LMFDB - Embedded newform 384.2.v.a.13.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			13.29
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.31365 + 0.523755i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.45136 + 1.37606i) q^{4} +(0.344860 + 3.50142i) q^{5} +(0.119870 - 1.40912i) q^{6} +(1.21392 - 1.81675i) q^{7} +(1.18586 + 2.56783i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(1.31365 + 0.523755i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.45136 + 1.37606i) q^{4} +(0.344860 + 3.50142i) q^{5} +(0.119870 - 1.40912i) q^{6} +(1.21392 - 1.81675i) q^{7} +(1.18586 + 2.56783i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-1.38086 + 4.78027i) q^{10} +(0.838508 - 0.448192i) q^{11} +(0.895504 - 1.78832i) q^{12} +(-4.53507 - 0.446666i) q^{13} +(2.54620 - 1.75079i) q^{14} +(3.25054 - 1.34642i) q^{15} +(0.212895 + 3.99433i) q^{16} +(5.82086 + 2.41108i) q^{17} +(-1.38324 + 0.294339i) q^{18} +(-2.76333 + 2.26781i) q^{19} +(-4.31767 + 5.55638i) q^{20} +(-2.09090 - 0.634269i) q^{21} +(1.33625 - 0.149595i) q^{22} +(1.01866 - 5.12116i) q^{23} +(2.11302 - 1.88020i) q^{24} +(-7.23711 + 1.43955i) q^{25} +(-5.72356 - 2.96203i) q^{26} +(0.773010 + 0.634393i) q^{27} +(4.26180 - 0.966338i) q^{28} +(2.86453 - 5.35916i) q^{29} +(4.97528 - 0.0662358i) q^{30} +(5.07838 - 5.07838i) q^{31} +(-1.81238 + 5.35866i) q^{32} +(-0.672299 - 0.672299i) q^{33} +(6.38376 + 6.21602i) q^{34} +(6.77985 + 3.62391i) q^{35} +(-1.97126 - 0.337823i) q^{36} +(0.734966 - 0.895559i) q^{37} +(-4.81783 + 1.53180i) q^{38} +(0.889030 + 4.46945i) q^{39} +(-8.58209 + 5.03774i) q^{40} +(-7.43439 - 1.47879i) q^{41} +(-2.41452 - 1.92833i) q^{42} +(0.662763 - 2.18484i) q^{43} +(1.83372 + 0.503353i) q^{44} +(-2.23203 - 2.71973i) q^{45} +(4.02040 - 6.19389i) q^{46} +(0.0750833 - 0.181267i) q^{47} +(3.76054 - 1.36322i) q^{48} +(0.851784 + 2.05639i) q^{49} +(-10.2610 - 1.89941i) q^{50} +(0.617552 - 6.27011i) q^{51} +(-5.96739 - 6.88883i) q^{52} +(-6.16699 - 11.5376i) q^{53} +(0.683199 + 1.23824i) q^{54} +(1.85848 + 2.78141i) q^{55} +(6.10464 + 0.962708i) q^{56} +(2.97231 + 1.98603i) q^{57} +(6.56988 - 5.53975i) q^{58} +(-4.87224 + 0.479874i) q^{59} +(6.57047 + 2.51882i) q^{60} +(0.0109391 - 0.00331835i) q^{61} +(9.33106 - 4.01140i) q^{62} +2.18499i q^{63} +(-5.18747 + 6.09017i) q^{64} -16.0332i q^{65} +(-0.531046 - 1.23529i) q^{66} +(-10.8712 + 3.29775i) q^{67} +(5.13037 + 11.5092i) q^{68} +(-5.19635 + 0.511796i) q^{69} +(7.00832 + 8.31153i) q^{70} +(-6.04869 - 4.04160i) q^{71} +(-2.41262 - 1.47624i) q^{72} +(-5.66473 - 8.47786i) q^{73} +(1.43454 - 0.791510i) q^{74} +(3.47838 + 6.50760i) q^{75} +(-7.13124 - 0.511115i) q^{76} +(0.203624 - 2.06743i) q^{77} +(-1.17303 + 6.33694i) q^{78} +(-2.80044 - 6.76087i) q^{79} +(-13.9124 + 2.12292i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-8.99167 - 5.83642i) q^{82} +(10.2385 + 12.4756i) q^{83} +(-2.16186 - 3.79777i) q^{84} +(-6.43482 + 21.2128i) q^{85} +(2.01496 - 2.52299i) q^{86} +(-5.95992 - 1.18550i) q^{87} +(2.14523 + 1.62165i) q^{88} +(2.36745 + 11.9020i) q^{89} +(-1.50763 - 4.74182i) q^{90} +(-6.31668 + 7.69689i) q^{91} +(8.52550 - 6.03091i) q^{92} +(-6.33389 - 3.38553i) q^{93} +(0.193573 - 0.198796i) q^{94} +(-8.89352 - 8.89352i) q^{95} +(5.65403 + 0.178805i) q^{96} +(5.26632 - 5.26632i) q^{97} +(0.0419027 + 3.14750i) q^{98} +(-0.448192 + 0.838508i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	1.31365	+	0.523755i	0.928892	+	0.370351i
$2$	1.31365	+	0.523755i	0.928892	+	0.370351i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	1.45136	+	1.37606i	0.725680	+	0.688032i
$5$	0.344860	+	3.50142i	0.154226	+	1.56588i	0.691438	+	0.722436i	$0.256978\pi$
$5$	0.344860	+	3.50142i	0.154226	+	1.56588i	−0.537211	+	0.843448i	$0.680522\pi$
$6$	0.119870	−	1.40912i	0.0489366	−	0.575273i
$7$	1.21392	−	1.81675i	0.458817	−	0.686668i	−0.527865	−	0.849328i	$-0.677007\pi$
$7$	1.21392	−	1.81675i	0.458817	−	0.686668i	0.986682	+	0.162660i	$0.0520074\pi$
$8$	1.18586	+	2.56783i	0.419265	+	0.907864i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	−1.38086	+	4.78027i	−0.436667	+	1.51165i
$11$	0.838508	−	0.448192i	0.252820	−	0.135135i	−0.340119	−	0.940382i	$-0.610468\pi$
$11$	0.838508	−	0.448192i	0.252820	−	0.135135i	0.592939	+	0.805247i	$0.297968\pi$
$12$	0.895504	−	1.78832i	0.258510	−	0.516242i
$13$	−4.53507	−	0.446666i	−1.25780	−	0.123883i	−0.552937	−	0.833223i	$-0.686493\pi$
$13$	−4.53507	−	0.446666i	−1.25780	−	0.123883i	−0.704866	+	0.709340i	$0.748993\pi$
$14$	2.54620	−	1.75079i	0.680499	−	0.467917i
$15$	3.25054	−	1.34642i	0.839287	−	0.347644i
$16$	0.212895	+	3.99433i	0.0532237	+	0.998583i
$17$	5.82086	+	2.41108i	1.41177	+	0.584773i	0.952777	−	0.303670i	$-0.0982120\pi$
$17$	5.82086	+	2.41108i	1.41177	+	0.584773i	0.458988	+	0.888442i	$0.348212\pi$
$18$	−1.38324	+	0.294339i	−0.326034	+	0.0693764i
$19$	−2.76333	+	2.26781i	−0.633952	+	0.520271i	−0.895582	−	0.444897i	$-0.853240\pi$
$19$	−2.76333	+	2.26781i	−0.633952	+	0.520271i	0.261630	+	0.965168i	$0.415740\pi$
$20$	−4.31767	+	5.55638i	−0.965459	+	1.24244i
$21$	−2.09090	−	0.634269i	−0.456273	−	0.138409i
$22$	1.33625	−	0.149595i	0.284889	−	0.0318937i
$23$	1.01866	−	5.12116i	0.212406	−	1.06784i	−0.716519	−	0.697568i	$-0.754266\pi$
$23$	1.01866	−	5.12116i	0.212406	−	1.06784i	0.928925	−	0.370269i	$-0.120734\pi$
$24$	2.11302	−	1.88020i	0.431318	−	0.383794i
$25$	−7.23711	+	1.43955i	−1.44742	+	0.287910i
$26$	−5.72356	−	2.96203i	−1.12248	−	0.580902i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	4.26180	−	0.966338i	0.805404	−	0.182621i
$29$	2.86453	−	5.35916i	0.531930	−	0.995170i	−0.462179	−	0.886786i	$-0.652932\pi$
$29$	2.86453	−	5.35916i	0.531930	−	0.995170i	0.994109	−	0.108384i	$-0.0345676\pi$
$30$	4.97528	−	0.0662358i	0.908357	−	0.0120930i
$31$	5.07838	−	5.07838i	0.912105	−	0.912105i	−0.0843329	−	0.996438i	$-0.526876\pi$
$31$	5.07838	−	5.07838i	0.912105	−	0.912105i	0.996438	+	0.0843329i	$0.0268759\pi$
$32$	−1.81238	+	5.35866i	−0.320387	+	0.947287i
$33$	−0.672299	−	0.672299i	−0.117032	−	0.117032i
$34$	6.38376	+	6.21602i	1.09481	+	1.06604i
$35$	6.77985	+	3.62391i	1.14600	+	0.612552i
$36$	−1.97126	−	0.337823i	−0.328544	−	0.0563038i
$37$	0.734966	−	0.895559i	0.120828	−	0.147229i	−0.709083	−	0.705125i	$-0.750891\pi$
$37$	0.734966	−	0.895559i	0.120828	−	0.147229i	0.829911	+	0.557896i	$0.188391\pi$
$38$	−4.81783	+	1.53180i	−0.781556	+	0.248491i
$39$	0.889030	+	4.46945i	0.142359	+	0.715686i
$40$	−8.58209	+	5.03774i	−1.35695	+	0.796537i
$41$	−7.43439	−	1.47879i	−1.16106	−	0.230948i	−0.423283	−	0.905997i	$-0.639122\pi$
$41$	−7.43439	−	1.47879i	−1.16106	−	0.230948i	−0.737773	+	0.675049i	$0.764122\pi$
$42$	−2.41452	−	1.92833i	−0.372568	−	0.297548i
$43$	0.662763	−	2.18484i	0.101070	−	0.333184i	−0.891793	−	0.452444i	$-0.850552\pi$
$43$	0.662763	−	2.18484i	0.101070	−	0.333184i	0.992863	+	0.119260i	$0.0380522\pi$
$44$	1.83372	+	0.503353i	0.276443	+	0.0758833i
$45$	−2.23203	−	2.71973i	−0.332731	−	0.405434i
$46$	4.02040	−	6.19389i	0.592776	−	0.913240i
$47$	0.0750833	−	0.181267i	0.0109520	−	0.0264405i	−0.918309	−	0.395865i	$-0.870445\pi$
$47$	0.0750833	−	0.181267i	0.0109520	−	0.0264405i	0.929261	+	0.369424i	$0.120445\pi$
$48$	3.76054	−	1.36322i	0.542787	−	0.196764i
$49$	0.851784	+	2.05639i	0.121683	+	0.293770i
$50$	−10.2610	−	1.89941i	−1.45113	−	0.268617i
$51$	0.617552	−	6.27011i	0.0864746	−	0.877992i
$52$	−5.96739	−	6.88883i	−0.827527	−	0.955308i
$53$	−6.16699	−	11.5376i	−0.847101	−	1.58481i	−0.810689	−	0.585477i	$-0.800907\pi$
$53$	−6.16699	−	11.5376i	−0.847101	−	1.58481i	−0.0364120	−	0.999337i	$-0.511593\pi$
$54$	0.683199	+	1.23824i	0.0929717	+	0.168503i
$55$	1.85848	+	2.78141i	0.250597	+	0.375045i
$56$	6.10464	+	0.962708i	0.815767	+	0.128647i
$57$	2.97231	+	1.98603i	0.393692	+	0.263057i
$58$	6.56988	−	5.53975i	0.862668	−	0.727405i
$59$	−4.87224	+	0.479874i	−0.634311	+	0.0624742i	−0.410062	−	0.912058i	$-0.634493\pi$
$59$	−4.87224	+	0.479874i	−0.634311	+	0.0624742i	−0.224249	+	0.974532i	$0.571993\pi$
$60$	6.57047	+	2.51882i	0.848244	+	0.325178i
$61$	0.0109391	−	0.00331835i	0.00140061	−	0.000424872i	−0.289584	−	0.957153i	$-0.593517\pi$
$61$	0.0109391	−	0.00331835i	0.00140061	−	0.000424872i	0.290985	+	0.956728i	$0.406017\pi$
$62$	9.33106	−	4.01140i	1.18505	−	0.509448i
$63$			2.18499i			0.275283i
$64$	−5.18747	+	6.09017i	−0.648434	+	0.761271i
$65$		−	16.0332i		−	1.98868i
$66$	−0.531046	−	1.23529i	−0.0653672	−	0.152053i
$67$	−10.8712	+	3.29775i	−1.32813	+	0.402885i	−0.873079	−	0.487579i	$-0.837880\pi$
$67$	−10.8712	+	3.29775i	−1.32813	+	0.402885i	−0.455054	+	0.890464i	$0.650380\pi$
$68$	5.13037	+	11.5092i	0.622148	+	1.39570i
$69$	−5.19635	+	0.511796i	−0.625567	+	0.0616130i
$70$	7.00832	+	8.31153i	0.837654	+	0.993418i
$71$	−6.04869	−	4.04160i	−0.717847	−	0.479650i	0.142217	−	0.989835i	$-0.454577\pi$
$71$	−6.04869	−	4.04160i	−0.717847	−	0.479650i	−0.860065	+	0.510185i	$0.829577\pi$
$72$	−2.41262	−	1.47624i	−0.284329	−	0.173977i
$73$	−5.66473	−	8.47786i	−0.663006	−	0.992259i	−0.998734	−	0.0503000i	$-0.983982\pi$
$73$	−5.66473	−	8.47786i	−0.663006	−	0.992259i	0.335728	−	0.941959i	$-0.391018\pi$
$74$	1.43454	−	0.791510i	0.166762	−	0.0920111i
$75$	3.47838	+	6.50760i	0.401649	+	0.751433i
$76$	−7.13124	−	0.511115i	−0.818010	−	0.0586290i
$77$	0.203624	−	2.06743i	0.0232051	−	0.235605i
