LMFDB - Embedded newform 669.2.m.b.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(19,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([0, 172])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.m (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [1368] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$1368$
Relative dimension:	$19$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	669.19
Dual form			669.2.m.b.493.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.261508 - 2.04215i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(-2.16654 + 0.564122i) q^{4} +(-3.76343 + 0.536159i) q^{5} +(1.52610 + 1.38195i) q^{6} +(0.345717 - 0.467440i) q^{7} +(0.183294 + 0.456145i) q^{8} +(0.155037 - 0.987909i) q^{9} +(2.07909 + 7.54530i) q^{10} +(-1.67175 + 0.537957i) q^{11} +(1.27978 - 1.83692i) q^{12} +(-0.184333 + 0.0651289i) q^{13} +(-1.04499 - 0.583768i) q^{14} +(2.51151 - 2.85363i) q^{15} +(-3.02538 + 1.69008i) q^{16} +(0.499058 - 2.31564i) q^{17} +(-2.05800 - 0.0582625i) q^{18} +(5.22206 + 5.60528i) q^{19} +(7.85115 - 3.28464i) q^{20} +(0.0411032 + 0.579941i) q^{21} +(1.53577 + 3.27328i) q^{22} +(5.51101 + 7.02640i) q^{23} +(-0.435782 - 0.227507i) q^{24} +(9.07490 - 2.63929i) q^{25} +(0.181208 + 0.359404i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-0.485315 + 1.20775i) q^{28} +(-5.05652 - 3.01559i) q^{29} +(-6.48433 - 4.38264i) q^{30} +(0.298219 - 3.00066i) q^{31} +(4.82719 + 6.52680i) q^{32} +(0.920773 - 1.49543i) q^{33} +(-4.85940 - 0.413596i) q^{34} +(-1.05046 + 1.94454i) q^{35} +(0.221409 + 2.22780i) q^{36} +(4.58990 - 4.15635i) q^{37} +(10.0812 - 12.1301i) q^{38} +(0.0977501 - 0.169308i) q^{39} +(-0.934382 - 1.61840i) q^{40} +(8.53704 + 1.46382i) q^{41} +(1.17358 - 0.235598i) q^{42} +(0.494568 + 2.01598i) q^{43} +(3.31842 - 2.10857i) q^{44} +(-0.0537935 + 3.80105i) q^{45} +(12.9078 - 13.0918i) q^{46} +(2.65915 - 2.85429i) q^{47} +(1.20060 - 3.25082i) q^{48} +(1.95078 + 6.36996i) q^{49} +(-7.76298 - 17.8421i) q^{50} +(1.12588 + 2.08414i) q^{51} +(0.362623 - 0.245090i) q^{52} +(-2.60422 + 0.147570i) q^{53} +(1.60184 - 1.29340i) q^{54} +(6.00308 - 2.92089i) q^{55} +(0.276588 + 0.0720180i) q^{56} +(-7.61184 - 0.865441i) q^{57} +(-4.83597 + 11.1148i) q^{58} +(-10.9346 + 0.930672i) q^{59} +(-3.83148 + 7.59929i) q^{60} +(-1.25815 + 6.76166i) q^{61} +(-6.20579 + 0.175687i) q^{62} +(-0.408189 - 0.414007i) q^{63} +(7.06257 - 6.76893i) q^{64} +(0.658805 - 0.343940i) q^{65} +(-3.29469 - 1.48929i) q^{66} +(-2.97202 + 10.7859i) q^{67} +(0.225075 + 5.29844i) q^{68} +(-8.75513 - 1.75761i) q^{69} +(4.24575 + 1.63669i) q^{70} +(-3.17672 + 6.77077i) q^{71} +(0.479047 - 0.110359i) q^{72} +(5.84379 + 2.84338i) q^{73} +(-9.68819 - 8.28636i) q^{74} +(-5.18093 + 7.90427i) q^{75} +(-14.4758 - 9.19815i) q^{76} +(-0.326488 + 0.967422i) q^{77} +(-0.371316 - 0.155345i) q^{78} +(-3.82276 - 10.3508i) q^{79} +(10.4797 - 7.98258i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(0.756846 - 17.8167i) q^{82} +(-2.02345 + 8.24809i) q^{83} +(-0.416209 - 1.23327i) q^{84} +(-0.636622 + 8.98233i) q^{85} +(3.98761 - 1.53718i) q^{86} +(5.80277 - 0.994986i) q^{87} +(-0.551808 - 0.663955i) q^{88} +(1.10070 + 0.156812i) q^{89} +(7.77640 - 0.884151i) q^{90} +(-0.0332831 + 0.108681i) q^{91} +(-15.9035 - 12.1141i) q^{92} +(1.72375 + 2.47418i) q^{93} +(-6.52428 - 4.68397i) q^{94} +(-22.6582 - 18.2952i) q^{95} +(-7.91073 - 1.82241i) q^{96} +(-7.25962 + 9.25584i) q^{97} +(12.4983 - 5.64958i) q^{98} +(0.272271 + 1.73494i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{86}{111}\right)$

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 $

$2$	−0.261508	−	2.04215i	−0.184914	−	1.44402i	−0.772581	−	0.634917i	$-0.781034\pi$
$2$	−0.261508	−	2.04215i	−0.184914	−	1.44402i	0.587667	−	0.809103i	$-0.300047\pi$
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$4$	−2.16654	+	0.564122i	−1.08327	+	0.282061i
$5$	−3.76343	+	0.536159i	−1.68306	+	0.239778i	−0.915822	−	0.401585i	$-0.868459\pi$
$5$	−3.76343	+	0.536159i	−1.68306	+	0.239778i	−0.767237	+	0.641363i	$0.778369\pi$
$6$	1.52610	+	1.38195i	0.623029	+	0.564179i
$7$	0.345717	−	0.467440i	0.130669	−	0.176676i	−0.733795	−	0.679371i	$-0.762253\pi$
$7$	0.345717	−	0.467440i	0.130669	−	0.176676i	0.864464	+	0.502695i	$0.167658\pi$
$8$	0.183294	+	0.456145i	0.0648043	+	0.161272i
$9$	0.155037	−	0.987909i	0.0516789	−	0.329303i
$10$	2.07909	+	7.54530i	0.657465	+	2.38603i
$11$	−1.67175	+	0.537957i	−0.504051	+	0.162200i	−0.547419	−	0.836859i	$-0.684389\pi$
$11$	−1.67175	+	0.537957i	−0.504051	+	0.162200i	0.0433680	+	0.999059i	$0.486191\pi$
$12$	1.27978	−	1.83692i	0.369440	−	0.530273i
$13$	−0.184333	+	0.0651289i	−0.0511247	+	0.0180635i	−0.358580	−	0.933499i	$-0.616739\pi$
$13$	−0.184333	+	0.0651289i	−0.0511247	+	0.0180635i	0.307455	+	0.951563i	$0.400523\pi$
$14$	−1.04499	−	0.583768i	−0.279286	−	0.156018i
$15$	2.51151	−	2.85363i	0.648470	−	0.736805i
$16$	−3.02538	+	1.69008i	−0.756344	+	0.422519i
$17$	0.499058	−	2.31564i	0.121039	−	0.561625i	−0.875834	−	0.482612i	$-0.839688\pi$
$17$	0.499058	−	2.31564i	0.121039	−	0.561625i	0.996874	−	0.0790128i	$-0.0251768\pi$
$18$	−2.05800	−	0.0582625i	−0.485076	−	0.0137326i
$19$	5.22206	+	5.60528i	1.19802	+	1.28594i	0.948210	+	0.317644i	$0.102892\pi$
$19$	5.22206	+	5.60528i	1.19802	+	1.28594i	0.249814	+	0.968294i	$0.419631\pi$
$20$	7.85115	−	3.28464i	1.75557	−	0.734469i
$21$	0.0411032	+	0.579941i	0.00896946	+	0.126553i
$22$	1.53577	+	3.27328i	0.327426	+	0.697866i
$23$	5.51101	+	7.02640i	1.14912	+	1.46511i	0.861782	+	0.507278i	$0.169348\pi$
$23$	5.51101	+	7.02640i	1.14912	+	1.46511i	0.287343	+	0.957828i	$0.407228\pi$
$24$	−0.435782	−	0.227507i	−0.0889536	−	0.0464397i
$25$	9.07490	−	2.63929i	1.81498	−	0.527857i
$26$	0.181208	+	0.359404i	0.0355378	+	0.0704849i
$27$	0.524307	+	0.851529i	0.100903	+	0.163877i
$28$	−0.485315	+	1.20775i	−0.0917159	+	0.228244i
$29$	−5.05652	−	3.01559i	−0.938973	−	0.559980i	−0.0405815	−	0.999176i	$-0.512921\pi$
$29$	−5.05652	−	3.01559i	−0.938973	−	0.559980i	−0.898391	+	0.439196i	$0.855263\pi$
$30$	−6.48433	−	4.38264i	−1.18387	−	0.800158i
$31$	0.298219	−	3.00066i	0.0535617	−	0.538934i	−0.931137	−	0.364669i	$-0.881182\pi$
$31$	0.298219	−	3.00066i	0.0535617	−	0.538934i	0.984699	−	0.174265i	$-0.0557549\pi$
$32$	4.82719	+	6.52680i	0.853335	+	1.15379i
$33$	0.920773	−	1.49543i	0.160286	−	0.260321i
$34$	−4.85940	−	0.413596i	−0.833379	−	0.0709310i
$35$	−1.05046	+	1.94454i	−0.177560	+	0.328687i
$36$	0.221409	+	2.22780i	0.0369014	+	0.371300i
$37$	4.58990	−	4.15635i	0.754575	−	0.683299i	−0.200490	−	0.979696i	$-0.564253\pi$
$37$	4.58990	−	4.15635i	0.754575	−	0.683299i	0.955065	+	0.296396i	$0.0957849\pi$
$38$	10.0812	−	12.1301i	1.63539	−	1.96776i
$39$	0.0977501	−	0.169308i	0.0156526	−	0.0271110i
$40$	−0.934382	−	1.61840i	−0.147739	−	0.255891i
$41$	8.53704	+	1.46382i	1.33326	+	0.228611i	0.791112	−	0.611671i	$-0.209503\pi$
$41$	8.53704	+	1.46382i	1.33326	+	0.228611i	0.542150	+	0.840282i	$0.317611\pi$
$42$	1.17358	−	0.235598i	0.181087	−	0.0363536i
$43$	0.494568	+	2.01598i	0.0754210	+	0.307435i	0.996670	−	0.0815380i	$-0.0259832\pi$
$43$	0.494568	+	2.01598i	0.0754210	+	0.307435i	−0.921249	+	0.388973i	$0.872830\pi$
$44$	3.31842	−	2.10857i	0.500271	−	0.317879i
$45$	−0.0537935	+	3.80105i	−0.00801906	+	0.566628i
$46$	12.9078	−	13.0918i	1.90315	−	1.93028i
$47$	2.65915	−	2.85429i	0.387877	−	0.416341i	−0.507498	−	0.861653i	$-0.669430\pi$
$47$	2.65915	−	2.85429i	0.387877	−	0.416341i	0.895376	+	0.445312i	$0.146907\pi$
$48$	1.20060	−	3.25082i	0.173291	−	0.469216i
$49$	1.95078	+	6.36996i	0.278683	+	0.909995i
$50$	−7.76298	−	17.8421i	−1.09785	−	2.52326i
$51$	1.12588	+	2.08414i	0.157654	+	0.291838i
$52$	0.362623	−	0.245090i	0.0502867	−	0.0339879i
$53$	−2.60422	+	0.147570i	−0.357718	+	0.0202704i	−0.234519	−	0.972112i	$-0.575351\pi$
$53$	−2.60422	+	0.147570i	−0.357718	+	0.0202704i	−0.123199	+	0.992382i	$0.539315\pi$
$54$	1.60184	−	1.29340i	0.217983	−	0.176009i
$55$	6.00308	−	2.92089i	0.809455	−	0.393853i
$56$	0.276588	+	0.0720180i	0.0369607	+	0.00962382i
$57$	−7.61184	−	0.865441i	−1.00821	−	0.114630i
$58$	−4.83597	+	11.1148i	−0.634993	+	1.45944i
$59$	−10.9346	+	0.930672i	−1.42356	+	0.121163i	−0.771128	−	0.636680i	$-0.780307\pi$
$59$	−10.9346	+	0.930672i	−1.42356	+	0.121163i	−0.652436	+	0.757844i	$0.726253\pi$
$60$	−3.83148	+	7.59929i	−0.494642	+	0.981064i
$61$	−1.25815	+	6.76166i	−0.161090	+	0.865742i	0.802155	+	0.597116i	$0.203687\pi$
$61$	−1.25815	+	6.76166i	−0.161090	+	0.865742i	−0.963244	+	0.268626i	$0.913430\pi$
$62$	−6.20579	+	0.175687i	−0.788136	+	0.0223123i
$63$	−0.408189	−	0.414007i	−0.0514270	−	0.0521600i
$64$	7.06257	−	6.76893i	0.882822	−	0.846116i
$65$	0.658805	−	0.343940i	0.0817147	−	0.0426605i
$66$	−3.29469	−	1.48929i	−0.405548	−	0.183319i
$67$	−2.97202	+	10.7859i	−0.363090	+	1.31770i	0.522263	+	0.852784i	$0.325088\pi$
$67$	−2.97202	+	10.7859i	−0.363090	+	1.31770i	−0.885353	+	0.464919i	$0.846083\pi$
$68$	0.225075	+	5.29844i	0.0272944	+	0.642531i
$69$	−8.75513	−	1.75761i	−1.05399	−	0.211591i
$70$	4.24575	+	1.63669i	0.507464	+	0.195622i
$71$	−3.17672	+	6.77077i	−0.377008	+	0.803542i	0.622769	+	0.782406i	$0.286008\pi$
$71$	−3.17672	+	6.77077i	−0.377008	+	0.803542i	−0.999777	+	0.0211363i	$0.993272\pi$
$72$	0.479047	−	0.110359i	0.0564562	−	0.0130059i
$73$	5.84379	+	2.84338i	0.683963	+	0.332793i	0.746628	−	0.665242i	$-0.231672\pi$
