LMFDB - Embedded newform 276.2.o.a.95.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			95.32
Character	$\chi$	$=$	276.95
Dual form			276.2.o.a.215.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.854631 - 1.12677i) q^{2} +(-1.36208 + 1.06992i) q^{3} +(-0.539212 - 1.92594i) q^{4} +(-0.639142 - 0.553820i) q^{5} +(0.0414785 + 2.44914i) q^{6} +(-1.43109 - 2.22681i) q^{7} +(-2.63092 - 1.03840i) q^{8} +(0.710529 - 2.91464i) q^{9} +O(q^{10})$	\(q+(0.854631 - 1.12677i) q^{2} +(-1.36208 + 1.06992i) q^{3} +(-0.539212 - 1.92594i) q^{4} +(-0.639142 - 0.553820i) q^{5} +(0.0414785 + 2.44914i) q^{6} +(-1.43109 - 2.22681i) q^{7} +(-2.63092 - 1.03840i) q^{8} +(0.710529 - 2.91464i) q^{9} +(-1.17026 + 0.246853i) q^{10} +(-0.134361 + 0.934503i) q^{11} +(2.79506 + 2.04637i) q^{12} +(-2.85860 - 1.83711i) q^{13} +(-3.73215 - 0.290602i) q^{14} +(1.46311 + 0.0705144i) q^{15} +(-3.41850 + 2.07698i) q^{16} +(0.501406 - 1.70763i) q^{17} +(-2.67689 - 3.29155i) q^{18} +(-1.49987 - 5.10810i) q^{19} +(-0.721991 + 1.52958i) q^{20} +(4.33178 + 1.50195i) q^{21} +(0.938139 + 0.950050i) q^{22} +(2.16393 + 4.27989i) q^{23} +(4.69453 - 1.40049i) q^{24} +(-0.609788 - 4.24117i) q^{25} +(-4.51305 + 1.65093i) q^{26} +(2.15065 + 4.73019i) q^{27} +(-3.51706 + 3.95691i) q^{28} +(-0.474656 + 1.61653i) q^{29} +(1.32987 - 1.58832i) q^{30} +(4.47775 - 2.04492i) q^{31} +(-0.581282 + 5.62691i) q^{32} +(-0.816836 - 1.41663i) q^{33} +(-1.49559 - 2.02436i) q^{34} +(-0.318586 + 2.21581i) q^{35} +(-5.99656 + 0.203173i) q^{36} +(6.10446 + 7.04492i) q^{37} +(-7.03748 - 2.67553i) q^{38} +(5.85921 - 0.556189i) q^{39} +(1.10644 + 2.12074i) q^{40} +(-4.13139 - 3.57987i) q^{41} +(5.39442 - 3.59729i) q^{42} +(4.32963 + 1.97727i) q^{43} +(1.87225 - 0.245123i) q^{44} +(-2.06832 + 1.46937i) q^{45} +(6.67180 + 1.21948i) q^{46} +10.8184 q^{47} +(2.43407 - 6.48655i) q^{48} +(-0.00278734 + 0.00610343i) q^{49} +(-5.29996 - 2.93754i) q^{50} +(1.14408 + 2.86240i) q^{51} +(-1.99678 + 6.49609i) q^{52} +(2.34204 + 3.64429i) q^{53} +(7.16784 + 1.61929i) q^{54} +(0.603422 - 0.522868i) q^{55} +(1.45274 + 7.34461i) q^{56} +(7.50823 + 5.35290i) q^{57} +(1.41580 + 1.91636i) q^{58} +(-8.58571 - 5.51770i) q^{59} +(-0.653118 - 2.85588i) q^{60} +(-2.08314 - 4.56144i) q^{61} +(1.52267 - 6.79304i) q^{62} +(-7.50720 + 2.58889i) q^{63} +(5.84344 + 5.46390i) q^{64} +(0.809623 + 2.75732i) q^{65} +(-2.29430 - 0.290308i) q^{66} +(-9.29956 + 1.33708i) q^{67} +(-3.55916 - 0.0449034i) q^{68} +(-7.52659 - 3.51432i) q^{69} +(2.22443 + 2.25268i) q^{70} +(-0.829574 - 5.76982i) q^{71} +(-4.89592 + 6.93037i) q^{72} +(5.76933 - 1.69403i) q^{73} +(13.1551 - 0.857501i) q^{74} +(5.36831 + 5.12439i) q^{75} +(-9.02916 + 5.64302i) q^{76} +(2.27325 - 1.03816i) q^{77} +(4.38077 - 7.07731i) q^{78} +(2.39274 - 3.72317i) q^{79} +(3.33518 + 0.565748i) q^{80} +(-7.99030 - 4.14188i) q^{81} +(-7.56450 + 1.59565i) q^{82} +(-3.69824 - 4.26800i) q^{83} +(0.556920 - 9.15261i) q^{84} +(-1.26619 + 0.813730i) q^{85} +(5.92816 - 3.18864i) q^{86} +(-1.08304 - 2.70969i) q^{87} +(1.32388 - 2.31908i) q^{88} +(-8.79914 - 4.01843i) q^{89} +(-0.112012 + 3.58628i) q^{90} +8.99463i q^{91} +(7.07599 - 6.47536i) q^{92} +(-3.91115 + 7.57619i) q^{93} +(9.24577 - 12.1899i) q^{94} +(-1.87033 + 4.09546i) q^{95} +(-5.22861 - 8.28623i) q^{96} +(7.68730 - 8.87162i) q^{97} +(0.00449500 + 0.00835687i) q^{98} +(2.62828 + 1.05561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$-1$	$-1$

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 $

$2$	0.854631	−	1.12677i	0.604315	−	0.796745i
$2$	0.854631	−	1.12677i	0.604315	−	0.796745i
$3$	−1.36208	+	1.06992i	−0.786398	+	0.617720i
$3$	−1.36208	+	1.06992i	−0.786398	+	0.617720i
$4$	−0.539212	−	1.92594i	−0.269606	−	0.962971i
$5$	−0.639142	−	0.553820i	−0.285833	−	0.247676i	0.500128	−	0.865951i	$-0.333286\pi$
$5$	−0.639142	−	0.553820i	−0.285833	−	0.247676i	−0.785961	+	0.618276i	$0.787832\pi$
$6$	0.0414785	+	2.44914i	0.0169335	+	0.999857i
$7$	−1.43109	−	2.22681i	−0.540900	−	0.841657i	0.457981	−	0.888962i	$-0.348573\pi$
$7$	−1.43109	−	2.22681i	−0.540900	−	0.841657i	−0.998880	+	0.0473056i	$0.984937\pi$
$8$	−2.63092	−	1.03840i	−0.930169	−	0.367131i
$9$	0.710529	−	2.91464i	0.236843	−	0.971548i
$10$	−1.17026	+	0.246853i	−0.370068	+	0.0780618i
$11$	−0.134361	+	0.934503i	−0.0405115	+	0.281763i	0.959489	+	0.281748i	$0.0909141\pi$
$11$	−0.134361	+	0.934503i	−0.0405115	+	0.281763i	−1.00000		1.57325e-5i	$0.999995\pi$
$12$	2.79506	+	2.04637i	0.806864	+	0.590737i
$13$	−2.85860	−	1.83711i	−0.792833	−	0.509523i	0.0804369	−	0.996760i	$-0.474368\pi$
$13$	−2.85860	−	1.83711i	−0.792833	−	0.509523i	−0.873270	+	0.487237i	$0.838005\pi$
$14$	−3.73215	−	0.290602i	−0.997460	−	0.0776667i
$15$	1.46311	+	0.0705144i	0.377773	+	0.0182067i
$16$	−3.41850	+	2.07698i	−0.854625	+	0.519245i
$17$	0.501406	−	1.70763i	0.121609	−	0.414161i	−0.876076	−	0.482174i	$-0.839847\pi$
$17$	0.501406	−	1.70763i	0.121609	−	0.414161i	0.997684	+	0.0680121i	$0.0216657\pi$
$18$	−2.67689	−	3.29155i	−0.630948	−	0.775825i
$19$	−1.49987	−	5.10810i	−0.344095	−	1.17188i	−0.931851	−	0.362841i	$-0.881807\pi$
$19$	−1.49987	−	5.10810i	−0.344095	−	1.17188i	0.587756	−	0.809038i	$-0.300011\pi$
$20$	−0.721991	+	1.52958i	−0.161442	+	0.342024i
$21$	4.33178	+	1.50195i	0.945271	+	0.327752i
$22$	0.938139	+	0.950050i	0.200012	+	0.202551i
$23$	2.16393	+	4.27989i	0.451210	+	0.892418i
$23$	2.16393	+	4.27989i	0.451210	+	0.892418i
$24$	4.69453	−	1.40049i	0.958267	−	0.285874i
$25$	−0.609788	−	4.24117i	−0.121958	−	0.848234i
$26$	−4.51305	+	1.65093i	−0.885081	+	0.323773i
$27$	2.15065	+	4.73019i	0.413892	+	0.910326i
$28$	−3.51706	+	3.95691i	−0.664661	+	0.747786i
$29$	−0.474656	+	1.61653i	−0.0881413	+	0.300182i	−0.991752	−	0.128173i	$-0.959089\pi$
$29$	−0.474656	+	1.61653i	−0.0881413	+	0.300182i	0.903610	+	0.428355i	$0.140907\pi$
$30$	1.32987	−	1.58832i	0.242800	−	0.289986i
$31$	4.47775	−	2.04492i	0.804228	−	0.367278i	0.0294929	−	0.999565i	$-0.490611\pi$
$31$	4.47775	−	2.04492i	0.804228	−	0.367278i	0.774735	+	0.632287i	$0.217883\pi$
$32$	−0.581282	+	5.62691i	−0.102757	+	0.994706i
$33$	−0.816836	−	1.41663i	−0.142193	−	0.246603i
$34$	−1.49559	−	2.02436i	−0.256491	−	0.347175i
$35$	−0.318586	+	2.21581i	−0.0538509	+	0.374541i
$36$	−5.99656	+	0.203173i	−0.999427	+	0.0338622i
$37$	6.10446	+	7.04492i	1.00357	+	1.15818i	0.987390	+	0.158309i	$0.0506042\pi$
$37$	6.10446	+	7.04492i	1.00357	+	1.15818i	0.0161776	+	0.999869i	$0.494850\pi$
$38$	−7.03748	−	2.67553i	−1.14163	−	0.434029i
$39$	5.85921	−	0.556189i	0.938225	−	0.0890615i
$40$	1.10644	+	2.12074i	0.174944	+	0.335318i
$41$	−4.13139	−	3.57987i	−0.645215	−	0.559082i	0.269592	−	0.962975i	$-0.413111\pi$
$41$	−4.13139	−	3.57987i	−0.645215	−	0.559082i	−0.914806	+	0.403893i	$0.867657\pi$
$42$	5.39442	−	3.59729i	0.832377	−	0.555075i
$43$	4.32963	+	1.97727i	0.660262	+	0.301532i	0.717222	−	0.696845i	$-0.245413\pi$
$43$	4.32963	+	1.97727i	0.660262	+	0.301532i	−0.0569598	+	0.998376i	$0.518141\pi$
$44$	1.87225	−	0.245123i	0.282252	−	0.0369537i
$45$	−2.06832	+	1.46937i	−0.308326	+	0.219040i
$46$	6.67180	+	1.21948i	0.983703	+	0.179803i
$47$	10.8184			1.57803			0.789016	−	0.614373i	$-0.210591\pi$
$47$	10.8184			1.57803			0.789016	+	0.614373i	$0.210591\pi$
$48$	2.43407	−	6.48655i	0.351327	−	0.936253i
$49$	−0.00278734	+	0.00610343i	−0.000398192	+	0.000871919i
$50$	−5.29996	−	2.93754i	−0.749527	−	0.415432i
$51$	1.14408	+	2.86240i	0.160203	+	0.400816i
$52$	−1.99678	+	6.49609i	−0.276903	+	0.900845i
$53$	2.34204	+	3.64429i	0.321704	+	0.500582i	0.964010	−	0.265867i	$-0.0856582\pi$
$53$	2.34204	+	3.64429i	0.321704	+	0.500582i	−0.642305	+	0.766449i	$0.722022\pi$
$54$	7.16784	+	1.61929i	0.975419	+	0.220357i
$55$	0.603422	−	0.522868i	0.0813654	−	0.0705036i
$56$	1.45274	+	7.34461i	0.194130	+	0.981464i
$57$	7.50823	+	5.35290i	0.994489	+	0.709009i
$58$	1.41580	+	1.91636i	0.185903	+	0.251631i
$59$	−8.58571	−	5.51770i	−1.11776	−	0.718344i	−0.154793	−	0.987947i	$-0.549471\pi$
$59$	−8.58571	−	5.51770i	−1.11776	−	0.718344i	−0.962971	+	0.269603i	$0.913107\pi$
$60$	−0.653118	−	2.85588i	−0.0843172	−	0.368693i
$61$	−2.08314	−	4.56144i	−0.266719	−	0.584033i	0.728126	−	0.685444i	$-0.240392\pi$
$61$	−2.08314	−	4.56144i	−0.266719	−	0.584033i	−0.994845	+	0.101411i	$0.967664\pi$
$62$	1.52267	−	6.79304i	0.193380	−	0.862716i
$63$	−7.50720	+	2.58889i	−0.945818	+	0.326170i
$64$	5.84344	+	5.46390i	0.730430	+	0.682988i
$65$	0.809623	+	2.75732i	0.100421	+	0.342004i
$66$	−2.29430	−	0.290308i	−0.282409	−	0.0357344i
$67$	−9.29956	+	1.33708i	−1.13612	+	0.163350i	−0.684606	−	0.728913i	$-0.740026\pi$
$67$	−9.29956	+	1.33708i	−1.13612	+	0.163350i	−0.451516	+	0.892263i	$0.649117\pi$
$68$	−3.55916	−	0.0449034i	−0.431612	−	0.00544534i
$69$	−7.52659	−	3.51432i	−0.906095	−	0.423074i
$70$	2.22443	+	2.25268i	0.265871	+	0.269246i
$71$	−0.829574	−	5.76982i	−0.0984524	−	0.684751i	−0.977949	−	0.208845i	$-0.933029\pi$
$71$	−0.829574	−	5.76982i	−0.0984524	−	0.684751i	0.879496	−	0.475906i	$-0.157880\pi$
$72$	−4.89592	+	6.93037i	−0.576989	+	0.816752i
$73$	5.76933	−	1.69403i	0.675249	−	0.198271i	0.0739100	−	0.997265i	$-0.476452\pi$
$73$	5.76933	−	1.69403i	0.675249	−	0.198271i	0.601339	+	0.798994i	$0.294634\pi$
$74$	13.1551	−	0.857501i	1.52924	−	0.0996824i
$75$	5.36831	+	5.12439i	0.619878	+	0.591713i
$76$	−9.02916	+	5.64302i	−1.03572	+	0.647299i
