LMFDB - Embedded newform 375.2.o.a.229.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [375,2,Mod(4,375)] 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("375.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(375, base_ring=CyclotomicField(50)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.o (of order $50$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$24$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			229.22
Character	$\chi$	$=$	375.229
Dual form			375.2.o.a.244.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.567280 + 2.20941i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-2.80706 + 1.54320i) q^{4} +(1.67876 - 1.47708i) q^{5} +(0.971233 + 2.06398i) q^{6} +(2.81586 - 3.87570i) q^{7} +(-1.87894 - 2.00087i) q^{8} +(0.929776 - 0.368125i) q^{9} +(4.21579 + 2.87116i) q^{10} +(-3.75267 + 0.963522i) q^{11} +(-2.46818 + 2.04185i) q^{12} +(1.84854 + 4.66888i) q^{13} +(10.1604 + 4.02278i) q^{14} +(1.37225 - 1.76548i) q^{15} +(-0.0779712 + 0.122863i) q^{16} +(1.82200 - 3.31421i) q^{17} +(1.34078 + 1.84543i) q^{18} +(-0.458606 + 2.40410i) q^{19} +(-2.43298 + 6.73691i) q^{20} +(2.03975 - 4.33469i) q^{21} +(-4.25763 - 7.74460i) q^{22} +(-8.02880 - 0.505129i) q^{23} +(-2.22058 - 1.61335i) q^{24} +(0.636493 - 4.95932i) q^{25} +(-9.26682 + 6.73274i) q^{26} +(0.844328 - 0.535827i) q^{27} +(-1.92333 + 15.2248i) q^{28} +(-4.60335 - 0.581538i) q^{29} +(4.67912 + 2.03034i) q^{30} +(0.301806 + 0.165919i) q^{31} +(-5.53659 - 1.79895i) q^{32} +(-3.50566 + 1.64964i) q^{33} +(8.35602 + 2.14546i) q^{34} +(-0.997539 - 10.6656i) q^{35} +(-2.04185 + 2.46818i) q^{36} +(2.44952 + 1.55451i) q^{37} +(-5.57179 + 0.350547i) q^{38} +(2.69066 + 4.23980i) q^{39} +(-6.10972 - 0.583646i) q^{40} +(0.525788 + 8.35715i) q^{41} +(10.7342 + 2.04766i) q^{42} +(-2.44296 + 0.793767i) q^{43} +(9.04708 - 8.49578i) q^{44} +(1.01713 - 1.99134i) q^{45} +(-3.43854 - 18.0254i) q^{46} +(-2.21434 + 2.35803i) q^{47} +(-0.0535679 + 0.135297i) q^{48} +(-4.92886 - 15.1695i) q^{49} +(11.3182 - 1.40705i) q^{50} +(1.16871 - 3.59691i) q^{51} +(-12.3940 - 10.2532i) q^{52} +(2.20511 + 1.03765i) q^{53} +(1.66283 + 1.56150i) q^{54} +(-4.87665 + 7.16051i) q^{55} +(-13.0456 + 1.64804i) q^{56} +2.44745i q^{57} +(-1.32653 - 10.5006i) q^{58} +(5.62404 + 6.79830i) q^{59} +(-1.12751 + 7.07347i) q^{60} +(0.439937 - 6.99261i) q^{61} +(-0.195375 + 0.760935i) q^{62} +(1.19138 - 4.64012i) q^{63} +(0.815539 - 12.9626i) q^{64} +(9.99955 + 5.10751i) q^{65} +(-5.63341 - 6.80962i) q^{66} +(1.81036 + 14.3304i) q^{67} +12.1149i q^{68} +(-7.98124 + 1.00827i) q^{69} +(22.9988 - 8.25436i) q^{70} +(-6.97546 - 6.55040i) q^{71} +(-2.48356 - 1.16867i) q^{72} +(1.81871 + 1.50457i) q^{73} +(-2.04499 + 6.29384i) q^{74} +(-0.304065 - 4.99075i) q^{75} +(-2.42266 - 7.45617i) q^{76} +(-6.83268 + 17.2574i) q^{77} +(-7.84109 + 8.34991i) q^{78} +(-1.94017 - 10.1707i) q^{79} +(0.0505827 + 0.321427i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-18.1661 + 5.90252i) q^{82} +(4.11441 + 0.784865i) q^{83} +(0.963569 + 15.3155i) q^{84} +(-1.83663 - 8.25501i) q^{85} +(-3.13960 - 4.94721i) q^{86} +(-4.63078 + 0.291344i) q^{87} +(8.97892 + 5.69819i) q^{88} +(3.42210 - 4.13661i) q^{89} +(4.97669 + 1.11760i) q^{90} +(23.3004 + 5.98252i) q^{91} +(23.3169 - 10.9721i) q^{92} +(0.327550 + 0.106428i) q^{93} +(-6.46601 - 3.55472i) q^{94} +(2.78114 + 4.71331i) q^{95} +(-5.77561 - 0.729629i) q^{96} +(0.705339 - 5.58333i) q^{97} +(30.7195 - 19.4952i) q^{98} +(-3.13445 + 2.27731i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 30 q^{8} + 10 q^{11} + 20 q^{16} - 10 q^{17} - 10 q^{19} - 20 q^{20} + 30 q^{22} - 180 q^{23} - 30 q^{24} - 40 q^{25} - 30 q^{28} - 20 q^{29} + 20 q^{30} + 10 q^{31} - 10 q^{33} + 20 q^{34} - 10 q^{35}+ \cdots - 60 q^{98}+O(q^{100}) $ 480 * q + 30 * q^8 + 10 * q^11 + 20 * q^16 - 10 * q^17 - 10 * q^19 - 20 * q^20 + 30 * q^22 - 180 * q^23 - 30 * q^24 - 40 * q^25 - 30 * q^28 - 20 * q^29 + 20 * q^30 + 10 * q^31 - 10 * q^33 + 20 * q^34 - 10 * q^35 + 10 * q^37 - 30 * q^38 - 10 * q^40 + 30 * q^41 + 10 * q^42 - 70 * q^44 + 20 * q^46 - 40 * q^47 + 80 * q^49 - 20 * q^50 + 40 * q^51 - 40 * q^52 - 10 * q^53 - 10 * q^55 - 240 * q^56 - 310 * q^58 - 40 * q^59 - 120 * q^60 + 20 * q^61 + 10 * q^62 + 10 * q^63 - 70 * q^64 + 70 * q^65 - 260 * q^67 - 30 * q^70 - 160 * q^71 + 30 * q^72 + 20 * q^73 + 100 * q^76 + 40 * q^77 - 20 * q^79 - 200 * q^82 - 10 * q^83 - 40 * q^84 + 20 * q^85 + 100 * q^86 - 40 * q^87 + 40 * q^88 - 50 * q^89 - 30 * q^90 - 120 * q^91 - 10 * q^92 - 300 * q^93 - 20 * q^94 - 60 * q^95 + 50 * q^96 - 40 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{21}{50}\right)$	$1$

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 $

$2$	0.567280	+	2.20941i	0.401127	+	1.56229i	0.773248	+	0.634103i	$0.218631\pi$
$2$	0.567280	+	2.20941i	0.401127	+	1.56229i	−0.372121	+	0.928184i	$0.621369\pi$
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$3$	0.982287	−	0.187381i	0.567124	−	0.108185i
$4$	−2.80706	+	1.54320i	−1.40353	+	0.771598i
$5$	1.67876	−	1.47708i	0.750766	−	0.660568i
$5$	1.67876	−	1.47708i	0.750766	−	0.660568i
$6$	0.971233	+	2.06398i	0.396504	+	0.842615i
$7$	2.81586	−	3.87570i	1.06430	−	1.46488i	0.188574	−	0.982059i	$-0.439613\pi$
$7$	2.81586	−	3.87570i	1.06430	−	1.46488i	0.875721	−	0.482818i	$-0.160387\pi$
$8$	−1.87894	−	2.00087i	−0.664305	−	0.707413i
$9$	0.929776	−	0.368125i	0.309925	−	0.122708i
$10$	4.21579	+	2.87116i	1.33315	+	0.907940i
$11$	−3.75267	+	0.963522i	−1.13147	+	0.290513i	−0.767596	−	0.640934i	$-0.778547\pi$
$11$	−3.75267	+	0.963522i	−1.13147	+	0.290513i	−0.363877	+	0.931447i	$0.618547\pi$
$12$	−2.46818	+	2.04185i	−0.712501	+	0.589432i
$13$	1.84854	+	4.66888i	0.512693	+	1.29491i	0.923642	+	0.383256i	$0.125197\pi$
$13$	1.84854	+	4.66888i	0.512693	+	1.29491i	−0.410950	+	0.911658i	$0.634803\pi$
$14$	10.1604	+	4.02278i	2.71548	+	1.07513i
$15$	1.37225	−	1.76548i	0.354314	−	0.455845i
$16$	−0.0779712	+	0.122863i	−0.0194928	+	0.0307157i
$17$	1.82200	−	3.31421i	0.441900	−	0.803814i	−0.557757	−	0.830004i	$-0.688338\pi$
$17$	1.82200	−	3.31421i	0.441900	−	0.803814i	0.999657	+	0.0261909i	$0.00833778\pi$
$18$	1.34078	+	1.84543i	0.316025	+	0.434971i
$19$	−0.458606	+	2.40410i	−0.105211	+	0.551538i	0.890177	+	0.455614i	$0.150580\pi$
$19$	−0.458606	+	2.40410i	−0.105211	+	0.551538i	−0.995389	+	0.0959233i	$0.969420\pi$
$20$	−2.43298	+	6.73691i	−0.544030	+	1.50642i
$21$	2.03975	−	4.33469i	0.445110	−	0.945907i
$22$	−4.25763	−	7.74460i	−0.907729	−	1.65115i
$23$	−8.02880	−	0.505129i	−1.67412	−	0.105327i	−0.802866	−	0.596159i	$-0.796693\pi$
$23$	−8.02880	−	0.505129i	−1.67412	−	0.105327i	−0.871254	+	0.490832i	$0.836693\pi$
$24$	−2.22058	−	1.61335i	−0.453274	−	0.329323i
$25$	0.636493	−	4.95932i	0.127299	−	0.991864i
$26$	−9.26682	+	6.73274i	−1.81737	+	1.32040i
$27$	0.844328	−	0.535827i	0.162491	−	0.103120i
$28$	−1.92333	+	15.2248i	−0.363476	+	2.87721i
$29$	−4.60335	−	0.581538i	−0.854821	−	0.107989i	−0.314304	−	0.949322i	$-0.601771\pi$
$29$	−4.60335	−	0.581538i	−0.854821	−	0.107989i	−0.540517	+	0.841333i	$0.681771\pi$
$30$	4.67912	+	2.03034i	0.854286	+	0.370688i
$31$	0.301806	+	0.165919i	0.0542059	+	0.0298000i	0.508626	−	0.860987i	$-0.330154\pi$
$31$	0.301806	+	0.165919i	0.0542059	+	0.0298000i	−0.454420	+	0.890787i	$0.650154\pi$
$32$	−5.53659	−	1.79895i	−0.978739	−	0.318012i
$33$	−3.50566	+	1.64964i	−0.610256	+	0.287165i
$34$	8.35602	+	2.14546i	1.43305	+	0.367944i
$35$	−0.997539	−	10.6656i	−0.168615	−	1.80282i
$36$	−2.04185	+	2.46818i	−0.340309	+	0.411363i
$37$	2.44952	+	1.55451i	0.402699	+	0.255561i	0.721717	−	0.692188i	$-0.243353\pi$
$37$	2.44952	+	1.55451i	0.402699	+	0.255561i	−0.319018	+	0.947749i	$0.603353\pi$
$38$	−5.57179	+	0.350547i	−0.903863	+	0.0568663i
$39$	2.69066	+	4.23980i	0.430850	+	0.678911i
$40$	−6.10972	−	0.583646i	−0.966032	−	0.0922826i
$41$	0.525788	+	8.35715i	0.0821142	+	1.30517i	0.796167	+	0.605077i	$0.206858\pi$
$41$	0.525788	+	8.35715i	0.0821142	+	1.30517i	−0.714053	+	0.700092i	$0.753142\pi$
$42$	10.7342	+	2.04766i	1.65632	+	0.315961i
$43$	−2.44296	+	0.793767i	−0.372548	+	0.121048i	−0.489306	−	0.872112i	$-0.662750\pi$
$43$	−2.44296	+	0.793767i	−0.372548	+	0.121048i	0.116758	+	0.993160i	$0.462750\pi$
$44$	9.04708	−	8.49578i	1.36390	−	1.28079i
$45$	1.01713	−	1.99134i	0.151624	−	0.296852i
$46$	−3.43854	−	18.0254i	−0.506985	−	2.65771i
$47$	−2.21434	+	2.35803i	−0.322995	+	0.343955i	−0.869889	−	0.493247i	$-0.835810\pi$
$47$	−2.21434	+	2.35803i	−0.322995	+	0.343955i	0.546894	+	0.837202i	$0.315810\pi$
$48$	−0.0535679	+	0.135297i	−0.00773186	+	0.0195284i
$49$	−4.92886	−	15.1695i	−0.704122	−	2.16707i
$50$	11.3182	−	1.40705i	1.60064	−	0.198987i
$51$	1.16871	−	3.59691i	0.163652	−	0.503669i
$52$	−12.3940	−	10.2532i	−1.71873	−	1.42186i
$53$	2.20511	+	1.03765i	0.302895	+	0.142532i	0.571220	−	0.820797i	$-0.306470\pi$
$53$	2.20511	+	1.03765i	0.302895	+	0.142532i	−0.268325	+	0.963328i	$0.586470\pi$
$54$	1.66283	+	1.56150i	0.226282	+	0.212493i
$55$	−4.87665	+	7.16051i	−0.657568	+	0.965523i
$56$	−13.0456	+	1.64804i	−1.74329	+	0.220229i
$57$			2.44745i			0.324172i
$58$	−1.32653	−	10.5006i	−0.174182	−	1.37879i
$59$	5.62404	+	6.79830i	0.732188	+	0.885063i	0.996853	−	0.0792771i	$-0.0252612\pi$
$59$	5.62404	+	6.79830i	0.732188	+	0.885063i	−0.264664	+	0.964341i	$0.585261\pi$
$60$	−1.12751	+	7.07347i	−0.145561	+	0.913182i
$61$	0.439937	−	6.99261i	0.0563282	−	0.895311i	−0.863835	−	0.503776i	$-0.831944\pi$
$61$	0.439937	−	6.99261i	0.0563282	−	0.895311i	0.920163	−	0.391536i	$-0.128056\pi$
