LMFDB - Embedded newform 110.2.k.a.63.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,2,Mod(7,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([5, 14])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	110.k (of order $20$, degree $8$, 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:	$0.878354422234$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			63.3
Character	$\chi$	$=$	110.63
Dual form			110.2.k.a.7.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.987688 - 0.156434i) q^{2} +(0.992087 - 1.94708i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.244349 - 2.22268i) q^{5} +(-1.28446 + 1.76791i) q^{6} +(-3.05681 + 1.55752i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-1.04353 - 1.43630i) q^{9} +(-0.589044 + 2.15709i) q^{10} +(3.24304 - 0.694771i) q^{11} +(1.54521 - 1.54521i) q^{12} +(0.387905 - 2.44914i) q^{13} +(3.26283 - 1.06016i) q^{14} +(-4.08532 - 2.68086i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.196982 - 1.24369i) q^{17} +(0.805997 + 1.58186i) q^{18} +(1.62761 + 5.00927i) q^{19} +(0.919234 - 2.03838i) q^{20} +7.49707i q^{21} +(-3.31180 + 0.178895i) q^{22} +(5.42684 + 5.42684i) q^{23} +(-1.76791 + 1.28446i) q^{24} +(-4.88059 - 1.08622i) q^{25} +(-0.766259 + 2.35830i) q^{26} +(2.64321 - 0.418643i) q^{27} +(-3.38851 + 0.536686i) q^{28} +(0.472216 - 1.45333i) q^{29} +(3.61564 + 3.28693i) q^{30} +(-6.34809 + 4.61215i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.86460 - 7.00373i) q^{33} +1.25920i q^{34} +(2.71495 + 7.17489i) q^{35} +(-0.548617 - 1.68847i) q^{36} +(2.60810 + 5.11868i) q^{37} +(-0.823949 - 5.20221i) q^{38} +(-4.38383 - 3.18504i) q^{39} +(-1.22679 + 1.86949i) q^{40} +(3.98871 - 1.29601i) q^{41} +(1.17280 - 7.40476i) q^{42} +(0.832964 - 0.832964i) q^{43} +(3.29901 + 0.341387i) q^{44} +(-3.44741 + 1.96848i) q^{45} +(-4.51108 - 6.20897i) q^{46} +(-4.97929 - 2.53708i) q^{47} +(1.94708 - 0.992087i) q^{48} +(2.80374 - 3.85901i) q^{49} +(4.65058 + 1.83634i) q^{50} +(-2.61699 - 0.850313i) q^{51} +(1.12574 - 2.20940i) q^{52} +(-9.00929 - 1.42693i) q^{53} -2.67615 q^{54} +(-0.751821 - 7.37799i) q^{55} +3.43074 q^{56} +(11.3682 + 1.80054i) q^{57} +(-0.693754 + 1.36157i) q^{58} +(2.65408 + 0.862364i) q^{59} +(-3.05694 - 3.81208i) q^{60} +(6.34618 - 8.73477i) q^{61} +(6.99143 - 3.56231i) q^{62} +(5.42695 + 2.76517i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-5.34886 - 1.46063i) q^{65} +(-2.93727 + 6.62581i) q^{66} +(-4.03846 + 4.03846i) q^{67} +(0.196982 - 1.24369i) q^{68} +(15.9504 - 5.18260i) q^{69} +(-1.55912 - 7.51127i) q^{70} +(-7.25478 - 5.27091i) q^{71} +(0.277728 + 1.75350i) q^{72} +(4.14012 + 8.12545i) q^{73} +(-1.77525 - 5.46365i) q^{74} +(-6.95692 + 8.42528i) q^{75} +5.26706i q^{76} +(-8.83124 + 7.17490i) q^{77} +(3.83161 + 3.83161i) q^{78} +(-11.2765 + 8.19287i) q^{79} +(1.50414 - 1.65456i) q^{80} +(3.45301 - 10.6273i) q^{81} +(-4.14235 + 0.656083i) q^{82} +(-11.9833 + 1.89797i) q^{83} +(-2.31672 + 7.13013i) q^{84} +(-2.81246 + 0.133932i) q^{85} +(-0.953013 + 0.692405i) q^{86} +(-2.36128 - 2.36128i) q^{87} +(-3.20499 - 0.853262i) q^{88} -4.89861i q^{89} +(3.71290 - 1.40495i) q^{90} +(2.62884 + 8.09073i) q^{91} +(3.48425 + 6.83822i) q^{92} +(2.68238 + 16.9359i) q^{93} +(4.52110 + 3.28477i) q^{94} +(11.5317 - 2.39364i) q^{95} +(-2.07831 + 0.675282i) q^{96} +(0.442255 - 2.79229i) q^{97} +(-3.37290 + 3.37290i) q^{98} +(-4.38211 - 3.93295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100}) $ 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$3$	0.992087	−	1.94708i	0.572782	−	1.12415i	−0.404960	−	0.914335i	$-0.632714\pi$
$3$	0.992087	−	1.94708i	0.572782	−	1.12415i	0.977742	−	0.209813i	$-0.0672856\pi$
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	0.244349	−	2.22268i	0.109276	−	0.994011i
$5$	0.244349	−	2.22268i	0.109276	−	0.994011i
$6$	−1.28446	+	1.76791i	−0.524380	+	0.721747i
$7$	−3.05681	+	1.55752i	−1.15537	+	0.588689i	−0.923326	−	0.384017i	$-0.874540\pi$
$7$	−3.05681	+	1.55752i	−1.15537	+	0.588689i	−0.232041	+	0.972706i	$0.574540\pi$
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	−1.04353	−	1.43630i	−0.347844	−	0.478766i
$10$	−0.589044	+	2.15709i	−0.186272	+	0.682131i
$11$	3.24304	−	0.694771i	0.977813	−	0.209481i
$11$	3.24304	−	0.694771i	0.977813	−	0.209481i
$12$	1.54521	−	1.54521i	0.446064	−	0.446064i
$13$	0.387905	−	2.44914i	0.107586	−	0.679268i	−0.873664	−	0.486529i	$-0.838263\pi$
$13$	0.387905	−	2.44914i	0.107586	−	0.679268i	0.981250	−	0.192739i	$-0.0617372\pi$
$14$	3.26283	−	1.06016i	0.872028	−	0.283339i
$15$	−4.08532	−	2.68086i	−1.05482	−	0.692194i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−0.196982	−	1.24369i	−0.0477751	−	0.301640i	0.952218	−	0.305420i	$-0.0987968\pi$
$17$	−0.196982	−	1.24369i	−0.0477751	−	0.301640i	−0.999993	+	0.00377992i	$0.998797\pi$
$18$	0.805997	+	1.58186i	0.189975	+	0.372848i
$19$	1.62761	+	5.00927i	0.373399	+	1.14920i	0.944552	+	0.328361i	$0.106496\pi$
$19$	1.62761	+	5.00927i	0.373399	+	1.14920i	−0.571153	+	0.820844i	$0.693504\pi$
$20$	0.919234	−	2.03838i	0.205547	−	0.455796i
$21$			7.49707i			1.63599i
$22$	−3.31180	+	0.178895i	−0.706077	+	0.0381405i
$23$	5.42684	+	5.42684i	1.13157	+	1.13157i	0.989915	+	0.141659i	$0.0452437\pi$
$23$	5.42684	+	5.42684i	1.13157	+	1.13157i	0.141659	+	0.989915i	$0.454756\pi$
$24$	−1.76791	+	1.28446i	−0.360874	+	0.262190i
$25$	−4.88059	−	1.08622i	−0.976117	−	0.217243i
$26$	−0.766259	+	2.35830i	−0.150276	+	0.462501i
$27$	2.64321	−	0.418643i	0.508685	−	0.0805679i
$28$	−3.38851	+	0.536686i	−0.640367	+	0.101424i
$29$	0.472216	−	1.45333i	0.0876883	−	0.269877i	−0.897591	−	0.440829i	$-0.854684\pi$
$29$	0.472216	−	1.45333i	0.0876883	−	0.269877i	0.985279	+	0.170952i	$0.0546844\pi$
$30$	3.61564	+	3.28693i	0.660123	+	0.600109i
$31$	−6.34809	+	4.61215i	−1.14015	+	0.828367i	−0.987140	−	0.159857i	$-0.948897\pi$
$31$	−6.34809	+	4.61215i	−1.14015	+	0.828367i	−0.153010	+	0.988225i	$0.548897\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.86460	−	7.00373i	0.324585	−	1.21919i
$34$			1.25920i			0.215950i
$35$	2.71495	+	7.17489i	0.458910	+	1.21278i
$36$	−0.548617	−	1.68847i	−0.0914361	−	0.281411i
$37$	2.60810	+	5.11868i	0.428768	+	0.841505i	0.999788	+	0.0205692i	$0.00654785\pi$
$37$	2.60810	+	5.11868i	0.428768	+	0.841505i	−0.571020	+	0.820936i	$0.693452\pi$
$38$	−0.823949	−	5.20221i	−0.133662	−	0.843910i
$39$	−4.38383	−	3.18504i	−0.701975	−	0.510015i
$40$	−1.22679	+	1.86949i	−0.193973	+	0.295592i
$41$	3.98871	−	1.29601i	0.622932	−	0.202403i	0.0194904	−	0.999810i	$-0.493796\pi$
$41$	3.98871	−	1.29601i	0.622932	−	0.202403i	0.603442	+	0.797407i	$0.293796\pi$
$42$	1.17280	−	7.40476i	0.180967	−	1.14258i
$43$	0.832964	−	0.832964i	0.127026	−	0.127026i	−0.640736	−	0.767762i	$-0.721371\pi$
$43$	0.832964	−	0.832964i	0.127026	−	0.127026i	0.767762	+	0.640736i	$0.221371\pi$
$44$	3.29901	+	0.341387i	0.497344	+	0.0514660i
$45$	−3.44741	+	1.96848i	−0.513910	+	0.293443i
$46$	−4.51108	−	6.20897i	−0.665123	−	0.915463i
$47$	−4.97929	−	2.53708i	−0.726305	−	0.370071i	0.0514190	−	0.998677i	$-0.483626\pi$
$47$	−4.97929	−	2.53708i	−0.726305	−	0.370071i	−0.777723	+	0.628607i	$0.783626\pi$
$48$	1.94708	−	0.992087i	0.281037	−	0.143195i
$49$	2.80374	−	3.85901i	0.400534	−	0.551287i
$50$	4.65058	+	1.83634i	0.657691	+	0.259697i
$51$	−2.61699	−	0.850313i	−0.366453	−	0.119068i
$52$	1.12574	−	2.20940i	0.156113	−	0.306388i
$53$	−9.00929	−	1.42693i	−1.23752	−	0.196004i	−0.496829	−	0.867849i	$-0.665502\pi$
$53$	−9.00929	−	1.42693i	−1.23752	−	0.196004i	−0.740692	+	0.671845i	$0.765502\pi$
$54$	−2.67615			−0.364179
$55$	−0.751821	−	7.37799i	−0.101375	−	0.994848i
$56$	3.43074			0.458452
$57$	11.3682	+	1.80054i	1.50575	+	0.238488i
$58$	−0.693754	+	1.36157i	−0.0910943	+	0.178783i
$59$	2.65408	+	0.862364i	0.345532	+	0.112270i	0.476642	−	0.879098i	$-0.341854\pi$
$59$	2.65408	+	0.862364i	0.345532	+	0.112270i	−0.131109	+	0.991368i	$0.541854\pi$
$60$	−3.05694	−	3.81208i	−0.394649	−	0.492137i
$61$	6.34618	−	8.73477i	0.812545	−	1.11837i	−0.178380	−	0.983962i	$-0.557086\pi$
$61$	6.34618	−	8.73477i	0.812545	−	1.11837i	0.990926	−	0.134411i	$-0.0429143\pi$
$62$	6.99143	−	3.56231i	0.887912	−	0.452414i
$63$	5.42695	+	2.76517i	0.683731	+	0.348378i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	−5.34886	−	1.46063i	−0.663444	−	0.181169i
$66$	−2.93727	+	6.62581i	−0.361553	+	0.815581i
$67$	−4.03846	+	4.03846i	−0.493376	+	0.493376i	−0.909368	−	0.415992i	$-0.863434\pi$
$67$	−4.03846	+	4.03846i	−0.493376	+	0.493376i	0.415992	+	0.909368i	$0.363434\pi$
$68$	0.196982	−	1.24369i	0.0238875	−	0.150820i
$69$	15.9504	−	5.18260i	1.92020	−	0.623912i
$70$	−1.55912	−	7.51127i	−0.186351	−	0.897768i
$71$	−7.25478	−	5.27091i	−0.860984	−	0.625541i	0.0671685	−	0.997742i	$-0.478603\pi$
$71$	−7.25478	−	5.27091i	−0.860984	−	0.625541i	−0.928152	+	0.372200i	$0.878603\pi$
$72$	0.277728	+	1.75350i	0.0327305	+	0.206652i
$73$	4.14012	+	8.12545i	0.484565	+	0.951012i	0.995799	+	0.0915704i	$0.0291887\pi$
$73$	4.14012	+	8.12545i	0.484565	+	0.951012i	−0.511234	+	0.859442i	$0.670811\pi$
$74$	−1.77525	−	5.46365i	−0.206368	−	0.635137i
$75$	−6.95692	+	8.42528i	−0.803316	+	0.972867i
$76$			5.26706i			0.604173i
$77$	−8.83124	+	7.17490i	−1.00641	+	0.817656i
$78$	3.83161	+	3.83161i	0.433844	+	0.433844i
$79$	−11.2765	+	8.19287i	−1.26871	+	0.921770i	−0.999150	−	0.0412138i	$-0.986878\pi$
