LMFDB - Embedded newform 384.2.v.a.229.24

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			229.24
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.986134 - 1.01368i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-0.0550803 - 1.99924i) q^{4} +(-0.677775 - 0.825871i) q^{5} +(0.391849 - 1.35884i) q^{6} +(1.41014 - 0.942226i) q^{7} +(-2.08090 - 1.91569i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.986134 - 1.01368i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-0.0550803 - 1.99924i) q^{4} +(-0.677775 - 0.825871i) q^{5} +(0.391849 - 1.35884i) q^{6} +(1.41014 - 0.942226i) q^{7} +(-2.08090 - 1.91569i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-1.50554 - 0.127375i) q^{10} +(-1.74200 + 0.528429i) q^{11} +(-0.991012 - 1.73721i) q^{12} +(2.10024 + 1.72362i) q^{13} +(0.435475 - 2.35859i) q^{14} +(-0.987057 - 0.408853i) q^{15} +(-3.99393 + 0.220238i) q^{16} +(-1.28276 + 0.531336i) q^{17} +(-0.294975 - 1.38311i) q^{18} +(0.136658 + 1.38751i) q^{19} +(-1.61378 + 1.40053i) q^{20} +(0.799471 - 1.49571i) q^{21} +(-1.18219 + 2.28692i) q^{22} +(3.76629 - 0.749161i) q^{23} +(-2.73824 - 0.708554i) q^{24} +(0.752767 - 3.78442i) q^{25} +(3.81832 - 0.429242i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-1.96141 - 2.76731i) q^{28} +(-1.26193 + 4.16002i) q^{29} +(-1.38782 + 0.597374i) q^{30} +(0.429538 + 0.429538i) q^{31} +(-3.71530 + 4.26574i) q^{32} +(-1.28720 + 1.28720i) q^{33} +(-0.726369 + 1.82427i) q^{34} +(-1.73392 - 0.525978i) q^{35} +(-1.69291 - 1.06492i) q^{36} +(9.15947 + 0.902129i) q^{37} +(1.54125 + 1.22974i) q^{38} +(2.66476 + 0.530054i) q^{39} +(-0.171727 + 3.01696i) q^{40} +(0.0409206 + 0.205722i) q^{41} +(-0.727776 - 2.28537i) q^{42} +(0.656154 + 0.350722i) q^{43} +(1.15241 + 3.45357i) q^{44} +(-1.06324 + 0.104720i) q^{45} +(2.95466 - 4.55657i) q^{46} +(-1.66400 - 4.01725i) q^{47} +(-3.41851 + 2.07696i) q^{48} +(-1.57808 + 3.80981i) q^{49} +(-3.09384 - 4.49500i) q^{50} +(-0.880823 + 1.07329i) q^{51} +(3.33026 - 4.29383i) q^{52} +(2.99320 + 9.86727i) q^{53} +(-0.912137 - 1.08074i) q^{54} +(1.61710 + 1.08051i) q^{55} +(-4.73937 - 0.740708i) q^{56} +(0.774588 + 1.15925i) q^{57} +(2.97248 + 5.38152i) q^{58} +(-1.91727 + 1.57346i) q^{59} +(-0.763028 + 1.99589i) q^{60} +(6.69473 + 12.5250i) q^{61} +(0.858994 - 0.0118307i) q^{62} -1.69596i q^{63} +(0.660296 + 7.97270i) q^{64} -2.90276i q^{65} +(0.0354532 + 2.57416i) q^{66} +(-5.87901 - 10.9988i) q^{67} +(1.13292 + 2.53528i) q^{68} +(2.96842 - 2.43612i) q^{69} +(-2.24304 + 1.23895i) q^{70} +(-1.22937 - 1.83988i) q^{71} +(-2.74892 + 0.665908i) q^{72} +(4.58079 + 3.06079i) q^{73} +(9.94692 - 8.39512i) q^{74} +(-1.12008 - 3.69241i) q^{75} +(2.76643 - 0.349636i) q^{76} +(-1.95856 + 2.38651i) q^{77} +(3.16511 - 2.17850i) q^{78} +(2.27553 - 5.49362i) q^{79} +(2.88888 + 3.14920i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(0.248889 + 0.161389i) q^{82} +(-7.02364 + 0.691768i) q^{83} +(-3.03431 - 1.51595i) q^{84} +(1.30824 + 0.699268i) q^{85} +(1.00257 - 0.319270i) q^{86} +(0.848098 + 4.26367i) q^{87} +(4.63723 + 2.23751i) q^{88} +(-14.5405 - 2.89228i) q^{89} +(-0.942344 + 1.18105i) q^{90} +(4.58568 + 0.451650i) q^{91} +(-1.70520 - 7.48846i) q^{92} +(0.581301 + 0.176336i) q^{93} +(-5.71312 - 2.27479i) q^{94} +(1.05328 - 1.05328i) q^{95} +(-1.26575 + 5.51343i) q^{96} +(7.28592 + 7.28592i) q^{97} +(2.30572 + 5.35665i) q^{98} +(-0.528429 + 1.74200i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.986134	−	1.01368i	0.697302	−	0.716778i
$2$	0.986134	−	1.01368i	0.697302	−	0.716778i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	−0.0550803	−	1.99924i	−0.0275402	−	0.999621i
$5$	−0.677775	−	0.825871i	−0.303110	−	0.369341i	0.599073	−	0.800695i	$-0.295536\pi$
$5$	−0.677775	−	0.825871i	−0.303110	−	0.369341i	−0.902183	+	0.431354i	$0.858036\pi$
$6$	0.391849	−	1.35884i	0.159971	−	0.554745i
$7$	1.41014	−	0.942226i	0.532983	−	0.356128i	−0.259770	−	0.965670i	$-0.583647\pi$
$7$	1.41014	−	0.942226i	0.532983	−	0.356128i	0.792753	+	0.609542i	$0.208647\pi$
$8$	−2.08090	−	1.91569i	−0.735710	−	0.677297i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−1.50554	−	0.127375i	−0.476095	−	0.0402795i
$11$	−1.74200	+	0.528429i	−0.525232	+	0.159327i	−0.541755	−	0.840536i	$-0.682240\pi$
$11$	−1.74200	+	0.528429i	−0.525232	+	0.159327i	0.0165237	+	0.999863i	$0.494740\pi$
$12$	−0.991012	−	1.73721i	−0.286081	−	0.501489i
$13$	2.10024	+	1.72362i	0.582502	+	0.478047i	0.878893	−	0.477020i	$-0.158283\pi$
$13$	2.10024	+	1.72362i	0.582502	+	0.478047i	−0.296390	+	0.955067i	$0.595783\pi$
$14$	0.435475	−	2.35859i	0.116386	−	0.630359i
$15$	−0.987057	−	0.408853i	−0.254857	−	0.105565i
$16$	−3.99393	+	0.220238i	−0.998483	+	0.0550594i
$17$	−1.28276	+	0.531336i	−0.311115	+	0.128868i	−0.532777	−	0.846255i	$-0.678852\pi$
$17$	−1.28276	+	0.531336i	−0.311115	+	0.128868i	0.221662	+	0.975123i	$0.428852\pi$
$18$	−0.294975	−	1.38311i	−0.0695262	−	0.326002i
$19$	0.136658	+	1.38751i	0.0313514	+	0.318316i	0.998051	+	0.0624025i	$0.0198762\pi$
$19$	0.136658	+	1.38751i	0.0313514	+	0.318316i	−0.966700	+	0.255914i	$0.917624\pi$
$20$	−1.61378	+	1.40053i	−0.360853	+	0.313167i
$21$	0.799471	−	1.49571i	0.174459	−	0.326390i
$22$	−1.18219	+	2.28692i	−0.252043	+	0.487574i
$23$	3.76629	−	0.749161i	0.785326	−	0.156211i	0.213890	−	0.976858i	$-0.431387\pi$
$23$	3.76629	−	0.749161i	0.785326	−	0.156211i	0.571436	+	0.820647i	$0.306387\pi$
$24$	−2.73824	−	0.708554i	−0.558941	−	0.144633i
$25$	0.752767	−	3.78442i	0.150553	−	0.756883i
$26$	3.81832	−	0.429242i	0.748834	−	0.0841813i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−1.96141	−	2.76731i	−0.370671	−	0.522973i
$29$	−1.26193	+	4.16002i	−0.234334	+	0.772496i	0.758360	+	0.651836i	$0.226001\pi$
$29$	−1.26193	+	4.16002i	−0.234334	+	0.772496i	−0.992694	+	0.120660i	$0.961499\pi$
$30$	−1.38782	+	0.597374i	−0.253379	+	0.109065i
$31$	0.429538	+	0.429538i	0.0771473	+	0.0771473i	0.744628	−	0.667480i	$-0.232627\pi$
$31$	0.429538	+	0.429538i	0.0771473	+	0.0771473i	−0.667480	+	0.744628i	$0.732627\pi$
$32$	−3.71530	+	4.26574i	−0.656779	+	0.754083i
$33$	−1.28720	+	1.28720i	−0.224073	+	0.224073i
$34$	−0.726369	+	1.82427i	−0.124571	+	0.312860i
$35$	−1.73392	−	0.525978i	−0.293085	−	0.0889065i
$36$	−1.69291	−	1.06492i	−0.282152	−	0.177487i
$37$	9.15947	+	0.902129i	1.50581	+	0.148309i	0.817001	−	0.576637i	$-0.195635\pi$
$37$	9.15947	+	0.902129i	1.50581	+	0.148309i	0.688806	+	0.724946i	$0.258135\pi$
$38$	1.54125	+	1.22974i	0.250023	+	0.199490i
$39$	2.66476	+	0.530054i	0.426703	+	0.0848765i
$40$	−0.171727	+	3.01696i	−0.0271525	+	0.477023i
$41$	0.0409206	+	0.205722i	0.00639073	+	0.0321283i	0.983849	−	0.179000i	$-0.0572862\pi$
$41$	0.0409206	+	0.205722i	0.00639073	+	0.0321283i	−0.977458	+	0.211128i	$0.932286\pi$
$42$	−0.727776	−	2.28537i	−0.112298	−	0.352640i
$43$	0.656154	+	0.350722i	0.100063	+	0.0534846i	0.520669	−	0.853759i	$-0.325683\pi$
$43$	0.656154	+	0.350722i	0.100063	+	0.0534846i	−0.420606	+	0.907243i	$0.638183\pi$
$44$	1.15241	+	3.45357i	0.173732	+	0.520645i
$45$	−1.06324	+	0.104720i	−0.158498	+	0.0156107i
$46$	2.95466	−	4.55657i	0.435640	−	0.671830i
$47$	−1.66400	−	4.01725i	−0.242719	−	0.585977i	0.754832	−	0.655919i	$-0.227719\pi$
$47$	−1.66400	−	4.01725i	−0.242719	−	0.585977i	−0.997551	+	0.0699421i	$0.977719\pi$
$48$	−3.41851	+	2.07696i	−0.493420	+	0.299783i
$49$	−1.57808	+	3.80981i	−0.225439	+	0.544259i
$50$	−3.09384	−	4.49500i	−0.437536	−	0.635689i
