LMFDB - Embedded newform 384.2.v.a.13.17

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			13.17
Character	$\chi$	$=$	384.13
Dual form			384.2.v.a.325.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156266 + 1.40555i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.95116 - 0.439279i) q^{4} +(-0.103867 - 1.05457i) q^{5} +(1.39039 - 0.258474i) q^{6} +(-0.0783117 + 0.117202i) q^{7} +(0.922330 - 2.67382i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})$	\(q+(-0.156266 + 1.40555i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.95116 - 0.439279i) q^{4} +(-0.103867 - 1.05457i) q^{5} +(1.39039 - 0.258474i) q^{6} +(-0.0783117 + 0.117202i) q^{7} +(0.922330 - 2.67382i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.49849 + 0.0188036i) q^{10} +(-2.29838 + 1.22851i) q^{11} +(0.146029 + 1.99466i) q^{12} +(-6.11996 - 0.602763i) q^{13} +(-0.152496 - 0.128386i) q^{14} +(-0.979014 + 0.405521i) q^{15} +(3.61407 + 1.71421i) q^{16} +(-6.95448 - 2.88064i) q^{17} +(-0.650954 - 1.25549i) q^{18} +(0.671982 - 0.551481i) q^{19} +(-0.260592 + 2.10327i) q^{20} +(0.134888 + 0.0409177i) q^{21} +(-1.36758 - 3.42248i) q^{22} +(1.85915 - 9.34658i) q^{23} +(-2.82642 - 0.106446i) q^{24} +(3.80259 - 0.756382i) q^{25} +(1.80355 - 8.50774i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.204283 - 0.194279i) q^{28} +(-3.35535 + 6.27741i) q^{29} +(-0.416995 - 1.43943i) q^{30} +(3.67878 - 3.67878i) q^{31} +(-2.97417 + 4.81189i) q^{32} +(1.84280 + 1.84280i) q^{33} +(5.13564 - 9.32475i) q^{34} +(0.131732 + 0.0704121i) q^{35} +(1.86638 - 0.718760i) q^{36} +(-1.42782 + 1.73980i) q^{37} +(0.670129 + 1.03068i) q^{38} +(1.19972 + 6.03141i) q^{39} +(-2.91554 - 0.694945i) q^{40} +(-6.97514 - 1.38744i) q^{41} +(-0.0785904 + 0.183198i) q^{42} +(-0.779364 + 2.56922i) q^{43} +(5.02418 - 1.38739i) q^{44} +(0.672252 + 0.819141i) q^{45} +(12.8466 + 4.07368i) q^{46} +(0.674420 - 1.62819i) q^{47} +(0.591288 - 3.95606i) q^{48} +(2.67118 + 6.44880i) q^{49} +(0.468922 + 5.46294i) q^{50} +(-0.737821 + 7.49122i) q^{51} +(11.6762 + 3.86446i) q^{52} +(-4.02295 - 7.52641i) q^{53} +(-1.01247 + 0.987374i) q^{54} +(1.53428 + 2.29622i) q^{55} +(0.241147 + 0.317490i) q^{56} +(-0.722801 - 0.482960i) q^{57} +(-8.29891 - 5.69706i) q^{58} +(-10.7263 + 1.05645i) q^{59} +(2.08835 - 0.361177i) q^{60} +(6.46233 - 1.96033i) q^{61} +(4.59585 + 5.74558i) q^{62} -0.140957i q^{63} +(-6.29862 - 4.93229i) q^{64} +6.51656i q^{65} +(-2.87812 + 2.30219i) q^{66} +(10.0367 - 3.04460i) q^{67} +(12.3039 + 8.67555i) q^{68} +(-9.48380 + 0.934073i) q^{69} +(-0.119553 + 0.174153i) q^{70} +(9.98888 + 6.67435i) q^{71} +(0.718605 + 2.73562i) q^{72} +(1.28206 + 1.91874i) q^{73} +(-2.22227 - 2.27875i) q^{74} +(-1.82765 - 3.41928i) q^{75} +(-1.55340 + 0.780842i) q^{76} +(0.0360066 - 0.365581i) q^{77} +(-8.66494 + 0.743772i) q^{78} +(-5.10188 - 12.3170i) q^{79} +(1.43238 - 3.98935i) q^{80} +(0.382683 - 0.923880i) q^{81} +(3.04010 - 9.58713i) q^{82} +(6.80230 + 8.28863i) q^{83} +(-0.245213 - 0.139090i) q^{84} +(-2.31551 + 7.63321i) q^{85} +(-3.48939 - 1.49692i) q^{86} +(6.98111 + 1.38863i) q^{87} +(1.16495 + 7.27856i) q^{88} +(-1.23326 - 6.20000i) q^{89} +(-1.25640 + 0.816883i) q^{90} +(0.549909 - 0.670066i) q^{91} +(-7.73326 + 17.4200i) q^{92} +(-4.58826 - 2.45248i) q^{93} +(2.18312 + 1.20236i) q^{94} +(-0.651374 - 0.651374i) q^{95} +(5.46805 + 1.44928i) q^{96} +(-12.5043 + 12.5043i) q^{97} +(-9.48155 + 2.74676i) q^{98} +(1.22851 - 2.29838i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{15}{32}\right)$	$1$

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 $

$2$	−0.156266	+	1.40555i	−0.110496	+	0.993877i
$2$	−0.156266	+	1.40555i	−0.110496	+	0.993877i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$3$	−0.290285	−	0.956940i	−0.167596	−	0.552490i
$4$	−1.95116	−	0.439279i	−0.975581	−	0.219640i
$5$	−0.103867	−	1.05457i	−0.0464505	−	0.471620i	−0.990069	−	0.140584i	$-0.955102\pi$
$5$	−0.103867	−	1.05457i	−0.0464505	−	0.471620i	0.943618	−	0.331036i	$-0.107398\pi$
$6$	1.39039	−	0.258474i	0.567625	−	0.105522i
$7$	−0.0783117	+	0.117202i	−0.0295990	+	0.0442981i	−0.845974	−	0.533224i	$-0.820980\pi$
$7$	−0.0783117	+	0.117202i	−0.0295990	+	0.0442981i	0.816375	+	0.577522i	$0.195980\pi$
$8$	0.922330	−	2.67382i	0.326093	−	0.945338i
$9$	−0.831470	+	0.555570i	−0.277157	+	0.185190i
$10$	1.49849	+	0.0188036i	0.473865	+	0.00594624i
$11$	−2.29838	+	1.22851i	−0.692989	+	0.370410i	−0.779985	−	0.625798i	$-0.784773\pi$
$11$	−2.29838	+	1.22851i	−0.692989	+	0.370410i	0.0869960	+	0.996209i	$0.472273\pi$
$12$	0.146029	+	1.99466i	0.0421548	+	0.575809i
$13$	−6.11996	−	0.602763i	−1.69737	−	0.167176i	−0.797496	−	0.603324i	$-0.793842\pi$
$13$	−6.11996	−	0.602763i	−1.69737	−	0.167176i	−0.899875	+	0.436148i	$0.856342\pi$
$14$	−0.152496	−	0.128386i	−0.0407562	−	0.0343126i
$15$	−0.979014	+	0.405521i	−0.252780	+	0.104705i
$16$	3.61407	+	1.71421i	0.903517	+	0.428552i
$17$	−6.95448	−	2.88064i	−1.68671	−	0.698658i	−0.687098	−	0.726565i	$-0.741116\pi$
$17$	−6.95448	−	2.88064i	−1.68671	−	0.698658i	−0.999611	+	0.0279073i	$0.991116\pi$
$18$	−0.650954	−	1.25549i	−0.153431	−	0.295922i
$19$	0.671982	−	0.551481i	0.154163	−	0.126519i	−0.554150	−	0.832417i	$-0.686957\pi$
$19$	0.671982	−	0.551481i	0.154163	−	0.126519i	0.708313	+	0.705898i	$0.249457\pi$
$20$	−0.260592	+	2.10327i	−0.0582702	+	0.470306i
$21$	0.134888	+	0.0409177i	0.0294349	+	0.00892898i
$22$	−1.36758	−	3.42248i	−0.291569	−	0.729674i
$23$	1.85915	−	9.34658i	0.387660	−	1.94890i	0.0825156	−	0.996590i	$-0.473705\pi$
$23$	1.85915	−	9.34658i	0.387660	−	1.94890i	0.305144	−	0.952306i	$-0.401295\pi$
$24$	−2.82642	−	0.106446i	−0.576941	−	0.0217282i
$25$	3.80259	−	0.756382i	0.760518	−	0.151276i
$26$	1.80355	−	8.50774i	0.353706	−	1.66850i
$27$	0.773010	+	0.634393i	0.148766	+	0.122089i
$28$	0.204283	−	0.194279i	0.0386059	−	0.0367152i
$29$	−3.35535	+	6.27741i	−0.623072	+	1.16569i	0.350340	+	0.936623i	$0.386066\pi$
$29$	−3.35535	+	6.27741i	−0.623072	+	1.16569i	−0.973412	+	0.229063i	$0.926434\pi$
$30$	−0.416995	−	1.43943i	−0.0761325	−	0.262802i
$31$	3.67878	−	3.67878i	0.660728	−	0.660728i	−0.294824	−	0.955552i	$-0.595261\pi$
$31$	3.67878	−	3.67878i	0.660728	−	0.660728i	0.955552	+	0.294824i	$0.0952610\pi$
$32$	−2.97417	+	4.81189i	−0.525764	+	0.850631i
$33$	1.84280	+	1.84280i	0.320790	+	0.320790i
$34$	5.13564	−	9.32475i	0.880755	−	1.59918i
$35$	0.131732	+	0.0704121i	0.0222667	+	0.0119018i
$36$	1.86638	−	0.718760i	0.311064	−	0.119793i
$37$	−1.42782	+	1.73980i	−0.234732	+	0.286022i	−0.877032	−	0.480431i	$-0.840480\pi$
$37$	−1.42782	+	1.73980i	−0.234732	+	0.286022i	0.642300	+	0.766453i	$0.277980\pi$
$38$	0.670129	+	1.03068i	0.108709	+	0.167199i
$39$	1.19972	+	6.03141i	0.192109	+	0.965798i
$40$	−2.91554	−	0.694945i	−0.460987	−	0.109880i
$41$	−6.97514	−	1.38744i	−1.08933	−	0.216682i	−0.382425	−	0.923987i	$-0.624911\pi$
$41$	−6.97514	−	1.38744i	−1.08933	−	0.216682i	−0.706909	+	0.707305i	$0.749911\pi$
$42$	−0.0785904	+	0.183198i	−0.0121268	+	0.0282680i
$43$	−0.779364	+	2.56922i	−0.118852	+	0.391802i	−0.996100	−	0.0882357i	$-0.971877\pi$
$43$	−0.779364	+	2.56922i	−0.118852	+	0.391802i	0.877248	+	0.480038i	$0.159377\pi$
$44$	5.02418	−	1.38739i	0.757424	−	0.209157i
$45$	0.672252	+	0.819141i	0.100213	+	0.122110i
$46$	12.8466	+	4.07368i	1.89413	+	0.600632i
$47$	0.674420	−	1.62819i	0.0983742	−	0.237496i	−0.867029	−	0.498257i	$-0.833973\pi$
$47$	0.674420	−	1.62819i	0.0983742	−	0.237496i	0.965403	+	0.260761i	$0.0839735\pi$
$48$	0.591288	−	3.95606i	0.0853450	−	0.571007i
$49$	2.67118	+	6.44880i	0.381597	+	0.921257i
$50$	0.468922	+	5.46294i	0.0663156	+	0.772576i
$51$	−0.737821	+	7.49122i	−0.103316	+	1.04898i
$52$	11.6762	+	3.86446i	1.61920	+	0.535904i
$53$	−4.02295	−	7.52641i	−0.552595	−	1.03383i	−0.990848	−	0.134980i	$-0.956903\pi$
$53$	−4.02295	−	7.52641i	−0.552595	−	1.03383i	0.438254	−	0.898851i	$-0.355597\pi$
$54$	−1.01247	+	0.987374i	−0.137780	+	0.134365i
$55$	1.53428	+	2.29622i	0.206883	+	0.309622i
$56$	0.241147	+	0.317490i	0.0322246	+	0.0424264i
$57$	−0.722801	−	0.482960i	−0.0957373	−	0.0639696i
$58$	−8.29891	−	5.69706i	−1.08970	−	0.748061i
$59$	−10.7263	+	1.05645i	−1.39645	+	0.137538i	−0.768067	−	0.640369i	$-0.778781\pi$
$59$	−10.7263	+	1.05645i	−1.39645	+	0.137538i	−0.628379	+	0.777907i	$0.716281\pi$
$60$	2.08835	−	0.361177i	0.269605	−	0.0466277i
$61$	6.46233	−	1.96033i	0.827417	−	0.250994i	0.151953	−	0.988388i	$-0.451444\pi$
$61$	6.46233	−	1.96033i	0.827417	−	0.250994i	0.675463	+	0.737393i	$0.263944\pi$
$62$	4.59585	+	5.74558i	0.583674	+	0.729690i
$63$		−	0.140957i		−	0.0177589i
$64$	−6.29862	−	4.93229i	−0.787327	−	0.616536i
$65$			6.51656i			0.808279i
$66$	−2.87812	+	2.30219i	−0.354272	+	0.283379i
$67$	10.0367	−	3.04460i	1.22618	−	0.371957i	0.390206	−	0.920728i	$-0.372404\pi$
$67$	10.0367	−	3.04460i	1.22618	−	0.371957i	0.835973	+	0.548770i	$0.184904\pi$
$68$	12.3039	+	8.67555i	1.49207	+	1.05206i
$69$	−9.48380	+	0.934073i	−1.14172	+	0.112449i
$70$	−0.119553	+	0.174153i	−0.0142893	+	0.0208153i
$71$	9.98888	+	6.67435i	1.18546	+	0.792100i	0.982349	−	0.187055i	$-0.0598944\pi$
$71$	9.98888	+	6.67435i	1.18546	+	0.792100i	0.203112	+	0.979155i	$0.434894\pi$
$72$	0.718605	+	2.73562i	0.0846884	+	0.322396i
$73$	1.28206	+	1.91874i	0.150054	+	0.224571i	0.898880	−	0.438195i	$-0.144382\pi$
$73$	1.28206	+	1.91874i	0.150054	+	0.224571i	−0.748826	+	0.662767i	$0.769382\pi$
