LMFDB - Embedded newform 740.2.n.a.223.61

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(223,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.223"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$108$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.61
Character	$\chi$	$=$	740.223
Dual form			740.2.n.a.667.61

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.191494 + 1.40119i) q^{2} +(1.30753 - 1.30753i) q^{3} +(-1.92666 + 0.536639i) q^{4} +(2.18104 - 0.493016i) q^{5} +(2.08247 + 1.58171i) q^{6} +(-2.86607 - 2.86607i) q^{7} +(-1.12088 - 2.59685i) q^{8} -0.419248i q^{9} +(1.10846 + 2.96164i) q^{10} -4.89109i q^{11} +(-1.81749 + 3.22083i) q^{12} +(-0.919494 - 0.919494i) q^{13} +(3.46706 - 4.56473i) q^{14} +(2.20714 - 3.49640i) q^{15} +(3.42404 - 2.06784i) q^{16} +(-0.216386 + 0.216386i) q^{17} +(0.587445 - 0.0802835i) q^{18} -7.36168 q^{19} +(-3.93755 + 2.12030i) q^{20} -7.49491 q^{21} +(6.85335 - 0.936616i) q^{22} +(3.80931 - 3.80931i) q^{23} +(-4.86103 - 1.92987i) q^{24} +(4.51387 - 2.15057i) q^{25} +(1.11231 - 1.46446i) q^{26} +(3.37440 + 3.37440i) q^{27} +(7.05998 + 3.98389i) q^{28} -3.68460i q^{29} +(5.32177 + 2.42307i) q^{30} +8.43848i q^{31} +(3.55312 + 4.40174i) q^{32} +(-6.39523 - 6.39523i) q^{33} +(-0.344635 - 0.261761i) q^{34} +(-7.66402 - 4.83799i) q^{35} +(0.224985 + 0.807748i) q^{36} +(-0.707107 + 0.707107i) q^{37} +(-1.40972 - 10.3151i) q^{38} -2.40452 q^{39} +(-3.72497 - 5.11123i) q^{40} +2.64586 q^{41} +(-1.43523 - 10.5018i) q^{42} +(3.28009 - 3.28009i) q^{43} +(2.62475 + 9.42347i) q^{44} +(-0.206696 - 0.914396i) q^{45} +(6.06703 + 4.60811i) q^{46} +(-1.62006 - 1.62006i) q^{47} +(1.77326 - 7.18077i) q^{48} +9.42867i q^{49} +(3.87774 + 5.91296i) q^{50} +0.565861i q^{51} +(2.26499 + 1.27812i) q^{52} +(4.23775 + 4.23775i) q^{53} +(-4.08199 + 5.37435i) q^{54} +(-2.41139 - 10.6677i) q^{55} +(-4.23024 + 10.6553i) q^{56} +(-9.62558 + 9.62558i) q^{57} +(5.16282 - 0.705580i) q^{58} +5.84695 q^{59} +(-2.37610 + 7.92080i) q^{60} +0.0623409 q^{61} +(-11.8239 + 1.61592i) q^{62} +(-1.20159 + 1.20159i) q^{63} +(-5.48727 + 5.82150i) q^{64} +(-2.45878 - 1.55213i) q^{65} +(7.73628 - 10.1856i) q^{66} +(7.24908 + 7.24908i) q^{67} +(0.300782 - 0.533024i) q^{68} -9.96155i q^{69} +(5.31132 - 11.6652i) q^{70} -13.0462i q^{71} +(-1.08872 + 0.469925i) q^{72} +(1.55730 + 1.55730i) q^{73} +(-1.12620 - 0.855383i) q^{74} +(3.09007 - 8.71393i) q^{75} +(14.1834 - 3.95056i) q^{76} +(-14.0182 + 14.0182i) q^{77} +(-0.460452 - 3.36919i) q^{78} +4.69910 q^{79} +(6.44848 - 6.19815i) q^{80} +10.0820 q^{81} +(0.506667 + 3.70735i) q^{82} +(5.12812 - 5.12812i) q^{83} +(14.4401 - 4.02206i) q^{84} +(-0.365265 + 0.578629i) q^{85} +(5.22414 + 3.96790i) q^{86} +(-4.81771 - 4.81771i) q^{87} +(-12.7014 + 5.48231i) q^{88} -3.96849i q^{89} +(1.24166 - 0.464721i) q^{90} +5.27066i q^{91} +(-5.29503 + 9.38348i) q^{92} +(11.0335 + 11.0335i) q^{93} +(1.95978 - 2.58024i) q^{94} +(-16.0561 + 3.62942i) q^{95} +(10.4012 + 1.10960i) q^{96} +(7.06893 - 7.06893i) q^{97} +(-13.2113 + 1.80554i) q^{98} -2.05058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{6} - 12 q^{8} - 16 q^{10} - 16 q^{12} + 8 q^{16} + 20 q^{20} - 16 q^{21} + 4 q^{22} + 16 q^{26} - 4 q^{28} - 24 q^{30} - 20 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 36 q^{40} - 40 q^{42}+ \cdots - 64 q^{98}+O(q^{100}) $ 216 * q - 8 * q^6 - 12 * q^8 - 16 * q^10 - 16 * q^12 + 8 * q^16 + 20 * q^20 - 16 * q^21 + 4 * q^22 + 16 * q^26 - 4 * q^28 - 24 * q^30 - 20 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 36 * q^40 - 40 * q^42 + 40 * q^46 - 36 * q^48 + 24 * q^50 - 20 * q^52 - 16 * q^56 - 32 * q^57 - 16 * q^58 + 20 * q^60 - 64 * q^61 + 4 * q^62 - 32 * q^65 + 52 * q^68 - 24 * q^70 + 40 * q^72 - 16 * q^73 - 24 * q^76 + 48 * q^77 + 24 * q^78 - 56 * q^80 - 136 * q^81 - 4 * q^82 + 48 * q^85 - 88 * q^86 - 64 * q^88 + 120 * q^90 + 56 * q^92 + 16 * q^96 - 80 * q^97 - 64 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.191494	+	1.40119i	0.135407	+	0.990790i
$2$	0.191494	+	1.40119i	0.135407	+	0.990790i
$3$	1.30753	−	1.30753i	0.754900	−	0.754900i	−0.220489	−	0.975389i	$-0.570765\pi$
$3$	1.30753	−	1.30753i	0.754900	−	0.754900i	0.975389	+	0.220489i	$0.0707653\pi$
$4$	−1.92666	+	0.536639i	−0.963330	+	0.268319i
$5$	2.18104	−	0.493016i	0.975391	−	0.220483i
$5$	2.18104	−	0.493016i	0.975391	−	0.220483i
$6$	2.08247	+	1.58171i	0.850167	+	0.645729i
$7$	−2.86607	−	2.86607i	−1.08327	−	1.08327i	−0.996202	−	0.0870688i	$-0.972250\pi$
$7$	−2.86607	−	2.86607i	−1.08327	−	1.08327i	−0.0870688	−	0.996202i	$-0.527750\pi$
$8$	−1.12088	−	2.59685i	−0.396290	−	0.918126i
$9$		−	0.419248i		−	0.139749i
$10$	1.10846	+	2.96164i	0.350527	+	0.936553i
$11$		−	4.89109i		−	1.47472i	−0.675500	−	0.737360i	$-0.736072\pi$
$11$		−	4.89109i		−	1.47472i	0.675500	−	0.737360i	$-0.263928\pi$
$12$	−1.81749	+	3.22083i	−0.524664	+	0.929773i
$13$	−0.919494	−	0.919494i	−0.255022	−	0.255022i	0.568004	−	0.823026i	$-0.307716\pi$
$13$	−0.919494	−	0.919494i	−0.255022	−	0.255022i	−0.823026	+	0.568004i	$0.807716\pi$
$14$	3.46706	−	4.56473i	0.926612	−	1.21998i
$15$	2.20714	−	3.49640i	0.569880	−	0.902766i
$16$	3.42404	−	2.06784i	0.856009	−	0.516960i
$17$	−0.216386	+	0.216386i	−0.0524814	+	0.0524814i	−0.732860	−	0.680379i	$-0.761815\pi$
$17$	−0.216386	+	0.216386i	−0.0524814	+	0.0524814i	0.680379	+	0.732860i	$0.261815\pi$
$18$	0.587445	−	0.0802835i	0.138462	−	0.0189230i
$19$	−7.36168			−1.68888			−0.844442	−	0.535646i	$-0.820068\pi$
$19$	−7.36168			−1.68888			−0.844442	+	0.535646i	$0.820068\pi$
$20$	−3.93755	+	2.12030i	−0.880463	+	0.474115i
$21$	−7.49491			−1.63552
$22$	6.85335	−	0.936616i	1.46114	−	0.199687i
$23$	3.80931	−	3.80931i	0.794297	−	0.794297i	−0.187893	−	0.982190i	$-0.560166\pi$
$23$	3.80931	−	3.80931i	0.794297	−	0.794297i	0.982190	+	0.187893i	$0.0601657\pi$
$24$	−4.86103	−	1.92987i	−0.992253	−	0.393934i
$25$	4.51387	−	2.15057i	0.902774	−	0.430115i
$26$	1.11231	−	1.46446i	0.218141	−	0.287205i
$27$	3.37440	+	3.37440i	0.649404	+	0.649404i
$28$	7.05998	+	3.98389i	1.33421	+	0.752885i
$29$		−	3.68460i		−	0.684214i	−0.939661	−	0.342107i	$-0.888860\pi$
$29$		−	3.68460i		−	0.684214i	0.939661	−	0.342107i	$-0.111140\pi$
$30$	5.32177	+	2.42307i	0.971617	+	0.442391i
$31$			8.43848i			1.51560i	0.652490	+	0.757798i	$0.273725\pi$
$31$			8.43848i			1.51560i	−0.652490	+	0.757798i	$0.726275\pi$
$32$	3.55312	+	4.40174i	0.628109	+	0.778126i
$33$	−6.39523	−	6.39523i	−1.11327	−	1.11327i
$34$	−0.344635	−	0.261761i	−0.0591044	−	0.0448917i
$35$	−7.66402	−	4.83799i	−1.29546	−	0.817769i
$36$	0.224985	+	0.807748i	0.0374975	+	0.134625i
$37$	−0.707107	+	0.707107i	−0.116248	+	0.116248i
$37$	−0.707107	+	0.707107i	−0.116248	+	0.116248i
$38$	−1.40972	−	10.3151i	−0.228687	−	1.67333i
$39$	−2.40452			−0.385032
$40$	−3.72497	−	5.11123i	−0.588969	−	0.808156i
$41$	2.64586			0.413214			0.206607	−	0.978424i	$-0.433758\pi$
$41$	2.64586			0.413214			0.206607	+	0.978424i	$0.433758\pi$
$42$	−1.43523	−	10.5018i	−0.221461	−	1.62046i
$43$	3.28009	−	3.28009i	0.500209	−	0.500209i	−0.411294	−	0.911503i	$-0.634923\pi$
$43$	3.28009	−	3.28009i	0.500209	−	0.500209i	0.911503	+	0.411294i	$0.134923\pi$
$44$	2.62475	+	9.42347i	0.395696	+	1.42064i
$45$	−0.206696	−	0.914396i	−0.0308124	−	0.136310i
$46$	6.06703	+	4.60811i	0.894535	+	0.679428i
$47$	−1.62006	−	1.62006i	−0.236310	−	0.236310i	0.579010	−	0.815320i	$-0.303439\pi$
$47$	−1.62006	−	1.62006i	−0.236310	−	0.236310i	−0.815320	+	0.579010i	$0.803439\pi$
$48$	1.77326	−	7.18077i	0.255948	−	1.03646i
$49$			9.42867i			1.34695i
$50$	3.87774	+	5.91296i	0.548395	+	0.836219i
$51$			0.565861i			0.0792365i
$52$	2.26499	+	1.27812i	0.314097	+	0.177243i
$53$	4.23775	+	4.23775i	0.582100	+	0.582100i	0.935480	−	0.353380i	$-0.114968\pi$
$53$	4.23775	+	4.23775i	0.582100	+	0.582100i	−0.353380	+	0.935480i	$0.614968\pi$
$54$	−4.08199	+	5.37435i	−0.555489	+	0.731356i
$55$	−2.41139	−	10.6677i	−0.325151	−	1.43843i
$56$	−4.23024	+	10.6553i	−0.565290	+	1.42387i
$57$	−9.62558	+	9.62558i	−1.27494	+	1.27494i
$58$	5.16282	−	0.705580i	0.677912	−	0.0926472i
$59$	5.84695			0.761208			0.380604	−	0.924738i	$-0.375716\pi$
$59$	5.84695			0.761208			0.380604	+	0.924738i	$0.375716\pi$
$60$	−2.37610	+	7.92080i	−0.306753	+	1.02257i
$61$	0.0623409			0.00798193			0.00399097	−	0.999992i	$-0.498730\pi$
$61$	0.0623409			0.00798193			0.00399097	+	0.999992i	$0.498730\pi$
$62$	−11.8239	+	1.61592i	−1.50164	+	0.205222i
$63$	−1.20159	+	1.20159i	−0.151386	+	0.151386i
$64$	−5.48727	+	5.82150i	−0.685909	+	0.727687i
$65$	−2.45878	−	1.55213i	−0.304974	−	0.192518i
$66$	7.73628	−	10.1856i	0.952270	−	1.25376i
$67$	7.24908	+	7.24908i	0.885616	+	0.885616i	0.994098	−	0.108482i	$-0.0345991\pi$
$67$	7.24908	+	7.24908i	0.885616	+	0.885616i	−0.108482	+	0.994098i	$0.534599\pi$
$68$	0.300782	−	0.533024i	0.0364751	−	0.0646387i
