LMFDB - Embedded newform 384.2.v.a.85.29

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			85.29
Character	$\chi$	$=$	384.85
Dual form			384.2.v.a.253.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23624 + 0.686806i) q^{2} +(0.634393 - 0.773010i) q^{3} +(1.05659 + 1.69812i) q^{4} +(-1.57885 + 0.478940i) q^{5} +(1.31517 - 0.519924i) q^{6} +(1.01743 + 0.202379i) q^{7} +(0.139929 + 2.82496i) q^{8} +(-0.195090 - 0.980785i) q^{9} +O(q^{10})$	\(q+(1.23624 + 0.686806i) q^{2} +(0.634393 - 0.773010i) q^{3} +(1.05659 + 1.69812i) q^{4} +(-1.57885 + 0.478940i) q^{5} +(1.31517 - 0.519924i) q^{6} +(1.01743 + 0.202379i) q^{7} +(0.139929 + 2.82496i) q^{8} +(-0.195090 - 0.980785i) q^{9} +(-2.28078 - 0.492280i) q^{10} +(6.16482 + 0.607182i) q^{11} +(1.98296 + 0.260517i) q^{12} +(0.803290 - 2.64809i) q^{13} +(1.11879 + 0.948966i) q^{14} +(-0.631388 + 1.52431i) q^{15} +(-1.76722 + 3.58845i) q^{16} +(1.52013 + 3.66992i) q^{17} +(0.432430 - 1.34648i) q^{18} +(-6.52569 + 3.48805i) q^{19} +(-2.48150 - 2.17503i) q^{20} +(0.801891 - 0.658095i) q^{21} +(7.20420 + 4.98466i) q^{22} +(1.64371 - 2.45998i) q^{23} +(2.27250 + 1.68397i) q^{24} +(-1.89396 + 1.26550i) q^{25} +(2.81179 - 2.72198i) q^{26} +(-0.881921 - 0.471397i) q^{27} +(0.731345 + 1.94155i) q^{28} +(-0.794337 - 8.06504i) q^{29} +(-1.82745 + 1.45077i) q^{30} +(-7.54803 - 7.54803i) q^{31} +(-4.64928 + 3.22246i) q^{32} +(4.38028 - 4.38028i) q^{33} +(-0.641274 + 5.58096i) q^{34} +(-1.70330 + 0.167760i) q^{35} +(1.45936 - 1.36758i) q^{36} +(3.34724 - 6.26224i) q^{37} +(-10.4630 - 0.169802i) q^{38} +(-1.53740 - 2.30088i) q^{39} +(-1.57391 - 4.39318i) q^{40} +(5.94091 + 3.96959i) q^{41} +(1.44332 - 0.262822i) q^{42} +(-0.180207 - 0.219583i) q^{43} +(5.48265 + 11.1101i) q^{44} +(0.777756 + 1.45508i) q^{45} +(3.72156 - 1.91223i) q^{46} +(-6.91097 + 2.86262i) q^{47} +(1.65280 + 3.64256i) q^{48} +(-5.47295 - 2.26697i) q^{49} +(-3.21054 + 0.263686i) q^{50} +(3.80125 + 1.15310i) q^{51} +(5.34553 - 1.43388i) q^{52} +(-0.0320936 + 0.325851i) q^{53} +(-0.766511 - 1.18847i) q^{54} +(-10.0241 + 1.99393i) q^{55} +(-0.429346 + 2.90252i) q^{56} +(-1.44355 + 7.25723i) q^{57} +(4.55712 - 10.5159i) q^{58} +(-4.12809 - 13.6085i) q^{59} +(-3.25557 + 0.538401i) q^{60} +(4.58212 + 3.76045i) q^{61} +(-4.14716 - 14.5152i) q^{62} -1.03736i q^{63} +(-7.96084 + 0.790587i) q^{64} +4.56568i q^{65} +(8.42349 - 2.40669i) q^{66} +(-4.00660 - 3.28813i) q^{67} +(-4.62581 + 6.45899i) q^{68} +(-0.858836 - 2.83120i) q^{69} +(-2.22091 - 0.962443i) q^{70} +(-1.36877 + 6.88127i) q^{71} +(2.74338 - 0.688363i) q^{72} +(-1.14730 + 0.228213i) q^{73} +(8.43894 - 5.44275i) q^{74} +(-0.223267 + 2.26687i) q^{75} +(-12.8181 - 7.39594i) q^{76} +(6.14938 + 1.86539i) q^{77} +(-0.320341 - 3.90035i) q^{78} +(9.75598 + 4.04106i) q^{79} +(1.07153 - 6.51202i) q^{80} +(-0.923880 + 0.382683i) q^{81} +(4.61807 + 8.98764i) q^{82} +(2.86644 + 5.36273i) q^{83} +(1.96480 + 0.666367i) q^{84} +(-4.15774 - 5.06622i) q^{85} +(-0.0719689 - 0.395226i) q^{86} +(-6.73828 - 4.50237i) q^{87} +(-0.852631 + 17.5004i) q^{88} +(6.07208 + 9.08751i) q^{89} +(-0.0378619 + 2.33300i) q^{90} +(1.35321 - 2.53168i) q^{91} +(5.91408 + 0.192008i) q^{92} +(-10.6231 + 1.04629i) q^{93} +(-10.5097 - 1.20761i) q^{94} +(8.63254 - 8.63254i) q^{95} +(-0.458477 + 5.63824i) q^{96} +(-2.11205 - 2.11205i) q^{97} +(-5.20893 - 6.56139i) q^{98} +(-0.607182 - 6.16482i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.23624	+	0.686806i	0.874156	+	0.485645i
$2$	1.23624	+	0.686806i	0.874156	+	0.485645i
$3$	0.634393	−	0.773010i	0.366267	−	0.446298i
$3$	0.634393	−	0.773010i	0.366267	−	0.446298i
$4$	1.05659	+	1.69812i	0.528297	+	0.849060i
$5$	−1.57885	+	0.478940i	−0.706084	+	0.214188i	−0.622850	−	0.782342i	$-0.714025\pi$
$5$	−1.57885	+	0.478940i	−0.706084	+	0.214188i	−0.0832348	+	0.996530i	$0.526525\pi$
$6$	1.31517	−	0.519924i	0.536917	−	0.212258i
$7$	1.01743	+	0.202379i	0.384552	+	0.0764921i	0.383581	−	0.923507i	$-0.374691\pi$
$7$	1.01743	+	0.202379i	0.384552	+	0.0764921i	0.000971238		1.00000i	$0.499691\pi$
$8$	0.139929	+	2.82496i	0.0494723	+	0.998775i
$9$	−0.195090	−	0.980785i	−0.0650301	−	0.326928i
$10$	−2.28078	−	0.492280i	−0.721247	−	0.155673i
$11$	6.16482	+	0.607182i	1.85876	+	0.183072i	0.964432	−	0.264332i	$-0.0851516\pi$
$11$	6.16482	+	0.607182i	1.85876	+	0.183072i	0.894332	+	0.447405i	$0.147652\pi$
$12$	1.98296	+	0.260517i	0.572431	+	0.0752047i
$13$	0.803290	−	2.64809i	0.222793	−	0.734449i	−0.772278	−	0.635284i	$-0.780883\pi$
$13$	0.803290	−	2.64809i	0.222793	−	0.734449i	0.995071	−	0.0991646i	$-0.0316170\pi$
$14$	1.11879	+	0.948966i	0.299010	+	0.253622i
$15$	−0.631388	+	1.52431i	−0.163024	+	0.393574i
$16$	−1.76722	+	3.58845i	−0.441804	+	0.897112i
$17$	1.52013	+	3.66992i	0.368686	+	0.890087i	0.993966	+	0.109687i	$0.0349848\pi$
$17$	1.52013	+	3.66992i	0.368686	+	0.890087i	−0.625280	+	0.780401i	$0.715015\pi$
$18$	0.432430	−	1.34648i	0.101925	−	0.317368i
$19$	−6.52569	+	3.48805i	−1.49710	+	0.800215i	−0.997805	−	0.0662198i	$-0.978906\pi$
$19$	−6.52569	+	3.48805i	−1.49710	+	0.800215i	−0.499291	+	0.866434i	$0.666406\pi$
$20$	−2.48150	−	2.17503i	−0.554881	−	0.486353i
$21$	0.801891	−	0.658095i	0.174987	−	0.143608i
$22$	7.20420	+	4.98466i	1.53594	+	1.06273i
$23$	1.64371	−	2.45998i	0.342737	−	0.512942i	−0.619558	−	0.784951i	$-0.712688\pi$
$23$	1.64371	−	2.45998i	0.342737	−	0.512942i	0.962295	+	0.272009i	$0.0876880\pi$
$24$	2.27250	+	1.68397i	0.463871	+	0.343739i
$25$	−1.89396	+	1.26550i	−0.378791	+	0.253100i
$26$	2.81179	−	2.72198i	0.551437	−	0.533825i
$27$	−0.881921	−	0.471397i	−0.169726	−	0.0907203i
$28$	0.731345	+	1.94155i	0.138211	+	0.366918i
$29$	−0.794337	−	8.06504i	−0.147505	−	1.49764i	−0.729238	−	0.684260i	$-0.760125\pi$
$29$	−0.794337	−	8.06504i	−0.147505	−	1.49764i	0.581733	−	0.813379i	$-0.302375\pi$
$30$	−1.82745	+	1.45077i	−0.333646	+	0.264873i
$31$	−7.54803	−	7.54803i	−1.35567	−	1.35567i	−0.879185	−	0.476481i	$-0.841912\pi$
$31$	−7.54803	−	7.54803i	−1.35567	−	1.35567i	−0.476481	−	0.879185i	$-0.658088\pi$
$32$	−4.64928	+	3.22246i	−0.821884	+	0.569655i
$33$	4.38028	−	4.38028i	0.762509	−	0.762509i
$34$	−0.641274	+	5.58096i	−0.109978	+	0.957126i
$35$	−1.70330	+	0.167760i	−0.287910	+	0.0283566i
$36$	1.45936	−	1.36758i	0.243226	−	0.227930i
$37$	3.34724	−	6.26224i	0.550282	−	1.02951i	−0.440970	−	0.897522i	$-0.645365\pi$
$37$	3.34724	−	6.26224i	0.550282	−	1.02951i	0.991252	−	0.131984i	$-0.0421347\pi$
$38$	−10.4630	−	0.169802i	−1.69732	−	0.0275455i
$39$	−1.53740	−	2.30088i	−0.246181	−	0.368436i
$40$	−1.57391	−	4.39318i	−0.248858	−	0.694623i
$41$	5.94091	+	3.96959i	0.927815	+	0.619946i	0.924966	−	0.380050i	$-0.124093\pi$
$41$	5.94091	+	3.96959i	0.927815	+	0.619946i	0.00284887	+	0.999996i	$0.499093\pi$
$42$	1.44332	−	0.262822i	0.222708	−	0.0405543i
$43$	−0.180207	−	0.219583i	−0.0274814	−	0.0334861i	0.759088	−	0.650988i	$-0.225645\pi$
$43$	−0.180207	−	0.219583i	−0.0274814	−	0.0334861i	−0.786570	+	0.617501i	$0.788145\pi$
$44$	5.48265	+	11.1101i	0.826540	+	1.67492i
$45$	0.777756	+	1.45508i	0.115941	+	0.216910i
$46$	3.72156	−	1.91223i	0.548714	−	0.281943i
$47$	−6.91097	+	2.86262i	−1.00807	+	0.417556i	−0.824750	−	0.565498i	$-0.808684\pi$
$47$	−6.91097	+	2.86262i	−1.00807	+	0.417556i	−0.183319	+	0.983054i	$0.558684\pi$
$48$	1.65280	+	3.64256i	0.238561	+	0.525759i
$49$	−5.47295	−	2.26697i	−0.781850	−	0.323853i
$50$	−3.21054	+	0.263686i	−0.454039	+	0.0372908i
$51$	3.80125	+	1.15310i	0.532282	+	0.161466i
$52$	5.34553	−	1.43388i	0.741291	−	0.198843i
$53$	−0.0320936	+	0.325851i	−0.00440839	+	0.0447591i	−0.997137	−	0.0756128i	$-0.975909\pi$
$53$	−0.0320936	+	0.325851i	−0.00440839	+	0.0447591i	0.992729	+	0.120372i	$0.0384087\pi$
$54$	−0.766511	−	1.18847i	−0.104309	−	0.161730i
$55$	−10.0241	+	1.99393i	−1.35166	+	0.268861i
$56$	−0.429346	+	2.90252i	−0.0573738	+	0.387865i
$57$	−1.44355	+	7.25723i	−0.191203	+	0.961243i
$58$	4.55712	−	10.5159i	0.598380	−	1.38081i
$59$	−4.12809	−	13.6085i	−0.537432	−	1.77167i	−0.630692	−	0.776033i	$-0.717229\pi$
$59$	−4.12809	−	13.6085i	−0.537432	−	1.77167i	0.0932605	−	0.995642i	$-0.470271\pi$
$60$	−3.25557	+	0.538401i	−0.420293	+	0.0695072i
$61$	4.58212	+	3.76045i	0.586680	+	0.481476i	0.880281	−	0.474452i	$-0.157354\pi$
$61$	4.58212	+	3.76045i	0.586680	+	0.481476i	−0.293601	+	0.955928i	$0.594854\pi$
$62$	−4.14716	−	14.5152i	−0.526690	−	1.84344i
$63$		−	1.03736i		−	0.130695i
$64$	−7.96084	+	0.790587i	−0.995105	+	0.0988234i
$65$			4.56568i			0.566302i
$66$	8.42349	−	2.40669i	1.03686	−	0.296243i
$67$	−4.00660	−	3.28813i	−0.489484	−	0.401709i	0.357016	−	0.934098i	$-0.383794\pi$
$67$	−4.00660	−	3.28813i	−0.489484	−	0.401709i	−0.846500	+	0.532389i	$0.821294\pi$
$68$	−4.62581	+	6.45899i	−0.560961	+	0.783267i
$69$	−0.858836	−	2.83120i	−0.103392	−	0.340837i
$70$	−2.22091	−	0.962443i	−0.265449	−	0.115034i
$71$	−1.36877	+	6.88127i	−0.162443	+	0.816656i	0.810523	+	0.585707i	$0.199183\pi$
$71$	−1.36877	+	6.88127i	−0.162443	+	0.816656i	−0.972966	+	0.230949i	$0.925817\pi$
$72$	2.74338	−	0.688363i	0.323311	−	0.0811244i
$73$	−1.14730	+	0.228213i	−0.134282	+	0.0267103i	−0.261774	−	0.965129i	$-0.584307\pi$
$73$	−1.14730	+	0.228213i	−0.134282	+	0.0267103i	0.127492	+	0.991840i	$0.459307\pi$
$74$	8.43894	−	5.44275i	0.981007	−	0.632707i
$75$	−0.223267	+	2.26687i	−0.0257807	+	0.261756i