$51$	−0.880823	+	1.07329i	−0.123340	+	0.150290i
$52$	3.33026	−	4.29383i	0.461824	−	0.595447i
$53$	2.99320	+	9.86727i	0.411148	+	1.35537i	0.881203	+	0.472737i	$0.156734\pi$
$53$	2.99320	+	9.86727i	0.411148	+	1.35537i	−0.470055	+	0.882637i	$0.655766\pi$
$54$	−0.912137	−	1.08074i	−0.124126	−	0.147070i
$55$	1.61710	+	1.08051i	0.218049	+	0.145696i
$56$	−4.73937	−	0.740708i	−0.633325	−	0.0989813i
$57$	0.774588	+	1.15925i	0.102597	+	0.153547i
$58$	2.97248	+	5.38152i	0.390306	+	0.706628i
$59$	−1.91727	+	1.57346i	−0.249607	+	0.204848i	−0.750874	−	0.660445i	$-0.770368\pi$
$59$	−1.91727	+	1.57346i	−0.249607	+	0.204848i	0.501267	+	0.865293i	$0.332868\pi$
$60$	−0.763028	+	1.99589i	−0.0985064	+	0.257668i
$61$	6.69473	+	12.5250i	0.857172	+	1.60366i	0.795815	+	0.605540i	$0.207043\pi$
$61$	6.69473	+	12.5250i	0.857172	+	1.60366i	0.0613567	+	0.998116i	$0.480457\pi$
$62$	0.858994	−	0.0118307i	0.109092	−	0.00150250i
$63$		−	1.69596i		−	0.213671i
$64$	0.660296	+	7.97270i	0.0825369	+	0.996588i
$65$		−	2.90276i		−	0.360043i
$66$	0.0354532	+	2.57416i	0.00436398	+	0.316858i
$67$	−5.87901	−	10.9988i	−0.718235	−	1.34372i	−0.930420	−	0.366494i	$-0.880558\pi$
$67$	−5.87901	−	10.9988i	−0.718235	−	1.34372i	0.212185	−	0.977229i	$-0.431942\pi$
$68$	1.13292	+	2.53528i	0.137387	+	0.307448i
$69$	2.96842	−	2.43612i	0.357356	−	0.293274i
$70$	−2.24304	+	1.23895i	−0.268095	+	0.148082i
$71$	−1.22937	−	1.83988i	−0.145899	−	0.218354i	0.751321	−	0.659937i	$-0.229417\pi$
$71$	−1.22937	−	1.83988i	−0.145899	−	0.218354i	−0.897220	+	0.441583i	$0.854417\pi$
$72$	−2.74892	+	0.665908i	−0.323963	+	0.0784780i
$73$	4.58079	+	3.06079i	0.536141	+	0.358238i	0.793974	−	0.607951i	$-0.208008\pi$
$73$	4.58079	+	3.06079i	0.536141	+	0.358238i	−0.257833	+	0.966190i	$0.583008\pi$
$74$	9.94692	−	8.39512i	1.15631	−	0.975912i
$75$	−1.12008	−	3.69241i	−0.129336	−	0.426363i
$76$	2.76643	−	0.349636i	0.317332	−	0.0401060i
$77$	−1.95856	+	2.38651i	−0.223199	+	0.271968i
$78$	3.16511	−	2.17850i	0.358378	−	0.246667i
$79$	2.27553	−	5.49362i	0.256017	−	0.618080i	−0.742651	−	0.669679i	$-0.766432\pi$
$79$	2.27553	−	5.49362i	0.256017	−	0.618080i	0.998668	+	0.0515989i	$0.0164317\pi$
$80$	2.88888	+	3.14920i	0.322986	+	0.352092i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	0.248889	+	0.161389i	0.0274851	+	0.0178224i
$83$	−7.02364	+	0.691768i	−0.770945	+	0.0759314i	−0.475838	−	0.879533i	$-0.657855\pi$
$83$	−7.02364	+	0.691768i	−0.770945	+	0.0759314i	−0.295107	+	0.955464i	$0.595355\pi$
$84$	−3.03431	−	1.51595i	−0.331070	−	0.165404i
$85$	1.30824	+	0.699268i	0.141898	+	0.0758462i
$86$	1.00257	−	0.319270i	0.108110	−	0.0344277i
$87$	0.848098	+	4.26367i	0.0909256	+	0.457114i
$88$	4.63723	+	2.23751i	0.494330	+	0.238519i
$89$	−14.5405	−	2.89228i	−1.54129	−	0.306581i	−0.649969	−	0.759960i	$-0.725218\pi$
$89$	−14.5405	−	2.89228i	−1.54129	−	0.306581i	−0.891318	+	0.453379i	$0.850218\pi$
$90$	−0.942344	+	1.18105i	−0.0993317	+	0.124493i
$91$	4.58568	+	0.451650i	0.480710	+	0.0473458i
$92$	−1.70520	−	7.48846i	−0.177780	−	0.780726i
$93$	0.581301	+	0.176336i	0.0602781	+	0.0182852i
$94$	−5.71312	−	2.27479i	−0.589264	−	0.234627i
$95$	1.05328	−	1.05328i	0.108064	−	0.108064i
$96$	−1.26575	+	5.51343i	−0.129185	+	0.562712i
$97$	7.28592	+	7.28592i	0.739773	+	0.739773i	0.972534	−	0.232761i	$-0.0747760\pi$
$97$	7.28592	+	7.28592i	0.739773	+	0.739773i	−0.232761	+	0.972534i	$0.574776\pi$
$98$	2.30572	+	5.35665i	0.232913	+	0.541103i
$99$	−0.528429	+	1.74200i	−0.0531091	+	0.175077i
$100$	−7.60742	−	1.29652i	−0.760742	−	0.129652i
$101$	0.538531	−	5.46779i	0.0535858	−	0.544066i	−0.930490	−	0.366317i	$-0.880619\pi$
$101$	0.538531	−	5.46779i	0.0535858	−	0.544066i	0.984076	−	0.177749i	$-0.0568815\pi$
$102$	0.219355	+	1.95127i	0.0217194	+	0.193205i
$103$	−0.0250551	+	0.125960i	−0.00246875	+	0.0124112i	−0.982000	−	0.188881i	$-0.939514\pi$
$103$	−0.0250551	+	0.125960i	−0.00246875	+	0.0124112i	0.979531	+	0.201292i	$0.0645140\pi$
$104$	−1.06847	−	7.61010i	−0.104772	−	0.746231i
$105$	−1.77712	+	0.353491i	−0.173429	+	0.0344972i
$106$	12.9539	+	6.69631i	1.25820	+	0.650403i
$107$	0.337680	−	0.631756i	0.0326448	−	0.0610741i	−0.865070	−	0.501651i	$-0.832726\pi$
$107$	0.337680	−	0.631756i	0.0326448	−	0.0610741i	0.897715	+	0.440577i	$0.145226\pi$
$108$	−1.99501	−	0.141145i	−0.191970	−	0.0135817i
$109$	0.714761	+	7.25709i	0.0684617	+	0.695103i	0.966755	+	0.255706i	$0.0823080\pi$
$109$	0.714761	+	7.25709i	0.0684617	+	0.695103i	−0.898293	+	0.439397i	$0.855192\pi$
$110$	2.68996	−	0.573686i	0.256478	−	0.0546988i
$111$	8.50319	−	3.52214i	0.807087	−	0.334306i
$112$	−5.42449	+	4.07375i	−0.512566	+	0.384934i
$113$	−4.43091	−	1.83534i	−0.416825	−	0.172655i	0.164407	−	0.986393i	$-0.447429\pi$
$113$	−4.43091	−	1.83534i	−0.416825	−	0.172655i	−0.581232	+	0.813738i	$0.697429\pi$
$114$	1.93895	+	0.357997i	0.181600	+	0.0335294i
$115$	−3.17141	−	2.60271i	−0.295735	−	0.242704i
$116$	8.38638	+	2.29376i	0.778656	+	0.212970i
$117$	2.59997	−	0.788693i	0.240368	−	0.0729147i
$118$	−0.295703	+	3.49514i	−0.0272216	+	0.321754i
$119$	−1.30823	+	1.95791i	−0.119925	+	0.179481i
$120$	1.27074	+	2.74167i	0.116002	+	0.250279i
$121$	−6.39085	+	4.27023i	−0.580986	+	0.388203i
$122$	19.2981	+	5.56499i	1.74717	+	0.503831i
$123$	0.133065	+	0.162141i	0.0119981	+	0.0146197i
$124$	0.835091	−	0.882409i	0.0749934	−	0.0792427i
$125$	−8.34680	+	4.46146i	−0.746560	+	0.399045i
$126$	−1.71916	−	1.67245i	−0.153155	−	0.148993i
$127$	−5.58316			−0.495426			−0.247713	−	0.968833i	$-0.579679\pi$
$127$	−5.58316			−0.495426			−0.247713	+	0.968833i	$0.579679\pi$
$128$	8.73288	+	7.19283i	0.771885	+	0.635762i
$129$	0.744006			0.0655060
$130$	−2.94246	−	2.86251i	−0.258071	−	0.251059i
$131$	2.91195	−	1.55647i	0.254418	−	0.135990i	−0.339258	−	0.940693i	$-0.610176\pi$
$131$	2.91195	−	1.55647i	0.254418	−	0.135990i	0.593676	+	0.804704i	$0.297676\pi$
$132$	2.64433	+	2.50253i	0.230159	+	0.217817i
$133$	1.50005	+	1.82782i	0.130071	+	0.158492i
$134$	−16.9468	−	4.88692i	−1.46398	−	0.422166i
$135$	−0.888328	+	0.593562i	−0.0764551	+	0.0510857i
$136$	3.68717	+	1.35171i	0.316172	+	0.115908i
$137$	11.1772	−	16.7278i	0.954931	−	1.42916i	0.0523532	−	0.998629i	$-0.483328\pi$
$137$	11.1772	−	16.7278i	0.954931	−	1.42916i	0.902578	−	0.430527i	$-0.141672\pi$
$138$	0.457822	−	5.41135i	0.0389724	−	0.460645i
$139$	−2.98195	+	0.904564i	−0.252925	+	0.0767241i	−0.414201	−	0.910185i	$-0.635939\pi$
$139$	−2.98195	+	0.904564i	−0.252925	+	0.0767241i	0.161276	+	0.986909i	$0.448439\pi$
$140$	−0.956052	+	3.49549i	−0.0808011	+	0.295423i
$141$	−3.36124	−	2.75850i	−0.283067	−	0.232307i
$142$	−3.07737	−	0.568187i	−0.258247	−	0.0476812i
$143$	−4.56943	−	1.89272i	−0.382115	−	0.158277i
$144$	−2.03579	+	3.44319i	−0.169649	+	0.286933i
$145$	4.29094	−	1.77737i	0.356343	−	0.147602i
$146$	7.61992	−	1.62510i	0.630629	−	0.134494i
$147$	0.404195	+	4.10386i	0.0333374	+	0.338480i
$148$	1.29907	−	18.3617i	0.106783	−	1.50932i
$149$	−2.09750	+	3.92414i	−0.171834	+	0.321478i	−0.953066	−	0.302762i	$-0.902091\pi$
$149$	−2.09750	+	3.92414i	−0.171834	+	0.321478i	0.781233	+	0.624240i	$0.214591\pi$
$150$	−4.84746	−	2.50581i	−0.395793	−	0.204599i
$151$	5.82458	−	1.15858i	0.473997	−	0.0942839i	0.0476897	−	0.998862i	$-0.484814\pi$
$151$	5.82458	−	1.15858i	0.473997	−	0.0942839i	0.426308	+	0.904578i	$0.359814\pi$
$152$	2.37366	−	3.14906i	0.192529	−	0.255422i
$153$	−0.270873	+	1.36177i	−0.0218988	+	0.110093i
$154$	0.487750	+	4.33877i	0.0393040	+	0.349628i
