LMFDB - Embedded newform 384.2.v.a.37.27

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			37.27
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15095 + 0.821770i) q^{2} +(0.471397 + 0.881921i) q^{3} +(0.649390 + 1.89164i) q^{4} +(-1.38739 + 1.13860i) q^{5} +(-0.182180 + 1.40243i) q^{6} +(-1.43779 + 0.960701i) q^{7} +(-0.807073 + 2.71084i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(1.15095 + 0.821770i) q^{2} +(0.471397 + 0.881921i) q^{3} +(0.649390 + 1.89164i) q^{4} +(-1.38739 + 1.13860i) q^{5} +(-0.182180 + 1.40243i) q^{6} +(-1.43779 + 0.960701i) q^{7} +(-0.807073 + 2.71084i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-2.53248 + 0.170363i) q^{10} +(-0.677175 - 2.23235i) q^{11} +(-1.36216 + 1.46442i) q^{12} +(-0.399914 + 0.487296i) q^{13} +(-2.44431 - 0.0758100i) q^{14} +(-1.65816 - 0.686834i) q^{15} +(-3.15659 + 2.45682i) q^{16} +(2.54925 - 1.05593i) q^{17} +(-1.32271 + 0.500432i) q^{18} +(7.35464 - 0.724369i) q^{19} +(-3.05477 - 1.88504i) q^{20} +(-1.52503 - 0.815147i) q^{21} +(1.05508 - 3.12581i) q^{22} +(1.24921 - 0.248483i) q^{23} +(-2.77120 + 0.566105i) q^{24} +(-0.347017 + 1.74457i) q^{25} +(-0.860728 + 0.232219i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-2.75098 - 2.09591i) q^{28} +(1.23304 + 0.374039i) q^{29} +(-1.34405 - 2.15314i) q^{30} +(5.60392 + 5.60392i) q^{31} +(-5.65202 + 0.233700i) q^{32} +(1.64954 - 1.64954i) q^{33} +(3.80181 + 0.879565i) q^{34} +(0.900919 - 2.96993i) q^{35} +(-1.93362 - 0.510990i) q^{36} +(0.0111882 - 0.113596i) q^{37} +(9.06011 + 5.21010i) q^{38} +(-0.618275 - 0.122983i) q^{39} +(-1.96683 - 4.67991i) q^{40} +(0.173208 + 0.870777i) q^{41} +(-1.08538 - 2.19142i) q^{42} +(2.86822 - 5.36607i) q^{43} +(3.78304 - 2.73063i) q^{44} +(-0.175920 - 1.78614i) q^{45} +(1.64198 + 0.740569i) q^{46} +(-1.87555 - 4.52799i) q^{47} +(-3.65473 - 1.62572i) q^{48} +(-1.53449 + 3.70458i) q^{49} +(-1.83304 + 1.72275i) q^{50} +(2.13296 + 1.75048i) q^{51} +(-1.18149 - 0.440047i) q^{52} +(2.71507 - 0.823606i) q^{53} +(-1.06486 - 0.930626i) q^{54} +(3.48125 + 2.32610i) q^{55} +(-1.44390 - 4.67297i) q^{56} +(4.10579 + 6.14475i) q^{57} +(1.11180 + 1.44378i) q^{58} +(-5.87743 - 7.16167i) q^{59} +(0.222447 - 3.58267i) q^{60} +(-8.35958 + 4.46829i) q^{61} +(1.84472 + 11.0550i) q^{62} -1.72922i q^{63} +(-6.69727 - 4.37568i) q^{64} -1.13141i q^{65} +(3.25408 - 0.543001i) q^{66} +(13.4696 - 7.19964i) q^{67} +(3.65290 + 4.13655i) q^{68} +(0.808015 + 0.984569i) q^{69} +(3.47751 - 2.67791i) q^{70} +(-0.0368105 - 0.0550907i) q^{71} +(-1.80559 - 2.17712i) q^{72} +(2.32216 + 1.55162i) q^{73} +(0.106227 - 0.121550i) q^{74} +(-1.70216 + 0.516344i) q^{75} +(6.14627 + 13.4419i) q^{76} +(3.11825 + 2.55908i) q^{77} +(-0.610543 - 0.649627i) q^{78} +(-1.80515 + 4.35801i) q^{79} +(1.58207 - 7.00265i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.516223 + 1.14456i) q^{82} +(-1.75957 - 17.8652i) q^{83} +(0.551622 - 3.41416i) q^{84} +(-2.33451 + 4.36757i) q^{85} +(7.71087 - 3.81908i) q^{86} +(0.251379 + 1.26377i) q^{87} +(6.59806 - 0.0340444i) q^{88} +(-4.69639 - 0.934170i) q^{89} +(1.26532 - 2.20033i) q^{90} +(0.106846 - 1.08483i) q^{91} +(1.28126 + 2.20169i) q^{92} +(-2.30055 + 7.58389i) q^{93} +(1.56229 - 6.75278i) q^{94} +(-9.37896 + 9.37896i) q^{95} +(-2.87045 - 4.87448i) q^{96} +(0.174862 + 0.174862i) q^{97} +(-4.81044 + 3.00281i) q^{98} +(2.23235 + 0.677175i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

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 $

$2$	1.15095	+	0.821770i	0.813847	+	0.581079i
$2$	1.15095	+	0.821770i	0.813847	+	0.581079i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$3$	0.471397	+	0.881921i	0.272161	+	0.509177i
$4$	0.649390	+	1.89164i	0.324695	+	0.945819i
$5$	−1.38739	+	1.13860i	−0.620458	+	0.509197i	−0.891292	−	0.453429i	$-0.850201\pi$
$5$	−1.38739	+	1.13860i	−0.620458	+	0.509197i	0.270834	+	0.962626i	$0.412701\pi$
$6$	−0.182180	+	1.40243i	−0.0743747	+	0.572540i
$7$	−1.43779	+	0.960701i	−0.543434	+	0.363111i	−0.796784	−	0.604264i	$-0.793467\pi$
$7$	−1.43779	+	0.960701i	−0.543434	+	0.363111i	0.253351	+	0.967375i	$0.418467\pi$
$8$	−0.807073	+	2.71084i	−0.285343	+	0.958425i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	−2.53248	+	0.170363i	−0.800842	+	0.0538734i
$11$	−0.677175	−	2.23235i	−0.204176	−	0.673078i	−0.997898	−	0.0647978i	$-0.979360\pi$
$11$	−0.677175	−	2.23235i	−0.204176	−	0.673078i	0.793722	−	0.608280i	$-0.208140\pi$
$12$	−1.36216	+	1.46442i	−0.393220	+	0.422742i
$13$	−0.399914	+	0.487296i	−0.110916	+	0.135152i	−0.825509	−	0.564389i	$-0.809112\pi$
$13$	−0.399914	+	0.487296i	−0.110916	+	0.135152i	0.714593	+	0.699540i	$0.246612\pi$
$14$	−2.44431	−	0.0758100i	−0.653268	−	0.0202611i
$15$	−1.65816	−	0.686834i	−0.428136	−	0.177340i
$16$	−3.15659	+	2.45682i	−0.789147	+	0.614205i
$17$	2.54925	−	1.05593i	0.618284	−	0.256102i	−0.0514817	−	0.998674i	$-0.516394\pi$
$17$	2.54925	−	1.05593i	0.618284	−	0.256102i	0.669766	+	0.742572i	$0.266394\pi$
$18$	−1.32271	+	0.500432i	−0.311766	+	0.117953i
$19$	7.35464	−	0.724369i	1.68727	−	0.166182i	0.791642	−	0.610985i	$-0.209227\pi$
$19$	7.35464	−	0.724369i	1.68727	−	0.166182i	0.895628	+	0.444804i	$0.146727\pi$
$20$	−3.05477	−	1.88504i	−0.683068	−	0.421508i
$21$	−1.52503	−	0.815147i	−0.332789	−	0.177880i
$22$	1.05508	−	3.12581i	0.224943	−	0.666425i
$23$	1.24921	−	0.248483i	0.260478	−	0.0518123i	−0.0631237	−	0.998006i	$-0.520106\pi$
$23$	1.24921	−	0.248483i	0.260478	−	0.0518123i	0.323602	+	0.946193i	$0.395106\pi$
$24$	−2.77120	+	0.566105i	−0.565668	+	0.115556i
$25$	−0.347017	+	1.74457i	−0.0694033	+	0.348914i
$26$	−0.860728	+	0.232219i	−0.168803	+	0.0455418i
$27$	−0.995185	−	0.0980171i	−0.191523	−	0.0188634i
$28$	−2.75098	−	2.09591i	−0.519887	−	0.396090i
$29$	1.23304	+	0.374039i	0.228970	+	0.0694574i	0.402685	−	0.915339i	$-0.368077\pi$
$29$	1.23304	+	0.374039i	0.228970	+	0.0694574i	−0.173715	+	0.984796i	$0.555577\pi$
$30$	−1.34405	−	2.15314i	−0.245389	−	0.393108i
$31$	5.60392	+	5.60392i	1.00649	+	1.00649i	0.999979	+	0.00651502i	$0.00207381\pi$
$31$	5.60392	+	5.60392i	1.00649	+	1.00649i	0.00651502	+	0.999979i	$0.497926\pi$
$32$	−5.65202	+	0.233700i	−0.999146	+	0.0413127i
$33$	1.64954	−	1.64954i	0.287147	−	0.287147i
$34$	3.80181	+	0.879565i	0.652004	+	0.150844i
$35$	0.900919	−	2.96993i	0.152283	−	0.502010i
$36$	−1.93362	−	0.510990i	−0.322270	−	0.0851650i
$37$	0.0111882	−	0.113596i	0.00183933	−	0.0186751i	−0.994221	−	0.107350i	$-0.965763\pi$
$37$	0.0111882	−	0.113596i	0.00183933	−	0.0186751i	0.996061	+	0.0886753i	$0.0282633\pi$
$38$	9.06011	+	5.21010i	1.46974	+	0.845190i
$39$	−0.618275	−	0.122983i	−0.0990033	−	0.0196930i
$40$	−1.96683	−	4.67991i	−0.310984	−	0.739959i
$41$	0.173208	+	0.870777i	0.0270506	+	0.135993i	0.991951	−	0.126625i	$-0.0404144\pi$
$41$	0.173208	+	0.870777i	0.0270506	+	0.135993i	−0.964900	+	0.262617i	$0.915414\pi$
$42$	−1.08538	−	2.19142i	−0.167478	−	0.338144i
$43$	2.86822	−	5.36607i	0.437400	−	0.818318i	−0.562564	−	0.826753i	$-0.690185\pi$
$43$	2.86822	−	5.36607i	0.437400	−	0.818318i	0.999964	+	0.00843556i	$0.00268515\pi$
$44$	3.78304	−	2.73063i	0.570315	−	0.411658i
$45$	−0.175920	−	1.78614i	−0.0262246	−	0.266262i
$46$	1.64198	+	0.740569i	0.242096	+	0.109191i
$47$	−1.87555	−	4.52799i	−0.273578	−	0.660475i	0.726053	−	0.687638i	$-0.241353\pi$
$47$	−1.87555	−	4.52799i	−0.273578	−	0.660475i	−0.999631	+	0.0271633i	$0.991353\pi$
$48$	−3.65473	−	1.62572i	−0.527514	−	0.234653i
$49$	−1.53449	+	3.70458i	−0.219213	+	0.529226i
$50$	−1.83304	+	1.72275i	−0.259230	+	0.243634i
$51$	2.13296	+	1.75048i	0.298674	+	0.245116i
$52$	−1.18149	−	0.440047i	−0.163843	−	0.0610235i
$53$	2.71507	−	0.823606i	0.372943	−	0.113131i	−0.0982487	−	0.995162i	$-0.531324\pi$
$53$	2.71507	−	0.823606i	0.372943	−	0.113131i	0.471192	+	0.882031i	$0.343824\pi$
$54$	−1.06486	−	0.930626i	−0.144910	−	0.126642i
$55$	3.48125	+	2.32610i	0.469412	+	0.313651i
$56$	−1.44390	−	4.67297i	−0.192949	−	0.624452i
$57$	4.10579	+	6.14475i	0.543825	+	0.813892i
$58$	1.11180	+	1.44378i	0.145987	+	0.189577i
$59$	−5.87743	−	7.16167i	−0.765177	−	0.932371i	0.234029	−	0.972230i	$-0.424809\pi$
$59$	−5.87743	−	7.16167i	−0.765177	−	0.932371i	−0.999205	+	0.0398592i	$0.987309\pi$
$60$	0.222447	−	3.58267i	0.0287177	−	0.462521i
$61$	−8.35958	+	4.46829i	−1.07034	+	0.572106i	−0.909852	−	0.414933i	$-0.863805\pi$
$61$	−8.35958	+	4.46829i	−1.07034	+	0.572106i	−0.160483	+	0.987039i	$0.551305\pi$
$62$	1.84472	+	11.0550i	0.234280	+	1.40398i
$63$		−	1.72922i		−	0.217861i
$64$	−6.69727	−	4.37568i	−0.837158	−	0.546961i
$65$		−	1.13141i		−	0.140334i
$66$	3.25408	−	0.543001i	0.400549	−	0.0668388i
$67$	13.4696	−	7.19964i	1.64557	−	0.879576i	0.653076	−	0.757292i	$-0.273478\pi$
$67$	13.4696	−	7.19964i	1.64557	−	0.879576i	0.992495	−	0.122284i	$-0.0390218\pi$
$68$	3.65290	+	4.13655i	0.442980	+	0.501630i
$69$	0.808015	+	0.984569i	0.0972736	+	0.118528i
$70$	3.47751	−	2.67791i	0.415643	−	0.320071i
$71$	−0.0368105	−	0.0550907i	−0.00436860	−	0.00653807i	0.829279	−	0.558835i	$-0.188751\pi$
$71$	−0.0368105	−	0.0550907i	−0.00436860	−	0.00653807i	−0.833647	+	0.552297i	$0.813751\pi$
$72$	−1.80559	−	2.17712i	−0.212791	−	0.256576i
$73$	2.32216	+	1.55162i	0.271788	+	0.181603i	0.683994	−	0.729488i	$-0.260242\pi$
$73$	2.32216	+	1.55162i	0.271788	+	0.181603i	−0.412206	+	0.911091i	$0.635242\pi$
$74$	0.106227	−	0.121550i	0.0123486	−	0.0141299i