$78$	−1.17303	+	6.33694i	−0.132819	+	0.717517i
$79$	−2.80044	−	6.76087i	−0.315074	−	0.760657i	−0.999501	−	0.0315754i	$-0.989948\pi$
$79$	−2.80044	−	6.76087i	−0.315074	−	0.760657i	0.684427	−	0.729081i	$-0.260052\pi$
$80$	−13.9124	+	2.12292i	−1.55546	+	0.237350i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	−8.99167	−	5.83642i	−0.992964	−	0.644524i
$83$	10.2385	+	12.4756i	1.12382	+	1.36938i	0.920723	+	0.390217i	$0.127600\pi$
$83$	10.2385	+	12.4756i	1.12382	+	1.36938i	0.203095	+	0.979159i	$0.434900\pi$
$84$	−2.16186	−	3.79777i	−0.235878	−	0.414371i
$85$	−6.43482	+	21.2128i	−0.697955	+	2.30085i
$86$	2.01496	−	2.52299i	0.217279	−	0.272061i
$87$	−5.95992	−	1.18550i	−0.638971	−	0.127099i
$88$	2.14523	+	1.62165i	0.228682	+	0.172868i
$89$	2.36745	+	11.9020i	0.250949	+	1.26161i	0.876492	+	0.481416i	$0.159877\pi$
$89$	2.36745	+	11.9020i	0.250949	+	1.26161i	−0.625543	+	0.780189i	$0.715123\pi$
$90$	−1.50763	−	4.74182i	−0.158918	−	0.499831i
$91$	−6.31668	+	7.69689i	−0.662168	+	0.806854i
$92$	8.52550	−	6.03091i	0.888844	−	0.628766i
$93$	−6.33389	−	3.38553i	−0.656794	−	0.351063i
$94$	0.193573	−	0.198796i	0.0199655	−	0.0205043i
$95$	−8.89352	−	8.89352i	−0.912456	−	0.912456i
$96$	5.65403	+	0.178805i	0.577062	+	0.0182492i
$97$	5.26632	−	5.26632i	0.534713	−	0.534713i	−0.387258	−	0.921971i	$-0.626578\pi$
$97$	5.26632	−	5.26632i	0.534713	−	0.534713i	0.921971	+	0.387258i	$0.126578\pi$
$98$	0.0419027	+	3.14750i	0.00423281	+	0.317946i
$99$	−0.448192	+	0.838508i	−0.0450450	+	0.0842732i
$100$	−12.4846	−	7.86942i	−1.24846	−	0.786942i
$101$	1.99538	+	1.63757i	0.198548	+	0.162944i	0.728414	−	0.685137i	$-0.240258\pi$
$101$	1.99538	+	1.63757i	0.198548	+	0.162944i	−0.529866	+	0.848081i	$0.677758\pi$
$102$	4.09525	−	7.91330i	0.405491	−	0.783533i
$103$	−0.0200763	+	0.00399343i	−0.00197818	+	0.000393485i	−0.196079	−	0.980588i	$-0.562821\pi$
$103$	−0.0200763	+	0.00399343i	−0.00197818	+	0.000393485i	0.194101	+	0.980982i	$0.437821\pi$
$104$	−4.23101	−	12.1750i	−0.414884	−	1.19385i
$105$	1.49977	−	7.53988i	0.146363	−	0.735817i
$106$	−2.05838	−	18.3864i	−0.199928	−	1.78585i
$107$	18.4978	+	5.61126i	1.78825	+	0.542461i	0.997564	−	0.0697553i	$-0.0222219\pi$
$107$	18.4978	+	5.61126i	1.78825	+	0.542461i	0.790690	+	0.612216i	$0.209722\pi$
$108$	0.248951	+	1.98445i	0.0239553	+	0.190953i
$109$	−7.59743	+	6.23505i	−0.727702	+	0.597209i	−0.923574	−	0.383420i	$-0.874746\pi$
$109$	−7.59743	+	6.23505i	−0.727702	+	0.597209i	0.195872	+	0.980629i	$0.437246\pi$
$110$	0.984613	+	4.62719i	0.0938792	+	0.441185i
$111$	−1.07035	−	0.443352i	−0.101593	−	0.0420811i
$112$	7.51515	+	4.46200i	0.710115	+	0.421620i
$113$	11.1376	−	4.61333i	1.04773	−	0.433985i	0.208651	−	0.977990i	$-0.433093\pi$
$113$	11.1376	−	4.61333i	1.04773	−	0.433985i	0.839082	+	0.544005i	$0.183093\pi$
$114$	2.86438	+	4.16572i	0.268274	+	0.390156i
$115$	18.2827	+	1.80068i	1.70487	+	0.167915i
$116$	11.5320	−	3.83629i	1.07072	−	0.356191i
$117$	4.01893	−	2.14816i	0.371550	−	0.198598i
$118$	−6.65176	−	1.92147i	−0.612344	−	0.176886i
$119$	11.4464	−	7.64822i	1.04929	−	0.701111i
$120$	7.31207	+	6.75017i	0.667497	+	0.616203i
$121$	−5.60905	+	8.39454i	−0.509914	+	0.763140i
$122$	0.0161082	+	0.00137028i	0.00145837	+	0.000124059i
$123$	0.742973	+	7.54353i	0.0669916	+	0.680178i
$124$	14.3587	−	0.382384i	1.28945	−	0.0343391i
$125$	−2.42962	−	8.00940i	−0.217312	−	0.716382i
$126$	−1.14440	+	2.87032i	−0.101951	+	0.255708i
$127$	10.7118			0.950522			0.475261	−	0.879845i	$-0.342354\pi$
$127$	10.7118			0.950522			0.475261	+	0.879845i	$0.342354\pi$
$128$	−10.0043	+	5.28340i	−0.884262	+	0.466991i
$129$	−2.28315			−0.201020
$130$	8.39750	−	21.0621i	0.736509	−	1.84727i
$131$	−3.96368	−	13.0665i	−0.346308	−	1.14162i	−0.941209	−	0.337825i	$-0.890309\pi$
$131$	−3.96368	−	13.0665i	−0.346308	−	1.14162i	0.594901	−	0.803799i	$-0.297191\pi$
$132$	−0.0506216	−	1.90087i	−0.00440604	−	0.165450i
$133$	0.765595	+	7.77322i	0.0663855	+	0.674024i
$134$	−16.0082	−	1.36177i	−1.38290	−	0.117639i
$135$	−1.95470	+	2.92541i	−0.168234	+	0.251779i
$136$	0.711496	+	17.8062i	0.0610103	+	1.52687i
$137$	3.20390	−	2.14077i	0.273727	−	0.182899i	−0.411128	−	0.911577i	$-0.634865\pi$
$137$	3.20390	−	2.14077i	0.273727	−	0.182899i	0.684856	+	0.728679i	$0.259865\pi$
$138$	−7.09425	−	2.04930i	−0.603903	−	0.174448i
$139$	4.35792	−	2.32936i	0.369634	−	0.197574i	−0.276112	−	0.961125i	$-0.589046\pi$
$139$	4.35792	−	2.32936i	0.369634	−	0.197574i	0.645747	+	0.763552i	$0.276546\pi$
$140$	4.85328	+	14.5891i	0.410177	+	1.23300i
$141$	−0.195257	−	0.0192312i	−0.0164436	−	0.00161956i
$142$	−5.82906	−	8.47729i	−0.489164	−	0.711399i
$143$	−4.00289	+	1.65805i	−0.334738	+	0.138653i
$144$	−2.39615	−	3.20289i	−0.199679	−	0.266907i
$145$	19.7525	+	8.18177i	1.64036	+	0.679459i
$146$	−3.00115	−	14.1039i	−0.248377	−	1.16725i
$147$	1.72058	−	1.41204i	0.141911	−	0.116463i
$148$	2.29905	−	0.288418i	0.188981	−	0.0237078i
$149$	3.76747	+	1.14285i	0.308643	+	0.0936259i	0.440807	−	0.897602i	$-0.354692\pi$
$149$	3.76747	+	1.14285i	0.308643	+	0.0936259i	−0.132164	+	0.991228i	$0.542192\pi$
$150$	1.16099	+	10.3705i	0.0947948	+	0.846751i
$151$	1.88016	−	9.45221i	0.153005	−	0.769210i	−0.825727	−	0.564070i	$-0.809235\pi$
$151$	1.88016	−	9.45221i	0.153005	−	0.769210i	0.978733	−	0.205140i	$-0.0657651\pi$
$152$	−9.10027	−	4.40645i	−0.738129	−	0.357411i
$153$	−6.17939	+	1.22916i	−0.499574	+	0.0993715i
$154$	1.35032	−	2.60923i	0.108812	−	0.210258i
$155$	19.5329	+	16.0302i	1.56892	+	1.28758i
$156$	−4.85995	+	7.71015i	−0.389108	+	0.617306i
$157$	−9.73990	+	18.2221i	−0.777329	+	1.45428i	0.110387	+	0.993889i	$0.464791\pi$
$157$	−9.73990	+	18.2221i	−0.777329	+	1.45428i	−0.887716	+	0.460391i	$0.847709\pi$
$158$	−0.137765	−	10.3482i	−0.0109600	−	0.823256i
$159$	−9.25063	+	9.25063i	−0.733623	+	0.733623i
$160$	−19.3880	−	4.49793i	−1.53275	−	0.355593i
$161$	−8.06732	−	8.06732i	−0.635794	−	0.635794i
$162$	0.986600	−	1.01322i	0.0775146	−	0.0796063i
$163$	−9.27279	−	4.95641i	−0.726301	−	0.388216i	0.0664271	−	0.997791i	$-0.478840\pi$
$163$	−9.27279	−	4.95641i	−0.726301	−	0.388216i	−0.792728	+	0.609575i	$0.791340\pi$
$164$	−8.75506	−	12.3765i	−0.683656	−	0.966439i
$165$	2.12215	−	2.58585i	0.165209	−	0.201308i
$166$	6.91561	+	21.7511i	0.536755	+	1.68821i
$167$	−0.738474	−	3.71256i	−0.0571449	−	0.287287i	0.941637	−	0.336630i	$-0.109287\pi$
$167$	−0.738474	−	3.71256i	−0.0571449	−	0.287287i	−0.998782	+	0.0493433i	$0.984287\pi$
$168$	−0.850829	−	6.12124i	−0.0656429	−	0.472264i
$169$	7.61717	+	1.51515i	0.585936	+	0.116550i
$170$	−19.5634	+	24.4959i	−1.50045	+	1.87875i
$171$	1.03770	−	3.42084i	0.0793549	−	0.261598i
$172$	3.96838	−	2.25898i	0.302586	−	0.172246i
$173$	15.3667	+	18.7244i	1.16831	+	1.42359i	0.885638	+	0.464376i	$0.153721\pi$
$173$	15.3667	+	18.7244i	1.16831	+	1.42359i	0.282674	+	0.959216i	$0.408779\pi$
$174$	−7.20835	−	4.67888i	−0.546463	−	0.354705i
$175$	−6.16993	+	14.8955i	−0.466403	+	1.12600i
$176$	1.96874	+	3.25386i	0.148399	+	0.245269i
$177$	1.87355	+	4.52314i	0.140824	+	0.339980i
$178$	−3.12372	+	16.8750i	−0.234132	+	1.26483i
$179$	0.491273	−	4.98798i	0.0367195	−	0.372819i	−0.959211	−	0.282692i	$-0.908773\pi$
$179$	0.491273	−	4.98798i	0.0367195	−	0.372819i	0.995930	−	0.0901272i	$-0.0287274\pi$
$180$	0.503051	−	7.01872i	0.0374952	−	0.523145i
$181$	5.50760	+	10.3040i	0.409377	+	0.765890i	0.999130	−	0.0416932i	$-0.0132752\pi$
$181$	5.50760	+	10.3040i	0.409377	+	0.765890i	−0.589754	+	0.807583i	$0.700775\pi$
$182$	−12.3292	+	6.80264i	−0.913901	+	0.504245i
$183$	−0.00635093	−	0.00950484i	−0.000469474	−	0.000702618i
$184$	14.3583	−	3.45724i	1.05850	−	0.254871i
$185$	3.38919	+	2.26458i	0.249178	+	0.166496i
$186$	−6.54733	−	7.76482i	−0.480073	−	0.569344i
$187$	5.96146	−	0.587153i	0.435945	−	0.0429368i
$188$	0.358408	−	0.159764i	0.0261396	−	0.0116520i
$189$	2.09090	−	0.634269i	0.152091	−	0.0461363i
$190$	−7.02496	−	16.3410i	−0.509644	−	1.18550i
$191$			23.0914i			1.67084i	0.549613	+	0.835419i	$0.314775\pi$
$191$			23.0914i			1.67084i	−0.549613	+	0.835419i	$0.685225\pi$
$192$	7.33377	+	3.19621i	0.529269	+	0.230667i
$193$			5.75082i			0.413953i	0.978346	+	0.206977i	$0.0663624\pi$
$193$			5.75082i			0.413953i	−0.978346	+	0.206977i	$0.933638\pi$
$194$	9.67637	−	4.15984i	0.694723	−	0.298659i
$195$	−15.3429	+	4.65421i	−1.09872	+	0.333295i
$196$	−1.59348	+	4.15667i	−0.113820	+	0.296905i
$197$	−14.6172	+	1.43966i	−1.04143	+	0.102572i	−0.604244	−	0.796800i	$-0.706525\pi$
$197$	−14.6172	+	1.43966i	−1.04143	+	0.102572i	−0.437185	+	0.899371i	$0.644025\pi$
$198$	−1.02794	+	0.866764i	−0.0730526	+	0.0615982i
$199$	−22.3654	−	14.9441i	−1.58544	−	1.05936i	−0.960348	−	0.278805i	$-0.910062\pi$
$199$	−22.3654	−	14.9441i	−1.58544	−	1.05936i	−0.625092	−	0.780551i	$-0.714938\pi$
$200$	−12.2787	−	16.8765i	−0.868236	−	1.19335i
$201$	6.31151	+	9.44584i	0.445180	+	0.666258i
$202$	1.76355	+	3.19628i	0.124083	+	0.224890i
$203$	−6.25897	−	11.7097i	−0.439293	−	0.821860i
$204$	9.52437	−	8.25040i	0.666839	−	0.577644i
$205$	2.61405	−	26.5409i	0.182573	−	1.85370i
$206$	−0.0284649	−	0.00526912i	−0.00198324	−	0.000367117i
$207$	1.99818	+	4.82403i	0.138883	+	0.335293i
$208$	0.818638	−	18.2097i	0.0567623	−	1.26261i
$209$	−1.30066	+	3.14008i	−0.0899687	+	0.217204i
$210$	5.91923	−	9.11925i	0.408466	−	0.629288i
