LMFDB - Embedded newform 552.2.t.a.451.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(19,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([11, 11, 0, 15]))

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

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

chi := DirichletCharacter("552.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			451.22
Character	$\chi$	$=$	552.451
Dual form			552.2.t.a.235.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.33194 + 0.475334i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.54812 + 1.26623i) q^{4} +(-0.462696 - 3.21812i) q^{5} +(0.513000 + 1.31789i) q^{6} +(1.43113 - 3.13375i) q^{7} +(1.46011 + 2.42241i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(1.33194 + 0.475334i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.54812 + 1.26623i) q^{4} +(-0.462696 - 3.21812i) q^{5} +(0.513000 + 1.31789i) q^{6} +(1.43113 - 3.13375i) q^{7} +(1.46011 + 2.42241i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.913400 - 4.50627i) q^{10} +(0.0298024 - 0.101497i) q^{11} +(0.0568468 + 1.99919i) q^{12} +(-0.610377 + 0.278750i) q^{13} +(3.39576 - 3.49369i) q^{14} +(2.12909 - 2.45710i) q^{15} +(0.793321 + 3.92054i) q^{16} +(0.598302 - 0.930977i) q^{17} +(-0.660050 + 1.25073i) q^{18} +(2.54616 + 3.96191i) q^{19} +(3.35858 - 5.56790i) q^{20} +(3.30552 - 0.970589i) q^{21} +(0.0879401 - 0.121022i) q^{22} +(-2.35594 - 4.17727i) q^{23} +(-0.874567 + 2.68982i) q^{24} +(-5.34475 + 1.56936i) q^{25} +(-0.945484 + 0.0811445i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(6.18361 - 3.03926i) q^{28} +(-2.63576 + 4.10132i) q^{29} +(4.00376 - 2.26068i) q^{30} +(-0.0721183 - 0.0624909i) q^{31} +(-0.806912 + 5.59901i) q^{32} +(0.0962231 - 0.0439436i) q^{33} +(1.23943 - 0.955609i) q^{34} +(-10.7470 - 3.15559i) q^{35} +(-1.47366 + 1.35215i) q^{36} +(-0.960068 + 6.67742i) q^{37} +(1.50810 + 6.48730i) q^{38} +(-0.610377 - 0.278750i) q^{39} +(7.12003 - 5.81965i) q^{40} +(0.346577 + 2.41050i) q^{41} +(4.86410 + 0.278463i) q^{42} +(1.63464 - 1.41643i) q^{43} +(0.174657 - 0.119393i) q^{44} +3.25121 q^{45} +(-1.15236 - 6.68372i) q^{46} +8.18987i q^{47} +(-2.44343 + 3.16696i) q^{48} +(-3.18820 - 3.67938i) q^{49} +(-7.86485 - 0.450252i) q^{50} +(1.09539 - 0.157493i) q^{51} +(-1.29790 - 0.341341i) q^{52} +(-2.84234 + 6.22386i) q^{53} +(-1.37748 + 0.320223i) q^{54} +(-0.340421 - 0.0489451i) q^{55} +(9.68084 - 1.10882i) q^{56} +(-1.32683 + 4.51876i) q^{57} +(-5.46017 + 4.20984i) q^{58} +(-6.33745 - 13.8771i) q^{59} +(6.40734 - 1.10796i) q^{60} +(-3.23927 + 3.73831i) q^{61} +(-0.0663530 - 0.117514i) q^{62} +(2.89818 + 1.86255i) q^{63} +(-3.73616 + 7.07398i) q^{64} +(1.17947 + 1.83529i) q^{65} +(0.149051 - 0.0127920i) q^{66} +(3.45689 + 11.7731i) q^{67} +(2.10507 - 0.683670i) q^{68} +(1.61416 - 4.51603i) q^{69} +(-12.8143 - 9.31145i) q^{70} +(-2.59002 - 8.82078i) q^{71} +(-2.60555 + 1.10050i) q^{72} +(-1.31153 + 0.842871i) q^{73} +(-4.45276 + 8.43755i) q^{74} +(-4.68611 - 3.01158i) q^{75} +(-1.07493 + 9.35752i) q^{76} +(-0.275416 - 0.238650i) q^{77} +(-0.680485 - 0.661410i) q^{78} +(-5.50717 - 12.0590i) q^{79} +(12.2497 - 4.36702i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.684172 + 3.37537i) q^{82} +(-15.2686 - 2.19529i) q^{83} +(6.34632 + 2.68297i) q^{84} +(-3.27283 - 1.49465i) q^{85} +(2.85052 - 1.10959i) q^{86} +(-4.82563 + 0.693821i) q^{87} +(0.289383 - 0.0760040i) q^{88} +(11.9248 - 10.3329i) q^{89} +(4.33041 + 1.54541i) q^{90} +2.31170i q^{91} +(1.64212 - 9.45005i) q^{92} -0.0954262i q^{93} +(-3.89292 + 10.9084i) q^{94} +(11.5718 - 10.0270i) q^{95} +(-4.75986 + 3.05675i) q^{96} +(8.96312 - 1.28870i) q^{97} +(-2.49755 - 6.41616i) q^{98} +(0.0962231 + 0.0439436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	$ 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) $ 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.33194	+	0.475334i	0.941822	+	0.336112i
$2$	1.33194	+	0.475334i	0.941822	+	0.336112i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$3$	0.654861	+	0.755750i	0.378084	+	0.436332i
$4$	1.54812	+	1.26623i	0.774058	+	0.633115i
$5$	−0.462696	−	3.21812i	−0.206924	−	1.43919i	−0.783117	−	0.621874i	$-0.786371\pi$
$5$	−0.462696	−	3.21812i	−0.206924	−	1.43919i	0.576193	−	0.817314i	$-0.304538\pi$
$6$	0.513000	+	1.31789i	0.209431	+	0.538026i
$7$	1.43113	−	3.13375i	0.540918	−	1.18444i	−0.419978	−	0.907534i	$-0.637962\pi$
$7$	1.43113	−	3.13375i	0.540918	−	1.18444i	0.960896	−	0.276911i	$-0.0893106\pi$
$8$	1.46011	+	2.42241i	0.516227	+	0.856452i
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$	0.913400	−	4.50627i	0.288843	−	1.42501i
$11$	0.0298024	−	0.101497i	0.00898575	−	0.0306026i	−0.954878	−	0.296998i	$-0.904015\pi$
$11$	0.0298024	−	0.101497i	0.00898575	−	0.0306026i	0.963864	+	0.266395i	$0.0858327\pi$
$12$	0.0568468	+	1.99919i	0.0164103	+	0.577117i
$13$	−0.610377	+	0.278750i	−0.169288	+	0.0773113i	−0.498257	−	0.867030i	$-0.666026\pi$
$13$	−0.610377	+	0.278750i	−0.169288	+	0.0773113i	0.328969	+	0.944341i	$0.393299\pi$
$14$	3.39576	−	3.49369i	0.907554	−	0.933727i
$15$	2.12909	−	2.45710i	0.549729	−	0.634421i
$16$	0.793321	+	3.92054i	0.198330	+	0.980135i
$17$	0.598302	−	0.930977i	0.145110	−	0.225795i	−0.761089	−	0.648648i	$-0.775335\pi$
$17$	0.598302	−	0.930977i	0.145110	−	0.225795i	0.906198	+	0.422853i	$0.138971\pi$
$18$	−0.660050	+	1.25073i	−0.155575	+	0.294801i
$19$	2.54616	+	3.96191i	0.584130	+	0.908924i	1.00000		0.000499791i	$-0.000159088\pi$
$19$	2.54616	+	3.96191i	0.584130	+	0.908924i	−0.415870	+	0.909424i	$0.636523\pi$
$20$	3.35858	−	5.56790i	0.751001	−	1.24502i
$21$	3.30552	−	0.970589i	0.721324	−	0.211800i
$22$	0.0879401	−	0.121022i	0.0187489	−	0.0258020i
$23$	−2.35594	−	4.17727i	−0.491247	−	0.871020i
$23$	−2.35594	−	4.17727i	−0.491247	−	0.871020i
$24$	−0.874567	+	2.68982i	−0.178520	+	0.549057i
$25$	−5.34475	+	1.56936i	−1.06895	+	0.313872i
$26$	−0.945484	+	0.0811445i	−0.185425	+	0.0159137i
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$	6.18361	−	3.03926i	1.16859	−	0.574365i
$29$	−2.63576	+	4.10132i	−0.489449	+	0.761597i	−0.994858	−	0.101283i	$-0.967705\pi$
$29$	−2.63576	+	4.10132i	−0.489449	+	0.761597i	0.505409	+	0.862880i	$0.331342\pi$
$30$	4.00376	−	2.26068i	0.730984	−	0.412742i
$31$	−0.0721183	−	0.0624909i	−0.0129528	−	0.0112237i	0.648360	−	0.761334i	$-0.275455\pi$
$31$	−0.0721183	−	0.0624909i	−0.0129528	−	0.0112237i	−0.661313	+	0.750110i	$0.730001\pi$
$32$	−0.806912	+	5.59901i	−0.142643	+	0.989774i
$33$	0.0962231	−	0.0439436i	0.0167503	−	0.00764960i
$34$	1.23943	−	0.955609i	0.212560	−	0.163886i
$35$	−10.7470	−	3.15559i	−1.81657	−	0.533392i
$36$	−1.47366	+	1.35215i	−0.245610	+	0.225359i
$37$	−0.960068	+	6.67742i	−0.157834	+	1.09776i	0.744780	+	0.667310i	$0.232555\pi$
$37$	−0.960068	+	6.67742i	−0.157834	+	1.09776i	−0.902614	+	0.430451i	$0.858355\pi$
$38$	1.50810	+	6.48730i	0.244646	+	1.05238i
$39$	−0.610377	−	0.278750i	−0.0977386	−	0.0446357i
$40$	7.12003	−	5.81965i	1.12578	−	0.920168i
$41$	0.346577	+	2.41050i	0.0541262	+	0.376456i	0.998823	+	0.0485101i	$0.0154473\pi$
$41$	0.346577	+	2.41050i	0.0541262	+	0.376456i	−0.944696	+	0.327946i	$0.893644\pi$
$42$	4.86410	+	0.278463i	0.750547	+	0.0429678i
$43$	1.63464	−	1.41643i	0.249281	−	0.216003i	−0.521253	−	0.853402i	$-0.674535\pi$
$43$	1.63464	−	1.41643i	0.249281	−	0.216003i	0.770534	+	0.637399i	$0.219990\pi$
$44$	0.174657	−	0.119393i	0.0263305	−	0.0179992i
$45$	3.25121			0.484662
$46$	−1.15236	−	6.68372i	−0.169907	−	0.985460i
$47$			8.18987i			1.19462i	0.802012	+	0.597308i	$0.203763\pi$
$47$			8.18987i			1.19462i	−0.802012	+	0.597308i	$0.796237\pi$
$48$	−2.44343	+	3.16696i	−0.352679	+	0.457111i
$49$	−3.18820	−	3.67938i	−0.455457	−	0.525625i
$50$	−7.86485	−	0.450252i	−1.11226	−	0.0636752i
$51$	1.09539	−	0.157493i	0.153385	−	0.0220535i
$52$	−1.29790	−	0.341341i	−0.179986	−	0.0473355i
$53$	−2.84234	+	6.22386i	−0.390426	+	0.854913i	0.607726	+	0.794147i	$0.292082\pi$
$53$	−2.84234	+	6.22386i	−0.390426	+	0.854913i	−0.998152	+	0.0607667i	$0.980645\pi$
$54$	−1.37748	+	0.320223i	−0.187452	+	0.0435769i
$55$	−0.340421	−	0.0489451i	−0.0459023	−	0.00659976i
$56$	9.68084	−	1.10882i	1.29366	−	0.148172i
$57$	−1.32683	+	4.51876i	−0.175743	+	0.598525i
$58$	−5.46017	+	4.20984i	−0.716955	+	0.552779i
$59$	−6.33745	−	13.8771i	−0.825066	−	1.80664i	−0.519493	−	0.854474i	$-0.673879\pi$
$59$	−6.33745	−	13.8771i	−0.825066	−	1.80664i	−0.305573	−	0.952169i	$-0.598848\pi$
$60$	6.40734	−	1.10796i	0.827184	−	0.143037i
$61$	−3.23927	+	3.73831i	−0.414746	+	0.478642i	−0.924229	−	0.381838i	$-0.875291\pi$
$61$	−3.23927	+	3.73831i	−0.414746	+	0.478642i	0.509483	+	0.860480i	$0.329837\pi$
$62$	−0.0663530	−	0.117514i	−0.00842684	−	0.0149243i
$63$	2.89818	+	1.86255i	0.365136	+	0.234659i
$64$	−3.73616	+	7.07398i	−0.467019	+	0.884247i
$65$	1.17947	+	1.83529i	0.146295	+	0.227640i
$66$	0.149051	−	0.0127920i	0.0183469	−	0.00157459i
$67$	3.45689	+	11.7731i	0.422326	+	1.43831i	0.846334	+	0.532653i	$0.178805\pi$
$67$	3.45689	+	11.7731i	0.422326	+	1.43831i	−0.424008	+	0.905659i	$0.639377\pi$
$68$	2.10507	−	0.683670i	0.255277	−	0.0829072i
$69$	1.61416	−	4.51603i	0.194322	−	0.543666i
$70$	−12.8143	−	9.31145i	−1.53160	−	1.11293i
$71$	−2.59002	−	8.82078i	−0.307378	−	1.04683i	−0.957842	−	0.287297i	$-0.907243\pi$
$71$	−2.59002	−	8.82078i	−0.307378	−	1.04683i	0.650463	−	0.759538i	$-0.274575\pi$
$72$	−2.60555	+	1.10050i	−0.307067	+	0.129696i
$73$	−1.31153	+	0.842871i	−0.153503	+	0.0986506i	−0.615138	−	0.788420i	$-0.710900\pi$
