LMFDB - Embedded newform 552.2.t.a.235.17

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			235.17
Character	$\chi$	$=$	552.235
Dual form			552.2.t.a.451.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.863512 + 1.11998i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-0.508693 + 1.93423i) q^{4} +(0.462696 - 3.21812i) q^{5} +(1.41190 + 0.0808295i) q^{6} +(-1.43113 - 3.13375i) q^{7} +(-2.60555 + 1.10050i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(0.863512 + 1.11998i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-0.508693 + 1.93423i) q^{4} +(0.462696 - 3.21812i) q^{5} +(1.41190 + 0.0808295i) q^{6} +(-1.43113 - 3.13375i) q^{7} +(-2.60555 + 1.10050i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(4.00376 - 2.26068i) q^{10} +(0.0298024 + 0.101497i) q^{11} +(1.12867 + 1.65109i) q^{12} +(0.610377 + 0.278750i) q^{13} +(2.27392 - 4.30886i) q^{14} +(-2.12909 - 2.45710i) q^{15} +(-3.48246 - 1.96786i) q^{16} +(0.598302 + 0.930977i) q^{17} +(0.985686 - 1.01411i) q^{18} +(2.54616 - 3.96191i) q^{19} +(5.98920 + 2.53200i) 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} +(0.214875 + 0.924312i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(6.78938 - 1.17402i) q^{28} +(2.63576 + 4.10132i) q^{29} +(0.913400 - 4.50627i) q^{30} +(0.0721183 - 0.0624909i) q^{31} +(-0.803197 - 5.59954i) q^{32} +(0.0962231 + 0.0439436i) q^{33} +(-0.526030 + 1.47399i) q^{34} +(-10.7470 + 3.15559i) q^{35} +(1.98693 + 0.228246i) q^{36} +(0.960068 + 6.67742i) q^{37} +(6.63589 - 0.569513i) q^{38} +(0.610377 - 0.278750i) q^{39} +(2.33598 + 8.89418i) q^{40} +(0.346577 - 2.41050i) q^{41} +(-1.76732 - 4.54022i) q^{42} +(1.63464 + 1.41643i) q^{43} +(-0.211479 + 0.00601339i) q^{44} -3.25121 q^{45} +(6.71282 - 0.968529i) q^{46} +8.18987i q^{47} +(-3.76773 + 1.34320i) q^{48} +(-3.18820 + 3.67938i) q^{49} +(-2.85761 - 7.34116i) q^{50} +(1.09539 + 0.157493i) q^{51} +(-0.849660 + 1.03881i) q^{52} +(2.84234 + 6.22386i) q^{53} +(-0.120928 - 1.40903i) q^{54} +(0.340421 - 0.0489451i) q^{55} +(7.17759 + 6.59017i) q^{56} +(-1.32683 - 4.51876i) q^{57} +(-2.31737 + 6.49353i) q^{58} +(-6.33745 + 13.8771i) q^{59} +(5.83565 - 2.86823i) q^{60} +(3.23927 + 3.73831i) q^{61} +(0.132263 + 0.0268092i) q^{62} +(-2.89818 + 1.86255i) q^{63} +(5.57778 - 5.73483i) q^{64} +(1.17947 - 1.83529i) q^{65} +(0.0338740 + 0.145713i) 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} +(1.46011 + 2.42241i) q^{72} +(-1.31153 - 0.842871i) q^{73} +(-6.64952 + 6.84129i) q^{74} +(-4.68611 + 3.01158i) q^{75} +(6.36801 + 6.94026i) q^{76} +(0.275416 - 0.238650i) q^{77} +(0.839261 + 0.442904i) q^{78} +(5.50717 - 12.0590i) q^{79} +(-7.94412 + 10.2965i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.99897 - 1.69333i) q^{82} +(-15.2686 + 2.19529i) q^{83} +(3.55883 - 5.89989i) q^{84} +(3.27283 - 1.49465i) q^{85} +(-0.174830 + 3.05387i) q^{86} +(4.82563 + 0.693821i) q^{87} +(-0.189350 - 0.231659i) q^{88} +(11.9248 + 10.3329i) q^{89} +(-2.80746 - 3.64128i) q^{90} -2.31170i q^{91} +(6.88133 + 6.68186i) q^{92} -0.0954262i q^{93} +(-9.17246 + 7.07205i) q^{94} +(-11.5718 - 10.0270i) q^{95} +(-4.75783 - 3.05990i) q^{96} +(8.96312 + 1.28870i) q^{97} +(-6.87386 - 0.393519i) 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 $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.863512	+	1.11998i	0.610595	+	0.791943i
$2$	0.863512	+	1.11998i	0.610595	+	0.791943i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$3$	0.654861	−	0.755750i	0.378084	−	0.436332i
$4$	−0.508693	+	1.93423i	−0.254347	+	0.967113i
$5$	0.462696	−	3.21812i	0.206924	−	1.43919i	−0.576193	−	0.817314i	$-0.695462\pi$
$5$	0.462696	−	3.21812i	0.206924	−	1.43919i	0.783117	−	0.621874i	$-0.213629\pi$
$6$	1.41190	+	0.0808295i	0.576406	+	0.0329985i
$7$	−1.43113	−	3.13375i	−0.540918	−	1.18444i	−0.960896	−	0.276911i	$-0.910689\pi$
$7$	−1.43113	−	3.13375i	−0.540918	−	1.18444i	0.419978	−	0.907534i	$-0.362038\pi$
$8$	−2.60555	+	1.10050i	−0.921201	+	0.389087i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	4.00376	−	2.26068i	1.26610	−	0.714889i
$11$	0.0298024	+	0.101497i	0.00898575	+	0.0306026i	0.963864	−	0.266395i	$-0.0858327\pi$
$11$	0.0298024	+	0.101497i	0.00898575	+	0.0306026i	−0.954878	+	0.296998i	$0.904015\pi$
$12$	1.12867	+	1.65109i	0.325818	+	0.476630i
$13$	0.610377	+	0.278750i	0.169288	+	0.0773113i	0.498257	−	0.867030i	$-0.333974\pi$
$13$	0.610377	+	0.278750i	0.169288	+	0.0773113i	−0.328969	+	0.944341i	$0.606701\pi$
$14$	2.27392	−	4.30886i	0.607731	−	1.15159i
$15$	−2.12909	−	2.45710i	−0.549729	−	0.634421i
$16$	−3.48246	−	1.96786i	−0.870616	−	0.491964i
$17$	0.598302	+	0.930977i	0.145110	+	0.225795i	0.906198	−	0.422853i	$-0.138971\pi$
$17$	0.598302	+	0.930977i	0.145110	+	0.225795i	−0.761089	+	0.648648i	$0.775335\pi$
$18$	0.985686	−	1.01411i	0.232328	−	0.239029i
$19$	2.54616	−	3.96191i	0.584130	−	0.908924i	−0.415870	−	0.909424i	$-0.636523\pi$
$19$	2.54616	−	3.96191i	0.584130	−	0.908924i	1.00000		0.000499791i	$0.000159088\pi$
$20$	5.98920	+	2.53200i	1.33923	+	0.566172i
$21$	−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
$26$	0.214875	+	0.924312i	0.0421404	+	0.181272i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	6.78938	−	1.17402i	1.28307	−	0.221869i
$29$	2.63576	+	4.10132i	0.489449	+	0.761597i	0.994858	−	0.101283i	$-0.0322948\pi$
$29$	2.63576	+	4.10132i	0.489449	+	0.761597i	−0.505409	+	0.862880i	$0.668658\pi$
$30$	0.913400	−	4.50627i	0.166763	−	0.822729i
$31$	0.0721183	−	0.0624909i	0.0129528	−	0.0112237i	−0.648360	−	0.761334i	$-0.724545\pi$
$31$	0.0721183	−	0.0624909i	0.0129528	−	0.0112237i	0.661313	+	0.750110i	$0.269999\pi$
$32$	−0.803197	−	5.59954i	−0.141986	−	0.989869i
$33$	0.0962231	+	0.0439436i	0.0167503	+	0.00764960i
$34$	−0.526030	+	1.47399i	−0.0902134	+	0.252788i
$35$	−10.7470	+	3.15559i	−1.81657	+	0.533392i
$36$	1.98693	+	0.228246i	0.331156	+	0.0380411i
$37$	0.960068	+	6.67742i	0.157834	+	1.09776i	0.902614	+	0.430451i	$0.141645\pi$
$37$	0.960068	+	6.67742i	0.157834	+	1.09776i	−0.744780	+	0.667310i	$0.767445\pi$
$38$	6.63589	−	0.569513i	1.07648	−	0.0923873i
$39$	0.610377	−	0.278750i	0.0977386	−	0.0446357i
$40$	2.33598	+	8.89418i	0.369350	+	1.40629i
$41$	0.346577	−	2.41050i	0.0541262	−	0.376456i	−0.944696	−	0.327946i	$-0.893644\pi$
$41$	0.346577	−	2.41050i	0.0541262	−	0.376456i	0.998823	−	0.0485101i	$-0.0154473\pi$
$42$	−1.76732	−	4.54022i	−0.272704	−	0.700571i
$43$	1.63464	+	1.41643i	0.249281	+	0.216003i	0.770534	−	0.637399i	$-0.219990\pi$
$43$	1.63464	+	1.41643i	0.249281	+	0.216003i	−0.521253	+	0.853402i	$0.674535\pi$
$44$	−0.211479	+	0.00601339i	−0.0318817	+	0.000906553i
$45$	−3.25121			−0.484662
$46$	6.71282	−	0.968529i	0.989751	−	0.142802i
$47$			8.18987i			1.19462i	0.802012	+	0.597308i	$0.203763\pi$
$47$			8.18987i			1.19462i	−0.802012	+	0.597308i	$0.796237\pi$
$48$	−3.76773	+	1.34320i	−0.543826	+	0.193874i
$49$	−3.18820	+	3.67938i	−0.455457	+	0.525625i
$50$	−2.85761	−	7.34116i	−0.404128	−	1.03820i
$51$	1.09539	+	0.157493i	0.153385	+	0.0220535i
$52$	−0.849660	+	1.03881i	−0.117827	+	0.144057i
$53$	2.84234	+	6.22386i	0.390426	+	0.854913i	0.998152	+	0.0607667i	$0.0193546\pi$
$53$	2.84234	+	6.22386i	0.390426	+	0.854913i	−0.607726	+	0.794147i	$0.707918\pi$
$54$	−0.120928	−	1.40903i	−0.0164562	−	0.191745i
$55$	0.340421	−	0.0489451i	0.0459023	−	0.00659976i
$56$	7.17759	+	6.59017i	0.959146	+	0.880648i
$57$	−1.32683	−	4.51876i	−0.175743	−	0.598525i
$58$	−2.31737	+	6.49353i	−0.304286	+	0.852643i
$59$	−6.33745	+	13.8771i	−0.825066	+	1.80664i	−0.305573	+	0.952169i	$0.598848\pi$
$59$	−6.33745	+	13.8771i	−0.825066	+	1.80664i	−0.519493	+	0.854474i	$0.673879\pi$
$60$	5.83565	−	2.86823i	0.753379	−	0.370287i
$61$	3.23927	+	3.73831i	0.414746	+	0.478642i	0.924229	−	0.381838i	$-0.124709\pi$
$61$	3.23927	+	3.73831i	0.414746	+	0.478642i	−0.509483	+	0.860480i	$0.670163\pi$
$62$	0.132263	+	0.0268092i	0.0167975	+	0.00340477i
$63$	−2.89818	+	1.86255i	−0.365136	+	0.234659i
$64$	5.57778	−	5.73483i	0.697223	−	0.716854i
$65$	1.17947	−	1.83529i	0.146295	−	0.227640i
$66$	0.0338740	+	0.145713i	0.00416960	+	0.0179361i
$67$	3.45689	−	11.7731i	0.422326	−	1.43831i	−0.424008	−	0.905659i	$-0.639377\pi$
$67$	3.45689	−	11.7731i	0.422326	−	1.43831i	0.846334	−	0.532653i	$-0.178805\pi$
$68$	−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	−0.650463	−	0.759538i	$-0.725425\pi$
$71$	2.59002	−	8.82078i	0.307378	−	1.04683i	0.957842	−	0.287297i	$-0.0927566\pi$
$72$	1.46011	+	2.42241i	0.172076	+	0.285484i
$73$	−1.31153	−	0.842871i	−0.153503	−	0.0986506i	0.461634	−	0.887070i	$-0.347263\pi$
$73$	−1.31153	−	0.842871i	−0.153503	−	0.0986506i	−0.615138	+	0.788420i	$0.710900\pi$
$74$	−6.64952	+	6.84129i	−0.772991	+	0.795284i
$75$	−4.68611	+	3.01158i	−0.541106	+	0.347748i
$76$	6.36801	+	6.94026i	0.730461	+	0.796102i
$77$	0.275416	−	0.238650i	0.0313866	−	0.0271966i
