LMFDB - Embedded newform 384.2.v.a.157.18

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			157.18
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.236404 + 1.39431i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.88823 + 0.659242i) q^{4} +(-1.27674 + 0.682433i) q^{5} +(1.41077 - 0.0985985i) q^{6} +(-0.687954 - 3.45858i) q^{7} +(-1.36557 - 2.47694i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(0.236404 + 1.39431i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.88823 + 0.659242i) q^{4} +(-1.27674 + 0.682433i) q^{5} +(1.41077 - 0.0985985i) q^{6} +(-0.687954 - 3.45858i) q^{7} +(-1.36557 - 2.47694i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.25335 - 1.61885i) q^{10} +(4.18657 - 5.10135i) q^{11} +(0.470989 + 1.94375i) q^{12} +(-1.37854 + 2.57906i) q^{13} +(4.65971 - 1.77685i) q^{14} +(0.554004 + 1.33748i) q^{15} +(3.13080 - 2.48960i) q^{16} +(2.00032 - 4.82920i) q^{17} +(0.0401562 - 1.41364i) q^{18} +(-0.106100 - 0.349765i) q^{19} +(1.96089 - 2.13027i) q^{20} +(-3.50936 + 0.345642i) q^{21} +(8.10261 + 4.63142i) q^{22} +(-4.11144 + 2.74718i) q^{23} +(-2.59886 + 1.11622i) q^{24} +(-1.61350 + 2.41477i) q^{25} +(-3.92192 - 1.31242i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(3.57906 + 6.07706i) q^{28} +(5.85942 - 4.80870i) q^{29} +(-1.73391 + 1.08864i) q^{30} +(2.89586 - 2.89586i) q^{31} +(4.21141 + 3.77677i) q^{32} +(-4.66643 - 4.66643i) q^{33} +(7.20631 + 1.64744i) q^{34} +(3.23859 + 3.94623i) q^{35} +(1.98056 - 0.278200i) q^{36} +(-10.8998 - 3.30641i) q^{37} +(0.462600 - 0.230623i) q^{38} +(2.43152 + 1.62469i) q^{39} +(3.43383 + 2.23049i) q^{40} +(-5.71849 - 8.55832i) q^{41} +(-1.31156 - 4.81144i) q^{42} +(0.299803 + 3.04395i) q^{43} +(-4.54217 + 12.3925i) q^{44} +(1.38535 - 0.420240i) q^{45} +(-4.80239 - 5.08320i) q^{46} +(-0.979176 - 0.405588i) q^{47} +(-2.17074 - 3.35975i) q^{48} +(-5.02134 + 2.07991i) q^{49} +(-3.74838 - 1.67886i) q^{50} +(-4.60988 - 2.46403i) q^{51} +(0.902766 - 5.77865i) q^{52} +(9.08346 + 7.45461i) q^{53} +(-1.40290 - 0.178524i) q^{54} +(-1.86384 + 9.37016i) q^{55} +(-7.62723 + 6.42697i) q^{56} +(-0.358481 + 0.0713062i) q^{57} +(8.09003 + 7.03308i) q^{58} +(-0.941833 - 1.76205i) q^{59} +(-1.92781 - 2.16025i) q^{60} +(6.75679 + 0.665486i) q^{61} +(4.72233 + 3.35314i) q^{62} +3.52634i q^{63} +(-4.27041 + 6.76488i) q^{64} -4.23356i q^{65} +(5.40331 - 7.60963i) q^{66} +(7.01002 + 0.690426i) q^{67} +(-0.593447 + 10.4373i) q^{68} +(2.33096 + 4.36092i) q^{69} +(-4.73668 + 5.44852i) q^{70} +(-7.00144 + 1.39267i) q^{71} +(0.856109 + 2.69575i) q^{72} +(-2.63451 + 13.2446i) q^{73} +(2.03343 - 15.9794i) q^{74} +(2.24499 + 1.84241i) q^{75} +(0.430921 + 0.590490i) q^{76} +(-20.5236 - 10.9701i) q^{77} +(-1.69051 + 3.77439i) q^{78} +(-1.48421 + 0.614781i) q^{79} +(-2.29824 + 5.31513i) q^{80} +(0.923880 + 0.382683i) q^{81} +(10.5811 - 9.99659i) q^{82} +(11.6004 - 3.51894i) q^{83} +(6.39860 - 2.96617i) q^{84} +(0.741712 + 7.53073i) q^{85} +(-4.17335 + 1.13762i) q^{86} +(-4.21122 - 6.30254i) q^{87} +(-18.3528 - 3.40359i) q^{88} +(-7.92861 - 5.29772i) q^{89} +(0.913448 + 1.83226i) q^{90} +(9.86827 + 2.99351i) q^{91} +(5.95228 - 7.89773i) q^{92} +(-2.59807 - 3.16576i) q^{93} +(0.334037 - 1.46116i) q^{94} +(0.374154 + 0.374154i) q^{95} +(4.17138 - 3.82095i) q^{96} +(-0.437798 + 0.437798i) q^{97} +(-4.08711 - 6.50963i) q^{98} +(-5.10135 + 4.18657i) 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 $

$2$	0.236404	+	1.39431i	0.167163	+	0.985929i
$2$	0.236404	+	1.39431i	0.167163	+	0.985929i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	−1.88823	+	0.659242i	−0.944113	+	0.329621i
$5$	−1.27674	+	0.682433i	−0.570976	+	0.305193i	−0.731503	−	0.681838i	$-0.761181\pi$
$5$	−1.27674	+	0.682433i	−0.570976	+	0.305193i	0.160527	+	0.987032i	$0.448681\pi$
$6$	1.41077	−	0.0985985i	0.575945	−	0.0402527i
$7$	−0.687954	−	3.45858i	−0.260022	−	1.30722i	−0.861266	−	0.508155i	$-0.830328\pi$
$7$	−0.687954	−	3.45858i	−0.260022	−	1.30722i	0.601243	−	0.799066i	$-0.294672\pi$
$8$	−1.36557	−	2.47694i	−0.482803	−	0.875729i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−1.25335	−	1.61885i	−0.396345	−	0.511926i
$11$	4.18657	−	5.10135i	1.26230	−	1.53811i	0.553074	−	0.833132i	$-0.313455\pi$
$11$	4.18657	−	5.10135i	1.26230	−	1.53811i	0.709225	−	0.704983i	$-0.249045\pi$
$12$	0.470989	+	1.94375i	0.135963	+	0.561113i
$13$	−1.37854	+	2.57906i	−0.382338	+	0.715303i	−0.997314	−	0.0732420i	$-0.976665\pi$
$13$	−1.37854	+	2.57906i	−0.382338	+	0.715303i	0.614977	+	0.788545i	$0.289165\pi$
$14$	4.65971	−	1.77685i	1.24536	−	0.474882i
$15$	0.554004	+	1.33748i	0.143043	+	0.345337i
$16$	3.13080	−	2.48960i	0.782700	−	0.622399i
$17$	2.00032	−	4.82920i	0.485149	−	1.17125i	−0.471985	−	0.881607i	$-0.656462\pi$
$17$	2.00032	−	4.82920i	0.485149	−	1.17125i	0.957134	−	0.289646i	$-0.0935377\pi$
$18$	0.0401562	−	1.41364i	0.00946490	−	0.333199i
$19$	−0.106100	−	0.349765i	−0.0243410	−	0.0802416i	0.943928	−	0.330150i	$-0.107099\pi$
$19$	−0.106100	−	0.349765i	−0.0243410	−	0.0802416i	−0.968269	+	0.249909i	$0.919599\pi$
$20$	1.96089	−	2.13027i	0.438468	−	0.476343i
$21$	−3.50936	+	0.345642i	−0.765805	+	0.0754252i
$22$	8.10261	+	4.63142i	1.72748	+	0.987422i
$23$	−4.11144	+	2.74718i	−0.857295	+	0.572826i	−0.904700	−	0.426049i	$-0.859905\pi$
$23$	−4.11144	+	2.74718i	−0.857295	+	0.572826i	0.0474048	+	0.998876i	$0.484905\pi$
$24$	−2.59886	+	1.11622i	−0.530490	+	0.227847i
$25$	−1.61350	+	2.41477i	−0.322699	+	0.482953i
$26$	−3.92192	−	1.31242i	−0.769151	−	0.257386i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	3.57906	+	6.07706i	0.676378	+	1.14846i
$29$	5.85942	−	4.80870i	1.08807	−	0.892954i	0.0933527	−	0.995633i	$-0.470242\pi$
$29$	5.85942	−	4.80870i	1.08807	−	0.892954i	0.994714	+	0.102679i	$0.0327416\pi$
$30$	−1.73391	+	1.08864i	−0.316566	+	0.198758i
$31$	2.89586	−	2.89586i	0.520111	−	0.520111i	−0.397494	−	0.917605i	$-0.630120\pi$
$31$	2.89586	−	2.89586i	0.520111	−	0.520111i	0.917605	+	0.397494i	$0.130120\pi$
$32$	4.21141	+	3.77677i	0.744480	+	0.667645i
$33$	−4.66643	−	4.66643i	−0.812321	−	0.812321i
$34$	7.20631	+	1.64744i	1.23587	+	0.282533i
$35$	3.23859	+	3.94623i	0.547422	+	0.667035i
$36$	1.98056	−	0.278200i	0.330093	−	0.0463667i
$37$	−10.8998	−	3.30641i	−1.79191	−	0.543571i	−0.793986	−	0.607936i	$-0.791998\pi$
$37$	−10.8998	−	3.30641i	−1.79191	−	0.543571i	−0.997926	+	0.0643655i	$0.979498\pi$
$38$	0.462600	−	0.230623i	0.0750437	−	0.0374119i
$39$	2.43152	+	1.62469i	0.389355	+	0.260159i
$40$	3.43383	+	2.23049i	0.542936	+	0.352672i
$41$	−5.71849	−	8.55832i	−0.893078	−	1.33659i	−0.941237	−	0.337746i	$-0.890336\pi$
$41$	−5.71849	−	8.55832i	−0.893078	−	1.33659i	0.0481595	−	0.998840i	$-0.484664\pi$
$42$	−1.31156	−	4.81144i	−0.202378	−	0.742421i
$43$	0.299803	+	3.04395i	0.0457195	+	0.464198i	0.990601	+	0.136785i	$0.0436769\pi$
$43$	0.299803	+	3.04395i	0.0457195	+	0.464198i	−0.944881	+	0.327413i	$0.893823\pi$
$44$	−4.54217	+	12.3925i	−0.684758	+	1.86823i
$45$	1.38535	−	0.420240i	0.206515	−	0.0626457i
$46$	−4.80239	−	5.08320i	−0.708074	−	0.749477i
$47$	−0.979176	−	0.405588i	−0.142828	−	0.0591611i	0.310125	−	0.950696i	$-0.399629\pi$
$47$	−0.979176	−	0.405588i	−0.142828	−	0.0591611i	−0.452952	+	0.891535i	$0.649629\pi$
$48$	−2.17074	−	3.35975i	−0.313319	−	0.484938i
$49$	−5.02134	+	2.07991i	−0.717334	+	0.297130i
$50$	−3.74838	−	1.67886i	−0.530101	−	0.237427i
$51$	−4.60988	−	2.46403i	−0.645512	−	0.345033i
$52$	0.902766	−	5.77865i	0.125191	−	0.801354i
$53$	9.08346	+	7.45461i	1.24771	+	1.02397i	0.998457	+	0.0555305i	$0.0176850\pi$
$53$	9.08346	+	7.45461i	1.24771	+	1.02397i	0.249253	+	0.968438i	$0.419815\pi$
$54$	−1.40290	−	0.178524i	−0.190911	−	0.0242940i
$55$	−1.86384	+	9.37016i	−0.251320	+	1.26347i
$56$	−7.62723	+	6.42697i	−1.01923	+	0.858840i
$57$	−0.358481	+	0.0713062i	−0.0474819	+	0.00944474i
$58$	8.09003	+	7.03308i	1.06227	+	0.923489i
$59$	−0.941833	−	1.76205i	−0.122616	−	0.229399i	0.813123	−	0.582092i	$-0.197766\pi$
$59$	−0.941833	−	1.76205i	−0.122616	−	0.229399i	−0.935739	+	0.352694i	$0.885266\pi$
$60$	−1.92781	−	2.16025i	−0.248879	−	0.278887i
$61$	6.75679	+	0.665486i	0.865119	+	0.0852068i	0.520833	−	0.853658i	$-0.325621\pi$
$61$	6.75679	+	0.665486i	0.865119	+	0.0852068i	0.344285	+	0.938865i	$0.388121\pi$
$62$	4.72233	+	3.35314i	0.599736	+	0.425850i
$63$			3.52634i			0.444277i
$64$	−4.27041	+	6.76488i	−0.533802	+	0.845610i
$65$		−	4.23356i		−	0.525108i
$66$	5.40331	−	7.60963i	0.665102	−	0.936681i
$67$	7.01002	+	0.690426i	0.856410	+	0.0843490i	0.516685	−	0.856176i	$-0.327166\pi$
$67$	7.01002	+	0.690426i	0.856410	+	0.0843490i	0.339725	+	0.940525i	$0.389666\pi$
$68$	−0.593447	+	10.4373i	−0.0719660	+	1.26571i
$69$	2.33096	+	4.36092i	0.280614	+	0.524993i
$70$	−4.73668	+	5.44852i	−0.566141	+	0.651222i
$71$	−7.00144	+	1.39267i	−0.830918	+	0.165280i	−0.592182	−	0.805805i	$-0.701733\pi$
$71$	−7.00144	+	1.39267i	−0.830918	+	0.165280i	−0.238736	+	0.971084i	$0.576733\pi$
$72$	0.856109	+	2.69575i	0.100893	+	0.317697i
$73$	−2.63451	+	13.2446i	−0.308346	+	1.55016i	0.446818	+	0.894625i	$0.352557\pi$
$73$	−2.63451	+	13.2446i	−0.308346	+	1.55016i	−0.755164	+	0.655535i	$0.772443\pi$
$74$	2.03343	−	15.9794i	0.236382	−	1.85756i
$75$	2.24499	+	1.84241i	0.259229	+	0.212744i
$76$	0.430921	+	0.590490i	0.0494300	+	0.0677339i
