LMFDB - Embedded newform 384.2.v.a.157.29

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			157.29
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.29

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34659 - 0.432078i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.62662 - 1.16367i) q^{4} +(-1.08115 + 0.577887i) q^{5} +(-0.298008 - 1.38246i) q^{6} +(-0.0529010 - 0.265951i) q^{7} +(1.68759 - 2.26981i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(1.34659 - 0.432078i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.62662 - 1.16367i) q^{4} +(-1.08115 + 0.577887i) q^{5} +(-0.298008 - 1.38246i) q^{6} +(-0.0529010 - 0.265951i) q^{7} +(1.68759 - 2.26981i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.20617 + 1.24532i) q^{10} +(1.36025 - 1.65747i) q^{11} +(-0.998625 - 1.73284i) q^{12} +(2.20431 - 4.12397i) q^{13} +(-0.186148 - 0.335270i) q^{14} +(0.469133 + 1.13259i) q^{15} +(1.29177 - 3.78568i) q^{16} +(1.67410 - 4.04163i) q^{17} +(-1.40501 + 0.161069i) q^{18} +(2.18807 + 7.21310i) q^{19} +(-1.08615 + 2.19810i) q^{20} +(-0.269856 + 0.0265785i) q^{21} +(1.11555 - 2.81967i) q^{22} +(-5.10966 + 3.41417i) q^{23} +(-2.09346 - 1.90195i) q^{24} +(-1.94292 + 2.90778i) q^{25} +(1.18643 - 6.50574i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-0.395528 - 0.371042i) q^{28} +(-5.38032 + 4.41551i) q^{29} +(1.12110 + 1.32243i) q^{30} +(-1.89571 + 1.89571i) q^{31} +(0.103775 - 5.65590i) q^{32} +(-1.51616 - 1.51616i) q^{33} +(0.508027 - 6.16577i) q^{34} +(0.210884 + 0.256962i) q^{35} +(-1.82238 + 0.823968i) q^{36} +(8.18737 + 2.48361i) q^{37} +(6.06306 + 8.76769i) q^{38} +(-3.88805 - 2.59791i) q^{39} +(-0.512852 + 3.42924i) q^{40} +(3.17234 + 4.74774i) q^{41} +(-0.351902 + 0.152389i) q^{42} +(0.379630 + 3.85445i) q^{43} +(0.283867 - 4.27895i) q^{44} +(1.17312 - 0.355861i) q^{45} +(-5.40544 + 6.80526i) q^{46} +(-6.08199 - 2.51924i) q^{47} +(-3.64083 - 1.65661i) q^{48} +(6.39923 - 2.65065i) q^{49} +(-1.35993 + 4.75509i) q^{50} +(-3.85808 - 2.06219i) q^{51} +(-1.21336 - 9.27320i) q^{52} +(5.46110 + 4.48181i) q^{53} +(0.0225780 + 1.41403i) q^{54} +(-0.512805 + 2.57805i) q^{55} +(-0.692933 - 0.328743i) q^{56} +(7.39284 - 1.47053i) q^{57} +(-5.33725 + 8.27061i) q^{58} +(1.97093 + 3.68735i) q^{59} +(2.08105 + 1.29637i) q^{60} +(-6.59197 - 0.649252i) q^{61} +(-1.73365 + 3.37183i) q^{62} +0.271162i q^{63} +(-2.30405 - 7.66103i) q^{64} +5.73247i q^{65} +(-2.69675 - 1.38655i) q^{66} +(7.25731 + 0.714782i) q^{67} +(-1.97999 - 8.52228i) q^{68} +(2.89689 + 5.41970i) q^{69} +(0.395002 + 0.254905i) q^{70} +(-11.3847 + 2.26456i) q^{71} +(-2.09799 + 1.89696i) q^{72} +(2.93329 - 14.7466i) q^{73} +(12.0982 - 0.193172i) q^{74} +(2.70334 + 2.21858i) q^{75} +(11.9528 + 9.18678i) q^{76} +(-0.512765 - 0.274079i) q^{77} +(-6.35812 - 1.81839i) q^{78} +(2.22197 - 0.920371i) q^{79} +(0.791097 + 4.83938i) q^{80} +(0.923880 + 0.382683i) q^{81} +(6.32324 + 5.02257i) q^{82} +(1.38287 - 0.419490i) q^{83} +(-0.408024 + 0.357255i) q^{84} +(0.525653 + 5.33705i) q^{85} +(2.17663 + 5.02634i) q^{86} +(3.86689 + 5.78721i) q^{87} +(-1.46659 - 5.88465i) q^{88} +(-6.65710 - 4.44813i) q^{89} +(1.42595 - 0.986077i) q^{90} +(-1.21339 - 0.368077i) q^{91} +(-4.33852 + 11.4995i) q^{92} +(1.70077 + 2.07239i) q^{93} +(-9.27847 - 0.764497i) q^{94} +(-6.53399 - 6.53399i) q^{95} +(-5.61850 - 0.657651i) q^{96} +(1.00262 - 1.00262i) q^{97} +(7.47186 - 6.33430i) q^{98} +(-1.65747 + 1.36025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.34659	−	0.432078i	0.952184	−	0.305525i
$2$	1.34659	−	0.432078i	0.952184	−	0.305525i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$3$	0.0980171	−	0.995185i	0.0565902	−	0.574570i
$4$	1.62662	−	1.16367i	0.813309	−	0.581833i
$5$	−1.08115	+	0.577887i	−0.483505	+	0.258439i	−0.695093	−	0.718920i	$-0.744637\pi$
$5$	−1.08115	+	0.577887i	−0.483505	+	0.258439i	0.211588	+	0.977359i	$0.432137\pi$
$6$	−0.298008	−	1.38246i	−0.121661	−	0.564386i
$7$	−0.0529010	−	0.265951i	−0.0199947	−	0.100520i	0.969499	−	0.245094i	$-0.0788188\pi$
$7$	−0.0529010	−	0.265951i	−0.0199947	−	0.100520i	−0.989494	+	0.144574i	$0.953819\pi$
$8$	1.68759	−	2.26981i	0.596655	−	0.802498i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−1.20617	+	1.24532i	−0.381426	+	0.393804i
$11$	1.36025	−	1.65747i	0.410131	−	0.499746i	−0.526446	−	0.850209i	$-0.676476\pi$
$11$	1.36025	−	1.65747i	0.410131	−	0.499746i	0.936577	+	0.350463i	$0.113976\pi$
$12$	−0.998625	−	1.73284i	−0.288278	−	0.500229i
$13$	2.20431	−	4.12397i	0.611365	−	1.14378i	−0.365678	−	0.930742i	$-0.619163\pi$
$13$	2.20431	−	4.12397i	0.611365	−	1.14378i	0.977043	−	0.213043i	$-0.0683373\pi$
$14$	−0.186148	−	0.335270i	−0.0497501	−	0.0896048i
$15$	0.469133	+	1.13259i	0.121130	+	0.292433i
$16$	1.29177	−	3.78568i	0.322942	−	0.946419i
$17$	1.67410	−	4.04163i	0.406028	−	0.980239i	−0.580143	−	0.814514i	$-0.697004\pi$
$17$	1.67410	−	4.04163i	0.406028	−	0.980239i	0.986172	−	0.165725i	$-0.0529965\pi$
$18$	−1.40501	+	0.161069i	−0.331164	+	0.0379643i
$19$	2.18807	+	7.21310i	0.501978	+	1.65480i	0.731764	+	0.681558i	$0.238697\pi$
$19$	2.18807	+	7.21310i	0.501978	+	1.65480i	−0.229786	+	0.973241i	$0.573803\pi$
$20$	−1.08615	+	2.19810i	−0.242871	+	0.491509i
$21$	−0.269856	+	0.0265785i	−0.0588874	+	0.00579990i
$22$	1.11555	−	2.81967i	0.237835	−	0.601156i
$23$	−5.10966	+	3.41417i	−1.06544	+	0.711903i	−0.959283	−	0.282447i	$-0.908854\pi$
$23$	−5.10966	+	3.41417i	−1.06544	+	0.711903i	−0.106155	+	0.994350i	$0.533854\pi$
$24$	−2.09346	−	1.90195i	−0.427327	−	0.388234i
$25$	−1.94292	+	2.90778i	−0.388584	+	0.581557i
$26$	1.18643	−	6.50574i	0.232677	−	1.27588i
$27$	−0.290285	+	0.956940i	−0.0558653	+	0.184163i
$28$	−0.395528	−	0.371042i	−0.0747477	−	0.0701203i
$29$	−5.38032	+	4.41551i	−0.999100	+	0.819941i	−0.983677	−	0.179941i	$-0.942409\pi$
$29$	−5.38032	+	4.41551i	−0.999100	+	0.819941i	−0.0154229	+	0.999881i	$0.504909\pi$
$30$	1.12110	+	1.32243i	0.204683	+	0.241441i
$31$	−1.89571	+	1.89571i	−0.340479	+	0.340479i	−0.856547	−	0.516068i	$-0.827395\pi$
$31$	−1.89571	+	1.89571i	−0.340479	+	0.340479i	0.516068	+	0.856547i	$0.327395\pi$
$32$	0.103775	−	5.65590i	0.0183451	−	0.999832i
$33$	−1.51616	−	1.51616i	−0.263930	−	0.263930i
$34$	0.508027	−	6.16577i	0.0871259	−	1.05742i
$35$	0.210884	+	0.256962i	0.0356458	+	0.0434346i
$36$	−1.82238	+	0.823968i	−0.303730	+	0.137328i
$37$	8.18737	+	2.48361i	1.34599	+	0.408303i	0.879364	−	0.476149i	$-0.157968\pi$
$37$	8.18737	+	2.48361i	1.34599	+	0.408303i	0.466630	+	0.884452i	$0.345468\pi$
$38$	6.06306	+	8.76769i	0.983558	+	1.42231i
$39$	−3.88805	−	2.59791i	−0.622587	−	0.415999i
$40$	−0.512852	+	3.42924i	−0.0810890	+	0.542210i
$41$	3.17234	+	4.74774i	0.495436	+	0.741473i	0.991960	−	0.126550i	$-0.0403904\pi$
$41$	3.17234	+	4.74774i	0.495436	+	0.741473i	−0.496524	+	0.868023i	$0.665390\pi$
$42$	−0.351902	+	0.152389i	−0.0542996	+	0.0235142i
$43$	0.379630	+	3.85445i	0.0578930	+	0.587798i	0.979744	+	0.200254i	$0.0641766\pi$
$43$	0.379630	+	3.85445i	0.0578930	+	0.587798i	−0.921851	+	0.387544i	$0.873323\pi$
$44$	0.283867	−	4.27895i	0.0427946	−	0.645076i
$45$	1.17312	−	0.355861i	0.174878	−	0.0530486i
$46$	−5.40544	+	6.80526i	−0.796988	+	1.00338i
$47$	−6.08199	−	2.51924i	−0.887150	−	0.367470i	−0.107884	−	0.994163i	$-0.534408\pi$
$47$	−6.08199	−	2.51924i	−0.887150	−	0.367470i	−0.779266	+	0.626694i	$0.784408\pi$
$48$	−3.64083	−	1.65661i	−0.525509	−	0.239111i
$49$	6.39923	−	2.65065i	0.914175	−	0.378664i
$50$	−1.35993	+	4.75509i	−0.192323	+	0.672471i
$51$	−3.85808	−	2.06219i	−0.540239	−	0.288764i
$52$	−1.21336	−	9.27320i	−0.168262	−	1.28596i
$53$	5.46110	+	4.48181i	0.750140	+	0.615624i	0.929783	−	0.368108i	$-0.119994\pi$
$53$	5.46110	+	4.48181i	0.750140	+	0.615624i	−0.179643	+	0.983732i	$0.557494\pi$
$54$	0.0225780	+	1.41403i	0.00307248	+	0.192426i
$55$	−0.512805	+	2.57805i	−0.0691466	+	0.347624i
$56$	−0.692933	−	0.328743i	−0.0925971	−	0.0439301i
$57$	7.39284	−	1.47053i	0.979205	−	0.194776i
$58$	−5.33725	+	8.27061i	−0.700815	+	1.08598i
$59$	1.97093	+	3.68735i	0.256593	+	0.480052i	0.976926	−	0.213576i	$-0.0685111\pi$
$59$	1.97093	+	3.68735i	0.256593	+	0.480052i	−0.720333	+	0.693628i	$0.756011\pi$
$60$	2.08105	+	1.29637i	0.268662	+	0.167361i
$61$	−6.59197	−	0.649252i	−0.844015	−	0.0831282i	−0.333239	−	0.942842i	$-0.608142\pi$
$61$	−6.59197	−	0.649252i	−0.844015	−	0.0831282i	−0.510776	+	0.859714i	$0.670642\pi$
$62$	−1.73365	+	3.37183i	−0.220174	+	0.428223i
$63$			0.271162i			0.0341631i
$64$	−2.30405	−	7.66103i	−0.288006	−	0.957629i
$65$			5.73247i			0.711026i
$66$	−2.69675	−	1.38655i	−0.331947	−	0.170673i
$67$	7.25731	+	0.714782i	0.886621	+	0.0873246i	0.531066	−	0.847331i	$-0.321792\pi$
$67$	7.25731	+	0.714782i	0.886621	+	0.0873246i	0.355555	+	0.934655i	$0.384292\pi$
$68$	−1.97999	−	8.52228i	−0.240109	−	1.03348i
$69$	2.89689	+	5.41970i	0.348745	+	0.652455i
$70$	0.395002	+	0.254905i	0.0472117	+	0.0304670i
$71$	−11.3847	+	2.26456i	−1.35112	+	0.268754i	−0.816991	−	0.576650i	$-0.804360\pi$
$71$	−11.3847	+	2.26456i	−1.35112	+	0.268754i	−0.534127	+	0.845404i	$0.679360\pi$
$72$	−2.09799	+	1.89696i	−0.247250	+	0.223559i
$73$	2.93329	−	14.7466i	0.343316	−	1.72596i	−0.294391	−	0.955685i	$-0.595117\pi$
$73$	2.93329	−	14.7466i	0.343316	−	1.72596i	0.637707	−	0.770279i	$-0.279883\pi$
$74$	12.0982	−	0.193172i	1.40638	−	0.0224558i
