LMFDB - Embedded newform 740.2.n.a.223.6

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			223.6
Character	$\chi$	$=$	740.223
Dual form			740.2.n.a.667.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40119 - 0.191494i) 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} +(-2.59685 - 1.12088i) q^{8} -0.419248i q^{9} +(-3.15046 + 0.273152i) q^{10} +4.89109i q^{11} +(-3.22083 + 1.81749i) 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} +(-0.0802835 + 0.587445i) q^{18} +7.36168 q^{19} +(4.46669 + 0.220558i) q^{20} -7.49491 q^{21} +(0.936616 - 6.85335i) 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} +(3.98389 + 7.05998i) q^{28} -3.68460i q^{29} +(3.76215 - 4.47646i) q^{30} -8.43848i q^{31} +(-4.40174 - 3.55312i) 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} +(-10.3151 - 1.40972i) q^{38} +2.40452 q^{39} +(-6.21645 - 1.16439i) q^{40} +2.64586 q^{41} +(10.5018 + 1.43523i) 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} +(-7.18077 + 1.77326i) q^{48} +9.42867i q^{49} +(-6.73661 + 2.14898i) q^{50} -0.565861i q^{51} +(-1.27812 - 2.26499i) 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} +(-0.705580 + 5.16282i) q^{58} -5.84695 q^{59} +(-6.12870 + 5.55193i) q^{60} +0.0623409 q^{61} +(-1.61592 + 11.8239i) 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} +(-0.533024 + 0.300782i) q^{68} -9.96155i q^{69} +(-9.81229 - 8.24655i) q^{70} +13.0462i q^{71} +(-0.469925 + 1.08872i) 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} +(-3.36919 - 0.460452i) q^{78} -4.69910 q^{79} +(8.48744 + 2.82194i) q^{80} +10.0820 q^{81} +(-3.70735 - 0.506667i) 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} +(5.48231 - 12.7014i) q^{88} -3.96849i q^{89} +(0.114518 + 1.32082i) q^{90} -5.27066i q^{91} +(-9.38348 + 5.29503i) 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} +(1.80554 - 13.2113i) 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 $

$2$	−1.40119	−	0.191494i	−0.990790	−	0.135407i
$2$	−1.40119	−	0.191494i	−0.990790	−	0.135407i
$3$	−1.30753	+	1.30753i	−0.754900	+	0.754900i	−0.975389	−	0.220489i	$-0.929235\pi$
$3$	−1.30753	+	1.30753i	−0.754900	+	0.754900i	0.220489	+	0.975389i	$0.429235\pi$
$4$	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	$0.0277500\pi$
$7$	2.86607	+	2.86607i	1.08327	+	1.08327i	0.0870688	+	0.996202i	$0.472250\pi$
$8$	−2.59685	−	1.12088i	−0.918126	−	0.396290i
$9$		−	0.419248i		−	0.139749i
$10$	−3.15046	+	0.273152i	−0.996262	+	0.0863781i
$11$			4.89109i			1.47472i	0.675500	+	0.737360i	$0.263928\pi$
$11$			4.89109i			1.47472i	−0.675500	+	0.737360i	$0.736072\pi$
$12$	−3.22083	+	1.81749i	−0.929773	+	0.524664i
$13$	−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	$0.261815\pi$
$18$	−0.0802835	+	0.587445i	−0.0189230	+	0.138462i
$19$	7.36168			1.68888			0.844442	−	0.535646i	$-0.179932\pi$
$19$	7.36168			1.68888			0.844442	+	0.535646i	$0.179932\pi$
$20$	4.46669	+	0.220558i	0.998783	+	0.0493182i
$21$	−7.49491			−1.63552
$22$	0.936616	−	6.85335i	0.199687	−	1.46114i
$23$	−3.80931	+	3.80931i	−0.794297	+	0.794297i	−0.982190	−	0.187893i	$-0.939834\pi$
$23$	−3.80931	+	3.80931i	−0.794297	+	0.794297i	0.187893	+	0.982190i	$0.439834\pi$
$24$	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
$28$	3.98389	+	7.05998i	0.752885	+	1.33421i
$29$		−	3.68460i		−	0.684214i	−0.939661	−	0.342107i	$-0.888860\pi$
$29$		−	3.68460i		−	0.684214i	0.939661	−	0.342107i	$-0.111140\pi$
$30$	3.76215	−	4.47646i	0.686872	−	0.817286i
$31$		−	8.43848i		−	1.51560i	−0.652490	−	0.757798i	$-0.726275\pi$
$31$		−	8.43848i		−	1.51560i	0.652490	−	0.757798i	$-0.273725\pi$
$32$	−4.40174	−	3.55312i	−0.778126	−	0.628109i
$33$	−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
$38$	−10.3151	−	1.40972i	−1.67333	−	0.228687i
$39$	2.40452			0.385032
$40$	−6.21645	−	1.16439i	−0.982906	−	0.184106i
$41$	2.64586			0.413214			0.206607	−	0.978424i	$-0.433758\pi$
$41$	2.64586			0.413214			0.206607	+	0.978424i	$0.433758\pi$
$42$	10.5018	+	1.43523i	1.62046	+	0.221461i
$43$	−3.28009	+	3.28009i	−0.500209	+	0.500209i	−0.911503	−	0.411294i	$-0.865077\pi$
$43$	−3.28009	+	3.28009i	−0.500209	+	0.500209i	0.411294	+	0.911503i	$0.365077\pi$
$44$	−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	0.815320	−	0.579010i	$-0.196561\pi$
$47$	1.62006	+	1.62006i	0.236310	+	0.236310i	−0.579010	+	0.815320i	$0.696561\pi$
$48$	−7.18077	+	1.77326i	−1.03646	+	0.255948i
$49$			9.42867i			1.34695i
$50$	−6.73661	+	2.14898i	−0.952700	+	0.303912i
$51$		−	0.565861i		−	0.0792365i
$52$	−1.27812	−	2.26499i	−0.177243	−	0.314097i
$53$	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
$58$	−0.705580	+	5.16282i	−0.0926472	+	0.677912i
$59$	−5.84695			−0.761208			−0.380604	−	0.924738i	$-0.624284\pi$
$59$	−5.84695			−0.761208			−0.380604	+	0.924738i	$0.624284\pi$
$60$	−6.12870	+	5.55193i	−0.791212	+	0.716751i
$61$	0.0623409			0.00798193			0.00399097	−	0.999992i	$-0.498730\pi$
$61$	0.0623409			0.00798193			0.00399097	+	0.999992i	$0.498730\pi$
$62$	−1.61592	+	11.8239i	−0.205222	+	1.50164i
$63$	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	0.108482	−	0.994098i	$-0.465401\pi$
$67$	−7.24908	−	7.24908i	−0.885616	−	0.885616i	−0.994098	+	0.108482i	$0.965401\pi$
$68$	−0.533024	+	0.300782i	−0.0646387	+	0.0364751i
$69$		−	9.96155i		−	1.19923i
$70$	−9.81229	−	8.24655i	−1.17279	−	0.985651i
$71$			13.0462i			1.54830i	0.632999	+	0.774152i	$0.281824\pi$
$71$			13.0462i			1.54830i	−0.632999	+	0.774152i	$0.718176\pi$
$72$	−0.469925	+	1.08872i	−0.0553812	+	0.128307i
$73$	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
$78$	−3.36919	−	0.460452i	−0.381486	−	0.0521360i