$76$	−12.8181	−	7.39594i	−1.47034	−	0.848373i
$77$	6.14938	+	1.86539i	0.700787	+	0.212581i
$78$	−0.320341	−	3.90035i	−0.0362714	−	0.441628i
$79$	9.75598	+	4.04106i	1.09763	+	0.454655i	0.856662	−	0.515878i	$-0.172534\pi$
$79$	9.75598	+	4.04106i	1.09763	+	0.454655i	0.240971	+	0.970532i	$0.422534\pi$
$80$	1.07153	−	6.51202i	0.119800	−	0.728066i
$81$	−0.923880	+	0.382683i	−0.102653	+	0.0425204i
$82$	4.61807	+	8.98764i	0.509981	+	0.992519i
$83$	2.86644	+	5.36273i	0.314633	+	0.588636i	0.988678	−	0.150054i	$-0.0479447\pi$
$83$	2.86644	+	5.36273i	0.314633	+	0.588636i	−0.674045	+	0.738690i	$0.735445\pi$
$84$	1.96480	+	0.666367i	0.214377	+	0.0727066i
$85$	−4.15774	−	5.06622i	−0.450970	−	0.549509i
$86$	−0.0719689	−	0.395226i	−0.00776061	−	0.0426183i
$87$	−6.73828	−	4.50237i	−0.722419	−	0.482705i
$88$	−0.852631	+	17.5004i	−0.0908907	+	1.86554i
$89$	6.07208	+	9.08751i	0.643639	+	0.963274i	0.999586	+	0.0287677i	$0.00915831\pi$
$89$	6.07208	+	9.08751i	0.643639	+	0.963274i	−0.355947	+	0.934506i	$0.615842\pi$
$90$	−0.0378619	+	2.33300i	−0.00399099	+	0.245920i
$91$	1.35321	−	2.53168i	0.141855	−	0.265392i
$92$	5.91408	+	0.192008i	0.616586	+	0.0200182i
$93$	−10.6231	+	1.04629i	−1.10157	+	0.108495i
$94$	−10.5097	−	1.20761i	−1.08399	−	0.124555i
$95$	8.63254	−	8.63254i	0.885680	−	0.885680i
$96$	−0.458477	+	5.63824i	−0.0467932	+	0.575451i
$97$	−2.11205	−	2.11205i	−0.214446	−	0.214446i	0.591707	−	0.806153i	$-0.298454\pi$
$97$	−2.11205	−	2.11205i	−0.214446	−	0.214446i	−0.806153	+	0.591707i	$0.798454\pi$
$98$	−5.20893	−	6.56139i	−0.526182	−	0.662800i
$99$	−0.607182	−	6.16482i	−0.0610241	−	0.619588i
$100$	−4.15011	−	1.87904i	−0.415011	−	0.187904i
$101$	3.25970	+	1.74235i	0.324352	+	0.173370i	0.625534	−	0.780197i	$-0.284881\pi$
$101$	3.25970	+	1.74235i	0.324352	+	0.173370i	−0.301182	+	0.953567i	$0.597381\pi$
$102$	3.90732	+	4.03623i	0.386882	+	0.399646i
$103$	−13.7140	+	9.16342i	−1.35128	+	0.902899i	−0.999450	−	0.0331641i	$-0.989442\pi$
$103$	−13.7140	+	9.16342i	−1.35128	+	0.902899i	−0.351833	+	0.936063i	$0.614442\pi$
$104$	7.59317	+	1.89872i	0.744571	+	0.186185i
$105$	−0.950880	+	1.42309i	−0.0927964	+	0.138880i
$106$	−0.263472	+	0.380790i	−0.0255907	+	0.0369855i
$107$	3.18881	−	2.61699i	0.308274	−	0.252994i	−0.467517	−	0.883984i	$-0.654851\pi$
$107$	3.18881	−	2.61699i	0.308274	−	0.252994i	0.775791	+	0.630990i	$0.217351\pi$
$108$	−0.131345	−	1.99568i	−0.0126387	−	0.192035i
$109$	6.32987	−	3.38339i	0.606292	−	0.324070i	−0.139527	−	0.990218i	$-0.544558\pi$
$109$	6.32987	−	3.38339i	0.606292	−	0.324070i	0.745819	+	0.666149i	$0.232058\pi$
$110$	−13.7617	−	4.41967i	−1.31213	−	0.421399i
$111$	−2.71731	−	6.56017i	−0.257916	−	0.622664i
$112$	−2.52424	+	3.29334i	−0.238519	+	0.311191i
$113$	3.06259	−	7.39376i	0.288105	−	0.695546i	−0.711872	−	0.702309i	$-0.752153\pi$
$113$	3.06259	−	7.39376i	0.288105	−	0.695546i	0.999977	+	0.00676259i	$0.00215261\pi$
$114$	−6.76889	+	7.98025i	−0.633965	+	0.747419i
$115$	−1.41699	+	4.67119i	−0.132135	+	0.435591i
$116$	12.8561	−	9.87035i	1.19366	−	0.916439i
$117$	−2.75392	−	0.271238i	−0.254600	−	0.0250759i
$118$	4.24307	−	19.6586i	0.390607	−	1.80972i
$119$	0.803910	+	4.04153i	0.0736943	+	0.370486i
$120$	−4.39446	−	1.57035i	−0.401157	−	0.143353i
$121$	26.8477	+	5.34034i	2.44070	+	0.485485i
$122$	3.08192	+	7.79586i	0.279024	+	0.705804i
$123$	6.83741	−	2.07411i	0.616509	−	0.187016i
$124$	4.84225	−	20.7927i	0.434846	−	1.86724i
$125$	7.61760	−	9.28207i	0.681338	−	0.830213i
$126$	0.712466	−	1.28243i	0.0634715	−	0.114248i
$127$	−16.5973			−1.47277			−0.736387	−	0.676561i	$-0.763469\pi$
$127$	−16.5973			−1.47277			−0.736387	+	0.676561i	$0.763469\pi$
$128$	−10.3845	−	4.49020i	−0.917870	−	0.396881i
$129$	−0.284062			−0.0250103
$130$	−3.13573	+	5.64429i	−0.275022	+	0.495037i
$131$	−5.56718	+	6.78362i	−0.486406	+	0.592688i	−0.957154	−	0.289580i	$-0.906484\pi$
$131$	−5.56718	+	6.78362i	−0.486406	+	0.592688i	0.470747	+	0.882268i	$0.343984\pi$
$132$	12.0664	+	2.81006i	1.05025	+	0.244584i
$133$	−7.34533	+	2.22818i	−0.636921	+	0.193208i
$134$	−2.69482	−	6.81668i	−0.232797	−	0.588872i
$135$	1.61819	+	0.321879i	0.139272	+	0.0277029i
$136$	−10.1547	+	4.80785i	−0.870758	+	0.412269i
$137$	−0.0712627	−	0.358262i	−0.00608838	−	0.0306084i	0.977622	−	0.210371i	$-0.0674671\pi$
$137$	−0.0712627	−	0.358262i	−0.00608838	−	0.0306084i	−0.983710	+	0.179762i	$0.942467\pi$
$138$	0.882757	−	4.08991i	0.0751453	−	0.348156i
$139$	−8.85581	−	0.872221i	−0.751140	−	0.0739809i	−0.284801	−	0.958587i	$-0.591927\pi$
$139$	−8.85581	−	0.872221i	−0.751140	−	0.0739809i	−0.466339	+	0.884606i	$0.654427\pi$
$140$	−2.08457	−	2.71515i	−0.176178	−	0.229472i
$141$	−2.17144	+	7.15828i	−0.182868	+	0.602836i
$142$	−6.41823	+	7.56684i	−0.538606	+	0.634995i
$143$	6.56001	−	15.8373i	0.548576	−	1.32438i
$144$	3.86426	+	1.03319i	0.322022	+	0.0860991i
$145$	5.11681	+	12.3531i	0.424928	+	1.02587i
$146$	−1.57508	−	0.505848i	−0.130355	−	0.0418643i
$147$	−5.22440	+	2.79250i	−0.430901	+	0.230321i
$148$	14.1707	−	0.932640i	1.16482	−	0.0766626i
$149$	0.642589	−	0.527360i	0.0526430	−	0.0432030i	−0.607704	−	0.794164i	$-0.707909\pi$
$149$	0.642589	−	0.527360i	0.0526430	−	0.0432030i	0.660347	+	0.750961i	$0.270409\pi$
$150$	−1.83291	+	2.64906i	−0.149657	+	0.216295i
$151$	0.900915	−	1.34831i	0.0733154	−	0.109724i	−0.793000	−	0.609222i	$-0.791482\pi$
$151$	0.900915	−	1.34831i	0.0733154	−	0.109724i	0.866315	+	0.499497i	$0.166482\pi$
$152$	−10.7668	−	17.9468i	−0.873299	−	1.45567i
$153$	3.30284	−	2.20689i	0.267019	−	0.178416i
$154$	6.32097	+	6.52952i	0.509358	+	0.526163i
$155$	15.5323	+	8.30217i	1.24758	+	0.666847i
$156$	2.28276	−	5.04179i	0.182767	−	0.403666i
$157$	0.239944	+	2.43619i	0.0191496	+	0.194429i	1.00000		0.000333722i	$-0.000106227\pi$
$157$	0.239944	+	2.43619i	0.0191496	+	0.194429i	−0.980850	+	0.194763i	$0.937606\pi$
$158$	9.28534	+	11.6962i	0.738702	+	0.930499i
$159$	0.231527	+	0.231527i	0.0183613	+	0.0183613i
$160$	5.79716	−	7.31451i	0.458306	−	0.578263i
$161$	2.17021	−	2.17021i	0.171036	−	0.171036i
$162$	−1.40497	−	0.161436i	−0.110385	−	0.0126836i
$163$	18.5939	−	1.83134i	1.45639	−	0.143441i	0.661384	−	0.750048i	$-0.269970\pi$
$163$	18.5939	−	1.83134i	1.45639	−	0.143441i	0.795002	+	0.606606i	$0.207470\pi$
$164$	−0.463703	+	14.2826i	−0.0362091	+	1.11529i
$165$	−4.81793	+	9.01370i	−0.375075	+	0.701716i
$166$	−0.139541	+	8.59833i	−0.0108305	+	0.667360i
$167$	6.57561	+	9.84110i	0.508836	+	0.761527i	0.993580	−	0.113129i	$-0.0360873\pi$
$167$	6.57561	+	9.84110i	0.508836	+	0.761527i	−0.484744	+	0.874656i	$0.661087\pi$
$168$	1.97130	+	2.17323i	0.152089	+	0.167668i
$169$	4.44199	+	2.96804i	0.341691	+	0.228311i
$170$	−1.66046	−	9.11864i	−0.127352	−	0.699368i
$171$	4.69413	+	5.71982i	0.358969	+	0.437405i
$172$	0.182472	−	0.538024i	0.0139134	−	0.0410239i
$173$	−1.15236	−	2.15592i	−0.0876127	−	0.163912i	0.834299	−	0.551313i	$-0.185873\pi$
$173$	−1.15236	−	2.15592i	−0.0876127	−	0.163912i	−0.921911	+	0.387401i	$0.873373\pi$
$174$	−5.23789	−	10.1939i	−0.397084	−	0.772799i
$175$	−2.18307	+	0.904259i	−0.165025	+	0.0683556i
$176$	−13.0734	+	21.0491i	−0.985446	+	1.58664i
$177$	−13.1383	−	5.44208i	−0.987538	−	0.409052i
$178$	1.26521	+	15.4047i	0.0948314	+	1.15463i
$179$	−1.47289	−	0.446797i	−0.110089	−	0.0333952i	0.234759	−	0.972054i	$-0.424570\pi$
$179$	−1.47289	−	0.446797i	−0.110089	−	0.0333952i	−0.344849	+	0.938658i	$0.612070\pi$
$180$	−1.64912	+	2.85815i	−0.122919	+	0.213034i
$181$	0.586753	−	5.95740i	0.0436130	−	0.442810i	−0.948437	−	0.316966i	$-0.897336\pi$
$181$	0.586753	−	5.95740i	0.0436130	−	0.442810i	0.992050	−	0.125844i	$-0.0401640\pi$
$182$	3.41167	−	2.20037i	0.252889	−	0.163103i
$183$	5.81373	−	1.15642i	0.429764	−	0.0854853i
$184$	7.17937	+	4.29920i	0.529270	+	0.316941i
$185$	−2.28556	+	11.4903i	−0.168038	+	0.844782i
$186$	−13.8514	−	6.00256i	−1.01563	−	0.440129i
$187$	7.14303	+	23.5474i	0.522350	+	1.72196i
$188$	−12.1632	−	8.71102i	−0.887089	−	0.635317i
$189$	−0.801891	−	0.658095i	−0.0583290	−	0.0478694i
$190$	16.6008	−	4.74303i	1.20435	−	0.344096i
$191$			9.54691i			0.690790i	0.938457	+	0.345395i	$0.112255\pi$
$191$			9.54691i			0.690790i	−0.938457	+	0.345395i	$0.887745\pi$
$192$	−4.43917	+	6.65536i	−0.320370	+	0.480309i
$193$		−	11.8629i		−	0.853909i	−0.904273	−	0.426954i	$-0.859586\pi$
$193$		−	11.8629i		−	0.853909i	0.904273	−	0.426954i	$-0.140414\pi$
$194$	−1.16044	−	4.06157i	−0.0833144	−	0.291604i
$195$	3.52932	+	2.89643i	0.252739	+	0.207418i
$196$	−1.93310	−	11.6890i	−0.138079	−	0.834928i
$197$	3.39073	+	11.1777i	0.241580	+	0.796381i	0.990950	+	0.134230i	$0.0428562\pi$
$197$	3.39073	+	11.1777i	0.241580	+	0.796381i	−0.749370	+	0.662151i	$0.769644\pi$
$198$	3.48341	−	8.03823i	0.247555	−	0.571252i
$199$	−1.72326	+	8.66341i	−0.122159	+	0.614133i	0.870398	+	0.492349i	$0.163862\pi$
$199$	−1.72326	+	8.66341i	−0.122159	+	0.614133i	−0.992557	+	0.121784i	$0.961138\pi$
$200$	−3.84001	−	5.17328i	−0.271530	−	0.365806i
$201$	−5.08352	+	1.01117i	−0.358564	+	0.0713227i
$202$	2.83313	+	4.39274i	0.199338	+	0.309072i
$203$	0.824014	−	8.36635i	0.0578344	−	0.587203i
$204$	2.05828	+	7.67333i	0.144109	+	0.537241i
$205$	−11.2810	−	3.42206i	−0.787901	−	0.239007i
$206$	−23.2474	+	1.90934i	−1.61972	+	0.133030i
$207$	−2.73339	−	1.13221i	−0.189984	−	0.0786938i
$208$	8.08295	+	7.56232i	0.560452	+	0.524352i
$209$	−42.3476	+	17.5409i	−2.92924	+	1.21333i
