LMFDB - Embedded newform 384.2.v.a.157.26

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			157.26
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24124 + 0.677730i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.08136 + 1.68245i) q^{4} +(-2.78687 + 1.48961i) q^{5} +(-0.796130 + 1.16884i) q^{6} +(-0.0876435 - 0.440614i) q^{7} +(0.201982 + 2.82121i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(1.24124 + 0.677730i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.08136 + 1.68245i) q^{4} +(-2.78687 + 1.48961i) q^{5} +(-0.796130 + 1.16884i) q^{6} +(-0.0876435 - 0.440614i) q^{7} +(0.201982 + 2.82121i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.46873 - 0.0397766i) q^{10} +(1.26346 - 1.53953i) q^{11} +(-1.78035 + 0.911246i) q^{12} +(-2.72548 + 5.09902i) q^{13} +(0.189830 - 0.606307i) q^{14} +(-1.20928 - 2.91946i) q^{15} +(-1.66131 + 3.63869i) q^{16} +(2.38060 - 5.74727i) q^{17} +(-1.08517 - 0.906862i) q^{18} +(1.73656 + 5.72469i) q^{19} +(-5.51982 - 3.07797i) q^{20} +(0.447082 - 0.0440338i) q^{21} +(2.61164 - 1.05464i) q^{22} +(-0.164730 + 0.110069i) q^{23} +(-2.82742 - 0.0755172i) q^{24} +(2.76984 - 4.14536i) q^{25} +(-6.83874 + 4.48197i) q^{26} +(0.290285 - 0.956940i) q^{27} +(0.646538 - 0.623919i) q^{28} +(5.96777 - 4.89762i) q^{29} +(0.477598 - 4.44332i) q^{30} +(-5.34556 + 5.34556i) q^{31} +(-4.52814 + 3.39057i) q^{32} +(1.40827 + 1.40827i) q^{33} +(6.85000 - 5.52035i) q^{34} +(0.900595 + 1.09738i) q^{35} +(-0.732354 - 1.86109i) q^{36} +(11.0850 + 3.36261i) q^{37} +(-1.72430 + 8.28264i) q^{38} +(-4.80732 - 3.21215i) q^{39} +(-4.76540 - 7.56146i) q^{40} +(-0.387580 - 0.580054i) q^{41} +(0.584781 + 0.248345i) q^{42} +(-0.575438 - 5.84252i) q^{43} +(3.95644 + 0.460922i) q^{44} +(3.02393 - 0.917299i) q^{45} +(-0.279066 + 0.0249797i) q^{46} +(11.4478 + 4.74184i) q^{47} +(-3.45833 - 2.00996i) q^{48} +(6.28070 - 2.60155i) q^{49} +(6.24749 - 3.26819i) q^{50} +(5.48626 + 2.93247i) q^{51} +(-11.5261 + 0.928388i) q^{52} +(-3.96058 - 3.25037i) q^{53} +(1.00886 - 0.991060i) q^{54} +(-1.22779 + 6.17252i) q^{55} +(1.22536 - 0.336256i) q^{56} +(-5.86733 + 1.16709i) q^{57} +(10.7267 - 2.03459i) q^{58} +(3.86979 + 7.23987i) q^{59} +(3.60419 - 5.19155i) q^{60} +(-0.782508 - 0.0770703i) q^{61} +(-10.2580 + 3.01228i) q^{62} +0.449246i q^{63} +(-7.91841 + 1.13967i) q^{64} -18.2702i q^{65} +(0.793578 + 2.70244i) q^{66} +(-5.42297 - 0.534115i) q^{67} +(12.2438 - 2.20964i) q^{68} +(-0.0933925 - 0.174725i) q^{69} +(0.374129 + 1.97247i) q^{70} +(-5.54100 + 1.10217i) q^{71} +(0.352289 - 2.80640i) q^{72} +(0.466609 - 2.34580i) q^{73} +(11.4803 + 11.6865i) q^{74} +(3.85391 + 3.16282i) q^{75} +(-7.75367 + 9.11216i) q^{76} +(-0.789070 - 0.421767i) q^{77} +(-3.79008 - 7.24512i) q^{78} +(-1.00966 + 0.418214i) q^{79} +(-0.790386 - 12.6153i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-0.0879599 - 0.982662i) q^{82} +(-2.85051 + 0.864694i) q^{83} +(0.557543 + 0.704580i) q^{84} +(1.92679 + 19.5631i) q^{85} +(3.24540 - 7.64197i) q^{86} +(4.28909 + 6.41908i) q^{87} +(4.59852 + 3.25352i) q^{88} +(-8.58661 - 5.73739i) q^{89} +(4.37511 + 0.910819i) q^{90} +(2.48557 + 0.753989i) q^{91} +(-0.363318 - 0.158126i) q^{92} +(-4.79586 - 5.84377i) q^{93} +(10.9958 + 13.6443i) q^{94} +(-13.3671 - 13.3671i) q^{95} +(-2.93041 - 4.83867i) q^{96} +(11.3641 - 11.3641i) q^{97} +(9.55901 + 1.02747i) q^{98} +(-1.53953 + 1.26346i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	1.24124	+	0.677730i	0.877691	+	0.479228i
$2$	1.24124	+	0.677730i	0.877691	+	0.479228i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	1.08136	+	1.68245i	0.540681	+	0.841227i
$5$	−2.78687	+	1.48961i	−1.24633	+	0.666175i	−0.956731	−	0.290974i	$-0.906021\pi$
$5$	−2.78687	+	1.48961i	−1.24633	+	0.666175i	−0.289595	+	0.957149i	$0.593521\pi$
$6$	−0.796130	+	1.16884i	−0.325019	+	0.477175i
$7$	−0.0876435	−	0.440614i	−0.0331261	−	0.166536i	0.960681	−	0.277654i	$-0.0895569\pi$
$7$	−0.0876435	−	0.440614i	−0.0331261	−	0.166536i	−0.993807	+	0.111118i	$0.964557\pi$
$8$	0.201982	+	2.82121i	0.0714114	+	0.997447i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−4.46873	−	0.0397766i	−1.41314	−	0.0125785i
$11$	1.26346	−	1.53953i	0.380947	−	0.464185i	−0.546872	−	0.837216i	$-0.684182\pi$
$11$	1.26346	−	1.53953i	0.380947	−	0.464185i	0.927819	+	0.373031i	$0.121682\pi$
$12$	−1.78035	+	0.911246i	−0.513941	+	0.263054i
$13$	−2.72548	+	5.09902i	−0.755913	+	1.41421i	0.149097	+	0.988823i	$0.452363\pi$
$13$	−2.72548	+	5.09902i	−0.755913	+	1.41421i	−0.905010	+	0.425391i	$0.860137\pi$
$14$	0.189830	−	0.606307i	0.0507343	−	0.162042i
$15$	−1.20928	−	2.91946i	−0.312234	−	0.753801i
$16$	−1.66131	+	3.63869i	−0.415327	+	0.909672i
$17$	2.38060	−	5.74727i	0.577380	−	1.39392i	−0.317777	−	0.948166i	$-0.602936\pi$
$17$	2.38060	−	5.74727i	0.577380	−	1.39392i	0.895156	−	0.445752i	$-0.147064\pi$
$18$	−1.08517	−	0.906862i	−0.255778	−	0.213750i
$19$	1.73656	+	5.72469i	0.398395	+	1.31333i	0.895275	+	0.445514i	$0.146979\pi$
$19$	1.73656	+	5.72469i	0.398395	+	1.31333i	−0.496880	+	0.867819i	$0.665521\pi$
$20$	−5.51982	−	3.07797i	−1.23427	−	0.688255i
$21$	0.447082	−	0.0440338i	0.0975614	−	0.00960896i
$22$	2.61164	−	1.05464i	0.556803	−	0.224850i
$23$	−0.164730	+	0.110069i	−0.0343485	+	0.0229509i	−0.572626	−	0.819817i	$-0.694075\pi$
$23$	−0.164730	+	0.110069i	−0.0343485	+	0.0229509i	0.538277	+	0.842768i	$0.319075\pi$
$24$	−2.82742	−	0.0755172i	−0.577144	−	0.0154149i
$25$	2.76984	−	4.14536i	0.553969	−	0.829073i
$26$	−6.83874	+	4.48197i	−1.34119	+	0.878987i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	0.646538	−	0.623919i	0.122184	−	0.117910i
$29$	5.96777	−	4.89762i	1.10819	−	0.909465i	0.111743	−	0.993737i	$-0.464357\pi$
$29$	5.96777	−	4.89762i	1.10819	−	0.909465i	0.996443	+	0.0842722i	$0.0268565\pi$
$30$	0.477598	−	4.44332i	0.0871970	−	0.811235i
$31$	−5.34556	+	5.34556i	−0.960090	+	0.960090i	−0.999234	−	0.0391434i	$-0.987537\pi$
$31$	−5.34556	+	5.34556i	−0.960090	+	0.960090i	0.0391434	+	0.999234i	$0.487537\pi$
$32$	−4.52814	+	3.39057i	−0.800469	+	0.599374i
$33$	1.40827	+	1.40827i	0.245149	+	0.245149i
$34$	6.85000	−	5.52035i	1.17477	−	0.946732i
$35$	0.900595	+	1.09738i	0.152228	+	0.185491i
$36$	−0.732354	−	1.86109i	−0.122059	−	0.310182i
$37$	11.0850	+	3.36261i	1.82237	+	0.552809i	0.999873	−	0.0159633i	$-0.00508149\pi$
$37$	11.0850	+	3.36261i	1.82237	+	0.552809i	0.822495	+	0.568772i	$0.192581\pi$
$38$	−1.72430	+	8.28264i	−0.279718	+	1.34362i
$39$	−4.80732	−	3.21215i	−0.769787	−	0.514356i
$40$	−4.76540	−	7.56146i	−0.753476	−	1.19557i
$41$	−0.387580	−	0.580054i	−0.0605298	−	0.0905892i	0.799970	−	0.600040i	$-0.204849\pi$
$41$	−0.387580	−	0.580054i	−0.0605298	−	0.0905892i	−0.860500	+	0.509451i	$0.829849\pi$
$42$	0.584781	+	0.248345i	0.0902336	+	0.0383204i
$43$	−0.575438	−	5.84252i	−0.0877535	−	0.890976i	−0.933783	−	0.357840i	$-0.883513\pi$
$43$	−0.575438	−	5.84252i	−0.0877535	−	0.890976i	0.846029	−	0.533136i	$-0.178987\pi$
$44$	3.95644	+	0.460922i	0.596456	+	0.0694866i
$45$	3.02393	−	0.917299i	0.450781	−	0.136743i
$46$	−0.279066	+	0.0249797i	−0.0411461	+	0.00368306i
$47$	11.4478	+	4.74184i	1.66983	+	0.691668i	0.998763	−	0.0497240i	$-0.0158342\pi$
$47$	11.4478	+	4.74184i	1.66983	+	0.691668i	0.671072	+	0.741392i	$0.265834\pi$
$48$	−3.45833	−	2.00996i	−0.499167	−	0.290113i
$49$	6.28070	−	2.60155i	0.897243	−	0.371650i
$50$	6.24749	−	3.26819i	0.883528	−	0.462192i
$51$	5.48626	+	2.93247i	0.768230	+	0.410627i
$52$	−11.5261	+	0.928388i	−1.59838	+	0.128744i
$53$	−3.96058	−	3.25037i	−0.544028	−	0.446472i	0.321805	−	0.946806i	$-0.395711\pi$
$53$	−3.96058	−	3.25037i	−0.544028	−	0.446472i	−0.865832	+	0.500334i	$0.833211\pi$
$54$	1.00886	−	0.991060i	0.137289	−	0.134866i
$55$	−1.22779	+	6.17252i	−0.165555	+	0.832303i
$56$	1.22536	−	0.336256i	0.163746	−	0.0449341i
$57$	−5.86733	+	1.16709i	−0.777147	+	0.154584i
$58$	10.7267	−	2.03459i	1.40849	−	0.267155i
$59$	3.86979	+	7.23987i	0.503804	+	0.942550i	0.997345	+	0.0728277i	$0.0232023\pi$
$59$	3.86979	+	7.23987i	0.503804	+	0.942550i	−0.493541	+	0.869723i	$0.664298\pi$
$60$	3.60419	−	5.19155i	0.465298	−	0.670226i
$61$	−0.782508	−	0.0770703i	−0.100190	−	0.00986784i	0.0477980	−	0.998857i	$-0.484780\pi$
$61$	−0.782508	−	0.0770703i	−0.100190	−	0.00986784i	−0.147988	+	0.988989i	$0.547280\pi$
$62$	−10.2580	+	3.01228i	−1.30276	+	0.382560i
$63$			0.449246i			0.0565996i
$64$	−7.91841	+	1.13967i	−0.989801	+	0.142458i
$65$		−	18.2702i		−	2.26614i
$66$	0.793578	+	2.70244i	0.0976827	+	0.332647i
$67$	−5.42297	−	0.534115i	−0.662521	−	0.0652526i	−0.238833	−	0.971061i	$-0.576765\pi$
$67$	−5.42297	−	0.534115i	−0.662521	−	0.0652526i	−0.423688	+	0.905808i	$0.639265\pi$
$68$	12.2438	−	2.20964i	1.48478	−	0.267958i
$69$	−0.0933925	−	0.174725i	−0.0112431	−	0.0210344i
$70$	0.374129	+	1.97247i	0.0447170	+	0.235755i
$71$	−5.54100	+	1.10217i	−0.657596	+	0.130804i	−0.512599	−	0.858628i	$-0.671317\pi$
$71$	−5.54100	+	1.10217i	−0.657596	+	0.130804i	−0.144997	+	0.989432i	$0.546317\pi$
$72$	0.352289	−	2.80640i	0.0415177	−	0.330738i
$73$	0.466609	−	2.34580i	0.0546125	−	0.274556i	−0.943824	−	0.330448i	$-0.892800\pi$
$73$	0.466609	−	2.34580i	0.0546125	−	0.274556i	0.998437	+	0.0558921i	$0.0178003\pi$
$74$	11.4803	+	11.6865i	1.33455	+	1.35852i
$75$	3.85391	+	3.16282i	0.445011	+	0.365211i
$76$	−7.75367	+	9.11216i	−0.889407	+	1.04524i
