930$	−1.79046	+	3.18176i	−0.0587114	+	0.104334i
$931$	−22.9296	+	19.8686i	−0.751488	+	0.651168i
$932$	−12.3403	−	46.3746i	−0.404221	−	1.51905i
$933$	6.12277	−	20.8523i	0.200451	−	0.682672i
$934$	33.6690	−	43.8000i	1.10168	−	1.43318i
$935$	−10.5322	−	6.76865i	−0.344441	−	0.221359i
$936$	−3.39846	−	1.41800i	−0.111082	−	0.0463488i
$937$	3.12261	−	21.7182i	0.102011	−	0.709503i	−0.873060	−	0.487612i	$-0.837868\pi$
$937$	3.12261	−	21.7182i	0.102011	−	0.709503i	0.975072	−	0.221891i	$-0.0712228\pi$
$938$	5.67418	+	27.7865i	0.185268	+	0.907260i
$939$	26.6313	−	3.82901i	0.869081	−	0.124955i
$940$	5.46609	+	46.3954i	0.178284	+	1.51325i
$941$	−4.03288	−	3.49451i	−0.131468	−	0.113918i	0.586645	−	0.809844i	$-0.300448\pi$
$941$	−4.03288	−	3.49451i	−0.131468	−	0.113918i	−0.718113	+	0.695927i	$0.754994\pi$
$942$	1.69718	−	7.34898i	0.0552972	−	0.239443i
$943$	−43.1816	−	36.7656i	−1.40619	−	1.19725i
$944$	29.6885	−	23.1820i	0.966279	−	0.754509i
$945$	−6.53596	+	7.54290i	−0.212615	+	0.245371i
$946$	−3.04584	−	8.49582i	−0.0990289	−	0.276223i
$947$	−4.70206	+	0.676054i	−0.152796	+	0.0219688i	−0.218289	−	0.975884i	$-0.570047\pi$
$947$	−4.70206	+	0.676054i	−0.152796	+	0.0219688i	0.0654921	+	0.997853i	$0.479138\pi$
$948$	−4.87913	−	0.124567i	−0.158467	−	0.00404574i
$949$	9.06473	+	1.30331i	0.294253	+	0.0423073i
$950$	4.00712	−	0.235237i	0.130008	−	0.00763209i
$951$	−19.1749	−	12.3230i	−0.621790	−	0.399600i
$952$	−11.8637	−	23.8547i	−0.384506	−	0.773137i
$953$	33.0944	+	9.71739i	1.07203	+	0.314777i	0.769687	−	0.638421i	$-0.220412\pi$
$953$	33.0944	+	9.71739i	1.07203	+	0.314777i	0.302346	+	0.953198i	$0.402230\pi$
$954$	−6.04389	−	11.4125i	−0.195678	−	0.369492i
$955$	29.7221	−	25.7544i	0.961785	−	0.833391i
$956$	−19.8373	−	18.0959i	−0.641585	−	0.585264i
$957$	−14.0324	−	6.40840i	−0.453604	−	0.207154i
$958$	2.31374	−	2.25542i	0.0747535	−	0.0728694i
$959$	−86.5044	+	25.4000i	−2.79337	+	0.820208i
$960$	−19.4213	+	1.28805i	−0.626818	+	0.0415717i
$961$	−12.4102	−	27.1744i	−0.400328	−	0.876595i
$962$	3.28720	+	0.277313i	0.105983	+	0.00894093i
$963$	3.82150	+	5.94636i	0.123146	+	0.191619i
$964$	−22.9234	+	9.76962i	−0.738314	+	0.314658i
$965$		−	5.85224i		−	0.188390i
$966$	9.61657	+	26.1079i	0.309408	+	0.840009i
$967$	−46.0017			−1.47931			−0.739657	−	0.672984i	$-0.765012\pi$
$967$	−46.0017			−1.47931			−0.739657	+	0.672984i	$0.765012\pi$
$968$	2.95891	+	16.6466i	0.0951031	+	0.535041i
$969$	−5.96305	+	3.83222i	−0.191561	+	0.123109i
$970$	−2.25424	+	26.7211i	−0.0723792	+	0.857963i
$971$	31.6135	−	14.4374i	1.01453	−	0.463318i	0.162438	−	0.986719i	$-0.448064\pi$
$971$	31.6135	−	14.4374i	1.01453	−	0.463318i	0.852087	+	0.523401i	$0.175337\pi$
$972$	−1.65436	−	1.12387i	−0.0530637	−	0.0360482i
$973$	−11.4669	−	39.0526i	−0.367611	−	1.25197i
