LMFDB - Embedded newform 384.2.v.a.157.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			157.20
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.521130 - 1.31470i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.45685 - 1.37025i) q^{4} +(-2.27128 + 1.21402i) q^{5} +(1.25729 + 0.647483i) q^{6} +(-0.00530364 - 0.0266632i) q^{7} +(-2.56067 + 1.20123i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(0.521130 - 1.31470i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.45685 - 1.37025i) q^{4} +(-2.27128 + 1.21402i) q^{5} +(1.25729 + 0.647483i) q^{6} +(-0.00530364 - 0.0266632i) q^{7} +(-2.56067 + 1.20123i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.412441 + 3.61870i) q^{10} +(-2.29916 + 2.80154i) q^{11} +(1.50645 - 1.31552i) q^{12} +(-1.83986 + 3.44214i) q^{13} +(-0.0378179 - 0.00692231i) q^{14} +(-0.985553 - 2.37934i) q^{15} +(0.244811 + 3.99250i) q^{16} +(0.672095 - 1.62258i) q^{17} +(-0.767601 + 1.18777i) q^{18} +(-0.274844 - 0.906039i) q^{19} +(4.97243 + 1.34358i) q^{20} +(0.0270547 - 0.00266465i) q^{21} +(2.48501 + 4.48266i) q^{22} +(-2.98873 + 1.99701i) q^{23} +(-0.944457 - 2.66608i) q^{24} +(0.906999 - 1.35742i) q^{25} +(3.56656 + 4.21266i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-0.0288087 + 0.0461115i) q^{28} +(-5.13823 + 4.21684i) q^{29} +(-3.64170 + 0.0557598i) q^{30} +(3.32015 - 3.32015i) q^{31} +(5.37650 + 1.75876i) q^{32} +(-2.56269 - 2.56269i) q^{33} +(-1.78295 - 1.72917i) q^{34} +(0.0444158 + 0.0541208i) q^{35} +(1.16153 + 1.62814i) q^{36} +(0.746322 + 0.226394i) q^{37} +(-1.33439 - 0.110828i) q^{38} +(-3.24522 - 2.16839i) q^{39} +(4.35768 - 5.83705i) q^{40} +(2.40985 + 3.60659i) q^{41} +(0.0105958 - 0.0369573i) q^{42} +(-0.735893 - 7.47165i) q^{43} +(7.18835 - 0.930979i) q^{44} +(2.46448 - 0.747592i) q^{45} +(1.06794 + 4.96998i) q^{46} +(-11.6664 - 4.83239i) q^{47} +(-3.99727 - 0.147701i) q^{48} +(6.46647 - 2.67850i) q^{49} +(-1.31193 - 1.89982i) q^{50} +(1.54889 + 0.827899i) q^{51} +(7.39700 - 2.49359i) q^{52} +(9.16863 + 7.52450i) q^{53} +(-1.10681 - 0.880326i) q^{54} +(1.82090 - 9.15431i) q^{55} +(0.0456095 + 0.0619048i) q^{56} +(0.928615 - 0.184713i) q^{57} +(2.86617 + 8.95272i) q^{58} +(-3.90628 - 7.30814i) q^{59} +(-1.82449 + 4.81679i) q^{60} +(-7.58662 - 0.747217i) q^{61} +(-2.63476 - 6.09522i) q^{62} +0.0271856i q^{63} +(5.11409 - 6.15192i) q^{64} -10.0517i q^{65} +(-4.70465 + 2.03366i) q^{66} +(12.1687 + 1.19851i) q^{67} +(-3.20248 + 1.44291i) q^{68} +(-1.69445 - 3.17008i) q^{69} +(0.0942987 - 0.0301893i) q^{70} +(-4.77220 + 0.949250i) q^{71} +(2.74582 - 0.678588i) q^{72} +(-1.00771 + 5.06608i) q^{73} +(0.686570 - 0.863205i) q^{74} +(1.26198 + 1.03568i) q^{75} +(-0.841097 + 1.69657i) q^{76} +(0.0868919 + 0.0464447i) q^{77} +(-4.54195 + 3.13647i) q^{78} +(-0.801401 + 0.331951i) q^{79} +(-5.40302 - 8.77087i) q^{80} +(0.923880 + 0.382683i) q^{81} +(5.99741 - 1.28871i) q^{82} +(-7.72407 + 2.34307i) q^{83} +(-0.0430658 - 0.0331897i) q^{84} +(0.443336 + 4.50127i) q^{85} +(-10.2064 - 2.92622i) q^{86} +(-3.69290 - 5.52681i) q^{87} +(2.52211 - 9.93565i) q^{88} +(14.3546 + 9.59147i) q^{89} +(0.301458 - 3.62963i) q^{90} +(0.101536 + 0.0308007i) q^{91} +(7.09054 + 1.18599i) q^{92} +(2.97873 + 3.62959i) q^{93} +(-12.4328 + 12.8195i) q^{94} +(1.72420 + 1.72420i) q^{95} +(-2.27728 + 5.17822i) q^{96} +(-3.52198 + 3.52198i) q^{97} +(-0.151542 - 9.89729i) q^{98} +(2.80154 - 2.29916i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.521130	−	1.31470i	0.368494	−	0.929630i
$2$	0.521130	−	1.31470i	0.368494	−	0.929630i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	−1.45685	−	1.37025i	−0.728424	−	0.685127i
$5$	−2.27128	+	1.21402i	−1.01575	+	0.542928i	−0.893259	−	0.449542i	$-0.851587\pi$
$5$	−2.27128	+	1.21402i	−1.01575	+	0.542928i	−0.122487	+	0.992470i	$0.539087\pi$
$6$	1.25729	+	0.647483i	0.513284	+	0.264334i
$7$	−0.00530364	−	0.0266632i	−0.00200459	−	0.0100777i	0.979770	−	0.200127i	$-0.0641354\pi$
$7$	−0.00530364	−	0.0266632i	−0.00200459	−	0.0100777i	−0.981775	+	0.190049i	$0.939135\pi$
$8$	−2.56067	+	1.20123i	−0.905334	+	0.424699i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	0.412441	+	3.61870i	0.130425	+	1.14433i
$11$	−2.29916	+	2.80154i	−0.693223	+	0.844695i	−0.994043	−	0.108986i	$-0.965240\pi$
$11$	−2.29916	+	2.80154i	−0.693223	+	0.844695i	0.300820	+	0.953681i	$0.402740\pi$
$12$	1.50645	−	1.31552i	0.434875	−	0.379759i
$13$	−1.83986	+	3.44214i	−0.510286	+	0.954677i	0.486432	+	0.873718i	$0.338298\pi$
$13$	−1.83986	+	3.44214i	−0.510286	+	0.954677i	−0.996717	+	0.0809586i	$0.974202\pi$
$14$	−0.0378179	−	0.00692231i	−0.0101072	−	0.00185007i
$15$	−0.985553	−	2.37934i	−0.254469	−	0.614342i
$16$	0.244811	+	3.99250i	0.0612028	+	0.998125i
$17$	0.672095	−	1.62258i	0.163007	−	0.393533i	−0.821179	−	0.570670i	$-0.806683\pi$
$17$	0.672095	−	1.62258i	0.163007	−	0.393533i	0.984186	+	0.177137i	$0.0566835\pi$
$18$	−0.767601	+	1.18777i	−0.180925	+	0.279959i
$19$	−0.274844	−	0.906039i	−0.0630535	−	0.207860i	0.919753	−	0.392497i	$-0.128389\pi$
$19$	−0.274844	−	0.906039i	−0.0630535	−	0.207860i	−0.982807	+	0.184638i	$0.940889\pi$
$20$	4.97243	+	1.34358i	1.11187	+	0.300433i
$21$	0.0270547	−	0.00266465i	0.00590381	−	0.000581474i
$22$	2.48501	+	4.48266i	0.529805	+	0.955707i
$23$	−2.98873	+	1.99701i	−0.623194	+	0.416405i	−0.826680	−	0.562673i	$-0.809773\pi$
$23$	−2.98873	+	1.99701i	−0.623194	+	0.416405i	0.203485	+	0.979078i	$0.434773\pi$
$24$	−0.944457	−	2.66608i	−0.192787	−	0.544212i
$25$	0.906999	−	1.35742i	0.181400	−	0.271484i
$26$	3.56656	+	4.21266i	0.699459	+	0.826170i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	−0.0288087	+	0.0461115i	−0.00544434	+	0.00871426i
$29$	−5.13823	+	4.21684i	−0.954145	+	0.783047i	−0.976236	−	0.216709i	$-0.930468\pi$
$29$	−5.13823	+	4.21684i	−0.954145	+	0.783047i	0.0220911	+	0.999756i	$0.492968\pi$
$30$	−3.64170	+	0.0557598i	−0.664881	+	0.0101803i
$31$	3.32015	−	3.32015i	0.596317	−	0.596317i	−0.343014	−	0.939330i	$-0.611448\pi$
$31$	3.32015	−	3.32015i	0.596317	−	0.596317i	0.939330	+	0.343014i	$0.111448\pi$
$32$	5.37650	+	1.75876i	0.950440	+	0.310908i
$33$	−2.56269	−	2.56269i	−0.446107	−	0.446107i
$34$	−1.78295	−	1.72917i	−0.305773	−	0.296551i
$35$	0.0444158	+	0.0541208i	0.00750764	+	0.00914808i
$36$	1.16153	+	1.62814i	0.193589	+	0.271357i
$37$	0.746322	+	0.226394i	0.122695	+	0.0372190i	0.351035	−	0.936362i	$-0.385830\pi$
$37$	0.746322	+	0.226394i	0.122695	+	0.0372190i	−0.228340	+	0.973581i	$0.573330\pi$
$38$	−1.33439	−	0.110828i	−0.216467	−	0.0179786i
$39$	−3.24522	−	2.16839i	−0.519652	−	0.347220i
$40$	4.35768	−	5.83705i	0.689009	−	0.922918i
$41$	2.40985	+	3.60659i	0.376355	+	0.563255i	0.970499	−	0.241104i	$-0.0775093\pi$
$41$	2.40985	+	3.60659i	0.376355	+	0.563255i	−0.594145	+	0.804358i	$0.702509\pi$
$42$	0.0105958	−	0.0369573i	0.00163496	−	0.00570263i
$43$	−0.735893	−	7.47165i	−0.112223	−	1.13942i	−0.872093	−	0.489341i	$-0.837238\pi$
$43$	−0.735893	−	7.47165i	−0.112223	−	1.13942i	0.759870	−	0.650075i	$-0.225262\pi$
$44$	7.18835	−	0.930979i	1.08368	−	0.140350i
$45$	2.46448	−	0.747592i	0.367383	−	0.111444i
$46$	1.06794	+	4.96998i	0.157459	+	0.732783i
$47$	−11.6664	−	4.83239i	−1.70172	−	0.704876i	−0.701750	−	0.712424i	$-0.747597\pi$
$47$	−11.6664	−	4.83239i	−1.70172	−	0.704876i	−0.999972	+	0.00754784i	$0.997597\pi$
$48$	−3.99727	−	0.147701i	−0.576957	−	0.0213188i
$49$	6.46647	−	2.67850i	0.923782	−	0.382643i
$50$	−1.31193	−	1.89982i	−0.185535	−	0.268675i
$51$	1.54889	+	0.827899i	0.216888	+	0.115929i
$52$	7.39700	−	2.49359i	1.02578	−	0.345799i
$53$	9.16863	+	7.52450i	1.25941	+	1.03357i	0.997656	+	0.0684348i	$0.0218005\pi$
$53$	9.16863	+	7.52450i	1.25941	+	1.03357i	0.261753	+	0.965135i	$0.415699\pi$
$54$	−1.10681	−	0.880326i	−0.150618	−	0.119797i
$55$	1.82090	−	9.15431i	0.245531	−	1.23437i
$56$	0.0456095	+	0.0619048i	0.00609483	+	0.00827238i
$57$	0.928615	−	0.184713i	0.122998	−	0.0244658i
$58$	2.86617	+	8.95272i	0.376347	+	1.17555i
$59$	−3.90628	−	7.30814i	−0.508555	−	0.951439i	−0.996892	−	0.0787837i	$-0.974896\pi$
$59$	−3.90628	−	7.30814i	−0.508555	−	0.951439i	0.488337	−	0.872655i	$-0.337604\pi$
$60$	−1.82449	+	4.81679i	−0.235541	+	0.621845i
$61$	−7.58662	−	0.747217i	−0.971367	−	0.0956713i	−0.400132	−	0.916458i	$-0.631036\pi$
$61$	−7.58662	−	0.747217i	−0.971367	−	0.0956713i	−0.571235	+	0.820786i	$0.693536\pi$
$62$	−2.63476	−	6.09522i	−0.334615	−	0.774093i
$63$			0.0271856i			0.00342506i
$64$	5.11409	−	6.15192i	0.639261	−	0.768990i
$65$		−	10.0517i		−	1.24676i
$66$	−4.70465	+	2.03366i	−0.579102	+	0.250327i
$67$	12.1687	+	1.19851i	1.48664	+	0.146422i	0.808495	−	0.588503i	$-0.200283\pi$
$67$	12.1687	+	1.19851i	1.48664	+	0.146422i	0.678149	+	0.734925i	$0.262783\pi$
$68$	−3.20248	+	1.44291i	−0.388358	+	0.174979i
$69$	−1.69445	−	3.17008i	−0.203987	−	0.381633i
$70$	0.0942987	−	0.0301893i	0.0112709	−	0.00360831i
$71$	−4.77220	+	0.949250i	−0.566356	+	0.112655i	−0.469960	−	0.882688i	$-0.655732\pi$
$71$	−4.77220	+	0.949250i	−0.566356	+	0.112655i	−0.0963964	+	0.995343i	$0.530732\pi$
$72$	2.74582	−	0.678588i	0.323598	−	0.0799723i
$73$	−1.00771	+	5.06608i	−0.117943	+	0.592940i	0.875932	+	0.482434i	$0.160247\pi$
$73$	−1.00771	+	5.06608i	−0.117943	+	0.592940i	−0.993875	+	0.110506i	$0.964753\pi$
$74$	0.686570	−	0.863205i	0.0798121	−	0.100346i
$75$	1.26198	+	1.03568i	0.145721	+	0.119590i
$76$	−0.841097	+	1.69657i	−0.0964805	+	0.194610i