$62$	−0.195375	+	0.760935i	−0.0248126	+	0.0966388i
$63$	1.19138	−	4.64012i	0.150100	−	0.584600i
$64$	0.815539	−	12.9626i	0.101942	−	1.62033i
$65$	9.99955	+	5.10751i	1.24029	+	0.633508i
$66$	−5.63341	−	6.80962i	−0.693424	−	0.838206i
$67$	1.81036	+	14.3304i	0.221170	+	1.75074i	0.577507	+	0.816385i	$0.304025\pi$
$67$	1.81036	+	14.3304i	0.221170	+	1.75074i	−0.356337	+	0.934357i	$0.615975\pi$
$68$			12.1149i			1.46915i
$69$	−7.98124	+	1.00827i	−0.960828	+	0.121381i
$70$	22.9988	−	8.25436i	2.74889	−	0.986585i
$71$	−6.97546	−	6.55040i	−0.827835	−	0.777389i	0.149573	−	0.988751i	$-0.452210\pi$
$71$	−6.97546	−	6.55040i	−0.827835	−	0.777389i	−0.977408	+	0.211362i	$0.932210\pi$
$72$	−2.48356	−	1.16867i	−0.292690	−	0.137730i
$73$	1.81871	+	1.50457i	0.212864	+	0.176096i	0.737745	−	0.675079i	$-0.235890\pi$
$73$	1.81871	+	1.50457i	0.212864	+	0.176096i	−0.524882	+	0.851175i	$0.675890\pi$
$74$	−2.04499	+	6.29384i	−0.237726	+	0.731644i
$75$	−0.304065	−	4.99075i	−0.0351104	−	0.576282i
$76$	−2.42266	−	7.45617i	−0.277898	−	0.855282i
$77$	−6.83268	+	17.2574i	−0.778656	+	1.96666i
$78$	−7.84109	+	8.34991i	−0.887828	+	0.945441i
$79$	−1.94017	−	10.1707i	−0.218286	−	1.14429i	−0.907601	−	0.419833i	$-0.862089\pi$
$79$	−1.94017	−	10.1707i	−0.218286	−	1.14429i	0.689316	−	0.724461i	$-0.257911\pi$
$80$	0.0505827	+	0.321427i	0.00565532	+	0.0359366i
$81$	0.728969	−	0.684547i	0.0809965	−	0.0760608i
$82$	−18.1661	+	5.90252i	−2.00611	+	0.651824i
$83$	4.11441	+	0.784865i	0.451615	+	0.0861502i	0.408171	−	0.912906i	$-0.366167\pi$
$83$	4.11441	+	0.784865i	0.451615	+	0.0861502i	0.0434444	+	0.999056i	$0.486167\pi$
$84$	0.963569	+	15.3155i	0.105134	+	1.67106i
$85$	−1.83663	−	8.25501i	−0.199210	−	0.895381i
$86$	−3.13960	−	4.94721i	−0.338551	−	0.533472i
$87$	−4.63078	+	0.291344i	−0.496472	+	0.0312354i
$88$	8.97892	+	5.69819i	0.957156	+	0.607429i
$89$	3.42210	−	4.13661i	0.362742	−	0.438480i	−0.557293	−	0.830316i	$-0.688160\pi$
$89$	3.42210	−	4.13661i	0.362742	−	0.438480i	0.920035	+	0.391836i	$0.128160\pi$
$90$	4.97669	+	1.11760i	0.524589	+	0.117805i
$91$	23.3004	+	5.98252i	2.44254	+	0.627139i
$92$	23.3169	−	10.9721i	2.43095	−	1.14392i
$93$	0.327550	+	0.106428i	0.0339654	+	0.0110360i
$94$	−6.46601	−	3.55472i	−0.666918	−	0.366641i
$95$	2.78114	+	4.71331i	0.285339	+	0.483575i
$96$	−5.77561	−	0.729629i	−0.589470	−	0.0744674i
$97$	0.705339	−	5.58333i	0.0716163	−	0.566902i	−0.914953	−	0.403560i	$-0.867773\pi$
$97$	0.705339	−	5.58333i	0.0716163	−	0.566902i	0.986570	−	0.163342i	$-0.0522273\pi$
$98$	30.7195	−	19.4952i	3.10314	−	1.96931i
$99$	−3.13445	+	2.27731i	−0.315024	+	0.228878i
$100$	5.86653	+	14.9034i	0.586653	+	1.49034i
$101$	1.85691	+	1.34912i	0.184769	+	0.134243i	0.676325	−	0.736604i	$-0.263572\pi$
$101$	1.85691	+	1.34912i	0.184769	+	0.134243i	−0.491556	+	0.870846i	$0.663572\pi$
$102$	8.61003	+	0.541697i	0.852520	+	0.0536360i
$103$	−0.920007	−	1.67349i	−0.0906509	−	0.164893i	0.827094	−	0.562063i	$-0.189992\pi$
$103$	−0.920007	−	1.67349i	−0.0906509	−	0.164893i	−0.917745	+	0.397170i	$0.869992\pi$
$104$	5.86851	−	12.4712i	0.575454	−	1.22290i
$105$	−2.97841	−	10.2898i	−0.290663	−	1.00418i
$106$	−1.04167	+	5.46062i	−0.101176	+	0.530382i
$107$	−3.01016	−	4.14313i	−0.291003	−	0.400532i	0.638336	−	0.769758i	$-0.279623\pi$
$107$	−3.01016	−	4.14313i	−0.291003	−	0.400532i	−0.929340	+	0.369226i	$0.879623\pi$
$108$	−1.54320	+	2.80706i	−0.148494	+	0.270110i
$109$	2.90884	−	4.58359i	0.278616	−	0.439029i	−0.675985	−	0.736915i	$-0.736282\pi$
$109$	2.90884	−	4.58359i	0.278616	−	0.439029i	0.954601	+	0.297887i	$0.0962817\pi$
$110$	−18.5869	−	6.71251i	−1.77219	−	0.640012i
$111$	2.69742	+	1.06799i	0.256028	+	0.101369i
$112$	0.256624	+	0.648158i	0.0242487	+	0.0612451i
$113$	−12.2707	+	10.1512i	−1.15433	+	0.954949i	−0.999456	−	0.0329845i	$-0.989499\pi$
$113$	−12.2707	+	10.1512i	−1.15433	+	0.954949i	−0.154879	+	0.987933i	$0.549499\pi$
$114$	−5.40741	+	1.38839i	−0.506450	+	0.130034i
$115$	−14.2246	+	11.0112i	−1.32645	+	1.02680i
$116$	13.8193	−	5.47146i	1.28309	−	0.508012i
$117$	3.43746	+	3.66052i	0.317793	+	0.338415i
$118$	−11.8298	+	16.2823i	−1.08902	+	1.49891i
$119$	−7.71437	−	16.3939i	−0.707175	−	1.50282i
$120$	−6.11087	+	0.571540i	−0.557843	+	0.0521742i
$121$	3.51479	−	1.93227i	0.319527	−	0.175661i
$122$	15.6991	−	2.99476i	1.42133	−	0.271133i
$123$	2.08245	+	8.11060i	0.187768	+	0.731308i
$124$	−1.10323			−0.0990734
$125$	−6.25677	−	9.26568i	−0.559623	−	0.828747i
$126$	10.9278			0.973523
$127$	−3.35526	−	13.0679i	−0.297731	−	1.15959i	−0.924748	−	0.380580i	$-0.875724\pi$
$127$	−3.35526	−	13.0679i	−0.297731	−	1.15959i	0.627017	−	0.779005i	$-0.284276\pi$
$128$	17.6656	−	3.36989i	1.56143	−	0.297859i
$129$	−2.25095	+	1.23747i	−0.198185	+	0.108953i
$130$	−5.61203	+	24.9905i	−0.492208	+	2.19181i
$131$	−5.79181	−	12.3082i	−0.506033	−	1.07538i	−0.980756	−	0.195240i	$-0.937452\pi$
$131$	−5.79181	−	12.3082i	−0.506033	−	1.07538i	0.474722	−	0.880136i	$-0.342548\pi$
$132$	7.29489	−	10.0405i	0.634938	−	0.873918i
$133$	8.02619	+	8.54702i	0.695959	+	0.741121i
$134$	−30.6348	+	12.1292i	−2.64645	+	1.04780i
$135$	0.625970	−	2.14666i	0.0538749	−	0.184755i
$136$	−10.0547	+	2.58161i	−0.862185	+	0.221371i
$137$	12.3116	−	10.1850i	1.05185	−	0.870166i	0.0600790	−	0.998194i	$-0.480865\pi$
$137$	12.3116	−	10.1850i	1.05185	−	0.870166i	0.991771	+	0.128028i	$0.0408647\pi$
$138$	−6.75526	−	17.0618i	−0.575046	−	1.45240i
$139$	18.5000	+	7.32469i	1.56915	+	0.621272i	0.982114	−	0.188286i	$-0.0602933\pi$
$139$	18.5000	+	7.32469i	1.56915	+	0.621272i	0.587039	+	0.809558i	$0.300293\pi$
$140$	19.2593	+	28.3997i	1.62771	+	2.40021i
$141$	−1.73327	+	2.73119i	−0.145967	+	0.230008i
$142$	10.5155	−	19.1275i	0.882438	−	1.60515i
$143$	−11.4355	−	15.7397i	−0.956287	−	1.31622i
$144$	−0.0272669	+	0.142938i	−0.00227224	+	0.0119115i
$145$	−8.58691	+	5.82323i	−0.713104	+	0.483593i
$146$	−2.29249	+	4.87178i	−0.189727	+	0.403191i
$147$	−7.68403	−	13.9772i	−0.633768	−	1.15282i
$148$	−9.27489	−	0.583527i	−0.762391	−	0.0479656i
$149$	6.71818	+	4.88104i	0.550375	+	0.399871i	0.827924	−	0.560841i	$-0.189522\pi$
$149$	6.71818	+	4.88104i	0.550375	+	0.399871i	−0.277549	+	0.960711i	$0.589522\pi$
$150$	10.8541	−	3.50295i	0.886234	−	0.286015i
$151$	11.0534	−	8.03078i	0.899514	−	0.653535i	−0.0388269	−	0.999246i	$-0.512362\pi$
$151$	11.0534	−	8.03078i	0.899514	−	0.653535i	0.938341	+	0.345711i	$0.112362\pi$
$152$	5.67197	−	3.59954i	0.460057	−	0.291961i
$153$	0.474013	−	3.75220i	0.0383217	−	0.303347i
$154$	−42.0046	−	5.30642i	−3.38483	−	0.427603i
$155$	0.751736	−	0.167251i	0.0603809	−	0.0134339i
$156$	−14.0957	−	7.74917i	−1.12856	−	0.620430i
$157$	20.1531	+	6.54813i	1.60839	+	0.522598i	0.969163	−	0.246421i	$-0.0792545\pi$
$157$	20.1531	+	6.54813i	1.60839	+	0.522598i	0.639227	+	0.769018i	$0.279254\pi$
$158$	21.3706	−	10.0563i	1.70016	−	0.800033i
$159$	2.36049	+	0.606070i	0.187199	+	0.0480645i
$160$	−11.9518	+	5.15795i	−0.944873	+	0.407772i
$161$	−24.5657	+	29.6948i	−1.93605	+	2.34028i
$162$	1.92597	+	1.22226i	0.151319	+	0.0960298i
$163$	−14.9780	+	0.942337i	−1.17317	+	0.0738095i	−0.637385	−	0.770546i	$-0.719984\pi$
$163$	−14.9780	+	0.942337i	−1.17317	+	0.0738095i	−0.535784	+	0.844355i	$0.679984\pi$
$164$	−14.3726	−	22.6477i	−1.12232	−	1.76849i
$165$	−3.44853	+	7.94747i	−0.268468	+	0.618710i
$166$	0.599932	+	9.53564i	0.0465637	+	0.740109i
$167$	−6.82501	−	1.30194i	−0.528135	−	0.100747i	−0.0835841	−	0.996501i	$-0.526637\pi$
$167$	−6.82501	−	1.30194i	−0.528135	−	0.100747i	−0.444551	+	0.895754i	$0.646637\pi$
$168$	−12.5057	+	4.06335i	−0.964835	+	0.313494i
$169$	−8.90473	+	8.36209i	−0.684979	+	0.643238i
$170$	17.1968	−	8.74076i	1.31893	−	0.670385i
$171$	0.458606	+	2.40410i	0.0350705	+	0.183846i
$172$	5.63261	−	5.99812i	0.429483	−	0.457353i
$173$	−1.81284	+	4.57872i	−0.137828	+	0.348114i	−0.982253	−	0.187560i	$-0.939942\pi$
$173$	−1.81284	+	4.57872i	−0.137828	+	0.348114i	0.844425	+	0.535673i	$0.179942\pi$
$174$	−3.27065	−	10.0660i	−0.247947	−	0.763103i
$175$	−17.4286	−	16.4316i	−1.31748	−	1.24211i
$176$	0.174219	−	0.536191i	0.0131323	−	0.0404169i
$177$	6.79830	+	5.62404i	0.510992	+	0.422729i
$178$	11.0807	+	5.21420i	0.830537	+	0.390821i
$179$	−5.38061	−	5.05273i	−0.402166	−	0.377659i	0.456905	−	0.889515i	$-0.348958\pi$
$179$	−5.38061	−	5.05273i	−0.402166	−	0.377659i	−0.859071	+	0.511857i	$0.828958\pi$
$180$	0.217896	+	7.15946i	0.0162410	+	0.533634i
$181$	−15.3003	+	1.93288i	−1.13726	+	0.143670i	−0.671336	−	0.741153i	$-0.734279\pi$
$181$	−15.3003	+	1.93288i	−1.13726	+	0.143670i	−0.465928	+	0.884823i	$0.654279\pi$
$182$			54.8738i			4.06752i
$183$	−0.878139	−	6.95118i	−0.0649139	−	0.513846i
$184$	14.0749	+	17.0137i	1.03762	+	1.25426i
$185$	6.40831	−	1.00847i	0.471148	−	0.0741441i
$186$	−0.0493293	+	0.784066i	−0.00361700	+	0.0574905i
$187$	−3.64406	+	14.1927i	−0.266480	+	1.03787i
$188$	2.57689	−	10.0363i	0.187939	−	0.731973i
$189$	0.300806	−	4.78117i	0.0218804	−	0.347779i
$190$	−8.83593	+	8.81844i	−0.641026	+	0.639757i
$191$	15.0035	+	18.1361i	1.08561	+	1.31228i	0.946750	+	0.321969i	$0.104345\pi$
$191$	15.0035	+	18.1361i	1.08561	+	1.31228i	0.138862	+	0.990312i	$0.455655\pi$
$192$	−1.62786	−	12.8858i	−0.117481	−	0.929955i
$193$			11.4283i			0.822630i	0.911493	+	0.411315i	$0.134930\pi$
$193$			11.4283i			0.822630i	−0.911493	+	0.411315i	$0.865070\pi$
$194$	12.7360	−	1.60893i	0.914391	−	0.115514i
$195$	10.7795	+	3.14331i	0.771934	+	0.225097i
$196$	37.2451	+	34.9755i	2.66036	+	2.49825i
$197$	−2.99789	−	1.41070i	−0.213591	−	0.100508i	0.316008	−	0.948757i	$-0.397657\pi$