$74$	−2.22227	−	2.27875i	−0.258333	−	0.264899i
$75$	−1.82765	−	3.41928i	−0.211038	−	0.394825i
$76$	−1.55340	+	0.780842i	−0.178187	+	0.0895687i
$77$	0.0360066	−	0.365581i	0.00410333	−	0.0416618i
$78$	−8.66494	+	0.743772i	−0.981111	+	0.0842156i
$79$	−5.10188	−	12.3170i	−0.574006	−	1.38577i	−0.898118	−	0.439754i	$-0.855066\pi$
$79$	−5.10188	−	12.3170i	−0.574006	−	1.38577i	0.324112	−	0.946019i	$-0.394934\pi$
$80$	1.43238	−	3.98935i	0.160145	−	0.446023i
$81$	0.382683	−	0.923880i	0.0425204	−	0.102653i
$82$	3.04010	−	9.58713i	0.335723	−	1.05872i
$83$	6.80230	+	8.28863i	0.746649	+	0.909795i	0.998315	−	0.0580192i	$-0.0184785\pi$
$83$	6.80230	+	8.28863i	0.746649	+	0.909795i	−0.251666	+	0.967814i	$0.580978\pi$
$84$	−0.245213	−	0.139090i	−0.0267550	−	0.0151760i
$85$	−2.31551	+	7.63321i	−0.251152	+	0.827938i
$86$	−3.48939	−	1.49692i	−0.376270	−	0.161417i
$87$	6.98111	+	1.38863i	0.748454	+	0.148877i
$88$	1.16495	+	7.27856i	0.124184	+	0.775897i
$89$	−1.23326	−	6.20000i	−0.130725	−	0.657198i	−0.989463	−	0.144784i	$-0.953751\pi$
$89$	−1.23326	−	6.20000i	−0.130725	−	0.657198i	0.858738	−	0.512414i	$-0.171249\pi$
$90$	−1.25640	+	0.816883i	−0.132436	+	0.0861070i
$91$	0.549909	−	0.670066i	0.0576461	−	0.0702420i
$92$	−7.73326	+	17.4200i	−0.806248	+	1.81616i
$93$	−4.58826	−	2.45248i	−0.475781	−	0.254310i
$94$	2.18312	+	1.20236i	0.225172	+	0.124014i
$95$	−0.651374	−	0.651374i	−0.0668296	−	0.0668296i
$96$	5.46805	+	1.44928i	0.558081	+	0.147917i
$97$	−12.5043	+	12.5043i	−1.26962	+	1.26962i	−0.323336	+	0.946284i	$0.604805\pi$
$97$	−12.5043	+	12.5043i	−1.26962	+	1.26962i	−0.946284	+	0.323336i	$0.895195\pi$
$98$	−9.48155	+	2.74676i	−0.957781	+	0.277465i
$99$	1.22851	−	2.29838i	0.123470	−	0.230996i
$100$	−7.75173	−	0.194574i	−0.775173	−	0.0194574i
$101$	−3.31742	−	2.72253i	−0.330095	−	0.270902i	0.454717	−	0.890636i	$-0.349741\pi$
$101$	−3.31742	−	2.72253i	−0.330095	−	0.270902i	−0.784812	+	0.619734i	$0.787241\pi$
$102$	−10.4140	−	2.20767i	−1.03114	−	0.218592i
$103$	1.76536	−	0.351151i	0.173946	−	0.0346000i	−0.107349	−	0.994221i	$-0.534236\pi$
$103$	1.76536	−	0.351151i	0.173946	−	0.0346000i	0.281295	+	0.959621i	$0.409236\pi$
$104$	−7.25630	+	15.8077i	−0.711539	+	1.55007i
$105$	0.0291405	−	0.146499i	0.00284382	−	0.0142968i
$106$	11.2074	−	4.47835i	1.08856	−	0.434976i
$107$	−2.80691	−	0.851465i	−0.271354	−	0.0823143i	0.151675	−	0.988430i	$-0.451533\pi$
$107$	−2.80691	−	0.851465i	−0.271354	−	0.0823143i	−0.423029	+	0.906116i	$0.639033\pi$
$108$	−1.22959	−	1.57737i	−0.118318	−	0.151783i
$109$	3.02571	−	2.48314i	0.289811	−	0.237842i	−0.478242	−	0.878228i	$-0.658726\pi$
$109$	3.02571	−	2.48314i	0.289811	−	0.237842i	0.768053	+	0.640386i	$0.221226\pi$
$110$	−3.46721	+	1.79770i	−0.330585	+	0.171404i
$111$	2.07936	+	0.861299i	0.197364	+	0.0817509i
$112$	−0.483932	+	0.289332i	−0.0457273	+	0.0273393i
$113$	7.38984	−	3.06097i	0.695177	−	0.287952i	−0.00697804	−	0.999976i	$-0.502221\pi$
$113$	7.38984	−	3.06097i	0.695177	−	0.287952i	0.702155	+	0.712024i	$0.252221\pi$
$114$	0.791775	−	0.940465i	0.0741565	−	0.0880827i
$115$	−10.0498	−	0.989815i	−0.937145	−	0.0923007i
$116$	9.30436	−	10.7743i	0.863888	−	1.00037i
$117$	5.42344	−	2.89889i	0.501397	−	0.268002i
$118$	0.191256	−	15.2415i	0.0176066	−	1.40309i
$119$	0.882232	−	0.589489i	0.0808741	−	0.0540384i
$120$	0.181316	+	2.99173i	0.0165518	+	0.273106i
$121$	−2.33795	+	3.49898i	−0.212541	+	0.318089i
$122$	1.74551	+	9.38949i	0.158031	+	0.850084i
$123$	0.697078	+	7.07755i	0.0628534	+	0.638161i
$124$	−8.79390	+	5.56188i	−0.789716	+	0.499472i
$125$	−2.73066	−	9.00179i	−0.244238	−	0.805144i
$126$	0.198123	+	0.0220268i	0.0176502	+	0.00196230i
$127$	13.3455			1.18422			0.592109	−	0.805858i	$-0.298295\pi$
$127$	13.3455			1.18422			0.592109	+	0.805858i	$0.298295\pi$
$128$	7.91685	−	8.08230i	0.699757	−	0.714381i
$129$	2.68483			0.236386
$130$	−9.15937	−	1.01831i	−0.803330	−	0.0893120i
$131$	4.43643	+	14.6250i	0.387613	+	1.27779i	0.906231	+	0.422782i	$0.138946\pi$
$131$	4.43643	+	14.6250i	0.387613	+	1.27779i	−0.518619	+	0.855006i	$0.673554\pi$
$132$	−2.78610	−	4.40510i	−0.242498	−	0.383415i
$133$	0.0120105	+	0.121945i	0.00104144	+	0.0105740i
$134$	2.71096	+	14.5829i	0.234191	+	1.25977i
$135$	0.588725	−	0.881089i	0.0506694	−	0.0758321i
$136$	−14.1166	+	15.9381i	−1.21049	+	1.36668i
$137$	9.06211	−	6.05511i	0.774229	−	0.517323i	−0.104569	−	0.994518i	$-0.533346\pi$
$137$	9.06211	−	6.05511i	0.774229	−	0.517323i	0.878798	+	0.477195i	$0.158346\pi$
$138$	0.169101	−	13.4760i	0.0143949	−	1.14715i
$139$	−11.9005	+	6.36096i	−1.00939	+	0.539530i	−0.891272	−	0.453470i	$-0.850186\pi$
$139$	−11.9005	+	6.36096i	−1.00939	+	0.539530i	−0.118118	+	0.993000i	$0.537686\pi$
$140$	−0.226100	−	0.195253i	−0.0191089	−	0.0165019i
$141$	−1.75386	−	0.172740i	−0.147701	−	0.0145473i
$142$	−10.9421	+	12.9969i	−0.918239	+	1.09068i
$143$	14.8065	−	6.13306i	1.23818	−	0.512872i
$144$	−3.95735	+	0.582555i	−0.329779	+	0.0485463i
$145$	6.96850	+	2.88645i	0.578703	+	0.239707i
$146$	−2.89723	+	1.50217i	−0.239776	+	0.124321i
$147$	5.39571	−	4.42815i	0.445031	−	0.365228i
$148$	3.55016	−	2.76742i	0.291822	−	0.227481i
$149$	−1.48330	−	0.449955i	−0.121517	−	0.0368618i	0.228940	−	0.973440i	$-0.426474\pi$
$149$	−1.48330	−	0.449955i	−0.121517	−	0.0368618i	−0.350457	+	0.936579i	$0.613974\pi$
$150$	5.09158	−	2.03454i	0.415726	−	0.166119i
$151$	0.244860	−	1.23100i	0.0199264	−	0.100177i	−0.969542	−	0.244924i	$-0.921237\pi$
$151$	0.244860	−	1.23100i	0.0199264	−	0.100177i	0.989469	+	0.144747i	$0.0462369\pi$
$152$	−0.854772	−	2.30541i	−0.0693312	−	0.186993i
$153$	7.38283	−	1.46854i	0.596867	−	0.118724i
$154$	0.508217	+	0.107737i	0.0409533	+	0.00868169i
$155$	−4.26164	−	3.49744i	−0.342304	−	0.280921i
$156$	0.308620	−	12.2953i	0.0247094	−	0.984409i
$157$	3.34032	−	6.24930i	0.266587	−	0.498748i	−0.712637	−	0.701533i	$-0.752499\pi$
$157$	3.34032	−	6.24930i	0.266587	−	0.498748i	0.979223	+	0.202785i	$0.0649992\pi$
$158$	18.1095	−	5.24624i	1.44071	−	0.417368i
$159$	−6.03452	+	6.03452i	−0.478569	+	0.478569i
$160$	5.38342	+	2.63669i	0.425596	+	0.208448i
$161$	0.949841	+	0.949841i	0.0748580	+	0.0748580i
$162$	1.23876	+	0.682253i	0.0973263	+	0.0536028i
$163$	−5.83421	−	3.11845i	−0.456970	−	0.244256i	0.226817	−	0.973937i	$-0.427168\pi$
$163$	−5.83421	−	3.11845i	−0.456970	−	0.244256i	−0.683787	+	0.729682i	$0.739668\pi$
$164$	13.0002	+	5.77116i	1.01514	+	0.450652i
$165$	1.75196	−	2.13477i	0.136390	−	0.166192i
$166$	−12.7131	+	8.26577i	−0.986726	+	0.641548i
$167$	−0.643466	−	3.23492i	−0.0497929	−	0.250326i	0.947870	−	0.318658i	$-0.103232\pi$
$167$	−0.643466	−	3.23492i	−0.0497929	−	0.250326i	−0.997663	+	0.0683322i	$0.978232\pi$
$168$	0.233818	−	0.322926i	0.0180394	−	0.0249143i
$169$	24.3404	+	4.84160i	1.87233	+	0.372431i
$170$	−10.3671	−	4.44738i	−0.795117	−	0.341099i
$171$	−0.252346	+	0.831873i	−0.0192974	+	0.0636149i
$172$	2.64927	−	4.67061i	0.202005	−	0.356130i
$173$	−15.8983	−	19.3722i	−1.20873	−	1.47284i	−0.839378	−	0.543548i	$-0.817080\pi$
$173$	−15.8983	−	19.3722i	−1.20873	−	1.47284i	−0.369350	−	0.929290i	$-0.620420\pi$
$174$	−3.04270	+	9.59533i	−0.230667	+	0.727420i
$175$	−0.209138	+	0.504903i	−0.0158093	+	0.0381671i
$176$	−10.4124	+	0.500013i	−0.784867	+	0.0376899i
$177$	4.12464	+	9.95777i	0.310027	+	0.748472i
$178$	8.90714	−	0.764562i	0.667619	−	0.0573063i
$179$	1.01765	−	10.3323i	0.0760625	−	0.772275i	−0.879188	−	0.476476i	$-0.841914\pi$
$179$	1.01765	−	10.3323i	0.0760625	−	0.772275i	0.955250	−	0.295800i	$-0.0955860\pi$
$180$	−0.951841	−	1.89358i	−0.0709460	−	0.141139i
$181$	−7.05716	−	13.2030i	−0.524555	−	0.981373i	−0.995088	−	0.0989907i	$-0.968439\pi$
$181$	−7.05716	−	13.2030i	−0.524555	−	0.981373i	0.470534	−	0.882382i	$-0.344061\pi$
$182$	0.855882	+	0.877635i	0.0634422	+	0.0650546i
$183$	−3.75183	−	5.61501i	−0.277343	−	0.415074i
$184$	−23.2763	−	13.5917i	−1.71595	−	1.00199i
$185$	1.98305	+	1.32503i	0.145797	+	0.0974184i
$186$	4.16408	−	6.06581i	0.305325	−	0.444767i
$187$	19.5230	−	1.92284i	1.42766	−	0.140612i
$188$	−2.03113	+	2.88061i	−0.148136	+	0.210090i
$189$	−0.134888	+	0.0409177i	−0.00981164	+	0.00297633i
$190$	1.01733	−	0.813754i	0.0738048	−	0.0590360i
$191$		−	8.64894i		−	0.625816i	−0.949784	−	0.312908i	$-0.898697\pi$
$191$		−	8.64894i		−	0.625816i	0.949784	−	0.312908i	$-0.101303\pi$
$192$	−2.89151	+	7.45917i	−0.208677	+	0.538319i
$193$		−	2.73991i		−	0.197223i	−0.995126	−	0.0986114i	$-0.968560\pi$
$193$		−	2.73991i		−	0.197223i	0.995126	−	0.0986114i	$-0.0314401\pi$
$194$	−15.6215	−	19.5295i	−1.12156	−	1.40213i
$195$	6.23596	−	1.89166i	0.446566	−	0.135464i
$196$	−2.37908	−	13.7560i	−0.169935	−	0.982575i
$197$	−1.33396	+	0.131383i	−0.0950406	+	0.00936068i	−0.145426	−	0.989369i	$-0.546455\pi$
$197$	−1.33396	+	0.131383i	−0.0950406	+	0.00936068i	0.0503850	+	0.998730i	$0.483955\pi$
$198$	3.03853	+	2.08590i	0.215939	+	0.148238i
$199$	7.18567	+	4.80131i	0.509378	+	0.340356i	0.783554	−	0.621324i	$-0.213405\pi$
$199$	7.18567	+	4.80131i	0.509378	+	0.340356i	−0.274175	+	0.961680i	$0.588405\pi$
$200$	1.48481	−	10.8651i	0.104992	−	0.768276i
$201$	−5.82701	−	8.72073i	−0.411005	−	0.615113i
$202$	4.34507	−	4.23737i	0.305718	−	0.298140i
$203$	−0.472960	−	0.884847i	−0.0331953	−	0.0621041i
$204$	4.73035	−	14.2925i	0.331191	−	1.00067i
$205$	−0.738677	+	7.49991i	−0.0515914	+	0.523817i
$206$	0.217698	+	2.53618i	0.0151677	+	0.176704i
$207$	3.64685	+	8.80428i	0.253474	+	0.611940i