$78$	0.839261	+	0.442904i	0.0950276	+	0.0501490i
$79$	5.50717	−	12.0590i	0.619605	−	1.35675i	−0.296201	−	0.955126i	$-0.595720\pi$
$79$	5.50717	−	12.0590i	0.619605	−	1.35675i	0.915806	−	0.401620i	$-0.131553\pi$
$80$	−7.94412	+	10.2965i	−0.888180	+	1.15118i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	2.99897	−	1.69333i	0.331181	−	0.186997i
$83$	−15.2686	+	2.19529i	−1.67594	+	0.240964i	−0.913718	−	0.406349i	$-0.866802\pi$
$83$	−15.2686	+	2.19529i	−1.67594	+	0.240964i	−0.762224	+	0.647313i	$0.775893\pi$
$84$	3.55883	−	5.89989i	0.388301	−	0.643731i
$85$	3.27283	−	1.49465i	0.354988	−	0.162118i
$86$	−0.174830	+	3.05387i	−0.0188524	+	0.329307i
$87$	4.82563	+	0.693821i	0.517362	+	0.0743854i
$88$	−0.189350	−	0.231659i	−0.0201848	−	0.0246950i
$89$	11.9248	+	10.3329i	1.26403	+	1.09529i	0.991082	+	0.133256i	$0.0425432\pi$
$89$	11.9248	+	10.3329i	1.26403	+	1.09529i	0.272945	+	0.962030i	$0.412002\pi$
$90$	−2.80746	−	3.64128i	−0.295933	−	0.383825i
$91$		−	2.31170i		−	0.242332i
$92$	6.88133	+	6.68186i	0.717428	+	0.696632i
$93$		−	0.0954262i		−	0.00989523i
$94$	−9.17246	+	7.07205i	−0.946067	+	0.729426i
$95$	−11.5718	−	10.0270i	−1.18724	−	1.02875i
$96$	−4.75783	−	3.05990i	−0.485594	−	0.312300i
$97$	8.96312	+	1.28870i	0.910067	+	0.130848i	0.581419	−	0.813605i	$-0.302498\pi$
$97$	8.96312	+	1.28870i	0.910067	+	0.130848i	0.328648	+	0.944452i	$0.393407\pi$
$98$	−6.87386	−	0.393519i	−0.694365	−	0.0397515i
$99$	0.0962231	−	0.0439436i	0.00967078	−	0.00441650i
$100$	5.75434	−	9.53964i	0.575434	−	0.953964i
$101$	−18.8396	+	2.70872i	−1.87461	+	0.269528i	−0.983045	−	0.183365i	$-0.941301\pi$
$101$	−18.8396	+	2.70872i	−1.87461	+	0.269528i	−0.891565	+	0.452893i	$0.850392\pi$
$102$	0.769494	+	1.36281i	0.0761912	+	0.134938i
$103$	0.453320	−	0.133107i	0.0446670	−	0.0131154i	−0.259323	−	0.965791i	$-0.583499\pi$
$103$	0.453320	−	0.133107i	0.0446670	−	0.0131154i	0.303990	+	0.952675i	$0.401681\pi$
$104$	−1.89713	−	0.0545747i	−0.186029	−	0.00535149i
$105$	−4.65292	+	10.1885i	−0.454079	+	0.994294i
$106$	−4.51618	+	8.55774i	−0.438650	+	0.831201i
$107$	−4.64627	+	4.02601i	−0.449172	+	0.389209i	−0.849863	−	0.527004i	$-0.823315\pi$
$107$	−4.64627	+	4.02601i	−0.449172	+	0.389209i	0.400691	+	0.916213i	$0.368770\pi$
$108$	1.47366	−	1.35215i	0.141803	−	0.130111i
$109$	5.58070	−	3.58650i	0.534534	−	0.343524i	−0.245364	−	0.969431i	$-0.578907\pi$
$109$	5.58070	−	3.58650i	0.534534	−	0.343524i	0.779898	+	0.625907i	$0.215271\pi$
$110$	0.348775	+	0.338998i	0.0332544	+	0.0323222i
$111$	5.67517	+	3.64721i	0.538663	+	0.346178i
$112$	−1.18289	+	13.7294i	−0.111773	+	1.29731i
$113$	−4.27392	+	14.5556i	−0.402057	+	1.36928i	0.471203	+	0.882025i	$0.343820\pi$
$113$	−4.27392	+	14.5556i	−0.402057	+	1.36928i	−0.873260	+	0.487255i	$0.837998\pi$
$114$	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
$118$	−21.0145	+	4.88524i	−1.93454	+	0.449723i
$119$	2.06119	−	3.20728i	0.188949	−	0.294011i
$120$	8.25151	+	4.05903i	0.753256	+	0.370537i
$121$	9.24438	−	5.94100i	0.840398	−	0.540091i
$122$	−1.38968	+	6.85598i	−0.125815	+	0.620711i
$123$	−1.59477	−	1.84046i	−0.143796	−	0.165949i
$124$	0.0841854	+	0.171282i	0.00756007	+	0.0153816i
$125$	−0.770377	+	1.68689i	−0.0689046	+	0.150880i
$126$	−4.58862	−	1.63756i	−0.408787	−	0.145885i
$127$	0.661229	+	2.25194i	0.0586746	+	0.199827i	0.983614	−	0.180287i	$-0.0577027\pi$
$127$	0.661229	+	2.25194i	0.0586746	+	0.199827i	−0.924939	+	0.380115i	$0.875885\pi$
$128$	11.2394	+	1.29489i	0.993429	+	0.114453i
$129$	2.14093	−	0.307819i	0.188498	−	0.0271020i
$130$	3.07397	−	0.263818i	0.269605	−	0.0231384i
$131$	−0.519254	−	1.13701i	−0.0453674	−	0.0993408i	0.885591	−	0.464466i	$-0.153754\pi$
$131$	−0.519254	−	1.13701i	−0.0453674	−	0.0993408i	−0.930959	+	0.365125i	$0.881026\pi$
$132$	−0.133945	+	0.163763i	−0.0116584	+	0.0142538i
$133$	−16.0595	−	2.30901i	−1.39254	−	0.200217i
$134$	16.1706	−	6.29457i	1.39693	−	0.543768i
$135$	−2.12909	+	2.45710i	−0.183243	+	0.211474i
$136$	−2.58345	−	1.76727i	−0.221529	−	0.151542i
$137$		−	11.9394i		−	1.02005i	−0.860159	−	0.510025i	$-0.829636\pi$
$137$		−	11.9394i		−	1.02005i	0.860159	−	0.510025i	$-0.170364\pi$
$138$	3.66400	−	5.70746i	0.311900	−	0.485851i
$139$	17.9863			1.52558			0.762789	−	0.646648i	$-0.223830\pi$
$139$	17.9863			1.52558			0.762789	+	0.646648i	$0.223830\pi$
$140$	−0.636722	−	22.3923i	−0.0538128	−	1.89249i
$141$	6.18949	+	5.36322i	0.521249	+	0.451665i
$142$	12.1156	−	4.71610i	1.01672	−	0.395766i
$143$	−0.0101017	+	0.0702592i	−0.000844750	+	0.00587537i
$144$	−1.45222	+	3.72707i	−0.121018	+	0.310589i
$145$	14.4181	−	6.58453i	1.19736	−	0.546816i
$146$	−0.188529	−	2.19672i	−0.0156028	−	0.181802i
$147$	0.692862	+	4.81896i	0.0571463	+	0.397461i
$148$	−13.4040	−	1.53977i	−1.10180	−	0.126568i
$149$	9.44712	−	2.77392i	0.773938	−	0.227249i	0.129165	−	0.991623i	$-0.458770\pi$
$149$	9.44712	−	2.77392i	0.773938	−	0.227249i	0.644773	+	0.764374i	$0.276952\pi$
$150$	−7.41942	−	2.64780i	−0.605793	−	0.216192i
$151$	5.97412	+	2.72829i	0.486167	+	0.222025i	0.643391	−	0.765538i	$-0.277527\pi$
$151$	5.97412	+	2.72829i	0.486167	+	0.222025i	−0.157224	+	0.987563i	$0.550254\pi$
$152$	−2.27406	+	13.1250i	−0.184451	+	1.06458i
$153$	0.836353	−	0.724704i	0.0676152	−	0.0585889i
$154$	0.505107	+	0.102383i	0.0407027	+	0.00825025i
$155$	−0.167734	−	0.261000i	−0.0134727	−	0.0209640i
$156$	0.228671	+	1.32241i	0.0183083	+	0.105877i
$157$	−3.74675	−	2.40789i	−0.299023	−	0.192171i	0.382522	−	0.923946i	$-0.375056\pi$
$157$	−3.74675	−	2.40789i	−0.299023	−	0.192171i	−0.681546	+	0.731776i	$0.738692\pi$
$158$	18.2613	−	4.24521i	1.45279	−	0.337731i
$159$	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	−0.637743	−	0.770250i	$-0.720132\pi$
$163$	−20.3084	−	5.96307i	−1.59067	−	0.467064i	−0.952932	+	0.303186i	$0.901950\pi$
$164$	4.48614	+	1.89656i	0.350309	+	0.148097i
$165$	0.185938	−	0.289325i	0.0144752	−	0.0225239i
$166$	−15.6433	−	15.2048i	−1.21415	−	1.18012i
$167$	−4.58653	−	7.13678i	−0.354917	−	0.552261i	0.617186	−	0.786817i	$-0.288273\pi$
$167$	−4.58653	−	7.13678i	−0.354917	−	0.552261i	−0.972103	+	0.234556i	$0.924636\pi$
$168$	9.68084	−	1.10882i	0.746893	−	0.0855473i
$169$	−8.21833	−	9.48446i	−0.632179	−	0.729574i
$170$	4.50010	+	2.37484i	0.345142	+	0.182142i
$171$	−4.28394	−	1.95641i	−0.327601	−	0.149610i
$172$	−3.57122	+	2.44125i	−0.272303	+	0.186143i
$173$	6.58548	+	22.4281i	0.500685	+	1.70518i	0.690480	+	0.723352i	$0.257400\pi$
$173$	6.58548	+	22.4281i	0.500685	+	1.70518i	−0.189795	+	0.981824i	$0.560782\pi$
$174$	3.38993	+	6.00371i	0.256990	+	0.455140i
$175$	2.73108	+	18.9951i	0.206450	+	1.43589i
$176$	0.0959469	−	0.412108i	0.00723227	−	0.0310638i
$177$	6.33745	+	13.8771i	0.476352	+	1.04307i
$178$	−1.27539	+	22.2781i	−0.0955945	+	1.66981i
$179$	1.32853	−	9.24014i	0.0992991	−	0.690640i	−0.877982	−	0.478693i	$-0.841111\pi$
$179$	1.32853	−	9.24014i	0.0992991	−	0.690640i	0.977281	−	0.211947i	$-0.0679804\pi$
$180$	1.65387	−	6.28858i	0.123272	−	0.468723i
$181$	−13.0027	+	15.0059i	−0.966480	+	1.11538i	0.0267994	+	0.999641i	$0.491468\pi$
$181$	−13.0027	+	15.0059i	−0.966480	+	1.11538i	−0.993280	+	0.115737i	$0.963077\pi$
$182$	2.58904	−	1.99618i	0.191913	−	0.147967i
$183$	4.94650			0.365656
$184$	−1.54141	+	13.4768i	−0.113635	+	0.993523i
$185$	21.9330			1.61254
$186$	0.106875	−	0.0824017i	0.00783646	−	0.00604198i
$187$	−0.0766610	+	0.0884715i	−0.00560601	+	0.00646967i
$188$	−15.8411	−	4.16613i	−1.15533	−	0.303846i
$189$	−0.490285	+	3.41001i	−0.0356630	+	0.248041i
$190$	1.23764	−	21.6186i	0.0897876	−	1.56838i
$191$	−7.70256	−	16.8663i	−0.557338	−	1.22040i	−0.953270	−	0.302120i	$-0.902306\pi$
$191$	−7.70256	−	16.8663i	−0.557338	−	1.22040i	0.395932	−	0.918280i	$-0.370422\pi$
$192$	−0.681427	−	7.97093i	−0.0491777	−	0.575252i
$193$	1.88981	+	13.1439i	0.136032	+	0.946122i	0.937475	+	0.348052i	$0.113157\pi$
$193$	1.88981	+	13.1439i	0.136032	+	0.946122i	−0.801444	+	0.598070i	$0.795934\pi$
$194$	6.29645	+	11.1513i	0.452059	+	0.800616i
$195$	−0.614632	−	2.09324i	−0.0440147	−	0.149900i
$196$	−5.49493	−	8.03837i	−0.392495	−	0.574169i
$197$	15.4327	+	7.04789i	1.09954	+	0.502142i	0.880726	−	0.473626i	$-0.157055\pi$
$197$	15.4327	+	7.04789i	1.09954	+	0.502142i	0.218811	+	0.975767i	$0.429782\pi$
$198$	0.132306	+	0.0698217i	0.00940255	+	0.00496201i
$199$	−4.69281	−	5.41579i	−0.332664	−	0.383915i	0.564633	−	0.825342i	$-0.309018\pi$
$199$	−4.69281	−	5.41579i	−0.332664	−	0.383915i	−0.897297	+	0.441427i	$0.854472\pi$
$200$	15.6531	−	1.79287i	1.10684	−	0.126775i
$201$	−6.63372	−	10.3223i	−0.467907	−	0.728077i
$202$	−19.3019	−	18.7609i	−1.35808	−	1.32001i
$203$	9.08038	−	14.1294i	0.637318	−	0.991686i
$204$	−0.861845	+	2.03862i	−0.0603412	+	0.142732i
$205$	−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
$210$	−15.4287	+	3.58671i	−1.06468	+	0.247507i