$197$	−2.99789	−	1.41070i	−0.213591	−	0.100508i	−0.529599	+	0.848248i	$0.677657\pi$
$198$	−6.80962	−	5.63341i	−0.483938	−	0.400349i
$199$	−0.802912	+	2.47111i	−0.0569169	+	0.175172i	−0.975473	−	0.220118i	$-0.929356\pi$
$199$	−0.802912	+	2.47111i	−0.0569169	+	0.175172i	0.918556	+	0.395290i	$0.129356\pi$
$200$	−11.1189	+	8.04472i	−0.786223	+	0.568848i
$201$	4.46355	+	13.7374i	0.314834	+	0.968961i
$202$	−1.92737	+	4.86799i	−0.135610	+	0.342511i
$203$	−15.2163	+	16.2037i	−1.06797	+	1.13727i
$204$	2.27011	+	11.9003i	0.158939	+	0.833189i
$205$	13.2268	+	13.2531i	0.923801	+	0.925634i
$206$	3.17551	−	2.98200i	0.221248	−	0.207766i
$207$	−7.65094	+	2.48594i	−0.531777	+	0.172785i
$208$	−0.717765	−	0.136921i	−0.0497680	−	0.00949376i
$209$	−0.595403	−	9.46366i	−0.0411849	−	0.654615i
$210$	21.0447	−	12.4177i	1.45223	−	0.856903i
$211$	−0.934410	−	1.47239i	−0.0643275	−	0.101364i	0.810642	−	0.585543i	$-0.199118\pi$
$211$	−0.934410	−	1.47239i	−0.0643275	−	0.101364i	−0.874969	+	0.484179i	$0.839118\pi$
$212$	−7.79117	+	0.490179i	−0.535100	+	0.0336656i
$213$	−8.07933	−	5.12730i	−0.553587	−	0.351317i
$214$	7.44627	−	9.00099i	0.509016	−	0.615295i
$215$	−2.92870	+	4.94099i	−0.199736	+	0.336973i
$216$	−2.65856	−	0.682601i	−0.180892	−	0.0464451i
$217$	1.49290	−	0.702504i	0.101344	−	0.0476891i
$218$	11.7772	+	3.82663i	0.797649	+	0.259172i
$219$	2.06842	+	1.13712i	0.139771	+	0.0768398i
$220$	2.63901	−	27.6256i	0.177922	−	1.86252i
$221$	18.8417	+	2.38026i	1.26743	+	0.160113i
$222$	−0.829422	+	6.56555i	−0.0556672	+	0.440651i
$223$	−12.5675	+	7.97559i	−0.841583	+	0.534085i	−0.885333	−	0.464958i	$-0.846070\pi$
$223$	−12.5675	+	7.97559i	−0.841583	+	0.534085i	0.0437498	+	0.999043i	$0.486070\pi$
$224$	−22.5624	+	16.3926i	−1.50752	+	1.09527i
$225$	−1.23385	−	4.84537i	−0.0822568	−	0.323025i
$226$	−29.3892	−	21.3525i	−1.95494	−	1.42035i
$227$	−6.31252	−	0.397150i	−0.418976	−	0.0263598i	−0.148097	−	0.988973i	$-0.547315\pi$
$227$	−6.31252	−	0.397150i	−0.418976	−	0.0263598i	−0.270880	+	0.962613i	$0.587315\pi$
$228$	−3.77689	−	6.87014i	−0.250131	−	0.454986i
$229$	2.22551	−	4.72945i	0.147066	−	0.312531i	−0.817698	−	0.575647i	$-0.804750\pi$
$229$	2.22551	−	4.72945i	0.147066	−	0.312531i	0.964764	+	0.263116i	$0.0847503\pi$
$230$	−32.3974	−	25.1815i	−2.13622	−	1.66042i
$231$	−3.47794	+	18.2320i	−0.228832	+	1.19958i
$232$	7.48583	+	10.3034i	0.491469	+	0.676449i
$233$	−0.970566	+	1.76545i	−0.0635839	+	0.115659i	−0.906188	−	0.422874i	$-0.861021\pi$
$233$	−0.970566	+	1.76545i	−0.0635839	+	0.115659i	0.842605	+	0.538533i	$0.181021\pi$
$234$	−6.13758	+	9.67128i	−0.401226	+	0.632231i
$235$	−0.234360	+	7.22933i	−0.0152880	+	0.471590i
$236$	−26.2782	−	10.4043i	−1.71056	−	0.677260i
$237$	−3.81160	−	9.62701i	−0.247590	−	0.625341i
$238$	31.8446	−	26.3441i	2.06418	−	1.70763i
$239$	−12.4399	+	3.19403i	−0.804672	+	0.206605i	−0.628555	−	0.777765i	$-0.716353\pi$
$239$	−12.4399	+	3.19403i	−0.804672	+	0.206605i	−0.176116	+	0.984369i	$0.556353\pi$
$240$	0.109916	+	0.306255i	0.00709506	+	0.0197687i
$241$	16.3933	−	6.49056i	1.05598	−	0.418094i	0.224982	−	0.974363i	$-0.427768\pi$
$241$	16.3933	−	6.49056i	1.05598	−	0.418094i	0.831002	+	0.556269i	$0.187768\pi$
$242$	6.26305	+	6.66948i	0.402604	+	0.428730i
$243$	0.587785	−	0.809017i	0.0377064	−	0.0518985i
$244$	9.55603	+	20.3076i	0.611762	+	1.30006i
$245$	−30.6808	−	18.1856i	−1.96013	−	1.16184i
$246$	−16.7383	+	9.20196i	−1.06720	+	0.586695i
$247$	−12.0722	+	2.30289i	−0.768135	+	0.146530i
$248$	−0.235093	−	0.915625i	−0.0149284	−	0.0581423i
$249$	4.18860			0.265442
$250$	16.9223	−	19.0800i	1.07026	−	1.20672i
$251$	6.97454			0.440229			0.220115	−	0.975474i	$-0.429357\pi$
$251$	6.97454			0.440229			0.220115	+	0.975474i	$0.429357\pi$
$252$	3.81634	+	14.8637i	0.240407	+	0.936322i
$253$	30.6162	−	5.84034i	1.92482	−	0.367179i
$254$	26.9689	−	14.8263i	1.69218	−	0.930282i
$255$	−3.35093	−	7.76464i	−0.209843	−	0.486240i
$256$	6.40652	+	13.6145i	0.400407	+	0.850909i
$257$	6.05119	−	8.32875i	0.377463	−	0.519533i	−0.577447	−	0.816428i	$-0.695951\pi$
$257$	6.05119	−	8.32875i	0.377463	−	0.519533i	0.954910	+	0.296895i	$0.0959510\pi$
$258$	−4.01100	−	4.27128i	−0.249714	−	0.265918i
$259$	12.9223	−	5.11632i	0.802956	−	0.317913i
$260$	−35.9513	+	1.09416i	−2.22960	+	0.0678572i
$261$	−4.49417	+	1.15391i	−0.278182	+	0.0714250i
$262$	23.9083	−	19.7787i	1.47706	−	1.22193i
$263$	−4.51988	−	11.4159i	−0.278707	−	0.703935i	−0.999937	−	0.0112384i	$-0.996423\pi$
$263$	−4.51988	−	11.4159i	−0.278707	−	0.703935i	0.721229	−	0.692696i	$-0.243577\pi$
$264$	9.88761	+	3.91478i	0.608540	+	0.240938i
$265$	5.23454	−	1.51515i	0.321555	−	0.0930750i
$266$	−14.3308	+	22.5817i	−0.878675	+	1.38457i
$267$	2.58636	−	4.70458i	0.158283	−	0.287915i
$268$	−27.1965	−	37.4327i	−1.66129	−	2.28657i
$269$	5.92484	−	31.0591i	0.361244	−	1.89371i	−0.0808316	−	0.996728i	$-0.525758\pi$
$269$	5.92484	−	31.0591i	0.361244	−	1.89371i	0.442075	−	0.896978i	$-0.354242\pi$
$270$	5.09795	+	0.165265i	0.310252	+	0.0100577i
$271$	−10.0467	+	21.3503i	−0.610294	+	1.29694i	0.325883	+	0.945410i	$0.394338\pi$
$271$	−10.0467	+	21.3503i	−0.610294	+	1.29694i	−0.936177	+	0.351530i	$0.885662\pi$
$272$	0.265130	+	0.482269i	0.0160758	+	0.0292419i
$273$	24.0087	+	1.51050i	1.45307	+	0.0914196i
$274$	29.4870	+	21.4236i	1.78137	+	1.29424i
$275$	2.38987	+	19.2240i	0.144114	+	1.15925i
$276$	20.8479	−	15.1469i	1.25490	−	0.911735i
$277$	−2.42883	+	1.54138i	−0.145934	+	0.0926128i	−0.606789	−	0.794863i	$-0.707543\pi$
$277$	−2.42883	+	1.54138i	−0.145934	+	0.0926128i	0.460855	+	0.887476i	$0.347543\pi$
$278$	−5.68852	+	45.0293i	−0.341175	+	2.70068i
$279$	0.341691	+	0.0431656i	0.0204565	+	0.00258426i
$280$	−19.4662	+	22.0360i	−1.16333	+	1.31690i
$281$	18.1854	+	9.99751i	1.08485	+	0.596401i	0.920794	−	0.390049i	$-0.127542\pi$
$281$	18.1854	+	9.99751i	1.08485	+	0.596401i	0.164056	+	0.986451i	$0.447542\pi$
$282$	−7.01757	−	2.28015i	−0.417890	−	0.135781i
$283$	−7.05298	+	3.31888i	−0.419256	+	0.197287i	−0.623823	−	0.781566i	$-0.714421\pi$
$283$	−7.05298	+	3.31888i	−0.419256	+	0.197287i	0.204567	+	0.978853i	$0.434421\pi$
$284$	29.6891	+	7.62287i	1.76172	+	0.452334i
$285$	3.61507	+	4.10869i	0.214138	+	0.243378i
$286$	28.2882	−	34.1945i	1.67271	−	2.02196i
$287$	33.8704	+	21.4948i	1.99930	+	1.26880i
$288$	−5.81002	+	0.365536i	−0.342359	+	0.0215394i
$289$	1.44477	+	2.27659i	0.0849864	+	0.133917i
$290$	−17.7371	−	15.6686i	−1.04156	−	0.920092i
$291$	−0.353367	−	5.61661i	−0.0207147	−	0.329251i
$292$	−7.42707	−	1.41679i	−0.434637	−	0.0829114i
$293$	10.5929	−	3.44185i	0.618846	−	0.201075i	0.0172180	−	0.999852i	$-0.494519\pi$
$293$	10.5929	−	3.44185i	0.618846	−	0.201075i	0.601628	+	0.798777i	$0.294519\pi$
$294$	26.5223	−	24.9061i	1.54681	−	1.45255i
$295$	19.4830	+	3.10560i	1.13435	+	0.180815i
$296$	−1.49213	−	7.82200i	−0.0867281	−	0.454645i
$297$	−2.65220	+	2.82431i	−0.153897	+	0.163883i
$298$	−6.97313	+	17.6121i	−0.403943	+	1.02024i
$299$	−12.4832	−	38.4192i	−0.721920	−	2.22184i
$300$	8.55523	+	13.5401i	0.493936	+	0.781739i
$301$	−3.80264	+	11.7033i	−0.219181	+	0.674568i
$302$	24.0136	+	19.8658i	1.38183	+	1.14315i
$303$	2.07682	+	0.977275i	0.119310	+	0.0561430i
$304$	−0.259616	−	0.243796i	−0.0148900	−	0.0139827i
$305$	−9.59006	−	12.3888i	−0.549125	−	0.709378i
$306$	8.55903	−	1.08126i	0.489287	−	0.0618113i
$307$		−	28.2816i		−	1.61411i	−0.590473	−	0.807057i	$-0.701059\pi$
$307$		−	28.2816i		−	1.61411i	0.590473	−	0.807057i	$-0.298941\pi$
$308$	−7.45175	−	58.9867i	−0.424603	−	3.36108i
$309$	−1.21729	−	1.47145i	−0.0692492	−	0.0837080i
$310$	0.795971	+	1.56601i	0.0452081	+	0.0889436i
$311$	1.10644	−	17.5864i	0.0627405	−	0.997232i	−0.833176	−	0.553009i	$-0.813480\pi$
$311$	1.10644	−	17.5864i	0.0627405	−	0.997232i	0.895916	−	0.444223i	$-0.146520\pi$
$312$	3.42769	−	13.3500i	0.194055	−	0.755793i
$313$	−0.445519	+	1.73518i	−0.0251822	+	0.0980782i	−0.979932	−	0.199332i	$-0.936123\pi$
$313$	−0.445519	+	1.73518i	−0.0251822	+	0.0980782i	0.954750	+	0.297410i	$0.0961228\pi$
$314$	−3.03506	+	48.2410i	−0.171279	+	2.72240i
$315$	−4.85377	−	9.54943i	−0.273479	−	0.538049i
$316$	21.1416	+	25.5558i	1.18931	+	1.43762i
$317$	0.294290	+	2.32955i	0.0165290	+	0.130840i	0.998220	−	0.0596402i	$-0.0189953\pi$
$317$	0.294290	+	2.32955i	0.0165290	+	0.130840i	−0.981691	+	0.190481i	$0.938995\pi$
$318$			5.55909i			0.311738i
$319$	17.8352	−	2.25311i	0.998579	−	0.126150i
$320$	−17.7777	−	22.9658i	−0.993803	−	1.28383i
$321$	−3.73319	−	3.50570i	−0.208366	−	0.195669i
$322$	−79.5436	−	37.4304i	−4.43279	−	2.08591i
$323$	7.13210	+	5.90018i	0.396840	+	0.328295i
$324$	−0.989871	+	3.04651i	−0.0549928	+	0.169251i
$325$	24.3311	−	6.19579i	1.34964	−	0.343681i
$326$	−10.5787	−	32.5580i	−0.585901	−	1.80322i
$327$	1.99843	−	5.04747i	0.110514	−	0.279126i
$328$	15.7336	−	16.7546i	0.868744	−	0.925118i
$329$	2.90375	+	15.2220i	0.160089	+	0.839217i
$330$	−19.5155	−	3.11077i	−1.07429	−	0.171242i
$331$	13.3317	−	12.5193i	0.732776	−	0.688122i	−0.225412	−	0.974264i	$-0.572373\pi$
$331$	13.3317	−	12.5193i	0.732776	−	0.688122i	0.958187	+	0.286141i	$0.0923727\pi$
$332$	−12.7606	+	4.14617i	−0.700329	+	0.227551i
$333$	2.84976	+	0.543622i	0.156166	+	0.0297903i
$334$	−0.995171	−	15.8178i	−0.0544533	−	0.865511i
$335$	24.2063	+	21.3834i	1.32253	+	1.16830i
$336$	0.373531	+	0.588590i	0.0203778	+	0.0321102i
$337$	−5.79823	+	0.364794i	−0.315850	+	0.0198716i	−0.219924	−	0.975517i	$-0.570581\pi$
$337$	−5.79823	+	0.364794i	−0.315850	+	0.0198716i	−0.0959254	+	0.995389i	$0.530581\pi$
$338$	−23.5267	−	14.9305i	−1.27969	−	0.812114i
$339$	−10.1512	+	12.2707i	−0.551340	+	0.666456i