$75$	2.70334	+	2.21858i	0.312155	+	0.256179i
$76$	11.9528	+	9.18678i	1.37108	+	1.05380i
$77$	−0.512765	−	0.274079i	−0.0584350	−	0.0312342i
$78$	−6.35812	−	1.81839i	−0.719916	−	0.205892i
$79$	2.22197	−	0.920371i	0.249991	−	0.103550i	−0.254169	−	0.967160i	$-0.581802\pi$
$79$	2.22197	−	0.920371i	0.249991	−	0.103550i	0.504160	+	0.863610i	$0.331802\pi$
$80$	0.791097	+	4.83938i	0.0884474	+	0.541059i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	6.32324	+	5.02257i	0.698285	+	0.554650i
$83$	1.38287	−	0.419490i	0.151790	−	0.0460450i	−0.213475	−	0.976948i	$-0.568478\pi$
$83$	1.38287	−	0.419490i	0.151790	−	0.0460450i	0.365265	+	0.930903i	$0.380978\pi$
$84$	−0.408024	+	0.357255i	−0.0445190	+	0.0389797i
$85$	0.525653	+	5.33705i	0.0570151	+	0.578884i
$86$	2.17663	+	5.02634i	0.234712	+	0.542004i
$87$	3.86689	+	5.78721i	0.414574	+	0.620454i
$88$	−1.46659	−	5.88465i	−0.156339	−	0.627305i
$89$	−6.65710	−	4.44813i	−0.705651	−	0.471501i	0.150245	−	0.988649i	$-0.451994\pi$
$89$	−6.65710	−	4.44813i	−0.705651	−	0.471501i	−0.855896	+	0.517148i	$0.826994\pi$
$90$	1.42595	−	0.986077i	0.150308	−	0.103942i
$91$	−1.21339	−	0.368077i	−0.127197	−	0.0385849i
$92$	−4.33852	+	11.4995i	−0.452321	+	1.19890i
$93$	1.70077	+	2.07239i	0.176361	+	0.214897i
$94$	−9.27847	−	0.764497i	−0.957001	−	0.0788519i
$95$	−6.53399	−	6.53399i	−0.670373	−	0.670373i
$96$	−5.61850	−	0.657651i	−0.573435	−	0.0671212i
$97$	1.00262	−	1.00262i	0.101801	−	0.101801i	−0.654372	−	0.756173i	$-0.727067\pi$
$97$	1.00262	−	1.00262i	0.101801	−	0.101801i	0.756173	+	0.654372i	$0.227067\pi$
$98$	7.47186	−	6.33430i	0.754771	−	0.639861i
$99$	−1.65747	+	1.36025i	−0.166582	+	0.136710i
$100$	0.223301	+	6.99076i	0.0223301	+	0.699076i
$101$	2.56663	−	8.46103i	0.255389	−	0.841904i	−0.731686	−	0.681642i	$-0.761266\pi$
$101$	2.56663	−	8.46103i	0.255389	−	0.841904i	0.987075	−	0.160262i	$-0.0512339\pi$
$102$	−6.08628	−	1.10993i	−0.602632	−	0.109900i
$103$	−6.08353	+	9.10465i	−0.599428	+	0.897108i	−0.999815	−	0.0192385i	$-0.993876\pi$
$103$	−6.08353	+	9.10465i	−0.599428	+	0.897108i	0.400387	+	0.916346i	$0.368876\pi$
$104$	−5.64064	−	11.9630i	−0.553110	−	1.17306i
$105$	0.276395	−	0.184681i	0.0269734	−	0.0180231i
$106$	9.29037	+	3.67555i	0.902360	+	0.357001i
$107$	−14.7404	+	1.45180i	−1.42501	+	0.140351i	−0.780934	−	0.624614i	$-0.785256\pi$
$107$	−14.7404	+	1.45180i	−1.42501	+	0.140351i	−0.644072	+	0.764965i	$0.722756\pi$
$108$	0.641376	+	1.89437i	0.0617164	+	0.182286i
$109$	2.49472	+	8.22399i	0.238951	+	0.787715i	0.991606	+	0.129300i	$0.0412729\pi$
$109$	2.49472	+	8.22399i	0.238951	+	0.787715i	−0.752655	+	0.658415i	$0.771227\pi$
$110$	0.423378	+	3.69315i	0.0403675	+	0.352128i
$111$	3.27415	−	7.90451i	0.310769	−	0.750263i
$112$	−1.07514	−	0.143281i	−0.101591	−	0.0135388i
$113$	−0.594816	−	1.43601i	−0.0559556	−	0.135089i	0.893429	−	0.449204i	$-0.148292\pi$
$113$	−0.594816	−	1.43601i	−0.0559556	−	0.135089i	−0.949385	+	0.314115i	$0.898292\pi$
$114$	9.31975	−	5.17448i	0.872875	−	0.484635i
$115$	3.55131	−	6.64403i	0.331161	−	0.619559i
$116$	−3.61354	+	13.4432i	−0.335509	+	1.24817i
$117$	−2.96650	+	3.61469i	−0.274253	+	0.334178i
$118$	4.24726	+	4.11376i	0.390992	+	0.378702i
$119$	−1.16344	−	0.231422i	−0.106652	−	0.0212144i
$120$	3.36246	+	0.846506i	0.306949	+	0.0772751i
$121$	1.24907	+	6.27948i	0.113552	+	0.570862i
$122$	−9.15722	+	1.97397i	−0.829056	+	0.178715i
$123$	5.03583	−	2.69171i	0.454065	−	0.242703i
$124$	−0.877621	+	5.28956i	−0.0788127	+	0.475016i
$125$	1.02101	−	10.3665i	0.0913223	−	0.927211i
$126$	0.117163	+	0.365144i	0.0104377	+	0.0325296i
$127$	−4.75290			−0.421751			−0.210876	−	0.977513i	$-0.567632\pi$
$127$	−4.75290			−0.421751			−0.210876	+	0.977513i	$0.567632\pi$
$128$	−6.41277	−	9.32075i	−0.566814	−	0.823846i
$129$	3.87310			0.341007
$130$	2.47688	+	7.71930i	0.217236	+	0.677027i
$131$	0.841887	−	8.54782i	0.0735560	−	0.746826i	−0.885694	−	0.464269i	$-0.846317\pi$
$131$	0.841887	−	8.54782i	0.0735560	−	0.746826i	0.959250	−	0.282558i	$-0.0911828\pi$
$132$	−4.23052	−	0.701910i	−0.368219	−	0.0610934i
$133$	1.80258	−	0.963501i	0.156304	−	0.0835461i
$134$	10.0815	−	2.17320i	0.870906	−	0.187736i
$135$	−0.239162	−	1.20235i	−0.0205838	−	0.103482i
$136$	−6.34852	−	10.6205i	−0.544381	−	0.910702i
$137$	−11.0881	−	2.20557i	−0.947324	−	0.188435i	−0.302831	−	0.953044i	$-0.597932\pi$
$137$	−11.0881	−	2.20557i	−0.947324	−	0.188435i	−0.644493	+	0.764610i	$0.722932\pi$
$138$	6.24266	+	6.04644i	0.531411	+	0.514707i
$139$	1.01207	−	1.23321i	0.0858425	−	0.104599i	−0.728318	−	0.685239i	$-0.759698\pi$
$139$	1.01207	−	1.23321i	0.0858425	−	0.104599i	0.814160	+	0.580640i	$0.197198\pi$
$140$	0.642045	+	0.172582i	0.0542627	+	0.0145858i
$141$	−3.10325	+	5.80578i	−0.261341	+	0.488935i
$142$	−14.3521	+	7.96853i	−1.20440	+	0.668704i
$143$	−3.83695	−	9.26322i	−0.320862	−	0.774629i
$144$	−2.00549	+	3.46092i	−0.167125	+	0.288410i
$145$	3.26527	−	7.88305i	0.271166	−	0.654651i
$146$	−2.42176	−	21.1251i	−0.200426	−	1.74833i
$147$	−2.01065	−	6.62822i	−0.165835	−	0.546686i
$148$	16.2078	−	5.48747i	1.33227	−	0.451067i
$149$	3.87810	−	0.381959i	0.317706	−	0.0312913i	0.0620927	−	0.998070i	$-0.480223\pi$
$149$	3.87810	−	0.381959i	0.317706	−	0.0312913i	0.255613	+	0.966779i	$0.417723\pi$
$150$	4.59890	+	1.81946i	0.375498	+	0.148558i
$151$	−4.25792	+	2.84505i	−0.346505	+	0.231527i	−0.716628	−	0.697455i	$-0.754315\pi$
$151$	−4.25792	+	2.84505i	−0.346505	+	0.231527i	0.370123	+	0.928983i	$0.379315\pi$
$152$	20.0649	+	7.20630i	1.62748	+	0.584508i
$153$	−2.43041	+	3.63737i	−0.196487	+	0.294064i
$154$	−0.808908	−	0.147517i	−0.0651837	−	0.0118873i
$155$	0.954039	−	3.14505i	0.0766303	−	0.252616i
$156$	−9.34748	+	0.298580i	−0.748397	+	0.0239055i
$157$	11.2532	−	9.23524i	0.898101	−	0.737053i	−0.0673245	−	0.997731i	$-0.521446\pi$
$157$	11.2532	−	9.23524i	0.898101	−	0.737053i	0.965426	+	0.260679i	$0.0839463\pi$
$158$	2.59442	−	2.19943i	0.206401	−	0.174977i
$159$	4.99551	−	4.99551i	0.396170	−	0.396170i
$160$	3.15627	+	6.17485i	0.249525	+	0.488165i
$161$	1.17831	+	1.17831i	0.0928637	+	0.0928637i
$162$	1.40944	+	0.116130i	0.110736	+	0.00912405i
$163$	10.1672	+	12.3888i	0.796358	+	0.970366i	0.999962	−	0.00868777i	$-0.00276544\pi$
$163$	10.1672	+	12.3888i	0.796358	+	0.970366i	−0.203604	+	0.979053i	$0.565265\pi$
$164$	10.6850	+	4.03122i	0.834356	+	0.314785i
$165$	2.51537	+	0.763028i	0.195821	+	0.0594017i
$166$	1.68091	−	1.16239i	0.130464	−	0.0902189i
$167$	−7.87786	−	5.26382i	−0.609607	−	0.407327i	0.212091	−	0.977250i	$-0.431973\pi$
$167$	−7.87786	−	5.26382i	−0.609607	−	0.407327i	−0.821698	+	0.569923i	$0.806973\pi$
$168$	−0.395079	+	0.657374i	−0.0304810	+	0.0507175i
$169$	−4.92576	−	7.37192i	−0.378904	−	0.567071i
$170$	3.01386	+	6.95970i	0.231153	+	0.533785i
$171$	−0.738821	−	7.50138i	−0.0564991	−	0.573645i
$172$	5.10280	+	5.82795i	0.389085	+	0.444377i
$173$	−10.9159	+	3.31131i	−0.829922	+	0.251754i	−0.676533	−	0.736412i	$-0.736519\pi$
$173$	−10.9159	+	3.31131i	−0.829922	+	0.251754i	−0.153388	+	0.988166i	$0.549019\pi$
$174$	7.70765	+	6.12221i	0.584315	+	0.464123i
$175$	0.876111	+	0.362897i	0.0662278	+	0.0274324i
$176$	−4.51752	−	7.29054i	−0.340521	−	0.549545i
$177$	3.86278	−	1.60002i	0.290344	−	0.120265i
$178$	−10.8863	−	3.11343i	−0.815965	−	0.233361i
$179$	13.2860	+	7.10151i	0.993042	+	0.530792i	0.886110	−	0.463474i	$-0.153397\pi$
$179$	13.2860	+	7.10151i	0.993042	+	0.530792i	0.106932	+	0.994266i	$0.465897\pi$
$180$	1.49411	−	1.94396i	0.111364	−	0.144894i
$181$	−14.4637	−	11.8701i	−1.07508	−	0.882297i	−0.0816430	−	0.996662i	$-0.526017\pi$
$181$	−14.4637	−	11.8701i	−1.07508	−	0.882297i	−0.993439	+	0.114365i	$0.963517\pi$
$182$	−1.79297	+	0.0286286i	−0.132904	+	0.00212209i
$183$	−1.29225	+	6.49659i	−0.0955260	+	0.480242i
$184$	−0.873538	+	17.3597i	−0.0643981	+	1.27977i
$185$	−10.2870	+	2.04621i	−0.756316	+	0.150441i
$186$	3.18567	+	2.05580i	0.233585	+	0.150738i
$187$	−4.42169	−	8.27240i	−0.323346	−	0.604938i
$188$	−12.8246	+	2.97956i	−0.935333	+	0.217307i
$189$	0.269856	+	0.0265785i	0.0196291	+	0.00193330i
$190$	−11.6218	−	5.97542i	−0.843134	−	0.433503i
$191$			7.97371i			0.576957i	0.957486	+	0.288479i	$0.0931494\pi$
$191$			7.97371i			0.576957i	−0.957486	+	0.288479i	$0.906851\pi$
$192$	−7.84998	+	1.54204i	−0.566523	+	0.111287i
$193$		−	22.3493i		−	1.60874i	−0.594129	−	0.804370i	$-0.702503\pi$
$193$		−	22.3493i		−	1.60874i	0.594129	−	0.804370i	$-0.297497\pi$
$194$	0.916910	−	1.78333i	0.0658303	−	0.128036i
$195$	5.70487	+	0.561881i	0.408534	+	0.0402371i
$196$	7.32463	−	11.7581i	0.523188	−	0.839867i
$197$	11.3014	+	21.1434i	0.805188	+	1.50640i	0.861368	+	0.507981i	$0.169608\pi$
$197$	11.3014	+	21.1434i	0.805188	+	1.50640i	−0.0561800	+	0.998421i	$0.517892\pi$
$198$	−1.64420	+	2.54786i	−0.116848	+	0.181068i
$199$	6.35943	−	1.26497i	0.450808	−	0.0896713i	0.0355357	−	0.999368i	$-0.488686\pi$
$199$	6.35943	−	1.26497i	0.450808	−	0.0896713i	0.415272	+	0.909697i	$0.363686\pi$
$200$	3.32125	+	9.31721i	0.234848	+	0.658826i
$201$	1.42268	−	7.15230i	0.100348	−	0.504484i
$202$	−0.199629	−	12.5025i	−0.0140459	−	0.879675i
$203$	1.45894	+	1.19732i	0.102397	+	0.0840352i
$204$	−8.67531	+	1.13512i	−0.607393	+	0.0794746i
$205$	−6.17343	−	3.29977i	−0.431171	−	0.230466i
$206$	−4.25811	+	14.8888i	−0.296677	+	1.03735i
$207$	5.67755	−	2.35172i	0.394617	−	0.163456i
$208$	−12.7646	−	13.6720i	−0.885064	−	0.947983i