$73$	5.84379	+	2.84338i	0.683963	+	0.332793i	−0.0626646	+	0.998035i	$0.519960\pi$
$74$	−9.68819	−	8.28636i	−1.12623	−	0.963270i
$75$	−5.18093	+	7.90427i	−0.598243	+	0.912707i
$76$	−14.4758	−	9.19815i	−1.66049	−	1.05510i
$77$	−0.326488	+	0.967422i	−0.0372068	+	0.110248i
$78$	−0.371316	−	0.155345i	−0.0420432	−	0.0175894i
$79$	−3.82276	−	10.3508i	−0.430094	−	1.16455i	−0.950525	−	0.310648i	$-0.899454\pi$
$79$	−3.82276	−	10.3508i	−0.430094	−	1.16455i	0.520431	−	0.853904i	$-0.325771\pi$
$80$	10.4797	−	7.98258i	1.17166	−	0.892479i
$81$	−0.951927	−	0.306324i	−0.105770	−	0.0340360i
$82$	0.756846	−	17.8167i	0.0835796	−	1.96753i
$83$	−2.02345	+	8.24809i	−0.222103	+	0.905346i	0.748204	+	0.663468i	$0.230916\pi$
$83$	−2.02345	+	8.24809i	−0.222103	+	0.905346i	−0.970307	+	0.241877i	$0.922237\pi$
$84$	−0.416209	−	1.23327i	−0.0454121	−	0.134561i
$85$	−0.636622	+	8.98233i	−0.0690513	+	0.974270i
$86$	3.98761	−	1.53718i	0.429996	−	0.165758i
$87$	5.80277	−	0.994986i	0.622123	−	0.106674i
$88$	−0.551808	−	0.663955i	−0.0588229	−	0.0707778i
$89$	1.10070	+	0.156812i	0.116674	+	0.0166220i	0.199133	−	0.979972i	$-0.436187\pi$
$89$	1.10070	+	0.156812i	0.116674	+	0.0166220i	−0.0824593	+	0.996594i	$0.526277\pi$
$90$	7.77640	−	0.884151i	0.819705	−	0.0931977i
$91$	−0.0332831	+	0.108681i	−0.00348902	+	0.0113928i
$92$	−15.9035	−	12.1141i	−1.65806	−	1.26298i
$93$	1.72375	+	2.47418i	0.178745	+	0.256560i
$94$	−6.52428	−	4.68397i	−0.672928	−	0.483115i
$95$	−22.6582	−	18.2952i	−2.32468	−	1.87705i
$96$	−7.91073	−	1.82241i	−0.807386	−	0.185999i
$97$	−7.25962	+	9.25584i	−0.737103	+	0.939789i	−0.999684	−	0.0251213i	$-0.992003\pi$
$97$	−7.25962	+	9.25584i	−0.737103	+	0.939789i	0.262581	+	0.964910i	$0.415426\pi$
$98$	12.4983	−	5.64958i	1.26252	−	0.570694i
$99$	0.272271	+	1.73494i	0.0273642	+	0.174368i
$100$	−18.1722	+	10.8375i	−1.81722	+	1.08375i
$101$	8.93254	+	0.506170i	0.888821	+	0.0503658i	0.495072	−	0.868852i	$-0.335142\pi$
$101$	8.93254	+	0.506170i	0.888821	+	0.0503658i	0.393749	+	0.919218i	$0.371178\pi$
$102$	3.96171	−	2.84423i	0.392268	−	0.281621i
$103$	13.1595	+	4.64954i	1.29664	+	0.458133i	0.890211	−	0.455549i	$-0.150557\pi$
$103$	13.1595	+	4.64954i	1.29664	+	0.458133i	0.406431	+	0.913682i	$0.366773\pi$
$104$	−0.0634954	−	0.0721448i	−0.00622623	−	0.00707438i
$105$	−0.465630	−	2.16053i	−0.0454408	−	0.210846i
$106$	0.982386	+	5.27963i	0.0954178	+	0.512803i
$107$	3.85324	+	1.12065i	0.372507	+	0.108338i	0.460212	−	0.887809i	$-0.347773\pi$
$107$	3.85324	+	1.12065i	0.372507	+	0.108338i	−0.0877056	+	0.996146i	$0.527953\pi$
$108$	−1.61630	−	1.54909i	−0.155528	−	0.149062i
$109$	−0.0447399	−	3.16133i	−0.00428531	−	0.302800i	−0.990514	−	0.137412i	$-0.956121\pi$
$109$	−0.0447399	−	3.16133i	−0.00428531	−	0.302800i	0.986229	−	0.165388i	$-0.0528876\pi$
$110$	−7.53475	−	11.4954i	−0.718411	−	1.09604i
$111$	−0.786510	+	6.14197i	−0.0746523	+	0.582970i
$112$	−0.255914	+	1.99847i	−0.0241816	+	0.188838i
$113$	−5.27626	−	8.04970i	−0.496348	−	0.757252i	0.497564	−	0.867427i	$-0.334228\pi$
$113$	−5.27626	−	8.04970i	−0.496348	−	0.757252i	−0.993912	+	0.110175i	$0.964859\pi$
$114$	0.223193	+	15.7709i	0.0209040	+	1.47708i
$115$	−24.5076	−	23.4886i	−2.28534	−	2.19033i
$116$	12.6563	+	3.68088i	1.17511	+	0.341761i
$117$	0.0357631	+	0.192201i	0.00330630	+	0.0177690i
$118$	4.76006	+	22.0868i	0.438199	+	2.03325i
$119$	−0.909890	−	1.03384i	−0.0834095	−	0.0947715i
$120$	1.76202	+	0.622560i	0.160849	+	0.0568317i
$121$	−6.43030	+	4.61650i	−0.584573	+	0.419682i
$122$	14.1374	+	0.801105i	1.27994	+	0.0725286i
$123$	−7.43915	+	4.43653i	−0.670766	+	0.400028i
$124$	1.04663	+	6.66926i	0.0939906	+	0.598917i
$125$	−15.4178	+	6.96930i	−1.37901	+	0.623353i
$126$	−0.738721	+	0.941851i	−0.0658105	+	0.0839068i
$127$	3.25099	+	0.748936i	0.288479	+	0.0664573i	0.366258	−	0.930513i	$-0.380639\pi$
$127$	3.25099	+	0.748936i	0.288479	+	0.0664573i	−0.0777791	+	0.996971i	$0.524783\pi$
$128$	−3.03802	−	2.45303i	−0.268525	−	0.216819i
$129$	−1.68621	−	1.21058i	−0.148462	−	0.106585i
$130$	−0.874661	−	1.25544i	−0.0767129	−	0.110109i
$131$	18.1305	+	13.8104i	1.58407	+	1.20662i	0.848555	+	0.529107i	$0.177473\pi$
$131$	18.1305	+	13.8104i	1.58407	+	1.20662i	0.735513	+	0.677511i	$0.236941\pi$
$132$	−1.15128	+	3.75933i	−0.100206	+	0.327208i
$133$	4.42549	−	0.503163i	0.383738	−	0.0436298i
$134$	22.8036	+	3.24872i	1.96993	+	0.280647i
$135$	−2.42975	−	2.92356i	−0.209120	−	0.251620i
$136$	1.14774	−	0.196800i	0.0984181	−	0.0168755i
$137$	−3.60579	+	1.38999i	−0.308063	+	0.118755i	−0.508785	−	0.860893i	$-0.669905\pi$
$137$	−3.60579	+	1.38999i	−0.308063	+	0.118755i	0.200722	+	0.979648i	$0.435671\pi$
$138$	−1.29977	+	18.3389i	−0.110644	+	1.56111i
$139$	−6.50147	−	19.2646i	−0.551448	−	1.63400i	−0.755578	−	0.655059i	$-0.772644\pi$
$139$	−6.50147	−	19.2646i	−0.551448	−	1.63400i	0.204130	−	0.978944i	$-0.434564\pi$
$140$	1.17890	−	4.80550i	0.0996354	−	0.406139i
$141$	−0.165564	+	3.89752i	−0.0139430	+	0.328230i
$142$	14.6577	+	4.71674i	1.23004	+	0.395820i
$143$	0.273121	−	0.208042i	0.0228395	−	0.0173974i
$144$	1.20060	+	3.25082i	0.100050	+	0.270902i
$145$	20.6467	+	8.63786i	1.71462	+	0.717335i
$146$	4.27843	−	12.6775i	0.354085	−	1.04919i
$147$	−5.62287	−	3.57285i	−0.463767	−	0.294684i
$148$	−7.59950	+	11.5941i	−0.624675	+	0.953032i
$149$	−4.53489	−	3.87871i	−0.371513	−	0.317757i	0.444513	−	0.895772i	$-0.353377\pi$
$149$	−4.53489	−	3.87871i	−0.371513	−	0.317757i	−0.816026	+	0.578016i	$0.803827\pi$
$150$	17.4966	+	8.51323i	1.42859	+	0.695102i
$151$	7.88950	−	1.81752i	0.642039	−	0.147907i	0.109059	−	0.994035i	$-0.465216\pi$
$151$	7.88950	−	1.81752i	0.642039	−	0.147907i	0.532980	+	0.846128i	$0.321072\pi$
$152$	−1.59965	+	3.40943i	−0.129748	+	0.276542i
$153$	−2.21027	−	0.852033i	−0.178690	−	0.0688828i
$154$	2.06100	+	0.413750i	0.166080	+	0.0333410i
$155$	0.486503	+	11.4527i	0.0390769	+	0.919901i
$156$	−0.116269	+	0.421955i	−0.00930894	+	0.0337835i
$157$	−12.3569	−	5.58569i	−0.986191	−	0.445786i	−0.146712	−	0.989179i	$-0.546869\pi$
$157$	−12.3569	−	5.58569i	−0.986191	−	0.445786i	−0.839478	+	0.543393i	$0.817139\pi$
$158$	−20.1382	+	10.5135i	−1.60211	+	0.836406i
$159$	1.88315	−	1.80485i	0.149344	−	0.143134i
$160$	−21.6662	−	21.9750i	−1.71287	−	1.73728i
$161$	5.18967	−	0.146921i	0.409003	−	0.0115790i
$162$	−0.376624	+	2.02409i	−0.0295904	+	0.159027i
$163$	−6.70769	+	13.3039i	−0.525387	+	1.04204i	0.462464	+	0.886638i	$0.346965\pi$
$163$	−6.70769	+	13.3039i	−0.525387	+	1.04204i	−0.987851	+	0.155405i	$0.950332\pi$
$164$	−19.3216	+	1.64451i	−1.50876	+	0.128415i
$165$	−2.66348	+	6.12163i	−0.207352	+	0.476569i
$166$	17.3730	+	1.97525i	1.34841	+	0.153309i
$167$	13.6589	+	3.55651i	1.05696	+	0.275211i	0.739567	−	0.673082i	$-0.235030\pi$
$167$	13.6589	+	3.55651i	1.05696	+	0.275211i	0.317394	+	0.948294i	$0.397192\pi$
$168$	−0.257003	+	0.125049i	−0.0198282	+	0.00964772i
$169$	−10.0847	+	8.14285i	−0.775748	+	0.626373i
$170$	18.5098	−	1.04887i	1.41963	−	0.0804447i
$171$	6.34711	−	4.28990i	0.485376	−	0.328057i
$172$	−2.20876	−	4.08870i	−0.168416	−	0.311761i
$173$	9.14829	+	21.0261i	0.695532	+	1.59858i	0.797166	+	0.603761i	$0.206332\pi$
$173$	9.14829	+	21.0261i	0.695532	+	1.59858i	−0.101634	+	0.994822i	$0.532407\pi$
$174$	−3.54938	−	11.5900i	−0.269078	−	0.878632i
$175$	1.90364	−	5.15442i	0.143901	−	0.389637i
$176$	4.14848	−	4.45290i	0.312703	−	0.335650i
$177$	7.70479	−	7.81460i	0.579127	−	0.587381i
$178$	0.0323918	−	2.28880i	0.00242787	−	0.171553i
$179$	−0.328771	+	0.208905i	−0.0245735	+	0.0156143i	−0.548535	−	0.836128i	$-0.684814\pi$
$179$	−0.328771	+	0.208905i	−0.0245735	+	0.0156143i	0.523961	+	0.851742i	$0.324454\pi$
$180$	−2.02771	−	8.26546i	−0.151137	−	0.616071i
$181$	10.9673	−	2.20171i	0.815194	−	0.163652i	0.228587	−	0.973523i	$-0.426589\pi$
$181$	10.9673	−	2.20171i	0.815194	−	0.163652i	0.586607	+	0.809872i	$0.300463\pi$
$182$	0.230646	+	0.0395483i	0.0170967	+	0.00293152i
$183$	−3.43886	−	5.95628i	−0.254208	−	0.440301i
$184$	−2.19492	+	3.80172i	−0.161812	+	0.280266i
$185$	−15.0453	+	18.1031i	−1.10615	+	1.33096i
$186$	4.60187	−	4.16719i	0.337426	−	0.305553i
$187$	0.411415	+	4.13963i	0.0300857	+	0.302720i
$188$	−4.15098	+	7.68400i	−0.302741	+	0.560413i
$189$	0.579301	+	0.0493058i	0.0421379	+	0.00358647i
$190$	−31.4363	+	51.0559i	−2.28063	+	3.70398i
$191$	−5.07955	−	6.86801i	−0.367544	−	0.496952i	0.580866	−	0.813999i	$-0.302714\pi$
$191$	−5.07955	−	6.86801i	−0.367544	−	0.496952i	−0.948410	+	0.317047i	$0.897309\pi$
$192$	−0.967468	+	9.73459i	−0.0698210	+	0.702534i
$193$	−12.5901	−	8.50940i	−0.906253	−	0.612520i	0.0156769	−	0.999877i	$-0.495010\pi$
$193$	−12.5901	−	8.50940i	−0.906253	−	0.612520i	−0.921930	+	0.387357i	$0.873388\pi$
$194$	20.8003	+	12.4048i	1.49337	+	0.890612i
$195$	−0.277100	+	0.689590i	−0.0198435	+	0.0493826i
$196$	−7.81987	−	12.7003i	−0.558562	−	0.907162i
$197$	3.29459	+	6.53443i	0.234730	+	0.465559i	0.979415	−	0.201857i	$-0.0646977\pi$
$197$	3.29459	+	6.53443i	0.234730	+	0.465559i	−0.744685	+	0.667416i	$0.767400\pi$
$198$	3.47180	−	1.00972i	0.246730	−	0.0717575i
$199$	10.6027	+	5.53534i	0.751608	+	0.392390i	0.794953	−	0.606671i	$-0.207495\pi$
$199$	10.6027	+	5.53534i	0.751608	+	0.392390i	−0.0433454	+	0.999060i	$0.513802\pi$
$200$	2.86727	+	3.65570i	0.202747	+	0.258497i
$201$	−4.75209	−	10.1284i	−0.335186	−	0.714406i
$202$	−1.30225	−	18.3740i	−0.0916263	−	1.29279i
$203$	−3.15773	+	1.32108i	−0.221629	+	0.0927218i
$204$	−3.61496	−	3.88024i	−0.253098	−	0.271671i