$79$	−11.2765	+	8.19287i	−1.26871	+	0.921770i	−0.269558	+	0.962984i	$0.586878\pi$
$80$	1.50414	−	1.65456i	0.168168	−	0.184985i
$81$	3.45301	−	10.6273i	0.383668	−	1.18081i
$82$	−4.14235	+	0.656083i	−0.457445	+	0.0724522i
$83$	−11.9833	+	1.89797i	−1.31534	+	0.208330i	−0.774382	−	0.632719i	$-0.781939\pi$
$83$	−11.9833	+	1.89797i	−1.31534	+	0.208330i	−0.540960	+	0.841048i	$0.681939\pi$
$84$	−2.31672	+	7.13013i	−0.252775	+	0.777961i
$85$	−2.81246	+	0.133932i	−0.305054	+	0.0145270i
$86$	−0.953013	+	0.692405i	−0.102766	+	0.0746639i
$87$	−2.36128	−	2.36128i	−0.253155	−	0.253155i
$88$	−3.20499	−	0.853262i	−0.341653	−	0.0909581i
$89$		−	4.89861i		−	0.519252i	−0.965709	−	0.259626i	$-0.916401\pi$
$89$		−	4.89861i		−	0.519252i	0.965709	−	0.259626i	$-0.0835993\pi$
$90$	3.71290	−	1.40495i	0.391374	−	0.148094i
$91$	2.62884	+	8.09073i	0.275577	+	0.848139i
$92$	3.48425	+	6.83822i	0.363258	+	0.712934i
$93$	2.68238	+	16.9359i	0.278150	+	1.75617i
$94$	4.52110	+	3.28477i	0.466316	+	0.338799i
$95$	11.5317	−	2.39364i	1.18313	−	0.245583i
$96$	−2.07831	+	0.675282i	−0.212116	+	0.0689207i
$97$	0.442255	−	2.79229i	0.0449042	−	0.283514i	−0.955011	−	0.296572i	$-0.904157\pi$
$97$	0.442255	−	2.79229i	0.0449042	−	0.283514i	0.999915	+	0.0130581i	$0.00415662\pi$
$98$	−3.37290	+	3.37290i	−0.340714	+	0.340714i
$99$	−4.38211	−	3.93295i	−0.440418	−	0.395276i
$100$	−4.30606	−	2.54124i	−0.430606	−	0.254124i
$101$	−3.41511	−	4.70050i	−0.339816	−	0.467717i	0.604572	−	0.796551i	$-0.293344\pi$
$101$	−3.41511	−	4.70050i	−0.339816	−	0.467717i	−0.944388	+	0.328834i	$0.893344\pi$
$102$	2.45176	+	1.24923i	0.242760	+	0.123692i
$103$	11.7021	−	5.96253i	1.15304	−	0.587505i	0.230376	−	0.973102i	$-0.426004\pi$
$103$	11.7021	−	5.96253i	1.15304	−	0.587505i	0.922667	+	0.385597i	$0.126004\pi$
$104$	−1.45751	+	2.00609i	−0.142921	+	0.196713i
$105$	16.6636	+	1.83190i	1.62620	+	0.178775i
$106$	8.67515	+	2.81873i	0.842605	+	0.273779i
$107$	3.35972	−	6.59383i	0.324797	−	0.637449i	−0.669652	−	0.742675i	$-0.733557\pi$
$107$	3.35972	−	6.59383i	0.324797	−	0.637449i	0.994448	+	0.105226i	$0.0335566\pi$
$108$	2.64321	+	0.418643i	0.254343	+	0.0402839i
$109$	−16.3020			−1.56145			−0.780726	−	0.624874i	$-0.785150\pi$
$109$	−16.3020			−1.56145			−0.780726	+	0.624874i	$0.785150\pi$
$110$	−0.411608	+	7.40477i	−0.0392452	+	0.706017i
$111$	12.5539			1.19157
$112$	−3.38851	−	0.536686i	−0.320184	−	0.0507121i
$113$	−5.71638	+	11.2190i	−0.537752	+	1.05540i	0.449056	+	0.893504i	$0.351760\pi$
$113$	−5.71638	+	11.2190i	−0.537752	+	1.05540i	−0.986808	+	0.161894i	$0.948240\pi$
$114$	−10.9466	−	3.55675i	−1.02524	−	0.333120i
$115$	13.3882	−	10.7361i	1.24845	−	1.00114i
$116$	0.898209	−	1.23628i	0.0833966	−	0.114786i
$117$	−3.92248	+	1.99860i	−0.362633	+	0.184771i
$118$	−2.48650	−	1.26694i	−0.228901	−	0.116631i
$119$	2.53922	+	3.49494i	0.232770	+	0.320380i
$120$	2.42296	+	4.24336i	0.221185	+	0.387364i
$121$	10.0346	−	4.50634i	0.912235	−	0.409667i
$122$	−7.63447	+	7.63447i	−0.691192	+	0.691192i
$123$	1.43371	−	9.05210i	0.129273	−	0.816200i
$124$	−7.46262	+	2.42475i	−0.670163	+	0.217749i
$125$	−3.60687	+	10.5826i	−0.322609	+	0.946532i
$126$	−4.92757	−	3.58009i	−0.438983	−	0.318939i
$127$	1.45179	+	9.16626i	0.128826	+	0.813374i	0.964487	+	0.264129i	$0.0850845\pi$
$127$	1.45179	+	9.16626i	0.128826	+	0.813374i	−0.835662	+	0.549245i	$0.814915\pi$
$128$	−0.453990	−	0.891007i	−0.0401275	−	0.0787546i
$129$	−0.795476	−	2.44822i	−0.0700377	−	0.215554i
$130$	5.05451	+	2.27939i	0.443310	+	0.199916i
$131$		−	12.4792i		−	1.09031i	−0.838335	−	0.545155i	$-0.816471\pi$
$131$		−	12.4792i		−	1.09031i	0.838335	−	0.545155i	$-0.183529\pi$
$132$	3.93761	−	6.08475i	0.342725	−	0.529610i
$133$	−12.7774	−	12.7774i	−1.10794	−	1.10794i
$134$	4.62049	−	3.35698i	0.399150	−	0.289999i
$135$	−0.284644	−	5.97729i	−0.0244982	−	0.514443i
$136$	−0.389113	+	1.19757i	−0.0333662	+	0.102691i
$137$	−6.34303	+	1.00464i	−0.541922	+	0.0858320i	−0.421394	−	0.906878i	$-0.638459\pi$
$137$	−6.34303	+	1.00464i	−0.541922	+	0.0858320i	−0.120528	+	0.992710i	$0.538459\pi$
$138$	−16.5648	+	2.62360i	−1.41009	+	0.223336i
$139$	0.806424	−	2.48192i	0.0684000	−	0.210514i	−0.911014	−	0.412375i	$-0.864699\pi$
$139$	0.806424	−	2.48192i	0.0684000	−	0.210514i	0.979414	+	0.201862i	$0.0646992\pi$
$140$	0.364904	+	7.66269i	0.0308400	+	0.647616i
$141$	−9.87979	+	7.17808i	−0.832028	+	0.604504i
$142$	6.34091	+	6.34091i	0.532117	+	0.532117i
$143$	−0.443599	−	8.21215i	−0.0370956	−	0.686734i
$144$		−	1.77536i		−	0.147947i
$145$	−3.11490	−	1.40470i	−0.258679	−	0.116654i
$146$	−2.81805	−	8.67307i	−0.233224	−	0.717789i
$147$	−4.73226	−	9.28757i	−0.390310	−	0.766026i
$148$	0.898689	+	5.67410i	0.0738718	+	0.466408i
$149$	4.53786	+	3.29695i	0.371756	+	0.270097i	0.757939	−	0.652326i	$-0.226207\pi$
$149$	4.53786	+	3.29695i	0.371756	+	0.270097i	−0.386183	+	0.922422i	$0.626207\pi$
$150$	8.18927	−	7.23325i	0.668651	−	0.590592i
$151$	−5.67179	+	1.84288i	−0.461563	+	0.149971i	−0.530563	−	0.847646i	$-0.678019\pi$
$151$	−5.67179	+	1.84288i	−0.461563	+	0.149971i	0.0689993	+	0.997617i	$0.478019\pi$
$152$	0.823949	−	5.20221i	0.0668311	−	0.421955i
$153$	−1.58076	+	1.58076i	−0.127797	+	0.127797i
$154$	9.84492	−	5.70505i	0.793326	−	0.459726i
$155$	8.70018	+	15.2367i	0.698816	+	1.22384i
$156$	−3.18504	−	4.38383i	−0.255007	−	0.350987i
$157$	7.72174	+	3.93442i	0.616262	+	0.314001i	0.734110	−	0.679030i	$-0.237600\pi$
$157$	7.72174	+	3.93442i	0.616262	+	0.314001i	−0.117848	+	0.993032i	$0.537600\pi$
$158$	12.4193	−	6.32797i	0.988030	−	0.503426i
$159$	−11.7164	+	16.1262i	−0.929167	+	1.27889i
$160$	−1.74445	+	1.39889i	−0.137911	+	0.110592i
$161$	−25.0413	−	8.13641i	−1.97353	−	0.641239i
$162$	−5.07297	+	9.95626i	−0.398570	+	0.782238i
$163$	6.63773	+	1.05131i	0.519907	+	0.0823452i	0.410873	−	0.911693i	$-0.365224\pi$
$163$	6.63773	+	1.05131i	0.519907	+	0.0823452i	0.109034	+	0.994038i	$0.465224\pi$
$164$	4.19398			0.327495
$165$	−15.1114	−	5.85576i	−1.17642	−	0.455870i
$166$	12.1327			0.941680
$167$	21.2637	+	3.36785i	1.64544	+	0.260612i	0.909276	−	0.416194i	$-0.136636\pi$
$167$	21.2637	+	3.36785i	1.64544	+	0.260612i	0.736162	+	0.676806i	$0.236636\pi$
$168$	3.40360	−	6.67993i	0.262593	−	0.515368i
$169$	6.51594	+	2.11716i	0.501226	+	0.162858i
$170$	2.79879	+	0.307683i	0.214657	+	0.0235982i
$171$	5.49634	−	7.56506i	0.420315	−	0.578514i
$172$	1.04960	−	0.534796i	0.0800310	−	0.0407778i
$173$	3.32549	+	1.69442i	0.252832	+	0.128824i	0.575814	−	0.817581i	$-0.304685\pi$
$173$	3.32549	+	1.69442i	0.252832	+	0.128824i	−0.322982	+	0.946405i	$0.604685\pi$
$174$	1.96282	+	2.70159i	0.148801	+	0.204807i
$175$	16.6109	−	4.28127i	1.25566	−	0.323634i
$176$	3.03205	+	1.34413i	0.228549	+	0.101317i
$177$	4.31218	−	4.31218i	0.324123	−	0.324123i
$178$	−0.766312	+	4.83830i	−0.0574375	+	0.362646i
$179$	−3.57423	+	1.16134i	−0.267151	+	0.0868025i	−0.439529	−	0.898228i	$-0.644855\pi$
$179$	−3.57423	+	1.16134i	−0.267151	+	0.0868025i	0.172379	+	0.985031i	$0.444855\pi$
$180$	−3.88697	+	0.806823i	−0.289718	+	0.0601370i
$181$	2.13510	+	1.55124i	0.158700	+	0.115303i	0.664301	−	0.747465i	$-0.268729\pi$
$181$	2.13510	+	1.55124i	0.158700	+	0.115303i	−0.505601	+	0.862767i	$0.668729\pi$
$182$	−1.33080	−	8.40236i	−0.0986457	−	0.622824i
$183$	−10.7113	−	21.0222i	−0.791805	−	1.55400i
$184$	−2.37162	−	7.29909i	−0.174838	−	0.538096i
$185$	12.0145	−	4.54621i	0.883320	−	0.334244i
$186$		−	17.1470i		−	1.25728i
$187$	−1.50290	−	3.89649i	−0.109903	−	0.284939i
$188$	−3.95159	−	3.95159i	−0.288199	−	0.288199i
$189$	−7.42775	+	5.39657i	−0.540289	+	0.392543i
$190$	−11.7642	+	0.560220i	−0.853462	+	0.0406426i
$191$	−6.80939	+	20.9572i	−0.492710	+	1.51641i	0.327784	+	0.944753i	$0.393698\pi$
$191$	−6.80939	+	20.9572i	−0.492710	+	1.51641i	−0.820495	+	0.571654i	$0.806302\pi$
$192$	2.15836	−	0.341850i	0.155766	−	0.0246709i
$193$	−1.63446	+	0.258873i	−0.117651	+	0.0186341i	−0.214982	−	0.976618i	$-0.568969\pi$
$193$	−1.63446	+	0.258873i	−0.117651	+	0.0186341i	0.0973313	+	0.995252i	$0.468969\pi$
$194$	−0.873619	+	2.68872i	−0.0627222	+	0.193039i
$195$	−8.15050	+	8.96558i	−0.583669	+	0.642039i
$196$	3.85901	−	2.80374i	0.275644	−	0.200267i
$197$	−0.368303	−	0.368303i	−0.0262405	−	0.0262405i	0.693865	−	0.720105i	$-0.255907\pi$
$197$	−0.368303	−	0.368303i	−0.0262405	−	0.0262405i	−0.720105	+	0.693865i	$0.755907\pi$
$198$	3.71291	+	4.57004i	0.263865	+	0.324779i
$199$		−	13.6983i		−	0.971047i	−0.874224	−	0.485524i	$-0.838629\pi$
$199$		−	13.6983i		−	0.971047i	0.874224	−	0.485524i	$-0.161371\pi$
$200$	3.85550	+	3.18357i	0.272625	+	0.225112i
$201$	3.85670	+	11.8697i	0.272031	+	0.837225i
$202$	2.63775	+	5.17687i	0.185591	+	0.364243i
$203$	0.820123	+	5.17806i	0.0575614	+	0.363428i
$204$	−2.22615	−	1.61739i	−0.155862	−	0.113240i
$205$	−1.90598	−	9.18230i	−0.133119	−	0.641319i
$206$	−12.4908	+	4.05850i	−0.870274	+	0.282769i
$207$	2.13148	−	13.4576i	0.148148	−	0.935370i
$208$	1.75339	−	1.75339i	0.121576	−	0.121576i
$209$	8.75870	+	15.1144i	0.605852	+	1.04549i
$210$	−16.1718	−	4.41610i	−1.11596	−	0.304740i
$211$	2.89876	+	3.98980i	0.199559	+	0.274669i	0.897055	−	0.441920i	$-0.145702\pi$
$211$	2.89876	+	3.98980i	0.199559	+	0.274669i	−0.697496	+	0.716589i	$0.745702\pi$
$212$	−8.12740	−	4.14112i	−0.558192	−	0.284413i
$213$	−17.4603	+	8.89644i	−1.19636	+	0.609574i
$214$	−4.34986	+	5.98707i	−0.297350	+	0.409268i
$215$	−1.64788	−	2.05494i	−0.112384	−	0.140146i
