LMFDB - Embedded newform 276.2.o.a.215.9

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			215.9
Character	$\chi$	$=$	276.215
Dual form			276.2.o.a.95.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.13746 + 0.840348i) q^{2} +(0.0833793 - 1.73004i) q^{3} +(0.587629 - 1.91172i) q^{4} +(0.639142 - 0.553820i) q^{5} +(1.35900 + 2.03792i) q^{6} +(1.43109 - 2.22681i) q^{7} +(0.938111 + 2.66832i) q^{8} +(-2.98610 - 0.288500i) q^{9} +O(q^{10})$	\(q+(-1.13746 + 0.840348i) q^{2} +(0.0833793 - 1.73004i) q^{3} +(0.587629 - 1.91172i) q^{4} +(0.639142 - 0.553820i) q^{5} +(1.35900 + 2.03792i) q^{6} +(1.43109 - 2.22681i) q^{7} +(0.938111 + 2.66832i) q^{8} +(-2.98610 - 0.288500i) q^{9} +(-0.261597 + 1.16705i) q^{10} +(-0.134361 - 0.934503i) q^{11} +(-3.25837 - 1.17602i) q^{12} +(-2.85860 + 1.83711i) q^{13} +(0.243497 + 3.73552i) q^{14} +(-0.904840 - 1.15192i) q^{15} +(-3.30938 - 2.24677i) q^{16} +(-0.501406 - 1.70763i) q^{17} +(3.63900 - 2.18120i) q^{18} +(1.49987 - 5.10810i) q^{19} +(-0.683173 - 1.54730i) q^{20} +(-3.73316 - 2.66151i) 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} +(1.70773 - 4.49186i) q^{26} +(-0.748095 + 5.14202i) q^{27} +(-3.41611 - 4.04438i) q^{28} +(0.474656 + 1.61653i) q^{29} +(1.99723 + 0.549881i) q^{30} +(-4.47775 - 2.04492i) q^{31} +(5.65236 - 0.225427i) q^{32} +(-1.62793 + 0.154533i) q^{33} +(2.00533 + 1.52101i) q^{34} +(-0.318586 - 2.21581i) q^{35} +(-2.30625 + 5.53906i) q^{36} +(6.10446 - 7.04492i) q^{37} +(2.58654 + 7.07068i) q^{38} +(2.93993 + 5.09868i) q^{39} +(2.07736 + 1.18589i) q^{40} +(4.13139 - 3.57987i) q^{41} +(6.48292 - 0.109794i) q^{42} +(-4.32963 + 1.97727i) q^{43} +(-1.86547 - 0.292279i) q^{44} +(-2.06832 + 1.46937i) q^{45} +(1.13522 + 6.68665i) q^{46} +10.8184 q^{47} +(-4.16294 + 5.53804i) q^{48} +(-0.00278734 - 0.00610343i) q^{49} +(-2.87045 - 5.33659i) q^{50} +(-2.99608 + 0.725072i) q^{51} +(1.83225 + 6.54440i) q^{52} +(-2.34204 + 3.64429i) q^{53} +(-3.47016 - 6.47750i) q^{54} +(-0.603422 - 0.522868i) q^{55} +(7.28438 + 1.72960i) q^{56} +(-8.71218 - 3.02076i) q^{57} +(-1.89835 - 1.43986i) q^{58} +(-8.58571 + 5.51770i) q^{59} +(-2.73386 + 1.05290i) q^{60} +(-2.08314 + 4.56144i) q^{61} +(6.81170 - 1.43686i) q^{62} +(-4.91580 + 6.23661i) q^{63} +(-6.23989 + 5.00637i) q^{64} +(-0.809623 + 2.75732i) q^{65} +(1.72185 - 1.54381i) q^{66} +(9.29956 + 1.33708i) q^{67} +(-3.55916 - 0.0449034i) q^{68} +(-7.22396 - 4.10054i) q^{69} +(2.22443 + 2.25268i) q^{70} +(-0.829574 + 5.76982i) q^{71} +(-2.03148 - 8.23851i) q^{72} +(5.76933 + 1.69403i) q^{73} +(-1.02339 + 13.1432i) q^{74} +(7.28656 + 1.40858i) q^{75} +(-8.88392 - 5.86902i) q^{76} +(-2.27325 - 1.03816i) q^{77} +(-7.62872 - 3.32897i) q^{78} +(-2.39274 - 3.72317i) q^{79} +(-3.35947 + 0.396798i) q^{80} +(8.83354 + 1.72297i) q^{81} +(-1.69095 + 7.54376i) q^{82} +(-3.69824 + 4.26800i) q^{83} +(-7.28179 + 5.57280i) q^{84} +(-1.26619 - 0.813730i) q^{85} +(3.26318 - 5.88747i) q^{86} +(2.83624 - 0.686390i) q^{87} +(2.36751 - 1.23519i) q^{88} +(8.79914 - 4.01843i) q^{89} +(1.11785 - 3.40945i) q^{90} +8.99463i q^{91} +(-6.91038 - 6.65182i) q^{92} +(-3.91115 + 7.57619i) q^{93} +(-12.3055 + 9.09126i) q^{94} +(-1.87033 - 4.09546i) q^{95} +(0.0812915 - 9.79762i) q^{96} +(7.68730 + 8.87162i) q^{97} +(0.00829950 + 0.00460007i) q^{98} +(0.131612 + 2.82928i) 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 $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$-1$	$-1$

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 $

$2$	−1.13746	+	0.840348i	−0.804305	+	0.594216i
$2$	−1.13746	+	0.840348i	−0.804305	+	0.594216i
$3$	0.0833793	−	1.73004i	0.0481391	−	0.998841i
$3$	0.0833793	−	1.73004i	0.0481391	−	0.998841i
$4$	0.587629	−	1.91172i	0.293814	−	0.955862i
$5$	0.639142	−	0.553820i	0.285833	−	0.247676i	−0.500128	−	0.865951i	$-0.666714\pi$
$5$	0.639142	−	0.553820i	0.285833	−	0.247676i	0.785961	+	0.618276i	$0.212168\pi$
$6$	1.35900	+	2.03792i	0.554809	+	0.831978i
$7$	1.43109	−	2.22681i	0.540900	−	0.841657i	−0.457981	−	0.888962i	$-0.651427\pi$
$7$	1.43109	−	2.22681i	0.540900	−	0.841657i	0.998880	+	0.0473056i	$0.0150635\pi$
$8$	0.938111	+	2.66832i	0.331672	+	0.943395i
$9$	−2.98610	−	0.288500i	−0.995365	−	0.0961665i
$10$	−0.261597	+	1.16705i	−0.0827241	+	0.369053i
$11$	−0.134361	−	0.934503i	−0.0405115	−	0.281763i	−1.00000		1.57325e-5i	$-0.999995\pi$
$11$	−0.134361	−	0.934503i	−0.0405115	−	0.281763i	0.959489	−	0.281748i	$-0.0909141\pi$
$12$	−3.25837	−	1.17602i	−0.940610	−	0.339488i
$13$	−2.85860	+	1.83711i	−0.792833	+	0.509523i	−0.873270	−	0.487237i	$-0.838005\pi$
$13$	−2.85860	+	1.83711i	−0.792833	+	0.509523i	0.0804369	+	0.996760i	$0.474368\pi$
$14$	0.243497	+	3.73552i	0.0650772	+	0.998360i
$15$	−0.904840	−	1.15192i	−0.233629	−	0.297424i
$16$	−3.30938	−	2.24677i	−0.827346	−	0.561692i
$17$	−0.501406	−	1.70763i	−0.121609	−	0.414161i	0.876076	−	0.482174i	$-0.160153\pi$
$17$	−0.501406	−	1.70763i	−0.121609	−	0.414161i	−0.997684	+	0.0680121i	$0.978334\pi$
$18$	3.63900	−	2.18120i	0.857721	−	0.514115i
$19$	1.49987	−	5.10810i	0.344095	−	1.17188i	−0.587756	−	0.809038i	$-0.699989\pi$
$19$	1.49987	−	5.10810i	0.344095	−	1.17188i	0.931851	−	0.362841i	$-0.118193\pi$
$20$	−0.683173	−	1.54730i	−0.152762	−	0.345988i
$21$	−3.73316	−	2.66151i	−0.814642	−	0.580789i
$22$	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
$26$	1.70773	−	4.49186i	0.334913	−	0.880926i
$27$	−0.748095	+	5.14202i	−0.143971	+	0.989582i
$28$	−3.41611	−	4.04438i	−0.645584	−	0.764317i
$29$	0.474656	+	1.61653i	0.0881413	+	0.300182i	0.991752	−	0.128173i	$-0.0409114\pi$
$29$	0.474656	+	1.61653i	0.0881413	+	0.300182i	−0.903610	+	0.428355i	$0.859093\pi$
$30$	1.99723	+	0.549881i	0.364643	+	0.100394i
$31$	−4.47775	−	2.04492i	−0.804228	−	0.367278i	−0.0294929	−	0.999565i	$-0.509389\pi$
$31$	−4.47775	−	2.04492i	−0.804228	−	0.367278i	−0.774735	+	0.632287i	$0.782117\pi$
$32$	5.65236	−	0.225427i	0.999206	−	0.0398503i
$33$	−1.62793	+	0.154533i	−0.283387	+	0.0269007i
$34$	2.00533	+	1.52101i	0.343912	+	0.260850i
$35$	−0.318586	−	2.21581i	−0.0538509	−	0.374541i
$36$	−2.30625	+	5.53906i	−0.384375	+	0.923177i
$37$	6.10446	−	7.04492i	1.00357	−	1.15818i	0.0161776	−	0.999869i	$-0.494850\pi$
$37$	6.10446	−	7.04492i	1.00357	−	1.15818i	0.987390	−	0.158309i	$-0.0506042\pi$
$38$	2.58654	+	7.07068i	0.419592	+	1.14702i
$39$	2.93993	+	5.09868i	0.470766	+	0.816442i
$40$	2.07736	+	1.18589i	0.328459	+	0.187506i
$41$	4.13139	−	3.57987i	0.645215	−	0.559082i	−0.269592	−	0.962975i	$-0.586889\pi$
$41$	4.13139	−	3.57987i	0.645215	−	0.559082i	0.914806	+	0.403893i	$0.132343\pi$
$42$	6.48292	−	0.109794i	1.00034	−	0.0169417i
$43$	−4.32963	+	1.97727i	−0.660262	+	0.301532i	−0.717222	−	0.696845i	$-0.754587\pi$
$43$	−4.32963	+	1.97727i	−0.660262	+	0.301532i	0.0569598	+	0.998376i	$0.481859\pi$
$44$	−1.86547	−	0.292279i	−0.281230	−	0.0440628i
$45$	−2.06832	+	1.46937i	−0.308326	+	0.219040i
$46$	1.13522	+	6.68665i	0.167379	+	0.985893i
$47$	10.8184			1.57803			0.789016	−	0.614373i	$-0.210591\pi$
$47$	10.8184			1.57803			0.789016	+	0.614373i	$0.210591\pi$
$48$	−4.16294	+	5.53804i	−0.600869	+	0.799348i
$49$	−0.00278734	−	0.00610343i	−0.000398192	−	0.000871919i
$50$	−2.87045	−	5.33659i	−0.405943	−	0.754708i
$51$	−2.99608	+	0.725072i	−0.419535	+	0.101530i
$52$	1.83225	+	6.54440i	0.254088	+	0.907544i
$53$	−2.34204	+	3.64429i	−0.321704	+	0.500582i	−0.964010	−	0.265867i	$-0.914342\pi$
$53$	−2.34204	+	3.64429i	−0.321704	+	0.500582i	0.642305	+	0.766449i	$0.277978\pi$
$54$	−3.47016	−	6.47750i	−0.472229	−	0.881476i
$55$	−0.603422	−	0.522868i	−0.0813654	−	0.0705036i
$56$	7.28438	+	1.72960i	0.973416	+	0.231128i
$57$	−8.71218	−	3.02076i	−1.15396	−	0.400109i
$58$	−1.89835	−	1.43986i	−0.249265	−	0.189063i
$59$	−8.58571	+	5.51770i	−1.11776	+	0.718344i	−0.962971	−	0.269603i	$-0.913107\pi$
$59$	−8.58571	+	5.51770i	−1.11776	+	0.718344i	−0.154793	+	0.987947i	$0.549471\pi$
$60$	−2.73386	+	1.05290i	−0.352940	+	0.135929i
$61$	−2.08314	+	4.56144i	−0.266719	+	0.584033i	−0.994845	−	0.101411i	$-0.967664\pi$
$61$	−2.08314	+	4.56144i	−0.266719	+	0.584033i	0.728126	+	0.685444i	$0.240392\pi$
$62$	6.81170	−	1.43686i	0.865087	−	0.182481i
$63$	−4.91580	+	6.23661i	−0.619332	+	0.785739i
$64$	−6.23989	+	5.00637i	−0.779987	+	0.625796i
$65$	−0.809623	+	2.75732i	−0.100421	+	0.342004i
$66$	1.72185	−	1.54381i	0.211945	−	0.190029i
$67$	9.29956	+	1.33708i	1.13612	+	0.163350i	0.684606	−	0.728913i	$-0.259974\pi$
$67$	9.29956	+	1.33708i	1.13612	+	0.163350i	0.451516	+	0.892263i	$0.350883\pi$
$68$	−3.55916	−	0.0449034i	−0.431612	−	0.00544534i
$69$	−7.22396	−	4.10054i	−0.869662	−	0.493647i
$70$	2.22443	+	2.25268i	0.265871	+	0.269246i
$71$	−0.829574	+	5.76982i	−0.0984524	+	0.684751i	0.879496	+	0.475906i	$0.157880\pi$
$71$	−0.829574	+	5.76982i	−0.0984524	+	0.684751i	−0.977949	+	0.208845i	$0.933029\pi$
$72$	−2.03148	−	8.23851i	−0.239412	−	0.970918i
$73$	5.76933	+	1.69403i	0.675249	+	0.198271i	0.601339	−	0.798994i	$-0.294634\pi$
$73$	5.76933	+	1.69403i	0.675249	+	0.198271i	0.0739100	+	0.997265i	$0.476452\pi$
$74$	−1.02339	+	13.1432i	−0.118966	+	1.52786i