$211$	−10.7164	−	13.0580i	−0.737749	−	0.898950i	0.260027	−	0.965601i	$-0.416268\pi$
$211$	−10.7164	−	13.0580i	−0.737749	−	0.898950i	−0.997776	+	0.0666513i	$0.978768\pi$
$212$	6.92599	−	25.2314i	0.475679	−	1.73290i
$213$	−2.11173	+	6.96145i	−0.144694	+	0.476991i
$214$	21.3608	+	17.0596i	1.46019	+	1.16617i
$215$	7.87859	+	1.56715i	0.537316	+	0.106879i
$216$	−0.712329	+	2.73726i	−0.0484679	+	0.186247i
$217$	−3.06144	−	15.3909i	−0.207824	−	1.04480i
$218$	−13.2460	+	4.21149i	−0.897133	+	0.285238i
$219$	−6.46843	+	7.88180i	−0.437096	+	0.532603i
$220$	−1.13007	+	6.59421i	−0.0761896	+	0.444581i
$221$	−25.3211	−	13.5344i	−1.70328	−	0.910422i
$222$	−1.17385	−	1.14301i	−0.0787839	−	0.0767138i
$223$	−0.770927	−	0.770927i	−0.0516251	−	0.0516251i	0.680823	−	0.732448i	$-0.261622\pi$
$223$	−0.770927	−	0.770927i	−0.0516251	−	0.0516251i	−0.732448	+	0.680823i	$0.761622\pi$
$224$	7.53529	+	9.79761i	0.503472	+	0.654631i
$225$	5.21766	−	5.21766i	0.347844	−	0.347844i
$226$	17.0471	−	0.226948i	1.13396	−	0.0150964i
$227$	−8.32972	+	15.5838i	−0.552863	+	1.03433i	0.437938	+	0.899005i	$0.355709\pi$
$227$	−8.32972	+	15.5838i	−0.552863	+	1.03433i	−0.990801	+	0.135329i	$0.956791\pi$
$228$	1.58098	+	6.97254i	0.104703	+	0.461768i
$229$	10.6273	+	8.72158i	0.702270	+	0.576338i	0.916302	−	0.400489i	$-0.131160\pi$
$229$	10.6273	+	8.72158i	0.702270	+	0.576338i	−0.214032	+	0.976827i	$0.568660\pi$
$230$	23.0739	+	11.9411i	1.52145	+	0.787373i
$231$	−2.03751	+	0.405287i	−0.134059	+	0.0266659i
$232$	17.1583	+	1.00040i	1.12650	+	0.0656795i
$233$	−4.35810	+	21.9096i	−0.285509	+	1.43535i	0.525739	+	0.850646i	$0.323789\pi$
$233$	−4.35810	+	21.9096i	−0.285509	+	1.43535i	−0.811248	+	0.584702i	$0.801211\pi$
$234$	6.40459	−	0.717001i	0.418681	−	0.0468718i
$235$	0.660586	+	0.200387i	0.0430919	+	0.0130718i
$236$	−7.73171	−	6.00804i	−0.503291	−	0.391090i
$237$	−5.65682	+	4.64243i	−0.367450	+	0.301558i
$238$	19.0423	−	4.05200i	1.23433	−	0.262652i
$239$	13.3446	+	5.52752i	0.863192	+	0.357546i	0.769955	−	0.638098i	$-0.220279\pi$
$239$	13.3446	+	5.52752i	0.863192	+	0.357546i	0.0932368	+	0.995644i	$0.470279\pi$
$240$	6.07007	+	12.6971i	0.391821	+	0.819595i
$241$	−13.3741	+	5.53975i	−0.861505	+	0.356847i	−0.769296	−	0.638893i	$-0.779393\pi$
$241$	−13.3741	+	5.53975i	−0.861505	+	0.356847i	−0.0922088	+	0.995740i	$0.529393\pi$
$242$	−11.7650	+	8.08973i	−0.756285	+	0.520028i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	0.0204429	+	0.0102368i	0.00130872	+	0.000655346i
$245$	−6.90654	+	3.69162i	−0.441243	+	0.235849i
$246$	−2.97496	+	10.2987i	−0.189676	+	0.656622i
$247$	13.5449	−	9.05039i	0.861839	−	0.575863i
$248$	19.0627	+	7.01815i	1.21048	+	0.445653i
$249$	8.96634	−	13.4191i	0.568219	−	0.850400i
$250$	1.00329	−	11.7941i	0.0634534	−	0.745923i
$251$	1.38358	+	14.0477i	0.0873308	+	0.886684i	0.934643	+	0.355588i	$0.115720\pi$
$251$	1.38358	+	14.0477i	0.0873308	+	0.886684i	−0.847312	+	0.531096i	$0.821780\pi$
$252$	−3.00669	+	3.17121i	−0.189403	+	0.199767i
$253$	−1.44111	−	4.75069i	−0.0906016	−	0.298673i
$254$	14.0716	+	5.61039i	0.882933	+	0.352027i
$255$	22.1673			1.38817
$256$	−15.9094	+	1.70074i	−0.994334	+	0.106296i
$257$	2.42891			0.151511			0.0757556	−	0.997126i	$-0.475863\pi$
$257$	2.42891			0.151511			0.0757556	+	0.997126i	$0.475863\pi$
$258$	−2.99926	−	1.19581i	−0.186726	−	0.0744479i
$259$	−0.734822	−	2.42238i	−0.0456596	−	0.150520i
$260$	22.0628	−	23.2700i	1.36828	−	1.44315i
$261$	0.595619	+	6.04742i	0.0368679	+	0.374326i
$262$	1.63676	−	19.2408i	0.101119	−	1.18870i
$263$	7.01483	−	10.4984i	0.432553	−	0.647362i	−0.549604	−	0.835426i	$-0.685221\pi$
$263$	7.01483	−	10.4984i	0.432553	−	0.647362i	0.982157	+	0.188064i	$0.0602212\pi$
$264$	0.929094	−	2.52360i	0.0571818	−	0.155317i
$265$	38.2713	−	25.5721i	2.35099	−	1.57088i
$266$	−3.06554	+	10.6123i	−0.187960	+	0.650681i
$267$	10.7022	−	5.72046i	0.654966	−	0.350087i
$268$	−20.3160	−	10.1733i	−1.24100	−	0.621433i
$269$	14.2376	+	1.40228i	0.868083	+	0.0854988i	0.522245	−	0.852795i	$-0.325095\pi$
$269$	14.2376	+	1.40228i	0.868083	+	0.0854988i	0.345838	+	0.938294i	$0.387595\pi$
$270$	−4.09999	+	2.81919i	−0.249518	+	0.171570i
$271$	−23.3363	+	9.66621i	−1.41758	+	0.587181i	−0.954251	−	0.299006i	$-0.903345\pi$
$271$	−23.3363	+	9.66621i	−1.41758	+	0.587181i	−0.463328	+	0.886187i	$0.653345\pi$
$272$	−8.39142	+	23.7637i	−0.508804	+	1.44089i
$273$	9.19910	+	3.81039i	0.556755	+	0.230615i
$274$	5.33004	−	1.13417i	0.322000	−	0.0685179i
$275$	−5.42317	+	4.45068i	−0.327030	+	0.268386i
$276$	−8.24604	−	6.40771i	−0.496353	−	0.385699i
$277$	−24.6647	−	7.48194i	−1.48196	−	0.449546i	−0.557287	−	0.830320i	$-0.688158\pi$
$277$	−24.6647	−	7.48194i	−1.48196	−	0.449546i	−0.924668	+	0.380774i	$0.875658\pi$
$278$	6.94481	−	0.777479i	0.416522	−	0.0466301i
$279$	−1.40112	+	7.04392i	−0.0838830	+	0.421709i
$280$	−1.26560	+	21.7069i	−0.0756342	+	1.29724i
$281$	−15.8102	+	3.14484i	−0.943157	+	0.187606i	−0.642638	−	0.766170i	$-0.722160\pi$
$281$	−15.8102	+	3.14484i	−0.943157	+	0.187606i	−0.300519	+	0.953776i	$0.597160\pi$
$282$	−0.246428	−	0.127530i	−0.0146746	−	0.00759431i
$283$	4.18382	+	3.43358i	0.248703	+	0.204105i	0.750482	−	0.660890i	$-0.229821\pi$
$283$	4.18382	+	3.43358i	0.248703	+	0.204105i	−0.501780	+	0.864995i	$0.667321\pi$
$284$	−3.21732	−	14.1892i	−0.190913	−	0.841975i
$285$	−5.92891	+	11.0922i	−0.351199	+	0.657046i
$286$	−6.12681	+	0.0815661i	−0.362286	+	0.00482311i
$287$	−11.7113	+	11.7113i	−0.691297	+	0.691297i
$288$	−1.47017	−	5.46247i	−0.0866307	−	0.321879i
$289$	16.0483	+	16.0483i	0.944017	+	0.944017i
$290$	21.6627	+	21.0935i	1.27208	+	1.23865i
$291$	−6.56828	−	3.51082i	−0.385039	−	0.205808i
$292$	3.44452	−	20.0995i	0.201575	−	1.17623i
$293$	−0.120508	+	0.146840i	−0.00704016	+	0.00857846i	−0.776519	−	0.630094i	$-0.783016\pi$
$293$	−0.120508	+	0.146840i	−0.00704016	+	0.00857846i	0.769478	+	0.638673i	$0.220516\pi$
$294$	2.99981	−	0.953771i	0.174953	−	0.0556250i
$295$	−3.36048	−	16.8943i	−0.195655	−	0.983623i
$296$	3.17121	+	0.825258i	0.184323	+	0.0479671i
$297$	0.932505	+	0.185487i	0.0541094	+	0.0107630i
$298$	4.35057	+	3.47454i	0.252022	+	0.201275i
$299$	−6.90716	+	22.7698i	−0.399451	+	1.31681i
$300$	−3.90648	+	14.2314i	−0.225541	+	0.821647i
$301$	−3.16477	−	3.85628i	−0.182414	−	0.222272i
$302$	7.42052	−	11.4322i	0.427003	−	0.657847i
$303$	0.987824	−	2.38482i	0.0567490	−	0.137004i
$304$	−9.64668	−	10.5549i	−0.553275	−	0.605363i
$305$	0.0153914	+	0.0371582i	0.000881311	+	0.00212767i
$306$	−8.76134	−	1.62181i	−0.500853	−	0.0927124i
$307$	1.03742	−	10.5331i	0.0592086	−	0.601155i	−0.919103	−	0.394017i	$-0.871085\pi$
$307$	1.03742	−	10.5331i	0.0592086	−	0.601155i	0.978312	−	0.207138i	$-0.0664150\pi$
$308$	3.14044	−	2.72038i	0.178943	−	0.155008i
$309$	0.00964933	+	0.0180526i	0.000548931	+	0.00102698i
$310$	17.2635	+	31.2886i	0.980501	+	1.77707i
$311$	−5.03727	−	7.53881i	−0.285637	−	0.427487i	0.660708	−	0.750643i	$-0.270256\pi$
$311$	−5.03727	−	7.53881i	−0.285637	−	0.427487i	−0.946346	+	0.323156i	$0.895256\pi$
$312$	−10.4225	+	7.58303i	−0.590059	+	0.429304i
$313$	20.8612	+	13.9390i	1.17915	+	0.787880i	0.981325	−	0.192358i	$-0.0616136\pi$
$313$	20.8612	+	13.9390i	1.17915	+	0.787880i	0.197821	+	0.980238i	$0.436614\pi$
$314$	−22.3387	+	18.8361i	−1.26065	+	1.06298i
$315$	−7.65057	+	0.753516i	−0.431061	+	0.0424558i
$316$	5.23893	−	13.6660i	0.294713	−	0.768775i
$317$	32.0995	−	9.73729i	1.80289	−	0.546900i	0.804027	−	0.594593i	$-0.202687\pi$
$317$	32.0995	−	9.73729i	1.80289	−	0.546900i	0.998862	+	0.0476921i	$0.0151866\pi$
$318$	−16.9972	+	7.30704i	−0.953154	+	0.409758i
$319$		−	5.77755i		−	0.323481i
$320$	−23.1132	−	16.0633i	−1.29207	−	0.897964i
$321$		−	19.3302i		−	1.07891i
$322$	−6.37234	−	14.8229i	−0.355117	−	0.826050i
$323$	−21.5528	+	6.53798i	−1.19923	+	0.363783i
$324$	1.82673	−	0.814285i	0.101485	−	0.0452381i
$325$	33.4638	−	3.29590i	1.85624	−	0.182823i
$326$	−9.58527	−	11.3677i	−0.530879	−	0.629597i
$327$	8.17199	+	5.46035i	0.451912	+	0.301958i
$328$	−5.01887	−	20.8439i	−0.277121	−	1.15091i
$329$	−0.238173	−	0.356451i	−0.0131309	−	0.0196518i
$330$	4.14212	−	2.28542i	0.228016	−	0.125808i
$331$	−17.0138	−	31.8306i	−0.935165	−	1.74957i	−0.579546	−	0.814940i	$-0.696770\pi$
$331$	−17.0138	−	31.8306i	−0.935165	−	1.74957i	−0.355619	−	0.934631i	$-0.615730\pi$
$332$	−2.30753	+	32.1954i	−0.126642	+	1.76695i
$333$	−0.113556	+	1.15296i	−0.00622284	+	0.0631816i
$334$	0.974376	−	5.26379i	0.0533155	−	0.288022i
$335$	−15.2959	−	36.9275i	−0.835704	−	2.01757i
$336$	2.08834	−	8.48680i	0.113928	−	0.462993i
$337$	−2.79867	+	6.75659i	−0.152453	+	0.368055i	−0.981592	−	0.190987i	$-0.938831\pi$
$337$	−2.79867	+	6.75659i	−0.152453	+	0.368055i	0.829139	+	0.559042i	$0.188831\pi$
$338$	9.21274	+	5.97991i	0.501107	+	0.325264i
$339$	−7.64774	−	9.31880i	−0.415368	−	0.506128i
$340$	−38.5294	+	21.9326i	−2.08955	+	1.18946i
$341$	1.98217	−	6.53435i	0.107341	−	0.353855i
$342$	3.15486	−	3.95029i	0.170595	−	0.213607i
$343$	19.7710	+	3.93269i	1.06753	+	0.212345i
$344$	6.39622	−	0.889051i	0.344861	−	0.0479344i
$345$	−3.58403	−	18.0181i	−0.192958	−	0.970063i
$346$	10.3795	+	32.6458i	0.558007	+	1.75505i
$347$	−3.57376	+	4.35464i	−0.191849	+	0.233769i	−0.860047	−	0.510214i	$-0.829566\pi$
$347$	−3.57376	+	4.35464i	−0.191849	+	0.233769i	0.668198	+	0.743984i	$0.267066\pi$
$348$	−7.01867	−	9.92183i	−0.376240	−	0.531866i