$211$	−0.102711	−	0.0660086i	−0.00707094	−	0.00454422i	0.537101	−	0.843518i	$-0.319520\pi$
$211$	−0.102711	−	0.0660086i	−0.00707094	−	0.00454422i	−0.544172	+	0.838974i	$0.683156\pi$
$212$	−13.4842	+	2.33170i	−0.926102	+	0.160142i
$213$	−4.97020	−	7.73379i	−0.340553	−	0.529910i
$214$	−8.52115	−	1.72720i	−0.582494	−	0.118069i
$215$	5.31458	−	4.60511i	0.362451	−	0.314066i
$216$	2.78691	+	0.482864i	0.189625	+	0.0328548i
$217$	−0.299041	−	0.136568i	−0.0203003	−	0.00927082i
$218$	8.83579	+	3.15326i	0.598435	+	0.213566i
$219$	−1.49587	+	0.439228i	−0.101082	+	0.0296802i
$220$	−0.0784988	+	0.683349i	−0.00529239	+	0.0460714i
$221$	0.105680	+	0.735024i	0.00710883	+	0.0494430i
$222$	0.815790	+	9.50546i	0.0547522	+	0.637965i
$223$	−11.7191	+	5.35195i	−0.784772	+	0.358393i	−0.767163	−	0.641452i	$-0.778332\pi$
$223$	−11.7191	+	5.35195i	−0.784772	+	0.358393i	−0.0176084	+	0.999845i	$0.505605\pi$
$224$	−16.3981	+	10.5307i	−1.09564	+	0.703613i
$225$	−0.792750	+	5.51370i	−0.0528500	+	0.367580i
$226$	−19.9925	+	7.78228i	−1.32988	+	0.517670i
$227$	21.2267	+	18.3930i	1.40886	+	1.22079i	0.941628	+	0.336655i	$0.109296\pi$
$227$	21.2267	+	18.3930i	1.40886	+	1.22079i	0.467236	+	0.884133i	$0.345250\pi$
$228$	9.41526	−	0.267722i	0.623541	−	0.0177303i
$229$	13.2720			0.877042			0.438521	−	0.898721i	$-0.355503\pi$
$229$	13.2720			0.877042			0.438521	+	0.898721i	$0.355503\pi$
$230$	−0.0108475	−	22.0508i	−0.000715266	−	1.45399i
$231$		−	0.364428i		−	0.0239776i
$232$	−11.3811	−	7.78554i	−0.747208	−	0.511146i
$233$	−0.740903	+	0.855047i	−0.0485381	+	0.0560160i	−0.779499	−	0.626403i	$-0.784527\pi$
$233$	−0.740903	+	0.855047i	−0.0485381	+	0.0560160i	0.730961	+	0.682419i	$0.239072\pi$
$234$	0.884324	−	0.344231i	0.0578101	−	0.0225031i
$235$	26.3560	+	3.78942i	1.71928	+	0.247194i
$236$	−23.6176	−	19.3173i	−1.53738	−	1.25745i
$237$	−5.50717	−	12.0590i	−0.357729	−	0.783317i
$238$	5.37194	−	0.461038i	0.348211	−	0.0298846i
$239$	2.49185	−	0.358274i	0.161184	−	0.0231748i	−0.0612501	−	0.998122i	$-0.519509\pi$
$239$	2.49185	−	0.358274i	0.161184	−	0.0231748i	0.222435	+	0.974948i	$0.428600\pi$
$240$	2.57926	+	12.7465i	0.166490	+	0.822784i
$241$	−2.28900	−	7.79562i	−0.147448	−	0.502160i	0.852335	−	0.522996i	$-0.175186\pi$
$241$	−2.28900	−	7.79562i	−0.147448	−	0.502160i	−0.999783	+	0.0208354i	$0.993367\pi$
$242$	14.6364	+	5.22335i	0.940864	+	0.335770i
$243$	−0.415415	+	0.909632i	−0.0266489	+	0.0583529i
$244$	−8.87854	+	4.36382i	−0.568390	+	0.279365i
$245$	10.3655	+	11.9624i	0.662229	+	0.764253i
$246$	0.684172	−	3.37537i	0.0436212	−	0.215206i
$247$	2.65850	−	1.70852i	0.169156	−	0.108710i
$248$	−0.119136	+	0.242189i	−0.00756517	+	0.0153790i
$249$	−8.33969	+	12.9768i	−0.528507	+	0.822372i
$250$	−2.55451	+	0.593847i	−0.161561	+	0.0375582i
$251$	−2.51440	+	8.56326i	−0.158707	+	0.540508i	−1.00000		7.21133e-5i	$-0.999977\pi$
$251$	−2.51440	+	8.56326i	−0.158707	+	0.540508i	0.841293	+	0.540580i	$0.181795\pi$
$252$	−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
$256$	8.25509	+	13.7060i	0.515943	+	0.856623i
$257$	−1.07112	−	0.688367i	−0.0668146	−	0.0429391i	0.506807	−	0.862060i	$-0.330826\pi$
$257$	−1.07112	−	0.688367i	−0.0668146	−	0.0429391i	−0.573622	+	0.819120i	$0.694462\pi$
$258$	2.19347	+	2.13198i	0.136559	+	0.132732i
$259$	19.5514	−	12.5649i	1.21486	−	0.780745i
$260$	2.94988	+	3.21496i	0.182944	+	0.199384i
$261$	3.68447	−	3.19261i	0.228063	−	0.197618i
$262$	0.825039	−	1.56337i	0.0509711	−	0.0965854i
$263$	2.32810	−	5.09783i	0.143557	−	0.314346i	−0.824172	−	0.566340i	$-0.808359\pi$
$263$	2.32810	−	5.09783i	0.143557	−	0.314346i	0.967729	+	0.251994i	$0.0810863\pi$
$264$	−0.299074	−	0.00860344i	−0.0184067	−	0.000529505i
$265$	21.3443	−	6.26725i	1.31117	−	0.384994i
$266$	−11.2816	−	19.9801i	−0.691717	−	1.22506i
$267$	15.6182	−	2.24555i	0.955817	−	0.137426i
$268$	21.0133	+	12.6753i	1.28359	+	0.774267i
$269$	−7.49425	+	3.42251i	−0.456932	+	0.208674i	−0.630565	−	0.776136i	$-0.717177\pi$
$269$	−7.49425	+	3.42251i	−0.456932	+	0.208674i	0.173633	+	0.984811i	$0.444449\pi$
$270$	−4.59040	−	0.262794i	−0.279363	−	0.0159931i
$271$	15.0886	+	2.16941i	0.916566	+	0.131782i	0.584425	−	0.811447i	$-0.301320\pi$
$271$	15.0886	+	2.16941i	0.916566	+	0.131782i	0.332141	+	0.943230i	$0.392229\pi$
$272$	−0.251537	−	4.41946i	−0.0152517	−	0.267969i
$273$	−1.74706	−	1.51384i	−0.105737	−	0.0916217i
$274$	13.3718	−	10.3098i	0.807821	−	0.622838i
$275$		−	0.589250i		−	0.0355331i
$276$	9.55613	−	0.824874i	0.575211	−	0.0496516i
$277$			1.21009i			0.0727071i	0.999339	+	0.0363536i	$0.0115742\pi$
$277$			1.21009i			0.0727071i	−0.999339	+	0.0363536i	$0.988426\pi$
$278$	15.5314	+	20.1442i	0.931511	+	1.20817i
$279$	−0.0721183	−	0.0624909i	−0.00431761	−	0.00374123i
$280$	24.5290	−	20.0491i	1.46589	−	1.19816i
$281$	−10.0984	−	1.45193i	−0.602418	−	0.0866147i	−0.165644	−	0.986186i	$-0.552970\pi$
$281$	−10.0984	−	1.45193i	−0.602418	−	0.0866147i	−0.436775	+	0.899571i	$0.643879\pi$
$282$	−0.661983	+	11.5633i	−0.0394205	+	0.688584i
$283$	−2.20786	+	1.00830i	−0.131244	+	0.0599370i	−0.479955	−	0.877293i	$-0.659347\pi$
$283$	−2.20786	+	1.00830i	−0.131244	+	0.0599370i	0.348711	+	0.937230i	$0.386620\pi$
$284$	15.7439	+	9.49675i	0.934226	+	0.563528i
$285$	−15.1558	+	2.17908i	−0.897755	+	0.129078i
$286$	−0.0874116	+	0.0493559i	−0.00516875	+	0.00291848i
$287$	−8.04988	+	2.36366i	−0.475169	+	0.139522i
$288$	−5.42824	+	1.59192i	−0.319862	+	0.0938047i
$289$	6.55330	−	14.3497i	0.385488	−	0.844102i
$290$	19.8247	+	10.4621i	1.16415	+	0.614357i
$291$	6.84353	−	5.92995i	0.401175	−	0.347620i
$292$	2.29747	−	2.10804i	0.134449	−	0.123364i
$293$	0.520259	−	0.334350i	0.0303938	−	0.0195329i	−0.525356	−	0.850883i	$-0.676068\pi$
$293$	0.520259	−	0.334350i	0.0303938	−	0.0195329i	0.555750	+	0.831350i	$0.312431\pi$
$294$	−4.79883	+	4.93722i	−0.279873	+	0.287944i
$295$	41.7258	+	26.8156i	2.42937	+	1.56126i
$296$	−9.85003	−	16.3418i	−0.572521	−	0.949848i
$297$	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
$302$	2.10311	+	9.04678i	0.121020	+	0.520584i
$303$	−10.2902	+	16.0119i	−0.591156	+	0.919857i
$304$	−16.6634	+	8.78672i	−0.955711	+	0.503953i
$305$	13.5291	−	8.69465i	0.774677	−	0.497854i
$306$	1.53385	+	0.310905i	0.0876845	+	0.0177732i
$307$	9.31105	+	10.7455i	0.531410	+	0.613279i	0.956450	−	0.291895i	$-0.0942857\pi$
$307$	9.31105	+	10.7455i	0.531410	+	0.613279i	−0.425041	+	0.905174i	$0.639740\pi$
$308$	0.321500	+	0.654117i	0.0183192	+	0.0372718i
$309$	0.196266	−	0.429763i	0.0111652	−	0.0244484i
$310$	0.147473	−	0.413235i	0.00837589	−	0.0234702i
$311$	−3.78112	−	12.8773i	−0.214407	−	0.730205i	−0.994518	−	0.104563i	$-0.966656\pi$
$311$	−3.78112	−	12.8773i	−0.214407	−	0.730205i	0.780111	−	0.625641i	$-0.215163\pi$
$312$	−1.28360	+	1.39802i	−0.0726697	+	0.0791472i
$313$	−4.83138	+	0.694648i	−0.273086	+	0.0392638i	−0.277497	−	0.960726i	$-0.589505\pi$
$313$	−4.83138	+	0.694648i	−0.273086	+	0.0392638i	0.00441126	+	0.999990i	$0.498596\pi$
$314$	−0.538585	−	6.27551i	−0.0303941	−	0.354148i
$315$	4.65292	+	10.1885i	0.262163	+	0.574056i
$316$	20.5234	+	16.7865i	1.15453	+	0.944312i
$317$	8.18367	+	1.17663i	0.459641	+	0.0660864i	0.368246	−	0.929728i	$-0.379958\pi$
$317$	8.18367	+	1.17663i	0.459641	+	0.0660864i	0.0913948	+	0.995815i	$0.470867\pi$
$318$	3.51004	+	9.01723i	0.196833	+	0.505661i
$319$	−0.337722	+	0.389752i	−0.0189088	+	0.0218219i
$320$	−15.8746	−	20.6035i	−0.887416	−	1.15177i
$321$			6.14789i			0.343142i
$322$	−12.6421	−	19.6502i	−0.704515	−	1.09506i
$323$	5.21182			0.289994
$324$	−0.0568468	−	1.99919i	−0.00315816	−	0.111066i
$325$	−2.82486	−	2.44775i	−0.156695	−	0.135777i
$326$	−10.8580	−	27.8941i	−0.601370	−	1.54491i
$327$	0.944086	−	6.56626i	0.0522081	−	0.363115i
$328$	1.74973	+	6.66208i	0.0966129	+	0.367852i
$329$	25.6650	−	11.7208i	1.41496	−	0.646189i
$330$	0.484597	−	0.0415897i	0.0266762	−	0.00228944i
$331$	3.88772	+	27.0397i	0.213688	+	1.48624i	0.760696	+	0.649108i	$0.224858\pi$
$331$	3.88772	+	27.0397i	0.213688	+	1.48624i	−0.547008	+	0.837128i	$0.684233\pi$
$332$	3.52083	−	30.6496i	0.193231	−	1.68211i
$333$	6.47282	−	1.90059i	0.354709	−	0.104152i
$334$	4.03250	−	11.2995i	0.220649	−	0.618282i
$335$	−36.2877	−	16.5720i	−1.98261	−	0.905428i
$336$	9.60137	+	9.88483i	0.523798	+	0.539262i
$337$	−4.57305	+	3.96257i	−0.249110	+	0.215855i	−0.770461	−	0.637487i	$-0.779974\pi$
$337$	−4.57305	+	3.96257i	−0.249110	+	0.215855i	0.521351	+	0.853343i	$0.325428\pi$
$338$	3.52574	−	17.3943i	0.191775	−	0.946124i
$339$	8.20159	+	12.7619i	0.445449	+	0.693133i
$340$	1.22613	+	7.09071i	0.0664960	+	0.384548i
$341$	0.00849196	+	0.00545745i	0.000459865	+	0.000295538i
$342$	−1.50810	−	6.48730i	−0.0815488	−	0.350793i
$343$	−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	0.932011	−	0.362430i	$-0.118053\pi$
$347$	28.3168	+	8.31455i	1.52012	+	0.446349i	0.588113	+	0.808779i	$0.299871\pi$
