LMFDB - Embedded newform 336.2.bo.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(5,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 6, 10]))

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

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

chi := DirichletCharacter("336.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bo (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	336.5
Dual form			336.2.bo.a.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40230 - 0.183144i) q^{2} +(1.05826 - 1.37116i) q^{3} +(1.93292 + 0.513647i) q^{4} +(0.478799 - 0.128294i) q^{5} +(-1.73512 + 1.72898i) q^{6} +(1.18449 - 2.36579i) q^{7} +(-2.61647 - 1.07429i) q^{8} +(-0.760185 - 2.90209i) q^{9} +O(q^{10})$	\(q+(-1.40230 - 0.183144i) q^{2} +(1.05826 - 1.37116i) q^{3} +(1.93292 + 0.513647i) q^{4} +(0.478799 - 0.128294i) q^{5} +(-1.73512 + 1.72898i) q^{6} +(1.18449 - 2.36579i) q^{7} +(-2.61647 - 1.07429i) q^{8} +(-0.760185 - 2.90209i) q^{9} +(-0.694919 + 0.0922180i) q^{10} +(-1.45091 - 0.388770i) q^{11} +(2.74982 - 2.10678i) q^{12} +(-0.486926 - 0.486926i) q^{13} +(-2.09430 + 3.10063i) q^{14} +(0.330780 - 0.792280i) q^{15} +(3.47233 + 1.98567i) q^{16} +(1.59268 + 2.75860i) q^{17} +(0.534512 + 4.20884i) q^{18} +(2.69513 - 0.722159i) q^{19} +(0.991377 - 0.00204771i) q^{20} +(-1.99039 - 4.12775i) q^{21} +(1.96342 + 0.810899i) q^{22} +(2.26818 - 3.92860i) q^{23} +(-4.24192 + 2.45073i) q^{24} +(-4.11734 + 2.37715i) q^{25} +(0.593642 + 0.771997i) q^{26} +(-4.78371 - 2.02882i) q^{27} +(3.50471 - 3.96447i) q^{28} +(-1.56573 - 1.56573i) q^{29} +(-0.608956 + 1.05044i) q^{30} +(-0.851744 + 0.491755i) q^{31} +(-4.50561 - 3.42045i) q^{32} +(-2.06850 + 1.57802i) q^{33} +(-1.72820 - 4.16009i) q^{34} +(0.263618 - 1.28470i) q^{35} +(0.0212733 - 5.99996i) q^{36} +(1.47622 - 0.395551i) q^{37} +(-3.91166 + 0.519090i) q^{38} +(-1.18295 + 0.152363i) q^{39} +(-1.39059 - 0.178693i) q^{40} -2.87800i q^{41} +(2.03517 + 6.15289i) q^{42} +(5.20338 + 5.20338i) q^{43} +(-2.60480 - 1.49671i) q^{44} +(-0.736296 - 1.29199i) q^{45} +(-3.90017 + 5.09369i) q^{46} +(6.34245 - 10.9854i) q^{47} +(6.39731 - 2.65979i) q^{48} +(-4.19395 - 5.60453i) q^{49} +(6.20912 - 2.57942i) q^{50} +(5.46796 + 0.735483i) q^{51} +(-0.691080 - 1.19130i) q^{52} +(1.68545 + 0.451615i) q^{53} +(6.33666 + 3.72112i) q^{54} -0.744571 q^{55} +(-5.64074 + 4.91753i) q^{56} +(1.86194 - 4.45970i) q^{57} +(1.90887 + 2.48238i) q^{58} +(-3.42524 + 12.7832i) q^{59} +(1.04632 - 1.36151i) q^{60} +(-11.6537 + 3.12260i) q^{61} +(1.28447 - 0.533599i) q^{62} +(-7.76617 - 1.63906i) q^{63} +(5.69180 + 5.62169i) q^{64} +(-0.295610 - 0.170670i) q^{65} +(3.18967 - 1.83403i) q^{66} +(12.3049 + 3.29710i) q^{67} +(1.66157 + 6.15022i) q^{68} +(-2.98644 - 7.26751i) q^{69} +(-0.604958 + 1.75326i) q^{70} +11.3218 q^{71} +(-1.12869 + 8.40988i) q^{72} +(5.65102 + 9.78785i) q^{73} +(-2.14255 + 0.284323i) q^{74} +(-1.09774 + 8.16118i) q^{75} +(5.58040 - 0.0115264i) q^{76} +(-2.63834 + 2.97205i) q^{77} +(1.68676 + 0.00299026i) q^{78} +(-3.58163 + 6.20356i) q^{79} +(1.91730 + 0.505259i) q^{80} +(-7.84424 + 4.41225i) q^{81} +(-0.527088 + 4.03584i) q^{82} +(-4.94774 + 4.94774i) q^{83} +(-1.72706 - 9.00096i) q^{84} +(1.11649 + 1.11649i) q^{85} +(-6.34375 - 8.24968i) q^{86} +(-3.80381 + 0.489929i) q^{87} +(3.37860 + 2.57590i) q^{88} +(9.31634 + 5.37879i) q^{89} +(0.795892 + 1.94661i) q^{90} +(-1.72873 + 0.575206i) q^{91} +(6.40211 - 6.42861i) q^{92} +(-0.227087 + 1.68828i) q^{93} +(-10.9060 + 14.2434i) q^{94} +(1.19778 - 0.691538i) q^{95} +(-9.45810 + 2.55821i) q^{96} -4.48178i q^{97} +(4.85476 + 8.62736i) q^{98} +(-0.0252849 + 4.50620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) $ 240 * q - 6 * q^3 - 4 * q^4	$ 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) $ 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.40230	−	0.183144i	−0.991579	−	0.129502i
$2$	−1.40230	−	0.183144i	−0.991579	−	0.129502i
$3$	1.05826	−	1.37116i	0.610985	−	0.791642i
$3$	1.05826	−	1.37116i	0.610985	−	0.791642i
$4$	1.93292	+	0.513647i	0.966458	+	0.256823i
$5$	0.478799	−	0.128294i	0.214126	−	0.0573748i	−0.150162	−	0.988661i	$-0.547979\pi$
$5$	0.478799	−	0.128294i	0.214126	−	0.0573748i	0.364287	+	0.931287i	$0.381313\pi$
$6$	−1.73512	+	1.72898i	−0.708359	+	0.705852i
$7$	1.18449	−	2.36579i	0.447696	−	0.894186i
$7$	1.18449	−	2.36579i	0.447696	−	0.894186i
$8$	−2.61647	−	1.07429i	−0.925061	−	0.379819i
$9$	−0.760185	−	2.90209i	−0.253395	−	0.967363i
$10$	−0.694919	+	0.0922180i	−0.219753	+	0.0291619i
$11$	−1.45091	−	0.388770i	−0.437465	−	0.117219i	0.0333630	−	0.999443i	$-0.489378\pi$
$11$	−1.45091	−	0.388770i	−0.437465	−	0.117219i	−0.470828	+	0.882225i	$0.656045\pi$
$12$	2.74982	−	2.10678i	0.793804	−	0.608174i
$13$	−0.486926	−	0.486926i	−0.135049	−	0.135049i	0.636351	−	0.771400i	$-0.280443\pi$
$13$	−0.486926	−	0.486926i	−0.135049	−	0.135049i	−0.771400	+	0.636351i	$0.780443\pi$
$14$	−2.09430	+	3.10063i	−0.559725	+	0.828678i
$15$	0.330780	−	0.792280i	0.0854072	−	0.204566i
$16$	3.47233	+	1.98567i	0.868084	+	0.496418i
$17$	1.59268	+	2.75860i	0.386282	+	0.669059i	0.991946	−	0.126661i	$-0.0404260\pi$
$17$	1.59268	+	2.75860i	0.386282	+	0.669059i	−0.605665	+	0.795720i	$0.707093\pi$
$18$	0.534512	+	4.20884i	0.125986	+	0.992032i
$19$	2.69513	−	0.722159i	0.618306	−	0.165675i	0.0639485	−	0.997953i	$-0.479631\pi$
$19$	2.69513	−	0.722159i	0.618306	−	0.165675i	0.554358	+	0.832279i	$0.312964\pi$
$20$	0.991377	−	0.00204771i	0.221679	−	0.000457881i
$21$	−1.99039	−	4.12775i	−0.434339	−	0.900749i
$22$	1.96342	+	0.810899i	0.418602	+	0.172884i
$23$	2.26818	−	3.92860i	0.472948	−	0.819169i	−0.526573	−	0.850130i	$-0.676523\pi$
$23$	2.26818	−	3.92860i	0.472948	−	0.819169i	0.999521	+	0.0309606i	$0.00985664\pi$
$24$	−4.24192	+	2.45073i	−0.865879	+	0.500253i
$25$	−4.11734	+	2.37715i	−0.823468	+	0.475429i
$26$	0.593642	+	0.771997i	0.116423	+	0.151401i
$27$	−4.78371	−	2.02882i	−0.920626	−	0.390446i
$28$	3.50471	−	3.96447i	0.662328	−	0.749214i
$29$	−1.56573	−	1.56573i	−0.290748	−	0.290748i	0.546627	−	0.837376i	$-0.315911\pi$
$29$	−1.56573	−	1.56573i	−0.290748	−	0.290748i	−0.837376	+	0.546627i	$0.815911\pi$
$30$	−0.608956	+	1.05044i	−0.111180	+	0.191783i
$31$	−0.851744	+	0.491755i	−0.152978	+	0.0883218i	−0.574535	−	0.818480i	$-0.694817\pi$
$31$	−0.851744	+	0.491755i	−0.152978	+	0.0883218i	0.421557	+	0.906802i	$0.361484\pi$
$32$	−4.50561	−	3.42045i	−0.796486	−	0.604657i
$33$	−2.06850	+	1.57802i	−0.360080	+	0.274697i
$34$	−1.72820	−	4.16009i	−0.296384	−	0.713450i
$35$	0.263618	−	1.28470i	0.0445596	−	0.217154i
$36$	0.0212733	−	5.99996i	0.00354556	−	0.999994i
$37$	1.47622	−	0.395551i	0.242688	−	0.0650282i	−0.135424	−	0.990788i	$-0.543240\pi$
$37$	1.47622	−	0.395551i	0.242688	−	0.0650282i	0.378113	+	0.925760i	$0.376573\pi$
$38$	−3.91166	+	0.519090i	−0.634555	+	0.0842075i
$39$	−1.18295	+	0.152363i	−0.189424	+	0.0243976i
$40$	−1.39059	−	0.178693i	−0.219871	−	0.0282538i
$41$		−	2.87800i		−	0.449468i	−0.974420	−	0.224734i	$-0.927849\pi$
$41$		−	2.87800i		−	0.449468i	0.974420	−	0.224734i	$-0.0721514\pi$
$42$	2.03517	+	6.15289i	0.314033	+	0.949412i
$43$	5.20338	+	5.20338i	0.793507	+	0.793507i	0.982063	−	0.188555i	$-0.0603805\pi$
