LMFDB - Embedded newform 230.2.l.a.33.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			33.7
Character	$\chi$	$=$	230.33
Dual form			230.2.l.a.7.7

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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	−0.613140	−	0.789974i	$-0.710094\pi$
$3$	−0.664372	−	3.05407i	−0.383575	−	1.76327i	0.229565	−	0.973293i	$-0.426270\pi$
$4$	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	0.999896	+	0.0143934i	$0.00458172\pi$
$7$	1.24726	+	2.28419i	0.471420	+	0.863341i	−0.528476	+	0.848948i	$0.677236\pi$
$8$	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	−0.0524072	−	0.998626i	$-0.516689\pi$
$11$	−3.47691	−	3.01276i	−1.04833	−	0.908380i	−0.995920	+	0.0902455i	$0.971235\pi$
$12$	−0.222970	−	3.11753i	−0.0643660	−	0.899954i
$13$	2.28489	+	1.24765i	0.633716	+	0.346035i	0.763786	−	0.645470i	$-0.223338\pi$
$13$	2.28489	+	1.24765i	0.633716	+	0.346035i	−0.130070	+	0.991505i	$0.541520\pi$
$14$	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	−0.985386	−	0.170334i	$-0.945515\pi$
$17$	−2.24436	+	2.99811i	−0.544337	+	0.727149i	0.441050	+	0.897483i	$0.354606\pi$
$18$	−6.34196	+	2.36543i	−1.49481	+	0.557537i
$19$	−0.215083	+	1.49593i	−0.0493434	+	0.343191i	0.950162	+	0.311755i	$0.100917\pi$
$19$	−0.215083	+	1.49593i	−0.0493434	+	0.343191i	−0.999506	+	0.0314355i	$0.989992\pi$
$20$	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	0.444006	−	0.896024i	$-0.353557\pi$
$29$	6.04466	−	0.869091i	1.12247	−	0.161386i	0.678460	+	0.734638i	$0.262648\pi$
$30$	−3.34390	−	6.13693i	−0.610510	−	1.12045i
$31$	4.50690	−	2.89641i	0.809464	−	0.520211i	−0.0692275	−	0.997601i	$-0.522053\pi$
$31$	4.50690	−	2.89641i	0.809464	−	0.520211i	0.878692	+	0.477390i	$0.158417\pi$
$32$	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	0.402065	+	0.915611i	$0.368293\pi$
$37$	−3.04986	+	8.17698i	−0.501393	+	1.34429i	−0.903458	+	0.428676i	$0.858980\pi$
$38$	−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	0.170252	+	0.985401i	$0.445542\pi$
$41$	−4.39226	+	9.61770i	−0.685955	+	1.50203i	−0.856207	+	0.516632i	$0.827186\pi$
$42$	6.51176	−	4.87465i	1.00479	−	0.752174i
$43$	0.661697	−	0.143943i	0.100908	−	0.0219511i	−0.161828	−	0.986819i	$-0.551739\pi$
$43$	0.661697	−	0.143943i	0.100908	−	0.0219511i	0.262736	+	0.964868i	$0.415375\pi$
$44$	−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	−0.552363	−	0.833604i	$-0.686274\pi$
$47$	1.92809	−	1.92809i	0.281241	−	0.281241i	0.833604	+	0.552363i	$0.186274\pi$
$48$	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	−0.0526122	−	0.998615i	$-0.516755\pi$
$53$	5.52584	−	3.01733i	0.759032	−	0.414463i	0.811644	+	0.584152i	$0.198573\pi$
$54$	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	−0.989745	−	0.142849i	$-0.954374\pi$
$59$	−1.80006	−	6.13045i	−0.234348	−	0.798117i	0.755396	−	0.655268i	$-0.227444\pi$
$60$	−2.89758	−	6.35985i	−0.374076	−	0.821053i
$61$	−4.00554	−	6.23274i	−0.512856	−	0.798020i	0.484179	−	0.874969i	$-0.339118\pi$
$61$	−4.00554	−	6.23274i	−0.512856	−	0.798020i	−0.997035	+	0.0769490i	$0.975482\pi$
$62$	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	0.844210	+	0.536012i	$0.180070\pi$
$67$	−0.554064	+	7.74682i	−0.0676897	+	0.946425i	−0.911900	+	0.410413i	$0.865385\pi$
$68$	−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	−0.986609	−	0.163101i	$-0.947851\pi$
$71$	−8.49053	−	9.79860i	−1.00764	−	1.16288i	−0.0210313	−	0.999779i	$-0.506695\pi$
$72$	−6.61404	+	1.43880i	−0.779472	+	0.169564i
$73$	1.19098	−	0.891553i	0.139393	−	0.104348i	−0.527306	−	0.849676i	$-0.676798\pi$
$73$	1.19098	−	0.891553i	0.139393	−	0.104348i	0.666699	+	0.745327i	$0.267707\pi$
$74$	−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	−0.0379052	−	0.999281i	$-0.512068\pi$
$79$	4.18153	−	1.22781i	0.470459	−	0.138139i	0.508364	+	0.861142i	$0.330250\pi$
