LMFDB - Embedded newform 483.2.u.a.113.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(113,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.113"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 0, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.34
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.645581 - 1.00454i) q^{2} +(0.990300 + 1.42102i) q^{3} +(0.238496 + 0.522234i) q^{4} +(-3.49538 - 1.02634i) q^{5} +(2.06680 - 0.0774141i) q^{6} +(0.755750 + 0.654861i) q^{7} +(3.04248 + 0.437442i) q^{8} +(-1.03861 + 2.81448i) q^{9} +(-3.28755 + 2.84868i) q^{10} +(1.94157 - 1.24777i) q^{11} +(-0.505924 + 0.856077i) q^{12} +(4.30148 + 4.96417i) q^{13} +(1.14573 - 0.336418i) q^{14} +(-2.00303 - 5.98339i) q^{15} +(1.65166 - 1.90612i) q^{16} +(-2.80287 + 6.13742i) q^{17} +(2.15676 + 2.86031i) q^{18} +(-1.15465 + 0.527310i) q^{19} +(-0.297647 - 2.07018i) q^{20} +(-0.182153 + 1.72245i) q^{21} -2.75593i q^{22} +(1.48214 - 4.56106i) q^{23} +(2.39135 + 4.75663i) q^{24} +(6.95802 + 4.47165i) q^{25} +(7.76368 - 1.11625i) q^{26} +(-5.02797 + 1.31129i) q^{27} +(-0.161747 + 0.550860i) q^{28} +(1.13436 + 0.518045i) q^{29} +(-7.30369 - 1.85064i) q^{30} +(0.899840 - 6.25852i) q^{31} +(0.883458 + 3.00878i) q^{32} +(3.69584 + 1.52335i) q^{33} +(4.35583 + 6.77781i) q^{34} +(-1.96952 - 3.06464i) q^{35} +(-1.71752 + 0.128844i) q^{36} +(-1.78916 - 6.09331i) q^{37} +(-0.215713 + 1.50032i) q^{38} +(-2.79445 + 11.0285i) q^{39} +(-10.1856 - 4.65162i) q^{40} +(0.966302 - 3.29092i) q^{41} +(1.61268 + 1.29496i) q^{42} +(-6.56447 + 0.943828i) q^{43} +(1.11468 + 0.716364i) q^{44} +(6.51894 - 8.77169i) q^{45} +(-3.62494 - 4.43341i) q^{46} +0.790600i q^{47} +(4.34428 + 0.459420i) q^{48} +(0.142315 + 0.989821i) q^{49} +(8.98394 - 4.10283i) q^{50} +(-11.4971 + 2.09495i) q^{51} +(-1.56657 + 3.43031i) q^{52} +(-3.57268 + 4.12309i) q^{53} +(-1.92872 + 5.89736i) q^{54} +(-8.06714 + 2.36873i) q^{55} +(2.01289 + 2.32299i) q^{56} +(-1.89277 - 1.11859i) q^{57} +(1.25272 - 0.805074i) q^{58} +(5.42727 - 4.70275i) q^{59} +(2.64702 - 2.47306i) q^{60} +(4.75318 + 0.683405i) q^{61} +(-5.70604 - 4.94431i) q^{62} +(-2.62802 + 1.44689i) q^{63} +(8.43279 + 2.47609i) q^{64} +(-9.94038 - 21.7664i) q^{65} +(3.91624 - 2.72919i) q^{66} +(7.39301 - 11.5037i) q^{67} -3.87364 q^{68} +(7.94913 - 2.41066i) q^{69} -4.35005 q^{70} +(0.909351 - 1.41498i) q^{71} +(-4.39112 + 8.10865i) q^{72} +(-6.72785 - 14.7319i) q^{73} +(-7.27604 - 2.13644i) q^{74} +(0.536213 + 14.3158i) q^{75} +(-0.550758 - 0.477235i) q^{76} +(2.28445 + 0.328455i) q^{77} +(9.27459 + 9.92695i) q^{78} +(7.83703 - 6.79083i) q^{79} +(-7.72950 + 4.96745i) q^{80} +(-6.84257 - 5.84630i) q^{81} +(-2.68205 - 3.09525i) q^{82} +(-3.54268 + 1.04022i) q^{83} +(-0.942963 + 0.315670i) q^{84} +(16.0961 - 18.5759i) q^{85} +(-3.28978 + 7.20362i) q^{86} +(0.387203 + 2.12497i) q^{87} +(6.45300 - 2.94699i) q^{88} +(-0.919136 - 6.39273i) q^{89} +(-4.60305 - 12.2114i) q^{90} +6.56854i q^{91} +(2.73543 - 0.313770i) q^{92} +(9.78461 - 4.91912i) q^{93} +(0.794193 + 0.510397i) q^{94} +(4.57712 - 0.658091i) q^{95} +(-3.40066 + 4.23501i) q^{96} +(-3.87096 + 13.1833i) q^{97} +(1.08620 + 0.496049i) q^{98} +(1.49528 + 6.76045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.645581	−	1.00454i	0.456495	−	0.710320i	−0.534359	−	0.845258i	$-0.679447\pi$
$2$	0.645581	−	1.00454i	0.456495	−	0.710320i	0.990854	+	0.134938i	$0.0430834\pi$
$3$	0.990300	+	1.42102i	0.571750	+	0.820428i
$3$	0.990300	+	1.42102i	0.571750	+	0.820428i
$4$	0.238496	+	0.522234i	0.119248	+	0.261117i
$5$	−3.49538	−	1.02634i	−1.56318	−	0.458991i	−0.618173	−	0.786042i	$-0.712127\pi$
$5$	−3.49538	−	1.02634i	−1.56318	−	0.458991i	−0.945007	+	0.327051i	$0.893945\pi$
$6$	2.06680	−	0.0774141i	0.843767	−	0.0316042i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	3.04248	+	0.437442i	1.07568	+	0.154659i
$9$	−1.03861	+	2.81448i	−0.346204	+	0.938159i
$10$	−3.28755	+	2.84868i	−1.03961	+	0.900831i
$11$	1.94157	−	1.24777i	0.585405	−	0.376217i	−0.214158	−	0.976799i	$-0.568701\pi$
$11$	1.94157	−	1.24777i	0.585405	−	0.376217i	0.799563	+	0.600582i	$0.205064\pi$
$12$	−0.505924	+	0.856077i	−0.146048	+	0.247128i
$13$	4.30148	+	4.96417i	1.19302	+	1.37681i	0.908363	+	0.418182i	$0.137333\pi$
$13$	4.30148	+	4.96417i	1.19302	+	1.37681i	0.284652	+	0.958631i	$0.408122\pi$
$14$	1.14573	−	0.336418i	0.306210	−	0.0899115i
$15$	−2.00303	−	5.98339i	−0.517179	−	1.54490i
$16$	1.65166	−	1.90612i	0.412916	−	0.476530i
$17$	−2.80287	+	6.13742i	−0.679795	+	1.48854i	0.183065	+	0.983101i	$0.441398\pi$
$17$	−2.80287	+	6.13742i	−0.679795	+	1.48854i	−0.862860	+	0.505442i	$0.831329\pi$
$18$	2.15676	+	2.86031i	0.508353	+	0.674181i
$19$	−1.15465	+	0.527310i	−0.264894	+	0.120973i	−0.543435	−	0.839451i	$-0.682877\pi$
$19$	−1.15465	+	0.527310i	−0.264894	+	0.120973i	0.278541	+	0.960424i	$0.410149\pi$
$20$	−0.297647	−	2.07018i	−0.0665559	−	0.462907i
$21$	−0.182153	+	1.72245i	−0.0397491	+	0.375869i
$22$		−	2.75593i		−	0.587566i
$23$	1.48214	−	4.56106i	0.309048	−	0.951046i
$23$	1.48214	−	4.56106i	0.309048	−	0.951046i
$24$	2.39135	+	4.75663i	0.488132	+	0.970942i
$25$	6.95802	+	4.47165i	1.39160	+	0.894330i
$26$	7.76368	−	1.11625i	1.52258	−	0.218914i
$27$	−5.02797	+	1.31129i	−0.967634	+	0.252357i
$28$	−0.161747	+	0.550860i	−0.0305673	+	0.104103i
$29$	1.13436	+	0.518045i	0.210645	+	0.0961985i	0.517944	−	0.855415i	$-0.326698\pi$
$29$	1.13436	+	0.518045i	0.210645	+	0.0961985i	−0.307298	+	0.951613i	$0.599425\pi$
$30$	−7.30369	−	1.85064i	−1.33347	−	0.337879i
$31$	0.899840	−	6.25852i	0.161616	−	1.12406i	−0.733972	−	0.679180i	$-0.762336\pi$
$31$	0.899840	−	6.25852i	0.161616	−	1.12406i	0.895588	−	0.444884i	$-0.146755\pi$
$32$	0.883458	+	3.00878i	0.156175	+	0.531882i
$33$	3.69584	+	1.52335i	0.643364	+	0.265181i
$34$	4.35583	+	6.77781i	0.747019	+	1.16238i
$35$	−1.96952	−	3.06464i	−0.332910	−	0.518018i
$36$	−1.71752	+	0.128844i	−0.286254	+	0.0214740i
$37$	−1.78916	−	6.09331i	−0.294136	−	1.00173i	−0.965456	−	0.260566i	$-0.916091\pi$
$37$	−1.78916	−	6.09331i	−0.294136	−	1.00173i	0.671320	−	0.741167i	$-0.265727\pi$
$38$	−0.215713	+	1.50032i	−0.0349932	+	0.243383i
$39$	−2.79445	+	11.0285i	−0.447469	+	1.76598i
$40$	−10.1856	−	4.65162i	−1.61049	−	0.735486i
$41$	0.966302	−	3.29092i	0.150911	−	0.513955i	−0.848984	−	0.528418i	$-0.822785\pi$
$41$	0.966302	−	3.29092i	0.150911	−	0.513955i	0.999895	+	0.0144623i	$0.00460366\pi$
$42$	1.61268	+	1.29496i	0.248842	+	0.199817i
$43$	−6.56447	+	0.943828i	−1.00107	+	0.143932i	−0.623314	−	0.781972i	$-0.714214\pi$
$43$	−6.56447	+	0.943828i	−1.00107	+	0.143932i	−0.377758	+	0.925904i	$0.623305\pi$
$44$	1.11468	+	0.716364i	0.168045	+	0.107996i
$45$	6.51894	−	8.77169i	0.971786	−	1.30761i
$46$	−3.62494	−	4.43341i	−0.534468	−	0.653671i
$47$			0.790600i			0.115321i	0.998336	+	0.0576604i	$0.0183641\pi$
$47$			0.790600i			0.115321i	−0.998336	+	0.0576604i	$0.981636\pi$
$48$	4.34428	+	0.459420i	0.627043	+	0.0663115i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	8.98394	−	4.10283i	1.27052	−	0.580228i
$51$	−11.4971	+	2.09495i	−1.60992	+	0.293352i
$52$	−1.56657	+	3.43031i	−0.217244	+	0.475699i
$53$	−3.57268	+	4.12309i	−0.490746	+	0.566351i	−0.946065	−	0.323978i	$-0.894980\pi$
$53$	−3.57268	+	4.12309i	−0.490746	+	0.566351i	0.455319	+	0.890328i	$0.349525\pi$
$54$	−1.92872	+	5.89736i	−0.262466	+	0.802530i
$55$	−8.06714	+	2.36873i	−1.08777	+	0.319399i
$56$	2.01289	+	2.32299i	0.268983	+	0.310423i
$57$	−1.89277	−	1.11859i	−0.250703	−	0.148160i
$58$	1.25272	−	0.805074i	0.164490	−	0.105711i
$59$	5.42727	−	4.70275i	0.706570	−	0.612246i	−0.225620	−	0.974215i	$-0.572441\pi$
$59$	5.42727	−	4.70275i	0.706570	−	0.612246i	0.932190	+	0.361969i	$0.117895\pi$
$60$	2.64702	−	2.47306i	0.341728	−	0.319271i
$61$	4.75318	+	0.683405i	0.608583	+	0.0875010i	0.439714	−	0.898138i	$-0.355080\pi$
$61$	4.75318	+	0.683405i	0.608583	+	0.0875010i	0.168868	+	0.985639i	$0.445989\pi$
$62$	−5.70604	−	4.94431i	−0.724668	−	0.627928i
$63$	−2.62802	+	1.44689i	−0.331100	+	0.182291i
$64$	8.43279	+	2.47609i	1.05410	+	0.309511i
$65$	−9.94038	−	21.7664i	−1.23295	−	2.69979i
$66$	3.91624	−	2.72919i	0.482055	−	0.335941i
$67$	7.39301	−	11.5037i	0.903200	−	1.40541i	−0.0109104	−	0.999940i	$-0.503473\pi$
$67$	7.39301	−	11.5037i	0.903200	−	1.40541i	0.914110	−	0.405466i	$-0.132891\pi$
$68$	−3.87364			−0.469748
$69$	7.94913	−	2.41066i	0.956963	−	0.290209i
$70$	−4.35005			−0.519930
$71$	0.909351	−	1.41498i	0.107920	−	0.167927i	−0.783093	−	0.621905i	$-0.786359\pi$
$71$	0.909351	−	1.41498i	0.107920	−	0.167927i	0.891013	+	0.453978i	$0.149995\pi$
$72$	−4.39112	+	8.10865i	−0.517499	+	0.955613i
$73$	−6.72785	−	14.7319i	−0.787436	−	1.72424i	−0.683850	−	0.729623i	$-0.739696\pi$
$73$	−6.72785	−	14.7319i	−0.787436	−	1.72424i	−0.103586	−	0.994620i	$-0.533032\pi$
$74$	−7.27604	−	2.13644i	−0.845823	−	0.248356i
$75$	0.536213	+	14.3158i	0.0619165	+	1.65304i
$76$	−0.550758	−	0.477235i	−0.0631763	−	0.0547426i
$77$	2.28445	+	0.328455i	0.260338	+	0.0374309i
$78$	9.27459	+	9.92695i	1.05014	+	1.12401i
$79$	7.83703	−	6.79083i	0.881735	−	0.764028i	−0.0910233	−	0.995849i	$-0.529014\pi$
$79$	7.83703	−	6.79083i	0.881735	−	0.764028i	0.972758	+	0.231821i	$0.0744683\pi$