$77$	−0.789070	−	0.421767i	−0.0899229	−	0.0480648i
$78$	−3.79008	−	7.24512i	−0.429142	−	0.820349i
$79$	−1.00966	+	0.418214i	−0.113595	+	0.0470527i	−0.438757	−	0.898606i	$-0.644581\pi$
$79$	−1.00966	+	0.418214i	−0.113595	+	0.0470527i	0.325162	+	0.945658i	$0.394581\pi$
$80$	−0.790386	−	12.6153i	−0.0883678	−	1.41043i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−0.0879599	−	0.982662i	−0.00971354	−	0.108517i
$83$	−2.85051	+	0.864694i	−0.312884	+	0.0949125i	−0.442822	−	0.896610i	$-0.646022\pi$
$83$	−2.85051	+	0.864694i	−0.312884	+	0.0949125i	0.129937	+	0.991522i	$0.458522\pi$
$84$	0.557543	+	0.704580i	0.0608330	+	0.0768759i
$85$	1.92679	+	19.5631i	0.208990	+	2.12191i
$86$	3.24540	−	7.64197i	0.349960	−	0.824055i
$87$	4.28909	+	6.41908i	0.459839	+	0.688198i
$88$	4.59852	+	3.25352i	0.490204	+	0.346826i
$89$	−8.58661	−	5.73739i	−0.910179	−	0.608162i	0.00987625	−	0.999951i	$-0.496856\pi$
$89$	−8.58661	−	5.73739i	−0.910179	−	0.608162i	−0.920055	+	0.391789i	$0.871856\pi$
$90$	4.37511	+	0.910819i	0.461177	+	0.0960088i
$91$	2.48557	+	0.753989i	0.260558	+	0.0790395i
$92$	−0.363318	−	0.158126i	−0.0378785	−	0.0164858i
$93$	−4.79586	−	5.84377i	−0.497307	−	0.605971i
$94$	10.9958	+	13.6443i	1.13413	+	1.40730i
$95$	−13.3671	−	13.3671i	−1.37144	−	1.37144i
$96$	−2.93041	−	4.83867i	−0.299084	−	0.493844i
$97$	11.3641	−	11.3641i	1.15385	−	1.15385i	0.168080	−	0.985773i	$-0.446243\pi$
$97$	11.3641	−	11.3641i	1.15385	−	1.15385i	0.985773	−	0.168080i	$-0.0537567\pi$
$98$	9.55901	+	1.02747i	0.965606	+	0.103790i
$99$	−1.53953	+	1.26346i	−0.154728	+	0.126982i
$100$	9.96959	+	0.177494i	0.996959	+	0.0177494i
$101$	−1.22246	+	4.02991i	−0.121639	+	0.400991i	−0.996521	−	0.0833462i	$-0.973439\pi$
$101$	−1.22246	+	4.02991i	−0.121639	+	0.400991i	0.874881	+	0.484337i	$0.160939\pi$
$102$	4.82235	+	7.35810i	0.477484	+	0.728561i
$103$	6.78479	−	10.1542i	0.668525	−	1.00052i	−0.329878	−	0.944024i	$-0.607008\pi$
$103$	6.78479	−	10.1542i	0.668525	−	1.00052i	0.998403	−	0.0564947i	$-0.0179924\pi$
$104$	−14.9359	−	6.65924i	−1.46458	−	0.652992i
$105$	−1.18037	+	0.788696i	−0.115192	+	0.0769689i
$106$	−2.71317	−	6.71870i	−0.263526	−	0.652577i
$107$	0.412500	−	0.0406277i	0.0398779	−	0.00392763i	−0.0780585	−	0.996949i	$-0.524872\pi$
$107$	0.412500	−	0.0406277i	0.0398779	−	0.00392763i	0.117936	+	0.993021i	$0.462372\pi$
$108$	1.92391	−	0.546409i	0.185129	−	0.0525782i
$109$	−3.56097	−	11.7390i	−0.341079	−	1.12439i	−0.944925	−	0.327287i	$-0.893866\pi$
$109$	−3.56097	−	11.7390i	−0.341079	−	1.12439i	0.603846	−	0.797101i	$-0.293634\pi$
$110$	−5.70729	+	6.82948i	−0.544169	+	0.651165i
$111$	−4.43294	+	10.7021i	−0.420756	+	1.01579i
$112$	1.74886	+	0.413088i	0.165252	+	0.0390331i
$113$	−1.26959	−	3.06506i	−0.119433	−	0.288336i	0.852845	−	0.522164i	$-0.174875\pi$
$113$	−1.26959	−	3.06506i	−0.119433	−	0.288336i	−0.972278	+	0.233827i	$0.924875\pi$
$114$	−8.07375	−	2.52784i	−0.756176	−	0.236754i
$115$	0.295120	−	0.552131i	0.0275201	−	0.0514864i
$116$	14.6933	+	4.74439i	1.36424	+	0.440506i
$117$	3.66788	−	4.46933i	0.339096	−	0.413189i
$118$	−0.103334	+	11.6091i	−0.00951262	+	1.06870i
$119$	−2.74097	−	0.545213i	−0.251264	−	0.0499796i
$120$	7.99214	−	4.00130i	0.729579	−	0.365267i
$121$	1.37217	+	6.89839i	0.124743	+	0.627126i
$122$	−0.919049	−	0.625992i	−0.0832067	−	0.0566747i
$123$	0.615250	−	0.328858i	0.0554753	−	0.0296521i
$124$	−14.7741	−	3.21317i	−1.32676	−	0.288551i
$125$	0.00446429	−	0.0453267i	0.000399298	−	0.00405414i
$126$	−0.304468	+	0.557623i	−0.0271241	+	0.0496770i
$127$	2.81642			0.249917			0.124958	−	0.992162i	$-0.460120\pi$
$127$	2.81642			0.249917			0.124958	+	0.992162i	$0.460120\pi$
$128$	−10.6010	−	3.95195i	−0.937009	−	0.349306i
$129$	5.87079			0.516894
$130$	12.3823	−	22.6778i	1.08600	−	1.98897i
$131$	0.109712	−	1.11393i	0.00958560	−	0.0973242i	−0.989201	−	0.146562i	$-0.953179\pi$
$131$	0.109712	−	1.11393i	0.00958560	−	0.0973242i	0.998787	+	0.0492378i	$0.0156792\pi$
$132$	−0.846502	+	3.89221i	−0.0736785	+	0.338773i
$133$	2.37018	−	1.26689i	0.205520	−	0.109853i
$134$	−6.36923	−	4.33828i	−0.550217	−	0.374770i
$135$	0.616485	+	3.09928i	0.0530586	+	0.266744i
$136$	16.6951	+	5.55531i	1.43159	+	0.476364i
$137$	2.24365	+	0.446291i	0.191688	+	0.0381292i	0.290001	−	0.957026i	$-0.406344\pi$
$137$	2.24365	+	0.446291i	0.191688	+	0.0381292i	−0.0983124	+	0.995156i	$0.531344\pi$
$138$	0.00249382	−	0.280171i	0.000212288	−	0.0238497i
$139$	−3.31671	+	4.04143i	−0.281320	+	0.342789i	−0.894430	−	0.447208i	$-0.852418\pi$
$139$	−3.31671	+	4.04143i	−0.281320	+	0.342789i	0.613110	+	0.789998i	$0.289918\pi$
$140$	−0.872419	+	2.70187i	−0.0737329	+	0.228350i
$141$	−5.84109	+	10.9279i	−0.491908	+	0.920296i
$142$	−7.62470	−	2.38724i	−0.639851	−	0.200333i
$143$	4.40655	+	10.6383i	0.368494	+	0.889623i
$144$	2.33926	−	3.24467i	0.194938	−	0.270389i
$145$	−9.33583	+	22.5387i	−0.775298	+	1.87174i
$146$	2.16900	−	2.59547i	0.179508	−	0.214803i
$147$	1.97341	+	6.50545i	0.162764	+	0.536561i
$148$	6.32950	+	22.2863i	0.520282	+	1.83192i
$149$	−7.55445	+	0.744048i	−0.618885	+	0.0609548i	−0.402601	−	0.915376i	$-0.631894\pi$
$149$	−7.55445	+	0.744048i	−0.618885	+	0.0609548i	−0.216284	+	0.976331i	$0.569394\pi$
$150$	2.64009	+	6.53774i	0.215563	+	0.533804i
$151$	−18.2293	+	12.1805i	−1.48348	+	0.991232i	−0.490698	+	0.871330i	$0.663258\pi$
$151$	−18.2293	+	12.1805i	−1.48348	+	0.991232i	−0.992786	+	0.119902i	$0.961742\pi$
$152$	−15.7998	+	6.05549i	−1.28153	+	0.491165i
$153$	−3.45609	+	5.17241i	−0.279408	+	0.418164i
$154$	−0.693583	−	1.05829i	−0.0558905	−	0.0852796i
$155$	6.93456	−	22.8602i	0.556997	−	1.83617i
$156$	0.205838	−	11.5616i	0.0164802	−	0.925669i
$157$	7.60880	−	6.24438i	0.607248	−	0.498356i	−0.279784	−	0.960063i	$-0.590263\pi$
$157$	7.60880	−	6.24438i	0.607248	−	0.498356i	0.887032	+	0.461707i	$0.152763\pi$
$158$	−1.53666	−	0.165171i	−0.122251	−	0.0131403i
$159$	3.62292	−	3.62292i	0.287316	−	0.287316i
$160$	7.56868	−	16.1943i	0.598357	−	1.28027i
$161$	0.0629353	+	0.0629353i	0.00496000	+	0.00496000i
$162$	0.887402	+	1.10114i	0.0697209	+	0.0865140i
$163$	6.92451	+	8.43754i	0.542369	+	0.660879i	0.970009	−	0.243070i	$-0.0781546\pi$
$163$	6.92451	+	8.43754i	0.542369	+	0.660879i	−0.427639	+	0.903949i	$0.640655\pi$
$164$	0.556800	−	1.27933i	0.0434788	−	0.0998992i
$165$	−6.02245	−	1.82689i	−0.468847	−	0.142223i
$166$	−4.12421	−	0.858585i	−0.320100	−	0.0666392i
$167$	−6.32978	−	4.22943i	−0.489813	−	0.327283i	0.286017	−	0.958225i	$-0.407669\pi$
$167$	−6.32978	−	4.22943i	−0.489813	−	0.327283i	−0.775830	+	0.630942i	$0.782669\pi$
$168$	0.214531	+	1.25242i	0.0165514	+	0.0966261i
$169$	−11.3493	−	16.9855i	−0.873025	−	1.30657i
$170$	−10.8669	+	25.5883i	−0.833451	+	1.96254i
$171$	−0.586366	−	5.95348i	−0.0448405	−	0.455274i
$172$	9.20752	−	7.28603i	0.702067	−	0.555555i
$173$	−3.78487	+	1.14813i	−0.287758	+	0.0872904i	−0.430864	−	0.902417i	$-0.641791\pi$
$173$	−3.78487	+	1.14813i	−0.287758	+	0.0872904i	0.143106	+	0.989707i	$0.454291\pi$
$174$	0.973395	+	10.8745i	0.0737929	+	0.824392i
$175$	−2.06926	−	0.857117i	−0.156422	−	0.0647919i
$176$	3.50287	+	7.15495i	0.264038	+	0.539325i
$177$	−7.58431	+	3.14152i	−0.570072	+	0.236131i
$178$	−6.76966	−	12.9409i	−0.507407	−	0.969961i
$179$	2.66403	+	1.42395i	0.199119	+	0.106431i	0.567943	−	0.823068i	$-0.307740\pi$
$179$	2.66403	+	1.42395i	0.199119	+	0.106431i	−0.368824	+	0.929499i	$0.620240\pi$
$180$	4.81328	+	4.09569i	0.358761	+	0.305275i
$181$	−9.93738	−	8.15539i	−0.738639	−	0.606186i	0.187986	−	0.982172i	$-0.439804\pi$
$181$	−9.93738	−	8.15539i	−0.738639	−	0.606186i	−0.926625	+	0.375986i	$0.877304\pi$
$182$	2.57419	+	2.62043i	0.190812	+	0.194239i
$183$	0.153398	−	0.771186i	0.0113395	−	0.0570077i
$184$	−0.343799	−	0.442504i	−0.0253452	−	0.0326218i
$185$	−35.9015	+	7.14125i	−2.63953	+	0.525035i
$186$	−1.99232	−	10.5038i	−0.146084	−	0.770179i
$187$	−5.84029	−	10.9264i	−0.427085	−	0.799019i
$188$	4.40131	+	24.3881i	0.320998	+	1.77868i
$189$	−0.447082	−	0.0440338i	−0.0325205	−	0.00320299i
$190$	−7.53254	−	25.6512i	−0.546468	−	1.86093i
$191$		−	17.8209i		−	1.28948i	−0.764404	−	0.644738i	$-0.776966\pi$
$191$		−	17.8209i		−	1.28948i	0.764404	−	0.644738i	$-0.223034\pi$
$192$	−0.358038	−	7.99198i	−0.0258392	−	0.576772i
$193$			7.42633i			0.534559i	0.963619	+	0.267279i	$0.0861247\pi$
$193$			7.42633i			0.534559i	−0.963619	+	0.267279i	$0.913875\pi$
$194$	21.8075	−	6.40382i	1.56568	−	0.459768i
$195$	18.1822	+	1.79079i	1.30206	+	0.128241i
$196$	11.1687	+	7.75377i	0.797765	+	0.553841i
$197$	0.634767	+	1.18757i	0.0452253	+	0.0846105i	0.903519	−	0.428549i	$-0.140975\pi$
$197$	0.634767	+	1.18757i	0.0452253	+	0.0846105i	−0.858293	+	0.513159i	$0.828475\pi$
$198$	−2.76721	+	0.524871i	−0.196657	+	0.0373010i
$199$	−10.2076	+	2.03041i	−0.723595	+	0.143932i	−0.543129	−	0.839649i	$-0.682761\pi$
$199$	−10.2076	+	2.03041i	−0.723595	+	0.143932i	−0.180466	+	0.983581i	$0.557761\pi$
$200$	12.2544	+	6.97701i	0.866516	+	0.493349i
$201$	1.06309	−	5.34450i	0.0749844	−	0.376972i
$202$	−4.24856	+	4.17360i	−0.298928	+	0.293653i
$203$	−2.68099	−	2.20023i	−0.188169	−	0.154426i
$204$	0.998894	+	12.4014i	0.0699365	+	0.868274i
$205$	1.94419	+	1.03919i	0.135788	+	0.0725803i
$206$	15.3033	−	8.00550i	1.06623	−	0.557770i
$207$	0.183038	−	0.0758167i	0.0127220	−	0.00526963i
$208$	−14.0259	−	18.3882i	−0.972519	−	1.27499i
$209$	11.0074	+	4.55941i	0.761397	+	0.315381i