$77$	−20.5236	−	10.9701i	−2.33888	−	1.25016i
$78$	−1.69051	+	3.77439i	−0.191413	+	0.427366i
$79$	−1.48421	+	0.614781i	−0.166987	+	0.0691683i	−0.464611	−	0.885515i	$-0.653806\pi$
$79$	−1.48421	+	0.614781i	−0.166987	+	0.0691683i	0.297624	+	0.954683i	$0.403806\pi$
$80$	−2.29824	+	5.31513i	−0.256951	+	0.594250i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	10.5811	−	9.99659i	1.16849	−	1.10394i
$83$	11.6004	−	3.51894i	1.27331	−	0.386254i	0.419935	−	0.907554i	$-0.362053\pi$
$83$	11.6004	−	3.51894i	1.27331	−	0.386254i	0.853373	+	0.521301i	$0.174553\pi$
$84$	6.39860	−	2.96617i	0.698145	−	0.323635i
$85$	0.741712	+	7.53073i	0.0804499	+	0.816822i
$86$	−4.17335	+	1.13762i	−0.450024	+	0.122673i
$87$	−4.21122	−	6.30254i	−0.451491	−	0.675703i
$88$	−18.3528	−	3.40359i	−1.95641	−	0.362824i
$89$	−7.92861	−	5.29772i	−0.840430	−	0.561558i	0.0591818	−	0.998247i	$-0.481151\pi$
$89$	−7.92861	−	5.29772i	−0.840430	−	0.561558i	−0.899612	+	0.436690i	$0.856151\pi$
$90$	0.913448	+	1.83226i	0.0962858	+	0.193137i
$91$	9.86827	+	2.99351i	1.03448	+	0.313805i
$92$	5.95228	−	7.89773i	0.620568	−	0.823395i
$93$	−2.59807	−	3.16576i	−0.269407	−	0.328274i
$94$	0.334037	−	1.46116i	0.0344532	−	0.150707i
$95$	0.374154	+	0.374154i	0.0383874	+	0.0383874i
$96$	4.17138	−	3.82095i	0.425739	−	0.389974i
$97$	−0.437798	+	0.437798i	−0.0444516	+	0.0444516i	−0.728983	−	0.684532i	$-0.760007\pi$
$97$	−0.437798	+	0.437798i	−0.0444516	+	0.0444516i	0.684532	+	0.728983i	$0.260007\pi$
$98$	−4.08711	−	6.50963i	−0.412860	−	0.657572i
$99$	−5.10135	+	4.18657i	−0.512705	+	0.420766i
$100$	1.45473	−	5.62331i	0.145473	−	0.562331i
$101$	−1.74937	+	5.76691i	−0.174069	+	0.573829i	0.825881	+	0.563845i	$0.190678\pi$
$101$	−1.74937	+	5.76691i	−0.174069	+	0.573829i	−0.999950	+	0.00998479i	$0.996822\pi$
$102$	2.34584	−	7.01013i	0.232273	−	0.694106i
$103$	−1.58977	+	2.37926i	−0.156645	+	0.234435i	−0.901488	−	0.432804i	$-0.857524\pi$
$103$	−1.58977	+	2.37926i	−0.156645	+	0.234435i	0.744843	+	0.667239i	$0.232524\pi$
$104$	8.27067	−	0.107353i	0.811006	−	0.0105268i
$105$	4.24467	−	2.83620i	0.414237	−	0.276784i
$106$	−8.24670	+	14.4275i	−0.800991	+	1.40132i
$107$	14.4493	−	1.42313i	1.39687	−	0.137580i	0.628611	−	0.777720i	$-0.283624\pi$
$107$	14.4493	−	1.42313i	1.39687	−	0.137580i	0.768258	+	0.640140i	$0.221124\pi$
$108$	−0.0827319	−	1.99829i	−0.00796088	−	0.192285i
$109$	1.26289	+	4.16321i	0.120963	+	0.398763i	0.996421	−	0.0845326i	$-0.0269397\pi$
$109$	1.26289	+	4.16321i	0.120963	+	0.398763i	−0.875457	+	0.483295i	$0.839440\pi$
$110$	−13.5056	−	0.383641i	−1.28771	−	0.0365788i
$111$	−4.35885	+	10.5232i	−0.413724	+	0.998819i
$112$	−10.7643	−	9.11540i	−1.01713	−	0.861324i
$113$	2.67842	+	6.46627i	0.251964	+	0.608295i	0.998362	−	0.0572042i	$-0.0182186\pi$
$113$	2.67842	+	6.46627i	0.251964	+	0.608295i	−0.746398	+	0.665499i	$0.768219\pi$
$114$	−0.184169	−	0.482978i	−0.0172490	−	0.0452350i
$115$	3.37449	−	6.31322i	0.314673	−	0.588711i
$116$	−7.89382	+	12.9427i	−0.732922	+	1.20170i
$117$	1.85520	−	2.26057i	0.171513	−	0.208990i
$118$	2.23419	−	1.72976i	0.205674	−	0.159238i
$119$	−18.0783	−	3.59600i	−1.65724	−	0.329645i
$120$	2.55633	−	3.19867i	0.233360	−	0.291997i
$121$	−6.35041	−	31.9257i	−0.577310	−	2.90233i
$122$	0.669433	+	9.57842i	0.0606076	+	0.867189i
$123$	−9.07762	+	4.85209i	−0.818502	+	0.437498i
$124$	−3.55896	+	7.37710i	−0.319604	+	0.662483i
$125$	1.12159	−	11.3877i	0.100318	−	1.01855i
$126$	−4.91682	+	0.833639i	−0.438026	+	0.0742665i
$127$	8.37877			0.743496			0.371748	−	0.928334i	$-0.378759\pi$
$127$	8.37877			0.743496			0.371748	+	0.928334i	$0.378759\pi$
$128$	−10.4419	−	4.35506i	−0.922943	−	0.384937i
$129$	3.05868			0.269302
$130$	5.90291	−	1.00083i	0.517720	−	0.0877784i
$131$	0.666389	−	6.76596i	0.0582227	−	0.591145i	−0.921167	−	0.389167i	$-0.872763\pi$
$131$	0.666389	−	6.76596i	0.0582227	−	0.591145i	0.979390	−	0.201978i	$-0.0647370\pi$
$132$	11.8876	+	5.73497i	1.03468	+	0.499165i
$133$	−1.13670	+	0.607578i	−0.0985643	+	0.0526837i
$134$	0.694521	+	9.93739i	0.0599975	+	0.858460i
$135$	−0.282429	−	1.41987i	−0.0243076	−	0.122203i
$136$	−14.6932	+	1.63997i	−1.25993	+	0.140626i
$137$	5.28033	+	1.05032i	0.451129	+	0.0897352i	0.415425	−	0.909627i	$-0.363633\pi$
$137$	5.28033	+	1.05032i	0.451129	+	0.0897352i	0.0357038	+	0.999362i	$0.488633\pi$
$138$	−5.52944	+	4.28102i	−0.470697	+	0.364425i
$139$	3.53726	−	4.31017i	0.300027	−	0.365584i	−0.601074	−	0.799193i	$-0.705260\pi$
$139$	3.53726	−	4.31017i	0.300027	−	0.365584i	0.901101	+	0.433610i	$0.142760\pi$
$140$	−8.71671	−	5.31637i	−0.736697	−	0.449315i
$141$	−0.499611	+	0.934707i	−0.0420748	+	0.0787165i
$142$	−3.59699	−	9.43298i	−0.301853	−	0.791598i
$143$	7.38536	+	17.8298i	0.617595	+	1.49101i
$144$	−3.55634	+	1.83097i	−0.296362	+	0.152581i
$145$	−4.19935	+	10.1381i	−0.348737	+	0.841926i
$146$	−19.0899	−	0.542271i	−1.57989	−	0.0448786i
$147$	1.57771	+	5.20103i	0.130128	+	0.428974i
$148$	22.7610	−	0.942336i	1.87094	−	0.0774595i
$149$	−0.873457	+	0.0860281i	−0.0715564	+	0.00704769i	−0.133732	−	0.991018i	$-0.542696\pi$
$149$	−0.873457	+	0.0860281i	−0.0715564	+	0.00704769i	0.0621756	+	0.998065i	$0.480196\pi$
$150$	−2.03818	+	3.56577i	−0.166417	+	0.291144i
$151$	0.0605200	−	0.0404381i	0.00492505	−	0.00329081i	−0.553105	−	0.833111i	$-0.686557\pi$
$151$	0.0605200	−	0.0404381i	0.00492505	−	0.00329081i	0.558030	+	0.829821i	$0.311557\pi$
$152$	−0.721458	+	0.740434i	−0.0585180	+	0.0600571i
$153$	−2.90401	+	4.34616i	−0.234776	+	0.351367i
$154$	10.4439	−	31.2097i	0.841594	−	2.51495i
$155$	−1.72103	+	5.67349i	−0.138237	+	0.455706i
$156$	−5.66233	−	1.46482i	−0.453349	−	0.117280i
$157$	−4.54190	+	3.72744i	−0.362483	+	0.297482i	−0.797951	−	0.602722i	$-0.794083\pi$
$157$	−4.54190	+	3.72744i	−0.362483	+	0.297482i	0.435468	+	0.900204i	$0.356583\pi$
$158$	−1.20807	−	1.92412i	−0.0961090	−	0.153075i
$159$	8.30905	−	8.30905i	0.658950	−	0.658950i
$160$	−7.95428	−	1.94796i	−0.628841	−	0.153999i
$161$	12.3298	+	12.3298i	0.971726	+	0.971726i
$162$	−0.315173	+	1.37865i	−0.0247623	+	0.108317i
$163$	3.27210	+	3.98707i	0.256291	+	0.312291i	0.885221	−	0.465170i	$-0.154007\pi$
$163$	3.27210	+	3.98707i	0.256291	+	0.312291i	−0.628930	+	0.777462i	$0.716507\pi$
$164$	16.4398	+	12.3902i	1.28373	+	0.967511i
$165$	9.14235	+	2.77330i	0.711731	+	0.215901i
$166$	7.64888	+	15.3427i	0.593668	+	1.19082i
$167$	15.2949	+	10.2198i	1.18356	+	0.790828i	0.982043	−	0.188657i	$-0.0604135\pi$
$167$	15.2949	+	10.2198i	1.18356	+	0.790828i	0.201515	+	0.979485i	$0.435413\pi$
$168$	5.64842	+	8.22045i	0.435785	+	0.634222i
$169$	2.47121	+	3.69843i	0.190093	+	0.284495i
$170$	−10.3249	+	2.81447i	−0.791880	+	0.215860i
$171$	0.0358256	+	0.363744i	0.00273965	+	0.0278162i
$172$	−2.57280	−	5.55003i	−0.196174	−	0.423186i
$173$	18.1625	−	5.50953i	1.38087	−	0.418882i	0.489438	−	0.872038i	$-0.337202\pi$
$173$	18.1625	−	5.50953i	1.38087	−	0.418882i	0.891431	+	0.453156i	$0.149702\pi$
$174$	7.79218	−	7.36171i	0.590723	−	0.558090i
$175$	9.46168	+	3.91915i	0.715235	+	0.296260i
$176$	0.407011	−	26.3942i	0.0306796	−	1.98954i
$177$	−1.84588	+	0.764587i	−0.138745	+	0.0574699i
$178$	5.51234	−	12.3074i	0.413168	−	0.922476i
$179$	15.8023	+	8.44650i	1.18112	+	0.631321i	0.940664	−	0.339339i	$-0.110203\pi$
$179$	15.8023	+	8.44650i	1.18112	+	0.631321i	0.240455	+	0.970660i	$0.422703\pi$
$180$	−2.33881	+	1.70679i	−0.174324	+	0.127216i
$181$	3.58289	+	2.94040i	0.266314	+	0.218558i	0.758067	−	0.652176i	$-0.226144\pi$
$181$	3.58289	+	2.94040i	0.266314	+	0.218558i	−0.491753	+	0.870735i	$0.663644\pi$
$182$	−1.84100	+	14.4671i	−0.136464	+	1.07238i
$183$	1.32456	−	6.65903i	0.0979145	−	0.492250i
$184$	12.4191	+	6.43230i	0.915545	+	0.474196i
$185$	16.1726	−	3.21693i	1.18903	−	0.236514i
$186$	3.79987	−	4.37092i	0.278620	−	0.320491i
$187$	−16.2610	−	30.4221i	−1.18912	−	2.22469i
$188$	2.11629	+	0.120328i	0.154346	+	0.00877584i
$189$	3.50936	+	0.345642i	0.255268	+	0.0251417i
$190$	−0.433237	+	0.610139i	−0.0314303	+	0.0442642i
$191$		−	2.70941i		−	0.196046i	−0.995184	−	0.0980230i	$-0.968748\pi$
$191$		−	2.70941i		−	0.196046i	0.995184	−	0.0980230i	$-0.0312519\pi$
$192$	6.31373	+	4.91292i	0.455654	+	0.354560i
$193$		−	4.02507i		−	0.289731i	−0.989451	−	0.144865i	$-0.953725\pi$
$193$		−	4.02507i		−	0.289731i	0.989451	−	0.144865i	$-0.0462749\pi$
$194$	−0.713925	−	0.506931i	−0.0512568	−	0.0363955i
$195$	−4.21317	−	0.414961i	−0.301712	−	0.0297160i
$196$	8.11027	−	7.23762i	0.579305	−	0.516973i
$197$	6.79856	+	12.7192i	0.484377	+	0.906206i	0.998815	+	0.0486778i	$0.0155008\pi$
$197$	6.79856	+	12.7192i	0.484377	+	0.906206i	−0.514437	+	0.857528i	$0.671999\pi$
$198$	−7.04337	−	6.12317i	−0.500551	−	0.435155i
$199$	−4.08138	+	0.811838i	−0.289322	+	0.0575497i	−0.337617	−	0.941283i	$-0.609621\pi$
$199$	−4.08138	+	0.811838i	−0.289322	+	0.0575497i	0.0482957	+	0.998833i	$0.484621\pi$
$200$	8.18457	+	0.698980i	0.578736	+	0.0494254i
$201$	1.37420	−	6.90859i	0.0969289	−	0.487294i
$202$	−8.45445	−	1.07586i	−0.594853	−	0.0756972i
$203$	−20.6623	−	16.9571i	−1.45021	−	1.19016i
$204$	10.3289	+	1.61363i	0.723167	+	0.112976i
$205$	13.1415	+	7.02429i	0.917843	+	0.490597i
$206$	−3.69326	−	1.65417i	−0.257322	−	0.115252i
$207$	4.56839	−	1.89229i	0.317525	−	0.131523i
$208$	2.10490	+	11.5065i	0.145949	+	0.797835i
$209$	−2.22847	−	0.923063i	−0.154147	−	0.0638496i
$210$	4.95800	+	5.24792i	0.342135	+	0.362141i
