LMFDB - Embedded newform 630.2.bw.a.493.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(103,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 10]))

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

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

chi := DirichletCharacter("630.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bw (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			493.45
Character	$\chi$	$=$	630.493
Dual form			630.2.bw.a.607.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(1.64201 + 0.551173i) q^{3} -1.00000i q^{4} +(-0.512049 - 2.17665i) q^{5} +(1.55082 - 0.771341i) q^{6} +(2.17879 + 1.50096i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.39242 + 1.81007i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(1.64201 + 0.551173i) q^{3} -1.00000i q^{4} +(-0.512049 - 2.17665i) q^{5} +(1.55082 - 0.771341i) q^{6} +(2.17879 + 1.50096i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.39242 + 1.81007i) q^{9} +(-1.90120 - 1.17705i) q^{10} +(1.02017 + 1.76699i) q^{11} +(0.551173 - 1.64201i) q^{12} +(-2.73645 - 0.733229i) q^{13} +(2.60197 - 0.479300i) q^{14} +(0.358919 - 3.85632i) q^{15} -1.00000 q^{16} +(7.04560 - 1.88786i) q^{17} +(2.97160 - 0.411784i) q^{18} +(-2.14232 - 3.71061i) q^{19} +(-2.17665 + 0.512049i) q^{20} +(2.75032 + 3.66548i) q^{21} +(1.97082 + 0.528078i) q^{22} +(-1.40119 + 0.375448i) q^{23} +(-0.771341 - 1.55082i) q^{24} +(-4.47561 + 2.22910i) q^{25} +(-2.45343 + 1.41649i) q^{26} +(2.93072 + 4.29079i) q^{27} +(1.50096 - 2.17879i) q^{28} +(3.89600 + 2.24936i) q^{29} +(-2.47303 - 2.98062i) q^{30} -6.04551i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.701217 + 3.46370i) q^{33} +(3.64707 - 6.31691i) q^{34} +(2.15141 - 5.51103i) q^{35} +(1.81007 - 2.39242i) q^{36} +(-10.6469 - 2.85282i) q^{37} +(-4.13865 - 1.10895i) q^{38} +(-4.08915 - 2.71223i) q^{39} +(-1.17705 + 1.90120i) q^{40} +(-7.89572 + 4.55860i) q^{41} +(4.53665 + 0.647121i) q^{42} +(-6.17601 + 1.65486i) q^{43} +(1.76699 - 1.02017i) q^{44} +(2.71485 - 6.13430i) q^{45} +(-0.725309 + 1.25627i) q^{46} +(0.768822 + 0.768822i) q^{47} +(-1.64201 - 0.551173i) q^{48} +(2.49425 + 6.54054i) q^{49} +(-1.58852 + 4.74095i) q^{50} +(12.6095 + 0.783447i) q^{51} +(-0.733229 + 2.73645i) q^{52} +(2.48435 - 0.665678i) q^{53} +(5.10638 + 0.961714i) q^{54} +(3.32373 - 3.12533i) q^{55} +(-0.479300 - 2.60197i) q^{56} +(-1.47253 - 7.27366i) q^{57} +(4.34543 - 1.16435i) q^{58} +8.54280 q^{59} +(-3.85632 - 0.358919i) q^{60} +12.7003i q^{61} +(-4.27482 - 4.27482i) q^{62} +(2.49574 + 7.53467i) q^{63} +1.00000i q^{64} +(-0.194787 + 6.33174i) q^{65} +(2.94504 + 1.95337i) q^{66} +(5.30820 - 5.30820i) q^{67} +(-1.88786 - 7.04560i) q^{68} +(-2.50771 - 0.155808i) q^{69} +(-2.37561 - 5.41816i) q^{70} -7.95478 q^{71} +(-0.411784 - 2.97160i) q^{72} +(3.52774 + 13.1657i) q^{73} +(-9.54572 + 5.51122i) q^{74} +(-8.57764 + 1.19338i) q^{75} +(-3.71061 + 2.14232i) q^{76} +(-0.429435 + 5.38112i) q^{77} +(-4.80930 + 0.973630i) q^{78} +2.57916i q^{79} +(0.512049 + 2.17665i) q^{80} +(2.44732 + 8.66087i) q^{81} +(-2.35970 + 8.80653i) q^{82} +(-0.288880 - 1.07812i) q^{83} +(3.66548 - 2.75032i) q^{84} +(-7.71691 - 14.3691i) q^{85} +(-3.19694 + 5.53726i) q^{86} +(5.15751 + 5.84085i) q^{87} +(0.528078 - 1.97082i) q^{88} +(-0.542567 - 0.939753i) q^{89} +(-2.41792 - 6.25729i) q^{90} +(-4.86160 - 5.70484i) q^{91} +(0.375448 + 1.40119i) q^{92} +(3.33212 - 9.92680i) q^{93} +1.08728 q^{94} +(-6.97973 + 6.56310i) q^{95} +(-1.55082 + 0.771341i) q^{96} +(2.04615 - 0.548265i) q^{97} +(6.38857 + 2.86116i) q^{98} +(-0.757691 + 6.07394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$	1.64201	+	0.551173i	0.948017	+	0.318220i
$3$	1.64201	+	0.551173i	0.948017	+	0.318220i
$4$		−	1.00000i		−	0.500000i
$5$	−0.512049	−	2.17665i	−0.228995	−	0.973428i
$5$	−0.512049	−	2.17665i	−0.228995	−	0.973428i
$6$	1.55082	−	0.771341i	0.633118	−	0.314899i
$7$	2.17879	+	1.50096i	0.823505	+	0.567309i
$7$	2.17879	+	1.50096i	0.823505	+	0.567309i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.39242	+	1.81007i	0.797472	+	0.603356i
$10$	−1.90120	−	1.17705i	−0.601211	−	0.372216i
$11$	1.02017	+	1.76699i	0.307593	+	0.532766i	0.977835	−	0.209376i	$-0.0671433\pi$
$11$	1.02017	+	1.76699i	0.307593	+	0.532766i	−0.670243	+	0.742142i	$0.733810\pi$
$12$	0.551173	−	1.64201i	0.159110	−	0.474008i
$13$	−2.73645	−	0.733229i	−0.758954	−	0.203361i	−0.141468	−	0.989943i	$-0.545182\pi$
$13$	−2.73645	−	0.733229i	−0.758954	−	0.203361i	−0.617486	+	0.786582i	$0.711849\pi$
$14$	2.60197	−	0.479300i	0.695407	−	0.128098i
$15$	0.358919	−	3.85632i	0.0926725	−	0.995697i
$16$	−1.00000			−0.250000
$17$	7.04560	−	1.88786i	1.70881	−	0.457874i	0.733676	−	0.679499i	$-0.237803\pi$
$17$	7.04560	−	1.88786i	1.70881	−	0.457874i	0.975132	+	0.221625i	$0.0711362\pi$
$18$	2.97160	−	0.411784i	0.700414	−	0.0970583i
$19$	−2.14232	−	3.71061i	−0.491482	−	0.851273i	0.508469	−	0.861080i	$-0.330211\pi$
$19$	−2.14232	−	3.71061i	−0.491482	−	0.851273i	−0.999952	+	0.00980745i	$0.996878\pi$
$20$	−2.17665	+	0.512049i	−0.486714	+	0.114498i
$21$	2.75032	+	3.66548i	0.600168	+	0.799874i
$22$	1.97082	+	0.528078i	0.420179	+	0.112587i
$23$	−1.40119	+	0.375448i	−0.292168	+	0.0782862i	−0.401926	−	0.915672i	$-0.631659\pi$
$23$	−1.40119	+	0.375448i	−0.292168	+	0.0782862i	0.109758	+	0.993958i	$0.464992\pi$
$24$	−0.771341	−	1.55082i	−0.157449	−	0.316559i
$25$	−4.47561	+	2.22910i	−0.895122	+	0.445821i
$26$	−2.45343	+	1.41649i	−0.481158	+	0.277796i
$27$	2.93072	+	4.29079i	0.564018	+	0.825763i
$28$	1.50096	−	2.17879i	0.283654	−	0.411753i
$29$	3.89600	+	2.24936i	0.723470	+	0.417695i	0.816028	−	0.578012i	$-0.196171\pi$
$29$	3.89600	+	2.24936i	0.723470	+	0.417695i	−0.0925587	+	0.995707i	$0.529505\pi$
$30$	−2.47303	−	2.98062i	−0.451512	−	0.544185i
$31$		−	6.04551i		−	1.08581i	−0.839796	−	0.542903i	$-0.817325\pi$
$31$		−	6.04551i		−	1.08581i	0.839796	−	0.542903i	$-0.182675\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	0.701217	+	3.46370i	0.122066	+	0.602953i
$34$	3.64707	−	6.31691i	0.625467	−	1.08334i
$35$	2.15141	−	5.51103i	0.363655	−	0.931534i
$36$	1.81007	−	2.39242i	0.301678	−	0.398736i
$37$	−10.6469	−	2.85282i	−1.75033	−	0.469001i	−0.765637	−	0.643273i	$-0.777576\pi$
$37$	−10.6469	−	2.85282i	−1.75033	−	0.469001i	−0.984697	+	0.174272i	$0.944243\pi$
$38$	−4.13865	−	1.10895i	−0.671378	−	0.179895i
$39$	−4.08915	−	2.71223i	−0.654788	−	0.434304i
$40$	−1.17705	+	1.90120i	−0.186108	+	0.300606i
$41$	−7.89572	+	4.55860i	−1.23310	+	0.711933i	−0.967676	−	0.252197i	$-0.918847\pi$
$41$	−7.89572	+	4.55860i	−1.23310	+	0.711933i	−0.265428	+	0.964131i	$0.585513\pi$
$42$	4.53665	+	0.647121i	0.700021	+	0.0998529i
$43$	−6.17601	+	1.65486i	−0.941832	+	0.252363i	−0.696893	−	0.717175i	$-0.745435\pi$
$43$	−6.17601	+	1.65486i	−0.941832	+	0.252363i	−0.244939	+	0.969538i	$0.578768\pi$
$44$	1.76699	−	1.02017i	0.266383	−	0.153796i
$45$	2.71485	−	6.13430i	0.404705	−	0.914447i
$46$	−0.725309	+	1.25627i	−0.106941	+	0.185227i
$47$	0.768822	+	0.768822i	0.112144	+	0.112144i	0.760952	−	0.648808i	$-0.224732\pi$
$47$	0.768822	+	0.768822i	0.112144	+	0.112144i	−0.648808	+	0.760952i	$0.724732\pi$
$48$	−1.64201	−	0.551173i	−0.237004	−	0.0795550i
$49$	2.49425	+	6.54054i	0.356322	+	0.934363i
$50$	−1.58852	+	4.74095i	−0.224651	+	0.670472i
$51$	12.6095	+	0.783447i	1.76568	+	0.109705i
$52$	−0.733229	+	2.73645i	−0.101681	+	0.379477i
$53$	2.48435	−	0.665678i	0.341251	−	0.0914379i	−0.0841235	−	0.996455i	$-0.526809\pi$
$53$	2.48435	−	0.665678i	0.341251	−	0.0914379i	0.425375	+	0.905017i	$0.360142\pi$
$54$	5.10638	+	0.961714i	0.694890	+	0.130873i
$55$	3.32373	−	3.12533i	0.448172	−	0.421420i
$56$	−0.479300	−	2.60197i	−0.0640492	−	0.347703i
$57$	−1.47253	−	7.27366i	−0.195042	−	0.963420i
$58$	4.34543	−	1.16435i	0.570583	−	0.152887i
$59$	8.54280			1.11218			0.556089	−	0.831123i	$-0.312301\pi$
$59$	8.54280			1.11218			0.556089	+	0.831123i	$0.312301\pi$
$60$	−3.85632	−	0.358919i	−0.497848	−	0.0463362i
$61$			12.7003i			1.62610i	0.582192	+	0.813052i	$0.302195\pi$
$61$			12.7003i			1.62610i	−0.582192	+	0.813052i	$0.697805\pi$
$62$	−4.27482	−	4.27482i	−0.542903	−	0.542903i
$63$	2.49574	+	7.53467i	0.314434	+	0.949279i
$64$			1.00000i			0.125000i
$65$	−0.194787	+	6.33174i	−0.0241604	+	0.785355i
$66$	2.94504	+	1.95337i	0.362510	+	0.240444i
$67$	5.30820	−	5.30820i	0.648500	−	0.648500i	−0.304130	−	0.952631i	$-0.598366\pi$
$67$	5.30820	−	5.30820i	0.648500	−	0.648500i	0.952631	+	0.304130i	$0.0983658\pi$
$68$	−1.88786	−	7.04560i	−0.228937	−	0.854404i
$69$	−2.50771	−	0.155808i	−0.301893	−	0.0187570i
$70$	−2.37561	−	5.41816i	−0.283939	−	0.647594i
$71$	−7.95478			−0.944059			−0.472030	−	0.881583i	$-0.656478\pi$
$71$	−7.95478			−0.944059			−0.472030	+	0.881583i	$0.656478\pi$
$72$	−0.411784	−	2.97160i	−0.0485292	−	0.350207i
$73$	3.52774	+	13.1657i	0.412891	+	1.54093i	0.789024	+	0.614363i	$0.210587\pi$
$73$	3.52774	+	13.1657i	0.412891	+	1.54093i	−0.376133	+	0.926566i	$0.622746\pi$
$74$	−9.54572	+	5.51122i	−1.10967	+	0.640667i
$75$	−8.57764	+	1.19338i	−0.990460	+	0.137800i
$76$	−3.71061	+	2.14232i	−0.425636	+	0.245741i
$77$	−0.429435	+	5.38112i	−0.0489386	+	0.613236i
