LMFDB - Embedded newform 640.2.bm.a.621.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			621.36
Character	$\chi$	$=$	640.621
Dual form			640.2.bm.a.101.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.272880 - 1.38764i) q^{2} +(0.276256 + 0.147662i) q^{3} +(-1.85107 - 0.757318i) q^{4} +(0.634393 - 0.773010i) q^{5} +(0.280286 - 0.343049i) q^{6} +(1.03637 + 0.692483i) q^{7} +(-1.55600 + 2.36196i) q^{8} +(-1.61220 - 2.41282i) q^{9} +(-0.899544 - 1.09125i) q^{10} +(-5.77435 - 1.75163i) q^{11} +(-0.399543 - 0.482547i) q^{12} +(2.08663 - 1.71246i) q^{13} +(1.24372 - 1.24915i) q^{14} +(0.289400 - 0.119873i) q^{15} +(2.85294 + 2.80370i) q^{16} +(-0.598387 - 0.247860i) q^{17} +(-3.78806 + 1.57873i) q^{18} +(0.300916 - 3.05525i) q^{19} +(-1.75972 + 0.950461i) q^{20} +(0.184051 + 0.344336i) q^{21} +(-4.00633 + 7.53471i) q^{22} +(-4.58900 - 0.912810i) q^{23} +(-0.778628 + 0.422743i) q^{24} +(-0.195090 - 0.980785i) q^{25} +(-1.80687 - 3.36279i) q^{26} +(-0.181207 - 1.83982i) q^{27} +(-1.39397 - 2.06670i) q^{28} +(-1.97757 - 6.51917i) q^{29} +(-0.0873690 - 0.434293i) q^{30} +(1.55671 - 1.55671i) q^{31} +(4.66903 - 3.19377i) q^{32} +(-1.33655 - 1.33655i) q^{33} +(-0.507228 + 0.762708i) q^{34} +(1.19277 - 0.361821i) q^{35} +(1.15702 + 5.68726i) q^{36} +(6.28174 - 0.618698i) q^{37} +(-4.15746 - 1.25128i) q^{38} +(0.829311 - 0.164960i) q^{39} +(0.838701 + 2.70122i) q^{40} +(-1.47840 + 7.43242i) q^{41} +(0.528037 - 0.161434i) q^{42} +(-4.66592 + 2.49398i) q^{43} +(9.36219 + 7.61541i) q^{44} +(-2.88790 - 0.284434i) q^{45} +(-2.51890 + 6.11878i) q^{46} +(0.164914 - 0.398137i) q^{47} +(0.374142 + 1.19581i) q^{48} +(-2.08425 - 5.03181i) q^{49} +(-1.41421 + 0.00307738i) q^{50} +(-0.128709 - 0.156832i) q^{51} +(-5.15939 + 1.58964i) q^{52} +(-1.79202 + 5.90749i) q^{53} +(-2.60246 - 0.250603i) q^{54} +(-5.01723 + 3.35241i) q^{55} +(-3.24822 + 1.37037i) q^{56} +(0.534274 - 0.799598i) q^{57} +(-9.58589 + 0.965193i) q^{58} +(7.41348 + 6.08408i) q^{59} +(-0.626482 + 0.00272651i) q^{60} +(2.35025 - 4.39702i) q^{61} +(-1.73535 - 2.58494i) q^{62} -3.61701i q^{63} +(-3.15770 - 7.35044i) q^{64} -2.69936i q^{65} +(-2.21937 + 1.48993i) q^{66} +(2.54468 - 4.76076i) q^{67} +(0.919949 + 0.911977i) q^{68} +(-1.13295 - 0.929791i) q^{69} +(-0.176594 - 1.75386i) q^{70} +(-7.18054 + 10.7464i) q^{71} +(8.20758 - 0.0535807i) q^{72} +(7.49988 - 5.01126i) q^{73} +(0.855637 - 8.88561i) q^{74} +(0.0909299 - 0.299756i) q^{75} +(-2.87081 + 5.42760i) q^{76} +(-4.77141 - 5.81398i) q^{77} +(-0.00260210 - 1.19580i) q^{78} +(3.96902 + 9.58207i) q^{79} +(3.97718 - 0.426702i) q^{80} +(-3.10989 + 7.50794i) q^{81} +(9.91007 + 4.07965i) q^{82} +(9.73115 + 0.958435i) q^{83} +(-0.0799207 - 0.776776i) q^{84} +(-0.571211 + 0.305319i) q^{85} +(2.18751 + 7.15516i) q^{86} +(0.416319 - 2.09298i) q^{87} +(13.1222 - 10.9132i) q^{88} +(9.51452 - 1.89256i) q^{89} +(-1.18274 + 3.92975i) q^{90} +(3.34838 - 0.329787i) q^{91} +(7.80329 + 5.16501i) q^{92} +(0.659917 - 0.200184i) q^{93} +(-0.507468 - 0.337484i) q^{94} +(-2.17084 - 2.17084i) q^{95} +(1.76145 - 0.192860i) q^{96} +(9.89096 - 9.89096i) q^{97} +(-7.55108 + 1.51909i) q^{98} +(5.08301 + 16.7565i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.272880	−	1.38764i	0.192956	−	0.981207i
$2$	0.272880	−	1.38764i	0.192956	−	0.981207i
$3$	0.276256	+	0.147662i	0.159497	+	0.0852528i	0.549214	−	0.835682i	$-0.314927\pi$
$3$	0.276256	+	0.147662i	0.159497	+	0.0852528i	−0.389717	+	0.920935i	$0.627427\pi$
$4$	−1.85107	−	0.757318i	−0.925536	−	0.378659i
$5$	0.634393	−	0.773010i	0.283709	−	0.345701i
$5$	0.634393	−	0.773010i	0.283709	−	0.345701i
$6$	0.280286	−	0.343049i	0.114426	−	0.140049i
$7$	1.03637	+	0.692483i	0.391713	+	0.261734i	0.735793	−	0.677206i	$-0.236809\pi$
$7$	1.03637	+	0.692483i	0.391713	+	0.261734i	−0.344081	+	0.938940i	$0.611809\pi$
$8$	−1.55600	+	2.36196i	−0.550131	+	0.835079i
$9$	−1.61220	−	2.41282i	−0.537399	−	0.804275i
$10$	−0.899544	−	1.09125i	−0.284461	−	0.345083i
$11$	−5.77435	−	1.75163i	−1.74103	−	0.528136i	−0.749962	−	0.661481i	$-0.769928\pi$
$11$	−5.77435	−	1.75163i	−1.74103	−	0.528136i	−0.991070	+	0.133345i	$0.957428\pi$
$12$	−0.399543	−	0.482547i	−0.115338	−	0.139299i
$13$	2.08663	−	1.71246i	0.578728	−	0.474950i	−0.298905	−	0.954283i	$-0.596621\pi$
$13$	2.08663	−	1.71246i	0.578728	−	0.474950i	0.877633	+	0.479333i	$0.159121\pi$
$14$	1.24372	−	1.24915i	0.332398	−	0.333848i
$15$	0.289400	−	0.119873i	0.0747226	−	0.0309511i
$16$	2.85294	+	2.80370i	0.713235	+	0.700925i
$17$	−0.598387	−	0.247860i	−0.145130	−	0.0601149i	0.308936	−	0.951083i	$-0.400027\pi$
$17$	−0.598387	−	0.247860i	−0.145130	−	0.0601149i	−0.454066	+	0.890968i	$0.650027\pi$
$18$	−3.78806	+	1.57873i	−0.892854	+	0.372111i
$19$	0.300916	−	3.05525i	0.0690348	−	0.700922i	−0.896917	−	0.442199i	$-0.854198\pi$
$19$	0.300916	−	3.05525i	0.0690348	−	0.700922i	0.965952	−	0.258723i	$-0.0833017\pi$
$20$	−1.75972	+	0.950461i	−0.393486	+	0.212530i
$21$	0.184051	+	0.344336i	0.0401633	+	0.0751403i
$22$	−4.00633	+	7.53471i	−0.854153	+	1.60641i
$23$	−4.58900	−	0.912810i	−0.956873	−	0.190334i	−0.308133	−	0.951343i	$-0.599704\pi$
$23$	−4.58900	−	0.912810i	−0.956873	−	0.190334i	−0.648741	+	0.761009i	$0.724704\pi$
$24$	−0.778628	+	0.422743i	−0.158937	+	0.0862921i
$25$	−0.195090	−	0.980785i	−0.0390181	−	0.196157i
$26$	−1.80687	−	3.36279i	−0.354356	−	0.659497i
$27$	−0.181207	−	1.83982i	−0.0348733	−	0.354074i
$28$	−1.39397	−	2.06670i	−0.263436	−	0.390570i
$29$	−1.97757	−	6.51917i	−0.367225	−	1.21058i	−0.924800	−	0.380453i	$-0.875768\pi$
$29$	−1.97757	−	6.51917i	−0.367225	−	1.21058i	0.557575	−	0.830127i	$-0.311732\pi$
$30$	−0.0873690	−	0.434293i	−0.0159513	−	0.0792906i
$31$	1.55671	−	1.55671i	0.279593	−	0.279593i	−0.553354	−	0.832946i	$-0.686652\pi$
$31$	1.55671	−	1.55671i	0.279593	−	0.279593i	0.832946	+	0.553354i	$0.186652\pi$
$32$	4.66903	−	3.19377i	0.825376	−	0.564584i
$33$	−1.33655	−	1.33655i	−0.232664	−	0.232664i
$34$	−0.507228	+	0.762708i	−0.0869889	+	0.130803i
$35$	1.19277	−	0.361821i	0.201614	−	0.0611590i
$36$	1.15702	+	5.68726i	0.192836	+	0.947876i
$37$	6.28174	−	0.618698i	1.03271	−	0.101713i	0.432565	−	0.901603i	$-0.357609\pi$
$37$	6.28174	−	0.618698i	1.03271	−	0.101713i	0.600147	+	0.799890i	$0.295109\pi$
$38$	−4.15746	−	1.25128i	−0.674430	−	0.202984i
$39$	0.829311	−	0.164960i	0.132796	−	0.0264148i
$40$	0.838701	+	2.70122i	0.132610	+	0.427100i
$41$	−1.47840	+	7.43242i	−0.230887	+	1.16075i	0.675192	+	0.737642i	$0.264061\pi$
$41$	−1.47840	+	7.43242i	−0.230887	+	1.16075i	−0.906080	+	0.423107i	$0.860939\pi$
$42$	0.528037	−	0.161434i	0.0814779	−	0.0249098i
$43$	−4.66592	+	2.49398i	−0.711546	+	0.380329i	−0.787111	−	0.616812i	$-0.788424\pi$
$43$	−4.66592	+	2.49398i	−0.711546	+	0.380329i	0.0755650	+	0.997141i	$0.475924\pi$
$44$	9.36219	+	7.61541i	1.41140	+	1.14807i
$45$	−2.88790	−	0.284434i	−0.430503	−	0.0424009i
$46$	−2.51890	+	6.11878i	−0.371391	+	0.902165i
$47$	0.164914	−	0.398137i	0.0240552	−	0.0580743i	−0.911396	−	0.411532i	$-0.864994\pi$
$47$	0.164914	−	0.398137i	0.0240552	−	0.0580743i	0.935451	+	0.353457i	$0.114994\pi$
$48$	0.374142	+	1.19581i	0.0540027	+	0.172600i
$49$	−2.08425	−	5.03181i	−0.297749	−	0.718831i
$50$	−1.41421	+	0.00307738i	−0.200000	+	0.000435207i
$51$	−0.128709	−	0.156832i	−0.0180228	−	0.0219609i
$52$	−5.15939	+	1.58964i	−0.715478	+	0.220443i
$53$	−1.79202	+	5.90749i	−0.246152	+	0.811456i	0.743595	+	0.668630i	$0.233119\pi$
$53$	−1.79202	+	5.90749i	−0.246152	+	0.811456i	−0.989748	+	0.142826i	$0.954381\pi$
$54$	−2.60246	−	0.250603i	−0.354149	−	0.0341027i
$55$	−5.01723	+	3.35241i	−0.676524	+	0.452039i
$56$	−3.24822	+	1.37037i	−0.434062	+	0.183123i
$57$	0.534274	−	0.799598i	0.0707664	−	0.105909i
$58$	−9.58589	+	0.965193i	−1.25869	+	0.126736i
$59$	7.41348	+	6.08408i	0.965152	+	0.792080i	0.978164	−	0.207835i	$-0.0666418\pi$
$59$	7.41348	+	6.08408i	0.965152	+	0.792080i	−0.0130115	+	0.999915i	$0.504142\pi$
$60$	−0.626482	+	0.00272651i	−0.0808784	+	0.000351991i
$61$	2.35025	−	4.39702i	0.300919	−	0.562980i	−0.685332	−	0.728230i	$-0.740343\pi$
$61$	2.35025	−	4.39702i	0.300919	−	0.562980i	0.986252	+	0.165250i	$0.0528431\pi$
$62$	−1.73535	−	2.58494i	−0.220390	−	0.328288i
$63$		−	3.61701i		−	0.455700i
$64$	−3.15770	−	7.35044i	−0.394713	−	0.918805i
$65$		−	2.69936i		−	0.334815i
$66$	−2.21937	+	1.48993i	−0.273185	+	0.183398i
$67$	2.54468	−	4.76076i	0.310882	−	0.581620i	−0.677154	−	0.735841i	$-0.736787\pi$
$67$	2.54468	−	4.76076i	0.310882	−	0.581620i	0.988036	+	0.154222i	$0.0492869\pi$
$68$	0.919949	+	0.911977i	0.111560	+	0.110593i
$69$	−1.13295	−	0.929791i	−0.136392	−	0.111934i
$70$	−0.176594	−	1.75386i	−0.0211071	−	0.209626i
$71$	−7.18054	+	10.7464i	−0.852173	+	1.27537i	0.107488	+	0.994206i	$0.465719\pi$
$71$	−7.18054	+	10.7464i	−0.852173	+	1.27537i	−0.959661	+	0.281160i	$0.909281\pi$
$72$	8.20758	−	0.0535807i	0.967272	−	0.00631454i
$73$	7.49988	−	5.01126i	0.877795	−	0.586524i	−0.0329668	−	0.999456i	$-0.510496\pi$
$73$	7.49988	−	5.01126i	0.877795	−	0.586524i	0.910761	+	0.412933i	$0.135496\pi$
$74$	0.855637	−	8.88561i	0.0994658	−	1.03293i
$75$	0.0909299	−	0.299756i	0.0104997	−	0.0346128i
$76$	−2.87081	+	5.42760i	−0.329305	+	0.622588i
$77$	−4.77141	−	5.81398i	−0.543753	−	0.662565i
$78$	−0.00260210	−	1.19580i	−0.000294630	−	0.135397i
