LMFDB - Embedded newform 640.2.bm.a.341.31

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			341.31
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.31

$q$-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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

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	−0.546172	−	0.837673i	$-0.683916\pi$
$3$	0.661571	−	0.806127i	0.381958	−	0.465417i	0.928130	+	0.372256i	$0.121416\pi$
$4$	−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	0.292767	−	0.956184i	$-0.405424\pi$
$7$	0.522095	+	0.103851i	0.197333	+	0.0392521i	−0.0954339	+	0.995436i	$0.530424\pi$
$8$	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	−0.520441	−	0.853898i	$-0.674232\pi$
$11$	−3.97156	−	0.391164i	−1.19747	−	0.117940i	−0.677028	+	0.735957i	$0.736732\pi$
$12$	−1.55044	+	1.39506i	−0.447574	+	0.402719i
$13$	−0.214570	+	0.707342i	−0.0595109	+	0.196181i	−0.981655	−	0.190665i	$-0.938936\pi$
$13$	−0.214570	+	0.707342i	−0.0595109	+	0.196181i	0.922144	+	0.386846i	$0.126436\pi$
$14$	−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	0.870145	+	0.492795i	$0.164025\pi$
$17$	2.48755	+	6.00547i	0.603318	+	1.45654i	−0.266827	+	0.963744i	$0.585975\pi$
$18$	−2.68491	+	0.326226i	−0.632840	+	0.0768921i
$19$	−5.94147	+	3.17578i	−1.36307	+	0.728574i	−0.980715	−	0.195443i	$-0.937385\pi$
$19$	−5.94147	+	3.17578i	−1.36307	+	0.728574i	−0.382351	+	0.924017i	$0.624885\pi$
$20$	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	−0.999968	−	0.00800203i	$-0.997453\pi$
$23$	−2.92500	+	4.37757i	−0.609904	+	0.912786i	0.390064	+	0.920788i	$0.372453\pi$
$24$	−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	−0.985538	−	0.169456i	$-0.945799\pi$
$29$	−0.280007	−	2.84296i	−0.0519960	−	0.527925i	0.933542	−	0.358469i	$-0.116701\pi$
$30$	−1.31613	−	0.665467i	−0.240291	−	0.121497i
$31$	5.31939	+	5.31939i	0.955391	+	0.955391i	0.999047	−	0.0436552i	$-0.0139003\pi$
$31$	5.31939	+	5.31939i	0.955391	+	0.955391i	−0.0436552	+	0.999047i	$0.513900\pi$
$32$	−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	−0.858759	−	0.512379i	$-0.828764\pi$
$37$	0.269889	−	0.504926i	0.0443694	−	0.0830094i	0.903129	+	0.429370i	$0.141264\pi$
$38$	−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	0.201774	−	0.979432i	$-0.435329\pi$
$41$	−4.00764	−	2.67782i	−0.625888	−	0.418205i	−0.827662	+	0.561227i	$0.810329\pi$
$42$	0.450889	+	0.642678i	0.0695737	+	0.0991674i
$43$	−6.00655	−	7.31900i	−0.915990	−	1.11614i	−0.992883	−	0.119097i	$-0.962000\pi$
$43$	−6.00655	−	7.31900i	−0.915990	−	1.11614i	0.0768928	−	0.997039i	$-0.475500\pi$
$44$	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	−0.657839	−	0.753158i	$-0.728529\pi$
$47$	−4.04784	+	1.67667i	−0.590439	+	0.244568i	0.0674006	+	0.997726i	$0.478529\pi$
$48$	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	0.741287	+	0.671188i	$0.234216\pi$
$53$	−0.849580	+	8.62593i	−0.116699	+	1.18486i	−0.857986	+	0.513674i	$0.828284\pi$
$54$	−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	0.962743	+	0.270418i	$0.0871619\pi$
$59$	2.40026	+	7.91261i	0.312488	+	1.03013i	−0.650255	+	0.759716i	$0.725338\pi$
$60$	1.07872	−	1.78506i	0.139262	−	0.230450i
$61$	10.4422	+	8.56968i	1.33699	+	1.09724i	0.987042	+	0.160465i	$0.0512993\pi$
$61$	10.4422	+	8.56968i	1.33699	+	1.09724i	0.349944	+	0.936771i	$0.386201\pi$
$62$	−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	−0.133201	−	0.991089i	$-0.542525\pi$
$67$	−9.25954	−	7.59910i	−1.13123	−	0.928378i	−0.998032	+	0.0627107i	$0.980025\pi$
$68$	−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	−0.515872	−	0.856666i	$-0.672532\pi$
$71$	2.43148	−	12.2239i	0.288563	−	1.45071i	0.804435	−	0.594040i	$-0.202468\pi$
$72$	5.40689	+	0.162080i	0.637208	+	0.0191013i
$73$	10.6243	−	2.11330i	1.24348	−	0.247343i	0.470855	−	0.882211i	$-0.343945\pi$
$73$	10.6243	−	2.11330i	1.24348	−	0.247343i	0.772621	+	0.634868i	$0.218945\pi$