$208$	−21.0847	−	12.6693i	−1.46196	−	0.878459i
$209$	−0.866971	+	2.09305i	−0.0599697	+	0.144780i
$210$	0.201359	+	0.0638513i	0.0138951	+	0.00440616i
$211$	−1.14765	−	1.39842i	−0.0790075	−	0.0962709i	0.732007	−	0.681298i	$-0.238584\pi$
$211$	−1.14765	−	1.39842i	−0.0790075	−	0.0962709i	−0.811014	+	0.585027i	$0.801084\pi$
$212$	4.54323	+	16.4524i	0.312030	+	1.12996i
$213$	3.48734	−	11.4962i	0.238949	−	0.787708i
$214$	1.63540	−	3.81220i	0.111794	−	0.260597i
$215$	2.79038	+	0.555042i	0.190303	+	0.0378535i
$216$	2.40922	−	1.48177i	0.163927	−	0.100822i
$217$	0.143068	+	0.719250i	0.00971207	+	0.0488259i
$218$	3.01737	+	4.64083i	0.204362	+	0.314317i
$219$	1.46395	−	1.78383i	0.0989249	−	0.120540i
$220$	−1.98495	−	5.15427i	−0.133826	−	0.347501i
$221$	40.8248	+	21.8213i	2.74617	+	1.46786i
$222$	−1.53553	+	2.78806i	−0.103058	+	0.187122i
$223$	−15.0544	−	15.0544i	−1.00812	−	1.00812i	−0.999967	−	0.00815115i	$-0.997405\pi$
$223$	−15.0544	−	15.0544i	−1.00812	−	1.00812i	−0.00815115	−	0.999967i	$-0.502595\pi$
$224$	−0.331050	−	0.725405i	−0.0221192	−	0.0484682i
$225$	−2.74151	+	2.74151i	−0.182768	+	0.182768i
$226$	3.14758	+	10.8651i	0.209374	+	0.722738i
$227$	2.12083	−	3.96780i	0.140765	−	0.263352i	−0.801654	−	0.597789i	$-0.796046\pi$
$227$	2.12083	−	3.96780i	0.140765	−	0.263352i	0.942418	+	0.334437i	$0.108546\pi$
$228$	1.19815	+	1.25984i	0.0793492	+	0.0834353i
$229$	−10.0026	−	8.20896i	−0.660993	−	0.542463i	0.242991	−	0.970029i	$-0.421871\pi$
$229$	−10.0026	−	8.20896i	−0.660993	−	0.542463i	−0.903984	+	0.427565i	$0.859371\pi$
$230$	2.96167	−	13.9708i	0.195287	−	0.921208i
$231$	−0.360292	+	0.0716665i	−0.0237054	+	0.00471531i
$232$	13.6899	+	14.7614i	0.898787	+	0.969135i
$233$	1.25420	−	6.30527i	0.0821651	−	0.413072i	−0.917710	−	0.397252i	$-0.869964\pi$
$233$	1.25420	−	6.30527i	0.0821651	−	0.413072i	0.999875	−	0.0158202i	$-0.00503594\pi$
$234$	3.22705	+	8.07593i	0.210959	+	0.527940i
$235$	−1.78710	−	0.542111i	−0.116578	−	0.0353634i
$236$	21.3929	+	2.65054i	1.39256	+	0.172535i
$237$	−10.3057	+	8.45763i	−0.669424	+	0.549382i
$238$	0.690696	+	1.33214i	0.0447712	+	0.0863499i
$239$	−18.6065	−	7.70705i	−1.20355	−	0.498528i	−0.311407	−	0.950277i	$-0.600800\pi$
$239$	−18.6065	−	7.70705i	−1.20355	−	0.498528i	−0.892145	+	0.451749i	$0.850800\pi$
$240$	−4.23337	−	0.212655i	−0.273263	−	0.0137268i
$241$	−5.13223	+	2.12584i	−0.330596	+	0.136937i	−0.541806	−	0.840503i	$-0.682259\pi$
$241$	−5.13223	+	2.12584i	−0.330596	+	0.136937i	0.211211	+	0.977441i	$0.432259\pi$
$242$	−4.55267	−	3.83288i	−0.292657	−	0.246387i
$243$	−0.995185	−	0.0980171i	−0.0638411	−	0.00628780i
$244$	−13.4702	+	0.986148i	−0.862340	+	0.0631317i
$245$	6.52329	−	3.48677i	0.416758	−	0.222762i
$246$	−10.0568	−	0.126197i	−0.641198	−	0.00804600i
$247$	−4.44491	+	2.97000i	−0.282823	+	0.188976i
$248$	−6.44334	−	13.2294i	−0.409152	−	0.840070i
$249$	5.95712	−	8.91546i	0.377517	−	0.564994i
$250$	13.0792	−	2.43142i	0.827201	−	0.153777i
$251$	−0.745501	−	7.56920i	−0.0470556	−	0.477764i	−0.989617	−	0.143730i	$-0.954090\pi$
$251$	−0.745501	−	7.56920i	−0.0470556	−	0.477764i	0.942561	−	0.334033i	$-0.108410\pi$
$252$	−0.0619196	+	0.275030i	−0.00390057	+	0.0173253i
$253$	7.20934	+	23.7660i	0.453247	+	1.49416i
$254$	−2.08544	+	18.7578i	−0.130852	+	1.17697i
$255$	7.97669			0.499520
$256$	10.1230	+	12.3905i	0.632686	+	0.774409i
$257$	−19.4962			−1.21614			−0.608068	−	0.793885i	$-0.708055\pi$
$257$	−19.4962			−1.21614			−0.608068	+	0.793885i	$0.708055\pi$
$258$	−0.419546	+	3.77367i	−0.0261198	+	0.234938i
$259$	−0.0920929	−	0.303589i	−0.00572237	−	0.0188641i
$260$	2.86259	−	12.7149i	0.177530	−	0.788542i
$261$	−0.697674	−	7.08361i	−0.0431850	−	0.438464i
$262$	−21.2494	+	3.95027i	−1.31279	+	0.244048i
$263$	−1.20983	+	1.81063i	−0.0746010	+	0.111648i	−0.866894	−	0.498492i	$-0.833887\pi$
$263$	−1.20983	+	1.81063i	−0.0746010	+	0.111648i	0.792293	+	0.610141i	$0.208887\pi$
$264$	6.62698	−	3.22764i	0.407862	−	0.198648i
$265$	−7.51931	+	5.02424i	−0.461907	+	0.308637i
$266$	−0.173277	−	0.00217434i	−0.0106243	−	0.000133318i
$267$	−5.57503	+	2.97992i	−0.341186	+	0.182368i
$268$	−20.9207	+	1.53160i	−1.27793	+	0.0935571i
$269$	9.15851	+	0.902035i	0.558404	+	0.0549980i	0.373283	−	0.927718i	$-0.378232\pi$
$269$	9.15851	+	0.902035i	0.558404	+	0.0549980i	0.185122	+	0.982716i	$0.440732\pi$
$270$	1.14642	+	0.965168i	0.0697689	+	0.0587383i
$271$	−19.9172	+	8.24997i	−1.20988	+	0.501150i	−0.894180	−	0.447708i	$-0.852241\pi$
$271$	−19.9172	+	8.24997i	−1.20988	+	0.501150i	−0.315704	+	0.948858i	$0.602241\pi$
$272$	−20.1959	−	22.3323i	−1.22456	−	1.35409i
$273$	−0.800843	−	0.331720i	−0.0484692	−	0.0200766i
$274$	7.09469	+	13.6835i	0.428606	+	0.826650i
$275$	−7.81058	+	6.40998i	−0.470996	+	0.386536i
$276$	18.9147	+	2.34351i	1.13853	+	0.141063i
$277$	−5.37601	−	1.63079i	−0.323013	−	0.0979850i	0.124614	−	0.992205i	$-0.460231\pi$
$277$	−5.37601	−	1.63079i	−0.323013	−	0.0979850i	−0.447627	+	0.894220i	$0.647731\pi$
$278$	−7.08103	−	17.7208i	−0.424692	−	1.06282i
$279$	−1.01497	+	5.10261i	−0.0607648	+	0.305485i
$280$	0.309769	−	0.287284i	0.0185123	−	0.0171685i
$281$	−2.68402	+	0.533885i	−0.160115	+	0.0318489i	−0.274497	−	0.961588i	$-0.588511\pi$
$281$	−2.68402	+	0.533885i	−0.160115	+	0.0318489i	0.114382	+	0.993437i	$0.463511\pi$
$282$	0.516863	−	2.43815i	0.0307787	−	0.145190i
$283$	−16.7485	−	13.7451i	−0.995595	−	0.817064i	−0.0124560	−	0.999922i	$-0.503965\pi$
$283$	−16.7485	−	13.7451i	−0.995595	−	0.817064i	−0.983139	+	0.182859i	$0.941465\pi$
$284$	−16.5580	−	17.4107i	−0.982537	−	1.03313i
$285$	−0.434242	+	0.812411i	−0.0257223	+	0.0481230i
$286$	6.30660	+	21.7697i	0.372917	+	1.28727i
$287$	0.708845	−	0.708845i	0.0418418	−	0.0418418i
$288$	−0.200415	−	5.65330i	−0.0118096	−	0.333124i
$289$	28.0459	+	28.0459i	1.64976	+	1.64976i
$290$	−5.14599	+	9.34355i	−0.302183	+	0.548672i
$291$	15.5957	+	8.33607i	0.914236	+	0.488669i
$292$	−1.65864	−	4.30695i	−0.0970648	−	0.252045i
$293$	0.185949	−	0.226579i	0.0108632	−	0.0132369i	−0.767551	−	0.640988i	$-0.778525\pi$
$293$	0.185949	−	0.226579i	0.0108632	−	0.0132369i	0.778414	+	0.627752i	$0.216025\pi$
$294$	5.38084	+	8.27593i	0.313817	+	0.482662i
$295$	2.22821	+	11.2020i	0.129731	+	0.652203i
$296$	3.33500	+	5.42240i	0.193843	+	0.315171i
$297$	−2.55603	−	0.508427i	−0.148316	−	0.0295019i
$298$	0.864226	−	2.01455i	0.0500633	−	0.116700i
$299$	−17.0117	+	56.0800i	−0.983811	+	3.24319i
$300$	2.06401	+	7.47442i	0.119166	+	0.431536i
$301$	−0.240084	−	0.292543i	−0.0138382	−	0.0168619i
$302$	1.69197	+	0.536526i	0.0973618	+	0.0308736i
$303$	−1.64231	+	3.96488i	−0.0943481	+	0.227776i
$304$	3.37394	−	0.841173i	0.193509	−	0.0482446i
$305$	−2.73853	−	6.61140i	−0.156808	−	0.378567i
$306$	0.910425	+	10.6065i	0.0520455	+	0.606330i
$307$	1.56090	−	15.8481i	0.0890852	−	0.904497i	−0.841947	−	0.539560i	$-0.818591\pi$
$307$	1.56090	−	15.8481i	0.0890852	−	0.904497i	0.931032	−	0.364937i	$-0.118909\pi$
$308$	−0.230847	+	0.697491i	−0.0131537	+	0.0397433i
$309$	−0.848487	−	1.58741i	−0.0482688	−	0.0903045i
$310$	5.58179	−	5.44344i	0.317024	−	0.309167i
$311$	−7.27811	−	10.8925i	−0.412703	−	0.617654i	0.565638	−	0.824654i	$-0.308630\pi$
$311$	−7.27811	−	10.8925i	−0.412703	−	0.617654i	−0.978341	+	0.207000i	$0.933630\pi$
$312$	17.2334	+	2.35511i	0.975651	+	0.133332i
$313$	17.0339	+	11.3817i	0.962811	+	0.643330i	0.934385	−	0.356266i	$-0.115950\pi$
$313$	17.0339	+	11.3817i	0.962811	+	0.643330i	0.0284266	+	0.999596i	$0.490950\pi$
$314$	8.26175	+	5.67155i	0.466237	+	0.320064i
$315$	−0.148650	+	0.0146407i	−0.00837547	+	0.000824912i
$316$	4.54398	+	26.2736i	0.255619	+	1.47801i
$317$	10.4002	−	3.15488i	0.584136	−	0.177196i	0.0156342	−	0.999878i	$-0.495023\pi$
$317$	10.4002	−	3.15488i	0.584136	−	0.177196i	0.568502	+	0.822682i	$0.307523\pi$
$318$	−7.53886	−	9.42483i	−0.422758	−	0.528518i
$319$		−	18.5500i		−	1.03860i
$320$	−4.54725	+	7.15466i	−0.254199	+	0.399958i
$321$			2.93321i			0.163716i
$322$	−1.48348	+	1.18663i	−0.0826711	+	0.0661281i
$323$	−6.26190	+	1.89953i	−0.348422	+	0.105693i
$324$	−1.15252	+	1.63453i	−0.0640288	+	0.0908074i
$325$	−23.7276	+	2.33696i	−1.31617	+	0.129631i
$326$	5.29483	−	7.71298i	0.293254	−	0.427183i
$327$	−3.25454	−	2.17461i	−0.179976	−	0.120256i
$328$	−10.1431	+	17.3706i	−0.560062	+	0.959130i
$329$	0.138012	+	0.206550i	0.00760885	+	0.0113875i
$330$	2.72677	+	2.79607i	0.150104	+	0.153919i
$331$	−8.16402	−	15.2738i	−0.448735	−	0.839525i	−0.999987	−	0.00518548i	$-0.998349\pi$
$331$	−8.16402	−	15.2738i	−0.448735	−	0.839525i	0.551251	−	0.834339i	$-0.314151\pi$
$332$	−9.63137	−	19.1606i	−0.528590	−	1.05157i
$333$	0.220606	−	2.23985i	0.0120891	−	0.122743i
$334$	4.64741	−	0.398920i	0.254295	−	0.0218279i
$335$	−4.25324	−	10.2682i	−0.232379	−	0.561013i
$336$	0.417352	+	0.379105i	0.0227684	+	0.0206819i
$337$	5.41421	−	13.0711i	0.294931	−	0.712027i	−0.705065	−	0.709143i	$-0.749082\pi$
$337$	5.41421	−	13.0711i	0.294931	−	0.712027i	0.999996	−	0.00288368i	$-0.000917906\pi$
$338$	−10.6087	+	33.4551i	−0.577036	+	1.81972i
$339$	−5.07432	−	6.18308i	−0.275599	−	0.335819i
$340$	7.87105	−	13.8765i	0.426868	−	0.752558i
$341$	−3.93582	+	12.9747i	−0.213137	+	0.702617i
$342$	−1.12981	−	0.484679i	−0.0610931	−	0.0262084i
$343$	−1.93274	−	0.384445i	−0.104358	−	0.0207581i
$344$	6.15080	+	4.45355i	0.331629	+	0.240119i
$345$	1.97010	+	9.90435i	0.106067	+	0.533232i
$346$	29.7130	−	19.3188i	1.59738	−	1.03858i