$43$	5.20338	+	5.20338i	0.793507	+	0.793507i	−0.188555	+	0.982063i	$0.560380\pi$
$44$	−2.60480	−	1.49671i	−0.392688	−	0.225638i
$45$	−0.736296	−	1.29199i	−0.109761	−	0.192599i
$46$	−3.90017	+	5.09369i	−0.575049	+	0.751023i
$47$	6.34245	−	10.9854i	0.925141	−	1.60239i	0.133807	−	0.991007i	$-0.457280\pi$
$47$	6.34245	−	10.9854i	0.925141	−	1.60239i	0.791334	−	0.611384i	$-0.209387\pi$
$48$	6.39731	−	2.65979i	0.923371	−	0.383908i
$49$	−4.19395	−	5.60453i	−0.599136	−	0.800647i
$50$	6.20912	−	2.57942i	0.878102	−	0.364785i
$51$	5.46796	+	0.735483i	0.765668	+	0.102988i
$52$	−0.691080	−	1.19130i	−0.0958356	−	0.165203i
$53$	1.68545	+	0.451615i	0.231514	+	0.0620341i	0.372711	−	0.927947i	$-0.378428\pi$
$53$	1.68545	+	0.451615i	0.231514	+	0.0620341i	−0.141197	+	0.989982i	$0.545095\pi$
$54$	6.33666	+	3.72112i	0.862310	+	0.506381i
$55$	−0.744571			−0.100398
$56$	−5.64074	+	4.91753i	−0.753775	+	0.657132i
$57$	1.86194	−	4.45970i	0.246621	−	0.590702i
$58$	1.90887	+	2.48238i	0.250648	+	0.325953i
$59$	−3.42524	+	12.7832i	−0.445928	+	1.66423i	0.267545	+	0.963545i	$0.413787\pi$
$59$	−3.42524	+	12.7832i	−0.445928	+	1.66423i	−0.713474	+	0.700682i	$0.752879\pi$
$60$	1.04632	−	1.36151i	0.135080	−	0.175770i
$61$	−11.6537	+	3.12260i	−1.49210	+	0.399808i	−0.910447	−	0.413626i	$-0.864262\pi$
$61$	−11.6537	+	3.12260i	−1.49210	+	0.399808i	−0.581657	+	0.813434i	$0.697595\pi$
$62$	1.28447	−	0.533599i	0.163127	−	0.0677671i
$63$	−7.76617	−	1.63906i	−0.978446	−	0.206503i
$64$	5.69180	+	5.62169i	0.711475	+	0.702712i
$65$	−0.295610	−	0.170670i	−0.0366659	−	0.0211691i
$66$	3.18967	−	1.83403i	0.392622	−	0.225753i
$67$	12.3049	+	3.29710i	1.50329	+	0.402804i	0.914199	−	0.405265i	$-0.132821\pi$
$67$	12.3049	+	3.29710i	1.50329	+	0.402804i	0.589087	+	0.808069i	$0.299487\pi$
$68$	1.66157	+	6.15022i	0.201495	+	0.745824i
$69$	−2.98644	−	7.26751i	−0.359525	−	0.874905i
$70$	−0.604958	+	1.75326i	−0.0723063	+	0.209555i
$71$	11.3218			1.34365			0.671827	−	0.740708i	$-0.265510\pi$
$71$	11.3218			1.34365			0.671827	+	0.740708i	$0.265510\pi$
$72$	−1.12869	+	8.40988i	−0.133017	+	0.991114i
$73$	5.65102	+	9.78785i	0.661402	+	1.14558i	0.980247	+	0.197775i	$0.0633715\pi$
$73$	5.65102	+	9.78785i	0.661402	+	1.14558i	−0.318846	+	0.947807i	$0.603295\pi$
$74$	−2.14255	+	0.284323i	−0.249066	+	0.0330519i
$75$	−1.09774	+	8.16118i	−0.126756	+	0.942372i
$76$	5.58040	−	0.0115264i	0.640116	−	0.00132217i
$77$	−2.63834	+	2.97205i	−0.300667	+	0.338697i
$78$	1.68676	+	0.00299026i	0.190988	+	0.000338581i
$79$	−3.58163	+	6.20356i	−0.402965	+	0.697955i	−0.994082	−	0.108630i	$-0.965354\pi$
$79$	−3.58163	+	6.20356i	−0.402965	+	0.697955i	0.591118	+	0.806585i	$0.298687\pi$
$80$	1.91730	+	0.505259i	0.214361	+	0.0564897i
$81$	−7.84424	+	4.41225i	−0.871582	+	0.490250i
$82$	−0.527088	+	4.03584i	−0.0582072	+	0.445684i
$83$	−4.94774	+	4.94774i	−0.543085	+	0.543085i	−0.924432	−	0.381347i	$-0.875460\pi$
$83$	−4.94774	+	4.94774i	−0.543085	+	0.543085i	0.381347	+	0.924432i	$0.375460\pi$
$84$	−1.72706	−	9.00096i	−0.188437	−	0.982085i
$85$	1.11649	+	1.11649i	0.121100	+	0.121100i
$86$	−6.34375	−	8.24968i	−0.684064	−	0.889586i
$87$	−3.80381	+	0.489929i	−0.407812	+	0.0525259i
$88$	3.37860	+	2.57590i	0.360160	+	0.274592i
$89$	9.31634	+	5.37879i	0.987530	+	0.570151i	0.904535	−	0.426399i	$-0.140218\pi$
$89$	9.31634	+	5.37879i	0.987530	+	0.570151i	0.0829951	+	0.996550i	$0.473551\pi$
$90$	0.795892	+	1.94661i	0.0838944	+	0.205191i
$91$	−1.72873	+	0.575206i	−0.181220	+	0.0602980i
$92$	6.40211	−	6.42861i	0.667466	−	0.670229i
$93$	−0.227087	+	1.68828i	−0.0235479	+	0.175067i
$94$	−10.9060	+	14.2434i	−1.12486	+	1.46909i
$95$	1.19778	−	0.691538i	0.122890	−	0.0709503i
$96$	−9.45810	+	2.55821i	−0.965313	+	0.261096i
$97$		−	4.48178i		−	0.455056i	−0.973772	−	0.227528i	$-0.926936\pi$
$97$		−	4.48178i		−	0.455056i	0.973772	−	0.227528i	$-0.0730643\pi$
$98$	4.85476	+	8.62736i	0.490405	+	0.871495i
$99$	−0.0252849	+	4.50620i	−0.00254123	+	0.452890i
$100$	−9.17948	+	2.47997i	−0.917948	+	0.247997i
$101$	−0.0952131	+	0.355340i	−0.00947406	+	0.0353577i	−0.970501	−	0.241097i	$-0.922493\pi$
$101$	−0.0952131	+	0.355340i	−0.00947406	+	0.0353577i	0.961027	+	0.276455i	$0.0891595\pi$
$102$	−7.53305	−	2.03279i	−0.745883	−	0.201277i
$103$	3.07387	−	5.32410i	0.302877	−	0.524599i	−0.673909	−	0.738814i	$-0.735386\pi$
$103$	3.07387	−	5.32410i	0.302877	−	0.524599i	0.976786	+	0.214215i	$0.0687194\pi$
$104$	0.750926	+	1.79713i	0.0736344	+	0.176223i
$105$	−1.48256	−	1.72101i	−0.144683	−	0.167953i
$106$	−2.28080	−	0.941981i	−0.221531	−	0.0914933i
$107$	4.76737	+	17.7921i	0.460879	+	1.72002i	0.670204	+	0.742177i	$0.266207\pi$
$107$	4.76737	+	17.7921i	0.460879	+	1.72002i	−0.209325	+	0.977846i	$0.567127\pi$
$108$	−8.20442	−	6.37867i	−0.789471	−	0.613788i
$109$	−5.74038	−	1.53813i	−0.549828	−	0.147326i	−0.0267992	−	0.999641i	$-0.508531\pi$
$109$	−5.74038	−	1.53813i	−0.549828	−	0.147326i	−0.523029	+	0.852315i	$0.675198\pi$
$110$	1.04412	+	0.136364i	0.0995525	+	0.0130018i
$111$	1.01985	−	2.44273i	0.0967999	−	0.231854i
$112$	8.81065	−	5.86281i	0.832528	−	0.553983i
$113$			8.26517i			0.777521i	0.921339	+	0.388761i	$0.127097\pi$
$113$			8.26517i			0.777521i	−0.921339	+	0.388761i	$0.872903\pi$
$114$	−3.42778	+	5.91286i	−0.321041	+	0.553790i
$115$	0.581986	−	2.17200i	0.0542705	−	0.202540i
$116$	−2.22219	−	3.83065i	−0.206325	−	0.355667i
$117$	−1.04295	+	1.78326i	−0.0964207	+	0.164862i
$118$	7.14439	−	17.2986i	0.657694	−	1.59246i
$119$	8.41280	−	0.500404i	0.771200	−	0.0458719i
$120$	−1.71662	+	1.71762i	−0.156705	+	0.156797i
$121$	−7.57228	−	4.37186i	−0.688390	−	0.397442i
$122$	16.9139	−	2.24453i	1.53131	−	0.203211i
$123$	−3.94622	−	3.04567i	−0.355818	−	0.274618i
$124$	−1.89894	+	0.513026i	−0.170530	+	0.0460711i
$125$	−3.41893	+	3.41893i	−0.305799	+	0.305799i
$126$	10.5904	+	3.72079i	0.943464	+	0.331475i
$127$	13.5133			1.19911			0.599557	−	0.800332i	$-0.295343\pi$
$127$	13.5133			1.19911			0.599557	+	0.800332i	$0.295343\pi$
$128$	−6.95206	−	8.92574i	−0.614481	−	0.788932i
$129$	12.6412	−	1.62818i	1.11299	−	0.143353i
$130$	0.383278	+	0.293471i	0.0336157	+	0.0257391i
$131$	−3.18143	−	11.8733i	−0.277963	−	1.03737i	−0.953830	−	0.300348i	$-0.902897\pi$
$131$	−3.18143	−	11.8733i	−0.277963	−	1.03737i	0.675867	−	0.737024i	$-0.263769\pi$
$132$	−4.80878	+	1.98770i	−0.418551	+	0.173007i
$133$	1.48389	−	7.23152i	0.128670	−	0.627052i
$134$	−16.6514	−	6.87710i	−1.43846	−	0.594091i
$135$	−2.55072	−	0.357674i	−0.219531	−	0.0307837i
$136$	−1.20365	−	8.92879i	−0.103212	−	0.765638i
$137$	5.89498	+	10.2104i	0.503642	+	0.872334i	0.999991	+	0.00421094i	$0.00134039\pi$
$137$	5.89498	+	10.2104i	0.503642	+	0.872334i	−0.496349	+	0.868123i	$0.665326\pi$
$138$	2.85690	+	10.7382i	0.243196	+	0.914097i
$139$	2.58545	−	2.58545i	0.219295	−	0.219295i	−0.588906	−	0.808201i	$-0.700441\pi$
$139$	2.58545	−	2.58545i	0.219295	−	0.219295i	0.808201	+	0.588906i	$0.200441\pi$
$140$	1.16943	−	2.34782i	0.0988353	−	0.198427i
$141$	−8.35091	−	20.3220i	−0.703274	−	1.71142i
$142$	−15.8767	−	2.07352i	−1.33234	−	0.174006i
$143$	0.517184	+	0.895788i	0.0432491	+	0.0749096i
$144$	3.12298	−	11.5865i	0.260248	−	0.965542i