$78$	−4.80930	+	0.973630i	−0.544546	+	0.110242i
$79$			2.57916i			0.290179i	0.989419	+	0.145089i	$0.0463469\pi$
$79$			2.57916i			0.290179i	−0.989419	+	0.145089i	$0.953653\pi$
$80$	0.512049	+	2.17665i	0.0572488	+	0.243357i
$81$	2.44732	+	8.66087i	0.271924	+	0.962319i
$82$	−2.35970	+	8.80653i	−0.260586	+	0.972519i
$83$	−0.288880	−	1.07812i	−0.0317087	−	0.118339i	0.948258	−	0.317502i	$-0.102844\pi$
$83$	−0.288880	−	1.07812i	−0.0317087	−	0.118339i	−0.979966	+	0.199164i	$0.936177\pi$
$84$	3.66548	−	2.75032i	0.399937	−	0.300084i
$85$	−7.71691	−	14.3691i	−0.837016	−	1.55855i
$86$	−3.19694	+	5.53726i	−0.344734	+	0.597098i
$87$	5.15751	+	5.84085i	0.552943	+	0.626205i
$88$	0.528078	−	1.97082i	0.0562934	−	0.210090i
$89$	−0.542567	−	0.939753i	−0.0575120	−	0.0996136i	0.835836	−	0.548979i	$-0.184983\pi$
$89$	−0.542567	−	0.939753i	−0.0575120	−	0.0996136i	−0.893348	+	0.449366i	$0.851650\pi$
$90$	−2.41792	−	6.25729i	−0.254871	−	0.659576i
$91$	−4.86160	−	5.70484i	−0.509634	−	0.598030i
$92$	0.375448	+	1.40119i	0.0391431	+	0.146084i
$93$	3.33212	−	9.92680i	0.345525	−	1.02936i
$94$	1.08728			0.112144
$95$	−6.97973	+	6.56310i	−0.716105	+	0.673360i
$96$	−1.55082	+	0.771341i	−0.158280	+	0.0787246i
$97$	2.04615	−	0.548265i	0.207755	−	0.0556679i	−0.153440	−	0.988158i	$-0.549035\pi$
$97$	2.04615	−	0.548265i	0.207755	−	0.0556679i	0.361196	+	0.932490i	$0.382369\pi$
$98$	6.38857	+	2.86116i	0.645343	+	0.289021i
$99$	−0.757691	+	6.07394i	−0.0761508	+	0.610454i
$100$	2.22910	+	4.47561i	0.222910	+	0.447561i
$101$	4.62401	−	2.66967i	0.460106	−	0.265642i	−0.251983	−	0.967732i	$-0.581083\pi$
$101$	4.62401	−	2.66967i	0.460106	−	0.265642i	0.712089	+	0.702089i	$0.247749\pi$
$102$	9.47025	−	8.36229i	0.937694	−	0.827990i
$103$	0.659670	+	2.46192i	0.0649992	+	0.242580i	0.990780	−	0.135480i	$-0.0432577\pi$
$103$	0.659670	+	2.46192i	0.0649992	+	0.242580i	−0.925781	+	0.378061i	$0.876591\pi$
$104$	1.41649	+	2.45343i	0.138898	+	0.240579i
$105$	6.57018	−	7.86338i	0.641184	−	0.767388i
$106$	1.28599	−	2.22740i	0.124907	−	0.216344i
$107$	−11.6202	−	3.11361i	−1.12336	−	0.301004i	−0.351119	−	0.936331i	$-0.614199\pi$
$107$	−11.6202	−	3.11361i	−1.12336	−	0.301004i	−0.772243	+	0.635327i	$0.780865\pi$
$108$	4.29079	−	2.93072i	0.412881	−	0.282009i
$109$	−13.3200	−	7.69030i	−1.27582	−	0.736597i	−0.299746	−	0.954019i	$-0.596902\pi$
$109$	−13.3200	−	7.69030i	−1.27582	−	0.736597i	−0.976078	+	0.217422i	$0.930235\pi$
$110$	0.140288	−	4.56018i	0.0133759	−	0.434796i
$111$	−15.9099	−	10.5526i	−1.51010	−	1.00161i
$112$	−2.17879	−	1.50096i	−0.205876	−	0.141827i
$113$	−4.65380	+	17.3682i	−0.437793	+	1.63387i	0.296499	+	0.955033i	$0.404181\pi$
$113$	−4.65380	+	17.3682i	−0.437793	+	1.63387i	−0.734293	+	0.678833i	$0.762486\pi$
$114$	−6.18450	−	4.10202i	−0.579231	−	0.384189i
$115$	1.53470	+	2.85765i	0.143111	+	0.266477i
$116$	2.24936	−	3.89600i	0.208848	−	0.361735i
$117$	−5.21953	−	6.70734i	−0.482546	−	0.620094i
$118$	6.04067	−	6.04067i	0.556089	−	0.556089i
$119$	18.1845	+	6.46189i	1.66697	+	0.592360i
$120$	−2.98062	+	2.47303i	−0.272092	+	0.225756i
$121$	3.41851	−	5.92103i	0.310774	−	0.538276i
$122$	8.98045	+	8.98045i	0.813052	+	0.813052i
$123$	−15.4775	+	3.13337i	−1.39555	+	0.282526i
$124$	−6.04551			−0.542903
$125$	7.14371	+	8.60043i	0.638953	+	0.769246i
$126$	7.09257	+	3.56306i	0.631857	+	0.317423i
$127$	−10.3960	+	10.3960i	−0.922492	+	0.922492i	−0.997205	−	0.0747130i	$-0.976196\pi$
$127$	−10.3960	+	10.3960i	−0.922492	+	0.922492i	0.0747130	+	0.997205i	$0.476196\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−11.0532	−	0.686752i	−0.973180	−	0.0604651i
$130$	4.33948	+	4.61495i	0.380598	+	0.404758i
$131$	0.0948553	+	0.0547647i	0.00828754	+	0.00478482i	0.504138	−	0.863623i	$-0.331810\pi$
$131$	0.0948553	+	0.0547647i	0.00828754	+	0.00478482i	−0.495851	+	0.868408i	$0.665144\pi$
$132$	3.46370	−	0.701217i	0.301477	−	0.0610331i
$133$	0.901799	−	11.3002i	0.0781959	−	0.979850i
$134$		−	7.50693i		−	0.648500i
$135$	7.83887	−	8.57625i	0.674663	−	0.738126i
$136$	−6.31691	−	3.64707i	−0.541671	−	0.312734i
$137$	12.3734	+	3.31543i	1.05713	+	0.283257i	0.745194	−	0.666847i	$-0.232357\pi$
$137$	12.3734	+	3.31543i	1.05713	+	0.283257i	0.311934	+	0.950104i	$0.399023\pi$
$138$	−1.88339	+	1.66304i	−0.160325	+	0.141568i
$139$	−7.75381	−	13.4300i	−0.657670	−	1.13912i	−0.981217	−	0.192905i	$-0.938209\pi$
$139$	−7.75381	−	13.4300i	−0.657670	−	1.13912i	0.323548	−	0.946212i	$-0.395124\pi$
$140$	−5.51103	−	2.15141i	−0.465767	−	0.181827i
$141$	0.838663	+	1.68617i	0.0706281	+	0.142001i
$142$	−5.62488	+	5.62488i	−0.472030	+	0.472030i
$143$	−1.49604	−	5.58328i	−0.125105	−	0.466897i
$144$	−2.39242	−	1.81007i	−0.199368	−	0.150839i
$145$	2.90112	−	9.63202i	0.240925	−	0.799896i
$146$	11.8040	+	6.81507i	0.976910	+	0.564019i
$147$	0.490627	+	12.1144i	0.0404662	+	0.999181i
$148$	−2.85282	+	10.6469i	−0.234500	+	0.875167i
$149$	−4.55867	−	2.63195i	−0.373461	−	0.215618i	0.301508	−	0.953464i	$-0.402510\pi$
$149$	−4.55867	−	2.63195i	−0.373461	−	0.215618i	−0.674969	+	0.737846i	$0.735843\pi$
$150$	−5.22146	+	6.90915i	−0.426330	+	0.564130i
$151$	−7.07650	−	12.2569i	−0.575878	−	0.997449i	−0.995946	−	0.0899566i	$-0.971327\pi$
$151$	−7.07650	−	12.2569i	−0.575878	−	0.997449i	0.420068	−	0.907493i	$-0.362006\pi$
$152$	−1.10895	+	4.13865i	−0.0899475	+	0.335689i
$153$	20.2732	+	8.23645i	1.63899	+	0.665877i
$154$	3.50137	+	4.10868i	0.282148	+	0.331087i
$155$	−13.1590	+	3.09560i	−1.05695	+	0.248644i
$156$	−2.71223	+	4.08915i	−0.217152	+	0.327394i
$157$	2.97768	+	2.97768i	0.237645	+	0.237645i	0.815874	−	0.578229i	$-0.196256\pi$
$157$	2.97768	+	2.97768i	0.237645	+	0.237645i	−0.578229	+	0.815874i	$0.696256\pi$
$158$	1.82374	+	1.82374i	0.145089	+	0.145089i
$159$	4.44623	+	0.276251i	0.352609	+	0.0219081i
$160$	1.90120	+	1.17705i	0.150303	+	0.0930540i
$161$	−3.61643	−	1.28510i	−0.285014	−	0.101280i
$162$	7.85467	+	4.39364i	0.617121	+	0.345197i
$163$	−4.81003	+	17.9513i	−0.376751	+	1.40605i	0.474019	+	0.880514i	$0.342803\pi$
$163$	−4.81003	+	17.9513i	−0.376751	+	1.40605i	−0.850770	+	0.525538i	$0.823864\pi$
$164$	4.55860	+	7.89572i	0.355967	+	0.616552i
$165$	7.18021	−	3.29989i	0.558979	−	0.256896i
$166$	−0.966612	−	0.558074i	−0.0750236	−	0.0433149i
$167$	3.61138	−	13.4779i	0.279457	−	1.04295i	−0.673338	−	0.739334i	$-0.735140\pi$
$167$	3.61138	−	13.4779i	0.279457	−	1.04295i	0.952795	−	0.303613i	$-0.0981931\pi$
$168$	0.647121	−	4.53665i	0.0499265	−	0.350010i
$169$	−4.30781	−	2.48712i	−0.331370	−	0.191317i
$170$	−15.6172	−	4.70383i	−1.19778	−	0.360767i
$171$	1.59113	−	12.7551i	0.121676	−	0.975405i
$172$	1.65486	+	6.17601i	0.126182	+	0.470916i
$173$	−4.73607	+	4.73607i	−0.360077	+	0.360077i	−0.863841	−	0.503764i	$-0.831948\pi$
$173$	−4.73607	+	4.73607i	−0.360077	+	0.360077i	0.503764	+	0.863841i	$0.331948\pi$
$174$	7.77701	+	0.483197i	0.589574	+	0.0366311i
$175$	−13.0972	−	1.86095i	−0.990056	−	0.140675i
$176$	−1.02017	−	1.76699i	−0.0768982	−	0.133192i
$177$	14.0274	+	4.70856i	1.05436	+	0.353917i
$178$	−1.04816	−	0.280853i	−0.0785628	−	0.0210508i
$179$	8.09360	+	4.67284i	0.604944	+	0.349265i	0.770984	−	0.636854i	$-0.219765\pi$
$179$	8.09360	+	4.67284i	0.604944	+	0.349265i	−0.166040	+	0.986119i	$0.553098\pi$
$180$	−6.13430	−	2.71485i	−0.457224	−	0.202353i
$181$		−	19.3483i		−	1.43815i	−0.694933	−	0.719075i	$-0.744566\pi$
$181$		−	19.3483i		−	1.43815i	0.694933	−	0.719075i	$-0.255434\pi$
$182$	−7.47160	−	0.596264i	−0.553832	−	0.0441980i
$183$	−7.00005	+	20.8540i	−0.517458	+	1.54157i
$184$	1.25627	+	0.725309i	0.0926136	+	0.0534705i
$185$	−0.757870	+	24.6353i	−0.0557197	+	1.81122i
$186$	−4.66315	−	9.37548i	−0.341918	−	0.687443i
$187$	10.5235	+	10.5235i	0.769556	+	0.769556i
$188$	0.768822	−	0.768822i	0.0560721	−	0.0560721i
$189$	−0.0548668	+	13.7476i	−0.00399097	+	0.999992i
$190$	−0.294599	+	9.57623i	−0.0213725	+	0.694732i
$191$	−0.890241			−0.0644156			−0.0322078	−	0.999481i	$-0.510254\pi$
$191$	−0.890241			−0.0644156			−0.0322078	+	0.999481i	$0.510254\pi$
$192$	−0.551173	+	1.64201i	−0.0397775	+	0.118502i
$193$	2.04448	+	2.04448i	0.147165	+	0.147165i	0.776850	−	0.629685i	$-0.216816\pi$
$193$	2.04448	+	2.04448i	0.147165	+	0.147165i	−0.629685	+	0.776850i	$0.716816\pi$
$194$	1.05917	−	1.83453i	0.0760438	−	0.131712i
$195$	−3.80973	+	10.2894i	−0.272820	+	0.736842i
$196$	6.54054	−	2.49425i	0.467182	−	0.178161i
$197$	10.7946	−	10.7946i	0.769084	−	0.769084i	−0.208861	−	0.977945i	$-0.566976\pi$
$197$	10.7946	−	10.7946i	0.769084	−	0.769084i	0.977945	+	0.208861i	$0.0669757\pi$
$198$	3.75916	+	4.83069i	0.267152	+	0.343302i
$199$	−7.63433	+	13.2230i	−0.541183	+	0.937357i	0.457653	+	0.889131i	$0.348690\pi$
$199$	−7.63433	+	13.2230i	−0.541183	+	0.937357i	−0.998836	+	0.0482262i	$0.984643\pi$
$200$	4.74095	+	1.58852i	0.335236	+	0.112325i
$201$	11.6419	−	5.79041i	0.821155	−	0.408424i
$202$	1.38192	−	5.15741i	0.0972319	−	0.362874i
$203$	5.11238	+	10.7486i	0.358819	+	0.754405i
$204$	0.783447	−	12.6095i	0.0548523	−	0.882842i
$205$	13.9655	+	14.8520i	0.975390	+	1.03731i
$206$	2.20730	+	1.27439i	0.153790	+	0.0887906i
$207$	−4.03181	−	1.63802i	−0.280230	−	0.113850i
$208$	2.73645	+	0.733229i	0.189738	+	0.0508403i
$209$	4.37106	−	7.57090i	0.302353	−	0.523690i