$77$	0.0868919	+	0.0464447i	0.00990225	+	0.00529286i
$78$	−4.54195	+	3.13647i	−0.514275	+	0.355135i
$79$	−0.801401	+	0.331951i	−0.0901646	+	0.0373474i	−0.427310	−	0.904105i	$-0.640539\pi$
$79$	−0.801401	+	0.331951i	−0.0901646	+	0.0373474i	0.337145	+	0.941453i	$0.390539\pi$
$80$	−5.40302	−	8.77087i	−0.604076	−	0.980613i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	5.99741	−	1.28871i	0.662303	−	0.142315i
$83$	−7.72407	+	2.34307i	−0.847827	+	0.257185i	−0.684161	−	0.729331i	$-0.739832\pi$
$83$	−7.72407	+	2.34307i	−0.847827	+	0.257185i	−0.163665	+	0.986516i	$0.552332\pi$
$84$	−0.0430658	−	0.0331897i	−0.00469886	−	0.00362130i
$85$	0.443336	+	4.50127i	0.0480866	+	0.488231i
$86$	−10.2064	−	2.92622i	−1.10059	−	0.315543i
$87$	−3.69290	−	5.52681i	−0.395920	−	0.592536i
$88$	2.52211	−	9.93565i	0.268857	−	1.05914i
$89$	14.3546	+	9.59147i	1.52159	+	1.01669i	0.984942	+	0.172887i	$0.0553097\pi$
$89$	14.3546	+	9.59147i	1.52159	+	1.01669i	0.536648	+	0.843806i	$0.319690\pi$
$90$	0.301458	−	3.62963i	0.0317765	−	0.382597i
$91$	0.101536	+	0.0308007i	0.0106439	+	0.00322879i
$92$	7.09054	+	1.18599i	0.739240	+	0.123648i
$93$	2.97873	+	3.62959i	0.308880	+	0.376371i
$94$	−12.4328	+	12.8195i	−1.28235	+	1.32223i
$95$	1.72420	+	1.72420i	0.176899	+	0.176899i
$96$	−2.27728	+	5.17822i	−0.232424	+	0.528500i
$97$	−3.52198	+	3.52198i	−0.357603	+	0.357603i	−0.862929	−	0.505326i	$-0.831372\pi$
$97$	−3.52198	+	3.52198i	−0.357603	+	0.357603i	0.505326	+	0.862929i	$0.331372\pi$
$98$	−0.151542	−	9.89729i	−0.0153081	−	0.999777i
$99$	2.80154	−	2.29916i	0.281565	−	0.231074i
$100$	−3.18137	+	0.734736i	−0.318137	+	0.0734736i
$101$	−3.92209	+	12.9294i	−0.390262	+	1.28652i	0.513353	+	0.858178i	$0.328403\pi$
$101$	−3.92209	+	12.9294i	−0.390262	+	1.28652i	−0.903615	+	0.428345i	$0.859097\pi$
$102$	1.89561	−	1.60488i	0.187693	−	0.158906i
$103$	−3.83568	+	5.74050i	−0.377941	+	0.565629i	−0.970864	−	0.239630i	$-0.922974\pi$
$103$	−3.83568	+	5.74050i	−0.377941	+	0.565629i	0.592923	+	0.805259i	$0.297974\pi$
$104$	0.576477	−	11.0243i	0.0565282	−	1.08102i
$105$	−0.0582137	+	0.0388971i	−0.00568107	+	0.00379597i
$106$	14.6705	−	8.13272i	1.42492	−	0.789919i
$107$	−1.37418	+	0.135344i	−0.132847	+	0.0130842i	−0.164222	−	0.986423i	$-0.552511\pi$
$107$	−1.37418	+	0.135344i	−0.132847	+	0.0130842i	0.0313753	+	0.999508i	$0.490011\pi$
$108$	−1.73415	+	0.996353i	−0.166869	+	0.0958741i
$109$	2.17271	+	7.16246i	0.208108	+	0.686039i	0.997403	+	0.0720251i	$0.0229462\pi$
$109$	2.17271	+	7.16246i	0.208108	+	0.686039i	−0.789295	+	0.614014i	$0.789554\pi$
$110$	−11.0862	−	7.16452i	−1.05703	−	0.683110i
$111$	−0.298456	+	0.720537i	−0.0283282	+	0.0683904i
$112$	0.105154	−	0.0277022i	0.00993616	−	0.00261762i
$113$	−5.97290	−	14.4199i	−0.561883	−	1.35651i	−0.908258	−	0.418409i	$-0.862588\pi$
$113$	−5.97290	−	14.4199i	−0.561883	−	1.35651i	0.346376	−	0.938096i	$-0.387412\pi$
$114$	0.241088	−	1.31711i	0.0225799	−	0.123358i
$115$	4.36383	−	8.16415i	0.406929	−	0.761311i
$116$	13.2637	+	0.897388i	1.23151	+	0.0833204i
$117$	2.47604	−	3.01706i	0.228910	−	0.278927i
$118$	−11.6437	+	1.32708i	−1.07189	+	0.122168i
$119$	−0.0468277	−	0.00931461i	−0.00429269	−	0.000853869i
$120$	5.38181	+	4.90882i	0.491290	+	0.448112i
$121$	−0.416471	−	2.09374i	−0.0378610	−	0.190340i
$122$	−4.93598	+	9.58470i	−0.446882	+	0.867758i
$123$	−3.82543	+	2.04473i	−0.344927	+	0.184367i
$124$	−9.38640	+	0.287507i	−0.842924	+	0.0258188i
$125$	0.850047	−	8.63067i	0.0760305	−	0.771951i
$126$	0.0357407	+	0.0141672i	0.00318404	+	0.00126211i
$127$	5.33644			0.473533			0.236766	−	0.971567i	$-0.423912\pi$
$127$	5.33644			0.473533			0.236766	+	0.971567i	$0.423912\pi$
$128$	−5.42280	−	9.92941i	−0.479312	−	0.877644i
$129$	7.50780			0.661025
$130$	−13.2149	−	5.23823i	−1.15902	−	0.459423i
$131$	−0.432385	+	4.39008i	−0.0377777	+	0.383563i	0.957642	+	0.287961i	$0.0929775\pi$
$131$	−0.432385	+	4.39008i	−0.0377777	+	0.383563i	−0.995420	+	0.0956017i	$0.969522\pi$
$132$	0.221915	+	7.24498i	0.0193152	+	0.630595i
$133$	−0.0227002	+	0.0121335i	−0.00196836	+	0.00105211i
$134$	7.91715	−	15.3736i	0.683938	−	1.32807i
$135$	0.502431	+	2.52589i	0.0432424	+	0.217394i
$136$	0.228080	+	4.96224i	0.0195577	+	0.425508i
$137$	−4.10563	−	0.816661i	−0.350768	−	0.0697720i	0.0165620	−	0.999863i	$-0.494728\pi$
$137$	−4.10563	−	0.816661i	−0.350768	−	0.0697720i	−0.367330	+	0.930091i	$0.619728\pi$
$138$	−5.05072	+	0.575655i	−0.429946	+	0.0490030i
$139$	−5.05884	+	6.16421i	−0.429085	+	0.522842i	−0.942007	−	0.335594i	$-0.891063\pi$
$139$	−5.05884	+	6.16421i	−0.429085	+	0.522842i	0.512922	+	0.858435i	$0.328563\pi$
$140$	0.00945216	−	0.139707i	0.000798853	−	0.0118074i
$141$	5.95262	−	11.1366i	0.501301	−	0.937869i
$142$	−1.23896	+	6.76868i	−0.103971	+	0.568015i
$143$	−5.41314	−	13.0685i	−0.452669	−	1.09284i
$144$	0.538791	−	3.96355i	0.0448993	−	0.330296i
$145$	6.55101	−	15.8155i	0.544032	−	1.31341i
$146$	6.13521	+	3.96491i	0.507753	+	0.328138i
$147$	2.03178	+	6.69788i	0.167578	+	0.552431i
$148$	−0.777060	−	1.35247i	−0.0638739	−	0.111172i
$149$	−3.36019	+	0.330950i	−0.275277	+	0.0271125i	−0.234714	−	0.972065i	$-0.575415\pi$
$149$	−3.36019	+	0.330950i	−0.275277	+	0.0271125i	−0.0405635	+	0.999177i	$0.512915\pi$
$150$	2.01926	−	1.11940i	0.164872	−	0.0913985i
$151$	1.26204	−	0.843265i	0.102703	−	0.0686239i	−0.503158	−	0.864194i	$-0.667829\pi$
$151$	1.26204	−	0.843265i	0.102703	−	0.0686239i	0.605861	+	0.795570i	$0.292829\pi$
$152$	1.79215	+	1.98992i	0.145362	+	0.161404i
$153$	−0.975730	+	1.46028i	−0.0788831	+	0.118057i
$154$	0.106343	−	0.0900326i	0.00856932	−	0.00725504i
$155$	−3.51024	+	11.5717i	−0.281950	+	0.929463i
$156$	1.75655	+	7.60579i	0.140637	+	0.608951i
$157$	−10.6191	+	8.71485i	−0.847495	+	0.695521i	−0.954330	−	0.298756i	$-0.903428\pi$
$157$	−10.6191	+	8.71485i	−0.847495	+	0.695521i	0.106835	+	0.994277i	$0.465928\pi$
$158$	0.0187809	+	1.22659i	0.00149412	+	0.0975821i
$159$	−8.38695	+	8.38695i	−0.665129	+	0.665129i
$160$	−14.3467	+	2.53257i	−1.13421	+	0.200217i
$161$	0.0690978	+	0.0690978i	0.00544567	+	0.00544567i
$162$	0.984573	−	1.01519i	0.0773554	−	0.0797611i
$163$	0.353069	+	0.430215i	0.0276545	+	0.0336971i	0.786654	−	0.617394i	$-0.211812\pi$
$163$	0.353069	+	0.430215i	0.0276545	+	0.0336971i	−0.759000	+	0.651091i	$0.774312\pi$
$164$	1.43116	−	8.55635i	0.111755	−	0.668139i
$165$	8.93175	+	2.70942i	0.695335	+	0.210928i
$166$	−0.944817	+	11.3758i	−0.0733320	+	0.882936i
$167$	17.8523	+	11.9285i	1.38145	+	0.923057i	0.999999	−	0.00133114i	$-0.000423716\pi$
$167$	17.8523	+	11.9285i	1.38145	+	0.923057i	0.381453	+	0.924388i	$0.375424\pi$
$168$	−0.0660772	+	0.0393222i	−0.00509797	+	0.00303377i
$169$	−1.24081	−	1.85700i	−0.0954467	−	0.142846i
$170$	6.14883	+	1.76289i	0.471594	+	0.135208i
$171$	0.0928034	+	0.942249i	0.00709685	+	0.0720556i
$172$	−9.16596	+	11.8934i	−0.698898	+	0.906864i
$173$	5.40780	−	1.64044i	0.411147	−	0.124720i	−0.0779336	−	0.996959i	$-0.524832\pi$
$173$	5.40780	−	1.64044i	0.411147	−	0.124720i	0.489081	+	0.872238i	$0.337332\pi$
$174$	−9.19055	+	1.97485i	−0.696734	+	0.149713i
$175$	−0.0410036	−	0.0169842i	−0.00309958	−	0.00128389i
$176$	−11.7480	−	8.49356i	−0.885539	−	0.640226i
$177$	7.65583	−	3.17115i	0.575448	−	0.238358i
$178$	20.0905	−	13.8736i	1.50585	−	1.03987i
$179$	13.4929	+	7.21208i	1.00850	+	0.539056i	0.890994	−	0.454015i	$-0.150009\pi$
$179$	13.4929	+	7.21208i	1.00850	+	0.539056i	0.117510	+	0.993072i	$0.462509\pi$
$180$	−4.61476	−	2.28783i	−0.343964	−	0.170525i
$181$	13.7226	+	11.2618i	1.01999	+	0.837086i	0.986731	−	0.162361i	$-0.0519108\pi$
$181$	13.7226	+	11.2618i	1.01999	+	0.837086i	0.0332608	+	0.999447i	$0.489411\pi$
$182$	0.0934071	−	0.117438i	0.00692380	−	0.00870510i
$183$	1.48724	−	7.47685i	0.109940	−	0.552705i
$184$	5.25430	−	8.70385i	0.387352	−	0.641656i
$185$	−1.96995	+	0.391848i	−0.144834	+	0.0288092i
$186$	6.32412	−	2.02464i	0.463707	−	0.148453i
$187$	3.00046	+	5.61347i	0.219416	+	0.410498i
$188$	10.3746	+	23.0260i	0.756645	+	1.67934i
$189$	−0.0270547	−	0.00266465i	−0.00196794	−	0.000193825i
$190$	3.16533	−	1.36827i	0.229637	−	0.0992644i
$191$			16.1697i			1.17000i	0.811033	+	0.585000i	$0.198905\pi$
$191$			16.1697i			1.17000i	−0.811033	+	0.585000i	$0.801095\pi$
$192$	5.62103	+	5.69245i	0.405663	+	0.410817i
$193$			23.4858i			1.69054i	0.534336	+	0.845272i	$0.320562\pi$
$193$			23.4858i			1.69054i	−0.534336	+	0.845272i	$0.679438\pi$
$194$	2.79492	+	6.46574i	0.200664	+	0.464213i
$195$	10.0033	+	0.985237i	0.716350	+	0.0705543i
$196$	−13.0909	−	4.95854i	−0.935064	−	0.354181i
$197$	1.71814	+	3.21441i	0.122412	+	0.229017i	0.935662	−	0.352898i	$-0.114804\pi$
$197$	1.71814	+	3.21441i	0.122412	+	0.229017i	−0.813250	+	0.581915i	$0.802304\pi$
$198$	−1.56273	−	4.88133i	−0.111059	−	0.346901i
$199$	−19.9922	+	3.97670i	−1.41721	+	0.281901i	−0.843487	−	0.537149i	$-0.819501\pi$
$199$	−19.9922	+	3.97670i	−1.41721	+	0.281901i	−0.573723	+	0.819049i	$0.694501\pi$
$200$	−0.691952	+	4.56543i	−0.0489284	+	0.322824i
$201$	−2.38548	+	11.9926i	−0.168259	+	0.845895i
$202$	14.9543	+	11.8942i	1.05218	+	0.836876i
$203$	0.139686	+	0.114637i	0.00980401	+	0.00804594i
$204$	−1.12207	−	3.32849i	−0.0785603	−	0.233041i
$205$	−9.85191	−	5.26596i	−0.688087	−	0.367790i
$206$	5.54813	+	8.03430i	0.386556	+	0.559776i
$207$	3.32090	−	1.37556i	0.230819	−	0.0956083i
$208$	−14.1932	−	6.50297i	−0.984118	−	0.450900i
$209$	3.17021	+	1.31314i	0.219288	+	0.0908321i
$210$	0.0208010	+	0.0968037i	0.00143541	+	0.00668009i
