LMFDB - Embedded newform 690.2.w.b.37.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.8
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.84527 - 1.26292i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33335 + 3.57484i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.84527 - 1.26292i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33335 + 3.57484i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.01431 - 1.99278i) q^{10} +(-0.290043 + 0.987796i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(-3.47860 - 1.29745i) q^{13} +(-0.542988 + 3.77657i) q^{14} +(1.75048 + 1.39134i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(4.48296 - 0.975208i) q^{17} +(0.800541 + 0.599278i) q^{18} +(-6.05358 + 3.89040i) q^{19} +(0.0648035 - 2.23513i) q^{20} +(-1.07492 - 3.66085i) q^{21} +(-0.727965 + 0.727965i) q^{22} +(-3.71643 + 3.03119i) q^{23} -1.00000i q^{24} +(1.81008 + 4.66086i) q^{25} +(-2.43129 - 2.80586i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-2.28648 + 3.05439i) q^{28} +(-0.296437 + 0.461265i) q^{29} +(0.869559 + 2.06006i) q^{30} +(-7.16746 + 8.27169i) q^{31} +(-0.800541 + 0.599278i) q^{32} +(0.359773 - 0.964588i) q^{33} +(4.40197 + 1.29253i) q^{34} +(2.05434 - 8.28047i) q^{35} +(0.415415 + 0.909632i) q^{36} +(2.74243 + 3.66346i) q^{37} +(-7.17757 + 0.513350i) q^{38} +(3.37718 + 1.54230i) q^{39} +(1.12806 - 1.93067i) q^{40} +(0.389544 + 2.70934i) q^{41} +(0.811022 - 3.72821i) q^{42} +(0.101394 - 1.41767i) q^{43} +(-0.987796 + 0.290043i) q^{44} +(-1.64676 - 1.51267i) q^{45} +(-4.71453 + 0.879319i) q^{46} +(3.43416 + 3.43416i) q^{47} +(0.479249 - 0.877679i) q^{48} +(-5.71142 + 4.94897i) q^{49} +(-0.645047 + 4.95822i) q^{50} +(-4.54111 + 0.652912i) q^{51} +(-0.789188 - 3.62784i) q^{52} +(2.86176 - 1.06738i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(1.78272 - 1.45645i) q^{55} +(-3.47061 + 1.58498i) q^{56} +(6.31569 - 3.44863i) q^{57} +(-0.481238 + 0.262776i) q^{58} +(1.04914 - 0.479127i) q^{59} +(-0.224091 + 2.22481i) q^{60} +(-0.855538 - 0.741328i) q^{61} +(-10.2549 + 3.82489i) q^{62} +(0.811022 + 3.72821i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(4.78039 + 6.78733i) q^{65} +(0.778043 - 0.674178i) q^{66} +(3.63231 - 6.65208i) q^{67} +(3.24407 + 3.24407i) q^{68} +(3.92321 - 2.75834i) q^{69} +(5.77146 - 6.28305i) q^{70} +(4.57883 - 1.34447i) q^{71} +(-0.0713392 + 0.997452i) q^{72} +(2.30460 - 10.5941i) q^{73} +(0.651266 + 4.52965i) q^{74} +(-1.47296 - 4.77811i) q^{75} +(-6.54563 - 2.98929i) q^{76} +(-3.91794 + 0.280217i) q^{77} +(2.22493 + 2.97216i) q^{78} +(-0.501877 - 1.09896i) q^{79} +(1.91535 - 1.15389i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-0.956552 + 2.56462i) q^{82} +(9.90017 - 7.41118i) q^{83} +(2.49856 - 2.88349i) q^{84} +(-9.50389 - 3.86208i) q^{85} +(0.768410 - 1.19567i) q^{86} +(0.328588 - 0.438943i) q^{87} +(-1.00597 - 0.218836i) q^{88} +(-3.18622 - 3.67709i) q^{89} +(-0.720380 - 2.11685i) q^{90} -14.1654i q^{91} +(-4.55926 - 1.48767i) q^{92} +(7.73930 - 7.73930i) q^{93} +(1.36827 + 4.65991i) q^{94} +(16.0838 + 0.466320i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-13.7543 - 10.2963i) q^{97} +(-7.38458 + 1.60642i) q^{98} +(-0.427669 + 0.936465i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	0.877679	+	0.479249i	0.620613	+	0.338880i
$2$	0.877679	+	0.479249i	0.620613	+	0.338880i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	−1.84527	−	1.26292i	−0.825232	−	0.564794i
$5$	−1.84527	−	1.26292i	−0.825232	−	0.564794i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	1.33335	+	3.57484i	0.503957	+	1.35116i	0.901182	+	0.433441i	$0.142701\pi$
$7$	1.33335	+	3.57484i	0.503957	+	1.35116i	−0.397225	+	0.917721i	$0.630027\pi$
$8$	0.0713392	+	0.997452i	0.0252222	+	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−1.01431	−	1.99278i	−0.320752	−	0.630173i
$11$	−0.290043	+	0.987796i	−0.0874513	+	0.297832i	−0.991592	−	0.129403i	$-0.958694\pi$
$11$	−0.290043	+	0.987796i	−0.0874513	+	0.297832i	0.904141	+	0.427235i	$0.140512\pi$
$12$	−0.479249	−	0.877679i	−0.138347	−	0.253364i
$13$	−3.47860	−	1.29745i	−0.964789	−	0.359848i	−0.182807	−	0.983149i	$-0.558518\pi$
$13$	−3.47860	−	1.29745i	−0.964789	−	0.359848i	−0.781982	+	0.623301i	$0.785791\pi$
$14$	−0.542988	+	3.77657i	−0.145120	+	1.00933i
$15$	1.75048	+	1.39134i	0.451971	+	0.359243i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	4.48296	−	0.975208i	1.08728	−	0.236523i	0.367008	−	0.930218i	$-0.380382\pi$
$17$	4.48296	−	0.975208i	1.08728	−	0.236523i	0.720269	+	0.693695i	$0.244018\pi$
$18$	0.800541	+	0.599278i	0.188689	+	0.141251i
$19$	−6.05358	+	3.89040i	−1.38879	+	0.892519i	−0.999590	−	0.0286357i	$-0.990884\pi$
$19$	−6.05358	+	3.89040i	−1.38879	+	0.892519i	−0.389197	+	0.921155i	$0.627247\pi$
$20$	0.0648035	−	2.23513i	0.0144905	−	0.499790i
$21$	−1.07492	−	3.66085i	−0.234567	−	0.798863i
$22$	−0.727965	+	0.727965i	−0.155203	+	0.155203i
$23$	−3.71643	+	3.03119i	−0.774930	+	0.632048i
$23$	−3.71643	+	3.03119i	−0.774930	+	0.632048i
$24$		−	1.00000i		−	0.204124i
$25$	1.81008	+	4.66086i	0.362015	+	0.932172i
$26$	−2.43129	−	2.80586i	−0.476815	−	0.550274i
$27$	−0.977147	−	0.212565i	−0.188052	−	0.0409082i
$28$	−2.28648	+	3.05439i	−0.432105	+	0.577225i
$29$	−0.296437	+	0.461265i	−0.0550470	+	0.0856549i	−0.867686	−	0.497112i	$-0.834394\pi$
$29$	−0.296437	+	0.461265i	−0.0550470	+	0.0856549i	0.812639	+	0.582767i	$0.198030\pi$
$30$	0.869559	+	2.06006i	0.158759	+	0.376115i
$31$	−7.16746	+	8.27169i	−1.28731	+	1.48564i	−0.504461	+	0.863435i	$0.668309\pi$
$31$	−7.16746	+	8.27169i	−1.28731	+	1.48564i	−0.782854	+	0.622205i	$0.786237\pi$
$32$	−0.800541	+	0.599278i	−0.141517	+	0.105938i
$33$	0.359773	−	0.964588i	0.0626284	−	0.167913i
$34$	4.40197	+	1.29253i	0.754931	+	0.221668i
$35$	2.05434	−	8.28047i	0.347247	−	1.39965i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	2.74243	+	3.66346i	0.450853	+	0.602270i	0.967171	−	0.254128i	$-0.0817884\pi$
$37$	2.74243	+	3.66346i	0.450853	+	0.602270i	−0.516317	+	0.856397i	$0.672697\pi$
$38$	−7.17757	+	0.513350i	−1.16436	+	0.0832764i
$39$	3.37718	+	1.54230i	0.540781	+	0.246966i
$40$	1.12806	−	1.93067i	0.178362	−	0.305265i
$41$	0.389544	+	2.70934i	0.0608365	+	0.423127i	0.997366	+	0.0725375i	$0.0231097\pi$
$41$	0.389544	+	2.70934i	0.0608365	+	0.423127i	−0.936529	+	0.350590i	$0.885981\pi$
$42$	0.811022	−	3.72821i	0.125143	−	0.575275i
$43$	0.101394	−	1.41767i	0.0154624	−	0.216193i	−0.983846	−	0.179016i	$-0.942709\pi$
$43$	0.101394	−	1.41767i	0.0154624	−	0.216193i	0.999309	−	0.0371776i	$-0.0118367\pi$
$44$	−0.987796	+	0.290043i	−0.148916	+	0.0437257i
$45$	−1.64676	−	1.51267i	−0.245485	−	0.225496i
$46$	−4.71453	+	0.879319i	−0.695120	+	0.129648i
$47$	3.43416	+	3.43416i	0.500924	+	0.500924i	0.911725	−	0.410801i	$-0.134751\pi$
$47$	3.43416	+	3.43416i	0.500924	+	0.500924i	−0.410801	+	0.911725i	$0.634751\pi$
$48$	0.479249	−	0.877679i	0.0691736	−	0.126682i
$49$	−5.71142	+	4.94897i	−0.815917	+	0.706996i
$50$	−0.645047	+	4.95822i	−0.0912234	+	0.701198i
$51$	−4.54111	+	0.652912i	−0.635882	+	0.0914260i
$52$	−0.789188	−	3.62784i	−0.109441	−	0.503090i
$53$	2.86176	−	1.06738i	0.393093	−	0.146616i	−0.145142	−	0.989411i	$-0.546364\pi$
$53$	2.86176	−	1.06738i	0.393093	−	0.146616i	0.538235	+	0.842795i	$0.319091\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	1.78272	−	1.45645i	0.240381	−	0.196388i
$56$	−3.47061	+	1.58498i	−0.463780	+	0.211801i
$57$	6.31569	−	3.44863i	0.836534	−	0.456782i
$58$	−0.481238	+	0.262776i	−0.0631896	+	0.0345041i
$59$	1.04914	−	0.479127i	0.136586	−	0.0623770i	−0.345949	−	0.938253i	$-0.612443\pi$
$59$	1.04914	−	0.479127i	0.136586	−	0.0623770i	0.482536	+	0.875876i	$0.339716\pi$
$60$	−0.224091	+	2.22481i	−0.0289300	+	0.287222i
$61$	−0.855538	−	0.741328i	−0.109540	−	0.0949173i	0.598369	−	0.801221i	$-0.295816\pi$
$61$	−0.855538	−	0.741328i	−0.109540	−	0.0949173i	−0.707909	+	0.706304i	$0.750361\pi$
$62$	−10.2549	+	3.82489i	−1.30238	+	0.485762i
$63$	0.811022	+	3.72821i	0.102179	+	0.469710i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	4.78039	+	6.78733i	0.592935	+	0.841865i
$66$	0.778043	−	0.674178i	0.0957705	−	0.0829856i
$67$	3.63231	−	6.65208i	0.443757	−	0.812681i	−0.556072	−	0.831134i	$-0.687692\pi$
$67$	3.63231	−	6.65208i	0.443757	−	0.812681i	0.999830	+	0.0184529i	$0.00587407\pi$
$68$	3.24407	+	3.24407i	0.393401	+	0.393401i
$69$	3.92321	−	2.75834i	0.472298	−	0.332065i
$70$	5.77146	−	6.28305i	0.689821	−	0.750968i
$71$	4.57883	−	1.34447i	0.543407	−	0.159559i	0.00150274	−	0.999999i	$-0.499522\pi$
$71$	4.57883	−	1.34447i	0.543407	−	0.159559i	0.541904	+	0.840440i	$0.317703\pi$
$72$	−0.0713392	+	0.997452i	−0.00840740	+	0.117551i
$73$	2.30460	−	10.5941i	0.269733	−	1.23994i	−0.620417	−	0.784272i	$-0.713037\pi$
$73$	2.30460	−	10.5941i	0.269733	−	1.23994i	0.890150	−	0.455669i	$-0.150600\pi$
$74$	0.651266	+	4.52965i	0.0757081	+	0.526562i
$75$	−1.47296	−	4.77811i	−0.170083	−	0.551729i
$76$	−6.54563	−	2.98929i	−0.750835	−	0.342895i
$77$	−3.91794	+	0.280217i	−0.446491	+	0.0319337i
$78$	2.22493	+	2.97216i	0.251923	+	0.336530i
$79$	−0.501877	−	1.09896i	−0.0564656	−	0.123642i	0.879296	−	0.476276i	$-0.158014\pi$
$79$	−0.501877	−	1.09896i	−0.0564656	−	0.123642i	−0.935762	+	0.352633i	$0.885286\pi$