$349$	−10.0580	−	5.37611i	−0.538393	−	0.287777i	0.179704	−	0.983721i	$-0.442486\pi$
$349$	−10.0580	−	5.37611i	−0.538393	−	0.287777i	−0.718096	+	0.695944i	$0.754986\pi$
$350$	−15.9067	+	16.3360i	−0.850251	+	0.873196i
$351$	−3.22230	−	3.22230i	−0.171994	−	0.171994i
$352$	0.882011	+	5.30557i	0.0470113	+	0.282788i
$353$	5.68079	−	5.68079i	0.302358	−	0.302358i	−0.539578	−	0.841936i	$-0.681416\pi$
$353$	5.68079	−	5.68079i	0.302358	−	0.302358i	0.841936	+	0.539578i	$0.181416\pi$
$354$	0.0921673	+	6.92311i	0.00489864	+	0.367959i
$355$	12.0654	−	22.5728i	0.640366	−	1.19804i
$356$	−12.9418	+	20.5318i	−0.685916	+	1.08818i
$357$	−10.6416	−	8.73333i	−0.563213	−	0.462217i
$358$	3.25784	−	6.29516i	0.172182	−	0.332709i
$359$	0.735560	−	0.146312i	0.0388214	−	0.00772205i	−0.175641	−	0.984454i	$-0.556200\pi$
$359$	0.735560	−	0.146312i	0.0388214	−	0.00772205i	0.214463	+	0.976732i	$0.431200\pi$
$360$	4.33693	−	8.95668i	0.228576	−	0.472059i
$361$	−1.21366	+	6.10150i	−0.0638771	+	0.321132i
$362$	1.83829	+	16.4205i	0.0966186	+	0.863042i
$363$	9.66130	+	2.93072i	0.507087	+	0.153823i
$364$	−19.7592	+	2.47881i	−1.03566	+	0.129925i
$365$	27.7310	−	22.7583i	1.45151	−	1.19122i
$366$	−0.00336470	−	0.0158124i	−0.000175876	−	0.000826526i
$367$	−0.0520128	−	0.0215444i	−0.00271505	−	0.00112461i	0.381325	−	0.924441i	$-0.375468\pi$
$367$	−0.0520128	−	0.0215444i	−0.00271505	−	0.00112461i	−0.384041	+	0.923316i	$0.625468\pi$
$368$	20.6725	+	2.97861i	1.07763	+	0.155271i
$369$	7.00304	−	2.90075i	0.364564	−	0.151007i
$370$	3.26613	+	4.74998i	0.169798	+	0.246940i
$371$	−28.4472	−	2.80181i	−1.47691	−	0.145462i
$372$	−4.53404	−	13.6295i	−0.235079	−	0.706655i
$373$	16.5170	−	8.82855i	0.855220	−	0.457125i	0.0153310	−	0.999882i	$-0.495120\pi$
$373$	16.5170	−	8.82855i	0.855220	−	0.457125i	0.839889	+	0.542758i	$0.182620\pi$
$374$	8.13881	+	2.35103i	0.420848	+	0.121569i
$375$	−6.95923	+	4.65001i	−0.359373	+	0.240126i
$376$	0.554501	−	0.0221567i	0.0285962	−	0.00114264i
$377$	−15.3846	+	23.0247i	−0.792347	+	1.18583i
$378$	3.07892	+	0.261914i	0.158363	+	0.0134714i
$379$	−0.351523	−	3.56907i	−0.0180565	−	0.183331i	0.981926	−	0.189266i	$-0.0606108\pi$
$379$	−0.351523	−	3.56907i	−0.0180565	−	0.183331i	−0.999982	+	0.00593506i	$0.998111\pi$
$380$	−0.669649	−	25.1458i	−0.0343523	−	1.28995i
$381$	−3.10948	−	10.2506i	−0.159304	−	0.525154i
$382$	−12.0943	+	30.3341i	−0.618797	+	1.55203i
$383$	−21.7924			−1.11354			−0.556770	−	0.830667i	$-0.687959\pi$
$383$	−21.7924			−1.11354			−0.556770	+	0.830667i	$0.687959\pi$
$384$	7.95999	+	8.03981i	0.406206	+	0.410280i
$385$	7.30916			0.372509
$386$	−3.01202	+	7.55457i	−0.153308	+	0.384518i
$387$	0.662763	+	2.18484i	0.0336901	+	0.111061i
$388$	14.8901	−	0.396534i	0.755931	−	0.0201310i
$389$	−3.04879	−	30.9549i	−0.154580	−	1.56947i	−0.689320	−	0.724457i	$-0.742090\pi$
$389$	−3.04879	−	30.9549i	−0.154580	−	1.56947i	0.534740	−	0.845017i	$-0.320410\pi$
$390$	−22.5928	−	1.92190i	−1.14403	−	0.0973193i
$391$	18.2770	−	27.3535i	0.924309	−	1.38333i
$392$	−4.27035	+	4.62583i	−0.215685	+	0.233639i
$393$	−11.3533	+	7.58600i	−0.572696	+	0.382663i
$394$	−19.9559	−	5.76460i	−1.00536	−	0.290416i
$395$	22.7069	−	12.1371i	1.14251	−	0.610683i
$396$	−1.80433	+	0.600236i	−0.0906709	+	0.0301630i
$397$	−20.4237	−	2.01156i	−1.02504	−	0.100957i	−0.428499	−	0.903542i	$-0.640957\pi$
$397$	−20.4237	−	2.01156i	−1.02504	−	0.100957i	−0.596538	+	0.802585i	$0.703457\pi$
$398$	−21.5533	−	31.3453i	−1.08037	−	1.57120i
$399$	7.21627	−	2.98908i	0.361265	−	0.149641i
$400$	−7.29078	−	28.6009i	−0.364539	−	1.43005i
$401$	−2.13045	−	0.882460i	−0.106389	−	0.0440679i	0.328854	−	0.944381i	$-0.393338\pi$
$401$	−2.13045	−	0.882460i	−0.106389	−	0.0440679i	−0.435243	+	0.900313i	$0.643338\pi$
$402$	3.34381	+	15.7142i	0.166774	+	0.783755i
$403$	−25.2992	+	20.7625i	−1.26024	+	1.03425i
$404$	0.642619	+	5.12247i	0.0319715	+	0.254852i
$405$	3.36686	+	1.02133i	0.167301	+	0.0507502i
$406$	−2.08908	−	18.6606i	−0.103679	−	0.926112i
$407$	0.214893	−	1.08034i	0.0106518	−	0.0535504i
$408$	16.8329	−	5.84972i	0.833353	−	0.289604i
$409$	−15.3685	+	3.05699i	−0.759926	+	0.151159i	−0.559818	−	0.828615i	$-0.689129\pi$
$409$	−15.3685	+	3.05699i	−0.759926	+	0.151159i	−0.200107	+	0.979774i	$0.564129\pi$
$410$	17.3349	−	33.4964i	0.856109	−	1.65427i
$411$	−2.97863	−	2.44450i	−0.146925	−	0.120578i
$412$	−0.0346332	−	0.0218304i	−0.00170626	−	0.00107551i
$413$	−5.04267	+	9.43418i	−0.248134	+	0.464225i
$414$	0.0982985	+	7.38365i	0.00483111	+	0.362887i
$415$	−40.1515	+	40.1515i	−1.97096	+	1.97096i
$416$	10.6128	−	23.4924i	0.520336	−	1.15181i
$417$	−3.49409	−	3.49409i	−0.171107	−	0.171107i
$418$	−3.35325	+	3.44374i	−0.164013	+	0.168439i
$419$	22.1008	+	11.8131i	1.07969	+	0.577109i	0.912609	−	0.408834i	$-0.134064\pi$
$419$	22.1008	+	11.8131i	1.07969	+	0.577109i	0.167085	+	0.985942i	$0.446564\pi$
$420$	12.5521	−	8.87929i	0.612478	−	0.433265i
$421$	16.2561	−	19.8081i	0.792275	−	0.965390i	−0.207643	−	0.978205i	$-0.566579\pi$
$421$	16.2561	−	19.8081i	0.792275	−	0.965390i	0.999918	+	0.0128148i	$0.00407919\pi$
$422$	−7.23845	−	22.7665i	−0.352362	−	1.10825i
$423$	0.0382771	+	0.192432i	0.00186110	+	0.00935637i
$424$	22.3134	−	29.5178i	1.08364	−	1.43351i
$425$	−45.5970	−	9.06982i	−2.21178	−	0.439951i
$426$	−6.42018	+	8.03889i	−0.311059	+	0.389485i
$427$	0.00725057	−	0.0239019i	0.000350880	−	0.00115669i
$428$	19.1256	+	33.5982i	0.924470	+	1.62403i
$429$	2.74863	+	3.34922i	0.132705	+	0.161702i
$430$	9.52892	+	6.18515i	0.459526	+	0.298274i
$431$	0.790280	−	1.90791i	0.0380665	−	0.0919006i	−0.903703	−	0.428160i	$-0.859162\pi$
$431$	0.790280	−	1.90791i	0.0380665	−	0.0919006i	0.941769	+	0.336260i	$0.109162\pi$
$432$	−2.36941	+	3.22272i	−0.113998	+	0.155053i
$433$	2.41408	+	5.82810i	0.116013	+	0.280081i	0.971211	−	0.238221i	$-0.0765643\pi$
$433$	2.41408	+	5.82810i	0.116013	+	0.280081i	−0.855198	+	0.518302i	$0.826564\pi$
$434$	4.03940	−	21.8217i	0.193897	−	1.04748i
$435$	2.09561	−	21.2770i	0.100477	−	1.02016i
$436$	−19.6064	−	1.40525i	−0.938978	−	0.0672991i
$437$	8.79891	+	16.4616i	0.420909	+	0.787466i
$438$	−12.6254	+	6.96607i	−0.603265	+	0.332852i
$439$	8.62333	+	12.9057i	0.411569	+	0.615957i	0.978113	−	0.208075i	$-0.0667198\pi$
$439$	8.62333	+	12.9057i	0.411569	+	0.615957i	−0.566544	+	0.824032i	$0.691720\pi$
$440$	−4.93827	+	8.07060i	−0.235423	+	0.384751i
$441$	−1.85070	−	1.23660i	−0.0881286	−	0.0588857i
$442$	−26.1744	−	31.0415i	−1.24499	−	1.47650i
$443$	1.85514	−	0.182715i	0.0881401	−	0.00868105i	−0.0538509	−	0.998549i	$-0.517150\pi$
$443$	1.85514	−	0.182715i	0.0881401	−	0.00868105i	0.141991	+	0.989868i	$0.454650\pi$
$444$	−0.943377	−	2.11633i	−0.0447707	−	0.100436i
$445$	−40.8574	+	12.3939i	−1.93682	+	0.587529i
$446$	−0.608952	−	1.41651i	−0.0288347	−	0.0670736i
$447$		−	3.93700i		−	0.186214i
$448$	4.76719	+	16.8173i	0.225228	+	0.794543i
$449$			22.7713i			1.07464i	0.843377	+	0.537322i	$0.180564\pi$
$449$			22.7713i			1.07464i	−0.843377	+	0.537322i	$0.819436\pi$
$450$	9.58697	−	4.12141i	0.451934	−	0.194285i
$451$	−6.89657	+	2.09205i	−0.324747	+	0.0985109i
$452$	22.5128	+	8.63039i	1.05891	+	0.405939i
$453$	−9.59098	+	0.944629i	−0.450624	+	0.0443826i
$454$	−19.1045	+	16.1090i	−0.896617	+	0.756031i
$455$	−29.1284	−	19.4630i	−1.36556	−	0.912440i
$456$	−1.57505	+	9.98754i	−0.0737583	+	0.467709i
$457$	−0.784330	−	1.17383i	−0.0366894	−	0.0549096i	0.812672	−	0.582722i	$-0.198012\pi$
$457$	−0.784330	−	1.17383i	−0.0366894	−	0.0549096i	−0.849361	+	0.527813i	$0.823012\pi$
$458$	9.39256	+	17.0232i	0.438885	+	0.795442i
$459$	2.97001	+	5.55650i	0.138628	+	0.259355i
$460$	24.0569	+	27.7715i	1.12166	+	1.29485i
$461$	−0.152271	+	1.54603i	−0.00709195	+	0.0720057i	−0.998079	−	0.0619501i	$-0.980268\pi$
$461$	−0.152271	+	1.54603i	−0.00709195	+	0.0720057i	0.990987	+	0.133956i	$0.0427680\pi$
$462$	−2.88885	−	0.534753i	−0.134402	−	0.0248790i
$463$	3.25592	+	7.86048i	0.151315	+	0.365308i	0.981302	−	0.192476i	$-0.0616518\pi$
$463$	3.25592	+	7.86048i	0.151315	+	0.365308i	−0.829986	+	0.557784i	$0.811652\pi$
$464$	22.0161	+	10.3009i	1.02207	+	0.478209i
$465$	9.66988	−	23.3452i	0.448430	−	1.08261i
$466$	−17.2003	+	26.4991i	−0.796789	+	1.22754i
$467$	−6.17517	−	7.52446i	−0.285753	−	0.348191i	0.610274	−	0.792190i	$-0.291059\pi$
$467$	−6.17517	−	7.52446i	−0.285753	−	0.348191i	−0.896027	+	0.443999i	$0.853559\pi$
$468$	8.78893	+	2.41255i	0.406268	+	0.111520i
$469$	−7.20556	+	23.7535i	−0.332722	+	1.09684i
$470$	0.762826	+	0.609223i	0.0351865	+	0.0281014i
$471$	20.2648	+	4.03092i	0.933752	+	0.185735i
$472$	−7.01003	−	11.9420i	−0.322663	−	0.549675i
$473$	−0.423494	−	2.12905i	−0.0194723	−	0.0978937i
$474$	−9.86259	+	3.13575i	−0.453004	+	0.144030i
$475$	16.7339	−	20.3903i	0.767804	−	0.935572i
$476$	27.1372	+	4.65061i	1.24383	+	0.213161i
$477$	11.5376	+	6.16699i	0.528271	+	0.282367i
$478$	14.6351	+	14.2506i	0.669394	+	0.651805i
$479$	−25.2679	−	25.2679i	−1.15452	−	1.15452i	−0.985636	−	0.168881i	$-0.945985\pi$
$479$	−25.2679	−	25.2679i	−1.15452	−	1.15452i	−0.168881	−	0.985636i	$-0.554015\pi$
$480$	1.32378	+	19.8588i	0.0604219	+	0.906426i
$481$	−3.73314	+	3.73314i	−0.170217	+	0.170217i
$482$	−20.4704	+	0.272523i	−0.932403	+	0.0124131i
$483$	−5.37812	+	10.0618i	−0.244713	+	0.457826i
$484$	−19.6922	+	4.46509i	−0.895099	+	0.202959i
$485$	20.2557	+	16.6235i	0.919766	+	0.754832i