$209$	14.9318	+	6.18497i	1.03286	+	0.427823i
$210$	0.292395	−	0.368115i	0.0201772	−	0.0254023i
$211$	−17.5774	+	5.33205i	−1.21008	+	0.367073i	−0.829938	−	0.557856i	$-0.811624\pi$
$211$	−17.5774	+	5.33205i	−1.21008	+	0.367073i	−0.380140	+	0.924929i	$0.624124\pi$
$212$	14.0984	+	0.935296i	0.968285	+	0.0642364i
$213$	1.13776	+	11.5519i	0.0779580	+	0.791521i
$214$	−19.2220	+	8.32397i	−1.31399	+	0.569015i
$215$	−2.63787	−	3.94785i	−0.179901	−	0.269241i
$216$	1.68219	+	2.27382i	0.114458	+	0.154714i
$217$	0.604450	+	0.403881i	0.0410328	+	0.0274172i
$218$	6.91277	+	9.99644i	0.468192	+	0.677044i
$219$	−14.3881	−	4.36459i	−0.972259	−	0.294932i
$220$	2.16584	+	4.79023i	0.146021	+	0.322957i
$221$	−12.9773	−	15.8129i	−0.872951	−	1.06369i
$222$	0.993584	−	12.0588i	0.0666850	−	0.809336i
$223$	3.48509	+	3.48509i	0.233379	+	0.233379i	0.814102	−	0.580723i	$-0.197230\pi$
$223$	3.48509	+	3.48509i	0.233379	+	0.233379i	−0.580723	+	0.814102i	$0.697230\pi$
$224$	−1.50968	+	0.271604i	−0.100870	+	0.0181473i
$225$	2.47287	−	2.47287i	0.164858	−	0.164858i
$226$	−1.42144	−	1.67672i	−0.0945531	−	0.111534i
$227$	14.3867	−	11.8069i	0.954882	−	0.783651i	−0.0214855	−	0.999769i	$-0.506840\pi$
$227$	14.3867	−	11.8069i	0.954882	−	0.783651i	0.976367	+	0.216118i	$0.0693396\pi$
$228$	10.3141	−	10.9948i	0.683069	−	0.728147i
$229$	−3.52564	+	11.6225i	−0.232981	+	0.768034i	0.760017	+	0.649903i	$0.225190\pi$
$229$	−3.52564	+	11.6225i	−0.232981	+	0.768034i	−0.992998	+	0.118132i	$0.962310\pi$
$230$	1.91142	−	10.4812i	0.126035	−	0.691112i
$231$	−0.323019	+	0.483432i	−0.0212531	+	0.0318075i
$232$	0.942566	+	19.6639i	0.0618825	+	1.29100i
$233$	3.91068	−	2.61303i	0.256197	−	0.171186i	−0.420839	−	0.907136i	$-0.638264\pi$
$233$	3.91068	−	2.61303i	0.256197	−	0.171186i	0.677036	+	0.735950i	$0.263264\pi$
$234$	−2.43284	+	6.14927i	−0.159039	+	0.401991i
$235$	8.03138	−	0.791022i	0.523910	−	0.0516006i
$236$	7.49679	+	3.70440i	0.487999	+	0.241136i
$237$	−0.698148	−	2.30148i	−0.0453496	−	0.149497i
$238$	−1.66667	+	0.191065i	−0.108034	+	0.0123849i
$239$	5.76140	−	13.9092i	0.372674	−	0.899714i	−0.620622	−	0.784110i	$-0.713120\pi$
$239$	5.76140	−	13.9092i	0.372674	−	0.899714i	0.993295	−	0.115604i	$-0.0368804\pi$
$240$	4.89362	−	0.312946i	0.315881	−	0.0202006i
$241$	−11.1449	−	26.9062i	−0.717907	−	1.73318i	−0.679225	−	0.733930i	$-0.737684\pi$
$241$	−11.1449	−	26.9062i	−0.717907	−	1.73318i	−0.0386819	−	0.999252i	$-0.512316\pi$
$242$	4.39521	+	7.91621i	0.282535	+	0.508873i
$243$	0.471397	−	0.881921i	0.0302401	−	0.0565753i
$244$	−11.4781	+	6.61476i	−0.734812	+	0.423467i
$245$	−5.38675	+	6.56377i	−0.344147	+	0.419344i
$246$	5.61817	−	5.80050i	0.358202	−	0.369826i
$247$	34.5698	+	6.87637i	2.19963	+	0.437533i
$248$	1.10370	+	7.50207i	0.0700852	+	0.476382i
$249$	−0.281924	−	1.41733i	−0.0178662	−	0.0898196i
$250$	−3.10426	−	14.4006i	−0.196331	−	0.910777i
$251$	20.9248	−	11.1845i	1.32076	−	0.705962i	0.347940	−	0.937517i	$-0.386881\pi$
$251$	20.9248	−	11.1845i	1.32076	−	0.705962i	0.972822	+	0.231555i	$0.0743814\pi$
$252$	0.315541	+	0.441076i	0.0198772	+	0.0277852i
$253$	−1.29154	+	13.1132i	−0.0811985	+	0.824422i
$254$	−6.40021	+	2.05362i	−0.401585	+	0.128856i
$255$	5.36287			0.335836
$256$	−12.6627	−	9.78042i	−0.791417	−	0.611276i
$257$	1.07490			0.0670503			0.0335252	−	0.999438i	$-0.489327\pi$
$257$	1.07490			0.0670503			0.0335252	+	0.999438i	$0.489327\pi$
$258$	5.21548	−	1.67348i	0.324702	−	0.104186i
$259$	0.227400	−	2.30883i	0.0141299	−	0.143463i
$260$	6.67068	+	9.32454i	0.413698	+	0.578283i
$261$	6.13836	−	3.28102i	0.379955	−	0.203090i
$262$	−2.55965	−	11.8742i	−0.158136	−	0.733589i
$263$	−3.38281	−	17.0065i	−0.208593	−	1.04867i	−0.933159	−	0.359463i	$-0.882960\pi$
$263$	−3.38281	−	17.0065i	−0.208593	−	1.04867i	0.724566	−	0.689205i	$-0.242040\pi$
$264$	−6.00006	+	0.882728i	−0.369278	+	0.0543282i
$265$	−8.49425	−	1.68961i	−0.521797	−	0.103792i
$266$	2.01104	−	2.07630i	0.123304	−	0.127306i
$267$	−5.07922	+	6.18905i	−0.310843	+	0.378764i
$268$	12.6366	−	7.28240i	0.771905	−	0.444843i
$269$	3.55551	−	6.65189i	0.216783	−	0.405573i	−0.749899	−	0.661552i	$-0.769898\pi$
$269$	3.55551	−	6.65189i	0.216783	−	0.405573i	0.966682	+	0.255979i	$0.0823980\pi$
$270$	−0.841561	−	1.51573i	−0.0512158	−	0.0922447i
$271$	−10.5998	−	25.5903i	−0.643894	−	1.55450i	−0.821384	−	0.570376i	$-0.806798\pi$
$271$	−10.5998	−	25.5903i	−0.643894	−	1.55450i	0.177489	−	0.984123i	$-0.443202\pi$
$272$	−13.1378	−	11.5584i	−0.796594	−	0.700833i
$273$	−0.485237	+	1.17147i	−0.0293679	+	0.0709003i
$274$	−15.8842	+	1.82094i	−0.959598	+	0.110007i
$275$	2.17671	+	7.17565i	0.131261	+	0.432708i
$276$	11.0189	+	5.44477i	0.663257	+	0.327737i
$277$	−19.8451	+	1.95458i	−1.19238	+	0.117439i	−0.674671	−	0.738118i	$-0.735715\pi$
$277$	−19.8451	+	1.95458i	−1.19238	+	0.117439i	−0.517708	+	0.855558i	$0.673215\pi$
$278$	0.830000	−	2.09792i	0.0497801	−	0.125825i
$279$	2.22911	−	1.48945i	0.133454	−	0.0891708i
$280$	0.939141	−	0.0450166i	0.0561244	−	0.00269026i
$281$	1.58068	−	2.36565i	0.0942955	−	0.141123i	−0.781322	−	0.624128i	$-0.785455\pi$
$281$	1.58068	−	2.36565i	0.0942955	−	0.141123i	0.875618	+	0.483004i	$0.160455\pi$
$282$	−1.67027	+	9.15886i	−0.0994629	+	0.545402i
$283$	−6.15575	+	20.2928i	−0.365922	+	1.20628i	0.559976	+	0.828509i	$0.310810\pi$
$283$	−6.15575	+	20.2928i	−0.365922	+	1.20628i	−0.925898	+	0.377773i	$0.876690\pi$
$284$	−15.8834	+	16.9316i	−0.942506	+	1.00470i
$285$	−7.14297	+	5.86208i	−0.423113	+	0.347240i
$286$	−9.16924	−	10.8159i	−0.542188	−	0.639558i
$287$	1.09485	−	1.09485i	0.0646269	−	0.0646269i
$288$	−1.20519	+	5.52698i	−0.0710167	+	0.325680i
$289$	−1.51136	−	1.51136i	−0.0889035	−	0.0889035i
$290$	0.990887	−	12.0261i	0.0581869	−	0.706197i
$291$	−0.899519	−	1.09607i	−0.0527307	−	0.0642526i
$292$	−12.3888	−	27.4005i	−0.725000	−	1.60349i
$293$	3.51539	+	1.06638i	0.205372	+	0.0622988i	0.391294	−	0.920266i	$-0.372027\pi$
$293$	3.51539	+	1.06638i	0.205372	+	0.0622988i	−0.185923	+	0.982564i	$0.559527\pi$
$294$	−5.57143	−	8.05675i	−0.324932	−	0.469879i
$295$	−4.26174	−	2.84760i	−0.248128	−	0.165794i
$296$	19.4543	−	14.3924i	1.13076	−	0.836542i
$297$	1.19124	+	1.78282i	0.0691228	+	0.103450i
$298$	5.05718	−	2.18998i	0.292954	−	0.126862i
$299$	2.81665	+	28.5980i	0.162891	+	1.65386i
$300$	6.97898	+	0.462988i	0.402932	+	0.0267306i
$301$	1.00501	−	0.304867i	0.0579280	−	0.0175723i
$302$	−4.50440	+	5.67088i	−0.259199	+	0.326323i
$303$	−8.16871	−	3.38359i	−0.469280	−	0.194382i
$304$	30.1329	+	1.03432i	1.72824	+	0.0593225i
$305$	7.50210	−	3.10747i	0.429569	−	0.177933i
$306$	−1.70115	+	5.94818i	−0.0972481	+	0.340035i
$307$	10.6121	+	5.67227i	0.605663	+	0.323734i	0.745566	−	0.666431i	$-0.232179\pi$
$307$	10.6121	+	5.67227i	0.605663	+	0.323734i	−0.139903	+	0.990165i	$0.544679\pi$
$308$	−1.15301	+	0.150866i	−0.0656987	+	0.00859638i
$309$	8.46452	+	6.94665i	0.481530	+	0.395181i
$310$	−0.0742040	−	4.64731i	−0.00421451	−	0.263950i
$311$	−5.51260	+	27.7137i	−0.312591	+	1.57150i	0.430677	+	0.902506i	$0.358275\pi$
$311$	−5.51260	+	27.7137i	−0.312591	+	1.57150i	−0.743267	+	0.668994i	$0.766725\pi$
$312$	−12.4582	+	4.44091i	−0.705308	+	0.251417i
$313$	3.71717	−	0.739391i	0.210107	−	0.0417929i	−0.0889145	−	0.996039i	$-0.528340\pi$
$313$	3.71717	−	0.739391i	0.210107	−	0.0417929i	0.299021	+	0.954246i	$0.403340\pi$
$314$	11.1631	−	17.2983i	0.629969	−	0.976202i
$315$	−0.156701	−	0.293166i	−0.00882908	−	0.0165180i
$316$	2.54329	−	4.08272i	0.143071	−	0.229671i
$317$	5.67406	+	0.558847i	0.318687	+	0.0313880i	0.256096	−	0.966651i	$-0.417564\pi$
$317$	5.67406	+	0.558847i	0.318687	+	0.0313880i	0.0625910	+	0.998039i	$0.480064\pi$
$318$	4.56846	−	8.88536i	0.256187	−	0.498266i
$319$			14.9239i			0.835580i
$320$	6.91823	+	6.95124i	0.386741	+	0.388586i
$321$			14.8117i			0.826708i
$322$	2.09582	+	1.07758i	0.116795	+	0.0600511i
$323$	32.8157	+	3.23207i	1.82592	+	0.179837i
$324$	1.94811	−	0.452607i	0.108229	−	0.0251448i
$325$	7.70883	+	14.4222i	0.427609	+	0.800000i
$326$	19.0440	+	12.2896i	1.05475	+	0.680659i
$327$	8.42891	−	1.67661i	0.466120	−	0.0927170i
$328$	16.1301	+	0.811666i	0.890635	+	0.0448167i
$329$	−0.348253	+	1.75078i	−0.0191998	+	0.0965239i
$330$	3.71686	−	0.0593474i	0.204606	−	0.00326697i
$331$	−26.4150	−	21.6782i	−1.45190	−	1.19154i	−0.943922	−	0.330170i	$-0.892894\pi$
$331$	−26.4150	−	21.6782i	−1.45190	−	1.19154i	−0.507976	−	0.861371i	$-0.669606\pi$
$332$	1.76126	−	2.29155i	0.0966616	−	0.125765i
$333$	−7.54552	−	4.03316i	−0.413492	−	0.221016i
$334$	−12.8826	−	3.68436i	−0.704907	−	0.201599i
$335$	−8.25930	+	3.42111i	−0.451254	+	0.186915i
$336$	−0.247973	+	1.05592i	−0.0135281	+	0.0576051i
$337$	4.09393	+	1.69576i	0.223011	+	0.0923741i	0.491391	−	0.870939i	$-0.336488\pi$
$337$	4.09393	+	1.69576i	0.223011	+	0.0923741i	−0.268381	+	0.963313i	$0.586488\pi$
$338$	−9.81823	−	7.79865i	−0.534041	−	0.424191i
$339$	−1.48740	+	0.451198i	−0.0807846	+	0.0245057i
$340$	7.06557	+	8.06965i	0.383184	+	0.437638i
$341$	0.563441	+	5.72071i	0.0305121	+	0.309794i
$342$	−4.23607	−	9.78206i	−0.229060	−	0.528953i
$343$	−2.09801	−	3.13990i	−0.113282	−	0.169539i
$344$	9.38951	+	5.64306i	0.506249	+	0.304253i
$345$	−6.26395	−	4.18544i	−0.337240	−	0.225336i
$346$	−13.2685	+	9.17551i	−0.713321	+	0.493278i
$347$	−14.3575	−	4.35530i	−0.770752	−	0.233805i	−0.119671	−	0.992814i	$-0.538184\pi$