$80$	1.91535	−	1.15389i	0.214142	−	0.129008i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	−0.956552	+	2.56462i	−0.105634	+	0.283214i
$83$	9.90017	−	7.41118i	1.08669	−	0.813482i	0.103234	−	0.994657i	$-0.467081\pi$
$83$	9.90017	−	7.41118i	1.08669	−	0.813482i	0.983451	+	0.181175i	$0.0579900\pi$
$84$	2.49856	−	2.88349i	0.272615	−	0.314614i
$85$	−9.50389	−	3.86208i	−1.03084	−	0.418902i
$86$	0.768410	−	1.19567i	0.0828598	−	0.128932i
$87$	0.328588	−	0.438943i	0.0352284	−	0.0470596i
$88$	−1.00597	−	0.218836i	−0.107237	−	0.0233280i
$89$	−3.18622	−	3.67709i	−0.337739	−	0.389771i	0.561320	−	0.827599i	$-0.310294\pi$
$89$	−3.18622	−	3.67709i	−0.337739	−	0.389771i	−0.899059	+	0.437827i	$0.855748\pi$
$90$	−0.720380	−	2.11685i	−0.0759347	−	0.223136i
$91$		−	14.1654i		−	1.48493i
$92$	−4.55926	−	1.48767i	−0.475335	−	0.155101i
$93$	7.73930	−	7.73930i	0.802528	−	0.802528i
$94$	1.36827	+	4.65991i	0.141127	+	0.480633i
$95$	16.0838	+	0.466320i	1.65016	+	0.0478434i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−13.7543	−	10.2963i	−1.39653	−	1.04543i	−0.991357	−	0.131192i	$-0.958119\pi$
$97$	−13.7543	−	10.2963i	−1.39653	−	1.04543i	−0.405176	−	0.914239i	$-0.632790\pi$
$98$	−7.38458	+	1.60642i	−0.745955	+	0.162273i
$99$	−0.427669	+	0.936465i	−0.0429824	+	0.0941182i
$100$	−2.94236	+	4.04258i	−0.294236	+	0.404258i
$101$	1.42916	−	9.94000i	0.142206	−	0.989067i	−0.786325	−	0.617813i	$-0.788019\pi$
$101$	1.42916	−	9.94000i	0.142206	−	0.989067i	0.928531	−	0.371254i	$-0.121072\pi$
$102$	−4.29854	−	1.60327i	−0.425619	−	0.158748i
$103$	2.28251	+	4.18010i	0.224902	+	0.411878i	0.965627	−	0.259931i	$-0.0836997\pi$
$103$	2.28251	+	4.18010i	0.224902	+	0.411878i	−0.740725	+	0.671808i	$0.765518\pi$
$104$	1.04598	−	3.56229i	0.102567	−	0.349312i
$105$	−2.63983	+	8.11281i	−0.257621	+	0.791730i
$106$	3.02325	+	0.434678i	0.293644	+	0.0422197i
$107$	0.0326501	+	0.456508i	0.00315641	+	0.0441323i	0.998786	−	0.0492556i	$-0.0156849\pi$
$107$	0.0326501	+	0.456508i	0.00315641	+	0.0441323i	−0.995630	+	0.0933879i	$0.970230\pi$
$108$	−0.349464	−	0.936950i	−0.0336272	−	0.0901580i
$109$	7.26470	+	4.66874i	0.695832	+	0.447184i	0.840155	−	0.542346i	$-0.182464\pi$
$109$	7.26470	+	4.66874i	0.695832	+	0.447184i	−0.144323	+	0.989531i	$0.546100\pi$
$110$	2.26266	−	0.423935i	0.215736	−	0.0404206i
$111$	−2.47410	−	3.84977i	−0.234831	−	0.365404i
$112$	−3.80568	−	0.272188i	−0.359603	−	0.0257193i
$113$	2.05598	+	1.12265i	0.193410	+	0.105610i	0.573036	−	0.819530i	$-0.305765\pi$
$113$	2.05598	+	1.12265i	0.193410	+	0.105610i	−0.379626	+	0.925140i	$0.623947\pi$
$114$	7.19591			0.673958
$115$	10.6860	−	0.899835i	0.996473	−	0.0839101i
$116$	−0.548307			−0.0509091
$117$	−3.25854	−	1.77930i	−0.301252	−	0.164496i
$118$	1.15043	+	0.0822804i	0.105906	+	0.00757452i
$119$	9.46355	+	14.7256i	0.867522	+	1.34989i
$120$	−1.26292	+	1.84527i	−0.115288	+	0.168450i
$121$	8.36217	+	5.37404i	0.760197	+	0.488549i
$122$	−0.395607	−	1.06066i	−0.0358166	−	0.0960280i
$123$	−0.195269	−	2.73022i	−0.0176068	−	0.246176i
$124$	−10.8336	−	1.55764i	−0.972887	−	0.139880i
$125$	2.54620	−	10.8865i	0.227739	−	0.973722i
$126$	−1.07492	+	3.66085i	−0.0957617	+	0.326135i
$127$	6.74062	+	12.3445i	0.598133	+	1.09540i	0.984884	+	0.173215i	$0.0554154\pi$
$127$	6.74062	+	12.3445i	0.598133	+	1.09540i	−0.386751	+	0.922184i	$0.626403\pi$
$128$	−0.936950	−	0.349464i	−0.0828154	−	0.0308886i
$129$	−0.202271	+	1.40683i	−0.0178090	+	0.123864i
$130$	0.942829	+	8.24810i	0.0826915	+	0.723406i
$131$	−5.81149	+	12.7254i	−0.507752	+	1.11182i	0.466119	+	0.884722i	$0.345652\pi$
$131$	−5.81149	+	12.7254i	−0.507752	+	1.11182i	−0.973871	+	0.227101i	$0.927075\pi$
$132$	1.00597	−	0.218836i	0.0875585	−	0.0190472i
$133$	−21.9791	−	16.4533i	−1.90583	−	1.42668i
$134$	6.37601	−	4.09761i	0.550803	−	0.353980i
$135$	1.53465	+	1.62630i	0.132082	+	0.139969i
$136$	1.29253	+	4.40197i	0.110834	+	0.377465i
$137$	−8.71161	+	8.71161i	−0.744283	+	0.744283i	−0.973399	−	0.229116i	$-0.926416\pi$
$137$	−8.71161	+	8.71161i	−0.744283	+	0.744283i	0.229116	+	0.973399i	$0.426416\pi$
$138$	4.76525	−	0.540747i	0.405645	−	0.0460315i
$139$			17.2008i			1.45895i	0.684007	+	0.729475i	$0.260236\pi$
$139$			17.2008i			1.45895i	−0.684007	+	0.729475i	$0.739764\pi$
$140$	8.07663	−	2.74854i	0.682600	−	0.232294i
$141$	−3.18042	−	3.67040i	−0.267840	−	0.309103i
$142$	4.66308	+	1.01439i	0.391317	+	0.0851257i
$143$	2.29056	−	3.05983i	0.191546	−	0.255876i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	1.12955	−	0.476785i	0.0938039	−	0.0395949i
$146$	7.09989	−	8.19371i	0.587591	−	0.678116i
$147$	6.04992	−	4.52891i	0.498989	−	0.373539i
$148$	−1.59923	+	4.28770i	−0.131456	+	0.352447i
$149$	8.33215	+	2.44654i	0.682597	+	0.200428i	0.604605	−	0.796526i	$-0.293331\pi$
$149$	8.33215	+	2.44654i	0.682597	+	0.200428i	0.0779917	+	0.996954i	$0.475149\pi$
$150$	0.997119	−	4.89957i	0.0814144	−	0.400048i
$151$	8.73996	+	19.1378i	0.711248	+	1.55741i	0.825778	+	0.563995i	$0.190736\pi$
$151$	8.73996	+	19.1378i	0.711248	+	1.55741i	−0.114530	+	0.993420i	$0.536536\pi$
$152$	−4.31235	−	5.76062i	−0.349777	−	0.467248i
$153$	4.57611	−	0.327290i	0.369957	−	0.0264598i
$154$	−3.57299	−	1.63173i	−0.287920	−	0.131488i
$155$	23.6724	−	6.21163i	1.90141	−	0.498930i
$156$	0.528370	+	3.67489i	0.0423034	+	0.294227i
$157$	−0.464306	+	2.13438i	−0.0370557	+	0.170342i	−0.991956	−	0.126585i	$-0.959598\pi$
$157$	−0.464306	+	2.13438i	−0.0370557	+	0.170342i	0.954900	+	0.296927i	$0.0959619\pi$
$158$	0.0861874	−	1.20506i	0.00685670	−	0.0958692i
$159$	−2.93062	+	0.860507i	−0.232413	+	0.0682426i
$160$	2.23406	−	0.0948139i	0.176618	−	0.00749569i
$161$	−15.7913	−	9.24402i	−1.24453	−	0.728531i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	11.8066	−	21.6221i	0.924763	−	1.69358i	0.231580	−	0.972816i	$-0.425610\pi$
$163$	11.8066	−	21.6221i	0.924763	−	1.69358i	0.693183	−	0.720762i	$-0.256208\pi$
$164$	−2.06863	+	1.79248i	−0.161533	+	0.139969i
$165$	−1.88208	+	1.32557i	−0.146519	+	0.103195i
$166$	12.2410	−	1.75999i	0.950084	−	0.136601i
$167$	−3.57900	−	16.4524i	−0.276951	−	1.27312i	−0.879829	−	0.475290i	$-0.842343\pi$
$167$	−3.57900	−	16.4524i	−0.276951	−	1.27312i	0.602878	−	0.797834i	$-0.294021\pi$
$168$	3.57484	−	1.33335i	0.275805	−	0.102870i
$169$	0.592519	+	0.513421i	0.0455784	+	0.0394939i
$170$	−6.49047	−	7.94440i	−0.497796	−	0.609308i
$171$	−6.54563	+	2.98929i	−0.500556	+	0.228596i
$172$	1.24744	−	0.681154i	0.0951165	−	0.0519375i
$173$	8.14810	−	4.44920i	0.619489	−	0.338266i	−0.138668	−	0.990339i	$-0.544282\pi$
$173$	8.14810	−	4.44920i	0.619489	−	0.338266i	0.758157	+	0.652073i	$0.226100\pi$
$174$	0.498758	−	0.227775i	0.0378107	−	0.0172676i
$175$	−14.2484	+	12.6853i	−1.07708	+	0.958917i
$176$	−0.778043	−	0.674178i	−0.0586472	−	0.0508181i
$177$	−1.08065	+	0.403061i	−0.0812265	+	0.0302959i
$178$	−1.03423	−	4.75430i	−0.0775192	−	0.356350i
$179$	−2.81402	+	0.404594i	−0.210329	+	0.0302408i	−0.246674	−	0.969099i	$-0.579338\pi$
$179$	−2.81402	+	0.404594i	−0.210329	+	0.0302408i	0.0363446	+	0.999339i	$0.488429\pi$
$180$	0.382236	−	2.20316i	0.0284902	−	0.164214i
$181$	−5.91992	+	5.12964i	−0.440024	+	0.381283i	−0.846509	−	0.532374i	$-0.821300\pi$
$181$	−5.91992	+	5.12964i	−0.440024	+	0.381283i	0.406485	+	0.913658i	$0.366754\pi$
$182$	6.78874	−	12.4327i	0.503215	−	0.921570i
$183$	0.800472	+	0.800472i	0.0591726	+	0.0591726i
$184$	−3.28860	−	3.49072i	−0.242439	−	0.257339i
$185$	−0.433890	−	10.2236i	−0.0319003	−	0.751652i
$186$	10.5017	−	3.08357i	0.770020	−	0.226098i
$187$	−0.336945	+	4.71110i	−0.0246398	+	0.344510i
$188$	−1.03235	+	4.74565i	−0.0752920	+	0.346112i
$189$	−0.542988	−	3.77657i	−0.0394966	−	0.274705i
$190$	13.8929	+	8.11741i	1.00790	+	0.588899i
$191$	−16.4572	−	7.51574i	−1.19080	−	0.543820i	−0.281338	−	0.959609i	$-0.590778\pi$
$191$	−16.4572	−	7.51574i	−1.19080	−	0.543820i	−0.909461	+	0.415789i	$0.863506\pi$
$192$	0.997452	−	0.0713392i	0.0719849	−	0.00514846i
$193$	13.8077	+	18.4450i	0.993903	+	1.32770i	0.944355	+	0.328927i	$0.106687\pi$
$193$	13.8077	+	18.4450i	0.993903	+	1.32770i	0.0495476	+	0.998772i	$0.484222\pi$
$194$	−7.13732	−	15.6286i	−0.512430	−	1.12207i
$195$	−4.28401	−	7.11107i	−0.306784	−	0.509234i
$196$	−7.25117	−	2.12913i	−0.517940	−	0.152081i
$197$	−6.86898	+	18.4164i	−0.489394	+	1.31212i	0.424229	+	0.905555i	$0.360545\pi$
$197$	−6.86898	+	18.4164i	−0.489394	+	1.31212i	−0.913623	+	0.406562i	$0.866728\pi$
$198$	−0.824156	+	0.616955i	−0.0585702	+	0.0438451i
$199$	5.67319	−	6.54721i	0.402162	−	0.464119i	−0.518159	−	0.855284i	$-0.673382\pi$
$199$	5.67319	−	6.54721i	0.402162	−	0.464119i	0.920320	+	0.391165i	$0.127928\pi$
$200$	−4.51986	+	2.13797i	−0.319602	+	0.151177i
$201$	−4.09761	+	6.37601i	−0.289023	+	0.449729i
$202$	6.01808	−	8.03921i	0.423430	−	0.565637i
$203$	−2.04420	−	0.444689i	−0.143475	−	0.0312111i
$204$	−3.00437	−	3.46723i	−0.210348	−	0.242755i
$205$	2.70285	−	5.49143i	0.188775	−	0.383538i
$206$			4.76268i			0.331831i
$207$	−4.10999	+	2.47144i	−0.285664	+	0.171777i
$208$	2.62526	−	2.62526i	0.182029	−	0.182029i
$209$	−2.08712	−	7.10809i	−0.144369	−	0.491677i
$210$	−6.20498	+	5.85531i	−0.428184	+	0.404055i
$211$	−1.08902	+	0.699869i	−0.0749711	+	0.0481810i	−0.577589	−	0.816327i	$-0.696006\pi$
$211$	−1.08902	+	0.699869i	−0.0749711	+	0.0481810i	0.502618	+	0.864508i	$0.332370\pi$
$212$	2.44513	+	1.83040i	0.167932	+	0.125712i