$80$	−7.72950	+	4.96745i	−0.864185	+	0.555378i
$81$	−6.84257	−	5.84630i	−0.760285	−	0.649589i
$82$	−2.68205	−	3.09525i	−0.296183	−	0.341813i
$83$	−3.54268	+	1.04022i	−0.388859	+	0.114179i	−0.470317	−	0.882497i	$-0.655861\pi$
$83$	−3.54268	+	1.04022i	−0.388859	+	0.114179i	0.0814580	+	0.996677i	$0.474042\pi$
$84$	−0.942963	+	0.315670i	−0.102886	+	0.0344425i
$85$	16.0961	−	18.5759i	1.74587	−	2.01484i
$86$	−3.28978	+	7.20362i	−0.354746	+	0.776786i
$87$	0.387203	+	2.12497i	0.0415125	+	0.227821i
$88$	6.45300	−	2.94699i	0.687892	−	0.314150i
$89$	−0.919136	−	6.39273i	−0.0974282	−	0.677628i	−0.978742	−	0.205096i	$-0.934249\pi$
$89$	−0.919136	−	6.39273i	−0.0974282	−	0.677628i	0.881314	−	0.472532i	$-0.156660\pi$
$90$	−4.60305	−	12.2114i	−0.485204	−	1.28719i
$91$			6.56854i			0.688570i
$92$	2.73543	−	0.313770i	0.285188	−	0.0327127i
$93$	9.78461	−	4.91912i	1.01462	−	0.510089i
$94$	0.794193	+	0.510397i	0.0819147	+	0.0526434i
$95$	4.57712	−	0.658091i	0.469603	−	0.0675187i
$96$	−3.40066	+	4.23501i	−0.347078	+	0.432234i
$97$	−3.87096	+	13.1833i	−0.393037	+	1.33856i	0.491007	+	0.871156i	$0.336629\pi$
$97$	−3.87096	+	13.1833i	−0.393037	+	1.33856i	−0.884044	+	0.467405i	$0.845189\pi$
$98$	1.08620	+	0.496049i	0.109722	+	0.0501085i
$99$	1.49528	+	6.76045i	0.150282	+	0.679451i
$100$	−0.675785	+	4.70019i	−0.0675785	+	0.470019i
$101$	−1.30636	−	4.44906i	−0.129988	−	0.442698i	0.868618	−	0.495482i	$-0.165009\pi$
$101$	−1.30636	−	4.44906i	−0.129988	−	0.442698i	−0.998606	+	0.0527841i	$0.983190\pi$
$102$	−5.31784	+	12.9018i	−0.526545	+	1.27747i
$103$	5.98548	+	9.31359i	0.589767	+	0.917696i	0.999984	+	0.00570752i	$0.00181677\pi$
$103$	5.98548	+	9.31359i	0.589767	+	0.917696i	−0.410217	+	0.911988i	$0.634547\pi$
$104$	10.9156	+	16.9850i	1.07036	+	1.66552i
$105$	2.40450	−	5.83365i	0.234655	−	0.569306i
$106$	1.83537	+	6.25071i	0.178267	+	0.607123i
$107$	0.104065	−	0.723790i	0.0100604	−	0.0699715i	−0.984173	−	0.177212i	$-0.943292\pi$
$107$	0.104065	−	0.723790i	0.0100604	−	0.0699715i	0.994233	+	0.107240i	$0.0342014\pi$
$108$	−1.88395	−	2.31304i	−0.181283	−	0.222573i
$109$	6.96431	+	3.18049i	0.667060	+	0.304636i	0.720013	−	0.693961i	$-0.244136\pi$
$109$	6.96431	+	3.18049i	0.667060	+	0.304636i	−0.0529526	+	0.998597i	$0.516863\pi$
$110$	−2.82851	+	9.63300i	−0.269687	+	0.918471i
$111$	6.88693	−	8.57664i	0.653678	−	0.814058i
$112$	2.49649	−	0.358941i	0.235896	−	0.0339167i
$113$	−9.71876	−	6.24587i	−0.914264	−	0.587562i	−0.00327623	−	0.999995i	$-0.501043\pi$
$113$	−9.71876	−	6.24587i	−0.914264	−	0.587562i	−0.910988	+	0.412433i	$0.864679\pi$
$114$	−2.34560	+	1.17923i	−0.219686	+	0.110445i
$115$	−9.86182	+	14.4214i	−0.919620	+	1.34481i
$116$			0.715953i			0.0664746i
$117$	−18.4391	+	6.95056i	−1.70470	+	0.642580i
$118$	−1.22038	−	8.48794i	−0.112345	−	0.781378i
$119$	−6.13742	+	2.80287i	−0.562616	+	0.256938i
$120$	−3.47677	−	19.0805i	−0.317384	−	1.74181i
$121$	−2.35681	+	5.16069i	−0.214255	+	0.469154i
$122$	3.75508	−	4.33359i	0.339969	−	0.392345i
$123$	5.63340	−	1.88586i	0.507947	−	0.170042i
$124$	3.48302	−	1.02271i	0.312785	−	0.0918419i
$125$	−7.80341	−	9.00561i	−0.697958	−	0.805486i
$126$	−0.243133	+	3.57405i	−0.0216600	+	0.318402i
$127$	−3.23098	+	2.07642i	−0.286703	+	0.184253i	−0.676085	−	0.736823i	$-0.736325\pi$
$127$	−3.23098	+	2.07642i	−0.286703	+	0.184253i	0.389382	+	0.921076i	$0.372689\pi$
$128$	3.19163	−	2.76556i	0.282103	−	0.244443i
$129$	−7.84200	−	8.39359i	−0.690449	−	0.739014i
$130$	−28.2826	−	4.06643i	−2.48055	−	0.356649i
$131$	−2.78897	−	2.41666i	−0.243673	−	0.211144i	0.524458	−	0.851436i	$-0.324268\pi$
$131$	−2.78897	−	2.41666i	−0.243673	−	0.211144i	−0.768132	+	0.640292i	$0.778813\pi$
$132$	0.0859020	+	2.29341i	0.00747681	+	0.199616i
$133$	−1.21794	−	0.357619i	−0.105609	−	0.0310095i
$134$	−6.78323	−	14.8532i	−0.585982	−	1.28312i
$135$	18.9205	+	0.576952i	1.62842	+	0.0496561i
$136$	−11.2124	+	17.4469i	−0.961457	+	1.49606i
$137$	14.6699			1.25333			0.626666	−	0.779288i	$-0.284419\pi$
$137$	14.6699			1.25333			0.626666	+	0.779288i	$0.284419\pi$
$138$	2.71020	−	9.54153i	0.230708	−	0.812229i
$139$	−15.4942			−1.31420			−0.657100	−	0.753804i	$-0.728217\pi$
$139$	−15.4942			−1.31420			−0.657100	+	0.753804i	$0.728217\pi$
$140$	1.13073	−	1.75946i	0.0955645	−	0.148701i
$141$	−1.12346	+	0.782931i	−0.0946125	+	0.0659347i
$142$	−0.834348	−	1.82697i	−0.0700169	−	0.153316i
$143$	14.5458	+	4.27102i	1.21638	+	0.357160i
$144$	3.64930	+	6.62829i	0.304108	+	0.552357i
$145$	−3.43333	−	2.97499i	−0.285122	−	0.247060i
$146$	−19.1423	−	2.75224i	−1.58422	−	0.227777i
$147$	−1.26562	+	1.18245i	−0.104387	+	0.0975271i
$148$	2.75543	−	2.38759i	0.226495	−	0.196259i
$149$	−12.2827	+	7.89361i	−1.00624	+	0.646670i	−0.936417	−	0.350890i	$-0.885879\pi$
$149$	−12.2827	+	7.89361i	−1.00624	+	0.646670i	−0.0698210	+	0.997560i	$0.522243\pi$
$150$	14.7270	+	8.70336i	1.20246	+	0.710626i
$151$	4.24438	+	4.89828i	0.345403	+	0.398616i	0.901696	−	0.432370i	$-0.142322\pi$
$151$	4.24438	+	4.89828i	0.345403	+	0.398616i	−0.556293	+	0.830986i	$0.687777\pi$
$152$	−3.74365	+	1.09924i	−0.303650	+	0.0891598i
$153$	−14.3625	−	14.2630i	−1.16114	−	1.15310i
$154$	1.80475	−	2.08279i	0.145431	−	0.167836i
$155$	−9.56862	+	20.9524i	−0.768570	+	1.68293i
$156$	−6.42593	+	1.17091i	−0.514486	+	0.0937474i
$157$	3.63267	−	1.65898i	0.289918	−	0.132401i	−0.265147	−	0.964208i	$-0.585421\pi$
$157$	3.63267	−	1.65898i	0.289918	−	0.132401i	0.555065	+	0.831807i	$0.312693\pi$
$158$	−1.76224	−	12.2567i	−0.140197	−	0.975089i
$159$	−9.39704	−	0.993763i	−0.745234	−	0.0788105i
$160$		−	11.4235i		−	0.903111i
$161$	4.10699	−	2.47642i	0.323676	−	0.195169i
$162$	−10.2903	+	3.09940i	−0.808483	+	0.243512i
$163$	1.47241	+	0.946262i	0.115328	+	0.0741170i	0.597033	−	0.802216i	$-0.296346\pi$
$163$	1.47241	+	0.946262i	0.115328	+	0.0741170i	−0.481705	+	0.876333i	$0.659982\pi$
$164$	1.94909	−	0.280237i	0.152198	−	0.0218828i
$165$	−11.3549	−	9.11784i	−0.883978	−	0.709823i
$166$	−1.24214	+	4.23032i	−0.0964084	+	0.328337i
$167$	−15.6864	−	7.16372i	−1.21385	−	0.554345i	−0.297497	−	0.954723i	$-0.596152\pi$
$167$	−15.6864	−	7.16372i	−1.21385	−	0.554345i	−0.916350	+	0.400378i	$0.868879\pi$
$168$	−1.30767	+	5.16082i	−0.100889	+	0.398166i
$169$	−4.29018	+	29.8388i	−0.330014	+	2.29530i
$170$	−8.26897	−	28.1615i	−0.634201	−	2.15989i
$171$	−0.284871	−	3.79740i	−0.0217846	−	0.290394i
$172$	−2.05850	−	3.20309i	−0.156959	−	0.244233i
$173$	12.4160	+	19.3197i	0.943971	+	1.46885i	0.882265	+	0.470752i	$0.156018\pi$
$173$	12.4160	+	19.3197i	0.943971	+	1.46885i	0.0617052	+	0.998094i	$0.480346\pi$
$174$	2.38460	+	0.982879i	0.180776	+	0.0745119i
$175$	2.33022	+	7.93599i	0.176148	+	0.599904i
$176$	0.828416	−	5.76176i	0.0624442	−	0.434309i
$177$	12.0573	+	3.05513i	0.906285	+	0.229638i
$178$	−7.01516	−	3.20372i	−0.525808	−	0.240129i
$179$	1.86189	−	6.34101i	0.139164	−	0.473949i	−0.860187	−	0.509979i	$-0.829653\pi$
$179$	1.86189	−	6.34101i	0.139164	−	0.473949i	0.999351	+	0.0360301i	$0.0114712\pi$
$180$	6.13562	+	1.31239i	0.457322	+	0.0978201i
$181$	20.2124	−	2.90611i	1.50238	−	0.216009i	0.658514	−	0.752568i	$-0.271185\pi$
$181$	20.2124	−	2.90611i	1.50238	−	0.216009i	0.843863	+	0.536559i	$0.180276\pi$
$182$	6.59839	+	4.24052i	0.489105	+	0.314329i
$183$	3.73594	+	7.43116i	0.276169	+	0.549327i
$184$	6.50458	−	13.2286i	0.479524	−	0.975222i
$185$			23.1347i			1.70090i
$186$	1.37529	−	13.0048i	0.100841	−	0.953556i
$187$	2.21613	+	15.4136i	0.162060	+	1.12715i
$188$	−0.412878	+	0.188555i	−0.0301123	+	0.0137518i
$189$	−4.65860	−	2.30162i	−0.338863	−	0.167418i
$190$	2.29382	−	5.02277i	0.166411	−	0.364390i
$191$	9.79738	−	11.3068i	0.708914	−	0.818130i	−0.281014	−	0.959704i	$-0.590671\pi$
$191$	9.79738	−	11.3068i	0.708914	−	0.818130i	0.989928	+	0.141573i	$0.0452161\pi$
$192$	4.83241	+	14.4353i	0.348749	+	1.04177i
$193$	9.20957	−	2.70417i	0.662919	−	0.194651i	0.0670715	−	0.997748i	$-0.478634\pi$
$193$	9.20957	−	2.70417i	0.662919	−	0.194651i	0.595848	+	0.803098i	$0.296816\pi$
$194$	10.7442	+	12.3994i	0.771387	+	0.890228i
$195$	21.0866	−	35.6808i	1.51004	−	2.55515i
$196$	−0.482977	+	0.310390i	−0.0344984	+	0.0221707i
$197$	1.44497	−	1.25208i	0.102950	−	0.0892067i	−0.601865	−	0.798598i	$-0.705575\pi$
$197$	1.44497	−	1.25208i	0.102950	−	0.0892067i	0.704815	+	0.709391i	$0.251030\pi$
$198$	7.75650	+	2.86234i	0.551230	+	0.203418i
$199$	0.135316	+	0.0194556i	0.00959233	+	0.00137917i	0.147109	−	0.989120i	$-0.453003\pi$
$199$	0.135316	+	0.0194556i	0.00959233	+	0.00137917i	−0.137517	+	0.990499i	$0.543912\pi$
$200$	19.2135	+	16.6486i	1.35860	+	1.17724i
$201$	23.6684	−	0.886524i	1.66944	−	0.0625306i
$202$	−5.31264	−	1.55993i	−0.373796	−	0.109756i
$203$	0.518045	+	1.13436i	0.0363596	+	0.0796164i
$204$	−3.83607	−	5.50454i	−0.268579	−	0.385395i
$205$	−6.75517	+	10.5113i	−0.471802	+	0.734138i
$206$	13.2200			0.921083
$207$	11.2976	+	8.90863i	0.785239	+	0.619193i
$208$	16.5669			1.14871
$209$	−1.58387	+	2.46454i	−0.109558	+	0.170476i
$210$	−4.30785	−	6.18152i	−0.297270	−	0.426565i
$211$	−2.76558	−	6.05578i	−0.190391	−	0.416897i	0.790231	−	0.612809i	$-0.209961\pi$
$211$	−2.76558	−	6.05578i	−0.190391	−	0.416897i	−0.980621	+	0.195912i	$0.937233\pi$