$211$	24.7605	−	7.51101i	1.70458	−	0.517079i	0.720296	−	0.693667i	$-0.244006\pi$
$211$	24.7605	−	7.51101i	1.70458	−	0.517079i	0.984285	+	0.176588i	$0.0565060\pi$
$212$	−3.04683	−	23.5254i	−0.209257	−	1.61573i
$213$	−0.476922	−	4.84227i	−0.0326781	−	0.331787i
$214$	−0.538187	+	1.87715i	−0.0367897	+	0.128320i
$215$	10.7422	+	16.0768i	0.732610	+	1.09643i
$216$	0.406183	+	2.79911i	0.0276372	+	0.190455i
$217$	−0.106135	−	0.0709169i	−0.00720489	−	0.00481416i
$218$	10.5487	+	0.876120i	0.714449	+	0.0593383i
$219$	−4.94291	−	1.49942i	−0.334011	−	0.101321i
$220$	−15.1965	+	10.8413i	−1.02455	+	0.730922i
$221$	4.34858	+	5.29876i	0.292517	+	0.356433i
$222$	0.791753	+	0.767873i	0.0531390	+	0.0515362i
$223$	−11.4849	−	11.4849i	−0.769083	−	0.769083i	0.208862	−	0.977945i	$-0.433024\pi$
$223$	−11.4849	−	11.4849i	−0.769083	−	0.769083i	−0.977945	+	0.208862i	$0.933024\pi$
$224$	0.0183791	−	0.152683i	0.00122801	−	0.0102015i
$225$	−1.15439	+	1.15439i	−0.0769594	+	0.0769594i
$226$	−22.0704	+	0.337930i	−1.46810	+	0.0224787i
$227$	11.2092	−	9.19912i	0.743978	−	0.610567i	−0.184120	−	0.982904i	$-0.558943\pi$
$227$	11.2092	−	9.19912i	0.743978	−	0.610567i	0.928098	+	0.372337i	$0.121443\pi$
$228$	−1.60596	−	1.00334i	−0.106357	−	0.0664478i
$229$	2.69185	−	8.87384i	0.177883	−	0.586400i	−0.821975	−	0.569524i	$-0.807128\pi$
$229$	2.69185	−	8.87384i	0.177883	−	0.586400i	0.999858	−	0.0168766i	$-0.00537226\pi$
$230$	−8.45925	−	9.99169i	−0.557787	−	0.658833i
$231$	−0.0547379	+	0.0819211i	−0.00360149	+	0.00539001i
$232$	8.09192	−	16.9701i	0.531261	−	1.11414i
$233$	−7.17838	+	4.79644i	−0.470272	+	0.314225i	−0.768028	−	0.640417i	$-0.778762\pi$
$233$	−7.17838	+	4.79644i	−0.470272	+	0.314225i	0.297756	+	0.954642i	$0.403762\pi$
$234$	−2.67618	−	4.82751i	−0.174947	−	0.315584i
$235$	32.3643	−	3.18760i	2.11121	−	0.207936i
$236$	−4.32314	+	15.9994i	−0.281413	+	1.04148i
$237$	−0.251802	−	0.830079i	−0.0163563	−	0.0539194i
$238$	−0.0366492	+	0.0567100i	−0.00237561	+	0.00367597i
$239$	6.77499	−	16.3563i	0.438238	−	1.05800i	−0.538319	−	0.842741i	$-0.680941\pi$
$239$	6.77499	−	16.3563i	0.438238	−	1.05800i	0.976557	−	0.215259i	$-0.0690594\pi$
$240$	9.25823	−	4.51731i	0.597616	−	0.291591i
$241$	−1.79409	−	4.33131i	−0.115567	−	0.279004i	0.855503	−	0.517798i	$-0.173248\pi$
$241$	−1.79409	−	4.33131i	−0.115567	−	0.279004i	−0.971070	+	0.238794i	$0.923248\pi$
$242$	−2.96966	−	0.543578i	−0.190897	−	0.0349425i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	10.0287	+	11.4842i	0.642020	+	0.735199i
$245$	−11.4354	+	13.9341i	−0.730581	+	0.890215i
$246$	0.694658	+	6.09485i	0.0442898	+	0.388593i
$247$	3.62438	+	0.720935i	0.230614	+	0.0458720i
$248$	−4.51355	+	12.4901i	−0.286611	+	0.793121i
$249$	−1.57470	−	7.91654i	−0.0997924	−	0.501690i
$250$	−10.9037	−	5.61525i	−0.689612	−	0.355140i
$251$	−10.6704	+	5.70344i	−0.673509	+	0.359998i	−0.772432	−	0.635097i	$-0.780960\pi$
$251$	−10.6704	+	5.70344i	−0.673509	+	0.359998i	0.0989234	+	0.995095i	$0.468460\pi$
$252$	0.0372511	−	0.0396052i	0.00234660	−	0.00249489i
$253$	1.27689	−	12.9645i	0.0802775	−	0.815071i
$254$	2.78098	−	7.01579i	0.174494	−	0.440210i
$255$	−4.52305			−0.283244
$256$	−15.8801	+	1.95482i	−0.992508	+	0.122176i
$257$	3.66814			0.228812			0.114406	−	0.993434i	$-0.463504\pi$
$257$	3.66814			0.228812			0.114406	+	0.993434i	$0.463504\pi$
$258$	3.91254	−	9.87047i	0.243584	−	0.614508i
$259$	0.00207817	−	0.0211000i	0.000129131	−	0.00131109i
$260$	−13.7734	+	14.6438i	−0.854187	+	0.908168i
$261$	5.86216	−	3.13339i	0.362859	−	0.193952i
$262$	5.54629	+	2.85626i	0.342651	+	0.176460i
$263$	2.05800	+	10.3462i	0.126902	+	0.637977i	0.990913	+	0.134505i	$0.0429444\pi$
$263$	2.05800	+	10.3462i	0.126902	+	0.637977i	−0.864011	+	0.503472i	$0.832056\pi$
$264$	9.64059	+	3.48383i	0.593337	+	0.214415i
$265$	−29.9594	−	5.95930i	−1.84039	−	0.366077i
$266$	0.00412213	+	0.0361670i	0.000252744	+	0.00221754i
$267$	−10.9523	+	13.3454i	−0.670269	+	0.816725i
$268$	−16.0857	−	18.4203i	−0.982589	−	1.12520i
$269$	−4.96214	+	9.28351i	−0.302547	+	0.566026i	−0.986551	−	0.163452i	$-0.947737\pi$
$269$	−4.96214	+	9.28351i	−0.302547	+	0.566026i	0.684004	+	0.729478i	$0.260237\pi$
$270$	3.58261	+	0.655773i	0.218031	+	0.0399091i
$271$	−10.7429	−	25.9357i	−0.652585	−	1.57548i	−0.809013	−	0.587791i	$-0.799998\pi$
$271$	−10.7429	−	25.9357i	−0.652585	−	1.57548i	0.156428	−	0.987689i	$-0.450002\pi$
$272$	6.64269	+	2.28611i	0.402772	+	0.138616i
$273$	−0.0406047	+	0.0980284i	−0.00245751	+	0.00593295i
$274$	−3.21323	+	4.97207i	−0.194118	+	0.300374i
$275$	1.71753	+	5.66192i	0.103571	+	0.341427i
$276$	−1.87527	+	6.94015i	−0.112878	+	0.417748i
$277$	−13.0519	+	1.28550i	−0.784216	+	0.0772385i	−0.482196	−	0.876063i	$-0.660161\pi$
$277$	−13.0519	+	1.28550i	−0.784216	+	0.0772385i	−0.302019	+	0.953302i	$0.597661\pi$
$278$	5.46775	+	9.86318i	0.327934	+	0.591555i
$279$	−3.90408	+	2.60863i	−0.233731	+	0.156174i
$280$	−0.178746	−	0.0852320i	−0.0106821	−	0.00509358i
$281$	14.0127	−	20.9715i	0.835928	−	1.25105i	−0.129811	−	0.991539i	$-0.541437\pi$
$281$	14.0127	−	20.9715i	0.835928	−	1.25105i	0.965739	−	0.259516i	$-0.0835630\pi$
$282$	−11.5391	−	13.6295i	−0.687144	−	0.811624i
$283$	−6.11698	+	20.1650i	−0.363617	+	1.19868i	0.564197	+	0.825640i	$0.309186\pi$
$283$	−6.11698	+	20.1650i	−0.363617	+	1.19868i	−0.927814	+	0.373044i	$0.878314\pi$
$284$	8.25309	+	5.15622i	0.489731	+	0.305965i
$285$	−1.88490	+	1.54690i	−0.111652	+	0.0916302i
$286$	−20.0020	+	0.306260i	−1.18274	+	0.0181095i
$287$	0.0833822	−	0.0833822i	0.00492190	−	0.00492190i
$288$	−4.93008	−	2.77387i	−0.290508	−	0.163452i
$289$	9.83976	+	9.83976i	0.578809	+	0.578809i
$290$	−17.3787	−	16.8545i	−1.02051	−	0.989732i
$291$	−3.15980	−	3.85023i	−0.185231	−	0.225705i
$292$	8.40989	−	5.99970i	0.492152	−	0.351106i
$293$	−20.7815	−	6.30401i	−1.21407	−	0.368284i	−0.382631	−	0.923901i	$-0.624982\pi$
$293$	−20.7815	−	6.30401i	−1.21407	−	0.368284i	−0.831438	+	0.555617i	$0.812482\pi$
$294$	9.86449	+	0.819292i	0.575308	+	0.0477821i
$295$	17.7445	+	11.8565i	1.03312	+	0.690312i
$296$	−2.18304	+	0.316784i	−0.126886	+	0.0184127i
$297$	2.01349	+	3.01340i	0.116835	+	0.174855i
$298$	−1.31600	+	4.59009i	−0.0762336	+	0.265897i
$299$	−1.37512	−	13.9619i	−0.0795254	−	0.807435i
$300$	−0.419369	−	3.23807i	−0.0242123	−	0.186950i
$301$	−0.195315	+	0.0592482i	−0.0112578	+	0.00341501i
$302$	−0.450953	−	2.09864i	−0.0259494	−	0.120763i
$303$	−12.4827	−	5.17051i	−0.717113	−	0.297038i
$304$	3.55008	−	1.31912i	0.203611	−	0.0756569i
$305$	18.1385	−	7.51320i	1.03861	−	0.430204i
$306$	1.41135	+	2.04378i	0.0806813	+	0.116835i
$307$	−20.0699	−	10.7276i	−1.14545	−	0.612257i	−0.214256	−	0.976777i	$-0.568733\pi$
$307$	−20.0699	−	10.7276i	−1.14545	−	0.612257i	−0.931195	+	0.364521i	$0.881233\pi$
$308$	−0.0629473	−	0.186727i	−0.00358675	−	0.0106397i
$309$	−5.33690	−	4.37988i	−0.303606	−	0.249163i
$310$	13.3840	+	10.6453i	0.760160	+	0.604611i
$311$	1.99309	−	10.0199i	0.113018	−	0.568179i	−0.882231	−	0.470817i	$-0.843959\pi$
$311$	1.99309	−	10.0199i	0.113018	−	0.568179i	0.995249	−	0.0973625i	$-0.0310406\pi$
$312$	10.9147	+	1.65427i	0.617923	+	0.0936546i
$313$	−18.7326	+	3.72615i	−1.05883	+	0.210615i	−0.693643	−	0.720319i	$-0.743995\pi$
$313$	−18.7326	+	3.72615i	−1.05883	+	0.210615i	−0.365188	+	0.930934i	$0.618995\pi$
$314$	5.92346	+	18.5024i	0.334280	+	1.04415i
$315$	−0.0330039	−	0.0617460i	−0.00185956	−	0.00347899i
$316$	1.62238	+	0.614520i	0.0912658	+	0.0345695i
$317$	−30.8998	−	3.04337i	−1.73551	−	0.170932i	−0.819765	−	0.572700i	$-0.805896\pi$
$317$	−30.8998	−	3.04337i	−1.73551	−	0.170932i	−0.915741	+	0.401768i	$0.868396\pi$
$318$	6.65560	+	15.3970i	0.373227	+	0.863420i
$319$		−	24.0901i		−	1.34879i
$320$	−4.14694	+	20.1813i	−0.231821	+	1.12817i
$321$		−	1.38082i		−	0.0770701i
$322$	0.126851	−	0.0548336i	0.00706916	−	0.00305576i
$323$	−1.65484	−	0.162988i	−0.0920778	−	0.00906888i
$324$	−0.821579	−	1.82346i	−0.0456433	−	0.101303i
$325$	3.00367	+	5.61948i	0.166614	+	0.311713i
$326$	0.749597	−	0.239980i	0.0415163	−	0.0132912i
$327$	−7.34093	+	1.46020i	−0.405954	+	0.0807494i
$328$	−10.5032	−	6.34051i	−0.579941	−	0.350096i
$329$	−0.0669724	+	0.336693i	−0.00369231	+	0.0185625i
$330$	8.21665	−	10.3306i	0.452312	−	0.568679i
$331$	22.8748	+	18.7729i	1.25731	+	1.03185i	0.997813	+	0.0661069i	$0.0210578\pi$
$331$	22.8748	+	18.7729i	1.25731	+	1.03185i	0.259500	+	0.965743i	$0.416442\pi$
$332$	14.4634	+	7.17043i	0.793782	+	0.393529i
$333$	−0.687814	−	0.367644i	−0.0376920	−	0.0201468i
$334$	24.9857	−	17.2540i	1.36716	−	0.944098i
$335$	−29.0935	+	12.0509i	−1.58955	+	0.658413i
$336$	0.0172619	+	0.107363i	0.000941714	+	0.00585715i
$337$	−25.8615	−	10.7122i	−1.40877	−	0.583531i	−0.456756	−	0.889592i	$-0.650989\pi$
$337$	−25.8615	−	10.7122i	−1.40877	−	0.583531i	−0.952012	+	0.306061i	$0.900989\pi$
$338$	−3.08801	+	0.663546i	−0.167966	+	0.0360922i
$339$	14.9359	−	4.53074i	0.811205	−	0.246076i
$340$	5.52200	−	7.16515i	0.299473	−	0.388585i
$341$	1.66796	+	16.9351i	0.0903251	+	0.917087i
$342$	1.28713	+	0.369026i	0.0696002	+	0.0199546i
$343$	−0.211438	−	0.316439i	−0.0114166	−	0.0170861i
$344$	10.8596	+	18.2485i	0.585508	+	0.983891i
$345$	7.69711	+	5.14305i	0.414399	+	0.276892i
$346$	0.661488	−	7.96449i	0.0355618	−	0.428174i
$347$	−0.984617	−	0.298680i	−0.0528570	−	0.0160340i	0.263745	−	0.964592i	$-0.415042\pi$
$347$	−0.984617	−	0.298680i	−0.0528570	−	0.0160340i	−0.316602	+	0.948558i	$0.602542\pi$