$347$	−10.5798	+	12.8915i	−0.567955	+	0.692055i	−0.975215	−	0.221257i	$-0.928984\pi$
$347$	−10.5798	+	12.8915i	−0.567955	+	0.692055i	0.407261	+	0.913312i	$0.366484\pi$
$348$	−13.0113	−	5.77610i	−0.697478	−	0.309631i
$349$	6.26290	+	3.34759i	0.335245	+	0.179192i	0.630427	−	0.776249i	$-0.282880\pi$
$349$	6.26290	+	3.34759i	0.335245	+	0.179192i	−0.295181	+	0.955441i	$0.595380\pi$
$350$	−0.676988	−	0.372853i	−0.0361865	−	0.0199298i
$351$	−4.34840	−	4.34840i	−0.232101	−	0.232101i
$352$	0.924310	−	14.7134i	0.0492659	−	0.784226i
$353$	−21.3140	+	21.3140i	−1.13443	+	1.13443i	−0.144999	+	0.989432i	$0.546318\pi$
$353$	−21.3140	+	21.3140i	−1.13443	+	1.13443i	−0.989432	+	0.144999i	$0.953682\pi$
$354$	−14.6407	+	4.24135i	−0.778145	+	0.225425i
$355$	6.00109	−	11.2273i	0.318505	−	0.595881i
$356$	−0.317247	+	12.6389i	−0.0168140	+	0.669863i
$357$	−0.820204	−	0.673124i	−0.0434098	−	0.0356255i
$358$	14.3636	+	3.04495i	0.759142	+	0.160930i
$359$	24.0195	−	4.77777i	1.26770	−	0.252161i	0.484974	−	0.874529i	$-0.338829\pi$
$359$	24.0195	−	4.77777i	1.26770	−	0.252161i	0.782725	+	0.622367i	$0.213829\pi$
$360$	2.81027	−	1.04196i	0.148114	−	0.0549162i
$361$	−3.55929	+	17.8937i	−0.187331	+	0.941776i
$362$	19.6603	−	7.85604i	1.03332	−	0.412904i
$363$	4.02699	+	1.22157i	0.211362	+	0.0641160i
$364$	−1.36731	+	1.06584i	−0.0716664	+	0.0558654i
$365$	1.89029	−	1.55132i	0.0989422	−	0.0811997i
$366$	8.47848	−	4.39597i	0.443177	−	0.229781i
$367$	−1.23284	−	0.510658i	−0.0643536	−	0.0266561i	0.350274	−	0.936647i	$-0.386088\pi$
$367$	−1.23284	−	0.510658i	−0.0643536	−	0.0266561i	−0.414628	+	0.909991i	$0.636088\pi$
$368$	22.7411	−	30.5922i	1.18546	−	1.59473i
$369$	6.57044	−	2.72157i	0.342043	−	0.141679i
$370$	−2.17229	+	2.58023i	−0.112932	+	0.134140i
$371$	1.19715	+	0.117909i	0.0621530	+	0.00612154i
$372$	7.87512	+	6.80071i	0.408306	+	0.352600i
$373$	3.02432	−	1.61654i	0.156594	−	0.0837010i	−0.391239	−	0.920289i	$-0.627953\pi$
$373$	3.02432	−	1.61654i	0.156594	−	0.0837010i	0.547832	+	0.836588i	$0.315453\pi$
$374$	−0.348105	+	27.7410i	−0.0180001	+	1.43445i
$375$	−7.82150	+	5.22616i	−0.403901	+	0.269878i
$376$	−3.73146	−	3.30501i	−0.192435	−	0.170443i
$377$	24.3184	−	36.3950i	1.25246	−	1.87444i
$378$	−0.0364338	−	0.195986i	−0.00187395	−	0.0100804i
$379$	0.312204	+	3.16986i	0.0160369	+	0.162825i	0.999868	−	0.0162762i	$-0.00518109\pi$
$379$	0.312204	+	3.16986i	0.0160369	+	0.162825i	−0.983831	+	0.179101i	$0.942681\pi$
$380$	0.984802	+	1.55707i	0.0505193	+	0.0798761i
$381$	−3.87398	−	12.7708i	−0.198470	−	0.654269i
$382$	12.1566	+	1.35153i	0.621983	+	0.0691504i
$383$	13.7153			0.700821			0.350410	−	0.936596i	$-0.386042\pi$
$383$	13.7153			0.700821			0.350410	+	0.936596i	$0.386042\pi$
$384$	−10.0324	−	5.22978i	−0.511965	−	0.266881i
$385$	−0.389272			−0.0198392
$386$	3.85109	+	0.428153i	0.196015	+	0.0217924i
$387$	−0.779364	−	2.56922i	−0.0396173	−	0.130601i
$388$	29.8908	−	18.9051i	1.51748	−	0.959759i
$389$	−0.794425	−	8.06593i	−0.0402790	−	0.408959i	−0.994091	−	0.108554i	$-0.965378\pi$
$389$	−0.794425	−	8.06593i	−0.0402790	−	0.408959i	0.953812	−	0.300405i	$-0.0971219\pi$
$390$	1.68436	+	9.06057i	0.0852909	+	0.458800i
$391$	−39.8535	+	59.6450i	−2.01548	+	3.01638i
$392$	19.7066	−	1.19433i	0.995335	−	0.0603229i
$393$	12.7074	−	8.49080i	0.641002	−	0.428304i
$394$	0.0237852	−	1.89548i	0.00119828	−	0.0954929i
$395$	−12.4593	+	6.65963i	−0.626895	+	0.335082i
$396$	−3.40666	+	3.94486i	−0.171191	+	0.198237i
$397$	15.7849	+	1.55468i	0.792223	+	0.0780272i	0.486030	−	0.873942i	$-0.338445\pi$
$397$	15.7849	+	1.55468i	0.792223	+	0.0780272i	0.306193	+	0.951969i	$0.400945\pi$
$398$	−7.87137	+	9.34956i	−0.394556	+	0.468651i
$399$	0.113207	−	0.0468921i	0.00566746	−	0.00234754i
$400$	15.0394	+	3.78482i	0.751970	+	0.189241i
$401$	9.54305	+	3.95286i	0.476557	+	0.197396i	0.608015	−	0.793925i	$-0.291966\pi$
$401$	9.54305	+	3.95286i	0.476557	+	0.197396i	−0.131458	+	0.991322i	$0.541966\pi$
$402$	13.1680	−	6.82742i	0.656761	−	0.340521i
$403$	−24.7314	+	20.2965i	−1.23196	+	1.01104i
$404$	5.27687	+	6.76938i	0.262534	+	0.336789i
$405$	−1.01405	−	0.307608i	−0.0503884	−	0.0152852i
$406$	1.31761	−	0.526500i	0.0653917	−	0.0261298i
$407$	1.14431	−	5.75282i	0.0567212	−	0.285157i
$408$	19.3497	+	8.88218i	0.957951	+	0.439733i
$409$	24.9033	−	4.95356i	1.23139	−	0.244938i	0.463833	−	0.885923i	$-0.346474\pi$
$409$	24.9033	−	4.95356i	1.23139	−	0.244938i	0.767554	+	0.640985i	$0.221474\pi$
$410$	−10.4261	−	2.21023i	−0.514908	−	0.109155i
$411$	−8.42497	−	6.91420i	−0.415573	−	0.341052i
$412$	−3.59875	−	0.0903313i	−0.177298	−	0.00445030i
$413$	0.716178	−	1.33987i	0.0352408	−	0.0659309i
$414$	−12.9448	+	3.75004i	−0.636201	+	0.184305i
$415$	8.03444	−	8.03444i	0.394395	−	0.394395i
$416$	21.1022	−	27.6559i	1.03462	−	1.35594i
$417$	9.54160	+	9.54160i	0.467254	+	0.467254i
$418$	−2.80642	−	1.54565i	−0.137267	−	0.0756000i
$419$	22.7138	+	12.1408i	1.10964	+	0.593115i	0.921247	−	0.388979i	$-0.127172\pi$
$419$	22.7138	+	12.1408i	1.10964	+	0.593115i	0.188393	+	0.982094i	$0.439672\pi$
$420$	−0.121212	+	0.273043i	−0.00591453	+	0.0133231i
$421$	−20.5197	+	25.0033i	−1.00007	+	1.21859i	−0.0243160	+	0.999704i	$0.507741\pi$
$421$	−20.5197	+	25.0033i	−1.00007	+	1.21859i	−0.975751	+	0.218881i	$0.929759\pi$
$422$	2.14489	−	1.39456i	0.104411	−	0.0678861i
$423$	0.343816	+	1.72848i	0.0167169	+	0.0840416i
$424$	−23.8347	+	3.81481i	−1.15752	+	0.185263i
$425$	−28.6239	−	5.69364i	−1.38846	−	0.276182i
$426$	15.6136	+	6.69811i	0.756482	+	0.324524i
$427$	−0.276322	+	0.910913i	−0.0133722	+	0.0440822i
$428$	5.10270	+	2.89436i	0.246648	+	0.139904i
$429$	−10.1671	−	12.3886i	−0.490871	−	0.598128i
$430$	−1.21618	+	3.83530i	−0.0586495	+	0.184955i
$431$	−3.55256	+	8.57663i	−0.171121	+	0.413122i	−0.986052	−	0.166435i	$-0.946774\pi$
$431$	−3.55256	+	8.57663i	−0.171121	+	0.413122i	0.814932	+	0.579557i	$0.196774\pi$
$432$	1.70623	+	3.61784i	0.0820910	+	0.174064i
$433$	−11.6714	−	28.1773i	−0.560892	−	1.35411i	−0.909054	−	0.416679i	$-0.863194\pi$
$433$	−11.6714	−	28.1773i	−0.560892	−	1.35411i	0.348162	−	0.937434i	$-0.386806\pi$
$434$	−1.03330	+	0.0886954i	−0.0496000	+	0.00425751i
$435$	0.739309	−	7.50633i	0.0354472	−	0.359901i
$436$	−6.99445	+	3.51588i	−0.334973	+	0.168380i
$437$	−3.90515	−	7.30602i	−0.186809	−	0.349494i
$438$	2.27851	+	2.33642i	0.108871	+	0.111638i
$439$	−9.89554	−	14.8097i	−0.472288	−	0.706829i	0.516478	−	0.856301i	$-0.327243\pi$
$439$	−9.89554	−	14.8097i	−0.472288	−	0.706829i	−0.988766	+	0.149471i	$0.952243\pi$
$440$	7.55478	−	1.98452i	0.360160	−	0.0946085i
$441$	−5.80377	−	3.87795i	−0.276370	−	0.184664i
$442$	−37.0505	+	53.9715i	−1.76231	+	2.56716i
$443$	17.1995	−	1.69400i	0.817173	−	0.0804846i	0.319212	−	0.947683i	$-0.396582\pi$
$443$	17.1995	−	1.69400i	0.817173	−	0.0804846i	0.497962	+	0.867199i	$0.334082\pi$
$444$	−3.67882	−	2.59395i	−0.174589	−	0.123104i
$445$	−6.41026	+	1.94453i	−0.303876	+	0.0921797i
$446$	23.5123	−	18.8073i	1.11334	−	0.890551i
$447$			1.55005i			0.0733148i
$448$	1.07133	−	0.351953i	0.0506155	−	0.0166282i
$449$			3.67205i			0.173295i	0.996239	+	0.0866474i	$0.0276154\pi$
$449$			3.67205i			0.173295i	−0.996239	+	0.0866474i	$0.972385\pi$
$450$	−3.42494	−	4.28175i	−0.161453	−	0.201844i
$451$	17.7360	−	5.38017i	0.835158	−	0.253342i
$452$	−15.7634	+	2.72625i	−0.741447	+	0.128232i
$453$	−1.24907	+	0.123022i	−0.0586864	+	0.00578010i
$454$	5.24554	+	3.60097i	0.246185	+	0.169002i
$455$	−0.763751	−	0.510322i	−0.0358052	−	0.0239243i
$456$	−1.95801	+	1.48719i	−0.0916921	+	0.0696441i
$457$	−22.6787	−	33.9411i	−1.06087	−	1.58770i	−0.777710	−	0.628624i	$-0.783619\pi$
$457$	−22.6787	−	33.9411i	−1.06087	−	1.58770i	−0.283156	−	0.959074i	$-0.591381\pi$
$458$	13.1012	−	12.7765i	0.612179	−	0.597006i
$459$	−3.54843	−	6.63864i	−0.165626	−	0.309865i
$460$	19.1739	+	6.34594i	0.893988	+	0.295881i
$461$	−1.72802	+	17.5449i	−0.0804819	+	0.817147i	0.867206	+	0.497949i	$0.165913\pi$
$461$	−1.72802	+	17.5449i	−0.0804819	+	0.817147i	−0.947688	+	0.319198i	$0.896587\pi$
$462$	−0.0444299	−	0.517608i	−0.00206707	−	0.0240813i
$463$	−4.21001	−	10.1639i	−0.195656	−	0.472355i	0.795354	−	0.606145i	$-0.207285\pi$
$463$	−4.21001	−	10.1639i	−0.195656	−	0.472355i	−0.991010	+	0.133791i	$0.957285\pi$
$464$	−22.8872	+	16.9352i	−1.06251	+	0.786198i
$465$	−2.10975	+	5.09339i	−0.0978374	+	0.236200i
$466$	8.66640	+	2.74813i	0.401463	+	0.127305i
$467$	0.515456	+	0.628085i	0.0238525	+	0.0290643i	0.784800	−	0.619749i	$-0.212766\pi$
$467$	0.515456	+	0.628085i	0.0238525	+	0.0290643i	−0.760948	+	0.648813i	$0.775266\pi$
$468$	−11.8554	+	3.27380i	−0.548017	+	0.151331i
$469$	−0.429159	+	1.41475i	−0.0198167	+	0.0653269i
$470$	1.04123	−	2.42715i	0.0480283	−	0.111956i
$471$	−6.94985	−	1.38241i	−0.320232	−	0.0636981i
$472$	−7.06844	+	29.6546i	−0.325351	+	1.36496i
$473$	−1.36504	−	6.86251i	−0.0627645	−	0.315539i
$474$	−10.2772	−	15.8068i	−0.472049	−	0.726030i
$475$	2.13814	−	2.60533i	0.0981046	−	0.119541i
$476$	−1.98033	+	0.762642i	−0.0907682	+	0.0349556i
$477$	7.52641	+	4.02295i	0.344611	+	0.184198i
$478$	13.7402	−	24.9480i	0.628463	−	1.14110i
$479$	27.8639	+	27.8639i	1.27313	+	1.27313i	0.944435	+	0.328698i	$0.106610\pi$
$479$	27.8639	+	27.8639i	1.27313	+	1.27313i	0.328698	+	0.944435i	$0.393390\pi$
$480$	0.960428	−	5.91700i	0.0438373	−	0.270073i
$481$	9.78688	−	9.78688i	0.446243	−	0.446243i
$482$	−2.18599	−	7.54582i	−0.0995691	−	0.343703i
$483$	0.633217	−	1.18467i	0.0288124	−	0.0539042i