$216$	−2.54517	−	0.826977i	−0.173177	−	0.0562687i
$217$	12.2214	−	23.9858i	0.829641	−	1.62826i
$218$	16.1013	+	2.55020i	1.09052	+	0.172721i
$219$	19.9283			1.34663
$220$	1.56490	−	7.24921i	0.105506	−	0.488742i
$221$	−3.12239			−0.210034
$222$	−12.3994	−	1.96387i	−0.832192	−	0.131806i
$223$	−1.52111	+	2.98535i	−0.101861	+	0.199914i	−0.936313	−	0.351168i	$-0.885785\pi$
$223$	−1.52111	+	2.98535i	−0.101861	+	0.199914i	0.834451	+	0.551082i	$0.185785\pi$
$224$	3.26283	+	1.06016i	0.218007	+	0.0708348i
$225$	3.53291	+	8.14347i	0.235528	+	0.542898i
$226$	7.40105	−	10.1867i	0.492310	−	0.677607i
$227$	−13.8508	+	7.05734i	−0.919310	+	0.468412i	−0.848570	−	0.529083i	$-0.822536\pi$
$227$	−13.8508	+	7.05734i	−0.919310	+	0.468412i	−0.0707400	+	0.997495i	$0.522536\pi$
$228$	10.2554	+	5.22538i	0.679179	+	0.346059i
$229$	0.0681452	+	0.0937938i	0.00450316	+	0.00619807i	0.811263	−	0.584682i	$-0.198781\pi$
$229$	0.0681452	+	0.0937938i	0.00450316	+	0.00619807i	−0.806759	+	0.590880i	$0.798781\pi$
$230$	−14.9028	+	8.50953i	−0.982663	+	0.561102i
$231$	5.20875	+	24.3133i	0.342710	+	1.59970i
$232$	−1.08055	+	1.08055i	−0.0709414	+	0.0709414i
$233$	−1.65061	+	10.4215i	−0.108135	+	0.682737i	0.872753	+	0.488162i	$0.162333\pi$
$233$	−1.65061	+	10.4215i	−0.108135	+	0.682737i	−0.980888	+	0.194574i	$0.937667\pi$
$234$	4.18684	−	1.36039i	0.273702	−	0.0889312i
$235$	−6.85579	+	10.4474i	−0.447222	+	0.681515i
$236$	2.25770	+	1.64031i	0.146964	+	0.106775i
$237$	4.76489	+	30.0844i	0.309513	+	1.95419i
$238$	−1.96123	−	3.84913i	−0.127128	−	0.249502i
$239$	−5.73518	−	17.6511i	−0.370978	−	1.14175i	−0.946152	−	0.323721i	$-0.895066\pi$
$239$	−5.73518	−	17.6511i	−0.370978	−	1.14175i	0.575175	−	0.818031i	$-0.304934\pi$
$240$	−1.72932	−	4.57015i	−0.111627	−	0.295002i
$241$			15.7897i			1.01711i	0.861031	+	0.508553i	$0.169819\pi$
$241$			15.7897i			1.01711i	−0.861031	+	0.508553i	$0.830181\pi$
$242$	−10.6160	+	2.88110i	−0.682422	+	0.185204i
$243$	−11.5895	−	11.5895i	−0.743466	−	0.743466i
$244$	8.73477	−	6.34618i	0.559186	−	0.406273i
$245$	−7.89225	−	7.17474i	−0.504217	−	0.458377i
$246$	−2.83212	+	8.71637i	−0.180569	+	0.555736i
$247$	12.8997	−	2.04312i	0.820791	−	0.130000i
$248$	7.75006	−	1.22749i	0.492129	−	0.0779456i
$249$	−8.19300	+	25.2155i	−0.519210	+	1.59797i
$250$	5.21794	−	9.88803i	0.330012	−	0.625374i
$251$	7.90964	−	5.74669i	0.499252	−	0.362728i	−0.309479	−	0.950906i	$-0.600155\pi$
$251$	7.90964	−	5.74669i	0.499252	−	0.362728i	0.808731	+	0.588178i	$0.200155\pi$
$252$	4.30685	+	4.30685i	0.271306	+	0.271306i
$253$	21.3699	+	13.8290i	1.34351	+	0.869424i
$254$		−	9.28052i		−	0.582311i
$255$	−2.52943	+	5.60896i	−0.158399	+	0.351247i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−8.84896	−	17.3671i	−0.551983	−	1.08333i	−0.983447	−	0.181197i	$-0.942003\pi$
$257$	−8.84896	−	17.3671i	−0.551983	−	1.08333i	0.431464	−	0.902130i	$-0.357997\pi$
$258$	0.402696	+	2.54252i	0.0250707	+	0.158290i
$259$	−15.9449	−	11.5847i	−0.990770	−	0.719837i
$260$	−4.63570	−	3.04203i	−0.287494	−	0.188659i
$261$	−2.58019	+	0.838354i	−0.159710	+	0.0518928i
$262$	−1.95217	+	12.3255i	−0.120606	+	0.761474i
$263$	8.03990	−	8.03990i	0.495761	−	0.495761i	−0.414354	−	0.910116i	$-0.635993\pi$
$263$	8.03990	−	8.03990i	0.495761	−	0.495761i	0.910116	+	0.414354i	$0.135993\pi$
$264$	−4.84100	+	5.39386i	−0.297943	+	0.331969i
$265$	−5.37301	+	19.6761i	−0.330062	+	1.20869i
$266$	10.6212	+	14.6189i	0.651229	+	0.896340i
$267$	−9.53799	−	4.85985i	−0.583716	−	0.297418i
$268$	−5.08875	+	2.59285i	−0.310845	+	0.158384i
$269$	5.39339	−	7.42336i	0.328841	−	0.452610i	−0.612300	−	0.790625i	$-0.709756\pi$
$269$	5.39339	−	7.42336i	0.328841	−	0.452610i	0.941141	+	0.338015i	$0.109756\pi$
$270$	−0.653915	+	5.94823i	−0.0397960	+	0.361998i
$271$	1.47444	+	0.479075i	0.0895658	+	0.0291017i	0.353457	−	0.935451i	$-0.385006\pi$
$271$	1.47444	+	0.479075i	0.0895658	+	0.0291017i	−0.263891	+	0.964552i	$0.585006\pi$
$272$	0.571663	−	1.12195i	0.0346622	−	0.0680283i
$273$	18.3613	+	2.90815i	1.11128	+	0.176009i
$274$	6.42210			0.387973
$275$	−16.5826	−	0.131748i	−0.999968	−	0.00794467i
$276$	16.7712			1.00951
$277$	−22.1707	−	3.51149i	−1.33211	−	0.210985i	−0.550542	−	0.834808i	$-0.685579\pi$
$277$	−22.1707	−	3.51149i	−1.33211	−	0.210985i	−0.781566	+	0.623823i	$0.785579\pi$
$278$	−1.18475	+	2.32521i	−0.0710568	+	0.139457i
$279$	13.2488	+	4.30481i	0.793188	+	0.257722i
$280$	0.838298	−	7.62543i	0.0500979	−	0.455707i
$281$	9.07909	−	12.4963i	0.541613	−	0.745467i	−0.447231	−	0.894418i	$-0.647590\pi$
$281$	9.07909	−	12.4963i	0.541613	−	0.745467i	0.988844	+	0.148952i	$0.0475898\pi$
$282$	10.8810	−	5.54417i	0.647957	−	0.330151i
$283$	−0.820505	−	0.418068i	−0.0487739	−	0.0248516i	0.429433	−	0.903099i	$-0.358713\pi$
$283$	−0.820505	−	0.418068i	−0.0487739	−	0.0248516i	−0.478207	+	0.878247i	$0.658713\pi$
$284$	−5.27091	−	7.25478i	−0.312771	−	0.430492i
$285$	6.77982	−	24.8278i	0.401602	−	1.47067i
$286$	−0.846525	+	8.18044i	−0.0500561	+	0.483719i
$287$	−10.1742	+	10.1742i	−0.600563	+	0.600563i
$288$	−0.277728	+	1.75350i	−0.0163653	+	0.103326i
$289$	14.6600	−	4.76332i	0.862352	−	0.280195i
$290$	2.85681	+	1.87469i	0.167758	+	0.110085i
$291$	−4.99805	−	3.63130i	−0.292991	−	0.212870i
$292$	1.42659	+	9.00713i	0.0834848	+	0.527103i
$293$	11.0146	+	21.6174i	0.643481	+	1.26290i	0.950360	+	0.311154i	$0.100715\pi$
$293$	11.0146	+	21.6174i	0.643481	+	1.26290i	−0.306879	+	0.951749i	$0.599285\pi$
$294$	3.22110	+	9.91352i	0.187858	+	0.578168i
$295$	2.56528	−	5.68846i	0.149356	−	0.331195i
$296$		−	5.74483i		−	0.333911i
$297$	8.28116	−	3.19410i	0.480522	−	0.185340i
$298$	−3.96624	−	3.96624i	−0.229758	−	0.229758i
$299$	15.3962	−	11.1860i	0.890384	−	0.646902i
$300$	−9.21998	+	5.86311i	−0.532316	+	0.338507i
$301$	−1.24885	+	3.84358i	−0.0719828	+	0.221540i
$302$	5.89025	−	0.932924i	0.338946	−	0.0536837i
$303$	−12.5403	+	1.98619i	−0.720423	+	0.114104i
$304$	−1.62761	+	5.00927i	−0.0933498	+	0.287301i
$305$	−17.8639	−	16.2398i	−1.02288	−	0.929891i
$306$	1.80858	−	1.31401i	0.103390	−	0.0751170i
$307$	−11.5434	−	11.5434i	−0.658817	−	0.658817i	0.296283	−	0.955100i	$-0.404253\pi$
$307$	−11.5434	−	11.5434i	−0.658817	−	0.658817i	−0.955100	+	0.296283i	$0.904253\pi$
$308$	−10.6162	+	4.09473i	−0.604913	+	0.233319i
$309$		−	28.7003i		−	1.63270i
$310$	−6.20952	−	16.4101i	−0.352677	−	0.932033i
$311$	1.89895	+	5.84437i	0.107680	+	0.331404i	0.990350	−	0.138589i	$-0.0442566\pi$
$311$	1.89895	+	5.84437i	0.107680	+	0.331404i	−0.882670	+	0.469992i	$0.844257\pi$
$312$	2.46004	+	4.82811i	0.139273	+	0.273338i
$313$	−2.07794	−	13.1196i	−0.117452	−	0.741562i	−0.974176	−	0.225788i	$-0.927504\pi$
$313$	−2.07794	−	13.1196i	−0.117452	−	0.741562i	0.856725	−	0.515774i	$-0.172496\pi$
$314$	−7.01119	−	5.09393i	−0.395665	−	0.287467i
$315$	7.47214	−	11.3867i	0.421008	−	0.641567i
$316$	−13.2563	+	4.30725i	−0.745728	+	0.242302i
$317$	0.265452	−	1.67600i	0.0149093	−	0.0941334i	−0.979112	−	0.203323i	$-0.934826\pi$
$317$	0.265452	−	1.67600i	0.0149093	−	0.0941334i	0.994021	+	0.109190i	$0.0348257\pi$
$318$	14.0948	−	14.0948i	0.790397	−	0.790397i
$319$	0.521681	−	5.04129i	0.0292085	−	0.282258i
$320$	1.94181	−	1.10877i	0.108550	−	0.0619824i
$321$	−9.50558	−	13.0833i	−0.530549	−	0.730239i
$322$	23.4602	+	11.9536i	1.30738	+	0.666146i
$323$	5.90938	−	3.01098i	0.328807	−	0.167535i
$324$	6.56802	−	9.04010i	0.364890	−	0.502228i
$325$	−4.55350	+	11.5319i	−0.252583	+	0.639673i
$326$	−6.39155	−	2.07674i	−0.353995	−	0.115020i
$327$	−16.1730	+	31.7414i	−0.894371	+	1.75530i
$328$	−4.14235	−	0.656083i	−0.228723	−	0.0362261i
$329$	19.1723			1.05701
$330$	14.0093	+	8.14761i	0.771188	+	0.448511i
$331$	−20.3380			−1.11788			−0.558940	−	0.829208i	$-0.688792\pi$
$331$	−20.3380			−1.11788			−0.558940	+	0.829208i	$0.688792\pi$
$332$	−11.9833	−	1.89797i	−0.657671	−	0.104165i
$333$	4.63031	−	9.08750i	0.253740	−	0.497992i
$334$	−20.4751	−	6.65276i	−1.12035	−	0.364023i
$335$	7.98940	+	9.96298i	0.436507	+	0.544336i
$336$	−4.40666	+	6.06525i	−0.240403	+	0.330887i
$337$	22.4259	−	11.4265i	1.22161	−	0.622444i	0.280280	−	0.959918i	$-0.409573\pi$
$337$	22.4259	−	11.4265i	1.22161	−	0.622444i	0.941335	+	0.337475i	$0.109573\pi$
$338$	−6.10452	−	3.11041i	−0.332042	−	0.169184i
$339$	16.1732	+	22.2605i	0.878408	+	1.20903i
$340$	−2.71620	−	0.741722i	−0.147306	−	0.0402255i
$341$	−17.3827	+	19.3679i	−0.941325	+	1.04883i
$342$	−6.61210	+	6.61210i	−0.357542	+	0.357542i
$343$	1.19681	−	7.55637i	0.0646217	−	0.408006i
$344$	−1.12033	+	0.364019i	−0.0604044	+	0.0196266i
$345$	−7.62179	−	36.7190i	−0.410343	−	1.97688i
$346$	−3.01948	−	2.19378i	−0.162328	−	0.117938i
$347$	−5.09851	−	32.1907i	−0.273702	−	1.72809i	−0.615345	−	0.788258i	$-0.710983\pi$
$347$	−5.09851	−	32.1907i	−0.273702	−	1.72809i	0.341643	−	0.939830i	$-0.389017\pi$
$348$	−1.51603	−	2.97538i	−0.0812678	−	0.159497i
$349$	7.28270	+	22.4138i	0.389834	+	1.19978i	0.932913	+	0.360103i	$0.117258\pi$
$349$	7.28270	+	22.4138i	0.389834	+	1.19978i	−0.543079	+	0.839682i	$0.682742\pi$
$350$	−17.0761	+	1.63005i	−0.912755	+	0.0871300i
$351$		−	6.63597i		−	0.354202i
$352$	−2.78445	−	1.80190i	−0.148412	−	0.0960414i
$353$	−13.3377	−	13.3377i	−0.709893	−	0.709893i	0.256620	−	0.966512i	$-0.417391\pi$
$353$	−13.3377	−	13.3377i	−0.709893	−	0.709893i	−0.966512	+	0.256620i	$0.917391\pi$
$354$	−4.93366	+	3.58451i	−0.262221	+	0.190515i
$355$	−13.4882	+	14.8371i	−0.715880	+	0.787471i