$74$	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	0.811214	−	0.584749i	$-0.198807\pi$
$79$	8.63355	+	3.57613i	0.971350	+	0.402346i	0.160135	+	0.987095i	$0.448807\pi$
$80$	−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	−0.896058	−	0.443936i	$-0.853582\pi$
$83$	−6.99093	−	13.0791i	−0.767355	−	1.43562i	0.128704	−	0.991683i	$-0.458918\pi$
$84$	−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	0.967180	−	0.254092i	$-0.0817765\pi$
$89$	3.41799	+	5.11538i	0.362306	+	0.542229i	−0.604874	+	0.796321i	$0.706777\pi$
$90$	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	0.546161	−	0.837680i	$-0.316089\pi$
$97$	−2.87112	−	2.87112i	−0.291519	−	0.291519i	−0.837680	+	0.546161i	$0.816089\pi$
$98$	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	0.980686	−	0.195591i	$-0.0626624\pi$
$101$	13.6970	+	7.32117i	1.36290	+	0.728484i	0.382212	+	0.924075i	$0.375162\pi$
$102$	−3.46633	+	8.93797i	−0.343218	+	0.884991i
$103$	5.66461	−	3.78497i	0.558150	−	0.372944i	−0.244267	−	0.969708i	$-0.578547\pi$
$103$	5.66461	−	3.78497i	0.558150	−	0.372944i	0.802417	+	0.596764i	$0.203547\pi$
$104$	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	−0.805032	−	0.593232i	$-0.797852\pi$
$107$	−3.93336	+	3.22803i	−0.380253	+	0.312065i	0.424779	+	0.905297i	$0.360352\pi$
$108$	−8.20744	−	6.13318i	−0.789761	−	0.590165i
$109$	10.9888	−	5.87362i	1.05253	−	0.562590i	0.147997	−	0.988988i	$-0.452717\pi$
$109$	10.9888	−	5.87362i	1.05253	−	0.562590i	0.904536	+	0.426397i	$0.140217\pi$
$110$	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	0.0888244	+	0.996047i	$0.471689\pi$
$113$	−7.21038	+	17.4074i	−0.678296	+	1.63755i	−0.767120	+	0.641503i	$0.778311\pi$
$114$	−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	−0.893484	−	0.449096i	$-0.851746\pi$
$131$	−3.18995	+	3.88697i	−0.278707	+	0.339606i	0.614776	+	0.788702i	$0.289246\pi$
$132$	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	−0.965666	−	0.259786i	$-0.916348\pi$
$137$	−2.02401	−	10.1754i	−0.172923	−	0.869341i	0.792744	−	0.609555i	$-0.208652\pi$
$138$	−7.57900	+	1.68753i	−0.645168	+	0.143652i
$139$	13.3520	+	1.31506i	1.13250	+	0.111542i	0.646856	−	0.762612i	$-0.276084\pi$
$139$	13.3520	+	1.31506i	1.13250	+	0.111542i	0.485648	+	0.874154i	$0.338584\pi$
$140$	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	−0.841422	−	0.540379i	$-0.818281\pi$
$149$	−5.80519	+	4.76419i	−0.475579	+	0.390298i	0.365842	+	0.930677i	$0.380781\pi$
$150$	1.45263	+	0.254761i	0.118607	+	0.0208012i
$151$	5.76297	−	8.62489i	0.468984	−	0.701884i	−0.519286	−	0.854600i	$-0.673802\pi$
$151$	5.76297	−	8.62489i	0.468984	−	0.701884i	0.988270	+	0.152717i	$0.0488022\pi$
$152$	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	−0.952183	−	0.305530i	$-0.901166\pi$
$157$	−0.976107	−	9.91058i	−0.0779018	−	0.790950i	0.874281	−	0.485421i	$-0.161334\pi$
$158$	−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	0.650956	−	0.759116i	$-0.274368\pi$
$163$	18.3528	−	1.80759i	1.43750	−	0.141581i	0.786544	+	0.617534i	$0.211868\pi$
$164$	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	0.661747	−	0.749727i	$-0.269815\pi$
$167$	−3.67203	−	5.49558i	−0.284150	−	0.425261i	−0.945897	+	0.324466i	$0.894815\pi$
$168$	−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	0.993847	+	0.110762i	$0.0353291\pi$
$173$	7.02091	+	13.1352i	0.533790	+	0.998651i	−0.460057	+	0.887890i	$0.652171\pi$
$174$	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	0.0416316	−	0.999133i	$-0.486744\pi$
$179$	−6.40646	−	1.94338i	−0.478842	−	0.145255i	−0.520473	+	0.853878i	$0.674244\pi$
$180$	1.27556	+	3.60601i	0.0950748	+	0.268776i
$181$	0.869814	−	8.83137i	0.0646528	−	0.656430i	−0.907177	−	0.420748i	$-0.861768\pi$
$181$	0.869814	−	8.83137i	0.0646528	−	0.656430i	0.971830	−	0.235682i	$-0.0757324\pi$
