LMFDB - Embedded newform 640.2.bm.a.381.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			381.31
Character	$\chi$	$=$	640.381
Dual form			640.2.bm.a.341.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.106586 - 1.41019i) q^{2} +(0.661571 + 0.806127i) q^{3} +(-1.97728 + 0.300613i) q^{4} +(-0.956940 - 0.290285i) q^{5} +(1.06628 - 1.01886i) q^{6} +(0.522095 - 0.103851i) q^{7} +(0.634671 + 2.75630i) q^{8} +(0.373107 - 1.87574i) q^{9} +O(q^{10})$	\(q+(-0.106586 - 1.41019i) q^{2} +(0.661571 + 0.806127i) q^{3} +(-1.97728 + 0.300613i) q^{4} +(-0.956940 - 0.290285i) q^{5} +(1.06628 - 1.01886i) q^{6} +(0.522095 - 0.103851i) q^{7} +(0.634671 + 2.75630i) q^{8} +(0.373107 - 1.87574i) q^{9} +(-0.307361 + 1.38041i) q^{10} +(-3.97156 + 0.391164i) q^{11} +(-1.55044 - 1.39506i) q^{12} +(-0.214570 - 0.707342i) q^{13} +(-0.202098 - 0.725185i) q^{14} +(-0.399078 - 0.963459i) q^{15} +(3.81926 - 1.18879i) q^{16} +(2.48755 - 6.00547i) q^{17} +(-2.68491 - 0.326226i) q^{18} +(-5.94147 - 3.17578i) q^{19} +(1.97940 + 0.286305i) q^{20} +(0.429120 + 0.352170i) q^{21} +(0.974927 + 5.55896i) q^{22} +(-2.92500 - 4.37757i) q^{23} +(-1.80205 + 2.33511i) q^{24} +(0.831470 + 0.555570i) q^{25} +(-0.974617 + 0.377977i) q^{26} +(4.51803 - 2.41494i) q^{27} +(-1.00111 + 0.362291i) q^{28} +(-0.280007 + 2.84296i) q^{29} +(-1.31613 + 0.665467i) q^{30} +(5.31939 - 5.31939i) q^{31} +(-2.08350 - 5.25918i) q^{32} +(-2.94279 - 2.94279i) q^{33} +(-8.73399 - 2.86782i) q^{34} +(-0.529760 - 0.0521769i) q^{35} +(-0.173867 + 3.82101i) q^{36} +(0.269889 + 0.504926i) q^{37} +(-3.84518 + 8.71710i) q^{38} +(0.428254 - 0.640927i) q^{39} +(0.192769 - 2.82185i) q^{40} +(-4.00764 + 2.67782i) q^{41} +(0.450889 - 0.642678i) q^{42} +(-6.00655 + 7.31900i) q^{43} +(7.73528 - 1.96734i) q^{44} +(-0.901539 + 1.68666i) q^{45} +(-5.86144 + 4.59139i) q^{46} +(-4.04784 - 1.67667i) q^{47} +(3.48503 + 2.29234i) q^{48} +(-6.20536 + 2.57034i) q^{49} +(0.694837 - 1.23175i) q^{50} +(6.48685 - 1.96777i) q^{51} +(0.636900 + 1.33411i) q^{52} +(-0.849580 - 8.62593i) q^{53} +(-3.88708 - 6.11388i) q^{54} +(3.91409 + 0.778561i) q^{55} +(0.617604 + 1.37314i) q^{56} +(-1.37062 - 6.89058i) q^{57} +(4.03896 + 0.0918445i) q^{58} +(2.40026 - 7.91261i) q^{59} +(1.07872 + 1.78506i) q^{60} +(10.4422 - 8.56968i) q^{61} +(-8.06834 - 6.93439i) q^{62} -1.01806i q^{63} +(-7.19439 + 3.49869i) q^{64} +0.739170i q^{65} +(-3.83624 + 4.46356i) q^{66} +(-9.25954 + 7.59910i) q^{67} +(-3.11325 + 12.6223i) q^{68} +(1.59378 - 5.25399i) q^{69} +(-0.0171144 + 0.752625i) q^{70} +(2.43148 + 12.2239i) q^{71} +(5.40689 - 0.162080i) q^{72} +(10.6243 + 2.11330i) q^{73} +(0.683276 - 0.434413i) q^{74} +(0.102216 + 1.03782i) q^{75} +(12.7026 + 4.49332i) q^{76} +(-2.03291 + 0.616676i) q^{77} +(-0.949475 - 0.535606i) q^{78} +(8.63355 - 3.57613i) q^{79} +(-3.99990 + 0.0289274i) q^{80} +(-0.364974 - 0.151177i) q^{81} +(4.20339 + 5.36612i) q^{82} +(-6.99093 + 13.0791i) q^{83} +(-0.954357 - 0.567339i) q^{84} +(-4.12373 + 5.02478i) q^{85} +(10.9614 + 7.69028i) q^{86} +(-2.47703 + 1.65510i) q^{87} +(-3.59880 - 10.6985i) q^{88} +(3.41799 - 5.11538i) q^{89} +(2.47460 + 1.09157i) q^{90} +(-0.185484 - 0.347016i) q^{91} +(7.09949 + 7.77638i) q^{92} +(7.80726 + 0.768948i) q^{93} +(-1.93299 + 5.88694i) q^{94} +(4.76375 + 4.76375i) q^{95} +(2.86119 - 5.15889i) q^{96} +(-2.87112 + 2.87112i) q^{97} +(4.28608 + 8.47678i) q^{98} +(-0.748095 + 7.59553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{3}{32}\right)$	$1$

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 $

$2$	−0.106586	−	1.41019i	−0.0753675	−	0.997156i
$2$	−0.106586	−	1.41019i	−0.0753675	−	0.997156i
$3$	0.661571	+	0.806127i	0.381958	+	0.465417i	0.928130	−	0.372256i	$-0.121416\pi$
$3$	0.661571	+	0.806127i	0.381958	+	0.465417i	−0.546172	+	0.837673i	$0.683916\pi$
$4$	−1.97728	+	0.300613i	−0.988639	+	0.150306i
$5$	−0.956940	−	0.290285i	−0.427957	−	0.129819i
$5$	−0.956940	−	0.290285i	−0.427957	−	0.129819i
$6$	1.06628	−	1.01886i	0.435306	−	0.415949i
$7$	0.522095	−	0.103851i	0.197333	−	0.0392521i	−0.0954339	−	0.995436i	$-0.530424\pi$
$7$	0.522095	−	0.103851i	0.197333	−	0.0392521i	0.292767	+	0.956184i	$0.405424\pi$
$8$	0.634671	+	2.75630i	0.224390	+	0.974499i
$9$	0.373107	−	1.87574i	0.124369	−	0.625245i
$10$	−0.307361	+	1.38041i	−0.0971960	+	0.436524i
$11$	−3.97156	+	0.391164i	−1.19747	+	0.117940i	−0.677028	−	0.735957i	$-0.736732\pi$
$11$	−3.97156	+	0.391164i	−1.19747	+	0.117940i	−0.520441	+	0.853898i	$0.674232\pi$
$12$	−1.55044	−	1.39506i	−0.447574	−	0.402719i
$13$	−0.214570	−	0.707342i	−0.0595109	−	0.196181i	0.922144	−	0.386846i	$-0.126436\pi$
$13$	−0.214570	−	0.707342i	−0.0595109	−	0.196181i	−0.981655	+	0.190665i	$0.938936\pi$
$14$	−0.202098	−	0.725185i	−0.0540130	−	0.193814i
$15$	−0.399078	−	0.963459i	−0.103041	−	0.248764i
$16$	3.81926	−	1.18879i	0.954816	−	0.297198i
$17$	2.48755	−	6.00547i	0.603318	−	1.45654i	−0.266827	−	0.963744i	$-0.585975\pi$
$17$	2.48755	−	6.00547i	0.603318	−	1.45654i	0.870145	−	0.492795i	$-0.164025\pi$
$18$	−2.68491	−	0.326226i	−0.632840	−	0.0768921i
$19$	−5.94147	−	3.17578i	−1.36307	−	0.728574i	−0.382351	−	0.924017i	$-0.624885\pi$
$19$	−5.94147	−	3.17578i	−1.36307	−	0.728574i	−0.980715	+	0.195443i	$0.937385\pi$
$20$	1.97940	+	0.286305i	0.442608	+	0.0640198i
$21$	0.429120	+	0.352170i	0.0936417	+	0.0768498i
$22$	0.974927	+	5.55896i	0.207855	+	1.18517i
$23$	−2.92500	−	4.37757i	−0.609904	−	0.912786i	0.390064	−	0.920788i	$-0.372453\pi$
$23$	−2.92500	−	4.37757i	−0.609904	−	0.912786i	−0.999968	+	0.00800203i	$0.997453\pi$
$24$	−1.80205	+	2.33511i	−0.367841	+	0.476653i
$25$	0.831470	+	0.555570i	0.166294	+	0.111114i
$26$	−0.974617	+	0.377977i	−0.191138	+	0.0741274i
$27$	4.51803	−	2.41494i	0.869495	−	0.464755i
$28$	−1.00111	+	0.362291i	−0.189192	+	0.0684666i
$29$	−0.280007	+	2.84296i	−0.0519960	+	0.527925i	0.933542	+	0.358469i	$0.116701\pi$
$29$	−0.280007	+	2.84296i	−0.0519960	+	0.527925i	−0.985538	+	0.169456i	$0.945799\pi$
$30$	−1.31613	+	0.665467i	−0.240291	+	0.121497i
$31$	5.31939	−	5.31939i	0.955391	−	0.955391i	−0.0436552	−	0.999047i	$-0.513900\pi$
$31$	5.31939	−	5.31939i	0.955391	−	0.955391i	0.999047	+	0.0436552i	$0.0139003\pi$
$32$	−2.08350	−	5.25918i	−0.368314	−	0.929701i
$33$	−2.94279	−	2.94279i	−0.512275	−	0.512275i
$34$	−8.73399	−	2.86782i	−1.49787	−	0.491827i
$35$	−0.529760	−	0.0521769i	−0.0895459	−	0.00881950i
$36$	−0.173867	+	3.82101i	−0.0289778	+	0.636836i
$37$	0.269889	+	0.504926i	0.0443694	+	0.0830094i	0.903129	−	0.429370i	$-0.141264\pi$
$37$	0.269889	+	0.504926i	0.0443694	+	0.0830094i	−0.858759	+	0.512379i	$0.828764\pi$
$38$	−3.84518	+	8.71710i	−0.623771	+	1.41410i
$39$	0.428254	−	0.640927i	0.0685755	−	0.102630i
$40$	0.192769	−	2.82185i	0.0304795	−	0.446174i
$41$	−4.00764	+	2.67782i	−0.625888	+	0.418205i	−0.827662	−	0.561227i	$-0.810329\pi$
$41$	−4.00764	+	2.67782i	−0.625888	+	0.418205i	0.201774	+	0.979432i	$0.435329\pi$
$42$	0.450889	−	0.642678i	0.0695737	−	0.0991674i
$43$	−6.00655	+	7.31900i	−0.915990	+	1.11614i	0.0768928	+	0.997039i	$0.475500\pi$
$43$	−6.00655	+	7.31900i	−0.915990	+	1.11614i	−0.992883	+	0.119097i	$0.962000\pi$
$44$	7.73528	−	1.96734i	1.16614	−	0.296588i
$45$	−0.901539	+	1.68666i	−0.134393	+	0.251432i
$46$	−5.86144	+	4.59139i	−0.864223	+	0.676964i
$47$	−4.04784	−	1.67667i	−0.590439	−	0.244568i	0.0674006	−	0.997726i	$-0.478529\pi$
$47$	−4.04784	−	1.67667i	−0.590439	−	0.244568i	−0.657839	+	0.753158i	$0.728529\pi$
$48$	3.48503	+	2.29234i	0.503021	+	0.330871i
$49$	−6.20536	+	2.57034i	−0.886480	+	0.367192i
$50$	0.694837	−	1.23175i	0.0982649	−	0.174195i
$51$	6.48685	−	1.96777i	0.908341	−	0.275542i
$52$	0.636900	+	1.33411i	0.0883221	+	0.185008i
$53$	−0.849580	−	8.62593i	−0.116699	−	1.18486i	−0.857986	−	0.513674i	$-0.828284\pi$
$53$	−0.849580	−	8.62593i	−0.116699	−	1.18486i	0.741287	−	0.671188i	$-0.234216\pi$
$54$	−3.88708	−	6.11388i	−0.528964	−	0.831994i
$55$	3.91409	+	0.778561i	0.527776	+	0.104981i
$56$	0.617604	+	1.37314i	0.0825308	+	0.183494i
$57$	−1.37062	−	6.89058i	−0.181543	−	0.912679i
$58$	4.03896	+	0.0918445i	0.530342	+	0.0120598i
$59$	2.40026	−	7.91261i	0.312488	−	1.03013i	−0.650255	−	0.759716i	$-0.725338\pi$
$59$	2.40026	−	7.91261i	0.312488	−	1.03013i	0.962743	−	0.270418i	$-0.0871619\pi$
$60$	1.07872	+	1.78506i	0.139262	+	0.230450i
$61$	10.4422	−	8.56968i	1.33699	−	1.09724i	0.349944	−	0.936771i	$-0.386201\pi$
$61$	10.4422	−	8.56968i	1.33699	−	1.09724i	0.987042	−	0.160465i	$-0.0512993\pi$
$62$	−8.06834	−	6.93439i	−1.02468	−	0.880669i
$63$		−	1.01806i		−	0.128264i
$64$	−7.19439	+	3.49869i	−0.899298	+	0.437336i
$65$			0.739170i			0.0916828i
$66$	−3.83624	+	4.46356i	−0.472209	+	0.549426i
$67$	−9.25954	+	7.59910i	−1.13123	+	0.928378i	−0.998032	−	0.0627107i	$-0.980025\pi$
$67$	−9.25954	+	7.59910i	−1.13123	+	0.928378i	−0.133201	+	0.991089i	$0.542525\pi$
$68$	−3.11325	+	12.6223i	−0.377537	+	1.53068i
$69$	1.59378	−	5.25399i	0.191869	−	0.632506i
$70$	−0.0171144	+	0.752625i	−0.00204556	+	0.0899559i
$71$	2.43148	+	12.2239i	0.288563	+	1.45071i	0.804435	+	0.594040i	$0.202468\pi$
$71$	2.43148	+	12.2239i	0.288563	+	1.45071i	−0.515872	+	0.856666i	$0.672532\pi$
$72$	5.40689	−	0.162080i	0.637208	−	0.0191013i
$73$	10.6243	+	2.11330i	1.24348	+	0.247343i	0.772621	−	0.634868i	$-0.218945\pi$
$73$	10.6243	+	2.11330i	1.24348	+	0.247343i	0.470855	+	0.882211i	$0.343945\pi$
