LMFDB - Embedded newform 230.2.l.a.7.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.7
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.664372 + 3.05407i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.09578 + 0.779553i) q^{5} +(-0.444805 + 3.09368i) q^{6} +(1.24726 - 2.28419i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-6.15705 - 2.81183i) q^{9} +(2.14605 + 0.628055i) q^{10} +(-3.47691 + 3.01276i) q^{11} +(-0.222970 + 3.11753i) q^{12} +(2.28489 - 1.24765i) q^{13} +(1.08113 - 2.36735i) q^{14} +(-3.77319 + 5.88275i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.24436 - 2.99811i) q^{17} +(-6.34196 - 2.36543i) q^{18} +(-0.215083 - 1.49593i) q^{19} +(2.18539 + 0.473357i) q^{20} +(6.14742 + 5.32677i) q^{21} +(-3.25312 + 3.25312i) q^{22} +(-4.73107 - 0.785478i) q^{23} +3.12550i q^{24} +(3.78459 + 3.26754i) q^{25} +(2.19007 - 1.40747i) q^{26} +(7.05898 - 9.42969i) q^{27} +(0.909491 - 2.43844i) q^{28} +(6.04466 + 0.869091i) q^{29} +(-3.34390 + 6.13693i) q^{30} +(4.50690 + 2.89641i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-6.89121 - 12.6203i) q^{33} +(-2.45252 - 2.83036i) q^{34} +(4.39463 - 3.81485i) q^{35} +(-6.49455 - 1.90697i) q^{36} +(-3.04986 - 8.17698i) q^{37} +(-0.321254 - 1.47678i) q^{38} +(2.29238 + 7.80713i) q^{39} +(2.21359 + 0.316247i) q^{40} +(-4.39226 - 9.61770i) q^{41} +(6.51176 + 4.87465i) q^{42} +(0.661697 + 0.143943i) q^{43} +(-3.01276 + 3.47691i) q^{44} +(-10.7119 - 10.6927i) q^{45} +(-4.77505 - 0.445966i) q^{46} +(1.92809 + 1.92809i) q^{47} +(0.222970 + 3.11753i) q^{48} +(0.122635 + 0.190823i) q^{49} +(4.00806 + 2.98923i) q^{50} +(10.6475 - 4.86256i) q^{51} +(2.08408 - 1.56012i) q^{52} +(5.52584 + 3.01733i) q^{53} +(6.36829 - 9.90925i) q^{54} +(-9.63544 + 3.60365i) q^{55} +(0.733218 - 2.49711i) q^{56} +(4.71158 + 0.336979i) q^{57} +(6.09126 + 0.435656i) q^{58} +(-1.80006 + 6.13045i) q^{59} +(-2.89758 + 6.35985i) q^{60} +(-4.00554 + 6.23274i) q^{61} +(4.70205 + 2.56751i) q^{62} +(-14.1022 + 10.5568i) q^{63} +(0.909632 - 0.415415i) q^{64} +(5.76124 - 0.833598i) q^{65} +(-7.77397 - 12.0965i) q^{66} +(-0.554064 - 7.74682i) q^{67} +(-2.64819 - 2.64819i) q^{68} +(5.54209 - 13.9272i) q^{69} +(4.11128 - 4.11864i) q^{70} +(-8.49053 + 9.79860i) q^{71} +(-6.61404 - 1.43880i) q^{72} +(1.19098 + 0.891553i) q^{73} +(-3.62542 - 7.93857i) q^{74} +(-12.4937 + 9.38755i) q^{75} +(-0.425787 - 1.45010i) q^{76} +(2.54509 + 11.6996i) q^{77} +(2.84349 + 7.62370i) q^{78} +(4.18153 + 1.22781i) q^{79} +(2.23051 + 0.157526i) q^{80} +(10.8114 + 12.4770i) q^{81} +(-5.06719 - 9.27986i) q^{82} +(-2.30068 + 0.858110i) q^{83} +(6.84293 + 4.39768i) q^{84} +(-2.36650 - 8.03298i) q^{85} +(0.670280 + 0.0963717i) q^{86} +(-6.67017 + 17.8834i) q^{87} +(-2.75704 + 3.68298i) q^{88} +(-13.5970 + 8.73826i) q^{89} +(-11.4474 - 9.90131i) q^{90} -6.77526i q^{91} +(-4.79470 - 0.104181i) q^{92} +(-11.8401 + 11.8401i) q^{93} +(2.06073 + 1.78563i) q^{94} +(0.715393 - 3.30282i) q^{95} +(0.444805 + 3.09368i) q^{96} +(-6.88907 - 2.56949i) q^{97} +(0.135936 + 0.181589i) q^{98} +(29.8789 - 8.77322i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$2$	0.997452	−	0.0713392i	0.705305	−	0.0504444i
$3$	−0.664372	+	3.05407i	−0.383575	+	1.76327i	0.229565	+	0.973293i	$0.426270\pi$
$3$	−0.664372	+	3.05407i	−0.383575	+	1.76327i	−0.613140	+	0.789974i	$0.710094\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	2.09578	+	0.779553i	0.937262	+	0.348627i
$5$	2.09578	+	0.779553i	0.937262	+	0.348627i
$6$	−0.444805	+	3.09368i	−0.181591	+	1.26299i
$7$	1.24726	−	2.28419i	0.471420	−	0.863341i	−0.528476	−	0.848948i	$-0.677236\pi$
$7$	1.24726	−	2.28419i	0.471420	−	0.863341i	0.999896	−	0.0143934i	$-0.00458172\pi$
$8$	0.977147	−	0.212565i	0.345474	−	0.0751532i
$9$	−6.15705	−	2.81183i	−2.05235	−	0.937277i
$10$	2.14605	+	0.628055i	0.678642	+	0.198609i
$11$	−3.47691	+	3.01276i	−1.04833	+	0.908380i	−0.995920	−	0.0902455i	$-0.971235\pi$
$11$	−3.47691	+	3.01276i	−1.04833	+	0.908380i	−0.0524072	+	0.998626i	$0.516689\pi$
$12$	−0.222970	+	3.11753i	−0.0643660	+	0.899954i
$13$	2.28489	−	1.24765i	0.633716	−	0.346035i	−0.130070	−	0.991505i	$-0.541520\pi$
$13$	2.28489	−	1.24765i	0.633716	−	0.346035i	0.763786	+	0.645470i	$0.223338\pi$
$14$	1.08113	−	2.36735i	0.288944	−	0.632700i
$15$	−3.77319	+	5.88275i	−0.974233	+	1.51892i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	−2.24436	−	2.99811i	−0.544337	−	0.727149i	0.441050	−	0.897483i	$-0.354606\pi$
$17$	−2.24436	−	2.99811i	−0.544337	−	0.727149i	−0.985386	+	0.170334i	$0.945515\pi$
$18$	−6.34196	−	2.36543i	−1.49481	−	0.557537i
$19$	−0.215083	−	1.49593i	−0.0493434	−	0.343191i	−0.999506	−	0.0314355i	$-0.989992\pi$
$19$	−0.215083	−	1.49593i	−0.0493434	−	0.343191i	0.950162	−	0.311755i	$-0.100917\pi$
$20$	2.18539	+	0.473357i	0.488668	+	0.105846i
$21$	6.14742	+	5.32677i	1.34148	+	1.16240i
$22$	−3.25312	+	3.25312i	−0.693568	+	0.693568i
$23$	−4.73107	−	0.785478i	−0.986496	−	0.163783i
$23$	−4.73107	−	0.785478i	−0.986496	−	0.163783i
$24$			3.12550i			0.637989i
$25$	3.78459	+	3.26754i	0.756919	+	0.653509i
$26$	2.19007	−	1.40747i	0.429507	−	0.276028i
$27$	7.05898	−	9.42969i	1.35850	−	1.81475i
$28$	0.909491	−	2.43844i	0.171878	−	0.460822i
$29$	6.04466	+	0.869091i	1.12247	+	0.161386i	0.678460	−	0.734638i	$-0.262648\pi$
$29$	6.04466	+	0.869091i	1.12247	+	0.161386i	0.444006	+	0.896024i	$0.353557\pi$
$30$	−3.34390	+	6.13693i	−0.610510	+	1.12045i
$31$	4.50690	+	2.89641i	0.809464	+	0.520211i	0.878692	−	0.477390i	$-0.158417\pi$
$31$	4.50690	+	2.89641i	0.809464	+	0.520211i	−0.0692275	+	0.997601i	$0.522053\pi$
$32$	0.936950	−	0.349464i	0.165631	−	0.0617771i
$33$	−6.89121	−	12.6203i	−1.19961	−	2.19691i
$34$	−2.45252	−	2.83036i	−0.420604	−	0.485403i
$35$	4.39463	−	3.81485i	0.742828	−	0.644827i
$36$	−6.49455	−	1.90697i	−1.08242	−	0.317829i
$37$	−3.04986	−	8.17698i	−0.501393	−	1.34429i	−0.903458	−	0.428676i	$-0.858980\pi$
$37$	−3.04986	−	8.17698i	−0.501393	−	1.34429i	0.402065	−	0.915611i	$-0.368293\pi$
$38$	−0.321254	−	1.47678i	−0.0521142	−	0.239565i
$39$	2.29238	+	7.80713i	0.367074	+	1.25014i
$40$	2.21359	+	0.316247i	0.350000	+	0.0500031i
$41$	−4.39226	−	9.61770i	−0.685955	−	1.50203i	−0.856207	−	0.516632i	$-0.827186\pi$
$41$	−4.39226	−	9.61770i	−0.685955	−	1.50203i	0.170252	−	0.985401i	$-0.445542\pi$
$42$	6.51176	+	4.87465i	1.00479	+	0.752174i
$43$	0.661697	+	0.143943i	0.100908	+	0.0219511i	0.262736	−	0.964868i	$-0.415375\pi$
$43$	0.661697	+	0.143943i	0.100908	+	0.0219511i	−0.161828	+	0.986819i	$0.551739\pi$
$44$	−3.01276	+	3.47691i	−0.454190	+	0.524163i
$45$	−10.7119	−	10.6927i	−1.59683	−	1.59398i
$46$	−4.77505	−	0.445966i	−0.704043	−	0.0657540i
$47$	1.92809	+	1.92809i	0.281241	+	0.281241i	0.833604	−	0.552363i	$-0.186274\pi$
$47$	1.92809	+	1.92809i	0.281241	+	0.281241i	−0.552363	+	0.833604i	$0.686274\pi$
$48$	0.222970	+	3.11753i	0.0321830	+	0.449977i
$49$	0.122635	+	0.190823i	0.0175193	+	0.0272605i
$50$	4.00806	+	2.98923i	0.566825	+	0.422741i
$51$	10.6475	−	4.86256i	1.49095	−	0.680895i
$52$	2.08408	−	1.56012i	0.289010	−	0.216350i
$53$	5.52584	+	3.01733i	0.759032	+	0.414463i	0.811644	−	0.584152i	$-0.198573\pi$
$53$	5.52584	+	3.01733i	0.759032	+	0.414463i	−0.0526122	+	0.998615i	$0.516755\pi$
$54$	6.36829	−	9.90925i	0.866614	−	1.34848i
$55$	−9.63544	+	3.60365i	−1.29924	+	0.485915i
$56$	0.733218	−	2.49711i	0.0979803	−	0.333690i
$57$	4.71158	+	0.336979i	0.624064	+	0.0446340i
$58$	6.09126	+	0.435656i	0.799822	+	0.0572044i
$59$	−1.80006	+	6.13045i	−0.234348	+	0.798117i	0.755396	+	0.655268i	$0.227444\pi$
$59$	−1.80006	+	6.13045i	−0.234348	+	0.798117i	−0.989745	+	0.142849i	$0.954374\pi$
$60$	−2.89758	+	6.35985i	−0.374076	+	0.821053i
$61$	−4.00554	+	6.23274i	−0.512856	+	0.798020i	−0.997035	−	0.0769490i	$-0.975482\pi$
$61$	−4.00554	+	6.23274i	−0.512856	+	0.798020i	0.484179	+	0.874969i	$0.339118\pi$
$62$	4.70205	+	2.56751i	0.597161	+	0.326075i
$63$	−14.1022	+	10.5568i	−1.77671	+	1.33003i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	5.76124	−	0.833598i	0.714594	−	0.103395i
$66$	−7.77397	−	12.0965i	−0.956910	−	1.48898i
$67$	−0.554064	−	7.74682i	−0.0676897	−	0.946425i	−0.911900	−	0.410413i	$-0.865385\pi$
$67$	−0.554064	−	7.74682i	−0.0676897	−	0.946425i	0.844210	−	0.536012i	$-0.180070\pi$
$68$	−2.64819	−	2.64819i	−0.321140	−	0.321140i
$69$	5.54209	−	13.9272i	0.667190	−	1.67663i
$70$	4.11128	−	4.11864i	0.491392	−	0.492272i
$71$	−8.49053	+	9.79860i	−1.00764	+	1.16288i	−0.0210313	+	0.999779i	$0.506695\pi$
$71$	−8.49053	+	9.79860i	−1.00764	+	1.16288i	−0.986609	+	0.163101i	$0.947851\pi$
$72$	−6.61404	−	1.43880i	−0.779472	−	0.169564i
$73$	1.19098	+	0.891553i	0.139393	+	0.104348i	0.666699	−	0.745327i	$-0.267707\pi$
$73$	1.19098	+	0.891553i	0.139393	+	0.104348i	−0.527306	+	0.849676i	$0.676798\pi$
$74$	−3.62542	−	7.93857i	−0.421447	−	0.922840i
$75$	−12.4937	+	9.38755i	−1.44265	+	1.08398i
$76$	−0.425787	−	1.45010i	−0.0488412	−	0.166338i
$77$	2.54509	+	11.6996i	0.290040	+	1.33329i
$78$	2.84349	+	7.62370i	0.321962	+	0.863214i
$79$	4.18153	+	1.22781i	0.470459	+	0.138139i	0.508364	−	0.861142i	$-0.330250\pi$
$79$	4.18153	+	1.22781i	0.470459	+	0.138139i	−0.0379052	+	0.999281i	$0.512068\pi$
$80$	2.23051	+	0.157526i	0.249379	+	0.0176119i