$212$	−3.00529	−	0.882433i	−0.206404	−	0.0606058i
$213$	2.91125	−	0.109044i	0.199475	−	0.00747156i
$214$	−0.659897	−	0.571804i	−0.0451096	−	0.0390877i
$215$	23.9140	+	3.43831i	1.63092	+	0.234491i
$216$	−15.8711	+	1.79011i	−1.07989	+	0.121801i
$217$	4.77851	−	4.14061i	0.324387	−	0.281083i
$218$	7.69098	−	4.94269i	0.520899	−	0.334761i
$219$	14.2718	−	24.1495i	0.964401	−	1.63187i
$220$	−3.16101	−	3.64800i	−0.213115	−	0.245948i
$221$	−42.5237	+	12.4861i	−2.86045	+	0.839904i
$222$	−4.16954	−	12.4551i	−0.279841	−	0.835934i
$223$	4.57184	−	5.27618i	0.306153	−	0.353319i	−0.581736	−	0.813378i	$-0.697626\pi$
$223$	4.57184	−	5.27618i	0.306153	−	0.353319i	0.887889	+	0.460059i	$0.152172\pi$
$224$	−1.30266	+	2.85243i	−0.0870376	+	0.190586i
$225$	−19.8121	+	14.9389i	−1.32080	+	0.995926i
$226$	−12.5485	+	5.73071i	−0.834714	+	0.381201i
$227$	1.87238	+	13.0227i	0.124274	+	0.864347i	0.952627	+	0.304140i	$0.0983692\pi$
$227$	1.87238	+	13.0227i	0.124274	+	0.864347i	−0.828353	+	0.560207i	$0.810722\pi$
$228$	0.132746	−	1.25525i	0.00879130	−	0.0831307i
$229$		−	2.63847i		−	0.174355i	−0.996193	−	0.0871773i	$-0.972215\pi$
$229$		−	2.63847i		−	0.174355i	0.996193	−	0.0871773i	$-0.0277847\pi$
$230$	8.12036	+	19.2168i	0.535441	+	1.26712i
$231$	1.79555	+	3.57153i	0.118139	+	0.234990i
$232$	3.22465	+	2.07235i	0.211708	+	0.136057i
$233$	−9.37149	+	1.34742i	−0.613947	+	0.0882722i	−0.442271	−	0.896881i	$-0.645827\pi$
$233$	−9.37149	+	1.34742i	−0.613947	+	0.0882722i	−0.171675	+	0.985154i	$0.554918\pi$
$234$	−4.92180	+	23.0101i	−0.321748	+	1.50421i
$235$	0.811421	−	2.76345i	0.0529313	−	0.180267i
$236$	3.75032	+	1.71271i	0.244125	+	0.111488i
$237$	17.4109	+	4.41165i	1.13096	+	0.286567i
$238$	−1.14660	+	7.97479i	−0.0743231	+	0.516929i
$239$	−1.82804	−	6.22572i	−0.118246	−	0.402709i	0.879005	−	0.476813i	$-0.158208\pi$
$239$	−1.82804	−	6.22572i	−0.118246	−	0.402709i	−0.997250	+	0.0741048i	$0.976390\pi$
$240$	−14.7134	−	6.06454i	−0.949745	−	0.391464i
$241$	−4.72289	−	7.34896i	−0.304228	−	0.473388i	0.655155	−	0.755495i	$-0.272603\pi$
$241$	−4.72289	−	7.34896i	−0.304228	−	0.473388i	−0.959383	+	0.282106i	$0.908967\pi$
$242$	3.66263	+	5.69916i	0.235443	+	0.366356i
$243$	1.53153	−	15.5130i	0.0982479	−	0.995162i
$244$	0.776720	+	2.64526i	0.0497244	+	0.169346i
$245$	0.518445	−	3.60586i	0.0331222	−	0.230370i
$246$	1.74239	−	6.87648i	0.111091	−	0.438428i
$247$	−7.58434	−	3.46365i	−0.482580	−	0.220387i
$248$	5.47548	−	18.6478i	0.347693	−	1.18413i
$249$	−4.98649	−	4.00409i	−0.316006	−	0.253749i
$250$	−14.0843	+	2.02501i	−0.890767	+	0.128073i
$251$	−5.81618	−	3.73783i	−0.367114	−	0.235930i	0.344057	−	0.938949i	$-0.388199\pi$
$251$	−5.81618	−	3.73783i	−0.367114	−	0.235930i	−0.711171	+	0.703019i	$0.751835\pi$
$252$	−1.38239	−	1.02736i	−0.0870824	−	0.0647178i
$253$	−2.81347	−	10.7050i	−0.176881	−	0.673016i
$254$			4.58616i			0.287761i
$255$	42.3368	+	4.47723i	2.65123	+	0.280375i
$256$	1.78388	+	12.4071i	0.111492	+	0.775447i
$257$	15.1562	−	6.92159i	0.945416	−	0.431757i	0.117791	−	0.993038i	$-0.462419\pi$
$257$	15.1562	−	6.92159i	0.945416	−	0.431757i	0.827625	+	0.561282i	$0.189691\pi$
$258$	−13.4944	+	2.45889i	−0.840123	+	0.153084i
$259$	2.63811	−	5.77666i	0.163924	−	0.358944i
$260$	8.99641	−	10.3824i	0.557934	−	0.643890i
$261$	−2.63618	+	2.65458i	−0.163176	+	0.164315i
$262$	−4.22815	+	1.24150i	−0.261216	+	0.0766998i
$263$	14.1602	+	16.3417i	0.873155	+	1.00768i	0.999876	+	0.0157366i	$0.00500932\pi$
$263$	14.1602	+	16.3417i	0.873155	+	1.00768i	−0.126721	+	0.991938i	$0.540445\pi$
$264$	10.5781	+	6.25146i	0.651039	+	0.384751i
$265$	16.7195	−	10.7450i	1.02707	−	0.660060i
$266$	−1.14552	+	0.992601i	−0.0702365	+	0.0608603i
$267$	8.17400	−	7.63683i	0.500241	−	0.467367i
$268$	7.77085	+	1.11728i	0.474681	+	0.0682488i
$269$	−0.361053	−	0.312854i	−0.0220138	−	0.0190751i	0.643784	−	0.765207i	$-0.277363\pi$
$269$	−0.361053	−	0.312854i	−0.0220138	−	0.0190751i	−0.665798	+	0.746132i	$0.731909\pi$
$270$	12.7943	−	18.6340i	0.778635	−	1.13403i
$271$	−20.9145	−	6.14105i	−1.27046	−	0.373042i	−0.424085	−	0.905622i	$-0.639404\pi$
$271$	−20.9145	−	6.14105i	−1.27046	−	0.373042i	−0.846380	+	0.532580i	$0.821222\pi$
$272$	7.06928	+	15.4796i	0.428638	+	0.938586i
$273$	−9.33404	+	6.50482i	−0.564922	+	0.393690i
$274$	9.47060	−	14.7365i	0.572140	−	0.890267i
$275$	19.0891			1.15111
$276$	3.15477	+	3.57638i	0.189895	+	0.215273i
$277$	−6.66902			−0.400703			−0.200351	−	0.979724i	$-0.564208\pi$
$277$	−6.66902			−0.400703			−0.200351	+	0.979724i	$0.564208\pi$
$278$	−10.0028	+	15.5646i	−0.599925	+	0.933502i
$279$	16.6799	+	9.03276i	0.998599	+	0.540777i
$280$	−4.65162	−	10.1856i	−0.277988	−	0.608708i
$281$	4.35758	+	1.27950i	0.259951	+	0.0763286i	0.409111	−	0.912485i	$-0.365839\pi$
$281$	4.35758	+	1.27950i	0.259951	+	0.0763286i	−0.149160	+	0.988813i	$0.547657\pi$
$282$	0.0612036	+	1.63401i	0.00364462	+	0.0973040i
$283$	−4.21781	−	3.65475i	−0.250723	−	0.217252i	0.520427	−	0.853906i	$-0.325773\pi$
$283$	−4.21781	−	3.65475i	−0.250723	−	0.217252i	−0.771150	+	0.636654i	$0.780318\pi$
$284$	0.955827	+	0.137427i	0.0567179	+	0.00815480i
$285$	5.46789	+	5.85249i	0.323890	+	0.346672i
$286$	13.6809	−	11.8546i	0.808968	−	0.700975i
$287$	2.88538	−	1.85432i	0.170318	−	0.109457i
$288$	−9.38572	−	0.638485i	−0.553059	−	0.0376231i
$289$	−18.6792	−	21.5570i	−1.09878	−	1.26806i
$290$	−5.20500	+	1.52833i	−0.305648	+	0.0897465i
$291$	−22.5672	+	7.55468i	−1.32291	+	0.442863i
$292$	6.08896	−	7.02703i	0.356329	−	0.411226i
$293$	−3.25625	+	7.13020i	−0.190232	+	0.416551i	−0.980583	−	0.196104i	$-0.937171\pi$
$293$	−3.25625	+	7.13020i	−0.190232	+	0.416551i	0.790351	+	0.612655i	$0.209898\pi$
$294$	0.370762	+	2.03475i	0.0216233	+	0.118669i
$295$	−23.7969	+	10.8677i	−1.38551	+	0.632742i
$296$	−2.77800	−	19.3214i	−0.161468	−	1.12303i
$297$	−8.12597	+	8.81971i	−0.471517	+	0.511771i
$298$			17.4345i			1.00995i
$299$	29.0173	−	12.2617i	1.67811	−	0.709111i
$300$	−7.34831	+	3.69429i	−0.424255	+	0.213290i
$301$	−5.57917	−	3.58552i	−0.321578	−	0.206666i
$302$	7.66063	−	1.10143i	0.440820	−	0.0633803i
$303$	5.02853	−	6.26228i	0.288881	−	0.359758i
$304$	−0.901972	+	3.07184i	−0.0517317	+	0.176182i
$305$	−15.9128	−	7.26712i	−0.911162	−	0.416114i
$306$	−23.6000	+	5.21988i	−1.34912	+	0.298401i
$307$	0.339026	−	2.35798i	0.0193492	−	0.134577i	−0.977857	−	0.209274i	$-0.932890\pi$
$307$	0.339026	−	2.35798i	0.0193492	−	0.134577i	0.997206	+	0.0746972i	$0.0237990\pi$
$308$	0.373304	+	1.27136i	0.0212710	+	0.0724422i
$309$	−7.30741	+	17.7288i	−0.415704	+	1.00855i
$310$	14.8702	+	23.1385i	0.844573	+	1.31418i
$311$	−6.00574	−	9.34512i	−0.340554	−	0.529913i	0.628162	−	0.778082i	$-0.283807\pi$
$311$	−6.00574	−	9.34512i	−0.340554	−	0.529913i	−0.968717	+	0.248169i	$0.920171\pi$
$312$	−13.3264	+	32.3316i	−0.754457	+	1.83041i
$313$	−3.28438	−	11.1856i	−0.185644	−	0.632246i	−0.998743	−	0.0501205i	$-0.984039\pi$
$313$	−3.28438	−	11.1856i	−0.185644	−	0.632246i	0.813099	−	0.582125i	$-0.197779\pi$
$314$	0.678660	−	4.72018i	0.0382990	−	0.266375i
$315$	10.6709	−	2.36021i	0.601238	−	0.132983i
$316$	5.41551	+	2.47318i	0.304646	+	0.139127i
$317$	−4.36662	+	14.8714i	−0.245254	+	0.835258i	0.741209	+	0.671274i	$0.234253\pi$
$317$	−4.36662	+	14.8714i	−0.245254	+	0.835258i	−0.986463	+	0.163984i	$0.947565\pi$
$318$	−7.06483	+	8.79818i	−0.396176	+	0.493378i
$319$	2.84884	−	0.409601i	0.159504	−	0.0229332i
$320$	−26.9345	−	17.3097i	−1.50568	−	0.967643i
$321$	1.13158	−	0.568890i	0.0631586	−	0.0317524i
$322$	0.163721	−	5.72438i	0.00912382	−	0.319007i
$323$		−	8.56454i		−	0.476544i
$324$	1.42121	−	4.96774i	0.0789562	−	0.275986i
$325$	7.73175	+	53.7755i	0.428880	+	2.98293i
$326$	1.90112	−	0.868214i	0.105294	−	0.0480859i
$327$	2.37720	+	13.0461i	0.131460	+	0.721450i
$328$	4.37954	−	9.58984i	0.241819	−	0.529511i
$329$	−0.517733	+	0.597496i	−0.0285435	+	0.0329410i
$330$	−16.4898	+	5.52019i	−0.907733	+	0.303877i
$331$	28.1055	−	8.25251i	1.54482	−	0.453599i	0.605270	−	0.796020i	$-0.293065\pi$
$331$	28.1055	−	8.25251i	1.54482	−	0.453599i	0.939546	+	0.342421i	$0.111247\pi$
$332$	−1.38816	−	1.60202i	−0.0761849	−	0.0879221i
$333$	19.0077	+	1.29304i	1.04162	+	0.0708583i
$334$	−17.3231	+	11.1329i	−0.947877	+	0.609164i
$335$	−37.6480	+	32.6222i	−2.05693	+	1.78234i
$336$	2.98233	+	3.19211i	0.162700	+	0.174144i
$337$	−6.86246	−	0.986673i	−0.373822	−	0.0537475i	−0.0471565	−	0.998888i	$-0.515016\pi$
$337$	−6.86246	−	0.986673i	−0.373822	−	0.0537475i	−0.326665	+	0.945140i	$0.605925\pi$
$338$	27.2048	+	23.5731i	1.47974	+	1.28221i
$339$	−0.748966	−	19.9959i	−0.0406782	−	1.08603i
$340$	13.5398	+	3.97566i	0.734301	+	0.215610i
$341$	−6.06210	−	13.2741i	−0.328281	−	0.718835i
$342$	−3.99856	−	2.16537i	−0.216218	−	0.117090i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	−20.3851			−1.09909
$345$	−30.2594	+	0.267671i	−1.62911	+	0.0144109i
$346$	27.4230			1.47427
$347$	−17.1744	+	26.7240i	−0.921973	+	1.43462i	−0.0214686	+	0.999770i	$0.506834\pi$
$347$	−17.1744	+	26.7240i	−0.921973	+	1.43462i	−0.900504	+	0.434848i	$0.856802\pi$
$348$	−1.01739	+	0.709008i	−0.0545376	+	0.0380068i
$349$	−8.92343	−	19.5396i	−0.477660	−	1.04593i	−0.983100	−	0.183068i	$-0.941397\pi$