$80$	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	0.220010	−	0.975498i	$-0.429391\pi$
$83$	−2.30068	−	0.858110i	−0.252533	−	0.0941898i	−0.472543	+	0.881308i	$0.656664\pi$
$84$	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	−0.999577	−	0.0290929i	$-0.990738\pi$
$89$	−13.5970	−	8.73826i	−1.44128	−	0.926254i	−0.441703	−	0.897161i	$-0.645626\pi$
$90$	−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	−0.673945	−	0.738782i	$-0.735401\pi$
$97$	−6.88907	+	2.56949i	−0.699479	+	0.260892i	−0.0255342	+	0.999674i	$0.508129\pi$
$98$	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	0.939389	+	0.342852i	$0.111393\pi$
$101$	5.86240	+	12.8369i	0.583330	+	1.27732i	−0.356059	+	0.934463i	$0.615880\pi$
$102$	10.2735	+	5.60976i	1.01723	+	0.555449i
$103$	0.942711	+	13.1808i	0.0928881	+	1.29874i	0.803561	+	0.595222i	$0.202936\pi$
$103$	0.942711	+	13.1808i	0.0928881	+	1.29874i	−0.710673	+	0.703522i	$0.751609\pi$
$104$	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	0.485013	−	0.874507i	$-0.338815\pi$
$107$	5.82282	+	1.26668i	0.562913	+	0.122454i	0.0778999	+	0.996961i	$0.475179\pi$
$108$	5.64514	+	10.3383i	0.543204	+	0.994804i
$109$	−0.132276	−	0.919999i	−0.0126697	−	0.0881199i	0.982505	−	0.186234i	$-0.0596282\pi$
$109$	−0.132276	−	0.919999i	−0.0126697	−	0.0881199i	−0.995175	+	0.0981138i	$0.968719\pi$
$110$	−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	0.0417639	−	0.999128i	$-0.486702\pi$
$113$	−0.628113	−	0.0449236i	−0.0590879	−	0.00422605i	−0.100852	+	0.994901i	$0.532157\pi$
$114$	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	−0.999040	−	0.0438045i	$-0.986052\pi$
$127$	−0.184850	−	2.58455i	−0.0164028	−	0.229341i	0.982637	−	0.185537i	$-0.0594024\pi$
$128$	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	−0.773485	−	0.633814i	$-0.781488\pi$
$131$	−20.2225	−	5.93786i	−1.76685	−	0.518794i	−0.993363	+	0.115021i	$0.963307\pi$
$132$	−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	0.542701	−	0.839926i	$-0.317402\pi$
$137$	−3.47894	−	3.47894i	−0.297226	−	0.297226i	−0.839926	+	0.542701i	$0.817402\pi$
$138$	4.53442	+	14.2870i	0.385996	+	1.21619i
$139$		−	9.56448i		−	0.811249i	−0.914040	−	0.405624i	$-0.867054\pi$
$139$		−	9.56448i		−	0.811249i	0.914040	−	0.405624i	$-0.132946\pi$
$140$	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	−0.296274	−	0.955103i	$-0.595744\pi$
$149$	8.43804	−	9.73802i	0.691271	−	0.797770i	0.987546	+	0.157333i	$0.0502897\pi$
$150$	−11.7922	−	10.2549i	−0.962825	−	0.837311i
$151$	−6.62240	+	1.94451i	−0.538924	+	0.158242i	−0.539856	−	0.841757i	$-0.681521\pi$
$151$	−6.62240	+	1.94451i	−0.538924	+	0.158242i	0.000932510		1.00000i	$0.499703\pi$
$152$	−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	−0.943059	−	0.332624i	$-0.892066\pi$
$157$	−11.1466	+	8.34427i	−0.889599	+	0.665946i	0.0534602	+	0.998570i	$0.482975\pi$
$158$	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	0.844829	+	0.535037i	$0.179702\pi$
$163$	−0.862351	+	12.0572i	−0.0675445	+	0.944396i	−0.912373	+	0.409359i	$0.865752\pi$
$164$	−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	0.871085	−	0.491132i	$-0.163417\pi$
$167$	8.33860	+	6.24220i	0.645260	+	0.483036i	−0.225825	+	0.974168i	$0.572508\pi$
$168$	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	−0.543236	−	0.839580i	$-0.682801\pi$
$173$	−12.6460	+	0.904460i	−0.961458	+	0.0687649i	−0.418222	+	0.908345i	$0.637347\pi$
$174$	−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	0.439714	−	0.898138i	$-0.355080\pi$
$179$	0.654216	+	0.298770i	0.0488984	+	0.0223311i	−0.390816	+	0.920469i	$0.627807\pi$
$180$	−12.1246	+	9.05944i	−0.903712	+	0.675251i
$181$	7.33618	−	11.4153i	0.545294	−	0.848494i	−0.453798	−	0.891105i	$-0.649931\pi$
$181$	7.33618	−	11.4153i	0.545294	−	0.848494i	0.999092	+	0.0426108i	$0.0135675\pi$
$182$	−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	0.557720	+	0.830029i	$0.311676\pi$