$73$	−1.31153	+	0.842871i	−0.153503	+	0.0986506i	0.461634	+	0.887070i	$0.347263\pi$
$74$	−4.45276	+	8.43755i	−0.517622	+	0.980846i
$75$	−4.68611	−	3.01158i	−0.541106	−	0.347748i
$76$	−1.07493	+	9.35752i	−0.123303	+	1.07338i
$77$	−0.275416	−	0.238650i	−0.0313866	−	0.0271966i
$78$	−0.680485	−	0.661410i	−0.0770497	−	0.0748900i
$79$	−5.50717	−	12.0590i	−0.619605	−	1.35675i	−0.915806	−	0.401620i	$-0.868447\pi$
$79$	−5.50717	−	12.0590i	−0.619605	−	1.35675i	0.296201	−	0.955126i	$-0.404280\pi$
$80$	12.2497	−	4.36702i	1.36956	−	0.488248i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−0.684172	+	3.37537i	−0.0755541	+	0.372747i
$83$	−15.2686	−	2.19529i	−1.67594	−	0.240964i	−0.762224	−	0.647313i	$-0.775893\pi$
$83$	−15.2686	−	2.19529i	−1.67594	−	0.240964i	−0.913718	+	0.406349i	$0.866802\pi$
$84$	6.34632	+	2.68297i	0.692440	+	0.292736i
$85$	−3.27283	−	1.49465i	−0.354988	−	0.162118i
$86$	2.85052	−	1.10959i	0.307380	−	0.119650i
$87$	−4.82563	+	0.693821i	−0.517362	+	0.0743854i
$88$	0.289383	−	0.0760040i	0.0308484	−	0.00810205i
$89$	11.9248	−	10.3329i	1.26403	−	1.09529i	0.272945	−	0.962030i	$-0.412002\pi$
$89$	11.9248	−	10.3329i	1.26403	−	1.09529i	0.991082	−	0.133256i	$-0.0425432\pi$
$90$	4.33041	+	1.54541i	0.456466	+	0.162901i
$91$			2.31170i			0.242332i
$92$	1.64212	−	9.45005i	0.171203	−	0.985236i
$93$		−	0.0954262i		−	0.00989523i
$94$	−3.89292	+	10.9084i	−0.401524	+	1.12511i
$95$	11.5718	−	10.0270i	1.18724	−	1.02875i
$96$	−4.75986	+	3.05675i	−0.485801	+	0.311978i
$97$	8.96312	−	1.28870i	0.910067	−	0.130848i	0.328648	−	0.944452i	$-0.393407\pi$
$97$	8.96312	−	1.28870i	0.910067	−	0.130848i	0.581419	+	0.813605i	$0.302498\pi$
$98$	−2.49755	−	6.41616i	−0.252290	−	0.648130i
$99$	0.0962231	+	0.0439436i	0.00967078	+	0.00441650i
$100$	−10.2615	−	4.33814i	−1.02615	−	0.433814i
$101$	18.8396	+	2.70872i	1.87461	+	0.269528i	0.983045	−	0.183365i	$-0.0586990\pi$
$101$	18.8396	+	2.70872i	1.87461	+	0.269528i	0.891565	+	0.452893i	$0.149608\pi$
$102$	1.53385	+	0.310905i	0.151874	+	0.0307842i
$103$	−0.453320	−	0.133107i	−0.0446670	−	0.0131154i	0.259323	−	0.965791i	$-0.416501\pi$
$103$	−0.453320	−	0.133107i	−0.0446670	−	0.0131154i	−0.303990	+	0.952675i	$0.598319\pi$
$104$	−1.56647	−	1.07158i	−0.153605	−	0.105077i
$105$	−4.65292	−	10.1885i	−0.454079	−	0.994294i
$106$	−6.74424	+	6.93874i	−0.655058	+	0.673950i
$107$	−4.64627	−	4.02601i	−0.449172	−	0.389209i	0.400691	−	0.916213i	$-0.368770\pi$
$107$	−4.64627	−	4.02601i	−0.449172	−	0.389209i	−0.849863	+	0.527004i	$0.823315\pi$
$108$	−1.98693	−	0.228246i	−0.191193	−	0.0219630i
$109$	−5.58070	−	3.58650i	−0.534534	−	0.343524i	0.245364	−	0.969431i	$-0.421093\pi$
$109$	−5.58070	−	3.58650i	−0.534534	−	0.343524i	−0.779898	+	0.625907i	$0.784729\pi$
$110$	−0.430154	−	0.227005i	−0.0410136	−	0.0216441i
$111$	−5.67517	+	3.64721i	−0.538663	+	0.346178i
$112$	13.4213	+	3.12475i	1.26820	+	0.295261i
$113$	−4.27392	−	14.5556i	−0.402057	−	1.36928i	−0.873260	−	0.487255i	$-0.837998\pi$
$113$	−4.27392	−	14.5556i	−0.402057	−	1.36928i	0.471203	−	0.882025i	$-0.343820\pi$
$114$	−3.91517	+	5.38802i	−0.366690	+	0.504635i
$115$	−12.3529	+	9.51450i	−1.15191	+	0.887231i
$116$	−9.27368	+	3.01184i	−0.861040	+	0.279642i
$117$	−0.189047	−	0.643835i	−0.0174774	−	0.0595225i
$118$	−1.84484	−	21.4958i	−0.169831	−	1.97885i
$119$	−2.06119	−	3.20728i	−0.188949	−	0.294011i
$120$	9.06083	+	1.56990i	0.827137	+	0.143311i
$121$	9.24438	+	5.94100i	0.840398	+	0.540091i
$122$	−6.09145	+	3.43947i	−0.551494	+	0.311395i
$123$	−1.59477	+	1.84046i	−0.143796	+	0.165949i
$124$	−0.0325196	−	0.188061i	−0.00292035	−	0.0168884i
$125$	0.770377	+	1.68689i	0.0689046	+	0.150880i
$126$	2.97486	+	3.85840i	0.265022	+	0.343733i
$127$	−0.661229	+	2.25194i	−0.0586746	+	0.199827i	−0.983614	−	0.180287i	$-0.942297\pi$
$127$	−0.661229	+	2.25194i	−0.0586746	+	0.199827i	0.924939	+	0.380115i	$0.124115\pi$
$128$	−8.33883	+	7.64617i	−0.737055	+	0.675833i
$129$	2.14093	+	0.307819i	0.188498	+	0.0271020i
$130$	0.698604	+	3.00514i	0.0612716	+	0.263568i
$131$	−0.519254	+	1.13701i	−0.0453674	+	0.0993408i	−0.930959	−	0.365125i	$-0.881026\pi$
$131$	−0.519254	+	1.13701i	−0.0453674	+	0.0993408i	0.885591	+	0.464466i	$0.153754\pi$
$132$	0.204607	+	0.0538108i	0.0178088	+	0.00468363i
$133$	16.0595	−	2.30901i	1.39254	−	0.200217i
$134$	−0.991786	+	17.3242i	−0.0856773	+	1.49658i
$135$	2.12909	+	2.45710i	0.183243	+	0.211474i
$136$	3.12880	+	0.0900058i	0.268292	+	0.00771794i
$137$			11.9394i			1.02005i	0.860159	+	0.510025i	$0.170364\pi$
$137$			11.9394i			1.02005i	−0.860159	+	0.510025i	$0.829636\pi$
$138$	4.29658	−	5.24780i	0.365749	−	0.446722i
$139$	17.9863			1.52558			0.762789	−	0.646648i	$-0.223830\pi$
$139$	17.9863			1.52558			0.762789	+	0.646648i	$0.223830\pi$
$140$	−12.6418	−	18.4933i	−1.06843	−	1.56297i
$141$	−6.18949	+	5.36322i	−0.521249	+	0.451665i
$142$	0.743079	−	12.9799i	0.0623578	−	1.08925i
$143$	0.0101017	+	0.0702592i	0.000844750	+	0.00587537i
$144$	−3.99354	+	0.227295i	−0.332795	+	0.0189413i
$145$	14.4181	+	6.58453i	1.19736	+	0.546816i
$146$	−2.14753	+	0.499236i	−0.177731	+	0.0413170i
$147$	0.692862	−	4.81896i	0.0571463	−	0.397461i
$148$	−9.94145	+	9.12175i	−0.817182	+	0.749803i
$149$	−9.44712	−	2.77392i	−0.773938	−	0.227249i	−0.129165	−	0.991623i	$-0.541230\pi$
$149$	−9.44712	−	2.77392i	−0.773938	−	0.227249i	−0.644773	+	0.764374i	$0.723048\pi$
$150$	−4.81010	−	6.23871i	−0.392743	−	0.509389i
$151$	−5.97412	+	2.72829i	−0.486167	+	0.222025i	−0.643391	−	0.765538i	$-0.722473\pi$
$151$	−5.97412	+	2.72829i	−0.486167	+	0.222025i	0.157224	+	0.987563i	$0.449746\pi$
$152$	−5.87969	+	11.9527i	−0.476906	+	0.969491i
$153$	0.836353	+	0.724704i	0.0676152	+	0.0585889i
$154$	−0.253399	−	0.448781i	−0.0204195	−	0.0361638i
$155$	−0.167734	+	0.261000i	−0.0134727	+	0.0209640i
$156$	−0.591973	−	1.20442i	−0.0473957	−	0.0964304i
$157$	3.74675	−	2.40789i	0.299023	−	0.192171i	−0.382522	−	0.923946i	$-0.624944\pi$
$157$	3.74675	−	2.40789i	0.299023	−	0.192171i	0.681546	+	0.731776i	$0.261308\pi$
$158$	−1.60314	−	18.6796i	−0.127539	−	1.48607i
$159$	−6.56502	+	1.92766i	−0.520640	+	0.152874i
$160$	18.3916	+	0.00610168i	1.45399	+	0.000482380i
$161$	−16.4622	+	1.40468i	−1.29740	+	0.110704i
$162$	−1.14407	−	0.831330i	−0.0898864	−	0.0653154i
$163$	−20.3084	+	5.96307i	−1.59067	+	0.467064i	−0.952932	−	0.303186i	$-0.901950\pi$
$163$	−20.3084	+	5.96307i	−1.59067	+	0.467064i	−0.637743	+	0.770250i	$0.720132\pi$
$164$	−2.51570	+	4.17057i	−0.196443	+	0.325667i
$165$	−0.185938	−	0.289325i	−0.0144752	−	0.0225239i
$166$	−19.2933	−	10.1817i	−1.49745	−	0.790250i
$167$	4.58653	−	7.13678i	0.354917	−	0.552261i	−0.617186	−	0.786817i	$-0.711727\pi$
$167$	4.58653	−	7.13678i	0.354917	−	0.552261i	0.972103	+	0.234556i	$0.0753637\pi$
$168$	7.17759	+	6.59017i	0.553763	+	0.508442i
$169$	−8.21833	+	9.48446i	−0.632179	+	0.729574i
$170$	−3.64874	−	3.54647i	−0.279846	−	0.272002i
$171$	−4.28394	+	1.95641i	−0.327601	+	0.149610i
$172$	4.32414	−	0.122956i	0.329713	−	0.00937534i
$173$	−6.58548	+	22.4281i	−0.500685	+	1.70518i	0.189795	+	0.981824i	$0.439218\pi$
$173$	−6.58548	+	22.4281i	−0.500685	+	1.70518i	−0.690480	+	0.723352i	$0.742600\pi$
$174$	−6.75724	−	1.36966i	−0.512265	−	0.103834i
$175$	−2.73108	+	18.9951i	−0.206450	+	1.43589i
$176$	0.421568	+	0.0363212i	0.0317769	+	0.00273781i
$177$	6.33745	−	13.8771i	0.476352	−	1.04307i
$178$	20.7947	−	8.09452i	1.55863	−	0.606710i
$179$	1.32853	+	9.24014i	0.0992991	+	0.690640i	0.977281	+	0.211947i	$0.0679804\pi$
$179$	1.32853	+	9.24014i	0.0992991	+	0.690640i	−0.877982	+	0.478693i	$0.841111\pi$
$180$	5.03325	+	4.11679i	0.375157	+	0.306847i
$181$	13.0027	+	15.0059i	0.966480	+	1.11538i	0.993280	+	0.115737i	$0.0369230\pi$
$181$	13.0027	+	15.0059i	0.966480	+	1.11538i	−0.0267994	+	0.999641i	$0.508532\pi$
$182$	−1.09883	+	3.07903i	−0.0814505	+	0.228233i
$183$	−4.94650			−0.365656
$184$	6.67913	−	11.8063i	0.492392	−	0.870373i
$185$	21.9330			1.61254
$186$	0.0453593	−	0.127102i	0.00332591	−	0.00931955i
$187$	−0.0766610	−	0.0884715i	−0.00560601	−	0.00646967i
$188$	−10.3703	+	12.6789i	−0.756329	+	0.924701i
$189$	0.490285	+	3.41001i	0.0356630	+	0.248041i
$190$	20.1791	−	7.85490i	1.46395	−	0.569854i
$191$	7.70256	−	16.8663i	0.557338	−	1.22040i	−0.395932	−	0.918280i	$-0.629578\pi$
$191$	7.70256	−	16.8663i	0.557338	−	1.22040i	0.953270	−	0.302120i	$-0.0976944\pi$
$192$	−7.79282	+	1.80887i	−0.562398	+	0.130544i
$193$	1.88981	−	13.1439i	0.136032	−	0.946122i	−0.801444	−	0.598070i	$-0.795934\pi$
$193$	1.88981	−	13.1439i	0.136032	−	0.946122i	0.937475	−	0.348052i	$-0.113157\pi$
$194$	12.5509	+	2.54400i	0.901101	+	0.182649i
$195$	−0.614632	+	2.09324i	−0.0440147	+	0.149900i
$196$	−0.276759	−	9.73309i	−0.0197685	−	0.695221i
$197$	−15.4327	+	7.04789i	−1.09954	+	0.502142i	−0.880726	−	0.473626i	$-0.842945\pi$
$197$	−15.4327	+	7.04789i	−1.09954	+	0.502142i	−0.218811	+	0.975767i	$0.570218\pi$
$198$	0.107275	+	0.104268i	0.00762372	+	0.00741002i
$199$	4.69281	−	5.41579i	0.332664	−	0.383915i	−0.564633	−	0.825342i	$-0.690982\pi$
$199$	4.69281	−	5.41579i	0.332664	−	0.383915i	0.897297	+	0.441427i	$0.145528\pi$
$200$	−11.6056	−	10.6558i	−0.820638	−	0.753476i
$201$	−6.63372	+	10.3223i	−0.467907	+	0.728077i
$202$	23.8056	+	12.5630i	1.67496	+	0.883926i
$203$	9.08038	+	14.1294i	0.637318	+	0.991686i
$204$	1.89521	+	1.14320i	0.132691	+	0.0800399i
$205$	7.59691	−	2.23065i	0.530591	−	0.155796i
$206$	−0.540524	−	0.392769i	−0.0376601	−	0.0273655i
$207$	4.47003	−	1.73747i	0.310689	−	0.120762i
$208$	−1.57708	−	2.17187i	−0.109351	−	0.150592i
$209$	0.478006	−	0.140355i	0.0330643	−	0.00970857i