$205$	−32.9134	−	0.931786i	−2.29877	−	0.0650787i
$206$	6.05376	−	28.0895i	0.421785	−	1.95709i
$207$	7.79585	−	4.35502i	0.541849	−	0.302695i
$208$	0.447603	−	0.508576i	0.0310357	−	0.0352634i
$209$	−11.7454	−	6.56135i	−0.812444	−	0.453858i
$210$	−4.29037	+	1.51588i	−0.296063	+	0.104606i
$211$	1.38873	−	1.99330i	0.0956041	−	0.137224i	−0.769827	−	0.638253i	$-0.779657\pi$
$211$	1.38873	−	1.99330i	0.0956041	−	0.137224i	0.865431	+	0.501028i	$0.167045\pi$
$212$	5.55889	−	1.78882i	0.381786	−	0.122856i
$213$	−1.98676	−	7.21024i	−0.136131	−	0.494038i
$214$	1.28089	−	8.16196i	0.0875599	−	0.557940i
$215$	−2.94216	−	7.32186i	−0.200654	−	0.499347i
$216$	−0.292318	+	0.395241i	−0.0198897	+	0.0268927i
$217$	−1.29953	−	1.17678i	−0.0882177	−	0.0798849i
$218$	−6.44421	+	0.918078i	−0.436457	+	0.0621801i
$219$	−6.28912	+	1.63756i	−0.424979	+	0.110656i
$220$	−11.3581	+	9.71468i	−0.765766	+	0.654963i
$221$	0.0588222	+	0.459351i	0.00395681	+	0.0308993i
$222$	12.7485			0.855625
$223$	7.30991	+	13.0217i	0.489508	+	0.871999i
$223$	7.30991	+	13.0217i	0.489508	+	0.871999i
$224$	4.71973			0.315350
$225$	−1.20043	−	9.37436i	−0.0800289	−	0.624957i
$226$	−15.0589	+	12.8800i	−1.00171	+	0.856764i
$227$	28.1938	−	7.34108i	1.87129	−	0.487245i	0.871291	−	0.490766i	$-0.163283\pi$
$227$	28.1938	−	7.34108i	1.87129	−	0.487245i	0.999994	+	0.00352117i	$0.00112082\pi$
$228$	16.9795	−	2.41900i	1.12450	−	0.160202i
$229$	−5.24535	−	4.74988i	−0.346622	−	0.313881i	0.479315	−	0.877643i	$-0.340885\pi$
$229$	−5.24535	−	4.74988i	−0.346622	−	0.313881i	−0.825937	+	0.563762i	$0.809354\pi$
$230$	−41.5584	+	56.1907i	−2.74028	+	3.70511i
$231$	−0.380697	−	0.947402i	−0.0250480	−	0.0623345i
$232$	0.448714	−	2.85925i	0.0294595	−	0.187719i
$233$	2.49169	+	9.04270i	0.163236	+	0.592407i	0.999058	+	0.0434055i	$0.0138208\pi$
$233$	2.49169	+	9.04270i	0.163236	+	0.592407i	−0.835821	+	0.549002i	$0.815008\pi$
$234$	0.383152	−	0.123296i	0.0250474	−	0.00806010i
$235$	−8.47719	+	12.1677i	−0.552991	+	0.793730i
$236$	23.1652	−	8.18478i	1.50793	−	0.532784i
$237$	9.63294	+	5.38128i	0.625727	+	0.349552i
$238$	−1.87331	+	2.12849i	−0.121428	+	0.137970i
$239$	−8.10258	+	4.52637i	−0.524112	+	0.292787i	−0.727261	−	0.686361i	$-0.759207\pi$
$239$	−8.10258	+	4.52637i	−0.524112	+	0.292787i	0.203149	+	0.979148i	$0.434883\pi$
$240$	−2.77541	+	12.8780i	−0.179152	+	0.831269i
$241$	−8.17180	−	0.231345i	−0.526392	−	0.0149023i	−0.235896	−	0.971778i	$-0.575802\pi$
$241$	−8.17180	−	0.231345i	−0.526392	−	0.0149023i	−0.290496	+	0.956876i	$0.593820\pi$
$242$	11.1092	+	11.9244i	0.714125	+	0.766530i
$243$	0.922520	−	0.385950i	0.0591797	−	0.0247587i
$244$	−1.08858	−	15.3591i	−0.0696890	−	0.983267i
$245$	−10.7569	−	22.9270i	−0.687236	−	1.46475i
$246$	11.0055	+	14.0317i	0.701683	+	0.894629i
$247$	−1.32766	−	0.693129i	−0.0844772	−	0.0441027i
$248$	1.42340	−	0.413972i	0.0903858	−	0.0262872i
$249$	−3.82343	−	7.58332i	−0.242300	−	0.480573i
$250$	18.2642	+	29.6630i	1.15513	+	1.87605i
$251$	−3.25658	+	8.10432i	−0.205554	+	0.511540i	−0.994718	−	0.102642i	$-0.967271\pi$
$251$	−3.25658	+	8.10432i	−0.205554	+	0.511540i	0.789165	+	0.614182i	$0.210514\pi$
$252$	1.11791	+	0.666692i	0.0704215	+	0.0419977i
$253$	−12.9929	−	8.78168i	−0.816858	−	0.552099i
$254$	0.679281	−	6.83487i	0.0426219	−	0.428858i
$255$	−5.35459	−	7.23988i	−0.335317	−	0.453379i
$256$	6.04313	−	9.81467i	0.377696	−	0.613417i
$257$	19.3741	+	1.64898i	1.20852	+	0.102860i	0.671692	−	0.740831i	$-0.265568\pi$
$257$	19.3741	+	1.64898i	1.20852	+	0.102860i	0.536829	+	0.843691i	$0.319622\pi$
$258$	−2.03123	+	3.76007i	−0.126459	+	0.234092i
$259$	−0.356037	−	3.58242i	−0.0221231	−	0.222601i
$260$	−1.23330	+	1.11680i	−0.0764860	+	0.0692613i
$261$	−3.76307	+	4.52786i	−0.232928	+	0.280267i
$262$	23.4616	−	40.6367i	1.44946	−	2.51055i
$263$	8.74010	+	15.1383i	0.538938	+	0.933468i	0.998962	+	0.0455612i	$0.0145076\pi$
$263$	8.74010	+	15.1383i	0.538938	+	0.933468i	−0.460024	+	0.887907i	$0.652159\pi$
$264$	0.850906	+	0.145902i	0.0523696	+	0.00897967i
$265$	9.72170	−	1.95165i	0.597199	−	0.119889i
$266$	−2.18484	−	8.90594i	−0.133961	−	0.546058i
$267$	−0.938398	+	0.596271i	−0.0574290	+	0.0364912i
$268$	0.354437	−	25.0445i	0.0216507	−	1.52984i
$269$	8.63195	−	8.75497i	0.526299	−	0.533800i	−0.397032	−	0.917805i	$-0.629960\pi$
$269$	8.63195	−	8.75497i	0.526299	−	0.533800i	0.923331	+	0.384005i	$0.125455\pi$
$270$	−5.33496	+	5.72646i	−0.324675	+	0.348501i
$271$	1.45087	−	3.92849i	0.0881344	−	0.238639i	−0.886382	−	0.462954i	$-0.846789\pi$
$271$	1.45087	−	3.92849i	0.0881344	−	0.238639i	0.974517	+	0.224316i	$0.0720146\pi$
$272$	2.40377	+	7.84913i	0.145750	+	0.475923i
$273$	−0.0453476	−	0.104225i	−0.00274456	−	0.00630799i
$274$	3.78151	+	7.00007i	0.228450	+	0.422890i
$275$	−13.7511	+	9.29413i	−0.829223	+	0.560457i
$276$	19.9598	−	1.13104i	1.20144	−	0.0680805i
$277$	−7.17740	+	5.79534i	−0.431248	+	0.348208i	−0.819237	−	0.573456i	$-0.805602\pi$
$277$	−7.17740	+	5.79534i	−0.431248	+	0.348208i	0.387989	+	0.921664i	$0.373170\pi$
$278$	−37.6411	+	18.3148i	−2.25756	+	1.09845i
$279$	−2.91814	−	0.759825i	−0.174705	−	0.0454895i
$280$	−1.07954	−	0.122740i	−0.0645146	−	0.00733510i
$281$	−7.60592	+	17.4812i	−0.453731	+	1.04284i	0.527421	+	0.849604i	$0.323159\pi$
$281$	−7.60592	+	17.4812i	−0.453731	+	1.04284i	−0.981153	+	0.193234i	$0.938102\pi$
$282$	8.00262	−	0.681123i	0.476549	−	0.0405603i
$283$	6.04624	−	11.9920i	0.359412	−	0.712851i	−0.638999	−	0.769208i	$-0.720651\pi$
$283$	6.04624	−	11.9920i	0.359412	−	0.712851i	0.998411	+	0.0563569i	$0.0179485\pi$
$284$	3.06295	−	16.4612i	0.181752	−	0.976790i
$285$	29.1107	−	0.824129i	1.72437	−	0.0488172i
$286$	−0.496277	−	0.503351i	−0.0293455	−	0.0297637i
$287$	3.63565	−	3.48449i	0.214606	−	0.205683i
$288$	7.19627	−	3.75693i	0.424044	−	0.221379i
$289$	10.3778	+	4.69104i	0.610456	+	0.275944i
$290$	12.2405	−	44.4226i	0.718789	−	2.60859i
$291$	−0.499244	−	11.7526i	−0.0292662	−	0.688949i
$292$	−14.2648	−	2.86368i	−0.834783	−	0.167584i
$293$	−24.7671	−	9.54744i	−1.44691	−	0.557767i	−0.496299	−	0.868152i	$-0.665308\pi$
$293$	−24.7671	−	9.54744i	−1.44691	−	0.557767i	−0.950611	+	0.310384i	$0.899542\pi$
$294$	−5.82588	+	12.4171i	−0.339772	+	0.724180i
$295$	40.6527	−	9.36521i	2.36689	−	0.545264i
$296$	2.73720	+	1.33183i	0.159097	+	0.0774108i
$297$	−1.33460	−	1.14149i	−0.0774411	−	0.0662357i
$298$	−6.73502	+	10.2753i	−0.390149	+	0.595229i
$299$	−1.47348	−	0.936271i	−0.0852137	−	0.0541459i
$300$	6.76571	−	20.0476i	0.390618	−	1.15745i
$301$	1.11333	+	0.465779i	0.0641714	+	0.0268470i
$302$	−5.77481	−	15.6363i	−0.332303	−	0.899767i
$303$	−7.11725	+	5.42136i	−0.408876	+	0.311449i
$304$	−25.2721	−	8.13238i	−1.44945	−	0.466424i
$305$	1.10963	−	26.1216i	0.0635374	−	1.49572i
$306$	−1.16198	+	4.73652i	−0.0664259	+	0.270769i
$307$	−7.03010	−	20.8310i	−0.401229	−	1.18889i	−0.938441	−	0.345441i	$-0.887730\pi$
$307$	−7.03010	−	20.8310i	−0.401229	−	1.18889i	0.537211	−	0.843448i	$-0.319478\pi$
$308$	0.161604	−	2.28013i	0.00920826	−	0.129923i
$309$	−13.0226	+	5.02007i	−0.740831	+	0.285582i
$310$	23.2609	−	3.98848i	1.32113	−	0.226530i
$311$	−14.7940	−	17.8006i	−0.838889	−	1.00938i	−0.999749	−	0.0224037i	$-0.992868\pi$
$311$	−14.7940	−	17.8006i	−0.838889	−	1.00938i	0.160860	−	0.986977i	$-0.448573\pi$
$312$	0.0951462	+	0.0135550i	0.00538659	+	0.000767403i
$313$	24.0247	−	2.73153i	1.35796	−	0.154395i	0.596502	−	0.802612i	$-0.296557\pi$
$313$	24.0247	−	2.73153i	1.35796	−	0.154395i	0.761456	+	0.648216i	$0.224485\pi$
$314$	−8.17539	+	26.6954i	−0.461364	+	1.50651i
$315$	1.75817	+	1.33923i	0.0990615	+	0.0754573i
$316$	14.1212	+	20.2688i	0.794382	+	1.14021i
$317$	−7.24759	−	5.20326i	−0.407065	−	0.292244i	0.361061	−	0.932542i	$-0.382414\pi$
$317$	−7.24759	−	5.20326i	−0.407065	−	0.292244i	−0.768127	+	0.640298i	$0.778811\pi$
$318$	−4.17825	−	3.37370i	−0.234304	−	0.189188i
$319$	10.0755	+	2.32110i	0.564119	+	0.129957i
$320$	−22.9503	+	29.2611i	−1.28296	+	1.63574i
$321$	−3.65666	+	1.65292i	−0.204095	+	0.0922568i
$322$	−1.65717	−	10.5597i	−0.0923507	−	0.588468i
$323$	15.5859	−	9.29505i	0.867223	−	0.517191i
$324$	2.23519	+	0.126659i	0.124177	+	0.00703660i
$325$	−1.50091	+	1.07755i	−0.0832554	+	0.0597715i
$326$	28.9227	+	10.2191i	1.60188	+	0.565981i
$327$	2.08882	+	2.37336i	0.115512	+	0.131247i
$328$	0.897074	+	4.16244i	0.0495326	+	0.229832i
$329$	−0.414896	−	2.22977i	−0.0228739	−	0.122931i
$330$	13.1978	+	3.83838i	0.726517	+	0.211296i
$331$	−24.0089	−	23.0107i	−1.31965	−	1.26478i	−0.940647	−	0.339388i	$-0.889780\pi$
$331$	−24.0089	−	23.0107i	−1.31965	−	1.26478i	−0.379004	−	0.925395i	$-0.623733\pi$
$332$	−0.269052	−	19.0113i	−0.0147662	−	1.04338i
$333$	−3.39449	−	5.17879i	−0.186017	−	0.283796i
$334$	3.69102	−	28.8237i	0.201964	−	1.57716i
$335$	5.40205	−	42.1854i	0.295145	−	2.30483i
$336$	−1.10450	−	1.68507i	−0.0602553	−	0.0919282i
$337$	−0.209410	−	14.7969i	−0.0114073	−	0.806041i	−0.920785	−	0.390070i	$-0.872451\pi$
$337$	−0.209410	−	14.7969i	−0.0114073	−	0.806041i	0.909378	−	0.415971i	$-0.136558\pi$
$338$	19.2662	+	18.4651i	1.04794	+	1.00437i
$339$	9.24186	+	2.68785i	0.501949	+	0.145984i
$340$	−3.68787	−	19.8197i	−0.200003	−	1.07487i
$341$	1.11568	+	5.17677i	0.0604174	+	0.280338i
$342$	−10.4204	−	11.8399i	−0.563473	−	0.640230i
$343$	7.48929	+	2.64613i	0.404383	+	0.142878i
$344$	−0.828930	+	0.595113i	−0.0446929	+	0.0320864i
$345$	33.8917	+	1.92050i	1.82467	+	0.103396i
$346$	40.5461	−	24.1807i	2.17977	−	1.29996i