$79$	−4.69910			−0.528690			−0.264345	−	0.964428i	$-0.585156\pi$
$79$	−4.69910			−0.528690			−0.264345	+	0.964428i	$0.585156\pi$
$80$	8.48744	+	2.82194i	0.948925	+	0.315503i
$81$	10.0820			1.12022
$82$	−3.70735	−	0.506667i	−0.409408	−	0.0559520i
$83$	−5.12812	+	5.12812i	−0.562885	+	0.562885i	−0.930126	−	0.367241i	$-0.880302\pi$
$83$	−5.12812	+	5.12812i	−0.562885	+	0.562885i	0.367241	+	0.930126i	$0.380302\pi$
$84$	−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
$88$	5.48231	−	12.7014i	0.584417	−	1.35398i
$89$		−	3.96849i		−	0.420659i	−0.977631	−	0.210330i	$-0.932546\pi$
$89$		−	3.96849i		−	0.420659i	0.977631	−	0.210330i	$-0.0674537\pi$
$90$	0.114518	+	1.32082i	0.0120713	+	0.139227i
$91$		−	5.27066i		−	0.552515i
$92$	−9.38348	+	5.29503i	−0.978295	+	0.552045i
$93$	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	$0.0805625\pi$
$98$	1.80554	−	13.2113i	0.182387	−	1.33455i
$99$	2.05058			0.206091
$100$	9.85078	−	1.72111i	0.985078	−	0.172111i
$101$	−7.56065			−0.752312			−0.376156	−	0.926556i	$-0.622754\pi$
$101$	−7.56065			−0.752312			−0.376156	+	0.926556i	$0.622754\pi$
$102$	−0.108359	+	0.792879i	−0.0107292	+	0.0785067i
$103$	5.31743	−	5.31743i	0.523942	−	0.523942i	−0.394817	−	0.918760i	$-0.629192\pi$
$103$	5.31743	−	5.31743i	0.523942	−	0.523942i	0.918760	+	0.394817i	$0.129192\pi$
$104$	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	$-0.918194\pi$
$107$	−12.6336	−	12.6336i	−1.22134	−	1.22134i	−0.254181	−	0.967157i	$-0.581806\pi$
$108$	−4.69049	−	8.31216i	−0.451342	−	0.799838i
$109$			15.9044i			1.52336i	0.647952	+	0.761681i	$0.275626\pi$
$109$			15.9044i			1.52336i	−0.647952	+	0.761681i	$0.724374\pi$
$110$	−1.33601	−	15.4092i	−0.127384	−	1.46921i
$111$		−	1.84912i		−	0.175511i
$112$	3.88695	+	15.7401i	0.367282	+	1.48730i
$113$	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
$118$	8.19268	+	1.11966i	0.754197	+	0.103073i
$119$	−1.24036			−0.113703
$120$	9.65063	−	6.60570i	0.880978	−	0.603015i
$121$	−12.9228			−1.17480
$122$	−0.0873513	−	0.0119379i	−0.00790842	−	0.00108081i
$123$	−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	0.982128	−	0.188216i	$-0.0602704\pi$
$127$	8.94693	+	8.94693i	0.793912	+	0.793912i	−0.188216	+	0.982128i	$0.560270\pi$
$128$	−6.57392	−	9.20780i	−0.581058	−	0.813862i
$129$		−	8.57760i		−	0.755215i
$130$	3.14799	+	2.64567i	0.276097	+	0.232040i
$131$		−	19.4576i		−	1.70002i	−0.526764	−	0.850011i	$-0.676595\pi$
$131$		−	19.4576i		−	1.70002i	0.526764	−	0.850011i	$-0.323405\pi$
$132$	−8.88951	−	15.7534i	−0.773732	−	1.37115i
$133$	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	$0.346900\pi$
$138$	−1.90758	+	13.9580i	−0.162384	+	1.18819i
$139$	14.2944			1.21244			0.606218	−	0.795299i	$-0.292686\pi$
$139$	14.2944			1.21244			0.606218	+	0.795299i	$0.292686\pi$
$140$	12.1697	+	13.4340i	1.02853	+	1.13538i
$141$	−4.23654			−0.356781
$142$	2.49828	−	18.2803i	0.209651	−	1.53405i
$143$	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
$148$	−1.74182	+	0.982893i	−0.143176	+	0.0807933i
$149$		−	8.36744i		−	0.685488i	−0.939429	−	0.342744i	$-0.888644\pi$
$149$		−	8.36744i		−	0.685488i	0.939429	−	0.342744i	$-0.111356\pi$
$150$	5.99844	−	11.6181i	0.489771	−	0.948617i
$151$			12.4276i			1.01134i	0.862727	+	0.505670i	$0.168755\pi$
$151$			12.4276i			1.01134i	−0.862727	+	0.505670i	$0.831245\pi$
$152$	−19.1172	−	8.25153i	−1.55061	−	0.669288i
$153$	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	$0.155899\pi$
$158$	6.58432	+	0.899850i	0.523820	+	0.0715882i
$159$	−11.0819			−0.878856
$160$	−11.3521	−	5.57937i	−0.897464	−	0.441088i
$161$	−21.8355			−1.72088
$162$	−14.1268	−	1.93064i	−1.10990	−	0.151685i
$163$	5.65113	−	5.65113i	0.442631	−	0.442631i	−0.450264	−	0.892895i	$-0.648670\pi$
$163$	5.65113	−	5.65113i	0.442631	−	0.442631i	0.892895	+	0.450264i	$0.148670\pi$
$164$	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	0.995326	−	0.0965697i	$-0.0307871\pi$
$167$	11.6145	+	11.6145i	0.898757	+	0.898757i	−0.0965697	+	0.995326i	$0.530787\pi$
$168$	19.4632	+	8.40087i	1.50162	+	0.648141i
$169$		−	11.3091i		−	0.869928i
$170$	0.622610	−	0.740822i	0.0477520	−	0.0568185i
$171$		−	3.08637i		−	0.236020i
$172$	−8.07984	+	4.55939i	−0.616082	+	0.347650i
$173$	−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
$178$	−0.759943	+	5.56061i	−0.0569601	+	0.416785i
$179$	12.6293			0.943955			0.471978	−	0.881611i	$-0.343540\pi$
$179$	12.6293			0.943955			0.471978	+	0.881611i	$0.343540\pi$
$180$	0.0924683	−	1.87265i	0.00689218	−	0.139579i
$181$	−9.40811			−0.699299			−0.349650	−	0.936881i	$-0.613699\pi$
$181$	−9.40811			−0.699299			−0.349650	+	0.936881i	$0.613699\pi$
$182$	−1.00930	+	7.38519i	−0.0748143	+	0.547427i
$183$	−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
$188$	2.25192	+	3.99069i	0.164238	+	0.291051i
$189$		−	19.3425i		−	1.40696i
$190$	−23.1927	+	2.01085i	−1.68257	+	0.145883i
$191$		−	3.52865i		−	0.255324i	−0.991818	−	0.127662i	$-0.959253\pi$
$191$		−	3.52865i		−	0.255324i	0.991818	−	0.127662i	$-0.0407473\pi$
$192$	−14.7865	−	0.437012i	−1.06712	−	0.0315387i
$193$	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	$0.165937\pi$
$198$	−2.87325	−	0.392674i	−0.204193	−	0.0279061i
$199$	2.32144			0.164562			0.0822812	−	0.996609i	$-0.473779\pi$
$199$	2.32144			0.164562			0.0822812	+	0.996609i	$0.473779\pi$
$200$	−14.1324	+	0.525227i	−0.999310	+	0.0371392i
$201$	18.9567			1.33710
$202$	10.5939	+	1.44782i	0.745384	+	0.101868i
$203$	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
$208$	−1.24701	−	5.04975i	−0.0864648	−	0.350137i
$209$			36.0067i			2.49063i