$210$	−1.35447	−	15.7821i	−0.0934675	−	1.08907i
$211$	−0.102711	+	0.0660086i	−0.00707094	+	0.00454422i	−0.544172	−	0.838974i	$-0.683156\pi$
$211$	−0.102711	+	0.0660086i	−0.00707094	+	0.00454422i	0.537101	+	0.843518i	$0.319520\pi$
$212$	−12.2811	+	6.03620i	−0.843471	+	0.414568i
$213$	4.97020	−	7.73379i	0.340553	−	0.529910i
$214$	−4.27484	−	7.57093i	−0.292222	−	0.517538i
$215$	−5.31458	−	4.60511i	−0.362451	−	0.314066i
$216$	−2.53798	−	1.24847i	−0.172688	−	0.0849474i
$217$	−0.299041	+	0.136568i	−0.0203003	+	0.00927082i
$218$	−5.72835	−	7.42968i	−0.387973	−	0.503202i
$219$	−1.49587	−	0.439228i	−0.101082	−	0.0296802i
$220$	−0.465035	−	0.506824i	−0.0313526	−	0.0341700i
$221$	−0.105680	+	0.735024i	−0.00710883	+	0.0494430i
$222$	−9.29261	+	2.16025i	−0.623679	+	0.144987i
$223$	11.7191	+	5.35195i	0.784772	+	0.358393i	0.767163	−	0.641452i	$-0.221668\pi$
$223$	11.7191	+	5.35195i	0.784772	+	0.358393i	0.0176084	+	0.999845i	$0.494395\pi$
$224$	16.3911	+	10.5416i	1.09517	+	0.704340i
$225$	−0.792750	−	5.51370i	−0.0528500	−	0.367580i
$226$	1.22619	−	21.4187i	0.0815652	−	1.42475i
$227$	21.2267	−	18.3930i	1.40886	−	1.22079i	0.467236	−	0.884133i	$-0.345250\pi$
$227$	21.2267	−	18.3930i	1.40886	−	1.22079i	0.941628	−	0.336655i	$-0.109296\pi$
$228$	−7.77588	+	5.31549i	−0.514970	+	0.352027i
$229$	−13.2720			−0.877042			−0.438521	−	0.898721i	$-0.644497\pi$
$229$	−13.2720			−0.877042			−0.438521	+	0.898721i	$0.644497\pi$
$230$	−20.9758	+	6.80097i	−1.38310	+	0.448443i
$231$		−	0.364428i		−	0.0239776i
$232$	−13.7836	−	0.396512i	−0.904937	−	0.0260323i
$233$	−0.740903	−	0.855047i	−0.0485381	−	0.0560160i	0.730961	−	0.682419i	$-0.239072\pi$
$233$	−0.740903	−	0.855047i	−0.0485381	−	0.0560160i	−0.779499	+	0.626403i	$0.784527\pi$
$234$	0.0542378	−	0.947408i	0.00354564	−	0.0619340i
$235$	26.3560	−	3.78942i	1.71928	−	0.247194i
$236$	7.76048	−	29.5080i	0.505164	−	1.92081i
$237$	5.50717	−	12.0590i	0.357729	−	0.783317i
$238$	−1.22085	−	5.25165i	−0.0791361	−	0.340414i
$239$	−2.49185	−	0.358274i	−0.161184	−	0.0231748i	0.0612501	−	0.998122i	$-0.480491\pi$
$239$	−2.49185	−	0.358274i	−0.161184	−	0.0231748i	−0.222435	+	0.974948i	$0.571400\pi$
$240$	11.3222	+	6.39792i	0.730847	+	0.412984i
$241$	−2.28900	+	7.79562i	−0.147448	+	0.502160i	−0.999783	−	0.0208354i	$-0.993367\pi$
$241$	−2.28900	+	7.79562i	−0.147448	+	0.502160i	0.852335	+	0.522996i	$0.175186\pi$
$242$	9.48897	+	12.3072i	0.609974	+	0.791137i
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$	−9.74833	+	1.68568i	−0.624073	+	0.107915i
$245$	−10.3655	+	11.9624i	−0.662229	+	0.764253i
$246$	−2.99897	+	1.69333i	−0.191207	+	0.107963i
$247$	−2.65850	−	1.70852i	−0.169156	−	0.108710i
$248$	0.0460779	−	0.265944i	0.00292595	−	0.0168874i
$249$	−8.33969	−	12.9768i	−0.528507	−	0.822372i
$250$	0.224258	+	2.61302i	0.0141833	+	0.165262i
$251$	−2.51440	−	8.56326i	−0.158707	−	0.540508i	0.841293	−	0.540580i	$-0.181795\pi$
$251$	−2.51440	−	8.56326i	−0.158707	−	0.540508i	−1.00000		7.21133e-5i	$0.999977\pi$
$252$	2.12830	+	6.55320i	0.134070	+	0.412813i
$253$	−0.494195	+	0.114629i	−0.0310697	+	0.00720668i
$254$	−1.95114	+	2.68514i	−0.122425	+	0.168480i
$255$	−1.01367	−	3.45223i	−0.0634782	−	0.216187i
$256$	−14.7413	+	6.22050i	−0.921330	+	0.388781i
$257$	−1.07112	+	0.688367i	−0.0668146	+	0.0429391i	−0.573622	−	0.819120i	$-0.694462\pi$
$257$	−1.07112	+	0.688367i	−0.0668146	+	0.0429391i	0.506807	+	0.862060i	$0.330826\pi$
$258$	2.70527	+	1.42765i	0.168423	+	0.0888817i
$259$	19.5514	+	12.5649i	1.21486	+	0.780745i
$260$	−0.497946	+	4.33472i	−0.0308813	+	0.268828i
$261$	−3.68447	−	3.19261i	−0.228063	−	0.197618i
$262$	−1.23207	+	1.26760i	−0.0761177	+	0.0783128i
$263$	−2.32810	−	5.09783i	−0.143557	−	0.314346i	0.824172	−	0.566340i	$-0.191641\pi$
$263$	−2.32810	−	5.09783i	−0.143557	−	0.314346i	−0.967729	+	0.251994i	$0.918914\pi$
$264$	0.246946	+	0.168929i	0.0151985	+	0.0103969i
$265$	21.3443	+	6.26725i	1.31117	+	0.384994i
$266$	22.4878	+	4.55818i	1.37882	+	0.279480i
$267$	15.6182	+	2.24555i	0.955817	+	0.137426i
$268$	−9.55577	+	22.6033i	−0.583712	+	1.38072i
$269$	7.49425	+	3.42251i	0.456932	+	0.208674i	0.630565	−	0.776136i	$-0.282823\pi$
$269$	7.49425	+	3.42251i	0.456932	+	0.208674i	−0.173633	+	0.984811i	$0.555551\pi$
$270$	1.66787	+	4.28474i	0.101504	+	0.260761i
$271$	−15.0886	+	2.16941i	−0.916566	+	0.131782i	−0.584425	−	0.811447i	$-0.698680\pi$
$271$	−15.0886	+	2.16941i	−0.916566	+	0.131782i	−0.332141	+	0.943230i	$0.607771\pi$
$272$	4.12458	+	1.60711i	0.250089	+	0.0974451i
$273$	−1.74706	+	1.51384i	−0.105737	+	0.0916217i
$274$	−5.67519	+	15.9025i	−0.342851	+	0.960706i
$275$			0.589250i			0.0355331i
$276$	8.21723	−	4.94743i	0.494619	−	0.297801i
$277$			1.21009i			0.0727071i	0.999339	+	0.0363536i	$0.0115742\pi$
$277$			1.21009i			0.0727071i	−0.999339	+	0.0363536i	$0.988426\pi$
$278$	23.9566	+	8.54950i	1.43682	+	0.512765i
$279$	0.0721183	−	0.0624909i	0.00431761	−	0.00374123i
$280$	−8.04760	−	30.6411i	−0.480936	−	1.83115i
$281$	−10.0984	+	1.45193i	−0.602418	+	0.0866147i	−0.436775	−	0.899571i	$-0.643879\pi$
$281$	−10.0984	+	1.45193i	−0.602418	+	0.0866147i	−0.165644	+	0.986186i	$0.552970\pi$
$282$	−10.7933	+	4.20140i	−0.642734	+	0.250190i
$283$	−2.20786	−	1.00830i	−0.131244	−	0.0599370i	0.348711	−	0.937230i	$-0.386620\pi$
$283$	−2.20786	−	1.00830i	−0.131244	−	0.0599370i	−0.479955	+	0.877293i	$0.659347\pi$
$284$	7.15950	−	16.9351i	0.424838	−	1.00492i
$285$	15.1558	+	2.17908i	0.897755	+	0.129078i
$286$	−0.0199417	+	0.0983825i	−0.00117918	+	0.00581748i
$287$	8.04988	+	2.36366i	0.475169	+	0.139522i
$288$	−5.42718	−	1.59552i	−0.319800	−	0.0940170i
$289$	6.55330	+	14.3497i	0.385488	+	0.844102i
$290$	16.0742	+	15.6236i	0.943908	+	0.917450i
$291$	6.84353	+	5.92995i	0.401175	+	0.347620i
$292$	−3.09767	−	0.355842i	−0.181278	−	0.0208241i
$293$	−0.520259	−	0.334350i	−0.0303938	−	0.0195329i	0.525356	−	0.850883i	$-0.323932\pi$
$293$	−0.520259	−	0.334350i	−0.0303938	−	0.0195329i	−0.555750	+	0.831350i	$0.687569\pi$
$294$	3.21346	−	6.08921i	0.187413	−	0.355130i
$295$	−41.7258	+	26.8156i	−2.42937	+	1.56126i
$296$	−17.5773	+	7.42409i	−1.02166	+	0.431517i
$297$	0.0298024	+	0.101497i	0.00172931	+	0.00588948i
$298$	−11.2644	−	8.18523i	−0.652531	−	0.474158i
$299$	2.60242	+	1.89299i	0.150502	+	0.109475i
$300$	−3.44129	−	10.5960i	−0.198683	−	0.611759i
$301$	−2.09933	−	7.14966i	−0.121003	−	0.412100i
$302$	−9.25400	+	0.794208i	−0.532508	+	0.0457015i
$303$	10.2902	+	16.0119i	0.591156	+	0.919857i
$304$	−13.5129	+	13.1254i	−0.775018	+	0.752794i
$305$	13.5291	+	8.69465i	0.774677	+	0.497854i
$306$	0.769494	+	1.36281i	0.0439890	+	0.0779065i
$307$	9.31105	−	10.7455i	0.531410	−	0.613279i	−0.425041	−	0.905174i	$-0.639740\pi$
$307$	9.31105	−	10.7455i	0.531410	−	0.613279i	0.956450	+	0.291895i	$0.0942857\pi$
$308$	−0.124191	−	0.718197i	−0.00707643	−	0.0409231i
$309$	−0.196266	−	0.429763i	−0.0111652	−	0.0244484i
$310$	−0.347474	+	0.267905i	−0.0197352	+	0.0152160i
$311$	3.78112	−	12.8773i	0.214407	−	0.730205i	−0.780111	−	0.625641i	$-0.784837\pi$
$311$	3.78112	−	12.8773i	0.214407	−	0.730205i	0.994518	−	0.104563i	$-0.0333445\pi$
$312$	−0.215971	−	1.88559i	−0.0122270	−	0.106751i
$313$	−4.83138	−	0.694648i	−0.273086	−	0.0392638i	0.00441126	−	0.999990i	$-0.498596\pi$
$313$	−4.83138	−	0.694648i	−0.273086	−	0.0392638i	−0.277497	+	0.960726i	$0.589505\pi$
$314$	6.13499	−	1.42620i	0.346218	−	0.0804852i
$315$	4.65292	−	10.1885i	0.262163	−	0.574056i
$316$	6.74376	−	25.6421i	0.379366	−	1.44248i
$317$	−8.18367	+	1.17663i	−0.459641	+	0.0660864i	−0.368246	−	0.929728i	$-0.620042\pi$
$317$	−8.18367	+	1.17663i	−0.459641	+	0.0660864i	−0.0913948	+	0.995815i	$0.529133\pi$
$318$	−9.66048	−	0.553049i	−0.541733	−	0.0310135i
$319$	0.337722	+	0.389752i	0.0189088	+	0.0218219i
$320$	24.4936	+	8.75030i	1.36924	+	0.489157i
$321$		−	6.14789i		−	0.343142i
$322$	−22.5943	−	5.95408i	−1.25913	−	0.331808i
$323$	5.21182			0.289994
$324$	−1.12867	−	1.65109i	−0.0627037	−	0.0917274i
$325$	2.82486	−	2.44775i	0.156695	−	0.135777i
$326$	−29.8839	−	1.71081i	−1.65512	−	0.0947532i
$327$	−0.944086	−	6.56626i	−0.0522081	−	0.363115i
$328$	−5.33317	+	4.35914i	−0.294475	+	0.240693i
$329$	25.6650	+	11.7208i	1.41496	+	0.646189i
$330$	−0.110132	−	0.473745i	−0.00606255	−	0.0260788i
$331$	3.88772	−	27.0397i	0.213688	−	1.48624i	−0.547008	−	0.837128i	$-0.684233\pi$
$331$	3.88772	−	27.0397i	0.213688	−	1.48624i	0.760696	−	0.649108i	$-0.224858\pi$
$332$	−20.8578	−	22.7321i	−1.14472	−	1.24758i
$333$	−6.47282	−	1.90059i	−0.354709	−	0.104152i
$334$	9.50133	−	7.32562i	0.519890	−	0.400840i
$335$	36.2877	−	16.5720i	1.98261	−	0.905428i
$336$	6.42757	+	12.1894i	0.350653	+	0.664989i
$337$	−4.57305	−	3.96257i	−0.249110	−	0.215855i	0.521351	−	0.853343i	$-0.325428\pi$
$337$	−4.57305	−	3.96257i	−0.249110	−	0.215855i	−0.770461	+	0.637487i	$0.779974\pi$
$338$	−15.4546	+	8.72626i	−0.840619	+	0.474646i
$339$	8.20159	−	12.7619i	0.445449	−	0.693133i
$340$	−3.17414	−	6.45805i	−0.172142	−	0.350237i
$341$	−0.00849196	+	0.00545745i	−0.000459865	+	0.000295538i
$342$	−6.63589	+	0.569513i	−0.358828	+	0.0307958i
$343$	7.04567	−	2.06880i	0.380431	−	0.111705i
$344$	5.81793	+	1.89164i	0.313682	+	0.101990i
$345$	−15.2800	−	3.10501i	−0.822647	−	0.167168i
$346$	−19.4323	+	26.7425i	−1.04469	+	1.43769i
$347$	28.3168	−	8.31455i	1.52012	−	0.446349i	0.588113	−	0.808779i	$-0.299871\pi$
$347$	28.3168	−	8.31455i	1.52012	−	0.446349i	0.932011	+	0.362430i	$0.118053\pi$
$348$	−8.34917	−	5.03625i	−0.447562	−	0.269971i
$349$	−4.02721	−	6.26645i	−0.215571	−	0.335436i	0.716580	−	0.697505i	$-0.245707\pi$