$347$	3.19272	+	20.3443i	0.171394	+	1.09214i	0.908965	+	0.416872i	$0.136874\pi$
$347$	3.19272	+	20.3443i	0.171394	+	1.09214i	−0.737571	+	0.675270i	$0.764027\pi$
$348$	−12.0106	+	5.42914i	−0.643837	+	0.291033i
$349$	2.46455	−	3.14223i	0.131924	−	0.168200i	−0.716378	−	0.697712i	$-0.754202\pi$
$349$	2.46455	−	3.14223i	0.131924	−	0.168200i	0.848302	+	0.529512i	$0.177625\pi$
$350$	−11.0239	−	2.53960i	−0.589254	−	0.135747i
$351$	−0.152106	−	0.122817i	−0.00811883	−	0.00655550i
$352$	−11.5810	−	8.31432i	−0.617268	−	0.443155i
$353$	5.13278	+	7.36729i	0.273190	+	0.392121i	0.933329	−	0.359022i	$-0.116890\pi$
$353$	5.13278	+	7.36729i	0.273190	+	0.392121i	−0.660139	+	0.751144i	$0.729502\pi$
$354$	−17.9735	−	13.6908i	−0.955279	−	0.727656i
$355$	8.32518	−	27.1846i	0.441855	−	1.44281i
$356$	−2.47317	+	0.281191i	−0.131078	+	0.0149031i
$357$	1.36345	+	0.194244i	0.0721612	+	0.0102805i
$358$	0.512593	+	0.616769i	0.0270914	+	0.0325973i
$359$	−11.7038	+	2.00681i	−0.617701	+	0.105915i	−0.469340	−	0.883018i	$-0.655508\pi$
$359$	−11.7038	+	2.00681i	−0.617701	+	0.105915i	−0.148361	+	0.988933i	$0.547400\pi$
$360$	−1.74369	+	0.672173i	−0.0919007	+	0.0354267i
$361$	−2.80592	+	39.5897i	−0.147680	+	2.08367i
$362$	−7.36427	−	21.8212i	−0.387057	−	1.14690i
$363$	1.88602	−	7.68790i	0.0989905	−	0.403510i
$364$	0.0107998	−	0.254236i	0.000566065	−	0.0133256i
$365$	−23.5172	−	7.56769i	−1.23095	−	0.396111i
$366$	−11.2643	+	8.58029i	−0.588797	+	0.448499i
$367$	−5.36483	−	14.5262i	−0.280042	−	0.758261i	−0.998061	−	0.0622378i	$-0.980176\pi$
$367$	−5.36483	−	14.5262i	−0.280042	−	0.758261i	0.718019	−	0.696023i	$-0.245049\pi$
$368$	−28.5480	−	11.9435i	−1.48817	−	0.622597i
$369$	2.76968	−	8.20687i	0.144184	−	0.427233i
$370$	40.9037	+	25.9908i	2.12648	+	1.35120i
$371$	−0.831344	+	1.26834i	−0.0431612	+	0.0658487i
$372$	−5.13031	−	4.38798i	−0.265994	−	0.227506i
$373$	13.9477	+	6.78647i	0.722185	+	0.351390i	0.761789	−	0.647825i	$-0.224321\pi$
$373$	13.9477	+	6.78647i	0.722185	+	0.351390i	−0.0396040	+	0.999215i	$0.512610\pi$
$374$	8.34618	−	1.92272i	0.431570	−	0.0994215i
$375$	7.18677	−	15.3177i	0.371123	−	0.791001i
$376$	1.78938	+	0.689784i	0.0922801	+	0.0355729i
$377$	1.12849	+	0.226546i	0.0581199	+	0.0116677i
$378$	−0.0508018	−	1.19591i	−0.00261296	−	0.0615112i
$379$	−0.766988	+	2.78351i	−0.0393975	+	0.142979i	−0.981115	−	0.193426i	$-0.938040\pi$
$379$	−0.766988	+	2.78351i	−0.0393975	+	0.142979i	0.941717	+	0.336405i	$0.109211\pi$
$380$	59.4106	+	26.8553i	3.04770	+	1.37765i
$381$	−2.95738	+	1.54395i	−0.151511	+	0.0790989i
$382$	−12.6972	+	12.1693i	−0.649644	+	0.622634i
$383$	3.56390	+	3.61469i	0.182107	+	0.184702i	0.797132	−	0.603805i	$-0.206350\pi$
$383$	3.56390	+	3.61469i	0.182107	+	0.184702i	−0.615025	+	0.788508i	$0.710854\pi$
$384$	3.90316	−	0.110499i	0.199183	−	0.00563890i
$385$	0.710025	−	3.81588i	0.0361862	−	0.194475i
$386$	−14.0851	+	27.9361i	−0.716912	+	1.42191i
$387$	2.06828	−	0.176037i	0.105137	−	0.00894846i
$388$	10.5068	−	24.1484i	0.533402	−	1.22595i
$389$	3.76129	+	0.427646i	0.190705	+	0.0216825i	0.207800	−	0.978171i	$-0.433370\pi$
$389$	3.76129	+	0.427646i	0.190705	+	0.0216825i	−0.0170950	+	0.999854i	$0.505442\pi$
$390$	1.48071	+	0.385547i	0.0749788	+	0.0195230i
$391$	19.0209	−	9.25492i	0.961930	−	0.468042i
$392$	−2.54806	+	2.05742i	−0.128697	+	0.103915i
$393$	−22.7547	+	1.28942i	−1.14782	+	0.0650424i
$394$	12.4827	−	8.43686i	0.628871	−	0.425043i
$395$	19.9364	+	36.9048i	1.00311	+	1.85688i
$396$	−1.56860	−	3.60521i	−0.0788251	−	0.181168i
$397$	8.38374	+	27.3758i	0.420768	+	1.37395i	0.875455	+	0.483300i	$0.160562\pi$
$397$	8.38374	+	27.3758i	0.420768	+	1.37395i	−0.454687	+	0.890651i	$0.650249\pi$
$398$	8.53130	−	23.0999i	0.427636	−	1.15790i
$399$	−3.03608	+	3.25888i	−0.151994	+	0.163148i
$400$	−22.9944	+	23.3221i	−1.14972	+	1.16611i
$401$	0.148683	−	10.5060i	0.00742489	−	0.524643i	−0.961164	−	0.275977i	$-0.910999\pi$
$401$	0.148683	−	10.5060i	0.00742489	−	0.524643i	0.968589	−	0.248666i	$-0.0799923\pi$
$402$	−19.4411	+	12.3532i	−0.969635	+	0.616120i
$403$	0.140458	+	0.572542i	0.00699672	+	0.0285204i
$404$	−19.6382	+	3.94241i	−0.977037	+	0.196142i
$405$	3.74675	+	0.642446i	0.186178	+	0.0319234i
$406$	3.52362	+	6.10310i	0.174875	+	0.302892i
$407$	−5.43721	+	9.41753i	−0.269513	+	0.466810i
$408$	−0.744305	+	0.895574i	−0.0368486	+	0.0443375i
$409$	−3.27524	+	2.96587i	−0.161950	+	0.146653i	−0.748189	−	0.663485i	$-0.769076\pi$
$409$	−3.27524	+	2.96587i	−0.161950	+	0.146653i	0.586239	+	0.810138i	$0.300608\pi$
$410$	6.70427	+	67.4579i	0.331100	+	3.33151i
$411$	1.83673	−	3.40003i	0.0905992	−	0.167711i
$412$	−31.1334	−	2.64984i	−1.53383	−	0.130548i
$413$	−3.34524	+	5.43302i	−0.164609	+	0.267342i
$414$	−10.9323	−	14.7814i	−0.537293	−	0.726469i
$415$	3.19283	−	32.1260i	0.156730	−	1.57701i
$416$	−1.31489	−	0.888713i	−0.0644679	−	0.0435727i
$417$	17.4625	+	10.4142i	0.855142	+	0.509986i
$418$	−10.3278	+	25.7017i	−0.505148	+	1.25711i
$419$	−2.98905	−	4.85452i	−0.146025	−	0.237159i	0.770220	−	0.637778i	$-0.220146\pi$
$419$	−2.98905	−	4.85452i	−0.146025	−	0.237159i	−0.916245	+	0.400619i	$0.868795\pi$
$420$	2.22761	+	4.41819i	0.108696	+	0.215586i
$421$	−14.2886	+	4.15561i	−0.696383	+	0.202532i	−0.608447	−	0.793594i	$-0.708207\pi$
$421$	−14.2886	+	4.15561i	−0.696383	+	0.202532i	−0.0879361	+	0.996126i	$0.528027\pi$
$422$	−4.43379	−	2.31473i	−0.215833	−	0.112679i
$423$	−2.40751	−	3.06952i	−0.117057	−	0.149245i
$424$	−0.544653	−	1.16086i	−0.0264507	−	0.0563761i
$425$	−1.58273	−	22.3313i	−0.0767738	−	1.08323i
$426$	−14.2049	+	5.94281i	−0.688228	+	0.287930i
$427$	2.72571	+	2.92573i	0.131906	+	0.141586i
$428$	−8.98036	−	0.254236i	−0.434082	−	0.0122890i
$429$	−0.0723329	+	0.335626i	−0.00349227	+	0.0162042i
$430$	−14.1830	+	7.92307i	−0.683963	+	0.382084i
$431$	21.7780	−	24.7447i	1.04901	−	1.19191i	0.0680542	−	0.997682i	$-0.478321\pi$
$431$	21.7780	−	24.7447i	1.04901	−	1.19191i	0.980957	−	0.194226i	$-0.0622196\pi$
$432$	−3.02538	−	1.69008i	−0.145559	−	0.0813139i
$433$	−27.2864	+	9.64089i	−1.31130	+	0.463312i	−0.895061	−	0.445943i	$-0.852868\pi$
$433$	−27.2864	+	9.64089i	−1.31130	+	0.463312i	−0.416239	+	0.909255i	$0.636652\pi$
$434$	−2.06332	+	2.96157i	−0.0990427	+	0.142160i
$435$	−21.3049	+	6.85577i	−1.02149	+	0.328709i
$436$	1.88030	+	6.82389i	0.0900503	+	0.326805i
$437$	−10.6061	+	67.5830i	−0.507358	+	3.23294i
$438$	4.98880	+	12.4151i	0.238374	+	0.593217i
$439$	16.6228	−	22.4755i	0.793361	−	1.07270i	−0.202271	−	0.979330i	$-0.564832\pi$
$439$	16.6228	−	22.4755i	0.793361	−	1.07270i	0.995632	−	0.0933656i	$-0.0297625\pi$
$440$	2.43268	+	2.20289i	0.115973	+	0.105019i
$441$	6.59538	−	0.939614i	0.314066	−	0.0447435i
$442$	0.922683	−	0.240248i	0.0438876	−	0.0114274i
$443$	2.97718	−	2.54640i	0.141450	−	0.120983i	−0.576440	−	0.817140i	$-0.695559\pi$
$443$	2.97718	−	2.54640i	0.141450	−	0.120983i	0.717890	+	0.696157i	$0.245108\pi$
$444$	−1.76082	−	13.7505i	−0.0835648	−	0.652569i
$445$	−4.22649			−0.200355
$446$	24.6807	−	18.3332i	1.16867	−	0.868104i
$447$	5.96738			0.282247
$448$	−0.722418	−	5.64146i	−0.0341310	−	0.266534i
$449$	−17.7479	+	15.1798i	−0.837574	+	0.716381i	−0.961172	−	0.275951i	$-0.911007\pi$
$449$	−17.7479	+	15.1798i	−0.837574	+	0.716381i	0.123598	+	0.992332i	$0.460557\pi$
$450$	−18.8299	+	4.90294i	−0.887652	+	0.231127i
$451$	−15.0592	+	2.14542i	−0.709112	+	0.101024i
$452$	15.9722	+	14.4635i	0.751269	+	0.680306i
$453$	−4.81424	+	6.50928i	−0.226193	+	0.305833i
$454$	−22.3645	−	55.6562i	−1.04962	−	2.61207i
$455$	0.0669886	−	0.426858i	0.00314047	−	0.0200114i
$456$	−1.00044	−	3.63073i	−0.0468498	−	0.170025i
$457$	0.896651	−	0.288536i	0.0419436	−	0.0134972i	−0.285278	−	0.958445i	$-0.592086\pi$
$457$	0.896651	−	0.288536i	0.0419436	−	0.0134972i	0.327221	+	0.944948i	$0.393888\pi$
$458$	−8.32828	+	11.9539i	−0.389155	+	0.558570i
$459$	2.23349	−	0.789144i	0.104251	−	0.0368341i
$460$	66.3470	+	37.0637i	3.09345	+	1.72810i
$461$	−8.04524	+	9.14117i	−0.374704	+	0.425747i	−0.907209	−	0.420680i	$-0.861791\pi$
$461$	−8.04524	+	9.14117i	−0.374704	+	0.425747i	0.532505	+	0.846427i	$0.321251\pi$
$462$	−1.83518	+	1.02520i	−0.0853805	+	0.0476964i
$463$	1.59074	−	7.38105i	0.0739279	−	0.343027i	−0.925428	−	0.378925i	$-0.876294\pi$
$463$	1.59074	−	7.38105i	0.0739279	−	0.343027i	0.999355	+	0.0358979i	$0.0114291\pi$
$464$	20.3945	+	0.577371i	0.946789	+	0.0268038i
$465$	−7.81379	−	8.38719i	−0.362356	−	0.388947i
$466$	17.8150	−	7.45316i	0.825263	−	0.345261i
$467$	−0.290891	−	4.10429i	−0.0134608	−	0.189924i	−0.999698	−	0.0245854i	$-0.992173\pi$
$467$	−0.290891	−	4.10429i	−0.0134608	−	0.189924i	0.986237	−	0.165338i	$-0.0528716\pi$
$468$	−0.185907	−	0.396236i	−0.00859356	−	0.0183160i
$469$	4.01427	+	5.11810i	0.185362	+	0.236332i
$470$	27.0651	+	14.1298i	1.24842	+	0.651758i
$471$	13.0212	−	3.78701i	0.599986	−	0.174496i
$472$	−2.42877	−	4.81718i	−0.111793	−	0.221729i
$473$	−1.91131	−	3.10416i	−0.0878820	−	0.142729i
$474$	8.47031	−	21.0792i	0.389054	−	0.968199i
$475$	62.1836	+	37.0848i	2.85318	+	1.70157i
$476$	2.55452	+	1.72655i	0.117086	+	0.0791364i
$477$	−0.257964	+	2.59561i	−0.0118114	+	0.118845i
$478$	11.3624	+	15.3630i	0.519705	+	0.702688i
$479$	−13.1398	+	21.3404i	−0.600372	+	0.975066i	0.397964	+	0.917401i	$0.369717\pi$
$479$	−13.1398	+	21.3404i	−0.600372	+	0.975066i	−0.998336	+	0.0576652i	$0.981634\pi$
$480$	30.7486	+	2.61709i	1.40348	+	0.119453i
$481$	−0.575371	+	1.06509i	−0.0262347	+	0.0485638i