$191$	−4.97822	+	16.9543i	−0.360211	+	1.22677i	−0.917932	+	0.396738i	$0.870142\pi$
$192$	0.664372	−	3.05407i	0.0479469	−	0.220408i
$193$	4.78257	−	12.8226i	0.344257	−	0.922989i	−0.643284	−	0.765628i	$-0.722429\pi$
$193$	4.78257	−	12.8226i	0.344257	−	0.922989i	0.987541	−	0.157361i	$-0.0502987\pi$
$194$	−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	−0.383634	−	0.923485i	$-0.625328\pi$
$197$	8.43065	−	15.4396i	0.600659	−	1.10003i	0.984293	−	0.176540i	$-0.0564905\pi$
$198$	29.1769	+	10.8824i	2.07351	+	0.773379i
$199$	−16.9934	+	10.9210i	−1.20463	+	0.774170i	−0.979752	−	0.200216i	$-0.935836\pi$
$199$	−16.9934	+	10.9210i	−1.20463	+	0.774170i	−0.224881	+	0.974386i	$0.572199\pi$
$200$	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	−0.967243	−	0.253851i	$-0.918303\pi$
$211$	0.469737	−	3.26709i	0.0323380	−	0.224916i	0.999581	+	0.0289354i	$0.00921170\pi$
$212$	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	0.965953	−	0.258719i	$-0.0833005\pi$
$223$	3.37595	+	6.18260i	0.226070	+	0.414017i	−0.739882	+	0.672737i	$0.765119\pi$
$224$	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	0.909967	−	0.414681i	$-0.136107\pi$
$227$	−1.35648	−	6.23564i	−0.0900327	−	0.413874i	−1.00000		0.000807034i	$0.999743\pi$
$228$	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	−0.775931	−	0.630818i	$-0.782719\pi$
$233$	−5.07036	−	23.3081i	−0.332171	−	1.52696i	0.443760	−	0.896146i	$-0.353644\pi$
$234$	−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	0.125758	−	0.992061i	$-0.459864\pi$
$239$	14.8082	−	6.76267i	0.957861	−	0.437440i	0.832103	+	0.554621i	$0.187137\pi$
$240$	−1.96298	−	6.70748i	−0.126710	−	0.432966i
$241$	14.7073	+	12.7439i	0.947378	+	0.820908i	0.983954	−	0.178423i	$-0.0570995\pi$
$241$	14.7073	+	12.7439i	0.947378	+	0.820908i	−0.0365754	+	0.999331i	$0.511645\pi$
$242$	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	−0.292221	−	0.956351i	$-0.594394\pi$
$251$	9.70871	−	8.41265i	0.612808	−	0.531002i	0.905029	+	0.425349i	$0.139849\pi$
$252$	−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	0.723961	−	0.689841i	$-0.242320\pi$
$257$	−2.27483	−	3.03881i	−0.141900	−	0.189556i	−0.865861	+	0.500285i	$0.833229\pi$
$258$	−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	−0.682617	−	0.730777i	$-0.739158\pi$
$263$	4.88468	−	8.94562i	0.301202	−	0.551610i	0.983819	+	0.179166i	$0.0573400\pi$
$264$	−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	−0.956870	−	0.290515i	$-0.906173\pi$
$269$	0.0847081	−	0.288489i	0.00516474	−	0.0175895i	0.962035	+	0.272926i	$0.0879914\pi$
$270$	21.0713	+	15.8032i	1.28236	+	0.961752i
$271$	−0.124734	+	0.273130i	−0.00757706	+	0.0165915i	−0.913383	−	0.407102i	$-0.866539\pi$
$271$	−0.124734	+	0.273130i	−0.00757706	+	0.0165915i	0.905806	+	0.423693i	$0.139267\pi$
$272$	−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	−0.564004	−	0.825772i	$-0.690740\pi$
$277$	4.35669	−	4.35669i	0.261768	−	0.261768i	0.825772	+	0.564004i	$0.190740\pi$
$278$	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	0.988698	−	0.149924i	$-0.0479029\pi$
$281$	25.5276	+	11.6581i	1.52285	+	0.695463i	0.534154	+	0.845387i	$0.320630\pi$
$282$	−6.82252	−	5.10728i	−0.406275	−	0.304134i
$283$	−5.47879	+	2.99164i	−0.325680	+	0.177835i	−0.633768	−	0.773523i	$-0.718493\pi$
$283$	−5.47879	+	2.99164i	−0.325680	+	0.177835i	0.308088	+	0.951358i	$0.400311\pi$
$284$	−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	0.918757	−	0.394823i	$-0.129194\pi$
$293$	13.6728	+	10.2353i	0.798772	+	0.597953i	−0.119986	+	0.992776i	$0.538285\pi$
$294$	−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	0.811106	+	0.584899i	$0.198866\pi$
$307$	−2.97299	+	13.6666i	−0.169678	+	0.779996i	−0.980784	+	0.195097i	$0.937498\pi$
$308$	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	−0.832848	−	0.553502i	$-0.813291\pi$
$311$	−2.93544	+	3.38768i	−0.166454	+	0.192098i	0.666394	+	0.745599i	$0.267837\pi$