$348$	−2.19314	+	13.1119i	−0.117565	+	0.702873i
$349$	−16.8220	−	20.4977i	−0.900461	−	1.09722i	−0.994817	−	0.101677i	$-0.967579\pi$
$349$	−16.8220	−	20.4977i	−0.900461	−	1.09722i	0.0943561	−	0.995539i	$-0.469921\pi$
$350$	−0.0436973	+	0.0450562i	−0.00233572	+	0.00240836i
$351$	2.75984	+	2.75984i	0.147309	+	0.147309i
$352$	−17.2887	+	11.0188i	−0.921490	+	0.587304i
$353$	19.3354	−	19.3354i	1.02912	−	1.02912i	0.0295586	−	0.999563i	$-0.490590\pi$
$353$	19.3354	−	19.3354i	1.02912	−	1.02912i	0.999563	−	0.0295586i	$-0.00941017\pi$
$354$	−0.179415	−	11.7177i	−0.00953578	−	0.622787i
$355$	9.68659	−	7.94958i	0.514111	−	0.421920i
$356$	−7.76979	−	33.6428i	−0.411798	−	1.78307i
$357$	0.0138597	−	0.0456892i	0.000733532	−	0.00241813i
$358$	16.5132	−	13.9806i	0.872751	−	0.738896i
$359$	1.85640	−	2.77829i	0.0979769	−	0.146633i	−0.779242	−	0.626723i	$-0.784396\pi$
$359$	1.85640	−	2.77829i	0.0979769	−	0.146633i	0.877219	+	0.480090i	$0.159396\pi$
$360$	−5.41270	+	4.87475i	−0.285274	+	0.256922i
$361$	15.0526	−	10.0578i	0.792240	−	0.529358i
$362$	21.9571	−	12.1721i	1.15404	−	0.639754i
$363$	2.12448	−	0.209243i	0.111506	−	0.0109824i
$364$	−0.105718	−	0.184002i	−0.00554114	−	0.00964435i
$365$	−3.86156	−	12.7299i	−0.202123	−	0.666311i
$366$	−9.05473	−	5.85167i	−0.473299	−	0.305872i
$367$	2.23600	−	5.39818i	0.116718	−	0.281783i	−0.854714	−	0.519099i	$-0.826268\pi$
$367$	2.23600	−	5.39818i	0.116718	−	0.281783i	0.971433	+	0.237316i	$0.0762677\pi$
$368$	−8.70474	−	11.4436i	−0.453766	−	0.596541i
$369$	−1.65993	−	4.00743i	−0.0864125	−	0.208618i
$370$	−0.511440	+	2.79409i	−0.0265885	+	0.145258i
$371$	0.152000	−	0.284372i	0.00789145	−	0.0147639i
$372$	0.633906	−	9.36938i	0.0328665	−	0.485780i
$373$	15.8929	−	19.3656i	0.822903	−	1.00271i	−0.176926	−	0.984224i	$-0.556615\pi$
$373$	15.8929	−	19.3656i	0.822903	−	1.00271i	0.999829	−	0.0184861i	$-0.00588465\pi$
$374$	8.94364	−	1.01935i	0.462464	−	0.0527093i
$375$	8.50579	+	1.69191i	0.439237	+	0.0873697i
$376$	35.6787	−	1.63990i	1.83999	−	0.0845716i
$377$	−5.06130	−	25.4449i	−0.260670	−	1.31048i
$378$	−0.0176022	+	0.0341800i	−0.000905359	+	0.00175803i
$379$	−25.9199	+	13.8545i	−1.33142	+	0.711657i	−0.974902	−	0.222634i	$-0.928535\pi$
$379$	−25.9199	+	13.8545i	−1.33142	+	0.711657i	−0.356514	+	0.934290i	$0.616035\pi$
$380$	−0.149306	−	4.87449i	−0.00765924	−	0.250056i
$381$	−0.523063	+	5.31074i	−0.0267973	+	0.272078i
$382$	21.2582	+	8.42652i	1.08767	+	0.431138i
$383$	11.2478			0.574738			0.287369	−	0.957820i	$-0.407219\pi$
$383$	11.2478			0.574738			0.287369	+	0.957820i	$0.407219\pi$
$384$	10.4131	−	4.42343i	0.531393	−	0.225732i
$385$	−0.253740			−0.0129318
$386$	30.8767	+	12.2391i	1.57158	+	0.622956i
$387$	−0.735893	+	7.47165i	−0.0374075	+	0.379805i
$388$	9.95699	−	0.304984i	0.505490	−	0.0154832i
$389$	27.6129	−	14.7594i	1.40003	−	0.748332i	0.413284	−	0.910602i	$-0.364382\pi$
$389$	27.6129	−	14.7594i	1.40003	−	0.748332i	0.986746	+	0.162270i	$0.0518816\pi$
$390$	6.50829	−	12.6378i	0.329560	−	0.639941i
$391$	1.23159	+	6.19164i	0.0622844	+	0.313125i
$392$	−13.3410	+	14.6265i	−0.673823	+	0.738750i
$393$	−4.32656	−	0.860606i	−0.218246	−	0.0434119i
$394$	5.12133	−	0.583703i	0.258009	−	0.0294065i
$395$	1.41721	−	1.72687i	0.0713075	−	0.0868884i
$396$	−7.23185	−	0.489286i	−0.363414	−	0.0245876i
$397$	−1.98308	+	3.71008i	−0.0995279	+	0.186204i	−0.926757	−	0.375661i	$-0.877416\pi$
$397$	−1.98308	+	3.71008i	−0.0995279	+	0.186204i	0.827229	+	0.561864i	$0.189916\pi$
$398$	−5.19039	+	28.3560i	−0.260171	+	1.42136i
$399$	−0.00985008	−	0.0237802i	−0.000493121	−	0.00119050i
$400$	5.64155	+	3.28888i	0.282077	+	0.164444i
$401$	1.41982	−	3.42774i	0.0709023	−	0.171173i	−0.884456	−	0.466624i	$-0.845470\pi$
$401$	1.41982	−	3.42774i	0.0709023	−	0.171173i	0.955358	+	0.295451i	$0.0954700\pi$
$402$	14.5235	+	9.38590i	0.724367	+	0.468126i
$403$	5.31980	+	17.5370i	0.264998	+	0.873582i
$404$	23.4304	−	13.4619i	1.16571	−	0.669755i
$405$	−2.56297	+	0.252431i	−0.127355	+	0.0125434i
$406$	0.223507	−	0.123903i	0.0110925	−	0.00614922i
$407$	−2.35017	+	1.57033i	−0.116493	+	0.0778384i
$408$	−4.96070	−	0.259403i	−0.245591	−	0.0128423i
$409$	−16.2160	+	24.2689i	−0.801828	+	1.20002i	0.174698	+	0.984622i	$0.444105\pi$
$409$	−16.2160	+	24.2689i	−0.801828	+	1.20002i	−0.976526	+	0.215398i	$0.930895\pi$
$410$	−12.0573	+	10.2080i	−0.595465	+	0.504138i
$411$	1.21515	−	4.00581i	0.0599390	−	0.197592i
$412$	13.4539	−	3.10718i	0.662828	−	0.153080i
$413$	−0.174141	+	0.142914i	−0.00856891	+	0.00703232i
$414$	−0.0778255	−	5.08282i	−0.00382491	−	0.249807i
$415$	14.6990	−	14.6990i	0.721544	−	0.721544i
$416$	−15.9459	+	15.2708i	−0.781812	+	0.748712i
$417$	−5.63868	−	5.63868i	−0.276127	−	0.276127i
$418$	3.37848	−	3.48354i	0.165247	−	0.170386i
$419$	−17.6466	−	21.5024i	−0.862090	−	1.05046i	−0.998212	−	0.0597681i	$-0.980964\pi$
$419$	−17.6466	−	21.5024i	−0.862090	−	1.05046i	0.136122	−	0.990692i	$-0.456536\pi$
$420$	0.138107	+	0.0231003i	0.00673895	+	0.00112718i
$421$	−0.0159121	−	0.00482687i	−0.000775506	−	0.000235247i	0.289897	−	0.957058i	$-0.406379\pi$
$421$	−0.0159121	−	0.00482687i	−0.000775506	−	0.000235247i	−0.290672	+	0.956823i	$0.593879\pi$
$422$	3.02873	−	36.4667i	0.147436	−	1.77517i
$423$	10.4995	+	7.01554i	0.510503	+	0.341107i
$424$	−32.5165	−	8.25413i	−1.57914	−	0.400856i
$425$	−1.59293	−	2.38399i	−0.0772686	−	0.115641i
$426$	−6.61464	−	1.89644i	−0.320481	−	0.0918829i
$427$	0.0203135	+	0.206246i	0.000983040	+	0.00998097i
$428$	2.18742	+	1.68579i	0.105733	+	0.0814858i
$429$	13.5361	−	4.10614i	0.653530	−	0.198246i
$430$	26.7341	−	5.74459i	1.28924	−	0.277029i
$431$	31.4805	+	13.0397i	1.51636	+	0.628098i	0.976859	−	0.213885i	$-0.0686119\pi$
$431$	31.4805	+	13.0397i	1.51636	+	0.628098i	0.539504	+	0.841983i	$0.318612\pi$
$432$	3.89165	+	0.924692i	0.187237	+	0.0444893i
$433$	−14.2319	+	5.89503i	−0.683939	+	0.283297i	−0.697472	−	0.716612i	$-0.745692\pi$
$433$	−14.2319	+	5.89503i	−0.683939	+	0.283297i	0.0135334	+	0.999908i	$0.495692\pi$
$434$	−0.148544	+	0.102578i	−0.00713035	+	0.00492390i
$435$	15.0973	+	8.06966i	0.723858	+	0.386910i
$436$	6.64908	−	13.4118i	0.318433	−	0.642307i
$437$	2.63080	+	2.15904i	0.125848	+	0.103281i
$438$	−4.54718	+	5.71704i	−0.217272	+	0.273171i
$439$	−4.80199	+	24.1412i	−0.229186	+	1.15220i	0.679164	+	0.733987i	$0.262343\pi$
$439$	−4.80199	+	24.1412i	−0.229186	+	1.15220i	−0.908350	+	0.418210i	$0.862657\pi$
$440$	6.33370	+	25.6285i	0.301947	+	1.22179i
$441$	−6.86477	+	1.36549i	−0.326894	+	0.0650232i
$442$	9.23243	−	2.95572i	0.439142	−	0.140589i
$443$	−19.1829	−	35.8887i	−0.911407	−	1.70512i	−0.681367	−	0.731942i	$-0.738614\pi$
$443$	−19.1829	−	35.8887i	−0.911407	−	1.70512i	−0.230040	−	0.973181i	$-0.573886\pi$
$444$	1.42212	−	0.640752i	0.0674910	−	0.0304088i
$445$	−44.2477	−	4.35801i	−2.09754	−	0.206590i
$446$	−21.0842	+	9.11399i	−0.998366	+	0.431560i
$447$		−	3.37645i		−	0.159700i
$448$	−0.191153	−	0.103730i	−0.00903114	−	0.00490080i
$449$		−	19.3252i		−	0.912015i	−0.889976	−	0.456007i	$-0.849279\pi$
$449$		−	19.3252i		−	0.912015i	0.889976	−	0.456007i	$-0.150721\pi$
$450$	0.916085	+	2.11926i	0.0431847	+	0.0999029i
$451$	−15.6446	−	1.54086i	−0.736676	−	0.0725563i
$452$	−11.0572	+	29.1919i	−0.520089	+	1.37307i
$453$	0.715503	+	1.33861i	0.0336173	+	0.0628935i
$454$	−6.25261	−	19.5306i	−0.293450	−	0.916614i
$455$	−0.268010	+	0.0533105i	−0.0125645	+	0.00249923i
$456$	−2.15600	+	1.58847i	−0.100964	+	0.0743870i
$457$	−6.66876	+	33.5261i	−0.311952	+	1.56829i	0.433142	+	0.901326i	$0.357405\pi$
$457$	−6.66876	+	33.5261i	−0.311952	+	1.56829i	−0.745093	+	0.666960i	$0.767595\pi$
$458$	−10.2636	−	8.16339i	−0.479586	−	0.381450i
$459$	−1.35761	−	1.11416i	−0.0633680	−	0.0520047i
$460$	−17.5444	+	5.91438i	−0.818012	+	0.275759i
$461$	22.9973	+	12.2923i	1.07109	+	0.572509i	0.910075	−	0.414443i	$-0.136024\pi$
$461$	22.9973	+	12.2923i	1.07109	+	0.572509i	0.161014	+	0.986952i	$0.448524\pi$
$462$	0.0791757	+	0.114655i	0.00368359	+	0.00533424i
$463$	−3.12568	+	1.29470i	−0.145263	+	0.0601698i	−0.454130	−	0.890935i	$-0.650050\pi$
$463$	−3.12568	+	1.29470i	−0.145263	+	0.0601698i	0.308868	+	0.951105i	$0.400050\pi$
$464$	−18.0936	−	19.4821i	−0.839975	−	0.904432i
$465$	−11.1719	−	4.62757i	−0.518086	−	0.214598i
$466$	2.56499	+	11.9370i	0.118821	+	0.552969i
$467$	−25.3762	+	7.69778i	−1.17427	+	0.356211i	−0.816359	−	0.577545i	$-0.804011\pi$
$467$	−25.3762	+	7.69778i	−1.17427	+	0.356211i	−0.357911	+	0.933756i	$0.616511\pi$
$468$	−7.74134	+	1.00260i	−0.357844	+	0.0463451i
$469$	−0.0325822	−	0.330813i	−0.00150451	−	0.0152755i
$470$	12.6753	−	44.2103i	0.584666	−	2.03927i
$471$	−7.63204	−	11.4221i	−0.351666	−	0.526305i
$472$	18.7815	+	14.0214i	0.864487	+	0.645387i
$473$	22.6240	+	15.1169i	1.04025	+	0.695076i
$474$	−1.22252	−	0.101536i	−0.0561523	−	0.00466371i
$475$	−1.47916	−	0.448698i	−0.0678685	−	0.0205877i
$476$	0.0554575	+	0.0777358i	0.00254189	+	0.00356301i
$477$	−7.52450	−	9.16863i	−0.344523	−	0.419803i
$478$	−17.9729	−	17.4308i	−0.822060	−	0.797266i
$479$	23.9632	+	23.9632i	1.09491	+	1.09491i	0.994996	+	0.0999116i	$0.0318560\pi$
$479$	23.9632	+	23.9632i	1.09491	+	1.09491i	0.0999116	+	0.994996i	$0.468144\pi$
$480$	−1.11415	−	14.5259i	−0.0508538	−	0.663012i
$481$	−2.15241	+	2.15241i	−0.0981413	+	0.0981413i
$482$	−6.62931	+	0.101504i	−0.301957	+	0.00462340i
$483$	−0.0755378	+	0.0619923i	−0.00343709	+	0.00282075i
$484$	−2.26222	+	3.62093i	−0.102828	+	0.164588i