$77$	2.27325	−	1.03816i	0.259061	−	0.118309i
$78$	4.38077	−	7.07731i	0.496024	−	0.801347i
$79$	2.39274	−	3.72317i	0.269204	−	0.418889i	−0.680162	−	0.733062i	$-0.738091\pi$
$79$	2.39274	−	3.72317i	0.269204	−	0.418889i	0.949366	+	0.314172i	$0.101727\pi$
$80$	3.33518	+	0.565748i	0.372884	+	0.0632525i
$81$	−7.99030	−	4.14188i	−0.887811	−	0.460208i
$82$	−7.56450	+	1.59565i	−0.835359	+	0.176210i
$83$	−3.69824	−	4.26800i	−0.405935	−	0.468474i	0.515566	−	0.856850i	$-0.327582\pi$
$83$	−3.69824	−	4.26800i	−0.405935	−	0.468474i	−0.921501	+	0.388376i	$0.873036\pi$
$84$	0.556920	−	9.15261i	0.0607650	−	0.998632i
$85$	−1.26619	+	0.813730i	−0.137337	+	0.0882614i
$86$	5.92816	−	3.18864i	0.639250	−	0.343840i
$87$	−1.08304	−	2.70969i	−0.116114	−	0.290509i
$88$	1.32388	−	2.31908i	0.141127	−	0.247215i
$89$	−8.79914	−	4.01843i	−0.932707	−	0.425953i	−0.109687	−	0.993966i	$-0.534985\pi$
$89$	−8.79914	−	4.01843i	−0.932707	−	0.425953i	−0.823019	+	0.568013i	$0.807712\pi$
$90$	−0.112012	+	3.58628i	−0.0118071	+	0.378027i
$91$			8.99463i			0.942894i
$92$	7.07599	−	6.47536i	0.737723	−	0.675103i
$93$	−3.91115	+	7.57619i	−0.405567	+	0.785615i
$94$	9.24577	−	12.1899i	0.953629	−	1.25729i
$95$	−1.87033	+	4.09546i	−0.191892	+	0.420186i
$96$	−5.22861	−	8.28623i	−0.533643	−	0.845710i
$97$	7.68730	−	8.87162i	0.780527	−	0.900776i	−0.216620	−	0.976256i	$-0.569503\pi$
$97$	7.68730	−	8.87162i	0.780527	−	0.900776i	0.997147	+	0.0754795i	$0.0240487\pi$
$98$	0.00449500	+	0.00835687i	0.000454064	+	0.000844172i
$99$	2.62828	+	1.05561i	0.264152	+	0.106092i
$100$	−7.83944	+	3.46130i	−0.783944	+	0.346130i
$101$	6.22731	−	5.39600i	0.619641	−	0.536922i	−0.287483	−	0.957786i	$-0.592818\pi$
$101$	6.22731	−	5.39600i	0.619641	−	0.536922i	0.907124	+	0.420864i	$0.138273\pi$
$102$	4.20302	+	1.15718i	0.416161	+	0.114578i
$103$	−3.26178	−	0.468973i	−0.321393	−	0.0462093i	−0.0202695	−	0.999795i	$-0.506452\pi$
$103$	−3.26178	−	0.468973i	−0.321393	−	0.0462093i	−0.301123	+	0.953585i	$0.597362\pi$
$104$	5.61308	+	7.80166i	0.550407	+	0.765016i
$105$	−1.93681	−	3.35898i	−0.189013	−	0.327803i
$106$	6.10785	+	0.475585i	0.593247	+	0.0461929i
$107$	−0.743662	−	1.62839i	−0.0718925	−	0.157423i	0.870274	−	0.492568i	$-0.163942\pi$
$107$	−0.743662	−	1.62839i	−0.0718925	−	0.157423i	−0.942166	+	0.335145i	$0.891215\pi$
$108$	7.95042	−	6.69260i	0.765029	−	0.643995i
$109$	16.5805	+	4.86848i	1.58813	+	0.466316i	0.952211	−	0.305442i	$-0.0988041\pi$
$109$	16.5805	+	4.86848i	1.58813	+	0.466316i	0.635917	+	0.771758i	$0.280622\pi$
$110$	−0.0734479	−	1.12678i	−0.00700298	−	0.107434i
$111$	−15.8523	−	3.06445i	−1.50463	−	0.290865i
$112$	9.51722	+	4.64003i	0.899293	+	0.438441i
$113$	−18.4025	+	2.64588i	−1.73116	+	0.248904i	−0.934613	−	0.355667i	$-0.884254\pi$
$113$	−18.4025	+	2.64588i	−1.73116	+	0.248904i	−0.796551	+	0.604571i	$0.793345\pi$
$114$	12.4482	−	3.88528i	1.16588	−	0.363889i
$115$	0.987228	−	3.93388i	0.0920595	−	0.366836i
$116$	3.36928	+	0.0425078i	0.312830	+	0.00394675i
$117$	−7.38564	+	7.02648i	−0.682803	+	0.649598i
$118$	−13.5548	+	4.95851i	−1.24782	+	0.456467i
$119$	−4.52013	+	1.32723i	−0.414360	+	0.121667i
$120$	−3.77609	−	1.70481i	−0.344708	−	0.155627i
$121$	9.69918	+	2.84794i	0.881744	+	0.258903i
$122$	−6.92001	−	1.55113i	−0.626508	−	0.140433i
$123$	9.45747	+	0.455802i	0.852752	+	0.0410983i
$124$	−6.35285	−	7.52124i	−0.570503	−	0.675427i
$125$	−4.24522	+	6.60569i	−0.379704	+	0.590831i
$126$	−3.49880	+	10.6714i	−0.311698	+	0.950685i
$127$	−19.4396	−	2.79500i	−1.72499	−	0.248016i	−0.792670	−	0.609651i	$-0.791309\pi$
$127$	−19.4396	−	2.79500i	−1.72499	−	0.248016i	−0.932320	+	0.361635i	$0.882219\pi$
$128$	11.1505	−	1.91458i	0.985577	−	0.169227i
$129$	−8.01283	+	1.93916i	−0.705491	+	0.170734i
$130$	3.79879	+	1.44424i	0.333176	+	0.126668i
$131$	−5.30305	+	3.40807i	−0.463330	+	0.297764i	−0.751402	−	0.659845i	$-0.770622\pi$
$131$	−5.30305	+	3.40807i	−0.463330	+	0.297764i	0.288072	+	0.957609i	$0.406986\pi$
$132$	−2.28789	+	2.33704i	−0.199135	+	0.203413i
$133$	−9.22835	+	10.6501i	−0.800199	+	0.923479i
$134$	−6.44112	+	11.6212i	−0.556428	+	1.00392i
$135$	1.24510	−	4.21433i	0.107162	−	0.362712i
$136$	−3.09237	+	3.97197i	−0.265168	+	0.340594i
$137$			20.5867i			1.75884i	0.476046	+	0.879421i	$0.342070\pi$
$137$			20.5867i			1.75884i	−0.476046	+	0.879421i	$0.657930\pi$
$138$	−10.3923	+	5.47728i	−0.884649	+	0.466257i
$139$			2.03732i			0.172804i	0.996260	+	0.0864018i	$0.0275369\pi$
$139$			2.03732i			0.172804i	−0.996260	+	0.0864018i	$0.972463\pi$
$140$	4.43931	−	0.581215i	0.375190	−	0.0491216i
$141$	−14.7356	+	11.5749i	−1.24096	+	0.974782i
$142$	−7.21022	−	3.99633i	−0.605069	−	0.335364i
$143$	2.10087	−	2.42453i	0.175684	−	0.202750i
$144$	3.62472	+	11.4395i	0.302060	+	0.953289i
$145$	1.19864	−	0.770318i	0.0995414	−	0.0639714i
$146$	3.02187	−	7.94847i	0.250092	−	0.657820i
$147$	−0.00273362	−	0.0112956i	−0.000225465	−	0.000931647i
$148$	10.2765	−	15.5555i	0.844724	−	1.27866i
$149$	17.4172	+	2.50422i	1.42687	+	0.205154i	0.812086	−	0.583538i	$-0.198332\pi$
$149$	17.4172	+	2.50422i	1.42687	+	0.205154i	0.614789	+	0.788692i	$0.289241\pi$
$150$	10.3619	−	1.66937i	0.846047	−	0.136304i
$151$	11.2333	−	17.4794i	0.914154	−	1.42245i	0.00778231	−	0.999970i	$-0.497523\pi$
$151$	11.2333	−	17.4794i	0.914154	−	1.42245i	0.906372	−	0.422481i	$-0.138841\pi$
$152$	−1.35822	+	14.9965i	−0.110167	+	1.21637i
$153$	−4.62087	−	2.67474i	−0.373576	−	0.216240i
$154$	0.773026	−	3.44866i	0.0622922	−	0.277901i
$155$	−3.99443	−	1.17287i	−0.320841	−	0.0942073i
$156$	−4.23054	−	10.9846i	−0.338715	−	0.879471i
$157$	−3.53249	+	1.03723i	−0.281923	+	0.0827801i	−0.419637	−	0.907692i	$-0.637843\pi$
$157$	−3.53249	+	1.03723i	−0.281923	+	0.0827801i	0.137714	+	0.990472i	$0.456024\pi$
$158$	−2.15024	−	5.87800i	−0.171064	−	0.467628i
$159$	−7.08916	−	2.45801i	−0.562207	−	0.194933i
$160$	3.48781	−	3.27447i	0.275736	−	0.258869i
$161$	6.43374	−	10.9435i	0.507050	−	0.862472i
$162$	−11.4957	+	5.46343i	−0.903187	+	0.429248i
$163$	−1.05528	+	0.151726i	−0.0826557	+	0.0118841i	−0.183519	−	0.983016i	$-0.558749\pi$
$163$	−1.05528	+	0.151726i	−0.0826557	+	0.0118841i	0.100863	+	0.994900i	$0.467840\pi$
$164$	−4.66693	+	9.88712i	−0.364426	+	0.772055i
$165$	−0.262481	+	1.35780i	−0.0204341	+	0.105705i
$166$	−7.96968	+	0.519496i	−0.618567	+	0.0403207i
$167$	4.22571	+	1.24078i	0.326995	+	0.0960145i	0.441110	−	0.897453i	$-0.354585\pi$
$167$	4.22571	+	1.24078i	0.326995	+	0.0960145i	−0.114115	+	0.993468i	$0.536403\pi$
$168$	−9.83691	−	8.44963i	−0.758934	−	0.651903i
$169$	−0.603777	−	1.32209i	−0.0464444	−	0.101699i
$170$	−0.165239	+	2.12214i	−0.0126733	+	0.162761i
$171$	−15.9540	+	0.742146i	−1.22003	+	0.0567533i
$172$	1.47353	−	9.40478i	0.112356	−	0.717108i
$173$	11.7982	+	1.69633i	0.897004	+	0.128970i	0.575369	−	0.817894i	$-0.304858\pi$
$173$	11.7982	+	1.69633i	0.897004	+	0.128970i	0.321635	+	0.946864i	$0.395768\pi$
$174$	−3.97879	−	1.09545i	−0.301631	−	0.0830456i
$175$	−8.57163	+	7.42736i	−0.647955	+	0.561456i
$176$	−1.48163	−	3.47367i	−0.111682	−	0.261838i
$177$	17.5980	−	1.67050i	1.32274	−	0.125562i
$178$	−12.0479	+	6.48031i	−0.903025	+	0.485720i
$179$	13.5567	−	15.6453i	1.01328	−	1.16938i	0.0277912	−	0.999614i	$-0.491153\pi$
$179$	13.5567	−	15.6453i	1.01328	−	1.16938i	0.985484	−	0.169768i	$-0.0543019\pi$
$180$	3.94517	+	3.19116i	0.294056	+	0.237855i
$181$	−5.79101	+	12.6805i	−0.430442	+	0.942537i	0.562812	+	0.826585i	$0.309719\pi$
$181$	−5.79101	+	12.6805i	−0.430442	+	0.942537i	−0.993255	+	0.115953i	$0.963008\pi$
$182$	10.1349	+	7.68709i	0.751246	+	0.569805i
$183$	7.71780	+	3.98425i	0.570516	+	0.294525i
$184$	−1.24886	−	13.5070i	−0.0920675	−	0.995753i
$185$		−	7.88348i		−	0.579605i
$186$	5.19402	+	10.8818i	0.380844	+	0.797893i
$187$	1.52842	+	0.698005i	0.111769	+	0.0510432i
$188$	−5.83343	−	20.8357i	−0.425447	−	1.51960i
$189$	7.45550	−	11.5584i	0.542308	−	0.840750i
$190$	3.01619	+	5.60754i	0.218817	+	0.406814i
$191$	−14.2051	+	9.12906i	−1.02784	+	0.660555i	−0.941951	−	0.335749i	$-0.891011\pi$
$191$	−14.2051	+	9.12906i	−1.02784	+	0.660555i	−0.0858927	+	0.996304i	$0.527374\pi$
$192$	−13.8052	−	1.19024i	−0.996304	−	0.0858985i
$193$	−11.2299	−	12.9600i	−0.808347	−	0.932882i	0.190461	−	0.981695i	$-0.439002\pi$
$193$	−11.2299	−	12.9600i	−0.808347	−	0.932882i	−0.998808	+	0.0488130i	$0.984456\pi$
$194$	−3.42645	−	16.2438i	−0.246005	−	1.16623i
$195$	−4.05290	−	2.88946i	−0.290234	−	0.206919i
$196$	0.0132578	+	0.00207722i	0.000946987	+	0.000148373i
$197$	5.22976	−	8.13766i	0.372605	−	0.579784i	−0.603425	−	0.797419i	$-0.706198\pi$
$197$	5.22976	−	8.13766i	0.372605	−	0.579784i	0.976030	+	0.217635i	$0.0698342\pi$
$198$	3.43563	−	2.05930i	0.244160	−	0.146348i
$199$	15.3369	−	7.00413i	1.08720	−	0.496510i	0.210527	−	0.977588i	$-0.432482\pi$
$199$	15.3369	−	7.00413i	1.08720	−	0.496510i	0.876678	+	0.481078i	$0.159755\pi$
$200$	−2.79974	+	11.7914i	−0.197972	+	0.833775i
$201$	11.2362	−	11.7710i	0.792540	−	0.830264i
$202$	−0.757982	−	11.6283i	−0.0533314	−	0.818166i
$203$	4.27898	−	1.25642i	0.300326	−	0.0881836i
$204$	4.89591	−	3.74687i	0.342782	−	0.262333i
$205$	0.657942	+	4.57609i	0.0459527	+	0.319608i
$206$	−3.31604	+	3.27447i	−0.231040	+	0.228143i
$207$	14.0119	−	3.26609i	0.973893	−	0.227009i
$208$	13.5878	+	0.342909i	0.942142	+	0.0237765i
$209$	4.97506	−	0.715306i	0.344132	−	0.0494788i
$210$	−5.44005	−	0.688352i	−0.375399	−	0.0475008i
