LMFDB - Embedded newform 384.2.v.a.37.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			37.10
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08984 - 0.901251i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(0.375495 + 1.96443i) q^{4} +(0.157832 - 0.129529i) q^{5} +(-0.281086 + 1.38600i) q^{6} +(-1.86560 + 1.24656i) q^{7} +(1.36122 - 2.47933i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-1.08984 - 0.901251i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(0.375495 + 1.96443i) q^{4} +(0.157832 - 0.129529i) q^{5} +(-0.281086 + 1.38600i) q^{6} +(-1.86560 + 1.24656i) q^{7} +(1.36122 - 2.47933i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-0.288750 - 0.00108010i) q^{10} +(-0.656510 - 2.16422i) q^{11} +(1.55547 - 1.25719i) q^{12} +(-1.87091 + 2.27971i) q^{13} +(3.15667 + 0.322831i) q^{14} +(-0.188636 - 0.0781357i) q^{15} +(-3.71801 + 1.47527i) q^{16} +(-7.53468 + 3.12097i) q^{17} +(1.35484 - 0.405459i) q^{18} +(-2.31226 + 0.227738i) q^{19} +(0.313717 + 0.261413i) q^{20} +(1.97880 + 1.05769i) q^{21} +(-1.23502 + 2.95033i) q^{22} +(1.89423 - 0.376786i) q^{23} +(-2.82825 - 0.0317392i) q^{24} +(-0.967319 + 4.86304i) q^{25} +(4.09357 - 0.798355i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-3.14930 - 3.19678i) q^{28} +(7.47173 + 2.26652i) q^{29} +(0.135163 + 0.255164i) q^{30} +(-5.52299 - 5.52299i) q^{31} +(5.38162 + 1.74305i) q^{32} +(-1.59920 + 1.59920i) q^{33} +(11.0244 + 3.38929i) q^{34} +(-0.132986 + 0.438397i) q^{35} +(-1.84198 - 0.779169i) q^{36} +(-0.462996 + 4.70088i) q^{37} +(2.72524 + 1.83573i) q^{38} +(2.89246 + 0.575346i) q^{39} +(-0.106302 - 0.567636i) q^{40} +(-0.488028 - 2.45348i) q^{41} +(-1.20333 - 2.93611i) q^{42} +(-4.72084 + 8.83208i) q^{43} +(4.00496 - 2.10233i) q^{44} +(0.0200130 + 0.203195i) q^{45} +(-2.40399 - 1.29654i) q^{46} +(1.77667 + 4.28926i) q^{47} +(3.05373 + 2.58355i) q^{48} +(-0.752210 + 1.81600i) q^{49} +(5.43704 - 4.42813i) q^{50} +(6.30427 + 5.17378i) q^{51} +(-5.18085 - 2.81925i) q^{52} +(-5.15970 + 1.56518i) q^{53} +(-0.996252 - 1.00373i) q^{54} +(-0.383949 - 0.256546i) q^{55} +(0.551132 + 6.32229i) q^{56} +(1.29084 + 1.93188i) q^{57} +(-6.10027 - 9.20404i) q^{58} +(-6.96321 - 8.48470i) q^{59} +(0.0826605 - 0.399903i) q^{60} +(8.12186 - 4.34122i) q^{61} +(1.04157 + 10.9968i) q^{62} -2.24374i q^{63} +(-4.29417 - 6.74982i) q^{64} +0.602148i q^{65} +(3.18414 - 0.301589i) q^{66} +(4.41544 - 2.36010i) q^{67} +(-8.96018 - 13.6295i) q^{68} +(-1.22523 - 1.49295i) q^{69} +(0.540039 - 0.357928i) q^{70} +(-9.35478 - 14.0004i) q^{71} +(1.30524 + 2.50925i) q^{72} +(3.88629 + 2.59674i) q^{73} +(4.74126 - 4.70592i) q^{74} +(4.74481 - 1.43932i) q^{75} +(-1.31562 - 4.45678i) q^{76} +(3.92261 + 3.21921i) q^{77} +(-2.63378 - 3.23386i) q^{78} +(-1.74009 + 4.20095i) q^{79} +(-0.395730 + 0.714436i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-1.67933 + 3.11374i) q^{82} +(-0.0428125 - 0.434683i) q^{83} +(-1.33474 + 4.28439i) q^{84} +(-0.784957 + 1.46855i) q^{85} +(13.1049 - 5.37087i) q^{86} +(-1.52325 - 7.65791i) q^{87} +(-6.25948 - 1.31828i) q^{88} +(-7.68770 - 1.52918i) q^{89} +(0.161319 - 0.239487i) q^{90} +(0.648587 - 6.58522i) q^{91} +(1.45145 + 3.57961i) q^{92} +(-2.26732 + 7.47437i) q^{93} +(1.92941 - 6.27582i) q^{94} +(-0.335451 + 0.335451i) q^{95} +(-0.999644 - 5.56783i) q^{96} +(-9.83661 - 9.83661i) q^{97} +(2.45646 - 1.30121i) q^{98} +(2.16422 + 0.656510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.08984	−	0.901251i	−0.770632	−	0.637280i
$2$	−1.08984	−	0.901251i	−0.770632	−	0.637280i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$4$	0.375495	+	1.96443i	0.187748	+	0.982217i
$5$	0.157832	−	0.129529i	0.0705846	−	0.0579273i	−0.598439	−	0.801168i	$-0.704212\pi$
$5$	0.157832	−	0.129529i	0.0705846	−	0.0579273i	0.669024	+	0.743241i	$0.266712\pi$
$6$	−0.281086	+	1.38600i	−0.114753	+	0.565831i
$7$	−1.86560	+	1.24656i	−0.705132	+	0.471154i	−0.855718	−	0.517443i	$-0.826884\pi$
$7$	−1.86560	+	1.24656i	−0.705132	+	0.471154i	0.150586	+	0.988597i	$0.451884\pi$
$8$	1.36122	−	2.47933i	0.481264	−	0.876576i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	−0.288750	−	0.00108010i	−0.0913107	−	0.000341556i
$11$	−0.656510	−	2.16422i	−0.197945	−	0.652538i	−0.998574	−	0.0533776i	$-0.983001\pi$
$11$	−0.656510	−	2.16422i	−0.197945	−	0.652538i	0.800629	−	0.599160i	$-0.204499\pi$
$12$	1.55547	−	1.25719i	0.449025	−	0.362918i
$13$	−1.87091	+	2.27971i	−0.518896	+	0.632276i	−0.964857	−	0.262776i	$-0.915362\pi$
$13$	−1.87091	+	2.27971i	−0.518896	+	0.632276i	0.445961	+	0.895052i	$0.352862\pi$
$14$	3.15667	+	0.322831i	0.843654	+	0.0862803i
$15$	−0.188636	−	0.0781357i	−0.0487057	−	0.0201745i
$16$	−3.71801	+	1.47527i	−0.929502	+	0.368818i
$17$	−7.53468	+	3.12097i	−1.82743	+	0.756946i	−0.857104	+	0.515144i	$0.827739\pi$
$17$	−7.53468	+	3.12097i	−1.82743	+	0.756946i	−0.970326	+	0.241802i	$0.922261\pi$
$18$	1.35484	−	0.405459i	0.319340	−	0.0955677i
$19$	−2.31226	+	0.227738i	−0.530470	+	0.0522467i	−0.359707	−	0.933065i	$-0.617123\pi$
$19$	−2.31226	+	0.227738i	−0.530470	+	0.0522467i	−0.170763	+	0.985312i	$0.554623\pi$
$20$	0.313717	+	0.261413i	0.0701493	+	0.0584537i
$21$	1.97880	+	1.05769i	0.431810	+	0.230807i
$22$	−1.23502	+	2.95033i	−0.263307	+	0.629013i
$23$	1.89423	−	0.376786i	0.394975	−	0.0785654i	0.00639289	−	0.999980i	$-0.497965\pi$
$23$	1.89423	−	0.376786i	0.394975	−	0.0785654i	0.388582	+	0.921414i	$0.372965\pi$
$24$	−2.82825	−	0.0317392i	−0.577314	−	0.00647873i
$25$	−0.967319	+	4.86304i	−0.193464	+	0.972608i
$26$	4.09357	−	0.798355i	0.802815	−	0.156570i
$27$	0.995185	+	0.0980171i	0.191523	+	0.0188634i
$28$	−3.14930	−	3.19678i	−0.595162	−	0.604135i
$29$	7.47173	+	2.26652i	1.38746	+	0.420883i	0.893681	−	0.448702i	$-0.148114\pi$
$29$	7.47173	+	2.26652i	1.38746	+	0.420883i	0.493783	+	0.869585i	$0.335614\pi$
$30$	0.135163	+	0.255164i	0.0246773	+	0.0465863i
$31$	−5.52299	−	5.52299i	−0.991959	−	0.991959i	0.00800888	−	0.999968i	$-0.497451\pi$
$31$	−5.52299	−	5.52299i	−0.991959	−	0.991959i	−0.999968	+	0.00800888i	$0.997451\pi$
$32$	5.38162	+	1.74305i	0.951344	+	0.308130i
$33$	−1.59920	+	1.59920i	−0.278385	+	0.278385i
$34$	11.0244	+	3.38929i	1.89066	+	0.581258i
$35$	−0.132986	+	0.438397i	−0.0224788	+	0.0741026i
$36$	−1.84198	−	0.779169i	−0.306997	−	0.129861i
$37$	−0.462996	+	4.70088i	−0.0761161	+	0.772820i	0.879046	+	0.476737i	$0.158181\pi$
$37$	−0.462996	+	4.70088i	−0.0761161	+	0.772820i	−0.955162	+	0.296083i	$0.904319\pi$
$38$	2.72524	+	1.83573i	0.442093	+	0.297795i
$39$	2.89246	+	0.575346i	0.463164	+	0.0921291i
$40$	−0.106302	−	0.567636i	−0.0168079	−	0.0897511i
$41$	−0.488028	−	2.45348i	−0.0762172	−	0.383170i	−1.00000		0.000252826i	$-0.999920\pi$
$41$	−0.488028	−	2.45348i	−0.0762172	−	0.383170i	0.923783	−	0.382917i	$-0.125080\pi$
$42$	−1.20333	−	2.93611i	−0.185678	−	0.453052i
$43$	−4.72084	+	8.83208i	−0.719922	+	1.34688i	0.209481	+	0.977813i	$0.432823\pi$
$43$	−4.72084	+	8.83208i	−0.719922	+	1.34688i	−0.929403	+	0.369067i	$0.879677\pi$
$44$	4.00496	−	2.10233i	0.603770	−	0.316938i
$45$	0.0200130	+	0.203195i	0.00298336	+	0.0302906i
$46$	−2.40399	−	1.29654i	−0.354448	−	0.191165i
$47$	1.77667	+	4.28926i	0.259154	+	0.625652i	0.998883	−	0.0472522i	$-0.0150465\pi$
$47$	1.77667	+	4.28926i	0.259154	+	0.625652i	−0.739729	+	0.672905i	$0.765046\pi$
$48$	3.05373	+	2.58355i	0.440768	+	0.372904i
$49$	−0.752210	+	1.81600i	−0.107459	+	0.259428i
$50$	5.43704	−	4.42813i	0.768913	−	0.626232i
$51$	6.30427	+	5.17378i	0.882775	+	0.724475i
$52$	−5.18085	−	2.81925i	−0.718454	−	0.390960i
$53$	−5.15970	+	1.56518i	−0.708739	+	0.214994i	−0.624017	−	0.781411i	$-0.714500\pi$
$53$	−5.15970	+	1.56518i	−0.708739	+	0.214994i	−0.0847222	+	0.996405i	$0.527000\pi$
$54$	−0.996252	−	1.00373i	−0.135573	−	0.136591i
$55$	−0.383949	−	0.256546i	−0.0517716	−	0.0345927i
$56$	0.551132	+	6.32229i	0.0736481	+	0.844851i
$57$	1.29084	+	1.93188i	0.170976	+	0.255884i
$58$	−6.10027	−	9.20404i	−0.801004	−	1.20855i
$59$	−6.96321	−	8.48470i	−0.906533	−	1.10461i	−0.994101	−	0.108456i	$-0.965409\pi$
$59$	−6.96321	−	8.48470i	−0.906533	−	1.10461i	0.0875679	−	0.996159i	$-0.472091\pi$
$60$	0.0826605	−	0.399903i	0.0106714	−	0.0516273i
$61$	8.12186	−	4.34122i	1.03990	−	0.555837i	0.139191	−	0.990266i	$-0.455550\pi$
$61$	8.12186	−	4.34122i	1.03990	−	0.555837i	0.900706	+	0.434429i	$0.143050\pi$
$62$	1.04157	+	10.9968i	0.132279	+	1.39659i
$63$		−	2.24374i		−	0.282685i
$64$	−4.29417	−	6.74982i	−0.536771	−	0.843728i
$65$			0.602148i			0.0746872i
$66$	3.18414	−	0.301589i	0.391941	−	0.0371231i
$67$	4.41544	−	2.36010i	0.539431	−	0.288332i	−0.179095	−	0.983832i	$-0.557317\pi$
$67$	4.41544	−	2.36010i	0.539431	−	0.288332i	0.718526	+	0.695500i	$0.244817\pi$
$68$	−8.96018	−	13.6295i	−1.08658	−	1.65282i
$69$	−1.22523	−	1.49295i	−0.147500	−	0.179730i
$70$	0.540039	−	0.357928i	0.0645470	−	0.0427806i
$71$	−9.35478	−	14.0004i	−1.11021	−	1.66154i	−0.589151	−	0.808023i	$-0.700538\pi$
$71$	−9.35478	−	14.0004i	−1.11021	−	1.66154i	−0.521057	−	0.853522i	$-0.674462\pi$
$72$	1.30524	+	2.50925i	0.153824	+	0.295719i
$73$	3.88629	+	2.59674i	0.454856	+	0.303925i	0.761811	−	0.647799i	$-0.224310\pi$
$73$	3.88629	+	2.59674i	0.454856	+	0.303925i	−0.306956	+	0.951724i	$0.599310\pi$
$74$	4.74126	−	4.70592i	0.551161	−	0.547053i
$75$	4.74481	−	1.43932i	0.547883	−	0.166199i
$76$	−1.31562	−	4.45678i	−0.150912	−	0.511227i