$485$	3.72363	−	12.2752i	0.169081	−	0.557386i
$486$	0.913799	+	1.07934i	0.0414508	+	0.0489598i
$487$	−8.93589	+	13.3735i	−0.404924	+	0.606011i	−0.976755	−	0.214360i	$-0.931233\pi$
$487$	−8.93589	+	13.3735i	−0.404924	+	0.606011i	0.571831	+	0.820372i	$0.306233\pi$
$488$	20.3244	−	7.19991i	0.920044	−	0.325925i
$489$	−0.462751	+	0.309200i	−0.0209263	+	0.0139825i
$490$	12.3597	+	22.2955i	0.558356	+	1.00721i
$491$	−3.18962	+	0.314150i	−0.143945	+	0.0141774i	−0.169733	−	0.985490i	$-0.554291\pi$
$491$	−3.18962	+	0.314150i	−0.143945	+	0.0141774i	0.0257877	+	0.999667i	$0.491791\pi$
$492$	8.37487	+	2.26294i	0.377568	+	0.102021i
$493$	3.38878	+	11.1713i	0.152623	+	0.503130i
$494$	2.83658	−	4.38926i	0.127624	−	0.197482i
$495$	−3.57183	+	8.62317i	−0.160542	+	0.387583i
$496$	14.0685	+	12.4429i	0.631695	+	0.558703i
$497$	0.0506201	+	0.122208i	0.00227062	+	0.00548177i
$498$	−11.2285	−	2.05529i	−0.503159	−	0.0920999i
$499$	−13.4974	+	25.2518i	−0.604226	+	1.13043i	0.374879	+	0.927074i	$0.377684\pi$
$499$	−13.4974	+	25.2518i	−0.604226	+	1.13043i	−0.979105	+	0.203354i	$0.934816\pi$
$500$	−13.0646	+	11.4088i	−0.584266	+	0.510217i
$501$	−13.6209	+	16.5971i	−0.608538	+	0.741505i
$502$	1.93763	+	17.0005i	0.0864808	+	0.758771i
$503$	10.3507	+	2.05889i	0.461517	+	0.0918014i	0.420372	−	0.907352i	$-0.361900\pi$
$503$	10.3507	+	2.05889i	0.461517	+	0.0918014i	0.0411447	+	0.999153i	$0.486900\pi$
$504$	−0.0326561	−	0.0696133i	−0.00145462	−	0.00310082i
$505$	−6.78843	−	34.1278i	−0.302081	−	1.51867i
$506$	−16.3789	−	8.43491i	−0.728133	−	0.374977i
$507$	1.96968	−	1.05281i	0.0874765	−	0.0467571i
$508$	−7.77438	−	7.31228i	−0.344932	−	0.324430i
$509$	3.37932	−	34.3108i	0.149786	−	1.52080i	−0.567123	−	0.823633i	$-0.691943\pi$
$509$	3.37932	−	34.3108i	0.149786	−	1.52080i	0.716909	−	0.697167i	$-0.245557\pi$
$510$	−2.35709	+	5.94643i	−0.104374	+	0.263312i
$511$	0.140422			0.00621192
$512$	−5.70562	+	21.8963i	−0.252155	+	0.967687i
$513$	−0.946808			−0.0418026
$514$	1.91157	−	4.82248i	0.0843159	−	0.212711i
$515$	1.74279	−	17.6949i	0.0767967	−	0.779730i
$516$	−10.9377	−	10.2876i	−0.481506	−	0.452886i
$517$	40.3611	−	21.5734i	1.77508	−	0.948799i
$518$	−0.0266571	−	0.0137280i	−0.00117125	−	0.000603174i
$519$	1.10248	+	5.54255i	0.0483936	+	0.243291i
$520$	12.0744	+	25.7391i	0.529497	+	1.12873i
$521$	−11.8588	−	2.35887i	−0.519544	−	0.103344i	−0.0716492	−	0.997430i	$-0.522826\pi$
$521$	−11.8588	−	2.35887i	−0.519544	−	0.103344i	−0.447895	+	0.894086i	$0.647826\pi$
$522$	−1.06451	−	9.33986i	−0.0465923	−	0.408795i
$523$	4.92501	−	6.00115i	0.215356	−	0.262412i	−0.654116	−	0.756394i	$-0.726959\pi$
$523$	4.92501	−	6.00115i	0.215356	−	0.262412i	0.869472	+	0.493982i	$0.164459\pi$
$524$	6.64544	−	5.80320i	0.290308	−	0.253514i
$525$	0.0209215	−	0.0391414i	0.000913089	−	0.00170827i
$526$	14.6746	+	2.68610i	0.639845	+	0.117119i
$527$	−3.15575	−	7.61866i	−0.137467	−	0.331874i
$528$	9.60417	−	10.8589i	0.417968	−	0.472574i
$529$	−3.85723	+	9.31217i	−0.167706	+	0.404877i
$530$	−23.4474	+	36.2820i	−1.01849	+	1.57599i
$531$	2.40548	+	7.92979i	0.104389	+	0.344124i
$532$	0.0496968	+	0.0134284i	0.00215463	+	0.000582193i
$533$	−16.8482	+	1.65940i	−0.729775	+	0.0718765i
$534$	11.8376	+	21.3536i	0.512262	+	0.924061i
$535$	2.95682	−	1.97569i	0.127835	−	0.0854163i
$536$	−32.5998	+	11.5484i	−1.40809	+	0.498816i
$537$	−8.49988	+	12.7210i	−0.366797	+	0.548951i
$538$	9.61907	+	11.3616i	0.414707	+	0.489834i
$539$	−7.36355	+	24.2744i	−0.317171	+	1.04557i
$540$	2.72914	−	4.36829i	0.117444	−	0.187981i
$541$	27.9311	−	22.9224i	1.20085	−	0.985513i	0.200868	−	0.979618i	$-0.435624\pi$
$541$	27.9311	−	22.9224i	1.20085	−	0.985513i	0.999983	−	0.00589470i	$-0.00187635\pi$
$542$	−39.6960	+	0.607803i	−1.70509	+	0.0261074i
$543$	−12.5527	+	12.5527i	−0.538686	+	0.538686i
$544$	6.46724	−	7.54175i	0.277281	−	0.323350i
$545$	−13.6302	−	13.6302i	−0.583854	−	0.583854i
$546$	0.107717	+	0.104468i	0.00460987	+	0.00447083i
$547$	−3.60020	−	4.38686i	−0.153933	−	0.187568i	0.690334	−	0.723491i	$-0.257464\pi$
$547$	−3.60020	−	4.38686i	−0.153933	−	0.187568i	−0.844267	+	0.535923i	$0.819964\pi$
$548$	4.86225	+	6.81551i	0.207705	+	0.291144i
$549$	7.29507	+	2.21294i	0.311346	+	0.0944458i
$550$	8.33876	+	0.692573i	0.355566	+	0.0295314i
$551$	5.23283	+	3.49646i	0.222926	+	0.148954i
$552$	8.14692	+	6.08213i	0.346756	+	0.258872i
$553$	0.0131012	+	0.0196074i	0.000557120	+	0.000833790i
$554$	−5.11171	+	17.8293i	−0.217176	+	0.757492i
$555$	−0.196872	−	1.99887i	−0.00835674	−	0.0848475i
$556$	15.8165	−	2.04843i	0.670769	−	0.0868727i
$557$	−1.64576	+	0.499236i	−0.0697332	+	0.0211533i	−0.324959	−	0.945728i	$-0.605350\pi$
$557$	−1.64576	+	0.499236i	−0.0697332	+	0.0211533i	0.255225	+	0.966882i	$0.417850\pi$
$558$	1.39501	+	6.49211i	0.0590557	+	0.274833i
$559$	27.0724	+	11.2137i	1.14504	+	0.474291i
$560$	−0.205204	+	0.190579i	−0.00867144	+	0.00805345i
$561$	−5.88054	+	2.43580i	−0.248277	+	0.102840i
$562$	−20.2687	−	29.3513i	−0.854983	−	1.23811i
$563$	−13.1757	−	7.04253i	−0.555288	−	0.296807i	0.169784	−	0.985481i	$-0.445693\pi$
$563$	−13.1757	−	7.04253i	−0.555288	−	0.296807i	−0.725071	+	0.688674i	$0.758193\pi$
$564$	−23.9320	+	8.06769i	−1.00772	+	0.339711i
$565$	31.0721	+	25.5003i	1.30721	+	1.07280i
$566$	23.3231	+	18.5505i	0.980342	+	0.779738i
$567$	0.00530364	−	0.0266632i	0.000222732	−	0.00111975i
$568$	11.0798	−	8.16324i	0.464897	−	0.342522i
$569$	23.7507	−	4.72431i	0.995681	−	0.198053i	0.329751	−	0.944068i	$-0.393035\pi$
$569$	23.7507	−	4.72431i	0.995681	−	0.198053i	0.665930	+	0.746015i	$0.268035\pi$
$570$	1.05142	+	3.28420i	0.0440392	+	0.137560i
$571$	−4.46787	−	8.35880i	−0.186975	−	0.349805i	0.770917	−	0.636936i	$-0.219798\pi$
$571$	−4.46787	−	8.35880i	−0.186975	−	0.349805i	−0.957891	+	0.287131i	$0.907298\pi$
$572$	−10.0210	+	26.4561i	−0.418999	+	1.10619i
$573$	−16.0919	−	1.58491i	−0.672247	−	0.0662105i
$574$	−0.0661693	−	0.153075i	−0.00276185	−	0.00638924i
$575$			5.86826i			0.244723i
$576$	−6.21600	+	5.03600i	−0.259000	+	0.209834i
$577$			30.9760i			1.28955i	0.764373	+	0.644775i	$0.223049\pi$
$577$			30.9760i			1.28955i	−0.764373	+	0.644775i	$0.776951\pi$
$578$	18.0641	−	7.80850i	0.751367	−	0.324791i
$579$	−23.3727	−	2.30201i	−0.971337	−	0.0956683i
$580$	−31.2151	+	14.0643i	−1.29614	+	0.583988i
$581$	0.103439	+	0.193522i	0.00429139	+	0.00802863i
$582$	−6.70855	+	2.14771i	−0.278078	+	0.0890255i
$583$	−42.1603	+	8.38621i	−1.74610	+	0.347321i
$584$	−3.50513	−	14.1831i	−0.145043	−	0.586899i
$585$	−1.96099	+	9.85854i	−0.0810768	+	0.407601i
$586$	−19.1177	+	24.0362i	−0.789746	+	0.992925i
$587$	−30.6759	−	25.1750i	−1.26613	−	1.03908i	−0.997112	−	0.0759488i	$-0.975801\pi$
$587$	−30.6759	−	25.1750i	−1.26613	−	1.03908i	−0.269016	−	0.963136i	$-0.586699\pi$
$588$	6.21779	−	12.5418i	0.256418	−	0.517217i
$589$	−3.92071	−	2.09566i	−0.161550	−	0.0863503i
$590$	24.8349	−	17.1498i	1.02244	−	0.706048i
$591$	−3.36733	+	1.39480i	−0.138514	+	0.0573742i
$592$	−0.721171	+	3.03511i	−0.0296400	+	0.124742i
$593$	1.74792	+	0.724012i	0.0717785	+	0.0297316i	0.418284	−	0.908316i	$-0.362632\pi$
$593$	1.74792	+	0.724012i	0.0717785	+	0.0297316i	−0.346505	+	0.938048i	$0.612632\pi$
$594$	5.01100	−	1.07675i	0.205604	−	0.0441798i
$595$	0.117667	−	0.0356939i	0.00482387	−	0.00146331i
$596$	5.34877	+	4.12217i	0.219094	+	0.168851i
$597$	−1.99797	−	20.2857i	−0.0817715	−	0.830240i
$598$	−19.0722	−	5.46807i	−0.779920	−	0.223606i
$599$	12.4943	+	18.6990i	0.510502	+	0.764020i	0.993770	−	0.111453i	$-0.0355504\pi$
$599$	12.4943	+	18.6990i	0.510502	+	0.764020i	−0.483268	+	0.875472i	$0.660550\pi$
$600$	−4.47562	−	1.13611i	−0.182716	−	0.0463815i
$601$	−0.898493	−	0.600354i	−0.0366503	−	0.0244889i	0.537110	−	0.843512i	$-0.319516\pi$
$601$	−0.898493	−	0.600354i	−0.0366503	−	0.0244889i	−0.573760	+	0.819023i	$0.694516\pi$
$602$	−0.0238912	+	0.287656i	−0.000973731	+	0.0117240i
$603$	−11.7011	−	3.54948i	−0.476504	−	0.144546i
$604$	−2.99408	−	0.500799i	−0.121827	−	0.0203772i
$605$	3.48777	+	4.24986i	0.141798	+	0.172781i
$606$	−13.3027	+	13.7164i	−0.540387	+	0.557193i
$607$	22.7561	+	22.7561i	0.923642	+	0.923642i	0.997285	−	0.0736429i	$-0.0234625\pi$
$607$	22.7561	+	22.7561i	0.923642	+	0.923642i	−0.0736429	+	0.997285i	$0.523463\pi$
$608$	0.115805	−	5.35470i	0.00469652	−	0.217162i
$609$	−0.127777	+	0.127777i	−0.00517777	+	0.00517777i
$610$	−0.425075	−	27.7619i	−0.0172108	−	1.12405i
$611$	38.0983	−	31.2665i	1.54129	−	1.26491i
$612$	3.42245	−	0.790413i	0.138344	−	0.0319506i
$613$	8.91751	−	29.3971i	0.360175	−	1.18734i	−0.570441	−	0.821339i	$-0.693228\pi$
$613$	8.91751	−	29.3971i	0.360175	−	1.18734i	0.930616	−	0.365998i	$-0.119272\pi$
$614$	−24.5626	+	20.7954i	−0.991265	+	0.839233i
$615$	6.20626	−	9.28832i	0.250260	−	0.374541i
$616$	−0.278292	−	0.0145523i	−0.0112127	−	0.000586330i
$617$	−36.4508	+	24.3557i	−1.46746	+	0.980523i	−0.472381	+	0.881394i	$0.656605\pi$
$617$	−36.4508	+	24.3557i	−1.46746	+	0.980523i	−0.995075	+	0.0991283i	$0.968395\pi$
$618$	−8.53942	+	4.73391i	−0.343506	+	0.190426i
$619$	−0.351250	+	0.0345951i	−0.0141179	+	0.00139049i	−0.105074	−	0.994464i	$-0.533508\pi$
$619$	−0.351250	+	0.0345951i	−0.0141179	+	0.00139049i	0.0909557	+	0.995855i	$0.471008\pi$
$620$	20.9701	−	12.0483i	0.842179	−	0.483872i
$621$	1.04343	+	3.43974i	0.0418716	+	0.138032i
$622$	−12.1345	−	7.84200i	−0.486550	−	0.314436i
$623$	0.179607	−	0.433610i	0.00719582	−	0.0173722i
$624$	7.86283	−	13.4874i	0.314765	−	0.539928i