$347$	−14.3575	−	4.35530i	−0.770752	−	0.233805i	−0.651081	+	0.759009i	$0.725684\pi$
$348$	13.0243	+	4.91381i	0.698177	+	0.263408i
$349$	−10.1663	−	12.3877i	−0.544192	−	0.663099i	0.426202	−	0.904628i	$-0.359851\pi$
$349$	−10.1663	−	12.3877i	−0.544192	−	0.663099i	−0.970394	+	0.241529i	$0.922351\pi$
$350$	1.33656	+	0.110126i	0.0714423	+	0.00588647i
$351$	3.30652	+	3.30652i	0.176489	+	0.176489i
$352$	−9.23333	−	7.86545i	−0.492138	−	0.419230i
$353$	−22.9017	+	22.9017i	−1.21893	+	1.21893i	−0.250926	+	0.968006i	$0.580735\pi$
$353$	−22.9017	+	22.9017i	−1.21893	+	1.21893i	−0.968006	+	0.250926i	$0.919265\pi$
$354$	4.51025	−	3.82359i	0.239717	−	0.203221i
$355$	10.9999	−	9.02741i	0.583816	−	0.479125i
$356$	−16.0047	+	0.511227i	−0.848246	+	0.0270950i
$357$	−0.344345	+	1.13515i	−0.0182247	+	0.0600786i
$358$	20.9592	+	3.82225i	1.10773	+	0.202012i
$359$	−13.4014	+	20.0565i	−0.707296	+	1.05854i	0.287611	+	0.957747i	$0.407139\pi$
$359$	−13.4014	+	20.0565i	−0.707296	+	1.05854i	−0.994907	+	0.100796i	$0.967861\pi$
$360$	1.17201	−	3.26330i	0.0617703	−	0.171991i
$361$	−31.4433	+	21.0097i	−1.65491	+	1.10578i
$362$	−24.6056	−	9.73470i	−1.29324	−	0.511644i
$363$	6.37168	−	0.627555i	0.334426	−	0.0329381i
$364$	−2.40203	+	0.813255i	−0.125901	+	0.0426261i
$365$	5.35056	+	17.6384i	0.280061	+	0.923238i
$366$	1.06690	+	9.30661i	0.0557676	+	0.486464i
$367$	−2.93744	+	7.09161i	−0.153333	+	0.370179i	−0.981816	−	0.189836i	$-0.939204\pi$
$367$	−2.93744	+	7.09161i	−0.153333	+	0.370179i	0.828483	+	0.560015i	$0.189204\pi$
$368$	6.32443	+	23.7538i	0.329684	+	1.23825i
$369$	−2.18515	−	5.27541i	−0.113754	−	0.274627i
$370$	−12.9683	+	7.20021i	−0.674189	+	0.374321i
$371$	0.903045	−	1.68948i	0.0468838	−	0.0877134i
$372$	5.17806	+	1.39186i	0.268470	+	0.0721647i
$373$	−9.04435	+	11.0206i	−0.468298	+	0.570623i	−0.952580	−	0.304289i	$-0.901581\pi$
$373$	−9.04435	+	11.0206i	−0.468298	+	0.570623i	0.484281	+	0.874912i	$0.339081\pi$
$374$	−9.52853	−	9.22903i	−0.492709	−	0.477222i
$375$	−10.2165	−	2.03220i	−0.527580	−	0.104942i
$376$	−15.9821	+	9.55349i	−0.824216	+	0.492684i
$377$	6.34957	+	31.9215i	0.327020	+	1.64404i
$378$	0.374870	−	0.0808084i	0.0192812	−	0.00415634i
$379$	1.65637	−	0.885347i	0.0850819	−	0.0454772i	−0.428307	−	0.903633i	$-0.640890\pi$
$379$	1.65637	−	0.885347i	0.0850819	−	0.0454772i	0.513389	+	0.858156i	$0.328390\pi$
$380$	−18.2317	−	3.02492i	−0.935265	−	0.155175i
$381$	−0.465865	+	4.73001i	−0.0238670	+	0.242326i
$382$	3.44526	+	10.7373i	0.176275	+	0.549369i
$383$	18.8871			0.965084			0.482542	−	0.875873i	$-0.339714\pi$
$383$	18.8871			0.965084			0.482542	+	0.875873i	$0.339714\pi$
$384$	−9.90443	+	5.46830i	−0.505433	+	0.279053i
$385$	0.712762			0.0363257
$386$	−9.65665	−	30.0954i	−0.491511	−	1.53182i
$387$	0.379630	−	3.85445i	0.0192977	−	0.195933i
$388$	0.464165	−	2.79759i	0.0235644	−	0.142026i
$389$	21.4353	−	11.4574i	1.08681	−	0.580914i	0.172126	−	0.985075i	$-0.444936\pi$
$389$	21.4353	−	11.4574i	1.08681	−	0.580914i	0.914688	+	0.404161i	$0.132436\pi$
$390$	7.92490	−	1.70832i	0.401293	−	0.0865044i
$391$	5.24472	+	26.3670i	0.265237	+	1.33344i
$392$	4.78284	−	18.9982i	0.241570	−	0.959555i
$393$	−8.42414	−	1.67567i	−0.424942	−	0.0845261i
$394$	24.3539	+	23.5884i	1.22693	+	1.18837i
$395$	−1.87041	+	2.27911i	−0.0941107	+	0.114674i
$396$	−1.11319	+	4.14135i	−0.0559401	+	0.208111i
$397$	3.37653	−	6.31704i	0.169463	−	0.317043i	−0.782826	−	0.622241i	$-0.786222\pi$
$397$	3.37653	−	6.31704i	0.169463	−	0.317043i	0.952289	+	0.305197i	$0.0987225\pi$
$398$	8.01699	−	4.45117i	0.401855	−	0.223117i
$399$	−0.782177	−	1.88834i	−0.0391578	−	0.0945354i
$400$	8.49813	+	11.1114i	0.424906	+	0.555572i
$401$	0.212080	−	0.512007i	0.0105908	−	0.0255684i	−0.918496	−	0.395431i	$-0.870595\pi$
$401$	0.212080	−	0.512007i	0.0105908	−	0.0255684i	0.929086	+	0.369863i	$0.120595\pi$
$402$	−1.17458	−	10.2459i	−0.0585828	−	0.511021i
$403$	3.63912	+	11.9966i	0.181277	+	0.597591i
$404$	−5.67089	−	16.7495i	−0.282137	−	0.833321i
$405$	−1.22000	+	0.120159i	−0.0606223	+	0.00597077i
$406$	2.48193	+	0.981924i	0.123176	+	0.0487321i
$407$	15.2534	−	10.1920i	0.756082	−	0.505198i
$408$	−11.1916	+	5.27696i	−0.554069	+	0.261248i
$409$	−17.3106	+	25.9072i	−0.855954	+	1.28103i	0.102197	+	0.994764i	$0.467413\pi$
$409$	−17.3106	+	25.9072i	−0.855954	+	1.28103i	−0.958151	+	0.286262i	$0.907587\pi$
$410$	−9.73885	−	1.77604i	−0.480968	−	0.0877122i
$411$	−3.28178	+	10.8186i	−0.161878	+	0.533641i
$412$	0.699185	+	21.8890i	0.0344464	+	1.07839i
$413$	0.876391	−	0.719236i	0.0431244	−	0.0353913i
$414$	6.62921	−	5.61995i	0.325808	−	0.276205i
$415$	−1.25267	+	1.25267i	−0.0614913	+	0.0614913i
$416$	−23.0960	−	12.8953i	−1.13238	−	0.632245i
$417$	−1.12807	−	1.12807i	−0.0552419	−	0.0552419i
$418$	22.7795	+	1.87691i	1.11418	+	0.0918026i
$419$	4.01521	+	4.89254i	0.196156	+	0.239016i	0.861794	−	0.507258i	$-0.169341\pi$
$419$	4.01521	+	4.89254i	0.196156	+	0.239016i	−0.665639	+	0.746274i	$0.731841\pi$
$420$	0.234682	−	0.622037i	0.0114513	−	0.0303523i
$421$	−19.7494	−	5.99092i	−0.962527	−	0.291979i	−0.230361	−	0.973105i	$-0.573991\pi$
$421$	−19.7494	−	5.99092i	−0.962527	−	0.291979i	−0.732166	+	0.681126i	$0.761491\pi$
$422$	−21.3657	+	14.7749i	−1.04007	+	0.719231i
$423$	5.47365	+	3.65738i	0.266138	+	0.177828i
$424$	19.3890	−	4.83217i	0.941612	−	0.234671i
$425$	8.49955	+	12.7205i	0.412289	+	0.617034i
$426$	6.52341	+	15.0640i	0.316060	+	0.729856i
$427$	0.176052	+	1.78749i	0.00851977	+	0.0865026i
$428$	−22.2875	+	19.5144i	−1.07731	+	0.943263i
$429$	−9.59470	+	2.91052i	−0.463236	+	0.140521i
$430$	−5.25791	−	4.17638i	−0.253559	−	0.201403i
$431$	14.4832	+	5.99912i	0.697629	+	0.288968i	0.703175	−	0.711017i	$-0.251765\pi$
$431$	14.4832	+	5.99912i	0.697629	+	0.288968i	−0.00554538	+	0.999985i	$0.501765\pi$
$432$	3.24769	+	2.33507i	0.156254	+	0.112346i
$433$	14.0481	−	5.81893i	0.675110	−	0.279640i	−0.0186708	−	0.999826i	$-0.505943\pi$
$433$	14.0481	−	5.81893i	0.675110	−	0.279640i	0.693781	+	0.720186i	$0.255943\pi$
$434$	0.988455	+	0.282693i	0.0474474	+	0.0135697i
$435$	−7.52504	−	4.02222i	−0.360798	−	0.192850i
$436$	13.6279	+	10.4743i	0.652659	+	0.501626i
$437$	−35.8070	−	29.3861i	−1.71288	−	1.40573i
$438$	−21.2608	+	0.339472i	−1.01588	+	0.0162206i
$439$	−5.00170	+	25.1453i	−0.238718	+	1.20012i	0.656443	+	0.754376i	$0.272060\pi$
$439$	−5.00170	+	25.1453i	−0.238718	+	1.20012i	−0.895161	+	0.445742i	$0.852940\pi$
$440$	4.98626	+	5.51466i	0.237711	+	0.262901i
$441$	−6.79338	+	1.35129i	−0.323494	+	0.0643470i
$442$	−24.3076	−	15.6863i	−1.15619	−	0.746123i
$443$	−11.1323	−	20.8271i	−0.528913	−	0.989527i	−0.994521	−	0.104536i	$-0.966664\pi$
$443$	−11.1323	−	20.8271i	−0.528913	−	0.989527i	0.465608	−	0.884991i	$-0.345836\pi$
$444$	−3.87240	−	16.6676i	−0.183776	−	0.791010i
$445$	9.76783	+	0.962047i	0.463040	+	0.0456054i
$446$	6.19883	+	3.18716i	0.293523	+	0.150917i
$447$		−	3.89686i		−	0.184315i
$448$	−1.91557	+	1.01804i	−0.0905024	+	0.0480979i
$449$			35.7993i			1.68948i	0.535181	+	0.844738i	$0.320243\pi$
$449$			35.7993i			1.68948i	−0.535181	+	0.844738i	$0.679757\pi$
$450$	2.26147	−	4.39841i	0.106607	−	0.207343i
$451$	12.1844	+	1.20006i	0.573742	+	0.0565087i
$452$	−2.63858	−	1.64368i	−0.124108	−	0.0773121i
$453$	2.41400	+	4.51629i	0.113420	+	0.212194i
$454$	14.2716	−	22.1153i	0.669798	−	1.03792i
$455$	1.52456	−	0.303254i	0.0714724	−	0.0142167i
$456$	9.13830	−	19.2620i	0.427940	−	0.902024i
$457$	−0.201394	+	1.01248i	−0.00942084	+	0.0473617i	−0.985210	−	0.171353i	$-0.945186\pi$
$457$	−0.201394	+	1.01248i	−0.00942084	+	0.0473617i	0.975789	+	0.218714i	$0.0701863\pi$
$458$	0.274220	+	17.1741i	0.0128135	+	0.802491i
$459$	3.38163	+	2.77524i	0.157841	+	0.129537i
$460$	−1.95481	−	14.9398i	−0.0911433	−	0.696573i
$461$	−2.19363	−	1.17252i	−0.102168	−	0.0546097i	0.419521	−	0.907745i	$-0.362198\pi$
$461$	−2.19363	−	1.17252i	−0.102168	−	0.0546097i	−0.521689	+	0.853136i	$0.674698\pi$
$462$	−0.226094	+	0.790554i	−0.0105188	+	0.0367799i
$463$	16.8934	−	6.99747i	0.785102	−	0.325200i	0.0461294	−	0.998935i	$-0.485311\pi$
$463$	16.8934	−	6.99747i	0.785102	−	0.325200i	0.738972	+	0.673736i	$0.235311\pi$
$464$	9.76558	+	26.0720i	0.453356	+	1.21036i
$465$	−3.03639	−	1.25771i	−0.140809	−	0.0583251i
$466$	4.13706	−	5.20841i	0.191645	−	0.241275i
$467$	−4.27141	+	1.29572i	−0.197657	+	0.0599587i	−0.387561	−	0.921844i	$-0.626682\pi$
$467$	−4.27141	+	1.29572i	−0.197657	+	0.0599587i	0.189904	+	0.981803i	$0.439182\pi$
$468$	−0.619071	+	9.33173i	−0.0286166	+	0.431360i
$469$	−0.193821	−	1.96790i	−0.00894984	−	0.0908693i
$470$	10.4732	−	4.53537i	0.483093	−	0.209201i
$471$	−8.08777	−	12.1042i	−0.372665	−	0.557732i
$472$	11.6957	+	1.74912i	0.538338	+	0.0805099i
$473$	6.90503	+	4.61379i	0.317494	+	0.212142i
$474$	−1.93454	−	2.79750i	−0.0888564	−	0.128494i
$475$	−25.2254	−	7.65204i	−1.15742	−	0.351100i
$476$	−2.16177	+	0.977417i	−0.0990844	+	0.0447998i
$477$	−4.48181	−	5.46110i	−0.205208	−	0.250047i
$478$	1.74837	−	21.2194i	0.0799686	−	0.970555i
$479$	−27.6632	−	27.6632i	−1.26397	−	1.26397i	−0.949155	−	0.314810i	$-0.898059\pi$
$479$	−27.6632	−	27.6632i	−1.26397	−	1.26397i	−0.314810	−	0.949155i	$-0.601941\pi$
$480$	6.45448	−	2.53583i	0.294606	−	0.115744i
$481$	28.2898	−	28.2898i	1.28991	−	1.28991i
$482$	−26.6332	−	31.4162i	−1.21311	−	1.43097i
$483$	1.28813	−	1.05714i	0.0586119	−	0.0481015i