$211$	0.599965	+	2.04329i	0.0413033	+	0.140666i	0.977563	−	0.210642i	$-0.0675553\pi$
$211$	0.599965	+	2.04329i	0.0413033	+	0.140666i	−0.936260	+	0.351308i	$0.885737\pi$
$212$	5.75583	−	6.47568i	0.395312	−	0.444752i
$213$	7.30321	+	6.97138i	0.500408	+	0.477671i
$214$	−2.47038	−	0.553741i	−0.168872	−	0.0378529i
$215$	−1.67219	−	3.66159i	−0.114043	−	0.249718i
$216$	−0.746328	−	14.6780i	−0.0507812	−	0.998710i
$217$	−10.9617	−	7.04466i	−0.744129	−	0.478223i
$218$	19.6559	−	14.5217i	1.33127	−	0.983531i
$219$	−6.04582	+	8.48014i	−0.408538	+	0.573035i
$220$	−1.33239	−	0.880219i	−0.0898295	−	0.0593444i
$221$	−4.57043	+	3.96030i	−0.307440	+	0.266398i
$222$	−17.0008	+	15.2429i	−1.14102	+	1.02304i
$223$	6.76613	+	10.5283i	0.453094	+	0.705028i	0.990380	−	0.138372i	$-0.0441869\pi$
$223$	6.76613	+	10.5283i	0.453094	+	0.705028i	−0.537286	+	0.843400i	$0.680551\pi$
$224$	13.3619	−	6.75819i	0.892783	−	0.451550i
$225$	−12.7948	−	1.23616i	−0.852985	−	0.0824105i
$226$	−12.7461	+	22.9966i	−0.847856	+	1.52971i
$227$	−0.384109	+	0.841081i	−0.0254942	+	0.0558245i	−0.921951	−	0.387307i	$-0.873405\pi$
$227$	−0.384109	+	0.841081i	−0.0254942	+	0.0558245i	0.896457	+	0.443132i	$0.146133\pi$
$228$	6.26085	−	17.3468i	0.414635	−	1.14882i
$229$	−19.0704			−1.26021			−0.630105	−	0.776510i	$-0.716988\pi$
$229$	−19.0704			−1.26021			−0.630105	+	0.776510i	$0.716988\pi$
$230$	−3.58885	−	4.47439i	−0.236642	−	0.295033i
$231$	−1.98560	+	3.84626i	−0.130643	+	0.253065i
$232$	2.92739	−	3.76007i	0.192192	−	0.246861i
$233$	9.50216	+	4.33949i	0.622507	+	0.284290i	0.701593	−	0.712578i	$-0.252473\pi$
$233$	9.50216	+	4.33949i	0.622507	+	0.284290i	−0.0790853	+	0.996868i	$0.525200\pi$
$234$	1.60522	+	14.3270i	0.104936	+	0.936582i
$235$	−6.91452	−	5.99146i	−0.451053	−	0.390840i
$236$	−5.99726	+	19.5108i	−0.390388	+	1.27004i
$237$	0.724406	+	7.63130i	0.0470552	+	0.495706i
$238$	−2.36756	+	6.22743i	−0.153466	+	0.403665i
$239$	2.06195	+	2.37962i	0.133377	+	0.153925i	0.818509	−	0.574494i	$-0.194801\pi$
$239$	2.06195	+	2.37962i	0.133377	+	0.153925i	−0.685132	+	0.728419i	$0.740256\pi$
$240$	−5.14809	+	2.79779i	−0.332308	+	0.180597i
$241$	2.22169	−	15.4522i	0.143112	−	0.995363i	−0.784049	−	0.620699i	$-0.786849\pi$
$241$	2.22169	−	15.4522i	0.143112	−	0.995363i	0.927161	−	0.374664i	$-0.122242\pi$
$242$	11.4982	−	8.49479i	0.739131	−	0.546066i
$243$	15.3149	−	2.90743i	0.982453	−	0.186512i
$244$	−7.66182	+	6.47159i	−0.490498	+	0.414301i
$245$	0.00516171	−	0.00235727i	0.000329770	−	0.000150601i
$246$	8.59623	−	10.2668i	0.548076	−	0.654589i
$247$	−5.09661	+	17.3575i	−0.324289	+	1.10443i
$248$	−13.9040	+	0.730304i	−0.882907	+	0.0463744i
$249$	9.60374	+	1.85652i	0.608612	+	0.117652i
$250$	3.81498	+	10.4288i	0.241281	+	0.659575i
$251$	2.79237	+	19.4214i	0.176253	+	1.22586i	0.865340	+	0.501186i	$0.167103\pi$
$251$	2.79237	+	19.4214i	0.176253	+	1.22586i	−0.689087	+	0.724679i	$0.741988\pi$
$252$	9.03402	+	13.0625i	0.569090	+	0.822858i
$253$	−4.29032	+	1.44715i	−0.269730	+	0.0909813i
$254$	−19.7630	+	19.5153i	−1.24004	+	1.22450i
$255$	0.854023	−	2.46309i	0.0534810	−	0.154245i
$256$	7.37230	−	14.2003i	0.460769	−	0.887520i
$257$	−5.76012	−	19.6172i	−0.359306	−	1.22369i	−0.918758	−	0.394822i	$-0.870806\pi$
$257$	−5.76012	−	19.6172i	−0.359306	−	1.22369i	0.559451	−	0.828863i	$-0.311012\pi$
$258$	−4.66303	+	10.6859i	−0.290308	+	0.665273i
$259$	6.95172	−	23.6754i	0.431959	−	1.47112i
$260$	4.87388	−	3.04607i	0.302265	−	0.188909i
$261$	4.37435	+	2.53204i	0.270765	+	0.156729i
$262$	−0.692055	+	8.88795i	−0.0427553	+	0.549099i
$263$	20.5212	+	13.1882i	1.26539	+	0.813218i	0.989013	−	0.147831i	$-0.0472292\pi$
$263$	20.5212	+	13.1882i	1.26539	+	0.813218i	0.276379	+	0.961049i	$0.410866\pi$
$264$	0.677999	+	4.57523i	0.0417279	+	0.281586i
$265$	0.521382	−	3.62629i	0.0320282	−	0.222761i
$266$	4.11334	+	19.5001i	0.252205	+	1.19563i
$267$	16.2846	−	3.94097i	0.996598	−	0.241184i
$268$	7.58956	+	17.1895i	0.463606	+	1.05001i
$269$	−10.9961	−	17.1102i	−0.670442	−	1.04323i	−0.995241	−	0.0974453i	$-0.968933\pi$
$269$	−10.9961	−	17.1102i	−0.670442	−	1.04323i	0.324799	−	0.945783i	$-0.394703\pi$
$270$	−3.68447	−	5.00464i	−0.224230	−	0.304573i
$271$	17.8428	+	15.4608i	1.08387	+	0.939179i	0.998365	−	0.0571588i	$-0.0182041\pi$
$271$	17.8428	+	15.4608i	1.08387	+	0.939179i	0.0855051	+	0.996338i	$0.472750\pi$
$272$	1.83266	+	6.87895i	0.111121	+	0.417098i
$273$	−9.62357	−	12.2514i	−0.582445	−	0.741490i
$274$	23.1964	+	17.5940i	1.40135	+	1.06289i
$275$	4.04532			0.243942
$276$	−2.70994	+	16.3907i	−0.163119	+	0.986606i
$277$	−0.377780			−0.0226986			−0.0113493	−	0.999936i	$-0.503613\pi$
$277$	−0.377780			−0.0226986			−0.0113493	+	0.999936i	$0.503613\pi$
$278$	2.29559	+	1.74116i	0.137680	+	0.104428i
$279$	−2.77864	−	14.5040i	−0.166353	−	0.868333i
$280$	3.13908	−	5.49880i	0.187596	−	0.328616i
$281$	19.1141	+	16.5625i	1.14025	+	0.988034i	0.999998	−	0.00208152i	$-0.000662568\pi$
$281$	19.1141	+	16.5625i	1.14025	+	0.988034i	0.140254	+	0.990116i	$0.455208\pi$
$282$	0.448733	+	26.4959i	0.0267217	+	1.57781i
$283$	3.63401	+	5.65464i	0.216020	+	0.336133i	0.932304	−	0.361675i	$-0.117795\pi$
$283$	3.63401	+	5.65464i	0.216020	+	0.336133i	−0.716284	+	0.697808i	$0.754159\pi$
$284$	−10.6650	+	4.70886i	−0.632852	+	0.279420i
$285$	−1.83428	−	7.57947i	−0.108654	−	0.448969i
$286$	−0.936418	−	4.43928i	−0.0553716	−	0.262500i
$287$	−2.05933	+	14.3229i	−0.121558	+	0.845456i
$288$	15.9874	+	5.69231i	0.942068	+	0.335423i
$289$	11.6367	+	7.47846i	0.684513	+	0.439909i
$290$	0.156424	−	2.00892i	0.00918552	−	0.117968i
$291$	−0.978776	+	20.3087i	−0.0573769	+	1.19052i
$292$	−6.37349	−	10.1980i	−0.372980	−	0.596790i
$293$	−3.06886	+	10.4516i	−0.179285	+	0.610587i	0.819985	+	0.572384i	$0.193981\pi$
$293$	−3.06886	+	10.4516i	−0.179285	+	0.610587i	−0.999270	+	0.0382027i	$0.987837\pi$
$294$	−0.0150638	−	0.00657343i	−0.000878537	−	0.000383370i
$295$	2.43168	+	8.28153i	0.141578	+	0.482169i
$296$	−8.74486	−	24.8735i	−0.508284	−	1.44574i
$297$	−4.70934	+	1.37423i	−0.273264	+	0.0797411i
$298$	17.7070	−	17.4850i	1.02574	−	1.01288i
$299$	1.67682	−	16.2099i	0.0969732	−	0.937440i
$300$	6.97462	−	13.1022i	0.402680	−	0.756454i
$301$	−1.79305	−	12.4709i	−0.103350	−	0.718812i
$302$	−10.0949	−	27.5957i	−0.580894	−	1.58796i
$303$	−2.70880	+	14.0125i	−0.155617	+	0.804999i
$304$	15.7368	+	14.3468i	0.902565	+	0.822848i
$305$	−1.19479	+	4.06909i	−0.0684137	+	0.232996i
$306$	−6.96295	+	2.92074i	−0.398046	+	0.166967i
$307$	−0.164871	+	0.0752942i	−0.00940970	+	0.00429727i	−0.420114	−	0.907471i	$-0.638010\pi$
$307$	−0.164871	+	0.0752942i	−0.00940970	+	0.00429727i	0.410705	+	0.911768i	$0.365283\pi$
$308$	−3.22519	−	3.81836i	−0.183772	−	0.217571i
$309$	4.94457	−	2.85107i	0.281287	−	0.162192i
$310$	−4.73532	+	3.49843i	−0.268948	+	0.198697i
$311$	1.50127	−	10.4416i	0.0851294	−	0.592088i	−0.901948	−	0.431844i	$-0.857863\pi$
$311$	1.50127	−	10.4416i	0.0851294	−	0.592088i	0.987078	−	0.160244i	$-0.0512280\pi$
$312$	−15.9926	−	4.62094i	−0.905405	−	0.261609i
$313$	19.8701	+	22.9314i	1.12313	+	1.29616i	0.950345	+	0.311197i	$0.100730\pi$
$313$	19.8701	+	22.9314i	1.12313	+	1.29616i	0.172781	+	0.984960i	$0.444725\pi$
$314$	−1.85025	+	4.86674i	−0.104416	+	0.274646i
$315$	6.23194	+	2.50296i	0.351130	+	0.141026i
$316$	−8.46080	−	2.60069i	−0.475957	−	0.146300i
$317$	−1.61828	−	1.40225i	−0.0908915	−	0.0787580i	0.608230	−	0.793761i	$-0.291880\pi$
$317$	−1.61828	−	1.40225i	−0.0908915	−	0.0787580i	−0.699121	+	0.715003i	$0.746425\pi$
$318$	−8.82823	+	5.88715i	−0.495063	+	0.330135i
$319$	−1.44688	−	0.660766i	−0.0810095	−	0.0369958i
$320$	−0.708771	−	6.72842i	−0.0396215	−	0.376130i
$321$	2.75518	+	1.42234i	0.153779	+	0.0793874i
$322$	−6.83236	−	16.6020i	−0.380753	−	0.925195i
$323$	−9.47480			−0.527192
$324$	−3.66855	+	17.6222i	−0.203808	+	0.979011i
$325$	−6.04836	+	13.2441i	−0.335502	+	0.734648i
$326$	−0.730913	+	1.31872i	−0.0404815	+	0.0730373i
$327$	−27.7929	+	11.1086i	−1.53695	+	0.614309i
$328$	7.15199	+	13.7084i	0.394903	+	0.756919i
$329$	−15.4821	−	24.0907i	−0.853557	−	1.32816i
$330$	1.30561	+	1.45618i	0.0718713	+	0.0801599i
$331$	−0.188652	+	0.163468i	−0.0103693	+	0.00898501i	−0.660030	−	0.751239i	$-0.729456\pi$
$331$	−0.188652	+	0.163468i	−0.0103693	+	0.00898501i	0.649661	+	0.760224i	$0.274911\pi$
$332$	−6.22578	+	9.42395i	−0.341684	+	0.517207i
$333$	24.8708	−	12.7867i	1.36291	−	0.700707i
$334$	5.00949	−	3.70098i	0.274107	−	0.202509i
$335$	6.68424	+	4.29570i	0.365199	+	0.234699i
$336$	−17.9277	+	3.86260i	−0.978036	+	0.210722i
$337$	−12.4687	−	27.3027i	−0.679214	−	1.48727i	−0.863474	−	0.504393i	$-0.831716\pi$
$337$	−12.4687	−	27.3027i	−0.679214	−	1.48727i	0.184260	−	0.982877i	$-0.441011\pi$
$338$	−2.00569	−	0.449580i	−0.109095	−	0.0244539i
$339$	22.2348	−	23.2932i	1.20763	−	1.26511i
$340$	2.24994	+	1.99983i	0.122020	+	0.108456i
$341$	1.30935	+	4.45923i	0.0709052	+	0.241481i
$342$	−12.7986	+	18.6107i	−0.692067	+	1.00635i
$343$	−18.3230	+	2.63444i	−0.989346	+	0.142247i
$344$	−9.33768	−	9.69794i	−0.503454	−	0.522878i
$345$	2.86426	+	6.41452i	0.154207	+	0.345346i
$346$	11.9945	−	11.8441i	0.644829	−	0.636745i
$347$	−0.192628	−	1.33976i	−0.0103408	−	0.0719219i	0.983998	−	0.178182i	$-0.0570215\pi$
$347$	−0.192628	−	1.33976i	−0.0103408	−	0.0719219i	−0.994338	+	0.106260i	$0.966112\pi$
$348$	−4.63471	+	3.54697i	−0.248447	+	0.190138i
$349$	−18.4632	+	5.42128i	−0.988312	+	0.290195i	−0.735651	−	0.677360i	$-0.763124\pi$