$356$	1.51375	−	4.65886i	0.0802288	−	0.246919i
$357$	9.32405	−	1.47678i	0.493481	−	0.0781597i
$358$	3.71190	−	0.587907i	0.196180	−	0.0310719i
$359$	5.78388	−	17.8010i	0.305262	−	0.939498i	−0.674318	−	0.738441i	$-0.735562\pi$
$359$	5.78388	−	17.8010i	0.305262	−	0.939498i	0.979579	−	0.201057i	$-0.0644378\pi$
$360$	3.96533	−	0.188833i	0.208991	−	0.00995236i
$361$	−7.07233	+	5.13835i	−0.372228	+	0.270439i
$362$	−1.86614	−	1.86614i	−0.0980822	−	0.0980822i
$363$	1.18098	−	24.0088i	0.0619851	−	1.26014i
$364$			8.50709i			0.445893i
$365$	19.0719	−	7.21672i	0.998268	−	0.377740i
$366$	7.29087	+	22.4390i	0.381100	+	1.17290i
$367$	−13.8443	−	27.1710i	−0.722668	−	1.41832i	−0.900766	−	0.434304i	$-0.856994\pi$
$367$	−13.8443	−	27.1710i	−0.722668	−	1.41832i	0.178098	−	0.984013i	$-0.443006\pi$
$368$	1.20059	+	7.58023i	0.0625851	+	0.395147i
$369$	−6.02380	−	4.37655i	−0.313587	−	0.227834i
$370$	−12.5777	+	2.61077i	−0.653884	+	0.135727i
$371$	29.7622	−	9.67033i	1.54518	−	0.502058i
$372$	−2.68238	+	16.9359i	−0.139075	+	0.878085i
$373$	8.76421	−	8.76421i	0.453794	−	0.453794i	−0.442818	−	0.896612i	$-0.646021\pi$
$373$	8.76421	−	8.76421i	0.453794	−	0.453794i	0.896612	+	0.442818i	$0.146021\pi$
$374$	0.874854	+	4.08362i	0.0452376	+	0.211159i
$375$	17.0268	+	17.5217i	0.879258	+	0.904816i
$376$	3.28477	+	4.52110i	0.169399	+	0.233158i
$377$	−3.37623	−	1.72028i	−0.173885	−	0.0885988i
$378$	8.18051	−	4.16818i	0.420760	−	0.214388i
$379$	−10.2229	+	14.0706i	−0.525114	+	0.722757i	−0.986376	−	0.164507i	$-0.947397\pi$
$379$	−10.2229	+	14.0706i	−0.525114	+	0.722757i	0.461262	+	0.887264i	$0.347397\pi$
$380$	11.7070	+	1.28700i	0.600555	+	0.0660216i
$381$	19.2877	+	6.26697i	0.988141	+	0.321067i
$382$	10.0040	−	19.6339i	0.511848	−	1.00456i
$383$	17.5345	+	2.77719i	0.895970	+	0.141908i	0.587403	−	0.809295i	$-0.300150\pi$
$383$	17.5345	+	2.77719i	0.895970	+	0.141908i	0.308567	+	0.951202i	$0.400150\pi$
$384$	−2.18526			−0.111516
$385$	13.7896	+	21.3822i	0.702782	+	1.08974i
$386$	1.65483			0.0842288
$387$	−2.06561	−	0.327160i	−0.105001	−	0.0166305i
$388$	1.28347	−	2.51896i	0.0651585	−	0.127881i
$389$	28.5785	+	9.28571i	1.44899	+	0.470804i	0.924687	−	0.380729i	$-0.124327\pi$
$389$	28.5785	+	9.28571i	1.44899	+	0.470804i	0.524300	+	0.851534i	$0.324327\pi$
$390$	9.45268	−	7.58018i	0.478655	−	0.383837i
$391$	5.68034	−	7.81832i	0.287267	−	0.395389i
$392$	−4.25010	+	2.16553i	−0.214662	+	0.109376i
$393$	−24.2979	−	12.3804i	−1.22567	−	0.624510i
$394$	0.306153	+	0.421384i	0.0154238	+	0.0212290i
$395$	15.4547	+	27.0660i	0.777611	+	1.36184i
$396$	−2.95228	−	5.09460i	−0.148358	−	0.256013i
$397$	24.1441	−	24.1441i	1.21176	−	1.21176i	0.241312	−	0.970448i	$-0.422422\pi$
$397$	24.1441	−	24.1441i	1.21176	−	1.21176i	0.970448	−	0.241312i	$-0.0775776\pi$
$398$	−2.14289	+	13.5297i	−0.107413	+	0.678180i
$399$	−37.5548	+	12.2023i	−1.88009	+	0.610879i
$400$	−3.31002	−	3.74750i	−0.165501	−	0.187375i
$401$	−20.4513	−	14.8588i	−1.02129	−	0.742012i	−0.0547443	−	0.998500i	$-0.517434\pi$
$401$	−20.4513	−	14.8588i	−1.02129	−	0.742012i	−0.966547	+	0.256489i	$0.917434\pi$
$402$	−1.95239	−	12.3269i	−0.0973763	−	0.614810i
$403$	8.83334	+	17.3364i	0.440020	+	0.863588i
$404$	−1.79543	−	5.52577i	−0.0893260	−	0.274917i
$405$	−22.7773	−	10.2717i	−1.13181	−	0.510404i
$406$		−	5.24260i		−	0.260186i
$407$	12.0145	+	14.7880i	0.595535	+	0.733016i
$408$	1.94573	+	1.94573i	0.0963278	+	0.0963278i
$409$	−27.1789	+	19.7466i	−1.34391	+	0.976408i	−0.344619	+	0.938742i	$0.611992\pi$
$409$	−27.1789	+	19.7466i	−1.34391	+	0.976408i	−0.999290	+	0.0376652i	$0.988008\pi$
$410$	0.446084	+	9.36741i	0.0220305	+	0.462623i
$411$	−4.33673	+	13.3471i	−0.213915	+	0.658363i
$412$	12.9719	−	2.05455i	0.639079	−	0.101220i
$413$	−9.45620	+	1.49771i	−0.465309	+	0.0736977i
$414$	−4.21048	+	12.9585i	−0.206934	+	0.636876i
$415$	1.29047	+	27.0988i	0.0633467	+	1.33023i
$416$	−2.00609	+	1.45751i	−0.0983567	+	0.0714603i
$417$	−4.03245	−	4.03245i	−0.197470	−	0.197470i
$418$	−6.28644	−	16.2985i	−0.307480	−	0.797186i
$419$			27.8874i			1.36239i	0.732102	+	0.681195i	$0.238539\pi$
$419$			27.8874i			1.36239i	−0.732102	+	0.681195i	$0.761461\pi$
$420$	15.2819	+	6.89156i	0.745680	+	0.336274i
$421$	−0.0125199	−	0.0385324i	−0.000610185	−	0.00187796i	0.950751	−	0.309956i	$-0.100314\pi$
$421$	−0.0125199	−	0.0385324i	−0.000610185	−	0.00187796i	−0.951361	+	0.308078i	$0.900314\pi$
$422$	−2.23893	−	4.39414i	−0.108989	−	0.213904i
$423$	1.55205	+	9.79926i	0.0754633	+	0.476456i
$424$	7.37952	+	5.36154i	0.358381	+	0.260379i
$425$	−0.389534	+	6.28392i	−0.0188952	+	0.304815i
$426$	18.6370	−	6.05553i	0.902966	−	0.293391i
$427$	−5.79448	+	36.5849i	−0.280415	+	1.77047i
$428$	5.23289	−	5.23289i	0.252941	−	0.252941i
$429$	−16.4298	−	7.28344i	−0.793238	−	0.351648i
$430$	1.30612	+	2.28743i	0.0629869	+	0.110310i
$431$	0.646083	+	0.889258i	0.0311207	+	0.0428340i	0.824294	−	0.566162i	$-0.191572\pi$
$431$	0.646083	+	0.889258i	0.0311207	+	0.0428340i	−0.793173	+	0.608996i	$0.791572\pi$
$432$	2.38447	+	1.21495i	0.114723	+	0.0584543i
$433$	−17.0092	+	8.66660i	−0.817408	+	0.416490i	−0.812116	−	0.583496i	$-0.801684\pi$
$433$	−17.0092	+	8.66660i	−0.817408	+	0.416490i	−0.00529194	+	0.999986i	$0.501684\pi$
$434$	−15.8231	+	21.7787i	−0.759534	+	1.04541i
$435$	−5.82533	+	4.67138i	−0.279303	+	0.223975i
$436$	−15.5042	−	5.03760i	−0.742514	−	0.241258i
$437$	−18.3517	+	36.0173i	−0.877882	+	1.72294i
$438$	−19.6829	−	3.11747i	−0.940487	−	0.148958i
$439$	−10.1829			−0.486006			−0.243003	−	0.970026i	$-0.578132\pi$
$439$	−10.1829			−0.486006			−0.243003	+	0.970026i	$0.578132\pi$
$440$	−2.67966	+	6.91516i	−0.127748	+	0.329667i
$441$	−8.46847			−0.403260
$442$	3.08394	+	0.488449i	0.146688	+	0.0232331i
$443$	−3.34974	+	6.57423i	−0.159151	+	0.312351i	−0.956788	−	0.290787i	$-0.906083\pi$
$443$	−3.34974	+	6.57423i	−0.159151	+	0.312351i	0.797637	+	0.603138i	$0.206083\pi$
$444$	11.9395	+	3.87938i	0.566624	+	0.184107i
$445$	−10.8880	−	1.19697i	−0.516142	−	0.0567418i
$446$	1.96940	−	2.71064i	0.0932537	−	0.128353i
$447$	10.9214	−	5.56472i	0.516564	−	0.263202i
$448$	−3.05681	−	1.55752i	−0.144421	−	0.0735861i
$449$	−22.8418	−	31.4390i	−1.07797	−	1.48370i	−0.861735	−	0.507358i	$-0.830622\pi$
$449$	−22.8418	−	31.4390i	−1.07797	−	1.48370i	−0.216236	−	0.976341i	$-0.569378\pi$
$450$	−2.21550	−	8.59588i	−0.104440	−	0.405214i
$451$	12.0351	−	6.97426i	0.566711	−	0.328405i
$452$	−8.90348	+	8.90348i	−0.418784	+	0.418784i
$453$	−2.03868	+	12.8717i	−0.0957856	+	0.604766i
$454$	14.7843	−	4.80371i	0.693861	−	0.225449i
$455$	18.6254	−	3.86610i	0.873174	−	0.181245i
$456$	−9.31169	−	6.76534i	−0.436060	−	0.316816i
$457$	5.52520	+	34.8847i	0.258458	+	1.63184i	0.685829	+	0.727762i	$0.259440\pi$
$457$	5.52520	+	34.8847i	0.258458	+	1.63184i	−0.427372	+	0.904076i	$0.640560\pi$
$458$	−0.0526336	−	0.103299i	−0.00245941	−	0.00482686i
$459$	−1.04133	−	3.20487i	−0.0486050	−	0.149591i
$460$	16.0505	−	6.07345i	0.748360	−	0.283176i
$461$		−	0.472430i		−	0.0220033i	−0.999939	−	0.0110016i	$-0.996498\pi$
$461$		−	0.472430i		−	0.0220033i	0.999939	−	0.0110016i	$-0.00350200\pi$
$462$	−1.34119	−	24.8288i	−0.0623976	−	1.15514i
$463$	−6.85802	−	6.85802i	−0.318719	−	0.318719i	0.529556	−	0.848275i	$-0.322359\pi$
$463$	−6.85802	−	6.85802i	−0.318719	−	0.318719i	−0.848275	+	0.529556i	$0.822359\pi$
$464$	1.23628	−	0.898209i	0.0573928	−	0.0416983i
$465$	38.2985	−	1.82381i	1.77605	−	0.0845770i
$466$	3.26057	−	10.0350i	0.151043	−	0.464863i
$467$	1.86900	−	0.296020i	0.0864868	−	0.0136982i	−0.113041	−	0.993590i	$-0.536059\pi$
$467$	1.86900	−	0.296020i	0.0864868	−	0.0136982i	0.199528	+	0.979892i	$0.436059\pi$
$468$	−4.34810	+	0.688672i	−0.200991	+	0.0318339i
$469$	6.05482	−	18.6348i	0.279586	−	0.860476i
$470$	8.40572	−	9.24632i	0.387727	−	0.426501i
$471$	15.3213	−	11.1316i	0.705967	−	0.512915i
$472$	−1.97330	−	1.97330i	−0.0908286	−	0.0908286i
$473$	2.12261	−	3.28005i	0.0975979	−	0.150817i
$474$		−	30.4594i		−	1.39904i
$475$	−2.50254	−	26.2161i	−0.114825	−	1.20288i
$476$	1.33495	+	4.10854i	0.0611872	+	0.188315i
$477$	7.35197	+	14.4291i	0.336624	+	0.660661i
$478$	2.90333	+	18.3309i	0.132795	+	0.838437i
$479$	−8.38889	−	6.09489i	−0.383298	−	0.278483i	0.379405	−	0.925231i	$-0.376129\pi$
$479$	−8.38889	−	6.09489i	−0.383298	−	0.278483i	−0.762704	+	0.646748i	$0.776129\pi$
$480$	0.993104	+	4.78441i	0.0453288	+	0.218377i
$481$	13.5480	−	4.40202i	0.617737	−	0.200715i
$482$	2.47006	−	15.5953i	0.112508	−	0.710348i
$483$	−40.6854	+	40.6854i	−1.85125	+	1.85125i
$484$	10.9360	−	1.18493i	0.497091	−	0.0538603i
$485$	−6.09829	−	1.66528i	−0.276909	−	0.0756165i
$486$	9.63381	+	13.2598i	0.436998	+	0.601477i
$487$	−13.9058	−	7.08537i	−0.630133	−	0.321069i	0.109593	−	0.993976i	$-0.465045\pi$
$487$	−13.9058	−	7.08537i	−0.630133	−	0.321069i	−0.739726	+	0.672908i	$0.765045\pi$
$488$	−9.61999	+	4.90163i	−0.435477	+	0.221886i
$489$	8.63220	−	11.8812i	0.390361	−	0.537286i
$490$	6.67270	+	8.32103i	0.301442	+	0.375906i
$491$	6.47769	+	2.10473i	0.292334	+	0.0949851i	0.451513	−	0.892265i	$-0.350885\pi$
$491$	6.47769	+	2.10473i	0.292334	+	0.0949851i	−0.159179	+	0.987250i	$0.550885\pi$
$492$	4.16079	−	8.16602i	0.187583	−	0.368153i
$493$	−1.90052	−	0.301012i	−0.0855950	−	0.0135569i
$494$	−13.0605			−0.587621
$495$	−9.81244	+	8.77900i	−0.441036	+	0.394587i
$496$	−7.84667			−0.352326
$497$	30.3861	+	4.81268i	1.36300	+	0.215878i
$498$	12.0367	−	23.6234i	0.539377	−	1.05859i
