LMFDB - Embedded newform 213.2.n.a.11.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(11,213)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("213.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([35, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.n (of order $70$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$528$
Relative dimension:	$22$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	213.11
Dual form			213.2.n.a.155.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.745900 + 0.401386i) q^{2} +(1.08290 - 1.35178i) q^{3} +(-0.706538 - 1.07036i) q^{4} +(-1.55927 + 0.506636i) q^{5} +(1.35032 - 0.573633i) q^{6} +(-0.558996 - 3.08032i) q^{7} +(-0.249236 - 2.76924i) q^{8} +(-0.654638 - 2.92770i) q^{9} +(-1.36641 - 0.247967i) q^{10} +(3.09104 + 2.70056i) q^{11} +(-2.21201 - 0.204010i) q^{12} +(3.02732 + 3.46504i) q^{13} +(0.819443 - 2.52199i) q^{14} +(-1.00367 + 2.65643i) q^{15} +(-0.0825005 + 0.193019i) q^{16} +(2.98406 + 2.16805i) q^{17} +(0.686844 - 2.44654i) q^{18} +(-3.32940 - 0.918855i) q^{19} +(1.64396 + 1.31102i) q^{20} +(-4.76927 - 2.58005i) q^{21} +(1.22164 + 3.25504i) q^{22} +(2.13292 + 1.02716i) q^{23} +(-4.01331 - 2.66190i) q^{24} +(-1.87045 + 1.35896i) q^{25} +(0.867256 + 3.79970i) q^{26} +(-4.66653 - 2.28549i) q^{27} +(-2.90210 + 2.77469i) q^{28} +(-0.0550900 + 0.146787i) q^{29} +(-1.81489 + 1.57857i) q^{30} +(9.98956 - 4.26974i) q^{31} +(-4.48667 + 3.57800i) q^{32} +(6.99786 - 1.25397i) q^{33} +(1.35559 + 2.81491i) q^{34} +(2.43223 + 4.51984i) q^{35} +(-2.67117 + 2.76923i) q^{36} +(0.960054 - 0.462338i) q^{37} +(-2.11458 - 2.02175i) q^{38} +(7.96229 - 0.339969i) q^{39} +(1.79162 + 4.19170i) q^{40} +(-1.80102 + 7.89078i) q^{41} +(-2.52180 - 3.83878i) q^{42} +(-1.76537 - 1.84643i) q^{43} +(0.706632 - 5.21657i) q^{44} +(2.50404 + 4.23341i) q^{45} +(1.17866 + 1.62228i) q^{46} +(-0.422326 - 9.40382i) q^{47} +(0.171580 + 0.320544i) q^{48} +(-2.62228 + 0.984157i) q^{49} +(-1.94064 + 0.262878i) q^{50} +(6.16219 - 1.68602i) q^{51} +(1.56993 - 5.68850i) q^{52} +(-5.61107 + 8.50041i) q^{53} +(-2.56340 - 3.57783i) q^{54} +(-6.18795 - 2.64486i) q^{55} +(-8.39082 + 2.31572i) q^{56} +(-4.84751 + 3.50559i) q^{57} +(-0.100010 + 0.0873758i) q^{58} +(-4.19746 + 2.50787i) q^{59} +(3.55247 - 0.802578i) q^{60} +(1.58548 - 8.73672i) q^{61} +(9.16503 + 0.824867i) q^{62} +(-8.65234 + 3.65307i) q^{63} +(-4.36968 + 0.792981i) q^{64} +(-6.47591 - 3.86918i) q^{65} +(5.72303 + 1.87351i) q^{66} +(-9.53314 + 6.29277i) q^{67} +(0.212237 - 4.72583i) q^{68} +(3.69825 - 1.77093i) q^{69} +4.34761i q^{70} +(5.50721 + 6.37736i) q^{71} +(-7.94434 + 2.54254i) q^{72} +(0.709630 - 1.31871i) q^{73} +(0.901680 + 0.0404945i) q^{74} +(-0.188496 + 4.00008i) q^{75} +(1.36884 + 4.21286i) q^{76} +(6.59071 - 11.0310i) q^{77} +(6.07553 + 2.94237i) q^{78} +(10.7654 - 0.968908i) q^{79} +(0.0308495 - 0.342766i) q^{80} +(-8.14290 + 3.83317i) q^{81} +(-4.51062 + 5.16283i) q^{82} +(1.95455 + 3.27136i) q^{83} +(0.608088 + 6.92774i) q^{84} +(-5.75136 - 1.86873i) q^{85} +(-0.575657 - 2.08585i) q^{86} +(0.138767 + 0.233426i) q^{87} +(6.70808 - 9.23288i) q^{88} +(6.02297 + 3.97573i) q^{89} +(0.168531 + 4.16278i) q^{90} +(8.98120 - 11.2621i) q^{91} +(-0.407559 - 3.00872i) q^{92} +(5.04597 - 18.1274i) q^{93} +(3.45955 - 7.18382i) q^{94} +(5.65694 - 0.254053i) q^{95} +(-0.0219504 + 9.93963i) q^{96} +(-9.04888 + 2.06535i) q^{97} +(-2.35098 - 0.318462i) q^{98} +(5.88292 - 10.8175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) $ 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{31}{70}\right)$	$-1$

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 $

$2$	0.745900	+	0.401386i	0.527431	+	0.283823i	0.715836	−	0.698269i	$-0.246046\pi$
$2$	0.745900	+	0.401386i	0.527431	+	0.283823i	−0.188405	+	0.982091i	$0.560332\pi$
$3$	1.08290	−	1.35178i	0.625215	−	0.780453i
$3$	1.08290	−	1.35178i	0.625215	−	0.780453i
$4$	−0.706538	−	1.07036i	−0.353269	−	0.535180i
$5$	−1.55927	+	0.506636i	−0.697325	+	0.226575i	−0.636165	−	0.771553i	$-0.719480\pi$
$5$	−1.55927	+	0.506636i	−0.697325	+	0.226575i	−0.0611603	+	0.998128i	$0.519480\pi$
$6$	1.35032	−	0.573633i	0.551268	−	0.234185i
$7$	−0.558996	−	3.08032i	−0.211281	−	1.16425i	−0.898891	−	0.438173i	$-0.855626\pi$
$7$	−0.558996	−	3.08032i	−0.211281	−	1.16425i	0.687610	−	0.726080i	$-0.258660\pi$
$8$	−0.249236	−	2.76924i	−0.0881181	−	0.979073i
$9$	−0.654638	−	2.92770i	−0.218213	−	0.975901i
$10$	−1.36641	−	0.247967i	−0.432098	−	0.0784142i
$11$	3.09104	+	2.70056i	0.931982	+	0.814249i	0.982841	−	0.184457i	$-0.0590528\pi$
$11$	3.09104	+	2.70056i	0.931982	+	0.814249i	−0.0508581	+	0.998706i	$0.516196\pi$
$12$	−2.21201	−	0.204010i	−0.638551	−	0.0588925i
$13$	3.02732	+	3.46504i	0.839627	+	0.961031i	0.999660	−	0.0260812i	$-0.00830285\pi$
$13$	3.02732	+	3.46504i	0.839627	+	0.961031i	−0.160033	+	0.987112i	$0.551160\pi$
$14$	0.819443	−	2.52199i	0.219005	−	0.674029i
$15$	−1.00367	+	2.65643i	−0.259147	+	0.685887i
$16$	−0.0825005	+	0.193019i	−0.0206251	+	0.0482549i
$17$	2.98406	+	2.16805i	0.723742	+	0.525829i	0.887578	−	0.460658i	$-0.152387\pi$
$17$	2.98406	+	2.16805i	0.723742	+	0.525829i	−0.163836	+	0.986488i	$0.552387\pi$
$18$	0.686844	−	2.44654i	0.161891	−	0.576654i
$19$	−3.32940	−	0.918855i	−0.763816	−	0.210800i	−0.137641	−	0.990482i	$-0.543952\pi$
$19$	−3.32940	−	0.918855i	−0.763816	−	0.210800i	−0.626175	+	0.779683i	$0.715380\pi$
$20$	1.64396	+	1.31102i	0.367601	+	0.293152i
$21$	−4.76927	−	2.58005i	−1.04074	−	0.563014i
$22$	1.22164	+	3.25504i	0.260454	+	0.693977i
$23$	2.13292	+	1.02716i	0.444745	+	0.214178i	0.642833	−	0.766006i	$-0.277759\pi$
$23$	2.13292	+	1.02716i	0.444745	+	0.214178i	−0.198088	+	0.980184i	$0.563473\pi$
$24$	−4.01331	−	2.66190i	−0.819213	−	0.543359i
$25$	−1.87045	+	1.35896i	−0.374091	+	0.271793i
$26$	0.867256	+	3.79970i	0.170083	+	0.745182i
$27$	−4.66653	−	2.28549i	−0.898075	−	0.439843i
$28$	−2.90210	+	2.77469i	−0.548446	+	0.524368i
$29$	−0.0550900	+	0.146787i	−0.0102299	+	0.0272576i	−0.941251	−	0.337709i	$-0.890348\pi$
$29$	−0.0550900	+	0.146787i	−0.0102299	+	0.0272576i	0.931021	+	0.364966i	$0.118920\pi$
$30$	−1.81489	+	1.57857i	−0.331352	+	0.288206i
$31$	9.98956	−	4.26974i	1.79418	−	0.766869i	0.810794	−	0.585331i	$-0.199036\pi$
$31$	9.98956	−	4.26974i	1.79418	−	0.766869i	0.983384	−	0.181537i	$-0.0581074\pi$
$32$	−4.48667	+	3.57800i	−0.793138	+	0.632506i
$33$	6.99786	−	1.25397i	1.21817	−	0.218288i
$34$	1.35559	+	2.81491i	0.232482	+	0.482753i
$35$	2.43223	+	4.51984i	0.411122	+	0.763992i
$36$	−2.67117	+	2.76923i	−0.445195	+	0.461539i
$37$	0.960054	−	0.462338i	0.157832	−	0.0760079i	−0.353300	−	0.935510i	$-0.614941\pi$
$37$	0.960054	−	0.462338i	0.157832	−	0.0760079i	0.511132	+	0.859502i	$0.329226\pi$
$38$	−2.11458	−	2.02175i	−0.343030	−	0.327970i
$39$	7.96229	−	0.339969i	1.27499	−	0.0544386i
$40$	1.79162	+	4.19170i	0.283280	+	0.662766i
$41$	−1.80102	+	7.89078i	−0.281272	+	1.23233i	0.614893	+	0.788611i	$0.289199\pi$
$41$	−1.80102	+	7.89078i	−0.281272	+	1.23233i	−0.896165	+	0.443722i	$0.853658\pi$
$42$	−2.52180	−	3.83878i	−0.389122	−	0.592336i
$43$	−1.76537	−	1.84643i	−0.269216	−	0.281578i	0.574342	−	0.818615i	$-0.305258\pi$
$43$	−1.76537	−	1.84643i	−0.269216	−	0.281578i	−0.843559	+	0.537037i	$0.819544\pi$
$44$	0.706632	−	5.21657i	0.106529	−	0.786427i
$45$	2.50404	+	4.23341i	0.373280	+	0.631079i
$46$	1.17866	+	1.62228i	0.173784	+	0.239193i
$47$	−0.422326	−	9.40382i	−0.0616026	−	1.37169i	−0.757166	−	0.653223i	$-0.773417\pi$
$47$	−0.422326	−	9.40382i	−0.0616026	−	1.37169i	0.695563	−	0.718465i	$-0.255155\pi$
$48$	0.171580	+	0.320544i	0.0247655	+	0.0462666i
$49$	−2.62228	+	0.984157i	−0.374611	+	0.140594i
$50$	−1.94064	+	0.262878i	−0.274448	+	0.0371765i
$51$	6.16219	−	1.68602i	0.862879	−	0.236090i
$52$	1.56993	−	5.68850i	0.217710	−	0.788854i
$53$	−5.61107	+	8.50041i	−0.770740	+	1.16762i	0.211018	+	0.977482i	$0.432322\pi$
$53$	−5.61107	+	8.50041i	−0.770740	+	1.16762i	−0.981757	+	0.190138i	$0.939106\pi$
$54$	−2.56340	−	3.57783i	−0.348835	−	0.486881i
$55$	−6.18795	−	2.64486i	−0.834383	−	0.356632i
$56$	−8.39082	+	2.31572i	−1.12127	+	0.309451i
$57$	−4.84751	+	3.50559i	−0.642068	+	0.464327i
$58$	−0.100010	+	0.0873758i	−0.0131319	+	0.0114730i
$59$	−4.19746	+	2.50787i	−0.546463	+	0.326496i	−0.759457	−	0.650557i	$-0.774536\pi$
$59$	−4.19746	+	2.50787i	−0.546463	+	0.326496i	0.212994	+	0.977053i	$0.431678\pi$
$60$	3.55247	−	0.802578i	0.458621	−	0.103612i
$61$	1.58548	−	8.73672i	0.203000	−	1.11862i	−0.707999	−	0.706214i	$-0.750402\pi$
$61$	1.58548	−	8.73672i	0.203000	−	1.11862i	0.910999	−	0.412409i	$-0.135312\pi$
$62$	9.16503	+	0.824867i	1.16396	+	0.104758i
$63$	−8.65234	+	3.65307i	−1.09009	+	0.460244i
$64$	−4.36968	+	0.792981i	−0.546210	+	0.0991226i
$65$	−6.47591	−	3.86918i	−0.803238	−	0.479912i
$66$	5.72303	+	1.87351i	0.704456	+	0.230613i
$67$	−9.53314	+	6.29277i	−1.16466	+	0.768785i	−0.976956	−	0.213441i	$-0.931533\pi$
$67$	−9.53314	+	6.29277i	−1.16466	+	0.768785i	−0.187703	+	0.982226i	$0.560104\pi$
$68$	0.212237	−	4.72583i	0.0257376	−	0.573091i
$69$	3.69825	−	1.77093i	0.445217	−	0.213195i
$70$			4.34761i			0.519638i
$71$	5.50721	+	6.37736i	0.653585	+	0.756853i
$71$	5.50721	+	6.37736i	0.653585	+	0.756853i
$72$	−7.94434	+	2.54254i	−0.936250	+	0.299641i
$73$	0.709630	−	1.31871i	0.0830559	−	0.154344i	−0.835680	−	0.549217i	$-0.814926\pi$
$73$	0.709630	−	1.31871i	0.0830559	−	0.154344i	0.918735	+	0.394874i	$0.129212\pi$