$349$	−4.02721	−	6.26645i	−0.215571	−	0.335436i	−0.932151	+	0.362070i	$0.882070\pi$
$350$	−12.6666	+	24.0021i	−0.677060	+	1.28297i
$351$	0.362778	−	0.564494i	0.0193637	−	0.0301305i
$352$	0.544237	+	0.248763i	0.0290080	+	0.0132591i
$353$	−19.1685	+	22.1216i	−1.02024	+	1.17741i	−0.0362179	+	0.999344i	$0.511531\pi$
$353$	−19.1685	+	22.1216i	−1.02024	+	1.17741i	−0.984018	+	0.178071i	$0.943014\pi$
$354$	15.0373	−	15.4710i	0.799226	−	0.822275i
$355$	−27.1880	+	12.4163i	−1.44299	+	0.658990i
$356$	31.5448	−	0.896973i	1.67187	−	0.0475395i
$357$	1.07411	−	3.65807i	0.0568477	−	0.193606i
$358$	−2.62263	+	12.9388i	−0.138610	+	0.683836i
$359$	−2.78692	+	19.3834i	−0.147088	+	1.02302i	0.773867	+	0.633348i	$0.218320\pi$
$359$	−2.78692	+	19.3834i	−0.147088	+	1.02302i	−0.920955	+	0.389670i	$0.872589\pi$
$360$	4.74713	+	7.87578i	0.250196	+	0.415090i
$361$	−1.32089	+	2.89234i	−0.0695205	+	0.152229i
$362$	10.1859	+	26.1675i	0.535361	+	1.37533i
$363$	1.56387	+	10.8770i	0.0820819	+	0.570892i
$364$	−2.92714	+	3.57877i	−0.153424	+	0.187579i
$365$	3.31930	+	3.83068i	0.173740	+	0.200507i
$366$	−6.58843	−	2.35124i	−0.344383	−	0.122901i
$367$	28.1273			1.46823			0.734117	−	0.679023i	$-0.237596\pi$
$367$	28.1273			1.46823			0.734117	+	0.679023i	$0.237596\pi$
$368$	14.5081	−	12.5505i	0.756289	−	0.654238i
$369$	−2.43528			−0.126776
$370$	29.2134	+	10.4255i	1.51873	+	0.541995i
$371$	15.4362	+	17.8144i	0.801410	+	0.924876i
$372$	0.120832	−	0.147731i	0.00626482	−	0.00765948i
$373$	−4.22177	−	29.3630i	−0.218595	−	1.52036i	−0.743231	−	0.669034i	$-0.766708\pi$
$373$	−4.22177	−	29.3630i	−0.218595	−	1.52036i	0.524636	−	0.851326i	$-0.324201\pi$
$374$	−0.0600541	−	0.154278i	−0.00310532	−	0.00797753i
$375$	−0.770377	+	1.68689i	−0.0397821	+	0.0871107i
$376$	−19.8392	+	11.9581i	−1.02313	+	0.616693i
$377$	0.465565	−	3.23807i	0.0239778	−	0.166769i
$378$	−0.967863	+	4.77496i	−0.0497815	+	0.245598i
$379$	6.59020	−	22.4442i	0.338516	−	1.15288i	−0.597778	−	0.801662i	$-0.703950\pi$
$379$	6.59020	−	22.4442i	0.338516	−	1.15288i	0.936294	−	0.351217i	$-0.114232\pi$
$380$	30.6110	−	0.870421i	1.57031	−	0.0446517i
$381$	−2.13491	+	0.974983i	−0.109375	+	0.0499499i
$382$	18.2764	−	18.8035i	0.935104	−	0.962072i
$383$	−14.6864	+	16.9490i	−0.750438	+	0.866051i	−0.994611	−	0.103681i	$-0.966938\pi$
$383$	−14.6864	+	16.9490i	−0.750438	+	0.866051i	0.244173	+	0.969732i	$0.421484\pi$
$384$	−11.2394	−	1.29489i	−0.573556	−	0.0660794i
$385$	−0.640569	+	0.996745i	−0.0326464	+	0.0507988i
$386$	8.76488	−	16.6086i	0.446121	−	0.845357i
$387$	1.16938	+	1.81958i	0.0594427	+	0.0924947i
$388$	15.5077	+	9.35431i	0.787286	+	0.474893i
$389$	30.1438	−	8.85103i	1.52835	−	0.448765i	0.593808	−	0.804607i	$-0.297624\pi$
$389$	30.1438	−	8.85103i	1.52835	−	0.448765i	0.934546	+	0.355842i	$0.115806\pi$
$390$	−1.81364	+	2.49592i	−0.0918373	+	0.126386i
$391$	−5.29850	−	0.305947i	−0.267957	−	0.0154724i
$392$	4.25784	−	13.0954i	0.215054	−	0.661419i
$393$	−1.19933	+	0.352156i	−0.0604983	+	0.0177639i
$394$	−23.9055	+	2.05165i	−1.20434	+	0.103361i
$395$	−36.2592	+	23.3024i	−1.82440	+	1.17247i
$396$	0.0933217	+	0.189870i	0.00468959	+	0.00954134i
$397$	11.3030	−	17.5878i	0.567280	−	0.882706i	−0.432541	−	0.901614i	$-0.642383\pi$
$397$	11.3030	−	17.5878i	0.567280	−	0.882706i	0.999821	+	0.0189088i	$0.00601921\pi$
$398$	8.82483	−	4.98284i	0.442349	−	0.249767i
$399$	12.2618	+	10.6249i	0.613857	+	0.531910i
$400$	−10.3929	−	19.7093i	−0.519643	−	0.985466i
$401$	20.7736	−	9.48697i	1.03738	−	0.473757i	0.177431	−	0.984133i	$-0.443221\pi$
$401$	20.7736	−	9.48697i	1.03738	−	0.473757i	0.859951	+	0.510377i	$0.170494\pi$
$402$	−13.7422	+	10.5954i	−0.685400	+	0.528450i
$403$	0.0614387	+	0.0180400i	0.00306048	+	0.000898638i
$404$	25.7360	+	28.0487i	1.28041	+	1.39547i
$405$	−0.462696	+	3.21812i	−0.0229916	+	0.159910i
$406$	5.37834	+	23.1356i	0.266923	+	1.14820i
$407$	0.649129	+	0.296447i	0.0321761	+	0.0146944i
$408$	1.98090	+	2.42353i	0.0980693	+	0.119982i
$409$	−4.21660	−	29.3271i	−0.208497	−	1.45013i	−0.778064	−	0.628185i	$-0.783798\pi$
$409$	−4.21660	−	29.3271i	−0.208497	−	1.45013i	0.569567	−	0.821945i	$-0.307111\pi$
$410$	11.1789	+	0.639977i	0.552087	+	0.0316062i
$411$	−9.02318	+	7.81863i	−0.445081	+	0.385665i
$412$	−0.533248	−	0.780073i	−0.0262712	−	0.0384314i
$413$	−52.5570			−2.58616
$414$	6.77968	−	0.189442i	0.333203	−	0.00931055i
$415$			50.1518i			2.46186i
$416$	−1.06820	−	3.64243i	−0.0523729	−	0.178585i
$417$	11.7785	+	13.5931i	0.576796	+	0.665659i
$418$	0.703389	+	0.0402681i	0.0344039	+	0.00196958i
$419$	−7.17754	+	1.03198i	−0.350646	+	0.0504153i	−0.315388	−	0.948963i	$-0.602135\pi$
$419$	−7.17754	+	1.03198i	−0.350646	+	0.0504153i	−0.0352584	+	0.999378i	$0.511225\pi$
$420$	5.69770	−	21.6646i	0.278019	−	1.05713i
$421$	7.47958	−	16.3780i	0.364532	−	0.798214i	−0.635135	−	0.772402i	$-0.719055\pi$
$421$	7.47958	−	16.3780i	0.364532	−	0.798214i	0.999667	−	0.0258128i	$-0.00821737\pi$
$422$	−0.168181	+	0.0390971i	−0.00818694	+	0.00190322i
$423$	−8.10651	−	1.16554i	−0.394152	−	0.0566705i
$424$	−19.2269	+	2.20220i	−0.933741	+	0.106948i
$425$	−1.73674	+	5.91479i	−0.0842443	+	0.286910i
$426$	10.2961	−	7.93841i	0.498849	−	0.384617i
$427$	7.07910	+	15.5011i	0.342582	+	0.750150i
$428$	−2.09510	−	12.1160i	−0.101270	−	0.585648i
$429$	−0.0464831	+	0.0536443i	−0.00224422	+	0.00258997i
$430$	−4.88972	−	8.65992i	−0.235803	−	0.417618i
$431$	29.8892	+	19.2086i	1.43971	+	0.925248i	0.999628	+	0.0272918i	$0.00868832\pi$
$431$	29.8892	+	19.2086i	1.43971	+	0.925248i	0.440086	+	0.897956i	$0.354948\pi$
$432$	−2.78699	−	2.86927i	−0.134089	−	0.138048i
$433$	−6.27023	−	9.75667i	−0.301328	−	0.468875i	0.657263	−	0.753661i	$-0.271714\pi$
$433$	−6.27023	−	9.75667i	−0.301328	−	0.468875i	−0.958591	+	0.284786i	$0.908078\pi$
$434$	−0.463220	+	0.0397550i	−0.0222353	+	0.00190830i
$435$	4.46560	+	15.2084i	0.214109	+	0.729189i
$436$	−4.09823	−	12.6188i	−0.196270	−	0.604329i
$437$	10.5514	−	19.9700i	0.504740	−	0.955296i
$438$	−1.78363	−	1.29606i	−0.0852250	−	0.0619282i
$439$	−3.47804	−	11.8451i	−0.165998	−	0.565337i	−0.999910	−	0.0134390i	$-0.995722\pi$
$439$	−3.47804	−	11.8451i	−0.165998	−	0.565337i	0.833912	−	0.551898i	$-0.186096\pi$
$440$	−0.378487	−	0.896104i	−0.0180436	−	0.0427201i
$441$	4.09565	−	2.63212i	0.195031	−	0.125339i
$442$	−0.490141	+	0.928772i	−0.0233136	+	0.0441772i
$443$	−28.9372	−	18.5968i	−1.37485	−	0.883562i	−0.375780	−	0.926709i	$-0.622625\pi$
$443$	−28.9372	−	18.5968i	−1.37485	−	0.883562i	−0.999069	+	0.0431468i	$0.986262\pi$
$444$	−13.4040	−	1.53977i	−0.636127	−	0.0730743i
$445$	−38.7701	−	33.5945i	−1.83788	−	1.59253i
$446$	13.0652	+	12.6990i	0.618655	+	0.601314i
$447$	−4.09016	−	8.95619i	−0.193458	−	0.423613i
$448$	16.8211	+	21.8320i	0.794723	+	1.03146i
$449$	3.61727	+	1.06213i	0.170709	+	0.0501248i	0.365970	−	0.930627i	$-0.380737\pi$
$449$	3.61727	+	1.06213i	0.170709	+	0.0501248i	−0.195261	+	0.980751i	$0.562555\pi$
$450$	1.56495	−	7.72072i	0.0737726	−	0.363958i
$451$	0.254988	+	0.0366617i	0.0120069	+	0.00172633i
$452$	11.8143	−	27.9456i	0.555696	−	1.31445i
$453$	−5.97412	−	2.72829i	−0.280688	−	0.128186i
$454$	37.0154	−	14.4086i	1.73722	−	0.676229i
$455$	7.43932	−	1.06961i	0.348761	−	0.0501442i
$456$	−12.8836	+	3.38377i	−0.603331	+	0.158459i
$457$	−27.0530	+	23.4416i	−1.26549	+	1.09655i	−0.274641	+	0.961547i	$0.588559\pi$
$457$	−27.0530	+	23.4416i	−1.26549	+	1.09655i	−0.990845	+	0.135003i	$0.956896\pi$
$458$	−17.6775	−	6.30866i	−0.826017	−	0.294784i
$459$			1.10665i			0.0516542i
$460$	−31.1712	−	0.912047i	−1.45337	−	0.0425244i
$461$		−	1.46696i		−	0.0683230i	−0.999416	−	0.0341615i	$-0.989124\pi$
$461$		−	1.46696i		−	0.0683230i	0.999416	−	0.0341615i	$-0.0108761\pi$
$462$	0.173225	−	0.485395i	0.00805916	−	0.0225826i
$463$	24.3753	−	21.1214i	1.13282	−	0.981593i	0.132864	−	0.991134i	$-0.457583\pi$
$463$	24.3753	−	21.1214i	1.13282	−	0.981593i	0.999954	+	0.00954138i	$0.00303716\pi$
$464$	−18.1704	−	7.07994i	−0.843540	−	0.328678i
$465$	−0.307093	+	0.0441533i	−0.0142411	+	0.00204756i
$466$	−0.580403	−	1.49105i	−0.0268866	−	0.0690714i
$467$	−19.6265	−	8.96312i	−0.908206	−	0.414764i	−0.0941553	−	0.995558i	$-0.530015\pi$
$467$	−19.6265	−	8.96312i	−0.908206	−	0.414764i	−0.814051	+	0.580794i	$0.802742\pi$
$468$	0.522577	−	1.23611i	0.0241561	−	0.0571391i
$469$	41.8411	+	6.01585i	1.93204	+	0.277786i
$470$	36.9058	+	7.48063i	1.70234	+	0.345056i
$471$	4.27336	+	1.25477i	0.196906	+	0.0578169i
$472$	24.3626	−	35.6140i	1.12138	−	1.63927i
$473$	−0.0950476	−	0.208125i	−0.00437029	−	0.00956961i
$474$	13.0673	−	13.4441i	0.600199	−	0.617509i
$475$	−19.8263	−	17.1796i	−0.909693	−	0.788253i
$476$	0.870190	−	7.57519i	0.0398851	−	0.347208i
$477$	−5.75601	−	3.69916i	−0.263549	−	0.169373i
$478$	−3.14869	−	1.66166i	−0.144018	−	0.0760026i
$479$	−28.0485	+	18.0257i	−1.28157	+	0.823615i	−0.991081	−	0.133263i	$-0.957454\pi$
$479$	−28.0485	+	18.0257i	−1.28157	+	0.823615i	−0.290489	+	0.956878i	$0.593818\pi$
$480$	12.0394	+	13.9035i	0.549519	+	0.634604i
$481$	−1.27533	−	4.34336i	−0.0581499	−	0.198040i
$482$	−6.75433	+	9.29524i	−0.307651	+	0.423387i
$483$	−11.8420	−	11.5214i	−0.538830	−	0.524242i
$484$	6.78868	+	20.9029i	0.308577	+	0.950130i
$485$	−8.29440	−	28.2481i	−0.376629	−	1.28268i
$486$	−0.120928	−	1.40903i	−0.00548540	−	0.0639151i
$487$	−9.94289	−	15.4714i	−0.450555	−	0.701078i	0.539464	−	0.842009i	$-0.318627\pi$
$487$	−9.94289	−	15.4714i	−0.450555	−	0.701078i	−0.990019	+	0.140931i	$0.954990\pi$
$488$	−13.7854	−	2.38849i	−0.624037	−	0.108122i
$489$	−17.8057	−	11.4431i	−0.805204	−	0.517473i
$490$	−19.4924	+	11.0061i	−0.880576	+	0.497207i