$499$	−10.3280	−	3.35578i	−0.462345	−	0.150225i	0.0685765	−	0.997646i	$-0.478154\pi$
$499$	−10.3280	−	3.35578i	−0.462345	−	0.150225i	−0.530922	+	0.847421i	$0.678154\pi$
$500$	−6.70053	+	8.95002i	−0.299657	+	0.400257i
$501$	27.6530	−	38.0610i	1.23544	−	1.70044i
$502$	−8.71124	+	4.43860i	−0.388802	+	0.198104i
$503$	8.04907	+	4.10121i	0.358890	+	0.182864i	0.624133	−	0.781318i	$-0.285452\pi$
$503$	8.04907	+	4.10121i	0.358890	+	0.182864i	−0.265243	+	0.964182i	$0.585452\pi$
$504$	−3.58009	−	4.92757i	−0.159470	−	0.219491i
$505$	−11.2822	+	6.44213i	−0.502050	+	0.286671i
$506$	−18.9434	−	17.0018i	−0.842138	−	0.755821i
$507$	10.5866	−	10.5866i	0.470170	−	0.470170i
$508$	−1.45179	+	9.16626i	−0.0644129	+	0.406687i
$509$	16.8242	−	5.46651i	0.745719	−	0.242299i	0.0885808	−	0.996069i	$-0.471767\pi$
$509$	16.8242	−	5.46651i	0.745719	−	0.242299i	0.657138	+	0.753770i	$0.271767\pi$
$510$	3.37572	−	5.14422i	0.149480	−	0.227790i
$511$	−25.3112	−	18.3897i	−1.11970	−	0.813510i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	6.39920	+	12.5591i	0.282532	+	0.554500i
$514$	6.02321	+	18.5375i	0.265672	+	0.817655i
$515$	−10.3934	−	27.4670i	−0.457987	−	1.21034i
$516$		−	2.57421i		−	0.113323i
$517$	−17.9107	−	4.76836i	−0.787713	−	0.209712i
$518$	13.9364	+	13.9364i	0.612330	+	0.612330i
$519$	6.59834	−	4.79398i	0.289635	−	0.210432i
$520$	4.10275	+	3.72976i	0.179918	+	0.163561i
$521$	−7.13389	+	21.9559i	−0.312542	+	0.961904i	0.664213	+	0.747543i	$0.268767\pi$
$521$	−7.13389	+	21.9559i	−0.312542	+	0.961904i	−0.976755	+	0.214361i	$0.931233\pi$
$522$	2.67957	−	0.424402i	0.117282	−	0.0185756i
$523$	31.6133	−	5.00705i	1.38235	−	0.218943i	0.579428	−	0.815024i	$-0.303276\pi$
$523$	31.6133	−	5.00705i	1.38235	−	0.218943i	0.802925	+	0.596080i	$0.203276\pi$
$524$	3.85627	−	11.8684i	0.168462	−	0.518473i
$525$	8.14344	−	36.5901i	0.355409	−	1.59692i
$526$	−9.19863	+	6.68320i	−0.401079	+	0.291401i
$527$	6.98656	+	6.98656i	0.304339	+	0.304339i
$528$	5.62518	−	4.57015i	0.244805	−	0.198890i
$529$			35.9012i			1.56092i
$530$	8.38488	−	18.5933i	0.364216	−	0.807641i
$531$	−1.53101	−	4.71196i	−0.0664401	−	0.204482i
$532$	−8.20357	−	16.1004i	−0.355670	−	0.698041i
$533$	−1.62687	−	10.2716i	−0.0704674	−	0.444914i
$534$	8.66032	+	6.29209i	0.374769	+	0.272285i
$535$	−13.8350	−	9.07877i	−0.598139	−	0.392510i
$536$	5.43171	−	1.76487i	0.234614	−	0.0762308i
$537$	−1.28473	+	8.11147i	−0.0554402	+	0.350036i
$538$	−6.48825	+	6.48825i	−0.279729	+	0.279729i
$539$	6.41149	−	14.4629i	0.276162	−	0.622960i
$540$	1.57637	−	5.77270i	0.0678363	−	0.248417i
$541$	−10.3718	−	14.2755i	−0.445917	−	0.613752i	0.525597	−	0.850734i	$-0.323842\pi$
$541$	−10.3718	−	14.2755i	−0.445917	−	0.613752i	−0.971514	+	0.236981i	$0.923842\pi$
$542$	−1.38134	−	0.703830i	−0.0593338	−	0.0302321i
$543$	5.13859	−	2.61824i	0.220518	−	0.112359i
$544$	−0.740137	+	1.01871i	−0.0317331	+	0.0436769i
$545$	−3.98338	+	36.2342i	−0.170629	+	1.55210i
$546$	−17.6803	−	5.74469i	−0.756649	−	0.245850i
$547$	−9.80680	+	19.2469i	−0.419309	+	0.822939i	0.580653	+	0.814151i	$0.302797\pi$
$547$	−9.80680	+	19.2469i	−0.419309	+	0.822939i	−0.999961	+	0.00878805i	$0.997203\pi$
$548$	−6.34303	−	1.00464i	−0.270961	−	0.0429160i
$549$	−19.1682			−0.818077
$550$	16.3578	+	2.72422i	0.697500	+	0.116161i
$551$	8.04871			0.342887
$552$	−16.5648	−	2.62360i	−0.705043	−	0.111668i
$553$	21.7096	−	42.6076i	0.923188	−	1.81186i
$554$	21.3484	+	6.93652i	0.907007	+	0.294704i
$555$	3.06754	−	27.9033i	0.130210	−	1.18443i
$556$	1.53391	−	2.11125i	0.0650523	−	0.0895368i
$557$	3.41172	−	1.73836i	0.144559	−	0.0736567i	−0.380215	−	0.924898i	$-0.624150\pi$
$557$	3.41172	−	1.73836i	0.144559	−	0.0736567i	0.524774	+	0.851242i	$0.324150\pi$
$558$	−12.4123	−	6.32439i	−0.525455	−	0.267733i
$559$	−1.71693	−	2.36315i	−0.0726185	−	0.0999508i
$560$	−2.02086	+	7.40041i	−0.0853968	+	0.312725i
$561$	−9.07779	−	0.939384i	−0.383264	−	0.0396608i
$562$	−10.9222	+	10.9222i	−0.460724	+	0.460724i
$563$	−0.651653	+	4.11438i	−0.0274639	+	0.173400i	−0.997608	−	0.0691305i	$-0.977978\pi$
$563$	−0.651653	+	4.11438i	−0.0274639	+	0.173400i	0.970144	+	0.242531i	$0.0779775\pi$
$564$	−11.6144	+	3.77374i	−0.489054	+	0.158903i
$565$	23.5395	+	15.4470i	0.990314	+	0.649861i
$566$	0.745003	+	0.541276i	0.0313148	+	0.0227515i
$567$	5.99703	+	37.8638i	0.251852	+	1.59013i
$568$	4.07111	+	7.99001i	0.170820	+	0.335253i
$569$	−6.89331	−	21.2154i	−0.288983	−	0.889397i	−0.985177	−	0.171543i	$-0.945125\pi$
$569$	−6.89331	−	21.2154i	−0.288983	−	0.889397i	0.696194	−	0.717854i	$-0.254875\pi$
$570$	−10.5803	+	23.4616i	−0.443159	+	0.982697i
$571$			43.1579i			1.80610i	0.429532	+	0.903051i	$0.358678\pi$
$571$			43.1579i			1.80610i	−0.429532	+	0.903051i	$0.641322\pi$
$572$	2.11580	−	7.94730i	0.0884662	−	0.332293i
$573$	34.0498	+	34.0498i	1.42245	+	1.42245i
$574$	11.6405	−	8.45733i	0.485866	−	0.353002i
$575$	−20.5915	−	32.3809i	−0.858723	−	1.35038i
$576$	0.548617	−	1.68847i	0.0228590	−	0.0703529i
$577$	−7.85149	+	1.24355i	−0.326862	+	0.0517698i	−0.317709	−	0.948188i	$-0.602913\pi$
$577$	−7.85149	+	1.24355i	−0.326862	+	0.0517698i	−0.00915278	+	0.999958i	$0.502913\pi$
$578$	−15.2246	+	2.41135i	−0.633262	+	0.100299i
$579$	−1.11748	+	3.43925i	−0.0464409	+	0.142930i
$580$	−2.52837	−	2.29851i	−0.104985	−	0.0954405i
$581$	33.6747	−	24.4661i	1.39706	−	1.01502i
$582$	4.36846	+	4.36846i	0.181078	+	0.181078i
$583$	−30.2089	+	1.63181i	−1.25112	+	0.0675825i
$584$		−	9.11941i		−	0.377364i
$585$	3.48380	+	9.20676i	0.144037	+	0.380653i
$586$	−7.49730	−	23.0743i	−0.309711	−	0.953192i
$587$	5.69486	+	11.1768i	0.235052	+	0.461315i	0.978159	−	0.207857i	$-0.0666488\pi$
$587$	5.69486	+	11.1768i	0.235052	+	0.461315i	−0.743107	+	0.669172i	$0.766649\pi$
$588$	−1.63062	−	10.2954i	−0.0672458	−	0.424573i
$589$	−33.4357	−	24.2925i	−1.37769	−	1.00095i
$590$	−3.42357	+	5.21712i	−0.140946	+	0.214786i
$591$	−1.08250	+	0.351727i	−0.0445283	+	0.0144681i
$592$	−0.898689	+	5.67410i	−0.0369359	+	0.233204i
$593$	0.117052	−	0.117052i	0.00480675	−	0.00480675i	−0.704699	−	0.709506i	$-0.748918\pi$
$593$	0.117052	−	0.117052i	0.00480675	−	0.00480675i	0.709506	+	0.704699i	$0.248918\pi$
$594$	−8.67887	+	1.85932i	−0.356098	+	0.0762887i
$595$	8.38857	−	4.78988i	0.343898	−	0.196366i
$596$	3.29695	+	4.53786i	0.135048	+	0.185878i
$597$	−26.6717	−	13.5899i	−1.09160	−	0.556198i
$598$	−16.9565	+	8.63977i	−0.693403	+	0.353306i
$599$	−9.73545	+	13.3997i	−0.397780	+	0.547497i	−0.960185	−	0.279365i	$-0.909876\pi$
$599$	−9.73545	+	13.3997i	−0.397780	+	0.547497i	0.562405	+	0.826862i	$0.309876\pi$
$600$	10.0237	−	4.34860i	0.409214	−	0.177531i
$601$	−25.6681	−	8.34007i	−1.04702	−	0.340198i	−0.265524	−	0.964104i	$-0.585545\pi$
$601$	−25.6681	−	8.34007i	−1.04702	−	0.340198i	−0.781499	+	0.623906i	$0.785545\pi$
$602$	1.83475	−	3.60090i	0.0747787	−	0.146762i
$603$	10.0147	+	1.58617i	0.407829	+	0.0645938i
$604$	−5.96367			−0.242658
$605$	−7.56420	−	23.4048i	−0.307529	−	0.951539i
$606$	12.6967			0.515766
$607$	−11.6605	−	1.84684i	−0.473286	−	0.0749611i	−0.0847647	−	0.996401i	$-0.527014\pi$
$607$	−11.6605	−	1.84684i	−0.473286	−	0.0749611i	−0.388521	+	0.921440i	$0.627014\pi$
$608$	2.39119	−	4.69298i	0.0969757	−	0.190326i
$609$	10.8957	+	3.54024i	0.441517	+	0.143458i
$610$	15.1035	+	18.8344i	0.611522	+	0.762584i
$611$	−8.14514	+	11.2108i	−0.329517	+	0.453541i
$612$	−1.99187	+	1.01491i	−0.0805166	+	0.0410252i
$613$	1.88363	+	0.959759i	0.0760793	+	0.0387643i	0.491616	−	0.870812i	$-0.336406\pi$
$613$	1.88363	+	0.959759i	0.0760793	+	0.0387643i	−0.415537	+	0.909576i	$0.636406\pi$
$614$	9.59550	+	13.2071i	0.387243	+	0.532994i
$615$	−19.7696	−	5.39855i	−0.797186	−	0.217690i
$616$	11.1260	−	2.38358i	0.448280	−	0.0960373i
$617$	5.33870	−	5.33870i	0.214928	−	0.214928i	−0.591429	−	0.806357i	$-0.701436\pi$
$617$	5.33870	−	5.33870i	0.214928	−	0.214928i	0.806357	+	0.591429i	$0.201436\pi$
$618$	−4.48972	+	28.3470i	−0.180603	+	1.14028i
$619$	6.85248	−	2.22651i	0.275424	−	0.0894908i	−0.168048	−	0.985779i	$-0.553746\pi$
$619$	6.85248	−	2.22651i	0.275424	−	0.0894908i	0.443472	+	0.896288i	$0.353746\pi$
$620$	3.56596	+	17.1795i	0.143212	+	0.689945i
$621$	16.6162	+	12.0724i	0.666784	+	0.484447i
$622$	−0.961310	−	6.06947i	−0.0385450	−	0.243364i
$623$	7.62971	+	14.9741i	0.305678	+	0.599927i
$624$	−1.67447	−	5.15350i	−0.0670326	−	0.206305i
$625$	22.6403	+	10.6027i	0.905611	+	0.424110i
$626$			13.2831i			0.530900i
$627$	38.1184	−	2.05906i	1.52230	−	0.0822309i
$628$	6.12801	+	6.12801i	0.244534	+	0.244534i
$629$	5.85232	−	4.25196i	0.233347	−	0.169537i
$630$	−9.16142	+	10.0776i	−0.365000	+	0.401501i
$631$	2.14008	−	6.58647i	0.0851951	−	0.262203i	−0.899380	−	0.437169i	$-0.855981\pi$
$631$	2.14008	−	6.58647i	0.0851951	−	0.262203i	0.984575	+	0.174965i	$0.0559813\pi$
$632$	13.7669	−	2.18047i	0.547620	−	0.0867344i
$633$	10.6443	−	1.68589i	0.423072	−	0.0670081i
$634$	−0.524368	+	1.61384i	−0.0208253	+	0.0640937i
$635$	20.7284	−	0.987103i	0.822580	−	0.0391720i
$636$	−16.1262	+	11.7164i	−0.639444	+	0.464584i
$637$	−8.36366	−	8.36366i	−0.331380	−	0.331380i
$638$	−1.30389	+	4.89762i	−0.0516215	+	0.193899i
$639$			15.9204i			0.629800i
$640$	−2.09135	+	0.791358i	−0.0826679	+	0.0312812i
$641$	−3.82612	−	11.7756i	−0.151123	−	0.465108i	0.846625	−	0.532190i	$-0.178631\pi$
$641$	−3.82612	−	11.7756i	−0.151123	−	0.465108i	−0.997747	+	0.0670825i	$0.978631\pi$