$75$	−1.70216	+	0.516344i	−0.196548	+	0.0596222i
$76$	6.14627	+	13.4419i	0.705025	+	1.54189i
$77$	3.11825	+	2.55908i	0.355358	+	0.291635i
$78$	−0.610543	−	0.649627i	−0.0691304	−	0.0735558i
$79$	−1.80515	+	4.35801i	−0.203095	+	0.490314i	−0.992306	−	0.123807i	$-0.960490\pi$
$79$	−1.80515	+	4.35801i	−0.203095	+	0.490314i	0.789211	+	0.614122i	$0.210490\pi$
$80$	1.58207	−	7.00265i	0.176881	−	0.782920i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−0.516223	+	1.14456i	−0.0570073	+	0.126396i
$83$	−1.75957	−	17.8652i	−0.193137	−	1.96096i	−0.267024	−	0.963690i	$-0.586040\pi$
$83$	−1.75957	−	17.8652i	−0.193137	−	1.96096i	0.0738864	−	0.997267i	$-0.476460\pi$
$84$	0.551622	−	3.41416i	0.0601869	−	0.372515i
$85$	−2.33451	+	4.36757i	−0.253213	+	0.473729i
$86$	7.71087	−	3.81908i	0.831484	−	0.411822i
$87$	0.251379	+	1.26377i	0.0269507	+	0.135490i
$88$	6.59806	−	0.0340444i	0.703355	−	0.00362914i
$89$	−4.69639	−	0.934170i	−0.497817	−	0.0990219i	−0.0602051	−	0.998186i	$-0.519175\pi$
$89$	−4.69639	−	0.934170i	−0.497817	−	0.0990219i	−0.437611	+	0.899164i	$0.644175\pi$
$90$	1.26532	−	2.20033i	0.133377	−	0.231935i
$91$	0.106846	−	1.08483i	0.0112005	−	0.113721i
$92$	1.28126	+	2.20169i	0.133581	+	0.229542i
$93$	−2.30055	+	7.58389i	−0.238556	+	0.786412i
$94$	1.56229	−	6.75278i	0.161138	−	0.696496i
$95$	−9.37896	+	9.37896i	−0.962261	+	0.962261i
$96$	−2.87045	−	4.87448i	−0.292964	−	0.497499i
$97$	0.174862	+	0.174862i	0.0177546	+	0.0177546i	0.715928	−	0.698174i	$-0.246004\pi$
$97$	0.174862	+	0.174862i	0.0177546	+	0.0177546i	−0.698174	+	0.715928i	$0.746004\pi$
$98$	−4.81044	+	3.00281i	−0.485928	+	0.303329i
$99$	2.23235	+	0.677175i	0.224359	+	0.0680586i
$100$	−3.52544	+	0.476476i	−0.352544	+	0.0476476i
$101$	−12.9973	−	1.28012i	−1.29328	−	0.127377i	−0.572133	−	0.820161i	$-0.693884\pi$
$101$	−12.9973	−	1.28012i	−1.29328	−	0.127377i	−0.721145	+	0.692784i	$0.756384\pi$
$102$	1.01645	+	3.76752i	0.100644	+	0.373040i
$103$	2.63837	−	13.2640i	0.259967	−	1.30694i	−0.601396	−	0.798951i	$-0.705389\pi$
$103$	2.63837	−	13.2640i	0.259967	−	1.30694i	0.861363	−	0.507990i	$-0.169611\pi$
$104$	−0.998221	−	1.47738i	−0.0978837	−	0.144869i
$105$	3.04394	−	0.605476i	0.297058	−	0.0590885i
$106$	3.80173	+	1.28323i	0.369257	+	0.124638i
$107$	0.763452	+	0.408074i	0.0738057	+	0.0394500i	0.507887	−	0.861424i	$-0.330427\pi$
$107$	0.763452	+	0.408074i	0.0738057	+	0.0394500i	−0.434081	+	0.900874i	$0.642927\pi$
$108$	−0.460850	−	1.94618i	−0.0443453	−	0.187271i
$109$	13.7792	−	1.35713i	1.31980	−	0.129989i	0.586533	−	0.809925i	$-0.300492\pi$
$109$	13.7792	−	1.35713i	1.31980	−	0.129989i	0.733272	+	0.679936i	$0.237992\pi$
$110$	2.09524	+	5.53802i	0.199774	+	0.528029i
$111$	0.105457	−	0.0436817i	0.0100095	−	0.00414608i
$112$	2.17824	−	6.56493i	0.205824	−	0.620327i
$113$	5.20806	+	2.15725i	0.489933	+	0.202937i	0.613953	−	0.789343i	$-0.289579\pi$
$113$	5.20806	+	2.15725i	0.489933	+	0.202937i	−0.124019	+	0.992280i	$0.539579\pi$
$114$	−0.323993	+	10.4463i	−0.0303447	+	0.978389i
$115$	−1.45021	+	1.76709i	−0.135233	+	0.164782i
$116$	0.0931781	+	2.57537i	0.00865137	+	0.239117i
$117$	−0.182992	−	0.603244i	−0.0169176	−	0.0557699i
$118$	−0.879410	−	13.0727i	−0.0809562	−	1.20344i
$119$	−2.65085	+	3.96728i	−0.243003	+	0.363680i
$120$	3.20015	−	3.94069i	0.292133	−	0.359734i
$121$	4.62136	−	3.08789i	0.420124	−	0.280718i
$122$	−13.2934	−	1.72685i	−1.20353	−	0.156342i
$123$	−0.686307	+	0.563238i	−0.0618822	+	0.0507854i
$124$	−6.96146	+	14.2397i	−0.625157	+	1.27876i
$125$	−5.73520	−	10.7298i	−0.512972	−	0.959703i
$126$	1.42102	−	1.99025i	0.126594	−	0.177305i
$127$	8.69033			0.771142			0.385571	−	0.922678i	$-0.374004\pi$
$127$	8.69033			0.771142			0.385571	+	0.922678i	$0.374004\pi$
$128$	−4.11244	−	10.5398i	−0.363492	−	0.931597i
$129$	6.08452			0.535712
$130$	0.929759	−	1.30220i	0.0815452	−	0.114211i
$131$	3.74484	+	7.00609i	0.327188	+	0.612125i	0.990704	−	0.136037i	$-0.0434365\pi$
$131$	3.74484	+	7.00609i	0.327188	+	0.612125i	−0.663516	+	0.748162i	$0.730937\pi$
$132$	4.19152	+	2.04913i	0.364825	+	0.178354i
$133$	−9.87853	+	8.10710i	−0.856577	+	0.702975i
$134$	21.4193	+	2.78244i	1.85035	+	0.240366i
$135$	1.49231	−	0.997129i	0.128437	−	0.0858192i
$136$	0.805035	+	7.76282i	0.0690311	+	0.665656i
$137$	−8.09159	+	12.1099i	−0.691311	+	1.03462i	0.305291	+	0.952259i	$0.401246\pi$
$137$	−8.09159	+	12.1099i	−0.691311	+	1.03462i	−0.996603	+	0.0823616i	$0.973754\pi$
$138$	0.120899	+	1.79720i	0.0102916	+	0.152987i
$139$	−4.88203	−	16.0939i	−0.414088	−	1.36507i	−0.877778	−	0.479068i	$-0.840975\pi$
$139$	−4.88203	−	16.0939i	−0.414088	−	1.36507i	0.463690	−	0.885998i	$-0.346525\pi$
$140$	6.20308	−	0.224431i	0.524256	−	0.0189679i
$141$	3.10920	−	3.78857i	0.261842	−	0.319055i
$142$	0.00290476	−	0.0936566i	0.000243762	−	0.00785949i
$143$	1.35863	+	0.562761i	0.113614	+	0.0470605i
$144$	−0.289066	−	3.98954i	−0.0240888	−	0.332462i
$145$	−2.13659	+	0.885004i	−0.177434	+	0.0734956i
$146$	1.39763	+	3.69412i	0.115668	+	0.305727i
$147$	−3.99050	+	0.393030i	−0.329131	+	0.0324166i
$148$	0.222148	−	0.0526040i	0.0182605	−	0.00432402i
$149$	−4.69346	−	2.50871i	−0.384503	−	0.205521i	0.267808	−	0.963472i	$-0.413701\pi$
$149$	−4.69346	−	2.50871i	−0.384503	−	0.205521i	−0.652311	+	0.757951i	$0.726201\pi$
$150$	−2.38342	−	0.804493i	−0.194605	−	0.0656866i
$151$	0.0952278	−	0.0189420i	0.00774953	−	0.00154148i	−0.191214	−	0.981548i	$-0.561242\pi$
$151$	0.0952278	−	0.0189420i	0.00774953	−	0.00154148i	0.198964	+	0.980007i	$0.436242\pi$
$152$	−3.97208	+	20.5218i	−0.322178	+	1.66454i
$153$	−0.538311	+	2.70627i	−0.0435199	+	0.218789i
$154$	1.48599	+	5.50787i	0.119744	+	0.443837i
$155$	−14.1554	−	1.39419i	−1.13699	−	0.111984i
$156$	−0.168863	−	1.24942i	−0.0135199	−	0.100033i
$157$	−10.7766	−	3.26906i	−0.860069	−	0.260899i	−0.170712	−	0.985321i	$-0.554607\pi$
$157$	−10.7766	−	3.26906i	−0.860069	−	0.260899i	−0.689357	+	0.724422i	$0.742107\pi$
$158$	−5.65892	+	3.53245i	−0.450199	+	0.281027i
$159$	2.00623	+	2.00623i	0.159104	+	0.159104i
$160$	7.57546	−	6.75962i	0.598892	−	0.534395i
$161$	−1.55738	+	1.55738i	−0.122739	+	0.122739i
$162$	0.318765	−	1.37782i	0.0250446	−	0.108252i
$163$	−5.65216	+	18.6327i	−0.442711	+	1.45942i	0.397721	+	0.917506i	$0.369801\pi$
$163$	−5.65216	+	18.6327i	−0.442711	+	1.45942i	−0.840432	+	0.541917i	$0.817699\pi$
$164$	−1.53472	+	0.893121i	−0.119841	+	0.0697410i
$165$	−0.410385	+	4.16670i	−0.0319484	+	0.324378i
$166$	12.6559	−	22.0079i	0.982286	−	1.70815i
$167$	2.41486	+	0.480346i	0.186868	+	0.0371703i	0.287637	−	0.957740i	$-0.407130\pi$
$167$	2.41486	+	0.480346i	0.186868	+	0.0371703i	−0.100769	+	0.994910i	$0.532130\pi$
$168$	3.44054	−	3.47623i	0.265444	−	0.268197i
$169$	2.45865	+	12.3605i	0.189127	+	0.950804i
$170$	−6.27605	+	3.10844i	−0.481351	+	0.238406i
$171$	−3.48373	+	6.51760i	−0.266407	+	0.498413i
$172$	12.0133	+	1.94097i	0.916002	+	0.147998i
$173$	−0.919291	−	9.33372i	−0.0698924	−	0.709630i	−0.964731	−	0.263239i	$-0.915209\pi$
$173$	−0.919291	−	9.33372i	−0.0698924	−	0.709630i	0.894838	−	0.446391i	$-0.147291\pi$
$174$	−0.749200	+	1.66111i	−0.0567967	+	0.125929i
$175$	−1.17707	−	2.84171i	−0.0889784	−	0.214813i
$176$	7.62203	+	5.38290i	0.574532	+	0.405751i
$177$	3.54543	−	8.55942i	0.266491	−	0.643366i
$178$	−4.63766	−	4.93454i	−0.347607	−	0.369859i
$179$	−16.1931	−	13.2894i	−1.21033	−	0.993294i	−0.999877	−	0.0156909i	$-0.995005\pi$
$179$	−16.1931	−	13.2894i	−1.21033	−	0.993294i	−0.210456	−	0.977603i	$-0.567495\pi$
$180$	3.26449	−	1.49268i	0.243321	−	0.111258i
$181$	−5.73681	+	1.74024i	−0.426414	+	0.129351i	−0.496195	−	0.868211i	$-0.665270\pi$
$181$	−5.73681	+	1.74024i	−0.426414	+	0.129351i	0.0697813	+	0.997562i	$0.477770\pi$
$182$	1.01445	−	1.16078i	0.0751963	−	0.0860430i
$183$	−7.88136	−	5.26616i	−0.582607	−	0.389286i
$184$	−0.334605	+	3.58694i	−0.0246674	+	0.264433i
$185$	0.113818	+	0.170341i	0.00836806	+	0.0125237i
$186$	−8.88003	+	6.83818i	−0.651115	+	0.501400i
$187$	−4.08350	−	4.97576i	−0.298615	−	0.363864i
$188$	7.34735	−	6.48830i	0.535861	−	0.473208i
$189$	1.52503	−	0.815147i	0.110930	−	0.0592932i
$190$	−18.5021	+	3.08741i	−1.34228	+	0.223984i
$191$			12.0933i			0.875040i	0.899209	+	0.437520i	$0.144143\pi$
$191$			12.0933i			0.875040i	−0.899209	+	0.437520i	$0.855857\pi$
$192$	0.701939	−	7.96915i	0.0506581	−	0.575124i
$193$		−	13.4303i		−	0.966732i	−0.875418	−	0.483366i	$-0.839414\pi$
$193$		−	13.4303i		−	0.966732i	0.875418	−	0.483366i	$-0.160586\pi$
$194$	0.0575619	+	0.344954i	0.00413270	+	0.0247663i
$195$	0.997815	−	0.533343i	0.0714550	−	0.0381935i
$196$	−8.00421	−	0.496979i	−0.571729	−	0.0354985i
$197$	11.7511	+	14.3188i	0.837232	+	1.02017i	0.999442	+	0.0334141i	$0.0106380\pi$
$197$	11.7511	+	14.3188i	0.837232	+	1.02017i	−0.162209	+	0.986756i	$0.551862\pi$
$198$	2.01285	+	2.61387i	0.143047	+	0.185760i
$199$	−5.19536	−	7.77540i	−0.368289	−	0.551184i	0.600324	−	0.799757i	$-0.295038\pi$
$199$	−5.19536	−	7.77540i	−0.368289	−	0.551184i	−0.968613	+	0.248573i	$0.920038\pi$
$200$	−4.44918	−	2.34870i	−0.314604	−	0.166078i
$201$	12.6990	+	8.48522i	0.895721	+	0.598501i
$202$	−13.9073	−	12.1541i	−0.978516	−	0.855162i
$203$	−2.13220	+	0.646795i	−0.149651	+	0.0453961i
$204$	−1.92614	+	5.17153i	−0.134857	+	0.362079i
$205$	−1.23177	−	1.01089i	−0.0860308	−	0.0706036i
$206$	13.9366	−	13.0981i	0.971009	−	0.912589i
$207$	−0.487417	+	1.17673i	−0.0338778	+	0.0817883i
$208$	0.0651630	−	2.52071i	0.00451824	−	0.174780i