$484$	9.33897	+	8.76082i	0.424499	+	0.398219i
$485$	−0.504582	+	1.66338i	−0.0229119	+	0.0755304i
$486$	0.253720	−	1.39127i	0.0115090	−	0.0631092i
$487$	19.8080	−	29.6447i	0.897584	−	1.34333i	−0.0413185	−	0.999146i	$-0.513156\pi$
$487$	19.8080	−	29.6447i	0.897584	−	1.34333i	0.938902	−	0.344183i	$-0.111844\pi$
$488$	−12.5983	+	13.8668i	−0.570296	+	0.627722i
$489$	13.3257	−	8.90395i	0.602609	−	0.402651i
$490$	−4.41769	+	11.1662i	−0.199571	+	0.504438i
$491$	33.5941	−	3.30873i	1.51608	−	0.149321i	0.694533	−	0.719461i	$-0.255611\pi$
$491$	33.5941	−	3.30873i	1.51608	−	0.149321i	0.821548	+	0.570140i	$0.193111\pi$
$492$	5.05912	−	10.2384i	0.228083	−	0.461582i
$493$	8.83870	+	29.1373i	0.398075	+	1.31228i
$494$	49.5226	−	5.67721i	2.22813	−	0.255430i
$495$	1.00590	−	2.42847i	0.0452120	−	0.109151i
$496$	4.72772	+	9.62534i	0.212281	+	0.432190i
$497$	1.20453	+	2.90798i	0.0540304	+	0.130441i
$498$	−0.992034	−	1.78675i	−0.0444541	−	0.0800662i
$499$	−17.2690	+	32.3080i	−0.773065	+	1.44630i	0.118282	+	0.992980i	$0.462261\pi$
$499$	−17.2690	+	32.3080i	−0.773065	+	1.44630i	−0.891347	+	0.453323i	$0.850239\pi$
$500$	−10.4024	−	18.0505i	−0.465208	−	0.807243i
$501$	−6.01064	+	7.32398i	−0.268536	+	0.327211i
$502$	23.3446	−	24.1021i	1.04192	−	1.07573i
$503$	35.9699	+	7.15485i	1.60382	+	0.319019i	0.914234	−	0.405187i	$-0.132794\pi$
$503$	35.9699	+	7.15485i	1.60382	+	0.319019i	0.689583	+	0.724206i	$0.257794\pi$
$504$	0.615484	+	0.457611i	0.0274159	+	0.0203836i
$505$	2.11461	+	10.6309i	0.0940989	+	0.473067i
$506$	3.92676	+	18.2162i	0.174566	+	0.809810i
$507$	−7.81923	+	4.17946i	−0.347264	+	0.185617i
$508$	−7.73114	+	5.53078i	−0.343014	+	0.245389i
$509$	4.19630	−	42.6057i	0.185998	−	1.88847i	−0.221353	−	0.975194i	$-0.571047\pi$
$509$	4.19630	−	42.6057i	0.185998	−	1.88847i	0.407351	−	0.913272i	$-0.366453\pi$
$510$	7.22160	−	2.31718i	0.319778	−	0.102606i
$511$	−4.07706			−0.180359
$512$	−21.2774	−	7.69897i	−0.940335	−	0.340250i
$513$	−7.53767			−0.332796
$514$	1.44745	−	0.464440i	0.0638442	−	0.0204856i
$515$	1.31575	−	13.3591i	0.0579791	−	0.588671i
$516$	6.30005	−	4.50699i	0.277344	−	0.198409i
$517$	−12.4486	+	6.65392i	−0.547489	+	0.292639i
$518$	−0.691379	−	3.20730i	−0.0303774	−	0.140921i
$519$	2.22542	+	11.1879i	0.0976849	+	0.491095i
$520$	13.0116	+	9.67409i	0.570597	+	0.424237i
$521$	−20.9923	−	4.17563i	−0.919691	−	0.182938i	−0.287527	−	0.957773i	$-0.592833\pi$
$521$	−20.9923	−	4.17563i	−0.919691	−	0.182938i	−0.632164	+	0.774835i	$0.717833\pi$
$522$	6.84821	−	7.07045i	0.299738	−	0.309465i
$523$	1.10825	−	1.35040i	0.0484602	−	0.0590490i	−0.748216	−	0.663455i	$-0.769089\pi$
$523$	1.10825	−	1.35040i	0.0484602	−	0.0590490i	0.796677	+	0.604406i	$0.206589\pi$
$524$	−8.57737	−	14.8837i	−0.374704	−	0.650198i
$525$	0.447024	−	0.836322i	0.0195097	−	0.0365001i
$526$	−11.9034	−	21.4392i	−0.519014	−	0.934794i
$527$	4.48815	+	10.8353i	0.195507	+	0.471995i
$528$	−7.69822	+	3.78117i	−0.335022	+	0.164554i
$529$	5.65038	−	13.6412i	0.245669	−	0.593097i
$530$	−12.1683	+	1.39496i	−0.528558	+	0.0605933i
$531$	−1.21369	−	4.00101i	−0.0526698	−	0.173629i
$532$	1.81092	−	3.66485i	0.0785133	−	0.158891i
$533$	26.5724	−	2.61715i	1.15098	−	0.113361i
$534$	−4.16548	+	10.5287i	−0.180258	+	0.455623i
$535$	15.0976	−	10.0879i	0.652725	−	0.436137i
$536$	13.8698	−	15.2664i	0.599085	−	0.659409i
$537$	8.36957	−	12.5260i	0.361174	−	0.540535i
$538$	1.91368	−	10.4936i	0.0825047	−	0.452413i
$539$	4.31119	−	14.2121i	0.185696	−	0.612157i
$540$	−1.78815	−	1.67745i	−0.0769499	−	0.0721862i
$541$	12.3961	−	10.1733i	0.532952	−	0.437382i	−0.329031	−	0.944319i	$-0.606722\pi$
$541$	12.3961	−	10.1733i	0.532952	−	0.437382i	0.861983	+	0.506937i	$0.169222\pi$
$542$	−25.3306	−	29.8797i	−1.08804	−	1.28344i
$543$	−13.2306	+	13.2306i	−0.567781	+	0.567781i
$544$	−22.6853	−	9.88796i	−0.972626	−	0.423943i
$545$	−7.44970	−	7.44970i	−0.319110	−	0.319110i
$546$	−0.147251	+	1.78715i	−0.00630178	+	0.0764828i
$547$	12.3020	+	14.9900i	0.525994	+	0.640926i	0.966452	−	0.256848i	$-0.0826839\pi$
$547$	12.3020	+	14.9900i	0.525994	+	0.640926i	−0.440458	+	0.897773i	$0.645184\pi$
$548$	−20.6027	+	9.31527i	−0.880104	+	0.397929i
$549$	6.33864	+	1.92281i	0.270527	+	0.0820634i
$550$	6.03158	+	8.72216i	0.257187	+	0.371914i
$551$	−43.6221	−	29.1473i	−1.85836	−	1.24172i
$552$	17.1905	+	2.57088i	0.731674	+	0.109424i
$553$	−0.362318	−	0.542248i	−0.0154073	−	0.0230587i
$554$	−25.8788	+	11.2067i	−1.09948	+	0.476125i
$555$	1.02806	+	10.4380i	0.0436386	+	0.443070i
$556$	0.211206	−	3.18367i	0.00895712	−	0.135018i
$557$	4.99575	−	1.51545i	0.211677	−	0.0642115i	−0.182665	−	0.983175i	$-0.558472\pi$
$557$	4.99575	−	1.51545i	0.211677	−	0.0642115i	0.394342	+	0.918964i	$0.370972\pi$
$558$	2.35815	−	2.96883i	0.0998284	−	0.125681i
$559$	16.7325	+	6.93081i	0.707708	+	0.293142i
$560$	1.24519	−	0.466401i	0.0526188	−	0.0197090i
$561$	−8.66597	+	3.58956i	−0.365878	+	0.151551i
$562$	1.10638	−	3.86855i	0.0466699	−	0.163185i
$563$	−9.83795	−	5.25849i	−0.414620	−	0.221619i	0.250878	−	0.968019i	$-0.419281\pi$
$563$	−9.83795	−	5.25849i	−0.414620	−	0.221619i	−0.665498	+	0.746400i	$0.731781\pi$
$564$	1.70818	+	13.0549i	0.0719272	+	0.549712i
$565$	1.47294	+	1.20881i	0.0619670	+	0.0508550i
$566$	0.478787	+	29.9859i	0.0201249	+	1.26040i
$567$	0.0529010	−	0.265951i	0.00222163	−	0.0111689i
$568$	−14.0727	+	29.6628i	−0.590477	+	1.24462i
$569$	16.0867	−	3.19985i	0.674390	−	0.134144i	0.153997	−	0.988071i	$-0.450785\pi$
$569$	16.0867	−	3.19985i	0.674390	−	0.134144i	0.520393	+	0.853927i	$0.325785\pi$
$570$	−7.08578	+	10.9801i	−0.296791	+	0.459908i
$571$	−21.0838	−	39.4450i	−0.882329	−	1.65072i	−0.751914	−	0.659262i	$-0.770869\pi$
$571$	−21.0838	−	39.4450i	−0.882329	−	1.65072i	−0.130415	−	0.991459i	$-0.541631\pi$
$572$	−17.0205	−	10.6028i	−0.711664	−	0.443325i
$573$	7.93531	+	0.781560i	0.331502	+	0.0326501i
$574$	1.00125	−	1.94737i	0.0417915	−	0.0812818i
$575$		−	21.4912i		−	0.896246i
$576$	0.765184	+	7.96332i	0.0318826	+	0.331805i
$577$			41.6027i			1.73194i	0.500092	+	0.865972i	$0.333300\pi$
$577$			41.6027i			1.73194i	−0.500092	+	0.865972i	$0.666700\pi$
$578$	−2.68821	−	1.38216i	−0.111815	−	0.0574902i
$579$	−22.2417	−	2.19062i	−0.924334	−	0.0910389i
$580$	−3.86189	−	16.6224i	−0.160356	−	0.690207i
$581$	−0.184719	−	0.345585i	−0.00766344	−	0.0143373i
$582$	−1.68487	−	1.08729i	−0.0698401	−	0.0450697i
$583$	14.8569	−	2.95523i	0.615312	−	0.122393i
$584$	−28.5218	−	31.5444i	−1.18024	−	1.30531i
$585$	1.11835	−	5.62232i	0.0462381	−	0.232455i
$586$	5.19456	−	0.0829420i	0.214585	−	0.00342630i
$587$	15.4373	+	12.6690i	0.637164	+	0.522907i	0.896593	−	0.442855i	$-0.146034\pi$
$587$	15.4373	+	12.6690i	0.637164	+	0.522907i	−0.259429	+	0.965762i	$0.583534\pi$
$588$	−10.9836	−	8.44185i	−0.452955	−	0.348136i
$589$	−17.8219	−	9.52599i	−0.734337	−	0.392511i
$590$	−6.96921	−	1.99315i	−0.286918	−	0.0820569i
$591$	22.1493	−	9.17453i	0.911099	−	0.377390i
$592$	19.9783	−	27.7865i	0.821104	−	1.14202i
$593$	29.9505	+	12.4059i	1.22992	+	0.509449i	0.900550	−	0.434753i	$-0.143164\pi$
$593$	29.9505	+	12.4059i	1.22992	+	0.509449i	0.329368	+	0.944202i	$0.393164\pi$
$594$	2.37443	+	1.88602i	0.0974241	+	0.0773843i
$595$	1.39159	−	0.422133i	0.0570495	−	0.0173058i
$596$	5.86371	−	5.13411i	0.240187	−	0.210301i
$597$	−0.635545	−	6.45280i	−0.0260111	−	0.264095i
$598$	16.1494	+	37.2928i	0.660400	+	1.52501i
$599$	5.05491	+	7.56521i	0.206538	+	0.309106i	0.920248	−	0.391335i	$-0.127987\pi$
$599$	5.05491	+	7.56521i	0.206538	+	0.309106i	−0.713710	+	0.700441i	$0.752987\pi$
$600$	9.59789	−	2.39201i	0.391832	−	0.0976534i
$601$	22.7620	+	15.2091i	0.928482	+	0.620392i	0.925150	−	0.379603i	$-0.123939\pi$
$601$	22.7620	+	15.2091i	0.928482	+	0.620392i	0.00333243	+	0.999994i	$0.498939\pi$
$602$	1.22161	−	0.844775i	0.0497893	−	0.0344305i
$603$	−6.97841	−	2.11688i	−0.284183	−	0.0862059i
$604$	−3.61532	+	9.58261i	−0.147105	+	0.389911i
$605$	−4.97926	−	6.06724i	−0.202436	−	0.246669i
$606$	−12.4619	−	1.02679i	−0.506230	−	0.0417107i
$607$	−18.1661	−	18.1661i	−0.737338	−	0.737338i	0.234724	−	0.972062i	$-0.424581\pi$
$607$	−18.1661	−	18.1661i	−0.737338	−	0.737338i	−0.972062	+	0.234724i	$0.924581\pi$
$608$	41.0237	−	11.6270i	1.66373	−	0.471536i
$609$	1.33455	−	1.33455i	0.0540788	−	0.0540788i
$610$	8.75960	−	7.42599i	0.354666	−	0.300669i
$611$	−23.7959	+	19.5288i	−0.962679	+	0.790050i
$612$	0.279329	+	8.74480i	0.0112912	+	0.353488i
$613$	13.4990	−	44.5003i	0.545220	−	1.79735i	−0.0562013	−	0.998419i	$-0.517899\pi$
$613$	13.4990	−	44.5003i	0.545220	−	1.79735i	0.601422	−	0.798932i	$-0.294601\pi$
$614$	16.7410	+	3.05299i	0.675612	+	0.123209i
$615$	−3.88898	+	5.82027i	−0.156819	+	0.234696i
$616$	−1.48745	+	0.701344i	−0.0599309	+	0.0282580i
$617$	−32.3548	+	21.6188i	−1.30256	+	0.870340i	−0.996655	−	0.0817227i	$-0.973958\pi$
$617$	−32.3548	+	21.6188i	−1.30256	+	0.870340i	−0.305901	+	0.952063i	$0.598958\pi$
$618$	14.3997	+	5.69697i	0.579243	+	0.229166i
$619$	−43.3591	+	4.27049i	−1.74275	+	0.171646i	−0.918721	−	0.394906i	$-0.870777\pi$
$619$	−43.3591	+	4.27049i	−1.74275	+	0.171646i	−0.824026	+	0.566552i	$0.808277\pi$
$620$	−2.10792	−	6.22597i	−0.0846562	−	0.250041i
$621$	−1.78390	−	5.88072i	−0.0715853	−	0.235985i
$622$	4.55127	+	39.7009i	0.182489	+	1.59186i
$623$	−0.830819	+	2.00577i	−0.0332860	+	0.0803596i
$624$	−14.8573	+	11.3630i	−0.594769	+	0.454884i