$81$	10.8114	+	12.4770i	1.20127	+	1.38634i
$82$	−5.06719	−	9.27986i	−0.559577	−	1.02479i
$83$	−2.30068	+	0.858110i	−0.252533	+	0.0941898i	−0.472543	−	0.881308i	$-0.656664\pi$
$83$	−2.30068	+	0.858110i	−0.252533	+	0.0941898i	0.220010	+	0.975498i	$0.429391\pi$
$84$	6.84293	+	4.39768i	0.746624	+	0.479826i
$85$	−2.36650	−	8.03298i	−0.256683	−	0.871299i
$86$	0.670280	+	0.0963717i	0.0722781	+	0.0103920i
$87$	−6.67017	+	17.8834i	−0.715117	+	1.91730i
$88$	−2.75704	+	3.68298i	−0.293902	+	0.392606i
$89$	−13.5970	+	8.73826i	−1.44128	+	0.926254i	−0.441703	+	0.897161i	$0.645626\pi$
$89$	−13.5970	+	8.73826i	−1.44128	+	0.926254i	−0.999577	+	0.0290929i	$0.990738\pi$
$90$	−11.4474	−	9.90131i	−1.20666	−	1.04369i
$91$		−	6.77526i		−	0.710241i
$92$	−4.79470	−	0.104181i	−0.499882	−	0.0108616i
$93$	−11.8401	+	11.8401i	−1.22776	+	1.22776i
$94$	2.06073	+	1.78563i	0.212548	+	0.184174i
$95$	0.715393	−	3.30282i	0.0733978	−	0.338862i
$96$	0.444805	+	3.09368i	0.0453977	+	0.315748i
$97$	−6.88907	−	2.56949i	−0.699479	−	0.260892i	−0.0255342	−	0.999674i	$-0.508129\pi$
$97$	−6.88907	−	2.56949i	−0.699479	−	0.260892i	−0.673945	+	0.738782i	$0.735401\pi$
$98$	0.135936	+	0.181589i	0.0137316	+	0.0183432i
$99$	29.8789	−	8.77322i	3.00294	−	0.881742i
$100$	4.21109	+	2.69568i	0.421109	+	0.269568i
$101$	5.86240	−	12.8369i	0.583330	−	1.27732i	−0.356059	−	0.934463i	$-0.615880\pi$
$101$	5.86240	−	12.8369i	0.583330	−	1.27732i	0.939389	−	0.342852i	$-0.111393\pi$
$102$	10.2735	−	5.60976i	1.01723	−	0.555449i
$103$	0.942711	−	13.1808i	0.0928881	−	1.29874i	−0.710673	−	0.703522i	$-0.751609\pi$
$103$	0.942711	−	13.1808i	0.0928881	−	1.29874i	0.803561	−	0.595222i	$-0.202936\pi$
$104$	1.96747	−	1.70482i	0.192926	−	0.167172i
$105$	8.73115	+	15.9560i	0.852073	+	1.55714i
$106$	5.72701	+	2.61544i	0.556256	+	0.254034i
$107$	5.82282	−	1.26668i	0.562913	−	0.122454i	0.0778999	−	0.996961i	$-0.475179\pi$
$107$	5.82282	−	1.26668i	0.562913	−	0.122454i	0.485013	+	0.874507i	$0.338815\pi$
$108$	5.64514	−	10.3383i	0.543204	−	0.994804i
$109$	−0.132276	+	0.919999i	−0.0126697	+	0.0881199i	−0.995175	−	0.0981138i	$-0.968719\pi$
$109$	−0.132276	+	0.919999i	−0.0126697	+	0.0881199i	0.982505	+	0.186234i	$0.0596282\pi$
$110$	−9.35381	+	4.28185i	−0.891850	+	0.408258i
$111$	26.9993	−	3.88191i	2.56266	−	0.368455i
$112$	0.553208	−	2.54306i	0.0522732	−	0.240296i
$113$	−0.628113	+	0.0449236i	−0.0590879	+	0.00422605i	−0.100852	−	0.994901i	$-0.532157\pi$
$113$	−0.628113	+	0.0449236i	−0.0590879	+	0.00422605i	0.0417639	+	0.999128i	$0.486702\pi$
$114$	4.72362			0.442407
$115$	−9.30296	−	5.33431i	−0.867506	−	0.497427i
$116$	6.10682			0.567004
$117$	−17.5764	+	1.25709i	−1.62494	+	0.116218i
$118$	−1.35814	+	6.24325i	−0.125027	+	0.574738i
$119$	−9.64755	+	1.38711i	−0.884389	+	0.127156i
$120$	−2.43649	+	6.55036i	−0.222420	+	0.597963i
$121$	1.44671	−	10.0621i	0.131519	−	0.914737i
$122$	−3.55069	+	6.50261i	−0.321465	+	0.588718i
$123$	32.2912	−	7.02452i	2.91160	−	0.633380i
$124$	4.87323	+	2.22553i	0.437629	+	0.199859i
$125$	5.38446	+	9.79835i	0.481601	+	0.876391i
$126$	−13.3132	+	11.5359i	−1.18603	+	1.02770i
$127$	−0.184850	+	2.58455i	−0.0164028	+	0.229341i	0.982637	+	0.185537i	$0.0594024\pi$
$127$	−0.184850	+	2.58455i	−0.0164028	+	0.229341i	−0.999040	+	0.0438045i	$0.986052\pi$
$128$	0.877679	−	0.479249i	0.0775766	−	0.0423600i
$129$	−0.879226	+	1.92524i	−0.0774115	+	0.169508i
$130$	5.68710	−	1.24248i	0.498791	−	0.108972i
$131$	−20.2225	+	5.93786i	−1.76685	+	0.518794i	−0.993363	−	0.115021i	$-0.963307\pi$
$131$	−20.2225	+	5.93786i	−1.76685	+	0.518794i	−0.773485	+	0.633814i	$0.781488\pi$
$132$	−8.61712	−	11.5111i	−0.750024	−	1.00191i
$133$	−3.68526	−	1.37453i	−0.319552	−	0.119187i
$134$	−1.10530	−	7.68756i	−0.0954837	−	0.664104i
$135$	22.1450	−	14.2597i	1.90594	−	1.22728i
$136$	−2.83036	−	2.45252i	−0.242702	−	0.210302i
$137$	−3.47894	+	3.47894i	−0.297226	+	0.297226i	−0.839926	−	0.542701i	$-0.817402\pi$
$137$	−3.47894	+	3.47894i	−0.297226	+	0.297226i	0.542701	+	0.839926i	$0.317402\pi$
$138$	4.53442	−	14.2870i	0.385996	−	1.21619i
$139$			9.56448i			0.811249i	0.914040	+	0.405624i	$0.132946\pi$
$139$			9.56448i			0.811249i	−0.914040	+	0.405624i	$0.867054\pi$
$140$	3.80699	−	4.40144i	0.321749	−	0.371990i
$141$	−7.16949	+	4.60755i	−0.603780	+	0.388026i
$142$	−7.76987	+	10.3793i	−0.652033	+	0.871015i
$143$	−4.18551	+	11.2218i	−0.350010	+	0.938412i
$144$	−6.69983	−	0.963290i	−0.558319	−	0.0802742i
$145$	11.9908	+	6.53356i	0.995781	+	0.542583i
$146$	1.25154	+	0.804318i	0.103579	+	0.0665659i
$147$	−0.664263	+	0.247757i	−0.0547875	+	0.0204347i
$148$	−4.18252	−	7.65971i	−0.343801	−	0.629624i
$149$	8.43804	+	9.73802i	0.691271	+	0.797770i	0.987546	−	0.157333i	$-0.0502897\pi$
$149$	8.43804	+	9.73802i	0.691271	+	0.797770i	−0.296274	+	0.955103i	$0.595744\pi$
$150$	−11.7922	+	10.2549i	−0.962825	+	0.837311i
$151$	−6.62240	−	1.94451i	−0.538924	−	0.158242i	0.000932510	−	1.00000i	$-0.499703\pi$
$151$	−6.62240	−	1.94451i	−0.538924	−	0.158242i	−0.539856	+	0.841757i	$0.681521\pi$
$152$	−0.528151	−	1.41603i	−0.0428387	−	0.114855i
$153$	5.38845	+	24.7703i	0.435630	+	2.00256i
$154$	3.37325	+	11.4882i	0.271824	+	0.925747i
$155$	7.18758	+	9.58362i	0.577320	+	0.769775i
$156$	3.38012	+	7.40142i	0.270626	+	0.592588i
$157$	−11.1466	−	8.34427i	−0.889599	−	0.665946i	0.0534602	−	0.998570i	$-0.482975\pi$
$157$	−11.1466	−	8.34427i	−0.889599	−	0.665946i	−0.943059	+	0.332624i	$0.892066\pi$
$158$	4.25847	+	0.926374i	0.338786	+	0.0736983i
$159$	−12.8864	+	14.8717i	−1.02195	+	1.17940i
$160$	2.23607	−	0.00199849i	0.176777	−	0.000157994i
$161$	−7.69505	+	9.82695i	−0.606455	+	0.774472i
$162$	11.6740	+	11.6740i	0.917194	+	0.917194i
$163$	−0.862351	−	12.0572i	−0.0675445	−	0.944396i	−0.912373	−	0.409359i	$-0.865752\pi$
$163$	−0.862351	−	12.0572i	−0.0675445	−	0.944396i	0.844829	−	0.535037i	$-0.179702\pi$
$164$	−5.71629	−	8.89472i	−0.446367	−	0.694561i
$165$	−4.60427	−	31.8215i	−0.358442	−	2.47730i
$166$	−2.23360	+	1.02005i	−0.173361	+	0.0791714i
$167$	8.33860	−	6.24220i	0.645260	−	0.483036i	−0.225825	−	0.974168i	$-0.572508\pi$
$167$	8.33860	−	6.24220i	0.645260	−	0.483036i	0.871085	+	0.491132i	$0.163417\pi$
$168$	7.13922	+	3.89831i	0.550803	+	0.300761i
$169$	−3.36421	+	5.23482i	−0.258786	+	0.402678i
$170$	−2.93353	−	7.84369i	−0.224992	−	0.601584i
$171$	−2.88204	+	9.81532i	−0.220395	+	0.750596i
$172$	0.675447	+	0.0483089i	0.0515023	+	0.00368352i
$173$	−12.6460	−	0.904460i	−0.961458	−	0.0687649i	−0.418222	−	0.908345i	$-0.637347\pi$
$173$	−12.6460	−	0.904460i	−0.961458	−	0.0687649i	−0.543236	+	0.839580i	$0.682801\pi$
$174$	−5.37739	+	18.3137i	−0.407659	+	1.38836i
$175$	12.1841	−	4.56924i	0.921028	−	0.345402i
$176$	−2.48728	+	3.87028i	−0.187485	+	0.291733i
$177$	−17.5269	−	9.57042i	−1.31740	−	0.719357i
$178$	−12.9390	+	9.68600i	−0.969818	+	0.725996i
$179$	0.654216	−	0.298770i	0.0488984	−	0.0223311i	−0.390816	−	0.920469i	$-0.627807\pi$
$179$	0.654216	−	0.298770i	0.0488984	−	0.0223311i	0.439714	+	0.898138i	$0.355080\pi$
$180$	−12.1246	−	9.05944i	−0.903712	−	0.675251i
$181$	7.33618	+	11.4153i	0.545294	+	0.848494i	0.999092	−	0.0426108i	$-0.0135675\pi$
$181$	7.33618	+	11.4153i	0.545294	+	0.848494i	−0.453798	+	0.891105i	$0.649931\pi$
$182$	−0.483342	−	6.75800i	−0.0358277	−	0.500936i
$183$	−16.3740	−	16.3740i	−1.21040	−	1.21040i
$184$	−4.78992	+	0.238134i	−0.353117	+	0.0175555i
$185$	−0.0174413	−	19.5147i	−0.00128231	−	1.43475i
$186$	−10.9653	+	12.6546i	−0.804013	+	0.927880i
$187$	16.8360	+	3.66245i	1.23117	+	0.267825i
$188$	2.18286	+	1.63407i	0.159201	+	0.119177i
$189$	−12.7348	−	27.8853i	−0.926320	−	2.02836i
$190$	0.477950	−	3.34544i	0.0346741	−	0.242704i
$191$	−4.97822	−	16.9543i	−0.360211	−	1.22677i	−0.917932	−	0.396738i	$-0.870142\pi$
$191$	−4.97822	−	16.9543i	−0.360211	−	1.22677i	0.557720	−	0.830029i	$-0.311676\pi$
$192$	0.664372	+	3.05407i	0.0479469	+	0.220408i
$193$	4.78257	+	12.8226i	0.344257	+	0.922989i	0.987541	+	0.157361i	$0.0502987\pi$
$193$	4.78257	+	12.8226i	0.344257	+	0.922989i	−0.643284	+	0.765628i	$0.722429\pi$
$194$	−7.05482	−	2.07148i	−0.506507	−	0.148724i
$195$	−1.28174	+	18.1491i	−0.0917875	+	1.29968i
$196$	0.148544	+	0.171428i	0.0106103	+	0.0122449i
$197$	8.43065	+	15.4396i	0.600659	+	1.10003i	0.984293	+	0.176540i	$0.0564905\pi$
$197$	8.43065	+	15.4396i	0.600659	+	1.10003i	−0.383634	+	0.923485i	$0.625328\pi$
$198$	29.1769	−	10.8824i	2.07351	−	0.773379i
$199$	−16.9934	−	10.9210i	−1.20463	−	0.774170i	−0.224881	−	0.974386i	$-0.572199\pi$
$199$	−16.9934	−	10.9210i	−1.20463	−	0.774170i	−0.979752	+	0.200216i	$0.935836\pi$
$200$	4.39267	+	2.38840i	0.310609	+	0.168885i
$201$	24.0274	+	3.45462i	1.69476	+	0.243670i
$202$	4.93169	−	13.2224i	0.346993	−	0.930323i
$203$	9.52443	−	12.7232i	0.668484	−	0.892990i
$204$	9.84714	−	6.32837i	0.689438	−	0.443075i
$205$	−1.70770	−	23.5806i	−0.119271	−	1.64694i
$206$		−	13.2145i		−	0.920697i
$207$	26.9208	+	18.1392i	1.87113	+	1.26076i
$208$	1.84084	−	1.84084i	0.127639	−	0.127639i
$209$	5.25471	+	4.55323i	0.363476	+	0.314954i
$210$	9.84719	+	15.2925i	0.679520	+	1.05528i
$211$	0.469737	+	3.26709i	0.0323380	+	0.224916i	0.999581	−	0.0289354i	$-0.00921170\pi$
$211$	0.469737	+	3.26709i	0.0323380	+	0.224916i	−0.967243	+	0.253851i	$0.918303\pi$