$69$		−	9.96155i		−	1.19923i
$70$	5.31132	−	11.6652i	0.634824	−	1.39426i
$71$		−	13.0462i		−	1.54830i	−0.632999	−	0.774152i	$-0.718176\pi$
$71$		−	13.0462i		−	1.54830i	0.632999	−	0.774152i	$-0.281824\pi$
$72$	−1.08872	+	0.469925i	−0.128307	+	0.0553812i
$73$	1.55730	+	1.55730i	0.182268	+	0.182268i	0.792343	−	0.610076i	$-0.208861\pi$
$73$	1.55730	+	1.55730i	0.182268	+	0.182268i	−0.610076	+	0.792343i	$0.708861\pi$
$74$	−1.12620	−	0.855383i	−0.130918	−	0.0994363i
$75$	3.09007	−	8.71393i	0.356811	−	1.00620i
$76$	14.1834	−	3.95056i	1.62695	−	0.453161i
$77$	−14.0182	+	14.0182i	−1.59752	+	1.59752i
$78$	−0.460452	−	3.36919i	−0.0521360	−	0.381486i
$79$	4.69910			0.528690			0.264345	−	0.964428i	$-0.414844\pi$
$79$	4.69910			0.528690			0.264345	+	0.964428i	$0.414844\pi$
$80$	6.44848	−	6.19815i	0.720962	−	0.692974i
$81$	10.0820			1.12022
$82$	0.506667	+	3.70735i	0.0559520	+	0.409408i
$83$	5.12812	−	5.12812i	0.562885	−	0.562885i	−0.367241	−	0.930126i	$-0.619698\pi$
$83$	5.12812	−	5.12812i	0.562885	−	0.562885i	0.930126	+	0.367241i	$0.119698\pi$
$84$	14.4401	−	4.02206i	1.57555	−	0.438843i
$85$	−0.365265	+	0.578629i	−0.0396186	+	0.0627611i
$86$	5.22414	+	3.96790i	0.563333	+	0.427870i
$87$	−4.81771	−	4.81771i	−0.516513	−	0.516513i
$88$	−12.7014	+	5.48231i	−1.35398	+	0.584417i
$89$		−	3.96849i		−	0.420659i	−0.977631	−	0.210330i	$-0.932546\pi$
$89$		−	3.96849i		−	0.420659i	0.977631	−	0.210330i	$-0.0674537\pi$
$90$	1.24166	−	0.464721i	0.130883	−	0.0489859i
$91$			5.27066i			0.552515i
$92$	−5.29503	+	9.38348i	−0.552045	+	0.978295i
$93$	11.0335	+	11.0335i	1.14412	+	1.14412i
$94$	1.95978	−	2.58024i	0.202135	−	0.266131i
$95$	−16.0561	+	3.62942i	−1.64732	+	0.372371i
$96$	10.4012	+	1.10960i	1.06157	+	0.113248i
$97$	7.06893	−	7.06893i	0.717741	−	0.717741i	−0.250401	−	0.968142i	$-0.580563\pi$
$97$	7.06893	−	7.06893i	0.717741	−	0.717741i	0.968142	+	0.250401i	$0.0805625\pi$
$98$	−13.2113	+	1.80554i	−1.33455	+	0.182387i
$99$	−2.05058			−0.206091
$100$	−7.54261	+	6.56574i	−0.754261	+	0.656574i
$101$	−7.56065			−0.752312			−0.376156	−	0.926556i	$-0.622754\pi$
$101$	−7.56065			−0.752312			−0.376156	+	0.926556i	$0.622754\pi$
$102$	−0.792879	+	0.108359i	−0.0785067	+	0.0107292i
$103$	−5.31743	+	5.31743i	−0.523942	+	0.523942i	−0.918760	−	0.394817i	$-0.870808\pi$
$103$	−5.31743	+	5.31743i	−0.523942	+	0.523942i	0.394817	+	0.918760i	$0.370808\pi$
$104$	−1.35715	+	3.41843i	−0.133079	+	0.335204i
$105$	−16.3467	+	3.69511i	−1.59527	+	0.360606i
$106$	−5.12639	+	6.74940i	−0.497919	+	0.655560i
$107$	12.6336	+	12.6336i	1.22134	+	1.22134i	0.967157	+	0.254181i	$0.0818058\pi$
$107$	12.6336	+	12.6336i	1.22134	+	1.22134i	0.254181	+	0.967157i	$0.418194\pi$
$108$	−8.31216	−	4.69049i	−0.799838	−	0.451342i
$109$			15.9044i			1.52336i	0.647952	+	0.761681i	$0.275626\pi$
$109$			15.9044i			1.52336i	−0.647952	+	0.761681i	$0.724374\pi$
$110$	14.4857	−	5.42160i	1.38115	−	0.516930i
$111$			1.84912i			0.175511i
$112$	−15.7401	−	3.88695i	−1.48730	−	0.367282i
$113$	7.36629	+	7.36629i	0.692962	+	0.692962i	0.962883	−	0.269920i	$-0.0869974\pi$
$113$	7.36629	+	7.36629i	0.692962	+	0.692962i	−0.269920	+	0.962883i	$0.586997\pi$
$114$	−15.3305	−	11.6440i	−1.43583	−	1.09056i
$115$	6.43021	−	10.1863i	0.599621	−	0.949879i
$116$	1.97730	+	7.09898i	0.183588	+	0.659123i
$117$	−0.385496	+	0.385496i	−0.0356391	+	0.0356391i
$118$	1.11966	+	8.19268i	0.103073	+	0.754197i
$119$	1.24036			0.113703
$120$	−11.5535	−	1.81257i	−1.05469	−	0.165464i
$121$	−12.9228			−1.17480
$122$	0.0119379	+	0.0873513i	0.00108081	+	0.00790842i
$123$	3.45953	−	3.45953i	0.311935	−	0.311935i
$124$	−4.52842	−	16.2581i	−0.406664	−	1.46002i
$125$	8.78467	−	6.91590i	0.785724	−	0.618577i
$126$	−1.91376	−	1.45356i	−0.170491	−	0.129493i
$127$	−8.94693	−	8.94693i	−0.793912	−	0.793912i	0.188216	−	0.982128i	$-0.439730\pi$
$127$	−8.94693	−	8.94693i	−0.793912	−	0.793912i	−0.982128	+	0.188216i	$0.939730\pi$
$128$	−9.20780	−	6.57392i	−0.813862	−	0.581058i
$129$		−	8.57760i		−	0.755215i
$130$	1.70398	−	3.74244i	0.149449	−	0.328233i
$131$			19.4576i			1.70002i	0.526764	+	0.850011i	$0.323405\pi$
$131$			19.4576i			1.70002i	−0.526764	+	0.850011i	$0.676595\pi$
$132$	15.7534	+	8.88951i	1.37115	+	0.773732i
$133$	21.0991	+	21.0991i	1.82952	+	1.82952i
$134$	−8.76917	+	11.5455i	−0.757541	+	0.997378i
$135$	9.02333	+	5.69607i	0.776605	+	0.490240i
$136$	0.804466	+	0.319381i	0.0689823	+	0.0273867i
$137$	−4.96158	+	4.96158i	−0.423897	+	0.423897i	−0.886543	−	0.462646i	$-0.846900\pi$
$137$	−4.96158	+	4.96158i	−0.423897	+	0.423897i	0.462646	+	0.886543i	$0.346900\pi$
$138$	13.9580	−	1.90758i	1.18819	−	0.162384i
$139$	−14.2944			−1.21244			−0.606218	−	0.795299i	$-0.707314\pi$
$139$	−14.2944			−1.21244			−0.606218	+	0.795299i	$0.707314\pi$
$140$	17.3622	+	5.20835i	1.46737	+	0.440186i
$141$	−4.23654			−0.356781
$142$	18.2803	−	2.49828i	1.53405	−	0.209651i
$143$	−4.49733	+	4.49733i	−0.376086	+	0.376086i
$144$	−0.866938	−	1.43552i	−0.0722449	−	0.119627i
$145$	−1.81657	−	8.03627i	−0.150858	−	0.667376i
$146$	−1.88385	+	2.48028i	−0.155909	+	0.205269i
$147$	12.3282	+	12.3282i	1.01682	+	1.01682i
$148$	0.982893	−	1.74182i	0.0807933	−	0.143176i
$149$		−	8.36744i		−	0.685488i	−0.939429	−	0.342744i	$-0.888644\pi$
$149$		−	8.36744i		−	0.685488i	0.939429	−	0.342744i	$-0.111356\pi$
$150$	12.8016	+	2.66111i	1.04525	+	0.217278i
$151$		−	12.4276i		−	1.01134i	−0.862727	−	0.505670i	$-0.831245\pi$
$151$		−	12.4276i		−	1.01134i	0.862727	−	0.505670i	$-0.168755\pi$
$152$	8.25153	+	19.1172i	0.669288	+	1.55061i
$153$	0.0907195	+	0.0907195i	0.00733424	+	0.00733424i
$154$	−22.3265	−	16.9577i	−1.79912	−	1.36649i
$155$	4.16030	+	18.4047i	0.334164	+	1.47830i
$156$	4.63270	−	1.29036i	0.370913	−	0.103312i
$157$	5.16255	−	5.16255i	0.412017	−	0.412017i	−0.470424	−	0.882441i	$-0.655899\pi$
$157$	5.16255	−	5.16255i	0.412017	−	0.412017i	0.882441	+	0.470424i	$0.155899\pi$
$158$	0.899850	+	6.58432i	0.0715882	+	0.523820i
$159$	11.0819			0.878856
$160$	9.91962	+	7.84863i	0.784215	+	0.620489i
$161$	−21.8355			−1.72088
$162$	1.93064	+	14.1268i	0.151685	+	1.10990i
$163$	−5.65113	+	5.65113i	−0.442631	+	0.442631i	−0.892895	−	0.450264i	$-0.851330\pi$
$163$	−5.65113	+	5.65113i	−0.442631	+	0.442631i	0.450264	+	0.892895i	$0.351330\pi$
$164$	−5.09767	+	1.41987i	−0.398061	+	0.110873i
$165$	−17.1012	−	10.7953i	−1.33133	−	0.840413i
$166$	8.16747	+	6.20346i	0.633919	+	0.481482i
$167$	−11.6145	−	11.6145i	−0.898757	−	0.898757i	0.0965697	−	0.995326i	$-0.469213\pi$
$167$	−11.6145	−	11.6145i	−0.898757	−	0.898757i	−0.995326	+	0.0965697i	$0.969213\pi$
$168$	8.40087	+	19.4632i	0.648141	+	1.50162i
$169$		−	11.3091i		−	0.869928i
$170$	−0.880715	−	0.401002i	−0.0675477	−	0.0307554i
$171$			3.08637i			0.236020i
$172$	−4.55939	+	8.07984i	−0.347650	+	0.616082i
$173$	−12.1079	−	12.1079i	−0.920549	−	0.920549i	0.0765194	−	0.997068i	$-0.475619\pi$
$173$	−12.1079	−	12.1079i	−0.920549	−	0.920549i	−0.997068	+	0.0765194i	$0.975619\pi$
$174$	5.82796	−	7.67309i	0.441817	−	0.581695i
$175$	−19.1007	−	6.77337i	−1.44388	−	0.512018i
$176$	−10.1140	−	16.7473i	−0.762372	−	1.26237i
$177$	7.64504	−	7.64504i	0.574636	−	0.574636i
$178$	5.56061	−	0.759943i	0.416785	−	0.0569601i
$179$	−12.6293			−0.943955			−0.471978	−	0.881611i	$-0.656460\pi$
$179$	−12.6293			−0.943955			−0.471978	+	0.881611i	$0.656460\pi$
$180$	0.888933	+	1.65081i	0.0662572	+	0.123044i
$181$	−9.40811			−0.699299			−0.349650	−	0.936881i	$-0.613699\pi$
$181$	−9.40811			−0.699299			−0.349650	+	0.936881i	$0.613699\pi$
$182$	−7.38519	+	1.00930i	−0.547427	+	0.0748143i
$183$	0.0815123	−	0.0815123i	0.00602556	−	0.00602556i
$184$	−14.1620	−	5.62245i	−1.04404	−	0.414493i
$185$	−1.19361	+	1.89084i	−0.0877562	+	0.139018i
$186$	−13.3472	+	17.5729i	−0.978664	+	1.28851i
$187$	1.05837	+	1.05837i	0.0773954	+	0.0773954i
$188$	3.99069	+	2.25192i	0.291051	+	0.164238i
$189$		−	19.3425i		−	1.40696i
$190$	−8.16016	−	21.8026i	−0.592000	−	1.58173i
$191$			3.52865i			0.255324i	0.991818	+	0.127662i	$0.0407473\pi$
$191$			3.52865i			0.255324i	−0.991818	+	0.127662i	$0.959253\pi$
$192$	0.437012	+	14.7865i	0.0315387	+	1.06712i
$193$	9.60875	+	9.60875i	0.691653	+	0.691653i	0.962595	−	0.270943i	$-0.0873354\pi$
$193$	9.60875	+	9.60875i	0.691653	+	0.691653i	−0.270943	+	0.962595i	$0.587335\pi$
$194$	11.2586	+	8.55125i	0.808318	+	0.613944i
$195$	−5.24436	+	1.18547i	−0.375557	+	0.0848931i
$196$	−5.05979	−	18.1658i	−0.361414	−	1.29756i
$197$	5.18132	−	5.18132i	0.369154	−	0.369154i	−0.498015	−	0.867169i	$-0.665937\pi$
$197$	5.18132	−	5.18132i	0.369154	−	0.369154i	0.867169	+	0.498015i	$0.165937\pi$
$198$	−0.392674	−	2.87325i	−0.0279061	−	0.204193i
$199$	−2.32144			−0.164562			−0.0822812	−	0.996609i	$-0.526221\pi$
$199$	−2.32144			−0.164562			−0.0822812	+	0.996609i	$0.526221\pi$
$200$	−10.6442	−	9.31132i	−0.752659	−	0.658410i