$486$	−1.25599	−	0.649994i	−0.0569728	−	0.0294843i
$487$	22.2562	−	4.42703i	1.00852	−	0.200608i	0.336932	−	0.941529i	$-0.390611\pi$
$487$	22.2562	−	4.42703i	1.00852	−	0.200608i	0.671592	+	0.740921i	$0.265611\pi$
$488$	0.0214933	+	0.0241547i	0.000972954	+	0.00109343i
$489$	−2.05124	+	10.3123i	−0.0927603	+	0.466337i
$490$	−11.0063	+	1.23217i	−0.497214	+	0.0556637i
$491$	−31.7760	−	9.63916i	−1.43403	−	0.435009i	−0.524775	−	0.851241i	$-0.675850\pi$
$491$	−31.7760	−	9.63916i	−1.43403	−	0.435009i	−0.909258	+	0.416232i	$0.863350\pi$
$492$	−9.30207	+	11.9708i	−0.419370	+	0.539684i
$493$	29.5954	−	24.2883i	1.33291	−	1.09389i
$494$	22.5334	−	4.79486i	1.01383	−	0.215731i
$495$	−3.09053	−	1.28014i	−0.138909	−	0.0575380i
$496$	21.3659	+	19.2036i	0.959357	+	0.862266i
$497$	−14.6852	+	6.08281i	−0.658721	+	0.272851i
$498$	18.8070	−	12.9318i	0.842760	−	0.579489i
$499$	28.3617	+	2.79338i	1.26964	+	0.125049i	0.710307	−	0.703892i	$-0.248556\pi$
$499$	28.3617	+	2.79338i	1.26964	+	0.125049i	0.559337	+	0.828941i	$0.311056\pi$
$500$	7.49518	−	14.9678i	0.335195	−	0.669382i
$501$	−3.33833	+	1.78438i	−0.149146	+	0.0797200i
$502$	−5.54003	+	19.1785i	−0.247264	+	0.855977i
$503$	−11.7920	+	7.87917i	−0.525780	+	0.351315i	−0.789960	−	0.613159i	$-0.789899\pi$
$503$	−11.7920	+	7.87917i	−0.525780	+	0.351315i	0.264180	+	0.964473i	$0.414899\pi$
$504$	−5.61068	+	2.59109i	−0.249919	+	0.115416i
$505$	−5.04568	+	7.55140i	−0.224530	+	0.336033i
$506$	0.595089	−	6.99554i	0.0264549	−	0.310990i
$507$	−0.761240	−	7.72900i	−0.0338079	−	0.343257i
$508$	15.5467	+	14.7402i	0.689775	+	0.653990i
$509$	−2.55696	−	8.42918i	−0.113335	−	0.373617i	0.881862	−	0.471508i	$-0.156290\pi$
$509$	−2.55696	−	8.42918i	−0.113335	−	0.373617i	−0.995197	+	0.0978913i	$0.968790\pi$
$510$	29.1201	+	11.6102i	1.28946	+	0.514110i
$511$	−22.2787			−0.985551
$512$	−21.7901	−	6.09843i	−0.962996	−	0.269515i
$513$	−3.57477			−0.157830
$514$	3.19074	+	1.27215i	0.140738	+	0.0561123i
$515$	−0.0209062	−	0.0689186i	−0.000921238	−	0.00303692i
$516$	−3.31367	−	3.14176i	−0.145876	−	0.138308i
$517$	−0.0182845	−	0.185646i	−0.000804151	−	0.00816468i
$518$	0.303437	−	3.56704i	0.0133322	−	0.156727i
$519$	13.4574	−	20.1405i	0.590716	−	0.884069i
$520$	41.1706	−	19.0132i	1.80545	−	0.833784i
$521$	37.5764	−	25.1078i	1.64625	−	1.09999i	0.744623	−	0.667486i	$-0.232629\pi$
$521$	37.5764	−	25.1078i	1.64625	−	1.09999i	0.901631	−	0.432506i	$-0.142371\pi$
$522$	−2.38493	+	8.25617i	−0.104386	+	0.361363i
$523$	−2.70208	+	1.44429i	−0.118154	+	0.0631544i	−0.529415	−	0.848363i	$-0.677588\pi$
$523$	−2.70208	+	1.44429i	−0.118154	+	0.0631544i	0.411261	+	0.911518i	$0.365088\pi$
$524$	12.2276	−	24.4185i	0.534165	−	1.06673i
$525$	16.0452	+	1.58031i	0.700268	+	0.0689704i
$526$	14.7137	−	10.1172i	0.641546	−	0.441132i
$527$	41.8049	−	17.3162i	1.82105	−	0.754304i
$528$	2.54225	−	2.82851i	0.110637	−	0.123095i
$529$	−3.93941	−	1.63176i	−0.171279	−	0.0709459i
$530$	63.6687	−	13.5480i	2.76559	−	0.588487i
$531$	3.78451	−	3.10587i	0.164234	−	0.134783i
$532$	−9.58529	+	12.3353i	−0.415575	+	0.534801i
$533$	33.0550	+	10.0271i	1.43177	+	0.434322i
$534$	17.0551	−	1.90934i	0.738047	−	0.0826253i
$535$	−13.2682	+	66.7039i	−0.573635	+	2.88386i
$536$	−21.3598	−	24.0048i	−0.922605	−	1.03685i
$537$	−4.91581	+	0.977815i	−0.212133	+	0.0421958i
$538$	17.9688	+	9.29915i	0.774691	+	0.400915i
$539$	1.63588	+	1.34254i	0.0704625	+	0.0578271i
$540$	−6.86253	+	1.55604i	−0.295316	+	0.0669612i
$541$	6.87287	−	12.8582i	0.295488	−	0.552819i	−0.689742	−	0.724055i	$-0.742276\pi$
$541$	6.87287	−	12.8582i	0.295488	−	0.552819i	0.985230	+	0.171236i	$0.0547761\pi$
$542$	−35.7185	+	0.475520i	−1.53424	+	0.0204253i
$543$	8.26154	−	8.26154i	0.354536	−	0.354536i
$544$	−23.4698	+	26.8222i	−1.00626	+	1.14999i
$545$	−24.4516	−	24.4516i	−1.04739	−	1.04739i
$546$	10.0887	+	9.82361i	0.431756	+	0.420412i
$547$	−4.75126	−	2.53960i	−0.203149	−	0.108586i	0.366685	−	0.930345i	$-0.380493\pi$
$547$	−4.75126	−	2.53960i	−0.203149	−	0.108586i	−0.569834	+	0.821760i	$0.692993\pi$
$548$	7.59585	+	1.30173i	0.324479	+	0.0556072i
$549$	−0.00725199	+	0.00883657i	−0.000309507	+	0.000377136i
$550$	−9.45523	+	3.00623i	−0.403172	+	0.128186i
$551$	4.23789	+	21.3053i	0.180540	+	0.907638i
$552$	−7.47635	−	12.7364i	−0.318215	−	0.542097i
$553$	−15.6823	−	3.11941i	−0.666880	−	0.132651i
$554$	−28.4821	−	22.7469i	−1.21009	−	0.966424i
$555$	1.18324	−	3.90063i	0.0502258	−	0.165572i
$556$	9.53026	+	2.61604i	0.404173	+	0.110945i
$557$	4.60978	+	5.61703i	0.195323	+	0.238001i	0.861457	−	0.507830i	$-0.169552\pi$
$557$	4.60978	+	5.61703i	0.195323	+	0.238001i	−0.666134	+	0.745832i	$0.732052\pi$
$558$	−5.52988	+	8.51941i	−0.234098	+	0.360655i
$559$	−3.98157	+	9.61236i	−0.168402	+	0.406559i
$560$	−13.0317	+	27.8525i	−0.550689	+	1.17698i
$561$	−2.29239	−	5.53432i	−0.0967848	−	0.233659i
$562$	−22.4162	−	4.14945i	−0.945571	−	0.175034i
$563$	0.671939	−	6.82232i	0.0283189	−	0.287526i	−0.970587	−	0.240752i	$-0.922606\pi$
$563$	0.671939	−	6.82232i	0.0283189	−	0.287526i	0.998905	−	0.0467741i	$-0.0148941\pi$
$564$	−0.256925	−	0.296598i	−0.0108185	−	0.0124890i
$565$	19.9941	+	37.4063i	0.841158	+	1.57370i
$566$	3.69773	+	6.70182i	0.155427	+	0.281699i
$567$	−1.21392	−	1.81675i	−0.0509797	−	0.0762964i
$568$	3.20524	−	20.3248i	0.134489	−	0.852808i
$569$	−14.2191	−	9.50091i	−0.596096	−	0.398299i	0.220602	−	0.975364i	$-0.429198\pi$
$569$	−14.2191	−	9.50091i	−0.596096	−	0.398299i	−0.816698	+	0.577065i	$0.804198\pi$
$570$	−13.5981	+	11.4660i	−0.569563	+	0.480258i
$571$	39.1475	−	3.85570i	1.63827	−	0.161356i	0.763473	−	0.645840i	$-0.223492\pi$
$571$	39.1475	−	3.85570i	1.63827	−	0.161356i	0.874800	+	0.484484i	$0.160992\pi$
$572$	−8.09121	−	3.10180i	−0.338311	−	0.129693i
$573$	22.0971	−	6.70309i	0.923121	−	0.280026i
$574$	−21.5184	+	9.25072i	−0.898163	+	0.386118i
$575$			38.5288i			1.60676i
$576$	0.929705	−	7.94579i	0.0387377	−	0.331075i
$577$		−	25.4250i		−	1.05845i	−0.848480	−	0.529227i	$-0.822482\pi$
$577$		−	25.4250i		−	1.05845i	0.848480	−	0.529227i	$-0.177518\pi$
$578$	12.6765	+	29.4872i	0.527272	+	1.22651i
$579$	5.50319	−	1.66937i	0.228705	−	0.0693769i
$580$	17.4094	+	39.0554i	0.722886	+	1.62169i
$581$	35.0937	−	3.45643i	1.45593	−	0.143397i
$582$	−6.78962	−	8.05217i	−0.281439	−	0.333773i
$583$	−10.3421	−	6.91039i	−0.428327	−	0.286199i
$584$	15.0521	−	24.5996i	0.622861	−	1.01794i
$585$	8.90759	+	13.3312i	0.368284	+	0.551175i
$586$	−0.235214	+	0.129779i	−0.00971659	+	0.00536113i
$587$	4.22577	+	7.90585i	0.174416	+	0.326309i	0.953906	−	0.300105i	$-0.0970218\pi$
$587$	4.22577	+	7.90585i	0.174416	+	0.326309i	−0.779490	+	0.626415i	$0.784522\pi$
$588$	4.44025	+	0.318245i	0.183113	+	0.0131242i
$589$	−2.51646	+	25.5501i	−0.103689	+	1.05277i
$590$	4.43397	−	23.9533i	0.182544	−	0.986140i
$591$	5.62081	+	13.5698i	0.231209	+	0.558188i
$592$	3.73363	+	2.74504i	0.153451	+	0.112820i
$593$	−1.96571	+	4.74565i	−0.0807221	+	0.194880i	−0.959088	−	0.283109i	$-0.908634\pi$
$593$	−1.96571	+	4.74565i	−0.0807221	+	0.194880i	0.878366	+	0.477989i	$0.158634\pi$
$594$	1.12784	+	0.732069i	0.0462757	+	0.0300372i
$595$	30.7270	+	37.4410i	1.25969	+	1.53493i
$596$	3.89532	+	6.84297i	0.159559	+	0.280299i
$597$	−7.80825	+	25.7404i	−0.319571	+	1.05348i
$598$	−20.9994	+	26.2940i	−0.858731	+	1.07524i
$599$	−22.3261	−	4.44094i	−0.912220	−	0.181452i	−0.283399	−	0.959002i	$-0.591462\pi$
$599$	−22.3261	−	4.44094i	−0.912220	−	0.181452i	−0.628821	+	0.777550i	$0.716462\pi$
$600$	−12.5855	+	16.6490i	−0.513801	+	0.679692i
$601$	−1.22048	−	6.13576i	−0.0497844	−	0.250283i	0.947877	−	0.318637i	$-0.103225\pi$
$601$	−1.22048	−	6.13576i	−0.0497844	−	0.250283i	−0.997661	+	0.0683543i	$0.978225\pi$
$602$	−2.13765	−	6.72338i	−0.0871243	−	0.274024i
$603$	7.20697	−	8.78172i	0.293491	−	0.357619i
$604$	15.7356	−	11.1313i	0.640274	−	0.452928i
$605$	−31.3272	−	16.7447i	−1.27363	−	0.680770i
$606$	2.54672	−	2.61544i	0.103453	−	0.106245i
$607$	19.2888	+	19.2888i	0.782907	+	0.782907i	0.980320	−	0.197413i	$-0.0632540\pi$
$607$	19.2888	+	19.2888i	0.782907	+	0.782907i	−0.197413	+	0.980320i	$0.563254\pi$
$608$	−7.14420	−	18.9179i	−0.289736	−	0.767222i
$609$	−9.38861	+	9.38861i	−0.380445	+	0.380445i
$610$	0.000757167		0.0568743i	3.06568e−5		0.00230277i
$611$	−0.421474	+	0.788522i	−0.0170510	+	0.0319002i
$612$	−10.6599	−	6.71929i	−0.430902	−	0.271611i
$613$	−6.56136	−	5.38477i	−0.265011	−	0.217489i	0.492498	−	0.870314i	$-0.336084\pi$
$613$	−6.56136	−	5.38477i	−0.265011	−	0.217489i	−0.757509	+	0.652825i	$0.773584\pi$
$614$	6.87957	−	13.2935i	0.277637	−	0.536480i
$615$	−26.1569	+	5.20293i	−1.05475	+	0.209802i
$616$	5.55027	−	1.92881i	0.223627	−	0.0777140i
$617$	−0.936590	+	4.70856i	−0.0377057	+	0.189559i	−0.995048	−	0.0993976i	$-0.968308\pi$
$617$	−0.936590	+	4.70856i	−0.0377057	+	0.189559i	0.957342	+	0.288957i	$0.0933084\pi$
$618$	0.00322070	+	0.0287688i	0.000129555	+	0.00115725i
$619$	−41.0030	−	12.4381i	−1.64805	−	0.499930i	−0.676434	−	0.736503i	$-0.736476\pi$
$619$	−41.0030	−	12.4381i	−1.64805	−	0.499930i	−0.971614	+	0.236573i	$0.923976\pi$
$620$	6.29064	+	50.1442i	0.252638	+	2.01384i
$621$	4.03627	−	3.31248i	0.161970	−	0.132925i
$622$	−2.66873	−	12.5417i	−0.107006	−	0.502875i
$623$	24.4968	+	10.1469i	0.981443	+	0.406527i
$624$	−17.6632	+	4.50260i	−0.707094	+	0.180248i