$484$	6.09874	−	5.80007i	0.277215	−	0.263640i
$485$	14.4855	+	11.8879i	0.657753	+	0.539804i
$486$	0.293281	−	1.38347i	0.0133035	−	0.0627554i
$487$	14.8136	−	2.94660i	0.671267	−	0.133523i	0.152322	−	0.988331i	$-0.451325\pi$
$487$	14.8136	−	2.94660i	0.671267	−	0.133523i	0.518945	+	0.854808i	$0.326325\pi$
$488$	0.718842	−	19.0872i	0.0325404	−	0.864036i
$489$	−1.29059	+	6.48822i	−0.0583624	+	0.293408i
$490$	3.88148	+	9.71370i	0.175347	+	0.438820i
$491$	1.06533	+	0.323166i	0.0480779	+	0.0145843i	0.314232	−	0.949346i	$-0.398253\pi$
$491$	1.06533	+	0.323166i	0.0480779	+	0.0145843i	−0.266154	+	0.963930i	$0.585753\pi$
$492$	1.74891	−	14.1157i	0.0788468	−	0.636383i
$493$	41.4176	−	33.9906i	1.86536	−	1.53086i
$494$	−3.47990	−	6.71167i	−0.156568	−	0.301972i
$495$	−2.55142	−	1.05683i	−0.114678	−	0.0475011i
$496$	19.6015	−	6.98915i	0.880135	−	0.313822i
$497$	−1.56449	+	0.648033i	−0.0701770	+	0.0290683i
$498$	11.6003	+	9.76623i	0.519820	+	0.437635i
$499$	−28.1704	−	2.77454i	−1.26108	−	0.124206i	−0.554707	−	0.832046i	$-0.687170\pi$
$499$	−28.1704	−	2.77454i	−1.26108	−	0.124206i	−0.706373	+	0.707840i	$0.749670\pi$
$500$	1.37367	+	18.7635i	0.0614323	+	0.839128i
$501$	−2.90884	+	1.55481i	−0.129957	+	0.0694637i
$502$	10.7554	+	0.134963i	0.480037	+	0.00602370i
$503$	−31.0230	+	20.7289i	−1.38325	+	0.924255i	−0.383246	+	0.923646i	$0.625194\pi$
$503$	−31.0230	+	20.7289i	−1.38325	+	0.924255i	−1.00000		0.000609030i	$0.999806\pi$
$504$	−0.376894	−	0.130009i	−0.0167882	−	0.00579106i
$505$	−2.52655	+	3.78124i	−0.112430	+	0.168263i
$506$	−34.5310	+	6.41931i	−1.53509	+	0.285373i
$507$	−2.43251	−	24.6977i	−0.108032	−	1.09686i
$508$	−26.0392	−	5.86238i	−1.15530	−	0.260101i
$509$	10.6325	+	35.0508i	0.471279	+	1.55360i	0.794493	+	0.607273i	$0.207737\pi$
$509$	10.6325	+	35.0508i	0.471279	+	1.55360i	−0.323214	+	0.946326i	$0.604763\pi$
$510$	−1.24648	+	11.2117i	−0.0551951	+	0.496461i
$511$	−0.325279			−0.0143895
$512$	−18.9974	+	12.2922i	−0.839576	+	0.543242i
$513$	0.869305			0.0383808
$514$	3.04658	−	27.4029i	0.134379	−	1.20869i
$515$	−0.553677	−	1.82523i	−0.0243979	−	0.0804291i
$516$	−5.23853	−	1.17939i	−0.230614	−	0.0519197i
$517$	0.450179	+	4.57075i	0.0197989	+	0.201021i
$518$	0.441102	−	0.0820009i	0.0193809	−	0.00360291i
$519$	−13.9230	+	20.8372i	−0.611151	+	0.914651i
$520$	17.4241	+	6.01041i	0.764097	+	0.263574i
$521$	−27.4576	+	18.3466i	−1.20294	+	0.803778i	−0.985062	−	0.172198i	$-0.944913\pi$
$521$	−27.4576	+	18.3466i	−1.20294	+	0.803778i	−0.217877	+	0.975976i	$0.569913\pi$
$522$	10.0654	+	0.126305i	0.440551	+	0.00552820i
$523$	21.0658	−	11.2599i	0.921143	−	0.492361i	0.0585639	−	0.998284i	$-0.481348\pi$
$523$	21.0658	−	11.2599i	0.921143	−	0.492361i	0.862579	+	0.505923i	$0.168848\pi$
$524$	−2.23176	−	30.4845i	−0.0974949	−	1.33172i
$525$	0.543872	+	0.0535667i	0.0237365	+	0.00233784i
$526$	−2.35589	−	1.98341i	−0.102721	−	0.0864809i
$527$	−36.1812	+	14.9867i	−1.57608	+	0.652833i
$528$	3.50105	+	9.81894i	0.152364	+	0.427314i
$529$	−62.6528	−	25.9517i	−2.72404	−	1.12833i
$530$	−5.88683	−	11.3539i	−0.255708	−	0.493182i
$531$	8.33167	−	6.83763i	0.361564	−	0.296728i
$532$	0.0301334	−	0.243210i	0.00130645	−	0.0105445i
$533$	41.8513	+	12.6954i	1.81278	+	0.549901i
$534$	−3.31725	−	8.30166i	−0.143551	−	0.359248i
$535$	−0.606390	+	3.04853i	−0.0262165	+	0.131799i
$536$	1.11644	−	29.6445i	0.0482228	−	1.28045i
$537$	−10.1828	+	2.02549i	−0.439422	+	0.0874065i
$538$	−2.69902	+	12.7318i	−0.116363	+	0.548908i
$539$	−14.0618	−	11.5402i	−0.605686	−	0.497073i
$540$	−1.53574	+	1.46053i	−0.0660878	+	0.0628513i
$541$	−3.77752	+	7.06724i	−0.162408	+	0.303844i	−0.949942	−	0.312428i	$-0.898858\pi$
$541$	−3.77752	+	7.06724i	−0.162408	+	0.303844i	0.787533	+	0.616272i	$0.211358\pi$
$542$	−8.48341	−	29.2839i	−0.364394	−	1.25785i
$543$	−10.5859	+	10.5859i	−0.454285	+	0.454285i
$544$	34.5451	−	24.8967i	1.48111	−	1.06744i
$545$	−2.93293	−	2.93293i	−0.125633	−	0.125633i
$546$	0.591395	−	1.07379i	0.0253094	−	0.0459540i
$547$	−6.03126	−	3.22378i	−0.257878	−	0.137839i	0.337392	−	0.941364i	$-0.390455\pi$
$547$	−6.03126	−	3.22378i	−0.257878	−	0.137839i	−0.595270	+	0.803525i	$0.702955\pi$
$548$	−20.3415	+	7.83371i	−0.868947	+	0.334639i
$549$	−4.28413	+	5.22023i	−0.182842	+	0.222794i
$550$	−7.78905	−	11.9799i	−0.332126	−	0.510823i
$551$	1.20714	+	6.06872i	0.0514260	+	0.258536i
$552$	−6.24965	+	26.2195i	−0.266003	+	1.11598i
$553$	1.84311	+	0.366618i	0.0783771	+	0.0155902i
$554$	3.13225	−	7.30143i	0.133077	−	0.310208i
$555$	0.692328	−	2.28230i	0.0293877	−	0.0968782i
$556$	26.0141	−	7.18362i	1.10324	−	0.304653i
$557$	18.7207	+	22.8113i	0.793224	+	0.966546i	0.999930	−	0.0118573i	$-0.00377438\pi$
$557$	18.7207	+	22.8113i	0.793224	+	0.966546i	−0.206706	+	0.978403i	$0.566274\pi$
$558$	−7.01339	−	2.22396i	−0.296900	−	0.0941477i
$559$	6.31831	−	15.2537i	0.267236	−	0.645165i
$560$	0.355387	+	0.480290i	0.0150178	+	0.0202960i
$561$	−7.50726	−	18.1241i	−0.316957	−	0.765201i
$562$	−0.330984	−	3.85596i	−0.0139617	−	0.162654i
$563$	−0.467006	+	4.74159i	−0.0196820	+	0.199834i	0.980315	+	0.197439i	$0.0632625\pi$
$563$	−0.467006	+	4.74159i	−0.0196820	+	0.199834i	−0.999997	+	0.00239533i	$0.999238\pi$
$564$	3.34618	+	1.10748i	0.140900	+	0.0466332i
$565$	−3.99558	−	7.47520i	−0.168095	−	0.314484i
$566$	21.9367	−	21.3930i	0.922070	−	0.899216i
$567$	0.0783117	+	0.117202i	0.00328878	+	0.00492201i
$568$	27.0591	−	20.5525i	1.13537	−	0.862363i
$569$	−20.9944	−	14.0280i	−0.880129	−	0.588083i	0.0313141	−	0.999510i	$-0.490031\pi$
$569$	−20.9944	−	14.0280i	−0.880129	−	0.588083i	−0.911443	+	0.411426i	$0.865031\pi$
$570$	−1.07403	−	0.737303i	−0.0449861	−	0.0308822i
$571$	6.87489	−	0.677118i	0.287705	−	0.0283365i	0.0468649	−	0.998901i	$-0.485077\pi$
$571$	6.87489	−	0.677118i	0.287705	−	0.0283365i	0.240840	+	0.970565i	$0.422577\pi$
$572$	−31.5840	+	5.46240i	−1.32059	+	0.228394i
$573$	−8.27652	+	2.51066i	−0.345757	+	0.104884i
$574$	0.885552	+	1.10709i	0.0369622	+	0.0462090i
$575$		−	36.9474i		−	1.54081i
$576$	7.97734	+	0.601722i	0.332389	+	0.0250718i
$577$		−	10.3866i		−	0.432399i	−0.976349	−	0.216199i	$-0.930634\pi$
$577$		−	10.3866i		−	0.432399i	0.976349	−	0.216199i	$-0.0693661\pi$
$578$	−43.8026	+	35.0374i	−1.82195	+	1.45736i
$579$	−2.62193	+	0.795353i	−0.108964	+	0.0330537i
$580$	−12.3287	−	8.69305i	−0.511922	−	0.360959i
$581$	−1.50414	+	0.148145i	−0.0624023	+	0.00614609i
$582$	−14.1539	+	20.6179i	−0.586696	+	0.854641i
$583$	18.4926	+	12.3563i	0.765884	+	0.511747i
$584$	6.31284	−	1.65829i	0.261227	−	0.0686203i
$585$	−3.62041	−	5.41832i	−0.149685	−	0.224020i
$586$	0.289412	+	0.296767i	0.0119555	+	0.0122593i
$587$	−0.883677	−	1.65324i	−0.0364732	−	0.0682366i	0.863024	−	0.505162i	$-0.168567\pi$
$587$	−0.883677	−	1.65324i	−0.0364732	−	0.0682366i	−0.899498	+	0.436926i	$0.856067\pi$
$588$	−12.4731	+	6.26981i	−0.514382	+	0.258563i
$589$	0.443295	−	4.50085i	0.0182656	−	0.185454i
$590$	−16.0932	+	1.38139i	−0.662545	+	0.0568708i
$591$	0.512954	+	1.23838i	0.0211001	+	0.0509401i
$592$	−8.14262	+	3.84018i	−0.334659	+	0.157830i
$593$	12.2578	−	29.5931i	0.503369	−	1.21524i	−0.444268	−	0.895894i	$-0.646536\pi$
$593$	12.2578	−	29.5931i	0.503369	−	1.21524i	0.947638	−	0.319348i	$-0.103464\pi$
$594$	1.11404	−	3.51319i	0.0457097	−	0.144148i
$595$	−0.713294	−	0.869151i	−0.0292422	−	0.0356317i
$596$	2.69651	+	1.52952i	0.110453	+	0.0626516i
$597$	2.50868	−	8.27000i	0.102673	−	0.338469i
$598$	−76.1651	−	32.6742i	−3.11462	−	1.33615i
$599$	28.3569	+	5.64054i	1.15863	+	0.230466i	0.736737	−	0.676179i	$-0.236365\pi$
$599$	28.3569	+	5.64054i	1.15863	+	0.230466i	0.421894	+	0.906645i	$0.361365\pi$
$600$	−10.8282	+	1.73309i	−0.442061	+	0.0707529i
$601$	2.94440	+	14.8025i	0.120105	+	0.603807i	0.993216	+	0.116286i	$0.0370989\pi$
$601$	2.94440	+	14.8025i	0.120105	+	0.603807i	−0.873111	+	0.487521i	$0.837901\pi$
$602$	0.448701	−	0.291736i	0.0182877	−	0.0118903i
$603$	−6.65373	+	8.10759i	−0.270961	+	0.330167i
$604$	−1.01851	+	2.29431i	−0.0414427	+	0.0933541i
$605$	3.93277	+	2.10211i	0.159890	+	0.0854629i
$606$	−5.31622	−	2.92792i	−0.215957	−	0.118939i
$607$	−1.59552	−	1.59552i	−0.0647603	−	0.0647603i	0.673985	−	0.738745i	$-0.264581\pi$
$607$	−1.59552	−	1.59552i	−0.0647603	−	0.0647603i	−0.738745	+	0.673985i	$0.764581\pi$
$608$	0.655083	+	4.87370i	0.0265671	+	0.197655i
$609$	−0.709452	+	0.709452i	−0.0287485	+	0.0287485i
$610$	9.72061	−	2.81602i	0.393576	−	0.114017i
$611$	−5.10884	+	9.55796i	−0.206681	+	0.386674i
$612$	−15.0502	−	0.377771i	−0.608368	−	0.0152705i
$613$	18.8336	+	15.4563i	0.760682	+	0.624276i	0.932632	−	0.360830i	$-0.117507\pi$
$613$	18.8336	+	15.4563i	0.760682	+	0.624276i	−0.171950	+	0.985106i	$0.555007\pi$
$614$	22.0314	+	4.67043i	0.889115	+	0.188483i
$615$	7.39140	−	1.47024i	0.298050	−	0.0592858i
$616$	−0.944288	−	0.433462i	−0.0380465	−	0.0174647i
$617$	−9.39486	+	47.2312i	−0.378223	+	1.90146i	0.0518387	+	0.998655i	$0.483492\pi$
$617$	−9.39486	+	47.2312i	−0.378223	+	1.90146i	−0.430062	+	0.902800i	$0.641508\pi$
$618$	2.36378	−	0.944537i	0.0950850	−	0.0379949i
$619$	22.1572	+	6.72131i	0.890573	+	0.270152i	0.702229	−	0.711951i	$-0.252188\pi$
$619$	22.1572	+	6.72131i	0.890573	+	0.270152i	0.188344	+	0.982103i	$0.439688\pi$
$620$	6.77881	+	8.69613i	0.272243	+	0.349245i
$621$	7.36655	−	6.04557i	0.295609	−	0.242600i
$622$	16.4472	−	8.52765i	0.659474	−	0.341928i
$623$	0.823228	+	0.340992i	0.0329819	+	0.0136616i