$974$	−4.00334	+	3.90243i	−0.128275	+	0.125042i
$975$	0.497274	−	1.08888i	0.0159255	−	0.0348720i
$976$	21.2154	−	8.40854i	0.679087	−	0.269151i
$977$	28.6259	+	33.0360i	0.915824	+	1.05692i	0.998179	+	0.0603137i	$0.0192101\pi$
$977$	28.6259	+	33.0360i	0.915824	+	1.05692i	−0.0823559	+	0.996603i	$0.526244\pi$
$978$	18.9833	−	10.0533i	0.607018	−	0.321469i
$979$	−0.513675	+	1.74942i	−0.0164171	+	0.0559116i
$980$	30.3857	+	36.9308i	0.970634	+	1.17971i
$981$	10.1484	−	15.7913i	0.324015	−	0.504177i
$982$	9.66966	−	0.567654i	0.308571	−	0.0181146i
$983$	−4.22453	+	29.3822i	−0.134742	+	0.937148i	0.804515	+	0.593932i	$0.202425\pi$
$983$	−4.22453	+	29.3822i	−0.134742	+	0.937148i	−0.939257	+	0.343216i	$0.888484\pi$
$984$	8.35561	−	32.3870i	0.266367	−	1.03246i
$985$	−0.234157	−	1.62860i	−0.00746086	−	0.0518914i
$986$	−21.0415	+	7.54360i	−0.670097	+	0.240237i
$987$	29.7644	+	25.7910i	0.947410	+	0.820935i
$988$	7.22420	+	3.52472i	0.229832	+	0.112136i
$989$	11.5528	+	7.28358i	0.367357	+	0.231604i
$990$	−1.73510	+	7.51318i	−0.0551451	+	0.238785i
$991$	15.3301	−	17.6919i	0.486976	−	0.562000i	−0.458079	−	0.888911i	$-0.651462\pi$
$991$	15.3301	−	17.6919i	0.486976	−	0.562000i	0.945055	+	0.326911i	$0.106008\pi$
$992$	−3.20673	+	5.07400i	−0.101814	+	0.161100i
$993$	3.76102	+	26.1584i	0.119352	+	0.830113i
$994$	−26.7686	+	5.46633i	−0.849049	+	0.173381i
$995$	−49.2543	−	7.08170i	−1.56147	−	0.224505i
$996$	13.3700	+	2.27200i	0.423646	+	0.0719912i
$997$	−0.290651	+	0.452261i	−0.00920500	+	0.0143233i	−0.845826	−	0.533460i	$-0.820892\pi$
$997$	−0.290651	+	0.452261i	−0.00920500	+	0.0143233i	0.836621	+	0.547783i	$0.184528\pi$
$998$	4.08681	−	5.31653i	0.129366	−	0.168292i
$999$	1.71911	+	0.504776i	0.0543902	+	0.0159704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.14	yes	480
8.5	even	2	inner	552.2.bb.a.85.41	yes	480
23.13	even	11	inner	552.2.bb.a.13.41	yes	480
184.13	even	22	inner	552.2.bb.a.13.14	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.14	✓	480	184.13	even	22	inner
552.2.bb.a.13.41	yes	480	23.13	even	11	inner
552.2.bb.a.85.14	yes	480	1.1	even	1	trivial
552.2.bb.a.85.41	yes	480	8.5	even	2	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.832989 - 1.14286i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.612258 + 1.90398i) q^{4} +(2.21313 - 1.01070i) q^{5} +(-0.511087 + 1.31863i) q^{6} +(-3.93606 + 1.15573i) q^{7} +(2.68599 - 0.886269i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.832989 - 1.14286i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-0.612258 + 1.90398i) q^{4} +(2.21313 - 1.01070i) q^{5} +(-0.511087 + 1.31863i) q^{6} +(-3.93606 + 1.15573i) q^{7} +(2.68599 - 0.886269i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-2.99860 - 