$74$	0.683276	−	0.434413i	0.0794293	−	0.0504995i
$75$	0.102216	+	1.03782i	0.0118029	+	0.119837i
$76$	12.7026	+	4.49332i	1.45709	+	0.515419i
$77$	−2.03291	+	0.616676i	−0.231671	+	0.0702767i
$78$	−0.949475	−	0.535606i	−0.107507	−	0.0606454i
$79$	8.63355	−	3.57613i	0.971350	−	0.402346i	0.160135	−	0.987095i	$-0.448807\pi$
$79$	8.63355	−	3.57613i	0.971350	−	0.402346i	0.811214	+	0.584749i	$0.198807\pi$
$80$	−3.99990	+	0.0289274i	−0.447202	+	0.00323418i
$81$	−0.364974	−	0.151177i	−0.0405526	−	0.0167974i
$82$	4.20339	+	5.36612i	0.464187	+	0.592588i
$83$	−6.99093	+	13.0791i	−0.767355	+	1.43562i	0.128704	+	0.991683i	$0.458918\pi$
$83$	−6.99093	+	13.0791i	−0.767355	+	1.43562i	−0.896058	+	0.443936i	$0.853582\pi$
$84$	−0.954357	−	0.567339i	−0.104129	−	0.0619018i
$85$	−4.12373	+	5.02478i	−0.447281	+	0.545014i
$86$	10.9614	+	7.69028i	1.18200	+	0.829264i
$87$	−2.47703	+	1.65510i	−0.265566	+	0.177445i
$88$	−3.59880	−	10.6985i	−0.383633	−	1.14047i
$89$	3.41799	−	5.11538i	0.362306	−	0.542229i	−0.604874	−	0.796321i	$-0.706777\pi$
$89$	3.41799	−	5.11538i	0.362306	−	0.542229i	0.967180	+	0.254092i	$0.0817765\pi$
$90$	2.47460	+	1.09157i	0.260846	+	0.115061i
$91$	−0.185484	−	0.347016i	−0.0194440	−	0.0363772i
$92$	7.09949	+	7.77638i	0.740173	+	0.810744i
$93$	7.80726	+	0.768948i	0.809575	+	0.0797362i
$94$	−1.93299	+	5.88694i	−0.199372	+	0.607192i
$95$	4.76375	+	4.76375i	0.488750	+	0.488750i
$96$	2.86119	−	5.15889i	0.292018	−	0.526527i
$97$	−2.87112	+	2.87112i	−0.291519	+	0.291519i	−0.837680	−	0.546161i	$-0.816089\pi$
$97$	−2.87112	+	2.87112i	−0.291519	+	0.291519i	0.546161	+	0.837680i	$0.316089\pi$
$98$	4.28608	+	8.47678i	0.432959	+	0.856284i
$99$	−0.748095	+	7.59553i	−0.0751864	+	0.763380i
$100$	−1.81106	−	0.848567i	−0.181106	−	0.0848567i
$101$	13.6970	−	7.32117i	1.36290	−	0.728484i	0.382212	−	0.924075i	$-0.375162\pi$
$101$	13.6970	−	7.32117i	1.36290	−	0.728484i	0.980686	+	0.195591i	$0.0626624\pi$
$102$	−3.46633	−	8.93797i	−0.343218	−	0.884991i
$103$	5.66461	+	3.78497i	0.558150	+	0.372944i	0.802417	−	0.596764i	$-0.203547\pi$
$103$	5.66461	+	3.78497i	0.558150	+	0.372944i	−0.244267	+	0.969708i	$0.578547\pi$
$104$	1.81346	−	1.04035i	0.177825	−	0.102015i
$105$	−0.308413	−	0.461573i	−0.0300980	−	0.0450449i
$106$	−12.0737	+	2.11747i	−1.17270	+	0.205667i
$107$	−3.93336	−	3.22803i	−0.380253	−	0.312065i	0.424779	−	0.905297i	$-0.360352\pi$
$107$	−3.93336	−	3.22803i	−0.380253	−	0.312065i	−0.805032	+	0.593232i	$0.797852\pi$
$108$	−8.20744	+	6.13318i	−0.789761	+	0.590165i
$109$	10.9888	+	5.87362i	1.05253	+	0.562590i	0.904536	−	0.426397i	$-0.140217\pi$
$109$	10.9888	+	5.87362i	1.05253	+	0.562590i	0.147997	+	0.988988i	$0.452717\pi$
$110$	0.680734	−	5.60260i	0.0649054	−	0.534187i
$111$	−0.228484	+	0.551609i	−0.0216867	+	0.0523564i
$112$	1.87056	−	1.01730i	0.176752	−	0.0961255i
$113$	−7.21038	−	17.4074i	−0.678296	−	1.63755i	−0.767120	−	0.641503i	$-0.778311\pi$
$113$	−7.21038	−	17.4074i	−0.678296	−	1.63755i	0.0888244	−	0.996047i	$-0.471689\pi$
$114$	−9.57094	+	2.66728i	−0.896401	+	0.249813i
$115$	1.52831	+	5.03815i	0.142515	+	0.469810i
$116$	−0.300978	−	5.70550i	−0.0279451	−	0.529742i
$117$	−1.40684	+	0.138562i	−0.130063	+	0.0128101i
$118$	−11.4141	−	2.54146i	−1.05076	−	0.233960i
$119$	0.675061	−	3.39376i	0.0618827	−	0.311106i
$120$	2.40230	−	1.71146i	0.219299	−	0.156234i
$121$	4.83160	−	0.961066i	0.439237	−	0.0873696i
$122$	−13.1979	−	13.8121i	−1.19488	−	1.25049i
$123$	−4.80999	−	1.45910i	−0.433703	−	0.131562i
$124$	−8.91885	+	12.1170i	−0.800936	+	1.08814i
$125$	−0.634393	−	0.773010i	−0.0567419	−	0.0691402i
$126$	−1.43566	+	0.108511i	−0.127899	+	0.00966691i
$127$	1.30781			0.116049			0.0580246	−	0.998315i	$-0.481520\pi$
$127$	1.30781			0.116049			0.0580246	+	0.998315i	$0.481520\pi$
$128$	5.70064	+	9.77255i	0.503870	+	0.863779i
$129$	−9.87380			−0.869339
$130$	1.04237	−	0.0787850i	0.0914220	−	0.00690990i
$131$	−3.18995	−	3.88697i	−0.278707	−	0.339606i	0.614776	−	0.788702i	$-0.289246\pi$
$131$	−3.18995	−	3.88697i	−0.278707	−	0.339606i	−0.893484	+	0.449096i	$0.851746\pi$
$132$	6.70337	+	4.93408i	0.583453	+	0.429457i
$133$	−3.43182	−	1.04103i	−0.297577	−	0.0902689i
$134$	11.7031	+	12.2478i	1.01100	+	1.05805i
$135$	−5.02450	+	0.999435i	−0.432440	+	0.0860177i
$136$	18.1316	+	3.04493i	1.55478	+	0.261100i
$137$	−2.02401	+	10.1754i	−0.172923	+	0.869341i	0.792744	+	0.609555i	$0.208652\pi$
$137$	−2.02401	+	10.1754i	−0.172923	+	0.869341i	−0.965666	+	0.259786i	$0.916348\pi$
$138$	−7.57900	−	1.68753i	−0.645168	−	0.143652i
$139$	13.3520	−	1.31506i	1.13250	−	0.111542i	0.485648	−	0.874154i	$-0.338584\pi$
$139$	13.3520	−	1.31506i	1.13250	−	0.111542i	0.646856	+	0.762612i	$0.276084\pi$
$140$	1.06317	−	0.0560845i	0.0898542	−	0.00474001i
$141$	−1.32633	−	4.37231i	−0.111697	−	0.368215i
$142$	16.9788	−	4.73174i	1.42483	−	0.397079i
$143$	1.12886	+	2.72531i	0.0944002	+	0.227902i
$144$	−0.804862	−	7.60748i	−0.0670718	−	0.633956i
$145$	1.09322	−	2.63926i	0.0907868	−	0.219179i
$146$	1.84776	−	15.2075i	0.152922	−	1.25858i
$147$	−6.17731	−	3.30184i	−0.509496	−	0.272331i
$148$	−0.685433	−	0.917248i	−0.0563422	−	0.0753973i
$149$	−5.80519	−	4.76419i	−0.475579	−	0.390298i	0.365842	−	0.930677i	$-0.380781\pi$
$149$	−5.80519	−	4.76419i	−0.475579	−	0.390298i	−0.841422	+	0.540379i	$0.818281\pi$
$150$	1.45263	−	0.254761i	0.118607	−	0.0208012i
$151$	5.76297	+	8.62489i	0.468984	+	0.701884i	0.988270	−	0.152717i	$-0.0488022\pi$
$151$	5.76297	+	8.62489i	0.468984	+	0.701884i	−0.519286	+	0.854600i	$0.673802\pi$
$152$	4.98253	−	18.3920i	0.404136	−	1.49179i
$153$	−10.3365	−	6.90666i	−0.835660	−	0.558370i
$154$	1.08631	+	2.80106i	0.0875373	+	0.225716i
$155$	−6.63448	+	3.54620i	−0.532894	+	0.284838i
$156$	−0.654106	+	1.39603i	−0.0523704	+	0.111772i
$157$	−0.976107	+	9.91058i	−0.0779018	+	0.790950i	0.874281	+	0.485421i	$0.161334\pi$
$157$	−0.976107	+	9.91058i	−0.0779018	+	0.790950i	−0.952183	+	0.305530i	$0.901166\pi$
$158$	−5.96324	−	11.7938i	−0.474410	−	0.938263i
$159$	6.39153	−	6.39153i	0.506881	−	0.506881i
$160$	0.467125	+	5.63753i	0.0369295	+	0.445686i
$161$	−1.98174	−	1.98174i	−0.156183	−	0.156183i
$162$	−0.174288	+	0.530796i	−0.0136933	+	0.0417033i
$163$	18.3528	+	1.80759i	1.43750	+	0.141581i	0.786544	−	0.617534i	$-0.211868\pi$
$163$	18.3528	+	1.80759i	1.43750	+	0.141581i	0.650956	+	0.759116i	$0.274368\pi$
$164$	7.11923	−	6.49954i	0.555918	−	0.507528i
$165$	1.96183	+	3.67033i	0.152728	+	0.285734i
$166$	19.1892	+	8.46451i	1.48937	+	0.656973i
$167$	−3.67203	+	5.49558i	−0.284150	+	0.425261i	−0.945897	−	0.324466i	$-0.894815\pi$
$167$	−3.67203	+	5.49558i	−0.284150	+	0.425261i	0.661747	+	0.749727i	$0.269815\pi$
$168$	−0.698336	+	1.40630i	−0.0538778	+	0.108498i
$169$	10.3548	−	6.91886i	0.796524	−	0.532220i
$170$	7.52543	+	5.27968i	0.577174	+	0.404933i
$171$	−8.17373	+	9.95972i	−0.625061	+	0.761638i
$172$	9.67644	−	16.2773i	0.737821	−	1.24114i
$173$	7.02091	−	13.1352i	0.533790	−	0.998651i	−0.460057	−	0.887890i	$-0.652171\pi$
$173$	7.02091	−	13.1352i	0.533790	−	0.998651i	0.993847	−	0.110762i	$-0.0353291\pi$
$174$	2.59802	+	3.31668i	0.196956	+	0.251437i
$175$	0.491803	+	0.203711i	0.0371768	+	0.0153991i
$176$	−14.7034	+	6.21530i	−1.10831	+	0.468496i
$177$	7.96651	−	3.29984i	0.598800	−	0.248031i
$178$	−7.57798	−	4.27479i	−0.567993	−	0.320409i
$179$	−6.40646	+	1.94338i	−0.478842	+	0.145255i	−0.520473	−	0.853878i	$-0.674244\pi$
$179$	−6.40646	+	1.94338i	−0.478842	+	0.145255i	0.0416316	+	0.999133i	$0.486744\pi$
$180$	1.27556	−	3.60601i	0.0950748	−	0.268776i
$181$	0.869814	+	8.83137i	0.0646528	+	0.656430i	0.971830	+	0.235682i	$0.0757324\pi$
$181$	0.869814	+	8.83137i	0.0646528	+	0.656430i	−0.907177	+	0.420748i	$0.861768\pi$
$182$	−0.469590	+	0.298555i	−0.0348083	+	0.0221304i
$183$	13.8165	+	2.74827i	1.02135	+	0.203158i
$184$	10.2095	−	10.8405i	0.752653	−	0.799171i
$185$	−0.111695	−	0.561529i	−0.00821198	−	0.0412844i
$186$	0.252221	−	11.0917i	0.0184937	−	0.813282i
$187$	−7.53030	+	24.8241i	−0.550670	+	1.81532i
$188$	8.50775	+	2.09842i	0.620491	+	0.153043i
$189$	2.10805	−	1.73003i	0.153338	−	0.125841i
$190$	6.21005	−	7.22554i	0.450524	−	0.524196i
$191$		−	14.3238i		−	1.03643i	−0.855250	−	0.518216i	$-0.826596\pi$
$191$		−	14.3238i		−	1.03643i	0.855250	−	0.518216i	$-0.173404\pi$
$192$	−7.57998	−	3.48495i	−0.547038	−	0.251505i
$193$		−	21.5180i		−	1.54890i	−0.632636	−	0.774449i	$-0.718027\pi$
$193$		−	21.5180i		−	1.54890i	0.632636	−	0.774449i	$-0.281973\pi$
$194$	4.35486	+	3.74281i	0.312660	+	0.268718i
$195$	−0.595865	+	0.489013i	−0.0426707	+	0.0350190i
$196$	11.4970	−	6.94770i	0.821218	−	0.496264i
$197$	−0.743232	+	2.45011i	−0.0529531	+	0.174563i	−0.979428	−	0.201793i	$-0.935323\pi$
$197$	−0.743232	+	2.45011i	−0.0529531	+	0.174563i	0.926475	+	0.376356i	$0.122823\pi$
$198$	10.7909	+	0.245381i	0.766875	+	0.0174385i
$199$	1.32753	+	6.67395i	0.0941062	+	0.473104i	0.998884	+	0.0472208i	$0.0150364\pi$
$199$	1.32753	+	6.67395i	0.0941062	+	0.473104i	−0.904778	+	0.425883i	$0.859964\pi$
$200$	−1.00361	+	2.64438i	−0.0709659	+	0.186986i
$201$	−12.2517	−	2.43701i	−0.864167	−	0.171893i
$202$	−11.7842	−	18.5350i	−0.829130	−	1.30412i
$203$	0.149054	+	1.51338i	0.0104616	+	0.106218i
$204$	−12.2348	+	5.84085i	−0.856606	+	0.408941i
$205$	4.61240	−	1.39916i	0.322144	−	0.0977213i
$206$	4.73376	−	8.39160i	0.329817	−	0.584671i
$207$	−9.30249	+	3.85322i	−0.646568	+	0.267817i