$75$	7.28656	+	1.40858i	0.841379	+	0.162649i
$76$	−8.88392	−	5.86902i	−1.01906	−	0.673222i
$77$	−2.27325	−	1.03816i	−0.259061	−	0.118309i
$78$	−7.62872	−	3.32897i	−0.863782	−	0.376932i
$79$	−2.39274	−	3.72317i	−0.269204	−	0.418889i	0.680162	−	0.733062i	$-0.261909\pi$
$79$	−2.39274	−	3.72317i	−0.269204	−	0.418889i	−0.949366	+	0.314172i	$0.898273\pi$
$80$	−3.35947	+	0.396798i	−0.375600	+	0.0443633i
$81$	8.83354	+	1.72297i	0.981504	+	0.191442i
$82$	−1.69095	+	7.54376i	−0.186734	+	0.833069i
$83$	−3.69824	+	4.26800i	−0.405935	+	0.468474i	−0.921501	−	0.388376i	$-0.873036\pi$
$83$	−3.69824	+	4.26800i	−0.405935	+	0.468474i	0.515566	+	0.856850i	$0.327582\pi$
$84$	−7.28179	+	5.57280i	−0.794508	+	0.608042i
$85$	−1.26619	−	0.813730i	−0.137337	−	0.0882614i
$86$	3.26318	−	5.88747i	0.351877	−	0.634862i
$87$	2.83624	−	0.686390i	0.304077	−	0.0735887i
$88$	2.36751	−	1.23519i	0.252378	−	0.131671i
$89$	8.79914	−	4.01843i	0.932707	−	0.425953i	0.109687	−	0.993966i	$-0.465015\pi$
$89$	8.79914	−	4.01843i	0.932707	−	0.425953i	0.823019	+	0.568013i	$0.192288\pi$
$90$	1.11785	−	3.40945i	0.117831	−	0.359388i
$91$			8.99463i			0.942894i
$92$	−6.91038	−	6.65182i	−0.720457	−	0.693500i
$93$	−3.91115	+	7.57619i	−0.405567	+	0.785615i
$94$	−12.3055	+	9.09126i	−1.26922	+	0.937692i
$95$	−1.87033	−	4.09546i	−0.191892	−	0.420186i
$96$	0.0812915	−	9.79762i	0.00829677	−	0.999966i
$97$	7.68730	+	8.87162i	0.780527	+	0.900776i	0.997147	−	0.0754795i	$-0.0240487\pi$
$97$	7.68730	+	8.87162i	0.780527	+	0.900776i	−0.216620	+	0.976256i	$0.569503\pi$
$98$	0.00829950	+	0.00460007i	0.000838376	+	0.000464677i
$99$	0.131612	+	2.82928i	0.0132275	+	0.284353i
$100$	7.74962	+	3.65798i	0.774962	+	0.365798i
$101$	−6.22731	−	5.39600i	−0.619641	−	0.536922i	0.287483	−	0.957786i	$-0.407182\pi$
$101$	−6.22731	−	5.39600i	−0.619641	−	0.536922i	−0.907124	+	0.420864i	$0.861727\pi$
$102$	2.79861	−	3.34249i	0.277104	−	0.330956i
$103$	3.26178	−	0.468973i	0.321393	−	0.0462093i	0.0202695	−	0.999795i	$-0.493548\pi$
$103$	3.26178	−	0.468973i	0.321393	−	0.0462093i	0.301123	+	0.953585i	$0.402638\pi$
$104$	−7.58369	−	5.90425i	−0.743642	−	0.578960i
$105$	−3.86002	+	0.366414i	−0.376699	+	0.0357584i
$106$	−0.398494	−	6.11337i	−0.0387052	−	0.593783i
$107$	−0.743662	+	1.62839i	−0.0718925	+	0.157423i	−0.942166	−	0.335145i	$-0.891215\pi$
$107$	−0.743662	+	1.62839i	−0.0718925	+	0.157423i	0.870274	+	0.492568i	$0.163942\pi$
$108$	9.39052	+	4.45175i	0.903603	+	0.428370i
$109$	16.5805	−	4.86848i	1.58813	−	0.466316i	0.635917	−	0.771758i	$-0.280622\pi$
$109$	16.5805	−	4.86848i	1.58813	−	0.466316i	0.952211	+	0.305442i	$0.0988041\pi$
$110$	1.12576	+	0.0876567i	0.107337	+	0.00835774i
$111$	−11.6790	−	11.1484i	−1.10852	−	1.05816i
$112$	−9.73915	+	4.15406i	−0.920264	+	0.392522i
$113$	18.4025	+	2.64588i	1.73116	+	0.248904i	0.934613	−	0.355667i	$-0.115746\pi$
$113$	18.4025	+	2.64588i	1.73116	+	0.248904i	0.796551	+	0.604571i	$0.206655\pi$
$114$	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
$117$	9.06606	−	4.66108i	0.838157	−	0.430917i
$118$	5.12911	−	13.4912i	0.472173	−	1.24196i
$119$	−4.52013	−	1.32723i	−0.414360	−	0.121667i
$120$	2.22485	−	3.49504i	0.203100	−	0.319052i
$121$	9.69918	−	2.84794i	0.881744	−	0.258903i
$122$	−1.46371	−	6.93902i	−0.132518	−	0.628230i
$123$	−5.84885	−	7.44597i	−0.527373	−	0.671380i
$124$	−6.54058	+	7.35857i	−0.587361	+	0.660819i
$125$	4.24522	+	6.60569i	0.379704	+	0.590831i
$126$	0.350592	−	11.2249i	0.0312332	−	0.999992i
$127$	19.4396	−	2.79500i	1.72499	−	0.248016i	0.792670	−	0.609651i	$-0.208691\pi$
$127$	19.4396	−	2.79500i	1.72499	−	0.248016i	0.932320	+	0.361635i	$0.117781\pi$
$128$	2.89054	−	10.9382i	0.255490	−	0.966812i
$129$	3.05977	+	7.65530i	0.269398	+	0.674012i
$130$	−1.39620	−	3.81671i	−0.122455	−	0.334748i
$131$	−5.30305	−	3.40807i	−0.463330	−	0.297764i	0.288072	−	0.957609i	$-0.406986\pi$
$131$	−5.30305	−	3.40807i	−0.463330	−	0.297764i	−0.751402	+	0.659845i	$0.770622\pi$
$132$	−0.661197	+	3.20297i	−0.0575498	+	0.278783i
$133$	−9.22835	−	10.6501i	−0.800199	−	0.923479i
$134$	−11.7015	+	6.29401i	−1.01085	+	0.543719i
$135$	2.36961	+	3.70079i	0.203944	+	0.318513i
$136$	4.08614	−	2.93986i	0.350383	−	0.252091i
$137$			20.5867i			1.75884i	0.476046	+	0.879421i	$0.342070\pi$
$137$			20.5867i			1.75884i	−0.476046	+	0.879421i	$0.657930\pi$
$138$	11.6628	−	1.40644i	0.992807	−	0.119725i
$139$			2.03732i			0.172804i	0.996260	+	0.0864018i	$0.0275369\pi$
$139$			2.03732i			0.172804i	−0.996260	+	0.0864018i	$0.972463\pi$
$140$	−4.42324	−	0.693027i	−0.373832	−	0.0585715i
$141$	0.902034	−	18.7164i	0.0759650	−	1.57620i
$142$	−3.90505	−	7.26006i	−0.327704	−	0.609251i
$143$	2.10087	+	2.42453i	0.175684	+	0.202750i
$144$	9.23395	+	7.66382i	0.769496	+	0.638652i
$145$	1.19864	+	0.770318i	0.0995414	+	0.0639714i
$146$	−7.98596	+	2.92136i	−0.660922	+	0.241773i
$147$	−0.0107916	+	0.00431333i	−0.000890077	+	0.000355757i
$148$	−9.88080	−	15.8098i	−0.812197	−	1.29956i
$149$	−17.4172	+	2.50422i	−1.42687	+	0.205154i	−0.812086	−	0.583538i	$-0.801668\pi$
$149$	−17.4172	+	2.50422i	−1.42687	+	0.205154i	−0.614789	+	0.788692i	$0.710759\pi$
$150$	−9.47187	+	4.52104i	−0.773375	+	0.369141i
$151$	−11.2333	−	17.4794i	−0.914154	−	1.42245i	−0.906372	−	0.422481i	$-0.861159\pi$
$151$	−11.2333	−	17.4794i	−0.914154	−	1.42245i	−0.00778231	−	0.999970i	$-0.502477\pi$
$152$	15.0371	−	0.789819i	1.21967	−	0.0640628i
$153$	1.00459	+	5.24381i	0.0812167	+	0.423937i
$154$	3.45814	−	0.729458i	0.278665	−	0.0587814i
$155$	−3.99443	+	1.17287i	−0.320841	+	0.0942073i
$156$	11.4749	−	2.62421i	0.918724	−	0.210105i
$157$	−3.53249	−	1.03723i	−0.281923	−	0.0827801i	0.137714	−	0.990472i	$-0.456024\pi$
$157$	−3.53249	−	1.03723i	−0.281923	−	0.0827801i	−0.419637	+	0.907692i	$0.637843\pi$
$158$	5.85040	+	2.22422i	0.465433	+	0.176950i
$159$	6.10950	+	4.35569i	0.484515	+	0.345429i
$160$	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	$-0.441251\pi$
$163$	1.05528	+	0.151726i	0.0826557	+	0.0118841i	−0.100863	+	0.994900i	$0.532160\pi$
$164$	−4.41600	−	10.0017i	−0.344832	−	0.781003i
$165$	−0.954898	+	1.00035i	−0.0743387	+	0.0778771i
$166$	0.619995	−	7.96249i	0.0481209	−	0.618009i
$167$	4.22571	−	1.24078i	0.326995	−	0.0960145i	−0.114115	−	0.993468i	$-0.536403\pi$
$167$	4.22571	−	1.24078i	0.326995	−	0.0960145i	0.441110	+	0.897453i	$0.354585\pi$
$168$	3.59965	−	12.4581i	0.277719	−	0.961161i
$169$	−0.603777	+	1.32209i	−0.0464444	+	0.101699i
$170$	2.12406	−	0.138455i	0.162908	−	0.0106190i
$171$	−5.95245	+	14.8206i	−0.455195	+	1.13336i
$172$	1.23579	+	9.43896i	0.0942282	+	0.719714i
$173$	−11.7982	+	1.69633i	−0.897004	+	0.128970i	−0.575369	−	0.817894i	$-0.695142\pi$
$173$	−11.7982	+	1.69633i	−0.897004	+	0.128970i	−0.321635	+	0.946864i	$0.604232\pi$
$174$	−2.64930	+	3.16417i	−0.200843	+	0.239875i
$175$	8.57163	+	7.42736i	0.647955	+	0.561456i
$176$	−1.65496	+	3.39451i	−0.124747	+	0.255871i
$177$	8.82999	+	15.3137i	0.663703	+	1.15105i
$178$	−6.63178	+	11.9651i	−0.497073	+	0.896826i
$179$	13.5567	+	15.6453i	1.01328	+	1.16938i	0.985484	+	0.169768i	$0.0543019\pi$
$179$	13.5567	+	15.6453i	1.01328	+	1.16938i	0.0277912	+	0.999614i	$0.491153\pi$
$180$	1.59362	+	4.81749i	0.118782	+	0.359075i
$181$	−5.79101	−	12.6805i	−0.430442	−	0.942537i	−0.993255	−	0.115953i	$-0.963008\pi$
$181$	−5.79101	−	12.6805i	−0.430442	−	0.942537i	0.562812	−	0.826585i	$-0.309719\pi$
$182$	−7.55863	−	10.2310i	−0.560283	−	0.758375i
$183$	7.71780	+	3.98425i	0.570516	+	0.294525i
$184$	13.4501	+	1.75905i	0.991556	+	0.129679i
$185$		−	7.88348i		−	0.579605i
$186$	−1.91787	−	11.9043i	−0.140625	−	0.872869i
$187$	−1.52842	+	0.698005i	−0.111769	+	0.0510432i
$188$	6.35723	−	20.6819i	0.463648	−	1.50838i
$189$	10.3797	+	9.02454i	0.755014	+	0.656439i
$190$	5.56905	+	3.08669i	0.404021	+	0.223932i
$191$	−14.2051	−	9.12906i	−1.02784	−	0.660555i	−0.0858927	−	0.996304i	$-0.527374\pi$
$191$	−14.2051	−	9.12906i	−1.02784	−	0.660555i	−0.941951	+	0.335749i	$0.891011\pi$
$192$	8.14095	+	11.2127i	0.587523	+	0.809208i
$193$	−11.2299	+	12.9600i	−0.808347	+	0.932882i	−0.998808	−	0.0488130i	$-0.984456\pi$
$193$	−11.2299	+	12.9600i	−0.808347	+	0.932882i	0.190461	+	0.981695i	$0.439002\pi$
$194$	−16.1992	−	3.63110i	−1.16304	−	0.260698i
$195$	4.70278	+	1.63059i	0.336773	+	0.116769i
$196$	−0.0133060	+	0.00174208i	−0.000950429	+	0.000124434i
$197$	−5.22976	−	8.13766i	−0.372605	−	0.579784i	0.603425	−	0.797419i	$-0.293802\pi$
$197$	−5.22976	−	8.13766i	−0.372605	−	0.579784i	−0.976030	+	0.217635i	$0.930166\pi$
$198$	−2.52728	−	3.10759i	−0.179606	−	0.220847i
$199$	−15.3369	−	7.00413i	−1.08720	−	0.496510i	−0.210527	−	0.977588i	$-0.567518\pi$
$199$	−15.3369	−	7.00413i	−1.08720	−	0.496510i	−0.876678	+	0.481078i	$0.840245\pi$
$200$	−11.8889	+	2.35158i	−0.840669	+	0.166282i
$201$	3.08859	−	15.9772i	0.217852	−	1.12694i
$202$	11.6178	+	0.904616i	0.817428	+	0.0636486i
$203$	4.27898	+	1.25642i	0.300326	+	0.0881836i
$204$	−0.374445	+	6.15376i	−0.0262164	+	0.430849i
$205$	0.657942	−	4.57609i	0.0459527	−	0.319608i
$206$	−3.31604	+	3.27447i	−0.231040	+	0.228143i
$207$	−7.69644	+	12.1559i	−0.534939	+	0.844890i