$209$	−6.59742	−	15.9276i	−0.456353	−	1.10173i
$210$	4.00099	+	1.80454i	0.276095	+	0.124525i
$211$	1.80095	+	18.2853i	0.123982	+	1.25881i	0.832860	+	0.553483i	$0.186702\pi$
$211$	1.80095	+	18.2853i	0.123982	+	1.25881i	−0.708878	+	0.705331i	$0.750798\pi$
$212$	3.32110	+	4.60108i	0.228094	+	0.316003i
$213$	0.0312334	−	0.0584335i	0.00214008	−	0.00400380i
$214$	0.543356	+	1.09706i	0.0371430	+	0.0749932i
$215$	2.13047	+	10.7106i	0.145297	+	0.730455i
$216$	1.06889	−	2.61868i	0.0727291	−	0.178178i
$217$	−13.4410	−	2.67357i	−0.912431	−	0.181494i
$218$	16.9744	+	9.76130i	1.14965	+	0.661119i
$219$	−0.273746	+	2.77939i	−0.0184980	+	0.187814i
$220$	−2.13945	+	8.09581i	−0.144241	+	0.545819i
$221$	−0.504928	+	1.66452i	−0.0339651	+	0.111968i
$222$	0.157272	+	0.0363857i	0.0105554	+	0.00244205i
$223$	−20.4582	+	20.4582i	−1.36998	+	1.36998i	−0.509528	+	0.860454i	$0.670180\pi$
$223$	−20.4582	+	20.4582i	−1.36998	+	1.36998i	−0.860454	+	0.509528i	$0.829820\pi$
$224$	7.90191	−	5.76592i	0.527969	−	0.385252i
$225$	−1.25777	−	1.25777i	−0.0838510	−	0.0838510i
$226$	4.22148	+	6.76272i	0.280808	+	0.449850i
$227$	15.6822	+	4.75714i	1.04086	+	0.315743i	0.764034	−	0.645176i	$-0.223216\pi$
$227$	15.6822	+	4.75714i	1.04086	+	0.315743i	0.276830	+	0.960919i	$0.410716\pi$
$228$	−8.95738	+	11.7570i	−0.593217	+	0.778626i
$229$	−28.9543	−	2.85175i	−1.91335	−	0.188449i	−0.929673	−	0.368386i	$-0.879910\pi$
$229$	−28.9543	−	2.85175i	−1.91335	−	0.188449i	−0.983678	+	0.179937i	$0.942410\pi$
$230$	−3.12127	+	0.842098i	−0.205810	+	0.0555263i
$231$	−0.786976	+	3.95640i	−0.0517792	+	0.260312i
$232$	−2.00911	+	3.04070i	−0.131905	+	0.199632i
$233$	20.7444	−	4.12633i	1.35901	−	0.270325i	0.538825	−	0.842418i	$-0.318868\pi$
$233$	20.7444	−	4.12633i	1.35901	−	0.270325i	0.820189	+	0.572093i	$0.193868\pi$
$234$	0.285112	−	0.844683i	0.0186384	−	0.0552186i
$235$	7.75769	+	4.14657i	0.506056	+	0.270492i
$236$	9.73055	−	15.7687i	0.633405	−	1.02645i
$237$	−4.69436	+	0.462354i	−0.304932	+	0.0300331i
$238$	−6.31120	+	2.38777i	−0.409094	+	0.154776i
$239$	−12.3524	+	5.11654i	−0.799011	+	0.330961i	−0.744560	−	0.667555i	$-0.767341\pi$
$239$	−12.3524	+	5.11654i	−0.799011	+	0.330961i	−0.0544508	+	0.998516i	$0.517341\pi$
$240$	6.92157	−	1.90576i	0.446785	−	0.123016i
$241$	7.82535	+	3.24136i	0.504075	+	0.208795i	0.620206	−	0.784439i	$-0.287049\pi$
$241$	7.82535	+	3.24136i	0.504075	+	0.208795i	−0.116131	+	0.993234i	$0.537049\pi$
$242$	7.85651	+	0.243669i	0.505036	+	0.0156637i
$243$	0.634393	−	0.773010i	0.0406963	−	0.0495886i
$244$	−13.8810	−	12.9116i	−0.888641	−	0.826583i
$245$	−2.08911	−	6.88686i	−0.133468	−	0.439985i
$246$	−1.25276	+	0.0842743i	−0.0798730	+	0.00537313i
$247$	−2.58824	+	3.87357i	−0.164686	+	0.246470i
$248$	−19.7141	+	10.6685i	−1.25185	+	0.677453i
$249$	14.9262	−	9.97338i	0.945910	−	0.632037i
$250$	2.21648	−	17.0625i	0.140182	−	1.07913i
$251$	−3.67555	+	3.01645i	−0.231999	+	0.190397i	−0.743209	−	0.669059i	$-0.766697\pi$
$251$	−3.67555	+	3.01645i	−0.231999	+	0.190397i	0.511210	+	0.859456i	$0.329197\pi$
$252$	3.27105	−	1.12293i	0.206057	−	0.0707383i
$253$	−1.40063	−	2.62040i	−0.0880570	−	0.164743i
$254$	10.0022	+	7.14145i	0.627592	+	0.448094i
$255$	−4.95233			−0.310127
$256$	3.92807	−	15.5103i	0.245505	−	0.969395i
$257$	−7.51945			−0.469050			−0.234525	−	0.972110i	$-0.575353\pi$
$257$	−7.51945			−0.469050			−0.234525	+	0.972110i	$0.575353\pi$
$258$	7.00300	+	5.00007i	0.435988	+	0.311291i
$259$	0.0930455	+	0.174076i	0.00578157	+	0.0108165i
$260$	2.14022	−	0.734726i	0.132731	−	0.0455658i
$261$	−0.996044	+	0.817432i	−0.0616536	+	0.0505978i
$262$	−1.44726	+	11.1411i	−0.0894122	+	0.688298i
$263$	9.51730	−	6.35926i	0.586862	−	0.392129i	−0.226393	−	0.974036i	$-0.572693\pi$
$263$	9.51730	−	6.35926i	0.586862	−	0.392129i	0.813255	+	0.581907i	$0.197693\pi$
$264$	3.14033	+	5.80292i	0.193274	+	0.357145i
$265$	−2.82909	+	4.23403i	−0.173790	+	0.260094i
$266$	−18.0319	+	1.21302i	−1.10561	+	0.0743752i
$267$	−1.39000	−	4.58221i	−0.0850666	−	0.280427i
$268$	22.3661	+	20.8042i	1.36623	+	1.27082i
$269$	14.3739	−	17.5147i	0.876394	−	1.06789i	−0.120774	−	0.992680i	$-0.538538\pi$
$269$	14.3739	−	17.5147i	0.876394	−	1.06789i	0.997168	−	0.0752089i	$-0.0239624\pi$
$270$	2.53699	+	0.0786846i	0.154396	+	0.00478859i
$271$	6.84425	+	2.83498i	0.415758	+	0.172213i	0.580750	−	0.814082i	$-0.302760\pi$
$271$	6.84425	+	2.83498i	0.415758	+	0.172213i	−0.164991	+	0.986295i	$0.552760\pi$
$272$	−5.45269	+	9.59620i	−0.330618	+	0.581855i
$273$	1.00710	−	0.417154i	0.0609525	−	0.0252473i
$274$	−19.2646	+	7.28854i	−1.16382	+	0.440317i
$275$	4.12948	−	0.406718i	0.249017	−	0.0245260i
$276$	−1.33773	+	2.16784i	−0.0805220	+	0.130489i
$277$	−20.6177	−	11.0204i	−1.23880	−	0.662152i	−0.283836	−	0.958873i	$-0.591607\pi$
$277$	−20.6177	−	11.0204i	−1.23880	−	0.662152i	−0.954964	+	0.296720i	$0.904107\pi$
$278$	7.60648	−	22.5352i	0.456206	−	1.35157i
$279$	−7.77286	+	1.54612i	−0.465349	+	0.0925637i
$280$	7.32389	+	4.83919i	0.437686	+	0.289197i
$281$	−4.62596	+	23.2563i	−0.275962	+	1.38735i	0.555383	+	0.831595i	$0.312572\pi$
$281$	−4.62596	+	23.2563i	−0.275962	+	1.38735i	−0.831344	+	0.555758i	$0.812428\pi$
$282$	6.69188	−	1.80542i	0.398496	−	0.107511i
$283$	12.7995	+	1.26064i	0.760850	+	0.0749371i	0.470998	−	0.882134i	$-0.343894\pi$
$283$	12.7995	+	1.26064i	0.760850	+	0.0749371i	0.289852	+	0.957072i	$0.406394\pi$
$284$	0.0803074	−	0.105407i	0.00476537	−	0.00625478i
$285$	−12.6927	−	3.85030i	−0.751852	−	0.228072i
$286$	1.10126	+	1.76419i	0.0651186	+	0.104319i
$287$	−1.08559	−	1.08559i	−0.0640806	−	0.0640806i
$288$	2.94578	−	4.82932i	0.173582	−	0.284571i
$289$	−6.63713	+	6.63713i	−0.390419	+	0.390419i
$290$	−3.18638	−	0.737185i	−0.187111	−	0.0432890i
$291$	−0.0717852	+	0.236644i	−0.00420812	+	0.0138723i
$292$	−1.42711	+	5.40029i	−0.0835153	+	0.316028i
$293$	−2.02254	+	20.5352i	−0.118158	+	1.19968i	0.735014	+	0.678052i	$0.237175\pi$
$293$	−2.02254	+	20.5352i	−0.118158	+	1.19968i	−0.853173	+	0.521629i	$0.825325\pi$
$294$	−4.91587	−	2.82691i	−0.286699	−	0.164869i
$295$	16.3086	+	3.24397i	0.949521	+	0.188871i
$296$	0.298911	+	0.122010i	0.0173738	+	0.00709167i
$297$	0.455106	+	2.28797i	0.0264079	+	0.132762i
$298$	−3.34038	−	6.74434i	−0.193503	−	0.390689i
$299$	−0.378491	+	0.708107i	−0.0218887	+	0.0409509i
$300$	−2.08210	−	2.88456i	−0.120210	−	0.166540i
$301$	1.03128	+	10.4708i	0.0594421	+	0.603526i
$302$	0.125169	+	0.0564539i	0.00720265	+	0.00324856i
$303$	−4.99791	−	12.0660i	−0.287123	−	0.693175i
$304$	−21.4359	+	20.3556i	−1.22943	+	1.16747i
$305$	6.51039	−	15.7175i	0.372784	−	0.899979i
$306$	−2.84350	+	2.67243i	−0.162552	+	0.152772i
$307$	1.40910	+	1.15642i	0.0804215	+	0.0660002i	0.673745	−	0.738964i	$-0.264685\pi$
$307$	1.40910	+	1.15642i	0.0804215	+	0.0660002i	−0.593324	+	0.804964i	$0.702185\pi$
$308$	−2.81590	+	7.56045i	−0.160451	+	0.430797i
$309$	12.9415	−	3.92577i	0.736218	−	0.223329i
$310$	−15.1465	−	13.2371i	−0.860266	−	0.751819i
$311$	17.3382	+	11.5850i	0.983159	+	0.656926i	0.939654	−	0.342127i	$-0.111147\pi$
$311$	17.3382	+	11.5850i	0.983159	+	0.656926i	0.0435054	+	0.999053i	$0.486147\pi$
$312$	0.832379	−	1.57679i	0.0471242	−	0.0892680i
$313$	−3.64373	−	5.45322i	−0.205956	−	0.308234i	0.714084	−	0.700060i	$-0.246844\pi$
$313$	−3.64373	−	5.45322i	−0.205956	−	0.308234i	−0.920039	+	0.391826i	$0.871844\pi$
$314$	−9.71700	−	12.6184i	−0.548362	−	0.712100i
$315$	1.96888	+	2.39909i	0.110934	+	0.135174i
$316$	−9.41602	−	0.584637i	−0.529692	−	0.0328884i
$317$	30.4575	−	16.2799i	1.71066	−	0.914368i	0.740449	−	0.672112i	$-0.234613\pi$
$317$	30.4575	−	16.2799i	1.71066	−	0.914368i	0.970213	−	0.242255i	$-0.0778872\pi$
$318$	0.660419	+	3.95773i	0.0370345	+	0.221939i
$319$		−	3.00587i		−	0.168296i
$320$	14.2739	−	1.55474i	0.797933	−	0.0869123i
$321$			0.865669i			0.0483169i
$322$	−3.07228	+	0.512666i	−0.171212	+	0.0285697i
$323$	17.9839	−	9.61262i	1.00065	−	0.534860i
$324$	1.49913	−	1.32386i	0.0832853	−	0.0735476i
$325$	−0.711346	−	0.866778i	−0.0394584	−	0.0480802i
$326$	−21.8171	+	16.8006i	−1.20834	+	0.930497i
$327$	7.69233	+	11.5124i	0.425387	+	0.636637i
$328$	−2.50033	−	0.233241i	−0.138057	−	0.0128786i
$329$	7.04670	+	4.70845i	0.388497	+	0.259585i
$330$	−3.89640	+	4.45844i	−0.214490	+	0.245429i
$331$	7.01219	−	2.12713i	0.385425	−	0.116917i	−0.0916249	−	0.995794i	$-0.529206\pi$
$331$	7.01219	−	2.12713i	0.385425	−	0.116917i	0.477050	+	0.878876i	$0.341706\pi$
$332$	32.6518	−	14.9299i	1.79200	−	0.819385i
$333$	0.0882358	+	0.0724133i	0.00483529	+	0.00396822i
$334$	2.38466	+	2.53732i	0.130483	+	0.138836i
$335$	−10.4900	+	25.3251i	−0.573131	+	1.38366i
$336$	6.81656	−	1.17365i	0.371874	−	0.0640278i
$337$	0.902557	+	2.17897i	0.0491654	+	0.118696i	0.946554	−	0.322545i	$-0.104538\pi$
$337$	0.902557	+	2.17897i	0.0491654	+	0.118696i	−0.897389	+	0.441241i	$0.854538\pi$
$338$	−7.32766	+	16.2468i	−0.398572	+	0.883707i
$339$	0.552539	+	5.61002i	0.0300098	+	0.304695i
$340$	−9.77786	−	1.57980i	−0.530279	−	0.0856767i
$341$	8.71506	−	16.3047i	0.471947	−	0.882950i
$342$	−9.36557	+	4.63863i	−0.506432	+	0.250828i
$343$	−3.71420	−	18.6725i	−0.200548	−	1.00822i
$344$	12.2317	+	12.1061i	0.659487	+	0.652717i
$345$	−2.24206	−	0.445973i	−0.120708	−	0.0240104i
$346$	6.61211	−	11.4981i	0.355469	−	0.618143i
$347$	0.808301	−	8.20681i	0.0433918	−	0.440565i	−0.948803	−	0.315868i	$-0.897704\pi$
$347$	0.808301	−	8.20681i	0.0433918	−	0.440565i	0.992195	−	0.124697i	$-0.0397957\pi$