$208$	−1.66038	−	2.44645i	−0.115127	−	0.169630i
$209$	24.8391	+	10.2887i	1.71816	+	0.711684i
$210$	−0.618033	+	0.484118i	−0.0426484	+	0.0334073i
$211$	−2.75990	+	5.16341i	−0.189999	+	0.355464i	−0.958826	−	0.283993i	$-0.908341\pi$
$211$	−2.75990	+	5.16341i	−0.189999	+	0.355464i	0.768827	+	0.639457i	$0.220841\pi$
$212$	4.27292	+	16.8005i	0.293465	+	1.15386i
$213$	−8.24539	+	10.0470i	−0.564965	+	0.688411i
$214$	−4.13290	+	5.89086i	−0.282519	+	0.402691i
$215$	7.87250	−	5.26024i	0.536900	−	0.358745i
$216$	9.52375	+	10.9204i	0.648009	+	0.743036i
$217$	2.22481	−	3.32966i	0.151030	−	0.226032i
$218$	7.11168	−	16.1223i	0.481664	−	1.09194i
$219$	5.32512	+	9.96260i	0.359838	+	0.673210i
$220$	−7.97329	−	0.362807i	−0.537559	−	0.0244605i
$221$	−4.78167	−	0.470953i	−0.321650	−	0.0316797i
$222$	0.802228	+	0.263412i	0.0538420	+	0.0176791i
$223$	−6.36213	−	6.36213i	−0.426039	−	0.426039i	0.461237	−	0.887277i	$-0.347406\pi$
$223$	−6.36213	−	6.36213i	−0.426039	−	0.426039i	−0.887277	+	0.461237i	$0.847406\pi$
$224$	−1.63396	−	2.52942i	−0.109173	−	0.169004i
$225$	1.35233	−	1.35233i	0.0901553	−	0.0901553i
$226$	−23.7792	+	12.0234i	−1.58177	+	0.799785i
$227$	2.23497	−	22.6921i	0.148340	−	1.50613i	−0.576437	−	0.817142i	$-0.695557\pi$
$227$	2.23497	−	22.6921i	0.148340	−	1.50613i	0.724777	−	0.688983i	$-0.241943\pi$
$228$	4.78150	+	13.2126i	0.316662	+	0.875024i
$229$	−21.9725	+	11.7445i	−1.45198	+	0.776100i	−0.993632	−	0.112673i	$-0.964059\pi$
$229$	−21.9725	+	11.7445i	−1.45198	+	0.776100i	−0.458348	+	0.888773i	$0.651559\pi$
$230$	6.94186	−	2.69220i	0.457733	−	0.177518i
$231$	−1.84203	−	1.23081i	−0.121197	−	0.0809811i
$232$	−8.01377	+	1.03256i	−0.526130	+	0.0677910i
$233$	−0.834537	−	1.24897i	−0.0546723	−	0.0818229i	0.803126	−	0.595809i	$-0.203168\pi$
$233$	−0.834537	−	1.24897i	−0.0546723	−	0.0818229i	−0.857799	+	0.513986i	$0.828168\pi$
$234$	0.345348	+	1.96915i	0.0225761	+	0.128727i
$235$	3.38683	+	2.77950i	0.220933	+	0.181315i
$236$	−2.36736	+	16.3670i	−0.154102	+	1.06540i
$237$	8.59452	+	4.59387i	0.558274	+	0.298404i
$238$	−4.85780	−	0.590238i	−0.314885	−	0.0382595i
$239$	5.57521	−	13.4597i	0.360630	−	0.870638i	−0.634578	−	0.772859i	$-0.718826\pi$
$239$	5.57521	−	13.4597i	0.360630	−	0.870638i	0.995208	−	0.0977794i	$-0.0311740\pi$
$240$	−2.66953	−	3.20528i	−0.172318	−	0.206900i
$241$	2.99072	+	7.22025i	0.192649	+	0.465097i	0.990458	−	0.137814i	$-0.0440075\pi$
$241$	2.99072	+	7.22025i	0.192649	+	0.465097i	−0.797809	+	0.602911i	$0.794008\pi$
$242$	−1.87027	−	6.71105i	−0.120225	−	0.431403i
$243$	−4.58092	−	15.1013i	−0.293866	−	0.968747i
$244$	−18.0710	+	20.0837i	−1.15688	+	1.28573i
$245$	6.68429	−	0.658345i	0.427044	−	0.0420601i
$246$	−1.54493	+	6.93853i	−0.0985010	+	0.442385i
$247$	−0.971502	+	4.88407i	−0.0618152	+	0.310766i
$248$	18.0379	+	11.2858i	1.14541	+	0.716648i
$249$	−15.1684	+	3.01719i	−0.961260	+	0.191206i
$250$	−1.02248	+	0.977008i	−0.0646670	+	0.0617914i
$251$	11.3336	+	3.43800i	0.715367	+	0.217004i	0.626928	−	0.779077i	$-0.284312\pi$
$251$	11.3336	+	3.43800i	0.715367	+	0.217004i	0.0884394	+	0.996082i	$0.471812\pi$
$252$	0.306042	+	2.01299i	0.0192788	+	0.126806i
$253$	13.3291	+	16.2416i	0.837995	+	1.02110i
$254$	−0.139394	−	1.84426i	−0.00874634	−	0.115719i
$255$	−6.77874			−0.424501
$256$	13.1736	−	9.08061i	0.823347	−	0.567538i
$257$	−15.8652			−0.989645			−0.494823	−	0.868994i	$-0.664767\pi$
$257$	−15.8652			−0.989645			−0.494823	+	0.868994i	$0.664767\pi$
$258$	1.05241	+	13.9239i	0.0655200	+	0.866867i
$259$	0.193345	+	0.235591i	0.0120139	+	0.0146389i
$260$	−0.222204	−	1.46155i	−0.0137805	−	0.0906412i
$261$	5.22817	+	1.58595i	0.323616	+	0.0981677i
$262$	−5.14137	+	4.91274i	−0.317635	+	0.303510i
$263$	−3.33454	+	0.663282i	−0.205617	+	0.0408997i	−0.296824	−	0.954932i	$-0.595927\pi$
$263$	−3.33454	+	0.663282i	−0.205617	+	0.0408997i	0.0912072	+	0.995832i	$0.470927\pi$
$264$	6.24352	−	9.97893i	0.384262	−	0.614161i
$265$	−1.69098	+	8.50112i	−0.103876	+	0.522219i
$266$	−1.10227	+	4.95048i	−0.0675845	+	0.303534i
$267$	6.38489	−	0.628857i	0.390749	−	0.0384854i
$268$	16.0243	−	17.8091i	0.978840	−	1.08786i
$269$	−1.05401	−	3.47459i	−0.0642639	−	0.211850i	0.918928	−	0.394426i	$-0.129056\pi$
$269$	−1.05401	−	3.47459i	−0.0642639	−	0.211850i	−0.983192	+	0.182576i	$0.941556\pi$
$270$	1.94494	+	6.97898i	0.118365	+	0.424727i
$271$	5.41921	+	13.0831i	0.329194	+	0.794744i	0.998653	+	0.0518950i	$0.0165261\pi$
$271$	5.41921	+	13.0831i	0.329194	+	0.794744i	−0.669459	+	0.742849i	$0.733474\pi$
$272$	2.36135	−	25.8936i	0.143178	−	1.57003i
$273$	0.157028	−	0.379100i	0.00950378	−	0.0229442i
$274$	14.5650	+	1.76969i	0.879901	+	0.106911i
$275$	−3.51955	−	1.88124i	−0.212237	−	0.113443i
$276$	−1.57193	+	10.8677i	−0.0946192	+	0.654159i
$277$	−24.7094	−	20.2785i	−1.48465	−	1.21842i	−0.919296	−	0.393566i	$-0.871241\pi$
$277$	−24.7094	−	20.2785i	−1.48465	−	1.21842i	−0.565350	−	0.824851i	$-0.691259\pi$
$278$	−3.27762	−	18.6887i	−0.196579	−	1.12088i
$279$	−7.99307	−	11.9625i	−0.478533	−	0.716175i
$280$	−0.192409	−	1.49329i	−0.0114986	−	0.0892414i
$281$	15.8181	+	10.5693i	0.943632	+	0.630514i	0.929277	−	0.369382i	$-0.120431\pi$
$281$	15.8181	+	10.5693i	0.943632	+	0.630514i	0.0143542	+	0.999897i	$0.495431\pi$
$282$	−6.02443	+	2.33640i	−0.358750	+	0.139131i
$283$	−8.90106	+	4.75771i	−0.529113	+	0.282817i	−0.714244	−	0.699897i	$-0.753229\pi$
$283$	−8.90106	+	4.75771i	−0.529113	+	0.282817i	0.185131	+	0.982714i	$0.440729\pi$
$284$	−8.48236	−	23.4391i	−0.503335	−	1.39085i
$285$	−0.688627	+	6.99174i	−0.0407907	+	0.414155i
$286$	3.72289	−	1.88239i	0.220139	−	0.111308i
$287$	−1.81427	+	1.81427i	−0.107093	+	0.107093i
$288$	−10.6422	+	1.94586i	−0.627098	+	0.114661i
$289$	−17.8569	−	17.8569i	−1.05041	−	1.05041i
$290$	−3.83839	−	1.26034i	−0.225398	−	0.0740096i
$291$	−4.21394	−	0.415037i	−0.247026	−	0.0243299i
$292$	−21.6424	−	0.984790i	−1.26653	−	0.0576305i
$293$	6.08207	+	11.3788i	0.355318	+	0.664754i	0.994550	−	0.104260i	$-0.0332476\pi$
$293$	6.08207	+	11.3788i	0.355318	+	0.664754i	−0.639232	+	0.769014i	$0.720748\pi$
$294$	−3.99781	+	9.06311i	−0.233157	+	0.528572i
$295$	−4.59382	+	6.87513i	−0.267462	+	0.400286i
$296$	−1.22044	+	1.06436i	−0.0709365	+	0.0618645i
$297$	−16.9990	+	11.3583i	−0.986380	+	0.659078i
$298$	−6.09967	+	8.69422i	−0.353345	+	0.503642i
$299$	−2.46882	+	3.00826i	−0.142775	+	0.173972i
$300$	−0.514092	−	2.02133i	−0.0296811	−	0.116702i
$301$	−2.37590	+	4.44500i	−0.136945	+	0.256206i
$302$	11.5485	−	9.04618i	0.664541	−	0.520549i
$303$	14.9633	+	6.19800i	0.859619	+	0.356066i
$304$	−26.4674	−	5.06599i	−1.51801	−	0.290554i
$305$	−12.4802	+	5.16947i	−0.714614	+	0.296003i
$306$	−8.63798	+	15.3127i	−0.493801	+	0.875367i
$307$	−21.8286	+	6.62164i	−1.24583	+	0.377917i	−0.843276	−	0.537481i	$-0.819376\pi$
$307$	−21.8286	+	6.62164i	−1.24583	+	0.377917i	−0.402550	+	0.915398i	$0.631876\pi$
$308$	3.83424	−	1.83046i	0.218476	−	0.104300i
$309$	0.696375	+	7.07041i	0.0396154	+	0.402222i
$310$	5.70797	+	8.97791i	0.324191	+	0.509911i
$311$	−9.64289	−	1.91809i	−0.546798	−	0.108765i	−0.0860418	−	0.996292i	$-0.527422\pi$
$311$	−9.64289	−	1.91809i	−0.546798	−	0.108765i	−0.460756	+	0.887527i	$0.652422\pi$
$312$	2.03839	+	0.773618i	0.115401	+	0.0437975i
$313$	−0.313435	−	1.57574i	−0.0177164	−	0.0890663i	0.970916	−	0.239422i	$-0.0769580\pi$
$313$	−0.313435	−	1.57574i	−0.0177164	−	0.0890663i	−0.988632	+	0.150356i	$0.951958\pi$
$314$	14.0799	+	0.320171i	0.794572	+	0.0180683i
$315$	−0.295527	+	0.974223i	−0.0166511	+	0.0548913i
$316$	−15.9959	+	9.66636i	−0.899840	+	0.543775i
$317$	−7.40186	+	6.07455i	−0.415730	+	0.341181i	−0.818892	−	0.573948i	$-0.805411\pi$
$317$	−7.40186	+	6.07455i	−0.415730	+	0.341181i	0.403162	+	0.915129i	$0.367911\pi$
$318$	−9.69453	−	8.33204i	−0.543642	−	0.467237i
$319$		−	11.4005i		−	0.638306i
$320$	7.90021	−	1.25962i	0.441635	−	0.0704147i
$321$		−	5.30636i		−	0.296172i
$322$	−2.58341	+	3.00586i	−0.143968	+	0.167510i
$323$	−33.8517	+	27.7814i	−1.88356	+	1.54580i
$324$	0.767100	+	0.189203i	0.0426167	+	0.0105113i
$325$	0.214570	−	0.707342i	0.0119022	−	0.0392363i
$326$	0.592904	−	26.0736i	0.0328379	−	1.44408i
$327$	2.53497	+	12.7441i	0.140184	+	0.704753i
$328$	−9.92440	−	9.34672i	−0.547983	−	0.516086i
$329$	−2.28749	−	0.455009i	−0.126113	−	0.0250855i
$330$	4.96676	−	3.15776i	0.273411	−	0.173829i
$331$	−0.245114	−	2.48868i	−0.0134727	−	0.136790i	0.986095	−	0.166181i	$-0.0531434\pi$
$331$	−0.245114	−	2.48868i	−0.0134727	−	0.136790i	−0.999568	+	0.0293902i	$0.990643\pi$
$332$	9.89128	−	27.9626i	0.542854	−	1.53465i
$333$	1.04781	−	0.317848i	0.0574194	−	0.0174180i
$334$	8.14121	+	4.59252i	0.445467	+	0.251291i
$335$	11.0667	−	4.58399i	0.604640	−	0.250450i
$336$	2.05758	+	0.834896i	0.112250	+	0.0455473i
$337$	−23.9239	−	9.90959i	−1.30322	−	0.539810i	−0.380319	−	0.924855i	$-0.624186\pi$
$337$	−23.9239	−	9.90959i	−1.30322	−	0.539810i	−0.922898	+	0.385045i	$0.874186\pi$
$338$	−10.8606	−	13.8648i	−0.590739	−	0.754146i
$339$	9.26239	−	17.3287i	0.503064	−	0.941167i
$340$	6.64325	−	11.1750i	0.360281	−	0.606051i
$341$	−19.0455	+	23.2070i	−1.03137	+	1.25673i
$342$	14.9163	+	10.4650i	0.806581	+	0.565880i
$343$	−6.07113	+	4.05660i	−0.327810	+	0.219036i
$344$	−23.9855	−	11.9107i	−1.29321	−	0.642181i
$345$	−3.05030	+	4.56510i	−0.164223	+	0.245777i
$346$	−19.2715	−	8.50081i	−1.03604	−	0.457006i