$348$	−3.79677	+	8.98092i	−0.203528	+	0.481428i
$349$	4.02721	−	6.26645i	0.215571	−	0.335436i	−0.716580	−	0.697505i	$-0.754293\pi$
$349$	4.02721	−	6.26645i	0.215571	−	0.335436i	0.932151	+	0.362070i	$0.117930\pi$
$350$	−18.9157	+	19.4612i	−1.01109	+	1.04025i
$351$	−0.362778	−	0.564494i	−0.0193637	−	0.0301305i
$352$	0.544402	−	0.248402i	0.0290167	−	0.0132399i
$353$	−19.1685	−	22.1216i	−1.02024	−	1.17741i	−0.984018	−	0.178071i	$-0.943014\pi$
$353$	−19.1685	−	22.1216i	−1.02024	−	1.17741i	−0.0362179	−	0.999344i	$-0.511531\pi$
$354$	−10.0695	+	19.0808i	−0.535190	+	1.01413i
$355$	−27.1880	−	12.4163i	−1.44299	−	0.658990i
$356$	−26.0522	+	17.8090i	−1.38077	+	0.943875i
$357$	−1.07411	−	3.65807i	−0.0568477	−	0.193606i
$358$	11.4959	−	6.49105i	0.607579	−	0.343063i
$359$	2.78692	+	19.3834i	0.147088	+	1.02302i	0.920955	+	0.389670i	$0.127411\pi$
$359$	2.78692	+	19.3834i	0.147088	+	1.02302i	−0.773867	+	0.633348i	$0.781680\pi$
$360$	8.47120	−	3.57797i	0.446472	−	0.188576i
$361$	−1.32089	−	2.89234i	−0.0695205	−	0.152229i
$362$	−28.0342	−	1.60492i	−1.47344	−	0.0843527i
$363$	1.56387	−	10.8770i	0.0820819	−	0.570892i
$364$	4.47134	+	1.17594i	0.234362	+	0.0616362i
$365$	−3.31930	+	3.83068i	−0.173740	+	0.200507i
$366$	4.27136	+	5.53996i	0.223268	+	0.289578i
$367$	−28.1273			−1.46823			−0.734117	−	0.679023i	$-0.762404\pi$
$367$	−28.1273			−1.46823			−0.734117	+	0.679023i	$0.762404\pi$
$368$	−16.4247	+	9.91103i	−0.856198	+	0.516648i
$369$	−2.43528			−0.126776
$370$	18.9394	+	24.5644i	0.984612	+	1.27704i
$371$	15.4362	−	17.8144i	0.801410	−	0.924876i
$372$	0.184576	+	0.0485427i	0.00956981	+	0.00251682i
$373$	4.22177	−	29.3630i	0.218595	−	1.52036i	−0.524636	−	0.851326i	$-0.675799\pi$
$373$	4.22177	−	29.3630i	0.218595	−	1.52036i	0.743231	−	0.669034i	$-0.233292\pi$
$374$	−0.165284	−	0.00946226i	−0.00854661	−	0.000489282i
$375$	0.770377	+	1.68689i	0.0397821	+	0.0871107i
$376$	−9.01298	−	21.3391i	−0.464809	−	1.10048i
$377$	0.465565	+	3.23807i	0.0239778	+	0.166769i
$378$	−4.24249	+	2.39547i	−0.218210	+	0.123210i
$379$	6.59020	+	22.4442i	0.338516	+	1.15288i	0.936294	+	0.351217i	$0.114232\pi$
$379$	6.59020	+	22.4442i	0.338516	+	1.15288i	−0.597778	+	0.801662i	$0.703950\pi$
$380$	25.2810	−	17.2818i	1.29689	−	0.886538i
$381$	2.13491	+	0.974983i	0.109375	+	0.0499499i
$382$	12.2386	−	23.1909i	0.626179	−	1.18655i
$383$	14.6864	+	16.9490i	0.750438	+	0.866051i	0.994611	−	0.103681i	$-0.0330620\pi$
$383$	14.6864	+	16.9490i	0.750438	+	0.866051i	−0.244173	+	0.969732i	$0.578516\pi$
$384$	8.33883	−	7.64617i	0.425539	−	0.390192i
$385$	−0.640569	−	0.996745i	−0.0326464	−	0.0507988i
$386$	−13.0890	+	13.4665i	−0.666214	+	0.685427i
$387$	1.16938	−	1.81958i	0.0594427	−	0.0924947i
$388$	−7.05212	+	16.6811i	−0.358017	+	0.846857i
$389$	−30.1438	−	8.85103i	−1.52835	−	0.448765i	−0.593808	−	0.804607i	$-0.702376\pi$
$389$	−30.1438	−	8.85103i	−1.52835	−	0.448765i	−0.934546	+	0.355842i	$0.884194\pi$
$390$	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
$394$	5.43288	+	23.3702i	0.273705	+	1.17738i
$395$	−36.2592	−	23.3024i	−1.82440	−	1.17247i
$396$	0.0360488	+	0.208471i	0.00181152	+	0.0104761i
$397$	−11.3030	−	17.5878i	−0.567280	−	0.882706i	0.432541	−	0.901614i	$-0.357617\pi$
$397$	−11.3030	−	17.5878i	−0.567280	−	0.882706i	−0.999821	+	0.0189088i	$0.993981\pi$
$398$	2.01326	−	9.93243i	0.100915	−	0.497868i
$399$	−12.2618	+	10.6249i	−0.613857	+	0.531910i
$400$	15.5246	+	15.9830i	0.776231	+	0.799148i
$401$	20.7736	+	9.48697i	1.03738	+	0.473757i	0.859951	−	0.510377i	$-0.170494\pi$
$401$	20.7736	+	9.48697i	1.03738	+	0.473757i	0.177431	+	0.984133i	$0.443221\pi$
$402$	5.83240	−	16.3430i	0.290894	−	0.815116i
$403$	0.0614387	−	0.0180400i	0.00306048	−	0.000898638i
$404$	4.34429	−	37.8179i	0.216137	−	1.88151i
$405$	0.462696	+	3.21812i	0.0229916	+	0.159910i
$406$	23.6656	−	2.03106i	1.17450	−	0.100800i
$407$	−0.649129	+	0.296447i	−0.0321761	+	0.0146944i
$408$	−3.02742	+	0.795124i	−0.149879	+	0.0393645i
$409$	−4.21660	+	29.3271i	−0.208497	+	1.45013i	0.569567	+	0.821945i	$0.307111\pi$
$409$	−4.21660	+	29.3271i	−0.208497	+	1.45013i	−0.778064	+	0.628185i	$0.783798\pi$
$410$	−4.06174	−	10.4346i	−0.200595	−	0.515326i
$411$	−9.02318	−	7.81863i	−0.445081	−	0.385665i
$412$	0.0268577	+	0.944535i	0.00132319	+	0.0465339i
$413$	52.5570			2.58616
$414$	−1.91400	−	6.50666i	−0.0940682	−	0.319785i
$415$			50.1518i			2.46186i
$416$	1.07062	−	3.64172i	0.0524914	−	0.178550i
$417$	11.7785	−	13.5931i	0.576796	−	0.665659i
$418$	0.255569	+	0.656553i	0.0125003	+	0.0321131i
$419$	−7.17754	−	1.03198i	−0.350646	−	0.0504153i	−0.0352584	−	0.999378i	$-0.511225\pi$
$419$	−7.17754	−	1.03198i	−0.350646	−	0.0504153i	−0.315388	+	0.948963i	$0.602135\pi$
$420$	−17.3399	−	14.1826i	−0.846101	−	0.692041i
$421$	−7.47958	−	16.3780i	−0.364532	−	0.798214i	−0.999667	−	0.0258128i	$-0.991783\pi$
$421$	−7.47958	−	16.3780i	−0.364532	−	0.798214i	0.635135	−	0.772402i	$-0.280945\pi$
$422$	−0.0147645	−	0.172034i	−0.000718723	−	0.00837446i
$423$	8.10651	−	1.16554i	0.394152	−	0.0566705i
$424$	−14.2553	−	13.0886i	−0.692296	−	0.635638i
$425$	−1.73674	−	5.91479i	−0.0842443	−	0.286910i
$426$	4.36983	−	12.2447i	0.211719	−	0.593259i
$427$	7.07910	−	15.5011i	0.342582	−	0.750150i
$428$	−5.42370	−	11.0349i	−0.262164	−	0.533394i
$429$	0.0464831	+	0.0536443i	0.00224422	+	0.00258997i
$430$	9.74682	+	1.97563i	0.470033	+	0.0952736i
$431$	−29.8892	+	19.2086i	−1.43971	+	0.925248i	−0.440086	+	0.897956i	$0.645052\pi$
$431$	−29.8892	+	19.2086i	−1.43971	+	0.925248i	−0.999628	+	0.0272918i	$0.991312\pi$
$432$	1.86573	+	3.53823i	0.0897650	+	0.170233i
$433$	−6.27023	+	9.75667i	−0.301328	+	0.468875i	−0.958591	−	0.284786i	$-0.908078\pi$
$433$	−6.27023	+	9.75667i	−0.301328	+	0.468875i	0.657263	+	0.753661i	$0.271714\pi$
$434$	−0.105273	−	0.452847i	−0.00505329	−	0.0217374i
$435$	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	−0.833912	−	0.551898i	$-0.813904\pi$
$439$	3.47804	−	11.8451i	0.165998	−	0.565337i	0.999910	−	0.0134390i	$-0.00427789\pi$
$440$	−0.833119	+	0.502163i	−0.0397174	+	0.0239397i
$441$	4.09565	+	2.63212i	0.195031	+	0.125339i
$442$	−0.731953	+	0.753061i	−0.0348154	+	0.0358195i
$443$	−28.9372	+	18.5968i	−1.37485	+	0.883562i	−0.999069	−	0.0431468i	$-0.986262\pi$
$443$	−28.9372	+	18.5968i	−1.37485	+	0.883562i	−0.375780	+	0.926709i	$0.622625\pi$
$444$	−9.94145	+	9.12175i	−0.471800	+	0.432899i
$445$	38.7701	−	33.5945i	1.83788	−	1.59253i
$446$	−16.1137	−	8.50368i	−0.763005	−	0.402661i
$447$	4.09016	−	8.95619i	0.193458	−	0.423613i
$448$	−25.9541	−	9.27205i	−1.22621	−	0.438063i
$449$	3.61727	−	1.06213i	0.170709	−	0.0501248i	−0.195261	−	0.980751i	$-0.562555\pi$
$449$	3.61727	−	1.06213i	0.170709	−	0.0501248i	0.365970	+	0.930627i	$0.380737\pi$
$450$	−6.85976	+	3.87328i	−0.323372	+	0.182588i
$451$	0.254988	−	0.0366617i	0.0120069	−	0.00172633i
$452$	−25.9798	−	15.6711i	−1.22199	−	0.737106i
$453$	5.97412	−	2.72829i	0.280688	−	0.128186i
$454$	−2.27025	+	39.6560i	−0.106548	+	1.86115i
$455$	−7.43932	−	1.06961i	−0.348761	−	0.0501442i
$456$	8.43003	+	10.3137i	0.394772	+	0.482982i
$457$	−27.0530	−	23.4416i	−1.26549	−	1.09655i	−0.990845	−	0.135003i	$-0.956896\pi$
$457$	−27.0530	−	23.4416i	−1.26549	−	1.09655i	−0.274641	−	0.961547i	$-0.588559\pi$
$458$	11.4606	+	14.8644i	0.535518	+	0.694567i
$459$		−	1.10665i		−	0.0516542i
$460$	24.6870	−	19.0533i	1.15104	−	0.888364i
$461$		−	1.46696i		−	0.0683230i	−0.999416	−	0.0341615i	$-0.989124\pi$
$461$		−	1.46696i		−	0.0683230i	0.999416	−	0.0341615i	$-0.0108761\pi$
$462$	0.408151	−	0.314688i	0.0189889	−	0.0146406i
$463$	−24.3753	−	21.1214i	−1.13282	−	0.981593i	−0.132864	−	0.991134i	$-0.542417\pi$
$463$	−24.3753	−	21.1214i	−1.13282	−	0.981593i	−0.999954	+	0.00954138i	$0.996963\pi$
$464$	−1.10812	−	19.4695i	−0.0514433	−	0.903849i
$465$	−0.307093	−	0.0441533i	−0.0142411	−	0.00204756i
$466$	−1.59741	−	0.0914496i	−0.0739986	−	0.00423632i
$467$	−19.6265	+	8.96312i	−0.908206	+	0.414764i	−0.814051	−	0.580794i	$-0.802742\pi$
$467$	−19.6265	+	8.96312i	−0.908206	+	0.414764i	−0.0941553	+	0.995558i	$0.530015\pi$
$468$	1.14915	+	0.693174i	0.0531197	+	0.0320420i
$469$	−41.8411	+	6.01585i	−1.93204	+	0.277786i
$470$	18.5147	+	32.7903i	0.854018	+	1.51250i
$471$	−4.27336	+	1.25477i	−0.196906	+	0.0578169i
$472$	1.24077	−	43.1318i	0.0571111	−	1.98530i
$473$	−0.0950476	+	0.208125i	−0.00437029	+	0.00956961i
$474$	8.75031	−	16.5810i	0.401915	−	0.761591i
$475$	−19.8263	+	17.1796i	−0.909693	+	0.788253i
$476$	5.15509	+	5.61834i	0.236283	+	0.257516i
$477$	5.75601	−	3.69916i	0.263549	−	0.169373i
$478$	2.55300	+	2.48144i	0.116772	+	0.113498i
$479$	28.0485	+	18.0257i	1.28157	+	0.823615i	0.991081	−	0.133263i	$-0.0425456\pi$
$479$	28.0485	+	18.0257i	1.28157	+	0.823615i	0.290489	+	0.956878i	$0.406182\pi$
$480$	−12.0486	+	13.8955i	−0.549940	+	0.634239i
$481$	−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