$349$	−18.4632	+	5.42128i	−0.988312	+	0.290195i	−0.252661	+	0.967555i	$0.581306\pi$
$350$	1.04333	+	16.0059i	0.0557683	+	0.855551i
$351$	2.54205	−	17.4727i	0.135684	−	0.932624i
$352$	−5.18026	−	1.29925i	−0.276109	−	0.0692502i
$353$	28.3503	−	12.9471i	1.50893	−	0.689107i	0.522405	−	0.852697i	$-0.325035\pi$
$353$	28.3503	−	12.9471i	1.50893	−	0.689107i	0.986528	+	0.163591i	$0.0523077\pi$
$354$	13.1575	−	21.2565i	0.699313	−	1.12977i
$355$	−2.66522	+	4.14717i	−0.141455	+	0.220109i
$356$	−2.99467	+	19.1134i	−0.158717	+	1.01301i
$357$	4.73675	−	6.64399i	0.250695	−	0.351637i
$358$	−6.04261	−	28.6462i	−0.319362	−	1.51400i
$359$	−5.09525	−	5.88023i	−0.268917	−	0.310347i	0.605189	−	0.796082i	$-0.293097\pi$
$359$	−5.09525	−	5.88023i	−0.268917	−	0.310347i	−0.874106	+	0.485735i	$0.838552\pi$
$360$	6.96736	−	1.71803i	0.367212	−	0.0905484i
$361$	−7.85927	+	5.05085i	−0.413646	+	0.265834i
$362$	9.33885	+	17.3623i	0.490839	+	0.912543i
$363$	−16.2581	+	6.49826i	−0.853331	+	0.341070i
$364$	17.3231	−	4.85001i	0.907979	−	0.254210i
$365$	−4.62561	−	2.11244i	−0.242115	−	0.110570i
$366$	11.0852	−	5.29110i	0.579433	−	0.276570i
$367$			18.1187i			0.945791i	0.881119	+	0.472895i	$0.156791\pi$
$367$			18.1187i			0.945791i	−0.881119	+	0.472895i	$0.843209\pi$
$368$	−16.2866	−	10.1364i	−0.848999	−	0.528394i
$369$	−13.3695	+	9.49793i	−0.695989	+	0.494442i
$370$	−8.88285	−	6.73746i	−0.461797	−	0.350264i
$371$	4.76349	−	10.4306i	0.247308	−	0.541529i
$372$	16.7002	+	3.44747i	0.865867	+	0.178743i
$373$	−2.92827	+	3.37940i	−0.151620	+	0.174979i	−0.826478	−	0.562968i	$-0.809659\pi$
$373$	−2.92827	+	3.37940i	−0.151620	+	0.174979i	0.674858	+	0.737947i	$0.264205\pi$
$374$	2.09272	−	1.12564i	0.108212	−	0.0582052i
$375$	−1.28525	−	13.5395i	−0.0663699	−	0.699179i
$376$	−28.4624	−	11.2339i	−1.46784	−	0.579344i
$377$	4.32659	−	3.74901i	0.222831	−	0.193084i
$378$	−6.65194	−	18.2788i	−0.342139	−	0.940159i
$379$	30.4353	+	4.37593i	1.56336	+	0.224777i	0.868984	−	0.494840i	$-0.164774\pi$
$379$	30.4353	+	4.37593i	1.56336	+	0.224777i	0.694371	+	0.719617i	$0.255683\pi$
$380$	8.89613	+	1.39383i	0.456362	+	0.0715022i
$381$	29.4688	−	16.9919i	1.50973	−	0.870522i
$382$	−1.85378	+	23.8078i	−0.0948477	+	1.21811i
$383$	5.87491	+	12.8643i	0.300194	+	0.657333i	0.998277	−	0.0586839i	$-0.0186904\pi$
$383$	5.87491	+	12.8643i	0.300194	+	0.657333i	−0.698082	+	0.716017i	$0.745963\pi$
$384$	−13.1395	+	14.5380i	−0.670521	+	0.741891i
$385$	−2.02788	−	0.595439i	−0.103350	−	0.0303464i
$386$	−24.2003	+	1.57748i	−1.23177	+	0.0802915i
$387$	8.83938	−	11.2144i	0.449331	−	0.570061i
$388$	−21.2313	−	10.0216i	−1.07786	−	0.508770i
$389$	−23.6117	+	3.39484i	−1.19716	+	0.172125i	−0.711923	−	0.702258i	$-0.752175\pi$
$389$	−23.6117	+	3.39484i	−1.19716	+	0.172125i	−0.485236	+	0.874383i	$0.661266\pi$
$390$	−6.71948	+	2.09725i	−0.340254	+	0.106198i
$391$	8.39347	−	1.54923i	0.424476	−	0.0783479i
$392$	0.0136711	−	0.0131632i	0.000690494	−	0.000664844i
$393$	3.57682	−	10.3159i	0.180427	−	0.520370i
$394$	−4.69974	−	12.8474i	−0.236770	−	0.647244i
$395$	−3.59126	+	1.05449i	−0.180696	+	0.0530572i
$396$	0.615839	−	5.63110i	0.0309471	−	0.282974i
$397$	−0.884980	−	0.259853i	−0.0444159	−	0.0130417i	0.259449	−	0.965757i	$-0.416459\pi$
$397$	−0.884980	−	0.259853i	−0.0444159	−	0.0130417i	−0.303865	+	0.952715i	$0.598277\pi$
$398$	5.21537	−	23.2671i	0.261423	−	1.16627i
$399$	1.17499	−	24.3799i	0.0588229	−	1.22052i
$400$	10.8934	+	13.2319i	0.544669	+	0.661596i
$401$	−13.2394	+	20.6009i	−0.661144	+	1.02876i	0.335101	+	0.942182i	$0.391230\pi$
$401$	−13.2394	+	20.6009i	−0.661144	+	1.02876i	−0.996245	+	0.0865785i	$0.972407\pi$
$402$	−3.66042	−	22.7205i	−0.182565	−	1.13319i
$403$	−16.5568	−	2.38051i	−0.824755	−	0.118582i
$404$	−13.7502	−	9.08386i	−0.684099	−	0.451939i
$405$	2.81308	+	7.07243i	0.139783	+	0.351432i
$406$	2.24125	−	5.89520i	0.111232	−	0.292574i
$407$	−7.40371	+	4.75807i	−0.366988	+	0.235849i
$408$	−0.0376542	−	8.71874i	−0.00186416	−	0.431642i
$409$	−18.2730	+	21.0881i	−0.903540	+	1.04274i	0.0953409	+	0.995445i	$0.469606\pi$
$409$	−18.2730	+	21.0881i	−0.903540	+	1.04274i	−0.998881	+	0.0472961i	$0.984940\pi$
$410$	5.71849	+	3.16952i	0.282416	+	0.156531i
$411$	−22.0262	−	28.0408i	−1.08647	−	1.38315i
$412$	0.855575	+	6.53487i	0.0421512	+	0.321950i
$413$			27.0151i			1.32933i
$414$	8.29485	−	18.5794i	0.407670	−	0.913129i
$415$			4.77602i			0.234445i
$416$	11.9989	−	15.0172i	0.588295	−	0.736279i
$417$	−2.17978	−	2.77500i	−0.106744	−	0.135892i
$418$	3.44586	−	6.21707i	0.168543	−	0.304087i
$419$	3.29741	−	3.80542i	0.161089	−	0.185907i	−0.669467	−	0.742842i	$-0.733477\pi$
$419$	3.29741	−	3.80542i	0.161089	−	0.185907i	0.830556	+	0.556935i	$0.188023\pi$
$420$	−5.42485	+	5.54139i	−0.264706	+	0.270392i
$421$	12.7210	−	8.17528i	0.619983	−	0.398439i	−0.192606	−	0.981276i	$-0.561694\pi$
$421$	12.7210	−	8.17528i	0.619983	−	0.398439i	0.812589	+	0.582838i	$0.198058\pi$
$422$	2.81506	+	1.07024i	0.137035	+	0.0520985i
$423$	7.68681	−	31.5319i	0.373746	−	1.53313i
$424$	−2.37748	−	12.0198i	−0.115461	−	0.583734i
$425$	−7.54810	−	1.08525i	−0.366137	−	0.0526425i
$426$	14.0967	−	2.27107i	0.682986	−	0.110034i
$427$	−7.17633	+	11.1666i	−0.347287	+	0.540389i
$428$	−2.73520	+	2.31030i	−0.132211	+	0.111673i
$429$	−0.267491	+	5.55018i	−0.0129146	+	0.267965i
$430$	−5.55487	−	1.24514i	−0.267880	−	0.0600458i
$431$	−2.90012	−	0.851552i	−0.139694	−	0.0410178i	0.211138	−	0.977456i	$-0.432283\pi$
$431$	−2.90012	−	0.851552i	−0.139694	−	0.0410178i	−0.350832	+	0.936438i	$0.614101\pi$
$432$	−17.1765	−	11.7033i	−0.826405	−	0.563076i
$433$	23.1370	−	6.79364i	1.11189	−	0.326482i	0.326327	−	0.945257i	$-0.394189\pi$
$433$	23.1370	−	6.79364i	1.11189	−	0.326482i	0.785568	+	0.618775i	$0.212371\pi$
$434$	−17.3059	+	6.33071i	−0.830710	+	0.303884i
$435$	−0.808461	+	2.33169i	−0.0387627	+	0.111796i
$436$	0.435997	−	34.5583i	0.0208805	−	1.65504i
$437$	18.6165	−	17.4728i	0.890547	−	0.835840i
$438$	4.38821	+	14.0596i	0.209677	+	0.671795i
$439$	−21.2628	+	3.05712i	−1.01482	+	0.145909i	−0.629601	−	0.776918i	$-0.716782\pi$
$439$	−21.2628	+	3.05712i	−1.01482	+	0.145909i	−0.385215	+	0.922827i	$0.625873\pi$
$440$	−2.13050	+	0.749027i	−0.101568	+	0.0357085i
$441$	0.0158088	+	0.0124608i	0.000752802	+	0.000593371i
$442$	0.556307	+	8.53440i	0.0264608	+	0.405940i
$443$	−39.0265	−	11.4592i	−1.85420	−	0.544443i	−0.999687	−	0.0250195i	$-0.992035\pi$
$443$	−39.0265	−	11.4592i	−1.85420	−	0.544443i	−0.854517	−	0.519424i	$-0.826147\pi$
$444$	2.64579	+	32.1830i	0.125564	+	1.52734i
$445$	3.39841	+	7.44148i	0.161100	+	0.352760i
$446$	17.6455	+	1.37396i	0.835539	+	0.0650588i
$447$	−26.4030	+	15.2241i	−1.24882	+	0.720077i
$448$	3.80463	−	20.8316i	0.179752	−	0.984199i
$449$	−19.3271	−	2.77882i	−0.912103	−	0.131141i	−0.329742	−	0.944071i	$-0.606962\pi$
$449$	−19.3271	−	2.77882i	−0.912103	−	0.131141i	−0.582361	+	0.812931i	$0.697871\pi$
$450$	−12.3277	+	13.3603i	−0.581132	+	0.629809i
$451$	3.90050	−	3.37980i	0.183667	−	0.159149i
$452$	15.0187	+	34.0155i	0.706419	+	1.59995i
$453$	3.40091	+	35.8271i	0.159789	+	1.68330i
$454$	0.619432	+	1.15162i	0.0290714	+	0.0540480i
$455$	4.98141	−	5.74885i	0.233532	−	0.269510i
$456$	−14.1951	−	21.8796i	−0.664744	−	1.02461i
$457$	−2.95823	+	6.47762i	−0.138380	+	0.303010i	−0.966116	−	0.258107i	$-0.916901\pi$
$457$	−2.95823	+	6.47762i	−0.138380	+	0.303010i	0.827736	+	0.561118i	$0.189628\pi$
$458$	−16.2982	+	21.4880i	−0.761564	+	1.00407i
$459$	9.15577	−	1.30077i	0.427355	−	0.0607146i
$460$	−8.10875	+	0.219850i	−0.378072	+	0.0102505i
$461$			20.4705i			0.953407i	0.879064	+	0.476703i	$0.158168\pi$
$461$			20.4705i			0.953407i	−0.879064	+	0.476703i	$0.841832\pi$
$462$	2.63688	+	5.52444i	0.122679	+	0.257020i
$463$	23.4379	+	10.7037i	1.08925	+	0.497445i	0.877353	−	0.479846i	$-0.159307\pi$
$463$	23.4379	+	10.7037i	1.08925	+	0.497445i	0.211901	+	0.977291i	$0.432035\pi$
$464$	−1.73489	−	6.51196i	−0.0805401	−	0.302310i
$465$	6.69562	−	2.67619i	0.310502	−	0.124105i
$466$	13.0104	−	6.99807i	0.602697	−	0.324179i
$467$	−7.61673	+	4.89498i	−0.352460	+	0.226512i	−0.704875	−	0.709331i	$-0.748997\pi$
$467$	−7.61673	+	4.89498i	−0.352460	+	0.226512i	0.352415	+	0.935844i	$0.385361\pi$
$468$	17.5150	+	10.4356i	0.809632	+	0.482384i
$469$	16.2859	+	18.7949i	0.752013	+	0.867869i
$470$	−12.6604	+	2.67057i	−0.583978	+	0.123184i
$471$	3.70177	−	5.19228i	0.170569	−	0.239248i
$472$	16.8587	+	23.4320i	0.775984	+	1.07855i
$473$	−2.42950	+	3.78038i	−0.111709	+	0.173822i
$474$	9.21781	+	5.70571i	0.423388	+	0.262072i
$475$	−20.7497	+	9.47608i	−0.952062	+	0.434792i
$476$	4.99348	+	7.98985i	0.228876	+	0.366214i
$477$	12.2859	−	4.23685i	0.562533	−	0.193992i
$478$	4.44349	−	0.289645i	0.203241	−	0.0132481i
$479$	17.3890	−	5.10586i	0.794523	−	0.233293i	0.140811	−	0.990037i	$-0.455029\pi$
$479$	17.3890	−	5.10586i	0.794523	−	0.233293i	0.653712	+	0.756744i	$0.273211\pi$
$480$	−1.24726	+	8.19178i	−0.0569292	+	0.373902i
$481$	−4.50791	−	31.3532i	−0.205543	−	1.42958i
$482$	−15.5123	−	15.7093i	−0.706566	−	0.715537i
$483$	2.94548	+	21.7896i	0.134024	+	0.991462i
$484$	0.255047	−	20.2157i	0.0115930	−	0.918895i
$485$	−9.82655	+	1.41285i	−0.446201	+	0.0641540i
$486$	9.81260	−	19.7411i	0.445109	−	0.895477i
$487$	−3.17527	−	10.8140i	−0.143885	−	0.490028i	0.855740	−	0.517406i	$-0.173102\pi$