$349$	−8.92343	−	19.5396i	−0.477660	−	1.04593i	0.505440	−	0.862862i	$-0.331330\pi$
$350$	9.47639	+	2.78252i	0.506534	+	0.148732i
$351$	−28.1372	−	19.3193i	−1.50185	−	1.03119i
$352$	5.46956	+	4.73940i	0.291529	+	0.252611i
$353$	−10.1153	−	1.45436i	−0.538383	−	0.0774078i	−0.132241	−	0.991218i	$-0.542217\pi$
$353$	−10.1153	−	1.45436i	−0.538383	−	0.0774078i	−0.406142	+	0.913810i	$0.633126\pi$
$354$	10.8530	−	10.1398i	0.576831	−	0.538924i
$355$	−4.63077	+	4.01258i	−0.245776	+	0.212966i
$356$	3.11929	−	2.00465i	0.165322	−	0.106246i
$357$	−10.0608	−	5.94574i	−0.532475	−	0.314682i
$358$	−5.16782	−	5.96399i	−0.273128	−	0.315206i
$359$	9.62329	−	2.82565i	0.507898	−	0.149132i	−0.0177368	−	0.999843i	$-0.505646\pi$
$359$	9.62329	−	2.82565i	0.507898	−	0.149132i	0.525635	+	0.850710i	$0.323828\pi$
$360$	23.6708	−	23.8360i	1.24756	−	1.25627i
$361$	−11.3872	+	13.1415i	−0.599326	+	0.691659i
$362$	10.1294	−	22.1804i	0.532392	−	1.16578i
$363$	−9.66741	+	1.76155i	−0.507407	+	0.0924575i
$364$	−3.43031	+	1.56657i	−0.179797	+	0.0821107i
$365$	8.39647	+	58.3987i	0.439491	+	3.05673i
$366$	9.87678	+	1.04450i	0.516268	+	0.0545967i
$367$		−	25.8793i		−	1.35089i	−0.737410	−	0.675445i	$-0.763952\pi$
$367$		−	25.8793i		−	1.35089i	0.737410	−	0.675445i	$-0.236048\pi$
$368$	−6.24593	−	10.3585i	−0.325591	−	0.539973i
$369$	8.25861	+	6.13762i	0.429926	+	0.319512i
$370$	23.2398	+	14.9353i	1.20818	+	0.776450i
$371$	−5.40011	+	0.776418i	−0.280359	+	0.0403096i
$372$	4.90253	+	3.93667i	0.254184	+	0.204107i
$373$	−2.70823	+	9.22340i	−0.140227	+	0.477570i	−0.999419	−	0.0340839i	$-0.989149\pi$
$373$	−2.70823	+	9.22340i	−0.140227	+	0.477570i	0.859192	+	0.511653i	$0.170967\pi$
$374$	16.9143	+	7.72450i	0.874617	+	0.399424i
$375$	5.06947	−	20.0071i	0.261786	−	1.03316i
$376$	−0.345842	+	2.40538i	−0.0178354	+	0.124048i
$377$	2.30776	+	7.85951i	0.118856	+	0.404785i
$378$	−5.31958	+	3.19389i	−0.273610	+	0.164276i
$379$	7.47787	+	11.6358i	0.384113	+	0.597691i	0.978440	−	0.206533i	$-0.0662179\pi$
$379$	7.47787	+	11.6358i	0.384113	+	0.597691i	−0.594327	+	0.804223i	$0.702582\pi$
$380$	1.43530	+	2.23338i	0.0736296	+	0.114570i
$381$	−6.15028	−	2.53501i	−0.315089	−	0.129873i
$382$	−5.03316	−	17.1414i	−0.257519	−	0.877028i
$383$	3.45926	−	24.0597i	0.176760	−	1.22939i	−0.687439	−	0.726242i	$-0.741265\pi$
$383$	3.45926	−	24.0597i	0.176760	−	1.22939i	0.864199	−	0.503150i	$-0.167826\pi$
$384$	7.09059	+	1.79664i	0.361840	+	0.0916844i
$385$	−7.64792	−	3.49269i	−0.389774	−	0.178004i
$386$	3.22906	−	10.9972i	0.164355	−	0.559742i
$387$	4.16156	−	19.4558i	0.211544	−	0.988995i
$388$	−7.80797	+	1.12262i	−0.396390	+	0.0569923i
$389$	15.1831	+	9.75760i	0.769815	+	0.494730i	0.865639	−	0.500668i	$-0.166912\pi$
$389$	15.1831	+	9.75760i	0.769815	+	0.494730i	−0.0958242	+	0.995398i	$0.530549\pi$
$390$	−22.2298	−	44.2172i	−1.12565	−	2.23903i
$391$	23.8389	+	21.8806i	1.20558	+	1.10655i
$392$			3.07376i			0.155248i
$393$	0.672207	−	6.35641i	0.0339084	−	0.320638i
$394$	−0.324918	−	2.25986i	−0.0163691	−	0.113850i
$395$	−34.3630	+	15.6931i	−1.72899	+	0.789604i
$396$	−3.17392	+	2.39323i	−0.159495	+	0.120264i
$397$	7.77375	−	17.0221i	0.390153	−	0.854317i	−0.608021	−	0.793921i	$-0.708036\pi$
$397$	7.77375	−	17.0221i	0.390153	−	0.854317i	0.998175	−	0.0603957i	$-0.0192363\pi$
$398$	0.106902	−	0.123371i	0.00535850	−	0.00618404i
$399$	−0.697940	−	2.08487i	−0.0349407	−	0.104374i
$400$	20.0158	−	5.87717i	1.00079	−	0.293859i
$401$	−11.0372	−	12.7376i	−0.551171	−	0.636085i	0.409985	−	0.912092i	$-0.365534\pi$
$401$	−11.0372	−	12.7376i	−0.551171	−	0.636085i	−0.961156	+	0.276007i	$0.910989\pi$
$402$	14.3893	−	24.3483i	0.717674	−	1.21438i
$403$	34.9390	−	22.4539i	1.74044	−	1.11851i
$404$	2.01189	−	1.74331i	0.100095	−	0.0867330i
$405$	17.9171	+	27.4578i	0.890307	+	1.36439i
$406$	1.47395	+	0.211923i	0.0731511	+	0.0105175i
$407$	−11.0768	−	9.59812i	−0.549057	−	0.475761i
$408$	−35.8960	+	1.34452i	−1.77712	+	0.0665638i
$409$	−29.7585	−	8.73790i	−1.47147	−	0.432061i	−0.554890	−	0.831924i	$-0.687240\pi$
$409$	−29.7585	−	8.73790i	−1.47147	−	0.432061i	−0.916575	+	0.399862i	$0.869058\pi$
$410$	6.19801	+	13.5717i	0.306098	+	0.670261i
$411$	14.5276	+	20.8462i	0.716593	+	1.02827i
$412$	−3.43636	+	5.34708i	−0.169297	+	0.263432i
$413$	7.18130			0.353369
$414$	16.2426	−	5.59772i	0.798283	−	0.275113i
$415$	13.4506			0.660264
$416$	−11.1359	+	17.3278i	−0.545984	+	0.849567i
$417$	−15.3439	−	22.0176i	−0.751393	−	1.07821i
$418$	1.45323	+	3.18212i	0.0710797	+	0.155643i
$419$	32.3698	+	9.50464i	1.58137	+	0.464332i	0.950285	−	0.311381i	$-0.100792\pi$
$419$	32.3698	+	9.50464i	1.58137	+	0.464332i	0.631085	+	0.775713i	$0.282610\pi$
$420$	3.61999	−	0.135591i	0.176638	−	0.00661614i
$421$	7.51224	+	6.50939i	0.366124	+	0.317248i	0.818421	−	0.574619i	$-0.194850\pi$
$421$	7.51224	+	6.50939i	0.366124	+	0.317248i	−0.452297	+	0.891867i	$0.649395\pi$
$422$	−7.86871	−	1.13135i	−0.383043	−	0.0550732i
$423$	−2.22513	−	0.821127i	−0.108189	−	0.0399246i
$424$	−12.6734	+	10.9816i	−0.615475	+	0.533312i
$425$	−46.9468	+	30.1709i	−2.27725	+	1.46350i
$426$	1.76991	−	2.99487i	0.0857523	−	0.145102i
$427$	3.14468	+	3.62916i	0.152182	+	0.175627i
$428$	0.402807	−	0.118275i	0.0194704	−	0.00571703i
$429$	8.33544	+	24.8994i	0.402439	+	1.20216i
$430$	18.8924	−	21.8029i	0.911070	−	1.05143i
$431$	−6.79045	+	14.8690i	−0.327084	+	0.716215i	−0.999718	−	0.0237612i	$-0.992436\pi$
$431$	−6.79045	+	14.8690i	−0.327084	+	0.716215i	0.672633	+	0.739976i	$0.265163\pi$
$432$	−5.80505	+	11.7497i	−0.279296	+	0.565309i
$433$	−4.18490	+	1.91118i	−0.201114	+	0.0918455i	−0.513426	−	0.858134i	$-0.671624\pi$
$433$	−4.18490	+	1.91118i	−0.201114	+	0.0918455i	0.312312	+	0.949980i	$0.398897\pi$
$434$	−1.07450	−	7.47333i	−0.0515777	−	0.358731i
$435$	0.827512	−	7.82497i	0.0396762	−	0.375179i
$436$			4.39554i			0.210508i
$437$	0.693737	+	6.04796i	0.0331859	+	0.289313i
$438$	−15.0456	−	29.9271i	−0.718906	−	1.42997i
$439$	−8.89332	−	5.71539i	−0.424455	−	0.272781i	0.310926	−	0.950434i	$-0.399361\pi$
$439$	−8.89332	−	5.71539i	−0.424455	−	0.272781i	−0.735382	+	0.677653i	$0.762997\pi$
$440$	−25.5803	+	3.67789i	−1.21949	+	0.175336i
$441$	−2.93364	−	0.627499i	−0.139697	−	0.0298809i
$442$	−14.9097	+	50.7777i	−0.709181	+	2.41525i
$443$	−2.18316	−	0.997016i	−0.103725	−	0.0473697i	0.362877	−	0.931837i	$-0.381795\pi$
$443$	−2.18316	−	0.997016i	−0.103725	−	0.0473697i	−0.466602	+	0.884467i	$0.654522\pi$
$444$	6.12152	+	1.55109i	0.290514	+	0.0736116i
$445$	−3.34836	+	23.2883i	−0.158727	+	1.10397i
$446$	−2.34866	−	7.99882i	−0.111212	−	0.378755i
$447$	−23.3806	−	9.63695i	−1.10586	−	0.455812i
$448$	4.75158	+	7.39360i	0.224491	+	0.349315i
$449$	−11.2160	−	17.4524i	−0.529316	−	0.823632i	0.468905	−	0.883248i	$-0.344649\pi$
$449$	−11.2160	−	17.4524i	−0.529316	−	0.823632i	−0.998221	+	0.0596166i	$0.981012\pi$
$450$	2.21649	+	29.5463i	0.104486	+	1.39283i
$451$	−2.23017	−	7.59527i	−0.105015	−	0.357647i
$452$	0.943917	−	6.56509i	0.0443981	−	0.308796i
$453$	−2.75735	+	10.8821i	−0.129552	+	0.511287i
$454$	14.2907	+	6.52632i	0.670694	+	0.306296i
$455$	6.74152	−	22.9595i	0.316047	−	1.07636i
$456$	−5.26938	−	4.23124i	−0.246761	−	0.198146i
$457$	−30.8485	+	4.43534i	−1.44303	+	0.207477i	−0.818942	−	0.573876i	$-0.805439\pi$
$457$	−30.8485	+	4.43534i	−1.44303	+	0.207477i	−0.624090	+	0.781353i	$0.714530\pi$
$458$	−2.65045	−	1.70334i	−0.123848	−	0.0795920i
$459$	6.04483	−	34.5342i	0.282149	−	1.61192i
$460$	−9.88338	−	1.71072i	−0.460815	−	0.0797628i
$461$		−	9.97732i		−	0.464690i	−0.972633	−	0.232345i	$-0.925360\pi$
$461$		−	9.97732i		−	0.464690i	0.972633	−	0.232345i	$-0.0746399\pi$
$462$	4.74694	+	0.502002i	0.220847	+	0.0233552i
$463$	−4.40559	−	30.6415i	−0.204745	−	1.42403i	−0.789962	−	0.613156i	$-0.789900\pi$
$463$	−4.40559	−	30.6415i	−0.204745	−	1.42403i	0.585217	−	0.810877i	$-0.301009\pi$
$464$	2.86104	−	1.30659i	0.132820	−	0.0606570i
$465$	−39.2496	+	7.15189i	−1.82016	+	0.331661i
$466$	−4.69652	+	10.2839i	−0.217562	+	0.476394i
$467$	0.351240	−	0.405353i	0.0162535	−	0.0187575i	−0.747565	−	0.664189i	$-0.768777\pi$
$467$	0.351240	−	0.405353i	0.0162535	−	0.0187575i	0.763818	+	0.645432i	$0.223322\pi$
$468$	−8.02748	−	7.97185i	−0.371070	−	0.368499i
$469$	13.1206	−	3.85256i	0.605854	−	0.177895i
$470$	−2.25216	−	2.59914i	−0.103885	−	0.119889i
$471$	5.95488	+	3.51921i	0.274386	+	0.162157i
$472$	18.5695	−	11.9339i	0.854731	−	0.549302i
$473$	−11.5677	+	10.0235i	−0.531883	+	0.460879i
$474$	15.6719	−	14.6420i	0.719833	−	0.672528i
$475$	−10.3920	−	1.49415i	−0.476818	−	0.0685561i
$476$	−2.92750	−	2.53670i	−0.134182	−	0.116269i
$477$	−7.89373	−	14.3375i	−0.361429	−	0.656470i
$478$	−7.43416	−	2.18287i	−0.340031	−	0.0998420i
$479$	9.27692	+	20.3136i	0.423873	+	0.928153i	0.994281	+	0.106792i	$0.0340579\pi$
$479$	9.27692	+	20.3136i	0.423873	+	0.928153i	−0.570408	+	0.821362i	$0.693215\pi$
$480$	16.2331	−	11.3127i	0.740937	−	0.516353i
$481$	22.5522	−	35.0919i	1.02829	−	1.60005i
$482$	−10.4314			−0.475136
$483$	7.58620	+	3.38372i	0.345184	+	0.153965i
$484$	−3.25718			−0.148054
$485$	27.0609	−	42.1077i	1.22877	−	1.91201i
$486$	−14.5948	−	11.5534i	−0.662034	−	0.524074i