$77$	3.92261	+	3.21921i	0.447023	+	0.366862i
$78$	−2.63378	−	3.23386i	−0.298217	−	0.366163i
$79$	−1.74009	+	4.20095i	−0.195776	+	0.472644i	−0.991031	−	0.133630i	$-0.957337\pi$
$79$	−1.74009	+	4.20095i	−0.195776	+	0.472644i	0.795256	+	0.606274i	$0.207337\pi$
$80$	−0.395730	+	0.714436i	−0.0442439	+	0.0798764i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−1.67933	+	3.11374i	−0.185451	+	0.343855i
$83$	−0.0428125	−	0.434683i	−0.00469928	−	0.0477126i	0.992549	−	0.121845i	$-0.0388812\pi$
$83$	−0.0428125	−	0.434683i	−0.00469928	−	0.0477126i	−0.997248	+	0.0741327i	$0.976381\pi$
$84$	−1.33474	+	4.28439i	−0.145632	+	0.467465i
$85$	−0.784957	+	1.46855i	−0.0851406	+	0.159287i
$86$	13.1049	−	5.37087i	1.41313	−	0.579156i
$87$	−1.52325	−	7.65791i	−0.163310	−	0.821014i
$88$	−6.25948	−	1.31828i	−0.667263	−	0.140529i
$89$	−7.68770	−	1.52918i	−0.814895	−	0.162093i	−0.229988	−	0.973193i	$-0.573869\pi$
$89$	−7.68770	−	1.52918i	−0.814895	−	0.162093i	−0.584907	+	0.811101i	$0.698869\pi$
$90$	0.161319	−	0.239487i	0.0170045	−	0.0252441i
$91$	0.648587	−	6.58522i	0.0679904	−	0.690318i
$92$	1.45145	+	3.57961i	0.151324	+	0.373201i
$93$	−2.26732	+	7.47437i	−0.235111	+	0.775056i
$94$	1.92941	−	6.27582i	0.199004	−	0.647301i
$95$	−0.335451	+	0.335451i	−0.0344165	+	0.0344165i
$96$	−0.999644	−	5.56783i	−0.102026	−	0.568264i
$97$	−9.83661	−	9.83661i	−0.998756	−	0.998756i	0.00124314	−	0.999999i	$-0.499604\pi$
$97$	−9.83661	−	9.83661i	−0.998756	−	0.998756i	−0.999999	+	0.00124314i	$0.999604\pi$
$98$	2.45646	−	1.30121i	0.248139	−	0.131442i
$99$	2.16422	+	0.656510i	0.217513	+	0.0659817i
$100$	−9.91634	−	0.0741871i	−0.991634	−	0.00741871i
$101$	−5.63220	−	0.554724i	−0.560425	−	0.0551971i	−0.186161	−	0.982519i	$-0.559605\pi$
$101$	−5.63220	−	0.554724i	−0.560425	−	0.0551971i	−0.374264	+	0.927322i	$0.622105\pi$
$102$	−2.20776	−	11.3203i	−0.218601	−	1.12088i
$103$	2.08252	−	10.4695i	0.205197	−	1.03159i	−0.731604	−	0.681730i	$-0.761228\pi$
$103$	2.08252	−	10.4695i	0.205197	−	1.03159i	0.936801	−	0.349864i	$-0.113772\pi$
$104$	3.10543	+	7.74177i	0.304513	+	0.759143i
$105$	0.449321	−	0.0893755i	0.0438492	−	0.00872216i
$106$	7.03385	+	2.94439i	0.683188	+	0.285984i
$107$	5.08690	+	2.71900i	0.491769	+	0.262856i	0.698589	−	0.715523i	$-0.253812\pi$
$107$	5.08690	+	2.71900i	0.491769	+	0.262856i	−0.206820	+	0.978379i	$0.566312\pi$
$108$	0.181139	+	1.99178i	0.0174301	+	0.191659i
$109$	8.87006	−	0.873625i	0.849598	−	0.0836781i	0.336160	−	0.941805i	$-0.390872\pi$
$109$	8.87006	−	0.873625i	0.849598	−	0.0836781i	0.513438	+	0.858127i	$0.328372\pi$
$110$	0.187230	+	0.625628i	0.0178516	+	0.0596513i
$111$	4.36406	−	1.80765i	0.414218	−	0.171575i
$112$	5.09732	−	7.38698i	0.481651	−	0.698004i
$113$	−12.8552	−	5.32480i	−1.20932	−	0.500915i	−0.315319	−	0.948986i	$-0.602111\pi$
$113$	−12.8552	−	5.32480i	−1.20932	−	0.500915i	−0.893998	+	0.448070i	$0.852111\pi$
$114$	0.334300	−	3.26881i	0.0313101	−	0.306152i
$115$	0.250166	−	0.304828i	0.0233281	−	0.0284253i
$116$	−1.64684	+	15.5288i	−0.152905	+	1.44181i
$117$	−0.856086	−	2.82214i	−0.0791452	−	0.260907i
$118$	−0.0580636	+	15.5226i	−0.00534518	+	1.42897i
$119$	10.1663	−	15.2149i	0.931940	−	1.39475i
$120$	−0.450499	+	0.361332i	−0.0411248	+	0.0329849i
$121$	4.89331	−	3.26961i	0.444846	−	0.297237i
$122$	−12.7640	−	2.58860i	−1.15560	−	0.234361i
$123$	−1.93372	+	1.58697i	−0.174358	+	0.143092i
$124$	8.77570	−	12.9234i	0.788081	−	1.16056i
$125$	0.958478	+	1.79319i	0.0857289	+	0.160387i
$126$	−2.02217	+	2.44532i	−0.180150	+	0.217846i
$127$	−1.24852			−0.110788			−0.0553939	−	0.998465i	$-0.517641\pi$
$127$	−1.24852			−0.110788			−0.0553939	+	0.998465i	$0.517641\pi$
$128$	−1.40334	+	11.2263i	−0.124039	+	0.992277i
$129$	10.0146			0.881735
$130$	0.542686	−	0.656244i	0.0475967	−	0.0575564i
$131$	1.84466	+	3.45112i	0.161169	+	0.301525i	0.949524	−	0.313695i	$-0.101567\pi$
$131$	1.84466	+	3.45112i	0.161169	+	0.301525i	−0.788355	+	0.615220i	$0.789067\pi$
$132$	−3.74201	−	2.54103i	−0.325700	−	0.221168i
$133$	4.02988	−	3.30724i	0.349435	−	0.286774i
$134$	−6.93915	−	1.40729i	−0.599452	−	0.121571i
$135$	0.169768	−	0.113435i	0.0146113	−	0.00976297i
$136$	−2.51844	+	22.9293i	−0.215954	+	1.96617i
$137$	−9.30086	+	13.9197i	−0.794626	+	1.18924i	0.183865	+	0.982952i	$0.441139\pi$
$137$	−9.30086	+	13.9197i	−0.794626	+	1.18924i	−0.978491	+	0.206290i	$0.933861\pi$
$138$	−0.0102167	+	2.73131i	−0.000869705	+	0.232505i
$139$	2.59575	+	8.55703i	0.220168	+	0.725798i	0.995544	+	0.0942975i	$0.0300605\pi$
$139$	2.59575	+	8.55703i	0.220168	+	0.725798i	−0.775376	+	0.631500i	$0.782440\pi$
$140$	−0.911138	−	0.0966270i	−0.0770052	−	0.00816647i
$141$	2.94527	−	3.58882i	0.248037	−	0.302233i
$142$	−2.42269	+	23.6892i	−0.203307	+	1.98795i
$143$	6.16206	+	2.55241i	0.515297	+	0.213443i
$144$	0.838971	−	3.91103i	0.0699142	−	0.325919i
$145$	1.47286	−	0.610078i	0.122314	−	0.0506642i
$146$	−1.89512	−	6.33254i	−0.156841	−	0.524085i
$147$	1.95616	−	0.192665i	0.161341	−	0.0158907i
$148$	−9.40843	+	0.855631i	−0.773368	+	0.0703325i
$149$	7.01821	+	3.75131i	0.574954	+	0.307320i	0.733127	−	0.680092i	$-0.238060\pi$
$149$	7.01821	+	3.75131i	0.574954	+	0.307320i	−0.158172	+	0.987412i	$0.550560\pi$
$150$	−6.46826	−	2.70763i	−0.528131	−	0.221077i
$151$	4.09188	−	0.813925i	0.332992	−	0.0662363i	−0.0257626	−	0.999668i	$-0.508201\pi$
$151$	4.09188	−	0.813925i	0.332992	−	0.0662363i	0.358755	+	0.933432i	$0.383201\pi$
$152$	−2.58286	+	6.04287i	−0.209498	+	0.490142i
$153$	1.59106	−	7.99878i	0.128629	−	0.646663i
$154$	−1.37370	−	7.04367i	−0.110696	−	0.567595i
$155$	−1.58710	−	0.156315i	−0.127479	−	0.0125555i
$156$	−0.0441253	+	5.89809i	−0.00353285	+	0.472225i
$157$	9.87857	+	2.99663i	0.788396	+	0.239157i	0.658709	−	0.752398i	$-0.271103\pi$
$157$	9.87857	+	2.99663i	0.788396	+	0.239157i	0.129687	+	0.991555i	$0.458603\pi$
$158$	5.68253	−	3.01010i	0.452078	−	0.239471i
$159$	3.81263	+	3.81263i	0.302361	+	0.302361i
$160$	1.07517	−	0.421968i	0.0849994	−	0.0333595i
$161$	−3.06420	+	3.06420i	−0.241493	+	0.241493i
$162$	−0.415584	+	1.35177i	−0.0326513	+	0.106205i
$163$	−1.90745	+	6.28801i	−0.149403	+	0.492515i	−0.999413	−	0.0342508i	$-0.989095\pi$
$163$	−1.90745	+	6.28801i	−0.149403	+	0.492515i	0.850011	+	0.526766i	$0.176595\pi$
$164$	4.63646	−	1.87997i	0.362046	−	0.146801i
$165$	−0.0452615	+	0.459548i	−0.00352360	+	0.0357757i
$166$	−0.345099	+	0.512319i	−0.0267849	+	0.0397636i
$167$	7.90867	+	1.57313i	0.611991	+	0.121733i	0.491348	−	0.870963i	$-0.336504\pi$
$167$	7.90867	+	1.57313i	0.611991	+	0.121733i	0.120643	+	0.992696i	$0.461504\pi$
$168$	5.31596	−	3.46636i	0.410135	−	0.267435i
$169$	0.839407	+	4.21998i	0.0645697	+	0.324614i
$170$	2.17901	−	0.893041i	0.167122	−	0.0684931i
$171$	1.09527	−	2.04910i	0.0837572	−	0.156699i
$172$	−19.1227	−	5.95739i	−1.45809	−	0.454247i
$173$	−1.84315	−	18.7138i	−0.140132	−	1.42279i	−0.765992	−	0.642850i	$-0.777752\pi$
$173$	−1.84315	−	18.7138i	−0.140132	−	1.42279i	0.625860	−	0.779936i	$-0.284748\pi$
$174$	−5.24159	+	9.71871i	−0.397364	+	0.736774i
$175$	−4.25742	−	10.2783i	−0.321831	−	0.776968i
$176$	5.63372	+	7.07807i	0.424658	+	0.533529i
$177$	−4.20040	+	10.1407i	−0.315722	+	0.762219i
$178$	7.00018	+	8.59511i	0.524686	+	0.644230i
$179$	−2.35524	−	1.93289i	−0.176039	−	0.144471i	0.542248	−	0.840219i	$-0.317573\pi$
$179$	−2.35524	−	1.93289i	−0.176039	−	0.144471i	−0.718287	+	0.695747i	$0.755073\pi$
$180$	−0.391649	+	0.115613i	−0.0291918	+	0.00861728i
$181$	12.0982	−	3.66994i	0.899251	−	0.272785i	0.193379	−	0.981124i	$-0.438055\pi$
$181$	12.0982	−	3.66994i	0.899251	−	0.272785i	0.705872	+	0.708339i	$0.250555\pi$
$182$	−6.64178	+	6.59228i	−0.492322	+	0.488652i
$183$	−7.65723	−	5.11640i	−0.566039	−	0.378215i
$184$	1.64429	−	5.20932i	0.121218	−	0.384036i
$185$	0.535827	+	0.801921i	0.0393948	+	0.0589584i
$186$	9.20729	−	6.10242i	0.675112	−	0.447451i
$187$	11.7011	+	14.2578i	0.855667	+	1.04263i
$188$	−7.75883	+	5.10074i	−0.565871	+	0.372010i
$189$	−1.97880	+	1.05769i	−0.143937	+	0.0769358i
$190$	0.667912	−	0.0632619i	0.0484554	−	0.00458950i
$191$			5.67297i			0.410481i	0.978712	+	0.205241i	$0.0657977\pi$
$191$			5.67297i			0.410481i	−0.978712	+	0.205241i	$0.934202\pi$
$192$	−3.92856	+	6.96896i	−0.283519	+	0.502942i
$193$		−	6.41422i		−	0.461706i	−0.972989	−	0.230853i	$-0.925848\pi$
$193$		−	6.41422i		−	0.461706i	0.972989	−	0.230853i	$-0.0741516\pi$
$194$	1.85506	+	19.5856i	0.133186	+	1.40616i
$195$	0.531047	−	0.283851i	0.0380291	−	0.0203270i
$196$	−3.84986	−	0.795770i	−0.274990	−	0.0568407i
$197$	4.67715	+	5.69913i	0.333233	+	0.406046i	0.912490	−	0.409099i	$-0.134157\pi$
$197$	4.67715	+	5.69913i	0.333233	+	0.406046i	−0.579256	+	0.815145i	$0.696657\pi$
$198$	−1.76697	−	2.66600i	−0.125573	−	0.189464i
$199$	−2.27840	−	3.40987i	−0.161512	−	0.241719i	0.741883	−	0.670529i	$-0.233933\pi$
$199$	−2.27840	−	3.40987i	−0.161512	−	0.241719i	−0.903395	+	0.428810i	$0.858933\pi$
$200$	10.7404	+	9.01796i	0.759458	+	0.637666i
$201$	−4.16284	−	2.78152i	−0.293624	−	0.196194i
$202$	5.63825	+	5.68059i	0.396706	+	0.399685i
$203$	−16.7646	+	5.08549i	−1.17665	+	0.356932i
$204$	−7.79634	+	14.3271i	−0.545853	+	1.00310i
$205$	−0.394825	−	0.324024i	−0.0275758	−	0.0226308i
$206$	−11.7053	+	9.53323i	−0.815546	+	0.664212i
$207$	−0.739093	+	1.78433i	−0.0513705	+	0.124019i
$208$	3.59286	−	11.2361i	0.249120	−	0.779080i
$209$	2.01090	+	4.85474i	0.139097	+	0.335810i