$79$	3.96902	+	9.58207i	0.446550	+	1.07807i	0.973606	+	0.228236i	$0.0732958\pi$
$79$	3.96902	+	9.58207i	0.446550	+	1.07807i	−0.527056	+	0.849831i	$0.676704\pi$
$80$	3.97718	−	0.426702i	0.444662	−	0.0477068i
$81$	−3.10989	+	7.50794i	−0.345543	+	0.834215i
$82$	9.91007	+	4.07965i	1.09438	+	0.450521i
$83$	9.73115	+	0.958435i	1.06813	+	0.105202i	0.616774	−	0.787141i	$-0.288439\pi$
$83$	9.73115	+	0.958435i	1.06813	+	0.105202i	0.451359	+	0.892343i	$0.350939\pi$
$84$	−0.0799207	−	0.776776i	−0.00872006	−	0.0847533i
$85$	−0.571211	+	0.305319i	−0.0619566	+	0.0331165i
$86$	2.18751	+	7.15516i	0.235885	+	0.771561i
$87$	0.416319	−	2.09298i	0.0446340	−	0.224390i
$88$	13.1222	−	10.9132i	1.39883	−	1.16335i
$89$	9.51452	−	1.89256i	1.00854	−	0.200611i	0.336940	−	0.941526i	$-0.390608\pi$
$89$	9.51452	−	1.89256i	1.00854	−	0.200611i	0.671598	+	0.740916i	$0.265608\pi$
$90$	−1.18274	+	3.92975i	−0.124672	+	0.414232i
$91$	3.34838	−	0.329787i	0.351006	−	0.0345711i
$92$	7.80329	+	5.16501i	0.813549	+	0.538490i
$93$	0.659917	−	0.200184i	0.0684302	−	0.0207581i
$94$	−0.507468	−	0.337484i	−0.0523414	−	0.0348089i
$95$	−2.17084	−	2.17084i	−0.222724	−	0.222724i
$96$	1.76145	−	0.192860i	0.179777	−	0.0196837i
$97$	9.89096	−	9.89096i	1.00428	−	1.00428i	0.00428436	−	0.999991i	$-0.498636\pi$
$97$	9.89096	−	9.89096i	1.00428	−	1.00428i	0.999991	−	0.00428436i	$-0.00136376\pi$
$98$	−7.55108	+	1.51909i	−0.762774	+	0.153451i
$99$	5.08301	+	16.7565i	0.510862	+	1.68409i
$100$	−0.381640	+	1.96325i	−0.0381640	+	0.196325i
$101$	−1.50716	−	15.3025i	−0.149968	−	1.52265i	−0.715902	−	0.698200i	$-0.753984\pi$
$101$	−1.50716	−	15.3025i	−0.149968	−	1.52265i	0.565934	−	0.824450i	$-0.308516\pi$
$102$	−0.252748	+	0.135805i	−0.0250258	+	0.0134467i
$103$	−2.68422	−	13.4945i	−0.264484	−	1.32965i	−0.853316	−	0.521394i	$-0.825412\pi$
$103$	−2.68422	−	13.4945i	−0.264484	−	1.32965i	0.588832	−	0.808255i	$-0.299588\pi$
$104$	0.797941	+	7.59314i	0.0782446	+	0.744568i
$105$	0.382936	+	0.0761708i	0.0373708	+	0.00743351i
$106$	7.70844	+	4.09871i	0.748710	+	0.398101i
$107$	−2.34240	−	4.38233i	−0.226449	−	0.423656i	0.742880	−	0.669425i	$-0.233459\pi$
$107$	−2.34240	−	4.38233i	−0.226449	−	0.423656i	−0.969328	+	0.245769i	$0.920959\pi$
$108$	−1.05791	+	3.54288i	−0.101797	+	0.340914i
$109$	1.09725	−	11.1405i	0.105097	−	1.06707i	−0.787531	−	0.616275i	$-0.788641\pi$
$109$	1.09725	−	11.1405i	0.105097	−	1.06707i	0.892628	−	0.450794i	$-0.148859\pi$
$110$	3.28282	+	7.87691i	0.313005	+	0.751034i
$111$	1.82673	+	0.756656i	0.173385	+	0.0718186i
$112$	1.01520	+	4.88130i	0.0959270	+	0.461239i
$113$	2.26020	−	0.936207i	0.212622	−	0.0880710i	−0.273830	−	0.961778i	$-0.588291\pi$
$113$	2.26020	−	0.936207i	0.212622	−	0.0880710i	0.486452	+	0.873707i	$0.338291\pi$
$114$	−0.963759	−	0.959574i	−0.0902643	−	0.0898723i
$115$	−3.61684	+	2.96827i	−0.337272	+	0.276792i
$116$	−1.27646	+	13.5651i	−0.118517	+	1.25949i
$117$	−7.49592	−	2.27386i	−0.692998	−	0.210219i
$118$	10.4655	−	8.62699i	0.963426	−	0.794178i
$119$	−0.448514	−	0.671249i	−0.0411152	−	0.0615333i
$120$	−0.167171	+	0.870073i	−0.0152606	+	0.0794264i
$121$	21.1287	+	14.1178i	1.92079	+	1.28343i
$122$	−5.46012	−	4.46116i	−0.494336	−	0.403894i
$123$	−1.50590	+	1.83495i	−0.135783	+	0.165452i
$124$	−4.06050	+	1.70265i	−0.364644	+	0.152903i
$125$	−0.881921	−	0.471397i	−0.0788814	−	0.0421630i
$126$	−5.01909	−	0.987011i	−0.447136	−	0.0879299i
$127$	−14.6884			−1.30339			−0.651693	−	0.758483i	$-0.725941\pi$
$127$	−14.6884			−1.30339			−0.651693	+	0.758483i	$0.725941\pi$
$128$	−11.0614	+	2.37595i	−0.977700	+	0.210007i
$129$	−1.65726			−0.145913
$130$	−3.74573	−	0.736603i	−0.328523	−	0.0646044i
$131$	6.84697	+	3.65978i	0.598223	+	0.319757i	0.742568	−	0.669771i	$-0.233608\pi$
$131$	6.84697	+	3.65978i	0.598223	+	0.319757i	−0.144345	+	0.989527i	$0.546108\pi$
$132$	1.46186	+	3.48625i	0.127238	+	0.303439i
$133$	2.42757	−	2.95800i	0.210497	−	0.256491i
$134$	−5.91182	−	4.83021i	−0.510703	−	0.417267i
$135$	−1.53716	−	1.02710i	−0.132298	−	0.0883985i
$136$	1.51653	−	1.02769i	0.130041	−	0.0881241i
$137$	−2.50689	−	3.75182i	−0.214178	−	0.320540i	0.708788	−	0.705422i	$-0.249242\pi$
$137$	−2.50689	−	3.75182i	−0.214178	−	0.320540i	−0.922966	+	0.384882i	$0.874242\pi$
$138$	−1.59937	+	1.31841i	−0.136148	+	0.112230i
$139$	11.0191	+	3.34262i	0.934631	+	0.283517i	0.720633	−	0.693317i	$-0.243851\pi$
$139$	11.0191	+	3.34262i	0.934631	+	0.283517i	0.213998	+	0.976834i	$0.431351\pi$
$140$	−2.48191	−	0.233545i	−0.209760	−	0.0197382i
$141$	0.104348	−	0.0856364i	0.00878771	−	0.00721189i
$142$	12.9527	+	12.8965i	1.08697	+	1.08225i
$143$	−15.0485	+	6.23331i	−1.25842	+	0.521256i
$144$	2.16534	−	11.4038i	0.180445	−	0.950313i
$145$	−6.29395	−	2.60704i	−0.522684	−	0.216503i
$146$	−4.90724	−	11.7746i	−0.406126	−	0.974472i
$147$	0.167222	−	1.69783i	0.0137922	−	0.140035i
$148$	−12.0965	−	3.61202i	−0.994327	−	0.296906i
$149$	8.36457	+	15.6490i	0.685252	+	1.28202i	0.948343	+	0.317245i	$0.102758\pi$
$149$	8.36457	+	15.6490i	0.685252	+	1.28202i	−0.263092	+	0.964771i	$0.584742\pi$
$150$	−0.391139	−	0.207975i	−0.0319364	−	0.0169811i
$151$	−2.41068	−	0.479515i	−0.196179	−	0.0390224i	0.0960229	−	0.995379i	$-0.469388\pi$
$151$	−2.41068	−	0.479515i	−0.196179	−	0.0390224i	−0.292202	+	0.956357i	$0.594388\pi$
$152$	6.74815	+	5.46473i	0.547347	+	0.443248i
$153$	0.366676	+	1.84340i	0.0296440	+	0.149030i
$154$	−9.36972	+	5.03446i	−0.755033	+	0.405689i
$155$	−0.215786	−	2.19092i	−0.0173324	−	0.175979i
$156$	−1.66004	−	0.322699i	−0.132910	−	0.0258366i
$157$	−4.72195	−	15.5662i	−0.376853	−	1.24232i	−0.916367	−	0.400340i	$-0.868892\pi$
$157$	−4.72195	−	15.5662i	−0.376853	−	1.24232i	0.539514	−	0.841976i	$-0.318608\pi$
$158$	14.3795	−	2.89280i	1.14397	−	0.230139i
$159$	−1.36737	+	1.36737i	−0.108439	+	0.108439i
$160$	0.493186	−	5.63531i	0.0389898	−	0.445511i
$161$	−4.12382	−	4.12382i	−0.325002	−	0.325002i
$162$	9.56966	+	6.36417i	0.751864	+	0.500016i
$163$	6.47209	−	1.96329i	0.506933	−	0.153776i	−0.0264503	−	0.999650i	$-0.508420\pi$
$163$	6.47209	−	1.96329i	0.506933	−	0.153776i	0.533383	+	0.845874i	$0.320920\pi$
$164$	8.36533	−	12.6383i	0.653223	−	0.986888i
$165$	−1.88107	+	0.185269i	−0.146441	+	0.0144232i
$166$	3.98540	−	13.2418i	0.309327	−	1.02776i
$167$	10.5270	−	2.09395i	0.814602	−	0.162034i	0.229829	−	0.973231i	$-0.426183\pi$
$167$	10.5270	−	2.09395i	0.814602	−	0.162034i	0.584774	+	0.811197i	$0.301183\pi$
$168$	−1.09969	−	0.101066i	−0.0848431	−	0.00779743i
$169$	−1.11464	+	5.60366i	−0.0857414	+	0.431051i
$170$	0.267799	+	0.875950i	0.0205393	+	0.0671823i
$171$	−7.85691	+	4.19961i	−0.600833	+	0.321152i
$172$	10.5257	−	1.08296i	0.802576	−	0.0825752i
$173$	7.68003	+	0.756417i	0.583902	+	0.0575093i	0.385655	−	0.922643i	$-0.373975\pi$
$173$	7.68003	+	0.756417i	0.583902	+	0.0575093i	0.198246	+	0.980152i	$0.436475\pi$
$174$	−2.79068	−	1.14883i	−0.211561	−	0.0870927i
$175$	0.476991	−	1.15156i	0.0360571	−	0.0870495i
$176$	−11.5628	−	21.1868i	−0.871580	−	1.59702i
$177$	1.14963	+	2.77546i	0.0864116	+	0.208616i
$178$	−0.0298534	−	13.7191i	−0.00223761	−	1.02829i
$179$	−0.743671	−	0.906166i	−0.0555846	−	0.0677300i	0.744476	−	0.667649i	$-0.232699\pi$
$179$	−0.743671	−	0.906166i	−0.0555846	−	0.0677300i	−0.800061	+	0.599919i	$0.795199\pi$
$180$	5.13031	+	2.71357i	0.382391	+	0.202258i
$181$	2.83138	−	9.33382i	0.210455	−	0.693777i	−0.786626	−	0.617430i	$-0.788174\pi$
$181$	2.83138	−	9.33382i	0.210455	−	0.693777i	0.997081	−	0.0763478i	$-0.0243259\pi$
$182$	0.456084	−	4.73633i	0.0338072	−	0.351080i
$183$	1.29855	−	0.867660i	0.0959912	−	0.0641393i
$184$	9.29653	−	9.41870i	0.685349	−	0.694356i
$185$	3.50684	−	5.24835i	0.257828	−	0.385866i
$186$	−0.0977037	−	0.970351i	−0.00716398	−	0.0711496i
$187$	3.02114	+	2.47938i	0.220927	+	0.181310i
$188$	−0.606784	+	0.612089i	−0.0442543	+	0.0446412i
$189$	1.08625	−	2.03223i	0.0790130	−	0.147823i
$190$	−3.60472	+	2.41996i	−0.261514	+	0.175562i
$191$			12.0810i			0.874152i	0.899425	+	0.437076i	$0.143986\pi$
$191$			12.0810i			0.874152i	−0.899425	+	0.437076i	$0.856014\pi$
$192$	0.213045	−	2.49688i	0.0153752	−	0.180197i
$193$			15.0820i			1.08563i	0.839853	+	0.542813i	$0.182641\pi$
$193$			15.0820i			1.08563i	−0.839853	+	0.542813i	$0.817359\pi$
$194$	−11.0260	−	16.4241i	−0.791622	−	1.17918i
$195$	0.398593	−	0.745716i	0.0285439	−	0.0534018i
$196$	0.0474060	+	10.8927i	0.00338615	+	0.778049i
$197$	−0.706695	−	0.579970i	−0.0503500	−	0.0413211i	0.608882	−	0.793261i	$-0.291618\pi$
$197$	−0.706695	−	0.579970i	−0.0503500	−	0.0413211i	−0.659232	+	0.751940i	$0.729118\pi$
$198$	24.6389	−	2.48087i	1.75101	−	0.176308i
$199$	−1.99013	+	2.97844i	−0.141077	+	0.211136i	−0.895279	−	0.445506i	$-0.853024\pi$
$199$	−1.99013	+	2.97844i	−0.141077	+	0.211136i	0.754202	+	0.656642i	$0.228024\pi$
$200$	2.62014	+	1.06531i	0.185272	+	0.0753288i
$201$	1.40597	−	0.939438i	0.0991694	−	0.0662629i
$202$	−21.6455	−	2.08435i	−1.52297	−	0.146654i
$203$	2.46491	−	8.12574i	0.173003	−	0.570315i
$204$	0.119477	+	0.387781i	0.00836510	+	0.0271501i
$205$	4.80745	+	5.85790i	0.335767	+	0.409133i
$206$	−19.4579	+	0.0423411i	−1.35570	+	0.00295005i
$207$	5.19593	+	12.5441i	0.361142	+	0.871874i
$208$	10.7543	+	0.964766i	0.745674	+	0.0668945i
$209$	−7.08926	+	17.1150i	−0.490374	+	1.18387i
$210$	0.210193	−	0.510591i	0.0145047	−	0.0352341i
$211$	7.63302	+	0.751787i	0.525479	+	0.0517552i	0.357279	−	0.933998i	$-0.383705\pi$