$210$	23.6124	−	2.04725i	1.62941	−	0.141273i
$211$			23.1345i			1.59265i	0.604870	+	0.796324i	$0.293225\pi$
$211$			23.1345i			1.59265i	−0.604870	+	0.796324i	$0.706775\pi$
$212$	5.89057	+	10.4389i	0.404566	+	0.716944i
$213$	−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
$218$	3.04559	−	22.2850i	0.206274	−	1.50933i
$219$	−4.07241			−0.275188
$220$	−1.07877	+	21.8470i	−0.0727305	+	1.47293i
$221$	0.397932			0.0267678
$222$	−0.354096	+	2.59097i	−0.0237654	+	0.173894i
$223$	−8.35787	+	8.35787i	−0.559684	+	0.559684i	−0.929217	−	0.369533i	$-0.879518\pi$
$223$	−8.35787	+	8.35787i	−0.559684	+	0.559684i	0.369533	+	0.929217i	$0.379518\pi$
$224$	−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	$-0.994798\pi$
$227$	−15.3107	−	15.3107i	−1.01621	−	1.01621i	−0.0163415	−	0.999866i	$-0.505202\pi$
$228$	−23.7107	+	13.3798i	−1.57028	+	0.886097i
$229$		−	5.83486i		−	0.385578i	−0.981240	−	0.192789i	$-0.938247\pi$
$229$		−	5.83486i		−	0.385578i	0.981240	−	0.192789i	$-0.0617533\pi$
$230$	10.9606	−	13.0416i	0.722718	−	0.859938i
$231$		−	36.6583i		−	2.41194i
$232$	−4.12999	+	9.56836i	−0.271147	+	0.628194i
$233$	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
$238$	1.73797	+	0.237521i	0.112656	+	0.0153962i
$239$	−19.5334			−1.26351			−0.631756	−	0.775168i	$-0.717665\pi$
$239$	−19.5334			−1.26351			−0.631756	+	0.775168i	$0.717665\pi$
$240$	−14.7873	+	7.40779i	−0.954517	+	0.478171i
$241$	−29.3763			−1.89229			−0.946145	−	0.323742i	$-0.895059\pi$
$241$	−29.3763			−1.89229			−0.946145	+	0.323742i	$0.895059\pi$
$242$	18.1073	+	2.47464i	1.16398	+	0.159076i
$243$	−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
$248$	−9.45849	+	21.9135i	−0.600615	+	1.39151i
$249$		−	13.4103i		−	0.849844i
$250$	−13.6333	+	8.00826i	−0.862248	+	0.506487i
$251$		−	11.6625i		−	0.736129i	−0.929800	−	0.368065i	$-0.880020\pi$
$251$		−	11.6625i		−	0.736129i	0.929800	−	0.368065i	$-0.119980\pi$
$252$	2.95988	−	1.67024i	0.186455	−	0.105215i
$253$	−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	$0.204319\pi$
$258$	−1.64256	+	12.0188i	−0.102261	+	0.748260i
$259$	−4.05323			−0.251855
$260$	−3.90430	−	4.30990i	−0.242134	−	0.267289i
$261$	−1.54476			−0.0956184
$262$	−3.72603	+	27.2638i	−0.230195	+	1.68437i
$263$	18.9610	−	18.9610i	1.16918	−	1.16918i	0.186781	−	0.982402i	$-0.440194\pi$
$263$	18.9610	−	18.9610i	1.16918	−	1.16918i	0.982402	−	0.186781i	$-0.0598056\pi$
$264$	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
$268$	−10.0764	−	17.8566i	−0.615512	−	1.09077i
$269$		−	12.3832i		−	0.755017i	−0.926006	−	0.377509i	$-0.876781\pi$
$269$		−	12.3832i		−	0.755017i	0.926006	−	0.377509i	$-0.123219\pi$
$270$	11.5526	+	9.70918i	0.703071	+	0.590882i
$271$		−	13.8912i		−	0.843832i	−0.906635	−	0.421916i	$-0.861358\pi$
$271$		−	13.8912i		−	0.843832i	0.906635	−	0.421916i	$-0.138642\pi$
$272$	−1.18837	+	0.293462i	−0.0720554	+	0.0177938i
$273$	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	$0.232765\pi$
$278$	−20.0292	−	2.73729i	−1.20127	−	0.164172i
$279$	−3.53781			−0.211803
$280$	−14.4795	−	21.1540i	−0.865317	−	1.26419i
$281$	18.5054			1.10394			0.551971	−	0.833863i	$-0.313876\pi$
$281$	18.5054			1.10394			0.551971	+	0.833863i	$0.313876\pi$
$282$	5.93619	+	0.811272i	0.353495	+	0.0483106i
$283$	18.4373	−	18.4373i	1.09599	−	1.09599i	0.101112	−	0.994875i	$-0.467760\pi$
$283$	18.4373	−	18.4373i	1.09599	−	1.09599i	0.994875	−	0.101112i	$-0.0322399\pi$
$284$	−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
$288$	−1.48964	+	1.84542i	−0.0877778	+	0.108743i
$289$			16.9064i			0.994491i
$290$	1.00645	+	11.6082i	0.0591011	+	0.681656i
$291$			18.4856i			1.08365i
$292$	2.16467	+	3.83608i	0.126678	+	0.224490i
$293$	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
$298$	−1.60232	+	11.7244i	−0.0928197	+	0.679174i
$299$	7.00528			0.405126
$300$	−10.6298	+	15.1305i	−0.613709	+	0.873562i
$301$	−18.8019			−1.08372
$302$	2.37981	−	17.4134i	0.136942	−	1.00203i
$303$	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	0.493151	−	0.869944i	$-0.335845\pi$
$307$	−6.60194	−	6.60194i	−0.376792	−	0.376792i	−0.869944	+	0.493151i	$0.835845\pi$
$308$	−34.5310	+	19.4856i	−1.96759	+	1.11029i
$309$			13.9054i			0.791049i
$310$	2.30498	+	26.5851i	0.130914	+	1.50993i
$311$			13.6125i			0.771891i	0.922521	+	0.385946i	$0.126125\pi$
$311$			13.6125i			0.771891i	−0.922521	+	0.385946i	$0.873875\pi$
$312$	−6.24419	−	2.69517i	−0.353508	−	0.152584i
$313$	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	$0.0785274\pi$
$318$	15.5279	+	2.12213i	0.870761	+	0.119003i
$319$	18.0217			1.00902
$320$	14.8380	+	9.99161i	0.829472	+	0.558548i
$321$	33.0376			1.84398
$322$	30.5956	+	4.18137i	1.70503	+	0.233019i
$323$	−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
$328$	−6.87091	−	2.96568i	−0.379382	−	0.163752i
$329$			9.28639i			0.511975i
$330$	21.8948	+	18.4010i	1.20527	+	1.01294i
$331$			11.4989i			0.632037i	0.948753	+	0.316019i	$0.102346\pi$
$331$			11.4989i			0.632037i	−0.948753	+	0.316019i	$0.897654\pi$
$332$	−12.6321	+	7.12820i	−0.693277	+	0.391211i
$333$	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	$0.0115490\pi$
$338$	−2.16562	+	15.8461i	−0.117794	+	0.861916i
$339$	−19.2632			−1.04624
$340$	−1.01426	+	0.918806i	−0.0550058	+	0.0498292i
$341$	41.2734			2.23508
$342$	−0.591021	+	4.32458i	−0.0319588	+	0.233847i
$343$	−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	$-0.807680\pi$
$347$	−25.9125	−	25.9125i	−1.39106	−	1.39106i	−0.568097	−	0.822962i	$-0.692320\pi$
$348$	6.69672	+	11.8675i	0.358982	+	0.636163i
$349$		−	0.108295i		−	0.00579688i	−0.999996	−	0.00289844i	$-0.999077\pi$