$487$	14.5891	+	31.9456i	0.661094	+	1.44759i	0.881500	+	0.472185i	$0.156534\pi$
$487$	14.5891	+	31.9456i	0.661094	+	1.44759i	−0.220406	+	0.975408i	$0.570738\pi$
$488$	14.1625	+	4.15848i	0.641106	+	0.188246i
$489$	0.113470	+	3.02942i	0.00513129	+	0.136995i
$490$	−3.28755	−	2.84868i	−0.148516	−	0.128690i
$491$	0.158482	+	0.0227862i	0.00715218	+	0.00102833i	0.145890	−	0.989301i	$-0.453395\pi$
$491$	0.158482	+	0.0227862i	0.00715218	+	0.00102833i	−0.138738	+	0.990329i	$0.544305\pi$
$492$	2.32841	+	2.49218i	0.104973	+	0.112356i
$493$	−6.35892	+	5.51003i	−0.286391	+	0.248159i
$494$	−8.37570	+	5.38274i	−0.376841	+	0.242181i
$495$	1.71190	−	25.1650i	0.0769444	−	1.13108i
$496$	−10.4433	−	12.0522i	−0.468917	−	0.541159i
$497$	1.61386	−	0.473871i	0.0723913	−	0.0212560i
$498$	−7.24147	+	2.42419i	−0.324498	+	0.108630i
$499$	−16.4941	+	19.0352i	−0.738376	+	0.852131i	−0.993388	−	0.114807i	$-0.963375\pi$
$499$	−16.4941	+	19.0352i	−0.738376	+	0.852131i	0.255012	+	0.966938i	$0.417921\pi$
$500$	2.84195	−	6.22301i	0.127096	−	0.278301i
$501$	−5.35439	−	29.3849i	−0.239216	−	1.31282i
$502$	−7.50964	+	3.42954i	−0.335171	+	0.153068i
$503$	−1.21178	−	8.42815i	−0.0540308	−	0.375792i	−0.998839	−	0.0481691i	$-0.984661\pi$
$503$	−1.21178	−	8.42815i	−0.0540308	−	0.375792i	0.944808	−	0.327623i	$-0.106248\pi$
$504$	−8.62862	+	3.25253i	−0.384349	+	0.144879i
$505$			16.8919i			0.751680i
$506$	−12.5699	−	4.08468i	−0.558802	−	0.181586i
$507$	−46.6502	+	23.4530i	−2.07181	+	1.04158i
$508$	−1.85496	−	1.19211i	−0.0823003	−	0.0528912i
$509$	−2.16408	+	0.311148i	−0.0959213	+	0.0137914i	−0.190108	−	0.981763i	$-0.560884\pi$
$509$	−2.16408	+	0.311148i	−0.0959213	+	0.0137914i	0.0941870	+	0.995555i	$0.469975\pi$
$510$	31.8294	−	39.6388i	1.40943	−	1.75523i
$511$	4.56280	−	15.5395i	0.201846	−	0.687426i
$512$	21.2982	+	9.72654i	0.941254	+	0.429856i
$513$	5.11408	−	4.16537i	0.225792	−	0.183906i
$514$	2.83150	−	19.6935i	0.124892	−	0.868643i
$515$	−11.3626	−	38.6976i	−0.500698	−	1.70522i
$516$	2.51313	−	6.09720i	0.110634	−	0.268414i
$517$	0.986487	+	1.53500i	0.0433857	+	0.0675094i
$518$	−4.09980	−	6.37941i	−0.180135	−	0.280295i
$519$	−15.1581	+	36.7757i	−0.665368	+	1.61427i
$520$	−20.7218	−	70.5721i	−0.908712	−	3.09479i
$521$	3.34473	−	23.2631i	0.146535	−	1.01917i	−0.775300	−	0.631593i	$-0.782402\pi$
$521$	3.34473	−	23.2631i	0.146535	−	1.01917i	0.921836	−	0.387581i	$-0.126689\pi$
$522$	0.964773	+	4.36191i	0.0422270	+	0.190916i
$523$	32.4459	+	14.8175i	1.41876	+	0.647926i	0.969414	−	0.245432i	$-0.0789299\pi$
$523$	32.4459	+	14.8175i	1.41876	+	0.647926i	0.449346	+	0.893358i	$0.351657\pi$
$524$	0.596901	−	2.03286i	0.0260758	−	0.0888059i
$525$	−8.96960	+	11.1703i	−0.391466	+	0.487512i
$526$	25.5576	−	3.67462i	1.11436	−	0.160221i
$527$	35.8891	+	23.0645i	1.56335	+	1.00471i
$528$	9.00797	−	4.52867i	0.392022	−	0.197085i
$529$	−18.6065	−	13.5203i	−0.808978	−	0.587839i
$530$		−	23.7323i		−	1.03086i
$531$	7.59897	+	20.1593i	0.329767	+	0.874837i
$532$	−0.103713	−	0.721340i	−0.00449653	−	0.0312741i
$533$	20.4932	−	9.35894i	0.887660	−	0.405381i
$534$	−2.39456	−	13.1413i	−0.103623	−	0.568681i
$535$	−1.10660	+	2.42311i	−0.0478424	+	0.104760i
$536$	27.5253	−	31.7659i	1.18891	−	1.37208i
$537$	10.8545	−	3.63371i	0.468408	−	0.156806i
$538$	−0.547365	+	0.160721i	−0.0235986	+	0.00692917i
$539$	1.51138	+	1.74423i	0.0650999	+	0.0751293i
$540$	4.21116	+	10.0185i	0.181220	+	0.431129i
$541$	−2.25474	+	1.44903i	−0.0969389	+	0.0622989i	−0.588212	−	0.808707i	$-0.700168\pi$
$541$	−2.25474	+	1.44903i	−0.0969389	+	0.0622989i	0.491273	+	0.871006i	$0.336532\pi$
$542$	−19.6710	+	17.0450i	−0.844940	+	0.732145i
$543$	24.1460	+	25.8444i	1.03620	+	1.10909i
$544$	−20.9424	−	3.01106i	−0.897897	−	0.129098i
$545$	−21.0786	−	18.2647i	−0.902910	−	0.782376i
$546$	0.508497	+	13.5758i	0.0217617	+	0.580993i
$547$	−17.4618	−	5.12726i	−0.746615	−	0.219226i	−0.113773	−	0.993507i	$-0.536294\pi$
$547$	−17.4618	−	5.12726i	−0.746615	−	0.219226i	−0.632842	+	0.774281i	$0.718112\pi$
$548$	3.49871	+	7.66111i	0.149458	+	0.327266i
$549$	−6.86014	+	12.6679i	−0.292784	+	0.540654i
$550$	12.3235	−	19.1758i	0.525478	−	0.817659i
$551$	−1.58296			−0.0674362
$552$	25.2396	−	3.85707i	1.07427	−	0.164168i
$553$	10.3699			0.440972
$554$	−4.30540	+	6.69933i	−0.182919	+	0.284627i
$555$	−32.8749	+	22.9103i	−1.39546	+	0.972487i
$556$	−3.69531	−	8.09159i	−0.156716	−	0.343160i
$557$	−20.5936	−	6.04681i	−0.872577	−	0.256212i	−0.185366	−	0.982670i	$-0.559347\pi$
$557$	−20.5936	−	6.04681i	−0.872577	−	0.256212i	−0.687211	+	0.726458i	$0.741165\pi$
$558$	19.8420	−	10.9243i	0.839980	−	0.462463i
$559$	−32.9222	−	28.5273i	−1.39246	−	1.20658i
$560$	−9.09456	−	1.30760i	−0.384315	−	0.0552562i
$561$	−19.7084	+	18.4132i	−0.832088	+	0.777407i
$562$	4.09848	−	3.55136i	0.172884	−	0.149805i
$563$	−24.5587	+	15.7829i	−1.03502	+	0.665170i	−0.943751	−	0.330656i	$-0.892730\pi$
$563$	−24.5587	+	15.7829i	−1.03502	+	0.665170i	−0.0912728	+	0.995826i	$0.529094\pi$
$564$	−0.676815	−	0.399983i	−0.0284990	−	0.0168423i
$565$	27.5604	+	31.8064i	1.15947	+	1.33810i
$566$	−6.39430	+	1.87754i	−0.268772	+	0.0789187i
$567$	−1.34276	−	8.89927i	−0.0563904	−	0.373734i
$568$	3.38565	−	3.90725i	0.142059	−	0.163945i
$569$	−3.81149	+	8.34600i	−0.159786	+	0.349882i	−0.972544	−	0.232719i	$-0.925238\pi$
$569$	−3.81149	+	8.34600i	−0.159786	+	0.349882i	0.812758	+	0.582601i	$0.197965\pi$
$570$	9.40905	−	1.71448i	0.394102	−	0.0718115i
$571$	−20.7224	+	9.46362i	−0.867207	+	0.396040i	−0.798785	−	0.601616i	$-0.794524\pi$
$571$	−20.7224	+	9.46362i	−0.867207	+	0.396040i	−0.0684218	+	0.997656i	$0.521796\pi$
$572$	1.23864	+	8.61491i	0.0517900	+	0.360207i
$573$	25.7695	+	2.72520i	1.07654	+	0.113847i
$574$		−	4.09560i		−	0.170947i
$575$	30.7083	−	25.1083i	1.28062	−	1.04709i
$576$	−15.7273	+	21.1622i	−0.655304	+	0.881758i
$577$	8.84490	+	5.68427i	0.368218	+	0.236639i	0.711644	−	0.702540i	$-0.247951\pi$
$577$	8.84490	+	5.68427i	0.368218	+	0.236639i	−0.343426	+	0.939180i	$0.611587\pi$
$578$	−33.7139	+	4.84733i	−1.40231	+	0.201622i
$579$	12.9629	+	10.4091i	0.538721	+	0.432586i
$580$	0.734808	−	2.50253i	0.0305112	−	0.103912i
$581$	−3.35858	−	1.53381i	−0.139337	−	0.0636332i
$582$	−6.97993	+	27.5469i	−0.289327	+	1.14186i
$583$	−1.79193	+	12.4632i	−0.0742142	+	0.516171i
$584$	−14.0250	−	47.7646i	−0.580357	−	1.97651i
$585$	71.5852	−	5.37013i	2.95969	−	0.222028i
$586$	5.06042	+	7.87417i	0.209044	+	0.325279i
$587$	20.1755	+	31.3937i	0.832732	+	1.29576i	0.952986	+	0.303014i	$0.0979928\pi$
$587$	20.1755	+	31.3937i	0.832732	+	1.29576i	−0.120254	+	0.992743i	$0.538371\pi$
$588$	−0.919364	−	0.378942i	−0.0379139	−	0.0156273i
$589$	2.26118	+	7.70088i	0.0931704	+	0.317309i
$590$	−4.44578	+	30.9211i	−0.183030	+	1.27300i
$591$	3.21018	+	0.813408i	0.132049	+	0.0334592i
$592$	−14.5697	−	6.65374i	−0.598810	−	0.273467i
$593$	−11.9982	+	40.8621i	−0.492707	+	1.67800i	0.219159	+	0.975689i	$0.429669\pi$
$593$	−11.9982	+	40.8621i	−0.492707	+	1.67800i	−0.711866	+	0.702316i	$0.752149\pi$
$594$	3.61381	+	13.8567i	0.148276	+	0.568549i
$595$	24.3293	−	3.49802i	0.997403	−	0.143405i
$596$	−7.05169	−	4.53185i	−0.288849	−	0.185632i
$597$	0.106357	+	0.211555i	0.00435290	+	0.00865835i
$598$	6.41561	−	37.0650i	0.262354	−	1.51570i
$599$			24.0444i			0.982427i	0.871039	+	0.491213i	$0.163447\pi$
$599$			24.0444i			0.982427i	−0.871039	+	0.491213i	$0.836553\pi$
$600$	−4.63091	+	43.7900i	−0.189056	+	1.78772i
$601$	−1.95206	−	13.5769i	−0.0796264	−	0.553814i	−0.990113	−	0.140274i	$-0.955202\pi$
$601$	−1.95206	−	13.5769i	−0.0796264	−	0.553814i	0.910486	−	0.413539i	$-0.135708\pi$
$602$	−7.20362	+	3.28978i	−0.293598	+	0.134082i
$603$	24.6986	+	32.7554i	1.00580	+	1.33390i
$604$	−1.54578	+	3.38478i	−0.0628968	+	0.137725i
$605$	13.5345	−	15.6197i	0.550257	−	0.635030i
$606$	−3.04441	−	9.09419i	−0.123671	−	0.369426i
$607$	13.5634	−	3.98259i	0.550523	−	0.161648i	0.00537142	−	0.999986i	$-0.498290\pi$
$607$	13.5634	−	3.98259i	0.550523	−	0.161648i	0.545152	+	0.838337i	$0.316472\pi$
$608$	−2.60664	−	3.00823i	−0.105713	−	0.122000i
$609$	−1.09893	+	1.85951i	−0.0445309	+	0.0753511i
$610$	−17.5731	+	11.2936i	−0.711515	+	0.457263i
$611$	−3.92467	+	3.40075i	−0.158775	+	0.137580i
$612$	4.02321	−	10.9023i	0.162629	−	0.440699i
$613$	−26.2321	−	3.77161i	−1.05951	−	0.152334i	−0.409536	−	0.912294i	$-0.634309\pi$
$613$	−26.2321	−	3.77161i	−1.05951	−	0.152334i	−0.649970	+	0.759960i	$0.725218\pi$
$614$	−2.14982	−	1.86283i	−0.0867598	−	0.0751778i
$615$	−21.6264	+	0.810039i	−0.872060	+	0.0326639i
$616$	6.80672	+	1.99863i	0.274250	+	0.0805272i
$617$	−2.25888	−	4.94627i	−0.0909393	−	0.199129i	0.858697	−	0.512484i	$-0.171274\pi$
$617$	−2.25888	−	4.94627i	−0.0909393	−	0.199129i	−0.949636	+	0.313354i	$0.898547\pi$
$618$	13.0918	+	18.7860i	0.526629	+	0.755683i
$619$	−18.0083	+	28.0214i	−0.723814	+	1.12628i	0.263059	+	0.964780i	$0.415269\pi$
$619$	−18.0083	+	28.0214i	−0.723814	+	1.12628i	−0.986873	+	0.161497i	$0.948368\pi$
$620$	−13.2241			−0.531093
$621$	−1.47133	+	24.8764i	−0.0590426	+	0.998255i
$622$	−13.2648			−0.531869
$623$	3.49171	−	5.43321i	0.139892	−	0.217677i
$624$	16.4062	+	23.5419i	0.656773	+	0.942432i