$213$	−4.66308	+	1.01439i	−0.319509	+	0.0695049i
$214$	−0.190125	+	0.416315i	−0.0129967	+	0.0284587i
$215$	−1.97751	+	2.48794i	−0.134865	+	0.169676i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	−39.1267	−	14.5935i	−2.65609	−	0.990671i
$218$	4.13859	+	7.57926i	0.280300	+	0.513332i
$219$	−3.05450	+	10.4027i	−0.206404	+	0.702946i
$220$	2.18906	+	0.712297i	0.147586	+	0.0480230i
$221$	−16.8597	−	2.42406i	−1.13411	−	0.163060i
$222$	−0.326465	−	4.56457i	−0.0219109	−	0.306354i
$223$	3.81862	+	10.2381i	0.255714	+	0.685595i	0.999846	+	0.0175623i	$0.00559055\pi$
$223$	3.81862	+	10.2381i	0.255714	+	0.685595i	−0.744132	+	0.668032i	$0.767137\pi$
$224$	−3.20972	−	2.06276i	−0.214458	−	0.137824i
$225$	1.12834	+	4.87102i	0.0752228	+	0.324735i
$226$	1.26646	+	1.97065i	0.0842437	+	0.131086i
$227$	10.7647	+	0.769905i	0.714476	+	0.0511004i	0.423845	−	0.905735i	$-0.360680\pi$
$227$	10.7647	+	0.769905i	0.714476	+	0.0511004i	0.290631	+	0.956835i	$0.406135\pi$
$228$	6.31569	+	3.44863i	0.418267	+	0.228391i
$229$	−20.3146			−1.34242			−0.671212	−	0.741265i	$-0.734226\pi$
$229$	−20.3146			−1.34242			−0.671212	+	0.741265i	$0.734226\pi$
$230$	9.81011	+	4.33148i	0.646860	+	0.285609i
$231$	3.92795			0.258440
$232$	−0.481238	−	0.262776i	−0.0315948	−	0.0172521i
$233$	21.3937	+	1.53011i	1.40155	+	0.100241i	0.751541	−	0.659686i	$-0.229311\pi$
$233$	21.3937	+	1.53011i	1.40155	+	0.100241i	0.650008	+	0.759927i	$0.274765\pi$
$234$	−2.00723	−	3.12331i	−0.131217	−	0.204177i
$235$	−1.99991	−	10.6740i	−0.130459	−	0.696297i
$236$	0.970275	+	0.623558i	0.0631595	+	0.0405902i
$237$	0.422200	+	1.13196i	0.0274248	+	0.0735288i
$238$	1.24874	+	17.4597i	0.0809440	+	1.13175i
$239$	11.0046	+	1.58222i	0.711827	+	0.102345i	0.488710	−	0.872446i	$-0.337468\pi$
$239$	11.0046	+	1.58222i	0.711827	+	0.102345i	0.223117	+	0.974792i	$0.428377\pi$
$240$	−1.99278	+	1.01431i	−0.128634	+	0.0654732i
$241$	−2.36498	+	8.05437i	−0.152341	+	0.518827i	−0.999930	−	0.0118266i	$-0.996235\pi$
$241$	−2.36498	+	8.05437i	−0.152341	+	0.518827i	0.847589	+	0.530654i	$0.178054\pi$
$242$	4.76380	+	8.72425i	0.306229	+	0.560816i
$243$	−0.936950	−	0.349464i	−0.0601054	−	0.0224181i
$244$	0.161106	−	1.12052i	0.0103138	−	0.0717337i
$245$	16.7893	−	1.91916i	1.07263	−	0.122611i
$246$	1.13707	−	2.48984i	0.0724971	−	0.158746i
$247$	26.1056	−	5.67892i	1.66106	−	0.361341i
$248$	−8.76194	−	6.55911i	−0.556384	−	0.416504i
$249$	−10.4037	+	6.68602i	−0.659305	+	0.423710i
$250$	7.45211	−	8.33463i	0.471313	−	0.527128i
$251$	−6.16980	−	21.0124i	−0.389434	−	1.32629i	−0.888161	−	0.459532i	$-0.848017\pi$
$251$	−6.16980	−	21.0124i	−0.389434	−	1.32629i	0.498727	−	0.866759i	$-0.333801\pi$
$252$	−2.69790	+	2.69790i	−0.169951	+	0.169951i
$253$	−1.91628	−	4.55026i	−0.120475	−	0.286072i
$254$			14.0650i			0.882514i
$255$	9.20416	+	4.53024i	0.576387	+	0.283695i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	22.2540	+	4.84106i	1.38817	+	0.301977i	0.843705	−	0.536808i	$-0.180370\pi$
$257$	22.2540	+	4.84106i	1.38817	+	0.301977i	0.544463	+	0.838785i	$0.316734\pi$
$258$	−0.851750	+	1.13781i	−0.0530277	+	0.0708367i
$259$	−9.43968	+	14.6884i	−0.586553	+	0.912695i
$260$	−3.12539	+	7.69103i	−0.193829	+	0.476978i
$261$	−0.359065	+	0.414383i	−0.0222256	+	0.0256497i
$262$	−11.1993	+	8.38366i	−0.691892	+	0.517944i
$263$	6.78779	−	18.1988i	0.418553	−	1.12218i	−0.541091	−	0.840964i	$-0.681988\pi$
$263$	6.78779	−	18.1988i	0.418553	−	1.12218i	0.959643	−	0.281220i	$-0.0907389\pi$
$264$	0.987796	+	0.290043i	0.0607947	+	0.0178509i
$265$	−6.62876	−	1.64456i	−0.407201	−	0.101024i
$266$	−11.4053	−	24.9742i	−0.699306	−	1.53127i
$267$	2.91578	+	3.89503i	0.178443	+	0.238372i
$268$	7.55986	−	0.540692i	0.461792	−	0.0330280i
$269$	7.19964	+	3.28796i	0.438970	+	0.200471i	0.622626	−	0.782520i	$-0.286066\pi$
$269$	7.19964	+	3.28796i	0.438970	+	0.200471i	−0.183656	+	0.982991i	$0.558793\pi$
$270$	0.567530	+	2.16285i	0.0345388	+	0.131627i
$271$	2.18535	+	15.1995i	0.132751	+	0.923301i	0.941947	+	0.335762i	$0.108994\pi$
$271$	2.18535	+	15.1995i	0.132751	+	0.923301i	−0.809196	+	0.587539i	$0.800097\pi$
$272$	−0.975208	+	4.48296i	−0.0591307	+	0.271819i
$273$	−1.01055	+	14.1293i	−0.0611611	+	0.855143i
$274$	−11.8210	+	3.47097i	−0.714134	+	0.209689i
$275$	−5.12898	+	0.436136i	−0.309289	+	0.0263000i
$276$	4.44151	+	1.80914i	0.267348	+	0.108897i
$277$	−18.8513	−	18.8513i	−1.13267	−	1.13267i	−0.989732	−	0.142934i	$-0.954346\pi$
$277$	−18.8513	−	18.8513i	−1.13267	−	1.13267i	−0.142934	−	0.989732i	$-0.545654\pi$
$278$	−8.24345	+	15.0968i	−0.494409	+	0.905443i
$279$	−8.27169	+	7.16746i	−0.495213	+	0.429105i
$280$	8.40592	+	1.45838i	0.502350	+	0.0871551i
$281$	−1.68682	+	0.242529i	−0.100628	+	0.0144681i	−0.192445	−	0.981308i	$-0.561642\pi$
$281$	−1.68682	+	0.242529i	−0.100628	+	0.0144681i	0.0918171	+	0.995776i	$0.470732\pi$
$282$	−1.03235	−	4.74565i	−0.0614757	−	0.282599i
$283$	−25.0799	+	9.35432i	−1.49085	+	0.556057i	−0.957143	−	0.289615i	$-0.906473\pi$
$283$	−25.0799	+	9.35432i	−1.49085	+	0.556057i	−0.533703	+	0.845672i	$0.679200\pi$
$284$	3.60654	+	3.12508i	0.214009	+	0.185440i
$285$	−16.0095	−	1.61254i	−0.948323	−	0.0955183i
$286$	3.47680	−	1.58780i	0.205587	−	0.0938886i
$287$	−9.16604	+	5.00504i	−0.541054	+	0.295438i
$288$	−0.877679	+	0.479249i	−0.0517177	+	0.0282400i
$289$	3.68214	−	1.68157i	0.216596	−	0.0989162i
$290$	1.21988	+	0.122871i	0.0716338	+	0.00721521i
$291$	12.9847	+	11.2513i	0.761175	+	0.659562i
$292$	10.1582	−	3.78883i	0.594467	−	0.221725i
$293$	0.387768	+	1.78254i	0.0226537	+	0.104137i	0.987085	−	0.160195i	$-0.0512122\pi$
$293$	0.387768	+	1.78254i	0.0226537	+	0.104137i	−0.964432	+	0.264332i	$0.914849\pi$
$294$	7.48037	−	1.07551i	0.436264	−	0.0627253i
$295$	−2.54105	−	0.440859i	−0.147946	−	0.0256678i
$296$	−3.45849	+	2.99680i	−0.201020	+	0.174185i
$297$	0.493386	−	0.903569i	0.0286292	−	0.0524304i
$298$	6.14045	+	6.14045i	0.355707	+	0.355707i
$299$	16.8608	−	5.72242i	0.975085	−	0.330936i
$300$	3.22326	−	3.82238i	0.186095	−	0.220685i
$301$	5.20315	−	1.52778i	0.299905	−	0.0880599i
$302$	−1.50091	+	20.9855i	−0.0863678	+	1.20758i
$303$	−2.13463	+	9.81272i	−0.122631	+	0.563726i
$304$	−1.02408	−	7.12266i	−0.0587352	−	0.408513i
$305$	0.642466	+	2.44843i	0.0367875	+	0.140197i
$306$	4.17321	+	1.90584i	0.238567	+	0.108950i
$307$	28.4412	−	2.03415i	1.62322	−	0.116095i	0.770142	−	0.637872i	$-0.220185\pi$
$307$	28.4412	−	2.03415i	1.62322	−	0.116095i	0.853082	+	0.521777i	$0.174731\pi$
$308$	−2.35393	−	3.14449i	−0.134128	−	0.179174i
$309$	−1.97849	−	4.33228i	−0.112552	−	0.246455i
$310$	23.7537	+	5.89316i	1.34912	+	0.334709i
$311$	−25.4157	−	7.46272i	−1.44119	−	0.423172i	−0.534573	−	0.845122i	$-0.679527\pi$
$311$	−25.4157	−	7.46272i	−1.44119	−	0.423172i	−0.906619	+	0.421950i	$0.861346\pi$
$312$	−1.29745	+	3.47860i	−0.0734536	+	0.196937i
$313$	−0.478924	+	0.358518i	−0.0270704	+	0.0202646i	−0.612727	−	0.790295i	$-0.709928\pi$
$313$	−0.478924	+	0.358518i	−0.0270704	+	0.0202646i	0.585657	+	0.810559i	$0.300837\pi$
$314$	−1.43041	+	1.65078i	−0.0807228	+	0.0931591i
$315$	3.21186	−	7.90382i	0.180968	−	0.445330i
$316$	0.653167	−	1.01635i	0.0367435	−	0.0571740i
$317$	−18.7229	+	25.0109i	−1.05159	+	1.40475i	−0.141693	+	0.989911i	$0.545254\pi$
$317$	−18.7229	+	25.0109i	−1.05159	+	1.40475i	−0.909893	+	0.414843i	$0.863836\pi$
$318$	−2.98454	−	0.649247i	−0.167365	−	0.0364079i
$319$	−0.369657	−	0.426607i	−0.0206968	−	0.0238854i
$320$	2.00622	+	0.987453i	0.112151	+	0.0552003i
$321$		−	0.457675i		−	0.0255449i
$322$	−9.42952	−	15.6813i	−0.525487	−	0.873882i
$323$	−23.3440	+	23.3440i	−1.29889	+	1.29889i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	−0.249293	−	18.5617i	−0.0138283	−	1.02962i
$326$	20.7248	−	13.3190i	1.14784	−	0.737672i
$327$	−6.91313	−	5.17510i	−0.382297	−	0.286184i
$328$	−2.67464	+	0.581833i	−0.147682	+	0.0321263i
$329$	−7.69765	+	16.8555i	−0.424385	+	0.929273i
$330$	−2.28713	+	0.261439i	−0.125903	+	0.0143918i
$331$	−3.22331	+	22.4186i	−0.177169	+	1.23224i	0.686104	+	0.727503i	$0.259319\pi$
$331$	−3.22331	+	22.4186i	−0.177169	+	1.23224i	−0.863274	+	0.504736i	$0.831590\pi$
$332$	11.5871	+	4.32177i	0.635926	+	0.237188i
$333$	2.19316	+	4.01646i	0.120184	+	0.220101i
$334$	4.74358	−	16.1551i	0.259557	−	0.883970i
$335$	−15.1036	+	7.68760i	−0.825200	+	0.420019i
$336$	3.77657	+	0.542988i	0.206029	+	0.0296224i
$337$	−1.23447	−	17.2601i	−0.0672458	−	0.940219i	−0.913343	−	0.407191i	$-0.866508\pi$
$337$	−1.23447	−	17.2601i	−0.0672458	−	0.940219i	0.846097	−	0.533028i	$-0.178946\pi$
$338$	0.273985	+	0.734583i	0.0149028	+	0.0399560i
$339$	−1.97065	−	1.26646i	−0.107031	−	0.0687847i
$340$	−1.88920	−	10.0832i	−0.102456	−	0.546837i
$341$	−6.09188	−	9.47914i	−0.329894	−	0.513324i
$342$	−7.17757	−	0.513350i	−0.388119	−	0.0277588i
$343$	−1.86619	−	1.01902i	−0.100765	−	0.0550219i
$344$	1.42129			0.0766311
$345$	−10.7230	+	0.135213i	−0.577304	+	0.00727962i
$346$	9.28369			0.499094
$347$	−15.7028	−	8.57440i	−0.842973	−	0.460298i	−0.00111612	−	0.999999i	$-0.500355\pi$
$347$	−15.7028	−	8.57440i	−0.842973	−	0.460298i	−0.841856	+	0.539702i	$0.818537\pi$
$348$	0.546910	+	0.0391158i	0.0293175	+	0.00209683i
$349$	14.4933	+	22.5519i	0.775806	+	1.20718i	0.973896	+	0.226994i	$0.0728897\pi$
$349$	14.4933	+	22.5519i	0.775806	+	1.20718i	−0.198090	+	0.980184i	$0.563474\pi$
$350$	−18.5849	+	4.30508i	−0.993405	+	0.230116i