$211$	8.30399	−	2.51899i	0.571670	−	0.173414i	0.00880246	−	0.999961i	$-0.497198\pi$
$211$	8.30399	−	2.51899i	0.571670	−	0.173414i	0.562868	+	0.826547i	$0.309698\pi$
$212$	−22.0660	−	8.08779i	−1.51550	−	0.555471i
$213$	0.699706	+	7.10423i	0.0479430	+	0.486774i
$214$	5.40017	+	19.8105i	0.369148	+	1.35422i
$215$	−2.46006	−	3.68174i	−0.167775	−	0.251093i
$216$	2.76668	−	0.587757i	0.188249	−	0.0399918i
$217$	−12.0078	−	8.02334i	−0.815141	−	0.544659i
$218$	−5.50627	+	2.74507i	−0.372931	+	0.185920i
$219$	12.9226	+	3.92002i	0.873226	+	0.264890i
$220$	−2.65785	−	18.9217i	−0.179192	−	1.27570i
$221$	9.69729	+	11.8162i	0.652310	+	0.794843i
$222$	−15.7031	−	3.58989i	−1.05392	−	0.240938i
$223$	−13.8982	−	13.8982i	−0.930690	−	0.930690i	0.0670588	−	0.997749i	$-0.478638\pi$
$223$	−13.8982	−	13.8982i	−0.930690	−	0.930690i	−0.997749	+	0.0670588i	$0.978638\pi$
$224$	10.1650	−	17.1638i	0.679178	−	1.14680i
$225$	2.05359	−	2.05359i	0.136906	−	0.136906i
$226$	−8.38282	+	5.26320i	−0.557617	+	0.350103i
$227$	−12.1616	+	9.98074i	−0.807191	+	0.662445i	−0.944656	−	0.328062i	$-0.893605\pi$
$227$	−12.1616	+	9.98074i	−0.807191	+	0.662445i	0.137465	+	0.990507i	$0.456105\pi$
$228$	0.629885	−	0.370968i	0.0417151	−	0.0245679i
$229$	−4.88546	+	16.1052i	−0.322840	+	1.06426i	0.633923	+	0.773396i	$0.281444\pi$
$229$	−4.88546	+	16.1052i	−0.322840	+	1.06426i	−0.956764	+	0.290866i	$0.906056\pi$
$230$	9.60036	+	3.21263i	0.633029	+	0.211834i
$231$	−12.9289	+	19.3495i	−0.850661	+	1.27310i
$232$	−19.9123	−	7.94676i	−1.30731	−	0.521731i
$233$	0.456538	−	0.305049i	0.0299088	−	0.0199844i	−0.540526	−	0.841327i	$-0.681775\pi$
$233$	0.456538	−	0.305049i	0.0299088	−	0.0199844i	0.570435	+	0.821343i	$0.306775\pi$
$234$	3.59052	+	2.05233i	0.234720	+	0.134165i
$235$	1.52694	−	0.150391i	0.0996067	−	0.00981040i
$236$	2.94001	+	2.70624i	0.191378	+	0.176162i
$237$	0.466343	+	1.53733i	0.0302922	+	0.0998600i
$238$	0.740177	−	26.0569i	0.0479786	−	1.68902i
$239$	7.01365	−	16.9325i	0.453676	−	1.09527i	−0.517238	−	0.855841i	$-0.673040\pi$
$239$	7.01365	−	16.9325i	0.453676	−	1.09527i	0.970914	−	0.239428i	$-0.0769600\pi$
$240$	5.06427	+	2.80815i	0.326897	+	0.181265i
$241$	−2.52091	−	6.08602i	−0.162386	−	0.392035i	0.821653	−	0.569989i	$-0.193052\pi$
$241$	−2.52091	−	6.08602i	−0.162386	−	0.392035i	−0.984039	+	0.177953i	$0.943052\pi$
$242$	43.0132	−	16.4018i	2.76499	−	1.05435i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	−13.1971	+	3.19777i	−0.844856	+	0.204716i
$245$	4.99156	−	6.08223i	0.318899	−	0.388580i
$246$	−8.91132	−	11.5100i	−0.568165	−	0.733851i
$247$	1.04833	+	0.208526i	0.0667036	+	0.0132682i
$248$	−11.1274	−	3.21834i	−0.706588	−	0.204365i
$249$	−2.36496	−	11.8894i	−0.149873	−	0.753463i
$250$	16.1432	−	1.12824i	1.02098	−	0.0713563i
$251$	−1.89051	+	1.01050i	−0.119328	+	0.0637821i	−0.529981	−	0.848010i	$-0.677801\pi$
$251$	−1.89051	+	1.01050i	−0.119328	+	0.0637821i	0.410653	+	0.911792i	$0.365301\pi$
$252$	−2.32471	−	6.65853i	−0.146443	−	0.419448i
$253$	−3.19852	+	32.4752i	−0.201090	+	2.04170i
$254$	1.98077	+	11.6826i	0.124285	+	0.733034i
$255$	7.56716			0.473874
$256$	3.60382	−	15.5889i	0.225239	−	0.974304i
$257$	7.13963			0.445358			0.222679	−	0.974892i	$-0.428520\pi$
$257$	7.13963			0.445358			0.222679	+	0.974892i	$0.428520\pi$
$258$	0.723083	+	4.26476i	0.0450172	+	0.265512i
$259$	−3.93694	+	39.9724i	−0.244630	+	2.48377i
$260$	2.79094	+	7.99392i	0.173087	+	0.495762i
$261$	−6.68497	+	3.57319i	−0.413789	+	0.221175i
$262$	9.59142	−	0.670341i	0.592560	−	0.0414138i
$263$	−2.21203	−	11.1206i	−0.136399	−	0.685726i	−0.987104	−	0.160081i	$-0.948824\pi$
$263$	−2.21203	−	11.1206i	−0.136399	−	0.685726i	0.850704	−	0.525644i	$-0.176176\pi$
$264$	−5.18609	+	17.9308i	−0.319182	+	1.10356i
$265$	−16.6845	−	3.31876i	−1.02492	−	0.203870i
$266$	−1.11588	−	1.44128i	−0.0684187	−	0.0883707i
$267$	−6.04935	+	7.37116i	−0.370214	+	0.451108i
$268$	−13.6917	+	3.31762i	−0.836351	+	0.202656i
$269$	3.93957	−	7.37041i	0.240200	−	0.449382i	−0.732718	−	0.680532i	$-0.761749\pi$
$269$	3.93957	−	7.37041i	0.240200	−	0.449382i	0.972918	+	0.231150i	$0.0742488\pi$
$270$	1.91297	−	0.729456i	0.116420	−	0.0443933i
$271$	−2.16211	−	5.21980i	−0.131339	−	0.317081i	0.844505	−	0.535547i	$-0.179895\pi$
$271$	−2.16211	−	5.21980i	−0.131339	−	0.317081i	−0.975844	+	0.218467i	$0.929895\pi$
$272$	−5.76016	−	20.0992i	−0.349261	−	1.21870i
$273$	3.94635	−	9.52733i	0.238844	−	0.576621i
$274$	−0.216192	+	7.61074i	−0.0130606	+	0.459782i
$275$	5.56356	+	18.3406i	0.335495	+	1.10598i
$276$	−7.27628	−	6.69773i	−0.437980	−	0.403156i
$277$	17.5183	−	1.72540i	1.05257	−	0.103669i	0.443097	−	0.896474i	$-0.353880\pi$
$277$	17.5183	−	1.72540i	1.05257	−	0.103669i	0.609477	+	0.792804i	$0.291380\pi$
$278$	6.84595	+	3.91312i	0.410593	+	0.234693i
$279$	−3.40517	+	2.27526i	−0.203862	+	0.136216i
$280$	5.35203	−	13.4106i	0.319845	−	0.801440i
$281$	−0.168566	+	0.252277i	−0.0100558	+	0.0150496i	−0.836463	−	0.548023i	$-0.815381\pi$
$281$	−0.168566	+	0.252277i	−0.0100558	+	0.0150496i	0.826408	+	0.563072i	$0.190381\pi$
$282$	−1.42138	−	0.475647i	−0.0846422	−	0.0283244i
$283$	3.86252	−	12.7330i	0.229603	−	0.756899i	−0.764125	−	0.645069i	$-0.776829\pi$
$283$	3.86252	−	12.7330i	0.229603	−	0.756899i	0.993727	−	0.111830i	$-0.0356712\pi$
$284$	12.3022	−	7.24532i	0.730001	−	0.429931i
$285$	0.409026	−	0.335679i	0.0242286	−	0.0198839i
$286$	−23.1145	+	14.5125i	−1.36679	+	0.858145i
$287$	−25.6656	+	25.6656i	−1.51499	+	1.51499i
$288$	−3.39368	−	4.52581i	−0.199975	−	0.266686i
$289$	−7.29907	−	7.29907i	−0.429357	−	0.429357i
$290$	−15.1285	−	3.45853i	−0.888376	−	0.203092i
$291$	0.392778	+	0.478601i	0.0230251	+	0.0280561i
$292$	−3.75683	−	26.7455i	−0.219852	−	1.56516i
$293$	−27.5198	−	8.34803i	−1.60772	−	0.487697i	−0.646371	−	0.763023i	$-0.723714\pi$
$293$	−27.5198	−	8.34803i	−1.60772	−	0.487697i	−0.961351	+	0.275326i	$0.911214\pi$
$294$	−6.87889	+	3.42937i	−0.401185	+	0.200005i
$295$	2.40495	+	1.60694i	0.140022	+	0.0935596i
$296$	6.69469	+	31.5132i	0.389121	+	1.83167i
$297$	3.66639	+	5.48714i	0.212746	+	0.318396i
$298$	−0.326439	−	1.19754i	−0.0189101	−	0.0693715i
$299$	−1.41737	−	14.3908i	−0.0819684	−	0.832239i
$300$	−5.45364	−	1.99891i	−0.314866	−	0.115407i
$301$	10.3215	−	3.13099i	0.594921	−	0.180467i
$302$	0.0706906	+	0.0748242i	0.00406779	+	0.00430565i
$303$	5.56768	+	2.30621i	0.319855	+	0.132488i
$304$	−1.20295	−	0.830899i	−0.0689941	−	0.0476553i
$305$	−9.08083	+	3.76140i	−0.519967	+	0.215377i
$306$	−6.74644	−	3.02166i	−0.385668	−	0.172737i
$307$	−17.2509	−	9.22079i	−0.984560	−	0.526259i	−0.101156	−	0.994871i	$-0.532254\pi$
$307$	−17.2509	−	9.22079i	−0.984560	−	0.526259i	−0.883404	+	0.468612i	$0.844754\pi$
$308$	45.9852	+	7.18400i	2.62025	+	0.409347i
$309$	2.21198	+	1.81532i	0.125835	+	0.103270i
$310$	−8.31749	−	1.05843i	−0.472402	−	0.0601148i
$311$	3.71423	−	18.6727i	0.210615	−	1.05883i	−0.720319	−	0.693643i	$-0.756004\pi$
$311$	3.71423	−	18.6727i	0.210615	−	1.05883i	0.930933	−	0.365189i	$-0.118996\pi$
$312$	0.703831	−	8.24136i	0.0398466	−	0.466575i
$313$	−29.8061	+	5.92880i	−1.68474	+	0.335116i	−0.942293	−	0.334789i	$-0.891335\pi$
$313$	−29.8061	+	5.92880i	−1.68474	+	0.335116i	−0.742447	+	0.669905i	$0.766335\pi$
$314$	−6.27095	−	5.45166i	−0.353890	−	0.307655i
$315$	−2.40649	−	4.50222i	−0.135590	−	0.253672i
$316$	2.39724	−	2.13930i	0.134855	−	0.120345i
$317$	1.90728	+	0.187851i	0.107124	+	0.0105508i	0.151437	−	0.988467i	$-0.451610\pi$
$317$	1.90728	+	0.187851i	0.107124	+	0.0105508i	−0.0443133	+	0.999018i	$0.514110\pi$
$318$	13.5497	+	9.62114i	0.759830	+	0.539527i
$319$		−	50.0229i		−	2.80075i
$320$	0.835643	−	11.5513i	0.0467139	−	0.645736i
$321$		−	14.5192i		−	0.810385i
$322$	−14.2768	+	20.1065i	−0.795617	+	1.12049i
$323$	−1.90132	−	0.187264i	−0.105792	−	0.0104196i
$324$	−1.99677	−	0.113533i	−0.110932	−	0.00630739i
$325$	−4.00357	−	7.49015i	−0.222078	−	0.415479i
$326$	−4.78569	+	5.50490i	−0.265055	+	0.304888i
$327$	4.26694	−	0.848748i	0.235963	−	0.0469359i
$328$	−13.3894	+	25.8513i	−0.739305	+	1.42740i
$329$	−0.729130	+	3.66559i	−0.0401983	+	0.202090i
$330$	−1.70557	+	13.4029i	−0.0938886	+	0.737807i
$331$	−15.6770	−	12.8658i	−0.861688	−	0.707169i	0.0958749	−	0.995393i	$-0.469435\pi$
$331$	−15.6770	−	12.8658i	−0.861688	−	0.707169i	−0.957563	+	0.288224i	$0.906935\pi$
$332$	−19.5843	+	14.2920i	−1.07483	+	0.784376i
$333$	10.0453	+	5.36932i	0.550479	+	0.294237i
$334$	−10.6338	+	23.7419i	−0.581854	+	1.29910i
$335$	−9.42115	+	3.90237i	−0.514733	+	0.213209i
$336$	−10.1266	+	9.81902i	−0.552451	+	0.535671i
$337$	33.1283	+	13.7222i	1.80462	+	0.747496i	0.984520	+	0.175270i	$0.0560798\pi$
$337$	33.1283	+	13.7222i	1.80462	+	0.747496i	0.820096	+	0.572226i	$0.193920\pi$
$338$	−4.57258	+	4.31997i	−0.248715	+	0.234976i
$339$	6.69766	−	2.03171i	0.363767	−	0.110348i
$340$	−6.36509	−	13.7307i	−0.345195	−	0.744654i
$341$	−2.64907	−	26.8965i	−0.143455	−	1.45653i
$342$	−0.498704	+	0.135943i	−0.0269668	+	0.00735093i
$343$	−3.06592	−	4.58847i	−0.165544	−	0.247754i
$344$	7.13026	−	4.89933i	0.384438	−	0.264154i
$345$	−5.95206	−	3.97704i	−0.320448	−	0.214117i
$346$	11.9757	+	24.0218i	0.643818	+	1.29142i
$347$	10.9543	+	3.32296i	0.588059	+	0.178386i	0.570272	−	0.821456i	$-0.306838\pi$
$347$	10.9543	+	3.32296i	0.588059	+	0.178386i	0.0177870	+	0.999842i	$0.494338\pi$