$210$	−0.914435	−	10.2061i	−0.0631020	−	0.704286i
$211$	−1.09372	−	1.89438i	−0.0752948	−	0.130414i	0.825920	−	0.563788i	$-0.190656\pi$
$211$	−1.09372	−	1.89438i	−0.0752948	−	0.130414i	−0.901214	+	0.433373i	$0.857323\pi$
$212$	−0.665678	−	2.48435i	−0.0457190	−	0.170626i
$213$	−13.0619	−	4.38446i	−0.894984	−	0.300418i
$214$	−10.4183	+	6.01503i	−0.712183	+	0.411179i
$215$	6.76446	+	12.5956i	0.461332	+	0.859015i
$216$	0.961714	−	5.10638i	0.0654363	−	0.347445i
$217$	9.07405	−	13.1719i	0.615987	−	0.894166i
$218$	−14.8565	+	3.98079i	−1.00621	+	0.269613i
$219$	−1.46398	+	23.5626i	−0.0989268	+	1.59222i
$220$	−3.12533	−	3.32373i	−0.210710	−	0.224086i
$221$	−20.6641			−1.39002
$222$	−18.7118	+	3.78816i	−1.25586	+	0.254245i
$223$	−2.18839	−	8.16719i	−0.146546	−	0.546916i	−0.999682	−	0.0252274i	$-0.991969\pi$
$223$	−2.18839	−	8.16719i	−0.146546	−	0.546916i	0.853136	−	0.521688i	$-0.174698\pi$
$224$	−2.60197	+	0.479300i	−0.173852	+	0.0320246i
$225$	−14.7424	−	2.76821i	−0.982824	−	0.184547i
$226$	8.99046	+	15.5719i	0.598037	+	1.03583i
$227$	3.61108	−	13.4767i	0.239676	−	0.894483i	−0.736309	−	0.676646i	$-0.763433\pi$
$227$	3.61108	−	13.4767i	0.239676	−	0.894483i	0.975985	−	0.217838i	$-0.0699004\pi$
$228$	−7.27366	+	1.47253i	−0.481710	+	0.0975209i
$229$	1.48473	−	2.57162i	0.0981135	−	0.169938i	−0.812790	−	0.582556i	$-0.802053\pi$
$229$	1.48473	−	2.57162i	0.0981135	−	0.169938i	0.910904	+	0.412619i	$0.135386\pi$
$230$	3.10586	+	0.935471i	0.204794	+	0.0616831i
$231$	−3.67107	+	8.59918i	−0.241538	+	0.565784i
$232$	−1.16435	−	4.34543i	−0.0764436	−	0.285291i
$233$	−1.95484	+	7.29558i	−0.128066	+	0.477949i	−0.999930	−	0.0117983i	$-0.996244\pi$
$233$	−1.95484	+	7.29558i	−0.128066	+	0.477949i	0.871864	+	0.489748i	$0.162911\pi$
$234$	−8.43357	−	1.05204i	−0.551320	−	0.0687741i
$235$	1.27978	−	2.06713i	0.0834838	−	0.134845i
$236$		−	8.54280i		−	0.556089i
$237$	−1.42157	+	4.23502i	−0.0923406	+	0.275094i
$238$	17.4276	−	8.28912i	1.12966	−	0.537304i
$239$	12.8950	−	7.44493i	0.834108	−	0.481573i	−0.0211491	−	0.999776i	$-0.506732\pi$
$239$	12.8950	−	7.44493i	0.834108	−	0.481573i	0.855257	+	0.518204i	$0.173399\pi$
$240$	−0.358919	+	3.85632i	−0.0231681	+	0.248924i
$241$	4.24046	−	2.44823i	0.273152	−	0.157704i	−0.357167	−	0.934040i	$-0.616257\pi$
$241$	4.24046	−	2.44823i	0.273152	−	0.157704i	0.630319	+	0.776336i	$0.282924\pi$
$242$	−1.76955	−	6.60405i	−0.113751	−	0.424525i
$243$	−0.755109	+	15.5702i	−0.0484403	+	0.998826i
$244$	12.7003			0.813052
$245$	12.9593	−	8.77820i	0.827939	−	0.560818i
$246$	−8.72859	+	13.1598i	−0.556514	+	0.839041i
$247$	3.14163	+	11.7247i	0.199897	+	0.746025i
$248$	−4.27482	+	4.27482i	−0.271451	+	0.271451i
$249$	0.119883	−	1.92950i	0.00759727	−	0.122277i
$250$	11.1328	+	1.03005i	0.704099	+	0.0651464i
$251$		−	15.4938i		−	0.977959i	−0.872295	−	0.488980i	$-0.837369\pi$
$251$		−	15.4938i		−	0.977959i	0.872295	−	0.488980i	$-0.162631\pi$
$252$	7.53467	−	2.49574i	0.474640	−	0.157217i
$253$	−2.09286	−	2.09286i	−0.131577	−	0.131577i
$254$			14.7021i			0.922492i
$255$	−4.75140	−	27.8476i	−0.297544	−	1.74389i
$256$	1.00000			0.0625000
$257$	9.66991	−	2.59104i	0.603192	−	0.161625i	0.0557168	−	0.998447i	$-0.482256\pi$
$257$	9.66991	−	2.59104i	0.603192	−	0.161625i	0.547475	+	0.836822i	$0.315589\pi$
$258$	−8.30140	+	7.33018i	−0.516822	+	0.456357i
$259$	−18.9153	−	22.1962i	−1.17534	−	1.37920i
$260$	6.33174	+	0.194787i	0.392678	+	0.0120802i
$261$	5.24938	+	12.4334i	0.324928	+	0.769610i
$262$	0.105797	−	0.0283483i	0.00653618	−	0.00175136i
$263$	−3.16754	+	11.8214i	−0.195319	+	0.728941i	0.796865	+	0.604157i	$0.206490\pi$
$263$	−3.16754	+	11.8214i	−0.195319	+	0.728941i	−0.992184	+	0.124783i	$0.960176\pi$
$264$	1.95337	−	2.94504i	0.120222	−	0.181255i
$265$	−2.72106	−	5.06669i	−0.167153	−	0.311244i
$266$	−7.35276	−	8.62810i	−0.450827	−	0.529023i
$267$	−0.372935	−	1.84214i	−0.0228233	−	0.112737i
$268$	−5.30820	−	5.30820i	−0.324250	−	0.324250i
$269$	9.74236	−	16.8743i	0.594002	−	1.02884i	−0.399685	−	0.916653i	$-0.630880\pi$
$269$	9.74236	−	16.8743i	0.594002	−	1.02884i	0.993687	−	0.112189i	$-0.0357863\pi$
$270$	−0.521403	−	11.6072i	−0.0317316	−	0.706394i
$271$	8.17466	−	4.71964i	0.496575	−	0.286698i	−0.230723	−	0.973019i	$-0.574109\pi$
$271$	8.17466	−	4.71964i	0.496575	−	0.286698i	0.727298	+	0.686322i	$0.240776\pi$
$272$	−7.04560	+	1.88786i	−0.427202	+	0.114468i
$273$	−4.83846	−	12.0470i	−0.292837	−	0.729118i
$274$	11.0937	−	6.40493i	0.670192	−	0.386936i
$275$	−8.50467	−	5.63428i	−0.512851	−	0.339760i
$276$	−0.155808	+	2.50771i	−0.00937852	+	0.150946i
$277$	5.08171	+	1.36164i	0.305330	+	0.0818130i	0.408231	−	0.912879i	$-0.366146\pi$
$277$	5.08171	+	1.36164i	0.305330	+	0.0818130i	−0.102901	+	0.994692i	$0.532812\pi$
$278$	−14.9792	−	4.01367i	−0.898393	−	0.240724i
$279$	10.9428	−	14.4634i	0.655127	−	0.865900i
$280$	−5.41816	+	2.37561i	−0.323797	+	0.141970i
$281$	1.29022	−	2.23473i	0.0769681	−	0.133313i	−0.824972	−	0.565173i	$-0.808809\pi$
$281$	1.29022	−	2.23473i	0.0769681	−	0.133313i	0.901940	+	0.431860i	$0.142143\pi$
$282$	1.78533	+	0.599279i	0.106315	+	0.0356865i
$283$	12.1915	−	12.1915i	0.724709	−	0.724709i	−0.244851	−	0.969561i	$-0.578739\pi$
$283$	12.1915	−	12.1915i	0.724709	−	0.724709i	0.969561	+	0.244851i	$0.0787391\pi$
$284$			7.95478i			0.472030i
$285$	−15.0782	+	6.92966i	−0.893156	+	0.410478i
$286$	−5.00583	−	2.89012i	−0.296001	−	0.170896i
$287$	−24.0454	−	1.91892i	−1.41935	−	0.113270i
$288$	−2.97160	+	0.411784i	−0.175103	+	0.0242646i
$289$	31.3540	−	18.1022i	1.84435	−	1.06484i
$290$	−4.75946	−	8.86227i	−0.279485	−	0.520410i
$291$	3.66200	+	0.227526i	0.214670	+	0.0133378i
$292$	13.1657	−	3.52774i	0.770464	−	0.206445i
$293$	−21.8856	−	5.86423i	−1.27857	−	0.342592i	−0.445263	−	0.895400i	$-0.646890\pi$
$293$	−21.8856	−	5.86423i	−1.27857	−	0.342592i	−0.833309	+	0.552808i	$0.813556\pi$
$294$	8.91312	+	8.21927i	0.519824	+	0.479357i
$295$	−4.37433	−	18.5947i	−0.254684	−	1.08262i
$296$	5.51122	+	9.54572i	0.320333	+	0.554834i
$297$	−4.59193	+	9.55587i	−0.266451	+	0.554488i
$298$	−5.08454	+	1.36240i	−0.294539	+	0.0789216i
$299$	4.10957			0.237663
$300$	1.19338	+	8.57764i	0.0689000	+	0.495230i
$301$	−15.9401	−	5.66434i	−0.918772	−	0.326487i
$302$	−13.6708	−	3.66307i	−0.786663	−	0.210786i
$303$	9.06414	−	1.83501i	0.520721	−	0.105419i
$304$	2.14232	+	3.71061i	0.122871	+	0.212818i
$305$	27.6440	−	6.50316i	1.58289	−	0.372370i
$306$	20.1593	−	8.51124i	1.15243	−	0.486555i
$307$	22.1004	+	22.1004i	1.26134	+	1.26134i	0.950445	+	0.310892i	$0.100628\pi$
$307$	22.1004	+	22.1004i	1.26134	+	1.26134i	0.310892	+	0.950445i	$0.399372\pi$
$308$	5.38112	+	0.429435i	0.306618	+	0.0244693i
$309$	−0.273758	+	4.40610i	−0.0155735	+	0.250654i
$310$	−7.11587	+	11.4937i	−0.404154	+	0.652798i
$311$		−	30.0068i		−	1.70153i	−0.525548	−	0.850764i	$-0.676140\pi$
$311$		−	30.0068i		−	1.70153i	0.525548	−	0.850764i	$-0.323860\pi$
$312$	0.973630	+	4.80930i	0.0551209	+	0.272273i
$313$	7.63266	−	7.63266i	0.431423	−	0.431423i	−0.457689	−	0.889112i	$-0.651323\pi$
$313$	7.63266	−	7.63266i	0.431423	−	0.431423i	0.889112	+	0.457689i	$0.151323\pi$
$314$	4.21107			0.237645
$315$	15.1224	−	9.29048i	0.852051	−	0.523459i
$316$	2.57916			0.145089
$317$	11.4800	−	11.4800i	0.644783	−	0.644783i	−0.306944	−	0.951728i	$-0.599306\pi$
$317$	11.4800	−	11.4800i	0.644783	−	0.644783i	0.951728	+	0.306944i	$0.0993065\pi$
$318$	3.33930	−	2.94862i	0.187259	−	0.165351i
$319$			9.17891i			0.513920i
$320$	2.17665	−	0.512049i	0.121678	−	0.0286244i
$321$	−17.3643	−	11.5173i	−0.969181	−	0.642833i
$322$	−3.46591	+	1.64850i	−0.193147	+	0.0918670i
$323$	−22.0991	−	22.0991i	−1.22962	−	1.22962i
$324$	8.66087	−	2.44732i	0.481159	−	0.135962i
$325$	13.8817	−	2.81818i	0.770019	−	0.156324i
$326$	9.29226	+	16.0947i	0.514651	+	0.891402i
$327$	−17.6329	−	19.9692i	−0.975103	−	1.10430i
$328$	8.80653	+	2.35970i	0.486259	+	0.130293i
$329$	0.521133	+	2.82907i	0.0287310	+	0.155972i
$330$	2.74380	−	7.41055i	0.151041	−	0.407937i
$331$	−24.3358			−1.33762			−0.668809	−	0.743435i	$-0.733195\pi$
$331$	−24.3358			−1.33762			−0.668809	+	0.743435i	$0.733195\pi$
$332$	−1.07812	+	0.288880i	−0.0591693	+	0.0158544i
$333$	−20.3080	−	26.0967i	−1.11287	−	1.43009i
$334$	−6.97665	−	12.0839i	−0.381745	−	0.661202i
$335$	−14.2722	−	8.83604i	−0.779772	−	0.482765i
$336$	−2.75032	−	3.66548i	−0.150042	−	0.199968i
$337$	26.9016	+	7.20827i	1.46542	+	0.392659i	0.901360	−	0.433071i	$-0.142570\pi$
$337$	26.9016	+	7.20827i	1.46542	+	0.392659i	0.564065	+	0.825730i	$0.309237\pi$
$338$	−4.80474	+	1.28743i	−0.261343	+	0.0700267i
$339$	−17.2145	+	25.9538i	−0.934964	+	1.40962i
$340$	−14.3691	+	7.71691i	−0.779275	+	0.418508i
$341$	10.6823	−	6.16744i	0.578480	−	0.333986i
$342$	−7.89410	−	10.1443i	−0.426864	−	0.548541i
$343$	−4.38262	+	17.9942i	−0.236639	+	0.971598i
$344$	5.53726	+	3.19694i	0.298549	+	0.172367i
$345$	0.944931	+	5.53818i	0.0508734	+	0.298166i
$346$			6.69782i			0.360077i
$347$	−13.6692	+	13.6692i	−0.733801	+	0.733801i	−0.971371	−	0.237569i	$-0.923649\pi$
$347$	−13.6692	+	13.6692i	−0.733801	+	0.733801i	0.237569	+	0.971371i	$0.423649\pi$
$348$	5.84085	−	5.15751i	0.313102	−	0.276471i
$349$	0.763709	−	1.32278i	0.0408804	−	0.0708069i	−0.844861	−	0.534985i	$-0.820317\pi$