$210$	−1.99964	+	0.178992i	−0.137989	+	0.0123516i
$211$	21.9816	−	6.66804i	1.51327	−	0.459047i	0.578917	−	0.815386i	$-0.303475\pi$
$211$	21.9816	−	6.66804i	1.51327	−	0.459047i	0.934356	+	0.356340i	$0.115975\pi$
$212$	1.18577	−	10.1783i	0.0814388	−	0.699050i
$213$	−0.553754	−	5.62236i	−0.0379426	−	0.385237i
$214$	0.539547	+	0.229135i	0.0368826	+	0.0156633i
$215$	10.3068	+	15.4252i	0.702916	+	1.05199i
$216$	2.75836	+	0.625668i	0.187682	+	0.0425713i
$217$	2.82383	+	1.88682i	0.191694	+	0.128086i
$218$	3.53582	−	16.9843i	0.239476	−	1.15032i
$219$	2.28877	+	0.694292i	0.154661	+	0.0469159i
$220$	−11.7127	+	4.60903i	−0.789668	+	0.310741i
$221$	22.8172	+	27.8028i	1.53485	+	1.87022i
$222$	−12.7555	+	10.2795i	−0.856090	+	0.689915i
$223$	−1.34365	−	1.34365i	−0.0899777	−	0.0899777i	0.660685	−	0.750663i	$-0.270266\pi$
$223$	−1.34365	−	1.34365i	−0.0899777	−	0.0899777i	−0.750663	+	0.660685i	$0.770266\pi$
$224$	1.89079	+	1.69800i	0.126334	+	0.113452i
$225$	−3.52534	+	3.52534i	−0.235023	+	0.235023i
$226$	0.501417	−	4.66492i	0.0333537	−	0.310306i
$227$	−15.8941	+	13.0440i	−1.05493	+	0.865759i	−0.991222	−	0.132209i	$-0.957793\pi$
$227$	−15.8941	+	13.0440i	−1.05493	+	0.865759i	−0.0637090	+	0.997969i	$0.520293\pi$
$228$	−8.30829	−	8.60948i	−0.550230	−	0.570177i
$229$	−4.31667	+	14.2301i	−0.285253	+	0.940354i	0.690841	+	0.723007i	$0.257240\pi$
$229$	−4.31667	+	14.2301i	−0.285253	+	0.940354i	−0.976094	+	0.217347i	$0.930260\pi$
$230$	0.740511	−	0.485316i	0.0488279	−	0.0320008i
$231$	0.497078	−	0.743930i	0.0327053	−	0.0489470i
$232$	15.0226	+	15.8471i	0.986280	+	1.04041i
$233$	17.4140	−	11.6357i	1.14083	−	0.762278i	0.166198	−	0.986092i	$-0.446851\pi$
$233$	17.4140	−	11.6357i	1.14083	−	0.762278i	0.974632	+	0.223814i	$0.0718509\pi$
$234$	7.58173	−	3.06168i	0.495633	−	0.200148i
$235$	−38.9671	+	3.83792i	−2.54193	+	0.250358i
$236$	−7.99610	+	14.3397i	−0.520502	+	0.933433i
$237$	−0.317236	−	1.04579i	−0.0206067	−	0.0679312i
$238$	−3.03270	−	2.53438i	−0.196581	−	0.164279i
$239$	9.72210	−	23.4712i	0.628870	−	1.51823i	−0.212158	−	0.977235i	$-0.568049\pi$
$239$	9.72210	−	23.4712i	0.628870	−	1.51823i	0.841028	−	0.540992i	$-0.181951\pi$
$240$	12.6320	+	0.449931i	0.815391	+	0.0290429i
$241$	5.37599	+	12.9788i	0.346298	+	0.836038i	0.997051	+	0.0767476i	$0.0244536\pi$
$241$	5.37599	+	12.9788i	0.346298	+	0.836038i	−0.650752	+	0.759290i	$0.725546\pi$
$242$	−2.97205	+	9.49253i	−0.191050	+	0.610203i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	−0.716508	−	1.39987i	−0.0458697	−	0.0896178i
$245$	−13.6282	+	16.6060i	−0.870673	+	1.06092i
$246$	0.986552	+	0.00878138i	0.0629002	+	0.000559880i
$247$	−33.9233	−	6.74776i	−2.15849	−	0.429349i
$248$	−16.1606	−	14.0012i	−1.02620	−	0.889078i
$249$	−0.581131	−	2.92154i	−0.0368277	−	0.185145i
$250$	0.0362605	−	0.0532358i	0.00229332	−	0.00336693i
$251$	−17.1310	+	9.15673i	−1.08130	+	0.577968i	−0.913080	−	0.407782i	$-0.866303\pi$
$251$	−17.1310	+	9.15673i	−1.08130	+	0.577968i	−0.168222	+	0.985749i	$0.553803\pi$
$252$	−0.755836	+	0.485798i	−0.0476132	+	0.0306024i
$253$	−0.0386749	+	0.392673i	−0.00243147	+	0.0246871i
$254$	3.49585	+	1.90877i	0.219349	+	0.119767i
$255$	−19.6577			−1.23101
$256$	−10.4801	−	12.0900i	−0.655007	−	0.755623i
$257$	1.17107			0.0730496			0.0365248	−	0.999333i	$-0.488371\pi$
$257$	1.17107			0.0730496			0.0365248	+	0.999333i	$0.488371\pi$
$258$	7.28707	+	3.97881i	0.453673	+	0.247710i
$259$	0.510080	−	5.17893i	0.0316948	−	0.321803i
$260$	30.7388	−	19.7567i	1.90634	−	1.22526i
$261$	−6.80857	+	3.63926i	−0.421440	+	0.225264i
$262$	0.891122	−	1.30830i	0.0550537	−	0.0808269i
$263$	5.82701	+	29.2944i	0.359309	+	1.80637i	0.562014	+	0.827128i	$0.310027\pi$
$263$	5.82701	+	29.2944i	0.359309	+	1.80637i	−0.202705	+	0.979240i	$0.564973\pi$
$264$	−3.68858	+	4.25747i	−0.227017	+	0.262029i
$265$	15.8794	+	3.15861i	0.975464	+	0.194032i
$266$	3.80057	+	0.0338292i	0.233028	+	0.00207420i
$267$	6.55140	−	7.98290i	0.400939	−	0.488546i
$268$	−4.96557	−	9.70147i	−0.303320	−	0.592611i
$269$	1.35649	−	2.53781i	0.0827064	−	0.154733i	−0.837168	−	0.546946i	$-0.815790\pi$
$269$	1.35649	−	2.53781i	0.0827064	−	0.154733i	0.919874	+	0.392213i	$0.128290\pi$
$270$	−1.33527	+	4.26477i	−0.0812619	+	0.259545i
$271$	1.30717	+	3.15579i	0.0794049	+	0.191700i	0.958596	−	0.284768i	$-0.0919166\pi$
$271$	1.30717	+	3.15579i	0.0794049	+	0.191700i	−0.879192	+	0.476469i	$0.841917\pi$
$272$	16.9576	+	18.2102i	1.02821	+	1.10416i
$273$	−0.993986	+	2.39970i	−0.0601588	+	0.145236i
$274$	2.48245	+	2.07455i	0.149970	+	0.125328i
$275$	−2.88232	−	9.50174i	−0.173810	−	0.572976i
$276$	0.192976	−	0.346070i	0.0116158	−	0.0208309i
$277$	−5.70574	+	0.561966i	−0.342825	+	0.0337653i	−0.267965	−	0.963429i	$-0.586351\pi$
$277$	−5.70574	+	0.561966i	−0.342825	+	0.0337653i	−0.0748601	+	0.997194i	$0.523851\pi$
$278$	−6.85584	+	2.76855i	−0.411186	+	0.166047i
$279$	6.28571	−	4.19998i	0.376316	−	0.251446i
$280$	−2.91402	+	2.76241i	−0.174146	+	0.165086i
$281$	10.9156	−	16.3364i	0.651173	−	0.974549i	−0.348138	−	0.937443i	$-0.613186\pi$
$281$	10.9156	−	16.3364i	0.651173	−	0.974549i	0.999311	−	0.0371060i	$-0.0118139\pi$
$282$	−14.6564	+	9.60549i	−0.872775	+	0.571999i
$283$	3.21099	−	10.5852i	0.190874	−	0.629227i	−0.808307	−	0.588761i	$-0.799616\pi$
$283$	3.21099	−	10.5852i	0.190874	−	0.629227i	0.999181	−	0.0404655i	$-0.0128841\pi$
$284$	−7.84620	−	8.13064i	−0.465586	−	0.482465i
$285$	14.6130	−	11.9926i	0.865599	−	0.710379i
$286$	−1.74034	+	16.1912i	−0.102908	+	0.957406i
$287$	−0.221611	+	0.221611i	−0.0130813	+	0.0130813i
$288$	5.10260	−	2.44203i	0.300673	−	0.143898i
$289$	−15.3431	−	15.3431i	−0.902533	−	0.902533i
$290$	−26.8632	+	21.6488i	−1.57746	+	1.27126i
$291$	10.1955	+	12.4233i	0.597673	+	0.728267i
$292$	4.45128	−	1.75162i	0.260492	−	0.102506i
$293$	9.81212	+	2.97647i	0.573230	+	0.173888i	0.563574	−	0.826066i	$-0.309426\pi$
$293$	9.81212	+	2.97647i	0.573230	+	0.173888i	0.00965671	+	0.999953i	$0.496926\pi$
$294$	−1.95947	+	9.41228i	−0.114278	+	0.548935i
$295$	−21.5692	−	14.4121i	−1.25581	−	0.839103i
$296$	−7.24763	+	31.9523i	−0.421260	+	1.85719i
$297$	−1.10647	−	1.65595i	−0.0642041	−	0.0960882i
$298$	−9.88116	−	4.19634i	−0.572400	−	0.243087i
$299$	−0.112275	−	1.13995i	−0.00649305	−	0.0659250i
$300$	−1.15383	+	9.90419i	−0.0666165	+	0.571819i
$301$	−2.52386	+	0.765605i	−0.145473	+	0.0441287i
$302$	−30.8821	+	2.76431i	−1.77707	+	0.159068i
$303$	−3.89069	−	1.61157i	−0.223514	−	0.0925825i
$304$	−23.7153	−	3.19165i	−1.36017	−	0.183054i
$305$	2.29555	−	0.950849i	0.131443	−	0.0544454i
$306$	−7.79534	+	4.07791i	−0.445630	+	0.233119i
$307$	13.6720	+	7.30786i	0.780304	+	0.417081i	0.812912	−	0.582387i	$-0.197881\pi$
$307$	13.6720	+	7.30786i	0.780304	+	0.417081i	−0.0326074	+	0.999468i	$0.510381\pi$
$308$	−0.143668	−	1.78366i	−0.00818622	−	0.101633i
$309$	9.44023	+	7.74740i	0.537036	+	0.440734i
$310$	24.1005	−	23.6752i	1.36882	−	1.34466i
$311$	−2.42437	+	12.1881i	−0.137473	+	0.691125i	0.849156	+	0.528143i	$0.177111\pi$
$311$	−2.42437	+	12.1881i	−0.137473	+	0.691125i	−0.986629	+	0.162982i	$0.947889\pi$
$312$	8.09114	−	14.2112i	0.458071	−	0.804553i
$313$	5.17831	−	1.03003i	0.292696	−	0.0582208i	−0.0465585	−	0.998916i	$-0.514825\pi$
$313$	5.17831	−	1.03003i	0.292696	−	0.0582208i	0.339254	+	0.940695i	$0.389825\pi$
$314$	13.6764	−	2.59407i	0.771802	−	0.146392i
$315$	−0.669202	−	1.25199i	−0.0377053	−	0.0705416i
$316$	−1.79543	−	1.24646i	−0.101001	−	0.0701190i
$317$	−17.0675	−	1.68100i	−0.958607	−	0.0944146i	−0.393404	−	0.919366i	$-0.628702\pi$
$317$	−17.0675	−	1.68100i	−0.958607	−	0.0944146i	−0.565204	+	0.824951i	$0.691202\pi$
$318$	6.95228	−	2.04156i	0.389865	−	0.114485i
$319$		−	15.3755i		−	0.860861i
$320$	20.3699	−	14.9715i	1.13871	−	0.836930i
$321$			0.414496i			0.0231349i
$322$	0.0354648	+	0.120771i	0.00197637	+	0.00673031i
$323$	37.0354	+	3.64767i	2.06070	+	0.202962i
$324$	0.355201	+	1.96821i	0.0197334	+	0.109345i
$325$	13.5881	+	25.4216i	0.753734	+	1.41014i
$326$	2.87661	+	15.1660i	0.159321	+	0.839966i
$327$	12.0315	−	2.39321i	0.665342	−	0.132345i
$328$	1.55817	−	1.21060i	0.0860354	−	0.0668443i
$329$	1.08599	−	5.45965i	0.0598727	−	0.301000i
$330$	−6.23718	−	6.34921i	−0.343346	−	0.349513i
$331$	22.6283	+	18.5705i	1.24376	+	1.02073i	0.998687	+	0.0512255i	$0.0163127\pi$
$331$	22.6283	+	18.5705i	1.24376	+	1.02073i	0.245075	+	0.969504i	$0.421187\pi$
$332$	−4.53725	−	3.86081i	−0.249014	−	0.211890i
$333$	−10.2160	−	5.46058i	−0.559835	−	0.299238i
$334$	−4.99038	−	9.53963i	−0.273061	−	0.521985i
$335$	15.9087	−	6.58961i	0.869186	−	0.360029i
$336$	−0.582517	+	1.69995i	−0.0317789	+	0.0927397i
$337$	23.7798	+	9.84991i	1.29537	+	0.536559i	0.920581	−	0.390552i	$-0.127716\pi$
$337$	23.7798	+	9.84991i	1.29537	+	0.536559i	0.374787	+	0.927111i	$0.377716\pi$
$338$	−2.57569	−	28.7748i	−0.140099	−	1.56515i
$339$	3.17474	−	0.963047i	0.172428	−	0.0523055i
$340$	−30.8304	+	24.3965i	−1.67201	+	1.32309i
$341$	1.47575	+	14.9835i	0.0799162	+	0.811402i
$342$	3.30703	−	7.78710i	0.178824	−	0.421078i
$343$	−3.44385	−	5.15409i	−0.185951	−	0.278295i
$344$	16.3667	−	2.80351i	0.882435	−	0.151155i
$345$	0.520545	+	0.347817i	0.0280252	+	0.0187258i
$346$	−5.47605	−	1.14002i	−0.294395	−	0.0612877i
$347$	6.52186	+	1.97838i	0.350112	+	0.106205i	0.460442	−	0.887690i	$-0.347691\pi$
$347$	6.52186	+	1.97838i	0.350112	+	0.106205i	−0.110330	+	0.993895i	$0.535191\pi$
