LMFDB - Embedded newform 273.2.cg.b.124.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [273,2,Mod(19,273)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(273, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("273.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			124.4
Character	$\chi$	$=$	273.124
Dual form			273.2.cg.b.262.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.185934 + 0.693915i) q^{2} -1.00000i q^{3} +(1.28510 + 0.741955i) q^{4} +(0.295002 + 1.10096i) q^{5} +(0.693915 + 0.185934i) q^{6} +(-0.650764 + 2.56447i) q^{7} +(-1.76976 + 1.76976i) q^{8} -1.00000 q^{9} -0.818827 q^{10} +(-1.26481 + 1.26481i) q^{11} +(0.741955 - 1.28510i) q^{12} +(3.60058 - 0.189346i) q^{13} +(-1.65853 - 0.928398i) q^{14} +(1.10096 - 0.295002i) q^{15} +(0.584904 + 1.01308i) q^{16} +(1.84581 - 3.19704i) q^{17} +(0.185934 - 0.693915i) q^{18} +(-0.439817 + 0.439817i) q^{19} +(-0.437757 + 1.63373i) q^{20} +(2.56447 + 0.650764i) q^{21} +(-0.642501 - 1.11284i) q^{22} +(-1.96021 + 1.13173i) q^{23} +(1.76976 + 1.76976i) q^{24} +(3.20503 - 1.85043i) q^{25} +(-0.538079 + 2.53370i) q^{26} +1.00000i q^{27} +(-2.73902 + 2.81277i) q^{28} +(-0.0743668 + 0.128807i) q^{29} +0.818827i q^{30} +(4.64644 + 1.24501i) q^{31} +(-5.64683 + 1.51306i) q^{32} +(1.26481 + 1.26481i) q^{33} +(1.87528 + 1.87528i) q^{34} +(-3.01537 + 0.0400569i) q^{35} +(-1.28510 - 0.741955i) q^{36} +(-4.33485 - 1.16152i) q^{37} +(-0.223419 - 0.386973i) q^{38} +(-0.189346 - 3.60058i) q^{39} +(-2.47053 - 1.42636i) q^{40} +(-1.12389 - 4.19440i) q^{41} +(-0.928398 + 1.65853i) q^{42} +(6.81492 - 3.93460i) q^{43} +(-2.56385 + 0.686981i) q^{44} +(-0.295002 - 1.10096i) q^{45} +(-0.420853 - 1.57064i) q^{46} +(-0.291034 + 0.0779824i) q^{47} +(1.01308 - 0.584904i) q^{48} +(-6.15301 - 3.33773i) q^{49} +(0.688114 + 2.56808i) q^{50} +(-3.19704 - 1.84581i) q^{51} +(4.76760 + 2.42814i) q^{52} +(-6.19942 - 10.7377i) q^{53} +(-0.693915 - 0.185934i) q^{54} +(-1.76564 - 1.01939i) q^{55} +(-3.38680 - 5.69020i) q^{56} +(0.439817 + 0.439817i) q^{57} +(-0.0755539 - 0.0755539i) q^{58} +(13.7549 - 3.68562i) q^{59} +(1.63373 + 0.437757i) q^{60} +2.90957i q^{61} +(-1.72786 + 2.99275i) q^{62} +(0.650764 - 2.56447i) q^{63} -1.86013i q^{64} +(1.27064 + 3.90825i) q^{65} +(-1.11284 + 0.642501i) q^{66} +(-8.53567 - 8.53567i) q^{67} +(4.74412 - 2.73902i) q^{68} +(1.13173 + 1.96021i) q^{69} +(0.532863 - 2.09986i) q^{70} +(-3.67037 + 13.6980i) q^{71} +(1.76976 - 1.76976i) q^{72} +(3.05289 - 11.3935i) q^{73} +(1.61199 - 2.79205i) q^{74} +(-1.85043 - 3.20503i) q^{75} +(-0.891535 + 0.238886i) q^{76} +(-2.42048 - 4.06667i) q^{77} +(2.53370 + 0.538079i) q^{78} +(-0.537165 + 0.930397i) q^{79} +(-0.942821 + 0.942821i) q^{80} +1.00000 q^{81} +3.11953 q^{82} +(-3.90388 + 3.90388i) q^{83} +(2.81277 + 2.73902i) q^{84} +(4.06435 + 1.08904i) q^{85} +(1.46315 + 5.46056i) q^{86} +(0.128807 + 0.0743668i) q^{87} -4.47683i q^{88} +(2.99167 - 11.1651i) q^{89} +0.818827 q^{90} +(-1.85755 + 9.35679i) q^{91} -3.35876 q^{92} +(1.24501 - 4.64644i) q^{93} -0.216453i q^{94} +(-0.613970 - 0.354476i) q^{95} +(1.51306 + 5.64683i) q^{96} +(-4.98572 - 1.33592i) q^{97} +(3.46016 - 3.64907i) q^{98} +(1.26481 - 1.26481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.185934	+	0.693915i	−0.131475	+	0.490672i	−0.999988	−	0.00499535i	$-0.998410\pi$
$2$	−0.185934	+	0.693915i	−0.131475	+	0.490672i	0.868512	+	0.495668i	$0.165077\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.28510	+	0.741955i	0.642552	+	0.370977i
$5$	0.295002	+	1.10096i	0.131929	+	0.492366i	0.999992	−	0.00408873i	$-0.00130149\pi$
$5$	0.295002	+	1.10096i	0.131929	+	0.492366i	−0.868063	+	0.496455i	$0.834635\pi$
$6$	0.693915	+	0.185934i	0.283290	+	0.0759073i
$7$	−0.650764	+	2.56447i	−0.245966	+	0.969279i
$7$	−0.650764	+	2.56447i	−0.245966	+	0.969279i
$8$	−1.76976	+	1.76976i	−0.625705	+	0.625705i
$9$	−1.00000			−0.333333
$10$	−0.818827			−0.258936
$11$	−1.26481	+	1.26481i	−0.381355	+	0.381355i	−0.871590	−	0.490235i	$-0.836911\pi$
$11$	−1.26481	+	1.26481i	−0.381355	+	0.381355i	0.490235	+	0.871590i	$0.336911\pi$
$12$	0.741955	−	1.28510i	0.214184	−	0.370977i
$13$	3.60058	−	0.189346i	0.998620	−	0.0525152i
$13$	3.60058	−	0.189346i	0.998620	−	0.0525152i
$14$	−1.65853	−	0.928398i	−0.443260	−	0.248125i
$15$	1.10096	−	0.295002i	0.284268	−	0.0761693i
$16$	0.584904	+	1.01308i	0.146226	+	0.253271i
$17$	1.84581	−	3.19704i	0.447675	−	0.775397i	−0.550559	−	0.834796i	$-0.685585\pi$
$17$	1.84581	−	3.19704i	0.447675	−	0.775397i	0.998234	+	0.0593997i	$0.0189187\pi$
$18$	0.185934	−	0.693915i	0.0438251	−	0.163557i
$19$	−0.439817	+	0.439817i	−0.100901	+	0.100901i	−0.755755	−	0.654854i	$-0.772730\pi$
$19$	−0.439817	+	0.439817i	−0.100901	+	0.100901i	0.654854	+	0.755755i	$0.272730\pi$
$20$	−0.437757	+	1.63373i	−0.0978855	+	0.365313i
$21$	2.56447	+	0.650764i	0.559613	+	0.142008i
$22$	−0.642501	−	1.11284i	−0.136982	−	0.237259i
$23$	−1.96021	+	1.13173i	−0.408731	+	0.235981i	−0.690244	−	0.723576i	$-0.742497\pi$
$23$	−1.96021	+	1.13173i	−0.408731	+	0.235981i	0.281513	+	0.959557i	$0.409164\pi$
$24$	1.76976	+	1.76976i	0.361251	+	0.361251i
$25$	3.20503	−	1.85043i	0.641006	−	0.370085i
$26$	−0.538079	+	2.53370i	−0.105526	+	0.496900i
$27$			1.00000i			0.192450i
$28$	−2.73902	+	2.81277i	−0.517626	+	0.531564i
$29$	−0.0743668	+	0.128807i	−0.0138096	+	0.0239189i	−0.872848	−	0.487993i	$-0.837729\pi$
$29$	−0.0743668	+	0.128807i	−0.0138096	+	0.0239189i	0.859038	+	0.511912i	$0.171063\pi$
$30$			0.818827i			0.149497i
$31$	4.64644	+	1.24501i	0.834525	+	0.223610i	0.650687	−	0.759346i	$-0.274481\pi$
$31$	4.64644	+	1.24501i	0.834525	+	0.223610i	0.183838	+	0.982956i	$0.441148\pi$
$32$	−5.64683	+	1.51306i	−0.998227	+	0.267474i
$33$	1.26481	+	1.26481i	0.220176	+	0.220176i
$34$	1.87528	+	1.87528i	0.321607	+	0.321607i
$35$	−3.01537	+	0.0400569i	−0.509690	+	0.00677085i
$36$	−1.28510	−	0.741955i	−0.214184	−	0.123659i
$37$	−4.33485	−	1.16152i	−0.712645	−	0.190953i	−0.115758	−	0.993277i	$-0.536930\pi$
$37$	−4.33485	−	1.16152i	−0.712645	−	0.190953i	−0.596888	+	0.802325i	$0.703596\pi$
$38$	−0.223419	−	0.386973i	−0.0362433	−	0.0627753i
$39$	−0.189346	−	3.60058i	−0.0303197	−	0.576554i
$40$	−2.47053	−	1.42636i	−0.390625	−	0.225527i
$41$	−1.12389	−	4.19440i	−0.175522	−	0.655056i	−0.996462	−	0.0840421i	$-0.973217\pi$
$41$	−1.12389	−	4.19440i	−0.175522	−	0.655056i	0.820941	−	0.571014i	$-0.193450\pi$
$42$	−0.928398	+	1.65853i	−0.143255	+	0.255916i
$43$	6.81492	−	3.93460i	1.03927	−	0.600021i	0.119641	−	0.992817i	$-0.461826\pi$
$43$	6.81492	−	3.93460i	1.03927	−	0.600021i	0.919625	+	0.392797i	$0.128492\pi$
$44$	−2.56385	+	0.686981i	−0.386515	+	0.103566i
$45$	−0.295002	−	1.10096i	−0.0439764	−	0.164122i
$46$	−0.420853	−	1.57064i	−0.0620513	−	0.231579i
$47$	−0.291034	+	0.0779824i	−0.0424517	+	0.0113749i	−0.279982	−	0.960005i	$-0.590329\pi$
$47$	−0.291034	+	0.0779824i	−0.0424517	+	0.0113749i	0.237531	+	0.971380i	$0.423662\pi$
$48$	1.01308	−	0.584904i	0.146226	−	0.0844236i
$49$	−6.15301	−	3.33773i	−0.879002	−	0.476819i
$50$	0.688114	+	2.56808i	0.0973141	+	0.363181i
$51$	−3.19704	−	1.84581i	−0.447675	−	0.258466i
$52$	4.76760	+	2.42814i	0.661147	+	0.336722i
$53$	−6.19942	−	10.7377i	−0.851556	−	1.47494i	−0.879804	−	0.475337i	$-0.842326\pi$
$53$	−6.19942	−	10.7377i	−0.851556	−	1.47494i	0.0282475	−	0.999601i	$-0.491007\pi$
$54$	−0.693915	−	0.185934i	−0.0944299	−	0.0253024i
$55$	−1.76564	−	1.01939i	−0.238078	−	0.137455i
$56$	−3.38680	−	5.69020i	−0.452580	−	0.760385i
$57$	0.439817	+	0.439817i	0.0582552	+	0.0582552i
$58$	−0.0755539	−	0.0755539i	−0.00992072	−	0.00992072i
$59$	13.7549	−	3.68562i	1.79074	−	0.479827i	0.798268	−	0.602303i	$-0.205750\pi$
$59$	13.7549	−	3.68562i	1.79074	−	0.479827i	0.992472	+	0.122476i	$0.0390833\pi$
$60$	1.63373	+	0.437757i	0.210914	+	0.0565142i
$61$			2.90957i			0.372533i	0.982499	+	0.186266i	$0.0596387\pi$
$61$			2.90957i			0.372533i	−0.982499	+	0.186266i	$0.940361\pi$
$62$	−1.72786	+	2.99275i	−0.219439	+	0.380079i
$63$	0.650764	−	2.56447i	0.0819886	−	0.323093i
$64$		−	1.86013i		−	0.232517i
$65$	1.27064	+	3.90825i	0.157604	+	0.484758i
$66$	−1.11284	+	0.642501i	−0.136982	+	0.0790864i
$67$	−8.53567	−	8.53567i	−1.04280	−	1.04280i	−0.999042	−	0.0437557i	$-0.986068\pi$
$67$	−8.53567	−	8.53567i	−1.04280	−	1.04280i	−0.0437557	−	0.999042i	$-0.513932\pi$
$68$	4.74412	−	2.73902i	0.575309	−	0.332155i
$69$	1.13173	+	1.96021i	0.136244	+	0.235981i
$70$	0.532863	−	2.09986i	0.0636893	−	0.250981i
$71$	−3.67037	+	13.6980i	−0.435593	+	1.62565i	0.304051	+	0.952656i	$0.401661\pi$
$71$	−3.67037	+	13.6980i	−0.435593	+	1.62565i	−0.739644	+	0.672999i	$0.765006\pi$
$72$	1.76976	−	1.76976i	0.208568	−	0.208568i
$73$	3.05289	−	11.3935i	0.357314	−	1.33351i	−0.520234	−	0.854024i	$-0.674155\pi$
$73$	3.05289	−	11.3935i	0.357314	−	1.33351i	0.877548	−	0.479490i	$-0.159178\pi$
$74$	1.61199	−	2.79205i	0.187390	−	0.324570i
$75$	−1.85043	−	3.20503i	−0.213669	−	0.370085i
$76$	−0.891535	+	0.238886i	−0.102266	+	0.0274021i
$77$	−2.42048	−	4.06667i	−0.275839	−	0.463440i
$78$	2.53370	+	0.538079i	0.286885	+	0.0609255i