$182$	−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	$0.173404\pi$
$191$			14.3238i			1.03643i	−0.855250	+	0.518216i	$0.826596\pi$
$192$	−7.57998	+	3.48495i	−0.547038	+	0.251505i
$193$			21.5180i			1.54890i	0.632636	+	0.774449i	$0.281973\pi$
$193$			21.5180i			1.54890i	−0.632636	+	0.774449i	$0.718027\pi$
$194$	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	0.926475	−	0.376356i	$-0.122823\pi$
$197$	−0.743232	−	2.45011i	−0.0529531	−	0.174563i	−0.979428	+	0.201793i	$0.935323\pi$
$198$	10.7909	−	0.245381i	0.766875	−	0.0174385i
$199$	1.32753	−	6.67395i	0.0941062	−	0.473104i	−0.904778	−	0.425883i	$-0.859964\pi$
$199$	1.32753	−	6.67395i	0.0941062	−	0.473104i	0.998884	−	0.0472208i	$-0.0150364\pi$
$200$	−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	0.768827	−	0.639457i	$-0.220841\pi$
$211$	−2.75990	−	5.16341i	−0.189999	−	0.355464i	−0.958826	+	0.283993i	$0.908341\pi$
$212$	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	−0.887277	−	0.461237i	$-0.847406\pi$
$223$	−6.36213	+	6.36213i	−0.426039	+	0.426039i	0.461237	+	0.887277i	$0.347406\pi$
$224$	−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	0.724777	+	0.688983i	$0.241943\pi$
$227$	2.23497	+	22.6921i	0.148340	+	1.50613i	−0.576437	+	0.817142i	$0.695557\pi$
$228$	4.78150	−	13.2126i	0.316662	−	0.875024i
$229$	−21.9725	−	11.7445i	−1.45198	−	0.776100i	−0.458348	−	0.888773i	$-0.651559\pi$
$229$	−21.9725	−	11.7445i	−1.45198	−	0.776100i	−0.993632	+	0.112673i	$0.964059\pi$
$230$	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	−0.857799	−	0.513986i	$-0.828168\pi$
$233$	−0.834537	+	1.24897i	−0.0546723	+	0.0818229i	0.803126	+	0.595809i	$0.203168\pi$
$234$	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	0.995208	+	0.0977794i	$0.0311740\pi$
$239$	5.57521	+	13.4597i	0.360630	+	0.870638i	−0.634578	+	0.772859i	$0.718826\pi$
$240$	−2.66953	+	3.20528i	−0.172318	+	0.206900i
$241$	2.99072	−	7.22025i	0.192649	−	0.465097i	−0.797809	−	0.602911i	$-0.794008\pi$
$241$	2.99072	−	7.22025i	0.192649	−	0.465097i	0.990458	+	0.137814i	$0.0440075\pi$
$242$	−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	0.0884394	−	0.996082i	$-0.471812\pi$
$251$	11.3336	−	3.43800i	0.715367	−	0.217004i	0.626928	+	0.779077i	$0.284312\pi$
$252$	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	0.0912072	−	0.995832i	$-0.470927\pi$
$263$	−3.33454	−	0.663282i	−0.205617	−	0.0408997i	−0.296824	+	0.954932i	$0.595927\pi$
$264$	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	−0.983192	−	0.182576i	$-0.941556\pi$
$269$	−1.05401	+	3.47459i	−0.0642639	+	0.211850i	0.918928	+	0.394426i	$0.129056\pi$
$270$	1.94494	−	6.97898i	0.118365	−	0.424727i
$271$	5.41921	−	13.0831i	0.329194	−	0.794744i	−0.669459	−	0.742849i	$-0.733474\pi$
$271$	5.41921	−	13.0831i	0.329194	−	0.794744i	0.998653	−	0.0518950i	$-0.0165261\pi$
$272$	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	−0.565350	+	0.824851i	$0.691259\pi$
$277$	−24.7094	+	20.2785i	−1.48465	+	1.21842i	−0.919296	+	0.393566i	$0.871241\pi$
$278$	−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	0.0143542	−	0.999897i	$-0.495431\pi$
$281$	15.8181	−	10.5693i	0.943632	−	0.630514i	0.929277	+	0.369382i	$0.120431\pi$
$282$	−6.02443	−	2.33640i	−0.358750	−	0.139131i
$283$	−8.90106	−	4.75771i	−0.529113	−	0.282817i	0.185131	−	0.982714i	$-0.440729\pi$
$283$	−8.90106	−	4.75771i	−0.529113	−	0.282817i	−0.714244	+	0.699897i	$0.753229\pi$
$284$	−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	−0.639232	−	0.769014i	$-0.720748\pi$
$293$	6.08207	−	11.3788i	0.355318	−	0.664754i	0.994550	+	0.104260i	$0.0332476\pi$
$294$	−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	−0.402550	−	0.915398i	$-0.631876\pi$
$307$	−21.8286	−	6.62164i	−1.24583	−	0.377917i	−0.843276	+	0.537481i	$0.819376\pi$
$308$	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	−0.460756	−	0.887527i	$-0.652422\pi$