$212$	5.89900	+	2.20021i	0.405145	+	0.151111i
$213$	−24.2847	−	32.4406i	−1.66396	−	2.22279i
$214$	5.71762	−	1.67884i	0.390848	−	0.114763i
$215$	1.27456	+	0.817501i	0.0869243	+	0.0557531i
$216$	4.89323	−	10.7147i	0.332942	−	0.729042i
$217$	12.2372	−	6.68203i	0.830717	−	0.453606i
$218$	−0.0663069	+	0.927091i	−0.00449087	+	0.0627905i
$219$	−3.51412	+	3.04500i	−0.237462	+	0.205762i
$220$	−9.02451	+	4.93823i	−0.608432	+	0.332935i
$221$	−8.86870	−	4.05020i	−0.596574	−	0.272446i
$222$	26.6536	−	5.79813i	1.78887	−	0.389145i
$223$	3.37595	−	6.18260i	0.226070	−	0.414017i	−0.739882	−	0.672737i	$-0.765119\pi$
$223$	3.37595	−	6.18260i	0.226070	−	0.414017i	0.965953	+	0.258719i	$0.0833005\pi$
$224$	0.370379	−	2.57604i	0.0247470	−	0.172119i
$225$	−14.1142	−	30.7601i	−0.940944	−	2.05067i
$226$	−0.623308	+	0.0896182i	−0.0414618	+	0.00596131i
$227$	−1.35648	+	6.23564i	−0.0900327	+	0.413874i	−1.00000		0.000807034i	$-0.999743\pi$
$227$	−1.35648	+	6.23564i	−0.0900327	+	0.413874i	0.909967	+	0.414681i	$0.136107\pi$
$228$	4.71158	−	0.336979i	0.312032	−	0.0223170i
$229$	0.740462			0.0489311			0.0244655	−	0.999701i	$-0.492212\pi$
$229$	0.740462			0.0489311			0.0244655	+	0.999701i	$0.492212\pi$
$230$	−9.65981	−	4.65705i	−0.636949	−	0.307077i
$231$	−37.4223			−2.46220
$232$	6.09126	−	0.435656i	0.399911	−	0.0286022i
$233$	−5.07036	+	23.3081i	−0.332171	+	1.52696i	0.443760	+	0.896146i	$0.353644\pi$
$233$	−5.07036	+	23.3081i	−0.332171	+	1.52696i	−0.775931	+	0.630818i	$0.782719\pi$
$234$	−17.4419	+	2.50777i	−1.14021	+	0.163938i
$235$	2.53781	+	5.54390i	0.165548	+	0.361644i
$236$	−0.909287	+	6.32423i	−0.0591895	+	0.411672i
$237$	−6.52791	+	11.9550i	−0.424033	+	0.776559i
$238$	−9.52401	+	2.07182i	−0.617350	+	0.134296i
$239$	14.8082	+	6.76267i	0.957861	+	0.437440i	0.832103	−	0.554621i	$-0.187137\pi$
$239$	14.8082	+	6.76267i	0.957861	+	0.437440i	0.125758	+	0.992061i	$0.459864\pi$
$240$	−1.96298	+	6.70748i	−0.126710	+	0.432966i
$241$	14.7073	−	12.7439i	0.947378	−	0.820908i	−0.0365754	−	0.999331i	$-0.511645\pi$
$241$	14.7073	−	12.7439i	0.947378	−	0.820908i	0.983954	+	0.178423i	$0.0570995\pi$
$242$	0.725204	−	10.1397i	0.0466179	−	0.651803i
$243$	−14.2736	+	7.79399i	−0.915654	+	0.499985i
$244$	−3.07776	+	6.73934i	−0.197033	+	0.431442i
$245$	0.108259	+	0.495525i	0.00691639	+	0.0316579i
$246$	31.7078	−	9.31026i	2.02162	−	0.593600i
$247$	−2.35784	−	3.14970i	−0.150026	−	0.200411i
$248$	5.01958	+	1.87221i	0.318744	+	0.118885i
$249$	−1.09222	−	7.59655i	−0.0692165	−	0.481412i
$250$	6.06974	+	9.38926i	0.383884	+	0.593829i
$251$	9.70871	+	8.41265i	0.612808	+	0.531002i	0.905029	−	0.425349i	$-0.139849\pi$
$251$	9.70871	+	8.41265i	0.612808	+	0.531002i	−0.292221	+	0.956351i	$0.594394\pi$
$252$	−12.4563	+	12.4563i	−0.784671	+	0.784671i
$253$	18.8159	−	11.5225i	1.18295	−	0.724415i
$254$			2.59115i			0.162583i
$255$	26.1055	−	1.89056i	1.63479	−	0.118391i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−2.27483	+	3.03881i	−0.141900	+	0.189556i	−0.865861	−	0.500285i	$-0.833229\pi$
$257$	−2.27483	+	3.03881i	−0.141900	+	0.189556i	0.723961	+	0.689841i	$0.242320\pi$
$258$	−0.739641	+	1.98305i	−0.0460480	+	0.123460i
$259$	−22.4817	−	3.23238i	−1.39695	−	0.200850i
$260$	5.58397	−	1.64502i	0.346303	−	0.102020i
$261$	−34.7736	−	22.3476i	−2.15243	−	1.38328i
$262$	−19.7474	+	7.36539i	−1.22000	+	0.455035i
$263$	4.88468	+	8.94562i	0.301202	+	0.551610i	0.983819	−	0.179166i	$-0.0573400\pi$
$263$	4.88468	+	8.94562i	0.301202	+	0.551610i	−0.682617	+	0.730777i	$0.739158\pi$
$264$	−9.41636	−	10.8671i	−0.579537	−	0.668821i
$265$	9.22877	+	10.6314i	0.566919	+	0.653079i
$266$	−3.77393	−	1.10812i	−0.231394	−	0.0679435i
$267$	−17.6538	−	47.3317i	−1.08039	−	2.89665i
$268$	−1.65091	−	7.58912i	−0.100845	−	0.463579i
$269$	0.0847081	+	0.288489i	0.00516474	+	0.0175895i	0.962035	−	0.272926i	$-0.0879914\pi$
$269$	0.0847081	+	0.288489i	0.00516474	+	0.0175895i	−0.956870	+	0.290515i	$0.906173\pi$
$270$	21.0713	−	15.8032i	1.28236	−	0.961752i
$271$	−0.124734	−	0.273130i	−0.00757706	−	0.0165915i	0.905806	−	0.423693i	$-0.139267\pi$
$271$	−0.124734	−	0.273130i	−0.00757706	−	0.0165915i	−0.913383	+	0.407102i	$0.866539\pi$
$272$	−2.99811	−	2.24436i	−0.181787	−	0.136084i
$273$	20.6921	+	4.50130i	1.25234	+	0.272431i
$274$	−3.22189	+	3.71826i	−0.194641	+	0.224628i
$275$	−23.0030	+	0.0411179i	−1.38713	+	0.00247950i
$276$	3.50364	−	14.5741i	0.210894	−	0.877260i
$277$	4.35669	+	4.35669i	0.261768	+	0.261768i	0.825772	−	0.564004i	$-0.190740\pi$
$277$	4.35669	+	4.35669i	0.261768	+	0.261768i	−0.564004	+	0.825772i	$0.690740\pi$
$278$	0.682322	+	9.54011i	0.0409230	+	0.572178i
$279$	−19.6050	−	30.5060i	−1.17372	−	1.82635i
$280$	3.48329	−	4.66181i	0.208167	−	0.278597i
$281$	25.5276	−	11.6581i	1.52285	−	0.695463i	0.534154	−	0.845387i	$-0.320630\pi$
$281$	25.5276	−	11.6581i	1.52285	−	0.695463i	0.988698	+	0.149924i	$0.0479029\pi$
$282$	−6.82252	+	5.10728i	−0.406275	+	0.304134i
$283$	−5.47879	−	2.99164i	−0.325680	−	0.177835i	0.308088	−	0.951358i	$-0.400311\pi$
$283$	−5.47879	−	2.99164i	−0.325680	−	0.177835i	−0.633768	+	0.773523i	$0.718493\pi$
$284$	−7.00962	+	10.9072i	−0.415945	+	0.647223i
$285$	9.61175	+	4.37916i	0.569351	+	0.259399i
$286$	−3.37429	+	11.4918i	−0.199526	+	0.679523i
$287$	−27.4469	−	1.96304i	−1.62014	−	0.115875i
$288$	−6.75148	−	0.482876i	−0.397835	−	0.0284537i
$289$	0.837923	−	2.85370i	0.0492896	−	0.167865i
$290$	12.4263	+	5.66150i	0.729699	+	0.332455i
$291$	12.4243	−	19.3326i	0.728326	−	1.13330i
$292$	1.30573	+	0.712985i	0.0764123	+	0.0417243i
$293$	13.6728	−	10.2353i	0.798772	−	0.597953i	−0.119986	−	0.992776i	$-0.538285\pi$
$293$	13.6728	−	10.2353i	0.798772	−	0.597953i	0.918757	+	0.394823i	$0.129194\pi$
$294$	−0.644896	+	0.294514i	−0.0376111	+	0.0171764i
$295$	−8.55155	+	11.4448i	−0.497891	+	0.666345i
$296$	−4.71830	−	7.34182i	−0.274246	−	0.426734i
$297$	3.86596	+	54.0531i	0.224326	+	3.13648i
$298$	9.11124	+	9.11124i	0.527800	+	0.527800i
$299$	−11.7900	+	4.10797i	−0.681833	+	0.237570i
$300$	−11.0305	+	11.0700i	−0.636848	+	0.639129i
$301$	1.15410	−	1.33190i	0.0665213	−	0.0767697i
$302$	−6.74425	−	1.46712i	−0.388088	−	0.0844234i
$303$	35.3099	+	26.4326i	2.02850	+	1.51851i
$304$	−0.627824	−	1.37474i	−0.0360082	−	0.0788469i
$305$	−13.2535	+	9.93992i	−0.758892	+	0.569158i
$306$	7.14181	+	24.3228i	0.408270	+	1.39044i
$307$	−2.97299	−	13.6666i	−0.169678	−	0.779996i	−0.980784	−	0.195097i	$-0.937498\pi$
$307$	−2.97299	−	13.6666i	−0.169678	−	0.779996i	0.811106	−	0.584899i	$-0.198866\pi$
$308$	4.18421	+	11.2183i	0.238418	+	0.639222i
$309$	39.6288	+	11.6361i	2.25440	+	0.661953i
$310$	7.85295	+	9.04644i	0.446018	+	0.513803i
$311$	−2.93544	−	3.38768i	−0.166454	−	0.192098i	0.666394	−	0.745599i	$-0.267837\pi$
$311$	−2.93544	−	3.38768i	−0.166454	−	0.192098i	−0.832848	+	0.553502i	$0.813291\pi$
$312$	3.89951	+	7.14143i	0.220767	+	0.404304i
$313$	−13.5390	+	5.04980i	−0.765272	+	0.285432i	−0.701630	−	0.712541i	$-0.747544\pi$
$313$	−13.5390	+	5.04980i	−0.765272	+	0.285432i	−0.0636414	+	0.997973i	$0.520271\pi$
$314$	−11.7135	−	7.52782i	−0.661032	−	0.424820i
$315$	−37.7847	+	11.1313i	−2.12892	+	0.627176i
$316$	4.31371	+	0.620217i	0.242665	+	0.0348900i
$317$	−4.51505	+	12.1053i	−0.253591	+	0.679902i	0.746307	+	0.665602i	$0.231825\pi$
$317$	−4.51505	+	12.1053i	−0.253591	+	0.679902i	−0.999898	+	0.0143009i	$0.995448\pi$
$318$	−11.7926	+	15.7531i	−0.661296	+	0.883388i
$319$	−23.6351	+	15.1893i	−1.32331	+	0.850440i
$320$	2.23023	−	0.161513i	0.124673	−	0.00902883i
$321$			18.6248i			1.03954i
$322$	−6.97440	+	10.3509i	−0.388668	+	0.576832i
$323$	−4.00226	+	4.00226i	−0.222691	+	0.222691i
$324$	12.4770	+	10.8114i	0.693169	+	0.600635i
$325$	12.7241	+	2.74415i	0.705808	+	0.152218i
$326$	−1.72031	−	11.9650i	−0.0952790	−	0.662680i
$327$	−2.72186	−	1.01520i	−0.150519	−	0.0561407i
$328$	−6.33627	−	8.46427i	−0.349862	−	0.467361i
$329$	6.80895	−	1.99929i	0.375389	−	0.110224i
$330$	−6.86265	−	31.4119i	−0.377777	−	1.72917i
$331$	−6.24039	+	13.6646i	−0.343003	+	0.751072i	−0.999996	−	0.00282474i	$-0.999101\pi$
$331$	−6.24039	+	13.6646i	−0.343003	+	0.751072i	0.656993	+	0.753897i	$0.271828\pi$
$332$	−2.15514	+	1.17680i	−0.118279	+	0.0645851i
$333$	−4.21417	+	58.9218i	−0.230935	+	3.22889i
$334$	7.87204	−	6.82116i	0.430739	−	0.373237i
$335$	4.87786	−	16.6676i	0.266506	−	0.910646i
$336$	7.39913	+	3.37907i	0.403656	+	0.184343i
$337$	4.27843	−	0.930715i	0.233061	−	0.0506993i	−0.0945180	−	0.995523i	$-0.530131\pi$
$337$	4.27843	−	0.930715i	0.233061	−	0.0506993i	0.327579	+	0.944824i	$0.393767\pi$
$338$	−2.98219	+	5.46148i	−0.162210	+	0.297065i
$339$	0.280101	−	1.94815i	0.0152130	−	0.105809i
$340$	−3.48562	−	7.61443i	−0.189034	−	0.412950i
$341$	−24.3963	+	3.50765i	−1.32113	+	0.189950i
$342$	−2.17448	+	9.99592i	−0.117582	+	0.540517i
$343$	18.7601	−	1.34175i	1.01295	−	0.0724478i
$344$	0.677172			0.0365107
$345$	22.4720	−	24.8679i	1.20985	−	1.33884i
$346$	−12.6783			−0.681590
$347$	13.4152	−	0.959472i	0.720164	−	0.0515072i	0.293554	−	0.955943i	$-0.405162\pi$
$347$	13.4152	−	0.959472i	0.720164	−	0.0515072i	0.426611	+	0.904435i	$0.359707\pi$
$348$	−4.05720	+	18.6507i	−0.217489	+	0.999780i
$349$	20.0416	−	2.88155i	1.07280	−	0.154246i	0.416795	−	0.909001i	$-0.363153\pi$