$491$	−5.53544	+	6.38824i	−0.249811	+	0.288297i	−0.866781	−	0.498690i	$-0.833815\pi$
$491$	−5.53544	+	6.38824i	−0.249811	+	0.288297i	0.616970	+	0.786987i	$0.288360\pi$
$492$	−4.79934	+	0.829903i	−0.216371	+	0.0374149i
$493$	2.24125	+	4.90766i	0.100941	+	0.221030i
$494$	−2.72884	−	3.53931i	−0.122776	−	0.159241i
$495$	0.0968938	−	0.329990i	0.00435505	−	0.0148320i
$496$	0.187785	−	0.332318i	0.00843179	−	0.0149215i
$497$	−31.3488	−	4.50727i	−1.40618	−	0.202179i
$498$	−4.93963	−	21.2485i	−0.221350	−	0.952166i
$499$	5.33738	−	11.6872i	0.238934	−	0.523192i	−0.751738	−	0.659462i	$-0.770784\pi$
$499$	5.33738	−	11.6872i	0.238934	−	0.523192i	0.990672	+	0.136270i	$0.0435114\pi$
$500$	−0.943360	+	3.58698i	−0.0421883	+	0.160414i
$501$	8.39716	−	1.20733i	0.375158	−	0.0539395i
$502$	0.721385	−	12.6009i	0.0321970	−	0.562406i
$503$	14.7464	+	17.0183i	0.657510	+	0.758807i	0.982368	−	0.186956i	$-0.0598622\pi$
$503$	14.7464	+	17.0183i	0.657510	+	0.758807i	−0.324859	+	0.945763i	$0.605317\pi$
$504$	−0.280193	+	9.74010i	−0.0124808	+	0.433859i
$505$		−	61.8814i		−	2.75369i
$506$	−0.712724	−	0.0822285i	−0.0316844	−	0.00365550i
$507$	−12.5497			−0.557353
$508$	−3.87513	+	2.64899i	−0.171931	+	0.117530i
$509$	−2.45914	+	2.13086i	−0.109000	+	0.0944487i	−0.707656	−	0.706558i	$-0.750247\pi$
$509$	−2.45914	+	2.13086i	−0.109000	+	0.0944487i	0.598656	+	0.801006i	$0.295702\pi$
$510$	0.290822	−	5.07998i	0.0128778	−	0.224945i
$511$	0.764365	+	5.31628i	0.0338135	+	0.235178i
$512$	−22.5913	+	1.27828i	−0.998403	+	0.0564926i
$513$	−4.28394	−	1.95641i	−0.189141	−	0.0863776i
$514$	−1.75387	+	0.407722i	−0.0773598	+	0.0179838i
$515$	−0.218605	+	1.52043i	−0.00963287	+	0.0669981i
$516$	2.92464	+	3.18745i	0.128750	+	0.140320i
$517$	0.831251	+	0.244077i	0.0365584	+	0.0107345i
$518$	20.0687	+	26.0291i	0.881767	+	1.14365i
$519$	−21.2626	+	9.71030i	−0.933324	+	0.426235i
$520$	−2.72367	+	5.53689i	−0.119441	+	0.242809i
$521$	20.1672	+	17.4750i	0.883541	+	0.765592i	0.973099	−	0.230389i	$-0.0739999\pi$
$521$	20.1672	+	17.4750i	0.883541	+	0.765592i	−0.0895578	+	0.995982i	$0.528545\pi$
$522$	−3.38993	−	6.00371i	−0.148373	−	0.262775i
$523$	−14.3532	+	22.3340i	−0.627622	+	0.976599i	0.371223	+	0.928544i	$0.378939\pi$
$523$	−14.3532	+	22.3340i	−0.627622	+	0.976599i	−0.998845	+	0.0480550i	$0.984698\pi$
$524$	−2.24358	+	1.10272i	−0.0980112	+	0.0481727i
$525$	−16.1440	+	10.3751i	−0.704582	+	0.452807i
$526$	−0.677713	−	7.89661i	−0.0295497	−	0.344309i
$527$	−0.101326	+	0.0297520i	−0.00441383	+	0.00129602i
$528$	0.248619	+	0.342385i	0.0108197	+	0.0149004i
$529$	−11.8991	+	19.6828i	−0.517353	+	0.855772i
$530$	25.4502	+	18.4933i	1.10549	+	0.803296i
$531$	14.6378	−	4.29803i	0.635224	−	0.186519i
$532$	27.7857	+	16.7604i	1.20466	+	0.726657i
$533$	−0.883468	−	1.37470i	−0.0382672	−	0.0595450i
$534$	19.7350	+	10.4148i	0.854019	+	0.450692i
$535$	−10.8064	+	16.8151i	−0.467201	+	0.726979i
$536$	−23.4718	+	25.5640i	−1.01383	+	1.10420i
$537$	−6.11323	+	7.05504i	−0.263805	+	0.304448i
$538$	8.35504	+	8.12084i	0.360211	+	0.350114i
$539$	−0.468463	+	0.213940i	−0.0201781	+	0.00921505i
$540$	0.184821	+	6.49980i	0.00795344	+	0.279707i
$541$	−10.1713	+	34.6402i	−0.437297	+	1.48930i	0.386434	+	0.922317i	$0.373707\pi$
$541$	−10.1713	+	34.6402i	−0.437297	+	1.48930i	−0.823731	+	0.566980i	$0.808112\pi$
$542$	−21.1283	−	4.28260i	−0.907536	−	0.183953i
$543$	−2.82575	+	19.6535i	−0.121265	+	0.843413i
$544$	4.72977	+	4.10112i	0.202787	+	0.175834i
$545$	−8.95961	+	19.6188i	−0.383788	+	0.840378i
$546$	−3.04656	+	1.18590i	−0.130381	+	0.0507518i
$547$	−4.84370	−	33.6887i	−0.207102	−	1.44043i	−0.782550	−	0.622587i	$-0.786082\pi$
$547$	−4.84370	−	33.6887i	−0.207102	−	1.44043i	0.575449	−	0.817838i	$-0.304827\pi$
$548$	−15.1180	+	18.4835i	−0.645809	+	0.789578i
$549$	−3.23927	−	3.73831i	−0.138249	−	0.159547i
$550$	−0.280090	+	0.784844i	−0.0119431	+	0.0334659i
$551$	−22.9602			−0.978136
$552$	13.2965	−	2.68374i	0.565938	−	0.114228i
$553$	−45.6714			−1.94215
$554$	−0.575196	+	1.61176i	−0.0244377	+	0.0684772i
$555$	14.3630	+	16.5758i	0.609677	+	0.703605i
$556$	27.8449	+	22.7748i	1.18088	+	0.965866i
$557$	−2.01391	−	14.0070i	−0.0853320	−	0.593497i	−0.986958	−	0.160980i	$-0.948535\pi$
$557$	−2.01391	−	14.0070i	−0.0853320	−	0.593497i	0.901626	−	0.432517i	$-0.142374\pi$
$558$	0.125761	−	0.0489536i	0.00532389	−	0.00207237i
$559$	−0.602921	+	1.32021i	−0.0255008	+	0.0558390i
$560$	3.84584	−	44.6373i	0.162516	−	1.88627i
$561$	0.0166600	−	0.115873i	0.000703387	−	0.00489216i
$562$	−14.1405	−	2.86622i	−0.596483	−	0.120904i
$563$	2.69371	−	9.17395i	0.113527	−	0.386636i	−0.883053	−	0.469273i	$-0.844516\pi$
$563$	2.69371	−	9.17395i	0.113527	−	0.386636i	0.996580	+	0.0826371i	$0.0263342\pi$
$564$	−16.3731	+	0.465568i	−0.689433	+	0.0196039i
$565$	−44.8643	+	20.4888i	−1.88745	+	0.861972i
$566$	−2.46146	−	2.39246i	−0.103463	−	0.100563i
$567$	−2.25604	+	2.60361i	−0.0947448	+	0.109341i
$568$	17.5859	−	19.1534i	0.737886	−	0.803659i
$569$	−3.64544	+	5.67242i	−0.152825	+	0.237800i	−0.909221	−	0.416314i	$-0.863322\pi$
$569$	−3.64544	+	5.67242i	−0.152825	+	0.237800i	0.756396	+	0.654114i	$0.226958\pi$
$570$	19.1508	+	10.1065i	0.802141	+	0.423314i
$571$	1.48323	+	2.30795i	0.0620712	+	0.0965846i	0.870902	−	0.491457i	$-0.163535\pi$
$571$	1.48323	+	2.30795i	0.0620712	+	0.0965846i	−0.808831	+	0.588042i	$0.799899\pi$
$572$	−0.0733256	+	0.121560i	−0.00306590	+	0.00508270i
$573$	17.7908	−	5.22384i	0.743220	−	0.218229i
$574$	9.59841	+	6.97463i	0.400630	+	0.291115i
$575$	19.1475	+	18.6292i	0.798508	+	0.776889i
$576$	−6.47026	−	4.70486i	−0.269594	−	0.196036i
$577$	−7.91014	+	2.32263i	−0.329303	+	0.0966922i	−0.442205	−	0.896914i	$-0.645804\pi$
$577$	−7.91014	+	2.32263i	−0.329303	+	0.0966922i	0.112902	+	0.993606i	$0.463985\pi$
$578$	1.90768	+	22.2280i	0.0793488	+	0.924561i
$579$	11.1711	−	7.17923i	0.464255	−	0.298359i
$580$	13.9834	+	28.4503i	0.580628	+	1.18133i
$581$	−28.7308	+	44.7061i	−1.19196	+	1.85472i
$582$	6.29645	+	11.1513i	0.260996	+	0.462236i
$583$	0.546998	+	0.473977i	0.0226543	+	0.0196301i
$584$	−3.95677	−	1.94639i	−0.163732	−	0.0805421i
$585$	−1.98447	+	0.906276i	−0.0820476	+	0.0374699i
$586$	−0.534024	−	0.692630i	−0.0220603	−	0.0286123i
$587$	−3.88206	−	1.13988i	−0.160230	−	0.0470477i	0.200634	−	0.979666i	$-0.435700\pi$
$587$	−3.88206	−	1.13988i	−0.160230	−	0.0470477i	−0.360864	+	0.932619i	$0.617518\pi$
$588$	7.17454	−	6.58298i	0.295873	−	0.271478i
$589$	0.0639581	−	0.444838i	0.00263535	−	0.0183292i
$590$	−68.3226	+	15.8830i	−2.81280	+	0.653891i
$591$	−15.4327	−	7.04789i	−0.634818	−	0.289912i
$592$	−26.9407	+	1.53335i	−1.10726	+	0.0630205i
$593$	2.47242	+	17.1961i	0.101530	+	0.706157i	0.975471	+	0.220126i	$0.0706468\pi$
$593$	2.47242	+	17.1961i	0.101530	+	0.706157i	−0.873941	+	0.486031i	$0.838444\pi$
$594$	−0.00855034	+	0.149354i	−0.000350825	+	0.00612808i
$595$	−9.36771	+	8.11717i	−0.384039	+	0.332771i
$596$	−11.1128	−	16.2566i	−0.455198	−	0.665896i
$597$	7.16611			0.293289
$598$	2.56646	+	3.75837i	0.104950	+	0.153691i
$599$			12.2519i			0.500598i	0.968169	+	0.250299i	$0.0805290\pi$
$599$			12.2519i			0.500598i	−0.968169	+	0.250299i	$0.919471\pi$
$600$	0.453049	−	15.7489i	0.0184956	−	0.642948i
$601$	−30.9481	−	35.7160i	−1.26240	−	1.45689i	−0.832515	−	0.554003i	$-0.813100\pi$
$601$	−30.9481	−	35.7160i	−1.26240	−	1.45689i	−0.429884	−	0.902884i	$-0.641446\pi$
$602$	0.602301	−	10.5208i	0.0245479	−	0.428795i
$603$	−12.1452	+	1.74622i	−0.494591	+	0.0711115i
$604$	−12.7033	−	3.34090i	−0.516888	−	0.135939i
$605$	14.8415	−	32.4984i	0.603394	−	1.32125i
$606$	6.09492	+	26.2181i	0.247589	+	1.06504i
$607$	39.9660	+	5.74624i	1.62217	+	0.233233i	0.892658	−	0.450736i	$-0.148838\pi$
$607$	39.9660	+	5.74624i	1.62217	+	0.233233i	0.729512	+	0.683968i	$0.239747\pi$
$608$	−24.2373	+	11.0591i	−0.982952	+	0.448505i
$609$	−4.73187	+	16.1153i	−0.191745	+	0.653023i
$610$	13.8871	+	18.0116i	0.562273	+	0.729268i
$611$	−2.28293	−	4.99891i	−0.0923573	−	0.202234i
$612$	0.377129	+	2.18094i	0.0152445	+	0.0881593i
$613$	0.430587	−	0.496924i	0.0173912	−	0.0200706i	−0.746987	−	0.664838i	$-0.768500\pi$
$613$	0.430587	−	0.496924i	0.0173912	−	0.0200706i	0.764379	+	0.644768i	$0.223046\pi$
$614$	17.5094	−	9.88651i	0.706624	−	0.398987i
$615$	6.66073	+	4.28059i	0.268587	+	0.172610i
$616$	0.175969	−	1.01563i	0.00709000	−	0.0409207i
$617$	1.64652	+	2.56204i	0.0662865	+	0.103144i	0.872815	−	0.488052i	$-0.162292\pi$
$617$	1.64652	+	2.56204i	0.0662865	+	0.103144i	−0.806528	+	0.591196i	$0.798656\pi$
$618$	−0.0571333	−	0.665710i	−0.00229824	−	0.0267788i
$619$	7.21768	+	24.5812i	0.290103	+	0.988000i	0.967603	+	0.252477i	$0.0812453\pi$
$619$	7.21768	+	24.5812i	0.290103	+	0.988000i	−0.677500	+	0.735523i	$0.736937\pi$
$620$	−0.590158	+	0.191667i	−0.0237013	+	0.00769754i
$621$	4.24034	+	2.24043i	0.170159	+	0.0899052i
$622$	11.1572	−	15.3545i	0.447364	−	0.615658i
$623$	−15.3147	−	52.1571i	−0.613571	−	2.08963i
$624$	0.608625	−	2.61415i	0.0243645	−	0.104650i
$625$	−18.3584	+	11.7982i	−0.734336	+	0.471929i
$626$	−6.10491	−	3.22175i	−0.244001	−	0.128767i
$627$	0.419100	+	0.269339i	0.0167373	+	0.0107564i
$628$	8.84935	+	1.01656i	0.353127	+	0.0405651i
$629$	5.64211	+	4.88892i	0.224966	+	0.194934i
$630$	11.0403	−	11.3587i	0.439858	−	0.452543i
$631$	−17.0712	−	37.3807i	−0.679594	−	1.48810i	−0.863073	−	0.505079i	$-0.831463\pi$
$631$	−17.0712	−	37.3807i	−0.679594	−	1.48810i	0.183480	−	0.983023i	$-0.441264\pi$
$632$	21.1708	−	30.9481i	0.842130	−	1.23105i
$633$	−0.117148	−	0.0343976i	−0.00465620	−	0.00136718i