$74$	0.901680	+	0.0404945i	0.104818	+	0.00470739i
$75$	−0.188496	+	4.00008i	−0.0217657	+	0.461889i
$76$	1.36884	+	4.21286i	0.157017	+	0.483248i
$77$	6.59071	−	11.0310i	0.751081	−	1.25710i
$78$	6.07553	+	2.94237i	0.687918	+	0.333157i
$79$	10.7654	−	0.968908i	1.21121	−	0.109011i	0.534439	−	0.845207i	$-0.320523\pi$
$79$	10.7654	−	0.968908i	1.21121	−	0.109011i	0.676768	+	0.736196i	$0.263380\pi$
$80$	0.0308495	−	0.342766i	0.00344908	−	0.0383224i
$81$	−8.14290	+	3.83317i	−0.904766	+	0.425908i
$82$	−4.51062	+	5.16283i	−0.498115	+	0.570139i
$83$	1.95455	+	3.27136i	0.214539	+	0.359079i	0.946734	−	0.322017i	$-0.104361\pi$
$83$	1.95455	+	3.27136i	0.214539	+	0.359079i	−0.732194	+	0.681096i	$0.761504\pi$
$84$	0.608088	+	6.92774i	0.0663478	+	0.755878i
$85$	−5.75136	−	1.86873i	−0.623823	−	0.202692i
$86$	−0.575657	−	2.08585i	−0.0620747	−	0.224923i
$87$	0.138767	+	0.233426i	0.0148774	+	0.0250258i
$88$	6.70808	−	9.23288i	0.715084	−	0.984228i
$89$	6.02297	+	3.97573i	0.638434	+	0.421427i	0.828223	−	0.560398i	$-0.189352\pi$
$89$	6.02297	+	3.97573i	0.638434	+	0.421427i	−0.189789	+	0.981825i	$0.560780\pi$
$90$	0.168531	+	4.16278i	0.0177647	+	0.438796i
$91$	8.98120	−	11.2621i	0.941486	−	1.18059i
$92$	−0.407559	−	3.00872i	−0.0424909	−	0.313681i
$93$	5.04597	−	18.1274i	0.523242	−	1.87973i
$94$	3.45955	−	7.18382i	0.356825	−	0.740954i
$95$	5.65694	−	0.254053i	0.580390	−	0.0260653i
$96$	−0.0219504	+	9.93963i	−0.00224031	+	1.01446i
$97$	−9.04888	+	2.06535i	−0.918774	+	0.209704i	−0.655656	−	0.755059i	$-0.727608\pi$
$97$	−9.04888	+	2.06535i	−0.918774	+	0.209704i	−0.263118	+	0.964764i	$0.584751\pi$
$98$	−2.35098	−	0.318462i	−0.237485	−	0.0321695i
$99$	5.88292	−	10.8175i	0.591256	−	1.08720i
$100$	2.77613	+	1.04190i	0.277613	+	0.104190i
$101$	−18.0998	−	4.13116i	−1.80100	−	0.411066i	−0.815223	−	0.579148i	$-0.803386\pi$
$101$	−18.0998	−	4.13116i	−1.80100	−	0.411066i	−0.985773	+	0.168082i	$0.946243\pi$
$102$	5.27312	+	1.21581i	0.522117	+	0.120383i
$103$	3.22823	+	4.04807i	0.318087	+	0.398868i	0.915011	−	0.403430i	$-0.132182\pi$
$103$	3.22823	+	4.04807i	0.318087	+	0.398868i	−0.596924	+	0.802298i	$0.703611\pi$
$104$	8.84101	−	9.24697i	0.866932	−	0.906740i
$105$	8.74371	+	1.60670i	0.853299	+	0.156798i
$106$	−7.59724	+	4.08825i	−0.737909	+	0.397086i
$107$	0.328431	−	0.176736i	0.0317506	−	0.0170857i	−0.457916	−	0.888995i	$-0.651404\pi$
$107$	0.328431	−	0.176736i	0.0317506	−	0.0170857i	0.489667	+	0.871910i	$0.337118\pi$
$108$	0.850785	+	6.60965i	0.0818668	+	0.636014i
$109$	0.0429090	−	0.0448793i	0.00410994	−	0.00429866i	−0.720737	−	0.693209i	$-0.756196\pi$
$109$	0.0429090	−	0.0448793i	0.00410994	−	0.00429866i	0.724847	+	0.688910i	$0.241911\pi$
$110$	−3.55398	−	4.45655i	−0.338859	−	0.424915i
$111$	0.414666	−	1.79845i	0.0393583	−	0.170702i
$112$	0.640680	+	0.146231i	0.0605386	+	0.0138175i
$113$	3.20481	+	1.20279i	0.301484	+	0.113149i	0.497532	−	0.867445i	$-0.334240\pi$
$113$	3.20481	+	1.20279i	0.301484	+	0.113149i	−0.196049	+	0.980594i	$0.562811\pi$
$114$	−5.02285	+	0.669099i	−0.470433	+	0.0626668i
$115$	−3.84619	−	0.521002i	−0.358659	−	0.0485837i
$116$	0.196038	−	0.0447443i	0.0182016	−	0.00415440i
$117$	8.16283	−	11.1314i	0.754653	−	1.02910i
$118$	−4.13751	+	0.185816i	−0.380888	+	0.0171057i
$119$	5.01022	−	10.4038i	0.459286	−	0.953717i
$120$	7.60643	+	2.11733i	0.694369	+	0.193285i
$121$	0.784930	+	5.79459i	0.0713573	+	0.526781i
$122$	4.68941	−	5.88033i	0.424559	−	0.532380i
$123$	8.71629	+	10.9795i	0.785922	+	0.989992i
$124$	−11.6282	−	7.67569i	−1.04424	−	0.689297i
$125$	7.04643	−	9.69858i	0.630252	−	0.867468i
$126$	−7.92007	−	0.748097i	−0.705576	−	0.0666458i
$127$	2.62589	+	9.51471i	0.233010	+	0.844294i	0.983117	+	0.182977i	$0.0585735\pi$
$127$	2.62589	+	9.51471i	0.233010	+	0.844294i	−0.750107	+	0.661317i	$0.769998\pi$
$128$	7.33794	+	2.38424i	0.648589	+	0.210739i
$129$	−4.40770	+	0.386890i	−0.388076	+	0.0340637i
$130$	−3.27735	−	5.48536i	−0.287442	−	0.481098i
$131$	−8.03679	+	9.19885i	−0.702178	+	0.803707i	−0.987980	−	0.154582i	$-0.950597\pi$
$131$	−8.03679	+	9.19885i	−0.702178	+	0.803707i	0.285802	+	0.958289i	$0.407740\pi$
$132$	−6.28645	−	6.60425i	−0.547166	−	0.574826i
$133$	−0.969250	+	10.7693i	−0.0840447	+	0.933813i
$134$	−9.63660	+	0.867310i	−0.832475	+	0.0749241i
$135$	8.43428	+	1.19946i	0.725907	+	0.103233i
$136$	5.26011	−	8.80393i	0.451050	−	0.754931i
$137$	−3.33819	−	10.2739i	−0.285200	−	0.877757i	−0.986339	−	0.164731i	$-0.947324\pi$
$137$	−3.33819	−	10.2739i	−0.285200	−	0.877757i	0.701138	−	0.713026i	$-0.252676\pi$
$138$	3.46935	+	0.163486i	0.295331	+	0.0139169i
$139$	−12.5052	−	0.561611i	−1.06068	−	0.0476352i	−0.492320	−	0.870414i	$-0.663851\pi$
$139$	−12.5052	−	0.561611i	−1.06068	−	0.0476352i	−0.568361	+	0.822779i	$0.692422\pi$
$140$	3.11939	−	5.79680i	0.263636	−	0.489919i
$141$	−13.1693	−	9.61254i	−1.10905	−	0.809522i
$142$	1.54805	+	6.96738i	0.129909	+	0.584690i
$143$			18.8860i			1.57933i
$144$	0.619112	+	0.115179i	0.0515926	+	0.00959825i
$145$	0.0115325	−	0.256790i	0.000957718	−	0.0213252i
$146$	1.05863	−	0.698792i	0.0876125	−	0.0578325i
$147$	−1.50931	+	4.61050i	−0.124485	+	0.380268i
$148$	−1.17318	−	0.700944i	−0.0964350	−	0.0576172i
$149$	−4.97626	+	0.903057i	−0.407671	+	0.0739813i	−0.378519	−	0.925594i	$-0.623566\pi$
$149$	−4.97626	+	0.903057i	−0.407671	+	0.0739813i	−0.0291521	+	0.999575i	$0.509281\pi$
$150$	−1.74617	+	2.90800i	−0.142574	+	0.237437i
$151$	0.526609	+	0.0473956i	0.0428548	+	0.00385700i	0.111046	−	0.993815i	$-0.464580\pi$
$151$	0.526609	+	0.0473956i	0.0428548	+	0.00385700i	−0.0681912	+	0.997672i	$0.521723\pi$
$152$	−1.71472	+	9.44889i	−0.139082	+	0.766406i
$153$	4.39392	−	10.1557i	0.355228	−	0.821043i
$154$	9.34370	−	5.58260i	0.752936	−	0.449859i
$155$	−13.4132	+	11.7187i	−1.07737	+	0.941272i
$156$	−5.98955	−	8.28231i	−0.479548	−	0.663115i
$157$	17.3672	−	4.79306i	1.38606	−	0.382528i	0.508113	−	0.861290i	$-0.330343\pi$
$157$	17.3672	−	4.79306i	1.38606	−	0.382528i	0.877944	+	0.478763i	$0.158915\pi$
$158$	8.41885	+	3.59839i	0.669768	+	0.286272i
$159$	5.41446	+	16.7901i	0.429395	+	1.33154i
$160$	5.18316	−	7.85216i	0.409765	−	0.620767i
$161$	1.97169	−	7.14427i	0.155391	−	0.563047i
$162$	−7.61237	−	0.409280i	−0.598084	−	0.0321560i
$163$	5.82325	−	0.788813i	0.456112	−	0.0617846i	0.0974260	−	0.995243i	$-0.468939\pi$
$163$	5.82325	−	0.788813i	0.456112	−	0.0617846i	0.358686	+	0.933458i	$0.383225\pi$
$164$	9.71846	−	3.64740i	0.758884	−	0.284814i
$165$	−10.2762	+	5.50064i	−0.800003	+	0.428224i
$166$	0.144819	+	3.22464i	0.0112401	+	0.250280i
$167$	−14.1164	−	19.4295i	−1.09236	−	1.50350i	−0.845144	−	0.534538i	$-0.820485\pi$
$167$	−14.1164	−	19.4295i	−1.09236	−	1.50350i	−0.247212	−	0.968961i	$-0.579515\pi$
$168$	−5.95610	+	13.8503i	−0.459523	+	1.06857i
$169$	−1.09685	+	8.09724i	−0.0843728	+	0.622865i
$170$	−3.53986	−	3.70240i	−0.271495	−	0.283961i
$171$	−0.510585	+	10.3490i	−0.0390454	+	0.791408i
$172$	−0.729045	+	3.19415i	−0.0555891	+	0.243552i
$173$	−8.84887	−	20.7030i	−0.672767	−	1.57402i	−0.811935	−	0.583748i	$-0.801586\pi$
$173$	−8.84887	−	20.7030i	−0.672767	−	1.57402i	0.139168	−	0.990269i	$-0.455557\pi$
$174$	0.00981234	+	0.229811i	0.000743872	+	0.0174219i
$175$	5.23163	+	5.00195i	0.395474	+	0.378112i
$176$	−0.776272	+	0.373833i	−0.0585137	+	0.0281787i
$177$	−1.15535	+	8.38984i	−0.0868418	+	0.630619i
$178$	2.89673	+	5.38303i	0.217119	+	0.403475i
$179$	−0.602750	−	1.25162i	−0.0450516	−	0.0935507i	0.877228	−	0.480074i	$-0.159390\pi$
$179$	−0.602750	−	1.25162i	−0.0450516	−	0.0935507i	−0.922280	+	0.386523i	$0.873676\pi$
$180$	2.76207	−	5.67128i	0.205872	−	0.422712i
$181$	3.33437	−	2.65907i	0.247841	−	0.197647i	−0.491687	−	0.870772i	$-0.663620\pi$
$181$	3.33437	−	2.65907i	0.247841	−	0.197647i	0.739529	+	0.673125i	$0.235048\pi$
$182$	11.2195	−	4.79545i	0.831645	−	0.355462i
$183$	−10.0932	−	11.6043i	−0.746113	−	0.857811i
$184$	2.31285	−	6.16257i	0.170506	−	0.454310i
$185$	−1.26274	+	1.20731i	−0.0928387	+	0.0887629i
$186$	11.0399	−	11.4959i	0.809484	−	0.842919i
$187$	3.36891	+	14.7602i	0.246359	+	1.07937i
$188$	−9.76708	+	7.09620i	−0.712337	+	0.517543i
$189$	−4.43148	+	15.6520i	−0.322343	+	1.13852i
$190$	4.32148	+	2.08112i	0.313513	+	0.150980i
$191$	−1.80406	−	4.80689i	−0.130537	−	0.347814i	0.854673	−	0.519167i	$-0.173758\pi$
$191$	−1.80406	−	4.80689i	−0.130537	−	0.347814i	−0.985210	+	0.171353i	$0.945186\pi$
$192$	−3.66001	+	6.76559i	−0.264138	+	0.488264i
$193$	3.81894	+	3.04551i	0.274894	+	0.219220i	0.751226	−	0.660045i	$-0.229463\pi$
$193$	3.81894	+	3.04551i	0.274894	+	0.219220i	−0.476333	+	0.879265i	$0.658034\pi$
$194$	−7.57856	−	2.09155i	−0.544109	−	0.150164i
$195$	−12.2431	+	4.56409i	−0.876745	+	0.326841i
$196$	2.90614	+	2.11143i	0.207581	+	0.150817i
$197$	−9.30452	+	21.7690i	−0.662920	+	1.55098i	0.162653	+	0.986683i	$0.447995\pi$
$197$	−9.30452	+	21.7690i	−0.662920	+	1.55098i	−0.825573	+	0.564295i	$0.809148\pi$
$198$	8.73007	−	5.70747i	0.620419	−	0.405612i
$199$	−0.996839	+	3.06795i	−0.0706640	+	0.217482i	−0.980152	−	0.198250i	$-0.936474\pi$
$199$	−0.996839	+	3.06795i	−0.0706640	+	0.217482i	0.909488	+	0.415731i	$0.136474\pi$
$200$	4.22948	+	4.84103i	0.299069	+	0.342312i
$201$	−1.81701	+	19.7012i	−0.128162	+	1.38962i
$202$	−11.8424	−	10.3464i	−0.833231	−	0.727972i
$203$	0.482946	+	0.0876417i	0.0338961	+	0.00615124i
$204$	−6.15847	−	5.40452i	−0.431179	−	0.378392i
$205$	−1.18949	−	13.2163i	−0.0830774	−	0.923065i