$349$	20.0416	−	2.88155i	1.07280	−	0.154246i	0.656007	+	0.754755i	$0.272244\pi$
$350$	11.8270	−	5.42680i	0.632182	−	0.290075i
$351$	4.36410	−	30.3530i	0.232938	−	1.62012i
$352$	−2.20484	+	4.03786i	−0.117518	+	0.215218i
$353$	32.8698	−	7.15039i	1.74948	−	0.380577i	0.780010	−	0.625767i	$-0.215214\pi$
$353$	32.8698	−	7.15039i	1.74948	−	0.380577i	0.969475	+	0.245190i	$0.0788504\pi$
$354$	−18.1650	−	8.29568i	−0.965459	−	0.440910i
$355$	−25.4328	+	13.9169i	−1.34983	+	0.738632i
$356$	−12.2150	+	10.5844i	−0.647395	+	0.560971i
$357$	2.17324	−	30.3858i	0.115020	−	1.60819i
$358$	0.631235	−	0.344680i	0.0333618	−	0.0182169i
$359$	7.61976	−	16.6849i	0.402155	−	0.880598i	−0.594892	−	0.803806i	$-0.702805\pi$
$359$	7.61976	−	16.6849i	0.402155	−	0.880598i	0.997047	−	0.0767917i	$-0.0244676\pi$
$360$	−12.7400	−	8.17140i	−0.671455	−	0.430670i
$361$	16.0388	−	4.70942i	0.844148	−	0.247864i
$362$	8.13185	+	10.8629i	0.427400	+	0.570940i
$363$	29.7692	+	11.1033i	1.56248	+	0.582775i
$364$	−0.964221	−	6.70630i	−0.0505389	−	0.351506i
$365$	1.80101	+	2.79693i	0.0942692	+	0.146398i
$366$	−17.5004	−	15.1642i	−0.914762	−	0.792646i
$367$	8.88352	−	8.88352i	0.463716	−	0.463716i	−0.436155	−	0.899871i	$-0.643660\pi$
$367$	8.88352	−	8.88352i	0.463716	−	0.463716i	0.899871	+	0.436155i	$0.143660\pi$
$368$	−4.76072	+	0.579236i	−0.248170	+	0.0301948i
$369$			71.5670i			3.72563i
$370$	−1.40956	−	19.4637i	−0.0732794	−	1.01187i
$371$	13.7843	−	8.85864i	0.715646	−	0.459918i
$372$	−10.0346	+	13.4046i	−0.520268	+	0.694997i
$373$	−3.12260	+	8.37203i	−0.161682	+	0.433487i	−0.992377	−	0.123242i	$-0.960671\pi$
$373$	−3.12260	+	8.37203i	−0.161682	+	0.433487i	0.830694	+	0.556729i	$0.187944\pi$
$374$	17.0544	+	2.45205i	0.881861	+	0.126793i
$375$	−33.5021	+	9.93476i	−1.73004	+	0.513029i
$376$	2.29387	+	1.47418i	0.118297	+	0.0760251i
$377$	14.8957	−	5.55582i	0.767169	−	0.286139i
$378$	−14.6917	−	26.9058i	−0.755658	−	1.38388i
$379$	8.15891	+	9.41588i	0.419095	+	0.483661i	0.925561	−	0.378599i	$-0.123594\pi$
$379$	8.15891	+	9.41588i	0.419095	+	0.483661i	−0.506466	+	0.862260i	$0.669048\pi$
$380$	0.238071	−	3.37101i	0.0122128	−	0.172929i
$381$	−7.77058	−	2.28165i	−0.398099	−	0.116892i
$382$	−6.17504	−	16.5559i	−0.315942	−	0.847075i
$383$	1.89043	+	8.69015i	0.0965963	+	0.444046i	0.999887	+	0.0150175i	$0.00478040\pi$
$383$	1.89043	+	8.69015i	0.0965963	+	0.444046i	−0.903291	+	0.429029i	$0.858856\pi$
$384$	0.880554	+	2.99889i	0.0449356	+	0.153037i
$385$	−3.78650	+	26.5038i	−0.192978	+	1.35076i
$386$	5.68514	+	12.4487i	0.289366	+	0.633623i
$387$	−3.66936	−	2.74685i	−0.186524	−	0.139630i
$388$	−7.18462	−	1.56292i	−0.364744	−	0.0793452i
$389$	18.6433	−	21.5155i	0.945253	−	1.09088i	−0.0504916	−	0.998724i	$-0.516079\pi$
$389$	18.6433	−	21.5155i	0.945253	−	1.09088i	0.995745	−	0.0921556i	$-0.0293757\pi$
$390$	0.0162611	+	18.1943i	0.000823414	+	0.921302i
$391$	8.26327	+	15.9472i	0.417891	+	0.806483i
$392$	0.160395	+	0.160395i	0.00810115	+	0.00810115i
$393$	−4.69938	−	65.7059i	−0.237052	−	3.31442i
$394$	9.51062	+	14.7988i	0.479138	+	0.745553i
$395$	7.80644	+	5.83295i	0.392784	+	0.293487i
$396$	28.3262	−	12.9361i	1.42344	−	0.650065i
$397$	14.5007	−	10.8551i	0.727767	−	0.544800i	−0.169907	−	0.985460i	$-0.554347\pi$
$397$	14.5007	−	10.8551i	0.727767	−	0.544800i	0.897674	+	0.440660i	$0.145256\pi$
$398$	−17.7292	−	9.68089i	−0.888686	−	0.485259i
$399$	6.64629	−	10.3418i	0.332731	−	0.517739i
$400$	4.55187	+	2.06894i	0.227593	+	0.103447i
$401$	−9.50070	+	32.3564i	−0.474442	+	1.61580i	0.280392	+	0.959886i	$0.409536\pi$
$401$	−9.50070	+	32.3564i	−0.474442	+	1.61580i	−0.754834	+	0.655916i	$0.772283\pi$
$402$	24.2127	+	1.73172i	1.20762	+	0.0863705i
$403$	13.9115	+	0.994970i	0.692981	+	0.0495630i
$404$	3.97585	−	13.5405i	0.197806	−	0.673665i
$405$	12.9319	+	34.5772i	0.642589	+	1.71816i
$406$	8.59251	−	13.3702i	0.426439	−	0.663552i
$407$	35.2393	+	19.2421i	1.74675	+	0.953796i
$408$	9.37059	−	7.01473i	0.463913	−	0.347281i
$409$	−24.1954	+	11.0497i	−1.19639	+	0.546372i	−0.911146	−	0.412084i	$-0.864801\pi$
$409$	−24.1954	+	11.0497i	−1.19639	+	0.546372i	−0.285241	+	0.958456i	$0.592074\pi$
$410$	−3.38557	−	23.3987i	−0.167201	−	1.15558i
$411$	−8.31361	−	12.9362i	−0.410080	−	0.638097i
$412$	−0.942711	−	13.1808i	−0.0464440	−	0.649372i
$413$	11.7580	+	11.7580i	0.578571	+	0.578571i
$414$	28.1463	+	16.1725i	1.38331	+	0.794834i
$415$	−5.49067	+	0.00490729i	−0.269526	+	0.000240889i
$416$	1.70482	−	1.96747i	0.0835858	−	0.0964632i
$417$	−29.2106	−	6.35437i	−1.43045	−	0.311175i
$418$	5.56614	+	4.16676i	0.272249	+	0.203803i
$419$	−6.02766	−	13.1987i	−0.294470	−	0.644800i	0.703346	−	0.710847i	$-0.251688\pi$
$419$	−6.02766	−	13.1987i	−0.294470	−	0.644800i	−0.997816	+	0.0660475i	$0.978961\pi$
$420$	10.9130	+	14.5510i	0.532502	+	0.710016i
$421$	2.59875	+	8.85054i	0.126656	+	0.431349i	0.998267	−	0.0588484i	$-0.0187428\pi$
$421$	2.59875	+	8.85054i	0.126656	+	0.431349i	−0.871611	+	0.490197i	$0.836925\pi$
$422$	0.701612	+	3.22526i	0.0341539	+	0.157003i
$423$	−6.44988	−	17.2928i	−0.313604	−	0.840805i
$424$	6.04093	+	1.77378i	0.293374	+	0.0861423i
$425$	1.30248	−	18.6802i	0.0631793	−	0.906122i
$426$	−26.5371	−	30.6255i	−1.28573	−	1.48381i
$427$	9.24079	+	16.9232i	0.447193	+	0.818973i
$428$	5.58328	−	2.08246i	0.269878	−	0.100659i
$429$	−31.4914	−	20.2383i	−1.52042	−	0.977113i
$430$	1.32963	+	0.724492i	0.0641206	+	0.0349381i
$431$	−23.2189	−	3.33838i	−1.11842	−	0.160804i	−0.441782	−	0.897123i	$-0.645653\pi$
$431$	−23.2189	−	3.33838i	−1.11842	−	0.160804i	−0.676635	+	0.736319i	$0.736562\pi$
$432$	4.11639	−	11.0365i	0.198050	−	0.530992i
$433$	−8.98558	+	12.0033i	−0.431820	+	0.576843i	−0.962689	−	0.270610i	$-0.912775\pi$
$433$	−8.98558	+	12.0033i	−0.431820	+	0.576843i	0.530869	+	0.847454i	$0.321865\pi$
$434$	11.7294	−	7.53800i	0.563027	−	0.361836i
$435$	−27.9203	+	32.2800i	−1.33868	+	1.54771i
$436$			0.929459i			0.0445130i
$437$	−0.157451	+	7.24631i	−0.00753189	+	0.346638i
$438$	−3.28794	+	3.28794i	−0.157104	+	0.157104i
$439$	−3.74540	−	3.24541i	−0.178758	−	0.154895i	0.560886	−	0.827893i	$-0.310461\pi$
$439$	−3.74540	−	3.24541i	−0.178758	−	0.154895i	−0.739644	+	0.672998i	$0.765006\pi$
$440$	−8.64923	+	5.56945i	−0.412336	+	0.265513i
$441$	−0.218505	−	1.51974i	−0.0104050	−	0.0723685i
$442$	−9.13505	−	3.40720i	−0.434510	−	0.162064i
$443$	−19.8275	−	26.4865i	−0.942034	−	1.25841i	−0.965959	−	0.258696i	$-0.916707\pi$
$443$	−19.8275	−	26.4865i	−0.942034	−	1.25841i	0.0239248	−	0.999714i	$-0.492384\pi$
$444$	26.1720	−	7.68480i	1.24207	−	0.364705i
$445$	−35.3083	+	7.71390i	−1.67377	+	0.365674i
$446$	2.92629	−	6.40768i	0.138564	−	0.303412i
$447$	−35.3466	+	19.3007i	−1.67184	+	0.912891i
$448$	0.185662	−	2.59590i	0.00877173	−	0.122645i
$449$	7.55683	−	6.54803i	0.356629	−	0.309021i	−0.458057	−	0.888923i	$-0.651455\pi$
$449$	7.55683	−	6.54803i	0.356629	−	0.309021i	0.814686	+	0.579902i	$0.196909\pi$
$450$	−16.2726	−	29.6748i	−0.767098	−	1.39888i
$451$	44.2473	+	20.2070i	2.08352	+	0.951513i
$452$	−0.615327	+	0.133856i	−0.0289425	+	0.00629606i
$453$	10.3384	−	18.9334i	0.485741	−	0.889569i
$454$	−0.908178	+	6.31652i	−0.0426229	+	0.296449i
$455$	5.28168	−	14.1995i	0.247609	−	0.665681i
$456$	4.67554	−	0.672241i	0.218952	−	0.0314806i
$457$	0.953406	−	4.38274i	0.0445985	−	0.205016i	−0.949456	−	0.313900i	$-0.898364\pi$
$457$	0.953406	−	4.38274i	0.0445985	−	0.205016i	0.994054	+	0.108884i	$0.0347279\pi$
$458$	0.738575	−	0.0528239i	0.0345113	−	0.00246830i
$459$	−44.1142			−2.05907
$460$	−9.96743	−	3.95606i	−0.464734	−	0.184452i
$461$	−34.9162			−1.62621			−0.813106	−	0.582116i	$-0.802225\pi$
$461$	−34.9162			−1.62621			−0.813106	+	0.582116i	$0.802225\pi$
$462$	−37.3269	+	2.66967i	−1.73661	+	0.124204i
$463$	−5.13139	+	23.5886i	−0.238476	+	1.09626i	0.689695	+	0.724100i	$0.257745\pi$
$463$	−5.13139	+	23.5886i	−0.238476	+	1.09626i	−0.928170	+	0.372155i	$0.878619\pi$
$464$	6.04466	−	0.869091i	0.280616	−	0.0403465i
$465$	−34.0443	+	15.5843i	−1.57876	+	0.722703i
$466$	−3.39467	+	23.6104i	−0.157255	+	1.09373i
$467$	15.2624	−	27.9510i	0.706260	−	1.29342i	−0.240239	−	0.970714i	$-0.577226\pi$
$467$	15.2624	−	27.9510i	0.706260	−	1.29342i	0.946499	−	0.322706i	$-0.104592\pi$
$468$	−17.2186	+	3.74567i	−0.795929	+	0.173144i
$469$	−18.3863	−	8.39672i	−0.848998	−	0.387724i
$470$	2.92684	+	5.34873i	0.135005	+	0.246719i
$471$	32.8895	−	28.4989i	1.51547	−	1.31316i
$472$	−0.455805	+	6.37298i	−0.0209801	+	0.293340i
$473$	−2.73432	+	1.49305i	−0.125724	+	0.0686507i
$474$	−5.65842	+	12.3902i	−0.259900	+	0.569101i
$475$	4.07403	−	6.36430i	0.186929	−	0.292014i
$476$	−9.35194	+	2.74598i	−0.428646	+	0.125862i
$477$	−25.5386	−	34.1156i	−1.16933	−	1.56205i
$478$	15.2529	+	5.68903i	0.697651	+	0.260210i
$479$	−0.570408	−	3.96728i	−0.0260626	−	0.181269i	0.972632	−	0.232352i	$-0.0746420\pi$
$479$	−0.570408	−	3.96728i	−0.0260626	−	0.181269i	−0.998694	+	0.0510823i	$0.983733\pi$
$480$	−1.47948	+	6.83043i	−0.0675286	+	0.311765i
$481$	−17.1706	−	14.8784i	−0.782911	−	0.678396i
$482$	13.7607	−	13.7607i	0.626781	−	0.626781i
$483$	−24.8998	−	30.0300i	−1.13298	−	1.36641i
$484$		−	10.1656i		−	0.462072i
$485$	−12.4349	−	10.7555i	−0.564641	−	0.488381i
$486$	−13.6813	+	8.79241i	−0.620594	+	0.398832i