$625$	11.6709	+	28.1761i	0.466836	+	1.12704i
$626$	−4.86337	+	26.5695i	−0.194380	+	1.06193i
$627$	−1.61756	+	3.02624i	−0.0645990	+	0.120856i
$628$	27.4119	+	1.85461i	1.09386	+	0.0740072i
$629$	0.868941	−	1.05881i	0.0346470	−	0.0422174i
$630$	−0.0983764	+	0.0112124i	−0.00391941	+	0.000446714i
$631$	31.3926	+	6.24438i	1.24972	+	0.248585i	0.775232	−	0.631676i	$-0.217633\pi$
$631$	31.3926	+	6.24438i	1.24972	+	0.248585i	0.474489	+	0.880261i	$0.342633\pi$
$632$	1.65338	−	1.81269i	0.0657677	−	0.0721048i
$633$	5.04789	+	25.3774i	0.200636	+	1.00866i
$634$	−20.1039	+	39.0378i	−0.798428	+	1.55039i
$635$	−12.1205	+	6.47856i	−0.480989	+	0.257094i
$636$	23.7108	−	0.726263i	0.940193	−	0.0287982i
$637$	−2.67764	+	27.1866i	−0.106092	+	1.07717i
$638$	−31.6712	−	12.5541i	−1.25387	−	0.497021i
$639$	4.86570			0.192484
$640$	24.3712	+	15.9691i	0.963357	+	0.631232i
$641$	39.1701			1.54712			0.773562	−	0.633720i	$-0.218473\pi$
$641$	39.1701			1.54712			0.773562	+	0.633720i	$0.218473\pi$
$642$	−1.81536	−	0.719589i	−0.0716467	−	0.0283999i
$643$	3.76185	−	38.1947i	0.148353	−	1.50625i	−0.576357	−	0.817198i	$-0.695526\pi$
$643$	3.76185	−	38.1947i	0.148353	−	1.50625i	0.724710	−	0.689054i	$-0.241974\pi$
$644$	−0.00598348	−	0.195346i	−0.000235782	−	0.00769773i
$645$	−17.0523	+	9.11464i	−0.671434	+	0.358889i
$646$	−1.07667	+	2.09067i	−0.0423609	+	0.0822565i
$647$	−4.83939	−	24.3293i	−0.190256	−	0.956482i	−0.951414	−	0.307915i	$-0.900369\pi$
$647$	−4.83939	−	24.3293i	−0.190256	−	0.956482i	0.761158	−	0.648567i	$-0.224631\pi$
$648$	−2.82544	+	0.129866i	−0.110994	+	0.00510163i
$649$	29.4552	+	5.85900i	1.15622	+	0.229986i
$650$	8.95321	−	1.02044i	0.351174	−	0.0400249i
$651$	0.0809785	−	0.0986726i	0.00317380	−	0.00386728i
$652$	0.0751368	−	1.11055i	0.00294258	−	0.0434926i
$653$	−20.0796	+	37.5662i	−0.785774	+	1.47008i	0.0944540	+	0.995529i	$0.469889\pi$
$653$	−20.0796	+	37.5662i	−0.785774	+	1.47008i	−0.880228	+	0.474551i	$0.842611\pi$
$654$	−1.90586	+	10.4120i	−0.0745249	+	0.407143i
$655$	−4.34759	−	10.4960i	−0.169875	−	0.410113i
$656$	−13.8094	+	10.5042i	−0.539165	+	0.410122i
$657$	1.97669	−	4.77214i	0.0771179	−	0.186179i
$658$	0.407747	+	0.263509i	0.0158957	+	0.0102727i
$659$	9.32446	+	30.7386i	0.363229	+	1.19741i	0.928133	+	0.372250i	$0.121414\pi$
$659$	9.32446	+	30.7386i	0.363229	+	1.19741i	−0.564903	+	0.825157i	$0.691086\pi$
$660$	−9.29961	−	16.1860i	−0.361987	−	0.630038i
$661$	22.7671	−	2.24237i	0.885538	−	0.0872179i	0.354987	−	0.934871i	$-0.384485\pi$
$661$	22.7671	−	2.24237i	0.885538	−	0.0872179i	0.530551	+	0.847653i	$0.321985\pi$
$662$	36.6013	−	20.2903i	1.42255	−	0.788605i
$663$	−5.69948	+	3.80827i	−0.221350	+	0.147901i
$664$	16.9642	−	15.2782i	0.658340	−	0.592910i
$665$	0.0368281	−	0.0551172i	0.00142813	−	0.00213735i
$666$	−0.841780	+	0.712675i	−0.0326183	+	0.0276156i
$667$	6.93575	−	22.8641i	0.268553	−	0.885301i
$668$	−9.66298	−	41.8402i	−0.373872	−	1.61885i
$669$	12.5553	−	10.3038i	0.485415	−	0.398370i
$670$	0.681808	+	44.5292i	0.0263405	+	1.72031i
$671$	19.5362	−	19.5362i	0.754188	−	0.754188i
$672$	0.150146	+	0.0332561i	0.00579200	+	0.00128288i
$673$	13.1151	+	13.1151i	0.505548	+	0.505548i	0.913157	−	0.407609i	$-0.133637\pi$
$673$	13.1151	+	13.1151i	0.505548	+	0.505548i	−0.407609	+	0.913157i	$0.633637\pi$
$674$	−27.5605	+	28.4176i	−1.06159	+	1.09461i
$675$	−1.03568	−	1.26198i	−0.0398634	−	0.0485737i
$676$	−0.736892	+	4.40559i	−0.0283420	+	0.169446i
$677$	−21.5365	−	6.53302i	−0.827714	−	0.251084i	−0.152124	−	0.988361i	$-0.548611\pi$
$677$	−21.5365	−	6.53302i	−0.827714	−	0.251084i	−0.675590	+	0.737277i	$0.736111\pi$
$678$	1.82697	−	21.9972i	0.0701644	−	0.844798i
$679$	0.112586	+	0.0752279i	0.00432067	+	0.00288698i
$680$	−6.54230	−	10.9937i	−0.250886	−	0.421590i
$681$	8.05613	+	12.0569i	0.308712	+	0.462020i
$682$	23.1337	+	6.63252i	0.885835	+	0.253972i
$683$	−3.40626	−	34.5843i	−0.130337	−	1.32333i	−0.808533	−	0.588451i	$-0.799738\pi$
$683$	−3.40626	−	34.5843i	−0.130337	−	1.32333i	0.678196	−	0.734881i	$-0.262762\pi$
$684$	1.15592	−	1.49988i	0.0441977	−	0.0573492i
$685$	10.3165	−	3.12947i	0.394172	−	0.119571i
$686$	−0.526207	+	0.113070i	−0.0200907	+	0.00431705i
$687$	8.56727	+	3.54868i	0.326862	+	0.135391i
$688$	29.6504	−	4.76720i	1.13041	−	0.181748i
$689$	−42.7694	+	17.7157i	−1.62938	+	0.674913i
$690$	10.7727	−	7.43916i	0.410111	−	0.283204i
$691$	−17.8722	−	9.55291i	−0.679892	−	0.363410i	0.0950233	−	0.995475i	$-0.469707\pi$
$691$	−17.8722	−	9.55291i	−0.679892	−	0.363410i	−0.774915	+	0.632065i	$0.782207\pi$
$692$	−10.1262	−	5.02019i	−0.384939	−	0.190839i
$693$	−0.0761614	−	0.0625040i	−0.00289313	−	0.00237433i
$694$	−0.905786	+	1.13882i	−0.0343832	+	0.0432290i
$695$	4.00653	−	20.1422i	0.151976	−	0.764037i
$696$	16.0953	+	9.71632i	0.610090	+	0.368296i
$697$	7.47162	−	1.48620i	0.283008	−	0.0562938i
$698$	−35.7146	+	11.4339i	−1.35182	+	0.432778i
$699$	−4.06974	−	7.61395i	−0.153932	−	0.287986i
$700$	0.0364633	+	0.0809287i	0.00137818	+	0.00305882i
$701$	33.3470	+	3.28439i	1.25950	+	0.124050i	0.705645	−	0.708565i	$-0.250657\pi$
$701$	33.3470	+	3.28439i	1.25950	+	0.124050i	0.553852	+	0.832615i	$0.313157\pi$
$702$	5.06658	−	2.19011i	0.191226	−	0.0826604i
$703$		−	0.738419i		−	0.0278500i
$704$	5.47672	+	28.4716i	0.206412	+	1.07306i
$705$			32.5209i			1.22481i
$706$	−15.3439	−	35.4965i	−0.577477	−	1.33593i
$707$	0.365540	+	0.0360026i	0.0137476	+	0.00135402i
$708$	−15.4987	−	5.87055i	−0.582475	−	0.220629i
$709$	1.89697	+	3.54898i	0.0712422	+	0.133285i	0.915021	−	0.403407i	$-0.132174\pi$
$709$	1.89697	+	3.54898i	0.0712422	+	0.133285i	−0.843779	+	0.536691i	$0.819674\pi$
$710$	−5.40330	−	16.8777i	−0.202782	−	0.633408i
$711$	0.850763	−	0.169227i	0.0319061	−	0.00634652i
$712$	−48.2791	−	7.31735i	−1.80934	−	0.274229i
$713$	−3.29268	+	16.5534i	−0.123312	+	0.619930i
$714$	−0.0528447	−	0.0420313i	−0.00197766	−	0.00157298i
$715$	28.1602	+	23.1105i	1.05313	+	0.864282i
$716$	−9.77466	−	28.9955i	−0.365296	−	1.08361i
$717$	15.6134	+	8.34556i	0.583095	+	0.311671i
$718$	−2.68519	−	3.88845i	−0.100210	−	0.145116i
$719$	−19.2016	+	7.95355i	−0.716098	+	0.296617i	−0.710825	−	0.703369i	$-0.751678\pi$
$719$	−19.2016	+	7.95355i	−0.716098	+	0.296617i	−0.00527264	+	0.999986i	$0.501678\pi$
$720$	3.58809	+	9.65642i	0.133720	+	0.359874i
$721$	0.173403	+	0.0718260i	0.00645787	+	0.00267494i
$722$	−5.37861	−	25.0309i	−0.200171	−	0.931555i
$723$	4.48631	−	1.36091i	0.166848	−	0.0506127i
$724$	−4.56015	−	35.2102i	−0.169477	−	1.30858i
$725$	1.06365	+	10.7994i	0.0395029	+	0.401080i
$726$	0.832038	−	2.90208i	0.0308798	−	0.107706i
$727$	−1.23069	−	1.84186i	−0.0456438	−	0.0683107i	0.807946	−	0.589257i	$-0.200579\pi$
$727$	−1.23069	−	1.84186i	−0.0456438	−	0.0683107i	−0.853590	+	0.520946i	$0.825579\pi$
$728$	−0.297000	+	0.0430981i	−0.0110076	+	0.00159732i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−18.7483	−	1.55713i	−0.693904	−	0.0576320i
$731$	−12.6179	−	3.82761i	−0.466691	−	0.141569i
$732$	−12.4119	+	8.85474i	−0.458755	+	0.327281i
$733$	26.3816	+	32.1461i	0.974427	+	1.18734i	0.982289	+	0.187374i	$0.0599977\pi$
$733$	26.3816	+	32.1461i	0.974427	+	1.18734i	−0.00786119	+	0.999969i	$0.502502\pi$
$734$	−5.93172	−	5.75281i	−0.218944	−	0.212340i
$735$	−12.7461	−	12.7461i	−0.470147	−	0.470147i
$736$	−19.5812	+	5.48046i	−0.721772	+	0.202012i
$737$	−31.3355	+	31.3355i	−1.15426	+	1.15426i
$738$	−6.13359	+	0.0939142i	−0.225780	+	0.00345703i
$739$	−17.0401	+	13.9844i	−0.626829	+	0.514426i	−0.893325	−	0.449410i	$-0.851634\pi$
$739$	−17.0401	+	13.9844i	−0.626829	+	0.514426i	0.266496	+	0.963836i	$0.414134\pi$
$740$	3.40685	+	2.12847i	0.125238	+	0.0782441i
$741$	−1.07272	+	3.53627i	−0.0394072	+	0.129908i
$742$	−0.294651	−	0.348029i	−0.0108170	−	0.0127765i
$743$	4.87472	−	7.29553i	0.178836	−	0.267647i	−0.731212	−	0.682151i	$-0.761045\pi$
$743$	4.87472	−	7.29553i	0.178836	−	0.267647i	0.910048	+	0.414504i	$0.136045\pi$
$744$	−11.9875	−	5.71606i	−0.439484	−	0.209561i
$745$	7.23014	−	4.83103i	0.264892	−	0.176995i
$746$	−17.1775	−	30.9863i	−0.628914	−	1.13449i
$747$	8.03276	−	0.791158i	0.293903	−	0.0289470i
$748$	3.32066	−	12.2894i	0.121415	−	0.449344i
$749$	0.0108968	+	0.0359221i	0.000398162	+	0.00131256i
$750$	6.65696	−	10.3008i	0.243078	−	0.376133i
$751$	7.83480	−	18.9149i	0.285896	−	0.690214i	−0.714055	−	0.700089i	$-0.753144\pi$
$751$	7.83480	−	18.9149i	0.285896	−	0.690214i	0.999951	+	0.00987549i	$0.00314352\pi$
$752$	16.4372	−	47.7612i	0.599404	−	1.74167i
$753$	−4.63010	−	11.1780i	−0.168730	−	0.407351i
$754$	−36.0899	−	6.60601i	−1.31431	−	0.240577i
$755$	−1.84269	+	3.44743i	−0.0670623	+	0.125465i
$756$	0.0357633	+	0.0409537i	0.00130070	+	0.00148947i
$757$	−16.0254	+	19.5270i	−0.582454	+	0.709722i	−0.977972	−	0.208736i	$-0.933065\pi$
$757$	−16.0254	+	19.5270i	−0.582454	+	0.709722i	0.395518	+	0.918458i	$0.370565\pi$
$758$	4.70679	+	41.2967i	0.170958	+	1.49997i
$759$	12.7769	+	2.54149i	0.463773	+	0.0922501i
$760$	−6.48627	−	2.34395i	−0.235282	−	0.0850239i
$761$	0.459198	+	2.30854i	0.0166459	+	0.0836847i	0.988215	−	0.153070i	$-0.0489161\pi$
$761$	0.459198	+	2.30854i	0.0166459	+	0.0836847i	−0.971569	+	0.236755i	$0.923916\pi$
$762$	6.70943	+	3.45525i	0.243057	+	0.125171i
$763$	0.179451	−	0.0959184i	0.00649655	−	0.00347248i
$764$	22.1566	−	23.5568i	0.801598	−	0.852256i
$765$	0.443336	−	4.50127i	0.0160289	−	0.162744i
$766$	5.86158	−	14.7875i	0.211787	−	0.534293i
$767$	32.3426			1.16782