$210$	−0.570237	−	0.307546i	−0.0393501	−	0.0212227i
$211$	1.71852	+	17.4484i	0.118308	+	1.20120i	0.852673	+	0.522445i	$0.174980\pi$
$211$	1.71852	+	17.4484i	0.118308	+	1.20120i	−0.734366	+	0.678754i	$0.762520\pi$
$212$	−5.01213	−	9.54817i	−0.344234	−	0.655771i
$213$	−7.93746	+	14.8499i	−0.543866	+	1.01750i
$214$	−3.09339	−	7.54784i	−0.211460	−	0.515960i
$215$	0.398913	+	2.00547i	0.0272057	+	0.136772i
$216$	1.59768	−	2.33397i	0.108708	−	0.158807i
$217$	17.1884	+	3.41899i	1.16683	+	0.232096i
$218$	−10.4543	−	7.04204i	−0.708054	−	0.476947i
$219$	0.458132	−	4.65149i	0.0309577	−	0.314319i
$220$	0.359798	−	0.850574i	0.0242576	−	0.0573457i
$221$	6.98180	−	23.0159i	0.469646	−	1.54822i
$222$	−6.38527	−	1.96306i	−0.428551	−	0.131752i
$223$	−10.3476	+	10.3476i	−0.692926	+	0.692926i	−0.962875	−	0.269949i	$-0.912993\pi$
$223$	−10.3476	+	10.3476i	−0.692926	+	0.692926i	0.269949	+	0.962875i	$0.412993\pi$
$224$	−12.2128	+	3.45665i	−0.816000	+	0.230957i
$225$	−3.50606	−	3.50606i	−0.233737	−	0.233737i
$226$	9.21112	+	17.3889i	0.612715	+	1.15670i
$227$	−3.54068	−	1.07405i	−0.235003	−	0.0712874i	0.170587	−	0.985343i	$-0.445434\pi$
$227$	−3.54068	−	1.07405i	−0.235003	−	0.0712874i	−0.405590	+	0.914055i	$0.632934\pi$
$228$	−3.31035	+	3.26118i	−0.219233	+	0.215977i
$229$	−5.40969	−	0.532808i	−0.357482	−	0.0352089i	−0.0823179	−	0.996606i	$-0.526232\pi$
$229$	−5.40969	−	0.532808i	−0.357482	−	0.0352089i	−0.275164	+	0.961397i	$0.588732\pi$
$230$	−0.547366	+	0.106751i	−0.0360923	+	0.00703895i
$231$	0.989979	−	4.97696i	0.0651358	−	0.327460i
$232$	15.7901	−	15.4396i	1.03667	−	1.01366i
$233$	5.53362	−	1.10071i	0.362520	−	0.0721097i	−0.0104698	−	0.999945i	$-0.503333\pi$
$233$	5.53362	−	1.10071i	0.362520	−	0.0721097i	0.372990	+	0.927836i	$0.378333\pi$
$234$	−1.61046	+	3.84722i	−0.105279	+	0.251501i
$235$	0.836000	+	0.446851i	0.0545346	+	0.0291494i
$236$	14.0530	−	16.8647i	0.914772	−	1.09780i
$237$	4.52518	−	0.445692i	0.293942	−	0.0289508i
$238$	−24.7920	+	7.41942i	−1.60703	+	0.480930i
$239$	−6.14276	+	2.54441i	−0.397342	+	0.164584i	−0.572402	−	0.819973i	$-0.693988\pi$
$239$	−6.14276	+	2.54441i	−0.397342	+	0.164584i	0.175060	+	0.984558i	$0.443988\pi$
$240$	0.816622	+	0.0122195i	0.0527127	+	0.000788763i
$241$	−5.29873	−	2.19481i	−0.341321	−	0.141380i	0.205437	−	0.978670i	$-0.434138\pi$
$241$	−5.29873	−	2.19481i	−0.341321	−	0.141380i	−0.546758	+	0.837290i	$0.684138\pi$
$242$	−8.27965	−	0.846757i	−0.532236	−	0.0544316i
$243$	−0.634393	+	0.773010i	−0.0406963	+	0.0495886i
$244$	11.5778	+	14.3248i	0.741191	+	0.917048i
$245$	0.116502	+	0.384056i	0.00744304	+	0.0245364i
$246$	3.53770	+	0.0132331i	0.225556	+	0.000843712i
$247$	3.80685	−	5.69736i	0.242224	−	0.362514i
$248$	−21.2113	+	6.17533i	−1.34692	+	0.392134i
$249$	−0.363174	+	0.242665i	−0.0230152	+	0.0153783i
$250$	0.571524	−	2.81811i	0.0361463	−	0.178233i
$251$	0.953967	−	0.782901i	0.0602139	−	0.0494163i	−0.603805	−	0.797132i	$-0.706349\pi$
$251$	0.953967	−	0.782901i	0.0602139	−	0.0494163i	0.664019	+	0.747716i	$0.268849\pi$
$252$	4.40769	−	0.842514i	0.277658	−	0.0530734i
$253$	−2.05903	−	3.85218i	−0.129450	−	0.242184i
$254$	1.36068	+	1.12522i	0.0853766	+	0.0706029i
$255$	1.66517			0.104277
$256$	11.6472	−	10.9701i	0.727947	−	0.685633i
$257$	−3.50851			−0.218855			−0.109427	−	0.993995i	$-0.534902\pi$
$257$	−3.50851			−0.218855			−0.109427	+	0.993995i	$0.534902\pi$
$258$	−10.9143	−	9.02565i	−0.679494	−	0.561913i
$259$	−4.99615	−	9.34713i	−0.310445	−	0.580802i
$260$	−1.18288	+	0.226104i	−0.0733591	+	0.0140223i
$261$	−6.03561	+	4.95330i	−0.373595	+	0.306602i
$262$	1.09994	−	5.42366i	0.0679545	−	0.335075i
$263$	−17.5127	+	11.7016i	−1.07988	+	0.721551i	−0.962430	−	0.271529i	$-0.912471\pi$
$263$	−17.5127	+	11.7016i	−1.07988	+	0.721551i	−0.117446	+	0.993079i	$0.537471\pi$
$264$	1.78808	+	6.14180i	0.110049	+	0.378002i
$265$	−0.611629	+	0.915368i	−0.0375721	+	0.0562306i
$266$	−7.37257	−	0.0275778i	−0.452041	−	0.00169090i
$267$	2.27534	+	7.50080i	0.139249	+	0.459041i
$268$	6.29424	+	7.78763i	0.384482	+	0.475705i
$269$	−12.2423	+	14.9173i	−0.746428	+	0.909525i	−0.998303	−	0.0582349i	$-0.981453\pi$
$269$	−12.2423	+	14.9173i	−0.746428	+	0.909525i	0.251875	+	0.967760i	$0.418953\pi$
$270$	−0.287254	−	0.0293773i	−0.0174817	−	0.00178785i
$271$	15.0332	+	6.22697i	0.913204	+	0.378261i	0.789282	−	0.614031i	$-0.210453\pi$
$271$	15.0332	+	6.22697i	0.913204	+	0.378261i	0.123922	+	0.992292i	$0.460453\pi$
$272$	23.4097	−	22.7195i	1.41942	−	1.37757i
$273$	−6.11338	+	2.53225i	−0.369999	+	0.153259i
$274$	22.6816	−	6.78784i	1.37024	−	0.410068i
$275$	11.1598	−	1.09914i	0.672958	−	0.0662806i
$276$	2.47273	−	2.96748i	0.148841	−	0.178621i
$277$	2.49751	+	1.33495i	0.150061	+	0.0802093i	0.544718	−	0.838619i	$-0.316637\pi$
$277$	2.49751	+	1.33495i	0.150061	+	0.0802093i	−0.394657	+	0.918828i	$0.629137\pi$
$278$	4.88308	−	11.6652i	0.292868	−	0.699632i
$279$	7.66061	−	1.52379i	0.458629	−	0.0912270i
$280$	0.905908	+	0.926471i	0.0541384	+	0.0553673i
$281$	−4.51856	+	22.7163i	−0.269554	+	1.35514i	0.574333	+	0.818622i	$0.305261\pi$
$281$	−4.51856	+	22.7163i	−0.269554	+	1.35514i	−0.843887	+	0.536520i	$0.819739\pi$
$282$	−6.44430	+	1.25681i	−0.383752	+	0.0748419i
$283$	−30.1801	−	2.97248i	−1.79402	−	0.176696i	−0.854560	−	0.519353i	$-0.826173\pi$
$283$	−30.1801	−	2.97248i	−1.79402	−	0.176696i	−0.939461	+	0.342657i	$0.888673\pi$
$284$	23.9902	−	23.6339i	1.42356	−	1.40242i
$285$	0.453971	+	0.137711i	0.0268909	+	0.00815728i
$286$	−4.41529	−	8.33527i	−0.261081	−	0.492875i
$287$	3.96887	+	3.96887i	0.234275	+	0.234275i
$288$	−4.43916	+	3.50626i	−0.261580	+	0.206609i
$289$	35.0102	−	35.0102i	2.05942	−	2.05942i
$290$	−2.15501	−	0.662528i	−0.126547	−	0.0389050i
$291$	−4.03817	+	13.3121i	−0.236722	+	0.780367i
$292$	−3.64183	+	8.60942i	−0.213122	+	0.503828i
$293$	3.17772	−	32.2640i	0.185645	−	1.88488i	−0.226862	−	0.973927i	$-0.572847\pi$
$293$	3.17772	−	32.2640i	0.185645	−	1.88488i	0.412507	−	0.910954i	$-0.364653\pi$
$294$	−2.30553	−	1.55301i	−0.134461	−	0.0905736i
$295$	−2.19804	−	0.437217i	−0.127975	−	0.0254557i
$296$	11.0248	+	7.54685i	0.640804	+	0.438652i
$297$	−0.441218	−	2.21815i	−0.0256020	−	0.128710i
$298$	−4.26784	−	10.4135i	−0.247230	−	0.603237i
$299$	−2.68497	+	5.02322i	−0.155276	+	0.290500i
$300$	4.60911	+	8.78041i	0.266107	+	0.506937i
$301$	−2.20246	−	22.3620i	−0.126948	−	1.28892i
$302$	−5.19304	−	2.80076i	−0.298826	−	0.161166i
$303$	2.16578	+	5.22866i	0.124421	+	0.300378i
$304$	8.26104	−	4.25795i	0.473803	−	0.244210i
$305$	0.719573	−	1.73720i	0.0412026	−	0.0994720i
$306$	−8.94290	+	7.28343i	−0.511231	+	0.416366i
$307$	21.1869	+	17.3876i	1.20920	+	0.992363i	0.999895	+	0.0145125i	$0.00461964\pi$
$307$	21.1869	+	17.3876i	1.20920	+	0.992363i	0.209303	+	0.977851i	$0.432880\pi$
$308$	−4.85100	+	8.91451i	−0.276411	+	0.507951i
$309$	−10.2150	+	3.09869i	−0.581111	+	0.176278i
$310$	1.58880	+	1.60073i	0.0902377	+	0.0909153i
$311$	22.8347	+	15.2576i	1.29484	+	0.865182i	0.996020	−	0.0891289i	$-0.0284083\pi$
$311$	22.8347	+	15.2576i	1.29484	+	0.865182i	0.298816	+	0.954311i	$0.403408\pi$
$312$	5.36374	−	6.38819i	0.303662	−	0.361660i
$313$	17.8359	+	26.6933i	1.00814	+	1.50879i	0.853683	+	0.520793i	$0.174364\pi$
$313$	17.8359	+	26.6933i	1.00814	+	1.50879i	0.154460	+	0.987999i	$0.450636\pi$
$314$	−8.06533	−	12.1689i	−0.455153	−	0.686731i
$315$	−0.290631	−	0.354134i	−0.0163752	−	0.0199532i
$316$	−8.90589	−	1.84086i	−0.500996	−	0.103556i
$317$	30.1511	−	16.1161i	1.69346	−	0.905171i	0.714891	−	0.699236i	$-0.246476\pi$
$317$	30.1511	−	16.1161i	1.69346	−	0.905171i	0.978566	−	0.205935i	$-0.0660237\pi$
$318$	−0.719015	−	7.59128i	−0.0403204	−	0.425698i
$319$		−	17.6585i		−	0.988685i
$320$	−1.55206	−	0.509118i	−0.0867627	−	0.0284605i
$321$		−	5.76797i		−	0.321937i
$322$	6.10110	−	0.577871i	0.340001	−	0.0322035i
$323$	16.7114	−	8.93244i	0.929848	−	0.497014i
$324$	1.67121	−	1.09867i	0.0928447	−	0.0610372i
$325$	−9.27653	−	11.3035i	−0.514569	−	0.627005i
$326$	7.74588	−	5.13383i	0.429005	−	0.284336i
$327$	−4.95179	−	7.41087i	−0.273834	−	0.409822i
$328$	−6.74731	−	2.12974i	−0.372558	−	0.117595i
$329$	−8.66136	−	5.78733i	−0.477516	−	0.319066i
$330$	0.463495	−	0.460041i	0.0255146	−	0.0253244i
$331$	−29.5070	+	8.95084i	−1.62185	+	0.491983i	−0.965046	−	0.262080i	$-0.915592\pi$
$331$	−29.5070	+	8.95084i	−1.62185	+	0.491983i	−0.656803	+	0.754062i	$0.728092\pi$
$332$	0.837830	−	0.247324i	0.0459819	−	0.0135736i
$333$	−3.65141	−	2.99664i	−0.200096	−	0.164215i
$334$	−7.20138	−	8.84215i	−0.394042	−	0.483821i
$335$	0.391195	−	0.944428i	0.0213733	−	0.0515996i
$336$	−8.91759	−	1.01324i	−0.486494	−	0.0552766i
$337$	−10.1563	−	24.5195i	−0.553250	−	1.33566i	−0.915025	−	0.403397i	$-0.867829\pi$
$337$	−10.1563	−	24.5195i	−0.553250	−	1.33566i	0.361775	−	0.932265i	$-0.382171\pi$
$338$	2.88844	−	5.35561i	0.157111	−	0.291307i
$339$	1.36385	+	13.8474i	0.0740741	+	0.752087i
$340$	−3.17962	−	0.990564i	−0.172439	−	0.0537209i
$341$	−8.32709	+	15.5789i	−0.450937	+	0.843644i
$342$	−3.04042	+	1.24608i	−0.164407	+	0.0673803i
$343$	−3.92454	−	19.7300i	−0.211905	−	1.06532i
$344$	15.4715	+	23.7269i	0.834170	+	1.27927i
$345$	−0.386761	−	0.0769316i	−0.0208225	−	0.00414186i
$346$	−14.8571	+	22.0562i	−0.798723	+	1.18575i
$347$	3.19069	−	32.3956i	0.171285	−	1.73909i	−0.398387	−	0.917218i	$-0.630430\pi$
$347$	3.19069	−	32.3956i	0.171285	−	1.73909i	0.569672	−	0.821872i	$-0.307070\pi$