$634$	−11.4594	−	2.32277i	−0.455112	−	0.0922492i
$635$	7.55296	+	1.08595i	0.299730	+	0.0430947i
$636$	−12.6043	−	5.32858i	−0.499792	−	0.211292i
$637$	2.97163	+	1.35710i	0.117740	+	0.0537702i
$638$	0.264562	+	0.679657i	0.0104741	+	0.0269079i
$639$	9.09960	−	1.30832i	0.359974	−	0.0517565i
$640$	28.4647	+	23.2975i	1.12516	+	0.920915i
$641$	−31.4539	+	27.2550i	−1.24236	+	1.07651i	−0.248183	+	0.968713i	$0.579833\pi$
$641$	−31.4539	+	27.2550i	−1.24236	+	1.07651i	−0.994173	+	0.107795i	$0.965621\pi$
$642$	2.92230	−	8.18861i	0.115334	−	0.323179i
$643$		−	22.5959i		−	0.891095i	−0.895258	−	0.445547i	$-0.853009\pi$
$643$		−	22.5959i		−	0.891095i	0.895258	−	0.445547i	$-0.146991\pi$
$644$	−27.2640	−	18.6703i	−1.07435	−	0.735712i
$645$		−	7.03220i		−	0.276893i
$646$	6.94182	+	2.47736i	0.273122	+	0.0974703i
$647$	−3.17903	+	2.75465i	−0.124981	+	0.108296i	−0.715109	−	0.699013i	$-0.753623\pi$
$647$	−3.17903	+	2.75465i	−0.124981	+	0.108296i	0.590128	+	0.807310i	$0.299077\pi$
$648$	−0.718493	−	2.73565i	−0.0282251	−	0.107466i
$649$	−1.59736	+	0.229666i	−0.0627019	+	0.00901517i
$650$	4.92603	−	1.91750i	0.193215	−	0.0752106i
$651$	−0.299041	−	0.136568i	−0.0117204	−	0.00535251i
$652$	−38.9903	−	16.4835i	−1.52698	−	0.645545i
$653$	41.1078	+	5.91041i	1.60867	+	0.231292i	0.887279	−	0.461233i	$-0.152593\pi$
$653$	41.1078	+	5.91041i	1.60867	+	0.231292i	0.721394	+	0.692525i	$0.243502\pi$
$654$	1.86370	−	9.19461i	0.0728766	−	0.359538i
$655$	3.89928	+	1.14493i	0.152358	+	0.0447362i
$656$	−9.17550	+	3.27107i	−0.358243	+	0.127714i
$657$	−0.647642	−	1.41814i	−0.0252669	−	0.0553268i
$658$	28.6128	+	27.8108i	1.11544	+	1.08418i
$659$	5.36910	+	4.65235i	0.209150	+	0.181230i	0.753136	−	0.657865i	$-0.228540\pi$
$659$	5.36910	+	4.65235i	0.209150	+	0.181230i	−0.543986	+	0.839094i	$0.683086\pi$
$660$	0.0784988	−	0.683349i	0.00305556	−	0.0265993i
$661$	3.97247	+	2.55295i	0.154511	+	0.0992983i	0.615612	−	0.788050i	$-0.288909\pi$
$661$	3.97247	+	2.55295i	0.154511	+	0.0992983i	−0.461101	+	0.887348i	$0.652545\pi$
$662$	18.0311	−	34.1672i	0.700798	−	1.32795i
$663$	−0.624700	+	0.401470i	−0.0242613	+	0.0155918i
$664$	−16.9759	−	40.1921i	−0.658793	−	1.55976i
$665$	−14.8614	−	50.6131i	−0.576299	−	1.96269i
$666$	−7.71798	−	5.60822i	−0.299066	−	0.217314i
$667$	23.3420	+	1.34782i	0.903806	+	0.0521878i
$668$	16.1373	−	5.24096i	0.624371	−	0.202779i
$669$	3.62967	+	12.3615i	0.140331	+	0.477924i
$670$	56.2102	−	4.82414i	2.17159	−	0.186373i
$671$	0.282892	+	0.440188i	0.0109209	+	0.0169933i
$672$	2.76707	+	19.2908i	0.106742	+	0.744160i
$673$	−41.1422	−	26.4405i	−1.58592	−	1.01921i	−0.973505	−	0.228667i	$-0.926563\pi$
$673$	−41.1422	−	26.4405i	−1.58592	−	1.01921i	−0.612411	−	0.790539i	$-0.709800\pi$
$674$	−4.20748	−	7.45163i	−0.162066	−	0.287026i
$675$	3.64783	−	4.20982i	0.140405	−	0.162036i
$676$	−24.7324	+	4.27674i	−0.951247	+	0.164490i
$677$	−7.28503	−	15.9520i	−0.279986	−	0.613085i	0.716431	−	0.697658i	$-0.245775\pi$
$677$	−7.28503	−	15.9520i	−0.279986	−	0.613085i	−0.996417	+	0.0845734i	$0.973047\pi$
$678$	16.9902	−	13.0996i	0.652504	−	0.503087i
$679$	8.78896	−	29.9325i	0.337289	−	1.14870i
$680$	−1.15803	−	10.1105i	−0.0444085	−	0.387720i
$681$	27.8010	+	3.99718i	1.06534	+	0.153172i
$682$	−0.0139049	+	0.00323247i	−0.000532445	+	0.000123778i
$683$	−11.6393	+	25.4866i	−0.445367	+	0.975217i	0.545215	+	0.838296i	$0.316448\pi$
$683$	−11.6393	+	25.4866i	−0.445367	+	0.975217i	−0.990582	+	0.136921i	$0.956279\pi$
$684$	−9.10930	−	2.39571i	−0.348303	−	0.0916022i
$685$	38.4224	−	5.52431i	1.46804	−	0.211073i
$686$	10.3678	+	0.593540i	0.395843	+	0.0226615i
$687$	−8.69134	−	10.0303i	−0.331595	−	0.382682i
$688$	6.84996	+	5.28501i	0.261152	+	0.201489i
$689$		−	4.59121i		−	0.174911i
$690$	−18.8761	−	11.3988i	−0.718600	−	0.433944i
$691$	−12.8621			−0.489298			−0.244649	−	0.969612i	$-0.578673\pi$
$691$	−12.8621			−0.489298			−0.244649	+	0.969612i	$0.578673\pi$
$692$	−38.5942	+	26.3825i	−1.46713	+	1.00291i
$693$	0.275416	−	0.238650i	0.0104622	−	0.00906555i
$694$	41.6684	+	2.38546i	1.58171	+	0.0905507i
$695$	−8.32219	−	57.8821i	−0.315679	−	2.19559i
$696$	−8.72667	−	10.6766i	−0.330784	−	0.404696i
$697$	2.45147	+	1.11955i	0.0928561	+	0.0424060i
$698$	−2.38533	−	10.2608i	−0.0902860	−	0.388377i
$699$	0.161014	−	1.11987i	0.00609009	−	0.0423575i
$700$	−28.2802	+	25.9484i	−1.06889	+	0.980757i
$701$	37.6862	+	11.0657i	1.42339	+	0.417944i	0.900648	−	0.434549i	$-0.143092\pi$
$701$	37.6862	+	11.0657i	1.42339	+	0.417944i	0.522738	+	0.852493i	$0.324910\pi$
$702$	0.751521	−	0.579430i	0.0283643	−	0.0218692i
$703$	−28.8998	+	13.1981i	−1.08998	+	0.497776i
$704$	0.606645	+	0.590032i	0.0228638	+	0.0222376i
$705$	20.1234	+	17.4370i	0.757890	+	0.656715i
$706$	−36.0464	+	20.3532i	−1.35662	+	0.766002i
$707$	35.4504	−	55.1620i	1.33325	−	2.07458i
$708$	27.3827	−	13.4587i	1.02910	−	0.505807i
$709$	26.9105	−	17.2943i	1.01064	−	0.649502i	0.0730846	−	0.997326i	$-0.476716\pi$
$709$	26.9105	−	17.2943i	1.01064	−	0.649502i	0.937560	+	0.347824i	$0.113079\pi$
$710$	−42.1146	+	3.61441i	−1.58053	+	0.135646i
$711$	12.7200	−	3.73494i	0.477038	−	0.140071i
$712$	42.4421	+	13.7996i	1.59058	+	0.517162i
$713$	−0.0911349	+	0.448482i	−0.00341303	+	0.0167958i
$714$	3.16945	−	4.36176i	0.118614	−	0.163235i
$715$	0.221428	−	0.0650173i	0.00828096	−	0.00243151i
$716$	−9.64342	+	15.9870i	−0.360392	+	0.597463i
$717$	−1.36105	−	2.11783i	−0.0508293	−	0.0790920i
$718$	−12.9256	+	24.4928i	−0.482379	+	0.914063i
$719$	11.4694	−	17.8467i	0.427736	−	0.665571i	−0.558765	−	0.829326i	$-0.688724\pi$
$719$	11.4694	−	17.8467i	0.427736	−	0.665571i	0.986501	+	0.163755i	$0.0523608\pi$
$720$	2.57926	+	12.7465i	0.0961233	+	0.475035i
$721$	−1.06589	+	1.23010i	−0.0396956	+	0.0458112i
$722$	−3.13417	+	3.22456i	−0.116642	+	0.120006i
$723$	−7.39052	+	3.37514i	−0.274856	+	0.125523i
$724$	1.12873	+	39.6952i	0.0419489	+	1.47526i
$725$	7.65104	−	26.0570i	0.284152	−	0.967734i
$726$	−3.08721	+	15.2308i	−0.114577	+	0.565268i
$727$	−4.20808	+	29.2679i	−0.156069	+	1.08549i	0.749720	+	0.661756i	$0.230188\pi$
$727$	−4.20808	+	29.2679i	−0.156069	+	1.08549i	−0.905789	+	0.423729i	$0.860721\pi$
$728$	−5.59988	+	3.37533i	−0.207545	+	0.125098i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	2.60025	+	6.68001i	0.0962397	+	0.247238i
$731$	−0.340649	−	2.36927i	−0.0125994	−	0.0876305i
$732$	−7.65775	−	6.26341i	−0.283039	−	0.231502i
$733$	−17.2557	−	19.9142i	−0.637354	−	0.735546i	0.341550	−	0.939864i	$-0.389048\pi$
$733$	−17.2557	−	19.9142i	−0.637354	−	0.735546i	−0.978905	+	0.204317i	$0.934503\pi$
$734$	37.4638	+	13.3699i	1.38281	+	0.493491i
$735$	−15.8286			−0.583846
$736$	25.2896	−	9.82022i	0.932187	−	0.361978i
$737$	1.29796			0.0478110
$738$	−3.24364	−	1.15757i	−0.119400	−	0.0426108i
$739$	25.7540	+	29.7217i	0.947377	+	1.09333i	0.995526	+	0.0944907i	$0.0301223\pi$
$739$	25.7540	+	29.7217i	0.947377	+	1.09333i	−0.0481492	+	0.998840i	$0.515332\pi$
$740$	33.9548	+	27.7722i	1.24820	+	1.02093i
$741$	−0.449739	−	3.12800i	−0.0165216	−	0.114910i
$742$	12.0923	+	31.0650i	0.443923	+	1.14043i
$743$	3.79546	−	8.31089i	0.139242	−	0.304897i	−0.827145	−	0.561988i	$-0.810037\pi$
$743$	3.79546	−	8.31089i	0.139242	−	0.304897i	0.966387	+	0.257091i	$0.0827640\pi$
$744$	0.231161	−	0.139333i	0.00847479	−	0.00510819i
$745$	−4.55568	+	31.6855i	−0.166907	+	1.16087i
$746$	8.33412	−	41.1165i	0.305134	−	1.50538i
$747$	4.34589	−	14.8007i	0.159008	−	0.541530i
$748$	−0.00665474	−	0.234034i	−0.000243322	−	0.00855715i
$749$	−19.2659	+	8.79846i	−0.703962	+	0.321489i
$750$	−1.82793	+	1.88065i	−0.0667466	+	0.0686715i
$751$	13.3625	−	15.4211i	0.487603	−	0.562724i	−0.457621	−	0.889148i	$-0.651298\pi$
$751$	13.3625	−	15.4211i	0.487603	−	0.562724i	0.945223	+	0.326424i	$0.105844\pi$
$752$	−32.1087	+	6.49720i	−1.17088	+	0.236928i
$753$	4.82510	−	7.50800i	0.175836	−	0.273607i
$754$	2.15927	−	4.09161i	0.0786359	−	0.149008i
$755$	11.5442	+	17.9631i	0.420135	+	0.653743i
$756$	−3.55883	+	5.89989i	−0.129434	+	0.214577i
$757$	−46.5747	+	13.6756i	−1.69279	+	0.497047i	−0.979093	−	0.203411i	$-0.934797\pi$
$757$	−46.5747	+	13.6756i	−1.69279	+	0.497047i	−0.713693	+	0.700458i	$0.752979\pi$
$758$	19.4462	−	26.7617i	0.706318	−	0.972028i
$759$	−0.410260	−	0.298421i	−0.0148915	−	0.0108320i
$760$	41.1857	+	13.3911i	1.49396	+	0.485747i
$761$	29.5113	−	8.66531i	1.06978	−	0.314117i	0.301000	−	0.953624i	$-0.402680\pi$
$761$	29.5113	−	8.66531i	1.06978	−	0.314117i	0.768785	+	0.639507i	$0.220862\pi$
$762$	−3.30702	+	0.283819i	−0.119801	+	0.0102817i
$763$	−19.2259	+	12.3557i	−0.696024	+	0.447307i
$764$	33.2810	−	16.3577i	1.20407	−	0.591801i
$765$	1.94521	−	3.02680i	0.0703292	−	0.109434i
$766$	−27.6177	+	15.5940i	−0.997869	+	0.563435i
$767$	7.73647	+	6.70369i	0.279348	+	0.242056i
$768$	−14.3546	−	7.06716i	−0.517978	−	0.255014i
$769$	39.9697	−	18.2535i	1.44134	−	0.658239i	0.467196	−	0.884154i	$-0.345264\pi$
$769$	39.9697	−	18.2535i	1.44134	−	0.658239i	0.974147	+	0.225915i	$0.0725371\pi$
$770$	−1.32699	+	1.02312i	−0.0478212	+	0.0368706i
$771$	−1.22167	−	0.358714i	−0.0439973	−	0.0129188i
$772$	19.5689	−	17.9554i	0.704301	−	0.646229i
$773$	2.36541	−	16.4518i	0.0850777	−	0.591729i	−0.902030	−	0.431673i	$-0.857924\pi$
$773$	2.36541	−	16.4518i	0.0850777	−	0.591729i	0.987108	−	0.160056i	$-0.0511674\pi$
$774$	0.692626	+	2.97942i	0.0248959	+	0.107093i
$775$	0.483525	+	0.220819i	0.0173687	+	0.00793204i
$776$	16.2089	+	19.8307i	0.581866	+	0.711881i
$777$	3.30750	+	23.0042i	0.118656	+	0.825271i
$778$	44.3569	+	2.53937i	1.59027	+	0.0910409i
$779$	−8.66772	+	7.51062i	−0.310553	+	0.269096i