$349$	0.763709	−	1.32278i	0.0408804	−	0.0708069i	0.885742	+	0.464179i	$0.153650\pi$
$350$	−10.5770	+	7.94523i	−0.565365	+	0.424691i
$351$	−4.87363	−	13.8904i	−0.260135	−	0.741415i
$352$	−1.97082	−	0.528078i	−0.105045	−	0.0281467i
$353$	25.4902	+	6.83008i	1.35671	+	0.363528i	0.862606	−	0.505877i	$-0.168831\pi$
$353$	25.4902	+	6.83008i	1.35671	+	0.363528i	0.494100	+	0.869405i	$0.335498\pi$
$354$	13.2483	−	6.58941i	0.704140	−	0.350223i
$355$	4.07324	+	17.3148i	0.216185	+	0.918973i
$356$	−0.939753	+	0.542567i	−0.0498068	+	0.0287560i
$357$	26.2975	+	20.6333i	1.39181	+	1.09203i
$358$	9.02724	−	2.41884i	0.477105	−	0.127840i
$359$	6.19249	−	3.57524i	0.326827	−	0.188694i	−0.327604	−	0.944815i	$-0.606241\pi$
$359$	6.19249	−	3.57524i	0.326827	−	0.188694i	0.654432	+	0.756121i	$0.272908\pi$
$360$	−6.25729	+	2.41792i	−0.329788	+	0.127435i
$361$	0.320910	−	0.555832i	0.0168900	−	0.0292543i
$362$	−13.6813	−	13.6813i	−0.719075	−	0.719075i
$363$	8.87675	−	7.83822i	0.465909	−	0.411400i
$364$	−5.70484	+	4.86160i	−0.299015	+	0.254817i
$365$	26.8507	−	14.4201i	1.40543	−	0.754784i
$366$	9.79624	+	19.6958i	0.512057	+	1.02952i
$367$	−5.31073	+	19.8199i	−0.277218	+	1.03459i	0.677122	+	0.735871i	$0.263227\pi$
$367$	−5.31073	+	19.8199i	−0.277218	+	1.03459i	−0.954340	+	0.298721i	$0.903440\pi$
$368$	1.40119	−	0.375448i	0.0730420	−	0.0195716i
$369$	−27.1412	−	3.38572i	−1.41292	−	0.176253i
$370$	16.8839	+	17.9557i	0.877751	+	0.933471i
$371$	6.41202	+	2.27852i	0.332896	+	0.118295i
$372$	−9.92680	−	3.33212i	−0.514681	−	0.172762i
$373$	0.437545	−	0.117240i	0.0226552	−	0.00607045i	−0.247474	−	0.968895i	$-0.579600\pi$
$373$	0.437545	−	0.117240i	0.0226552	−	0.00607045i	0.270129	+	0.962824i	$0.412934\pi$
$374$	14.8825			0.769556
$375$	6.98975	+	18.0594i	0.360949	+	0.932586i
$376$		−	1.08728i		−	0.0560721i
$377$	−9.01191	−	9.01191i	−0.464137	−	0.464137i
$378$	9.68224	+	9.75983i	0.498001	+	0.501992i
$379$		−	35.6704i		−	1.83226i	−0.400877	−	0.916132i	$-0.631294\pi$
$379$		−	35.6704i		−	1.83226i	0.400877	−	0.916132i	$-0.368706\pi$
$380$	6.56310	+	6.97973i	0.336680	+	0.358052i
$381$	−22.8003	+	11.3403i	−1.16809	+	0.580983i
$382$	−0.629495	+	0.629495i	−0.0322078	+	0.0322078i
$383$	0.985194	+	3.67680i	0.0503411	+	0.187875i	0.986518	−	0.163654i	$-0.0523282\pi$
$383$	0.985194	+	3.67680i	0.0503411	+	0.187875i	−0.936177	+	0.351530i	$0.885662\pi$
$384$	0.771341	+	1.55082i	0.0393623	+	0.0791398i
$385$	11.9327	−	1.82067i	0.608147	−	0.0927899i
$386$	2.89133			0.147165
$387$	−17.7710	−	7.21988i	−0.903350	−	0.367007i
$388$	−0.548265	−	2.04615i	−0.0278339	−	0.103878i
$389$	0.702002	−	0.405301i	0.0355929	−	0.0205496i	−0.482098	−	0.876117i	$-0.660125\pi$
$389$	0.702002	−	0.405301i	0.0355929	−	0.0205496i	0.517691	+	0.855568i	$0.326792\pi$
$390$	4.58185	+	9.96961i	0.232011	+	0.504831i
$391$	−9.16342	+	5.29050i	−0.463414	+	0.267552i
$392$	2.86116	−	6.38857i	0.144510	−	0.322671i
$393$	0.125569	+	0.142206i	0.00633411	+	0.00717335i
$394$		−	15.2659i		−	0.769084i
$395$	5.61394	−	1.32066i	0.282468	−	0.0664495i
$396$	6.07394	+	0.757691i	0.305227	+	0.0380754i
$397$	−0.998137	+	3.72510i	−0.0500950	+	0.186957i	−0.986439	−	0.164126i	$-0.947520\pi$
$397$	−0.998137	+	3.72510i	−0.0500950	+	0.186957i	0.936344	+	0.351083i	$0.114186\pi$
$398$	3.95182	+	14.7484i	0.198087	+	0.739270i
$399$	7.70912	−	18.0580i	0.385939	−	0.904031i
$400$	4.47561	−	2.22910i	0.223781	−	0.111455i
$401$	11.7601	−	20.3690i	0.587269	−	1.01718i	−0.407319	−	0.913286i	$-0.633536\pi$
$401$	11.7601	−	20.3690i	0.587269	−	1.01718i	0.994588	−	0.103894i	$-0.0331302\pi$
$402$	4.13762	−	12.3265i	0.206366	−	0.614789i
$403$	−4.43274	+	16.5432i	−0.220811	+	0.824076i
$404$	−2.66967	−	4.62401i	−0.132821	−	0.230053i
$405$	17.5985	−	9.76174i	0.874478	−	0.485065i
$406$	11.2154	+	3.98542i	0.556612	+	0.197793i
$407$	−5.82072	−	21.7232i	−0.288522	−	1.07678i
$408$	−8.36229	−	9.47025i	−0.413995	−	0.468847i
$409$	−17.3266			−0.856746			−0.428373	−	0.903602i	$-0.640913\pi$
$409$	−17.3266			−0.856746			−0.428373	+	0.903602i	$0.640913\pi$
$410$	20.3770	+	0.626871i	1.00635	+	0.0309589i
$411$	18.4899	+	12.2639i	0.912037	+	0.604931i
$412$	2.46192	−	0.659670i	0.121290	−	0.0324996i
$413$	18.6130	+	12.8224i	0.915884	+	0.630948i
$414$	−4.00918	+	1.69267i	−0.197040	+	0.0831901i
$415$	−2.19876	+	1.18084i	−0.107933	+	0.0579651i
$416$	2.45343	−	1.41649i	0.120289	−	0.0694491i
$417$	−5.32961	−	26.3259i	−0.260992	−	1.28919i
$418$	−2.26263	−	8.44425i	−0.110669	−	0.413022i
$419$	−17.8933	−	30.9922i	−0.874147	−	1.51407i	−0.857668	−	0.514203i	$-0.828088\pi$
$419$	−17.8933	−	30.9922i	−0.874147	−	1.51407i	−0.0164788	−	0.999864i	$-0.505246\pi$
$420$	−7.86338	−	6.57018i	−0.383694	−	0.320592i
$421$	−9.58742	+	16.6059i	−0.467262	+	0.809322i	−0.999300	−	0.0373983i	$-0.988093\pi$
$421$	−9.58742	+	16.6059i	−0.467262	+	0.809322i	0.532038	+	0.846720i	$0.321426\pi$
$422$	−2.11291	−	0.566151i	−0.102855	−	0.0275598i
$423$	0.447724	+	3.23096i	0.0217691	+	0.157095i
$424$	−2.22740	−	1.28599i	−0.108172	−	0.0624533i
$425$	−27.3251	+	24.1547i	−1.32546	+	1.17168i
$426$	−12.3364	+	6.13585i	−0.597701	+	0.297283i
$427$	−19.0626	+	27.6712i	−0.922502	+	1.33910i
$428$	−3.11361	+	11.6202i	−0.150502	+	0.561681i
$429$	0.620842	−	9.99239i	0.0299745	−	0.482437i
$430$	13.6897	+	4.12326i	0.660174	+	0.198841i
$431$	−3.44883	+	5.97354i	−0.166124	+	0.287735i	−0.937054	−	0.349185i	$-0.886459\pi$
$431$	−3.44883	+	5.97354i	−0.166124	+	0.287735i	0.770930	+	0.636920i	$0.219792\pi$
$432$	−2.93072	−	4.29079i	−0.141004	−	0.206441i
$433$	−7.31840	+	7.31840i	−0.351700	+	0.351700i	−0.860742	−	0.509042i	$-0.830000\pi$
$433$	−7.31840	+	7.31840i	−0.351700	+	0.351700i	0.509042	+	0.860742i	$0.330000\pi$
$434$	−2.89761	−	15.7303i	−0.139090	−	0.755076i
$435$	10.0726	−	14.2169i	0.482944	−	0.681648i
$436$	−7.69030	+	13.3200i	−0.368299	+	0.637912i
$437$	4.39494	+	4.39494i	0.210238	+	0.210238i
$438$	15.6261	+	17.6965i	0.746645	+	0.845572i
$439$	20.7268			0.989237			0.494619	−	0.869110i	$-0.335308\pi$
$439$	20.7268			0.989237			0.494619	+	0.869110i	$0.335308\pi$
$440$	−4.56018	−	0.140288i	−0.217398	−	0.00668794i
$441$	−5.87153	+	20.1625i	−0.279597	+	0.960118i
$442$	−14.6118	+	14.6118i	−0.695010	+	0.695010i
$443$	6.49240	+	6.49240i	0.308463	+	0.308463i	0.844313	−	0.535850i	$-0.180009\pi$
$443$	6.49240	+	6.49240i	0.308463	+	0.308463i	−0.535850	+	0.844313i	$0.680009\pi$
$444$	−10.5526	+	15.9099i	−0.500806	+	0.755051i
$445$	−1.76769	+	1.66218i	−0.0837967	+	0.0787948i
$446$	−7.32251	−	4.22765i	−0.346731	−	0.200185i
$447$	−6.03474	−	6.83432i	−0.285433	−	0.323252i
$448$	−1.50096	+	2.17879i	−0.0709136	+	0.102938i
$449$			21.1898i			1.00001i	0.866022	+	0.500005i	$0.166669\pi$
$449$			21.1898i			1.00001i	−0.866022	+	0.500005i	$0.833331\pi$
$450$	−12.3818	+	8.46700i	−0.583685	+	0.399138i
$451$	−16.1099	−	9.30108i	−0.758588	−	0.437971i
$452$	17.3682	+	4.65380i	0.816933	+	0.218897i
$453$	−4.86406	−	24.0263i	−0.228534	−	1.12885i
$454$	−6.97608	−	12.0829i	−0.327404	−	0.567080i
$455$	−9.92807	+	13.5032i	−0.465435	+	0.633038i
$456$	−4.10202	+	6.18450i	−0.192095	+	0.289616i
$457$	13.3723	−	13.3723i	0.625531	−	0.625531i	−0.321410	−	0.946940i	$-0.604157\pi$
$457$	13.3723	−	13.3723i	0.625531	−	0.625531i	0.946940	+	0.321410i	$0.104157\pi$
$458$	−0.768551	−	2.86827i	−0.0359120	−	0.134026i
$459$	28.7491	+	24.6984i	1.34189	+	1.15282i
$460$	2.85765	−	1.53470i	0.133239	−	0.0715556i
$461$	19.4589	+	11.2346i	0.906291	+	0.523247i	0.879236	−	0.476386i	$-0.158054\pi$
$461$	19.4589	+	11.2346i	0.906291	+	0.523247i	0.0270552	+	0.999634i	$0.491387\pi$
$462$	3.48470	+	8.67637i	0.162123	+	0.403661i
$463$	−4.02103	+	15.0067i	−0.186873	+	0.697420i	0.807349	+	0.590075i	$0.200902\pi$
$463$	−4.02103	+	15.0067i	−0.186873	+	0.697420i	−0.994222	+	0.107346i	$0.965765\pi$
$464$	−3.89600	−	2.24936i	−0.180867	−	0.104424i
$465$	−23.3134	−	2.16985i	−1.08113	−	0.100624i
$466$	3.77647	+	6.54104i	0.174942	+	0.303008i
$467$	−8.61114	+	32.1372i	−0.398476	+	1.48713i	0.417302	+	0.908768i	$0.362976\pi$
$467$	−8.61114	+	32.1372i	−0.398476	+	1.48713i	−0.815778	+	0.578365i	$0.803691\pi$
$468$	−6.70734	+	5.21953i	−0.310047	+	0.241273i
$469$	19.5329	−	3.59807i	0.901943	−	0.166144i
$470$	−0.556740	−	2.36663i	−0.0256805	−	0.109164i
$471$	3.24817	+	6.53061i	0.149668	+	0.300914i
$472$	−6.04067	−	6.04067i	−0.278044	−	0.278044i
$473$	−9.22468	−	9.22468i	−0.424151	−	0.424151i
$474$	1.98941	+	3.99981i	0.0913768	+	0.183717i
$475$	17.8595	+	11.8318i	0.819452	+	0.542880i
$476$	6.46189	−	18.1845i	0.296180	−	0.833484i
$477$	7.14851	+	2.90425i	0.327308	+	0.132977i
$478$	3.85378	−	14.3825i	0.176268	−	0.657840i
$479$	−8.15578	−	14.1262i	−0.372647	−	0.645444i	0.617325	−	0.786709i	$-0.288217\pi$
$479$	−8.15578	−	14.1262i	−0.372647	−	0.645444i	−0.989972	+	0.141265i	$0.954883\pi$
$480$	2.47303	+	2.98062i	0.112878	+	0.136046i
$481$	27.0428	+	15.6132i	1.23305	+	0.711900i
$482$	1.26730	−	4.72962i	0.0577238	−	0.215428i
$483$	−5.22991	−	4.10344i	−0.237969	−	0.186713i
$484$	−5.92103	−	3.41851i	−0.269138	−	0.155387i
$485$	−2.24111	−	4.17302i	−0.101764	−	0.189487i
$486$	10.4758	+	11.5437i	0.475193	+	0.523633i
$487$	−7.18763	−	26.8246i	−0.325703	−	1.21554i	−0.913604	−	0.406606i	$-0.866712\pi$