$348$	14.4715	−	5.86784i	0.775753	−	0.314549i
$349$	−8.11619	+	26.7555i	−0.434450	+	1.43219i	0.417554	+	0.908652i	$0.362887\pi$
$349$	−8.11619	+	26.7555i	−0.434450	+	1.43219i	−0.852004	+	0.523536i	$0.824613\pi$
$350$	−4.62344	+	15.0387i	−0.247133	+	0.803853i
$351$	−2.08535	+	2.08535i	−0.111308	+	0.111308i
$352$	0.239263	−	12.7913i	0.0127528	−	0.681781i
$353$	−18.2638	−	18.2638i	−0.972084	−	0.972084i	0.0275365	−	0.999621i	$-0.491234\pi$
$353$	−18.2638	−	18.2638i	−0.972084	−	0.972084i	−0.999621	+	0.0275365i	$0.991234\pi$
$354$	13.7170	−	7.26607i	0.729053	−	0.386187i
$355$	−3.28995	−	0.997996i	−0.174612	−	0.0529681i
$356$	0.117278	−	15.6762i	0.00621573	−	0.830836i
$357$	−18.2107	−	1.79360i	−0.963812	−	0.0949272i
$358$	0.824807	+	4.22920i	0.0435924	+	0.223520i
$359$	0.0386436	−	0.194275i	0.00203953	−	0.0102534i	−0.979752	−	0.200214i	$-0.935836\pi$
$359$	0.0386436	−	0.194275i	0.00203953	−	0.0102534i	0.981792	+	0.189961i	$0.0608361\pi$
$360$	0.531030	+	0.226974i	0.0279878	+	0.0119626i
$361$	−13.3402	+	2.65353i	−0.702117	+	0.139660i
$362$	−16.4926	−	6.90385i	−0.866832	−	0.362858i
$363$	−5.19023	−	2.77423i	−0.272416	−	0.145609i
$364$	13.1798	−	1.19861i	0.690807	−	0.0628242i
$365$	0.949735	−	0.0935407i	0.0497114	−	0.00489614i
$366$	3.73399	+	12.4771i	0.195179	+	0.652190i
$367$	−33.6017	+	13.9183i	−1.75399	+	0.726527i	−0.756638	+	0.653834i	$0.773160\pi$
$367$	−33.6017	+	13.9183i	−1.75399	+	0.726527i	−0.997354	+	0.0726936i	$0.976840\pi$
$368$	−6.48691	+	4.19540i	−0.338153	+	0.218700i
$369$	2.31113	+	0.957302i	0.120313	+	0.0498351i
$370$	0.138768	−	1.35688i	0.00721418	−	0.0705408i
$371$	7.67487	−	9.35185i	0.398459	−	0.485524i
$372$	−15.5343	−	1.64742i	−0.805415	−	0.0854149i
$373$	8.34167	+	27.4988i	0.431915	+	1.42383i	0.855417	+	0.517939i	$0.173301\pi$
$373$	8.34167	+	27.4988i	0.431915	+	1.42383i	−0.423502	+	0.905895i	$0.639199\pi$
$374$	0.0975707	−	26.0843i	0.00504526	−	1.34879i
$375$	1.12963	−	1.69060i	0.0583336	−	0.0873024i
$376$	13.0529	+	1.43367i	0.673153	+	0.0739358i
$377$	−19.1459	+	12.7929i	−0.986064	+	0.658867i
$378$	3.10982	+	0.630684i	0.159952	+	0.0324389i
$379$	−9.57836	+	7.86075i	−0.492007	+	0.403780i	−0.847415	−	0.530932i	$-0.821842\pi$
$379$	−9.57836	+	7.86075i	−0.492007	+	0.403780i	0.355408	+	0.934711i	$0.384342\pi$
$380$	−0.784931	−	0.533011i	−0.0402661	−	0.0273429i
$381$	0.588546	+	1.10109i	0.0301521	+	0.0564107i
$382$	5.11276	−	6.18262i	0.261592	−	0.316330i
$383$	−7.21602			−0.368721			−0.184361	−	0.982859i	$-0.559021\pi$
$383$	−7.21602			−0.368721			−0.184361	+	0.982859i	$0.559021\pi$
$384$	10.5623	−	4.05443i	0.539004	−	0.206902i
$385$	1.03610			0.0528043
$386$	−5.78082	+	6.99046i	−0.294236	+	0.355805i
$387$	−4.72084	−	8.83208i	−0.239974	−	0.448960i
$388$	15.6298	−	23.0170i	0.793482	−	1.16851i
$389$	−5.28030	+	4.33343i	−0.267722	+	0.219714i	−0.758670	−	0.651475i	$-0.774150\pi$
$389$	−5.28030	+	4.33343i	−0.267722	+	0.219714i	0.490948	+	0.871189i	$0.336650\pi$
$390$	−0.834576	−	0.169255i	−0.0422604	−	0.00857057i
$391$	−13.0965	+	8.75081i	−0.662319	+	0.442547i
$392$	3.47853	+	4.33695i	0.175693	+	0.219049i
$393$	2.17405	−	3.25369i	0.109666	−	0.164127i
$394$	0.0390010	−	10.4264i	0.00196484	−	0.525275i
$395$	0.269505	+	0.888438i	0.0135603	+	0.0447022i
$396$	−0.477016	+	4.49799i	−0.0239709	+	0.226033i
$397$	8.23267	−	10.0315i	0.413186	−	0.503468i	−0.524280	−	0.851546i	$-0.675665\pi$
$397$	8.23267	−	10.0315i	0.413186	−	0.503468i	0.937466	+	0.348078i	$0.113165\pi$
$398$	−0.590057	+	5.76962i	−0.0295769	+	0.289205i
$399$	−4.81640	−	1.99502i	−0.241121	−	0.0998757i
$400$	−3.57780	−	19.5079i	−0.178890	−	0.975393i
$401$	−13.1424	+	5.44376i	−0.656301	+	0.271849i	−0.685881	−	0.727714i	$-0.740583\pi$
$401$	−13.1424	+	5.44376i	−0.656301	+	0.271849i	0.0295803	+	0.999562i	$0.490583\pi$
$402$	2.02998	+	6.78318i	0.101246	+	0.338314i
$403$	22.9238	−	2.25780i	1.14192	−	0.112469i
$404$	−1.02515	−	11.2724i	−0.0510029	−	0.560823i
$405$	−0.180069	−	0.0962490i	−0.00894771	−	0.00478265i
$406$	22.8540	+	9.56676i	1.13423	+	0.474790i
$407$	10.4777	−	2.08415i	0.519361	−	0.103307i
$408$	21.4090	−	8.58773i	1.05990	−	0.425156i
$409$	4.43387	−	22.2906i	0.219241	−	1.10220i	−0.701693	−	0.712479i	$-0.747572\pi$
$409$	4.43387	−	22.2906i	0.219241	−	1.10220i	0.920934	−	0.389718i	$-0.127428\pi$
$410$	0.138268	+	0.708970i	0.00682858	+	0.0350135i
$411$	16.6605	+	1.64092i	0.821801	+	0.0809404i
$412$	21.3487	+	0.159716i	1.05177	+	0.00786863i
$413$	23.5673	+	7.14905i	1.15967	+	0.351782i
$414$	2.41362	−	1.27852i	0.118623	−	0.0628359i
$415$	−0.0630614	−	0.0630614i	−0.00309556	−	0.00309556i
$416$	−14.0421	+	9.00742i	−0.688472	+	0.441625i
$417$	6.32300	−	6.32300i	0.309639	−	0.309639i
$418$	2.18378	−	7.10321i	0.106812	−	0.347429i
$419$	−6.74019	+	22.2194i	−0.329280	+	1.08549i	0.623499	+	0.781824i	$0.285711\pi$
$419$	−6.74019	+	22.2194i	−0.329280	+	1.08549i	−0.952779	+	0.303666i	$0.901789\pi$
$420$	0.344290	+	0.849102i	0.0167996	+	0.0414319i
$421$	1.77456	−	18.0174i	0.0864868	−	0.878116i	−0.849853	−	0.527020i	$-0.823309\pi$
$421$	1.77456	−	18.0174i	0.0864868	−	0.878116i	0.936340	−	0.351096i	$-0.114191\pi$
$422$	13.8525	−	20.5648i	0.674329	−	1.00108i
$423$	−4.55345	−	0.905738i	−0.221396	−	0.0440385i
$424$	−3.14288	+	14.9231i	−0.152632	+	0.724732i
$425$	−7.88895	−	39.6604i	−0.382670	−	1.92381i
$426$	22.0341	−	9.03039i	1.06755	−	0.437524i
$427$	−9.74059	+	18.2234i	−0.471380	+	0.881890i
$428$	−3.43120	+	11.0138i	−0.165853	+	0.532374i
$429$	−0.653751	−	6.63765i	−0.0315634	−	0.320469i
$430$	1.37268	−	2.54516i	0.0661966	−	0.122739i
$431$	11.4563	+	27.6580i	0.551831	+	1.33224i	0.916102	+	0.400944i	$0.131318\pi$
$431$	11.4563	+	27.6580i	0.551831	+	1.33224i	−0.364272	+	0.931293i	$0.618682\pi$
$432$	−3.84471	+	1.10374i	−0.184978	+	0.0531037i
$433$	−1.73211	+	4.18169i	−0.0832400	+	0.200959i	−0.960019	−	0.279934i	$-0.909687\pi$
$433$	−1.73211	+	4.18169i	−0.0832400	+	0.200959i	0.876779	+	0.480893i	$0.159687\pi$
$434$	−15.6513	−	19.2172i	−0.751284	−	0.922457i
$435$	−1.23234	−	1.01136i	−0.0590863	−	0.0484909i
$436$	5.04684	+	17.0966i	0.241700	+	0.818780i
$437$	−4.29416	+	1.30262i	−0.205417	+	0.0623127i
$438$	−4.69145	+	4.65648i	−0.224166	+	0.222495i
$439$	23.5427	+	15.7307i	1.12363	+	0.750787i	0.971374	−	0.237553i	$-0.0763455\pi$
$439$	23.5427	+	15.7307i	1.12363	+	0.750787i	0.152258	+	0.988341i	$0.451345\pi$
$440$	−1.15870	+	0.602720i	−0.0552389	+	0.0287336i
$441$	−1.09204	−	1.63435i	−0.0520019	−	0.0778264i
$442$	−28.3521	+	18.7913i	−1.34857	+	0.893809i
$443$	−4.17534	−	5.08766i	−0.198376	−	0.241722i	0.664315	−	0.747452i	$-0.268723\pi$
$443$	−4.17534	−	5.08766i	−0.198376	−	0.241722i	−0.862692	+	0.505730i	$0.831223\pi$
$444$	5.18970	+	7.89415i	0.246292	+	0.374640i
$445$	−1.41144	+	0.754430i	−0.0669087	+	0.0357634i
$446$	20.6030	−	1.95143i	0.975579	−	0.0924028i
$447$		−	7.95787i		−	0.376394i
$448$	16.4252	+	7.23958i	0.776020	+	0.342038i
$449$			20.0456i			0.946010i	0.881060	+	0.473005i	$0.156831\pi$
$449$			20.0456i			0.946010i	−0.881060	+	0.473005i	$0.843169\pi$
$450$	0.661199	+	6.98087i	0.0311692	+	0.329081i
$451$	−4.98949	+	2.66694i	−0.234946	+	0.125581i
$452$	5.63316	−	27.2527i	0.264962	−	1.28186i
$453$	−2.64672	−	3.22503i	−0.124354	−	0.151525i
$454$	2.89078	+	4.36158i	0.135671	+	0.204699i
$455$	−0.750611	−	1.12337i	−0.0351892	−	0.0526644i
$456$	6.54689	−	0.570711i	0.306586	−	0.0267260i
$457$	18.5511	+	12.3954i	0.867783	+	0.579834i	0.907818	−	0.419364i	$-0.137747\pi$
$457$	18.5511	+	12.3954i	0.867783	+	0.579834i	−0.0400351	+	0.999198i	$0.512747\pi$
$458$	5.41549	+	5.45616i	0.253049	+	0.254950i
$459$	−7.80431	+	2.36741i	−0.364274	+	0.110501i
$460$	0.692750	+	0.376973i	0.0322996	+	0.0175764i
$461$	3.97095	+	3.25887i	0.184945	+	0.151781i	0.722310	−	0.691569i	$-0.243080\pi$
$461$	3.97095	+	3.25887i	0.184945	+	0.151781i	−0.537365	+	0.843350i	$0.680580\pi$
$462$	−5.56440	+	4.53186i	−0.258879	+	0.210841i
$463$	−10.7306	+	25.9061i	−0.498695	+	1.20396i	0.451491	+	0.892275i	$0.350892\pi$
$463$	−10.7306	+	25.9061i	−0.498695	+	1.20396i	−0.950187	+	0.311681i	$0.899108\pi$
$464$	−31.1237	+	2.59587i	−1.44488	+	0.120510i
$465$	0.610294	+	1.47338i	0.0283017	+	0.0683264i
$466$	−7.02277	−	3.78759i	−0.325323	−	0.175457i
$467$	1.89208	+	19.2106i	0.0875548	+	0.888959i	0.934188	+	0.356782i	$0.116126\pi$
$467$	1.89208	+	19.2106i	0.0875548	+	0.888959i	−0.846633	+	0.532177i	$0.821374\pi$
$468$	5.22245	−	2.74142i	0.241408	−	0.126722i
$469$	−5.29546	+	9.90710i	−0.244521	+	0.457467i
$470$	−0.508380	−	1.24044i	−0.0234498	−	0.0572173i
$471$	−2.01393	−	10.1247i	−0.0927971	−	0.466523i
$472$	−30.5148	+	5.71458i	−1.40456	+	0.263035i
$473$	22.2139	+	4.41861i	1.02139	+	0.203168i
$474$	−5.33340	−	3.59259i	−0.244971	−	0.165013i
$475$	1.12920	−	11.4649i	0.0518111	−	0.526047i
$476$	33.7061	+	14.2579i	1.54491	+	0.653508i
$477$	1.56518	−	5.15970i	0.0716645	−	0.236246i
$478$	8.98777	+	2.76316i	0.411091	+	0.126384i
$479$	−8.75596	+	8.75596i	−0.400070	+	0.400070i	−0.878258	−	0.478188i	$-0.841294\pi$
$479$	−8.75596	+	8.75596i	−0.400070	+	0.400070i	0.478188	+	0.878258i	$0.341294\pi$
$480$	−0.878973	−	0.749298i	−0.0401195	−	0.0342006i
$481$	−9.85040	−	9.85040i	−0.449140	−	0.449140i
$482$	3.79669	+	7.16747i	0.172934	+	0.326469i
$483$	4.14684	+	1.25793i	0.188688	+	0.0572378i
$484$	8.26034	+	8.38487i	0.375470	+	0.381130i
$485$	−2.82666	−	0.278402i	−0.128352	−	0.0126416i