$210$	−2.15291	+	1.10622i	−0.148565	+	0.0763363i
$211$	−4.44126	−	8.30901i	−0.305749	−	0.572016i	0.681383	−	0.731928i	$-0.261379\pi$
$211$	−4.44126	−	8.30901i	−0.305749	−	0.572016i	−0.987131	+	0.159912i	$0.948879\pi$
$212$	−0.587244	+	0.289794i	−0.0403321	+	0.0199031i
$213$	4.45095	+	5.42350i	0.304974	+	0.371612i
$214$	5.73951	−	1.04514i	0.392345	−	0.0714443i
$215$	0.389688	+	0.260381i	0.0265765	+	0.0177578i
$216$	1.20827	−	2.55736i	0.0822125	−	0.174006i
$217$	−6.15201	−	9.20714i	−0.417626	−	0.625021i
$218$	10.1490	+	0.164706i	0.687376	+	0.0111553i
$219$	−0.551431	+	1.03165i	−0.0372622	+	0.0697127i
$220$	−13.9774	−	14.9154i	−0.942355	−	1.00560i
$221$	10.9394	−	1.07744i	0.735864	−	0.0724763i
$222$	1.14631	−	9.97623i	0.0769352	−	0.669561i
$223$	−12.9554	+	12.9554i	−0.867555	+	0.867555i	−0.992201	−	0.124646i	$-0.960220\pi$
$223$	−12.9554	+	12.9554i	−0.867555	+	0.867555i	0.124646	+	0.992201i	$0.460220\pi$
$224$	−5.38246	+	2.33770i	−0.359631	+	0.156194i
$225$	1.61068	+	1.61068i	0.107378	+	0.107378i
$226$	8.86419	−	7.03707i	0.589637	−	0.468099i
$227$	−1.18491	−	12.0306i	−0.0786451	−	0.798497i	−0.950911	−	0.309465i	$-0.899850\pi$
$227$	−1.18491	−	12.0306i	−0.0786451	−	0.798497i	0.872266	−	0.489032i	$-0.162650\pi$
$228$	−13.8489	+	5.21662i	−0.917165	+	0.345479i
$229$	2.76795	+	1.47950i	0.182912	+	0.0977682i	0.560311	−	0.828282i	$-0.310682\pi$
$229$	2.76795	+	1.47950i	0.182912	+	0.0977682i	−0.377399	+	0.926051i	$0.623182\pi$
$230$	−4.95995	+	4.80153i	−0.327049	+	0.316604i
$231$	5.34310	−	3.57014i	0.351550	−	0.234898i
$232$	22.6723	−	3.37250i	1.48851	−	0.221416i
$233$	−14.7684	+	22.1025i	−0.967512	+	1.44798i	−0.0748836	+	0.997192i	$0.523859\pi$
$233$	−14.7684	+	22.1025i	−0.967512	+	1.44798i	−0.892629	+	0.450792i	$0.851141\pi$
$234$	−3.21823	−	2.22673i	−0.210382	−	0.145566i
$235$	9.54038	−	7.82959i	0.622346	−	0.510746i
$236$	18.7471	−	21.3886i	1.22033	−	1.39228i
$237$	9.31291	−	4.97785i	0.604938	−	0.323346i
$238$	−1.78192	+	5.54844i	−0.115505	+	0.359652i
$239$	9.29804	+	22.4475i	0.601440	+	1.45201i	0.872099	+	0.489330i	$0.162759\pi$
$239$	9.29804	+	22.4475i	0.601440	+	1.45201i	−0.270658	+	0.962676i	$0.587241\pi$
$240$	−4.35409	−	4.95948i	−0.281055	−	0.320133i
$241$	1.44233	−	3.48209i	0.0929085	−	0.224301i	−0.870593	−	0.492004i	$-0.836265\pi$
$241$	1.44233	−	3.48209i	0.0929085	−	0.224301i	0.963502	+	0.267703i	$0.0862646\pi$
$242$	29.5225	+	25.0411i	1.89778	+	1.60970i
$243$	−0.290285	+	0.956940i	−0.0186218	+	0.0613878i
$244$	−1.54425	+	11.7543i	−0.0988603	+	0.752489i
$245$	9.72673	+	0.957999i	0.621418	+	0.0612043i
$246$	9.87721	+	2.13188i	0.629748	+	0.135924i
$247$	3.99467	+	20.0826i	0.254175	+	1.27782i
$248$	20.2667	−	22.3791i	1.28694	−	1.42107i
$249$	5.96390	+	1.18629i	0.377947	+	0.0751783i
$250$	15.7922	−	6.24308i	0.998785	−	0.394847i
$251$	20.6752	−	6.27174i	1.30501	−	0.395869i	0.440165	−	0.897917i	$-0.354920\pi$
$251$	20.6752	−	6.27174i	1.30501	−	0.395869i	0.864840	+	0.502048i	$0.167420\pi$
$252$	1.76156	−	1.09607i	0.110968	−	0.0690459i
$253$	11.6268	−	14.1673i	0.730973	−	0.890693i
$254$	−20.5183	−	11.3991i	−1.28743	−	0.715245i
$255$	−6.55388			−0.410420
$256$	−9.75389	−	12.6831i	−0.609618	−	0.792695i
$257$	19.9130			1.24214			0.621068	−	0.783757i	$-0.286699\pi$
$257$	19.9130			1.24214			0.621068	+	0.783757i	$0.286699\pi$
$258$	−0.351170	−	0.195096i	−0.0218629	−	0.0121461i
$259$	4.67292	−	5.69397i	0.290361	−	0.353806i
$260$	−7.75306	+	4.82407i	−0.480824	+	0.299176i
$261$	−7.75510	+	2.35248i	−0.480029	+	0.145615i
$262$	−11.5414	+	4.56264i	−0.713031	+	0.281881i
$263$	−18.0966	−	3.59964i	−1.11589	−	0.221963i	−0.397496	−	0.917604i	$-0.630121\pi$
$263$	−18.0966	−	3.59964i	−1.11589	−	0.221963i	−0.718390	+	0.695641i	$0.755121\pi$
$264$	12.9871	+	11.7612i	0.799298	+	0.723852i
$265$	−0.105392	−	0.529842i	−0.00647419	−	0.0325480i
$266$	−10.6109	−	2.29025i	−0.650599	−	0.140424i
$267$	10.8768	+	1.07127i	0.665651	+	0.0655609i
$268$	1.35029	−	10.2779i	0.0824819	−	0.627823i
$269$	2.71599	−	8.95342i	0.165597	−	0.545900i	−0.834389	−	0.551176i	$-0.814179\pi$
$269$	2.71599	−	8.95342i	0.165597	−	0.545900i	0.999986	+	0.00527585i	$0.00167936\pi$
$270$	1.77941	+	1.50931i	0.108292	+	0.0918535i
$271$	7.99638	−	19.3050i	0.485745	−	1.17269i	−0.471096	−	0.882082i	$-0.656141\pi$
$271$	7.99638	−	19.3050i	0.485745	−	1.17269i	0.956841	−	0.290611i	$-0.0938585\pi$
$272$	−15.8557	−	1.03064i	−0.961395	−	0.0624916i
$273$	−1.09855	−	2.65212i	−0.0664870	−	0.160514i
$274$	0.157958	−	0.491842i	0.00954261	−	0.0297133i
$275$	−12.4443	+	6.65161i	−0.750419	+	0.401107i
$276$	3.90028	−	4.44984i	0.234769	−	0.267849i
$277$	4.51659	−	3.70667i	0.271376	−	0.222712i	−0.488856	−	0.872365i	$-0.662586\pi$
$277$	4.51659	−	3.70667i	0.271376	−	0.222712i	0.760231	+	0.649652i	$0.225086\pi$
$278$	−10.3489	−	7.16050i	−0.620685	−	0.429459i
$279$	−5.93045	+	8.87554i	−0.355047	+	0.531365i
$280$	−0.712257	−	4.78828i	−0.0425655	−	0.286154i
$281$	0.994244	−	0.664333i	0.0593116	−	0.0396308i	−0.525561	−	0.850756i	$-0.676145\pi$
$281$	0.994244	−	0.664333i	0.0593116	−	0.0396308i	0.584873	+	0.811125i	$0.301145\pi$
$282$	−7.60077	+	7.35801i	−0.452620	+	0.438163i
$283$	13.2329	+	7.07315i	0.786616	+	0.420455i	0.815231	−	0.579135i	$-0.196610\pi$
$283$	13.2329	+	7.07315i	0.786616	+	0.420455i	−0.0286150	+	0.999591i	$0.509110\pi$
$284$	−13.1314	+	4.94637i	−0.779208	+	0.293513i
$285$	−1.19662	−	12.1495i	−0.0708815	−	0.719672i
$286$	18.9869	−	15.0733i	1.12272	−	0.891301i
$287$	5.24109	+	5.24109i	0.309372	+	0.309372i
$288$	4.06757	+	3.93127i	0.239684	+	0.231652i
$289$	0.863273	−	0.863273i	0.0507808	−	0.0507808i
$290$	−2.15854	+	18.7856i	−0.126754	+	1.10313i
$291$	−2.97250	+	0.292766i	−0.174251	+	0.0171622i
$292$	−1.59977	−	1.70713i	−0.0936193	−	0.0999022i
$293$	−7.75247	+	14.5038i	−0.452904	+	0.847324i	0.547044	+	0.837104i	$0.315753\pi$
$293$	−7.75247	+	14.5038i	−0.452904	+	0.847324i	−0.999948	+	0.0102197i	$0.996747\pi$
$294$	−8.37653	−	0.135941i	−0.488529	−	0.00792827i
$295$	13.0353	+	19.5087i	0.758944	+	1.13584i
$296$	18.1590	+	8.57955i	1.05547	+	0.498676i
$297$	−5.15066	−	3.44156i	−0.298872	−	0.199700i
$298$	1.15659	−	0.210610i	0.0669995	−	0.0122003i
$299$	−5.19389	−	6.32878i	−0.300371	−	0.366003i
$300$	−4.08532	+	2.01603i	−0.235866	+	0.116396i
$301$	−0.138909	−	0.259880i	−0.00800658	−	0.0149793i
$302$	2.03978	−	1.04809i	0.117376	−	0.0603108i
$303$	3.41478	−	1.41445i	0.196174	−	0.0812580i
$304$	−0.984385	−	29.5812i	−0.0564584	−	1.69660i
$305$	−9.03552	−	3.74264i	−0.517373	−	0.214303i
$306$	5.59883	−	0.459839i	0.320064	−	0.0262872i
$307$	19.6377	+	5.95703i	1.12078	+	0.339986i	0.795695	−	0.605698i	$-0.207106\pi$
$307$	19.6377	+	5.95703i	1.12078	+	0.339986i	0.325089	+	0.945684i	$0.394606\pi$
$308$	3.32974	+	12.4133i	0.189730	+	0.707316i
$309$	−1.61667	+	16.4143i	−0.0919690	+	0.933777i
$310$	13.4997	+	20.9312i	0.766730	+	1.18881i
$311$	−3.82681	+	0.761199i	−0.216998	+	0.0431636i	−0.302392	−	0.953184i	$-0.597785\pi$
$311$	−3.82681	+	0.761199i	−0.216998	+	0.0431636i	0.0853938	+	0.996347i	$0.472785\pi$
$312$	6.28479	−	4.66506i	0.355806	−	0.264107i
$313$	0.0743662	−	0.373864i	0.00420342	−	0.0211320i	−0.978627	−	0.205645i	$-0.934071\pi$
$313$	0.0743662	−	0.373864i	0.00420342	−	0.0211320i	0.982830	+	0.184513i	$0.0590708\pi$
$314$	−1.37656	+	3.17652i	−0.0776839	+	0.179261i
$315$	0.496833	+	1.63784i	0.0279934	+	0.0922818i
$316$	3.44591	+	20.8366i	0.193848	+	1.17215i
$317$	−23.6482	−	19.4076i	−1.32822	−	1.09004i	−0.988775	−	0.149411i	$-0.952262\pi$
$317$	−23.6482	−	19.4076i	−1.32822	−	1.09004i	−0.339441	−	0.940627i	$-0.610238\pi$
$318$	0.127209	+	0.445237i	0.00713354	+	0.0249677i
$319$		−	50.2018i		−	2.81076i
$320$	12.1904	−	5.06098i	0.681461	−	0.282918i
$321$		−	4.12518i		−	0.230245i
$322$	4.17341	−	1.19239i	0.232575	−	0.0664494i
$323$	−22.7208	−	18.6465i	−1.26422	−	1.03752i
$324$	−1.62601	−	1.16452i	−0.0903338	−	0.0646953i
$325$	1.82977	+	6.03193i	0.101497	+	0.334591i
$326$	24.2443	+	10.5064i	1.34277	+	0.581897i
$327$	1.40023	−	7.03945i	0.0774332	−	0.389283i
$328$	−10.3826	+	17.3383i	−0.573286	+	0.957349i
$329$	−7.61075	+	1.51387i	−0.419594	+	0.0834625i
$330$	−12.1468	+	7.83415i	−0.668659	+	0.431256i
$331$	−0.668252	+	6.78488i	−0.0367305	+	0.372931i	0.959195	+	0.282747i	$0.0912456\pi$
$331$	−0.668252	+	6.78488i	−0.0367305	+	0.372931i	−0.995925	+	0.0901841i	$0.971254\pi$
$332$	−6.07789	+	10.5338i	−0.333568	+	0.578117i
$333$	−6.79493	−	2.06122i	−0.372360	−	0.112954i
$334$	1.37013	+	16.6822i	0.0749700	+	0.912807i
$335$	7.90064	+	3.27255i	0.431658	+	0.178799i
$336$	0.944423	+	4.04054i	0.0515225	+	0.220429i
$337$	2.20817	−	0.914655i	0.120287	−	0.0498244i	−0.321728	−	0.946832i	$-0.604264\pi$
$337$	2.20817	−	0.914655i	0.120287	−	0.0498244i	0.442015	+	0.897008i	$0.354264\pi$
$338$	3.45291	+	6.72000i	0.187813	+	0.365520i
$339$	−3.77256	−	7.05797i	−0.204897	−	0.383336i
$340$	4.21000	−	12.4133i	0.228319	−	0.673204i
$341$	−41.9492	−	51.1153i	−2.27168	−	2.76805i
$342$	1.87468	+	10.2950i	0.101371	+	0.556692i
$343$	−11.1473	−	7.44838i	−0.601897	−	0.402175i
$344$	0.595098	−	0.539805i	0.0320856	−	0.0291043i
$345$	2.71195	+	4.05872i	0.146007	+	0.218514i
$346$	0.0560982	−	3.45670i	0.00301586	−	0.185833i
$347$	−1.83776	+	3.43820i	−0.0986559	+	0.184572i	−0.926407	−	0.376523i	$-0.877120\pi$
$347$	−1.83776	+	3.43820i	−0.0986559	+	0.184572i	0.827752	+	0.561095i	$0.189620\pi$