$312$	3.89951	−	7.14143i	0.220767	−	0.404304i
$313$	−13.5390	−	5.04980i	−0.765272	−	0.285432i	−0.0636414	−	0.997973i	$-0.520271\pi$
$313$	−13.5390	−	5.04980i	−0.765272	−	0.285432i	−0.701630	+	0.712541i	$0.747544\pi$
$314$	−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	−0.999898	−	0.0143009i	$-0.995448\pi$
$317$	−4.51505	−	12.1053i	−0.253591	−	0.679902i	0.746307	−	0.665602i	$-0.231825\pi$
$318$	−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	0.656993	−	0.753897i	$-0.271828\pi$
$331$	−6.24039	−	13.6646i	−0.343003	−	0.751072i	−0.999996	+	0.00282474i	$0.999101\pi$
$332$	−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	0.327579	−	0.944824i	$-0.393767\pi$
$337$	4.27843	+	0.930715i	0.233061	+	0.0506993i	−0.0945180	+	0.995523i	$0.530131\pi$
$338$	−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	0.426611	−	0.904435i	$-0.359707\pi$
$347$	13.4152	+	0.959472i	0.720164	+	0.0515072i	0.293554	+	0.955943i	$0.405162\pi$
$348$	−4.05720	−	18.6507i	−0.217489	−	0.999780i
$349$	20.0416	+	2.88155i	1.07280	+	0.154246i	0.656007	−	0.754755i	$-0.272244\pi$
$349$	20.0416	+	2.88155i	1.07280	+	0.154246i	0.416795	+	0.909001i	$0.363153\pi$
$350$	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	0.969475	−	0.245190i	$-0.0788504\pi$
$353$	32.8698	+	7.15039i	1.74948	+	0.380577i	0.780010	+	0.625767i	$0.215214\pi$
$354$	−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	0.997047	+	0.0767917i	$0.0244676\pi$
$359$	7.61976	+	16.6849i	0.402155	+	0.880598i	−0.594892	+	0.803806i	$0.702805\pi$
$360$	−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	0.899871	−	0.436155i	$-0.143660\pi$
$367$	8.88352	+	8.88352i	0.463716	+	0.463716i	−0.436155	+	0.899871i	$0.643660\pi$
$368$	−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	0.830694	−	0.556729i	$-0.187944\pi$
$373$	−3.12260	−	8.37203i	−0.161682	−	0.433487i	−0.992377	+	0.123242i	$0.960671\pi$
$374$	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	−0.506466	−	0.862260i	$-0.669048\pi$
$379$	8.15891	−	9.41588i	0.419095	−	0.483661i	0.925561	+	0.378599i	$0.123594\pi$
$380$	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	−0.903291	−	0.429029i	$-0.858856\pi$
$383$	1.89043	−	8.69015i	0.0965963	−	0.444046i	0.999887	−	0.0150175i	$-0.00478040\pi$
$384$	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	0.995745	+	0.0921556i	$0.0293757\pi$
$389$	18.6433	+	21.5155i	0.945253	+	1.09088i	−0.0504916	+	0.998724i	$0.516079\pi$
$390$	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	0.897674	−	0.440660i	$-0.145256\pi$
$397$	14.5007	+	10.8551i	0.727767	+	0.544800i	−0.169907	+	0.985460i	$0.554347\pi$
$398$	−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	−0.754834	−	0.655916i	$-0.772283\pi$
$401$	−9.50070	−	32.3564i	−0.474442	−	1.61580i	0.280392	−	0.959886i	$-0.409536\pi$
$402$	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	−0.285241	−	0.958456i	$-0.592074\pi$
$409$	−24.1954	−	11.0497i	−1.19639	−	0.546372i	−0.911146	+	0.412084i	$0.864801\pi$
$410$	−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	−0.997816	−	0.0660475i	$-0.978961\pi$
$419$	−6.02766	+	13.1987i	−0.294470	+	0.644800i	0.703346	+	0.710847i	$0.251688\pi$
$420$	10.9130	−	14.5510i	0.532502	−	0.710016i
$421$	2.59875	−	8.85054i	0.126656	−	0.431349i	−0.871611	−	0.490197i	$-0.836925\pi$
$421$	2.59875	−	8.85054i	0.126656	−	0.431349i	0.998267	+	0.0588484i	$0.0187428\pi$
$422$	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	−0.676635	−	0.736319i	$-0.736562\pi$
$431$	−23.2189	+	3.33838i	−1.11842	+	0.160804i	−0.441782	+	0.897123i	$0.645653\pi$
$432$	4.11639	+	11.0365i	0.198050	+	0.530992i
$433$	−8.98558	−	12.0033i	−0.431820	−	0.576843i	0.530869	−	0.847454i	$-0.321865\pi$
$433$	−8.98558	−	12.0033i	−0.431820	−	0.576843i	−0.962689	+	0.270610i	$0.912775\pi$
$434$	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	−0.739644	−	0.672998i	$-0.765006\pi$