$155$	0.0636130	−	0.645873i	0.00510952	−	0.0518778i
$156$	0.912929	−	5.35669i	0.0730928	−	0.428879i
$157$	−2.30349	+	7.59359i	−0.183839	+	0.606034i	0.815779	+	0.578364i	$0.196309\pi$
$157$	−2.30349	+	7.59359i	−0.183839	+	0.606034i	−0.999617	+	0.0276700i	$0.991191\pi$
$158$	−3.32477	−	7.72409i	−0.264505	−	0.614496i
$159$	7.29117	+	7.29117i	0.578227	+	0.578227i
$160$	6.04109	+	0.177149i	0.477590	+	0.0140049i
$161$	4.60512	−	4.60512i	0.362934	−	0.362934i
$162$	−1.31389	−	0.523152i	−0.103229	−	0.0411027i
$163$	−21.7001	−	6.58266i	−1.69969	−	0.515594i	−0.716404	−	0.697685i	$-0.754213\pi$
$163$	−21.7001	−	6.58266i	−1.69969	−	0.515594i	−0.983282	+	0.182091i	$0.941713\pi$
$164$	0.409034	−	0.0931414i	0.0319402	−	0.00727312i
$165$	1.93550	+	0.190630i	0.150678	+	0.0148405i
$166$	−6.22502	+	7.80188i	−0.483155	+	0.605543i
$167$	0.379987	+	0.0755842i	0.0294043	+	0.00584888i	0.209771	−	0.977751i	$-0.432728\pi$
$167$	0.379987	+	0.0755842i	0.0294043	+	0.00584888i	−0.180366	+	0.983600i	$0.557728\pi$
$168$	−4.52892	+	1.58088i	−0.349414	+	0.121967i
$169$	−1.09604	−	5.51015i	−0.0843106	−	0.423858i
$170$	1.99893	−	0.636559i	0.153311	−	0.0488218i
$171$	1.22959	+	0.657231i	0.0940293	+	0.0502597i
$172$	0.665036	−	1.33113i	0.0507085	−	0.101498i
$173$	−13.1260	+	1.29280i	−0.997952	+	0.0982897i	−0.583782	−	0.811910i	$-0.698428\pi$
$173$	−13.1260	+	1.29280i	−0.997952	+	0.0982897i	−0.414169	+	0.910200i	$0.635928\pi$
$174$	5.15833	+	3.34486i	0.391052	+	0.253573i
$175$	−2.50427	−	6.04584i	−0.189305	−	0.457022i
$176$	6.84104	−	2.49416i	0.515662	−	0.188005i
$177$	−0.949157	+	2.29147i	−0.0713430	+	0.172237i
$178$	−17.2707	+	11.8872i	−1.29449	+	0.890980i
$179$	−7.86075	+	9.57836i	−0.587540	+	0.715920i	−0.978905	−	0.204316i	$-0.934503\pi$
$179$	−7.86075	+	9.57836i	−0.587540	+	0.715920i	0.391365	+	0.920236i	$0.372003\pi$
$180$	0.267924	+	2.11990i	0.0199699	+	0.158008i
$181$	−1.58944	−	5.23969i	−0.118142	−	0.389463i	0.877846	−	0.478942i	$-0.158980\pi$
$181$	−1.58944	−	5.23969i	−0.118142	−	0.389463i	−0.995989	+	0.0894792i	$0.971480\pi$
$182$	4.97992	−	4.20301i	0.369136	−	0.311548i
$183$	11.8084	+	7.89015i	0.872905	+	0.583257i
$184$	−9.27243	−	5.65610i	−0.683573	−	0.416973i
$185$	−5.46302	−	8.17598i	−0.401649	−	0.601110i
$186$	0.751988	−	0.415361i	0.0551385	−	0.0304557i
$187$	1.95379	−	1.60343i	0.142875	−	0.117255i
$188$	−7.93980	+	3.54801i	−0.579070	+	0.258765i
$189$	−0.799471	−	1.49571i	−0.0581530	−	0.108797i
$190$	−0.0290102	−	2.10636i	−0.00210462	−	0.152811i
$191$		−	24.9554i		−	1.80571i	−0.429943	−	0.902856i	$-0.641466\pi$
$191$		−	24.9554i		−	1.80571i	0.429943	−	0.902856i	$-0.358534\pi$
$192$	4.34064	+	6.72004i	0.313258	+	0.484977i
$193$		−	4.07046i		−	0.292998i	−0.989211	−	0.146499i	$-0.953199\pi$
$193$		−	4.07046i		−	0.292998i	0.989211	−	0.146499i	$-0.0468006\pi$
$194$	14.5705	−	0.200674i	1.04610	−	0.0144076i
$195$	−1.36835	−	2.56001i	−0.0979897	−	0.183326i
$196$	7.70366	+	2.94511i	0.550261	+	0.210365i
$197$	−10.1042	+	8.29227i	−0.719892	+	0.590800i	−0.921367	−	0.388694i	$-0.872926\pi$
$197$	−10.1042	+	8.29227i	−0.719892	+	0.590800i	0.201475	+	0.979494i	$0.435426\pi$
$198$	1.24472	+	2.25350i	0.0884584	+	0.160149i
$199$	−9.53553	−	14.2709i	−0.675956	−	1.01164i	−0.997893	−	0.0648784i	$-0.979334\pi$
$199$	−9.53553	−	14.2709i	−0.675956	−	1.01164i	0.321937	−	0.946761i	$-0.395666\pi$
$200$	−8.81619	+	6.43293i	−0.623398	+	0.454877i
$201$	−10.3696	−	6.92877i	−0.731418	−	0.488718i
$202$	−5.01151	−	5.93787i	−0.352609	−	0.417787i
$203$	2.14018	+	7.05523i	0.150211	+	0.495180i
$204$	2.19427	+	1.70186i	0.153630	+	0.119154i
$205$	0.142165	−	0.173228i	0.00992922	−	0.0120988i
$206$	0.102975	+	0.149612i	0.00717464	+	0.0104239i
$207$	1.46953	−	3.54777i	0.102140	−	0.246587i
$208$	−8.76783	−	6.42149i	−0.607940	−	0.445250i
$209$	−0.971256	−	2.34482i	−0.0671832	−	0.162195i
$210$	−1.39415	+	2.15002i	−0.0962057	+	0.148365i
$211$	−23.3461	+	2.29939i	−1.60721	+	0.158296i	−0.861423	−	0.507888i	$-0.830426\pi$
$211$	−23.3461	+	2.29939i	−1.60721	+	0.158296i	−0.745787	+	0.666184i	$0.767926\pi$
$212$	19.5622	−	6.52763i	1.34354	−	0.448320i
$213$	−1.95152	−	1.04311i	−0.133716	−	0.0714728i
$214$	−0.307398	−	0.965294i	−0.0210133	−	0.0659861i
$215$	−0.155074	−	0.779610i	−0.0105760	−	0.0531689i
$216$	−2.11043	+	1.88311i	−0.143596	+	0.128129i
$217$	1.01043	+	0.200987i	0.0685925	+	0.0136439i
$218$	8.06120	+	6.43193i	0.545973	+	0.435625i
$219$	5.48275	+	0.540003i	0.370490	+	0.0364900i
$220$	2.07113	−	3.29248i	0.139635	−	0.221979i
$221$	−3.60993	−	1.09506i	−0.242830	−	0.0736617i
$222$	4.81497	−	12.0928i	0.323160	−	0.811614i
$223$	6.80299	−	6.80299i	0.455562	−	0.455562i	−0.441634	−	0.897195i	$-0.645601\pi$
$223$	6.80299	−	6.80299i	0.455562	−	0.455562i	0.897195	+	0.441634i	$0.145601\pi$
$224$	−1.21981	+	9.51595i	−0.0815019	+	0.635811i
$225$	−2.72841	−	2.72841i	−0.181894	−	0.181894i
$226$	−6.22991	+	2.68162i	−0.414408	+	0.178378i
$227$	−2.08805	+	6.88337i	−0.138589	+	0.456865i	−0.998570	−	0.0534601i	$-0.982975\pi$
$227$	−2.08805	+	6.88337i	−0.138589	+	0.456865i	0.859981	+	0.510325i	$0.170475\pi$
$228$	2.27496	−	1.61244i	0.150663	−	0.106786i
$229$	1.28708	−	13.0680i	0.0850528	−	0.863556i	−0.854112	−	0.520089i	$-0.825899\pi$
$229$	1.28708	−	13.0680i	0.0850528	−	0.863556i	0.939165	−	0.343467i	$-0.111601\pi$
$230$	−5.76574	+	0.648164i	−0.380181	+	0.0427387i
$231$	−0.602302	+	3.02798i	−0.0396286	+	0.199226i
$232$	10.5952	−	6.23912i	0.695611	−	0.409619i
$233$	−8.92830	+	1.77595i	−0.584913	+	0.116346i	−0.478672	−	0.877994i	$-0.658882\pi$
$233$	−8.92830	+	1.77595i	−0.584913	+	0.116346i	−0.106241	+	0.994340i	$0.533882\pi$
$234$	1.76444	−	3.41329i	0.115345	−	0.223134i
$235$	−2.18992	+	4.09704i	−0.142854	+	0.267262i
$236$	3.25134	+	3.74642i	0.211644	+	0.243871i
$237$	−0.582834	−	5.91761i	−0.0378591	−	0.384390i
$238$	0.694594	+	3.25688i	0.0450238	+	0.211112i
$239$	−11.6520	+	4.82641i	−0.753705	+	0.312195i	−0.726252	−	0.687428i	$-0.758740\pi$
$239$	−11.6520	+	4.82641i	−0.753705	+	0.312195i	−0.0274527	+	0.999623i	$0.508740\pi$
$240$	4.03229	+	1.41554i	0.260283	+	0.0913729i
$241$	−13.0308	−	5.39755i	−0.839390	−	0.347687i	−0.0787770	−	0.996892i	$-0.525101\pi$
$241$	−13.0308	−	5.39755i	−0.839390	−	0.347687i	−0.760613	+	0.649206i	$0.775101\pi$
$242$	−1.97360	+	10.6893i	−0.126868	+	0.687133i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	24.6717	−	14.0743i	1.57944	−	0.901012i
$245$	4.21600	−	1.27891i	0.269350	−	0.0817065i
$246$	0.295578	+	0.0250071i	0.0188454	+	0.00159439i
$247$	−2.10453	+	3.14965i	−0.133908	+	0.200407i
$248$	−0.0709661	−	1.71669i	−0.00450635	−	0.109010i
$249$	−5.86820	+	3.92101i	−0.371882	+	0.248484i
$250$	−3.70859	+	12.8605i	−0.234552	+	0.813372i
$251$	16.4905	+	20.0937i	1.04087	+	1.26830i	0.962472	+	0.271380i	$0.0874800\pi$
$251$	16.4905	+	20.0937i	1.04087	+	1.26830i	0.0783966	+	0.996922i	$0.475020\pi$
$252$	−3.39064	+	0.0934142i	−0.213590	+	0.00588454i
$253$	−6.16498	+	3.29525i	−0.387589	+	0.207171i
$254$	−5.50575	+	5.65952i	−0.345461	+	0.355110i
$255$	1.48340			0.0928938
$256$	15.9030	−	1.75923i	0.993937	−	0.109952i
$257$	23.9118			1.49158			0.745788	−	0.666184i	$-0.232073\pi$
$257$	23.9118			1.49158			0.745788	+	0.666184i	$0.232073\pi$
$258$	0.733689	−	0.754181i	0.0456775	−	0.0469533i
$259$	13.7661	−	7.35816i	0.855387	−	0.457214i
$260$	−5.80332	+	0.159885i	−0.359907	+	0.00991565i
$261$	2.75784	+	3.36044i	0.170706	+	0.208006i
$262$	1.29382	−	4.48667i	0.0799323	−	0.277187i