$340$	17.8946	+	20.3381i	0.970472	+	1.10299i
$341$	−1.29245	−	0.331844i	−0.0699898	−	0.0179703i
$342$	−5.05147	+	2.37704i	−0.273152	+	0.128536i
$343$	−40.7781	−	13.2496i	−2.20181	−	0.715412i
$344$	6.17840	+	3.39660i	0.333117	+	0.183132i
$345$	−11.9093	+	13.4815i	−0.641177	+	0.725822i
$346$	−11.1447	−	1.40790i	−0.599140	−	0.0756890i
$347$	−0.859589	+	6.80435i	−0.0461452	+	0.365277i	0.952086	+	0.305829i	$0.0989337\pi$
$347$	−0.859589	+	6.80435i	−0.0461452	+	0.365277i	−0.998231	+	0.0594471i	$0.981066\pi$
$348$	12.5493	−	7.96403i	0.672713	−	0.426917i
$349$	−13.5550	+	9.84830i	−0.725584	+	0.527168i	−0.888163	−	0.459528i	$-0.848019\pi$
$349$	−13.5550	+	9.84830i	−0.725584	+	0.527168i	0.162579	+	0.986695i	$0.448019\pi$
$350$	26.4173	−	47.8281i	1.41206	−	2.55652i
$351$	4.06248	+	2.95157i	0.216839	+	0.157543i
$352$	22.5103	+	1.41623i	1.19980	+	0.0754853i
$353$	11.2993	+	20.5534i	0.601402	+	1.09395i	0.985342	+	0.170589i	$0.0545669\pi$
$353$	11.2993	+	20.5534i	0.601402	+	1.09395i	−0.383940	+	0.923358i	$0.625433\pi$
$354$	−8.56927	+	18.2106i	−0.455452	+	0.967884i
$355$	−21.3856	−	0.693277i	−1.13503	−	0.0367953i
$356$	−3.22246	+	16.8927i	−0.170790	+	0.895312i
$357$	−10.6496	−	14.6580i	−0.563639	−	0.775782i
$358$	8.11123	−	14.7543i	0.428692	−	0.779787i
$359$	−13.5691	+	21.3815i	−0.716150	+	1.12847i	0.270040	+	0.962849i	$0.412963\pi$
$359$	−13.5691	+	21.3815i	−0.716150	+	1.12847i	−0.986189	+	0.165622i	$0.947037\pi$
$360$	−5.89553	+	1.70648i	−0.310722	+	0.0899393i
$361$	12.0964	+	4.78930i	0.636652	+	0.252068i
$362$	−12.9501	−	32.7082i	−0.680641	−	1.71910i
$363$	3.09047	−	2.55666i	0.162207	−	0.134190i
$364$	−74.6379	+	19.1638i	−3.91209	+	1.00445i
$365$	5.27554	−	0.160559i	0.276134	−	0.00840406i
$366$	14.8599	−	5.88343i	0.776737	−	0.307532i
$367$	16.3693	+	17.4315i	0.854471	+	0.909919i	0.996803	−	0.0799001i	$-0.0254601\pi$
$367$	16.3693	+	17.4315i	0.854471	+	0.909919i	−0.142332	+	0.989819i	$0.545460\pi$
$368$	0.688077	−	0.947056i	0.0358685	−	0.0493687i
$369$	3.56534	+	7.57673i	0.185604	+	0.394429i
$370$	5.86342	+	13.5865i	0.304825	+	0.706328i
$371$	10.2309	−	5.62447i	0.531161	−	0.292008i
$372$	−1.08369	+	0.206726i	−0.0561869	+	0.0107182i
$373$	5.70760	+	22.2296i	0.295528	+	1.15101i	0.926834	+	0.375472i	$0.122520\pi$
$373$	5.70760	+	22.2296i	0.295528	+	1.15101i	−0.631305	+	0.775534i	$0.717480\pi$
$374$	−33.4246			−1.72835
$375$	−7.88216	−	7.92915i	−0.407033	−	0.409460i
$376$	8.87872			0.457885
$377$	−5.79434	−	22.5675i	−0.298424	−	1.16228i
$378$	10.7342	−	2.04766i	0.552108	−	0.105320i
$379$	2.05752	−	1.13113i	0.105688	−	0.0581024i	−0.428033	−	0.903763i	$-0.640793\pi$
$379$	2.05752	−	1.13113i	0.105688	−	0.0581024i	0.533721	+	0.845661i	$0.320793\pi$
$380$	−15.0804	−	8.93870i	−0.773608	−	0.458546i
$381$	−5.74450	−	12.2077i	−0.294300	−	0.625418i
$382$	−31.5588	+	43.4370i	−1.61469	+	2.22243i
$383$	−10.5896	−	11.2768i	−0.541104	−	0.576217i	0.399067	−	0.916922i	$-0.369334\pi$
$383$	−10.5896	−	11.2768i	−0.541104	−	0.576217i	−0.940170	+	0.340705i	$0.889334\pi$
$384$	16.7212	−	6.62040i	0.853301	−	0.337846i
$385$	14.0200	+	39.0634i	0.714525	+	1.99086i
$386$	−25.2499	+	6.48307i	−1.28519	+	0.329979i
$387$	−1.97920	+	1.63734i	−0.100609	+	0.0832307i
$388$	6.63625	+	16.7613i	0.336905	+	0.850924i
$389$	6.82399	+	2.70181i	0.345990	+	0.136987i	0.534692	−	0.845047i	$-0.320428\pi$
$389$	6.82399	+	2.70181i	0.345990	+	0.136987i	−0.188701	+	0.982035i	$0.560428\pi$
$390$	−0.829880	+	25.5994i	−0.0420226	+	1.29628i
$391$	−16.3026	+	25.6888i	−0.824457	+	1.29914i
$392$	−21.0910	+	38.3645i	−1.06526	+	1.93770i
$393$	−7.99556	−	11.0049i	−0.403323	−	0.555126i
$394$	1.41617	−	7.42383i	0.0713456	−	0.374007i
$395$	−18.2800	−	14.2084i	−0.919766	−	0.714904i
$396$	5.28426	−	11.2296i	0.265544	−	0.564310i
$397$	12.5478	+	22.8244i	0.629757	+	1.14552i	0.978096	+	0.208155i	$0.0667457\pi$
$397$	12.5478	+	22.8244i	0.629757	+	1.14552i	−0.348339	+	0.937369i	$0.613254\pi$
$398$	−5.91516	−	0.372151i	−0.296500	−	0.0186542i
$399$	9.48557	+	6.89167i	0.474873	+	0.345015i
$400$	0.559689	+	0.464886i	0.0279844	+	0.0232443i
$401$	3.18921	−	2.31710i	0.159262	−	0.115710i	−0.505300	−	0.862944i	$-0.668618\pi$
$401$	3.18921	−	2.31710i	0.159262	−	0.115710i	0.664562	+	0.747233i	$0.268618\pi$
$402$	−27.8194	+	17.6547i	−1.38751	+	0.880538i
$403$	−0.216756	+	1.71580i	−0.0107974	+	0.0854702i
$404$	−7.29442	−	0.921499i	−0.362911	−	0.0458463i
$405$	0.212638	−	2.22593i	0.0105661	−	0.110608i
$406$	−44.4324	−	24.4269i	−2.20514	−	1.21229i
$407$	−10.6901	−	3.47341i	−0.529887	−	0.172171i
$408$	−9.39287	+	4.41995i	−0.465016	+	0.218820i
$409$	9.47735	+	2.43337i	0.468625	+	0.120322i	0.475616	−	0.879653i	$-0.342225\pi$
$409$	9.47735	+	2.43337i	0.468625	+	0.120322i	−0.00699086	+	0.999976i	$0.502225\pi$
$410$	−21.7781	+	36.7416i	−1.07554	+	1.81454i
$411$	10.1850	−	12.3116i	0.502390	−	0.607286i
$412$	5.16503	+	3.27783i	0.254463	+	0.161487i
$413$	42.1847	−	2.65404i	2.07577	−	0.130597i
$414$	−9.83268	−	15.4938i	−0.483250	−	0.761480i
$415$	8.06642	−	4.75969i	0.395965	−	0.233644i
$416$	−1.83554	−	29.1751i	−0.0899947	−	1.43043i
$417$	19.5449	+	3.72838i	0.957116	+	0.182580i
$418$	20.5713	−	6.68403i	1.00618	−	0.326927i
$419$	5.54646	−	5.20847i	0.270962	−	0.254451i	−0.537139	−	0.843493i	$-0.680495\pi$
$419$	5.54646	−	5.20847i	0.270962	−	0.254451i	0.808102	+	0.589043i	$0.200495\pi$
$420$	24.2397	+	24.2878i	1.18278	+	1.18512i
$421$	−5.17597	−	27.1334i	−0.252261	−	1.32240i	−0.852562	−	0.522625i	$-0.824953\pi$
$421$	−5.17597	−	27.1334i	−0.252261	−	1.32240i	0.600301	−	0.799774i	$-0.295047\pi$
$422$	2.72305	−	2.89975i	0.132556	−	0.141158i
$423$	−1.19079	+	3.00760i	−0.0578983	+	0.146234i
$424$	−2.06707	−	6.36180i	−0.100386	−	0.308956i
$425$	−15.2765	−	11.1454i	−0.741021	−	0.540630i
$426$	6.74506	−	20.7591i	0.326799	−	1.00578i
$427$	−25.8624	−	21.3953i	−1.25157	−	1.03539i
$428$	14.8434	+	6.98477i	0.717482	+	0.337622i
$429$	−14.1823	−	13.3181i	−0.684727	−	0.643002i
$430$	−12.5780	−	3.66778i	−0.606567	−	0.176876i
$431$	32.3113	−	4.08186i	1.55638	−	0.196616i	0.700447	−	0.713704i	$-0.252984\pi$
$431$	32.3113	−	4.08186i	1.55638	−	0.196616i	0.855932	+	0.517088i	$0.172984\pi$
$432$			0.145516i			0.00700112i
$433$	−1.15618	−	9.15208i	−0.0555623	−	0.439821i	−0.995216	−	0.0976950i	$-0.968853\pi$
$433$	−1.15618	−	9.15208i	−0.0555623	−	0.439821i	0.939654	−	0.342126i	$-0.111147\pi$
$434$	2.39901	+	2.89990i	0.115156	+	0.139200i
$435$	−7.34365	+	7.32912i	−0.352101	+	0.351404i
$436$	−1.09191	+	17.3553i	−0.0522928	+	0.831170i
$437$	4.89644	−	19.0704i	0.234228	−	0.912259i
$438$	−1.33900	+	5.21506i	−0.0639798	+	0.249185i
$439$	1.43433	−	22.7980i	0.0684567	−	1.08809i	−0.802476	−	0.596685i	$-0.796484\pi$
$439$	1.43433	−	22.7980i	0.0684567	−	1.08809i	0.870932	−	0.491403i	$-0.163516\pi$
$440$	23.4901	−	3.69662i	1.11985	−	0.176230i
$441$	−10.1670	−	12.2898i	−0.484142	−	0.585227i
$442$	5.42954	+	42.9792i	0.258257	+	2.04431i
$443$			13.8803i			0.659472i	0.944073	+	0.329736i	$0.106960\pi$
$443$			13.8803i			0.659472i	−0.944073	+	0.329736i	$0.893040\pi$
$444$	−9.21995	+	1.16475i	−0.437559	+	0.0552766i
$445$	−0.365188	−	11.9991i	−0.0173116	−	0.568812i
$446$	−24.7506	−	23.2424i	−1.17198	−	1.10056i
$447$	7.51380	+	3.53572i	0.355390	+	0.167234i
$448$	−47.9428	−	39.6617i	−2.26508	−	1.87384i
$449$	−9.18319	+	28.2630i	−0.433382	+	1.33381i	0.461354	+	0.887216i	$0.347364\pi$
$449$	−9.18319	+	28.2630i	−0.433382	+	1.33381i	−0.894736	+	0.446595i	$0.852636\pi$
$450$	10.0055	−	5.47476i	0.471662	−	0.258083i
$451$	−10.0254	−	30.8550i	−0.472078	−	1.45291i
$452$	18.7794	−	47.4314i	0.883309	−	2.23098i
$453$	9.35281	−	9.95973i	0.439434	−	0.467949i
$454$	−2.70350	−	14.1722i	−0.126881	−	0.665135i
$455$	47.9525	−	24.3732i	2.24805	−	1.14263i
$456$	4.89701	−	4.59860i	0.229324	−	0.215349i
$457$	−20.1884	+	6.55961i	−0.944373	+	0.306845i	−0.740427	−	0.672137i	$-0.765377\pi$
$457$	−20.1884	+	6.55961i	−0.944373	+	0.306845i	−0.203946	+	0.978982i	$0.565377\pi$
$458$	11.7118	+	2.23414i	0.547255	+	0.104394i
$459$	−0.237475	−	3.77456i	−0.0110844	−	0.176181i
$460$	22.9369	−	52.8603i	1.06944	−	2.46463i
$461$	14.9374	+	23.5376i	0.695704	+	1.09625i	0.990072	+	0.140561i	$0.0448907\pi$
$461$	14.9374	+	23.5376i	0.695704	+	1.09625i	−0.294368	+	0.955692i	$0.595109\pi$
$462$	−42.2549	+	2.65845i	−1.96588	+	0.123682i
$463$	7.04506	+	4.47093i	0.327412	+	0.207782i	0.689365	−	0.724415i	$-0.257890\pi$
$463$	7.04506	+	4.47093i	0.327412	+	0.207782i	−0.361953	+	0.932196i	$0.617890\pi$
$464$	0.430378	−	0.520238i	0.0199798	−	0.0241514i
$465$	0.707081	−	0.305150i	0.0327901	−	0.0141510i
$466$	−4.45119	−	1.14287i	−0.206197	−	0.0529425i
$467$	−28.5262	+	13.4234i	−1.32004	+	0.621162i	−0.951270	−	0.308360i	$-0.900220\pi$
$467$	−28.5262	+	13.4234i	−1.32004	+	0.621162i	−0.368767	+	0.929522i	$0.620220\pi$
$468$	−15.2981	−	4.97064i	−0.707153	−	0.229768i
$469$	60.6382	+	33.3361i	2.80001	+	1.53932i
$470$	−16.1055	+	3.58325i	−0.742891	+	0.165283i
$471$	21.0231	+	2.65583i	0.968693	+	0.122374i
$472$	3.03526	−	24.0265i	0.139709	−	1.10591i
$473$	8.40282	−	5.33259i	0.386362	−	0.245193i
$474$	19.1077	−	13.8826i	0.877648	−	0.637648i
$475$	11.6308	+	3.80457i	0.533657	+	0.174565i
$476$	46.9537	+	34.1139i	2.15212	+	1.56361i
$477$	2.43224	+	0.153024i	0.111365	+	0.00700647i
$478$	−14.1138	−	25.6730i	−0.645551	−	1.17425i
$479$	3.07899	−	6.54318i	0.140682	−	0.298965i	−0.822053	−	0.569411i	$-0.807171\pi$
$479$	3.07899	−	6.54318i	0.140682	−	0.298965i	0.962735	+	0.270446i	$0.0871711\pi$
$480$	−10.7736	+	7.30614i	−0.491745	+	0.333478i
$481$	−2.72980	+	14.3101i	−0.124468	+	0.652485i