$624$	−6.00322	+	23.8545i	−0.240321	+	0.954944i
$625$	8.70037	−	3.60381i	0.348015	−	0.144152i
$626$	−18.6594	+	22.1635i	−0.745778	+	0.885830i
$627$	2.25460	+	0.222058i	0.0900399	+	0.00886815i
$628$	−9.26269	+	10.7261i	−0.369622	+	0.428016i
$629$	14.9415	−	7.98638i	0.595755	−	0.318438i
$630$	0.00265051	−	0.211223i	0.000105599	−	0.00841534i
$631$	−12.2990	+	8.21795i	−0.489617	+	0.327152i	−0.775752	−	0.631038i	$-0.782629\pi$
$631$	−12.2990	+	8.21795i	−0.489617	+	0.327152i	0.286135	+	0.958189i	$0.407629\pi$
$632$	−37.6391	+	2.28114i	−1.49720	+	0.0907389i
$633$	−1.00506	+	1.50417i	−0.0399474	+	0.0597854i
$634$	2.80915	+	15.1111i	0.111566	+	0.600138i
$635$	−1.38615	−	14.0738i	−0.0550076	−	0.558501i
$636$	14.4252	−	9.12349i	0.571995	−	0.361770i
$637$	−12.4604	−	41.0765i	−0.493700	−	1.62751i
$638$	26.0730	+	2.89872i	1.03224	+	0.114762i
$639$	−12.0135			−0.475247
$640$	−9.34568	−	7.50942i	−0.369420	−	0.296836i
$641$	12.6929			0.501339			0.250669	−	0.968073i	$-0.419349\pi$
$641$	12.6929			0.501339			0.250669	+	0.968073i	$0.419349\pi$
$642$	−4.12278	−	0.458359i	−0.162713	−	0.0180900i
$643$	3.02364	+	9.96762i	0.119241	+	0.393085i	0.996160	−	0.0875539i	$-0.0279050\pi$
$643$	3.02364	+	9.96762i	0.119241	+	0.393085i	−0.876919	+	0.480638i	$0.840405\pi$
$644$	−1.43605	−	2.27054i	−0.0565883	−	0.0894718i
$645$	−0.278864	−	2.83135i	−0.0109802	−	0.111484i
$646$	−1.69137	−	9.09827i	−0.0665460	−	0.357967i
$647$	15.6543	−	23.4284i	0.615436	−	0.921065i	−0.384562	−	0.923099i	$-0.625648\pi$
$647$	15.6543	−	23.4284i	0.615436	−	0.921065i	0.999998	+	0.00203450i	$0.000647602\pi$
$648$	−2.11733	−	1.87535i	−0.0831764	−	0.0736706i
$649$	23.3553	−	15.6055i	0.916777	−	0.612570i
$650$	0.423076	−	33.7156i	0.0165944	−	1.32243i
$651$	0.646749	−	0.345694i	0.0253481	−	0.0135488i
$652$	10.0136	+	8.64744i	0.392163	+	0.338660i
$653$	−28.3692	−	2.79412i	−1.11017	−	0.109342i	−0.473733	−	0.880669i	$-0.657094\pi$
$653$	−28.3692	−	2.79412i	−1.11017	−	0.109342i	−0.636440	+	0.771326i	$0.719594\pi$
$654$	3.56510	−	4.23461i	0.139407	−	0.165586i
$655$	14.9623	−	6.19759i	0.584625	−	0.242160i
$656$	−22.8303	−	16.9712i	−0.891372	−	0.662613i
$657$	−2.13199	−	0.883098i	−0.0831767	−	0.0344529i
$658$	−0.311883	+	0.161707i	−0.0121585	+	0.00630399i
$659$	36.4723	−	29.9320i	1.42076	−	1.16599i	0.460231	−	0.887799i	$-0.347766\pi$
$659$	36.4723	−	29.9320i	1.42076	−	1.16599i	0.960527	−	0.278187i	$-0.0897336\pi$
$660$	−4.35612	+	3.39569i	−0.169562	+	0.132177i
$661$	−7.69719	−	2.33492i	−0.299386	−	0.0908178i	0.137018	−	0.990569i	$-0.456248\pi$
$661$	−7.69719	−	2.33492i	−0.299386	−	0.0908178i	−0.436404	+	0.899751i	$0.643748\pi$
$662$	22.7439	−	9.08820i	0.883968	−	0.353223i
$663$	9.03087	−	45.4012i	0.350730	−	1.76324i
$664$	28.4362	−	10.5433i	1.10354	−	0.409158i
$665$	0.127352	−	0.0253320i	0.00493851	−	0.000982332i
$666$	3.11375	+	0.660084i	0.120655	+	0.0255777i
$667$	52.4342	+	43.0316i	2.03026	+	1.66619i
$668$	−0.165527	+	6.59452i	−0.00640444	+	0.255150i
$669$	−10.0361	+	18.7762i	−0.388018	+	0.725931i
$670$	15.0972	−	4.37358i	0.583255	−	0.168966i
$671$	−12.4446	+	12.4446i	−0.480420	+	0.480420i
$672$	−0.598070	+	0.527369i	−0.0230711	+	0.0203437i
$673$	−19.3932	−	19.3932i	−0.747551	−	0.747551i	0.226468	−	0.974019i	$-0.427282\pi$
$673$	−19.3932	−	19.3932i	−0.747551	−	0.747551i	−0.974019	+	0.226468i	$0.927282\pi$
$674$	17.5260	+	9.65253i	0.675078	+	0.371801i
$675$	3.41928	+	1.82765i	0.131608	+	0.0703461i
$676$	−45.3652	−	20.1389i	−1.74481	−	0.774575i
$677$	8.90415	−	10.8497i	0.342214	−	0.416989i	−0.573255	−	0.819377i	$-0.694320\pi$
$677$	8.90415	−	10.8497i	0.342214	−	0.416989i	0.915469	+	0.402388i	$0.131820\pi$
$678$	9.48359	−	6.16603i	0.364215	−	0.236805i
$679$	−0.486293	−	2.44476i	−0.0186622	−	0.0938213i
$680$	18.2742	+	13.2316i	0.700782	+	0.507409i
$681$	−4.41259	−	0.877719i	−0.169091	−	0.0336343i
$682$	−17.6215	−	7.55950i	−0.674764	−	0.289468i
$683$	−0.906663	+	2.98887i	−0.0346925	+	0.114366i	−0.972577	−	0.232583i	$-0.925282\pi$
$683$	−0.906663	+	2.98887i	−0.0346925	+	0.114366i	0.937884	+	0.346949i	$0.112782\pi$
$684$	0.857792	−	1.51227i	0.0327985	−	0.0578231i
$685$	−7.32681	−	8.92775i	−0.279943	−	0.341112i
$686$	0.842378	−	2.65649i	0.0321622	−	0.101425i
$687$	−4.95187	+	11.9549i	−0.188926	+	0.456107i
$688$	−7.22086	+	7.94934i	−0.275293	+	0.303066i
$689$	20.0836	+	48.4862i	0.765126	+	1.84718i
$690$	−14.2290	+	1.22137i	−0.541687	+	0.0464968i
$691$	3.86155	−	39.2070i	0.146900	−	1.49150i	−0.585523	−	0.810655i	$-0.699111\pi$
$691$	3.86155	−	39.2070i	0.146900	−	1.49150i	0.732424	−	0.680849i	$-0.238389\pi$
$692$	22.5104	+	44.7821i	0.855718	+	1.70236i
$693$	0.173168	+	0.323974i	0.00657810	+	0.0123068i
$694$	−16.4665	−	16.8850i	−0.625060	−	0.640946i
$695$	7.94417	+	11.8893i	0.301340	+	0.450987i
$696$	10.1518	−	17.3855i	0.384804	−	0.658994i
$697$	44.5117	+	29.7418i	1.68600	+	1.12655i
$698$	−5.68389	+	8.27973i	−0.215139	+	0.313392i
$699$	−6.39784	+	0.630132i	−0.241988	+	0.0238338i
$700$	0.629855	−	0.893278i	0.0238063	−	0.0337627i
$701$	−26.1772	+	7.94077i	−0.988699	+	0.299919i	−0.742900	−	0.669402i	$-0.766550\pi$
$701$	−26.1772	+	7.94077i	−0.988699	+	0.299919i	−0.245799	+	0.969321i	$0.579050\pi$
$702$	6.79142	−	5.43241i	0.256326	−	0.205033i
$703$			1.95653i			0.0737919i
$704$	20.5360	+	3.59836i	0.773980	+	0.135618i
$705$			1.86751i			0.0703347i
$706$	−26.6273	−	33.2886i	−1.00213	−	1.25283i
$707$	0.578878	−	0.175601i	0.0217709	−	0.00660414i
$708$	−3.67361	−	21.2411i	−0.138063	−	0.798289i
$709$	−30.5152	+	3.00549i	−1.14602	+	0.112873i	−0.653151	−	0.757228i	$-0.726553\pi$
$709$	−30.5152	+	3.00549i	−1.14602	+	0.112873i	−0.492873	+	0.870101i	$0.664053\pi$
$710$	14.8427	+	10.1893i	0.557038	+	0.382397i
$711$	11.0850	+	7.40678i	0.415721	+	0.277776i
$712$	−17.7151	−	2.42094i	−0.663903	−	0.0907285i
$713$	−27.5446	−	41.2234i	−1.03155	−	1.54383i
$714$	1.07428	−	1.04765i	0.0402040	−	0.0392075i
$715$	−8.00567	−	14.9775i	−0.299395	−	0.560129i
$716$	−6.52438	+	19.7130i	−0.243827	+	0.736711i
$717$	−1.97402	+	20.0425i	−0.0737210	+	0.748501i
$718$	2.96200	+	34.5073i	0.110541	+	1.28780i
$719$	−2.83397	−	6.84181i	−0.105689	−	0.255156i	0.862184	−	0.506595i	$-0.169096\pi$
$719$	−2.83397	−	6.84181i	−0.105689	−	0.255156i	−0.967873	+	0.251439i	$0.919096\pi$
$720$	1.02538	+	4.11281i	0.0382138	+	0.153275i
$721$	−0.0970925	+	0.234402i	−0.00361592	+	0.00872959i
$722$	−24.5944	−	7.79895i	−0.915310	−	0.290247i
$723$	3.52411	+	4.29414i	0.131063	+	0.159701i
$724$	7.96985	+	28.8613i	0.296197	+	1.07262i
$725$	−8.01088	+	26.4083i	−0.297517	+	0.980781i
$726$	−2.34627	+	5.46926i	−0.0870781	+	0.202983i
$727$	7.31693	+	1.45543i	0.271370	+	0.0539789i	0.328899	−	0.944365i	$-0.393322\pi$
$727$	7.31693	+	1.45543i	0.271370	+	0.0539789i	−0.0575294	+	0.998344i	$0.518322\pi$
$728$	−1.28444	−	2.08838i	−0.0476044	−	0.0774005i
$729$	0.195090	+	0.980785i	0.00722557	+	0.0363254i
$730$	1.88508	+	2.89932i	0.0697698	+	0.107309i
$731$	12.8211	−	15.6225i	0.474204	−	0.577820i
$732$	4.85387	+	12.6039i	0.179404	+	0.465854i
$733$	31.0973	+	16.6219i	1.14861	+	0.613942i	0.932051	−	0.362328i	$-0.118018\pi$
$733$	31.0973	+	16.6219i	1.14861	+	0.613942i	0.216555	+	0.976270i	$0.430518\pi$
$734$	0.910408	−	1.65302i	0.0336038	−	0.0610141i
$735$	−5.23025	−	5.23025i	−0.192921	−	0.192921i
$736$	39.4453	+	36.7443i	1.45397	+	1.35441i
$737$	−19.3279	+	19.3279i	−0.711952	+	0.711952i
$738$	2.79857	+	9.66039i	0.103017	+	0.355604i
$739$	17.2427	−	32.2588i	0.634283	−	1.18666i	−0.335349	−	0.942094i	$-0.608854\pi$
$739$	17.2427	−	32.2588i	0.634283	−	1.18666i	0.969633	−	0.244566i	$-0.0786456\pi$
$740$	−3.28720	−	3.45647i	−0.120840	−	0.127062i
$741$	4.13240	+	3.39137i	0.151808	+	0.124585i
$742$	−0.352801	+	1.66424i	−0.0129517	+	0.0610960i
$743$	−11.4017	+	2.26794i	−0.418288	+	0.0832026i	−0.399747	−	0.916626i	$-0.630902\pi$
$743$	−11.4017	+	2.26794i	−0.418288	+	0.0832026i	−0.0185407	+	0.999828i	$0.505902\pi$
$744$	−10.7894	+	10.0062i	−0.395558	+	0.366845i
$745$	−0.320446	+	1.61099i	−0.0117402	+	0.0590221i
$746$	1.79953	+	4.50346i	0.0658854	+	0.164883i
$747$	−10.2608	−	3.11259i	−0.375424	−	0.113884i
$748$	−38.9371	−	4.82425i	−1.42368	−	0.176392i
$749$	0.319607	−	0.262294i	0.0116782	−	0.00958403i
$750$	−6.12342	−	11.8102i	−0.223596	−	0.431248i
$751$	36.8545	+	15.2656i	1.34484	+	0.557051i	0.934852	−	0.355039i	$-0.115532\pi$
$751$	36.8545	+	15.2656i	1.34484	+	0.557051i	0.409990	+	0.912090i	$0.365532\pi$
$752$	5.22846	−	4.72830i	0.190662	−	0.172423i
$753$	−7.02686	+	2.91062i	−0.256073	+	0.106069i
$754$	47.3550	+	39.8681i	1.72457	+	1.45191i
$755$	−1.32361	−	0.130364i	−0.0481711	−	0.00474444i
$756$	0.281162	−	0.0205838i	0.0102258	−	0.000748625i
$757$	26.4216	−	14.1226i	0.960309	−	0.513296i	0.0847473	−	0.996402i	$-0.472992\pi$
$757$	26.4216	−	14.1226i	0.960309	−	0.513296i	0.875561	+	0.483107i	$0.160492\pi$
$758$	−4.50420	−	0.0565204i	−0.163600	−	0.00205291i
$759$	20.6499	−	13.7978i	0.749544	−	0.500829i
$760$	−2.34244	+	1.14088i	−0.0849692	+	0.0413839i
$761$	18.1829	−	27.2126i	0.659128	−	0.986455i	−0.339815	−	0.940492i	$-0.610365\pi$
$761$	18.1829	−	27.2126i	0.659128	−	0.986455i	0.998943	−	0.0459623i	$-0.0146354\pi$
$762$	18.5554	−	3.44945i	0.672192	−	0.124961i
$763$	0.0540794	+	0.549078i	0.00195781	+	0.0198779i
$764$	−3.79930	+	16.8755i	−0.137454	+	0.610534i
$765$	−2.31551	−	7.63321i	−0.0837175	−	0.275979i
$766$	−2.14323	+	19.2776i	−0.0774382	+	0.696529i
$767$	66.2814			2.39328