$625$	0.853539	+	1.86899i	0.0341416	+	0.0747596i
$626$	−13.3567	−	3.92189i	−0.533843	−	0.156750i
$627$	−5.07067	+	0.189927i	−0.202503	+	0.00758496i
$628$	1.73275	+	1.50144i	0.0691444	+	0.0599140i
$629$	42.4120	+	6.09792i	1.69108	+	0.243140i
$630$	4.51802	−	12.2431i	0.180002	−	0.487778i
$631$	33.6632	−	29.1693i	1.34011	−	1.16121i	0.367169	−	0.930154i	$-0.380327\pi$
$631$	33.6632	−	29.1693i	1.34011	−	1.16121i	0.972940	−	0.231057i	$-0.0742184\pi$
$632$	26.8146	−	17.2327i	1.06663	−	0.685479i
$633$	5.86665	−	9.92700i	0.233178	−	0.394563i
$634$	12.1199	+	13.9871i	0.481343	+	0.555500i
$635$	13.4246	−	3.94182i	0.532739	−	0.156426i
$636$	−1.72218	−	5.14446i	−0.0682890	−	0.203991i
$637$	−4.30148	+	4.96417i	−0.170431	+	0.196688i
$638$	1.42769	−	3.12621i	0.0565229	−	0.123768i
$639$	3.03796	+	4.02896i	0.120180	+	0.159383i
$640$	−13.9943	+	6.39099i	−0.553174	+	0.252626i
$641$	−5.71495	−	39.7483i	−0.225727	−	1.56997i	−0.715814	−	0.698291i	$-0.753944\pi$
$641$	−5.71495	−	39.7483i	−0.225727	−	1.56997i	0.490087	−	0.871674i	$-0.336965\pi$
$642$	0.159051	−	1.50399i	0.00627723	−	0.0593576i
$643$			5.01701i			0.197852i	0.995095	+	0.0989258i	$0.0315406\pi$
$643$			5.01701i			0.197852i	−0.995095	+	0.0989258i	$0.968459\pi$
$644$	2.27277	+	1.55419i	0.0895598	+	0.0612437i
$645$	18.7961	+	37.3873i	0.740095	+	1.47212i
$646$	−8.60345	−	5.52910i	−0.338498	−	0.217540i
$647$	0.410793	−	0.0590632i	0.0161500	−	0.00232201i	−0.134235	−	0.990950i	$-0.542858\pi$
$647$	0.410793	−	0.0590632i	0.0161500	−	0.00232201i	0.150385	+	0.988627i	$0.451949\pi$
$648$	−18.2609	−	20.7805i	−0.717357	−	0.816333i
$649$	4.66945	−	15.9027i	0.183292	−	0.624235i
$650$	59.0114	+	26.9496i	2.31462	+	1.05705i
$651$	10.6161	+	2.68994i	0.416076	+	0.105427i
$652$	−0.143005	+	0.994624i	−0.00560052	+	0.0389525i
$653$	12.0158	+	40.9221i	0.470215	+	1.60141i	0.763786	+	0.645469i	$0.223338\pi$
$653$	12.0158	+	40.9221i	0.470215	+	1.60141i	−0.293571	+	0.955937i	$0.594844\pi$
$654$	14.6401	+	6.03431i	0.572471	+	0.235960i
$655$	7.26820	+	11.3095i	0.283992	+	0.441900i
$656$	−4.67689	−	7.27738i	−0.182602	−	0.284134i
$657$	48.4504	−	3.63462i	1.89023	−	0.141800i
$658$	0.265972	+	0.905818i	0.0103687	+	0.0353125i
$659$	−1.42931	+	9.94105i	−0.0556779	+	0.387248i	0.942860	+	0.333190i	$0.108125\pi$
$659$	−1.42931	+	9.94105i	−0.0556779	+	0.387248i	−0.998538	+	0.0540587i	$0.982784\pi$
$660$	2.05355	−	8.10449i	0.0799342	−	0.315467i
$661$	2.52156	+	1.15156i	0.0980774	+	0.0447905i	0.463850	−	0.885914i	$-0.346468\pi$
$661$	2.52156	+	1.15156i	0.0980774	+	0.0447905i	−0.365772	+	0.930704i	$0.619195\pi$
$662$	9.85435	−	33.5608i	0.383000	−	1.30438i
$663$	−59.8542	−	48.0621i	−2.32454	−	1.86658i
$664$	−11.2335	+	1.61514i	−0.435946	+	0.0626796i
$665$	3.89012	+	2.50003i	0.150852	+	0.0969469i
$666$	13.5699	−	18.2593i	0.525825	−	0.707535i
$667$	4.04412	−	4.40606i	0.156589	−	0.170603i
$668$		−	9.90047i		−	0.383061i
$669$	12.0251	+	1.27168i	0.464916	+	0.0491661i
$670$	8.46558	+	58.8794i	0.327054	+	2.27471i
$671$	10.0814	−	4.60400i	0.389187	−	0.177736i
$672$	−5.34339	+	0.973649i	−0.206126	+	0.0375593i
$673$	4.91897	−	10.7710i	0.189612	−	0.415193i	−0.790820	−	0.612049i	$-0.790346\pi$
$673$	4.91897	−	10.7710i	0.189612	−	0.415193i	0.980433	+	0.196855i	$0.0630730\pi$
$674$	−5.42143	+	6.25667i	−0.208826	+	0.240998i
$675$	−40.8484	−	13.3594i	−1.57225	−	0.514203i
$676$	−16.6061	+	4.87598i	−0.638694	+	0.187538i
$677$	−0.0544833	−	0.0628771i	−0.00209396	−	0.00241656i	0.754702	−	0.656068i	$-0.227782\pi$
$677$	−0.0544833	−	0.0628771i	−0.00209396	−	0.00241656i	−0.756796	+	0.653652i	$0.773236\pi$
$678$	−20.5703	−	12.1566i	−0.789996	−	0.466871i
$679$	−11.5587	+	7.42832i	−0.443582	+	0.285073i
$680$	57.0979	−	49.4756i	2.18961	−	1.89730i
$681$	−16.6513	+	15.5571i	−0.638081	+	0.596149i
$682$	−17.2480	−	2.47989i	−0.660461	−	0.0949600i
$683$	15.3535	+	13.3039i	0.587485	+	0.509059i	0.897114	−	0.441798i	$-0.145659\pi$
$683$	15.3535	+	13.3039i	0.587485	+	0.509059i	−0.309629	+	0.950857i	$0.600205\pi$
$684$	1.91519	−	1.05444i	0.0732292	−	0.0403173i
$685$	−51.2767	−	15.0562i	−1.95918	−	0.575268i
$686$	0.496049	+	1.08620i	0.0189392	+	0.0414711i
$687$	3.74932	−	2.61287i	0.143045	−	0.0996873i
$688$	−9.04324	+	14.0716i	−0.344770	+	0.536473i
$689$	−35.8355			−1.36523
$690$	−19.2660	+	30.5697i	−0.733444	+	1.16377i
$691$	−48.7979			−1.85636			−0.928180	−	0.372131i	$-0.878627\pi$
$691$	−48.7979			−1.85636			−0.928180	+	0.372131i	$0.878627\pi$
$692$	−7.12822	+	11.0917i	−0.270974	+	0.421644i
$693$	−3.29709	+	6.08841i	−0.125246	+	0.231280i
$694$	15.7579	+	34.5050i	0.598162	+	1.30979i
$695$	54.1580	+	15.9022i	2.05433	+	0.603206i
$696$	0.248504	+	6.63455i	0.00941952	+	0.251482i
$697$	17.4894	+	15.1546i	0.662456	+	0.574022i
$698$	−25.3892	−	3.65041i	−0.960994	−	0.138170i
$699$	−11.1953	−	11.9828i	−0.423445	−	0.453229i
$700$	−3.58869	+	3.10962i	−0.135640	+	0.117533i
$701$	−39.9445	+	25.6708i	−1.50868	+	0.969572i	−0.515019	+	0.857179i	$0.672215\pi$
$701$	−39.9445	+	25.6708i	−1.50868	+	0.969572i	−0.993664	+	0.112393i	$0.964148\pi$
$702$	−37.5719	+	15.7929i	−1.41806	+	0.596063i
$703$	5.27891	+	6.09218i	0.199098	+	0.229771i
$704$	19.4624	−	5.71468i	0.733517	−	0.215380i
$705$	4.73047	−	1.58359i	0.178160	−	0.0596415i
$706$	−7.99122	+	9.22236i	−0.300754	+	0.347088i
$707$	1.92623	−	4.21786i	0.0724434	−	0.158629i
$708$	1.28014	+	7.02539i	0.0481105	+	0.264030i
$709$	−26.0213	+	11.8835i	−0.977249	+	0.446295i	−0.839017	−	0.544105i	$-0.816869\pi$
$709$	−26.0213	+	11.8835i	−0.977249	+	0.446295i	−0.138232	+	0.990400i	$0.544142\pi$
$710$	1.04128	+	7.24226i	0.0390785	+	0.271797i
$711$	10.9730	+	29.1102i	0.411519	+	1.09172i
$712$		−	19.8518i		−	0.743978i
$713$	−27.2118	−	13.3802i	−1.01909	−	0.501094i
$714$	−12.4678	+	6.26808i	−0.466597	+	0.234577i
$715$	−46.4594	−	29.8576i	−1.73748	−	1.11661i
$716$	3.75554	−	0.539966i	0.140351	−	0.0201795i
$717$	7.03659	−	8.76302i	0.262786	−	0.327261i
$718$	3.37412	−	11.4912i	0.125921	−	0.428848i
$719$	−46.5737	−	21.2695i	−1.73690	−	0.793218i	−0.992028	−	0.126015i	$-0.959781\pi$
$719$	−46.5737	−	21.2695i	−1.73690	−	0.793218i	−0.744876	−	0.667202i	$-0.767492\pi$
$720$	−5.95282	−	26.9138i	−0.221849	−	1.00302i
$721$	−1.57558	+	10.9584i	−0.0586777	+	0.408112i
$722$	5.84988	+	19.9229i	0.217710	+	0.741452i
$723$	5.76597	−	13.9890i	0.214439	−	0.520257i
$724$	6.33826	+	9.86252i	0.235559	+	0.366538i
$725$	5.57639	+	8.67703i	0.207102	+	0.322257i
$726$	−4.47154	+	10.8486i	−0.165954	+	0.402628i
$727$	11.0720	+	37.7077i	0.410637	+	1.39850i	0.862338	+	0.506333i	$0.168999\pi$
$727$	11.0720	+	37.7077i	0.410637	+	1.39850i	−0.451701	+	0.892170i	$0.649182\pi$
$728$	−2.87335	+	19.9846i	−0.106494	+	0.740679i
$729$	23.5611	−	13.1862i	0.872632	−	0.488378i
$730$	64.0847	+	29.2665i	2.37188	+	1.08320i
$731$	12.6067	−	42.9343i	0.466274	−	1.58798i
$732$	−2.98980	+	3.72334i	−0.110506	+	0.137619i
$733$	−20.6136	+	2.96379i	−0.761381	+	0.109470i	−0.512059	−	0.858950i	$-0.671117\pi$
$733$	−20.6136	+	2.96379i	−0.761381	+	0.109470i	−0.249322	+	0.968421i	$0.580208\pi$
$734$	−25.9969	−	16.7072i	−0.959564	−	0.616674i
$735$	5.63743	−	2.83416i	0.207940	−	0.104540i
$736$	15.0326	+	0.429944i	0.554110	+	0.0158479i
$737$		−	31.5601i		−	1.16253i
$738$	11.4971	−	4.33380i	0.423215	−	0.159529i
$739$	3.19627	+	22.2306i	0.117577	+	0.817764i	0.960211	+	0.279277i	$0.0900948\pi$
$739$	3.19627	+	22.2306i	0.117577	+	0.817764i	−0.842634	+	0.538487i	$0.818996\pi$
$740$	−12.0817	+	5.51754i	−0.444133	+	0.202829i
$741$	−2.58884	−	14.2076i	−0.0951035	−	0.521929i
$742$	−2.70626	+	5.92588i	−0.0993500	+	0.217546i
$743$	−14.7789	+	17.0558i	−0.542187	+	0.625717i	−0.959045	−	0.283255i	$-0.908586\pi$
$743$	−14.7789	+	17.0558i	−0.542187	+	0.625717i	0.416858	+	0.908972i	$0.363131\pi$
$744$	31.9213	−	10.6861i	1.17029	−	0.391772i
$745$	51.0341	−	14.9850i	1.86975	−	0.549007i
$746$	7.51693	+	8.67500i	0.275214	+	0.317614i
$747$	0.751781	−	11.0512i	0.0275062	−	0.404341i
$748$	−7.52094	+	4.83342i	−0.274993	+	0.176727i
$749$	0.552629	−	0.478856i	0.0201926	−	0.0174970i
$750$	−16.8252	−	18.0087i	−0.614371	−	0.657585i
$751$	−30.6659	−	4.40909i	−1.11901	−	0.160890i	−0.442110	−	0.896961i	$-0.645770\pi$
$751$	−30.6659	−	4.40909i	−1.11901	−	0.160890i	−0.676904	+	0.736071i	$0.736679\pi$
$752$	1.50698	+	1.30581i	0.0549539	+	0.0476178i
$753$	−0.448218	−	11.9665i	−0.0163340	−	0.436084i
$754$	9.38507	+	2.75571i	0.341784	+	0.100357i
$755$	−9.80844	−	21.4775i	−0.356966	−	0.781646i
$756$	0.0909258	−	2.98181i	0.00330694	−	0.108447i
$757$	−5.27472	+	8.20763i	−0.191713	+	0.298311i	−0.923782	−	0.382920i	$-0.874919\pi$
$757$	−5.27472	+	8.20763i	−0.191713	+	0.298311i	0.732069	+	0.681231i	$0.238555\pi$
$758$	16.5162			0.599897
$759$	12.4258	−	14.5991i	0.451030	−	0.529915i
$760$	14.2137			0.515584
$761$	19.2298	−	29.9221i	0.697079	−	1.08468i	−0.294560	−	0.955633i	$-0.595173\pi$
$761$	19.2298	−	29.9221i	0.697079	−	1.08468i	0.991639	−	0.129043i	$-0.0411905\pi$
$762$	−6.51704	+	4.54167i	−0.236087	+	0.164527i
$763$	3.18049	+	6.96431i	0.115142	+	0.252125i
$764$	8.24143	+	2.41990i	0.298164	+	0.0875490i
$765$	35.5639	+	64.5954i	1.28581	+	2.33545i
$766$	−21.9358	−	19.0075i	−0.792572	−	0.686767i