$486$	−1.37748	+	0.320223i	−0.0624839	+	0.0145256i
$487$	9.94289	−	15.4714i	0.450555	−	0.701078i	−0.539464	−	0.842009i	$-0.681373\pi$
$487$	9.94289	−	15.4714i	0.450555	−	0.701078i	0.990019	+	0.140931i	$0.0450095\pi$
$488$	−12.5541	−	6.17554i	−0.568298	−	0.279554i
$489$	−17.8057	+	11.4431i	−0.805204	+	0.517473i
$490$	−4.44690	+	21.9388i	−0.200891	+	0.991096i
$491$	−5.53544	−	6.38824i	−0.249811	−	0.288297i	0.616970	−	0.786987i	$-0.288360\pi$
$491$	−5.53544	−	6.38824i	−0.249811	−	0.288297i	−0.866781	+	0.498690i	$0.833815\pi$
$492$	4.37112	−	2.14842i	0.197065	−	0.0968581i
$493$	−2.24125	+	4.90766i	−0.100941	+	0.221030i
$494$	4.20915	+	1.50214i	0.189378	+	0.0675843i
$495$	−0.0968938	−	0.329990i	−0.00435505	−	0.0148320i
$496$	−0.374122	+	0.0757036i	−0.0167986	+	0.00339919i
$497$	−31.3488	+	4.50727i	−1.40618	+	0.202179i
$498$	−21.7352	+	1.86538i	−0.973976	+	0.0835897i
$499$	5.33738	+	11.6872i	0.238934	+	0.523192i	0.990672	−	0.136270i	$-0.0435114\pi$
$499$	5.33738	+	11.6872i	0.238934	+	0.523192i	−0.751738	+	0.659462i	$0.770784\pi$
$500$	−2.87094	−	2.34819i	−0.128392	−	0.105014i
$501$	−8.39716	−	1.20733i	−0.375158	−	0.0539395i
$502$	−11.7619	+	4.57841i	−0.524957	+	0.204344i
$503$	−14.7464	+	17.0183i	−0.657510	+	0.758807i	−0.982368	−	0.186956i	$-0.940138\pi$
$503$	−14.7464	+	17.0183i	−0.657510	+	0.758807i	0.324859	+	0.945763i	$0.394683\pi$
$504$	5.50161	−	8.04241i	0.245061	−	0.358238i
$505$			61.8814i			2.75369i
$506$	0.298361	+	0.652470i	0.0132638	+	0.0290058i
$507$	−12.5497			−0.557353
$508$	−4.69212	+	0.133420i	−0.208179	+	0.00591955i
$509$	2.45914	+	2.13086i	0.109000	+	0.0944487i	0.707656	−	0.706558i	$-0.249753\pi$
$509$	2.45914	+	2.13086i	0.109000	+	0.0944487i	−0.598656	+	0.801006i	$0.704298\pi$
$510$	4.74172	−	1.84576i	0.209967	−	0.0817316i
$511$	−0.764365	+	5.31628i	−0.0338135	+	0.235178i
$512$	−8.22199	+	21.0808i	−0.363364	+	0.931647i
$513$	−4.28394	+	1.95641i	−0.189141	+	0.0863776i
$514$	−0.153970	−	1.79404i	−0.00679135	−	0.0791318i
$515$	−0.218605	−	1.52043i	−0.00963287	−	0.0669981i
$516$	−0.493685	+	4.29763i	−0.0217333	+	0.189192i
$517$	−0.831251	+	0.244077i	−0.0365584	+	0.0107345i
$518$	30.9552	+	11.0471i	1.36009	+	0.485382i
$519$	21.2626	+	9.71030i	0.933324	+	0.426235i
$520$	−1.05342	+	6.07996i	−0.0461957	+	0.266624i
$521$	20.1672	−	17.4750i	0.883541	−	0.765592i	−0.0895578	−	0.995982i	$-0.528545\pi$
$521$	20.1672	−	17.4750i	0.883541	−	0.765592i	0.973099	+	0.230389i	$0.0739999\pi$
$522$	6.75724	+	1.36966i	0.295756	+	0.0599484i
$523$	−14.3532	−	22.3340i	−0.627622	−	0.976599i	−0.998845	−	0.0480550i	$-0.984698\pi$
$523$	−14.3532	−	22.3340i	−0.627622	−	0.976599i	0.371223	−	0.928544i	$-0.378939\pi$
$524$	2.46337	−	0.425966i	0.107613	−	0.0186084i
$525$	16.1440	+	10.3751i	0.704582	+	0.452807i
$526$	7.71979	−	1.79462i	0.336599	−	0.0782492i
$527$	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
$532$	12.6355	−	29.8882i	0.547819	−	1.29582i
$533$	0.883468	−	1.37470i	0.0382672	−	0.0595450i
$534$	16.0015	+	15.5529i	0.692451	+	0.673041i
$535$	10.8064	+	16.8151i	0.467201	+	0.726979i
$536$	3.94922	+	34.4797i	0.170580	+	1.48930i
$537$	−6.11323	−	7.05504i	−0.263805	−	0.304448i
$538$	−10.3045	−	5.43800i	−0.444259	−	0.234449i
$539$	−0.468463	−	0.213940i	−0.0201781	−	0.00921505i
$540$	−3.66954	−	5.36806i	−0.157912	−	0.231004i
$541$	10.1713	+	34.6402i	0.437297	+	1.48930i	0.823731	+	0.566980i	$0.191888\pi$
$541$	10.1713	+	34.6402i	0.437297	+	1.48930i	−0.386434	+	0.922317i	$0.626293\pi$
$542$	10.5995	+	18.7722i	0.455287	+	0.806334i
$543$	2.82575	+	19.6535i	0.121265	+	0.843413i
$544$	4.73249	−	4.09798i	0.202904	−	0.175699i
$545$	−8.95961	−	19.6188i	−0.383788	−	0.840378i
$546$	0.186853	−	3.26389i	0.00799658	−	0.139681i
$547$	−4.84370	+	33.6887i	−0.207102	+	1.44043i	0.575449	+	0.817838i	$0.304827\pi$
$547$	−4.84370	+	33.6887i	−0.207102	+	1.44043i	−0.782550	+	0.622587i	$0.786082\pi$
$548$	23.0935	+	6.07348i	0.986504	+	0.259446i
$549$	3.23927	−	3.73831i	0.138249	−	0.159547i
$550$	0.659946	−	0.508824i	0.0281402	−	0.0216963i
$551$	22.9602			0.978136
$552$	9.17567	+	9.99035i	0.390543	+	0.425217i
$553$	−45.6714			−1.94215
$554$	−1.35527	+	1.04493i	−0.0575799	+	0.0443946i
$555$	14.3630	−	16.5758i	0.609677	−	0.703605i
$556$	−9.14951	+	34.7896i	−0.388026	+	1.47541i
$557$	2.01391	−	14.0070i	0.0853320	−	0.593497i	−0.901626	−	0.432517i	$-0.857626\pi$
$557$	2.01391	−	14.0070i	0.0853320	−	0.593497i	0.986958	−	0.160980i	$-0.0514654\pi$
$558$	0.00771325	−	0.134732i	0.000326528	−	0.00570368i
$559$	0.602921	+	1.32021i	0.0255008	+	0.0558390i
$560$	43.6356	+	10.1592i	1.84394	+	0.429306i
$561$	0.0166600	+	0.115873i	0.000703387	+	0.00489216i
$562$	−7.09394	−	12.5637i	−0.299240	−	0.529967i
$563$	2.69371	+	9.17395i	0.113527	+	0.386636i	0.996580	−	0.0826371i	$-0.0263342\pi$
$563$	2.69371	+	9.17395i	0.113527	+	0.386636i	−0.883053	+	0.469273i	$0.844516\pi$
$564$	−13.5222	+	9.24364i	−0.569389	+	0.389227i
$565$	44.8643	+	20.4888i	1.88745	+	0.861972i
$566$	−3.03579	−	1.60208i	−0.127604	−	0.0673403i
$567$	2.25604	+	2.60361i	0.0947448	+	0.109341i
$568$	2.95889	+	25.8333i	0.124152	+	1.08394i
$569$	−3.64544	−	5.67242i	−0.152825	−	0.237800i	0.756396	−	0.654114i	$-0.226958\pi$
$569$	−3.64544	−	5.67242i	−0.152825	−	0.237800i	−0.909221	+	0.416314i	$0.863322\pi$
$570$	−15.5278	−	15.0925i	−0.650387	−	0.632156i
$571$	1.48323	−	2.30795i	0.0620712	−	0.0965846i	−0.808831	−	0.588042i	$-0.799899\pi$
$571$	1.48323	−	2.30795i	0.0620712	−	0.0965846i	0.870902	+	0.491457i	$0.163535\pi$
$572$	−0.130758	−	0.0552794i	−0.00546728	−	0.00231135i
$573$	−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	0.112902	−	0.993606i	$-0.463985\pi$
$577$	−7.91014	−	2.32263i	−0.329303	−	0.0966922i	−0.442205	+	0.896914i	$0.645804\pi$
$578$	21.7302	−	5.05163i	0.903858	−	0.210120i
$579$	11.1711	+	7.17923i	0.464255	+	0.298359i
$580$	5.40158	+	31.2374i	0.224288	+	1.29706i
$581$	28.7308	+	44.7061i	1.19196	+	1.85472i
$582$	12.5509	+	2.54400i	0.520251	+	0.105452i
$583$	−0.546998	+	0.473977i	−0.0226543	+	0.0196301i
$584$	4.34485	+	0.752797i	0.179791	+	0.0311509i
$585$	−1.98447	−	0.906276i	−0.0820476	−	0.0374699i
$586$	0.823714	+	0.293962i	0.0340273	+	0.0121435i
$587$	−3.88206	+	1.13988i	−0.160230	+	0.0470477i	−0.360864	−	0.932619i	$-0.617518\pi$
$587$	−3.88206	+	1.13988i	−0.160230	+	0.0470477i	0.200634	+	0.979666i	$0.435700\pi$
$588$	−9.67341	−	1.11122i	−0.398925	−	0.0458260i
$589$	−0.0639581	−	0.444838i	−0.00263535	−	0.0183292i
$590$	5.99797	+	69.8875i	0.246933	+	2.87722i
$591$	15.4327	−	7.04789i	0.634818	−	0.289912i
$592$	9.79680	−	25.1431i	0.402646	−	1.03338i
$593$	2.47242	−	17.1961i	0.101530	−	0.706157i	−0.873941	−	0.486031i	$-0.838444\pi$
$593$	2.47242	−	17.1961i	0.101530	−	0.706157i	0.975471	−	0.220126i	$-0.0706468\pi$
$594$	0.139409	−	0.0542664i	0.00572004	−	0.00222658i
$595$	−9.36771	−	8.11717i	−0.384039	−	0.332771i
$596$	0.559711	+	19.6839i	0.0229266	+	0.806286i
$597$	−7.16611			−0.293289
$598$	4.36733	+	1.28003i	0.178593	+	0.0523443i
$599$			12.2519i			0.500598i	0.968169	+	0.250299i	$0.0805290\pi$
$599$			12.2519i			0.500598i	−0.968169	+	0.250299i	$0.919471\pi$
$600$	8.89565	−	13.0039i	0.363163	−	0.530883i
$601$	−30.9481	+	35.7160i	−1.26240	+	1.45689i	−0.429884	+	0.902884i	$0.641446\pi$
$601$	−30.9481	+	35.7160i	−1.26240	+	1.45689i	−0.832515	+	0.554003i	$0.813100\pi$
$602$	9.82025	−	3.82262i	0.400243	−	0.155798i
$603$	−12.1452	−	1.74622i	−0.494591	−	0.0711115i
$604$	−8.31612	+	10.1674i	−0.338378	+	0.413707i
$605$	−14.8415	−	32.4984i	−0.603394	−	1.32125i
$606$	−26.8186	+	2.30166i	−1.08943	+	0.0934985i
$607$	−39.9660	+	5.74624i	−1.62217	+	0.233233i	−0.892658	−	0.450736i	$-0.851162\pi$
$607$	−39.9660	+	5.74624i	−1.62217	+	0.233233i	−0.729512	+	0.683968i	$0.760253\pi$
$608$	−24.2300	−	11.0752i	−0.982654	−	0.449157i
$609$	−4.73187	−	16.1153i	−0.191745	−	0.653023i
$610$	21.4204	+	7.64438i	0.867286	+	0.309512i
$611$	−2.28293	+	4.99891i	−0.0923573	+	0.202234i
$612$	0.976295	+	1.98635i	0.0394644	+	0.0802934i
$613$	−0.430587	−	0.496924i	−0.0173912	−	0.0200706i	0.746987	−	0.664838i	$-0.231500\pi$
$613$	−0.430587	−	0.496924i	−0.0173912	−	0.0200706i	−0.764379	+	0.644768i	$0.776954\pi$
$614$	−3.99453	+	19.7070i	−0.161206	+	0.795312i
$615$	−6.66073	+	4.28059i	−0.268587	+	0.172610i
$616$	−0.454976	+	0.924910i	−0.0183315	+	0.0372657i
$617$	1.64652	−	2.56204i	0.0662865	−	0.103144i	−0.806528	−	0.591196i	$-0.798656\pi$
$617$	1.64652	−	2.56204i	0.0662865	−	0.103144i	0.872815	+	0.488052i	$0.162292\pi$
$618$	0.650803	−	0.151292i	0.0261791	−	0.00608586i
$619$	7.21768	−	24.5812i	0.290103	−	0.988000i	−0.677500	−	0.735523i	$-0.736937\pi$
$619$	7.21768	−	24.5812i	0.290103	−	0.988000i	0.967603	−	0.252477i	$-0.0812453\pi$
$620$	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
$624$	−2.67415	−	0.230398i	−0.107052	−	0.00922332i