$211$	7.63302	+	0.751787i	0.525479	+	0.0517552i	0.168200	+	0.985753i	$0.446205\pi$
$212$	7.79100	−	9.57806i	0.535088	−	0.657824i
$213$	−3.57051	+	1.90848i	−0.244647	+	0.130767i
$214$	−6.72028	+	2.05455i	−0.459389	+	0.140446i
$215$	−1.03215	+	5.18897i	−0.0703921	+	0.353885i
$216$	4.62755	+	2.43477i	0.314865	+	0.165665i
$217$	2.69132	−	0.535338i	0.182699	−	0.0363411i
$218$	−15.1596	−	4.56261i	−1.02674	−	0.309019i
$219$	2.81186	−	0.276944i	0.190008	−	0.0187142i
$220$	11.8261	−	2.40591i	0.797316	−	0.162206i
$221$	−1.67307	+	0.507519i	−0.112543	+	0.0341394i
$222$	1.54844	−	2.32836i	0.103925	−	0.156269i
$223$	12.7251	+	12.7251i	0.852133	+	0.852133i	0.990396	−	0.138263i	$-0.0441519\pi$
$223$	12.7251	+	12.7251i	0.852133	+	0.852133i	−0.138263	+	0.990396i	$0.544152\pi$
$224$	7.05049	−	0.0767136i	0.471081	−	0.00512564i
$225$	−2.05194	+	2.05194i	−0.136796	+	0.136796i
$226$	−0.682350	−	3.39182i	−0.0453893	−	0.225620i
$227$	−8.37948	−	27.6235i	−0.556166	−	1.83343i	−0.552611	−	0.833439i	$-0.686368\pi$
$227$	−8.37948	−	27.6235i	−0.556166	−	1.83343i	−0.00355471	−	0.999994i	$-0.501132\pi$
$228$	−1.59453	+	1.07550i	−0.105600	+	0.0712266i
$229$	−0.718465	−	7.29470i	−0.0474775	−	0.482047i	−0.989296	−	0.145925i	$-0.953384\pi$
$229$	−0.718465	−	7.29470i	−0.0474775	−	0.482047i	0.941818	−	0.336123i	$-0.109116\pi$
$230$	3.13191	+	5.82885i	0.206512	+	0.384343i
$231$	−0.459628	−	2.31071i	−0.0302413	−	0.152033i
$232$	18.4751	+	5.47292i	1.21295	+	0.359315i
$233$	−13.1190	−	2.60954i	−0.859457	−	0.170957i	−0.254361	−	0.967109i	$-0.581865\pi$
$233$	−13.1190	−	2.60954i	−0.859457	−	0.170957i	−0.605096	+	0.796153i	$0.706865\pi$
$234$	−5.20079	+	9.78113i	−0.339986	+	0.639412i
$235$	−0.203144	−	0.380056i	−0.0132517	−	0.0247921i
$236$	−9.11530	−	16.8764i	−0.593355	−	1.09856i
$237$	−0.318441	+	3.23318i	−0.0206849	+	0.210018i
$238$	−1.05384	+	0.439204i	−0.0683103	+	0.0284694i
$239$	−20.5945	−	8.53051i	−1.33214	−	0.551793i	−0.400878	−	0.916131i	$-0.631295\pi$
$239$	−20.5945	−	8.53051i	−1.33214	−	0.551793i	−0.931266	+	0.364339i	$0.881295\pi$
$240$	1.16173	+	0.469399i	0.0749892	+	0.0302996i
$241$	−16.8061	+	6.96132i	−1.08258	+	0.448418i	−0.851413	−	0.524496i	$-0.824254\pi$
$241$	−16.8061	+	6.96132i	−1.08258	+	0.448418i	−0.231165	+	0.972915i	$0.574254\pi$
$242$	25.3559	−	25.4665i	1.62994	−	1.63705i
$243$	−6.25502	+	5.13336i	−0.401260	+	0.329305i
$244$	−7.68043	+	6.35931i	−0.491689	+	0.407113i
$245$	−5.21188	−	1.58101i	−0.332975	−	0.101007i
$246$	2.13531	+	2.59037i	0.136143	+	0.165156i
$247$	−4.60408	−	6.89050i	−0.292951	−	0.438432i
$248$	1.25464	+	6.09912i	0.0796695	+	0.387295i
$249$	2.54677	+	1.70170i	0.161395	+	0.107841i
$250$	−0.894787	+	1.09515i	−0.0565913	+	0.0692635i
$251$	−1.77765	+	2.16607i	−0.112204	+	0.136721i	−0.826084	−	0.563547i	$-0.809436\pi$
$251$	−1.77765	+	2.16607i	−0.112204	+	0.136721i	0.713880	+	0.700268i	$0.246936\pi$
$252$	−2.73922	+	6.69534i	−0.172555	+	0.421767i
$253$	24.8996	+	13.3091i	1.56542	+	0.836737i
$254$	−4.00818	+	20.3822i	−0.251496	+	1.27889i
$255$	−0.202885			−0.0127051
$256$	0.278518	+	15.9976i	0.0174074	+	0.999848i
$257$	9.16276			0.571557			0.285779	−	0.958296i	$-0.407748\pi$
$257$	9.16276			0.571557			0.285779	+	0.958296i	$0.407748\pi$
$258$	−0.452233	+	2.29967i	−0.0281548	+	0.143171i
$259$	6.93867	+	3.70880i	0.431148	+	0.230453i
$260$	−2.04428	+	4.99671i	−0.126781	+	0.309883i
$261$	−12.5414	+	15.2817i	−0.776292	+	0.945915i
$262$	6.94686	−	8.50243i	0.429178	−	0.525282i
$263$	−10.4111	−	6.95649i	−0.641977	−	0.428956i	0.191513	−	0.981490i	$-0.438661\pi$
$263$	−10.4111	−	6.95649i	−0.641977	−	0.428956i	−0.833490	+	0.552535i	$0.813661\pi$
$264$	5.23656	−	1.07720i	0.322288	−	0.0662971i
$265$	3.42971	+	5.13292i	0.210685	+	0.315313i
$266$	−3.44220	−	4.17577i	−0.211055	−	0.256033i
$267$	2.90791	+	0.882104i	0.177961	+	0.0539839i
$268$	−8.31580	+	6.88538i	−0.507968	+	0.420592i
$269$	16.7567	−	13.7518i	1.02167	−	0.838464i	0.0347058	−	0.999398i	$-0.488951\pi$
$269$	16.7567	−	13.7518i	1.02167	−	0.838464i	0.986965	+	0.160934i	$0.0514506\pi$
$270$	−1.84470	+	1.85275i	−0.112265	+	0.112754i
$271$	−6.73454	+	2.78954i	−0.409094	+	0.169452i	−0.577734	−	0.816225i	$-0.696063\pi$
$271$	−6.73454	+	2.78954i	−0.409094	+	0.169452i	0.168639	+	0.985678i	$0.446063\pi$
$272$	−1.01224	−	2.38483i	−0.0613759	−	0.144601i
$273$	0.973709	+	0.403323i	0.0589315	+	0.0244102i
$274$	−5.89025	+	2.45485i	−0.355843	+	0.148303i
$275$	−0.591453	+	6.00512i	−0.0356659	+	0.362122i
$276$	1.39303	+	2.57912i	0.0838507	+	0.155245i
$277$	−6.75781	−	12.6430i	−0.406037	−	0.759643i	0.592922	−	0.805260i	$-0.297974\pi$
$277$	−6.75781	−	12.6430i	−0.406037	−	0.759643i	−0.998959	+	0.0456176i	$0.985474\pi$
$278$	7.64525	−	14.3784i	0.458531	−	0.862360i
$279$	−6.26578	−	1.24634i	−0.375122	−	0.0746165i
$280$	−1.00134	+	3.38026i	−0.0598415	+	0.202009i
$281$	0.770936	+	3.87576i	0.0459902	+	0.231208i	0.996943	−	0.0781263i	$-0.0248937\pi$
$281$	0.770936	+	3.87576i	0.0459902	+	0.231208i	−0.950953	+	0.309334i	$0.899894\pi$
$282$	−0.0903577	−	0.168166i	−0.00538072	−	0.0100141i
$283$	2.56392	+	26.0319i	0.152409	+	1.54744i	0.702105	+	0.712073i	$0.252244\pi$
$283$	2.56392	+	26.0319i	0.152409	+	1.54744i	−0.549696	+	0.835365i	$0.685256\pi$
$284$	21.4302	−	14.4545i	1.27165	−	0.857715i
$285$	−0.279158	−	0.920260i	−0.0165359	−	0.0545115i
$286$	4.54312	+	22.5829i	0.268640	+	1.33535i
$287$	−6.67900	+	6.67900i	−0.394249	+	0.394249i
$288$	−15.2334	−	6.11656i	−0.897637	−	0.360422i
$289$	−11.7242	−	11.7242i	−0.689658	−	0.689658i
$290$	−5.33512	+	8.02230i	−0.313289	+	0.471086i
$291$	4.19296	−	1.27192i	0.245796	−	0.0745613i
$292$	−17.6779	+	3.59641i	−1.03452	+	0.210464i
$293$	−0.686214	+	0.0675862i	−0.0400891	+	0.00394843i	−0.118042	−	0.993009i	$-0.537662\pi$
$293$	−0.686214	+	0.0675862i	−0.0400891	+	0.00394843i	0.0779527	+	0.996957i	$0.475162\pi$
$294$	−2.31035	−	0.695349i	−0.134742	−	0.0405536i
$295$	9.40612	−	1.87099i	0.547645	−	0.108933i
$296$	−8.31308	+	15.7999i	−0.483188	+	0.918351i
$297$	−2.17634	+	10.9412i	−0.126284	+	0.634872i
$298$	23.9977	−	7.33667i	1.39015	−	0.425002i
$299$	−11.1387	+	5.95377i	−0.644169	+	0.344315i
$300$	−0.395328	+	0.486007i	−0.0228243	+	0.0280596i
$301$	−6.56268	−	0.646367i	−0.378266	−	0.0372560i
$302$	−1.32322	+	3.21430i	−0.0761428	+	0.184962i
$303$	1.84323	−	4.44995i	0.105891	−	0.255643i
$304$	9.42450	−	7.87276i	0.540532	−	0.451534i
$305$	−1.90795	−	4.60621i	−0.109249	−	0.263751i
$306$	2.65803	−	0.00578398i	0.151950	−	0.000330648i
$307$	5.83289	+	7.10740i	0.332901	+	0.405641i	0.912379	−	0.409347i	$-0.134243\pi$
$307$	5.83289	+	7.10740i	0.332901	+	0.405641i	−0.579478	+	0.814988i	$0.696743\pi$
$308$	4.42919	+	14.3756i	0.252377	+	0.819124i
$309$	1.25109	−	4.12429i	0.0711720	−	0.234623i
$310$	−3.09908	−	0.298425i	−0.176016	−	0.0169494i
$311$	−20.0396	+	13.3900i	−1.13634	+	0.759277i	−0.973796	−	0.227424i	$-0.926970\pi$
$311$	−20.0396	+	13.3900i	−1.13634	+	0.759277i	−0.162543	+	0.986701i	$0.551970\pi$
$312$	−0.900782	+	2.21548i	−0.0509967	+	0.125427i
$313$	−18.9073	+	28.2968i	−1.06870	+	1.59943i	−0.306758	+	0.951787i	$0.599244\pi$
$313$	−18.9073	+	28.2968i	−1.06870	+	1.59943i	−0.761946	+	0.647641i	$0.775756\pi$
$314$	−22.8887	+	2.30464i	−1.29169	+	0.130059i
$315$	−2.79598	−	2.29461i	−0.157536	−	0.129286i
$316$	−0.0902752	−	20.7429i	−0.00507837	−	1.16688i
$317$	11.6009	−	21.7038i	0.651572	−	1.21901i	−0.311624	−	0.950206i	$-0.600873\pi$
$317$	11.6009	−	21.7038i	0.651572	−	1.21901i	0.963196	−	0.268800i	$-0.0866272\pi$
$318$	1.52428	+	2.27054i	0.0854775	+	0.127325i
$319$			41.1079i			2.30160i
$320$	−7.68519	−	2.22213i	−0.429615	−	0.124221i
$321$		−	1.55653i		−	0.0868770i
$322$	−6.84767	+	4.59705i	−0.381606	+	0.256184i
$323$	−0.937339	+	1.75364i	−0.0521549	+	0.0975750i
$324$	11.4425	−	11.5426i	0.635696	−	0.641253i
$325$	−2.08663	−	1.71246i	−0.115746	−	0.0949900i
$326$	−0.958222	−	9.51665i	−0.0530710	−	0.527078i
$327$	1.94816	−	2.91562i	0.107733	−	0.161234i
$328$	−15.2547	−	15.0568i	−0.842299	−	0.831373i
$329$	0.446616	−	0.298419i	0.0246227	−	0.0164524i
$330$	−0.256220	+	2.66079i	−0.0141045	+	0.146472i
$331$	3.42756	−	11.2991i	0.188396	−	0.621057i	−0.810958	−	0.585105i	$-0.801053\pi$
$331$	3.42756	−	11.2991i	0.188396	−	0.621057i	0.999353	−	0.0359526i	$-0.0114465\pi$
$332$	−17.2872	−	9.14371i	−0.948760	−	0.501826i
$333$	−11.6202	−	14.1593i	−0.636784	−	0.775923i
$334$	−0.0330301	−	15.1790i	−0.00180733	−	0.830559i
$335$	−2.06579	−	4.98726i	−0.112866	−	0.272483i
$336$	−0.440328	+	1.49839i	−0.0240219	+	0.0817441i
$337$	−6.29770	+	15.2040i	−0.343057	+	0.828214i	0.654346	+	0.756195i	$0.272944\pi$
$337$	−6.29770	+	15.2040i	−0.343057	+	0.828214i	−0.997403	+	0.0720186i	$0.977056\pi$
$338$	7.47169	+	3.07584i	0.406406	+	0.167304i
$339$	0.762638	+	0.0751133i	0.0414208	+	0.00407959i
$340$	1.28858	−	0.132579i	0.0698829	−	0.00719008i
$341$	−11.7157	+	6.26219i	−0.634443	+	0.339117i
$342$	3.68353	+	12.0485i	0.199183	+	0.651510i
$343$	3.02656	−	15.2156i	0.163419	−	0.821563i
$344$	1.36950	−	14.9014i	0.0738383	−	0.803427i
$345$	−1.43748	+	0.285932i	−0.0773911	+	0.0153941i
$346$	3.14536	−	10.4507i	0.169096	−	0.561832i
$347$	−23.5082	+	2.31535i	−1.26199	+	0.124295i	−0.706789	−	0.707425i	$-0.749857\pi$
$347$	−23.5082	+	2.31535i	−1.26199	+	0.124295i	−0.555196	+	0.831719i	$0.687357\pi$