$347$	6.88181	+	12.8750i	0.369435	+	0.691164i	0.996110	−	0.0881166i	$-0.0280848\pi$
$347$	6.88181	+	12.8750i	0.369435	+	0.691164i	−0.626675	+	0.779280i	$0.715585\pi$
$348$	4.40024	−	4.01722i	0.235877	−	0.215346i
$349$	11.8524	+	1.16736i	0.634444	+	0.0624872i	0.410126	−	0.912029i	$-0.365485\pi$
$349$	11.8524	+	1.16736i	0.634444	+	0.0624872i	0.224318	+	0.974516i	$0.427985\pi$
$350$	0.234853	−	0.715249i	0.0125534	−	0.0382317i
$351$	−2.67762	−	2.67762i	−0.142921	−	0.142921i
$352$	10.3319	+	20.0722i	0.550694	+	1.06985i
$353$	16.4417	−	16.4417i	0.875103	−	0.875103i	−0.117920	−	0.993023i	$-0.537623\pi$
$353$	16.4417	−	16.4417i	0.875103	−	0.875103i	0.993023	+	0.117920i	$0.0376228\pi$
$354$	−5.50252	−	10.8826i	−0.292455	−	0.578403i
$355$	1.22162	−	12.4033i	0.0648369	−	0.658300i
$356$	−5.22057	+	11.1420i	−0.276690	+	0.590526i
$357$	3.18240	−	1.70103i	0.168431	−	0.0900280i
$358$	3.42337	+	8.82720i	0.180931	+	0.466532i
$359$	−18.6921	−	12.4897i	−0.986533	−	0.659180i	−0.0460206	−	0.998940i	$-0.514654\pi$
$359$	−18.6921	−	12.4897i	−0.986533	−	0.659180i	−0.940512	+	0.339760i	$0.889654\pi$
$360$	−5.22112	−	1.41444i	−0.275177	−	0.0745474i
$361$	14.6596	+	21.9397i	0.771558	+	1.15472i
$362$	12.3612	−	2.16790i	0.649691	−	0.113942i
$363$	3.97119	+	3.25907i	0.208433	+	0.171057i
$364$	0.471071	+	0.630389i	0.0246908	+	0.0330414i
$365$	−9.55333	−	5.10636i	−0.500044	−	0.267279i
$366$	2.40295	−	19.7768i	0.125604	−	1.03375i
$367$	−1.07935	+	2.60579i	−0.0563418	+	0.136021i	−0.949544	−	0.313635i	$-0.898453\pi$
$367$	−1.07935	+	2.60579i	−0.0563418	+	0.136021i	0.893202	+	0.449656i	$0.148453\pi$
$368$	−16.3753	−	13.2419i	−0.853624	−	0.690280i
$369$	3.52760	+	8.51638i	0.183639	+	0.443345i
$370$	−0.779958	+	0.217362i	−0.0405481	+	0.0113001i
$371$	−1.33937	−	4.41533i	−0.0695369	−	0.229232i
$372$	−15.6683	+	0.826537i	−0.812363	+	0.0428539i
$373$	−0.610250	+	0.0601043i	−0.0315975	+	0.00311208i	−0.113804	−	0.993503i	$-0.536303\pi$
$373$	−0.610250	+	0.0601043i	−0.0315975	+	0.00311208i	0.0822060	+	0.996615i	$0.473803\pi$
$374$	35.8093	+	7.97327i	1.85166	+	0.412288i
$375$	0.203448	−	1.02280i	0.0105060	−	0.0528173i
$376$	2.05236	−	12.2212i	0.105843	−	0.630261i
$377$	2.07103	−	0.411953i	0.106663	−	0.0212166i
$378$	−2.66436	−	2.78835i	−0.137040	−	0.143417i
$379$	20.9600	+	6.35814i	1.07664	+	0.326596i	0.778319	−	0.627869i	$-0.216073\pi$
$379$	20.9600	+	6.35814i	1.07664	+	0.326596i	0.298323	+	0.954465i	$0.403573\pi$
$380$	−10.8513	−	7.98722i	−0.556660	−	0.409736i
$381$	0.865208	+	1.05426i	0.0443259	+	0.0540113i
$382$	−20.1993	+	1.52671i	−1.03349	+	0.0781134i
$383$	15.1489			0.774071			0.387036	−	0.922065i	$-0.373499\pi$
$383$	15.1489			0.774071			0.387036	+	0.922065i	$0.373499\pi$
$384$	−4.10653	+	11.0607i	−0.209561	+	0.564438i
$385$	2.12438			0.108269
$386$	−30.3445	+	2.29351i	−1.54449	+	0.116737i
$387$	11.4874	+	13.9975i	0.583939	+	0.711531i
$388$	4.81392	−	6.54011i	0.244390	−	0.332024i
$389$	22.8665	+	6.93646i	1.15938	+	0.351693i	0.810649	−	0.585532i	$-0.199114\pi$
$389$	22.8665	+	6.93646i	1.15938	+	0.351693i	0.348726	+	0.937225i	$0.386614\pi$
$390$	0.753113	+	0.788161i	0.0381354	+	0.0399101i
$391$	−33.5654	+	6.67657i	−1.69747	+	0.337649i
$392$	−11.0230	−	15.4725i	−0.556746	−	0.781480i
$393$	1.02301	−	5.14301i	0.0516040	−	0.259431i
$394$	3.53434	+	0.786953i	0.178057	+	0.0396461i
$395$	−9.29988	+	0.915959i	−0.467928	+	0.0460869i
$396$	−0.804122	−	15.2434i	−0.0404086	−	0.766009i
$397$	8.47830	+	27.9492i	0.425513	+	1.40273i	0.863773	+	0.503881i	$0.168095\pi$
$397$	8.47830	+	27.9492i	0.425513	+	1.40273i	−0.438259	+	0.898849i	$0.644405\pi$
$398$	9.27005	−	2.58342i	0.464666	−	0.129495i
$399$	−1.43119	−	3.45520i	−0.0716491	−	0.172976i
$400$	3.83606	+	1.13343i	0.191803	+	0.0566713i
$401$	5.82601	−	14.0652i	0.290937	−	0.702384i	−0.709059	−	0.705149i	$-0.750880\pi$
$401$	5.82601	−	14.0652i	0.290937	−	0.702384i	0.999996	+	0.00276478i	$0.000880057\pi$
$402$	−2.13080	+	17.5370i	−0.106274	+	0.874664i
$403$	−4.90401	−	2.62125i	−0.244286	−	0.130574i
$404$	−24.8819	+	18.5935i	−1.23792	+	0.925060i
$405$	0.305374	+	0.250614i	0.0151741	+	0.0124531i
$406$	2.11826	−	0.371500i	0.105128	−	0.0184372i
$407$	−1.26939	−	1.89977i	−0.0629212	−	0.0941682i
$408$	9.54077	+	16.6308i	0.472339	+	0.823349i
$409$	−22.2351	−	14.8570i	−1.09946	−	0.734633i	−0.132911	−	0.991128i	$-0.542432\pi$
$409$	−22.2351	−	14.8570i	−1.09946	−	0.734633i	−0.966546	+	0.256495i	$0.917432\pi$
$410$	−2.46469	−	6.35523i	−0.121722	−	0.313863i
$411$	−9.54167	+	5.10013i	−0.470656	+	0.251571i
$412$	−12.3383	−	5.78109i	−0.607865	−	0.284814i
$413$	0.431432	−	4.38041i	0.0212294	−	0.215546i
$414$	6.42529	+	12.7076i	0.315786	+	0.624544i
$415$	10.4866	−	10.4866i	0.514766	−	0.514766i
$416$	−3.27298	+	2.60221i	−0.160471	+	0.127584i
$417$	9.89342	+	9.89342i	0.484483	+	0.484483i
$418$	11.8615	−	36.1245i	0.580167	−	1.76691i
$419$	−7.44623	−	0.733390i	−0.363772	−	0.0358285i	−0.0855200	−	0.996336i	$-0.527255\pi$
$419$	−7.44623	−	0.733390i	−0.363772	−	0.0358285i	−0.278252	+	0.960508i	$0.589755\pi$
$420$	0.748573	+	0.819945i	0.0365266	+	0.0400092i
$421$	−8.18252	−	15.3084i	−0.398792	−	0.746087i	0.599744	−	0.800192i	$-0.295269\pi$
$421$	−8.18252	−	15.3084i	−0.398792	−	0.746087i	−0.998535	+	0.0541055i	$0.982769\pi$
$422$	7.57557	+	3.34164i	0.368773	+	0.162669i
$423$	−4.65527	+	6.96711i	−0.226347	+	0.338752i
$424$	23.2364	−	7.81632i	1.12846	−	0.379594i
$425$	5.40478	−	3.61136i	0.262170	−	0.175177i
$426$	15.0471	+	10.5567i	0.729033	+	0.511474i
$427$	4.56185	−	5.55863i	0.220763	−	0.269001i
$428$	8.74775	+	5.20029i	0.422838	+	0.251366i
$429$	−1.45013	+	2.71299i	−0.0700127	+	0.130985i
$430$	−8.25704	−	10.5411i	−0.398190	−	0.508335i
$431$	16.4455	+	6.81195i	0.792152	+	0.328120i	0.741808	−	0.670612i	$-0.233968\pi$
$431$	16.4455	+	6.81195i	0.792152	+	0.328120i	0.0503434	+	0.998732i	$0.483968\pi$
$432$	14.3847	−	14.5943i	0.692084	−	0.702167i
$433$	5.94474	−	2.46239i	0.285686	−	0.118335i	−0.235239	−	0.971938i	$-0.575587\pi$
$433$	5.94474	−	2.46239i	0.285686	−	0.118335i	0.520925	+	0.853603i	$0.325587\pi$
$434$	−4.93258	−	2.78251i	−0.236772	−	0.133565i
$435$	2.85082	−	0.864787i	0.136686	−	0.0414634i
$436$	−23.4935	−	8.31042i	−1.12514	−	0.397997i
$437$	3.47658	+	35.2983i	0.166307	+	1.68855i
$438$	13.4816	−	8.57131i	0.644175	−	0.409553i
$439$	7.51875	+	1.49557i	0.358850	+	0.0713798i	0.371223	−	0.928544i	$-0.378938\pi$
$439$	7.51875	+	1.49557i	0.358850	+	0.0713798i	−0.0123728	+	0.999923i	$0.503938\pi$
$440$	0.338212	+	11.2825i	0.0161236	+	0.537874i
$441$	2.50602	+	12.5986i	0.119334	+	0.599935i
$442$	−0.154476	+	6.79326i	−0.00734769	+	0.323123i
$443$	3.80608	−	12.5469i	0.180832	−	0.596123i	−0.818921	−	0.573906i	$-0.805427\pi$
$443$	3.80608	−	12.5469i	0.180832	−	0.596123i	0.999753	−	0.0222173i	$-0.00707258\pi$
$444$	0.285956	−	1.15937i	0.0135709	−	0.0550213i
$445$	−4.75573	+	3.90293i	−0.225443	+	0.185016i
$446$	−8.29370	+	9.64993i	−0.392718	+	0.456937i
$447$		−	7.83157i		−	0.370420i
$448$	−3.39281	+	2.57379i	−0.160295	+	0.121600i
$449$		−	5.11657i		−	0.241466i	−0.992685	−	0.120733i	$-0.961476\pi$
$449$		−	5.11657i		−	0.241466i	0.992685	−	0.120733i	$-0.0385245\pi$
$450$	−2.05118	−	1.76291i	−0.0966937	−	0.0831041i
$451$	14.8691	−	12.2027i	0.700158	−	0.574605i
$452$	19.4898	+	32.2518i	0.916724	+	1.51700i
$453$	−3.14014	+	10.3517i	−0.147537	+	0.486363i
$454$	−32.2384	−	0.733089i	−1.51302	−	0.0344056i
$455$	0.0767637	+	0.385917i	0.00359874	+	0.0180921i
$456$	18.1226	−	8.15110i	0.848669	−	0.381710i
$457$	22.4447	+	4.46453i	1.04992	+	0.208842i	0.689752	−	0.724046i	$-0.257720\pi$
$457$	22.4447	+	4.46453i	1.04992	+	0.208842i	0.360167	+	0.932888i	$0.382720\pi$
$458$	18.9040	+	29.7336i	0.883325	+	1.38936i
$459$	−3.26402	−	33.1401i	−0.152351	−	1.54685i
$460$	−4.53642	−	9.50240i	−0.211512	−	0.443052i
$461$	27.3277	−	8.28975i	1.27278	−	0.386092i	0.419597	−	0.907711i	$-0.362171\pi$
$461$	27.3277	−	8.28975i	1.27278	−	0.386092i	0.853179	+	0.521618i	$0.174671\pi$
$462$	−1.53934	+	2.72880i	−0.0716165	+	0.126955i
$463$	27.3252	−	11.3185i	1.26991	−	0.526014i	0.356973	−	0.934115i	$-0.383809\pi$
$463$	27.3252	−	11.3185i	1.26991	−	0.526014i	0.912937	+	0.408101i	$0.133809\pi$
$464$	2.31026	+	11.1909i	0.107251	+	0.519524i
$465$	−7.24787	−	3.00217i	−0.336112	−	0.139222i
$466$	−1.67234	+	1.30998i	−0.0774697	+	0.0606836i
$467$	−4.16188	+	7.78632i	−0.192589	+	0.360308i	−0.959619	−	0.281303i	$-0.909233\pi$
$467$	−4.16188	+	7.78632i	−0.192589	+	0.360308i	0.767030	+	0.641611i	$0.221733\pi$
$468$	2.74007	−	0.696891i	0.126660	−	0.0322138i
$469$	−4.04518	+	4.92907i	−0.186789	+	0.227603i
$470$	3.55864	−	5.07234i	0.164148	−	0.233970i
$471$	−8.63495	+	5.76969i	−0.397877	+	0.265853i
$472$	23.3329	+	1.59394i	1.07398	+	0.0733672i
$473$	20.9924	−	31.4174i	0.965232	−	1.44457i
$474$	5.56218	−	12.6096i	0.255479	−	0.579176i
$475$	−3.17578	−	5.94147i	−0.145715	−	0.272613i
$476$	−0.314576	+	6.91334i	−0.0144186	+	0.316873i
$477$	−16.4969	−	1.62481i	−0.755343	−	0.0743948i
$478$	−19.5750	−	6.42749i	−0.895342	−	0.293987i
$479$	−24.3323	−	24.3323i	−1.11177	−	1.11177i	−0.992911	−	0.118858i	$-0.962077\pi$
$479$	−24.3323	−	24.3323i	−1.11177	−	1.11177i	−0.118858	−	0.992911i	$-0.537923\pi$
$480$	−4.23553	+	4.10619i	−0.193325	+	0.187421i
$481$	0.299245	−	0.299245i	0.0136444	−	0.0136444i
$482$	9.86316	−	4.98707i	0.449255	−	0.227155i