$145$	−0.950543	−	0.548796i	−0.0789383	−	0.0455750i
$146$	−6.13187	−	14.7605i	−0.507477	−	1.22159i
$147$	−12.1230	−	0.180437i	−0.999889	−	0.0148822i
$148$	3.05658	−	0.00631342i	0.251249	−	0.000518960i
$149$	4.69419	+	17.5190i	0.384563	+	1.43521i	0.838854	+	0.544356i	$0.183226\pi$
$149$	4.69419	+	17.5190i	0.384563	+	1.43521i	−0.454291	+	0.890853i	$0.650107\pi$
$150$	3.03404	−	11.2434i	0.247728	−	0.918021i
$151$	11.0224	−	6.36377i	0.896987	−	0.517876i	0.0207658	−	0.999784i	$-0.493390\pi$
$151$	11.0224	−	6.36377i	0.896987	−	0.517876i	0.876222	+	0.481908i	$0.160056\pi$
$152$	−7.82754	−	1.00585i	−0.634897	−	0.0815854i
$153$	6.79498	−	6.71915i	0.549341	−	0.543211i
$154$	4.24407	−	3.68453i	0.341997	−	0.296908i
$155$	−0.344725	+	0.344725i	−0.0276890	+	0.0276890i
$156$	−2.36480	−	0.313113i	−0.189336	−	0.0250691i
$157$	−3.30638	+	12.3396i	−0.263878	+	0.984805i	0.699056	+	0.715067i	$0.253604\pi$
$157$	−3.30638	+	12.3396i	−0.263878	+	0.984805i	−0.962934	+	0.269738i	$0.913063\pi$
$158$	6.15868	−	8.04333i	0.489958	−	0.639893i
$159$	2.40288	−	1.83310i	0.190561	−	0.145375i
$160$	−2.59610	−	1.05967i	−0.205240	−	0.0837742i
$161$	−6.60761	−	10.0194i	−0.520752	−	0.789642i
$162$	11.8081	−	4.75070i	0.927731	−	0.373250i
$163$	−2.65609	−	9.91268i	−0.208041	−	0.776421i	−0.988501	−	0.151215i	$-0.951682\pi$
$163$	−2.65609	−	9.91268i	−0.208041	−	0.776421i	0.780460	−	0.625206i	$-0.214985\pi$
$164$	1.47828	−	5.56294i	0.115434	−	0.434393i
$165$	−0.787947	+	1.02093i	−0.0613416	+	0.0794792i
$166$	7.84438	−	6.03209i	0.608842	−	0.468181i
$167$			11.7120i			0.906298i	0.891435	+	0.453149i	$0.149700\pi$
$167$			11.7120i			0.906298i	−0.891435	+	0.453149i	$0.850300\pi$
$168$	0.773392	+	12.9384i	0.0596685	+	0.998218i
$169$		−	12.5258i		−	0.963523i
$170$	−1.36118	−	1.77013i	−0.104397	−	0.135763i
$171$	−4.14457	−	7.27254i	−0.316943	−	0.556145i
$172$	7.38499	+	12.7304i	0.563101	+	0.970683i
$173$	−6.70016	−	25.0053i	−0.509404	−	1.90112i	−0.426304	−	0.904580i	$-0.640185\pi$
$173$	−6.70016	−	25.0053i	−0.509404	−	1.90112i	−0.0830993	−	0.996541i	$-0.526482\pi$
$174$	5.42383	+	0.00961529i	0.411180	+	0.000728933i
$175$	0.746875	+	12.5565i	0.0564584	+	0.949181i
$176$	−4.26607	−	4.23097i	−0.321567	−	0.318921i
$177$	13.9030	+	18.2244i	1.04502	+	1.36983i
$178$	−12.0793	−	9.24894i	−0.905379	−	0.693237i
$179$	−1.57850	+	5.89102i	−0.117982	+	0.440316i	−0.999493	−	0.0318487i	$-0.989861\pi$
$179$	−1.57850	+	5.89102i	−0.117982	+	0.440316i	0.881510	+	0.472165i	$0.156527\pi$
$180$	−0.759573	−	2.87551i	−0.0566152	−	0.214328i
$181$	−4.18491	+	4.18491i	−0.311062	+	0.311062i	−0.845321	−	0.534259i	$-0.820591\pi$
$181$	−4.18491	+	4.18491i	−0.311062	+	0.311062i	0.534259	+	0.845321i	$0.320591\pi$
$182$	2.52955	−	0.490008i	0.187503	−	0.0363218i
$183$	−8.05101	+	19.2837i	−0.595148	+	1.42549i
$184$	−10.1551	+	7.84236i	−0.748642	+	0.578147i
$185$	0.656064	−	0.378779i	0.0482348	−	0.0278484i
$186$	0.627645	−	2.32590i	0.0460211	−	0.170543i
$187$	−1.23837	−	4.62167i	−0.0905587	−	0.337970i
$188$	17.9021	−	17.9762i	1.30564	−	1.31105i
$189$	−10.4660	+	8.91415i	−0.761292	+	0.648409i
$190$	−1.80630	+	0.750381i	−0.131043	+	0.0544384i
$191$	−11.4487	−	6.60991i	−0.828399	−	0.478276i	0.0249054	−	0.999690i	$-0.492072\pi$
$191$	−11.4487	−	6.60991i	−0.828399	−	0.478276i	−0.853304	+	0.521414i	$0.825405\pi$
$192$	13.7317	−	1.85520i	0.990997	−	0.133887i
$193$	9.96849	+	17.2659i	0.717548	+	1.24283i	0.961969	+	0.273160i	$0.0880689\pi$
$193$	9.96849	+	17.2659i	0.717548	+	1.24283i	−0.244421	+	0.969669i	$0.578598\pi$
$194$	−0.820811	+	6.28483i	−0.0589308	+	0.451224i
$195$	−0.546848	+	0.224717i	−0.0391606	+	0.0160923i
$196$	−5.22781	−	12.9873i	−0.373415	−	0.927664i
$197$	−8.37075	+	8.37075i	−0.596391	+	0.596391i	−0.939350	−	0.342959i	$-0.888571\pi$
$197$	−8.37075	+	8.37075i	−0.596391	+	0.596391i	0.342959	+	0.939350i	$0.388571\pi$
$198$	0.860740	−	6.31444i	0.0611701	−	0.448748i
$199$	−8.18748	−	14.1811i	−0.580395	−	1.00527i	−0.995432	−	0.0954689i	$-0.969565\pi$
$199$	−8.18748	−	14.1811i	−0.580395	−	1.00527i	0.415038	−	0.909804i	$-0.363768\pi$
$200$	13.3266	−	1.79651i	0.942335	−	0.127032i
$201$	17.5426	−	13.3829i	1.23736	−	0.943958i
$202$	0.198596	−	0.480858i	0.0139732	−	0.0338330i
$203$	−5.55878	+	1.84959i	−0.390150	+	0.129816i
$204$	10.1913	+	4.23023i	0.713536	+	0.296175i
$205$	−0.369230	−	1.37799i	−0.0257881	−	0.0962427i
$206$	−5.28558	+	6.90305i	−0.368264	+	0.480958i
$207$	−13.1254	−	3.59599i	−0.912277	−	0.249938i
$208$	−0.723895	−	2.65765i	−0.0501931	−	0.184275i
$209$	−4.19115			−0.289908
$210$	1.76381	+	2.68490i	0.121715	+	0.185276i
$211$	−8.45390	+	8.45390i	−0.581990	+	0.581990i	−0.935450	−	0.353460i	$-0.885005\pi$
$211$	−8.45390	+	8.45390i	−0.581990	+	0.581990i	0.353460	+	0.935450i	$0.385005\pi$
$212$	3.02586	+	1.73866i	0.207817	+	0.119412i
$213$	11.9814	−	15.5241i	0.820953	−	1.06369i
$214$	−3.42680	−	25.8230i	−0.234251	−	1.76522i
$215$	3.15893	+	1.82381i	0.215437	+	0.124383i
$216$	10.3369	+	10.4474i	0.703336	+	0.710857i
$217$	0.154504	+	2.59753i	0.0104884	+	0.176332i
$218$	7.76806	+	3.20824i	0.526119	+	0.217289i
$219$	19.4010	+	2.60958i	1.31100	+	0.176339i
$220$	−1.43919	−	0.382446i	−0.0970304	−	0.0257845i
$221$	0.567719	−	2.11875i	0.0381889	−	0.142523i
$222$	−1.87751	+	3.23867i	−0.126010	+	0.217365i
$223$		−	17.2064i		−	1.15222i	−0.817371	−	0.576112i	$-0.804569\pi$
$223$		−	17.2064i		−	1.15222i	0.817371	−	0.576112i	$-0.195431\pi$
$224$	−13.4289	+	6.60783i	−0.897259	+	0.441504i
$225$	10.0286	+	10.1418i	0.668575	+	0.676120i
$226$	1.51371	−	11.5903i	0.100691	−	0.770974i
$227$	−17.6305	−	4.72407i	−1.17018	−	0.313547i	−0.379152	−	0.925334i	$-0.623784\pi$
$227$	−17.6305	−	4.72407i	−1.17018	−	0.313547i	−0.791023	+	0.611787i	$0.790451\pi$
$228$	5.88970	−	7.66385i	0.390055	−	0.507551i
$229$	1.71004	+	6.38196i	0.113003	+	0.421732i	0.999130	−	0.0417108i	$-0.0132808\pi$
$229$	1.71004	+	6.38196i	0.113003	+	0.421732i	−0.886127	+	0.463442i	$0.846614\pi$
$230$	−1.21391	+	2.93922i	−0.0800429	+	0.193807i
$231$	1.28313	+	6.76280i	0.0844240	+	0.444959i
$232$	2.41463	+	5.77872i	0.158528	+	0.379392i
$233$	1.23993	−	2.14762i	0.0812304	−	0.140695i	−0.822548	−	0.568695i	$-0.807448\pi$
$233$	1.23993	−	2.14762i	0.0812304	−	0.140695i	0.903779	+	0.428000i	$0.140782\pi$
$234$	1.78913	−	2.30966i	0.116959	−	0.150987i
$235$	1.62739	−	6.07352i	0.106159	−	0.396193i
$236$	−13.1867	+	22.9494i	−0.858384	+	1.49388i
$237$	4.71582	+	11.4760i	0.306326	+	0.745444i
$238$	−11.8890	−	0.839033i	−0.770646	−	0.0543865i
$239$			19.9191i			1.28846i	0.764833	+	0.644229i	$0.222821\pi$
$239$			19.9191i			1.28846i	−0.764833	+	0.644229i	$0.777179\pi$
$240$	2.72179	−	2.09424i	0.175691	−	0.135183i
$241$	−7.32694	+	4.23021i	−0.471970	+	0.272492i	−0.717064	−	0.697007i	$-0.754514\pi$
$241$	−7.32694	+	4.23021i	−0.471970	+	0.272492i	0.245094	+	0.969499i	$0.421181\pi$
$242$	9.81797	+	7.51750i	0.631123	+	0.483243i
$243$	−2.25129	+	15.4250i	−0.144421	+	0.989516i
$244$	−24.1296	+	0.0498400i	−1.54474	+	0.00319068i
$245$	−2.72709	−	2.14539i	−0.174227	−	0.137064i
$246$	4.97600	+	4.99368i	0.317258	+	0.318385i
$247$	−1.66397	−	0.960694i	−0.105876	−	0.0611275i
$248$	2.75685	−	0.371639i	0.175060	−	0.0235991i