$642$	7.34187	+	14.4092i	0.289760	+	0.568687i
$643$	1.19624	+	7.55275i	0.0471750	+	0.297851i	0.999984	−	0.00572029i	$-0.00182083\pi$
$643$	1.19624	+	7.55275i	0.0471750	+	0.297851i	−0.952809	+	0.303572i	$0.901821\pi$
$644$	−21.3014	−	15.4764i	−0.839393	−	0.609854i
$645$	−5.63598	+	1.16987i	−0.221917	+	0.0460634i
$646$	−6.30765	+	2.04948i	−0.248171	+	0.0806357i
$647$	2.60262	−	16.4323i	0.102319	−	0.646019i	−0.882218	−	0.470842i	$-0.843950\pi$
$647$	2.60262	−	16.4323i	0.102319	−	0.646019i	0.984537	−	0.175177i	$-0.0560498\pi$
$648$	−7.90134	+	7.90134i	−0.310394	+	0.310394i
$649$	9.20644	+	0.952698i	0.361384	+	0.0373967i
$650$	6.30142	−	10.6776i	0.247162	−	0.418809i
$651$	−34.5776	−	47.5920i	−1.35520	−	1.86528i
$652$	5.98798	+	3.05103i	0.234507	+	0.119488i
$653$	4.39031	−	2.23698i	0.171806	−	0.0875397i	−0.365972	−	0.930626i	$-0.619264\pi$
$653$	4.39031	−	2.23698i	0.171806	−	0.0875397i	0.537779	+	0.843086i	$0.319264\pi$
$654$	20.9394	−	28.8206i	0.818794	−	1.12697i
$655$	−27.7372	−	3.04927i	−1.08378	−	0.119145i
$656$	3.98871	+	1.29601i	0.155733	+	0.0506007i
$657$	7.35021	−	14.4256i	0.286759	−	0.562797i
$658$	−18.9363	−	2.99921i	−0.738213	−	0.116922i
$659$	−8.64436			−0.336736			−0.168368	−	0.985724i	$-0.553850\pi$
$659$	−8.64436			−0.336736			−0.168368	+	0.985724i	$0.553850\pi$
$660$	−12.5623	−	10.2388i	−0.488986	−	0.398546i
$661$	47.7979			1.85912			0.929562	−	0.368667i	$-0.120186\pi$
$661$	47.7979			1.85912			0.929562	+	0.368667i	$0.120186\pi$
$662$	20.0876	+	3.18157i	0.780729	+	0.123655i
$663$	−3.09768	+	6.07954i	−0.120304	+	0.236110i
$664$	11.5389	+	3.74921i	0.447796	+	0.145498i
$665$	−31.5221	+	25.2778i	−1.22237	+	0.980232i
$666$	−5.99490	+	8.25128i	−0.232298	+	0.319730i
$667$	10.4496	−	5.32436i	0.404612	−	0.206160i
$668$	19.1823	+	9.77387i	0.742185	+	0.378162i
$669$	4.30365	+	5.92346i	0.166389	+	0.229014i
$670$	−6.33248	−	11.0901i	−0.244645	−	0.428449i
$671$	14.5122	−	32.7363i	0.560239	−	1.26377i
$672$	5.30123	−	5.30123i	0.204499	−	0.204499i
$673$	−0.0252234	+	0.159254i	−0.000972291	+	0.00613880i	−0.988170	−	0.153364i	$-0.950989\pi$
$673$	−0.0252234	+	0.159254i	−0.000972291	+	0.00613880i	0.987197	+	0.159503i	$0.0509892\pi$
$674$	−23.9373	+	7.77769i	−0.922029	+	0.299585i
$675$	−13.3551	−	0.827872i	−0.514040	−	0.0318648i
$676$	5.54279	+	4.02707i	0.213184	+	0.154887i
$677$	0.260996	+	1.64786i	0.0100309	+	0.0633326i	0.992196	−	0.124688i	$-0.0397929\pi$
$677$	0.260996	+	1.64786i	0.0100309	+	0.0633326i	−0.982165	+	0.188020i	$0.939793\pi$
$678$	−12.4918	−	24.5165i	−0.479744	−	0.941551i
$679$	2.99716	+	9.22432i	0.115021	+	0.353997i
$680$	2.56673	+	1.15750i	0.0984294	+	0.0443880i
$681$			33.9701i			1.30174i
$682$	20.1985	−	16.4102i	0.773440	−	0.628377i
$683$	−26.1231	−	26.1231i	−0.999572	−	0.999572i	0.000427547	−	1.00000i	$-0.499864\pi$
$683$	−26.1231	−	26.1231i	−0.999572	−	0.999572i	−1.00000		0.000427547i	$0.999864\pi$
$684$	7.56506	−	5.49634i	0.289257	−	0.210158i
$685$	0.683074	+	14.3440i	0.0260989	+	0.548056i
$686$	−2.36415	+	7.27611i	−0.0902638	+	0.277803i
$687$	0.250230	−	0.0396325i	0.00954687	−	0.00151208i
$688$	1.16349	−	0.184278i	0.0443575	−	0.00702554i
$689$	−6.98950	+	21.5115i	−0.266279	+	0.819521i
$690$	1.78384	+	37.4592i	0.0679096	+	1.42605i
$691$	−14.8900	+	10.8182i	−0.566441	+	0.411543i	−0.833811	−	0.552051i	$-0.813845\pi$
$691$	−14.8900	+	10.8182i	−0.566441	+	0.411543i	0.267370	+	0.963594i	$0.413845\pi$
$692$	2.63912	+	2.63912i	0.100324	+	0.100324i
$693$	19.5210	+	5.19706i	0.741540	+	0.197420i
$694$			32.5920i			1.23717i
$695$	−5.31946	−	2.39887i	−0.201778	−	0.0909945i
$696$	1.03192	+	3.17591i	0.0391146	+	0.120382i
$697$	−2.39754	−	4.70544i	−0.0908134	−	0.178231i
$698$	−3.68674	−	23.2771i	−0.139545	−	0.881053i
$699$	18.6540	+	13.5529i	0.705559	+	0.512619i
$700$	17.1209	+	1.06130i	0.647107	+	0.0401135i
$701$	3.47892	−	1.13037i	0.131397	−	0.0426935i	−0.242580	−	0.970131i	$-0.577994\pi$
$701$	3.47892	−	1.13037i	0.131397	−	0.0426935i	0.373977	+	0.927438i	$0.377994\pi$
$702$	−1.03809	+	6.55427i	−0.0391803	+	0.247375i
$703$	−21.3959	+	21.3959i	−0.806960	+	0.806960i
$704$	2.46829	+	2.21530i	0.0930272	+	0.0834921i
$705$	13.5405	+	23.7135i	0.509963	+	0.893103i
$706$	11.0870	+	15.2599i	0.417264	+	0.574315i
$707$	17.7605	+	9.04943i	0.667952	+	0.340339i
$708$	5.43366	−	2.76859i	0.204209	−	0.104050i
$709$	7.74978	−	10.6667i	0.291049	−	0.400594i	−0.638306	−	0.769783i	$-0.720364\pi$
$709$	7.74978	−	10.6667i	0.291049	−	0.400594i	0.929354	+	0.369189i	$0.120364\pi$
$710$	15.6432	−	12.5444i	0.587078	−	0.470783i
$711$	23.5348	+	7.64692i	0.882624	+	0.286782i
$712$	−2.22392	+	4.36470i	−0.0833451	+	0.163574i
$713$	−59.4795	−	9.42063i	−2.22752	−	0.352805i
$714$	−9.44028			−0.353293
$715$	−18.3613	−	1.02065i	−0.686675	−	0.0381701i
$716$	−3.75817			−0.140449
$717$	−40.0578	−	6.34454i	−1.49599	−	0.236941i
$718$	−8.49735	+	16.6770i	−0.317118	+	0.622380i
$719$	−42.2831	−	13.7386i	−1.57689	−	0.512364i	−0.615639	−	0.788028i	$-0.711102\pi$
$719$	−42.2831	−	13.7386i	−1.57689	−	0.512364i	−0.961254	+	0.275665i	$0.911102\pi$
$720$	−3.94605	−	0.433807i	−0.147061	−	0.0161670i
$721$	−26.4844	+	36.4527i	−0.986331	+	1.35757i
$722$	7.78907	−	3.96873i	0.289879	−	0.147701i
$723$	30.7439	+	15.6648i	1.14338	+	0.582580i
$724$	1.55124	+	2.13510i	0.0576513	+	0.0793502i
$725$	−3.88333	+	6.58019i	−0.144223	+	0.244382i
$726$	−4.92224	+	23.5285i	−0.182682	+	0.873224i
$727$	20.6798	−	20.6798i	0.766971	−	0.766971i	−0.210601	−	0.977572i	$-0.567542\pi$
$727$	20.6798	−	20.6798i	0.766971	−	0.766971i	0.977572	+	0.210601i	$0.0675420\pi$
$728$	1.33080	−	8.40236i	0.0493228	−	0.311412i
$729$	−2.18164	+	0.708858i	−0.0808015	+	0.0262540i
$730$	−19.9660	+	4.14437i	−0.738976	+	0.153390i
$731$	−1.20003	−	0.871874i	−0.0443847	−	0.0322474i
$732$	−3.69088	−	23.3033i	−0.136419	−	0.861314i
$733$	−3.76215	−	7.38363i	−0.138958	−	0.272721i	0.811031	−	0.585003i	$-0.198907\pi$
$733$	−3.76215	−	7.38363i	−0.138958	−	0.272721i	−0.949989	+	0.312282i	$0.898907\pi$
$734$	9.42340	+	29.0022i	0.347824	+	1.07049i
$735$	−21.7996	+	8.24887i	−0.804090	+	0.304264i
$736$		−	7.67471i		−	0.282894i
$737$	−10.2911	+	15.9027i	−0.379076	+	0.585783i
$738$	5.26500	+	5.26500i	0.193807	+	0.193807i
$739$	23.7967	−	17.2893i	0.875376	−	0.635998i	−0.0566481	−	0.998394i	$-0.518041\pi$
$739$	23.7967	−	17.2893i	0.875376	−	0.635998i	0.932024	+	0.362396i	$0.118041\pi$
$740$	12.8313	−	0.611037i	0.471687	−	0.0224622i
$741$	8.81955	−	27.1438i	0.323994	−	0.997152i
$742$	−30.9086	+	4.89543i	−1.13469	+	0.179717i
$743$	7.44870	−	1.17976i	0.273266	−	0.0432811i	−0.0182973	−	0.999833i	$-0.505825\pi$
$743$	7.44870	−	1.17976i	0.273266	−	0.0432811i	0.291563	+	0.956551i	$0.405825\pi$
$744$	5.29872	−	16.3078i	0.194260	−	0.597872i
$745$	8.43688	−	9.28060i	0.309103	−	0.340015i
$746$	−10.0273	+	7.28529i	−0.367127	+	0.266733i
$747$	15.2310	+	15.2310i	0.557274	+	0.557274i
$748$	−0.225264	−	4.17020i	−0.00823646	−	0.152478i
$749$			25.3890i			0.927692i
$750$	−14.0761	−	19.9695i	−0.513988	−	0.729185i
$751$	3.35816	+	10.3354i	0.122541	+	0.377143i	0.993445	−	0.114310i	$-0.0364659\pi$
$751$	3.35816	+	10.3354i	0.122541	+	0.377143i	−0.870904	+	0.491453i	$0.836466\pi$
$752$	−2.53708	−	4.97929i	−0.0925177	−	0.181576i
$753$	−3.34222	−	21.1019i	−0.121797	−	0.768997i
$754$	3.06556	+	2.22726i	0.111641	+	0.0811119i
$755$	2.71022	+	13.0569i	0.0986351	+	0.475188i
$756$	−8.73184	+	2.83715i	−0.317574	+	0.103186i
$757$	1.60621	−	10.1412i	0.0583786	−	0.368588i	−0.941153	−	0.337981i	$-0.890256\pi$
$757$	1.60621	−	10.1412i	0.0583786	−	0.368588i	0.999531	−	0.0306069i	$-0.00974399\pi$
$758$	12.2981	−	12.2981i	0.446688	−	0.446688i
$759$	48.1270	−	27.8892i	1.74690	−	1.01232i
$760$	−11.3615	−	3.10253i	−0.412125	−	0.112540i
$761$	21.0629	+	28.9906i	0.763530	+	1.05091i	0.996912	+	0.0785242i	$0.0250208\pi$
$761$	21.0629	+	28.9906i	0.763530	+	1.05091i	−0.233382	+	0.972385i	$0.574979\pi$
$762$	−18.0699	−	9.20708i	−0.654604	−	0.333537i
$763$	49.8323	−	25.3908i	1.80405	−	0.919209i
$764$	−12.9522	+	17.8272i	−0.468595	+	0.644966i
$765$	3.12726	+	3.89977i	0.113066	+	0.140996i
$766$	−16.8842	−	5.48599i	−0.610049	−	0.198217i
$767$	3.14158	−	6.16570i	0.113436	−	0.222631i
$768$	2.15836	+	0.341850i	0.0778830	+	0.0123354i
$769$	19.6409			0.708269			0.354134	−	0.935195i	$-0.384776\pi$
$769$	19.6409			0.708269			0.354134	+	0.935195i	$0.384776\pi$
$770$	−10.2749	−	23.2761i	−0.370282	−	0.838812i
$771$	−42.5940			−1.53399
$772$	−1.63446	−	0.258873i	−0.0588255	−	0.00931704i
$773$	14.7844	−	29.0160i	0.531757	−	1.04363i	−0.456341	−	0.889805i	$-0.650840\pi$
$773$	14.7844	−	29.0160i	0.531757	−	1.04363i	0.988098	−	0.153827i	$-0.0491598\pi$
$774$	1.98900	+	0.646265i	0.0714931	+	0.0232295i
$775$	35.9922	−	15.6146i	1.29288	−	0.560894i
$776$	−1.66172	+	2.28717i	−0.0596524	+	0.0821045i
$777$	−38.3751	+	19.5531i	−1.37670	+	0.701462i
$778$	−26.7740	−	13.6420i	−0.959895	−	0.489091i
$779$	12.9841	+	17.8711i	0.465205	+	0.640300i
$780$	−10.5221	+	6.00813i	−0.376752	+	0.215126i
$781$	−27.1896	−	12.0533i	−0.972920	−	0.431302i
$782$	−6.83346	+	6.83346i	−0.244364	+	0.244364i
$783$	0.639738	−	4.03915i	0.0228624	−	0.144347i
$784$	4.53654	−	1.47401i	0.162019	−	0.0526432i
$785$	10.6317	−	16.2016i	0.379463	−	0.578259i
$786$	22.0621	+	16.0290i	0.786928	+	0.571737i
$787$	−4.69715	−	29.6567i	−0.167435	−	1.05715i	−0.918067	−	0.396425i	$-0.870251\pi$
$787$	−4.69715	−	29.6567i	−0.167435	−	1.05715i	0.750632	−	0.660721i	$-0.229749\pi$