$348$	0.525940	−	16.1996i	0.0281933	−	0.868389i
$349$	12.2136	−	1.20293i	0.653778	−	0.0643915i	0.234310	−	0.972162i	$-0.424717\pi$
$349$	12.2136	−	1.20293i	0.653778	−	0.0643915i	0.419468	+	0.907770i	$0.362217\pi$
$350$	−3.31986	−	0.381465i	−0.177454	−	0.0203902i
$351$	−1.95674	+	1.95674i	−0.104443	+	0.104443i
$352$	−30.6186	+	17.0429i	−1.63198	+	0.908390i
$353$	0.293385	+	0.293385i	0.0156153	+	0.0156153i	0.714871	−	0.699256i	$-0.246485\pi$
$353$	0.293385	+	0.293385i	0.0156153	+	0.0156153i	−0.699256	+	0.714871i	$0.746485\pi$
$354$	−12.5045	−	15.7512i	−0.664608	−	0.837168i
$355$	−1.13463	−	11.5201i	−0.0602198	−	0.611421i
$356$	−9.01595	+	19.9129i	−0.477844	+	1.05538i
$357$	3.63414	+	1.94249i	0.192339	+	0.102807i
$358$	−1.51399	−	1.56394i	−0.0800169	−	0.0826569i
$359$	0.125093	−	0.0835842i	0.00660214	−	0.00441141i	−0.552265	−	0.833669i	$-0.686236\pi$
$359$	0.125093	−	0.0835842i	0.00660214	−	0.00441141i	0.558867	+	0.829257i	$0.311236\pi$
$360$	−4.00171	+	2.40074i	−0.210909	+	0.126530i
$361$	19.8623	−	29.7260i	1.04538	−	1.56453i
$362$	4.81695	−	6.96181i	0.253173	−	0.365905i
$363$	21.1601	−	17.3657i	1.11062	−	0.911462i
$364$	5.72888	−	0.377044i	0.300275	−	0.0197625i
$365$	1.70212	−	0.909803i	0.0890932	−	0.0476213i
$366$	7.98143	+	2.56329i	0.417196	+	0.133985i
$367$	−0.134841	−	0.325535i	−0.00703865	−	0.0169928i	0.920321	−	0.391164i	$-0.127927\pi$
$367$	−0.134841	−	0.325535i	−0.00703865	−	0.0169928i	−0.927360	+	0.374171i	$0.877927\pi$
$368$	5.92273	+	10.2457i	0.308744	+	0.534093i
$369$	2.73430	−	6.60119i	0.142342	−	0.343644i
$370$	−10.7171	+	12.6350i	−0.557156	+	0.656865i
$371$	−0.0985984	+	0.325035i	−0.00511897	+	0.0168750i
$372$	−13.0010	−	16.9338i	−0.674073	−	0.877978i
$373$	−17.4983	−	1.72343i	−0.906028	−	0.0892360i	−0.365741	−	0.930717i	$-0.619184\pi$
$373$	−17.4983	−	1.72343i	−0.906028	−	0.0892360i	−0.540287	+	0.841481i	$0.681684\pi$
$374$	−7.34199	+	34.0162i	−0.379645	+	1.75894i
$375$	−2.34258	−	11.7770i	−0.120970	−	0.608160i
$376$	−9.05383	−	19.1227i	−0.466916	−	0.986176i
$377$	−21.9950	−	4.37509i	−1.13280	−	0.225328i
$378$	−0.539349	−	1.36431i	−0.0277411	−	0.0701725i
$379$	−12.5815	+	3.81657i	−0.646270	+	0.196044i	−0.596369	−	0.802710i	$-0.703391\pi$
$379$	−12.5815	+	3.81657i	−0.646270	+	0.196044i	−0.0499010	+	0.998754i	$0.515891\pi$
$380$	23.7802	+	5.53799i	1.21990	+	0.284093i
$381$	−10.5292	+	12.8299i	−0.539428	+	0.657295i
$382$	−6.55688	+	11.8023i	−0.335479	+	0.603859i
$383$	−5.29622			−0.270624			−0.135312	−	0.990803i	$-0.543204\pi$
$383$	−5.29622			−0.270624			−0.135312	+	0.990803i	$0.543204\pi$
$384$	−10.0588	+	5.17879i	−0.513313	+	0.264279i
$385$	−10.6024			−0.540347
$386$	8.14750	−	14.6654i	0.414697	−	0.746449i
$387$	−0.180207	+	0.219583i	−0.00916045	+	0.0111620i
$388$	1.35493	−	5.81808i	0.0687861	−	0.295368i
$389$	3.14249	−	0.953264i	0.159331	−	0.0483324i	−0.209612	−	0.977785i	$-0.567220\pi$
$389$	3.14249	−	0.953264i	0.159331	−	0.0483324i	0.368942	+	0.929452i	$0.379720\pi$
$390$	2.37380	+	6.00465i	0.120202	+	0.304057i
$391$	11.5266	+	2.29279i	0.582926	+	0.115951i
$392$	5.63829	−	15.7781i	0.284777	−	0.796915i
$393$	1.71203	+	8.60697i	0.0863606	+	0.434164i
$394$	−3.48518	+	16.1472i	−0.175581	+	0.813484i
$395$	−17.3387	−	1.70771i	−0.872403	−	0.0859242i
$396$	9.82705	−	7.54478i	0.493828	−	0.379140i
$397$	−4.58840	+	15.1259i	−0.230285	+	0.759148i	0.763298	+	0.646046i	$0.223579\pi$
$397$	−4.58840	+	15.1259i	−0.230285	+	0.759148i	−0.993583	+	0.113102i	$0.963921\pi$
$398$	−8.08045	+	9.52654i	−0.405037	+	0.477522i
$399$	−2.93742	+	7.09156i	−0.147055	+	0.355022i
$400$	−1.19415	−	9.03277i	−0.0597075	−	0.451639i
$401$	−2.46428	−	5.94930i	−0.123060	−	0.297094i	0.850329	−	0.526251i	$-0.176403\pi$
$401$	−2.46428	−	5.94930i	−0.123060	−	0.297094i	−0.973389	+	0.229158i	$0.926403\pi$
$402$	−6.97894	−	2.24133i	−0.348078	−	0.111788i
$403$	−26.0511	+	13.9246i	−1.29770	+	0.693635i
$404$	0.485470	+	7.37631i	0.0241530	+	0.366985i
$405$	1.27539	−	1.04668i	0.0633745	−	0.0520101i
$406$	6.76475	−	9.77691i	0.335729	−	0.485220i
$407$	24.4374	−	36.5732i	1.21132	−	1.81287i
$408$	−2.72555	+	10.8997i	−0.134935	+	0.539618i
$409$	2.82623	−	1.88842i	0.139748	−	0.0933765i	−0.483731	−	0.875217i	$-0.660719\pi$
$409$	2.82623	−	1.88842i	0.139748	−	0.0933765i	0.623479	+	0.781840i	$0.285719\pi$
$410$	−11.5958	−	11.9784i	−0.572676	−	0.591570i
$411$	−0.322149	−	0.172192i	−0.0158904	−	0.00849361i
$412$	−30.0507	−	13.6060i	−1.48049	−	0.670321i
$413$	−1.44596	−	14.6811i	−0.0711512	−	0.722410i
$414$	−2.60153	−	3.27699i	−0.127858	−	0.161055i
$415$	−7.09411	−	7.09411i	−0.348236	−	0.348236i
$416$	4.79864	+	14.9003i	0.235273	+	0.730546i
$417$	−6.29230	+	6.29230i	−0.308135	+	0.308135i
$418$	−64.3992	−	7.39972i	−3.14987	−	0.361932i
$419$	1.17182	−	0.115414i	0.0572472	−	0.00563835i	−0.0693530	−	0.997592i	$-0.522093\pi$
$419$	1.17182	−	0.115414i	0.0572472	−	0.00563835i	0.126600	+	0.991954i	$0.459593\pi$
$420$	−3.42127	−	0.111076i	−0.166941	−	0.00541995i
$421$	−18.3216	+	34.2772i	−0.892938	+	1.67057i	−0.163477	+	0.986547i	$0.552271\pi$
$421$	−18.3216	+	34.2772i	−0.892938	+	1.67057i	−0.729461	+	0.684022i	$0.760229\pi$
$422$	0.216205	−	13.3222i	0.0105247	−	0.648516i
$423$	4.15588	+	6.21971i	0.202066	+	0.302412i
$424$	−0.925009	−	0.0450672i	−0.0449224	−	0.00218865i
$425$	−7.52335	−	5.02694i	−0.364936	−	0.243843i
$426$	1.77757	+	9.76171i	0.0861233	+	0.472956i
$427$	3.90094	+	4.75331i	0.188780	+	0.230029i
$428$	7.81324	+	2.64988i	0.377667	+	0.128087i
$429$	−8.08075	−	15.1180i	−0.390142	−	0.729905i
$430$	0.302918	+	0.589534i	0.0146080	+	0.0284299i
$431$	25.0822	−	10.3894i	1.20817	−	0.500440i	0.314539	−	0.949244i	$-0.398150\pi$
$431$	25.0822	−	10.3894i	1.20817	−	0.500440i	0.893630	+	0.448804i	$0.148150\pi$
$432$	3.25013	−	2.33167i	0.156372	−	0.112182i
$433$	−26.7931	−	11.0981i	−1.28760	−	0.533339i	−0.369328	−	0.929299i	$-0.620412\pi$
$433$	−26.7931	−	11.0981i	−1.28760	−	0.533339i	−0.918268	+	0.395960i	$0.870412\pi$
$434$	−1.28186	−	15.6075i	−0.0615315	−	0.749184i
$435$	12.7951	+	3.88136i	0.613479	+	0.186097i
$436$	12.4335	+	7.17401i	0.595457	+	0.343573i
$437$	−2.14578	+	21.7864i	−0.102646	+	1.04219i
$438$	−1.39025	+	0.896649i	−0.0664286	+	0.0428436i
$439$	−1.27533	+	0.253680i	−0.0608684	+	0.0121075i	−0.225431	−	0.974259i	$-0.572379\pi$
$439$	−1.27533	+	0.253680i	−0.0608684	+	0.0121075i	0.164562	+	0.986367i	$0.447379\pi$
$440$	−7.03544	−	28.0388i	−0.335401	−	1.33670i
$441$	−1.15569	+	5.81006i	−0.0550330	+	0.276669i
$442$	14.2638	+	6.18128i	0.678458	+	0.294013i
$443$	11.2279	+	37.0134i	0.533453	+	1.75856i	0.644353	+	0.764728i	$0.277127\pi$
$443$	11.2279	+	37.0134i	0.533453	+	1.75856i	−0.110899	+	0.993832i	$0.535373\pi$
$444$	8.26886	−	11.5458i	0.392423	−	0.547937i
$445$	−13.9393	−	11.4397i	−0.660785	−	0.542293i
$446$	−24.9138	+	7.11815i	−1.17970	+	0.337054i
$447$		−	0.831282i		−	0.0393183i
$448$	−8.25958	−	0.806741i	−0.390229	−	0.0381149i
$449$		−	10.5560i		−	0.498170i	−0.968482	−	0.249085i	$-0.919870\pi$
$449$		−	10.5560i		−	0.498170i	0.968482	−	0.249085i	$-0.0801298\pi$
$450$	0.884965	+	3.09741i	0.0417177	+	0.146013i
$451$	34.2144	+	28.0790i	1.61109	+	1.32219i
$452$	15.7914	−	2.61155i	0.742765	−	0.122837i
$453$	−0.470727	−	1.55178i	−0.0221167	−	0.0729089i
$454$	6.79784	−	15.6865i	0.319038	−	0.736204i
$455$	−0.923997	+	4.64525i	−0.0433177	+	0.217773i
$456$	−20.7034	−	3.06249i	−0.969525	−	0.143414i
$457$	25.4652	−	5.06533i	1.19121	−	0.236946i	0.440607	−	0.897700i	$-0.354763\pi$
$457$	25.4652	−	5.06533i	1.19121	−	0.236946i	0.750603	+	0.660754i	$0.229763\pi$
$458$	2.40573	+	3.73007i	0.112412	+	0.174295i
$459$	0.389353	−	3.95317i	0.0181735	−	0.184518i
$460$	−9.42942	+	2.52934i	−0.439649	+	0.117931i
$461$	35.7342	+	10.8398i	1.66431	+	0.504862i	0.975484	−	0.220069i	$-0.0706281\pi$
$461$	35.7342	+	10.8398i	1.66431	+	0.504862i	0.688822	+	0.724930i	$0.258128\pi$
$462$	9.05736	−	0.743893i	0.421387	−	0.0346090i
$463$	−11.7986	−	4.88715i	−0.548329	−	0.227125i	0.0912806	−	0.995825i	$-0.470904\pi$
$463$	−11.7986	−	4.88715i	−0.548329	−	0.227125i	−0.639610	+	0.768700i	$0.720904\pi$
$464$	30.3447	+	11.4022i	1.40872	+	0.529335i
$465$	16.2712	−	6.73977i	0.754560	−	0.312549i
$466$	−33.4375	+	17.1810i	−1.54896	+	0.795896i
$467$	−14.8622	−	27.8053i	−0.687742	−	1.28668i	−0.947114	−	0.320898i	$-0.896015\pi$
$467$	−14.8622	−	27.8053i	−0.687742	−	1.28668i	0.259372	−	0.965778i	$-0.416485\pi$
$468$	−2.44919	−	4.96308i	−0.113214	−	0.229418i
$469$	−3.41098	−	4.15629i	−0.157504	−	0.191920i
$470$	17.1716	−	3.12688i	0.792069	−	0.144232i
$471$	2.03542	+	1.36002i	0.0937872	+	0.0626666i
$472$	37.8659	−	13.5659i	1.74292	−	0.624422i
$473$	−0.977619	−	1.46311i	−0.0449510	−	0.0672739i
$474$	14.9318	+	0.242327i	0.685842	+	0.0111304i
$475$	7.94523	−	14.8645i	0.364552	−	0.682029i
$476$	−6.01359	+	5.63539i	−0.275632	+	0.258298i
$477$	0.325851	−	0.0320936i	0.0149197	−	0.00146946i
$478$	−3.92242	+	34.1365i	−0.179407	+	1.56137i
$479$	−12.3475	+	12.3475i	−0.564171	+	0.564171i	−0.930489	−	0.366319i	$-0.880618\pi$
$479$	−12.3475	+	12.3475i	−0.564171	+	0.564171i	0.366319	+	0.930489i	$0.380618\pi$
$480$	−1.97651	−	9.12154i	−0.0902150	−	0.416339i
$481$	−13.8942	−	13.8942i	−0.633520	−	0.633520i
$482$	4.17459	−	3.31411i	0.190147	−	0.150954i
$483$	−0.300828	−	3.05436i	−0.0136881	−	0.138978i