$201$	18.9567			1.33710
$202$	−1.44782	−	10.5939i	−0.101868	−	0.745384i
$203$	−10.5603	+	10.5603i	−0.741189	+	0.741189i
$204$	−0.303663	−	1.09022i	−0.0212607	−	0.0763309i
$205$	5.77073	−	1.30445i	0.403045	−	0.0911068i
$206$	−8.46899	−	6.43247i	−0.590062	−	0.448171i
$207$	−1.59705	−	1.59705i	−0.111002	−	0.111002i
$208$	−5.04975	−	1.24701i	−0.350137	−	0.0864648i
$209$			36.0067i			2.49063i
$210$	−8.30784	−	22.1972i	−0.573296	−	1.53175i
$211$		−	23.1345i		−	1.59265i	−0.604870	−	0.796324i	$-0.706775\pi$
$211$		−	23.1345i		−	1.59265i	0.604870	−	0.796324i	$-0.293225\pi$
$212$	−10.4389	−	5.89057i	−0.716944	−	0.404566i
$213$	−17.0583	−	17.0583i	−1.16882	−	1.16882i
$214$	−15.2828	+	20.1213i	−1.04471	+	1.37547i
$215$	5.53687	−	8.77114i	0.377611	−	0.598187i
$216$	4.98053	−	12.5451i	0.338882	−	0.853586i
$217$	24.1852	−	24.1852i	1.64180	−	1.64180i
$218$	−22.2850	+	3.04559i	−1.50933	+	0.206274i
$219$	4.07241			0.275188
$220$	10.3706	+	19.2589i	0.699186	+	1.29844i
$221$	0.397932			0.0267678
$222$	−2.59097	+	0.354096i	−0.173894	+	0.0237654i
$223$	8.35787	−	8.35787i	0.559684	−	0.559684i	−0.369533	−	0.929217i	$-0.620482\pi$
$223$	8.35787	−	8.35787i	0.559684	−	0.559684i	0.929217	+	0.369533i	$0.120482\pi$
$224$	2.43221	−	22.7992i	0.162509	−	1.52333i
$225$	−0.901624	−	1.89243i	−0.0601082	−	0.126162i
$226$	−8.91096	+	11.7322i	−0.592748	+	0.780412i
$227$	15.3107	+	15.3107i	1.01621	+	1.01621i	0.999866	+	0.0163415i	$0.00520188\pi$
$227$	15.3107	+	15.3107i	1.01621	+	1.01621i	0.0163415	+	0.999866i	$0.494798\pi$
$228$	13.3798	−	23.7107i	0.886097	−	1.57028i
$229$		−	5.83486i		−	0.385578i	−0.981240	−	0.192789i	$-0.938247\pi$
$229$		−	5.83486i		−	0.385578i	0.981240	−	0.192789i	$-0.0617533\pi$
$230$	15.5043	+	7.05932i	1.02232	+	0.465478i
$231$			36.6583i			2.41194i
$232$	−9.56836	+	4.12999i	−0.628194	+	0.271147i
$233$	5.57483	+	5.57483i	0.365219	+	0.365219i	0.865730	−	0.500511i	$-0.166854\pi$
$233$	5.57483	+	5.57483i	0.365219	+	0.365219i	−0.500511	+	0.865730i	$0.666854\pi$
$234$	−0.613973	−	0.466332i	−0.0401366	−	0.0304851i
$235$	−4.33213	−	2.73470i	−0.282597	−	0.178392i
$236$	−11.2651	+	3.13770i	−0.733294	+	0.204247i
$237$	6.14419	−	6.14419i	0.399108	−	0.399108i
$238$	0.237521	+	1.73797i	0.0153962	+	0.112656i
$239$	19.5334			1.26351			0.631756	−	0.775168i	$-0.282335\pi$
$239$	19.5334			1.26351			0.631756	+	0.775168i	$0.282335\pi$
$240$	0.327319	−	16.5358i	0.0211283	−	1.06738i
$241$	−29.3763			−1.89229			−0.946145	−	0.323742i	$-0.895059\pi$
$241$	−29.3763			−1.89229			−0.946145	+	0.323742i	$0.895059\pi$
$242$	−2.47464	−	18.1073i	−0.159076	−	1.16398i
$243$	3.05924	−	3.05924i	0.196251	−	0.196251i
$244$	−0.120110	+	0.0334545i	−0.00768923	+	0.00214171i
$245$	4.64848	+	20.5643i	0.296981	+	1.31381i
$246$	5.50994	+	4.18498i	0.351301	+	0.266824i
$247$	6.76902	+	6.76902i	0.430702	+	0.430702i
$248$	21.9135	−	9.45849i	1.39151	−	0.600615i
$249$		−	13.4103i		−	0.849844i
$250$	11.3727	+	10.9846i	0.719272	+	0.694729i
$251$			11.6625i			0.736129i	0.929800	+	0.368065i	$0.119980\pi$
$251$			11.6625i			0.736129i	−0.929800	+	0.368065i	$0.880020\pi$
$252$	1.67024	−	2.95988i	0.105215	−	0.186455i
$253$	−18.6317	−	18.6317i	−1.17137	−	1.17137i
$254$	10.8231	−	14.2496i	0.679099	−	0.894101i
$255$	0.278979	+	1.23417i	0.0174703	+	0.0772865i
$256$	7.44806	−	14.1607i	0.465504	−	0.885046i
$257$	3.24245	−	3.24245i	0.202258	−	0.202258i	−0.598709	−	0.800967i	$-0.704319\pi$
$257$	3.24245	−	3.24245i	0.202258	−	0.202258i	0.800967	+	0.598709i	$0.204319\pi$
$258$	12.0188	−	1.64256i	0.748260	−	0.102261i
$259$	4.05323			0.251855
$260$	5.57016	+	1.67095i	0.345447	+	0.103628i
$261$	−1.54476			−0.0956184
$262$	−27.2638	+	3.72603i	−1.68437	+	0.230195i
$263$	−18.9610	+	18.9610i	−1.16918	+	1.16918i	−0.186781	+	0.982402i	$0.559806\pi$
$263$	−18.9610	+	18.9610i	−1.16918	+	1.16918i	−0.982402	+	0.186781i	$0.940194\pi$
$264$	−9.43920	+	23.7757i	−0.580942	+	1.46330i
$265$	11.3320	+	7.15343i	0.696119	+	0.439432i
$266$	−25.5234	+	33.6041i	−1.56494	+	2.06040i
$267$	−5.18891	−	5.18891i	−0.317556	−	0.317556i
$268$	−17.8566	−	10.0764i	−1.09077	−	0.615512i
$269$		−	12.3832i		−	0.755017i	−0.926006	−	0.377509i	$-0.876781\pi$
$269$		−	12.3832i		−	0.755017i	0.926006	−	0.377509i	$-0.123219\pi$
$270$	−6.25335	+	13.7342i	−0.380567	+	0.835834i
$271$			13.8912i			0.843832i	0.906635	+	0.421916i	$0.138642\pi$
$271$			13.8912i			0.843832i	−0.906635	+	0.421916i	$0.861358\pi$
$272$	−0.293462	+	1.18837i	−0.0177938	+	0.0720554i
$273$	6.89152	+	6.89152i	0.417094	+	0.417094i
$274$	−7.90223	−	6.00200i	−0.477391	−	0.362594i
$275$	−10.5187	−	22.0778i	−0.634299	−	1.33134i
$276$	5.34576	+	19.1925i	0.321777	+	1.15525i
$277$	1.27380	−	1.27380i	0.0765353	−	0.0765353i	−0.667803	−	0.744338i	$-0.732765\pi$
$277$	1.27380	−	1.27380i	0.0765353	−	0.0765353i	0.744338	+	0.667803i	$0.232765\pi$
$278$	−2.73729	−	20.0292i	−0.164172	−	1.20127i
$279$	3.53781			0.211803
$280$	−3.97312	+	25.3251i	−0.237439	+	1.51346i
$281$	18.5054			1.10394			0.551971	−	0.833863i	$-0.313876\pi$
$281$	18.5054			1.10394			0.551971	+	0.833863i	$0.313876\pi$
$282$	−0.811272	−	5.93619i	−0.0483106	−	0.353495i
$283$	−18.4373	+	18.4373i	−1.09599	+	1.09599i	−0.101112	+	0.994875i	$0.532240\pi$
$283$	−18.4373	+	18.4373i	−1.09599	+	1.09599i	−0.994875	+	0.101112i	$0.967760\pi$
$284$	7.00113	+	25.1357i	0.415440	+	1.49153i
$285$	−16.2482	+	25.7393i	−0.962462	+	1.52467i
$286$	−7.16282	−	5.44040i	−0.423547	−	0.321697i
$287$	−7.58321	−	7.58321i	−0.447623	−	0.447623i
$288$	1.84542	−	1.48964i	0.108743	−	0.0877778i
$289$			16.9064i			0.994491i
$290$	10.9125	−	4.08425i	0.640802	−	0.239835i
$291$		−	18.4856i		−	1.08365i
$292$	−3.83608	−	2.16467i	−0.224490	−	0.126678i
$293$	17.4340	+	17.4340i	1.01850	+	1.01850i	0.999826	+	0.0186790i	$0.00594606\pi$
$293$	17.4340	+	17.4340i	1.01850	+	1.01850i	0.0186790	+	0.999826i	$0.494054\pi$
$294$	−14.9134	+	19.6350i	−0.869767	+	1.14513i
$295$	12.7524	−	2.88264i	0.742475	−	0.167834i
$296$	2.62883	+	1.04367i	0.152798	+	0.0606622i
$297$	16.5045	−	16.5045i	0.957689	−	0.957689i
$298$	11.7244	−	1.60232i	0.679174	−	0.0928197i
$299$	−7.00528			−0.405126
$300$	−1.27728	+	18.4470i	−0.0737439	+	1.06504i
$301$	−18.8019			−1.08372
$302$	17.4134	−	2.37981i	1.00203	−	0.136942i
$303$	−9.88574	+	9.88574i	−0.567921	+	0.567921i
$304$	−25.2067	+	15.2228i	−1.44570	+	0.873087i
$305$	0.135968	−	0.0307350i	0.00778550	−	0.00175988i
$306$	−0.109743	+	0.144487i	−0.00627358	+	0.00825980i
$307$	6.60194	+	6.60194i	0.376792	+	0.376792i	0.869944	−	0.493151i	$-0.164155\pi$
$307$	6.60194	+	6.60194i	0.376792	+	0.376792i	−0.493151	+	0.869944i	$0.664155\pi$
$308$	19.4856	−	34.5310i	1.11029	−	1.96759i
$309$			13.9054i			0.791049i
$310$	−24.9917	+	9.35375i	−1.41943	+	0.531258i
$311$		−	13.6125i		−	0.771891i	−0.922521	−	0.385946i	$-0.873875\pi$
$311$		−	13.6125i		−	0.771891i	0.922521	−	0.385946i	$-0.126125\pi$
$312$	2.69517	+	6.24419i	0.152584	+	0.353508i
$313$	12.6725	+	12.6725i	0.716293	+	0.716293i	0.967844	−	0.251551i	$-0.0809406\pi$
$313$	12.6725	+	12.6725i	0.716293	+	0.716293i	−0.251551	+	0.967844i	$0.580941\pi$
$314$	8.22231	+	6.24511i	0.464012	+	0.352432i
$315$	−2.02832	+	3.21312i	−0.114283	+	0.181039i
$316$	−9.05356	+	2.52172i	−0.509303	+	0.141858i
$317$	12.9175	−	12.9175i	0.725517	−	0.725517i	−0.244206	−	0.969723i	$-0.578527\pi$
$317$	12.9175	−	12.9175i	0.725517	−	0.725517i	0.969723	+	0.244206i	$0.0785274\pi$
$318$	2.12213	+	15.5279i	0.119003	+	0.870761i
$319$	−18.0217			−1.00902
$320$	−9.09787	+	15.4022i	−0.508586	+	0.861011i
$321$	33.0376			1.84398
$322$	−4.18137	−	30.5956i	−0.233019	−	1.70503i
$323$	1.59297	−	1.59297i	0.0886350	−	0.0886350i
$324$	−19.4245	+	5.41038i	−1.07914	+	0.300577i
$325$	−6.12792	−	2.17304i	−0.339916	−	0.120538i
$326$	−9.00046	−	6.83614i	−0.498489	−	0.378619i
$327$	20.7954	+	20.7954i	1.14999	+	1.14999i
$328$	−2.96568	−	6.87091i	−0.163752	−	0.379382i
$329$			9.28639i			0.511975i
$330$	11.8515	−	26.0293i	0.652403	−	1.43286i
$331$		−	11.4989i		−	0.632037i	−0.948753	−	0.316019i	$-0.897654\pi$
$331$		−	11.4989i		−	0.632037i	0.948753	−	0.316019i	$-0.102346\pi$
$332$	−7.12820	+	12.6321i	−0.391211	+	0.693277i
$333$	0.296453	+	0.296453i	0.0162455	+	0.0162455i
$334$	14.0500	−	18.4982i	0.768781	−	1.01218i
$335$	19.3844	+	12.2366i	1.05909	+	0.668558i
$336$	−25.6629	+	15.4983i	−1.40002	+	0.845501i
$337$	17.6796	−	17.6796i	0.963068	−	0.963068i	−0.0362743	−	0.999342i	$-0.511549\pi$
$337$	17.6796	−	17.6796i	0.963068	−	0.963068i	0.999342	+	0.0362743i	$0.0115490\pi$
$338$	15.8461	−	2.16562i	0.861916	−	0.117794i
$339$	19.2632			1.04624
$340$	0.393227	−	1.31084i	0.0213257	−	0.0710901i
$341$	41.2734			2.23508
$342$	−4.32458	+	0.591021i	−0.233847	+	0.0319588i
$343$	6.96073	−	6.96073i	0.375844	−	0.375844i
$344$	−12.1945	−	4.84132i	−0.657482	−	0.261027i
$345$	−4.91120	−	21.7265i	−0.264410	−	1.16972i