$788$	−0.236465	−	0.464089i	−0.00842372	−	0.0165325i
$789$	−7.67805	−	23.6306i	−0.273346	−	0.841272i
$790$	−11.0304	−	29.1504i	−0.392443	−	1.03713i
$791$		−	43.1979i		−	1.53594i
$792$	2.11897	+	5.49372i	0.0752941	+	0.195211i
$793$	−18.9309	−	18.9309i	−0.672257	−	0.672257i
$794$	−27.6239	+	20.0699i	−0.980334	+	0.712254i
$795$	32.9804	+	29.9821i	1.16969	+	1.06335i
$796$	4.23301	−	13.0279i	0.150035	−	0.461760i
$797$	−8.91423	+	1.41187i	−0.315758	+	0.0500112i	−0.312302	−	0.949983i	$-0.601100\pi$
$797$	−8.91423	+	1.41187i	−0.315758	+	0.0500112i	−0.00345606	+	0.999994i	$0.501100\pi$
$798$	39.0013	−	6.17720i	1.38063	−	0.218671i
$799$	−2.17452	+	6.69247i	−0.0769288	+	0.236763i
$800$	2.68303	+	4.21917i	0.0948593	+	0.149170i
$801$	−7.03586	+	5.11185i	−0.248600	+	0.180618i
$802$	17.8751	+	17.8751i	0.631193	+	0.631193i
$803$	19.0719	+	23.4747i	0.673033	+	0.828404i
$804$			12.4805i			0.440155i
$805$	−24.2034	+	53.6706i	−0.853058	+	1.89164i
$806$	−6.01258	−	18.5048i	−0.211784	−	0.651804i
$807$	−9.10317	−	17.8660i	−0.320447	−	0.628912i
$808$	0.908905	+	5.73860i	0.0319752	+	0.201883i
$809$	13.8867	+	10.0893i	0.488231	+	0.354721i	0.804504	−	0.593948i	$-0.202431\pi$
$809$	13.8867	+	10.0893i	0.488231	+	0.354721i	−0.316272	+	0.948668i	$0.602431\pi$
$810$	20.8900	+	13.7084i	0.733999	+	0.481663i
$811$	−5.74240	+	1.86582i	−0.201643	+	0.0655178i	−0.408097	−	0.912938i	$-0.633808\pi$
$811$	−5.74240	+	1.86582i	−0.201643	+	0.0655178i	0.206454	+	0.978456i	$0.433808\pi$
$812$	−0.820123	+	5.17806i	−0.0287807	+	0.181714i
$813$	2.39557	−	2.39557i	0.0840163	−	0.0840163i
$814$	−9.55319	−	16.4854i	−0.334839	−	0.577814i
$815$	3.95865	−	14.4966i	0.138665	−	0.507795i
$816$	−1.61739	−	2.22615i	−0.0566200	−	0.0779308i
$817$	5.52828	+	2.81680i	0.193410	+	0.0985474i
$818$	29.9333	−	15.2518i	1.04659	−	0.533266i
$819$	8.87742	−	12.2187i	0.310202	−	0.426956i
$820$	1.02479	−	9.32186i	0.0357873	−	0.325534i
$821$	48.1064	+	15.6307i	1.67893	+	0.545516i	0.984703	−	0.174243i	$-0.0557479\pi$
$821$	48.1064	+	15.6307i	1.67893	+	0.545516i	0.694224	+	0.719759i	$0.255748\pi$
$822$	6.37128	−	12.5043i	0.222224	−	0.436139i
$823$	−11.6049	−	1.83804i	−0.404523	−	0.0640702i	−0.0491423	−	0.998792i	$-0.515649\pi$
$823$	−11.6049	−	1.83804i	−0.404523	−	0.0640702i	−0.355381	+	0.934722i	$0.615649\pi$
$824$	−13.1336			−0.457530
$825$	−16.7079	+	32.1570i	−0.581695	+	1.11956i
$826$	9.57407			0.333125
$827$	24.7958	+	3.92727i	0.862235	+	0.136565i	0.571863	−	0.820349i	$-0.306221\pi$
$827$	24.7958	+	3.92727i	0.862235	+	0.136565i	0.290372	+	0.956914i	$0.406221\pi$
$828$	6.18580	−	12.1403i	0.214971	−	0.421905i
$829$	−26.8536	−	8.72525i	−0.932662	−	0.303040i	−0.197011	−	0.980401i	$-0.563124\pi$
$829$	−26.8536	−	8.72525i	−0.932662	−	0.303040i	−0.735651	+	0.677361i	$0.763124\pi$
$830$	2.96461	−	26.9671i	0.102903	−	0.936041i
$831$	−28.8324	+	39.6844i	−1.00019	+	1.37664i
$832$	2.20940	−	1.12574i	0.0765971	−	0.0390282i
$833$	−5.35171	−	2.72683i	−0.185426	−	0.0944792i
$834$	3.35199	+	4.61362i	0.116070	+	0.159757i
$835$	12.6814	−	46.4395i	0.438858	−	1.60711i
$836$	3.65940	+	17.0813i	0.126563	+	0.590768i
$837$	−14.8485	+	14.8485i	−0.513238	+	0.513238i
$838$	4.36255	−	27.5441i	0.150702	−	0.951494i
$839$	20.9970	−	6.82234i	0.724897	−	0.235533i	0.0767521	−	0.997050i	$-0.475545\pi$
$839$	20.9970	−	6.82234i	0.724897	−	0.235533i	0.648145	+	0.761517i	$0.275545\pi$
$840$	−14.0157	−	9.19733i	−0.483587	−	0.317338i
$841$	21.5723	+	15.6732i	0.743873	+	0.540455i
$842$	0.00633800	+	0.0400166i	0.000218422	+	0.00137906i
$843$	−15.3241	−	30.0752i	−0.527789	−	1.03584i
$844$	1.52397	+	4.69029i	0.0524571	+	0.161446i
$845$	6.29791	−	13.9655i	0.216655	−	0.480428i
$846$		−	9.92141i		−	0.341105i
$847$	−23.6551	+	29.4042i	−0.812800	+	1.01034i
$848$	−6.44994	−	6.44994i	−0.221492	−	0.221492i
$849$	−1.62802	+	1.18283i	−0.0558737	+	0.0405946i
$850$	1.36776	−	6.14562i	0.0469138	−	0.210793i
$851$	−13.6245	+	41.9320i	−0.467043	+	1.43741i
$852$	−19.3548	+	3.06551i	−0.663086	+	0.105022i
$853$	25.8504	−	4.09430i	0.885100	−	0.140186i	0.302698	−	0.953087i	$-0.402113\pi$
$853$	25.8504	−	4.09430i	0.885100	−	0.140186i	0.582403	+	0.812901i	$0.302113\pi$
$854$	11.4463	−	35.2280i	0.391684	−	1.20548i
$855$	−15.4717	−	14.0651i	−0.529119	−	0.481016i
$856$	−5.98707	+	4.34986i	−0.204634	+	0.148675i
$857$	−27.1635	−	27.1635i	−0.927888	−	0.927888i	0.0696817	−	0.997569i	$-0.477802\pi$
$857$	−27.1635	−	27.1635i	−0.927888	−	0.927888i	−0.997569	+	0.0696817i	$0.977802\pi$
$858$	15.0881	+	9.76396i	0.515101	+	0.333336i
$859$		−	27.8087i		−	0.948822i	−0.880304	−	0.474411i	$-0.842661\pi$
$859$		−	27.8087i		−	0.948822i	0.880304	−	0.474411i	$-0.157339\pi$
$860$	−0.932211	−	2.46359i	−0.0317881	−	0.0840077i
$861$	9.71628	+	29.9036i	0.331130	+	1.01911i
$862$	−0.499019	−	0.979379i	−0.0169966	−	0.0333578i
$863$	−4.53111	−	28.6083i	−0.154241	−	0.973838i	−0.936445	−	0.350815i	$-0.885905\pi$
$863$	−4.53111	−	28.6083i	−0.154241	−	0.973838i	0.782204	−	0.623022i	$-0.214095\pi$
$864$	−2.16505	−	1.57300i	−0.0736567	−	0.0535147i
$865$	4.57872	−	6.97745i	0.155681	−	0.237240i
$866$	18.1555	−	5.89908i	0.616949	−	0.200459i
$867$	5.26942	−	33.2698i	0.178959	−	1.12990i
$868$	19.0352	−	19.0352i	0.646098	−	0.646098i
$869$	−30.8780	+	34.4044i	−1.04746	+	1.16709i
$870$	6.48437	−	3.70258i	0.219841	−	0.125529i
$871$	8.32420	+	11.4573i	0.282055	+	0.388215i
$872$	14.5252	+	7.40097i	0.491886	+	0.250628i
$873$	−4.47206	+	2.27863i	−0.151356	+	0.0771199i
$874$	23.7601	−	32.7030i	0.803698	−	1.10620i
$875$	−5.45705	−	37.9667i	−0.184482	−	1.28351i
$876$	18.9529	+	6.15818i	0.640360	+	0.208065i
$877$	−10.3378	+	20.2890i	−0.349082	+	0.685112i	−0.997066	−	0.0765416i	$-0.975612\pi$
$877$	−10.3378	+	20.2890i	−0.349082	+	0.685112i	0.647984	+	0.761654i	$0.275612\pi$
$878$	10.0576	+	1.59296i	0.339427	+	0.0537599i
$879$	53.0183			1.78826
$880$	3.72844	−	6.41083i	0.125686	−	0.216109i
$881$	−15.3181			−0.516080			−0.258040	−	0.966134i	$-0.583077\pi$
$881$	−15.3181			−0.516080			−0.258040	+	0.966134i	$0.583077\pi$
$882$	8.36421	+	1.32476i	0.281638	+	0.0446070i
$883$	−15.6628	+	30.7400i	−0.527096	+	1.03448i	0.461954	+	0.886904i	$0.347149\pi$
$883$	−15.6628	+	30.7400i	−0.527096	+	1.03448i	−0.989050	+	0.147580i	$0.952851\pi$
$884$	−2.96956	−	0.964870i	−0.0998773	−	0.0324521i
$885$	−8.53090	−	10.6383i	−0.286763	−	0.357601i
$886$	4.33693	−	5.96928i	0.145702	−	0.200542i
$887$	−23.6624	+	12.0566i	−0.794507	+	0.404821i	−0.803624	−	0.595137i	$-0.797098\pi$
$887$	−23.6624	+	12.0566i	−0.794507	+	0.404821i	0.00911764	+	0.999958i	$0.497098\pi$
$888$	−11.1856	−	5.69937i	−0.375365	−	0.191258i
$889$	−18.7145	−	25.7583i	−0.627665	−	0.863907i
$890$	10.5667	+	2.88550i	0.354198	+	0.0967221i
$891$	3.81472	−	36.8637i	0.127798	−	1.23498i
$892$	−2.36919	+	2.36919i	−0.0793263	+	0.0793263i
$893$	4.60455	−	29.0720i	0.154085	−	0.972857i
$894$	−11.6574	+	3.78773i	−0.389883	+	0.126681i
$895$	1.70792	+	8.22813i	0.0570895	+	0.275036i
$896$	2.77553	+	2.01654i	0.0927239	+	0.0673679i
$897$	−6.50565	−	41.0751i	−0.217217	−	1.37146i
$898$	17.6424	+	34.6252i	0.588735	+	1.15546i
$899$	3.70532	+	11.4038i	0.123579	+	0.380338i
$900$	0.843529	+	8.83663i	0.0281176	+	0.294554i
$901$			11.4859i			0.382650i
$902$	−12.9780	+	5.00569i	−0.432119	+	0.166671i
$903$	6.24479	+	6.24479i	0.207814	+	0.207814i
$904$	10.1867	−	7.40105i	0.338804	−	0.246155i
$905$	3.96961	−	4.36659i	0.131954	−	0.145150i
$906$	4.02716	−	12.3943i	0.133793	−	0.411774i
$907$	−5.39312	+	0.854186i	−0.179076	+	0.0283628i	−0.245328	−	0.969440i	$-0.578896\pi$
$907$	−5.39312	+	0.854186i	−0.179076	+	0.0283628i	0.0662526	+	0.997803i	$0.478896\pi$
$908$	−15.3537	+	2.43179i	−0.509532	+	0.0807019i
$909$	−3.18754	+	9.81023i	−0.105724	+	0.325385i
$910$	−19.0009	+	0.904840i	−0.629874	+	0.0299952i
$911$	−31.0215	+	22.5384i	−1.02779	+	0.746731i	−0.967864	−	0.251472i	$-0.919085\pi$
$911$	−31.0215	+	22.5384i	−1.02779	+	0.746731i	−0.0599221	+	0.998203i	$0.519085\pi$
$912$	8.13872	+	8.13872i	0.269500	+	0.269500i
$913$	−37.5437	+	14.4809i	−1.24252	+	0.479247i
$914$		−	35.3196i		−	1.16827i
$915$	−49.3428	+	18.6711i	−1.63122	+	0.617248i
$916$	0.0358260	+	0.110261i	0.00118373	+	0.00364313i
$917$	19.4366	+	38.1465i	0.641854	+	1.25971i
$918$	0.527154	+	3.32832i	0.0173987	+	0.109851i
$919$	36.5168	+	26.5310i	1.20458	+	0.875178i	0.994727	−	0.102556i	$-0.0327020\pi$
$919$	36.5168	+	26.5310i	1.20458	+	0.875178i	0.209851	+	0.977733i	$0.432702\pi$
$920$	−16.8030	+	3.48782i	−0.553979	+	0.114990i
$921$	−33.9280	+	11.0239i	−1.11797	+	0.363249i
$922$	−0.0739044	+	0.466614i	−0.00243391	+	0.0153671i
$923$	−15.7233	+	15.7233i	−0.517540	+	0.517540i
$924$	−2.55940	+	24.7329i	−0.0841980	+	0.813652i
$925$	−7.16905	−	27.8151i	−0.235717	−	0.914555i
$926$	5.70076	+	7.84642i	0.187338	+	0.257849i
$927$	−20.7755	−	10.5856i	−0.682356	−	0.347678i
$928$	−1.36157	+	0.693754i	−0.0446957	+	0.0227736i
$929$	−29.3205	+	40.3562i	−0.961975	+	1.32404i	−0.0159768	+	0.999872i	$0.505086\pi$
$929$	−29.3205	+	40.3562i	−0.961975	+	1.32404i	−0.945998	+	0.324172i	$0.894914\pi$
$930$	−38.1123	−	4.18985i	−1.24975	−	0.137390i
$931$	23.8942	+	7.76370i	0.783101	+	0.254445i
$932$	−4.79025	+	9.40139i	−0.156910	+	0.307953i
$933$	13.2634	+	2.10071i	0.434223	+	0.0687742i
$934$	−1.89229			−0.0619177
$935$	−9.02787	+	2.38836i	−0.295243	+	0.0781079i
$936$	4.40230			0.143894