$206$	0.783097	+	4.31522i	0.0545609	+	0.300655i
$207$	1.61093	−	6.91698i	0.111967	−	0.480763i
$208$	−0.918576	+	0.298464i	−0.0636918	+	0.0206947i
$209$	−7.80986	−	11.8314i	−0.540219	−	0.818397i
$210$	5.87702	+	4.70804i	0.405553	+	0.324886i
$211$	18.9145	+	10.1783i	1.30213	+	0.700704i	0.970132	−	0.242577i	$-0.0779927\pi$
$211$	18.9145	+	10.1783i	1.30213	+	0.700704i	0.331995	+	0.943281i	$0.392278\pi$
$212$	13.0629			0.897165
$213$	14.5846	−	0.538491i	0.999319	−	0.0368968i
$214$	0.315916			0.0215956
$215$	3.68815	+	1.98468i	0.251530	+	0.135354i
$216$	−5.16600	+	13.4924i	−0.351502	+	0.918038i
$217$	−18.7363	−	28.3843i	−1.27190	−	1.92685i
$218$	0.0500198	−	0.0162524i	0.00338777	−	0.00110075i
$219$	−1.01415	−	2.38731i	−0.0685302	−	0.161319i
$220$	1.54107	+	8.49202i	0.103899	+	0.572532i
$221$	1.52132	+	16.9033i	0.102335	+	1.13704i
$222$	1.03117	−	1.17502i	0.0692078	−	0.0788625i
$223$	−20.5102	−	3.72206i	−1.37347	−	0.249248i	−0.558861	−	0.829261i	$-0.688761\pi$
$223$	−20.5102	−	3.72206i	−1.37347	−	0.249248i	−0.814607	+	0.580014i	$0.803047\pi$
$224$	13.5294	+	11.8203i	0.903972	+	0.789777i
$225$	5.20312	+	4.58651i	0.346875	+	0.305767i
$226$	1.90769	+	2.18353i	0.126898	+	0.145246i
$227$	−5.68080	+	17.4837i	−0.377048	+	1.16043i	0.565039	+	0.825064i	$0.308861\pi$
$227$	−5.68080	+	17.4837i	−0.377048	+	1.16043i	−0.942087	+	0.335369i	$0.891139\pi$
$228$	7.17719	+	2.71174i	0.475321	+	0.179590i
$229$	−9.44317	+	22.0934i	−0.624022	+	1.45997i	0.247142	+	0.968979i	$0.420509\pi$
$229$	−9.44317	+	22.0934i	−0.624022	+	1.45997i	−0.871164	+	0.490993i	$0.836634\pi$
$230$	−2.65975	−	1.93242i	−0.175379	−	0.127420i
$231$	−7.77441	−	20.8547i	−0.511519	−	1.37214i
$232$	0.420217	+	0.115973i	0.0275886	+	0.00761397i
$233$	−15.6711	−	12.4973i	−1.02665	−	0.818725i	−0.0430459	−	0.999073i	$-0.513706\pi$
$233$	−15.6711	−	12.4973i	−1.02665	−	0.818725i	−0.983603	+	0.180348i	$0.942278\pi$
$234$	10.5567	−	5.02650i	0.690110	−	0.328592i
$235$	5.42283	+	14.4491i	0.353747	+	0.942554i
$236$	5.64999	+	2.72089i	0.367783	+	0.177115i
$237$	10.3482	−	15.6018i	0.672187	−	1.01344i
$238$	7.91306	−	5.74918i	0.512928	−	0.372664i
$239$	3.02725	+	13.2633i	0.195817	+	0.857929i	0.973393	+	0.229141i	$0.0735916\pi$
$239$	3.02725	+	13.2633i	0.195817	+	0.857929i	−0.777577	+	0.628788i	$0.783551\pi$
$240$	−0.429939	−	0.412885i	−0.0277524	−	0.0266516i
$241$	−12.4732	+	11.9256i	−0.803467	+	0.768193i	−0.976222	−	0.216772i	$-0.930447\pi$
$241$	−12.4732	+	11.9256i	−0.803467	+	0.768193i	0.172756	+	0.984965i	$0.444733\pi$
$242$	−1.74039	+	4.63724i	−0.111876	+	0.298093i
$243$	−3.63635	+	15.1584i	−0.233272	+	0.972411i
$244$	−10.4716	+	4.47579i	−0.670378	+	0.286533i
$245$	3.59022	−	2.86310i	0.229371	−	0.182917i
$246$	2.09445	+	11.6882i	0.133537	+	0.745214i
$247$	−6.89527	−	14.3182i	−0.438735	−	0.911043i
$248$	−14.3137	−	26.5993i	−0.908920	−	1.68906i
$249$	6.53876	+	0.900445i	0.414377	+	0.0570634i
$250$	9.14881	−	4.40583i	0.578621	−	0.278649i
$251$	6.86977	+	6.56818i	0.433616	+	0.414580i	0.876049	−	0.482222i	$-0.160170\pi$
$251$	6.86977	+	6.56818i	0.433616	+	0.414580i	−0.442433	+	0.896802i	$0.645884\pi$
$252$	10.0233	+	6.68007i	0.631409	+	0.420805i
$253$	3.81903	+	8.93507i	0.240100	+	0.561743i
$254$	−1.86042	+	8.15102i	−0.116733	+	0.511440i
$255$	−8.75429	+	5.75094i	−0.548215	+	0.360138i
$256$	10.6545	+	11.1437i	0.665904	+	0.696481i
$257$	3.05024	−	22.5178i	0.190269	−	1.40462i	−0.603967	−	0.797009i	$-0.706414\pi$
$257$	3.05024	−	22.5178i	0.190269	−	1.40462i	0.794236	−	0.607610i	$-0.207871\pi$
$258$	−3.44300	−	1.48061i	−0.214352	−	0.0921786i
$259$	−1.96082	−	2.69883i	−0.121839	−	0.167697i
$260$	0.434068	+	9.66527i	0.0269198	+	0.599415i
$261$	0.465812	+	0.0651949i	0.0288330	+	0.00403546i
$262$	−9.68692	+	3.63556i	−0.598460	+	0.224606i
$263$	18.0694	−	2.44767i	1.11421	−	0.150930i	0.446091	−	0.894987i	$-0.352816\pi$
$263$	18.0694	−	2.44767i	1.11421	−	0.150930i	0.668115	+	0.744058i	$0.267101\pi$
$264$	−5.21665	−	19.0662i	−0.321063	−	1.17344i
$265$	4.44253	−	16.0972i	0.272903	−	0.988841i
$266$	−5.04559	+	7.64374i	−0.309365	+	0.468668i
$267$	11.8966	−	3.83642i	0.728062	−	0.234785i
$268$	13.4711	+	5.75781i	0.822876	+	0.351714i
$269$	−7.79896	+	2.15238i	−0.475511	+	0.131233i	−0.495573	−	0.868566i	$-0.665042\pi$
$269$	−7.79896	+	2.15238i	−0.475511	+	0.131233i	0.0200626	+	0.999799i	$0.493613\pi$
$270$	5.80968	+	4.28007i	0.353566	+	0.260477i
$271$	−4.37471	+	3.82207i	−0.265745	+	0.232174i	−0.780489	−	0.625170i	$-0.785030\pi$
$271$	−4.37471	+	3.82207i	−0.265745	+	0.232174i	0.514744	+	0.857344i	$0.327887\pi$
$272$	−0.664663	+	0.397117i	−0.0403011	+	0.0240788i
$273$	−5.49811	−	24.3364i	−0.332760	−	1.47290i
$274$	1.63384	−	9.00318i	0.0987037	−	0.543902i
$275$	−9.45160	−	0.850660i	−0.569953	−	0.0512967i
$276$	−4.50849	−	2.70722i	−0.271379	−	0.162956i
$277$	−7.62274	+	1.38332i	−0.458006	+	0.0831159i	−0.402657	−	0.915351i	$-0.631913\pi$
$277$	−7.62274	+	1.38332i	−0.458006	+	0.0831159i	−0.0553497	+	0.998467i	$0.517627\pi$
$278$	−9.10224	−	5.43833i	−0.545916	−	0.326170i
$279$	−19.0401	−	26.4513i	−1.13990	−	1.58360i
$280$	11.9103	−	7.86192i	0.711776	−	0.469839i
$281$	−0.216169	+	4.81338i	−0.0128956	+	0.287142i	0.982175	+	0.187970i	$0.0601908\pi$
$281$	−0.216169	+	4.81338i	−0.0128956	+	0.287142i	−0.995070	+	0.0991719i	$0.968381\pi$
$282$	−5.96462	−	12.4559i	−0.355188	−	0.741741i
$283$		−	11.8172i		−	0.702459i	−0.936289	−	0.351230i	$-0.885764\pi$
$283$		−	11.8172i		−	0.702459i	0.936289	−	0.351230i	$-0.114236\pi$
$284$	2.93501	−	10.4005i	0.174161	−	0.617158i
$285$	5.78250	−	7.92207i	0.342525	−	0.469263i
$286$	−7.58058	+	14.0871i	−0.448249	+	0.832986i
$287$	25.3129	+	1.13680i	1.49417	+	0.0671034i
$288$	13.4125	+	10.7933i	0.790337	+	0.636003i
$289$	−1.04909	−	3.22876i	−0.0617110	−	0.189927i
$290$	0.111674	−	0.186911i	0.00655772	−	0.0109758i
$291$	−7.00716	+	14.4687i	−0.410767	+	0.848170i
$292$	−1.91288	+	0.172162i	−0.111943	+	0.0100750i
$293$	−0.807370	+	8.97061i	−0.0471670	+	0.524069i	0.937303	+	0.348516i	$0.113314\pi$
$293$	−0.807370	+	8.97061i	−0.0471670	+	0.524069i	−0.984470	+	0.175553i	$0.943829\pi$
$294$	−2.97638	+	2.83316i	−0.173586	+	0.165233i
$295$	5.27438	−	6.03702i	0.307086	−	0.351489i
$296$	−1.51960	−	2.54339i	−0.0883251	−	0.147831i
$297$	−8.25232	−	19.6668i	−0.478848	−	1.14118i
$298$	−4.07426	−	1.32381i	−0.236016	−	0.0766861i
$299$	2.89787	+	10.5002i	0.167588	+	0.607243i
$300$	4.41470	−	2.62445i	0.254883	−	0.151523i
$301$	−4.70077	+	6.47006i	−0.270948	+	0.372928i
$302$	0.373773	+	0.246726i	0.0215082	+	0.0141975i
$303$	−25.1848	+	19.9933i	−1.44683	+	1.14859i
$304$	0.452034	−	0.566832i	0.0259259	−	0.0325101i
$305$	1.95415	+	14.4261i	0.111894	+	0.826038i
$306$	7.35380	−	5.81151i	0.420389	−	0.332222i
$307$	3.68288	−	7.64759i	0.210193	−	0.436471i	−0.769042	−	0.639198i	$-0.779266\pi$
$307$	3.68288	−	7.64759i	0.210193	−	0.436471i	0.979235	+	0.202728i	$0.0649806\pi$
$308$	−16.4637	+	0.739386i	−0.938107	+	0.0421305i
$309$	8.96797	+	0.0198047i	0.510170	+	0.00112665i
$310$	−14.7086	+	3.35715i	−0.835394	+	0.190673i
$311$	27.2382	+	3.68967i	1.54454	+	0.209222i	0.856383	−	0.516342i	$-0.172707\pi$
$311$	27.2382	+	3.68967i	1.54454	+	0.209222i	0.688155	+	0.725564i	$0.258421\pi$
$312$	−2.92594	−	21.9647i	−0.165649	−	1.24351i
$313$	−27.7243	−	10.4051i	−1.56707	−	0.588131i	−0.591208	−	0.806519i	$-0.701349\pi$
$313$	−27.7243	−	10.4051i	−1.56707	−	0.588131i	−0.975862	+	0.218388i	$0.929920\pi$
$314$	14.8781	+	3.39583i	0.839619	+	0.191638i
$315$	11.6405	−	10.0797i	0.655869	−	0.567927i
$316$	−8.64328	−	10.8383i	−0.486222	−	0.609703i
$317$	5.19840	−	5.43710i	0.291971	−	0.305378i	−0.560498	−	0.828156i	$-0.689390\pi$
$317$	5.19840	−	5.43710i	0.291971	−	0.305378i	0.852469	+	0.522778i	$0.175104\pi$
$318$	−2.70065	+	14.6970i	−0.151445	+	0.824167i
$319$	−0.566691	+	0.304949i	−0.0317286	+	0.0170739i
$320$	6.41175	−	3.45031i	0.358428	−	0.192878i
$321$	0.116750	−	0.635356i	0.00651635	−	0.0354621i
$322$	4.33829	−	4.53750i	0.241764	−	0.252865i
$323$	−7.94301	−	9.96022i	−0.441961	−	0.554201i
$324$	9.85614	+	6.00754i	0.547563	+	0.333752i
$325$	−10.3713	−	2.36719i	−0.575298	−	0.131308i
$326$	4.66018	+	1.74899i	0.258104	+	0.0968679i
$327$	−0.0142008	−	0.106604i	−0.000785306	−	0.00589520i
$328$	22.3003	+	3.02078i	1.23133	+	0.166795i
$329$	−28.7307	+	6.55760i	−1.58398	+	0.361532i
$330$	−9.87291	−	0.0218031i	−0.543486	−	0.00120022i
$331$	32.0738	−	1.44043i	1.76293	−	0.0791735i	0.860354	−	0.509696i	$-0.170242\pi$
$331$	32.0738	−	1.44043i	1.76293	−	0.0791735i	0.902580	+	0.430523i	$0.141671\pi$
$332$	2.12057	−	4.40341i	0.116381	−	0.241669i
$333$	−1.98208	−	2.50809i	−0.108617	−	0.137442i
$334$	−2.73066	−	20.1586i	−0.149415	−	1.10303i
$335$	11.6766	−	14.6419i	0.637959	−	0.799975i
$336$	0.891468	−	0.707707i	0.0486335	−	0.0386086i
$337$	17.6875	+	11.6754i	0.963502	+	0.636002i	0.931599	−	0.363489i	$-0.118414\pi$
$337$	17.6875	+	11.6754i	0.963502	+	0.636002i	0.0319035	+	0.999491i	$0.489843\pi$
$338$	−4.06825	+	5.59947i	−0.221284	+	0.304571i
$339$	5.09641	−	3.02971i	0.276799	−	0.164551i
$340$	2.06334	+	7.47636i	0.111901	+	0.405462i
$341$	42.4088	+	13.7794i	2.29656	+	0.746199i
$342$	−4.53479	+	7.51438i	−0.245213	+	0.406331i
$343$	−6.74254	−	11.2851i	−0.364063	−	0.609338i
$344$	−4.67321	+	5.34892i	−0.251963	+	0.288394i
$345$	−4.86933	+	4.63502i	−0.262156	+	0.249541i
$346$	1.70950	−	18.9941i	0.0919035	−	1.02113i