$348$	−6.16175	+	14.1576i	−0.330304	+	0.758925i
$349$	−9.12028	−	11.1131i	−0.488197	−	0.594870i	0.469398	−	0.882987i	$-0.344471\pi$
$349$	−9.12028	−	11.1131i	−0.488197	−	0.594870i	−0.957595	+	0.288117i	$0.906971\pi$
$350$	−1.98756	−	2.46629i	−0.106240	−	0.131829i
$351$	4.08829	+	4.08829i	0.218217	+	0.218217i
$352$	−0.501227	+	11.2550i	−0.0267155	+	0.599895i
$353$	9.77975	−	9.77975i	0.520524	−	0.520524i	−0.397206	−	0.917729i	$-0.630020\pi$
$353$	9.77975	−	9.77975i	0.520524	−	0.520524i	0.917729	+	0.397206i	$0.130020\pi$
$354$	−11.5431	−	1.24073i	−0.613507	−	0.0659439i
$355$	13.8002	−	11.3256i	0.732441	−	0.601099i
$356$	0.367658	−	20.6508i	0.0194858	−	1.09449i
$357$	0.811249	−	2.67433i	0.0429359	−	0.141541i
$358$	2.34164	+	3.57296i	0.123760	+	0.188837i
$359$	7.38753	−	11.0562i	0.389899	−	0.583525i	−0.583650	−	0.812006i	$-0.698376\pi$
$359$	7.38753	−	11.0562i	0.389899	−	0.583525i	0.973548	+	0.228481i	$0.0733758\pi$
$360$	3.19867	+	8.34585i	0.168585	+	0.439865i
$361$	−13.9585	+	9.32675i	−0.734656	+	0.490881i
$362$	−6.80753	−	16.8577i	−0.357796	−	0.886020i
$363$	−6.99967	+	0.689407i	−0.367387	+	0.0361845i
$364$	1.41925	+	4.99719i	0.0743888	+	0.261924i
$365$	2.19396	+	7.23252i	0.114837	+	0.378567i
$366$	0.713060	−	0.853265i	0.0372723	−	0.0446009i
$367$	14.1821	−	34.2386i	0.740299	−	1.78724i	0.135634	−	0.990759i	$-0.456693\pi$
$367$	14.1821	−	34.2386i	0.740299	−	1.78724i	0.604664	−	0.796480i	$-0.293307\pi$
$368$	−0.126839	−	0.782258i	−0.00661196	−	0.0407780i
$369$	0.266970	+	0.644521i	0.0138979	+	0.0335524i
$370$	−49.4023	−	15.4675i	−2.56830	−	0.804118i
$371$	−1.08504	+	2.02996i	−0.0563323	+	0.105390i
$372$	4.64582	−	14.3881i	0.240874	−	0.745986i
$373$	23.8735	−	29.0900i	1.23612	−	1.50622i	0.443795	−	0.896128i	$-0.353632\pi$
$373$	23.8735	−	29.0900i	1.23612	−	1.50622i	0.792329	−	0.610094i	$-0.208868\pi$
$374$	0.155951	−	17.5205i	0.00806405	−	0.905962i
$375$	0.0446708	+	0.00888558i	0.00230679	+	0.000458849i
$376$	−11.0655	+	33.2544i	−0.570657	+	1.71496i
$377$	8.70801	+	43.7781i	0.448485	+	2.25469i
$378$	−0.525094	−	0.357658i	−0.0270079	−	0.0183959i
$379$	18.5448	−	9.91239i	0.952581	−	0.509165i	0.0795506	−	0.996831i	$-0.474651\pi$
$379$	18.5448	−	9.91239i	0.952581	−	0.509165i	0.873030	+	0.487666i	$0.162151\pi$
$380$	8.03488	−	36.9444i	0.412181	−	1.89521i
$381$	−0.276057	+	2.80285i	−0.0141428	+	0.143595i
$382$	12.0778	−	22.1201i	0.617953	−	1.13176i
$383$	9.07025			0.463468			0.231734	−	0.972779i	$-0.425560\pi$
$383$	9.07025			0.463468			0.231734	+	0.972779i	$0.425560\pi$
$384$	4.97200	−	10.1626i	0.253726	−	0.518610i
$385$	2.82730			0.144093
$386$	−5.03305	+	9.21787i	−0.256176	+	0.469177i
$387$	−0.575438	+	5.84252i	−0.0292512	+	0.296992i
$388$	31.4084	+	6.83089i	1.59452	+	0.346786i
$389$	−20.0703	+	10.7278i	−1.01760	+	0.543920i	−0.893837	−	0.448391i	$-0.851997\pi$
$389$	−20.0703	+	10.7278i	−1.01760	+	0.543920i	−0.123766	+	0.992311i	$0.539497\pi$
$390$	21.3549	+	14.5455i	1.08135	+	0.736538i
$391$	0.240440	+	1.20878i	0.0121596	+	0.0611304i
$392$	8.60810	+	17.1937i	0.434775	+	0.868412i
$393$	1.09781	+	0.218368i	0.0553772	+	0.0110152i
$394$	−0.0169499	+	1.90426i	−0.000853926	+	0.0959351i
$395$	2.19081	−	2.66951i	0.110231	−	0.134317i
$396$	−3.79050	−	1.22393i	−0.190480	−	0.0615047i
$397$	8.45622	−	15.8205i	0.424406	−	0.794007i	−0.575308	−	0.817937i	$-0.695118\pi$
$397$	8.45622	−	15.8205i	0.424406	−	0.794007i	0.999714	+	0.0239298i	$0.00761782\pi$
$398$	−14.0461	−	4.39775i	−0.704069	−	0.220439i
$399$	1.02847	+	2.48294i	0.0514878	+	0.124302i
$400$	10.4821	+	16.9653i	0.524106	+	0.848266i
$401$	13.6935	−	33.0590i	0.683819	−	1.65089i	−0.0730578	−	0.997328i	$-0.523276\pi$
$401$	13.6935	−	33.0590i	0.683819	−	1.65089i	0.756877	−	0.653557i	$-0.226724\pi$
$402$	4.94168	−	5.91333i	0.246469	−	0.294930i
$403$	−12.6879	−	41.8263i	−0.632028	−	2.08352i
$404$	−8.10207	+	2.30106i	−0.403093	+	0.114482i
$405$	−3.14478	+	0.309734i	−0.156265	+	0.0153908i
$406$	−1.83660	−	4.54801i	−0.0911487	−	0.225714i
$407$	19.1823	−	12.8172i	0.950830	−	0.635324i
$408$	−7.16496	+	16.0702i	−0.354719	+	0.795592i
$409$	1.36330	−	2.04032i	0.0674108	−	0.100887i	−0.796233	−	0.604991i	$-0.793177\pi$
$409$	1.36330	−	2.04032i	0.0674108	−	0.100887i	0.863643	+	0.504103i	$0.168177\pi$
$410$	1.70892	+	2.60752i	0.0843975	+	0.128776i
$411$	−0.664058	+	2.18911i	−0.0327556	+	0.107981i
$412$	24.4207	+	0.434776i	1.20312	+	0.0214199i
$413$	2.85082	−	2.33961i	0.140280	−	0.115125i
$414$	0.278577	+	0.0299434i	0.0136913	+	0.00147164i
$415$	6.65595	−	6.65595i	0.326728	−	0.326728i
$416$	−4.94724	−	32.3300i	−0.242558	−	1.58511i
$417$	−3.69687	−	3.69687i	−0.181037	−	0.181037i
$418$	10.5728	+	13.1194i	0.517131	+	0.641689i
$419$	−6.96872	−	8.49141i	−0.340444	−	0.414832i	0.574441	−	0.818546i	$-0.305219\pi$
$419$	−6.96872	−	8.49141i	−0.340444	−	0.414832i	−0.914886	+	0.403713i	$0.867719\pi$
$420$	−2.60335	−	1.13305i	−0.127031	−	0.0552871i
$421$	−3.15368	−	0.956660i	−0.153701	−	0.0466247i	0.212496	−	0.977162i	$-0.431841\pi$
$421$	−3.15368	−	0.956660i	−0.153701	−	0.0466247i	−0.366198	+	0.930537i	$0.619341\pi$
$422$	31.8036	+	6.62093i	1.54817	+	0.322302i
$423$	−10.3028	−	6.88408i	−0.500937	−	0.334716i
$424$	8.36998	−	11.8301i	0.406482	−	0.574522i
$425$	−17.2306	−	25.7875i	−0.835809	−	1.25088i
$426$	3.12310	−	7.35400i	0.151315	−	0.356302i
$427$	0.0346235	+	0.351538i	0.00167555	+	0.0170121i
$428$	0.514416	+	0.650079i	0.0248652	+	0.0314228i
$429$	−11.0190	+	3.34259i	−0.532004	+	0.161382i
$430$	2.33909	+	26.1316i	0.112801	+	1.26018i
$431$	7.52312	+	3.11618i	0.362376	+	0.150101i	0.556440	−	0.830888i	$-0.312167\pi$
$431$	7.52312	+	3.11618i	0.362376	+	0.150101i	−0.194064	+	0.980989i	$0.562167\pi$
$432$	2.99976	+	2.64603i	0.144326	+	0.127307i
$433$	2.72567	−	1.12901i	0.130987	−	0.0542567i	−0.316227	−	0.948684i	$-0.602416\pi$
$433$	2.72567	−	1.12901i	0.130987	−	0.0542567i	0.447214	+	0.894427i	$0.352416\pi$
$434$	2.22630	+	4.25580i	0.106866	+	0.204285i
$435$	−21.5151	−	11.5000i	−1.03157	−	0.551385i
$436$	15.8996	−	18.6853i	0.761451	−	0.894861i
$437$	−0.916173	−	0.751884i	−0.0438265	−	0.0359675i
$438$	2.37038	+	2.41295i	0.113261	+	0.115295i
$439$	−2.92301	+	14.6950i	−0.139508	+	0.701352i	0.846197	+	0.532870i	$0.178887\pi$
$439$	−2.92301	+	14.6950i	−0.139508	+	0.701352i	−0.985705	+	0.168482i	$0.946113\pi$
$440$	−17.6619	−	2.21711i	−0.842000	−	0.105697i
$441$	−6.66755	+	1.32626i	−0.317503	+	0.0631552i
$442$	9.47882	+	49.9739i	0.450861	+	2.37702i
$443$	−14.7942	−	27.6780i	−0.702894	−	1.31502i	−0.939209	−	0.343345i	$-0.888440\pi$
$443$	−14.7942	−	27.6780i	−0.702894	−	1.31502i	0.236316	−	0.971676i	$-0.424060\pi$
$444$	−22.7993	+	4.11459i	−1.08201	+	0.195270i
$445$	32.4762	+	3.19863i	1.53952	+	0.151630i
$446$	−0.757164	−	2.57843i	−0.0358528	−	0.122092i
$447$		−	7.59100i		−	0.359042i
$448$	1.19615	+	3.38907i	0.0565127	+	0.160119i
$449$			22.4558i			1.05976i	0.848074	+	0.529878i	$0.177762\pi$
$449$			22.4558i			1.05976i	−0.848074	+	0.529878i	$0.822238\pi$
$450$	−6.76503	+	1.98657i	−0.318907	+	0.0936478i
$451$	−1.38270	−	0.136184i	−0.0651087	−	0.00641265i
$452$	3.78394	−	5.45047i	0.177981	−	0.256368i
$453$	−10.3350	−	19.3355i	−0.485582	−	0.908459i
$454$	−28.5688	+	5.41879i	−1.34080	+	0.254317i
$455$	−8.05010	+	1.60127i	−0.377395	+	0.0750685i
$456$	−4.47768	−	16.3172i	−0.209687	−	0.764124i
$457$	−4.47572	+	22.5010i	−0.209365	+	1.05255i	0.722949	+	0.690901i	$0.242786\pi$
$457$	−4.47572	+	22.5010i	−0.209365	+	1.05255i	−0.932314	+	0.361649i	$0.882214\pi$
$458$	−15.0022	+	14.7375i	−0.701008	+	0.688639i
$459$	−4.80874	−	3.94643i	−0.224453	−	0.184204i
$460$	1.24807	−	0.100528i	0.0581914	−	0.00468712i
$461$	−6.23961	−	3.33514i	−0.290607	−	0.155333i	0.319651	−	0.947535i	$-0.396434\pi$
$461$	−6.23961	−	3.33514i	−0.290607	−	0.155333i	−0.610258	+	0.792202i	$0.708934\pi$
$462$	1.12118	−	0.586512i	0.0521619	−	0.0272870i
$463$	0.562375	−	0.232943i	0.0261358	−	0.0108258i	−0.369577	−	0.929200i	$-0.620497\pi$
$463$	0.562375	−	0.232943i	0.0261358	−	0.0108258i	0.395713	+	0.918374i	$0.370497\pi$
$464$	7.90661	+	29.8513i	0.367055	+	1.38581i
$465$	22.0704	+	9.14186i	1.02349	+	0.423943i
$466$	29.5008	−	2.64068i	1.36660	−	0.122327i
$467$	2.66636	−	0.808830i	0.123384	−	0.0374282i	−0.227989	−	0.973664i	$-0.573215\pi$
$467$	2.66636	−	0.808830i	0.123384	−	0.0374282i	0.351373	+	0.936236i	$0.385715\pi$
$468$	11.4858	+	1.33808i	0.530929	+	0.0618528i
$469$	0.239949	+	2.43624i	0.0110798	+	0.112495i
$470$	−50.9686	−	21.6454i	−2.35101	−	0.998427i
$471$	5.46852	+	8.18422i	0.251976	+	0.377109i
$472$	−19.6435	+	12.3798i	−0.904167	+	0.569826i
$473$	−9.72176	−	6.49587i	−0.447007	−	0.298680i
$474$	0.314995	−	1.51308i	0.0144682	−	0.0694979i
$475$	28.5409	+	8.65779i	1.30955	+	0.397247i
$476$	−2.04669	−	5.20113i	−0.0938097	−	0.238393i
$477$	3.25037	+	3.96058i	0.148824	+	0.181343i
$478$	27.9746	−	22.5445i	1.27953	−	1.03116i
$479$	22.1521	+	22.1521i	1.01216	+	1.01216i	0.999925	+	0.0122311i	$0.00389337\pi$
$479$	22.1521	+	22.1521i	1.01216	+	1.01216i	0.0122311	+	0.999925i	$0.496107\pi$
$480$	15.3744	+	9.11955i	0.701743	+	0.416249i
$481$	−47.3580	+	47.3580i	−2.15934	+	2.15934i
$482$	−2.12322	+	19.7533i	−0.0967099	+	0.899738i
$483$	−0.0688010	+	0.0564635i	−0.00313055	+	0.00256918i
$484$	−10.1224	+	9.76828i	−0.460109	+	0.444013i
$485$	−14.7422	+	48.5985i	−0.669409	+	2.20675i