$348$	−2.22735	+	1.29620i	−0.119398	+	0.0694834i
$349$	1.13572	−	3.74398i	0.0607940	−	0.200411i	−0.921282	−	0.388894i	$-0.872857\pi$
$349$	1.13572	−	3.74398i	0.0607940	−	0.200411i	0.982076	+	0.188483i	$0.0603572\pi$
$350$	0.980471	−	4.23796i	0.0524084	−	0.226528i
$351$	0.445752	−	0.445752i	0.0237925	−	0.0237925i
$352$	4.34911	+	12.4590i	0.231808	+	0.664068i
$353$	−12.4307	−	12.4307i	−0.661621	−	0.661621i	0.294141	−	0.955762i	$-0.404967\pi$
$353$	−12.4307	−	12.4307i	−0.661621	−	0.661621i	−0.955762	+	0.294141i	$0.904967\pi$
$354$	11.1145	−	6.93798i	0.590729	−	0.368749i
$355$	0.113797	+	0.0345198i	0.00603970	+	0.00183212i
$356$	−1.28268	−	9.49051i	−0.0679817	−	0.502996i
$357$	−4.74843	−	0.467680i	−0.251314	−	0.0247522i
$358$	−7.71676	−	28.6025i	−0.407844	−	1.51169i
$359$	0.198756	−	0.999213i	0.0104899	−	0.0527364i	−0.975186	−	0.221388i	$-0.928941\pi$
$359$	0.198756	−	0.999213i	0.0104899	−	0.0527364i	0.985676	+	0.168652i	$0.0539413\pi$
$360$	4.98392	+	0.964657i	0.262676	+	0.0508419i
$361$	34.9311	−	6.94822i	1.83848	−	0.365696i
$362$	−8.03288	−	2.71140i	−0.422199	−	0.142508i
$363$	4.90177	+	2.62005i	0.257276	+	0.137517i
$364$	2.12149	−	0.502362i	0.111196	−	0.0263309i
$365$	−4.98840	+	0.491315i	−0.261105	+	0.0257166i
$366$	−4.74352	−	12.5378i	−0.247948	−	0.655360i
$367$	13.3569	−	5.53259i	0.697222	−	0.288799i	−0.00578340	−	0.999983i	$-0.501841\pi$
$367$	13.3569	−	5.53259i	0.697222	−	0.288799i	0.703005	+	0.711184i	$0.251841\pi$
$368$	−3.33276	+	3.85344i	−0.173732	+	0.200874i
$369$	−0.820254	−	0.339760i	−0.0427007	−	0.0176872i
$370$	−0.00898151	+	0.289586i	−0.000466926	+	0.0150549i
$371$	−3.11246	+	3.79254i	−0.161591	+	0.196899i
$372$	−15.8399	+	0.573096i	−0.821261	+	0.0297137i
$373$	−6.89077	−	22.7158i	−0.356790	−	1.17618i	−0.933302	−	0.359092i	$-0.883087\pi$
$373$	−6.89077	−	22.7158i	−0.356790	−	1.17618i	0.576512	−	0.817089i	$-0.304413\pi$
$374$	−0.610993	−	9.08257i	−0.0315937	−	0.469648i
$375$	6.75929	−	10.1160i	0.349048	−	0.522387i
$376$	13.7883	−	1.42990i	0.711080	−	0.0737417i
$377$	−0.675379	+	0.451274i	−0.0347838	+	0.0232418i
$378$	2.42510	+	0.315029i	0.124734	+	0.0162033i
$379$	−17.0397	+	13.9842i	−0.875273	+	0.718318i	−0.960570	−	0.278038i	$-0.910316\pi$
$379$	−17.0397	+	13.9842i	−0.875273	+	0.718318i	0.0852973	+	0.996356i	$0.472816\pi$
$380$	−23.8322	−	11.6510i	−1.22257	−	0.597684i
$381$	4.09659	+	7.66419i	0.209875	+	0.392648i
$382$	−9.93790	+	13.9188i	−0.508467	+	0.712149i
$383$	11.3514			0.580030			0.290015	−	0.957022i	$-0.406340\pi$
$383$	11.3514			0.580030			0.290015	+	0.957022i	$0.406340\pi$
$384$	7.35670	−	8.59529i	0.375420	−	0.438626i
$385$	−7.24000			−0.368984
$386$	11.0366	−	15.4576i	0.561747	−	0.786772i
$387$	2.86822	+	5.36607i	0.145800	+	0.272773i
$388$	−0.217222	+	0.444329i	−0.0110278	+	0.0225574i
$389$	24.7473	−	20.3096i	1.25474	−	1.02974i	0.256741	−	0.966480i	$-0.417351\pi$
$389$	24.7473	−	20.3096i	1.25474	−	1.02974i	0.997997	−	0.0632570i	$-0.0201488\pi$
$390$	1.58672	+	0.206121i	0.0803469	+	0.0104373i
$391$	2.92216	−	1.95253i	0.147780	−	0.0987436i
$392$	−8.80408	−	7.14962i	−0.444673	−	0.361110i
$393$	−4.41352	+	6.60530i	−0.222633	+	0.333193i
$394$	1.75826	+	26.1370i	0.0885798	+	1.31676i
$395$	−2.45759	−	8.10158i	−0.123655	−	0.407635i
$396$	0.168693	+	4.66254i	0.00847715	+	0.234302i
$397$	18.7603	−	22.8595i	0.941553	−	1.14729i	−0.0473730	−	0.998877i	$-0.515085\pi$
$397$	18.7603	−	22.8595i	0.941553	−	1.14729i	0.988926	−	0.148409i	$-0.0474150\pi$
$398$	0.409972	−	13.2185i	0.0205500	−	0.662584i
$399$	−11.8065	−	4.89042i	−0.591066	−	0.244827i
$400$	−3.19071	−	6.35945i	−0.159535	−	0.317972i
$401$	2.54762	−	1.05526i	0.127222	−	0.0526970i	−0.318164	−	0.948036i	$-0.603066\pi$
$401$	2.54762	−	1.05526i	0.127222	−	0.0526970i	0.445386	+	0.895339i	$0.353066\pi$
$402$	7.64310	+	20.2018i	0.381203	+	1.00757i
$403$	−4.97186	+	0.489685i	−0.247666	+	0.0243930i
$404$	−6.01878	−	25.4175i	−0.299446	−	1.26457i
$405$	1.58286	+	0.846056i	0.0786529	+	0.0420408i
$406$	−2.98558	−	1.00774i	−0.148172	−	0.0500135i
$407$	−0.261162	+	0.0519484i	−0.0129453	+	0.00257499i
$408$	−6.46671	+	4.36935i	−0.320150	+	0.216315i
$409$	5.50653	−	27.6832i	0.272281	−	1.36885i	−0.566358	−	0.824159i	$-0.691648\pi$
$409$	5.50653	−	27.6832i	0.272281	−	1.36885i	0.838639	−	0.544688i	$-0.183352\pi$
$410$	−0.586995	−	2.17572i	−0.0289896	−	0.107451i
$411$	−14.4944	−	1.42757i	−0.714954	−	0.0704168i
$412$	26.8040	−	3.62266i	1.32054	−	0.178476i
$413$	15.3307	+	4.65053i	0.754377	+	0.228838i
$414$	−1.52799	+	0.953816i	−0.0750968	+	0.0468775i
$415$	22.7825	+	22.7825i	1.11835	+	1.11835i
$416$	2.14644	−	2.84767i	0.105238	−	0.139619i
$417$	11.8922	−	11.8922i	0.582362	−	0.582362i
$418$	5.49547	−	23.7535i	0.268792	−	1.16182i
$419$	4.40040	−	14.5062i	0.214973	−	0.708673i	−0.781434	−	0.623988i	$-0.785512\pi$
$419$	4.40040	−	14.5062i	0.214973	−	0.708673i	0.996408	−	0.0846850i	$-0.0269884\pi$
$420$	3.12204	+	5.36483i	0.152340	+	0.261777i
$421$	−0.352666	+	3.58068i	−0.0171879	+	0.174512i	−0.999946	−	0.0103839i	$-0.996695\pi$
$421$	−0.352666	+	3.58068i	−0.0171879	+	0.174512i	0.982758	+	0.184895i	$0.0591946\pi$
$422$	−12.9535	+	22.5255i	−0.630568	+	1.09653i
$423$	4.80689	+	0.956149i	0.233719	+	0.0464896i
$424$	0.0414061	+	8.02481i	0.00201086	+	0.389719i
$425$	0.957520	+	4.81378i	0.0464465	+	0.233503i
$426$	0.0839671	−	0.0415877i	0.00406822	−	0.00201493i
$427$	7.72664	−	14.4555i	0.373918	−	0.699552i
$428$	−0.276150	+	1.70917i	−0.0133482	+	0.0826160i
$429$	0.144141	+	1.46349i	0.00695918	+	0.0706577i
$430$	−6.34956	+	14.0781i	−0.306203	+	0.678908i
$431$	−4.44087	−	10.7212i	−0.213909	−	0.516422i	0.780108	−	0.625645i	$-0.215164\pi$
$431$	−4.44087	−	10.7212i	−0.213909	−	0.516422i	−0.994017	+	0.109222i	$0.965164\pi$
$432$	3.38220	−	2.13559i	0.162726	−	0.102749i
$433$	7.29237	−	17.6053i	0.350449	−	0.846058i	−0.646116	−	0.763239i	$-0.723608\pi$
$433$	7.29237	−	17.6053i	0.350449	−	0.846058i	0.996565	−	0.0828189i	$-0.0263923\pi$
$434$	−13.2729	−	14.1225i	−0.637118	−	0.677903i
$435$	−1.78768	−	1.46711i	−0.0857129	−	0.0703428i
$436$	11.5152	+	25.1839i	0.551480	+	1.20609i
$437$	9.00748	−	2.73239i	0.430886	−	0.130708i
$438$	−2.59908	+	2.97399i	−0.124189	+	0.142103i
$439$	−28.3309	−	18.9301i	−1.35216	−	0.903484i	−0.352680	−	0.935744i	$-0.614730\pi$
$439$	−28.3309	−	18.9301i	−1.35216	−	0.903484i	−0.999480	+	0.0322597i	$0.989730\pi$
$440$	−9.11529	+	7.55977i	−0.434555	+	0.360398i
$441$	−2.22773	−	3.33404i	−0.106082	−	0.158764i
$442$	−1.94900	+	1.50086i	−0.0927047	+	0.0713885i
$443$	−1.41758	−	1.72733i	−0.0673513	−	0.0820678i	0.738245	−	0.674533i	$-0.235655\pi$
$443$	−1.41758	−	1.72733i	−0.0673513	−	0.0820678i	−0.805596	+	0.592465i	$0.798155\pi$
$444$	0.151112	+	0.171120i	0.00717148	+	0.00812099i
$445$	7.57936	−	4.05125i	0.359296	−	0.192048i
$446$	−40.3584	+	6.73452i	−1.91102	+	0.318889i
$447$		−	5.32186i		−	0.251715i
$448$	13.8330	−	0.142754i	0.653547	−	0.00674448i
$449$			26.4042i			1.24609i	0.782185	+	0.623047i	$0.214105\pi$
$449$			26.4042i			1.24609i	−0.782185	+	0.623047i	$0.785895\pi$
$450$	−0.414037	−	2.48122i	−0.0195179	−	0.116966i
$451$	1.82658	−	0.976329i	0.0860105	−	0.0459736i
$452$	−0.698674	+	11.2527i	−0.0328628	+	0.529281i
$453$	0.0615954	+	0.0750542i	0.00289400	+	0.00352636i
$454$	14.1402	+	18.3624i	0.663633	+	0.861791i
$455$	1.08695	+	1.62673i	0.0509569	+	0.0762623i
$456$	−19.9711	+	6.17086i	−0.935231	+	0.288977i
$457$	4.49468	+	3.00325i	0.210252	+	0.140486i	0.656238	−	0.754554i	$-0.272147\pi$
$457$	4.49468	+	3.00325i	0.210252	+	0.140486i	−0.445986	+	0.895040i	$0.647147\pi$
$458$	−30.9815	−	27.0760i	−1.44767	−	1.26518i
$459$	−2.64048	+	0.800980i	−0.123247	+	0.0373865i
$460$	−4.28445	−	1.59575i	−0.199763	−	0.0744021i
$461$	29.9438	+	24.5742i	1.39462	+	1.14454i	0.971106	+	0.238647i	$0.0767039\pi$
$461$	29.9438	+	24.5742i	1.39462	+	1.14454i	0.423515	+	0.905889i	$0.360796\pi$
$462$	−4.15702	+	3.90692i	−0.193402	+	0.181766i
$463$	9.57436	−	23.1145i	0.444958	−	1.07422i	−0.529228	−	0.848479i	$-0.677518\pi$
$463$	9.57436	−	23.1145i	0.444958	−	1.07422i	0.974186	−	0.225745i	$-0.0724815\pi$
$464$	−4.81115	+	1.84868i	−0.223352	+	0.0858226i
$465$	−5.44326	−	13.1412i	−0.252425	−	0.609408i
$466$	27.2668	+	12.2979i	1.26311	+	0.569691i
$467$	2.71341	+	27.5497i	0.125562	+	1.27485i	0.827034	+	0.562152i	$0.190026\pi$
$467$	2.71341	+	27.5497i	0.125562	+	1.27485i	−0.701472	+	0.712697i	$0.747474\pi$
$468$	1.02229	−	0.737895i	0.0472552	−	0.0341092i
$469$	−12.4497	+	23.2918i	−0.574875	+	1.07552i
$470$	5.52121	+	11.1475i	0.254675	+	0.514198i
$471$	−2.19702	−	11.0452i	−0.101233	−	0.508934i
$472$	24.1576	−	10.1528i	1.11195	−	0.467319i
$473$	−13.9212	−	2.76910i	−0.640098	−	0.127323i
$474$	−5.78294	−	3.32553i	−0.265619	−	0.152747i
$475$	−1.28847	+	13.0821i	−0.0591191	+	0.600246i
$476$	−9.22610	−	2.43814i	−0.422877	−	0.111752i
$477$	−0.823606	+	2.71507i	−0.0377103	+	0.124314i
$478$	−18.4217	−	4.26194i	−0.842588	−	0.194937i
$479$	−26.9672	+	26.9672i	−1.23216	+	1.23216i	−0.269033	+	0.963131i	$0.586704\pi$
$479$	−26.9672	+	26.9672i	−1.23216	+	1.23216i	−0.963131	+	0.269033i	$0.913296\pi$
$480$	9.53250	+	3.49449i	0.435097	+	0.159501i
$481$	0.0508806	+	0.0508806i	0.00231996	+	0.00231996i
$482$	6.34296	+	10.1613i	0.288914	+	0.462834i
$483$	−2.10763	−	0.639344i	−0.0959006	−	0.0290911i
$484$	8.84224	+	6.73669i	0.401920	+	0.306213i