$263$	−7.18426	+	4.80037i	−0.443000	+	0.296003i	−0.756994	−	0.653422i	$-0.773333\pi$
$263$	−7.18426	+	4.80037i	−0.443000	+	0.296003i	0.313994	+	0.949425i	$0.398333\pi$
$264$	5.14442	−	0.212665i	0.316617	−	0.0130886i
$265$	6.12038	−	9.15980i	0.375972	−	0.562682i
$266$	3.33207	+	0.281906i	0.204302	+	0.0172848i
$267$	−14.1870	+	4.30357i	−0.868228	+	0.263374i
$268$	−21.6655	+	12.3594i	−1.32343	+	0.754969i
$269$	−12.3584	−	10.1423i	−0.753504	−	0.618385i	0.177193	−	0.984176i	$-0.443298\pi$
$269$	−12.3584	−	10.1423i	−0.753504	−	0.618385i	−0.930697	+	0.365791i	$0.880798\pi$
$270$	−0.274331	+	1.48581i	−0.0166952	+	0.0904235i
$271$	20.5938	+	8.53022i	1.25098	+	0.518174i	0.907130	−	0.420850i	$-0.138268\pi$
$271$	20.5938	+	8.53022i	1.25098	+	0.518174i	0.343852	+	0.939024i	$0.388268\pi$
$272$	5.00623	−	2.40463i	0.303548	−	0.145802i
$273$	4.25712	−	1.76336i	0.257652	−	0.106723i
$274$	−5.93442	−	27.8259i	−0.358511	−	1.68103i
$275$	0.688477	+	6.99022i	0.0415167	+	0.421526i
$276$	−5.03389	−	5.80040i	−0.303004	−	0.349143i
$277$	13.7345	−	25.6954i	0.825226	−	1.54389i	−0.0138689	−	0.999904i	$-0.504415\pi$
$277$	13.7345	−	25.6954i	0.825226	−	1.54389i	0.839095	−	0.543985i	$-0.183085\pi$
$278$	−2.02366	+	3.91475i	−0.121371	+	0.234791i
$279$	0.595786	−	0.118509i	0.0356688	−	0.00709496i
$280$	2.60050	+	4.41615i	0.155410	+	0.263915i
$281$	1.76032	−	8.84975i	0.105012	−	0.527932i	−0.892090	−	0.451858i	$-0.850761\pi$
$281$	1.76032	−	8.84975i	0.105012	−	0.527932i	0.997102	−	0.0760741i	$-0.0242385\pi$
$282$	−6.11085	+	0.686961i	−0.363896	+	0.0409079i
$283$	1.49039	−	15.1322i	0.0885944	−	0.899514i	−0.843459	−	0.537193i	$-0.819485\pi$
$283$	1.49039	−	15.1322i	0.0885944	−	0.899514i	0.932054	−	0.362320i	$-0.118015\pi$
$284$	−3.61066	+	2.55915i	−0.214253	+	0.151858i
$285$	0.432397	−	1.42542i	0.0256130	−	0.0844347i
$286$	−6.42467	+	2.76545i	−0.379899	+	0.163524i
$287$	0.251540	+	0.251540i	0.0148480	+	0.0148480i
$288$	1.48272	+	5.45908i	0.0873702	+	0.321679i
$289$	−10.6577	+	10.6577i	−0.626921	+	0.626921i
$290$	2.42977	−	6.10235i	0.142681	−	0.358342i
$291$	9.86016	+	2.99105i	0.578013	+	0.175338i
$292$	5.86694	−	9.32670i	0.343337	−	0.545804i
$293$	13.0217	+	1.28253i	0.760738	+	0.0749262i	0.470944	−	0.882163i	$-0.343913\pi$
$293$	13.0217	+	1.28253i	0.760738	+	0.0749262i	0.289794	+	0.957089i	$0.406413\pi$
$294$	4.55857	+	3.63723i	0.265861	+	0.212127i
$295$	2.59896	+	0.516965i	0.151317	+	0.0300989i
$296$	−17.3317	−	19.4239i	−1.00739	−	1.12899i
$297$	0.355139	+	1.78540i	0.0206072	+	0.103600i
$298$	1.90940	+	5.99591i	0.110608	+	0.347334i
$299$	9.20139	+	4.91825i	0.532130	+	0.284430i
$300$	−7.32032	+	2.44269i	−0.422639	+	0.141029i
$301$	1.25573	−	0.123679i	0.0723790	−	0.00712871i
$302$	4.56939	−	7.04675i	0.262939	−	0.405495i
$303$	−2.10256	−	5.07603i	−0.120789	−	0.291610i
$304$	−0.851382	−	5.51151i	−0.0488301	−	0.316107i
$305$	5.80648	−	14.0181i	0.332478	−	0.802673i
$306$	1.11328	+	1.61747i	0.0636418	+	0.0924643i
$307$	−18.4607	+	22.4944i	−1.05361	+	1.28382i	−0.0961130	+	0.995370i	$0.530641\pi$
$307$	−18.4607	+	22.4944i	−1.05361	+	1.28382i	−0.957494	+	0.288453i	$0.906859\pi$
$308$	4.87909	+	3.78419i	0.278012	+	0.215624i
$309$	0.0372807	+	0.122898i	0.00212083	+	0.00699143i
$310$	−0.591976	−	0.701400i	−0.0336220	−	0.0398369i
$311$	20.7759	+	13.8820i	1.17809	+	0.787177i	0.981152	−	0.193238i	$-0.0618991\pi$
$311$	20.7759	+	13.8820i	1.17809	+	0.787177i	0.196942	+	0.980415i	$0.436899\pi$
$312$	−4.52968	−	6.20783i	−0.256443	−	0.351449i
$313$	−3.91668	−	5.86173i	−0.221384	−	0.331325i	0.704107	−	0.710094i	$-0.251347\pi$
$313$	−3.91668	−	5.86173i	−0.221384	−	0.331325i	−0.925491	+	0.378769i	$0.876347\pi$
$314$	5.42589	+	9.82329i	0.306201	+	0.554360i
$315$	−1.40065	+	1.14948i	−0.0789175	+	0.0647659i
$316$	−11.1084	−	4.24674i	−0.624896	−	0.238898i
$317$	11.0775	+	20.7245i	0.622172	+	1.16400i	0.973702	+	0.227825i	$0.0731614\pi$
$317$	11.0775	+	20.7245i	0.622172	+	1.16400i	−0.351530	+	0.936176i	$0.614339\pi$
$318$	14.5810	−	0.200819i	0.817660	−	0.0112614i
$319$		−	7.91357i		−	0.443075i
$320$	6.13690	−	5.94902i	0.343063	−	0.332560i
$321$		−	0.716340i		−	0.0399822i
$322$	−0.126838	−	9.20936i	−0.00706839	−	0.513218i
$323$	−0.912532	−	1.70723i	−0.0507746	−	0.0949926i
$324$	−1.82598	+	0.815964i	−0.101443	+	0.0453313i
$325$	8.10390	−	6.65070i	0.449524	−	0.368915i
$326$	−28.0719	+	15.5055i	−1.55476	+	0.858772i
$327$	4.05133	+	6.06325i	0.224039	+	0.335298i
$328$	0.308947	−	0.506478i	0.0170587	−	0.0279656i
$329$	−6.13164	−	4.09703i	−0.338048	−	0.225876i
$330$	2.10190	−	1.77398i	0.115706	−	0.0976546i
$331$	−1.54930	−	5.10737i	−0.0851574	−	0.280726i	0.904011	−	0.427508i	$-0.140608\pi$
$331$	−1.54930	−	5.10737i	−0.0851574	−	0.280726i	−0.989169	+	0.146782i	$0.953108\pi$
$332$	1.76988	+	14.0039i	0.0971346	+	0.768561i
$333$	5.83882	−	7.11462i	0.319965	−	0.389879i
$334$	0.451336	−	0.310648i	0.0246960	−	0.0169979i
$335$	−5.09899	+	12.3101i	−0.278588	+	0.672570i
$336$	−2.86362	+	6.14982i	−0.156223	+	0.335500i
$337$	−0.160820	−	0.388254i	−0.00876042	−	0.0211495i	0.919439	−	0.393233i	$-0.128643\pi$
$337$	−0.160820	−	0.388254i	−0.00876042	−	0.0211495i	−0.928199	+	0.372084i	$0.878643\pi$
$338$	−6.66635	−	4.32272i	−0.362602	−	0.235125i
$339$	−4.77289	+	0.470088i	−0.259228	+	0.0255317i
$340$	1.32595	−	2.65400i	0.0719096	−	0.143933i
$341$	−0.975234	−	0.521273i	−0.0528119	−	0.0282285i
$342$	1.87876	−	0.598292i	0.101592	−	0.0323519i
$343$	3.68046	+	18.5029i	0.198726	+	0.999063i
$344$	−0.693519	−	1.98680i	−0.0373920	−	0.107121i
$345$	−4.02384	−	0.800392i	−0.216636	−	0.0430916i
$346$	−11.6335	+	14.5804i	−0.625422	+	0.783847i
$347$	35.3011	+	3.47685i	1.89506	+	0.186647i	0.977498	−	0.210944i	$-0.0676538\pi$
$347$	35.3011	+	3.47685i	1.89506	+	0.186647i	0.917563	+	0.397591i	$0.130154\pi$
$348$	8.47740	−	1.93040i	0.454436	−	0.103480i
$349$	15.7894	+	4.78966i	0.845186	+	0.256384i	0.683039	−	0.730382i	$-0.260658\pi$
$349$	15.7894	+	4.78966i	0.845186	+	0.256384i	0.162147	+	0.986767i	$0.448158\pi$
$350$	−8.59807	−	3.42349i	−0.459586	−	0.182993i
$351$	1.92118	−	1.92118i	0.102545	−	0.102545i
$352$	4.21790	−	9.39418i	0.224815	−	0.500711i
$353$	20.0365	+	20.0365i	1.06644	+	1.06644i	0.997630	+	0.0688069i	$0.0219192\pi$
$353$	20.0365	+	20.0365i	1.06644	+	1.06644i	0.0688069	+	0.997630i	$0.478081\pi$
$354$	1.38681	+	3.22183i	0.0737082	+	0.171238i
$355$	−0.686270	+	2.26233i	−0.0364234	+	0.120072i
$356$	−4.98147	+	29.2292i	−0.264017	+	1.54915i
$357$	−0.230806	+	2.34342i	−0.0122156	+	0.124027i
$358$	1.95760	+	17.4138i	0.103462	+	0.920348i
$359$	−2.81218	+	14.1378i	−0.148421	+	0.746165i	0.832845	+	0.553507i	$0.186711\pi$
$359$	−2.81218	+	14.1378i	−0.148421	+	0.746165i	−0.981266	+	0.192658i	$0.938289\pi$
$360$	2.41310	+	1.81892i	0.127182	+	0.0958655i
$361$	16.7284	−	3.32749i	0.880443	−	0.175131i
$362$	−6.87876	−	3.55586i	−0.361539	−	0.186892i
$363$	−3.62325	+	6.77863i	−0.190172	+	0.355786i
$364$	0.650377	−	9.19276i	0.0340890	−	0.481832i
$365$	−0.576930	−	5.85767i	−0.0301979	−	0.306605i
$366$	19.6428	−	4.18920i	1.02674	−	0.218973i
$367$	−20.5175	+	8.49864i	−1.07101	+	0.443625i	−0.847346	−	0.531042i	$-0.821801\pi$
$367$	−20.5175	+	8.49864i	−1.07101	+	0.443625i	−0.223661	+	0.974667i	$0.571801\pi$
$368$	−14.8773	+	3.82158i	−0.775533	+	0.199214i
$369$	0.193786	+	0.0802687i	0.0100881	+	0.00417862i
$370$	−13.6751	−	2.52488i	−0.710933	−	0.131262i
$371$	13.5180	+	11.0940i	0.701822	+	0.575970i
$372$	0.320520	−	1.17187i	0.0166182	−	0.0607589i