1.68739i) q^{10} +(-1.69367 + 1.46758i) q^{11} +(1.93274 - 0.514305i) q^{12} +(-0.366797 + 1.24920i) q^{13} +(4.59954 + 3.53566i) q^{14} +(-2.04676 - 1.31537i) q^{15} +(-3.25028 - 2.33146i) q^{16} +(-0.326777 + 2.27279i) q^{17} +(1.38562 - 0.282952i) q^{18} +(-3.05560 + 0.439329i) q^{19} +(0.569349 + 4.83256i) q^{20} +(3.10026 + 2.68639i) q^{21} +(3.08804 + 0.713156i) q^{22} +(-4.34498 + 2.03006i) q^{23} +(-2.19773 - 1.78044i) q^{24} +(0.602107 - 0.694868i) q^{25} +(1.73319 - 0.621369i) q^{26} +(0.989821 - 0.142315i) q^{27} +(0.209396 - 8.20179i) q^{28} +(-6.81354 - 0.979640i) q^{29} +(0.201642 + 3.43485i) q^{30} +(0.892638 + 0.573664i) q^{31} +(0.0429204 + 5.65669i) q^{32} +(2.15027 + 0.631376i) q^{33} +(2.86968 - 1.51975i) q^{34} +(-7.54290 + 6.53596i) q^{35} +(-1.47758 - 1.34787i) q^{36} +(1.62977 + 0.744293i) q^{37} +(3.04738 + 3.12617i) q^{38} +(1.24920 - 0.366797i) q^{39} +(5.04868 - 4.67615i) q^{40} +(4.91248 + 10.7568i) q^{41} +(0.487686 - 5.78090i) q^{42} +(-1.53959 - 2.39564i) q^{43} +(-1.75727 - 4.12325i) q^{44} +2.43299i q^{45} +(5.93939 + 3.27469i) q^{46} +9.60060 q^{47} +(-0.204111 + 3.99479i) q^{48} +(8.26810 - 5.31359i) q^{49} +(-1.29569 - 0.109306i) q^{50} +(2.08866 - 0.953858i) q^{51} +(-2.15387 - 1.46320i) q^{52} +(-2.57267 - 8.76172i) q^{53} +(-0.987156 - 1.01268i) q^{54} +(-2.26503 + 4.95972i) q^{55} +(-9.54793 + 6.59269i) q^{56} +(2.02157 + 2.33302i) q^{57} +(4.55602 + 8.60296i) q^{58} +(-2.65301 + 9.03534i) q^{59} +(3.75759 - 3.09164i) q^{60} +(-3.08448 + 4.79955i) q^{61} +(-0.0879405 - 1.49802i) q^{62} +(0.583809 - 4.06048i) q^{63} +(6.42905 - 4.76101i) q^{64} +(0.450795 + 3.13535i) q^{65} +(-1.06958 - 2.98339i) q^{66} +(3.69443 + 3.20124i) q^{67} +(-4.12727 - 2.01371i) q^{68} +(4.05687 + 2.55770i) q^{69} +(13.7528 + 3.17610i) q^{70} +(-3.08398 + 3.55910i) q^{71} +(-0.309621 + 2.81143i) q^{72} +(-1.00106 - 6.96251i) q^{73} +(-0.506962 - 2.48259i) q^{74} +(-0.910084 - 0.130850i) q^{75} +(1.03434 - 6.08679i) q^{76} +(4.97028 - 7.73390i) q^{77} +(-1.45976 - 1.12212i) q^{78} +(-2.34151 - 0.687529i) q^{79} +(-9.54968 - 1.87474i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.20151 - 14.5746i) q^{82} +(6.16808 + 2.81687i) q^{83} +(-7.01300 + 4.25807i) q^{84} +(1.57391 + 5.36024i) q^{85} +(-1.45543 + 3.75508i) q^{86} +(2.85955 + 6.26155i) q^{87} +(-3.24851 + 5.44294i) q^{88} +(0.684426 - 0.439854i) q^{89} +(2.78057 - 2.02665i) q^{90} -5.34083i q^{91} +(-1.20494 - 9.51568i) q^{92} -1.06108i q^{93} +(-7.99719 - 10.9721i) q^{94} +(-6.31840 + 4.06059i) q^{95} +(4.73551 - 3.09435i) q^{96} +(-3.23759 - 7.08933i) q^{97} +(-12.9599 - 5.02313i) q^{98} +(-0.631376 - 2.15027i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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