$485$	−0.441699	−	0.0435036i	−0.0200565	−	0.00197540i
$486$	1.36539	−	0.368374i	0.0619355	−	0.0167098i
$487$	5.47693	−	27.5344i	0.248183	−	1.24770i	−0.632711	−	0.774388i	$-0.718058\pi$
$487$	5.47693	−	27.5344i	0.248183	−	1.24770i	0.880894	−	0.473313i	$-0.156942\pi$
$488$	−5.36601	−	26.2677i	−0.242908	−	1.18908i
$489$	−19.0970	+	3.79862i	−0.863594	+	0.171780i
$490$	3.25495	−	9.64322i	0.147043	−	0.435636i
$491$	−6.73860	−	3.60186i	−0.304109	−	0.162549i	0.312283	−	0.949989i	$-0.398906\pi$
$491$	−6.73860	−	3.60186i	−0.304109	−	0.162549i	−0.616392	+	0.787440i	$0.711406\pi$
$492$	−1.51112	−	0.932483i	−0.0681266	−	0.0420396i
$493$	3.53830	−	0.348492i	0.159357	−	0.0156953i
$494$	−6.16213	+	2.33137i	−0.277247	+	0.104893i
$495$	−3.86816	+	1.60224i	−0.173861	+	0.0720155i
$496$	−31.4571	−	3.92144i	−1.41246	−	0.176078i
$497$	0.105851	+	0.0438451i	0.00474809	+	0.00196672i
$498$	25.3752	+	0.787011i	1.13709	+	0.0352668i
$499$	−13.0952	+	15.9565i	−0.586221	+	0.714312i	−0.978665	−	0.205464i	$-0.934130\pi$
$499$	−13.0952	+	15.9565i	−0.586221	+	0.714312i	0.392444	+	0.919776i	$0.371630\pi$
$500$	16.5725	−	17.8167i	0.741145	−	0.796789i
$501$	0.714732	+	2.35615i	0.0319319	+	0.105265i
$502$	−6.70922	+	0.451336i	−0.299447	+	0.0201441i
$503$	−17.5909	+	26.3267i	−0.784340	+	1.17385i	0.196780	+	0.980448i	$0.436951\pi$
$503$	−17.5909	+	26.3267i	−0.784340	+	1.17385i	−0.981120	+	0.193400i	$0.938049\pi$
$504$	4.68762	+	1.39560i	0.208803	+	0.0621651i
$505$	19.4898	−	13.0227i	0.867286	−	0.579502i
$506$	0.541301	−	4.16696i	0.0240638	−	0.185244i
$507$	−9.74195	+	7.99501i	−0.432655	+	0.355071i
$508$	5.64341	+	16.4390i	0.250386	+	0.729361i
$509$	6.82928	+	12.7767i	0.302703	+	0.566317i	0.986580	−	0.163280i	$-0.0522075\pi$
$509$	6.82928	+	12.7767i	0.302703	+	0.566317i	−0.683877	+	0.729597i	$0.739708\pi$
$510$	−5.69990	−	4.06968i	−0.252396	−	0.180208i
$511$	−4.82942			−0.213641
$512$	17.2669	−	14.6237i	0.763098	−	0.646282i
$513$	−7.39022			−0.326286
$514$	−8.65454	−	6.17925i	−0.381735	−	0.272555i
$515$	11.4419	+	21.4064i	0.504192	+	0.943277i
$516$	3.95123	+	11.5097i	0.173943	+	0.506687i
$517$	−8.83796	+	7.25313i	−0.388693	+	0.318992i
$518$	−0.0359592	+	0.276815i	−0.00157996	+	0.0121626i
$519$	7.79826	−	5.21063i	0.342305	−	0.228721i
$520$	3.06707	+	0.913131i	0.134500	+	0.0400434i
$521$	−10.7051	+	16.0213i	−0.468997	+	0.701904i	−0.988272	−	0.152703i	$-0.951202\pi$
$521$	−10.7051	+	16.0213i	−0.468997	+	0.701904i	0.519275	+	0.854607i	$0.326202\pi$
$522$	−1.81814	+	0.122308i	−0.0795779	+	0.00535328i
$523$	−4.49169	−	14.8071i	−0.196408	−	0.647470i	−0.998721	−	0.0505663i	$-0.983897\pi$
$523$	−4.49169	−	14.8071i	−0.196408	−	0.647470i	0.802313	−	0.596904i	$-0.203603\pi$
$524$	−10.8211	+	11.6336i	−0.472723	+	0.508214i
$525$	1.95129	−	2.37766i	0.0851614	−	0.103769i
$526$	16.1798	+	0.501817i	0.705474	+	0.0218802i
$527$	20.2032	+	8.36843i	0.880064	+	0.364535i
$528$	−1.15429	+	9.25951i	−0.0502340	+	0.402969i
$529$	−19.7505	+	8.18090i	−0.858715	+	0.355692i
$530$	−6.73555	+	2.54832i	−0.292574	+	0.110692i
$531$	9.22004	−	0.908095i	0.400116	−	0.0394080i
$532$	−21.7507	−	13.4219i	−0.943013	−	0.581914i
$533$	−0.493595	−	0.263832i	−0.0213800	−	0.0114278i
$534$	2.16570	−	6.41617i	0.0937189	−	0.277655i
$535$	−1.52384	+	0.303110i	−0.0658812	+	0.0131046i
$536$	8.64612	+	42.3245i	0.373455	+	1.82814i
$537$	4.08678	−	20.5456i	0.176358	−	0.886610i
$538$	30.9368	−	8.34653i	1.33378	−	0.359845i
$539$	9.30903	+	0.916860i	0.400968	+	0.0394919i
$540$	2.85530	+	2.17538i	0.122872	+	0.0936135i
$541$	2.95675	+	0.896921i	0.127121	+	0.0385616i	0.353204	−	0.935546i	$-0.385092\pi$
$541$	2.95675	+	0.896921i	0.127121	+	0.0385616i	−0.226083	+	0.974108i	$0.572592\pi$
$542$	5.54771	+	8.88732i	0.238295	+	0.381743i
$543$	−4.23907	−	4.23907i	−0.181916	−	0.181916i
$544$	−14.1617	+	6.56393i	−0.607176	+	0.281426i
$545$	−17.5718	+	17.5718i	−0.752694	+	0.752694i
$546$	1.50193	+	0.347478i	0.0642767	+	0.0148707i
$547$	−6.84441	+	22.5630i	−0.292646	+	0.964724i	0.680152	+	0.733071i	$0.261914\pi$
$547$	−6.84441	+	22.5630i	−0.292646	+	0.964724i	−0.972798	+	0.231653i	$0.925586\pi$
$548$	−28.1622	−	7.44230i	−1.20303	−	0.317919i
$549$	0.929088	−	9.43319i	0.0396525	−	0.402599i
$550$	5.08707	+	2.92537i	0.216913	+	0.124738i
$551$	9.33953	+	1.85775i	0.397877	+	0.0791427i
$552$	−3.32113	+	1.39578i	−0.141357	+	0.0594082i
$553$	−1.59132	−	8.00011i	−0.0676698	−	0.340199i
$554$	−14.6738	−	29.6270i	−0.623431	−	1.25873i
$555$	−0.0965736	+	0.180676i	−0.00409932	+	0.00766929i
$556$	27.2735	−	19.6862i	1.15665	−	0.834882i
$557$	0.881057	+	8.94552i	0.0373316	+	0.379034i	0.995639	+	0.0932936i	$0.0297395\pi$
$557$	0.881057	+	8.94552i	0.0373316	+	0.379034i	−0.958307	+	0.285740i	$0.907760\pi$
$558$	−10.2168	−	4.60799i	−0.432510	−	0.195072i
$559$	1.46782	+	3.54364i	0.0620823	+	0.149880i
$560$	4.45276	+	11.5882i	0.188163	+	0.489692i
$561$	2.46328	−	5.94688i	0.104000	−	0.251078i
$562$	−24.4356	+	22.9654i	−1.03075	+	0.968738i
$563$	−30.7164	−	25.2083i	−1.29454	−	1.06240i	−0.994085	−	0.108608i	$-0.965361\pi$
$563$	−30.7164	−	25.2083i	−1.29454	−	1.06240i	−0.300458	−	0.953795i	$-0.597139\pi$
$564$	9.18569	+	3.42122i	0.386787	+	0.144059i
$565$	−9.68184	+	2.93695i	−0.407318	+	0.123559i
$566$	13.6956	+	11.9692i	0.575671	+	0.503101i
$567$	1.43779	+	0.960701i	0.0603815	+	0.0403456i
$568$	0.179051	−	0.0553249i	0.00751280	−	0.00232138i
$569$	−0.441823	−	0.661235i	−0.0185222	−	0.0277204i	0.822093	−	0.569353i	$-0.192806\pi$
$569$	−0.441823	−	0.661235i	−0.0185222	−	0.0277204i	−0.840615	+	0.541633i	$0.817806\pi$
$570$	−11.4447	−	14.8620i	−0.479365	−	0.622501i
$571$	15.9314	+	19.4125i	0.666708	+	0.812386i	0.991041	−	0.133557i	$-0.0426399\pi$
$571$	15.9314	+	19.4125i	0.666708	+	0.812386i	−0.324333	+	0.945943i	$0.605140\pi$
$572$	−0.182263	+	2.93548i	−0.00762079	+	0.122739i
$573$	−10.6653	+	5.70074i	−0.445551	+	0.238152i
$574$	−0.357360	−	2.14158i	−0.0149159	−	0.0893877i
$575$			2.26556i			0.0944804i
$576$	7.35905	−	3.13757i	0.306627	−	0.130732i
$577$			23.1912i			0.965463i	0.875768	+	0.482731i	$0.160355\pi$
$577$			23.1912i			0.965463i	−0.875768	+	0.482731i	$0.839645\pi$
$578$	−13.0932	+	2.18484i	−0.544606	+	0.0908773i
$579$	11.8444	−	6.33099i	0.492238	−	0.263107i
$580$	−3.06159	−	3.46694i	−0.127125	−	0.143957i
$581$	19.6930	+	23.9959i	0.817002	+	0.995520i
$582$	−0.277088	+	0.213375i	−0.0114857	+	0.00884470i
$583$	−3.67715	−	5.50324i	−0.152292	−	0.227921i
$584$	−6.08033	+	5.04272i	−0.251606	+	0.208669i
$585$	0.940733	+	0.628578i	0.0388945	+	0.0259885i
$586$	−19.2031	+	21.9730i	−0.793272	+	0.907697i
$587$	−36.4041	+	11.0431i	−1.50256	+	0.455796i	−0.931078	−	0.364820i	$-0.881131\pi$
$587$	−36.4041	+	11.0431i	−1.50256	+	0.455796i	−0.571480	+	0.820616i	$0.693631\pi$
$588$	−3.33486	−	7.29336i	−0.137527	−	0.300773i
$589$	45.2741	+	37.1555i	1.86549	+	1.53097i
$590$	16.1046	+	17.1355i	0.663016	+	0.705459i
$591$	−7.08860	+	17.1134i	−0.291586	+	0.703950i
$592$	0.243768	+	0.386063i	0.0100188	+	0.0158671i
$593$	−11.6963	−	28.2374i	−0.480310	−	1.15957i	−0.959462	−	0.281839i	$-0.909056\pi$
$593$	−11.6963	−	28.2374i	−0.480310	−	1.15957i	0.479152	−	0.877732i	$-0.340944\pi$
$594$	−1.35638	+	3.00734i	−0.0556529	+	0.123393i
$595$	−0.839385	−	8.52241i	−0.0344114	−	0.349385i
$596$	1.69768	−	10.5074i	0.0695396	−	0.430402i
$597$	4.40822	−	8.24720i	0.180416	−	0.337535i
$598$	−1.01753	+	0.503966i	−0.0416097	+	0.0206087i
$599$	−9.07754	−	45.6359i	−0.370898	−	1.86463i	−0.489960	−	0.871745i	$-0.662988\pi$
$599$	−9.07754	−	45.6359i	−0.370898	−	1.86463i	0.119061	−	0.992887i	$-0.462012\pi$
$600$	−0.0259587	−	5.03099i	−0.00105976	−	0.205390i
$601$	−40.2119	−	7.99864i	−1.64028	−	0.326271i	−0.713148	−	0.701014i	$-0.752731\pi$
$601$	−40.2119	−	7.99864i	−1.64028	−	0.326271i	−0.927129	+	0.374742i	$0.877731\pi$
$602$	−7.41762	+	12.8989i	−0.302319	+	0.525719i
$603$	−1.49702	+	15.1995i	−0.0609632	+	0.618970i
$604$	0.0976713	+	0.167836i	0.00397419	+	0.00682914i
$605$	−2.89574	+	9.54598i	−0.117729	+	0.388099i
$606$	4.16313	−	17.9946i	0.169116	−	0.730980i
$607$	6.01560	−	6.01560i	0.244166	−	0.244166i	−0.574405	−	0.818571i	$-0.694767\pi$
$607$	6.01560	−	6.01560i	0.244166	−	0.244166i	0.818571	+	0.574405i	$0.194767\pi$
$608$	−41.3993	+	5.81293i	−1.67896	+	0.235745i
$609$	−1.57553	−	1.57553i	−0.0638438	−	0.0638438i
$610$	20.4093	−	12.7400i	0.826348	−	0.515829i
$611$	2.95653	+	0.896855i	0.119609	+	0.0362829i
$612$	−5.46886	+	0.739136i	−0.221066	+	0.0298778i
$613$	1.75047	+	0.172407i	0.0707009	+	0.00696343i	0.133306	−	0.991075i	$-0.457441\pi$
$613$	1.75047	+	0.172407i	0.0707009	+	0.00696343i	−0.0626048	+	0.998038i	$0.519941\pi$
$614$	0.671499	+	2.48894i	0.0270995	+	0.100445i
$615$	0.310872	−	1.56286i	0.0125356	−	0.0630205i
$616$	−9.45392	+	6.38771i	−0.380909	+	0.257368i
$617$	−19.5302	+	3.88479i	−0.786255	+	0.156396i	−0.571860	−	0.820351i	$-0.693778\pi$
$617$	−19.5302	+	3.88479i	−0.786255	+	0.156396i	−0.214395	+	0.976747i	$0.568778\pi$
$618$	18.1212	+	6.11657i	0.728941	+	0.246045i
$619$	22.5927	+	12.0760i	0.908077	+	0.485377i	0.858163	−	0.513377i	$-0.171606\pi$
$619$	22.5927	+	12.0760i	0.908077	+	0.485377i	0.0499131	+	0.998754i	$0.484106\pi$
$620$	−6.55509	−	27.6823i	−0.263259	−	1.11175i
$621$	−1.26755	+	0.124843i	−0.0508650	+	0.00500976i
$622$	10.4353	+	27.5818i	0.418416	+	1.10593i
$623$	7.64989	−	3.16869i	0.306486	−	0.126951i
$624$	2.25379	−	1.13079i	0.0902236	−	0.0452677i