$484$	19.2986	+	51.2332i	0.877209	+	2.32878i
$485$	4.34615	+	2.32307i	0.197349	+	0.105485i
$486$	−1.01610	+	0.983642i	−0.0460910	+	0.0446189i
$487$	16.3616	−	10.9325i	0.741417	−	0.495399i	−0.126587	−	0.991955i	$-0.540402\pi$
$487$	16.3616	−	10.9325i	0.741417	−	0.495399i	0.868004	+	0.496556i	$0.165402\pi$
$488$	−9.98196	+	13.4705i	−0.451862	+	0.609782i
$489$	10.3802	−	15.5351i	0.469409	−	0.702520i
$490$	11.3666	+	7.86470i	0.513493	+	0.355291i
$491$	−22.9805	+	18.8596i	−1.03709	+	0.851122i	−0.989029	−	0.147722i	$-0.952806\pi$
$491$	−22.9805	+	18.8596i	−1.03709	+	0.851122i	−0.0480661	+	0.998844i	$0.515306\pi$
$492$	10.7465	+	9.41925i	0.484487	+	0.424653i
$493$	28.3906	−	15.1751i	1.27865	−	0.683451i
$494$	−8.85444	+	27.5705i	−0.398380	+	1.24045i
$495$	3.91123	+	9.44254i	0.175797	+	0.424411i
$496$	40.4247	−	13.7467i	1.81512	−	0.617244i
$497$	−2.78525	+	6.72419i	−0.124935	+	0.301621i
$498$	6.55808	+	5.56259i	0.293874	+	0.249266i
$499$	−5.41342	+	17.8457i	−0.242338	+	0.798881i	0.748418	+	0.663227i	$0.230814\pi$
$499$	−5.41342	+	17.8457i	−0.242338	+	0.798881i	−0.990756	+	0.135654i	$0.956686\pi$
$500$	23.8108	+	3.12820i	1.06485	+	0.139898i
$501$	11.7788	+	1.16011i	0.526238	+	0.0518299i
$502$	29.8670	+	6.44644i	1.33303	+	0.287718i
$503$	−1.05940	−	5.32598i	−0.0472365	−	0.237474i	0.949953	−	0.312392i	$-0.101130\pi$
$503$	−1.05940	−	5.32598i	−0.0472365	−	0.237474i	−0.997190	+	0.0749186i	$0.976130\pi$
$504$	2.93051	−	0.145157i	0.130535	−	0.00646579i
$505$	−5.98106	−	1.18971i	−0.266154	−	0.0529413i
$506$	24.1038	−	9.52889i	1.07154	−	0.423611i
$507$	5.11229	−	1.55080i	0.227045	−	0.0688733i
$508$	−17.5366	−	28.1842i	−0.778062	−	1.25047i
$509$	−5.68958	+	6.93277i	−0.252186	+	0.307290i	−0.883680	−	0.468091i	$-0.844942\pi$
$509$	−5.68958	+	6.93277i	−0.252186	+	0.307290i	0.631494	+	0.775381i	$0.282442\pi$
$510$	−8.10219	−	4.50125i	−0.358771	−	0.199319i
$511$	−1.21348			−0.0536814
$512$	−3.34733	−	22.3785i	−0.147933	−	0.988997i
$513$	7.39940			0.326692
$514$	24.6173	+	13.6763i	1.08582	+	0.603238i
$515$	17.2637	−	21.0359i	0.760730	−	0.926952i
$516$	−0.300139	−	0.482372i	−0.0132129	−	0.0212352i
$517$	−44.3430	+	13.4513i	−1.95020	+	0.591588i
$518$	9.68752	−	3.82974i	0.425645	−	0.168269i
$519$	−2.39760	−	0.476913i	−0.105243	−	0.0209342i
$520$	−12.8979	+	0.638869i	−0.565609	+	0.0280163i
$521$	−1.56794	−	7.88259i	−0.0686929	−	0.345342i	0.931119	−	0.364714i	$-0.118833\pi$
$521$	−1.56794	−	7.88259i	−0.0686929	−	0.345342i	−0.999812	+	0.0193719i	$0.993833\pi$
$522$	−11.2029	−	2.41801i	−0.490337	−	0.105833i
$523$	−26.0592	−	2.56661i	−1.13949	−	0.112230i	−0.489380	−	0.872071i	$-0.662777\pi$
$523$	−26.0592	−	2.56661i	−1.13949	−	0.112230i	−0.650109	+	0.759841i	$0.725277\pi$
$524$	−17.4016	−	2.28619i	−0.760194	−	0.0998726i
$525$	−0.685926	+	2.26120i	−0.0299363	+	0.0986867i
$526$	−19.8996	−	16.8789i	−0.867662	−	0.735955i
$527$	16.2267	−	39.1747i	0.706846	−	1.70648i
$528$	7.97749	+	23.4593i	0.347176	+	1.02093i
$529$	5.45197	+	13.1622i	0.237042	+	0.572271i
$530$	0.233609	−	0.727398i	0.0101473	−	0.0315961i
$531$	−12.5417	+	6.70366i	−0.544262	+	0.290914i
$532$	−11.5448	−	10.1190i	−0.500529	−	0.438713i
$533$	15.2841	−	12.5434i	0.662029	−	0.543313i
$534$	12.7106	+	8.79462i	0.550043	+	0.380581i
$535$	−3.78128	+	5.65909i	−0.163479	+	0.244664i
$536$	8.72821	−	11.7786i	0.377001	−	0.508758i
$537$	−1.27977	+	0.855117i	−0.0552263	+	0.0369010i
$538$	9.50689	−	9.20325i	0.409871	−	0.396780i
$539$	−32.3633	−	17.2985i	−1.39399	−	0.745101i
$540$	1.16319	+	3.08798i	0.0500556	+	0.132886i
$541$	3.56822	+	36.2288i	0.153410	+	1.55760i	0.696274	+	0.717776i	$0.254840\pi$
$541$	3.56822	+	36.2288i	0.153410	+	1.55760i	−0.542865	+	0.839820i	$0.682660\pi$
$542$	23.1442	−	18.3737i	0.994130	−	0.789216i
$543$	−4.23290	−	4.23290i	−0.181651	−	0.181651i
$544$	−18.8937	−	12.1639i	−0.810060	−	0.521524i
$545$	−8.37350	+	8.37350i	−0.358681	+	0.358681i
$546$	0.463425	−	4.03316i	0.0198328	−	0.172603i
$547$	−7.73612	+	0.761942i	−0.330773	+	0.0325783i	−0.262041	−	0.965057i	$-0.584395\pi$
$547$	−7.73612	+	0.761942i	−0.330773	+	0.0325783i	−0.0687322	+	0.997635i	$0.521895\pi$
$548$	0.533075	−	0.499550i	0.0227718	−	0.0213397i
$549$	2.79427	−	5.22770i	0.119256	−	0.223113i
$550$	−19.9525	−	0.323807i	−0.850779	−	0.0138072i
$551$	33.3149	+	49.8592i	1.41926	+	2.12407i
$552$	7.87787	−	2.82235i	0.335304	−	0.120127i
$553$	9.10818	+	6.08589i	0.387319	+	0.258799i
$554$	8.12937	−	1.48032i	0.345384	−	0.0628929i
$555$	7.43216	+	9.05612i	0.315478	+	0.384411i
$556$	−7.87587	−	15.9598i	−0.334011	−	0.676847i
$557$	−4.32502	−	8.09155i	−0.183257	−	0.342850i	0.773472	−	0.633831i	$-0.218518\pi$
$557$	−4.32502	−	8.09155i	−0.183257	−	0.342850i	−0.956729	+	0.290981i	$0.906018\pi$
$558$	−13.4273	+	6.89926i	−0.568421	+	0.292069i
$559$	−0.726235	+	0.300817i	−0.0307165	+	0.0127232i
$560$	2.40810	−	6.40866i	0.101761	−	0.270815i
$561$	22.7339	+	9.41669i	0.959826	+	0.397573i
$562$	1.68540	−	0.138424i	0.0710941	−	0.00583905i
$563$	−32.9666	−	10.0003i	−1.38938	−	0.421463i	−0.495046	−	0.868867i	$-0.664849\pi$
$563$	−32.9666	−	10.0003i	−1.38938	−	0.421463i	−0.894332	+	0.447403i	$0.852349\pi$
$564$	−14.4499	+	3.87603i	−0.608452	+	0.163210i
$565$	−1.29422	+	13.1405i	−0.0544483	+	0.552823i
$566$	11.5012	+	17.8326i	0.483433	+	0.749560i
$567$	−1.01743	+	0.202379i	−0.0427280	+	0.00849912i
$568$	−19.6309	−	2.90384i	−0.823692	−	0.121842i
$569$	−3.09301	+	15.5496i	−0.129666	+	0.651874i	0.860210	+	0.509940i	$0.170332\pi$
$569$	−3.09301	+	15.5496i	−0.129666	+	0.651874i	−0.989876	+	0.141935i	$0.954668\pi$
$570$	6.86502	−	15.8415i	0.287544	−	0.663529i
$571$	−1.86414	−	6.14525i	−0.0780119	−	0.257171i	0.909256	−	0.416237i	$-0.136651\pi$
$571$	−1.86414	−	6.14525i	−0.0780119	−	0.257171i	−0.987268	+	0.159067i	$0.949151\pi$
$572$	33.8248	−	5.59389i	1.41429	−	0.233892i
$573$	7.37986	+	6.05650i	0.308298	+	0.253014i
$574$	2.87965	+	10.0789i	0.120194	+	0.420684i
$575$			6.73922i			0.281045i
$576$	2.32848	+	7.65364i	0.0970200	+	0.318902i
$577$		−	0.810917i		−	0.0337589i	−0.999858	−	0.0168795i	$-0.994627\pi$
$577$		−	0.810917i		−	0.0337589i	0.999858	−	0.0168795i	$-0.00537315\pi$
$578$	1.66012	−	0.474314i	0.0690518	−	0.0197289i
$579$	−9.17013	−	7.52573i	−0.381098	−	0.312759i
$580$	−15.5706	+	21.7411i	−0.646533	+	0.902751i
$581$	1.83109	+	6.03630i	0.0759665	+	0.250428i
$582$	−3.87581	−	1.67960i	−0.160657	−	0.0696217i
$583$	−0.395702	+	1.98933i	−0.0163883	+	0.0823896i
$584$	−0.805234	−	3.20916i	−0.0333208	−	0.132796i
$585$	4.47795	−	0.890719i	0.185140	−	0.0368267i
$586$	−19.5453	+	12.6058i	−0.807407	+	0.520742i
$587$	4.66946	−	47.4098i	0.192729	−	1.95681i	−0.0856110	−	0.996329i	$-0.527284\pi$
$587$	4.66946	−	47.4098i	0.192729	−	1.95681i	0.278340	−	0.960483i	$-0.410216\pi$
$588$	−10.2621	−	5.92111i	−0.423200	−	0.244182i
$589$	75.5840	+	22.9282i	3.11439	+	0.944738i
$590$	2.71610	+	33.0702i	0.111820	+	1.36148i
$591$	10.7916	+	4.47002i	0.443906	+	0.183872i
$592$	16.5564	+	23.0781i	0.680464	+	0.948505i
$593$	9.14567	−	3.78826i	0.375568	−	0.155565i	−0.186911	−	0.982377i	$-0.559848\pi$
$593$	9.14567	−	3.78826i	0.375568	−	0.155565i	0.562479	+	0.826812i	$0.309848\pi$
$594$	−4.00378	−	7.79212i	−0.164277	−	0.319714i
$595$	−3.20490	−	5.99595i	−0.131388	−	0.245810i
$596$	1.57448	+	0.533988i	0.0644930	+	0.0218730i
$597$	5.60368	+	6.82811i	0.229344	+	0.279456i
$598$	−2.07427	−	11.3911i	−0.0848232	−	0.465817i
$599$	6.89653	+	4.60811i	0.281785	+	0.188282i	0.688428	−	0.725304i	$-0.258301\pi$
$599$	6.89653	+	4.60811i	0.281785	+	0.188282i	−0.406644	+	0.913587i	$0.633301\pi$
$600$	−6.43507	−	0.313522i	−0.262711	−	0.0127995i
$601$	21.4222	+	32.0606i	0.873830	+	1.30778i	0.950500	+	0.310723i	$0.100571\pi$
$601$	21.4222	+	32.0606i	0.873830	+	1.30778i	−0.0766701	+	0.997057i	$0.524429\pi$
$602$	0.00676222	−	0.416679i	0.000275607	−	0.0169826i
$603$	−2.44330	+	4.57109i	−0.0994989	+	0.186149i
$604$	3.24150	+	0.105239i	0.131895	+	0.00428213i
$605$	−44.9463	+	4.42682i	−1.82733	+	0.179976i
$606$	5.19295	+	0.596691i	0.210949	+	0.0242389i
$607$	25.1106	−	25.1106i	1.01921	−	1.01921i	0.0193941	−	0.999812i	$-0.493826\pi$
$607$	25.1106	−	25.1106i	1.01921	−	1.01921i	0.999812	−	0.0193941i	$-0.00617372\pi$
$608$	19.0996	−	37.2457i	0.774593	−	1.51051i
$609$	−5.94453	−	5.94453i	−0.240885	−	0.240885i
$610$	−8.59964	−	10.8325i	−0.348189	−	0.438594i
$611$	2.02896	+	20.6004i	0.0820830	+	0.833403i
$612$	7.23733	+	3.27684i	0.292552	+	0.132458i
$613$	6.29005	+	3.36210i	0.254053	+	0.135794i	0.593508	−	0.804828i	$-0.297743\pi$
$613$	6.29005	+	3.36210i	0.254053	+	0.135794i	−0.339455	+	0.940622i	$0.610243\pi$
$614$	20.1857	+	20.8516i	0.814627	+	0.841504i
$615$	−9.80189	+	6.54942i	−0.395251	+	0.264098i
$616$	−4.40920	+	17.6328i	−0.177652	+	0.710446i
$617$	−8.23818	+	12.3293i	−0.331656	+	0.496359i	−0.959395	−	0.282065i	$-0.908981\pi$
$617$	−8.23818	+	12.3293i	−0.331656	+	0.496359i	0.627739	+	0.778424i	$0.283981\pi$
$618$	−13.2720	+	19.1817i	−0.533880	+	0.771602i
$619$	−9.65799	+	7.92610i	−0.388187	+	0.318577i	−0.808164	−	0.588958i	$-0.799538\pi$
$619$	−9.65799	+	7.92610i	−0.388187	+	0.318577i	0.419976	+	0.907535i	$0.362038\pi$
$620$	2.31323	+	35.1477i	0.0929017	+	1.41156i
$621$	−2.60925	+	1.39467i	−0.104706	+	0.0559663i
$622$	−5.25366	−	1.68725i	−0.210653	−	0.0676525i
$623$	4.33878	+	10.4747i	0.173830	+	0.419662i
$624$	10.9735	−	1.45072i	0.439292	−	0.0580753i