$487$	−3.17527	−	10.8140i	−0.143885	−	0.490028i	−0.999625	+	0.0273783i	$0.991284\pi$
$488$	0.743955	+	14.1639i	0.0336772	+	0.641170i
$489$	1.27504	−	1.33573i	0.0576592	−	0.0604037i
$490$	0.00175526	−	0.00783065i	7.92944e−5	−	0.000353753i
$491$	−1.72925	−	3.78653i	−0.0780399	−	0.170884i	0.866590	−	0.499020i	$-0.166307\pi$
$491$	−1.72925	−	3.78653i	−0.0780399	−	0.170884i	−0.944630	+	0.328137i	$0.893579\pi$
$492$	−4.22173	−	18.4603i	−0.190330	−	0.832255i
$493$	2.52244	+	1.62107i	0.113605	+	0.0730095i
$494$	15.2021	+	20.5769i	0.683975	+	0.925799i
$495$	−1.09523	−	2.13027i	−0.0492268	−	0.0957487i
$496$	−11.0599	+	16.2908i	−0.496606	+	0.731477i
$497$	−11.6611	+	10.1044i	−0.523073	+	0.453245i
$498$	10.2995	−	9.23454i	0.461533	−	0.413810i
$499$	−11.1808	−	17.3977i	−0.500523	−	0.778829i	0.495436	−	0.868645i	$-0.335008\pi$
$499$	−11.1808	−	17.3977i	−0.500523	−	0.778829i	−0.995958	+	0.0898161i	$0.971372\pi$
$500$	15.0112	+	4.61418i	0.671323	+	0.206352i
$501$	−7.08330	+	2.83114i	−0.316458	+	0.126486i
$502$	24.2698	+	13.4517i	1.08321	+	0.600380i
$503$	−14.4896	+	31.7279i	−0.646062	+	1.41468i	0.248898	+	0.968530i	$0.419932\pi$
$503$	−14.4896	+	31.7279i	−0.646062	+	1.41468i	−0.894959	+	0.446148i	$0.852796\pi$
$504$	22.4391	+	0.984338i	0.999518	+	0.0438459i
$505$	−6.96855			−0.310096
$506$	−2.03604	+	6.07097i	−0.0905130	+	0.269887i
$507$	2.23692	+	1.15479i	0.0993453	+	0.0512862i
$508$	5.09908	+	38.9467i	0.226235	+	1.72798i
$509$	−13.1509	−	6.00579i	−0.582901	−	0.266202i	0.102064	−	0.994778i	$-0.467455\pi$
$509$	−13.1509	−	6.00579i	−0.582901	−	0.266202i	−0.684965	+	0.728576i	$0.740183\pi$
$510$	−2.04546	−	3.06732i	−0.0905744	−	0.135823i
$511$	−12.0287	−	10.4229i	−0.532118	−	0.461083i
$512$	−9.69987	−	20.4429i	−0.428678	−	0.903458i
$513$	20.9366	−	18.0804i	0.924374	−	0.798270i
$514$	−27.0268	−	10.2751i	−1.19210	−	0.453216i
$515$	1.82501	+	2.10618i	0.0804197	+	0.0928093i
$516$	8.05532	+	14.3866i	0.354616	+	0.633336i
$517$	−1.45358	+	10.1099i	−0.0639284	+	0.444632i
$518$	−20.7355	−	28.0667i	−0.911066	−	1.23318i
$519$	−17.8851	+	10.3127i	−0.785069	+	0.452676i
$520$	0.733162	−	8.09500i	0.0321513	−	0.354989i
$521$	−19.4837	+	8.89790i	−0.853595	+	0.389824i	−0.793648	−	0.608378i	$-0.791821\pi$
$521$	−19.4837	+	8.89790i	−0.853595	+	0.389824i	−0.0599476	+	0.998202i	$0.519093\pi$
$522$	6.59148	−	2.76491i	0.288501	−	0.121017i
$523$	8.87401	−	30.2221i	0.388033	−	1.32152i	−0.501701	−	0.865041i	$-0.667292\pi$
$523$	8.87401	−	30.2221i	0.388033	−	1.32152i	0.889734	−	0.456479i	$-0.150890\pi$
$524$	9.42321	+	8.37570i	0.411655	+	0.365894i
$525$	3.72855	−	19.2877i	0.162727	−	0.841783i
$526$	32.3981	−	11.8516i	1.41262	−	0.516755i
$527$	−1.24680	−	8.67168i	−0.0543114	−	0.377744i
$528$	5.73466	+	3.14618i	0.249569	+	0.136920i
$529$	−13.6348	+	18.5227i	−0.592819	+	0.805336i
$530$	−3.64040	−	3.68661i	−0.158129	−	0.160136i
$531$	−22.1825	+	21.1038i	−0.962640	+	0.915827i
$532$	25.4875	+	12.0306i	1.10502	+	0.521593i
$533$	5.23337	+	17.8232i	0.226683	+	0.772010i
$534$	9.47672	−	21.7170i	0.410098	−	0.939786i
$535$	−0.426530	+	1.45263i	−0.0184405	+	0.0628026i
$536$	25.8548	+	6.13896i	1.11676	+	0.265163i
$537$	−1.72609	+	35.8147i	−0.0744862	+	1.54552i
$538$	−28.6768	−	2.23290i	−1.23635	−	0.0962674i
$539$	−0.00532917	−	0.00342485i	−0.000229544	−	0.000147519i
$540$	−8.78794	−	0.125579i	−0.378173	−	0.00540406i
$541$	6.24616	−	43.4430i	0.268543	−	1.86776i	−0.193776	−	0.981046i	$-0.562073\pi$
$541$	6.24616	−	43.4430i	0.268543	−	1.86776i	0.462319	−	0.886714i	$-0.347018\pi$
$542$	32.6697	−	6.89133i	1.40329	−	0.296008i
$543$	−5.67938	−	23.4679i	−0.243726	−	1.00710i
$544$	9.31723	+	3.81398i	0.399473	+	0.163523i
$545$	−7.90105	−	12.2943i	−0.338444	−	0.526629i
$546$	−22.0291	+	0.373084i	−0.942759	+	0.0159665i
$547$	29.1989	+	25.3010i	1.24845	+	1.08179i	0.993380	+	0.114871i	$0.0366454\pi$
$547$	29.1989	+	25.3010i	1.24845	+	1.08179i	0.255074	+	0.966921i	$0.417900\pi$
$548$	39.6488	−	11.1006i	1.69371	−	0.474194i
$549$	−14.7751	+	2.83058i	−0.630587	+	0.120806i
$550$	3.45725	−	4.55813i	0.147418	−	0.194360i
$551$	8.96932			0.382106
$552$	16.1526	+	17.0615i	0.687498	+	0.726186i
$553$	−11.7150			−0.498173
$554$	−0.322862	+	0.425670i	−0.0137171	+	0.0180850i
$555$	8.43471	+	10.7379i	0.358034	+	0.455800i
$556$	3.92377	−	1.09855i	0.166405	−	0.0465889i
$557$	−28.8275	−	24.9792i	−1.22146	−	1.05840i	−0.996462	−	0.0840417i	$-0.973217\pi$
$557$	−28.8275	−	24.9792i	−1.22146	−	1.05840i	−0.224998	−	0.974359i	$-0.572237\pi$
$558$	−18.7174	−	9.26470i	−0.792370	−	0.392206i
$559$	−8.74420	−	13.6062i	−0.369840	−	0.575483i
$560$	−3.51312	−	8.23646i	−0.148456	−	0.348054i
$561$	−2.82864	+	0.684550i	−0.119425	+	0.0289017i
$562$	34.9976	−	7.38236i	1.47628	−	0.311406i
$563$	4.12961	−	28.7221i	0.174042	−	1.21049i	−0.696193	−	0.717855i	$-0.745124\pi$
$563$	4.12961	−	28.7221i	0.174042	−	1.21049i	0.870235	−	0.492636i	$-0.163967\pi$
$564$	30.2382	+	22.1386i	1.27326	+	0.932202i
$565$	13.2272	+	8.50058i	0.556471	+	0.357622i
$566$	9.47720	+	0.737937i	0.398356	+	0.0310178i
$567$	2.21162	+	23.7203i	0.0928793	+	0.996159i
$568$	−3.80885	+	16.0413i	−0.159816	+	0.673079i
$569$	0.405597	−	1.38134i	0.0170035	−	0.0579086i	−0.950554	−	0.310559i	$-0.899484\pi$
$569$	0.405597	−	1.38134i	0.0170035	−	0.0579086i	0.967558	+	0.252650i	$0.0813021\pi$
$570$	−10.1079	−	4.41084i	−0.423375	−	0.184750i
$571$	7.00602	+	23.8603i	0.293193	+	0.998523i	0.965965	+	0.258673i	$0.0832853\pi$
$571$	7.00602	+	23.8603i	0.293193	+	0.998523i	−0.672772	+	0.739850i	$0.734896\pi$
$572$	−5.80233	−	2.73882i	−0.242607	−	0.114516i
$573$	9.58109	−	27.6329i	0.400256	−	1.15438i
$574$	14.3787	+	14.5612i	0.600154	+	0.607773i
$575$	16.8322	−	11.7874i	0.701950	−	0.491569i
$576$	20.0773	−	13.1493i	0.836552	−	0.547887i
$577$	2.39174	+	16.6349i	0.0995693	+	0.692520i	0.977066	+	0.212937i	$0.0683029\pi$
$577$	2.39174	+	16.6349i	0.0995693	+	0.692520i	−0.877497	+	0.479583i	$0.840788\pi$
$578$	18.3716	−	6.72055i	0.764157	−	0.279538i
$579$	29.1623	+	5.63744i	1.21194	+	0.234284i
$580$	−2.12991	−	1.89314i	−0.0884395	−	0.0786084i
$581$	−4.21154	+	14.3432i	−0.174724	+	0.595055i
$582$	22.0467	+	18.4593i	0.913864	+	0.765162i
$583$	−3.72028	+	1.69900i	−0.154078	+	0.0703652i
$584$	−16.9377	−	1.53404i	−0.700887	−	0.0634792i
$585$	8.61188	−	0.400606i	0.356057	−	0.0165630i
$586$	9.15375	+	12.3901i	0.378138	+	0.511831i
$587$	−1.76746	+	12.2929i	−0.0729508	+	0.507384i	0.920283	+	0.391253i	$0.127958\pi$
$587$	−1.76746	+	12.2929i	−0.0729508	+	0.507384i	−0.993234	+	0.116131i	$0.962951\pi$
$588$	−0.0202807	+	0.0113555i	−0.000836362	+	0.000468293i
$589$	−17.1617	−	19.8057i	−0.707136	−	0.816079i
$590$	11.4095	+	4.33772i	0.469724	+	0.178581i
$591$	1.58332	+	16.6796i	0.0651291	+	0.686107i
$592$	−35.5003	−	11.4042i	−1.45905	−	0.468711i
$593$	1.39579	+	1.20946i	0.0573184	+	0.0496667i	0.683049	−	0.730373i	$-0.260654\pi$
$593$	1.39579	+	1.20946i	0.0573184	+	0.0496667i	−0.625731	+	0.780039i	$0.715199\pi$
$594$	−2.47631	+	6.48080i	−0.101604	+	0.265910i
$595$	3.62405	+	1.65505i	0.148572	+	0.0678504i
$596$	−4.56859	−	34.8949i	−0.187137	−	1.42935i
$597$	−13.3962	+	25.9495i	−0.548271	+	1.06204i
$598$	−16.8317	−	15.7428i	−0.688298	−	0.643772i
$599$	5.26349			0.215060			0.107530	−	0.994202i	$-0.465706\pi$
$599$	5.26349			0.215060			0.107530	+	0.994202i	$0.465706\pi$
$600$	−8.80238	−	19.0563i	−0.359356	−	0.777970i
$601$	−8.87395	+	19.4312i	−0.361976	+	0.792617i	0.637773	+	0.770224i	$0.279856\pi$
$601$	−8.87395	+	19.4312i	−0.361976	+	0.792617i	−0.999749	+	0.0223929i	$0.992872\pi$
$602$	−15.5842	−	8.63769i	−0.635166	−	0.352046i
$603$	−2.71051	+	28.0549i	−0.110380	+	1.14249i
$604$	−39.7214	−	12.2096i	−1.61624	−	0.496802i
$605$	−4.62191	−	7.19183i	−0.187907	−	0.292389i
$606$	13.4738	+	15.0277i	0.547338	+	0.610460i
$607$	−15.2048	+	13.1750i	−0.617143	+	0.534758i	−0.906360	−	0.422506i	$-0.861151\pi$
$607$	−15.2048	+	13.1750i	−0.617143	+	0.534758i	0.289217	+	0.957264i	$0.406605\pi$
$608$	29.6147	−	5.47041i	1.20103	−	0.221854i
$609$	−4.48404	+	6.28953i	−0.181703	+	0.254865i
$610$	3.56382	+	4.82383i	0.144295	+	0.195311i
$611$	−30.9256	−	19.8747i	−1.25112	−	0.804043i
$612$	−2.65976	+	10.3418i	−0.107515	+	0.418042i
$613$	3.13093	+	6.85578i	0.126457	+	0.276902i	0.962262	−	0.272124i	$-0.0877260\pi$
$613$	3.13093	+	6.85578i	0.126457	+	0.276902i	−0.835805	+	0.549026i	$0.814999\pi$
$614$	−0.0560650	+	0.250120i	−0.00226260	+	0.0100940i
$615$	−5.79223	−	5.52906i	−0.233565	−	0.222953i
$616$	−7.05875	+	0.370758i	−0.284405	+	0.0149383i
$617$	5.35216	+	18.2278i	0.215470	+	0.733823i	0.994303	+	0.106592i	$0.0339937\pi$
$617$	5.35216	+	18.2278i	0.215470	+	0.733823i	−0.778833	+	0.627231i	$0.784188\pi$
$618$	1.01329	−	8.00800i	0.0407603	−	0.322129i
$619$	1.69912	−	0.244297i	0.0682934	−	0.00981911i	−0.108083	−	0.994142i	$-0.534471\pi$
$619$	1.69912	−	0.244297i	0.0682934	−	0.00981911i	0.176377	+	0.984323i	$0.443562\pi$
$620$	−0.105036	+	8.32547i	−0.00421837	+	0.334359i
$621$	−15.5908	+	19.4403i	−0.625639	+	0.780113i
$622$	−10.4822	−	10.6153i	−0.420298	−	0.425634i
$623$	3.64403	+	25.3448i	0.145995	+	1.01542i
$624$	−18.8745	+	14.0708i	−0.755586	+	0.563283i
$625$	−14.1844	+	4.16493i	−0.567377	+	0.166597i
$626$	42.8200	−	2.79118i	1.71143	−	0.111558i
$627$	−6.01112	+	6.29724i	−0.240061	+	0.251488i
$628$	3.90240	+	6.24407i	0.155723	+	0.249166i
$629$	15.0909	−	6.89180i	0.601715	−	0.274794i
$630$	8.14627	−	4.88284i	0.324555	−	0.194537i