$486$	1.38806	−	0.270709i	0.0629638	−	0.0122796i
$487$	−8.31451	+	41.7999i	−0.376766	+	1.89413i	0.0665772	+	0.997781i	$0.478792\pi$
$487$	−8.31451	+	41.7999i	−0.376766	+	1.89413i	−0.443344	+	0.896352i	$0.646208\pi$
$488$	0.292295	−	26.0461i	0.0132316	−	1.17905i
$489$	6.44469	−	1.28193i	0.291439	−	0.0579708i
$490$	0.219162	−	0.523556i	0.00990073	−	0.0236519i
$491$	−2.35721	−	1.25996i	−0.106379	−	0.0568610i	0.417349	−	0.908746i	$-0.362959\pi$
$491$	−2.35721	−	1.25996i	−0.106379	−	0.0568610i	−0.523728	+	0.851885i	$0.675459\pi$
$492$	−3.84360	−	3.20278i	−0.173283	−	0.144392i
$493$	−63.3708	+	6.24148i	−2.85408	+	0.281102i
$494$	−9.28360	+	2.77827i	−0.417689	+	0.125000i
$495$	0.426621	−	0.176712i	0.0191752	−	0.00794262i
$496$	28.6824	+	12.3866i	1.28788	+	0.556176i
$497$	34.9046	+	14.4580i	1.56569	+	0.648529i
$498$	0.614503	+	0.0628451i	0.0275366	+	0.00281615i
$499$	27.2650	−	33.2225i	1.22055	−	1.48724i	0.399155	−	0.916883i	$-0.369303\pi$
$499$	27.2650	−	33.2225i	1.22055	−	1.48724i	0.821394	−	0.570361i	$-0.193197\pi$
$500$	−3.16269	+	2.55620i	−0.141440	+	0.114317i
$501$	−2.34074	−	7.71639i	−0.104577	−	0.344743i
$502$	−1.74526	−	0.00652831i	−0.0778948	−	0.000291373i
$503$	−10.9834	+	16.4379i	−0.489727	+	0.732928i	−0.991218	−	0.132234i	$-0.957785\pi$
$503$	−10.9834	+	16.4379i	−0.489727	+	0.732928i	0.501492	+	0.865162i	$0.332785\pi$
$504$	−5.56298	−	3.05422i	−0.247795	−	0.136046i
$505$	−0.960795	+	0.641983i	−0.0427548	+	0.0285679i
$506$	−1.22777	+	6.05395i	−0.0545808	+	0.269131i
$507$	3.32600	−	2.72958i	0.147713	−	0.121225i
$508$	−0.468811	−	2.45263i	−0.0208001	−	0.108818i
$509$	−1.82049	−	3.40590i	−0.0806918	−	0.150964i	0.838339	−	0.545149i	$-0.183527\pi$
$509$	−1.82049	−	3.40590i	−0.0806918	−	0.150964i	−0.919031	+	0.394185i	$0.871027\pi$
$510$	−1.81477	−	1.50074i	−0.0803594	−	0.0664538i
$511$	−10.4873			−0.463929
$512$	−22.5804	+	1.45867i	−0.997920	+	0.0644649i
$513$	−2.32345			−0.102583
$514$	3.82371	+	3.16205i	0.168657	+	0.139472i
$515$	−1.02742	−	1.92218i	−0.0452737	−	0.0847012i
$516$	3.76043	+	19.6730i	0.165544	+	0.866056i
$517$	8.11651	−	6.66104i	0.356964	−	0.292952i
$518$	−2.97912	+	14.6896i	−0.130895	+	0.645426i
$519$	−15.6353	+	10.4472i	−0.686312	+	0.458579i
$520$	1.49292	+	0.819655i	0.0654690	+	0.0359442i
$521$	2.97047	−	4.44563i	0.130139	−	0.194767i	−0.760678	−	0.649130i	$-0.775133\pi$
$521$	2.97047	−	4.44563i	0.130139	−	0.194767i	0.890816	+	0.454363i	$0.150133\pi$
$522$	11.0420	+	0.0413037i	0.483296	+	0.00180781i
$523$	−5.45894	−	17.9957i	−0.238703	−	0.786898i	−0.991666	−	0.128835i	$-0.958876\pi$
$523$	−5.45894	−	17.9957i	−0.238703	−	0.786898i	0.752963	−	0.658063i	$-0.228624\pi$
$524$	−6.08683	+	4.91959i	−0.265904	+	0.214913i
$525$	−7.05773	+	8.59987i	−0.308025	+	0.375329i
$526$	29.6320	+	3.03046i	1.29202	+	0.132134i
$527$	58.8511	+	24.3769i	2.56359	+	1.06188i
$528$	3.58658	−	8.30508i	0.156086	−	0.361432i
$529$	−17.8031	+	7.37428i	−0.774047	+	0.320621i
$530$	1.49155	−	0.446372i	0.0647889	−	0.0193891i
$531$	10.9233	−	1.07585i	0.474032	−	0.0466881i
$532$	8.01005	+	6.67459i	0.347280	+	0.289380i
$533$	6.50628	+	3.47768i	0.281818	+	0.150635i
$534$	4.28034	−	10.2253i	0.185229	−	0.442493i
$535$	1.15507	−	0.229757i	0.0499378	−	0.00993326i
$536$	0.158906	−	14.1599i	0.00686368	−	0.611616i
$537$	−0.594409	+	2.98829i	−0.0256506	+	0.128954i
$538$	26.7864	−	5.22406i	1.15484	−	0.225225i
$539$	4.42405	+	0.435731i	0.190558	+	0.0187683i
$540$	0.286584	+	0.290904i	0.0123326	+	0.0125185i
$541$	−34.2306	−	10.3837i	−1.47169	−	0.446432i	−0.550264	−	0.834991i	$-0.685473\pi$
$541$	−34.2306	−	10.3837i	−1.47169	−	0.446432i	−0.921424	+	0.388559i	$0.872973\pi$
$542$	−10.7717	−	20.3351i	−0.462686	−	0.873467i
$543$	−8.93964	−	8.93964i	−0.383637	−	0.383637i
$544$	−45.9888	+	3.66253i	−1.97175	+	0.157030i
$545$	1.28682	−	1.28682i	0.0551213	−	0.0551213i
$546$	8.94479	+	2.74995i	0.382802	+	0.117687i
$547$	9.86405	−	32.5174i	0.421756	−	1.39034i	−0.446747	−	0.894660i	$-0.647418\pi$
$547$	9.86405	−	32.5174i	0.421756	−	1.39034i	0.868503	−	0.495684i	$-0.165082\pi$
$548$	−30.8368	−	13.0441i	−1.31728	−	0.557218i
$549$	−0.902667	+	9.16493i	−0.0385249	+	0.391150i
$550$	−13.1529	−	8.85985i	−0.560843	−	0.377785i
$551$	−17.7928	−	3.53920i	−0.757998	−	0.150775i
$552$	−5.36932	+	1.00552i	−0.228533	+	0.0427979i
$553$	−1.99040	−	10.0064i	−0.0846406	−	0.425517i
$554$	−1.51876	−	3.70577i	−0.0645261	−	0.157443i
$555$	0.454645	−	0.850580i	0.0192986	−	0.0361051i
$556$	−15.8350	+	8.31230i	−0.671555	+	0.352520i
$557$	1.92446	+	19.5393i	0.0815418	+	0.827908i	0.945776	+	0.324819i	$0.105303\pi$
$557$	1.92446	+	19.5393i	0.0815418	+	0.827908i	−0.864235	+	0.503089i	$0.832197\pi$
$558$	−9.72215	−	5.24345i	−0.411571	−	0.221973i
$559$	−11.3023	−	27.2861i	−0.478036	−	1.15408i
$560$	−0.152311	−	1.82615i	−0.00643629	−	0.0771691i
$561$	7.05840	−	17.0405i	0.298006	−	0.719450i
$562$	25.3976	−	20.6848i	1.07133	−	0.872534i
$563$	−30.1092	−	24.7100i	−1.26895	−	1.04140i	−0.996865	−	0.0791274i	$-0.974787\pi$
$563$	−30.1092	−	24.7100i	−1.26895	−	1.04140i	−0.272086	−	0.962273i	$-0.587713\pi$
$564$	8.15594	+	4.43821i	0.343427	+	0.186882i
$565$	−2.71868	+	0.824704i	−0.114376	+	0.0346955i
$566$	30.2125	+	30.4393i	1.26993	+	1.27946i
$567$	1.86560	+	1.24656i	0.0783480	+	0.0523504i
$568$	−47.4456	+	4.13597i	−1.99077	+	0.173541i
$569$	21.2159	+	31.7519i	0.889418	+	1.33111i	0.943086	+	0.332549i	$0.107909\pi$
$569$	21.2159	+	31.7519i	0.889418	+	1.33111i	−0.0536677	+	0.998559i	$0.517091\pi$
$570$	−0.370644	−	0.559224i	−0.0155246	−	0.0234233i
$571$	6.89150	+	8.39731i	0.288400	+	0.351417i	0.896976	−	0.442079i	$-0.145759\pi$
$571$	6.89150	+	8.39731i	0.288400	+	0.351417i	−0.608576	+	0.793496i	$0.708259\pi$
$572$	−2.70022	+	13.0634i	−0.112902	+	0.546207i
$573$	5.00311	−	2.67422i	0.209008	−	0.111717i
$574$	−0.748481	−	7.90238i	−0.0312410	−	0.329839i
$575$			9.57620i			0.399355i
$576$	7.99799	+	0.179533i	0.333249	+	0.00748052i
$577$			15.0899i			0.628201i	0.949390	+	0.314100i	$0.101703\pi$
$577$			15.0899i			0.628201i	−0.949390	+	0.314100i	$0.898297\pi$
$578$	−69.7084	+	6.60250i	−2.89949	+	0.274628i
$579$	−5.65684	+	3.02364i	−0.235090	+	0.125658i
$580$	1.75151	+	2.66425i	0.0727275	+	0.110627i
$581$	0.621728	+	0.757577i	0.0257936	+	0.0314296i
$582$	16.3984	−	10.8686i	0.679738	−	0.450517i
$583$	6.77478	+	10.1392i	0.280583	+	0.419922i
$584$	11.7283	−	6.10067i	0.485319	−	0.252448i
$585$	−0.500668	−	0.334535i	−0.0207001	−	0.0138313i
$586$	−32.5411	+	32.2986i	−1.34426	+	1.33424i
$587$	15.6442	−	4.74563i	0.645707	−	0.195873i	0.0495888	−	0.998770i	$-0.484209\pi$
$587$	15.6442	−	4.74563i	0.645707	−	0.195873i	0.596118	+	0.802897i	$0.296709\pi$
$588$	1.11300	+	3.77040i	0.0458995	+	0.155488i
$589$	14.0284	+	11.5128i	0.578031	+	0.474378i
$590$	2.00146	+	2.45748i	0.0823989	+	0.101173i
$591$	2.82139	−	6.81143i	0.116056	−	0.280185i
$592$	−5.21365	−	18.1610i	−0.214280	−	0.746411i
$593$	8.43383	+	20.3611i	0.346336	+	0.836129i	0.997046	+	0.0768028i	$0.0244712\pi$
$593$	8.43383	+	20.3611i	0.346336	+	0.836129i	−0.650710	+	0.759326i	$0.725529\pi$
$594$	−1.51825	+	2.81507i	−0.0622947	+	0.115504i
$595$	−0.366214	−	3.71823i	−0.0150133	−	0.152433i
$596$	−4.73390	+	15.1954i	−0.193908	+	0.622429i
$597$	−1.93321	+	3.61678i	−0.0791209	+	0.148025i
$598$	7.45336	−	3.05467i	0.304791	−	0.124915i
$599$	3.63836	+	18.2913i	0.148659	+	0.747362i	0.981139	+	0.193305i	$0.0619208\pi$
$599$	3.63836	+	18.2913i	0.148659	+	0.747362i	−0.832479	+	0.554056i	$0.813079\pi$
$600$	2.89017	−	13.7232i	0.117991	−	0.560247i
$601$	−19.6744	−	3.91348i	−0.802534	−	0.159634i	−0.223252	−	0.974761i	$-0.571667\pi$
$601$	−19.6744	−	3.91348i	−0.802534	−	0.159634i	−0.579283	+	0.815127i	$0.696667\pi$
$602$	−17.7534	+	26.3559i	−0.723574	+	1.07419i
$603$	−0.490734	+	4.98250i	−0.0199842	+	0.202903i
$604$	3.13538	+	7.73260i	0.127577	+	0.314635i
$605$	0.348811	−	1.14988i	0.0141812	−	0.0467491i
$606$	2.35198	−	7.65030i	0.0955426	−	0.310772i
$607$	1.52507	−	1.52507i	0.0619008	−	0.0619008i	−0.675479	−	0.737380i	$-0.736063\pi$
$607$	1.52507	−	1.52507i	0.0619008	−	0.0619008i	0.737380	+	0.675479i	$0.236063\pi$
$608$	−12.8407	−	2.80479i	−0.520758	−	0.113749i
$609$	12.3878	+	12.3878i	0.501979	+	0.501979i
$610$	−2.34987	+	1.24476i	−0.0951436	+	0.0503987i
$611$	−13.1022	−	3.97451i	−0.530059	−	0.160792i
$612$	16.3105	+	0.122024i	0.659313	+	0.00493251i
$613$	−7.41618	−	0.730430i	−0.299537	−	0.0295018i	−0.0528676	−	0.998602i	$-0.516836\pi$
$613$	−7.41618	−	0.730430i	−0.299537	−	0.0295018i	−0.246669	+	0.969100i	$0.579336\pi$
$614$	−7.41966	−	38.0444i	−0.299433	−	1.53535i
$615$	−0.0996448	+	0.500948i	−0.00401807	+	0.0202002i
$616$	13.3210	−	5.34341i	0.536719	−	0.215292i
$617$	2.82997	−	0.562917i	0.113930	−	0.0226622i	−0.137796	−	0.990461i	$-0.544002\pi$
$617$	2.82997	−	0.562917i	0.113930	−	0.0226622i	0.251726	+	0.967798i	$0.419002\pi$
$618$	13.9254	+	5.82921i	0.560161	+	0.234485i
$619$	−1.65443	−	0.884310i	−0.0664971	−	0.0355434i	0.437813	−	0.899066i	$-0.355753\pi$
$619$	−1.65443	−	0.884310i	−0.0664971	−	0.0355434i	−0.504310	+	0.863523i	$0.668253\pi$
$620$	−0.288875	−	3.17644i	−0.0116015	−	0.127569i
$621$	1.92204	−	0.189305i	0.0771289	−	0.00759654i
$622$	−11.1352	−	37.2081i	−0.446479	−	1.49191i
$623$	16.2484	−	6.73031i	0.650979	−	0.269644i
$624$	−11.6030	+	2.12802i	−0.464491	+	0.0851890i
$625$	−22.5209	−	9.32845i	−0.900834	−	0.373138i