$346$	14.6469	−	19.2841i	0.787422	−	1.03672i
$347$	25.9125	+	25.9125i	1.39106	+	1.39106i	0.822962	+	0.568097i	$0.192320\pi$
$347$	25.9125	+	25.9125i	1.39106	+	1.39106i	0.568097	+	0.822962i	$0.307680\pi$
$348$	11.8675	+	6.69672i	0.636163	+	0.358982i
$349$		−	0.108295i		−	0.00579688i	−0.999996	−	0.00289844i	$-0.999077\pi$
$349$		−	0.108295i		−	0.00579688i	0.999996	−	0.00289844i	$-0.000922604\pi$
$350$	5.83308	−	28.0608i	0.311791	−	1.49991i
$351$		−	6.20548i		−	0.331224i
$352$	21.5293	−	17.3786i	1.14752	−	0.926285i
$353$	14.2283	+	14.2283i	0.757296	+	0.757296i	0.975830	−	0.218533i	$-0.0701272\pi$
$353$	14.2283	+	14.2283i	0.757296	+	0.757296i	−0.218533	+	0.975830i	$0.570127\pi$
$354$	12.1761	+	9.24816i	0.647153	+	0.491534i
$355$	−6.43200	−	28.4544i	−0.341375	−	1.51020i
$356$	2.12965	+	7.64593i	0.112871	+	0.405234i
$357$	1.62180	−	1.62180i	0.0858346	−	0.0858346i
$358$	−2.41843	−	17.6960i	−0.127818	−	0.935261i
$359$	−8.75756			−0.462206			−0.231103	−	0.972929i	$-0.574233\pi$
$359$	−8.75756			−0.462206			−0.231103	+	0.972929i	$0.574233\pi$
$360$	−2.14287	+	1.56168i	−0.112939	+	0.0823080i
$361$	35.1943			1.85233
$362$	−1.80160	−	13.1825i	−0.0946899	−	0.692859i
$363$	−16.8969	+	16.8969i	−0.886857	+	0.886857i
$364$	−2.82844	−	10.1548i	−0.148251	−	0.532255i
$365$	4.16429	+	2.62875i	0.217969	+	0.137595i
$366$	0.129823	+	0.0986050i	0.00678597	+	0.00515417i
$367$	11.8048	+	11.8048i	0.616204	+	0.616204i	0.944556	−	0.328352i	$-0.106493\pi$
$367$	11.8048	+	11.8048i	0.616204	+	0.616204i	−0.328352	+	0.944556i	$0.606493\pi$
$368$	5.16617	−	20.9203i	0.269305	−	1.09055i
$369$		−	1.10927i		−	0.0577464i
$370$	−2.87800	−	1.31039i	−0.149620	−	0.0681241i
$371$		−	24.2914i		−	1.26114i
$372$	−27.1789	−	15.3368i	−1.40916	−	0.795178i
$373$	−10.8527	−	10.8527i	−0.561931	−	0.561931i	0.367925	−	0.929856i	$-0.380068\pi$
$373$	−10.8527	−	10.8527i	−0.561931	−	0.561931i	−0.929856	+	0.367925i	$0.880068\pi$
$374$	−1.28030	+	1.68564i	−0.0662027	+	0.0871624i
$375$	2.44347	−	20.5289i	0.126180	−	1.06011i
$376$	−2.39117	+	6.02294i	−0.123315	+	0.310609i
$377$	−3.38797	+	3.38797i	−0.174489	+	0.174489i
$378$	27.1025	−	3.70398i	1.39400	−	0.190512i
$379$	14.8932			0.765015			0.382507	−	0.923952i	$-0.375061\pi$
$379$	14.8932			0.765015			0.382507	+	0.923952i	$0.375061\pi$
$380$	28.9870	−	15.6090i	1.48700	−	0.800725i
$381$	−23.3967			−1.19865
$382$	−4.94430	+	0.675716i	−0.252973	+	0.0345726i
$383$	7.82161	−	7.82161i	0.399666	−	0.399666i	−0.478449	−	0.878115i	$-0.658801\pi$
$383$	7.82161	−	7.82161i	0.399666	−	0.399666i	0.878115	+	0.478449i	$0.158801\pi$
$384$	−20.6350	+	3.44387i	−1.05303	+	0.175744i
$385$	−23.6631	+	37.4854i	−1.20598	+	1.91043i
$386$	−11.6237	+	15.3037i	−0.591628	+	0.778937i
$387$	−1.37517	−	1.37517i	−0.0699038	−	0.0699038i
$388$	−9.82596	+	17.4129i	−0.498838	+	0.884005i
$389$		−	18.1292i		−	0.919187i	−0.888129	−	0.459593i	$-0.847995\pi$
$389$		−	18.1292i		−	0.919187i	0.888129	−	0.459593i	$-0.152005\pi$
$390$	−2.66533	−	7.12133i	−0.134964	−	0.360603i
$391$			1.64857i			0.0833716i
$392$	24.4848	−	10.5684i	1.23667	−	0.533784i
$393$	25.4414	+	25.4414i	1.28335	+	1.28335i
$394$	8.25220	+	6.26782i	0.415740	+	0.315768i
$395$	10.2489	−	2.31673i	0.515679	−	0.116567i
$396$	3.95077	−	1.10042i	0.198534	−	0.0552983i
$397$	−4.54863	+	4.54863i	−0.228289	+	0.228289i	−0.811978	−	0.583689i	$-0.801609\pi$
$397$	−4.54863	+	4.54863i	−0.228289	+	0.228289i	0.583689	+	0.811978i	$0.301609\pi$
$398$	−0.444542	−	3.25277i	−0.0222829	−	0.163047i
$399$	55.1751			2.76221
$400$	11.0086	−	16.6976i	0.550431	−	0.834881i
$401$	−13.4064			−0.669483			−0.334741	−	0.942310i	$-0.608649\pi$
$401$	−13.4064			−0.669483			−0.334741	+	0.942310i	$0.608649\pi$
$402$	3.63010	+	26.5619i	0.181053	+	1.32479i
$403$	7.75913	−	7.75913i	0.386510	−	0.386510i
$404$	14.5668	−	4.05734i	0.724725	−	0.201860i
$405$	21.9892	−	4.97057i	1.09265	−	0.246990i
$406$	−16.8192	−	12.7748i	−0.834724	−	0.634000i
$407$	3.45853	+	3.45853i	0.171433	+	0.171433i
$408$	1.46946	−	0.634261i	0.0727490	−	0.0314006i
$409$		−	37.9316i		−	1.87560i	−0.347180	−	0.937799i	$-0.612861\pi$
$409$		−	37.9316i		−	1.87560i	0.347180	−	0.937799i	$-0.387139\pi$
$410$	2.93284	+	7.83609i	0.144843	+	0.386997i
$411$			12.9748i			0.640000i
$412$	7.39134	−	13.0984i	0.364145	−	0.645313i
$413$	−16.7577	−	16.7577i	−0.824595	−	0.824595i
$414$	1.93194	−	2.54359i	0.0949496	−	0.125011i
$415$	8.65640	−	13.7129i	0.424926	−	0.673139i
$416$	0.780304	−	7.31445i	0.0382575	−	0.358620i
$417$	−18.6903	+	18.6903i	−0.915268	+	0.915268i
$418$	−50.4521	+	6.89506i	−2.46769	+	0.337249i
$419$	−34.8854			−1.70426			−0.852131	−	0.523329i	$-0.824690\pi$
$419$	−34.8854			−1.70426			−0.852131	+	0.523329i	$0.824690\pi$
$420$	29.5116	−	15.8915i	1.44002	−	0.775426i
$421$	−35.9432			−1.75177			−0.875883	−	0.482524i	$-0.839720\pi$
$421$	−35.9432			−1.75177			−0.875883	+	0.482524i	$0.839720\pi$
$422$	32.4159	−	4.43013i	1.57798	−	0.215655i
$423$	−0.679206	+	0.679206i	−0.0330241	+	0.0330241i
$424$	6.25482	−	15.7548i	0.303761	−	0.765122i
$425$	−0.511385	+	1.44209i	−0.0248058	+	0.0699519i
$426$	20.6353	−	27.1685i	0.999786	−	1.31632i
$427$	−0.178673	−	0.178673i	−0.00864659	−	0.00864659i
$428$	−31.1204	−	17.5610i	−1.50426	−	0.848842i
$429$			11.7608i			0.567814i
$430$	13.3503	+	6.07857i	0.643808	+	0.293135i
$431$		−	4.48617i		−	0.216091i	−0.994146	−	0.108046i	$-0.965541\pi$
$431$		−	4.48617i		−	0.216091i	0.994146	−	0.108046i	$-0.0344593\pi$
$432$	18.5318	+	4.57635i	0.891612	+	0.220180i
$433$	13.2572	+	13.2572i	0.637102	+	0.637102i	0.949839	−	0.312738i	$-0.101246\pi$
$433$	13.2572	+	13.2572i	0.637102	+	0.637102i	−0.312738	+	0.949839i	$0.601246\pi$
$434$	38.5194	+	29.2567i	1.84899	+	1.40437i
$435$	−12.8828	−	8.13242i	−0.617685	−	0.389920i
$436$	−8.53490	−	30.6423i	−0.408748	−	1.46750i
$437$	−28.0429	+	28.0429i	−1.34148	+	1.34148i
$438$	0.779842	+	5.70621i	0.0372623	+	0.272653i
$439$	12.7409			0.608088			0.304044	−	0.952658i	$-0.401663\pi$
$439$	12.7409			0.608088			0.304044	+	0.952658i	$0.401663\pi$
$440$	−24.9995	+	18.2192i	−1.19180	+	0.868564i
$441$	3.95295			0.188236
$442$	0.0762016	+	0.557578i	0.00362454	+	0.0265213i
$443$	−0.640705	+	0.640705i	−0.0304408	+	0.0304408i	−0.722163	−	0.691723i	$-0.756852\pi$
$443$	−0.640705	+	0.640705i	−0.0304408	+	0.0304408i	0.691723	+	0.722163i	$0.256852\pi$
$444$	−0.992310	−	3.56263i	−0.0470930	−	0.169075i
$445$	−1.95653	−	8.65544i	−0.0927483	−	0.410307i
$446$	13.3114	+	10.1105i	0.630315	+	0.478745i
$447$	−10.9406	−	10.9406i	−0.517475	−	0.517475i
$448$	32.4117	−	0.957921i	1.53131	−	0.0452575i
$449$		−	1.79037i		−	0.0844927i	−0.999107	−	0.0422464i	$-0.986549\pi$
$449$		−	1.79037i		−	0.0844927i	0.999107	−	0.0422464i	$-0.0134514\pi$
$450$	2.47900	−	1.62573i	0.116861	−	0.0766379i
$451$		−	12.9412i		−	0.609375i
$452$	−18.1454	−	10.2393i	−0.853487	−	0.481616i
$453$	−16.2494	−	16.2494i	−0.763461	−	0.763461i
$454$	−18.5213	+	24.3851i	−0.869247	+	1.14445i
$455$	2.59852	+	11.4955i	0.121820	+	0.538918i
$456$	35.7853	+	14.2071i	1.67580	+	0.665309i
$457$	24.7951	−	24.7951i	1.15987	−	1.15987i	0.175364	−	0.984504i	$-0.443890\pi$
$457$	24.7951	−	24.7951i	1.15987	−	1.15987i	0.984504	−	0.175364i	$-0.0561102\pi$
$458$	8.17574	−	1.11734i	0.382027	−	0.0522099i
$459$	−1.46035			−0.0681632
$460$	−6.92246	+	23.0763i	−0.322761	+	1.07594i
$461$	18.8538			0.878109			0.439054	−	0.898461i	$-0.355314\pi$
$461$	18.8538			0.878109			0.439054	+	0.898461i	$0.355314\pi$
$462$	−51.3652	+	7.01985i	−2.38973	+	0.326593i
$463$	19.9055	−	19.9055i	0.925089	−	0.925089i	−0.0722940	−	0.997383i	$-0.523032\pi$
$463$	19.9055	−	19.9055i	0.925089	−	0.925089i	0.997383	+	0.0722940i	$0.0230320\pi$
$464$	−7.61917	−	12.6162i	−0.353711	−	0.585693i
$465$	29.5043	+	18.6249i	1.36823	+	0.863707i
$466$	−6.74385	+	8.87894i	−0.312403	+	0.411309i
$467$	12.4846	+	12.4846i	0.577719	+	0.577719i	0.934274	−	0.356555i	$-0.116049\pi$
$467$	12.4846	+	12.4846i	0.577719	+	0.577719i	−0.356555	+	0.934274i	$0.616049\pi$
$468$	0.535847	−	0.949592i	0.0247696	−	0.0438949i
$469$		−	41.5527i		−	1.91872i
$470$	3.00225	−	6.59381i	0.138484	−	0.304150i
$471$		−	13.5003i		−	0.622063i
$472$	−6.55371	−	15.1837i	−0.301659	−	0.698884i
$473$	−16.0432	−	16.0432i	−0.737668	−	0.737668i
$474$	9.78575	+	7.43259i	0.449474	+	0.341390i
$475$	−33.2297	+	15.8318i	−1.52468	+	0.726414i
$476$	−2.38974	+	0.665623i	−0.109534	+	0.0305088i
$477$	1.77667	−	1.77667i	0.0813481	−	0.0813481i
$478$	3.74053	+	27.3700i	0.171088	+	1.25187i
$479$	1.80115			0.0822967			0.0411483	−	0.999153i	$-0.486898\pi$
$479$	1.80115			0.0822967			0.0411483	+	0.999153i	$0.486898\pi$
$480$	23.2325	−	2.70787i	1.06041	−	0.123597i
$481$	1.30036			0.0592913
$482$	−5.62538	−	41.1617i	−0.256229	−	1.87486i
$483$	−28.5505	+	28.5505i	−1.29909	+	1.29909i
$484$	24.8978	−	6.93488i	1.13172	−	0.315222i