$625$	−3.22305	+	7.78113i	−0.128922	+	0.311245i
$626$	0.348707	−	0.411112i	0.0139371	−	0.0164313i
$627$	−13.3057	+	43.8630i	−0.531378	+	1.75172i
$628$	−3.88342	+	2.98152i	−0.154965	+	0.118976i
$629$	28.0702	+	2.76467i	1.11923	+	0.110235i
$630$	−0.510672	+	2.36600i	−0.0203457	+	0.0942636i
$631$	4.98820	+	25.0774i	0.198577	+	0.998314i	0.943553	+	0.331222i	$0.107461\pi$
$631$	4.98820	+	25.0774i	0.198577	+	0.998314i	−0.744976	+	0.667092i	$0.767539\pi$
$632$	−10.0507	+	28.1257i	−0.399795	+	1.11878i
$633$	−9.24046	−	1.83804i	−0.367275	−	0.0730556i
$634$	−15.9057	−	40.2342i	−0.631696	−	1.59791i
$635$	26.2047	−	7.94911i	1.03990	−	0.315451i
$636$	−0.148530	+	0.637789i	−0.00588960	+	0.0252900i
$637$	−10.3995	+	12.6719i	−0.412044	+	0.502077i
$638$	34.4789	−	62.0616i	1.36503	−	2.45704i
$639$	7.01608			0.277552
$640$	18.5462	+	2.11580i	0.733101	+	0.0836344i
$641$	40.1106			1.58427			0.792136	−	0.610344i	$-0.208969\pi$
$641$	40.1106			1.58427			0.792136	+	0.610344i	$0.208969\pi$
$642$	2.83320	−	5.09973i	0.111818	−	0.201270i
$643$	−13.9728	+	17.0259i	−0.551034	+	0.671436i	−0.971820	−	0.235723i	$-0.924254\pi$
$643$	−13.9728	+	17.0259i	−0.551034	+	0.671436i	0.420787	+	0.907160i	$0.361754\pi$
$644$	5.97830	+	1.39224i	0.235578	+	0.0548620i
$645$	0.448493	−	0.136049i	0.0176594	−	0.00535692i
$646$	−15.2819	−	38.6564i	−0.601259	−	1.52092i
$647$	5.32774	+	1.05975i	0.209455	+	0.0416632i	0.298702	−	0.954346i	$-0.403446\pi$
$647$	5.32774	+	1.05975i	0.209455	+	0.0416632i	−0.0892475	+	0.996009i	$0.528446\pi$
$648$	−1.21034	−	2.55638i	−0.0475468	−	0.100424i
$649$	−17.1861	−	86.4004i	−0.674614	−	3.39151i
$650$	−1.88073	+	8.71363i	−0.0737684	+	0.341777i
$651$	−11.0200	−	1.08538i	−0.431908	−	0.0425393i
$652$	22.7560	+	29.6397i	0.891195	+	1.16078i
$653$	−3.81106	+	12.5634i	−0.149138	+	0.491643i	−0.999397	−	0.0347222i	$-0.988945\pi$
$653$	−3.81106	+	12.5634i	−0.149138	+	0.491643i	0.850259	+	0.526365i	$0.176445\pi$
$654$	6.56577	−	7.74079i	0.256742	−	0.302689i
$655$	5.54080	−	13.3767i	0.216497	−	0.522670i
$656$	−24.7435	+	14.3035i	−0.966073	+	0.558459i
$657$	0.447655	+	1.08074i	0.0174647	+	0.0421635i
$658$	−10.4485	−	3.35560i	−0.407324	−	0.130815i
$659$	−29.1988	+	15.6071i	−1.13742	+	0.607966i	−0.929003	−	0.370073i	$-0.879333\pi$
$659$	−29.1988	+	15.6071i	−1.13742	+	0.607966i	−0.208422	+	0.978039i	$0.566833\pi$
$660$	−20.3969	+	1.34242i	−0.793950	+	0.0522536i
$661$	24.0058	−	19.7010i	0.933716	−	0.766281i	−0.0387689	−	0.999248i	$-0.512344\pi$
$661$	24.0058	−	19.7010i	0.933716	−	0.766281i	0.972484	+	0.232968i	$0.0748436\pi$
$662$	−5.48602	+	7.92880i	−0.213220	+	0.308162i
$663$	6.10702	−	9.13979i	0.237177	−	0.354960i
$664$	−14.7484	+	8.84799i	−0.572350	+	0.343369i
$665$	10.5300	−	7.03594i	0.408337	−	0.272842i
$666$	−6.98452	−	7.21496i	−0.270645	−	0.279574i
$667$	−21.1455	−	11.3025i	−0.818758	−	0.437635i
$668$	−9.76360	+	21.5642i	−0.377765	+	0.834345i
$669$	1.79583	+	18.2334i	0.0694310	+	0.704945i
$670$	7.51951	+	9.47188i	0.290504	+	0.365931i
$671$	25.9647	+	25.9647i	1.00236	+	1.00236i
$672$	−1.60753	+	5.64372i	−0.0620118	+	0.217711i
$673$	−1.86675	+	1.86675i	−0.0719578	+	0.0719578i	−0.742170	−	0.670212i	$-0.766203\pi$
$673$	−1.86675	+	1.86675i	−0.0719578	+	0.0719578i	0.670212	+	0.742170i	$0.266203\pi$
$674$	3.35803	+	0.385851i	0.129346	+	0.0148624i
$675$	2.26687	−	0.223267i	0.0872520	−	0.00859357i
$676$	−0.346708	+	10.6790i	−0.0133349	+	0.410732i
$677$	0.855848	−	1.60118i	0.0328929	−	0.0615383i	−0.864938	−	0.501879i	$-0.832642\pi$
$677$	0.855848	−	1.60118i	0.0328929	−	0.0615383i	0.897831	+	0.440341i	$0.145142\pi$
$678$	0.183652	−	11.3164i	0.00705311	−	0.434603i
$679$	−1.72142	−	2.57629i	−0.0660621	−	0.0988689i
$680$	13.7301	−	12.4544i	0.526525	−	0.477603i
$681$	−10.0515	−	6.71617i	−0.385173	−	0.257364i
$682$	−16.7531	−	92.0019i	−0.641511	−	3.52293i
$683$	4.23751	+	5.16343i	0.162144	+	0.197573i	0.847744	−	0.530405i	$-0.177960\pi$
$683$	4.23751	+	5.16343i	0.162144	+	0.197573i	−0.685600	+	0.727978i	$0.740460\pi$
$684$	−4.75314	+	14.0147i	−0.181741	+	0.535866i
$685$	0.284099	+	0.531512i	0.0108549	+	0.0203080i
$686$	−8.66517	−	16.8640i	−0.330838	−	0.643872i
$687$	2.89964	−	1.20107i	0.110628	−	0.0458237i
$688$	1.10643	−	0.258613i	0.0421822	−	0.00985953i
$689$	0.837104	+	0.346740i	0.0318911	+	0.0132097i
$690$	0.565076	+	6.88015i	0.0215121	+	0.261923i
$691$	6.91040	+	2.09625i	0.262884	+	0.0797450i	0.418975	−	0.907998i	$-0.362389\pi$
$691$	6.91040	+	2.09625i	0.262884	+	0.0797450i	−0.156091	+	0.987743i	$0.549889\pi$
$692$	2.44343	−	4.23479i	0.0928853	−	0.160983i
$693$	0.629867	−	6.39514i	0.0239267	−	0.242931i
$694$	−4.63329	+	2.98827i	−0.175877	+	0.113433i
$695$	14.3998	−	2.86429i	0.546214	−	0.108649i
$696$	11.7762	−	19.6654i	0.446374	−	0.745415i
$697$	−5.53713	+	27.8370i	−0.209734	+	1.05440i
$698$	15.9251	+	6.90125i	0.602775	+	0.261216i
$699$	7.71649	+	25.4379i	0.291864	+	0.962148i
$700$	−3.84216	−	2.75169i	−0.145220	−	0.104004i
$701$	20.5368	+	16.8541i	0.775664	+	0.636571i	0.936602	−	0.350394i	$-0.113952\pi$
$701$	20.5368	+	16.8541i	0.775664	+	0.636571i	−0.160939	+	0.986964i	$0.551452\pi$
$702$	−3.76291	+	1.07511i	−0.142022	+	0.0405772i
$703$			52.5408i			1.98161i
$704$	−49.5572	+	0.0401526i	−1.86776	+	0.00151331i
$705$		−	12.3419i		−	0.464821i
$706$	0.161196	+	0.564193i	0.00606671	+	0.0212337i
$707$	2.96390	+	2.43241i	0.111469	+	0.0914801i
$708$	−4.64060	−	28.0605i	−0.174404	−	1.05458i
$709$	−10.4034	−	34.2954i	−0.390708	−	1.28799i	−0.903171	−	0.429281i	$-0.858767\pi$
$709$	−10.4034	−	34.2954i	−0.390708	−	1.28799i	0.512463	−	0.858709i	$-0.328733\pi$
$710$	6.50938	−	15.0209i	0.244293	−	0.563723i
$711$	2.06011	−	10.3569i	0.0772603	−	0.388414i
$712$	−24.8222	+	18.4250i	−0.930252	+	0.690506i
$713$	−30.9748	+	6.16127i	−1.16002	+	0.230741i
$714$	3.15857	+	4.89734i	0.118206	+	0.183278i
$715$	−2.77220	+	28.1466i	−0.103674	+	1.05262i
$716$	−0.797536	−	2.97323i	−0.0298053	−	0.111115i
$717$	23.2507	+	7.05304i	0.868315	+	0.263400i
$718$	0.212051	−	0.0174160i	0.00791368	−	0.000649960i
$719$	−33.2788	−	13.7845i	−1.24109	−	0.514076i	−0.337034	−	0.941492i	$-0.609424\pi$
$719$	−33.2788	−	13.7845i	−1.24109	−	0.514076i	−0.904055	+	0.427416i	$0.859424\pi$
$720$	−6.59594	+	0.219495i	−0.245816	+	0.00818011i
$721$	−15.8075	+	6.54769i	−0.588703	+	0.243849i
$722$	44.9706	−	23.1070i	1.67363	−	0.859955i
$723$	−1.77669	−	3.32395i	−0.0660757	−	0.123619i
$724$	10.7363	−	5.29818i	0.399013	−	0.196905i
$725$	11.7107	+	14.2696i	0.434926	+	0.529959i
$726$	38.0859	−	6.93528i	1.41350	−	0.257393i
$727$	−14.8004	−	9.88928i	−0.548915	−	0.366773i	0.249973	−	0.968253i	$-0.419578\pi$
$727$	−14.8004	−	9.88928i	−0.548915	−	0.366773i	−0.798888	+	0.601480i	$0.794578\pi$
$728$	7.34124	+	3.46851i	0.272085	+	0.128552i
$729$	0.555570	+	0.831470i	0.0205767	+	0.0307952i
$730$	2.72910	+	0.0442901i	0.101008	+	0.00163925i
$731$	0.531915	−	0.995143i	0.0196736	−	0.0368067i
$732$	8.10650	+	8.65054i	0.299625	+	0.319733i
$733$	−47.5284	+	4.68114i	−1.75550	+	0.172902i	−0.923942	−	0.382532i	$-0.875052\pi$
$733$	−47.5284	+	4.68114i	−1.75550	+	0.172902i	−0.831560	+	0.555434i	$0.812552\pi$
$734$	0.0568833	−	0.495051i	0.00209960	−	0.0182727i
$735$	6.91112	−	6.91112i	0.254920	−	0.254920i
$736$	0.285134	+	16.7339i	0.0105102	+	0.616821i
$737$	−22.7035	−	22.7035i	−0.836293	−	0.836293i
$738$	7.91400	−	6.28274i	0.291318	−	0.231271i
$739$	−3.51990	−	35.7381i	−0.129481	−	1.31465i	−0.811948	−	0.583730i	$-0.801593\pi$
$739$	−3.51990	−	35.7381i	−0.129481	−	1.31465i	0.682466	−	0.730917i	$-0.260907\pi$
$740$	−21.9268	+	8.25941i	−0.806044	+	0.303622i
$741$	18.0582	+	9.65232i	0.663385	+	0.354587i
$742$	−0.345128	+	0.334105i	−0.0126700	+	0.0122654i
$743$	−4.57464	+	3.05668i	−0.167827	+	0.112139i	−0.636647	−	0.771155i	$-0.719679\pi$
$743$	−4.57464	+	3.05668i	−0.167827	+	0.112139i	0.468820	+	0.883294i	$0.344679\pi$
$744$	−4.44220	−	29.8635i	−0.162859	−	1.09485i
$745$	−0.761981	+	1.14038i	−0.0279168	+	0.0417805i
$746$	−20.4485	−	14.1485i	−0.748673	−	0.518014i
$747$	4.70047	−	3.85758i	0.171981	−	0.141141i
$748$	−32.4390	+	37.0098i	−1.18609	+	1.35321i
$749$	3.77401	−	2.01725i	0.137899	−	0.0737087i
$750$	5.19249	−	16.1681i	0.189603	−	0.590375i
$751$	0.436225	+	1.05314i	0.0159181	+	0.0384296i	0.931639	−	0.363386i	$-0.118379\pi$
$751$	0.436225	+	1.05314i	0.0159181	+	0.0384296i	−0.915721	+	0.401815i	$0.868379\pi$
$752$	1.94083	−	29.8585i	0.0707749	−	1.08883i
$753$	8.26807	−	19.9609i	0.301305	−	0.727415i
$754$	−24.1864	−	20.5150i	−0.880816	−	0.747112i
$755$	−0.776651	+	2.56027i	−0.0282652	+	0.0931779i
$756$	0.270250	−	2.05705i	0.00982890	−	0.0748140i
$757$	−33.5953	−	3.30885i	−1.22104	−	0.120262i	−0.533115	−	0.846043i	$-0.678979\pi$
$757$	−33.5953	−	3.30885i	−1.22104	−	0.120262i	−0.687926	+	0.725781i	$0.741479\pi$
$758$	−18.1751	−	3.92287i	−0.660149	−	0.142485i
$759$	−3.57551	−	17.9753i	−0.129783	−	0.652463i
$760$	25.5945	+	23.1787i	0.928412	+	0.840778i
$761$	30.0195	+	5.97125i	1.08821	+	0.216458i	0.706420	−	0.707793i	$-0.250309\pi$
$761$	30.0195	+	5.97125i	1.08821	+	0.216458i	0.381786	+	0.924251i	$0.375309\pi$
$762$	−21.8283	+	8.62933i	−0.790757	+	0.312608i
$763$	7.12492	−	2.16132i	0.257939	−	0.0782450i
$764$	−16.2118	+	10.0872i	−0.586522	+	0.364943i
$765$	−4.15774	+	5.06622i	−0.150323	+	0.183170i
$766$	−6.54741	−	3.63747i	−0.236568	−	0.131427i