$631$	19.9461	−	31.0367i	0.794040	−	1.23555i	−0.173997	−	0.984746i	$-0.555668\pi$
$631$	19.9461	−	31.0367i	0.794040	−	1.23555i	0.968038	−	0.250805i	$-0.0806952\pi$
$632$	−10.1612	+	7.31073i	−0.404192	+	0.290805i
$633$	−3.00337	−	2.14121i	−0.119373	−	0.0851056i
$634$	−2.96304	+	0.625021i	−0.117677	+	0.0248227i
$635$	10.8768	+	12.5525i	0.431631	+	0.498129i
$636$	−0.911428	+	14.9787i	−0.0361405	+	0.593944i
$637$	0.0191806	−	0.0123266i	0.000759962	−	0.000488398i
$638$	−1.98108	+	1.06558i	−0.0784315	+	0.0421868i
$639$	−17.4064	−	1.68171i	−0.688586	−	0.0665273i
$640$	−8.18710	−	4.95170i	−0.323624	−	0.195733i
$641$	39.5617	+	18.0672i	1.56259	+	0.713613i	0.994038	−	0.109032i	$-0.0347751\pi$
$641$	39.5617	+	18.0672i	1.56259	+	0.713613i	0.568556	+	0.822645i	$0.307502\pi$
$642$	3.95731	−	1.88888i	0.156183	−	0.0745480i
$643$			46.8659i			1.84821i	0.382140	+	0.924104i	$0.375187\pi$
$643$			46.8659i			1.84821i	−0.382140	+	0.924104i	$0.624813\pi$
$644$	−24.5458	−	6.49012i	−0.967239	−	0.255747i
$645$	6.19528	+	3.19827i	0.243939	+	0.125932i
$646$	−8.09746	+	10.6759i	−0.318590	+	0.420038i
$647$	6.02883	−	13.2013i	0.237018	−	0.518997i	−0.753323	−	0.657651i	$-0.771550\pi$
$647$	6.02883	−	13.2013i	0.237018	−	0.518997i	0.990341	+	0.138654i	$0.0442775\pi$
$648$	16.7209	+	19.1941i	0.656858	+	0.754015i
$649$	6.30990	−	7.28201i	0.247685	−	0.285844i
$650$	9.75386	+	18.1339i	0.382578	+	0.711269i
$651$	22.4680	−	2.13278i	0.880589	−	0.0835904i
$652$	0.861233	+	1.95059i	0.0337285	+	0.0763910i
$653$	6.00373	−	5.20226i	0.234944	−	0.203580i	−0.529429	−	0.848354i	$-0.677594\pi$
$653$	6.00373	−	5.20226i	0.234944	−	0.203580i	0.764373	+	0.644774i	$0.223048\pi$
$654$	−11.2359	+	40.8100i	−0.439357	+	1.59580i
$655$	5.27686	+	0.758698i	0.206184	+	0.0296448i
$656$	21.5585	+	3.65697i	0.841717	+	0.142781i
$657$	−0.838214	−	18.0192i	−0.0327018	−	0.702996i
$658$	−40.3761	−	3.14386i	−1.57402	−	0.122560i
$659$	−16.8520	−	36.9008i	−0.656461	−	1.43745i	−0.885783	−	0.464099i	$-0.846378\pi$
$659$	−16.8520	−	36.9008i	−0.656461	−	1.43745i	0.229322	−	0.973351i	$-0.426349\pi$
$660$	2.75658	−	0.226621i	0.107300	−	0.00882122i
$661$	−4.44158	−	1.30417i	−0.172757	−	0.0507262i	0.194210	−	0.980960i	$-0.437786\pi$
$661$	−4.44158	−	1.30417i	−0.172757	−	0.0507262i	−0.366967	+	0.930234i	$0.619604\pi$
$662$	0.0229625	+	0.352272i	0.000892464	+	0.0136914i
$663$	1.98808	−	10.2842i	0.0772105	−	0.399407i
$664$	5.29786	+	15.0690i	0.205597	+	0.584791i
$665$	11.7964	−	1.69607i	0.457446	−	0.0657709i
$666$	6.84774	−	38.9516i	0.265344	−	1.50934i
$667$	−7.94568	+	1.46658i	−0.307658	+	0.0567861i
$668$	0.111118	−	8.80751i	0.00429929	−	0.340773i
$669$	−20.4805	−	7.10117i	−0.791822	−	0.274547i
$670$	10.5528	−	3.86035i	0.407691	−	0.149138i
$671$	4.54258	−	1.33382i	0.175364	−	0.0514916i
$672$	−10.9693	+	23.5015i	−0.423150	+	0.906588i
$673$	37.7614	+	11.0878i	1.45560	+	0.427402i	0.911388	−	0.411549i	$-0.135012\pi$
$673$	37.7614	+	11.0878i	1.45560	+	0.427402i	0.544208	+	0.838950i	$0.316830\pi$
$674$	−41.4199	−	9.28436i	−1.59543	−	0.357620i
$675$	18.7501	−	12.0057i	0.721692	−	0.462099i
$676$	−2.22070	+	1.87572i	−0.0854115	+	0.0721432i
$677$	18.5326	−	28.8373i	0.712266	−	1.10831i	−0.276813	−	0.960924i	$-0.589278\pi$
$677$	18.5326	−	28.8373i	0.712266	−	1.10831i	0.989079	−	0.147384i	$-0.0470854\pi$
$678$	−7.24345	−	44.9606i	−0.278183	−	1.72670i
$679$	−30.7566	−	4.42214i	−1.18033	−	0.169706i
$680$	4.17622	−	0.826042i	0.160151	−	0.0316773i
$681$	−0.376705	−	1.55659i	−0.0144354	−	0.0596486i
$682$	6.14353	+	2.33566i	0.235248	+	0.0894372i
$683$	24.0879	−	15.4804i	0.921699	−	0.592340i	0.00854858	−	0.999963i	$-0.497279\pi$
$683$	24.0879	−	15.4804i	0.921699	−	0.592340i	0.913150	+	0.407624i	$0.133643\pi$
$684$	10.0319	+	30.3263i	0.383580	+	1.15956i
$685$	11.4013	−	13.1578i	0.435622	−	0.502735i
$686$	−12.6910	+	22.8972i	−0.484543	+	0.874219i
$687$	25.9755	−	20.4039i	0.991027	−	0.778458i
$688$	−18.9076	+	2.23324i	−0.720845	+	0.0851413i
$689$		−	14.7202i		−	0.560794i
$690$	9.67556	+	2.25469i	0.368342	+	0.0858345i
$691$			3.84217i			0.146163i	0.997326	+	0.0730815i	$0.0232833\pi$
$691$			3.84217i			0.146163i	−0.997326	+	0.0730815i	$0.976717\pi$
$692$	−3.09472	−	23.6374i	−0.117644	−	0.898560i
$693$	−1.41065	−	7.36335i	−0.0535862	−	0.279711i
$694$	−1.67422	−	0.927950i	−0.0635525	−	0.0352245i
$695$	1.12831	−	1.30214i	0.0427992	−	0.0493930i
$696$	0.0356454	+	8.25360i	0.00135113	+	0.312852i
$697$	−8.18460	+	5.25992i	−0.310014	+	0.199234i
$698$	−9.67069	+	25.4369i	−0.366041	+	0.962802i
$699$	−17.5856	+	4.25584i	−0.665150	+	0.160971i
$700$	18.9266	+	12.5035i	0.715358	+	0.472590i
$701$	2.18584	+	0.314276i	0.0825580	+	0.0118701i	0.183470	−	0.983025i	$-0.441267\pi$
$701$	2.18584	+	0.314276i	0.0825580	+	0.0118701i	−0.100912	+	0.994895i	$0.532176\pi$
$702$	−17.5152	−	17.7970i	−0.661068	−	0.671705i
$703$	26.8303	−	41.7487i	1.01192	−	1.57458i
$704$	−5.89117	+	4.72658i	−0.222032	+	0.178140i
$705$	15.8285	+	0.762856i	0.596137	+	0.0287308i
$706$	9.64061	−	43.0092i	0.362829	−	1.61867i
$707$	−20.9277	−	6.14493i	−0.787067	−	0.231104i
$708$	−12.7063	−	32.9919i	−0.477532	−	1.23991i
$709$	18.1997	−	5.34391i	0.683504	−	0.200695i	0.0784960	−	0.996914i	$-0.474988\pi$
$709$	18.1997	−	5.34391i	0.683504	−	0.200695i	0.605008	+	0.796220i	$0.293170\pi$
$710$	2.39511	+	6.54738i	0.0898870	+	0.245719i
$711$	−9.15161	−	9.61940i	−0.343212	−	0.360756i
$712$	18.9770	+	19.7092i	0.711195	+	0.738634i
$713$	18.4415	+	14.7392i	0.690641	+	0.551987i
$714$	−3.43806	−	11.0154i	−0.128666	−	0.412240i
$715$	−2.68551	+	0.386118i	−0.100432	+	0.0144400i
$716$	−37.4418	−	17.6733i	−1.39927	−	0.660482i
$717$	−5.35456	−	1.03511i	−0.199970	−	0.0386567i
$718$	−10.9802	+	0.715735i	−0.409778	+	0.0267110i
$719$	6.14401	+	1.80405i	0.229133	+	0.0672795i	0.394284	−	0.918989i	$-0.370993\pi$
$719$	6.14401	+	1.80405i	0.229133	+	0.0672795i	−0.165150	+	0.986268i	$0.552811\pi$
$720$	4.01869	−	9.31888i	0.149768	−	0.347294i
$721$	3.62357	+	7.93452i	0.134949	+	0.295497i
$722$	−1.02564	+	13.1722i	−0.0381705	+	0.490218i
$723$	13.5065	+	23.4242i	0.502314	+	0.871155i
$724$	27.5446	+	4.31565i	1.02369	+	0.160390i
$725$	7.14541	+	1.02735i	0.265374	+	0.0381550i
$726$	−6.57268	+	23.8728i	−0.243935	+	0.886001i
$727$	7.55910	−	6.54999i	0.280351	−	0.242926i	−0.503322	−	0.864099i	$-0.667889\pi$
$727$	7.55910	−	6.54999i	0.280351	−	0.242926i	0.783673	+	0.621173i	$0.213344\pi$
$728$	9.34005	−	23.6641i	0.346165	−	0.877051i
$729$	−17.7494	+	20.3460i	−0.657386	+	0.753554i
$730$	−6.33342	+	3.40663i	−0.234410	+	0.126085i
$731$	5.54736	−	6.40199i	0.205176	−	0.236786i
$732$	3.51191	−	17.0124i	0.129804	−	0.628796i
$733$	7.57521	−	16.5874i	0.279797	−	0.612670i	−0.716600	−	0.697485i	$-0.754303\pi$
$733$	7.57521	−	16.5874i	0.279797	−	0.612670i	0.996397	+	0.0848148i	$0.0270299\pi$
$734$	20.4156	+	15.4848i	0.753554	+	0.571556i
$735$	−0.00450856	+	0.00873343i	−0.000166301	+	0.000322137i
$736$	−25.3404	+	9.68840i	−0.934059	+	0.357119i
$737$		−	8.87013i		−	0.326735i
$738$	−0.724041	+	23.1816i	−0.0266523	+	0.853325i
$739$	38.8144	+	17.7259i	1.42781	+	0.652060i	0.971343	−	0.237680i	$-0.0763870\pi$
$739$	38.8144	+	17.7259i	1.42781	+	0.652060i	0.456468	+	0.889740i	$0.349114\pi$
$740$	−15.1831	+	4.25086i	−0.558142	+	0.156265i
$741$	−11.6292	−	29.0952i	−0.427208	−	1.06884i
$742$	−7.68183	−	14.2817i	−0.282009	−	0.524296i
$743$	−3.91823	+	2.51809i	−0.143746	+	0.0923798i	−0.610537	−	0.791988i	$-0.709046\pi$
$743$	−3.91823	+	2.51809i	−0.143746	+	0.0923798i	0.466791	+	0.884368i	$0.345410\pi$
$744$	18.1570	−	15.8710i	0.665670	−	0.581858i
$745$	−9.74519	−	11.2465i	−0.357036	−	0.412042i
$746$	1.30521	+	6.18762i	0.0477872	+	0.226545i
$747$	−15.0674	+	7.74652i	−0.551288	+	0.283430i
$748$	0.520176	−	3.32002i	0.0190195	−	0.121392i
$749$	−2.56188	+	3.98637i	−0.0936092	+	0.145659i
$750$	−16.3543	−	10.1231i	−0.597176	−	0.369644i
$751$	−19.9866	+	9.12757i	−0.729321	+	0.333070i	−0.745233	−	0.666804i	$-0.767662\pi$
$751$	−19.9866	+	9.12757i	−0.729321	+	0.333070i	0.0159124	+	0.999873i	$0.494935\pi$
$752$	−36.9829	+	22.4697i	−1.34863	+	0.819385i
$753$	−24.5828	−	23.4658i	−0.895847	−	0.855142i
$754$	−0.526628	−	8.07909i	−0.0191787	−	0.294223i
$755$	−16.8601	+	4.95057i	−0.613602	+	0.180170i
$756$	−26.2809	−	8.12642i	−0.955827	−	0.295555i
$757$	−2.24723	−	15.6298i	−0.0816768	−	0.568075i	−0.989031	−	0.147708i	$-0.952811\pi$
$757$	−2.24723	−	15.6298i	−0.0816768	−	0.568075i	0.907354	−	0.420367i	$-0.138099\pi$
$758$	30.9416	−	30.5537i	1.12385	−	1.10976i
$759$	4.29542	−	6.56144i	0.155914	−	0.238165i
$760$	9.17343	−	8.83266i	0.332755	−	0.320394i
$761$	43.6135	−	6.27067i	1.58099	−	0.227312i	0.704844	−	0.709362i	$-0.251017\pi$
$761$	43.6135	−	6.27067i	1.58099	−	0.227312i	0.876143	+	0.482050i	$0.160108\pi$
$762$	6.03901	−	47.7263i	0.218770	−	1.72894i
$763$	−12.8870	−	43.8890i	−0.466540	−	1.58889i
$764$	25.2416	+	22.4357i	0.913208	+	0.811694i
$765$	1.47207	+	4.26867i	0.0532228	+	0.154334i
$766$	19.5159	+	4.37454i	0.705139	+	0.158058i
$767$	14.4065	+	31.5458i	0.520188	+	1.13905i
$768$	5.15158	+	27.2298i	0.185892	+	0.982570i
$769$	5.14057	+	3.30364i	0.185374	+	0.119132i	0.630036	−	0.776566i	$-0.283040\pi$
$769$	5.14057	+	3.30364i	0.185374	+	0.119132i	−0.444663	+	0.895698i	$0.646676\pi$
$770$	−2.40401	+	1.77607i	−0.0866345	+	0.0640051i
$771$	28.8346	+	20.5573i	1.03845	+	0.740352i