$625$	−1.80472	−	4.35697i	−0.0721887	−	0.174279i
$626$	4.68604	−	2.60177i	0.187292	−	0.103987i
$627$	7.61876	−	14.2537i	0.304264	−	0.569238i
$628$	7.55788	−	28.1171i	0.301592	−	1.12200i
$629$	23.7443	−	28.9325i	0.946747	−	1.15361i
$630$	−0.337682	−	0.327068i	−0.0134536	−	0.0130307i
$631$	4.70744	+	0.936368i	0.187400	+	0.0372762i	0.287898	−	0.957661i	$-0.407044\pi$
$631$	4.70744	+	0.936368i	0.187400	+	0.0372762i	−0.100498	+	0.994937i	$0.532044\pi$
$632$	1.66072	−	6.59666i	0.0660600	−	0.262401i
$633$	3.58349	+	18.0154i	0.142431	+	0.716048i
$634$	7.88211	−	1.69910i	0.313039	−	0.0674799i
$635$	5.13859	−	2.74663i	0.203919	−	0.108997i
$636$	2.31268	−	13.9389i	0.0917038	−	0.552713i
$637$	3.17468	−	32.2331i	0.125785	−	1.27712i
$638$	6.44830	+	20.0964i	0.255291	+	0.795626i
$639$	11.6078			0.459196
$640$	12.3195	+	6.37127i	0.486971	+	0.251847i
$641$	−47.2206			−1.86510			−0.932551	−	0.361037i	$-0.882423\pi$
$641$	−47.2206			−1.86510			−0.932551	+	0.361037i	$0.882423\pi$
$642$	6.39981	+	19.9453i	0.252580	+	0.787178i
$643$	2.27368	−	23.0850i	0.0896650	−	0.910384i	−0.840149	−	0.542355i	$-0.817533\pi$
$643$	2.27368	−	23.0850i	0.0896650	−	0.910384i	0.929814	−	0.368029i	$-0.119967\pi$
$644$	3.28781	+	0.545500i	0.129558	+	0.0214957i
$645$	−4.18740	+	2.23821i	−0.164879	+	0.0881295i
$646$	45.5859	−	9.82669i	1.79355	−	0.386626i
$647$	−0.971395	−	4.88353i	−0.0381895	−	0.191991i	0.956981	−	0.290149i	$-0.0937050\pi$
$647$	−0.971395	−	4.88353i	−0.0381895	−	0.191991i	−0.995171	+	0.0981579i	$0.968705\pi$
$648$	2.42775	−	1.45121i	0.0953711	−	0.0570091i
$649$	8.79263	+	1.74896i	0.345141	+	0.0686528i
$650$	16.6122	+	16.0900i	0.651582	+	0.631102i
$651$	0.461182	−	0.561952i	0.0180752	−	0.0220246i
$652$	30.9546	+	8.32059i	1.21228	+	0.325859i
$653$	12.0330	−	22.5121i	0.470887	−	0.880968i	−0.528598	−	0.848872i	$-0.677282\pi$
$653$	12.0330	−	22.5121i	0.470887	−	0.880968i	0.999485	−	0.0320952i	$-0.0102180\pi$
$654$	10.6259	−	5.89966i	0.415504	−	0.230695i
$655$	4.02946	+	9.72799i	0.157444	+	0.380104i
$656$	22.0713	−	5.87647i	0.861741	−	0.229438i
$657$	−5.75385	+	13.8910i	−0.224479	+	0.541941i
$658$	0.287521	+	2.50806i	0.0112088	+	0.0977745i
$659$	−0.357717	−	1.17923i	−0.0139347	−	0.0459364i	0.949697	−	0.313169i	$-0.101391\pi$
$659$	−0.357717	−	1.17923i	−0.0139347	−	0.0459364i	−0.963632	+	0.267233i	$0.913891\pi$
$660$	4.97945	−	1.68589i	0.193825	−	0.0656232i
$661$	24.9092	−	2.45334i	0.968856	−	0.0954240i	0.398807	−	0.917035i	$-0.369424\pi$
$661$	24.9092	−	2.45334i	0.968856	−	0.0954240i	0.570049	+	0.821611i	$0.306924\pi$
$662$	−44.9368	−	17.7783i	−1.74652	−	0.690975i
$663$	−17.0088	+	11.3649i	−0.660567	+	0.441377i
$664$	1.38157	−	3.84678i	0.0536152	−	0.149284i
$665$	−1.39207	+	2.08338i	−0.0539821	+	0.0807899i
$666$	−11.9034	−	2.17077i	−0.461246	−	0.0841157i
$667$	12.4163	−	40.9311i	0.480761	−	1.58486i
$668$	−18.9396	+	0.604974i	−0.732795	+	0.0234072i
$669$	3.80991	−	3.12671i	0.147300	−	0.120886i
$670$	−9.64371	+	8.17550i	−0.372569	+	0.315847i
$671$	−10.0429	+	10.0429i	−0.387700	+	0.387700i
$672$	0.122321	+	1.52904i	0.00471863	+	0.0589839i
$673$	−3.90644	−	3.90644i	−0.150582	−	0.150582i	0.627796	−	0.778378i	$-0.283957\pi$
$673$	−3.90644	−	3.90644i	−0.150582	−	0.150582i	−0.778378	+	0.627796i	$0.783957\pi$
$674$	6.24556	+	0.514601i	0.240570	+	0.0198217i
$675$	−2.21858	−	2.70334i	−0.0853930	−	0.104052i
$676$	−16.5908	−	6.25936i	−0.638106	−	0.240744i
$677$	36.4517	+	11.0575i	1.40095	+	0.424974i	0.898250	−	0.439485i	$-0.144839\pi$
$677$	36.4517	+	11.0575i	1.40095	+	0.424974i	0.502702	+	0.864459i	$0.332339\pi$
$678$	−1.80797	+	1.25025i	−0.0694346	+	0.0480157i
$679$	−0.319688	−	0.213609i	−0.0122685	−	0.00819754i
$680$	13.0012	+	7.81364i	0.498572	+	0.299639i
$681$	−10.3399	−	15.4747i	−0.396226	−	0.592994i
$682$	3.23052	+	7.46001i	0.123703	+	0.285659i
$683$	1.92840	+	19.5794i	0.0737883	+	0.749185i	0.958888	+	0.283784i	$0.0915899\pi$
$683$	1.92840	+	19.5794i	0.0737883	+	0.749185i	−0.885100	+	0.465401i	$0.845910\pi$
$684$	−9.93087	−	11.3421i	−0.379716	−	0.433677i
$685$	13.2625	−	4.02314i	0.506735	−	0.153716i
$686$	−4.18185	−	3.32166i	−0.159664	−	0.126821i
$687$	11.2209	+	4.64786i	0.428105	+	0.177327i
$688$	15.0821	+	3.54189i	0.574999	+	0.135033i
$689$	30.5208	−	12.6421i	1.16275	−	0.481627i
$690$	−10.2434	−	2.92956i	−0.389960	−	0.111526i
$691$	−20.4159	−	10.9125i	−0.776659	−	0.415133i	0.0349092	−	0.999390i	$-0.488886\pi$
$691$	−20.4159	−	10.9125i	−0.776659	−	0.415133i	−0.811568	+	0.584258i	$0.801386\pi$
$692$	−13.9028	+	18.0887i	−0.528504	+	0.687629i
$693$	0.449442	+	0.368848i	0.0170729	+	0.0140114i
$694$	−21.2155	+	0.338750i	−0.805331	+	0.0128588i
$695$	−0.381543	+	1.91814i	−0.0144727	+	0.0727594i
$696$	19.6616	+	0.989371i	0.745271	+	0.0375020i
$697$	24.4994	−	4.87324i	0.927982	−	0.184587i
$698$	−19.0424	−	12.2885i	−0.720764	−	0.465128i
$699$	−2.21714	−	4.14797i	−0.0838599	−	0.156891i
$700$	1.84739	−	0.429205i	0.0698247	−	0.0162224i
$701$	−17.7186	−	1.74513i	−0.669221	−	0.0659125i	−0.242300	−	0.970201i	$-0.577902\pi$
$701$	−17.7186	−	1.74513i	−0.669221	−	0.0659125i	−0.426921	+	0.904289i	$0.640402\pi$
$702$	5.88120	+	3.02386i	0.221972	+	0.114128i
$703$			64.4906i			2.43231i
$704$	−15.8320	−	6.60203i	−0.596692	−	0.248823i
$705$		−	8.07024i		−	0.303943i
$706$	−20.9439	+	40.7345i	−0.788233	+	1.53306i
$707$	−2.38600	−	0.235000i	−0.0897347	−	0.00883810i
$708$	4.42138	−	7.09759i	0.166166	−	0.266744i
$709$	3.21425	+	6.01343i	0.120714	+	0.225839i	0.935019	−	0.354597i	$-0.115382\pi$
$709$	3.21425	+	6.01343i	0.120714	+	0.225839i	−0.814306	+	0.580436i	$0.802882\pi$
$710$	10.9119	−	16.9091i	0.409515	−	0.634586i
$711$	−2.35883	+	0.469201i	−0.0884631	+	0.0175964i
$712$	−21.3309	+	7.60368i	−0.799408	+	0.284960i
$713$	3.21416	−	16.1587i	0.120371	−	0.605147i
$714$	0.0267827	+	1.67737i	0.00100232	+	0.0627740i
$715$	9.50141	+	7.79760i	0.355332	+	0.291614i
$716$	29.8750	−	3.90901i	1.11648	−	0.146086i
$717$	−13.2776	−	7.09700i	−0.495859	−	0.265042i
$718$	−9.38016	+	32.7984i	−0.350064	+	1.22403i
$719$	16.8420	−	6.97617i	0.628099	−	0.260167i	−0.0458459	−	0.998949i	$-0.514598\pi$
$719$	16.8420	−	6.97617i	0.628099	−	0.260167i	0.673945	+	0.738781i	$0.264598\pi$
$720$	0.168219	−	4.90073i	0.00626915	−	0.182639i
$721$	2.74322	+	1.13628i	0.102163	+	0.0423172i
$722$	−33.2634	+	41.8775i	−1.23794	+	1.55852i
$723$	−27.8690	+	8.45398i	−1.03646	+	0.314407i
$724$	−37.3398	−	2.47714i	−1.38772	−	0.0920620i
$725$	−2.38584	−	24.2238i	−0.0886077	−	0.899649i
$726$	8.30889	−	3.59812i	0.308372	−	0.133539i
$727$	−16.6268	−	24.8838i	−0.616655	−	0.922890i	0.383344	−	0.923605i	$-0.374772\pi$
$727$	−16.6268	−	24.8838i	−0.616655	−	0.922890i	−1.00000		0.000715586i	$0.999772\pi$
$728$	−2.88317	+	2.13299i	−0.106857	+	0.0790538i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	14.8262	+	21.4399i	0.548742	+	0.793527i
$731$	16.2138	+	4.91840i	0.599689	+	0.181914i
$732$	5.45786	+	12.0712i	0.201728	+	0.446165i
$733$	7.82637	+	9.53646i	0.289073	+	0.352237i	0.897217	−	0.441590i	$-0.145585\pi$
$733$	7.82637	+	9.53646i	0.289073	+	0.352237i	−0.608143	+	0.793827i	$0.708085\pi$
$734$	−0.891404	+	10.8187i	−0.0329023	+	0.399326i
$735$	6.00417	+	6.00417i	0.221467	+	0.221467i
$736$	18.7799	+	29.2540i	0.692237	+	1.07832i
$737$	11.0565	−	11.0565i	0.407271	−	0.407271i
$738$	−5.22189	−	6.15967i	−0.192220	−	0.226741i
$739$	−28.2001	+	23.1432i	−1.03736	+	0.851336i	−0.989062	−	0.147497i	$-0.952878\pi$
$739$	−28.2001	+	23.1432i	−1.03736	+	0.851336i	−0.0482934	+	0.998833i	$0.515378\pi$
$740$	−14.3519	+	15.2990i	−0.527587	+	0.562404i
$741$	10.2317	−	33.7294i	0.375871	−	1.23908i
$742$	0.486046	−	2.66522i	0.0178433	−	0.0978435i
$743$	−20.5217	+	30.7129i	−0.752869	+	1.12675i	0.235081	+	0.971976i	$0.424465\pi$
$743$	−20.5217	+	30.7129i	−0.752869	+	1.12675i	−0.987950	+	0.154773i	$0.950535\pi$
$744$	7.57413	−	0.363057i	0.277681	−	0.0133103i
$745$	−3.97208	+	2.65406i	−0.145526	+	0.0972371i
$746$	−7.41729	+	18.7481i	−0.271566	+	0.686415i
$747$	−1.43814	+	0.141644i	−0.0526187	+	0.00518249i
$748$	−16.8187	−	8.31066i	−0.614953	−	0.303868i
$749$	1.16589	+	3.84342i	0.0426006	+	0.140435i
$750$	−14.6356	+	1.67780i	−0.534416	+	0.0612648i
$751$	4.44883	−	10.7404i	0.162340	−	0.391924i	−0.821688	−	0.569938i	$-0.806967\pi$
$751$	4.44883	−	10.7404i	0.162340	−	0.391924i	0.984028	+	0.178014i	$0.0569673\pi$
$752$	−17.3936	+	19.7702i	−0.634278	+	0.720944i
$753$	−9.07969	−	21.9203i	−0.330882	−	0.798821i
$754$	22.3428	+	40.2416i	0.813678	+	1.46551i
$755$	2.95934	−	5.53653i	0.107701	−	0.201495i
$756$	0.469881	−	0.270789i	0.0170894	−	0.00984849i
$757$	−10.3734	+	12.6400i	−0.377028	+	0.459410i	−0.926607	−	0.376032i	$-0.877288\pi$
$757$	−10.3734	+	12.6400i	−0.377028	+	0.459410i	0.549578	+	0.835442i	$0.314788\pi$
$758$	1.84791	−	1.90788i	0.0671192	−	0.0692973i
$759$	12.9235	+	2.57064i	0.469093	+	0.0933085i
$760$	−25.8576	+	3.80417i	−0.937954	+	0.137992i
$761$	−7.14684	−	35.9296i	−0.259073	−	1.30245i	−0.862918	−	0.505345i	$-0.831365\pi$
$761$	−7.14684	−	35.9296i	−0.259073	−	1.30245i	0.603845	−	0.797102i	$-0.293635\pi$
$762$	1.41640	+	6.57068i	0.0513109	+	0.238031i
$763$	2.05521	−	1.09853i	0.0744035	−	0.0397695i
$764$	9.27872	+	12.9702i	0.335692	+	0.469244i
$765$	0.525653	−	5.33705i	0.0190050	−	0.192961i
$766$	25.4332	−	8.16069i	0.918937	−	0.294858i
$767$	19.5511			0.705948