$487$	−7.18763	−	26.8246i	−0.325703	−	1.21554i	0.587901	−	0.808933i	$-0.299954\pi$
$488$	8.98045	−	8.98045i	0.406526	−	0.406526i
$489$	−17.7924	+	26.8251i	−0.804600	+	1.21307i
$490$	2.95648	−	15.3707i	0.133560	−	0.694379i
$491$	−9.70454	−	16.8088i	−0.437960	−	0.758569i	0.559572	−	0.828782i	$-0.310965\pi$
$491$	−9.70454	−	16.8088i	−0.437960	−	0.758569i	−0.997532	+	0.0702129i	$0.977632\pi$
$492$	3.13337	+	15.4775i	0.141263	+	0.697777i
$493$	31.6962	+	8.49296i	1.42752	+	0.382504i
$494$	10.5121	+	6.06915i	0.472961	+	0.273064i
$495$	13.6088	−	1.46093i	0.611671	−	0.0656638i
$496$			6.04551i			0.271451i
$497$	−17.3318	−	11.9398i	−0.777438	−	0.535573i
$498$	−1.27959	−	1.44913i	−0.0573400	−	0.0649373i
$499$	3.11042	+	1.79580i	0.139241	+	0.0803911i	0.568002	−	0.823027i	$-0.307716\pi$
$499$	3.11042	+	1.79580i	0.139241	+	0.0803911i	−0.428761	+	0.903418i	$0.641050\pi$
$500$	8.60043	−	7.14371i	0.384623	−	0.319477i
$501$	13.3586	−	20.1403i	0.596817	−	0.899803i
$502$	−10.9558	−	10.9558i	−0.488980	−	0.488980i
$503$	22.4946	−	22.4946i	1.00298	−	1.00298i	0.00298850	−	0.999996i	$-0.499049\pi$
$503$	22.4946	−	22.4946i	1.00298	−	1.00298i	0.999996	−	0.00298850i	$-0.000951269\pi$
$504$	3.56306	−	7.09257i	0.158711	−	0.315928i
$505$	−8.17866	−	8.69785i	−0.363946	−	0.387049i
$506$	−2.95975			−0.131577
$507$	−5.70265	−	6.45823i	−0.253264	−	0.286820i
$508$	10.3960	+	10.3960i	0.461246	+	0.461246i
$509$	−2.54377	+	4.40595i	−0.112751	+	0.195290i	−0.916878	−	0.399167i	$-0.869300\pi$
$509$	−2.54377	+	4.40595i	−0.112751	+	0.195290i	0.804128	+	0.594457i	$0.202633\pi$
$510$	−23.0510	−	16.3315i	−1.02072	−	0.723172i
$511$	−12.0750	+	33.9803i	−0.534164	+	1.50320i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	9.64290	−	20.0670i	0.425745	−	0.885981i
$514$	5.00551	−	8.66980i	0.220784	−	0.382409i
$515$	5.02096	−	2.69650i	0.221250	−	0.118822i
$516$	−0.686752	+	11.0532i	−0.0302326	+	0.486590i
$517$	−0.574169	+	2.14283i	−0.0252519	+	0.0942414i
$518$	−29.0702	−	2.31992i	−1.27727	−	0.101931i
$519$	−10.3871	+	5.16630i	−0.455943	+	0.226775i
$520$	4.61495	−	4.33948i	0.202379	−	0.190299i
$521$	−8.81828	−	5.09124i	−0.386336	−	0.223051i	0.294235	−	0.955733i	$-0.404935\pi$
$521$	−8.81828	−	5.09124i	−0.386336	−	0.223051i	−0.680571	+	0.732682i	$0.738268\pi$
$522$	12.5036	+	5.07989i	0.547269	+	0.222341i
$523$	−4.57877	−	1.22688i	−0.200216	−	0.0536477i	0.157317	−	0.987548i	$-0.449715\pi$
$523$	−4.57877	−	1.22688i	−0.200216	−	0.0536477i	−0.357533	+	0.933900i	$0.616382\pi$
$524$	0.0547647	−	0.0948553i	0.00239241	−	0.00414377i
$525$	−20.4801	−	10.2745i	−0.893824	−	0.448418i
$526$	6.11922	+	10.5988i	0.266811	+	0.462130i
$527$	−11.4131	−	42.5942i	−0.497162	−	1.85543i
$528$	−0.701217	−	3.46370i	−0.0305166	−	0.150738i
$529$	−18.0962	+	10.4479i	−0.786792	+	0.454255i
$530$	−5.50677	−	1.65861i	−0.239199	−	0.0720456i
$531$	20.4379	+	15.4630i	0.886931	+	0.671039i
$532$	−11.3002	−	0.901799i	−0.489925	−	0.0390979i
$533$	24.9487	−	6.68499i	1.08065	−	0.289559i
$534$	−1.56629	−	1.03888i	−0.0677801	−	0.0449568i
$535$	−0.827151	+	26.8873i	−0.0357609	+	1.16244i
$536$	−7.50693			−0.324250
$537$	10.7143	+	12.1338i	0.462354	+	0.523614i
$538$	−5.04302	−	18.8208i	−0.217420	−	0.811422i
$539$	−9.01248	+	11.0798i	−0.388195	+	0.477239i
$540$	−8.57625	−	7.83887i	−0.369063	−	0.337331i
$541$	13.7148	+	23.7548i	0.589646	+	1.02130i	0.994279	+	0.106817i	$0.0340661\pi$
$541$	13.7148	+	23.7548i	0.589646	+	1.02130i	−0.404633	+	0.914479i	$0.632601\pi$
$542$	2.44307	−	9.11765i	0.104939	−	0.391636i
$543$	10.6643	−	31.7702i	0.457648	−	1.36339i
$544$	−3.64707	+	6.31691i	−0.156367	+	0.270835i
$545$	−9.91860	+	32.9308i	−0.424866	+	1.41060i
$546$	−11.9398	−	5.09722i	−0.510977	−	0.218141i
$547$	1.36315	+	5.08735i	0.0582842	+	0.217519i	0.988925	−	0.148413i	$-0.0474166\pi$
$547$	1.36315	+	5.08735i	0.0582842	+	0.217519i	−0.930641	+	0.365933i	$0.880750\pi$
$548$	3.31543	−	12.3734i	0.141628	−	0.528564i
$549$	−22.9883	+	30.3843i	−0.981118	+	1.29677i
$550$	−9.99775	+	2.02968i	−0.426305	+	0.0865458i
$551$		−	19.2754i		−	0.821160i
$552$	1.66304	+	1.88339i	0.0707839	+	0.0801624i
$553$	−3.87121	+	5.61946i	−0.164621	+	0.238964i
$554$	4.55614	−	2.63049i	0.193572	−	0.111759i
$555$	−14.8227	+	40.0338i	−0.629190	+	1.69934i
$556$	−13.4300	+	7.75381i	−0.569559	+	0.328835i
$557$	5.29922	+	19.7770i	0.224535	+	0.837977i	0.982590	+	0.185786i	$0.0594833\pi$
$557$	5.29922	+	19.7770i	0.224535	+	0.837977i	−0.758055	+	0.652191i	$0.773850\pi$
$558$	−2.48944	−	17.9649i	−0.105386	−	0.760513i
$559$	18.1137			0.766128
$560$	−2.15141	+	5.51103i	−0.0909137	+	0.232883i
$561$	11.4795	+	23.0801i	0.484664	+	0.974441i
$562$	−0.667867	−	2.49251i	−0.0281723	−	0.105140i
$563$	2.26517	−	2.26517i	0.0954655	−	0.0954655i	−0.657761	−	0.753227i	$-0.728496\pi$
$563$	2.26517	−	2.26517i	0.0954655	−	0.0954655i	0.753227	+	0.657761i	$0.228496\pi$
$564$	1.68617	−	0.838663i	0.0710006	−	0.0353141i
$565$	40.1876	+	1.23631i	1.69070	+	0.0520121i
$566$		−	17.2414i		−	0.724709i
$567$	−7.66741	+	22.5435i	−0.322001	+	0.946739i
$568$	5.62488	+	5.62488i	0.236015	+	0.236015i
$569$			25.2808i			1.05983i	0.848051	+	0.529914i	$0.177776\pi$
$569$			25.2808i			1.05983i	−0.848051	+	0.529914i	$0.822224\pi$
$570$	−5.76189	+	15.5619i	−0.241339	+	0.651817i
$571$	−15.2250			−0.637144			−0.318572	−	0.947899i	$-0.603203\pi$
$571$	−15.2250			−0.637144			−0.318572	+	0.947899i	$0.603203\pi$
$572$	−5.58328	+	1.49604i	−0.233449	+	0.0625524i
$573$	−1.46179	−	0.490677i	−0.0610671	−	0.0204983i
$574$	−18.3595	+	15.6458i	−0.766312	+	0.653042i
$575$	5.43427	−	4.80375i	0.226625	−	0.200330i
$576$	−1.81007	+	2.39242i	−0.0754194	+	0.0996840i
$577$	−34.0132	+	9.11382i	−1.41599	+	0.379413i	−0.884059	−	0.467375i	$-0.845200\pi$
$577$	−34.0132	+	9.11382i	−1.41599	+	0.379413i	−0.531930	+	0.846788i	$0.678533\pi$
$578$	9.37040	−	34.9708i	0.389757	−	1.45459i
$579$	2.23020	+	4.48393i	0.0926840	+	0.186346i
$580$	−9.63202	−	2.90112i	−0.399948	−	0.120463i
$581$	0.988796	−	2.78258i	0.0410222	−	0.115441i
$582$	2.75031	−	2.42854i	0.114004	−	0.100666i
$583$	3.71070	+	3.71070i	0.153681	+	0.153681i
$584$	6.81507	−	11.8040i	0.282009	−	0.488455i
$585$	−11.9269	+	14.7956i	−0.493116	+	0.611722i
$586$	−19.6221	+	11.3288i	−0.810582	+	0.467990i
$587$	20.6779	−	5.54063i	0.853469	−	0.228686i	0.194543	−	0.980894i	$-0.437678\pi$
$587$	20.6779	−	5.54063i	0.853469	−	0.228686i	0.658926	+	0.752208i	$0.271011\pi$
$588$	12.1144	−	0.490627i	0.499590	−	0.0202331i
$589$	−22.4325	+	12.9514i	−0.924316	+	0.533654i
$590$	−16.2416	−	10.0553i	−0.668654	−	0.413970i
$591$	23.6746	−	11.7752i	0.973842	−	0.484367i
$592$	10.6469	+	2.85282i	0.437584	+	0.117250i
$593$	−26.0301	−	6.97475i	−1.06893	−	0.286419i	−0.318876	−	0.947796i	$-0.603305\pi$
$593$	−26.0301	−	6.97475i	−1.06893	−	0.286419i	−0.750053	+	0.661378i	$0.769972\pi$
$594$	3.51004	+	10.0040i	0.144019	+	0.410469i
$595$	4.75392	−	42.8901i	0.194892	−	1.75832i
$596$	−2.63195	+	4.55867i	−0.107809	+	0.186730i
$597$	−19.8239	+	17.5046i	−0.811337	+	0.716415i
$598$	2.90590	−	2.90590i	0.118831	−	0.118831i
$599$			31.6035i			1.29129i	0.763639	+	0.645643i	$0.223411\pi$
$599$			31.6035i			1.29129i	−0.763639	+	0.645643i	$0.776589\pi$
$600$	6.90915	+	5.22146i	0.282065	+	0.213165i
$601$	25.4446	+	14.6905i	1.03791	+	0.599237i	0.919240	−	0.393697i	$-0.128804\pi$
$601$	25.4446	+	14.6905i	1.03791	+	0.599237i	0.118668	+	0.992934i	$0.462138\pi$
$602$	−15.2766	+	7.26605i	−0.622629	+	0.296142i
$603$	22.3076	−	3.09123i	0.908437	−	0.125885i
$604$	−12.2569	+	7.07650i	−0.498725	+	0.287939i
$605$	−14.6385	−	4.40904i	−0.595138	−	0.179253i
$606$	5.11176	−	7.70686i	0.207651	−	0.313070i
$607$	−8.46555	+	2.26834i	−0.343606	+	0.0920689i	−0.426495	−	0.904490i	$-0.640252\pi$
$607$	−8.46555	+	2.26834i	−0.343606	+	0.0920689i	0.0828893	+	0.996559i	$0.473585\pi$
$608$	4.13865	+	1.10895i	0.167844	+	0.0449738i
$609$	2.47025	+	20.4672i	0.100100	+	0.829372i
$610$	14.9489	−	24.1457i	0.605262	−	0.977632i
$611$	−1.54012	−	2.66756i	−0.0623066	−	0.107918i
$612$	8.23645	−	20.2732i	0.332939	−	0.819494i
$613$	−7.64709	+	2.04903i	−0.308863	+	0.0827596i	−0.409921	−	0.912121i	$-0.634444\pi$
$613$	−7.64709	+	2.04903i	−0.308863	+	0.0827596i	0.101058	+	0.994881i	$0.467777\pi$
$614$	31.2547			1.26134
$615$	14.7455	+	32.0846i	0.594595	+	1.29377i
$616$	4.10868	−	3.50137i	0.165544	−	0.141074i
$617$	−30.6120	−	8.20246i	−1.23239	−	0.330219i	−0.416882	−	0.908961i	$-0.636877\pi$
$617$	−30.6120	−	8.20246i	−1.23239	−	0.330219i	−0.815511	+	0.578742i	$0.803544\pi$
$618$	2.92201	+	3.30916i	0.117540	+	0.133114i
$619$	11.9435	+	20.6868i	0.480052	+	0.831474i	0.999738	−	0.0228830i	$-0.00728453\pi$
$619$	11.9435	+	20.6868i	0.480052	+	0.831474i	−0.519686	+	0.854357i	$0.673951\pi$
$620$	3.09560	+	13.1590i	0.124322	+	0.528476i
$621$	−5.71746	−	4.91188i	−0.229434	−	0.197107i
$622$	−21.2180	−	21.2180i	−0.850764	−	0.850764i
$623$	0.228391	−	2.86189i	0.00915027	−	0.114659i
$624$	4.08915	+	2.71223i	0.163697	+	0.108576i
$625$	15.0622	−	19.9532i	0.602488	−	0.798128i
$626$		−	10.7942i		−	0.431423i
$627$	11.3502	−	10.0223i	0.453284	−	0.400253i
$628$	2.97768	−	2.97768i	0.118822	−	0.118822i
$629$	−80.3993			−3.20573