$768$	−0.388880	−	15.9953i	−0.0140325	−	0.577180i
$769$	34.9837			1.26154			0.630772	−	0.775968i	$-0.282738\pi$
$769$	34.9837			1.26154			0.630772	+	0.775968i	$0.282738\pi$
$770$	−0.132232	+	0.333591i	−0.00476530	+	0.0120218i
$771$	−0.359540	+	3.65047i	−0.0129485	+	0.131469i
$772$	32.1815	−	34.2152i	1.15824	−	1.23143i
$773$	36.9562	−	19.7535i	1.32922	−	0.710485i	0.354745	−	0.934963i	$-0.384568\pi$
$773$	36.9562	−	19.7535i	1.32922	−	0.710485i	0.974479	+	0.224478i	$0.0720678\pi$
$774$	9.43944	+	4.86117i	0.339294	+	0.174731i
$775$	−1.49547	−	7.51821i	−0.0537187	−	0.270062i
$776$	4.78792	−	13.2493i	0.171876	−	0.475624i
$777$	0.0207947	+	0.00413633i	0.000746007	+	0.000148390i
$778$	−5.01422	−	43.9941i	−0.179769	−	1.57727i
$779$	2.60538	−	3.17466i	0.0933474	−	0.113744i
$780$	−13.2232	−	15.1424i	−0.473468	−	0.542184i
$781$	8.31271	−	15.5520i	0.297452	−	0.556494i
$782$	8.78194	+	1.60748i	0.314041	+	0.0574832i
$783$	2.54371	+	6.14106i	0.0909048	+	0.219464i
$784$	12.2770	+	25.1617i	0.438464	+	0.898631i
$785$	13.5388	−	32.6857i	0.483222	−	1.16660i
$786$	−3.38613	+	5.23962i	−0.120779	+	0.186891i
$787$	6.93079	+	22.8478i	0.247056	+	0.814435i	0.989501	+	0.144528i	$0.0461662\pi$
$787$	6.93079	+	22.8478i	0.247056	+	0.814435i	−0.742445	+	0.669907i	$0.766334\pi$
$788$	1.90149	−	7.03718i	0.0677377	−	0.250689i
$789$	−10.4981	+	1.03398i	−0.373744	+	0.0368106i
$790$	−1.53176	−	2.76312i	−0.0544977	−	0.0983074i
$791$	−0.352801	+	0.235734i	−0.0125442	+	0.00838174i
$792$	−4.41199	+	9.25270i	−0.156773	+	0.328780i
$793$	16.5303	−	24.7394i	0.587010	−	0.878522i
$794$	3.84418	+	4.54058i	0.136425	+	0.161139i
$795$	8.86714	−	29.2311i	0.314485	−	1.03672i
$796$	34.5747	+	21.6010i	1.22547	+	0.765625i
$797$	−10.2018	+	8.37244i	−0.361368	+	0.296567i	−0.797504	−	0.603314i	$-0.793847\pi$
$797$	−10.2018	+	8.37244i	−0.361368	+	0.296567i	0.436136	+	0.899881i	$0.356347\pi$
$798$	−0.0363969		0.000557290i	−0.00128844		1.97278e-5i
$799$	−15.6819	+	15.6819i	−0.554784	+	0.554784i
$800$	7.26386	−	5.70298i	0.256816	−	0.201631i
$801$	−12.2076	−	12.2076i	−0.431335	−	0.431335i
$802$	−3.76653	−	3.65293i	−0.133001	−	0.128989i
$803$	−11.8759	−	14.4709i	−0.419093	−	0.510666i
$804$	19.9082	−	14.2027i	0.702109	−	0.500891i
$805$	−0.240827	−	0.0730540i	−0.00848802	−	0.00257481i
$806$	25.8282	+	2.14515i	0.909758	+	0.0755597i
$807$	−8.75243	−	5.84819i	−0.308100	−	0.205866i
$808$	−5.48801	−	37.8193i	−0.193068	−	1.33048i
$809$	13.1168	+	19.6306i	0.461161	+	0.690176i	0.987056	−	0.160373i	$-0.0512697\pi$
$809$	13.1168	+	19.6306i	0.461161	+	0.690176i	−0.525896	+	0.850549i	$0.676270\pi$
$810$	−1.00377	+	3.50108i	−0.0352689	+	0.123015i
$811$	0.259108	+	2.63077i	0.00909851	+	0.0923788i	0.998662	−	0.0517221i	$-0.0164710\pi$
$811$	0.259108	+	2.63077i	0.00909851	+	0.0923788i	−0.989563	+	0.144101i	$0.953971\pi$
$812$	−0.0464189	−	0.358413i	−0.00162898	−	0.0125778i
$813$	26.8638	−	8.14904i	0.942154	−	0.285799i
$814$	0.839765	+	3.90810i	0.0294338	+	0.136979i
$815$	−1.32421	−	0.548505i	−0.0463850	−	0.0192133i
$816$	−2.92620	+	6.38662i	−0.102438	+	0.223577i
$817$	−6.56735	+	2.72028i	−0.229762	+	0.0951707i
$818$	23.4556	+	33.9663i	0.820106	+	1.18760i
$819$	−0.0935764	−	0.0500176i	−0.00326982	−	0.00174776i
$820$	7.13704	+	21.1713i	0.249236	+	0.739334i
$821$	12.7787	+	10.4872i	0.445979	+	0.366006i	0.830414	−	0.557146i	$-0.188104\pi$
$821$	12.7787	+	10.4872i	0.445979	+	0.366006i	−0.384435	+	0.923152i	$0.625604\pi$
$822$	−4.63318	−	3.68510i	−0.161601	−	0.128533i
$823$	4.56432	−	22.9464i	0.159102	−	0.799860i	−0.815991	−	0.578064i	$-0.803808\pi$
$823$	4.56432	−	22.9464i	0.159102	−	0.799860i	0.975093	−	0.221796i	$-0.0711918\pi$
$824$	2.92625	−	19.3071i	0.101941	−	0.672594i
$825$	−5.80301	+	1.15429i	−0.202035	+	0.0401872i
$826$	0.0971380	+	0.303419i	0.00337986	+	0.0105573i
$827$	20.5803	+	38.5031i	0.715648	+	1.33888i	0.931961	+	0.362559i	$0.118097\pi$
$827$	20.5803	+	38.5031i	0.715648	+	1.33888i	−0.216313	+	0.976324i	$0.569403\pi$
$828$	−6.72292	−	2.54649i	−0.233638	−	0.0884968i
$829$	−42.2851	−	4.16472i	−1.46862	−	0.144647i	−0.668155	−	0.744022i	$-0.732916\pi$
$829$	−42.2851	−	4.16472i	−1.46862	−	0.144647i	−0.800468	+	0.599375i	$0.795416\pi$
$830$	−11.6646	−	26.9847i	−0.404884	−	0.936653i
$831$		−	13.1151i		−	0.454958i
$832$	11.7665	+	28.9221i	0.407932	+	1.00269i
$833$		−	12.2926i		−	0.425913i
$834$	−10.3516	+	4.47466i	−0.358447	+	0.154945i
$835$	−55.0290	−	5.41989i	−1.90436	−	0.187563i
$836$	−2.81918	−	6.25705i	−0.0975032	−	0.216404i
$837$	−2.21340	−	4.14097i	−0.0765062	−	0.143133i
$838$	−37.4652	+	11.9943i	−1.29421	+	0.414337i
$839$	32.9320	−	6.55059i	1.13694	−	0.226151i	0.409492	−	0.912314i	$-0.365706\pi$
$839$	32.9320	−	6.55059i	1.13694	−	0.226151i	0.727448	+	0.686163i	$0.240706\pi$
$840$	0.102342	−	0.169531i	0.00353112	−	0.00584937i
$841$	2.96207	−	14.8913i	0.102140	−	0.513495i
$842$	−0.0146381	+	0.0184041i	−0.000504462	+	0.000634247i
$843$	19.4970	+	16.0008i	0.671513	+	0.551097i
$844$	−46.3642	−	22.9857i	−1.59592	−	0.791201i
$845$	5.07266	+	2.71139i	0.174505	+	0.0932747i
$846$	14.6949	−	10.1476i	0.505221	−	0.348883i
$847$	−0.0536170	+	0.0222089i	−0.00184230	+	0.000763106i
$848$	−27.7970	+	38.4479i	−0.954553	+	1.32030i
$849$	−19.4683	−	8.06404i	−0.668151	−	0.276757i
$850$	−3.96435	+	0.851853i	−0.135976	+	0.0292183i
$851$	−2.68267	+	0.813779i	−0.0919607	+	0.0278960i
$852$	−5.94033	+	7.70795i	−0.203512	+	0.264070i
$853$	−2.66353	−	27.0432i	−0.0911974	−	0.925943i	−0.926536	−	0.376207i	$-0.877228\pi$
$853$	−2.66353	−	27.0432i	−0.0911974	−	0.925943i	0.835338	−	0.549736i	$-0.185272\pi$
$854$	0.281737	+	0.0807751i	0.00964085	+	0.00276407i
$855$	−1.35469	−	2.02744i	−0.0463296	−	0.0693371i
$856$	3.35623	−	1.99728i	0.114714	−	0.0682655i
$857$	36.8053	+	24.5925i	1.25725	+	0.840064i	0.992259	−	0.124188i	$-0.0396325\pi$
$857$	36.8053	+	24.5925i	1.25725	+	0.840064i	0.264986	+	0.964252i	$0.414633\pi$
$858$	1.65575	−	19.9357i	0.0565265	−	0.680594i
$859$	11.5009	+	3.48877i	0.392407	+	0.119035i	0.480321	−	0.877093i	$-0.340520\pi$
$859$	11.5009	+	3.48877i	0.392407	+	0.119035i	−0.0879142	+	0.996128i	$0.528020\pi$
$860$	6.37957	−	38.1409i	0.217542	−	1.30060i
$861$	0.0748078	+	0.0911536i	0.00254944	+	0.00310651i
$862$	33.5486	−	34.5919i	1.14267	−	1.17821i
$863$	2.13473	+	2.13473i	0.0726670	+	0.0726670i	0.742506	−	0.669839i	$-0.233637\pi$
$863$	2.13473	+	2.13473i	0.0726670	+	0.0726670i	−0.669839	+	0.742506i	$0.733637\pi$
$864$	3.24374	−	4.63445i	0.110354	−	0.157667i
$865$	−10.2911	+	10.2911i	−0.349907	+	0.349907i
$866$	0.333524	+	21.7826i	0.0113336	+	0.740204i
$867$	−10.7568	+	8.82791i	−0.365322	+	0.299812i
$868$	0.0574479	+	0.248747i	0.00194991	+	0.00844301i
$869$	0.912577	−	3.00836i	0.0309571	−	0.102052i
$870$	18.4768	−	15.6430i	0.626421	−	0.530346i
$871$	−26.5142	+	39.6812i	−0.898398	+	1.34455i
$872$	−14.1674	−	15.7308i	−0.479767	−	0.532712i
$873$	4.14141	−	2.76720i	0.140165	−	0.0936556i
$874$	4.20947	−	2.33356i	0.142388	−	0.0789339i
$875$	−0.234630	+	0.0231090i	−0.00793193	+	0.000781227i
$876$	5.14649	+	8.95747i	0.173884	+	0.302645i
$877$	−5.01369	−	16.5279i	−0.169300	−	0.558109i	−0.999999	−	0.00138630i	$-0.999559\pi$
$877$	−5.01369	−	16.5279i	−0.169300	−	0.558109i	0.830699	−	0.556722i	$-0.187941\pi$
$878$	29.2359	+	18.8938i	0.986663	+	0.637636i
$879$	8.31060	−	20.0636i	0.280310	−	0.676727i
$880$	36.9944	+	5.02889i	1.24708	+	0.169524i
$881$	15.8993	+	38.3844i	0.535662	+	1.29320i	0.927725	+	0.373264i	$0.121762\pi$
$881$	15.8993	+	38.3844i	0.535662	+	1.29320i	−0.392063	+	0.919938i	$0.628238\pi$
$882$	−1.78224	+	9.73668i	−0.0600110	+	0.327851i
$883$	19.3436	−	36.1893i	0.650964	−	1.21787i	−0.312472	−	0.949927i	$-0.601157\pi$
$883$	19.3436	−	36.1893i	0.650964	−	1.21787i	0.963436	−	0.267940i	$-0.0863430\pi$
$884$	0.925425	−	13.6781i	0.0311254	−	0.460046i
$885$	−13.5387	+	16.4969i	−0.455097	+	0.554538i
$886$	−57.1795	+	6.51702i	−1.92098	+	0.218943i
$887$	3.40697	+	0.677688i	0.114395	+	0.0227546i	0.251956	−	0.967739i	$-0.418926\pi$
$887$	3.40697	+	0.677688i	0.114395	+	0.0227546i	−0.137561	+	0.990493i	$0.543926\pi$
$888$	−0.101283	−	2.20358i	−0.00339884	−	0.0739471i
$889$	−0.0283026	−	0.142287i	−0.000949237	−	0.00477214i
$890$	−28.7882	+	55.9011i	−0.964984	+	1.87381i
$891$	−3.19625	+	1.70843i	−0.107078	+	0.0572346i
$892$	0.994525	+	32.4689i	0.0332992	+	1.08714i
$893$	−1.17189	+	11.8984i	−0.0392157	+	0.398164i
$894$	−4.43900	−	1.75957i	−0.148462	−	0.0588487i
$895$	−39.4017			−1.31705
$896$	−0.235989	+	0.197251i	−0.00788385	+	0.00658970i
$897$	14.0294			0.468428
$898$	−25.4068	−	10.0710i	−0.847836	−	0.336072i
$899$	−3.05916	+	31.0602i	−0.102029	+	1.03592i
$900$	3.26358	−	0.0999638i	0.108786	−	0.00333213i
$901$	18.3713	−	9.81966i	0.612036	−	0.327140i
$902$	−10.1786	+	19.7649i	−0.338912	+	0.658100i
$903$	−0.0398187	−	0.200182i	−0.00132508	−	0.00666164i
$904$	32.6162	+	29.7497i	1.08480	+	0.989460i
$905$	−44.8400	−	8.91922i	−1.49053	−	0.296485i
$906$	2.13274	−	0.243078i	0.0708555	−	0.00807573i
$907$	5.03755	−	6.13827i	0.167269	−	0.203818i	−0.682629	−	0.730765i	$-0.739163\pi$
$907$	5.03755	−	6.13827i	0.167269	−	0.203818i	0.849898	+	0.526947i	$0.176663\pi$
$908$	−28.9352	−	1.95767i	−0.960247	−	0.0649676i
$909$	6.36913	−	11.9158i	0.211251	−	0.395222i
$910$	−0.0695809	+	0.380133i	−0.00230658	+	0.0126013i
$911$	9.05153	+	21.8523i	0.299890	+	0.724000i	0.999951	+	0.00991599i	$0.00315641\pi$
$911$	9.05153	+	21.8523i	0.299890	+	0.724000i	−0.700060	+	0.714084i	$0.746844\pi$