$626$	4.61910	−	45.1659i	0.184617	−	1.80519i
$627$	3.33357	−	4.06197i	0.133130	−	0.162219i
$628$	−2.17733	+	20.5310i	−0.0868850	+	0.819277i
$629$	−11.1828	−	36.8647i	−0.445886	−	1.46989i
$630$	−0.00242346	+	0.647880i	−9.65528e−5	+	0.0258122i
$631$	14.3410	−	21.4628i	0.570905	−	0.854420i	−0.427873	−	0.903839i	$-0.640737\pi$
$631$	14.3410	−	21.4628i	0.570905	−	0.854420i	0.998778	+	0.0494187i	$0.0157369\pi$
$632$	8.04691	+	10.0327i	0.320089	+	0.399079i
$633$	14.5780	−	9.74073i	0.579425	−	0.387159i
$634$	−47.3845	−	9.60976i	−1.88188	−	0.381652i
$635$	−0.197056	+	0.161719i	−0.00781992	+	0.00641764i
$636$	−6.05803	+	8.92128i	−0.240217	+	0.353752i
$637$	−2.73262	−	5.11238i	−0.108270	−	0.202560i
$638$	−15.9147	+	19.2449i	−0.630069	+	0.761912i
$639$	16.8382			0.666108
$640$	1.23265	+	1.95365i	0.0487248	+	0.0772248i
$641$	3.55832			0.140545			0.0702726	−	0.997528i	$-0.477613\pi$
$641$	3.55832			0.140545			0.0702726	+	0.997528i	$0.477613\pi$
$642$	−5.19839	+	6.28615i	−0.205164	+	0.248095i
$643$	3.31625	+	6.20427i	0.130780	+	0.244673i	0.938785	−	0.344503i	$-0.111953\pi$
$643$	3.31625	+	6.20427i	0.130780	+	0.244673i	−0.808005	+	0.589176i	$0.799453\pi$
$644$	−7.17002	−	4.86883i	−0.282538	−	0.191859i
$645$	1.58062	−	1.29718i	0.0622370	−	0.0510766i
$646$	−26.2631	−	5.32626i	−1.03331	−	0.209559i
$647$	−2.33680	+	1.56140i	−0.0918689	+	0.0613849i	−0.600656	−	0.799507i	$-0.705094\pi$
$647$	−2.33680	+	1.56140i	−0.0918689	+	0.0613849i	0.508787	+	0.860892i	$0.330094\pi$
$648$	−2.81152	−	0.308803i	−0.110447	−	0.0121309i
$649$	−13.7914	+	20.6402i	−0.541358	+	0.810200i
$650$	−0.0773534	+	20.6795i	−0.00303405	+	0.811115i
$651$	−5.08729	−	16.7706i	−0.199387	−	0.657290i
$652$	−13.0686	−	1.38594i	−0.511807	−	0.0542775i
$653$	16.8283	−	20.5054i	0.658543	−	0.802436i	−0.331463	−	0.943468i	$-0.607542\pi$
$653$	16.8283	−	20.5054i	0.658543	−	0.802436i	0.990005	+	0.141032i	$0.0450420\pi$
$654$	−1.28241	+	12.5395i	−0.0501460	+	0.490332i
$655$	0.738167	+	0.305759i	0.0288426	+	0.0119470i
$656$	5.43405	+	8.40210i	0.212164	+	0.328047i
$657$	−4.31821	+	1.78866i	−0.168470	+	0.0697824i
$658$	4.22364	+	14.1133i	0.164655	+	0.550194i
$659$	−16.9604	+	1.67046i	−0.660685	+	0.0650718i	−0.422802	−	0.906222i	$-0.638953\pi$
$659$	−16.9604	+	1.67046i	−0.660685	+	0.0650718i	−0.237883	+	0.971294i	$0.576453\pi$
$660$	−0.919747	+	0.0836446i	−0.0358011	+	0.00325586i
$661$	15.3531	+	8.20640i	0.597166	+	0.319192i	0.742142	−	0.670243i	$-0.233810\pi$
$661$	15.3531	+	8.20640i	0.597166	+	0.319192i	−0.144975	+	0.989435i	$0.546310\pi$
$662$	40.2248	+	16.8382i	1.56338	+	0.654435i
$663$	−23.5894	+	4.69222i	−0.916137	+	0.182231i
$664$	−1.13600	−	0.485552i	−0.0440853	−	0.0188431i
$665$	0.207660	−	1.04398i	0.00805270	−	0.0404837i
$666$	1.27873	+	6.55669i	0.0495497	+	0.254066i
$667$	15.0072	+	1.47808i	0.581080	+	0.0572314i
$668$	−0.120649	+	16.1268i	−0.00466805	+	0.623963i
$669$	14.0036	+	4.24794i	0.541410	+	0.164235i
$670$	−1.27751	+	0.676709i	−0.0493544	+	0.0261436i
$671$	−14.7275	−	14.7275i	−0.568547	−	0.568547i
$672$	8.80555	+	9.14125i	0.339682	+	0.352631i
$673$	14.2735	−	14.2735i	0.550202	−	0.550202i	−0.376297	−	0.926499i	$-0.622803\pi$
$673$	14.2735	−	14.2735i	0.550202	−	0.550202i	0.926499	+	0.376297i	$0.122803\pi$
$674$	−11.0295	+	35.8757i	−0.424840	+	1.38188i
$675$	−1.43932	+	4.74481i	−0.0553995	+	0.182628i
$676$	−7.97469	+	3.23354i	−0.306719	+	0.124367i
$677$	−4.93841	+	50.1405i	−0.189799	+	1.92706i	0.154110	+	0.988054i	$0.450749\pi$
$677$	−4.93841	+	50.1405i	−0.189799	+	1.92706i	−0.343908	+	0.939003i	$0.611751\pi$
$678$	10.9936	−	16.3206i	0.422206	−	0.626788i
$679$	30.6131	+	6.08932i	1.17482	+	0.233687i
$680$	2.57253	+	3.94519i	0.0986520	+	0.151291i
$681$	0.721834	+	3.62890i	0.0276607	+	0.139060i
$682$	23.1157	−	9.47368i	0.885145	−	0.362766i
$683$	−2.08075	+	3.89281i	−0.0796178	+	0.148954i	−0.918580	−	0.395236i	$-0.870663\pi$
$683$	−2.08075	+	3.89281i	−0.0796178	+	0.148954i	0.838962	+	0.544190i	$0.183163\pi$
$684$	4.43660	+	1.38215i	0.169637	+	0.0528480i
$685$	0.335039	+	3.40171i	0.0128012	+	0.129973i
$686$	−13.5046	+	25.0395i	−0.515607	+	0.956013i
$687$	2.08021	+	5.02208i	0.0793651	+	0.191604i
$688$	4.52242	−	39.8023i	0.172416	−	1.51745i
$689$	6.08517	−	14.6909i	0.231826	−	0.559678i
$690$	0.352173	+	0.432412i	0.0134070	+	0.0164616i
$691$	−19.4552	−	15.9665i	−0.740110	−	0.607393i	0.186922	−	0.982375i	$-0.440149\pi$
$691$	−19.4552	−	15.9665i	−0.740110	−	0.607393i	−0.927032	+	0.374982i	$0.877649\pi$
$692$	36.0700	−	10.6477i	1.37118	−	0.404765i
$693$	−4.85596	+	1.47304i	−0.184463	+	0.0559561i
$694$	−32.6739	+	32.4304i	−1.24029	+	1.23104i
$695$	1.51808	+	1.01435i	0.0575840	+	0.0384764i
$696$	−21.0600	−	6.64744i	−0.798276	−	0.251971i
$697$	11.3344	+	16.9631i	0.429320	+	0.642523i
$698$	32.9587	−	21.8444i	1.24751	−	0.826824i
$699$	−3.57927	−	4.36135i	−0.135380	−	0.164961i
$700$	18.5924	−	12.2229i	0.702728	−	0.461981i
$701$	24.3494	−	13.0150i	0.919663	−	0.491570i	0.0575820	−	0.998341i	$-0.481661\pi$
$701$	24.3494	−	13.0150i	0.919663	−	0.491570i	0.862081	+	0.506771i	$0.169161\pi$
$702$	4.15211	−	0.393271i	0.156711	−	0.0148431i
$703$		−	10.9751i		−	0.413935i
$704$	−11.7890	+	13.7249i	−0.444313	+	0.517275i
$705$		−	0.947930i		−	0.0357011i
$706$	3.44433	+	36.3649i	0.129629	+	1.36861i
$707$	11.1990	−	5.98597i	0.421180	−	0.225125i
$708$	−21.4979	−	4.44364i	−0.807941	−	0.167002i
$709$	5.38805	+	6.56536i	0.202353	+	0.246567i	0.864292	−	0.502990i	$-0.167767\pi$
$709$	5.38805	+	6.56536i	0.202353	+	0.246567i	−0.661940	+	0.749557i	$0.730267\pi$
$710$	2.68607	+	4.05272i	0.100806	+	0.152096i
$711$	−2.52622	−	3.78076i	−0.0947407	−	0.141790i
$712$	−14.2560	+	16.9788i	−0.534266	+	0.636308i
$713$	−12.5428	−	8.38085i	−0.469732	−	0.313865i
$714$	18.2302	+	18.3671i	0.682249	+	0.687372i
$715$	1.30318	−	0.395316i	0.0487362	−	0.0147840i
$716$	2.91266	−	5.35250i	0.108851	−	0.200032i
$717$	5.13965	+	4.21800i	0.191944	+	0.157524i
$718$	−0.217205	+	0.176900i	−0.00810604	+	0.00660186i
$719$	−3.54609	+	8.56102i	−0.132247	+	0.319272i	−0.976107	−	0.217291i	$-0.930278\pi$
$719$	−3.54609	+	8.56102i	−0.132247	+	0.319272i	0.843860	+	0.536564i	$0.180278\pi$
$720$	−0.374176	−	0.725957i	−0.0139447	−	0.0270548i
$721$	9.16571	+	22.1280i	0.341349	+	0.824089i
$722$	16.9302	+	9.13095i	0.630076	+	0.339819i
$723$	0.562158	+	5.70769i	0.0209069	+	0.212271i
$724$	11.7522	+	22.3880i	0.436766	+	0.832045i
$725$	−18.2497	+	34.1428i	−0.677778	+	1.26803i
$726$	3.15623	+	7.70116i	0.117139	+	0.285817i
$727$	−3.55907	−	17.8926i	−0.131999	−	0.663602i	−0.988955	−	0.148213i	$-0.952648\pi$
$727$	−3.55907	−	17.8926i	−0.131999	−	0.663602i	0.856957	−	0.515388i	$-0.172352\pi$
$728$	−15.4441	−	10.5720i	−0.572395	−	0.391824i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	−1.11936	−	0.754005i	−0.0414294	−	0.0279070i
$731$	8.00543	−	81.2805i	0.296092	−	3.00627i
$732$	7.17558	−	16.9633i	0.265217	−	0.626982i
$733$	−3.67754	+	12.1232i	−0.135833	+	0.447782i	−0.998297	−	0.0583369i	$-0.981420\pi$
$733$	−3.67754	+	12.1232i	−0.135833	+	0.447782i	0.862464	+	0.506119i	$0.168920\pi$
$734$	49.1642	+	15.1149i	1.81468	+	0.557900i
$735$	0.283788	−	0.283788i	0.0104677	−	0.0104677i
$736$	10.8508	+	1.27402i	0.399965	+	0.0469610i
$737$	−8.00656	−	8.00656i	−0.294925	−	0.294925i
$738$	−1.65599	−	3.12621i	−0.0609579	−	0.115077i
$739$	−24.9149	−	7.55784i	−0.916508	−	0.278020i	−0.203418	−	0.979092i	$-0.565205\pi$
$739$	−24.9149	−	7.55784i	−0.916508	−	0.278020i	−0.713090	+	0.701072i	$0.752705\pi$
$740$	−1.37412	+	1.35371i	−0.0505137	+	0.0497635i
$741$	−6.81916	−	0.671629i	−0.250508	−	0.0246729i
$742$	−16.7927	+	3.27503i	−0.616480	+	0.120230i
$743$	6.25338	−	31.4379i	0.229414	−	1.15334i	−0.678634	−	0.734477i	$-0.737428\pi$
$743$	6.25338	−	31.4379i	0.229414	−	1.15334i	0.908048	−	0.418866i	$-0.137572\pi$
$744$	15.4451	+	15.7957i	0.566245	+	0.579098i
$745$	1.59360	−	0.316988i	0.0583851	−	0.0116135i
$746$	15.6922	−	37.4872i	0.574534	−	1.37250i
$747$	0.385211	+	0.205899i	0.0140941	+	0.00753347i
$748$	−23.6148	+	28.3397i	−0.863443	+	1.03620i
$749$	−12.8795	+	1.26852i	−0.470607	+	0.0463508i
$750$	−2.75477	+	0.824409i	−0.100590	+	0.0301032i
$751$	−3.42555	+	1.41891i	−0.125000	+	0.0517768i	−0.444307	−	0.895875i	$-0.646550\pi$
$751$	−3.42555	+	1.41891i	−0.125000	+	0.0517768i	0.319307	+	0.947651i	$0.396550\pi$
$752$	−12.9335	−	13.3264i	−0.471635	−	0.485964i
$753$	−1.14015	−	0.472267i	−0.0415495	−	0.0172104i
$754$	32.3955	+	3.31308i	1.17978	+	0.120655i
$755$	0.540402	−	0.658482i	0.0196672	−	0.0239646i
$756$	−2.82080	−	3.49007i	−0.102591	−	0.126933i
$757$	−4.52339	−	14.9116i	−0.164405	−	0.541972i	0.835567	−	0.549388i	$-0.185139\pi$
$757$	−4.52339	−	14.9116i	−0.164405	−	0.541972i	−0.999972	+	0.00741647i	$0.997639\pi$
$758$	17.5234	+	0.0655478i	0.636477	+	0.00238080i
$759$	−2.42670	+	3.63181i	−0.0880835	+	0.131826i
$760$	0.375072	+	1.28832i	0.0136053	+	0.0467321i
$761$	38.9519	−	26.0268i	1.41201	−	0.943472i	0.412536	−	0.910941i	$-0.364643\pi$
$761$	38.9519	−	26.0268i	1.41201	−	0.943472i	0.999471	−	0.0325310i	$-0.0103568\pi$
$762$	0.350940	−	1.73044i	0.0127132	−	0.0626872i
$763$	−15.4590	+	12.6869i	−0.559653	+	0.459296i
$764$	−11.1442	+	2.13017i	−0.403182	+	0.0770669i
$765$	−0.784957	−	1.46855i	−0.0283802	−	0.0530956i
$766$	7.86430	+	6.50344i	0.284149	+	0.234979i
$767$	32.3701			1.16882
$768$	−15.1652	−	5.10058i	−0.547228	−	0.184051i