$630$	4.12379	−	17.2625i	0.164296	−	0.687755i
$631$	−5.43850			−0.216503			−0.108252	−	0.994124i	$-0.534525\pi$
$631$	−5.43850			−0.216503			−0.108252	+	0.994124i	$0.534525\pi$
$632$	1.82374	−	1.82374i	0.0725446	−	0.0725446i
$633$	−0.751773	−	3.71343i	−0.0298803	−	0.147595i
$634$		−	16.2352i		−	0.644783i
$635$	27.9516	+	17.3051i	1.10923	+	0.686733i
$636$	0.276251	−	4.44623i	0.0109541	−	0.176305i
$637$	−2.02968	−	19.7267i	−0.0804187	−	0.781601i
$638$	6.49047	+	6.49047i	0.256960	+	0.256960i
$639$	−19.0312	−	14.3987i	−0.752861	−	0.569603i
$640$	1.17705	−	1.90120i	0.0465270	−	0.0751514i
$641$	5.48545	+	9.50109i	0.216662	+	0.375270i	0.953786	−	0.300488i	$-0.0971496\pi$
$641$	5.48545	+	9.50109i	0.216662	+	0.375270i	−0.737123	+	0.675758i	$0.763816\pi$
$642$	−20.4224	+	4.13446i	−0.806007	+	0.163174i
$643$	−21.3742	−	5.72720i	−0.842916	−	0.225859i	−0.188576	−	0.982059i	$-0.560387\pi$
$643$	−21.3742	−	5.72720i	−0.842916	−	0.225859i	−0.654341	+	0.756200i	$0.727054\pi$
$644$	−1.28510	+	3.61643i	−0.0506402	+	0.142507i
$645$	4.16496	+	24.4106i	0.163995	+	0.961166i
$646$	−31.2528			−1.22962
$647$	24.0076	−	6.43281i	0.943835	−	0.252900i	0.246091	−	0.969247i	$-0.420854\pi$
$647$	24.0076	−	6.43281i	0.943835	−	0.252900i	0.697744	+	0.716347i	$0.254187\pi$
$648$	4.39364	−	7.85467i	0.172599	−	0.308561i
$649$	8.71510	+	15.0950i	0.342098	+	0.592531i
$650$	7.82310	−	11.8086i	0.306847	−	0.463172i
$651$	22.1597	−	16.6271i	0.868507	−	0.651666i
$652$	17.9513	+	4.81003i	0.703026	+	0.188375i
$653$	20.9034	−	5.60104i	0.818013	−	0.219186i	0.174535	−	0.984651i	$-0.444158\pi$
$653$	20.9034	−	5.60104i	0.818013	−	0.219186i	0.643477	+	0.765465i	$0.277491\pi$
$654$	−26.5887	−	1.65200i	−1.03970	−	0.0645982i
$655$	0.0706331	−	0.234509i	0.00275986	−	0.00916302i
$656$	7.89572	−	4.55860i	0.308276	−	0.177983i
$657$	−15.3910	+	37.8833i	−0.600459	+	1.47797i
$658$	2.36895	+	1.63196i	0.0923514	+	0.0636204i
$659$	34.6743	+	20.0192i	1.35072	+	0.779838i	0.988350	−	0.152197i	$-0.0486348\pi$
$659$	34.6743	+	20.0192i	1.35072	+	0.779838i	0.362369	+	0.932035i	$0.381968\pi$
$660$	−3.29989	−	7.18021i	−0.128448	−	0.279489i
$661$		−	35.8298i		−	1.39362i	−0.717256	−	0.696810i	$-0.754602\pi$
$661$		−	35.8298i		−	1.39362i	0.717256	−	0.696810i	$-0.245398\pi$
$662$	−17.2080	+	17.2080i	−0.668809	+	0.668809i
$663$	−33.9308	−	11.3895i	−1.31776	−	0.442332i
$664$	−0.558074	+	0.966612i	−0.0216575	+	0.0375118i
$665$	−25.0583	+	3.82335i	−0.971719	+	0.148263i
$666$	−32.8130	−	4.09325i	−1.27148	−	0.158610i
$667$	−6.30356	−	1.68903i	−0.244075	−	0.0653996i
$668$	−13.4779	−	3.61138i	−0.521474	−	0.139729i
$669$	0.908165	−	14.6168i	0.0351117	−	0.565119i
$670$	−16.3400	+	3.84392i	−0.631268	+	0.148504i
$671$	−22.4412	+	12.9564i	−0.866332	+	0.500177i
$672$	−4.53665	−	0.647121i	−0.175005	−	0.0249632i
$673$	4.18746	−	1.12203i	0.161415	−	0.0432510i	−0.177207	−	0.984174i	$-0.556706\pi$
$673$	4.18746	−	1.12203i	0.161415	−	0.0432510i	0.338621	+	0.940923i	$0.390039\pi$
$674$	24.1193	−	13.9253i	0.929042	−	0.536383i
$675$	−22.6814	−	12.6710i	−0.873007	−	0.487708i
$676$	−2.48712	+	4.30781i	−0.0956583	+	0.165685i
$677$	−11.4193	−	11.4193i	−0.438880	−	0.438880i	0.452755	−	0.891635i	$-0.350441\pi$
$677$	−11.4193	−	11.4193i	−0.438880	−	0.438880i	−0.891635	+	0.452755i	$0.850441\pi$
$678$	6.17963	+	30.5246i	0.237327	+	1.17229i
$679$	5.28106	+	1.87663i	0.202669	+	0.0720186i
$680$	−4.70383	+	15.6172i	−0.180383	+	0.598892i
$681$	13.3575	−	20.1387i	0.511859	−	0.771716i
$682$	3.19250	−	11.9146i	0.122247	−	0.456233i
$683$	−1.96557	+	0.526673i	−0.0752105	+	0.0201526i	−0.296228	−	0.955117i	$-0.595729\pi$
$683$	−1.96557	+	0.526673i	−0.0752105	+	0.0201526i	0.221018	+	0.975270i	$0.429062\pi$
$684$	−12.7551	−	1.59113i	−0.487702	−	0.0608382i
$685$	0.880767	−	28.6302i	0.0336524	−	1.09390i
$686$	9.62486	+	15.8228i	0.367479	+	0.604118i
$687$	3.85535	−	3.40430i	0.147091	−	0.129882i
$688$	6.17601	−	1.65486i	0.235458	−	0.0630908i
$689$	−7.28637			−0.277589
$690$	4.58426	+	3.24792i	0.174520	+	0.123646i
$691$		−	18.5952i		−	0.707393i	−0.935360	−	0.353697i	$-0.884925\pi$
$691$		−	18.5952i		−	0.707393i	0.935360	−	0.353697i	$-0.115075\pi$
$692$	4.73607	+	4.73607i	0.180039	+	0.180039i
$693$	−10.7676	+	12.0966i	−0.409026	+	0.459511i
$694$			19.3312i			0.733801i
$695$	−25.2621	+	23.7541i	−0.958245	+	0.901046i
$696$	0.483197	−	7.77701i	0.0183155	−	0.294787i
$697$	−47.0241	+	47.0241i	−1.78116	+	1.78116i
$698$	−0.395325	−	1.47537i	−0.0149633	−	0.0558437i
$699$	−7.23101	+	10.9020i	−0.273502	+	0.412351i
$700$	−1.86095	+	13.0972i	−0.0703374	+	0.495028i
$701$	26.2072			0.989834			0.494917	−	0.868940i	$-0.335199\pi$
$701$	26.2072			0.989834			0.494917	+	0.868940i	$0.335199\pi$
$702$	−13.2682	−	6.37582i	−0.500775	−	0.240640i
$703$	12.2233	+	45.6180i	0.461011	+	1.72052i
$704$	−1.76699	+	1.02017i	−0.0665958	+	0.0384491i
$705$	3.24077	−	2.68888i	0.122054	−	0.101269i
$706$	22.8539	−	13.1947i	0.860117	−	0.496589i
$707$	14.0818	+	1.12378i	0.529601	+	0.0422643i
$708$	4.70856	−	14.0274i	0.176959	−	0.527182i
$709$		−	30.1555i		−	1.13251i	−0.824229	−	0.566257i	$-0.808391\pi$
$709$		−	30.1555i		−	1.13251i	0.824229	−	0.566257i	$-0.191609\pi$
$710$	15.1236	+	9.36318i	0.567579	+	0.351394i
$711$	−4.66846	+	6.17043i	−0.175081	+	0.231409i
$712$	−0.280853	+	1.04816i	−0.0105254	+	0.0392814i
$713$	2.26977	+	8.47090i	0.0850036	+	0.317238i
$714$	33.1851	−	4.00523i	1.24192	−	0.149892i
$715$	−11.3868	+	6.11526i	−0.425842	+	0.228698i
$716$	4.67284	−	8.09360i	0.174632	−	0.302472i
$717$	25.2772	−	5.11730i	0.943995	−	0.191109i
$718$	1.85068	−	6.90683i	0.0690667	−	0.257761i
$719$	−23.4845	−	40.6763i	−0.875823	−	1.51697i	−0.855883	−	0.517169i	$-0.826986\pi$
$719$	−23.4845	−	40.6763i	−0.875823	−	1.51697i	−0.0199400	−	0.999801i	$-0.506348\pi$
$720$	−2.71485	+	6.13430i	−0.101176	+	0.228612i
$721$	−2.25796	+	6.35415i	−0.0840908	+	0.236641i
$722$	−0.166115	−	0.619950i	−0.00618217	−	0.0230722i
$723$	8.31229	−	1.68280i	0.309138	−	0.0625841i
$724$	−19.3483			−0.719075
$725$	−22.4511	−	1.38266i	−0.833811	−	0.0513507i
$726$	0.734349	−	11.8193i	0.0272542	−	0.438654i
$727$	30.7512	−	8.23977i	1.14050	−	0.305596i	0.361348	−	0.932431i	$-0.382317\pi$
$727$	30.7512	−	8.23977i	1.14050	−	0.305596i	0.779152	+	0.626835i	$0.215650\pi$
$728$	−0.596264	+	7.47160i	−0.0220990	+	0.276916i
$729$	−9.82175	+	25.1502i	−0.363768	+	0.931489i
$730$	8.78977	−	29.1829i	0.325324	−	1.08011i
$731$	−40.3895	+	23.3189i	−1.49386	+	0.862481i
$732$	20.8540	+	7.00005i	0.770787	+	0.258729i
$733$	−13.9064	−	51.8993i	−0.513644	−	1.91695i	−0.376583	−	0.926383i	$-0.622901\pi$
$733$	−13.9064	−	51.8993i	−0.513644	−	1.91695i	−0.137061	−	0.990563i	$-0.543766\pi$
$734$	10.2596	+	17.7701i	0.378687	+	0.655905i
$735$	26.1176	−	7.27110i	0.963364	−	0.268199i
$736$	0.725309	−	1.25627i	0.0267352	−	0.0463068i
$737$	14.7948	+	3.96425i	0.544973	+	0.146025i
$738$	−21.5858	+	16.7977i	−0.794584	+	0.618331i
$739$	−11.0385	−	6.37309i	−0.406058	−	0.234438i	0.283036	−	0.959109i	$-0.408658\pi$
$739$	−11.0385	−	6.37309i	−0.406058	−	0.234438i	−0.689095	+	0.724671i	$0.741992\pi$
$740$	24.6353	+	0.757870i	0.905611	+	0.0278599i
$741$	−1.30375	+	20.9837i	−0.0478944	+	0.770856i
$742$	6.14514	−	2.92282i	0.225595	−	0.107300i
$743$	3.39116	−	12.6560i	0.124410	−	0.464303i	−0.875408	−	0.483384i	$-0.839407\pi$
$743$	3.39116	−	12.6560i	0.124410	−	0.464303i	0.999818	+	0.0190810i	$0.00607405\pi$
$744$	−9.37548	+	4.66315i	−0.343722	+	0.170959i
$745$	−3.39457	+	11.2703i	−0.124367	+	0.412913i
$746$	0.226490	−	0.392292i	0.00829239	−	0.0143628i
$747$	1.26034	−	3.10219i	0.0461134	−	0.113503i
$748$	10.5235	−	10.5235i	0.384778	−	0.384778i
$749$	−20.6445	−	24.2253i	−0.754333	−	0.885172i
$750$	17.7125	+	7.82746i	0.646767	+	0.285818i
$751$	−7.61280	+	13.1858i	−0.277795	+	0.481155i	−0.970836	−	0.239743i	$-0.922937\pi$
$751$	−7.61280	+	13.1858i	−0.277795	+	0.481155i	0.693041	+	0.720898i	$0.256270\pi$
$752$	−0.768822	−	0.768822i	−0.0280361	−	0.0280361i
$753$	8.53976	−	25.4410i	0.311206	−	0.927122i
$754$	−12.7448			−0.464137
$755$	−23.0554	+	21.6792i	−0.839071	+	0.788986i
$756$	13.7476	+	0.0548668i	0.499996	+	0.00199549i
$757$	−15.6585	+	15.6585i	−0.569117	+	0.569117i	−0.931881	−	0.362764i	$-0.881833\pi$
$757$	−15.6585	+	15.6585i	−0.569117	+	0.569117i	0.362764	+	0.931881i	$0.381833\pi$
$758$	−25.2228	−	25.2228i	−0.916132	−	0.916132i
$759$	−2.28298	−	4.59003i	−0.0828668	−	0.166608i
$760$	9.57623	+	0.294599i	0.347366	+	0.0106862i
$761$	44.0153	+	25.4122i	1.59555	+	0.921192i	0.992330	+	0.123619i	$0.0394500\pi$
$761$	44.0153	+	25.4122i	1.59555	+	0.921192i	0.603222	+	0.797573i	$0.293883\pi$
$762$	−8.10340	+	24.1411i	−0.293555	+	0.874538i
$763$	−17.4787	−	36.7483i	−0.632770	−	1.33038i
$764$			0.890241i			0.0322078i
$765$	7.54701	−	48.3450i	0.272863	−	1.74792i
$766$	3.29652	+	1.90325i	0.119108	+	0.0687672i
$767$	−23.3769	−	6.26383i	−0.844092	−	0.226174i
$768$	1.64201	+	0.551173i	0.0592511	+	0.0198887i
$769$	19.6040	+	33.9551i	0.706938	+	1.22445i	0.965988	+	0.258588i	$0.0832572\pi$
$769$	19.6040	+	33.9551i	0.706938	+	1.22445i	−0.259050	+	0.965864i	$0.583410\pi$
$770$	7.15029	−	9.72511i	0.257679	−	0.350469i
$771$	17.3062	+	1.07526i	0.623269	+	0.0387246i