$625$	−6.87962	+	2.84963i	−0.275185	+	0.113985i
$626$	20.1037	+	29.2372i	0.803507	+	1.16855i
$627$	3.38243	+	0.333140i	0.135081	+	0.0133043i
$628$	−39.2109	+	13.0441i	−1.56468	+	0.520515i
$629$	6.43740	−	3.44086i	0.256676	−	0.137196i
$630$	−10.4448	−	3.01717i	−0.416133	−	0.120207i
$631$	22.7231	−	15.1831i	0.904591	−	0.604429i	−0.0138855	−	0.999904i	$-0.504420\pi$
$631$	22.7231	−	15.1831i	0.904591	−	0.604429i	0.918477	+	0.395475i	$0.129420\pi$
$632$	14.0398	−	15.2085i	0.558473	−	0.604962i
$633$	−9.38492	+	14.0455i	−0.373017	+	0.558259i
$634$	47.2676	+	4.02090i	1.87723	+	0.159690i
$635$	3.69409	+	37.5067i	0.146595	+	1.48841i
$636$	−26.1555	+	0.696539i	−1.03713	+	0.0276195i
$637$	−2.94439	−	9.70634i	−0.116661	−	0.384579i
$638$	3.02602	−	7.58969i	0.119801	−	0.300479i
$639$	7.27470			0.287783
$640$	−21.9495	−	33.2072i	−0.867629	−	1.31263i
$641$	29.7433			1.17479			0.587396	−	0.809300i	$-0.300153\pi$
$641$	29.7433			1.17479			0.587396	+	0.809300i	$0.300153\pi$
$642$	10.1243	−	25.3931i	0.399574	−	1.00219i
$643$	1.12094	+	3.69523i	0.0442054	+	0.145726i	0.976265	−	0.216579i	$-0.0694900\pi$
$643$	1.12094	+	3.69523i	0.0442054	+	0.145726i	−0.932060	+	0.362305i	$0.881990\pi$
$644$	−0.607439	−	22.8097i	−0.0239365	−	0.898829i
$645$	−0.787366	−	7.99426i	−0.0310025	−	0.314774i
$646$	−31.7372	−	2.69979i	−1.24868	−	0.106222i
$647$	−27.4918	+	41.1444i	−1.08081	+	1.61755i	−0.347473	+	0.937690i	$0.612960\pi$
$647$	−27.4918	+	41.1444i	−1.08081	+	1.61755i	−0.733340	+	0.679862i	$0.762040\pi$
$648$	2.82617	−	0.112928i	0.111023	−	0.00443622i
$649$	−3.87033	+	2.58607i	−0.151924	+	0.101512i
$650$	45.6860	+	13.1972i	1.79195	+	0.517636i
$651$	−13.8395	+	7.39736i	−0.542412	+	0.289925i
$652$	−6.63783	−	19.9535i	−0.259957	−	0.781439i
$653$	4.62974	+	0.455990i	0.181176	+	0.0178443i	0.188198	−	0.982131i	$-0.439735\pi$
$653$	4.62974	+	0.455990i	0.181176	+	0.0178443i	−0.00702227	+	0.999975i	$0.502235\pi$
$654$	7.87526	+	11.4531i	0.307947	+	0.447852i
$655$	44.3844	−	18.3846i	1.73424	−	0.718346i
$656$	4.32404	−	30.0102i	0.168825	−	1.17170i
$657$	9.42010	+	3.90193i	0.367513	+	0.152229i
$658$	−0.126183	−	0.592996i	−0.00491912	−	0.0231174i
$659$	16.8443	−	13.8238i	0.656161	−	0.538498i	−0.246341	−	0.969183i	$-0.579228\pi$
$659$	16.8443	−	13.8238i	0.656161	−	0.538498i	0.902502	+	0.430686i	$0.141728\pi$
$660$	6.63830	−	0.832783i	0.258396	−	0.0324160i
$661$	−3.86297	−	1.17182i	−0.150252	−	0.0455784i	0.214263	−	0.976776i	$-0.431265\pi$
$661$	−3.86297	−	1.17182i	−0.150252	−	0.0455784i	−0.364515	+	0.931198i	$0.618765\pi$
$662$	−5.67878	−	50.7255i	−0.220712	−	1.97150i
$663$	−5.60129	+	28.1596i	−0.217536	+	1.09363i
$664$	−19.8938	+	41.0849i	−0.772029	+	1.59441i
$665$	−26.9533	+	5.36135i	−1.04520	+	0.207904i
$666$	−0.753040	+	1.45511i	−0.0291797	+	0.0563842i
$667$	−24.5271	−	20.1289i	−0.949694	−	0.779394i
$668$	4.03693	−	6.40445i	0.156194	−	0.247796i
$669$	−0.513943	+	0.961520i	−0.0198702	+	0.0371745i
$670$	−0.752467	−	56.5212i	−0.0290703	−	2.18361i
$671$	0.00768530	−	0.00768530i	0.000296688	−	0.000296688i
$672$	7.18835	−	10.0549i	0.277297	−	0.387877i
$673$	−8.21709	−	8.21709i	−0.316746	−	0.316746i	0.530770	−	0.847516i	$-0.321903\pi$
$673$	−8.21709	−	8.21709i	−0.316746	−	0.316746i	−0.847516	+	0.530770i	$0.821903\pi$
$674$	−7.21528	+	7.40998i	−0.277922	+	0.285422i
$675$	−6.50760	−	3.47838i	−0.250478	−	0.133883i
$676$	8.97032	+	12.6807i	0.345012	+	0.487721i
$677$	−24.7351	+	30.1398i	−0.950647	+	1.15837i	0.0366253	+	0.999329i	$0.488339\pi$
$677$	−24.7351	+	30.1398i	−0.950647	+	1.15837i	−0.987272	+	0.159038i	$0.949161\pi$
$678$	−5.16569	−	16.2472i	−0.198387	−	0.623970i
$679$	−3.17473	−	15.9605i	−0.121835	−	0.612506i
$680$	−62.1015	+	8.63188i	−2.38148	+	0.331018i
$681$	17.3308	+	3.44731i	0.664117	+	0.132101i
$682$	6.02629	−	7.54569i	0.230759	−	0.288939i
$683$	1.75049	−	5.77060i	0.0669808	−	0.220806i	−0.917060	−	0.398749i	$-0.869444\pi$
$683$	1.75049	−	5.77060i	0.0669808	−	0.220806i	0.984041	+	0.177943i	$0.0569444\pi$
$684$	6.21337	−	3.53693i	0.237574	−	0.135238i
$685$	8.60065	+	10.4799i	0.328614	+	0.400417i
$686$	23.9124	+	15.5213i	0.912980	+	0.592608i
$687$	5.26109	−	12.7014i	0.200723	−	0.484589i
$688$	8.86806	+	2.18215i	0.338091	+	0.0831938i
$689$	22.8143	+	55.0785i	0.869155	+	2.09833i
$690$	4.72893	−	25.5467i	0.180027	−	0.972546i
$691$	3.32423	−	33.7515i	0.126460	−	1.28397i	−0.697197	−	0.716879i	$-0.745570\pi$
$691$	3.32423	−	33.7515i	0.126460	−	1.28397i	0.823657	−	0.567088i	$-0.191930\pi$
$692$	−3.46333	+	48.3215i	−0.131656	+	1.83691i
$693$	0.979294	+	1.83213i	0.0372003	+	0.0695969i
$694$	−6.97544	+	3.84870i	−0.264784	+	0.146095i
$695$	9.65894	+	14.4556i	0.366384	+	0.548333i
$696$	−4.02347	−	16.7099i	−0.152509	−	0.633387i
$697$	−39.7090	−	26.5327i	−1.50409	−	1.00500i
$698$	−10.3969	−	12.3303i	−0.393530	−	0.466708i
$699$	22.2313	−	2.18959i	0.840865	−	0.0828180i
$700$	−29.4520	+	13.1286i	−1.11318	+	0.496213i
$701$	−27.6273	+	8.38066i	−1.04347	+	0.316533i	−0.765080	−	0.643935i	$-0.777301\pi$
$701$	−27.6273	+	8.38066i	−1.04347	+	0.316533i	−0.278390	+	0.960468i	$0.589801\pi$
$702$	−2.54528	−	5.92067i	−0.0960654	−	0.223461i
$703$			4.14149i			0.156199i
$704$	−1.62017	+	7.43163i	−0.0610624	+	0.280090i
$705$		−	0.690310i		−	0.0259986i
$706$	10.4379	−	4.48724i	0.392837	−	0.168879i
$707$	5.39727	−	1.63724i	0.202985	−	0.0615749i
$708$	−3.50494	+	9.14283i	−0.131724	+	0.343609i
$709$	−37.9118	+	3.73399i	−1.42381	+	0.140233i	−0.780395	−	0.625287i	$-0.784982\pi$
$709$	−37.9118	+	3.73399i	−1.42381	+	0.140233i	−0.643413	+	0.765519i	$0.722482\pi$
$710$	27.6724	−	23.3335i	1.03853	−	0.875689i
$711$	6.08462	+	4.06561i	0.228191	+	0.152472i
$712$	−27.7547	+	20.1933i	−1.04015	+	0.756774i
$713$	−20.8341	−	31.1804i	−0.780242	−	1.16771i
$714$	−9.40521	−	17.0461i	−0.351981	−	0.637936i
$715$	−7.18597	−	13.4440i	−0.268740	−	0.502777i
$716$	7.57679	−	6.56333i	0.283158	−	0.245283i
$717$	1.41577	−	14.3746i	0.0528729	−	0.536828i
$718$	1.04290	+	0.193051i	0.0389207	+	0.00720458i
$719$	1.51608	+	3.66014i	0.0565402	+	0.136500i	0.949625	−	0.313388i	$-0.101464\pi$
$719$	1.51608	+	3.66014i	0.0565402	+	0.136500i	−0.893085	+	0.449888i	$0.851464\pi$
$720$	10.3883	−	9.49447i	0.387150	−	0.353838i
$721$	−0.0171159	+	0.0413214i	−0.000637430	+	0.00153889i
$722$	−4.79003	+	7.37958i	−0.178266	+	0.274640i
$723$	9.18352	+	11.1902i	0.341539	+	0.416166i
$724$	−6.18544	+	22.5336i	−0.229880	+	0.837455i
$725$	−13.0161	+	42.9084i	−0.483407	+	1.59358i
$726$	11.1566	+	8.91011i	0.414060	+	0.330685i
$727$	40.4215	+	8.04034i	1.49915	+	0.298200i	0.875391	−	0.483416i	$-0.160604\pi$
$727$	40.4215	+	8.04034i	1.49915	+	0.298200i	0.623761	+	0.781615i	$0.285604\pi$
$728$	−27.2550	−	7.09269i	−1.01014	−	0.262872i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	48.3487	−	15.3722i	1.78947	−	0.568949i
$731$	9.12566	−	11.1196i	0.337525	−	0.411275i
$732$	0.00386178	−	0.0225342i	0.000142735	−	0.000832889i
$733$	2.50709	+	1.34007i	0.0926016	+	0.0494966i	0.517047	−	0.855957i	$-0.327031\pi$
$733$	2.50709	+	1.34007i	0.0926016	+	0.0494966i	−0.424446	+	0.905453i	$0.639531\pi$
$734$	−0.0570427	−	0.0555439i	−0.00210549	−	0.00205016i
$735$	5.53753	+	5.53753i	0.204255	+	0.204255i
$736$	25.5964	+	14.7402i	0.943495	+	0.543330i
$737$	−7.63759	+	7.63759i	−0.281334	+	0.281334i
$738$	10.7188	−	0.142700i	0.394566	−	0.00525285i
$739$	−22.6506	+	42.3763i	−0.833216	+	1.55884i	−0.00394341	+	0.999992i	$0.501255\pi$
$739$	−22.6506	+	42.3763i	−0.833216	+	1.55884i	−0.829272	+	0.558845i	$0.811245\pi$
$740$	1.80272	+	7.95047i	0.0662694	+	0.292265i
$741$	−12.5926	−	10.3344i	−0.462599	−	0.379645i
$742$	−35.9023	−	18.5800i	−1.31801	−	0.682092i
$743$	15.1307	−	3.00969i	0.555092	−	0.110415i	0.0904300	−	0.995903i	$-0.471176\pi$
$743$	15.1307	−	3.00969i	0.555092	−	0.110415i	0.464662	+	0.885488i	$0.346176\pi$
$744$	1.18235	−	20.2791i	0.0433472	−	0.743468i
$745$	−2.70235	+	13.5856i	−0.0990064	+	0.497739i
$746$	26.3216	−	2.94674i	0.963704	−	0.107888i
$747$	−15.4441	−	4.68490i	−0.565068	−	0.171412i
$748$	9.46019	+	7.35118i	0.345899	+	0.268786i
$749$	32.6491	−	26.7944i	1.19297	−	0.979047i
$750$	−11.5775	+	2.46356i	−0.422750	+	0.0899564i
$751$	−35.9956	−	14.9098i	−1.31350	−	0.544068i	−0.387594	−	0.921830i	$-0.626694\pi$
$751$	−35.9956	−	14.9098i	−1.31350	−	0.544068i	−0.925903	+	0.377762i	$0.876694\pi$
$752$	0.740025	+	0.261317i	0.0269859	+	0.00952924i
$753$	13.0412	−	5.40184i	0.475248	−	0.196854i
$754$	−32.2693	+	22.1886i	−1.17518	+	0.808063i
$755$	33.7446	+	3.32355i	1.22809	+	0.120956i
$756$	3.90745	+	1.95667i	0.142113	+	0.0711633i
$757$	12.8509	−	6.86893i	0.467073	−	0.249656i	−0.221033	−	0.975266i	$-0.570943\pi$
$757$	12.8509	−	6.86893i	0.467073	−	0.249656i	0.688105	+	0.725611i	$0.258443\pi$
$758$	1.40754	−	4.87263i	0.0511242	−	0.176982i
$759$	−4.12780	+	2.75811i	−0.149830	+	0.100113i
$760$	12.2905	−	33.3835i	0.445825	−	1.21095i
$761$	−0.378294	+	0.566156i	−0.0137131	+	0.0205232i	−0.838263	−	0.545266i	$-0.816429\pi$
$761$	−0.378294	+	0.566156i	−0.0137131	+	0.0205232i	0.824550	+	0.565789i	$0.191429\pi$
$762$	1.28403	−	15.0943i	0.0465154	−	0.546809i
$763$	2.10491	+	21.3715i	0.0762027	+	0.773699i
$764$	−31.7753	+	33.5140i	−1.14959	+	1.21249i
$765$	−6.43482	−	21.2128i	−0.232652	−	0.766949i
$766$	−28.6276	−	11.4139i	−1.03436	−	0.412400i
$767$	22.3103			0.805578
$768$	6.24575	+	14.7306i	0.225374	+	0.531545i