$311$	−9.64289	+	1.91809i	−0.546798	+	0.108765i	−0.0860418	+	0.996292i	$0.527422\pi$
$312$	2.03839	−	0.773618i	0.115401	−	0.0437975i
$313$	−0.313435	+	1.57574i	−0.0177164	+	0.0890663i	−0.988632	−	0.150356i	$-0.951958\pi$
$313$	−0.313435	+	1.57574i	−0.0177164	+	0.0890663i	0.970916	+	0.239422i	$0.0769580\pi$
$314$	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	0.403162	−	0.915129i	$-0.367911\pi$
$317$	−7.40186	−	6.07455i	−0.415730	−	0.341181i	−0.818892	+	0.573948i	$0.805411\pi$
$318$	−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	−0.999568	−	0.0293902i	$-0.990643\pi$
$331$	−0.245114	+	2.48868i	−0.0134727	+	0.136790i	0.986095	+	0.166181i	$0.0531434\pi$
$332$	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	−0.922898	−	0.385045i	$-0.874186\pi$
$337$	−23.9239	+	9.90959i	−1.30322	+	0.539810i	−0.380319	+	0.924855i	$0.624186\pi$
$338$	−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	−0.626675	−	0.779280i	$-0.715585\pi$
$347$	6.88181	−	12.8750i	0.369435	−	0.691164i	0.996110	+	0.0881166i	$0.0280848\pi$
$348$	4.40024	+	4.01722i	0.235877	+	0.215346i
$349$	11.8524	−	1.16736i	0.634444	−	0.0624872i	0.224318	−	0.974516i	$-0.427985\pi$
$349$	11.8524	−	1.16736i	0.634444	−	0.0624872i	0.410126	+	0.912029i	$0.365485\pi$
$350$	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	0.993023	−	0.117920i	$-0.0376228\pi$
$353$	16.4417	+	16.4417i	0.875103	+	0.875103i	−0.117920	+	0.993023i	$0.537623\pi$
$354$	−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	−0.940512	−	0.339760i	$-0.889654\pi$
$359$	−18.6921	+	12.4897i	−0.986533	+	0.659180i	−0.0460206	+	0.998940i	$0.514654\pi$
$360$	−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	0.893202	−	0.449656i	$-0.148453\pi$
$367$	−1.07935	−	2.60579i	−0.0563418	−	0.136021i	−0.949544	+	0.313635i	$0.898453\pi$
$368$	−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	0.0822060	−	0.996615i	$-0.473803\pi$
$373$	−0.610250	−	0.0601043i	−0.0315975	−	0.00311208i	−0.113804	+	0.993503i	$0.536303\pi$
$374$	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	0.298323	−	0.954465i	$-0.403573\pi$
$379$	20.9600	−	6.35814i	1.07664	−	0.326596i	0.778319	+	0.627869i	$0.216073\pi$
$380$	−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	0.348726	−	0.937225i	$-0.386614\pi$
$389$	22.8665	−	6.93646i	1.15938	−	0.351693i	0.810649	+	0.585532i	$0.199114\pi$
$390$	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	−0.438259	−	0.898849i	$-0.644405\pi$
$397$	8.47830	−	27.9492i	0.425513	−	1.40273i	0.863773	−	0.503881i	$-0.168095\pi$
$398$	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	0.999996	−	0.00276478i	$-0.000880057\pi$
$401$	5.82601	+	14.0652i	0.290937	+	0.702384i	−0.709059	+	0.705149i	$0.750880\pi$
$402$	−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	−0.966546	−	0.256495i	$-0.917432\pi$
$409$	−22.2351	+	14.8570i	−1.09946	+	0.734633i	−0.132911	+	0.991128i	$0.542432\pi$
$410$	−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	−0.278252	−	0.960508i	$-0.589755\pi$
$419$	−7.44623	+	0.733390i	−0.363772	+	0.0358285i	−0.0855200	+	0.996336i	$0.527255\pi$
$420$	0.748573	−	0.819945i	0.0365266	−	0.0400092i
$421$	−8.18252	+	15.3084i	−0.398792	+	0.746087i	−0.998535	−	0.0541055i	$-0.982769\pi$
$421$	−8.18252	+	15.3084i	−0.398792	+	0.746087i	0.599744	+	0.800192i	$0.295269\pi$
$422$	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	0.0503434	−	0.998732i	$-0.483968\pi$
$431$	16.4455	−	6.81195i	0.792152	−	0.328120i	0.741808	+	0.670612i	$0.233968\pi$
$432$	14.3847	+	14.5943i	0.692084	+	0.702167i
$433$	5.94474	+	2.46239i	0.285686	+	0.118335i	0.520925	−	0.853603i	$-0.325587\pi$
$433$	5.94474	+	2.46239i	0.285686	+	0.118335i	−0.235239	+	0.971938i	$0.575587\pi$
$434$	−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	−0.0123728	−	0.999923i	$-0.503938\pi$
$439$	7.51875	−	1.49557i	0.358850	−	0.0713798i	0.371223	+	0.928544i	$0.378938\pi$