$485$	11.9325	−	18.9027i	0.541828	−	0.858328i
$486$	4.87240	+	3.70075i	0.221017	+	0.167869i
$487$	−5.08360	−	5.08360i	−0.230360	−	0.230360i	0.582483	−	0.812843i	$-0.302081\pi$
$487$	−5.08360	−	5.08360i	−0.230360	−	0.230360i	−0.812843	+	0.582483i	$0.802081\pi$
$488$	−0.0698764	−	0.161890i	−0.00316316	−	0.00732841i
$489$			14.7780i			0.668284i
$490$	−27.9243	+	10.4513i	−1.26149	+	0.472144i
$491$			34.2409i			1.54527i	0.634851	+	0.772635i	$0.281062\pi$
$491$			34.2409i			1.54527i	−0.634851	+	0.772635i	$0.718938\pi$
$492$	−4.80882	+	8.52186i	−0.216798	+	0.384195i
$493$	0.797298	+	0.797298i	0.0359085	+	0.0359085i
$494$	−8.18844	+	10.7809i	−0.368415	+	0.485056i
$495$	−4.47240	+	1.01097i	−0.201019	+	0.0454397i
$496$	17.4494	+	28.8937i	0.783503	+	1.29736i
$497$	−37.3914	+	37.3914i	−1.67723	+	1.67723i
$498$	18.7904	−	2.56800i	0.842017	−	0.115075i
$499$	33.0682			1.48034			0.740169	−	0.672421i	$-0.234746\pi$
$499$	33.0682			1.48034			0.740169	+	0.672421i	$0.234746\pi$
$500$	−13.2137	+	18.0388i	−0.590936	+	0.806719i
$501$	−30.3725			−1.35694
$502$	−16.3413	+	2.23330i	−0.729350	+	0.0996769i
$503$	−5.35078	+	5.35078i	−0.238580	+	0.238580i	−0.816262	−	0.577682i	$-0.803957\pi$
$503$	−5.35078	+	5.35078i	−0.238580	+	0.238580i	0.577682	+	0.816262i	$0.303957\pi$
$504$	4.46719	+	1.77352i	0.198985	+	0.0789988i
$505$	−16.4901	+	3.72752i	−0.733799	+	0.165872i
$506$	22.5387	−	29.6744i	1.00197	−	1.31919i
$507$	−14.7869	−	14.7869i	−0.656709	−	0.656709i
$508$	22.0390	+	12.4364i	0.977821	+	0.551777i
$509$			35.9659i			1.59416i	0.603873	+	0.797081i	$0.293623\pi$
$509$			35.9659i			1.59416i	−0.603873	+	0.797081i	$0.706377\pi$
$510$	−1.67588	+	0.627237i	−0.0742091	+	0.0277745i
$511$		−	8.92662i		−	0.394891i
$512$	21.2681	+	7.72444i	0.939927	+	0.341375i
$513$	−24.8412	−	24.8412i	−1.09677	−	1.09677i
$514$	5.16419	+	3.92237i	0.227783	+	0.173009i
$515$	−8.97596	+	14.2191i	−0.395528	+	0.626569i
$516$	4.60307	+	16.5261i	0.202639	+	0.727522i
$517$	−7.92386	+	7.92386i	−0.348491	+	0.348491i
$518$	0.776170	+	5.67934i	0.0341029	+	0.249536i
$519$	−31.6629			−1.38985
$520$	−1.27466	+	8.12482i	−0.0558975	+	0.356297i
$521$	23.5994			1.03391			0.516955	−	0.856012i	$-0.327065\pi$
$521$	23.5994			1.03391			0.516955	+	0.856012i	$0.327065\pi$
$522$	−0.295813	−	2.16450i	−0.0129474	−	0.0947377i
$523$	−23.2708	+	23.2708i	−1.01756	+	1.01756i	−0.0177193	+	0.999843i	$0.505641\pi$
$523$	−23.2708	+	23.2708i	−1.01756	+	1.01756i	−0.999843	+	0.0177193i	$0.994359\pi$
$524$	−10.4417	−	37.4883i	−0.456149	−	1.63768i
$525$	−33.8311	+	16.1184i	−1.47651	+	0.703463i
$526$	−30.1988	−	22.9370i	−1.31673	−	1.00010i
$527$	−1.82597	−	1.82597i	−0.0795406	−	0.0795406i
$528$	−35.1218	−	8.67318i	−1.52848	−	0.377452i
$529$		−	6.02175i		−	0.261815i
$530$	−7.85330	+	17.2481i	−0.341125	+	0.749210i
$531$		−	2.45132i		−	0.106378i
$532$	−51.9733	−	29.3281i	−2.25333	−	1.27154i
$533$	−2.43285	−	2.43285i	−0.105379	−	0.105379i
$534$	6.27699	−	8.26428i	0.271632	−	0.357630i
$535$	33.7830	+	21.3258i	1.46057	+	0.921997i
$536$	10.6995	−	26.9501i	0.462146	−	1.16407i
$537$	−16.5131	+	16.5131i	−0.712592	+	0.712592i
$538$	17.3512	−	2.37131i	0.748063	−	0.102234i
$539$	46.1165			1.98638
$540$	−20.4416	−	6.13212i	−0.879668	−	0.263884i
$541$	28.4406			1.22276			0.611378	−	0.791339i	$-0.290616\pi$
$541$	28.4406			1.22276			0.611378	+	0.791339i	$0.290616\pi$
$542$	−19.4642	+	2.66009i	−0.836060	+	0.114261i
$543$	−12.3013	+	12.3013i	−0.527901	+	0.527901i
$544$	−1.72132	−	0.183630i	−0.0738011	−	0.00787309i
$545$	7.84110	+	34.6881i	0.335876	+	1.48587i
$546$	−8.33664	+	10.9760i	−0.356775	+	0.469730i
$547$	−19.8937	−	19.8937i	−0.850591	−	0.850591i	0.139614	−	0.990206i	$-0.455414\pi$
$547$	−19.8937	−	19.8937i	−0.850591	−	0.850591i	−0.990206	+	0.139614i	$0.955414\pi$
$548$	6.89671	−	12.2219i	0.294613	−	0.522092i
$549$		−	0.0261363i		−	0.00111547i
$550$	28.9209	−	18.9664i	1.23319	−	0.808730i
$551$			27.1249i			1.15556i
$552$	−25.8687	+	11.1657i	−1.10104	+	0.475243i
$553$	−13.4679	−	13.4679i	−0.572714	−	0.572714i
$554$	2.02876	+	1.54091i	0.0861938	+	0.0654670i
$555$	0.911646	+	4.03301i	0.0386972	+	0.171192i
$556$	27.5405	−	7.67093i	1.16798	−	0.325320i
$557$	−20.4590	+	20.4590i	−0.866876	+	0.866876i	−0.992125	−	0.125250i	$-0.960027\pi$
$557$	−20.4590	+	20.4590i	−0.866876	+	0.866876i	0.125250	+	0.992125i	$0.460027\pi$
$558$	0.677471	+	4.95715i	0.0286796	+	0.209853i
$559$	−6.03204			−0.255128
$560$	−36.2461	−	0.717475i	−1.53168	−	0.0303189i
$561$	2.76768			0.116852
$562$	3.54369	+	25.9296i	0.149481	+	1.09378i
$563$	25.7265	−	25.7265i	1.08424	−	1.08424i	0.0881327	−	0.996109i	$-0.471910\pi$
$563$	25.7265	−	25.7265i	1.08424	−	1.08424i	0.996109	−	0.0881327i	$-0.0280900\pi$
$564$	8.16237	−	2.27349i	0.343698	−	0.0957312i
$565$	19.6979	+	12.4345i	0.828696	+	0.523122i
$566$	−29.3649	−	22.3036i	−1.23430	−	0.937489i
$567$	−28.8956	−	28.8956i	−1.21350	−	1.21350i
$568$	−33.8792	+	14.6232i	−1.42154	+	0.613577i
$569$		−	8.84476i		−	0.370792i	−0.982664	−	0.185396i	$-0.940643\pi$
$569$		−	8.84476i		−	0.370792i	0.982664	−	0.185396i	$-0.0593568\pi$
$570$	−39.1771	−	17.8379i	−1.64095	−	0.747147i
$571$			29.2747i			1.22511i	0.790429	+	0.612554i	$0.209858\pi$
$571$			29.2747i			1.22511i	−0.790429	+	0.612554i	$0.790142\pi$
$572$	6.25138	−	11.0783i	0.261383	−	0.463206i
$573$	4.61380	+	4.61380i	0.192744	+	0.192744i
$574$	9.17337	−	12.0777i	0.382889	−	0.504111i
$575$	9.00254	−	25.3870i	0.375432	−	1.05871i
$576$	2.44065	+	2.30053i	0.101694	+	0.0958553i
$577$	18.8365	−	18.8365i	0.784175	−	0.784175i	−0.196357	−	0.980532i	$-0.562911\pi$
$577$	18.8365	−	18.8365i	0.784175	−	0.784175i	0.980532	+	0.196357i	$0.0629112\pi$
$578$	−23.6890	+	3.23747i	−0.985332	+	0.134661i
$579$	25.1274			1.04426
$580$	7.81248	+	14.5083i	0.324396	+	0.602425i
$581$	−29.3951			−1.21951
$582$	25.9018	−	3.53989i	1.07367	−	0.146733i
$583$	20.7273	−	20.7273i	0.858435	−	0.858435i
$584$	2.29853	−	5.78960i	0.0951138	−	0.239575i
$585$	−0.650726	+	1.03084i	−0.0269042	+	0.0426199i
$586$	−21.0898	+	27.7668i	−0.871212	+	1.14704i
$587$	−25.3068	−	25.3068i	−1.04452	−	1.04452i	−0.998961	−	0.0455624i	$-0.985492\pi$
$587$	−25.3068	−	25.3068i	−1.04452	−	1.04452i	−0.0455624	−	0.998961i	$-0.514508\pi$
$588$	−30.3681	−	17.1365i	−1.25236	−	0.706697i
$589$		−	62.1214i		−	2.55967i
$590$	6.48114	+	17.3166i	0.266824	+	0.712911i
$591$		−	13.5494i		−	0.557349i
$592$	−0.958975	+	3.88334i	−0.0394136	+	0.159604i
$593$	11.5376	+	11.5376i	0.473794	+	0.473794i	0.903140	−	0.429346i	$-0.141256\pi$
$593$	11.5376	+	11.5376i	0.473794	+	0.473794i	−0.429346	+	0.903140i	$0.641256\pi$
$594$	26.2864	+	19.9654i	1.07855	+	0.819191i
$595$	2.70526	−	0.611514i	0.110905	−	0.0250697i
$596$	4.49030	+	16.1212i	0.183930	+	0.660351i
$597$	−3.03534	+	3.03534i	−0.124228	+	0.124228i
$598$	−1.34147	−	9.81572i	−0.0548568	−	0.401395i
$599$	−34.1685			−1.39609			−0.698043	−	0.716056i	$-0.745945\pi$
$599$	−34.1685			−1.39609			−0.698043	+	0.716056i	$0.745945\pi$
$600$	−26.0924	+	1.74279i	−1.06522	+	0.0711490i
$601$	−27.6480			−1.12779			−0.563893	−	0.825848i	$-0.690697\pi$
$601$	−27.6480			−1.12779			−0.563893	+	0.825848i	$0.690697\pi$
$602$	−3.60045	−	26.3450i	−0.146744	−	1.07374i
$603$	3.03916	−	3.03916i	0.123764	−	0.123764i
$604$	6.66911	+	23.9437i	0.271362	+	0.974255i
$605$	−28.1851	+	6.37114i	−1.14589	+	0.259024i
$606$	−15.7449	−	11.9587i	−0.639591	−	0.485790i
$607$	13.3196	+	13.3196i	0.540624	+	0.540624i	0.923712	−	0.383088i	$-0.125139\pi$
$607$	13.3196	+	13.3196i	0.540624	+	0.540624i	−0.383088	+	0.923712i	$0.625139\pi$
$608$	−26.1569	−	32.4042i	−1.06080	−	1.31416i
$609$			27.6158i			1.11905i
$610$	0.0691026	+	0.184631i	0.00279788	+	0.00747550i
$611$			2.97927i			0.120528i
$612$	−0.223469	−	0.126102i	−0.00903321	−	0.00509737i
$613$	5.34620	+	5.34620i	0.215931	+	0.215931i	0.806781	−	0.590850i	$-0.201208\pi$
$613$	5.34620	+	5.34620i	0.215931	+	0.215931i	−0.590850	+	0.806781i	$0.701208\pi$
$614$	−7.98633	+	10.5148i	−0.322302	+	0.424343i
$615$	5.83977	−	9.25098i	0.235482	−	0.373036i
$616$	52.1158	+	20.6905i	2.09981	+	0.833644i
$617$	5.76663	−	5.76663i	0.232156	−	0.232156i	−0.581436	−	0.813592i	$-0.697509\pi$
$617$	5.76663	−	5.76663i	0.232156	−	0.232156i	0.813592	+	0.581436i	$0.197509\pi$
$618$	−19.4840	+	2.66280i	−0.783763	+	0.107113i
$619$	−29.1731			−1.17257			−0.586283	−	0.810107i	$-0.699409\pi$
$619$	−29.1731			−1.17257			−0.586283	+	0.810107i	$0.699409\pi$
$620$	−17.8921	−	33.2269i	−0.718566	−	1.33443i
$621$	25.7083			1.03164
$622$	19.0736	−	2.60671i	0.764782	−	0.104519i
$623$	−11.3740	+	11.3740i	−0.455688	+	0.455688i
$624$	−8.23318	+	4.97217i	−0.329591	+	0.199046i
$625$	15.7501	−	19.4148i	0.630003	−	0.776593i
$626$	−15.3299	+	20.1833i	−0.612705	+	0.806687i
$627$	47.0796	+	47.0796i	1.88018	+	1.88018i
$628$	−7.17606	+	12.7169i	−0.286356	+	0.507460i
$629$		−	0.306016i		−	0.0122017i