$625$	11.9571	+	4.95281i	0.478285	+	0.198112i
$626$	0.287531	−	9.27071i	0.0114920	−	0.370532i
$627$	10.9369	−	13.3266i	0.436776	−	0.532214i
$628$	−0.814365	−	22.5084i	−0.0324967	−	0.898182i
$629$	−0.0914284	−	0.301399i	−0.00364549	−	0.0120176i
$630$	0.294594	+	4.37921i	0.0117369	+	0.174472i
$631$	−11.3395	+	16.9708i	−0.451419	+	0.675597i	−0.985469	−	0.169856i	$-0.945670\pi$
$631$	−11.3395	+	16.9708i	−0.451419	+	0.675597i	0.534049	+	0.845453i	$0.320670\pi$
$632$	−10.3570	−	8.41069i	−0.411978	−	0.334559i
$633$	−15.2773	+	10.2079i	−0.607217	+	0.405729i
$634$	48.4334	+	6.29166i	1.92354	+	0.249874i
$635$	−12.0569	+	9.89480i	−0.478462	+	0.392663i
$636$	−2.49223	+	5.09788i	−0.0988235	+	0.202144i
$637$	−1.19157	−	2.22927i	−0.0472116	−	0.0883267i
$638$	2.47013	−	3.45962i	0.0977934	−	0.136968i
$639$	0.0662571			0.00262109
$640$	17.7062	+	9.94039i	0.699898	+	0.392928i
$641$	−40.8810			−1.61470			−0.807351	−	0.590072i	$-0.799100\pi$
$641$	−40.8810			−1.61470			−0.807351	+	0.590072i	$0.799100\pi$
$642$	−0.711380	+	0.996345i	−0.0280759	+	0.0393226i
$643$	7.81035	+	14.6121i	0.308010	+	0.576247i	0.987534	−	0.157407i	$-0.0503135\pi$
$643$	7.81035	+	14.6121i	0.308010	+	0.576247i	−0.679524	+	0.733654i	$0.737813\pi$
$644$	−3.95735	−	1.93465i	−0.155941	−	0.0762361i
$645$	−8.44159	+	6.92783i	−0.332387	+	0.272783i
$646$	28.5980	+	3.71498i	1.12517	+	0.146164i
$647$	20.0496	−	13.3967i	0.788233	−	0.526680i	−0.0950771	−	0.995470i	$-0.530310\pi$
$647$	20.0496	−	13.3967i	0.788233	−	0.526680i	0.883310	+	0.468790i	$0.155310\pi$
$648$	2.81334	−	0.291754i	0.110518	−	0.0114612i
$649$	−12.0073	+	17.9702i	−0.471327	+	0.705391i
$650$	−0.106435	−	1.58218i	−0.00417473	−	0.0620584i
$651$	−3.97814	−	13.1142i	−0.155916	−	0.513985i
$652$	−38.9167	+	1.40803i	−1.52410	+	0.0551426i
$653$	−27.9973	+	34.1148i	−1.09562	+	1.33502i	−0.157966	+	0.987444i	$0.550494\pi$
$653$	−27.9973	+	34.1148i	−1.09562	+	1.33502i	−0.937653	+	0.347572i	$0.887006\pi$
$654$	−0.607011	+	19.5716i	−0.0237360	+	0.765308i
$655$	−13.1727	−	5.45630i	−0.514699	−	0.213195i
$656$	−2.68609	−	2.32314i	−0.104874	−	0.0907034i
$657$	−2.58024	+	1.06877i	−0.100665	+	0.0416968i
$658$	4.24116	+	11.2100i	0.165338	+	0.437010i
$659$	−1.99566	+	0.196556i	−0.0777399	+	0.00765672i	−0.136812	−	0.990597i	$-0.543686\pi$
$659$	−1.99566	+	0.196556i	−0.0777399	+	0.00765672i	0.0590724	+	0.998254i	$0.481186\pi$
$660$	−8.14840	+	1.92952i	−0.317176	+	0.0751063i
$661$	32.0304	+	17.1206i	1.24584	+	0.665914i	0.956617	−	0.291348i	$-0.0941039\pi$
$661$	32.0304	+	17.1206i	1.24584	+	0.665914i	0.289221	+	0.957262i	$0.406604\pi$
$662$	9.81872	+	3.31418i	0.381615	+	0.128809i
$663$	−1.70600	+	0.339345i	−0.0662556	+	0.0131791i
$664$	49.8496	+	9.64859i	1.93454	+	0.374438i
$665$	4.47461	−	22.4954i	0.173518	−	0.872333i
$666$	0.0420483	+	0.155854i	0.00162934	+	0.00603921i
$667$	1.63327	+	0.160863i	0.0632404	+	0.00622864i
$668$	0.659547	+	4.87998i	0.0255186	+	0.188812i
$669$	−27.6864	−	8.39859i	−1.07042	−	0.324708i
$670$	−32.8850	+	20.5277i	−1.27046	+	0.793054i
$671$	15.6357	+	15.6357i	0.603608	+	0.603608i
$672$	8.81002	+	4.25083i	0.339854	+	0.163979i
$673$	−10.0344	+	10.0344i	−0.386799	+	0.386799i	−0.873544	−	0.486745i	$-0.838184\pi$
$673$	−10.0344	+	10.0344i	−0.386799	+	0.386799i	0.486745	+	0.873544i	$0.338184\pi$
$674$	−0.751806	+	3.24958i	−0.0289585	+	0.125169i
$675$	0.516344	−	1.70216i	0.0198741	−	0.0655160i
$676$	−21.7849	+	12.6776i	−0.837880	+	0.487601i
$677$	0.0193445	−	0.196408i	0.000743469	−	0.00754857i	−0.994806	−	0.101791i	$-0.967543\pi$
$677$	0.0193445	−	0.196408i	0.000743469	−	0.00754857i	0.995549	+	0.0942422i	$0.0300428\pi$
$678$	−3.97420	+	6.91094i	−0.152628	+	0.265413i
$679$	−0.419405	−	0.0834249i	−0.0160953	−	0.00320155i
$680$	−9.95564	−	9.85343i	−0.381781	−	0.377862i
$681$	3.19711	+	16.0730i	0.122514	+	0.615917i
$682$	23.4294	−	11.6042i	0.897156	−	0.444349i
$683$	6.77389	−	12.6731i	0.259196	−	0.484921i	−0.718340	−	0.695692i	$-0.755098\pi$
$683$	6.77389	−	12.6731i	0.259196	−	0.484921i	0.977535	+	0.210772i	$0.0675976\pi$
$684$	−14.5912	−	2.35749i	−0.557909	−	0.0901409i
$685$	−2.56218	−	26.0142i	−0.0978958	−	0.993953i
$686$	11.0696	−	24.5434i	0.422641	−	0.937073i
$687$	−11.1339	−	26.8797i	−0.424786	−	1.02552i
$688$	4.12967	+	23.9852i	0.157442	+	0.914426i
$689$	−0.684452	+	1.65241i	−0.0260755	+	0.0629519i
$690$	−2.21402	−	2.35575i	−0.0842863	−	0.0896819i
$691$	−9.60092	−	7.87928i	−0.365236	−	0.299742i	0.433818	−	0.901001i	$-0.357166\pi$
$691$	−9.60092	−	7.87928i	−0.365236	−	0.299742i	−0.799054	+	0.601259i	$0.794666\pi$
$692$	17.0590	−	7.80019i	0.648487	−	0.296519i
$693$	−3.86021	+	1.17098i	−0.146637	+	0.0444819i
$694$	7.67443	−	8.78143i	0.291317	−	0.333338i
$695$	25.0977	+	16.7698i	0.952012	+	0.636114i
$696$	−3.62875	−	0.338505i	−0.137547	−	0.0128310i
$697$	1.36104	+	2.03693i	0.0515529	+	0.0771544i
$698$	4.38386	−	3.37585i	0.165931	−	0.127778i
$699$	13.4180	+	16.3498i	0.507514	+	0.618407i
$700$	4.61110	−	4.07197i	0.174283	−	0.153906i
$701$	−10.7404	+	5.74087i	−0.405660	+	0.216830i	−0.661590	−	0.749865i	$-0.730118\pi$
$701$	−10.7404	+	5.74087i	−0.405660	+	0.216830i	0.255930	+	0.966695i	$0.417618\pi$
$702$	0.879345	−	0.146734i	0.0331887	−	0.00553813i
$703$		−	0.843562i		−	0.0318156i
$704$	−5.23282	+	17.9137i	−0.197219	+	0.675149i
$705$			8.79635i			0.331290i
$706$	−4.09200	−	24.5224i	−0.154005	−	0.922913i
$707$	19.9172	−	10.6460i	0.749063	−	0.400383i
$708$	18.4937	+	1.14827i	0.695036	+	0.0431545i
$709$	7.63466	+	9.30286i	0.286726	+	0.349376i	0.896376	−	0.443294i	$-0.146190\pi$
$709$	7.63466	+	9.30286i	0.286726	+	0.349376i	−0.609651	+	0.792670i	$0.708690\pi$
$710$	0.102607	+	0.133245i	0.00385078	+	0.00500061i
$711$	−2.62067	−	3.92210i	−0.0982827	−	0.147090i
$712$	6.32271	−	11.9772i	0.236954	−	0.448865i
$713$	8.39294	+	5.60798i	0.314318	+	0.210021i
$714$	−5.08090	−	4.44040i	−0.190148	−	0.166178i
$715$	−2.52570	+	0.766163i	−0.0944558	+	0.0286529i
$716$	14.6230	−	39.2615i	0.546488	−	1.46727i
$717$	−10.3353	−	8.48194i	−0.385978	−	0.316764i
$718$	1.04988	−	0.986716i	0.0391812	−	0.0368239i
$719$	20.2384	−	48.8598i	0.754765	−	1.82216i	0.224142	−	0.974556i	$-0.428042\pi$
$719$	20.2384	−	48.8598i	0.754765	−	1.82216i	0.530623	−	0.847608i	$-0.321958\pi$
$720$	4.94353	+	5.20591i	0.184235	+	0.194013i
$721$	8.94931	+	21.6055i	0.333290	+	0.804632i
$722$	45.9139	+	20.7082i	1.70874	+	0.770680i
$723$	0.830214	+	8.42931i	0.0308760	+	0.313489i
$724$	−7.01733	−	9.72187i	−0.260797	−	0.361310i
$725$	−1.08042	+	2.02133i	−0.0401260	+	0.0750704i
$726$	3.48864	+	7.04369i	0.129475	+	0.261416i
$727$	−8.31967	−	41.8258i	−0.308560	−	1.55123i	−0.754578	−	0.656210i	$-0.772158\pi$
$727$	−8.31967	−	41.8258i	−0.308560	−	1.55123i	0.446019	−	0.895024i	$-0.352842\pi$
$728$	2.85456	+	1.16518i	0.105797	+	0.0431844i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−6.14517	−	3.53384i	−0.227443	−	0.130793i
$731$	1.64561	−	16.7081i	0.0608649	−	0.617972i
$732$	4.84359	−	18.3285i	0.179024	−	0.677440i
$733$	−7.52152	+	24.7951i	−0.277814	+	0.915830i	0.701360	+	0.712807i	$0.252576\pi$
$733$	−7.52152	+	24.7951i	−0.277814	+	0.915830i	−0.979174	+	0.203023i	$0.934924\pi$
$734$	19.9196	+	4.60850i	0.735247	+	0.170103i
$735$	5.08887	−	5.08887i	0.187706	−	0.187706i
$736$	−7.00249	+	1.69637i	−0.258115	+	0.0625291i
$737$	−25.1934	−	25.1934i	−0.928009	−	0.928009i
$738$	−0.664870	−	1.06511i	−0.0244742	−	0.0392072i
$739$	−26.2478	−	7.96217i	−0.965539	−	0.292893i	−0.232133	−	0.972684i	$-0.574571\pi$
$739$	−26.2478	−	7.96217i	−0.965539	−	0.292893i	−0.733406	+	0.679791i	$0.762071\pi$
$740$	−0.248311	+	0.325920i	−0.00912808	+	0.0119810i
$741$	−4.63628	−	0.456633i	−0.170318	−	0.0167748i
$742$	−6.69889	+	1.80732i	−0.245924	+	0.0663486i
$743$	4.06044	−	20.4132i	0.148963	−	0.748887i	−0.832013	−	0.554757i	$-0.812811\pi$
$743$	4.06044	−	20.4132i	0.148963	−	0.748887i	0.980976	−	0.194131i	$-0.0621886\pi$
$744$	−18.7020	−	12.3572i	−0.685647	−	0.453035i
$745$	9.36805	−	1.86342i	0.343219	−	0.0682705i
$746$	10.7362	−	31.8075i	0.393081	−	1.16455i
$747$	15.8319	+	8.46233i	0.579259	+	0.309620i
$748$	6.76055	−	10.9557i	0.247190	−	0.400581i
$749$	−1.48972	+	0.146725i	−0.0544332	+	0.00536120i
$750$	16.0926	−	6.08846i	0.587620	−	0.222319i
$751$	−7.69905	+	3.18905i	−0.280942	+	0.116370i	−0.518705	−	0.854953i	$-0.673586\pi$
$751$	−7.69905	+	3.18905i	−0.280942	+	0.116370i	0.237763	+	0.971323i	$0.423586\pi$
$752$	17.0448	+	9.68509i	0.621560	+	0.353179i
$753$	−4.39292	−	1.81961i	−0.160087	−	0.0663101i
$754$	−1.14817	−	0.0356105i	−0.0418140	−	0.00129686i
$755$	−0.110550	+	0.134706i	−0.00402334	+	0.00490246i
$756$	2.53230	+	2.35546i	0.0920990	+	0.0856673i
$757$	−10.3443	−	34.1008i	−0.375972	−	1.23941i	−0.917163	−	0.398513i	$-0.869526\pi$
$757$	−10.3443	−	34.1008i	−0.375972	−	1.23941i	0.541191	−	0.840900i	$-0.317974\pi$
$758$	−31.1037	+	2.09238i	−1.12974	+	0.0759985i
$759$	1.65073	−	2.47050i	0.0599178	−	0.0896733i
$760$	−17.8553	−	32.9943i	−0.647681	−	1.19683i
$761$	−42.4044	+	28.3337i	−1.53716	+	1.02710i	−0.556620	+	0.830767i	$0.687902\pi$
$761$	−42.4044	+	28.3337i	−1.53716	+	1.02710i	−0.980538	+	0.196329i	$0.937098\pi$
$762$	−1.58321	+	12.1876i	−0.0573535	+	0.441510i
$763$	−18.5078	+	15.1889i	−0.670026	+	0.549876i
$764$	−22.8761	+	7.85326i	−0.827629	+	0.284121i
$765$	−2.33451	−	4.36757i	−0.0844045	−	0.157910i
$766$	13.0650	+	9.32825i	0.472056	+	0.337043i
$767$	5.84033			0.210882