$373$	−29.2886	+	8.88459i	−1.51650	+	0.460027i	−0.935337	−	0.353757i	$-0.884904\pi$
$373$	−29.2886	+	8.88459i	−1.51650	+	0.460027i	−0.581167	+	0.813784i	$0.697404\pi$
$374$	0.301335	−	3.56171i	0.0155816	−	0.184172i
$375$	−5.25810	+	7.86931i	−0.271527	+	0.406369i
$376$	−4.23317	+	11.5472i	−0.218309	+	0.595502i
$377$	−9.82066	+	6.56195i	−0.505790	+	0.337958i
$378$	−2.30455	−	0.664560i	−0.118533	−	0.0341813i
$379$	4.07833	+	4.96946i	0.209490	+	0.255264i	0.867146	−	0.498054i	$-0.165952\pi$
$379$	4.07833	+	4.96946i	0.209490	+	0.255264i	−0.657656	+	0.753318i	$0.728452\pi$
$380$	−2.16378	−	2.04775i	−0.110999	−	0.105047i
$381$	−4.92391	+	2.63189i	−0.252260	+	0.134836i
$382$	−25.2967	−	24.6094i	−1.29429	−	1.25913i
$383$	31.3628			1.60256			0.801281	−	0.598288i	$-0.204152\pi$
$383$	31.3628			1.60256			0.801281	+	0.598288i	$0.204152\pi$
$384$	11.0924	+	2.22685i	0.566056	+	0.113639i
$385$	3.29842			0.168103
$386$	−4.12613	−	4.01402i	−0.210015	−	0.204308i
$387$	0.656154	−	0.350722i	0.0333542	−	0.0178282i
$388$	14.1650	−	14.9676i	0.719119	−	0.759866i
$389$	−5.31838	−	6.48047i	−0.269653	−	0.328573i	0.620525	−	0.784187i	$-0.286920\pi$
$389$	−5.31838	−	6.48047i	−0.269653	−	0.328573i	−0.890177	+	0.455614i	$0.849420\pi$
$390$	−3.94440	−	1.13744i	−0.199732	−	0.0575966i
$391$	−4.43319	+	2.96216i	−0.224196	+	0.149803i
$392$	10.5822	−	4.90475i	0.534483	−	0.247727i
$393$	1.83440	−	2.74537i	0.0925331	−	0.138486i
$394$	−1.55837	+	18.4196i	−0.0785098	+	0.927968i
$395$	−6.07932	+	1.84414i	−0.305884	+	0.0927888i
$396$	3.51178	+	0.960507i	0.176473	+	0.0482673i
$397$	−1.53545	−	1.26011i	−0.0770622	−	0.0632433i	0.595074	−	0.803671i	$-0.297123\pi$
$397$	−1.53545	−	1.26011i	−0.0770622	−	0.0632433i	−0.672136	+	0.740428i	$0.734623\pi$
$398$	−23.8694	−	4.40710i	−1.19647	−	0.220908i
$399$	2.18456	+	0.904872i	0.109365	+	0.0453003i
$400$	−2.17303	+	15.2805i	−0.108651	+	0.764024i
$401$	10.0009	−	4.14250i	0.499421	−	0.206867i	−0.118730	−	0.992927i	$-0.537882\pi$
$401$	10.0009	−	4.14250i	0.499421	−	0.206867i	0.618150	+	0.786060i	$0.287882\pi$
$402$	−17.2494	+	3.67877i	−0.860321	+	0.183480i
$403$	0.161772	+	1.64250i	0.00805842	+	0.0818185i
$404$	−10.9611	−	0.775485i	−0.545335	−	0.0385818i
$405$	−0.503632	+	0.942230i	−0.0250257	+	0.0468198i
$406$	9.26222	+	4.78795i	0.459677	+	0.237622i
$407$	−16.4325	+	3.26862i	−0.814527	+	0.162020i
$408$	3.88898	−	0.546021i	0.192533	−	0.0270321i
$409$	−1.71397	+	8.61670i	−0.0847503	+	0.426068i	0.914994	+	0.403467i	$0.132195\pi$
$409$	−1.71397	+	8.61670i	−0.0847503	+	0.426068i	−0.999745	+	0.0226016i	$0.992805\pi$
$410$	−0.0354040	−	0.314935i	−0.00174848	−	0.0155536i
$411$	1.97195	−	20.0215i	0.0972690	−	0.987589i
$412$	0.253205	+	0.0431532i	0.0124745	+	0.00212601i
$413$	−1.22106	+	4.02531i	−0.0600846	+	0.198072i
$414$	−2.14713	−	4.98820i	−0.105526	−	0.245157i
$415$	5.33176	+	5.33176i	0.261726	+	0.261726i
$416$	−15.1556	+	2.55530i	−0.743063	+	0.125284i
$417$	−2.20343	+	2.20343i	−0.107903	+	0.107903i
$418$	−3.33468	−	1.32777i	−0.163104	−	0.0649432i
$419$	10.4599	+	3.17297i	0.510998	+	0.155010i	0.535246	−	0.844696i	$-0.320219\pi$
$419$	10.4599	+	3.17297i	0.510998	+	0.155010i	−0.0242475	+	0.999706i	$0.507719\pi$
$420$	0.804599	+	3.53342i	0.0392604	+	0.172413i
$421$	16.1254	+	1.58821i	0.785903	+	0.0774047i	0.483004	−	0.875618i	$-0.339545\pi$
$421$	16.1254	+	1.58821i	0.785903	+	0.0774047i	0.302899	+	0.953023i	$0.402045\pi$
$422$	−20.6915	+	25.9329i	−1.00725	+	1.26239i
$423$	−4.26469	−	0.848300i	−0.207356	−	0.0412458i
$424$	12.6740	−	26.2669i	0.615505	−	1.27563i
$425$	1.04518	+	5.25447i	0.0506986	+	0.254879i
$426$	−2.98184	+	0.949567i	−0.144471	+	0.0460067i
$427$	21.2418	+	11.3540i	1.02796	+	0.549459i
$428$	−1.28163	−	0.640307i	−0.0619500	−	0.0309504i
$429$	−4.92210	+	0.484784i	−0.237641	+	0.0234056i
$430$	−0.943196	−	0.611605i	−0.0454849	−	0.0294942i
$431$	−12.6513	−	30.5430i	−0.609394	−	1.47121i	−0.863661	−	0.504073i	$-0.831834\pi$
$431$	−12.6513	−	30.5430i	−0.609394	−	1.47121i	0.254267	−	0.967134i	$-0.418166\pi$
$432$	−0.172297	+	3.99629i	−0.00828962	+	0.192271i
$433$	−14.9074	+	35.9897i	−0.716406	+	1.72956i	−0.0330695	+	0.999453i	$0.510528\pi$
$433$	−14.9074	+	35.9897i	−0.716406	+	1.72956i	−0.683336	+	0.730104i	$0.739472\pi$
$434$	1.20016	−	0.826050i	0.0576093	−	0.0396517i
$435$	2.94643	−	3.59023i	0.141270	−	0.172138i
$436$	14.4693	−	1.82870i	0.692954	−	0.0875790i
$437$	1.55416	+	5.12337i	0.0743455	+	0.245084i
$438$	5.95411	−	5.02521i	0.284498	−	0.240114i
$439$	16.2217	+	10.8390i	0.774218	+	0.517316i	0.878794	−	0.477201i	$-0.158349\pi$
$439$	16.2217	+	10.8390i	0.774218	+	0.517316i	−0.104576	+	0.994517i	$0.533349\pi$
$440$	−1.29510	−	5.34628i	−0.0617415	−	0.254874i
$441$	2.29101	+	3.42874i	0.109096	+	0.163273i
$442$	−4.66991	+	2.57943i	−0.222125	+	0.122691i
$443$	−11.0033	+	9.03015i	−0.522781	+	0.429035i	−0.858414	−	0.512958i	$-0.828550\pi$
$443$	−11.0033	+	9.03015i	−0.522781	+	0.429035i	0.335633	+	0.941993i	$0.391050\pi$
$444$	−7.50996	−	16.8059i	−0.356407	−	0.797574i
$445$	7.46652	+	13.9689i	0.353947	+	0.662188i
$446$	−0.187373	−	13.6047i	−0.00887238	−	0.644200i
$447$			4.44954i			0.210456i
$448$	8.44320	+	10.6205i	0.398904	+	0.501771i
$449$		−	9.83505i		−	0.464145i	−0.972699	−	0.232072i	$-0.925449\pi$
$449$		−	9.83505i		−	0.464145i	0.972699	−	0.232072i	$-0.0745506\pi$
$450$	−5.45631	+	0.0751480i	−0.257213	+	0.00354251i
$451$	−0.179993	−	0.336743i	−0.00847553	−	0.0158566i
$452$	−3.42524	+	8.95955i	−0.161110	+	0.421422i
$453$	4.59067	−	3.76746i	0.215688	−	0.177011i
$454$	4.91841	+	8.90452i	0.230833	+	0.417910i
$455$	−2.73506	−	4.09330i	−0.128221	−	0.191897i
$456$	0.608923	−	3.89616i	0.0285154	−	0.182454i
$457$	−16.1096	−	10.7641i	−0.753574	−	0.503522i	0.118465	−	0.992958i	$-0.462203\pi$
$457$	−16.1096	−	10.7641i	−0.753574	−	0.503522i	−0.872039	+	0.489436i	$0.837203\pi$
$458$	−11.9775	−	14.1915i	−0.559670	−	0.663123i
$459$	0.403045	+	1.32866i	0.0188125	+	0.0620167i
$460$	−5.02876	+	6.48377i	−0.234467	+	0.302307i
$461$	17.1894	−	20.9453i	0.800590	−	0.975522i	−0.199400	−	0.979918i	$-0.563899\pi$
$461$	17.1894	−	20.9453i	0.800590	−	0.975522i	0.999990	+	0.00439649i	$0.00139945\pi$
$462$	2.47544	+	3.59653i	0.115168	+	0.167326i
$463$	−7.41847	+	17.9098i	−0.344766	+	0.832338i	0.652455	+	0.757828i	$0.273739\pi$
$463$	−7.41847	+	17.9098i	−0.344766	+	0.832338i	−0.997220	+	0.0745102i	$0.976261\pi$
$464$	4.12386	−	16.8927i	0.191445	−	0.784226i
$465$	−0.248361	−	0.599596i	−0.0115175	−	0.0278056i
$466$	−7.00426	+	10.8017i	−0.324466	+	0.500381i
$467$	36.3494	−	3.58010i	1.68205	−	0.165667i	0.788623	−	0.614877i	$-0.210794\pi$
$467$	36.3494	−	3.58010i	1.68205	−	0.165667i	0.893426	+	0.449210i	$0.148294\pi$
$468$	−1.72000	−	5.15453i	−0.0795068	−	0.238268i
$469$	−18.6536	−	9.97057i	−0.861345	−	0.460398i
$470$	1.99353	+	6.26010i	0.0919546	+	0.288757i
$471$	1.54810	+	7.78280i	0.0713325	+	0.358613i
$472$	7.00391	+	0.398667i	0.322381	+	0.0183502i
$473$	−1.32835	−	0.264225i	−0.0610776	−	0.0121491i
$474$	−6.57330	−	5.24475i	−0.301922	−	0.240900i
$475$	5.35378	+	0.527301i	0.245648	+	0.0241942i
$476$	3.98639	+	2.50763i	0.182716	+	0.114937i
$477$	9.86727	+	2.99320i	0.451791	+	0.137049i
$478$	−6.59800	+	16.5708i	−0.301786	+	0.757933i
$479$	18.1864	−	18.1864i	0.830959	−	0.830959i	−0.156689	−	0.987648i	$-0.550082\pi$
$479$	18.1864	−	18.1864i	0.830959	−	0.830959i	0.987648	+	0.156689i	$0.0500819\pi$
$480$	5.41128	−	2.69152i	0.246990	−	0.122850i
$481$	17.6822	+	17.6822i	0.806237	+	0.806237i