$630$	−4.89060	−	2.22676i	−0.194846	−	0.0887163i
$631$			1.00145i			0.0398673i	0.999801	+	0.0199336i	$0.00634549\pi$
$631$			1.00145i			0.0398673i	−0.999801	+	0.0199336i	$0.993655\pi$
$632$	−5.26711	−	12.2029i	−0.209514	−	0.485403i
$633$	−30.2490	−	30.2490i	−1.20229	−	1.20229i
$634$	20.5734	+	15.6262i	0.817075	+	0.620595i
$635$	−23.9246	−	15.1026i	−0.949419	−	0.599330i
$636$	−21.3511	+	5.94700i	−0.846628	+	0.235814i
$637$	8.66960	−	8.66960i	0.343502	−	0.343502i
$638$	−3.45106	−	25.2519i	−0.136629	−	0.999730i
$639$	−5.46961			−0.216375
$640$	−23.3236	−	9.79839i	−0.921947	−	0.387315i
$641$	−39.4064			−1.55646			−0.778230	−	0.627979i	$-0.783882\pi$
$641$	−39.4064			−1.55646			−0.778230	+	0.627979i	$0.783882\pi$
$642$	6.32650	+	46.2918i	0.249687	+	1.82699i
$643$	−6.04020	+	6.04020i	−0.238202	+	0.238202i	−0.816105	−	0.577903i	$-0.803871\pi$
$643$	−6.04020	+	6.04020i	−0.238202	+	0.238202i	0.577903	+	0.816105i	$0.303871\pi$
$644$	42.0696	−	11.7178i	1.65777	−	0.461745i
$645$	−4.22889	−	18.7081i	−0.166512	−	0.736630i
$646$	2.53709	+	1.92700i	0.0998205	+	0.0758169i
$647$	−26.4847	−	26.4847i	−1.04122	−	1.04122i	−0.999113	−	0.0421082i	$-0.986593\pi$
$647$	−26.4847	−	26.4847i	−1.04122	−	1.04122i	−0.0421082	−	0.999113i	$-0.513407\pi$
$648$	−11.3007	−	26.1814i	−0.443931	−	1.02850i
$649$		−	28.5980i		−	1.12257i
$650$	1.87138	−	9.00249i	0.0734014	−	0.353107i
$651$		−	63.2456i		−	2.47879i
$652$	7.85519	−	13.9204i	0.307633	−	0.545166i
$653$	7.72375	+	7.72375i	0.302254	+	0.302254i	0.841895	−	0.539641i	$-0.181440\pi$
$653$	7.72375	+	7.72375i	0.302254	+	0.302254i	−0.539641	+	0.841895i	$0.681440\pi$
$654$	−25.1560	+	33.1204i	−0.983679	+	1.29511i
$655$	9.59293	+	42.4379i	0.374827	+	1.65819i
$656$	9.05953	−	5.47122i	0.353715	−	0.213615i
$657$	0.652893	−	0.652893i	0.0254718	−	0.0254718i
$658$	−13.0120	+	1.77829i	−0.507260	+	0.0693249i
$659$	−12.3464			−0.480949			−0.240474	−	0.970655i	$-0.577303\pi$
$659$	−12.3464			−0.480949			−0.240474	+	0.970655i	$0.577303\pi$
$660$	38.7414	+	11.6217i	1.50801	+	0.452375i
$661$	−3.74124			−0.145517			−0.0727587	−	0.997350i	$-0.523180\pi$
$661$	−3.74124			−0.145517			−0.0727587	+	0.997350i	$0.523180\pi$
$662$	16.1121	−	2.20197i	0.626216	−	0.0855822i
$663$	0.520306	−	0.520306i	0.0202070	−	0.0202070i
$664$	−19.0650	−	7.56898i	−0.739864	−	0.293733i
$665$	56.4200	+	35.6157i	2.18788	+	1.38112i
$666$	−0.358618	+	0.472156i	−0.0138962	+	0.0182957i
$667$	−14.0358	−	14.0358i	−0.543469	−	0.543469i
$668$	28.6100	+	16.1444i	1.10695	+	0.624645i
$669$		−	21.8563i		−	0.845012i
$670$	−13.4338	+	29.5045i	−0.518993	+	1.13986i
$671$		−	0.304915i		−	0.0117711i
$672$	−26.6303	−	32.9907i	−1.02729	−	1.27264i
$673$	7.67036	+	7.67036i	0.295671	+	0.295671i	0.839315	−	0.543645i	$-0.182956\pi$
$673$	7.67036	+	7.67036i	0.295671	+	0.295671i	−0.543645	+	0.839315i	$0.682956\pi$
$674$	28.1579	+	21.3869i	1.08460	+	0.823792i
$675$	22.4885	+	7.97471i	0.865583	+	0.306947i
$676$	6.06888	+	21.7887i	0.233419	+	0.838028i
$677$	13.3337	−	13.3337i	0.512455	−	0.512455i	−0.402823	−	0.915278i	$-0.631971\pi$
$677$	13.3337	−	13.3337i	0.512455	−	0.512455i	0.915278	+	0.402823i	$0.131971\pi$
$678$	3.68880	+	26.9914i	0.141667	+	1.03660i
$679$	−40.5200			−1.55502
$680$	1.91203	+	0.299968i	0.0733230	+	0.0115032i
$681$	40.0383			1.53427
$682$	7.90361	+	57.8318i	0.302645	+	2.21449i
$683$	−12.3615	+	12.3615i	−0.473001	+	0.473001i	−0.902884	−	0.429883i	$-0.858555\pi$
$683$	−12.3615	+	12.3615i	−0.473001	+	0.473001i	0.429883	+	0.902884i	$0.358555\pi$
$684$	−1.65627	−	5.94638i	−0.0633289	−	0.227366i
$685$	−8.37528	+	13.2676i	−0.320003	+	0.506927i
$686$	11.0862	+	8.42035i	0.423274	+	0.321491i
$687$	−7.62923	−	7.62923i	−0.291073	−	0.291073i
$688$	4.44844	−	18.0138i	0.169595	−	0.686771i
$689$		−	7.79318i		−	0.296896i
$690$	29.5025	−	11.0420i	1.12314	−	0.420363i
$691$		−	39.0056i		−	1.48384i	−0.670487	−	0.741921i	$-0.733915\pi$
$691$		−	39.0056i		−	1.48384i	0.670487	−	0.741921i	$-0.266085\pi$
$692$	29.8254	+	16.8303i	1.13379	+	0.639791i
$693$	5.87710	+	5.87710i	0.223253	+	0.223253i
$694$	−31.3463	+	41.2705i	−1.18989	+	1.56661i
$695$	−31.1767	+	7.04736i	−1.18260	+	0.267322i
$696$	−7.11082	+	17.9109i	−0.269535	+	0.678913i
$697$	−0.572528	+	0.572528i	−0.0216861	+	0.0216861i
$698$	0.151741	−	0.0207378i	0.00574349	−	0.000784938i
$699$	14.5785			0.551409
$700$	40.4355	+	2.79977i	1.52832	+	0.105821i
$701$	1.00217			0.0378513			0.0189257	−	0.999821i	$-0.493975\pi$
$701$	1.00217			0.0378513			0.0189257	+	0.999821i	$0.493975\pi$
$702$	8.69505	−	1.18831i	0.328173	−	0.0448500i
$703$	5.20549	−	5.20549i	0.196329	−	0.196329i
$704$	28.4735	+	26.8388i	1.07314	+	1.01152i
$705$	−9.24006	+	2.08868i	−0.348001	+	0.0786642i
$706$	−17.2119	+	22.6612i	−0.647779	+	0.852865i
$707$	21.6693	+	21.6693i	0.814958	+	0.814958i
$708$	−10.6268	+	18.8320i	−0.399378	+	0.707750i
$709$			33.4480i			1.25617i	0.778146	+	0.628084i	$0.216160\pi$
$709$			33.4480i			1.25617i	−0.778146	+	0.628084i	$0.783840\pi$
$710$	38.6383	−	14.4613i	1.45007	−	0.542723i
$711$		−	1.97009i		−	0.0738840i
$712$	−10.3056	+	4.44819i	−0.386218	+	0.166703i
$713$	32.1448	+	32.1448i	1.20383	+	1.20383i
$714$	2.58301	+	1.96188i	0.0966666	+	0.0734215i
$715$	−7.59160	+	12.0261i	−0.283910	+	0.449751i
$716$	24.3323	−	6.77735i	0.909340	−	0.253282i
$717$	25.5404	−	25.5404i	0.953825	−	0.953825i
$718$	−1.67702	−	12.2710i	−0.0625859	−	0.457949i
$719$	28.6775			1.06949			0.534745	−	0.845014i	$-0.320408\pi$
$719$	28.6775			1.06949			0.534745	+	0.845014i	$0.320408\pi$
$720$	−2.59856	−	2.70351i	−0.0968427	−	0.100754i
$721$	30.4802			1.13514
$722$	6.73950	+	49.3139i	0.250818	+	1.83527i
$723$	−38.4102	+	38.4102i	−1.42849	+	1.42849i
$724$	18.1262	−	5.04876i	0.673656	−	0.187636i
$725$	−7.92401	−	16.6318i	−0.294290	−	0.617690i
$726$	−26.9114	−	20.4401i	−0.998775	−	0.758602i
$727$	9.48022	+	9.48022i	0.351602	+	0.351602i	0.860705	−	0.509104i	$-0.170023\pi$
$727$	9.48022	+	9.48022i	0.351602	+	0.351602i	−0.509104	+	0.860705i	$0.670023\pi$
$728$	13.6871	−	5.90776i	0.507278	−	0.218956i
$729$			22.2458i			0.823920i
$730$	−2.88594	+	6.33835i	−0.106813	+	0.234593i
$731$			1.41953i			0.0525033i
$732$	−0.113304	+	0.200789i	−0.00418783	+	0.00742138i
$733$	−35.9030	−	35.9030i	−1.32611	−	1.32611i	−0.908735	−	0.417373i	$-0.862951\pi$
$733$	−35.9030	−	35.9030i	−1.32611	−	1.32611i	−0.417373	−	0.908735i	$-0.637049\pi$
$734$	−14.2802	+	18.8013i	−0.527091	+	0.693967i
$735$	32.9664	+	20.8104i	1.21598	+	0.767601i
$736$	30.3026	+	3.23267i	1.11697	+	0.119158i
$737$	35.4559	−	35.4559i	1.30604	−	1.30604i
$738$	1.55430	−	0.212419i	0.0572145	−	0.00781925i
$739$	21.6438			0.796182			0.398091	−	0.917346i	$-0.369673\pi$
$739$	21.6438			0.796182			0.398091	+	0.917346i	$0.369673\pi$
$740$	1.28499	−	4.28355i	0.0472371	−	0.157466i
$741$	17.7013			0.650275
$742$	34.0368	−	4.65166i	1.24953	−	0.170768i
$743$	−32.2288	+	32.2288i	−1.18236	+	1.18236i	−0.203228	+	0.979131i	$0.565143\pi$
$743$	−32.2288	+	32.2288i	−1.18236	+	1.18236i	−0.979131	+	0.203228i	$0.934857\pi$
$744$	16.2852	−	41.0197i	0.597045	−	1.50385i
$745$	−4.12528	−	18.2497i	−0.151139	−	0.668618i
$746$	13.1284	−	17.2849i	0.480666	−	0.632845i
$747$	−2.14995	−	2.14995i	−0.0786627	−	0.0786627i
$748$	−2.60707	−	1.47115i	−0.0953240	−	0.0537906i
$749$		−	72.4175i		−	2.64608i
$750$	29.2328	−	0.507407i	1.06743	−	0.0185279i
$751$			17.9121i			0.653621i	0.945090	+	0.326810i	$0.105974\pi$
$751$			17.9121i			0.653621i	−0.945090	+	0.326810i	$0.894026\pi$
$752$	−8.89717	−	2.19712i	−0.324446	−	0.0801206i
$753$	15.2490	+	15.2490i	0.555704	+	0.555704i
$754$	−5.39596	−	4.09841i	−0.196509	−	0.149255i
$755$	−6.12698	−	27.1050i	−0.222984	−	0.986452i
$756$	10.3799	+	37.2664i	0.377515	+	1.35537i
$757$	−7.71522	+	7.71522i	−0.280415	+	0.280415i	−0.833274	−	0.552860i	$-0.813537\pi$
$757$	−7.71522	+	7.71522i	−0.280415	+	0.280415i	0.552860	+	0.833274i	$0.313537\pi$
$758$	2.85197	+	20.8683i	0.103588	+	0.757969i
$759$	−48.7229			−1.76853
$760$	27.4220	+	37.6272i	0.994700	+	1.36488i
$761$	17.4074			0.631019			0.315509	−	0.948922i	$-0.397825\pi$
$761$	17.4074			0.631019			0.315509	+	0.948922i	$0.397825\pi$
$762$	−4.48033	−	32.7832i	−0.162305	−	1.18761i
$763$	45.5830	−	45.5830i	1.65021	−	1.65021i
$764$	−1.89361	−	6.79851i	−0.0685084	−	0.245961i
$765$	0.242589	+	0.153137i	0.00877083	+	0.00553667i
$766$	12.4574	+	9.46177i	0.450102	+	0.341867i
$767$	−5.37623	−	5.37623i	−0.194125	−	0.194125i
$768$	−8.77699	−	28.2541i	−0.316712	−	1.01953i
$769$			10.7498i			0.387646i	0.981037	+	0.193823i	$0.0620888\pi$
$769$			10.7498i			0.387646i	−0.981037	+	0.193823i	$0.937911\pi$
$770$	−57.0555	−	25.9782i	−2.05614	−	0.936188i
$771$		−	8.47917i		−	0.305370i
$772$	−23.6692	−	13.3564i	−0.851874	−	0.480706i
$773$	−25.7268	−	25.7268i	−0.925328	−	0.925328i	0.0720711	−	0.997399i	$-0.477039\pi$