$440$	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	0.999753	+	0.0222173i	$0.00707258\pi$
$443$	3.80608	+	12.5469i	0.180832	+	0.596123i	−0.818921	+	0.573906i	$0.805427\pi$
$444$	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	$0.0385245\pi$
$449$			5.11657i			0.241466i	−0.992685	+	0.120733i	$0.961476\pi$
$450$	−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	0.360167	−	0.932888i	$-0.382720\pi$
$457$	22.4447	−	4.46453i	1.04992	−	0.208842i	0.689752	+	0.724046i	$0.257720\pi$
$458$	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	0.853179	−	0.521618i	$-0.174671\pi$
$461$	27.3277	+	8.28975i	1.27278	+	0.386092i	0.419597	+	0.907711i	$0.362171\pi$
$462$	−1.53934	−	2.72880i	−0.0716165	−	0.126955i
$463$	27.3252	+	11.3185i	1.26991	+	0.526014i	0.912937	−	0.408101i	$-0.133809\pi$
$463$	27.3252	+	11.3185i	1.26991	+	0.526014i	0.356973	+	0.934115i	$0.383809\pi$
$464$	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	0.767030	−	0.641611i	$-0.221733\pi$
$467$	−4.16188	−	7.78632i	−0.192589	−	0.360308i	−0.959619	+	0.281303i	$0.909233\pi$
$468$	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	−0.118858	+	0.992911i	$0.537923\pi$
$479$	−24.3323	+	24.3323i	−1.11177	+	1.11177i	−0.992911	+	0.118858i	$0.962077\pi$
$480$	−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	−0.119563	−	0.992827i	$-0.538149\pi$
$487$	16.5938	−	11.0876i	0.751935	−	0.502427i	0.871498	+	0.490400i	$0.163149\pi$
$488$	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	−0.835950	−	0.548805i	$-0.815083\pi$
$491$	−10.2101	+	8.37922i	−0.460776	+	0.378149i	0.375174	+	0.926954i	$0.377583\pi$
$492$	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	−0.994176	−	0.107770i	$-0.965629\pi$
$499$	−2.40527	+	7.92912i	−0.107675	+	0.354956i	0.886501	+	0.462727i	$0.153129\pi$
$500$	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	0.965165	+	0.261641i	$0.0842635\pi$
$503$	3.89332	+	19.5730i	0.173594	+	0.872718i	−0.791571	+	0.611077i	$0.790737\pi$
$504$	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	−0.187268	−	0.982309i	$-0.559963\pi$
$509$	18.3354	−	22.3417i	0.812701	−	0.990278i	0.999968	−	0.00796952i	$-0.00253680\pi$
$510$	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	−0.987986	−	0.154547i	$-0.950608\pi$
$521$	−3.06656	−	15.4166i	−0.134348	−	0.675415i	0.853637	−	0.520868i	$-0.174392\pi$
$522$	1.67924	+	7.54176i	0.0734984	+	0.330094i
$523$	−1.99504	−	0.196495i	−0.0872372	−	0.00859212i	0.0543043	−	0.998524i	$-0.482706\pi$
$523$	−1.99504	−	0.196495i	−0.0872372	−	0.00859212i	−0.141542	+	0.989932i	$0.545206\pi$
$524$	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	0.323599	+	0.946194i	$0.395107\pi$
$541$	4.43816	+	45.0613i	0.190811	+	1.93734i	−0.132788	+	0.991144i	$0.542393\pi$
$542$	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	0.696447	−	0.717608i	$-0.254763\pi$
$547$	35.5384	−	3.50022i	1.51951	−	0.149659i	0.823064	+	0.567949i	$0.192263\pi$
$548$	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	0.999954	+	0.00955415i	$0.00304123\pi$
$557$	10.6759	+	19.9733i	0.452353	+	0.846294i	−0.547601	+	0.836740i	$0.684459\pi$
$558$	−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	−0.435173	−	0.900347i	$-0.643313\pi$
$563$	−30.7798	−	9.33694i	−1.29721	−	0.393505i	−0.862039	+	0.506842i	$0.830813\pi$
$564$	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	−0.762872	−	0.646549i	$-0.776212\pi$
$569$	4.51678	−	22.7074i	0.189353	−	0.951944i	0.952226	−	0.305395i	$-0.0987884\pi$
$570$	9.93309	−	0.225875i	0.416051	−	0.00946086i
$571$	2.16499	+	7.13701i	0.0906019	+	0.298674i	0.990517	−	0.137391i	$-0.0438717\pi$
$571$	2.16499	+	7.13701i	0.0906019	+	0.298674i	−0.899915	+	0.436065i	$0.856372\pi$
$572$	−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	$-0.915940\pi$
$577$		−	12.5400i		−	0.522047i	0.965332	−	0.261024i	$-0.0840601\pi$