$348$	−2.35568	+	3.55896i	−0.126278	+	0.190780i
$349$	0.341545	−	0.103607i	0.0182825	−	0.00554593i	−0.281130	−	0.959670i	$-0.590709\pi$
$349$	0.341545	−	0.103607i	0.0182825	−	0.00554593i	0.299413	+	0.954124i	$0.403209\pi$
$350$	−1.46778	−	0.976127i	−0.0784562	−	0.0521762i
$351$	−3.52873	−	3.52873i	−0.188350	−	0.188350i
$352$	−32.5549	+	10.2635i	−1.73518	+	0.547047i
$353$	−0.0661558	+	0.0661558i	−0.00352112	+	0.00352112i	−0.708865	−	0.705344i	$-0.750793\pi$
$353$	−0.0661558	+	0.0661558i	−0.00352112	+	0.00352112i	0.705344	+	0.708865i	$0.250793\pi$
$354$	4.16504	−	0.837903i	0.221369	−	0.0445341i
$355$	3.75182	+	12.3681i	0.199126	+	0.656430i
$356$	−19.0453	−	3.70226i	−1.00940	−	0.196219i
$357$	−0.0247869	−	0.251665i	−0.00131186	−	0.0133195i
$358$	−1.46036	+	0.784670i	−0.0771825	+	0.0414711i
$359$	2.23324	+	11.2273i	0.117866	+	0.592552i	0.993898	+	0.110300i	$0.0351811\pi$
$359$	2.23324	+	11.2273i	0.117866	+	0.592552i	−0.876032	+	0.482252i	$0.839819\pi$
$360$	5.16541	−	6.37853i	0.272241	−	0.336178i
$361$	9.39092	+	1.86797i	0.494259	+	0.0983142i
$362$	−12.1793	−	6.47595i	−0.640131	−	0.340368i
$363$	3.75228	+	7.02003i	0.196944	+	0.368456i
$364$	−6.44785	−	1.92533i	−0.337959	−	0.100915i
$365$	0.884118	−	8.97660i	0.0462768	−	0.469857i
$366$	−0.849650	−	2.03868i	−0.0444119	−	0.106563i
$367$	−18.5466	−	7.68225i	−0.968124	−	0.401010i	−0.158111	−	0.987421i	$-0.550540\pi$
$367$	−18.5466	−	7.68225i	−0.968124	−	0.401010i	−0.810013	+	0.586411i	$0.800540\pi$
$368$	−10.5329	−	15.4704i	−0.549065	−	0.806450i
$369$	20.3166	−	8.41541i	1.05764	−	0.438089i
$370$	−6.32586	−	6.29839i	−0.328866	−	0.327438i
$371$	−5.94803	+	4.88142i	−0.308806	+	0.253431i
$372$	−1.37316	−	0.129213i	−0.0711948	−	0.00669936i
$373$	28.3572	+	8.60207i	1.46828	+	0.445398i	0.920340	−	0.391119i	$-0.127912\pi$
$373$	28.3572	+	8.60207i	1.46828	+	0.445398i	0.547941	+	0.836517i	$0.315412\pi$
$374$	4.26489	−	3.51567i	0.220532	−	0.181791i
$375$	−0.174029	−	0.260453i	−0.00898681	−	0.0134497i
$376$	0.683777	+	1.00902i	0.0352631	+	0.0520364i
$377$	−15.2903	−	10.2166i	−0.787489	−	0.526183i
$378$	−2.52358	−	2.06188i	−0.129799	−	0.106051i
$379$	−2.53629	+	3.09048i	−0.130281	+	0.158747i	−0.834065	−	0.551666i	$-0.813992\pi$
$379$	−2.53629	+	3.09048i	−0.130281	+	0.158747i	0.703784	+	0.710414i	$0.251492\pi$
$380$	2.37437	+	5.66240i	0.121802	+	0.290475i
$381$	−4.05777	−	2.16892i	−0.207886	−	0.111117i
$382$	16.7641	+	3.29668i	0.857725	+	0.168673i
$383$	30.0427			1.53511			0.767555	−	0.640983i	$-0.221473\pi$
$383$	30.0427			1.53511			0.767555	+	0.640983i	$0.221473\pi$
$384$	−3.40662	−	0.976979i	−0.173844	−	0.0498562i
$385$	−7.52122			−0.383317
$386$	20.9284	+	4.11559i	1.06523	+	0.209478i
$387$	13.5399	+	7.23724i	0.688273	+	0.367890i
$388$	−25.7995	+	10.8183i	−1.30977	+	0.549215i
$389$	−19.1087	+	23.2840i	−0.968849	+	1.18055i	0.0146979	+	0.999892i	$0.495321\pi$
$389$	−19.1087	+	23.2840i	−0.968849	+	1.18055i	−0.983547	+	0.180654i	$0.942179\pi$
$390$	−0.926015	−	0.756594i	−0.0468906	−	0.0383116i
$391$	2.51975	+	1.68364i	0.127429	+	0.0851456i
$392$	15.1280	+	2.90662i	0.764081	+	0.146806i
$393$	1.35111	+	2.02208i	0.0681544	+	0.102000i
$394$	−0.997631	+	0.822374i	−0.0502599	+	0.0414306i
$395$	9.92496	+	3.01070i	0.499379	+	0.151485i
$396$	3.28094	−	34.8669i	0.164873	−	1.75213i
$397$	−25.1604	+	20.6486i	−1.26276	+	1.03632i	−0.265371	+	0.964146i	$0.585495\pi$
$397$	−25.1604	+	20.6486i	−1.26276	+	1.03632i	−0.997392	+	0.0721766i	$0.977005\pi$
$398$	3.58993	+	3.57434i	0.179947	+	0.179165i
$399$	1.10742	−	0.458707i	0.0554402	−	0.0229641i
$400$	2.19325	−	3.34510i	0.109662	−	0.167255i
$401$	−11.0457	−	4.57530i	−0.551598	−	0.228479i	0.0894350	−	0.995993i	$-0.471494\pi$
$401$	−11.0457	−	4.57530i	−0.551598	−	0.228479i	−0.641033	+	0.767513i	$0.721494\pi$
$402$	−0.919938	−	2.20733i	−0.0458823	−	0.110092i
$403$	0.582485	−	5.91407i	0.0290157	−	0.294601i
$404$	−8.79896	+	29.4673i	−0.437765	+	1.46606i
$405$	3.83082	+	7.16696i	0.190355	+	0.356129i
$406$	−10.6029	−	5.63776i	−0.526215	−	0.279797i
$407$	−37.3567	−	7.43071i	−1.85170	−	0.368326i
$408$	0.570702	−	0.0599735i	0.0282540	−	0.00296913i
$409$	6.03684	+	30.3492i	0.298502	+	1.50067i	0.780864	+	0.624701i	$0.214779\pi$
$409$	6.03684	+	30.3492i	0.298502	+	1.50067i	−0.482362	+	0.875972i	$0.660221\pi$
$410$	9.44049	−	5.07249i	0.466233	−	0.250513i
$411$	−0.138542	−	1.40664i	−0.00683376	−	0.0693843i
$412$	−5.25093	+	27.0121i	−0.258695	+	1.33079i
$413$	3.47001	+	11.4391i	0.170748	+	0.562881i
$414$	18.8245	−	3.78703i	0.925174	−	0.186122i
$415$	6.91426	−	6.91426i	0.339407	−	0.339407i
$416$	4.27337	−	14.6597i	0.209519	−	0.718753i
$417$	2.55053	+	2.55053i	0.124900	+	0.124900i
$418$	21.8149	+	14.5077i	1.06700	+	0.709593i
$419$	22.6425	−	6.86852i	1.10616	−	0.335549i	0.316188	−	0.948696i	$-0.397597\pi$
$419$	22.6425	−	6.86852i	1.10616	−	0.335549i	0.789968	+	0.613148i	$0.210097\pi$
$420$	−0.651157	−	0.431002i	−0.0317732	−	0.0210308i
$421$	−16.1951	+	1.59508i	−0.789300	+	0.0777393i	−0.484631	−	0.874719i	$-0.661046\pi$
$421$	−16.1951	+	1.59508i	−0.789300	+	0.0777393i	−0.304669	+	0.952458i	$0.598546\pi$
$422$	3.12611	−	10.3867i	0.152177	−	0.505618i
$423$	−1.22651	+	0.243968i	−0.0596349	+	0.0118621i
$424$	−11.1649	−	13.4247i	−0.542213	−	0.651963i
$425$	−0.126358	+	0.635245i	−0.00612926	+	0.0308139i
$426$	1.67395	+	5.47536i	0.0811032	+	0.265282i
$427$	5.48060	−	2.92944i	0.265225	−	0.141766i
$428$	1.01714	+	9.88595i	0.0491654	+	0.477855i
$429$	−5.07768	−	0.500108i	−0.245153	−	0.0241454i
$430$	6.91875	+	2.84822i	0.333652	+	0.137353i
$431$	12.5398	−	30.2737i	0.604020	−	1.45823i	−0.265390	−	0.964141i	$-0.585501\pi$
$431$	12.5398	−	30.2737i	0.604020	−	1.45823i	0.869410	−	0.494092i	$-0.164499\pi$
$432$	4.64135	−	5.75696i	0.223307	−	0.276982i
$433$	9.52831	+	23.0034i	0.457901	+	1.10547i	0.969246	+	0.246096i	$0.0791478\pi$
$433$	9.52831	+	23.0034i	0.457901	+	1.10547i	−0.511344	+	0.859376i	$0.670852\pi$
$434$	−0.00844447	−	3.88066i	−0.000405348	−	0.186278i
$435$	−1.35378	−	1.64959i	−0.0649089	−	0.0790917i
$436$	−10.4680	+	19.7910i	−0.501327	+	0.947815i
$437$	−4.16976	+	13.7459i	−0.199467	+	0.657554i
$438$	0.383004	−	3.97742i	0.0183007	−	0.190048i
$439$	27.9309	−	18.6629i	1.33307	−	0.890730i	0.334409	−	0.942428i	$-0.391463\pi$
$439$	27.9309	−	18.6629i	1.33307	−	0.890730i	0.998663	+	0.0516984i	$0.0164634\pi$
$440$	−0.111416	−	17.0669i	−0.00531154	−	0.813631i
$441$	−8.78066	+	13.1412i	−0.418127	+	0.625771i
$442$	0.247705	+	2.46010i	0.0117821	+	0.117015i
$443$	−28.5412	−	23.4232i	−1.35603	−	1.11287i	−0.982707	−	0.185167i	$-0.940717\pi$
$443$	−28.5412	−	23.4232i	−1.35603	−	1.11287i	−0.373326	−	0.927700i	$-0.621783\pi$
$444$	−2.80838	−	2.78404i	−0.133280	−	0.132125i
$445$	4.57298	−	8.55545i	0.216780	−	0.405567i
$446$	21.1302	−	14.1853i	1.00054	−	0.671695i
$447$			5.55827i			0.262897i
$448$	1.81749	−	9.80446i	0.0858684	−	0.463217i
$449$		−	15.9088i		−	0.750780i	−0.926867	−	0.375390i	$-0.877509\pi$
$449$		−	15.9088i		−	0.750780i	0.926867	−	0.375390i	$-0.122491\pi$
$450$	2.28741	+	3.40728i	0.107830	+	0.160621i
$451$	21.5556	−	40.3278i	1.01502	−	1.89896i
$452$	−4.89281	+	0.0212940i	−0.230138	+	0.00100158i
$453$	−0.595161	−	0.488436i	−0.0279631	−	0.0229487i
$454$	−40.6179	+	4.08978i	−1.90629	+	0.191943i
$455$	1.86926	−	2.79755i	0.0876324	−	0.131151i
$456$	1.05729	+	2.50611i	0.0495119	+	0.117359i
$457$	4.12822	−	2.75839i	0.193110	−	0.129032i	−0.455256	−	0.890360i	$-0.650452\pi$
$457$	4.12822	−	2.75839i	0.193110	−	0.129032i	0.648367	+	0.761328i	$0.275452\pi$
$458$	−10.3184	−	0.993612i	−0.482149	−	0.0464284i
$459$	−0.347587	+	1.14584i	−0.0162240	+	0.0534833i
$460$	8.94296	−	2.75538i	0.416968	−	0.128470i
$461$	−1.90324	−	2.31910i	−0.0886426	−	0.108011i	0.726800	−	0.686849i	$-0.241007\pi$
$461$	−1.90324	−	2.31910i	−0.0886426	−	0.108011i	−0.815443	+	0.578837i	$0.803507\pi$
$462$	−3.33184	+	0.00725022i	−0.155011	+	0.000337311i
$463$	−5.22716	−	12.6195i	−0.242927	−	0.586477i	0.754644	−	0.656134i	$-0.227809\pi$
$463$	−5.22716	−	12.6195i	−0.242927	−	0.586477i	−0.997571	+	0.0696573i	$0.977809\pi$
$464$	12.6359	−	24.1433i	0.586608	−	1.12083i
$465$	0.263903	−	0.637118i	0.0122382	−	0.0295456i
$466$	−7.20103	+	17.4924i	−0.333581	+	0.810319i
$467$	11.0509	+	1.08842i	0.511377	+	0.0503662i	0.350415	−	0.936595i	$-0.386041\pi$
$467$	11.0509	+	1.08842i	0.511377	+	0.0503662i	0.160961	+	0.986961i	$0.448541\pi$
$468$	12.1535	+	9.88589i	0.561794	+	0.456975i
$469$	5.93399	−	3.17178i	0.274006	−	0.146459i
$470$	−0.582813	+	0.178180i	−0.0268832	+	0.00821885i
$471$	0.994066	−	4.99751i	0.0458042	−	0.230273i
$472$	−25.9058	+	8.04347i	−1.19241	+	0.370231i
$473$	31.3112	−	6.22818i	1.43969	−	0.286372i
$474$	4.39958	+	1.32415i	0.202080	+	0.0608203i
$475$	−3.05525	+	0.300916i	−0.140184	+	0.0138070i
$476$	0.321883	+	1.58220i	0.0147535	+	0.0725199i
$477$	17.1428	−	5.20021i	0.784915	−	0.238101i
$478$	−17.4571	+	26.2498i	−0.798468	+	1.20064i
$479$	7.68334	+	7.68334i	0.351061	+	0.351061i	0.860504	−	0.509443i	$-0.170149\pi$
$479$	7.68334	+	7.68334i	0.351061	+	0.351061i	−0.509443	+	0.860504i	$0.670149\pi$
$480$	0.968368	−	1.48397i	0.0441998	−	0.0677335i
$481$	12.0482	−	12.0482i	0.549351	−	0.549351i
$482$	5.07373	+	25.2204i	0.231102	+	1.14876i
$483$	−0.530299	−	1.74816i	−0.0241295	−	0.0795442i