$482$	1.66455	+	16.7486i	0.0758181	+	0.762876i
$483$	−3.84838	+	3.48487i	−0.175107	+	0.158567i
$484$	11.3272	−	13.6293i	0.514873	−	0.619513i
$485$	22.3585	−	38.7261i	1.01525	−	1.75846i
$486$	−1.02941	−	1.78300i	−0.0466952	−	0.0808784i
$487$	−23.7286	−	4.06868i	−1.07525	−	0.184369i	−0.395978	−	0.918260i	$-0.629594\pi$
$487$	−23.7286	−	4.06868i	−1.07525	−	0.184369i	−0.679268	+	0.733891i	$0.737702\pi$
$488$	−3.31491	+	0.665475i	−0.150059	+	0.0301246i
$489$	−3.54987	−	14.4702i	−0.160531	−	0.654363i
$490$	−44.0074	+	27.9629i	−1.98805	+	1.26324i
$491$	0.170635	−	12.0571i	0.00770065	−	0.544128i	−0.958325	−	0.285681i	$-0.907780\pi$
$491$	0.170635	−	12.0571i	0.00770065	−	0.544128i	0.966025	−	0.258447i	$-0.0832108\pi$
$492$	13.6144	−	13.8085i	0.613787	−	0.622535i
$493$	−9.50651	+	10.2041i	−0.428152	+	0.459571i
$494$	−1.06828	+	2.89255i	−0.0480642	+	0.130142i
$495$	−1.95488	−	6.38334i	−0.0878651	−	0.286910i
$496$	4.16912	+	9.58213i	0.187199	+	0.430251i
$497$	2.06668	+	3.82570i	0.0927033	+	0.171606i
$498$	−14.4864	+	9.79113i	−0.649153	+	0.438751i
$499$	33.6706	−	1.90797i	1.50731	−	0.0854127i	0.716546	−	0.697540i	$-0.245722\pi$
$499$	33.6706	−	1.90797i	1.50731	−	0.0854127i	0.790759	+	0.612127i	$0.209686\pi$
$500$	29.4717	−	23.7968i	1.31802	−	1.06422i
$501$	−12.6918	+	6.17537i	−0.567026	+	0.275895i
$502$	17.4019	+	4.53110i	0.776684	+	0.202233i
$503$	29.3611	+	3.33826i	1.30915	+	0.148846i	0.739562	−	0.673088i	$-0.235032\pi$
$503$	29.3611	+	3.33826i	1.30915	+	0.148846i	0.569583	+	0.821934i	$0.307105\pi$
$504$	0.114029	−	0.262079i	0.00507924	−	0.0116739i
$505$	−33.8884	+	2.88433i	−1.50801	+	0.128351i
$506$	−14.5358	+	28.8300i	−0.646194	+	1.28165i
$507$	2.37111	−	12.7431i	0.105305	−	0.565939i
$508$	−7.46588	+	0.211361i	−0.331245	+	0.00937761i
$509$	−21.0839	−	21.3844i	−0.934527	−	0.947846i	0.0642176	−	0.997936i	$-0.479545\pi$
$509$	−21.0839	−	21.3844i	−0.934527	−	0.947846i	−0.998745	+	0.0500895i	$0.984049\pi$
$510$	−13.3847	+	12.8282i	−0.592684	+	0.568041i
$511$	3.34941	−	1.74861i	0.148169	−	0.0773541i
$512$	−28.7396	−	12.9911i	−1.27012	−	0.574131i
$513$	−2.03509	+	7.38563i	−0.0898514	+	0.326083i
$514$	−1.69901	−	39.9960i	−0.0749401	−	1.76415i
$515$	−52.0177	−	10.4427i	−2.29217	−	0.460158i
$516$	4.33614	+	1.67153i	0.190888	+	0.0735851i
$517$	−2.90994	+	6.20216i	−0.127979	+	0.272771i
$518$	−7.22275	+	1.66392i	−0.317349	+	0.0731082i
$519$	−20.6189	−	10.0324i	−0.905068	−	0.440374i
$520$	0.277642	+	0.237468i	0.0121754	+	0.0104137i
$521$	10.8365	−	16.5327i	0.474756	−	0.724310i	−0.516496	−	0.856290i	$-0.672764\pi$
$521$	10.8365	−	16.5327i	0.474756	−	0.724310i	0.991252	+	0.131979i	$0.0421333\pi$
$522$	10.2306	+	6.50069i	0.447783	+	0.284528i
$523$	−8.61135	+	25.5164i	−0.376548	+	1.11576i	0.577574	+	0.816338i	$0.303999\pi$
$523$	−8.61135	+	25.5164i	−0.376548	+	1.11576i	−0.954122	+	0.299417i	$0.903208\pi$
$524$	−47.0711	−	19.6929i	−2.05631	−	0.860287i
$525$	1.90364	+	5.15442i	0.0830815	+	0.224957i
$526$	28.6291	−	21.8074i	1.24829	−	0.950848i
$527$	−6.79961	−	2.18807i	−0.296196	−	0.0953138i
$528$	−0.258293	+	6.08042i	−0.0112408	+	0.264616i
$529$	−13.5192	+	55.1075i	−0.587790	+	2.39598i
$530$	−6.52787	−	19.3428i	−0.283553	−	0.840199i
$531$	−0.775845	+	10.9467i	−0.0336688	+	0.475045i
$532$	−9.30413	+	3.58663i	−0.403385	+	0.155500i
$533$	−1.66899	+	0.286178i	−0.0722921	+	0.0123957i
$534$	1.46307	+	1.76042i	0.0633134	+	0.0761809i
$535$	−15.1023	−	2.15155i	−0.652928	−	0.0930196i
$536$	−5.46467	+	0.621315i	−0.236038	+	0.0268367i
$537$	0.114062	−	0.372453i	0.00492216	−	0.0160725i
$538$	−20.1363	−	15.3383i	−0.868138	−	0.661279i
$539$	−6.68798	−	9.59953i	−0.288072	−	0.413481i
$540$	6.91339	+	4.96332i	0.297505	+	0.213587i
$541$	30.0346	+	24.2512i	1.29129	+	1.04264i	0.996193	+	0.0871728i	$0.0277832\pi$
$541$	30.0346	+	24.2512i	1.29129	+	1.04264i	0.295093	+	0.955468i	$0.404649\pi$
$542$	−8.40199	−	1.93558i	−0.360896	−	0.0831402i
$543$	−6.90349	+	8.80178i	−0.296257	+	0.377721i
$544$	17.5228	−	7.92078i	0.751282	−	0.339601i
$545$	1.86335	+	11.8735i	0.0798172	+	0.508603i
$546$	−0.200985	+	0.119862i	−0.00860135	+	0.00512964i
$547$	33.4891	+	1.89769i	1.43189	+	0.0811393i	0.755377	−	0.655290i	$-0.227454\pi$
$547$	33.4891	+	1.89769i	1.43189	+	0.0811393i	0.676515	+	0.736429i	$0.263490\pi$
$548$	7.02794	−	5.04556i	0.300219	−	0.215536i
$549$	6.48485	+	2.29124i	0.276766	+	0.0977878i
$550$	22.5760	+	25.6514i	0.962646	+	1.09378i
$551$	−9.50229	−	44.0908i	−0.404811	−	1.87833i
$552$	−0.803040	−	4.31577i	−0.0341797	−	0.183691i
$553$	−6.15996	−	1.79152i	−0.261948	−	0.0761833i
$554$	13.7119	+	13.1418i	0.582564	+	0.558342i
$555$	−0.333096	−	23.5366i	−0.0141391	−	0.999073i
$556$	24.9533	+	38.0698i	1.05825	+	1.61452i
$557$	−5.15109	+	40.2256i	−0.218259	+	1.70441i	0.398423	+	0.917202i	$0.369558\pi$
$557$	−5.15109	+	40.2256i	−0.218259	+	1.70441i	−0.616681	+	0.787213i	$0.711523\pi$
$558$	−0.788561	+	6.15799i	−0.0333825	+	0.260688i
$559$	−0.222464	−	0.339401i	−0.00940923	−	0.0143551i
$560$	−0.108383	−	7.65833i	−0.00458000	−	0.323623i
$561$	−3.00336	−	2.87848i	−0.126802	−	0.121530i
$562$	37.6882	+	10.9610i	1.58978	+	0.462362i
$563$	4.83643	+	25.9924i	0.203831	+	1.09545i	0.918331	+	0.395813i	$0.129537\pi$
$563$	4.83643	+	25.9924i	0.203831	+	1.09545i	−0.714500	+	0.699636i	$0.753346\pi$
$564$	−1.83997	−	8.53751i	−0.0774768	−	0.359494i
$565$	24.1728	+	27.4656i	1.01696	+	1.15549i
$566$	−26.0706	−	9.21134i	−1.09583	−	0.387182i
$567$	−0.472286	+	0.339068i	−0.0198341	+	0.0142395i
$568$	−3.67073	−	0.208005i	−0.154020	−	0.00872768i
$569$	3.72549	−	2.22179i	0.156181	−	0.0931423i	−0.431993	−	0.901877i	$-0.642189\pi$
$569$	3.72549	−	2.22179i	0.156181	−	0.0931423i	0.588174	+	0.808735i	$0.299847\pi$
$570$	−9.29566	−	59.2329i	−0.389353	−	2.48099i
$571$	−15.7494	+	7.11917i	−0.659091	+	0.297928i	−0.713567	−	0.700587i	$-0.752922\pi$
$571$	−15.7494	+	7.11917i	−0.659091	+	0.297928i	0.0544757	+	0.998515i	$0.482651\pi$
$572$	−0.474366	+	0.604805i	−0.0198342	+	0.0252881i
$573$	8.32430	+	1.91768i	0.347753	+	0.0801122i
$574$	−8.06660	−	6.51333i	−0.336694	−	0.271861i
$575$	68.5565	+	49.2187i	2.85901	+	2.05256i
$576$	−5.59213	−	8.02661i	−0.233005	−	0.334442i
$577$	29.1507	+	22.2047i	1.21356	+	0.924395i	0.998635	−	0.0522357i	$-0.0166347\pi$
$577$	29.1507	+	22.2047i	1.21356	+	0.924395i	0.214925	+	0.976630i	$0.431049\pi$
$578$	6.86596	−	22.4197i	0.285586	−	0.932537i
$579$	15.0988	−	1.71668i	0.627483	−	0.0713428i
$580$	−49.6047	−	7.06695i	−2.05972	−	0.293439i
$581$	3.15595	+	3.79735i	0.130931	+	0.157541i
$582$	−23.8700	+	4.09293i	−0.989445	+	0.169657i
$583$	4.27422	−	1.64766i	0.177020	−	0.0682392i
$584$	−0.225863	+	3.18679i	−0.00934630	+	0.131870i
$585$	−0.237643	−	0.704163i	−0.00982531	−	0.0291135i
$586$	−13.0205	+	53.0750i	−0.537873	+	2.19251i
$587$	−1.07277	+	25.2539i	−0.0442780	+	1.04234i	0.830258	+	0.557379i	$0.188193\pi$
$587$	−1.07277	+	25.2539i	−0.0442780	+	1.04234i	−0.874536	+	0.484961i	$0.838834\pi$
$588$	14.1977	+	4.56872i	0.585502	+	0.188411i
$589$	18.3768	−	13.9980i	0.757204	−	0.576779i
$590$	−29.7562	−	80.5699i	−1.22504	−	3.31701i
$591$	−6.75100	−	2.82438i	−0.277699	−	0.116179i
$592$	−6.86163	+	20.3318i	−0.282011	+	0.835632i
$593$	−8.97883	−	5.70527i	−0.368717	−	0.234287i	0.338996	−	0.940788i	$-0.389913\pi$
$593$	−8.97883	−	5.70527i	−0.368717	−	0.234287i	−0.707713	+	0.706500i	$0.750273\pi$
$594$	−1.98208	+	3.02395i	−0.0813258	+	0.124074i
$595$	3.97861	+	3.40293i	0.163107	+	0.139506i
$596$	12.0131	+	5.84514i	0.492074	+	0.239426i
$597$	−11.6554	+	2.68507i	−0.477024	+	0.109893i
$598$	−1.52668	+	3.25392i	−0.0624306	+	0.133063i
$599$	3.76972	+	1.45318i	0.154027	+	0.0593755i	0.435475	−	0.900201i	$-0.356581\pi$
$599$	3.76972	+	1.45318i	0.154027	+	0.0593755i	−0.281448	+	0.959576i	$0.590815\pi$
$600$	−4.55513	−	0.914451i	−0.185962	−	0.0373323i
$601$	0.636521	+	14.9842i	0.0259642	+	0.611218i	0.964193	+	0.265202i	$0.0854387\pi$
$601$	0.636521	+	14.9842i	0.0259642	+	0.611218i	−0.938229	+	0.346016i	$0.887534\pi$
$602$	0.660046	−	2.39540i	0.0269015	−	0.0976292i
$603$	10.1947	+	4.60829i	0.415159	+	0.187664i
$604$	−16.0676	+	8.38835i	−0.653781	+	0.341317i
$605$	21.7248	−	20.8216i	0.883241	−	0.846518i
$606$	12.9325	+	13.1168i	0.525346	+	0.532833i
$607$	−35.3583	+	1.00100i	−1.43515	+	0.0406293i	−0.737275	−	0.675593i	$-0.763888\pi$
$607$	−35.3583	+	1.00100i	−1.43515	+	0.0406293i	−0.697872	+	0.716222i	$0.745870\pi$
$608$	−11.3766	+	61.1411i	−0.461381	+	2.47960i
$609$	1.54102	−	3.05643i	0.0624453	−	0.123853i
$610$	−53.6346	+	4.56497i	−2.17160	+	0.184830i
$611$	−0.304272	+	0.699327i	−0.0123095	+	0.0282917i
$612$	5.26927	+	0.599099i	0.212998	+	0.0242171i
$613$	−10.4165	−	2.71225i	−0.420720	−	0.109547i	0.0355930	−	0.999366i	$-0.488668\pi$
$613$	−10.4165	−	2.71225i	−0.420720	−	0.109547i	−0.456313	+	0.889819i	$0.650830\pi$
$614$	−40.7017	+	19.8040i	−1.64259	+	0.799225i
$615$	25.6181	−	20.6852i	1.03302	−	0.834106i
$616$	−0.501128	+	0.0283969i	−0.0201910	+	0.00114414i
$617$	−16.3706	+	11.0646i	−0.659057	+	0.445445i	−0.843305	−	0.537435i	$-0.819393\pi$
$617$	−16.3706	+	11.0646i	−0.659057	+	0.445445i	0.184248	+	0.982880i	$0.441015\pi$
$618$	13.6573	+	25.2814i	0.549376	+	1.01697i
$619$	−3.46167	−	7.95616i	−0.139136	−	0.319785i	0.833350	−	0.552746i	$-0.186420\pi$
$619$	−3.46167	−	7.95616i	−0.139136	−	0.319785i	−0.972486	+	0.232961i	$0.925159\pi$
$620$	−7.51473	−	24.5382i	−0.301799	−	0.985477i
$621$	−3.09372	+	8.37678i	−0.124147	+	0.336149i