$578$	−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	0.880599	+	0.473862i	$0.157140\pi$
$587$	−1.82984	+	18.5786i	−0.0755254	+	0.766822i	−0.956125	+	0.292960i	$0.905360\pi$
$588$	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	−0.125760	−	0.992061i	$-0.540137\pi$
$593$	11.8545	−	4.91031i	0.486807	−	0.201642i	0.612567	+	0.790419i	$0.290137\pi$
$594$	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	0.993311	−	0.115468i	$-0.0368367\pi$
$599$	31.0032	+	20.7157i	1.26676	+	0.846420i	0.273446	+	0.961887i	$0.411837\pi$
$600$	−2.79567	−	0.940412i	−0.114133	−	0.0383922i
$601$	7.18889	+	10.7589i	0.293241	+	0.438866i	0.948612	−	0.316441i	$-0.102488\pi$
$601$	7.18889	+	10.7589i	0.293241	+	0.438866i	−0.655371	+	0.755307i	$0.727488\pi$
$602$	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	−0.787442	−	0.616389i	$-0.788595\pi$
$607$	−4.21430	+	4.21430i	−0.171053	+	0.171053i	0.616389	+	0.787442i	$0.288595\pi$
$608$	−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	0.999471	−	0.0325319i	$-0.0103570\pi$
$613$	37.8240	+	20.2174i	1.52770	+	0.816571i	0.528227	+	0.849103i	$0.322857\pi$
$614$	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	−0.552218	−	0.833700i	$-0.686218\pi$
$617$	10.6647	−	15.9609i	0.429345	−	0.642560i	0.981563	+	0.191140i	$0.0612184\pi$
$618$	9.89641	+	1.73563i	0.398092	+	0.0698172i
$619$	1.05545	−	0.866186i	0.0424221	−	0.0348150i	−0.612943	−	0.790127i	$-0.710015\pi$
$619$	1.05545	−	0.866186i	0.0424221	−	0.0348150i	0.655365	+	0.755312i	$0.272515\pi$
$620$	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	0.846063	+	0.533083i	$0.178967\pi$
$631$	6.74225	+	33.8956i	0.268405	+	1.34936i	−0.577658	+	0.816279i	$0.696033\pi$
$632$	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	−0.881860	−	0.471512i	$-0.843708\pi$
$643$	−6.27255	+	7.64313i	−0.247365	+	0.301416i	0.634494	+	0.772928i	$0.281208\pi$
$644$	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	−0.652639	−	0.757669i	$-0.726338\pi$
$647$	−39.3128	−	7.81980i	−1.54555	−	0.307428i	−0.892907	+	0.450241i	$0.851338\pi$
$648$	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	−0.906266	−	0.422707i	$-0.861080\pi$
$653$	2.09824	−	6.91696i	0.0821103	−	0.270681i	0.988376	+	0.152026i	$0.0485798\pi$
$654$	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	−0.932638	−	0.360814i	$-0.882499\pi$
$659$	−29.5416	+	15.7903i	−1.15078	+	0.615104i	−0.218140	+	0.975917i	$0.569999\pi$
$660$	−4.98243	+	6.66751i	−0.193941	+	0.259532i
$661$	−21.8890	+	17.9638i	−0.851383	+	0.698712i	−0.955224	−	0.295882i	$-0.904386\pi$
$661$	−21.8890	+	17.9638i	−0.851383	+	0.698712i	0.103842	+	0.994594i	$0.466886\pi$
$662$	−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	−0.746503	−	0.665382i	$-0.768269\pi$
$673$	−2.10444	+	2.10444i	−0.0811203	+	0.0811203i	0.665382	+	0.746503i	$0.268269\pi$
$674$	−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	0.544602	+	0.838695i	$0.316681\pi$
$677$	−11.8469	+	22.1639i	−0.455312	+	0.851828i	−0.999914	+	0.0131336i	$0.995819\pi$
$678$	−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	0.877547	−	0.479491i	$-0.159179\pi$
$683$	6.16947	+	7.51752i	0.236068	+	0.287650i	−0.641479	+	0.767141i	$0.721679\pi$
$684$	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	0.555839	−	0.831290i	$-0.312397\pi$
$691$	14.6198	+	4.43485i	0.556162	+	0.168710i	0.000322946		1.00000i	$0.499897\pi$
$692$	−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	0.989770	−	0.142672i	$-0.0455695\pi$
$701$	27.6131	+	22.6615i	1.04293	+	0.855914i	0.0531638	+	0.998586i	$0.483069\pi$
$702$	−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	−0.751049	−	0.660246i	$-0.770452\pi$
$709$	−13.1375	−	43.3084i	−0.493388	−	1.62648i	0.257661	−	0.966235i	$-0.417048\pi$
$710$	−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	0.942489	−	0.334238i	$-0.108479\pi$
$719$	36.8048	+	15.2450i	1.37259	+	0.568544i	0.430098	+	0.902782i	$0.358479\pi$