$769$	6.28975			0.226814			0.113407	−	0.993549i	$-0.463824\pi$
$769$	6.28975			0.226814			0.113407	+	0.993549i	$0.463824\pi$
$770$	9.60169	+	3.82821i	0.346021	+	0.137959i
$771$	−0.705075	−	2.32432i	−0.0253927	−	0.0837084i
$772$	−7.91350	+	8.34651i	−0.284813	+	0.300398i
$773$	−1.60379	−	16.2835i	−0.0576842	−	0.585677i	−0.979967	−	0.199161i	$-0.936178\pi$
$773$	−1.60379	−	16.2835i	−0.0576842	−	0.585677i	0.922283	−	0.386516i	$-0.126322\pi$
$774$	−0.273680	+	3.21724i	−0.00983724	+	0.115641i
$775$	−29.4422	+	44.0634i	−1.05760	+	1.58280i
$776$	19.7681	+	7.27787i	0.709634	+	0.261260i
$777$	−2.10477	+	1.40636i	−0.0755082	+	0.0504530i
$778$	12.2077	−	42.2607i	0.437668	−	1.51512i
$779$	23.8973	−	12.7734i	0.856210	−	0.457654i
$780$	−28.6725	−	14.3578i	−1.02664	−	0.514093i
$781$	−6.88328	−	0.677944i	−0.246303	−	0.0242588i
$782$	38.3362	−	26.3603i	1.37090	−	0.942641i
$783$	5.61412	−	2.32545i	0.200632	−	0.0831047i
$784$	−8.03256	+	3.84010i	−0.286877	+	0.137146i
$785$	−67.1621	−	27.8194i	−2.39712	−	0.992919i
$786$	−18.8874	+	4.01903i	−0.673692	+	0.143354i
$787$	−17.2974	+	14.1956i	−0.616585	+	0.506018i	−0.890049	−	0.455864i	$-0.849330\pi$
$787$	−17.2974	+	14.1956i	−0.616585	+	0.506018i	0.273465	+	0.961882i	$0.411830\pi$
$788$	−23.1958	−	18.0247i	−0.826317	−	0.642102i
$789$	−12.0827	−	3.66524i	−0.430155	−	0.130486i
$790$	36.1858	−	4.05104i	1.28743	−	0.144130i
$791$	5.13878	−	25.8344i	0.182714	−	0.918564i
$792$	−2.68464	−	0.156525i	−0.0953944	−	0.00556188i
$793$	−0.0510920	+	0.0101628i	−0.00181433	+	0.000360893i
$794$	−25.7761	−	13.3395i	−0.914758	−	0.473402i
$795$	−35.5806	−	29.2002i	−1.26191	−	1.03562i
$796$	−11.8962	−	52.4654i	−0.421651	−	1.85959i
$797$	−9.23124	+	17.2704i	−0.326987	+	0.611750i	−0.990673	−	0.136261i	$-0.956491\pi$
$797$	−9.23124	+	17.2704i	−0.326987	+	0.611750i	0.663686	+	0.748012i	$0.268991\pi$
$798$	11.0452	−	0.147045i	0.390996	−	0.00520533i
$799$	0.874098	−	0.874098i	0.0309234	−	0.0309234i
$800$	5.40234	−	41.3902i	0.191002	−	1.46337i
$801$	−8.58083	−	8.58083i	−0.303189	−	0.303189i
$802$	−2.33647	−	2.27508i	−0.0825037	−	0.0803358i
$803$	−8.54963	−	4.56987i	−0.301710	−	0.161267i
$804$	−3.83781	+	22.3944i	−0.135349	+	0.789788i
$805$	25.4650	−	31.0292i	0.897523	−	1.09363i
$806$	−44.1088	+	14.0241i	−1.55367	+	0.493978i
$807$	−2.79106	−	14.0316i	−0.0982501	−	0.493936i
$808$	−1.83874	+	7.06571i	−0.0646867	+	0.248571i
$809$	35.0316	+	6.96823i	1.23165	+	0.244990i	0.767663	−	0.640854i	$-0.221420\pi$
$809$	35.0316	+	6.96823i	1.23165	+	0.244990i	0.463984	+	0.885844i	$0.346420\pi$
$810$	3.88796	+	3.10508i	0.136609	+	0.109101i
$811$	0.234433	−	0.772821i	0.00823204	−	0.0271374i	−0.952728	−	0.303824i	$-0.901736\pi$
$811$	0.234433	−	0.772821i	0.00823204	−	0.0271374i	0.960960	+	0.276687i	$0.0892365\pi$
$812$	7.02929	−	25.6077i	0.246680	−	0.898656i
$813$	16.0242	+	19.5255i	0.561992	+	0.684789i
$814$	0.848127	−	1.30664i	0.0297268	−	0.0457976i
$815$	14.1567	−	34.1772i	0.495887	−	1.19718i
$816$	25.1764	+	1.13183i	0.881350	+	0.0396221i
$817$	3.12336	+	7.54045i	0.109272	+	0.263807i
$818$	−21.7900	−	4.03353i	−0.761870	−	0.141029i
$819$	0.975960	−	9.90909i	0.0341028	−	0.346252i
$820$	40.3159	−	34.9233i	1.40789	−	1.21958i
$821$	−14.6187	−	27.3497i	−0.510198	−	0.954513i	−0.996726	−	0.0808481i	$-0.974237\pi$
$821$	−14.6187	−	27.3497i	−0.510198	−	0.954513i	0.486529	−	0.873665i	$-0.338263\pi$
$822$	−2.63257	−	4.77130i	−0.0918213	−	0.166418i
$823$	−5.93196	−	8.87781i	−0.206775	−	0.309461i	0.713558	−	0.700596i	$-0.247082\pi$
$823$	−5.93196	−	8.87781i	−0.206775	−	0.309461i	−0.920333	+	0.391135i	$0.872082\pi$
$824$	−0.0340622	−	0.0468169i	−0.00118661	−	0.00163094i
$825$	5.83330	+	3.89769i	0.203090	+	0.135700i
$826$	−11.5655	+	9.75209i	−0.402416	+	0.339319i
$827$	2.76519	−	0.272348i	0.0961552	−	0.00947046i	−0.0498251	−	0.998758i	$-0.515866\pi$
$827$	2.76519	−	0.272348i	0.0961552	−	0.00947046i	0.145980	+	0.989287i	$0.453366\pi$
$828$	−3.73810	+	9.75103i	−0.129908	+	0.338872i
$829$	10.9858	−	3.33251i	0.381553	−	0.115743i	−0.0936809	−	0.995602i	$-0.529863\pi$
$829$	10.9858	−	3.33251i	0.381553	−	0.115743i	0.475234	+	0.879859i	$0.342363\pi$
$830$	−73.7747	+	31.7155i	−2.56076	+	1.10086i
$831$			25.7745i			0.894107i
$832$	26.2458	−	25.3023i	0.909910	−	0.877200i
$833$			14.0237i			0.485891i
$834$	−2.75997	−	6.42007i	−0.0955700	−	0.222309i
$835$	12.7446	−	3.86602i	0.441044	−	0.133789i
$836$	−6.20868	+	2.76759i	−0.214732	+	0.0957191i
$837$	7.14734	−	0.703951i	0.247048	−	0.0243321i
$838$	22.8456	+	27.0937i	0.789186	+	0.935937i
$839$	−13.6521	−	9.12205i	−0.471323	−	0.314928i	0.297127	−	0.954838i	$-0.403972\pi$
$839$	−13.6521	−	9.12205i	−0.471323	−	0.314928i	−0.768450	+	0.639910i	$0.778972\pi$
$840$	21.1396	−	5.09008i	0.729386	−	0.175625i
$841$	−4.40350	−	6.59030i	−0.151845	−	0.227252i
$842$	31.7295	−	17.5068i	1.09347	−	0.603323i
$843$	7.59888	+	14.2165i	0.261719	+	0.489643i
$844$	2.41525	−	33.6984i	0.0831364	−	1.15995i
$845$	−2.67832	+	27.1935i	−0.0921370	+	0.935483i
$846$	−0.0505046	+	0.272837i	−0.00173638	+	0.00938031i
$847$	8.44189	+	20.3805i	0.290067	+	0.700283i
$848$	44.7722	−	27.0893i	1.53748	−	0.930250i
$849$	2.07123	−	5.00039i	0.0710843	−	0.171613i
$850$	−55.1483	−	35.7963i	−1.89157	−	1.22780i
$851$	−3.83762	−	4.67615i	−0.131552	−	0.160297i
$852$	−12.6443	+	7.19769i	−0.433186	+	0.246589i
$853$	7.86322	−	25.9216i	0.269232	−	0.887538i	−0.713207	−	0.700953i	$-0.752758\pi$
$853$	7.86322	−	25.9216i	0.269232	−	0.887538i	0.982439	−	0.186585i	$-0.0597418\pi$
$854$	0.0220435	−	0.0276013i	0.000754312	−	0.000944496i
$855$	12.3357	+	2.45372i	0.421871	+	0.0839153i
$856$	7.52713	+	54.1534i	0.257272	+	1.85093i
$857$	11.0657	+	55.6312i	0.377998	+	1.90033i	0.432165	+	0.901795i	$0.357750\pi$
$857$	11.0657	+	55.6312i	0.377998	+	1.90033i	−0.0541665	+	0.998532i	$0.517250\pi$
$858$	1.85657	+	5.83931i	0.0633823	+	0.199351i
$859$	−6.49461	+	7.91370i	−0.221593	+	0.270012i	−0.871926	−	0.489637i	$-0.837129\pi$
$859$	−6.49461	+	7.91370i	−0.221593	+	0.270012i	0.650333	+	0.759649i	$0.274629\pi$
$860$	9.27818	+	13.1160i	0.316383	+	0.447250i
$861$	14.6066	+	7.80741i	0.497793	+	0.266076i
$862$	2.03743	−	2.09241i	0.0693951	−	0.0712677i
$863$	−13.9330	−	13.9330i	−0.474287	−	0.474287i	0.429012	−	0.903299i	$-0.358862\pi$
$863$	−13.9330	−	13.9330i	−0.474287	−	0.474287i	−0.903299	+	0.429012i	$0.858862\pi$
$864$	−4.80049	+	2.99254i	−0.163316	+	0.101808i
$865$	−60.2628	+	60.2628i	−2.04900	+	2.04900i
$866$	0.118758	+	8.92048i	0.00403557	+	0.303130i
$867$	10.6987	−	20.0158i	0.363346	−	0.679773i
$868$	16.7356	−	26.5505i	0.568044	−	0.901182i
$869$	−5.37836	−	4.41390i	−0.182448	−	0.149731i
$870$	13.8969	−	26.8530i	0.471148	−	0.910403i
$871$	50.7749	−	10.0997i	1.72044	−	0.342217i
$872$	−25.0200	−	12.1150i	−0.847285	−	0.410265i
$873$	−1.45297	+	7.30459i	−0.0491757	+	0.247223i
$874$	2.93685	+	26.2333i	0.0993404	+	0.887355i
$875$	−17.5005	−	5.30870i	−0.591623	−	0.179467i
$876$	−20.2339	+	2.53836i	−0.683640	+	0.0857634i
$877$	−10.0098	+	8.21486i	−0.338008	+	0.277396i	−0.788050	−	0.615611i	$-0.788909\pi$
$877$	−10.0098	+	8.21486i	−0.338008	+	0.277396i	0.450042	+	0.893008i	$0.351409\pi$
$878$	4.56861	+	21.4701i	0.154183	+	0.724582i
$879$	0.175498	+	0.0726938i	0.00591941	+	0.00245190i
$880$	−10.7142	+	8.01551i	−0.361175	+	0.270203i
$881$	−16.3655	+	6.77883i	−0.551369	+	0.228385i	−0.640933	−	0.767596i	$-0.721453\pi$
$881$	−16.3655	+	6.77883i	−0.551369	+	0.228385i	0.0895643	+	0.995981i	$0.471453\pi$
$882$	−1.78350	−	2.59377i	−0.0600536	−	0.0873369i
$883$	42.4014	+	4.17618i	1.42692	+	0.140540i	0.781795	−	0.623536i	$-0.214304\pi$
$883$	42.4014	+	4.17618i	1.42692	+	0.140540i	0.645127	+	0.764075i	$0.276804\pi$
$884$	−18.1258	−	54.4867i	−0.609637	−	1.83259i
$885$	−15.1913	+	8.11993i	−0.510651	+	0.272948i
$886$	2.53270	+	0.731614i	0.0850877	+	0.0245790i
$887$	−23.7081	+	15.8413i	−0.796041	+	0.531898i	−0.885801	−	0.464066i	$-0.846390\pi$
$887$	−23.7081	+	15.8413i	−0.796041	+	0.531898i	0.0897595	+	0.995963i	$0.471390\pi$
$888$	−0.130831	−	3.27422i	−0.00439039	−	0.109876i
$889$	13.0033	−	19.4608i	0.436116	−	0.652693i
$890$	−60.1637	−	5.11794i	−2.01669	−	0.171554i
$891$	−0.0931921	−	0.946196i	−0.00312205	−	0.0316987i
$892$	−0.0580480	−	2.17974i	−0.00194359	−	0.0729831i
$893$	0.203599	+	0.671176i	0.00681318	+	0.0224600i
$894$	2.06202	−	5.17184i	0.0689644	−	0.172972i
$895$	17.6344			0.589454
$896$	−2.54573	+	24.5889i	−0.0850469	+	0.821458i
$897$	23.7944			0.794473
$898$	−11.9266	+	29.9135i	−0.397995	+	0.998228i
$899$	−12.6687	−	41.7630i	−0.422524	−	1.39288i
$900$	14.7525	−	0.392871i	0.491752	−	0.0130957i
$901$	−8.07905	−	82.0280i	−0.269152	−	2.73275i
$902$	−10.1554	−	0.863889i	−0.338138	−	0.0287644i
$903$	−2.77155	+	4.14791i	−0.0922313	+	0.138034i
$904$	25.0538	+	23.1285i	0.833277	+	0.769244i
$905$	−34.1793	+	22.8379i	−1.13616	+	0.759156i
$906$	−13.0940	−	3.78242i	−0.435018	−	0.125662i
$907$	36.9546	−	19.7526i	1.22706	−	0.655875i	0.274896	−	0.961474i	$-0.411357\pi$
$907$	36.9546	−	19.7526i	1.22706	−	0.655875i	0.952160	+	0.305599i	$0.0988566\pi$
$908$	−33.5338	+	11.1555i	−1.11286	+	0.370208i
$909$	−2.56888	−	0.253013i	−0.0852044	−	0.00839190i
$910$	−28.0708	−	40.8238i	−0.930537	−	1.35330i
$911$	30.3698	−	12.5796i	1.00620	−	0.416780i	0.182130	−	0.983274i	$-0.441701\pi$