$482$	−18.3215	+	7.88635i	−0.834522	+	0.359213i
$483$	1.89051	−	6.23219i	0.0860214	−	0.283574i
$484$	8.88923	+	12.5416i	0.404056	+	0.570075i
$485$	1.07902	−	10.9554i	0.0489957	−	0.497461i
$486$	−1.40536	+	0.157986i	−0.0637485	+	0.00716639i
$487$	2.54727	−	12.8060i	0.115428	−	0.580295i	−0.879172	−	0.476505i	$-0.841903\pi$
$487$	2.54727	−	12.8060i	0.115428	−	0.580295i	0.994599	−	0.103789i	$-0.0330967\pi$
$488$	10.0628	−	38.8882i	0.455522	−	1.76038i
$489$	−22.2409	+	4.42398i	−1.00577	+	0.200059i
$490$	2.86114	−	5.53483i	0.129253	−	0.250038i
$491$	16.2082	−	30.3234i	0.731466	−	1.36848i	−0.190687	−	0.981651i	$-0.561072\pi$
$491$	16.2082	−	30.3234i	0.731466	−	1.36848i	0.922153	−	0.386825i	$-0.126428\pi$
$492$	0.316829	−	0.274960i	0.0142837	−	0.0123962i
$493$	−0.591619	−	6.00681i	−0.0266452	−	0.270533i
$494$	1.11738	+	5.23928i	0.0502732	+	0.235727i
$495$	1.79682	−	0.744268i	0.0807611	−	0.0334523i
$496$	−1.81015	−	1.62094i	−0.0812779	−	0.0727826i
$497$	−3.46717	−	1.43615i	−0.155524	−	0.0644201i
$498$	−1.81220	+	9.81510i	−0.0812066	+	0.439825i
$499$	−13.8786	−	11.3898i	−0.621290	−	0.509880i	0.270269	−	0.962785i	$-0.412888\pi$
$499$	−13.8786	−	11.3898i	−0.621290	−	0.509880i	−0.891559	+	0.452905i	$0.850388\pi$
$500$	9.37927	+	16.4415i	0.419454	+	0.735287i
$501$	0.370749	−	0.112466i	0.0165639	−	0.00502459i
$502$	36.6303	+	3.09907i	1.63489	+	0.138318i
$503$	−18.1245	+	27.1252i	−0.808129	+	1.20945i	0.166592	+	0.986026i	$0.446724\pi$
$503$	−18.1245	+	27.1252i	−0.808129	+	1.20945i	−0.974721	+	0.223425i	$0.928276\pi$
$504$	−3.24893	+	3.52913i	−0.144719	+	0.157200i
$505$	−4.88070	+	3.26118i	−0.217188	+	0.145121i
$506$	−2.73918	+	9.49886i	−0.121771	+	0.422276i
$507$	−3.56409	−	4.34285i	−0.158287	−	0.192873i
$508$	0.307523	+	11.1621i	0.0136441	+	0.495238i
$509$	−39.6905	+	21.2150i	−1.75925	+	0.940339i	−0.845633	+	0.533765i	$0.820777\pi$
$509$	−39.6905	+	21.2150i	−1.75925	+	0.940339i	−0.913618	+	0.406574i	$0.866723\pi$
$510$	1.46283	−	1.50368i	0.0647750	−	0.0665842i
$511$	9.34352			0.413333
$512$	13.8992	−	17.8553i	0.614263	−	0.789101i
$513$	1.39422			0.0615564
$514$	23.5802	−	24.2388i	1.04008	−	1.06913i
$515$	0.121009	−	0.0646806i	0.00533229	−	0.00285017i
$516$	−0.0409801	−	1.48745i	−0.00180405	−	0.0654812i
$517$	5.02152	+	6.11873i	0.220846	+	0.269102i
$518$	6.11647	−	21.2105i	0.268742	−	0.931938i
$519$	−10.9667	+	7.32770i	−0.481384	+	0.321650i
$520$	−5.56078	+	6.04036i	−0.243856	+	0.264887i
$521$	12.9095	−	19.3204i	0.565575	−	0.846443i	−0.432912	−	0.901436i	$-0.642514\pi$
$521$	12.9095	−	19.3204i	0.565575	−	0.846443i	0.998487	+	0.0549935i	$0.0175138\pi$
$522$	6.12599	+	0.518283i	0.268127	+	0.0226846i
$523$	−24.0145	+	7.28472i	−1.05008	+	0.318538i	−0.767730	−	0.640773i	$-0.778614\pi$
$523$	−24.0145	+	7.28472i	−1.05008	+	0.318538i	−0.282350	+	0.959311i	$0.591114\pi$
$524$	−3.27215	−	5.73597i	−0.142945	−	0.250577i
$525$	−5.05855	−	4.15145i	−0.220773	−	0.181184i
$526$	−2.21862	+	12.0163i	−0.0967364	+	0.523936i
$527$	−0.779223	−	0.322765i	−0.0339435	−	0.0140599i
$528$	4.85752	−	5.42450i	0.211396	−	0.236071i
$529$	−7.62554	+	3.15860i	−0.331545	+	0.137331i
$530$	−3.24956	−	15.2369i	−0.141152	−	0.661847i
$531$	0.243109	+	2.46832i	0.0105500	+	0.107116i
$532$	3.57163	−	3.09964i	0.154850	−	0.134387i
$533$	−0.268644	+	0.502597i	−0.0116363	+	0.0217699i
$534$	−9.62782	+	18.6249i	−0.416636	+	0.805978i
$535$	−0.750620	+	0.149308i	−0.0324521	+	0.00645513i
$536$	−8.83671	+	34.1498i	−0.381688	+	1.47505i
$537$	−2.41736	+	12.1529i	−0.104317	+	0.524436i
$538$	−22.4680	+	2.52578i	−0.968665	+	0.108894i
$539$	0.735788	−	7.47058i	0.0316926	−	0.321781i
$540$	1.23560	+	1.74329i	0.0531719	+	0.0750192i
$541$	8.61351	−	28.3949i	0.370324	−	1.22079i	−0.551825	−	0.833960i	$-0.686068\pi$
$541$	8.61351	−	28.3949i	0.370324	−	1.22079i	0.922149	−	0.386834i	$-0.126432\pi$
$542$	28.9551	−	12.4635i	1.24373	−	0.535353i
$543$	−3.87174	−	3.87174i	−0.166152	−	0.166152i
$544$	2.49930	−	7.44599i	0.107156	−	0.319244i
$545$	5.50898	−	5.50898i	0.235979	−	0.235979i
$546$	2.41061	−	6.05424i	0.103165	−	0.259098i
$547$	−28.8394	−	8.74834i	−1.23308	−	0.374052i	−0.394536	−	0.918880i	$-0.629095\pi$
$547$	−28.8394	−	8.74834i	−1.23308	−	0.374052i	−0.838547	+	0.544829i	$0.816595\pi$
$548$	−34.0586	−	21.4245i	−1.45491	−	0.915210i
$549$	14.1335	+	1.39203i	0.603203	+	0.0594103i
$550$	7.76476	+	6.19540i	0.331090	+	0.264173i
$551$	−5.94450	−	1.18244i	−0.253244	−	0.0503734i
$552$	−10.8438	−	0.617237i	−0.461544	−	0.0262714i
$553$	−1.96741	−	9.89084i	−0.0836628	−	0.420601i
$554$	−12.5028	−	39.2615i	−0.531193	−	1.66806i
$555$	−8.67208	−	4.63532i	−0.368109	−	0.196759i
$556$	1.97269	+	5.91181i	0.0836606	+	0.250717i
$557$	20.8581	−	2.05435i	0.883787	−	0.0870454i	0.354069	−	0.935219i	$-0.384798\pi$
$557$	20.8581	−	2.05435i	0.883787	−	0.0870454i	0.529718	+	0.848174i	$0.322298\pi$
$558$	0.467395	−	0.720800i	0.0197864	−	0.0305139i
$559$	0.773570	+	1.86756i	0.0327185	+	0.0789895i
$560$	7.04098	+	1.71885i	0.297536	+	0.0726345i
$561$	0.967235	−	2.33511i	0.0408367	−	0.0985885i
$562$	−7.23487	−	10.5114i	−0.305184	−	0.443398i
$563$	14.4000	−	17.5465i	0.606888	−	0.739496i	−0.375402	−	0.926862i	$-0.622495\pi$
$563$	14.4000	−	17.5465i	0.606888	−	0.739496i	0.982290	+	0.187367i	$0.0599952\pi$
$564$	−5.32976	+	6.87186i	−0.224423	+	0.289358i
$565$	1.48740	+	4.90331i	0.0625755	+	0.206284i
$566$	−13.8694	−	16.4331i	−0.582974	−	0.690735i
$567$	−1.41014	−	0.942226i	−0.0592204	−	0.0395698i
$568$	−0.966440	+	6.18370i	−0.0405509	+	0.259462i
$569$	−0.167503	−	0.250686i	−0.00702211	−	0.0105093i	0.827942	−	0.560814i	$-0.189512\pi$
$569$	−0.167503	−	0.250686i	−0.00702211	−	0.0105093i	−0.834964	+	0.550304i	$0.814512\pi$
$570$	−1.01852	−	1.84397i	−0.0426609	−	0.0772353i
$571$	31.8080	−	26.1042i	1.33112	−	1.09243i	0.342907	−	0.939369i	$-0.388588\pi$
$571$	31.8080	−	26.1042i	1.33112	−	1.09243i	0.988217	−	0.153056i	$-0.0489116\pi$
$572$	−3.53232	+	9.23964i	−0.147694	+	0.386329i
$573$	−11.7639	−	22.0087i	−0.491444	−	0.919428i
$574$	0.503033	−	0.00692812i	0.0209962	−	0.000289174i
$575$		−	14.8171i		−	0.617918i
$576$	6.99590	+	3.88038i	0.291496	+	0.161683i
$577$			21.8396i			0.909194i	0.890697	+	0.454597i	$0.150217\pi$
$577$			21.8396i			0.909194i	−0.890697	+	0.454597i	$0.849783\pi$
$578$	0.293542	+	21.3133i	0.0122097	+	0.886517i
$579$	−1.91880	−	3.58983i	−0.0797427	−	0.149188i
$580$	−3.78973	−	8.48073i	−0.157360	−	0.352143i
$581$	−9.25252	+	7.59335i	−0.383859	+	0.315025i
$582$	12.7554	−	7.04544i	0.528728	−	0.292043i
$583$	−10.4283	−	15.6071i	−0.431896	−	0.646378i
$584$	−3.66867	−	15.1446i	−0.151811	−	0.626686i
$585$	−2.41356	−	1.61269i	−0.0997883	−	0.0666764i
$586$	14.1412	−	11.9351i	0.584169	−	0.493034i
$587$	−5.66369	−	18.6707i	−0.233765	−	0.770622i	−0.992822	−	0.119597i	$-0.961840\pi$
$587$	−5.66369	−	18.6707i	−0.233765	−	0.770622i	0.759057	−	0.651024i	$-0.225660\pi$
$588$	8.18234	−	1.03412i	0.337434	−	0.0426466i
$589$	−0.537287	+	0.654687i	−0.0221385	+	0.0269759i
$590$	3.08696	−	2.12471i	0.127088	−	0.0874728i
$591$	−5.00213	+	12.0762i	−0.205760	+	0.496749i
$592$	−36.7810	−	1.58578i	−1.51169	−	0.0651752i
$593$	−3.92114	−	9.46647i	−0.161022	−	0.388741i	0.822691	−	0.568489i	$-0.192472\pi$
$593$	−3.92114	−	9.46647i	−0.161022	−	0.388741i	−0.983713	+	0.179748i	$0.942472\pi$
$594$	2.16004	+	1.40065i	0.0886273	+	0.0574694i
$595$	2.50367	−	0.246590i	0.102640	−	0.0101092i
$596$	7.96083	+	3.97726i	0.326088	+	0.162915i
$597$	−15.1369	−	8.09082i	−0.619510	−	0.331135i