$768$	−10.9745	+	11.6431i	−0.396008	+	0.420132i
$769$	−15.7610			−0.568355			−0.284178	−	0.958772i	$-0.591721\pi$
$769$	−15.7610			−0.568355			−0.284178	+	0.958772i	$0.591721\pi$
$770$	0.959800	−	0.307969i	0.0345888	−	0.0110984i
$771$	0.105358	−	1.06972i	0.00379439	−	0.0385251i
$772$	−26.0071	−	36.3538i	−0.936017	−	1.30840i
$773$	−31.6710	+	16.9285i	−1.13913	+	0.608876i	−0.929470	−	0.368899i	$-0.879735\pi$
$773$	−31.6710	+	16.9285i	−1.13913	+	0.608876i	−0.209658	+	0.977775i	$0.567235\pi$
$774$	−1.15422	−	5.35440i	−0.0414874	−	0.192460i
$775$	−1.82910	−	9.19551i	−0.0657032	−	0.330312i
$776$	−0.583738	−	3.96777i	−0.0209550	−	0.142435i
$777$	−2.27542	−	0.452609i	−0.0816302	−	0.0162373i
$778$	23.9141	−	24.6902i	0.857363	−	0.885187i
$779$	−27.3047	+	33.2708i	−0.978291	+	1.19205i
$780$	9.93348	−	5.72459i	0.355676	−	0.204973i
$781$	−11.7326	+	21.9502i	−0.419827	+	0.785441i
$782$	18.4551	+	33.2395i	0.659953	+	1.18864i
$783$	−2.66356	−	6.43040i	−0.0951879	−	0.229804i
$784$	−1.76818	−	27.6494i	−0.0631492	−	0.987479i
$785$	−6.82944	+	16.4877i	−0.243753	+	0.588473i
$786$	−12.0679	+	1.38345i	−0.430447	+	0.0493460i
$787$	−8.09856	−	26.6974i	−0.288682	−	0.951659i	−0.974595	−	0.223975i	$-0.928097\pi$
$787$	−8.09856	−	26.6974i	−0.288682	−	0.951659i	0.685913	−	0.727684i	$-0.259403\pi$
$788$	42.9868	+	21.2411i	1.53134	+	0.756684i
$789$	−17.2562	+	1.69959i	−0.614338	+	0.0605070i
$790$	−1.53393	+	3.87719i	−0.0545749	+	0.137944i
$791$	−0.350443	+	0.234159i	−0.0124603	+	0.00832573i
$792$	0.290369	+	6.05769i	0.0103178	+	0.215251i
$793$	−17.2082	+	25.7540i	−0.611083	+	0.914550i
$794$	1.81735	−	9.96540i	0.0644954	−	0.353659i
$795$	−2.51406	+	8.28773i	−0.0891644	+	0.293936i
$796$	8.87236	−	9.45787i	0.314472	−	0.335225i
$797$	−6.63086	+	5.44180i	−0.234877	+	0.192759i	−0.744468	−	0.667658i	$-0.767297\pi$
$797$	−6.63086	+	5.44180i	−0.234877	+	0.192759i	0.509591	+	0.860417i	$0.329797\pi$
$798$	−1.86918	−	2.20486i	−0.0661684	−	0.0780514i
$799$	−20.3637	+	20.3637i	−0.720416	+	0.720416i
$800$	16.2445	+	11.2907i	0.574330	+	0.399187i
$801$	5.66139	+	5.66139i	0.200036	+	0.200036i
$802$	0.0643585	−	0.781099i	0.00227258	−	0.0275816i
$803$	−20.4521	−	24.9210i	−0.721740	−	0.879442i
$804$	−6.00872	−	13.2896i	−0.211911	−	0.468687i
$805$	−1.95486	−	0.592999i	−0.0688996	−	0.0209005i
$806$	10.0839	+	14.5821i	0.355189	+	0.513632i
$807$	−6.27136	−	4.19039i	−0.220762	−	0.147509i
$808$	−14.8735	−	20.1045i	−0.523247	−	0.707275i
$809$	21.0993	+	31.5773i	0.741811	+	1.11020i	0.989942	+	0.141473i	$0.0451838\pi$
$809$	21.0993	+	31.5773i	0.741811	+	1.11020i	−0.248131	+	0.968727i	$0.579816\pi$
$810$	−1.59092	+	0.688941i	−0.0558993	+	0.0242069i
$811$	2.25550	+	22.9004i	0.0792012	+	0.804143i	0.949947	+	0.312410i	$0.101136\pi$
$811$	2.25550	+	22.9004i	0.0792012	+	0.804143i	−0.870746	+	0.491733i	$0.836364\pi$
$812$	3.76641	+	0.249865i	0.132175	+	0.00876854i
$813$	−26.5060	+	8.04051i	−0.929607	+	0.281993i
$814$	16.1363	−	20.3151i	0.565579	−	0.712044i
$815$	−18.1516	−	7.51864i	−0.635823	−	0.263367i
$816$	−12.7905	+	11.9416i	−0.447757	+	0.418039i
$817$	−26.9719	+	11.1721i	−0.943626	+	0.390863i
$818$	−12.1164	+	42.3659i	−0.423640	+	1.48129i
$819$	1.11826	+	0.597724i	0.0390753	+	0.0208862i
$820$	−13.8816	+	1.81635i	−0.484768	+	0.0634296i
$821$	−15.4260	−	12.6598i	−0.538369	−	0.441828i	0.325502	−	0.945542i	$-0.394467\pi$
$821$	−15.4260	−	12.6598i	−0.538369	−	0.441828i	−0.863871	+	0.503713i	$0.831967\pi$
$822$	0.255253	+	15.9862i	0.00890296	+	0.557582i
$823$	6.39011	−	32.1252i	0.222745	−	1.11982i	−0.693887	−	0.720084i	$-0.744103\pi$
$823$	6.39011	−	32.1252i	0.222745	−	1.11982i	0.916632	−	0.399732i	$-0.130897\pi$
$824$	10.3993	+	29.1734i	0.362275	+	1.01630i
$825$	7.35445	−	1.46289i	0.256049	−	0.0509313i
$826$	0.869375	−	1.34719i	0.0302494	−	0.0468746i
$827$	5.50745	+	10.3037i	0.191513	+	0.358295i	0.959291	−	0.282421i	$-0.0911375\pi$
$827$	5.50745	+	10.3037i	0.191513	+	0.358295i	−0.767778	+	0.640716i	$0.778638\pi$
$828$	6.49859	−	10.4321i	0.225842	−	0.362541i
$829$	40.6245	+	4.00116i	1.41095	+	0.138966i	0.774607	−	0.632443i	$-0.217948\pi$
$829$	40.6245	+	4.00116i	1.41095	+	0.138966i	0.636339	+	0.771409i	$0.280448\pi$
$830$	−1.14559	+	2.22809i	−0.0397639	+	0.0773382i
$831$			19.9412i			0.691751i
$832$	−36.6727	−	7.38545i	−1.27140	−	0.256044i
$833$		−	30.3007i		−	1.04986i
$834$	−2.00647	−	1.03164i	−0.0694782	−	0.0357226i
$835$	11.5590	+	1.13847i	0.400017	+	0.0393982i
$836$	31.4856	−	7.31508i	1.08895	−	0.252997i
$837$	−1.26378	−	2.36437i	−0.0436827	−	0.0817247i
$838$	7.52080	+	4.85338i	0.259802	+	0.167657i
$839$	−3.15908	+	0.628379i	−0.109063	+	0.0216941i	−0.249320	−	0.968421i	$-0.580207\pi$
$839$	−3.15908	+	0.628379i	−0.109063	+	0.0216941i	0.140257	+	0.990115i	$0.455207\pi$
$840$	0.0472520	−	0.939031i	0.00163035	−	0.0323997i
$841$	3.79346	−	19.0710i	0.130809	−	0.657621i
$842$	−29.1829	+	0.465966i	−1.00571	+	0.0160583i
$843$	−2.19933	−	1.80494i	−0.0757489	−	0.0621655i
$844$	−22.3870	+	29.1274i	−0.770592	+	1.00261i
$845$	9.58561	+	5.12362i	0.329755	+	0.176258i
$846$	8.95104	+	2.55995i	0.307743	+	0.0880128i
$847$	1.60396	−	0.664382i	0.0551127	−	0.0228284i
$848$	24.0212	−	14.8845i	0.824890	−	0.511136i
$849$	19.5917	+	8.11516i	0.672386	+	0.278511i
$850$	16.9417	+	13.4568i	0.581094	+	0.461565i
$851$	−50.3141	+	15.2626i	−1.72475	+	0.523196i
$852$	15.2932	+	17.4665i	0.523937	+	0.598392i
$853$	2.38430	+	24.2082i	0.0816370	+	0.828874i	0.945603	+	0.325324i	$0.105473\pi$
$853$	2.38430	+	24.2082i	0.0816370	+	0.828874i	−0.863966	+	0.503551i	$0.832027\pi$
$854$	1.00941	+	2.33095i	0.0345411	+	0.0797634i
$855$	5.13372	+	7.68316i	0.175570	+	0.262758i
$856$	−21.5805	+	35.9079i	−0.737605	+	1.22731i
$857$	8.02276	+	5.36064i	0.274052	+	0.183116i	0.685000	−	0.728543i	$-0.259802\pi$
$857$	8.02276	+	5.36064i	0.274052	+	0.183116i	−0.410948	+	0.911659i	$0.634802\pi$
$858$	−11.6626	+	8.06494i	−0.398154	+	0.275333i
$859$	−21.2698	−	6.45213i	−0.725717	−	0.220144i	−0.0942520	−	0.995548i	$-0.530046\pi$
$859$	−21.2698	−	6.45213i	−0.725717	−	0.220144i	−0.631465	+	0.775405i	$0.717546\pi$
$860$	−8.88478	−	3.35205i	−0.302969	−	0.114304i
$861$	−0.982263	−	1.19689i	−0.0334754	−	0.0407899i
$862$	22.0950	+	1.82051i	0.752558	+	0.0620069i
$863$	18.5943	+	18.5943i	0.632956	+	0.632956i	0.948808	−	0.315852i	$-0.102290\pi$
$863$	18.5943	+	18.5943i	0.632956	+	0.632956i	−0.315852	+	0.948808i	$0.602290\pi$
$864$	5.38224	+	1.74113i	0.183107	+	0.0592344i
$865$	9.88818	−	9.88818i	0.336208	−	0.336208i
$866$	16.4029	−	13.9056i	0.557392	−	0.472532i
$867$	−1.65222	+	1.35594i	−0.0561124	+	0.0460502i
$868$	1.45319	−	0.0464183i	0.0493245	−	0.00157554i
$869$	1.49695	−	4.93479i	0.0507806	−	0.167401i
$870$	−11.8711	−	2.16488i	−0.402467	−	0.0733963i
$871$	18.9451	−	28.3533i	0.641930	−	0.960716i
$872$	22.8769	+	8.21623i	0.774711	+	0.278237i
$873$	−1.17896	+	0.787754i	−0.0399016	+	0.0266614i
$874$	−60.9145	−	24.0996i	−2.06046	−	0.815181i
$875$	−2.81101	+	0.276860i	−0.0950293	+	0.00935957i
$876$	−28.4829	+	9.64344i	−0.962347	+	0.325822i
$877$	14.8215	+	48.8598i	0.500485	+	1.64988i	0.735228	+	0.677820i	$0.237075\pi$
$877$	14.8215	+	48.8598i	0.500485	+	1.64988i	−0.234743	+	0.972058i	$0.575425\pi$
$878$	4.12946	+	36.0215i	0.139363	+	1.21567i
$879$	1.40582	−	3.39394i	0.0474170	−	0.114475i
$880$	9.09722	+	5.27155i	0.306667	+	0.177704i
$881$	−5.90029	−	14.2446i	−0.198786	−	0.479912i	0.792781	−	0.609506i	$-0.208632\pi$
$881$	−5.90029	−	14.2446i	−0.198786	−	0.479912i	−0.991567	+	0.129595i	$0.958632\pi$
$882$	−8.56405	+	4.75490i	−0.288366	+	0.160106i
$883$	−2.55923	+	4.78799i	−0.0861251	+	0.161129i	−0.921296	−	0.388861i	$-0.872868\pi$
$883$	−2.55923	+	4.78799i	−0.0861251	+	0.161129i	0.835171	+	0.549990i	$0.185368\pi$
$884$	−39.5101	−	10.6203i	−1.32887	−	0.357200i
$885$	−3.25162	+	3.96210i	−0.109302	+	0.133185i
$886$	−23.9897	−	23.2356i	−0.805948	−	0.780615i
$887$	−13.0294	−	2.59172i	−0.437486	−	0.0870213i	−0.0285665	−	0.999592i	$-0.509094\pi$
$887$	−13.0294	−	2.59172i	−0.437486	−	0.0870213i	−0.408919	+	0.912571i	$0.634094\pi$
$888$	−12.4163	−	20.7713i	−0.416662	−	0.697039i
$889$	0.251433	+	1.26404i	0.00843279	+	0.0423945i
$890$	13.5690	−	2.92498i	0.454833	−	0.0980456i
$891$	1.89099	−	1.01076i	0.0633507	−	0.0338617i
$892$	9.72439	+	1.61343i	0.325597	+	0.0540217i
$893$	4.86374	−	49.3823i	0.162759	−	1.65252i
$894$	−1.68375	−	5.24748i	−0.0563130	−	0.175502i
$895$	−18.4680			−0.617318
$896$	−2.13962	+	2.19856i	−0.0714798	+	0.0734488i
$897$	28.7363			0.959479
$898$	15.4681	+	48.2071i	0.516177	+	1.60869i
$899$	1.82899	−	18.5700i	0.0610002	−	0.619345i
$900$	1.14482	−	6.90000i	0.0381606	−	0.230000i
$901$	27.2562	−	14.5688i	0.908037	−	0.485356i
$902$	16.9260	−	3.64863i	0.563573	−	0.121486i
$903$	−0.204891	−	1.03006i	−0.00681834	−	0.0342781i
$904$	−4.26328	−	1.07329i	−0.141795	−	0.0356971i
$905$	22.4970	+	4.47494i	0.747827	+	0.148752i
$906$	5.20207	+	5.03855i	0.172827	+	0.167395i
$907$	20.6191	−	25.1245i	0.684646	−	0.834244i	−0.308487	−	0.951228i	$-0.599823\pi$
$907$	20.6191	−	25.1245i	0.684646	−	0.834244i	0.993134	+	0.116984i	$0.0373228\pi$
$908$	9.66245	−	35.9467i	0.320660	−	1.19293i
$909$	−4.16797	+	7.79773i	−0.138243	+	0.258634i
$910$	1.92193	−	1.06709i	0.0637113	−	0.0353736i
$911$	−2.79355	−	6.74422i	−0.0925544	−	0.223446i	0.870822	−	0.491598i	$-0.163587\pi$