$351$	3.12331	+	2.00723i	0.166710	+	0.107138i
$352$	−0.359773	−	0.964588i	−0.0191760	−	0.0514127i
$353$	−2.20089	−	30.7725i	−0.117142	−	1.63785i	−0.628018	−	0.778199i	$-0.716134\pi$
$353$	−2.20089	−	30.7725i	−0.117142	−	1.63785i	0.510877	−	0.859654i	$-0.329321\pi$
$354$	−1.14163	−	0.164141i	−0.0606769	−	0.00872402i
$355$	−10.1471	−	3.30178i	−0.538555	−	0.175240i
$356$	1.37077	−	4.66841i	0.0726505	−	0.247425i
$357$	−8.38892	−	15.3632i	−0.443989	−	0.813105i
$358$	−2.66370	−	0.993510i	−0.140781	−	0.0525086i
$359$	4.69707	−	32.6688i	0.247902	−	1.72419i	−0.362397	−	0.932024i	$-0.618042\pi$
$359$	4.69707	−	32.6688i	0.247902	−	1.72419i	0.610299	−	0.792171i	$-0.291049\pi$
$360$	1.39134	−	1.75048i	0.0733301	−	0.0922583i
$361$	13.6177	−	29.8187i	0.716723	−	1.56940i
$362$	−7.65416	+	1.66506i	−0.402294	+	0.0875137i
$363$	−7.95749	−	5.95690i	−0.417660	−	0.312656i
$364$	11.9167	−	7.65838i	0.624603	−	0.401408i
$365$	−17.6320	+	16.6384i	−0.922903	+	0.870895i
$366$	0.318932	+	1.08618i	0.0166709	+	0.0567757i
$367$	22.9270	−	22.9270i	1.19678	−	1.19678i	0.221653	−	0.975126i	$-0.428855\pi$
$367$	22.9270	−	22.9270i	1.19678	−	1.19678i	0.975126	−	0.221653i	$-0.0711451\pi$
$368$	−1.21341	−	4.63979i	−0.0632533	−	0.241866i
$369$			2.73720i			0.142493i
$370$	4.51882	−	9.18095i	0.234922	−	0.477295i
$371$	7.63144	+	8.80715i	0.396205	+	0.457245i
$372$	10.6949	+	2.32653i	0.554504	+	0.120625i
$373$	−14.2826	+	19.0794i	−0.739527	+	0.987893i	0.260223	+	0.965549i	$0.416204\pi$
$373$	−14.2826	+	19.0794i	−0.739527	+	0.987893i	−0.999750	+	0.0223443i	$0.992887\pi$
$374$	−2.55352	+	3.97335i	−0.132039	+	0.205457i
$375$	−3.31635	+	10.6772i	−0.171255	+	0.551366i
$376$	−3.18042	+	3.67040i	−0.164018	+	0.189286i
$377$	1.62965	−	1.21994i	0.0839315	−	0.0628303i
$378$	1.33335	−	3.57484i	0.0685799	−	0.183870i
$379$	−3.87869	−	1.13889i	−0.199235	−	0.0585006i	0.180593	−	0.983558i	$-0.442198\pi$
$379$	−3.87869	−	1.13889i	−0.199235	−	0.0585006i	−0.379827	+	0.925057i	$0.624017\pi$
$380$	8.30325	+	13.7826i	0.425948	+	0.707035i
$381$	−5.84279	−	12.7939i	−0.299335	−	0.655453i
$382$	−10.8422	−	14.4835i	−0.554736	−	0.741040i
$383$	−0.468204	+	0.0334866i	−0.0239241	+	0.00171108i	−0.0832961	−	0.996525i	$-0.526545\pi$
$383$	−0.468204	+	0.0334866i	−0.0239241	+	0.00171108i	0.0593720	+	0.998236i	$0.481090\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	7.58357	+	4.43096i	0.386494	+	0.225823i
$386$	3.27902	+	22.8061i	0.166898	+	1.16080i
$387$	0.302118	−	1.38881i	0.0153575	−	0.0705974i
$388$	1.22569	−	17.1374i	0.0622251	−	0.870020i
$389$	−9.23702	+	2.71223i	−0.468335	+	0.137516i	−0.507381	−	0.861722i	$-0.669386\pi$
$389$	−9.23702	+	2.71223i	−0.468335	+	0.137516i	0.0390458	+	0.999237i	$0.487568\pi$
$390$	−0.352014	−	8.29435i	−0.0178249	−	0.420000i
$391$	−13.7046	+	17.2130i	−0.693070	+	0.870499i
$392$	−5.34381	−	5.34381i	−0.269903	−	0.269903i
$393$	6.70450	−	12.2784i	0.338198	−	0.619363i
$394$	−14.8548	+	12.8718i	−0.748375	+	0.648470i
$395$	−0.461793	+	2.66171i	−0.0232353	+	0.133925i
$396$	−1.01902	+	0.146513i	−0.0512077	+	0.00736255i
$397$	3.13101	+	14.3930i	0.157141	+	0.722364i	0.986515	+	0.163671i	$0.0523335\pi$
$397$	3.13101	+	14.3930i	0.157141	+	0.722364i	−0.829374	+	0.558693i	$0.811303\pi$
$398$	8.11698	−	3.02748i	0.406867	−	0.151754i
$399$	20.7493	+	17.9794i	1.03876	+	0.900095i
$400$	−4.99160	−	0.289688i	−0.249580	−	0.0144844i
$401$	29.1288	−	13.3027i	1.45462	−	0.664304i	0.477823	−	0.878456i	$-0.341426\pi$
$401$	29.1288	−	13.3027i	1.45462	−	0.664304i	0.976800	+	0.214152i	$0.0686988\pi$
$402$	−6.65208	+	3.63231i	−0.331776	+	0.181163i
$403$	35.6648	−	19.4745i	1.77659	−	0.970092i
$404$	9.13472	−	4.17169i	0.454469	−	0.207549i
$405$	−1.41472	−	1.73163i	−0.0702981	−	0.0860456i
$406$	−1.58104	−	1.36998i	−0.0784656	−	0.0679908i
$407$	−4.41418	+	1.64640i	−0.218803	+	0.0816092i
$408$	−0.975208	−	4.48296i	−0.0482800	−	0.221939i
$409$	−19.7446	+	2.83885i	−0.976309	+	0.140372i	−0.611959	−	0.790890i	$-0.709618\pi$
$409$	−19.7446	+	2.83885i	−0.976309	+	0.140372i	−0.364351	+	0.931262i	$0.618709\pi$
$410$	5.00400	−	3.52437i	0.247130	−	0.174056i
$411$	9.31089	−	8.06793i	0.459272	−	0.397962i
$412$	−2.28251	+	4.18010i	−0.112451	+	0.205939i
$413$	3.11167	+	3.11167i	0.153115	+	0.153115i
$414$	−4.79168	+	0.199421i	−0.235498	+	0.00980099i
$415$	−27.6282	+	1.17255i	−1.35622	+	0.0575582i
$416$	3.56229	−	1.04598i	0.174656	−	0.0512836i
$417$	1.22709	−	17.1569i	0.0600908	−	0.840179i
$418$	1.57472	−	7.23887i	0.0770221	−	0.354065i
$419$	2.06280	+	14.3471i	0.100774	+	0.700902i	0.976093	+	0.217355i	$0.0697428\pi$
$419$	2.06280	+	14.3471i	0.100774	+	0.700902i	−0.875318	+	0.483547i	$0.839348\pi$
$420$	−8.25213	+	2.16535i	−0.402663	+	0.105659i
$421$	−3.29265	−	1.50370i	−0.160474	−	0.0732861i	0.333559	−	0.942729i	$-0.391750\pi$
$421$	−3.29265	−	1.50370i	−0.160474	−	0.0732861i	−0.494033	+	0.869443i	$0.664478\pi$
$422$	−1.29122	+	0.0923498i	−0.0628556	+	0.00449552i
$423$	2.91047	+	3.88794i	0.141512	+	0.189038i
$424$	1.26882	+	2.77833i	0.0616193	+	0.134927i
$425$	12.6598	+	19.1292i	0.614091	+	0.927905i
$426$	−4.57883	−	1.34447i	−0.221845	−	0.0651396i
$427$	1.50940	−	4.04686i	0.0730450	−	0.195841i
$428$	−0.366387	+	0.274274i	−0.0177100	+	0.0132575i
$429$	−2.50301	+	2.88863i	−0.120846	+	0.139464i
$430$	−2.92796	+	1.23590i	−0.141199	+	0.0596004i
$431$	−22.2301	+	34.5908i	−1.07079	+	1.66618i	−0.418475	+	0.908229i	$0.637435\pi$
$431$	−22.2301	+	34.5908i	−1.07079	+	1.66618i	−0.652313	+	0.757950i	$0.726201\pi$
$432$	0.599278	−	0.800541i	0.0288328	−	0.0385161i
$433$	10.8524	+	2.36080i	0.521535	+	0.113453i	0.465624	−	0.884983i	$-0.345830\pi$
$433$	10.8524	+	2.36080i	0.521535	+	0.113453i	0.0559112	+	0.998436i	$0.482194\pi$
$434$	−27.3468	−	31.5598i	−1.31269	−	1.51492i
$435$	−1.16068	+	0.394990i	−0.0556506	+	0.0189383i
$436$			8.63557i			0.413569i
$437$	10.7052	−	32.8080i	0.512097	−	1.56942i
$438$	−7.66633	+	7.66633i	−0.366311	+	0.366311i
$439$	3.64758	+	12.4225i	0.174089	+	0.592894i	0.999594	+	0.0284983i	$0.00907253\pi$
$439$	3.64758	+	12.4225i	0.174089	+	0.592894i	−0.825504	+	0.564396i	$0.809109\pi$
$440$	1.57992	+	1.67427i	0.0753198	+	0.0798177i
$441$	−6.35760	+	4.08578i	−0.302743	+	0.194561i
$442$	−13.6357	−	10.2075i	−0.648583	−	0.485523i
$443$	−37.2575	+	8.10486i	−1.77015	+	0.385074i	−0.975153	−	0.221533i	$-0.928894\pi$
$443$	−37.2575	+	8.10486i	−1.77015	+	0.385074i	−0.795002	+	0.606607i	$0.792530\pi$
$444$	1.90104	−	4.16269i	0.0902192	−	0.197552i
$445$	1.23558	+	10.8092i	0.0585722	+	0.512404i
$446$	−1.55508	+	10.8158i	−0.0736354	+	0.512145i
$447$	−8.13639	−	3.03472i	−0.384838	−	0.143537i
$448$	−1.82853	−	3.34870i	−0.0863898	−	0.158211i
$449$	−7.14049	+	24.3183i	−0.336981	+	1.14765i	0.600503	+	0.799622i	$0.294967\pi$
$449$	−7.14049	+	24.3183i	−0.336981	+	1.14765i	−0.937484	+	0.348029i	$0.886851\pi$
$450$	−1.34411	+	4.81595i	−0.0633619	+	0.227026i
$451$	−2.78926	−	0.401035i	−0.131341	−	0.0188840i
$452$	0.167113	+	2.33655i	0.00786035	+	0.109902i
$453$	−7.35241	−	19.7126i	−0.345446	−	0.926178i
$454$	9.07895	+	5.83469i	0.426096	+	0.273835i
$455$	−17.8897	+	26.1390i	−0.838683	+	1.22542i
$456$	3.89040	+	6.05358i	0.182185	+	0.283485i
$457$	−0.00420444		0.000300707i	−0.000196675		1.40665e-5i	0.0712408	−	0.997459i	$-0.477304\pi$
$457$	−0.00420444		0.000300707i	−0.000196675		1.40665e-5i	−0.0714375	+	0.997445i	$0.522759\pi$
$458$	−17.8297	−	9.73573i	−0.833126	−	0.454921i
$459$	−4.58780			−0.214140
$460$	6.53427	+	8.50314i	0.304662	+	0.396461i
$461$	8.86813			0.413030			0.206515	−	0.978443i	$-0.433788\pi$
$461$	8.86813			0.413030			0.206515	+	0.978443i	$0.433788\pi$
$462$	3.44748	+	1.88247i	0.160391	+	0.0875802i
$463$	14.5584	+	1.04124i	0.676586	+	0.0483904i	0.405404	−	0.914138i	$-0.367131\pi$
$463$	14.5584	+	1.04124i	0.676586	+	0.0483904i	0.271182	+	0.962528i	$0.412585\pi$
$464$	−0.296437	−	0.461265i	−0.0137618	−	0.0214137i
$465$	−24.0552	+	4.50703i	−1.11553	+	0.209009i
$466$	18.0435	+	11.5959i	0.835850	+	0.537168i
$467$	10.8235	+	29.0190i	0.500853	+	1.34284i	0.903933	+	0.427675i	$0.140667\pi$
$467$	10.8235	+	29.0190i	0.500853	+	1.34284i	−0.403080	+	0.915165i	$0.632060\pi$
$468$	−0.264860	−	3.70322i	−0.0122431	−	0.171182i
$469$	28.6232	+	4.11540i	1.32170	+	0.190032i
$470$	3.36024	−	10.3268i	0.154996	−	0.476341i
$471$	0.615388	−	2.09582i	0.0283556	−	0.0965702i
$472$	0.552751	+	1.01229i	0.0254424	+	0.0465943i
$473$	1.37096	+	0.511343i	0.0630370	+	0.0235116i
$474$	−0.171936	+	1.19584i	−0.00789726	+	0.0549267i
$475$	−29.0901	−	21.1730i	−1.33474	−	0.971483i
$476$	−7.27155	+	15.9225i	−0.333291	+	0.729806i
$477$	2.98454	−	0.649247i	0.136653	−	0.0297270i
$478$	8.90021	+	6.66261i	0.407086	+	0.304741i
$479$	7.85520	−	5.04823i	0.358913	−	0.230660i	−0.348740	−	0.937220i	$-0.613390\pi$
$479$	7.85520	−	5.04823i	0.358913	−	0.230660i	0.707653	+	0.706560i	$0.249754\pi$
$480$	−2.23513	−	0.0648035i	−0.102019	−	0.00295786i
$481$	−4.78667	−	16.3019i	−0.218253	−	0.743302i
$482$	−5.93574	+	5.93574i	−0.270365	+	0.270365i
$483$	15.0916	+	10.3470i	0.686693	+	0.470805i
$484$			9.94013i			0.451824i
$485$	12.3770	+	36.3700i	0.562010	+	1.65148i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	19.0944	+	4.15374i	0.865251	+	0.188224i	0.623222	−	0.782045i	$-0.285823\pi$
$487$	19.0944	+	4.15374i	0.865251	+	0.188224i	0.242029	+	0.970269i	$0.422187\pi$