$439$	−3.74540	+	3.24541i	−0.178758	+	0.154895i	0.560886	+	0.827893i	$0.310461\pi$
$440$	−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	0.0239248	+	0.999714i	$0.492384\pi$
$443$	−19.8275	+	26.4865i	−0.942034	+	1.25841i	−0.965959	+	0.258696i	$0.916707\pi$
$444$	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	0.814686	−	0.579902i	$-0.196909\pi$
$449$	7.55683	+	6.54803i	0.356629	+	0.309021i	−0.458057	+	0.888923i	$0.651455\pi$
$450$	−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	0.994054	−	0.108884i	$-0.0347279\pi$
$457$	0.953406	+	4.38274i	0.0445985	+	0.205016i	−0.949456	+	0.313900i	$0.898364\pi$
$458$	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	−0.928170	−	0.372155i	$-0.878619\pi$
$463$	−5.13139	−	23.5886i	−0.238476	−	1.09626i	0.689695	−	0.724100i	$-0.257745\pi$
$464$	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	0.946499	+	0.322706i	$0.104592\pi$
$467$	15.2624	+	27.9510i	0.706260	+	1.29342i	−0.240239	+	0.970714i	$0.577226\pi$
$468$	−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	−0.998694	−	0.0510823i	$-0.983733\pi$
$479$	−0.570408	+	3.96728i	−0.0260626	+	0.181269i	0.972632	+	0.232352i	$0.0746420\pi$
$480$	−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	−0.993604	−	0.112920i	$-0.963980\pi$
$487$	−18.1404	−	24.2327i	−0.822019	−	1.09809i	0.171585	−	0.985169i	$-0.445111\pi$
$488$	−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	−0.424983	−	0.905201i	$-0.639720\pi$
$491$	4.91636	−	3.15956i	0.221872	−	0.142589i	0.646856	+	0.762613i	$0.276084\pi$
$492$	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	−0.305108	−	0.952318i	$-0.598692\pi$
$499$	10.4192	−	35.4845i	0.466427	−	1.58851i	0.771535	−	0.636187i	$-0.219489\pi$
$500$	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	−0.330921	−	0.943658i	$-0.607359\pi$
$503$	−5.38101	+	1.17057i	−0.239928	+	0.0521930i	0.0909935	+	0.995851i	$0.470996\pi$
$504$	−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	−0.0856244	−	0.996327i	$-0.527289\pi$
$509$	19.3176	−	30.0587i	0.856237	−	1.33233i	0.941861	−	0.336003i	$-0.109075\pi$
$510$	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	0.523155	−	0.852238i	$-0.324755\pi$
$521$	−10.7141	−	16.6715i	−0.469394	−	0.730391i	−0.992549	+	0.121846i	$0.961118\pi$
$522$	−36.2792	+	19.8100i	−1.58790	+	0.867058i
$523$	9.06364	+	6.78495i	0.396325	+	0.296685i	0.778790	−	0.627285i	$-0.215834\pi$
$523$	9.06364	+	6.78495i	0.396325	+	0.296685i	−0.382465	+	0.923970i	$0.624925\pi$
$524$	−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	−0.474466	−	0.880274i	$-0.657359\pi$
$541$	10.8010	−	12.4650i	0.464372	−	0.535914i	0.938838	+	0.344360i	$0.111904\pi$
$542$	−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	−0.579365	−	0.815068i	$-0.696699\pi$
$547$	−15.7931	−	42.3431i	−0.675266	−	1.81046i	−0.0959013	−	0.995391i	$-0.530573\pi$
$548$	−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	−0.220400	−	0.975410i	$-0.570736\pi$
$557$	5.94246	−	2.21642i	0.251790	−	0.0939128i	0.472190	+	0.881497i	$0.343464\pi$
$558$	−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	0.999932	+	0.0116254i	$0.00370058\pi$
$563$	0.280753	+	3.92544i	0.0118323	+	0.165438i	−0.988100	+	0.153812i	$0.950845\pi$
$564$	−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	0.648139	+	0.761522i	$0.275547\pi$
$569$	5.74397	+	39.9502i	0.240800	+	1.67480i	−0.407340	+	0.913277i	$0.633543\pi$
$570$	9.89967	−	3.68231i	0.414651	−	0.154235i
$571$	−17.5505	−	2.52338i	−0.734466	−	0.105600i	−0.235075	−	0.971977i	$-0.575534\pi$
$571$	−17.5505	−	2.52338i	−0.734466	−	0.105600i	−0.499391	+	0.866377i	$0.666443\pi$
$572$	−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	0.267006	−	0.963695i	$-0.413966\pi$
$577$	9.46769	+	0.677143i	0.394145	+	0.0281898i	0.127140	+	0.991885i	$0.459420\pi$
$578$	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	0.942312	+	0.334735i	$0.108647\pi$