$767$	−39.3526			−1.42094
$768$	−15.9920	−	0.506229i	−0.577061	−	0.0182670i
$769$	50.0874			1.80620			0.903098	−	0.429434i	$-0.141287\pi$
$769$	50.0874			1.80620			0.903098	+	0.429434i	$0.141287\pi$
$770$	−13.1071	−	7.28178i	−0.472348	−	0.262417i
$771$	12.6326	−	15.3929i	0.454954	−	0.554363i
$772$	20.1446	−	12.5343i	0.725019	−	0.451118i
$773$	4.63900	−	1.40723i	0.166853	−	0.0506144i	−0.205753	−	0.978604i	$-0.565964\pi$
$773$	4.63900	−	1.40723i	0.166853	−	0.0506144i	0.372606	+	0.927990i	$0.378464\pi$
$774$	−0.373591	+	0.147691i	−0.0134285	+	0.00530863i
$775$	23.8477	+	4.74359i	0.856633	+	0.170395i
$776$	5.67092	−	6.26199i	0.203574	−	0.224792i
$777$	−1.43703	−	7.22443i	−0.0515531	−	0.259175i
$778$	4.53959	+	0.979816i	0.162752	+	0.0351281i
$779$	−52.6147	−	5.18210i	−1.88512	−	0.185668i
$780$	−1.18944	+	9.05355i	−0.0425886	+	0.324169i
$781$	−12.6164	+	41.5907i	−0.451450	+	1.48823i
$782$	12.6750	+	10.7510i	0.453257	+	0.384455i
$783$	−3.10129	+	7.48717i	−0.110831	+	0.267570i
$784$	17.8068	−	15.6332i	0.635957	−	0.558327i
$785$	−1.54563	−	3.73147i	−0.0551657	−	0.133182i
$786$	−3.79483	+	11.8161i	−0.135357	+	0.421468i
$787$	34.7608	−	18.5800i	1.23909	−	0.662307i	0.284057	−	0.958807i	$-0.408320\pi$
$787$	34.7608	−	18.5800i	1.23909	−	0.662307i	0.955033	+	0.296500i	$0.0958195\pi$
$788$	−15.3985	+	17.5682i	−0.548549	+	0.625842i
$789$	−14.2629	+	11.7053i	−0.507774	+	0.416719i
$790$	−20.2620	−	14.0195i	−0.720888	−	0.498790i
$791$	4.61231	−	6.90281i	0.163995	−	0.245436i
$792$	17.3304	−	2.57790i	0.615810	−	0.0916018i
$793$	13.6388	−	9.11315i	0.484328	−	0.323617i
$794$	−16.0609	+	15.5480i	−0.569982	+	0.551777i
$795$	−0.476434	−	0.254659i	−0.0168974	−	0.00903183i
$796$	−16.5323	+	6.22741i	−0.585972	+	0.220725i
$797$	−1.00437	−	10.1975i	−0.0355766	−	0.361215i	−0.996447	−	0.0842179i	$-0.973161\pi$
$797$	−1.00437	−	10.1975i	−0.0355766	−	0.361215i	0.960871	−	0.276997i	$-0.0893392\pi$
$798$	−8.50190	+	6.74946i	−0.300964	+	0.238928i
$799$	−21.0112	−	21.0112i	−0.743322	−	0.743322i
$800$	4.72750	−	11.9869i	0.167142	−	0.423799i
$801$	7.72829	−	7.72829i	0.273066	−	0.273066i
$802$	1.03957	−	9.04726i	0.0367083	−	0.319470i
$803$	−7.21148	+	0.710269i	−0.254488	+	0.0250649i
$804$	−7.08831	−	7.56402i	−0.249985	−	0.266762i
$805$	−2.38704	+	4.46583i	−0.0841320	+	0.157400i
$806$	−41.7690	−	0.677863i	−1.47125	−	0.0238767i
$807$	−5.19808	−	7.77948i	−0.182981	−	0.273851i
$808$	−4.46594	+	9.45234i	−0.157111	+	0.332532i
$809$	42.0531	+	28.0990i	1.47851	+	0.987907i	0.993553	+	0.113367i	$0.0361636\pi$
$809$	42.0531	+	28.0990i	1.47851	+	0.987907i	0.484954	+	0.874540i	$0.338836\pi$
$810$	2.29556	−	0.418011i	0.0806577	−	0.0146874i
$811$	−22.6590	−	27.6100i	−0.795664	−	0.969520i	0.204292	−	0.978910i	$-0.434511\pi$
$811$	−22.6590	−	27.6100i	−0.795664	−	0.969520i	−0.999956	+	0.00939023i	$0.997011\pi$
$812$	15.0777	−	7.44057i	0.529124	−	0.261113i
$813$	−9.85009	−	18.4282i	−0.345458	−	0.646306i
$814$	55.3293	−	28.4296i	1.93929	−	0.996456i
$815$	−28.4799	+	11.7968i	−0.997608	+	0.413223i
$816$	−10.8555	+	11.6028i	−0.380017	+	0.406180i
$817$	1.94190	+	0.804359i	0.0679383	+	0.0281410i
$818$	4.79088	−	0.393481i	0.167509	−	0.0137578i
$819$	−2.74703	−	0.833302i	−0.0959889	−	0.0291179i
$820$	−6.10840	−	22.7723i	−0.213315	−	0.795242i
$821$	1.60705	−	16.3167i	0.0560865	−	0.569456i	−0.925541	−	0.378648i	$-0.876389\pi$
$821$	1.60705	−	16.3167i	0.0560865	−	0.569456i	0.981627	−	0.190808i	$-0.0611108\pi$
$822$	−0.279991	−	0.434125i	−0.00976582	−	0.0151418i
$823$	−23.1597	+	4.60676i	−0.807297	+	0.160581i	−0.581451	−	0.813581i	$-0.697515\pi$
$823$	−23.1597	+	4.60676i	−0.807297	+	0.160581i	−0.225846	+	0.974163i	$0.572515\pi$
$824$	−27.8053	−	37.4594i	−0.968644	−	1.30496i
$825$	−2.75281	+	13.8393i	−0.0958404	+	0.481822i
$826$	8.29551	−	19.1425i	0.288638	−	0.666053i
$827$	13.0646	+	43.0682i	0.454300	+	1.49763i	0.822980	+	0.568070i	$0.192310\pi$
$827$	13.0646	+	43.0682i	0.454300	+	1.49763i	−0.368680	+	0.929556i	$0.620190\pi$
$828$	−0.965461	−	5.83790i	−0.0335521	−	0.202881i
$829$	3.69482	+	3.03226i	0.128327	+	0.105315i	0.696367	−	0.717685i	$-0.254798\pi$
$829$	3.69482	+	3.03226i	0.128327	+	0.105315i	−0.568041	+	0.823000i	$0.692298\pi$
$830$	−3.89777	−	13.6423i	−0.135293	−	0.473532i
$831$		−	5.84286i		−	0.202687i
$832$	−4.30131	+	21.7161i	−0.149121	+	0.752871i
$833$		−	23.5314i		−	0.815315i
$834$	−12.1004	+	3.45722i	−0.419003	+	0.119714i
$835$	−15.0952	−	12.3883i	−0.522391	−	0.428716i
$836$	−74.5308	−	53.3776i	−2.57770	−	1.84610i
$837$	3.09865	+	10.2149i	0.107105	+	0.353078i
$838$	1.52792	+	0.662134i	0.0527812	+	0.0228730i
$839$	−1.36656	+	6.87014i	−0.0471788	+	0.237184i	−0.997178	−	0.0750671i	$-0.976083\pi$
$839$	−1.36656	+	6.87014i	−0.0471788	+	0.237184i	0.950000	+	0.312251i	$0.101083\pi$
$840$	−4.15324	−	2.48707i	−0.143300	−	0.0858121i
$841$	−35.9711	+	7.15509i	−1.24038	+	0.246727i
$842$	−46.1917	+	29.7916i	−1.59187	+	1.02669i
$843$	0.117206	−	1.19001i	0.00403678	−	0.0409861i
$844$	9.41708	−	16.3210i	0.324149	−	0.561793i
$845$	−8.43475	−	2.55865i	−0.290164	−	0.0880204i
$846$	0.865939	+	10.5434i	0.0297716	+	0.362488i
$847$	26.2348	+	10.8668i	0.901440	+	0.373389i
$848$	−1.11258	−	0.691016i	−0.0382063	−	0.0237296i
$849$	13.8625	−	5.74204i	0.475760	−	0.197066i
$850$	−5.84816	−	11.3816i	−0.200590	−	0.390386i
$851$	−9.90313	−	18.5275i	−0.339475	−	0.635113i
$852$	−4.50690	+	13.2887i	−0.154404	+	0.455263i
$853$	8.78758	+	10.7077i	0.300881	+	0.366625i	0.901401	−	0.432985i	$-0.142540\pi$
$853$	8.78758	+	10.7077i	0.300881	+	0.366625i	−0.600520	+	0.799610i	$0.705040\pi$
$854$	1.55791	+	8.55544i	0.0533106	+	0.292761i
$855$	−10.1508	−	6.78254i	−0.347150	−	0.231958i
$856$	7.83910	+	8.64208i	0.267935	+	0.295380i
$857$	−18.9089	−	28.2992i	−0.645917	−	0.966684i	−0.999511	−	0.0312843i	$-0.990040\pi$
$857$	−18.9089	−	28.2992i	−0.645917	−	0.966684i	0.353593	−	0.935399i	$-0.384960\pi$
$858$	0.393378	−	24.2395i	0.0134297	−	0.827521i
$859$	−13.3024	+	24.8870i	−0.453871	+	0.849133i	0.546064	+	0.837743i	$0.316126\pi$
$859$	−13.3024	+	24.8870i	−0.453871	+	0.849133i	−0.999935	+	0.0113897i	$0.996374\pi$
$860$	−0.0304161	+	0.936854i	−0.00103718	+	0.0319464i
$861$	7.37633	−	0.726505i	0.251385	−	0.0247592i
$862$	38.1433	+	4.38281i	1.29916	+	0.149279i
$863$	−12.3219	+	12.3219i	−0.419443	+	0.419443i	−0.885012	−	0.465569i	$-0.845850\pi$
$863$	−12.3219	+	12.3219i	−0.419443	+	0.419443i	0.465569	+	0.885012i	$0.345850\pi$
$864$	5.61935	−	0.650299i	0.191174	−	0.0221236i
$865$	2.85197	+	2.85197i	0.0969700	+	0.0969700i
$866$	−25.5006	−	32.1216i	−0.866545	−	1.09154i
$867$	−0.119665	−	1.21497i	−0.00406402	−	0.0412627i
$868$	9.13464	−	20.1751i	0.310050	−	0.684786i
$869$	57.6902	+	30.8361i	1.95701	+	1.04604i
$870$	13.1521	+	13.5861i	0.445899	+	0.460611i
$871$	−11.9257	+	7.96852i	−0.404088	+	0.270003i
$872$	10.4437	+	17.4082i	0.353668	+	0.589517i
$873$	−1.65942	+	2.48350i	−0.0561630	+	0.0840538i
$874$	−17.6158	+	25.4596i	−0.595862	+	0.861184i
$875$	9.62885	−	7.90220i	0.325515	−	0.267143i
$876$	−2.33451	+	0.153645i	−0.0788758	+	0.00519119i
$877$	−2.61563	+	1.39808i	−0.0883236	+	0.0472099i	−0.514967	−	0.857210i	$-0.672196\pi$
$877$	−2.61563	+	1.39808i	−0.0883236	+	0.0472099i	0.426644	+	0.904420i	$0.359696\pi$
$878$	−1.75085	−	0.562298i	−0.0590884	−	0.0189766i
$879$	6.29351	+	15.1939i	0.212275	+	0.512477i
$880$	10.5597	−	39.4948i	0.355969	−	1.33137i
$881$	6.49905	−	15.6901i	0.218959	−	0.528613i	−0.775786	−	0.630996i	$-0.782647\pi$
$881$	6.49905	−	15.6901i	0.218959	−	0.528613i	0.994745	+	0.102383i	$0.0326466\pi$
$882$	−5.41910	+	6.38891i	−0.182471	+	0.215126i
$883$	9.43444	−	31.1012i	0.317494	−	1.04664i	−0.642422	−	0.766351i	$-0.722070\pi$
$883$	9.43444	−	31.1012i	0.317494	−	1.04664i	0.959916	−	0.280287i	$-0.0904297\pi$
$884$	13.3881	+	17.4380i	0.450292	+	0.586503i
$885$	23.3499	+	2.29977i	0.784899	+	0.0773058i
$886$	−11.5406	+	53.4690i	−0.387715	+	1.79632i
$887$	−5.15377	−	25.9097i	−0.173047	−	0.869964i	−0.965574	−	0.260128i	$-0.916235\pi$
$887$	−5.15377	−	25.9097i	−0.173047	−	0.869964i	0.792528	−	0.609836i	$-0.208765\pi$
$888$	18.1520	−	8.59426i	0.609142	−	0.288405i
$889$	−16.8866	−	3.35895i	−0.566358	−	0.112656i
$890$	−9.37551	−	23.7158i	−0.314268	−	0.794956i
$891$	−5.92791	+	1.79821i	−0.198592	+	0.0602424i
$892$	−35.6883	−	8.31118i	−1.19493	−	0.278279i
$893$	35.1139	−	42.7864i	1.17504	−	1.43179i
$894$	0.570929	−	1.02767i	0.0190947	−	0.0343703i
$895$	2.53947			0.0848851
$896$	−9.65678	−	6.67006i	−0.322610	−	0.222831i
$897$	−8.18718			−0.273362
$898$	7.24995	−	13.0498i	0.241934	−	0.435478i
$899$	−54.8794	+	66.8708i	−1.83033	+	2.23027i
$900$	−1.03329	+	4.43695i	−0.0344430	+	0.147898i
$901$	−1.24464	+	0.377556i	−0.0414649	+	0.0125782i
$902$	23.0125	+	58.2112i	0.766231	+	1.93822i
$903$	−0.289013	−	0.0574883i	−0.00961776	−	0.00191309i
$904$	21.3156	+	7.61712i	0.708948	+	0.253342i
$905$	1.92684	+	9.68688i	0.0640503	+	0.322003i
$906$	0.483838	−	2.24167i	0.0160745	−	0.0744746i
$907$	−14.3160	−	1.41000i	−0.475354	−	0.0468183i	−0.142496	−	0.989795i	$-0.545513\pi$
$907$	−14.3160	−	1.41000i	−0.475354	−	0.0468183i	−0.332858	+	0.942977i	$0.608013\pi$
$908$	19.1774	−	14.7235i	0.636423	−	0.488618i
$909$	1.07293	−	3.53698i	0.0355869	−	0.117314i
$910$	−4.33267	+	5.10805i	−0.143627	+	0.169330i
$911$	−10.6398	+	25.6867i	−0.352511	+	0.851037i	0.643798	+	0.765196i	$0.277358\pi$