$768$	8.91846	−	13.2839i	0.321817	−	0.479340i
$769$	−1.43086			−0.0515983			−0.0257992	−	0.999667i	$-0.508213\pi$
$769$	−1.43086			−0.0515983			−0.0257992	+	0.999667i	$0.508213\pi$
$770$	0.0608299	−	0.547143i	0.00219216	−	0.0197177i
$771$	5.65943	+	18.6567i	0.203820	+	0.671903i
$772$	−1.20358	+	5.34600i	−0.0433179	+	0.192407i
$773$	0.278167	+	2.82428i	0.0100050	+	0.101582i	0.998890	−	0.0470983i	$-0.0149974\pi$
$773$	0.278167	+	2.82428i	0.0100050	+	0.101582i	−0.988885	+	0.148681i	$0.952497\pi$
$774$	3.73296	−	0.693958i	0.134179	−	0.0249438i
$775$	11.2063	−	16.7714i	0.402543	−	0.602448i
$776$	21.9012	+	44.9674i	0.786206	+	1.61423i
$777$	−0.263784	+	0.176255i	−0.00946319	+	0.00632310i
$778$	11.4612	+	0.143820i	0.410905	+	0.00515620i
$779$	−5.45232	+	2.91432i	−0.195350	+	0.104417i
$780$	−12.9983	+	0.951604i	−0.465415	+	0.0340729i
$781$	−31.1578	−	3.06877i	−1.11491	−	0.109809i
$782$	−77.6065	−	65.3367i	−2.77520	−	2.33644i
$783$	−6.57606	+	2.72389i	−0.235009	+	0.0973441i
$784$	−1.40077	+	27.8854i	−0.0500274	+	0.995906i
$785$	−6.93730	−	2.87352i	−0.247603	−	0.102560i
$786$	9.94855	+	19.1877i	0.354853	+	0.684403i
$787$	26.0830	−	21.4057i	0.929757	−	0.763032i	−0.0419751	−	0.999119i	$-0.513365\pi$
$787$	26.0830	−	21.4057i	0.929757	−	0.763032i	0.971732	+	0.236087i	$0.0758650\pi$
$788$	2.66048	+	0.329630i	0.0947758	+	0.0117426i
$789$	2.08386	+	0.632132i	0.0741874	+	0.0225045i
$790$	−7.41351	−	18.5529i	−0.263761	−	0.660082i
$791$	−0.219959	+	1.10581i	−0.00782086	+	0.0393181i
$792$	−5.01237	−	5.40469i	−0.178107	−	0.192047i
$793$	−40.7308	+	8.10186i	−1.44639	+	0.287706i
$794$	−4.65183	+	21.9436i	−0.165087	+	0.778750i
$795$	6.99064	+	5.73707i	0.247932	+	0.203473i
$796$	−11.9113	−	12.5246i	−0.422184	−	0.443924i
$797$	−8.80199	+	16.4674i	−0.311783	+	0.583304i	−0.988192	−	0.153222i	$-0.951035\pi$
$797$	−8.80199	+	16.4674i	−0.311783	+	0.583304i	0.676409	+	0.736526i	$0.263535\pi$
$798$	0.0482189	+	0.166447i	0.00170693	+	0.00589215i
$799$	−9.38047	+	9.38047i	−0.331857	+	0.331857i
$800$	−7.66990	+	20.5473i	−0.271172	+	0.726455i
$801$	4.46995	+	4.46995i	0.157938	+	0.157938i
$802$	−7.04720	+	12.7956i	−0.248845	+	0.451827i
$803$	−5.30385	−	2.83497i	−0.187169	−	0.100044i
$804$	7.53860	+	19.5752i	0.265866	+	0.690365i
$805$	0.903022	−	1.10034i	0.0318273	−	0.0387817i
$806$	−24.6632	−	37.9329i	−0.868724	−	1.33613i
$807$	−1.79538	−	9.02600i	−0.0632004	−	0.317730i
$808$	−10.3393	+	6.35910i	−0.363736	+	0.223712i
$809$	2.82797	+	0.562518i	0.0994262	+	0.0197771i	0.244553	−	0.969636i	$-0.421359\pi$
$809$	2.82797	+	0.562518i	0.0994262	+	0.0197771i	−0.145126	+	0.989413i	$0.546359\pi$
$810$	0.590820	−	1.37723i	0.0207593	−	0.0483909i
$811$	−10.2495	+	33.7881i	−0.359909	+	1.18646i	0.570920	+	0.821006i	$0.306587\pi$
$811$	−10.2495	+	33.7881i	−0.359909	+	1.18646i	−0.930829	+	0.365455i	$0.880913\pi$
$812$	0.534128	+	1.93424i	0.0187442	+	0.0678785i
$813$	13.6764	+	16.6647i	0.479652	+	0.584458i
$814$	7.90709	+	2.50735i	0.277143	+	0.0878827i
$815$	−2.68266	+	6.47651i	−0.0939694	+	0.226862i
$816$	−15.5081	+	25.8090i	−0.542891	+	0.903496i
$817$	0.893158	+	2.15627i	0.0312476	+	0.0754385i
$818$	3.07098	+	35.7769i	0.107374	+	1.25091i
$819$	−0.0849639	+	0.862653i	−0.00296888	+	0.0301435i
$820$	4.73583	−	14.3091i	0.165382	−	0.499694i
$821$	−9.00869	−	16.8541i	−0.314405	−	0.588211i	0.674234	−	0.738518i	$-0.264474\pi$
$821$	−9.00869	−	16.8541i	−0.314405	−	0.588211i	−0.988639	+	0.150307i	$0.951974\pi$
$822$	11.0348	−	10.7613i	0.384883	−	0.375343i
$823$	18.5427	+	27.7511i	0.646357	+	0.967342i	0.999495	+	0.0317708i	$0.0101147\pi$
$823$	18.5427	+	27.7511i	0.646357	+	0.967342i	−0.353138	+	0.935571i	$0.614885\pi$
$824$	0.689326	−	5.04412i	0.0240138	−	0.175720i
$825$	8.40126	+	5.61354i	0.292494	+	0.195438i
$826$	1.77135	+	1.21600i	0.0616332	+	0.0423101i
$827$	49.0219	−	4.82824i	1.70466	−	0.167894i	0.801730	−	0.597686i	$-0.203913\pi$
$827$	49.0219	−	4.82824i	1.70466	−	0.167894i	0.902928	+	0.429791i	$0.141413\pi$
$828$	−3.24806	−	18.7806i	−0.112878	−	0.652670i
$829$	44.5469	−	13.5132i	1.54718	−	0.469331i	0.602717	−	0.797955i	$-0.294085\pi$
$829$	44.5469	−	13.5132i	1.54718	−	0.469331i	0.944461	+	0.328623i	$0.106585\pi$
$830$	10.0373	+	12.5483i	0.348401	+	0.435559i
$831$			5.61792i			0.194883i
$832$	35.5743	+	33.9820i	1.23332	+	1.17811i
$833$		−	52.5427i		−	1.82050i
$834$	−14.9023	+	11.9202i	−0.516023	+	0.412763i
$835$	−3.34463	+	1.01458i	−0.115746	+	0.0351111i
$836$	2.61104	−	3.70304i	0.0903046	−	0.128072i
$837$	5.17752	−	0.509942i	0.178961	−	0.0176262i
$838$	−20.6139	+	30.0282i	−0.712094	+	1.03731i
$839$	−27.7993	−	18.5749i	−0.959739	−	0.641277i	−0.0261637	−	0.999658i	$-0.508329\pi$
$839$	−27.7993	−	18.5749i	−0.959739	−	0.641277i	−0.933576	+	0.358380i	$0.883329\pi$
$840$	−0.364835	−	0.213037i	−0.0125880	−	0.00735047i
$841$	−12.0360	−	18.0131i	−0.415034	−	0.621143i
$842$	−31.9369	−	32.7486i	−1.10062	−	1.12859i
$843$	1.29003	+	2.41347i	0.0444308	+	0.0831243i
$844$	1.62496	+	3.23267i	0.0559333	+	0.111273i
$845$	2.57768	−	26.1716i	0.0886748	−	0.900330i
$846$	−2.48320	+	0.213150i	−0.0853741	+	0.00732825i
$847$	−0.226998	−	0.548022i	−0.00779975	−	0.0188303i
$848$	−1.63737	−	34.0971i	−0.0562275	−	1.17090i
$849$	−8.29145	+	20.0173i	−0.284562	+	0.686993i
$850$	12.4756	−	39.3427i	0.427911	−	1.34944i
$851$	13.6067	+	16.5798i	0.466430	+	0.568347i
$852$	−11.8544	+	20.8991i	−0.406126	+	0.715991i
$853$	−1.42366	+	4.69319i	−0.0487453	+	0.160692i	−0.977934	−	0.208914i	$-0.933007\pi$
$853$	−1.42366	+	4.69319i	−0.0487453	+	0.160692i	0.929189	+	0.369606i	$0.120507\pi$
$854$	−1.23716	−	0.530730i	−0.0423346	−	0.0181612i
$855$	0.903482	+	0.179714i	0.0308984	+	0.00614608i
$856$	−4.86556	+	6.71982i	−0.166301	+	0.229679i
$857$	1.52493	+	7.66633i	0.0520905	+	0.261877i	0.998051	−	0.0624055i	$-0.0198772\pi$
$857$	1.52493	+	7.66633i	0.0520905	+	0.261877i	−0.945960	+	0.324282i	$0.894877\pi$
$858$	19.0016	−	12.3545i	0.648705	−	0.421774i
$859$	35.3231	−	43.0414i	1.20521	−	1.46855i	0.360978	−	0.932574i	$-0.382443\pi$
$859$	35.3231	−	43.0414i	1.20521	−	1.46855i	0.844232	−	0.535978i	$-0.180057\pi$
$860$	−5.20067	−	2.30873i	−0.177341	−	0.0787272i
$861$	−0.884090	−	0.472556i	−0.0301297	−	0.0161047i
$862$	−11.4998	−	6.33354i	−0.391684	−	0.215721i
$863$	−3.88293	−	3.88293i	−0.132176	−	0.132176i	0.637923	−	0.770100i	$-0.279794\pi$
$863$	−3.88293	−	3.88293i	−0.132176	−	0.132176i	−0.770100	+	0.637923i	$0.779794\pi$
$864$	−5.35170	+	1.83285i	−0.182068	+	0.0623549i
$865$	−18.7781	+	18.7781i	−0.638474	+	0.638474i
$866$	41.4285	−	12.0017i	1.40780	−	0.407833i
$867$	18.6969	−	34.9795i	0.634981	−	1.18797i
$868$	0.0368032	−	1.46622i	0.00124918	−	0.0497667i
$869$	26.8577	+	22.0415i	0.911084	+	0.747707i
$870$	10.4350	+	2.21212i	0.353781	+	0.0749979i
$871$	−63.2594	+	12.5831i	−2.14346	+	0.426361i
$872$	−3.84876	−	10.3805i	−0.130335	−	0.351528i
$873$	3.44993	−	17.3440i	0.116763	−	0.587005i
$874$	10.8792	−	4.34722i	0.367996	−	0.147047i
$875$	1.26887	+	0.384907i	0.0428955	+	0.0130122i
$876$	−3.64001	+	2.83746i	−0.122985	+	0.0958690i
$877$	−24.4715	+	20.0832i	−0.826344	+	0.678163i	−0.949342	−	0.314244i	$-0.898249\pi$
$877$	−24.4715	+	20.0832i	−0.826344	+	0.678163i	0.122998	+	0.992407i	$0.460749\pi$
$878$	22.3622	−	11.5945i	0.754687	−	0.391294i
$879$	−0.270801	−	0.112169i	−0.00913388	−	0.00378338i
$880$	1.60880	+	10.9288i	0.0542328	+	0.368408i
$881$	−0.00798067	+	0.00330570i	−0.000268876	+	0.000111372i	−0.382818	−	0.923824i	$-0.625046\pi$
$881$	−0.00798067	+	0.00330570i	−0.000268876	+	0.000111372i	0.382549	+	0.923935i	$0.375046\pi$
$882$	6.35760	−	7.55152i	0.214072	−	0.254273i
$883$	−31.3035	−	3.08312i	−1.05345	−	0.103755i	−0.443560	−	0.896245i	$-0.646285\pi$
$883$	−31.3035	−	3.08312i	−1.05345	−	0.103755i	−0.609886	+	0.792490i	$0.708785\pi$
$884$	−70.0701	−	60.5103i	−2.35671	−	2.03518i
$885$	10.0728	−	5.38402i	0.338593	−	0.180982i
$886$	−0.306677	+	24.4395i	−0.0103030	+	0.821063i
$887$	5.36587	−	3.58536i	0.180168	−	0.120385i	−0.462216	−	0.886768i	$-0.652945\pi$
$887$	5.36587	−	3.58536i	0.180168	−	0.120385i	0.642384	+	0.766383i	$0.277945\pi$
$888$	4.22081	−	4.76543i	0.141641	−	0.159917i
$889$	−1.04511	+	1.56411i	−0.0350517	+	0.0524586i
$890$	−1.73144	−	9.31383i	−0.0580380	−	0.312200i
$891$	0.255443	+	2.59356i	0.00855768	+	0.0868876i
$892$	22.7605	+	35.9867i	0.762078	+	1.20492i
$893$	−0.444720	−	1.46605i	−0.0148820	−	0.0490594i
$894$	−2.17868	−	0.242219i	−0.0728658	−	0.00810102i
$895$	−11.0019			−0.367754
$896$	0.327277	+	1.56081i	0.0109336	+	0.0521429i
$897$	58.6035			1.95671
$898$	−5.16127	−	0.573815i	−0.172234	−	0.0191485i
$899$	10.7496	+	35.4368i	0.358520	+	1.18188i
$900$	6.55343	−	4.14485i	0.218448	−	0.138162i
$901$	6.29664	+	63.9309i	0.209772	+	2.12985i
$902$	4.79058	+	25.7697i	0.159509	+	0.858037i
$903$	−0.210253	+	0.314666i	−0.00699679	+	0.0104714i
$904$	−1.36862	−	22.5823i	−0.0455195	−	0.751076i
$905$	−13.1906	+	8.81365i	−0.438469	+	0.292976i
$906$	0.0222716	−	1.77486i	0.000739924	−	0.0589657i
$907$	−11.3608	+	6.07249i	−0.377230	+	0.201634i	−0.649105	−	0.760699i	$-0.724856\pi$
$907$	−11.3608	+	6.07249i	−0.377230	+	0.201634i	0.271875	+	0.962333i	$0.412356\pi$
$908$	−5.88106	+	6.81018i	−0.195170	+	0.226004i
$909$	4.27089	+	0.420646i	0.141656	+	0.0139519i
$910$	0.836634	−	0.993748i	0.0277341	−	0.0329424i
$911$	−42.3843	+	17.5562i	−1.40425	+	0.581661i	−0.950852	−	0.309645i	$-0.899790\pi$