$587$	1.38655	+	19.3865i	0.0572291	+	0.800168i	−0.885083	+	0.465433i	$0.845899\pi$
$588$	−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	−0.981705	−	0.190408i	$-0.939019\pi$
$593$	−38.9367	+	14.5226i	−1.59894	+	0.596373i	−0.617232	+	0.786781i	$0.711746\pi$
$594$	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	$0.293047\pi$
$599$			38.9627i			1.59197i	−0.605315	+	0.795986i	$0.706953\pi$
$600$	−10.2127	−	11.8287i	−0.416932	−	0.482906i
$601$	−1.12932	−	0.725767i	−0.0460658	−	0.0296047i	0.517405	−	0.855740i	$-0.326898\pi$
$601$	−1.12932	−	0.725767i	−0.0460658	−	0.0296047i	−0.563471	+	0.826136i	$0.690534\pi$
$602$	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	0.833226	−	0.552933i	$-0.186491\pi$
$607$	27.1219	+	10.1159i	1.10084	+	0.410593i	0.267616	+	0.963526i	$0.413764\pi$
$608$	−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	−0.999882	−	0.0153887i	$-0.995101\pi$
$613$	−2.07887	+	9.55639i	−0.0839646	+	0.385979i	0.915917	+	0.401368i	$0.131465\pi$
$614$	−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	−0.360459	−	0.932775i	$-0.617380\pi$
$617$	10.7550	−	8.05106i	0.432978	−	0.324124i	0.793438	+	0.608651i	$0.208289\pi$
$618$	40.3580	−	8.77934i	1.62344	−	0.353157i
$619$	−2.29681	−	2.65066i	−0.0923165	−	0.106539i	0.707712	−	0.706501i	$-0.249728\pi$
$619$	−2.29681	−	2.65066i	−0.0923165	−	0.106539i	−0.800028	+	0.599962i	$0.795182\pi$
$620$	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	0.999948	−	0.0102039i	$-0.00324805\pi$
$631$	3.84888	+	13.1081i	0.153222	+	0.521825i	−0.846726	+	0.532029i	$0.821430\pi$
$632$	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	−0.741577	−	0.670867i	$-0.765922\pi$
$641$	4.47438	−	6.96227i	0.176727	−	0.274993i	0.918305	+	0.395874i	$0.129558\pi$
$642$	1.32868	−	18.5774i	0.0524388	−	0.733190i
$643$	3.79292	−	3.79292i	0.149578	−	0.149578i	−0.628351	−	0.777930i	$-0.716270\pi$
$643$	3.79292	−	3.79292i	0.149578	−	0.149578i	0.777930	+	0.628351i	$0.216270\pi$
$644$	−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	−0.0887542	−	0.996054i	$-0.528289\pi$
$647$	6.21375	−	1.35172i	0.244288	−	0.0531415i	0.333042	+	0.942912i	$0.391925\pi$
$648$	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	−0.895010	−	0.446046i	$-0.852832\pi$
$653$	1.87799	−	5.03508i	0.0734913	−	0.197038i	0.968501	+	0.249008i	$0.0801046\pi$
$654$	−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	−0.629601	−	0.776919i	$-0.716782\pi$
$659$	−4.73466	+	3.04278i	−0.184436	+	0.118530i	0.445165	+	0.895449i	$0.353145\pi$
$660$	−9.08607	+	30.8423i	−0.353675	+	1.20053i
$661$	−31.5886	+	4.54176i	−1.22865	+	0.176654i	−0.725915	−	0.687784i	$-0.758584\pi$
$661$	−31.5886	+	4.54176i	−1.22865	+	0.176654i	−0.502739	+	0.864438i	$0.667674\pi$
$662$	−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	−0.836600	−	0.547814i	$-0.815460\pi$
$673$	−1.95290	+	2.60877i	−0.0752789	+	0.100561i	0.761321	+	0.648375i	$0.224551\pi$
$674$	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	0.482810	−	0.875725i	$-0.339616\pi$
$677$	0.185501	+	0.101291i	0.00712938	+	0.00389293i	−0.475680	+	0.879618i	$0.657798\pi$
$678$	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	0.972730	+	0.231939i	$0.0745070\pi$
$683$	16.7769	+	30.7247i	0.641952	+	1.17565i	−0.330778	+	0.943709i	$0.607311\pi$
$684$	−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	0.334264	−	0.942479i	$-0.391512\pi$
$701$	−14.5899	−	12.6422i	−0.551051	−	0.477489i	−0.885316	+	0.464991i	$0.846058\pi$
$702$	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	0.917412	+	0.397939i	$0.130275\pi$
$709$	−1.99572	+	13.8805i	−0.0749509	+	0.521295i	−0.992363	+	0.123355i	$0.960635\pi$
$710$	−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	0.278710	−	0.960375i	$-0.410093\pi$
$719$	21.8991	−	3.14862i	0.816699	−	0.117424i	0.537989	+	0.842952i	$0.319184\pi$