$79$	−0.537165	+	0.930397i	−0.0604358	+	0.104678i	−0.894660	−	0.446747i	$-0.852582\pi$
$79$	−0.537165	+	0.930397i	−0.0604358	+	0.104678i	0.834224	+	0.551425i	$0.185916\pi$
$80$	−0.942821	+	0.942821i	−0.105411	+	0.105411i
$81$	1.00000			0.111111
$82$	3.11953			0.344494
$83$	−3.90388	+	3.90388i	−0.428507	+	0.428507i	−0.888119	−	0.459613i	$-0.847988\pi$
$83$	−3.90388	+	3.90388i	−0.428507	+	0.428507i	0.459613	+	0.888119i	$0.347988\pi$
$84$	2.81277	+	2.73902i	0.306899	+	0.298852i
$85$	4.06435	+	1.08904i	0.440840	+	0.118123i
$86$	1.46315	+	5.46056i	0.157776	+	0.588827i
$87$	0.128807	+	0.0743668i	0.0138096	+	0.00797296i
$88$		−	4.47683i		−	0.477232i
$89$	2.99167	−	11.1651i	0.317117	−	1.18350i	−0.604886	−	0.796312i	$-0.706781\pi$
$89$	2.99167	−	11.1651i	0.317117	−	1.18350i	0.922003	−	0.387184i	$-0.126552\pi$
$90$	0.818827			0.0863119
$91$	−1.85755	+	9.35679i	−0.194724	+	0.980858i
$92$	−3.35876			−0.350175
$93$	1.24501	−	4.64644i	0.129102	−	0.481813i
$94$		−	0.216453i		−	0.0223254i
$95$	−0.613970	−	0.354476i	−0.0629920	−	0.0363684i
$96$	1.51306	+	5.64683i	0.154426	+	0.576327i
$97$	−4.98572	−	1.33592i	−0.506224	−	0.135642i	−0.00333671	−	0.999994i	$-0.501062\pi$
$97$	−4.98572	−	1.33592i	−0.506224	−	0.135642i	−0.502887	+	0.864352i	$0.667729\pi$
$98$	3.46016	−	3.64907i	0.349529	−	0.368612i
$99$	1.26481	−	1.26481i	0.127118	−	0.127118i
$100$	5.49173			0.549173
$101$	3.91219			0.389277			0.194639	−	0.980875i	$-0.437647\pi$
$101$	3.91219			0.389277			0.194639	+	0.980875i	$0.437647\pi$
$102$	1.87528	−	1.87528i	0.185680	−	0.185680i
$103$	−0.950036	+	1.64551i	−0.0936098	+	0.162137i	−0.909028	−	0.416736i	$-0.863174\pi$
$103$	−0.950036	+	1.64551i	−0.0936098	+	0.162137i	0.815418	+	0.578873i	$0.196507\pi$
$104$	−6.03706	+	6.70726i	−0.591983	+	0.657701i
$105$	0.0400569	+	3.01537i	0.00390915	+	0.294270i
$106$	8.60375	−	2.30537i	0.835670	−	0.223917i
$107$	4.28971	+	7.43000i	0.414702	+	0.718285i	0.995397	−	0.0958359i	$-0.0305524\pi$
$107$	4.28971	+	7.43000i	0.414702	+	0.718285i	−0.580695	+	0.814121i	$0.697219\pi$
$108$	−0.741955	+	1.28510i	−0.0713946	+	0.123659i
$109$	−1.31677	+	4.91424i	−0.126123	+	0.470698i	−0.999877	−	0.0156698i	$-0.995012\pi$
$109$	−1.31677	+	4.91424i	−0.126123	+	0.470698i	0.873754	+	0.486368i	$0.161679\pi$
$110$	1.03566	−	1.03566i	0.0987466	−	0.0987466i
$111$	−1.16152	+	4.33485i	−0.110247	+	0.411446i
$112$	−2.97866	+	0.840690i	−0.281457	+	0.0794378i
$113$	−4.23850	−	7.34129i	−0.398724	−	0.690611i	0.594844	−	0.803841i	$-0.297214\pi$
$113$	−4.23850	−	7.34129i	−0.398724	−	0.690611i	−0.993569	+	0.113230i	$0.963880\pi$
$114$	−0.386973	+	0.223419i	−0.0362433	+	0.0209251i
$115$	−1.82425	−	1.82425i	−0.170113	−	0.170113i
$116$	−0.191138	+	0.110354i	−0.0177467	+	0.0102461i
$117$	−3.60058	+	0.189346i	−0.332873	+	0.0175051i
$118$			10.2300i			0.941752i
$119$	6.99753	+	6.81405i	0.641463	+	0.624643i
$120$	−1.42636	+	2.47053i	−0.130208	+	0.225527i
$121$			7.80050i			0.709136i
$122$	−2.01900	−	0.540989i	−0.182791	−	0.0489788i
$123$	−4.19440	+	1.12389i	−0.378197	+	0.101337i
$124$	5.04742	+	5.04742i	0.453271	+	0.453271i
$125$	7.01255	+	7.01255i	0.627222	+	0.627222i
$126$	1.65853	+	0.928398i	0.147753	+	0.0827082i
$127$	−11.4302	−	6.59920i	−1.01426	−	0.585584i	−0.101825	−	0.994802i	$-0.532468\pi$
$127$	−11.4302	−	6.59920i	−1.01426	−	0.585584i	−0.912437	+	0.409218i	$0.865802\pi$
$128$	−10.0029	−	2.68026i	−0.884138	−	0.236904i
$129$	−3.93460	−	6.81492i	−0.346422	−	0.600021i
$130$	−2.94825	+	0.155042i	−0.258579	+	0.0135981i
$131$	2.88915	+	1.66805i	0.252426	+	0.145738i	0.620875	−	0.783910i	$-0.286778\pi$
$131$	2.88915	+	1.66805i	0.252426	+	0.145738i	−0.368449	+	0.929648i	$0.620111\pi$
$132$	0.686981	+	2.56385i	0.0597940	+	0.223154i
$133$	−0.841680	−	1.41411i	−0.0729829	−	0.122619i
$134$	7.51010	−	4.33596i	0.648774	−	0.374570i
$135$	−1.10096	+	0.295002i	−0.0947559	+	0.0253898i
$136$	2.39135	+	8.92465i	0.205057	+	0.765282i
$137$	0.619181	+	2.31082i	0.0529002	+	0.197426i	0.987319	−	0.158751i	$-0.0507466\pi$
$137$	0.619181	+	2.31082i	0.0529002	+	0.197426i	−0.934418	+	0.356177i	$0.884080\pi$
$138$	−1.57064	+	0.420853i	−0.133702	+	0.0358254i
$139$	−8.38216	+	4.83944i	−0.710965	+	0.410476i	−0.811418	−	0.584466i	$-0.801304\pi$
$139$	−8.38216	+	4.83944i	−0.710965	+	0.410476i	0.100453	+	0.994942i	$0.467971\pi$
$140$	−3.90478	−	2.18579i	−0.330014	−	0.184733i
$141$	0.0779824	+	0.291034i	0.00656731	+	0.0245095i
$142$	−8.82281	−	5.09385i	−0.740394	−	0.427467i
$143$	−4.31457	+	4.79354i	−0.360802	+	0.400856i
$144$	−0.584904	−	1.01308i	−0.0487420	−	0.0844236i
$145$	−0.163750	−	0.0438768i	−0.0135987	−	0.00364377i
$146$	7.33852	+	4.23690i	0.607340	+	0.350648i
$147$	−3.33773	+	6.15301i	−0.275291	+	0.507492i
$148$	−4.70894	−	4.70894i	−0.387072	−	0.387072i
$149$	13.6133	+	13.6133i	1.11524	+	1.11524i	0.992430	+	0.122812i	$0.0391912\pi$
$149$	13.6133	+	13.6133i	1.11524	+	1.11524i	0.122812	+	0.992430i	$0.460809\pi$
$150$	2.56808	−	0.688114i	0.209683	−	0.0561843i
$151$	7.46774	+	2.00097i	0.607716	+	0.162837i	0.549537	−	0.835469i	$-0.314804\pi$
$151$	7.46774	+	2.00097i	0.607716	+	0.162837i	0.0581786	+	0.998306i	$0.481471\pi$
$152$		−	1.55674i		−	0.126268i
$153$	−1.84581	+	3.19704i	−0.149225	+	0.258466i
$154$	3.27197	−	0.923475i	0.263663	−	0.0744158i
$155$			5.48285i			0.440393i
$156$	2.42814	−	4.76760i	0.194406	−	0.381713i
$157$	−15.0022	+	8.66153i	−1.19731	+	0.691265i	−0.959954	−	0.280158i	$-0.909613\pi$
$157$	−15.0022	+	8.66153i	−1.19731	+	0.691265i	−0.237353	+	0.971424i	$0.576280\pi$
$158$	−0.545740	−	0.545740i	−0.0434167	−	0.0434167i
$159$	−10.7377	+	6.19942i	−0.851556	+	0.491646i
$160$	−3.33165	−	5.77060i	−0.263390	−	0.456206i
$161$	−1.62664	−	5.76338i	−0.128197	−	0.454218i
$162$	−0.185934	+	0.693915i	−0.0146084	+	0.0545191i
$163$	−4.17954	+	4.17954i	−0.327367	+	0.327367i	−0.851584	−	0.524218i	$-0.824358\pi$
$163$	−4.17954	+	4.17954i	−0.327367	+	0.327367i	0.524218	+	0.851584i	$0.324358\pi$
$164$	1.66775	−	6.22412i	0.130229	−	0.486022i
$165$	−1.01939	+	1.76564i	−0.0793594	+	0.137455i
$166$	−1.98310	−	3.43483i	−0.153918	−	0.266594i
$167$	2.99467	−	0.802421i	0.231735	−	0.0620932i	−0.141083	−	0.989998i	$-0.545058\pi$
$167$	2.99467	−	0.802421i	0.231735	−	0.0620932i	0.372818	+	0.927905i	$0.378392\pi$
$168$	−5.69020	+	3.38680i	−0.439008	+	0.261297i
$169$	12.9283	−	1.36351i	0.994484	−	0.104886i
$170$	−1.51140	+	2.61782i	−0.115919	+	0.200778i
$171$	0.439817	−	0.439817i	0.0336336	−	0.0336336i
$172$	11.6772			0.890377
$173$	24.8480			1.88916			0.944578	−	0.328287i	$-0.106471\pi$
$173$	24.8480			1.88916			0.944578	+	0.328287i	$0.106471\pi$
$174$	−0.0755539	+	0.0755539i	−0.00572773	+	0.00572773i
$175$	2.65964	+	9.42340i	0.201050	+	0.712342i
$176$	−2.02115	−	0.541567i	−0.152350	−	0.0408221i
$177$	−3.68562	−	13.7549i	−0.277028	−	1.03388i
$178$	7.19137	+	4.15194i	0.539016	+	0.311201i
$179$		−	8.87577i		−	0.663406i	−0.943384	−	0.331703i	$-0.892377\pi$
$179$		−	8.87577i		−	0.663406i	0.943384	−	0.331703i	$-0.107623\pi$
$180$	0.437757	−	1.63373i	0.0326285	−	0.121771i
$181$	3.34068			0.248311			0.124155	−	0.992263i	$-0.460378\pi$
$181$	3.34068			0.248311			0.124155	+	0.992263i	$0.460378\pi$
$182$	−6.14744	−	3.02873i	−0.455678	−	0.224504i
$183$	2.90957			0.215082
$184$	1.46621	−	5.47198i	0.108091	−	0.403400i
$185$		−	5.11517i		−	0.376075i
$186$	2.99275	+	1.72786i	0.219439	+	0.126693i
$187$	1.70905	+	6.37827i	0.124978	+	0.466425i
$188$	−0.431869	−	0.115719i	−0.0314973	−	0.00843967i
$189$	−2.56447	−	0.650764i	−0.186538	−	0.0473361i
$190$	0.360134	−	0.360134i	0.0261269	−	0.0261269i
$191$	15.7320			1.13833			0.569164	−	0.822224i	$-0.307267\pi$
$191$	15.7320			1.13833			0.569164	+	0.822224i	$0.307267\pi$
$192$	−1.86013			−0.134244
$193$	2.81149	−	2.81149i	0.202376	−	0.202376i	−0.598641	−	0.801017i	$-0.704293\pi$
$193$	2.81149	−	2.81149i	0.202376	−	0.202376i	0.801017	+	0.598641i	$0.204293\pi$
$194$	1.85403	−	3.21128i	0.133112	−	0.230556i
$195$	3.90825	−	1.27064i	0.279875	−	0.0909926i
$196$	−5.43081	−	8.85459i	−0.387915	−	0.632471i
$197$	11.2932	−	3.02601i	0.804609	−	0.215594i	0.167002	−	0.985956i	$-0.446591\pi$
$197$	11.2932	−	3.02601i	0.804609	−	0.215594i	0.637607	+	0.770362i	$0.279925\pi$
$198$	0.642501	+	1.11284i	0.0456606	+	0.0790864i
$199$	7.62525	−	13.2073i	0.540540	−	0.936242i	−0.458333	−	0.888780i	$-0.651553\pi$
$199$	7.62525	−	13.2073i	0.540540	−	0.936242i	0.998873	−	0.0474620i	$-0.0151133\pi$
$200$	−2.39733	+	8.94695i	−0.169517	+	0.632645i
$201$	−8.53567	+	8.53567i	−0.602060	+	0.602060i
$202$	−0.727409	+	2.71473i	−0.0511803	+	0.191008i
$203$	−0.281927	−	0.274535i	−0.0197874	−	0.0192686i
$204$	−2.73902	−	4.74412i	−0.191770	−	0.332155i
$205$	4.28634	−	2.47472i	0.299371	−	0.172842i
$206$	−0.965201	−	0.965201i	−0.0672487	−	0.0672487i
$207$	1.96021	−	1.13173i	0.136244	−	0.0786603i
$208$	2.29782	+	3.53694i	0.159325	+	0.245242i
$209$		−	1.11257i		−	0.0769582i
$210$	−2.09986	−	0.532863i	−0.144904	−	0.0367711i
$211$	−12.3892	+	21.4587i	−0.852907	+	1.47728i	0.0256666	+	0.999671i	$0.491829\pi$