$769$	39.3407			1.41866			0.709330	−	0.704876i	$-0.248997\pi$
$769$	39.3407			1.41866			0.709330	+	0.704876i	$0.248997\pi$
$770$	−1.12918	−	0.933782i	−0.0406927	−	0.0336512i
$771$	1.65390	+	3.09423i	0.0595638	+	0.111436i
$772$	12.6003	−	2.40851i	0.453495	−	0.0866841i
$773$	26.4529	−	21.7093i	0.951445	−	0.780831i	−0.0243082	−	0.999705i	$-0.507738\pi$
$773$	26.4529	−	21.7093i	0.951445	−	0.780831i	0.975753	+	0.218874i	$0.0702383\pi$
$774$	−2.81496	+	13.8802i	−0.101182	+	0.498914i
$775$	32.2010	−	21.5160i	1.15670	−	0.772879i
$776$	−37.7780	+	10.9984i	−1.35615	+	0.394821i
$777$	−5.88827	+	8.81241i	−0.211240	+	0.316144i
$778$	9.66018	+	0.0361348i	0.346334	+	0.00129550i
$779$	1.68720	+	5.56196i	0.0604503	+	0.199278i
$780$	0.757011	+	0.936623i	0.0271054	+	0.0335365i
$781$	−24.1585	+	29.4372i	−0.864460	+	1.05335i
$782$	22.1597	+	2.26627i	0.792431	+	0.0810416i
$783$	7.21359	+	2.98797i	0.257793	+	0.106781i
$784$	0.117636	−	7.86160i	0.00420130	−	0.280772i
$785$	1.94731	−	0.806601i	0.0695024	−	0.0287888i
$786$	−5.30175	+	1.58664i	−0.189107	+	0.0565934i
$787$	37.1054	−	3.65456i	1.32267	−	0.130271i	0.588088	−	0.808797i	$-0.299881\pi$
$787$	37.1054	−	3.65456i	1.32267	−	0.130271i	0.734577	+	0.678526i	$0.237381\pi$
$788$	−9.43932	+	11.3280i	−0.336262	+	0.403542i
$789$	18.5753	+	9.92870i	0.661298	+	0.353471i
$790$	0.506989	−	1.21115i	0.0180378	−	0.0430906i
$791$	30.6204	−	6.09078i	1.08874	−	0.216563i
$792$	4.57369	−	4.47217i	0.162519	−	0.158912i
$793$	−5.29852	+	26.6375i	−0.188156	+	0.945924i
$794$	−18.0132	+	3.51305i	−0.639265	+	0.124674i
$795$	1.09560	+	0.107907i	0.0388570	+	0.00382708i
$796$	5.84294	−	5.75617i	0.207098	−	0.204022i
$797$	−4.01068	−	1.21663i	−0.142065	−	0.0430951i	0.218451	−	0.975848i	$-0.429900\pi$
$797$	−4.01068	−	1.21663i	−0.142065	−	0.0430951i	−0.360517	+	0.932753i	$0.617400\pi$
$798$	3.45108	+	6.51502i	0.122167	+	0.230629i
$799$	−26.7733	−	26.7733i	−0.947170	−	0.947170i
$800$	−13.6822	+	24.4849i	−0.483741	+	0.865673i
$801$	5.54253	−	5.54253i	0.195836	−	0.195836i
$802$	19.2293	+	5.91178i	0.679010	+	0.208752i
$803$	3.06853	−	10.1156i	0.108286	−	0.356971i
$804$	3.90099	−	9.22208i	0.137577	−	0.325238i
$805$	−0.0867250	+	0.880533i	−0.00305665	+	0.0310347i
$806$	−27.0181	−	18.1995i	−0.951671	−	0.641048i
$807$	18.9269	+	3.76479i	0.666258	+	0.132527i
$808$	−9.04201	+	13.2090i	−0.318097	+	0.464691i
$809$	0.287022	+	1.44296i	0.0100911	+	0.0507316i	0.985503	−	0.169659i	$-0.0542667\pi$
$809$	0.287022	+	1.44296i	0.0100911	+	0.0507316i	−0.975412	+	0.220391i	$0.929267\pi$
$810$	0.109502	+	0.267183i	0.00384750	+	0.00938787i
$811$	12.8002	−	23.9474i	0.449475	−	0.840908i	−0.550507	−	0.834831i	$-0.685566\pi$
$811$	12.8002	−	23.9474i	0.449475	−	0.840908i	0.999982	−	0.00607725i	$-0.00193446\pi$
$812$	−16.2852	−	31.0234i	−0.571497	−	1.08871i
$813$	−1.59492	−	16.1935i	−0.0559363	−	0.567931i
$814$	−13.2974	−	7.17166i	−0.466072	−	0.251367i
$815$	0.513426	+	1.23952i	0.0179845	+	0.0434185i
$816$	−31.0721	−	9.93565i	−1.08774	−	0.347817i
$817$	8.90444	−	21.4972i	0.311527	−	0.752092i
$818$	−24.9216	+	20.2971i	−0.871363	+	0.709671i
$819$	5.11507	+	4.19783i	0.178735	+	0.146684i
$820$	0.488270	−	0.897277i	0.0170511	−	0.0313343i
$821$	0.940875	−	0.285411i	0.0328368	−	0.00996092i	−0.273824	−	0.961780i	$-0.588288\pi$
$821$	0.940875	−	0.285411i	0.0328368	−	0.00996092i	0.306660	+	0.951819i	$0.400788\pi$
$822$	−16.6784	−	16.8036i	−0.581725	−	0.586093i
$823$	−18.3955	−	12.2915i	−0.641226	−	0.428453i	0.191994	−	0.981396i	$-0.438505\pi$
$823$	−18.3955	−	12.2915i	−0.641226	−	0.428453i	−0.833219	+	0.552943i	$0.813505\pi$
$824$	−23.1227	−	19.4146i	−0.805517	−	0.676339i
$825$	−6.23003	−	9.32389i	−0.216902	−	0.324616i
$826$	−19.2414	−	29.0313i	−0.669494	−	1.01013i
$827$	−15.1641	−	18.4775i	−0.527308	−	0.642527i	0.439435	−	0.898274i	$-0.355179\pi$
$827$	−15.1641	−	18.4775i	−0.527308	−	0.642527i	−0.966744	+	0.255747i	$0.917679\pi$
$828$	−3.78272	−	0.781893i	−0.131459	−	0.0271727i
$829$	10.9709	−	5.86405i	0.381034	−	0.203667i	−0.269749	−	0.962931i	$-0.586941\pi$
$829$	10.9709	−	5.86405i	0.381034	−	0.203667i	0.650783	+	0.759264i	$0.274441\pi$
$830$	0.0118926	+	0.125561i	0.000412798	+	0.00435828i
$831$		−	2.83190i		−	0.0982376i
$832$	23.4216	+	2.83885i	0.811998	+	0.0984195i
$833$		−	16.0306i		−	0.555427i
$834$	−12.5897	+	1.19244i	−0.435944	+	0.0412908i
$835$	1.45201	−	0.776114i	0.0502488	−	0.0268585i
$836$	−8.78174	+	5.77321i	−0.303723	+	0.199671i
$837$	−4.95505	−	6.03775i	−0.171272	−	0.208695i
$838$	27.3710	−	18.1410i	0.945515	−	0.626670i
$839$	2.55491	+	3.82370i	0.0882054	+	0.132009i	0.872948	−	0.487813i	$-0.162205\pi$
$839$	2.55491	+	3.82370i	0.0882054	+	0.132009i	−0.784743	+	0.619821i	$0.787205\pi$
$840$	0.390033	−	1.23568i	0.0134574	−	0.0426348i
$841$	26.5769	+	17.7581i	0.916446	+	0.612350i
$842$	−18.1722	+	18.0368i	−0.626255	+	0.621588i
$843$	22.1640	−	6.72339i	0.763370	−	0.231566i
$844$	−33.6310	+	9.92771i	−1.15763	+	0.341726i
$845$	0.679097	+	0.557321i	0.0233616	+	0.0191724i
$846$	4.14623	+	5.09091i	0.142550	+	0.175029i
$847$	−5.05323	+	12.1996i	−0.173631	+	0.419182i
$848$	16.8747	−	13.4313i	0.579481	−	0.461232i
$849$	11.6053	+	28.0177i	0.398293	+	0.961564i
$850$	−27.1463	+	50.3334i	−0.931111	+	1.72642i
$851$	0.894205	+	9.07901i	0.0306529	+	0.311225i
$852$	−32.1522	−	10.0165i	−1.10152	−	0.343161i
$853$	−12.5693	+	23.5154i	−0.430363	+	0.805153i	−0.999858	−	0.0168417i	$-0.994639\pi$
$853$	−12.5693	+	23.5154i	−0.430363	+	0.805153i	0.569495	+	0.821995i	$0.307139\pi$
$854$	27.0395	−	11.0818i	0.925272	−	0.379211i
$855$	−0.0925506	−	0.465283i	−0.00316516	−	0.0159124i
$856$	13.6657	−	8.91094i	0.467083	−	0.304570i
$857$	−26.0427	−	5.18022i	−0.889602	−	0.176953i	−0.270927	−	0.962600i	$-0.587330\pi$
$857$	−26.0427	−	5.18022i	−0.889602	−	0.176953i	−0.618675	+	0.785647i	$0.712330\pi$
$858$	−5.26970	+	7.82316i	−0.179905	+	0.267078i
$859$	0.188150	−	1.91032i	0.00641961	−	0.0651794i	−0.991441	−	0.130554i	$-0.958324\pi$
$859$	0.188150	−	1.91032i	0.00641961	−	0.0651794i	0.997861	+	0.0653749i	$0.0208243\pi$
$860$	−3.78983	+	1.53668i	−0.129232	+	0.0524005i
$861$	1.62932	−	5.37115i	0.0555271	−	0.183048i
$862$	12.4412	−	40.4677i	0.423750	−	1.37834i
$863$	−19.3952	+	19.3952i	−0.660219	+	0.660219i	−0.955432	−	0.295213i	$-0.904610\pi$
$863$	−19.3952	+	19.3952i	−0.660219	+	0.660219i	0.295213	+	0.955432i	$0.404610\pi$
$864$	5.18485	+	2.26215i	0.176392	+	0.0769598i
$865$	−2.71490	−	2.71490i	−0.0923094	−	0.0923094i
$866$	5.65647	−	2.99630i	0.192215	−	0.101818i
$867$	−47.3799	−	14.3725i	−1.60911	−	0.488117i
$868$	−0.262215	+	35.0494i	−0.00890014	+	1.18965i
$869$	10.2342	+	1.00798i	0.347171	+	0.0341934i
$870$	0.431568	+	2.21286i	0.0146315	+	0.0750231i
$871$	−2.88053	+	14.4814i	−0.0976031	+	0.490684i
$872$	9.90809	−	23.1810i	0.335530	−	0.785008i
$873$	13.6438	−	2.71391i	0.461771	−	0.0918521i
$874$	5.85392	+	2.45047i	0.198012	+	0.0828883i
$875$	−4.02345	−	2.15058i	−0.136017	−	0.0727028i
$876$	9.30958	−	0.846642i	0.314542	−	0.0286054i
$877$	−47.0648	+	4.63547i	−1.58926	+	0.156529i	−0.853641	−	0.520862i	$-0.825611\pi$
$877$	−47.0648	+	4.63547i	−1.58926	+	0.156529i	−0.735623	+	0.677391i	$0.763111\pi$
$878$	−11.4804	−	38.3619i	−0.387445	−	1.29465i
$879$	−29.9523	+	12.4066i	−1.01026	+	0.418465i
$880$	1.80600	+	0.387413i	0.0608802	+	0.0130597i
$881$	23.1626	+	9.59427i	0.780368	+	0.323239i	0.737064	−	0.675823i	$-0.236212\pi$
$881$	23.1626	+	9.59427i	0.780368	+	0.323239i	0.0433040	+	0.999062i	$0.486212\pi$
$882$	−0.282815	+	2.76538i	−0.00952287	+	0.0931153i
$883$	17.4252	−	21.2327i	0.586406	−	0.714538i	−0.392293	−	0.919841i	$-0.628318\pi$
$883$	17.4252	−	21.2327i	0.586406	−	0.714538i	0.978699	+	0.205303i	$0.0658179\pi$
$884$	47.8349	+	5.07293i	1.60886	+	0.170621i
$885$	0.650557	+	2.14460i	0.0218682	+	0.0720899i
$886$	−0.0348165	+	9.30776i	−0.00116968	+	0.312700i
$887$	−31.5197	+	47.1726i	−1.05833	+	1.58390i	−0.275874	+	0.961194i	$0.588967\pi$
$887$	−31.5197	+	47.1726i	−1.05833	+	1.58390i	−0.782455	+	0.622708i	$0.786033\pi$
$888$	1.45867	−	13.2806i	0.0489498	−	0.445667i
$889$	2.32923	−	1.55634i	0.0781200	−	0.0521981i
$890$	2.21817	+	0.449854i	0.0743533	+	0.0150791i
$891$	−1.74825	+	1.43475i	−0.0585684	+	0.0480659i
$892$	−24.2126	−	16.4417i	−0.810699	−	0.550509i
$893$	−5.08495	−	9.51328i	−0.170161	−	0.318350i
$894$	−7.17203	+	8.67279i	−0.239869	+	0.290061i
$895$	−0.622098			−0.0207945
$896$	−11.3762	−	22.6932i	−0.380052	−	0.758128i
$897$	5.69577			0.190176
$898$	18.0661	−	21.8465i	0.602874	−	0.729026i
$899$	−28.7483	−	53.7843i	−0.958810	−	1.79381i
$900$	5.57091	−	8.20392i	0.185697	−	0.273464i
$901$	33.9918	−	27.8964i	1.13243	−	0.929363i
$902$	7.84132	+	1.59025i	0.261087	+	0.0529495i
$903$	−18.6833	+	12.4837i	−0.621740	+	0.415433i
$904$	−30.7007	+	24.6241i	−1.02109	+	0.818986i
$905$	1.43411	−	2.14630i	0.0476716	−	0.0713456i
$906$	−0.0220699	+	5.90012i	−0.000733225	+	0.196018i
$907$	6.83485	+	22.5315i	0.226947	+	0.748145i	0.994271	+	0.106886i	$0.0340879\pi$
$907$	6.83485	+	22.5315i	0.226947	+	0.748145i	−0.767324	+	0.641260i	$0.778412\pi$
$908$	0.780400	−	7.35873i	0.0258985	−	0.244208i
$909$	3.59032	−	4.37482i	0.119083	−	0.145104i
$910$	−0.194392	+	1.90078i	−0.00644404	+	0.0630102i
$911$	−23.1656	−	9.59550i	−0.767510	−	0.317913i	−0.0356468	−	0.999364i	$-0.511349\pi$
$911$	−23.1656	−	9.59550i	−0.767510	−	0.317913i	−0.731863	+	0.681451i	$0.761349\pi$