$772$	−18.9049	+	28.6163i	−0.680403	+	1.02992i
$773$	24.0941	−	20.8776i	0.866603	−	0.750916i	−0.103237	−	0.994657i	$-0.532920\pi$
$773$	24.0941	−	20.8776i	0.866603	−	0.750916i	0.969840	+	0.243741i	$0.0783746\pi$
$774$	−5.08163	−	19.5441i	−0.182656	−	0.702498i
$775$	−11.4033	−	17.7439i	−0.409620	−	0.637380i
$776$	−29.4370	+	15.3580i	−1.05673	+	0.551319i
$777$	15.8620	+	39.6856i	0.569048	+	1.42371i
$778$	−16.3541	+	29.5062i	−0.586321	+	1.05785i
$779$	−12.0898	+	26.4729i	−0.433161	+	0.948491i
$780$	−3.37957	+	9.36367i	−0.121008	+	0.335273i
$781$	5.50338			0.196926
$782$	5.42770	−	10.7815i	0.194094	−	0.385546i
$783$	−8.66731	+	1.23137i	−0.309744	+	0.0440056i
$784$	−0.00314817	−	0.0266539i	−0.000112435	−	0.000951923i
$785$	2.83220	+	1.29342i	0.101086	+	0.0461642i
$786$	−8.56679	−	12.8466i	−0.305567	−	0.458221i
$787$	−41.1818	−	35.6842i	−1.46797	−	1.27201i	−0.890009	−	0.455944i	$-0.849302\pi$
$787$	−41.1818	−	35.6842i	−1.46797	−	1.27201i	−0.577964	−	0.816062i	$-0.696153\pi$
$788$	−18.4926	−	5.68429i	−0.658772	−	0.202494i
$789$	−42.0619	+	3.99275i	−1.49744	+	0.142146i
$790$	−1.88104	+	4.94772i	−0.0669244	+	0.176032i
$791$	32.2275	+	37.1925i	1.14588	+	1.32241i
$792$	−5.81863	−	5.50642i	−0.206756	−	0.195662i
$793$	−2.42501	+	16.8663i	−0.0861146	+	0.598940i
$794$	−1.04913	+	0.775088i	−0.0372321	+	0.0275068i
$795$	3.16969	+	5.49714i	0.112417	+	0.194963i
$796$	−21.7594	−	25.7613i	−0.771241	−	0.913084i
$797$	−28.6032	+	13.0627i	−1.01318	+	0.462703i	−0.851620	−	0.524160i	$-0.824379\pi$
$797$	−28.6032	+	13.0627i	−1.01318	+	0.462703i	−0.161559	+	0.986863i	$0.551652\pi$
$798$	−26.4663	−	22.1597i	−0.936897	−	0.784446i
$799$	5.42443	−	18.4739i	0.191902	−	0.653560i
$800$	24.2191	−	0.965906i	0.856276	−	0.0341499i
$801$	−17.9643	+	22.7911i	−0.634739	+	0.805285i
$802$	11.8976	+	32.5239i	0.420121	+	1.14846i
$803$	0.807901	+	5.61907i	0.0285102	+	0.198293i
$804$	−28.7290	−	15.2932i	−1.01319	−	0.539349i
$805$	−10.1728	+	3.43135i	−0.358545	+	0.120939i
$806$	−16.8323	+	16.6213i	−0.592892	+	0.585459i
$807$	33.2842	+	11.5406i	1.17166	+	0.406247i
$808$	−21.9868	+	7.72996i	−0.773491	+	0.271939i
$809$	−4.95696	−	16.8818i	−0.174277	−	0.593534i	−0.999584	−	0.0288489i	$-0.990816\pi$
$809$	−4.95696	−	16.8818i	−0.174277	−	0.593534i	0.825306	−	0.564685i	$-0.191002\pi$
$810$	10.3731	+	2.87463i	0.364475	+	0.101004i
$811$	5.93418	−	20.2100i	0.208377	−	0.709668i	−0.787282	−	0.616593i	$-0.788512\pi$
$811$	5.93418	−	20.2100i	0.208377	−	0.709668i	0.995659	−	0.0930748i	$-0.0296696\pi$
$812$	−4.72707	−	7.56359i	−0.165888	−	0.265430i
$813$	−40.8452	−	1.96853i	−1.43250	−	0.0690394i
$814$	−0.966193	+	12.4087i	−0.0338651	+	0.434923i
$815$	0.758501	+	0.487459i	0.0265691	+	0.0170749i
$816$	−9.85618	−	7.40888i	−0.345035	−	0.259363i
$817$	3.60622	−	25.0818i	0.126166	−	0.877503i
$818$	8.14478	+	38.6120i	0.284776	+	1.35004i
$819$	26.2162	+	6.39095i	0.916067	+	0.223318i
$820$	8.45851	−	3.73464i	0.295384	−	0.130419i
$821$	6.90186	+	10.7395i	0.240877	+	0.374811i	0.940552	−	0.339649i	$-0.110308\pi$
$821$	6.90186	+	10.7395i	0.240877	+	0.374811i	−0.699675	+	0.714461i	$0.746672\pi$
$822$	−50.4197	+	0.853907i	−1.75859	+	0.0297834i
$823$	11.4168	+	9.89269i	0.397964	+	0.344837i	0.830737	−	0.556665i	$-0.187919\pi$
$823$	11.4168	+	9.89269i	0.397964	+	0.344837i	−0.432773	+	0.901503i	$0.642465\pi$
$824$	8.09448	+	4.62087i	0.281985	+	0.160976i
$825$	−5.51005	+	4.32818i	−0.191835	+	0.150688i
$826$	30.4397	+	23.0879i	1.05913	+	0.803332i
$827$	0.545286			0.0189614			0.00948072	−	0.999955i	$-0.496982\pi$
$827$	0.545286			0.0189614			0.00948072	+	0.999955i	$0.496982\pi$
$828$	−13.8457	−	25.2249i	−0.481170	−	0.876627i
$829$	−6.82275			−0.236964			−0.118482	−	0.992956i	$-0.537803\pi$
$829$	−6.82275			−0.236964			−0.118482	+	0.992956i	$0.537803\pi$
$830$	5.38146	+	4.08173i	0.186793	+	0.141679i
$831$	0.514566	−	0.404195i	0.0178501	−	0.0140214i
$832$	−6.66626	−	26.3542i	−0.231111	−	0.913666i
$833$	0.00902482	+	0.00782005i	0.000312692	+	0.000270949i
$834$	−4.98969	+	0.0845052i	−0.172779	+	0.00292618i
$835$	−2.01366	−	3.13332i	−0.0696856	−	0.108433i
$836$	−4.06025	−	9.19598i	−0.140427	−	0.318050i
$837$	19.3029	+	16.7827i	0.667207	+	0.580095i
$838$	−1.46975	−	6.96765i	−0.0507717	−	0.240693i
$839$	1.96581	−	13.6725i	0.0678674	−	0.472028i	−0.927338	−	0.374224i	$-0.877909\pi$
$839$	1.96581	−	13.6725i	0.0678674	−	0.472028i	0.995206	−	0.0978039i	$-0.0311818\pi$
$840$	1.60761	+	10.8484i	0.0554679	+	0.374305i
$841$	22.0085	+	14.1440i	0.758913	+	0.487724i
$842$	1.66010	−	21.3204i	0.0572110	−	0.734751i
$843$	−43.7555	−	2.10879i	−1.50702	−	0.0726308i
$844$	3.61175	−	2.25726i	0.124322	−	0.0776982i
$845$	−0.346299	+	1.17938i	−0.0119130	+	0.0405721i
$846$	−28.9597	−	35.6094i	−0.995657	−	1.22428i
$847$	−7.53854	−	25.6739i	−0.259027	−	0.882166i
$848$	−15.5754	−	7.59364i	−0.534861	−	0.260767i
$849$	−10.9998	−	3.81396i	−0.377514	−	0.130895i
$850$	−7.67367	+	7.57747i	−0.263205	+	0.259905i
$851$	−16.9419	+	41.3711i	−0.580760	+	1.41818i
$852$	9.48849	−	17.8246i	0.325070	−	0.610661i
$853$	−1.28380	−	8.92902i	−0.0439565	−	0.305724i	−0.999925	−	0.0122545i	$-0.996099\pi$
$853$	−1.28380	−	8.92902i	−0.0439565	−	0.305724i	0.955968	−	0.293469i	$-0.0948099\pi$
$854$	6.44904	+	17.6294i	0.220682	+	0.603265i
$855$	10.6079	+	8.36130i	0.362782	+	0.285951i
$856$	0.265585	+	5.05639i	0.00907751	+	0.172824i
$857$	8.72744	−	29.7229i	0.298124	−	1.01532i	−0.665131	−	0.746727i	$-0.731624\pi$
$857$	8.72744	−	29.7229i	0.298124	−	1.01532i	0.963255	−	0.268589i	$-0.0865575\pi$
$858$	6.02516	+	5.04476i	0.205696	+	0.172225i
$859$	−7.51823	+	3.43346i	−0.256519	+	0.117148i	−0.539524	−	0.841970i	$-0.681396\pi$
$859$	−7.51823	+	3.43346i	−0.256519	+	0.117148i	0.283005	+	0.959118i	$0.408669\pi$
$860$	−6.15035	+	5.19492i	−0.209725	+	0.177145i
$861$	−12.5195	−	21.7123i	−0.426663	−	0.739954i
$862$	−3.43804	+	2.54000i	−0.117100	+	0.0865128i
$863$	−5.04909	+	35.1172i	−0.171873	+	1.19540i	0.703050	+	0.711141i	$0.251821\pi$
$863$	−5.04909	+	35.1172i	−0.171873	+	1.19540i	−0.874923	+	0.484263i	$0.839088\pi$
$864$	−27.8665	+	9.35192i	−0.948037	+	0.318159i
$865$	−6.60129	−	7.61830i	−0.224451	−	0.259030i
$866$	12.1188	−	31.8761i	0.411812	−	1.08319i
$867$	−23.8515	+	2.26412i	−0.810040	+	0.0768935i
$868$	−7.65692	+	24.9102i	−0.259893	+	0.845506i
$869$	3.15782	+	2.73627i	0.107122	+	0.0928216i
$870$	1.93633	+	2.90368i	0.0656478	+	0.0984439i
$871$	29.0401	+	13.2622i	0.983986	+	0.449371i
$872$	−38.5666	−	30.0259i	−1.30603	−	1.01680i
$873$	−20.3956	−	28.7093i	−0.690285	−	0.971662i
$874$	−3.77763	−	35.9093i	−0.127780	−	1.21465i
$875$	20.7849			0.702658
$876$	19.5922	+	7.07129i	0.661960	+	0.238917i
$877$	19.9538	−	43.6927i	0.673791	−	1.47540i	−0.195299	−	0.980744i	$-0.562568\pi$
$877$	19.9538	−	43.6927i	0.673791	−	1.47540i	0.869090	−	0.494653i	$-0.164705\pi$
$878$	−14.7272	+	26.5709i	−0.497017	+	0.896725i
$879$	−7.00234	−	17.5193i	−0.236183	−	0.590912i
$880$	−0.976812	+	3.04072i	−0.0329283	+	0.102503i
$881$	15.2633	+	23.7502i	0.514234	+	0.800164i	0.997145	−	0.0755056i	$-0.0240571\pi$
$881$	15.2633	+	23.7502i	0.514234	+	0.800164i	−0.482911	+	0.875669i	$0.660421\pi$
$882$	0.0275511	−	0.00716353i	0.000927695	−	0.000241209i
$883$	−11.8468	+	10.2653i	−0.398677	+	0.345456i	−0.831009	−	0.556259i	$-0.812236\pi$
$883$	−11.8468	+	10.2653i	−0.398677	+	0.345456i	0.432332	+	0.901714i	$0.357691\pi$
$884$	10.0917	+	6.66693i	0.339422	+	0.224233i
$885$	−12.1727	−	8.67841i	−0.409182	−	0.291721i
$886$	−46.2651	+	34.1804i	−1.55431	+	1.14831i
$887$	−11.9658	−	7.68993i	−0.401771	−	0.258203i	0.324115	−	0.946018i	$-0.394934\pi$
$887$	−11.9658	−	7.68993i	−0.401771	−	0.258203i	−0.725886	+	0.687815i	$0.758570\pi$
$888$	38.5239	+	24.5234i	1.29278	+	0.822951i
$889$	21.5959	+	47.2884i	0.724302	+	1.58600i
$890$	11.2892	+	2.53050i	0.378415	+	0.0848226i
$891$	4.94418	−	6.91045i	0.165636	−	0.231509i
$892$	16.6285	−	18.7082i	0.556764	−	0.626396i
$893$	−16.2263	−	55.2617i	−0.542992	−	1.84926i
$894$	−5.41074	+	42.7611i	−0.180962	+	1.43014i
$895$	−17.3293	+	2.49158i	−0.579255	+	0.0832843i
$896$	−20.2208	−	22.0902i	−0.675529	−	0.737983i
$897$	15.0593	+	23.8732i	0.502816	+	0.797103i
$898$	−19.6486	+	19.4023i	−0.655683	+	0.647463i
$899$	1.18028	+	8.20904i	0.0393646	+	0.273787i
$900$	4.51832	+	25.3085i	0.150611	+	0.843618i
$901$	7.39742	−	2.17208i	0.246444	−	0.0723624i
$902$	−0.474765	−	7.28344i	−0.0158079	−	0.242512i
$903$	15.7852	+	15.0680i	0.525299	+	0.501431i
$904$	51.1630	+	12.1481i	1.70166	+	0.404041i
$905$	10.7240	−	4.89749i	0.356478	−	0.162798i
$906$	43.2753	+	26.7869i	1.43773	+	0.889936i
$907$	3.50117	−	5.44793i	0.116255	−	0.180896i	−0.778250	−	0.627955i	$-0.783892\pi$
$907$	3.50117	−	5.44793i	0.116255	−	0.180896i	0.894504	+	0.447059i	$0.147529\pi$
$908$	1.82699	+	0.286250i	0.0606308	+	0.00949956i
$909$	−11.3027	−	21.9844i	−0.374888	−	0.729177i
$910$	−2.22035	−	10.5260i	−0.0736040	−	0.348935i
$911$	0.954839	+	1.10194i	0.0316352	+	0.0365090i	0.771347	−	0.636415i	$-0.219583\pi$
$911$	0.954839	+	1.10194i	0.0316352	+	0.0365090i	−0.739711	+	0.672924i	$0.765038\pi$
$912$	−36.7848	−	2.70445i	−1.21806	−	0.0895533i
$913$	4.48536	−	2.88257i	0.148444	−	0.0953990i
$914$	4.77058	+	8.86921i	0.157797	+	0.293367i
$915$	−2.72621	−	6.82077i	−0.0901258	−	0.225488i
$916$	10.2830	+	36.7286i	0.339760	+	1.21355i
$917$	15.1783	+	6.93168i	0.501230	+	0.228904i