$483$	0.286472	−	2.90860i	0.0130349	−	0.132346i
$484$	−9.26452	+	3.35274i	−0.421115	+	0.152397i
$485$	3.58094	−	1.91405i	0.162602	−	0.0869126i
$486$	−20.8074	+	8.06955i	−0.943843	+	0.366042i
$487$	16.5938	+	11.0876i	0.751935	+	0.502427i	0.871498	−	0.490400i	$-0.163149\pi$
$487$	16.5938	+	11.0876i	0.751935	+	0.502427i	−0.119563	+	0.992827i	$0.538149\pi$
$488$	30.2480	+	23.3429i	1.36926	+	1.05668i
$489$	10.6845	+	15.9905i	0.483170	+	0.723115i
$490$	−1.64084	−	9.35596i	−0.0741257	−	0.422659i
$491$	−10.2101	−	8.37922i	−0.460776	−	0.378149i	0.375174	−	0.926954i	$-0.377583\pi$
$491$	−10.2101	−	8.37922i	−0.460776	−	0.378149i	−0.835950	+	0.548805i	$0.815083\pi$
$492$	9.94932	+	1.43909i	0.448550	+	0.0648794i
$493$	16.3768	+	8.75357i	0.737573	+	0.394241i
$494$	6.99102	+	0.849432i	0.314541	+	0.0382177i
$495$	2.92075	−	7.05131i	0.131278	−	0.316933i
$496$	13.9925	−	26.6398i	0.628283	−	1.19616i
$497$	2.53893	+	6.12951i	0.113886	+	0.274946i
$498$	5.87155	+	21.0688i	0.263110	+	0.944115i
$499$	−2.40527	−	7.92912i	−0.107675	−	0.354956i	0.886501	−	0.462727i	$-0.153129\pi$
$499$	−2.40527	−	7.92912i	−0.107675	−	0.354956i	−0.994176	+	0.107770i	$0.965629\pi$
$500$	1.48675	+	1.33775i	0.0664894	+	0.0598260i
$501$	−6.85945	+	0.675596i	−0.306457	+	0.0301834i
$502$	3.64024	−	16.3489i	0.162472	−	0.729688i
$503$	3.89332	−	19.5730i	0.173594	−	0.872718i	−0.791571	−	0.611077i	$-0.790737\pi$
$503$	3.89332	−	19.5730i	0.173594	−	0.872718i	0.965165	−	0.261641i	$-0.0842635\pi$
$504$	2.80608	−	0.646134i	0.124993	−	0.0287811i
$505$	−15.2324	+	3.02991i	−0.677833	+	0.134829i
$506$	21.4831	−	20.5277i	0.955038	−	0.912570i
$507$	12.4279	+	3.76997i	0.551944	+	0.167430i
$508$	−2.58590	+	0.393143i	−0.114731	+	0.0174429i
$509$	18.3354	+	22.3417i	0.812701	+	0.990278i	0.999968	+	0.00796952i	$0.00253680\pi$
$509$	18.3354	+	22.3417i	0.812701	+	0.990278i	−0.187268	+	0.982309i	$0.559963\pi$
$510$	0.722518	+	9.55933i	0.0319936	+	0.423294i
$511$	5.76635			0.255088
$512$	−14.2095	−	17.6094i	−0.627977	−	0.778232i
$513$	−34.5130			−1.52379
$514$	1.69101	+	22.3730i	0.0745871	+	0.986830i
$515$	−4.32197	−	5.26634i	−0.190449	−	0.232063i
$516$	19.5233	−	2.96819i	0.859463	−	0.130667i
$517$	16.7321	+	5.07563i	0.735877	+	0.223226i
$518$	0.311621	−	0.297764i	0.0136918	−	0.0130830i
$519$	15.2335	−	3.03013i	0.668675	−	0.133008i
$520$	−2.03737	+	0.469130i	−0.0893448	+	0.0205727i
$521$	−3.06656	+	15.4166i	−0.134348	+	0.675415i	0.853637	+	0.520868i	$0.174392\pi$
$521$	−3.06656	+	15.4166i	−0.134348	+	0.675415i	−0.987986	+	0.154547i	$0.950608\pi$
$522$	1.67924	−	7.54176i	0.0734984	−	0.330094i
$523$	−1.99504	+	0.196495i	−0.0872372	+	0.00859212i	−0.141542	−	0.989932i	$-0.545206\pi$
$523$	−1.99504	+	0.196495i	−0.0872372	+	0.00859212i	0.0543043	+	0.998524i	$0.482706\pi$
$524$	7.47590	+	6.72668i	0.326586	+	0.293856i
$525$	0.161145	+	0.531225i	0.00703296	+	0.0231846i
$526$	1.29077	+	4.63165i	0.0562802	+	0.201949i
$527$	−18.7132	−	45.1777i	−0.815160	−	1.96797i
$528$	−14.7377	−	7.74094i	−0.641375	−	0.336881i
$529$	−1.80576	+	4.35950i	−0.0785115	+	0.189544i
$530$	12.1684	+	1.47850i	0.528563	+	0.0642221i
$531$	−13.9464	−	7.45451i	−0.605223	−	0.323498i
$532$	7.09861	+	1.02676i	0.307764	+	0.0445157i
$533$	2.75405	+	2.26019i	0.119291	+	0.0978996i
$534$	−1.56735	−	8.93689i	−0.0678257	−	0.386737i
$535$	2.82695	+	4.23083i	0.122220	+	0.182915i
$536$	−26.8222	−	20.6991i	−1.15854	−	0.894066i
$537$	−5.80494	−	3.87874i	−0.250502	−	0.167380i
$538$	−4.78750	+	1.85669i	−0.206404	+	0.0800477i
$539$	23.6395	−	12.6356i	1.01823	−	0.544253i
$540$	9.63440	−	3.48659i	0.414598	−	0.150039i
$541$	4.43816	−	45.0613i	0.190811	−	1.93734i	−0.132788	−	0.991144i	$-0.542393\pi$
$541$	4.43816	−	45.0613i	0.190811	−	1.93734i	0.323599	−	0.946194i	$-0.395107\pi$
$542$	17.8721	−	9.03661i	0.767673	−	0.388155i
$543$	−6.54376	+	6.54376i	−0.280820	+	0.280820i
$544$	−36.7667	−	0.570069i	−1.57636	−	0.0244415i
$545$	−8.81057	−	8.81057i	−0.377403	−	0.377403i
$546$	−0.551340	−	0.181033i	−0.0235952	−	0.00774751i
$547$	35.5384	+	3.50022i	1.51951	+	0.149659i	0.823064	−	0.567949i	$-0.192263\pi$
$547$	35.5384	+	3.50022i	1.51951	+	0.149659i	0.696447	+	0.717608i	$0.254763\pi$
$548$	0.943182	−	20.7280i	0.0402907	−	0.885456i
$549$	−12.1784	−	22.7842i	−0.519762	−	0.972406i
$550$	−2.27777	+	5.16375i	−0.0971245	+	0.220183i
$551$	10.6923	−	16.0021i	0.455506	−	0.681713i
$552$	15.4931	+	1.05838i	0.659430	+	0.0450477i
$553$	4.13615	−	2.76369i	0.175887	−	0.117524i
$554$	−25.9629	+	37.0064i	−1.10306	+	1.57225i
$555$	0.378769	−	0.461532i	0.0160779	−	0.0195909i
$556$	−26.0054	+	6.61403i	−1.10287	+	0.280497i
$557$	10.6759	−	19.9733i	0.452353	−	0.846294i	−0.547601	−	0.836740i	$-0.684459\pi$
$557$	10.6759	−	19.9733i	0.452353	−	0.846294i	0.999954	−	0.00955415i	$-0.00304123\pi$
$558$	−16.0174	+	12.5468i	−0.678072	+	0.531148i
$559$	6.46585	+	2.67824i	0.273477	+	0.113278i
$560$	−2.08532	+	0.430497i	−0.0881210	+	0.0181918i
$561$	−24.9932	+	10.3525i	−1.05521	+	0.437084i
$562$	13.2188	−	23.4332i	0.557602	−	0.988468i
$563$	−30.7798	+	9.33694i	−1.29721	+	0.393505i	−0.862039	−	0.506842i	$-0.830813\pi$
$563$	−30.7798	+	9.33694i	−1.29721	+	0.393505i	−0.435173	+	0.900347i	$0.643313\pi$
$564$	3.93689	+	8.24657i	0.165773	+	0.347243i
$565$	1.84680	+	18.7509i	0.0776956	+	0.788857i
$566$	7.65801	+	12.0451i	0.321890	+	0.506293i
$567$	−0.206251	−	0.0410259i	−0.00866173	−	0.00172292i
$568$	−32.1495	+	14.4600i	−1.34896	+	0.606729i
$569$	4.51678	+	22.7074i	0.189353	+	0.951944i	0.952226	+	0.305395i	$0.0987884\pi$
$569$	4.51678	+	22.7074i	0.189353	+	0.951944i	−0.762872	+	0.646549i	$0.776212\pi$
$570$	9.93309	+	0.225875i	0.416051	+	0.00946086i
$571$	2.16499	−	7.13701i	0.0906019	−	0.298674i	−0.899915	−	0.436065i	$-0.856372\pi$
$571$	2.16499	−	7.13701i	0.0906019	−	0.298674i	0.990517	+	0.137391i	$0.0438717\pi$
$572$	−3.05134	−	5.04936i	−0.127583	−	0.211124i
$573$	11.5468	−	9.47620i	0.482374	−	0.395874i
$574$	2.75185	+	2.36510i	0.114860	+	0.0987172i
$575$		−	5.26485i		−	0.219560i
$576$	3.87834	+	14.8002i	0.161597	+	0.616673i
$577$			12.5400i			0.522047i	0.965332	+	0.261024i	$0.0840601\pi$
$577$			12.5400i			0.522047i	−0.965332	+	0.261024i	$0.915940\pi$
$578$	−23.2784	+	27.0850i	−0.968253	+	1.12659i
$579$	17.3462	−	14.2357i	0.720884	−	0.591614i
$580$	−1.36820	+	5.54719i	−0.0568115	+	0.230335i
$581$	−2.29165	+	7.55456i	−0.0950737	+	0.313416i
$582$	−0.136135	+	5.98670i	−0.00564300	+	0.248157i
$583$	6.74830	+	33.9260i	0.279486	+	1.40507i
$584$	0.918031	+	30.6249i	0.0379884	+	1.26727i
$585$	1.38649	+	0.275790i	0.0573242	+	0.0114025i
$586$	15.3980	−	9.78969i	0.636084	−	0.404408i
$587$	−1.82984	−	18.5786i	−0.0755254	−	0.766822i	−0.956125	−	0.292960i	$-0.905360\pi$
$587$	−1.82984	−	18.5786i	−0.0755254	−	0.766822i	0.880599	−	0.473862i	$-0.157140\pi$
$588$	13.2068	+	4.67168i	0.544641	+	0.192657i
$589$	−48.4982	+	14.7118i	−1.99833	+	0.606188i
$590$	10.1849	+	5.74537i	0.419305	+	0.236533i
$591$	−2.46680	+	1.02178i	−0.101471	+	0.0420305i
$592$	1.63103	+	1.60761i	0.0670348	+	0.0660722i
$593$	11.8545	+	4.91031i	0.486807	+	0.201642i	0.612567	−	0.790419i	$-0.290137\pi$
$593$	11.8545	+	4.91031i	0.486807	+	0.201642i	−0.125760	+	0.992061i	$0.540137\pi$
$594$	17.8293	+	22.7611i	0.731544	+	0.933901i
$595$	−1.63115	+	3.05167i	−0.0668706	+	0.125106i
$596$	12.9106	+	7.67503i	0.528841	+	0.314381i
$597$	−4.50179	+	5.48545i	−0.184246	+	0.224504i
$598$	4.50537	+	3.16087i	0.184238	+	0.129258i
$599$	31.0032	−	20.7157i	1.26676	−	0.846420i	0.273446	−	0.961887i	$-0.411837\pi$
$599$	31.0032	−	20.7157i	1.26676	−	0.846420i	0.993311	+	0.115468i	$0.0368367\pi$
$600$	−2.79567	+	0.940412i	−0.114133	+	0.0383922i
$601$	7.18889	−	10.7589i	0.293241	−	0.438866i	−0.655371	−	0.755307i	$-0.727488\pi$
$601$	7.18889	−	10.7589i	0.293241	−	0.438866i	0.948612	+	0.316441i	$0.102488\pi$
$602$	6.52154	+	2.87670i	0.265798	+	0.117246i
$603$	10.7991	+	20.2037i	0.439774	+	0.822759i
$604$	−13.9877	−	15.3214i	−0.569153	−	0.623419i
$605$	−4.90254	−	0.482858i	−0.199317	−	0.0196310i
$606$	7.14549	−	21.7617i	0.290266	−	0.884010i
$607$	−4.21430	−	4.21430i	−0.171053	−	0.171053i	0.616389	−	0.787442i	$-0.288595\pi$
$607$	−4.21430	−	4.21430i	−0.171053	−	0.171053i	−0.787442	+	0.616389i	$0.788595\pi$
$608$	−4.32296	+	37.8640i	−0.175319	+	1.53559i
$609$	−1.12136	+	1.12136i	−0.0454399	+	0.0454399i
$610$	8.62015	+	17.0485i	0.349020	+	0.690273i
$611$	−0.317435	+	3.22297i	−0.0128420	+	0.130387i
$612$	22.5145	+	10.5491i	0.910093	+	0.426422i
$613$	37.8240	−	20.2174i	1.52770	−	0.816571i	0.528227	−	0.849103i	$-0.322857\pi$
$613$	37.8240	−	20.2174i	1.52770	−	0.816571i	0.999471	+	0.0325319i	$0.0103570\pi$
$614$	11.6644	+	30.0768i	0.470737	+	1.21380i
$615$	4.17932	+	2.79254i	0.168527	+	0.112606i
$616$	−2.98997	−	5.21192i	−0.120469	−	0.209994i
$617$	10.6647	+	15.9609i	0.429345	+	0.642560i	0.981563	−	0.191140i	$-0.0612184\pi$
$617$	10.6647	+	15.9609i	0.429345	+	0.642560i	−0.552218	+	0.833700i	$0.686218\pi$
$618$	9.89641	−	1.73563i	0.398092	−	0.0698172i
$619$	1.05545	+	0.866186i	0.0424221	+	0.0348150i	0.655365	−	0.755312i	$-0.272515\pi$
$619$	1.05545	+	0.866186i	0.0424221	+	0.0348150i	−0.612943	+	0.790127i	$0.710015\pi$
$620$	12.0522	−	9.00624i	0.484027	−	0.361699i
$621$	−23.7868	−	12.7143i	−0.954530	−	0.510207i
$622$	−1.67708	+	13.8028i	−0.0672448	+	0.553440i
$623$	1.25328	−	3.02568i	0.0502115	−	0.121221i