$249$	1.54819	+	12.0201i	0.0981124	+	0.761746i
$250$	5.42054	−	4.16823i	0.342825	−	0.263622i
$251$	−11.5508	−	11.5508i	−0.729078	−	0.729078i	0.241358	−	0.970436i	$-0.422407\pi$
$251$	−11.5508	−	11.5508i	−0.729078	−	0.729078i	−0.970436	+	0.241358i	$0.922407\pi$
$252$	−14.1695	−	7.15724i	−0.892593	−	0.450864i
$253$	−4.81824	+	4.81824i	−0.302920	+	0.302920i
$254$	−18.9498	−	2.47488i	−1.18902	−	0.155288i
$255$	2.71241	−	0.349357i	0.169858	−	0.0218776i
$256$	8.11421	+	13.7898i	0.507138	+	0.861865i
$257$	8.29276	−	14.3635i	0.517288	−	0.895970i	−0.482510	−	0.875890i	$-0.660275\pi$
$257$	8.29276	−	14.3635i	0.517288	−	0.895970i	0.999798	−	0.0200792i	$-0.00639184\pi$
$258$	−18.0250	−	0.0319544i	−1.12219	−	0.00198940i
$259$	0.812777	−	3.96095i	0.0505035	−	0.246121i
$260$	−0.483725	−	0.481731i	−0.0299993	−	0.0298757i
$261$	−3.35364	+	5.73413i	−0.207585	+	0.354933i
$262$	2.28682	+	17.2326i	0.141280	+	1.06463i
$263$	−8.90599	−	15.4256i	−0.549167	−	0.951185i	−0.998332	−	0.0577361i	$-0.981612\pi$
$263$	−8.90599	−	15.4256i	−0.549167	−	0.951185i	0.449165	−	0.893449i	$-0.351722\pi$
$264$	7.10742	−	1.90666i	0.437431	−	0.117347i
$265$	0.864932			0.0531323
$266$	−3.40527	+	9.86903i	−0.208791	+	0.605109i
$267$	17.2343	−	7.08210i	1.05472	−	0.433417i
$268$	22.0909	+	12.6934i	1.34941	+	0.775373i
$269$	19.2683	+	5.16292i	1.17481	+	0.314789i	0.792865	−	0.609397i	$-0.208588\pi$
$269$	19.2683	+	5.16292i	1.17481	+	0.314789i	0.381943	+	0.924186i	$0.375255\pi$
$270$	3.51138	+	0.968717i	0.213696	+	0.0589543i
$271$	−22.5220	−	13.0031i	−1.36811	−	0.789879i	−0.377425	−	0.926040i	$-0.623190\pi$
$271$	−22.5220	−	13.0031i	−1.36811	−	0.789879i	−0.990687	+	0.136161i	$0.956524\pi$
$272$	0.0526351	+	12.7413i	0.00319147	+	0.772557i
$273$	−1.04074	+	2.97909i	−0.0629882	+	0.180303i
$274$	−6.39659	−	15.3977i	−0.386432	−	0.930211i
$275$	6.89804	−	1.84833i	0.415968	−	0.111458i
$276$	−2.03961	−	15.5815i	−0.122770	−	0.937894i
$277$	−7.98946	+	29.8171i	−0.480040	+	1.79153i	0.121386	+	0.992605i	$0.461266\pi$
$277$	−7.98946	+	29.8171i	−0.480040	+	1.79153i	−0.601426	+	0.798929i	$0.705400\pi$
$278$	−4.09910	+	3.15208i	−0.245848	+	0.189049i
$279$	2.07460	+	2.09801i	0.124203	+	0.125605i
$280$	−2.06989	+	3.07818i	−0.123700	+	0.183956i
$281$	9.67354			0.577075			0.288537	−	0.957469i	$-0.406831\pi$
$281$	9.67354			0.577075			0.288537	+	0.957469i	$0.406831\pi$
$282$	7.98868	+	30.0270i	0.475719	+	1.78808i
$283$	−25.5777	−	6.85354i	−1.52044	−	0.407400i	−0.600553	−	0.799585i	$-0.705053\pi$
$283$	−25.5777	−	6.85354i	−1.52044	−	0.407400i	−0.919886	+	0.392185i	$0.871719\pi$
$284$	21.8842	+	5.81542i	1.29859	+	0.345082i
$285$	0.319345	−	2.37418i	0.0189164	−	0.140634i
$286$	−0.561191	−	1.35089i	−0.0331839	−	0.0798796i
$287$	−6.80876	−	3.40897i	−0.401908	−	0.201225i
$288$	−6.50137	+	15.6758i	−0.383097	+	0.923708i
$289$	3.42674	−	5.93529i	0.201573	−	0.349135i
$290$	1.23244	+	0.943665i	0.0723715	+	0.0554139i
$291$	−6.14526	−	4.74288i	−0.360242	−	0.278032i
$292$	5.89545	+	21.8217i	0.345005	+	1.27702i
$293$	4.86775	+	4.86775i	0.284377	+	0.284377i	0.834852	−	0.550475i	$-0.185553\pi$
$293$	4.86775	+	4.86775i	0.284377	+	0.284377i	−0.550475	+	0.834852i	$0.685553\pi$
$294$	16.9671	+	2.47328i	0.989542	+	0.144245i
$295$			6.56001i			0.381939i
$296$	−4.28741	−	0.550940i	−0.249201	−	0.0320227i
$297$	6.15199	+	4.80339i	0.356975	+	0.278721i
$298$	−3.37420	−	25.4266i	−0.195462	−	1.47293i
$299$	−3.01737	+	0.808503i	−0.174499	+	0.0467569i
$300$	−6.31381	+	15.2110i	−0.364528	+	0.878209i
$301$	18.4735	−	6.14674i	1.06479	−	0.354292i
$302$	−16.6222	+	6.90526i	−0.956500	+	0.397353i
$303$	0.386470	+	0.506594i	0.0222021	+	0.0291031i
$304$	10.7924	+	2.84408i	0.618985	+	0.163119i
$305$	−5.17917	+	2.99020i	−0.296559	+	0.171218i
$306$	−10.7592	+	8.17783i	−0.615062	+	0.467496i
$307$	−6.83909	−	6.83909i	−0.390327	−	0.390327i	0.484477	−	0.874804i	$-0.339010\pi$
$307$	−6.83909	−	6.83909i	−0.390327	−	0.390327i	−0.874804	+	0.484477i	$0.839010\pi$
$308$	−6.62628	+	4.38956i	−0.377567	+	0.250118i
$309$	−4.04727	−	9.84904i	−0.230241	−	0.560292i
$310$	0.546544	−	0.420276i	0.0310416	−	0.0238701i
$311$	20.0828	−	11.5948i	1.13879	−	0.657481i	0.192660	−	0.981266i	$-0.438289\pi$
$311$	20.0828	−	11.5948i	1.13879	−	0.657481i	0.946131	+	0.323785i	$0.104955\pi$
$312$	3.25883	+	0.872179i	0.184495	+	0.0493774i
$313$	−0.557103	+	0.964930i	−0.0314893	+	0.0545411i	−0.881341	−	0.472482i	$-0.843358\pi$
$313$	−0.557103	+	0.964930i	−0.0314893	+	0.0545411i	0.849851	+	0.527023i	$0.176692\pi$
$314$	6.89647	−	16.6983i	0.389190	−	0.942340i
$315$	−3.92872	+	0.211570i	−0.221358	+	0.0119206i
$316$	−10.1094	+	10.1513i	−0.568700	+	0.571054i
$317$	21.6251	−	5.79442i	1.21458	−	0.325447i	0.406025	−	0.913862i	$-0.366915\pi$
$317$	21.6251	−	5.79442i	1.21458	−	0.325447i	0.808559	+	0.588415i	$0.200248\pi$
$318$	−3.70529	+	2.13050i	−0.207782	+	0.119472i
$319$	1.66302	+	2.88044i	0.0931113	+	0.161274i
$320$	3.44646	+	1.96144i	0.192663	+	0.109648i
$321$	29.4409	+	12.2917i	1.64323	+	0.686057i
$322$	7.43088	+	15.2604i	0.414107	+	0.850431i
$323$	6.28463	+	6.28463i	0.349686	+	0.349686i
$324$	−17.4286	+	4.49935i	−0.968255	+	0.249964i
$325$	3.16234	+	0.847345i	0.175415	+	0.0470023i
$326$	1.90921	+	14.3870i	0.105741	+	0.796824i
$327$	−8.18382	+	6.24327i	−0.452566	+	0.345253i
$328$	−3.09181	+	7.53020i	−0.170717	+	0.415786i
$329$	−18.4767	−	28.0171i	−1.01865	−	1.54463i
$330$	1.29192	−	1.28735i	0.0711178	−	0.0708661i
$331$	25.8676	−	6.93122i	1.42181	−	0.380974i	0.535687	−	0.844416i	$-0.320053\pi$
$331$	25.8676	−	6.93122i	1.42181	−	0.380974i	0.886127	+	0.463442i	$0.153386\pi$
$332$	−12.1050	+	7.02218i	−0.664346	+	0.385392i
$333$	−2.27012	−	3.98342i	−0.124402	−	0.218290i
$334$	2.14497	−	16.4237i	0.117368	−	0.898667i
$335$	6.31459			0.345003
$336$	1.28505	−	18.2852i	0.0701054	−	0.997540i
$337$	1.87049			0.101892			0.0509462	−	0.998701i	$-0.483776\pi$
$337$	1.87049			0.101892			0.0509462	+	0.998701i	$0.483776\pi$
$338$	−2.29402	+	17.5650i	−0.124778	+	0.955410i
$339$	11.3329	+	8.74667i	0.615519	+	0.475054i
$340$	1.58459	+	2.73155i	0.0859367	+	0.148139i
$341$	1.42698	−	0.382359i	0.0772755	−	0.0207059i
$342$	4.48003	+	10.9574i	0.242252	+	0.592507i
$343$	−18.2269	+	3.28348i	−0.984158	+	0.177292i
$344$	−8.02452	−	19.2044i	−0.432653	−	1.03543i
$345$	−2.36228	−	3.09654i	−0.127181	−	0.166712i
$346$	4.81609	+	36.2922i	0.258915	+	1.95108i
$347$	−4.17378	−	1.11836i	−0.224060	−	0.0600368i	0.145042	−	0.989425i	$-0.453668\pi$
$347$	−4.17378	−	1.11836i	−0.224060	−	0.0600368i	−0.369103	+	0.929389i	$0.620335\pi$
$348$	−7.60411	−	1.00682i	−0.407623	−	0.0539715i
$349$	0.764040	+	0.764040i	0.0408981	+	0.0408981i	0.727260	−	0.686362i	$-0.240793\pi$
$349$	0.764040	+	0.764040i	0.0408981	+	0.0408981i	−0.686362	+	0.727260i	$0.740793\pi$
$350$	1.25230	−	17.7448i	0.0669380	−	0.948499i
$351$	1.34143	+	3.31720i	0.0716004	+	0.177059i
$352$	5.20746	+	6.71441i	0.277558	+	0.357879i
$353$	−13.8774	−	24.0364i	−0.738620	−	1.27933i	−0.953117	−	0.302602i	$-0.902145\pi$
$353$	−13.8774	−	24.0364i	−0.738620	−	1.27933i	0.214497	−	0.976725i	$-0.431189\pi$
$354$	−16.1586	−	28.1025i	−0.858821	−	1.49363i
$355$	5.42089	−	1.45252i	0.287711	−	0.0770919i