$911$	−2.79355	−	6.74422i	−0.0925544	−	0.223446i	−0.963377	+	0.268152i	$0.913587\pi$
$912$	3.98289	−	29.8865i	0.131887	−	0.989640i
$913$	1.18576	−	2.86268i	0.0392430	−	0.0947409i
$914$	0.166274	+	1.45041i	0.00549984	+	0.0479754i
$915$	−2.35717	−	7.77056i	−0.0779258	−	0.256887i
$916$	7.78980	+	23.0080i	0.257382	+	0.760205i
$917$	−2.31784	+	0.228287i	−0.0765418	+	0.00753871i
$918$	5.75280	+	2.27598i	0.189871	+	0.0751185i
$919$	23.6728	−	15.8177i	0.780895	−	0.521777i	−0.100058	−	0.994982i	$-0.531903\pi$
$919$	23.6728	−	15.8177i	0.780895	−	0.521777i	0.880953	+	0.473204i	$0.156903\pi$
$920$	−9.08749	−	19.2732i	−0.299606	−	0.635419i
$921$	6.68513	−	10.0050i	0.220282	−	0.329676i
$922$	−3.46055	−	0.631086i	−0.113967	−	0.0207837i
$923$	−15.7565	+	51.9421i	−0.518630	+	1.70969i
$924$	0.0371248	+	1.16224i	0.00122131	+	0.0382350i
$925$	−23.1292	+	18.9816i	−0.760483	+	0.624113i
$926$	19.7250	−	16.7220i	0.648205	−	0.549519i
$927$	7.74287	−	7.74287i	0.254309	−	0.254309i
$928$	24.4154	+	30.8888i	0.801474	+	1.01397i
$929$	19.5226	+	19.5226i	0.640515	+	0.640515i	0.950682	−	0.310167i	$-0.100385\pi$
$929$	19.5226	+	19.5226i	0.640515	+	0.640515i	−0.310167	+	0.950682i	$0.600385\pi$
$930$	−4.63221	−	0.381669i	−0.151896	−	0.0125154i
$931$	33.1213	+	40.3585i	1.08551	+	1.32270i
$932$	3.32049	−	8.80113i	0.108766	−	0.288291i
$933$	27.0399	+	8.20248i	0.885248	+	0.268537i
$934$	−5.19200	+	3.59039i	−0.169887	+	0.117481i
$935$	9.56102	+	6.38847i	0.312679	+	0.208925i
$936$	3.19840	+	12.8335i	0.104543	+	0.419477i
$937$	14.2402	+	21.3120i	0.465209	+	0.696234i	0.987691	−	0.156416i	$-0.0499941\pi$
$937$	14.2402	+	21.3120i	0.465209	+	0.696234i	−0.522483	+	0.852650i	$0.674994\pi$
$938$	−1.11129	−	2.56621i	−0.0362848	−	0.0837899i
$939$	−0.371484	−	3.77175i	−0.0121229	−	0.123086i
$940$	12.1435	−	10.6325i	0.396077	−	0.346795i
$941$	21.6556	−	6.56914i	0.705951	−	0.214148i	0.0831602	−	0.996536i	$-0.473499\pi$
$941$	21.6556	−	6.56914i	0.705951	−	0.214148i	0.622791	+	0.782388i	$0.285999\pi$
$942$	−16.1209	−	12.8049i	−0.525247	−	0.417205i
$943$	−32.4192	−	13.4285i	−1.05571	−	0.437291i
$944$	16.5051	−	2.69810i	0.537195	−	0.0878158i
$945$	−0.307114	+	0.127211i	−0.00999042	+	0.00413817i
$946$	11.2918	+	3.22938i	0.367127	+	0.104996i
$947$	43.4906	+	23.2462i	1.41326	+	0.755401i	0.988687	−	0.149995i	$-0.0479258\pi$
$947$	43.4906	+	23.2462i	1.41326	+	0.755401i	0.424569	+	0.905396i	$0.360426\pi$
$948$	−3.81378	−	2.93122i	−0.123866	−	0.0952017i
$949$	−54.3489	−	44.6030i	−1.76424	−	1.44787i
$950$	−37.2746	+	0.595166i	−1.20935	+	0.0193097i
$951$	1.11231	−	5.59197i	0.0360692	−	0.181332i
$952$	−2.48870	+	2.25023i	−0.0806591	+	0.0729305i
$953$	34.5013	−	6.86274i	1.11761	−	0.222306i	0.398475	−	0.917179i	$-0.369540\pi$
$953$	34.5013	−	6.86274i	1.11761	−	0.222306i	0.719132	+	0.694873i	$0.244540\pi$
$954$	−8.39479	−	5.41738i	−0.271791	−	0.175394i
$955$	−4.60790	−	8.62077i	−0.149108	−	0.278962i
$956$	−6.81411	−	29.3294i	−0.220384	−	0.948579i
$957$	14.8521	+	1.46280i	0.480099	+	0.0472857i
$958$	−49.2037	−	25.2984i	−1.58970	−	0.817354i
$959$			3.06558i			0.0989928i
$960$	7.59587	−	6.20357i	0.245156	−	0.200219i
$961$			23.8126i			0.768148i
$962$	25.8714	−	50.3183i	0.834128	−	1.62233i
$963$	14.7404	+	1.45180i	0.475002	+	0.0467836i
$964$	−49.4383	−	30.7972i	−1.59230	−	0.991910i
$965$	12.9154	+	24.1630i	0.415761	+	0.777833i
$966$	1.27782	−	1.98011i	0.0411130	−	0.0637089i
$967$	−4.60837	+	0.916662i	−0.148195	+	0.0294779i	−0.268630	−	0.963243i	$-0.586571\pi$
$967$	−4.60837	+	0.916662i	−0.148195	+	0.0294779i	0.120435	+	0.992721i	$0.461571\pi$
$968$	16.3611	+	7.76208i	0.525867	+	0.249483i
$969$	6.43301	−	32.3409i	0.206658	−	1.03894i
$970$	0.0392458	+	2.45792i	0.00126011	+	0.0789190i
$971$	−28.2962	−	23.2221i	−0.908069	−	0.745233i	0.0593967	−	0.998234i	$-0.481082\pi$
$971$	−28.2962	−	23.2221i	−0.908069	−	0.745233i	−0.967466	+	0.253001i	$0.918582\pi$
$972$	−0.259479	−	1.98310i	−0.00832279	−	0.0636078i
$973$	−0.381513	−	0.203923i	−0.0122307	−	0.00653747i
$974$	13.8644	−	48.4779i	0.444244	−	1.55333i
$975$	15.1084	−	6.25808i	0.483854	−	0.200419i
$976$	−10.9731	+	24.1164i	−0.351242	+	0.771946i
$977$	0.422172	+	0.174869i	0.0135065	+	0.00559457i	0.389426	−	0.921058i	$-0.372673\pi$
$977$	0.422172	+	0.174869i	0.0135065	+	0.00559457i	−0.375920	+	0.926652i	$0.622673\pi$
$978$	14.0971	−	17.7477i	0.450775	−	0.567510i
$979$	−16.4280	+	4.98337i	−0.525040	+	0.159269i
$980$	−1.12415	+	16.9451i	−0.0359095	+	0.541292i
$981$	−0.842364	−	8.55266i	−0.0268946	−	0.273065i
$982$	43.8079	−	18.9708i	1.39797	−	0.605382i
$983$	22.7614	+	34.0648i	0.725975	+	1.08650i	0.992449	+	0.122657i	$0.0391414\pi$
$983$	22.7614	+	34.0648i	0.725975	+	1.08650i	−0.266474	+	0.963842i	$0.585859\pi$
$984$	2.38878	−	15.9729i	0.0761516	−	0.509196i
$985$	−24.4369	−	16.3282i	−0.778625	−	0.520261i
$986$	24.4917	+	35.4170i	0.779974	+	1.12791i
$987$	1.70822	+	0.518183i	0.0543732	+	0.0164939i
$988$	64.2337	−	29.0425i	2.04355	−	0.923965i
$989$	−15.0995	−	18.3988i	−0.480136	−	0.585048i
$990$	0.305254	−	3.70478i	0.00970162	−	0.117746i
$991$	−20.0242	−	20.0242i	−0.636089	−	0.636089i	0.313499	−	0.949588i	$-0.398499\pi$
$991$	−20.0242	−	20.0242i	−0.636089	−	0.636089i	−0.949588	+	0.313499i	$0.898499\pi$
$992$	10.5252	+	10.9187i	0.334175	+	0.346668i
$993$	−24.1629	+	24.1629i	−0.766787	+	0.766787i
$994$	2.87848	+	3.39542i	0.0912999	+	0.107696i
$995$	−6.14449	+	5.04265i	−0.194793	+	0.159863i
$996$	−2.10788	−	1.97739i	−0.0667908	−	0.0626559i
$997$	9.35887	−	30.8521i	0.296399	−	0.977095i	−0.674635	−	0.738151i	$-0.735699\pi$
$997$	9.35887	−	30.8521i	0.296399	−	0.977095i	0.971033	−	0.238943i	$-0.0768010\pi$
$998$	−9.29468	+	50.9672i	−0.294218	+	1.61334i
$999$	−4.75333	+	7.11387i	−0.150389	+	0.225073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.29	✓	512
128.53	even	32	inner	384.2.v.a.181.29	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.29	✓	512	1.1	even	1	trivial
384.2.v.a.181.29	yes	512	128.53	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.34659 - 0.432078i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.62662 - 1.16367i) q^{4} +(-1.08115 + 0.577887i) q^{5} +(-0.298008 - 1.38246i) q^{6} +(-0.0529010 - 0.265951i) q^{7} +(1.68759 - 2.26981i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.34659 - 0.432078i) q^{2} +(0.0980171 - 0.995185i) q^{3} +(1.62662 - 1.16367i) q^{4} +(-1.08115 + 0.577887i) q^{5} +(-0.298008 - 1.38246i) q^{6} +(-0.0529010 - 0.265951i) q^{7} +(1.68759 - 2.26981i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-1.20617 + 1.24532i) q^{10} +(1.36025 - 1.65747i) q^{11} +(-0.998625 - 1.73284i) q^{12} +(2.20431 - 4.12397i) q^{13} +(-0.186148 - 0.335270i) q^{14} +(0.469133 + 1.13259i) q^{15} +(1.29177 - 3.78568i) q^{16} +(1.67410 - 4.04163i) q^{17} +(-1.40501 + 0.161069i) q^{18} +(2.18807 + 7.21310i) q^{19} +(-1.08615 + 2.19810i) q^{20} +(-0.269856 + 0.0265785i) q^{21} +(1.11555 - 2.81967i) q^{22} +(-5.10966 + 3.41417i) q^{23} +(-2.09346 - 1.90195i) q^{24} +(-1.94292 + 2.90778i) q^{25} +(1.18643 - 6.50574i) q^{26} +(-0.290285 + 0.956940i) q^{27} +(-0.395528 - 0.371042i) q^{28} +(-5.38032 + 4.41551i) q^{29} +(1.12110 + 1.32243i) q^{30} +(-1.89571 + 1.89571i) q^{31} +(0.103775 - 5.65590i) q^{32} +(-1.51616 - 1.51616i) q^{33} +(0.508027 - 6.16577i) q^{34} +(0.210884 + 0.256962i) q^{35} +(-1.82238 + 0.823968i) q^{36} +(8.18737 + 2.48361i) q^{37} +(6.06306 + 8.76769i) q^{38} +(-3.88805 - 2.59791i) q^{39} +(-0.512852 + 3.42924i) q^{40} +(3.17234 + 4.74774i) q^{41} +(-0.351902 + 0.152389i) q^{42} +(0.379630 + 3.85445i) q^{43} +(0.283867 - 4.27895i) q^{44} +(1.17312 - 0.355861i) q^{45} +(-5.40544 + 6.80526i) q^{46} +(-6.08199 - 2.51924i) q^{47} +(-3.64083 - 1.65661i) q^{48} +(6.39923 - 2.65065i) q^{49} +(-1.35993 + 4.75509i) q^{50} +(-3.85808 - 2.06219i) q^{51} +(-1.21336 - 9.27320i) q^{52} +(5.46110 + 4.48181i) q^{53} +(0.0225780 + 1.41403i) q^{54} +(-0.512805 + 2.57805i) q^{55} +(-0.692933 - 0.328743i) q^{56} +(7.39284 - 1.47053i) q^{57} +(-5.33725 + 8.27061i) q^{58} +(1.97093 + 3.68735i) q^{59} +(2.08105 + 1.29637i) q^{60} +(-6.59197 - 0.649252i) q^{61} +(-1.73365 + 3.37183i) q^{62} +0.271162i q^{63} +(-2.30405 - 7.66103i) q^{64} +5.73247i q^{65} +(-2.69675 - 1.38655i) q^{66} +(7.25731 + 0.714782i) q^{67} +(-1.97999 - 8.52228i) q^{68} +(2.89689 + 5.41970i) q^{69} +(0.395002 + 0.254905i) q^{70} +(-11.3847 + 2.26456i) q^{71} +(-2.09799 + 1.89696i) q^{72} +(2.93329 - 14.7466i) q^{73} +(12.0982 - 0.193172i) q^{74} +(2.70334 + 2.21858i) q^{75} +(11.9528 + 9.18678i) q^{76} +(-0.512765 - 0.274079i) q^{77} +(-6.35812 - 1.81839i) q^{78} +(2.22197 - 0.920371i) q^{79} +(0.791097 + 4.83938i) q^{80} +(0.923880 + 0.382683i) q^{81} +(6.32324 + 5.02257i) q^{82} +(1.38287 - 0.419490i) q^{83} +(-0.408024 + 0.357255i) q^{84} +(0.525653 + 5.33705i) q^{85} +(2.17663 + 5.02634i) q^{86} +(3.86689 + 5.78721i) q^{87} +(-1.46659 - 5.88465i) q^{88} +(-6.65710 - 4.44813i) q^{89} +(1.42595 - 0.986077i) q^{90} +(-1.21339 - 0.368077i) q^{91} +(-4.33852 + 11.4995i) q^{92} +(1.70077 + 2.07239i) q^{93} +(-9.27847 - 0.764497i) q^{94} +(-6.53399 - 6.53399i) q^{95} +(-5.61850 - 0.657651i) q^{96} +(1.00262 - 1.00262i) q^{97} +(7.47186 - 6.33430i) q^{98} +(-1.65747 + 1.36025i) 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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