$482$	23.6399	+	32.5375i	1.07677	+	1.48204i
$483$	−18.5663	+	33.7720i	−0.844797	+	1.53668i
$484$	−6.88437	+	10.8480i	−0.312926	+	0.493093i
$485$	−7.06291	−	10.4149i	−0.320710	−	0.472918i
$486$	2.12089	+	0.839719i	0.0962054	+	0.0380904i
$487$	1.62623	+	4.10740i	0.0736917	+	0.186124i	0.961953	−	0.273214i	$-0.0880867\pi$
$487$	1.62623	+	4.10740i	0.0736917	+	0.186124i	−0.888262	+	0.459338i	$0.848087\pi$
$488$	−14.8179	+	12.2584i	−0.670774	+	0.554912i
$489$	−14.5361	+	3.73224i	−0.657347	+	0.168778i
$490$	22.7749	−	78.1028i	1.02886	−	3.52833i
$491$	−17.0048	+	6.73269i	−0.767418	+	0.303842i	−0.719023	−	0.694986i	$-0.755411\pi$
$491$	−17.0048	+	6.73269i	−0.767418	+	0.303842i	−0.0483946	+	0.998828i	$0.515411\pi$
$492$	−18.3618	−	19.5534i	−0.827815	−	0.881533i
$493$	−10.3147	+	14.1969i	−0.464549	+	0.639396i
$494$	−11.9363	−	25.3660i	−0.537041	−	1.14127i
$495$	−1.89824	+	8.45289i	−0.0853195	+	0.379929i
$496$	−0.0439175	+	0.0241438i	−0.00197195	+	0.00108409i
$497$	−45.0293	+	8.58980i	−2.01984	+	0.385305i
$498$	2.37611	+	9.25432i	0.106476	+	0.414696i
$499$	−20.6663			−0.925149			−0.462574	−	0.886581i	$-0.653074\pi$
$499$	−20.6663			−0.925149			−0.462574	+	0.886581i	$0.653074\pi$
$500$	31.8619	+	16.3539i	1.42491	+	0.731370i
$501$	−6.94808			−0.310417
$502$	3.95651	+	15.4096i	0.176588	+	0.687764i
$503$	35.6710	−	6.80460i	1.59049	−	0.303402i	0.685252	−	0.728306i	$-0.259692\pi$
$503$	35.6710	−	6.80460i	1.59049	−	0.303402i	0.905239	+	0.424904i	$0.139692\pi$
$504$	−11.5228	+	6.33471i	−0.513266	+	0.282170i
$505$	5.11006	−	0.477936i	0.227395	−	0.0212679i
$506$	30.2716	+	64.3305i	1.34574	+	2.85984i
$507$	−7.18010	+	9.88256i	−0.318879	+	0.438900i
$508$	29.5847	+	31.5045i	1.31261	+	1.39779i
$509$	38.2342	−	15.1380i	1.69470	−	0.670979i	0.695816	−	0.718220i	$-0.255043\pi$
$509$	38.2342	−	15.1380i	1.69470	−	0.670979i	0.998884	+	0.0472410i	$0.0150429\pi$
$510$	15.2543	−	11.8083i	0.675473	−	0.522880i
$511$	10.9525	−	2.81212i	0.484509	−	0.124401i
$512$	1.26822	−	1.04916i	0.0560479	−	0.0463668i
$513$	0.900966	+	2.27558i	0.0397786	+	0.100469i
$514$	21.8343	+	8.64482i	0.963071	+	0.381307i
$515$	−4.01634	−	1.45047i	−0.176981	−	0.0639152i
$516$	4.40891	−	6.94733i	0.194091	−	0.305839i
$517$	6.03768	−	10.9825i	0.265537	−	0.483009i
$518$	18.6346	+	25.6484i	0.818758	+	1.12692i
$519$	−0.922767	+	4.83731i	−0.0405050	+	0.212334i
$520$	−8.56909	−	29.6044i	−0.375779	−	1.29824i
$521$	4.66770	−	9.91938i	0.204496	−	0.434576i	−0.776102	−	0.630608i	$-0.782806\pi$
$521$	4.66770	−	9.91938i	0.204496	−	0.434576i	0.980597	+	0.196032i	$0.0628057\pi$
$522$	−5.09890	−	9.27486i	−0.223173	−	0.405950i
$523$	−7.17988	−	0.451720i	−0.313954	−	0.0197523i	−0.0949682	−	0.995480i	$-0.530275\pi$
$523$	−7.17988	−	0.451720i	−0.313954	−	0.0197523i	−0.218986	+	0.975728i	$0.570275\pi$
$524$	35.2520	+	25.6121i	1.53999	+	1.11887i
$525$	−20.1988	−	12.8748i	−0.881549	−	0.561901i
$526$	22.6584	−	16.4623i	0.987951	−	0.717789i
$527$	1.09978	−	0.697943i	0.0479072	−	0.0304029i
$528$	0.0706609	−	0.559339i	0.00307512	−	0.0243421i
$529$	41.3878	+	5.22850i	1.79947	+	0.227326i
$530$	6.31703	+	10.7057i	0.274394	+	0.465026i
$531$	7.73173	+	4.25055i	0.335528	+	0.184458i
$532$	−35.7197	−	11.6060i	−1.54865	−	0.503186i
$533$	−38.0466	+	17.9034i	−1.64798	+	0.775481i
$534$	11.8615	+	3.04552i	0.513298	+	0.131793i
$535$	−11.1731	−	2.50910i	−0.483054	−	0.108478i
$536$	25.2718	−	30.5483i	1.09157	−	1.31949i
$537$	−6.23209	−	3.95500i	−0.268935	−	0.170671i
$538$	71.9832	−	4.52880i	3.10342	−	0.195250i
$539$	33.1125	+	52.1769i	1.42626	+	2.24742i
$540$	1.55558	+	6.99181i	0.0669417	+	0.300880i
$541$	−1.93159	−	30.7018i	−0.0830456	−	1.31997i	−0.790172	−	0.612885i	$-0.790009\pi$
$541$	−1.93159	−	30.7018i	−0.0830456	−	1.31997i	0.707126	−	0.707087i	$-0.249991\pi$
$542$	−52.8709	−	10.0857i	−2.27100	−	0.433216i
$543$	−14.6671	+	4.76564i	−0.629427	+	0.204513i
$544$	−16.0497	+	15.0717i	−0.688127	+	0.646195i
$545$	−1.88707	−	11.9913i	−0.0808330	−	0.513653i
$546$	10.2823	+	53.9019i	0.440043	+	2.30679i
$547$	0.144391	−	0.153761i	0.00617371	−	0.00657434i	−0.725874	−	0.687827i	$-0.758565\pi$
$547$	0.144391	−	0.153761i	0.00617371	−	0.00657434i	0.732048	+	0.681253i	$0.238565\pi$
$548$	−18.8419	+	47.5892i	−0.804886	+	2.03291i
$549$	−2.16511	−	6.66351i	−0.0924045	−	0.284392i
$550$	−41.1179	+	16.1856i	−1.75327	+	0.690155i
$551$	3.50920	−	10.8002i	0.149497	−	0.460104i
$552$	17.0137	+	14.0749i	0.724149	+	0.599068i
$553$	−44.8818	−	21.1198i	−1.90857	−	0.898105i
$554$	−4.78338	−	4.49189i	−0.203226	−	0.190842i
$555$	6.10583	−	2.19140i	0.259178	−	0.0930199i
$556$	−63.2342	+	7.98834i	−2.68173	+	0.338781i
$557$			4.30738i			0.182509i	0.995828	+	0.0912547i	$0.0290877\pi$
$557$			4.30738i			0.182509i	−0.995828	+	0.0912547i	$0.970912\pi$
$558$	0.0984639	+	0.779422i	0.00416831	+	0.0329956i
$559$	−8.22191	−	9.93858i	−0.347750	−	0.420357i
$560$	1.38819	+	0.709050i	0.0586617	+	0.0299629i
$561$	−0.920071	+	14.6241i	−0.0388454	+	0.617430i
$562$	−11.7724	+	45.8504i	−0.496588	+	1.93408i
$563$	0.979683	−	3.81561i	0.0412887	−	0.160809i	−0.944596	−	0.328236i	$-0.893546\pi$
$563$	0.979683	−	3.81561i	0.0412887	−	0.160809i	0.985884	+	0.167427i	$0.0535459\pi$
$564$	0.650626	−	10.3414i	0.0273963	−	0.435452i
$565$	−5.60552	+	35.1664i	−0.235826	+	1.47946i
$566$	−11.3338	−	13.7002i	−0.476394	−	0.575862i
$567$	−0.600425	−	4.75285i	−0.0252155	−	0.199601i
$568$			26.2647i			1.10204i
$569$	−24.4838	+	3.09303i	−1.02642	+	0.129666i	−0.620469	−	0.784231i	$-0.713058\pi$
$569$	−24.4838	+	3.09303i	−1.02642	+	0.129666i	−0.405946	+	0.913897i	$0.633058\pi$
$570$	−7.02701	+	10.3179i	−0.294329	+	0.432170i
$571$	−10.8473	−	10.1863i	−0.453946	−	0.426284i	0.423546	−	0.905874i	$-0.360785\pi$
$571$	−10.8473	−	10.1863i	−0.453946	−	0.426284i	−0.877492	+	0.479591i	$0.840785\pi$
$572$	56.3896	+	26.5349i	2.35777	+	1.10948i
$573$	18.1361	+	15.0035i	0.757645	+	0.626779i
$574$	−28.2768	+	87.0270i	−1.18025	+	3.63244i
$575$	−7.61538	+	39.4959i	−0.317583	+	1.64709i
$576$	−4.01359	−	12.3526i	−0.167233	−	0.514690i
$577$	3.99679	−	10.0947i	0.166388	−	0.420249i	−0.822528	−	0.568725i	$-0.807437\pi$
$577$	3.99679	−	10.0947i	0.166388	−	0.420249i	0.988916	+	0.148476i	$0.0474368\pi$
$578$	−4.21033	+	4.48354i	−0.175127	+	0.186491i
$579$	2.14146	+	11.2259i	0.0889960	+	0.466533i
$580$	15.1176	−	29.5975i	0.627725	−	1.22897i
$581$	14.6275	−	13.7361i	0.606851	−	0.569871i
$582$	12.2089	−	3.96692i	0.506076	−	0.164434i
$583$	−9.27484	−	1.76927i	−0.384125	−	0.0732757i
$584$	−0.406805	−	6.46598i	−0.0168337	−	0.267564i
$585$	11.1775	+	1.06776i	0.462134	+	0.0441465i
$586$	13.6136	+	21.4516i	0.562373	+	0.886158i
$587$	−7.72839	+	0.486229i	−0.318985	+	0.0200688i	−0.221476	−	0.975166i	$-0.571087\pi$
$587$	−7.72839	+	0.486229i	−0.318985	+	0.0200688i	−0.0975089	+	0.995235i	$0.531087\pi$
$588$	43.1391	+	27.3769i	1.77903	+	1.12900i
$589$	−0.537296	+	0.649479i	−0.0221389	+	0.0267613i
$590$	4.19080	+	44.8077i	0.172532	+	1.84471i
$591$	−3.20913	−	0.823964i	−0.132006	−	0.0338934i
$592$	−0.381984	+	0.179748i	−0.0156995	+	0.00738761i
$593$	−0.156214	−	0.0507571i	−0.00641495	−	0.00208434i	0.305808	−	0.952093i	$-0.401074\pi$
$593$	−0.156214	−	0.0507571i	−0.00641495	−	0.00208434i	−0.312223	+	0.950009i	$0.601074\pi$
$594$	−7.74460	−	4.25763i	−0.317765	−	0.174693i
$595$	−37.1656	−	16.1267i	−1.52364	−	0.661131i
$596$	−26.3908	−	3.33393i	−1.08101	−	0.136563i
$597$	−0.325651	+	2.57779i	−0.0133280	+	0.105502i
$598$	77.8023	−	49.3749i	3.18157	−	2.01909i
$599$	21.6046	−	15.6966i	0.882739	−	0.641347i	−0.0512358	−	0.998687i	$-0.516316\pi$
$599$	21.6046	−	15.6966i	0.882739	−	0.641347i	0.933975	+	0.357339i	$0.116316\pi$
$600$	−9.41449	+	9.98569i	−0.384345	+	0.407664i
$601$	−19.3469	−	14.0564i	−0.789178	−	0.573372i	0.118541	−	0.992949i	$-0.462178\pi$
$601$	−19.3469	−	14.0564i	−0.789178	−	0.573372i	−0.907719	+	0.419578i	$0.862178\pi$
$602$	−28.0146	−	1.76253i	−1.14179	−	0.0718353i
$603$	6.95862	+	12.6577i	0.283377	+	0.515460i
$604$	−18.6346	+	39.6005i	−0.758230	+	1.61132i
$605$	3.04639	−	8.43545i	0.123853	−	0.342950i
$606$	−0.981065	+	5.14292i	−0.0398530	+	0.208917i
$607$	23.0017	+	31.6591i	0.933610	+	1.28500i	0.958435	+	0.285312i	$0.0920973\pi$
$607$	23.0017	+	31.6591i	0.933610	+	1.28500i	−0.0248244	+	0.999692i	$0.507903\pi$
$608$	6.86395	−	12.4855i	0.278370	−	0.506353i
$609$	−11.9105	+	18.7679i	−0.482637	+	0.760514i
$610$	21.9316	−	28.2162i	0.887983	−	1.14244i
$611$	−15.1027	−	5.97957i	−0.610988	−	0.241907i
$612$	4.45979	+	11.2641i	0.180276	+	0.455326i
$613$	−15.1122	+	12.5019i	−0.610375	+	0.504946i	−0.890480	−	0.455023i	$-0.849631\pi$
$613$	−15.1122	+	12.5019i	−0.610375	+	0.504946i	0.280104	+	0.959970i	$0.409631\pi$
$614$	62.4855	−	16.0436i	2.52171	−	0.647465i
$615$	15.4759	+	10.5398i	0.624049	+	0.425008i
$616$	47.3679	−	18.7543i	1.90851	−	0.755631i
$617$	−0.480579	−	0.511764i	−0.0193474	−	0.0206029i	0.719222	−	0.694780i	$-0.244498\pi$
$617$	−0.480579	−	0.511764i	−0.0193474	−	0.0206029i	−0.738570	+	0.674177i	$0.764498\pi$
$618$	2.56049	−	3.52422i	0.102998	−	0.141765i
$619$	14.3339	+	30.4610i	0.576126	+	1.22433i	0.954371	+	0.298625i	$0.0965280\pi$
$619$	14.3339	+	30.4610i	0.576126	+	1.22433i	−0.378244	+	0.925706i	$0.623472\pi$
$620$	−1.85207	+	1.62956i	−0.0743809	+	0.0654448i
$621$	−7.04960	+	3.87555i	−0.282891	+	0.155521i
$622$	39.4831	−	7.53181i	1.58313	−	0.301998i
$623$	−6.39610	−	24.9112i	−0.256254	−	0.998044i
$624$	−0.730707			−0.0292517
$625$	−24.1898	−	6.31315i	−0.967590	−	0.252526i
$626$	−4.08646			−0.163328
$627$	−2.35817	−	9.18447i	−0.0941763	−	0.366792i