$487$	−18.1404	+	24.2327i	−0.822019	+	1.09809i	0.171585	+	0.985169i	$0.445111\pi$
$487$	−18.1404	+	24.2327i	−0.822019	+	1.09809i	−0.993604	+	0.112920i	$0.963980\pi$
$488$	−2.58913	+	6.94174i	−0.117205	+	0.314238i
$489$	37.3966	+	5.37682i	1.69113	+	0.243148i
$490$	0.143333	+	0.486539i	0.00647513	+	0.0219796i
$491$	4.91636	+	3.15956i	0.221872	+	0.142589i	0.646856	−	0.762613i	$-0.276084\pi$
$491$	4.91636	+	3.15956i	0.221872	+	0.142589i	−0.424983	+	0.905201i	$0.639720\pi$
$492$	30.9628	−	11.5485i	1.39591	−	0.520649i
$493$	−10.9608	−	20.0731i	−0.493648	−	0.904048i
$494$	−2.57653	−	2.97347i	−0.115923	−	0.133783i
$495$	69.4587	+	4.90539i	3.12194	+	0.220481i
$496$	5.14036	+	1.50935i	0.230809	+	0.0677716i
$497$	11.7919	+	31.6154i	0.528940	+	1.41814i
$498$	−1.63137	−	7.49927i	−0.0731033	−	0.336050i
$499$	10.4192	+	35.4845i	0.466427	+	1.58851i	0.771535	+	0.636187i	$0.219489\pi$
$499$	10.4192	+	35.4845i	0.466427	+	1.58851i	−0.305108	+	0.952318i	$0.598692\pi$
$500$	6.72410	+	8.93233i	0.300711	+	0.399466i
$501$	13.5242	+	29.6138i	0.604215	+	1.32305i
$502$	10.2841	+	7.69860i	0.459003	+	0.343605i
$503$	−5.38101	−	1.17057i	−0.239928	−	0.0521930i	0.0909935	−	0.995851i	$-0.470996\pi$
$503$	−5.38101	−	1.17057i	−0.239928	−	0.0521930i	−0.330921	+	0.943658i	$0.607359\pi$
$504$	−11.5359	+	13.3132i	−0.513850	+	0.593015i
$505$	22.2933	−	22.3332i	0.992040	−	0.993814i
$506$	17.9460	−	12.8355i	0.797797	−	0.570607i
$507$	−13.7524	−	13.7524i	−0.610766	−	0.610766i
$508$	0.184850	+	2.58455i	0.00820141	+	0.114671i
$509$	19.3176	+	30.0587i	0.856237	+	1.33233i	0.941861	+	0.336003i	$0.109075\pi$
$509$	19.3176	+	30.0587i	0.856237	+	1.33233i	−0.0856244	+	0.996327i	$0.527289\pi$
$510$	25.9041	−	3.74809i	1.14705	−	0.165968i
$511$	3.52193	−	1.60841i	0.155801	−	0.0711520i
$512$	0.800541	−	0.599278i	0.0353793	−	0.0264846i
$513$	−15.6245	−	8.53160i	−0.689837	−	0.376680i
$514$	−2.05225	+	3.19336i	−0.0905207	+	0.140853i
$515$	12.2509	−	26.8892i	0.539837	−	1.18488i
$516$	−0.596287	+	2.03077i	−0.0262501	+	0.0893995i
$517$	−12.5127	−	0.894923i	−0.550306	−	0.0393586i
$518$	−22.6550	−	1.62032i	−0.995405	−	0.0711928i
$519$	11.1639	−	38.0209i	0.490043	−	1.66893i
$520$	5.45239	−	2.03919i	0.239103	−	0.0894243i
$521$	−10.7141	+	16.6715i	−0.469394	+	0.730391i	−0.992549	−	0.121846i	$-0.961118\pi$
$521$	−10.7141	+	16.6715i	−0.469394	+	0.730391i	0.523155	+	0.852238i	$0.324755\pi$
$522$	−36.2792	−	19.8100i	−1.58790	−	0.867058i
$523$	9.06364	−	6.78495i	0.396325	−	0.296685i	−0.382465	−	0.923970i	$-0.624925\pi$
$523$	9.06364	−	6.78495i	0.396325	−	0.296685i	0.778790	+	0.627285i	$0.215834\pi$
$524$	−19.1716	+	8.75539i	−0.837516	+	0.382481i
$525$	5.86004	+	40.2466i	0.255753	+	1.75651i
$526$	5.51040	+	8.57436i	0.240265	+	0.373860i
$527$	−1.43134	−	20.0128i	−0.0623503	−	0.871771i
$528$	−10.1676	−	10.1676i	−0.442489	−	0.442489i
$529$	21.7660	+	7.43230i	0.946350	+	0.323143i
$530$	9.96369	+	9.94589i	0.432795	+	0.432022i
$531$	28.3209	−	32.6840i	1.22902	−	1.41837i
$532$	−3.84336	−	0.836073i	−0.166631	−	0.0362483i
$533$	−22.0353	−	16.4954i	−0.954456	−	0.714497i
$534$	−20.9854	−	45.9517i	−0.908128	−	1.98852i
$535$	13.1908	+	1.88452i	0.570287	+	0.0814748i
$536$	−2.18811	−	7.45201i	−0.0945118	−	0.321878i
$537$	0.477822	+	2.19651i	0.0206196	+	0.0947866i
$538$	0.105073	+	0.281711i	0.00453001	+	0.0121454i
$539$	−1.00129	−	0.294007i	−0.0431288	−	0.0126638i
$540$	19.8902	−	17.2661i	0.855940	−	0.743016i
$541$	10.8010	+	12.4650i	0.464372	+	0.535914i	0.938838	−	0.344360i	$-0.111904\pi$
$541$	10.8010	+	12.4650i	0.464372	+	0.535914i	−0.474466	+	0.880274i	$0.657359\pi$
$542$	−0.143901	−	0.263535i	−0.00618109	−	0.0113198i
$543$	−39.7371	+	14.8212i	−1.70528	+	0.636038i
$544$	−3.15058	−	2.02476i	−0.135080	−	0.0868108i
$545$	−0.994409	+	1.82500i	−0.0425958	+	0.0781744i
$546$	20.9605	+	3.01367i	0.897028	+	0.128973i
$547$	−15.7931	+	42.3431i	−0.675266	+	1.81046i	−0.0959013	+	0.995391i	$0.530573\pi$
$547$	−15.7931	+	42.3431i	−0.675266	+	1.81046i	−0.579365	+	0.815068i	$0.696699\pi$
$548$	−2.94842	+	3.93863i	−0.125950	+	0.168250i
$549$	42.1877	−	27.1124i	1.80053	−	1.15713i
$550$	−22.9415	+	1.68203i	−0.978227	+	0.0717219i
$551$		−	9.22935i		−	0.393183i
$552$	2.45501	−	14.7869i	0.104492	−	0.629374i
$553$	8.02001	−	8.02001i	0.341045	−	0.341045i
$554$	4.65639	+	4.03479i	0.197831	+	0.171422i
$555$	59.6108	+	12.9117i	2.53034	+	0.548073i
$556$	1.36117	+	9.46713i	0.0577264	+	0.401496i
$557$	5.94246	+	2.21642i	0.251790	+	0.0939128i	0.472190	−	0.881497i	$-0.343464\pi$
$557$	5.94246	+	2.21642i	0.251790	+	0.0939128i	−0.220400	+	0.975410i	$0.570736\pi$
$558$	−21.7313	−	29.0297i	−0.919961	−	1.22892i
$559$	1.69150	−	0.496668i	0.0715427	−	0.0210068i
$560$	3.14185	−	4.89843i	0.132767	−	0.206997i
$561$	−22.3707	+	48.9851i	−0.944494	+	2.06815i
$562$	24.6309	−	13.4495i	1.03899	−	0.567333i
$563$	0.280753	−	3.92544i	0.0118323	−	0.165438i	−0.988100	−	0.153812i	$-0.950845\pi$
$563$	0.280753	−	3.92544i	0.0118323	−	0.165438i	0.999932	−	0.0116254i	$-0.00370058\pi$
$564$	−6.44079	+	5.58098i	−0.271206	+	0.235002i
$565$	−1.35141	−	0.395498i	−0.0568542	−	0.0166387i
$566$	−5.67825	−	2.59317i	−0.238675	−	0.108999i
$567$	41.9846	−	9.13318i	1.76319	−	0.383558i
$568$	−6.21365	+	11.3795i	−0.260719	+	0.477472i
$569$	5.74397	−	39.9502i	0.240800	−	1.67480i	−0.407340	−	0.913277i	$-0.633543\pi$
$569$	5.74397	−	39.9502i	0.240800	−	1.67480i	0.648139	−	0.761522i	$-0.275547\pi$
$570$	9.89967	+	3.68231i	0.414651	+	0.154235i
$571$	−17.5505	+	2.52338i	−0.734466	+	0.105600i	−0.499391	−	0.866377i	$-0.666443\pi$
$571$	−17.5505	+	2.52338i	−0.734466	+	0.105600i	−0.235075	+	0.971977i	$0.575534\pi$
$572$	−2.54588	+	11.7032i	−0.106449	+	0.489336i
$573$	55.0869	−	3.93989i	2.30129	−	0.164591i
$574$	−27.5170			−1.14854
$575$	−15.3386	−	18.4317i	−0.639664	−	0.768655i
$576$	−6.76873			−0.282030
$577$	9.46769	−	0.677143i	0.394145	−	0.0281898i	0.127140	−	0.991885i	$-0.459420\pi$
$577$	9.46769	−	0.677143i	0.394145	−	0.0281898i	0.267006	+	0.963695i	$0.413966\pi$
$578$	0.632207	−	2.90621i	0.0262964	−	0.120882i
$579$	−42.3384	+	6.08735i	−1.75952	+	0.252981i
$580$	12.7986	+	4.76059i	0.531431	+	0.197673i
$581$	−0.909466	+	6.32547i	−0.0377310	+	0.262425i
$582$	11.0135	−	20.1697i	0.456523	−	0.836060i
$583$	−28.3033	+	6.15701i	−1.17220	+	0.254997i
$584$	1.35327	+	0.618018i	0.0559988	+	0.0255738i
$585$	−37.8162	−	11.0671i	−1.56351	−	0.457570i
$586$	12.9078	−	11.1846i	0.533214	−	0.462033i
$587$	1.38655	−	19.3865i	0.0572291	−	0.800168i	−0.885083	−	0.465433i	$-0.845899\pi$
$587$	1.38655	−	19.3865i	0.0572291	−	0.800168i	0.942312	−	0.334735i	$-0.108647\pi$
$588$	−0.622242	+	0.339770i	−0.0256608	+	0.0140119i
$589$	3.36348	−	7.36500i	0.138590	−	0.303470i
$590$	−7.71330	+	12.0257i	−0.317551	+	0.495092i
$591$	−52.7547	+	15.4902i	−2.17004	+	0.637180i
$592$	−5.23004	−	6.98651i	−0.214953	−	0.287144i
$593$	−38.9367	−	14.5226i	−1.59894	−	0.596373i	−0.617232	−	0.786781i	$-0.711746\pi$
$593$	−38.9367	−	14.5226i	−1.59894	−	0.596373i	−0.981705	+	0.190408i	$0.939019\pi$
$594$	7.71221	+	53.6396i	0.316436	+	2.20086i
$595$	−21.3005	−	4.61370i	−0.873234	−	0.189143i
$596$	9.73802	+	8.43804i	0.398885	+	0.345636i
$597$	44.6435	−	44.6435i	1.82714	−	1.82714i
$598$	−11.4669	+	4.93859i	−0.468916	+	0.201954i
$599$		−	38.9627i		−	1.59197i	−0.605315	−	0.795986i	$-0.706953\pi$
$599$		−	38.9627i		−	1.59197i	0.605315	−	0.795986i	$-0.293047\pi$
$600$	−10.2127	+	11.8287i	−0.416932	+	0.482906i
$601$	−1.12932	+	0.725767i	−0.0460658	+	0.0296047i	−0.563471	−	0.826136i	$-0.690534\pi$
$601$	−1.12932	+	0.725767i	−0.0460658	+	0.0296047i	0.517405	+	0.855740i	$0.326898\pi$
$602$	1.05614	−	1.41084i	0.0430452	−	0.0575017i
$603$	−18.3714	+	49.2555i	−0.748140	+	2.00584i
$604$	−6.83173	−	0.982255i	−0.277979	−	0.0399674i
$605$	10.8759	−	19.9602i	0.442170	−	0.811497i
$606$	37.1056	+	23.8463i	1.50731	+	0.968690i
$607$	27.1219	−	10.1159i	1.10084	−	0.410593i	0.267616	−	0.963526i	$-0.413764\pi$
$607$	27.1219	−	10.1159i	1.10084	−	0.410593i	0.833226	+	0.552933i	$0.186491\pi$
$608$	−0.724297	−	1.32645i	−0.0293741	−	0.0537947i
$609$	32.5296	+	37.5412i	1.31817	+	1.52125i
$610$	−12.5106	+	10.8601i	−0.506539	+	0.439712i
$611$	6.81105	+	1.99991i	0.275546	+	0.0809075i
$612$	8.85878	+	23.7513i	0.358095	+	0.960090i
$613$	−2.07887	−	9.55639i	−0.0839646	−	0.385979i	0.915917	−	0.401368i	$-0.131465\pi$
$613$	−2.07887	−	9.55639i	−0.0839646	−	0.385979i	−0.999882	+	0.0153887i	$0.995101\pi$
$614$	−3.94038	−	13.4197i	−0.159021	−	0.541576i
$615$	73.1513	+	10.4508i	2.94975	+	0.421419i
$616$	4.97386	+	10.8912i	0.200402	+	0.438820i
$617$	10.7550	+	8.05106i	0.432978	+	0.324124i	0.793438	−	0.608651i	$-0.208289\pi$
$617$	10.7550	+	8.05106i	0.432978	+	0.324124i	−0.360459	+	0.932775i	$0.617380\pi$
$618$	40.3580	+	8.77934i	1.62344	+	0.353157i
$619$	−2.29681	+	2.65066i	−0.0923165	+	0.106539i	−0.800028	−	0.599962i	$-0.795182\pi$
$619$	−2.29681	+	2.65066i	−0.0923165	+	0.106539i	0.707712	+	0.706501i	$0.249728\pi$
$620$	8.47831	+	8.46317i	0.340497	+	0.339889i
$621$	−40.8033	+	39.0679i	−1.63738	+	1.56774i
$622$	−3.16964	−	3.16964i	−0.127091	−	0.127091i
$623$	3.00082	+	41.9570i	0.120225	+	1.68097i
$624$	4.39904	+	6.84504i	0.176103	+	0.274021i
$625$	3.64631	+	24.7327i	0.145853	+	0.989306i