$625$	−18.3584	−	11.7982i	−0.734336	−	0.471929i
$626$	−4.94995	−	4.81120i	−0.197840	−	0.192294i
$627$	0.419100	−	0.269339i	0.0167373	−	0.0107564i
$628$	6.56335	−	6.02219i	0.261906	−	0.240311i
$629$	−5.64211	+	4.88892i	−0.224966	+	0.194934i
$630$	−7.39300	+	14.0090i	−0.294544	+	0.558134i
$631$	17.0712	−	37.3807i	0.679594	−	1.48810i	−0.183480	−	0.983023i	$-0.558736\pi$
$631$	17.0712	−	37.3807i	0.679594	−	1.48810i	0.863073	−	0.505079i	$-0.168537\pi$
$632$	−1.07821	+	37.4810i	−0.0428891	+	1.49092i
$633$	−0.117148	+	0.0343976i	−0.00465620	+	0.00136718i
$634$	5.74890	+	10.1816i	0.228318	+	0.404361i
$635$	7.55296	−	1.08595i	0.299730	−	0.0430947i
$636$	−7.06812	+	11.7176i	−0.280269	+	0.464635i
$637$	−2.97163	+	1.35710i	−0.117740	+	0.0537702i
$638$	−0.728141	−	0.0416851i	−0.0288274	−	0.00165033i
$639$	−9.09960	−	1.30832i	−0.359974	−	0.0517565i
$640$	9.36751	−	35.5705i	0.370283	−	1.40605i
$641$	−31.4539	−	27.2550i	−1.24236	−	1.07651i	−0.994173	−	0.107795i	$-0.965621\pi$
$641$	−31.4539	−	27.2550i	−1.24236	−	1.07651i	−0.248183	−	0.968713i	$-0.579833\pi$
$642$	−6.88549	+	5.30878i	−0.271749	+	0.209521i
$643$			22.5959i			0.891095i	0.895258	+	0.445547i	$0.146991\pi$
$643$			22.5959i			0.891095i	−0.895258	+	0.445547i	$0.853009\pi$
$644$	11.0912	−	31.1270i	0.437053	−	1.22658i
$645$		−	7.03220i		−	0.276893i
$646$	4.50047	+	5.83712i	0.177069	+	0.229658i
$647$	3.17903	+	2.75465i	0.124981	+	0.108296i	0.715109	−	0.699013i	$-0.246377\pi$
$647$	3.17903	+	2.75465i	0.124981	+	0.108296i	−0.590128	+	0.807310i	$0.700923\pi$
$648$	2.18996	−	1.78999i	0.0860297	−	0.0703176i
$649$	−1.59736	−	0.229666i	−0.0627019	−	0.00901517i
$650$	0.302126	−	5.27744i	0.0118504	−	0.206998i
$651$	−0.299041	+	0.136568i	−0.0117204	+	0.00535251i
$652$	21.8647	−	36.2476i	0.856286	−	1.41957i
$653$	−41.1078	+	5.91041i	−1.60867	+	0.231292i	−0.887279	−	0.461233i	$-0.847407\pi$
$653$	−41.1078	+	5.91041i	−1.60867	+	0.231292i	−0.721394	+	0.692525i	$0.756498\pi$
$654$	8.16929	−	4.61269i	0.319444	−	0.180371i
$655$	−3.89928	+	1.14493i	−0.152358	+	0.0447362i
$656$	−5.95045	+	7.71244i	−0.232326	+	0.301120i
$657$	−0.647642	+	1.41814i	−0.0252669	+	0.0553268i
$658$	35.2890	+	18.6231i	1.37571	+	0.726004i
$659$	5.36910	−	4.65235i	0.209150	−	0.181230i	−0.543986	−	0.839094i	$-0.683086\pi$
$659$	5.36910	−	4.65235i	0.209150	−	0.181230i	0.753136	+	0.657865i	$0.228540\pi$
$660$	0.465035	+	0.506824i	0.0181015	+	0.0197281i
$661$	−3.97247	+	2.55295i	−0.154511	+	0.0992983i	−0.615612	−	0.788050i	$-0.711091\pi$
$661$	−3.97247	+	2.55295i	−0.154511	+	0.0992983i	0.461101	+	0.887348i	$0.347455\pi$
$662$	−26.9267	+	27.7033i	−1.04654	+	1.07672i
$663$	0.624700	+	0.401470i	0.0242613	+	0.0155918i
$664$	37.3671	−	22.5230i	1.45012	−	0.874063i
$665$	−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
$670$	−12.7746	−	54.9516i	−0.493526	−	2.12296i
$671$	−0.282892	+	0.440188i	−0.0109209	+	0.0169933i
$672$	−2.77987	+	19.2890i	−0.107236	+	0.744089i
$673$	−41.1422	+	26.4405i	−1.58592	+	1.01921i	−0.612411	+	0.790539i	$0.709800\pi$
$673$	−41.1422	+	26.4405i	−1.58592	+	1.01921i	−0.973505	+	0.228667i	$0.926563\pi$
$674$	−8.38688	−	1.69998i	−0.323050	−	0.0654808i
$675$	3.64783	+	4.20982i	0.140405	+	0.162036i
$676$	22.5257	−	11.0714i	0.866373	−	0.425824i
$677$	7.28503	−	15.9520i	0.279986	−	0.613085i	−0.716431	−	0.697658i	$-0.754225\pi$
$677$	7.28503	−	15.9520i	0.279986	−	0.613085i	0.996417	+	0.0845734i	$0.0269528\pi$
$678$	−7.21088	+	20.2057i	−0.276932	+	0.775994i
$679$	−8.78896	−	29.9325i	−0.337289	−	1.14870i
$680$	−6.88265	+	7.49615i	−0.263938	+	0.287464i
$681$	27.8010	−	3.99718i	1.06534	−	0.153172i
$682$	0.00122070	+	0.0142234i	4.67428e−5	+	0.000544641i
$683$	−11.6393	−	25.4866i	−0.445367	−	0.975217i	−0.990582	−	0.136921i	$-0.956279\pi$
$683$	−11.6393	−	25.4866i	−0.445367	−	0.975217i	0.545215	−	0.838296i	$-0.316448\pi$
$684$	5.96335	−	7.29090i	0.228014	−	0.278774i
$685$	−38.4224	−	5.52431i	−1.46804	−	0.211073i
$686$	−3.76702	−	9.67742i	−0.143826	−	0.369486i
$687$	8.69134	−	10.0303i	0.331595	−	0.382682i
$688$	−2.90526	−	8.14940i	−0.110762	−	0.310693i
$689$			4.59121i			0.174911i
$690$	−16.6720	−	14.4320i	−0.634692	−	0.549417i
$691$	−12.8621			−0.489298			−0.244649	−	0.969612i	$-0.578673\pi$
$691$	−12.8621			−0.489298			−0.244649	+	0.969612i	$0.578673\pi$
$692$	−46.7310	+	1.32879i	−1.77645	+	0.0505130i
$693$	−0.275416	−	0.238650i	−0.0104622	−	0.00906555i
$694$	15.1398	+	38.8938i	0.574698	+	1.47639i
$695$	8.32219	−	57.8821i	0.315679	−	2.19559i
$696$	−13.3370	+	3.50284i	−0.505537	+	0.132775i
$697$	2.45147	−	1.11955i	0.0928561	−	0.0424060i
$698$	10.4958	−	0.900785i	0.397273	−	0.0340952i
$699$	0.161014	+	1.11987i	0.00609009	+	0.0423575i
$700$	−38.1301	−	4.38014i	−1.44118	−	0.165554i
$701$	−37.6862	+	11.0657i	−1.42339	+	0.417944i	−0.900648	−	0.434549i	$-0.856908\pi$
$701$	−37.6862	+	11.0657i	−1.42339	+	0.417944i	−0.522738	+	0.852493i	$0.675090\pi$
$702$	0.318956	−	0.893751i	0.0120382	−	0.0337324i
$703$	28.8998	+	13.1981i	1.08998	+	0.497776i
$704$	0.748302	+	0.395220i	0.0282027	+	0.0148954i
$705$	20.1234	−	17.4370i	0.757890	−	0.656715i
$706$	8.22346	−	40.5705i	0.309494	−	1.52689i
$707$	35.4504	+	55.1620i	1.33325	+	2.07458i
$708$	−30.0653	+	5.19889i	−1.12992	+	0.195386i
$709$	−26.9105	−	17.2943i	−1.01064	−	0.649502i	−0.0730846	−	0.997326i	$-0.523284\pi$
$709$	−26.9105	−	17.2943i	−1.01064	−	0.649502i	−0.937560	+	0.347824i	$0.886921\pi$
$710$	−9.57115	−	41.1715i	−0.359199	−	1.54514i
$711$	−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
$716$	17.1967	+	7.27008i	0.642671	+	0.271696i
$717$	1.36105	−	2.11783i	0.0508293	−	0.0790920i
$718$	−19.3024	+	19.8591i	−0.720361	+	0.741135i
$719$	−11.4694	−	17.8467i	−0.427736	−	0.665571i	0.558765	−	0.829326i	$-0.311276\pi$
$719$	−11.4694	−	17.8467i	−0.427736	−	0.665571i	−0.986501	+	0.163755i	$0.947639\pi$
$720$	11.3222	+	6.39792i	0.421955	+	0.238436i
$721$	−1.06589	−	1.23010i	−0.0396956	−	0.0458112i
$722$	2.09875	−	3.97694i	0.0781075	−	0.148006i
$723$	−7.39052	−	3.37514i	−0.274856	−	0.125523i
$724$	−22.4104	−	32.7835i	−0.832876	−	1.21839i
$725$	−7.65104	−	26.0570i	−0.284152	−	0.967734i
$726$	13.5324	−	7.64089i	0.502233	−	0.283580i
$727$	4.20808	+	29.2679i	0.156069	+	1.08549i	0.905789	+	0.423729i	$0.139279\pi$
$727$	4.20808	+	29.2679i	0.156069	+	1.08549i	−0.749720	+	0.661756i	$0.769812\pi$
$728$	2.54403	+	6.02324i	0.0942880	+	0.223236i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−7.15653	−	0.409702i	−0.264875	−	0.0151637i
$731$	−0.340649	+	2.36927i	−0.0125994	+	0.0876305i
$732$	−2.51625	+	9.56765i	−0.0930033	+	0.353630i
$733$	17.2557	−	19.9142i	0.637354	−	0.735546i	−0.341550	−	0.939864i	$-0.610952\pi$
$733$	17.2557	−	19.9142i	0.637354	−	0.735546i	0.978905	+	0.204317i	$0.0654974\pi$
$734$	−24.2883	−	31.5019i	−0.896497	−	1.16276i
$735$	15.8286			0.583846
$736$	−25.2831	−	9.83700i	−0.931946	−	0.362597i
$737$	1.29796			0.0478110
$738$	−2.10290	−	2.72746i	−0.0774087	−	0.100399i
$739$	25.7540	−	29.7217i	0.947377	−	1.09333i	−0.0481492	−	0.998840i	$-0.515332\pi$
$739$	25.7540	−	29.7217i	0.947377	−	1.09333i	0.995526	−	0.0944907i	$-0.0301223\pi$
$740$	−11.1572	+	42.4233i	−0.410145	+	1.55951i
$741$	0.449739	−	3.12800i	0.0165216	−	0.114910i
$742$	33.2810	+	1.90529i	1.22179	+	0.0699456i
$743$	−3.79546	−	8.31089i	−0.139242	−	0.304897i	0.827145	−	0.561988i	$-0.189963\pi$
$743$	−3.79546	−	8.31089i	−0.139242	−	0.304897i	−0.966387	+	0.257091i	$0.917236\pi$
$744$	0.105017	+	0.248638i	0.00385010	+	0.00911550i
$745$	−4.55568	−	31.6855i	−0.166907	−	1.16087i
$746$	36.5315	−	20.6271i	1.33751	−	0.755211i
$747$	4.34589	+	14.8007i	0.159008	+	0.541530i
$748$	−0.132127	−	0.193285i	−0.00483104	−	0.00706718i
$749$	19.2659	+	8.79846i	0.703962	+	0.321489i
$750$	−1.22405	+	2.31945i	−0.0446959	+	0.0846945i
$751$	−13.3625	−	15.4211i	−0.487603	−	0.562724i	0.457621	−	0.889148i	$-0.348702\pi$
$751$	−13.3625	−	15.4211i	−0.487603	−	0.562724i	−0.945223	+	0.326424i	$0.894156\pi$
$752$	16.1165	−	28.5209i	0.587708	−	1.04005i
$753$	4.82510	+	7.50800i	0.175836	+	0.273607i
$754$	−3.22454	+	3.31754i	−0.117431	+	0.120818i
$755$	11.5442	−	17.9631i	0.420135	−	0.653743i
$756$	−6.34632	−	2.68297i	−0.230813	−	0.0975786i
$757$	46.5747	+	13.6756i	1.69279	+	0.497047i	0.979093	−	0.203411i	$-0.0652029\pi$
$757$	46.5747	+	13.6756i	1.69279	+	0.497047i	0.713693	+	0.700458i	$0.247021\pi$
$758$	−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	0.768785	−	0.639507i	$-0.220862\pi$
$761$	29.5113	+	8.66531i	1.06978	+	0.314117i	0.301000	+	0.953624i	$0.402680\pi$
$762$	0.751567	+	3.23296i	0.0272264	+	0.117118i
$763$	−19.2259	−	12.3557i	−0.696024	−	0.447307i
$764$	36.5414	−	6.31875i	1.32202	−	0.228604i
$765$	−1.94521	−	3.02680i	−0.0703292	−	0.109434i
$766$	−6.30058	+	31.0840i	−0.227649	+	1.12311i
$767$	−7.73647	+	6.70369i	−0.279348	+	0.242056i