$628$	−66.6760	+	12.7191i	−2.66066	+	0.507548i
$629$	9.61502	−	5.28590i	0.383376	−	0.210763i
$630$	18.3451	−	16.1411i	0.730888	−	0.643078i
$631$	−16.9750	−	36.0738i	−0.675766	−	1.43608i	−0.888459	−	0.458956i	$-0.848223\pi$
$631$	−16.9750	−	36.0738i	−0.675766	−	1.43608i	0.212693	−	0.977119i	$-0.431777\pi$
$632$	−16.7048	+	22.9921i	−0.664480	+	0.914578i
$633$	−1.19376	−	1.27122i	−0.0474476	−	0.0505266i
$634$	−4.97998	+	1.97171i	−0.197780	+	0.0783067i
$635$	−24.9349	−	16.9819i	−0.989511	−	0.673905i
$636$	−7.56132	+	1.94142i	−0.299826	+	0.0769822i
$637$	61.7132	−	51.0536i	2.44516	−	2.02282i
$638$	15.0956	+	38.1271i	0.597639	+	1.50947i
$639$	−8.89698	−	3.52256i	−0.351959	−	0.139350i
$640$	24.6787	−	31.7506i	0.975513	−	1.25505i
$641$	−6.53804	+	10.3023i	−0.258237	+	0.406916i	−0.948566	−	0.316579i	$-0.897466\pi$
$641$	−6.53804	+	10.3023i	−0.258237	+	0.406916i	0.690329	+	0.723495i	$0.257466\pi$
$642$	5.62776	−	10.2369i	0.222110	−	0.404016i
$643$	−2.89532	−	3.98507i	−0.114180	−	0.157156i	0.748102	−	0.663584i	$-0.230965\pi$
$643$	−2.89532	−	3.98507i	−0.114180	−	0.157156i	−0.862282	+	0.506428i	$0.830965\pi$
$644$	23.1325	−	121.265i	0.911550	−	4.77851i
$645$	−1.95098	+	5.40225i	−0.0768197	+	0.212713i
$646$	−8.99002	+	19.1048i	−0.353708	+	0.751667i
$647$	4.32583	+	7.86866i	0.170066	+	0.309349i	0.947581	−	0.319515i	$-0.103520\pi$
$647$	4.32583	+	7.86866i	0.170066	+	0.309349i	−0.777515	+	0.628864i	$0.783520\pi$
$648$	−2.73937	−	0.172347i	−0.107613	−	0.00677042i
$649$	−27.6555	−	20.0929i	−1.08557	−	0.788715i
$650$	27.4915	+	50.2425i	1.07831	+	1.97067i
$651$	1.33482	−	0.969801i	0.0523156	−	0.0380095i
$652$	40.5900	−	25.7592i	1.58963	−	1.00881i
$653$	−0.517263	+	4.09456i	−0.0202421	+	0.160233i	−0.998996	−	0.0448077i	$-0.985733\pi$
$653$	−0.517263	+	4.09456i	−0.0202421	+	0.160233i	0.978754	+	0.205040i	$0.0657325\pi$
$654$	12.2856	+	1.55203i	0.480404	+	0.0606892i
$655$	−27.9033	−	12.1077i	−1.09027	−	0.473085i
$656$	−1.06778	−	0.587017i	−0.0416898	−	0.0229192i
$657$	2.24486	+	0.729399i	0.0875804	+	0.0284566i
$658$	−31.9844	+	15.0507i	−1.24688	+	0.586738i
$659$	−11.1992	−	2.87546i	−0.436258	−	0.112012i	0.0241726	−	0.999708i	$-0.492305\pi$
$659$	−11.1992	−	2.87546i	−0.436258	−	0.112012i	−0.460430	+	0.887696i	$0.652305\pi$
$660$	−2.58427	−	27.6308i	−0.100592	−	1.07553i
$661$	−21.0157	+	25.4036i	−0.817416	+	0.988086i	0.182572	+	0.983192i	$0.441558\pi$
$661$	−21.0157	+	25.4036i	−0.817416	+	0.988086i	−0.999988	+	0.00489356i	$0.998442\pi$
$662$	35.2230	+	22.3532i	1.36898	+	0.868782i
$663$	18.9540	−	1.19248i	0.736110	−	0.0463121i
$664$	−6.16031	−	9.70709i	−0.239066	−	0.376708i
$665$	26.0987	+	2.49314i	1.01206	+	0.0966798i
$666$	0.415531	+	6.60468i	0.0161015	+	0.255926i
$667$	36.6656	+	6.99434i	1.41970	+	0.270822i
$668$	21.1674	−	6.87770i	0.818991	−	0.266106i
$669$	−10.8504	+	10.1892i	−0.419502	+	0.393939i
$670$	−33.5129	+	65.6120i	−1.29472	+	2.53481i
$671$	5.08659	+	26.6648i	0.196366	+	1.02938i
$672$	−19.0911	+	20.3300i	−0.736456	+	0.784246i
$673$	−3.42408	+	8.64824i	−0.131989	+	0.333365i	−0.980708	−	0.195478i	$-0.937374\pi$
$673$	−3.42408	+	8.64824i	−0.131989	+	0.333365i	0.848719	+	0.528843i	$0.177374\pi$
$674$	−4.09519	−	12.6037i	−0.157741	−	0.485477i
$675$	−2.11993	−	4.52834i	−0.0815961	−	0.174296i
$676$	12.0918	−	37.2147i	0.465068	−	1.43133i
$677$	−28.2974	−	23.4096i	−1.08756	−	0.899705i	−0.0921790	−	0.995742i	$-0.529383\pi$
$677$	−28.2974	−	23.4096i	−1.08756	−	0.899705i	−0.995378	+	0.0960373i	$0.969383\pi$
$678$	−32.8697	−	15.4673i	−1.26235	−	0.594018i
$679$	−19.6532	−	18.4556i	−0.754220	−	0.708260i
$680$	−13.0662	+	19.1855i	−0.501068	+	0.735730i
$681$	−6.27512	+	0.792732i	−0.240463	+	0.0303776i
$682$		−	3.04379i		−	0.116553i
$683$	−2.81652	−	22.2951i	−0.107771	−	0.853097i	−0.949624	−	0.313390i	$-0.898535\pi$
$683$	−2.81652	−	22.2951i	−0.107771	−	0.853097i	0.841853	−	0.539707i	$-0.181465\pi$
$684$	−4.99733	−	6.04073i	−0.191078	−	0.230973i
$685$	5.62418	−	35.2834i	0.214889	−	1.34811i
$686$	6.14121	−	97.6118i	0.234473	−	3.72684i
$687$	1.29988	−	5.06269i	0.0495935	−	0.193154i
$688$	0.0929562	−	0.362040i	0.00354392	−	0.0138027i
$689$	−0.768409	+	12.2135i	−0.0292741	+	0.465298i
$690$	−36.5421	−	18.6648i	−1.39114	−	0.710556i
$691$	−22.0874	−	26.6991i	−0.840244	−	1.01568i	−0.999595	−	0.0284581i	$-0.990940\pi$
$691$	−22.0874	−	26.6991i	−0.840244	−	1.01568i	0.159351	−	0.987222i	$-0.449060\pi$
$692$	−1.97710	−	15.6503i	−0.0751580	−	0.594937i
$693$			18.5608i			0.705065i
$694$	−15.5212	+	1.96078i	−0.589177	+	0.0744304i
$695$	41.8763	−	15.0296i	1.58846	−	0.570104i
$696$	9.28389	+	8.71816i	0.351905	+	0.330461i
$697$	28.6553	+	13.4842i	1.08540	+	0.510750i
$698$	−29.4484	−	24.3618i	−1.11464	−	0.922109i
$699$	−0.622562	+	1.91605i	−0.0235474	+	0.0724716i
$700$	74.2803	+	19.2289i	2.80753	+	0.726784i
$701$	13.0202	+	40.0719i	0.491765	+	1.51350i	0.821939	+	0.569576i	$0.192892\pi$
$701$	13.0202	+	40.0719i	0.491765	+	1.51350i	−0.330174	+	0.943920i	$0.607108\pi$
$702$	−4.21665	+	10.6500i	−0.159147	+	0.401960i
$703$	−4.86057	+	5.17598i	−0.183320	+	0.195216i
$704$	9.42933	+	49.4303i	0.355381	+	1.86297i
$705$	1.12443	+	7.14519i	0.0423486	+	0.269104i
$706$	−39.0010	+	36.6243i	−1.46782	+	1.37837i
$707$	10.4576	−	3.39787i	0.393298	−	0.127790i
$708$	−27.7623	−	5.29594i	−1.04337	−	0.199033i
$709$	0.443259	+	7.04541i	0.0166470	+	0.264596i	0.997543	+	0.0700615i	$0.0223196\pi$
$709$	0.443259	+	7.04541i	0.0166470	+	0.264596i	−0.980896	+	0.194534i	$0.937680\pi$
$710$	−10.5999	−	47.6428i	−0.397806	−	1.78800i
$711$	−5.54801	−	8.74226i	−0.208067	−	0.327860i
$712$	−14.7067	+	0.925268i	−0.551158	+	0.0346759i
$713$	−2.33933	−	1.48458i	−0.0876086	−	0.0555981i
$714$	26.3441	−	31.8446i	0.985904	−	1.19175i
$715$	−42.4462	−	9.53201i	−1.58740	−	0.356477i
$716$	22.9011	+	5.87999i	0.855853	+	0.219746i
$717$	−11.6211	+	5.46846i	−0.433997	+	0.204223i
$718$	−54.9379	−	17.8504i	−2.05026	−	0.666171i
$719$	28.4907	+	15.6629i	1.06252	+	0.584127i	0.914387	−	0.404840i	$-0.132673\pi$
$719$	28.4907	+	15.6629i	1.06252	+	0.584127i	0.148135	+	0.988967i	$0.452673\pi$
$720$	0.165356	+	0.280235i	0.00616245	+	0.0104437i
$721$	−9.07654	−	1.14663i	−0.338028	−	0.0427029i
$722$	−3.71948	+	29.4427i	−0.138425	+	1.09575i
$723$	14.8867	−	9.44739i	0.553643	−	0.351352i
$724$	39.9662	−	29.0371i	1.48533	−	1.07916i
$725$	−5.81404	+	22.4594i	−0.215928	+	0.834120i
$726$	7.40185	+	5.37776i	0.274709	+	0.199587i
$727$	−32.0917	−	2.01904i	−1.19022	−	0.0748820i	−0.544701	−	0.838630i	$-0.683357\pi$
$727$	−32.0917	−	2.01904i	−1.19022	−	0.0748820i	−0.645514	+	0.763748i	$0.723357\pi$
$728$	−31.8098	−	57.8618i	−1.17895	−	2.14450i
$729$	0.425779	−	0.904827i	0.0157696	−	0.0335121i
$730$	3.34745	+	11.5647i	0.123895	+	0.428030i
$731$	−1.82037	+	9.54273i	−0.0673289	+	0.352951i
$732$	13.1920	+	18.1573i	0.487592	+	0.671112i
$733$	−5.88940	+	10.7128i	−0.217530	+	0.395685i	−0.962446	−	0.271473i	$-0.912489\pi$
$733$	−5.88940	+	10.7128i	−0.217530	+	0.395685i	0.744916	+	0.667158i	$0.232489\pi$
$734$	−29.2274	+	46.0550i	−1.07880	+	1.69992i
$735$	−33.5450	−	12.1145i	−1.23733	−	0.446850i
$736$	43.5434	+	17.2401i	1.60503	+	0.635477i
$737$	−20.6014	−	52.0331i	−0.758862	−	1.91667i
$738$	−14.7175	+	12.1754i	−0.541760	+	0.448183i
$739$	−46.3501	+	11.9007i	−1.70502	+	0.437774i	−0.970556	−	0.240876i	$-0.922565\pi$
$739$	−46.3501	+	11.9007i	−1.70502	+	0.437774i	−0.734462	+	0.678650i	$0.762565\pi$
$740$	−16.4323	+	12.7201i	−0.604062	+	0.467601i
$741$	−11.4268	+	4.52420i	−0.419775	+	0.166201i
$742$	18.2305	+	19.4135i	0.669264	+	0.712693i
$743$	3.49681	−	4.81295i	0.128286	−	0.176570i	−0.740043	−	0.672560i	$-0.765195\pi$
$743$	3.49681	−	4.81295i	0.128286	−	0.176570i	0.868328	+	0.495990i	$0.165195\pi$
$744$	−0.402499	−	0.855355i	−0.0147563	−	0.0313588i
$745$	18.4879	−	1.72914i	0.677344	−	0.0633509i
$746$	−45.8765	+	25.2208i	−1.67966	+	0.923400i
$747$	4.11441	−	0.784865i	0.150538	−	0.0287167i
$748$	−11.6730	−	45.4632i	−0.426806	−	1.66230i
$749$	−24.5337			−0.896443
$750$	13.0473	−	21.9130i	0.476422	−	0.800148i
$751$	−24.6183			−0.898334			−0.449167	−	0.893448i	$-0.648279\pi$
$751$	−24.6183			−0.898334			−0.449167	+	0.893448i	$0.648279\pi$
$752$	−0.117060	−	0.455919i	−0.00426874	−	0.0166257i
$753$	6.85100	−	1.30690i	0.249664	−	0.0476260i
$754$	46.5738	−	25.6041i	1.69612	−	0.932448i
$755$	6.69400	−	29.8085i	0.243620	−	1.08484i
$756$	6.53391	+	13.8853i	0.237636	+	0.505002i
$757$	16.4498	−	22.6412i	0.597878	−	0.822908i	−0.397634	−	0.917544i	$-0.630169\pi$
$757$	16.4498	−	22.6412i	0.597878	−	0.822908i	0.995512	+	0.0946359i	$0.0301687\pi$
$758$	3.66633	+	3.90424i	0.133167	+	0.141808i
$759$	28.9795	−	11.4738i	1.05189	−	0.416472i
$760$	4.20510	−	14.4207i	0.152535	−	0.523094i
$761$	−9.16345	+	2.35277i	−0.332175	+	0.0852880i	−0.411094	−	0.911593i	$-0.634853\pi$
$761$	−9.16345	+	2.35277i	−0.332175	+	0.0852880i	0.0789190	+	0.996881i	$0.474853\pi$
$762$	23.7130	−	19.6171i	0.859032	−	0.710653i
$763$	−9.57375	−	24.1805i	−0.346593	−	0.875394i
$764$	−70.1032	−	27.7558i	−2.53625	−	1.00417i
$765$	−4.74652	−	6.99920i	−0.171611	−	0.253057i
$766$	18.9077	−	29.7938i	0.683165	−	1.07650i
$767$	−21.3442	+	38.8249i	−0.770693	+	1.40189i
$768$	8.84415	+	12.1729i	0.319136	+	0.439253i
$769$	−2.41862	+	12.6789i	−0.0872178	+	0.457212i	0.911707	+	0.410842i	$0.134765\pi$
$769$	−2.41862	+	12.6789i	−0.0872178	+	0.457212i	−0.998924	+	0.0463698i	$0.985235\pi$
$770$	−78.3538	+	53.1358i	−2.82367	+	1.91488i
$771$	4.38336	−	9.31511i	0.157863	−	0.335475i
$772$	−17.6362	−	32.0801i	−0.634740	−	1.15459i