$768$	15.5306	−	3.84727i	0.560411	−	0.138826i
$769$	8.75470			0.315703			0.157851	−	0.987463i	$-0.449543\pi$
$769$	8.75470			0.315703			0.157851	+	0.987463i	$0.449543\pi$
$770$	−8.33290	−	5.94961i	−0.300297	−	0.214409i
$771$	−3.54464	−	6.63156i	−0.127657	−	0.238830i
$772$	25.4052	−	8.72148i	0.914353	−	0.313893i
$773$	14.4056	−	11.8224i	0.518133	−	0.425221i	−0.338639	−	0.940917i	$-0.609966\pi$
$773$	14.4056	−	11.8224i	0.518133	−	0.425221i	0.856772	+	0.515695i	$0.172466\pi$
$774$	−1.10848	+	8.53312i	−0.0398435	+	0.306717i
$775$	−11.7211	+	7.83178i	−0.421034	+	0.281326i
$776$	−0.615149	+	0.332896i	−0.0220826	+	0.0119503i
$777$	−0.109660	+	0.164118i	−0.00393403	+	0.00588769i
$778$	45.1728	−	3.03882i	1.61952	−	0.108947i
$779$	1.90465	+	6.27878i	0.0682411	+	0.224961i
$780$	1.65686	+	1.54116i	0.0593252	+	0.0551823i
$781$	−0.0980545	+	0.119480i	−0.00350867	+	0.00427532i
$782$	4.96781	+	0.154076i	0.177648	+	0.00550976i
$783$	−1.19044	−	0.493098i	−0.0425430	−	0.0176219i
$784$	−4.25775	−	15.4638i	−0.152062	−	0.552279i
$785$	18.6735	−	7.73482i	0.666486	−	0.276068i
$786$	−10.5078	+	3.97550i	−0.374801	+	0.141801i
$787$	−9.99970	+	0.984885i	−0.356451	+	0.0351073i	−0.274658	−	0.961542i	$-0.588565\pi$
$787$	−9.99970	+	0.984885i	−0.356451	+	0.0351073i	−0.0817929	+	0.996649i	$0.526065\pi$
$788$	−19.4549	+	31.5273i	−0.693052	+	1.12311i
$789$	10.0948	+	5.39578i	0.359384	+	0.192095i
$790$	3.82906	−	11.3441i	0.136232	−	0.403606i
$791$	−9.56057	+	1.90172i	−0.339935	+	0.0676173i
$792$	−3.63738	+	5.50500i	−0.129249	+	0.195612i
$793$	1.16573	−	5.86053i	0.0413963	−	0.208113i
$794$	40.3775	−	10.8936i	1.43294	−	0.386599i
$795$	−5.06771	−	0.499125i	−0.179733	−	0.0177022i
$796$	11.3344	−	14.8770i	0.401738	−	0.527301i
$797$	−46.5187	−	14.1113i	−1.64778	−	0.499848i	−0.676229	−	0.736691i	$-0.736387\pi$
$797$	−46.5187	−	14.1113i	−1.64778	−	0.499848i	−0.971548	+	0.236844i	$0.923887\pi$
$798$	−9.56997	−	15.3309i	−0.338773	−	0.542708i
$799$	−9.56252	−	9.56252i	−0.338298	−	0.338298i
$800$	1.55364	−	9.94146i	0.0549295	−	0.351484i
$801$	3.38591	−	3.38591i	0.119635	−	0.119635i
$802$	3.79937	+	0.879001i	0.134160	+	0.0310386i
$803$	1.89124	−	6.23458i	0.0667404	−	0.220013i
$804$	−7.80435	+	29.5322i	−0.275238	+	1.04152i
$805$	0.387458	−	3.93393i	0.0136561	−	0.138653i
$806$	−6.12479	−	3.52211i	−0.215736	−	0.124061i
$807$	22.2224	+	4.42031i	0.782265	+	0.155602i
$808$	13.9600	−	34.2004i	0.491110	−	1.20317i
$809$	−6.57045	−	33.0319i	−0.231005	−	1.16134i	−0.905922	−	0.423445i	$-0.860821\pi$
$809$	−6.57045	−	33.0319i	−0.231005	−	1.16134i	0.674917	−	0.737894i	$-0.264179\pi$
$810$	1.12653	+	2.27452i	0.0395824	+	0.0799183i
$811$	18.1367	−	33.9313i	0.636864	−	1.19149i	−0.331855	−	0.943330i	$-0.607675\pi$
$811$	18.1367	−	33.9313i	0.636864	−	1.19149i	0.968719	−	0.248159i	$-0.0798254\pi$
$812$	−2.60813	−	3.61332i	−0.0915274	−	0.126803i
$813$	0.726127	+	7.37249i	0.0254664	+	0.258564i
$814$	−0.343275	−	0.154825i	−0.0120318	−	0.00542661i
$815$	−13.3734	−	32.2863i	−0.468450	−	1.13094i
$816$	−11.0335	−	0.285227i	−0.386249	−	0.00998494i
$817$	17.2077	−	41.5432i	0.602023	−	1.45341i
$818$	29.0870	−	27.3370i	1.01700	−	0.955816i
$819$	0.842641	+	0.691537i	0.0294443	+	0.0241643i
$820$	1.11234	−	2.98653i	0.0388445	−	0.104294i
$821$	28.9615	−	8.78537i	1.01076	−	0.306612i	0.258881	−	0.965909i	$-0.416646\pi$
$821$	28.9615	−	8.78537i	1.01076	−	0.306612i	0.751882	+	0.659298i	$0.229146\pi$
$822$	−15.5092	−	13.5541i	−0.540945	−	0.472753i
$823$	−31.3619	−	20.9554i	−1.09321	−	0.730458i	−0.127956	−	0.991780i	$-0.540841\pi$
$823$	−31.3619	−	20.9554i	−1.09321	−	0.730458i	−0.965252	+	0.261322i	$0.915841\pi$
$824$	33.8272	+	17.8572i	1.17843	+	0.622085i
$825$	2.30532	+	3.45015i	0.0802608	+	0.120119i
$826$	13.8233	+	17.9509i	0.480975	+	0.624591i
$827$	20.6666	+	25.1824i	0.718650	+	0.875677i	0.996383	−	0.0849812i	$-0.0270830\pi$
$827$	20.6666	+	25.1824i	0.718650	+	0.875677i	−0.277733	+	0.960658i	$0.589583\pi$
$828$	−2.54247	−	0.157861i	−0.0883569	−	0.00548605i
$829$	25.4910	−	13.6252i	0.885340	−	0.473224i	0.0349576	−	0.999389i	$-0.488870\pi$
$829$	25.4910	−	13.6252i	0.885340	−	0.473224i	0.850383	+	0.526164i	$0.176370\pi$
$830$	7.49963	+	44.9435i	0.260316	+	1.56001i
$831$		−	23.3782i		−	0.810981i
$832$	4.81059	−	1.51366i	0.166777	−	0.0524766i
$833$			11.0642i			0.383353i
$834$	23.4600	−	3.91471i	0.812352	−	0.135555i
$835$	−3.89727	+	2.08314i	−0.134871	+	0.0720899i
$836$	25.8449	−	22.8231i	0.893865	−	0.789354i
$837$	−5.02766	−	6.12622i	−0.173781	−	0.211753i
$838$	16.9854	−	13.0798i	0.586750	−	0.451835i
$839$	11.3738	+	17.0221i	0.392668	+	0.587669i	0.974153	−	0.225888i	$-0.0725282\pi$
$839$	11.3738	+	17.0221i	0.392668	+	0.587669i	−0.581485	+	0.813557i	$0.697528\pi$
$840$	−0.815330	+	8.74027i	−0.0281316	+	0.301568i
$841$	−22.7321	−	15.1891i	−0.783867	−	0.523763i
$842$	−3.34839	+	3.83138i	−0.115393	+	0.132038i
$843$	−22.6909	+	6.88320i	−0.781515	+	0.237070i
$844$	−33.4197	+	15.2811i	−1.15035	+	0.525996i
$845$	−17.4847	−	14.3493i	−0.601492	−	0.493632i
$846$	4.74677	+	5.05064i	0.163197	+	0.173645i
$847$	−3.67801	+	8.87949i	−0.126378	+	0.305103i
$848$	−6.54689	+	9.27021i	−0.224821	+	0.318340i
$849$	4.92185	+	11.8824i	0.168917	+	0.407802i
$850$	−2.85375	+	6.32730i	−0.0978830	+	0.217024i
$851$	−0.0142503	−	0.144685i	−0.000488492	−	0.00495975i
$852$	0.130818	+	0.0211361i	0.00448174	+	0.000724111i
$853$	−12.9508	+	24.2293i	−0.443428	+	0.829596i	−0.999999	−	0.00120436i	$-0.999617\pi$
$853$	−12.9508	+	24.2293i	−0.443428	+	0.829596i	0.556571	+	0.830800i	$0.312117\pi$
$854$	20.7721	−	10.2881i	0.710807	−	0.352052i
$855$	−2.58765	−	13.0090i	−0.0884958	−	0.444898i
$856$	−1.72238	+	1.74025i	−0.0588698	+	0.0594805i
$857$	−2.23041	−	0.443657i	−0.0761895	−	0.0151550i	0.156848	−	0.987623i	$-0.449867\pi$
$857$	−2.23041	−	0.443657i	−0.0761895	−	0.0151550i	−0.233038	+	0.972468i	$0.574867\pi$
$858$	−1.03675	+	1.80285i	−0.0353940	+	0.0615484i
$859$	−0.478493	+	4.85822i	−0.0163260	+	0.165760i	−0.999891	−	0.0147965i	$-0.995290\pi$
$859$	−0.478493	+	4.85822i	−0.0163260	+	0.165760i	0.983565	+	0.180557i	$0.0577899\pi$
$860$	−18.8770	+	10.9854i	−0.643701	+	0.374599i
$861$	0.445663	−	1.46915i	0.0151881	−	0.0500686i
$862$	3.69913	−	15.9890i	0.125993	−	0.544587i
$863$	4.53778	−	4.53778i	0.154468	−	0.154468i	−0.625642	−	0.780110i	$-0.715163\pi$
$863$	4.53778	−	4.53778i	0.154468	−	0.154468i	0.780110	+	0.625642i	$0.215163\pi$
$864$	5.64772	+	0.321421i	0.192139	+	0.0109350i
$865$	11.9028	+	11.9028i	0.404707	+	0.404707i
$866$	22.8607	−	14.2703i	0.776838	−	0.484924i
$867$	−8.98214	−	2.72470i	−0.305050	−	0.0925358i
$868$	−3.67099	−	27.1616i	−0.124601	−	0.921925i
$869$	10.9510	+	1.07858i	0.371487	+	0.0365883i
$870$	−0.851912	−	3.15765i	−0.0288825	−	0.107054i
$871$	−1.87831	+	9.44292i	−0.0636442	+	0.319961i
$872$	−7.44183	+	38.4484i	−0.252012	+	1.30203i
$873$	−0.242541	+	0.0482443i	−0.00820876	+	0.00163282i
$874$	12.6126	+	4.25722i	0.426627	+	0.144003i
$875$	18.5541	+	9.91740i	0.627245	+	0.335269i
$876$	−5.43536	+	1.28708i	−0.183644	+	0.0434863i
$877$	28.4677	−	2.80383i	0.961287	−	0.0946785i	0.394816	−	0.918760i	$-0.370808\pi$
$877$	28.4677	−	2.80383i	0.961287	−	0.0946785i	0.566471	+	0.824082i	$0.308308\pi$
$878$	−17.0514	−	45.0691i	−0.575456	−	1.52101i
$879$	−19.0639	+	7.89651i	−0.643008	+	0.266343i
$880$	−16.7037	+	1.21028i	−0.563081	+	0.0407985i
$881$	48.5637	+	20.1158i	1.63615	+	0.677717i	0.995901	−	0.0904472i	$-0.0288296\pi$
$881$	48.5637	+	20.1158i	1.63615	+	0.677717i	0.640253	+	0.768164i	$0.278830\pi$
$882$	0.175793	−	5.66801i	0.00591926	−	0.190852i
$883$	5.69669	−	6.94144i	0.191709	−	0.233598i	−0.668281	−	0.743909i	$-0.732970\pi$
$883$	5.69669	−	6.94144i	0.191709	−	0.233598i	0.859990	+	0.510311i	$0.170470\pi$
$884$	−3.47657	+	0.125784i	−0.116930	+	0.00423058i
$885$	4.82687	+	15.9121i	0.162253	+	0.534878i
$886$	−0.212105	−	3.15300i	−0.00712582	−	0.105927i
$887$	−26.6229	+	39.8440i	−0.893910	+	1.33783i	0.0469009	+	0.998900i	$0.485066\pi$
$887$	−26.6229	+	39.8440i	−0.893910	+	1.33783i	−0.940811	+	0.338932i	$0.889934\pi$
$888$	0.0333025	+	0.321131i	0.00111756	+	0.0107764i
$889$	−12.4949	+	8.34881i	−0.419065	+	0.280010i
$890$	12.0527	+	1.56568i	0.404007	+	0.0524818i
$891$	−1.80328	+	1.47991i	−0.0604120	+	0.0495789i
$892$	−51.9848	−	25.4142i	−1.74058	−	0.850929i
$893$	−17.0740	−	31.9431i	−0.571358	−	1.06894i
$894$	4.37334	−	6.12521i	0.146266	−	0.204858i
$895$	37.5974			1.25674
$896$	16.0384	+	11.2032i	0.535807	+	0.374274i
$897$	−0.802914			−0.0268085
$898$	−21.6982	+	30.3901i	−0.724078	+	1.01413i
$899$	4.81379	+	9.00596i	0.160549	+	0.300366i
$900$	1.56246	−	3.19602i	0.0520819	−	0.106534i
$901$	6.05171	−	4.96651i	0.201612	−	0.165458i
$902$	2.90463	+	0.377321i	0.0967137	+	0.0125634i
$903$	−8.74827	+	5.84541i	−0.291124	+	0.194523i
$904$	−10.0512	+	12.3771i	−0.334299	+	0.411658i
$905$	5.97774	−	8.94631i	0.198707	−	0.297386i
$906$	0.00921620	+	0.137001i	0.000306188	+	0.00455156i
$907$	−4.23364	−	13.9564i	−0.140576	−	0.463416i	0.858177	−	0.513355i	$-0.171597\pi$
$907$	−4.23364	−	13.9564i	−0.140576	−	0.463416i	−0.998752	+	0.0499387i	$0.984097\pi$
$908$	1.18507	+	32.7543i	0.0393278	+	1.08699i
$909$	8.28529	−	10.0957i	0.274806	−	0.334852i
$910$	−0.0857723	+	2.76551i	−0.00284332	+	0.0916759i
$911$	27.6037	+	11.4338i	0.914552	+	0.378820i	0.789797	−	0.613368i	$-0.210186\pi$
$911$	27.6037	+	11.4338i	0.914552	+	0.378820i	0.124754	+	0.992188i	$0.460186\pi$