$348$	12.1066	+	9.12441i	0.648984	+	0.489120i
$349$	−4.28928	−	5.22651i	−0.229600	−	0.279769i	0.645448	−	0.763804i	$-0.276671\pi$
$349$	−4.28928	−	5.22651i	−0.229600	−	0.279769i	−0.875048	+	0.484035i	$0.839171\pi$
$350$	−3.22776	+	14.1191i	−0.172531	+	0.754695i
$351$	−2.06784	−	2.06784i	−0.110373	−	0.110373i
$352$	36.8980	−	5.67218i	1.96667	−	0.302328i
$353$	−2.51073	+	2.51073i	−0.133633	+	0.133633i	−0.770759	−	0.637126i	$-0.780123\pi$
$353$	−2.51073	+	2.51073i	−0.133633	+	0.133633i	0.637126	+	0.770759i	$0.280123\pi$
$354$	−1.50245	−	2.39298i	−0.0798541	−	0.127186i
$355$	7.98863	−	6.55610i	0.423992	−	0.347961i
$356$	18.4635	+	4.77644i	0.978563	+	0.253151i
$357$	−5.35067	+	17.6388i	−0.283187	+	0.933543i
$358$	−8.04136	+	24.0302i	−0.424999	+	1.27003i
$359$	0.565678	−	0.846597i	0.0298553	−	0.0446817i	−0.816242	−	0.577710i	$-0.803946\pi$
$359$	0.565678	−	0.846597i	0.0298553	−	0.0446817i	0.846097	+	0.533029i	$0.178946\pi$
$360$	−2.93270	−	2.85754i	−0.154567	−	0.150606i
$361$	15.6868	−	10.4816i	0.825623	−	0.551664i
$362$	−3.25284	+	5.69080i	−0.170965	+	0.299102i
$363$	−32.3944	+	3.19057i	−1.70026	+	0.167461i
$364$	−20.6070	+	0.853157i	−1.08010	+	0.0447176i
$365$	−5.67494	−	18.7078i	−0.297040	−	0.979210i
$366$	9.59791	+	0.272640i	0.501691	+	0.0142511i
$367$	−0.0475153	+	0.114712i	−0.00248028	+	0.00598792i	−0.925115	−	0.379687i	$-0.876032\pi$
$367$	−0.0475153	+	0.114712i	−0.00248028	+	0.00598792i	0.922635	+	0.385675i	$0.126032\pi$
$368$	−6.03274	+	18.8367i	−0.314478	+	0.981931i
$369$	3.93896	+	9.50950i	0.205054	+	0.495045i
$370$	8.30868	+	21.7892i	0.431948	+	1.13277i
$371$	19.5333	−	36.5443i	1.01412	−	1.89729i
$372$	6.99274	+	4.26491i	0.362557	+	0.221125i
$373$	−23.8312	+	29.0384i	−1.23393	+	1.50355i	−0.437024	+	0.899450i	$0.643967\pi$
$373$	−23.8312	+	29.0384i	−1.23393	+	1.50355i	−0.796908	+	0.604100i	$0.793533\pi$
$374$	38.5738	−	29.8648i	1.99461	−	1.54427i
$375$	−11.2229	−	2.23238i	−0.579549	−	0.115280i
$376$	0.332522	+	2.97922i	0.0171485	+	0.153641i
$377$	4.32451	+	21.7408i	0.222724	+	1.11971i
$378$	0.347692	+	4.97486i	0.0178833	+	0.255879i
$379$	15.2925	−	8.17403i	0.785525	−	0.419872i	−0.0293061	−	0.999570i	$-0.509330\pi$
$379$	15.2925	−	8.17403i	0.785525	−	0.419872i	0.814831	+	0.579699i	$0.196830\pi$
$380$	−0.953145	−	0.459829i	−0.0488953	−	0.0235887i
$381$	0.821263	−	8.33843i	0.0420746	−	0.427191i
$382$	3.77777	−	0.640514i	0.193287	−	0.0327715i
$383$	−5.47282			−0.279648			−0.139824	−	0.990176i	$-0.544654\pi$
$383$	−5.47282			−0.279648			−0.139824	+	0.990176i	$0.544654\pi$
$384$	−5.35758	+	9.96476i	−0.273403	+	0.508512i
$385$	33.6897			1.71699
$386$	5.61222	−	0.951541i	0.285654	−	0.0484322i
$387$	0.299803	−	3.04395i	0.0152398	−	0.154733i
$388$	0.538047	−	1.11528i	0.0273152	−	0.0566196i
$389$	−2.20561	+	1.17892i	−0.111829	+	0.0597737i	−0.526363	−	0.850260i	$-0.676445\pi$
$389$	−2.20561	+	1.17892i	−0.111829	+	0.0597737i	0.414534	+	0.910034i	$0.363945\pi$
$390$	−0.417422	−	5.97259i	−0.0211370	−	0.302434i
$391$	5.04247	+	25.3502i	0.255009	+	1.28202i
$392$	12.0088	+	9.59727i	0.606536	+	0.484735i
$393$	−6.66806	−	1.32636i	−0.336359	−	0.0669060i
$394$	−16.1274	+	12.4862i	−0.812485	+	0.629045i
$395$	1.47541	−	1.79779i	0.0742360	−	0.0904568i
$396$	6.87254	−	11.2682i	0.345358	−	0.566249i
$397$	−1.44341	+	2.70042i	−0.0724424	+	0.135530i	−0.915535	−	0.402238i	$-0.868232\pi$
$397$	−1.44341	+	2.70042i	−0.0724424	+	0.135530i	0.843093	+	0.537768i	$0.180732\pi$
$398$	−2.09681	−	5.49881i	−0.105104	−	0.275631i
$399$	0.493237	+	1.19078i	0.0246927	+	0.0596135i
$400$	0.960262	+	11.5771i	0.0480131	+	0.578855i
$401$	−14.9311	+	36.0470i	−0.745626	+	1.80010i	−0.164333	+	0.986405i	$0.552547\pi$
$401$	−14.9311	+	36.0470i	−0.745626	+	1.80010i	−0.581293	+	0.813694i	$0.697453\pi$
$402$	9.95761	+	0.282857i	0.496641	+	0.0141076i
$403$	3.47655	+	11.4606i	0.173179	+	0.570895i
$404$	−0.498576	−	12.0425i	−0.0248051	−	0.599137i
$405$	−1.44071	+	0.141898i	−0.0715895	+	0.00705095i
$406$	18.7589	−	32.8185i	0.930989	−	1.62875i
$407$	−62.4998	+	41.7611i	−3.09800	+	2.07002i
$408$	0.191886	+	14.7832i	0.00949975	+	0.731877i
$409$	−10.3954	+	15.5579i	−0.514021	+	0.769287i	−0.994161	−	0.107905i	$-0.965586\pi$
$409$	−10.3954	+	15.5579i	−0.514021	+	0.769287i	0.480140	+	0.877192i	$0.340586\pi$
$410$	−6.68736	+	19.9840i	−0.330265	+	0.986938i
$411$	1.56283	−	5.15196i	0.0770887	−	0.254127i
$412$	1.43334	−	5.54062i	0.0706155	−	0.272967i
$413$	−5.44624	+	4.46961i	−0.267992	+	0.219935i
$414$	3.71843	+	5.92243i	0.182751	+	0.291072i
$415$	−12.4093	+	12.4093i	−0.609147	+	0.609147i
$416$	−15.5461	+	5.65508i	−0.762211	+	0.277263i
$417$	−3.94270	−	3.94270i	−0.193075	−	0.193075i
$418$	0.760221	−	3.32540i	0.0371836	−	0.162651i
$419$	5.91259	+	7.20451i	0.288849	+	0.351963i	0.897137	−	0.441753i	$-0.145643\pi$
$419$	5.91259	+	7.20451i	0.288849	+	0.351963i	−0.608288	+	0.793717i	$0.708143\pi$
$420$	−6.14516	+	8.15364i	−0.299853	+	0.397857i
$421$	−2.66339	−	0.807931i	−0.129806	−	0.0393762i	0.224713	−	0.974425i	$-0.427855\pi$
$421$	−2.66339	−	0.807931i	−0.129806	−	0.0393762i	−0.354519	+	0.935049i	$0.615355\pi$
$422$	5.47535	+	10.9829i	0.266536	+	0.534638i
$423$	0.881235	+	0.588823i	0.0428471	+	0.0286295i
$424$	6.06043	−	32.6790i	0.294321	−	1.58703i
$425$	8.43388	+	12.6222i	0.409103	+	0.612266i
$426$	−9.74012	+	2.65508i	−0.471910	+	0.128639i
$427$	−2.34673	−	23.8267i	−0.113566	−	1.15306i
$428$	−26.3454	+	12.2128i	−1.27345	+	0.590328i
$429$	18.4679	−	5.60217i	0.891637	−	0.270475i
$430$	4.55194	−	4.30048i	0.219514	−	0.207388i
$431$	7.41153	+	3.06996i	0.357001	+	0.147875i	0.553973	−	0.832534i	$-0.313111\pi$
$431$	7.41153	+	3.06996i	0.357001	+	0.147875i	−0.196972	+	0.980409i	$0.563111\pi$
$432$	1.47357	+	3.71868i	0.0708973	+	0.178915i
$433$	15.9927	−	6.62438i	0.768558	−	0.318347i	0.0362701	−	0.999342i	$-0.488452\pi$
$433$	15.9927	−	6.62438i	0.768558	−	0.318347i	0.732288	+	0.680995i	$0.238452\pi$
$434$	8.34837	−	18.6394i	0.400735	−	0.894718i
$435$	9.67771	+	5.17284i	0.464011	+	0.248019i
$436$	−5.12919	−	7.02852i	−0.245644	−	0.336605i
$437$	1.39709	+	1.14656i	0.0668320	+	0.0548476i
$438$	−2.41080	+	18.9448i	−0.115192	+	0.905219i
$439$	4.65214	−	23.3879i	0.222035	−	1.11624i	−0.695481	−	0.718544i	$-0.744809\pi$
$439$	4.65214	−	23.3879i	0.222035	−	1.11624i	0.917516	−	0.397699i	$-0.130191\pi$
$440$	25.7545	−	8.17904i	1.22780	−	0.389920i
$441$	5.33063	−	1.06033i	0.253839	−	0.0504918i
$442$	−14.1830	+	16.3145i	−0.674617	+	0.776000i
$443$	9.75857	+	18.2570i	0.463644	+	0.867416i	0.999730	+	0.0232529i	$0.00740230\pi$
$443$	9.75857	+	18.2570i	0.463644	+	0.867416i	−0.536086	+	0.844163i	$0.680098\pi$
$444$	1.29317	−	22.7437i	0.0613710	−	1.07937i
$445$	13.7381	+	1.35309i	0.651250	+	0.0641425i
$446$	16.0928	−	22.6640i	0.762018	−	1.07317i
$447$			0.877684i			0.0415130i
$448$	26.3347	+	10.1156i	1.24420	+	0.477919i
$449$		−	7.40143i		−	0.349295i	−0.984631	−	0.174648i	$-0.944121\pi$
$449$		−	7.40143i		−	0.349295i	0.984631	−	0.174648i	$-0.0558786\pi$
$450$	3.34883	+	2.37787i	0.157865	+	0.112094i
$451$	−67.5999	−	6.65800i	−3.18315	−	0.313513i
$452$	−9.32029	−	10.4441i	−0.438390	−	0.491247i
$453$	−0.0343114	−	0.0641922i	−0.00161209	−	0.00301601i
$454$	−16.7913	−	14.5976i	−0.788056	−	0.685098i
$455$	−14.6421	+	2.91249i	−0.686432	+	0.136540i
$456$	0.666153	+	0.790559i	0.0311955	+	0.0370213i
$457$	−2.37264	+	11.9281i	−0.110988	+	0.557972i	0.884776	+	0.466017i	$0.154312\pi$
$457$	−2.37264	+	11.9281i	−0.110988	+	0.557972i	−0.995763	+	0.0919550i	$0.970688\pi$
$458$	−23.6107	−	3.00454i	−1.10325	−	0.140393i
$459$	4.04059	+	3.31603i	0.188599	+	0.154779i
$460$	−2.20986	+	14.1454i	−0.103035	+	0.659533i
$461$	−27.7294	−	14.8217i	−1.29149	−	0.690315i	−0.324681	−	0.945823i	$-0.605257\pi$
$461$	−27.7294	−	14.8217i	−1.29149	−	0.690315i	−0.966807	+	0.255509i	$0.917757\pi$
$462$	−30.0358	−	13.4527i	−1.39739	−	0.625877i
$463$	4.34404	−	1.79936i	0.201885	−	0.0836234i	−0.279450	−	0.960160i	$-0.590152\pi$
$463$	4.34404	−	1.79936i	0.201885	−	0.0836234i	0.481335	+	0.876537i	$0.340152\pi$
$464$	6.37295	−	29.6427i	0.295857	−	1.37613i
$465$	5.47748	+	2.26885i	0.254012	+	0.105215i
$466$	0.533261	+	0.564443i	0.0247028	+	0.0261473i
$467$	−30.5429	+	9.26507i	−1.41335	+	0.428736i	−0.902410	−	0.430877i	$-0.858204\pi$
$467$	−30.5429	+	9.26507i	−1.41335	+	0.428736i	−0.510944	+	0.859614i	$0.670704\pi$
$468$	−2.01278	+	5.49149i	−0.0930406	+	0.253844i
$469$	−2.43468	−	24.7197i	−0.112423	−	1.14145i
$470$	0.570666	+	2.09348i	0.0263229	+	0.0965652i
$471$	3.26431	+	4.88538i	0.150411	+	0.225107i
$472$	−3.07833	+	4.73906i	−0.141692	+	0.218133i
$473$	16.7834	+	11.2143i	0.771702	+	0.515635i
$474$	−2.03327	+	1.01366i	−0.0933912	+	0.0465588i
$475$	1.01579	+	0.308138i	0.0466078	+	0.0141383i
$476$	36.5066	−	5.12792i	1.67328	−	0.235038i
$477$	−7.45461	−	9.08346i	−0.341323	−	0.415903i
$478$	25.2672	+	5.77635i	1.15570	+	0.264204i
$479$	9.95147	+	9.95147i	0.454694	+	0.454694i	0.896909	−	0.442215i	$-0.145807\pi$
$479$	9.95147	+	9.95147i	0.454694	+	0.454694i	−0.442215	+	0.896909i	$0.645807\pi$
$480$	−2.71823	+	7.72505i	−0.124070	+	0.352598i
$481$	23.5532	−	23.5532i	1.07393	−	1.07393i
$482$	7.88988	−	4.95370i	0.359374	−	0.225635i
$483$	13.4790	−	11.0619i	0.613315	−	0.503335i
$484$	33.0378	+	56.0965i	1.50172	+	2.54984i
$485$	0.260187	−	0.857722i	0.0118145	−	0.0389472i