$347$	3.88748	−	0.349880i	0.208691	−	0.0187825i	0.0151995	−	0.999884i	$-0.495162\pi$
$347$	3.88748	−	0.349880i	0.208691	−	0.0187825i	0.193492	+	0.981102i	$0.438019\pi$
$348$	0.151805	−	0.313454i	0.00813762	−	0.0168029i
$349$	8.05611	−	13.4837i	0.431234	−	0.721764i	−0.563292	−	0.826258i	$-0.690465\pi$
$349$	8.05611	−	13.4837i	0.431234	−	0.721764i	0.994525	+	0.104494i	$0.0333224\pi$
$350$	1.89456	+	5.83086i	0.101268	+	0.311672i
$351$	−6.20775	−	23.0887i	−0.331345	−	1.23238i
$352$	−23.5310	−	1.05678i	−1.25421	−	0.0563265i
$353$	11.4277	−	21.2362i	0.608234	−	1.13029i	−0.371205	−	0.928551i	$-0.621055\pi$
$353$	11.4277	−	21.2362i	0.608234	−	1.13029i	0.979440	−	0.201738i	$-0.0646590\pi$
$354$	−4.22934	+	5.79424i	−0.224787	+	0.307960i
$355$	−11.8182	−	7.15384i	−0.627245	−	0.379687i
$356$		−	9.25575i		−	0.490554i
$357$	−8.63813	−	18.0391i	−0.457178	−	0.954729i
$358$	0.0527927	−	1.17552i	0.00279018	−	0.0621282i
$359$	8.19776	−	5.41130i	0.432661	−	0.285597i	−0.315737	−	0.948847i	$-0.602252\pi$
$359$	8.19776	−	5.41130i	0.432661	−	0.285597i	0.748398	+	0.663249i	$0.230823\pi$
$360$	11.0992	−	7.98938i	0.584979	−	0.421077i
$361$	−6.06995	−	3.62663i	−0.319471	−	0.190875i
$362$	3.55441	−	0.645031i	0.186816	−	0.0339021i
$363$	8.68304	+	5.21393i	0.455741	+	0.273660i
$364$	−18.4000	−	1.65603i	−0.964423	−	0.0867997i
$365$	−0.438394	+	2.41575i	−0.0229466	+	0.126446i
$366$	−2.87076	−	12.7069i	−0.150057	−	0.664200i
$367$	28.2566	−	16.8825i	1.47498	−	0.881261i	0.474983	−	0.879995i	$-0.342454\pi$
$367$	28.2566	−	16.8825i	1.47498	−	0.881261i	0.999999	−	0.00126538i	$-0.000402784\pi$
$368$	−0.374229	+	0.326954i	−0.0195080	+	0.0170437i
$369$	24.2809	+	0.107243i	1.26401	+	0.00558285i
$370$	−1.42647	+	0.393682i	−0.0741589	+	0.0204666i
$371$	29.3206	+	12.5322i	1.52225	+	0.650640i
$372$	−22.9681	+	7.40674i	−1.19084	+	0.384021i
$373$	−1.83803	+	2.78449i	−0.0951694	+	0.144175i	−0.879039	−	0.476750i	$-0.841815\pi$
$373$	−1.83803	+	2.78449i	−0.0951694	+	0.144175i	0.783869	+	0.620926i	$0.213243\pi$
$374$	−3.41165	+	12.3618i	−0.176412	+	0.639215i
$375$	−5.47978	−	20.0279i	−0.282974	−	1.03424i
$376$	−25.9361	+	3.51329i	−1.33755	+	0.181184i
$377$	−0.675397	+	0.253481i	−0.0347847	+	0.0130549i
$378$	−9.58794	+	9.89610i	−0.493150	+	0.509000i
$379$	1.25968	+	28.0490i	0.0647054	+	1.44078i	0.724470	+	0.689306i	$0.242085\pi$
$379$	1.25968	+	28.0490i	0.0647054	+	1.44078i	−0.659765	+	0.751472i	$0.729344\pi$
$380$	−4.26877	−	5.87546i	−0.218983	−	0.301405i
$381$	15.7054	+	6.75388i	0.804613	+	0.346012i
$382$	0.583772	−	4.30958i	0.0298684	−	0.220497i
$383$	−0.0431797	−	0.0451625i	−0.00220638	−	0.00230769i	0.721691	−	0.692216i	$-0.243365\pi$
$383$	−0.0431797	−	0.0451625i	−0.00220638	−	0.00230769i	−0.723897	+	0.689908i	$0.757651\pi$
$384$	11.1693	−	7.33741i	0.569979	−	0.374436i
$385$	−4.68797	+	20.5393i	−0.238921	+	1.04678i
$386$	1.62613	+	3.80451i	0.0827677	+	0.193645i
$387$	−4.25013	+	6.37722i	−0.216046	+	0.324172i
$388$	8.60404	+	8.22630i	0.436804	+	0.417627i
$389$	6.76384	−	3.25729i	0.342940	−	0.165151i	−0.254483	−	0.967077i	$-0.581905\pi$
$389$	6.76384	−	3.25729i	0.342940	−	0.165151i	0.597424	+	0.801926i	$0.296191\pi$
$390$	−10.9641	−	1.50985i	−0.555187	−	0.0764542i
$391$	4.13784	+	7.68939i	0.209260	+	0.388869i
$392$	3.37893	+	7.01641i	0.170662	+	0.354382i
$393$	3.73178	+	20.8255i	0.188243	+	1.05051i
$394$	−15.6780	+	12.5028i	−0.789847	+	0.629882i
$395$	−16.2953	+	6.96495i	−0.819906	+	0.350445i
$396$	−15.7351	+	1.34616i	−0.790721	+	0.0676468i
$397$	4.15115	−	11.0607i	0.208340	−	0.555121i	−0.789975	−	0.613139i	$-0.789907\pi$
$397$	4.15115	−	11.0607i	0.208340	−	0.555121i	0.998316	+	0.0580180i	$0.0184781\pi$
$398$	−1.97498	+	1.88827i	−0.0989966	+	0.0946504i
$399$	13.5081	+	12.9723i	0.676251	+	0.649426i
$400$	−0.107993	−	0.473149i	−0.00539966	−	0.0236575i
$401$	−22.5034	+	16.3497i	−1.12376	+	0.816463i	−0.984776	−	0.173831i	$-0.944385\pi$
$401$	−22.5034	+	16.3497i	−1.12376	+	0.816463i	−0.138989	+	0.990294i	$0.544385\pi$
$402$	−9.26309	+	13.9658i	−0.462001	+	0.696551i
$403$	45.0364	+	21.6884i	2.24342	+	1.08038i
$404$	8.36636	+	22.2921i	0.416242	+	1.10907i
$405$	10.7549	−	10.1024i	0.534416	−	0.501994i
$406$	0.325051	+	0.259219i	0.0161320	+	0.0128648i
$407$	4.21613	+	1.16358i	0.208986	+	0.0576764i
$408$	−6.20483	−	16.6443i	−0.307185	−	0.824018i
$409$	2.95487	+	2.14684i	0.146109	+	0.106154i	0.658438	−	0.752635i	$-0.271217\pi$
$409$	2.95487	+	2.14684i	0.146109	+	0.106154i	−0.512329	+	0.858789i	$0.671217\pi$
$410$	4.41759	−	10.3355i	0.218169	−	0.510432i
$411$	−17.5030	−	6.61312i	−0.863359	−	0.326201i
$412$	2.05202	−	6.31548i	0.101096	−	0.311141i
$413$	10.0714	+	11.5277i	0.495582	+	0.567239i
$414$	3.97797	−	4.51277i	0.195507	−	0.221790i
$415$	−4.70505	−	4.11068i	−0.230962	−	0.201785i
$416$	−25.9805	−	4.71476i	−1.27380	−	0.231160i
$417$	−14.3012	+	16.2962i	−0.700331	+	0.798029i
$418$	−1.07640	−	11.9598i	−0.0526487	−	0.584974i
$419$	0.584837	+	3.22272i	0.0285712	+	0.157440i	0.995061	−	0.0992644i	$-0.0316490\pi$
$419$	0.584837	+	3.22272i	0.0285712	+	0.157440i	−0.966490	+	0.256705i	$0.917363\pi$
$420$	−4.45802	−	10.4941i	−0.217529	−	0.512060i
$421$	13.3499	−	4.33765i	0.650635	−	0.211404i	0.0349410	−	0.999389i	$-0.488876\pi$
$421$	13.3499	−	4.33765i	0.650635	−	0.211404i	0.615694	+	0.787985i	$0.288876\pi$
$422$	10.0229	+	15.1840i	0.487906	+	0.739146i
$423$	−27.2551	+	7.39254i	−1.32519	+	0.359438i
$424$	24.9381	+	13.4198i	1.21110	+	0.651721i
$425$	−8.52786			−0.413662
$426$	11.0948	+	5.45238i	0.537544	+	0.264169i
$427$	−27.7982			−1.34525
$428$	−0.421220	−	0.226668i	−0.0203605	−	0.0109564i
$429$	25.5298	+	20.4517i	1.23259	+	0.987420i
$430$	1.95437	+	2.96074i	0.0942480	+	0.142780i
$431$	−14.3045	+	4.64783i	−0.689026	+	0.223878i	−0.632543	−	0.774526i	$-0.717989\pi$
$431$	−14.3045	+	4.64783i	−0.689026	+	0.223878i	−0.0564831	+	0.998404i	$0.517989\pi$
$432$	0.826136	−	0.712177i	0.0397475	−	0.0342646i
$433$	3.16704	+	17.4518i	0.152198	+	0.838680i	0.966195	+	0.257811i	$0.0830014\pi$
$433$	3.16704	+	17.4518i	0.152198	+	0.838680i	−0.813997	+	0.580869i	$0.802713\pi$
$434$	−2.58236	−	28.6924i	−0.123957	−	1.37728i
$435$	−0.334636	−	0.293668i	−0.0160446	−	0.0140803i
$436$	−0.0783539	−	0.0142191i	−0.00375247	−	0.000680973i
$437$	−6.15753	−	5.37967i	−0.294554	−	0.257344i
$438$	0.201773	−	2.18776i	0.00964110	−	0.104535i
$439$	−19.8449	−	22.7143i	−0.947144	−	1.08409i	−0.996355	−	0.0853053i	$-0.972813\pi$
$439$	−19.8449	−	22.7143i	−0.947144	−	1.08409i	0.0492107	−	0.998788i	$-0.484329\pi$
$440$	−5.78197	+	17.7951i	−0.275645	+	0.848347i
$441$	4.59796	+	7.03298i	0.218951	+	0.334904i
$442$	−5.64999	+	13.2188i	−0.268742	+	0.628754i
$443$	−16.8800	−	12.2640i	−0.801992	−	0.582681i	0.109506	−	0.993986i	$-0.465073\pi$
$443$	−16.8800	−	12.2640i	−0.801992	−	0.582681i	−0.911498	+	0.411305i	$0.865073\pi$
$444$	−2.21797	+	0.826834i	−0.105260	+	0.0392398i
$445$	−11.4057	−	3.14776i	−0.540681	−	0.149218i
$446$	−13.8046	−	11.0088i	−0.653667	−	0.521282i
$447$	−4.16807	+	7.70475i	−0.197143	+	0.364422i
$448$	4.88527	+	13.0168i	0.230808	+	0.614985i
$449$	−19.9278	−	9.59670i	−0.940449	−	0.452896i	−0.100121	−	0.994975i	$-0.531923\pi$
$449$	−19.9278	−	9.59670i	−0.940449	−	0.452896i	−0.840328	+	0.542079i	$0.817637\pi$
$450$	2.04005	+	5.50953i	0.0961687	+	0.259722i
$451$	−26.8765	+	19.5269i	−1.26557	+	0.919487i
$452$	−0.976909	−	4.28012i	−0.0459499	−	0.201320i
$453$	0.634335	−	0.660536i	0.0298037	−	0.0310347i
$454$	−11.2550	+	10.7609i	−0.528224	+	0.505034i
$455$	−8.29831	+	22.1108i	−0.389031	+	1.03657i
$456$	10.9160	+	12.5502i	0.511188	+	0.587716i
$457$	17.4385	−	7.45359i	0.815740	−	0.348664i	0.0556244	−	0.998452i	$-0.482285\pi$
$457$	17.4385	−	7.45359i	0.815740	−	0.348664i	0.760116	+	0.649788i	$0.225142\pi$
$458$	−15.9116	+	12.6891i	−0.743502	+	0.592923i
$459$	−8.97017	−	16.9373i	−0.418692	−	0.790567i
$460$	2.15982	+	4.48491i	0.100702	+	0.209110i
$461$	8.71316	+	16.1918i	0.405812	+	0.754126i	0.998690	−	0.0511668i	$-0.0162940\pi$
$461$	8.71316	+	16.1918i	0.405812	+	0.754126i	−0.592878	+	0.805292i	$0.702008\pi$
$462$	2.57186	−	18.6761i	0.119654	−	0.868889i
$463$	−7.15508	+	3.44571i	−0.332525	+	0.160136i	−0.592694	−	0.805427i	$-0.701936\pi$
$463$	−7.15508	+	3.44571i	−0.332525	+	0.160136i	0.260170	+	0.965563i	$0.416222\pi$
$464$	−0.0237877	−	0.0227434i	−0.00110432	−	0.00105584i
$465$	1.31602	+	30.8220i	0.0610290	+	1.42934i
$466$	−6.67284	−	15.6119i	−0.309113	−	0.723207i
$467$	4.40072	−	19.2808i	0.203641	−	0.892210i	−0.765056	−	0.643964i	$-0.777289\pi$
$467$	4.40072	−	19.2808i	0.203641	−	0.892210i	0.968697	−	0.248246i	$-0.0798541\pi$
$468$	−17.6820	−	0.872370i	−0.817350	−	0.0403253i
$469$	24.7128	+	25.8475i	1.14113	+	1.19353i
$470$	−1.75477	+	12.9542i	−0.0809414	+	0.597534i
$471$	12.3279	−	28.6672i	0.568039	−	1.32091i
$472$	7.99103	+	10.9987i	0.367817	+	0.506257i
$473$	−0.470427	−	10.4749i	−0.0216302	−	0.481635i
$474$	13.9810	−	7.48375i	0.642171	−	0.343740i
$475$	7.47617	−	2.80586i	0.343030	−	0.128741i
$476$	−14.6757	+	1.98796i	−0.672661	+	0.0911182i
$477$	28.5599	+	10.8629i	1.30767	+	0.497376i
$478$	−3.06566	+	11.1082i	−0.140220	+	0.508075i
$479$	−0.466077	+	0.706077i	−0.0212956	+	0.0322615i	−0.845065	−	0.534663i	$-0.820438\pi$
$479$	−0.466077	+	0.706077i	−0.0212956	+	0.0322615i	0.823770	+	0.566925i	$0.191867\pi$
$480$	−5.00155	−	15.5096i	−0.228288	−	0.707915i
$481$	4.50841	+	1.92699i	0.205566	+	0.0878631i
$482$	−14.0905	+	3.88872i	−0.641804	+	0.177127i