$349$		−	0.108295i		−	0.00579688i	0.999996	−	0.00289844i	$-0.000922604\pi$
$350$	−25.4667	−	13.1484i	−1.36125	−	0.702814i
$351$			6.20548i			0.331224i
$352$	17.3786	−	21.5293i	0.926285	−	1.14752i
$353$	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
$358$	−17.6960	−	2.41843i	−0.935261	−	0.127818i
$359$	8.75756			0.462206			0.231103	−	0.972929i	$-0.425767\pi$
$359$	8.75756			0.462206			0.231103	+	0.972929i	$0.425767\pi$
$360$	−0.488167	+	2.60623i	−0.0257287	+	0.137360i
$361$	35.1943			1.85233
$362$	13.1825	+	1.80160i	0.692859	+	0.0946899i
$363$	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	0.328352	−	0.944556i	$-0.393507\pi$
$367$	−11.8048	−	11.8048i	−0.616204	−	0.616204i	−0.944556	+	0.328352i	$0.893507\pi$
$368$	−20.9203	+	5.16617i	−1.09055	+	0.269305i
$369$		−	1.10927i		−	0.0577464i
$370$	2.03456	−	2.42086i	0.105772	−	0.125854i
$371$			24.2914i			1.26114i
$372$	15.3368	+	27.1789i	0.795178	+	1.40916i
$373$	−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
$378$	−3.70398	+	27.1025i	−0.190512	+	1.39400i
$379$	−14.8932			−0.765015			−0.382507	−	0.923952i	$-0.624939\pi$
$379$	−14.8932			−0.765015			−0.382507	+	0.923952i	$0.624939\pi$
$380$	32.8824	+	1.62367i	1.68683	+	0.0832927i
$381$	−23.3967			−1.19865
$382$	−0.675716	+	4.94430i	−0.0345726	+	0.252973i
$383$	−7.82161	+	7.82161i	−0.399666	+	0.399666i	−0.878115	−	0.478449i	$-0.841199\pi$
$383$	−7.82161	+	7.82161i	−0.399666	+	0.399666i	0.478449	+	0.878115i	$0.341199\pi$
$384$	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
$388$	17.4129	−	9.82596i	0.884005	−	0.498838i
$389$		−	18.1292i		−	0.919187i	−0.888129	−	0.459593i	$-0.847995\pi$
$389$		−	18.1292i		−	0.919187i	0.888129	−	0.459593i	$-0.152005\pi$
$390$	−7.57535	+	0.656799i	−0.383593	+	0.0332583i
$391$		−	1.64857i		−	0.0833716i
$392$	10.5684	−	24.4848i	0.533784	−	1.23667i
$393$	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	$0.301609\pi$
$398$	−3.25277	−	0.444542i	−0.163047	−	0.0222829i
$399$	−55.1751			−2.76221
$400$	19.9027	+	1.97033i	0.995135	+	0.0985163i
$401$	−13.4064			−0.669483			−0.334741	−	0.942310i	$-0.608649\pi$
$401$	−13.4064			−0.669483			−0.334741	+	0.942310i	$0.608649\pi$
$402$	−26.5619	−	3.63010i	−1.32479	−	0.181053i
$403$	−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
$408$	−0.634261	+	1.46946i	−0.0314006	+	0.0727490i
$409$		−	37.9316i		−	1.87560i	−0.347180	−	0.937799i	$-0.612861\pi$
$409$		−	37.9316i		−	1.87560i	0.347180	−	0.937799i	$-0.387139\pi$
$410$	−8.33567	+	0.722721i	−0.411670	+	0.0356926i
$411$		−	12.9748i		−	0.640000i
$412$	13.0984	−	7.39134i	0.645313	−	0.364145i
$413$	−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
$418$	6.89506	−	50.4521i	0.337249	−	2.46769i
$419$	34.8854			1.70426			0.852131	−	0.523329i	$-0.175310\pi$
$419$	34.8854			1.70426			0.852131	+	0.523329i	$0.175310\pi$
$420$	−33.4775	−	1.65306i	−1.63353	−	0.0806610i
$421$	−35.9432			−1.75177			−0.875883	−	0.482524i	$-0.839720\pi$
$421$	−35.9432			−1.75177			−0.875883	+	0.482524i	$0.839720\pi$
$422$	4.43013	−	32.4159i	0.215655	−	1.57798i
$423$	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
$428$	−17.5610	−	31.1204i	−0.848842	−	1.50426i
$429$			11.7608i			0.567814i
$430$	9.43782	−	11.2297i	0.455132	−	0.541546i
$431$			4.48617i			0.216091i	0.994146	+	0.108046i	$0.0344593\pi$
$431$			4.48617i			0.216091i	−0.994146	+	0.108046i	$0.965541\pi$
$432$	−4.57635	−	18.5318i	−0.220180	−	0.891612i
$433$	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
$438$	5.70621	+	0.779842i	0.272653	+	0.0372623i
$439$	−12.7409			−0.608088			−0.304044	−	0.952658i	$-0.598337\pi$
$439$	−12.7409			−0.608088			−0.304044	+	0.952658i	$0.598337\pi$
$440$	5.69513	−	30.4052i	0.271505	−	1.44951i
$441$	3.95295			0.188236
$442$	−0.557578	−	0.0762016i	−0.0265213	−	0.00362454i
$443$	0.640705	−	0.640705i	0.0304408	−	0.0304408i	−0.691723	−	0.722163i	$-0.743148\pi$
$443$	0.640705	−	0.640705i	0.0304408	−	0.0304408i	0.722163	+	0.691723i	$0.243148\pi$
$444$	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
$448$	−0.957921	+	32.4117i	−0.0452575	+	1.53131i
$449$		−	1.79037i		−	0.0844927i	−0.999107	−	0.0422464i	$-0.986549\pi$
$449$		−	1.79037i		−	0.0844927i	0.999107	−	0.0422464i	$-0.0134514\pi$
$450$	0.900955	+	2.82431i	0.0424714	+	0.133139i
$451$			12.9412i			0.609375i
$452$	10.2393	+	18.1454i	0.481616	+	0.853487i
$453$	−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	$-0.0561102\pi$
$458$	−1.11734	+	8.17574i	−0.0522099	+	0.382027i
$459$	1.46035			0.0681632
$460$	−17.8552	+	16.1749i	−0.832504	+	0.754157i
$461$	18.8538			0.878109			0.439054	−	0.898461i	$-0.355314\pi$
$461$	18.8538			0.878109			0.439054	+	0.898461i	$0.355314\pi$
$462$	−7.01985	+	51.3652i	−0.326593	+	2.38973i
$463$	−19.9055	+	19.9055i	−0.925089	+	0.925089i	−0.997383	−	0.0722940i	$-0.976968\pi$
$463$	−19.9055	+	19.9055i	−0.925089	+	0.925089i	0.0722940	+	0.997383i	$0.476968\pi$
$464$	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	0.356555	−	0.934274i	$-0.383951\pi$
$467$	−12.4846	−	12.4846i	−0.577719	−	0.577719i	−0.934274	+	0.356555i	$0.883951\pi$
$468$	−0.949592	+	0.535847i	−0.0438949	+	0.0247696i
$469$		−	41.5527i		−	1.91872i
$470$	−5.54645	−	4.66141i	−0.255839	−	0.215015i
$471$			13.5003i			0.622063i
$472$	15.1837	+	6.55371i	0.698884	+	0.301659i
$473$	−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
$478$	27.3700	+	3.74053i	1.25187	+	0.171088i
$479$	−1.80115			−0.0822967			−0.0411483	−	0.999153i	$-0.513102\pi$
$479$	−1.80115			−0.0822967			−0.0411483	+	0.999153i	$0.513102\pi$
$480$	22.1384	−	7.54802i	1.01047	−	0.344519i