$486$	1.34112	+	0.448786i	0.0608342	+	0.0203573i
$487$	6.54685	−	9.79806i	0.296666	−	0.443992i	−0.652953	−	0.757398i	$-0.726470\pi$
$487$	6.54685	−	9.79806i	0.296666	−	0.443992i	0.949619	+	0.313406i	$0.101470\pi$
$488$	−7.57854	−	17.6449i	−0.343064	−	0.798747i
$489$	4.28859	−	2.86555i	0.193937	−	0.129584i
$490$	9.66057	+	5.52194i	0.436420	+	0.249456i
$491$	11.8769	−	1.16977i	0.535995	−	0.0527909i	0.173602	−	0.984816i	$-0.444460\pi$
$491$	11.8769	−	1.16977i	0.535995	−	0.0527909i	0.362394	+	0.932025i	$0.381960\pi$
$492$	13.9419	−	15.1462i	0.628550	−	0.682843i
$493$	−11.5015	−	37.9153i	−0.518000	−	1.70762i
$494$	−0.0429216	+	1.51100i	−0.00193113	+	0.0679830i
$495$	3.65606	−	8.82650i	0.164327	−	0.396722i
$496$	1.85683	−	16.2759i	0.0833743	−	0.730808i
$497$	9.63334	+	23.2569i	0.432114	+	1.04322i
$498$	16.0185	−	6.10820i	0.717808	−	0.273715i
$499$	−17.7094	+	33.1319i	−0.792781	+	1.48319i	0.0809172	+	0.996721i	$0.474215\pi$
$499$	−17.7094	+	33.1319i	−0.792781	+	1.48319i	−0.873698	+	0.486468i	$0.838285\pi$
$500$	5.38943	+	22.2419i	0.241023	+	0.994690i
$501$	11.6697	−	14.2196i	0.521364	−	0.635284i
$502$	−1.85588	−	2.39708i	−0.0828318	−	0.106987i
$503$	2.86027	+	0.568943i	0.127533	+	0.0253679i	0.258444	−	0.966026i	$-0.416790\pi$
$503$	2.86027	+	0.568943i	0.127533	+	0.0253679i	−0.130911	+	0.991394i	$0.541790\pi$
$504$	8.73451	−	4.81548i	0.389066	−	0.214498i
$505$	−1.70203	−	8.55669i	−0.0757394	−	0.380768i
$506$	−46.0367	+	3.21750i	−2.04658	+	0.143035i
$507$	3.92285	−	2.09680i	0.174220	−	0.0931224i
$508$	−15.8210	+	5.52364i	−0.701944	+	0.245072i
$509$	1.64613	−	16.7135i	0.0729636	−	0.740812i	−0.887202	−	0.461381i	$-0.847354\pi$
$509$	1.64613	−	16.7135i	0.0729636	−	0.740812i	0.960166	−	0.279431i	$-0.0901459\pi$
$510$	1.78890	+	10.5510i	0.0792140	+	0.467206i
$511$	47.6198			2.10658
$512$	22.5877	+	1.33960i	0.998246	+	0.0592024i
$513$	0.365504			0.0161374
$514$	1.68783	+	9.95489i	0.0744472	+	0.439091i
$515$	0.406042	−	4.12261i	0.0178923	−	0.181664i
$516$	−5.77548	+	2.01641i	−0.254251	+	0.0887675i
$517$	−6.16844	+	3.29710i	−0.271287	+	0.145006i
$518$	−56.6648	+	3.96029i	−2.48971	+	0.174005i
$519$	−3.70277	−	18.6151i	−0.162533	−	0.817111i
$520$	−10.4862	+	5.78124i	−0.459852	+	0.253524i
$521$	−29.5982	−	5.88745i	−1.29672	−	0.257934i	−0.501979	−	0.864880i	$-0.667395\pi$
$521$	−29.5982	−	5.88745i	−1.29672	−	0.257934i	−0.794743	+	0.606946i	$0.792395\pi$
$522$	−6.56250	−	8.47623i	−0.287233	−	0.370995i
$523$	−9.32242	+	11.3594i	−0.407641	+	0.496712i	−0.935848	−	0.352404i	$-0.885364\pi$
$523$	−9.32242	+	11.3594i	−0.407641	+	0.496712i	0.528207	+	0.849116i	$0.322864\pi$
$524$	3.20211	+	13.2150i	0.139885	+	0.577299i
$525$	4.82769	−	9.03197i	0.210698	−	0.394188i
$526$	14.9827	−	5.71321i	0.653276	−	0.249108i
$527$	−8.19203	−	19.7773i	−0.356850	−	0.861513i
$528$	−26.2272	−	2.99213i	−1.14139	−	0.130216i
$529$	0.555255	−	1.34050i	0.0241415	−	0.0582828i
$530$	0.683112	−	24.0480i	0.0296725	−	1.04458i
$531$	0.579978	+	1.91193i	0.0251689	+	0.0829707i
$532$	1.74580	−	1.89661i	0.0756902	−	0.0822283i
$533$	29.9556	−	2.95037i	1.29752	−	0.127795i
$534$	−11.7078	−	6.69213i	−0.506646	−	0.289597i
$535$	−17.4769	+	11.6777i	−0.755591	+	0.504870i
$536$	−7.86256	−	18.3062i	−0.339611	−	0.790707i
$537$	9.95473	−	14.8983i	0.429578	−	0.642909i
$538$	11.2080	+	3.75061i	0.483211	+	0.161700i
$539$	−10.4119	+	34.3233i	−0.448470	+	1.47841i
$540$	1.46932	+	2.49484i	0.0632297	+	0.107361i
$541$	−4.69382	+	3.85212i	−0.201803	+	0.165616i	−0.729867	−	0.683589i	$-0.760418\pi$
$541$	−4.69382	+	3.85212i	−0.201803	+	0.165616i	0.528064	+	0.849205i	$0.322918\pi$
$542$	6.76692	−	4.24865i	0.290664	−	0.182495i
$543$	3.27743	−	3.27743i	0.140648	−	0.140648i
$544$	26.6630	−	12.7830i	1.14316	−	0.548067i
$545$	−4.45350	−	4.45350i	−0.190767	−	0.190767i
$546$	14.2170	+	3.25016i	0.608433	+	0.139094i
$547$	−12.0069	−	14.6305i	−0.513379	−	0.625555i	0.450216	−	0.892920i	$-0.351347\pi$
$547$	−12.0069	−	14.6305i	−0.513379	−	0.625555i	−0.963595	+	0.267365i	$0.913847\pi$
$548$	−10.6629	+	1.49777i	−0.455496	+	0.0639815i
$549$	−6.49713	−	1.97088i	−0.277291	−	0.0841153i
$550$	−24.2573	+	12.0931i	−1.03434	+	0.515653i
$551$	−2.30360	−	1.53922i	−0.0981368	−	0.0655729i
$552$	7.61861	−	11.7288i	0.324270	−	0.499210i
$553$	3.14734	+	4.71033i	0.133839	+	0.200304i
$554$	6.54715	+	24.0182i	0.278162	+	1.02043i
$555$	−1.61625	−	16.4100i	−0.0686059	−	0.696568i
$556$	−3.83771	+	10.4705i	−0.162755	+	0.444047i
$557$	15.2308	−	4.62022i	0.645351	−	0.195765i	0.0493913	−	0.998780i	$-0.484272\pi$
$557$	15.2308	−	4.62022i	0.645351	−	0.195765i	0.595959	+	0.803014i	$0.296772\pi$
$558$	−3.97742	−	4.20999i	−0.168378	−	0.178223i
$559$	−8.26383	−	3.42299i	−0.349523	−	0.144777i
$560$	19.9639	+	4.29209i	0.843629	+	0.181374i
$561$	−31.8695	+	13.2008i	−1.34553	+	0.557337i
$562$	−0.391603	−	0.175395i	−0.0165188	−	0.00739859i
$563$	−23.6677	−	12.6507i	−0.997476	−	0.533162i	−0.109958	−	0.993936i	$-0.535072\pi$
$563$	−23.6677	−	12.6507i	−0.997476	−	0.533162i	−0.887517	+	0.460774i	$0.847572\pi$
$564$	0.327181	−	2.09430i	0.0137768	−	0.0881860i
$565$	−7.83244	−	6.42792i	−0.329513	−	0.270424i
$566$	18.6669	+	2.37543i	0.784630	+	0.0998469i
$567$	0.687954	−	3.45858i	0.0288914	−	0.145247i
$568$	13.0105	+	15.4403i	0.545910	+	0.647861i
$569$	−4.84846	+	0.964420i	−0.203258	+	0.0404306i	−0.295669	−	0.955290i	$-0.595543\pi$
$569$	−4.84846	+	0.964420i	−0.203258	+	0.0404306i	0.0924110	+	0.995721i	$0.470543\pi$
$570$	0.564737	+	0.490955i	0.0236542	+	0.0205638i
$571$	15.5113	+	29.0195i	0.649126	+	1.21443i	0.964153	+	0.265347i	$0.0854866\pi$
$571$	15.5113	+	29.0195i	0.649126	+	1.21443i	−0.315026	+	0.949083i	$0.602013\pi$
$572$	−25.6994	−	28.7980i	−1.07455	−	1.20411i
$573$	−2.69636	−	0.265569i	−0.112642	−	0.0110943i
$574$	−41.8533	−	29.7185i	−1.74692	−	1.24042i
$575$		−	14.3607i		−	0.598884i
$576$	5.50812	−	5.80178i	0.229505	−	0.241741i
$577$			17.3249i			0.721243i	0.932712	+	0.360622i	$0.117435\pi$
$577$			17.3249i			0.721243i	−0.932712	+	0.360622i	$0.882565\pi$
$578$	8.45167	−	11.9027i	0.351543	−	0.495088i
$579$	−4.00569	−	0.394526i	−0.166471	−	0.0163959i
$580$	1.24585	−	21.9115i	0.0517310	−	0.909825i
$581$	−20.1511	−	37.7000i	−0.836007	−	1.56406i
$582$	−0.574467	+	0.660799i	−0.0238124	+	0.0273910i
$583$	76.0571	−	15.1287i	3.14996	−	0.626567i
$584$	36.4036	−	11.5609i	1.50639	−	0.478395i
$585$	−0.825926	+	4.15221i	−0.0341478	+	0.171673i
$586$	5.13401	−	40.3447i	0.212084	−	1.66663i
$587$	−3.51352	−	2.88347i	−0.145019	−	0.119014i	0.559087	−	0.829109i	$-0.311152\pi$
$587$	−3.51352	−	2.88347i	−0.145019	−	0.119014i	−0.704106	+	0.710095i	$0.748652\pi$
$588$	−6.40782	−	8.78062i	−0.264254	−	0.362107i
$589$	−1.32012	−	0.705619i	−0.0543946	−	0.0290745i
$590$	−1.67204	+	3.73315i	−0.0688368	+	0.153691i
$591$	13.3243	−	5.51912i	0.548090	−	0.227026i
$592$	−42.3567	+	16.7843i	−1.74085	+	0.689832i
$593$	−2.90597	−	1.20369i	−0.119334	−	0.0494298i	0.322217	−	0.946666i	$-0.395572\pi$
$593$	−2.90597	−	1.20369i	−0.119334	−	0.0494298i	−0.441552	+	0.897236i	$0.645572\pi$
$594$	−6.78405	+	6.40928i	−0.278353	+	0.262976i
$595$	25.5354	−	7.74607i	1.04685	−	0.317558i
$596$	1.59257	−	0.738260i	0.0652343	−	0.0302403i
$597$	0.407883	+	4.14131i	0.0166935	+	0.169492i
$598$	19.7302	−	5.37828i	0.806827	−	0.219934i
$599$	−0.527098	−	0.788858i	−0.0215367	−	0.0322319i	0.820545	−	0.571582i	$-0.193670\pi$
$599$	−0.527098	−	0.788858i	−0.0215367	−	0.0322319i	−0.842082	+	0.539350i	$0.818670\pi$
$600$	1.49784	−	8.07664i	0.0611492	−	0.329728i
$601$	20.1693	+	13.4767i	0.822723	+	0.549726i	0.894175	−	0.447718i	$-0.147763\pi$
$601$	20.1693	+	13.4767i	0.822723	+	0.549726i	−0.0714521	+	0.997444i	$0.522763\pi$
$602$	6.80563	+	13.6512i	0.277377	+	0.556383i
$603$	−6.74063	−	2.04475i	−0.274500	−	0.0832685i
$604$	−0.0876169	+	0.116254i	−0.00356508	+	0.00473030i
$605$	29.8950	+	36.4271i	1.21540	+	1.48097i
$606$	−1.89936	+	8.30829i	−0.0771562	+	0.337501i
$607$	13.3535	+	13.3535i	0.542000	+	0.542000i	0.924115	−	0.382115i	$-0.124804\pi$
$607$	13.3535	+	13.3535i	0.542000	+	0.542000i	−0.382115	+	0.924115i	$0.624804\pi$
$608$	0.874152	−	1.87372i	0.0354515	−	0.0759895i
$609$	−18.9007	+	18.9007i	−0.765896	+	0.765896i
$610$	−7.39132	−	11.7723i	−0.299266	−	0.476648i
$611$	2.39587	−	1.96624i	0.0969265	−	0.0795455i
$612$	2.61826	−	10.1210i	0.105837	−	0.409117i
$613$	3.29705	−	10.8689i	0.133167	−	0.438992i	−0.864844	−	0.502041i	$-0.832583\pi$
$613$	3.29705	−	10.8689i	0.133167	−	0.438992i	0.998010	+	0.0630493i	$0.0200825\pi$
$614$	8.77852	−	26.2330i	0.354272	−	1.05868i
$615$	8.27856	−	12.3897i	0.333824	−	0.499602i
$616$	0.854292	+	65.8161i	0.0344204	+	2.65181i
$617$	22.4225	−	14.9823i	0.902697	−	0.603163i	−0.0152422	−	0.999884i	$-0.504852\pi$
$617$	22.4225	−	14.9823i	0.902697	−	0.603163i	0.917939	+	0.396721i	$0.129852\pi$
$618$	−2.00821	+	3.51334i	−0.0807821	+	0.141327i
$619$	38.7546	−	3.81700i	1.55768	−	0.153418i	0.717823	−	0.696226i	$-0.245139\pi$
$619$	38.7546	−	3.81700i	1.55768	−	0.153418i	0.839857	+	0.542808i	$0.182639\pi$
$620$	−0.490499	−	11.8474i	−0.0196989	−	0.475804i
$621$	−1.43540	−	4.73187i	−0.0576005	−	0.189883i
$622$	26.9137	+	0.764514i	1.07914	+	0.0306542i
$623$	−12.8681	+	31.0663i	−0.515549	+	1.24465i
$624$	11.6574	−	0.966926i	0.466671	−	0.0387080i
$625$	0.782381	+	1.88883i	0.0312952	+	0.0755534i