$211$	−12.3892	+	21.4587i	−0.852907	+	1.47728i	−0.878573	+	0.477607i	$0.841504\pi$
$212$		−	18.3988i		−	1.26363i
$213$	13.6980	+	3.67037i	0.938572	+	0.251490i
$214$	−5.95340	+	1.59521i	−0.406966	+	0.109046i
$215$	6.34227	+	6.34227i	0.432539	+	0.432539i
$216$	−1.76976	−	1.76976i	−0.120417	−	0.120417i
$217$	−6.21653	+	11.1054i	−0.422005	+	0.753887i
$218$	−3.16523	−	1.82745i	−0.214377	−	0.123770i
$219$	−11.3935	−	3.05289i	−0.769904	−	0.206295i
$220$	−1.51268	−	2.62004i	−0.101985	−	0.176643i
$221$	6.04064	−	11.8607i	0.406338	−	0.797836i
$222$	−2.79205	−	1.61199i	−0.187390	−	0.108190i
$223$	−3.00869	−	11.2286i	−0.201477	−	0.751922i	−0.990495	−	0.137552i	$-0.956077\pi$
$223$	−3.00869	−	11.2286i	−0.201477	−	0.751922i	0.789018	−	0.614370i	$-0.210590\pi$
$224$	−0.205451	−	15.4658i	−0.0137273	−	1.03335i
$225$	−3.20503	+	1.85043i	−0.213669	+	0.123362i
$226$	5.88232	−	1.57616i	0.391286	−	0.104845i
$227$	4.29157	+	16.0164i	0.284842	+	1.06304i	0.948955	+	0.315412i	$0.102143\pi$
$227$	4.29157	+	16.0164i	0.284842	+	1.06304i	−0.664113	+	0.747632i	$0.731191\pi$
$228$	0.238886	+	0.891535i	0.0158206	+	0.0590433i
$229$	−26.6978	+	7.15366i	−1.76424	+	0.472727i	−0.987570	−	0.157179i	$-0.949760\pi$
$229$	−26.6978	+	7.15366i	−1.76424	+	0.472727i	−0.776672	+	0.629906i	$0.783093\pi$
$230$	1.60507	−	0.926687i	0.105835	−	0.0611040i
$231$	−4.06667	+	2.42048i	−0.267567	+	0.159256i
$232$	−0.0963463	−	0.359569i	−0.00632545	−	0.0236069i
$233$	11.6318	+	6.71565i	0.762028	+	0.439957i	0.830023	−	0.557729i	$-0.188327\pi$
$233$	11.6318	+	6.71565i	0.762028	+	0.439957i	−0.0679957	+	0.997686i	$0.521660\pi$
$234$	0.538079	−	2.53370i	0.0351754	−	0.165633i
$235$	−0.171712	−	0.297413i	−0.0112012	−	0.0194011i
$236$	20.4111	+	5.46913i	1.32865	+	0.356010i
$237$	0.930397	+	0.537165i	0.0604358	+	0.0348926i
$238$	−6.02946	+	3.58873i	−0.390832	+	0.232623i
$239$	−16.8627	−	16.8627i	−1.09076	−	1.09076i	−0.995448	−	0.0953106i	$-0.969616\pi$
$239$	−16.8627	−	16.8627i	−1.09076	−	1.09076i	−0.0953106	−	0.995448i	$-0.530384\pi$
$240$	0.942821	+	0.942821i	0.0608588	+	0.0608588i
$241$	8.04154	−	2.15473i	0.518001	−	0.138798i	0.00965940	−	0.999953i	$-0.496925\pi$
$241$	8.04154	−	2.15473i	0.518001	−	0.138798i	0.508342	+	0.861155i	$0.330259\pi$
$242$	−5.41289	−	1.45038i	−0.347954	−	0.0932339i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.15877	+	3.73910i	−0.138201	+	0.239371i
$245$	1.85957	−	7.75888i	0.118803	−	0.495697i
$246$		−	3.11953i		−	0.198894i
$247$	−1.50032	+	1.66687i	−0.0954628	+	0.106061i
$248$	−10.4265	+	6.01972i	−0.662081	+	0.382253i
$249$	3.90388	+	3.90388i	0.247398	+	0.247398i
$250$	−6.16999	+	3.56225i	−0.390225	+	0.225296i
$251$	−13.0929	−	22.6775i	−0.826414	−	1.43139i	−0.900834	−	0.434165i	$-0.857044\pi$
$251$	−13.0929	−	22.6775i	−0.826414	−	1.43139i	0.0744193	−	0.997227i	$-0.476290\pi$
$252$	2.73902	−	2.81277i	0.172542	−	0.177188i
$253$	1.04787	−	3.91071i	0.0658792	−	0.245864i
$254$	6.70454	−	6.70454i	0.420680	−	0.420680i
$255$	1.08904	−	4.06435i	0.0681983	−	0.254519i
$256$	5.57988	−	9.66464i	0.348743	−	0.604040i
$257$	−6.72087	−	11.6409i	−0.419237	−	0.726139i	0.576626	−	0.817008i	$-0.304369\pi$
$257$	−6.72087	−	11.6409i	−0.419237	−	0.726139i	−0.995863	+	0.0908690i	$0.971036\pi$
$258$	5.46056	−	1.46315i	0.339959	−	0.0910919i
$259$	5.79965	−	10.3607i	0.360373	−	0.643784i
$260$	−1.26684	+	5.96526i	−0.0785659	+	0.369950i
$261$	0.0743668	−	0.128807i	0.00460319	−	0.00797296i
$262$	−1.69468	+	1.69468i	−0.104698	+	0.104698i
$263$	−16.4817			−1.01630			−0.508151	−	0.861268i	$-0.669671\pi$
$263$	−16.4817			−1.01630			−0.508151	+	0.861268i	$0.669671\pi$
$264$	−4.47683			−0.275530
$265$	9.99299	−	9.99299i	0.613865	−	0.613865i
$266$	1.13777	−	0.321123i	0.0697613	−	0.0196893i
$267$	−11.1651	−	2.99167i	−0.683292	−	0.183087i
$268$	−4.63614	−	17.3023i	−0.283197	−	1.05691i
$269$	−20.3123	−	11.7273i	−1.23846	−	0.715026i	−0.269681	−	0.962950i	$-0.586918\pi$
$269$	−20.3123	−	11.7273i	−1.23846	−	0.715026i	−0.968780	+	0.247924i	$0.920252\pi$
$270$		−	0.818827i		−	0.0498322i
$271$	0.840222	−	3.13575i	0.0510398	−	0.190483i	−0.935699	−	0.352799i	$-0.885230\pi$
$271$	0.840222	−	3.13575i	0.0510398	−	0.190483i	0.986739	+	0.162316i	$0.0518965\pi$
$272$	4.31850			0.261847
$273$	9.35679	+	1.85755i	0.566299	+	0.112424i
$274$	−1.71864			−0.103827
$275$	−1.71332	+	6.39420i	−0.103317	+	0.385585i
$276$			3.35876i			0.202173i
$277$	19.0308	+	10.9874i	1.14345	+	0.660170i	0.947282	−	0.320401i	$-0.103818\pi$
$277$	19.0308	+	10.9874i	1.14345	+	0.660170i	0.196166	+	0.980571i	$0.437151\pi$
$278$	−1.79963	−	6.71632i	−0.107935	−	0.402818i
$279$	−4.64644	−	1.24501i	−0.278175	−	0.0745368i
$280$	5.26559	−	5.40737i	0.314679	−	0.323152i
$281$	−3.80908	+	3.80908i	−0.227230	+	0.227230i	−0.811535	−	0.584304i	$-0.801367\pi$
$281$	−3.80908	+	3.80908i	−0.227230	+	0.227230i	0.584304	+	0.811535i	$0.301367\pi$
$282$	−0.216453			−0.0128896
$283$	−31.6565			−1.88178			−0.940891	−	0.338711i	$-0.890009\pi$
$283$	−31.6565			−1.88178			−0.940891	+	0.338711i	$0.890009\pi$
$284$	−14.8801	+	14.8801i	−0.882972	+	0.882972i
$285$	−0.354476	+	0.613970i	−0.0209973	+	0.0363684i
$286$	−2.52409	−	3.88523i	−0.149252	−	0.229738i
$287$	11.4878	−	0.152607i	0.678104	−	0.00900810i
$288$	5.64683	−	1.51306i	0.332742	−	0.0891581i
$289$	1.68595	+	2.92015i	0.0991733	+	0.171773i
$290$	0.0608936	−	0.105471i	0.00357579	−	0.00619346i
$291$	−1.33592	+	4.98572i	−0.0783131	+	0.292268i
$292$	12.3768	−	12.3768i	0.724296	−	0.724296i
$293$	−2.39685	+	8.94515i	−0.140025	+	0.522581i	0.859901	+	0.510460i	$0.170525\pi$
$293$	−2.39685	+	8.94515i	−0.140025	+	0.522581i	−0.999927	+	0.0121210i	$0.996142\pi$
$294$	−3.64907	−	3.46016i	−0.212818	−	0.201800i
$295$	8.11548	+	14.0564i	0.472501	+	0.818396i
$296$	9.72727	−	5.61604i	0.565386	−	0.326426i
$297$	−1.26481	−	1.26481i	−0.0733919	−	0.0733919i
$298$	−11.9776	+	6.91528i	−0.693845	+	0.400592i
$299$	−6.84358	+	4.44602i	−0.395775	+	0.257120i
$300$		−	5.49173i		−	0.317065i
$301$	5.65525	+	20.0372i	0.325963	+	1.15492i
$302$	−2.77701	+	4.80993i	−0.159799	+	0.276780i
$303$		−	3.91219i		−	0.224749i
$304$	−0.702822	−	0.188321i	−0.0403096	−	0.0108009i
$305$	−3.20333	+	0.858331i	−0.183422	+	0.0491479i
$306$	−1.87528	−	1.87528i	−0.107202	−	0.107202i
$307$	−7.50306	−	7.50306i	−0.428222	−	0.428222i	0.459800	−	0.888022i	$-0.347921\pi$
$307$	−7.50306	−	7.50306i	−0.428222	−	0.428222i	−0.888022	+	0.459800i	$0.847921\pi$
$308$	−0.0932817	−	7.02198i	−0.00531522	−	0.400114i
$309$	1.64551	+	0.950036i	0.0936098	+	0.0540457i
$310$	−3.80463	−	1.01945i	−0.216089	−	0.0579007i
$311$	17.4012	+	30.1398i	0.986732	+	1.70907i	0.633973	+	0.773356i	$0.281423\pi$
$311$	17.4012	+	30.1398i	0.986732	+	1.70907i	0.352759	+	0.935714i	$0.385243\pi$
$312$	6.70726	+	6.03706i	0.379724	+	0.341781i
$313$	5.98235	+	3.45391i	0.338142	+	0.195226i	0.659450	−	0.751748i	$-0.270789\pi$
$313$	5.98235	+	3.45391i	0.338142	+	0.195226i	−0.321308	+	0.946975i	$0.604122\pi$
$314$	−3.22095	−	12.0207i	−0.181769	−	0.678369i
$315$	3.01537	−	0.0400569i	0.169897	−	0.00225695i
$316$	−1.38063	+	0.797105i	−0.0776663	+	0.0448406i
$317$	−28.2016	+	7.55659i	−1.58396	+	0.424420i	−0.940148	−	0.340766i	$-0.889314\pi$
$317$	−28.2016	+	7.55659i	−1.58396	+	0.424420i	−0.643809	+	0.765186i	$0.722647\pi$
$318$	−2.30537	−	8.60375i	−0.129279	−	0.482474i
$319$	−0.0688568	−	0.256977i	−0.00385524	−	0.0143879i
$320$	2.04794	−	0.548744i	0.114483	−	0.0306757i
$321$	7.43000	−	4.28971i	0.414702	−	0.239428i
$322$	4.30174	−	0.0571455i	0.239727	−	0.00318459i
$323$	0.594293	+	2.21793i	0.0330674	+	0.123409i
$324$	1.28510	+	0.741955i	0.0713946	+	0.0412197i
$325$	11.1896	−	7.26946i	0.620687	−	0.403237i
$326$	−2.12313	−	3.67737i	−0.117589	−	0.203670i
$327$	4.91424	+	1.31677i	0.271758	+	0.0728173i
$328$	9.41210	+	5.43408i	0.519697	+	0.300047i
$329$	−0.0105888	−	0.797097i	−0.000583782	−	0.0439454i
$330$	−1.03566	−	1.03566i	−0.0570113	−	0.0570113i
$331$	−10.5622	−	10.5622i	−0.580553	−	0.580553i	0.354502	−	0.935055i	$-0.384650\pi$
$331$	−10.5622	−	10.5622i	−0.580553	−	0.580553i	−0.935055	+	0.354502i	$0.884650\pi$
$332$	−7.91340	+	2.12039i	−0.434304	+	0.116371i
$333$	4.33485	+	1.16152i	0.237548	+	0.0636509i
$334$			2.22725i			0.121870i
$335$	6.87942	−	11.9155i	0.375863	−	0.651014i
$336$	0.840690	+	2.97866i	0.0458634	+	0.162499i
$337$		−	32.4956i		−	1.77015i	−0.465450	−	0.885074i	$-0.654108\pi$
$337$		−	32.4956i		−	1.77015i	0.465450	−	0.885074i	$-0.345892\pi$
$338$	−1.45765	+	9.22467i	−0.0792857	+	0.501756i
$339$	−7.34129	+	4.23850i	−0.398724	+	0.230204i
$340$	4.41509	+	4.41509i	0.239442	+	0.239442i
$341$	−7.45158	+	4.30217i	−0.403526	+	0.232976i
$342$	0.223419	+	0.386973i	0.0120811	+	0.0209251i
$343$	12.5637	−	13.6071i	0.678374	−	0.734716i
$344$	−5.09749	+	19.0241i	−0.274838	+	1.02571i
$345$	−1.82425	+	1.82425i	−0.0982146	+	0.0982146i
$346$	−4.62008	+	17.2424i	−0.248377	+	0.926957i
$347$	−16.4298	+	28.4572i	−0.881997	+	1.52766i	−0.0328796	+	0.999459i	$0.510468\pi$
$347$	−16.4298	+	28.4572i	−0.881997	+	1.52766i	−0.849117	+	0.528204i	$0.822866\pi$
$348$	0.110354	+	0.191138i	0.00591558	+	0.0102461i