$780$	−3.60205	+	2.46232i	−0.128974	+	0.0881651i
$781$	−0.972476			−0.0347979
$782$	−6.91184	−	2.92606i	−0.247167	−	0.104636i
$783$		−	4.87525i		−	0.174227i
$784$	11.8959	−	15.4184i	0.424853	−	0.550657i
$785$	−9.48249	−	10.9434i	−0.338445	−	0.390586i
$786$	−1.76483	−	0.101034i	−0.0629493	−	0.00360376i
$787$	34.0937	−	4.90193i	1.21531	−	0.174735i	0.495313	−	0.868714i	$-0.335053\pi$
$787$	34.0937	−	4.90193i	1.21531	−	0.174735i	0.719995	+	0.693979i	$0.244144\pi$
$788$	−32.8159	−	8.63045i	−1.16902	−	0.307447i
$789$	2.32810	−	5.09783i	0.0828826	−	0.181488i
$790$	−59.3715	+	13.8021i	−2.11234	+	0.491056i
$791$	−51.7302	−	7.43768i	−1.83932	−	0.264454i
$792$	0.0340468	+	0.297254i	0.00120980	+	0.0105625i
$793$	0.935120	−	3.18473i	0.0332071	−	0.113093i
$794$	23.4149	−	18.0531i	0.830965	−	0.640682i
$795$	9.24107	+	20.2351i	0.327747	+	0.717666i
$796$	14.1226	−	2.44209i	0.500564	−	0.0865575i
$797$	−22.6795	+	26.1736i	−0.803350	+	0.927115i	−0.998560	−	0.0536466i	$-0.982916\pi$
$797$	−22.6795	+	26.1736i	−0.803350	+	0.927115i	0.195210	+	0.980761i	$0.437461\pi$
$798$	11.2816	+	19.9801i	0.399363	+	0.707290i
$799$	7.62458	+	4.90002i	0.269738	+	0.173350i
$800$	−4.47412	−	31.1917i	−0.158184	−	1.10279i
$801$	8.53065	+	13.2740i	0.301416	+	0.469012i
$802$	32.1786	−	2.76167i	1.13626	−	0.0975179i
$803$	0.0464626	+	0.158237i	0.00163963	+	0.00558406i
$804$	−23.3401	+	7.58025i	−0.823143	+	0.267335i
$805$	12.1374	+	52.3273i	0.427787	+	1.84429i
$806$	0.0732574	+	0.0532321i	0.00258038	+	0.00187502i
$807$	2.32113	+	7.90504i	0.0817076	+	0.278271i
$808$	20.9462	+	49.5923i	0.736886	+	1.74465i
$809$	33.1023	−	21.2735i	1.16381	−	0.747938i	0.191471	−	0.981498i	$-0.438674\pi$
$809$	33.1023	−	21.2735i	1.16381	−	0.747938i	0.972342	+	0.233561i	$0.0750377\pi$
$810$	−2.14596	+	4.06640i	−0.0754015	+	0.142879i
$811$	7.39709	+	4.75382i	0.259747	+	0.166929i	0.664033	−	0.747703i	$-0.268844\pi$
$811$	7.39709	+	4.75382i	0.259747	+	0.166929i	−0.404286	+	0.914633i	$0.632480\pi$
$812$	−3.83354	+	33.3717i	−0.134531	+	1.17112i
$813$	−11.5205	−	9.98253i	−0.404040	−	0.350103i
$814$	0.723688	+	0.703403i	0.0253653	+	0.0246542i
$815$	28.5865	+	62.5957i	1.00134	+	2.19263i
$816$	1.48645	+	4.16958i	0.0520363	+	0.145964i
$817$	9.77383	+	2.86986i	0.341943	+	0.100404i
$818$	8.32391	−	41.0661i	0.291039	−	1.43584i
$819$	−2.28817	−	0.328989i	−0.0799550	−	0.0114958i
$820$	14.5854	+	6.16613i	0.509345	+	0.215330i
$821$	0.283354	+	0.129403i	0.00988912	+	0.00451621i	0.420353	−	0.907360i	$-0.361906\pi$
$821$	0.283354	+	0.129403i	0.00988912	+	0.00451621i	−0.410464	+	0.911877i	$0.634633\pi$
$822$	−15.7348	+	6.12491i	−0.548813	+	0.213631i
$823$	−18.2817	+	2.62852i	−0.637262	+	0.0916244i	−0.453370	−	0.891322i	$-0.649779\pi$
$823$	−18.2817	+	2.62852i	−0.637262	+	0.0916244i	−0.183891	+	0.982947i	$0.558869\pi$
$824$	−0.339458	−	1.29248i	−0.0118256	−	0.0450256i
$825$	−0.445325	+	0.385877i	−0.0155042	+	0.0134345i
$826$	−70.0027	−	24.9821i	−2.43570	−	0.869240i
$827$			10.5440i			0.366652i	0.983052	+	0.183326i	$0.0586864\pi$
$827$			10.5440i			0.366652i	−0.983052	+	0.183326i	$0.941314\pi$
$828$	9.12016	+	2.97029i	0.316948	+	0.103225i
$829$			5.62524i			0.195373i	0.995217	+	0.0976863i	$0.0311442\pi$
$829$			5.62524i			0.195373i	−0.995217	+	0.0976863i	$0.968856\pi$
$830$	−23.8389	+	66.7991i	−0.827459	+	2.31863i
$831$	−0.914523	+	0.792439i	−0.0317245	+	0.0274894i
$832$	0.308593	−	5.35925i	0.0106986	−	0.185798i
$833$	−5.33292	+	0.766758i	−0.184775	+	0.0265666i
$834$	9.22697	+	23.7039i	0.319504	+	0.820800i
$835$	−25.0892	−	11.4579i	−0.868248	−	0.396516i
$836$	0.917730	+	0.387979i	0.0317403	+	0.0134185i
$837$	0.0944549	+	0.0135806i	0.00326484	+	0.000469413i
$838$	−10.0506	−	2.03720i	−0.347191	−	0.0703741i
$839$	−29.6480	−	8.70544i	−1.02356	−	0.300545i	−0.273472	−	0.961880i	$-0.588172\pi$
$839$	−29.6480	−	8.70544i	−1.02356	−	0.300545i	−0.750091	+	0.661335i	$0.769990\pi$
$840$	17.8869	−	26.1476i	0.617157	−	0.902178i
$841$	2.17341	+	4.75911i	0.0749452	+	0.164107i
$842$	17.7473	−	18.2592i	0.611614	−	0.629252i
$843$	−7.71032	−	6.68103i	−0.265557	−	0.230107i
$844$	−0.242591	−	0.0278674i	−0.00835033	−	0.000959234i
$845$	34.3247	+	22.0592i	1.18081	+	0.758858i
$846$	−10.2433	−	5.40572i	−0.352173	−	0.185853i
$847$	31.8475	−	20.4672i	1.09429	−	0.703260i
$848$	−26.6558	−	6.20600i	−0.915364	−	0.213115i
$849$	−0.683822	−	2.32889i	−0.0234687	−	0.0799271i
$850$	−5.12473	+	7.05260i	−0.175777	+	0.241902i
$851$	30.1552	−	11.7211i	1.03371	−	0.401795i
$852$	17.4872	−	5.67937i	0.599102	−	0.194572i
$853$	9.69898	+	33.0317i	0.332087	+	1.13098i	0.941186	+	0.337890i	$0.109713\pi$
$853$	9.69898	+	33.0317i	0.332087	+	1.13098i	−0.609099	+	0.793094i	$0.708469\pi$
$854$	2.06074	+	24.0114i	0.0705169	+	0.821653i
$855$	8.27813	+	12.8810i	0.283106	+	0.440522i
$856$	2.96860	−	17.1336i	0.101465	−	0.585614i
$857$	4.60502	+	2.95947i	0.157305	+	0.101094i	0.616925	−	0.787022i	$-0.288378\pi$
$857$	4.60502	+	2.95947i	0.157305	+	0.101094i	−0.459620	+	0.888115i	$0.652015\pi$
$858$	−0.0874116	+	0.0493559i	−0.00298418	+	0.00168498i
$859$	7.95606	−	9.18179i	0.271457	−	0.313278i	−0.603610	−	0.797280i	$-0.706272\pi$
$859$	7.95606	−	9.18179i	0.271457	−	0.313278i	0.875067	+	0.484001i	$0.160817\pi$
$860$	−2.39645	−	13.8587i	−0.0817183	−	0.472579i
$861$	3.48522	+	7.63156i	0.118776	+	0.260083i
$862$	30.6801	+	39.7921i	1.04497	+	1.35532i
$863$	−1.87657	+	6.39100i	−0.0638791	+	0.217552i	−0.985247	−	0.171140i	$-0.945255\pi$
$863$	−1.87657	+	6.39100i	−0.0638791	+	0.217552i	0.921368	+	0.388692i	$0.127073\pi$
$864$	−2.34823	−	5.14643i	−0.0798886	−	0.175085i
$865$	75.2234	+	10.8155i	2.55767	+	0.367738i
$866$	−3.71388	−	15.9757i	−0.126203	−	0.542877i
$867$	−6.55330	+	14.3497i	−0.222562	+	0.487342i
$868$	−0.635877	−	0.167233i	−0.0215831	−	0.00567625i
$869$	−1.38809	+	0.199577i	−0.0470876	+	0.00677018i
$870$	−1.28119	+	22.3793i	−0.0434363	+	0.758731i
$871$	−5.39175	−	6.22241i	−0.182693	−	0.210838i
$872$	0.539536	−	18.7554i	0.0182710	−	0.635139i
$873$			9.05529i			0.306475i
$874$	23.5462	−	21.5834i	0.796461	−	0.730069i
$875$	6.38880			0.215981
$876$	−1.75962	−	2.57409i	−0.0594520	−	0.0869705i
$877$	34.4822	−	29.8790i	1.16438	−	1.00894i	0.164636	−	0.986354i	$-0.447355\pi$
$877$	34.4822	−	29.8790i	1.16438	−	1.00894i	0.999745	−	0.0225871i	$-0.00719032\pi$
$878$	0.997854	−	17.4302i	0.0336760	−	0.588240i
$879$	−0.0880122	−	0.612138i	−0.00296858	−	0.0206469i
$880$	−0.0781717	−	1.37346i	−0.00263517	−	0.0462994i
$881$	1.47707	+	0.674557i	0.0497639	+	0.0227264i	0.440142	−	0.897928i	$-0.354928\pi$
$881$	1.47707	+	0.674557i	0.0497639	+	0.0227264i	−0.390378	+	0.920655i	$0.627656\pi$
$882$	6.70629	−	1.55901i	0.225813	−	0.0524947i
$883$	−1.50472	+	10.4655i	−0.0506378	+	0.352194i	0.948712	+	0.316141i	$0.102387\pi$
$883$	−1.50472	+	10.4655i	−0.0506378	+	0.352194i	−0.999350	+	0.0360524i	$0.988522\pi$
$884$	−1.09431	+	1.00409i	−0.0368058	+	0.0337710i
$885$	−47.5905	−	13.9738i	−1.59974	−	0.469725i
$886$	−29.7029	−	38.5247i	−0.997888	−	1.29426i
$887$	−4.40843	+	2.01326i	−0.148021	+	0.0675988i	−0.488048	−	0.872817i	$-0.662291\pi$
$887$	−4.40843	+	2.01326i	−0.148021	+	0.0675988i	0.340027	+	0.940416i	$0.389564\pi$
$888$	−17.1214	−	8.42227i	−0.574557	−	0.282633i
$889$	6.11070	+	5.29495i	0.204946	+	0.177587i
$890$	−35.6708	−	63.1745i	−1.19569	−	2.11761i
$891$	−0.0571903	+	0.0889898i	−0.00191595	+	0.00298127i
$892$	11.3658	+	23.1246i	0.380554	+	0.774268i
$893$	−32.4475	+	20.8528i	−1.08581	+	0.697811i
$894$	−1.19065	−	13.8733i	−0.0398213	−	0.463992i
$895$	29.1212	−	8.55075i	0.973414	−	0.285820i
$896$	12.0272	+	37.0745i	0.401800	+	1.23857i
$897$	0.273597	+	3.20643i	0.00913514	+	0.107059i
$898$	4.31311	+	3.13410i	0.143930	+	0.104586i
$899$	0.446382	−	0.131070i	0.0148877	−	0.00437141i
$900$	5.75434	−	9.53964i	0.191811	−	0.317988i
$901$	4.09369	+	6.36991i	0.136381	+	0.212212i
$902$	0.322202	+	0.170036i	0.0107281	+	0.00566157i
$903$	4.02858	−	6.26860i	0.134063	−	0.208606i
$904$	29.0193	−	31.6060i	0.965169	−	1.05120i
$905$	42.2745	−	48.7873i	1.40525	−	1.62175i
$906$	−6.66030	−	6.47361i	−0.221274	−	0.215071i
$907$	−14.5423	+	6.64126i	−0.482870	+	0.220519i	−0.641950	−	0.766746i	$-0.721874\pi$
$907$	−14.5423	+	6.64126i	−0.482870	+	0.220519i	0.159080	+	0.987266i	$0.449147\pi$
$908$	56.1511	−	1.59665i	1.86344	−	0.0529867i
$909$	−5.36231	+	18.2623i	−0.177857	+	0.605724i
$910$	10.4171	+	2.11150i	0.345325	+	0.0699957i
$911$	−5.92335	+	41.1978i	−0.196249	+	1.36494i	0.618798	+	0.785550i	$0.287620\pi$
$911$	−5.92335	+	41.1978i	−0.196249	+	1.36494i	−0.815048	+	0.579394i	$0.803289\pi$
$912$	−18.7686	−	1.61705i	−0.621490	−	0.0535460i
$913$	−0.677855	+	1.48430i	−0.0224337	+	0.0491230i
$914$	−47.1755	+	18.3635i	−1.56043	+	0.607410i
$915$	2.28873	+	15.9184i	0.0756629	+	0.526247i
$916$	−20.5467	−	16.8055i	−0.678881	−	0.555268i
$917$	2.81997	+	3.25442i	0.0931237	+	0.107470i
$918$	−0.526030	+	1.47399i	−0.0173616	+	0.0486491i
$919$	9.52582			0.314228			0.157114	−	0.987580i	$-0.449781\pi$
$919$	9.52582			0.314228			0.157114	+	0.987580i	$0.449781\pi$
$920$	−41.0846	−	16.0315i	−1.35452	−	0.528544i
$921$	14.2184			0.468511
$922$	0.697294	−	1.95389i	0.0229642	−	0.0643481i
$923$	4.03968	+	4.66204i	0.132968	+	0.153453i
$924$	0.461450	−	0.564176i	0.0151806	−	0.0185600i
$925$	−5.34796	−	37.1959i	−0.175840	−	1.22299i
$926$	42.5061	−	16.5459i	1.39684	−	0.543732i
$927$	0.196266	−	0.429763i	0.00644623	−	0.0141153i
$928$	−20.8365	−	18.0671i	−0.683992	−	0.593080i
$929$	−5.33843	+	37.1296i	−0.175148	+	1.21818i	0.692653	+	0.721271i	$0.256442\pi$