$768$	15.7642	+	2.73672i	0.568842	+	0.0987530i
$769$	39.9697	+	18.2535i	1.44134	+	0.658239i	0.974147	−	0.225915i	$-0.0725371\pi$
$769$	39.9697	+	18.2535i	1.44134	+	0.658239i	0.467196	+	0.884154i	$0.345264\pi$
$770$	0.563192	−	1.57812i	0.0202960	−	0.0568716i
$771$	−1.22167	+	0.358714i	−0.0439973	+	0.0129188i
$772$	−26.3847	−	3.03091i	−0.949606	−	0.109085i
$773$	−2.36541	−	16.4518i	−0.0850777	−	0.591729i	−0.987108	−	0.160056i	$-0.948833\pi$
$773$	−2.36541	−	16.4518i	−0.0850777	−	0.591729i	0.902030	−	0.431673i	$-0.142076\pi$
$774$	3.04766	−	0.261560i	0.109546	−	0.00940159i
$775$	−0.483525	+	0.220819i	−0.0173687	+	0.00793204i
$776$	−24.7721	+	6.50617i	−0.889266	+	0.233558i
$777$	3.30750	−	23.0042i	0.118656	−	0.825271i
$778$	−16.1166	−	41.4034i	−0.577809	−	1.48438i
$779$	−8.66772	−	7.51062i	−0.310553	−	0.269096i
$780$	4.36147	−	0.124018i	0.156166	−	0.00444055i
$781$	0.972476			0.0347979
$782$	4.91797	+	5.67001i	0.175866	+	0.202759i
$783$		−	4.87525i		−	0.174227i
$784$	18.3433	−	6.53938i	0.655117	−	0.233549i
$785$	−9.48249	+	10.9434i	−0.338445	+	0.390586i
$786$	−0.641232	−	1.64731i	−0.0228720	−	0.0587577i
$787$	34.0937	+	4.90193i	1.21531	+	0.174735i	0.719995	−	0.693979i	$-0.244144\pi$
$787$	34.0937	+	4.90193i	1.21531	+	0.174735i	0.495313	+	0.868714i	$0.335053\pi$
$788$	−21.4827	+	26.2652i	−0.765291	+	0.935658i
$789$	−2.32810	−	5.09783i	−0.0828826	−	0.181488i
$790$	−5.21217	−	60.7314i	−0.185441	−	2.16073i
$791$	51.7302	−	7.43768i	1.83932	−	0.264454i
$792$	−0.202354	+	0.220391i	−0.00719034	+	0.00783126i
$793$	0.935120	+	3.18473i	0.0332071	+	0.113093i
$794$	9.93764	−	27.8463i	0.352674	−	0.988230i
$795$	9.24107	−	20.2351i	0.327747	−	0.717666i
$796$	12.8626	−	6.32197i	0.455901	−	0.224076i
$797$	22.6795	+	26.1736i	0.803350	+	0.927115i	0.998560	−	0.0536466i	$-0.0170844\pi$
$797$	22.6795	+	26.1736i	0.803350	+	0.927115i	−0.195210	+	0.980761i	$0.562539\pi$
$798$	−22.4878	−	4.55818i	−0.796061	−	0.161358i
$799$	−7.62458	+	4.90002i	−0.269738	+	0.173350i
$800$	−4.49482	+	31.1887i	−0.158916	+	1.10269i
$801$	8.53065	−	13.2740i	0.301416	−	0.469012i
$802$	7.31305	+	31.4580i	0.258233	+	1.11082i
$803$	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
$808$	46.1066	−	27.7908i	1.62202	−	0.977675i
$809$	33.1023	+	21.2735i	1.16381	+	0.747938i	0.972342	−	0.233561i	$-0.0750377\pi$
$809$	33.1023	+	21.2735i	1.16381	+	0.747938i	0.191471	+	0.981498i	$0.438674\pi$
$810$	−3.20468	+	3.29710i	−0.112601	+	0.115848i
$811$	7.39709	−	4.75382i	0.259747	−	0.166929i	−0.404286	−	0.914633i	$-0.632480\pi$
$811$	7.39709	−	4.75382i	0.259747	−	0.166929i	0.664033	+	0.747703i	$0.268844\pi$
$812$	22.7102	+	24.7510i	0.796973	+	0.868591i
$813$	11.5205	−	9.98253i	0.404040	−	0.350103i
$814$	−0.892545	−	0.471023i	−0.0312837	−	0.0165094i
$815$	−28.5865	+	62.5957i	−1.00134	+	2.19263i
$816$	−3.50473	−	2.70403i	−0.122690	−	0.0946601i
$817$	9.77383	−	2.86986i	0.341943	−	0.100404i
$818$	−36.4867	+	20.6018i	−1.27573	+	0.720325i
$819$	−2.28817	+	0.328989i	−0.0799550	+	0.0114958i
$820$	8.17908	−	13.5594i	0.285626	−	0.473515i
$821$	−0.283354	+	0.129403i	−0.00988912	+	0.00451621i	−0.420353	−	0.907360i	$-0.638094\pi$
$821$	−0.283354	+	0.129403i	−0.00988912	+	0.00451621i	0.410464	+	0.911877i	$0.365367\pi$
$822$	0.965054	−	16.8572i	0.0336601	−	0.587964i
$823$	18.2817	+	2.62852i	0.637262	+	0.0916244i	0.453370	−	0.891322i	$-0.350221\pi$
$823$	18.2817	+	2.62852i	0.637262	+	0.0916244i	0.183891	+	0.982947i	$0.441131\pi$
$824$	−1.03466	+	0.845697i	−0.0360442	+	0.0294613i
$825$	−0.445325	−	0.385877i	−0.0155042	−	0.0134345i
$826$	45.3836	+	58.8626i	1.57910	+	2.04809i
$827$		−	10.5440i		−	0.366652i	−0.983052	−	0.183326i	$-0.941314\pi$
$827$		−	10.5440i		−	0.366652i	0.983052	−	0.183326i	$-0.0586864\pi$
$828$	5.63454	−	7.76222i	0.195814	−	0.269756i
$829$			5.62524i			0.195373i	0.995217	+	0.0976863i	$0.0311442\pi$
$829$			5.62524i			0.195373i	−0.995217	+	0.0976863i	$0.968856\pi$
$830$	−56.1689	+	43.3067i	−1.94965	+	1.50320i
$831$	0.914523	+	0.792439i	0.0317245	+	0.0274894i
$832$	5.00314	−	1.94561i	0.173453	−	0.0674517i
$833$	−5.33292	−	0.766758i	−0.184775	−	0.0265666i
$834$	25.3949	+	1.45382i	0.879353	+	0.0503417i
$835$	−25.0892	+	11.4579i	−0.868248	+	0.396516i
$836$	−0.514637	+	0.853173i	−0.0177991	+	0.0295076i
$837$	−0.0944549	+	0.0135806i	−0.00326484	+	0.000469413i
$838$	−5.04211	−	8.92980i	−0.174177	−	0.308475i
$839$	29.6480	−	8.70544i	1.02356	−	0.300545i	0.273472	−	0.961880i	$-0.411828\pi$
$839$	29.6480	−	8.70544i	1.02356	−	0.300545i	0.750091	+	0.661335i	$0.230010\pi$
$840$	0.910967	−	31.6672i	0.0314313	−	1.09262i
$841$	2.17341	−	4.75911i	0.0749452	−	0.164107i
$842$	11.8843	−	22.5195i	0.409558	−	0.776075i
$843$	−7.71032	+	6.68103i	−0.265557	+	0.230107i
$844$	0.179924	−	0.165089i	0.00619325	−	0.00568260i
$845$	−34.3247	+	22.0592i	−1.18081	+	0.758858i
$846$	8.30544	+	8.07264i	0.285547	+	0.277543i
$847$	−31.8475	−	20.4672i	−1.09429	−	0.703260i
$848$	2.34931	−	27.2677i	0.0806758	−	0.936376i
$849$	−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	0.609099	+	0.793094i	$0.291531\pi$
$853$	−9.69898	+	33.0317i	−0.332087	+	1.13098i	−0.941186	+	0.337890i	$0.890287\pi$
$854$	23.4737	−	5.45694i	0.803254	−	0.186733i
$855$	−8.27813	+	12.8810i	−0.283106	+	0.440522i
$856$	7.67544	−	15.6032i	0.262341	−	0.533307i
$857$	4.60502	−	2.95947i	0.157305	−	0.101094i	−0.459620	−	0.888115i	$-0.652015\pi$
$857$	4.60502	−	2.95947i	0.157305	−	0.101094i	0.616925	+	0.787022i	$0.288378\pi$
$858$	−0.0199417	+	0.0983825i	−0.000680798	+	0.00335872i
$859$	7.95606	+	9.18179i	0.271457	+	0.313278i	0.875067	−	0.484001i	$-0.160817\pi$
$859$	7.95606	+	9.18179i	0.271457	+	0.313278i	−0.603610	+	0.797280i	$0.706272\pi$
$860$	6.20383	+	12.6222i	0.211549	+	0.430413i
$861$	−3.48522	+	7.63156i	−0.118776	+	0.260083i
$862$	−47.3229	−	16.8883i	−1.61183	−	0.575219i
$863$	1.87657	+	6.39100i	0.0638791	+	0.217552i	0.985247	−	0.171140i	$-0.0547451\pi$
$863$	1.87657	+	6.39100i	0.0638791	+	0.217552i	−0.921368	+	0.388692i	$0.872927\pi$
$864$	−2.35165	+	5.14488i	−0.0800047	+	0.175032i
$865$	75.2234	−	10.8155i	2.55767	−	0.367738i
$866$	−16.3417	+	1.40249i	−0.555312	+	0.0476587i
$867$	−6.55330	−	14.3497i	−0.222562	−	0.487342i
$868$	0.416273	−	0.508943i	0.0141292	−	0.0172746i
$869$	1.38809	+	0.199577i	0.0470876	+	0.00677018i
$870$	20.8892	−	8.13131i	0.708210	−	0.275677i
$871$	5.39175	−	6.22241i	0.182693	−	0.210838i
$872$	−10.5938	+	15.4864i	−0.358752	+	0.524435i
$873$		−	9.05529i		−	0.306475i
$874$	13.2547	−	29.0616i	0.448348	−	0.983024i
$875$	6.38880			0.215981
$876$	−0.0886255	−	3.11679i	−0.00299438	−	0.105306i
$877$	−34.4822	−	29.8790i	−1.16438	−	1.00894i	−0.999745	−	0.0225871i	$-0.992810\pi$
$877$	−34.4822	−	29.8790i	−1.16438	−	1.00894i	−0.164636	−	0.986354i	$-0.552645\pi$
$878$	16.2696	−	6.33308i	0.549072	−	0.213731i
$879$	0.0880122	−	0.612138i	0.00296858	−	0.0206469i
$880$	−1.28182	−	0.499449i	−0.0432101	−	0.0168364i
$881$	1.47707	−	0.674557i	0.0497639	−	0.0227264i	−0.390378	−	0.920655i	$-0.627656\pi$
$881$	1.47707	−	0.674557i	0.0497639	−	0.0227264i	0.440142	+	0.897928i	$0.354928\pi$
$882$	0.588739	+	6.85990i	0.0198239	+	0.230985i
$883$	−1.50472	−	10.4655i	−0.0506378	−	0.352194i	−0.999350	−	0.0360524i	$-0.988522\pi$
$883$	−1.50472	−	10.4655i	−0.0506378	−	0.352194i	0.948712	−	0.316141i	$-0.102387\pi$
$884$	−1.47546	−	0.169492i	−0.0496251	−	0.00570062i
$885$	47.5905	−	13.9738i	1.59974	−	0.469725i
$886$	−45.8157	−	16.3504i	−1.53921	−	0.549303i
$887$	4.40843	+	2.01326i	0.148021	+	0.0675988i	0.488048	−	0.872817i	$-0.337709\pi$
$887$	4.40843	+	2.01326i	0.148021	+	0.0675988i	−0.340027	+	0.940416i	$0.610436\pi$
$888$	−18.8007	−	3.25744i	−0.630910	−	0.109313i
$889$	6.11070	−	5.29495i	0.204946	−	0.177587i
$890$	71.1035	+	14.4123i	2.38339	+	0.483103i
$891$	−0.0571903	−	0.0889898i	−0.00191595	−	0.00298127i
$892$	−4.39044	−	25.3900i	−0.147003	−	0.850119i
$893$	32.4475	+	20.8528i	1.08581	+	0.697811i
$894$	13.5626	−	3.15290i	0.453602	−	0.105449i
$895$	−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
$900$	−10.2615	−	4.33814i	−0.342049	−	0.144605i
$901$	−4.09369	+	6.36991i	−0.136381	+	0.212212i
$902$	0.261246	+	0.253923i	0.00869852	+	0.00845470i
$903$	−4.02858	−	6.26860i	−0.134063	−	0.208606i
$904$	−4.88261	−	42.6289i	−0.162393	−	1.41782i
$905$	42.2745	+	48.7873i	1.40525	+	1.62175i
$906$	8.21434	+	4.33496i	0.272903	+	0.144019i
$907$	−14.5423	−	6.64126i	−0.482870	−	0.220519i	0.159080	−	0.987266i	$-0.449147\pi$
$907$	−14.5423	−	6.64126i	−0.482870	−	0.220519i	−0.641950	+	0.766746i	$0.721874\pi$
$908$	−46.3741	+	31.7008i	−1.53898	+	1.05203i
$909$	5.36231	+	18.2623i	0.177857	+	0.605724i
$910$	−5.22600	−	9.25548i	−0.173240	−	0.306816i
$911$	5.92335	+	41.1978i	0.196249	+	1.36494i	0.815048	+	0.579394i	$0.196711\pi$
$911$	5.92335	+	41.1978i	0.196249	+	1.36494i	−0.618798	+	0.785550i	$0.712380\pi$