$484$	−28.4192	−	42.1341i	−1.29178	−	1.91519i
$485$	−1.37106	−	13.9206i	−0.0622565	−	0.632101i
$486$	5.41637	+	10.0805i	0.245692	+	0.457260i
$487$	−7.36905	−	37.0467i	−0.333923	−	1.67875i	−0.674300	−	0.738457i	$-0.735555\pi$
$487$	−7.36905	−	37.0467i	−0.333923	−	1.67875i	0.340377	−	0.940289i	$-0.389445\pi$
$488$	6.72857	+	12.3930i	0.304588	+	0.561004i
$489$	2.07786	+	0.413312i	0.0939640	+	0.0186906i
$490$	−3.61608	+	6.80077i	−0.163358	+	0.307227i
$491$	−6.29024	−	11.7682i	−0.283874	−	0.531092i	0.699057	−	0.715066i	$-0.253604\pi$
$491$	−6.29024	−	11.7682i	−0.283874	−	0.531092i	−0.982931	+	0.183975i	$0.941104\pi$
$492$	4.17718	−	2.25618i	0.188322	−	0.101716i
$493$	−0.432491	+	4.39115i	−0.0194784	+	0.197767i
$494$	−10.8179	+	4.50851i	−0.486719	+	0.202848i
$495$	16.1775	+	6.70096i	0.727126	+	0.301186i
$496$	8.80573	−	0.0766482i	0.395389	−	0.00344161i
$497$	−14.8834	+	6.16492i	−0.667614	+	0.276535i
$498$	3.05630	−	3.06963i	0.136956	−	0.137553i
$499$	27.5352	−	22.5975i	1.23264	−	1.01160i	0.233412	−	0.972378i	$-0.425011\pi$
$499$	27.5352	−	22.5975i	1.23264	−	1.01160i	0.999230	−	0.0392260i	$-0.0124892\pi$
$500$	1.27550	+	1.54048i	0.0570422	+	0.0688926i
$501$	3.21734	+	0.975970i	0.143740	+	0.0436031i
$502$	2.52063	+	3.05781i	0.112501	+	0.136477i
$503$	1.32753	+	1.98679i	0.0591916	+	0.0885865i	0.859885	−	0.510488i	$-0.170535\pi$
$503$	1.32753	+	1.98679i	0.0591916	+	0.0885865i	−0.800693	+	0.599075i	$0.795535\pi$
$504$	8.54322	+	5.62808i	0.380545	+	0.250695i
$505$	−12.7851	−	8.54272i	−0.568929	−	0.380146i
$506$	25.2628	−	30.9198i	1.12307	−	1.37455i
$507$	−1.13537	+	1.38346i	−0.0504237	+	0.0614415i
$508$	27.1893	+	11.1238i	1.20633	+	0.493539i
$509$	−27.6770	−	14.7937i	−1.22676	−	0.655717i	−0.274672	−	0.961538i	$-0.588569\pi$
$509$	−27.6770	−	14.7937i	−1.22676	−	0.655717i	−0.952089	+	0.305821i	$0.901069\pi$
$510$	−0.0553633	+	0.281530i	−0.00245153	+	0.0124664i
$511$	11.2429			0.497356
$512$	22.2748	+	3.97894i	0.984418	+	0.175846i
$513$	−5.67565			−0.250586
$514$	2.50034	−	12.7146i	0.110285	−	0.560816i
$515$	−12.1342	−	6.48587i	−0.534697	−	0.285802i
$516$	3.06770	+	1.25507i	0.135048	+	0.0552514i
$517$	−1.64966	+	2.01012i	−0.0725519	+	0.0884048i
$518$	7.03989	−	8.61630i	0.309315	−	0.378578i
$519$	2.00996	+	1.34301i	0.0882276	+	0.0589518i
$520$	6.37578	+	4.20022i	0.279597	+	0.184192i
$521$	14.4802	+	21.6711i	0.634388	+	0.949429i	0.999827	+	0.0185938i	$0.00591893\pi$
$521$	14.4802	+	21.6711i	0.634388	+	0.949429i	−0.365439	+	0.930835i	$0.619081\pi$
$522$	17.7832	+	21.5730i	0.778349	+	0.944223i
$523$	−20.8075	−	6.31189i	−0.909849	−	0.276000i	−0.199540	−	0.979890i	$-0.563945\pi$
$523$	−20.8075	−	6.31189i	−0.909849	−	0.276000i	−0.710309	+	0.703890i	$0.751445\pi$
$524$	−9.90263	−	11.9599i	−0.432598	−	0.522469i
$525$	0.301813	−	0.247692i	0.0131722	−	0.0108101i
$526$	−12.4941	+	12.5486i	−0.544768	+	0.547144i
$527$	−1.31736	+	0.545668i	−0.0573851	+	0.0237697i
$528$	−0.0658083	−	7.56039i	−0.00286394	−	0.329024i
$529$	−1.02350	−	0.423947i	−0.0445000	−	0.0184325i
$530$	8.05852	−	3.35851i	0.350040	−	0.145884i
$531$	2.72783	−	27.6961i	0.118378	−	1.20191i
$532$	−6.73376	+	3.63703i	−0.291945	+	0.157685i
$533$	9.64282	+	18.0404i	0.417677	+	0.781418i
$534$	2.01755	−	3.79441i	0.0873080	−	0.164200i
$535$	−4.87359	−	0.969417i	−0.210704	−	0.0419116i
$536$	7.28519	+	13.4182i	0.314672	+	0.579578i
$537$	−0.0716375	−	0.360146i	−0.00309139	−	0.0155414i
$538$	−14.5100	−	27.0048i	−0.625570	−	1.16426i
$539$	3.22129	+	32.7063i	0.138751	+	1.40876i
$540$	2.06756	+	3.06535i	0.0889734	+	0.131912i
$541$	4.07809	+	13.4437i	0.175331	+	0.577988i	0.999925	+	0.0122634i	$0.00390366\pi$
$541$	4.07809	+	13.4437i	0.175331	+	0.577988i	−0.824594	+	0.565725i	$0.808596\pi$
$542$	2.03314	+	10.1063i	0.0873309	+	0.434103i
$543$	2.16044	−	2.16044i	0.0927133	−	0.0927133i
$544$	−3.58550	+	0.753843i	−0.153727	+	0.0323208i
$545$	−7.91566	−	7.91566i	−0.339070	−	0.339070i
$546$	0.825373	−	1.24110i	0.0353227	−	0.0531140i
$547$	39.6448	−	12.0261i	1.69509	−	0.514200i	0.712769	−	0.701399i	$-0.247441\pi$
$547$	39.6448	−	12.0261i	1.69509	−	0.514200i	0.982322	+	0.187198i	$0.0599407\pi$
$548$	1.79911	+	8.84341i	0.0768541	+	0.377772i
$549$	−14.3983	+	1.41811i	−0.614504	+	0.0605234i
$550$	8.17153	+	2.45940i	0.348435	+	0.104869i
$551$	−20.5128	+	4.08025i	−0.873874	+	0.173824i
$552$	3.95901	−	1.22923i	0.168507	−	0.0523196i
$553$	−2.52203	+	12.6791i	−0.107247	+	0.539170i
$554$	−19.3879	+	5.92737i	−0.823714	+	0.251830i
$555$	1.74377	−	0.932063i	0.0740188	−	0.0395639i
$556$	−17.8658	−	14.5324i	−0.757678	−	0.616312i
$557$	−21.5605	−	2.12353i	−0.913548	−	0.0899767i	−0.369691	−	0.929155i	$-0.620537\pi$
$557$	−21.5605	−	2.12353i	−0.913548	−	0.0899767i	−0.543857	+	0.839178i	$0.683037\pi$
$558$	−3.43928	+	8.35452i	−0.145596	+	0.353675i
$559$	−5.46522	+	13.1942i	−0.231154	+	0.558056i
$560$	4.41733	+	2.31190i	0.186666	+	0.0976958i
$561$	0.468497	+	1.13105i	0.0197800	+	0.0477531i
$562$	5.58851	−	0.0121608i	0.235737	−	0.000512973i
$563$	−20.1353	−	24.5350i	−0.848603	−	1.03403i	−0.998969	−	0.0453954i	$-0.985545\pi$
$563$	−20.1353	−	24.5350i	−0.848603	−	1.03403i	0.150366	−	0.988630i	$-0.451955\pi$
$564$	−0.258010	+	0.0794944i	−0.0108642	+	0.00334732i
$565$	0.710160	−	2.34109i	0.0298767	−	0.0984902i
$566$	36.8225	+	3.54582i	1.54777	+	0.149042i
$567$	−8.42213	+	5.62749i	−0.353696	+	0.236332i
$568$	−14.2097	−	33.6816i	−0.596225	−	1.41325i
$569$	9.14227	−	13.6824i	0.383264	−	0.573595i	−0.588809	−	0.808272i	$-0.700403\pi$
$569$	9.14227	−	13.6824i	0.383264	−	0.573595i	0.972073	+	0.234677i	$0.0754032\pi$
$570$	−1.35316	+	0.136249i	−0.0566778	+	0.00570683i
$571$	18.5683	+	15.2386i	0.777057	+	0.637714i	0.936967	−	0.349417i	$-0.113620\pi$
$571$	18.5683	+	15.2386i	0.777057	+	0.637714i	−0.159910	+	0.987132i	$0.551120\pi$
$572$	32.5765	−	0.141776i	1.36209	−	0.00592796i
$573$	−1.78391	+	3.33746i	−0.0745239	+	0.139424i
$574$	7.44546	+	11.0906i	0.310767	+	0.462913i
$575$			4.67891i			0.195124i
$576$	−12.6445	+	19.4693i	−0.526853	+	0.811222i
$577$		−	1.62108i		−	0.0674864i	−0.999431	−	0.0337432i	$-0.989257\pi$
$577$		−	1.62108i		−	0.0674864i	0.999431	−	0.0337432i	$-0.0107428\pi$
$578$	−19.4682	+	13.0696i	−0.809771	+	0.543624i
$579$	−2.22704	+	4.16650i	−0.0925527	+	0.173154i
$580$	9.67619	+	9.59233i	0.401782	+	0.398300i
$581$	9.42141	+	7.73195i	0.390866	+	0.320775i
$582$	−0.620787	−	6.16539i	−0.0257325	−	0.255564i
$583$	20.6954	−	30.9729i	0.857118	−	1.28277i
$584$	0.166547	+	25.5120i	0.00689177	+	1.05569i
$585$	−6.51308	+	4.35190i	−0.269283	+	0.179929i
$586$	−0.0934694	+	0.970660i	−0.00386119	+	0.0400976i
$587$	10.2006	−	33.6270i	0.421025	−	1.38793i	−0.448385	−	0.893841i	$-0.648000\pi$
$587$	10.2006	−	33.6270i	0.421025	−	1.38793i	0.869409	−	0.494092i	$-0.164500\pi$
$588$	−1.59534	+	3.01617i	−0.0657908	+	0.124385i
$589$	−4.28769	−	5.22457i	−0.176671	−	0.215274i
$590$	−0.0295132	−	13.5628i	−0.00121504	−	0.558373i
$591$	−0.109590	−	0.264572i	−0.00450791	−	0.0108831i
$592$	19.6561	+	15.8470i	0.807859	+	0.651309i
$593$	−2.59360	+	6.26151i	−0.106506	+	0.257129i	−0.968144	−	0.250395i	$-0.919439\pi$
$593$	−2.59360	+	6.26151i	−0.106506	+	0.257129i	0.861637	+	0.507525i	$0.169439\pi$
$594$	14.5885	+	6.00561i	0.598574	+	0.246413i
$595$	−0.803417	−	0.0791296i	−0.0329369	−	0.00324400i
$596$	−3.63215	−	35.3021i	−0.148778	−	1.44603i
$597$	−0.989589	+	0.528946i	−0.0405012	+	0.0216483i
$598$	5.22213	+	17.0812i	0.213549	+	0.698501i
$599$	−7.01013	+	35.2423i	−0.286426	+	1.43996i	0.522796	+	0.852458i	$0.324889\pi$
$599$	−7.01013	+	35.2423i	−0.286426	+	1.43996i	−0.809222	+	0.587503i	$0.800111\pi$
$600$	0.566523	+	0.681194i	0.0231282	+	0.0278096i
$601$	19.2881	−	3.83664i	0.786778	−	0.156500i	0.214679	−	0.976685i	$-0.431129\pi$
$601$	19.2881	−	3.83664i	0.786778	−	0.156500i	0.572099	+	0.820185i	$0.306129\pi$
$602$	−2.68775	+	8.93023i	−0.109545	+	0.363969i
$603$	−15.5894	+	1.53542i	−0.634850	+	0.0625272i
$604$	4.09921	+	2.71327i	0.166794	+	0.110401i
$605$	24.3171	−	7.37651i	0.988630	−	0.299898i
$606$	−5.67193	−	3.77204i	−0.230407	−	0.153229i
$607$	4.62016	+	4.62016i	0.187526	+	0.187526i	0.794626	−	0.607099i	$-0.207667\pi$
$607$	4.62016	+	4.62016i	0.187526	+	0.187526i	−0.607099	+	0.794626i	$0.707667\pi$
$608$	−8.35277	−	15.2261i	−0.338750	−	0.617500i
$609$	1.88081	−	1.88081i	0.0762143	−	0.0762143i
$610$	−6.91239	+	1.39060i	−0.279874	+	0.0563039i
$611$	−0.337678	−	1.11318i	−0.0136610	−	0.0450342i
$612$	0.717299	−	3.68996i	0.0289951	−	0.149158i
$613$	2.70115	+	27.4253i	0.109099	+	1.10770i	0.881378	+	0.472413i	$0.156617\pi$
$613$	2.70115	+	27.4253i	0.109099	+	1.10770i	−0.772279	+	0.635283i	$0.780883\pi$
$614$	11.4542	−	6.15447i	0.462253	−	0.248374i
$615$	0.463100	+	2.32816i	0.0186740	+	0.0938805i
$616$	21.1567	−	2.22330i	0.852428	−	0.0895793i
$617$	17.3749	+	3.45609i	0.699488	+	0.139137i	0.532009	−	0.846739i	$-0.321437\pi$
$617$	17.3749	+	3.45609i	0.699488	+	0.139137i	0.167479	+	0.985876i	$0.446437\pi$
$618$	−5.38162	−	2.86150i	−0.216480	−	0.115106i
$619$	−15.1505	−	28.3446i	−0.608950	−	1.13927i	−0.977753	−	0.209758i	$-0.932732\pi$
$619$	−15.1505	−	28.3446i	−0.608950	−	1.13927i	0.368803	−	0.929508i	$-0.379768\pi$
$620$	−1.25978	+	4.21896i	−0.0505941	+	0.169438i
$621$	−0.847850	+	8.60837i	−0.0340231	+	0.345442i
$622$	13.1121	+	31.4615i	0.525746	+	1.26149i