$911$	30.3698	−	12.5796i	1.00620	−	0.416780i	0.824066	+	0.566494i	$0.191701\pi$
$912$	−7.30009	+	12.2952i	−0.241730	+	0.407135i
$913$	14.1765	+	5.87210i	0.469174	+	0.194338i
$914$	−0.415535	−	1.95280i	−0.0137447	−	0.0645930i
$915$	0.0310903	−	0.0255151i	0.00102781	−	0.000843504i
$916$	3.42255	+	27.2820i	0.113084	+	0.901421i
$917$	−28.5501	−	8.66059i	−0.942809	−	0.285998i
$918$	0.991313	+	8.85487i	0.0327182	+	0.292254i
$919$	−2.64715	+	13.3081i	−0.0873215	+	0.438995i	0.912248	+	0.409639i	$0.134345\pi$
$919$	−2.64715	+	13.3081i	−0.0873215	+	0.438995i	−0.999569	+	0.0293554i	$0.990655\pi$
$920$	17.0568	+	49.0820i	0.562347	+	1.61819i
$921$	−10.3807	+	2.06485i	−0.342055	+	0.0680390i
$922$	−1.00977	+	1.95119i	−0.0332550	+	0.0642590i
$923$	25.6260	+	21.0307i	0.843490	+	0.692234i
$924$	−3.51487	−	2.21553i	−0.115631	−	0.0728857i
$925$	−4.02983	+	7.53927i	−0.132500	+	0.247890i
$926$	0.160172	+	12.0312i	0.00526357	+	0.395371i
$927$	0.0144742	−	0.0144742i	0.000475396	−	0.000475396i
$928$	23.5263	+	25.0629i	0.772288	+	0.822730i
$929$	−35.1803	−	35.1803i	−1.15423	−	1.15423i	−0.985696	−	0.168533i	$-0.946097\pi$
$929$	−35.1803	−	35.1803i	−1.15423	−	1.15423i	−0.168533	−	0.985696i	$-0.553903\pi$
$930$	24.9300	−	25.6027i	0.817487	−	0.839547i
$931$	−7.01726	−	3.75080i	−0.229981	−	0.122928i
$932$	−36.4742	+	25.8018i	−1.19475	+	0.845165i
$933$	−5.75195	+	7.00877i	−0.188310	+	0.229457i
$934$	−4.17104	−	13.1188i	−0.136481	−	0.429260i
$935$	4.11174	+	20.6711i	0.134468	+	0.676017i
$936$	10.2820	+	7.77249i	0.336078	+	0.254052i
$937$	29.7168	+	5.91104i	0.970806	+	0.193105i	0.654925	−	0.755694i	$-0.272700\pi$
$937$	29.7168	+	5.91104i	0.970806	+	0.193105i	0.315881	+	0.948799i	$0.397700\pi$
$938$	−21.9066	+	27.4299i	−0.715277	+	0.895619i
$939$	7.28312	−	24.0092i	0.237676	−	0.783511i
$940$	0.683003	+	1.19984i	0.0222771	+	0.0391345i
$941$	−9.52045	−	11.6007i	−0.310358	−	0.378172i	0.594349	−	0.804208i	$-0.297410\pi$
$941$	−9.52045	−	11.6007i	−0.310358	−	0.378172i	−0.904707	+	0.426035i	$0.859910\pi$
$942$	24.5096	+	15.9090i	0.798567	+	0.518343i
$943$	−15.1463	+	36.5663i	−0.493230	+	1.19076i
$944$	−2.95405	−	19.3592i	−0.0961460	−	0.630087i
$945$	2.94191	+	7.10241i	0.0957005	+	0.231041i
$946$	0.558777	−	3.01863i	0.0181674	−	0.0981442i
$947$	−0.983800	+	9.98869i	−0.0319692	+	0.324589i	0.965877	+	0.258999i	$0.0833928\pi$
$947$	−0.983800	+	9.98869i	−0.0319692	+	0.324589i	−0.997847	+	0.0655895i	$0.979107\pi$
$948$	−14.5984	−	1.04630i	−0.474133	−	0.0339824i
$949$	21.9032	+	40.9780i	0.711007	+	1.33020i
$950$	32.6621	−	18.0213i	1.05970	−	0.584688i
$951$	−18.6360	−	27.8908i	−0.604314	−	0.904420i
$952$	33.2131	+	20.3226i	1.07644	+	0.658658i
$953$	11.8943	+	7.94752i	0.385294	+	0.257445i	0.733099	−	0.680121i	$-0.238073\pi$
$953$	11.8943	+	7.94752i	0.385294	+	0.257445i	−0.347805	+	0.937567i	$0.613073\pi$
$954$	11.9264	+	14.1442i	0.386132	+	0.457934i
$955$	−80.8529	+	7.96332i	−2.61634	+	0.257687i
$956$	11.7616	+	26.3855i	0.380398	+	0.853368i
$957$	−5.52877	+	1.67713i	−0.178720	+	0.0542141i
$958$	−19.9590	−	46.4273i	−0.644845	−	1.50000i
$959$		−	8.41940i		−	0.271877i
$960$	−8.66217	+	26.7809i	−0.279570	+	0.864349i
$961$		−	20.5800i		−	0.663870i
$962$	−6.85930	+	2.94879i	−0.221153	+	0.0950729i
$963$	−18.4978	+	5.61126i	−0.596085	+	0.180820i
$964$	−27.0338	−	10.3635i	−0.870699	−	0.333786i
$965$	−20.1361	+	1.98323i	−0.648202	+	0.0638424i
$966$	−12.3349	+	10.4008i	−0.396868	+	0.334641i
$967$	35.6771	+	23.8387i	1.14730	+	0.766600i	0.975817	−	0.218588i	$-0.0701450\pi$
$967$	35.6771	+	23.8387i	1.14730	+	0.766600i	0.171480	+	0.985188i	$0.445145\pi$
$968$	−28.2073	−	4.44832i	−0.906616	−	0.142974i
$969$	12.5129	+	18.7269i	0.401973	+	0.601595i
$970$	17.9024	+	32.4465i	0.574810	+	1.04179i
$971$	1.27784	+	2.39068i	0.0410080	+	0.0767205i	0.901591	−	0.432590i	$-0.142400\pi$
$971$	1.27784	+	2.39068i	0.0410080	+	0.0767205i	−0.860583	+	0.509311i	$0.829900\pi$
$972$	−1.30949	−	1.51170i	−0.0420020	−	0.0484877i
$973$	1.05828	−	10.7449i	0.0339269	−	0.344466i
$974$	31.5556	+	5.84122i	1.01111	+	0.187165i
$975$	−12.8680	−	31.0661i	−0.412106	−	0.994912i
$976$	0.0155835	+	0.0429881i	0.000498815	+	0.00137602i
$977$	−15.1187	+	36.4998i	−0.483690	+	1.16773i	0.474154	+	0.880442i	$0.342754\pi$
$977$	−15.1187	+	36.4998i	−0.483690	+	1.16773i	−0.957844	+	0.287289i	$0.907246\pi$
$978$	−8.09573	+	12.4724i	−0.258873	+	0.398823i
$979$	7.31948	+	8.91881i	0.233932	+	0.285047i
$980$	−15.1038	−	4.14597i	−0.482473	−	0.132438i
$981$	2.85302	−	9.40516i	0.0910900	−	0.300284i
$982$	−36.6941	−	29.3054i	−1.17096	−	0.935172i
$983$	20.1127	+	4.00066i	0.641495	+	0.127601i	0.505111	−	0.863055i	$-0.331452\pi$
$983$	20.1127	+	4.00066i	0.641495	+	0.127601i	0.136385	+	0.990656i	$0.456452\pi$
$984$	−18.4894	+	10.8534i	−0.589421	+	0.345994i
$985$	−10.0817	−	50.6844i	−0.321231	−	1.61494i
$986$	51.5991	−	16.4056i	1.64325	−	0.522461i
$987$	−0.271964	+	0.331389i	−0.00865671	+	0.0105482i
$988$	32.1124	+	5.50323i	1.02163	+	0.175081i
$989$	−10.5138	−	5.61973i	−0.334318	−	0.178697i
$990$	−3.38940	−	3.30034i	−0.107722	−	0.104892i
$991$	−8.79387	−	8.79387i	−0.279347	−	0.279347i	0.553502	−	0.832848i	$-0.313291\pi$
$991$	−8.79387	−	8.79387i	−0.279347	−	0.279347i	−0.832848	+	0.553502i	$0.813291\pi$
$992$	18.0094	+	36.4173i	0.571798	+	1.15625i
$993$	−25.5212	+	25.5212i	−0.809890	+	0.809890i
$994$	−22.4771	+	0.299238i	−0.712931	+	0.00949125i
$995$	44.6126	−	83.4642i	1.41431	−	2.64599i
$996$	31.4789	−	7.13766i	0.997448	−	0.226165i
$997$	13.5437	+	11.1150i	0.428934	+	0.352017i	0.823955	−	0.566655i	$-0.191763\pi$
$997$	13.5437	+	11.1150i	0.428934	+	0.352017i	−0.395021	+	0.918672i	$0.629263\pi$
$998$	35.7943	+	18.5241i	1.13305	+	0.586371i
$999$	1.13627	−	0.226019i	0.0359501	−	0.00715092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.29	✓	512
128.69	even	32	inner	384.2.v.a.325.29	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.29	✓	512	1.1	even	1	trivial
384.2.v.a.325.29	yes	512	128.69	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31365 + 0.523755i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.45136 + 1.37606i) q^{4} +(0.344860 + 3.50142i) q^{5} +(0.119870 - 1.40912i) q^{6} +(1.21392 - 1.81675i) q^{7} +(1.18586 + 2.56783i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(1.31365 + 0.523755i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(1.45136 + 1.37606i) q^{4} +(0.344860 + 3.50142i) q^{5} +(0.119870 - 1.40912i) q^{6} +(1.21392 - 1.81675i) q^{7} +(1.18586 + 2.56783i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(-1.38086 + 4.78027i) q^{10} +(0.838508 - 0.448192i) q^{11} +(0.895504 - 1.78832i) q^{12} +(-4.53507 - 0.446666i) q^{13} +(2.54620 - 1.75079i) q^{14} +(3.25054 - 1.34642i) q^{15} +(0.212895 + 3.99433i) q^{16} +(5.82086 + 2.41108i) q^{17} +(-1.38324 + 0.294339i) q^{18} +(-2.76333 + 2.26781i) q^{19} +(-4.31767 + 5.55638i) q^{20} +(-2.09090 - 0.634269i) q^{21} +(1.33625 - 0.149595i) q^{22} +(1.01866 - 5.12116i) q^{23} +(2.11302 - 1.88020i) q^{24} +(-7.23711 + 1.43955i) q^{25} +(-5.72356 - 2.96203i) q^{26} +(0.773010 + 0.634393i) q^{27} +(4.26180 - 0.966338i) q^{28} +(2.86453 - 5.35916i) q^{29} +(4.97528 - 0.0662358i) q^{30} +(5.07838 - 5.07838i) q^{31} +(-1.81238 + 5.35866i) q^{32} +(-0.672299 - 0.672299i) q^{33} +(6.38376 + 6.21602i) q^{34} +(6.77985 + 3.62391i) q^{35} +(-1.97126 - 0.337823i) q^{36} +(0.734966 - 0.895559i) q^{37} +(-4.81783 + 1.53180i) q^{38} +(0.889030 + 4.46945i) q^{39} +(-8.58209 + 5.03774i) q^{40} +(-7.43439 - 1.47879i) q^{41} +(-2.41452 - 1.92833i) q^{42} +(0.662763 - 2.18484i) q^{43} +(1.83372 + 0.503353i) q^{44} +(-2.23203 - 2.71973i) q^{45} +(4.02040 - 6.19389i) q^{46} +(0.0750833 - 0.181267i) q^{47} +(3.76054 - 1.36322i) q^{48} +(0.851784 + 2.05639i) q^{49} +(-10.2610 - 1.89941i) q^{50} +(0.617552 - 6.27011i) q^{51} +(-5.96739 - 6.88883i) q^{52} +(-6.16699 - 11.5376i) q^{53} +(0.683199 + 1.23824i) q^{54} +(1.85848 + 2.78141i) q^{55} +(6.10464 + 0.962708i) q^{56} +(2.97231 + 1.98603i) q^{57} +(6.56988 - 5.53975i) q^{58} +(-4.87224 + 0.479874i) q^{59} +(6.57047 + 2.51882i) q^{60} +(0.0109391 - 0.00331835i) q^{61} +(9.33106 - 4.01140i) q^{62} +2.18499i q^{63} +(-5.18747 + 6.09017i) q^{64} -16.0332i q^{65} +(-0.531046 - 1.23529i) q^{66} +(-10.8712 + 3.29775i) q^{67} +(5.13037 + 11.5092i) q^{68} +(-5.19635 + 0.511796i) q^{69} +(7.00832 + 8.31153i) q^{70} +(-6.04869 - 4.04160i) q^{71} +(-2.41262 - 1.47624i) q^{72} +(-5.66473 - 8.47786i) q^{73} +(1.43454 - 0.791510i) q^{74} +(3.47838 + 6.50760i) q^{75} +(-7.13124 - 0.511115i) q^{76} +(0.203624 - 2.06743i) q^{77} +(-1.17303 + 6.33694i) q^{78} +(-2.80044 - 6.76087i) q^{79} +(-13.9124 + 2.12292i) q^{80} +(0.382683 - 0.923880i) q^{81} +(-8.99167 - 5.83642i) q^{82} +(10.2385 + 12.4756i) q^{83} +(-2.16186 - 3.79777i) q^{84} +(-6.43482 + 21.2128i) q^{85} +(2.01496 - 2.52299i) q^{86} +(-5.95992 - 1.18550i) q^{87} +(2.14523 + 1.62165i) q^{88} +(2.36745 + 11.9020i) q^{89} +(-1.50763 - 4.74182i) q^{90} +(-6.31668 + 7.69689i) q^{91} +(8.52550 - 6.03091i) q^{92} +(-6.33389 - 3.38553i) q^{93} +(0.193573 - 0.198796i) q^{94} +(-8.89352 - 8.89352i) q^{95} +(5.65403 + 0.178805i) q^{96} +(5.26632 - 5.26632i) q^{97} +(0.0419027 + 3.14750i) q^{98} +(-0.448192 + 0.838508i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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