$720$	−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	−0.999744	−	0.0226041i	$-0.992804\pi$
$727$	−6.18491	+	16.5824i	−0.229385	+	0.615006i	0.770359	+	0.637610i	$0.220077\pi$
$728$	−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	−0.546659	−	0.837355i	$-0.684101\pi$
$733$	−18.8453	+	4.09955i	−0.696068	+	0.151420i	−0.149409	+	0.988776i	$0.547737\pi$
$734$	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	−0.754228	−	0.656613i	$-0.771988\pi$
$739$	4.25075	−	6.61429i	0.156366	−	0.243311i	0.910594	+	0.413303i	$0.135625\pi$
$740$	−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	−0.703365	−	0.710829i	$-0.748320\pi$
$743$	−13.2377	+	7.22835i	−0.485646	+	0.265183i	0.217719	+	0.976011i	$0.430138\pi$
$744$	−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	0.958065	−	0.286552i	$-0.0925090\pi$
$751$	8.20525	+	12.7676i	0.299414	+	0.465897i	−0.658651	+	0.752448i	$0.728873\pi$
$752$	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	−0.833917	−	0.551890i	$-0.813907\pi$
$757$	1.92744	−	26.9491i	0.0700540	−	0.979483i	0.903971	−	0.427593i	$-0.140639\pi$
$758$	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	0.972608	−	0.232451i	$-0.0746746\pi$
$761$	16.6650	+	19.2325i	0.604106	+	0.697176i	−0.368502	+	0.929627i	$0.620129\pi$
$762$	−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	0.322625	−	0.946527i	$-0.395435\pi$
$769$	30.6638	−	9.00371i	1.10577	−	0.324682i	0.783140	+	0.621845i	$0.213617\pi$
$770$	−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	−0.149678	−	0.988735i	$-0.547824\pi$
$773$	−25.3084	−	9.43955i	−0.910281	−	0.339517i	−0.760603	+	0.649218i	$0.775096\pi$
$774$	−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	0.00453983	−	0.999990i	$-0.498555\pi$
$787$	18.5946	−	6.93542i	0.662825	−	0.247221i	0.658285	+	0.752769i	$0.271282\pi$
$788$	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	−0.224407	−	0.974495i	$-0.572045\pi$
$797$	−23.5266	−	5.11790i	−0.833356	−	0.181285i	−0.608948	+	0.793210i	$0.708408\pi$
$798$	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	0.104147	−	0.994562i	$-0.466789\pi$
$809$	−2.16520	−	0.311308i	−0.0761242	−	0.0109450i	−0.180272	+	0.983617i	$0.557698\pi$
$810$	15.3656	−	33.5666i	0.539893	−	1.17941i
$811$	1.89548	+	13.1833i	0.0665592	+	0.462929i	0.995657	+	0.0930956i	$0.0296762\pi$
$811$	1.89548	+	13.1833i	0.0665592	+	0.462929i	−0.929098	+	0.369834i	$0.879415\pi$
$812$	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	0.613179	−	0.789944i	$-0.289890\pi$
$821$	20.1128	+	5.90566i	0.701943	+	0.206109i	0.0887634	+	0.996053i	$0.471709\pi$
$822$	−9.21529	+	12.3102i	−0.321420	+	0.429367i
$823$	−13.2986	+	4.96012i	−0.463560	+	0.172899i	−0.570383	−	0.821379i	$-0.693205\pi$
$823$	−13.2986	+	4.96012i	−0.463560	+	0.172899i	0.106823	+	0.994278i	$0.465932\pi$
$824$	−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	−0.870790	−	0.491656i	$-0.836392\pi$
$827$	−39.1807	−	39.1807i	−1.36245	−	1.36245i	−0.491656	−	0.870790i	$-0.663608\pi$
$828$	29.2283	−	14.1233i	1.01575	−	0.490820i
$829$			45.0301i			1.56396i	0.623303	+	0.781980i	$0.285790\pi$
$829$			45.0301i			1.56396i	−0.623303	+	0.781980i	$0.714210\pi$
$830$	−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	−0.0867177	+	0.996233i	$0.527638\pi$
$839$	−30.7170	+	35.4493i	−1.06047	+	1.22385i	−0.973751	+	0.227614i	$0.926908\pi$
$840$	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	0.960574	+	0.278026i	$0.0896801\pi$
$853$	−0.870050	+	12.1649i	−0.0297899	+	0.416518i	−0.990364	+	0.138492i	$0.955774\pi$
$854$	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	−0.00214954	−	0.999998i	$-0.500684\pi$
$857$	−28.1693	−	21.0873i	−0.962246	−	0.720328i	−0.960096	+	0.279669i	$0.909775\pi$
$858$	−32.8549	+	17.9401i	−1.12165	+	0.612466i
$859$	20.5494	+	31.9755i	0.701136	+	1.09099i	0.990992	+	0.133919i	$0.0427561\pi$