$483$	−7.52235	−	10.4019i	−0.342279	−	0.473301i
$484$	5.64771	−	4.93426i	0.256714	−	0.224284i
$485$	13.0632	−	7.80491i	0.593171	−	0.354403i
$486$	−8.79672	+	9.84706i	−0.399027	+	0.446672i
$487$	−0.624836	+	3.44313i	−0.0283140	+	0.156023i	−0.994989	−	0.0999832i	$-0.968121\pi$
$487$	−0.624836	+	3.44313i	−0.0283140	+	0.156023i	0.966675	+	0.256006i	$0.0824068\pi$
$488$	−24.5892	−	2.21307i	−1.11310	−	0.100181i
$489$	5.23972	−	8.72599i	0.236948	−	0.394603i
$490$	3.82715	−	0.694526i	0.172893	−	0.0313755i
$491$	−16.8023	−	10.0389i	−0.758275	−	0.453048i	0.0810282	−	0.996712i	$-0.474180\pi$
$491$	−16.8023	−	10.0389i	−0.758275	−	0.453048i	−0.839303	+	0.543664i	$0.817037\pi$
$492$	5.59366	−	17.0870i	0.252182	−	0.770343i
$493$	−0.482633	+	0.318583i	−0.0217367	+	0.0143483i
$494$	0.603932	−	13.4476i	0.0271722	−	0.605035i
$495$	−3.69249	+	19.8479i	−0.165965	+	0.892097i
$496$			2.28044i			0.102395i
$497$	16.5658	−	20.5289i	0.743078	−	0.920847i
$498$	4.51583	+	3.29621i	0.202359	+	0.147707i
$499$	−7.55121	+	14.0325i	−0.338039	+	0.628181i	−0.991695	−	0.128610i	$-0.958948\pi$
$499$	−7.55121	+	14.0325i	−0.338039	+	0.628181i	0.653657	+	0.756791i	$0.273234\pi$
$500$	−15.3595	−	0.689798i	−0.686900	−	0.0308487i
$501$	−41.5511	−	1.95802i	−1.85637	−	0.0874778i
$502$	2.48779	+	7.65663i	0.111036	+	0.341732i
$503$	19.0110	−	31.8191i	0.847659	−	1.41874i	−0.0596234	−	0.998221i	$-0.518990\pi$
$503$	19.0110	−	31.8191i	0.847659	−	1.41874i	0.907283	−	0.420521i	$-0.138153\pi$
$504$	12.2727	+	23.0499i	0.546669	+	1.02672i
$505$	30.3154	−	2.72843i	1.34902	−	0.121414i
$506$	−0.737794	+	8.19757i	−0.0327990	+	0.364426i
$507$	9.75794	+	10.2512i	0.433365	+	0.455273i
$508$	8.32887	−	9.53315i	0.369534	−	0.422965i
$509$	−2.67081	−	4.47018i	−0.118381	−	0.198137i	0.793522	−	0.608541i	$-0.208245\pi$
$509$	−2.67081	−	4.47018i	−0.118381	−	0.198137i	−0.911904	+	0.410404i	$0.865388\pi$
$510$	−8.83817	+	0.775778i	−0.391361	+	0.0343520i
$511$	−4.45874	−	1.44873i	−0.197243	−	0.0640882i
$512$	−0.631012	−	2.28642i	−0.0278871	−	0.101047i
$513$	13.4367	+	11.8972i	0.593245	+	0.525273i
$514$	11.3135	−	15.5717i	0.499016	−	0.686837i
$515$	−7.08456	−	4.67648i	−0.312183	−	0.206070i
$516$	3.52832	+	4.44447i	0.155326	+	0.195657i
$517$	24.0901	−	30.2081i	1.05948	−	1.32855i
$518$	−0.379300	−	2.80010i	−0.0166655	−	0.123029i
$519$	−37.5684	−	10.4576i	−1.64907	−	0.459036i
$520$	−9.10063	+	18.8977i	−0.399089	+	0.828717i
$521$	22.6094	−	1.01539i	0.990535	−	0.0444850i	0.456304	−	0.889824i	$-0.349173\pi$
$521$	22.6094	−	1.01539i	0.990535	−	0.0444850i	0.534231	+	0.845339i	$0.320601\pi$
$522$	0.321281	+	0.235599i	0.0140621	+	0.0103119i
$523$	16.5013	−	3.76631i	0.721551	−	0.164689i	0.154051	−	0.988063i	$-0.450768\pi$
$523$	16.5013	−	3.76631i	0.721551	−	0.164689i	0.567500	+	0.823374i	$0.307911\pi$
$524$	15.5244	+	2.10292i	0.678185	+	0.0918664i
$525$	12.4269	−	1.65540i	0.542355	−	0.0722476i
$526$	14.4604	+	5.42709i	0.630504	+	0.236632i
$527$	39.0665	+	8.91668i	1.70176	+	0.388417i
$528$	−0.335287	+	1.45418i	−0.0145915	+	0.0632849i
$529$	−10.8460	−	13.6004i	−0.471564	−	0.591323i
$530$	9.77486	−	10.2237i	0.424593	−	0.444089i
$531$	10.0901	+	10.6472i	0.437873	+	0.462048i
$532$	12.2118	−	6.57144i	0.529448	−	0.284908i
$533$	−32.7942	+	17.6473i	−1.42047	+	0.764389i
$534$	10.4136	+	1.91355i	0.450640	+	0.0828074i
$535$	−0.422570	+	0.441974i	−0.0182693	+	0.0191082i
$536$	19.8022	+	24.8311i	0.855323	+	1.07254i
$537$	−2.34464	−	0.540600i	−0.101179	−	0.0233286i
$538$	−6.68117	−	1.52493i	−0.288046	−	0.0657446i
$539$	−10.7633	−	4.03954i	−0.463609	−	0.173995i
$540$	−4.67529	−	9.87517i	−0.201192	−	0.424960i
$541$	28.0997	+	3.80637i	1.20810	+	0.163649i	0.710463	−	0.703735i	$-0.248486\pi$
$541$	28.0997	+	3.80637i	1.20810	+	0.163649i	0.497640	+	0.867384i	$0.334200\pi$
$542$	−4.79722	+	1.09493i	−0.206058	+	0.0470314i
$543$	0.0163130	−	7.38686i	0.000700056	−	0.317000i
$544$	−21.1458	+	0.949658i	−0.906618	+	0.0407162i
$545$	−0.0441691	+	0.0917181i	−0.00189200	+	0.00392877i
$546$	5.66724	−	20.3594i	0.242536	−	0.871300i
$547$	−4.35179	−	32.1262i	−0.186069	−	1.37362i	−0.807370	−	0.590046i	$-0.799110\pi$
$547$	−4.35179	−	32.1262i	−0.186069	−	1.37362i	0.621300	−	0.783572i	$-0.286605\pi$
$548$	−8.63819	+	10.8319i	−0.369005	+	0.462718i
$549$	−26.6164	+	1.07757i	−1.13596	+	0.0459897i
$550$	−6.70851	−	4.42825i	−0.286052	−	0.188821i
$551$	0.318292	−	0.438091i	0.0135597	−	0.0186633i
$552$	−5.82586	−	9.79994i	−0.247965	−	0.417113i
$553$	−9.00239	−	32.6194i	−0.382821	−	1.38712i
$554$	−6.24105	−	2.02784i	−0.265157	−	0.0861546i
$555$	0.264587	+	3.01435i	0.0112311	+	0.127952i
$556$	8.23431	+	13.7819i	0.349212	+	0.584483i
$557$	−17.8530	+	20.4344i	−0.756454	+	0.865832i	−0.994426	−	0.105440i	$-0.966375\pi$
$557$	−17.8530	+	20.4344i	−0.756454	+	0.865832i	0.237971	+	0.971272i	$0.423518\pi$
$558$	−3.58481	−	27.3725i	−0.151757	−	1.15877i
$559$	1.05363	−	11.7068i	0.0445639	−	0.495146i
$560$	−1.07308	+	0.0965786i	−0.0453458	+	0.00408119i
$561$	23.6007	+	11.4298i	0.996424	+	0.482566i
$562$	−2.09326	+	3.50353i	−0.0882989	+	0.147787i
$563$	−8.38636	−	25.8106i	−0.353443	−	1.08779i	−0.956907	−	0.290395i	$-0.906213\pi$
$563$	−8.38636	−	25.8106i	−0.353443	−	1.08779i	0.603464	−	0.797390i	$-0.293787\pi$
$564$	−0.984282	+	20.8875i	−0.0414458	+	0.879521i
$565$	−5.60653	−	0.251790i	−0.235869	−	0.0105929i
$566$	4.74325	−	8.81444i	0.199374	−	0.370499i
$567$	16.3593	+	22.9400i	0.687025	+	0.963391i
$568$	16.2878	−	16.8402i	0.683421	−	0.706600i
$569$			21.3115i			0.893426i	0.894677	+	0.446713i	$0.147405\pi$
$569$			21.3115i			0.893426i	−0.894677	+	0.446713i	$0.852595\pi$
$570$	7.49297	−	3.58806i	0.313846	−	0.150287i
$571$	−0.955503	+	21.2759i	−0.0399865	+	0.890370i	0.874321	+	0.485348i	$0.161307\pi$
$571$	−0.955503	+	21.2759i	−0.0399865	+	0.890370i	−0.914307	+	0.405021i	$0.867264\pi$
$572$	20.2148	−	13.3437i	0.845225	−	0.557928i
$573$	−8.45150	−	2.76671i	−0.353066	−	0.115581i
$574$	18.4246	+	11.0082i	0.769028	+	0.459473i
$575$	−5.38541	+	0.977307i	−0.224587	+	0.0407565i
$576$	5.18217	+	12.2740i	0.215924	+	0.511418i
$577$	−10.3175	−	0.928593i	−0.429524	−	0.0386578i	−0.127231	−	0.991873i	$-0.540609\pi$
$577$	−10.3175	−	0.928593i	−0.429524	−	0.0386578i	−0.302292	+	0.953215i	$0.597752\pi$
$578$	0.513463	−	2.82942i	0.0213573	−	0.117688i
$579$	8.25242	−	1.86440i	0.342959	−	0.0774817i
$580$	−0.283006	+	0.169088i	−0.0117512	+	0.00702100i
$581$	8.98427	−	7.84932i	0.372730	−	0.325645i
$582$	−11.0342	+	7.97962i	−0.457381	+	0.330766i
$583$	−40.2998	+	11.1220i	−1.66905	+	0.460628i
$584$	−3.82869	−	1.63646i	−0.158432	−	0.0677173i
$585$	−7.08842	+	21.4925i	−0.293070	+	0.888604i
$586$	−4.20289	+	6.36711i	−0.173620	+	0.263023i
$587$	3.34666	−	12.1264i	0.138132	−	0.500509i	−0.861846	−	0.507170i	$-0.830692\pi$
$587$	3.34666	−	12.1264i	0.138132	−	0.500509i	0.999978	+	0.00666101i	$0.00212028\pi$
$588$	6.00127	−	1.64199i	0.247488	−	0.0677146i
$589$	−37.1825	+	5.03671i	−1.53208	+	0.207534i
$590$	6.35733	−	2.38595i	0.261727	−	0.0982279i
$591$	19.3511	+	36.1515i	0.795998	+	1.48707i
$592$	0.0100353	+	0.223452i	0.000412446	+	0.00918383i
$593$	1.40984	+	1.94049i	0.0578954	+	0.0796862i	0.836983	−	0.547229i	$-0.184317\pi$
$593$	1.40984	+	1.94049i	0.0578954	+	0.0796862i	−0.779088	+	0.626915i	$0.784317\pi$
$594$	1.73856	−	17.9818i	0.0713341	−	0.737802i
$595$	−2.54131	+	18.7607i	−0.104183	+	0.769113i
$596$	4.48251	+	4.68834i	0.183611	+	0.192042i
$597$	3.06773	+	4.66981i	0.125554	+	0.191123i
$598$	−2.05311	+	8.99527i	−0.0839580	+	0.367844i
$599$	−9.23432	−	21.6048i	−0.377304	−	0.882747i	−0.995325	−	0.0965850i	$-0.969208\pi$
$599$	−9.23432	−	21.6048i	−0.377304	−	0.882747i	0.618021	−	0.786162i	$-0.287935\pi$
$600$	11.1241	−	0.474972i	0.454141	−	0.0193907i
$601$	10.2799	+	9.82859i	0.419326	+	0.400917i	0.871013	−	0.491260i	$-0.163463\pi$
$601$	10.2799	+	9.82859i	0.419326	+	0.400917i	−0.451687	+	0.892176i	$0.649178\pi$
$602$	−6.10329	+	2.93919i	−0.248752	+	0.119793i
$603$	24.6641	+	23.7907i	1.00440	+	0.968833i
$604$	−0.321339	−	0.597147i	−0.0130751	−	0.0242976i
$605$	−4.15966	−	8.63763i	−0.169114	−	0.351170i
$606$	−26.8103	+	4.80423i	−1.08910	+	0.195158i
$607$	5.22442	−	4.16633i	0.212052	−	0.169106i	−0.511704	−	0.859162i	$-0.670985\pi$
$607$	5.22442	−	4.16633i	0.212052	−	0.169106i	0.723756	+	0.690056i	$0.242414\pi$
$608$	18.2255	−	7.78997i	0.739143	−	0.315925i
$609$	0.641456	−	0.557930i	0.0259931	−	0.0226085i
$610$	−4.33284	+	11.5448i	−0.175432	+	0.467436i
$611$	31.3061	−	29.9317i	1.26651	−	1.21091i
$612$	−13.9748	+	2.47234i	−0.564897	+	0.0999385i
$613$	−3.23477	−	14.1725i	−0.130651	−	0.572420i	−0.997296	−	0.0734940i	$-0.976585\pi$
$613$	−3.23477	−	14.1725i	−0.130651	−	0.572420i	0.866644	−	0.498926i	$-0.166272\pi$
$614$	5.81669	−	4.22607i	0.234743	−	0.170551i
$615$	−19.1537	−	12.7040i	−0.772350	−	0.512276i
$616$	−32.1901	−	15.5019i	−1.29697	−	0.624590i
$617$	0.683852	+	1.82212i	0.0275309	+	0.0733557i	0.949282	−	0.314427i	$-0.101812\pi$
$617$	0.683852	+	1.82212i	0.0275309	+	0.0733557i	−0.921751	+	0.387783i	$0.873241\pi$
$618$	6.68126	+	3.61439i	0.268760	+	0.145392i
$619$	−18.3893	−	14.6650i	−0.739128	−	0.589435i	0.179873	−	0.983690i	$-0.442431\pi$
$619$	−18.3893	−	14.6650i	−0.739128	−	0.589435i	−0.919001	+	0.394255i	$0.871003\pi$
$620$	22.0202	+	6.07719i	0.884352	+	0.244066i
$621$	−7.60578	−	9.66805i	−0.305209	−	0.387966i
$622$	18.8360	+	13.6852i	0.755255	+	0.548725i