$626$	−13.1443	+	6.00280i	−0.525352	+	0.239920i
$627$	−17.3970	+	13.0232i	−0.694768	+	0.520097i
$628$	−12.2207	−	6.67301i	−0.487659	−	0.266282i
$629$	−17.6705	+	27.4959i	−0.704570	+	1.09633i
$630$	−36.8943	+	13.7984i	−1.46990	+	0.549743i
$631$	3.84888	−	13.1081i	0.153222	−	0.521825i	−0.846726	−	0.532029i	$-0.821430\pi$
$631$	3.84888	−	13.1081i	0.153222	−	0.521825i	0.999948	+	0.0102039i	$0.00324805\pi$
$632$	4.34696	+	0.310901i	0.172913	+	0.0123670i
$633$	−10.2900	−	0.735956i	−0.408991	−	0.0292516i
$634$	−3.63996	+	12.3966i	−0.144561	+	0.492331i
$635$	−2.40220	+	5.27254i	−0.0953283	+	0.209234i
$636$	−10.6387	+	16.5542i	−0.421853	+	0.656417i
$637$	0.518288	+	0.283007i	0.0205353	+	0.0112131i
$638$	−22.4913	+	16.8368i	−0.890438	+	0.666574i
$639$	79.8286	−	36.4565i	3.15797	−	1.44220i
$640$	2.21302	−	0.320204i	0.0874774	−	0.0126572i
$641$	4.47438	+	6.96227i	0.176727	+	0.274993i	0.918305	−	0.395874i	$-0.129558\pi$
$641$	4.47438	+	6.96227i	0.176727	+	0.274993i	−0.741577	+	0.670867i	$0.765922\pi$
$642$	1.32868	+	18.5774i	0.0524388	+	0.733190i
$643$	3.79292	+	3.79292i	0.149578	+	0.149578i	0.777930	−	0.628351i	$-0.216270\pi$
$643$	3.79292	+	3.79292i	0.149578	+	0.149578i	−0.628351	+	0.777930i	$0.716270\pi$
$644$	−6.21821	+	10.8220i	−0.245032	+	0.426448i
$645$	−3.34349	+	3.34947i	−0.131650	+	0.131885i
$646$	−3.70654	+	4.27758i	−0.145832	+	0.168299i
$647$	6.21375	+	1.35172i	0.244288	+	0.0531415i	0.333042	−	0.942912i	$-0.391925\pi$
$647$	6.21375	+	1.35172i	0.244288	+	0.0531415i	−0.0887542	+	0.996054i	$0.528289\pi$
$648$	13.2165	+	9.89377i	0.519194	+	0.388664i
$649$	−12.2109	−	26.7382i	−0.479320	−	1.04956i
$650$	12.8875	+	1.82943i	0.505489	+	0.0717563i
$651$	12.2773	+	41.8127i	0.481186	+	1.63877i
$652$	−2.56950	−	11.8118i	−0.100629	−	0.462585i
$653$	1.87799	+	5.03508i	0.0734913	+	0.197038i	0.968501	−	0.249008i	$-0.0801046\pi$
$653$	1.87799	+	5.03508i	0.0734913	+	0.197038i	−0.895010	+	0.446046i	$0.852832\pi$
$654$	−2.78735	−	0.818439i	−0.108994	−	0.0320035i
$655$	−47.0108	−	3.32005i	−1.83686	−	0.129725i
$656$	−6.92396	−	7.99068i	−0.270335	−	0.311983i
$657$	−4.82600	−	8.83816i	−0.188280	−	0.344810i
$658$	6.64897	−	2.47994i	0.259204	−	0.0966780i
$659$	−4.73466	−	3.04278i	−0.184436	−	0.118530i	0.445165	−	0.895449i	$-0.353145\pi$
$659$	−4.73466	−	3.04278i	−0.184436	−	0.118530i	−0.629601	+	0.776919i	$0.716782\pi$
$660$	−9.08607	−	30.8423i	−0.353675	−	1.20053i
$661$	−31.5886	−	4.54176i	−1.22865	−	0.176654i	−0.502739	−	0.864438i	$-0.667674\pi$
$661$	−31.5886	−	4.54176i	−1.22865	−	0.176654i	−0.725915	+	0.687784i	$0.758584\pi$
$662$	−5.24968	+	14.0749i	−0.204034	+	0.547038i
$663$	18.2617	−	24.3948i	0.709226	−	0.947415i
$664$	−2.06570	+	1.32754i	−0.0801647	+	0.0515187i
$665$	−6.65197	−	5.75357i	−0.257952	−	0.223114i
$666$			59.0723i			2.28900i
$667$	−27.9151	−	8.85968i	−1.08088	−	0.343048i
$668$	7.36537	−	7.36537i	0.284975	−	0.284975i
$669$	16.6392	+	14.4179i	0.643308	+	0.557430i
$670$	3.67638	−	16.9731i	0.142031	−	0.655727i
$671$	−4.85084	−	33.7383i	−0.187265	−	1.30245i
$672$	7.62134	+	2.84261i	0.293999	+	0.109656i
$673$	−1.95290	−	2.60877i	−0.0752789	−	0.100561i	0.761321	−	0.648375i	$-0.224551\pi$
$673$	−1.95290	−	2.60877i	−0.0752789	−	0.100561i	−0.836600	+	0.547814i	$0.815460\pi$
$674$	4.20113	−	1.23356i	0.161821	−	0.0475151i
$675$	57.5273	−	12.6220i	2.21423	−	0.485823i
$676$	−2.58498	+	5.66031i	−0.0994222	+	0.217704i
$677$	0.185501	−	0.101291i	0.00712938	−	0.00389293i	−0.475680	−	0.879618i	$-0.657798\pi$
$677$	0.185501	−	0.101291i	0.00712938	−	0.00389293i	0.482810	+	0.875725i	$0.339616\pi$
$678$	0.140408	−	1.96317i	0.00539235	−	0.0753949i
$679$	−14.4617	+	12.5311i	−0.554987	+	0.480899i
$680$	−4.01995	−	7.34637i	−0.154158	−	0.281720i
$681$	−18.1429	−	8.28557i	−0.695236	−	0.317504i
$682$	−24.0839	+	5.23913i	−0.922219	+	0.200617i
$683$	16.7769	−	30.7247i	0.641952	−	1.17565i	−0.330778	−	0.943709i	$-0.607311\pi$
$683$	16.7769	−	30.7247i	0.641952	−	1.17565i	0.972730	−	0.231939i	$-0.0745070\pi$
$684$	−1.45584	+	10.1256i	−0.0556653	+	0.387161i
$685$	−10.0031	+	4.57908i	−0.382199	+	0.174957i
$686$	18.6166	−	2.67667i	0.710786	−	0.102196i
$687$	−0.491942	+	2.26142i	−0.0187688	+	0.0862786i
$688$	0.675447	−	0.0483089i	0.0257512	−	0.00184176i
$689$	16.3905			0.624429
$690$	20.6407	−	26.4077i	0.785777	−	1.00532i
$691$	27.6793			1.05297			0.526485	−	0.850185i	$-0.323510\pi$
$691$	27.6793			1.05297			0.526485	+	0.850185i	$0.323510\pi$
$692$	−12.6460	+	0.904460i	−0.480729	+	0.0343824i
$693$	17.2270	−	79.1914i	0.654401	−	3.00823i
$694$	13.3125	−	1.91406i	0.505337	−	0.0726566i
$695$	−7.45602	+	20.0451i	−0.282823	+	0.760352i
$696$	−2.71634	+	18.8926i	−0.102963	+	0.716121i
$697$	−18.9771	+	34.7540i	−0.718811	+	1.31640i
$698$	19.7850	−	4.30396i	0.748872	−	0.162907i
$699$	−67.8159	−	30.9705i	−2.56503	−	1.17141i
$700$	11.4098	−	6.25671i	0.431249	−	0.236481i
$701$	−14.5899	+	12.6422i	−0.551051	+	0.477489i	−0.885316	−	0.464991i	$-0.846058\pi$
$701$	−14.5899	+	12.6422i	−0.551051	+	0.477489i	0.334264	+	0.942479i	$0.391512\pi$
$702$	2.18762	−	30.5870i	0.0825665	−	1.15443i
$703$	−11.5763	+	6.32111i	−0.436607	+	0.238405i
$704$	−1.91116	+	4.18486i	−0.0720296	+	0.157723i
$705$	−18.6175	+	4.06742i	−0.701176	+	0.153188i
$706$	32.2760	−	9.47708i	1.21472	−	0.356675i
$707$	−22.0099	−	29.4017i	−0.827766	−	1.10577i
$708$	−18.7105	−	6.97867i	−0.703185	−	0.262274i
$709$	−1.99572	−	13.8805i	−0.0749509	−	0.521295i	−0.992363	−	0.123355i	$-0.960635\pi$
$709$	−1.99572	−	13.8805i	−0.0749509	−	0.521295i	0.917412	−	0.397939i	$-0.130275\pi$
$710$	−24.3752	+	15.6958i	−0.914785	+	0.589052i
$711$	−22.2935	−	19.3175i	−0.836073	−	0.724461i
$712$	−11.4288	+	11.4288i	−0.428313	+	0.428313i
$713$	−19.0474	−	17.2432i	−0.713331	−	0.645763i
$714$		−	30.4634i		−	1.14007i
$715$	−17.5199	+	20.2556i	−0.655206	+	0.757515i
$716$	0.605037	−	0.388834i	0.0226113	−	0.0145314i
$717$	−30.4918	+	40.7323i	−1.13874	+	1.52117i
$718$	6.41005	−	17.1860i	0.239221	−	0.641376i
$719$	21.8991	+	3.14862i	0.816699	+	0.117424i	0.537989	−	0.842952i	$-0.319184\pi$
$719$	21.8991	+	3.14862i	0.816699	+	0.117424i	0.278710	+	0.960375i	$0.410093\pi$
$720$	−13.2904	−	7.24172i	−0.495306	−	0.269883i
$721$	−28.9316	−	18.5932i	−1.07747	−	0.692448i
$722$	15.6620	−	5.84162i	0.582878	−	0.217402i
$723$	29.1497	+	53.3837i	1.08409	+	1.98536i
$724$	8.88608	+	10.2551i	0.330248	+	0.381127i
$725$	20.0368	+	23.0404i	0.744148	+	0.855697i
$726$	30.4855	+	8.95134i	1.13142	+	0.332216i
$727$	−6.18491	−	16.5824i	−0.229385	−	0.615006i	0.770359	−	0.637610i	$-0.220077\pi$
$727$	−6.18491	−	16.5824i	−0.229385	−	0.615006i	−0.999744	+	0.0226041i	$0.992804\pi$
$728$	−1.44019	−	6.62043i	−0.0533768	−	0.245369i
$729$	−0.366606	−	1.24854i	−0.0135780	−	0.0462424i
$730$	1.99595	+	2.66132i	0.0738735	+	0.0984999i
$731$	−1.05353	−	2.30690i	−0.0389661	−	0.0853238i
$732$	−18.5376	−	13.8771i	−0.685171	−	0.512913i
$733$	−18.8453	−	4.09955i	−0.696068	−	0.151420i	−0.149409	−	0.988776i	$-0.547737\pi$
$733$	−18.8453	−	4.09955i	−0.696068	−	0.151420i	−0.546659	+	0.837355i	$0.684101\pi$
$734$	8.22714	−	9.49463i	0.303669	−	0.350453i
$735$	−1.58529	+	0.00141685i	−0.0584743	+	5.22615e-5i
$736$	−4.70727	+	0.917387i	−0.173512	+	0.0338153i
$737$	25.2657	+	25.2657i	0.930675	+	0.930675i
$738$	5.10553	+	71.3846i	0.187937	+	2.62770i
$739$	4.25075	+	6.61429i	0.156366	+	0.243311i	0.910594	−	0.413303i	$-0.135625\pi$
$739$	4.25075	+	6.61429i	0.156366	+	0.243311i	−0.754228	+	0.656613i	$0.771988\pi$
$740$	−2.79449	−	19.3136i	−0.102728	−	0.709981i
$741$	11.1859	−	5.10843i	0.410924	−	0.187663i
$742$	13.1172	−	9.81943i	0.481548	−	0.360483i
$743$	−13.2377	−	7.22835i	−0.485646	−	0.265183i	0.217719	−	0.976011i	$-0.430138\pi$
$743$	−13.2377	−	7.22835i	−0.485646	−	0.265183i	−0.703365	+	0.710829i	$0.748320\pi$
$744$	−9.05273	+	14.0863i	−0.331889	+	0.516429i
$745$	10.0930	+	26.9867i	0.369778	+	0.988714i
$746$	−2.51739	+	8.57346i	−0.0921684	+	0.313897i
$747$	16.5783	+	1.18570i	0.606567	+	0.0433826i
$748$	17.1859	+	1.22916i	0.628377	+	0.0449424i
$749$	4.36924	−	14.8803i	0.159649	−	0.543713i
$750$	−32.7080	+	12.2995i	−1.19433	+	0.449113i
$751$	8.20525	−	12.7676i	0.299414	−	0.465897i	−0.658651	−	0.752448i	$-0.728873\pi$
$751$	8.20525	−	12.7676i	0.299414	−	0.465897i	0.958065	+	0.286552i	$0.0925090\pi$
$752$	2.39319	+	1.30678i	0.0872708	+	0.0476535i
$753$	−32.1430	+	24.0619i	−1.17136	+	0.876866i
$754$	14.4614	−	6.60431i	0.526654	−	0.240515i
$755$	−12.3633	−	9.23779i	−0.449945	−	0.336198i
$756$	−16.5737	−	25.7891i	−0.602778	−	0.937941i
$757$	1.92744	+	26.9491i	0.0700540	+	0.979483i	0.903971	+	0.427593i	$0.140639\pi$
$757$	1.92744	+	26.9491i	0.0700540	+	0.979483i	−0.833917	+	0.551890i	$0.813907\pi$
$758$	8.80984	+	8.80984i	0.319988	+	0.319988i
$759$	22.6898	+	65.1204i	0.823588	+	2.36372i
$760$	−0.00302035	−	3.37941i	−0.000109560	−	0.122584i
$761$	16.6650	−	19.2325i	0.604106	−	0.697176i	−0.368502	−	0.929627i	$-0.620129\pi$
$761$	16.6650	−	19.2325i	0.604106	−	0.697176i	0.972608	+	0.232451i	$0.0746746\pi$
$762$	−7.91355	−	1.72149i	−0.286678	−	0.0623629i
$763$	1.93647	+	1.44962i	0.0701048	+	0.0524798i
$764$	−7.34039	−	16.0732i	−0.265566	−	0.581509i
$765$	−8.01675	+	56.1137i	−0.289846	+	2.02879i
$766$	2.50556	+	8.53315i	0.0905295	+	0.308315i