$937$	34.9131	+	5.52969i	1.14056	+	0.180647i	0.698004	−	0.716094i	$-0.254072\pi$
$937$	34.9131	+	5.52969i	1.14056	+	0.180647i	0.442556	+	0.896741i	$0.354072\pi$
$938$	−8.89540	+	17.4582i	−0.290445	+	0.570031i
$939$	−27.6064	−	8.96985i	−0.900900	−	0.292720i
$940$	−9.74867	+	7.81754i	−0.317967	+	0.254980i
$941$	1.47624	−	2.03188i	0.0481242	−	0.0662373i	−0.784277	−	0.620411i	$-0.786966\pi$
$941$	1.47624	−	2.03188i	0.0481242	−	0.0662373i	0.832401	+	0.554174i	$0.186966\pi$
$942$	−16.8740	+	8.59774i	−0.549785	+	0.280129i
$943$	28.6794	+	14.6129i	0.933928	+	0.475860i
$944$	1.64031	+	2.25770i	0.0533877	+	0.0734819i
$945$	10.1799	+	17.8281i	0.331152	+	0.579949i
$946$	−2.60960	+	2.90762i	−0.0848453	+	0.0945349i
$947$	−32.6819	+	32.6819i	−1.06202	+	1.06202i	−0.0640730	+	0.997945i	$0.520409\pi$
$947$	−32.6819	+	32.6819i	−1.06202	+	1.06202i	−0.997945	+	0.0640730i	$0.979591\pi$
$948$	−4.76489	+	30.0844i	−0.154757	+	0.977094i
$949$	21.5063	−	6.98783i	0.698125	−	0.226834i
$950$	−1.62937	+	26.2848i	−0.0528637	+	0.852792i
$951$	−2.99995	−	2.17959i	−0.0972801	−	0.0706781i
$952$	−0.675794	−	4.26679i	−0.0219026	−	0.138288i
$953$	9.21853	+	18.0924i	0.298617	+	0.586070i	0.990750	−	0.135701i	$-0.0433286\pi$
$953$	9.21853	+	18.0924i	0.298617	+	0.586070i	−0.692132	+	0.721771i	$0.743329\pi$
$954$	−5.00426	−	15.4015i	−0.162019	−	0.498643i
$955$	44.9171	+	20.2559i	1.45348	+	0.655467i
$956$		−	18.5594i		−	0.600255i
$957$	−9.29825	−	6.01716i	−0.300570	−	0.194507i
$958$	7.33216	+	7.33216i	0.236891	+	0.236891i
$959$	17.8247	−	12.9504i	0.575591	−	0.418191i
$960$	−0.232431	−	4.88086i	−0.00750167	−	0.157529i
$961$	9.44670	−	29.0739i	0.304732	−	0.937869i
$962$	−14.0699	+	2.22845i	−0.453631	+	0.0718480i
$963$	−12.9767	+	2.05530i	−0.418167	+	0.0662312i
$964$	−4.87930	+	15.0169i	−0.157152	+	0.483663i
$965$	0.176013	+	3.69613i	0.00566606	+	0.118983i
$966$	46.5491	−	33.8199i	1.49769	−	1.08814i
$967$	8.86927	+	8.86927i	0.285217	+	0.285217i	0.835185	−	0.549969i	$-0.185360\pi$
$967$	8.86927	+	8.86927i	0.285217	+	0.285217i	−0.549969	+	0.835185i	$0.685360\pi$
$968$	−10.9867	−	0.540428i	−0.353126	−	0.0173700i
$969$		−	14.4932i		−	0.465589i
$970$	5.76270	+	2.59876i	0.185029	+	0.0834412i
$971$	10.9331	+	33.6487i	0.350860	+	1.07984i	0.958371	+	0.285526i	$0.0921682\pi$
$971$	10.9331	+	33.6487i	0.350860	+	1.07984i	−0.607511	+	0.794312i	$0.707832\pi$
$972$	−7.44091	−	14.6036i	−0.238667	−	0.468411i
$973$	1.40056	+	8.84279i	0.0448999	+	0.283487i
$974$	12.6262	+	9.17349i	0.404570	+	0.293938i
$975$	17.9360	+	20.3067i	0.574413	+	0.650333i
$976$	10.2683	−	3.33639i	0.328682	−	0.106795i
$977$	1.43474	−	9.05860i	0.0459015	−	0.289810i	−0.954050	−	0.299647i	$-0.903131\pi$
$977$	1.43474	−	9.05860i	0.0459015	−	0.289810i	0.999952	+	0.00983656i	$0.00313113\pi$
$978$	−10.3845	+	10.3845i	−0.332061	+	0.332061i
$979$	−3.40342	−	15.8864i	−0.108774	−	0.507731i
$980$	−5.28885	−	9.26242i	−0.168946	−	0.295877i
$981$	17.0117	+	23.4146i	0.543141	+	0.747569i
$982$	−6.06869	−	3.09215i	−0.193660	−	0.0986745i
$983$	−29.8234	+	15.1958i	−0.951220	+	0.484671i	−0.859512	−	0.511115i	$-0.829233\pi$
$983$	−29.8234	+	15.1958i	−0.951220	+	0.484671i	−0.0917077	+	0.995786i	$0.529233\pi$
$984$	−5.38701	+	7.41459i	−0.171732	+	0.236368i
$985$	−0.908613	+	0.728624i	−0.0289508	+	0.0232159i
$986$	1.83003	+	0.594613i	0.0582800	+	0.0189363i
$987$	19.0206	−	37.3301i	0.605433	−	1.18823i
$988$	12.8997	+	2.04312i	0.410395	+	0.0650002i
$989$	9.04073			0.287479
$990$	11.0650	−	7.13591i	0.351668	−	0.226794i
$991$	52.6621			1.67287			0.836433	−	0.548069i	$-0.184637\pi$
$991$	52.6621			1.67287			0.836433	+	0.548069i	$0.184637\pi$
$992$	7.75006	+	1.22749i	0.246065	+	0.0389728i
$993$	−20.1771	+	39.5998i	−0.640301	+	1.25666i
$994$	−29.2591	−	9.50686i	−0.928043	−	0.301539i
$995$	−30.4469	−	3.34716i	−0.965232	−	0.106112i
$996$	−15.5840	+	21.4496i	−0.493798	+	0.679655i
$997$	41.2437	−	21.0147i	1.30620	−	0.665543i	0.344279	−	0.938867i	$-0.388123\pi$
$997$	41.2437	−	21.0147i	1.30620	−	0.665543i	0.961922	+	0.273325i	$0.0881234\pi$
$998$	9.67590	+	4.93012i	0.306285	+	0.156060i
$999$	9.03664	+	12.4379i	0.285907	+	0.393517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.2.k.a.63.3	yes	48
3.2	odd	2		990.2.bh.c.613.4		48
4.3	odd	2		880.2.cm.c.833.2		48
5.2	odd	4	inner	110.2.k.a.107.4	yes	48
5.3	odd	4		550.2.bh.b.107.3		48
5.4	even	2		550.2.bh.b.393.4		48
11.7	odd	10	inner	110.2.k.a.73.4	yes	48
15.2	even	4		990.2.bh.c.217.3		48
20.7	even	4		880.2.cm.c.657.5		48
33.29	even	10		990.2.bh.c.73.3		48
44.7	even	10		880.2.cm.c.513.5		48
55.7	even	20	inner	110.2.k.a.7.3	✓	48
55.18	even	20		550.2.bh.b.7.4		48
55.29	odd	10		550.2.bh.b.293.3		48
165.62	odd	20		990.2.bh.c.667.4		48
220.7	odd	20		880.2.cm.c.337.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.k.a.7.3	✓	48	55.7	even	20	inner
110.2.k.a.63.3	yes	48	1.1	even	1	trivial
110.2.k.a.73.4	yes	48	11.7	odd	10	inner
110.2.k.a.107.4	yes	48	5.2	odd	4	inner
550.2.bh.b.7.4		48	55.18	even	20
550.2.bh.b.107.3		48	5.3	odd	4
550.2.bh.b.293.3		48	55.29	odd	10
550.2.bh.b.393.4		48	5.4	even	2
880.2.cm.c.337.2		48	220.7	odd	20
880.2.cm.c.513.5		48	44.7	even	10
880.2.cm.c.657.5		48	20.7	even	4
880.2.cm.c.833.2		48	4.3	odd	2
990.2.bh.c.73.3		48	33.29	even	10
990.2.bh.c.217.3		48	15.2	even	4
990.2.bh.c.613.4		48	3.2	odd	2
990.2.bh.c.667.4		48	165.62	odd	20

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	110.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(0.992087 - 1.94708i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.244349 - 2.22268i) q^{5} +(-1.28446 + 1.76791i) q^{6} +(-3.05681 + 1.55752i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(-1.04353 - 1.43630i) q^{9} +(-0.589044 + 2.15709i) q^{10} +(3.24304 - 0.694771i) q^{11} +(1.54521 - 1.54521i) q^{12} +(0.387905 - 2.44914i) q^{13} +(3.26283 - 1.06016i) q^{14} +(-4.08532 - 2.68086i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-0.196982 - 1.24369i) q^{17} +(0.805997 + 1.58186i) q^{18} +(1.62761 + 5.00927i) q^{19} +(0.919234 - 2.03838i) q^{20} +7.49707i q^{21} +(-3.31180 + 0.178895i) q^{22} +(5.42684 + 5.42684i) q^{23} +(-1.76791 + 1.28446i) q^{24} +(-4.88059 - 1.08622i) q^{25} +(-0.766259 + 2.35830i) q^{26} +(2.64321 - 0.418643i) q^{27} +(-3.38851 + 0.536686i) q^{28} +(0.472216 - 1.45333i) q^{29} +(3.61564 + 3.28693i) q^{30} +(-6.34809 + 4.61215i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.86460 - 7.00373i) q^{33} +1.25920i q^{34} +(2.71495 + 7.17489i) q^{35} +(-0.548617 - 1.68847i) q^{36} +(2.60810 + 5.11868i) q^{37} +(-0.823949 - 5.20221i) q^{38} +(-4.38383 - 3.18504i) q^{39} +(-1.22679 + 1.86949i) q^{40} +(3.98871 - 1.29601i) q^{41} +(1.17280 - 7.40476i) q^{42} +(0.832964 - 0.832964i) q^{43} +(3.29901 + 0.341387i) q^{44} +(-3.44741 + 1.96848i) q^{45} +(-4.51108 - 6.20897i) q^{46} +(-4.97929 - 2.53708i) q^{47} +(1.94708 - 0.992087i) q^{48} +(2.80374 - 3.85901i) q^{49} +(4.65058 + 1.83634i) q^{50} +(-2.61699 - 0.850313i) q^{51} +(1.12574 - 2.20940i) q^{52} +(-9.00929 - 1.42693i) q^{53} -2.67615 q^{54} +(-0.751821 - 7.37799i) q^{55} +3.43074 q^{56} +(11.3682 + 1.80054i) q^{57} +(-0.693754 + 1.36157i) q^{58} +(2.65408 + 0.862364i) q^{59} +(-3.05694 - 3.81208i) q^{60} +(6.34618 - 8.73477i) q^{61} +(6.99143 - 3.56231i) q^{62} +(5.42695 + 2.76517i) q^{63} +(0.587785 + 0.809017i) q^{64} +(-5.34886 - 1.46063i) q^{65} +(-2.93727 + 6.62581i) q^{66} +(-4.03846 + 4.03846i) q^{67} +(0.196982 - 1.24369i) q^{68} +(15.9504 - 5.18260i) q^{69} +(-1.55912 - 7.51127i) q^{70} +(-7.25478 - 5.27091i) q^{71} +(0.277728 + 1.75350i) q^{72} +(4.14012 + 8.12545i) q^{73} +(-1.77525 - 5.46365i) q^{74} +(-6.95692 + 8.42528i) q^{75} +5.26706i q^{76} +(-8.83124 + 7.17490i) q^{77} +(3.83161 + 3.83161i) q^{78} +(-11.2765 + 8.19287i) q^{79} +(1.50414 - 1.65456i) q^{80} +(3.45301 - 10.6273i) q^{81} +(-4.14235 + 0.656083i) q^{82} +(-11.9833 + 1.89797i) q^{83} +(-2.31672 + 7.13013i) q^{84} +(-2.81246 + 0.133932i) q^{85} +(-0.953013 + 0.692405i) q^{86} +(-2.36128 - 2.36128i) q^{87} +(-3.20499 - 0.853262i) q^{88} -4.89861i q^{89} +(3.71290 - 1.40495i) q^{90} +(2.62884 + 8.09073i) q^{91} +(3.48425 + 6.83822i) q^{92} +(2.68238 + 16.9359i) q^{93} +(4.52110 + 3.28477i) q^{94} +(11.5317 - 2.39364i) q^{95} +(-2.07831 + 0.675282i) q^{96} +(0.442255 - 2.79229i) q^{97} +(-3.37290 + 3.37290i) q^{98} +(-4.38211 - 3.93295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 8 q^{5} - 20 q^{7} + 12 q^{11} - 16 q^{12} - 16 q^{15} + 12 q^{16} - 20 q^{17} - 4 q^{20} - 4 q^{22} - 8 q^{23} - 20 q^{25} + 8 q^{26} + 8 q^{27} - 20 q^{28} + 16 q^{31} - 104 q^{33} - 4 q^{36}+ \cdots + 72 q^{97}+O(q^{100}) \) 48 * q - 4 * q^3 - 8 * q^5 - 20 * q^7 + 12 * q^11 - 16 * q^12 - 16 * q^15 + 12 * q^16 - 20 * q^17 - 4 * q^20 - 4 * q^22 - 8 * q^23 - 20 * q^25 + 8 * q^26 + 8 * q^27 - 20 * q^28 + 16 * q^31 - 104 * q^33 - 4 * q^36 + 20 * q^37 - 36 * q^38 - 20 * q^41 - 20 * q^42 + 16 * q^45 + 40 * q^46 + 40 * q^47 + 4 * q^48 + 40 * q^50 + 40 * q^51 + 40 * q^52 + 96 * q^55 - 8 * q^56 + 48 * q^58 + 20 * q^60 + 80 * q^61 + 40 * q^62 + 100 * q^63 + 24 * q^66 + 20 * q^68 - 56 * q^70 - 56 * q^71 - 20 * q^73 - 76 * q^75 - 96 * q^77 + 16 * q^78 - 12 * q^80 - 68 * q^81 - 80 * q^85 - 56 * q^86 - 4 * q^88 - 80 * q^90 - 68 * q^91 - 12 * q^92 + 76 * q^93 + 20 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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