$488$	0.678406	−	0.906244i	0.0307100	−	0.0410237i
$489$	−13.3190	+	20.7248i	−0.602307	+	0.937207i
$490$	15.6554	+	6.36184i	0.707237	+	0.287399i
$491$	18.5970	−	21.4621i	0.839272	−	0.968571i	−0.160558	−	0.987026i	$-0.551329\pi$
$491$	18.5970	−	21.4621i	0.839272	−	0.968571i	0.999830	+	0.0184554i	$0.00587486\pi$
$492$	2.19124	−	1.64034i	0.0987887	−	0.0739523i
$493$	−0.879086	+	2.35692i	−0.0395921	+	0.106150i
$494$	25.6339	+	7.52680i	1.15332	+	0.338647i
$495$	1.97184	−	1.18792i	0.0886278	−	0.0533932i
$496$	−4.54673	−	9.95594i	−0.204154	−	0.447035i
$497$	10.9114	+	14.5759i	0.489444	+	0.653820i
$498$	−12.3353	+	0.882241i	−0.552760	+	0.0395342i
$499$	−2.56408	−	1.17098i	−0.114784	−	0.0524202i	0.357195	−	0.934030i	$-0.383733\pi$
$499$	−2.56408	−	1.17098i	−0.114784	−	0.0524202i	−0.471979	+	0.881610i	$0.656460\pi$
$500$	10.5349	−	3.74371i	0.471136	−	0.167424i
$501$	2.39618	+	16.6658i	0.107053	+	0.744573i
$502$	4.65507	−	21.3990i	0.207766	−	0.955084i
$503$	−2.69869	+	37.7326i	−0.120329	+	1.68241i	0.475822	+	0.879542i	$0.342151\pi$
$503$	−2.69869	+	37.7326i	−0.120329	+	1.68241i	−0.596151	+	0.802872i	$0.703304\pi$
$504$	−3.66085	+	1.07492i	−0.163067	+	0.0478809i
$505$	−15.1906	+	16.5371i	−0.675973	+	0.735892i
$506$	0.498830	−	4.91204i	0.0221757	−	0.218367i
$507$	−0.554382	−	0.554382i	−0.0246210	−	0.0246210i
$508$	−6.74062	+	12.3445i	−0.299066	+	0.547699i
$509$	−0.981047	+	0.850082i	−0.0434841	+	0.0376792i	−0.676332	−	0.736597i	$-0.736431\pi$
$509$	−0.981047	+	0.850082i	−0.0434841	+	0.0376792i	0.632848	+	0.774276i	$0.281886\pi$
$510$	5.90719	+	8.38718i	0.261575	+	0.371391i
$511$	40.9449	−	5.88699i	1.81130	−	0.260425i
$512$	−0.212565	−	0.977147i	−0.00939415	−	0.0431842i
$513$	6.74220	−	2.51471i	0.297675	−	0.111027i
$514$	17.2118	+	14.9141i	0.759180	+	0.657833i
$515$	1.06727	−	10.5961i	0.0470296	−	0.466918i
$516$	−1.29286	+	0.590427i	−0.0569148	+	0.0259921i
$517$	−4.38831	+	2.39620i	−0.192997	+	0.105385i
$518$	−15.3244	+	8.36777i	−0.673317	+	0.367659i
$519$	−8.44474	+	3.85658i	−0.370683	+	0.169285i
$520$	−6.42901	+	5.25242i	−0.281931	+	0.230334i
$521$	0.334956	+	0.290241i	0.0146747	+	0.0127157i	0.662167	−	0.749356i	$-0.269637\pi$
$521$	0.334956	+	0.290241i	0.0146747	+	0.0127157i	−0.647493	+	0.762072i	$0.724182\pi$
$522$	−0.513736	+	0.191614i	−0.0224856	+	0.00838671i
$523$	−5.59147	−	25.7036i	−0.244498	−	1.12394i	−0.921628	−	0.388075i	$-0.873140\pi$
$523$	−5.59147	−	25.7036i	−0.244498	−	1.12394i	0.677130	−	0.735864i	$-0.263224\pi$
$524$	−13.8472	+	1.99093i	−0.604918	+	0.0869741i
$525$	15.1170	−	11.6365i	0.659761	−	0.507858i
$526$	14.6792	−	12.7196i	0.640045	−	0.554602i
$527$	−24.0648	+	44.0714i	−1.04828	+	1.91978i
$528$	0.727965	+	0.727965i	0.0316806	+	0.0316806i
$529$	4.62373	−	22.5304i	0.201032	−	0.979585i
$530$	−5.02977	−	4.62022i	−0.218479	−	0.200689i
$531$	1.10665	−	0.324941i	0.0480245	−	0.0141013i
$532$	1.95864	−	27.3853i	0.0849177	−	1.18730i
$533$	2.16016	−	9.93010i	0.0935670	−	0.430120i
$534$	0.692432	+	4.81597i	0.0299645	+	0.208407i
$535$	0.516284	−	0.883618i	0.0223209	−	0.0382021i
$536$	6.89426	+	3.14850i	0.297787	+	0.135995i
$537$	2.83571	−	0.202814i	0.122370	−	0.00875207i
$538$	4.74322	+	6.33619i	0.204495	+	0.273173i
$539$	−3.23202	−	7.07713i	−0.139213	−	0.304834i
$540$	−0.538433	+	2.17027i	−0.0231705	+	0.0933937i
$541$	33.7081	+	9.89759i	1.44922	+	0.425531i	0.909285	−	0.416174i	$-0.136629\pi$
$541$	33.7081	+	9.89759i	1.44922	+	0.425531i	0.539939	+	0.841704i	$0.318447\pi$
$542$	−5.36629	+	14.3876i	−0.230502	+	0.617999i
$543$	6.27078	−	4.69425i	0.269105	−	0.201449i
$544$	−3.00437	+	3.46723i	−0.128811	+	0.148656i
$545$	−7.50913	−	17.7898i	−0.321656	−	0.762033i
$546$	−7.65838	+	11.9167i	−0.327748	+	0.509987i
$547$	−24.2196	+	32.3536i	−1.03556	+	1.38334i	−0.114717	+	0.993398i	$0.536596\pi$
$547$	−24.2196	+	32.3536i	−1.03556	+	1.38334i	−0.920839	+	0.389943i	$0.872495\pi$
$548$	−12.0385	−	2.61882i	−0.514260	−	0.111870i
$549$	−0.741328	−	0.855538i	−0.0316391	−	0.0365135i
$550$	−4.71062	−	2.07527i	−0.200861	−	0.0884899i
$551$		−	3.94557i		−	0.168087i
$552$	3.03119	+	3.71643i	0.129016	+	0.158182i
$553$	3.25942	−	3.25942i	0.138605	−	0.138605i
$554$	−7.51094	−	25.5799i	−0.319109	−	1.08679i
$555$	−0.296556	+	10.2285i	−0.0125881	+	0.434174i
$556$	−14.4702	+	9.29944i	−0.613673	+	0.394384i
$557$	−1.27195	−	0.952173i	−0.0538944	−	0.0403448i	0.571991	−	0.820260i	$-0.306171\pi$
$557$	−1.27195	−	0.952173i	−0.0538944	−	0.0403448i	−0.625885	+	0.779915i	$0.715262\pi$
$558$	−10.6949	+	2.32653i	−0.452751	+	0.0984899i
$559$	−2.19207	+	4.79996i	−0.0927146	+	0.203017i
$560$	6.67877	+	5.30852i	0.282230	+	0.224326i
$561$	0.672172	−	4.67506i	0.0283791	−	0.197381i
$562$	−1.59672	−	0.595546i	−0.0673536	−	0.0251216i
$563$	−4.61729	−	8.45593i	−0.194595	−	0.356375i	0.762103	−	0.647456i	$-0.224167\pi$
$563$	−4.61729	−	8.45593i	−0.194595	−	0.356375i	−0.956698	+	0.291081i	$0.905985\pi$
$564$	1.36827	−	4.65991i	0.0576147	−	0.196217i
$565$	−2.37603	−	4.66813i	−0.0999604	−	0.196390i
$566$	−26.4952	−	3.80943i	−1.11367	−	0.160122i
$567$	0.272188	+	3.80568i	0.0114308	+	0.159824i
$568$	1.66769	+	4.47125i	0.0699747	+	0.187609i
$569$	−14.4415	−	9.28100i	−0.605420	−	0.389080i	0.201717	−	0.979444i	$-0.435348\pi$
$569$	−14.4415	−	9.28100i	−0.605420	−	0.389080i	−0.807137	+	0.590364i	$0.798984\pi$
$570$	−13.2784	−	9.08784i	−0.556172	−	0.380648i
$571$	−18.2223	−	28.3544i	−0.762579	−	1.18660i	−0.977700	−	0.210008i	$-0.932651\pi$
$571$	−18.2223	−	28.3544i	−0.762579	−	1.18660i	0.215121	−	0.976587i	$-0.430985\pi$
$572$	3.81246	+	0.272673i	0.159407	+	0.0114010i
$573$	15.8791	+	8.67063i	0.663358	+	0.362221i
$574$	−10.4435			−0.435903
$575$	−20.8550	−	11.8351i	−0.869713	−	0.493557i
$576$	−1.00000			−0.0416667
$577$	10.8099	+	5.90263i	0.450020	+	0.245730i	0.688242	−	0.725481i	$-0.258383\pi$
$577$	10.8099	+	5.90263i	0.450020	+	0.245730i	−0.238222	+	0.971211i	$0.576565\pi$
$578$	4.03763	+	0.288777i	0.167943	+	0.0120115i
$579$	−12.4567	−	19.3830i	−0.517683	−	0.805531i
$580$	1.01178	+	0.692467i	0.0420118	+	0.0287531i
$581$	39.6941	+	25.5099i	1.64679	+	1.05833i
$582$	6.00421	+	16.0979i	0.248883	+	0.667280i
$583$	0.224322	+	3.13643i	0.00929045	+	0.129898i
$584$	10.7315	+	1.54295i	0.444072	+	0.0638479i
$585$	3.76580	+	7.39857i	0.155697	+	0.305893i
$586$	−0.513945	+	1.75034i	−0.0212309	+	0.0723057i
$587$	−4.30420	−	7.88255i	−0.177653	−	0.325348i	0.773645	−	0.633619i	$-0.218431\pi$
$587$	−4.30420	−	7.88255i	−0.177653	−	0.325348i	−0.951298	+	0.308271i	$0.900249\pi$
$588$	7.08080	+	2.64100i	0.292007	+	0.108913i
$589$	11.2086	−	77.9577i	0.461843	−	3.21219i
$590$	−2.01895	−	1.60473i	−0.0831187	−	0.0660656i
$591$	8.16529	−	17.8795i	0.335875	−	0.735464i
$592$	−4.47165	+	0.972748i	−0.183784	+	0.0399797i
$593$	−21.4421	−	16.0513i	−0.880520	−	0.659149i	0.0602539	−	0.998183i	$-0.480809\pi$
$593$	−21.4421	−	16.0513i	−0.880520	−	0.659149i	−0.940774	+	0.339034i	$0.889900\pi$
$594$	0.866069	−	0.556589i	0.0355352	−	0.0228371i
$595$	1.13434	−	39.1244i	0.0465034	−	1.60394i
$596$	2.44654	+	8.33215i	0.100214	+	0.341298i
$597$	−6.12580	+	6.12580i	−0.250712	+	0.250712i
$598$	17.5408	+	3.05807i	0.717298	+	0.125054i
$599$		−	37.2455i		−	1.52181i	−0.648865	−	0.760904i	$-0.724756\pi$
$599$		−	37.2455i		−	1.52181i	0.648865	−	0.760904i	$-0.275244\pi$
$600$	4.66086	−	1.81008i	0.190279	−	0.0738961i
$601$	8.09365	+	9.34057i	0.330147	+	0.381010i	0.896418	−	0.443209i	$-0.146160\pi$
$601$	8.09365	+	9.34057i	0.330147	+	0.381010i	−0.566271	+	0.824219i	$0.691615\pi$
$602$	5.29888	+	1.15270i	0.215966	+	0.0469806i
$603$	4.54203	−	6.06744i	0.184966	−	0.247085i
$604$	−11.3746	+	17.6992i	−0.462826	+	0.720171i
$605$	−8.64353	−	20.4773i	−0.351409	−	0.832521i
$606$	−6.57625	+	7.58940i	−0.267142	+	0.308298i
$607$	−1.74871	+	1.30907i	−0.0709779	+	0.0531334i	−0.634177	−	0.773188i	$-0.718661\pi$
$607$	−1.74871	+	1.30907i	−0.0709779	+	0.0531334i	0.563200	+	0.826321i	$0.309570\pi$
$608$	2.51471	−	6.74220i	0.101985	−	0.273432i
$609$	2.00727	+	0.589388i	0.0813387	+	0.0238832i
$610$	−0.609528	+	2.45683i	−0.0246790	+	0.0994743i
$611$	−7.49041	−	16.4017i	−0.303030	−	0.663542i
$612$	2.74937	+	3.67273i	0.111137	+	0.148461i
$613$	29.2896	−	2.09484i	1.18300	−	0.0846096i	0.534056	−	0.845449i	$-0.320667\pi$
$613$	29.2896	−	2.09484i	1.18300	−	0.0846096i	0.648940	+	0.760839i	$0.275212\pi$
$614$	25.9371	+	11.8451i	1.04674	+	0.478028i
$615$	−3.08772	+	5.28462i	−0.124509	+	0.213096i
$616$	−0.559006	−	3.88797i	−0.0225230	−	0.156651i
$617$	−7.55232	+	34.7174i	−0.304045	+	1.39767i	0.530945	+	0.847406i	$0.321837\pi$
$617$	−7.55232	+	34.7174i	−0.304045	+	1.39767i	−0.834990	+	0.550265i	$0.814527\pi$
$618$	0.339766	−	4.75054i	0.0136674	−	0.191095i
$619$	40.0749	−	11.7671i	1.61075	−	0.472958i	0.652237	−	0.758015i	$-0.273831\pi$
$619$	40.0749	−	11.7671i	1.61075	−	0.472958i	0.958511	+	0.285056i	$0.0920123\pi$
$620$	18.0238	+	16.5562i	0.723854	+	0.664915i
$621$	4.27583	−	2.17194i	0.171583	−	0.0871568i
$622$	−18.7303	−	18.7303i	−0.751017	−	0.751017i
$623$	8.89669	−	16.2931i	0.356438	−	0.652768i
$624$	−2.80586	+	2.43129i	−0.112324	+	0.0973295i
$625$	−18.4472	+	16.8730i	−0.737890	+	0.674921i
$626$	−0.592160	+	0.0851398i	−0.0236675	+	0.00340287i
$627$	1.57472	+	7.23887i	0.0628883	+	0.289093i
$628$	−2.04658	+	0.763334i	−0.0816674	+	0.0304603i