$912$	−28.0568	−	9.30924i	−0.929054	−	0.308260i
$913$	−38.6897	+	16.0258i	−1.28044	+	0.530377i
$914$	2.70519	+	7.15020i	0.0894798	+	0.236507i
$915$	16.9305	−	1.66751i	0.559706	−	0.0551263i
$916$	−13.4081	−	56.6229i	−0.443017	−	1.87087i
$917$	−12.1151	−	6.47563i	−0.400074	−	0.213844i
$918$	−3.69729	−	1.24797i	−0.122029	−	0.0411892i
$919$	4.39365	−	0.873952i	0.144933	−	0.0288290i	−0.122090	−	0.992519i	$-0.538960\pi$
$919$	4.39365	−	0.873952i	0.144933	−	0.0288290i	0.267024	+	0.963690i	$0.413960\pi$
$920$	−3.61986	−	5.35746i	−0.119343	−	0.176630i
$921$	−0.355625	+	1.78785i	−0.0117182	+	0.0589115i
$922$	14.2696	+	52.8907i	0.469943	+	1.74186i
$923$	0.0415665	+	0.00409395i	0.00136818	+	0.000134754i
$924$	−7.99513	+	1.08057i	−0.263020	+	0.0355481i
$925$	0.194294	+	0.0589384i	0.00638834	+	0.00193788i
$926$	30.0145	−	18.7359i	0.986337	−	0.615699i
$927$	9.56281	+	9.56281i	0.314084	+	0.314084i
$928$	−7.05660	−	1.82592i	−0.231644	−	0.0599387i
$929$	−3.59959	+	3.59959i	−0.118099	+	0.118099i	−0.763686	−	0.645588i	$-0.776613\pi$
$929$	−3.59959	+	3.59959i	−0.118099	+	0.118099i	0.645588	+	0.763686i	$0.276613\pi$
$930$	4.53409	−	19.5980i	0.148679	−	0.642644i
$931$	−8.60212	+	28.3574i	−0.281923	+	0.929376i
$932$	21.2767	+	36.5614i	0.696943	+	1.19761i
$933$	−2.04390	+	20.7521i	−0.0669143	+	0.679392i
$934$	−19.5165	+	33.9383i	−0.638600	+	1.11049i
$935$	11.3308	+	2.25384i	0.370557	+	0.0737083i
$936$	1.78298	−	0.00919977i	0.0582786	−	0.000300704i
$937$	0.0436105	+	0.219245i	0.00142469	+	0.00716242i	0.981491	−	0.191508i	$-0.0613377\pi$
$937$	0.0436105	+	0.219245i	0.00142469	+	0.00716242i	−0.980066	+	0.198670i	$0.936338\pi$
$938$	−33.4696	+	16.5770i	−1.09282	+	0.541258i
$939$	3.09167	−	5.78411i	0.100893	−	0.188757i
$940$	−2.80605	+	17.3675i	−0.0915231	+	0.566464i
$941$	0.380716	+	3.86547i	0.0124110	+	0.126011i	0.999394	−	0.0348151i	$-0.0110842\pi$
$941$	0.380716	+	3.86547i	0.0124110	+	0.126011i	−0.986983	+	0.160826i	$0.948584\pi$
$942$	6.54791	−	14.5179i	0.213342	−	0.473019i
$943$	0.432747	+	1.04474i	0.0140922	+	0.0340215i
$944$	36.1476	+	8.16665i	1.17650	+	0.265802i
$945$	−1.18768	+	2.86732i	−0.0386354	+	0.0932741i
$946$	−13.7471	−	14.6271i	−0.446957	−	0.475569i
$947$	−28.0688	−	23.0355i	−0.912113	−	0.748552i	0.0561661	−	0.998421i	$-0.482112\pi$
$947$	−28.0688	−	23.0355i	−0.912113	−	0.748552i	−0.968280	+	0.249869i	$0.919612\pi$
$948$	−3.92308	−	8.57978i	−0.127416	−	0.278658i
$949$	−1.68476	+	0.511066i	−0.0546896	+	0.0165899i
$950$	−12.2334	+	13.9980i	−0.396904	+	0.454156i
$951$	28.7151	+	19.1868i	0.931151	+	0.622175i
$952$	−8.61522	−	10.3879i	−0.279221	−	0.336674i
$953$	29.2529	+	43.7801i	0.947594	+	1.41818i	0.908005	+	0.418959i	$0.137605\pi$
$953$	29.2529	+	43.7801i	0.947594	+	1.41818i	0.0395895	+	0.999216i	$0.487395\pi$
$954$	−3.17909	+	2.44810i	−0.102927	+	0.0792602i
$955$	−13.7694	−	16.7781i	−0.445568	−	0.542926i
$956$	−17.7002	−	20.0437i	−0.572464	−	0.648258i
$957$	2.65094	−	1.41696i	0.0856927	−	0.0458037i
$958$	−53.1989	+	8.87719i	−1.71878	+	0.286809i
$959$		−	25.1851i		−	0.813270i
$960$	8.09980	+	11.8555i	0.261420	+	0.382635i
$961$			31.8078i			1.02606i
$962$	0.0167491	+	0.100373i	0.000540013	+	0.00323617i
$963$	−0.763452	+	0.408074i	−0.0246019	+	0.0131500i
$964$	−1.04979	+	16.9076i	−0.0338114	+	0.544558i
$965$	15.2917	+	18.6330i	0.492257	+	0.599817i
$966$	−1.90040	−	2.46784i	−0.0611442	−	0.0794016i
$967$	−3.54865	−	5.31094i	−0.114117	−	0.170788i	0.770014	−	0.638027i	$-0.220249\pi$
$967$	−3.54865	−	5.31094i	−0.114117	−	0.170788i	−0.884131	+	0.467238i	$0.845249\pi$
$968$	4.64100	+	15.0199i	0.149167	+	0.482758i
$969$	16.9551	+	11.3291i	0.544678	+	0.363942i
$970$	−0.472625	−	0.413046i	−0.0151751	−	0.0132621i
$971$	3.60240	−	1.09278i	0.115607	−	0.0350689i	−0.231951	−	0.972727i	$-0.574511\pi$
$971$	3.60240	−	1.09278i	0.115607	−	0.0350689i	0.347558	+	0.937659i	$0.387011\pi$
$972$	1.87422	+	0.698057i	0.0601158	+	0.0223902i
$973$	22.4807	+	18.4495i	0.720699	+	0.591463i
$974$	28.9306	−	27.1900i	0.926996	−	0.871224i
$975$	0.429104	−	1.03595i	0.0137423	−	0.0331769i
$976$	15.4100	−	34.6425i	0.493261	−	1.10888i
$977$	12.4276	+	30.0029i	0.397595	+	0.959878i	0.988235	+	0.152943i	$0.0488752\pi$
$977$	12.4276	+	30.0029i	0.397595	+	0.959878i	−0.590640	+	0.806935i	$0.701125\pi$
$978$	−25.1013	−	11.3213i	−0.802651	−	0.362014i
$979$	1.09489	+	11.1166i	0.0349927	+	0.355287i
$980$	11.6708	−	8.42409i	0.372810	−	0.269098i
$981$	−6.52688	+	12.2109i	−0.208387	+	0.389865i
$982$	−4.79592	−	9.68314i	−0.153044	−	0.309001i
$983$	2.64922	+	13.3185i	0.0844969	+	0.424795i	0.999759	+	0.0219365i	$0.00698317\pi$
$983$	2.64922	+	13.3185i	0.0844969	+	0.424795i	−0.915262	+	0.402858i	$0.868017\pi$
$984$	−0.972945	−	2.31504i	−0.0310164	−	0.0738008i
$985$	−32.6067	−	6.48587i	−1.03894	−	0.206657i
$986$	4.35880	+	2.50657i	0.138812	+	0.0798254i
$987$	−0.830694	+	8.43418i	−0.0264413	+	0.268463i
$988$	−9.00818	−	2.38055i	−0.286588	−	0.0757355i
$989$	2.24963	−	7.41604i	0.0715341	−	0.235816i
$990$	−5.76875	−	1.33463i	−0.183343	−	0.0424172i
$991$	7.16895	−	7.16895i	0.227729	−	0.227729i	−0.584014	−	0.811743i	$-0.698519\pi$
$991$	7.16895	−	7.16895i	0.227729	−	0.227729i	0.811743	+	0.584014i	$0.198519\pi$
$992$	−32.9831	−	30.3639i	−1.04722	−	0.964054i
$993$	5.18148	+	5.18148i	0.164429	+	0.164429i
$994$	0.0857996	+	0.137449i	0.00272140	+	0.00435962i
$995$	16.0610	+	4.87206i	0.509169	+	0.154455i
$996$	28.5589	+	21.7584i	0.904925	+	0.689441i
$997$	−16.5017	−	1.62528i	−0.522614	−	0.0514730i	−0.166729	−	0.986003i	$-0.553321\pi$
$997$	−16.5017	−	1.62528i	−0.522614	−	0.0514730i	−0.355885	+	0.934530i	$0.615821\pi$
$998$	−28.1845	+	7.60400i	−0.892165	+	0.240700i
$999$	−0.0222687	+	0.111952i	−0.000704551	+	0.00354202i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.27	✓	512
128.45	even	32	inner	384.2.v.a.301.27	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.27	✓	512	1.1	even	1	trivial
384.2.v.a.301.27	yes	512	128.45	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)

\(f(q)\)	\(=\)	\(q+(1.15095 + 0.821770i) q^{2} +(0.471397 + 0.881921i) q^{3} +(0.649390 + 1.89164i) q^{4} +(-1.38739 + 1.13860i) q^{5} +(-0.182180 + 1.40243i) q^{6} +(-1.43779 + 0.960701i) q^{7} +(-0.807073 + 2.71084i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.15095 + 0.821770i) q^{2} +(0.471397 + 0.881921i) q^{3} +(0.649390 + 1.89164i) q^{4} +(-1.38739 + 1.13860i) q^{5} +(-0.182180 + 1.40243i) q^{6} +(-1.43779 + 0.960701i) q^{7} +(-0.807073 + 2.71084i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-2.53248 + 0.170363i) q^{10} +(-0.677175 - 2.23235i) q^{11} +(-1.36216 + 1.46442i) q^{12} +(-0.399914 + 0.487296i) q^{13} +(-2.44431 - 0.0758100i) q^{14} +(-1.65816 - 0.686834i) q^{15} +(-3.15659 + 2.45682i) q^{16} +(2.54925 - 1.05593i) q^{17} +(-1.32271 + 0.500432i) q^{18} +(7.35464 - 0.724369i) q^{19} +(-3.05477 - 1.88504i) q^{20} +(-1.52503 - 0.815147i) q^{21} +(1.05508 - 3.12581i) q^{22} +(1.24921 - 0.248483i) q^{23} +(-2.77120 + 0.566105i) q^{24} +(-0.347017 + 1.74457i) q^{25} +(-0.860728 + 0.232219i) q^{26} +(-0.995185 - 0.0980171i) q^{27} +(-2.75098 - 2.09591i) q^{28} +(1.23304 + 0.374039i) q^{29} +(-1.34405 - 2.15314i) q^{30} +(5.60392 + 5.60392i) q^{31} +(-5.65202 + 0.233700i) q^{32} +(1.64954 - 1.64954i) q^{33} +(3.80181 + 0.879565i) q^{34} +(0.900919 - 2.96993i) q^{35} +(-1.93362 - 0.510990i) q^{36} +(0.0111882 - 0.113596i) q^{37} +(9.06011 + 5.21010i) q^{38} +(-0.618275 - 0.122983i) q^{39} +(-1.96683 - 4.67991i) q^{40} +(0.173208 + 0.870777i) q^{41} +(-1.08538 - 2.19142i) q^{42} +(2.86822 - 5.36607i) q^{43} +(3.78304 - 2.73063i) q^{44} +(-0.175920 - 1.78614i) q^{45} +(1.64198 + 0.740569i) q^{46} +(-1.87555 - 4.52799i) q^{47} +(-3.65473 - 1.62572i) q^{48} +(-1.53449 + 3.70458i) q^{49} +(-1.83304 + 1.72275i) q^{50} +(2.13296 + 1.75048i) q^{51} +(-1.18149 - 0.440047i) q^{52} +(2.71507 - 0.823606i) q^{53} +(-1.06486 - 0.930626i) q^{54} +(3.48125 + 2.32610i) q^{55} +(-1.44390 - 4.67297i) q^{56} +(4.10579 + 6.14475i) q^{57} +(1.11180 + 1.44378i) q^{58} +(-5.87743 - 7.16167i) q^{59} +(0.222447 - 3.58267i) q^{60} +(-8.35958 + 4.46829i) q^{61} +(1.84472 + 11.0550i) q^{62} -1.72922i q^{63} +(-6.69727 - 4.37568i) q^{64} -1.13141i q^{65} +(3.25408 - 0.543001i) q^{66} +(13.4696 - 7.19964i) q^{67} +(3.65290 + 4.13655i) q^{68} +(0.808015 + 0.984569i) q^{69} +(3.47751 - 2.67791i) q^{70} +(-0.0368105 - 0.0550907i) q^{71} +(-1.80559 - 2.17712i) q^{72} +(2.32216 + 1.55162i) q^{73} +(0.106227 - 0.121550i) q^{74} +(-1.70216 + 0.516344i) q^{75} +(6.14627 + 13.4419i) q^{76} +(3.11825 + 2.55908i) q^{77} +(-0.610543 - 0.649627i) q^{78} +(-1.80515 + 4.35801i) q^{79} +(1.58207 - 7.00265i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.516223 + 1.14456i) q^{82} +(-1.75957 - 17.8652i) q^{83} +(0.551622 - 3.41416i) q^{84} +(-2.33451 + 4.36757i) q^{85} +(7.71087 - 3.81908i) q^{86} +(0.251379 + 1.26377i) q^{87} +(6.59806 - 0.0340444i) q^{88} +(-4.69639 - 0.934170i) q^{89} +(1.26532 - 2.20033i) q^{90} +(0.106846 - 1.08483i) q^{91} +(1.28126 + 2.20169i) q^{92} +(-2.30055 + 7.58389i) q^{93} +(1.56229 - 6.75278i) q^{94} +(-9.37896 + 9.37896i) q^{95} +(-2.87045 - 4.87448i) q^{96} +(0.174862 + 0.174862i) q^{97} +(-4.81044 + 3.00281i) q^{98} +(2.23235 + 0.677175i) 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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