$349$	18.3049	−	4.90477i	0.979837	−	0.262547i	0.266861	−	0.963735i	$-0.414014\pi$
$349$	18.3049	−	4.90477i	0.979837	−	0.262547i	0.712976	+	0.701189i	$0.247347\pi$
$350$	−7.03356	+	0.0934356i	−0.375960	+	0.00499434i
$351$	0.189346	+	3.60058i	0.0101066	+	0.192185i
$352$	5.22843	−	9.05591i	0.278677	−	0.482682i
$353$	−12.0733	+	12.0733i	−0.642598	+	0.642598i	−0.951193	−	0.308595i	$-0.900141\pi$
$353$	−12.0733	+	12.0733i	−0.642598	+	0.642598i	0.308595	+	0.951193i	$0.400141\pi$
$354$	10.2300			0.543721
$355$	−16.1638			−0.857885
$356$	12.1286	−	12.1286i	0.642814	−	0.642814i
$357$	6.81405	−	6.99753i	0.360638	−	0.370349i
$358$	6.15903	+	1.65031i	0.325515	+	0.0872215i
$359$	6.96207	+	25.9828i	0.367444	+	1.37132i	0.864077	+	0.503359i	$0.167903\pi$
$359$	6.96207	+	25.9828i	0.367444	+	1.37132i	−0.496633	+	0.867960i	$0.665431\pi$
$360$	2.47053	+	1.42636i	0.130208	+	0.0751758i
$361$			18.6131i			0.979638i
$362$	−0.621147	+	2.31815i	−0.0326467	+	0.121839i
$363$	7.80050			0.409420
$364$	−9.32946	+	10.6462i	−0.488997	+	0.558014i
$365$	13.4445			0.703717
$366$	−0.540989	+	2.01900i	−0.0282779	+	0.105535i
$367$		−	21.3768i		−	1.11586i	−0.829887	−	0.557931i	$-0.811595\pi$
$367$		−	21.3768i		−	1.11586i	0.829887	−	0.557931i	$-0.188405\pi$
$368$	−2.29306	−	1.32390i	−0.119534	−	0.0690131i
$369$	1.12389	+	4.19440i	0.0585072	+	0.218352i
$370$	3.54949	+	0.951084i	0.184529	+	0.0494445i
$371$	31.5709	−	8.91051i	1.63908	−	0.462611i
$372$	5.04742	−	5.04742i	0.261696	−	0.261696i
$373$	12.2273			0.633108			0.316554	−	0.948574i	$-0.397474\pi$
$373$	12.2273			0.633108			0.316554	+	0.948574i	$0.397474\pi$
$374$	−4.74375			−0.245293
$375$	7.01255	−	7.01255i	0.362127	−	0.362127i
$376$	0.377051	−	0.653072i	0.0194449	−	0.0336796i
$377$	−0.243374	+	0.477861i	−0.0125344	+	0.0246111i
$378$	0.928398	−	1.65853i	0.0477516	−	0.0853054i
$379$	−6.48058	+	1.73647i	−0.332885	+	0.0891963i	−0.421390	−	0.906879i	$-0.638458\pi$
$379$	−6.48058	+	1.73647i	−0.332885	+	0.0891963i	0.0885051	+	0.996076i	$0.471791\pi$
$380$	−0.526010	−	0.911076i	−0.0269837	−	0.0467372i
$381$	−6.59920	+	11.4302i	−0.338087	+	0.585584i
$382$	−2.92512	+	10.9167i	−0.149662	+	0.558546i
$383$	12.4967	−	12.4967i	0.638550	−	0.638550i	−0.311648	−	0.950198i	$-0.600881\pi$
$383$	12.4967	−	12.4967i	0.638550	−	0.638550i	0.950198	+	0.311648i	$0.100881\pi$
$384$	−2.68026	+	10.0029i	−0.136777	+	0.510457i
$385$	3.76321	−	3.86454i	0.191791	−	0.196955i
$386$	1.42819	+	2.47369i	0.0726928	+	0.125908i
$387$	−6.81492	+	3.93460i	−0.346422	+	0.200007i
$388$	−5.41598	−	5.41598i	−0.274955	−	0.274955i
$389$	−2.12342	+	1.22596i	−0.107662	+	0.0621584i	−0.552864	−	0.833272i	$-0.686465\pi$
$389$	−2.12342	+	1.22596i	−0.107662	+	0.0621584i	0.445202	+	0.895430i	$0.353132\pi$
$390$	0.155042	+	2.94825i	0.00785085	+	0.149290i
$391$			8.35581i			0.422572i
$392$	16.7963	−	4.98238i	0.848344	−	0.251648i
$393$	1.66805	−	2.88915i	0.0841420	−	0.145738i
$394$			8.39918i			0.423145i
$395$	−1.18280	−	0.316930i	−0.0595131	−	0.0159465i
$396$	2.56385	−	0.686981i	0.128838	−	0.0345221i
$397$	−22.7971	−	22.7971i	−1.14415	−	1.14415i	−0.987683	−	0.156471i	$-0.949988\pi$
$397$	−22.7971	−	22.7971i	−1.14415	−	1.14415i	−0.156471	−	0.987683i	$-0.550012\pi$
$398$	7.74697	+	7.74697i	0.388321	+	0.388321i
$399$	−1.41411	+	0.841680i	−0.0707943	+	0.0421367i
$400$	3.74927	+	2.16464i	0.187464	+	0.108232i
$401$	8.08577	+	2.16657i	0.403784	+	0.108194i	0.454994	−	0.890494i	$-0.349641\pi$
$401$	8.08577	+	2.16657i	0.403784	+	0.108194i	−0.0512105	+	0.998688i	$0.516308\pi$
$402$	−4.33596	−	7.51010i	−0.216258	−	0.374570i
$403$	16.9656	+	3.60297i	0.845117	+	0.179477i
$404$	5.02757	+	2.90267i	0.250131	+	0.144413i
$405$	0.295002	+	1.10096i	0.0146588	+	0.0547073i
$406$	0.242924	−	0.144588i	0.0120561	−	0.00717578i
$407$	6.95188	−	4.01367i	0.344592	−	0.198950i
$408$	8.92465	−	2.39135i	0.441836	−	0.118390i
$409$	−1.92771	−	7.19431i	−0.0953191	−	0.355736i	0.901749	−	0.432261i	$-0.142284\pi$
$409$	−1.92771	−	7.19431i	−0.0953191	−	0.355736i	−0.997068	+	0.0765252i	$0.975617\pi$
$410$	0.920269	+	3.43449i	0.0454489	+	0.169617i
$411$	2.31082	−	0.619181i	0.113984	−	0.0305420i
$412$	−2.44179	+	1.40977i	−0.120298	+	0.0694543i
$413$	0.500452	+	37.6726i	0.0246256	+	1.85375i
$414$	0.420853	+	1.57064i	0.0206838	+	0.0771929i
$415$	−5.44969	−	3.14638i	−0.267515	−	0.154450i
$416$	−20.0453	+	6.51710i	−0.982803	+	0.319527i
$417$	4.83944	+	8.38216i	0.236988	+	0.410476i
$418$	0.772031	+	0.206865i	0.0377613	+	0.0101181i
$419$	−34.7153	−	20.0429i	−1.69595	−	0.979159i	−0.949525	−	0.313693i	$-0.898434\pi$
$419$	−34.7153	−	20.0429i	−1.69595	−	0.979159i	−0.746428	−	0.665466i	$-0.768233\pi$
$420$	−2.18579	+	3.90478i	−0.106656	+	0.190534i
$421$	−0.669436	−	0.669436i	−0.0326263	−	0.0326263i	0.690605	−	0.723232i	$-0.257344\pi$
$421$	−0.669436	−	0.669436i	−0.0326263	−	0.0326263i	−0.723232	+	0.690605i	$0.757344\pi$
$422$	−12.5870	−	12.5870i	−0.612723	−	0.612723i
$423$	0.291034	−	0.0779824i	0.0141506	−	0.00379164i
$424$	29.9747	+	8.03169i	1.45570	+	0.390053i
$425$		−	13.6622i		−	0.662712i
$426$	−5.09385	+	8.82281i	−0.246798	+	0.427467i
$427$	−7.46151	−	1.89345i	−0.361088	−	0.0916302i
$428$			12.7311i			0.615381i
$429$	4.79354	+	4.31457i	0.231434	+	0.208309i
$430$	−5.58024	+	3.22176i	−0.269103	+	0.155367i
$431$	−4.16513	−	4.16513i	−0.200627	−	0.200627i	0.599642	−	0.800269i	$-0.295310\pi$
$431$	−4.16513	−	4.16513i	−0.200627	−	0.200627i	−0.800269	+	0.599642i	$0.795310\pi$
$432$	−1.01308	+	0.584904i	−0.0487420	+	0.0281412i
$433$	2.92894	+	5.07307i	0.140756	+	0.243796i	0.927781	−	0.373124i	$-0.121713\pi$
$433$	2.92894	+	5.07307i	0.140756	+	0.243796i	−0.787026	+	0.616920i	$0.788380\pi$
$434$	−6.55038	−	6.37863i	−0.314428	−	0.306184i
$435$	−0.0438768	+	0.163750i	−0.00210373	+	0.00785123i
$436$	−5.33832	+	5.33832i	−0.255659	+	0.255659i
$437$	0.364380	−	1.35988i	0.0174306	−	0.0650520i
$438$	4.23690	−	7.33852i	0.202447	−	0.350648i
$439$	1.63187	+	2.82648i	0.0778850	+	0.134901i	0.902337	−	0.431031i	$-0.141850\pi$
$439$	1.63187	+	2.82648i	0.0778850	+	0.134901i	−0.824452	+	0.565932i	$0.808517\pi$
$440$	4.92883	−	1.32068i	0.234973	−	0.0629608i
$441$	6.15301	+	3.33773i	0.293001	+	0.158940i
$442$	7.10716	+	6.39700i	0.338053	+	0.304274i
$443$	−11.0985	+	19.2231i	−0.527305	+	0.913319i	0.472189	+	0.881498i	$0.343464\pi$
$443$	−11.0985	+	19.2231i	−0.527305	+	0.913319i	−0.999494	+	0.0318214i	$0.989869\pi$
$444$	−4.70894	+	4.70894i	−0.223476	+	0.223476i
$445$	13.1749			0.624550
$446$	8.35111			0.395437
$447$	13.6133	−	13.6133i	0.643885	−	0.643885i
$448$	4.77025	+	1.21051i	0.225373	+	0.0571911i
$449$	−14.5184	−	3.89019i	−0.685165	−	0.183589i	−0.100588	−	0.994928i	$-0.532073\pi$
$449$	−14.5184	−	3.89019i	−0.685165	−	0.183589i	−0.584576	+	0.811339i	$0.698739\pi$
$450$	−0.688114	−	2.56808i	−0.0324380	−	0.121060i
$451$	6.72664	+	3.88363i	0.316745	+	0.182873i
$452$		−	12.5791i		−	0.591671i
$453$	2.00097	−	7.46774i	0.0940140	−	0.350865i
$454$	−11.9120			−0.559056
$455$	−10.8495	+	0.715176i	−0.508631	+	0.0335280i
$456$	−1.55674			−0.0729011
$457$	0.713145	−	2.66149i	0.0333595	−	0.124499i	−0.947238	−	0.320531i	$-0.896139\pi$
$457$	0.713145	−	2.66149i	0.0333595	−	0.124499i	0.980598	+	0.196031i	$0.0628054\pi$
$458$		−	19.8561i		−	0.927816i
$459$	3.19704	+	1.84581i	0.149225	+	0.0861552i
$460$	−0.990842	−	3.69787i	−0.0461982	−	0.172414i
$461$	−16.7183	−	4.47966i	−0.778650	−	0.208639i	−0.152461	−	0.988310i	$-0.548720\pi$
$461$	−16.7183	−	4.47966i	−0.778650	−	0.208639i	−0.626190	+	0.779671i	$0.715386\pi$
$462$	−0.923475	−	3.27197i	−0.0429640	−	0.152226i
$463$	−12.0995	+	12.0995i	−0.562309	+	0.562309i	−0.929963	−	0.367653i	$-0.880161\pi$
$463$	−12.0995	+	12.0995i	−0.562309	+	0.562309i	0.367653	+	0.929963i	$0.380161\pi$
$464$	−0.173990			−0.00807728
$465$	5.48285			0.254261
$466$	−6.82285	+	6.82285i	−0.316062	+	0.316062i
$467$	0.693713	−	1.20155i	0.0321012	−	0.0556009i	−0.849528	−	0.527543i	$-0.823113\pi$
$467$	0.693713	−	1.20155i	0.0321012	−	0.0556009i	0.881630	+	0.471942i	$0.156447\pi$
$468$	−4.76760	−	2.42814i	−0.220382	−	0.112241i
$469$	27.4442	−	16.3348i	1.26725	−	0.754269i
$470$	0.238307	−	0.0638541i	0.0109923	−	0.00294537i
$471$	8.66153	+	15.0022i	0.399102	+	0.691265i
$472$	−17.8203	+	30.8656i	−0.820244	+	1.42070i
$473$	−3.64307	+	13.5961i	−0.167509	+	0.625151i
$474$	−0.545740	+	0.545740i	−0.0250667	+	0.0250667i
$475$	−0.595778	+	2.22348i	−0.0273362	+	0.102020i
$476$	3.93683	+	13.9486i	0.180444	+	0.639334i
$477$	6.19942	+	10.7377i	0.283852	+	0.491646i
$478$	14.8366	−	8.56594i	0.678613	−	0.391797i
$479$	−2.07532	−	2.07532i	−0.0948238	−	0.0948238i	0.658104	−	0.752927i	$-0.271359\pi$
$479$	−2.07532	−	2.07532i	−0.0948238	−	0.0948238i	−0.752927	+	0.658104i	$0.771359\pi$
$480$	−5.77060	+	3.33165i	−0.263390	+	0.152069i
$481$	−15.8279	−	3.36135i	−0.721690	−	0.153265i
$482$			5.98079i			0.272417i
$483$	−5.76338	+	1.62664i	−0.262243	+	0.0740149i
$484$	−5.78762	+	10.0245i	−0.263074	+	0.455657i
$485$		−	5.88320i		−	0.267143i
$486$	0.693915	+	0.185934i	0.0314766	+	0.00843414i