$773$	−25.7268	−	25.7268i	−0.925328	−	0.925328i	−0.997399	+	0.0720711i	$0.977039\pi$
$774$	1.66354	−	2.19021i	0.0597945	−	0.0787255i
$775$	18.1476	+	38.0902i	0.651880	+	1.36824i
$776$	−26.2804	−	10.4336i	−0.943410	−	0.374543i
$777$	5.29970	−	5.29970i	0.190126	−	0.190126i
$778$	25.4024	−	3.47164i	0.910721	−	0.124464i
$779$	−19.4780			−0.697871
$780$	9.46794	−	5.09832i	0.339006	−	0.182549i
$781$	−63.8104			−2.28332
$782$	−2.30995	+	0.315691i	−0.0826038	+	0.0112891i
$783$	12.4333	−	12.4333i	0.444331	−	0.444331i
$784$	19.4970	+	32.2841i	0.696321	+	1.15300i
$785$	8.71452	−	13.8050i	0.311034	−	0.492720i
$786$	−30.7763	+	40.5201i	−1.09775	+	1.44530i
$787$	−10.1230	−	10.1230i	−0.360846	−	0.360846i	0.503278	−	0.864124i	$-0.332127\pi$
$787$	−10.1230	−	10.1230i	−0.360846	−	0.360846i	−0.864124	+	0.503278i	$0.832127\pi$
$788$	−7.20215	+	12.7631i	−0.256566	+	0.454668i
$789$			49.5839i			1.76523i
$790$	5.20878	+	13.9170i	0.185320	+	0.495146i
$791$		−	42.2246i		−	1.50133i
$792$	2.29845	+	5.32505i	0.0816718	+	0.189218i
$793$	−0.0573220	−	0.0573220i	−0.00203557	−	0.00203557i
$794$	−7.24452	−	5.50245i	−0.257098	−	0.195275i
$795$	24.1702	−	5.46357i	0.857228	−	0.193773i
$796$	4.47262	−	1.24577i	0.158528	−	0.0441553i
$797$	−33.0322	+	33.0322i	−1.17006	+	1.17006i	−0.187868	+	0.982194i	$0.560158\pi$
$797$	−33.0322	+	33.0322i	−1.17006	+	1.17006i	−0.982194	+	0.187868i	$0.939842\pi$
$798$	10.5657	+	77.3108i	0.374022	+	2.73677i
$799$	0.701117			0.0248037
$800$	25.5046	+	12.2277i	0.901724	+	0.432313i
$801$	−1.66378			−0.0587868
$802$	−2.56724	−	18.7849i	−0.0906526	−	0.663317i
$803$	7.61688	−	7.61688i	0.268794	−	0.268794i
$804$	−36.5231	+	10.1729i	−1.28807	+	0.358771i
$805$	−47.6241	+	10.7652i	−1.67853	+	0.379425i
$806$	12.3578	+	9.38618i	0.435286	+	0.330614i
$807$	−16.1914	−	16.1914i	−0.569963	−	0.569963i
$808$	8.47455	+	19.6339i	0.298134	+	0.690717i
$809$			34.9239i			1.22786i	0.789361	+	0.613930i	$0.210412\pi$
$809$			34.9239i			1.22786i	−0.789361	+	0.613930i	$0.789588\pi$
$810$	11.1755	+	29.8592i	0.392667	+	1.04914i
$811$			20.4586i			0.718398i	0.933261	+	0.359199i	$0.116950\pi$
$811$			20.4586i			0.718398i	−0.933261	+	0.359199i	$0.883050\pi$
$812$	14.6791	−	26.0132i	0.515134	−	0.912885i
$813$	18.1631	+	18.1631i	0.637009	+	0.637009i
$814$	−4.18376	+	5.50833i	−0.146641	+	0.193067i
$815$	−9.53925	+	15.1114i	−0.334145	+	0.529331i
$816$	1.17011	+	1.93753i	0.0409621	+	0.0678271i
$817$	−24.1469	+	24.1469i	−0.844795	+	0.844795i
$818$	53.1493	−	7.26368i	1.85832	−	0.253969i
$819$	2.20971			0.0772136
$820$	−10.4182	+	5.61003i	−0.363820	+	0.195911i
$821$	−25.5454			−0.891541			−0.445771	−	0.895147i	$-0.647070\pi$
$821$	−25.5454			−0.891541			−0.445771	+	0.895147i	$0.647070\pi$
$822$	−18.1801	+	2.48460i	−0.634105	+	0.0866603i
$823$	−5.51659	+	5.51659i	−0.192296	+	0.192296i	−0.796688	−	0.604391i	$-0.793416\pi$
$823$	−5.51659	+	5.51659i	−0.192296	+	0.192296i	0.604391	+	0.796688i	$0.293416\pi$
$824$	19.7688	+	7.84840i	0.688678	+	0.273412i
$825$	−42.6207	−	15.1138i	−1.48386	−	0.526196i
$826$	20.2717	−	26.6898i	0.705344	−	0.928656i
$827$	−39.1590	−	39.1590i	−1.36169	−	1.36169i	−0.871764	−	0.489926i	$-0.837024\pi$
$827$	−39.1590	−	39.1590i	−1.36169	−	1.36169i	−0.489926	−	0.871764i	$-0.662976\pi$
$828$	3.93400	+	2.21993i	0.136716	+	0.0771479i
$829$			45.5969i			1.58365i	0.610750	+	0.791823i	$0.290868\pi$
$829$			45.5969i			1.58365i	−0.610750	+	0.791823i	$0.709132\pi$
$830$	20.8720	+	9.50331i	0.724477	+	0.329865i
$831$		−	3.33105i		−	0.115553i
$832$	10.3983	−	0.307321i	0.360498	−	0.0106544i
$833$	−2.04024	−	2.04024i	−0.0706900	−	0.0706900i
$834$	−29.7677	−	22.6096i	−1.03077	−	0.782905i
$835$	−31.0578	−	19.6055i	−1.07480	−	0.678478i
$836$	−19.3226	−	69.3726i	−0.668285	−	2.39930i
$837$	−28.4748	+	28.4748i	−0.984233	+	0.984233i
$838$	−6.68034	−	48.8810i	−0.230769	−	1.68856i
$839$	−38.7658			−1.33835			−0.669173	−	0.743107i	$-0.733351\pi$
$839$	−38.7658			−1.33835			−0.669173	+	0.743107i	$0.733351\pi$
$840$	27.9183	+	38.3082i	0.963272	+	1.32176i
$841$	15.4237			0.531852
$842$	−6.88292	−	50.3632i	−0.237201	−	1.73563i
$843$	24.1964	−	24.1964i	0.833367	−	0.833367i
$844$	12.4149	+	44.5724i	0.427339	+	1.53425i
$845$	−5.57554	−	24.6655i	−0.191805	−	0.848520i
$846$	−1.08176	−	0.821632i	−0.0371917	−	0.0282483i
$847$	37.0376	+	37.0376i	1.27263	+	1.27263i
$848$	23.2732	+	5.74722i	0.799206	+	0.197360i
$849$			48.2146i			1.65472i
$850$	−2.11857	−	0.440395i	−0.0726665	−	0.0151054i
$851$			5.38718i			0.184670i
$852$	42.0197	+	23.7114i	1.43957	+	0.812339i
$853$	−12.2711	−	12.2711i	−0.420155	−	0.420155i	0.465102	−	0.885257i	$-0.346018\pi$
$853$	−12.2711	−	12.2711i	−0.420155	−	0.420155i	−0.885257	+	0.465102i	$0.846018\pi$
$854$	0.216140	−	0.284570i	0.00739615	−	0.00973777i
$855$	1.52163	+	6.73149i	0.0520386	+	0.230212i
$856$	18.6469	−	46.9683i	0.637338	−	1.60534i
$857$	−1.85798	+	1.85798i	−0.0634672	+	0.0634672i	−0.738128	−	0.674661i	$-0.764290\pi$
$857$	−1.85798	+	1.85798i	−0.0634672	+	0.0634672i	0.674661	+	0.738128i	$0.264290\pi$
$858$	−16.4790	+	2.25212i	−0.562585	+	0.0768860i
$859$	−0.911505			−0.0311002			−0.0155501	−	0.999879i	$-0.504950\pi$
$859$	−0.911505			−0.0311002			−0.0155501	+	0.999879i	$0.504950\pi$
$860$	−5.96073	+	19.8703i	−0.203259	+	0.677571i
$861$	−19.8305			−0.675821
$862$	6.28597	−	0.859076i	0.214101	−	0.0292602i
$863$	−19.9864	+	19.9864i	−0.680347	+	0.680347i	−0.960078	−	0.279732i	$-0.909755\pi$
$863$	−19.9864	+	19.9864i	−0.680347	+	0.680347i	0.279732	+	0.960078i	$0.409755\pi$
$864$	−2.86359	+	26.8429i	−0.0974215	+	0.913214i
$865$	−32.3773	−	20.4385i	−1.10086	−	0.694929i
$866$	−16.0372	+	21.1146i	−0.544966	+	0.717502i
$867$	22.1055	+	22.1055i	0.750742	+	0.750742i
$868$	−33.6180	+	59.5755i	−1.14107	+	2.02212i
$869$		−	22.9837i		−	0.779669i
$870$	8.92806	−	19.6086i	0.302690	−	0.664794i
$871$		−	13.3310i		−	0.451703i
$872$	41.3013	−	17.8268i	1.39864	−	0.603693i
$873$	−2.96363	−	2.96363i	−0.100304	−	0.100304i
$874$	−44.6635	−	33.9234i	−1.51077	−	1.14748i
$875$	−44.9989	−	5.35602i	−1.52124	−	0.181066i
$876$	−7.84615	+	2.18541i	−0.265097	+	0.0738383i
$877$	5.91287	−	5.91287i	0.199663	−	0.199663i	−0.600192	−	0.799856i	$-0.704909\pi$
$877$	5.91287	−	5.91287i	0.199663	−	0.199663i	0.799856	+	0.600192i	$0.204909\pi$
$878$	2.43980	+	17.8523i	0.0823392	+	0.602487i
$879$	45.5908			1.53774
$880$	−30.3157	−	31.5401i	−1.02194	−	1.06322i
$881$	7.91044			0.266509			0.133255	−	0.991082i	$-0.457457\pi$
$881$	7.91044			0.266509			0.133255	+	0.991082i	$0.457457\pi$
$882$	0.756967	+	5.53883i	0.0254884	+	0.186502i
$883$	14.4972	−	14.4972i	0.487868	−	0.487868i	−0.419765	−	0.907633i	$-0.637887\pi$
$883$	14.4972	−	14.4972i	0.487868	−	0.487868i	0.907633	+	0.419765i	$0.137887\pi$
$884$	−0.766679	+	0.213546i	−0.0257862	+	0.00718232i
$885$	12.9050	−	20.4433i	0.433797	−	0.687192i
$886$	−1.02044	−	0.775057i	−0.0342823	−	0.0260386i
$887$	−27.6203	−	27.6203i	−0.927398	−	0.927398i	0.0701388	−	0.997537i	$-0.477656\pi$
$887$	−27.6203	−	27.6203i	−0.927398	−	0.927398i	−0.997537	+	0.0701388i	$0.977656\pi$
$888$	4.80189	−	2.07264i	0.161141	−	0.0695531i
$889$			51.2850i			1.72004i
$890$	11.7532	−	4.39893i	0.393969	−	0.147453i
$891$		−	49.3119i		−	1.65201i
$892$	−11.6176	+	20.5879i	−0.388986	+	0.689335i
$893$	11.9263	+	11.9263i	0.399100	+	0.399100i
$894$	13.2348	−	17.4250i	0.442639	−	0.582779i
$895$	−27.5449	+	6.22642i	−0.920725	+	0.208126i
$896$	7.54888	+	45.2315i	0.252190	+	1.51108i
$897$	−9.15959	+	9.15959i	−0.305830	+	0.305830i
$898$	2.50864	−	0.342845i	0.0837145	−	0.0114409i
$899$	31.0924			1.03699
$900$	2.75267	+	3.16222i	0.0917558	+	0.105407i
$901$	−1.83398			−0.0610989
$902$	18.1330	−	2.47816i	0.603763	−	0.0825136i
$903$	−24.5840	+	24.5840i	−0.818103	+	0.818103i
$904$	10.8725	−	27.3859i	0.361613	−	0.910840i
$905$	−20.5195	+	4.63835i	−0.682090	+	0.154184i
$906$	19.6568	−	25.8801i	0.653052	−	0.859808i
$907$	−12.6017	−	12.6017i	−0.418431	−	0.418431i	0.466231	−	0.884663i	$-0.345611\pi$
$907$	−12.6017	−	12.6017i	−0.418431	−	0.418431i	−0.884663	+	0.466231i	$0.845611\pi$
$908$	−37.7149	−	21.2822i	−1.25161	−	0.706275i
$909$			3.16979i			0.105135i
$910$	−15.6098	+	5.84234i	−0.517460	+	0.193672i
$911$			2.65754i			0.0880484i	0.999030	+	0.0440242i	$0.0140179\pi$
$911$			2.65754i			0.0880484i	−0.999030	+	0.0440242i	$0.985982\pi$
$912$	−13.0542	+	52.8625i	−0.432267	+	1.75045i
$913$	−25.0821	−	25.0821i	−0.830097	−	0.830097i
$914$	39.4908	+	29.9945i	1.30624	+	0.992131i
$915$	0.137595	−	0.217968i	0.00454874	−	0.00720581i
$916$	3.13121	+	11.2418i	0.103458	+	0.371439i
$917$	55.7669	−	55.7669i	1.84159	−	1.84159i
$918$	−0.279648	−	2.04622i	−0.00922977	−	0.0675354i
$919$	36.3493			1.19905			0.599526	−	0.800356i	$-0.295356\pi$
$919$	36.3493			1.19905			0.599526	+	0.800356i	$0.295356\pi$
$920$	−33.6598	−	5.28070i	−1.10973	−	0.174100i