$356$	15.2449	+	15.1821i	0.807979	+	0.804648i
$357$	8.21677	−	12.0649i	0.434877	−	0.638542i
$358$	3.29244	−	7.97192i	0.174011	−	0.421329i
$359$	11.5863	−	20.0681i	0.611504	−	1.05916i	−0.379484	−	0.925198i	$-0.623898\pi$
$359$	11.5863	−	20.0681i	0.611504	−	1.05916i	0.990987	−	0.133957i	$-0.0427684\pi$
$360$	0.538521	+	4.17145i	0.0283826	+	0.219855i
$361$	−9.71225	+	5.60737i	−0.511171	+	0.295125i
$362$	6.63496	−	5.10208i	0.348726	−	0.268159i
$363$	−14.0080	+	5.75630i	−0.735227	+	0.302127i
$364$	−3.63694	+	0.223869i	−0.190627	+	0.0117339i
$365$	3.96142	+	3.96142i	0.207350	+	0.207350i
$366$	14.8217	−	25.5671i	0.774740	−	1.33641i
$367$	3.58369	−	2.06904i	0.187067	−	0.108003i	−0.403542	−	0.914961i	$-0.632221\pi$
$367$	3.58369	−	2.06904i	0.187067	−	0.108003i	0.590609	+	0.806958i	$0.298888\pi$
$368$	15.6768	−	9.13755i	0.817209	−	0.476328i
$369$	−8.35222	+	2.18782i	−0.434799	+	0.113893i
$370$	−0.989373	+	0.411009i	−0.0514351	+	0.0213674i
$371$	3.06483	−	3.45249i	0.159118	−	0.179244i
$372$	−1.30612	+	3.14667i	−0.0677193	+	0.163147i
$373$	17.0023	−	4.55576i	0.880348	−	0.235888i	0.209791	−	0.977746i	$-0.432722\pi$
$373$	17.0023	−	4.55576i	0.880348	−	0.235888i	0.670557	+	0.741858i	$0.266055\pi$
$374$	0.890145	+	6.70778i	0.0460283	+	0.346851i
$375$	1.06981	+	8.30603i	0.0552448	+	0.428921i
$376$	−28.3964	+	21.9294i	−1.46443	+	1.13092i
$377$			1.52479i			0.0785306i
$378$	16.3091	−	10.5836i	0.838852	−	0.544360i
$379$	−7.35479	−	7.35479i	−0.377790	−	0.377790i	0.492514	−	0.870304i	$-0.336078\pi$
$379$	−7.35479	−	7.35479i	−0.377790	−	0.377790i	−0.870304	+	0.492514i	$0.836078\pi$
$380$	2.67041	−	0.721450i	0.136989	−	0.0370096i
$381$	14.3006	−	18.5290i	0.732641	−	0.949270i
$382$	14.8440	+	11.3659i	0.759485	+	0.581528i
$383$	8.74610	−	15.1487i	0.446905	−	0.774062i	−0.551278	−	0.834322i	$-0.685860\pi$
$383$	8.74610	−	15.1487i	0.446905	−	0.774062i	0.998183	+	0.0602596i	$0.0191928\pi$
$384$	−19.5957	+	0.0866875i	−0.999990	+	0.00442375i
$385$	−0.881939	+	1.76150i	−0.0449478	+	0.0897744i
$386$	−10.8167	−	26.0378i	−0.550556	−	1.32529i
$387$	11.1451	−	19.0562i	0.566539	−	0.968680i
$388$	2.30205	−	8.66291i	0.116869	−	0.439793i
$389$	−18.5400	−	4.96778i	−0.940016	−	0.251877i	−0.243896	−	0.969802i	$-0.578425\pi$
$389$	−18.5400	−	4.96778i	−0.940016	−	0.251877i	−0.696120	+	0.717925i	$0.745092\pi$
$390$	0.808003	−	0.214969i	0.0409148	−	0.0108854i
$391$	14.4499			0.730764
$392$	4.95243	+	19.1696i	0.250136	+	0.968211i
$393$	−19.6470	−	8.20269i	−0.991058	−	0.413771i
$394$	13.2714	−	10.2053i	0.668603	−	0.514135i
$395$	−0.919002	+	3.42976i	−0.0462400	+	0.172570i
$396$	−2.36347	+	8.69713i	−0.118769	+	0.437047i
$397$	7.93727	−	2.12679i	0.398360	−	0.106740i	−0.0540765	−	0.998537i	$-0.517222\pi$
$397$	7.93727	−	2.12679i	0.398360	−	0.106740i	0.452437	+	0.891797i	$0.350555\pi$
$398$	8.88415	+	21.3857i	0.445322	+	1.07197i
$399$	−8.34527	−	9.68746i	−0.417786	−	0.484980i
$400$	−19.0170	+	0.0785603i	−0.950850	+	0.00392802i
$401$	−28.7394	−	16.5927i	−1.43517	−	0.828599i	−0.437666	−	0.899138i	$-0.644195\pi$
$401$	−28.7394	−	16.5927i	−1.43517	−	0.828599i	−0.997509	+	0.0705391i	$0.977528\pi$
$402$	−27.0511	+	15.5541i	−1.34919	+	0.775768i
$403$	0.654185	+	0.175288i	0.0325873	+	0.00873174i
$404$	−0.366558	+	0.637937i	−0.0182370	+	0.0317386i
$405$	−3.18975	+	3.11895i	−0.158500	+	0.154982i
$406$	8.13385	−	1.57564i	0.403676	−	0.0781976i
$407$	−2.29563			−0.113790
$408$	−13.5166	−	7.79855i	−0.669172	−	0.386086i
$409$	8.76642	+	15.1839i	0.433471	+	0.750794i	0.997169	−	0.0751865i	$-0.0239552\pi$
$409$	8.76642	+	15.1839i	0.433471	+	0.750794i	−0.563698	+	0.825981i	$0.690622\pi$
$410$	0.265404	+	1.99998i	0.0131073	+	0.0987718i
$411$	20.2386	+	2.72224i	0.998294	+	0.134278i
$412$	8.67624	−	8.71215i	0.427448	−	0.429217i
$413$	26.1852	+	23.2450i	1.28849	+	1.14381i
$414$	17.7472	+	7.44650i	0.872227	+	0.365976i
$415$	−1.73421	+	3.00374i	−0.0851290	+	0.147448i
$416$	0.528389	+	3.85941i	0.0259064	+	0.189223i
$417$	−0.809009	−	6.28116i	−0.0396173	−	0.307590i
$418$	5.87727	+	0.767583i	0.287466	+	0.0375437i
$419$	−11.8036	+	11.8036i	−0.576645	+	0.576645i	−0.933977	−	0.357332i	$-0.883686\pi$
$419$	−11.8036	+	11.8036i	−0.576645	+	0.576645i	0.357332	+	0.933977i	$0.383686\pi$
$420$	−1.98168	−	4.08808i	−0.0966962	−	0.199478i
$421$	−27.0336	−	27.0336i	−1.31753	−	1.31753i	−0.915722	−	0.401813i	$-0.868380\pi$
$421$	−27.0336	−	27.0336i	−1.31753	−	1.31753i	−0.401813	−	0.915722i	$-0.631620\pi$
$422$	13.4032	−	10.3067i	0.652458	−	0.501720i
$423$	−36.7022	−	10.0554i	−1.78452	−	0.488909i
$424$	−3.92476	−	2.99230i	−0.190603	−	0.145319i
$425$	−13.1152	−	7.57206i	−0.636181	−	0.367299i
$426$	−19.6447	+	19.5752i	−0.951790	+	0.948421i
$427$	−6.41631	+	31.2689i	−0.310507	+	1.51321i
$428$	0.0760923	+	36.8393i	0.00367806	+	1.78070i
$429$	1.77559	+	0.238830i	0.0857261	+	0.0115308i
$430$	−4.09577	−	3.13608i	−0.197515	−	0.151235i
$431$	−23.2323	+	13.4132i	−1.11906	+	0.646090i	−0.941161	−	0.337959i	$-0.890264\pi$
$431$	−23.2323	+	13.4132i	−1.11906	+	0.646090i	−0.177900	+	0.984049i	$0.556930\pi$
$432$	−12.5821	−	16.5436i	−0.605356	−	0.795955i
$433$		−	6.51222i		−	0.312958i	−0.987681	−	0.156479i	$-0.949986\pi$
$433$		−	6.51222i		−	0.312958i	0.987681	−	0.156479i	$-0.0500143\pi$
$434$	0.259060	−	3.67083i	0.0124353	−	0.176205i
$435$	−1.75841	+	0.722584i	−0.0843092	+	0.0346452i
$436$	−10.3056	−	5.92160i	−0.493549	−	0.283593i
$437$	3.27597	−	12.2261i	0.156711	−	0.584853i
$438$	−26.7282	−	7.21260i	−1.27712	−	0.344631i
$439$	−10.8000	+	18.7062i	−0.515457	+	0.892798i	0.484382	+	0.874857i	$0.339045\pi$
$439$	−10.8000	+	18.7062i	−0.515457	+	0.892798i	−0.999839	+	0.0179414i	$0.994289\pi$
$440$	1.94814	+	0.799886i	0.0928742	+	0.0381331i
$441$	−13.0767	+	16.4317i	−0.622699	+	0.782462i
$442$	−1.18415	+	2.86717i	−0.0563243	+	0.136377i
$443$	3.73136	+	13.9256i	0.177282	+	0.661627i	0.996152	+	0.0876466i	$0.0279346\pi$
$443$	3.73136	+	13.9256i	0.177282	+	0.661627i	−0.818869	+	0.573980i	$0.805399\pi$
$444$	3.22599	−	4.19775i	0.153099	−	0.199216i
$445$	5.15072	+	1.38013i	0.244168	+	0.0654245i
$446$	−3.15124	+	24.1286i	−0.149216	+	1.14252i
$447$	28.9891	+	12.1031i	1.37114	+	0.572455i
$448$	20.0417	−	6.80676i	0.946879	−	0.321589i
$449$			17.3114i			0.816977i	0.912764	+	0.408488i	$0.133944\pi$
$449$			17.3114i			0.816977i	−0.912764	+	0.408488i	$0.866056\pi$
$450$	−12.2058	−	16.0586i	−0.575386	−	0.757009i
$451$	−1.11888	+	4.17572i	−0.0526860	+	0.196627i
$452$	−4.24538	+	15.9759i	−0.199686	+	0.751442i
$453$	2.93872	−	21.8480i	0.138073	−	1.02651i
$454$	23.8581	+	9.85349i	1.11972	+	0.462447i
$455$	−0.753918	+	0.497193i	−0.0353442	+	0.0233088i
$456$	−9.66273	+	9.66839i	−0.452499	+	0.452764i
$457$	3.12831	+	1.80613i	0.146336	+	0.0844873i	0.571380	−	0.820685i	$-0.306408\pi$
$457$	3.12831	+	1.80613i	0.146336	+	0.0844873i	−0.425044	+	0.905173i	$0.639741\pi$
$458$	−1.22918	−	9.26263i	−0.0574359	−	0.432814i
$459$	−2.02223	−	16.4276i	−0.0943895	−	0.766775i
$460$	2.24057	−	3.89937i	0.104467	−	0.181809i
$461$	−10.9932	+	10.9932i	−0.512005	+	0.512005i	−0.915141	−	0.403135i	$-0.867920\pi$
$461$	−10.9932	+	10.9932i	−0.512005	+	0.512005i	0.403135	+	0.915141i	$0.367920\pi$