$626$	−15.3129	−	40.1575i	−0.612026	−	1.60502i
$627$	−1.13705	+	2.12726i	−0.0454093	+	0.0849547i
$628$	6.11885	−	10.0325i	0.244169	−	0.400339i
$629$	−37.7704	+	46.0233i	−1.50600	+	1.83507i
$630$	5.70861	−	4.41974i	0.227437	−	0.176087i
$631$	25.2787	+	5.02825i	1.00633	+	0.200171i	0.670626	−	0.741796i	$-0.266026\pi$
$631$	25.2787	+	5.02825i	1.00633	+	0.200171i	0.335704	+	0.941967i	$0.391026\pi$
$632$	3.54958	+	2.83677i	0.141195	+	0.112841i
$633$	−1.69292	−	8.51091i	−0.0672877	−	0.338278i
$634$	0.188965	+	2.70376i	0.00750476	+	0.107380i
$635$	−10.6975	+	5.71795i	−0.424519	+	0.226910i
$636$	−10.2117	+	21.1670i	−0.404920	+	0.839327i
$637$	1.55790	−	15.8176i	0.0617261	−	0.626716i
$638$	69.7477	−	11.8256i	2.76134	−	0.468180i
$639$	7.13861			0.282399
$640$	16.3037	−	1.56561i	0.644459	−	0.0618863i
$641$	22.0597			0.871308			0.435654	−	0.900114i	$-0.356517\pi$
$641$	22.0597			0.871308			0.435654	+	0.900114i	$0.356517\pi$
$642$	20.2444	−	3.43240i	0.798982	−	0.135466i
$643$	−2.90570	+	29.5021i	−0.114590	+	1.16345i	0.750163	+	0.661252i	$0.229975\pi$
$643$	−2.90570	+	29.5021i	−0.114590	+	1.16345i	−0.864753	+	0.502197i	$0.832525\pi$
$644$	−31.4098	−	15.1532i	−1.23772	−	0.597118i
$645$	−3.90514	+	2.08734i	−0.153765	+	0.0821891i
$646$	−0.188374	−	2.69531i	−0.00741149	−	0.106045i
$647$	−0.963473	−	4.84371i	−0.0378780	−	0.190426i	0.957214	−	0.289382i	$-0.0934497\pi$
$647$	−0.963473	−	4.84371i	−0.0378780	−	0.190426i	−0.995092	+	0.0989560i	$0.968450\pi$
$648$	−0.313744	−	2.81097i	−0.0123250	−	0.110425i
$649$	−12.9319	−	2.57231i	−0.507620	−	0.100972i
$650$	9.49717	−	7.35294i	0.372510	−	0.288406i
$651$	−9.16167	+	11.1635i	−0.359074	+	0.437533i
$652$	−8.80692	−	5.37138i	−0.344905	−	0.210360i
$653$	−2.97021	+	5.55688i	−0.116233	+	0.217458i	−0.933310	−	0.359072i	$-0.883093\pi$
$653$	−2.97021	+	5.55688i	−0.116233	+	0.217458i	0.817076	+	0.576529i	$0.195593\pi$
$654$	2.19214	+	5.74882i	0.0857196	+	0.224796i
$655$	3.76651	+	9.09315i	0.147170	+	0.355299i
$656$	−39.2102	−	12.5577i	−1.53090	−	0.490295i
$657$	5.16778	−	12.4761i	0.201614	−	0.486740i
$658$	−5.28335	−	0.150080i	−0.205966	−	0.00585071i
$659$	−7.34412	−	24.2103i	−0.286086	−	0.943101i	−0.975735	−	0.218956i	$-0.929735\pi$
$659$	−7.34412	−	24.2103i	−0.286086	−	0.943101i	0.689648	−	0.724145i	$-0.257765\pi$
$660$	−19.0911	+	0.790399i	−0.743121	+	0.0307662i
$661$	41.2018	−	4.05802i	1.60256	−	0.157839i	0.743152	−	0.669123i	$-0.233330\pi$
$661$	41.2018	−	4.05802i	1.60256	−	0.157839i	0.859412	+	0.511284i	$0.170830\pi$
$662$	14.2329	−	24.9002i	0.553177	−	0.967776i
$663$	12.7098	−	8.49241i	0.493607	−	0.329818i
$664$	−24.5574	−	23.9280i	−0.953011	−	0.928588i
$665$	1.03664	−	1.55144i	0.0401992	−	0.0601623i
$666$	−5.11178	+	15.2756i	−0.198077	+	0.591918i
$667$	−10.8803	+	35.8676i	−0.421287	+	1.38880i
$668$	−35.6176	−	9.21414i	−1.37809	−	0.356506i
$669$	−15.1935	+	12.4690i	−0.587415	+	0.482079i
$670$	−7.66833	−	12.2135i	−0.296253	−	0.471849i
$671$	31.6827	−	31.6827i	1.22310	−	1.22310i
$672$	−16.0848	−	11.7984i	−0.620483	−	0.455133i
$673$	−9.48973	−	9.48973i	−0.365802	−	0.365802i	0.500141	−	0.865944i	$-0.333281\pi$
$673$	−9.48973	−	9.48973i	−0.365802	−	0.365802i	−0.865944	+	0.500141i	$0.833281\pi$
$674$	−11.3014	+	49.4353i	−0.435314	+	1.90418i
$675$	−1.84241	−	2.24499i	−0.0709146	−	0.0864097i
$676$	−7.10437	−	5.35435i	−0.273245	−	0.205937i
$677$	−25.9765	−	7.87990i	−0.998359	−	0.302849i	−0.251519	−	0.967852i	$-0.580930\pi$
$677$	−25.9765	−	7.87990i	−0.998359	−	0.302849i	−0.746840	+	0.665003i	$0.768430\pi$
$678$	4.41620	+	8.85834i	0.169603	+	0.340203i
$679$	1.81534	+	1.21297i	0.0696665	+	0.0465497i
$680$	17.6403	−	12.1209i	0.676473	−	0.464817i
$681$	8.74064	+	13.0813i	0.334942	+	0.501276i
$682$	36.8759	−	10.0521i	1.41205	−	0.384913i
$683$	−2.84255	−	28.8609i	−0.108767	−	1.10433i	−0.882336	−	0.470620i	$-0.844030\pi$
$683$	−2.84255	−	28.8609i	−0.108767	−	1.10433i	0.773569	−	0.633712i	$-0.218470\pi$
$684$	−0.307442	−	0.663213i	−0.0117553	−	0.0253586i
$685$	−7.45840	+	2.26248i	−0.284971	+	0.0864449i
$686$	5.67298	−	5.35959i	0.216595	−	0.204630i
$687$	15.5488	+	6.44053i	0.593224	+	0.245721i
$688$	8.51683	+	8.78361i	0.324701	+	0.334872i
$689$	−31.7478	+	13.1504i	−1.20949	+	0.500989i
$690$	4.13816	−	9.23924i	0.157537	−	0.351732i
$691$	37.5342	+	20.0624i	1.42787	+	0.763211i	0.990686	−	0.136163i	$-0.0434772\pi$
$691$	37.5342	+	20.0624i	1.42787	+	0.763211i	0.437180	+	0.899374i	$0.355977\pi$
$692$	−30.6628	+	22.3767i	−1.16562	+	0.850636i
$693$	17.9891	+	14.7633i	0.683349	+	0.560810i
$694$	−2.04361	+	16.0593i	−0.0775743	+	0.609604i
$695$	−1.57477	+	7.91691i	−0.0597345	+	0.300306i
$696$	−9.86025	+	19.0375i	−0.373752	+	0.721615i
$697$	−52.7687	+	10.4963i	−1.99876	+	0.397577i
$698$	6.27339	−	7.21618i	0.237451	−	0.273136i
$699$	−0.258831	−	0.484239i	−0.00978990	−	0.0183156i
$700$	−20.4495	−	1.16272i	−0.772917	−	0.0439466i
$701$	−33.0544	−	3.25557i	−1.24845	−	0.122961i	−0.547885	−	0.836553i	$-0.684567\pi$
$701$	−33.0544	−	3.25557i	−1.24845	−	0.122961i	−0.700561	+	0.713592i	$0.747067\pi$
$702$	2.39438	−	3.37207i	0.0903699	−	0.127270i
$703$			4.16317i			0.157017i
$704$	16.6316	+	50.1065i	0.626828	+	1.88846i
$705$		−	1.53433i		−	0.0577862i
$706$	−4.09430	−	2.90720i	−0.154091	−	0.109414i
$707$	21.1488	+	2.08298i	0.795383	+	0.0783384i
$708$	2.98138	−	2.66059i	0.112047	−	0.0999912i
$709$	0.773853	+	1.44778i	0.0290626	+	0.0543724i	0.896033	−	0.443987i	$-0.146436\pi$
$709$	0.773853	+	1.44778i	0.0290626	+	0.0543724i	−0.866971	+	0.498359i	$0.833936\pi$
$710$	11.0298	+	9.58877i	0.413941	+	0.359860i
$711$	1.57563	−	0.313413i	0.0590908	−	0.0117539i
$712$	−2.29502	+	26.8731i	−0.0860095	+	1.00711i
$713$	−3.95071	+	19.8616i	−0.147955	+	0.743822i
$714$	−25.8589	−	3.29064i	−0.967746	−	0.123149i
$715$	−21.5969	−	17.7241i	−0.807677	−	0.662843i
$716$	−35.4066	−	5.53138i	−1.32321	−	0.206717i
$717$	−16.1635	−	8.63955i	−0.603636	−	0.322650i
$718$	1.31415	+	0.588595i	0.0490437	+	0.0219662i
$719$	13.4078	−	5.55368i	0.500026	−	0.207117i	−0.118392	−	0.992967i	$-0.537774\pi$
$719$	13.4078	−	5.55368i	0.500026	−	0.207117i	0.618418	+	0.785849i	$0.287774\pi$
$720$	3.29101	−	4.76464i	0.122649	−	0.177568i
$721$	9.32254	+	3.86152i	0.347190	+	0.143811i
$722$	18.3231	+	19.3945i	0.681915	+	0.721789i
$723$	−6.30381	+	1.91224i	−0.234441	+	0.0711170i
$724$	−8.70375	−	3.19015i	−0.323472	−	0.118561i
$725$	2.15775	+	21.9080i	0.0801366	+	0.813641i
$726$	−12.1068	−	44.4137i	−0.449326	−	1.64835i
$727$	6.96454	+	10.4232i	0.258300	+	0.386574i	0.937842	−	0.347064i	$-0.112821\pi$
$727$	6.96454	+	10.4232i	0.258300	+	0.386574i	−0.679541	+	0.733637i	$0.737821\pi$
$728$	−6.06113	−	28.5309i	−0.224640	−	1.05743i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	24.7430	−	12.3352i	0.915778	−	0.456548i
$731$	15.2995	+	4.64107i	0.565874	+	0.171656i
$732$	1.88884	+	13.4470i	0.0698134	+	0.497014i
$733$	20.3839	+	24.8378i	0.752895	+	0.917405i	0.998651	−	0.0519264i	$-0.0165361\pi$
$733$	20.3839	+	24.8378i	0.752895	+	0.917405i	−0.245756	+	0.969332i	$0.579036\pi$
$734$	−0.171177	−	0.0391329i	−0.00631827	−	0.00144442i
$735$	−5.56369	−	5.56369i	−0.205220	−	0.205220i
$736$	−27.6904	−	3.95848i	−1.02068	−	0.145911i
$737$	32.8700	−	32.8700i	1.21078	−	1.21078i
$738$	−12.3280	+	7.74023i	−0.453802	+	0.284922i
$739$	−28.1500	+	23.1021i	−1.03552	+	0.849826i	−0.988825	−	0.149084i	$-0.952368\pi$
$739$	−28.1500	+	23.1021i	−1.03552	+	0.849826i	−0.0466910	+	0.998909i	$0.514868\pi$
$740$	−28.4168	+	16.7360i	−1.04462	+	0.615226i
$741$	0.310276	−	1.02284i	0.0113983	−	0.0375751i
$742$	55.5720	+	18.5964i	2.04011	+	0.682696i
$743$	−9.67872	+	14.4852i	−0.355078	+	0.531411i	−0.965411	−	0.260733i	$-0.916036\pi$
$743$	−9.67872	+	14.4852i	−0.355078	+	0.531411i	0.610333	+	0.792145i	$0.291036\pi$
$744$	−4.29352	+	10.7583i	−0.157408	+	0.394419i
$745$	1.05647	−	0.705912i	0.0387061	−	0.0258626i
$746$	−46.1224	−	26.3634i	−1.68866	−	0.965232i
$747$	−12.0640	+	1.18820i	−0.441399	+	0.0434740i
$748$	50.7599	+	46.7239i	1.85597	+	1.70840i
$749$	−14.8625	−	48.9951i	−0.543064	−	1.79024i
$750$	0.459499	−	16.1760i	0.0167785	−	0.590665i
$751$	−5.95613	+	14.3794i	−0.217342	+	0.524711i	−0.994517	−	0.104574i	$-0.966652\pi$
$751$	−5.95613	+	14.3794i	−0.217342	+	0.524711i	0.777175	+	0.629285i	$0.216652\pi$
$752$	−4.07536	+	1.16794i	−0.148613	+	0.0425903i
$753$	0.820330	+	1.98045i	0.0298945	+	0.0721717i
$754$	−29.2912	+	11.1693i	−1.06672	+	0.406763i
$755$	−0.0496721	+	0.0929299i	−0.00180775	+	0.00338207i
$756$	−6.85432	+	1.66087i	−0.249289	+	0.0604051i
$757$	25.5218	−	31.0984i	0.927604	−	1.13029i	−0.0636038	−	0.997975i	$-0.520259\pi$
$757$	25.5218	−	31.0984i	0.927604	−	1.13029i	0.991208	−	0.132314i	$-0.0422406\pi$
$758$	15.0124	+	19.3902i	0.545274	+	0.704285i
$759$	32.0053	+	6.36625i	1.16172	+	0.231080i
$760$	0.415820	−	1.43769i	0.0150834	−	0.0521505i
$761$	3.28999	+	16.5399i	0.119262	+	0.599571i	0.993477	+	0.114032i	$0.0363766\pi$
$761$	3.28999	+	16.5399i	0.119262	+	0.599571i	−0.874215	+	0.485539i	$0.838623\pi$
$762$	11.8205	−	0.826134i	0.428213	−	0.0299277i
$763$	13.5300	−	7.23192i	0.489818	−	0.261813i
$764$	1.78616	+	5.11598i	0.0646209	+	0.185090i
$765$	0.741712	−	7.53073i	0.0268166	−	0.272274i
$766$	−1.29379	−	7.63083i	−0.0467467	−	0.275713i
$767$	5.84278			0.210970
$768$	−15.1606	−	5.11444i	−0.547059	−	0.184552i