$720$	−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	0.853164	−	0.521642i	$-0.174680\pi$
$727$	18.8126	+	12.5702i	0.697722	+	0.466203i	−0.155443	+	0.987845i	$0.549680\pi$
$728$	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	−0.204808	−	0.978802i	$-0.565657\pi$
$733$	−5.81346	+	0.572576i	−0.214725	+	0.0211486i	−0.00991747	+	0.999951i	$0.503157\pi$
$734$	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	0.881471	+	0.472238i	$0.156554\pi$
$739$	2.96492	+	30.1033i	0.109066	+	1.10737i	−0.772405	+	0.635131i	$0.780946\pi$
$740$	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	−0.690879	−	0.722971i	$-0.742776\pi$
$743$	−7.83201	+	5.23318i	−0.287329	+	0.191987i	0.403550	+	0.914958i	$0.367776\pi$
$744$	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	−0.999621	−	0.0275452i	$-0.991231\pi$
$751$	−8.55728	−	20.6591i	−0.312259	−	0.753861i	0.687361	−	0.726316i	$-0.258769\pi$
$752$	−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	−0.00983508	−	0.999952i	$-0.503131\pi$
$757$	−5.90338	−	0.581432i	−0.214562	−	0.0211325i	−0.204727	+	0.978819i	$0.565631\pi$
$758$	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	0.559764	−	0.828652i	$-0.310892\pi$
$761$	20.9602	+	4.16924i	0.759806	+	0.151135i	0.200043	+	0.979787i	$0.435892\pi$
$762$	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	−0.329030	−	0.944319i	$-0.606722\pi$
$773$	−2.16789	+	0.657622i	−0.0779736	+	0.0236530i	0.251057	+	0.967972i	$0.419222\pi$
$774$	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	−0.853936	−	0.520379i	$-0.825791\pi$
$787$	−25.1269	+	13.4306i	−0.895678	+	0.478750i	−0.0417420	+	0.999128i	$0.513291\pi$
$788$	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	−0.931506	−	0.363725i	$-0.881505\pi$
$797$	−2.50856	−	25.4699i	−0.0888579	−	0.902189i	0.842648	−	0.538464i	$-0.180995\pi$
$798$	−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	0.160677	−	0.987007i	$-0.448632\pi$
$809$	−19.6174	−	13.1079i	−0.689710	−	0.460850i	−0.850387	+	0.526157i	$0.823632\pi$
$810$	0.320865	+	0.457347i	0.0112740	+	0.0160695i
$811$	7.96434	+	9.70457i	0.279666	+	0.340774i	0.893831	−	0.448404i	$-0.148007\pi$
$811$	7.96434	+	9.70457i	0.279666	+	0.340774i	−0.614166	+	0.789177i	$0.710507\pi$
$812$	−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	0.956384	+	0.292112i	$0.0943579\pi$
$821$	−1.10634	+	11.2329i	−0.0386115	+	0.392029i	−0.994996	+	0.0999176i	$0.968142\pi$
$822$	8.20916	−	12.9120i	0.286327	−	0.450357i
$823$	7.56742	−	1.50525i	0.263784	−	0.0524698i	−0.0614265	−	0.998112i	$-0.519565\pi$
$823$	7.56742	−	1.50525i	0.263784	−	0.0524698i	0.325210	+	0.945642i	$0.394565\pi$
$824$	−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	0.954969	−	0.296704i	$-0.0958875\pi$
$827$	−0.112115	−	0.369592i	−0.00389860	−	0.0128520i	−0.958868	+	0.283852i	$0.908388\pi$
$828$	17.2353	+	10.4153i	0.598968	+	0.361958i
$829$	−7.70041	−	6.31956i	−0.267446	−	0.219487i	0.491106	−	0.871100i	$-0.336593\pi$
$829$	−7.70041	−	6.31956i	−0.267446	−	0.219487i	−0.758552	+	0.651612i	$0.774093\pi$
$830$	−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	−0.397436	−	0.917630i	$-0.630100\pi$
$839$	9.29528	−	46.7305i	0.320909	−	1.61332i	0.718344	−	0.695688i	$-0.244900\pi$
$840$	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	−0.984372	−	0.176100i	$-0.943652\pi$
$853$	−28.1853	−	34.3439i	−0.965047	−	1.17591i	0.0193247	−	0.999813i	$-0.493848\pi$
$854$	−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	0.717513	−	0.696545i	$-0.245280\pi$
$857$	−5.87222	−	8.78840i	−0.200591	−	0.300206i	−0.918104	+	0.396339i	$0.870280\pi$
$858$	3.98040	−	1.75579i	0.135889	−	0.0599416i
$859$	−17.2641	+	32.2989i	−0.589044	+	1.10202i	0.394079	+	0.919077i	$0.371064\pi$
$859$	−17.2641	+	32.2989i	−0.589044	+	1.10202i	−0.983123	+	0.182947i	$0.941436\pi$