$462$	−0.560780	−	9.71850i	−0.0260899	−	0.452146i
$463$	−8.28850			−0.385199			−0.192600	−	0.981277i	$-0.561692\pi$
$463$	−8.28850			−0.385199			−0.192600	+	0.981277i	$0.561692\pi$
$464$	−2.32771	−	8.54576i	−0.108061	−	0.396727i
$465$	0.107867	+	0.837483i	0.00500223	+	0.0388374i
$466$	−2.13208	+	2.78453i	−0.0987667	+	0.128991i
$467$	0.583107	+	2.17619i	0.0269830	+	0.100702i	0.978104	−	0.208116i	$-0.0667332\pi$
$467$	0.583107	+	2.17619i	0.0269830	+	0.100702i	−0.951121	+	0.308818i	$0.900067\pi$
$468$	−2.93190	+	2.91118i	−0.135527	+	0.134569i
$469$	22.3754	−	25.2055i	1.03320	−	1.16388i
$470$	−3.39443	+	8.21887i	−0.156573	+	0.379108i
$471$	13.4206	+	17.5920i	0.618388	+	0.810598i
$472$	22.6949	−	29.7670i	1.04462	−	1.37014i
$473$	−5.52671	−	9.57254i	−0.254118	−	0.440146i
$474$	−4.51127	−	16.9565i	−0.207209	−	0.778836i
$475$	−9.38010	+	9.38010i	−0.430388	+	0.430388i
$476$	16.5183	+	3.35397i	0.757114	+	0.153729i
$477$	0.0293723	−	5.23464i	0.00134486	−	0.239678i
$478$	3.64805	−	27.9326i	0.166858	−	1.27761i
$479$	3.53273	+	6.11886i	0.161414	+	0.279578i	0.935376	−	0.353654i	$-0.115061\pi$
$479$	3.53273	+	6.11886i	0.161414	+	0.279578i	−0.773962	+	0.633232i	$0.781728\pi$
$480$	−4.20033	+	2.43828i	−0.191718	+	0.111292i
$481$	−0.911413	−	0.526205i	−0.0415569	−	0.0239929i
$482$	11.0493	−	4.59016i	0.503284	−	0.209076i
$483$	−20.7308	−	1.54302i	−0.943286	−	0.0702097i
$484$	−12.3910	−	12.3399i	−0.563227	−	0.560906i
$485$	−0.574985	−	2.14587i	−0.0261087	−	0.0974391i
$486$	5.98200	−	21.2183i	0.271349	−	0.962481i
$487$	19.5940	−	11.3126i	0.887890	−	0.512623i	0.0146380	−	0.999893i	$-0.495340\pi$
$487$	19.5940	−	11.3126i	0.887890	−	0.512623i	0.873252	+	0.487270i	$0.162007\pi$
$488$	33.8461	+	4.34929i	1.53214	+	0.196883i
$489$	−16.4027	−	6.84821i	−0.741758	−	0.309687i
$490$	3.43129	+	3.50794i	0.155010	+	0.158472i
$491$	25.4191	−	25.4191i	1.14715	−	1.14715i	0.160034	−	0.987111i	$-0.448839\pi$
$491$	25.4191	−	25.4191i	1.14715	−	1.14715i	0.987111	−	0.160034i	$-0.0511605\pi$
$492$	−6.06331	−	7.91398i	−0.273355	−	0.356790i
$493$	1.82552	−	6.81293i	0.0822172	−	0.306839i
$494$	2.15745	+	1.65193i	0.0970682	+	0.0743239i
$495$	0.566012	+	2.16081i	0.0254403	+	0.0971212i
$496$	−3.93401	+	0.0162516i	−0.176642	+	0.000729718i
$497$	13.4106	−	26.7851i	0.601549	−	1.20148i
$498$	0.0303845	−	17.1394i	0.00136156	−	0.768037i
$499$	3.51324	+	13.1116i	0.157274	+	0.586955i	0.998900	+	0.0468940i	$0.0149323\pi$
$499$	3.51324	+	13.1116i	0.157274	+	0.586955i	−0.841626	+	0.540061i	$0.818401\pi$
$500$	−8.36463	+	4.85239i	−0.374078	+	0.217005i
$501$	16.0590	+	12.3943i	0.717464	+	0.553735i
$502$	14.0822	+	18.3131i	0.628521	+	0.817356i
$503$			16.8100i			0.749519i	0.927122	+	0.374760i	$0.122275\pi$
$503$			16.8100i			0.749519i	−0.927122	+	0.374760i	$0.877725\pi$
$504$	18.5591	+	12.6317i	0.826688	+	0.562660i
$505$			0.182352i			0.00811455i
$506$	7.63907	−	5.87421i	0.339598	−	0.261140i
$507$	−17.1749	−	13.2555i	−0.762766	−	0.588698i
$508$	26.1202	+	6.94108i	1.15889	+	0.307961i
$509$	3.74932	+	13.9927i	0.166186	+	0.620214i	0.997886	+	0.0649891i	$0.0207013\pi$
$509$	3.74932	+	13.9927i	0.166186	+	0.620214i	−0.831700	+	0.555225i	$0.812632\pi$
$510$	−3.86761	−	0.00685644i	−0.171261	−	0.000303608i
$511$	29.8496	−	1.77549i	1.32047	−	0.0785432i
$512$	−8.85307	−	20.8236i	−0.391254	−	0.920283i
$513$	−14.3579	−	2.01333i	−0.633916	−	0.0888906i
$514$	−14.2596	+	18.6232i	−0.628962	+	0.821435i
$515$	0.788717	−	2.94353i	0.0347550	−	0.129708i
$516$	25.2707	+	3.34597i	1.11248	+	0.147298i
$517$	−13.4731	+	13.4731i	−0.592547	+	0.592547i
$518$	−1.86518	+	5.40560i	−0.0819515	+	0.237509i
$519$	−41.3769	−	17.2750i	−1.81625	−	0.758290i
$520$	0.590103	+	0.764124i	0.0258777	+	0.0335091i
$521$	−17.9780	+	10.3796i	−0.787632	+	0.454739i	−0.839128	−	0.543934i	$-0.816934\pi$
$521$	−17.9780	+	10.3796i	−0.787632	+	0.454739i	0.0514964	+	0.998673i	$0.483601\pi$
$522$	5.75299	−	7.42679i	0.251802	−	0.325062i
$523$	−0.492550	−	1.83822i	−0.0215377	−	0.0803798i	0.954321	−	0.298785i	$-0.0965813\pi$
$523$	−0.492550	−	1.83822i	−0.0215377	−	0.0803798i	−0.975858	+	0.218405i	$0.929915\pi$
$524$	−0.0507790	−	24.5841i	−0.00221829	−	1.07396i
$525$	18.0074	+	12.2639i	0.785907	+	0.535240i
$526$	9.66380	+	23.2625i	0.421362	+	1.01429i
$527$	−2.71311	−	1.56642i	−0.118185	−	0.0682342i
$528$	−10.3160	+	1.37203i	−0.448944	+	0.0597101i
$529$	1.21074	+	2.09707i	0.0526411	+	0.0911770i
$530$	−1.21290	−	0.158407i	−0.0526849	−	0.00688075i
$531$	39.7017	+	0.222772i	1.72291	+	0.00966748i
$532$	6.58268	−	13.2157i	0.285396	−	0.572975i
$533$	−1.40138	+	1.40138i	−0.0607003	+	0.0607003i
$534$	−25.4648	+	6.77490i	−1.10197	+	0.293179i
$535$	4.56522	+	7.90720i	0.197372	+	0.341858i
$536$	−28.6534	−	21.8458i	−1.23764	−	0.943596i
$537$	6.40711	+	8.39859i	0.276487	+	0.362426i
$538$	−26.0744	−	10.7689i	−1.12415	−	0.464278i
$539$	3.90617	+	9.76215i	0.168251	+	0.420485i
$540$	−4.74662	−	2.00152i	−0.204262	−	0.0861319i
$541$	−4.44435	−	16.5866i	−0.191078	−	0.713112i	−0.993247	−	0.116016i	$-0.962988\pi$
$541$	−4.44435	−	16.5866i	−0.191078	−	0.713112i	0.802170	−	0.597096i	$-0.203679\pi$
$542$	29.2012	+	22.3590i	1.25430	+	0.960401i
$543$	1.30949	+	10.1669i	0.0561957	+	0.436304i
$544$	2.25968	−	17.8769i	0.0968832	−	0.766464i
$545$	−2.94582			−0.126185
$546$	2.00503	−	3.98698i	0.0858074	−	0.170627i
$547$	14.2581	−	14.2581i	0.609631	−	0.609631i	−0.333218	−	0.942850i	$-0.608135\pi$
$547$	14.2581	−	14.2581i	0.609631	−	0.609631i	0.942850	+	0.333218i	$0.108135\pi$
$548$	6.14997	+	22.7638i	0.262714	+	0.972422i
$549$	17.9210	+	31.4463i	0.764851	+	1.34210i
$550$	−10.0117	+	1.32858i	−0.426899	+	0.0566509i
$551$	−5.35055	−	3.08914i	−0.227941	−	0.131602i
$552$	0.00650556	+	22.2235i	0.000276895	+	0.945895i
$553$	10.4339	+	15.8215i	0.443696	+	0.672797i
$554$	16.6645	−	40.3494i	0.708005	−	1.71428i
$555$	0.174916	−	1.30042i	0.00742478	−	0.0551997i
$556$	6.32548	−	3.66946i	0.268260	−	0.155620i
$557$	−3.16690	+	11.8190i	−0.134186	+	0.500789i	0.865814	+	0.500366i	$0.166801\pi$
$557$	−3.16690	+	11.8190i	−0.134186	+	0.500789i	−1.00000		0.000422644i	$0.999865\pi$
$558$	−2.52498	−	3.32200i	−0.106891	−	0.140632i
$559$		−	5.06732i		−	0.214325i
$560$	3.46637	−	3.93746i	0.146481	−	0.166388i
$561$	−7.64758	−	3.19290i	−0.322881	−	0.134804i
$562$	−13.5652	−	1.77165i	−0.572215	−	0.0747325i
$563$	−25.5634	−	6.84970i	−1.07737	−	0.288680i	−0.323852	−	0.946108i	$-0.604978\pi$
$563$	−25.5634	−	6.84970i	−1.07737	−	0.288680i	−0.753518	+	0.657427i	$0.771645\pi$
$564$	−5.70331	−	43.5701i	−0.240153	−	1.83463i
$565$	1.06037	+	3.95735i	0.0446101	+	0.166487i
$566$	34.6126	+	14.2952i	1.45488	+	0.600870i
$567$	1.14702	+	23.7841i	0.0481704	+	0.998839i
$568$	−29.6232	−	12.1629i	−1.24296	−	0.510346i
$569$	−14.6506	+	25.3756i	−0.614187	+	1.06380i	0.376340	+	0.926482i	$0.377182\pi$
$569$	−14.6506	+	25.3756i	−0.614187	+	1.06380i	−0.990527	+	0.137321i	$0.956151\pi$
$570$	−0.882635	+	3.27083i	−0.0369695	+	0.137000i
$571$	6.15367	−	22.9658i	0.257523	−	0.961090i	−0.709146	−	0.705062i	$-0.750919\pi$
$571$	6.15367	−	22.9658i	0.257523	−	0.961090i	0.966669	−	0.256028i	$-0.0824140\pi$
$572$	0.539554	+	1.99713i	0.0225599	+	0.0835044i