$481$	1.30036			0.0592913
$482$	41.1617	+	5.62538i	1.87486	+	0.256229i
$483$	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	0.812843	−	0.582483i	$-0.197919\pi$
$487$	5.08360	+	5.08360i	0.230360	+	0.230360i	−0.582483	+	0.812843i	$0.697919\pi$
$488$	−0.161890	−	0.0698764i	−0.00732841	−	0.00316316i
$489$			14.7780i			0.668284i
$490$	−2.57546	−	29.7046i	−0.116347	−	1.34192i
$491$		−	34.2409i		−	1.54527i	−0.634851	−	0.772635i	$-0.718938\pi$
$491$		−	34.2409i		−	1.54527i	0.634851	−	0.772635i	$-0.281062\pi$
$492$	−8.52186	+	4.80882i	−0.384195	+	0.216798i
$493$	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
$498$	−2.56800	+	18.7904i	−0.115075	+	0.842017i
$499$	−33.0682			−1.48034			−0.740169	−	0.672421i	$-0.765254\pi$
$499$	−33.0682			−1.48034			−0.740169	+	0.672421i	$0.765254\pi$
$500$	20.6364	−	8.61039i	0.922888	−	0.385068i
$501$	−30.3725			−1.35694
$502$	−2.23330	+	16.3413i	−0.0996769	+	0.729350i
$503$	5.35078	−	5.35078i	0.238580	−	0.238580i	−0.577682	−	0.816262i	$-0.696043\pi$
$503$	5.35078	−	5.35078i	0.238580	−	0.238580i	0.816262	+	0.577682i	$0.196043\pi$
$504$	−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
$508$	12.4364	+	22.0390i	0.551777	+	0.977821i
$509$			35.9659i			1.59416i	0.603873	+	0.797081i	$0.293623\pi$
$509$			35.9659i			1.59416i	−0.603873	+	0.797081i	$0.706377\pi$
$510$	0.154566	+	1.78272i	0.00684430	+	0.0789403i
$511$			8.92662i			0.394891i
$512$	−7.72444	−	21.2681i	−0.341375	−	0.939927i
$513$	−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
$518$	5.67934	+	0.776170i	0.249536	+	0.0341029i
$519$	31.6629			1.38985
$520$	4.64534	+	6.78663i	0.203711	+	0.297613i
$521$	23.5994			1.03391			0.516955	−	0.856012i	$-0.327065\pi$
$521$	23.5994			1.03391			0.516955	+	0.856012i	$0.327065\pi$
$522$	2.16450	+	0.295813i	0.0947377	+	0.0129474i
$523$	23.2708	−	23.2708i	1.01756	−	1.01756i	0.0177193	−	0.999843i	$-0.494359\pi$
$523$	23.2708	−	23.2708i	1.01756	−	1.01756i	0.999843	−	0.0177193i	$-0.00564052\pi$
$524$	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
$528$	−8.67318	−	35.1218i	−0.377452	−	1.52848i
$529$		−	6.02175i		−	0.261815i
$530$	−14.5084	−	12.1933i	−0.630205	−	0.529644i
$531$			2.45132i			0.106378i
$532$	29.3281	+	51.9733i	1.27154	+	2.25333i
$533$	−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
$538$	−2.37131	+	17.3512i	−0.102234	+	0.748063i
$539$	−46.1165			−1.98638
$540$	−14.3282	−	15.8167i	−0.616586	−	0.680641i
$541$	28.4406			1.22276			0.611378	−	0.791339i	$-0.290616\pi$
$541$	28.4406			1.22276			0.611378	+	0.791339i	$0.290616\pi$
$542$	−2.66009	+	19.4642i	−0.114261	+	0.836060i
$543$	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	0.990206	−	0.139614i	$-0.0445863\pi$
$547$	19.8937	+	19.8937i	0.850591	+	0.850591i	−0.139614	+	0.990206i	$0.544586\pi$
$548$	−12.2219	+	6.89671i	−0.522092	+	0.294613i
$549$		−	0.0261363i		−	0.00111547i
$550$	−10.5109	−	32.9494i	−0.448185	−	1.40497i
$551$		−	27.1249i		−	1.15556i
$552$	−11.1657	+	25.8687i	−0.475243	+	1.10104i
$553$	−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	$0.460027\pi$
$558$	4.95715	+	0.677471i	0.209853	+	0.0286796i
$559$	6.03204			0.255128
$560$	16.2377	+	32.4134i	0.686168	+	1.36972i
$561$	2.76768			0.116852
$562$	−25.9296	−	3.54369i	−1.09378	−	0.149481i
$563$	−25.7265	+	25.7265i	−1.08424	+	1.08424i	−0.0881327	+	0.996109i	$0.528090\pi$
$563$	−25.7265	+	25.7265i	−1.08424	+	1.08424i	−0.996109	+	0.0881327i	$0.971910\pi$
$564$	−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
$568$	14.6232	−	33.8792i	0.613577	−	1.42154i
$569$		−	8.84476i		−	0.370792i	−0.982664	−	0.185396i	$-0.940643\pi$
$569$		−	8.84476i		−	0.370792i	0.982664	−	0.185396i	$-0.0593568\pi$
$570$	27.6958	−	32.9542i	1.16005	−	1.38030i
$571$		−	29.2747i		−	1.22511i	−0.790429	−	0.612554i	$-0.790142\pi$
$571$		−	29.2747i		−	1.22511i	0.790429	−	0.612554i	$-0.209858\pi$
$572$	11.0783	−	6.25138i	0.463206	−	0.261383i
$573$	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	$0.0629112\pi$
$578$	3.23747	−	23.6890i	0.134661	−	0.985332i
$579$	−25.1274			−1.04426
$580$	0.812667	−	16.4580i	0.0337442	−	0.683381i
$581$	−29.3951			−1.21951
$582$	3.53989	−	25.9018i	0.146733	−	1.07367i
$583$	−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	$0.0145080\pi$
$587$	25.3068	+	25.3068i	1.04452	+	1.04452i	0.0455624	+	0.998961i	$0.485492\pi$
$588$	−17.1365	−	30.3681i	−0.706697	−	1.25236i
$589$		−	62.1214i		−	2.55967i
$590$	18.4206	−	1.59710i	0.758363	−	0.0657517i
$591$			13.5494i			0.557349i
$592$	−3.88334	+	0.958975i	−0.159604	+	0.0394136i
$593$	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
$598$	−9.81572	−	1.34147i	−0.401395	−	0.0548568i
$599$	34.1685			1.39609			0.698043	−	0.716056i	$-0.254055\pi$
$599$	34.1685			1.39609			0.698043	+	0.716056i	$0.254055\pi$
$600$	17.7917	−	19.1652i	0.726343	−	0.782416i
$601$	−27.6480			−1.12779			−0.563893	−	0.825848i	$-0.690697\pi$
$601$	−27.6480			−1.12779			−0.563893	+	0.825848i	$0.690697\pi$
$602$	26.3450	+	3.60045i	1.07374	+	0.146744i
$603$	−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	0.383088	−	0.923712i	$-0.374861\pi$
$607$	−13.3196	−	13.3196i	−0.540624	−	0.540624i	−0.923712	+	0.383088i	$0.874861\pi$
$608$	−32.4042	−	26.1569i	−1.31416	−	1.06080i
$609$			27.6158i			1.11905i
$610$	−0.196402	+	0.0170285i	−0.00795210	+	0.000689464i
$611$		−	2.97927i		−	0.120528i
$612$	0.126102	+	0.223469i	0.00509737	+	0.00903321i
$613$	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	$0.197509\pi$
$618$	2.66280	−	19.4840i	0.107113	−	0.783763i
$619$	29.1731			1.17257			0.586283	−	0.810107i	$-0.300591\pi$