$624$	0.873686	−	2.95697i	0.0349754	−	0.118374i
$625$	0.382683	+	0.923880i	0.0153073	+	0.0369552i
$626$	−2.18869	+	0.609955i	−0.0874778	+	0.0243787i
$627$	8.13884	+	26.8302i	0.325034	+	1.07149i
$628$	−1.04921	−	19.8894i	−0.0418680	−	0.793674i
$629$	3.70368	−	0.364781i	0.147675	−	0.0145448i
$630$	1.40534	+	0.312912i	0.0559901	+	0.0124667i
$631$	6.74225	−	33.8956i	0.268405	−	1.34936i	−0.577658	−	0.816279i	$-0.696033\pi$
$631$	6.74225	−	33.8956i	0.268405	−	1.34936i	0.846063	−	0.533083i	$-0.178967\pi$
$632$	15.3364	+	21.5270i	0.610048	+	0.856297i
$633$	−5.98824	+	1.19113i	−0.238011	+	0.0473433i
$634$	9.35521	+	9.79057i	0.371543	+	0.388833i
$635$	−1.25149	−	0.379636i	−0.0496640	−	0.0150654i
$636$	−10.7165	+	14.5592i	−0.424936	+	0.577310i
$637$	3.14959	+	3.83779i	0.124791	+	0.152059i
$638$	−16.0769	+	1.21513i	−0.636490	+	0.0481075i
$639$	23.8359			0.942935
$640$	−2.61835	−	11.0066i	−0.103499	−	0.435072i
$641$	−33.2596			−1.31368			−0.656838	−	0.754031i	$-0.728107\pi$
$641$	−33.2596			−1.31368			−0.656838	+	0.754031i	$0.728107\pi$
$642$	−7.48298	+	0.565583i	−0.295330	+	0.0223218i
$643$	−6.27255	−	7.64313i	−0.247365	−	0.301416i	0.634494	−	0.772928i	$-0.281208\pi$
$643$	−6.27255	−	7.64313i	−0.247365	−	0.301416i	−0.881860	+	0.471512i	$0.843708\pi$
$644$	4.51419	+	3.32272i	0.177884	+	0.130934i
$645$	9.44863	+	2.86621i	0.372040	+	0.112857i
$646$	42.7852	+	44.7763i	1.68336	+	1.76170i
$647$	−39.3128	+	7.81980i	−1.54555	+	0.307428i	−0.892907	−	0.450241i	$-0.851338\pi$
$647$	−39.3128	+	7.81980i	−1.54555	+	0.307428i	−0.652639	+	0.757669i	$0.726338\pi$
$648$	0.185051	−	1.10192i	0.00726949	−	0.0432877i
$649$	−6.43765	+	32.3643i	−0.252700	+	1.27041i
$650$	−1.02036	−	0.227192i	−0.0400217	−	0.00891120i
$651$	4.15599	−	0.409329i	0.162886	−	0.0160429i
$652$	−36.8319	+	1.94296i	−1.44245	+	0.0760924i
$653$	2.09824	+	6.91696i	0.0821103	+	0.270681i	0.988376	−	0.152026i	$-0.0485798\pi$
$653$	2.09824	+	6.91696i	0.0821103	+	0.270681i	−0.906266	+	0.422707i	$0.861080\pi$
$654$	17.7015	−	4.93314i	0.692183	−	0.192901i
$655$	1.92427	+	4.64559i	0.0751873	+	0.181518i
$656$	−12.1229	+	14.9915i	−0.473318	+	0.585321i
$657$	7.92797	−	19.1398i	0.309300	−	0.746716i
$658$	−0.397836	+	3.27429i	−0.0155093	+	0.127645i
$659$	−29.5416	−	15.7903i	−1.15078	−	0.615104i	−0.218140	−	0.975917i	$-0.569999\pi$
$659$	−29.5416	−	15.7903i	−1.15078	−	0.615104i	−0.932638	+	0.360814i	$0.882499\pi$
$660$	−4.98243	−	6.66751i	−0.193941	−	0.259532i
$661$	−21.8890	−	17.9638i	−0.851383	−	0.698712i	0.103842	−	0.994594i	$-0.466886\pi$
$661$	−21.8890	−	17.9638i	−0.851383	−	0.698712i	−0.955224	+	0.295882i	$0.904386\pi$
$662$	−3.48339	+	0.610915i	−0.135386	+	0.0237439i
$663$	−2.78377	−	4.16620i	−0.108112	−	0.161802i
$664$	−40.4869	−	10.9682i	−1.57120	−	0.425648i
$665$	2.98185	+	1.99241i	0.115631	+	0.0772623i
$666$	−0.559908	−	1.44373i	−0.0216960	−	0.0559433i
$667$	13.2643	−	7.08990i	0.513595	−	0.274522i
$668$	5.60859	−	11.9702i	0.217003	−	0.463139i
$669$	0.919681	−	9.33768i	0.0355569	−	0.361015i
$670$	−7.64386	−	15.1176i	−0.295308	−	0.584044i
$671$	−38.1196	+	38.1196i	−1.47159	+	1.47159i
$672$	0.958054	−	2.99057i	0.0369578	−	0.115364i
$673$	−2.10444	−	2.10444i	−0.0811203	−	0.0811203i	0.665382	−	0.746503i	$-0.268269\pi$
$673$	−2.10444	−	2.10444i	−0.0811203	−	0.0811203i	−0.746503	+	0.665382i	$0.768269\pi$
$674$	−11.4245	+	34.7935i	−0.440054	+	1.34019i
$675$	5.09827	+	0.502136i	0.196232	+	0.0193272i
$676$	−18.3945	+	16.7933i	−0.707479	+	0.645897i
$677$	−11.8469	−	22.1639i	−0.455312	−	0.851828i	−0.999914	−	0.0131336i	$-0.995819\pi$
$677$	−11.8469	−	22.1639i	−0.455312	−	0.851828i	0.544602	−	0.838695i	$-0.316681\pi$
$678$	−25.4240	−	11.2147i	−0.976404	−	0.430700i
$679$	−1.20083	+	1.79717i	−0.0460837	+	0.0689691i
$680$	−16.4670	−	8.17715i	−0.631481	−	0.313579i
$681$	19.7713	−	13.2107i	0.757637	−	0.506237i
$682$	34.7563	+	24.3843i	1.33089	+	0.933722i
$683$	6.16947	−	7.51752i	0.236068	−	0.287650i	−0.641479	−	0.767141i	$-0.721679\pi$
$683$	6.16947	−	7.51752i	0.236068	−	0.287650i	0.877547	+	0.479491i	$0.159179\pi$
$684$	13.1677	−	22.1503i	0.503480	−	0.846936i
$685$	4.89061	−	9.14969i	0.186861	−	0.349592i
$686$	6.36768	+	8.12908i	0.243119	+	0.310370i
$687$	−24.0039	−	9.94274i	−0.915806	−	0.379339i
$688$	−14.2398	+	35.0937i	−0.542889	+	1.33794i
$689$	−5.91918	+	2.45181i	−0.225503	+	0.0934064i
$690$	6.76279	+	3.81494i	0.257455	+	0.145232i
$691$	14.6198	−	4.43485i	0.556162	−	0.168710i	0.000322946	−	1.00000i	$-0.499897\pi$
$691$	14.6198	−	4.43485i	0.556162	−	0.168710i	0.555839	+	0.831290i	$0.312397\pi$
$692$	−9.93370	+	28.0825i	−0.377623	+	1.06754i
$693$	0.398229	+	4.04328i	0.0151275	+	0.153592i
$694$	17.4226	−	11.0770i	0.661355	−	0.420475i
$695$	−13.1588	−	2.61745i	−0.499143	−	0.0992857i
$696$	−6.13405	−	5.77700i	−0.232511	−	0.218977i
$697$	6.11236	+	30.7289i	0.231522	+	1.16394i
$698$	0.382903	−	16.8386i	0.0144931	−	0.637349i
$699$	0.454725	−	1.49903i	0.0171993	−	0.0566984i
$700$	−1.03367	−	0.254952i	−0.0390691	−	0.00963629i
$701$	27.6131	−	22.6615i	1.04293	−	0.855914i	0.0531638	−	0.998586i	$-0.483069\pi$
$701$	27.6131	−	22.6615i	1.04293	−	0.855914i	0.989770	+	0.142672i	$0.0455695\pi$
$702$	−3.49056	+	4.06135i	−0.131743	+	0.153286i
$703$		−	3.85711i		−	0.145474i
$704$	27.2043	−	16.7094i	1.02530	−	0.629760i
$705$			4.56906i			0.172081i
$706$	−24.9384	−	21.4335i	−0.938568	−	0.806659i
$707$	6.39080	−	5.24480i	0.240351	−	0.197251i
$708$	−14.7600	+	8.91953i	−0.554716	+	0.335216i
$709$	−13.1375	+	43.3084i	−0.493388	+	1.62648i	0.257661	+	0.966235i	$0.417048\pi$
$709$	−13.1375	+	43.3084i	−0.493388	+	1.62648i	−0.751049	+	0.660246i	$0.770452\pi$
$710$	−17.6213	−	0.400701i	−0.661315	−	0.0150381i
$711$	−3.48664	−	17.5285i	−0.130759	−	0.657371i
$712$	16.2688	+	6.17442i	0.609700	+	0.231396i
$713$	−38.8452	−	7.72679i	−1.45476	−	0.289371i
$714$	−2.73797	−	4.30649i	−0.102466	−	0.161166i
$715$	−0.289137	−	2.93565i	−0.0108131	−	0.109787i
$716$	12.0832	−	5.76847i	0.451569	−	0.215578i
$717$	14.5387	−	4.41025i	0.542956	−	0.164704i
$718$	−15.6205	+	27.6907i	−0.582953	+	1.03341i
$719$	36.8048	−	15.2450i	1.37259	−	0.568544i	0.430098	−	0.902782i	$-0.358479\pi$
$719$	36.8048	−	15.2450i	1.37259	−	0.568544i	0.942489	+	0.334238i	$0.108479\pi$
$720$	−1.43813	+	7.51354i	−0.0535959	+	0.280013i
$721$	3.35054	+	1.38784i	0.124781	+	0.0516858i
$722$	29.3766	−	23.0113i	1.09328	−	0.856392i
$723$	−3.84186	+	7.18761i	−0.142880	+	0.267310i
$724$	−4.37469	−	17.2006i	−0.162584	−	0.639255i
$725$	−1.81228	+	2.20827i	−0.0673065	+	0.0820132i
$726$	4.17264	−	5.94751i	0.154861	−	0.220733i
$727$	18.8126	−	12.5702i	0.697722	−	0.466203i	−0.155443	−	0.987845i	$-0.549680\pi$
$727$	18.8126	−	12.5702i	0.697722	−	0.466203i	0.853164	+	0.521642i	$0.174680\pi$
$728$	0.838760	−	0.731491i	0.0310865	−	0.0271109i
$729$	8.48450	−	12.6980i	0.314241	−	0.470295i
$730$	−6.18270	+	14.0163i	−0.228832	+	0.518766i
$731$	29.0124	+	54.2785i	1.07306	+	2.00756i
$732$	−28.1452	−	1.28069i	−1.04028	−	0.0473356i
$733$	−5.81346	−	0.572576i	−0.214725	−	0.0211486i	−0.00991747	−	0.999951i	$-0.503157\pi$
$733$	−5.81346	−	0.572576i	−0.214725	−	0.0211486i	−0.204808	+	0.978802i	$0.565657\pi$
$734$	3.78970	+	1.24435i	0.139881	+	0.0459299i
$735$	4.95284	+	4.95284i	0.182688	+	0.182688i
$736$	−16.9282	+	24.5038i	−0.623982	+	0.903221i
$737$	33.8023	−	33.8023i	1.24512	−	1.24512i
$738$	11.6337	−	5.88231i	0.428244	−	0.216531i
$739$	2.96492	−	30.1033i	0.109066	−	1.10737i	−0.772405	−	0.635131i	$-0.780946\pi$
$739$	2.96492	−	30.1033i	0.109066	−	1.10737i	0.881471	−	0.472238i	$-0.156554\pi$
$740$	0.389655	+	1.07672i	0.0143240	+	0.0395811i
$741$	−4.57990	+	2.44801i	−0.168247	+	0.0899298i
$742$	−6.08370	+	2.35939i	−0.223339	+	0.0866157i
$743$	−7.83201	−	5.23318i	−0.287329	−	0.191987i	0.403550	−	0.914958i	$-0.367776\pi$
$743$	−7.83201	−	5.23318i	−0.287329	−	0.191987i	−0.690879	+	0.722971i	$0.742776\pi$
$744$	2.83559	+	22.0072i	0.103958	+	0.806823i
$745$	4.17224	+	6.24420i	0.152859	+	0.228770i
$746$	0.149803	+	0.854162i	0.00548466	+	0.0312731i
$747$	21.9246	+	17.9931i	0.802179	+	0.658331i
$748$	7.42708	−	51.3478i	0.271561	−	1.87746i
$749$	−2.38883	−	1.27685i	−0.0872858	−	0.0466552i
$750$	−1.46403	−	0.177885i	−0.0534589	−	0.00649542i
$751$	−8.55728	+	20.6591i	−0.312259	+	0.753861i	0.687361	+	0.726316i	$0.258769\pi$
$751$	−8.55728	+	20.6591i	−0.312259	+	0.753861i	−0.999621	+	0.0275452i	$0.991231\pi$
$752$	−17.4530	−	1.59162i	−0.636445	−	0.0580403i
$753$	4.72649	+	11.4108i	0.172243	+	0.415831i
$754$	−0.801674	−	2.87663i	−0.0291952	−	0.104761i
$755$	−3.01114	−	9.92641i	−0.109587	−	0.361259i
$756$	−3.64813	+	4.05446i	−0.132681	+	0.147459i
$757$	−5.90338	+	0.581432i	−0.214562	+	0.0211325i	−0.204727	−	0.978819i	$-0.565631\pi$
$757$	−5.90338	+	0.581432i	−0.214562	+	0.0211325i	−0.00983508	+	0.999952i	$0.503131\pi$
$758$	6.73216	−	30.2353i	0.244523	−	1.09819i
$759$	−4.27461	+	21.4899i	−0.155159	+	0.780035i
$760$	−10.1069	+	16.1537i	−0.366616	+	0.585958i
$761$	20.9602	−	4.16924i	0.759806	−	0.151135i	0.200043	−	0.979787i	$-0.435892\pi$
$761$	20.9602	−	4.16924i	0.759806	−	0.151135i	0.559764	+	0.828652i	$0.310892\pi$
$762$	1.39449	−	1.33248i	0.0505169	−	0.0482706i
$763$	6.34716	+	1.92539i	0.229783	+	0.0697038i
$764$	4.30591	+	28.3221i	0.155782	+	1.02466i
$765$	7.88656	+	9.60980i	0.285139	+	0.347443i
$766$	−1.61465	−	21.3628i	−0.0583398	−	0.771869i