$573$	−21.1789	+	8.70307i	−0.884763	+	0.363576i
$574$	8.92362	+	6.02740i	0.372465	+	0.251579i
$575$			21.5672i			0.899412i
$576$	11.9878	−	20.7916i	0.499493	−	0.866318i
$577$	−6.62027	+	3.82222i	−0.275606	+	0.159121i	−0.631432	−	0.775431i	$-0.717533\pi$
$577$	−6.62027	+	3.82222i	−0.275606	+	0.159121i	0.355827	+	0.934552i	$0.384199\pi$
$578$	−5.89235	+	7.69550i	−0.245089	+	0.320091i
$579$	34.2237	+	4.60335i	1.42229	+	0.191309i
$580$	−1.55543	−	1.54902i	−0.0645858	−	0.0643196i
$581$	5.84476	+	17.5659i	0.242481	+	0.728756i
$582$	7.74890	+	7.77643i	0.321202	+	0.322343i
$583$	−2.26986	−	1.31050i	−0.0940080	−	0.0542755i
$584$	−4.27070	−	31.6804i	−0.176723	−	1.31095i
$585$	−0.270582	+	0.987627i	−0.0111872	+	0.0408333i
$586$	−5.93457	−	7.71757i	−0.245155	−	0.318810i
$587$	−29.4710	−	29.4710i	−1.21640	−	1.21640i	−0.968885	−	0.247513i	$-0.920387\pi$
$587$	−29.4710	−	29.4710i	−1.21640	−	1.21640i	−0.247513	−	0.968885i	$-0.579613\pi$
$588$	−23.3401	−	6.57572i	−0.962529	−	0.271178i
$589$	−1.94044	+	1.94044i	−0.0799544	+	0.0799544i
$590$	1.20142	−	9.19913i	0.0494619	−	0.378722i
$591$	2.61927	+	20.3361i	0.107742	+	0.836514i
$592$	5.91135	+	1.55780i	0.242955	+	0.0640251i
$593$	−1.89529	+	3.28274i	−0.0778303	+	0.134806i	−0.902314	−	0.431080i	$-0.858133\pi$
$593$	−1.89529	+	3.28274i	−0.0778303	+	0.134806i	0.824483	+	0.565886i	$0.191466\pi$
$594$	−7.74725	−	7.86251i	−0.317874	−	0.322603i
$595$	3.96384	−	1.31890i	0.162502	−	0.0540698i
$596$	0.0749244	+	36.2739i	0.00306902	+	1.48584i
$597$	−28.1091	−	3.78089i	−1.15043	−	0.154742i
$598$	4.37935	−	0.581154i	0.179085	−	0.0237652i
$599$	−20.1244	−	34.8564i	−0.822260	−	1.42420i	−0.903996	−	0.427542i	$-0.859380\pi$
$599$	−20.1244	−	34.8564i	−0.822260	−	1.42420i	0.0817360	−	0.996654i	$-0.473954\pi$
$600$	11.6397	−	20.1742i	0.475188	−	0.823607i
$601$	−22.9360			−0.935578			−0.467789	−	0.883840i	$-0.654949\pi$
$601$	−22.9360			−0.935578			−0.467789	+	0.883840i	$0.654949\pi$
$602$	−27.0312	+	5.23631i	−1.10171	+	0.213416i
$603$	0.214438	−	38.2164i	0.00873257	−	1.55629i
$604$	24.5740	−	6.63903i	0.999904	−	0.270138i
$605$	−4.18649	−	1.12177i	−0.170205	−	0.0456063i
$606$	−0.449169	−	0.781179i	−0.0182463	−	0.0317332i
$607$	12.7058	+	7.33571i	0.515714	+	0.297747i	0.735179	−	0.677873i	$-0.237098\pi$
$607$	12.7058	+	7.33571i	0.515714	+	0.297747i	−0.219466	+	0.975620i	$0.570431\pi$
$608$	−14.6133	−	5.96482i	−0.592649	−	0.241905i
$609$	−3.34652	+	9.57935i	−0.135608	+	0.388175i
$610$	7.81041	−	3.24463i	0.316234	−	0.131371i
$611$	−8.43741	+	2.26080i	−0.341341	+	0.0914620i
$612$	16.5854	−	9.49733i	0.670425	−	0.383907i
$613$	1.43715	−	5.36352i	0.0580460	−	0.216631i	−0.930811	−	0.365502i	$-0.880897\pi$
$613$	1.43715	−	5.36352i	0.0580460	−	0.216631i	0.988857	+	0.148871i	$0.0475640\pi$
$614$	8.33795	+	10.8430i	0.336492	+	0.437589i
$615$	−2.28018	−	0.951987i	−0.0919459	−	0.0383878i
$616$	10.0960	−	4.94194i	0.406779	−	0.199116i
$617$	13.1235			0.528332			0.264166	−	0.964477i	$-0.414903\pi$
$617$	13.1235			0.528332			0.264166	+	0.964477i	$0.414903\pi$
$618$	3.87172	+	14.5526i	0.155743	+	0.585391i
$619$	30.0918	+	8.06306i	1.20949	+	0.324082i	0.806562	−	0.591150i	$-0.201326\pi$
$619$	30.0918	+	8.06306i	1.20949	+	0.324082i	0.402928	+	0.915232i	$0.367993\pi$
$620$	−0.843393	+	0.489258i	−0.0338715	+	0.0196491i
$621$	−18.8207	+	14.1916i	−0.755249	+	0.569488i
$622$	−30.2857	+	12.5814i	−1.21435	+	0.504469i
$623$	23.7603	−	15.6694i	0.951934	−	0.627781i
$624$	−4.41014	−	1.81989i	−0.176547	−	0.0728541i
$625$	10.6874	−	18.5111i	0.427495	−	0.740443i
$626$	0.957948	−	1.25110i	0.0382873	−	0.0500038i
$627$	−4.43531	+	5.74675i	−0.177129	+	0.229503i
$628$	−12.7291	+	22.1531i	−0.507948	+	0.884003i
$629$	3.44231	+	3.44231i	0.137254	+	0.137254i
$630$	5.54801	+	0.422835i	0.221038	+	0.0168462i
$631$			44.2183i			1.76030i	0.474695	+	0.880150i	$0.342558\pi$
$631$			44.2183i			1.76030i	−0.474695	+	0.880150i	$0.657442\pi$
$632$	16.0356	−	12.3837i	0.637863	−	0.492597i
$633$	2.64529	+	20.5381i	0.105141	+	0.816315i
$634$	−31.3861	+	4.16504i	−1.24650	+	0.165415i
$635$	6.47018	−	1.73368i	0.256761	−	0.0687989i
$636$	5.58613	−	2.30901i	0.221504	−	0.0915582i
$637$	−0.686850	+	4.77114i	−0.0272140	+	0.189039i
$638$	−1.80453	−	4.34382i	−0.0714420	−	0.171974i
$639$	−8.60669	−	32.8570i	−0.340476	−	1.29980i
$640$	−4.47376	−	3.38173i	−0.176841	−	0.133675i
$641$	16.4206	−	9.48043i	0.648574	−	0.374454i	−0.139336	−	0.990245i	$-0.544497\pi$
$641$	16.4206	−	9.48043i	0.648574	−	0.374454i	0.787910	+	0.615791i	$0.211163\pi$
$642$	−39.0340	−	22.6287i	−1.54055	−	0.893082i
$643$	13.2656	+	13.2656i	0.523144	+	0.523144i	0.918520	−	0.395375i	$-0.129385\pi$
$643$	13.2656	+	13.2656i	0.523144	+	0.523144i	−0.395375	+	0.918520i	$0.629385\pi$
$644$	−7.62550	−	22.7607i	−0.300487	−	0.896898i
$645$	5.84371	−	2.40136i	0.230096	−	0.0945534i
$646$	−7.66198	−	9.96396i	−0.301457	−	0.392027i
$647$	−8.74834	+	5.05086i	−0.343933	+	0.198570i	−0.662010	−	0.749495i	$-0.730296\pi$
$647$	−8.74834	+	5.05086i	−0.343933	+	0.198570i	0.318077	+	0.948065i	$0.396963\pi$
$648$	25.2642	−	3.11752i	0.992473	−	0.122468i
$649$	9.93942	−	17.2156i	0.390157	−	0.675771i
$650$	−4.27937	−	1.76740i	−0.167851	−	0.0693231i
$651$	3.72515	+	2.53700i	0.146000	+	0.0994330i
$652$	−0.0423941	−	20.5247i	−0.00166028	−	0.803808i
$653$	8.32848	−	2.23161i	0.325919	−	0.0873296i	−0.0921499	−	0.995745i	$-0.529374\pi$
$653$	8.32848	−	2.23161i	0.325919	−	0.0873296i	0.418068	+	0.908416i	$0.362707\pi$
$654$	12.6196	−	7.25615i	0.493466	−	0.283738i
$655$	−3.04653	−	5.27675i	−0.119038	−	0.206180i
$656$	5.71477	−	9.99339i	0.223124	−	0.390176i
$657$	24.1094	−	23.8403i	0.940597	−	0.930100i
$658$	20.7788	+	42.6724i	0.810042	+	1.66354i
$659$	−3.66207	−	3.66207i	−0.142654	−	0.142654i	0.632173	−	0.774827i	$-0.282163\pi$
$659$	−3.66207	−	3.66207i	−0.142654	−	0.142654i	−0.774827	+	0.632173i	$0.782163\pi$
$660$	−2.04743	+	1.56864i	−0.0796962	+	0.0610594i
$661$	9.22313	+	2.47133i	0.358738	+	0.0961236i	0.433687	−	0.901064i	$-0.357213\pi$
$661$	9.22313	+	2.47133i	0.358738	+	0.0961236i	−0.0749483	+	0.997187i	$0.523879\pi$
$662$	−37.5437	+	4.98218i	−1.45918	+	0.193638i
$663$	−2.30437	−	3.02062i	−0.0894943	−	0.117311i
$664$	18.2609	−	7.63028i	0.708661	−	0.296112i
$665$	−0.217274	−	3.65282i	−0.00842553	−	0.141650i
$666$	2.45386	+	6.00173i	0.0950853	+	0.232562i
$667$	−9.70247	+	2.59977i	−0.375681	+	0.100663i
$668$	−6.01581	+	22.6382i	−0.232759	+	0.875900i
$669$	−23.5928	−	18.2088i	−0.912149	−	0.703991i
$670$	−8.85498	−	1.15648i	−0.342098	−	0.0446786i
$671$	18.1224			0.699609
$672$	−5.15086	+	25.4061i	−0.198699	+	0.980061i
$673$	−40.0505			−1.54383			−0.771916	−	0.635724i	$-0.780702\pi$
$673$	−40.0505			−1.54383			−0.771916	+	0.635724i	$0.780702\pi$
$674$	−2.62300	−	0.342569i	−0.101034	−	0.0131953i
$675$	24.5190	−	3.01827i	0.943735	−	0.116173i
$676$	6.43384	−	24.2113i	0.247455	−	0.931205i
$677$	−24.4871	+	6.56130i	−0.941115	+	0.252171i	−0.696588	−	0.717471i	$-0.745299\pi$
$677$	−24.4871	+	6.56130i	−0.941115	+	0.252171i	−0.244527	+	0.969642i	$0.578633\pi$
$678$	−14.2903	−	14.3410i	−0.548815	−	0.550764i
$679$	−10.6030	−	5.30864i	−0.406905	−	0.203727i
$680$	−1.72182	−	4.12068i	−0.0660287	−	0.158021i