$912$	−7.64940	−	5.27840i	−0.253297	−	0.174785i
$913$	−0.912643	+	0.378029i	−0.0302041	+	0.0125109i
$914$	−9.04629	−	30.2282i	−0.299225	−	0.999860i
$915$	−1.87128	+	0.184305i	−0.0618627	+	0.00609294i
$916$	−0.984645	−	10.8270i	−0.0325336	−	0.357736i
$917$	−7.74341	−	4.13894i	−0.255710	−	0.136680i
$918$	10.6391	+	4.45354i	0.351142	+	0.146989i
$919$	11.7121	−	2.32968i	0.386346	−	0.0768490i	0.00190409	−	0.999998i	$-0.499394\pi$
$919$	11.7121	−	2.32968i	0.386346	−	0.0768490i	0.384442	+	0.923149i	$0.374394\pi$
$920$	−0.415239	−	1.03518i	−0.0136900	−	0.0341289i
$921$	5.34708	−	26.8816i	0.176192	−	0.885779i
$922$	−1.39063	−	7.13046i	−0.0457980	−	0.234829i
$923$	49.4188	+	4.86732i	1.62664	+	0.160210i
$924$	10.1486	+	0.0759249i	0.333866	+	0.00249775i
$925$	−22.4127	−	6.79882i	−0.736925	−	0.223544i
$926$	35.0425	−	18.5624i	1.15157	−	0.609999i
$927$	7.54812	+	7.54812i	0.247913	+	0.247913i
$928$	36.2593	+	25.2211i	1.19027	+	0.827924i
$929$	−19.4036	+	19.4036i	−0.636610	+	0.636610i	−0.949718	−	0.313108i	$-0.898630\pi$
$929$	−19.4036	+	19.4036i	−0.636610	+	0.636610i	0.313108	+	0.949718i	$0.398630\pi$
$930$	0.662763	−	2.15577i	0.0217328	−	0.0706906i
$931$	1.32574	−	4.37037i	0.0434493	−	0.143233i
$932$	4.24011	+	10.4571i	0.138890	+	0.342535i
$933$	2.69185	−	27.3308i	0.0881272	−	0.894770i
$934$	15.2515	−	22.6417i	0.499044	−	0.740857i
$935$	3.69361	+	0.734704i	0.120794	+	0.0240274i
$936$	−8.16233	−	1.71903i	−0.266794	−	0.0561881i
$937$	−8.76578	−	44.0686i	−0.286366	−	1.43966i	−0.809356	−	0.587319i	$-0.800184\pi$
$937$	−8.76578	−	44.0686i	−0.286366	−	1.43966i	0.522990	−	0.852339i	$-0.324816\pi$
$938$	14.7000	−	6.02461i	0.479971	−	0.196710i
$939$	15.1336	−	28.3129i	0.493866	−	0.923958i
$940$	−0.563896	+	1.81006i	−0.0183923	+	0.0590376i
$941$	−0.829429	−	8.42133i	−0.0270386	−	0.274528i	−0.999192	−	0.0401834i	$-0.987206\pi$
$941$	−0.829429	−	8.42133i	−0.0270386	−	0.274528i	0.972154	−	0.234344i	$-0.0752942\pi$
$942$	−6.93005	+	12.8494i	−0.225793	+	0.418655i
$943$	−1.84888	−	4.46359i	−0.0602078	−	0.145354i
$944$	38.4065	+	21.2736i	1.25003	+	0.692395i
$945$	−0.175316	+	0.423251i	−0.00570304	+	0.0137684i
$946$	−20.2272	−	24.8358i	−0.657644	−	0.807483i
$947$	28.3547	+	23.2701i	0.921403	+	0.756176i	0.970117	−	0.242637i	$-0.0780124\pi$
$947$	28.3547	+	23.2701i	0.921403	+	0.756176i	−0.0487144	+	0.998813i	$0.515512\pi$
$948$	2.57472	+	8.72207i	0.0836229	+	0.283280i
$949$	−13.1907	+	4.00135i	−0.428187	+	0.129889i
$950$	−11.5634	+	11.4772i	−0.375167	+	0.372370i
$951$	−28.4263	−	18.9938i	−0.921786	−	0.615918i
$952$	−23.8843	−	45.9164i	−0.774093	−	1.48816i
$953$	30.0619	+	44.9907i	0.973799	+	1.45739i	0.887328	+	0.461139i	$0.152559\pi$
$953$	30.0619	+	44.9907i	0.973799	+	1.45739i	0.0864710	+	0.996254i	$0.472441\pi$
$954$	−6.35597	+	4.21262i	−0.205782	+	0.136389i
$955$	0.734816	+	0.895376i	0.0237781	+	0.0289737i
$956$	−7.30491	−	11.1116i	−0.236258	−	0.359376i
$957$	−15.5734	+	8.32415i	−0.503416	+	0.269081i
$958$	17.4339	−	1.65127i	0.563263	−	0.0533500i
$959$		−	37.5627i		−	1.21296i
$960$	0.282633	+	1.60879i	0.00912195	+	0.0519235i
$961$			30.0069i			0.967965i
$962$	1.85767	+	19.6130i	0.0598935	+	0.632349i
$963$	−5.08690	+	2.71900i	−0.163923	+	0.0876186i
$964$	2.32191	−	11.2332i	0.0747836	−	0.361795i
$965$	−0.830830	−	1.01237i	−0.0267454	−	0.0325893i
$966$	−3.38567	−	5.10828i	−0.108932	−	0.164356i
$967$	−4.18079	−	6.25699i	−0.134445	−	0.201211i	0.758138	−	0.652094i	$-0.226109\pi$
$967$	−4.18079	−	6.25699i	−0.134445	−	0.201211i	−0.892583	+	0.450883i	$0.851109\pi$
$968$	−1.44557	−	16.5828i	−0.0464623	−	0.532991i
$969$	−15.7554	−	10.5274i	−0.506137	−	0.338190i
$970$	2.82969	+	2.85094i	0.0908560	+	0.0915383i
$971$	−49.8437	+	15.1199i	−1.59956	+	0.485221i	−0.959170	−	0.282830i	$-0.908727\pi$
$971$	−49.8437	+	15.1199i	−1.59956	+	0.485221i	−0.640389	+	0.768051i	$0.721227\pi$
$972$	−1.75674	−	0.955963i	−0.0563475	−	0.0306625i
$973$	−15.5095	−	12.7283i	−0.497210	−	0.408050i
$974$	46.7336	−	38.0616i	1.49744	−	1.21957i
$975$	−5.59586	+	13.5096i	−0.179211	+	0.432653i
$976$	−23.7926	+	28.1226i	−0.761584	+	0.900184i
$977$	−5.26858	−	12.7195i	−0.168557	−	0.406932i	0.816918	−	0.576754i	$-0.195681\pi$
$977$	−5.26858	−	12.7195i	−0.168557	−	0.406932i	−0.985475	+	0.169822i	$0.945681\pi$
$978$	−8.17901	−	4.41119i	−0.261536	−	0.141054i
$979$	1.73757	+	17.6418i	0.0555329	+	0.563835i
$980$	−0.710707	+	0.373072i	−0.0227027	+	0.0119173i
$981$	−4.20155	+	7.86055i	−0.134145	+	0.250968i
$982$	1.43344	+	3.49759i	0.0457430	+	0.111612i
$983$	−10.9051	−	54.8235i	−0.347818	−	1.74860i	−0.618363	−	0.785892i	$-0.712204\pi$
$983$	−10.9051	−	54.8235i	−0.347818	−	1.74860i	0.270545	−	0.962707i	$-0.412796\pi$
$984$	1.30239	+	6.95455i	0.0415188	+	0.221703i
$985$	1.47641	+	0.293676i	0.0470423	+	0.00935730i
$986$	74.6891	+	50.3108i	2.37859	+	1.60222i
$987$	−1.02104	+	10.3668i	−0.0325000	+	0.329978i
$988$	12.6215	+	5.33898i	0.401545	+	0.169856i
$989$	−5.61457	+	18.5088i	−0.178533	+	0.588544i
$990$	−0.624210	−	0.191905i	−0.0198387	−	0.00609913i
$991$	33.9011	−	33.9011i	1.07690	−	1.07690i	0.0801197	−	0.996785i	$-0.474470\pi$
$991$	33.9011	−	33.9011i	1.07690	−	1.07690i	0.996785	−	0.0801197i	$-0.0255303\pi$
$992$	−20.0958	−	39.3495i	−0.638042	−	1.24935i
$993$	21.8034	+	21.8034i	0.691911	+	0.691911i
$994$	−25.0102	−	47.2147i	−0.793274	−	1.49756i
$995$	−0.801284	−	0.243067i	−0.0254024	−	0.00770574i
$996$	−0.613070	−	0.622312i	−0.0194259	−	0.0197187i
$997$	−21.4928	−	2.11686i	−0.680684	−	0.0670415i	−0.248235	−	0.968700i	$-0.579850\pi$
$997$	−21.4928	−	2.11686i	−0.680684	−	0.0670415i	−0.432449	+	0.901658i	$0.642350\pi$
$998$	−59.6563	+	11.6346i	−1.88839	+	0.368286i
$999$	−0.921534	+	4.63286i	−0.0291560	+	0.146577i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.10	✓	512
128.45	even	32	inner	384.2.v.a.301.10	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.10	✓	512	1.1	even	1	trivial
384.2.v.a.301.10	yes	512	128.45	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.08984 - 0.901251i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(0.375495 + 1.96443i) q^{4} +(0.157832 - 0.129529i) q^{5} +(-0.281086 + 1.38600i) q^{6} +(-1.86560 + 1.24656i) q^{7} +(1.36122 - 2.47933i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-1.08984 - 0.901251i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(0.375495 + 1.96443i) q^{4} +(0.157832 - 0.129529i) q^{5} +(-0.281086 + 1.38600i) q^{6} +(-1.86560 + 1.24656i) q^{7} +(1.36122 - 2.47933i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(-0.288750 - 0.00108010i) q^{10} +(-0.656510 - 2.16422i) q^{11} +(1.55547 - 1.25719i) q^{12} +(-1.87091 + 2.27971i) q^{13} +(3.15667 + 0.322831i) q^{14} +(-0.188636 - 0.0781357i) q^{15} +(-3.71801 + 1.47527i) q^{16} +(-7.53468 + 3.12097i) q^{17} +(1.35484 - 0.405459i) q^{18} +(-2.31226 + 0.227738i) q^{19} +(0.313717 + 0.261413i) q^{20} +(1.97880 + 1.05769i) q^{21} +(-1.23502 + 2.95033i) q^{22} +(1.89423 - 0.376786i) q^{23} +(-2.82825 - 0.0317392i) q^{24} +(-0.967319 + 4.86304i) q^{25} +(4.09357 - 0.798355i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-3.14930 - 3.19678i) q^{28} +(7.47173 + 2.26652i) q^{29} +(0.135163 + 0.255164i) q^{30} +(-5.52299 - 5.52299i) q^{31} +(5.38162 + 1.74305i) q^{32} +(-1.59920 + 1.59920i) q^{33} +(11.0244 + 3.38929i) q^{34} +(-0.132986 + 0.438397i) q^{35} +(-1.84198 - 0.779169i) q^{36} +(-0.462996 + 4.70088i) q^{37} +(2.72524 + 1.83573i) q^{38} +(2.89246 + 0.575346i) q^{39} +(-0.106302 - 0.567636i) q^{40} +(-0.488028 - 2.45348i) q^{41} +(-1.20333 - 2.93611i) q^{42} +(-4.72084 + 8.83208i) q^{43} +(4.00496 - 2.10233i) q^{44} +(0.0200130 + 0.203195i) q^{45} +(-2.40399 - 1.29654i) q^{46} +(1.77667 + 4.28926i) q^{47} +(3.05373 + 2.58355i) q^{48} +(-0.752210 + 1.81600i) q^{49} +(5.43704 - 4.42813i) q^{50} +(6.30427 + 5.17378i) q^{51} +(-5.18085 - 2.81925i) q^{52} +(-5.15970 + 1.56518i) q^{53} +(-0.996252 - 1.00373i) q^{54} +(-0.383949 - 0.256546i) q^{55} +(0.551132 + 6.32229i) q^{56} +(1.29084 + 1.93188i) q^{57} +(-6.10027 - 9.20404i) q^{58} +(-6.96321 - 8.48470i) q^{59} +(0.0826605 - 0.399903i) q^{60} +(8.12186 - 4.34122i) q^{61} +(1.04157 + 10.9968i) q^{62} -2.24374i q^{63} +(-4.29417 - 6.74982i) q^{64} +0.602148i q^{65} +(3.18414 - 0.301589i) q^{66} +(4.41544 - 2.36010i) q^{67} +(-8.96018 - 13.6295i) q^{68} +(-1.22523 - 1.49295i) q^{69} +(0.540039 - 0.357928i) q^{70} +(-9.35478 - 14.0004i) q^{71} +(1.30524 + 2.50925i) q^{72} +(3.88629 + 2.59674i) q^{73} +(4.74126 - 4.70592i) q^{74} +(4.74481 - 1.43932i) q^{75} +(-1.31562 - 4.45678i) q^{76} +(3.92261 + 3.21921i) q^{77} +(-2.63378 - 3.23386i) q^{78} +(-1.74009 + 4.20095i) q^{79} +(-0.395730 + 0.714436i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-1.67933 + 3.11374i) q^{82} +(-0.0428125 - 0.434683i) q^{83} +(-1.33474 + 4.28439i) q^{84} +(-0.784957 + 1.46855i) q^{85} +(13.1049 - 5.37087i) q^{86} +(-1.52325 - 7.65791i) q^{87} +(-6.25948 - 1.31828i) q^{88} +(-7.68770 - 1.52918i) q^{89} +(0.161319 - 0.239487i) q^{90} +(0.648587 - 6.58522i) q^{91} +(1.45145 + 3.57961i) q^{92} +(-2.26732 + 7.47437i) q^{93} +(1.92941 - 6.27582i) q^{94} +(-0.335451 + 0.335451i) q^{95} +(-0.999644 - 5.56783i) q^{96} +(-9.83661 - 9.83661i) q^{97} +(2.45646 - 1.30121i) q^{98} +(2.16422 + 0.656510i) 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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