$598$	14.0593	−	4.47719i	0.574928	−	0.183086i
$599$	−6.83727	−	34.3733i	−0.279363	−	1.40445i	−0.824384	−	0.566031i	$-0.808478\pi$
$599$	−6.83727	−	34.3733i	−0.279363	−	1.40445i	0.545021	−	0.838423i	$-0.316522\pi$
$600$	−4.74272	+	9.82926i	−0.193621	+	0.401278i
$601$	36.0926	+	7.17927i	1.47225	+	0.292849i	0.865044	−	0.501696i	$-0.167290\pi$
$601$	36.0926	+	7.17927i	1.47225	+	0.292849i	0.607206	+	0.794545i	$0.292290\pi$
$602$	1.11295	−	1.39487i	0.0453603	−	0.0568505i
$603$	−12.4114	−	1.22242i	−0.505432	−	0.0497807i
$604$	−2.63710	−	11.5809i	−0.107302	−	0.471221i
$605$	7.85822	+	2.38377i	0.319482	+	0.0969138i
$606$	−7.21885	−	2.87433i	−0.293246	−	0.116762i
$607$	−20.5070	+	20.5070i	−0.832355	+	0.832355i	−0.987838	−	0.155484i	$-0.950306\pi$
$607$	−20.5070	+	20.5070i	−0.832355	+	0.832355i	0.155484	+	0.987838i	$0.450306\pi$
$608$	−6.42647	−	4.57206i	−0.260628	−	0.185422i
$609$	5.21328	+	5.21328i	0.211253	+	0.211253i
$610$	−8.48384	−	19.7096i	−0.343501	−	0.798018i
$611$	3.42943	−	11.3053i	0.138740	−	0.457364i
$612$	2.73743	+	0.466534i	0.110654	+	0.0188585i
$613$	1.69953	−	17.2556i	0.0686433	−	0.696947i	−0.897858	−	0.440285i	$-0.854877\pi$
$613$	1.69953	−	17.2556i	0.0686433	−	0.696947i	0.966501	−	0.256662i	$-0.0826227\pi$
$614$	4.59735	+	40.8957i	0.185534	+	1.65041i
$615$	0.0437189	−	0.219790i	0.00176292	−	0.00886278i
$616$	8.64738	−	1.21411i	0.348413	−	0.0489179i
$617$	3.76363	−	0.748632i	0.151518	−	0.0301388i	−0.118748	−	0.992924i	$-0.537888\pi$
$617$	3.76363	−	0.748632i	0.151518	−	0.0301388i	0.270266	+	0.962786i	$0.412888\pi$
$618$	0.161343	+	0.0834033i	0.00649015	+	0.00335497i
$619$	14.0463	−	26.2788i	0.564569	−	1.05623i	−0.424028	−	0.905649i	$-0.639384\pi$
$619$	14.0463	−	26.2788i	0.564569	−	1.05623i	0.988597	−	0.150586i	$-0.0481159\pi$
$620$	−1.29476	−	0.0916028i	−0.0519988	−	0.00367886i
$621$	−0.376393	−	3.82158i	−0.0151041	−	0.153355i
$622$	34.5597	−	7.37052i	1.38572	−	0.295531i
$623$	−23.2293	+	9.62189i	−0.930662	+	0.385493i
$624$	−10.7596	−	1.53012i	−0.430729	−	0.0612537i
$625$	−8.48237	−	3.51351i	−0.339295	−	0.140540i
$626$	−9.80427	−	1.81020i	−0.391858	−	0.0723502i
$627$	−1.96191	−	1.61010i	−0.0783512	−	0.0643012i
$628$	15.3083	+	4.18697i	0.610867	+	0.167078i
$629$	−12.2287	+	3.70954i	−0.487591	+	0.147909i
$630$	−0.216023	+	2.55334i	−0.00860656	+	0.101728i
$631$	−1.85509	+	2.77634i	−0.0738500	+	0.110524i	−0.866556	−	0.499080i	$-0.833672\pi$
$631$	−1.85509	+	2.77634i	−0.0738500	+	0.110524i	0.792706	+	0.609604i	$0.208672\pi$
$632$	−15.2592	+	7.07247i	−0.606978	+	0.281328i
$633$	−19.5055	+	13.0331i	−0.775273	+	0.518021i
$634$	31.9317	+	9.20813i	1.26817	+	0.365702i
$635$	3.78413	+	4.61098i	0.150169	+	0.182981i
$636$	14.1752	−	14.9784i	0.562084	−	0.593933i
$637$	−9.88103	+	5.28152i	−0.391501	+	0.209261i
$638$	−8.02180	−	7.80384i	−0.317586	−	0.308957i
$639$	−2.21281			−0.0875374
$640$	0.0214188	−	12.0874i	0.000846653	−	0.477795i
$641$	30.8070			1.21680			0.608401	−	0.793630i	$-0.291811\pi$
$641$	30.8070			1.21680			0.608401	+	0.793630i	$0.291811\pi$
$642$	−0.726137	−	0.706407i	−0.0286583	−	0.0278797i
$643$	27.2808	−	14.5819i	1.07585	−	0.575053i	0.164370	−	0.986399i	$-0.447441\pi$
$643$	27.2808	−	14.5819i	1.07585	−	0.575053i	0.911480	+	0.411345i	$0.134941\pi$
$644$	−9.46040	−	8.95309i	−0.372792	−	0.352801i
$645$	−0.504268	−	0.614453i	−0.0198556	−	0.0241941i
$646$	−2.63045	−	0.758542i	−0.103494	−	0.0298444i
$647$	−21.3630	+	14.2743i	−0.839865	+	0.561180i	−0.899440	−	0.437044i	$-0.856025\pi$
$647$	−21.3630	+	14.2743i	−0.839865	+	0.561180i	0.0595753	+	0.998224i	$0.481025\pi$
$648$	−0.973537	+	2.65560i	−0.0382441	+	0.104322i
$649$	2.50842	−	3.75411i	0.0984639	−	0.147362i
$650$	1.24987	−	14.7732i	0.0490240	−	0.579453i
$651$	0.985865	−	0.299059i	0.0386391	−	0.0117210i
$652$	−11.9651	+	43.7464i	−0.468589	+	1.71324i
$653$	−31.4707	−	25.8273i	−1.23154	−	1.01070i	−0.999276	−	0.0380489i	$-0.987886\pi$
$653$	−31.4707	−	25.8273i	−1.23154	−	1.01070i	−0.232267	−	0.972652i	$-0.574614\pi$
$654$	10.1413	+	1.87243i	0.396557	+	0.0732179i
$655$	−3.25909	−	1.34996i	−0.127343	−	0.0527473i
$656$	−0.208742	−	0.812627i	−0.00815000	−	0.0317277i
$657$	5.08991	−	2.10831i	0.198576	−	0.0822529i
$658$	−10.1997	+	2.17528i	−0.397625	+	0.0848011i
$659$	4.27579	+	43.4128i	0.166561	+	1.69112i	0.608084	+	0.793873i	$0.291939\pi$
$659$	4.27579	+	43.4128i	0.166561	+	1.69112i	−0.441523	+	0.897250i	$0.645561\pi$
$660$	0.274508	−	3.88003i	0.0106852	−	0.151030i
$661$	11.5912	−	21.6855i	0.450844	−	0.843470i	−0.549126	−	0.835740i	$-0.685039\pi$
$661$	11.5912	−	21.6855i	0.450844	−	0.843470i	0.999970	−	0.00773042i	$-0.00246069\pi$
$662$	−6.70504	−	3.46606i	−0.260599	−	0.134712i
$663$	−3.69988	+	0.735952i	−0.143691	+	0.0285820i
$664$	15.9407	+	12.0156i	0.618620	+	0.466295i
$665$	0.492845	−	2.47770i	0.0191117	−	0.0960811i
$666$	−1.45407	−	12.9346i	−0.0563440	−	0.501207i
$667$	−1.63626	+	16.6132i	−0.0633562	+	0.643266i
$668$	0.130181	−	0.763850i	0.00503686	−	0.0295542i
$669$	2.79279	−	9.20660i	0.107976	−	0.355948i
$670$	7.45012	+	17.3081i	0.287823	+	0.668670i
$671$	−18.2807	−	18.2807i	−0.705720	−	0.705720i
$672$	3.41001	+	8.96733i	0.131544	+	0.345922i
$673$	−9.90839	+	9.90839i	−0.381940	+	0.381940i	−0.871801	−	0.489861i	$-0.837048\pi$
$673$	−9.90839	+	9.90839i	−0.381940	+	0.381940i	0.489861	+	0.871801i	$0.337048\pi$
$674$	−0.552154	−	0.219851i	−0.0212682	−	0.00846834i
$675$	−3.69241	−	1.12008i	−0.142121	−	0.0431119i
$676$	−10.9558	+	2.49474i	−0.421375	+	0.0959517i
$677$	11.8509	+	1.16721i	0.455467	+	0.0448596i	0.323150	−	0.946348i	$-0.395258\pi$
$677$	11.8509	+	1.16721i	0.455467	+	0.0448596i	0.132317	+	0.991207i	$0.457758\pi$
$678$	−4.23019	+	5.30173i	−0.162459	+	0.203612i
$679$	17.1392	+	3.40919i	0.657740	+	0.130833i
$680$	−1.38274	−	3.96128i	−0.0530255	−	0.151908i
$681$	1.40330	+	7.05489i	0.0537747	+	0.270344i
$682$	−1.49011	+	0.474526i	−0.0570594	+	0.0181706i
$683$	−28.4993	−	15.2332i	−1.09049	−	0.582881i	−0.174738	−	0.984615i	$-0.555908\pi$
$683$	−28.4993	−	15.2332i	−1.09049	−	0.582881i	−0.915757	+	0.401734i	$0.868408\pi$
$684$	1.24624	−	2.49445i	0.0476511	−	0.0953778i
$685$	−21.3907	+	2.10680i	−0.817295	+	0.0804965i
$686$	22.3854	+	14.5155i	0.854678	+	0.554206i
$687$	−5.02509	−	12.1316i	−0.191719	−	0.462851i
$688$	−2.69788	−	1.25625i	−0.102856	−	0.0478940i
$689$	−10.7210	+	25.8828i	−0.408438	+	0.986057i
$690$	−4.77938	+	3.28958i	−0.181948	+	0.125232i
$691$	1.39108	−	1.69504i	0.0529193	−	0.0644823i	−0.745878	−	0.666082i	$-0.767970\pi$
$691$	1.39108	−	1.69504i	0.0529193	−	0.0644823i	0.798797	+	0.601600i	$0.205470\pi$
$692$	3.30760	+	26.1708i	0.125736	+	0.994866i
$693$	0.896195	+	2.95436i	0.0340436	+	0.112227i
$694$	38.3360	−	32.3552i	1.45521	−	1.22819i
$695$	2.76814	+	1.84961i	0.105002	+	0.0701599i
$696$	6.40305	−	10.4970i	0.242707	−	0.397887i
$697$	−0.161799	−	0.242149i	−0.00612857	−	0.00917205i
$698$	20.4256	−	11.2821i	0.773121	−	0.427033i
$699$	−7.03688	+	5.77502i	−0.266159	+	0.218431i
$700$	−11.9492	+	5.33964i	−0.451635	+	0.201819i
$701$	2.52679	+	4.72729i	0.0954355	+	0.178547i	0.925109	−	0.379702i	$-0.123973\pi$
$701$	2.52679	+	4.72729i	0.0954355	+	0.178547i	−0.829673	+	0.558249i	$0.811473\pi$
$702$	−0.0529148	−	3.84200i	−0.00199714	−	0.145007i
$703$			12.8321i			0.483972i
$704$	−5.36324	−	13.5395i	−0.202135	−	0.510289i
$705$			4.64559i			0.174963i
$706$	40.0693	−	0.551862i	1.50803	−	0.0207696i
$707$	−4.39249	−	8.21778i	−0.165197	−	0.309061i