$859$	20.5494	+	31.9755i	0.701136	+	1.09099i	−0.289856	+	0.957070i	$0.593608\pi$
$860$	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	−0.203004	−	0.979178i	$-0.565070\pi$
$863$	−7.77284	+	0.555924i	−0.264590	+	0.0189239i	−0.0615863	+	0.998102i	$0.519616\pi$
$864$	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	0.184285	−	0.982873i	$-0.441003\pi$
$877$	22.5132	−	4.89744i	0.760216	−	0.165375i	0.575931	+	0.817498i	$0.304640\pi$
$878$	−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	−0.861410	−	0.507909i	$-0.830418\pi$
$881$	4.09163	−	13.9348i	0.137851	−	0.469476i	0.999261	+	0.0384331i	$0.0122366\pi$
$882$	−0.326366	+	1.50028i	−0.0109893	+	0.0505170i
$883$	2.98263	−	7.99675i	0.100374	−	0.269112i	−0.877051	−	0.480398i	$-0.840492\pi$
$883$	2.98263	−	7.99675i	0.100374	−	0.269112i	0.977424	+	0.211286i	$0.0677651\pi$
$884$	−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	−0.844271	−	0.535917i	$-0.819966\pi$
$887$	1.87685	−	3.43719i	0.0630184	−	0.115410i	0.907289	+	0.420507i	$0.138148\pi$
$888$	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	0.991605	−	0.129303i	$-0.0412738\pi$
$907$	42.7332	+	23.3341i	1.41893	+	0.774795i	0.427326	+	0.904098i	$0.359456\pi$
$908$	−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	0.0518375	−	0.998656i	$-0.483492\pi$
$911$	25.3691	−	11.5857i	0.840517	−	0.383851i	0.788680	+	0.614804i	$0.210765\pi$
$912$	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	−0.874780	−	0.484520i	$-0.838994\pi$
$929$	−32.9625	+	15.0535i	−1.08146	+	0.493888i	−0.206684	+	0.978408i	$0.566267\pi$
$930$	−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	−0.878971	−	0.476876i	$-0.841769\pi$
$937$	−5.31939	+	7.10587i	−0.173777	+	0.232139i	0.705194	+	0.709015i	$0.250860\pi$
$938$	−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	−0.183405	−	0.983038i	$-0.558712\pi$
$941$	23.4217	−	20.2950i	0.763526	−	0.661599i	0.946930	+	0.321439i	$0.104166\pi$
$942$	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	0.977156	+	0.212525i	$0.0681686\pi$
$947$	27.8737	+	37.2350i	0.905775	+	1.20997i	−0.0713807	+	0.997449i	$0.522741\pi$
$948$	−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	−0.846137	−	0.532965i	$-0.821078\pi$
$953$	1.84229	−	3.37390i	0.0596775	−	0.109291i	0.905815	+	0.423674i	$0.139260\pi$
$954$	−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	−0.866822	−	0.498617i	$-0.833841\pi$
$967$	−11.4499	+	11.4499i	−0.368205	+	0.368205i	0.498617	+	0.866822i	$0.333841\pi$
$968$	−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	−0.0211077	−	0.999777i	$-0.506719\pi$
$971$	−24.6330	−	11.2495i	−0.790511	−	0.361015i	−0.769404	+	0.638763i	$0.779447\pi$
$972$	−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	−0.372276	−	0.928122i	$-0.621423\pi$
$977$	−19.0254	+	1.36073i	−0.608678	+	0.0435335i	−0.236401	+	0.971655i	$0.575968\pi$
$978$	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	0.190969	−	0.981596i	$-0.438837\pi$
$983$	−21.8549	−	16.3604i	−0.697063	−	0.521815i	−0.888032	+	0.459781i	$0.847928\pi$
$984$	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	−0.990730	−	0.135846i	$-0.956625\pi$
$991$	−30.9827	−	35.7559i	−0.984198	−	1.13582i	0.00653234	−	0.999979i	$-0.497921\pi$
$992$	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	−0.794043	−	0.607862i	$-0.792027\pi$
$997$	5.70752	−	26.2370i	0.180759	−	0.830935i	0.974802	−	0.223073i	$-0.0716090\pi$
$998$	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.33.7	yes	240
5.2	odd	4	inner	230.2.l.a.217.1	yes	240
23.7	odd	22	inner	230.2.l.a.53.1	yes	240
115.7	even	44	inner	230.2.l.a.7.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.7	✓	240	115.7	even	44	inner
230.2.l.a.33.7	yes	240	1.1	even	1	trivial
230.2.l.a.53.1	yes	240	23.7	odd	22	inner
230.2.l.a.217.1	yes	240	5.2	odd	4	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

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