$629$	15.8669	+	13.7487i	0.632653	+	0.548197i
$630$	6.60688	−	5.39774i	0.263225	−	0.215051i
$631$	−31.1664	+	14.2332i	−1.24072	+	0.566616i	−0.924177	−	0.381964i	$-0.875248\pi$
$631$	−31.1664	+	14.2332i	−1.24072	+	0.566616i	−0.316539	+	0.948580i	$0.602521\pi$
$632$	1.06035	−	0.578998i	0.0421786	−	0.0230313i
$633$	1.13617	−	0.620396i	0.0451587	−	0.0246585i
$634$	−28.4192	+	12.9786i	−1.12867	+	0.515447i
$635$	3.15183	−	31.2919i	0.125076	−	1.24178i
$636$	−2.30832	−	2.00017i	−0.0915307	−	0.0793118i
$637$	26.2888	−	9.80520i	1.04160	−	0.388496i
$638$	−0.119989	−	0.551581i	−0.00475042	−	0.0218373i
$639$	4.72356	−	0.679146i	0.186861	−	0.0268666i
$640$	1.28758	+	1.82815i	0.0508963	+	0.0722639i
$641$	21.1563	−	18.3321i	0.835625	−	0.724073i	−0.127873	−	0.991791i	$-0.540815\pi$
$641$	21.1563	−	18.3321i	0.835625	−	0.724073i	0.963497	+	0.267718i	$0.0862694\pi$
$642$	0.219340	−	0.401691i	0.00865666	−	0.0158535i
$643$	−3.13320	−	3.13320i	−0.123561	−	0.123561i	0.642622	−	0.766183i	$-0.277847\pi$
$643$	−3.13320	−	3.13320i	−0.123561	−	0.123561i	−0.766183	+	0.642622i	$0.777847\pi$
$644$	−0.760870	−	18.2822i	−0.0299825	−	0.720419i
$645$	2.14995	−	2.34053i	0.0846544	−	0.0921584i
$646$	−31.6761	+	9.30095i	−1.24628	+	0.365941i
$647$	2.70394	−	37.8060i	0.106303	−	1.48631i	−0.612155	−	0.790738i	$-0.709697\pi$
$647$	2.70394	−	37.8060i	0.106303	−	1.48631i	0.718458	−	0.695570i	$-0.244848\pi$
$648$	−0.212565	+	0.977147i	−0.00835035	+	0.0383860i
$649$	0.168983	+	1.17530i	0.00663318	+	0.0461348i
$650$	8.67690	−	16.4107i	0.340336	−	0.643682i
$651$	37.9859	+	17.3476i	1.48879	+	0.679905i
$652$	24.5728	−	1.75748i	0.962346	−	0.0688284i
$653$	−9.88293	−	13.2020i	−0.386749	−	0.516636i	0.564345	−	0.825539i	$-0.309129\pi$
$653$	−9.88293	−	13.2020i	−0.386749	−	0.516636i	−0.951093	+	0.308903i	$0.900038\pi$
$654$	−3.58734	−	7.85519i	−0.140276	−	0.307162i
$655$	26.7949	−	16.1424i	1.04696	−	0.630736i
$656$	−2.62632	−	0.771157i	−0.102541	−	0.0301086i
$657$	3.78883	−	10.1582i	0.147816	−	0.396311i
$658$	−14.8340	+	11.1046i	−0.578291	+	0.432903i
$659$	−5.14042	+	5.93236i	−0.200242	+	0.231092i	−0.846986	−	0.531616i	$-0.821585\pi$
$659$	−5.14042	+	5.93236i	−0.200242	+	0.231092i	0.646743	+	0.762708i	$0.276130\pi$
$660$	−2.13266	−	0.866647i	−0.0830138	−	0.0337342i
$661$	8.01024	−	12.4642i	0.311562	−	0.484801i	−0.649793	−	0.760111i	$-0.725144\pi$
$661$	8.01024	−	12.4642i	0.311562	−	0.484801i	0.961355	+	0.275311i	$0.0887808\pi$
$662$	−13.5731	+	18.1316i	−0.527535	+	0.704704i
$663$	16.6438	+	3.62064i	0.646392	+	0.140614i
$664$	8.09856	+	9.34624i	0.314285	+	0.362704i
$665$	19.7782	+	58.1187i	0.766966	+	2.25375i
$666$			4.57623i			0.177325i
$667$	−0.296496	−	2.61282i	−0.0114804	−	0.101169i
$668$	11.9057	−	11.9057i	0.460645	−	0.460645i
$669$	−3.07851	−	10.4844i	−0.119022	−	0.405352i
$670$	−16.9404	−	0.491157i	−0.654466	−	0.0189751i
$671$	0.980424	−	0.630080i	0.0378488	−	0.0243240i
$672$	3.05439	+	2.28648i	0.117826	+	0.0882031i
$673$	−0.784141	+	0.170579i	−0.0302264	+	0.00657535i	−0.227653	−	0.973742i	$-0.573105\pi$
$673$	−0.784141	+	0.170579i	−0.0302264	+	0.00657535i	0.197427	+	0.980318i	$0.436742\pi$
$674$	7.18843	−	15.7405i	0.276888	−	0.606300i
$675$	−0.777973	−	4.93910i	−0.0299442	−	0.190106i
$676$	−0.111577	+	0.776035i	−0.00429142	+	0.0298475i
$677$	30.6231	+	11.4218i	1.17694	+	0.438976i	0.860408	−	0.509606i	$-0.170209\pi$
$677$	30.6231	+	11.4218i	1.17694	+	0.438976i	0.316532	+	0.948582i	$0.397481\pi$
$678$	−1.12265	−	2.05598i	−0.0431151	−	0.0789594i
$679$	18.4685	−	62.8978i	0.708754	−	2.41380i
$680$	3.17424	−	9.75520i	0.121727	−	0.374095i
$681$	−10.6823	−	1.53589i	−0.409347	−	0.0588553i
$682$	−0.803841	−	11.2392i	−0.0307807	−	0.430370i
$683$	8.23038	+	22.0665i	0.314927	+	0.844351i	0.993910	+	0.110197i	$0.0351483\pi$
$683$	8.23038	+	22.0665i	0.314927	+	0.844351i	−0.678983	+	0.734154i	$0.737579\pi$
$684$	−6.05358	−	3.89040i	−0.231464	−	0.148753i
$685$	27.0773	−	5.07326i	1.03457	−	0.193839i
$686$	−1.14956	−	1.78874i	−0.0438902	−	0.0682946i
$687$	20.2628	+	1.44922i	0.773074	+	0.0552914i
$688$	1.24744	+	0.681154i	0.0475582	+	0.0259688i
$689$	−11.3398			−0.432012
$690$	−9.47611	−	5.02029i	−0.360749	−	0.191119i
$691$	0.344921			0.0131214			0.00656070	−	0.999978i	$-0.497912\pi$
$691$	0.344921			0.0131214			0.00656070	+	0.999978i	$0.497912\pi$
$692$	8.14810	+	4.44920i	0.309744	+	0.169133i
$693$	−3.91794	−	0.280217i	−0.148830	−	0.0106446i
$694$	−9.67278	−	15.0511i	−0.367174	−	0.571333i
$695$	21.7232	−	31.7401i	0.824006	−	1.20397i
$696$	0.461265	+	0.296437i	0.0174842	+	0.0112364i
$697$	4.38847	+	11.7660i	0.166225	+	0.445667i
$698$	1.91243	+	26.7392i	0.0723865	+	1.01210i
$699$	−21.2301	−	3.05242i	−0.802995	−	0.115453i
$700$	−18.3748	−	5.12832i	−0.694501	−	0.193832i
$701$	−4.35467	+	14.8307i	−0.164474	+	0.560146i	0.835470	+	0.549536i	$0.185196\pi$
$701$	−4.35467	+	14.8307i	−0.164474	+	0.560146i	−0.999944	+	0.0106100i	$0.996623\pi$
$702$	1.77930	+	3.25854i	0.0671553	+	0.122986i
$703$	−30.8539	−	11.5079i	−1.16368	−	0.434029i
$704$	0.146513	−	1.01902i	0.00552191	−	0.0384057i
$705$	1.23333	+	10.7895i	0.0464500	+	0.406356i
$706$	12.8160	−	28.0631i	0.482336	−	1.05617i
$707$	37.4395	−	8.14446i	1.40806	−	0.306304i
$708$	−0.923319	−	0.691188i	−0.0347004	−	0.0259764i
$709$	20.3042	−	13.0487i	0.762539	−	0.490054i	−0.100658	−	0.994921i	$-0.532095\pi$
$709$	20.3042	−	13.0487i	0.762539	−	0.490054i	0.863197	+	0.504867i	$0.168459\pi$
$710$	−7.32356	−	7.76091i	−0.274848	−	0.291262i
$711$	−0.340371	−	1.15920i	−0.0127649	−	0.0434733i
$712$	3.44042	−	3.44042i	0.128935	−	0.128935i
$713$	1.56429	−	52.4672i	0.0585830	−	1.96491i
$714$		−	17.5043i		−	0.655082i
$715$	−8.09103	+	2.75344i	−0.302587	+	0.102973i
$716$	−1.86174	−	2.14856i	−0.0695764	−	0.0802955i
$717$	−10.8637	−	2.36325i	−0.405711	−	0.0882570i
$718$	19.7790	−	26.4217i	0.738146	−	0.986048i
$719$	−26.8722	+	41.8140i	−1.00216	+	1.55940i	−0.185208	+	0.982699i	$0.559296\pi$
$719$	−26.8722	+	41.8140i	−1.00216	+	1.55940i	−0.816957	+	0.576699i	$0.804341\pi$
$720$	2.06006	−	0.869559i	0.0767741	−	0.0324065i
$721$	−11.8998	+	13.7331i	−0.443172	+	0.511448i
$722$	26.2426	−	19.6450i	0.976648	−	0.731109i
$723$	2.93354	−	7.86513i	0.109100	−	0.292507i
$724$	−7.51588	−	2.20686i	−0.279325	−	0.0820173i
$725$	−2.68647	−	0.546727i	−0.0997729	−	0.0203049i
$726$	−4.12928	−	9.04186i	−0.153252	−	0.335575i
$727$	21.1933	+	28.3110i	0.786017	+	1.05000i	0.997362	+	0.0725843i	$0.0231246\pi$
$727$	21.1933	+	28.3110i	0.786017	+	1.05000i	−0.211345	+	0.977411i	$0.567784\pi$
$728$	14.1293	−	1.01055i	0.523666	−	0.0374533i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	−23.4492	+	6.15306i	−0.867895	+	0.227735i
$731$	−0.927981	−	6.45425i	−0.0343226	−	0.238719i
$732$	−0.240632	+	1.10617i	−0.00889402	+	0.0408852i
$733$	−0.948714	+	13.2648i	−0.0350415	+	0.489945i	0.949381	+	0.314127i	$0.101712\pi$
$733$	−0.948714	+	13.2648i	−0.0350415	+	0.489945i	−0.984423	+	0.175818i	$0.943743\pi$
$734$	31.1103	−	9.13479i	1.14830	−	0.337171i
$735$	−16.8834	+	0.716536i	−0.622754	+	0.0264298i
$736$	1.15863	−	4.65377i	0.0427077	−	0.171540i
$737$	5.51737	+	5.51737i	0.203235	+	0.203235i
$738$	−1.31180	+	2.40238i	−0.0482880	+	0.0884328i
$739$	20.1494	−	17.4595i	0.741206	−	0.642259i	−0.200114	−	0.979773i	$-0.564131\pi$
$739$	20.1494	−	17.4595i	0.741206	−	0.642259i	0.941321	+	0.337514i	$0.109586\pi$
$740$	8.36603	−	5.89229i	0.307541	−	0.216605i
$741$	−26.4442	+	3.80210i	−0.971451	+	0.139674i
$742$	2.47714	+	11.3872i	0.0909386	+	0.418038i
$743$	−5.30052	+	1.97699i	−0.194457	+	0.0725288i	−0.444806	−	0.895627i	$-0.646727\pi$
$743$	−5.30052	+	1.97699i	−0.194457	+	0.0725288i	0.250349	+	0.968156i	$0.419455\pi$
$744$	8.27169	+	7.16746i	0.303255	+	0.262772i
$745$	−12.2853	−	15.0374i	−0.450100	−	0.550926i
$746$	−21.6794	+	9.90063i	−0.793737	+	0.362488i
$747$	10.8541	−	5.92680i	0.397132	−	0.216850i
$748$	−4.14540	+	2.26356i	−0.151571	+	0.0827639i
$749$	−1.58841	+	0.725403i	−0.0580393	+	0.0265056i
$750$	−8.02771	+	7.78177i	−0.293130	+	0.284150i
$751$	25.0146	+	21.6753i	0.912795	+	0.790941i	0.978361	−	0.206907i	$-0.0663398\pi$
$751$	25.0146	+	21.6753i	0.912795	+	0.790941i	−0.0655658	+	0.997848i	$0.520885\pi$
$752$	−4.55042	+	1.69722i	−0.165937	+	0.0618912i
$753$	4.65507	+	21.3990i	0.169640	+	0.779823i
$754$	2.01497	−	0.289709i	0.0733809	−	0.0105506i
$755$	8.04190	−	46.3524i	0.292675	−	1.68694i
$756$	2.88349	−	2.49856i	0.104871	−	0.0908716i
$757$	0.855857	−	1.56738i	0.0311066	−	0.0569675i	−0.861663	−	0.507480i	$-0.830577\pi$
$757$	0.855857	−	1.56738i	0.0311066	−	0.0569675i	0.892770	+	0.450513i	$0.148759\pi$
$758$	−2.85843	−	2.85843i	−0.103823	−	0.103823i
$759$	1.58678	+	4.67537i	0.0575965	+	0.169705i
$760$	0.682272	+	16.0761i	0.0247486	+	0.583140i
$761$	−19.8104	+	5.81687i	−0.718128	+	0.210861i	−0.620325	−	0.784345i	$-0.712999\pi$
$761$	−19.8104	+	5.81687i	−0.718128	+	0.210861i	−0.0978022	+	0.995206i	$0.531181\pi$
$762$	1.00338	−	14.0291i	0.0363487	−	0.508221i
$763$	−7.00363	+	32.1952i	−0.253549	+	1.16554i
$764$	−2.57478	−	17.9080i	−0.0931522	−	0.647888i
$765$	−8.85753	−	5.17532i	−0.320245	−	0.187114i
$766$	−0.426981	−	0.194996i	−0.0154275	−	0.00704548i
$767$	−4.27118	+	0.305481i	−0.154223	+	0.0110303i
$768$	0.599278	+	0.800541i	0.0216246	+	0.0288870i