$623$	8.87972	−	20.7751i	0.355758	−	0.832338i
$624$	−0.591272	+	1.56492i	−0.0236698	+	0.0626471i
$625$	−2.50136	+	7.69839i	−0.100054	+	0.307936i
$626$	−16.5031	−	18.8893i	−0.659596	−	0.754968i
$627$	−24.4509	−	2.25506i	−0.976474	−	0.0900585i
$628$	−17.4009	−	15.2027i	−0.694372	−	0.606655i
$629$	3.86724	+	0.701800i	0.154197	+	0.0279826i
$630$	12.7285	−	2.84611i	0.507116	−	0.113392i
$631$	0.475893	+	5.28761i	0.0189450	+	0.210496i	0.999870	+	0.0161107i	$0.00512842\pi$
$631$	0.475893	+	5.28761i	0.0189450	+	0.210496i	−0.980925	+	0.194386i	$0.937729\pi$
$632$	−5.36627	−	29.5706i	−0.213459	−	1.17625i
$633$	34.2415	−	14.5461i	1.36098	−	0.578158i
$634$	6.05986	−	1.96897i	0.240668	−	0.0781977i
$635$	−8.91496	−	13.5056i	−0.353779	−	0.535953i
$636$	14.1459	−	17.6582i	0.560921	−	0.700195i
$637$	−11.3486	−	6.10695i	−0.449648	−	0.241966i
$638$	−0.545097			−0.0215806
$639$	15.0658	−	20.2983i	0.595993	−	0.802990i
$640$	−12.6498			−0.500025
$641$	−13.1311	−	7.06616i	−0.518649	−	0.279097i	0.193531	−	0.981094i	$-0.438006\pi$
$641$	−13.1311	−	7.06616i	−0.518649	−	0.279097i	−0.712179	+	0.701998i	$0.752292\pi$
$642$	0.342107	−	0.427050i	0.0135019	−	0.0168543i
$643$	−19.8947	−	30.1393i	−0.784572	−	1.18858i	−0.978233	−	0.207508i	$-0.933465\pi$
$643$	−19.8947	−	30.1393i	−0.784572	−	1.18858i	0.193661	−	0.981068i	$-0.437964\pi$
$644$	−9.04001	+	2.93728i	−0.356226	+	0.115745i
$645$	6.67677	−	2.83637i	0.262897	−	0.111682i
$646$	−1.92680	−	10.6175i	−0.0758089	−	0.417741i
$647$	−0.893306	−	9.92544i	−0.0351195	−	0.390209i	−0.994237	−	0.107202i	$-0.965811\pi$
$647$	−0.893306	−	9.92544i	−0.0351195	−	0.390209i	0.959118	−	0.283007i	$-0.0913320\pi$
$648$	12.6445	+	21.5942i	0.496721	+	0.848302i
$649$	−19.7471	−	3.58358i	−0.775143	−	0.140668i
$650$	−6.78582	−	5.92859i	−0.266162	−	0.232539i
$651$	−58.6591	−	5.41003i	−2.29903	−	0.212036i
$652$	−4.95866	−	5.67565i	−0.194196	−	0.222275i
$653$	1.37885	−	4.24367i	0.0539586	−	0.166068i	−0.920446	−	0.390871i	$-0.872174\pi$
$653$	1.37885	−	4.24367i	0.0539586	−	0.166068i	0.974404	+	0.224803i	$0.0721739\pi$
$654$	0.0321969	−	0.0852157i	0.00125900	−	0.00333220i
$655$	7.87102	−	18.4152i	0.307546	−	0.719540i
$656$	−1.37449	−	0.998624i	−0.0536648	−	0.0389897i
$657$	−4.32535	−	1.21431i	−0.168748	−	0.0473746i
$658$	−24.0624	−	6.64079i	−0.938049	−	0.258885i
$659$	22.8570	+	18.2279i	0.890384	+	0.710057i	0.957729	−	0.287672i	$-0.0928814\pi$
$659$	22.8570	+	18.2279i	0.890384	+	0.710057i	−0.0673452	+	0.997730i	$0.521453\pi$
$660$	13.1482	+	7.11284i	0.511793	+	0.276867i
$661$	5.80397	+	15.4646i	0.225748	+	0.601505i	0.999488	−	0.0319994i	$-0.0101875\pi$
$661$	5.80397	+	15.4646i	0.225748	+	0.601505i	−0.773739	+	0.633504i	$0.781616\pi$
$662$	24.5020	+	11.7995i	0.952297	+	0.458602i
$663$	24.4970	+	16.2481i	0.951387	+	0.631026i
$664$	8.57203	−	6.22794i	0.332659	−	0.241691i
$665$	−3.94478	−	17.2832i	−0.152972	−	0.670213i
$666$	−0.471718	−	2.66636i	−0.0182787	−	0.103319i
$667$	−0.268276	+	0.256498i	−0.0103877	+	0.00993165i
$668$	−10.8228	+	28.8373i	−0.418747	+	1.11575i
$669$	−27.2420	+	23.6948i	−1.05324	+	0.916093i
$670$	14.5866	−	6.23462i	0.563530	−	0.240864i
$671$	28.4948	−	22.7238i	1.10003	−	0.877244i
$672$	30.6295	−	5.48860i	1.18156	−	0.211727i
$673$	0.359767	+	0.747063i	0.0138680	+	0.0287972i	0.907788	−	0.419430i	$-0.137770\pi$
$673$	0.359767	+	0.747063i	0.0138680	+	0.0287972i	−0.893920	+	0.448227i	$0.852056\pi$
$674$	8.50678	+	15.8082i	0.327669	+	0.608911i
$675$	11.8344	−	2.06674i	0.455508	−	0.0795490i
$676$	9.44192	−	4.54699i	0.363151	−	0.174884i
$677$	5.52140	+	5.27899i	0.212204	+	0.202888i	0.789679	−	0.613521i	$-0.210247\pi$
$677$	5.52140	+	5.27899i	0.212204	+	0.202888i	−0.577474	+	0.816409i	$0.695962\pi$
$678$	5.01750	−	0.214234i	0.192696	−	0.00822762i
$679$	11.4202	+	26.7190i	0.438268	+	1.02538i
$680$	−3.74151	+	16.3926i	−0.143480	+	0.628629i
$681$	17.4824	+	26.6124i	0.669927	+	1.01979i
$682$	26.1018	+	27.3004i	0.999491	+	1.04539i
$683$	−3.77176	+	27.8442i	−0.144322	+	1.06543i	0.763420	+	0.645902i	$0.223519\pi$
$683$	−3.77176	+	27.8442i	−0.144322	+	1.06543i	−0.907743	+	0.419528i	$0.862196\pi$
$684$	11.4379	−	6.76545i	0.437339	−	0.258684i
$685$	10.4102	+	14.3285i	0.397755	+	0.547462i
$686$	−0.499576	−	11.1239i	−0.0190739	−	0.424713i
$687$	19.6394	+	36.6901i	0.749291	+	1.39982i
$688$	0.502041	−	0.188419i	0.0191401	−	0.00718341i
$689$	−46.4408	+	6.29083i	−1.76925	+	0.239662i
$690$	−5.49247	+	1.50278i	−0.209095	+	0.0572098i
$691$	9.15832	−	33.1844i	0.348399	−	1.26239i	−0.554371	−	0.832270i	$-0.687041\pi$
$691$	9.15832	−	33.1844i	0.348399	−	1.26239i	0.902769	−	0.430125i	$-0.141530\pi$
$692$	−15.9075	+	24.0989i	−0.604714	+	0.916102i
$693$	−36.6100	−	12.0743i	−1.39070	−	0.458666i
$694$	3.04011	+	1.29941i	0.115401	+	0.0493248i
$695$	19.7835	−	5.45991i	0.750432	−	0.207106i
$696$	0.611825	−	0.442456i	0.0231912	−	0.0167712i
$697$	−22.4820	+	19.6419i	−0.851565	+	0.743990i
$698$	11.4212	−	6.82385i	0.432299	−	0.258287i
$699$	−33.8640	+	7.65059i	−1.28085	+	0.289372i
$700$	1.65754	−	9.13379i	0.0626491	−	0.345225i
$701$	18.2167	+	1.63953i	0.688035	+	0.0619243i	0.428140	−	0.903712i	$-0.359169\pi$
$701$	18.2167	+	1.63953i	0.688035	+	0.0619243i	0.259895	+	0.965637i	$0.416312\pi$
$702$	4.63710	−	19.7135i	0.175016	−	0.744039i
$703$	−3.62122	+	0.657155i	−0.136577	+	0.0247851i
$704$	−15.6483	−	9.34945i	−0.589769	−	0.352371i
$705$	25.4044	+	8.31648i	0.956787	+	0.313217i
$706$	17.0478	−	11.2532i	0.641603	−	0.423518i
$707$	−2.60759	+	58.0625i	−0.0980685	+	2.18367i
$708$	9.79645	−	4.69110i	0.368173	−	0.176302i
$709$			7.23934i			0.271879i	0.990717	+	0.135940i	$0.0434053\pi$
$709$			7.23934i			0.271879i	−0.990717	+	0.135940i	$0.956595\pi$
$710$	−5.94374	−	10.0797i	−0.223065	−	0.378285i
$711$	−9.88415	−	30.8837i	−0.370684	−	1.15823i
$712$	9.50859	−	17.6699i	0.356350	−	0.662209i
$713$	25.6927	+	1.15386i	0.962198	+	0.0432123i
$714$	0.797443	−	16.9226i	0.0298436	−	0.633311i
$715$	−9.56834	−	29.4483i	−0.357836	−	1.10131i
$716$	−0.913821	+	1.52948i	−0.0341511	+	0.0571593i
$717$	21.2073	+	10.2706i	0.792001	+	0.383564i
$718$	8.28673	−	0.745819i	0.309258	−	0.0278337i
$719$	3.43965	−	38.2176i	0.128277	−	1.42528i	−0.631642	−	0.775260i	$-0.717619\pi$
$719$	3.43965	−	38.2176i	0.128277	−	1.42528i	0.759919	−	0.650018i	$-0.225238\pi$
$720$	−1.02371	+	0.134070i	−0.0381516	+	0.00499648i
$721$	10.6648	−	12.2068i	0.397178	−	0.454607i
$722$	−3.07190	−	5.14149i	−0.114324	−	0.191346i
$723$	2.61355	+	29.7752i	0.0971988	+	1.10735i
$724$	−5.20202	−	1.69024i	−0.193331	−	0.0628172i
$725$	−0.0964347	−	0.349423i	−0.00358149	−	0.0129772i
$726$	4.38388	+	7.37431i	0.162701	+	0.273686i
$727$	−24.3844	+	33.5623i	−0.904369	+	1.24476i	0.0646841	+	0.997906i	$0.479396\pi$
$727$	−24.3844	+	33.5623i	−0.904369	+	1.24476i	−0.969053	+	0.246852i	$0.920604\pi$
$728$	−33.4258	−	22.0642i	−1.23884	−	0.817752i
$729$	16.5530	+	21.3306i	0.613076	+	0.790024i
$730$	−1.29664	+	1.62594i	−0.0479910	+	0.0601788i
$731$	−1.26482	−	9.33728i	−0.0467811	−	0.345352i
$732$	−5.28947	+	19.0022i	−0.195505	+	0.702343i
$733$	20.2580	−	42.0662i	0.748247	−	1.55375i	−0.0821762	−	0.996618i	$-0.526187\pi$
$733$	20.2580	−	42.0662i	0.748247	−	1.55375i	0.830423	−	0.557133i	$-0.188099\pi$
$734$	27.8530	−	1.25088i	1.02807	−	0.0461708i
$735$	0.0175647	−	7.95366i	0.000647883	−	0.293375i
$736$	−13.2449	+	3.02306i	−0.488213	+	0.111431i
$737$	−46.4613	−	6.29361i	−1.71142	−	0.231828i
$738$	18.0681	+	9.82599i	0.665094	+	0.361700i
$739$	−7.57873	−	2.84435i	−0.278788	−	0.104631i	0.208064	−	0.978115i	$-0.433284\pi$
$739$	−7.57873	−	2.84435i	−0.278788	−	0.104631i	−0.486853	+	0.873484i	$0.661855\pi$
$740$	2.18443	+	0.498581i	0.0803011	+	0.0183282i
$741$	−26.8220	−	6.18429i	−0.985330	−	0.227186i
$742$	16.8400	+	21.1166i	0.618214	+	0.775216i
$743$	3.79736	−	3.97172i	0.139311	−	0.145708i	−0.649458	−	0.760397i	$-0.725004\pi$
$743$	3.79736	−	3.97172i	0.139311	−	0.145708i	0.788770	+	0.614689i	$0.210718\pi$
$744$	−51.4568	−	9.45546i	−1.88650	−	0.346654i
$745$	7.30178	−	3.92926i	0.267517	−	0.143957i
$746$	−2.48864	+	1.33919i	−0.0911155	+	0.0490314i
$747$	8.29806	−	7.86390i	0.303610	−	0.287725i
$748$	13.4184	−	14.0346i	0.490626	−	0.513154i
$749$	−0.727997	−	0.912879i	−0.0266004	−	0.0333559i
$750$	3.95154	−	17.1383i	0.144290	−	0.625802i
$751$	−36.4166	−	8.31184i	−1.32886	−	0.303303i	−0.501588	−	0.865107i	$-0.667251\pi$
$751$	−36.4166	−	8.31184i	−1.32886	−	0.303303i	−0.827271	+	0.561803i	$0.810108\pi$
$752$	1.84996	+	0.694302i	0.0674612	+	0.0253186i
$753$	16.3181	−	2.17374i	0.594663	−	0.0792157i
$754$	−0.605522	−	0.0820235i	−0.0220518	−	0.00298712i
$755$	−0.845135	+	0.192897i	−0.0307576	+	0.00702023i
$756$	19.8843	−	6.31547i	0.723185	−	0.229691i
$757$	−6.50264	+	0.292034i	−0.236342	+	0.0106142i	−0.162721	−	0.986672i	$-0.552027\pi$
$757$	−6.50264	+	0.292034i	−0.236342	+	0.0106142i	−0.0736214	+	0.997286i	$0.523456\pi$
$758$	−10.3189	+	21.4273i	−0.374798	+	0.778276i
$759$	16.2139	+	4.51331i	0.588528	+	0.163823i
$760$	−2.11344	−	15.6021i	−0.0766627	−	0.565947i
$761$	−6.11857	+	7.67245i	−0.221798	+	0.278126i	−0.880264	−	0.474485i	$-0.842634\pi$
$761$	−6.11857	+	7.67245i	−0.221798	+	0.278126i	0.658466	+	0.752611i	$0.271206\pi$
$762$	9.00376	+	11.3416i	0.326172	+	0.410865i
$763$	−0.162229	−	0.107086i	−0.00587308	−	0.00387679i
$764$	−3.87047	+	5.32724i	−0.140029	+	0.192733i
$765$	−1.70603	+	18.0616i	−0.0616816	+	0.653020i
$766$	−0.0140802	−	0.0510184i	−0.000508738	−	0.00184337i