$912$	−4.27164	+	18.3474i	−0.141448	+	0.607544i
$913$	−0.677855	−	1.48430i	−0.0224337	−	0.0491230i
$914$	2.89339	−	50.5408i	0.0957049	−	1.67174i
$915$	2.28873	−	15.9184i	0.0756629	−	0.526247i
$916$	−6.75140	+	25.6711i	−0.223073	+	0.848198i
$917$	−2.81997	+	3.25442i	−0.0931237	+	0.107470i
$918$	1.23943	−	0.955609i	0.0409072	−	0.0315398i
$919$	−9.52582			−0.314228			−0.157114	−	0.987580i	$-0.550219\pi$
$919$	−9.52582			−0.314228			−0.157114	+	0.987580i	$0.550219\pi$
$920$	42.6568	+	11.1961i	1.40635	+	0.369125i
$921$	14.2184			0.468511
$922$	1.64296	−	1.26673i	0.0541079	−	0.0417177i
$923$	4.03968	−	4.66204i	0.132968	−	0.153453i
$924$	0.704886	+	0.185382i	0.0231891	+	0.00609862i
$925$	5.34796	−	37.1959i	0.175840	−	1.22299i
$926$	2.60701	−	45.5384i	0.0856716	−	1.49648i
$927$	−0.196266	−	0.429763i	−0.00644623	−	0.0141153i
$928$	20.8485	−	18.0532i	0.684386	−	0.592626i
$929$	−5.33843	−	37.1296i	−0.175148	−	1.21818i	−0.867801	−	0.496911i	$-0.834468\pi$
$929$	−5.33843	−	37.1296i	−0.175148	−	1.21818i	0.692653	−	0.721271i	$-0.256442\pi$
$930$	−0.215728	−	0.382064i	−0.00707400	−	0.0125284i
$931$	6.45968	+	21.9997i	0.211708	+	0.721010i
$932$	−1.27696	−	1.86803i	−0.0418283	−	0.0611894i
$933$	−12.2081	−	5.57526i	−0.399676	−	0.182526i
$934$	−26.9862	−	14.2414i	−0.883016	−	0.465994i
$935$	0.249241	+	0.287640i	0.00815106	+	0.00940683i
$936$	0.215971	+	1.88559i	0.00705923	+	0.0616324i
$937$	11.9622	+	18.6136i	0.390788	+	0.608078i	0.979784	−	0.200058i	$-0.0641130\pi$
$937$	11.9622	+	18.6136i	0.390788	+	0.608078i	−0.588996	+	0.808136i	$0.700477\pi$
$938$	−42.8679	−	41.6663i	−1.39969	−	1.36045i
$939$	−2.63890	+	4.10621i	−0.0861174	+	0.134001i
$940$	−20.7367	+	49.0508i	−0.676357	+	1.59986i
$941$	5.14805	+	1.51160i	0.167822	+	0.0492769i	0.364564	−	0.931178i	$-0.381218\pi$
$941$	5.14805	+	1.51160i	0.167822	+	0.0492769i	−0.196742	+	0.980455i	$0.563036\pi$
$942$	−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
$946$	−0.315170	+	0.0732676i	−0.0102471	+	0.00238214i
$947$	−6.68081	−	4.29349i	−0.217097	−	0.139520i	0.427573	−	0.903981i	$-0.359369\pi$
$947$	−6.68081	−	4.29349i	−0.217097	−	0.139520i	−0.644670	+	0.764461i	$0.723005\pi$
$948$	26.1263	−	4.51777i	0.848544	−	0.146730i
$949$	−0.565580	−	0.880059i	−0.0183595	−	0.0285679i
$950$	−36.3610	−	7.37020i	−1.17971	−	0.239121i
$951$	6.24841	−	5.41428i	0.202619	−	0.175570i
$952$	−1.84092	+	10.6251i	−0.0596646	+	0.344361i
$953$	−27.2980	−	12.4666i	−0.884270	−	0.403832i	−0.0790929	−	0.996867i	$-0.525202\pi$
$953$	−27.2980	−	12.4666i	−0.884270	−	0.403832i	−0.805177	+	0.593035i	$0.797930\pi$
$954$	9.11335	+	3.25232i	0.295056	+	0.105298i
$955$	−57.8416	+	16.9838i	−1.87171	+	0.549584i
$956$	−0.574605	+	5.00206i	−0.0185841	+	0.161778i
$957$	0.0733941	+	0.510467i	0.00237249	+	0.0165011i
$958$	4.03190	+	46.9791i	0.130265	+	1.51783i
$959$	−37.4150	+	17.0869i	−1.20819	+	0.551763i
$960$	−25.9667	−	1.49520i	−0.838072	−	0.0482574i
$961$	−4.41046	+	30.6755i	−0.142273	+	0.989531i
$962$	−5.96572	+	2.32221i	−0.192343	+	0.0748711i
$963$	4.64627	+	4.02601i	0.149724	+	0.129736i
$964$	16.2429	−	0.461865i	0.523149	−	0.0148757i
$965$	43.1732			1.38980
$966$	−23.1294	−	3.31389i	−0.744177	−	0.106623i
$967$			29.5149i			0.949135i	0.880219	+	0.474568i	$0.157396\pi$
$967$			29.5149i			0.949135i	−0.880219	+	0.474568i	$0.842604\pi$
$968$	−17.5486	+	25.6530i	−0.564033	+	0.824520i
$969$	3.41302	−	3.93883i	0.109642	−	0.126534i
$970$	38.7996	−	15.1031i	1.24578	−	0.484931i
$971$	−0.0375125	−	0.00539348i	−0.00120383	−	0.000173085i	0.141713	−	0.989908i	$-0.454739\pi$
$971$	−0.0375125	−	0.00539348i	−0.00120383	−	0.000173085i	−0.142917	+	0.989735i	$0.545648\pi$
$972$	−1.54812	−	1.26623i	−0.0496558	−	0.0406144i
$973$	−25.7408	−	56.3645i	−0.825212	−	1.80696i
$974$	25.9134	−	2.22398i	0.830320	−	0.0712608i
$975$	−3.69978	+	0.531947i	−0.118488	+	0.0170360i
$976$	−3.92416	−	19.3929i	−0.125609	−	0.620753i
$977$	6.37952	+	21.7267i	0.204099	+	0.695097i	0.996385	+	0.0849479i	$0.0270724\pi$
$977$	6.37952	+	21.7267i	0.204099	+	0.695097i	−0.792286	+	0.610149i	$0.791109\pi$
$978$	−28.1914	−	10.0608i	−0.901462	−	0.321709i
$979$	−0.693376	+	1.51828i	−0.0221604	+	0.0485245i
$980$	−28.4109	+	13.9640i	−0.907554	+	0.446065i
$981$	−4.34421	−	5.01348i	−0.138700	−	0.160068i
$982$	2.37476	−	11.7159i	0.0757815	−	0.373869i
$983$	18.7739	−	12.0653i	0.598795	−	0.384822i	−0.205846	−	0.978584i	$-0.565994\pi$
$983$	18.7739	−	12.0653i	0.598795	−	0.384822i	0.804640	+	0.593762i	$0.202358\pi$
$984$	6.18069	+	3.04037i	0.197033	+	0.0969235i
$985$	29.8216	−	46.4034i	0.950197	−	1.47853i
$986$	−7.43182	+	1.72768i	−0.236677	+	0.0550204i
$987$	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	−0.626601	−	0.779340i	$-0.715554\pi$
$991$	10.1326	−	34.5084i	0.321872	−	1.09620i	0.948473	−	0.316857i	$-0.102627\pi$
$992$	−0.407845	−	0.353637i	−0.0129491	−	0.0112280i
$993$	22.9811	+	14.7691i	0.729285	+	0.468683i
$994$	−32.1181	−	31.2178i	−1.01872	−	0.990168i
$995$	−19.6000	+	12.5962i	−0.621362	+	0.399325i
$996$	−20.8578	−	22.7321i	−0.660903	−	0.720293i
$997$	−22.6172	+	19.5979i	−0.716295	+	0.620673i	−0.934805	−	0.355162i	$-0.884426\pi$
$997$	−22.6172	+	19.5979i	−0.716295	+	0.620673i	0.218510	+	0.975835i	$0.429880\pi$
$998$	−8.48053	+	16.0698i	−0.268446	+	0.508681i
$999$	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.235.17	✓	240
8.3	odd	2	inner	552.2.t.a.235.22	yes	240
23.14	odd	22	inner	552.2.t.a.451.22	yes	240
184.83	even	22	inner	552.2.t.a.451.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.t.a.235.17	✓	240	1.1	even	1	trivial
552.2.t.a.235.22	yes	240	8.3	odd	2	inner
552.2.t.a.451.17	yes	240	184.83	even	22	inner
552.2.t.a.451.22	yes	240	23.14	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.863512 + 1.11998i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-0.508693 + 1.93423i) q^{4} +(0.462696 - 3.21812i) q^{5} +(1.41190 + 0.0808295i) q^{6} +(-1.43113 - 3.13375i) q^{7} +(-2.60555 + 1.10050i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.863512 + 1.11998i) q^{2} +(0.654861 - 0.755750i) q^{3} +(-0.508693 + 1.93423i) q^{4} +(0.462696 - 3.21812i) q^{5} +(1.41190 + 0.0808295i) q^{6} +(-1.43113 - 3.13375i) q^{7} +(-2.60555 + 1.10050i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(4.00376 - 2.26068i) q^{10} +(0.0298024 + 0.101497i) q^{11} +(1.12867 + 1.65109i) q^{12} +(0.610377 + 0.278750i) q^{13} +(2.27392 - 4.30886i) q^{14} +(-2.12909 - 2.45710i) q^{15} +(-3.48246 - 1.96786i) q^{16} +(0.598302 + 0.930977i) q^{17} +(0.985686 - 1.01411i) q^{18} +(2.54616 - 3.96191i) q^{19} +(5.98920 + 2.53200i) 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} +(0.214875 + 0.924312i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(6.78938 - 1.17402i) q^{28} +(2.63576 + 4.10132i) q^{29} +(0.913400 - 4.50627i) q^{30} +(0.0721183 - 0.0624909i) q^{31} +(-0.803197 - 5.59954i) q^{32} +(0.0962231 + 0.0439436i) q^{33} +(-0.526030 + 1.47399i) q^{34} +(-10.7470 + 3.15559i) q^{35} +(1.98693 + 0.228246i) q^{36} +(0.960068 + 6.67742i) q^{37} +(6.63589 - 0.569513i) q^{38} +(0.610377 - 0.278750i) q^{39} +(2.33598 + 8.89418i) q^{40} +(0.346577 - 2.41050i) q^{41} +(-1.76732 - 4.54022i) q^{42} +(1.63464 + 1.41643i) q^{43} +(-0.211479 + 0.00601339i) q^{44} -3.25121 q^{45} +(6.71282 - 0.968529i) q^{46} +8.18987i q^{47} +(-3.76773 + 1.34320i) q^{48} +(-3.18820 + 3.67938i) q^{49} +(-2.85761 - 7.34116i) q^{50} +(1.09539 + 0.157493i) q^{51} +(-0.849660 + 1.03881i) q^{52} +(2.84234 + 6.22386i) q^{53} +(-0.120928 - 1.40903i) q^{54} +(0.340421 - 0.0489451i) q^{55} +(7.17759 + 6.59017i) q^{56} +(-1.32683 - 4.51876i) q^{57} +(-2.31737 + 6.49353i) q^{58} +(-6.33745 + 13.8771i) q^{59} +(5.83565 - 2.86823i) q^{60} +(3.23927 + 3.73831i) q^{61} +(0.132263 + 0.0268092i) q^{62} +(-2.89818 + 1.86255i) q^{63} +(5.57778 - 5.73483i) q^{64} +(1.17947 - 1.83529i) q^{65} +(0.0338740 + 0.145713i) 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} +(1.46011 + 2.42241i) q^{72} +(-1.31153 - 0.842871i) q^{73} +(-6.64952 + 6.84129i) q^{74} +(-4.68611 + 3.01158i) q^{75} +(6.36801 + 6.94026i) q^{76} +(0.275416 - 0.238650i) q^{77} +(0.839261 + 0.442904i) q^{78} +(5.50717 - 12.0590i) q^{79} +(-7.94412 + 10.2965i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(2.99897 - 1.69333i) q^{82} +(-15.2686 + 2.19529i) q^{83} +(3.55883 - 5.89989i) q^{84} +(3.27283 - 1.49465i) q^{85} +(-0.174830 + 3.05387i) q^{86} +(4.82563 + 0.693821i) q^{87} +(-0.189350 - 0.231659i) q^{88} +(11.9248 + 10.3329i) q^{89} +(-2.80746 - 3.64128i) q^{90} -2.31170i q^{91} +(6.88133 + 6.68186i) q^{92} -0.0954262i q^{93} +(-9.17246 + 7.07205i) q^{94} +(-11.5718 - 10.0270i) q^{95} +(-4.75783 - 3.05990i) q^{96} +(8.96312 + 1.28870i) q^{97} +(-6.87386 - 0.393519i) 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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