$619$	29.1731			1.17257			0.586283	+	0.810107i	$0.300591\pi$
$620$	1.86117	−	37.6921i	0.0747464	−	1.51375i
$621$	25.7083			1.03164
$622$	2.60671	−	19.0736i	0.104519	−	0.764782i
$623$	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
$628$	12.7169	−	7.17606i	0.507460	−	0.286356i
$629$		−	0.306016i		−	0.0122017i
$630$	−3.45735	+	4.11378i	−0.137744	+	0.163897i
$631$		−	1.00145i		−	0.0398673i	−0.999801	−	0.0199336i	$-0.993655\pi$
$631$		−	1.00145i		−	0.0398673i	0.999801	−	0.0199336i	$-0.00634549\pi$
$632$	12.2029	+	5.26711i	0.485403	+	0.209514i
$633$	−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
$638$	−25.2519	−	3.45106i	−0.999730	−	0.136629i
$639$	5.46961			0.216375
$640$	−18.8776	−	16.8415i	−0.746202	−	0.665720i
$641$	−39.4064			−1.55646			−0.778230	−	0.627979i	$-0.783882\pi$
$641$	−39.4064			−1.55646			−0.778230	+	0.627979i	$0.783882\pi$
$642$	−46.2918	−	6.32650i	−1.82699	−	0.249687i
$643$	6.04020	−	6.04020i	0.238202	−	0.238202i	−0.577903	−	0.816105i	$-0.696129\pi$
$643$	6.04020	−	6.04020i	0.238202	−	0.238202i	0.816105	+	0.577903i	$0.196129\pi$
$644$	−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	$0.0134074\pi$
$647$	26.4847	+	26.4847i	1.04122	+	1.04122i	0.0421082	+	0.999113i	$0.486593\pi$
$648$	−26.1814	−	11.3007i	−1.02850	−	0.443931i
$649$		−	28.5980i		−	1.12257i
$650$	8.17024	+	4.21830i	0.320463	+	0.165455i
$651$			63.2456i			2.47879i
$652$	13.9204	−	7.85519i	0.545166	−	0.307633i
$653$	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
$658$	1.77829	−	13.0120i	0.0693249	−	0.507260i
$659$	12.3464			0.480949			0.240474	−	0.970655i	$-0.422697\pi$
$659$	12.3464			0.480949			0.240474	+	0.970655i	$0.422697\pi$
$660$	−27.1550	−	29.9761i	−1.05701	−	1.16682i
$661$	−3.74124			−0.145517			−0.0727587	−	0.997350i	$-0.523180\pi$
$661$	−3.74124			−0.145517			−0.0727587	+	0.997350i	$0.523180\pi$
$662$	2.20197	−	16.1121i	0.0855822	−	0.626216i
$663$	−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
$668$	16.1444	+	28.6100i	0.624645	+	1.10695i
$669$		−	21.8563i		−	0.845012i
$670$	24.8180	+	20.8578i	0.958804	+	0.805808i
$671$			0.304915i			0.0117711i
$672$	32.9907	+	26.6303i	1.27264	+	1.02729i
$673$	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	$0.131971\pi$
$678$	26.9914	+	3.68880i	1.03660	+	0.141667i
$679$	40.5200			1.55502
$680$	1.59711	−	1.09320i	0.0612464	−	0.0419222i
$681$	40.0383			1.53427
$682$	−57.8318	−	7.90361i	−2.21449	−	0.302645i
$683$	12.3615	−	12.3615i	0.473001	−	0.473001i	−0.429883	−	0.902884i	$-0.641445\pi$
$683$	12.3615	−	12.3615i	0.473001	−	0.473001i	0.902884	+	0.429883i	$0.141445\pi$
$684$	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
$688$	−18.0138	+	4.44844i	−0.686771	+	0.169595i
$689$		−	7.79318i		−	0.296896i
$690$	2.72101	+	31.3835i	0.103587	+	1.19475i
$691$			39.0056i			1.48384i	0.670487	+	0.741921i	$0.266085\pi$
$691$			39.0056i			1.48384i	−0.670487	+	0.741921i	$0.733915\pi$
$692$	−16.8303	−	29.8254i	−0.639791	−	1.13379i
$693$	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
$698$	−0.0207378	+	0.151741i	−0.000784938	+	0.00574349i
$699$	−14.5785			−0.551409
$700$	33.1658	+	23.3002i	1.25355	+	0.880664i
$701$	1.00217			0.0378513			0.0189257	−	0.999821i	$-0.493975\pi$
$701$	1.00217			0.0378513			0.0189257	+	0.999821i	$0.493975\pi$
$702$	1.18831	−	8.69505i	0.0448500	−	0.328173i
$703$	−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
$708$	18.8320	−	10.6268i	0.707750	−	0.399378i
$709$			33.4480i			1.25617i	0.778146	+	0.628084i	$0.216160\pi$
$709$			33.4480i			1.25617i	−0.778146	+	0.628084i	$0.783840\pi$
$710$	−3.56360	−	41.1017i	−0.133740	−	1.54252i
$711$			1.97009i			0.0738840i
$712$	−4.44819	+	10.3056i	−0.166703	+	0.386218i
$713$	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
$718$	−12.2710	−	1.67702i	−0.457949	−	0.0625859i
$719$	−28.6775			−1.06949			−0.534745	−	0.845014i	$-0.679592\pi$
$719$	−28.6775			−1.06949			−0.534745	+	0.845014i	$0.679592\pi$
$720$	1.18309	−	3.55834i	0.0440913	−	0.132612i
$721$	30.4802			1.13514
$722$	−49.3139	−	6.73950i	−1.83527	−	0.250818i
$723$	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	0.509104	−	0.860705i	$-0.329977\pi$
$727$	−9.48022	−	9.48022i	−0.351602	−	0.351602i	−0.860705	+	0.509104i	$0.829977\pi$
$728$	−5.90776	+	13.6871i	−0.218956	+	0.507278i
$729$			22.2458i			0.823920i
$730$	−5.33157	−	4.48082i	−0.197330	−	0.165842i
$731$		−	1.41953i		−	0.0525033i
$732$	−0.200789	+	0.113304i	−0.00742138	+	0.00418783i
$733$	−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
$738$	−0.212419	+	1.55430i	−0.00781925	+	0.0572145i
$739$	−21.6438			−0.796182			−0.398091	−	0.917346i	$-0.630327\pi$
$739$	−21.6438			−0.796182			−0.398091	+	0.917346i	$0.630327\pi$
$740$	−3.31439	+	3.00247i	−0.121839	+	0.110373i
$741$	17.7013			0.650275
$742$	4.65166	−	34.0368i	0.170768	−	1.24953i
$743$	32.2288	−	32.2288i	1.18236	−	1.18236i	0.203228	−	0.979131i	$-0.434857\pi$
$743$	32.2288	−	32.2288i	1.18236	−	1.18236i	0.979131	−	0.203228i	$-0.0651434\pi$
$744$	−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
$748$	−1.47115	−	2.60707i	−0.0537906	−	0.0953240i
$749$		−	72.4175i		−	2.64608i
$750$	7.35492	−	28.2969i	0.268564	−	1.03326i
$751$		−	17.9121i		−	0.653621i	−0.945090	−	0.326810i	$-0.894026\pi$
$751$		−	17.9121i		−	0.653621i	0.945090	−	0.326810i	$-0.105974\pi$
$752$	2.19712	+	8.89717i	0.0801206	+	0.324446i
$753$	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	$0.313537\pi$
$758$	20.8683	+	2.85197i	0.757969	+	0.103588i
$759$	48.7229			1.76853
$760$	−45.7635	−	8.57185i	−1.66002	−	0.310934i
$761$	17.4074			0.631019			0.315509	−	0.948922i	$-0.397825\pi$