$773$	21.8777	+	1.37643i	0.786887	+	0.0495067i	0.451149	−	0.892449i	$-0.351014\pi$
$773$	21.8777	+	1.37643i	0.786887	+	0.0495067i	0.335738	+	0.941955i	$0.391014\pi$
$774$	−4.74031	−	3.44404i	−0.170387	−	0.123793i
$775$	1.01494	−	1.39115i	0.0364579	−	0.0499715i
$776$	−12.4968	+	9.07945i	−0.448609	+	0.325933i
$777$	11.7348	−	7.44710i	0.420982	−	0.267163i
$778$	−2.09829	+	16.6097i	−0.0752273	+	0.595485i
$779$	−20.3325	−	2.56860i	−0.728489	−	0.0920295i
$780$	−35.1094	+	7.81138i	−1.25712	+	0.279692i
$781$	32.4881	+	17.8605i	1.16251	+	0.639098i
$782$	−66.0051	−	21.4464i	−2.36034	−	0.766920i
$783$	−4.19834	+	1.97559i	−0.150036	+	0.0706018i
$784$	2.24807	+	0.577207i	0.0802883	+	0.0206145i
$785$	43.5043	−	18.7749i	1.55274	−	0.670103i
$786$	19.7787	−	23.9083i	0.705482	−	0.852782i
$787$	−28.2877	−	17.9519i	−1.00835	−	0.639918i	−0.0743643	−	0.997231i	$-0.523693\pi$
$787$	−28.2877	−	17.9519i	−1.00835	−	0.639918i	−0.933984	+	0.357314i	$0.883693\pi$
$788$	10.5923	−	0.666408i	0.377334	−	0.0237398i
$789$	−6.57894	−	10.3668i	−0.234217	−	0.369066i
$790$	21.0224	−	48.4481i	0.747943	−	1.72371i
$791$	4.79046	+	76.1422i	0.170329	+	2.70731i
$792$	10.4460	+	1.99269i	0.371183	+	0.0708070i
$793$	33.4609	−	10.8721i	1.18823	−	0.386079i
$794$	−43.3103	+	40.6710i	−1.53702	+	1.44336i
$795$	4.85791	−	2.46917i	0.172292	−	0.0875724i
$796$	−1.55958	−	8.17561i	−0.0552779	−	0.289777i
$797$	17.0928	−	18.2019i	0.605457	−	0.644746i	−0.351084	−	0.936344i	$-0.614187\pi$
$797$	17.0928	−	18.2019i	0.605457	−	0.644746i	0.956541	+	0.291598i	$0.0941869\pi$
$798$	−9.84554	+	24.8670i	−0.348528	+	0.880282i
$799$	3.78048	+	11.6351i	0.133744	+	0.411621i
$800$	−12.4456	+	26.3127i	−0.440017	+	0.930294i
$801$	1.65900	−	5.10588i	0.0586180	−	0.180408i
$802$	6.92860	+	5.73183i	0.244657	+	0.202398i
$803$	−8.27470	−	3.89378i	−0.292008	−	0.137408i
$804$	−33.7290	−	31.6736i	−1.18953	−	1.11704i
$805$	2.62152	+	86.1360i	0.0923964	+	3.03590i
$806$	−3.91387	+	0.494437i	−0.137860	+	0.0174158i
$807$		−	31.6191i		−	1.11305i
$808$	−0.789601	−	6.25034i	−0.0277781	−	0.219886i
$809$	−28.4602	−	34.4024i	−1.00061	−	1.20953i	−0.977747	−	0.209787i	$-0.932723\pi$
$809$	−28.4602	−	34.4024i	−1.00061	−	1.20953i	−0.0228592	−	0.999739i	$-0.507277\pi$
$810$	5.03862	−	0.792923i	0.177039	−	0.0278605i
$811$	−1.74945	+	27.8067i	−0.0614316	+	0.976427i	0.839747	+	0.542978i	$0.182703\pi$
$811$	−1.74945	+	27.8067i	−0.0614316	+	0.976427i	−0.901178	+	0.433449i	$0.857297\pi$
$812$	17.7076	−	68.9664i	0.621414	−	2.42025i
$813$	−5.86809	+	22.8547i	−0.205803	+	0.801550i
$814$	1.60993	−	25.5891i	0.0564280	−	0.896898i
$815$	−23.7526	+	23.7056i	−0.832018	+	0.830372i
$816$	0.350802	+	0.424046i	0.0122805	+	0.0148446i
$817$	−0.787935	−	6.23714i	−0.0275663	−	0.218210i
$818$			22.3197i			0.780391i
$819$	23.8665	−	3.01504i	0.833962	−	0.105354i
$820$	−57.5806	−	16.7906i	−2.01080	−	0.586353i
$821$	−24.6043	−	23.1050i	−0.858697	−	0.806370i	0.123866	−	0.992299i	$-0.460471\pi$
$821$	−24.6043	−	23.1050i	−0.858697	−	0.806370i	−0.982563	+	0.185929i	$0.940471\pi$
$822$	32.9791	+	15.5188i	1.15028	+	0.541279i
$823$	2.11739	+	1.75165i	0.0738074	+	0.0610588i	0.673596	−	0.739100i	$-0.264749\pi$
$823$	2.11739	+	1.75165i	0.0738074	+	0.0610588i	−0.599789	+	0.800158i	$0.704749\pi$
$824$	−1.61978	+	4.98519i	−0.0564279	+	0.173667i
$825$	5.94975	+	18.4357i	0.207144	+	0.641847i
$826$	29.7944	+	91.6976i	1.03668	+	3.19057i
$827$	17.8647	−	45.1211i	0.621217	−	1.56902i	−0.188422	−	0.982088i	$-0.560337\pi$
$827$	17.8647	−	45.1211i	0.621217	−	1.56902i	0.809639	−	0.586928i	$-0.199663\pi$
$828$	17.6404	−	18.7851i	0.613046	−	0.652827i
$829$	−3.34775	−	17.5495i	−0.116272	−	0.609520i	−0.991951	−	0.126626i	$-0.959585\pi$
$829$	−3.34775	−	17.5495i	−0.116272	−	0.609520i	0.875678	−	0.482895i	$-0.160415\pi$
$830$	15.0920	+	15.1219i	0.523851	+	0.524890i
$831$	−2.09699	+	1.96920i	−0.0727436	+	0.0683108i
$832$	62.0285	−	20.1543i	2.15045	−	0.698724i
$833$	−59.2551	−	11.3035i	−2.05307	−	0.391644i
$834$	2.84989	+	45.2976i	0.0986835	+	1.56853i
$835$	−13.3806	+	7.89541i	−0.463056	+	0.273232i
$836$	16.2756	+	25.6463i	0.562904	+	0.886995i
$837$	0.343727	−	0.0216255i	0.0118809	−	0.000747486i
$838$	14.6540	+	9.29973i	0.506215	+	0.321254i
$839$	18.9668	−	22.9269i	0.654806	−	0.791524i	−0.333705	−	0.942678i	$-0.608299\pi$
$839$	18.9668	−	22.9269i	0.654806	−	0.791524i	0.988510	+	0.151153i	$0.0482988\pi$
$840$	−14.9922	+	25.2933i	−0.517281	+	0.872700i
$841$	−7.23626	−	1.85796i	−0.249526	−	0.0640674i
$842$	57.0125	−	26.8280i	1.96478	−	0.924555i
$843$	19.7366	+	6.41282i	0.679766	+	0.220869i
$844$	4.89514	+	2.69113i	0.168498	+	0.0926324i
$845$	−2.59748	+	27.1909i	−0.0893560	+	0.935397i
$846$	−7.32052	−	0.924797i	−0.251685	−	0.0317952i
$847$	2.40826	−	19.0633i	0.0827486	−	0.655023i
$848$	−0.299423	+	0.190020i	−0.0102822	+	0.00652530i
$849$	−6.30616	+	4.58169i	−0.216427	+	0.157243i
$850$	15.9586	−	40.0746i	0.547375	−	1.37455i
$851$	−18.8815	−	13.7182i	−0.647250	−	0.470254i
$852$	30.5916	+	1.92466i	1.04805	+	0.0659378i
$853$	−9.82028	−	17.8630i	−0.336240	−	0.611618i	0.653095	−	0.757276i	$-0.273470\pi$
$853$	−9.82028	−	17.8630i	−0.336240	−	0.611618i	−0.989335	+	0.145658i	$0.953470\pi$
$854$	32.5996	−	69.2778i	1.11554	−	2.37064i
$855$	4.32092	+	3.35851i	0.147772	+	0.114859i
$856$	−2.63394	+	13.8076i	−0.0900264	+	0.471935i
$857$	−3.83746	−	5.28181i	−0.131085	−	0.180423i	0.738429	−	0.674331i	$-0.235568\pi$
$857$	−3.83746	−	5.28181i	−0.131085	−	0.180423i	−0.869514	+	0.493908i	$0.835568\pi$
$858$	21.3797	−	38.8895i	0.729891	−	1.32767i
$859$	28.2517	−	44.5176i	0.963936	−	1.51892i	0.113038	−	0.993591i	$-0.463942\pi$
$859$	28.2517	−	44.5176i	0.963936	−	1.51892i	0.850899	−	0.525330i	$-0.176058\pi$
$860$	0.596141	−	18.3892i	0.0203282	−	0.627068i
$861$	37.2981	+	14.7674i	1.27112	+	0.503271i
$862$	27.3480	+	69.0732i	0.931478	+	2.35264i
$863$	20.2860	−	16.7821i	0.690545	−	0.571268i	−0.224572	−	0.974458i	$-0.572098\pi$
$863$	20.2860	−	16.7821i	0.690545	−	0.571268i	0.915117	+	0.403189i	$0.132098\pi$
$864$	−5.63862	+	1.44775i	−0.191830	+	0.0492535i
$865$	3.71978	+	10.3643i	0.126476	+	0.352397i
$866$	19.5648	−	7.74625i	0.664839	−	0.263228i
$867$	1.84577	+	1.96554i	0.0626856	+	0.0667533i
$868$	−3.10655	+	4.27581i	−0.105443	+	0.145130i
$869$	17.0805	+	36.2979i	0.579417	+	1.23132i
$870$	−20.3589	−	12.0675i	−0.690232	−	0.409125i
$871$	−63.5606	+	34.9427i	−2.15367	+	1.18399i
$872$	−14.6367	+	2.79210i	−0.495660	+	0.0945523i
$873$	−1.39955	−	5.45091i	−0.0473677	−	0.184485i
$874$	44.9118			1.51917
$875$	−53.5292	−	1.84148i	−1.80962	−	0.0622535i
$876$	−7.56100			−0.255463
$877$	8.85506	+	34.4882i	0.299014	+	1.16458i	0.923516	+	0.383560i	$0.125302\pi$
$877$	8.85506	+	34.4882i	0.299014	+	1.16458i	−0.624502	+	0.781023i	$0.714698\pi$
$878$	51.1837	−	9.76381i	1.72737	−	0.329513i
$879$	9.76036	−	5.36581i	0.329209	−	0.180984i
$880$	−0.499522	−	1.15747i	−0.0168389	−	0.0390184i
$881$	9.80969	+	20.8466i	0.330497	+	0.702341i	0.999150	−	0.0412334i	$-0.0131287\pi$
$881$	9.80969	+	20.8466i	0.330497	+	0.702341i	−0.668653	+	0.743575i	$0.733129\pi$
$882$	21.3856	−	29.4348i	0.720091	−	0.991120i
$883$	25.4542	+	27.1059i	0.856601	+	0.912188i	0.996960	−	0.0779131i	$-0.0248257\pi$
$883$	25.4542	+	27.1059i	0.856601	+	0.912188i	−0.140359	+	0.990101i	$0.544826\pi$
$884$	−56.5630	+	22.3949i	−1.90242	+	0.753221i
$885$	19.7199	−	0.600168i	0.662876	−	0.0201744i
$886$	−30.6672	+	7.87400i	−1.03028	+	0.264532i
$887$	−32.4866	+	26.8753i	−1.09079	+	0.902383i	−0.995659	−	0.0930814i	$-0.970328\pi$
$887$	−32.4866	+	26.8753i	−1.09079	+	0.902383i	−0.0951352	+	0.995464i	$0.530328\pi$
$888$	−2.93140	−	7.40386i	−0.0983712	−	0.248457i
$889$	−60.0950	−	23.7933i	−2.01552	−	0.798002i
$890$	26.3037	−	7.61369i	0.881703	−	0.255211i
$891$	−2.07600	+	3.27126i	−0.0695487	+	0.109591i
$892$	22.9699	−	41.7821i	0.769090	−	1.39897i
$893$	−4.65343	−	6.40490i	−0.155721	−	0.214332i
$894$	−3.54943	+	18.6068i	−0.118711	+	0.622304i
$895$	−16.4960	−	0.534767i	−0.551401	−	0.0178753i
$896$	36.6831	−	77.9556i	1.22550	−	2.60431i
$897$	−19.4611	−	35.3996i	−0.649787	−	1.18196i
$898$	−67.6538	−	4.25642i	−2.25764	−	0.142039i
$899$	−1.29283	−	0.939296i	−0.0431183	−	0.0313273i
$900$	10.9409	+	11.6972i	0.364695	+	0.389906i
$901$	7.45668	−	5.41760i	0.248418	−	0.180486i
$902$	62.4842	−	39.6537i	2.08050	−	1.32032i
$903$	−1.54230	+	12.2086i	−0.0513246	+	0.406276i
$904$	43.3673	+	5.47856i	1.44237	+	0.182214i
$905$	−22.8306	+	25.8446i	−0.758916	+	0.859103i
$906$	27.3108	+	15.0142i	0.907340	+	0.498814i
$907$	45.6809	+	14.8426i	1.51681	+	0.492842i	0.944868	−	0.327452i	$-0.106190\pi$
$907$	45.6809	+	14.8426i	1.51681	+	0.492842i	0.571943	+	0.820294i	$0.306190\pi$
$908$	18.3325	−	8.62663i	0.608386	−	0.286285i
$909$	2.22315	+	0.570809i	0.0737373	+	0.0189325i
$910$	81.0528	+	92.1202i	2.68687	+	3.05375i
$911$	16.0907	−	19.4503i	0.533108	−	0.644417i	−0.433355	−	0.901223i	$-0.642670\pi$
$911$	16.0907	−	19.4503i	0.533108	−	0.644417i	0.966463	+	0.256807i	$0.0826703\pi$
$912$	−0.300701	−	0.190830i	−0.00995719	−	0.00631902i
$913$	−16.1963	+	1.01898i	−0.536018	+	0.0337234i
$914$	−25.9453	−	40.8833i	−0.858194	−	1.35230i
$915$	−11.7416	−	10.3723i	−0.388166	−	0.342898i
$916$	1.05132	+	16.7103i	0.0347366	+	0.552122i
$917$	−64.0119	−	12.2109i	−2.11386	−	0.403240i
$918$	8.20482	−	2.66591i	0.270799	−	0.0879881i
$919$	−2.95826	+	2.77799i	−0.0975841	+	0.0916376i	−0.731804	−	0.681515i	$-0.761321\pi$
$919$	−2.95826	+	2.77799i	−0.0975841	+	0.0916376i	0.634220	+	0.773153i	$0.281321\pi$
$920$	48.7589	+	7.77218i	1.60753	+	0.256241i