$767$	46.6905	+	6.71308i	1.68590	+	0.242395i
$768$	−15.8643	+	14.8217i	−0.572453	+	0.534833i
$769$	−20.6495	+	17.8929i	−0.744642	+	0.645236i	−0.942198	−	0.335056i	$-0.891245\pi$
$769$	−20.6495	+	17.8929i	−0.744642	+	0.645236i	0.197557	+	0.980291i	$0.436699\pi$
$770$	−8.44592	+	5.42786i	−0.304370	+	0.195607i
$771$	24.8449	+	14.6828i	0.894767	+	0.528789i
$772$	3.60866	+	4.16461i	0.129878	+	0.149888i
$773$	42.0392	−	12.3438i	1.51205	−	0.443977i	0.582546	−	0.812798i	$-0.302057\pi$
$773$	42.0392	−	12.3438i	1.51205	−	0.443977i	0.929500	+	0.368821i	$0.120239\pi$
$774$	−16.8576	−	16.7408i	−0.605934	−	0.601735i
$775$	34.2470	−	39.5232i	1.23019	−	1.41971i
$776$	−17.5442	+	38.4165i	−0.629801	+	1.37907i
$777$	10.8213	−	1.97181i	0.388212	−	0.0707383i
$778$	19.6039	−	8.95279i	0.702833	−	0.320973i
$779$	0.619597	+	4.30939i	0.0221994	+	0.154400i
$780$	23.6628	+	2.50240i	0.847264	+	0.0896005i
$781$		−	3.88194i		−	0.138907i
$782$	37.3699	−	9.82152i	1.33635	−	0.351217i
$783$	−6.38284	−	1.11725i	−0.228104	−	0.0399271i
$784$	2.12178	+	1.36358i	0.0757777	+	0.0486994i
$785$	−14.4002	+	2.07044i	−0.513965	+	0.0738971i
$786$	−5.95133	−	4.77884i	−0.212277	−	0.170456i
$787$	10.1457	−	34.5532i	0.361656	−	1.23169i	−0.554945	−	0.831887i	$-0.687261\pi$
$787$	10.1457	−	34.5532i	0.361656	−	1.23169i	0.916602	−	0.399801i	$-0.130921\pi$
$788$	0.998497	+	0.455998i	0.0355700	+	0.0162443i
$789$	−9.19915	+	36.3052i	−0.327498	+	1.29250i
$790$	−6.41975	+	44.6504i	−0.228405	+	1.58859i
$791$	−3.25478	−	11.0847i	−0.115727	−	0.394128i
$792$	1.59206	+	21.2226i	0.0565715	+	0.754112i
$793$	17.0532	+	26.5353i	0.605576	+	0.942295i
$794$	−12.0809	−	18.7982i	−0.428735	−	0.667125i
$795$	31.8263	+	13.1181i	1.12876	+	0.465250i
$796$	0.0221121	+	0.0753069i	0.000783743	+	0.00266918i
$797$	−2.81145	+	19.5541i	−0.0995866	+	0.692640i	0.877465	+	0.479640i	$0.159233\pi$
$797$	−2.81145	+	19.5541i	−0.0995866	+	0.692640i	−0.977052	+	0.213000i	$0.931676\pi$
$798$	−2.54492	−	0.644841i	−0.0900892	−	0.0228271i
$799$	−4.85225	−	2.21595i	−0.171660	−	0.0783946i
$800$	−7.30710	+	24.8857i	−0.258345	+	0.879842i
$801$	18.9468	+	4.05268i	0.669453	+	0.143194i
$802$	−19.9209	+	2.86419i	−0.703431	+	0.101138i
$803$	−31.4447	−	20.2083i	−1.10966	−	0.713134i
$804$	6.10780	+	12.1490i	0.215405	+	0.428462i
$805$	−16.8971	+	4.44087i	−0.595545	+	0.156520i
$806$		−	49.5936i		−	1.74686i
$807$	0.0870223	−	0.822884i	0.00306333	−	0.0289669i
$808$	−2.02837	−	14.1076i	−0.0713578	−	0.496304i
$809$	−31.4253	+	14.3514i	−1.10485	+	0.504570i	−0.882460	−	0.470388i	$-0.844114\pi$
$809$	−31.4253	+	14.3514i	−1.10485	+	0.504570i	−0.222393	+	0.974957i	$0.571387\pi$
$810$	39.1495	−	0.272268i	1.37557	−	0.00956652i
$811$	7.96128	−	17.4328i	0.279558	−	0.612148i	−0.716812	−	0.697266i	$-0.754400\pi$
$811$	7.96128	−	17.4328i	0.279558	−	0.612148i	0.996371	+	0.0851185i	$0.0271269\pi$
$812$	−0.468850	+	0.541081i	−0.0164534	+	0.0189882i
$813$	−11.9850	−	35.8015i	−0.420334	−	1.25561i
$814$	−16.7927	+	4.93079i	−0.588584	+	0.172824i
$815$	−4.17545	−	4.81873i	−0.146260	−	0.168793i
$816$	−14.9961	+	25.3750i	−0.524968	+	0.888303i
$817$	7.08196	−	4.55130i	0.247766	−	0.159230i
$818$	−27.9892	+	24.2528i	−0.978618	+	0.847978i
$819$	−18.4870	−	6.82216i	−0.645988	−	0.238386i
$820$	−7.10042	−	1.02089i	−0.247957	−	0.0356509i
$821$	24.7732	+	21.4661i	0.864592	+	0.749173i	0.969443	−	0.245315i	$-0.0788913\pi$
$821$	24.7732	+	21.4661i	0.864592	+	0.749173i	−0.104852	+	0.994488i	$0.533437\pi$
$822$	30.3197	−	1.13566i	1.05752	−	0.0396105i
$823$	35.2933	+	10.3630i	1.23025	+	0.361233i	0.831343	−	0.555759i	$-0.187572\pi$
$823$	35.2933	+	10.3630i	1.23025	+	0.361233i	0.398904	+	0.916993i	$0.369391\pi$
$824$	14.1365	+	30.9547i	0.492469	+	1.07836i
$825$	18.9039	+	27.1260i	0.658149	+	0.944406i
$826$	4.63611	−	7.21393i	0.161311	−	0.251005i
$827$	5.47546			0.190400			0.0952002	−	0.995458i	$-0.469651\pi$
$827$	5.47546			0.190400			0.0952002	+	0.995458i	$0.469651\pi$
$828$	−1.95795	+	8.02468i	−0.0680434	+	0.278877i
$829$	−5.12354			−0.177948			−0.0889740	−	0.996034i	$-0.528359\pi$
$829$	−5.12354			−0.177948			−0.0889740	+	0.996034i	$0.528359\pi$
$830$	8.68346	−	13.5117i	0.301407	−	0.468999i
$831$	−6.60433	−	9.47683i	−0.229102	−	0.328748i
$832$	23.9817	+	52.5126i	0.831416	+	1.82055i
$833$	−6.47384	−	1.90089i	−0.224305	−	0.0658620i
$834$	−32.0234	+	1.19947i	−1.10888	+	0.0415342i
$835$	47.4773	+	41.1394i	1.64302	+	1.42369i
$836$	−1.66481	−	0.239364i	−0.0575788	−	0.00827858i
$837$	3.68234	+	32.6476i	0.127280	+	1.12847i
$838$	30.4452	−	26.3809i	1.05171	−	0.911314i
$839$	4.69843	−	3.01950i	0.162208	−	0.104245i	−0.457019	−	0.889457i	$-0.651083\pi$
$839$	4.69843	−	3.01950i	0.162208	−	0.104245i	0.619226	+	0.785213i	$0.287446\pi$
$840$	9.86752	−	16.6969i	0.340462	−	0.576098i
$841$	−17.9726	−	20.7414i	−0.619743	−	0.715222i
$842$	11.3887	−	3.34403i	0.392482	−	0.115243i
$843$	2.49711	+	7.45930i	0.0860050	+	0.256912i
$844$	2.50295	−	2.88856i	0.0861553	−	0.0994285i
$845$	45.6204	−	99.8948i	1.56939	−	3.43649i
$846$	−2.26136	+	1.70513i	−0.0777471	+	0.0586237i
$847$	−5.16069	+	2.35681i	−0.177323	+	0.0809809i
$848$	1.95825	+	13.6199i	0.0672466	+	0.467710i
$849$	1.01659	−	9.61290i	0.0348893	−	0.329914i
$850$			66.6379i			2.28566i
$851$	−30.4437	−	0.870711i	−1.04360	−	0.0298476i
$852$	0.751268	+	1.49435i	0.0257380	+	0.0511955i
$853$	7.24059	+	4.65324i	0.247913	+	0.159324i	0.658696	−	0.752409i	$-0.271108\pi$
$853$	7.24059	+	4.65324i	0.247913	+	0.159324i	−0.410783	+	0.911733i	$0.634745\pi$
$854$	5.67580	−	0.816056i	0.194222	−	0.0279249i
$855$	−2.90167	+	13.5657i	−0.0992352	+	0.463938i
$856$	0.633233	−	2.15659i	0.0216434	−	0.0737108i
$857$	33.1325	+	15.1311i	1.13178	+	0.516868i	0.891132	−	0.453744i	$-0.149912\pi$
$857$	33.1325	+	15.1311i	1.13178	+	0.516868i	0.240651	+	0.970612i	$0.422639\pi$
$858$	30.3938	+	7.70129i	1.03763	+	0.262918i
$859$	−5.88357	+	40.9211i	−0.200745	+	1.39621i	0.601336	+	0.798996i	$0.294635\pi$
$859$	−5.88357	+	40.9211i	−0.200745	+	1.39621i	−0.802081	+	0.597215i	$0.796274\pi$
$860$	3.90779	+	13.3087i	0.133255	+	0.453824i
$861$	5.49242	+	2.26385i	0.187181	+	0.0771520i
$862$	10.5528	+	16.4205i	0.359429	+	0.559283i
$863$	0.0675389	+	0.105093i	0.00229905	+	0.00357739i	0.842401	−	0.538851i	$-0.181141\pi$
$863$	0.0675389	+	0.105093i	0.00229905	+	0.00357739i	−0.840102	+	0.542428i	$0.817505\pi$
$864$	−8.38737	−	13.9696i	−0.285344	−	0.475256i
$865$	−23.5701	−	80.2725i	−0.801408	−	2.72935i
$866$	−0.781829	+	5.43774i	−0.0265676	+	0.184782i
$867$	12.1349	−	47.8915i	0.412124	−	1.62648i
$868$	3.30202	+	1.50798i	0.112078	+	0.0511843i
$869$	6.74274	−	22.9637i	0.228732	−	0.778989i
$870$	−7.32630	−	5.88293i	−0.248385	−	0.199450i
$871$	88.9074	−	12.7830i	3.01251	−	0.433134i
$872$	19.7975	+	12.7231i	0.670427	+	0.430857i
$873$	−33.0836	−	24.5871i	−1.11971	−	0.832146i
$874$	6.52331	+	3.20756i	0.220654	+	0.108497i
$875$		−	11.9161i		−	0.402839i
$876$	16.0155	+	1.69368i	0.541112	+	0.0572241i
$877$	−1.24458	−	8.65623i	−0.0420264	−	0.292300i	−0.999985	−	0.00539507i	$-0.998283\pi$
$877$	−1.24458	−	8.65623i	−0.0420264	−	0.292300i	0.957959	−	0.286905i	$-0.0926264\pi$
$878$	−11.4827	+	5.24399i	−0.387523	+	0.176976i
$879$	−13.3568	+	2.43383i	−0.450515	+	0.0820909i
$880$	−8.80912	+	19.2893i	−0.296955	+	0.650242i
$881$	7.69712	−	8.88295i	0.259323	−	0.299274i	−0.611126	−	0.791533i	$-0.709283\pi$
$881$	7.69712	−	8.88295i	0.259323	−	0.299274i	0.870449	+	0.492259i	$0.163829\pi$
$882$	−2.52425	+	2.54187i	−0.0849960	+	0.0855892i
$883$	−14.8565	+	4.36226i	−0.499961	+	0.146802i	−0.521983	−	0.852956i	$-0.674808\pi$
$883$	−14.8565	+	4.36226i	−0.499961	+	0.146802i	0.0220225	+	0.999757i	$0.492989\pi$
$884$	−16.6624	−	19.2294i	−0.560417	−	0.646756i
$885$	−39.0093	−	23.0537i	−1.31128	−	0.774942i
$886$	−2.41095	+	1.54943i	−0.0809976	+	0.0520540i
$887$	27.1437	−	23.5202i	0.911397	−	0.789730i	−0.0667226	−	0.997772i	$-0.521254\pi$
$887$	27.1437	−	23.5202i	0.911397	−	0.789730i	0.978120	+	0.208041i	$0.0667088\pi$
$888$	24.7051	−	23.0816i	0.829049	−	0.774567i
$889$	−3.80158	−	0.546584i	−0.127501	−	0.0183319i
$890$	21.2325	+	18.3981i	0.711716	+	0.616705i
$891$	−20.5802	−	2.81304i	−0.689461	−	0.0942404i
$892$	3.84577	+	1.12922i	0.128766	+	0.0378091i
$893$	−0.416891	−	0.912865i	−0.0139507	−	0.0305478i
$894$	−24.7748	+	17.2654i	−0.828593	+	0.577440i
$895$	−13.0160	+	20.2533i	−0.435077	+	0.676993i
$896$	4.22313			0.141085
$897$	46.1599	+	29.0915i	1.54123	+	0.971336i
$898$	−24.7726			−0.826672
$899$	4.26294	−	6.63326i	0.142177	−	0.221232i
$900$	−12.5267	−	6.78366i	−0.417557	−	0.226122i
$901$	−15.2914	−	33.4835i	−0.509431	−	1.11550i
$902$	−9.06954	−	2.66306i	−0.301983	−	0.0886701i
$903$	−0.429953	−	11.4789i	−0.0143079	−	0.381993i
$904$	−26.8369	−	23.2543i	−0.892582	−	0.773427i
$905$	−73.6326	−	10.5868i	−2.44763	−	0.351916i
$906$	9.15148	+	9.79518i	0.304038	+	0.325423i
$907$	−8.54108	+	7.40088i	−0.283602	+	0.245742i	−0.785031	−	0.619456i	$-0.787353\pi$
$907$	−8.54108	+	7.40088i	−0.283602	+	0.245742i	0.501429	+	0.865199i	$0.332808\pi$
$908$	−6.35434	+	4.08369i	−0.210876	+	0.135522i
$909$	13.8786	+	0.944122i	0.460324	+	0.0313146i
$910$	−18.7116	−	21.5944i	−0.620285	−	0.715847i