$487$	6.02834	−	1.61529i	0.273170	−	0.0731957i	−0.119633	−	0.992818i	$-0.538172\pi$
$487$	6.02834	−	1.61529i	0.273170	−	0.0731957i	0.392803	+	0.919622i	$0.371505\pi$
$488$	−5.14925	−	5.14925i	−0.233096	−	0.233096i
$489$	4.17954	+	4.17954i	0.189005	+	0.189005i
$490$	5.03825	+	2.73302i	0.227605	+	0.123465i
$491$	32.7858	+	18.9289i	1.47960	+	0.854249i	0.999733	−	0.0230905i	$-0.00735060\pi$
$491$	32.7858	+	18.9289i	1.47960	+	0.854249i	0.479870	+	0.877340i	$0.340684\pi$
$492$	−6.22412	−	1.66775i	−0.280605	−	0.0751878i
$493$	0.274535	+	0.475508i	0.0123644	+	0.0214158i
$494$	−0.877708	−	1.35102i	−0.0394900	−	0.0607853i
$495$	1.76564	+	1.01939i	0.0793594	+	0.0458182i
$496$	1.45642	+	5.43544i	0.0653953	+	0.244059i
$497$	−32.7396	−	18.3267i	−1.46857	−	0.822066i
$498$	−3.43483	+	1.98310i	−0.153918	+	0.0888648i
$499$	−19.5207	+	5.23054i	−0.873864	+	0.234151i	−0.667758	−	0.744378i	$-0.732746\pi$
$499$	−19.5207	+	5.23054i	−0.873864	+	0.234151i	−0.206106	+	0.978530i	$0.566079\pi$
$500$	3.80886	+	14.2149i	0.170337	+	0.635708i
$501$	−0.802421	−	2.99467i	−0.0358495	−	0.133792i
$502$	18.1707	−	4.86882i	0.810997	−	0.217306i
$503$	−15.6016	+	9.00759i	−0.695641	+	0.401629i	−0.805722	−	0.592294i	$-0.798222\pi$
$503$	−15.6016	+	9.00759i	−0.695641	+	0.401629i	0.110081	+	0.993923i	$0.464889\pi$
$504$	3.38680	+	5.69020i	0.150860	+	0.253462i
$505$	1.15411	+	4.30718i	0.0513570	+	0.191667i
$506$	2.51887	+	1.45427i	0.111977	+	0.0646502i
$507$	−1.36351	−	12.9283i	−0.0605557	−	0.574166i
$508$	−9.79262	−	16.9613i	−0.434477	−	0.752537i
$509$	−35.1353	−	9.41446i	−1.55734	−	0.417289i	−0.625522	−	0.780207i	$-0.715114\pi$
$509$	−35.1353	−	9.41446i	−1.55734	−	0.417289i	−0.931821	+	0.362918i	$0.881780\pi$
$510$	2.61782	+	1.51140i	0.115919	+	0.0669260i
$511$	27.2317	+	15.2436i	1.20466	+	0.674335i
$512$	−8.97627	−	8.97627i	−0.396699	−	0.396699i
$513$	−0.439817	−	0.439817i	−0.0194184	−	0.0194184i
$514$	9.32744	−	2.49928i	0.411416	−	0.110238i
$515$	−2.09191	−	0.560526i	−0.0921806	−	0.0246997i
$516$		−	11.6772i		−	0.514059i
$517$	0.269471	−	0.466737i	0.0118513	−	0.0205271i
$518$	6.11111	+	5.95088i	0.268507	+	0.261467i
$519$		−	24.8480i		−	1.09070i
$520$	−9.16540	−	4.66793i	−0.401929	−	0.204702i
$521$	3.65298	−	2.10905i	0.160040	−	0.0923992i	−0.417841	−	0.908520i	$-0.637213\pi$
$521$	3.65298	−	2.10905i	0.160040	−	0.0923992i	0.577881	+	0.816121i	$0.303880\pi$
$522$	0.0755539	+	0.0755539i	0.00330691	+	0.00330691i
$523$	−4.80837	+	2.77611i	−0.210255	+	0.121391i	−0.601430	−	0.798925i	$-0.705402\pi$
$523$	−4.80837	+	2.77611i	−0.210255	+	0.121391i	0.391175	+	0.920316i	$0.372069\pi$
$524$	2.47524	+	4.28724i	0.108131	+	0.187289i
$525$	9.42340	−	2.65964i	0.411271	−	0.116076i
$526$	3.06450	−	11.4369i	0.133619	−	0.498672i
$527$	12.5568	−	12.5568i	0.546983	−	0.546983i
$528$	−0.541567	+	2.02115i	−0.0235687	+	0.0879595i
$529$	−8.93840	+	15.4818i	−0.388626	+	0.673120i
$530$	5.07625	+	8.79233i	0.220498	+	0.381914i
$531$	−13.7549	+	3.68562i	−0.596913	+	0.159942i
$532$	−0.0324371	−	2.44177i	−0.00140633	−	0.105864i
$533$	−4.84084	−	14.8895i	−0.209680	−	0.644934i
$534$	4.15194	−	7.19137i	0.179672	−	0.311201i
$535$	−6.91469	+	6.91469i	−0.298948	+	0.298948i
$536$	30.2122			1.30497
$537$	−8.87577			−0.383018
$538$	11.9145	−	11.9145i	0.513670	−	0.513670i
$539$	12.0040	−	3.56080i	0.517049	−	0.153375i
$540$	−1.63373	−	0.437757i	−0.0703046	−	0.0188381i
$541$	−5.70004	−	21.2728i	−0.245064	−	0.914590i	−0.973351	−	0.229319i	$-0.926350\pi$
$541$	−5.70004	−	21.2728i	−0.245064	−	0.914590i	0.728288	−	0.685272i	$-0.240317\pi$
$542$	2.01972	+	1.16609i	0.0867544	+	0.0500877i
$543$		−	3.34068i		−	0.143362i
$544$	−5.58566	+	20.8460i	−0.239483	+	0.893764i
$545$	−5.79885			−0.248395
$546$	−3.02873	+	6.14744i	−0.129618	+	0.263086i
$547$	13.7598			0.588326			0.294163	−	0.955755i	$-0.404959\pi$
$547$	13.7598			0.588326			0.294163	+	0.955755i	$0.404959\pi$
$548$	−0.918809	+	3.42904i	−0.0392496	+	0.146481i
$549$		−	2.90957i		−	0.124178i
$550$	−4.11847	−	2.37780i	−0.175612	−	0.101390i
$551$	−0.0239438	−	0.0893593i	−0.00102004	−	0.00380684i
$552$	−5.47198	−	1.46621i	−0.232903	−	0.0624062i
$553$	−2.03641	−	1.98301i	−0.0865969	−	0.0843263i
$554$	−11.1628	+	11.1628i	−0.474262	+	0.474262i
$555$	−5.11517			−0.217127
$556$	−14.3626			−0.609109
$557$	14.2481	−	14.2481i	0.603709	−	0.603709i	−0.337585	−	0.941295i	$-0.609610\pi$
$557$	14.2481	−	14.2481i	0.603709	−	0.603709i	0.941295	+	0.337585i	$0.109610\pi$
$558$	1.72786	−	2.99275i	0.0731463	−	0.126693i
$559$	23.7927	−	15.4572i	1.00632	−	0.653770i
$560$	−1.80428	−	3.03139i	−0.0762448	−	0.128100i
$561$	6.37827	−	1.70905i	0.269291	−	0.0721562i
$562$	−1.93494	−	3.35141i	−0.0816205	−	0.141371i
$563$	8.17826	−	14.1652i	0.344673	−	0.596991i	−0.640622	−	0.767857i	$-0.721323\pi$
$563$	8.17826	−	14.1652i	0.344673	−	0.596991i	0.985294	+	0.170866i	$0.0546566\pi$
$564$	−0.115719	+	0.431869i	−0.00487265	+	0.0181850i
$565$	6.83214	−	6.83214i	0.287430	−	0.287430i
$566$	5.88601	−	21.9669i	0.247408	−	0.923338i
$567$	−0.650764	+	2.56447i	−0.0273295	+	0.107698i
$568$	−17.7465	−	30.7379i	−0.744628	−	1.28973i
$569$	11.0711	−	6.39190i	0.464125	−	0.267963i	−0.249652	−	0.968336i	$-0.580316\pi$
$569$	11.0711	−	6.39190i	0.464125	−	0.267963i	0.713777	+	0.700373i	$0.246983\pi$
$570$	−0.360134	−	0.360134i	−0.0150844	−	0.0150844i
$571$	−9.47759	+	5.47189i	−0.396625	+	0.228991i	−0.685027	−	0.728518i	$-0.740209\pi$
$571$	−9.47759	+	5.47189i	−0.396625	+	0.228991i	0.288402	+	0.957509i	$0.406876\pi$
$572$	−9.10126	+	2.95898i	−0.380543	+	0.123721i
$573$		−	15.7320i		−	0.657214i
$574$	−2.03008	+	7.99994i	−0.0847338	+	0.333911i
$575$	−4.18835	+	7.25443i	−0.174666	+	0.302531i
$576$			1.86013i			0.0775055i
$577$	34.6623	+	9.28774i	1.44301	+	0.386654i	0.893587	−	0.448890i	$-0.148180\pi$
$577$	34.6623	+	9.28774i	1.44301	+	0.386654i	0.549424	+	0.835544i	$0.314847\pi$
$578$	−2.33981	+	0.626950i	−0.0973232	+	0.0260777i
$579$	−2.81149	−	2.81149i	−0.116842	−	0.116842i
$580$	−0.177882	−	0.177882i	−0.00738614	−	0.00738614i
$581$	−7.47088	−	12.5519i	−0.309944	−	0.520740i
$582$	−3.21128	−	1.85403i	−0.133112	−	0.0768521i
$583$	21.4223	+	5.74009i	0.887221	+	0.237730i
$584$	14.7610	+	25.5667i	0.610813	+	1.05796i
$585$	−1.27064	−	3.90825i	−0.0525346	−	0.161586i
$586$	−5.76152	−	3.32642i	−0.238006	−	0.137413i
$587$	−6.71060	−	25.0443i	−0.276976	−	1.03369i	−0.954506	−	0.298193i	$-0.903616\pi$
$587$	−6.71060	−	25.0443i	−0.276976	−	1.03369i	0.677530	−	0.735496i	$-0.263051\pi$
$588$	−8.85459	+	5.43081i	−0.365157	+	0.223963i
$589$	−2.59116	+	1.49601i	−0.106767	+	0.0616419i
$590$	−11.2629	+	3.01789i	−0.463687	+	0.124244i
$591$	−3.02601	−	11.2932i	−0.124473	−	0.464541i
$592$	−1.35876	−	5.07095i	−0.0558445	−	0.208415i
$593$	−30.8591	+	8.26866i	−1.26723	+	0.339553i	−0.828969	−	0.559295i	$-0.811072\pi$
$593$	−30.8591	+	8.26866i	−1.26723	+	0.339553i	−0.438261	+	0.898848i	$0.644405\pi$
$594$	1.11284	−	0.642501i	0.0456606	−	0.0263621i
$595$	−5.43774	+	9.71419i	−0.222926	+	0.398243i
$596$	7.39403	+	27.5949i	0.302871	+	1.13033i
$597$	−13.2073	−	7.62525i	−0.540540	−	0.312081i
$598$	−1.81271	−	5.57553i	−0.0741271	−	0.228001i
$599$	0.468153	+	0.810865i	0.0191282	+	0.0331311i	0.875431	−	0.483343i	$-0.160578\pi$
$599$	0.468153	+	0.810865i	0.0191282	+	0.0331311i	−0.856303	+	0.516474i	$0.827244\pi$
$600$	8.94695	+	2.39733i	0.365258	+	0.0978705i
$601$	15.2342	+	8.79548i	0.621417	+	0.358775i	0.777420	−	0.628981i	$-0.216528\pi$
$601$	15.2342	+	8.79548i	0.621417	+	0.358775i	−0.156004	+	0.987756i	$0.549861\pi$
$602$	−14.9556	+	0.198674i	−0.609545	+	0.00809735i
$603$	8.53567	+	8.53567i	0.347599	+	0.347599i
$604$	8.11218	+	8.11218i	0.330080	+	0.330080i
$605$	−8.58807	+	2.30117i	−0.349155	+	0.0935557i
$606$	2.71473	+	0.727409i	0.110278	+	0.0295490i
$607$		−	31.2424i		−	1.26809i	−0.773297	−	0.634044i	$-0.781394\pi$
$607$		−	31.2424i		−	1.26809i	0.773297	−	0.634044i	$-0.218606\pi$
$608$	1.81810	−	3.14904i	0.0737336	−	0.127710i
$609$	−0.274535	+	0.281927i	−0.0111247	+	0.0114242i
$610$		−	2.38244i		−	0.0964620i
$611$	−1.03313	+	0.335888i	−0.0417958	+	0.0135886i
$612$	−4.74412	+	2.73902i	−0.191770	+	0.110718i
$613$	−21.0552	−	21.0552i	−0.850411	−	0.850411i	0.139773	−	0.990184i	$-0.455363\pi$
$613$	−21.0552	−	21.0552i	−0.850411	−	0.850411i	−0.990184	+	0.139773i	$0.955363\pi$
$614$	6.60156	−	3.81141i	0.266417	−	0.153816i
$615$	−2.47472	−	4.28634i	−0.0997903	−	0.172842i
$616$	11.4807	+	2.91336i	0.462571	+	0.117383i
$617$	10.0184	−	37.3893i	0.403327	−	1.50524i	−0.403794	−	0.914850i	$-0.632309\pi$
$617$	10.0184	−	37.3893i	0.403327	−	1.50524i	0.807121	−	0.590386i	$-0.201025\pi$
$618$	−0.965201	+	0.965201i	−0.0388261	+	0.0388261i
$619$	4.36560	−	16.2926i	0.175468	−	0.654857i	−0.821003	−	0.570924i	$-0.806585\pi$
$619$	4.36560	−	16.2926i	0.175468	−	0.654857i	0.996471	−	0.0839329i	$-0.0267481\pi$
$620$	−4.06802	+	7.04602i	−0.163376	+	0.282975i
$621$	−1.13173	−	1.96021i	−0.0454146	−	0.0786603i
$622$	−24.1499	+	6.47095i	−0.968324	+	0.259462i
$623$	26.6856	+	14.9379i	1.06914	+	0.598474i
$624$	3.53694	−	2.29782i	0.141591	−	0.0919862i