$208$	13.5878	+	0.342909i	0.942142	+	0.0237765i
$209$	−4.97506	−	0.715306i	−0.344132	−	0.0494788i
$210$	4.08270	−	3.66054i	0.281733	−	0.252601i
$211$	−0.599965	+	2.04329i	−0.0413033	+	0.140666i	−0.977563	−	0.210642i	$-0.932445\pi$
$211$	−0.599965	+	2.04329i	−0.0413033	+	0.140666i	0.936260	+	0.351308i	$0.114263\pi$
$212$	5.59063	+	6.61883i	0.383966	+	0.454583i
$213$	9.91286	+	1.91628i	0.679218	+	0.131301i
$214$	−0.522532	−	2.47717i	−0.0357196	−	0.169336i
$215$	−1.67219	+	3.66159i	−0.114043	+	0.249718i
$216$	−14.4224	+	2.82763i	−0.981317	+	0.192396i
$217$	−10.9617	+	7.04466i	−0.744129	+	0.478223i
$218$	−14.7685	+	19.4711i	−1.00025	+	1.31875i
$219$	3.41178	−	9.83994i	0.230547	−	0.664922i
$220$	−1.35417	+	0.846325i	−0.0912980	+	0.0570592i
$221$	4.57043	+	3.96030i	0.307440	+	0.266398i
$222$	22.6530	+	2.86637i	1.52037	+	0.192378i
$223$	−6.76613	+	10.5283i	−0.453094	+	0.705028i	−0.990380	−	0.138372i	$-0.955813\pi$
$223$	−6.76613	+	10.5283i	−0.453094	+	0.705028i	0.537286	+	0.843400i	$0.319449\pi$
$224$	7.58703	−	12.9094i	0.506930	−	0.862543i
$225$	3.04446	−	12.4886i	0.202964	−	0.832574i
$226$	−23.1556	+	12.4549i	−1.54029	+	0.828491i
$227$	−0.384109	−	0.841081i	−0.0254942	−	0.0558245i	0.896457	−	0.443132i	$-0.146133\pi$
$227$	−0.384109	−	0.841081i	−0.0254942	−	0.0558245i	−0.921951	+	0.387307i	$0.873405\pi$
$228$	−10.8944	+	14.8802i	−0.721498	+	0.985466i
$229$	−19.0704			−1.26021			−0.630105	−	0.776510i	$-0.716988\pi$
$229$	−19.0704			−1.26021			−0.630105	+	0.776510i	$0.716988\pi$
$230$	4.42876	+	3.64501i	0.292024	+	0.240345i
$231$	−1.98560	+	3.84626i	−0.130643	+	0.253065i
$232$	−3.86814	+	2.78302i	−0.253956	+	0.182714i
$233$	−9.50216	+	4.33949i	−0.622507	+	0.284290i	−0.701593	−	0.712578i	$-0.747527\pi$
$233$	−9.50216	+	4.33949i	−0.622507	+	0.284290i	0.0790853	+	0.996868i	$0.474800\pi$
$234$	−6.39534	+	12.9204i	−0.418077	+	0.844636i
$235$	6.91452	−	5.99146i	0.451053	−	0.390840i
$236$	5.50312	+	19.6559i	0.358222	+	1.27949i
$237$	−6.64075	+	3.82910i	−0.431363	+	0.248727i
$238$	6.25680	−	2.28882i	0.405568	−	0.148362i
$239$	2.06195	−	2.37962i	0.133377	−	0.153925i	−0.685132	−	0.728419i	$-0.740256\pi$
$239$	2.06195	−	2.37962i	0.133377	−	0.153925i	0.818509	+	0.574494i	$0.194801\pi$
$240$	0.406367	+	5.84511i	0.0262309	+	0.377300i
$241$	2.22169	+	15.4522i	0.143112	+	0.995363i	0.927161	+	0.374664i	$0.122242\pi$
$241$	2.22169	+	15.4522i	0.143112	+	0.995363i	−0.784049	+	0.620699i	$0.786849\pi$
$242$	−8.63917	+	11.3901i	−0.555347	+	0.732184i
$243$	3.71735	−	15.1387i	0.238468	−	0.971150i
$244$	7.49611	+	6.66283i	0.479889	+	0.426544i
$245$	−0.00516171	−	0.00235727i	−0.000329770	−	0.000150601i
$246$	12.9100	+	3.55441i	0.823114	+	0.226621i
$247$	5.09661	+	17.3575i	0.324289	+	1.10443i
$248$	1.25588	−	13.8664i	0.0797484	−	0.880520i
$249$	7.07546	+	6.75398i	0.448389	+	0.428016i
$250$	−10.3798	−	3.94624i	−0.656479	−	0.249582i
$251$	2.79237	−	19.4214i	0.176253	−	1.22586i	−0.689087	−	0.724679i	$-0.741988\pi$
$251$	2.79237	−	19.4214i	0.176253	−	1.22586i	0.865340	−	0.501186i	$-0.167103\pi$
$252$	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
$255$	−1.51336	+	2.12271i	−0.0947704	+	0.132929i
$256$	5.90405	+	14.8708i	0.369003	+	0.929428i
$257$	5.76012	−	19.6172i	0.359306	−	1.22369i	−0.559451	−	0.828863i	$-0.688988\pi$
$257$	5.76012	−	19.6172i	0.359306	−	1.22369i	0.918758	−	0.394822i	$-0.129194\pi$
$258$	−9.91349	−	6.13633i	−0.617187	−	0.382031i
$259$	−6.95172	−	23.6754i	−0.431959	−	1.47112i
$260$	4.79549	+	3.16806i	0.297403	+	0.196475i
$261$	−0.951000	−	4.96405i	−0.0588654	−	0.307267i
$262$	8.89597	−	0.579876i	0.549595	−	0.0358249i
$263$	20.5212	−	13.1882i	1.26539	−	0.813218i	0.276379	−	0.961049i	$-0.410866\pi$
$263$	20.5212	−	13.1882i	1.26539	−	0.813218i	0.989013	+	0.147831i	$0.0472292\pi$
$264$	−1.93953	−	4.19888i	−0.119370	−	0.258423i
$265$	0.521382	+	3.62629i	0.0320282	+	0.222761i
$266$	19.4466	+	4.35901i	1.19235	+	0.267268i
$267$	−6.21839	−	15.5579i	−0.380559	−	0.952130i
$268$	8.02081	−	16.9925i	0.489949	−	1.03798i
$269$	10.9961	−	17.1102i	0.670442	−	1.04323i	−0.324799	−	0.945783i	$-0.605297\pi$
$269$	10.9961	−	17.1102i	0.670442	−	1.04323i	0.995241	−	0.0974453i	$-0.0310671\pi$
$270$	−5.80529	−	2.21820i	−0.353299	−	0.134995i
$271$	−17.8428	+	15.4608i	−1.08387	+	0.939179i	−0.998365	−	0.0571588i	$-0.981796\pi$
$271$	−17.8428	+	15.4608i	−1.08387	+	0.939179i	−0.0855051	+	0.996338i	$0.527250\pi$
$272$	−2.17731	+	6.77775i	−0.132019	+	0.410962i
$273$	15.5611	+	0.749966i	0.941801	+	0.0453900i
$274$	−17.3000	−	23.4165i	−1.04513	−	1.41465i
$275$	4.04532			0.243942
$276$	−12.0841	+	11.4006i	−0.727378	+	0.686237i
$277$	−0.377780			−0.0226986			−0.0113493	−	0.999936i	$-0.503613\pi$
$277$	−0.377780			−0.0226986			−0.0113493	+	0.999936i	$0.503613\pi$
$278$	−1.71206	−	2.31737i	−0.102683	−	0.138987i
$279$	12.7810	+	7.39815i	0.765180	+	0.442916i
$280$	5.61364	−	2.92877i	0.335479	−	0.175027i
$281$	−19.1141	+	16.5625i	−1.14025	+	0.988034i	−0.999998	−	0.00208152i	$-0.999337\pi$
$281$	−19.1141	+	16.5625i	−1.14025	+	0.988034i	−0.140254	+	0.990116i	$0.544792\pi$
$282$	14.7022	+	22.0471i	0.875506	+	1.31289i
$283$	−3.63401	+	5.65464i	−0.216020	+	0.336133i	−0.932304	−	0.361675i	$-0.882205\pi$
$283$	−3.63401	+	5.65464i	−0.216020	+	0.336133i	0.716284	+	0.697808i	$0.245841\pi$
$284$	10.5428	+	4.97643i	0.625601	+	0.295297i
$285$	−7.24127	+	2.89428i	−0.428936	+	0.171443i
$286$	−4.42711	−	0.992346i	−0.261781	−	0.0586787i
$287$	−2.05933	−	14.3229i	−0.121558	−	0.845456i
$288$	−16.9435	−	0.957557i	−0.998407	−	0.0564246i
$289$	11.6367	−	7.47846i	0.684513	−	0.439909i
$290$	−2.01074	+	0.131068i	−0.118075	+	0.00769659i
$291$	15.9892	−	12.5597i	0.937306	−	0.736260i
$292$	6.62874	−	10.0339i	0.387918	−	0.587190i
$293$	3.06886	+	10.4516i	0.179285	+	0.610587i	0.999270	+	0.0382027i	$0.0121633\pi$
$293$	3.06886	+	10.4516i	0.179285	+	0.610587i	−0.819985	+	0.572384i	$0.806019\pi$
$294$	0.00865032	−	0.0139749i	0.000504497	−	0.000815035i
$295$	−2.43168	+	8.28153i	−0.141578	+	0.482169i
$296$	24.5248	+	9.67975i	1.42547	+	0.562624i
$297$	4.90575	+	0.00820908i	0.284660	+	0.000476339i
$298$	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
$302$	27.4662	+	10.4422i	1.58050	+	0.600880i
$303$	−9.85454	+	10.3236i	−0.566128	+	0.593076i
$304$	−16.4404	+	13.5348i	−0.942921	+	0.776274i
$305$	1.19479	+	4.06909i	0.0684137	+	0.232996i
$306$	−5.54931	−	5.12041i	−0.317233	−	0.292714i
$307$	0.164871	+	0.0752942i	0.00940970	+	0.00429727i	0.420114	−	0.907471i	$-0.361990\pi$
$307$	0.164871	+	0.0752942i	0.00940970	+	0.00429727i	−0.410705	+	0.911768i	$0.634717\pi$
$308$	−3.32050	+	3.73577i	−0.189203	+	0.212865i
$309$	−0.539379	−	5.68212i	−0.0306842	−	0.323245i
$310$	3.55789	−	4.69081i	0.202074	−	0.266420i
$311$	1.50127	+	10.4416i	0.0851294	+	0.592088i	0.987078	+	0.160244i	$0.0512280\pi$
$311$	1.50127	+	10.4416i	0.0851294	+	0.592088i	−0.901948	+	0.431844i	$0.857863\pi$
$312$	−10.8469	+	12.6278i	−0.614087	+	0.714909i
$313$	19.8701	−	22.9314i	1.12313	−	1.29616i	0.172781	−	0.984960i	$-0.444725\pi$
$313$	19.8701	−	22.9314i	1.12313	−	1.29616i	0.950345	−	0.311197i	$-0.100730\pi$
$314$	4.88970	−	1.78871i	0.275941	−	0.100943i
$315$	0.312067	+	6.70854i	0.0175830	+	0.377984i
$316$	−8.52372	+	2.38641i	−0.479497	+	0.134246i
$317$	1.61828	−	1.40225i	0.0908915	−	0.0787580i	−0.608230	−	0.793761i	$-0.708120\pi$
$317$	1.61828	−	1.40225i	0.0908915	−	0.0787580i	0.699121	+	0.715003i	$0.253575\pi$
$318$	−10.6096	+	0.179684i	−0.594958	+	0.0100762i
$319$	1.44688	−	0.660766i	0.0810095	−	0.0369958i
$320$	−1.21555	+	6.65556i	−0.0679515	+	0.372057i
$321$	2.75518	+	1.42234i	0.153779	+	0.0793874i
$322$	16.5145	+	7.04126i	0.920318	+	0.392394i
$323$	−9.47480			−0.527192
$324$	8.48469	−	15.8748i	0.471372	−	0.881935i
$325$	−6.04836	−	13.2441i	−0.335502	−	0.734648i
$326$	−1.32784	+	0.714218i	−0.0735421	+	0.0395569i
$327$	−7.04021	−	29.0910i	−0.389325	−	1.60873i
$328$	13.4280	+	7.66557i	0.741435	+	0.423260i
$329$	15.4821	−	24.0907i	0.853557	−	1.32816i
$330$	0.245515	−	1.94030i	0.0135151	−	0.106810i
$331$	0.188652	+	0.163468i	0.0103693	+	0.00898501i	0.660030	−	0.751239i	$-0.270544\pi$
$331$	0.188652	+	0.163468i	0.0103693	+	0.00898501i	−0.649661	+	0.760224i	$0.725089\pi$
$332$	5.98605	+	9.57802i	0.328527	+	0.525662i
$333$	−20.2610	+	19.2757i	−1.11029	+	1.05630i
$334$	−3.76389	+	4.96241i	−0.205951	+	0.271531i
$335$	6.68424	−	4.29570i	0.365199	−	0.234699i
$336$	6.37466	+	17.1955i	0.347766	+	0.938092i
$337$	−12.4687	+	27.3027i	−0.679214	+	1.48727i	0.184260	+	0.982877i	$0.441011\pi$
$337$	−12.4687	+	27.3027i	−0.679214	+	1.48727i	−0.863474	+	0.504393i	$0.831716\pi$
$338$	−0.424242	−	2.01120i	−0.0230757	−	0.109395i
$339$	6.11188	−	31.6165i	0.331952	−	1.71717i
$340$	−2.29968	+	1.94243i	−0.124718	+	0.105343i
$341$	−1.30935	+	4.45923i	−0.0709052	+	0.241481i
$342$	−5.68377	−	21.8599i	−0.307343	−	1.18205i
$343$	18.3230	+	2.63444i	0.989346	+	0.142247i
$344$	−9.33768	−	9.69794i	−0.503454	−	0.522878i
$345$	−6.88809	+	1.37994i	−0.370842	+	0.0742937i
$346$	11.9945	−	11.8441i	0.644829	−	0.636745i