$929$	−5.33843	+	37.1296i	−0.175148	+	1.21818i	−0.867801	+	0.496911i	$0.834468\pi$
$930$	−0.430016	−	0.0871623i	−0.0141008	−	0.00285816i
$931$	6.45968	−	21.9997i	0.211708	−	0.721010i
$932$	−0.0643159	−	2.26186i	−0.00210674	−	0.0740898i
$933$	12.2081	−	5.57526i	0.399676	−	0.182526i
$934$	−21.8808	−	21.2675i	−0.715961	−	0.695893i
$935$	−0.249241	+	0.287640i	−0.00815106	+	0.00940683i
$936$	1.28360	−	1.39802i	0.0419559	−	0.0456957i
$937$	11.9622	−	18.6136i	0.390788	−	0.608078i	−0.588996	−	0.808136i	$-0.700477\pi$
$937$	11.9622	−	18.6136i	0.390788	−	0.608078i	0.979784	+	0.200058i	$0.0641130\pi$
$938$	52.8702	+	27.9012i	1.72627	+	0.911008i
$939$	−2.63890	−	4.10621i	−0.0861174	−	0.134001i
$940$	45.6004	+	27.5063i	1.48732	+	0.897157i
$941$	−5.14805	+	1.51160i	−0.167822	+	0.0492769i	−0.364564	−	0.931178i	$-0.618782\pi$
$941$	−5.14805	+	1.51160i	−0.167822	+	0.0492769i	0.196742	+	0.980455i	$0.436964\pi$
$942$	5.09542	+	3.70255i	0.166018	+	0.120636i
$943$	9.25277	−	7.12672i	0.301312	−	0.232078i
$944$	49.3781	−	35.8552i	1.60712	−	1.16699i
$945$	10.7470	−	3.15559i	0.349599	−	0.102651i
$946$	−0.0276685	−	0.322389i	−0.000899580	−	0.0104818i
$947$	−6.68081	+	4.29349i	−0.217097	+	0.139520i	−0.644670	−	0.764461i	$-0.723005\pi$
$947$	−6.68081	+	4.29349i	−0.217097	+	0.139520i	0.427573	+	0.903981i	$0.359369\pi$
$948$	23.7952	−	11.6954i	0.772833	−	0.379849i
$949$	0.565580	−	0.880059i	0.0183595	−	0.0285679i
$950$	−18.2413	−	32.3062i	−0.591827	−	1.04815i
$951$	−6.24841	−	5.41428i	−0.202619	−	0.175570i
$952$	4.75978	−	9.67604i	0.154265	−	0.313602i
$953$	−27.2980	+	12.4666i	−0.884270	+	0.403832i	−0.805177	−	0.593035i	$-0.797930\pi$
$953$	−27.2980	+	12.4666i	−0.884270	+	0.403832i	−0.0790929	+	0.996867i	$0.525202\pi$
$954$	−5.90830	−	7.66308i	−0.191288	−	0.248101i
$955$	−57.8416	−	16.9838i	−1.87171	−	0.549584i
$956$	−3.40401	−	3.70991i	−0.110094	−	0.119987i
$957$	−0.0733941	+	0.510467i	−0.00237249	+	0.0165011i
$958$	−45.9271	+	10.6767i	−1.48384	+	0.344948i
$959$	37.4150	+	17.0869i	1.20819	+	0.551763i
$960$	9.42687	+	24.2413i	0.304251	+	0.782384i
$961$	−4.41046	−	30.6755i	−0.142273	−	0.989531i
$962$	0.365893	−	6.39130i	0.0117969	−	0.206064i
$963$	4.64627	−	4.02601i	0.149724	−	0.129736i
$964$	−13.4147	+	9.17012i	−0.432058	+	0.295350i
$965$	−43.1732			−1.38980
$966$	−10.2963	−	20.9747i	−0.331278	−	0.674850i
$967$			29.5149i			0.949135i	0.880219	+	0.474568i	$0.157396\pi$
$967$			29.5149i			0.949135i	−0.880219	+	0.474568i	$0.842604\pi$
$968$	−0.893736	+	31.0682i	−0.0287258	+	0.998570i
$969$	3.41302	+	3.93883i	0.109642	+	0.126534i
$970$	2.37967	−	41.5674i	0.0764067	−	1.33465i
$971$	−0.0375125	+	0.00539348i	−0.00120383	+	0.000173085i	−0.142917	−	0.989735i	$-0.545648\pi$
$971$	−0.0375125	+	0.00539348i	−0.00120383	+	0.000173085i	0.141713	+	0.989908i	$0.454739\pi$
$972$	0.508693	−	1.93423i	0.0163163	−	0.0620403i
$973$	25.7408	−	56.3645i	0.825212	−	1.80696i
$974$	−5.88921	−	25.3332i	−0.188702	−	0.811727i
$975$	3.69978	+	0.531947i	0.118488	+	0.0170360i
$976$	−17.2260	−	9.73400i	−0.551391	−	0.311578i
$977$	6.37952	−	21.7267i	0.204099	−	0.695097i	−0.792286	−	0.610149i	$-0.791109\pi$
$977$	6.37952	−	21.7267i	0.204099	−	0.695097i	0.996385	−	0.0849479i	$-0.0270724\pi$
$978$	−18.2769	−	23.7051i	−0.584430	−	0.758006i
$979$	−0.693376	−	1.51828i	−0.0221604	−	0.0485245i
$980$	−31.1942	+	5.39411i	−0.996463	+	0.172309i
$981$	4.34421	−	5.01348i	0.138700	−	0.160068i
$982$	−10.4094	+	5.87756i	−0.332178	+	0.187560i
$983$	−18.7739	−	12.0653i	−0.598795	−	0.384822i	0.205846	−	0.978584i	$-0.434006\pi$
$983$	−18.7739	−	12.0653i	−0.598795	−	0.384822i	−0.804640	+	0.593762i	$0.797642\pi$
$984$	−6.78690	−	1.17591i	−0.216359	−	0.0374867i
$985$	29.8216	+	46.4034i	0.950197	+	1.47853i
$986$	0.652432	+	7.60205i	0.0207777	+	0.242098i
$987$	7.94899	+	27.0718i	0.253019	+	0.861704i
$988$	−1.95229	−	6.01126i	−0.0621107	−	0.191244i
$989$	−9.76792	−	3.49133i	−0.310602	−	0.111018i
$990$	0.285912	−	0.393469i	0.00908688	−	0.0125053i
$991$	−10.1326	−	34.5084i	−0.321872	−	1.09620i	−0.948473	−	0.316857i	$-0.897373\pi$
$991$	−10.1326	−	34.5084i	−0.321872	−	1.09620i	0.626601	−	0.779340i	$-0.284446\pi$
$992$	0.408080	−	0.353366i	0.0129565	−	0.0112194i
$993$	22.9811	−	14.7691i	0.729285	−	0.468683i
$994$	−39.6121	−	20.9045i	−1.25642	−	0.663052i
$995$	−19.6000	−	12.5962i	−0.621362	−	0.399325i
$996$	3.52083	−	30.6496i	0.111562	−	0.971169i
$997$	22.6172	+	19.5979i	0.716295	+	0.620673i	0.934805	−	0.355162i	$-0.115574\pi$
$997$	22.6172	+	19.5979i	0.716295	+	0.620673i	−0.218510	+	0.975835i	$0.570120\pi$
$998$	12.6644	−	13.0296i	0.400884	−	0.412446i
$999$	−2.80243	−	6.13646i	−0.0886648	−	0.194149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.t.a.451.22	yes	240
8.3	odd	2	inner	552.2.t.a.451.17	yes	240
23.5	odd	22	inner	552.2.t.a.235.17	✓	240
184.51	even	22	inner	552.2.t.a.235.22	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.17	✓	240	23.5	odd	22	inner
552.2.t.a.235.22	yes	240	184.51	even	22	inner
552.2.t.a.451.17	yes	240	8.3	odd	2	inner
552.2.t.a.451.22	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.33194 + 0.475334i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.54812 + 1.26623i) q^{4} +(-0.462696 - 3.21812i) q^{5} +(0.513000 + 1.31789i) q^{6} +(1.43113 - 3.13375i) q^{7} +(1.46011 + 2.42241i) q^{8} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(1.33194 + 0.475334i) q^{2} +(0.654861 + 0.755750i) q^{3} +(1.54812 + 1.26623i) q^{4} +(-0.462696 - 3.21812i) q^{5} +(0.513000 + 1.31789i) q^{6} +(1.43113 - 3.13375i) q^{7} +(1.46011 + 2.42241i) q^{8} +(-0.142315 + 0.989821i) q^{9} +(0.913400 - 4.50627i) q^{10} +(0.0298024 - 0.101497i) q^{11} +(0.0568468 + 1.99919i) q^{12} +(-0.610377 + 0.278750i) q^{13} +(3.39576 - 3.49369i) q^{14} +(2.12909 - 2.45710i) q^{15} +(0.793321 + 3.92054i) q^{16} +(0.598302 - 0.930977i) q^{17} +(-0.660050 + 1.25073i) q^{18} +(2.54616 + 3.96191i) q^{19} +(3.35858 - 5.56790i) q^{20} +(3.30552 - 0.970589i) q^{21} +(0.0879401 - 0.121022i) q^{22} +(-2.35594 - 4.17727i) q^{23} +(-0.874567 + 2.68982i) q^{24} +(-5.34475 + 1.56936i) q^{25} +(-0.945484 + 0.0811445i) q^{26} +(-0.841254 + 0.540641i) q^{27} +(6.18361 - 3.03926i) q^{28} +(-2.63576 + 4.10132i) q^{29} +(4.00376 - 2.26068i) q^{30} +(-0.0721183 - 0.0624909i) q^{31} +(-0.806912 + 5.59901i) q^{32} +(0.0962231 - 0.0439436i) q^{33} +(1.23943 - 0.955609i) q^{34} +(-10.7470 - 3.15559i) q^{35} +(-1.47366 + 1.35215i) q^{36} +(-0.960068 + 6.67742i) q^{37} +(1.50810 + 6.48730i) q^{38} +(-0.610377 - 0.278750i) q^{39} +(7.12003 - 5.81965i) q^{40} +(0.346577 + 2.41050i) q^{41} +(4.86410 + 0.278463i) q^{42} +(1.63464 - 1.41643i) q^{43} +(0.174657 - 0.119393i) q^{44} +3.25121 q^{45} +(-1.15236 - 6.68372i) q^{46} +8.18987i q^{47} +(-2.44343 + 3.16696i) q^{48} +(-3.18820 - 3.67938i) q^{49} +(-7.86485 - 0.450252i) q^{50} +(1.09539 - 0.157493i) q^{51} +(-1.29790 - 0.341341i) q^{52} +(-2.84234 + 6.22386i) q^{53} +(-1.37748 + 0.320223i) q^{54} +(-0.340421 - 0.0489451i) q^{55} +(9.68084 - 1.10882i) q^{56} +(-1.32683 + 4.51876i) q^{57} +(-5.46017 + 4.20984i) q^{58} +(-6.33745 - 13.8771i) q^{59} +(6.40734 - 1.10796i) q^{60} +(-3.23927 + 3.73831i) q^{61} +(-0.0663530 - 0.117514i) q^{62} +(2.89818 + 1.86255i) q^{63} +(-3.73616 + 7.07398i) q^{64} +(1.17947 + 1.83529i) q^{65} +(0.149051 - 0.0127920i) q^{66} +(3.45689 + 11.7731i) q^{67} +(2.10507 - 0.683670i) q^{68} +(1.61416 - 4.51603i) q^{69} +(-12.8143 - 9.31145i) q^{70} +(-2.59002 - 8.82078i) q^{71} +(-2.60555 + 1.10050i) q^{72} +(-1.31153 + 0.842871i) q^{73} +(-4.45276 + 8.43755i) q^{74} +(-4.68611 - 3.01158i) q^{75} +(-1.07493 + 9.35752i) q^{76} +(-0.275416 - 0.238650i) q^{77} +(-0.680485 - 0.661410i) q^{78} +(-5.50717 - 12.0590i) q^{79} +(12.2497 - 4.36702i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-0.684172 + 3.37537i) q^{82} +(-15.2686 - 2.19529i) q^{83} +(6.34632 + 2.68297i) q^{84} +(-3.27283 - 1.49465i) q^{85} +(2.85052 - 1.10959i) q^{86} +(-4.82563 + 0.693821i) q^{87} +(0.289383 - 0.0760040i) q^{88} +(11.9248 - 10.3329i) q^{89} +(4.33041 + 1.54541i) q^{90} +2.31170i q^{91} +(1.64212 - 9.45005i) q^{92} -0.0954262i q^{93} +(-3.89292 + 10.9084i) q^{94} +(11.5718 - 10.0270i) q^{95} +(-4.75986 + 3.05675i) q^{96} +(8.96312 - 1.28870i) q^{97} +(-2.49755 - 6.41616i) q^{98} +(0.0962231 + 0.0439436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9}+O(q^{10}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9	\( 240 q + 24 q^{3} - 4 q^{4} + 11 q^{6} - 24 q^{9} + 4 q^{12} - 4 q^{16} + 44 q^{17} - 55 q^{20} - 24 q^{25} + 24 q^{27} + 33 q^{34} + 7 q^{36} - 132 q^{38} + 11 q^{40} - 66 q^{42} + 77 q^{44} + 37 q^{48} - 56 q^{49} - 37 q^{50} - 55 q^{52} - 11 q^{54} + 132 q^{56} + 37 q^{58} + 11 q^{60} + 51 q^{62} - 4 q^{64} - 55 q^{66} - 132 q^{70} + 144 q^{73} + 44 q^{74} + 24 q^{75} - 55 q^{76} - 198 q^{80} - 24 q^{81} - 26 q^{82} + 44 q^{84} - 110 q^{86} + 22 q^{88} - 139 q^{92} - 117 q^{94} - 209 q^{98}+O(q^{100}) \) 240 * q + 24 * q^3 - 4 * q^4 + 11 * q^6 - 24 * q^9 + 4 * q^12 - 4 * q^16 + 44 * q^17 - 55 * q^20 - 24 * q^25 + 24 * q^27 + 33 * q^34 + 7 * q^36 - 132 * q^38 + 11 * q^40 - 66 * q^42 + 77 * q^44 + 37 * q^48 - 56 * q^49 - 37 * q^50 - 55 * q^52 - 11 * q^54 + 132 * q^56 + 37 * q^58 + 11 * q^60 + 51 * q^62 - 4 * q^64 - 55 * q^66 - 132 * q^70 + 144 * q^73 + 44 * q^74 + 24 * q^75 - 55 * q^76 - 198 * q^80 - 24 * q^81 - 26 * q^82 + 44 * q^84 - 110 * q^86 + 22 * q^88 - 139 * q^92 - 117 * q^94 - 209 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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