$769$	−20.7896	−	45.5228i	−0.749691	−	1.64159i	−0.766920	−	0.641743i	$-0.778212\pi$
$769$	−20.7896	−	45.5228i	−0.749691	−	1.64159i	0.0172292	−	0.999852i	$-0.494516\pi$
$770$	4.53240	+	7.52338i	0.163337	+	0.271124i
$771$	−21.8520	−	6.41631i	−0.786979	−	0.231078i
$772$	−8.05188	+	21.5879i	−0.289793	+	0.776966i
$773$	−2.83318	+	2.12089i	−0.101902	+	0.0762832i	−0.649014	−	0.760777i	$-0.724818\pi$
$773$	−2.83318	+	2.12089i	−0.101902	+	0.0762832i	0.547111	+	0.837060i	$0.315727\pi$
$774$	0.930750	−	1.07414i	0.0334551	−	0.0386093i
$775$	−51.5269	−	18.4342i	−1.85090	−	0.662174i
$776$	9.28885	−	14.4537i	0.333450	−	0.518859i
$777$	10.4635	−	13.9776i	0.375376	−	0.501443i
$778$	−9.40697	−	2.04636i	−0.337256	−	0.0733656i
$779$	−12.8985	−	14.8857i	−0.462138	−	0.533336i
$780$	3.66610	−	7.44847i	0.131267	−	0.266698i
$781$			4.91290i			0.175798i
$782$	−20.2775	+	8.53959i	−0.725123	+	0.305375i
$783$	0.387712	−	0.387712i	0.0138557	−	0.0138557i
$784$	−2.12913	−	7.25117i	−0.0760405	−	0.258970i
$785$	3.55232	−	3.35214i	0.126788	−	0.119643i
$786$	11.7688	−	7.56335i	0.419779	−	0.269776i
$787$	14.1011	+	10.5559i	0.502649	+	0.376278i	0.820304	−	0.571928i	$-0.193804\pi$
$787$	14.1011	+	10.5559i	0.502649	+	0.376278i	−0.317655	+	0.948206i	$0.602895\pi$
$788$	−19.2065	+	4.17813i	−0.684205	+	0.148840i
$789$	−8.06878	+	17.6682i	−0.287256	+	0.629003i
$790$	−1.68093	+	2.11481i	−0.0598047	+	0.0752417i
$791$	−1.27196	+	8.84668i	−0.0452257	+	0.314552i
$792$	−0.964588	−	0.359773i	−0.0342751	−	0.0127840i
$793$	2.01424	+	3.68880i	0.0715276	+	0.130993i
$794$	−4.14981	+	14.1330i	−0.147271	+	0.501560i
$795$	6.49454	+	2.11326i	0.230338	+	0.0749496i
$796$	8.57502	+	1.23290i	0.303933	+	0.0436990i
$797$	−0.0877591	−	1.22703i	−0.00310859	−	0.0434637i	0.995661	−	0.0930541i	$-0.0296630\pi$
$797$	−0.0877591	−	1.22703i	−0.00310859	−	0.0434637i	−0.998770	+	0.0495904i	$0.984208\pi$
$798$	9.59463	+	25.7242i	0.339646	+	0.910627i
$799$	18.7442	+	12.0462i	0.663123	+	0.426163i
$800$	−4.24219	−	2.64647i	−0.149984	−	0.0935670i
$801$	−2.63048	−	4.09311i	−0.0929436	−	0.144623i
$802$	31.9410	+	2.28447i	1.12788	+	0.0806674i
$803$	9.79634	+	5.34921i	0.345705	+	0.188769i
$804$	−7.57917			−0.267297
$805$	17.4649	+	37.0009i	0.615556	+	1.30411i
$806$	40.6354			1.43132
$807$	−6.94673	−	3.79320i	−0.244537	−	0.133527i
$808$	10.0166	+	0.716404i	0.352384	+	0.0252030i
$809$	0.263428	+	0.409902i	0.00926164	+	0.0144114i	0.845853	−	0.533415i	$-0.179092\pi$
$809$	0.263428	+	0.409902i	0.00926164	+	0.0144114i	−0.836592	+	0.547827i	$0.815455\pi$
$810$	−0.411788	−	2.19782i	−0.0144688	−	0.0772237i
$811$	22.8471	+	14.6830i	0.802271	+	0.515588i	0.876356	−	0.481663i	$-0.159967\pi$
$811$	22.8471	+	14.6830i	0.802271	+	0.515588i	−0.0740850	+	0.997252i	$0.523604\pi$
$812$	−0.731084	−	1.96011i	−0.0256560	−	0.0687864i
$813$	−1.09547	−	15.3166i	−0.0384197	−	0.537178i
$814$	−4.66327	−	0.670477i	−0.163448	−	0.0235002i
$815$	−49.0934	+	24.9881i	−1.71967	+	0.875293i
$816$	1.29253	−	4.40197i	0.0452477	−	0.154100i
$817$	4.90152	+	8.97646i	0.171482	+	0.314047i
$818$	−18.6900	−	6.97100i	−0.653479	−	0.243735i
$819$	2.01594	−	14.0212i	0.0704428	−	0.489940i
$820$	6.08096	−	0.695106i	0.212356	−	0.0242741i
$821$	10.7216	−	23.4771i	0.374188	−	0.819357i	−0.625060	−	0.780577i	$-0.714925\pi$
$821$	10.7216	−	23.4771i	0.374188	−	0.819357i	0.999248	−	0.0387803i	$-0.0123472\pi$
$822$	12.0385	−	2.61882i	0.419892	−	0.0913418i
$823$	20.4610	+	15.3169i	0.713225	+	0.533913i	0.893146	−	0.449768i	$-0.148493\pi$
$823$	20.4610	+	15.3169i	0.713225	+	0.533913i	−0.179921	+	0.983681i	$0.557584\pi$
$824$	−4.00662	+	2.57490i	−0.139577	+	0.0897008i
$825$	5.14703	−	0.0691271i	0.179196	−	0.00240670i
$826$	1.23978	+	4.22231i	0.0431375	+	0.146913i
$827$	23.7447	−	23.7447i	0.825684	−	0.825684i	−0.161232	−	0.986916i	$-0.551547\pi$
$827$	23.7447	−	23.7447i	0.825684	−	0.825684i	0.986916	+	0.161232i	$0.0515469\pi$
$828$	−4.30113	−	2.12138i	−0.149475	−	0.0737231i
$829$		−	33.8608i		−	1.17603i	−0.808849	−	0.588017i	$-0.799909\pi$
$829$		−	33.8608i		−	1.17603i	0.808849	−	0.588017i	$-0.200091\pi$
$830$	−24.8107	−	12.2117i	−0.861191	−	0.423874i
$831$	17.4585	+	20.1481i	0.605627	+	0.698931i
$832$	3.62784	+	0.789188i	0.125773	+	0.0273602i
$833$	−20.7778	+	27.7559i	−0.719907	+	0.961683i
$834$	9.29944	−	14.4702i	0.322013	−	0.501062i
$835$	−14.1738	+	34.8792i	−0.490504	+	1.20704i
$836$	4.85132	−	5.59872i	0.167786	−	0.193636i
$837$	8.76194	−	6.55911i	0.302857	−	0.226716i
$838$	−5.06536	+	13.5807i	−0.174980	+	0.469139i
$839$	38.3300	+	11.2547i	1.32330	+	0.388555i	0.865682	−	0.500595i	$-0.166885\pi$
$839$	38.3300	+	11.2547i	1.32330	+	0.388555i	0.457616	+	0.889150i	$0.348704\pi$
$840$	−8.28047	−	2.05434i	−0.285703	−	0.0708814i
$841$	11.9221	+	26.1059i	0.411108	+	0.900202i
$842$	−2.16924	−	2.89777i	−0.0747571	−	0.0998638i
$843$	1.69983	−	0.121574i	0.0585452	−	0.00418724i
$844$	−1.17753	−	0.537762i	−0.0405324	−	0.0185105i
$845$	−0.444952	−	1.69571i	−0.0153068	−	0.0583340i
$846$	0.691171	+	4.80720i	0.0237630	+	0.165275i
$847$	−8.06167	+	37.0589i	−0.277002	+	1.27336i
$848$	−0.217894	+	3.04656i	−0.00748252	+	0.104619i
$849$	25.6833	−	7.54131i	0.881450	−	0.258817i
$850$	1.94357	+	22.8565i	0.0666640	+	0.783973i
$851$	−21.2967	−	5.30216i	−0.730043	−	0.181756i
$852$	−3.37441	−	3.37441i	−0.115605	−	0.115605i
$853$	1.65418	−	3.02940i	0.0566380	−	0.103725i	−0.847826	−	0.530274i	$-0.822089\pi$
$853$	1.65418	−	3.02940i	0.0566380	−	0.103725i	0.904464	+	0.426549i	$0.140271\pi$
$854$	3.26422	−	2.82846i	0.111699	−	0.0967880i
$855$	15.8537	+	2.75053i	0.542185	+	0.0940663i
$856$	−0.453016	+	0.0651339i	−0.0154838	+	0.00222623i
$857$	5.17170	+	23.7739i	0.176662	+	0.812102i	0.977116	+	0.212708i	$0.0682282\pi$
$857$	5.17170	+	23.7739i	0.176662	+	0.812102i	−0.800454	+	0.599394i	$0.795408\pi$
$858$	−3.58121	+	1.33572i	−0.122260	+	0.0456008i
$859$	−6.39478	−	5.54111i	−0.218187	−	0.189060i	0.538909	−	0.842364i	$-0.318837\pi$
$859$	−6.39478	−	5.54111i	−0.218187	−	0.189060i	−0.757096	+	0.653304i	$0.773382\pi$
$860$	−3.16211	−	0.318499i	−0.107827	−	0.0108607i
$861$	9.49974	−	4.33839i	0.323750	−	0.147852i
$862$	−36.0885	+	19.7058i	−1.22918	+	0.671183i
$863$	−5.40437	+	2.95101i	−0.183967	+	0.100453i	−0.568593	−	0.822619i	$-0.692512\pi$
$863$	−5.40437	+	2.95101i	−0.183967	+	0.100453i	0.384626	+	0.923072i	$0.374330\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	−20.6545	−	2.08039i	−0.702273	−	0.0707353i
$866$	8.39355	+	7.27305i	0.285224	+	0.247148i
$867$	−3.79272	+	1.41461i	−0.128807	+	0.0480427i
$868$	−8.87665	−	40.8053i	−0.301293	−	1.38502i
$869$	1.23111	−	0.177007i	0.0417627	−	0.00600456i
$870$	−1.20801	−	0.209583i	−0.0409553	−	0.00710552i
$871$	−21.2661	+	18.4272i	−0.720574	+	0.624381i
$872$	−4.13859	+	7.57926i	−0.140150	+	0.256666i
$873$	−12.1489	−	12.1489i	−0.411179	−	0.411179i
$874$	25.1189	−	23.6644i	0.849659	−	0.800461i
$875$	42.3126	−	5.41329i	1.43043	−	0.183002i
$876$	−10.4027	+	3.05450i	−0.351473	+	0.103202i
$877$	−2.85336	+	39.8952i	−0.0963511	+	1.34716i	0.687486	+	0.726198i	$0.258714\pi$
$877$	−2.85336	+	39.8952i	−0.0963511	+	1.34716i	−0.783837	+	0.620966i	$0.786740\pi$
$878$	−2.75207	+	12.6511i	−0.0928779	+	0.426953i
$879$	−0.259615	−	1.80566i	−0.00875660	−	0.0609035i
$880$	0.584271	+	2.22665i	0.0196958	+	0.0750603i
$881$	−46.2812	−	21.1359i	−1.55925	−	0.712087i	−0.565612	−	0.824672i	$-0.691360\pi$
$881$	−46.2812	−	21.1359i	−1.55925	−	0.712087i	−0.993642	+	0.112584i	$0.964087\pi$
$882$	−7.53803	+	0.539131i	−0.253819	+	0.0181535i
$883$	20.0155	+	26.7376i	0.673575	+	0.899790i	0.998951	−	0.0457942i	$-0.0145818\pi$
$883$	20.0155	+	26.7376i	0.673575	+	0.899790i	−0.325376	+	0.945585i	$0.605491\pi$
$884$	−7.07579	−	15.4938i	−0.237985	−	0.521113i
$885$	2.50313	+	0.621012i	0.0841416	+	0.0208751i
$886$	−36.5843	−	10.7421i	−1.22907	−	0.360889i
$887$	−9.01827	+	24.1789i	−0.302804	+	0.811849i	0.693051	+	0.720889i	$0.256266\pi$
$887$	−9.01827	+	24.1789i	−0.302804	+	0.811849i	−0.995855	+	0.0909597i	$0.971007\pi$
$888$	3.66346	−	2.74243i	0.122938	−	0.0920301i
$889$	−35.1421	+	40.5561i	−1.17863	+	1.36021i
$890$	−4.09584	+	10.0791i	−0.137293	+	0.337854i
$891$	−0.556589	+	0.866069i	−0.0186464	+	0.0290144i
$892$	−6.54835	+	8.74757i	−0.219255	+	0.292890i
$893$	−34.1492	−	7.42871i	−1.14276	−	0.248592i
$894$	−5.68675	−	6.56286i	−0.190193	−	0.219495i
$895$	5.70360	+	2.80728i	0.190650	+	0.0938371i
$896$		−	3.81540i		−	0.127464i
$897$	−17.2261	+	4.50500i	−0.575162	+	0.150418i
$898$	−17.9216	+	17.9216i	−0.598051	+	0.598051i
$899$	−1.69074	−	5.75814i	−0.0563894	−	0.192045i
$900$	−3.48774	+	3.58269i	−0.116258	+	0.119423i
$901$	11.7882	−	7.57584i	0.392723	−	0.252388i
$902$	−2.25588	−	1.68873i	−0.0751125	−	0.0562285i
$903$	−5.29888	+	1.15270i	−0.176336	+	0.0383595i
$904$	−0.973117	+	2.13083i	−0.0323654	+	0.0708703i
$905$	17.4022	−	1.98922i	0.578468	−	0.0661239i
$906$	2.99418	−	20.8249i	0.0994748	−	0.691863i
$907$	−3.46619	−	1.29282i	−0.115093	−	0.0429275i	0.291258	−	0.956645i	$-0.405926\pi$
$907$	−3.46619	−	1.29282i	−0.115093	−	0.0429275i	−0.406351	+	0.913717i	$0.633199\pi$
$908$	5.17214	+	9.47206i	0.171643	+	0.314341i
$909$	2.82922	−	9.63544i	0.0938393	−	0.319587i
$910$	−28.2285	+	14.3680i	−0.935766	+	0.476296i
$911$	18.6794	+	2.68569i	0.618875	+	0.0889808i	0.444619	−	0.895720i	$-0.353339\pi$