$769$	−2.32400			−0.0838056			−0.0419028	−	0.999122i	$-0.513342\pi$
$769$	−2.32400			−0.0838056			−0.0419028	+	0.999122i	$0.513342\pi$
$770$	7.96436	+	46.9740i	0.287016	+	1.69283i
$771$	0.699806	−	7.10525i	0.0252029	−	0.255889i
$772$	2.65350	+	7.60025i	0.0955014	+	0.273539i
$773$	18.4698	−	9.87231i	0.664312	−	0.355082i	−0.104529	−	0.994522i	$-0.533334\pi$
$773$	18.4698	−	9.87231i	0.664312	−	0.355082i	0.768841	+	0.639439i	$0.220834\pi$
$774$	4.31510	−	0.301581i	0.155103	−	0.0108401i
$775$	2.32037	+	11.6653i	0.0833500	+	0.419029i
$776$	1.68224	+	0.486551i	0.0603890	+	0.0174662i
$777$	39.3941	+	7.83596i	1.41325	+	0.281114i
$778$	−2.16520	−	2.79661i	−0.0776262	−	0.100263i
$779$	−2.38667	+	2.90817i	−0.0855114	+	0.104196i
$780$	8.22898	−	1.99396i	0.294645	−	0.0713952i
$781$	−22.2075	+	41.5473i	−0.794647	+	1.48668i
$782$	−34.1541	+	13.0237i	−1.22135	+	0.465726i
$783$	2.90074	+	7.00301i	0.103664	+	0.250267i
$784$	−10.5427	+	19.0129i	−0.376524	+	0.679032i
$785$	3.25511	−	7.85852i	0.116180	−	0.280483i
$786$	0.273010	−	9.61094i	0.00973793	−	0.342811i
$787$	1.39283	+	4.59154i	0.0496489	+	0.163671i	0.978259	−	0.207386i	$-0.0664956\pi$
$787$	1.39283	+	4.59154i	0.0496489	+	0.163671i	−0.928610	+	0.371057i	$0.878996\pi$
$788$	−21.2222	−	19.5348i	−0.756011	−	0.695900i
$789$	−11.2839	+	1.11136i	−0.401716	+	0.0395656i
$790$	2.85548	+	1.63218i	0.101593	+	0.0580704i
$791$	20.5215	−	13.7120i	0.729660	−	0.487543i
$792$	17.3361	+	6.91864i	0.616013	+	0.245843i
$793$	−11.0308	+	16.5088i	−0.391716	+	0.586245i
$794$	−4.10646	−	1.37417i	−0.145733	−	0.0487675i
$795$	−4.93814	+	16.2789i	−0.175138	+	0.577352i
$796$	7.17138	−	4.22355i	0.254183	−	0.149700i
$797$	−4.54655	+	3.73126i	−0.161047	+	0.132168i	−0.711466	−	0.702721i	$-0.751968\pi$
$797$	−4.54655	+	3.73126i	−0.161047	+	0.132168i	0.550418	+	0.834889i	$0.314468\pi$
$798$	−1.54372	+	0.969232i	−0.0546470	+	0.0343104i
$799$	−3.91733	+	3.91733i	−0.138585	+	0.138585i
$800$	−15.9151	+	4.07578i	−0.562684	+	0.144100i
$801$	6.74272	+	6.74272i	0.238242	+	0.238242i
$802$	−53.7906	−	12.2971i	−1.89941	−	0.434225i
$803$	56.5356	+	68.8889i	1.99510	+	2.43104i
$804$	1.95962	+	13.9509i	0.0691106	+	0.492011i
$805$	−24.1563	−	7.32773i	−0.851397	−	0.258268i
$806$	−15.1579	+	7.55674i	−0.533913	+	0.266175i
$807$	−6.94878	−	4.64302i	−0.244609	−	0.163442i
$808$	16.6732	−	3.54206i	0.586560	−	0.124609i
$809$	12.4445	+	18.6245i	0.437524	+	0.654801i	0.983059	−	0.183287i	$-0.0586737\pi$
$809$	12.4445	+	18.6245i	0.437524	+	0.654801i	−0.545535	+	0.838088i	$0.683674\pi$
$810$	−0.538439	−	1.97526i	−0.0189188	−	0.0694036i
$811$	−2.13305	−	21.6572i	−0.0749014	−	0.760487i	−0.957129	−	0.289663i	$-0.906457\pi$
$811$	−2.13305	−	21.6572i	−0.0749014	−	0.760487i	0.882227	−	0.470824i	$-0.156043\pi$
$812$	50.1939	+	18.3974i	1.76146	+	0.645623i
$813$	−5.40659	+	1.64007i	−0.189618	+	0.0575198i
$814$	−73.0032	−	77.2720i	−2.55876	−	2.70838i
$815$	−6.89854	−	2.85747i	−0.241645	−	0.100093i
$816$	−20.5671	+	3.76235i	−0.719991	+	0.131709i
$817$	1.03286	−	0.427824i	0.0361352	−	0.0149677i
$818$	−24.1501	−	10.8166i	−0.844388	−	0.378193i
$819$	−9.09465	−	4.86119i	−0.317793	−	0.169864i
$820$	−29.4449	−	4.60001i	−1.02826	−	0.160639i
$821$	4.48517	+	3.68089i	0.156534	+	0.128464i	0.709400	−	0.704806i	$-0.248966\pi$
$821$	4.48517	+	3.68089i	0.156534	+	0.128464i	−0.552866	+	0.833270i	$0.686466\pi$
$822$	7.55291	+	0.961134i	0.263438	+	0.0335234i
$823$	5.54523	−	27.8777i	0.193295	−	0.971757i	−0.755328	−	0.655347i	$-0.772522\pi$
$823$	5.54523	−	27.8777i	0.193295	−	0.971757i	0.948622	−	0.316410i	$-0.102478\pi$
$824$	8.06421	+	0.688702i	0.280930	+	0.0239921i
$825$	18.7976	−	3.73908i	0.654449	−	0.130178i
$826$	−7.51955	−	6.53714i	−0.261639	−	0.227456i
$827$	−2.85637	−	5.34389i	−0.0993256	−	0.185825i	0.827351	−	0.561686i	$-0.189847\pi$
$827$	−2.85637	−	5.34389i	−0.0993256	−	0.185825i	−0.926676	+	0.375861i	$0.877347\pi$
$828$	−7.37868	+	6.58475i	−0.256427	+	0.228836i
$829$	−26.8519	−	2.64468i	−0.932606	−	0.0918537i	−0.379712	−	0.925105i	$-0.623977\pi$
$829$	−26.8519	−	2.64468i	−0.932606	−	0.0918537i	−0.552895	+	0.833251i	$0.686477\pi$
$830$	−20.2360	−	14.3688i	−0.702402	−	0.498749i
$831$		−	17.6031i		−	0.610644i
$832$	−11.5601	−	20.3393i	−0.400775	−	0.705139i
$833$			28.4095i			0.984332i
$834$	4.56529	−	6.42943i	0.158083	−	0.222633i
$835$	−26.5020	−	2.61022i	−0.917139	−	0.0903303i
$836$	4.81638	+	0.273850i	0.166578	+	0.00947132i
$837$	1.93054	+	3.61178i	0.0667292	+	0.124842i
$838$	−8.64759	+	9.94718i	−0.298726	+	0.343620i
$839$	45.8041	−	9.11100i	1.58133	−	0.314547i	0.675231	−	0.737606i	$-0.264044\pi$
$839$	45.8041	−	9.11100i	1.58133	−	0.314547i	0.906102	+	0.423060i	$0.139044\pi$
$840$	−12.8215	−	6.64073i	−0.442383	−	0.229127i
$841$	5.55157	−	27.9097i	0.191434	−	0.962402i
$842$	0.496875	−	3.90461i	0.0171234	−	0.134562i
$843$	0.234540	+	0.192482i	0.00807798	+	0.00662943i
$844$	−14.0192	+	10.2308i	−0.482560	+	0.352157i
$845$	−5.67904	−	3.03551i	−0.195365	−	0.104425i
$846$	−0.612677	+	1.36792i	−0.0210643	+	0.0470300i
$847$	−106.049	+	43.9268i	−3.64388	+	1.50934i
$848$	46.9975	+	0.724723i	1.61390	+	0.0248871i
$849$	−12.2931	−	5.09197i	−0.421898	−	0.174756i
$850$	−15.6055	+	14.7434i	−0.535265	+	0.505695i
$851$	53.8971	−	16.3495i	1.84757	−	0.560454i
$852$	−6.00461	−	12.9531i	−0.205715	−	0.443767i
$853$	−4.63452	−	47.0550i	−0.158683	−	1.61113i	−0.663683	−	0.748014i	$-0.731008\pi$
$853$	−4.63452	−	47.0550i	−0.158683	−	1.61113i	0.505000	−	0.863119i	$-0.331492\pi$
$854$	32.6672	−	8.90480i	1.11785	−	0.304716i
$855$	−0.293971	−	0.439958i	−0.0100536	−	0.0150463i
$856$	−23.2566	−	33.8466i	−0.794895	−	1.15685i
$857$	−34.8620	−	23.2940i	−1.19086	−	0.795709i	−0.207656	−	0.978202i	$-0.566583\pi$
$857$	−34.8620	−	23.2940i	−1.19086	−	0.795709i	−0.983207	+	0.182493i	$0.941583\pi$
$858$	12.1771	+	24.4256i	0.415718	+	0.833878i
$859$	12.0600	+	3.65835i	0.411481	+	0.124821i	0.489237	−	0.872151i	$-0.337275\pi$
$859$	12.0600	+	3.65835i	0.411481	+	0.124821i	−0.0777558	+	0.996972i	$0.524775\pi$
$860$	7.07232	+	5.33019i	0.241164	+	0.181758i
$861$	23.0263	+	28.0577i	0.784735	+	0.956203i
$862$	−2.52837	+	11.0598i	−0.0861167	+	0.376697i
$863$	31.3811	+	31.3811i	1.06823	+	1.06823i	0.997495	+	0.0707303i	$0.0225330\pi$
$863$	31.3811	+	31.3811i	1.06823	+	1.06823i	0.0707303	+	0.997495i	$0.477467\pi$
$864$	−4.83665	+	2.93373i	−0.164546	+	0.0998076i
$865$	−19.4289	+	19.4289i	−0.660604	+	0.660604i
$866$	13.0172	+	20.7328i	0.442342	+	0.704529i
$867$	−7.97936	+	6.54849i	−0.270993	+	0.222398i
$868$	27.9627	+	7.23385i	0.949116	+	0.245533i
$869$	−3.07755	+	10.1453i	−0.104399	+	0.344156i
$870$	−4.92473	+	14.7166i	−0.166964	+	0.498941i
$871$	−11.4442	+	17.1275i	−0.387773	+	0.580343i
$872$	8.58741	−	8.81327i	0.290807	−	0.298455i
$873$	0.514796	−	0.343975i	0.0174232	−	0.0116418i
$874$	−1.26839	+	2.21904i	−0.0429040	+	0.0750601i
$875$	−40.1569	+	3.95511i	−1.35755	+	0.133707i
$876$	−26.9850	+	1.11722i	−0.911738	+	0.0377472i
$877$	6.54295	+	21.5692i	0.220940	+	0.728340i	0.995408	+	0.0957271i	$0.0305176\pi$
$877$	6.54295	+	21.5692i	0.220940	+	0.728340i	−0.774468	+	0.632613i	$0.781982\pi$
$878$	33.7099	+	0.957568i	1.13765	+	0.0323163i
$879$	−11.0052	+	26.5690i	−0.371198	+	0.896150i
$880$	17.4926	+	33.9763i	0.589676	+	1.14534i
$881$	16.4362	+	39.6805i	0.553750	+	1.33687i	0.914643	+	0.404263i	$0.132472\pi$
$881$	16.4362	+	39.6805i	0.553750	+	1.33687i	−0.360893	+	0.932607i	$0.617528\pi$
$882$	2.73861	+	7.18191i	0.0922138	+	0.241827i
$883$	12.1241	−	22.6826i	0.408008	−	0.763330i	−0.591054	−	0.806632i	$-0.701288\pi$
$883$	12.1241	−	22.6826i	0.408008	−	0.763330i	0.999062	+	0.0433023i	$0.0137879\pi$
$884$	−26.1004	−	15.9188i	−0.877852	−	0.535406i
$885$	1.83493	−	2.23587i	0.0616804	−	0.0751578i
$886$	−23.1490	+	17.9225i	−0.777707	+	0.602119i
$887$	2.26393	+	0.450325i	0.0760155	+	0.0151204i	0.232952	−	0.972488i	$-0.425162\pi$
$887$	2.26393	+	0.450325i	0.0760155	+	0.0151204i	−0.156936	+	0.987609i	$0.550162\pi$
$888$	32.0176	−	3.57362i	1.07444	−	0.119923i
$889$	−5.76421	−	28.9787i	−0.193326	−	0.971913i
$890$	1.36111	+	19.4751i	0.0456246	+	0.652808i
$891$	5.82009	−	3.11090i	0.194980	−	0.104219i
$892$	35.4051	+	17.0806i	1.18545	+	0.571902i
$893$	−0.0379699	+	0.385515i	−0.00127061	+	0.0129008i
$894$	−1.22377	+	0.207488i	−0.0409289	+	0.00693942i
$895$	−25.9396			−0.867066
$896$	−7.87877	+	39.1103i	−0.263211	+	1.30658i
$897$	−14.4604			−0.482818
$898$	10.3199	−	1.74972i	0.344380	−	0.0583891i
$899$	3.04273	−	30.8934i	0.101481	−	1.03035i
$900$	−2.52383	+	5.23146i	−0.0841277	+	0.174382i
$901$	54.1696	−	28.9543i	1.80465	−	0.964606i
$902$	−6.69749	−	95.8294i	−0.223002	−	3.19077i
$903$	−2.10423	−	10.5787i	−0.0700244	−	0.352037i
$904$	12.3589	−	15.4644i	0.411052	−	0.514339i
$905$	−6.58105	−	1.30905i	−0.218762	−	0.0435144i
$906$	0.0813928	−	0.0630162i	0.00270409	−	0.00209357i
$907$	−2.45422	+	2.99048i	−0.0814911	+	0.0992972i	−0.812160	−	0.583435i	$-0.801708\pi$
$907$	−2.45422	+	2.99048i	−0.0814911	+	0.0992972i	0.730669	+	0.682732i	$0.239208\pi$
$908$	16.3841	−	26.8633i	0.543724	−	0.891490i
$909$	2.84083	−	5.31482i	0.0942244	−	0.176281i
$910$	−7.52238	−	19.7272i	−0.249364	−	0.653949i
$911$	−1.62060	−	3.91248i	−0.0536930	−	0.129626i	0.894757	−	0.446554i	$-0.147349\pi$
$911$	−1.62060	−	3.91248i	−0.0536930	−	0.129626i	−0.948450	+	0.316927i	$0.897349\pi$