$623$	11.1712	+	4.62725i	0.447563	+	0.185387i
$624$	2.82847	+	1.85452i	0.113230	+	0.0742402i
$625$	−0.923880	+	0.382683i	−0.0369552	+	0.0153073i
$626$	34.1062	+	33.9581i	1.36316	+	1.35724i
$627$	−4.48569	+	3.68131i	−0.179141	+	0.147017i
$628$	−3.04788	+	32.3901i	−0.121624	+	1.29251i
$629$	−3.91227	−	1.18677i	−0.155992	−	0.0473197i
$630$	−3.94705	+	3.25366i	−0.157254	+	0.129629i
$631$	−2.17947	−	3.26181i	−0.0867633	−	0.129850i	0.785549	−	0.618799i	$-0.212381\pi$
$631$	−2.17947	−	3.26181i	−0.0867633	−	0.129850i	−0.872313	+	0.488949i	$0.837381\pi$
$632$	−28.8083	−	5.53507i	−1.14593	−	0.220173i
$633$	1.99766	+	1.33479i	0.0793999	+	0.0530533i
$634$	−26.9513	−	22.0204i	−1.07037	−	0.874542i
$635$	−9.31823	+	11.3543i	−0.369783	+	0.450582i
$636$	3.56663	−	1.49556i	0.141426	−	0.0593030i
$637$	−12.9658	−	6.93038i	−0.513725	−	0.274592i
$638$	57.0429	+	11.2176i	2.25835	+	0.444107i
$639$	37.5057			1.48370
$640$	−5.18065	+	10.0579i	−0.204783	+	0.397572i
$641$	44.7672			1.76820			0.884099	−	0.467299i	$-0.154773\pi$
$641$	44.7672			1.76820			0.884099	+	0.467299i	$0.154773\pi$
$642$	−2.15990	−	0.424747i	−0.0852444	−	0.0167634i
$643$	18.5446	+	9.91228i	0.731327	+	0.390902i	0.794632	−	0.607092i	$-0.207664\pi$
$643$	18.5446	+	9.91228i	0.731327	+	0.390902i	−0.0633048	+	0.997994i	$0.520164\pi$
$644$	4.51045	+	10.7565i	0.177736	+	0.423867i
$645$	−1.05135	+	1.28108i	−0.0413970	+	0.0504423i
$646$	2.17763	+	1.77922i	0.0856777	+	0.0700025i
$647$	11.2677	+	7.52883i	0.442979	+	0.295989i	0.756985	−	0.653432i	$-0.226671\pi$
$647$	11.2677	+	7.52883i	0.442979	+	0.295989i	−0.314007	+	0.949421i	$0.601671\pi$
$648$	−12.8944	−	19.0278i	−0.506541	−	0.747483i
$649$	−32.1509	−	48.1173i	−1.26203	−	1.88877i
$650$	−2.94567	+	2.42820i	−0.115539	+	0.0952417i
$651$	0.822544	+	0.249516i	0.0322381	+	0.00977931i
$652$	−13.4671	−	1.26724i	−0.527414	−	0.0496291i
$653$	−2.88046	+	2.36393i	−0.112721	+	0.0925079i	−0.689065	−	0.724699i	$-0.741979\pi$
$653$	−2.88046	+	2.36393i	−0.112721	+	0.0925079i	0.576344	+	0.817207i	$0.304479\pi$
$654$	−3.51421	−	3.49895i	−0.137416	−	0.136820i
$655$	7.17273	−	2.97104i	0.280262	−	0.116088i
$656$	−25.0561	+	17.0592i	−0.978275	+	0.666052i
$657$	−24.1826	−	10.0168i	−0.943452	−	0.390791i
$658$	−0.292225	−	0.701173i	−0.0113921	−	0.0273346i
$659$	−1.32556	+	13.4586i	−0.0516365	+	0.524274i	0.934222	+	0.356693i	$0.116096\pi$
$659$	−1.32556	+	13.4586i	−0.0516365	+	0.524274i	−0.985858	+	0.167581i	$0.946404\pi$
$660$	3.62230	+	1.08162i	0.140998	+	0.0421020i
$661$	−1.38502	−	2.59119i	−0.0538711	−	0.100786i	0.853545	−	0.521019i	$-0.174448\pi$
$661$	−1.38502	−	2.59119i	−0.0538711	−	0.100786i	−0.907416	+	0.420234i	$0.861948\pi$
$662$	−14.7438	−	7.83952i	−0.573034	−	0.304692i
$663$	−0.537136	−	0.106843i	−0.0208606	−	0.00414944i
$664$	−17.4055	+	21.4932i	−0.675464	+	0.834100i
$665$	−0.746533	−	3.75307i	−0.0289493	−	0.145538i
$666$	−22.8189	+	12.2609i	−0.884213	+	0.475098i
$667$	3.12431	+	31.7217i	0.120974	+	1.22827i
$668$	−21.0720	−	4.09623i	−0.815300	−	0.158488i
$669$	1.63637	+	5.39438i	0.0632657	+	0.208559i
$670$	−7.48422	+	1.50564i	−0.289141	+	0.0581680i
$671$	−21.2731	+	21.2731i	−0.821240	+	0.821240i
$672$	1.95907	+	1.01990i	0.0755728	+	0.0393434i
$673$	−31.8009	−	31.8009i	−1.22584	−	1.22584i	−0.965525	−	0.260311i	$-0.916175\pi$
$673$	−31.8009	−	31.8009i	−1.22584	−	1.22584i	−0.260311	−	0.965525i	$-0.583825\pi$
$674$	19.3791	+	12.8878i	0.746455	+	0.496419i
$675$	−1.76912	+	0.536657i	−0.0680935	+	0.0206559i
$676$	6.30703	−	9.52865i	0.242578	−	0.366487i
$677$	−0.798559	+	0.0786512i	−0.0306911	+	0.00302281i	−0.113351	−	0.993555i	$-0.536158\pi$
$677$	−0.798559	+	0.0786512i	−0.0306911	+	0.00302281i	0.0826599	+	0.996578i	$0.473658\pi$
$678$	0.312339	−	1.03777i	0.0119953	−	0.0398552i
$679$	17.1001	−	3.40141i	0.656240	−	0.130534i
$680$	0.167657	−	1.82426i	0.00642934	−	0.0699570i
$681$	1.76405	−	8.86849i	0.0675986	−	0.339841i
$682$	5.49265	+	17.9660i	0.210325	+	0.687955i
$683$	4.31205	−	2.30484i	0.164996	−	0.0881921i	−0.386832	−	0.922150i	$-0.626431\pi$
$683$	4.31205	−	2.30484i	0.164996	−	0.0881921i	0.551828	+	0.833958i	$0.313931\pi$
$684$	17.7242	−	1.82360i	0.677700	−	0.0697269i
$685$	−4.49055	−	0.442281i	−0.171575	−	0.0168987i
$686$	−20.2878	−	8.35180i	−0.774591	−	0.318873i
$687$	0.878670	−	2.12130i	0.0335233	−	0.0809325i
$688$	−20.3040	−	5.96665i	−0.774081	−	0.227476i
$689$	6.37703	+	15.3955i	0.242946	+	0.586523i
$690$	0.00451032	+	2.07272i	0.000171705	+	0.0789071i
$691$	−20.1199	−	24.5162i	−0.765397	−	0.932639i	0.233817	−	0.972281i	$-0.424878\pi$
$691$	−20.1199	−	24.5162i	−0.765397	−	0.932639i	−0.999214	+	0.0396417i	$0.987378\pi$
$692$	−13.6434	−	7.21641i	−0.518646	−	0.274327i
$693$	−6.33565	+	20.8859i	−0.240672	+	0.793388i
$694$	−3.20205	+	33.2526i	−0.121548	+	1.26225i
$695$	9.57434	−	6.39737i	0.363176	−	0.242666i
$696$	4.29573	+	4.24001i	0.162829	+	0.160717i
$697$	2.72686	−	4.08103i	0.103287	−	0.154580i
$698$	−0.0505673	−	0.502213i	−0.00191400	−	0.0190090i
$699$	−3.23889	−	2.65809i	−0.122506	−	0.100538i
$700$	−1.75504	+	1.77038i	−0.0663342	+	0.0669142i
$701$	10.5812	−	19.7961i	0.399647	−	0.747687i	−0.598942	−	0.800793i	$-0.704412\pi$
$701$	10.5812	−	19.7961i	0.399647	−	0.747687i	0.998589	+	0.0531055i	$0.0169120\pi$
$702$	−5.85952	+	3.93368i	−0.221153	+	0.148467i
$703$		−	19.3785i		−	0.730873i
$704$	5.35843	+	47.9751i	0.201954	+	1.80813i
$705$		−	0.134989i		−	0.00508400i
$706$	0.0737476	+	0.109853i	0.00277553	+	0.00413437i
$707$	9.03471	−	16.9027i	0.339785	−	0.635693i
$708$	−0.0261483	−	6.00821i	−0.000982713	−	0.225802i
$709$	1.36111	+	1.11703i	0.0511174	+	0.0419509i	0.659605	−	0.751612i	$-0.270724\pi$
$709$	1.36111	+	1.11703i	0.0511174	+	0.0419509i	−0.608488	+	0.793563i	$0.708224\pi$
$710$	18.1862	−	1.83115i	0.682517	−	0.0687219i
$711$	16.7210	−	25.0247i	0.627086	−	0.938501i
$712$	−10.3345	+	25.4177i	−0.387302	+	0.952570i
$713$	−8.56471	+	5.72276i	−0.320751	+	0.214319i
$714$	−0.355984	−	0.0342794i	−0.0133224	−	0.00128287i
$715$	−4.72828	+	15.5871i	−0.176828	+	0.582923i
$716$	0.690333	+	2.24057i	0.0257990	+	0.0837342i
$717$	−4.42972	−	5.39763i	−0.165431	−	0.201578i
$718$	16.1888	−	0.0352274i	0.604159	−	0.00131467i
$719$	−2.83544	−	6.84536i	−0.105744	−	0.255289i	0.862147	−	0.506658i	$-0.169119\pi$
$719$	−2.83544	−	6.84536i	−0.105744	−	0.255289i	−0.967891	+	0.251369i	$0.919119\pi$
$720$	−7.44155	−	8.90830i	−0.277330	−	0.331993i
$721$	6.56284	−	15.8441i	0.244413	−	0.590065i
$722$	5.15466	−	12.5215i	0.191837	−	0.466000i
$723$	−5.67072	−	0.558517i	−0.210896	−	0.0207715i
$724$	−12.3098	+	15.1333i	−0.457489	+	0.562425i
$725$	−6.00810	+	3.21140i	−0.223135	+	0.119268i
$726$	10.7652	−	3.29118i	0.399533	−	0.122147i
$727$	0.134717	−	0.677270i	0.00499639	−	0.0251185i	−0.978207	−	0.207634i	$-0.933424\pi$
$727$	0.134717	−	0.677270i	0.00499639	−	0.0251185i	0.983203	+	0.182515i	$0.0584238\pi$
$728$	−4.43115	+	8.42189i	−0.164229	+	0.312136i
$729$	21.4252	−	4.26173i	0.793524	−	0.157842i
$730$	−12.2150	−	3.67637i	−0.452097	−	0.136069i
$731$	3.41018	−	0.335874i	0.126130	−	0.0124227i
$732$	−3.06080	+	0.622690i	−0.113130	+	0.0230153i
$733$	35.3317	−	10.7178i	1.30501	−	0.395869i	0.440166	−	0.897916i	$-0.354920\pi$
$733$	35.3317	−	10.7178i	1.30501	−	0.395869i	0.864840	+	0.502047i	$0.167420\pi$
$734$	−15.7212	+	23.6396i	−0.580279	+	0.872553i
$735$	−1.20636	−	1.20636i	−0.0444972	−	0.0444972i
$736$	−24.3415	+	10.3943i	−0.897240	+	0.383138i
$737$	−23.0330	+	23.0330i	−0.848430	+	0.848430i
$738$	−6.13353	−	30.4885i	−0.225778	−	1.12230i
$739$	14.0339	+	46.2635i	0.516245	+	1.70183i	0.695933	+	0.718107i	$0.254991\pi$
$739$	14.0339	+	46.2635i	0.516245	+	1.70183i	−0.179689	+	0.983724i	$0.557509\pi$
$740$	−10.4661	+	7.05929i	−0.384741	+	0.259505i
$741$	−0.254442	−	2.58339i	−0.00934716	−	0.0949033i
$742$	5.15054	+	9.58576i	0.189082	+	0.351904i
$743$	−8.24284	−	41.4396i	−0.302401	−	1.52027i	−0.770986	−	0.636852i	$-0.780236\pi$
$743$	−8.24284	−	41.4396i	−0.302401	−	1.52027i	0.468585	−	0.883418i	$-0.344764\pi$
$744$	−0.554008	+	1.87018i	−0.0203109	+	0.0685642i
$745$	17.4033	+	3.46173i	0.637606	+	0.126828i
$746$	19.6747	−	37.0022i	0.720341	−	1.35475i
$747$	−13.3760	−	25.0247i	−0.489402	−	0.915607i
$748$	−3.71466	−	6.87748i	−0.135821	−	0.251466i
$749$	0.607082	−	6.16381i	0.0221823	−	0.225221i
$750$	−0.408903	+	0.170417i	−0.0149310	+	0.00622273i
$751$	8.49157	+	3.51732i	0.309862	+	0.128349i	0.532195	−	0.846622i	$-0.321367\pi$
$751$	8.49157	+	3.51732i	0.309862	+	0.128349i	−0.222333	+	0.974971i	$0.571367\pi$
$752$	1.58675	−	0.673492i	0.0578627	−	0.0245597i
$753$	−0.810932	+	0.335899i	−0.0295520	+	0.0122408i
$754$	−18.3494	+	18.4294i	−0.668245	+	0.671160i
$755$	−1.89999	+	1.55928i	−0.0691478	+	0.0567481i
$756$	−3.54977	+	2.93917i	−0.129104	+	0.106896i
$757$	29.8625	+	9.05870i	1.08537	+	0.329244i	0.781778	−	0.623557i	$-0.214313\pi$
$757$	29.8625	+	9.05870i	1.08537	+	0.329244i	0.303594	+	0.952801i	$0.401813\pi$
$758$	3.59636	+	4.36278i	0.130626	+	0.158463i
$759$	4.91342	+	7.35345i	0.178346	+	0.266913i
$760$	8.50528	−	1.74960i	0.308519	−	0.0634647i
$761$	43.2375	+	28.8904i	1.56736	+	1.04728i	0.969318	+	0.245810i	$0.0790539\pi$
$761$	43.2375	+	28.8904i	1.56736	+	1.04728i	0.598041	+	0.801466i	$0.295946\pi$
$762$	−4.11696	+	5.03885i	−0.149142	+	0.182538i
$763$	8.85179	−	10.7859i	0.320456	−	0.390477i