$708$	4.63347	+	1.77138i	0.174137	+	0.0665725i
$709$	19.5173	−	16.0175i	0.732988	−	0.601548i	−0.192066	−	0.981382i	$-0.561519\pi$
$709$	19.5173	−	16.0175i	0.732988	−	0.601548i	0.925055	+	0.379834i	$0.124019\pi$
$710$	1.61652	+	2.92662i	0.0606668	+	0.109834i
$711$	−3.30356	−	4.94412i	−0.123893	−	0.185419i
$712$	24.7166	+	33.8735i	0.926293	+	1.26946i
$713$	1.93956	+	1.29597i	0.0726370	+	0.0485345i
$714$	2.14786	+	2.54489i	0.0803817	+	0.0952400i
$715$	1.53390	+	5.05660i	0.0573647	+	0.189106i
$716$	19.5824	+	15.1880i	0.731829	+	0.567601i
$717$	−8.00099	+	9.74923i	−0.298802	+	0.364092i
$718$	11.5580	+	16.7924i	0.431340	+	0.626687i
$719$	−2.69537	+	6.50720i	−0.100520	+	0.242677i	−0.966137	−	0.258030i	$-0.916927\pi$
$719$	−2.69537	+	6.50720i	−0.100520	+	0.242677i	0.865617	+	0.500707i	$0.166927\pi$
$720$	4.22344	−	0.652409i	0.157398	−	0.0243139i
$721$	0.0833520	+	0.201229i	0.00310419	+	0.00749418i
$722$	13.1235	−	20.2386i	0.488405	−	0.753201i
$723$	−14.0366	+	1.38248i	−0.522025	+	0.0514150i
$724$	−10.3879	+	3.46628i	−0.386062	+	0.128823i
$725$	14.7933	+	7.90718i	0.549409	+	0.293665i
$726$	3.29833	+	10.3574i	0.122412	+	0.384401i
$727$	−3.89879	−	19.6006i	−0.144598	−	0.726945i	−0.983248	−	0.182273i	$-0.941654\pi$
$727$	−3.89879	−	19.6006i	−0.144598	−	0.726945i	0.838650	−	0.544671i	$-0.183346\pi$
$728$	−8.67713	−	9.72456i	−0.321596	−	0.360416i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−6.50672	−	5.19163i	−0.240824	−	0.192151i
$731$	−1.02804	−	0.101253i	−0.0380234	−	0.00374498i
$732$	15.1239	−	24.0425i	0.558995	−	0.888637i
$733$	−9.07751	−	2.75363i	−0.335285	−	0.101708i	0.118153	−	0.992995i	$-0.462303\pi$
$733$	−9.07751	−	2.75363i	−0.335285	−	0.101708i	−0.453438	+	0.891288i	$0.649803\pi$
$734$	−11.6182	+	29.1789i	−0.428834	+	1.07701i
$735$	3.11530	−	3.11530i	0.114910	−	0.114910i
$736$	−10.7972	+	18.8494i	−0.397989	+	0.694797i
$737$	16.0533	+	16.0533i	0.591332	+	0.591332i
$738$	0.272465	−	0.117280i	0.0100296	−	0.00431715i
$739$	0.751026	−	2.47580i	0.0276269	−	0.0910738i	−0.942043	−	0.335493i	$-0.891097\pi$
$739$	0.751026	−	2.47580i	0.0276269	−	0.0910738i	0.969670	+	0.244419i	$0.0785972\pi$
$740$	−16.0449	+	11.3722i	−0.589821	+	0.418051i
$741$	−0.371294	+	3.76981i	−0.0136398	+	0.138487i
$742$	24.5763	−	2.76278i	0.902224	−	0.101425i
$743$	4.11877	−	20.7065i	0.151103	−	0.759646i	−0.828702	−	0.559690i	$-0.810920\pi$
$743$	4.11877	−	20.7065i	0.151103	−	0.759646i	0.979805	−	0.199956i	$-0.0640799\pi$
$744$	−0.871826	−	1.48053i	−0.0319627	−	0.0542788i
$745$	4.66247	−	0.927422i	0.170820	−	0.0339781i
$746$	−19.8763	+	38.4505i	−0.727725	+	1.40777i
$747$	−3.32694	+	6.22427i	−0.121726	+	0.227734i
$748$	−3.31327	−	3.81778i	−0.121145	−	0.139592i
$749$	−0.119080	−	1.20904i	−0.00435107	−	0.0441772i
$750$	2.79174	+	13.0902i	0.101940	+	0.477987i
$751$	−47.5456	+	19.6940i	−1.73496	+	0.718646i	−0.735825	+	0.677172i	$0.763205\pi$
$751$	−47.5456	+	19.6940i	−1.73496	+	0.718646i	−0.999140	+	0.0414740i	$0.986795\pi$
$752$	7.53066	+	15.6782i	0.274615	+	0.571724i
$753$	24.0154	+	9.94750i	0.875169	+	0.362507i
$754$	−3.03278	+	16.4259i	−0.110447	+	0.598197i
$755$	−4.90459	−	4.02509i	−0.178496	−	0.146488i
$756$	−2.94624	+	1.68072i	−0.107154	+	0.0611272i
$757$	−33.2599	+	10.0893i	−1.20885	+	0.366701i	−0.829477	−	0.558541i	$-0.811361\pi$
$757$	−33.2599	+	10.0893i	−1.20885	+	0.366701i	−0.379376	+	0.925243i	$0.623861\pi$
$758$	9.05920	+	0.766444i	0.329045	+	0.0278385i
$759$	−3.88366	+	5.81231i	−0.140968	+	0.210973i
$760$	−4.20952	+	0.174017i	−0.152695	+	0.00631228i
$761$	−1.17737	+	0.786691i	−0.0426795	+	0.0285175i	−0.576727	−	0.816937i	$-0.695670\pi$
$761$	−1.17737	+	0.786691i	−0.0426795	+	0.0285175i	0.534047	+	0.845454i	$0.320670\pi$
$762$	−2.18775	+	7.58664i	−0.0792540	+	0.274835i
$763$	7.84574	+	9.56006i	0.284035	+	0.346097i
$764$	−49.8919	+	1.37455i	−1.80503	+	0.0497296i
$765$	1.30824	−	0.699268i	0.0472994	−	0.0252821i
$766$	30.9279	−	31.7917i	1.11747	−	1.14868i
$767$	−6.73879			−0.243324
$768$	13.1959	−	9.04812i	0.476166	−

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.986134 - 1.01368i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-0.0550803 - 1.99924i) q^{4} +(-0.677775 - 0.825871i) q^{5} +(0.391849 - 1.35884i) q^{6} +(1.41014 - 0.942226i) q^{7} +(-2.08090 - 1.91569i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.986134 - 1.01368i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-0.0550803 - 1.99924i) q^{4} +(-0.677775 - 0.825871i) q^{5} +(0.391849 - 1.35884i) q^{6} +(1.41014 - 0.942226i) q^{7} +(-2.08090 - 1.91569i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-1.50554 - 0.127375i) q^{10} +(-1.74200 + 0.528429i) q^{11} +(-0.991012 - 1.73721i) q^{12} +(2.10024 + 1.72362i) q^{13} +(0.435475 - 2.35859i) q^{14} +(-0.987057 - 0.408853i) q^{15} +(-3.99393 + 0.220238i) q^{16} +(-1.28276 + 0.531336i) q^{17} +(-0.294975 - 1.38311i) q^{18} +(0.136658 + 1.38751i) q^{19} +(-1.61378 + 1.40053i) q^{20} +(0.799471 - 1.49571i) q^{21} +(-1.18219 + 2.28692i) q^{22} +(3.76629 - 0.749161i) q^{23} +(-2.73824 - 0.708554i) q^{24} +(0.752767 - 3.78442i) q^{25} +(3.81832 - 0.429242i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-1.96141 - 2.76731i) q^{28} +(-1.26193 + 4.16002i) q^{29} +(-1.38782 + 0.597374i) q^{30} +(0.429538 + 0.429538i) q^{31} +(-3.71530 + 4.26574i) q^{32} +(-1.28720 + 1.28720i) q^{33} +(-0.726369 + 1.82427i) q^{34} +(-1.73392 - 0.525978i) q^{35} +(-1.69291 - 1.06492i) q^{36} +(9.15947 + 0.902129i) q^{37} +(1.54125 + 1.22974i) q^{38} +(2.66476 + 0.530054i) q^{39} +(-0.171727 + 3.01696i) q^{40} +(0.0409206 + 0.205722i) q^{41} +(-0.727776 - 2.28537i) q^{42} +(0.656154 + 0.350722i) q^{43} +(1.15241 + 3.45357i) q^{44} +(-1.06324 + 0.104720i) q^{45} +(2.95466 - 4.55657i) q^{46} +(-1.66400 - 4.01725i) q^{47} +(-3.41851 + 2.07696i) q^{48} +(-1.57808 + 3.80981i) q^{49} +(-3.09384 - 4.49500i) q^{50} +(-0.880823 + 1.07329i) q^{51} +(3.33026 - 4.29383i) q^{52} +(2.99320 + 9.86727i) q^{53} +(-0.912137 - 1.08074i) q^{54} +(1.61710 + 1.08051i) q^{55} +(-4.73937 - 0.740708i) q^{56} +(0.774588 + 1.15925i) q^{57} +(2.97248 + 5.38152i) q^{58} +(-1.91727 + 1.57346i) q^{59} +(-0.763028 + 1.99589i) q^{60} +(6.69473 + 12.5250i) q^{61} +(0.858994 - 0.0118307i) q^{62} -1.69596i q^{63} +(0.660296 + 7.97270i) q^{64} -2.90276i q^{65} +(0.0354532 + 2.57416i) q^{66} +(-5.87901 - 10.9988i) q^{67} +(1.13292 + 2.53528i) q^{68} +(2.96842 - 2.43612i) q^{69} +(-2.24304 + 1.23895i) q^{70} +(-1.22937 - 1.83988i) q^{71} +(-2.74892 + 0.665908i) q^{72} +(4.58079 + 3.06079i) q^{73} +(9.94692 - 8.39512i) q^{74} +(-1.12008 - 3.69241i) q^{75} +(2.76643 - 0.349636i) q^{76} +(-1.95856 + 2.38651i) q^{77} +(3.16511 - 2.17850i) q^{78} +(2.27553 - 5.49362i) q^{79} +(2.88888 + 3.14920i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(0.248889 + 0.161389i) q^{82} +(-7.02364 + 0.691768i) q^{83} +(-3.03431 - 1.51595i) q^{84} +(1.30824 + 0.699268i) q^{85} +(1.00257 - 0.319270i) q^{86} +(0.848098 + 4.26367i) q^{87} +(4.63723 + 2.23751i) q^{88} +(-14.5405 - 2.89228i) q^{89} +(-0.942344 + 1.18105i) q^{90} +(4.58568 + 0.451650i) q^{91} +(-1.70520 - 7.48846i) q^{92} +(0.581301 + 0.176336i) q^{93} +(-5.71312 - 2.27479i) q^{94} +(1.05328 - 1.05328i) q^{95} +(-1.26575 + 5.51343i) q^{96} +(7.28592 + 7.28592i) q^{97} +(2.30572 + 5.35665i) q^{98} +(-0.528429 + 1.74200i) 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

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