$347$	−0.192628	+	1.33976i	−0.0103408	+	0.0719219i	−0.994338	−	0.106260i	$-0.966112\pi$
$347$	−0.192628	+	1.33976i	−0.0103408	+	0.0719219i	0.983998	+	0.178182i	$0.0570215\pi$
$348$	0.354468	−	5.82545i	0.0190015	−	0.312277i
$349$	−18.4632	−	5.42128i	−0.988312	−	0.290195i	−0.252661	−	0.967555i	$-0.581306\pi$
$349$	−18.4632	−	5.42128i	−0.988312	−	0.290195i	−0.735651	+	0.677360i	$0.763124\pi$
$350$	−15.9915	−	1.24517i	−0.854780	−	0.0665569i
$351$	−7.30795	−	16.0733i	−0.390070	−	0.857930i
$352$	−0.970121	−	5.25186i	−0.0517076	−	0.279925i
$353$	−28.3503	−	12.9471i	−1.50893	−	0.689107i	−0.522405	−	0.852697i	$-0.674965\pi$
$353$	−28.3503	−	12.9471i	−1.50893	−	0.689107i	−0.986528	+	0.163591i	$0.947692\pi$
$354$	−22.9126	−	9.99846i	−1.21779	−	0.531412i
$355$	2.66522	+	4.14717i	0.141455	+	0.220109i
$356$	−2.51151	−	19.1829i	−0.133110	−	1.01669i
$357$	−2.67305	+	7.70936i	−0.141473	+	0.408023i
$358$	−28.5677	−	6.40350i	−1.50985	−	0.338436i
$359$	−5.09525	+	5.88023i	−0.268917	+	0.310347i	−0.874106	−	0.485735i	$-0.838552\pi$
$359$	−5.09525	+	5.88023i	−0.268917	+	0.310347i	0.605189	+	0.796082i	$0.293097\pi$
$360$	−5.86105	−	4.14051i	−0.308905	−	0.218224i
$361$	−7.85927	−	5.05085i	−0.413646	−	0.265834i
$362$	17.2431	+	9.55714i	0.906278	+	0.502312i
$363$	−4.11834	−	17.0175i	−0.216157	−	0.893185i
$364$	17.1953	+	5.28551i	0.901277	+	0.277036i
$365$	4.62561	−	2.11244i	0.242115	−	0.110570i
$366$	−12.1268	+	1.95372i	−0.633881	+	0.102122i
$367$			18.1187i			0.945791i	0.881119	+	0.472895i	$0.156791\pi$
$367$			18.1187i			0.945791i	−0.881119	+	0.472895i	$0.843209\pi$
$368$	−16.7772	+	9.30194i	−0.874571	+	0.484897i
$369$	−13.3695	+	9.49793i	−0.695989	+	0.494442i
$370$	6.62487	+	8.96714i	0.344410	+	0.466179i
$371$	4.76349	+	10.4306i	0.247308	+	0.541529i
$372$	12.1853	+	11.9290i	0.631778	+	0.618492i
$373$	−2.92827	−	3.37940i	−0.151620	−	0.174979i	0.674858	−	0.737947i	$-0.264205\pi$
$373$	−2.92827	−	3.37940i	−0.151620	−	0.174979i	−0.826478	+	0.562968i	$0.809659\pi$
$374$	1.15195	−	2.07836i	0.0595657	−	0.107469i
$375$	11.7821	−	6.79363i	0.608424	−	0.350822i
$376$	10.1489	+	28.8671i	0.523390	+	1.48871i
$377$	−4.32659	−	3.74901i	−0.222831	−	0.193084i
$378$	−19.3903	−	1.54246i	−0.997329	−	0.0793357i
$379$	−30.4353	+	4.37593i	−1.56336	+	0.224777i	−0.868984	−	0.494840i	$-0.835226\pi$
$379$	−30.4353	+	4.37593i	−1.56336	+	0.224777i	−0.694371	+	0.719617i	$0.744317\pi$
$380$	−8.92846	+	1.16895i	−0.458020	+	0.0599661i
$381$	−3.21460	−	33.8645i	−0.164689	−	1.73493i
$382$	23.8293	−	1.55329i	1.21921	−	0.0794733i
$383$	5.87491	−	12.8643i	0.300194	−	0.657333i	−0.698082	−	0.716017i	$-0.745963\pi$
$383$	5.87491	−	12.8643i	0.300194	−	0.657333i	0.998277	+	0.0586839i	$0.0186904\pi$
$384$	−18.6826	−	5.91277i	−0.953392	−	0.301735i
$385$	−2.02788	+	0.595439i	−0.103350	+	0.0303464i
$386$	1.88265	−	24.1785i	0.0958242	−	1.23065i
$387$	13.4991	−	4.65524i	0.686199	−	0.236639i
$388$	21.4774	−	9.48279i	1.09035	−	0.481416i
$389$	23.6117	+	3.39484i	1.19716	+	0.172125i	0.711923	−	0.702258i	$-0.247825\pi$
$389$	23.6117	+	3.39484i	1.19716	+	0.172125i	0.485236	+	0.874383i	$0.338734\pi$
$390$	−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
$393$	−6.33827	+	8.89035i	−0.319723	+	0.448459i
$394$	12.7871	+	4.86144i	0.644205	+	0.244916i
$395$	−3.59126	−	1.05449i	−0.180696	−	0.0530572i
$396$	5.48614	+	1.41096i	0.275689	+	0.0709034i
$397$	−0.884980	+	0.259853i	−0.0444159	+	0.0130417i	−0.303865	−	0.952715i	$-0.598277\pi$
$397$	−0.884980	+	0.259853i	−0.0444159	+	0.0130417i	0.259449	+	0.965757i	$0.416459\pi$
$398$	23.3310	−	4.92143i	1.16948	−	0.246689i
$399$	−19.1945	+	15.0774i	−0.960929	+	0.754816i
$400$	11.5470	−	12.6656i	0.577348	−	0.633280i
$401$	13.2394	+	20.6009i	0.661144	+	1.02876i	0.996245	+	0.0865785i	$0.0275933\pi$
$401$	13.2394	+	20.6009i	0.661144	+	1.02876i	−0.335101	+	0.942182i	$0.608770\pi$
$402$	9.91324	+	20.7689i	0.494427	+	1.03586i
$403$	16.5568	−	2.38051i	0.824755	−	0.118582i
$404$	−13.9750	+	8.73407i	−0.695283	+	0.434536i
$405$	6.60010	−	3.79096i	0.327962	−	0.188374i
$406$	−5.92300	+	2.16671i	−0.293954	+	0.107532i
$407$	−7.40371	−	4.75807i	−0.366988	−	0.235849i
$408$	−4.74539	−	7.31432i	−0.234932	−	0.362113i
$409$	−18.2730	−	21.0881i	−0.903540	−	1.04274i	−0.998881	−	0.0472961i	$-0.984940\pi$
$409$	−18.2730	−	21.0881i	−0.903540	−	1.04274i	0.0953409	−	0.995445i	$-0.469606\pi$
$410$	3.09713	+	5.75802i	0.152956	+	0.284368i
$411$	35.6159	+	1.71651i	1.75680	+	0.0846690i
$412$	1.02017	−	6.51121i	0.0502601	−	0.320784i
$413$			27.0151i			1.32933i
$414$	−1.46077	−	20.2945i	−0.0717929	−	0.997420i
$415$			4.77602i			0.234445i
$416$	−15.7437	+	11.0284i	−0.771899	+	0.540713i
$417$	3.52466	+	0.169871i	0.172603	+	0.00831860i
$418$	6.26004	−	3.36716i	0.306189	−	0.164693i
$419$	3.29741	+	3.80542i	0.161089	+	0.185907i	0.830556	−	0.556935i	$-0.188023\pi$
$419$	3.29741	+	3.80542i	0.161089	+	0.185907i	−0.669467	+	0.742842i	$0.733477\pi$
$420$	−1.56777	+	7.59461i	−0.0764995	+	0.370579i
$421$	12.7210	+	8.17528i	0.619983	+	0.398439i	0.812589	−	0.582838i	$-0.198058\pi$
$421$	12.7210	+	8.17528i	0.619983	+	0.398439i	−0.192606	+	0.981276i	$0.561694\pi$
$422$	−1.03464	−	2.82834i	−0.0503656	−	0.137682i
$423$	−32.3049	−	3.12111i	−1.57072	−	0.151754i
$424$	−11.9212	−	2.83058i	−0.578947	−	0.137465i
$425$	7.54810	−	1.08525i	0.366137	−	0.0526425i
$426$	−12.8858	+	6.15056i	−0.624320	+	0.297996i
$427$	7.17633	+	11.1666i	0.347287	+	0.540389i
$428$	2.67604	+	2.37857i	0.129351	+	0.114972i
$429$	4.36972	−	3.43244i	0.210972	−	0.165720i
$430$	−1.17496	−	5.57014i	−0.0566617	−	0.268616i
$431$	−2.90012	+	0.851552i	−0.139694	+	0.0410178i	−0.350832	−	0.936438i	$-0.614101\pi$
$431$	−2.90012	+	0.851552i	−0.139694	+	0.0410178i	0.211138	+	0.977456i	$0.432283\pi$
$432$	14.0287	−	15.3361i	0.674954	−	0.737859i
$433$	23.1370	+	6.79364i	1.11189	+	0.326482i	0.785568	−	0.618775i	$-0.212371\pi$
$433$	23.1370	+	6.79364i	1.11189	+	0.326482i	0.326327	+	0.945257i	$0.394189\pi$
$434$	6.54853	−	17.2247i	0.314339	−	0.826810i
$435$	1.43262	−	2.00947i	0.0686891	−	0.0963465i
$436$	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	$-0.283218\pi$
$439$	21.2628	+	3.05712i	1.01482	+	0.145909i	0.385215	+	0.922827i	$0.374127\pi$
$440$	0.829105	−	2.10063i	0.0395260	−	0.100144i
$441$	0.00656244	+	0.0190296i	0.000312497	+	0.000906171i
$442$	−8.52670	−	0.663927i	−0.405574	−	0.0315798i
$443$	−39.0265	+	11.4592i	−1.85420	+	0.544443i	−0.854517	+	0.519424i	$0.826147\pi$
$443$	−39.0265	+	11.4592i	−1.85420	+	0.544443i	−0.999687	+	0.0250195i	$0.992035\pi$
$444$	−28.1756	+	15.7760i	−1.33715	+	0.748695i
$445$	3.39841	−	7.44148i	0.161100	−	0.352760i
$446$	−1.15125	−	17.6614i	−0.0545130	−	0.836293i
$447$	2.88017	+	30.3413i	0.136227	+	1.43510i
$448$	2.21842	+	21.0596i	0.104810	+	0.994974i
$449$	19.3271	−	2.77882i	0.912103	−	0.131141i	0.329742	−	0.944071i	$-0.393038\pi$
$449$	19.3271	−	2.77882i	0.912103	−	0.131141i	0.582361	+	0.812931i	$0.302129\pi$
$450$	7.03184	+	16.7637i	0.331484	+	0.790248i
$451$	−3.90050	−	3.37980i	−0.183667	−	0.159149i
$452$	15.8721	−	33.6258i	0.746559	−	1.58162i
$453$	−31.1767	+	17.9767i	−1.46481	+	0.844619i
$454$	1.14371	+	0.633911i	0.0536770	+	0.0297509i
$455$	4.98141	+	5.74885i	0.233532	+	0.269510i
$456$	−0.112637	−	26.0807i	−0.00527469	−	1.22134i
$457$	−2.95823	−	6.47762i	−0.138380	−	0.303010i	0.827736	−	0.561118i	$-0.189628\pi$
$457$	−2.95823	−	6.47762i	−0.138380	−	0.303010i	−0.966116	+	0.258107i	$0.916901\pi$
$458$	21.6919	−	16.0258i	1.01359	−	0.748837i
$459$	9.15577	−	1.30077i	0.427355	−	0.0607146i
$460$	−8.10062	−	0.424352i	−0.377693	−	0.0197855i
$461$			20.4705i			0.953407i	0.879064	+	0.476703i	$0.158168\pi$
$461$			20.4705i			0.953407i	−0.879064	+	0.476703i	$0.841832\pi$
$462$	−0.973656	−	6.04356i	−0.0452986	−	0.281172i
$463$	−23.4379	+	10.7037i	−1.08925	+	0.497445i	−0.877353	−	0.479846i	$-0.840693\pi$
$463$	−23.4379	+	10.7037i	−1.08925	+	0.497445i	−0.211901	+	0.977291i	$0.567965\pi$
$464$	2.06115	−	6.41616i	0.0956864	−	0.297863i
$465$	1.69606	+	7.00833i	0.0786531	+	0.325004i
$466$	7.16164	−	12.9211i	0.331757	−	0.598560i
$467$	−7.61673	−	4.89498i	−0.352460	−	0.226512i	0.352415	−	0.935844i	$-0.385361\pi$
$467$	−7.61673	−	4.89498i	−0.352460	−	0.226512i	−0.704875	+	0.709331i	$0.748997\pi$
$468$	−3.58323	−	20.0708i	−0.165635	−	0.927773i
$469$	16.2859	−	18.7949i	0.752013	−	0.867869i
$470$	−2.83007	+	12.6257i	−0.130541	+	0.582378i
$471$	−2.08899	+	6.02487i	−0.0962556	+	0.277611i
$472$	−22.7774	−	17.7332i	−1.04841	−	0.816238i
$473$	2.42950	+	3.78038i	0.111709	+	0.173822i
$474$	4.33581	−	9.93599i	0.199150	−	0.456375i
$475$	20.7497	+	9.47608i	0.952062	+	0.434792i
$476$	−5.19346	+	7.86133i	−0.238042	+	0.360324i
$477$	8.04494	−	10.2065i	0.368353	−	0.467325i
$478$	−0.345678	+	4.43949i	−0.0158109	+	0.203057i
$479$	17.3890	+	5.10586i	0.794523	+	0.233293i	0.653712	−	0.756744i	$-0.273211\pi$
$479$	17.3890	+	5.10586i	0.794523	+	0.233293i	0.140811	+	0.990037i	$0.455029\pi$
$480$	−5.37416	−	6.30709i	−0.245296	−	0.287878i
$481$	−4.50791	+	31.3532i	−0.205543	+	1.42958i
$482$	−15.5123	−	15.7093i	−0.706566	−	0.715537i
$483$	−19.4692	+	10.2182i	−0.885881	+	0.464944i