$921$	17.2644			0.568882
$922$	3.61039	+	26.4177i	0.118902	+	0.870021i
$923$	−11.9959	+	11.9959i	−0.394851	+	0.394851i
$924$	−19.6723	−	70.6281i	−0.647170	−	2.32349i
$925$	−1.67110	+	4.71247i	−0.0549455	+	0.154945i
$926$	31.7032	+	24.0796i	1.04183	+	0.791306i
$927$	2.22932	+	2.22932i	0.0732206	+	0.0732206i
$928$	16.2187	−	13.0918i	0.532404	−	0.429761i
$929$			2.72649i			0.0894533i	0.998999	+	0.0447266i	$0.0142417\pi$
$929$			2.72649i			0.0894533i	−0.998999	+	0.0447266i	$0.985758\pi$
$930$	−20.4471	+	44.9076i	−0.670485	+	1.47258i
$931$		−	69.4108i		−	2.27485i
$932$	−13.7325	−	7.74914i	−0.449822	−	0.253831i
$933$	−17.7986	−	17.7986i	−0.582701	−	0.582701i
$934$	−15.1026	+	19.8840i	−0.494172	+	0.650626i
$935$	2.83013	+	1.78655i	0.0925551	+	0.0584263i
$936$	1.43317	+	0.568982i	0.0468446	+	0.0185978i
$937$	−18.5367	+	18.5367i	−0.605568	+	0.605568i	−0.941785	−	0.336217i	$-0.890853\pi$
$937$	−18.5367	+	18.5367i	−0.605568	+	0.605568i	0.336217	+	0.941785i	$0.390853\pi$
$938$	58.2231	−	7.95710i	1.90105	−	0.259808i
$939$	33.1393			1.08146
$940$	9.81408	+	2.94405i	0.320100	+	0.0960242i
$941$	2.09390			0.0682591			0.0341296	−	0.999417i	$-0.489134\pi$
$941$	2.09390			0.0682591			0.0341296	+	0.999417i	$0.489134\pi$
$942$	18.9165	−	2.58524i	0.616334	−	0.0842316i
$943$	10.0789	−	10.0789i	0.328215	−	0.328215i
$944$	20.0202	−	12.0906i	0.651601	−	0.393514i
$945$	−9.53616	−	42.1868i	−0.310211	−	1.37234i
$946$	19.4074	−	25.5518i	0.630989	−	0.830759i
$947$	−17.4442	−	17.4442i	−0.566859	−	0.566859i	0.364388	−	0.931247i	$-0.381278\pi$
$947$	−17.4442	−	17.4442i	−0.566859	−	0.566859i	−0.931247	+	0.364388i	$0.881278\pi$
$948$	−8.54055	+	15.1350i	−0.277384	+	0.491561i
$949$		−	2.86385i		−	0.0929644i
$950$	−28.5467	−	43.5293i	−0.926176	−	1.41228i
$951$		−	33.7798i		−	1.09539i
$952$	−1.39029	−	3.22102i	−0.0450594	−	0.104394i
$953$	−3.55331	−	3.55331i	−0.115103	−	0.115103i	0.647209	−	0.762312i	$-0.275936\pi$
$953$	−3.55331	−	3.55331i	−0.115103	−	0.115103i	−0.762312	+	0.647209i	$0.775936\pi$
$954$	2.82967	+	2.14923i	0.0916140	+	0.0695838i
$955$	1.73968	+	7.69612i	0.0562947	+	0.249041i
$956$	−37.6342	+	10.4824i	−1.21718	+	0.339025i
$957$	−23.5639	+	23.5639i	−0.761712	+	0.761712i
$958$	0.344910	+	2.52375i	0.0111435	+	0.0815387i
$959$	28.4405			0.918390
$960$	8.24312	+	32.0345i	0.266046	+	1.03391i
$961$	−40.2079			−1.29703
$962$	0.249011	+	1.82205i	0.00802845	+	0.0587453i
$963$	5.29662	−	5.29662i	0.170681	−	0.170681i
$964$	56.5981	−	15.7644i	1.82290	−	0.507739i
$965$	25.6943	+	16.2198i	0.827130	+	0.522134i
$966$	−45.4718	−	34.5373i	−1.46303	−	1.11122i
$967$	35.7408	+	35.7408i	1.14935	+	1.14935i	0.986681	+	0.162666i	$0.0520092\pi$
$967$	35.7408	+	35.7408i	1.14935	+	1.14935i	0.162666	+	0.986681i	$0.447991\pi$
$968$	14.4849	+	33.5586i	0.465561	+	1.07861i
$969$		−	4.16569i		−	0.133821i
$970$	28.7713	+	13.1000i	0.923790	+	0.420614i
$971$			21.3031i			0.683651i	0.939764	+	0.341825i	$0.111045\pi$
$971$			21.3031i			0.683651i	−0.939764	+	0.341825i	$0.888955\pi$
$972$	−4.25241	+	7.53583i	−0.136396	+	0.241712i
$973$	40.9687	+	40.9687i	1.31340	+	1.31340i
$974$	6.14961	−	8.09657i	0.197046	−	0.259431i
$975$	−10.8537	+	5.17111i	−0.347597	+	0.165608i
$976$	0.213457	−	0.128911i	0.00683261	−	0.00412634i
$977$	−14.6023	+	14.6023i	−0.467169	+	0.467169i	−0.900996	−	0.433827i	$-0.857163\pi$
$977$	−14.6023	+	14.6023i	−0.467169	+	0.467169i	0.433827	+	0.900996i	$0.357163\pi$
$978$	−20.7068	+	2.82990i	−0.662129	+	0.0904903i
$979$	−19.4103			−0.620355
$980$	−19.9917	−	37.1259i	−0.638610	−	1.18594i
$981$	6.66787			0.212889
$982$	−47.9780	+	6.55693i	−1.53104	+	0.209240i
$983$	−19.9634	+	19.9634i	−0.636734	+	0.636734i	−0.949748	−	0.313014i	$-0.898661\pi$
$983$	−19.9634	+	19.9634i	−0.636734	+	0.636734i	0.313014	+	0.949748i	$0.398661\pi$
$984$	−12.8616	−	5.10618i	−0.410013	−	0.162779i
$985$	8.74620	−	13.8551i	0.278677	−	0.441462i
$986$	−0.964487	+	1.26984i	−0.0307155	+	0.0404400i
$987$	12.1422	+	12.1422i	0.386490	+	0.386490i
$988$	−16.6741	−	9.40908i	−0.530474	−	0.299343i
$989$		−	24.9898i		−	0.794628i
$990$	−2.27300	−	6.07308i	−0.0722406	−	0.193015i
$991$			31.1421i			0.989262i	0.869103	+	0.494631i	$0.164697\pi$
$991$			31.1421i			0.989262i	−0.869103	+	0.494631i	$0.835303\pi$
$992$	−37.1440	+	29.9829i	−1.17932	+	0.951959i
$993$	−15.0351	−	15.0351i	−0.477125	−	0.477125i
$994$	−59.5527	−	45.2322i	−1.88890	−	1.43468i
$995$	−5.06315	+	1.14451i	−0.160513	+	0.0362833i
$996$	7.19649	+	25.8371i	0.228030	+	0.818680i
$997$	−25.2726	+	25.2726i	−0.800392	+	0.800392i	−0.983157	−	0.182765i	$-0.941495\pi$
$997$	−25.2726	+	25.2726i	−0.800392	+	0.800392i	0.182765	+	0.983157i	$0.441495\pi$
$998$	6.33238	+	46.3348i	0.200448	+	1.46670i
$999$	−4.77212			−0.150983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.n.a.223.61	yes	216
4.3	odd	2	inner	740.2.n.a.223.6	✓	216
5.2	odd	4	inner	740.2.n.a.667.6	yes	216
20.7	even	4	inner	740.2.n.a.667.61	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.n.a.223.6	✓	216	4.3	odd	2	inner
740.2.n.a.223.61	yes	216	1.1	even	1	trivial
740.2.n.a.667.6	yes	216	5.2	odd	4	inner
740.2.n.a.667.61	yes	216	20.7	even	4	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.191494 + 1.40119i) q^{2} +(1.30753 - 1.30753i) q^{3} +(-1.92666 + 0.536639i) q^{4} +(2.18104 - 0.493016i) q^{5} +(2.08247 + 1.58171i) q^{6} +(-2.86607 - 2.86607i) q^{7} +(-1.12088 - 2.59685i) q^{8} -0.419248i q^{9} +(1.10846 + 2.96164i) q^{10} -4.89109i q^{11} +(-1.81749 + 3.22083i) q^{12} +(-0.919494 - 0.919494i) q^{13} +(3.46706 - 4.56473i) q^{14} +(2.20714 - 3.49640i) q^{15} +(3.42404 - 2.06784i) q^{16} +(-0.216386 + 0.216386i) q^{17} +(0.587445 - 0.0802835i) q^{18} -7.36168 q^{19} +(-3.93755 + 2.12030i) q^{20} -7.49491 q^{21} +(6.85335 - 0.936616i) q^{22} +(3.80931 - 3.80931i) q^{23} +(-4.86103 - 1.92987i) q^{24} +(4.51387 - 2.15057i) q^{25} +(1.11231 - 1.46446i) q^{26} +(3.37440 + 3.37440i) q^{27} +(7.05998 + 3.98389i) q^{28} -3.68460i q^{29} +(5.32177 + 2.42307i) q^{30} +8.43848i q^{31} +(3.55312 + 4.40174i) q^{32} +(-6.39523 - 6.39523i) q^{33} +(-0.344635 - 0.261761i) q^{34} +(-7.66402 - 4.83799i) q^{35} +(0.224985 + 0.807748i) q^{36} +(-0.707107 + 0.707107i) q^{37} +(-1.40972 - 10.3151i) q^{38} -2.40452 q^{39} +(-3.72497 - 5.11123i) q^{40} +2.64586 q^{41} +(-1.43523 - 10.5018i) q^{42} +(3.28009 - 3.28009i) q^{43} +(2.62475 + 9.42347i) q^{44} +(-0.206696 - 0.914396i) q^{45} +(6.06703 + 4.60811i) q^{46} +(-1.62006 - 1.62006i) q^{47} +(1.77326 - 7.18077i) q^{48} +9.42867i q^{49} +(3.87774 + 5.91296i) q^{50} +0.565861i q^{51} +(2.26499 + 1.27812i) q^{52} +(4.23775 + 4.23775i) q^{53} +(-4.08199 + 5.37435i) q^{54} +(-2.41139 - 10.6677i) q^{55} +(-4.23024 + 10.6553i) q^{56} +(-9.62558 + 9.62558i) q^{57} +(5.16282 - 0.705580i) q^{58} +5.84695 q^{59} +(-2.37610 + 7.92080i) q^{60} +0.0623409 q^{61} +(-11.8239 + 1.61592i) q^{62} +(-1.20159 + 1.20159i) q^{63} +(-5.48727 + 5.82150i) q^{64} +(-2.45878 - 1.55213i) q^{65} +(7.73628 - 10.1856i) q^{66} +(7.24908 + 7.24908i) q^{67} +(0.300782 - 0.533024i) q^{68} -9.96155i q^{69} +(5.31132 - 11.6652i) q^{70} -13.0462i q^{71} +(-1.08872 + 0.469925i) q^{72} +(1.55730 + 1.55730i) q^{73} +(-1.12620 - 0.855383i) q^{74} +(3.09007 - 8.71393i) q^{75} +(14.1834 - 3.95056i) q^{76} +(-14.0182 + 14.0182i) q^{77} +(-0.460452 - 3.36919i) q^{78} +4.69910 q^{79} +(6.44848 - 6.19815i) q^{80} +10.0820 q^{81} +(0.506667 + 3.70735i) q^{82} +(5.12812 - 5.12812i) q^{83} +(14.4401 - 4.02206i) q^{84} +(-0.365265 + 0.578629i) q^{85} +(5.22414 + 3.96790i) q^{86} +(-4.81771 - 4.81771i) q^{87} +(-12.7014 + 5.48231i) q^{88} -3.96849i q^{89} +(1.24166 - 0.464721i) q^{90} +5.27066i q^{91} +(-5.29503 + 9.38348i) q^{92} +(11.0335 + 11.0335i) q^{93} +(1.95978 - 2.58024i) q^{94} +(-16.0561 + 3.62942i) q^{95} +(10.4012 + 1.10960i) q^{96} +(7.06893 - 7.06893i) q^{97} +(-13.2113 + 1.80554i) q^{98} -2.05058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{6} - 12 q^{8} - 16 q^{10} - 16 q^{12} + 8 q^{16} + 20 q^{20} - 16 q^{21} + 4 q^{22} + 16 q^{26} - 4 q^{28} - 24 q^{30} - 20 q^{32} + 16 q^{33} + 32 q^{36} - 12 q^{38} - 36 q^{40} - 40 q^{42}+ \cdots - 64 q^{98}+O(q^{100}) \) 216 * q - 8 * q^6 - 12 * q^8 - 16 * q^10 - 16 * q^12 + 8 * q^16 + 20 * q^20 - 16 * q^21 + 4 * q^22 + 16 * q^26 - 4 * q^28 - 24 * q^30 - 20 * q^32 + 16 * q^33 + 32 * q^36 - 12 * q^38 - 36 * q^40 - 40 * q^42 + 40 * q^46 - 36 * q^48 + 24 * q^50 - 20 * q^52 - 16 * q^56 - 32 * q^57 - 16 * q^58 + 20 * q^60 - 64 * q^61 + 4 * q^62 - 32 * q^65 + 52 * q^68 - 24 * q^70 + 40 * q^72 - 16 * q^73 - 24 * q^76 + 48 * q^77 + 24 * q^78 - 56 * q^80 - 136 * q^81 - 4 * q^82 + 48 * q^85 - 88 * q^86 - 64 * q^88 + 120 * q^90 + 56 * q^92 + 16 * q^96 - 80 * q^97 - 64 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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