$622$	−32.4829	+	34.8666i	−1.30244	+	1.39802i
$623$	0.453831	−	0.460299i	0.0181823	−	0.0184415i
$624$	−0.00958712	+	0.677427i	−0.000383792	+	0.0271188i
$625$	14.4033	−	9.15208i	0.576134	−	0.366083i
$626$	−11.8609	−	48.3478i	−0.474055	−	1.93237i
$627$	13.1906	−	2.64805i	0.526783	−	0.105753i
$628$	29.9227	+	5.13077i	1.19405	+	0.204740i
$629$	−7.33397	−	12.7028i	−0.292425	−	0.506494i
$630$	2.27515	−	3.94067i	0.0906440	−	0.157000i
$631$	22.3955	−	26.9470i	0.891550	−	1.07274i	−0.105379	−	0.994432i	$-0.533605\pi$
$631$	22.3955	−	26.9470i	0.891550	−	1.07274i	0.996929	−	0.0783123i	$-0.0249531\pi$
$632$	4.02076	−	3.64097i	0.159937	−	0.144830i
$633$	0.240258	+	2.41746i	0.00954938	+	0.0960852i
$634$	−8.73054	+	16.1614i	−0.346734	+	0.641850i
$635$	−12.6364	−	1.07552i	−0.501462	−	0.0426807i
$636$	−3.06176	+	4.97261i	−0.121407	+	0.197177i
$637$	−0.774462	−	1.04714i	−0.0306853	−	0.0414892i
$638$	2.10523	−	21.1827i	0.0833468	−	0.838629i
$639$	6.19639	+	4.18803i	0.245125	+	0.165676i
$640$	12.7486	+	7.60295i	0.503933	+	0.300533i
$641$	−2.49430	+	6.20730i	−0.0985189	+	0.245174i	−0.969015	−	0.247001i	$-0.920555\pi$
$641$	−2.49430	+	6.20730i	−0.0985189	+	0.245174i	0.870496	+	0.492175i	$0.163798\pi$
$642$	4.33175	+	7.03521i	0.170961	+	0.277658i
$643$	−16.7508	−	33.2232i	−0.660587	−	1.31020i	−0.937058	−	0.349173i	$-0.886463\pi$
$643$	−16.7508	−	33.2232i	−0.660587	−	1.31020i	0.276472	−	0.961022i	$-0.410835\pi$
$644$	−11.1607	+	3.24592i	−0.439794	+	0.127907i
$645$	6.99499	+	3.65185i	0.275428	+	0.143792i
$646$	−23.0578	−	29.3981i	−0.907195	−	1.15665i
$647$	−1.22583	−	2.61269i	−0.0481922	−	0.102715i	0.879754	−	0.475428i	$-0.157707\pi$
$647$	−1.22583	−	2.61269i	−0.0481922	−	0.102715i	−0.927947	+	0.372713i	$0.878428\pi$
$648$	−0.0347545	−	0.490364i	−0.00136529	−	0.0192633i
$649$	17.7792	−	7.43820i	0.697896	−	0.291975i
$650$	2.59301	+	2.78330i	0.101706	+	0.109170i
$651$	1.75246	+	0.0496125i	0.0686844	+	0.00194447i
$652$	7.02742	−	32.6073i	0.275215	−	1.27700i
$653$	42.7791	−	23.8979i	1.67408	−	0.935195i	0.698478	−	0.715631i	$-0.253861\pi$
$653$	42.7791	−	23.8979i	1.67408	−	0.935195i	0.975598	−	0.219564i	$-0.0704634\pi$
$654$	4.30052	−	4.88634i	0.168164	−	0.191071i
$655$	−75.6374	−	42.2536i	−2.95540	−	1.65099i
$656$	−28.3017	+	9.99964i	−1.10500	+	0.390420i
$657$	3.71500	−	5.33230i	0.144936	−	0.208033i
$658$	−4.44503	+	1.43038i	−0.173285	+	0.0557621i
$659$	11.0572	+	40.1280i	0.430726	+	1.56316i	0.779775	+	0.626059i	$0.215333\pi$
$659$	11.0572	+	40.1280i	0.430726	+	1.56316i	−0.349050	+	0.937104i	$0.613496\pi$
$660$	2.31717	−	14.7653i	0.0901959	−	0.574737i
$661$	−9.55766	−	23.7851i	−0.371750	−	0.925135i	−0.990244	−	0.139345i	$-0.955500\pi$
$661$	−9.55766	−	23.7851i	−0.371750	−	0.925135i	0.618494	−	0.785789i	$-0.287743\pi$
$662$	−40.7128	+	55.0474i	−1.58235	+	2.13948i
$663$	−0.343274	−	0.310849i	−0.0133316	−	0.0120724i
$664$	−4.13321	+	0.588840i	−0.160400	+	0.0228514i
$665$	−16.3853	+	4.26639i	−0.635393	+	0.165443i
$666$	−9.68819	+	8.28636i	−0.375410	+	0.321090i
$667$	−6.67782	−	52.1481i	−0.258566	−	2.01918i
$668$	−31.5989			−1.22260
$669$	−14.0191	−	5.14447i	−0.542009	−	0.198897i
$670$	−87.5617			−3.38280
$671$	−1.53418	−	11.9806i	−0.0592263	−	0.462507i
$672$	−3.58674	+	3.06776i	−0.138361	+	0.118341i
$673$	−26.2526	+	6.83566i	−1.01197	+	0.263495i	−0.720774	−	0.693170i	$-0.756214\pi$
$673$	−26.2526	+	6.83566i	−1.01197	+	0.263495i	−0.291191	+	0.956665i	$0.594051\pi$
$674$	−30.1629	+	4.29716i	−1.16183	+	0.165521i
$675$	7.00546	+	6.34374i	0.269640	+	0.244171i
$676$	17.2554	−	23.3308i	0.663668	−	0.897338i
$677$	7.36848	+	18.3372i	0.283194	+	0.704754i	0.999972	+	0.00745350i	$0.00237254\pi$
$677$	7.36848	+	18.3372i	0.283194	+	0.704754i	−0.716779	+	0.697301i	$0.754384\pi$
$678$	3.07217	−	19.5762i	0.117986	−	0.751819i
$679$	1.81678	+	6.59334i	0.0697215	+	0.253029i
$680$	−4.21393	+	1.35602i	−0.161597	+	0.0520009i
$681$	−16.6541	+	23.9044i	−0.638188	+	0.916018i
$682$	10.2800	−	3.63215i	0.393641	−	0.139082i
$683$	4.92089	+	2.74897i	0.188293	+	0.105187i	0.578997	−	0.815330i	$-0.303444\pi$
$683$	4.92089	+	2.74897i	0.188293	+	0.105187i	−0.390704	+	0.920516i	$0.627769\pi$
$684$	−11.3312	+	12.8748i	−0.433260	+	0.492279i
$685$	12.8249	−	7.16441i	0.490014	−	0.273738i
$686$	3.44530	−	15.9863i	0.131542	−	0.610358i
$687$	7.07354	+	0.200253i	0.269872	+	0.00764014i
$688$	−4.90343	−	5.26326i	−0.186941	−	0.200660i
$689$	0.470433	−	0.196812i	0.0179221	−	0.00749795i
$690$	−4.94100	−	69.7143i	−0.188100	−	2.65398i
$691$	13.8422	+	29.5028i	0.526582	+	1.12234i	0.973693	+	0.227862i	$0.0731737\pi$
$691$	13.8422	+	29.5028i	0.526582	+	1.12234i	−0.447111	+	0.894479i	$0.647547\pi$
$692$	−31.6814	−	40.3930i	−1.20434	−	1.53551i
$693$	0.905107	+	0.472527i	0.0343822	+	0.0179498i
$694$	40.7113	−	11.8402i	1.54538	−	0.449449i
$695$	34.7968	+	69.0153i	1.31992	+	2.61790i
$696$	1.51747	+	2.46453i	0.0575197	+	0.0934178i
$697$	7.65016	−	19.0382i	0.289771	−	0.721122i
$698$	−7.06142	−	4.21126i	−0.267279	−	0.159398i
$699$	−7.77118	−	5.25240i	−0.293933	−	0.198664i
$700$	−1.21658	+	12.2411i	−0.0459823	+	0.462671i
$701$	−11.7041	−	15.8250i	−0.442058	−	0.597702i	0.525362	−	0.850879i	$-0.323930\pi$
$701$	−11.7041	−	15.8250i	−0.442058	−	0.597702i	−0.967420	+	0.253177i	$0.918524\pi$
$702$	−0.211034	+	0.342742i	−0.00796498	+	0.0129360i
$703$	47.2662	+	4.02295i	1.78268	+	0.151728i
$704$	−8.16544	+	15.1153i	−0.307747	+	0.569679i
$705$	−1.46660	−	14.7568i	−0.0552353	−	0.555774i
$706$	13.7029	−	12.4085i	0.515714	−	0.467001i
$707$	3.32473	−	4.00044i	0.125040	−	0.150452i
$708$	−12.2843	+	21.2770i	−0.461673	+	0.799640i
$709$	4.92319	+	8.52722i	0.184894	+	0.320247i	0.943541	−	0.331256i	$-0.107472\pi$
$709$	4.92319	+	8.52722i	0.184894	+	0.320247i	−0.758647	+	0.651502i	$0.774139\pi$
$710$	−57.6921	−	9.89231i	−2.16515	−	0.371252i
$711$	−10.8183	+	2.17179i	−0.405717	+	0.0814485i
$712$	0.130223	+	0.530822i	0.00488031	+	0.0198934i
$713$	22.7273	−	14.4412i	0.851145	−	0.540829i
$714$	0.0401239	−	2.83516i	0.00150160	−	0.106103i
$715$	−0.916330	+	0.929390i	−0.0342688	+	0.0347572i
$716$	0.594445	−	0.638067i	0.0222155	−	0.0238457i
$717$	3.21544	−	8.70636i	0.120083	−	0.325145i
$718$	7.15884	+	23.3761i	0.267166	+	0.872388i
$719$	0.568825	+	1.30736i	0.0212136	+	0.0487564i	0.927249	−	0.374446i	$-0.122167\pi$
$719$	0.568825	+	1.30736i	0.0212136	+	0.0487564i	−0.906035	+	0.423203i	$0.860906\pi$
$720$	−6.26133	−	11.5905i	−0.233346	−	0.431954i
$721$	6.72283	−	4.54384i	0.250371	−	0.169222i
$722$	81.5821	−	4.62291i	3.03617	−	0.172047i
$723$	6.36050	−	5.13574i	0.236549	−	0.191000i
$724$	−22.5190	+	10.9570i	−0.836914	+	0.407213i
$725$	−53.8464	−	14.0205i	−1.99981	−	0.520709i
$726$	−16.1931	−	1.84110i	−0.600982	−	0.0683296i
$727$	17.7459	−	40.7866i	0.658161	−	1.51269i	−0.189349	−	0.981910i	$-0.560638\pi$
$727$	17.7459	−	40.7866i	0.658161	−	1.51269i	0.847510	−	0.530780i	$-0.178101\pi$
$728$	−0.0556748	+	0.00473862i	−0.00206345	+	0.000175625i
$729$	−0.450204	+	0.892926i	−0.0166742	+	0.0330713i
$730$	−9.30443	+	50.0047i	−0.344373	+	1.85076i
$731$	4.91511	−	0.139148i	0.181792	−	0.00514657i
$732$	10.8105	+	10.9646i	0.399567	+	0.405262i
$733$	−24.5000	+	23.4814i	−0.904929	+	0.867304i	−0.991654	−	0.128928i	$-0.958846\pi$
$733$	−24.5000	+	23.4814i	−0.904929	+	0.867304i	0.0867253	+	0.996232i	$0.472360\pi$
$734$	−28.2618	+	14.7545i	−1.04316	+	0.544599i
$735$	23.0769	+	10.4314i	0.851206	+	0.384769i
$736$	−19.2572	+	69.8870i	−0.709829	+	2.57607i
$737$	−0.833875	−	19.6301i	−0.0307162	−	0.723082i
$738$	−17.4840	−	3.50994i	−0.643594	−	0.129203i
$739$	17.5727	+	6.77409i	0.646423	+	0.249189i	0.660632	−	0.750710i	$-0.270289\pi$
$739$	17.5727	+	6.77409i	0.646423	+	0.249189i	−0.0142084	+	0.999899i	$0.504523\pi$
$740$	22.3839	−	47.7083i	0.822848	−	1.75379i
$741$	1.45948	−	0.336222i	0.0536152	−	0.0123514i
$742$	2.80754	+	1.36605i	0.103068	+	0.0501493i
$743$	9.31365	+	7.96602i	0.341685	+	0.292245i	0.804191	−	0.594371i	$-0.202599\pi$
$743$	9.31365	+	7.96602i	0.341685	+	0.292245i	−0.462506	+	0.886616i	$0.653050\pi$
$744$	−0.812629	+	1.23978i	−0.0297924	+	0.0454527i
$745$	19.1464	+	12.1659i	0.701469	+	0.445723i
$746$	10.2116	−	30.2581i	0.373872	−	1.10783i
$747$	7.83465	+	3.27774i	0.286655	+	0.119926i
$748$	−3.22660	−	8.73657i	−0.117976	−	0.319441i
$749$	1.85597	−	1.41373i	0.0678156	−	0.0516566i
$750$	−33.1604	−	10.6708i	−1.21085	−	0.389643i
$751$	1.96186	−	46.1837i	0.0715893	−	1.68527i	−0.501018	−	0.865437i	$-0.667041\pi$
$751$	1.96186	−	46.1837i	0.0715893	−	1.68527i	0.572607	−	0.819830i	$-0.305932\pi$
$752$	−3.22097	+	13.1295i	−0.117457	+	0.478782i
$753$	−2.79286	−	8.27558i	−0.101778	−	0.301579i
$754$	0.167533	−	2.36378i	0.00610119	−	0.0860839i
$755$	−28.7171	+	11.0701i	−1.04512	+	0.402883i
$756$	−1.28289	+	0.219974i	−0.0466583	+	0.00800036i
$757$	−29.2447	−	35.1882i	−1.06292	−	1.27894i	−0.958711	−	0.284382i	$-0.908211\pi$
$757$	−29.2447	−	35.1882i	−1.06292	−	1.27894i	−0.104205	−	0.994556i	$-0.533230\pi$
$758$	5.88492	+	0.838397i	0.213750	+	0.0304520i
$759$	15.5819	−	1.77161i	0.565587	−	0.0643053i
$760$	4.19216	−	13.6888i	0.152066	−	0.496547i
$761$	−17.6730	−	13.4619i	−0.640645	−	0.487993i	0.234332	−	0.972157i	$-0.424710\pi$
$761$	−17.6730	−	13.4619i	−0.640645	−	0.487993i	−0.874978	+	0.484163i	$0.839124\pi$
$762$	3.92636	+	5.63566i	0.142237	+	0.204158i
$763$	−1.49320	−	1.07201i	−0.0540574	−	0.0388094i
$764$	14.8794	+	12.0143i	0.538319	+	0.434662i