$912$	0.964803	+	3.66228i	0.0319478	+	0.121270i
$913$	11.1947	−	27.0264i	0.370490	−	0.894442i
$914$	40.6014	+	26.2389i	1.34297	+	0.867904i
$915$	5.69914	+	18.7875i	0.188408	+	0.621097i
$916$	−16.0810	+	9.23932i	−0.531332	+	0.305276i
$917$	0.119347	−	0.0117546i	0.00394118	−	0.000388172i
$918$	−2.17228	+	1.20422i	−0.0716959	+	0.0397453i
$919$	−5.97061	+	3.98944i	−0.196952	+	0.131599i	−0.650136	−	0.759818i	$-0.725288\pi$
$919$	−5.97061	+	3.98944i	−0.196952	+	0.131599i	0.453184	+	0.891417i	$0.350288\pi$
$920$	−1.36730	+	26.1477i	−0.0450787	+	0.862064i
$921$	12.6431	−	18.9218i	0.416606	−	0.623495i
$922$	28.1452	−	23.8285i	0.926912	−	0.784750i
$923$	5.51274	−	18.1731i	0.181454	−	0.598174i
$924$	0.191997	−	0.0443417i	0.00631625	−	0.00145874i
$925$	0.984225	−	0.807733i	0.0323611	−	0.0265581i
$926$	0.0732505	+	4.78403i	0.00240716	+	0.157213i
$927$	4.88190	−	4.88190i	0.160343	−	0.160343i
$928$	−35.0421	+	13.6349i	−1.15031	+	0.447588i
$929$	4.73822	+	4.73822i	0.155456	+	0.155456i	0.780550	−	0.625094i	$-0.214939\pi$
$929$	4.73822	+	4.73822i	0.155456	+	0.155456i	−0.625094	+	0.780550i	$0.714939\pi$
$930$	−11.9059	+	12.2761i	−0.390409	+	0.402550i
$931$	−4.20410	−	5.12271i	−0.137784	−	0.167890i
$932$	17.0302	+	2.84852i	0.557841	+	0.0933063i
$933$	9.77634	+	2.96562i	0.320063	+	0.0970901i
$934$	−3.10404	+	37.3735i	−0.101567	+	1.22290i
$935$	−13.6298	−	9.10712i	−0.445741	−	0.297835i
$936$	−2.71613	+	10.7000i	−0.0887795	+	0.349740i
$937$	−22.2596	−	33.3139i	−0.727191	−	1.08832i	−0.992271	−	0.124092i	$-0.960398\pi$
$937$	−22.2596	−	33.3139i	−0.727191	−	1.08832i	0.265080	−	0.964227i	$-0.414602\pi$
$938$	−0.451898	−	0.129561i	−0.0147550	−	0.00423031i
$939$	−1.87209	−	19.0077i	−0.0610934	−	0.620291i
$940$	−51.5177	−	39.7034i	−1.68032	−	1.29498i
$941$	−3.10662	+	0.942382i	−0.101273	+	0.0307208i	−0.340514	−	0.940239i	$-0.610601\pi$
$941$	−3.10662	+	0.942382i	−0.101273	+	0.0307208i	0.239242	+	0.970960i	$0.423101\pi$
$942$	−18.9939	+	4.08138i	−0.618856	+	0.132979i
$943$	−14.4048	−	5.96666i	−0.469084	−	0.194301i
$944$	28.2215	−	17.3850i	0.918530	−	0.565832i
$945$	0.0646836	−	0.0267928i	0.00210416	−	0.000871570i
$946$	31.6642	−	21.8658i	1.02949	−	0.710920i
$947$	17.7010	+	9.46140i	0.575206	+	0.307454i	0.733230	−	0.679981i	$-0.238012\pi$
$947$	17.7010	+	9.46140i	0.575206	+	0.307454i	−0.158023	+	0.987435i	$0.550512\pi$
$948$	−0.770582	+	1.55433i	−0.0250273	+	0.0504823i
$949$	−15.5841	−	12.7895i	−0.505882	−	0.415166i
$950$	−1.36073	+	1.71081i	−0.0441481	+	0.0555061i
$951$	6.05742	−	30.4527i	0.196425	−	0.987497i
$952$	0.131099	−	0.0323992i	0.00424896	−	0.00105007i
$953$	−28.1949	+	5.60831i	−0.913322	+	0.181671i	−0.629314	−	0.777151i	$-0.716664\pi$
$953$	−28.1949	+	5.60831i	−0.913322	+	0.181671i	−0.284008	+	0.958822i	$0.591664\pi$
$954$	−15.9752	+	5.11438i	−0.517216	+	0.165584i
$955$	−19.6304	−	36.7259i	−0.635225	−	1.18842i
$956$	−32.2824	+	14.5451i	−1.04409	+	0.470424i
$957$	23.9741	+	2.36125i	0.774973	+	0.0763282i
$958$	43.9923	−	19.0164i	1.42133	−	0.614392i
$959$			0.113801i			0.00367481i
$960$	−19.6777	−	6.10508i	−0.635095	−	0.197041i
$961$			8.95320i			0.288813i
$962$	1.70808	+	3.95144i	0.0550706	+	0.127400i
$963$	1.37418	+	0.135344i	0.0442822	+	0.00436141i
$964$	−3.32128	+	8.76842i	−0.106971	+	0.282412i
$965$	−28.5123	−	53.3428i	−0.917844	−	1.71716i
$966$	0.0421360	+	0.131615i	0.00135570	+	0.00423465i
$967$	−40.1701	+	7.99034i	−1.29178	+	0.256952i	−0.792706	−	0.609604i	$-0.791328\pi$
$967$	−40.1701	+	7.99034i	−1.29178	+	0.256952i	−0.499079	+	0.866556i	$0.666328\pi$
$968$	3.58151	+	4.86110i	0.115114	+	0.156242i
$969$	0.324406	−	1.63090i	0.0104214	−	0.0523920i
$970$	−14.1976	−	11.2924i	−0.455857	−	0.362577i
$971$	8.34251	+	6.84652i	0.267724	+	0.219715i	0.758671	−	0.651474i	$-0.225849\pi$
$971$	8.34251	+	6.84652i	0.267724	+	0.219715i	−0.490947	+	0.871189i	$0.663349\pi$
$972$	1.89521	−	0.638892i	0.0607889	−	0.0204925i
$973$	0.191188	+	0.102192i	0.00612920	+	0.00327613i
$974$	12.9253	+	18.7173i	0.414154	+	0.599741i
$975$	−5.88683	+	2.43841i	−0.188530	+	0.0780915i
$976$	1.12597	−	30.4725i	0.0360416	−	0.975402i
$977$	−6.09538	−	2.52479i	−0.195009	−	0.0807752i	0.283042	−	0.959108i	$-0.408656\pi$
$977$	−6.09538	−	2.52479i	−0.195009	−	0.0807752i	−0.478051	+	0.878332i	$0.658656\pi$
$978$	0.165351	+	0.769509i	0.00528734	+	0.0246062i
$979$	−59.8745	+	18.1627i	−1.91360	+	0.580484i
$980$	35.7528	−	4.63043i	1.14208	−	0.147914i
$981$	−0.733634	−	7.44871i	−0.0234231	−	0.237819i
$982$	−1.24919	+	4.35709i	−0.0398634	+	0.139040i
$983$	−7.04648	−	10.5458i	−0.224748	−	0.336359i	0.701909	−	0.712266i	$-0.252331\pi$
$983$	−7.04648	−	10.5458i	−0.224748	−	0.336359i	−0.926657	+	0.375907i	$0.877331\pi$
$984$	7.33947	−	9.83112i	0.233974	−	0.313405i
$985$	−7.80473	−	5.21495i	−0.248679	−	0.166162i
$986$	16.4528	+	1.36649i	0.523965	+	0.0435178i
$987$	−0.328507	−	0.0996516i	−0.0104565	−	0.00317195i
$988$	−4.29231	−	6.01662i	−0.136557	−	0.191414i
$989$	17.1203	+	20.8612i	0.544395	+	0.663347i
$990$	9.47545	+	9.18966i	0.301150	+	0.292067i
$991$	35.2464	+	35.2464i	1.11964	+	1.11964i	0.991794	+	0.127844i	$0.0408056\pi$
$991$	35.2464	+	35.2464i	1.11964	+	1.11964i	0.127844	+	0.991794i	$0.459194\pi$
$992$	23.6901	−	12.0115i	0.752163	−	0.381364i
$993$	−20.9246	+	20.9246i	−0.664022	+	0.664022i
$994$	0.187046	−	0.00286394i	0.00593272	−	9.08387e-5i
$995$	40.5801	−	33.3032i	1.28647	−	1.05578i
$996$	−8.55357	+	13.6909i	−0.271030	+	0.433813i
$997$	−7.64278	+	25.1949i	−0.242049	+	0.797930i	0.748781	+	0.662818i	$0.230640\pi$
$997$	−7.64278	+	25.1949i	−0.242049	+	0.797930i	−0.990830	+	0.135112i	$0.956860\pi$
$998$	26.1646	+	30.9044i	0.828226	+	0.978263i
$999$	0.433291	−	0.648466i	0.0137087	−	0.0205166i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.20	✓	512
128.53	even	32	inner	384.2.v.a.181.20	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.20	✓	512	1.1	even	1	trivial
384.2.v.a.181.20	yes	512	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.521130 - 1.31470i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.45685 - 1.37025i) q^{4} +(-2.27128 + 1.21402i) q^{5} +(1.25729 + 0.647483i) q^{6} +(-0.00530364 - 0.0266632i) q^{7} +(-2.56067 + 1.20123i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(0.521130 - 1.31470i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-1.45685 - 1.37025i) q^{4} +(-2.27128 + 1.21402i) q^{5} +(1.25729 + 0.647483i) q^{6} +(-0.00530364 - 0.0266632i) q^{7} +(-2.56067 + 1.20123i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(0.412441 + 3.61870i) q^{10} +(-2.29916 + 2.80154i) q^{11} +(1.50645 - 1.31552i) q^{12} +(-1.83986 + 3.44214i) q^{13} +(-0.0378179 - 0.00692231i) q^{14} +(-0.985553 - 2.37934i) q^{15} +(0.244811 + 3.99250i) q^{16} +(0.672095 - 1.62258i) q^{17} +(-0.767601 + 1.18777i) q^{18} +(-0.274844 - 0.906039i) q^{19} +(4.97243 + 1.34358i) q^{20} +(0.0270547 - 0.00266465i) q^{21} +(2.48501 + 4.48266i) q^{22} +(-2.98873 + 1.99701i) q^{23} +(-0.944457 - 2.66608i) q^{24} +(0.906999 - 1.35742i) q^{25} +(3.56656 + 4.21266i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-0.0288087 + 0.0461115i) q^{28} +(-5.13823 + 4.21684i) q^{29} +(-3.64170 + 0.0557598i) q^{30} +(3.32015 - 3.32015i) q^{31} +(5.37650 + 1.75876i) q^{32} +(-2.56269 - 2.56269i) q^{33} +(-1.78295 - 1.72917i) q^{34} +(0.0444158 + 0.0541208i) q^{35} +(1.16153 + 1.62814i) q^{36} +(0.746322 + 0.226394i) q^{37} +(-1.33439 - 0.110828i) q^{38} +(-3.24522 - 2.16839i) q^{39} +(4.35768 - 5.83705i) q^{40} +(2.40985 + 3.60659i) q^{41} +(0.0105958 - 0.0369573i) q^{42} +(-0.735893 - 7.47165i) q^{43} +(7.18835 - 0.930979i) q^{44} +(2.46448 - 0.747592i) q^{45} +(1.06794 + 4.96998i) q^{46} +(-11.6664 - 4.83239i) q^{47} +(-3.99727 - 0.147701i) q^{48} +(6.46647 - 2.67850i) q^{49} +(-1.31193 - 1.89982i) q^{50} +(1.54889 + 0.827899i) q^{51} +(7.39700 - 2.49359i) q^{52} +(9.16863 + 7.52450i) q^{53} +(-1.10681 - 0.880326i) q^{54} +(1.82090 - 9.15431i) q^{55} +(0.0456095 + 0.0619048i) q^{56} +(0.928615 - 0.184713i) q^{57} +(2.86617 + 8.95272i) q^{58} +(-3.90628 - 7.30814i) q^{59} +(-1.82449 + 4.81679i) q^{60} +(-7.58662 - 0.747217i) q^{61} +(-2.63476 - 6.09522i) q^{62} +0.0271856i q^{63} +(5.11409 - 6.15192i) q^{64} -10.0517i q^{65} +(-4.70465 + 2.03366i) q^{66} +(12.1687 + 1.19851i) q^{67} +(-3.20248 + 1.44291i) q^{68} +(-1.69445 - 3.17008i) q^{69} +(0.0942987 - 0.0301893i) q^{70} +(-4.77220 + 0.949250i) q^{71} +(2.74582 - 0.678588i) q^{72} +(-1.00771 + 5.06608i) q^{73} +(0.686570 - 0.863205i) q^{74} +(1.26198 + 1.03568i) q^{75} +(-0.841097 + 1.69657i) q^{76} +(0.0868919 + 0.0464447i) q^{77} +(-4.54195 + 3.13647i) q^{78} +(-0.801401 + 0.331951i) q^{79} +(-5.40302 - 8.77087i) q^{80} +(0.923880 + 0.382683i) q^{81} +(5.99741 - 1.28871i) q^{82} +(-7.72407 + 2.34307i) q^{83} +(-0.0430658 - 0.0331897i) q^{84} +(0.443336 + 4.50127i) q^{85} +(-10.2064 - 2.92622i) q^{86} +(-3.69290 - 5.52681i) q^{87} +(2.52211 - 9.93565i) q^{88} +(14.3546 + 9.59147i) q^{89} +(0.301458 - 3.62963i) q^{90} +(0.101536 + 0.0308007i) q^{91} +(7.09054 + 1.18599i) q^{92} +(2.97873 + 3.62959i) q^{93} +(-12.4328 + 12.8195i) q^{94} +(1.72420 + 1.72420i) q^{95} +(-2.27728 + 5.17822i) q^{96} +(-3.52198 + 3.52198i) q^{97} +(-0.151542 - 9.89729i) q^{98} +(2.80154 - 2.29916i) 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

Related objects

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