$625$	3.60028	−	6.23587i	0.144011	−	0.249435i
$626$	−3.50904	+	3.50904i	−0.140250	+	0.140250i
$627$	−1.11257			−0.0444318
$628$	−25.7059			−1.02578
$629$	−11.7148	+	11.7148i	−0.467098	+	0.467098i
$630$	−0.532863	+	2.09986i	−0.0212298	+	0.0836603i
$631$	−42.5020	−	11.3884i	−1.69198	−	0.453364i	−0.721079	−	0.692853i	$-0.756354\pi$
$631$	−42.5020	−	11.3884i	−1.69198	−	0.453364i	−0.970899	+	0.239488i	$0.923020\pi$
$632$	−0.695927	−	2.59724i	−0.0276825	−	0.103312i
$633$	21.4587	+	12.3892i	0.852907	+	0.492426i
$634$		−	20.9745i		−	0.833005i
$635$	3.89356	−	14.5310i	0.154511	−	0.576644i
$636$	−18.3988			−0.729559
$637$	−22.7864	−	10.8527i	−0.902829	−	0.430000i
$638$	0.191123			0.00756664
$639$	3.67037	−	13.6980i	0.145198	−	0.541885i
$640$		−	11.8035i		−	0.466574i
$641$	−9.22123	−	5.32388i	−0.364217	−	0.210281i	0.306712	−	0.951802i	$-0.400771\pi$
$641$	−9.22123	−	5.32388i	−0.364217	−	0.210281i	−0.670929	+	0.741522i	$0.734104\pi$
$642$	1.59521	+	5.95340i	0.0629578	+	0.234962i
$643$	−8.17038	−	2.18925i	−0.322208	−	0.0863355i	0.0940895	−	0.995564i	$-0.470006\pi$
$643$	−8.17038	−	2.18925i	−0.322208	−	0.0863355i	−0.416298	+	0.909228i	$0.636673\pi$
$644$	2.18576	−	8.61343i	0.0861310	−	0.339417i
$645$	6.34227	−	6.34227i	0.249727	−	0.249727i
$646$	−1.64956			−0.0649010
$647$	16.8410			0.662087			0.331044	−	0.943615i	$-0.392599\pi$
$647$	16.8410			0.662087			0.331044	+	0.943615i	$0.392599\pi$
$648$	−1.76976	+	1.76976i	−0.0695228	+	0.0695228i
$649$	−12.7358	+	22.0590i	−0.499923	+	0.865892i
$650$	2.96386	+	9.11627i	0.116252	+	0.357569i
$651$	11.1054	+	6.21653i	0.435257	+	0.243645i
$652$	−8.47217	+	2.27011i	−0.331796	+	0.0889044i
$653$	−0.711699	−	1.23270i	−0.0278509	−	0.0482392i	0.851764	−	0.523926i	$-0.175533\pi$
$653$	−0.711699	−	1.23270i	−0.0278509	−	0.0482392i	−0.879615	+	0.475686i	$0.842200\pi$
$654$	−1.82745	+	3.16523i	−0.0714589	+	0.123770i
$655$	−0.984158	+	3.67293i	−0.0384542	+	0.143513i
$656$	3.59192	−	3.59192i	0.140241	−	0.140241i
$657$	−3.05289	+	11.3935i	−0.119105	+	0.444505i
$658$	0.555087	+	0.140860i	0.0216395	+	0.00549129i
$659$	−16.2369	−	28.1232i	−0.632501	−	1.09552i	−0.987039	−	0.160483i	$-0.948695\pi$
$659$	−16.2369	−	28.1232i	−0.632501	−	1.09552i	0.354537	−	0.935042i	$-0.384638\pi$
$660$	−2.62004	+	1.51268i	−0.101985	+	0.0588811i
$661$	7.44155	+	7.44155i	0.289443	+	0.289443i	0.836860	−	0.547417i	$-0.184389\pi$
$661$	7.44155	+	7.44155i	0.289443	+	0.289443i	−0.547417	+	0.836860i	$0.684389\pi$
$662$	9.29318	−	5.36542i	0.361190	−	0.208533i
$663$	−11.8607	−	6.04064i	−0.460631	−	0.234599i
$664$		−	13.8179i		−	0.536238i
$665$	1.30859	−	1.34383i	0.0507450	−	0.0521114i
$666$	−1.61199	+	2.79205i	−0.0624635	+	0.108190i
$667$		−	0.336651i		−	0.0130352i
$668$	4.44383	+	1.19072i	0.171937	+	0.0460703i
$669$	−11.2286	+	3.00869i	−0.434122	+	0.116323i
$670$	6.98924	+	6.98924i	0.270018	+	0.270018i
$671$	−3.68006	−	3.68006i	−0.142067	−	0.142067i
$672$	−15.4658	+	0.205451i	−0.596605	+	0.00792545i
$673$	41.3188	+	23.8554i	1.59272	+	0.919558i	0.992838	+	0.119471i	$0.0381200\pi$
$673$	41.3188	+	23.8554i	1.59272	+	0.919558i	0.599884	+	0.800087i	$0.295213\pi$
$674$	22.5492	+	6.04204i	0.868563	+	0.232731i
$675$	1.85043	+	3.20503i	0.0712229	+	0.123362i
$676$	17.6259	+	7.83996i	0.677918	+	0.301537i
$677$	17.7371	+	10.2405i	0.681692	+	0.393575i	0.800492	−	0.599343i	$-0.204571\pi$
$677$	17.7371	+	10.2405i	0.681692	+	0.393575i	−0.118800	+	0.992918i	$0.537905\pi$
$678$	−1.57616	−	5.88232i	−0.0605322	−	0.225909i
$679$	6.67046	−	11.9164i	0.255989	−	0.457308i
$680$	−9.12027	+	5.26559i	−0.349746	+	0.201926i
$681$	16.0164	−	4.29157i	0.613748	−	0.164453i
$682$	−1.59984	−	5.97069i	−0.0612611	−	0.228629i
$683$	11.3947	+	42.5257i	0.436007	+	1.62720i	0.738646	+	0.674094i	$0.235466\pi$
$683$	11.3947	+	42.5257i	0.436007	+	1.62720i	−0.302639	+	0.953105i	$0.597868\pi$
$684$	0.891535	−	0.238886i	0.0340887	−	0.00913403i
$685$	−2.36147	+	1.36339i	−0.0902269	+	0.0520925i
$686$	7.10619	+	11.2482i	0.271316	+	0.429457i
$687$	7.15366	+	26.6978i	0.272929	+	1.01859i
$688$	7.97215	+	4.60273i	0.303936	+	0.175477i
$689$	−24.3546	−	37.4881i	−0.927838	−	1.42818i
$690$	−0.926687	−	1.60507i	−0.0352784	−	0.0611040i
$691$	26.2316	+	7.02872i	0.997895	+	0.267385i	0.720564	−	0.693389i	$-0.243883\pi$
$691$	26.2316	+	7.02872i	0.997895	+	0.267385i	0.277332	+	0.960774i	$0.410550\pi$
$692$	31.9322	+	18.4361i	1.21388	+	0.700834i
$693$	2.42048	+	4.06667i	0.0919464	+	0.154480i
$694$	−16.6920	−	16.6920i	−0.633621	−	0.633621i
$695$	−7.80081	−	7.80081i	−0.295901	−	0.295901i
$696$	−0.359569	+	0.0963463i	−0.0136294	+	0.00365200i
$697$	−15.4842	−	4.14897i	−0.586505	−	0.157153i
$698$			13.6140i			0.515297i
$699$	6.71565	−	11.6318i	0.254009	−	0.439957i
$700$	−3.57382	+	14.0834i	−0.135078	+	0.532302i
$701$		−	26.8903i		−	1.01563i	−0.861465	−	0.507817i	$-0.830453\pi$
$701$		−	26.8903i		−	1.01563i	0.861465	−	0.507817i	$-0.169547\pi$
$702$	−2.53370	−	0.538079i	−0.0956284	−	0.0203085i
$703$	2.41740	−	1.39569i	0.0911739	−	0.0526393i
$704$	2.35272	+	2.35272i	0.0886714	+	0.0886714i
$705$	−0.297413	+	0.171712i	−0.0112012	+	0.00646704i
$706$	−6.13303	−	10.6227i	−0.230819	−	0.399791i
$707$	−2.54591	+	10.0327i	−0.0957489	+	0.377318i
$708$	5.46913	−	20.4111i	0.205543	−	0.767095i
$709$	−27.1687	+	27.1687i	−1.02034	+	1.02034i	−0.0205514	+	0.999789i	$0.506542\pi$
$709$	−27.1687	+	27.1687i	−1.02034	+	1.02034i	−0.999789	+	0.0205514i	$0.993458\pi$
$710$	3.00540	−	11.2163i	0.112791	−	0.420940i
$711$	0.537165	−	0.930397i	0.0201453	−	0.0348926i
$712$	14.4650	+	25.0541i	0.542098	+	0.938941i
$713$	−10.5170	+	2.81802i	−0.393864	+	0.105536i
$714$	3.58873	+	6.02946i	0.134305	+	0.225647i
$715$	−6.55032	−	3.33608i	−0.244968	−	0.124762i
$716$	6.58542	−	11.4063i	0.246109	−	0.426273i
$717$	−16.8627	+	16.8627i	−0.629750	+	0.629750i
$718$	−19.3243			−0.721178
$719$	24.5648			0.916111			0.458056	−	0.888923i	$-0.348546\pi$
$719$	24.5648			0.916111			0.458056	+	0.888923i	$0.348546\pi$
$720$	0.942821	−	0.942821i	0.0351369	−	0.0351369i
$721$	−3.60161	−	3.50718i	−0.134131	−	0.130614i
$722$	−12.9159	−	3.46081i	−0.480681	−	0.128798i
$723$	−2.15473	−	8.04154i	−0.0801351	−	0.299068i
$724$	4.29312	+	2.47864i	0.159553	+	0.0921178i
$725$			0.550441i			0.0204429i
$726$	−1.45038	+	5.41289i	−0.0538286	+	0.200891i
$727$	45.2245			1.67728			0.838642	−	0.544684i	$-0.183350\pi$
$727$	45.2245			1.67728			0.838642	+	0.544684i	$0.183350\pi$
$728$	−13.2719	−	19.8467i	−0.491888	−	0.735568i
$729$	−1.00000			−0.0370370
$730$	−2.49979	+	9.32934i	−0.0925214	+	0.345294i
$731$		−	29.0501i		−	1.07446i
$732$	3.73910	+	2.15877i	0.138201	+	0.0797905i
$733$	6.13373	+	22.8914i	0.226555	+	0.845513i	0.981776	+	0.190043i	$0.0608627\pi$
$733$	6.13373	+	22.8914i	0.226555	+	0.845513i	−0.755221	+	0.655470i	$0.772471\pi$
$734$	14.8337	+	3.97468i	0.547523	+	0.146708i
$735$	−7.75888	−	1.85957i	−0.286191	−	0.0685912i
$736$	9.35657	−	9.35657i	0.344888	−	0.344888i
$737$	21.5920			0.795353
$738$	−3.11953			−0.114831
$739$	−2.34942	+	2.34942i	−0.0864249	+	0.0864249i	−0.748998	−	0.662573i	$-0.769465\pi$
$739$	−2.34942	+	2.34942i	−0.0864249	+	0.0864249i	0.662573	+	0.748998i	$0.269465\pi$
$740$	3.79522	−	6.57352i	0.139515	−	0.241647i
$741$	1.66687	+	1.50032i	0.0612341	+	0.0551155i
$742$	0.313034	+	23.5643i	0.0114918	+	0.865073i
$743$	4.57486	−	1.22583i	0.167835	−	0.0449713i	−0.173923	−	0.984759i	$-0.555644\pi$
$743$	4.57486	−	1.22583i	0.167835	−	0.0449713i	0.341758	+	0.939788i	$0.388978\pi$
$744$	6.01972	+	10.4265i	0.220694	+	0.382253i
$745$	−10.9718	+	19.0037i	−0.401974	+	0.696240i
$746$	−2.27348	+	8.48474i	−0.0832380	+	0.310649i
$747$	3.90388	−	3.90388i	0.142836	−	0.142836i
$748$	−2.53608	+	9.46477i	−0.0927282	+	0.346066i
$749$	−21.8456	+	6.16566i	−0.798221	+	0.225288i
$750$	3.56225	+	6.16999i	0.130075	+	0.225296i
$751$	17.9224	−	10.3475i	0.653999	−	0.377587i	−0.135987	−	0.990711i	$-0.543421\pi$
$751$	17.9224	−	10.3475i	0.653999	−	0.377587i	0.789987	+	0.613124i	$0.210087\pi$
$752$	−0.249230	−	0.249230i	−0.00908848	−	0.00908848i
$753$	−22.6775	+	13.0929i	−0.826414	+	0.477131i
$754$	−0.286344	−	0.257732i	−0.0104280	−	0.00938604i
$755$			8.81200i			0.320702i
$756$	−2.81277	−	2.73902i	−0.102300	−	0.0996172i
$757$	−17.9148	+	31.0293i	−0.651124	+	1.12778i	0.331727	+	0.943375i	$0.392369\pi$
$757$	−17.9148	+	31.0293i	−0.651124	+	1.12778i	−0.982851	+	0.184404i	$0.940965\pi$
$758$		−	4.81984i		−	0.175065i
$759$	−3.91071	−	1.04787i	−0.141950	−	0.0380354i
$760$	1.71392	−	0.459243i	0.0621703	−	0.0166585i
$761$	−13.3852	−	13.3852i	−0.485214	−	0.485214i	0.421578	−	0.906792i	$-0.361476\pi$
$761$	−13.3852	−	13.3852i	−0.485214	−	0.485214i	−0.906792	+	0.421578i	$0.861476\pi$
$762$	−6.70454	−	6.70454i	−0.242880	−	0.242880i
$763$	−11.7455	−	6.57481i	−0.425216	−	0.238024i
$764$	20.2173	+	11.6724i	0.731435	+	0.422294i
$765$	−4.06435	−	1.08904i	−0.146947	−	0.0393743i
$766$	6.34807	+	10.9952i	0.229365	+	0.397272i
$767$	48.8278	−	15.8748i	1.76307	−	0.573206i
$768$	−9.66464	−	5.57988i	−0.348743	−	0.201347i
$769$	5.11103	+	19.0746i	0.184309	+	0.687849i	0.994777	+	0.102067i	$0.0325457\pi$