$911$	−42.3843	+	17.5562i	−1.40425	+	0.581661i	−0.453402	+	0.891306i	$0.649790\pi$
$912$	−1.78436	−	2.98448i	−0.0590859	−	0.0988261i
$913$	−25.8170	−	10.6937i	−0.854417	−	0.353911i
$914$	51.2499	−	26.5723i	1.69520	−	0.878935i
$915$	−5.53176	+	4.53980i	−0.182874	+	0.150081i
$916$	15.9108	+	20.4110i	0.525706	+	0.674397i
$917$	−2.06149	−	0.625347i	−0.0680765	−	0.0206508i
$918$	9.88546	−	3.95011i	0.326269	−	0.130373i
$919$	−6.60131	+	33.1870i	−0.217757	+	1.09474i	0.704956	+	0.709251i	$0.250967\pi$
$919$	−6.60131	+	33.1870i	−0.217757	+	1.09474i	−0.922713	+	0.385488i	$0.874033\pi$
$920$	−11.9158	+	25.9583i	−0.392852	+	0.855820i
$921$	−15.6188	+	3.10677i	−0.514656	+	0.102371i
$922$	−24.3902	−	5.17049i	−0.803250	−	0.170281i
$923$	−57.1084	−	46.8677i	−1.87975	−	1.54267i
$924$	0.734469	+	0.0184357i	0.0241623	+	0.000606490i
$925$	−4.11345	+	7.69572i	−0.135249	+	0.253034i
$926$	14.9437	−	4.32913i	0.491082	−	0.142264i
$927$	−1.27275	+	1.27275i	−0.0418027	+	0.0418027i
$928$	−20.2269	−	34.8156i	−0.663980	−	1.14288i
$929$	9.41012	+	9.41012i	0.308736	+	0.308736i	0.844419	−	0.535683i	$-0.179946\pi$
$929$	9.41012	+	9.41012i	0.308736	+	0.308736i	−0.535683	+	0.844419i	$0.679946\pi$
$930$	−6.82936	−	3.76129i	−0.223943	−	0.123338i
$931$	5.35138	+	2.86037i	0.175384	+	0.0937449i
$932$	−5.21691	+	11.7517i	−0.170886	+	0.384938i
$933$	−8.31071	+	10.1266i	−0.272080	+	0.331531i
$934$	−0.963356	+	0.626353i	−0.0315220	+	0.0204949i
$935$	−4.05556	−	20.3887i	−0.132631	−	0.666781i
$936$	−2.74890	−	17.1750i	−0.0898507	−	0.561383i
$937$	−15.5236	−	3.08783i	−0.507134	−	0.100875i	−0.0651091	−	0.997878i	$-0.520740\pi$
$937$	−15.5236	−	3.08783i	−0.507134	−	0.100875i	−0.442024	+	0.897003i	$0.645740\pi$
$938$	−1.92144	−	0.824282i	−0.0627372	−	0.0269138i
$939$	5.94691	−	19.6043i	0.194070	−	0.639763i
$940$	3.24878	+	1.84278i	0.105964	+	0.0601049i
$941$	−6.53028	−	7.95717i	−0.212881	−	0.259396i	0.655612	−	0.755098i	$-0.272411\pi$
$941$	−6.53028	−	7.95717i	−0.212881	−	0.259396i	−0.868493	+	0.495702i	$0.834911\pi$
$942$	3.02907	−	9.55236i	0.0986926	−	0.311233i
$943$	−25.9357	+	62.6142i	−0.844581	+	2.03900i
$944$	−40.5766	−	14.5691i	−1.32066	−	0.474183i
$945$	0.0571611	+	0.137999i	0.00185945	+	0.00448911i
$946$	9.85894	−	0.846261i	0.320542	−	0.0275143i
$947$	0.299245	−	3.03828i	0.00972415	−	0.0987309i	−0.989098	−	0.147262i	$-0.952954\pi$
$947$	0.299245	−	3.03828i	0.00972415	−	0.0987309i	0.998822	+	0.0485310i	$0.0154540\pi$
$948$	23.8233	−	11.9752i	0.773744	−	0.388935i
$949$	−6.68960	−	12.5154i	−0.217154	−	0.406266i
$950$	3.32782	+	3.41239i	0.107969	+	0.110713i
$951$	−6.03806	−	9.03660i	−0.195798	−	0.293032i
$952$	−0.762477	−	2.90263i	−0.0247120	−	0.0940749i
$953$	9.01545	+	6.02393i	0.292039	+	0.195134i	0.692956	−	0.720980i	$-0.256308\pi$
$953$	9.01545	+	6.02393i	0.292039	+	0.195134i	−0.400916	+	0.916115i	$0.631308\pi$
$954$	−6.83059	+	9.95012i	−0.221148	+	0.322147i
$955$	−9.12095	+	0.898335i	−0.295147	+	0.0290695i
$956$	32.9187	+	23.2111i	1.06467	+	0.750702i
$957$	−17.7512	+	5.38477i	−0.573816	+	0.174065i
$958$	−43.5183	+	34.8100i	−1.40601	+	1.12466i
$959$			1.53628i			0.0496091i
$960$	8.16658	+	2.27456i	0.263575	+	0.0734110i
$961$			3.93320i			0.126878i
$962$	12.2266	+	15.2853i	0.394202	+	0.492819i
$963$	2.80691	−	0.851465i	0.0904513	−	0.0274381i
$964$	10.9476	−	1.89338i	0.352600	−	0.0609815i
$965$	−2.88943	+	0.284585i	−0.0930142	+	0.00916110i
$966$	1.56616	+	1.07514i	0.0503904	+	0.0345922i
$967$	35.5700	+	23.7671i	1.14385	+	0.764299i	0.975189	−	0.221375i	$-0.0710544\pi$
$967$	35.5700	+	23.7671i	1.14385	+	0.764299i	0.168665	+	0.985673i	$0.446054\pi$
$968$	7.19929	+	9.47846i	0.231394	+	0.304649i
$969$	3.63547	+	5.44086i	0.116788	+	0.174786i
$970$	−18.9727	+	18.5025i	−0.609178	+	0.594079i
$971$	18.2104	+	34.0692i	0.584399	+	1.09333i	0.984255	+	0.176756i	$0.0565603\pi$
$971$	18.2104	+	34.0692i	0.584399	+	1.09333i	−0.399855	+	0.916578i	$0.630940\pi$
$972$	1.89871	+	0.628411i	0.0609011	+	0.0201563i
$973$	0.186434	−	1.89290i	0.00597681	−	0.0606836i
$974$	1.82676	+	21.2817i	0.0585331	+	0.681910i
$975$	9.12409	+	22.0275i	0.292205	+	0.705445i
$976$	26.7157	+	3.99304i	0.855149	+	0.127814i
$977$	6.70098	−	16.1776i	0.214383	−	0.517567i	−0.779704	−	0.626148i	$-0.784631\pi$
$977$	6.70098	−	16.1776i	0.214383	−	0.517567i	0.994088	+	0.108581i	$0.0346306\pi$
$978$	−8.91787	−	2.82788i	−0.285162	−	0.0904255i
$979$	10.4513	+	12.7349i	0.334024	+	0.407009i
$980$	−14.2597	+	3.93771i	−0.455508	+	0.125786i
$981$	−1.13623	+	3.74565i	−0.0362771	+	0.119589i
$982$	−0.620702	+	1.44689i	−0.0198074	+	0.0461720i
$983$	−27.2129	−	5.41299i	−0.867958	−	0.172648i	−0.259026	−	0.965870i	$-0.583402\pi$
$983$	−27.2129	−	5.41299i	−0.867958	−	0.172648i	−0.608932	+	0.793223i	$0.708402\pi$
$984$	19.5670	+	4.66397i	0.623774	+	0.148682i
$985$	0.277107	+	1.39311i	0.00882937	+	0.0443882i
$986$	41.3034	+	63.5262i	1.31537	+	2.02309i
$987$	0.157593	−	0.192027i	0.00501624	−	0.00611230i
$988$	9.97741	−	3.84239i	0.317424	−	0.122243i
$989$	22.5645	+	12.0610i	0.717508	+	0.383516i
$990$	1.88413	−	3.42101i	0.0598817	−	0.108727i
$991$	17.7481	+	17.7481i	0.563789	+	0.563789i	0.930381	−	0.366593i	$-0.119476\pi$
$991$	17.7481	+	17.7481i	0.563789	+	0.563789i	−0.366593	+	0.930381i	$0.619476\pi$
$992$	6.76059	+	28.6432i	0.214649	+	0.909422i
$993$	−12.2462	+	12.2462i	−0.388623	+	0.388623i
$994$	−0.666370	−	2.30024i	−0.0211360	−	0.0729592i
$995$	4.31699	−	8.07652i	0.136858	−	0.256043i
$996$	−15.5397	+	14.7787i	−0.492393	+	0.468280i
$997$	−26.7385	−	21.9437i	−0.846817	−	0.694965i	0.107356	−	0.994221i	$-0.465762\pi$
$997$	−26.7385	−	21.9437i	−0.846817	−	0.694965i	−0.954173	+	0.299256i	$0.903262\pi$
$998$	8.30183	−	39.1614i	0.262790	−	1.23963i
$999$	−2.20744	+	0.439087i	−0.0698402	+	0.0138921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.13.17	✓	512
128.69	even	32	inner	384.2.v.a.325.17	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.13.17	✓	512	1.1	even	1	trivial
384.2.v.a.325.17	yes	512	128.69	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)

\(f(q)\)	\(=\)	\(q+(-0.156266 + 1.40555i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.95116 - 0.439279i) q^{4} +(-0.103867 - 1.05457i) q^{5} +(1.39039 - 0.258474i) q^{6} +(-0.0783117 + 0.117202i) q^{7} +(0.922330 - 2.67382i) q^{8} +(-0.831470 + 0.555570i) q^{9} +O(q^{10})\)	\(q+(-0.156266 + 1.40555i) q^{2} +(-0.290285 - 0.956940i) q^{3} +(-1.95116 - 0.439279i) q^{4} +(-0.103867 - 1.05457i) q^{5} +(1.39039 - 0.258474i) q^{6} +(-0.0783117 + 0.117202i) q^{7} +(0.922330 - 2.67382i) q^{8} +(-0.831470 + 0.555570i) q^{9} +(1.49849 + 0.0188036i) q^{10} +(-2.29838 + 1.22851i) q^{11} +(0.146029 + 1.99466i) q^{12} +(-6.11996 - 0.602763i) q^{13} +(-0.152496 - 0.128386i) q^{14} +(-0.979014 + 0.405521i) q^{15} +(3.61407 + 1.71421i) q^{16} +(-6.95448 - 2.88064i) q^{17} +(-0.650954 - 1.25549i) q^{18} +(0.671982 - 0.551481i) q^{19} +(-0.260592 + 2.10327i) q^{20} +(0.134888 + 0.0409177i) q^{21} +(-1.36758 - 3.42248i) q^{22} +(1.85915 - 9.34658i) q^{23} +(-2.82642 - 0.106446i) q^{24} +(3.80259 - 0.756382i) q^{25} +(1.80355 - 8.50774i) q^{26} +(0.773010 + 0.634393i) q^{27} +(0.204283 - 0.194279i) q^{28} +(-3.35535 + 6.27741i) q^{29} +(-0.416995 - 1.43943i) q^{30} +(3.67878 - 3.67878i) q^{31} +(-2.97417 + 4.81189i) q^{32} +(1.84280 + 1.84280i) q^{33} +(5.13564 - 9.32475i) q^{34} +(0.131732 + 0.0704121i) q^{35} +(1.86638 - 0.718760i) q^{36} +(-1.42782 + 1.73980i) q^{37} +(0.670129 + 1.03068i) q^{38} +(1.19972 + 6.03141i) q^{39} +(-2.91554 - 0.694945i) q^{40} +(-6.97514 - 1.38744i) q^{41} +(-0.0785904 + 0.183198i) q^{42} +(-0.779364 + 2.56922i) q^{43} +(5.02418 - 1.38739i) q^{44} +(0.672252 + 0.819141i) q^{45} +(12.8466 + 4.07368i) q^{46} +(0.674420 - 1.62819i) q^{47} +(0.591288 - 3.95606i) q^{48} +(2.67118 + 6.44880i) q^{49} +(0.468922 + 5.46294i) q^{50} +(-0.737821 + 7.49122i) q^{51} +(11.6762 + 3.86446i) q^{52} +(-4.02295 - 7.52641i) q^{53} +(-1.01247 + 0.987374i) q^{54} +(1.53428 + 2.29622i) q^{55} +(0.241147 + 0.317490i) q^{56} +(-0.722801 - 0.482960i) q^{57} +(-8.29891 - 5.69706i) q^{58} +(-10.7263 + 1.05645i) q^{59} +(2.08835 - 0.361177i) q^{60} +(6.46233 - 1.96033i) q^{61} +(4.59585 + 5.74558i) q^{62} -0.140957i q^{63} +(-6.29862 - 4.93229i) q^{64} +6.51656i q^{65} +(-2.87812 + 2.30219i) q^{66} +(10.0367 - 3.04460i) q^{67} +(12.3039 + 8.67555i) q^{68} +(-9.48380 + 0.934073i) q^{69} +(-0.119553 + 0.174153i) q^{70} +(9.98888 + 6.67435i) q^{71} +(0.718605 + 2.73562i) q^{72} +(1.28206 + 1.91874i) q^{73} +(-2.22227 - 2.27875i) q^{74} +(-1.82765 - 3.41928i) q^{75} +(-1.55340 + 0.780842i) q^{76} +(0.0360066 - 0.365581i) q^{77} +(-8.66494 + 0.743772i) q^{78} +(-5.10188 - 12.3170i) q^{79} +(1.43238 - 3.98935i) q^{80} +(0.382683 - 0.923880i) q^{81} +(3.04010 - 9.58713i) q^{82} +(6.80230 + 8.28863i) q^{83} +(-0.245213 - 0.139090i) q^{84} +(-2.31551 + 7.63321i) q^{85} +(-3.48939 - 1.49692i) q^{86} +(6.98111 + 1.38863i) q^{87} +(1.16495 + 7.27856i) q^{88} +(-1.23326 - 6.20000i) q^{89} +(-1.25640 + 0.816883i) q^{90} +(0.549909 - 0.670066i) q^{91} +(-7.73326 + 17.4200i) q^{92} +(-4.58826 - 2.45248i) q^{93} +(2.18312 + 1.20236i) q^{94} +(-0.651374 - 0.651374i) q^{95} +(5.46805 + 1.44928i) q^{96} +(-12.5043 + 12.5043i) q^{97} +(-9.48155 + 2.74676i) q^{98} +(1.22851 - 2.29838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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