$486$	−1.18282	+	0.775198i	−0.0536539	+	0.0351637i
$487$	12.1526	−	18.1877i	0.550687	−	0.824162i	−0.446827	−	0.894620i	$-0.647446\pi$
$487$	12.1526	−	18.1877i	0.550687	−	0.824162i	0.997515	+	0.0704582i	$0.0224461\pi$
$488$	0.0593787	−	2.22318i	0.00268795	−	0.100639i
$489$	−9.07563	+	6.06414i	−0.410414	+	0.274230i
$490$	−28.1703	+	11.3758i	−1.27260	+	0.513907i
$491$	−37.3429	+	3.67796i	−1.68526	+	0.165984i	−0.894782	−	0.446504i	$-0.852669\pi$
$491$	−37.3429	+	3.67796i	−1.68526	+	0.165984i	−0.790480	+	0.612488i	$0.790169\pi$
$492$	1.21860	+	0.679516i	0.0549386	+	0.0306349i
$493$	−13.9411	−	45.9576i	−0.627875	−	2.06983i
$494$	−37.5338	−	31.3664i	−1.68873	−	1.41124i
$495$	2.40840	−	5.81439i	0.108249	−	0.261337i
$496$	−10.5702	−	28.3314i	−0.474616	−	1.27212i
$497$	0.971266	+	2.34484i	0.0435672	+	0.105181i
$498$	1.25869	−	4.02019i	0.0564034	−	0.180149i
$499$	−11.6590	+	21.8124i	−0.521927	+	0.976457i	0.473487	+	0.880801i	$0.342995\pi$
$499$	−11.6590	+	21.8124i	−0.521927	+	0.976457i	−0.995414	+	0.0956562i	$0.969505\pi$
$500$	0.0810876	−	0.0415036i	0.00362635	−	0.00185610i
$501$	4.82949	−	5.88475i	0.215766	−	0.262911i
$502$	−27.4696	−	0.244509i	−1.22603	−	0.0109130i
$503$	11.9700	+	2.38098i	0.533716	+	0.106163i	0.454588	−	0.890702i	$-0.349787\pi$
$503$	11.9700	+	2.38098i	0.533716	+	0.106163i	0.0791277	+	0.996864i	$0.474787\pi$
$504$	−1.26741	+	0.0907395i	−0.0564551	+	0.00404186i
$505$	−2.59617	−	13.0518i	−0.115528	−	0.580799i
$506$	−0.314131	+	0.461191i	−0.0139648	+	0.0205024i
$507$	18.0161	−	9.62981i	0.800123	−	0.427675i
$508$	3.04557	+	4.73849i	0.135125	+	0.210237i
$509$	−0.228333	+	2.31830i	−0.0101207	+	0.102757i	−0.998918	−	0.0465080i	$-0.985191\pi$
$509$	−0.228333	+	2.31830i	−0.0101207	+	0.102757i	0.988797	+	0.149265i	$0.0476907\pi$
$510$	−24.4000	−	13.3226i	−1.08045	−	0.589936i
$511$	−1.07449			−0.0475326
$512$	−4.81461	−	22.1093i	−0.212778	−	0.977101i
$513$	5.98228			0.264124
$514$	1.45359	+	0.793673i	0.0641150	+	0.0350074i
$515$	−3.78256	+	38.4050i	−0.166680	+	1.69233i
$516$	6.34846	+	9.87734i	0.279475	+	0.434826i
$517$	21.7640	−	11.6331i	0.957180	−	0.511623i
$518$	4.14305	−	6.08260i	0.182035	−	0.267254i
$519$	−0.771616	−	3.87918i	−0.0338702	−	0.170277i
$520$	51.5440	−	3.69025i	2.26036	−	0.161828i
$521$	−16.5625	−	3.29448i	−0.725616	−	0.144334i	−0.181556	−	0.983381i	$-0.558113\pi$
$521$	−16.5625	−	3.29448i	−0.725616	−	0.144334i	−0.544059	+	0.839047i	$0.683113\pi$
$522$	−10.9175	−	0.0971778i	−0.477847	−	0.00425336i
$523$	−24.5157	+	29.8725i	−1.07200	+	1.30623i	−0.122497	+	0.992469i	$0.539090\pi$
$523$	−24.5157	+	29.8725i	−1.07200	+	1.30623i	−0.949501	+	0.313765i	$0.898410\pi$
$524$	1.99277	−	1.01997i	0.0870546	−	0.0445577i
$525$	1.05581	−	1.97529i	0.0460794	−	0.0862086i
$526$	−12.6210	+	40.3105i	−0.550300	+	1.75762i
$527$	17.9967	+	43.4480i	0.783950	+	1.89262i
$528$	−7.46384	+	2.78469i	−0.324822	+	0.121188i
$529$	−8.78670	+	21.2130i	−0.382030	+	0.922303i
$530$	17.5695	+	14.6826i	0.763170	+	0.637770i
$531$	−2.38300	−	7.85571i	−0.103414	−	0.340909i
$532$	4.69450	+	2.61775i	0.203532	+	0.113494i
$533$	4.01405	−	0.395349i	0.173868	−	0.0171245i
$534$	13.5421	−	5.46863i	0.586025	−	0.236651i
$535$	−1.08906	+	0.727689i	−0.0470843	+	0.0314607i
$536$	0.411509	−	15.4072i	0.0177745	−	0.665489i
$537$	−1.67821	+	2.51163i	−0.0724203	+	0.108385i
$538$	3.40368	−	2.23070i	0.146743	−	0.0961723i
$539$	3.93023	−	12.9562i	0.169287	−	0.558065i
$540$	−4.54775	+	4.38865i	−0.195704	+	0.188858i
$541$	19.5172	−	16.0174i	0.839111	−	0.688640i	−0.113266	−	0.993565i	$-0.536131\pi$
$541$	19.5172	−	16.0174i	0.839111	−	0.688640i	0.952377	+	0.304924i	$0.0986312\pi$
$542$	−0.516259	+	4.80301i	−0.0221752	+	0.206307i
$543$	9.09016	−	9.09016i	0.390096	−	0.390096i
$544$	8.70687	+	34.0960i	0.373304	+	1.46185i
$545$	27.4105	+	27.4105i	1.17414	+	1.17414i
$546$	−2.86012	+	2.30495i	−0.122402	+	0.0986426i
$547$	−12.2483	−	14.9247i	−0.523701	−	0.638132i	0.442239	−	0.896897i	$-0.354184\pi$
$547$	−12.2483	−	14.9247i	−0.523701	−	0.638132i	−0.965940	+	0.258765i	$0.916684\pi$
$548$	1.67534	+	4.25745i	0.0715670	+	0.181869i
$549$	0.752436	+	0.228249i	0.0321132	+	0.00974143i
$550$	2.86196	−	13.7474i	0.122034	−	0.586191i
$551$	38.4007	+	25.6586i	1.63593	+	1.09309i
$552$	0.474072	−	0.298771i	0.0201778	−	0.0127165i
$553$	0.272761	+	0.408215i	0.0115990	+	0.0173591i
$554$	−7.46307	−	3.16942i	−0.317075	−	0.134656i
$555$	−3.58790	−	36.4286i	−0.152298	−	1.54631i
$556$	−10.3861	−	1.20997i	−0.440468	−	0.0513142i
$557$	−34.4373	+	10.4464i	−1.45915	+	0.442629i	−0.917420	−	0.397921i	$-0.869732\pi$
$557$	−34.4373	+	10.4464i	−1.45915	+	0.442629i	−0.541734	+	0.840550i	$0.682232\pi$
$558$	10.6485	−	0.953170i	0.450789	−	0.0403509i
$559$	31.3595	+	12.9895i	1.32636	+	0.549398i
$560$	−5.48918	+	1.45390i	−0.231960	+	0.0614385i
$561$	11.4463	−	4.74120i	0.483261	−	0.200173i
$562$	24.6206	−	12.8796i	1.03856	−	0.543292i
$563$	−35.4943	−	18.9721i	−1.49591	−	0.799578i	−0.498186	−	0.867070i	$-0.666000\pi$
$563$	−35.4943	−	18.9721i	−1.49591	−	0.799578i	−0.997720	+	0.0674920i	$0.978500\pi$
$564$	−24.7020	+	1.98967i	−1.04014	+	0.0837800i
$565$	8.10393	+	6.65072i	0.340935	+	0.279798i
$566$	11.1596	−	10.9626i	0.469071	−	0.460794i
$567$	0.0876435	−	0.440614i	0.00368068	−	0.0185040i
$568$	−4.22864	−	15.4097i	−0.177430	−	0.646577i
$569$	−20.9874	+	4.17465i	−0.879837	+	0.175010i	−0.614283	−	0.789086i	$-0.710555\pi$
$569$	−20.9874	+	4.17465i	−0.879837	+	0.175010i	−0.265554	+	0.964096i	$0.585555\pi$
$570$	26.2660	−	4.98201i	1.10016	−	0.208674i
$571$	16.6457	+	31.1420i	0.696603	+	1.30325i	0.942581	+	0.333977i	$0.108391\pi$
$571$	16.6457	+	31.1420i	0.696603	+	1.30325i	−0.245978	+	0.969275i	$0.579109\pi$
$572$	−13.1335	+	18.9177i	−0.549137	+	0.790990i
$573$	17.7351	+	1.74676i	0.740895	+	0.0729717i
$574$	−0.425265	+	0.124880i	−0.0177502	+	0.00521240i
$575$			0.987737i			0.0411915i
$576$	7.98859	+	0.427038i	0.332858	+	0.0177932i
$577$		−	35.0007i		−	1.45710i	−0.684993	−	0.728549i	$-0.740195\pi$
$577$		−	35.0007i		−	1.45710i	0.684993	−	0.728549i	$-0.259805\pi$
$578$	−8.64599	−	29.4429i	−0.359626	−	1.22466i
$579$	−7.39057	−	0.727908i	−0.307142	−	0.0302508i
$580$	−48.0157	+	8.66538i	−1.99374	+	0.359810i
$581$	0.630825	+	1.18019i	0.0261710	+	0.0489625i
$582$	4.23548	+	22.3301i	0.175566	+	0.925614i
$583$	−10.0080	+	1.99072i	−0.414491	+	0.0824474i
$584$	6.71224	+	0.842591i	0.277755	+	0.0348667i
$585$	−3.56434	+	17.9192i	−0.147367	+	0.740866i
$586$	10.1620	+	10.3445i	0.419787	+	0.427327i
$587$	−12.0546	−	9.89294i	−0.497546	−	0.408325i	0.351870	−	0.936049i	$-0.385546\pi$
$587$	−12.0546	−	9.89294i	−0.497546	−	0.408325i	−0.849416	+	0.527723i	$0.823046\pi$
$588$	−8.81116	+	10.3549i	−0.363366	+	0.427030i
$589$	−39.8845	−	21.3187i	−1.64341	−	0.878423i
$590$	−17.0051	−	32.5070i	−0.700088	−	1.33829i
$591$	−1.24406	+	0.515309i	−0.0511740	+	0.0211970i
$592$	−30.6511	+	34.7486i	−1.25975	+	1.42816i
$593$	−38.7980	−	16.0707i	−1.59324	−	0.659943i	−0.602803	−	0.797890i	$-0.705950\pi$
$593$	−38.7980	−	16.0707i	−1.59324	−	0.659943i	−0.990440	+	0.137947i	$0.955950\pi$
$594$	−0.251110	−	2.80533i	−0.0103032	−	0.115104i
$595$	8.45088	−	2.56355i	0.346452	−	0.105095i
$596$	−9.42093	−	11.9054i	−0.385896	−	0.487666i
$597$	−1.02012	−	10.3574i	−0.0417506	−	0.423901i
$598$	0.633218	−	1.49105i	0.0258942	−	0.0609734i
$599$	−5.75547	−	8.61367i	−0.235162	−	0.351945i	0.695054	−	0.718958i	$-0.255381\pi$
$599$	−5.75547	−	8.61367i	−0.235162	−	0.351945i	−0.930216	+	0.367013i	$0.880381\pi$
$600$	−8.14455	+	11.5115i	−0.332500	+	0.469955i
$601$	18.3882	+	12.2866i	0.750071	+	0.501181i	0.870881	−	0.491494i	$-0.163549\pi$
$601$	18.3882	+	12.2866i	0.750071	+	0.501181i	−0.120810	+	0.992676i	$0.538549\pi$
$602$	−3.65160	−	0.760197i	−0.148828	−	0.0309833i
$603$	5.21456	+	1.58182i	0.212353	+	0.0644167i
$604$	−40.2056	−	17.4986i	−1.63594	−	0.712006i
$605$	−14.1000	−	17.1809i	−0.573246	−	0.698503i
$606$	−3.73707	−	4.63719i	−0.151808	−	0.188373i
$607$	6.70800	+	6.70800i	0.272269	+	0.272269i	0.830013	−	0.557744i	$-0.188333\pi$
$607$	6.70800	+	6.70800i	0.272269	+	0.272269i	−0.557744	+	0.830013i	$0.688333\pi$
$608$	−27.2734	−	20.0342i	−1.10608	−	0.812495i
$609$	2.45242	−	2.45242i	0.0993772	−	0.0993772i
$610$	3.49375	+	0.375532i	0.141458	+	0.0152049i
$611$	−55.3795	+	45.4488i	−2.24042	+	1.83866i
$612$	−12.4396	−	0.221470i	−0.502842	−	0.00895239i
$613$	−11.8899	+	39.1959i	−0.480231	+	1.58311i	0.297637	+	0.954679i	$0.403802\pi$
$613$	−11.8899	+	39.1959i	−0.480231	+	1.58311i	−0.777867	+	0.628429i	$0.783698\pi$
$614$	12.0175	+	18.3368i	0.484989	+	0.740012i
$615$	−1.22475	+	1.83297i	−0.0493867	+	0.0739125i
$616$	1.03051	−	2.31132i	0.0415206	−	0.0931257i
$617$	22.0312	−	14.7208i	0.886944	−	0.592637i	−0.0264787	−	0.999649i	$-0.508429\pi$
$617$	22.0312	−	14.7208i	0.886944	−	0.592637i	0.913423	+	0.407012i	$0.133429\pi$
$618$	6.46696	+	16.0143i	0.260139	+	0.644191i
$619$	−24.5648	+	2.41942i	−0.987342	+	0.0972447i	−0.578778	−	0.815485i	$-0.696470\pi$
$619$	−24.5648	+	2.41942i	−0.987342	+	0.0972447i	−0.408564	+	0.912730i	$0.633970\pi$
$620$	45.9600	−	13.0531i	1.84580	−	0.524224i
$621$	0.0575108	+	0.189588i	0.00230783	+	0.00760789i
$622$	−11.2695	+	13.4853i	−0.451865	+	0.540713i
$623$	−1.77541	+	4.28622i	−0.0711303	+	0.171724i
$624$	19.6745	−	12.1560i	0.787609	−	0.486628i
$625$	9.59458	+	23.1634i	0.383783	+	0.926535i