$764$	9.14918	−	22.3629i	0.331006	−	0.809060i
$765$	1.65759	+	0.885998i	0.0599301	+	0.0320333i
$766$	8.19806	−	41.6883i	0.296208	−	1.50626i
$767$	25.8879			0.934760
$768$	−2.28529	+	4.46056i	−0.0824634	+	0.160957i
$769$	−50.9206			−1.83624			−0.918121	−	0.396300i	$-0.870294\pi$
$769$	−50.9206			−1.83624			−0.918121	+	0.396300i	$0.870294\pi$
$770$	−2.05239	+	10.4367i	−0.0739631	+	0.376113i
$771$	2.53127	+	1.35299i	0.0911615	+	0.0487268i
$772$	11.4219	−	27.9179i	0.411082	−	1.00479i
$773$	20.4483	−	24.9163i	0.735474	−	0.896178i	−0.262153	−	0.965026i	$-0.584433\pi$
$773$	20.4483	−	24.9163i	0.735474	−	0.896178i	0.997627	+	0.0688486i	$0.0219325\pi$
$774$	13.7374	−	16.8136i	0.493782	−	0.604352i
$775$	−1.83049	−	1.22310i	−0.0657533	−	0.0439349i
$776$	7.97167	+	38.7524i	0.286166	+	1.39113i
$777$	1.36920	+	2.04916i	0.0491199	+	0.0735131i
$778$	27.0954	+	32.8697i	0.971415	+	1.17843i
$779$	22.2630	+	6.75342i	0.797656	+	0.241966i
$780$	−1.30257	+	1.07851i	−0.0466395	+	0.0386169i
$781$	60.2867	−	49.4760i	2.15723	−	1.77039i
$782$	3.02388	−	3.03707i	0.108134	−	0.108605i
$783$	−11.6358	+	4.81970i	−0.415829	+	0.172242i
$784$	8.16148	−	20.1991i	0.291481	−	0.721395i
$785$	−15.0284	−	6.22496i	−0.536386	−	0.222178i
$786$	3.17460	−	1.32306i	0.113234	−	0.0471921i
$787$	−5.01630	+	50.9314i	−0.178812	+	1.81551i	0.318485	+	0.947928i	$0.396826\pi$
$787$	−5.01630	+	50.9314i	−0.178812	+	1.81551i	−0.497297	+	0.867580i	$0.665674\pi$
$788$	0.868923	+	1.60876i	0.0309541	+	0.0573097i
$789$	−1.84893	−	3.45910i	−0.0658236	−	0.123147i
$790$	6.88609	−	12.9507i	0.244996	−	0.460764i
$791$	2.99073	+	0.594892i	0.106338	+	0.0211519i
$792$	−47.4872	−	14.0672i	−1.68739	−	0.499857i
$793$	−2.62558	−	13.1997i	−0.0932370	−	0.468734i
$794$	21.7870	+	40.5481i	0.773191	+	1.43900i
$795$	0.189541	+	1.92444i	0.00672231	+	0.0682528i
$796$	5.93950	−	4.00615i	0.210520	−	0.141994i
$797$	12.1751	+	40.1358i	0.431263	+	1.42168i	0.856286	+	0.516501i	$0.172766\pi$
$797$	12.1751	+	40.1358i	0.431263	+	1.42168i	−0.425023	+	0.905182i	$0.639734\pi$
$798$	−0.334326	−	1.66186i	−0.0118350	−	0.0588294i
$799$	−0.197365	+	0.197365i	−0.00698226	+	0.00698226i
$800$	−4.04328	−	3.95624i	−0.142952	−	0.139874i
$801$	−19.9057	−	19.9057i	−0.703333	−	0.703333i
$802$	−9.36302	+	14.0790i	−0.330620	+	0.497146i
$803$	−52.0848	+	15.7997i	−1.83803	+	0.557561i
$804$	−3.31400	+	0.674203i	−0.116876	+	0.0237773i
$805$	−5.80388	+	0.571632i	−0.204560	+	0.0201474i
$806$	−8.04764	−	2.42211i	−0.283466	−	0.0853153i
$807$	6.65975	−	1.32471i	0.234434	−	0.0466319i
$808$	38.4889	+	20.2508i	1.35404	+	0.712422i
$809$	3.13331	−	15.7522i	0.110161	−	0.553818i	−0.885803	−	0.464062i	$-0.846391\pi$
$809$	3.13331	−	15.7522i	0.110161	−	0.553818i	0.995964	−	0.0897556i	$-0.0286086\pi$
$810$	10.9905	−	3.36006i	0.386167	−	0.118061i
$811$	41.7563	−	22.3192i	1.46626	−	0.783733i	0.471109	−	0.882075i	$-0.343854\pi$
$811$	41.7563	−	22.3192i	1.46626	−	0.783733i	0.995153	+	0.0983423i	$0.0313540\pi$
$812$	−10.7165	+	13.1746i	−0.376076	+	0.462338i
$813$	−2.27237	−	0.223809i	−0.0796955	−	0.00784932i
$814$	−20.5050	+	49.8098i	−0.718701	+	1.74583i
$815$	2.58821	−	6.24849i	0.0906609	−	0.218875i
$816$	0.0725121	−	0.808293i	0.00253843	−	0.0282959i
$817$	6.21570	+	15.0060i	0.217460	+	0.524994i
$818$	43.7611	−	0.0952257i	1.53007	−	0.00332949i
$819$	−6.19397	−	7.54737i	−0.216435	−	0.263727i
$820$	−4.46265	−	14.4842i	−0.155843	−	0.505809i
$821$	−14.4559	+	47.6546i	−0.504513	+	1.66316i	0.221254	+	0.975216i	$0.428985\pi$
$821$	−14.4559	+	47.6546i	−0.504513	+	1.66316i	−0.725767	+	0.687941i	$0.758515\pi$
$822$	−1.98971	−	0.191598i	−0.0693990	−	0.00668276i
$823$	−5.09702	+	3.40572i	−0.177671	+	0.118716i	−0.641226	−	0.767352i	$-0.721574\pi$
$823$	−5.09702	+	3.40572i	−0.177671	+	0.118716i	0.463555	+	0.886068i	$0.346574\pi$
$824$	36.0500	+	14.6574i	1.25586	+	0.510616i
$825$	−1.05012	+	1.57162i	−0.0365605	+	0.0547167i
$826$	16.8202	−	1.69361i	0.585250	−	0.0589282i
$827$	−22.0684	−	18.1111i	−0.767395	−	0.629785i	0.167027	−	0.985952i	$-0.446583\pi$
$827$	−22.0684	−	18.1111i	−0.767395	−	0.629785i	−0.934422	+	0.356168i	$0.884083\pi$
$828$	−0.118181	−	27.1550i	−0.00410708	−	0.943701i
$829$	−9.15367	+	17.1253i	−0.317920	+	0.594787i	−0.989226	−	0.146393i	$-0.953234\pi$
$829$	−9.15367	+	17.1253i	−0.317920	+	0.594787i	0.671306	+	0.741180i	$0.265734\pi$
$830$	−7.70771	−	11.4812i	−0.267539	−	0.398520i
$831$		−	4.49057i		−	0.155776i
$832$	−19.1763	−	9.93025i	−0.664818	−	0.344269i
$833$			3.52757i			0.122223i
$834$	4.23520	−	2.84322i	0.146653	−	0.0984526i
$835$	5.05960	−	9.46585i	0.175095	−	0.327579i
$836$	26.0842	−	26.3122i	0.902141	−	0.910028i
$837$	−3.14615	−	2.58198i	−0.108747	−	0.0892463i
$838$	−3.35232	−	33.2938i	−0.115804	−	1.15012i
$839$	5.79664	−	8.67528i	0.200122	−	0.299504i	−0.717812	−	0.696237i	$-0.754856\pi$
$839$	5.79664	−	8.67528i	0.200122	−	0.299504i	0.917934	+	0.396733i	$0.129856\pi$
$840$	−0.775763	+	0.785958i	−0.0267664	+	0.0271181i
$841$	−14.4762	+	9.67270i	−0.499180	+	0.333541i
$842$	−2.20593	+	22.9082i	−0.0760215	+	0.789467i
$843$	−0.359326	+	1.18454i	−0.0123759	+	0.0407977i
$844$	−13.5599	−	7.17224i	−0.466752	−	0.246879i
$845$	3.62457	+	4.41655i	0.124689	+	0.151934i
$846$	0.00384837	+	1.76852i	0.000132310	+	0.0608031i
$847$	12.1209	+	29.2626i	0.416481	+	1.00547i
$848$	−21.6753	+	11.8294i	−0.744334	+	0.406224i
$849$	−3.13563	+	7.57008i	−0.107615	+	0.259805i
$850$	0.847008	+	0.348685i	0.0290521	+	0.0119598i
$851$	−29.3917	−	2.89483i	−1.00753	−	0.0992334i
$852$	8.05460	−	0.828718i	0.275946	−	0.0283914i
$853$	−36.5444	+	19.5334i	−1.25126	+	0.668811i	−0.957875	−	0.287184i	$-0.907281\pi$
$853$	−36.5444	+	19.5334i	−1.25126	+	0.668811i	−0.293382	+	0.955995i	$0.594781\pi$
$854$	−2.56945	−	8.40447i	−0.0879249	−	0.287595i
$855$	−1.73803	+	8.73768i	−0.0594395	+	0.298822i
$856$	13.9957	+	1.28626i	0.478362	+	0.0439634i
$857$	41.4037	−	8.23571i	1.41432	−	0.281326i	0.571980	−	0.820267i	$-0.306175\pi$
$857$	41.4037	−	8.23571i	1.41432	−	0.281326i	0.842344	+	0.538941i	$0.181175\pi$
$858$	−2.07957	+	6.90951i	−0.0709953	+	0.235887i
$859$	−26.0274	+	2.56348i	−0.888044	+	0.0874647i	−0.531742	−	0.846906i	$-0.678462\pi$
$859$	−26.0274	+	2.56348i	−0.888044	+	0.0874647i	−0.356302	+	0.934371i	$0.615962\pi$
$860$	5.84029	−	8.82349i	0.199152	−	0.300879i
$861$	−2.83135	+	0.858881i	−0.0964922	+	0.0292706i
$862$	−38.5870	−	25.6618i	−1.31428	−	0.874043i
$863$	−6.92860	−	6.92860i	−0.235852	−	0.235852i	0.579278	−	0.815130i	$-0.303335\pi$
$863$	−6.92860	−	6.92860i	−0.235852	−	0.235852i	−0.815130	+	0.579278i	$0.803335\pi$
$864$	−6.72203	−	8.01146i	−0.228688	−	0.272556i
$865$	5.45688	−	5.45688i	0.185539	−	0.185539i
$866$	34.5204	−	6.94466i	1.17305	−	0.235989i
$867$	−1.50766	−	4.97010i	−0.0512029	−	0.168793i
$868$	−5.38726	−	1.04724i	−0.182855	−	0.0355456i
$869$	−6.13428	−	62.2824i	−0.208091	−	2.11279i
$870$	−2.65845	+	1.42842i	−0.0901299	+	0.0484279i
$871$	−2.84278	−	14.2916i	−0.0963240	−	0.484253i
$872$	24.6062	+	19.9264i	0.833270	+	0.674792i
$873$	−39.8113	−	7.91897i	−1.34741	−	0.268016i
$874$	17.9364	+	9.53710i	0.606709	+	0.322597i
$875$	−0.587566	−	1.09926i	−0.0198634	−	0.0371617i
$876$	−5.41470	−	1.61683i	−0.182946	−	0.0546276i
$877$	−4.74979	+	48.2254i	−0.160389	+	1.62846i	0.492016	+	0.870586i	$0.336260\pi$
$877$	−4.74979	+	48.2254i	−0.160389	+	1.62846i	−0.652405	+	0.757871i	$0.726240\pi$
$878$	−18.2755	−	43.8507i	−0.616767	−	1.47989i
$879$	−0.199551	−	0.0826567i	−0.00673069	−	0.00278794i
$880$	−23.7130	−	4.50261i	−0.799366	−	0.151783i
$881$	26.1790	−	10.8437i	0.881993	−	0.365333i	0.104723	−	0.994501i	$-0.466604\pi$
$881$	26.1790	−	10.8437i	0.881993	−	0.365333i	0.777269	+	0.629168i	$0.216604\pi$
$882$	15.8391	+	15.7703i	0.533331	+	0.531015i
$883$	17.1727	−	14.0932i	0.577906	−	0.474275i	−0.299452	−	0.954111i	$-0.596804\pi$
$883$	17.1727	−	14.0932i	0.577906	−	0.474275i	0.877358	+	0.479836i	$0.159304\pi$
$884$	3.48132	+	0.327589i	0.117089	+	0.0110180i
$885$	2.87477	+	0.872053i	0.0966345	+	0.0293138i
$886$	−40.2912	+	33.2131i	−1.35361	+	1.11582i
$887$	−7.20335	−	10.7806i	−0.241865	−	0.361976i	0.690600	−	0.723237i	$-0.257347\pi$
$887$	−7.20335	−	10.7806i	−0.241865	−	0.361976i	−0.932465	+	0.361260i	$0.882347\pi$
$888$	−4.62959	+	3.13730i	−0.155359	+	0.105281i
$889$	−15.2227	−	10.1715i	−0.510553	−	0.341140i
$890$	−10.6240	−	8.68026i	−0.356117	−	0.290963i
$891$	31.1087	−	37.9061i	1.04218	−	1.26990i
$892$	−13.9181	−	33.1919i	−0.466012	−	1.11135i
$893$	−1.16678	−	0.623659i	−0.0390449	−	0.0208699i
$894$	7.71285	+	1.51674i	0.257956	+	0.0507274i
$895$	−1.17226			−0.0391842
$896$	−13.1091	−	5.19746i	−0.437943	−	0.173635i
$897$	−3.95629			−0.132097
$898$	−22.0756	−	4.34119i	−0.736671	−	0.144867i
$899$	−13.2269	−	7.06995i	−0.441143	−	0.235796i
$900$	5.35226	−	2.24432i	0.178409	−	0.0748105i
$901$	2.53655	−	3.09080i	0.0845047	−	0.102969i
$902$	−50.0782	−	40.9161i	−1.66742	−	1.36236i
$903$	−1.71754	−	1.14762i	−0.0571561	−	0.0381905i
$904$	−1.30560	+	6.79525i	−0.0434237	+	0.226007i
$905$	−5.41893	−	8.11000i	−0.180131	−	0.269586i
$906$	−0.840179	+	0.692582i	−0.0279131	+	0.0230095i
$907$	−26.6081	−	8.07147i	−0.883507	−	0.268009i	−0.184250	−	0.982879i	$-0.558986\pi$
$907$	−26.6081	−	8.07147i	−0.883507	−	0.268009i	−0.699257	+	0.714870i	$0.746486\pi$
$908$	−5.40871	+	57.4789i	−0.179494	+	1.90751i