$765$	8.77502	+	2.02151i	0.317262	+	0.0730880i
$766$	6.44977	−	8.22330i	0.233040	−	0.297120i
$767$	1.95499	−	0.883712i	0.0705907	−	0.0319090i
$768$	1.78694	+	11.3866i	0.0644807	+	0.410878i
$769$	−7.37492	+	4.39822i	−0.265946	+	0.158604i	−0.639002	−	0.769205i	$-0.720652\pi$
$769$	−7.37492	+	4.39822i	−0.265946	+	0.158604i	0.373056	+	0.927809i	$0.378310\pi$
$770$	−7.97829	−	0.452096i	−0.287518	−	0.0162924i
$771$	−15.7951	+	11.3397i	−0.568845	+	0.408391i
$772$	32.0772	+	11.3336i	1.15448	+	0.407905i
$773$	33.9224	+	38.5433i	1.22010	+	1.38631i	0.898231	+	0.439525i	$0.144853\pi$
$773$	33.9224	+	38.5433i	1.22010	+	1.38631i	0.321873	+	0.946783i	$0.395687\pi$
$774$	−0.900367	−	4.17772i	−0.0323630	−	0.150165i
$775$	−5.21329	−	28.0177i	−0.187267	−	1.00643i
$776$	−5.55265	−	1.61490i	−0.199329	−	0.0579715i
$777$	2.59909	+	2.49103i	0.0932420	+	0.0893652i
$778$	−0.110288	−	7.79296i	−0.00395402	−	0.279391i
$779$	36.3758	+	55.4966i	1.30330	+	1.98837i
$780$	0.211334	−	1.65034i	0.00756698	−	0.0590916i
$781$	1.66829	−	13.0279i	0.0596962	−	0.466177i
$782$	−23.8741	−	36.4234i	−0.853736	−	1.30250i
$783$	−0.0833125	−	5.88687i	−0.00297735	−	0.210380i
$784$	−16.6676	−	15.9746i	−0.595270	−	0.570521i
$785$	49.4993	+	14.3961i	1.76671	+	0.513818i
$786$	8.58373	+	46.1315i	0.306171	+	1.64545i
$787$	−1.26090	−	5.85060i	−0.0449463	−	0.208551i	0.949505	−	0.313753i	$-0.101586\pi$
$787$	−1.26090	−	5.85060i	−0.0449463	−	0.208551i	−0.994451	+	0.105201i	$0.966451\pi$
$788$	−10.8241	−	12.2985i	−0.385591	−	0.438117i
$789$	−16.4817	−	5.82335i	−0.586764	−	0.207317i
$790$	70.1517	−	50.3640i	2.49589	−	1.79187i
$791$	−5.58684	−	0.316583i	−0.198645	−	0.0112564i
$792$	−0.741477	+	0.442199i	−0.0263472	+	0.0157128i
$793$	−0.208462	−	1.32834i	−0.00740269	−	0.0471707i
$794$	53.7131	−	24.2799i	1.90621	−	0.861660i
$795$	−6.11943	+	7.80212i	−0.217034	+	0.276713i
$796$	−26.0938	−	6.01127i	−0.924870	−	0.213064i
$797$	−14.5952	−	11.7848i	−0.516990	−	0.417440i	0.334039	−	0.942559i	$-0.391588\pi$
$797$	−14.5952	−	11.7848i	−0.516990	−	0.417440i	−0.851029	+	0.525119i	$0.824021\pi$
$798$	7.44909	+	5.34792i	0.263695	+	0.189314i
$799$	−5.28243	−	7.58209i	−0.186879	−	0.268235i
$800$	61.0324	+	46.4897i	2.15782	+	1.64366i
$801$	0.325564	−	1.06308i	0.0115033	−	0.0375621i
$802$	−21.4937	+	2.44376i	−0.758968	+	0.0862922i
$803$	−11.2989	−	1.60971i	−0.398731	−	0.0568054i
$804$	16.0092	+	19.2629i	0.564603	+	0.679350i
$805$	−19.4522	+	3.33542i	−0.685601	+	0.117558i
$806$	1.13249	−	0.436561i	0.0398902	−	0.0153772i
$807$	−0.869207	+	12.2640i	−0.0305975	+	0.431712i
$808$	1.40640	+	4.16731i	0.0494768	+	0.146606i
$809$	−4.91821	+	20.0479i	−0.172915	+	0.704846i	0.818546	+	0.574441i	$0.194781\pi$
$809$	−4.91821	+	20.0479i	−0.172915	+	0.704846i	−0.991461	+	0.130404i	$0.958372\pi$
$810$	0.332166	−	7.81945i	0.0116711	−	0.274747i
$811$	−33.6158	−	10.8173i	−1.18041	−	0.379848i	−0.349865	−	0.936800i	$-0.613772\pi$
$811$	−33.6158	−	10.8173i	−1.18041	−	0.379848i	−0.830545	+	0.556952i	$0.811971\pi$
$812$	6.09609	−	4.64352i	0.213931	−	0.162956i
$813$	1.45087	+	3.92849i	0.0508844	+	0.137778i
$814$	20.6539	+	8.64086i	0.723919	+	0.302862i
$815$	18.1109	−	53.6648i	0.634398	−	1.87980i
$816$	−6.92856	−	4.40250i	−0.242548	−	0.154118i
$817$	−8.71748	+	13.2998i	−0.304986	+	0.465301i
$818$	6.91326	+	5.91295i	0.241717	+	0.206741i
$819$	0.102207	+	0.0497302i	0.00357139	+	0.00173771i
$820$	71.8337	−	16.5484i	2.50854	−	0.577897i
$821$	5.29518	−	11.2860i	0.184803	−	0.393884i	−0.791226	−	0.611524i	$-0.790557\pi$
$821$	5.29518	−	11.2860i	0.184803	−	0.393884i	0.976029	+	0.217640i	$0.0698360\pi$
$822$	−7.42370	−	2.86175i	−0.258931	−	0.0998150i
$823$	−4.31338	−	0.865919i	−0.150355	−	0.0301840i	0.121068	−	0.992644i	$-0.461368\pi$
$823$	−4.31338	−	0.865919i	−0.150355	−	0.0301840i	−0.271423	+	0.962460i	$0.587494\pi$
$824$	0.291191	+	6.85486i	0.0101441	+	0.238801i
$825$	4.40905	−	16.0011i	0.153503	−	0.557085i
$826$	11.9699	+	5.41072i	0.416485	+	0.188263i
$827$	24.2604	−	12.6656i	0.843617	−	0.440425i	0.0147643	−	0.999891i	$-0.495300\pi$
$827$	24.2604	−	12.6656i	0.843617	−	0.440425i	0.828853	+	0.559466i	$0.188994\pi$
$828$	−14.4332	+	13.8331i	−0.501589	+	0.480734i
$829$	−18.4425	−	18.7054i	−0.640535	−	0.649664i	0.313420	−	0.949615i	$-0.398525\pi$
$829$	−18.4425	−	18.7054i	−0.640535	−	0.649664i	−0.953955	+	0.299951i	$0.903030\pi$
$830$	−66.4412	+	1.88096i	−2.30621	+	0.0652892i
$831$	1.68754	−	9.06936i	0.0585403	−	0.314612i
$832$	−0.861011	+	1.70771i	−0.0298502	+	0.0592043i
$833$	15.7241	−	1.33832i	0.544807	−	0.0463699i
$834$	16.7008	−	38.3845i	0.578302	−	1.32915i
$835$	−53.3114	−	6.06133i	−1.84492	−	0.209761i
$836$	29.1482	+	7.58959i	1.00811	+	0.262491i
$837$	2.71151	−	1.31932i	0.0937233	−	0.0456025i
$838$	−9.13202	+	7.37359i	−0.315460	+	0.254716i
$839$	−20.2024	+	1.14478i	−0.697463	+	0.0395223i	−0.401743	−	0.915752i	$-0.631596\pi$
$839$	−20.2024	+	1.14478i	−0.697463	+	0.0395223i	−0.295720	+	0.955275i	$0.595559\pi$
$840$	0.900168	−	0.608407i	0.0310588	−	0.0209921i
$841$	2.69119	+	4.98175i	0.0927997	+	0.171784i
$842$	12.2230	+	28.0928i	0.421231	+	0.968141i
$843$	−5.58241	−	18.2285i	−0.192268	−	0.627822i
$844$	−1.88427	+	5.10197i	−0.0648591	+	0.175617i
$845$	33.5873	−	36.0521i	1.15544	−	1.24023i
$846$	−5.63884	+	5.71921i	−0.193867	+	0.196630i
$847$	−0.0651257	+	4.60179i	−0.00223775	+	0.158119i
$848$	7.62935	−	4.84779i	0.261993	−	0.166474i
$849$	3.19982	+	13.0433i	0.109817	+	0.447643i
$850$	−45.1901	+	9.07200i	−1.55001	+	0.311167i
$851$	54.4992	+	9.34482i	1.86821	+	0.320336i
$852$	8.37185	+	14.5005i	0.286815	+	0.496778i
$853$	1.13201	−	1.96070i	0.0387593	−	0.0671330i	−0.845995	−	0.533191i	$-0.820993\pi$
$853$	1.13201	−	1.96070i	0.0387593	−	0.0671330i	0.884754	+	0.466058i	$0.154326\pi$
$854$	5.26199	−	6.33142i	0.180062	−	0.216657i
$855$	−21.5869	+	19.5478i	−0.738255	+	0.668521i
$856$	0.195096	+	1.96305i	0.00666825	+	0.0670955i
$857$	−22.1818	+	41.0614i	−0.757716	+	1.40263i	0.152417	+	0.988316i	$0.451294\pi$
$857$	−22.1818	+	41.0614i	−0.757716	+	1.40263i	−0.910133	+	0.414315i	$0.864021\pi$
$858$	0.704315	+	0.0599460i	0.0240449	+	0.00204652i
$859$	−25.4607	+	41.3509i	−0.868710	+	1.41087i	0.0425735	+	0.999093i	$0.486444\pi$
$859$	−25.4607	+	41.3509i	−0.868710	+	1.41087i	−0.911283	+	0.411781i	$0.864907\pi$
$860$	10.5047	+	14.2033i	0.358208	+	0.484329i
$861$	−0.498030	+	5.01114i	−0.0169728	+	0.170779i
$862$	−56.2275	−	38.0031i	−1.91512	−	1.29439i
$863$	−40.9117	−	24.3987i	−1.39265	−	0.830542i	−0.396486	−	0.918041i	$-0.629770\pi$
$863$	−40.9117	−	24.3987i	−1.39265	−	0.830542i	−0.996165	+	0.0874986i	$0.972113\pi$
$864$	−3.02682	+	7.53254i	−0.102975	+	0.256262i
$865$	−45.7023	−	74.2253i	−1.55393	−	2.52374i
$866$	26.8238	+	53.2018i	0.911509	+	1.80787i
$867$	−10.9357	+	3.18046i	−0.371394	+	0.108014i
$868$	3.47932	+	1.81644i	0.118096	+	0.0616539i
$869$	11.9590	+	15.2474i	0.405680	+	0.517232i
$870$	19.5719	+	41.7150i	0.663551	+	1.41427i
$871$	−0.154632	−	2.18175i	−0.00523949	−	0.0739259i
$872$	1.43382	−	0.599861i	0.0485554	−	0.0203138i
$873$	8.01842	+	8.60684i	0.271382	+	0.291297i
$874$	140.788	+	3.98575i	4.76224	+	0.134820i
$875$	−2.07247	+	9.61631i	−0.0700624	+	0.325091i
$876$	12.7018	−	7.09566i	0.429155	−	0.239740i
$877$	22.9856	−	26.1167i	0.776169	−	0.881899i	−0.219429	−	0.975629i	$-0.570419\pi$
$877$	22.9856	−	26.1167i	0.776169	−	0.881899i	0.995598	+	0.0937292i	$0.0298788\pi$
$878$	−50.2453	−	28.0687i	−1.69570	−	0.947273i
$879$	25.0274	−	8.84274i	0.844153	−	0.298258i
$880$	−13.2250	+	18.9825i	−0.445816	+	0.639898i
$881$	30.8171	−	9.91675i	1.03826	−	0.334104i	0.262363	−	0.964969i	$-0.415498\pi$
$881$	30.8171	−	9.91675i	1.03826	−	0.334104i	0.775892	+	0.630865i	$0.217300\pi$
$882$	−3.64358	−	13.2231i	−0.122686	−	0.445244i
$883$	−3.77045	+	24.0257i	−0.126886	+	0.808529i	0.837964	+	0.545726i	$0.183746\pi$
$883$	−3.77045	+	24.0257i	−0.126886	+	0.808529i	−0.964849	+	0.262803i	$0.915353\pi$
$884$	−0.386571	−	0.962018i	−0.0130018	−	0.0323562i
$885$	−24.8066	+	33.5407i	−0.833864	+	1.12746i
$886$	−5.97869	−	5.41395i	−0.200858	−	0.181885i
$887$	12.3259	−	1.75601i	0.413862	−	0.0589610i	0.0690049	−	0.997616i	$-0.478018\pi$
$887$	12.3259	−	1.75601i	0.413862	−	0.0589610i	0.344857	+	0.938655i	$0.387927\pi$
$888$	−2.94579	+	0.767025i	−0.0988544	+	0.0257397i
$889$	1.47401	−	1.26072i	0.0494366	−	0.0422833i
$890$	1.10526	+	8.63113i	0.0370484	+	0.289316i
$891$	1.75617			0.0588339
$892$	−23.1830	−	24.0883i	−0.776225	−	0.806537i
$893$	29.8853			1.00007
$894$	−1.56052	−	12.1863i	−0.0521915	−	0.407571i
$895$	1.12530	−	0.962475i	0.0376146	−	0.0321720i
$896$	−2.19694	+	0.572038i	−0.0733946	+	0.0191105i
$897$	1.72833	−	0.246227i	0.0577073	−	0.00822129i
$898$	35.6408	+	32.2742i	1.18935	+	1.07700i
$899$	−10.5567	+	14.2736i	−0.352085	+	0.476051i
$900$	7.88906	+	19.6327i	0.262969	+	0.654423i
$901$	−0.957940	+	6.10409i	−0.0319136	+	0.203357i
$902$	8.31939	+	30.1922i	0.277005	+	1.00529i
$903$	−1.14882	+	0.369684i	−0.0382304	+	0.0123023i
$904$	2.70472	−	3.88220i	0.0899578	−	0.129120i
$905$	−40.0943	+	14.1662i	−1.33278	+	0.470901i
$906$	14.5519	+	8.12918i	0.483455	+	0.270074i
$907$	−10.0088	+	11.3722i	−0.332338	+	0.377609i	−0.892710	−	0.450632i	$-0.851199\pi$
$907$	−10.0088	+	11.3722i	−0.332338	+	0.377609i	0.560372	+	0.828241i	$0.310658\pi$
$908$	−56.9415	+	31.8094i	−1.88967	+	1.05563i
$909$	1.88492	−	8.74606i	0.0625189	−	0.290088i
$910$	−0.889227	−	0.0251742i	−0.0294776	−	0.000834516i