$626$	7.12562	+	2.23098i	0.284797	+	0.0891680i
$627$	−5.61636	+	10.5075i	−0.224296	+	0.419628i
$628$	18.7338	+	6.04902i	0.747558	+	0.241382i
$629$	45.7148	−	55.7037i	1.82277	−	2.22105i
$630$	0.0178695	−	2.00756i	0.000711936	−	0.0799831i
$631$	−1.31344	−	0.261260i	−0.0522873	−	0.0104006i	0.168877	−	0.985637i	$-0.445986\pi$
$631$	−1.31344	−	0.261260i	−0.0522873	−	0.0104006i	−0.221165	+	0.975236i	$0.570986\pi$
$632$	−1.38380	−	2.76398i	−0.0550446	−	0.109945i
$633$	4.48136	+	22.5293i	0.178118	+	0.895460i
$634$	−20.0457	−	13.6537i	−0.796115	−	0.542258i
$635$	−7.84898	+	4.19537i	−0.311477	+	0.166488i
$636$	10.0131	+	2.17771i	0.397045	+	0.0863517i
$637$	−3.85258	+	39.1159i	−0.152645	+	1.54983i
$638$	10.4204	−	19.0847i	0.412548	−	0.755569i
$639$	5.64956			0.223493
$640$	35.4306	−	4.77789i	1.40052	−	0.188863i
$641$	−10.9018			−0.430595			−0.215297	−	0.976549i	$-0.569072\pi$
$641$	−10.9018			−0.430595			−0.215297	+	0.976549i	$0.569072\pi$
$642$	−0.280916	+	0.514489i	−0.0110869	+	0.0203053i
$643$	−1.12589	+	11.4314i	−0.0444008	+	0.450808i	0.947122	+	0.320874i	$0.103977\pi$
$643$	−1.12589	+	11.4314i	−0.0444008	+	0.450808i	−0.991523	+	0.129934i	$0.958523\pi$
$644$	−0.0378299	+	0.173942i	−0.00149071	+	0.00685426i
$645$	−16.3611	+	8.74520i	−0.644219	+	0.344342i
$646$	43.4977	+	29.6277i	1.71140	+	1.16568i
$647$	−7.16480	−	36.0199i	−0.281677	−	1.41609i	−0.819524	−	0.573045i	$-0.805762\pi$
$647$	−7.16480	−	36.0199i	−0.281677	−	1.41609i	0.537846	−	0.843043i	$-0.319238\pi$
$648$	−0.893022	+	2.68375i	−0.0350812	+	0.105428i
$649$	16.0353	+	3.18962i	0.629440	+	0.125203i
$650$	−0.362839	+	40.7634i	−0.0142317	+	1.59887i
$651$	−2.15452	+	2.62529i	−0.0844423	+	0.102893i
$652$	−6.70787	+	20.7742i	−0.262701	+	0.813581i
$653$	14.6097	−	27.3328i	0.571721	−	1.06962i	−0.415400	−	0.909639i	$-0.636358\pi$
$653$	14.6097	−	27.3328i	0.571721	−	1.06962i	0.987121	−	0.159976i	$-0.0511418\pi$
$654$	16.5559	+	5.18354i	0.647387	+	0.202693i
$655$	1.35357	+	3.26780i	0.0528882	+	0.127683i
$656$	2.75453	−	0.446633i	0.107546	−	0.0174381i
$657$	−0.915287	+	2.20970i	−0.0357088	+	0.0862086i
$658$	5.04815	−	6.04074i	0.196797	−	0.235493i
$659$	7.96165	+	26.2460i	0.310142	+	1.02240i	0.964027	+	0.265806i	$0.0856381\pi$
$659$	7.96165	+	26.2460i	0.310142	+	1.02240i	−0.653885	+	0.756594i	$0.726862\pi$
$660$	−3.43880	−	12.1080i	−0.133855	−	0.471305i
$661$	12.7588	−	1.25664i	0.496262	−	0.0488775i	0.153209	−	0.988194i	$-0.451039\pi$
$661$	12.7588	−	1.25664i	0.496262	−	0.0488775i	0.343052	+	0.939316i	$0.388539\pi$
$662$	15.5013	+	38.3864i	0.602477	+	1.49193i
$663$	−29.9054	+	19.9821i	−1.16143	+	0.776042i
$664$	−3.01523	−	7.86723i	−0.117014	−	0.305308i
$665$	−4.71820	+	7.06129i	−0.182964	+	0.273825i
$666$	−8.97975	−	13.7016i	−0.347958	−	0.530926i
$667$	−0.443993	+	1.46365i	−0.0171915	+	0.0566727i
$668$	0.271026	−	15.2231i	0.0104863	−	0.589000i
$669$	1.46888	−	1.20548i	0.0567904	−	0.0466066i
$670$	24.2125	+	2.60253i	0.935412	+	0.100544i
$671$	−1.10732	+	1.10732i	−0.0427475	+	0.0427475i
$672$	−1.87515	+	1.71526i	−0.0723355	+	0.0661675i
$673$	−5.58602	−	5.58602i	−0.215325	−	0.215325i	0.591200	−	0.806525i	$-0.298654\pi$
$673$	−5.58602	−	5.58602i	−0.215325	−	0.215325i	−0.806525	+	0.591200i	$0.798654\pi$
$674$	22.8409	+	28.3424i	0.879798	+	1.09171i
$675$	−3.16282	−	3.85391i	−0.121737	−	0.148337i
$676$	16.3045	−	37.4622i	0.627098	−	1.44085i
$677$	21.8643	+	6.63246i	0.840313	+	0.254906i	0.680965	−	0.732316i	$-0.261561\pi$
$677$	21.8643	+	6.63246i	0.840313	+	0.254906i	0.159348	+	0.987222i	$0.449061\pi$
$678$	4.59331	+	0.956244i	0.176405	+	0.0367243i
$679$	−6.00319	−	4.01120i	−0.230381	−	0.153936i
$680$	−54.8023	+	9.38727i	−2.10157	+	0.359985i
$681$	−11.4233	−	17.0961i	−0.437741	−	0.655125i
$682$	−8.32302	+	19.5983i	−0.318705	+	0.750458i
$683$	4.25139	+	43.1650i	0.162675	+	1.65166i	0.636669	+	0.771137i	$0.280312\pi$
$683$	4.25139	+	43.1650i	0.162675	+	1.65166i	−0.473995	+	0.880528i	$0.657188\pi$
$684$	9.38238	−	7.42440i	0.358744	−	0.283879i
$685$	−6.91757	+	2.09842i	−0.264307	+	0.0801766i
$686$	−0.781571	−	8.73148i	−0.0298405	−	0.333369i
$687$	−13.7385	−	5.69068i	−0.524157	−	0.217113i
$688$	22.2151	+	7.61239i	0.846943	+	0.290220i
$689$	27.3682	−	11.3363i	1.04264	−	0.431877i
$690$	0.410396	+	0.784515i	0.0156235	+	0.0298660i
$691$	−26.6139	−	14.2254i	−1.01244	−	0.541161i	−0.120214	−	0.992748i	$-0.538358\pi$
$691$	−26.6139	−	14.2254i	−1.01244	−	0.541161i	−0.892227	+	0.451587i	$0.850858\pi$
$692$	−6.02448	−	5.12633i	−0.229017	−	0.194874i
$693$	0.691626	+	0.567603i	0.0262727	+	0.0215614i
$694$	6.75440	+	6.87572i	0.256393	+	0.260999i
$695$	3.22309	−	16.2035i	0.122259	−	0.614635i
$696$	−17.2432	+	13.3969i	−0.653603	+	0.507810i
$697$	−4.25640	+	0.846650i	−0.161223	+	0.0320692i
$698$	−3.78879	−	19.9751i	−0.143408	−	0.756069i
$699$	9.87277	+	18.4707i	0.373422	+	0.698624i
$700$	−0.795564	−	4.40829i	−0.0300695	−	0.166618i
$701$	13.6725	+	1.34662i	0.516403	+	0.0508612i	0.352862	−	0.935675i	$-0.385209\pi$
$701$	13.6725	+	1.34662i	0.516403	+	0.0508612i	0.163541	+	0.986537i	$0.447709\pi$
$702$	2.30380	+	7.84532i	0.0869513	+	0.296102i
$703$			69.2977i			2.61361i
$704$	−8.25002	+	13.6305i	−0.310934	+	0.513719i
$705$		−	39.1556i		−	1.47469i
$706$	18.7671	−	5.51100i	0.706308	−	0.207409i
$707$	1.88277	+	0.185437i	0.0708090	+	0.00697408i
$708$	−13.4869	−	9.36313i	−0.506867	−	0.351888i
$709$	−15.4604	−	28.9243i	−0.580627	−	1.08628i	−0.985141	−	0.171745i	$-0.945059\pi$
$709$	−15.4604	−	28.9243i	−0.580627	−	1.08628i	0.404514	−	0.914532i	$-0.367441\pi$
$710$	24.8051	−	4.70492i	0.930920	−	0.176573i
$711$	1.07185	−	0.213204i	0.0401974	−	0.00799576i
$712$	14.4520	−	25.3834i	0.541612	−	0.951285i
$713$	0.292192	−	1.46895i	0.0109427	−	0.0550126i
$714$	2.81943	−	2.76968i	0.105515	−	0.103653i
$715$	−28.1275	−	23.0836i	−1.05191	−	0.863279i
$716$	0.485044	+	6.02191i	0.0181270	+	0.225049i
$717$	22.4053	+	11.9759i	0.836740	+	0.447247i
$718$	16.6628	−	8.71669i	0.621852	−	0.325304i
$719$	−7.66081	+	3.17321i	−0.285700	+	0.118341i	−0.520931	−	0.853599i	$-0.674415\pi$
$719$	−7.66081	+	3.17321i	−0.285700	+	0.118341i	0.235231	+	0.971939i	$0.424415\pi$
$720$	−1.68592	+	12.5271i	−0.0628304	+	0.466856i
$721$	−5.06870	−	2.09952i	−0.188768	−	0.0781904i
$722$	−23.6468	+	2.11667i	−0.880045	+	0.0787744i
$723$	−13.4432	+	4.07796i	−0.499959	+	0.151661i
$724$	2.97517	−	25.5381i	0.110571	−	0.949117i
$725$	−3.77263	−	38.3042i	−0.140112	−	1.42258i
$726$	−9.15551	−	3.88817i	−0.339793	−	0.144303i
$727$	12.5784	+	18.8249i	0.466508	+	0.698179i	0.987892	−	0.155144i	$-0.0495840\pi$
$727$	12.5784	+	18.8249i	0.466508	+	0.698179i	−0.521384	+	0.853322i	$0.674584\pi$
$728$	−1.62512	+	7.16459i	−0.0602309	+	0.265537i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−2.17846	+	10.4642i	−0.0806285	+	0.387298i
$731$	−34.9484	−	10.6015i	−1.29261	−	0.392110i
$732$	1.46336	−	0.575846i	0.0540875	−	0.0212839i
$733$	−30.6297	−	37.3224i	−1.13133	−	1.37853i	−0.915605	−	0.402080i	$-0.868287\pi$
$733$	−30.6297	−	37.3224i	−1.13133	−	1.37853i	−0.215728	−	0.976453i	$-0.569213\pi$
$734$	40.8079	−	32.8867i	1.50625	−	1.21387i
$735$	−15.1902	−	15.1902i	−0.560300	−	0.560300i
$736$	0.372722	−	1.05693i	0.0137387	−	0.0389591i
$737$	−7.67397	+	7.67397i	−0.282674	+	0.282674i
$738$	−0.105438	+	0.980940i	−0.00388123	+	0.0361089i
$739$	8.79249	−	7.21581i	0.323437	−	0.265438i	−0.458637	−	0.888624i	$-0.651662\pi$
$739$	8.79249	−	7.21581i	0.323437	−	0.265438i	0.782074	+	0.623186i	$0.214162\pi$
$740$	−50.8374	−	52.6804i	−1.86882	−	1.93657i
$741$	10.0403	−	33.0985i	0.368841	−	1.21590i
$742$	−2.72256	+	1.78431i	−0.0999482	+	0.0655040i
$743$	4.45629	−	6.66931i	0.163485	−	0.244673i	−0.740678	−	0.671860i	$-0.765495\pi$
$743$	4.45629	−	6.66931i	0.163485	−	0.244673i	0.904163	+	0.427187i	$0.140495\pi$
$744$	15.5178	−	14.7104i	0.568910	−	0.539311i
$745$	19.9449	−	13.3268i	0.730725	−	0.488255i
$746$	49.3480	−	19.9279i	1.80676	−	0.729612i
$747$	2.96443	−	0.291971i	0.108463	−	0.0106827i
$748$	12.0677	−	21.6415i	0.441240	−	0.791290i
$749$	−0.0540540	−	0.178192i	−0.00197509	−	0.00651100i
$750$	0.0494253	+	0.0413039i	0.00180476	+	0.00150821i
$751$	−11.6996	+	28.2454i	−0.426926	+	1.03069i	0.553331	+	0.832962i	$0.313357\pi$
$751$	−11.6996	+	28.2454i	−0.426926	+	1.03069i	−0.980257	+	0.197729i	$0.936643\pi$
$752$	−36.2724	+	33.7774i	−1.32272	+	1.23173i
$753$	−7.43350	−	17.9461i	−0.270892	−	0.653991i
$754$	−18.8610	+	60.2409i	−0.686878	+	2.19384i
$755$	32.6586	−	61.1000i	1.18857	−	2.22366i
$756$	−0.409374	−	0.799813i	−0.0148888	−	0.0290889i
$757$	−4.73203	+	5.76600i	−0.171989	+	0.209569i	−0.851870	−	0.523753i	$-0.824531\pi$
$757$	−4.73203	+	5.76600i	−0.171989	+	0.209569i	0.679881	+	0.733322i	$0.262031\pi$
$758$	29.7365	+	0.264687i	1.08008	+	0.00961386i
$759$	−0.386991	−	0.0769773i	−0.0140469	−	0.00279410i
$760$	35.0115	−	40.4114i	1.27000	−	1.46588i
$761$	4.80004	+	24.1314i	0.174001	+	0.874764i	0.964860	+	0.262765i	$0.0846343\pi$
$761$	4.80004	+	24.1314i	0.174001	+	0.874764i	−0.790859	+	0.611999i	$0.790366\pi$
$762$	−2.24223	+	3.29193i	−0.0812276	+	0.119254i
$763$	−4.86025	+	2.59786i	−0.175953	+	0.0940487i
$764$	29.9829	−	19.2709i	1.08474	−	0.697196i
$765$	1.92679	−	19.5631i	0.0696634	−	0.707304i
$766$	11.2584	+	6.14719i	0.406782	+	0.222107i
$767$	−47.4632			−1.71380
$768$	13.0590	−	9.24462i	0.471225	−	0.333586i