$761$	17.4074			0.631019			0.315509	+	0.948922i	$0.397825\pi$
$762$	32.7832	+	4.48033i	1.18761	+	0.162305i
$763$	−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
$768$	−28.2541	−	8.77699i	−1.01953	−	0.316712i
$769$			10.7498i			0.387646i	0.981037	+	0.193823i	$0.0620888\pi$
$769$			10.7498i			0.387646i	−0.981037	+	0.193823i	$0.937911\pi$
$770$	40.3347	−	47.9928i	1.45356	−	1.72954i
$771$			8.47917i			0.305370i
$772$	13.3564	+	23.6692i	0.480706	+	0.851874i
$773$	−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
$778$	−3.47164	+	25.4024i	−0.124464	+	0.910721i
$779$	19.4780			0.697871
$780$	10.7403	+	0.530336i	0.384563	+	0.0189891i
$781$	−63.8104			−2.28332
$782$	−0.315691	+	2.30995i	−0.0112891	+	0.0826038i
$783$	−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	0.864124	−	0.503278i	$-0.167873\pi$
$787$	10.1230	+	10.1230i	0.360846	+	0.360846i	−0.503278	+	0.864124i	$0.667873\pi$
$788$	12.7631	−	7.20215i	0.454668	−	0.256566i
$789$			49.5839i			1.76523i
$790$	14.8043	−	1.28357i	0.526714	−	0.0456672i
$791$			42.2246i			1.50133i
$792$	−5.32505	−	2.29845i	−0.189218	−	0.0816718i
$793$	−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	$0.939842\pi$
$798$	77.3108	+	10.5657i	2.73677	+	0.374022i
$799$	−0.701117			−0.0248037
$800$	−27.5101	−	6.57205i	−0.972631	−	0.232357i
$801$	−1.66378			−0.0587868
$802$	18.7849	+	2.56724i	0.663317	+	0.0906526i
$803$	−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
$808$	19.6339	+	8.47455i	0.690717	+	0.298134i
$809$			34.9239i			1.22786i	0.789361	+	0.613930i	$0.210412\pi$
$809$			34.9239i			1.22786i	−0.789361	+	0.613930i	$0.789588\pi$
$810$	−31.7628	+	2.75391i	−1.11603	+	0.0967624i
$811$		−	20.4586i		−	0.718398i	−0.933261	−	0.359199i	$-0.883050\pi$
$811$		−	20.4586i		−	0.718398i	0.933261	−	0.359199i	$-0.116950\pi$
$812$	26.0132	−	14.6791i	0.912885	−	0.515134i
$813$	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
$818$	−7.26368	+	53.1493i	−0.253969	+	1.85832i
$819$	−2.20971			−0.0772136
$820$	11.8183	+	0.583565i	0.412711	+	0.0203790i
$821$	−25.5454			−0.891541			−0.445771	−	0.895147i	$-0.647070\pi$
$821$	−25.5454			−0.891541			−0.445771	+	0.895147i	$0.647070\pi$
$822$	−2.48460	+	18.1801i	−0.0866603	+	0.634105i
$823$	5.51659	−	5.51659i	0.192296	−	0.192296i	−0.604391	−	0.796688i	$-0.706584\pi$
$823$	5.51659	−	5.51659i	0.192296	−	0.192296i	0.796688	+	0.604391i	$0.206584\pi$
$824$	−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	$0.162976\pi$
$827$	39.1590	+	39.1590i	1.36169	+	1.36169i	0.489926	+	0.871764i	$0.337024\pi$
$828$	2.21993	+	3.93400i	0.0771479	+	0.136716i
$829$			45.5969i			1.58365i	0.610750	+	0.791823i	$0.290868\pi$
$829$			45.5969i			1.58365i	−0.610750	+	0.791823i	$0.709132\pi$
$830$	14.7552	−	17.5567i	0.512160	−	0.609402i
$831$			3.33105i			0.115553i
$832$	0.307321	−	10.3983i	0.0106544	−	0.360498i
$833$	−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
$838$	−48.8810	−	6.68034i	−1.68856	−	0.230769i
$839$	38.7658			1.33835			0.669173	−	0.743107i	$-0.266649\pi$
$839$	38.7658			1.33835			0.669173	+	0.743107i	$0.266649\pi$
$840$	46.5917	+	8.72699i	1.60757	+	0.301110i
$841$	15.4237			0.531852
$842$	50.3632	+	6.88292i	1.73563	+	0.237201i
$843$	−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
$848$	5.74722	+	23.2732i	0.197360	+	0.799206i
$849$			48.2146i			1.65472i
$850$	0.992700	−	1.92272i	0.0340493	−	0.0659487i
$851$		−	5.38718i		−	0.184670i
$852$	−23.7114	−	42.0197i	−0.812339	−	1.43957i
$853$	−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	$0.264290\pi$
$858$	2.25212	−	16.4790i	0.0768860	−	0.562585i
$859$	0.911505			0.0311002			0.0155501	−	0.999879i	$-0.495050\pi$
$859$	0.911505			0.0311002			0.0155501	+	0.999879i	$0.495050\pi$
$860$	−15.3746	+	13.9277i	−0.524269	+	0.474931i
$861$	−19.8305			−0.675821
$862$	0.859076	−	6.28597i	0.0292602	−	0.214101i
$863$	19.9864	−	19.9864i	0.680347	−	0.680347i	−0.279732	−	0.960078i	$-0.590245\pi$
$863$	19.9864	−	19.9864i	0.680347	−	0.680347i	0.960078	+	0.279732i	$0.0902455\pi$
$864$	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
$868$	59.5755	−	33.6180i	2.02212	−	1.14107i
$869$		−	22.9837i		−	0.779669i
$870$	−16.4940	−	13.8620i	−0.559198	−	0.469967i
$871$			13.3310i			0.451703i
$872$	17.8268	−	41.3013i	0.603693	−	1.39864i
$873$	−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	$0.204909\pi$
$878$	17.8523	+	2.43980i	0.602487	+	0.0823392i
$879$	−45.5908			−1.53774
$880$	−13.8024	+	41.5129i	−0.465278	+	1.39940i
$881$	7.91044			0.266509			0.133255	−	0.991082i	$-0.457457\pi$
$881$	7.91044			0.266509			0.133255	+	0.991082i	$0.457457\pi$
$882$	−5.53883	−	0.756967i	−0.186502	−	0.0254884i
$883$	−14.4972	+	14.4972i	−0.487868	+	0.487868i	−0.907633	−	0.419765i	$-0.862113\pi$
$883$	−14.4972	+	14.4972i	−0.487868	+	0.487868i	0.419765	+	0.907633i	$0.362113\pi$
$884$	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	0.997537	−	0.0701388i	$-0.0223442\pi$
$887$	27.6203	+	27.6203i	0.927398	+	0.927398i	−0.0701388	+	0.997537i	$0.522344\pi$
$888$	−2.07264	+	4.80189i	−0.0695531	+	0.161141i
$889$			51.2850i			1.72004i
$890$	1.08400	+	12.5026i	0.0363358	+	0.419087i
$891$			49.3119i			1.65201i
$892$	−20.5879	+	11.6176i	−0.689335	+	0.388986i
$893$	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
$898$	−0.342845	+	2.50864i	−0.0114409	+	0.0837145i
$899$	−31.0924			−1.03699
$900$	−0.721570	−	4.12992i	−0.0240523	−	0.137664i
$901$	−1.83398			−0.0610989
$902$	2.47816	−	18.1330i	0.0825136	−	0.603763i
$903$	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	0.884663	−	0.466231i	$-0.154389\pi$