$767$	3.53568	+	16.2533i	0.127666	+	0.586872i
$768$	1.09225	+	2.92843i	0.0394131	+	0.105671i
$769$	30.6638	+	9.00371i	1.10577	+	0.324682i	0.783140	−	0.621845i	$-0.213617\pi$
$769$	30.6638	+	9.00371i	1.10577	+	0.324682i	0.322625	+	0.946527i	$0.395435\pi$
$770$	−1.88609	+	26.7064i	−0.0679700	+	0.962433i
$771$	−7.76942	−	8.96639i	−0.279809	−	0.322917i
$772$	6.55873	+	12.0114i	0.236054	+	0.432301i
$773$	−25.3084	+	9.43955i	−0.910281	+	0.339517i	−0.760603	−	0.649218i	$-0.775096\pi$
$773$	−25.3084	+	9.43955i	−0.910281	+	0.339517i	−0.149678	+	0.988735i	$0.547824\pi$
$774$	−3.85597	−	2.47808i	−0.138600	−	0.0890727i
$775$	7.59266	+	25.6883i	0.272736	+	0.922749i
$776$	−7.27782	−	1.04639i	−0.261258	−	0.0375633i
$777$	24.8081	−	66.5132i	0.889987	−	2.38615i
$778$	17.0609	−	22.7907i	0.611663	−	0.817086i
$779$	−13.4428	+	8.63913i	−0.481637	+	0.309529i
$780$	1.31418	+	18.1467i	0.0470553	+	0.649757i
$781$		−	59.6487i		−	2.13440i
$782$	9.37987	+	15.3170i	0.335424	+	0.547736i
$783$	50.8644	−	50.8644i	1.81775	−	1.81775i
$784$	0.171428	+	0.148544i	0.00612244	+	0.00530513i
$785$	−16.8561	−	26.1772i	−0.601621	−	0.934303i
$786$	−9.37481	−	65.2032i	−0.334388	−	2.32572i
$787$	18.5946	+	6.93542i	0.662825	+	0.247221i	0.658285	−	0.752769i	$-0.271282\pi$
$787$	18.5946	+	6.93542i	0.662825	+	0.247221i	0.00453983	+	0.999990i	$0.498555\pi$
$788$	10.5421	+	14.0826i	0.375548	+	0.501673i
$789$	−30.5658	+	8.97492i	−1.08817	+	0.319516i
$790$	8.20266	+	5.26118i	0.291838	+	0.187184i
$791$	−0.680807	+	1.49076i	−0.0242067	+	0.0530053i
$792$	27.3311	−	14.9239i	0.971170	−	0.530299i
$793$	−1.37597	+	19.2386i	−0.0488623	+	0.683184i
$794$	13.6893	−	11.8619i	0.485816	−	0.420962i
$795$	−38.6002	+	21.1221i	−1.36901	+	0.749125i
$796$	−18.3747	−	8.39144i	−0.651274	−	0.297427i
$797$	−23.5266	+	5.11790i	−0.833356	+	0.181285i	−0.608948	−	0.793210i	$-0.708408\pi$
$797$	−23.5266	+	5.11790i	−0.833356	+	0.181285i	−0.224407	+	0.974495i	$0.572045\pi$
$798$	5.89158	−	10.7896i	0.208560	−	0.381949i
$799$	1.45330	−	10.1080i	0.0514142	−	0.357594i
$800$	4.68786	+	1.73894i	0.165741	+	0.0614810i
$801$	108.288	−	15.5695i	3.82617	−	0.550120i
$802$	−7.16821	+	32.9517i	−0.253118	+	1.16357i
$803$	−6.82694	+	0.488273i	−0.240918	+	0.0172308i
$804$	24.2745			0.856096
$805$	−23.7878	+	14.5964i	−0.838409	+	0.514457i
$806$	13.9470			0.491263
$807$	−0.937344	+	0.0670402i	−0.0329961	+	0.00235993i
$808$	2.99975	−	13.7896i	0.105531	−	0.485118i
$809$	−2.16520	+	0.311308i	−0.0761242	+	0.0109450i	−0.180272	−	0.983617i	$-0.557698\pi$
$809$	−2.16520	+	0.311308i	−0.0761242	+	0.0109450i	0.104147	+	0.994562i	$0.466789\pi$
$810$	15.3656	+	33.5666i	0.539893	+	1.17941i
$811$	1.89548	−	13.1833i	0.0665592	−	0.462929i	−0.929098	−	0.369834i	$-0.879415\pi$
$811$	1.89548	−	13.1833i	0.0665592	−	0.462929i	0.995657	−	0.0930956i	$-0.0296762\pi$
$812$	7.61680	−	13.9491i	0.267297	−	0.489518i
$813$	0.917027	−	0.199487i	0.0321615	−	0.00699632i
$814$	36.5222	+	16.6791i	1.28010	+	0.584604i
$815$	7.59196	−	25.9416i	0.265935	−	0.908694i
$816$	8.84629	−	7.66535i	0.309682	−	0.268341i
$817$	0.0730101	−	1.02081i	0.00255430	−	0.0357138i
$818$	−23.3455	+	12.7476i	−0.816257	+	0.445710i
$819$	−19.0509	+	41.7157i	−0.665692	+	1.45766i
$820$	−5.04619	−	23.0975i	−0.176221	−	0.806601i
$821$	20.1128	−	5.90566i	0.701943	−	0.206109i	0.0887634	−	0.996053i	$-0.471709\pi$
$821$	20.1128	−	5.90566i	0.701943	−	0.206109i	0.613179	+	0.789944i	$0.289890\pi$
$822$	−9.21529	−	12.3102i	−0.321420	−	0.429367i
$823$	−13.2986	−	4.96012i	−0.463560	−	0.172899i	0.106823	−	0.994278i	$-0.465932\pi$
$823$	−13.2986	−	4.96012i	−0.463560	−	0.172899i	−0.570383	+	0.821379i	$0.693205\pi$
$824$	−1.88062	−	13.0800i	−0.0655144	−	0.455663i
$825$	15.1570	−	70.2801i	0.527698	−	2.44684i
$826$	12.5668	+	10.8892i	0.437255	+	0.378883i
$827$	−39.1807	+	39.1807i	−1.36245	+	1.36245i	−0.491656	+	0.870790i	$0.663608\pi$
$827$	−39.1807	+	39.1807i	−1.36245	+	1.36245i	−0.870790	+	0.491656i	$0.836392\pi$
$828$	29.2283	+	14.1233i	1.01575	+	0.490820i
$829$		−	45.0301i		−	1.56396i	−0.623303	−	0.781980i	$-0.714210\pi$
$829$		−	45.0301i		−	1.56396i	0.623303	−	0.781980i	$-0.285790\pi$
$830$	−5.47633	+	0.396595i	−0.190086	+	0.0137660i
$831$	−16.2001	+	10.4112i	−0.561975	+	0.361159i
$832$	1.56012	−	2.08408i	0.0540875	−	0.0722524i
$833$	0.296874	−	0.795949i	0.0102861	−	0.0275780i
$834$	−29.5895	−	4.25432i	−1.02460	−	0.147315i
$835$	22.3420	−	6.58190i	0.773177	−	0.227776i
$836$	5.84922	+	3.75906i	0.202299	+	0.130010i
$837$	59.1264	−	22.0530i	2.04371	−	0.762264i
$838$	−6.95388	−	12.7351i	−0.240218	−	0.439926i
$839$	−30.7170	−	35.4493i	−1.06047	−	1.22385i	−0.973751	−	0.227614i	$-0.926908\pi$
$839$	−30.7170	−	35.4493i	−1.06047	−	1.22385i	−0.0867177	−	0.996233i	$-0.527638\pi$
$840$	11.9233	+	13.7354i	0.411393	+	0.473916i
$841$	7.95733	+	2.33648i	0.274391	+	0.0805684i
$842$	3.22352	+	8.64260i	0.111090	+	0.297844i
$843$	18.6447	+	85.7085i	0.642159	+	2.95196i
$844$	0.929912	+	3.16699i	0.0320089	+	0.109012i
$845$	−11.1315	+	8.34845i	−0.382934	+	0.287195i
$846$	−7.66711	−	16.7886i	−0.263601	−	0.577205i
$847$	−21.1793	−	15.8546i	−0.727730	−	0.544772i
$848$	6.15208	+	1.33830i	0.211263	+	0.0459575i
$849$	12.7766	−	14.7450i	0.438493	−	0.506048i
$850$	−0.0334719	−	18.7255i	−0.00114808	−	0.642279i
$851$	8.00625	+	41.0815i	0.274451	+	1.40825i
$852$	−28.6543	−	28.6543i	−0.981680	−	0.981680i
$853$	−0.870050	−	12.1649i	−0.0297899	−	0.416518i	−0.990364	−	0.138492i	$-0.955774\pi$
$853$	−0.870050	−	12.1649i	−0.0297899	−	0.416518i	0.960574	−	0.278026i	$-0.0896801\pi$
$854$	10.4245	+	16.2209i	0.356720	+	0.555067i
$855$	−13.6917	+	18.3241i	−0.468246	+	0.626670i
$856$	5.42049	−	2.47546i	0.185269	−	0.0846094i
$857$	−28.1693	+	21.0873i	−0.962246	+	0.720328i	−0.960096	−	0.279669i	$-0.909775\pi$
$857$	−28.1693	+	21.0873i	−0.962246	+	0.720328i	−0.00214954	+	0.999998i	$0.500684\pi$
$858$	−32.8549	−	17.9401i	−1.12165	−	0.612466i
$859$	20.5494	−	31.9755i	0.701136	−	1.09099i	−0.289856	−	0.957070i	$-0.593608\pi$
$859$	20.5494	−	31.9755i	0.701136	−	1.09099i	0.990992	−	0.133919i	$-0.0427561\pi$
$860$	1.37793	+	0.627791i	0.0469870	+	0.0214075i
$861$	24.2302	−	82.5206i	0.825764	−	2.81229i
$862$	−23.3979	−	1.67345i	−0.796937	−	0.0569980i
$863$	−7.77284	−	0.555924i	−0.264590	−	0.0189239i	−0.0615863	−	0.998102i	$-0.519616\pi$
$863$	−7.77284	−	0.555924i	−0.264590	−	0.0189239i	−0.203004	+	0.979178i	$0.565070\pi$
$864$	3.31857	−	11.3020i	0.112900	−	0.384502i
$865$	−25.7982	−	11.7538i	−0.877165	−	0.399641i
$866$	−8.10638	+	12.6138i	−0.275466	+	0.428634i
$867$	8.15872	+	4.45500i	0.277085	+	0.151300i
$868$	11.1617	−	8.35556i	0.378853	−	0.283606i
$869$	−18.2379	+	8.32897i	−0.618678	+	0.282541i
$870$	−25.5463	+	34.1895i	−0.866101	+	1.15913i
$871$	−10.9313	−	17.0094i	−0.370392	−	0.576341i
$872$	0.0663069	+	0.927091i	0.00224543	+	0.0313953i
$873$	35.1914	+	35.1914i	1.19105	+	1.19105i
$874$	0.359897	+	7.23908i	0.0121737	+	0.244866i
$875$	29.0971	−	0.0780168i	0.983661	−	0.00263745i
$876$	−3.04500	+	3.51412i	−0.102881	+	0.118731i
$877$	22.5132	+	4.89744i	0.760216	+	0.165375i	0.575931	−	0.817498i	$-0.304640\pi$
$877$	22.5132	+	4.89744i	0.760216	+	0.165375i	0.184285	+	0.982873i	$0.441003\pi$
$878$	−3.96739	−	2.96995i	−0.133893	−	0.100231i
$879$	22.1755	+	48.5576i	0.747962	+	1.63781i
$880$	−8.22987	+	6.17229i	−0.277429	+	0.208068i
$881$	4.09163	+	13.9348i	0.137851	+	0.469476i	0.999261	−	0.0384331i	$-0.0122366\pi$
$881$	4.09163	+	13.9348i	0.137851	+	0.469476i	−0.861410	+	0.507909i	$0.830418\pi$
$882$	−0.326366	−	1.50028i	−0.0109893	−	0.0505170i
$883$	2.98263	+	7.99675i	0.100374	+	0.269112i	0.977424	−	0.211286i	$-0.0677651\pi$
$883$	2.98263	+	7.99675i	0.100374	+	0.269112i	−0.877051	+	0.480398i	$0.840492\pi$
$884$	−9.35484	−	2.74683i	−0.314637	−	0.0923858i
$885$	−29.2719	−	33.7207i	−0.983965	−	1.13351i
$886$	−21.6665	−	25.0045i	−0.727901	−	0.840043i
$887$	1.87685	+	3.43719i	0.0630184	+	0.115410i	0.907289	−	0.420507i	$-0.138148\pi$
$887$	1.87685	+	3.43719i	0.0630184	+	0.115410i	−0.844271	+	0.535917i	$0.819966\pi$
$888$	25.5571	−	9.53231i	0.857641	−	0.319883i
$889$	5.67303	+	3.64584i	0.190267	+	0.122277i
$890$	−34.6680	+	10.2131i	−1.16207	+	0.342344i
$891$	−75.1806	−	10.8093i	−2.51864	−	0.362126i
$892$	2.46172	−	6.60011i	0.0824243	−	0.220988i
$893$	2.46960	−	3.29899i	0.0826419	−	0.110397i
$894$	−33.8796	+	21.7731i	−1.13310	+	0.728202i
$895$	1.60400	−	0.116161i	0.0536158	−	0.00388285i
$896$		−	2.60253i		−	0.0869445i
$897$	−4.71308	−	38.7367i	−0.157365	−	1.29338i
$898$	7.07044	−	7.07044i	0.235944	−	0.235944i
$899$	24.7255	+	21.4247i	0.824641	+	0.714555i
$900$	−18.3481	−	28.4383i	−0.611604	−	0.947944i
$901$	−3.35565	−	23.3391i	−0.111793	−	0.777537i
$902$	45.5761	+	16.9990i	1.51752	+	0.566005i
$903$	3.30097	+	4.40959i	0.109850	+	0.146742i
$904$	−0.604210	+	0.177412i	−0.0200957	+	0.00590064i
$905$	6.47618	+	29.6429i	0.215276	+	0.985365i
$906$	8.96138	−	19.6227i	0.297722	−	0.651920i
$907$	42.7332	−	23.3341i	1.41893	−	0.774795i	0.427326	−	0.904098i	$-0.359456\pi$
$907$	42.7332	−	23.3341i	1.41893	−	0.774795i	0.991605	+	0.129303i	$0.0412738\pi$
$908$	−0.455249	+	6.36521i	−0.0151080	+	0.211237i
$909$	−72.1902	+	62.5531i	−2.39440	+	2.07476i
$910$	4.25524	−	14.5401i	0.141060	−	0.481999i