$860$	−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	−0.923168	−	0.384396i	$-0.874410\pi$
$863$	−15.8274	+	15.8274i	−0.538772	+	0.538772i	0.384396	+	0.923168i	$0.374410\pi$
$864$	−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	−0.810107	−	0.586282i	$-0.800591\pi$
$877$	−22.8830	+	12.2312i	−0.772704	+	0.413019i	0.0374038	+	0.999300i	$0.488091\pi$
$878$	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	−0.161023	−	0.986951i	$-0.551479\pi$
$881$	19.3143	−	46.6290i	0.650717	−	1.57097i	0.811740	−	0.584019i	$-0.198521\pi$
$882$	17.4994	+	4.87681i	0.589234	+	0.164211i
$883$	−9.77632	+	32.2282i	−0.328999	+	1.08457i	0.623957	+	0.781459i	$0.285524\pi$
$883$	−9.77632	+	32.2282i	−0.328999	+	1.08457i	−0.952957	+	0.303107i	$0.901976\pi$
$884$	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	−0.927721	−	0.373275i	$-0.878235\pi$
$887$	−6.35752	−	31.9614i	−0.213465	−	1.07316i	0.714256	−	0.699884i	$-0.246765\pi$
$888$	−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	0.242924	−	0.970045i	$-0.421893\pi$
$907$	8.79201	+	0.865937i	0.291934	+	0.0287530i	0.0490098	+	0.998798i	$0.484393\pi$
$908$	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	−0.759044	−	0.651039i	$-0.774333\pi$
$911$	7.18456	−	17.3451i	0.238035	−	0.574668i	0.997079	+	0.0763713i	$0.0243334\pi$
$912$	−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	−0.962783	−	0.270275i	$-0.912885\pi$
$919$	−10.4478	+	15.6362i	−0.344640	+	0.515790i	0.618143	+	0.786066i	$0.287885\pi$
$920$	−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	−0.754739	−	0.656025i	$-0.772237\pi$
$929$	−3.00877	+	3.00877i	−0.0987144	+	0.0987144i	0.656025	+	0.754739i	$0.272237\pi$
$930$	−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	−0.917565	−	0.397585i	$-0.869848\pi$
$937$	−50.0794	−	33.4620i	−1.63602	−	1.09316i	−0.718458	−	0.695571i	$-0.755152\pi$
$938$	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	0.979125	−	0.203260i	$-0.0651538\pi$
$941$	8.16426	+	15.2743i	0.266147	+	0.497926i	−0.712977	+	0.701187i	$0.752654\pi$
$942$	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	0.536021	−	0.844205i	$-0.319927\pi$
$947$	15.7772	+	4.78597i	0.512691	+	0.155523i	−0.0233297	+	0.999728i	$0.507427\pi$
$948$	−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	−0.958630	−	0.284656i	$-0.908121\pi$
$953$	1.11016	−	5.58116i	0.0359616	−	0.180791i	0.994591	+	0.103864i	$0.0331207\pi$
$954$	−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	−0.923514	−	0.383565i	$-0.874696\pi$
$967$	2.37845	−	11.9573i	0.0764857	−	0.384520i	1.00000		0.000954529i	$-0.000303836\pi$
$968$	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	0.916252	+	0.400601i	$0.131199\pi$
$971$	−1.88673	+	19.1563i	−0.0605479	+	0.614754i	−0.976800	+	0.214152i	$0.931301\pi$
$972$	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	−0.372084	−	0.928199i	$-0.621357\pi$
$977$	0.661067	−	0.273823i	0.0211494	−	0.00876037i	0.393233	+	0.919439i	$0.371357\pi$
$978$	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	0.109968	−	0.993935i	$-0.464925\pi$
$983$	−24.0233	−	16.0519i	−0.766226	−	0.511976i	−0.876193	+	0.481959i	$0.839925\pi$
$984$	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	0.353897	−	0.935285i	$-0.384857\pi$
$991$	40.5836	−	40.5836i	1.28918	−	1.28918i	0.935285	−	0.353897i	$-0.115143\pi$
$992$	−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	0.971430	−	0.237328i	$-0.0762716\pi$
$997$	41.4835	+	22.1734i	1.31380	+	0.702239i	0.342366	+	0.939566i	$0.388772\pi$
$998$	−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.341.31	✓	1024
128.125	even	32	inner	640.2.bm.a.381.31	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.31	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.31	yes	1024	128.125	even	32	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 $\F_{q}$

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

Related objects

Downloads

Learn more