$907$	12.6017	+	12.6017i	0.418431	+	0.418431i	−0.466231	+	0.884663i	$0.654389\pi$
$908$	−21.2822	−	37.7149i	−0.706275	−	1.25161i
$909$			3.16979i			0.105135i
$910$	1.43969	+	16.6050i	0.0477252	+	0.550450i
$911$		−	2.65754i		−	0.0880484i	−0.999030	−	0.0440242i	$-0.985982\pi$
$911$		−	2.65754i		−	0.0880484i	0.999030	−	0.0440242i	$-0.0140179\pi$
$912$	−52.8625	+	13.0542i	−1.75045	+	0.432267i
$913$	−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
$918$	−2.04622	−	0.279648i	−0.0675354	−	0.00922977i
$919$	−36.3493			−1.19905			−0.599526	−	0.800356i	$-0.704644\pi$
$919$	−36.3493			−1.19905			−0.599526	+	0.800356i	$0.704644\pi$
$920$	28.1159	−	19.2449i	0.926954	−	0.634485i
$921$	17.2644			0.568882
$922$	−26.4177	−	3.61039i	−0.870021	−	0.118902i
$923$	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
$928$	−13.0918	+	16.2187i	−0.429761	+	0.532404i
$929$			2.72649i			0.0894533i	0.998999	+	0.0447266i	$0.0142417\pi$
$929$			2.72649i			0.0894533i	−0.998999	+	0.0447266i	$0.985758\pi$
$930$	−37.7745	−	31.7468i	−1.23867	−	1.04102i
$931$			69.4108i			2.27485i
$932$	7.74914	+	13.7325i	0.253831	+	0.449822i
$933$	−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	$0.390853\pi$
$938$	−7.95710	+	58.2231i	−0.259808	+	1.90105i
$939$	−33.1393			−1.08146
$940$	6.87899	+	7.59362i	0.224368	+	0.247677i
$941$	2.09390			0.0682591			0.0341296	−	0.999417i	$-0.489134\pi$
$941$	2.09390			0.0682591			0.0341296	+	0.999417i	$0.489134\pi$
$942$	2.58524	−	18.9165i	0.0842316	−	0.616334i
$943$	−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	0.931247	−	0.364388i	$-0.118722\pi$
$947$	17.4442	+	17.4442i	0.566859	+	0.566859i	−0.364388	+	0.931247i	$0.618722\pi$
$948$	15.1350	−	8.54055i	0.491561	−	0.277384i
$949$		−	2.86385i		−	0.0929644i
$950$	−49.5927	+	15.8201i	−1.60900	+	0.513272i
$951$			33.7798i			1.09539i
$952$	3.22102	+	1.39029i	0.104394	+	0.0450594i
$953$	−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
$958$	2.52375	+	0.344910i	0.0815387	+	0.0111435i
$959$	−28.4405			−0.918390
$960$	−32.4654	+	6.33684i	−1.04782	+	0.204521i
$961$	−40.2079			−1.29703
$962$	−1.82205	−	0.249011i	−0.0587453	−	0.00802845i
$963$	−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	$-0.947991\pi$
$967$	−35.7408	−	35.7408i	−1.14935	−	1.14935i	−0.162666	−	0.986681i	$-0.552009\pi$
$968$	33.5586	+	14.4849i	1.07861	+	0.465561i
$969$		−	4.16569i		−	0.133821i
$970$	−20.3395	+	24.2013i	−0.653061	+	0.777056i
$971$		−	21.3031i		−	0.683651i	−0.939764	−	0.341825i	$-0.888955\pi$
$971$		−	21.3031i		−	0.683651i	0.939764	−	0.341825i	$-0.111045\pi$
$972$	−7.53583	+	4.25241i	−0.241712	+	0.136396i
$973$	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	$0.357163\pi$
$978$	2.82990	−	20.7068i	0.0904903	−	0.662129i
$979$	19.4103			0.620355
$980$	−2.07956	+	42.1150i	−0.0664292	+	1.34531i
$981$	6.66787			0.212889
$982$	−6.55693	+	47.9780i	−0.209240	+	1.53104i
$983$	19.9634	−	19.9634i	0.636734	−	0.636734i	−0.313014	−	0.949748i	$-0.601339\pi$
$983$	19.9634	−	19.9634i	0.636734	−	0.636734i	0.949748	+	0.313014i	$0.101339\pi$
$984$	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
$988$	−9.40908	−	16.6741i	−0.299343	−	0.530474i
$989$		−	24.9898i		−	0.794628i
$990$	−6.46027	+	0.560119i	−0.205321	+	0.0178018i
$991$		−	31.1421i		−	0.989262i	−0.869103	−	0.494631i	$-0.835303\pi$
$991$		−	31.1421i		−	0.989262i	0.869103	−	0.494631i	$-0.164697\pi$
$992$	−29.9829	+	37.1440i	−0.951959	+	1.17932i
$993$	−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	$0.441495\pi$
$998$	46.3348	+	6.33238i	1.46670	+	0.200448i
$999$	4.77212			0.150983

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.n.a.223.6	✓	216	1.1	even	1	trivial
740.2.n.a.223.61	yes	216	4.3	odd	2	inner
740.2.n.a.667.6	yes	216	20.7	even	4	inner
740.2.n.a.667.61	yes	216	5.2	odd	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+(-1.40119 - 0.191494i) 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} +(-2.59685 - 1.12088i) q^{8} -0.419248i q^{9} +(-3.15046 + 0.273152i) q^{10} +4.89109i q^{11} +(-3.22083 + 1.81749i) 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} +(-0.0802835 + 0.587445i) q^{18} +7.36168 q^{19} +(4.46669 + 0.220558i) q^{20} -7.49491 q^{21} +(0.936616 - 6.85335i) 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} +(3.98389 + 7.05998i) q^{28} -3.68460i q^{29} +(3.76215 - 4.47646i) q^{30} -8.43848i q^{31} +(-4.40174 - 3.55312i) 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} +(-10.3151 - 1.40972i) q^{38} +2.40452 q^{39} +(-6.21645 - 1.16439i) q^{40} +2.64586 q^{41} +(10.5018 + 1.43523i) 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} +(-7.18077 + 1.77326i) q^{48} +9.42867i q^{49} +(-6.73661 + 2.14898i) q^{50} -0.565861i q^{51} +(-1.27812 - 2.26499i) 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} +(-0.705580 + 5.16282i) q^{58} -5.84695 q^{59} +(-6.12870 + 5.55193i) q^{60} +0.0623409 q^{61} +(-1.61592 + 11.8239i) 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} +(-0.533024 + 0.300782i) q^{68} -9.96155i q^{69} +(-9.81229 - 8.24655i) q^{70} +13.0462i q^{71} +(-0.469925 + 1.08872i) 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} +(-3.36919 - 0.460452i) q^{78} -4.69910 q^{79} +(8.48744 + 2.82194i) q^{80} +10.0820 q^{81} +(-3.70735 - 0.506667i) 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} +(5.48231 - 12.7014i) q^{88} -3.96849i q^{89} +(0.114518 + 1.32082i) q^{90} -5.27066i q^{91} +(-9.38348 + 5.29503i) 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} +(1.80554 - 13.2113i) 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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