$769$	5.11103	+	19.0746i	0.184309	+	0.687849i	−0.810469	+	0.585782i	$0.800788\pi$
$770$	1.98195	+	3.32990i	0.0714246	+	0.120001i
$771$	−11.6409	+	6.72087i	−0.419237	+	0.242046i
$772$	5.69906	−	1.52706i	0.205114	−	0.0549601i
$773$	1.64193	+	6.12777i	0.0590562	+	0.220401i	0.989147	−	0.146929i	$-0.0469388\pi$
$773$	1.64193	+	6.12777i	0.0590562	+	0.220401i	−0.930091	+	0.367329i	$0.880272\pi$
$774$	−1.46315	−	5.46056i	−0.0525919	−	0.196276i
$775$	17.1958	−	4.60760i	0.617691	−	0.165510i
$776$	11.1878	−	6.45928i	0.401619	−	0.231875i
$777$	−10.3607	−	5.79965i	−0.371689	−	0.208061i
$778$	−0.455894	−	1.70142i	−0.0163446	−	0.0609988i
$779$	2.33907	+	1.35046i	0.0838060	+	0.0483854i
$780$	5.96526	+	1.26684i	0.213591	+	0.0453600i
$781$	−12.6831	−	21.9677i	−0.453836	−	0.786067i
$782$	−5.79823	−	1.55363i	−0.207344	−	0.0555577i
$783$	−0.128807	−	0.0743668i	−0.00460319	−	0.00265765i
$784$	−0.217522	−	8.18577i	−0.00776864	−	0.292349i
$785$	−13.9617	−	13.9617i	−0.498315	−	0.498315i
$786$	1.69468	+	1.69468i	0.0604471	+	0.0604471i
$787$	−3.07224	+	0.823204i	−0.109514	+	0.0293441i	−0.313160	−	0.949701i	$-0.601387\pi$
$787$	−3.07224	+	0.823204i	−0.109514	+	0.0293441i	0.203646	+	0.979045i	$0.434721\pi$
$788$	16.7581	+	4.49033i	0.596984	+	0.159961i
$789$			16.4817i			0.586763i
$790$	0.439845	−	0.761835i	0.0156490	−	0.0271049i
$791$	21.5848	−	6.09205i	0.767467	−	0.216608i
$792$			4.47683i			0.159077i
$793$	0.550917	+	10.4761i	0.0195636	+	0.372018i
$794$	20.0580	−	11.5805i	0.711832	−	0.410977i
$795$	−9.99299	−	9.99299i	−0.354415	−	0.354415i
$796$	19.5985	−	11.3152i	0.694650	−	0.401056i
$797$	20.0820	+	34.7831i	0.711342	+	1.23208i	0.964354	+	0.264617i	$0.0852455\pi$
$797$	20.0820	+	34.7831i	0.711342	+	1.23208i	−0.253012	+	0.967463i	$0.581421\pi$
$798$	−0.321123	−	1.13777i	−0.0113676	−	0.0402767i
$799$	−0.287882	+	1.07439i	−0.0101845	+	0.0380092i
$800$	−15.2984	+	15.2984i	−0.540882	+	0.540882i
$801$	−2.99167	+	11.1651i	−0.105706	+	0.394499i
$802$	−3.00684	+	5.20800i	−0.106175	+	0.183901i
$803$	10.5494	+	18.2720i	0.372279	+	0.644806i
$804$	−17.3023	+	4.63614i	−0.610205	+	0.163504i
$805$	5.86541	−	3.49109i	0.206728	−	0.123045i
$806$	−5.65464	+	11.1028i	−0.199176	+	0.391079i
$807$	−11.7273	+	20.3123i	−0.412820	+	0.715026i
$808$	−6.92364	+	6.92364i	−0.243573	+	0.243573i
$809$	31.2254			1.09783			0.548913	−	0.835879i	$-0.315042\pi$
$809$	31.2254			1.09783			0.548913	+	0.835879i	$0.315042\pi$
$810$	−0.818827			−0.0287706
$811$	−39.2451	+	39.2451i	−1.37808	+	1.37808i	−0.530221	+	0.847859i	$0.677891\pi$
$811$	−39.2451	+	39.2451i	−1.37808	+	1.37808i	−0.847859	+	0.530221i	$0.822109\pi$
$812$	−0.158613	−	0.561982i	−0.00556622	−	0.0197217i
$813$	−3.13575	−	0.840222i	−0.109976	−	0.0294679i
$814$	1.49256	+	5.57030i	0.0523141	+	0.195239i
$815$	−5.83450	−	3.36855i	−0.204374	−	0.117995i
$816$		−	4.31850i		−	0.151178i
$817$	−1.26682	+	4.72782i	−0.0443203	+	0.165406i
$818$	5.35067			0.187082
$819$	1.85755	−	9.35679i	0.0649082	−	0.326953i
$820$	7.34452			0.256482
$821$	−3.38289	+	12.6251i	−0.118064	+	0.440620i	−0.999498	−	0.0316873i	$-0.989912\pi$
$821$	−3.38289	+	12.6251i	−0.118064	+	0.440620i	0.881434	+	0.472307i	$0.156579\pi$
$822$			1.71864i			0.0599444i
$823$	−33.0094	−	19.0580i	−1.15064	−	0.664320i	−0.201594	−	0.979469i	$-0.564612\pi$
$823$	−33.0094	−	19.0580i	−1.15064	−	0.664320i	−0.949042	+	0.315149i	$0.897946\pi$
$824$	−1.23082	−	4.59350i	−0.0428778	−	0.160022i
$825$	6.39420	+	1.71332i	0.222618	+	0.0596502i
$826$	−26.2346	−	6.65734i	−0.912820	−	0.231639i
$827$	9.67947	−	9.67947i	0.336588	−	0.336588i	−0.518493	−	0.855082i	$-0.673507\pi$
$827$	9.67947	−	9.67947i	0.336588	−	0.336588i	0.855082	+	0.518493i	$0.173507\pi$
$828$	3.35876			0.116725
$829$	5.89972			0.204906			0.102453	−	0.994738i	$-0.467331\pi$
$829$	5.89972			0.204906			0.102453	+	0.994738i	$0.467331\pi$
$830$	3.19660	−	3.19660i	0.110956	−	0.110956i
$831$	10.9874	−	19.0308i	0.381149	−	0.660170i
$832$	−0.352209	−	6.69755i	−0.0122107	−	0.232196i
$833$	−22.0282	+	13.5106i	−0.763231	+	0.468115i
$834$	−6.71632	+	1.79963i	−0.232567	+	0.0623162i
$835$	1.76687	+	3.06031i	0.0611452	+	0.105907i
$836$	0.825478	−	1.42977i	0.0285498	−	0.0494496i
$837$	−1.24501	+	4.64644i	−0.0430338	+	0.160604i
$838$	20.3628	−	20.3628i	0.703422	−	0.703422i
$839$	0.684157	−	2.55331i	0.0236197	−	0.0881499i	−0.953110	−	0.302624i	$-0.902137\pi$
$839$	0.684157	−	2.55331i	0.0236197	−	0.0881499i	0.976730	+	0.214474i	$0.0688039\pi$
$840$	−5.40737	−	5.26559i	−0.186572	−	0.181680i
$841$	14.4889	+	25.0956i	0.499619	+	0.865365i
$842$	0.589003	−	0.340061i	0.0202984	−	0.0117193i
$843$	3.80908	+	3.80908i	0.131192	+	0.131192i
$844$	−31.8428	+	18.3844i	−1.09607	+	0.632818i
$845$	5.31506	+	13.8314i	0.182844	+	0.475813i
$846$			0.216453i			0.00744180i
$847$	−20.0041	−	5.07629i	−0.687351	−	0.174423i
$848$	7.25213	−	12.5611i	0.249039	−	0.431349i
$849$			31.6565i			1.08645i
$850$	9.48038	+	2.54026i	0.325175	+	0.0871302i
$851$	9.81173	−	2.62904i	0.336342	−	0.0901225i
$852$	14.8801	+	14.8801i	0.509784	+	0.509784i
$853$	−6.42738	−	6.42738i	−0.220069	−	0.220069i	0.588458	−	0.808528i	$-0.299735\pi$
$853$	−6.42738	−	6.42738i	−0.220069	−	0.220069i	−0.808528	+	0.588458i	$0.799735\pi$
$854$	2.70124	−	4.82560i	0.0924345	−	0.165129i
$855$	0.613970	+	0.354476i	0.0209973	+	0.0121228i
$856$	−20.7411	−	5.55756i	−0.708916	−	0.189954i
$857$	19.4950	+	33.7663i	0.665935	+	1.15343i	0.979031	+	0.203712i	$0.0653007\pi$
$857$	19.4950	+	33.7663i	0.665935	+	1.15343i	−0.313096	+	0.949722i	$0.601366\pi$
$858$	−3.88523	+	2.52409i	−0.132639	+	0.0861709i
$859$	28.9041	+	16.6878i	0.986197	+	0.569381i	0.904135	−	0.427246i	$-0.140516\pi$
$859$	28.9041	+	16.6878i	0.986197	+	0.569381i	0.0820614	+	0.996627i	$0.473850\pi$
$860$	3.44480	+	12.8562i	0.117467	+	0.438391i
$861$	−0.152607	−	11.4878i	−0.00520083	−	0.391503i
$862$	3.66468	−	2.11581i	0.124820	−	0.0720647i
$863$	−50.0676	+	13.4156i	−1.70432	+	0.456671i	−0.974021	−	0.226457i	$-0.927286\pi$
$863$	−50.0676	+	13.4156i	−1.70432	+	0.456671i	−0.730299	+	0.683128i	$0.760619\pi$
$864$	−1.51306	−	5.64683i	−0.0514754	−	0.192109i
$865$	7.33021	+	27.3567i	0.249235	+	0.930157i
$866$	−4.06487	+	1.08918i	−0.138130	+	0.0370118i
$867$	2.92015	−	1.68595i	0.0991733	−	0.0572578i
$868$	−16.2286	+	9.65927i	−0.550835	+	0.327857i
$869$	−0.497365	−	1.85619i	−0.0168719	−	0.0629670i
$870$	−0.105471	−	0.0608936i	−0.00357579	−	0.00206449i
$871$	−32.3495	−	29.1171i	−1.09612	−	0.986596i
$872$	−6.36666	−	11.0274i	−0.215602	−	0.373434i
$873$	4.98572	+	1.33592i	0.168741	+	0.0452141i
$874$	0.875894	+	0.505697i	0.0296275	+	0.0171055i
$875$	−22.5470	+	13.4200i	−0.762228	+	0.453678i
$876$	−12.3768	−	12.3768i	−0.418173	−	0.418173i
$877$	−6.94698	−	6.94698i	−0.234583	−	0.234583i	0.580020	−	0.814603i	$-0.303045\pi$
$877$	−6.94698	−	6.94698i	−0.234583	−	0.234583i	−0.814603	+	0.580020i	$0.803045\pi$
$878$	−2.26476	+	0.606841i	−0.0764320	+	0.0204799i
$879$	8.94515	+	2.39685i	0.301713	+	0.0808436i
$880$		−	2.38498i		−	0.0803977i
$881$	9.37414	−	16.2365i	0.315823	−	0.547021i	−0.663789	−	0.747920i	$-0.731053\pi$
$881$	9.37414	−	16.2365i	0.315823	−	0.547021i	0.979612	+	0.200899i	$0.0643862\pi$
$882$	−3.46016	+	3.64907i	−0.116510	+	0.122871i
$883$			22.1170i			0.744297i	0.928173	+	0.372148i	$0.121379\pi$
$883$			22.1170i			0.744297i	−0.928173	+	0.372148i	$0.878621\pi$
$884$	16.5630	−	10.7603i	0.557072	−	0.361909i
$885$	14.0564	−	8.11548i	0.472501	−	0.272799i
$886$	−11.2756	−	11.2756i	−0.378813	−	0.378813i
$887$	26.2767	−	15.1709i	0.882285	−	0.509387i	0.0108738	−	0.999941i	$-0.496539\pi$
$887$	26.2767	−	15.1709i	0.882285	−	0.509387i	0.871411	+	0.490553i	$0.163205\pi$
$888$	−5.61604	−	9.72727i	−0.188462	−	0.326426i
$889$	24.3618	−	25.0178i	0.817068	−	0.839069i
$890$	−2.44966	+	9.14227i	−0.0821129	+	0.306450i
$891$	−1.26481	+	1.26481i	−0.0423728	+	0.0423728i
$892$	4.46463	−	16.6622i	0.149487	−	0.557892i
$893$	0.0937039	−	0.162300i	0.00313568	−	0.00543116i
$894$	6.91528	+	11.9776i	0.231282	+	0.400592i
$895$	9.77190	−	2.61837i	0.326639	−	0.0875226i
$896$	13.3830	−	23.9079i	0.447094	−	0.798705i
$897$	4.44602	+	6.84358i	0.148448	+	0.228501i
$898$	5.39892	−	9.35121i	0.180164	−	0.312054i
$899$	−0.505907	+	0.505907i	−0.0168730	+	0.0168730i
$900$	−5.49173			−0.183058
$901$	−45.7719			−1.52488
$902$	−3.94562	+	3.94562i	−0.131375	+	0.131375i
$903$	20.0372	−	5.65525i	0.666795	−	0.188195i
$904$	20.4935	+	5.49121i	0.681603	+	0.182635i
$905$	0.985509	+	3.67797i	0.0327594	+	0.122260i
$906$	4.80993	+	2.77701i	0.159799	+	0.0922601i
$907$		−	33.4843i		−	1.11183i	−0.831240	−	0.555914i	$-0.812369\pi$
$907$		−	33.4843i		−	1.11183i	0.831240	−	0.555914i	$-0.187631\pi$
$908$	−6.36831	+	23.7668i	−0.211340	+	0.788730i
$909$	−3.91219			−0.129759
$910$	1.52101	−	7.66159i	0.0504211	−	0.253979i
$911$	4.56752			0.151329			0.0756643	−	0.997133i	$-0.475892\pi$
$911$	4.56752			0.151329			0.0756643	+	0.997133i	$0.475892\pi$
$912$	−0.188321	+	0.702822i	−0.00623592	+	0.0232728i
$913$		−	9.87535i		−	0.326827i