$772$	2.04448	−	2.04448i	0.0735824	−	0.0735824i
$773$	9.91157	+	36.9905i	0.356494	+	1.33045i	0.878594	+	0.477570i	$0.158482\pi$
$773$	9.91157	+	36.9905i	0.356494	+	1.33045i	−0.522099	+	0.852885i	$0.674851\pi$
$774$	−17.6712	+	7.46076i	−0.635178	+	0.268171i
$775$	13.4761	+	27.0573i	0.484074	+	0.971928i
$776$	−1.83453	−	1.05917i	−0.0658558	−	0.0380219i
$777$	−18.8253	−	46.8721i	−0.675353	−	1.68153i
$778$	0.209799	−	0.782981i	0.00752167	−	0.0280712i
$779$	33.8304	+	19.5320i	1.21210	+	0.699805i
$780$	10.2894	+	3.80973i	0.368421	+	0.136410i
$781$	−8.11523	−	14.0560i	−0.290386	−	0.502963i
$782$	−2.73857	+	10.2205i	−0.0979309	+	0.365483i
$783$	1.76658	+	23.3092i	0.0631322	+	0.833002i
$784$	−2.49425	−	6.54054i	−0.0890805	−	0.233591i
$785$	4.95665	−	8.00608i	0.176910	−	0.285749i
$786$	0.189345	+	0.0117643i	0.00675373	+	0.000419619i
$787$	12.1652	+	12.1652i	0.433643	+	0.433643i	0.889866	−	0.456223i	$-0.150798\pi$
$787$	12.1652	+	12.1652i	0.433643	+	0.433643i	−0.456223	+	0.889866i	$0.650798\pi$
$788$	−10.7946	−	10.7946i	−0.384542	−	0.384542i
$789$	−11.7168	+	17.6651i	−0.417129	+	0.628894i
$790$	3.03581	−	4.90350i	0.108009	−	0.174459i
$791$	−36.2087	+	30.8566i	−1.28743	+	1.09713i
$792$	4.83069	−	3.75916i	0.171651	−	0.133576i
$793$	9.31220	−	34.7536i	0.330686	−	1.23414i
$794$	1.92825	+	3.33983i	0.0684311	+	0.118526i
$795$	−1.67539	−	9.81935i	−0.0594199	−	0.348256i
$796$	13.2230	+	7.63433i	0.468678	+	0.270592i
$797$	5.24363	−	19.5695i	0.185739	−	0.693187i	−0.808732	−	0.588177i	$-0.799846\pi$
$797$	5.24363	−	19.5695i	0.185739	−	0.693187i	0.994471	−	0.105010i	$-0.0334875\pi$
$798$	−7.31776	−	18.2201i	−0.259046	−	0.644985i
$799$	6.86824	+	3.96538i	0.242981	+	0.140285i
$800$	1.58852	−	4.74095i	0.0561627	−	0.167618i
$801$	0.402970	−	3.23036i	0.0142383	−	0.114139i
$802$	−6.08745	−	22.7187i	−0.214955	−	0.802224i
$803$	−19.6647	+	19.6647i	−0.693952	+	0.693952i
$804$	−5.79041	−	11.6419i	−0.204212	−	0.410578i
$805$	−0.945433	+	8.52974i	−0.0333221	+	0.300634i
$806$	8.56340	+	14.8322i	0.301633	+	0.522443i
$807$	25.2977	−	22.3380i	0.890522	−	0.786336i
$808$	−5.15741	−	1.38192i	−0.181437	−	0.0486159i
$809$	11.4356	+	6.60235i	0.402055	+	0.232126i	0.687370	−	0.726307i	$-0.258765\pi$
$809$	11.4356	+	6.60235i	0.402055	+	0.232126i	−0.285315	+	0.958434i	$0.592098\pi$
$810$	5.54145	−	19.3466i	0.194707	−	0.679772i
$811$			6.68954i			0.234902i	0.993079	+	0.117451i	$0.0374722\pi$
$811$			6.68954i			0.234902i	−0.993079	+	0.117451i	$0.962528\pi$
$812$	10.7486	−	5.11238i	0.377203	−	0.179409i
$813$	16.0242	−	3.24406i	0.561995	−	0.113774i
$814$	−19.4765	−	11.2448i	−0.682651	−	0.394129i
$815$	41.5366	+	1.27782i	1.45496	+	0.0447599i
$816$	−12.6095	−	0.783447i	−0.441421	−	0.0274261i
$817$	19.3715	+	19.3715i	0.677724	+	0.677724i
$818$	−12.2518	+	12.2518i	−0.428373	+	0.428373i
$819$	−1.30482	−	22.4482i	−0.0455943	−	0.784403i
$820$	14.8520	−	13.9655i	0.518654	−	0.487695i
$821$	−37.7439			−1.31727			−0.658635	−	0.752462i	$-0.728866\pi$
$821$	−37.7439			−1.31727			−0.658635	+	0.752462i	$0.728866\pi$
$822$	21.7462	−	4.40245i	0.758484	−	0.153553i
$823$	0.405430	+	0.405430i	0.0141324	+	0.0141324i	0.714138	−	0.700005i	$-0.246819\pi$
$823$	0.405430	+	0.405430i	0.0141324	+	0.0141324i	−0.700005	+	0.714138i	$0.746819\pi$
$824$	1.27439	−	2.20730i	0.0443953	−	0.0768949i
$825$	−10.8593	−	13.9391i	−0.378073	−	0.485297i
$826$	22.2281	−	4.09456i	0.773416	−	0.142468i
$827$	18.6169	−	18.6169i	0.647374	−	0.647374i	−0.304984	−	0.952358i	$-0.598651\pi$
$827$	18.6169	−	18.6169i	0.647374	−	0.647374i	0.952358	+	0.304984i	$0.0986510\pi$
$828$	−1.63802	+	4.03181i	−0.0569251	+	0.140115i
$829$	14.9831	−	25.9516i	0.520386	−	0.901335i	−0.479333	−	0.877633i	$-0.659121\pi$
$829$	14.9831	−	25.9516i	0.520386	−	0.901335i	0.999719	−	0.0237017i	$-0.00754519\pi$
$830$	−0.719778	+	2.38974i	−0.0249839	+	0.0829490i
$831$	7.59374	+	5.03673i	0.263424	+	0.174722i
$832$	0.733229	−	2.73645i	0.0254201	−	0.0948692i
$833$	29.9211	+	41.3732i	1.03671	+	1.43350i
$834$	−22.3838	−	14.8466i	−0.775089	−	0.514097i
$835$	−31.1858	−	0.959387i	−1.07923	−	0.0332010i
$836$	−7.57090	−	4.37106i	−0.261845	−	0.151176i
$837$	25.9400	−	17.7177i	0.896618	−	0.612413i
$838$	−34.5673	−	9.26228i	−1.19411	−	0.319960i
$839$	−11.7317	+	20.3199i	−0.405023	+	0.701520i	−0.994324	−	0.106393i	$-0.966070\pi$
$839$	−11.7317	+	20.3199i	−0.405023	+	0.701520i	0.589301	+	0.807913i	$0.299403\pi$
$840$	−10.2061	+	0.914435i	−0.352143	+	0.0315510i
$841$	−4.38077	−	7.58772i	−0.151061	−	0.261645i
$842$	4.96281	+	18.5215i	0.171030	+	0.638292i
$843$	3.35028	−	2.95832i	0.115390	−	0.101890i
$844$	−1.89438	+	1.09372i	−0.0652072	+	0.0376474i
$845$	−3.20777	+	10.6501i	−0.110351	+	0.366375i
$846$	2.60122	+	1.96805i	0.0894319	+	0.0676629i
$847$	16.3354	−	7.76965i	0.561292	−	0.266968i
$848$	−2.48435	+	0.665678i	−0.0853128	+	0.0228595i
$849$	26.7382	−	13.2990i	0.917654	−	0.456420i
$850$	−2.24182	+	36.4017i	−0.0768937	+	1.24857i
$851$	15.9894			0.548108
$852$	−4.38446	+	13.0619i	−0.150209	+	0.447492i
$853$	14.3191	+	53.4394i	0.490275	+	1.82973i	0.555030	+	0.831831i	$0.312707\pi$
$853$	14.3191	+	53.4394i	0.490275	+	1.82973i	−0.0647544	+	0.997901i	$0.520626\pi$
$854$	6.08724	+	33.0458i	0.208301	+	1.13080i
$855$	−28.5781	+	3.06790i	−0.977349	+	0.104920i
$856$	6.01503	+	10.4183i	0.205590	+	0.356092i
$857$	−8.13093	+	30.3450i	−0.277747	+	1.03657i	0.676231	+	0.736690i	$0.263612\pi$
$857$	−8.13093	+	30.3450i	−0.277747	+	1.03657i	−0.953978	+	0.299877i	$0.903054\pi$
$858$	−6.62669	−	7.50469i	−0.226231	−	0.256206i
$859$	−16.9865	+	29.4215i	−0.579573	+	1.00385i	0.415955	+	0.909385i	$0.363447\pi$
$859$	−16.9865	+	29.4215i	−0.579573	+	1.00385i	−0.995528	+	0.0944645i	$0.969886\pi$
$860$	12.5956	−	6.76446i	0.429508	−	0.230666i
$861$	−38.4252	−	16.4040i	−1.30953	−	0.559048i
$862$	1.78524	+	6.66262i	0.0608057	+	0.226930i
$863$	−1.10932	+	4.14004i	−0.0377617	+	0.140929i	−0.982233	−	0.187665i	$-0.939908\pi$
$863$	−1.10932	+	4.14004i	−0.0377617	+	0.140929i	0.944471	+	0.328594i	$0.106575\pi$
$864$	−5.10638	−	0.961714i	−0.173723	−	0.0327182i
$865$	12.7339	+	7.88367i	0.432965	+	0.268053i
$866$			10.3498i			0.351700i
$867$	61.4611	−	12.4426i	2.08733	−	0.422574i
$868$	−13.1719	−	9.07405i	−0.447083	−	0.307993i
$869$	−4.55734	+	2.63118i	−0.154597	+	0.0892568i
$870$	−2.93046	−	17.1753i	−0.0993519	−	0.582296i
$871$	−18.4178	+	10.6335i	−0.624062	+	0.360302i
$872$	3.98079	+	14.8565i	0.134807	+	0.503105i
$873$	5.88765	+	2.39200i	0.199267	+	0.0809568i
$874$	6.21538			0.210238
$875$	2.65577	+	29.4609i	0.0897814	+	0.995961i
$876$	23.5626	+	1.46398i	0.796108	+	0.0494634i
$877$	−11.2078	−	41.8280i	−0.378460	−	1.41243i	−0.848223	−	0.529640i	$-0.822327\pi$
$877$	−11.2078	−	41.8280i	−0.378460	−	1.41243i	0.469763	−	0.882793i	$-0.344340\pi$
$878$	14.6561	−	14.6561i	0.494619	−	0.494619i
$879$	−32.7043	−	21.6919i	−1.10309	−	0.731650i
$880$	−3.32373	+	3.12533i	−0.112043	+	0.105355i
$881$			13.2732i			0.447186i	0.974683	+	0.223593i	$0.0717786\pi$
$881$			13.2732i			0.447186i	−0.974683	+	0.223593i	$0.928221\pi$
$882$	10.1052	+	18.4088i	0.340261	+	0.619857i
$883$	4.65552	+	4.65552i	0.156671	+	0.156671i	0.781090	−	0.624419i	$-0.214664\pi$
$883$	4.65552	+	4.65552i	0.156671	+	0.156671i	−0.624419	+	0.781090i	$0.714664\pi$
$884$			20.6641i			0.695010i
$885$	3.06617	−	32.9437i	0.103068	−	1.10739i
$886$	9.18164			0.308463
$887$	−22.6689	+	6.07412i	−0.761147	+	0.203949i	−0.618457	−	0.785819i	$-0.712242\pi$
$887$	−22.6689	+	6.07412i	−0.761147	+	0.203949i	−0.142690	+	0.989767i	$0.545575\pi$
$888$	3.78816	+	18.7118i	0.127122	+	0.627928i
$889$	−38.2545	+	7.04672i	−1.28301	+	0.236339i
$890$	−0.0746105	+	2.42528i	−0.00250095	+	0.0812957i
$891$	−12.8069	+	13.1599i	−0.429049	+	0.440874i
$892$	−8.16719	+	2.18839i	−0.273458	+	0.0732728i
$893$	1.20574	−	4.49987i	0.0403484	−	0.150582i
$894$	−9.09980	−	0.565384i	−0.304343	−	0.0189093i
$895$	6.02682	−	20.0097i	0.201454	−	0.668849i
$896$	0.479300	+	2.60197i	0.0160123	+	0.0869259i
$897$	6.74797	+	2.26508i	0.225308	+	0.0756289i
$898$	14.9835	+	14.9835i	0.500005	+	0.500005i
$899$	13.5985	−	23.5533i	0.453536	−	0.785547i
$900$	−2.76821	+	14.7424i	−0.0922737	+	0.491412i
$901$	16.2470	−	9.38020i	0.541266	−	0.312500i
$902$	−17.9683	+	4.81459i	−0.598279	+	0.160308i
$903$	−23.0518	−	18.0867i	−0.767116	−	0.601887i
$904$	15.5719	−	8.99046i	0.517915	−	0.299018i
$905$	−42.1145	+	9.90729i	−1.39993	+	0.329330i
$906$	−20.4286	−	13.5498i	−0.678694	−	0.450160i
$907$	−50.0561	−	13.4125i	−1.66209	−	0.445355i	−0.699127	−	0.714998i	$-0.746428\pi$
$907$	−50.0561	−	13.4125i	−1.66209	−	0.445355i	−0.962960	+	0.269643i	$0.913094\pi$
$908$	−13.4767	−	3.61108i	−0.447242	−	0.119838i
$909$	15.8948	+	1.98279i	0.527199	+	0.0657652i
$910$	2.52797	+	16.5684i	0.0838014	+	0.549236i
$911$	12.5567	−	21.7488i	0.416021	−	0.720570i	−0.579514	−	0.814963i	$-0.696757\pi$
$911$	12.5567	−	21.7488i	0.416021	−	0.720570i	0.995535	+	0.0943923i	$0.0300908\pi$
$912$	1.47253	+	7.27366i	0.0487605	+	0.240855i
$913$	1.61031	−	1.61031i	0.0532934	−	0.0532934i
$914$		−	18.9113i		−	0.625531i
$915$	48.9763	+	4.55837i	1.61911	+	0.150695i
$916$	−2.57162	−	1.48473i	−0.0849688	−	0.0490567i
$917$	0.124470	+	0.261695i	0.00411037	+	0.00864192i