$921$	−5.29944	−	27.7806i	−0.174622	−	0.915403i
$922$	−43.5304	+	46.3552i	−1.43360	+	1.52663i
$923$	17.6886	−	44.6762i	0.582227	−	1.47054i
$924$	−18.3728	−	56.5456i	−0.604420	−	1.86021i
$925$	9.26845	−	11.1585i	0.304745	−	0.366890i
$926$	−5.88160	+	18.1017i	−0.193281	+	0.594858i
$927$	−1.47145	−	1.21729i	−0.0483288	−	0.0399811i
$928$	24.4407	+	11.5009i	0.802305	+	0.377536i
$929$	8.40490	+	7.89272i	0.275756	+	0.258952i	0.810069	−	0.586335i	$-0.199430\pi$
$929$	8.40490	+	7.89272i	0.275756	+	0.258952i	−0.534313	+	0.845287i	$0.679430\pi$
$930$	1.07531	+	1.38913i	0.0352609	+	0.0455512i
$931$	38.7293	−	4.89264i	1.26930	−	0.160350i
$932$		−	6.45351i		−	0.211392i
$933$	−2.20852	−	17.4822i	−0.0723036	−	0.572342i
$934$	−45.8402	−	55.4113i	−1.49994	−	1.81311i
$935$	14.8461	+	29.2087i	0.485521	+	0.955226i
$936$	0.865440	−	13.7558i	0.0282878	−	0.449622i
$937$	−12.9084	+	50.2748i	−0.421698	+	1.64241i	0.302746	+	0.953071i	$0.402097\pi$
$937$	−12.9084	+	50.2748i	−0.421698	+	1.64241i	−0.724444	+	0.689334i	$0.757903\pi$
$938$	−39.2543	+	152.885i	−1.28170	+	4.99189i
$939$	−0.112487	+	1.78793i	−0.00367087	+	0.0583468i
$940$	−10.4984	−	20.6549i	−0.342420	−	0.673687i
$941$	4.46318	+	5.39506i	0.145496	+	0.175874i	0.838227	−	0.545322i	$-0.183593\pi$
$941$	4.46318	+	5.39506i	0.145496	+	0.175874i	−0.692731	+	0.721196i	$0.743593\pi$
$942$	6.05815	+	47.9552i	0.197385	+	1.56246i
$943$		−	67.3635i		−	2.19366i
$944$	−1.27377	+	0.160915i	−0.0414578	+	0.00523733i
$945$	−6.55718	−	8.47077i	−0.213305	−	0.275554i
$946$	16.5486	+	15.5402i	0.538042	+	0.505255i
$947$	32.8903	+	15.4770i	1.06879	+	0.502936i	0.877983	−	0.478692i	$-0.158889\pi$
$947$	32.8903	+	15.4770i	1.06879	+	0.502936i	0.190809	+	0.981627i	$0.438889\pi$
$948$	25.5558	+	21.1416i	0.830013	+	0.686646i
$949$	−3.66268	+	11.2726i	−0.118896	+	0.365923i
$950$	−1.80793	+	27.8554i	−0.0586570	+	0.903749i
$951$	0.725592	+	2.23314i	0.0235289	+	0.0724146i
$952$	−18.3071	+	46.2385i	−0.593337	+	1.49860i
$953$	−19.8381	+	21.1254i	−0.642619	+	0.684320i	−0.964988	−	0.262294i	$-0.915521\pi$
$953$	−19.8381	+	21.1254i	−0.642619	+	0.684320i	0.322369	+	0.946614i	$0.395521\pi$
$954$	1.04167	+	5.46062i	0.0337253	+	0.176794i
$955$	51.9756	+	8.28492i	1.68189	+	0.268094i
$956$	29.9906	−	28.1631i	0.969967	−	0.910859i
$957$	17.0971	−	5.55518i	0.552670	−	0.179573i
$958$	16.2032	+	3.09093i	0.523502	+	0.0998633i
$959$	−4.80640	−	76.3956i	−0.155207	−	2.46694i
$960$	−21.7662	−	19.2278i	−0.702500	−	0.620575i
$961$	−16.5471	−	26.0740i	−0.533777	−	0.841097i
$962$	−33.1654	+	2.08659i	−1.06930	+	0.0672744i
$963$	−4.32397	−	2.74407i	−0.139338	−	0.0884265i
$964$	−36.0008	+	43.5175i	−1.15951	+	1.40160i
$965$	16.8805	+	19.1855i	0.543404	+	0.617603i
$966$	−85.1485	−	21.8624i	−2.73961	−	0.703412i
$967$	44.0766	−	20.7409i	1.41741	−	0.666982i	0.443993	−	0.896030i	$-0.353561\pi$
$967$	44.0766	−	20.7409i	1.41741	−	0.666982i	0.973415	+	0.229049i	$0.0735615\pi$
$968$	−10.4703	−	3.40201i	−0.336528	−	0.109345i
$969$	8.11135	+	4.45925i	0.260574	+	0.143252i
$970$	19.0042	−	21.5130i	0.610188	−	0.690742i
$971$	−17.1967	−	2.17245i	−0.551868	−	0.0697171i	−0.155546	−	0.987829i	$-0.549714\pi$
$971$	−17.1967	−	2.17245i	−0.551868	−	0.0697171i	−0.396322	+	0.918112i	$0.629714\pi$
$972$	−0.401479	+	3.17803i	−0.0128774	+	0.101935i
$973$	80.4818	−	51.0753i	2.58013	−	1.63740i
$974$	−8.15238	+	5.92305i	−0.261219	+	0.189787i
$975$	22.7391	−	10.6452i	0.728234	−	0.340920i
$976$	0.824829	+	0.599274i	0.0264021	+	0.0191823i
$977$	−23.4713	−	1.47669i	−0.750913	−	0.0472434i	−0.317279	−	0.948332i	$-0.602769\pi$
$977$	−23.4713	−	1.47669i	−0.750913	−	0.0472434i	−0.433634	+	0.901089i	$0.642769\pi$
$978$	−16.4921	−	29.9990i	−0.527359	−	0.959263i
$979$	−8.85631	+	18.8206i	−0.283049	+	0.601509i
$980$	114.187	+	3.70171i	3.64757	+	0.118247i
$981$	1.01723	−	5.33253i	0.0324778	−	0.170255i
$982$	−24.5218	−	33.7513i	−0.782521	−	1.07705i
$983$	15.6491	−	28.4656i	0.499129	−	0.907912i	−0.499994	−	0.866029i	$-0.666664\pi$
$983$	15.6491	−	28.4656i	0.499129	−	0.907912i	0.999123	−	0.0418830i	$-0.0133357\pi$
$984$	12.3154	−	19.4060i	0.392602	−	0.618641i
$985$	−7.11646	+	2.05988i	−0.226749	+	0.0656332i
$986$	−37.2180	−	14.7357i	−1.18526	−	0.469279i
$987$	5.70464	+	14.4083i	0.181581	+	0.458621i
$988$	30.3336	−	25.0941i	0.965040	−	0.798350i
$989$	20.0150	−	5.13898i	0.636440	−	0.163410i
$990$	−19.7527	+	0.601167i	−0.627782	+	0.0191063i
$991$	−1.86464	+	0.738263i	−0.0592322	+	0.0234517i	−0.397554	−	0.917579i	$-0.630141\pi$
$991$	−1.86464	+	0.738263i	−0.0592322	+	0.0234517i	0.338322	+	0.941031i	$0.390141\pi$
$992$	−1.37249	−	1.46156i	−0.0435768	−	0.0464045i
$993$	10.7497	−	14.7956i	0.341130	−	0.469526i
$994$	−44.5226	−	94.6153i	−1.41217	−	3.00101i
$995$	2.30212	+	5.33437i	0.0729820	+	0.169111i
$996$	−11.7577	+	6.46383i	−0.372556	+	0.204814i
$997$	−18.1987	+	3.47158i	−0.576357	+	0.109946i	−0.467315	−	0.884091i	$-0.654778\pi$
$997$	−18.1987	+	3.47158i	−0.576357	+	0.109946i	−0.109043	+	0.994037i	$0.534778\pi$
$998$	−11.7235	−	45.6602i	−0.371102	−	1.44535i
$999$	2.90115			0.0917884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.o.a.229.22	✓	480
125.119	even	50	inner	375.2.o.a.244.22	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
375.2.o.a.229.22	✓	480	1.1	even	1	trivial
375.2.o.a.244.22	yes	480	125.119	even	50	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.o (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.567280 + 2.20941i) q^{2} +(0.982287 - 0.187381i) q^{3} +(-2.80706 + 1.54320i) q^{4} +(1.67876 - 1.47708i) q^{5} +(0.971233 + 2.06398i) q^{6} +(2.81586 - 3.87570i) q^{7} +(-1.87894 - 2.00087i) q^{8} +(0.929776 - 0.368125i) q^{9} +(4.21579 + 2.87116i) q^{10} +(-3.75267 + 0.963522i) q^{11} +(-2.46818 + 2.04185i) q^{12} +(1.84854 + 4.66888i) q^{13} +(10.1604 + 4.02278i) q^{14} +(1.37225 - 1.76548i) q^{15} +(-0.0779712 + 0.122863i) q^{16} +(1.82200 - 3.31421i) q^{17} +(1.34078 + 1.84543i) q^{18} +(-0.458606 + 2.40410i) q^{19} +(-2.43298 + 6.73691i) q^{20} +(2.03975 - 4.33469i) q^{21} +(-4.25763 - 7.74460i) q^{22} +(-8.02880 - 0.505129i) q^{23} +(-2.22058 - 1.61335i) q^{24} +(0.636493 - 4.95932i) q^{25} +(-9.26682 + 6.73274i) q^{26} +(0.844328 - 0.535827i) q^{27} +(-1.92333 + 15.2248i) q^{28} +(-4.60335 - 0.581538i) q^{29} +(4.67912 + 2.03034i) q^{30} +(0.301806 + 0.165919i) q^{31} +(-5.53659 - 1.79895i) q^{32} +(-3.50566 + 1.64964i) q^{33} +(8.35602 + 2.14546i) q^{34} +(-0.997539 - 10.6656i) q^{35} +(-2.04185 + 2.46818i) q^{36} +(2.44952 + 1.55451i) q^{37} +(-5.57179 + 0.350547i) q^{38} +(2.69066 + 4.23980i) q^{39} +(-6.10972 - 0.583646i) q^{40} +(0.525788 + 8.35715i) q^{41} +(10.7342 + 2.04766i) q^{42} +(-2.44296 + 0.793767i) q^{43} +(9.04708 - 8.49578i) q^{44} +(1.01713 - 1.99134i) q^{45} +(-3.43854 - 18.0254i) q^{46} +(-2.21434 + 2.35803i) q^{47} +(-0.0535679 + 0.135297i) q^{48} +(-4.92886 - 15.1695i) q^{49} +(11.3182 - 1.40705i) q^{50} +(1.16871 - 3.59691i) q^{51} +(-12.3940 - 10.2532i) q^{52} +(2.20511 + 1.03765i) q^{53} +(1.66283 + 1.56150i) q^{54} +(-4.87665 + 7.16051i) q^{55} +(-13.0456 + 1.64804i) q^{56} +2.44745i q^{57} +(-1.32653 - 10.5006i) q^{58} +(5.62404 + 6.79830i) q^{59} +(-1.12751 + 7.07347i) q^{60} +(0.439937 - 6.99261i) q^{61} +(-0.195375 + 0.760935i) q^{62} +(1.19138 - 4.64012i) q^{63} +(0.815539 - 12.9626i) q^{64} +(9.99955 + 5.10751i) q^{65} +(-5.63341 - 6.80962i) q^{66} +(1.81036 + 14.3304i) q^{67} +12.1149i q^{68} +(-7.98124 + 1.00827i) q^{69} +(22.9988 - 8.25436i) q^{70} +(-6.97546 - 6.55040i) q^{71} +(-2.48356 - 1.16867i) q^{72} +(1.81871 + 1.50457i) q^{73} +(-2.04499 + 6.29384i) q^{74} +(-0.304065 - 4.99075i) q^{75} +(-2.42266 - 7.45617i) q^{76} +(-6.83268 + 17.2574i) q^{77} +(-7.84109 + 8.34991i) q^{78} +(-1.94017 - 10.1707i) q^{79} +(0.0505827 + 0.321427i) q^{80} +(0.728969 - 0.684547i) q^{81} +(-18.1661 + 5.90252i) q^{82} +(4.11441 + 0.784865i) q^{83} +(0.963569 + 15.3155i) q^{84} +(-1.83663 - 8.25501i) q^{85} +(-3.13960 - 4.94721i) q^{86} +(-4.63078 + 0.291344i) q^{87} +(8.97892 + 5.69819i) q^{88} +(3.42210 - 4.13661i) q^{89} +(4.97669 + 1.11760i) q^{90} +(23.3004 + 5.98252i) q^{91} +(23.3169 - 10.9721i) q^{92} +(0.327550 + 0.106428i) q^{93} +(-6.46601 - 3.55472i) q^{94} +(2.78114 + 4.71331i) q^{95} +(-5.77561 - 0.729629i) q^{96} +(0.705339 - 5.58333i) q^{97} +(30.7195 - 19.4952i) q^{98} +(-3.13445 + 2.27731i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 30 q^{8} + 10 q^{11} + 20 q^{16} - 10 q^{17} - 10 q^{19} - 20 q^{20} + 30 q^{22} - 180 q^{23} - 30 q^{24} - 40 q^{25} - 30 q^{28} - 20 q^{29} + 20 q^{30} + 10 q^{31} - 10 q^{33} + 20 q^{34} - 10 q^{35}+ \cdots - 60 q^{98}+O(q^{100}) \) 480 * q + 30 * q^8 + 10 * q^11 + 20 * q^16 - 10 * q^17 - 10 * q^19 - 20 * q^20 + 30 * q^22 - 180 * q^23 - 30 * q^24 - 40 * q^25 - 30 * q^28 - 20 * q^29 + 20 * q^30 + 10 * q^31 - 10 * q^33 + 20 * q^34 - 10 * q^35 + 10 * q^37 - 30 * q^38 - 10 * q^40 + 30 * q^41 + 10 * q^42 - 70 * q^44 + 20 * q^46 - 40 * q^47 + 80 * q^49 - 20 * q^50 + 40 * q^51 - 40 * q^52 - 10 * q^53 - 10 * q^55 - 240 * q^56 - 310 * q^58 - 40 * q^59 - 120 * q^60 + 20 * q^61 + 10 * q^62 + 10 * q^63 - 70 * q^64 + 70 * q^65 - 260 * q^67 - 30 * q^70 - 160 * q^71 + 30 * q^72 + 20 * q^73 + 100 * q^76 + 40 * q^77 - 20 * q^79 - 200 * q^82 - 10 * q^83 - 40 * q^84 + 20 * q^85 + 100 * q^86 - 40 * q^87 + 40 * q^88 - 50 * q^89 - 30 * q^90 - 120 * q^91 - 10 * q^92 - 300 * q^93 - 20 * q^94 - 60 * q^95 + 50 * q^96 - 40 * q^97 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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