$912$	−0.944808	+	1.11572i	−0.0312857	+	0.0369451i
$913$	30.6145	−	73.9099i	1.01319	−	2.44606i
$914$	−17.1924	−	0.488370i	−0.568674	−	0.0161538i
$915$	2.85321	+	9.40579i	0.0943244	+	0.310946i
$916$	−1.39237	−	33.6310i	−0.0460052	−	1.11120i
$917$	−23.8591	+	2.34991i	−0.787896	+	0.0776010i
$918$	−3.66838	+	6.41778i	−0.121074	+	0.211818i
$919$	8.49162	−	5.67392i	0.280113	−	0.187165i	−0.407575	−	0.913172i	$-0.633626\pi$
$919$	8.49162	−	5.67392i	0.280113	−	0.187165i	0.687688	+	0.726006i	$0.258626\pi$
$920$	−20.2456	+	0.262787i	−0.667476	+	0.00866383i
$921$	−10.8673	+	16.2640i	−0.358089	+	0.535918i
$922$	14.1108	−	42.1674i	0.464713	−	1.38871i
$923$	6.05996	−	19.9770i	0.199466	−	0.657551i
$924$	11.6567	−	45.0596i	0.383479	−	1.48235i
$925$	25.5710	−	20.9855i	0.840768	−	0.690000i
$926$	3.53582	+	5.63159i	0.116194	+	0.185065i
$927$	2.02339	−	2.02339i	0.0664569	−	0.0664569i
$928$	42.8378	+	1.87826i	1.40622	+	0.0616569i
$929$	−28.2830	−	28.2830i	−0.927936	−	0.927936i	0.0696368	−	0.997572i	$-0.477816\pi$
$929$	−28.2830	−	28.2830i	−0.927936	−	0.927936i	−0.997572	+	0.0696368i	$0.977816\pi$
$930$	−1.86859	+	8.17369i	−0.0612735	+	0.268026i
$931$	1.26024	+	1.53561i	0.0413028	+	0.0503277i
$932$	−0.660946	+	0.876970i	−0.0216500	+	0.0287261i
$933$	−18.2187	−	5.52659i	−0.596455	−	0.180933i
$934$	−20.1389	−	40.3961i	−0.658964	−	1.32180i
$935$	41.5221	+	27.7442i	1.35792	+	0.907332i
$936$	−8.13269	−	1.50824i	−0.265825	−	0.0492983i
$937$	33.1748	+	49.6496i	1.08377	+	1.62198i	0.725286	+	0.688448i	$0.241708\pi$
$937$	33.1748	+	49.6496i	1.08377	+	1.62198i	0.358488	+	0.933534i	$0.383292\pi$
$938$	33.8915	−	9.23853i	1.10660	−	0.301649i
$939$	2.97874	+	30.2437i	0.0972076	+	0.986966i
$940$	−2.78407	+	1.29060i	−0.0908063	+	0.0420946i
$941$	−26.2340	+	7.95799i	−0.855203	+	0.259423i	−0.687294	−	0.726380i	$-0.741201\pi$
$941$	−26.2340	+	7.95799i	−0.855203	+	0.259423i	−0.167909	+	0.985802i	$0.553701\pi$
$942$	−6.04007	+	5.70639i	−0.196796	+	0.185924i
$943$	47.0225	+	19.4773i	1.53126	+	0.634270i
$944$	−7.33547	−	3.17183i	−0.238749	−	0.103234i
$945$	−4.71642	+	1.95361i	−0.153425	+	0.0635508i
$946$	−11.6686	+	26.0524i	−0.379380	+	0.847038i
$947$	−18.2983	−	9.78065i	−0.594615	−	0.317828i	0.146496	−	0.989211i	$-0.453201\pi$
$947$	−18.2983	−	9.78065i	−0.594615	−	0.317828i	−0.741111	+	0.671383i	$0.765701\pi$
$948$	−1.89403	−	2.59539i	−0.0615152	−	0.0842942i
$949$	−30.5268	−	25.0527i	−0.990942	−	0.813245i
$950$	−0.189504	+	1.48918i	−0.00614831	+	0.0483154i
$951$	0.373893	−	1.87969i	0.0121243	−	0.0609530i
$952$	15.7802	+	49.6894i	0.511440	+	1.61044i
$953$	5.82596	−	1.15886i	0.188721	−	0.0375390i	−0.0998247	−	0.995005i	$-0.531828\pi$
$953$	5.82596	−	1.15886i	0.188721	−	0.0375390i	0.288546	+	0.957466i	$0.406828\pi$
$954$	10.9029	−	12.5414i	0.352995	−	0.406044i
$955$	1.84899	+	3.45922i	0.0598319	+	0.111938i
$956$	−2.08078	+	36.5960i	−0.0672973	+	1.18360i
$957$	−49.7821	−	4.90310i	−1.60923	−	0.158495i
$958$	−11.5229	+	16.2280i	−0.372289	+	0.524304i
$959$		−	18.9850i		−	0.613059i
$960$	−11.4137	−	1.96384i	−0.368377	−	0.0633827i
$961$			14.2280i			0.458969i
$962$	38.4086	+	27.2725i	1.23834	+	0.879301i
$963$	−14.4493	−	1.42313i	−0.465623	−	0.0458599i
$964$	8.77222	+	9.82990i	0.282534	+	0.316600i
$965$	2.74684	+	5.13898i	0.0884239	+	0.165430i
$966$	18.6103	+	16.1789i	0.598776	+	0.520547i
$967$	−43.2701	+	8.60696i	−1.39147	+	0.276781i	−0.833244	−	0.552906i	$-0.813519\pi$
$967$	−43.2701	+	8.60696i	−1.39147	+	0.276781i	−0.558229	+	0.829687i	$0.688519\pi$
$968$	−70.4059	+	59.3264i	−2.26293	+	1.90682i
$969$	−0.372724	+	1.87381i	−0.0119736	+	0.0601954i
$970$	1.25744	+	0.160014i	0.0403741	+	0.00513775i
$971$	45.5569	+	37.3876i	1.46199	+	1.19982i	0.937296	+	0.348534i	$0.113320\pi$
$971$	45.5569	+	37.3876i	1.46199	+	1.19982i	0.524695	+	0.851291i	$0.324180\pi$
$972$	−0.308704	+	1.97603i	−0.00990170	+	0.0633812i
$973$	−17.3405	−	9.26871i	−0.555912	−	0.297141i
$974$	15.2093	+	6.81208i	0.487337	+	0.218273i
$975$	−7.84650	+	3.25013i	−0.251289	+	0.104087i
$976$	22.8110	−	14.7382i	0.730161	−	0.471758i
$977$	−46.0888	−	19.0906i	−1.47451	−	0.610763i	−0.506629	−	0.862164i	$-0.669109\pi$
$977$	−46.0888	−	19.0906i	−1.47451	−	0.610763i	−0.967883	+	0.251401i	$0.919109\pi$
$978$	5.00931	+	5.30222i	0.160180	+	0.169546i
$979$	−60.2192	+	18.2673i	−1.92461	+	0.583825i
$980$	−5.41553	+	14.7753i	−0.172993	+	0.471979i
$981$	−0.426427	−	4.32959i	−0.0136148	−	0.138233i
$982$	4.43876	+	16.2835i	0.141647	+	0.519629i
$983$	−32.2146	−	48.2126i	−1.02749	−	1.53774i	−0.830254	−	0.557386i	$-0.811805\pi$
$983$	−32.2146	−	48.2126i	−1.02749	−	1.53774i	−0.197233	−	0.980357i	$-0.563195\pi$
$984$	24.4145	+	15.8588i	0.778305	+	0.505560i
$985$	−17.3600	−	11.5996i	−0.553136	−	0.369593i
$986$	50.1468	−	25.0000i	1.59700	−	0.796161i
$987$	3.57647	+	1.08491i	0.113840	+	0.0345331i
$988$	−2.11695	+	0.297359i	−0.0673492	+	0.00946025i
$989$	−9.59490	−	11.6914i	−0.305100	−	0.371765i
$990$	13.1712	+	3.01108i	0.418609	+	0.0956983i
$991$	−28.8687	−	28.8687i	−0.917045	−	0.917045i	0.0797686	−	0.996813i	$-0.474582\pi$
$991$	−28.8687	−	28.8687i	−0.917045	−	0.917045i	−0.996813	+	0.0797686i	$0.974582\pi$
$992$	23.1326	−	1.25866i	0.734462	−	0.0399625i
$993$	−14.3405	+	14.3405i	−0.455081	+	0.455081i
$994$	−30.1501	+	18.9299i	−0.956304	+	0.600421i
$995$	4.65685	−	3.82178i	0.147632	−	0.121159i
$996$	12.3036	+	20.8909i	0.389854	+	0.661953i
$997$	−4.86605	+	16.0412i	−0.154109	+	0.508030i	−0.999666	−	0.0258560i	$-0.991769\pi$
$997$	−4.86605	+	16.0412i	−0.154109	+	0.508030i	0.845556	+	0.533886i	$0.179269\pi$
$998$	−50.3829	−	16.8600i	−1.59484	−	0.533692i
$999$	6.32808	−	9.47064i	0.200211	−	0.299638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.18	✓	512
128.53	even	32	inner	384.2.v.a.181.18	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.18	✓	512	1.1	even	1	trivial
384.2.v.a.181.18	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)

\(f(q)\)	\(=\)	\(q+(0.236404 + 1.39431i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.88823 + 0.659242i) q^{4} +(-1.27674 + 0.682433i) q^{5} +(1.41077 - 0.0985985i) q^{6} +(-0.687954 - 3.45858i) q^{7} +(-1.36557 - 2.47694i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(0.236404 + 1.39431i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(-1.88823 + 0.659242i) q^{4} +(-1.27674 + 0.682433i) q^{5} +(1.41077 - 0.0985985i) q^{6} +(-0.687954 - 3.45858i) q^{7} +(-1.36557 - 2.47694i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.25335 - 1.61885i) q^{10} +(4.18657 - 5.10135i) q^{11} +(0.470989 + 1.94375i) q^{12} +(-1.37854 + 2.57906i) q^{13} +(4.65971 - 1.77685i) q^{14} +(0.554004 + 1.33748i) q^{15} +(3.13080 - 2.48960i) q^{16} +(2.00032 - 4.82920i) q^{17} +(0.0401562 - 1.41364i) q^{18} +(-0.106100 - 0.349765i) q^{19} +(1.96089 - 2.13027i) q^{20} +(-3.50936 + 0.345642i) q^{21} +(8.10261 + 4.63142i) q^{22} +(-4.11144 + 2.74718i) q^{23} +(-2.59886 + 1.11622i) q^{24} +(-1.61350 + 2.41477i) q^{25} +(-3.92192 - 1.31242i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(3.57906 + 6.07706i) q^{28} +(5.85942 - 4.80870i) q^{29} +(-1.73391 + 1.08864i) q^{30} +(2.89586 - 2.89586i) q^{31} +(4.21141 + 3.77677i) q^{32} +(-4.66643 - 4.66643i) q^{33} +(7.20631 + 1.64744i) q^{34} +(3.23859 + 3.94623i) q^{35} +(1.98056 - 0.278200i) q^{36} +(-10.8998 - 3.30641i) q^{37} +(0.462600 - 0.230623i) q^{38} +(2.43152 + 1.62469i) q^{39} +(3.43383 + 2.23049i) q^{40} +(-5.71849 - 8.55832i) q^{41} +(-1.31156 - 4.81144i) q^{42} +(0.299803 + 3.04395i) q^{43} +(-4.54217 + 12.3925i) q^{44} +(1.38535 - 0.420240i) q^{45} +(-4.80239 - 5.08320i) q^{46} +(-0.979176 - 0.405588i) q^{47} +(-2.17074 - 3.35975i) q^{48} +(-5.02134 + 2.07991i) q^{49} +(-3.74838 - 1.67886i) q^{50} +(-4.60988 - 2.46403i) q^{51} +(0.902766 - 5.77865i) q^{52} +(9.08346 + 7.45461i) q^{53} +(-1.40290 - 0.178524i) q^{54} +(-1.86384 + 9.37016i) q^{55} +(-7.62723 + 6.42697i) q^{56} +(-0.358481 + 0.0713062i) q^{57} +(8.09003 + 7.03308i) q^{58} +(-0.941833 - 1.76205i) q^{59} +(-1.92781 - 2.16025i) q^{60} +(6.75679 + 0.665486i) q^{61} +(4.72233 + 3.35314i) q^{62} +3.52634i q^{63} +(-4.27041 + 6.76488i) q^{64} -4.23356i q^{65} +(5.40331 - 7.60963i) q^{66} +(7.01002 + 0.690426i) q^{67} +(-0.593447 + 10.4373i) q^{68} +(2.33096 + 4.36092i) q^{69} +(-4.73668 + 5.44852i) q^{70} +(-7.00144 + 1.39267i) q^{71} +(0.856109 + 2.69575i) q^{72} +(-2.63451 + 13.2446i) q^{73} +(2.03343 - 15.9794i) q^{74} +(2.24499 + 1.84241i) q^{75} +(0.430921 + 0.590490i) q^{76} +(-20.5236 - 10.9701i) q^{77} +(-1.69051 + 3.77439i) q^{78} +(-1.48421 + 0.614781i) q^{79} +(-2.29824 + 5.31513i) q^{80} +(0.923880 + 0.382683i) q^{81} +(10.5811 - 9.99659i) q^{82} +(11.6004 - 3.51894i) q^{83} +(6.39860 - 2.96617i) q^{84} +(0.741712 + 7.53073i) q^{85} +(-4.17335 + 1.13762i) q^{86} +(-4.21122 - 6.30254i) q^{87} +(-18.3528 - 3.40359i) q^{88} +(-7.92861 - 5.29772i) q^{89} +(0.913448 + 1.83226i) q^{90} +(9.86827 + 2.99351i) q^{91} +(5.95228 - 7.89773i) q^{92} +(-2.59807 - 3.16576i) q^{93} +(0.334037 - 1.46116i) q^{94} +(0.374154 + 0.374154i) q^{95} +(4.17138 - 3.82095i) q^{96} +(-0.437798 + 0.437798i) q^{97} +(-4.08711 - 6.50963i) q^{98} +(-5.10135 + 4.18657i) 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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