$767$	−21.3969	−	6.95228i	−0.772598	−	0.251032i
$768$	26.6016	−	2.33498i	0.959903	−	0.0842563i
$769$	23.0563	+	38.5897i	0.831430	+	1.39158i	0.918518	+	0.395379i	$0.129387\pi$
$769$	23.0563	+	38.5897i	0.831430	+	1.39158i	−0.0870880	+	0.996201i	$0.527756\pi$
$770$	−11.7410	+	13.4386i	−0.423115	+	0.484294i
$771$	−27.1360	−	28.5078i	−0.977280	−	1.02668i
$772$	0.561557	−	6.23941i	0.0202109	−	0.224561i
$773$	−28.4300	+	2.55874i	−1.02255	+	0.0920316i	−0.588204	−	0.808712i	$-0.700165\pi$
$773$	−28.4300	+	2.55874i	−1.02255	+	0.0920316i	−0.434350	+	0.900744i	$0.643022\pi$
$774$	−5.72989	+	3.05083i	−0.205957	+	0.109660i
$775$	−12.8826	+	21.5618i	−0.462756	+	0.774524i
$776$	7.97474	+	24.5437i	0.286276	+	0.881068i
$777$	−5.77162	−	0.271976i	−0.207056	−	0.00975710i
$778$	6.35258	+	0.285295i	0.227751	+	0.0102283i
$779$	13.2468	−	24.6166i	0.474615	−	0.881983i
$780$	13.5354	+	9.87980i	0.484646	+	0.353754i
$781$	−0.199432	+	34.5852i	−0.00713624	+	1.23755i
$782$			7.39639i			0.264494i
$783$	0.592559	−	0.559077i	0.0211763	−	0.0199798i
$784$	0.0263776	−	0.587344i	0.000942059	−	0.0209766i
$785$	−24.6518	+	16.2725i	−0.879861	+	0.580791i
$786$	−5.57551	+	17.0316i	−0.198872	+	0.607497i
$787$	40.7091	+	24.3226i	1.45112	+	0.867006i	0.999680	−	0.0252943i	$-0.00805229\pi$
$787$	40.7091	+	24.3226i	1.45112	+	0.867006i	0.451443	+	0.892300i	$0.350909\pi$
$788$	29.8747	−	5.42145i	1.06424	−	0.193131i
$789$	16.2587	−	27.0765i	0.578825	−	0.963949i
$790$	−14.9503	−	1.34555i	−0.531908	−	0.0478726i
$791$	1.91349	−	10.5442i	0.0680360	−	0.374909i
$792$	−31.4225	−	13.5951i	−1.11655	−	0.483080i
$793$	35.0729	−	20.9551i	1.24547	−	0.744136i
$794$	7.53595	−	6.58396i	0.267441	−	0.233656i
$795$	−16.9490	−	23.4370i	−0.601121	−	0.831226i
$796$	3.98812	−	1.10065i	0.141355	−	0.0390115i
$797$	−21.1457	−	9.03809i	−0.749018	−	0.320146i	−0.0155585	−	0.999879i	$-0.504953\pi$
$797$	−21.1457	−	9.03809i	−0.749018	−	0.320146i	−0.733459	+	0.679733i	$0.762095\pi$
$798$	4.86880	+	15.0980i	0.172354	+	0.534463i
$799$	19.1277	−	28.9772i	0.676689	−	1.02514i
$800$	3.52973	−	12.7897i	0.124795	−	0.452184i
$801$	7.69689	−	20.2362i	0.271956	−	0.715009i
$802$	−23.3478	+	3.16267i	−0.824439	+	0.111678i
$803$	5.75475	−	2.15979i	0.203081	−	0.0762175i
$804$	22.3712	−	11.9748i	0.788970	−	0.422319i
$805$	0.545152	+	12.1387i	0.0192141	+	0.427835i
$806$	24.8873	+	34.2544i	0.876616	+	1.20656i
$807$	−5.53598	+	12.8733i	−0.194876	+	0.453162i
$808$	−6.92904	+	51.1522i	−0.243763	+	1.79953i
$809$	17.2337	+	18.0251i	0.605906	+	0.633728i	0.952591	−	0.304253i	$-0.0984069\pi$
$809$	17.2337	+	18.0251i	0.605906	+	0.633728i	−0.346685	+	0.937982i	$0.612693\pi$
$810$	12.0771	−	3.21852i	0.424345	−	0.113087i
$811$	−1.05463	+	4.62066i	−0.0370332	+	0.162253i	−0.990063	−	0.140623i	$-0.955090\pi$
$811$	−1.05463	+	4.62066i	−0.0370332	+	0.162253i	0.953030	+	0.302876i	$0.0979467\pi$
$812$	−0.247411	−	0.578848i	−0.00868244	−	0.0203136i
$813$	0.429220	+	10.0526i	0.0150534	+	0.352560i
$814$	2.67777	+	2.56021i	0.0938557	+	0.0897352i
$815$	−8.68036	+	4.18024i	−0.304060	+	0.146427i
$816$	−0.182949	+	1.32852i	−0.00640449	+	0.0465075i
$817$	4.18101	+	7.76962i	0.146275	+	0.271825i
$818$	1.34233	+	2.78737i	0.0469334	+	0.0974581i
$819$	−38.8514	−	18.9217i	−1.35758	−	0.661178i
$820$	−13.3058	+	10.6110i	−0.464657	+	0.370552i
$821$	−37.9826	+	16.2345i	−1.32560	+	0.566589i	−0.935221	−	0.354065i	$-0.884799\pi$
$821$	−37.9826	+	16.2345i	−1.32560	+	0.566589i	−0.390380	+	0.920654i	$0.627656\pi$
$822$	−10.4011	−	11.9582i	−0.362779	−	0.417089i
$823$	6.29853	−	16.7824i	0.219553	−	0.584997i	−0.779594	−	0.626285i	$-0.784575\pi$
$823$	6.29853	−	16.7824i	0.219553	−	0.584997i	0.999147	+	0.0412880i	$0.0131461\pi$
$824$	10.4055	−	9.94864i	0.362492	−	0.346577i
$825$	−11.3851	+	11.8553i	−0.396378	+	0.412750i
$826$	2.88522	+	12.6410i	0.100390	+	0.439836i
$827$	−17.0734	+	12.4045i	−0.593700	+	0.431348i	−0.843637	−	0.536914i	$-0.819590\pi$
$827$	−17.0734	+	12.4045i	−0.593700	+	0.431348i	0.249937	+	0.968262i	$0.419590\pi$
$828$	−8.54184	+	3.16284i	−0.296849	+	0.109916i
$829$	−33.9057	−	16.3281i	−1.17759	−	0.567100i	−0.260385	−	0.965505i	$-0.583850\pi$
$829$	−33.9057	−	16.3281i	−1.17759	−	0.567100i	−0.917210	+	0.398405i	$0.869564\pi$
$830$	−1.85953	−	4.95469i	−0.0645452	−	0.171980i
$831$	−6.38474	+	11.8023i	−0.221484	+	0.409417i
$832$	−15.9761	−	12.7405i	−0.553873	−	0.441699i
$833$	−9.95875	−	2.74844i	−0.345050	−	0.0952278i
$834$	−17.2083	+	6.41506i	−0.595875	+	0.222135i
$835$	31.8548	+	23.1439i	1.10238	+	0.800928i
$836$	−7.14592	+	16.7187i	−0.247147	+	0.578229i
$837$	−56.3751	−	2.90617i	−1.94861	−	0.100452i
$838$	−0.857324	+	2.63857i	−0.0296158	+	0.0911479i
$839$	31.2682	+	35.7893i	1.07950	+	1.23558i	0.970387	+	0.241554i	$0.0776570\pi$
$839$	31.2682	+	35.7893i	1.07950	+	1.23558i	0.109109	+	0.994030i	$0.465200\pi$
$840$	2.27009	−	24.6138i	0.0783257	−	0.849258i
$841$	21.8206	+	19.0641i	0.752433	+	0.657381i
$842$	11.6988	+	2.12301i	0.403166	+	0.0731639i
$843$	6.27255	+	5.50464i	0.216038	+	0.189590i
$844$	−2.46934	−	27.4367i	−0.0849983	−	0.944409i
$845$	−2.39208	−	13.1815i	−0.0822901	−	0.453456i
$846$	−23.2968	−	5.42572i	−0.800962	−	0.186540i
$847$	17.4104	−	5.65699i	0.598230	−	0.194377i
$848$	−1.17783	−	1.78433i	−0.0404468	−	0.0612742i
$849$	−15.9743	−	12.7969i	−0.548236	−	0.439188i
$850$	−6.36093	−	3.42296i	−0.218178	−	0.117407i
$851$	2.52262			0.0864741
$852$	−10.8809	−	15.2303i	−0.372775	−	0.521781i
$853$	−12.5011			−0.428029			−0.214014	−	0.976830i	$-0.568654\pi$
$853$	−12.5011			−0.428029			−0.214014	+	0.976830i	$0.568654\pi$
$854$	−20.7347	−	11.1578i	−0.709526	−	0.381812i
$855$	−4.44704	−	16.3955i	−0.152086	−	0.560715i
$856$	−0.571281	−	0.865454i	−0.0195260	−	0.0295806i
$857$	18.2897	−	5.94269i	0.624765	−	0.202998i	0.0205100	−	0.999790i	$-0.493471\pi$
$857$	18.2897	−	5.94269i	0.624765	−	0.202998i	0.604255	+	0.796791i	$0.293471\pi$
$858$	10.8336	+	25.5023i	0.369855	+	0.870633i
$859$	0.665740	+	3.66853i	0.0227148	+	0.125169i	0.993295	−	0.115611i	$-0.0368826\pi$
$859$	0.665740	+	3.66853i	0.0227148	+	0.125169i	−0.970580	+	0.240780i	$0.922597\pi$
$860$	−0.481499	−	5.34990i	−0.0164190	−	0.182430i
$861$	28.9482	−	32.9865i	0.986551	−	1.12418i
$862$	−12.5353	−	2.27483i	−0.426955	−	0.0774809i
$863$	−41.6731	−	36.4087i	−1.41857	−	1.23937i	−0.930365	−	0.366635i	$-0.880510\pi$
$863$	−41.6731	−	36.4087i	−1.41857	−	1.23937i	−0.488202	−	0.872730i	$-0.662347\pi$
$864$	29.1147	−	6.44260i	0.990501	−	0.219182i
$865$	24.2866	+	27.7983i	0.825769	+	0.945169i
$866$	−4.64262	+	14.2885i	−0.157762	+	0.485543i
$867$	−5.50064	−	2.07829i	−0.186812	−	0.0705826i
$868$	−17.1435	+	40.1092i	−0.581888	+	1.36140i
$869$	35.8930	+	26.0778i	1.21759	+	0.884628i
$870$	−0.131731	−	0.353365i	−0.00446609	−	0.0119802i
$871$	−50.6646	−	13.9825i	−1.71670	−	0.473780i
$872$	−0.134976	−	0.107640i	−0.00457086	−	0.00364514i
$873$	11.9705	+	25.1404i	0.405139	+	0.850873i
$874$	−2.43357	−	6.48424i	−0.0823169	−	0.219333i
$875$	−33.8137	−	16.2838i	−1.14311	−	0.550494i
$876$	−1.83874	+	2.77223i	−0.0621252	+	0.0936650i
$877$	−32.9040	+	23.9061i	−1.11109	+	0.807253i	−0.982835	−	0.184488i	$-0.940937\pi$
$877$	−32.9040	+	23.9061i	−1.11109	+	0.807253i	−0.128254	+	0.991741i	$0.540937\pi$
$878$	−5.68510	−	24.9080i	−0.191863	−	0.840605i
$879$	11.2520	+	10.8057i	0.379521	+	0.364467i
$880$	1.02102	−	0.976192i	0.0344185	−	0.0329074i
$881$	3.99770	−	10.6518i	0.134686	−	0.358869i	−0.851536	−	0.524296i	$-0.824329\pi$
$881$	3.99770	−	10.6518i	0.134686	−	0.358869i	0.986222	+	0.165427i	$0.0529001\pi$
$882$	0.606680	+	7.09146i	0.0204280	+	0.238782i
$883$	42.6542	−	18.2313i	1.43543	−	0.613531i	0.472024	−	0.881586i	$-0.343524\pi$
$883$	42.6542	−	18.2313i	1.43543	−	0.613531i	0.963404	+	0.268054i	$0.0863807\pi$
$884$	17.0177	−	13.5712i	0.572368	−	0.456448i
$885$	−2.44909	−	13.6673i	−0.0823253	−	0.459422i
$886$	−7.66816	−	15.9231i	−0.257617	−	0.534947i
$887$	18.2202	+	33.8587i	0.611773	+	1.13686i	0.978444	+	0.206514i	$0.0662118\pi$
$887$	18.2202	+	33.8587i	0.611773	+	1.13686i	−0.366671	+	0.930351i	$0.619503\pi$
$888$	−5.08369	−	0.700069i	−0.170597	−	0.0234928i
$889$	27.8405	−	13.4073i	0.933741	−	0.449666i
$890$	−7.24402	−	6.92599i	−0.242820	−	0.232160i
$891$	−35.5217	−	10.1419i	−1.19002	−	0.339766i
$892$	10.5073	+	24.5831i	0.351811	+	0.823103i
$893$	−7.23465	+	31.6971i	−0.242098	+	1.06070i
$894$	−6.20154	+	4.07396i	−0.207410	+	0.136254i
$895$	1.57396	+	1.64624i	0.0526118	+	0.0550277i
$896$	3.24236	−	23.9360i	0.108320	−	0.799647i
$897$	17.3321	+	7.45342i	0.578703	+	0.248862i
$898$	−11.0121	−	15.1569i	−0.367479	−	0.505792i
$899$	0.0764169	+	1.70155i	0.00254865	+	0.0567500i
$900$	1.23301	−	8.80975i	0.0411003	−	0.293658i
$901$	−35.1731	+	13.2007i	−1.17179	+	0.439779i
$902$	−27.8850	+	3.77728i	−0.928469	+	0.125770i
$903$	3.65563	+	13.3609i	0.121652	+	0.444622i
$904$	2.53205	−	9.17466i	0.0842146	−	0.305145i
$905$	−3.85198	+	5.83551i	−0.128044	+	0.193979i
$906$	0.738280	−	0.238081i	0.0245277	−	0.00790970i
$907$	14.2799	+	6.10352i	0.474157	+	0.202664i	0.616816	−	0.787108i	$-0.288422\pi$
$907$	14.2799	+	6.10352i	0.474157	+	0.202664i	−0.142659	+	0.989772i	$0.545565\pi$
$908$	22.7275	−	6.27240i	0.754240	−	0.208157i
$909$	−0.245993	+	55.6952i	−0.00815908	+	1.84729i
$910$	−15.0647	+	13.1616i	−0.499388	+	0.436302i
$911$	17.5822	−	10.5049i	0.582523	−	0.348041i	−0.191214	−	0.981548i	$-0.561242\pi$