$918$	6.35914	−	11.4281i	0.209883	−	0.377184i
$919$			5.66520i			0.186878i	0.995625	+	0.0934389i	$0.0297860\pi$
$919$			5.66520i			0.186878i	−0.995625	+	0.0934389i	$0.970214\pi$
$920$	−6.68227	+	9.32457i	−0.220308	+	0.307422i
$921$	0.144009	−	0.278956i	0.00474526	−	0.00919192i
$922$	23.0655	+	17.4947i	0.759622	+	0.576158i
$923$	−8.22837	+	18.0176i	−0.270840	+	0.593057i
$924$	8.47832	+	1.75020i	0.278916	+	0.0575774i
$925$	26.1563	−	30.1860i	0.860013	−	0.992508i
$926$	32.0914	−	17.2614i	1.05459	−	0.567244i
$927$	−3.68448	+	9.17371i	−0.121014	+	0.301304i
$928$	−8.82015	−	3.61050i	−0.289536	−	0.118521i
$929$	−7.37482	+	6.39032i	−0.241960	+	0.209660i	−0.767396	−	0.641174i	$-0.778448\pi$
$929$	−7.37482	+	6.39032i	−0.241960	+	0.209660i	0.525436	+	0.850833i	$0.323902\pi$
$930$	2.70684	−	9.83157i	0.0887608	−	0.322390i
$931$	0.0353576	+	0.00508366i	0.00115880	+	0.000166610i
$932$	3.23393	−	20.6405i	0.105931	−	0.676103i
$933$	9.12684	+	15.8285i	0.298799	+	0.518203i
$934$	−0.993993	+	12.7657i	−0.0325244	+	0.417706i
$935$	−0.590307	−	1.29259i	−0.0193051	−	0.0422723i
$936$	26.7273	−	10.8168i	0.873610	−	0.353559i
$937$	−9.84323	−	2.89023i	−0.321564	−	0.0944198i	0.116967	−	0.993136i	$-0.462683\pi$
$937$	−9.84323	−	2.89023i	−0.321564	−	0.0944198i	−0.438531	+	0.898716i	$0.644501\pi$
$938$	35.0960	−	2.28770i	1.14592	−	0.0746960i
$939$	−51.5995	−	9.97485i	−1.68389	−	0.325517i
$940$	−7.81082	+	16.5476i	−0.254761	+	0.539724i
$941$	11.9775	−	1.72211i	0.390456	−	0.0561391i	0.0557086	−	0.998447i	$-0.482258\pi$
$941$	11.9775	−	1.72211i	0.390456	−	0.0561391i	0.334747	+	0.942308i	$0.391349\pi$
$942$	−2.68685	−	8.60852i	−0.0875422	−	0.280481i
$943$	6.38141	−	25.4285i	0.207807	−	0.828064i
$944$	40.8104	+	1.02992i	1.32827	+	0.0335209i
$945$	−11.1664	+	3.25846i	−0.363243	+	0.105998i
$946$	2.18328	+	5.96832i	0.0709847	+	0.194047i
$947$	8.67359	−	2.54680i	0.281854	−	0.0827597i	−0.137750	−	0.990467i	$-0.543987\pi$
$947$	8.67359	−	2.54680i	0.281854	−	0.0827597i	0.419604	+	0.907707i	$0.362169\pi$
$948$	14.3068	−	5.51005i	0.464664	−	0.178958i
$949$	−19.6043	−	5.75635i	−0.636383	−	0.186859i
$950$	−7.05601	+	31.4787i	−0.228927	+	1.02130i
$951$	3.70452	+	0.178539i	0.120127	+	0.00578953i
$952$	13.2703	+	1.20189i	0.430093	+	0.0389533i
$953$	−8.52263	+	13.2615i	−0.276075	+	0.429581i	−0.951409	−	0.307931i	$-0.900363\pi$
$953$	−8.52263	+	13.2615i	−0.276075	+	0.429581i	0.675333	+	0.737512i	$0.264000\pi$
$954$	5.72596	−	17.4643i	0.185385	−	0.565428i
$955$	14.1349	+	2.03229i	0.457395	+	0.0657635i
$956$	3.47118	−	5.25433i	0.112266	−	0.169937i
$957$	2.67773	−	0.648029i	0.0865588	−	0.0209478i
$958$	9.10803	−	23.9570i	0.294267	−	0.774015i
$959$	45.8428	−	29.4614i	1.48034	−	0.951357i
$960$	8.16430	+	8.40632i	0.263502	+	0.271313i
$961$	−4.43214	+	5.11496i	−0.142972	+	0.164999i
$962$	−39.1804	−	21.7160i	−1.26323	−	0.700153i
$963$	−5.27458	+	1.01049i	−0.169971	+	0.0325626i
$964$	−30.9580	+	4.05316i	−0.997090	+	0.130543i
$965$			14.5026i			0.466856i
$966$	27.0691	+	15.3032i	0.870935	+	0.492373i
$967$			18.2886i			0.588120i	0.955787	+	0.294060i	$0.0950066\pi$
$967$			18.2886i			0.588120i	−0.955787	+	0.294060i	$0.904993\pi$
$968$	−22.5604	−	17.5643i	−0.725119	−	0.564539i
$969$	12.9054	−	10.1373i	0.414583	−	0.325657i
$970$	−6.80613	+	12.2797i	−0.218532	+	0.394278i
$971$	28.5686	−	32.9699i	0.916808	−	1.05805i	−0.0813070	−	0.996689i	$-0.525909\pi$
$971$	28.5686	−	32.9699i	0.916808	−	1.05805i	0.998115	−	0.0613642i	$-0.0195451\pi$
$972$	−13.8575	−	27.9279i	−0.444481	−	0.895788i
$973$	4.53674	−	2.91559i	0.145441	−	0.0934694i
$974$	−14.8985	−	5.66416i	−0.477379	−	0.181491i
$975$	−5.93177	−	24.5107i	−0.189969	−	0.784972i
$976$	16.5953	+	11.2667i	0.531201	+	0.360637i
$977$	−34.9345	−	5.02283i	−1.11765	−	0.160694i	−0.441363	−	0.897329i	$-0.645505\pi$
$977$	−34.9345	−	5.02283i	−1.11765	−	0.160694i	−0.676292	+	0.736634i	$0.736414\pi$
$978$	−0.415369	−	2.57823i	−0.0132820	−	0.0824426i
$979$	4.93750	−	7.68290i	0.157803	−	0.245547i
$980$	−0.00732323	−	0.00867008i	−0.000233932	−	0.000276956i
$981$	25.9708	−	44.8672i	0.829185	−	1.43250i
$982$	−5.74441	−	1.28762i	−0.183311	−	0.0410896i
$983$	−55.7187	−	16.3605i	−1.77715	−	0.521819i	−0.782276	−	0.622932i	$-0.785941\pi$
$983$	−55.7187	−	16.3605i	−1.77715	−	0.521819i	−0.994875	+	0.101113i	$0.967760\pi$
$984$	−24.4085	−	11.0198i	−0.778115	−	0.351300i
$985$	−7.84935	+	2.30478i	−0.250101	+	0.0734363i
$986$	3.98233	−	1.45678i	0.126823	−	0.0463935i
$987$	46.8631	+	16.2487i	1.49167	+	0.517203i
$988$	36.1776	+	0.456427i	1.15096	+	0.0145209i
$989$	0.906487	+	22.8090i	0.0288246	+	0.725284i
$990$	−3.33634	−	0.586532i	−0.106036	−	0.0186412i
$991$	0.421248	−	0.0605663i	0.0133814	−	0.00192395i	−0.135621	−	0.990761i	$-0.543303\pi$
$991$	0.421248	−	0.0605663i	0.0133814	−	0.00192395i	0.149002	+	0.988837i	$0.452394\pi$
$992$	8.90374	+	26.3846i	0.282694	+	0.837711i
$993$	0.0820612	−	0.424500i	0.00260413	−	0.0134711i
$994$	1.41938	+	21.7749i	0.0450200	+	0.690658i
$995$	−13.6815	−	4.01725i	−0.433732	−	0.127355i
$996$	−1.60289	−	19.4973i	−0.0507895	−	0.617795i
$997$	9.11291	+	19.9545i	0.288609	+	0.631965i	0.997291	−	0.0735632i	$-0.0234371\pi$
$997$	9.11291	+	19.9545i	0.288609	+	0.631965i	−0.708682	+	0.705528i	$0.750710\pi$
$998$	−29.1587	−	2.27042i	−0.923002	−	0.0718690i
$999$	−20.1953	+	44.0264i	−0.638951	+	1.39293i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.95.32	yes	440
3.2	odd	2	inner	276.2.o.a.95.13	yes	440
4.3	odd	2	inner	276.2.o.a.95.36	yes	440
12.11	even	2	inner	276.2.o.a.95.9	✓	440
23.8	even	11	inner	276.2.o.a.215.9	yes	440
69.8	odd	22	inner	276.2.o.a.215.36	yes	440
92.31	odd	22	inner	276.2.o.a.215.13	yes	440
276.215	even	22	inner	276.2.o.a.215.32	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.95.9	✓	440	12.11	even	2	inner
276.2.o.a.95.13	yes	440	3.2	odd	2	inner
276.2.o.a.95.32	yes	440	1.1	even	1	trivial
276.2.o.a.95.36	yes	440	4.3	odd	2	inner
276.2.o.a.215.9	yes	440	23.8	even	11	inner
276.2.o.a.215.13	yes	440	92.31	odd	22	inner
276.2.o.a.215.32	yes	440	276.215	even	22	inner
276.2.o.a.215.36	yes	440	69.8	odd	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.854631 - 1.12677i) q^{2} +(-1.36208 + 1.06992i) q^{3} +(-0.539212 - 1.92594i) q^{4} +(-0.639142 - 0.553820i) q^{5} +(0.0414785 + 2.44914i) q^{6} +(-1.43109 - 2.22681i) q^{7} +(-2.63092 - 1.03840i) q^{8} +(0.710529 - 2.91464i) q^{9} +O(q^{10})\)	\(q+(0.854631 - 1.12677i) q^{2} +(-1.36208 + 1.06992i) q^{3} +(-0.539212 - 1.92594i) q^{4} +(-0.639142 - 0.553820i) q^{5} +(0.0414785 + 2.44914i) q^{6} +(-1.43109 - 2.22681i) q^{7} +(-2.63092 - 1.03840i) q^{8} +(0.710529 - 2.91464i) q^{9} +(-1.17026 + 0.246853i) q^{10} +(-0.134361 + 0.934503i) q^{11} +(2.79506 + 2.04637i) q^{12} +(-2.85860 - 1.83711i) q^{13} +(-3.73215 - 0.290602i) q^{14} +(1.46311 + 0.0705144i) q^{15} +(-3.41850 + 2.07698i) q^{16} +(0.501406 - 1.70763i) q^{17} +(-2.67689 - 3.29155i) q^{18} +(-1.49987 - 5.10810i) q^{19} +(-0.721991 + 1.52958i) q^{20} +(4.33178 + 1.50195i) q^{21} +(0.938139 + 0.950050i) q^{22} +(2.16393 + 4.27989i) q^{23} +(4.69453 - 1.40049i) q^{24} +(-0.609788 - 4.24117i) q^{25} +(-4.51305 + 1.65093i) q^{26} +(2.15065 + 4.73019i) q^{27} +(-3.51706 + 3.95691i) q^{28} +(-0.474656 + 1.61653i) q^{29} +(1.32987 - 1.58832i) q^{30} +(4.47775 - 2.04492i) q^{31} +(-0.581282 + 5.62691i) q^{32} +(-0.816836 - 1.41663i) q^{33} +(-1.49559 - 2.02436i) q^{34} +(-0.318586 + 2.21581i) q^{35} +(-5.99656 + 0.203173i) q^{36} +(6.10446 + 7.04492i) q^{37} +(-7.03748 - 2.67553i) q^{38} +(5.85921 - 0.556189i) q^{39} +(1.10644 + 2.12074i) q^{40} +(-4.13139 - 3.57987i) q^{41} +(5.39442 - 3.59729i) q^{42} +(4.32963 + 1.97727i) q^{43} +(1.87225 - 0.245123i) q^{44} +(-2.06832 + 1.46937i) q^{45} +(6.67180 + 1.21948i) q^{46} +10.8184 q^{47} +(2.43407 - 6.48655i) q^{48} +(-0.00278734 + 0.00610343i) q^{49} +(-5.29996 - 2.93754i) q^{50} +(1.14408 + 2.86240i) q^{51} +(-1.99678 + 6.49609i) q^{52} +(2.34204 + 3.64429i) q^{53} +(7.16784 + 1.61929i) q^{54} +(0.603422 - 0.522868i) q^{55} +(1.45274 + 7.34461i) q^{56} +(7.50823 + 5.35290i) q^{57} +(1.41580 + 1.91636i) q^{58} +(-8.58571 - 5.51770i) q^{59} +(-0.653118 - 2.85588i) q^{60} +(-2.08314 - 4.56144i) q^{61} +(1.52267 - 6.79304i) q^{62} +(-7.50720 + 2.58889i) q^{63} +(5.84344 + 5.46390i) q^{64} +(0.809623 + 2.75732i) q^{65} +(-2.29430 - 0.290308i) q^{66} +(-9.29956 + 1.33708i) q^{67} +(-3.55916 - 0.0449034i) q^{68} +(-7.52659 - 3.51432i) q^{69} +(2.22443 + 2.25268i) q^{70} +(-0.829574 - 5.76982i) q^{71} +(-4.89592 + 6.93037i) q^{72} +(5.76933 - 1.69403i) q^{73} +(13.1551 - 0.857501i) q^{74} +(5.36831 + 5.12439i) q^{75} +(-9.02916 + 5.64302i) q^{76} +(2.27325 - 1.03816i) q^{77} +(4.38077 - 7.07731i) q^{78} +(2.39274 - 3.72317i) q^{79} +(3.33518 + 0.565748i) q^{80} +(-7.99030 - 4.14188i) q^{81} +(-7.56450 + 1.59565i) q^{82} +(-3.69824 - 4.26800i) q^{83} +(0.556920 - 9.15261i) q^{84} +(-1.26619 + 0.813730i) q^{85} +(5.92816 - 3.18864i) q^{86} +(-1.08304 - 2.70969i) q^{87} +(1.32388 - 2.31908i) q^{88} +(-8.79914 - 4.01843i) q^{89} +(-0.112012 + 3.58628i) q^{90} +8.99463i q^{91} +(7.07599 - 6.47536i) q^{92} +(-3.91115 + 7.57619i) q^{93} +(9.24577 - 12.1899i) q^{94} +(-1.87033 + 4.09546i) q^{95} +(-5.22861 - 8.28623i) q^{96} +(7.68730 - 8.87162i) q^{97} +(0.00449500 + 0.00835687i) q^{98} +(2.62828 + 1.05561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more