$484$	0.255047	−	20.2157i	0.0115930	−	0.918895i
$485$	9.82655	+	1.41285i	0.446201	+	0.0641540i
$486$	8.49347	+	20.3436i	0.385272	+	0.922803i
$487$	3.17527	−	10.8140i	0.143885	−	0.490028i	−0.855740	−	0.517406i	$-0.826898\pi$
$487$	3.17527	−	10.8140i	0.143885	−	0.490028i	0.999625	+	0.0273783i	$0.00871588\pi$
$488$	−14.1256	−	1.27935i	−0.639437	−	0.0579136i
$489$	0.350481	−	1.81302i	0.0158493	−	0.0819878i
$490$	0.00785217	−	0.00165633i	0.000354725	−	7.48254e-5i
$491$	−1.72925	+	3.78653i	−0.0780399	+	0.170884i	−0.944630	−	0.328137i	$-0.893579\pi$
$491$	−1.72925	+	3.78653i	−0.0780399	+	0.170884i	0.866590	+	0.499020i	$0.166307\pi$
$492$	−17.6716	+	6.80594i	−0.796697	+	0.306835i
$493$	2.52244	−	1.62107i	0.113605	−	0.0730095i
$494$	−20.3835	−	15.4605i	−0.917097	−	0.695600i
$495$	1.65103	+	1.73542i	0.0742083	+	0.0780014i
$496$	10.2241	+	16.8279i	0.459077	+	0.755595i
$497$	11.6611	+	10.1044i	0.523073	+	0.453245i
$498$	−13.7238	−	1.73652i	−0.614976	−	0.0778155i
$499$	11.1808	−	17.3977i	0.500523	−	0.778829i	−0.495436	−	0.868645i	$-0.664992\pi$
$499$	11.1808	−	17.3977i	0.500523	−	0.778829i	0.995958	+	0.0898161i	$0.0286279\pi$
$500$	15.1229	−	4.23400i	0.676315	−	0.189350i
$501$	−1.79427	−	7.41411i	−0.0801619	−	0.331238i
$502$	13.1445	+	24.4376i	0.586668	+	1.09070i
$503$	−14.4896	−	31.7279i	−0.646062	−	1.41468i	−0.894959	−	0.446148i	$-0.852796\pi$
$503$	−14.4896	−	31.7279i	−0.646062	−	1.41468i	0.248898	−	0.968530i	$-0.419932\pi$
$504$	−21.2529	−	7.26630i	−0.946678	−	0.323667i
$505$	−6.96855			−0.310096
$506$	6.09617	−	1.95929i	0.271008	−	0.0871011i
$507$	2.23692	+	1.15479i	0.0993453	+	0.0512862i
$508$	6.08002	−	38.8057i	0.269757	−	1.72172i
$509$	13.1509	−	6.00579i	0.582901	−	0.266202i	−0.102064	−	0.994778i	$-0.532545\pi$
$509$	13.1509	−	6.00579i	0.582901	−	0.266202i	0.684965	+	0.728576i	$0.259817\pi$
$510$	−0.0624303	−	3.68625i	−0.00276446	−	0.163230i
$511$	12.0287	−	10.4229i	0.532118	−	0.461083i
$512$	−19.2123	−	11.9535i	−0.849073	−	0.528276i
$513$	25.1439	+	11.5337i	1.11013	+	0.509227i
$514$	9.93335	+	27.1542i	0.438141	+	1.19772i
$515$	1.82501	−	2.10618i	0.0804197	−	0.0928093i
$516$	16.4328	−	1.35096i	0.723416	−	0.0594726i
$517$	−1.45358	−	10.1099i	−0.0639284	−	0.444632i
$518$	27.8029	+	21.0879i	1.22159	+	0.926551i
$519$	1.95100	+	20.5529i	0.0856393	+	0.902173i
$520$	−8.11694	+	0.426340i	−0.355952	+	0.0186962i
$521$	19.4837	+	8.89790i	0.853595	+	0.389824i	0.793648	−	0.608378i	$-0.208179\pi$
$521$	19.4837	+	8.89790i	0.853595	+	0.389824i	0.0599476	+	0.998202i	$0.480907\pi$
$522$	5.25325	+	4.84723i	0.229929	+	0.212158i
$523$	−8.87401	−	30.2221i	−0.388033	−	1.32152i	−0.889734	−	0.456479i	$-0.849110\pi$
$523$	−8.87401	−	30.2221i	−0.388033	−	1.32152i	0.501701	−	0.865041i	$-0.332708\pi$
$524$	−9.63151	+	8.13530i	−0.420755	+	0.355392i
$525$	13.5644	−	14.2100i	0.591997	−	0.620176i
$526$	−12.2594	+	32.2460i	−0.534534	+	1.40599i
$527$	−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
$531$	27.2296	−	13.9994i	1.18166	−	0.607523i
$532$	−25.7829	+	11.3838i	−1.11783	+	0.493549i
$533$	−5.23337	+	17.8232i	−0.226683	+	0.772010i
$534$	20.1473	+	12.4709i	0.871857	+	0.539669i
$535$	0.426530	+	1.45263i	0.0184405	+	0.0628026i
$536$	5.15628	+	26.0686i	0.222717	+	1.12599i
$537$	28.1973	−	22.1492i	1.21680	−	0.955807i
$538$	1.87096	+	28.7027i	0.0806629	+	1.23746i
$539$	−0.00532917	+	0.00342485i	−0.000229544	+	0.000147519i
$540$	8.46734	−	2.35536i	0.364376	−	0.101358i
$541$	6.24616	+	43.4430i	0.268543	+	1.86776i	0.462319	+	0.886714i	$0.347018\pi$
$541$	6.24616	+	43.4430i	0.268543	+	1.86776i	−0.193776	+	0.981046i	$0.562073\pi$
$542$	7.30292	−	32.5802i	0.313687	−	1.39944i
$543$	−22.4207	+	8.96140i	−0.962166	+	0.384571i
$544$	−3.21907	−	9.53912i	−0.138017	−	0.408986i
$545$	7.90105	−	12.2943i	0.338444	−	0.526629i
$546$	−18.3304	+	12.2237i	−0.784467	+	0.523126i
$547$	−29.1989	+	25.3010i	−1.24845	+	1.08179i	−0.255074	+	0.966921i	$0.582100\pi$
$547$	−29.1989	+	25.3010i	−1.24845	+	1.08179i	−0.993380	+	0.114871i	$0.963355\pi$
$548$	39.3561	+	12.0973i	1.68121	+	0.516773i
$549$	7.53643	−	13.0199i	0.321647	−	0.555677i
$550$	−4.60139	+	3.39948i	−0.196204	+	0.144954i
$551$	8.96932			0.382106
$552$	4.16469	−	23.1226i	0.177261	−	0.984164i
$553$	−11.7150			−0.498173
$554$	0.429709	−	0.317467i	0.0182566	−	0.0134879i
$555$	−13.6387	−	0.657319i	−0.578933	−	0.0279016i
$556$	3.89480	+	1.19719i	0.165176	+	0.0507722i
$557$	28.8275	−	24.9792i	1.22146	−	1.05840i	0.224998	−	0.974359i	$-0.427763\pi$
$557$	28.8275	−	24.9792i	1.22146	−	1.05840i	0.996462	−	0.0840417i	$-0.0267829\pi$
$558$	−20.7549	+	2.32542i	−0.878626	+	0.0984428i
$559$	8.74420	−	13.6062i	0.369840	−	0.575483i
$560$	−3.92410	+	8.04877i	−0.165823	+	0.340123i
$561$	1.08014	+	2.70243i	0.0456035	+	0.114097i
$562$	7.82328	−	34.9016i	0.330005	−	1.47224i
$563$	4.12961	+	28.7221i	0.174042	+	1.21049i	0.870235	+	0.492636i	$0.163967\pi$
$563$	4.12961	+	28.7221i	0.174042	+	1.21049i	−0.696193	+	0.717855i	$0.745124\pi$
$564$	−35.2505	−	12.7227i	−1.48431	−	0.535723i
$565$	13.2272	−	8.50058i	0.556471	−	0.357622i
$566$	−0.618321	−	9.48576i	−0.0259900	−	0.398716i
$567$	16.4783	−	17.2049i	0.692023	−	0.722539i
$568$	−16.1740	+	3.19916i	−0.678645	+	0.134234i
$569$	−0.405597	−	1.38134i	−0.0170035	−	0.0579086i	0.950554	−	0.310559i	$-0.100516\pi$
$569$	−0.405597	−	1.38134i	−0.0170035	−	0.0579086i	−0.967558	+	0.252650i	$0.918698\pi$
$570$	5.80445	−	9.37732i	0.243122	−	0.392773i
$571$	−7.00602	+	23.8603i	−0.293193	+	0.998523i	0.672772	+	0.739850i	$0.265104\pi$
$571$	−7.00602	+	23.8603i	−0.293193	+	0.998523i	−0.965965	+	0.258673i	$0.916715\pi$
$572$	5.86958	−	2.59156i	0.245419	−	0.108359i
$573$	−16.9781	+	23.8142i	−0.709269	+	0.994854i
$574$	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	−0.877497	−	0.479583i	$-0.840788\pi$
$577$	2.39174	−	16.6349i	0.0995693	−	0.692520i	0.977066	−	0.212937i	$-0.0683029\pi$
$578$	−6.95178	+	18.2853i	−0.289156	+	0.760570i
$579$	21.4850	+	20.5088i	0.892887	+	0.852317i
$580$	2.17699	−	1.83880i	0.0903946	−	0.0763522i
$581$	4.21154	+	14.3432i	0.174724	+	0.595055i
$582$	−7.63263	+	27.7226i	−0.316383	+	1.14914i
$583$	3.72028	+	1.69900i	0.154078	+	0.0703652i
$584$	0.892059	+	16.9836i	0.0369137	+	0.702787i
$585$	3.21310	−	8.00005i	0.132845	−	0.330762i
$586$	−12.2737	−	9.30933i	−0.507020	−	0.384565i
$587$	−1.76746	−	12.2929i	−0.0729508	−	0.507384i	−0.993234	−	0.116131i	$-0.962951\pi$
$587$	−1.76746	−	12.2929i	−0.0729508	−	0.507384i	0.920283	−	0.391253i	$-0.127958\pi$
$588$	0.00190443	+	0.0231652i	7.85375e−5	+	0.000955318i
$589$	−17.1617	+	19.8057i	−0.707136	+	0.816079i
$590$	−4.19344	−	11.4634i	−0.172641	−	0.471939i
$591$	−14.5146	+	8.36919i	−0.597049	+	0.344263i
$592$	−36.0303	+	9.59905i	−1.48084	+	0.394518i
$593$	−1.39579	+	1.20946i	−0.0573184	+	0.0496667i	−0.683049	−	0.730373i	$-0.739346\pi$
$593$	−1.39579	+	1.20946i	−0.0573184	+	0.0496667i	0.625731	+	0.780039i	$0.284801\pi$
$594$	−5.58699	+	4.11320i	−0.229237	+	0.168767i
$595$	−3.62405	+	1.65505i	−0.148572	+	0.0678504i
$596$	−5.44748	+	34.7685i	−0.223138	+	1.42417i
$597$	−13.3962	+	25.9495i	−0.548271	+	1.06204i
$598$	−15.5292	−	17.0289i	−0.635038	−	0.696365i
$599$	5.26349			0.215060			0.107530	−	0.994202i	$-0.465706\pi$
$599$	5.26349			0.215060			0.107530	+	0.994202i	$0.465706\pi$
$600$	3.07704	+	20.7643i	0.125620	+	0.847699i
$601$	−8.87395	−	19.4312i	−0.361976	−	0.792617i	−0.999749	−	0.0223929i	$-0.992872\pi$
$601$	−8.87395	−	19.4312i	−0.361976	−	0.792617i	0.637773	−	0.770224i	$-0.279856\pi$
$602$	−8.44040	−	15.6920i	−0.344005	−	0.639557i
$603$	−27.3836	−	6.67556i	−1.11515	−	0.271850i
$604$	−40.0168	+	11.2036i	−1.62826	+	0.455869i
$605$	4.62191	−	7.19183i	0.187907	−	0.292389i
$606$	2.53371	−	20.0239i	0.102925	−	0.813416i
$607$	15.2048	+	13.1750i	0.617143	+	0.534758i	0.906360	−	0.422506i	$-0.138849\pi$
$607$	15.2048	+	13.1750i	0.617143	+	0.534758i	−0.289217	+	0.957264i	$0.593395\pi$
$608$	7.32633	−	29.2110i	0.297122	−	1.18466i
$609$	2.53044	−	7.29806i	0.102539	−	0.295732i
$610$	−4.77849	−	3.62439i	−0.193475	−	0.146747i
$611$	−30.9256	+	19.8747i	−1.25112	+	0.804043i
$612$	10.6150	+	1.16090i	0.429088	+	0.0469267i
$613$	3.13093	−	6.85578i	0.126457	−	0.276902i	−0.835805	−	0.549026i	$-0.814999\pi$
$613$	3.13093	−	6.85578i	0.126457	−	0.276902i	0.962262	+	0.272124i	$0.0877260\pi$
$614$	−0.250808	+	0.0529052i	−0.0101218	+	0.00213508i
$615$	−7.86197	−	1.51982i	−0.317025	−	0.0612850i
$616$	0.637580	−	7.03967i	0.0256888	−	0.283636i
$617$	−5.35216	+	18.2278i	−0.215470	+	0.733823i	0.778833	+	0.627231i	$0.215812\pi$
$617$	−5.35216	+	18.2278i	−0.215470	+	0.733823i	−0.994303	+	0.106592i	$0.966006\pi$
$618$	5.38848	+	6.00992i	0.216757	+	0.241754i
$619$	−1.69912	−	0.244297i	−0.0682934	−	0.00981911i	0.108083	−	0.994142i	$-0.465529\pi$
$619$	−1.69912	−	0.244297i	−0.0682934	−	0.00981911i	−0.176377	+	0.984323i	$0.556438\pi$
$620$	−0.105036	+	8.32547i	−0.00421837	+	0.334359i
$621$	20.3884	+	14.3287i	0.818159	+	0.574991i
$622$	−10.4822	−	10.6153i	−0.420298	−	0.425634i
$623$	3.64403	−	25.3448i	0.145995	−	1.01542i