$911$	17.5822	−	10.5049i	0.582523	−	0.348041i	0.773737	+	0.633507i	$0.218385\pi$
$912$	−0.276726	−	1.22488i	−0.00916330	−	0.0405597i
$913$	−2.79292	+	15.3903i	−0.0924322	+	0.509343i
$914$	15.9992	+	1.43995i	0.529205	+	0.0476293i
$915$	21.6172	+	12.9805i	0.714642	+	0.429123i
$916$	30.3198	−	5.50224i	1.00180	−	0.181799i
$917$	32.8280	+	19.6138i	1.08407	+	0.647705i
$918$	0.107554	−	16.2341i	0.00354981	−	0.535804i
$919$	10.0103	−	6.60776i	0.330210	−	0.217970i	−0.374904	−	0.927064i	$-0.622324\pi$
$919$	10.0103	−	6.60776i	0.330210	−	0.217970i	0.705114	+	0.709094i	$0.250896\pi$
$920$	−0.484169	+	10.7809i	−0.0159626	+	0.355434i
$921$	−6.34967	−	13.2601i	−0.209229	−	0.436934i
$922$			15.5748i			0.512928i
$923$	−5.42575	+	38.3890i	−0.178591	+	1.26359i
$924$	−16.8291	+	23.0561i	−0.553638	+	0.758489i
$925$	−1.16744	+	2.16946i	−0.0383851	+	0.0713315i
$926$	−6.72003	−	0.301797i	−0.220834	−	0.00991767i
$927$	9.73822	−	12.1013i	0.319845	−	0.397459i
$928$	−0.278032	−	0.855694i	−0.00912685	−	0.0280895i
$929$	−22.7333	+	38.0492i	−0.745856	+	1.24835i	0.216426	+	0.976299i	$0.430560\pi$
$929$	−22.7333	+	38.0492i	−0.745856	+	1.24835i	−0.962282	+	0.272053i	$0.912297\pi$
$930$	−11.3899	+	23.5183i	−0.373489	+	0.771197i
$931$	9.63489	−	0.867156i	0.315771	−	0.0284199i
$932$	−2.30436	+	25.6035i	−0.0754818	+	0.838672i
$933$	34.4840	−	32.8246i	1.12896	−	1.07463i
$934$	11.0215	−	12.6152i	0.360636	−	0.412781i
$935$	−12.7311	−	21.3082i	−0.416350	−	0.696853i
$936$	−32.8601	−	19.8304i	−1.07406	−	0.648178i
$937$	−49.5570	−	16.1021i	−1.61896	−	0.526031i	−0.647262	−	0.762267i	$-0.724086\pi$
$937$	−49.5570	−	16.1021i	−1.61896	−	0.526031i	−0.971696	+	0.236236i	$0.924086\pi$
$938$	8.05842	+	29.1990i	0.263117	+	0.953382i
$939$	−44.0882	+	26.2095i	−1.43876	+	0.855316i
$940$	11.6343	−	16.0132i	0.379468	−	0.522293i
$941$	45.7799	+	30.2190i	1.49238	+	0.985112i	0.992921	+	0.118775i	$0.0378966\pi$
$941$	45.7799	+	30.2190i	1.49238	+	0.985112i	0.499460	+	0.866337i	$0.333532\pi$
$942$	20.7020	−	16.4346i	0.674507	−	0.535468i
$943$	−11.9465	+	14.9805i	−0.389032	+	0.487831i
$944$	−0.137774	−	1.01709i	−0.00448418	−	0.0331035i
$945$	−1.02002	−	26.6508i	−0.0331812	−	0.866951i
$946$	3.85357	−	8.00202i	0.125290	−	0.260168i
$947$	−33.7808	+	1.51710i	−1.09773	+	0.0492991i	−0.586351	−	0.810057i	$-0.699436\pi$
$947$	−33.7808	+	1.51710i	−1.09773	+	0.0492991i	−0.511378	+	0.859356i	$0.670865\pi$
$948$	−24.0109	−	0.0530251i	−0.779838	−	0.00172218i
$949$	6.71768	−	1.53327i	0.218065	−	0.0497719i
$950$	6.70271	+	0.907943i	0.217465	+	0.0294576i
$951$	−1.72042	−	12.9150i	−0.0557883	−	0.418797i
$952$	−30.0594	−	11.2815i	−0.974229	−	0.365634i
$953$	32.7584	+	7.47690i	1.06115	+	0.242201i	0.717257	−	0.696808i	$-0.245397\pi$
$953$	32.7584	+	7.47690i	1.06115	+	0.242201i	0.343893	+	0.939009i	$0.388254\pi$
$954$	16.9426	+	19.5661i	0.548538	+	0.633477i
$955$	5.24835	+	6.58122i	0.169833	+	0.212963i
$956$	12.0576	−	12.6112i	0.389970	−	0.407877i
$957$	−0.201446	+	1.09627i	−0.00651183	+	0.0354375i
$958$	−0.631056	+	0.339586i	−0.0203885	+	0.0109715i
$959$	−29.7808	+	16.0258i	−0.961674	+	0.517499i
$960$	2.27924	−	12.4036i	0.0735620	−	0.400326i
$961$	60.1377	−	62.8991i	1.93993	−	2.02900i
$962$	2.58936	+	3.24695i	0.0834842	+	0.104686i
$963$	−0.732435	−	0.845850i	−0.0236024	−	0.0272571i
$964$	21.5774	+	4.92490i	0.694961	+	0.158620i
$965$	−7.49772	−	2.81394i	−0.241360	−	0.0905839i
$966$	−1.43576	−	10.7781i	−0.0461949	−	0.346780i
$967$	5.74319	+	0.777968i	0.184689	+	0.0250178i	0.225993	−	0.974129i	$-0.427437\pi$
$967$	5.74319	+	0.777968i	0.184689	+	0.0250178i	−0.0413049	+	0.999147i	$0.513151\pi$
$968$	15.8509	−	3.61788i	0.509469	−	0.116283i
$969$	−22.0656	−	0.0487291i	−0.708848	−	0.00156540i
$970$	12.8766	−	0.578291i	0.413444	−	0.0185678i
$971$	17.6949	−	36.7437i	0.567855	−	1.17916i	−0.397350	−	0.917667i	$-0.630070\pi$
$971$	17.6949	−	36.7437i	0.567855	−	1.17916i	0.965205	−	0.261495i	$-0.0842156\pi$
$972$	18.7942	−	6.81778i	0.602823	−	0.218680i
$973$	5.26044	+	38.8342i	0.168642	+	1.24497i
$974$	−1.84809	+	2.31743i	−0.0592166	+	0.0742553i
$975$	−14.4311	+	11.4564i	−0.462165	+	0.366897i
$976$	1.55555	+	1.02681i	0.0497921	+	0.0328675i
$977$	−4.26039	+	5.86392i	−0.136302	+	0.187604i	−0.871712	−	0.490019i	$-0.836990\pi$
$977$	−4.26039	+	5.86392i	−0.136302	+	0.187604i	0.735410	+	0.677623i	$0.236990\pi$
$978$	7.41079	−	4.40556i	0.236971	−	0.140874i
$979$	7.88054	+	28.5545i	0.251863	+	0.912606i
$980$	−5.60117	−	1.81993i	−0.178923	−	0.0581356i
$981$	−0.159483	−	0.0962452i	−0.00509191	−	0.00307287i
$982$	−8.50333	−	14.2322i	−0.271352	−	0.454167i
$983$	3.11584	−	3.56636i	0.0993798	−	0.113749i	−0.701231	−	0.712934i	$-0.747366\pi$
$983$	3.11584	−	3.56636i	0.0993798	−	0.113749i	0.800611	+	0.599185i	$0.204509\pi$
$984$	28.2325	−	26.8740i	0.900020	−	0.856711i
$985$	3.47926	−	38.6577i	0.110858	−	1.23174i
$986$	−0.487870	+	0.0439091i	−0.0155370	+	0.00139835i
$987$	−22.2482	+	45.9390i	−0.708167	+	1.46225i
$988$	−10.4538	+	17.4967i	−0.332580	+	0.556646i
$989$	−1.86881	−	5.75161i	−0.0594248	−	0.182891i
$990$	−10.7209	+	13.3224i	−0.340732	+	0.423415i
$991$	−36.5054	−	1.63946i	−1.15963	−	0.0520791i	−0.543281	−	0.839551i	$-0.682818\pi$
$991$	−36.5054	−	1.63946i	−1.15963	−	0.0520791i	−0.616351	+	0.787472i	$0.711390\pi$
$992$	−29.5427	+	54.8995i	−0.937982	+	1.74306i
$993$	32.7857	−	44.9167i	1.04042	−	1.42539i
$994$	20.5964	−	8.66322i	0.653280	−	0.274781i
$995$		−	5.28879i		−	0.167666i
$996$	−3.65608	−	7.63502i	−0.115847	−	0.241925i
$997$	−0.374711	+	8.34358i	−0.0118672	+	0.264244i	0.984284	+	0.176593i	$0.0565075\pi$
$997$	−0.374711	+	8.34358i	−0.0118672	+	0.264244i	−0.996151	+	0.0876512i	$0.972064\pi$
$998$	−11.2649	+	7.43589i	−0.356584	+	0.235379i
$999$	−5.53679	−	0.0366824i	−0.175176	−	0.00116058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.n.a.11.15	yes	528
3.2	odd	2	inner	213.2.n.a.11.8	✓	528
71.13	odd	70	inner	213.2.n.a.155.8	yes	528
213.155	even	70	inner	213.2.n.a.155.15	yes	528

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.n.a.11.8	✓	528	3.2	odd	2	inner
213.2.n.a.11.15	yes	528	1.1	even	1	trivial
213.2.n.a.155.8	yes	528	71.13	odd	70	inner
213.2.n.a.155.15	yes	528	213.155	even	70	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.n (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.745900 + 0.401386i) q^{2} +(1.08290 - 1.35178i) q^{3} +(-0.706538 - 1.07036i) q^{4} +(-1.55927 + 0.506636i) q^{5} +(1.35032 - 0.573633i) q^{6} +(-0.558996 - 3.08032i) q^{7} +(-0.249236 - 2.76924i) q^{8} +(-0.654638 - 2.92770i) q^{9} +(-1.36641 - 0.247967i) q^{10} +(3.09104 + 2.70056i) q^{11} +(-2.21201 - 0.204010i) q^{12} +(3.02732 + 3.46504i) q^{13} +(0.819443 - 2.52199i) q^{14} +(-1.00367 + 2.65643i) q^{15} +(-0.0825005 + 0.193019i) q^{16} +(2.98406 + 2.16805i) q^{17} +(0.686844 - 2.44654i) q^{18} +(-3.32940 - 0.918855i) q^{19} +(1.64396 + 1.31102i) q^{20} +(-4.76927 - 2.58005i) q^{21} +(1.22164 + 3.25504i) q^{22} +(2.13292 + 1.02716i) q^{23} +(-4.01331 - 2.66190i) q^{24} +(-1.87045 + 1.35896i) q^{25} +(0.867256 + 3.79970i) q^{26} +(-4.66653 - 2.28549i) q^{27} +(-2.90210 + 2.77469i) q^{28} +(-0.0550900 + 0.146787i) q^{29} +(-1.81489 + 1.57857i) q^{30} +(9.98956 - 4.26974i) q^{31} +(-4.48667 + 3.57800i) q^{32} +(6.99786 - 1.25397i) q^{33} +(1.35559 + 2.81491i) q^{34} +(2.43223 + 4.51984i) q^{35} +(-2.67117 + 2.76923i) q^{36} +(0.960054 - 0.462338i) q^{37} +(-2.11458 - 2.02175i) q^{38} +(7.96229 - 0.339969i) q^{39} +(1.79162 + 4.19170i) q^{40} +(-1.80102 + 7.89078i) q^{41} +(-2.52180 - 3.83878i) q^{42} +(-1.76537 - 1.84643i) q^{43} +(0.706632 - 5.21657i) q^{44} +(2.50404 + 4.23341i) q^{45} +(1.17866 + 1.62228i) q^{46} +(-0.422326 - 9.40382i) q^{47} +(0.171580 + 0.320544i) q^{48} +(-2.62228 + 0.984157i) q^{49} +(-1.94064 + 0.262878i) q^{50} +(6.16219 - 1.68602i) q^{51} +(1.56993 - 5.68850i) q^{52} +(-5.61107 + 8.50041i) q^{53} +(-2.56340 - 3.57783i) q^{54} +(-6.18795 - 2.64486i) q^{55} +(-8.39082 + 2.31572i) q^{56} +(-4.84751 + 3.50559i) q^{57} +(-0.100010 + 0.0873758i) q^{58} +(-4.19746 + 2.50787i) q^{59} +(3.55247 - 0.802578i) q^{60} +(1.58548 - 8.73672i) q^{61} +(9.16503 + 0.824867i) q^{62} +(-8.65234 + 3.65307i) q^{63} +(-4.36968 + 0.792981i) q^{64} +(-6.47591 - 3.86918i) q^{65} +(5.72303 + 1.87351i) q^{66} +(-9.53314 + 6.29277i) q^{67} +(0.212237 - 4.72583i) q^{68} +(3.69825 - 1.77093i) q^{69} +4.34761i q^{70} +(5.50721 + 6.37736i) q^{71} +(-7.94434 + 2.54254i) q^{72} +(0.709630 - 1.31871i) q^{73} +(0.901680 + 0.0404945i) q^{74} +(-0.188496 + 4.00008i) q^{75} +(1.36884 + 4.21286i) q^{76} +(6.59071 - 11.0310i) q^{77} +(6.07553 + 2.94237i) q^{78} +(10.7654 - 0.968908i) q^{79} +(0.0308495 - 0.342766i) q^{80} +(-8.14290 + 3.83317i) q^{81} +(-4.51062 + 5.16283i) q^{82} +(1.95455 + 3.27136i) q^{83} +(0.608088 + 6.92774i) q^{84} +(-5.75136 - 1.86873i) q^{85} +(-0.575657 - 2.08585i) q^{86} +(0.138767 + 0.233426i) q^{87} +(6.70808 - 9.23288i) q^{88} +(6.02297 + 3.97573i) q^{89} +(0.168531 + 4.16278i) q^{90} +(8.98120 - 11.2621i) q^{91} +(-0.407559 - 3.00872i) q^{92} +(5.04597 - 18.1274i) q^{93} +(3.45955 - 7.18382i) q^{94} +(5.65694 - 0.254053i) q^{95} +(-0.0219504 + 9.93963i) q^{96} +(-9.04888 + 2.06535i) q^{97} +(-2.35098 - 0.318462i) q^{98} +(5.88292 - 10.8175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) \) 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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