$767$	−6.11194			−0.220689
$768$	16.0354	+	4.61209i	0.578626	+	0.166424i
$769$	47.4508			1.71112			0.855559	−	0.517705i	$-0.173213\pi$
$769$	47.4508			1.71112			0.855559	+	0.517705i	$0.173213\pi$
$770$	−0.226429	−	2.99579i	−0.00815993	−	0.107961i
$771$	−10.4960	−	12.7894i	−0.378003	−	0.460598i
$772$	6.46858	+	42.5471i	0.232809	+	1.53130i
$773$	−2.16789	−	0.657622i	−0.0779736	−	0.0236530i	0.251057	−	0.967972i	$-0.419222\pi$
$773$	−2.16789	−	0.657622i	−0.0779736	−	0.0236530i	−0.329030	+	0.944319i	$0.606722\pi$
$774$	18.5147	−	17.6914i	0.665497	−	0.635904i
$775$	7.37821	−	1.46762i	0.265033	−	0.0527184i
$776$	−9.73590	−	6.09146i	−0.349499	−	0.218671i
$777$	−0.0620051	+	0.311721i	−0.00222442	+	0.0111829i
$778$	7.34450	−	32.9854i	0.263313	−	1.18258i
$779$	32.3154	−	3.18279i	1.15782	−	0.114035i
$780$	1.03119	−	1.14604i	0.0369224	−	0.0410348i
$781$	−14.4383	−	47.5966i	−0.516642	−	1.70314i
$782$	12.9928	+	46.6220i	0.464623	+	1.66720i
$783$	5.60049	+	13.5208i	0.200145	+	0.483193i
$784$	−20.6443	+	17.1937i	−0.737297	+	0.614060i
$785$	3.81096	−	9.20048i	0.136019	−	0.328379i
$786$	−7.36167	−	0.894466i	−0.262582	−	0.0319045i
$787$	−25.1269	−	13.4306i	−0.895678	−	0.478750i	−0.0417420	−	0.999128i	$-0.513291\pi$
$787$	−25.1269	−	13.4306i	−0.895678	−	0.478750i	−0.853936	+	0.520379i	$0.825791\pi$
$788$	0.733044	−	5.06797i	0.0261136	−	0.180539i
$789$	−2.74073	−	2.24926i	−0.0975724	−	0.0800756i
$790$	2.28291	+	13.0170i	0.0812224	+	0.463124i
$791$	−5.57229	−	8.33952i	−0.198128	−	0.296519i
$792$	−21.4104	+	2.75869i	−0.760784	+	0.0980259i
$793$	−8.30227	−	5.54740i	−0.294822	−	0.196994i
$794$	38.5100	−	14.9350i	1.36667	−	0.530024i
$795$	−7.97168	+	4.26095i	−0.282726	+	0.151120i
$796$	−4.63117	−	12.7972i	−0.164148	−	0.453584i
$797$	−2.50856	+	25.4699i	−0.0888579	+	0.902189i	0.842648	+	0.538464i	$0.180995\pi$
$797$	−2.50856	+	25.4699i	−0.0888579	+	0.902189i	−0.931506	+	0.363725i	$0.881505\pi$
$798$	−4.71995	+	2.38653i	−0.167084	+	0.0844821i
$799$	−20.1384	+	20.1384i	−0.712445	+	0.712445i
$800$	1.18948	−	5.53038i	0.0420544	−	0.195529i
$801$	−8.31983	−	8.31983i	−0.293967	−	0.293967i
$802$	−20.4556	−	6.71664i	−0.722314	−	0.237173i
$803$	−43.0215	−	4.23725i	−1.51820	−	0.149529i
$804$	24.9576	+	1.13564i	0.880186	+	0.0400509i
$805$	1.32114	+	2.47168i	0.0465641	+	0.0871152i
$806$	−3.17376	+	7.19498i	−0.111791	+	0.253432i
$807$	2.10366	−	3.14835i	0.0740524	−	0.110827i
$808$	28.8724	+	33.1064i	1.01573	+	1.16468i
$809$	−19.6174	+	13.1079i	−0.689710	+	0.460850i	−0.850387	−	0.526157i	$-0.823632\pi$
$809$	−19.6174	+	13.1079i	−0.689710	+	0.460850i	0.160677	+	0.987007i	$0.448632\pi$
$810$	0.320865	−	0.457347i	0.0112740	−	0.0160695i
$811$	7.96434	−	9.70457i	0.279666	−	0.340774i	−0.614166	−	0.789177i	$-0.710507\pi$
$811$	7.96434	−	9.70457i	0.279666	−	0.340774i	0.893831	+	0.448404i	$0.148007\pi$
$812$	−0.749662	−	2.94756i	−0.0263080	−	0.103439i
$813$	−6.96147	+	13.0240i	−0.244150	+	0.456772i
$814$	−2.54374	+	1.99257i	−0.0891582	+	0.0698395i
$815$	−17.0378	−	7.05728i	−0.596808	−	0.247206i
$816$	22.4357	−	15.2269i	0.785408	−	0.533049i
$817$	58.9312	−	24.4101i	2.06174	−	0.854002i
$818$	−18.5813	+	32.9393i	−0.649681	+	1.15170i
$819$	−0.720116	+	0.218445i	−0.0251629	+	0.00763308i
$820$	−8.69939	+	4.15307i	−0.303796	+	0.145031i
$821$	−1.10634	−	11.2329i	−0.0386115	−	0.392029i	−0.994996	−	0.0999176i	$-0.968142\pi$
$821$	−1.10634	−	11.2329i	−0.0386115	−	0.392029i	0.956384	−	0.292112i	$-0.0943579\pi$
$822$	8.20916	+	12.9120i	0.286327	+	0.450357i
$823$	7.56742	+	1.50525i	0.263784	+	0.0524698i	0.325210	−	0.945642i	$-0.394565\pi$
$823$	7.56742	+	1.50525i	0.263784	+	0.0524698i	−0.0614265	+	0.998112i	$0.519565\pi$
$824$	−6.83735	+	18.0156i	−0.238190	+	0.627602i
$825$	−0.811915	−	4.08177i	−0.0282673	−	0.142109i
$826$	−6.22320	−	0.141513i	−0.216533	−	0.00492387i
$827$	−0.112115	+	0.369592i	−0.00389860	+	0.0128520i	−0.958868	−	0.283852i	$-0.908388\pi$
$827$	−0.112115	+	0.369592i	−0.00389860	+	0.0128520i	0.954969	+	0.296704i	$0.0958875\pi$
$828$	17.2353	−	10.4153i	0.598968	−	0.361958i
$829$	−7.70041	+	6.31956i	−0.267446	+	0.219487i	−0.758552	−	0.651612i	$-0.774093\pi$
$829$	−7.70041	+	6.31956i	−0.267446	+	0.219487i	0.491106	+	0.871100i	$0.336593\pi$
$830$	−15.9058	−	13.6704i	−0.552098	−	0.474505i
$831$		−	33.3346i		−	1.15636i
$832$	4.01847	+	4.33817i	0.139315	+	0.150399i
$833$			43.6599i			1.51273i
$834$	12.8971	−	15.0061i	0.446591	−	0.519619i
$835$	5.10920	−	4.19301i	0.176811	−	0.145105i
$836$	−52.2068	−	12.8767i	−1.80561	−	0.445349i
$837$	11.1872	−	36.8792i	0.386685	−	1.27473i
$838$	−0.240558	+	10.5788i	−0.00830993	+	0.365438i
$839$	9.29528	+	46.7305i	0.320909	+	1.61332i	0.718344	+	0.695688i	$0.244900\pi$
$839$	9.29528	+	46.7305i	0.320909	+	1.61332i	−0.397436	+	0.917630i	$0.630100\pi$
$840$	1.07649	−	1.14303i	0.0371425	−	0.0394381i
$841$	20.4388	+	4.06552i	0.704785	+	0.140190i
$842$	−20.7157	+	13.1706i	−0.713909	+	0.453888i
$843$	1.94460	+	19.7438i	0.0669754	+	0.680013i
$844$	3.90491	−	11.0392i	0.134412	−	0.379984i
$845$	−11.9174	+	3.61510i	−0.409970	+	0.124363i
$846$	10.3211	+	5.82223i	0.354848	+	0.200172i
$847$	2.42275	−	1.00354i	0.0832467	−	0.0344819i
$848$	−13.4992	−	31.9347i	−0.463564	−	1.09664i
$849$	−9.72400	−	4.02781i	−0.333727	−	0.138234i
$850$	−5.66878	−	7.23685i	−0.194437	−	0.248222i
$851$	1.42092	−	2.65836i	0.0487087	−	0.0911275i
$852$	13.2832	−	22.3445i	0.455074	−	0.765508i
$853$	−28.1853	+	34.3439i	−0.965047	+	1.17591i	0.0193247	+	0.999813i	$0.493848\pi$
$853$	−28.1853	+	34.3439i	−0.965047	+	1.17591i	−0.984372	+	0.176100i	$0.943652\pi$
$854$	−8.32495	−	5.84061i	−0.284874	−	0.199861i
$855$	10.7129	−	7.15815i	0.366374	−	0.244803i
$856$	6.40103	−	12.8903i	0.218783	−	0.440580i
$857$	−5.87222	+	8.78840i	−0.200591	+	0.300206i	−0.918104	−	0.396339i	$-0.870280\pi$
$857$	−5.87222	+	8.78840i	−0.200591	+	0.300206i	0.717513	+	0.696545i	$0.245280\pi$
$858$	3.98040	+	1.75579i	0.135889	+	0.0599416i
$859$	−17.2641	−	32.2989i	−0.589044	−	1.10202i	−0.983123	−	0.182947i	$-0.941436\pi$
$859$	−17.2641	−	32.2989i	−0.589044	−	1.10202i	0.394079	−	0.919077i	$-0.371064\pi$
$860$	−13.9848	+	12.7675i	−0.476879	+	0.435369i
$861$	−2.66280	−	0.262263i	−0.0907481	−	0.00893791i
$862$	7.85329	−	23.9174i	0.267484	−	0.814628i
$863$	−15.8274	−	15.8274i	−0.538772	−	0.538772i	0.384396	−	0.923168i	$-0.374410\pi$
$863$	−15.8274	−	15.8274i	−0.538772	−	0.538772i	−0.923168	+	0.384396i	$0.874410\pi$
$864$	−22.1139	−	18.7296i	−0.752330	−	0.637195i
$865$	−10.5315	+	10.5315i	−0.358083	+	0.358083i
$866$	−4.10607	−	8.12077i	−0.139530	−	0.275955i
$867$	2.58132	−	26.2086i	0.0876662	−	0.890090i
$868$	−3.39812	+	7.25246i	−0.115340	+	0.246165i
$869$	−32.8898	+	17.5799i	−1.11571	+	0.596359i
$870$	−1.52337	−	3.92803i	−0.0516471	−	0.133173i
$871$	7.36198	+	4.91912i	0.249451	+	0.166678i
$872$	−9.21520	+	34.0161i	−0.312066	+	1.15193i
$873$	4.31423	+	6.45671i	0.146015	+	0.218526i
$874$	49.4068	−	8.66494i	1.67121	−	0.293096i
$875$	−0.411492	−	0.337703i	−0.0139110	−	0.0114164i
$876$	−13.5241	−	18.0980i	−0.456938	−	0.611476i
$877$	−22.8830	−	12.2312i	−0.772704	−	0.413019i	0.0374038	−	0.999300i	$-0.488091\pi$
$877$	−22.8830	−	12.2312i	−0.772704	−	0.413019i	−0.810107	+	0.586282i	$0.800591\pi$
$878$	1.30765	−	10.7623i	0.0441311	−	0.363209i
$879$	−5.14899	+	12.4308i	−0.173671	+	0.419279i
$880$	15.8745	−	1.67950i	0.535129	−	0.0566160i
$881$	19.3143	+	46.6290i	0.650717	+	1.57097i	0.811740	+	0.584019i	$0.198521\pi$
$881$	19.3143	+	46.6290i	0.650717	+	1.57097i	−0.161023	+	0.986951i	$0.551479\pi$
$882$	17.4994	−	4.87681i	0.589234	−	0.164211i
$883$	−9.77632	−	32.2282i	−0.328999	−	1.08457i	−0.952957	−	0.303107i	$-0.901976\pi$
$883$	−9.77632	−	32.2282i	−0.328999	−	1.08457i	0.623957	−	0.781459i	$-0.285524\pi$
$884$	9.59627	−	0.506224i	0.322757	−	0.0170262i
$885$	−8.58137	+	0.845191i	−0.288459	+	0.0284108i
$886$	−18.0993	−	4.02997i	−0.608057	−	0.135389i
$887$	−6.35752	+	31.9614i	−0.213465	+	1.07316i	0.714256	+	0.699884i	$0.246765\pi$
$887$	−6.35752	+	31.9614i	−0.213465	+	1.07316i	−0.927721	+	0.373275i	$0.878235\pi$
$888$	−1.66541	−	0.279680i	−0.0558876	−	0.00938545i
$889$	0.682800	−	0.135817i	0.0229004	−	0.00455517i
$890$	6.01076	+	6.29049i	0.201481	+	0.210858i
$891$	1.50865	+	0.457643i	0.0505416	+	0.0153316i
$892$	14.4922	+	10.6672i	0.485236	+	0.357163i
$893$	18.7254	+	22.8170i	0.626621	+	0.763540i
$894$	−11.0440	+	0.834734i	−0.369367	+	0.0279177i
$895$	6.69474			0.223780
$896$	3.99117	+	4.51018i	0.133336	+	0.150675i
$897$	−4.05834			−0.135504
$898$	−7.21535	+	0.545354i	−0.240779	+	0.0181987i
$899$	13.6334	+	16.6123i	0.454698	+	0.554051i
$900$	−2.26741	+	3.08046i	−0.0755802	+	0.102682i
$901$	−53.9161	−	16.3553i	−1.79621	−	0.544873i
$902$	−18.7930	−	19.6676i	−0.625739	−	0.654860i
$903$	−5.15506	+	1.02541i	−0.171550	+	0.0341234i
$904$	43.4038	−	30.9220i	1.44359	−	1.02845i
$905$	1.73125	−	8.70359i	0.0575487	−	0.289317i
$906$	14.9325	+	3.32486i	0.496100	+	0.110461i
$907$	8.79201	−	0.865937i	0.291934	−	0.0287530i	0.0490098	−	0.998798i	$-0.484393\pi$
$907$	8.79201	−	0.865937i	0.291934	−	0.0287530i	0.242924	+	0.970045i	$0.421893\pi$
$908$	2.40236	+	45.5404i	0.0797250	+	1.51131i
$909$	−8.62216	−	28.4234i	−0.285979	−	0.942746i
$910$	0.536035	−	0.149385i	0.0177694	−	0.00495206i
$911$	7.18456	+	17.3451i	0.238035	+	0.574668i	0.997079	−	0.0763713i	$-0.0243334\pi$