$909$	−34.4923	+	28.3071i	−1.14404	+	0.938887i
$910$	−3.37190	−	3.35725i	−0.111777	−	0.111292i
$911$	−24.2919	+	10.0620i	−0.804827	+	0.333370i	−0.746888	−	0.664950i	$-0.768453\pi$
$911$	−24.2919	+	10.0620i	−0.804827	+	0.333370i	−0.0579387	+	0.998320i	$0.518453\pi$
$912$	3.76609	−	0.783259i	0.124708	−	0.0259363i
$913$	−54.5122	−	22.5797i	−1.80409	−	0.747279i
$914$	−2.70113	−	6.48119i	−0.0893455	−	0.214379i
$915$	0.153078	−	1.55423i	0.00506060	−	0.0513812i
$916$	−4.19448	+	14.0471i	−0.138589	+	0.464130i
$917$	4.56169	+	8.53432i	0.150640	+	0.281828i
$918$	1.49516	+	0.795003i	0.0493477	+	0.0262390i
$919$	−32.1417	−	6.39338i	−1.06026	−	0.210898i	−0.365992	−	0.930618i	$-0.619270\pi$
$919$	−32.1417	−	6.39338i	−1.06026	−	0.210898i	−0.694264	+	0.719720i	$0.744270\pi$
$920$	−1.38310	−	13.1615i	−0.0455995	−	0.433921i
$921$	0.561880	+	2.82476i	0.0185146	+	0.0930791i
$922$	−3.73743	+	2.00817i	−0.123086	+	0.0661354i
$923$	3.41965	+	34.7202i	0.112559	+	1.14283i
$924$	−0.899134	+	4.62537i	−0.0295794	+	0.152163i
$925$	−1.83232	−	6.04034i	−0.0602462	−	0.198605i
$926$	−18.9376	+	3.80979i	−0.622329	+	0.125197i
$927$	−28.2323	+	28.2323i	−0.927270	+	0.927270i
$928$	−30.0541	−	24.1223i	−0.986573	−	0.791854i
$929$	39.8794	+	39.8794i	1.30840	+	1.30840i	0.922569	+	0.385833i	$0.126086\pi$
$929$	39.8794	+	39.8794i	1.30840	+	1.30840i	0.385833	+	0.922569i	$0.373914\pi$
$930$	−0.812074	−	0.540058i	−0.0266290	−	0.0177092i
$931$	−16.0006	+	4.85374i	−0.524399	+	0.159075i
$932$	22.3081	+	14.7657i	0.730725	+	0.483668i
$933$	−7.51325	+	0.739990i	−0.245973	+	0.0242262i
$934$	4.52592	−	15.0377i	0.148093	−	0.492048i
$935$	3.83318	−	0.762466i	0.125358	−	0.0249353i
$936$	17.0345	−	14.1669i	0.556789	−	0.463060i
$937$	0.913940	−	4.59469i	0.0298571	−	0.150102i	−0.962981	−	0.269569i	$-0.913119\pi$
$937$	0.913940	−	4.59469i	0.0298571	−	0.150102i	0.992838	+	0.119467i	$0.0381187\pi$
$938$	−2.78201	−	9.09974i	−0.0908360	−	0.297117i
$939$	−9.40162	+	5.02527i	−0.306810	+	0.163994i
$940$	0.0882112	+	0.857355i	0.00287713	+	0.0279639i
$941$	−17.2255	−	1.69657i	−0.561536	−	0.0553065i	−0.186733	−	0.982411i	$-0.559790\pi$
$941$	−17.2255	−	1.69657i	−0.561536	−	0.0553065i	−0.374803	+	0.927104i	$0.622290\pi$
$942$	−6.66347	−	2.74313i	−0.217107	−	0.0893759i
$943$	13.5688	−	32.7579i	0.441860	−	1.06674i
$944$	4.09224	+	38.1427i	0.133191	+	1.24144i
$945$	−0.881825	−	2.12891i	−0.0286858	−	0.0692536i
$946$	−0.0982439	−	45.1481i	−0.00319419	−	1.46789i
$947$	6.46208	+	7.87406i	0.209989	+	0.255873i	0.867345	−	0.497708i	$-0.165825\pi$
$947$	6.46208	+	7.87406i	0.209989	+	0.255873i	−0.657355	+	0.753581i	$0.728325\pi$
$948$	3.03800	−	5.74369i	0.0986697	−	0.186546i
$949$	7.06795	−	23.2999i	0.229435	−	0.756347i
$950$	−0.416156	+	4.32169i	−0.0135019	+	0.140214i
$951$	6.40965	−	4.28279i	0.207847	−	0.138879i
$952$	2.28335	−	0.0149062i	0.0740039	−	0.000483112i
$953$	22.5172	−	33.6993i	0.729403	−	1.09163i	−0.262537	−	0.964922i	$-0.584559\pi$
$953$	22.5172	−	33.6993i	0.729403	−	1.09163i	0.991940	−	0.126707i	$-0.0404407\pi$
$954$	−2.53807	−	25.2070i	−0.0821731	−	0.816108i
$955$	9.33876	+	7.66412i	0.302195	+	0.248005i
$956$	31.6615	+	31.3871i	1.02401	+	1.01513i
$957$	−6.07008	+	11.3563i	−0.196218	+	0.367098i
$958$	12.7583	−	8.56506i	0.412203	−	0.276724i
$959$		−	5.62427i		−	0.181617i
$960$	−1.79496	−	1.74869i	−0.0579320	−	0.0564387i
$961$			26.1533i			0.843656i
$962$	−13.4308	−	20.0063i	−0.433027	−	0.645028i
$963$	−6.79737	+	12.7170i	−0.219042	+	0.409799i
$964$	36.3813	−	0.158335i	1.17176	−	0.00509962i
$965$	11.6586	+	9.56793i	0.375302	+	0.308002i
$966$	−2.57052	+	0.258824i	−0.0827052	+	0.00832751i
$967$	4.19769	−	6.28229i	0.134989	−	0.202025i	−0.757817	−	0.652468i	$-0.773734\pi$
$967$	4.19769	−	6.28229i	0.134989	−	0.202025i	0.892805	+	0.450443i	$0.148734\pi$
$968$	−66.2219	+	27.9379i	−2.12845	+	0.897957i
$969$	−0.517892	+	0.346044i	−0.0166371	+	0.0111165i
$970$	−19.6908	−	1.89612i	−0.632235	−	0.0608809i
$971$	−4.47472	+	14.7512i	−0.143601	+	0.473388i	−0.999006	−	0.0445709i	$-0.985808\pi$
$971$	−4.47472	+	14.7512i	−0.143601	+	0.473388i	0.855406	+	0.517959i	$0.173308\pi$
$972$	15.4661	−	4.76519i	0.496075	−	0.152843i
$973$	9.10524	+	11.0948i	0.291901	+	0.355682i
$974$	−53.4183	+	0.116240i	−1.71163	+	0.00372457i
$975$	−0.323581	−	0.781194i	−0.0103629	−	0.0250182i
$976$	19.0331	−	5.95501i	0.609233	−	0.190615i
$977$	9.38422	−	22.6555i	0.300228	−	0.724814i	−0.699718	−	0.714419i	$-0.746691\pi$
$977$	9.38422	−	22.6555i	0.300228	−	0.724814i	0.999946	−	0.0103950i	$-0.00330888\pi$
$978$	1.14053	−	2.77053i	0.0364702	−	0.0885917i
$979$	−58.2552	−	5.73764i	−1.86184	−	0.183376i
$980$	8.45024	+	6.87360i	0.269933	+	0.219569i
$981$	−28.6491	+	15.3133i	−0.914696	+	0.488915i
$982$	−18.0465	+	5.51725i	−0.575886	+	0.176063i
$983$	6.40020	−	32.1760i	0.204135	−	1.02625i	−0.733780	−	0.679387i	$-0.762246\pi$
$983$	6.40020	−	32.1760i	0.204135	−	1.02625i	0.937914	−	0.346867i	$-0.112754\pi$
$984$	−1.99088	−	6.41207i	−0.0634670	−	0.204409i
$985$	−0.896646	+	0.178354i	−0.0285695	+	0.00568283i
$986$	5.97531	+	1.79840i	0.190292	+	0.0572727i
$987$	0.167446	−	0.0164920i	0.00532985	−	0.000524945i
$988$	3.30419	+	16.2416i	0.105120	+	0.516713i
$989$	23.6884	−	7.18581i	0.753249	−	0.228495i
$990$	13.7130	−	20.6200i	0.435829	−	0.655346i
$991$	−16.5224	−	16.5224i	−0.524852	−	0.524852i	0.394181	−	0.919033i	$-0.371028\pi$
$991$	−16.5224	−	16.5224i	−0.524852	−	0.524852i	−0.919033	+	0.394181i	$0.871028\pi$
$992$	2.29655	−	12.2401i	0.0729156	−	0.388623i
$993$	2.61534	−	2.61534i	0.0829953	−	0.0829953i
$994$	4.49327	+	22.3351i	0.142518	+	0.708426i
$995$	1.03984	+	3.42789i	0.0329651	+	0.108672i
$996$	−3.42553	−	5.07867i	−0.108542	−	0.160924i
$997$	−4.03571	−	40.9752i	−0.127812	−	1.29770i	−0.818484	−	0.574529i	$-0.805185\pi$
$997$	−4.03571	−	40.9752i	−0.127812	−	1.29770i	0.690672	−	0.723168i	$-0.257315\pi$
$998$	−23.8433	−	44.3752i	−0.754748	−	1.40467i
$999$	−2.27659	−	11.4452i	−0.0720281	−	0.362110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.621.36	yes	1024
128.101	even	32	inner	640.2.bm.a.101.36	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.36	✓	1024	128.101	even	32	inner
640.2.bm.a.621.36	yes	1024	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.272880 - 1.38764i) q^{2} +(0.276256 + 0.147662i) q^{3} +(-1.85107 - 0.757318i) q^{4} +(0.634393 - 0.773010i) q^{5} +(0.280286 - 0.343049i) q^{6} +(1.03637 + 0.692483i) q^{7} +(-1.55600 + 2.36196i) q^{8} +(-1.61220 - 2.41282i) q^{9} +(-0.899544 - 1.09125i) q^{10} +(-5.77435 - 1.75163i) q^{11} +(-0.399543 - 0.482547i) q^{12} +(2.08663 - 1.71246i) q^{13} +(1.24372 - 1.24915i) q^{14} +(0.289400 - 0.119873i) q^{15} +(2.85294 + 2.80370i) q^{16} +(-0.598387 - 0.247860i) q^{17} +(-3.78806 + 1.57873i) q^{18} +(0.300916 - 3.05525i) q^{19} +(-1.75972 + 0.950461i) q^{20} +(0.184051 + 0.344336i) q^{21} +(-4.00633 + 7.53471i) q^{22} +(-4.58900 - 0.912810i) q^{23} +(-0.778628 + 0.422743i) q^{24} +(-0.195090 - 0.980785i) q^{25} +(-1.80687 - 3.36279i) q^{26} +(-0.181207 - 1.83982i) q^{27} +(-1.39397 - 2.06670i) q^{28} +(-1.97757 - 6.51917i) q^{29} +(-0.0873690 - 0.434293i) q^{30} +(1.55671 - 1.55671i) q^{31} +(4.66903 - 3.19377i) q^{32} +(-1.33655 - 1.33655i) q^{33} +(-0.507228 + 0.762708i) q^{34} +(1.19277 - 0.361821i) q^{35} +(1.15702 + 5.68726i) q^{36} +(6.28174 - 0.618698i) q^{37} +(-4.15746 - 1.25128i) q^{38} +(0.829311 - 0.164960i) q^{39} +(0.838701 + 2.70122i) q^{40} +(-1.47840 + 7.43242i) q^{41} +(0.528037 - 0.161434i) q^{42} +(-4.66592 + 2.49398i) q^{43} +(9.36219 + 7.61541i) q^{44} +(-2.88790 - 0.284434i) q^{45} +(-2.51890 + 6.11878i) q^{46} +(0.164914 - 0.398137i) q^{47} +(0.374142 + 1.19581i) q^{48} +(-2.08425 - 5.03181i) q^{49} +(-1.41421 + 0.00307738i) q^{50} +(-0.128709 - 0.156832i) q^{51} +(-5.15939 + 1.58964i) q^{52} +(-1.79202 + 5.90749i) q^{53} +(-2.60246 - 0.250603i) q^{54} +(-5.01723 + 3.35241i) q^{55} +(-3.24822 + 1.37037i) q^{56} +(0.534274 - 0.799598i) q^{57} +(-9.58589 + 0.965193i) q^{58} +(7.41348 + 6.08408i) q^{59} +(-0.626482 + 0.00272651i) q^{60} +(2.35025 - 4.39702i) q^{61} +(-1.73535 - 2.58494i) q^{62} -3.61701i q^{63} +(-3.15770 - 7.35044i) q^{64} -2.69936i q^{65} +(-2.21937 + 1.48993i) q^{66} +(2.54468 - 4.76076i) q^{67} +(0.919949 + 0.911977i) q^{68} +(-1.13295 - 0.929791i) q^{69} +(-0.176594 - 1.75386i) q^{70} +(-7.18054 + 10.7464i) q^{71} +(8.20758 - 0.0535807i) q^{72} +(7.49988 - 5.01126i) q^{73} +(0.855637 - 8.88561i) q^{74} +(0.0909299 - 0.299756i) q^{75} +(-2.87081 + 5.42760i) q^{76} +(-4.77141 - 5.81398i) q^{77} +(-0.00260210 - 1.19580i) q^{78} +(3.96902 + 9.58207i) q^{79} +(3.97718 - 0.426702i) q^{80} +(-3.10989 + 7.50794i) q^{81} +(9.91007 + 4.07965i) q^{82} +(9.73115 + 0.958435i) q^{83} +(-0.0799207 - 0.776776i) q^{84} +(-0.571211 + 0.305319i) q^{85} +(2.18751 + 7.15516i) q^{86} +(0.416319 - 2.09298i) q^{87} +(13.1222 - 10.9132i) q^{88} +(9.51452 - 1.89256i) q^{89} +(-1.18274 + 3.92975i) q^{90} +(3.34838 - 0.329787i) q^{91} +(7.80329 + 5.16501i) q^{92} +(0.659917 - 0.200184i) q^{93} +(-0.507468 - 0.337484i) q^{94} +(-2.17084 - 2.17084i) q^{95} +(1.76145 - 0.192860i) q^{96} +(9.89096 - 9.89096i) q^{97} +(-7.55108 + 1.51909i) q^{98} +(5.08301 + 16.7565i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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