$911$	25.3691	+	11.5857i	0.840517	+	0.383851i	0.788680	−	0.614804i	$-0.210765\pi$
$911$	25.3691	+	11.5857i	0.840517	+	0.383851i	0.0518375	+	0.998656i	$0.483492\pi$
$912$	4.61567	−	1.00408i	0.152840	−	0.0332483i
$913$	5.41398	−	9.91496i	0.179177	−	0.328137i
$914$	0.638316	−	4.43959i	0.0211136	−	0.146848i
$915$	−21.5520	−	47.0808i	−0.712486	−	1.55644i
$916$	0.732925	−	0.105379i	0.0242165	−	0.00348181i
$917$	−11.6595	+	53.5980i	−0.385032	+	1.76996i
$918$	−44.0018	+	3.14707i	−1.45227	+	0.103869i
$919$	25.1171			0.828537			0.414269	−	0.910155i	$-0.364037\pi$
$919$	25.1171			0.828537			0.414269	+	0.910155i	$0.364037\pi$
$920$	−10.2243	−	3.23492i	−0.337084	−	0.106652i
$921$	43.7140			1.44043
$922$	−34.8273	+	2.49090i	−1.14698	+	0.0820333i
$923$	−7.17478	+	32.9819i	−0.236161	+	1.08561i
$924$	−37.0414	+	5.32574i	−1.21857	+	0.175204i
$925$	15.1762	−	40.9121i	0.498989	−	1.34518i
$926$	−3.43552	+	23.8946i	−0.112898	+	0.785224i
$927$	−42.8666	+	78.5042i	−1.40792	+	2.57842i
$928$	5.96726	−	1.29810i	0.195885	−	0.0426122i
$929$	−32.9625	−	15.0535i	−1.08146	−	0.493888i	−0.206684	−	0.978408i	$-0.566267\pi$
$929$	−32.9625	−	15.0535i	−1.08146	−	0.493888i	−0.874780	+	0.484520i	$0.838994\pi$
$930$	−32.8457	+	17.9733i	−1.07705	+	0.589366i
$931$	0.259083	−	0.224496i	0.00849109	−	0.00735758i
$932$	−1.70167	+	23.7924i	−0.0557400	+	0.779347i
$933$	12.2964	−	6.71436i	0.402567	−	0.219818i
$934$	13.2295	−	28.9686i	0.432883	−	0.947882i
$935$	32.4295	+	20.8002i	1.06056	+	0.680241i
$936$	−16.9075	+	4.96449i	−0.552639	+	0.162269i
$937$	−5.31939	−	7.10587i	−0.173777	−	0.232139i	0.705194	−	0.709015i	$-0.250860\pi$
$937$	−5.31939	−	7.10587i	−0.173777	−	0.232139i	−0.878971	+	0.476876i	$0.841769\pi$
$938$	−18.9384	−	7.06367i	−0.618361	−	0.230637i
$939$	−6.42748	−	44.7041i	−0.209753	−	1.45886i
$940$	3.30095	+	5.12630i	0.107665	+	0.167202i
$941$	23.4217	+	20.2950i	0.763526	+	0.661599i	0.946930	−	0.321439i	$-0.104166\pi$
$941$	23.4217	+	20.2950i	0.763526	+	0.661599i	−0.183405	+	0.983038i	$0.558712\pi$
$942$	30.7726	−	30.7726i	1.00263	−	1.00263i
$943$	13.2256	+	48.9520i	0.430684	+	1.59410i
$944$			6.38926i			0.207953i
$945$	−4.95126	−	68.3689i	−0.161065	−	2.22404i
$946$	−2.62084	+	1.68431i	−0.0852110	+	0.0547618i
$947$	27.8737	−	37.2350i	0.905775	−	1.20997i	−0.0713807	−	0.997449i	$-0.522741\pi$
$947$	27.8737	−	37.2350i	0.905775	−	1.20997i	0.977156	−	0.212525i	$-0.0681686\pi$
$948$	−4.76009	+	12.7623i	−0.154601	+	0.414500i
$949$	3.83360	+	0.551188i	0.124444	+	0.0178923i
$950$	3.60963	−	6.63872i	0.117112	−	0.215389i
$951$	−33.9708	−	21.8317i	−1.10158	−	0.707942i
$952$	−9.13222	+	3.40614i	−0.295977	+	0.110394i
$953$	1.84229	+	3.37390i	0.0596775	+	0.109291i	0.905815	−	0.423674i	$-0.139260\pi$
$953$	1.84229	+	3.37390i	0.0596775	+	0.109291i	−0.846137	+	0.532965i	$0.821078\pi$
$954$	−27.9073	−	32.2068i	−0.903533	−	1.04273i
$955$	2.78348	−	39.4132i	0.0900714	−	1.27538i
$956$	15.6199	+	4.58641i	0.505183	+	0.148335i
$957$	−30.6868	−	82.2746i	−0.991964	−	2.65956i
$958$	−0.851977	−	3.91647i	−0.0275261	−	0.126536i
$959$	3.60740	+	12.2857i	0.116489	+	0.396725i
$960$	−0.988430	+	6.91857i	−0.0319014	+	0.223296i
$961$	−0.954875	−	2.09088i	−0.0308024	−	0.0674479i
$962$	−18.1882	−	13.6155i	−0.586412	−	0.438983i
$963$	−39.4131	−	8.57379i	−1.27007	−	0.276286i
$964$	12.7439	−	14.7073i	0.410454	−	0.473689i
$965$	0.0273502	+	30.6016i	0.000880433	+	0.985099i
$966$	−26.9787	−	28.1771i	−0.868025	−	0.906584i
$967$	−11.4499	−	11.4499i	−0.368205	−	0.368205i	0.498617	−	0.866822i	$-0.333841\pi$
$967$	−11.4499	−	11.4499i	−0.368205	−	0.368205i	−0.866822	+	0.498617i	$0.833841\pi$
$968$	−0.725204	−	10.1397i	−0.0233089	−	0.325902i
$969$	−9.56418	−	14.8822i	−0.307246	−	0.478084i
$970$	−13.1705	−	9.84098i	−0.422880	−	0.315975i
$971$	−24.6330	+	11.2495i	−0.790511	+	0.361015i	−0.769404	−	0.638763i	$-0.779447\pi$
$971$	−24.6330	+	11.2495i	−0.790511	+	0.361015i	−0.0211077	+	0.999777i	$0.506719\pi$
$972$	−13.0191	+	9.74601i	−0.417589	+	0.312604i
$973$	21.8471	+	11.9294i	0.700385	+	0.382439i
$974$	−16.3654	+	25.4651i	−0.524382	+	0.815954i
$975$	−16.8344	+	37.0373i	−0.539132	+	1.18614i
$976$	−2.08732	+	7.10876i	−0.0668135	+	0.227546i
$977$	−19.0254	−	1.36073i	−0.608678	−	0.0435335i	−0.236401	−	0.971655i	$-0.575968\pi$
$977$	−19.0254	−	1.36073i	−0.608678	−	0.0435335i	−0.372276	+	0.928122i	$0.621423\pi$
$978$	37.6849	+	2.69528i	1.20503	+	0.0861854i
$979$	20.9493	−	71.3466i	0.669541	−	2.28025i
$980$	0.177677	+	0.475074i	0.00567569	+	0.0151757i
$981$	3.40131	−	5.29254i	0.108595	−	0.168978i
$982$	5.12924	+	2.80078i	0.163681	+	0.0893763i
$983$	−21.8549	+	16.3604i	−0.697063	+	0.521815i	−0.888032	−	0.459781i	$-0.847928\pi$
$983$	−21.8549	+	16.3604i	−0.697063	+	0.521815i	0.190969	+	0.981596i	$0.438837\pi$
$984$	30.0601	−	13.7280i	0.958281	−	0.437632i
$985$	5.63283	+	38.9301i	0.179477	+	1.24042i
$986$	−12.3648	−	19.2401i	−0.393776	−	0.612728i
$987$	1.58229	+	22.1233i	0.0503648	+	0.704191i
$988$	−2.78209	−	2.78209i	−0.0885100	−	0.0885100i
$989$	−3.01747	−	1.20075i	−0.0959499	−	0.0381817i
$990$	69.6317	−	0.0622334i	2.21304	−	0.00197791i
$991$	−30.9827	+	35.7559i	−0.984198	+	1.13582i	0.00653234	+	0.999979i	$0.497921\pi$
$991$	−30.9827	+	35.7559i	−0.984198	+	1.13582i	−0.990730	+	0.135846i	$0.956625\pi$
$992$	5.23494	+	1.13879i	0.166209	+	0.0361566i
$993$	−37.5866	−	28.1369i	−1.19277	−	0.892899i
$994$	14.0173	+	30.6936i	0.444601	+	0.973541i
$995$	−27.1010	−	36.1353i	−0.859160	−	1.14557i
$996$	−2.16220	−	7.36379i	−0.0685120	−	0.233330i
$997$	5.70752	+	26.2370i	0.180759	+	0.830935i	0.974802	+	0.223073i	$0.0716090\pi$
$997$	5.70752	+	26.2370i	0.180759	+	0.830935i	−0.794043	+	0.607862i	$0.792027\pi$
$998$	12.9241	+	34.6508i	0.409105	+	1.09685i
$999$	−98.6353	−	28.9619i	−3.12068	−	0.916315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.7	✓	240
5.3	odd	4	inner	230.2.l.a.53.1	yes	240
23.10	odd	22	inner	230.2.l.a.217.1	yes	240
115.33	even	44	inner	230.2.l.a.33.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.7	✓	240	1.1	even	1	trivial
230.2.l.a.33.7	yes	240	115.33	even	44	inner
230.2.l.a.53.1	yes	240	5.3	odd	4	inner
230.2.l.a.217.1	yes	240	23.10	odd	22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 - 0.0713392i) q^{2} +(-0.664372 + 3.05407i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.09578 + 0.779553i) q^{5} +(-0.444805 + 3.09368i) q^{6} +(1.24726 - 2.28419i) q^{7} +(0.977147 - 0.212565i) q^{8} +(-6.15705 - 2.81183i) q^{9} +(2.14605 + 0.628055i) q^{10} +(-3.47691 + 3.01276i) q^{11} +(-0.222970 + 3.11753i) q^{12} +(2.28489 - 1.24765i) q^{13} +(1.08113 - 2.36735i) q^{14} +(-3.77319 + 5.88275i) q^{15} +(0.959493 - 0.281733i) q^{16} +(-2.24436 - 2.99811i) q^{17} +(-6.34196 - 2.36543i) q^{18} +(-0.215083 - 1.49593i) q^{19} +(2.18539 + 0.473357i) q^{20} +(6.14742 + 5.32677i) q^{21} +(-3.25312 + 3.25312i) q^{22} +(-4.73107 - 0.785478i) q^{23} +3.12550i q^{24} +(3.78459 + 3.26754i) q^{25} +(2.19007 - 1.40747i) q^{26} +(7.05898 - 9.42969i) q^{27} +(0.909491 - 2.43844i) q^{28} +(6.04466 + 0.869091i) q^{29} +(-3.34390 + 6.13693i) q^{30} +(4.50690 + 2.89641i) q^{31} +(0.936950 - 0.349464i) q^{32} +(-6.89121 - 12.6203i) q^{33} +(-2.45252 - 2.83036i) q^{34} +(4.39463 - 3.81485i) q^{35} +(-6.49455 - 1.90697i) q^{36} +(-3.04986 - 8.17698i) q^{37} +(-0.321254 - 1.47678i) q^{38} +(2.29238 + 7.80713i) q^{39} +(2.21359 + 0.316247i) q^{40} +(-4.39226 - 9.61770i) q^{41} +(6.51176 + 4.87465i) q^{42} +(0.661697 + 0.143943i) q^{43} +(-3.01276 + 3.47691i) q^{44} +(-10.7119 - 10.6927i) q^{45} +(-4.77505 - 0.445966i) q^{46} +(1.92809 + 1.92809i) q^{47} +(0.222970 + 3.11753i) q^{48} +(0.122635 + 0.190823i) q^{49} +(4.00806 + 2.98923i) q^{50} +(10.6475 - 4.86256i) q^{51} +(2.08408 - 1.56012i) q^{52} +(5.52584 + 3.01733i) q^{53} +(6.36829 - 9.90925i) q^{54} +(-9.63544 + 3.60365i) q^{55} +(0.733218 - 2.49711i) q^{56} +(4.71158 + 0.336979i) q^{57} +(6.09126 + 0.435656i) q^{58} +(-1.80006 + 6.13045i) q^{59} +(-2.89758 + 6.35985i) q^{60} +(-4.00554 + 6.23274i) q^{61} +(4.70205 + 2.56751i) q^{62} +(-14.1022 + 10.5568i) q^{63} +(0.909632 - 0.415415i) q^{64} +(5.76124 - 0.833598i) q^{65} +(-7.77397 - 12.0965i) q^{66} +(-0.554064 - 7.74682i) q^{67} +(-2.64819 - 2.64819i) q^{68} +(5.54209 - 13.9272i) q^{69} +(4.11128 - 4.11864i) q^{70} +(-8.49053 + 9.79860i) q^{71} +(-6.61404 - 1.43880i) q^{72} +(1.19098 + 0.891553i) q^{73} +(-3.62542 - 7.93857i) q^{74} +(-12.4937 + 9.38755i) q^{75} +(-0.425787 - 1.45010i) q^{76} +(2.54509 + 11.6996i) q^{77} +(2.84349 + 7.62370i) q^{78} +(4.18153 + 1.22781i) q^{79} +(2.23051 + 0.157526i) q^{80} +(10.8114 + 12.4770i) q^{81} +(-5.06719 - 9.27986i) q^{82} +(-2.30068 + 0.858110i) q^{83} +(6.84293 + 4.39768i) q^{84} +(-2.36650 - 8.03298i) q^{85} +(0.670280 + 0.0963717i) q^{86} +(-6.67017 + 17.8834i) q^{87} +(-2.75704 + 3.68298i) q^{88} +(-13.5970 + 8.73826i) q^{89} +(-11.4474 - 9.90131i) q^{90} -6.77526i q^{91} +(-4.79470 - 0.104181i) q^{92} +(-11.8401 + 11.8401i) q^{93} +(2.06073 + 1.78563i) q^{94} +(0.715393 - 3.30282i) q^{95} +(0.444805 + 3.09368i) q^{96} +(-6.88907 - 2.56949i) q^{97} +(0.135936 + 0.181589i) q^{98} +(29.8789 - 8.77322i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more