$769$	−52.1275			−1.87977			−0.939883	−	0.341496i	$-0.889067\pi$
$769$	−52.1275			−1.87977			−0.939883	+	0.341496i	$0.889067\pi$
$770$	3.50937	+	1.91615i	0.126469	+	0.0690533i
$771$	−0.114785	+	1.16544i	−0.00413389	+	0.0419721i
$772$	−12.4945	+	8.03056i	−0.449686	+	0.289026i
$773$	22.3024	−	11.9209i	0.802162	−	0.428764i	−0.0187466	−	0.999824i	$-0.505968\pi$
$773$	22.3024	−	11.9209i	0.802162	−	0.428764i	0.820908	+	0.571060i	$0.193468\pi$
$774$	−4.67391	+	6.86199i	−0.168000	+	0.246649i
$775$	7.35292	+	36.9656i	0.264125	+	1.32784i
$776$	34.3559	+	29.7652i	1.23331	+	1.06851i
$777$	5.10399	+	1.01525i	0.183105	+	0.0364218i
$778$	−32.1826	−	0.286460i	−1.15380	−	0.0102701i
$779$	2.64757	−	3.22607i	0.0948590	−	0.115586i
$780$	16.6487	+	32.5273i	0.596118	+	1.16466i
$781$	−5.30399	+	9.92307i	−0.189792	+	0.355076i
$782$	−0.520779	+	1.66334i	−0.0186230	+	0.0594808i
$783$	−2.95438	−	7.13250i	−0.105581	−	0.254895i
$784$	−0.967948	+	27.1755i	−0.0345696	+	0.970553i
$785$	−11.9030	+	28.7364i	−0.424837	+	1.02565i
$786$	1.21465	+	1.01507i	0.0433252	+	0.0362062i
$787$	−3.85617	−	12.7121i	−0.137458	−	0.453137i	0.861003	−	0.508600i	$-0.169837\pi$
$787$	−3.85617	−	12.7121i	−0.137458	−	0.453137i	−0.998461	+	0.0554624i	$0.982337\pi$
$788$	−1.31161	+	2.35216i	−0.0467242	+	0.0837921i
$789$	−29.7245	+	2.92760i	−1.05822	+	0.104225i
$790$	4.52853	−	1.82873i	0.161118	−	0.0650631i
$791$	−1.23924	+	0.828030i	−0.0440621	+	0.0294414i
$792$	−3.87543	−	4.08813i	−0.137707	−	0.145265i
$793$	2.52569	−	3.77997i	0.0896900	−	0.134231i
$794$	21.2182	−	13.9060i	0.753007	−	0.493505i
$795$	−4.69986	+	15.4933i	−0.166687	+	0.549492i
$796$	−14.4542	−	14.9782i	−0.512314	−	0.530887i
$797$	1.87262	−	1.53682i	0.0663316	−	0.0544370i	−0.600643	−	0.799517i	$-0.705089\pi$
$797$	1.87262	−	1.53682i	0.0663316	−	0.0544370i	0.666975	+	0.745080i	$0.267589\pi$
$798$	−0.406187	+	3.77895i	−0.0143789	+	0.133773i
$799$	54.5053	−	54.5053i	1.92826	−	1.92826i
$800$	1.51293	+	28.1621i	0.0534901	+	0.995682i
$801$	7.30231	+	7.30231i	0.258014	+	0.258014i
$802$	39.4020	−	31.7537i	1.39133	−	1.12126i
$803$	−3.02189	−	3.68218i	−0.106640	−	0.129941i
$804$	10.1415	−	3.99075i	0.357662	−	0.140743i
$805$	−0.269142	−	0.0816432i	−0.00948600	−	0.00287755i
$806$	12.5982	−	60.5155i	0.443754	−	2.13157i
$807$	2.39263	+	1.59870i	0.0842245	+	0.0562770i
$808$	−11.6161	−	2.63484i	−0.408654	−	0.0926935i
$809$	16.4602	+	24.6344i	0.578710	+	0.866100i	0.999150	−	0.0412197i	$-0.0131244\pi$
$809$	16.4602	+	24.6344i	0.578710	+	0.866100i	−0.420440	+	0.907320i	$0.638124\pi$
$810$	−4.11335	−	1.74686i	−0.144528	−	0.0613784i
$811$	2.03941	+	20.7065i	0.0716134	+	0.727103i	0.962210	+	0.272309i	$0.0877872\pi$
$811$	2.03941	+	20.7065i	0.0716134	+	0.727103i	−0.890597	+	0.454794i	$0.849713\pi$
$812$	0.802668	−	6.88990i	0.0281681	−	0.241788i
$813$	−3.26872	+	0.991554i	−0.114639	+	0.0347753i
$814$	32.4964	−	2.90882i	1.13900	−	0.101954i
$815$	−31.8664	−	13.1995i	−1.11623	−	0.462358i
$816$	−19.7847	+	15.0910i	−0.692603	+	0.528292i
$817$	32.4473	−	13.4401i	1.13519	−	0.470210i
$818$	3.07497	−	1.60858i	0.107514	−	0.0562428i
$819$	−2.29071	−	1.22441i	−0.0800440	−	0.0427844i
$820$	0.353982	+	4.39475i	0.0123616	+	0.153471i
$821$	−20.6859	−	16.9764i	−0.721942	−	0.592482i	0.200007	−	0.979794i	$-0.435904\pi$
$821$	−20.6859	−	16.9764i	−0.721942	−	0.592482i	−0.921949	+	0.387312i	$0.873404\pi$
$822$	−2.30788	+	2.26716i	−0.0804966	+	0.0790762i
$823$	4.27859	−	21.5099i	0.149142	−	0.749788i	−0.831737	−	0.555170i	$-0.812653\pi$
$823$	4.27859	−	21.5099i	0.149142	−	0.749788i	0.980879	−	0.194618i	$-0.0623468\pi$
$824$	30.0174	+	17.0903i	1.04570	+	0.595370i
$825$	9.73850	−	1.93711i	0.339051	−	0.0674414i
$826$	5.12418	−	0.971932i	0.178293	−	0.0338178i
$827$	−3.17140	−	5.93327i	−0.110280	−	0.206320i	0.820727	−	0.571321i	$-0.193569\pi$
$827$	−3.17140	−	5.93327i	−0.110280	−	0.206320i	−0.931007	+	0.365001i	$0.881069\pi$
$828$	0.325488	+	0.225967i	0.0113115	+	0.00785291i
$829$	−53.9311	−	5.31175i	−1.87311	−	0.184485i	−0.903406	−	0.428785i	$-0.858942\pi$
$829$	−53.9311	−	5.31175i	−1.87311	−	0.184485i	−0.969700	+	0.244301i	$0.921442\pi$
$830$	12.7726	−	3.75070i	0.443343	−	0.130189i
$831$		−	5.73335i		−	0.198888i
$832$	15.7703	−	43.4822i	0.546737	−	1.50748i
$833$		−	42.2901i		−	1.46527i
$834$	−2.08323	−	7.09419i	−0.0721363	−	0.245652i
$835$	23.9405	+	2.35793i	0.828494	+	0.0815996i
$836$	4.23198	+	23.4498i	0.146366	+	0.811028i
$837$	3.56365	+	6.66711i	0.123178	+	0.230449i
$838$	−2.89498	−	15.2628i	−0.100005	−	0.527245i
$839$	35.9441	−	7.14973i	1.24093	−	0.246836i	0.469375	−	0.882999i	$-0.344479\pi$
$839$	35.9441	−	7.14973i	1.24093	−	0.246836i	0.771555	+	0.636163i	$0.219479\pi$
$840$	−2.46349	−	3.17076i	−0.0849984	−	0.109402i
$841$	5.96994	−	30.0129i	0.205860	−	1.03493i
$842$	−3.26613	−	3.32479i	−0.112558	−	0.114580i
$843$	15.1878	+	12.4643i	0.523097	+	0.429295i
$844$	34.9887	+	29.7724i	1.20436	+	1.02481i
$845$	56.9308	+	30.4302i	1.95848	+	1.04683i
$846$	−8.12266	−	15.5273i	−0.279263	−	0.533840i
$847$	2.91926	−	1.20920i	0.100307	−	0.0415485i
$848$	18.4068	−	9.01146i	0.632093	−	0.309455i
$849$	10.2195	+	4.23307i	0.350733	+	0.145278i
$850$	−3.91044	−	43.6862i	−0.134127	−	1.49843i
$851$	−2.19615	+	0.666195i	−0.0752831	+	0.0228369i
$852$	8.86055	−	7.01147i	0.303557	−	0.240209i
$853$	−1.71422	−	17.4047i	−0.0586936	−	0.595926i	−0.978879	−	0.204442i	$-0.934462\pi$
$853$	−1.71422	−	17.4047i	−0.0586936	−	0.595926i	0.920185	−	0.391484i	$-0.128038\pi$
$854$	−0.195272	+	0.459809i	−0.00668207	+	0.0157344i
$855$	10.5025	+	15.7181i	0.359178	+	0.537548i
$856$	0.197937	+	1.15554i	0.00676533	+	0.0394956i
$857$	−17.6676	−	11.8051i	−0.603514	−	0.403255i	0.215934	−	0.976408i	$-0.430720\pi$
$857$	−17.6676	−	11.8051i	−0.603514	−	0.403255i	−0.819449	+	0.573153i	$0.805720\pi$
$858$	−15.9427	−	3.31897i	−0.544273	−	0.113308i
$859$	−22.7996	−	6.91619i	−0.777913	−	0.235977i	−0.123732	−	0.992316i	$-0.539486\pi$
$859$	−22.7996	−	6.91619i	−0.777913	−	0.235977i	−0.654180	+	0.756338i	$0.726986\pi$
$860$	−14.8068	+	34.0209i	−0.504907	+	1.16010i
$861$	−0.198822	−	0.242265i	−0.00677584	−	0.00825638i
$862$	7.22608	+	8.96658i	0.246121	+	0.305403i
$863$	−25.1291	−	25.1291i	−0.855404	−	0.855404i	0.135388	−	0.990793i	$-0.456772\pi$
$863$	−25.1291	−	25.1291i	−0.855404	−	0.855404i	−0.990793	+	0.135388i	$0.956772\pi$
$864$	1.93013	+	5.31739i	0.0656643	+	0.180901i
$865$	8.83766	−	8.83766i	0.300490	−	0.300490i
$866$	4.14838	+	0.445895i	0.140968	+	0.0151521i
$867$	16.7731	−	13.7653i	0.569643	−	0.467494i
$868$	−0.120909	+	6.79130i	−0.00410393	+	0.230512i
$869$	−0.631807	+	2.08279i	−0.0214326	+	0.0706538i
$870$	−18.9115	−	28.8558i	−0.641159	−	0.978302i
$871$	17.5037	−	26.1961i	0.593089	−	0.887620i
$872$	32.3988	−	12.4173i	1.09716	−	0.420503i
$873$	−13.3628	+	8.92875i	−0.452263	+	0.302192i
$874$	−0.627618	−	1.55419i	−0.0212295	−	0.0525712i
$875$	−0.0203628	+	0.00200556i	−0.000688389	+	6.78004e-5i
$876$	1.30688	+	4.60154i	0.0441554	+	0.155472i
$877$	−1.83277	−	6.04183i	−0.0618882	−	0.204018i	0.920544	−	0.390640i	$-0.127746\pi$
$877$	−1.83277	−	6.04183i	−0.0618882	−	0.204018i	−0.982432	+	0.186622i	$0.940246\pi$
$878$	−13.5874	+	16.2590i	−0.458552	+	0.548714i
$879$	−3.92390	+	9.47313i	−0.132350	+	0.319521i
$880$	−20.4201	−	14.7220i	−0.688363	−	0.496279i
$881$	13.0433	+	31.4894i	0.439440	+	1.06090i	0.976142	+	0.217131i	$0.0696700\pi$
$881$	13.0433	+	31.4894i	0.439440	+	1.06090i	−0.536702	+	0.843772i	$0.680330\pi$
$882$	−9.17489	−	2.87260i	−0.308935	−	0.0967253i
$883$	−8.33038	+	15.5850i	−0.280340	+	0.524479i	−0.982201	−	0.187835i	$-0.939853\pi$
$883$	−8.33038	+	15.5850i	−0.280340	+	0.524479i	0.701861	+	0.712314i	$0.252353\pi$
$884$	−22.1033	+	68.4538i	−0.743415	+	2.30235i
$885$	16.4568	−	20.0527i	0.553190	−	0.674064i
$886$	0.395044	−	44.3816i	0.0132718	−	1.49103i
$887$	−47.8310	−	9.51418i	−1.60601	−	0.319455i	−0.690989	−	0.722866i	$-0.742825\pi$
$887$	−47.8310	−	9.51418i	−1.60601	−	0.319455i	−0.915019	+	0.403411i	$0.867825\pi$
$888$	−31.0881	−	10.3446i	−1.04325	−	0.347142i
$889$	−0.246841	−	1.24095i	−0.00827877	−	0.0416202i
$890$	38.1431	+	25.9804i	1.27856	+	0.870865i
$891$	1.75643	−	0.938833i	0.0588427	−	0.0314521i
$892$	0.807660	−	3.71361i	0.0270424	−	0.124341i
$893$	−7.26568	+	73.7696i	−0.243137	+	2.46861i
$894$	5.14465	−	9.42227i	0.172063	−	0.315128i
$895$	−9.54543			−0.319068
$896$	−0.812168	+	5.01733i	−0.0271326	+	0.167617i
$897$	1.14547			0.0382460
$898$	−15.2190	+	27.8731i	−0.507865	+	0.930138i
$899$	−5.72053	+	58.0815i	−0.190790	+	1.93713i
$900$	−9.74340	−	2.11906i	−0.324780	−	0.0706352i
$901$	−28.1093	+	15.0247i	−0.936456	+	0.500546i
$902$	−1.62397	−	1.10613i	−0.0540722	−	0.0368302i
$903$	−0.514537	−	2.58675i	−0.0171227	−	0.0860817i
$904$	8.39073	−	4.20086i	0.279071	−	0.139718i
$905$	39.8425	+	7.92518i	1.32441	+	0.263442i
$906$	0.275972	−	31.0043i	0.00916856	−	1.03005i
$907$	24.7445	−	30.1513i	0.821629	−	1.00116i	−0.178224	−	0.983990i	$-0.557035\pi$
$907$	24.7445	−	30.1513i	0.821629	−	1.00116i	0.999853	−	0.0171676i	$-0.00546488\pi$
$908$	−39.1332	−	12.6359i	−1.29868	−	0.419337i
$909$	1.98517	−	3.71399i	0.0658439	−	0.123185i
$910$	−11.0774	−	3.46824i	−0.367211	−	0.114971i
$911$	10.5569	+	25.4866i	0.349765	+	0.844407i	0.996647	+	0.0818176i	$0.0260725\pi$
$911$	10.5569	+	25.4866i	0.349765	+	0.844407i	−0.646882	+	0.762590i	$0.723928\pi$