$911$	18.6794	+	2.68569i	0.618875	+	0.0889808i	0.174256	+	0.984700i	$0.444248\pi$
$912$	0.513350	+	7.17757i	0.0169987	+	0.237673i
$913$	4.44926	+	11.9289i	0.147249	+	0.394790i
$914$	−0.00354603	−	0.00227890i	−0.000117292	−	7.53792e-5i
$915$	−0.466160	−	2.48802i	−0.0154108	−	0.0822515i
$916$	−10.9829	−	17.0897i	−0.362885	−	0.564660i
$917$	−53.2400	−	3.80780i	−1.75814	−	0.125745i
$918$	−4.02662	−	2.19870i	−0.132898	−	0.0725679i
$919$	−32.4521			−1.07050			−0.535248	−	0.844695i	$-0.679782\pi$
$919$	−32.4521			−1.07050			−0.535248	+	0.844695i	$0.679782\pi$
$920$	1.65987	+	10.5946i	0.0547244	+	0.349292i
$921$	−28.5138			−0.939563
$922$	7.78337	+	4.25004i	0.256332	+	0.139968i
$923$	−17.6723	−	1.26395i	−0.581690	−	0.0416033i
$924$	2.12361	+	3.30440i	0.0698616	+	0.108707i
$925$	−12.1109	+	19.4133i	−0.398203	+	0.638304i
$926$	12.2786	+	7.89097i	0.403499	+	0.259313i
$927$	1.66439	+	4.46239i	0.0546656	+	0.146564i
$928$	−0.0391158	−	0.546910i	−0.00128404	−	0.0179532i
$929$	24.8890	+	3.57849i	0.816581	+	0.117407i	0.537934	−	0.842987i	$-0.319205\pi$
$929$	24.8890	+	3.57849i	0.816581	+	0.117407i	0.278647	+	0.960394i	$0.410114\pi$
$930$	−23.2728	−	7.57272i	−0.763144	−	0.248319i
$931$	15.3210	−	52.1787i	0.502127	−	1.71009i
$932$	10.2791	+	18.8248i	0.336704	+	0.616626i
$933$	24.8186	+	9.25684i	0.812523	+	0.303055i
$934$	−4.40774	+	30.6565i	−0.144226	+	1.00311i
$935$	6.57149	−	8.26774i	0.214911	−	0.270384i
$936$	1.54230	−	3.37718i	0.0504118	−	0.110386i
$937$	29.4632	−	6.40933i	0.962522	−	0.209384i	0.296265	−	0.955106i	$-0.404259\pi$
$937$	29.4632	−	6.40933i	0.962522	−	0.209384i	0.666257	+	0.745722i	$0.267895\pi$
$938$	23.1497	+	17.3297i	0.755865	+	0.565834i
$939$	0.503280	−	0.323438i	0.0164239	−	0.0105550i
$940$	7.89833	−	7.45324i	0.257615	−	0.243098i
$941$	9.37971	+	31.9443i	0.305770	+	1.04136i	0.958814	+	0.284036i	$0.0916735\pi$
$941$	9.37971	+	31.9443i	0.305770	+	1.04136i	−0.653044	+	0.757320i	$0.726508\pi$
$942$	1.54453	−	1.54453i	0.0503236	−	0.0503236i
$943$	−9.66023	−	8.88828i	−0.314580	−	0.289442i
$944$			1.15337i			0.0375389i
$945$	−3.76753	+	7.65455i	−0.122558	+	0.249003i
$946$	0.958206	+	1.10583i	0.0311540	+	0.0359536i
$947$	1.56098	+	0.339570i	0.0507250	+	0.0110346i	0.237856	−	0.971300i	$-0.423555\pi$
$947$	1.56098	+	0.339570i	0.0507250	+	0.0110346i	−0.187131	+	0.982335i	$0.559919\pi$
$948$	−0.724008	+	0.967162i	−0.0235147	+	0.0314120i
$949$	−21.7620	+	33.8624i	−0.706425	+	1.09922i
$950$	−15.3846	−	32.5245i	−0.499142	−	1.05523i
$951$	20.4595	−	23.6115i	0.663445	−	0.765656i
$952$	−14.0129	+	10.4899i	−0.454161	+	0.339981i
$953$	8.13731	−	21.8170i	0.263593	−	0.706721i	−0.735965	−	0.677019i	$-0.763271\pi$
$953$	8.13731	−	21.8170i	0.263593	−	0.706721i	0.999559	−	0.0297021i	$-0.00945587\pi$
$954$	2.93062	+	0.860507i	0.0948823	+	0.0278599i
$955$	20.8762	+	34.6527i	0.675539	+	1.12133i
$956$	4.61848	+	10.1131i	0.149372	+	0.327080i
$957$	0.338281	+	0.451891i	0.0109351	+	0.0146076i
$958$	9.31371	−	0.666130i	0.300912	−	0.0215217i
$959$	−42.7582	−	19.5270i	−1.38073	−	0.630560i
$960$	−1.93067	−	1.12806i	−0.0623121	−	0.0364080i
$961$	−12.6366	−	87.8897i	−0.407633	−	2.83515i
$962$	3.61151	−	16.6018i	0.116440	−	0.535264i
$963$	−0.0326501	+	0.456508i	−0.00105214	+	0.0147108i
$964$	−8.05437	+	2.36498i	−0.259414	+	0.0761707i
$965$	−2.18457	−	51.4741i	−0.0703239	−	1.65701i
$966$	8.28681	+	16.3140i	0.266624	+	0.524894i
$967$	−10.1273	−	10.1273i	−0.325671	−	0.325671i	0.525267	−	0.850938i	$-0.323966\pi$
$967$	−10.1273	−	10.1273i	−0.325671	−	0.325671i	−0.850938	+	0.525267i	$0.823966\pi$
$968$	−4.76380	+	8.72425i	−0.153114	+	0.280408i
$969$	24.9499	−	21.6192i	0.801505	−	0.694508i
$970$	−6.56727	+	37.8528i	−0.210862	+	1.21538i
$971$	−7.73364	+	1.11193i	−0.248184	+	0.0356835i	−0.265284	−	0.964170i	$-0.585466\pi$
$971$	−7.73364	+	1.11193i	−0.248184	+	0.0356835i	0.0170999	+	0.999854i	$0.494557\pi$
$972$	−0.212565	−	0.977147i	−0.00681803	−	0.0313420i
$973$	−61.4900	+	22.9346i	−1.97128	+	0.735249i
$974$	14.7681	+	12.7966i	0.473200	+	0.410030i
$975$	−1.07552	+	18.5322i	−0.0344442	+	0.593506i
$976$	1.02974	−	0.470266i	0.0329611	−	0.0150528i
$977$	52.5983	−	28.7209i	1.68277	−	0.918862i	0.704993	−	0.709215i	$-0.250950\pi$
$977$	52.5983	−	28.7209i	1.68277	−	0.918862i	0.977777	−	0.209647i	$-0.0672316\pi$
$978$	−21.6221	+	11.8066i	−0.691400	+	0.377533i
$979$	4.55636	−	2.08082i	0.145622	−	0.0665033i
$980$	10.6915	+	13.0865i	0.341526	+	0.418032i
$981$	6.52633	+	5.65509i	0.208370	+	0.180553i
$982$	26.6079	−	9.92423i	0.849092	−	0.316695i
$983$	9.07269	+	41.7065i	0.289374	+	1.33023i	0.860534	+	0.509392i	$0.170130\pi$
$983$	9.07269	+	41.7065i	0.289374	+	1.33023i	−0.571160	+	0.820839i	$0.693507\pi$
$984$	2.70934	−	0.389544i	0.0863705	−	0.0124182i
$985$	35.9336	−	25.3084i	1.14494	−	0.806394i
$986$	−1.90111	+	1.64732i	−0.0605436	+	0.0524613i
$987$	8.88049	−	16.2634i	0.282669	−	0.517670i
$988$	18.8911	+	18.8911i	0.601007	+	0.601007i
$989$	3.92042	+	5.57603i	0.124662	+	0.177308i
$990$	2.29996	−	0.0976107i	0.0730975	−	0.00310227i
$991$	−23.2773	+	6.83484i	−0.739428	+	0.217116i	−0.629692	−	0.776845i	$-0.716819\pi$
$991$	−23.2773	+	6.83484i	−0.739428	+	0.217116i	−0.109736	+	0.993961i	$0.535001\pi$
$992$	0.780809	−	10.9171i	0.0247907	−	0.346619i
$993$	4.81443	−	22.1316i	0.152781	−	0.702324i
$994$	2.59121	+	18.0223i	0.0821883	+	0.571632i
$995$	−18.7372	+	4.91662i	−0.594008	+	0.155867i
$996$	−11.2493	−	5.13737i	−0.356447	−	0.162784i
$997$	−38.2169	+	2.73333i	−1.21034	+	0.0865654i	−0.661880	−	0.749610i	$-0.730241\pi$
$997$	−38.2169	+	2.73333i	−1.21034	+	0.0865654i	−0.548462	+	0.836175i	$0.684787\pi$
$998$	−1.68925	−	2.25658i	−0.0534724	−	0.0714307i
$999$	−1.90104	−	4.16269i	−0.0601461	−	0.131702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.8	✓	240
5.3	odd	4	inner	690.2.w.b.313.9	yes	240
23.5	odd	22	inner	690.2.w.b.97.9	yes	240
115.28	even	44	inner	690.2.w.b.373.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.8	✓	240	1.1	even	1	trivial
690.2.w.b.97.9	yes	240	23.5	odd	22	inner
690.2.w.b.313.9	yes	240	5.3	odd	4	inner
690.2.w.b.373.8	yes	240	115.28	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.84527 - 1.26292i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33335 + 3.57484i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.84527 - 1.26292i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(1.33335 + 3.57484i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.01431 - 1.99278i) q^{10} +(-0.290043 + 0.987796i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(-3.47860 - 1.29745i) q^{13} +(-0.542988 + 3.77657i) q^{14} +(1.75048 + 1.39134i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(4.48296 - 0.975208i) q^{17} +(0.800541 + 0.599278i) q^{18} +(-6.05358 + 3.89040i) q^{19} +(0.0648035 - 2.23513i) q^{20} +(-1.07492 - 3.66085i) q^{21} +(-0.727965 + 0.727965i) q^{22} +(-3.71643 + 3.03119i) q^{23} -1.00000i q^{24} +(1.81008 + 4.66086i) q^{25} +(-2.43129 - 2.80586i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(-2.28648 + 3.05439i) q^{28} +(-0.296437 + 0.461265i) q^{29} +(0.869559 + 2.06006i) q^{30} +(-7.16746 + 8.27169i) q^{31} +(-0.800541 + 0.599278i) q^{32} +(0.359773 - 0.964588i) q^{33} +(4.40197 + 1.29253i) q^{34} +(2.05434 - 8.28047i) q^{35} +(0.415415 + 0.909632i) q^{36} +(2.74243 + 3.66346i) q^{37} +(-7.17757 + 0.513350i) q^{38} +(3.37718 + 1.54230i) q^{39} +(1.12806 - 1.93067i) q^{40} +(0.389544 + 2.70934i) q^{41} +(0.811022 - 3.72821i) q^{42} +(0.101394 - 1.41767i) q^{43} +(-0.987796 + 0.290043i) q^{44} +(-1.64676 - 1.51267i) q^{45} +(-4.71453 + 0.879319i) q^{46} +(3.43416 + 3.43416i) q^{47} +(0.479249 - 0.877679i) q^{48} +(-5.71142 + 4.94897i) q^{49} +(-0.645047 + 4.95822i) q^{50} +(-4.54111 + 0.652912i) q^{51} +(-0.789188 - 3.62784i) q^{52} +(2.86176 - 1.06738i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(1.78272 - 1.45645i) q^{55} +(-3.47061 + 1.58498i) q^{56} +(6.31569 - 3.44863i) q^{57} +(-0.481238 + 0.262776i) q^{58} +(1.04914 - 0.479127i) q^{59} +(-0.224091 + 2.22481i) q^{60} +(-0.855538 - 0.741328i) q^{61} +(-10.2549 + 3.82489i) q^{62} +(0.811022 + 3.72821i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(4.78039 + 6.78733i) q^{65} +(0.778043 - 0.674178i) q^{66} +(3.63231 - 6.65208i) q^{67} +(3.24407 + 3.24407i) q^{68} +(3.92321 - 2.75834i) q^{69} +(5.77146 - 6.28305i) q^{70} +(4.57883 - 1.34447i) q^{71} +(-0.0713392 + 0.997452i) q^{72} +(2.30460 - 10.5941i) q^{73} +(0.651266 + 4.52965i) q^{74} +(-1.47296 - 4.77811i) q^{75} +(-6.54563 - 2.98929i) q^{76} +(-3.91794 + 0.280217i) q^{77} +(2.22493 + 2.97216i) q^{78} +(-0.501877 - 1.09896i) q^{79} +(1.91535 - 1.15389i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-0.956552 + 2.56462i) q^{82} +(9.90017 - 7.41118i) q^{83} +(2.49856 - 2.88349i) q^{84} +(-9.50389 - 3.86208i) q^{85} +(0.768410 - 1.19567i) q^{86} +(0.328588 - 0.438943i) q^{87} +(-1.00597 - 0.218836i) q^{88} +(-3.18622 - 3.67709i) q^{89} +(-0.720380 - 2.11685i) q^{90} -14.1654i q^{91} +(-4.55926 - 1.48767i) q^{92} +(7.73930 - 7.73930i) q^{93} +(1.36827 + 4.65991i) q^{94} +(16.0838 + 0.466320i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-13.7543 - 10.2963i) q^{97} +(-7.38458 + 1.60642i) q^{98} +(-0.427669 + 0.936465i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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