$624$	1.72619	−	23.4788i	0.0691027	−	0.939906i
$625$	−14.1844	−	4.16493i	−0.567377	−	0.166597i
$626$	−3.33115	+	42.7813i	−0.133139	+	1.70989i
$627$	−1.65233	+	8.54743i	−0.0659876	+	0.341352i
$628$	−4.05869	+	6.14363i	−0.161959	+	0.245158i
$629$	−15.0909	−	6.89180i	−0.601715	−	0.274794i
$630$	−5.99248	−	7.36845i	−0.238746	−	0.293566i
$631$	−19.9461	−	31.0367i	−0.794040	−	1.23555i	−0.968038	−	0.250805i	$-0.919305\pi$
$631$	−19.9461	−	31.0367i	−0.794040	−	1.23555i	0.173997	−	0.984746i	$-0.444332\pi$
$632$	7.68997	−	9.87734i	0.305891	−	0.392900i
$633$	3.48496	+	1.20833i	0.138515	+	0.0480269i
$634$	−0.662351	+	2.95491i	−0.0263053	+	0.117355i
$635$	10.8768	−	12.5525i	0.431631	−	0.498129i
$636$	11.9170	−	9.12016i	0.472540	−	0.361638i
$637$	0.0191806	+	0.0123266i	0.000759962	+	0.000488398i
$638$	−1.09049	+	1.96748i	−0.0431729	+	0.0778931i
$639$	4.14178	−	16.9899i	0.163846	−	0.672110i
$640$	−4.21034	−	8.59191i	−0.166428	−	0.339625i
$641$	−39.5617	+	18.0672i	−1.56259	+	0.713613i	−0.994038	−	0.109032i	$-0.965225\pi$
$641$	−39.5617	+	18.0672i	−1.56259	+	0.713613i	−0.568556	+	0.822645i	$0.692498\pi$
$642$	−4.32917	+	0.697458i	−0.170859	+	0.0275265i
$643$			46.8659i			1.84821i	0.382140	+	0.924104i	$0.375187\pi$
$643$			46.8659i			1.84821i	−0.382140	+	0.924104i	$0.624813\pi$
$644$	−24.7017	+	5.86880i	−0.973384	+	0.231263i
$645$	6.19528	+	3.19827i	0.243939	+	0.125932i
$646$	10.7772	−	7.96214i	0.424023	−	0.313266i
$647$	6.02883	+	13.2013i	0.237018	+	0.518997i	0.990341	−	0.138654i	$-0.0442775\pi$
$647$	6.02883	+	13.2013i	0.237018	+	0.518997i	−0.753323	+	0.657651i	$0.771550\pi$
$648$	3.68939	+	25.1871i	0.144933	+	0.989442i
$649$	6.30990	+	7.28201i	0.247685	+	0.285844i
$650$	18.0094	+	9.98185i	0.706386	+	0.391520i
$651$	11.2736	+	19.5516i	0.441846	+	0.766287i
$652$	0.910170	−	1.92824i	0.0356450	−	0.0755158i
$653$	−6.00373	−	5.20226i	−0.234944	−	0.203580i	0.529429	−	0.848354i	$-0.322406\pi$
$653$	−6.00373	−	5.20226i	−0.234944	−	0.203580i	−0.764373	+	0.644774i	$0.776952\pi$
$654$	32.4545	+	27.1736i	1.26907	+	1.06257i
$655$	−5.27686	+	0.758698i	−0.206184	+	0.0296448i
$656$	−21.7155	+	2.56489i	−0.847848	+	0.100142i
$657$	−16.7390	−	6.72298i	−0.653052	−	0.262288i
$658$	2.63425	+	40.4125i	0.102694	+	1.57544i
$659$	−16.8520	+	36.9008i	−0.656461	+	1.43745i	0.229322	+	0.973351i	$0.426349\pi$
$659$	−16.8520	+	36.9008i	−0.656461	+	1.43745i	−0.885783	+	0.464099i	$0.846378\pi$
$660$	1.35127	+	2.41334i	0.0525981	+	0.0939390i
$661$	−4.44158	+	1.30417i	−0.172757	+	0.0507262i	−0.366967	−	0.930234i	$-0.619604\pi$
$661$	−4.44158	+	1.30417i	−0.172757	+	0.0507262i	0.194210	+	0.980960i	$0.437786\pi$
$662$	−0.351954	−	0.0274047i	−0.0136791	−	0.00106511i
$663$	7.23256	−	7.57683i	0.280889	−	0.294260i
$664$	−14.8578	−	5.86425i	−0.576593	−	0.227577i
$665$	−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
$669$	17.6503	+	12.5835i	0.682399	+	0.486508i
$670$	−3.99317	+	10.5033i	−0.154270	+	0.405777i
$671$	4.54258	+	1.33382i	0.175364	+	0.0514916i
$672$	−21.7011	−	14.2023i	−0.837140	−	0.547864i
$673$	37.7614	−	11.0878i	1.45560	−	0.427402i	0.544208	−	0.838950i	$-0.316830\pi$
$673$	37.7614	−	11.0878i	1.45560	−	0.427402i	0.911388	+	0.411549i	$0.135012\pi$
$674$	−8.76110	−	41.5337i	−0.337465	−	1.59982i
$675$	−21.3520	−	6.30834i	−0.821838	−	0.242808i
$676$	2.17267	+	1.93115i	0.0835642	+	0.0742751i
$677$	−18.5326	−	28.8373i	−0.712266	−	1.10831i	−0.989079	−	0.147384i	$-0.952915\pi$
$677$	−18.5326	−	28.8373i	−0.712266	−	1.10831i	0.276813	−	0.960924i	$-0.410722\pi$
$678$	19.6169	+	41.0987i	0.753382	+	1.57838i
$679$	30.7566	−	4.42214i	1.18033	−	0.169706i
$680$	0.983469	−	4.14197i	0.0377143	−	0.158837i
$681$	−1.48713	+	0.594396i	−0.0569871	+	0.0227773i
$682$	−2.25798	−	6.17250i	−0.0864624	−	0.236357i
$683$	24.0879	+	15.4804i	0.921699	+	0.592340i	0.913150	−	0.407624i	$-0.133643\pi$
$683$	24.0879	+	15.4804i	0.921699	+	0.592340i	0.00854858	+	0.999963i	$0.497279\pi$
$684$	24.8350	+	20.0884i	0.949591	+	0.768101i
$685$	11.4013	+	13.1578i	0.435622	+	0.502735i
$686$	−23.0555	+	12.4011i	−0.880262	+	0.473476i
$687$	−1.59008	+	32.9927i	−0.0606653	+	1.25875i
$688$	18.7709	+	3.18411i	0.715633	+	0.121393i
$689$		−	14.7202i		−	0.560794i
$690$	6.67530	−	7.35803i	0.254124	−	0.280115i
$691$			3.84217i			0.146163i	0.997326	+	0.0730815i	$0.0232833\pi$
$691$			3.84217i			0.146163i	−0.997326	+	0.0730815i	$0.976717\pi$
$692$	−3.69007	+	23.5518i	−0.140275	+	0.895306i
$693$	6.48863	+	3.75587i	0.246483	+	0.142674i
$694$	−0.906756	−	1.68579i	−0.0344200	−	0.0639918i
$695$	1.12831	+	1.30214i	0.0427992	+	0.0493930i
$696$	4.49222	+	6.92410i	0.170277	+	0.262457i
$697$	−8.18460	−	5.25992i	−0.310014	−	0.199234i
$698$	25.5569	−	9.34903i	0.967343	−	0.353866i
$699$	6.71522	+	16.8010i	0.253993	+	0.635471i
$700$	19.2360	−	12.0221i	0.727053	−	0.454392i
$701$	−2.18584	+	0.314276i	−0.0825580	+	0.0118701i	−0.183470	−	0.983025i	$-0.558733\pi$
$701$	−2.18584	+	0.314276i	−0.0825580	+	0.0118701i	0.100912	+	0.994895i	$0.467824\pi$
$702$	21.8197	+	12.1415i	0.823531	+	0.458252i
$703$	−26.8303	−	41.7487i	−1.01192	−	1.57458i
$704$	5.51687	+	5.15854i	0.207925	+	0.194420i
$705$	−9.78896	−	12.4620i	−0.368674	−	0.469345i
$706$	43.1274	−	9.09727i	1.62312	−	0.342380i
$707$	−20.9277	+	6.14493i	−0.787067	+	0.231104i
$708$	34.4644	−	7.88173i	1.29525	−	0.296214i
$709$	18.1997	+	5.34391i	0.683504	+	0.200695i	0.605008	−	0.796220i	$-0.293170\pi$
$709$	18.1997	+	5.34391i	0.683504	+	0.200695i	0.0784960	+	0.996914i	$0.474988\pi$
$710$	−6.51665	−	2.47752i	−0.244565	−	0.0929796i
$711$	6.07081	+	11.8080i	0.227673	+	0.442836i
$712$	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
$716$	37.8757	−	16.7231i	1.41548	−	0.624970i
$717$	−3.94492	−	3.76568i	−0.147326	−	0.140632i
$718$	0.854197	−	10.9703i	0.0318783	−	0.409408i
$719$	6.14401	−	1.80405i	0.229133	−	0.0672795i	−0.165150	−	0.986268i	$-0.552811\pi$
$719$	6.14401	−	1.80405i	0.229133	−	0.0672795i	0.394284	+	0.918989i	$0.370993\pi$
$720$	10.1462	−	0.215670i	0.378126	−	0.00803755i
$721$	3.62357	−	7.93452i	0.134949	−	0.295497i
$722$	13.1841	−	0.859392i	0.490661	−	0.0319833i
$723$	26.9182	−	2.55523i	1.00110	−	0.0950299i
$724$	−27.6447	+	3.61937i	−1.02741	+	0.134513i
$725$	−7.14541	+	1.02735i	−0.265374	+	0.0381550i
$726$	18.9850	+	15.8958i	0.704601	+	0.589949i
$727$	−7.55910	−	6.54999i	−0.280351	−	0.242926i	0.503322	−	0.864099i	$-0.332111\pi$
$727$	−7.55910	−	6.54999i	−0.280351	−	0.242926i	−0.783673	+	0.621173i	$0.786656\pi$
$728$	−24.0006	+	8.43797i	−0.889521	+	0.312732i
$729$	−25.8807	−	7.69344i	−0.958545	−	0.284942i
$730$	−3.48625	+	6.28994i	−0.129032	+	0.232801i
$731$	5.54736	+	6.40199i	0.205176	+	0.236786i
$732$	12.1520	−	12.4131i	0.449151	−	0.458800i
$733$	7.57521	+	16.5874i	0.279797	+	0.612670i	0.996397	−	0.0848148i	$-0.0270299\pi$
$733$	7.57521	+	16.5874i	0.279797	+	0.612670i	−0.716600	+	0.697485i	$0.754303\pi$
$734$	−15.2261	−	20.6093i	−0.562004	−	0.760704i
$735$	−0.00450856	+	0.00873343i	−0.000166301	+	0.000322137i
$736$	11.2665	−	24.6793i	0.415288	−	0.909690i
$737$		−	8.87013i		−	0.326735i
$738$	7.22571	−	22.0386i	0.265982	−	0.811251i
$739$	−38.8144	+	17.7259i	−1.42781	+	0.652060i	−0.971343	−	0.237680i	$-0.923613\pi$
$739$	−38.8144	+	17.7259i	−1.42781	+	0.652060i	−0.456468	+	0.889740i	$0.650886\pi$
$740$	−15.0710	−	4.63256i	−0.554022	−	0.170296i
$741$	30.4541	−	7.37010i	1.11876	−	0.270747i
$742$	−14.1836	−	7.86138i	−0.520697	−	0.288600i
$743$	−3.91823	−	2.51809i	−0.143746	−	0.0923798i	0.466791	−	0.884368i	$-0.345410\pi$
$743$	−3.91823	−	2.51809i	−0.143746	−	0.0923798i	−0.610537	+	0.791988i	$0.709046\pi$
$744$	−23.8848	−	3.32890i	−0.875660	−	0.122043i
$745$	−9.74519	+	11.2465i	−0.357036	+	0.412042i
$746$	6.17067	+	1.38317i	0.225924	+	0.0506414i
$747$	12.2746	−	11.6777i	0.449105	−	0.427265i
$748$	0.436251	+	3.33208i	0.0159509	+	0.121833i
$749$	2.56188	+	3.98637i	0.0936092	+	0.145659i
$750$	−7.69263	+	17.6285i	−0.280895	+	0.643703i
$751$	19.9866	+	9.12757i	0.729321	+	0.333070i	0.745233	−	0.666804i	$-0.232338\pi$
$751$	19.9866	+	9.12757i	0.729321	+	0.333070i	−0.0159124	+	0.999873i	$0.505065\pi$
$752$	−35.8024	−	24.3065i	−1.30558	−	0.886368i
$753$	−33.3669	−	6.45026i	−1.21596	−	0.235060i
$754$	8.07180	+	0.628506i	0.293958	+	0.0228889i
$755$	−16.8601	−	4.95057i	−0.613602	−	0.180170i
$756$	23.3519	−	14.5401i	0.849299	−	0.528819i
$757$	−2.24723	+	15.6298i	−0.0816768	+	0.568075i	0.907354	+	0.420367i	$0.138099\pi$
$757$	−2.24723	+	15.6298i	−0.0816768	+	0.568075i	−0.989031	+	0.147708i	$0.952811\pi$
$758$	30.9416	−	30.5537i	1.12385	−	1.10976i
$759$	−2.86135	+	7.30177i	−0.103860	+	0.265037i
$760$	9.17343	−	8.83266i	0.332755	−	0.320394i
$761$	−43.6135	−	6.27067i	−1.58099	−	0.227312i	−0.704844	−	0.709362i	$-0.748983\pi$
$761$	−43.6135	−	6.27067i	−1.58099	−	0.227312i	−0.876143	+	0.482050i	$0.839892\pi$
$762$	32.1144	+	35.8181i	1.16338	+	1.29755i
$763$	12.8870	−	43.8890i	0.466540	−	1.58889i
$764$	−25.7996	+	21.7917i	−0.933396	+	0.788397i
$765$	3.54620	+	2.79517i	0.128213	+	0.101060i
$766$	4.12799	+	19.5696i	0.149150	+	0.707077i
$767$	14.4065	−	31.5458i	0.520188	−	1.13905i