$914$	1.71425	+	0.989725i	0.0567025	+	0.0327372i
$915$	0.858331	+	3.20333i	0.0283755	+	0.105899i
$916$	−39.6172	−	10.6154i	−1.30899	−	0.350742i
$917$	−6.15782	+	6.32363i	−0.203349	+	0.208825i
$918$	−1.87528	+	1.87528i	−0.0618934	+	0.0618934i
$919$	−1.13762			−0.0375265			−0.0187633	−	0.999824i	$-0.505973\pi$
$919$	−1.13762			−0.0375265			−0.0187633	+	0.999824i	$0.505973\pi$
$920$	6.45699			0.212881
$921$	−7.50306	+	7.50306i	−0.247234	+	0.247234i
$922$	6.21701	−	10.7682i	0.204746	−	0.354631i
$923$	−10.6218	+	50.0157i	−0.349620	+	1.64629i
$924$	−7.02198	+	0.0932817i	−0.231006	+	0.00306874i
$925$	−16.0426	+	4.29861i	−0.527479	+	0.141338i
$926$	−6.14630	−	10.6457i	−0.201980	−	0.349839i
$927$	0.950036	−	1.64551i	0.0312033	−	0.0540457i
$928$	0.225043	−	0.839873i	0.00738741	−	0.0275702i
$929$	7.02783	−	7.02783i	0.230576	−	0.230576i	−0.582357	−	0.812933i	$-0.697870\pi$
$929$	7.02783	−	7.02783i	0.230576	−	0.230576i	0.812933	+	0.582357i	$0.197870\pi$
$930$	−1.01945	+	3.80463i	−0.0334290	+	0.124759i
$931$	4.17419	−	1.23821i	0.136804	−	0.0405806i
$932$	9.96542	+	17.2606i	0.326428	+	0.565390i
$933$	30.1398	−	17.4012i	0.986732	−	0.569690i
$934$	0.704786	+	0.704786i	0.0230613	+	0.0230613i
$935$	−6.51807	+	3.76321i	−0.213164	+	0.123070i
$936$	6.03706	−	6.70726i	0.197328	−	0.219234i
$937$			38.1135i			1.24511i	0.782574	+	0.622557i	$0.213906\pi$
$937$			38.1135i			1.24511i	−0.782574	+	0.622557i	$0.786094\pi$
$938$	6.23213	+	22.0811i	0.203486	+	0.720974i
$939$	3.45391	−	5.98235i	0.112714	−	0.195226i
$940$		−	0.509610i		−	0.0166216i
$941$	34.3121	+	9.19390i	1.11854	+	0.299712i	0.770293	−	0.637690i	$-0.220110\pi$
$941$	34.3121	+	9.19390i	1.11854	+	0.299712i	0.348249	+	0.937402i	$0.386776\pi$
$942$	−12.0207	+	3.22095i	−0.391657	+	0.104944i
$943$	6.94996	+	6.94996i	0.226322	+	0.226322i
$944$	11.7792	+	11.7792i	0.383379	+	0.383379i
$945$	−0.0400569	−	3.01537i	−0.00130305	−	0.0980899i
$946$	−8.75719	−	5.05597i	−0.284721	−	0.164384i
$947$	2.76408	+	0.740632i	0.0898204	+	0.0240673i	0.303449	−	0.952848i	$-0.401862\pi$
$947$	2.76408	+	0.740632i	0.0898204	+	0.0240673i	−0.213629	+	0.976915i	$0.568528\pi$
$948$	0.797105	+	1.38063i	0.0258888	+	0.0448406i
$949$	8.83484	−	41.6014i	0.286791	−	1.35044i
$950$	−1.43213	−	0.826840i	−0.0464644	−	0.0268262i
$951$	7.55659	+	28.2016i	0.245039	+	0.914498i
$952$	−24.4432	+	0.324710i	−0.792209	+	0.0105239i
$953$	−3.30028	+	1.90542i	−0.106907	+	0.0617226i	−0.552500	−	0.833513i	$-0.686326\pi$
$953$	−3.30028	+	1.90542i	−0.106907	+	0.0617226i	0.445593	+	0.895235i	$0.352993\pi$
$954$	−8.60375	+	2.30537i	−0.278557	+	0.0746390i
$955$	4.64098	+	17.3204i	0.150179	+	0.560474i
$956$	−9.15896	−	34.1817i	−0.296222	−	1.10552i
$957$	−0.256977	+	0.0688568i	−0.00830689	+	0.00222582i
$958$	1.82597	−	1.05422i	0.0589944	−	0.0340604i
$959$	−6.32896	+	0.0840755i	−0.204373	+	0.00271494i
$960$	−0.548744	−	2.04794i	−0.0177106	−	0.0660970i
$961$	−6.80743	−	3.93027i	−0.219595	−	0.126783i
$962$	5.27544	−	10.3582i	0.170087	−	0.333963i
$963$	−4.28971	−	7.43000i	−0.138234	−	0.239428i
$964$	11.9329	+	3.19742i	0.384334	+	0.102982i
$965$	3.92475	+	2.26596i	0.126342	+	0.0729437i
$966$	−0.0571455	−	4.30174i	−0.00183862	−	0.138406i
$967$	18.1751	+	18.1751i	0.584472	+	0.584472i	0.936129	−	0.351657i	$-0.114382\pi$
$967$	18.1751	+	18.1751i	0.584472	+	0.584472i	−0.351657	+	0.936129i	$0.614382\pi$
$968$	−13.8050	−	13.8050i	−0.443710	−	0.443710i
$969$	2.21793	−	0.594293i	0.0712503	−	0.0190915i
$970$	4.08245	+	1.09389i	0.131079	+	0.0351226i
$971$			18.0500i			0.579252i	0.957140	+	0.289626i	$0.0935310\pi$
$971$			18.0500i			0.579252i	−0.957140	+	0.289626i	$0.906469\pi$
$972$	0.741955	−	1.28510i	0.0237982	−	0.0412197i
$973$	−6.95579	−	24.6451i	−0.222992	−	0.790086i
$974$			4.48349i			0.143660i
$975$	−7.26946	−	11.1896i	−0.232809	−	0.358354i
$976$	−2.94764	+	1.70182i	−0.0943517	+	0.0544740i
$977$	−41.5873	−	41.5873i	−1.33050	−	1.33050i	−0.904925	−	0.425571i	$-0.860073\pi$
$977$	−41.5873	−	41.5873i	−1.33050	−	1.33050i	−0.425571	−	0.904925i	$-0.639927\pi$
$978$	−3.67737	+	2.12313i	−0.117589	+	0.0678902i
$979$	10.3378	+	17.9056i	0.330398	+	0.572267i
$980$	8.14648	−	8.59126i	0.260230	−	0.274438i
$981$	1.31677	−	4.91424i	0.0420411	−	0.156899i
$982$	−19.2311	+	19.2311i	−0.613688	+	0.613688i
$983$	3.07898	−	11.4909i	0.0982041	−	0.366503i	−0.899282	−	0.437370i	$-0.855910\pi$
$983$	3.07898	−	11.4909i	0.0982041	−	0.366503i	0.997486	+	0.0708673i	$0.0225767\pi$
$984$	5.43408	−	9.41210i	0.173232	−	0.300047i
$985$	6.66306	+	11.5408i	0.212303	+	0.367719i
$986$	−0.381008	+	0.102091i	−0.0121338	+	0.00325123i
$987$	−0.797097	+	0.0105888i	−0.0253719	+	0.000337047i
$988$	−3.16481	+	1.02894i	−0.100686	+	0.0327348i
$989$	−8.90577	+	15.4252i	−0.283187	+	0.490494i
$990$	−1.03566	+	1.03566i	−0.0329155	+	0.0329155i
$991$	55.7812			1.77195			0.885975	−	0.463734i	$-0.153491\pi$
$991$	55.7812			1.77195			0.885975	+	0.463734i	$0.153491\pi$
$992$	−28.1214			−0.892856
$993$	−10.5622	+	10.5622i	−0.335183	+	0.335183i
$994$	18.8046	−	19.3109i	0.596446	−	0.612506i
$995$	16.7903	+	4.49894i	0.532287	+	0.142626i
$996$	2.12039	+	7.91340i	0.0671871	+	0.250746i
$997$	34.4398	+	19.8839i	1.09072	+	0.629728i	0.933768	−	0.357878i	$-0.116500\pi$
$997$	34.4398	+	19.8839i	1.09072	+	0.629728i	0.156953	+	0.987606i	$0.449833\pi$
$998$		−	14.5182i		−	0.459566i
$999$	1.16152	−	4.33485i	0.0367489	−	0.137149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.124.4	yes	40
3.2	odd	2		819.2.gh.d.397.7		40
7.3	odd	6		273.2.bt.b.241.4	yes	40
13.2	odd	12		273.2.bt.b.145.4	✓	40
21.17	even	6		819.2.et.d.514.7		40
39.2	even	12		819.2.et.d.145.7		40
91.80	even	12	inner	273.2.cg.b.262.4	yes	40
273.80	odd	12		819.2.gh.d.262.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.145.4	✓	40	13.2	odd	12
273.2.bt.b.241.4	yes	40	7.3	odd	6
273.2.cg.b.124.4	yes	40	1.1	even	1	trivial
273.2.cg.b.262.4	yes	40	91.80	even	12	inner
819.2.et.d.145.7		40	39.2	even	12
819.2.et.d.514.7		40	21.17	even	6
819.2.gh.d.262.7		40	273.80	odd	12
819.2.gh.d.397.7		40	3.2	odd	2

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.185934 + 0.693915i) q^{2} -1.00000i q^{3} +(1.28510 + 0.741955i) q^{4} +(0.295002 + 1.10096i) q^{5} +(0.693915 + 0.185934i) q^{6} +(-0.650764 + 2.56447i) q^{7} +(-1.76976 + 1.76976i) q^{8} -1.00000 q^{9} -0.818827 q^{10} +(-1.26481 + 1.26481i) q^{11} +(0.741955 - 1.28510i) q^{12} +(3.60058 - 0.189346i) q^{13} +(-1.65853 - 0.928398i) q^{14} +(1.10096 - 0.295002i) q^{15} +(0.584904 + 1.01308i) q^{16} +(1.84581 - 3.19704i) q^{17} +(0.185934 - 0.693915i) q^{18} +(-0.439817 + 0.439817i) q^{19} +(-0.437757 + 1.63373i) q^{20} +(2.56447 + 0.650764i) q^{21} +(-0.642501 - 1.11284i) q^{22} +(-1.96021 + 1.13173i) q^{23} +(1.76976 + 1.76976i) q^{24} +(3.20503 - 1.85043i) q^{25} +(-0.538079 + 2.53370i) q^{26} +1.00000i q^{27} +(-2.73902 + 2.81277i) q^{28} +(-0.0743668 + 0.128807i) q^{29} +0.818827i q^{30} +(4.64644 + 1.24501i) q^{31} +(-5.64683 + 1.51306i) q^{32} +(1.26481 + 1.26481i) q^{33} +(1.87528 + 1.87528i) q^{34} +(-3.01537 + 0.0400569i) q^{35} +(-1.28510 - 0.741955i) q^{36} +(-4.33485 - 1.16152i) q^{37} +(-0.223419 - 0.386973i) q^{38} +(-0.189346 - 3.60058i) q^{39} +(-2.47053 - 1.42636i) q^{40} +(-1.12389 - 4.19440i) q^{41} +(-0.928398 + 1.65853i) q^{42} +(6.81492 - 3.93460i) q^{43} +(-2.56385 + 0.686981i) q^{44} +(-0.295002 - 1.10096i) q^{45} +(-0.420853 - 1.57064i) q^{46} +(-0.291034 + 0.0779824i) q^{47} +(1.01308 - 0.584904i) q^{48} +(-6.15301 - 3.33773i) q^{49} +(0.688114 + 2.56808i) q^{50} +(-3.19704 - 1.84581i) q^{51} +(4.76760 + 2.42814i) q^{52} +(-6.19942 - 10.7377i) q^{53} +(-0.693915 - 0.185934i) q^{54} +(-1.76564 - 1.01939i) q^{55} +(-3.38680 - 5.69020i) q^{56} +(0.439817 + 0.439817i) q^{57} +(-0.0755539 - 0.0755539i) q^{58} +(13.7549 - 3.68562i) q^{59} +(1.63373 + 0.437757i) q^{60} +2.90957i q^{61} +(-1.72786 + 2.99275i) q^{62} +(0.650764 - 2.56447i) q^{63} -1.86013i q^{64} +(1.27064 + 3.90825i) q^{65} +(-1.11284 + 0.642501i) q^{66} +(-8.53567 - 8.53567i) q^{67} +(4.74412 - 2.73902i) q^{68} +(1.13173 + 1.96021i) q^{69} +(0.532863 - 2.09986i) q^{70} +(-3.67037 + 13.6980i) q^{71} +(1.76976 - 1.76976i) q^{72} +(3.05289 - 11.3935i) q^{73} +(1.61199 - 2.79205i) q^{74} +(-1.85043 - 3.20503i) q^{75} +(-0.891535 + 0.238886i) q^{76} +(-2.42048 - 4.06667i) q^{77} +(2.53370 + 0.538079i) q^{78} +(-0.537165 + 0.930397i) q^{79} +(-0.942821 + 0.942821i) q^{80} +1.00000 q^{81} +3.11953 q^{82} +(-3.90388 + 3.90388i) q^{83} +(2.81277 + 2.73902i) q^{84} +(4.06435 + 1.08904i) q^{85} +(1.46315 + 5.46056i) q^{86} +(0.128807 + 0.0743668i) q^{87} -4.47683i q^{88} +(2.99167 - 11.1651i) q^{89} +0.818827 q^{90} +(-1.85755 + 9.35679i) q^{91} -3.35876 q^{92} +(1.24501 - 4.64644i) q^{93} -0.216453i q^{94} +(-0.613970 - 0.354476i) q^{95} +(1.51306 + 5.64683i) q^{96} +(-4.98572 - 1.33592i) q^{97} +(3.46016 - 3.64907i) q^{98} +(1.26481 - 1.26481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32}+ \cdots - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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