$911$	7.18456	+	17.3451i	0.238035	+	0.574668i	−0.759044	+	0.651039i	$0.774333\pi$
$912$	−13.4262	−	24.6876i	−0.444586	−	0.817487i
$913$	22.6488	−	54.6790i	0.749566	−	1.80961i
$914$	3.90355	−	32.1272i	0.129118	−	1.06267i
$915$	−12.4238	−	6.64065i	−0.410718	−	0.219533i
$916$	39.9151	−	29.8274i	1.31883	−	0.985525i
$917$	−2.06913	−	1.69809i	−0.0683285	−	0.0560758i
$918$	−46.3860	+	8.13515i	−1.53097	+	0.268500i
$919$	−10.4478	−	15.6362i	−0.344640	−	0.515790i	0.618143	−	0.786066i	$-0.287885\pi$
$919$	−10.4478	−	15.6362i	−0.344640	−	0.515790i	−0.962783	+	0.270275i	$0.912885\pi$
$920$	−12.9167	+	7.41004i	−0.425851	+	0.244302i
$921$	−19.7791	−	13.2160i	−0.651743	−	0.435480i
$922$	−14.6029	−	37.6537i	−0.480920	−	1.24006i
$923$	8.12473	−	4.34276i	0.267429	−	0.142944i
$924$	4.01221	+	1.87991i	0.131992	+	0.0618445i
$925$	−0.0561177	+	0.569773i	−0.00184514	+	0.0187340i
$926$	−18.8737	−	37.3274i	−0.620228	−	1.22665i
$927$	9.21310	−	9.21310i	0.302598	−	0.302598i
$928$	15.5351	−	4.45070i	0.509963	−	0.146101i
$929$	−3.00877	−	3.00877i	−0.0987144	−	0.0987144i	0.656025	−	0.754739i	$-0.272237\pi$
$929$	−3.00877	−	3.00877i	−0.0987144	−	0.0987144i	−0.754739	+	0.656025i	$0.772237\pi$
$930$	−3.46111	+	10.5409i	−0.113494	+	0.345649i
$931$	45.0318	+	4.43524i	1.47586	+	0.145359i
$932$	2.02557	+	2.21870i	0.0663497	+	0.0726758i
$933$	−4.83323	−	9.04235i	−0.158233	−	0.296033i
$934$	11.4238	+	5.03913i	0.373798	+	0.164885i
$935$	14.4121	−	21.5692i	0.471326	−	0.705389i
$936$	−1.27480	−	3.78974i	−0.0416682	−	0.123872i
$937$	−50.0794	+	33.4620i	−1.63602	+	1.09316i	−0.718458	+	0.695571i	$0.755152\pi$
$937$	−50.0794	+	33.4620i	−1.63602	+	1.09316i	−0.917565	+	0.397585i	$0.869848\pi$
$938$	7.38209	+	5.17911i	0.241034	+	0.169104i
$939$	1.06289	−	1.29514i	0.0346861	−	0.0422651i
$940$	−7.53227	−	4.47773i	−0.245676	−	0.146047i
$941$	8.16426	−	15.2743i	0.266147	−	0.497926i	−0.712977	−	0.701187i	$-0.752654\pi$
$941$	8.16426	−	15.2743i	0.266147	−	0.497926i	0.979125	+	0.203260i	$0.0651538\pi$
$942$	9.05672	+	11.5620i	0.295084	+	0.376709i
$943$	23.4446	+	9.71109i	0.763462	+	0.316237i
$944$	−0.239190	−	33.0738i	−0.00778499	−	1.07646i
$945$	−2.51948	+	1.04360i	−0.0819586	+	0.0339483i
$946$	−46.5420	−	26.2547i	−1.51321	−	0.853613i
$947$	15.7772	−	4.78597i	0.512691	−	0.155523i	−0.0233297	−	0.999728i	$-0.507427\pi$
$947$	15.7772	−	4.78597i	0.512691	−	0.155523i	0.536021	+	0.844205i	$0.319927\pi$
$948$	−18.3747	−	6.49973i	−0.596784	−	0.211102i
$949$	−0.784822	−	7.96843i	−0.0254764	−	0.258666i
$950$	−8.04011	+	5.11173i	−0.260856	+	0.165847i
$951$	−9.79371	−	1.94809i	−0.317583	−	0.0631711i
$952$	9.78267	−	0.293251i	0.317058	−	0.00950432i
$953$	1.11016	+	5.58116i	0.0359616	+	0.180791i	0.994591	−	0.103864i	$-0.0331207\pi$
$953$	1.11016	+	5.58116i	0.0359616	+	0.180791i	−0.958630	+	0.284656i	$0.908121\pi$
$954$	−0.532949	+	23.4370i	−0.0172549	+	0.758802i
$955$	−4.15798	+	13.7070i	−0.134549	+	0.443548i
$956$	−6.97757	+	28.2896i	−0.225671	+	0.914952i
$957$	9.19025	−	7.54224i	0.297079	−	0.243806i
$958$	−31.7197	+	36.9066i	−1.02482	+	1.19240i
$959$			5.52271i			0.178338i
$960$	6.24196	+	5.53525i	0.201458	+	0.178649i
$961$		−	25.5919i		−	0.825546i
$962$	−0.453889	−	0.390098i	−0.0146340	−	0.0125773i
$963$	−7.52250	+	6.17355i	−0.242409	+	0.198940i
$964$	−8.08399	−	13.3774i	−0.260368	−	0.430857i
$965$	−6.24634	+	20.5914i	−0.201077	+	0.662862i
$966$	−4.13221	−	0.0939650i	−0.132952	−	0.00302328i
$967$	2.37845	+	11.9573i	0.0764857	+	0.384520i	1.00000		0.000954529i	$0.000303836\pi$
$967$	2.37845	+	11.9573i	0.0764857	+	0.384520i	−0.923514	+	0.383565i	$0.874696\pi$
$968$	5.71547	+	12.7074i	0.183702	+	0.408431i
$969$	−44.7906	−	8.90941i	−1.43888	−	0.286211i
$970$	−3.08086	−	4.84580i	−0.0989203	−	0.155589i
$971$	−1.88673	−	19.1563i	−0.0605479	−	0.614754i	−0.976800	−	0.214152i	$-0.931301\pi$
$971$	−1.88673	−	19.1563i	−0.0605479	−	0.614754i	0.916252	−	0.400601i	$-0.131199\pi$
$972$	13.5974	+	28.4823i	0.436136	+	0.913571i
$973$	6.83446	−	2.07321i	0.219103	−	0.0664641i
$974$	13.8670	−	24.5822i	0.444326	−	0.787663i
$975$	0.712160	−	0.294986i	0.0228074	−	0.00944712i
$976$	29.6939	−	45.1435i	0.950479	−	1.44501i
$977$	0.661067	+	0.273823i	0.0211494	+	0.00876037i	0.393233	−	0.919439i	$-0.371357\pi$
$977$	0.661067	+	0.273823i	0.0211494	+	0.00876037i	−0.372084	+	0.928199i	$0.621357\pi$
$978$	21.4108	−	16.7716i	0.684643	−	0.536296i
$979$	−11.5738	+	21.6530i	−0.369900	+	0.692033i
$980$	−13.0188	+	3.31111i	−0.415870	+	0.105770i
$981$	15.1173	−	18.4205i	0.482659	−	0.588122i
$982$	−10.7281	+	15.2913i	−0.342346	+	0.487965i
$983$	−24.0233	+	16.0519i	−0.766226	+	0.511976i	−0.876193	−	0.481959i	$-0.839925\pi$
$983$	−24.0233	+	16.0519i	−0.766226	+	0.511976i	0.109968	+	0.993935i	$0.464925\pi$
$984$	0.968942	−	14.1838i	0.0308887	−	0.452164i
$985$	1.42246	−	2.12886i	0.0453233	−	0.0678311i
$986$	10.5987	−	24.0274i	0.337531	−	0.765188i
$987$	−1.14654	−	2.14502i	−0.0364947	−	0.0682769i
$988$	0.452717	−	9.94922i	0.0144029	−	0.316527i
$989$	49.6085	+	4.88601i	1.57746	+	0.155366i
$990$	−10.2550	−	3.36725i	−0.325926	−	0.107018i
$991$	40.5836	+	40.5836i	1.28918	+	1.28918i	0.935285	+	0.353897i	$0.115143\pi$
$991$	40.5836	+	40.5836i	1.28918	+	1.28918i	0.353897	+	0.935285i	$0.384857\pi$
$992$	−39.0586	−	16.8927i	−1.24011	−	0.536344i
$993$	1.84403	−	1.84403i	0.0585186	−	0.0585186i
$994$	8.37317	−	4.23369i	0.265581	−	0.134285i
$995$	0.666977	−	6.77193i	0.0211446	−	0.214685i
$996$	29.0852	−	10.5256i	0.921600	−	0.333518i
$997$	41.4835	−	22.1734i	1.31380	−	0.702239i	0.342366	−	0.939566i	$-0.388772\pi$
$997$	41.4835	−	22.1734i	1.31380	−	0.702239i	0.971430	+	0.237328i	$0.0762716\pi$
$998$	−10.9252	+	4.23703i	−0.345831	+	0.134121i
$999$	2.43873	+	1.62951i	0.0771580	+	0.0515553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.381.31	yes	1024
128.85	even	32	inner	640.2.bm.a.341.31	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.31	✓	1024	128.85	even	32	inner
640.2.bm.a.381.31	yes	1024	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.106586 - 1.41019i) q^{2} +(0.661571 + 0.806127i) q^{3} +(-1.97728 + 0.300613i) q^{4} +(-0.956940 - 0.290285i) q^{5} +(1.06628 - 1.01886i) q^{6} +(0.522095 - 0.103851i) q^{7} +(0.634671 + 2.75630i) q^{8} +(0.373107 - 1.87574i) q^{9} +O(q^{10})\)	\(q+(-0.106586 - 1.41019i) q^{2} +(0.661571 + 0.806127i) q^{3} +(-1.97728 + 0.300613i) q^{4} +(-0.956940 - 0.290285i) q^{5} +(1.06628 - 1.01886i) q^{6} +(0.522095 - 0.103851i) q^{7} +(0.634671 + 2.75630i) q^{8} +(0.373107 - 1.87574i) q^{9} +(-0.307361 + 1.38041i) q^{10} +(-3.97156 + 0.391164i) q^{11} +(-1.55044 - 1.39506i) q^{12} +(-0.214570 - 0.707342i) q^{13} +(-0.202098 - 0.725185i) q^{14} +(-0.399078 - 0.963459i) q^{15} +(3.81926 - 1.18879i) q^{16} +(2.48755 - 6.00547i) q^{17} +(-2.68491 - 0.326226i) q^{18} +(-5.94147 - 3.17578i) q^{19} +(1.97940 + 0.286305i) q^{20} +(0.429120 + 0.352170i) q^{21} +(0.974927 + 5.55896i) q^{22} +(-2.92500 - 4.37757i) q^{23} +(-1.80205 + 2.33511i) q^{24} +(0.831470 + 0.555570i) q^{25} +(-0.974617 + 0.377977i) q^{26} +(4.51803 - 2.41494i) q^{27} +(-1.00111 + 0.362291i) q^{28} +(-0.280007 + 2.84296i) q^{29} +(-1.31613 + 0.665467i) q^{30} +(5.31939 - 5.31939i) q^{31} +(-2.08350 - 5.25918i) q^{32} +(-2.94279 - 2.94279i) q^{33} +(-8.73399 - 2.86782i) q^{34} +(-0.529760 - 0.0521769i) q^{35} +(-0.173867 + 3.82101i) q^{36} +(0.269889 + 0.504926i) q^{37} +(-3.84518 + 8.71710i) q^{38} +(0.428254 - 0.640927i) q^{39} +(0.192769 - 2.82185i) q^{40} +(-4.00764 + 2.67782i) q^{41} +(0.450889 - 0.642678i) q^{42} +(-6.00655 + 7.31900i) q^{43} +(7.73528 - 1.96734i) q^{44} +(-0.901539 + 1.68666i) q^{45} +(-5.86144 + 4.59139i) q^{46} +(-4.04784 - 1.67667i) q^{47} +(3.48503 + 2.29234i) q^{48} +(-6.20536 + 2.57034i) q^{49} +(0.694837 - 1.23175i) q^{50} +(6.48685 - 1.96777i) q^{51} +(0.636900 + 1.33411i) q^{52} +(-0.849580 - 8.62593i) q^{53} +(-3.88708 - 6.11388i) q^{54} +(3.91409 + 0.778561i) q^{55} +(0.617604 + 1.37314i) q^{56} +(-1.37062 - 6.89058i) q^{57} +(4.03896 + 0.0918445i) q^{58} +(2.40026 - 7.91261i) q^{59} +(1.07872 + 1.78506i) q^{60} +(10.4422 - 8.56968i) q^{61} +(-8.06834 - 6.93439i) q^{62} -1.01806i q^{63} +(-7.19439 + 3.49869i) q^{64} +0.739170i q^{65} +(-3.83624 + 4.46356i) q^{66} +(-9.25954 + 7.59910i) q^{67} +(-3.11325 + 12.6223i) q^{68} +(1.59378 - 5.25399i) q^{69} +(-0.0171144 + 0.752625i) q^{70} +(2.43148 + 12.2239i) q^{71} +(5.40689 - 0.162080i) q^{72} +(10.6243 + 2.11330i) q^{73} +(0.683276 - 0.434413i) q^{74} +(0.102216 + 1.03782i) q^{75} +(12.7026 + 4.49332i) q^{76} +(-2.03291 + 0.616676i) q^{77} +(-0.949475 - 0.535606i) q^{78} +(8.63355 - 3.57613i) q^{79} +(-3.99990 + 0.0289274i) q^{80} +(-0.364974 - 0.151177i) q^{81} +(4.20339 + 5.36612i) q^{82} +(-6.99093 + 13.0791i) q^{83} +(-0.954357 - 0.567339i) q^{84} +(-4.12373 + 5.02478i) q^{85} +(10.9614 + 7.69028i) q^{86} +(-2.47703 + 1.65510i) q^{87} +(-3.59880 - 10.6985i) q^{88} +(3.41799 - 5.11538i) q^{89} +(2.47460 + 1.09157i) q^{90} +(-0.185484 - 0.347016i) q^{91} +(7.09949 + 7.77638i) q^{92} +(7.80726 + 0.768948i) q^{93} +(-1.93299 + 5.88694i) q^{94} +(4.76375 + 4.76375i) q^{95} +(2.86119 - 5.15889i) q^{96} +(-2.87112 + 2.87112i) q^{97} +(4.28608 + 8.47678i) q^{98} +(-0.748095 + 7.59553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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