$911$	38.8681	−	11.4127i	1.28776	−	0.378120i	0.435002	−	0.900430i	$-0.356748\pi$
$911$	38.8681	−	11.4127i	1.28776	−	0.378120i	0.852756	+	0.522310i	$0.174930\pi$
$912$	−5.25837	+	1.76032i	−0.174122	+	0.0582899i
$913$	−5.58039	+	6.44011i	−0.184684	+	0.213137i
$914$	−15.4597	+	33.8520i	−0.511362	+	1.11973i
$915$	−5.43167	−	29.8090i	−0.179565	−	0.985456i
$916$	1.37790	−	0.629264i	0.0455270	−	0.0207915i
$917$	−0.525190	−	3.65277i	−0.0173433	−	0.120625i
$918$	−30.7887	−	28.3669i	−1.01618	−	0.936247i
$919$		−	19.9493i		−	0.658068i	−0.944318	−	0.329034i	$-0.893277\pi$
$919$		−	19.9493i		−	0.658068i	0.944318	−	0.329034i	$-0.106723\pi$
$920$	−36.3129	+	39.5629i	−1.19720	+	1.30435i
$921$	3.68648	−	1.85334i	0.121474	−	0.0610697i
$922$	−10.0227	−	6.44117i	−0.330079	−	0.212129i
$923$	10.9357	−	1.57232i	0.359955	−	0.0517536i
$924$	−1.43694	+	1.78950i	−0.0472719	+	0.0588701i
$925$	14.7982	−	50.3979i	0.486560	−	1.65707i
$926$	−33.6249	−	15.3560i	−1.10498	−	0.504629i
$927$	−32.4295	+	7.17280i	−1.06512	+	0.235586i
$928$	−0.556524	+	3.87071i	−0.0182688	+	0.127062i
$929$	16.1192	+	54.8970i	0.528854	+	1.80111i	0.595526	+	0.803336i	$0.296944\pi$
$929$	16.1192	+	54.8970i	0.528854	+	1.80111i	−0.0666722	+	0.997775i	$0.521238\pi$
$930$	−18.1544	+	44.0451i	−0.595306	+	1.44429i
$931$	−0.686266	−	1.06785i	−0.0224915	−	0.0349974i
$932$	−2.93873	−	4.57276i	−0.0962614	−	0.149786i
$933$	7.33214	−	17.7888i	0.240044	−	0.582378i
$934$	−0.180441	−	0.614525i	−0.00590420	−	0.0201079i
$935$	8.07325	−	56.1507i	0.264023	−	1.83632i
$936$	−59.1410	+	13.0809i	−1.93308	+	0.427562i
$937$	−16.7770	−	7.66182i	−0.548082	−	0.250301i	0.122074	−	0.992521i	$-0.461046\pi$
$937$	−16.7770	−	7.66182i	−0.548082	−	0.250301i	−0.670156	+	0.742220i	$0.733773\pi$
$938$	4.60036	−	15.6674i	0.150207	−	0.511558i
$939$	12.6424	−	15.7443i	0.412570	−	0.513794i
$940$	1.63669	−	0.235320i	0.0533828	−	0.00767529i
$941$	26.9248	+	17.3035i	0.877722	+	0.564078i	0.900106	−	0.435672i	$-0.143489\pi$
$941$	26.9248	+	17.3035i	0.877722	+	0.564078i	−0.0223834	+	0.999749i	$0.507125\pi$
$942$	7.37956	−	3.71000i	0.240439	−	0.120878i
$943$	−13.5779	−	9.28497i	−0.442157	−	0.302360i
$944$		−	18.1124i		−	0.589508i
$945$	13.9213	+	12.8263i	0.452861	+	0.417240i
$946$	2.60112	+	18.0912i	0.0845698	+	0.588196i
$947$	9.10663	−	4.15886i	0.295926	−	0.135145i	−0.261920	−	0.965090i	$-0.584355\pi$
$947$	9.10663	−	4.15886i	0.295926	−	0.135145i	0.557845	+	0.829945i	$0.311628\pi$
$948$	1.84853	+	10.1447i	0.0600375	+	0.329486i
$949$	44.1922	−	96.7673i	1.43454	−	3.14120i
$950$	−8.20982	+	9.47464i	−0.266362	+	0.307398i
$951$	−25.4568	+	8.52203i	−0.825493	+	0.276346i
$952$	−19.8990	+	5.84289i	−0.644932	+	0.189369i
$953$	−21.8202	−	25.1819i	−0.706826	−	0.815721i	0.282831	−	0.959170i	$-0.408726\pi$
$953$	−21.8202	−	25.1819i	−0.706826	−	0.815721i	−0.989658	+	0.143448i	$0.954181\pi$
$954$	−19.4987	−	1.32644i	−0.631294	−	0.0429452i
$955$	−45.8501	+	29.4661i	−1.48367	+	0.953500i
$956$	2.81531	−	2.43948i	0.0910535	−	0.0788983i
$957$	3.40325	+	3.64263i	0.110012	+	0.117750i
$958$	26.3949	+	3.79502i	0.852782	+	0.122612i
$959$	11.0868	+	9.60673i	0.358010	+	0.310217i
$960$	−2.07568	−	55.4163i	−0.0669921	−	1.78855i
$961$	−8.61511	−	2.52962i	−0.277907	−	0.0816007i
$962$	−20.6921	−	45.3094i	−0.667140	−	1.46083i
$963$	1.92901	+	1.04463i	0.0621614	+	0.0336626i
$964$	2.71149	−	4.21916i	0.0873311	−	0.135890i
$965$	−34.9663			−1.12560
$966$	8.29661	−	5.43620i	0.266939	−	0.174907i
$967$	19.7368			0.634692			0.317346	−	0.948310i	$-0.397208\pi$
$967$	19.7368			0.634692			0.317346	+	0.948310i	$0.397208\pi$
$968$	−9.42804	+	14.6703i	−0.303029	+	0.471522i
$969$	12.1704	−	8.48146i	0.390970	−	0.272464i
$970$	−24.8290	−	54.3678i	−0.797210	−	1.74565i
$971$	−28.1350	−	8.26119i	−0.902897	−	0.265114i	−0.202849	−	0.979210i	$-0.565020\pi$
$971$	−28.1350	−	8.26119i	−0.902897	−	0.265114i	−0.700048	+	0.714096i	$0.746838\pi$
$972$	8.46670	−	2.89998i	0.271570	−	0.0930170i
$973$	−11.7097	−	10.1465i	−0.375396	−	0.325283i
$974$	41.5092	+	5.96812i	1.33004	+	0.191231i
$975$	−68.7595	+	64.2409i	−2.20207	+	2.05735i
$976$	9.15331	−	7.93139i	0.292990	−	0.253878i
$977$	12.6148	−	8.10704i	0.403583	−	0.259367i	−0.323065	−	0.946377i	$-0.604713\pi$
$977$	12.6148	−	8.10704i	0.403583	−	0.259367i	0.726648	+	0.687010i	$0.241077\pi$
$978$	3.11644	+	1.84175i	0.0996526	+	0.0588926i
$979$	−9.76122	−	11.2651i	−0.311970	−	0.360033i
$980$	2.00675	−	0.589235i	0.0641033	−	0.0188224i
$981$	−16.1847	+	16.2976i	−0.516736	+	0.520342i
$982$	0.125203	−	0.144492i	0.00399538	−	0.00461091i
$983$	−10.2457	+	22.4349i	−0.326786	+	0.715562i	−0.999708	−	0.0241513i	$-0.992312\pi$
$983$	−10.2457	+	22.4349i	−0.326786	+	0.715562i	0.672922	+	0.739713i	$0.265039\pi$
$984$	17.9644	−	3.27340i	0.572685	−	0.104352i
$985$	−6.33577	+	2.89345i	−0.201874	+	0.0921930i
$986$	1.42987	+	9.94499i	0.0455364	+	0.316713i
$987$	−1.36177	−	0.144011i	−0.0433455	−	0.00458391i
$988$		−	4.78687i		−	0.152291i
$989$	−5.42463	+	31.3398i	−0.172493	+	0.996548i
$990$	−24.1742	−	17.9657i	−0.768305	−	0.570988i
$991$	−8.79998	−	5.65541i	−0.279541	−	0.179650i	0.393356	−	0.919386i	$-0.371314\pi$
$991$	−8.79998	−	5.65541i	−0.279541	−	0.179650i	−0.672897	+	0.739736i	$0.734950\pi$
$992$	19.6255	−	2.82172i	0.623110	−	0.0895897i
$993$	39.5598	+	31.7661i	1.25539	+	1.00807i
$994$	0.565851	−	1.92711i	0.0179477	−	0.0611243i
$995$	−0.453014	−	0.206885i	−0.0143615	−	0.00655868i
$996$	0.901813	−	3.55908i	0.0285750	−	0.112774i
$997$	−8.43287	+	58.6519i	−0.267072	+	1.85752i	0.208732	+	0.977973i	$0.433066\pi$
$997$	−8.43287	+	58.6519i	−0.267072	+	1.85752i	−0.475804	+	0.879551i	$0.657843\pi$
$998$	8.47340	+	28.8578i	0.268221	+	0.913477i
$999$	16.9859	+	28.2909i	0.537410	+	0.895085i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.34	yes	480
3.2	odd	2	inner	483.2.u.a.113.15	✓	480
23.11	odd	22	inner	483.2.u.a.218.15	yes	480
69.11	even	22	inner	483.2.u.a.218.34	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.15	✓	480	3.2	odd	2	inner
483.2.u.a.113.34	yes	480	1.1	even	1	trivial
483.2.u.a.218.15	yes	480	23.11	odd	22	inner
483.2.u.a.218.34	yes	480	69.11	even	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.645581 - 1.00454i) q^{2} +(0.990300 + 1.42102i) q^{3} +(0.238496 + 0.522234i) q^{4} +(-3.49538 - 1.02634i) q^{5} +(2.06680 - 0.0774141i) q^{6} +(0.755750 + 0.654861i) q^{7} +(3.04248 + 0.437442i) q^{8} +(-1.03861 + 2.81448i) q^{9} +(-3.28755 + 2.84868i) q^{10} +(1.94157 - 1.24777i) q^{11} +(-0.505924 + 0.856077i) q^{12} +(4.30148 + 4.96417i) q^{13} +(1.14573 - 0.336418i) q^{14} +(-2.00303 - 5.98339i) q^{15} +(1.65166 - 1.90612i) q^{16} +(-2.80287 + 6.13742i) q^{17} +(2.15676 + 2.86031i) q^{18} +(-1.15465 + 0.527310i) q^{19} +(-0.297647 - 2.07018i) q^{20} +(-0.182153 + 1.72245i) q^{21} -2.75593i q^{22} +(1.48214 - 4.56106i) q^{23} +(2.39135 + 4.75663i) q^{24} +(6.95802 + 4.47165i) q^{25} +(7.76368 - 1.11625i) q^{26} +(-5.02797 + 1.31129i) q^{27} +(-0.161747 + 0.550860i) q^{28} +(1.13436 + 0.518045i) q^{29} +(-7.30369 - 1.85064i) q^{30} +(0.899840 - 6.25852i) q^{31} +(0.883458 + 3.00878i) q^{32} +(3.69584 + 1.52335i) q^{33} +(4.35583 + 6.77781i) q^{34} +(-1.96952 - 3.06464i) q^{35} +(-1.71752 + 0.128844i) q^{36} +(-1.78916 - 6.09331i) q^{37} +(-0.215713 + 1.50032i) q^{38} +(-2.79445 + 11.0285i) q^{39} +(-10.1856 - 4.65162i) q^{40} +(0.966302 - 3.29092i) q^{41} +(1.61268 + 1.29496i) q^{42} +(-6.56447 + 0.943828i) q^{43} +(1.11468 + 0.716364i) q^{44} +(6.51894 - 8.77169i) q^{45} +(-3.62494 - 4.43341i) q^{46} +0.790600i q^{47} +(4.34428 + 0.459420i) q^{48} +(0.142315 + 0.989821i) q^{49} +(8.98394 - 4.10283i) q^{50} +(-11.4971 + 2.09495i) q^{51} +(-1.56657 + 3.43031i) q^{52} +(-3.57268 + 4.12309i) q^{53} +(-1.92872 + 5.89736i) q^{54} +(-8.06714 + 2.36873i) q^{55} +(2.01289 + 2.32299i) q^{56} +(-1.89277 - 1.11859i) q^{57} +(1.25272 - 0.805074i) q^{58} +(5.42727 - 4.70275i) q^{59} +(2.64702 - 2.47306i) q^{60} +(4.75318 + 0.683405i) q^{61} +(-5.70604 - 4.94431i) q^{62} +(-2.62802 + 1.44689i) q^{63} +(8.43279 + 2.47609i) q^{64} +(-9.94038 - 21.7664i) q^{65} +(3.91624 - 2.72919i) q^{66} +(7.39301 - 11.5037i) q^{67} -3.87364 q^{68} +(7.94913 - 2.41066i) q^{69} -4.35005 q^{70} +(0.909351 - 1.41498i) q^{71} +(-4.39112 + 8.10865i) q^{72} +(-6.72785 - 14.7319i) q^{73} +(-7.27604 - 2.13644i) q^{74} +(0.536213 + 14.3158i) q^{75} +(-0.550758 - 0.477235i) q^{76} +(2.28445 + 0.328455i) q^{77} +(9.27459 + 9.92695i) q^{78} +(7.83703 - 6.79083i) q^{79} +(-7.72950 + 4.96745i) q^{80} +(-6.84257 - 5.84630i) q^{81} +(-2.68205 - 3.09525i) q^{82} +(-3.54268 + 1.04022i) q^{83} +(-0.942963 + 0.315670i) q^{84} +(16.0961 - 18.5759i) q^{85} +(-3.28978 + 7.20362i) q^{86} +(0.387203 + 2.12497i) q^{87} +(6.45300 - 2.94699i) q^{88} +(-0.919136 - 6.39273i) q^{89} +(-4.60305 - 12.2114i) q^{90} +6.56854i q^{91} +(2.73543 - 0.313770i) q^{92} +(9.78461 - 4.91912i) q^{93} +(0.794193 + 0.510397i) q^{94} +(4.57712 - 0.658091i) q^{95} +(-3.40066 + 4.23501i) q^{96} +(-3.87096 + 13.1833i) q^{97} +(1.08620 + 0.496049i) q^{98} +(1.49528 + 6.76045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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