$911$	−10.6398	+	25.6867i	−0.352511	+	0.851037i	−0.996309	+	0.0858412i	$0.972642\pi$
$912$	−23.4911	−	18.0052i	−0.777868	−	0.596212i
$913$	14.4149	+	34.8007i	0.477065	+	1.15174i
$914$	34.9600	+	11.2276i	1.15637	+	0.371377i
$915$	−8.62517	+	4.61025i	−0.285139	+	0.152410i
$916$	0.412234	+	6.26355i	0.0136206	+	0.206953i
$917$	−7.03707	+	5.77517i	−0.232384	+	0.190713i
$918$	3.19640	−	4.61967i	0.105497	−	0.152472i
$919$	29.6966	−	44.4441i	0.979601	−	1.46608i	0.0973774	−	0.995248i	$-0.468955\pi$
$919$	29.6966	−	44.4441i	0.979601	−	1.46608i	0.882224	−	0.470830i	$-0.156045\pi$
$920$	−13.3942	−	3.34931i	−0.441594	−	0.110424i
$921$	17.0629	−	11.4011i	0.562241	−	0.375677i
$922$	36.7313	+	37.9431i	1.20968	+	1.24959i
$923$	17.1227	+	9.15228i	0.563601	+	0.301251i
$924$	11.7080	+	5.30102i	0.385165	+	0.174391i
$925$	1.58535	+	16.0963i	0.0521260	+	0.529244i
$926$	−11.2295	−	14.1451i	−0.369023	−	0.464836i
$927$	11.6628	+	11.6628i	0.383057	+	0.383057i
$928$	29.6823	+	34.9369i	0.974370	+	1.14686i
$929$	19.2577	−	19.2577i	0.631824	−	0.631824i	−0.316702	−	0.948525i	$-0.602575\pi$
$929$	19.2577	−	19.2577i	0.631824	−	0.631824i	0.948525	+	0.316702i	$0.102575\pi$
$930$	24.7441	+	2.84320i	0.811392	+	0.0932321i
$931$	43.6221	−	4.29640i	1.42966	−	0.140809i
$932$	−53.1370	−	1.72516i	−1.74056	−	0.0565094i
$933$	−1.83929	+	3.44106i	−0.0602155	+	0.112655i
$934$	0.723508	−	44.5816i	0.0236739	−	1.45875i
$935$	−22.5556	−	33.7568i	−0.737647	−	1.10397i
$936$	0.380884	−	7.81769i	0.0124496	−	0.255529i
$937$	−11.0704	−	7.39700i	−0.361654	−	0.241649i	0.361446	−	0.932393i	$-0.382283\pi$
$937$	−11.0704	−	7.39700i	−0.361654	−	0.241649i	−0.723100	+	0.690744i	$0.757283\pi$
$938$	−1.36223	−	7.48086i	−0.0444785	−	0.244259i
$939$	−0.241823	−	0.294663i	−0.00789161	−	0.00961595i
$940$	23.3759	+	7.92800i	0.762437	+	0.258583i
$941$	−9.70877	−	18.1638i	−0.316497	−	0.592124i	0.672494	−	0.740103i	$-0.265223\pi$
$941$	−9.70877	−	18.1638i	−0.316497	−	0.592124i	−0.988991	+	0.147979i	$0.952723\pi$
$942$	1.58220	+	3.07926i	0.0515509	+	0.100328i
$943$	19.5303	−	8.08970i	0.635993	−	0.263437i
$944$	56.1286	+	9.23572i	1.82683	+	0.300597i
$945$	1.58126	+	0.654977i	0.0514382	+	0.0213064i
$946$	−0.203701	−	2.48019i	−0.00662291	−	0.0806381i
$947$	22.2261	+	6.74220i	0.722250	+	0.219092i	0.629946	−	0.776639i	$-0.283077\pi$
$947$	22.2261	+	6.74220i	0.722250	+	0.219092i	0.0923038	+	0.995731i	$0.470577\pi$
$948$	18.2930	+	10.5549i	0.594127	+	0.342806i
$949$	−0.317289	+	3.22149i	−0.0102996	+	0.104574i
$950$	20.0313	−	12.9193i	0.649900	−	0.419157i
$951$	−30.0045	+	5.96827i	−0.972964	+	0.193535i
$952$	−11.3047	+	2.83654i	−0.366387	+	0.0919329i
$953$	0.952741	−	4.78975i	0.0308623	−	0.155155i	−0.962281	−	0.272057i	$-0.912296\pi$
$953$	0.952741	−	4.78975i	0.0308623	−	0.155155i	0.993144	+	0.116901i	$0.0372962\pi$
$954$	0.424874	+	0.184121i	0.0137558	+	0.00596115i
$955$	−4.57240	−	15.0732i	−0.147959	−	0.487756i
$956$	−28.2942	+	39.5071i	−0.915100	+	1.27775i
$957$	−38.8065	−	31.8477i	−1.25444	−	1.02949i
$958$	−23.7448	+	6.78416i	−0.767160	+	0.219186i
$959$		−	0.378928i		−	0.0122362i
$960$	3.82128	−	12.6339i	0.123331	−	0.407758i
$961$			82.9454i			2.67566i
$962$	−7.63398	−	26.7192i	−0.246129	−	0.861462i
$963$	−3.18881	−	2.61699i	−0.102758	−	0.0843313i
$964$	7.43696	−	1.22991i	0.239528	−	0.0396127i
$965$	5.68160	+	18.7297i	0.182897	+	0.602932i
$966$	1.72585	−	3.98254i	0.0555285	−	0.128136i
$967$	4.19071	−	21.0681i	0.134764	−	0.677505i	−0.853045	−	0.521837i	$-0.825247\pi$
$967$	4.19071	−	21.0681i	0.134764	−	0.677505i	0.987809	−	0.155668i	$-0.0497530\pi$
$968$	−11.3295	+	76.5910i	−0.364144	+	2.46173i
$969$	−28.8279	+	5.73422i	−0.926084	+	0.184210i
$970$	3.77740	+	5.85684i	0.121285	+	0.188052i
$971$	−2.01497	+	20.4584i	−0.0646635	+	0.656540i	0.907153	+	0.420801i	$0.138251\pi$
$971$	−2.01497	+	20.4584i	−0.0646635	+	0.656540i	−0.971816	+	0.235739i	$0.924249\pi$
$972$	−1.93171	+	0.518160i	−0.0619597	+	0.0166200i
$973$	−8.83364	−	2.67965i	−0.283193	−	0.0859058i
$974$	27.7355	−	2.27795i	0.888702	−	0.0729903i
$975$	5.82354	+	2.41219i	0.186503	+	0.0772519i
$976$	−21.5918	+	9.79716i	−0.691136	+	0.313600i
$977$	−22.4820	+	9.31237i	−0.719264	+	0.297929i	−0.712132	−	0.702046i	$-0.752270\pi$
$977$	−22.4820	+	9.31237i	−0.719264	+	0.297929i	−0.00713216	+	0.999975i	$0.502270\pi$
$978$	23.5020	−	12.0759i	0.751512	−	0.386146i
$979$	31.9155	+	59.7097i	1.02002	+	1.90833i
$980$	8.65041	+	17.5294i	0.276327	+	0.559955i
$981$	−4.55327	−	5.54818i	−0.145375	−	0.177140i
$982$	−41.3624	+	7.53191i	−1.31993	+	0.240353i
$983$	40.0771	+	26.7786i	1.27826	+	0.854106i	0.994495	−	0.104788i	$-0.0334163\pi$
$983$	40.0771	+	26.7786i	1.27826	+	0.854106i	0.283765	+	0.958894i	$0.408416\pi$
$984$	6.81603	+	19.0252i	0.217287	+	0.606502i
$985$	−10.7069	−	16.0241i	−0.341151	−	0.510569i
$986$	45.5200	+	0.738737i	1.44965	+	0.0235262i
$987$	−3.65797	+	6.84358i	−0.116434	+	0.217834i
$988$	−29.8818	+	28.0025i	−0.950667	+	0.890879i
$989$	−0.836380	+	0.0823762i	−0.0265953	+	0.00261941i
$990$	−1.64997	+	14.3595i	−0.0524394	+	0.456376i
$991$	11.8698	−	11.8698i	0.377056	−	0.377056i	−0.492983	−	0.870039i	$-0.664094\pi$
$991$	11.8698	−	11.8698i	0.377056	−	0.377056i	0.870039	+	0.492983i	$0.164094\pi$
$992$	59.4161	+	10.7697i	1.88646	+	0.341938i
$993$	4.82085	+	4.82085i	0.152985	+	0.152985i
$994$	−8.06146	+	6.39980i	−0.255694	+	0.202989i
$995$	−1.42848	−	14.5036i	−0.0452858	−	0.459795i
$996$	4.28696	+	11.3808i	0.135837	+	0.360616i
$997$	−35.2329	−	18.8324i	−1.11584	−	0.596428i	−0.192839	−	0.981230i	$-0.561770\pi$
$997$	−35.2329	−	18.8324i	−1.11584	−	0.596428i	−0.922999	+	0.384802i	$0.874270\pi$
$998$	−18.9488	+	18.3436i	−0.599814	+	0.580657i
$999$	−5.90400	+	3.94493i	−0.186794	+	0.124812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.85.29	✓	512
128.125	even	32	inner	384.2.v.a.253.29	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.85.29	✓	512	1.1	even	1	trivial
384.2.v.a.253.29	yes	512	128.125	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.23624 + 0.686806i) q^{2} +(0.634393 - 0.773010i) q^{3} +(1.05659 + 1.69812i) q^{4} +(-1.57885 + 0.478940i) q^{5} +(1.31517 - 0.519924i) q^{6} +(1.01743 + 0.202379i) q^{7} +(0.139929 + 2.82496i) q^{8} +(-0.195090 - 0.980785i) q^{9} +O(q^{10})\)	\(q+(1.23624 + 0.686806i) q^{2} +(0.634393 - 0.773010i) q^{3} +(1.05659 + 1.69812i) q^{4} +(-1.57885 + 0.478940i) q^{5} +(1.31517 - 0.519924i) q^{6} +(1.01743 + 0.202379i) q^{7} +(0.139929 + 2.82496i) q^{8} +(-0.195090 - 0.980785i) q^{9} +(-2.28078 - 0.492280i) q^{10} +(6.16482 + 0.607182i) q^{11} +(1.98296 + 0.260517i) q^{12} +(0.803290 - 2.64809i) q^{13} +(1.11879 + 0.948966i) q^{14} +(-0.631388 + 1.52431i) q^{15} +(-1.76722 + 3.58845i) q^{16} +(1.52013 + 3.66992i) q^{17} +(0.432430 - 1.34648i) q^{18} +(-6.52569 + 3.48805i) q^{19} +(-2.48150 - 2.17503i) q^{20} +(0.801891 - 0.658095i) q^{21} +(7.20420 + 4.98466i) q^{22} +(1.64371 - 2.45998i) q^{23} +(2.27250 + 1.68397i) q^{24} +(-1.89396 + 1.26550i) q^{25} +(2.81179 - 2.72198i) q^{26} +(-0.881921 - 0.471397i) q^{27} +(0.731345 + 1.94155i) q^{28} +(-0.794337 - 8.06504i) q^{29} +(-1.82745 + 1.45077i) q^{30} +(-7.54803 - 7.54803i) q^{31} +(-4.64928 + 3.22246i) q^{32} +(4.38028 - 4.38028i) q^{33} +(-0.641274 + 5.58096i) q^{34} +(-1.70330 + 0.167760i) q^{35} +(1.45936 - 1.36758i) q^{36} +(3.34724 - 6.26224i) q^{37} +(-10.4630 - 0.169802i) q^{38} +(-1.53740 - 2.30088i) q^{39} +(-1.57391 - 4.39318i) q^{40} +(5.94091 + 3.96959i) q^{41} +(1.44332 - 0.262822i) q^{42} +(-0.180207 - 0.219583i) q^{43} +(5.48265 + 11.1101i) q^{44} +(0.777756 + 1.45508i) q^{45} +(3.72156 - 1.91223i) q^{46} +(-6.91097 + 2.86262i) q^{47} +(1.65280 + 3.64256i) q^{48} +(-5.47295 - 2.26697i) q^{49} +(-3.21054 + 0.263686i) q^{50} +(3.80125 + 1.15310i) q^{51} +(5.34553 - 1.43388i) q^{52} +(-0.0320936 + 0.325851i) q^{53} +(-0.766511 - 1.18847i) q^{54} +(-10.0241 + 1.99393i) q^{55} +(-0.429346 + 2.90252i) q^{56} +(-1.44355 + 7.25723i) q^{57} +(4.55712 - 10.5159i) q^{58} +(-4.12809 - 13.6085i) q^{59} +(-3.25557 + 0.538401i) q^{60} +(4.58212 + 3.76045i) q^{61} +(-4.14716 - 14.5152i) q^{62} -1.03736i q^{63} +(-7.96084 + 0.790587i) q^{64} +4.56568i q^{65} +(8.42349 - 2.40669i) q^{66} +(-4.00660 - 3.28813i) q^{67} +(-4.62581 + 6.45899i) q^{68} +(-0.858836 - 2.83120i) q^{69} +(-2.22091 - 0.962443i) q^{70} +(-1.36877 + 6.88127i) q^{71} +(2.74338 - 0.688363i) q^{72} +(-1.14730 + 0.228213i) q^{73} +(8.43894 - 5.44275i) q^{74} +(-0.223267 + 2.26687i) q^{75} +(-12.8181 - 7.39594i) q^{76} +(6.14938 + 1.86539i) q^{77} +(-0.320341 - 3.90035i) q^{78} +(9.75598 + 4.04106i) q^{79} +(1.07153 - 6.51202i) q^{80} +(-0.923880 + 0.382683i) q^{81} +(4.61807 + 8.98764i) q^{82} +(2.86644 + 5.36273i) q^{83} +(1.96480 + 0.666367i) q^{84} +(-4.15774 - 5.06622i) q^{85} +(-0.0719689 - 0.395226i) q^{86} +(-6.73828 - 4.50237i) q^{87} +(-0.852631 + 17.5004i) q^{88} +(6.07208 + 9.08751i) q^{89} +(-0.0378619 + 2.33300i) q^{90} +(1.35321 - 2.53168i) q^{91} +(5.91408 + 0.192008i) q^{92} +(-10.6231 + 1.04629i) q^{93} +(-10.5097 - 1.20761i) q^{94} +(8.63254 - 8.63254i) q^{95} +(-0.458477 + 5.63824i) q^{96} +(-2.11205 - 2.11205i) q^{97} +(-5.20893 - 6.56139i) q^{98} +(-0.607182 - 6.16482i) 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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