$768$	26.2195	−	8.97435i	0.946114	−	0.323834i
$769$	5.14057	−	3.30364i	0.185374	−	0.119132i	−0.444663	−	0.895698i	$-0.646676\pi$
$769$	5.14057	−	3.30364i	0.185374	−	0.119132i	0.630036	+	0.776566i	$0.283040\pi$
$770$	1.80626	−	2.38141i	0.0650929	−	0.0858202i
$771$	−33.4583	−	11.6009i	−1.20497	−	0.417797i
$772$	18.1769	+	29.0842i	0.654203	+	1.04676i
$773$	−24.0941	−	20.8776i	−0.866603	−	0.750916i	0.103237	−	0.994657i	$-0.467080\pi$
$773$	−24.0941	−	20.8776i	−0.866603	−	0.750916i	−0.969840	+	0.243741i	$0.921625\pi$
$774$	−11.4427	+	16.6391i	−0.411299	+	0.598081i
$775$	11.4033	−	17.7439i	0.409620	−	0.637380i
$776$	−16.4608	+	28.8348i	−0.590908	+	1.03511i
$777$	−41.5391	+	10.0527i	−1.49021	+	0.360640i
$778$	−29.7102	+	15.9805i	−1.06516	+	0.572930i
$779$	−12.0898	−	26.4729i	−0.433161	−	0.948491i
$780$	5.88072	−	8.03224i	0.210564	−	0.287600i
$781$	5.50338			0.196926
$782$	10.8491	−	5.29126i	0.387964	−	0.189215i
$783$	−8.66731	+	1.23137i	−0.309744	+	0.0440056i
$784$	−0.00448861	+	0.0264611i	−0.000160308	+	0.000945040i
$785$	−2.83220	+	1.29342i	−0.101086	+	0.0461642i
$786$	−0.261470	−	15.4388i	−0.00932634	−	0.550683i
$787$	41.1818	−	35.6842i	1.46797	−	1.27201i	0.577964	−	0.816062i	$-0.303847\pi$
$787$	41.1818	−	35.6842i	1.46797	−	1.27201i	0.890009	−	0.455944i	$-0.150698\pi$
$788$	−18.6301	+	5.21593i	−0.663671	+	0.185810i
$789$	−21.1051	−	36.6022i	−0.751360	−	1.30307i
$790$	4.97106	−	1.81847i	0.176862	−	0.0646984i
$791$	32.2275	−	37.1925i	1.14588	−	1.32241i
$792$	−7.42597	+	3.00536i	−0.263870	+	0.106791i
$793$	−2.42501	−	16.8663i	−0.0861146	−	0.598940i
$794$	0.788261	−	1.03926i	0.0279743	−	0.0368821i
$795$	6.31711	−	0.599655i	0.224045	−	0.0212676i
$796$	−22.4024	+	25.2041i	−0.794031	+	0.893336i
$797$	28.6032	+	13.0627i	1.01318	+	0.462703i	0.851620	−	0.524160i	$-0.175621\pi$
$797$	28.6032	+	13.0627i	1.01318	+	0.462703i	0.161559	+	0.986863i	$0.448348\pi$
$798$	9.16272	−	33.2801i	0.324357	−	1.17810i
$799$	−5.42443	−	18.4739i	−0.191902	−	0.653560i
$800$	−2.49067	+	24.1101i	−0.0880584	+	0.852420i
$801$	−27.4344	+	9.46088i	−0.969346	+	0.334284i
$802$	−32.3712	−	12.3070i	−1.14307	−	0.434575i
$803$	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
$807$	−28.6846	−	20.4503i	−1.00974	−	0.719885i
$808$	8.55635	−	21.6785i	0.301011	−	0.762648i
$809$	4.95696	−	16.8818i	0.174277	−	0.593534i	−0.825306	−	0.564685i	$-0.808998\pi$
$809$	4.95696	−	16.8818i	0.174277	−	0.593534i	0.999584	−	0.0288489i	$-0.00918418\pi$
$810$	−4.32162	+	9.85845i	−0.151846	+	0.346391i
$811$	−5.93418	−	20.2100i	−0.208377	−	0.709668i	−0.995659	−	0.0930748i	$-0.970330\pi$
$811$	−5.93418	−	20.2100i	−0.208377	−	0.709668i	0.787282	−	0.616593i	$-0.211488\pi$
$812$	4.91639	−	7.44193i	0.172531	−	0.261160i
$813$	25.2602	+	32.1578i	0.885914	+	1.12782i
$814$	12.4199	−	0.809578i	0.435316	−	0.0283757i
$815$	0.758501	−	0.487459i	0.0265691	−	0.0170749i
$816$	11.5443	+	4.33196i	0.404130	+	0.151649i
$817$	3.60622	+	25.0818i	0.126166	+	0.877503i
$818$	38.5061	+	8.63123i	1.34634	+	0.301784i
$819$	2.59495	−	26.8588i	0.0906748	−	0.938524i
$820$	−8.36160	−	3.94685i	−0.292000	−	0.137830i
$821$	−6.90186	+	10.7395i	−0.240877	+	0.374811i	−0.940552	−	0.339649i	$-0.889692\pi$
$821$	−6.90186	+	10.7395i	−0.240877	+	0.374811i	0.699675	+	0.714461i	$0.253328\pi$
$822$	−41.9541	+	27.9773i	−1.46332	+	0.975820i
$823$	−11.4168	+	9.89269i	−0.397964	+	0.344837i	−0.830737	−	0.556665i	$-0.812081\pi$
$823$	−11.4168	+	9.89269i	−0.397964	+	0.344837i	0.432773	+	0.901503i	$0.357535\pi$
$824$	4.31128	+	8.26353i	0.150191	+	0.287874i
$825$	0.337296	−	6.99857i	0.0117431	−	0.243659i
$826$	−22.7021	−	30.7286i	−0.789907	−	1.06918i
$827$	0.545286			0.0189614			0.00948072	−	0.999955i	$-0.496982\pi$
$827$	0.545286			0.0189614			0.00948072	+	0.999955i	$0.496982\pi$
$828$	18.7160	+	21.8566i	0.650426	+	0.759569i
$829$	−6.82275			−0.236964			−0.118482	−	0.992956i	$-0.537803\pi$
$829$	−6.82275			−0.236964			−0.118482	+	0.992956i	$0.537803\pi$
$830$	−4.01352	−	5.43253i	−0.139311	−	0.188566i
$831$	−0.0314990	+	0.653575i	−0.00109269	+	0.0226723i
$832$	8.64011	−	25.7746i	0.299542	−	0.893573i
$833$	−0.00902482	+	0.00782005i	−0.000312692	+	0.000270949i
$834$	−4.15191	+	2.76872i	−0.143769	+	0.0958729i
$835$	2.01366	−	3.13332i	0.0696856	−	0.108433i
$836$	−4.29096	+	9.09062i	−0.148406	+	0.314406i
$837$	13.8648	−	21.4949i	0.479237	−	0.742972i
$838$	−6.94855	−	1.55753i	−0.240034	−	0.0538041i
$839$	1.96581	+	13.6725i	0.0678674	+	0.472028i	0.995206	+	0.0978039i	$0.0311818\pi$
$839$	1.96581	+	13.6725i	0.0678674	+	0.472028i	−0.927338	+	0.374224i	$0.877909\pi$
$840$	−4.59884	−	9.95603i	−0.158675	−	0.343516i
$841$	22.0085	−	14.1440i	0.758913	−	0.487724i
$842$	−21.3397	+	1.39101i	−0.735414	+	0.0479373i
$843$	27.0601	+	34.4492i	0.931998	+	1.18649i
$844$	3.55366	+	2.34767i	0.122322	+	0.0808100i
$845$	0.346299	+	1.17938i	0.0119130	+	0.0405721i
$846$	39.3683	−	23.5972i	1.35351	−	0.811290i
$847$	7.53854	−	25.6739i	0.259027	−	0.882166i
$848$	15.9386	−	6.79833i	0.547334	−	0.233456i
$849$	9.47976	+	6.75848i	0.325344	+	0.231950i
$850$	−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	0.955968	+	0.293469i	$0.0948099\pi$
$853$	−1.28380	+	8.92902i	−0.0439565	+	0.305724i	−0.999925	+	0.0122545i	$0.996099\pi$
$854$	−17.5466	−	6.67093i	−0.600433	−	0.228274i
$855$	4.40346	+	12.7690i	0.150595	+	0.436692i
$856$	−5.04272	−	0.456717i	−0.172357	−	0.0156103i
$857$	−8.72744	−	29.7229i	−0.298124	−	1.01532i	−0.963255	−	0.268589i	$-0.913443\pi$
$857$	−8.72744	−	29.7229i	−0.298124	−	1.01532i	0.665131	−	0.746727i	$-0.268376\pi$
$858$	−2.08593	+	7.57635i	−0.0712125	+	0.258652i
$859$	7.51823	+	3.43346i	0.256519	+	0.117148i	0.539524	−	0.841970i	$-0.318604\pi$
$859$	7.51823	+	3.43346i	0.256519	+	0.117148i	−0.283005	+	0.959118i	$0.591331\pi$
$860$	6.01733	+	5.34843i	0.205189	+	0.182380i
$861$	−24.9510	+	2.36849i	−0.850328	+	0.0807179i
$862$	2.58317	−	3.40572i	0.0879831	−	0.115999i
$863$	−5.04909	−	35.1172i	−0.171873	−	1.19540i	−0.874923	−	0.484263i	$-0.839088\pi$
$863$	−5.04909	−	35.1172i	−0.171873	−	1.19540i	0.703050	−	0.711141i	$-0.251821\pi$
$864$	−3.06935	+	29.2332i	−0.104422	+	0.994533i
$865$	−6.60129	+	7.61830i	−0.224451	+	0.259030i
$866$	−32.0265	+	11.7157i	−1.08830	+	0.398115i
$867$	−11.9678	−	20.7556i	−0.406448	−	0.704896i
$868$	7.02604	+	25.0954i	0.238479	+	0.851794i
$869$	−3.15782	+	2.73627i	−0.107122	+	0.0928216i
$870$	0.0590996	+	3.48959i	0.00200366	+	0.118308i
$871$	−29.0401	+	13.2622i	−0.983986	+	0.449371i
$872$	28.5451	+	39.6750i	0.966658	+	1.34357i
$873$	−20.3956	−	28.7093i	−0.690285	−	0.971662i
$874$	35.8588	+	4.23033i	1.21294	+	0.143093i
$875$	20.7849			0.702658
$876$	−16.8064	−	12.3046i	−0.567836	−	0.415735i
$877$	19.9538	+	43.6927i	0.673791	+	1.47540i	0.869090	+	0.494653i	$0.164705\pi$
$877$	19.9538	+	43.6927i	0.673791	+	1.47540i	−0.195299	+	0.980744i	$0.562568\pi$
$878$	−26.7546	+	14.3908i	−0.902924	+	0.485665i
$879$	18.3375	−	4.43781i	0.618510	−	0.149684i
$880$	0.822192	+	3.08612i	0.0277161	+	0.104033i
$881$	−15.2633	+	23.7502i	−0.514234	+	0.800164i	−0.997145	−	0.0755056i	$-0.975943\pi$
$881$	−15.2633	+	23.7502i	−0.514234	+	0.800164i	0.482911	+	0.875669i	$0.339579\pi$
$882$	−0.0234560	−	0.0161306i	−0.000789804	−	0.000543147i
$883$	11.8468	+	10.2653i	0.398677	+	0.345456i	0.831009	−	0.556259i	$-0.187764\pi$
$883$	11.8468	+	10.2653i	0.398677	+	0.345456i	−0.432332	+	0.901714i	$0.642309\pi$
$884$	10.2567	−	6.41021i	0.344971	−	0.215599i
$885$	14.1247	+	4.89741i	0.474795	+	0.164625i
$886$	34.7613	−	45.8302i	1.16783	−	1.53970i
$887$	−11.9658	+	7.68993i	−0.401771	+	0.258203i	−0.725886	−	0.687815i	$-0.758570\pi$
$887$	−11.9658	+	7.68993i	−0.401771	+	0.258203i	0.324115	+	0.946018i	$0.394934\pi$
$888$	18.7912	−	41.6218i	0.630593	−	1.39674i
$889$	21.5959	−	47.2884i	0.724302	−	1.58600i
$890$	2.38788	+	11.3202i	0.0800420	+	0.379455i
$891$	0.423240	−	8.48647i	0.0141791	−	0.284307i
$892$	16.1513	+	19.1217i	0.540784	+	0.640243i
$893$	16.2263	−	55.2617i	0.542992	−	1.84926i
$894$	−28.7734	−	32.0917i	−0.962326	−	1.07331i
$895$	17.3293	+	2.49158i	0.579255	+	0.0832843i
$896$	−20.2208	−	22.0902i	−0.675529	−	0.737983i
$897$	28.1836	−	1.54941i	0.941021	−	0.0517333i
$898$	−19.6486	+	19.4023i	−0.655683	+	0.647463i
$899$	1.18028	−	8.20904i	0.0393646	−	0.273787i
$900$	−22.0858	−	13.1588i	−0.736193	−	0.438628i
$901$	7.39742	+	2.17208i	0.246444	+	0.0723624i
$902$	7.27687	+	0.566609i	0.242293	+	0.0188660i
$903$	21.4257	+	4.14187i	0.713004	+	0.137833i
$904$	10.2035	+	51.5860i	0.339365	+	1.71573i
$905$	−10.7240	−	4.89749i	−0.356478	−	0.162798i
$906$	20.3555	−	46.6470i	0.676267	−	1.54974i
$907$	−3.50117	−	5.44793i	−0.116255	−	0.180896i	0.778250	−	0.627955i	$-0.216108\pi$
$907$	−3.50117	−	5.44793i	−0.116255	−	0.180896i	−0.894504	+	0.447059i	$0.852471\pi$
$908$	−1.83363	+	0.240067i	−0.0608511	+	0.00796691i
$909$	17.0386	+	17.9095i	0.565135	+	0.594022i
$910$	−10.4972	−	2.35297i	−0.347978	−	0.0780001i
$911$	0.954839	−	1.10194i	0.0316352	−	0.0365090i	−0.739711	−	0.672924i	$-0.765038\pi$
$911$	0.954839	−	1.10194i	0.0316352	−	0.0365090i	0.771347	+	0.636415i	$0.219583\pi$