$918$	37.7931	−	2.86429i	1.24736	−	0.0945357i
$919$	14.9323	−	8.62117i	0.492571	−	0.284386i	−0.233069	−	0.972460i	$-0.574877\pi$
$919$	14.9323	−	8.62117i	0.492571	−	0.284386i	0.725641	+	0.688074i	$0.241544\pi$
$920$	0.935471	−	3.10586i	0.0308416	−	0.102397i
$921$	24.1080	+	48.4703i	0.794387	+	1.59715i
$922$	21.7036	−	5.81546i	0.714769	−	0.191522i
$923$	21.7678	+	5.83268i	0.716497	+	0.191985i
$924$	8.59918	+	3.67107i	0.282892	+	0.120769i
$925$	54.0105	−	10.9649i	1.77585	−	0.360522i
$926$	7.76804	+	13.4546i	0.255274	+	0.442147i
$927$	−2.87804	+	7.08399i	−0.0945272	+	0.232669i
$928$	−4.34543	+	1.16435i	−0.142646	+	0.0382218i
$929$	−33.4755			−1.09830			−0.549148	−	0.835725i	$-0.685048\pi$
$929$	−33.4755			−1.09830			−0.549148	+	0.835725i	$0.685048\pi$
$930$	−18.0194	+	14.9507i	−0.590878	+	0.490254i
$931$	18.9259	−	23.2672i	0.620272	−	0.762550i
$932$	7.29558	+	1.95484i	0.238975	+	0.0640331i
$933$	16.5389	−	49.2715i	0.541460	−	1.61308i
$934$	16.6355	+	28.8134i	0.544329	+	0.942805i
$935$	17.5175	−	28.2946i	0.572883	−	0.925332i
$936$	−1.05204	+	8.43357i	−0.0343871	+	0.275660i
$937$	−5.95231	−	5.95231i	−0.194453	−	0.194453i	0.603164	−	0.797617i	$-0.293907\pi$
$937$	−5.95231	−	5.95231i	−0.194453	−	0.194453i	−0.797617	+	0.603164i	$0.793907\pi$
$938$	11.2676	−	16.3560i	0.367900	−	0.534043i
$939$	16.7398	−	8.32601i	0.546284	−	0.271709i
$940$	−2.06713	−	1.27978i	−0.0674224	−	0.0417419i
$941$			58.3486i			1.90211i	0.309023	+	0.951055i	$0.399998\pi$
$941$			58.3486i			1.90211i	−0.309023	+	0.951055i	$0.600002\pi$
$942$	6.91464	+	2.32103i	0.225291	+	0.0756233i
$943$	9.35188	−	9.35188i	0.304539	−	0.304539i
$944$	−8.54280			−0.278044
$945$	29.9518	−	6.92003i	0.974334	−	0.225109i
$946$	−13.0457			−0.424151
$947$	3.49869	−	3.49869i	0.113692	−	0.113692i	−0.647972	−	0.761664i	$-0.724383\pi$
$947$	3.49869	−	3.49869i	0.113692	−	0.113692i	0.761664	+	0.647972i	$0.224383\pi$
$948$	4.23502	+	1.42157i	0.137547	+	0.0461703i
$949$		−	38.6139i		−	1.25346i
$950$	20.9949	−	4.26226i	0.681166	−	0.138286i
$951$	25.1779	−	12.5229i	0.816448	−	0.406083i
$952$	−8.28912	−	17.4276i	−0.268652	−	0.564832i
$953$	−7.44417	−	7.44417i	−0.241140	−	0.241140i	0.576181	−	0.817322i	$-0.304542\pi$
$953$	−7.44417	−	7.44417i	−0.241140	−	0.241140i	−0.817322	+	0.576181i	$0.804542\pi$
$954$	7.10838	−	3.00115i	0.230142	−	0.0971657i
$955$	0.455847	+	1.93774i	0.0147509	+	0.0627039i
$956$	−7.44493	−	12.8950i	−0.240786	−	0.417054i
$957$	−5.05917	+	15.0719i	−0.163540	+	0.487205i
$958$	−15.7558	−	4.22174i	−0.509046	−	0.136398i
$959$	21.9826	+	25.7955i	0.709857	+	0.832981i
$960$	3.85632	+	0.358919i	0.124462	+	0.0115841i
$961$	−5.54816			−0.178973
$962$	30.1624	−	8.08198i	0.972473	−	0.260573i
$963$	−22.1644	−	28.4823i	−0.714238	−	0.917829i
$964$	−2.44823	−	4.24046i	−0.0788522	−	0.136576i
$965$	3.40324	−	5.49699i	0.109554	−	0.176954i
$966$	−6.59967	+	0.796537i	−0.212341	+	0.0256282i
$967$	29.5599	+	7.92056i	0.950583	+	0.254708i	0.700610	−	0.713545i	$-0.252912\pi$
$967$	29.5599	+	7.92056i	0.950583	+	0.254708i	0.249973	+	0.968253i	$0.419578\pi$
$968$	−6.60405	+	1.76955i	−0.212262	+	0.0568755i
$969$	−24.1066	−	48.4674i	−0.774414	−	1.55700i
$970$	−4.53548	−	1.36607i	−0.145625	−	0.0438617i
$971$	26.8212	−	15.4852i	0.860733	−	0.496944i	−0.00352468	−	0.999994i	$-0.501122\pi$
$971$	26.8212	−	15.4852i	0.860733	−	0.496944i	0.864258	+	0.503049i	$0.167789\pi$
$972$	15.5702	+	0.755109i	0.499413	+	0.0242201i
$973$	3.26392	−	40.8993i	0.104637	−	1.31117i
$974$	−24.0503	−	13.8854i	−0.770621	−	0.444918i
$975$	24.3473	+	3.02374i	0.779737	+	0.0968372i
$976$		−	12.7003i		−	0.406526i
$977$	10.1129	−	10.1129i	0.323540	−	0.323540i	−0.526583	−	0.850124i	$-0.676527\pi$
$977$	10.1129	−	10.1129i	0.323540	−	0.323540i	0.850124	+	0.526583i	$0.176527\pi$
$978$	6.38708	+	31.5493i	0.204236	+	1.00884i
$979$	1.10702	−	1.91741i	0.0353805	−	0.0612808i
$980$	−8.77820	−	12.9593i	−0.280409	−	0.413969i
$981$	−17.9470	−	42.5085i	−0.573004	−	1.35719i
$982$	−18.7477	−	5.02344i	−0.598264	−	0.160304i
$983$	−22.6384	−	6.06595i	−0.722054	−	0.193474i	−0.120966	−	0.992657i	$-0.538599\pi$
$983$	−22.6384	−	6.06595i	−0.722054	−	0.193474i	−0.601088	+	0.799183i	$0.705266\pi$
$984$	13.1598	+	8.72859i	0.419520	+	0.278257i
$985$	−29.0235	−	17.9687i	−0.924764	−	0.572531i
$986$	28.4180	−	16.4071i	0.905013	−	0.522510i
$987$	−0.703601	+	4.93261i	−0.0223959	+	0.157007i
$988$	11.7247	−	3.14163i	0.373013	−	0.0999484i
$989$	8.03244	−	4.63753i	0.255417	−	0.147465i
$990$	8.58985	−	10.6559i	0.273003	−	0.338667i
$991$	7.11579	−	12.3249i	0.226041	−	0.391514i	−0.730591	−	0.682816i	$-0.760755\pi$
$991$	7.11579	−	12.3249i	0.226041	−	0.391514i	0.956631	+	0.291302i	$0.0940885\pi$
$992$	4.27482	+	4.27482i	0.135726	+	0.135726i
$993$	−39.9597	−	13.4132i	−1.26808	−	0.425656i
$994$	−20.6981	+	3.81273i	−0.656505	+	0.120932i
$995$	32.6911	+	9.84641i	1.03638	+	0.312152i
$996$	−1.92950	−	0.119883i	−0.0611386	−	0.00379863i
$997$	4.26839	−	15.9299i	0.135181	−	0.504503i	−0.864816	−	0.502089i	$-0.832565\pi$
$997$	4.26839	−	15.9299i	0.135181	−	0.504503i	0.999997	−	0.00241416i	$-0.000768452\pi$
$998$	3.46922	−	0.929575i	0.109816	−	0.0294252i
$999$	−18.9622	−	54.0443i	−0.599936	−	1.70989i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.493.45	yes	192
5.2	odd	4	inner	630.2.bw.a.367.40	yes	192
7.5	odd	6		630.2.cg.a.313.19	yes	192
9.4	even	3		630.2.cg.a.283.33	yes	192
35.12	even	12		630.2.cg.a.187.33	yes	192
45.22	odd	12		630.2.cg.a.157.19	yes	192
63.40	odd	6	inner	630.2.bw.a.103.40	✓	192
315.292	even	12	inner	630.2.bw.a.607.45	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.40	✓	192	63.40	odd	6	inner
630.2.bw.a.367.40	yes	192	5.2	odd	4	inner
630.2.bw.a.493.45	yes	192	1.1	even	1	trivial
630.2.bw.a.607.45	yes	192	315.292	even	12	inner
630.2.cg.a.157.19	yes	192	45.22	odd	12
630.2.cg.a.187.33	yes	192	35.12	even	12
630.2.cg.a.283.33	yes	192	9.4	even	3
630.2.cg.a.313.19	yes	192	7.5	odd	6

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.64201 + 0.551173i) q^{3} -1.00000i q^{4} +(-0.512049 - 2.17665i) q^{5} +(1.55082 - 0.771341i) q^{6} +(2.17879 + 1.50096i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.39242 + 1.81007i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(1.64201 + 0.551173i) q^{3} -1.00000i q^{4} +(-0.512049 - 2.17665i) q^{5} +(1.55082 - 0.771341i) q^{6} +(2.17879 + 1.50096i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.39242 + 1.81007i) q^{9} +(-1.90120 - 1.17705i) q^{10} +(1.02017 + 1.76699i) q^{11} +(0.551173 - 1.64201i) q^{12} +(-2.73645 - 0.733229i) q^{13} +(2.60197 - 0.479300i) q^{14} +(0.358919 - 3.85632i) q^{15} -1.00000 q^{16} +(7.04560 - 1.88786i) q^{17} +(2.97160 - 0.411784i) q^{18} +(-2.14232 - 3.71061i) q^{19} +(-2.17665 + 0.512049i) q^{20} +(2.75032 + 3.66548i) q^{21} +(1.97082 + 0.528078i) q^{22} +(-1.40119 + 0.375448i) q^{23} +(-0.771341 - 1.55082i) q^{24} +(-4.47561 + 2.22910i) q^{25} +(-2.45343 + 1.41649i) q^{26} +(2.93072 + 4.29079i) q^{27} +(1.50096 - 2.17879i) q^{28} +(3.89600 + 2.24936i) q^{29} +(-2.47303 - 2.98062i) q^{30} -6.04551i q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.701217 + 3.46370i) q^{33} +(3.64707 - 6.31691i) q^{34} +(2.15141 - 5.51103i) q^{35} +(1.81007 - 2.39242i) q^{36} +(-10.6469 - 2.85282i) q^{37} +(-4.13865 - 1.10895i) q^{38} +(-4.08915 - 2.71223i) q^{39} +(-1.17705 + 1.90120i) q^{40} +(-7.89572 + 4.55860i) q^{41} +(4.53665 + 0.647121i) q^{42} +(-6.17601 + 1.65486i) q^{43} +(1.76699 - 1.02017i) q^{44} +(2.71485 - 6.13430i) q^{45} +(-0.725309 + 1.25627i) q^{46} +(0.768822 + 0.768822i) q^{47} +(-1.64201 - 0.551173i) q^{48} +(2.49425 + 6.54054i) q^{49} +(-1.58852 + 4.74095i) q^{50} +(12.6095 + 0.783447i) q^{51} +(-0.733229 + 2.73645i) q^{52} +(2.48435 - 0.665678i) q^{53} +(5.10638 + 0.961714i) q^{54} +(3.32373 - 3.12533i) q^{55} +(-0.479300 - 2.60197i) q^{56} +(-1.47253 - 7.27366i) q^{57} +(4.34543 - 1.16435i) q^{58} +8.54280 q^{59} +(-3.85632 - 0.358919i) q^{60} +12.7003i q^{61} +(-4.27482 - 4.27482i) q^{62} +(2.49574 + 7.53467i) q^{63} +1.00000i q^{64} +(-0.194787 + 6.33174i) q^{65} +(2.94504 + 1.95337i) q^{66} +(5.30820 - 5.30820i) q^{67} +(-1.88786 - 7.04560i) q^{68} +(-2.50771 - 0.155808i) q^{69} +(-2.37561 - 5.41816i) q^{70} -7.95478 q^{71} +(-0.411784 - 2.97160i) q^{72} +(3.52774 + 13.1657i) q^{73} +(-9.54572 + 5.51122i) q^{74} +(-8.57764 + 1.19338i) q^{75} +(-3.71061 + 2.14232i) q^{76} +(-0.429435 + 5.38112i) q^{77} +(-4.80930 + 0.973630i) q^{78} +2.57916i q^{79} +(0.512049 + 2.17665i) q^{80} +(2.44732 + 8.66087i) q^{81} +(-2.35970 + 8.80653i) q^{82} +(-0.288880 - 1.07812i) q^{83} +(3.66548 - 2.75032i) q^{84} +(-7.71691 - 14.3691i) q^{85} +(-3.19694 + 5.53726i) q^{86} +(5.15751 + 5.84085i) q^{87} +(0.528078 - 1.97082i) q^{88} +(-0.542567 - 0.939753i) q^{89} +(-2.41792 - 6.25729i) q^{90} +(-4.86160 - 5.70484i) q^{91} +(0.375448 + 1.40119i) q^{92} +(3.33212 - 9.92680i) q^{93} +1.08728 q^{94} +(-6.97973 + 6.56310i) q^{95} +(-1.55082 + 0.771341i) q^{96} +(2.04615 - 0.548265i) q^{97} +(6.38857 + 2.86116i) q^{98} +(-0.757691 + 6.07394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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