$912$	5.50079	−	23.2883i	0.182149	−	0.771152i
$913$	−2.27028	+	5.48094i	−0.0751353	+	0.181393i
$914$	−20.8050	+	24.8958i	−0.688169	+	0.823480i
$915$	0.721267	+	2.37770i	0.0238443	+	0.0786043i
$916$	−28.6095	+	8.12535i	−0.945283	+	0.268469i
$917$	−0.500427	+	0.0492877i	−0.0165256	+	0.00162762i
$918$	−3.29420	−	8.15751i	−0.108725	−	0.269238i
$919$	−25.5558	+	17.0759i	−0.843009	+	0.563281i	−0.900396	−	0.435071i	$-0.856723\pi$
$919$	−25.5558	+	17.0759i	−0.843009	+	0.563281i	0.0573869	+	0.998352i	$0.481723\pi$
$920$	1.61728	+	0.721074i	0.0533202	+	0.0237731i
$921$	−8.61276	+	12.8899i	−0.283800	+	0.424737i
$922$	−5.48453	−	8.36848i	−0.180624	−	0.275601i
$923$	9.48190	−	31.2576i	0.312101	−	1.02886i
$924$	1.78915	+	0.0318533i	0.0588587	+	0.00104790i
$925$	44.6430	−	36.6376i	1.46785	−	1.20464i
$926$	0.855916	+	0.0919996i	0.0281272	+	0.00302330i
$927$	−8.63540	+	8.63540i	−0.283624	+	0.283624i
$928$	−10.4171	+	42.4112i	−0.341959	+	1.39222i
$929$	10.6517	+	10.6517i	0.349470	+	0.349470i	0.859912	−	0.510442i	$-0.170518\pi$
$929$	10.6517	+	10.6517i	0.349470	+	0.349470i	−0.510442	+	0.859912i	$0.670518\pi$
$930$	21.1990	+	26.3050i	0.695142	+	0.862576i
$931$	25.7999	+	31.4373i	0.845558	+	1.03031i
$932$	38.4074	+	16.7159i	1.25807	+	0.547548i
$933$	−11.8918	−	3.60734i	−0.389320	−	0.118099i
$934$	3.85776	+	0.803117i	0.126230	+	0.0262788i
$935$	32.5523	+	21.7507i	1.06457	+	0.711325i
$936$	13.3497	+	9.44513i	0.436350	+	0.308724i
$937$	−0.449735	−	0.673076i	−0.0146922	−	0.0219884i	0.824051	−	0.566516i	$-0.191709\pi$
$937$	−0.449735	−	0.673076i	−0.0146922	−	0.0219884i	−0.838743	+	0.544527i	$0.816709\pi$
$938$	−1.35328	+	3.18659i	−0.0441862	+	0.104046i
$939$	0.517507	+	5.25434i	0.0168882	+	0.171469i
$940$	−48.5947	−	61.4101i	−1.58498	−	2.00298i
$941$	−7.79715	+	2.36524i	−0.254180	+	0.0771046i	−0.414803	−	0.909911i	$-0.636150\pi$
$941$	−7.79715	+	2.36524i	−0.254180	+	0.0771046i	0.160623	+	0.987016i	$0.448650\pi$
$942$	1.24106	+	13.8648i	0.0404360	+	0.451739i
$943$	0.127692	+	0.0528916i	0.00415821	+	0.00172239i
$944$	−32.7725	+	2.05330i	−1.06666	+	0.0668293i
$945$	1.31155	−	0.543263i	0.0426648	−	0.0176724i
$946$	−7.66460	−	14.6517i	−0.249198	−	0.476367i
$947$	−27.9980	−	14.9653i	−0.909814	−	0.486306i	−0.0510612	−	0.998696i	$-0.516260\pi$
$947$	−27.9980	−	14.9653i	−0.909814	−	0.486306i	−0.858753	+	0.512390i	$0.828760\pi$
$948$	1.41644	−	1.66461i	0.0460039	−	0.0540641i
$949$	10.6896	+	8.77270i	0.346998	+	0.284774i
$950$	29.5585	+	30.0895i	0.959006	+	0.976231i
$951$	3.34582	−	16.8206i	0.108496	−	0.545444i
$952$	0.984531	−	7.84296i	0.0319088	−	0.254192i
$953$	−22.9685	+	4.56872i	−0.744023	+	0.147995i	−0.552523	−	0.833497i	$-0.686335\pi$
$953$	−22.9685	+	4.56872i	−0.744023	+	0.147995i	−0.191499	+	0.981493i	$0.561335\pi$
$954$	1.35028	+	7.11891i	0.0437170	+	0.230483i
$955$	26.5463	+	49.6646i	0.859017	+	1.60711i
$956$	50.0024	−	9.02392i	1.61719	−	0.291854i
$957$	15.3014	+	1.50706i	0.494625	+	0.0487163i
$958$	12.4830	+	42.5093i	0.403307	+	1.37341i
$959$		−	1.02770i		−	0.0331861i
$960$	12.9028	+	21.7393i	0.416435	+	0.701632i
$961$		−	26.1499i		−	0.843546i
$962$	−90.8788	+	26.6868i	−2.93005	+	0.860417i
$963$	−0.412500	−	0.0406277i	−0.0132926	−	0.00130921i
$964$	−16.0228	+	23.0797i	−0.516061	+	0.743345i
$965$	−11.0624	−	20.6962i	−0.356110	−	0.666235i
$966$	−0.123666	+	0.0234563i	−0.00397888	+	0.000754696i
$967$	0.406436	−	0.0808451i	0.0130701	−	0.00259980i	−0.188551	−	0.982063i	$-0.560379\pi$
$967$	0.406436	−	0.0808451i	0.0130701	−	0.00259980i	0.201621	+	0.979464i	$0.435379\pi$
$968$	−19.1846	+	5.26454i	−0.616617	+	0.169209i
$969$	−7.26021	+	36.4995i	−0.233231	+	1.17253i
$970$	−51.2353	+	50.3313i	−1.64507	+	1.61604i
$971$	40.1363	+	32.9390i	1.28803	+	1.05706i	0.994887	+	0.100994i	$0.0322024\pi$
$971$	40.1363	+	32.9390i	1.28803	+	1.05706i	0.293147	+	0.956067i	$0.405298\pi$
$972$	−1.99354	+	0.160573i	−0.0639429	+	0.00515039i
$973$	2.07140	+	1.10718i	0.0664059	+	0.0354947i
$974$	27.4107	−	14.3391i	0.878295	−	0.459454i
$975$	−26.6311	+	11.0309i	−0.852876	+	0.353273i
$976$	1.58042	−	2.71926i	0.0505881	−	0.0870415i
$977$	−0.723846	−	0.299827i	−0.0231579	−	0.00959231i	0.371074	−	0.928603i	$-0.378989\pi$
$977$	−0.723846	−	0.299827i	−0.0231579	−	0.00959231i	−0.394232	+	0.919011i	$0.628989\pi$
$978$	−15.3749	+	1.37624i	−0.491635	+	0.0440072i
$979$	−19.6817	+	5.97037i	−0.629029	+	0.190814i
$980$	−42.6758	−	4.97170i	−1.36323	−	0.158815i
$981$	1.20239	+	12.2081i	0.0383895	+	0.389775i
$982$	−48.8442	−	20.7432i	−1.55868	−	0.661942i
$983$	18.2287	+	27.2812i	0.581406	+	0.870136i	0.999263	−	0.0383766i	$-0.0122186\pi$
$983$	18.2287	+	27.2812i	0.581406	+	0.870136i	−0.417857	+	0.908513i	$0.637219\pi$
$984$	1.05205	+	1.66932i	0.0335380	+	0.0532161i
$985$	−3.53803	−	2.36403i	−0.112731	−	0.0753243i
$986$	13.8426	−	66.4928i	0.440839	−	2.11756i
$987$	5.32692	+	1.61590i	0.169558	+	0.0514347i
$988$	−25.3306	−	64.3711i	−0.805872	−	2.04792i
$989$	0.737871	+	0.899098i	0.0234629	+	0.0285897i
$990$	6.92999	−	5.58482i	0.220250	−	0.177497i
$991$	3.97696	+	3.97696i	0.126332	+	0.126332i	0.767446	−	0.641114i	$-0.221527\pi$
$991$	3.97696	+	3.97696i	0.126332	+	0.126332i	−0.641114	+	0.767446i	$0.721527\pi$
$992$	6.08091	−	42.3299i	0.193069	−	1.34398i
$993$	−20.6991	+	20.6991i	−0.656866	+	0.656866i
$994$	−0.383596	+	3.56877i	−0.0121669	+	0.113195i
$995$	25.4226	−	20.8638i	0.805951	−	0.661427i
$996$	4.28695	−	4.13697i	0.135837	−	0.131085i
$997$	1.05923	−	3.49182i	0.0335462	−	0.110587i	−0.938568	−	0.345093i	$-0.887847\pi$
$997$	1.05923	−	3.49182i	0.0335462	−	0.110587i	0.972115	+	0.234506i	$0.0753473\pi$
$998$	−29.2545	+	19.1728i	−0.926036	+	0.606905i
$999$	6.43563	−	9.63160i	0.203614	−	0.304730i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.26	✓	512
128.53	even	32	inner	384.2.v.a.181.26	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.26	✓	512	1.1	even	1	trivial
384.2.v.a.181.26	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(1.24124 + 0.677730i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.08136 + 1.68245i) q^{4} +(-2.78687 + 1.48961i) q^{5} +(-0.796130 + 1.16884i) q^{6} +(-0.0876435 - 0.440614i) q^{7} +(0.201982 + 2.82121i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.24124 + 0.677730i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.08136 + 1.68245i) q^{4} +(-2.78687 + 1.48961i) q^{5} +(-0.796130 + 1.16884i) q^{6} +(-0.0876435 - 0.440614i) q^{7} +(0.201982 + 2.82121i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-4.46873 - 0.0397766i) q^{10} +(1.26346 - 1.53953i) q^{11} +(-1.78035 + 0.911246i) q^{12} +(-2.72548 + 5.09902i) q^{13} +(0.189830 - 0.606307i) q^{14} +(-1.20928 - 2.91946i) q^{15} +(-1.66131 + 3.63869i) q^{16} +(2.38060 - 5.74727i) q^{17} +(-1.08517 - 0.906862i) q^{18} +(1.73656 + 5.72469i) q^{19} +(-5.51982 - 3.07797i) q^{20} +(0.447082 - 0.0440338i) q^{21} +(2.61164 - 1.05464i) q^{22} +(-0.164730 + 0.110069i) q^{23} +(-2.82742 - 0.0755172i) q^{24} +(2.76984 - 4.14536i) q^{25} +(-6.83874 + 4.48197i) q^{26} +(0.290285 - 0.956940i) q^{27} +(0.646538 - 0.623919i) q^{28} +(5.96777 - 4.89762i) q^{29} +(0.477598 - 4.44332i) q^{30} +(-5.34556 + 5.34556i) q^{31} +(-4.52814 + 3.39057i) q^{32} +(1.40827 + 1.40827i) q^{33} +(6.85000 - 5.52035i) q^{34} +(0.900595 + 1.09738i) q^{35} +(-0.732354 - 1.86109i) q^{36} +(11.0850 + 3.36261i) q^{37} +(-1.72430 + 8.28264i) q^{38} +(-4.80732 - 3.21215i) q^{39} +(-4.76540 - 7.56146i) q^{40} +(-0.387580 - 0.580054i) q^{41} +(0.584781 + 0.248345i) q^{42} +(-0.575438 - 5.84252i) q^{43} +(3.95644 + 0.460922i) q^{44} +(3.02393 - 0.917299i) q^{45} +(-0.279066 + 0.0249797i) q^{46} +(11.4478 + 4.74184i) q^{47} +(-3.45833 - 2.00996i) q^{48} +(6.28070 - 2.60155i) q^{49} +(6.24749 - 3.26819i) q^{50} +(5.48626 + 2.93247i) q^{51} +(-11.5261 + 0.928388i) q^{52} +(-3.96058 - 3.25037i) q^{53} +(1.00886 - 0.991060i) q^{54} +(-1.22779 + 6.17252i) q^{55} +(1.22536 - 0.336256i) q^{56} +(-5.86733 + 1.16709i) q^{57} +(10.7267 - 2.03459i) q^{58} +(3.86979 + 7.23987i) q^{59} +(3.60419 - 5.19155i) q^{60} +(-0.782508 - 0.0770703i) q^{61} +(-10.2580 + 3.01228i) q^{62} +0.449246i q^{63} +(-7.91841 + 1.13967i) q^{64} -18.2702i q^{65} +(0.793578 + 2.70244i) q^{66} +(-5.42297 - 0.534115i) q^{67} +(12.2438 - 2.20964i) q^{68} +(-0.0933925 - 0.174725i) q^{69} +(0.374129 + 1.97247i) q^{70} +(-5.54100 + 1.10217i) q^{71} +(0.352289 - 2.80640i) q^{72} +(0.466609 - 2.34580i) q^{73} +(11.4803 + 11.6865i) q^{74} +(3.85391 + 3.16282i) q^{75} +(-7.75367 + 9.11216i) q^{76} +(-0.789070 - 0.421767i) q^{77} +(-3.79008 - 7.24512i) q^{78} +(-1.00966 + 0.418214i) q^{79} +(-0.790386 - 12.6153i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-0.0879599 - 0.982662i) q^{82} +(-2.85051 + 0.864694i) q^{83} +(0.557543 + 0.704580i) q^{84} +(1.92679 + 19.5631i) q^{85} +(3.24540 - 7.64197i) q^{86} +(4.28909 + 6.41908i) q^{87} +(4.59852 + 3.25352i) q^{88} +(-8.58661 - 5.73739i) q^{89} +(4.37511 + 0.910819i) q^{90} +(2.48557 + 0.753989i) q^{91} +(-0.363318 - 0.158126i) q^{92} +(-4.79586 - 5.84377i) q^{93} +(10.9958 + 13.6443i) q^{94} +(-13.3671 - 13.3671i) q^{95} +(-2.93041 - 4.83867i) q^{96} +(11.3641 - 11.3641i) q^{97} +(9.55901 + 1.02747i) q^{98} +(-1.53953 + 1.26346i) 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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