$911$	−19.3559	−	20.7764i	−0.641291	−	0.688351i	0.325026	−	0.945705i	$-0.394627\pi$
$911$	−19.3559	−	20.7764i	−0.641291	−	0.688351i	−0.966317	+	0.257354i	$0.917149\pi$
$912$	24.4913	−	10.2463i	0.810989	−	0.339289i
$913$	−1.05442	−	14.8772i	−0.0348963	−	0.492365i
$914$	−0.823717	−	1.75564i	−0.0272461	−	0.0580715i
$915$	16.1354	+	20.5723i	0.533421	+	0.680099i
$916$	14.0437	+	7.33177i	0.464018	+	0.242249i
$917$	12.7235	−	3.70044i	0.420168	−	0.122199i
$918$	−2.19563	−	4.35477i	−0.0724665	−	0.143729i
$919$	−29.1933	−	47.4130i	−0.962998	−	1.56401i	−0.818502	−	0.574504i	$-0.805195\pi$
$919$	−29.1933	−	47.4130i	−0.962998	−	1.56401i	−0.144496	−	0.989505i	$-0.546156\pi$
$920$	6.22212	−	15.4843i	0.205137	−	0.510504i
$921$	18.8824	+	11.2610i	0.622195	+	0.371062i
$922$	20.7716	+	14.0391i	0.684075	+	0.462354i
$923$	0.144602	−	1.45497i	0.00475962	−	0.0478910i
$924$	1.35924	+	1.83782i	0.0447159	+	0.0604598i
$925$	30.6831	−	49.8325i	1.00885	−	1.63848i
$926$	−15.4892	−	1.31833i	−0.509008	−	0.0433229i
$927$	6.63352	−	12.2795i	0.217873	−	0.403312i
$928$	−4.72670	−	47.5597i	−0.155161	−	1.56122i
$929$	32.7295	−	29.6379i	1.07382	−	0.972389i	0.0741293	−	0.997249i	$-0.476382\pi$
$929$	32.7295	−	29.6379i	1.07382	−	0.972389i	0.999691	+	0.0248593i	$0.00791378\pi$
$930$	−15.0846	+	18.1503i	−0.494642	+	0.595171i
$931$	−25.5183	+	44.1990i	−0.836329	+	1.44856i
$932$	−10.4995	−	18.1857i	−0.343923	−	0.595693i
$933$	22.8128	+	3.91164i	0.746857	+	0.128061i
$934$	−8.30551	+	1.66735i	−0.271765	+	0.0545573i
$935$	−3.76784	−	15.3587i	−0.123221	−	0.502282i
$936$	−0.0811166	+	0.0515426i	−0.00265138	+	0.00168472i
$937$	−0.276349	+	19.5268i	−0.00902793	+	0.637914i	0.943150	+	0.332369i	$0.107848\pi$
$937$	−0.276349	+	19.5268i	−0.00902793	+	0.637914i	−0.952177	+	0.305545i	$0.901161\pi$
$938$	9.40217	−	9.53618i	0.306992	−	0.311367i
$939$	−16.4820	+	17.6916i	−0.537871	+	0.577342i
$940$	11.5021	−	31.1438i	0.375157	−	1.01580i
$941$	−8.48892	−	27.7192i	−0.276731	−	0.903622i	−0.981053	−	0.193741i	$-0.937938\pi$
$941$	−8.48892	−	27.7192i	−0.276731	−	0.903622i	0.704322	−	0.709881i	$-0.251251\pi$
$942$	−11.1388	−	25.6010i	−0.362922	−	0.834125i
$943$	36.7623	+	68.0518i	1.19715	+	2.21607i
$944$	31.5084	−	21.2960i	1.02551	−	0.693124i
$945$	−2.20660	+	0.125039i	−0.0717806	+	0.00406751i
$946$	−5.83934	+	4.71494i	−0.189853	+	0.153296i
$947$	−24.7543	+	12.0446i	−0.804406	+	0.391396i	−0.793520	−	0.608545i	$-0.791754\pi$
$947$	−24.7543	+	12.0446i	−0.804406	+	0.391396i	−0.0108863	+	0.999941i	$0.503465\pi$
$948$	−23.9058	−	6.22459i	−0.776425	−	0.202165i
$949$	−1.26239	−	0.143529i	−0.0409788	−	0.00465916i
$950$	59.4713	−	136.686i	1.92950	−	4.43469i
$951$	8.88982	−	0.756635i	0.288272	−	0.0245356i
$952$	0.304802	−	0.604538i	0.00987867	−	0.0195932i
$953$	3.78547	−	20.3442i	0.122623	−	0.659014i	−0.864950	−	0.501857i	$-0.832650\pi$
$953$	3.78547	−	20.3442i	0.122623	−	0.659014i	0.987574	−	0.157156i	$-0.0502327\pi$
$954$	5.36810	−	0.151972i	0.173799	−	0.00492027i
$955$	22.7989	+	23.1239i	0.737756	+	0.748270i
$956$	15.0011	−	14.3774i	0.485170	−	0.464998i
$957$	−9.16551	+	4.78501i	−0.296279	+	0.154677i
$958$	47.0164	+	21.2528i	1.51903	+	0.686646i
$959$	−0.596845	+	2.16603i	−0.0192731	+	0.0699448i
$960$	−1.57829	−	37.1542i	−0.0509392	−	1.19915i
$961$	21.4786	+	4.31187i	0.692858	+	0.139092i
$962$	2.32553	+	0.896467i	0.0749782	+	0.0289032i
$963$	1.70450	−	3.63291i	0.0549266	−	0.117069i
$964$	17.8350	−	4.10867i	0.574427	−	0.132331i
$965$	51.9443	+	25.2743i	1.67215	+	0.813608i
$966$	8.12301	+	6.94765i	0.261354	+	0.223537i
$967$	−1.48728	+	2.26906i	−0.0478277	+	0.0729681i	−0.859469	−	0.511189i	$-0.829205\pi$
$967$	−1.48728	+	2.26906i	−0.0478277	+	0.0729681i	0.811641	+	0.584157i	$0.198575\pi$
$968$	−3.28443	−	2.08697i	−0.105566	−	0.0670779i
$969$	−5.80280	+	17.1944i	−0.186413	+	0.552362i
$970$	−84.9315	−	35.5323i	−2.72699	−	1.14087i
$971$	4.93918	+	13.3737i	0.158506	+	0.429181i	0.992447	−	0.122672i	$-0.0391462\pi$
$971$	4.93918	+	13.3737i	0.158506	+	0.429181i	−0.833941	+	0.551853i	$0.813921\pi$
$972$	−1.78095	+	1.35659i	−0.0571240	+	0.0435125i
$973$	−11.2527	−	3.62105i	−0.360746	−	0.116086i
$974$	−2.10364	+	49.5214i	−0.0674051	+	1.58677i
$975$	0.440220	−	1.79445i	0.0140983	−	0.0574682i
$976$	−7.62135	−	22.5829i	−0.243954	−	0.722863i
$977$	−1.37725	+	19.4321i	−0.0440621	+	0.621689i	0.925797	+	0.378022i	$0.123395\pi$
$977$	−1.37725	+	19.4321i	−0.0440621	+	0.621689i	−0.969859	+	0.243667i	$0.921650\pi$
$978$	−28.6220	+	11.0334i	−0.915229	+	0.352810i
$979$	−1.92445	+	0.329980i	−0.0615057	+	0.0105462i
$980$	36.2389	+	43.6039i	1.15761	+	1.39288i
$981$	−3.13004	−	0.445922i	−0.0999345	−	0.0142372i
$982$	−24.6670	+	2.80456i	−0.787156	+	0.0894970i
$983$	−3.90390	+	12.7476i	−0.124515	+	0.406584i	−0.996563	−	0.0828358i	$-0.973602\pi$
$983$	−3.90390	+	12.7476i	−0.124515	+	0.406584i	0.872048	+	0.489420i	$0.162791\pi$
$984$	−3.38725	−	2.58014i	−0.107982	−	0.0822520i
$985$	−15.9025	−	22.8255i	−0.506695	−	0.727280i
$986$	23.3244	+	16.7453i	0.742801	+	0.533278i
$987$	1.76462	+	1.42483i	0.0561684	+	0.0453528i
$988$	3.26744	+	0.752724i	0.103951	+	0.0239474i
$989$	−11.4395	+	14.5851i	−0.363756	+	0.463781i
$990$	−12.5245	+	5.66145i	−0.398056	+	0.179933i
$991$	4.33876	+	27.6470i	0.137825	+	0.878236i	0.953864	+	0.300239i	$0.0970665\pi$
$991$	4.33876	+	27.6470i	0.137825	+	0.878236i	−0.816039	+	0.577997i	$0.803834\pi$
$992$	21.0242	−	12.5383i	0.667520	−	0.398093i
$993$	33.2021	+	1.88143i	1.05364	+	0.0597052i
$994$	7.27220	−	5.22093i	0.230660	−	0.165598i
$995$	−42.8705	−	15.1471i	−1.35909	−	0.480196i
$996$	12.5615	+	14.2727i	0.398027	+	0.452246i
$997$	11.7711	+	54.6179i	0.372793	+	1.72977i	0.642017	+	0.766690i	$0.278098\pi$
$997$	11.7711	+	54.6179i	0.372793	+	1.72977i	−0.269224	+	0.963078i	$0.586767\pi$
$998$	−12.7015	−	68.2617i	−0.402059	−	2.16078i
$999$	5.94577	+	1.72923i	0.188116	+	0.0547104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.m.b.19.3	✓	1368
223.47	even	111	inner	669.2.m.b.493.3	yes	1368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.m.b.19.3	✓	1368	1.1	even	1	trivial
669.2.m.b.493.3	yes	1368	223.47	even	111	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:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.m (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261508 - 2.04215i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(-2.16654 + 0.564122i) q^{4} +(-3.76343 + 0.536159i) q^{5} +(1.52610 + 1.38195i) q^{6} +(0.345717 - 0.467440i) q^{7} +(0.183294 + 0.456145i) q^{8} +(0.155037 - 0.987909i) q^{9} +(2.07909 + 7.54530i) q^{10} +(-1.67175 + 0.537957i) q^{11} +(1.27978 - 1.83692i) q^{12} +(-0.184333 + 0.0651289i) q^{13} +(-1.04499 - 0.583768i) q^{14} +(2.51151 - 2.85363i) q^{15} +(-3.02538 + 1.69008i) q^{16} +(0.499058 - 2.31564i) q^{17} +(-2.05800 - 0.0582625i) q^{18} +(5.22206 + 5.60528i) q^{19} +(7.85115 - 3.28464i) q^{20} +(0.0411032 + 0.579941i) q^{21} +(1.53577 + 3.27328i) q^{22} +(5.51101 + 7.02640i) q^{23} +(-0.435782 - 0.227507i) q^{24} +(9.07490 - 2.63929i) q^{25} +(0.181208 + 0.359404i) q^{26} +(0.524307 + 0.851529i) q^{27} +(-0.485315 + 1.20775i) q^{28} +(-5.05652 - 3.01559i) q^{29} +(-6.48433 - 4.38264i) q^{30} +(0.298219 - 3.00066i) q^{31} +(4.82719 + 6.52680i) q^{32} +(0.920773 - 1.49543i) q^{33} +(-4.85940 - 0.413596i) q^{34} +(-1.05046 + 1.94454i) q^{35} +(0.221409 + 2.22780i) q^{36} +(4.58990 - 4.15635i) q^{37} +(10.0812 - 12.1301i) q^{38} +(0.0977501 - 0.169308i) q^{39} +(-0.934382 - 1.61840i) q^{40} +(8.53704 + 1.46382i) q^{41} +(1.17358 - 0.235598i) q^{42} +(0.494568 + 2.01598i) q^{43} +(3.31842 - 2.10857i) q^{44} +(-0.0537935 + 3.80105i) q^{45} +(12.9078 - 13.0918i) q^{46} +(2.65915 - 2.85429i) q^{47} +(1.20060 - 3.25082i) q^{48} +(1.95078 + 6.36996i) q^{49} +(-7.76298 - 17.8421i) q^{50} +(1.12588 + 2.08414i) q^{51} +(0.362623 - 0.245090i) q^{52} +(-2.60422 + 0.147570i) q^{53} +(1.60184 - 1.29340i) q^{54} +(6.00308 - 2.92089i) q^{55} +(0.276588 + 0.0720180i) q^{56} +(-7.61184 - 0.865441i) q^{57} +(-4.83597 + 11.1148i) q^{58} +(-10.9346 + 0.930672i) q^{59} +(-3.83148 + 7.59929i) q^{60} +(-1.25815 + 6.76166i) q^{61} +(-6.20579 + 0.175687i) q^{62} +(-0.408189 - 0.414007i) q^{63} +(7.06257 - 6.76893i) q^{64} +(0.658805 - 0.343940i) q^{65} +(-3.29469 - 1.48929i) q^{66} +(-2.97202 + 10.7859i) q^{67} +(0.225075 + 5.29844i) q^{68} +(-8.75513 - 1.75761i) q^{69} +(4.24575 + 1.63669i) q^{70} +(-3.17672 + 6.77077i) q^{71} +(0.479047 - 0.110359i) q^{72} +(5.84379 + 2.84338i) q^{73} +(-9.68819 - 8.28636i) q^{74} +(-5.18093 + 7.90427i) q^{75} +(-14.4758 - 9.19815i) q^{76} +(-0.326488 + 0.967422i) q^{77} +(-0.371316 - 0.155345i) q^{78} +(-3.82276 - 10.3508i) q^{79} +(10.4797 - 7.98258i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(0.756846 - 17.8167i) q^{82} +(-2.02345 + 8.24809i) q^{83} +(-0.416209 - 1.23327i) q^{84} +(-0.636622 + 8.98233i) q^{85} +(3.98761 - 1.53718i) q^{86} +(5.80277 - 0.994986i) q^{87} +(-0.551808 - 0.663955i) q^{88} +(1.10070 + 0.156812i) q^{89} +(7.77640 - 0.884151i) q^{90} +(-0.0332831 + 0.108681i) q^{91} +(-15.9035 - 12.1141i) q^{92} +(1.72375 + 2.47418i) q^{93} +(-6.52428 - 4.68397i) q^{94} +(-22.6582 - 18.2952i) q^{95} +(-7.91073 - 1.82241i) q^{96} +(-7.25962 + 9.25584i) q^{97} +(12.4983 - 5.64958i) q^{98} +(0.272271 + 1.73494i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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