$912$	22.0450	+	29.5711i	0.729983	+	0.979197i
$913$	4.48536	+	2.88257i	0.148444	+	0.0953990i
$914$	8.80832	+	4.88209i	0.291353	+	0.161485i
$915$	7.13933	−	1.72777i	0.236019	−	0.0571182i
$916$	−11.2063	+	36.4574i	−0.370268	+	1.20459i
$917$	−15.1783	+	6.93168i	−0.501230	+	0.228904i
$918$	−9.32122	+	9.17361i	−0.307646	+	0.302774i
$919$			5.66520i			0.186878i	0.995625	+	0.0934389i	$0.0297860\pi$
$919$			5.66520i			0.186878i	−0.995625	+	0.0934389i	$0.970214\pi$
$920$	9.57073	−	6.32466i	0.315538	−	0.208518i
$921$	0.144009	−	0.278956i	0.00474526	−	0.00919192i
$922$	−17.2024	−	23.2844i	−0.566530	−	0.766830i
$923$	−8.22837	−	18.0176i	−0.270840	−	0.593057i
$924$	6.18619	+	6.05609i	0.203511	+	0.199231i
$925$	26.1563	+	30.1860i	0.860013	+	0.992508i
$926$	17.6648	−	31.8711i	0.580502	−	1.04735i
$927$	−9.87528	+	0.459377i	−0.324347	+	0.0150879i
$928$	3.04733	+	9.03020i	0.100034	+	0.296431i
$929$	7.37482	+	6.39032i	0.241960	+	0.209660i	0.767396	−	0.641174i	$-0.221552\pi$
$929$	7.37482	+	6.39032i	0.241960	+	0.209660i	−0.525436	+	0.850833i	$0.676098\pi$
$930$	−7.81865	−	6.54641i	−0.256384	−	0.214665i
$931$	−0.0353576	+	0.00508366i	−0.00115880	+	0.000166610i
$932$	2.71217	+	20.7155i	0.0888401	+	0.678560i
$933$	18.1896	−	1.72665i	0.595500	−	0.0565281i
$934$	12.7772	−	0.832871i	0.418083	−	0.0272524i
$935$	−0.590307	+	1.29259i	−0.0193051	+	0.0422723i
$936$	20.9422	+	19.8186i	0.684519	+	0.647790i
$937$	−9.84323	+	2.89023i	−0.321564	+	0.0944198i	−0.438531	−	0.898716i	$-0.644501\pi$
$937$	−9.84323	+	2.89023i	−0.321564	+	0.0944198i	0.116967	+	0.993136i	$0.462683\pi$
$938$	−2.73026	+	35.0643i	−0.0891462	+	1.14489i
$939$	−38.0155	−	36.2882i	−1.24059	−	1.18422i
$940$	−7.39086	−	16.7394i	−0.241063	−	0.545980i
$941$	−11.9775	−	1.72211i	−0.390456	−	0.0561391i	−0.0557086	−	0.998447i	$-0.517742\pi$
$941$	−11.9775	−	1.72211i	−0.390456	−	0.0561391i	−0.334747	+	0.942308i	$0.608651\pi$
$942$	−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
$945$	11.6321	+	0.0194647i	0.378392	+	0.000633185i
$946$	−5.94030	−	2.25840i	−0.193136	−	0.0734270i
$947$	8.67359	+	2.54680i	0.281854	+	0.0827597i	0.419604	−	0.907707i	$-0.362169\pi$
$947$	8.67359	+	2.54680i	0.281854	+	0.0827597i	−0.137750	+	0.990467i	$0.543987\pi$
$948$	3.41789	+	14.9454i	0.111008	+	0.485403i
$949$	−19.6043	+	5.75635i	−0.636383	+	0.186859i
$950$	−31.5652	+	6.65834i	−1.02411	+	0.216025i
$951$	−2.29101	−	2.91661i	−0.0742912	−	0.0945775i
$952$	−0.698907	−	13.3063i	−0.0226517	−	0.431258i
$953$	8.52263	+	13.2615i	0.276075	+	0.429581i	0.951409	−	0.307931i	$-0.0996367\pi$
$953$	8.52263	+	13.2615i	0.276075	+	0.429581i	−0.675333	+	0.737512i	$0.736000\pi$
$954$	−0.573761	+	18.3701i	−0.0185762	+	0.594753i
$955$	−14.1349	+	2.03229i	−0.457395	+	0.0657635i
$956$	−3.33752	−	5.34023i	−0.107943	−	0.172715i
$957$	−1.02251	−	2.55825i	−0.0330532	−	0.0826965i
$958$	−24.0700	+	8.80509i	−0.777665	+	0.284479i
$959$	45.8428	+	29.4614i	1.48034	+	0.951357i
$960$	11.4130	+	2.65790i	0.368354	+	0.0857832i
$961$	−4.43214	−	5.11496i	−0.142972	−	0.164999i
$962$	−21.2200	−	39.4512i	−0.684162	−	1.27196i
$963$	2.69044	−	4.64799i	0.0866981	−	0.149779i
$964$	30.8459	+	4.83289i	0.993479	+	0.155657i
$965$			14.5026i			0.466856i
$966$	13.5586	−	27.9837i	0.436242	−	0.900362i
$967$			18.2886i			0.588120i	0.955787	+	0.294060i	$0.0950066\pi$
$967$			18.2886i			0.588120i	−0.955787	+	0.294060i	$0.904993\pi$
$968$	16.6981	+	23.2089i	0.536698	+	0.745961i
$969$	−0.790002	+	16.3918i	−0.0253785	+	0.526581i
$970$	−12.3646	+	6.65068i	−0.397003	+	0.213540i
$971$	28.5686	+	32.9699i	0.916808	+	1.05805i	0.998115	+	0.0613642i	$0.0195451\pi$
$971$	28.5686	+	32.9699i	0.916808	+	1.05805i	−0.0813070	+	0.996689i	$0.525909\pi$
$972$	−26.7567	−	16.0025i	−0.858221	−	0.513281i
$973$	4.53674	+	2.91559i	0.145441	+	0.0934694i
$974$	5.47576	+	14.9688i	0.175455	+	0.479631i
$975$	−23.4171	+	9.35963i	−0.749947	+	0.299748i
$976$	17.1424	−	10.4152i	0.548716	−	0.333384i
$977$	34.9345	−	5.02283i	1.11765	−	0.160694i	0.441363	−	0.897329i	$-0.354495\pi$
$977$	34.9345	−	5.02283i	1.11765	−	0.160694i	0.676292	+	0.736634i	$0.263586\pi$
$978$	1.12491	+	2.35677i	0.0359708	+	0.0753611i
$979$	−4.93750	−	7.68290i	−0.157803	−	0.245547i
$980$	−0.00753963	+	0.00848257i	−0.000240845	+	0.000270966i
$981$	−50.9156	+	9.75429i	−1.62561	+	0.311430i
$982$	−1.21505	−	5.76019i	−0.0387739	−	0.183815i
$983$	−55.7187	+	16.3605i	−1.77715	+	0.521819i	−0.994875	−	0.101113i	$-0.967760\pi$
$983$	−55.7187	+	16.3605i	−1.77715	+	0.521819i	−0.782276	+	0.622932i	$0.785941\pi$
$984$	14.3814	−	22.5918i	0.458461	−	0.720200i
$985$	−7.84935	−	2.30478i	−0.250101	−	0.0734363i
$986$	−1.50691	+	3.96363i	−0.0479897	+	0.126228i
$987$	−40.3870	−	28.7934i	−1.28553	−	0.916504i
$988$	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	$-0.456697\pi$
$991$	−0.421248	−	0.0605663i	−0.0133814	−	0.00192395i	−0.149002	+	0.988837i	$0.547606\pi$
$992$	−25.7708	−	10.5492i	−0.818225	−	0.334938i
$993$	0.298536	−	0.312746i	0.00947376	−	0.00992470i
$994$	−21.7553	−	1.69396i	−0.690035	−	0.0537292i
$995$	−13.6815	+	4.01725i	−0.433732	+	0.127355i
$996$	17.0695	−	9.55751i	0.540868	−	0.302841i
$997$	9.11291	−	19.9545i	0.288609	−	0.631965i	−0.708682	−	0.705528i	$-0.750710\pi$
$997$	9.11291	−	19.9545i	0.288609	−	0.631965i	0.997291	+	0.0735632i	$0.0234371\pi$
$998$	1.90240	+	29.1850i	0.0602193	+	0.923835i
$999$	31.6584	+	36.6595i	1.00163	+	1.15986i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.95.9	✓	440	276.95	even	22	inner
276.2.o.a.95.13	yes	440	69.26	odd	22	inner
276.2.o.a.95.32	yes	440	23.3	even	11	inner
276.2.o.a.95.36	yes	440	92.3	odd	22	inner
276.2.o.a.215.9	yes	440	1.1	even	1	trivial
276.2.o.a.215.13	yes	440	4.3	odd	2	inner
276.2.o.a.215.32	yes	440	12.11	even	2	inner
276.2.o.a.215.36	yes	440	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13746 + 0.840348i) q^{2} +(0.0833793 - 1.73004i) q^{3} +(0.587629 - 1.91172i) q^{4} +(0.639142 - 0.553820i) q^{5} +(1.35900 + 2.03792i) q^{6} +(1.43109 - 2.22681i) q^{7} +(0.938111 + 2.66832i) q^{8} +(-2.98610 - 0.288500i) q^{9} +O(q^{10})\)	\(q+(-1.13746 + 0.840348i) q^{2} +(0.0833793 - 1.73004i) q^{3} +(0.587629 - 1.91172i) q^{4} +(0.639142 - 0.553820i) q^{5} +(1.35900 + 2.03792i) q^{6} +(1.43109 - 2.22681i) q^{7} +(0.938111 + 2.66832i) q^{8} +(-2.98610 - 0.288500i) q^{9} +(-0.261597 + 1.16705i) q^{10} +(-0.134361 - 0.934503i) q^{11} +(-3.25837 - 1.17602i) q^{12} +(-2.85860 + 1.83711i) q^{13} +(0.243497 + 3.73552i) q^{14} +(-0.904840 - 1.15192i) q^{15} +(-3.30938 - 2.24677i) q^{16} +(-0.501406 - 1.70763i) q^{17} +(3.63900 - 2.18120i) q^{18} +(1.49987 - 5.10810i) q^{19} +(-0.683173 - 1.54730i) q^{20} +(-3.73316 - 2.66151i) 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} +(1.70773 - 4.49186i) q^{26} +(-0.748095 + 5.14202i) q^{27} +(-3.41611 - 4.04438i) q^{28} +(0.474656 + 1.61653i) q^{29} +(1.99723 + 0.549881i) q^{30} +(-4.47775 - 2.04492i) q^{31} +(5.65236 - 0.225427i) q^{32} +(-1.62793 + 0.154533i) q^{33} +(2.00533 + 1.52101i) q^{34} +(-0.318586 - 2.21581i) q^{35} +(-2.30625 + 5.53906i) q^{36} +(6.10446 - 7.04492i) q^{37} +(2.58654 + 7.07068i) q^{38} +(2.93993 + 5.09868i) q^{39} +(2.07736 + 1.18589i) q^{40} +(4.13139 - 3.57987i) q^{41} +(6.48292 - 0.109794i) q^{42} +(-4.32963 + 1.97727i) q^{43} +(-1.86547 - 0.292279i) q^{44} +(-2.06832 + 1.46937i) q^{45} +(1.13522 + 6.68665i) q^{46} +10.8184 q^{47} +(-4.16294 + 5.53804i) q^{48} +(-0.00278734 - 0.00610343i) q^{49} +(-2.87045 - 5.33659i) q^{50} +(-2.99608 + 0.725072i) q^{51} +(1.83225 + 6.54440i) q^{52} +(-2.34204 + 3.64429i) q^{53} +(-3.47016 - 6.47750i) q^{54} +(-0.603422 - 0.522868i) q^{55} +(7.28438 + 1.72960i) q^{56} +(-8.71218 - 3.02076i) q^{57} +(-1.89835 - 1.43986i) q^{58} +(-8.58571 + 5.51770i) q^{59} +(-2.73386 + 1.05290i) q^{60} +(-2.08314 + 4.56144i) q^{61} +(6.81170 - 1.43686i) q^{62} +(-4.91580 + 6.23661i) q^{63} +(-6.23989 + 5.00637i) q^{64} +(-0.809623 + 2.75732i) q^{65} +(1.72185 - 1.54381i) q^{66} +(9.29956 + 1.33708i) q^{67} +(-3.55916 - 0.0449034i) q^{68} +(-7.22396 - 4.10054i) q^{69} +(2.22443 + 2.25268i) q^{70} +(-0.829574 + 5.76982i) q^{71} +(-2.03148 - 8.23851i) q^{72} +(5.76933 + 1.69403i) q^{73} +(-1.02339 + 13.1432i) q^{74} +(7.28656 + 1.40858i) q^{75} +(-8.88392 - 5.86902i) q^{76} +(-2.27325 - 1.03816i) q^{77} +(-7.62872 - 3.32897i) q^{78} +(-2.39274 - 3.72317i) q^{79} +(-3.35947 + 0.396798i) q^{80} +(8.83354 + 1.72297i) q^{81} +(-1.69095 + 7.54376i) q^{82} +(-3.69824 + 4.26800i) q^{83} +(-7.28179 + 5.57280i) q^{84} +(-1.26619 - 0.813730i) q^{85} +(3.26318 - 5.88747i) q^{86} +(2.83624 - 0.686390i) q^{87} +(2.36751 - 1.23519i) q^{88} +(8.79914 - 4.01843i) q^{89} +(1.11785 - 3.40945i) q^{90} +8.99463i q^{91} +(-6.91038 - 6.65182i) q^{92} +(-3.91115 + 7.57619i) q^{93} +(-12.3055 + 9.09126i) q^{94} +(-1.87033 - 4.09546i) q^{95} +(0.0812915 - 9.79762i) q^{96} +(7.68730 + 8.87162i) q^{97} +(0.00829950 + 0.00460007i) q^{98} +(0.131612 + 2.82928i) 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

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