$681$	−25.1350	+	19.1750i	−0.963177	+	0.734787i
$682$	−2.07109	+	0.274841i	−0.0793062	+	0.0105242i
$683$	42.3377	+	11.3444i	1.62001	+	0.434080i	0.951004	−	0.309178i	$-0.100054\pi$
$683$	42.3377	+	11.3444i	1.62001	+	0.434080i	0.669005	+	0.743258i	$0.266721\pi$
$684$	−4.27559	−	16.1861i	−0.163481	−	0.618890i
$685$	4.13245	+	4.13245i	0.157893	+	0.157893i
$686$	26.1610	−	1.26631i	0.998831	−	0.0483479i
$687$	10.5604	+	4.40900i	0.402903	+	0.168214i
$688$	7.73566	+	28.4001i	0.294919	+	1.08274i
$689$	−0.600787	−	1.04059i	−0.0228882	−	0.0396435i
$690$	2.74553	+	4.77492i	0.104520	+	0.181778i
$691$	−38.7972	+	10.3957i	−1.47591	+	0.395470i	−0.904955	−	0.425508i	$-0.860095\pi$
$691$	−38.7972	+	10.3957i	−1.47591	+	0.395470i	−0.570960	+	0.820978i	$0.693429\pi$
$692$	−0.106942	−	51.7748i	−0.00406532	−	1.96818i
$693$	10.6308	+	5.39739i	0.403830	+	0.205030i
$694$	5.64810	+	2.33269i	0.214399	+	0.0885476i
$695$	0.906215	−	1.56961i	0.0343747	−	0.0595387i
$696$	10.4789	+	2.80452i	0.397201	+	0.106305i
$697$	7.93926	−	4.58374i	0.300721	−	0.173621i
$698$	−0.931488	−	1.21135i	−0.0352573	−	0.0458501i
$699$	−1.63258	−	3.97288i	−0.0617497	−	0.150268i
$700$	−5.00595	+	24.6543i	−0.189207	+	0.931844i
$701$	0.587547	+	0.587547i	0.0221914	+	0.0221914i	0.718115	−	0.695924i	$-0.245005\pi$
$701$	0.587547	+	0.587547i	0.0221914	+	0.0221914i	−0.695924	+	0.718115i	$0.745005\pi$
$702$	−1.27357	−	4.89740i	−0.0480679	−	0.184840i
$703$	3.69295	−	2.13213i	0.139282	−	0.0804146i
$704$	−6.07274	−	10.3694i	−0.228875	−	0.390810i
$705$	−6.60559	−	8.65877i	−0.248781	−	0.326108i
$706$	15.0582	+	36.2479i	0.566724	+	1.36421i
$707$	0.727882	+	0.646153i	0.0273748	+	0.0243011i
$708$	17.5125	+	42.3676i	0.658160	+	1.59227i
$709$	−2.14857	+	0.575708i	−0.0806913	+	0.0216212i	−0.298939	−	0.954272i	$-0.596633\pi$
$709$	−2.14857	+	0.575708i	−0.0806913	+	0.0216212i	0.218248	+	0.975893i	$0.429966\pi$
$710$	−7.86775	+	1.04408i	−0.295272	+	0.0391835i
$711$	20.7260	+	5.67834i	0.777285	+	0.212955i
$712$	−18.5975	−	24.0819i	−0.696971	−	0.902507i
$713$			4.46155i			0.167086i
$714$	−13.7320	+	15.4138i	−0.513908	+	0.576847i
$715$	0.362551	+	0.362551i	0.0135586	+	0.0135586i
$716$	−6.07701	+	10.5761i	−0.227108	+	0.395246i
$717$	27.3123	+	21.0795i	1.02000	+	0.787228i
$718$	−19.9229	+	26.0197i	−0.743517	+	0.971045i
$719$	−25.3872	+	43.9719i	−0.946783	+	1.63988i	−0.194641	+	0.980875i	$0.562354\pi$
$719$	−25.3872	+	43.9719i	−0.946783	+	1.63988i	−0.752142	+	0.659001i	$0.770979\pi$
$720$	0.00880373	−	5.94827i	0.000328096	−	0.221679i
$721$	−8.95473	−	13.5785i	−0.333492	−	0.505690i
$722$	14.6465	−	6.08450i	0.545086	−	0.226442i
$723$	−1.95347	+	14.5231i	−0.0726503	+	0.540120i
$724$	−10.2387	+	5.93952i	−0.380517	+	0.220741i
$725$	10.1686	+	2.72467i	0.377652	+	0.101192i
$726$	20.6977	−	5.50661i	0.768162	−	0.204370i
$727$	26.5391			0.984281			0.492141	−	0.870516i	$-0.336215\pi$
$727$	26.5391			0.984281			0.492141	+	0.870516i	$0.336215\pi$
$728$	5.14110	+	0.352150i	0.190542	+	0.0130515i
$729$	18.7678	+	19.4105i	0.695104	+	0.718909i
$730$	−4.82961	−	6.28063i	−0.178752	−	0.232457i
$731$	−6.06673	+	22.6414i	−0.224386	+	0.837421i
$732$	−25.4669	+	33.1383i	−0.941284	+	1.22483i
$733$	19.8491	−	5.31855i	0.733143	−	0.196445i	0.127115	−	0.991888i	$-0.459428\pi$
$733$	19.8491	−	5.31855i	0.733143	−	0.196445i	0.606029	+	0.795443i	$0.292762\pi$
$734$	−5.40435	+	2.24510i	−0.199478	+	0.0828681i
$735$	−5.82764	+	1.46891i	−0.214956	+	0.0541817i
$736$	−23.6571	+	9.94252i	−0.872012	+	0.366486i
$737$	−16.5715	−	9.56757i	−0.610420	−	0.352426i
$738$	12.1130	−	1.53833i	0.445887	−	0.0566266i
$739$	3.38680	+	0.907491i	0.124586	+	0.0333826i	0.320573	−	0.947224i	$-0.396125\pi$
$739$	3.38680	+	0.907491i	0.124586	+	0.0333826i	−0.195988	+	0.980606i	$0.562791\pi$
$740$	1.46268	−	0.395163i	0.0537691	−	0.0145265i
$741$	−3.07818	+	1.26492i	−0.113080	+	0.0464679i
$742$	−4.93013	+	4.28014i	−0.180991	+	0.157129i
$743$	−21.4331			−0.786303			−0.393152	−	0.919474i	$-0.628615\pi$
$743$	−21.4331			−0.786303			−0.393152	+	0.919474i	$0.628615\pi$
$744$	2.40788	−	4.17338i	0.0882770	−	0.153004i
$745$	4.49515	+	7.78583i	0.164690	+	0.285251i
$746$	−24.6768	+	3.27470i	−0.903483	+	0.119895i
$747$	18.1200	+	10.5976i	0.662975	+	0.387745i
$748$	−0.0197657	−	9.56938i	−0.000722707	−	0.349891i
$749$	47.7392	+	9.79597i	1.74435	+	0.357937i
$750$	0.0209960	−	11.8435i	0.000766665	−	0.432464i
$751$	−22.4704	+	38.9198i	−0.819955	+	1.42020i	0.0857599	+	0.996316i	$0.472668\pi$
$751$	−22.4704	+	38.9198i	−0.819955	+	1.42020i	−0.905715	+	0.423888i	$0.860665\pi$
$752$	43.8366	−	25.5511i	1.59856	−	0.931753i
$753$	−28.0617	+	3.61433i	−1.02262	+	0.131713i
$754$	0.279256	−	2.13822i	0.0101699	−	0.0778693i
$755$	4.46107	−	4.46107i	0.162355	−	0.162355i
$756$	−24.8087	+	11.8545i	−0.902284	+	0.431143i
$757$	8.74678	+	8.74678i	0.317907	+	0.317907i	0.847963	−	0.530056i	$-0.177829\pi$
$757$	8.74678	+	8.74678i	0.317907	+	0.317907i	−0.530056	+	0.847963i	$0.677829\pi$
$758$	8.96667	+	11.6606i	0.325684	+	0.423534i
$759$	1.50767	+	11.7055i	0.0547248	+	0.424884i
$760$	−3.87686	+	0.522624i	−0.140629	+	0.0189575i
$761$	−19.1228	−	11.0405i	−0.693200	−	0.400219i	0.111609	−	0.993752i	$-0.464399\pi$
$761$	−19.1228	−	11.0405i	−0.693200	−	0.400219i	−0.804810	+	0.593533i	$0.797733\pi$
$762$	−23.4472	+	23.3643i	−0.849404	+	0.846398i
$763$	−10.4383	+	11.7586i	−0.377893	+	0.425691i
$764$	−18.7342	−	18.6570i	−0.677780	−	0.674986i
$765$	2.39140	−	4.08888i	0.0864614	−	0.147834i
$766$	−15.0391	+	19.6413i	−0.543385	+	0.709669i
$767$	7.89231	−	4.55662i	0.284975	−	0.164530i
$768$	27.4951	+	3.46727i	0.992142	+	0.125114i
$769$			17.2185i			0.620915i	0.950587	+	0.310457i	$0.100482\pi$
$769$			17.2185i			0.620915i	−0.950587	+	0.310457i	$0.899518\pi$
$770$	1.55936	−	2.30864i	0.0561953	−	0.0831975i
$771$	−10.9188	−	26.5710i	−0.393232	−	0.956931i
$772$	10.3997	+	38.4939i	0.374293	+	1.38543i
$773$	2.15882	−	8.05682i	0.0776473	−	0.289784i	−0.916173	−	0.400783i	$-0.868738\pi$
$773$	2.15882	−	8.05682i	0.0776473	−	0.289784i	0.993821	+	0.110999i	$0.0354050\pi$
$774$	−19.1189	+	24.6814i	−0.687214	+	0.887155i
$775$	2.33795	−	4.04944i	0.0839815	−	0.145460i
$776$	−4.81474	+	11.7264i	−0.172839	+	0.420955i
$777$	−4.57099	−	5.30615i	−0.163983	−	0.190357i
$778$	25.0889	+	10.3618i	0.899482	+	0.371490i
$779$	−2.07838	−	7.75660i	−0.0744655	−	0.277909i
$780$	−1.17244	+	0.153472i	−0.0419800	+	0.00549517i
$781$	−16.4270	−	4.40159i	−0.587803	−	0.157501i
$782$	−20.2632	−	2.64641i	−0.724610	−	0.0946355i
$783$	4.31342	+	10.6666i	0.154149	+	0.381192i
$784$	−3.43403	−	27.7886i	−0.122644	−	0.992451i
$785$			6.33237i			0.226012i
$786$	26.0487	+	15.1009i	0.929128	+	0.538631i
$787$	−0.732027	+	2.73196i	−0.0260939	+	0.0973839i	−0.977745	−	0.209798i	$-0.932719\pi$
$787$	−0.732027	+	2.73196i	−0.0260939	+	0.0973839i	0.951651	+	0.307182i	$0.0993860\pi$
$788$	−20.4796	+	11.8803i	−0.729554	+	0.423220i
$789$	−30.5759	−	4.11269i	−1.08853	−	0.146416i
$790$	1.91686	−	4.64126i	0.0681988	−	0.165129i
$791$	19.5537	+	9.79004i	0.695248	+	0.348094i
$792$	4.90713	−	11.7632i	0.174367	−	0.417986i
$793$	7.19497	+	4.15402i	0.255501	+	0.147514i
$794$	−11.5200	+	1.52874i	−0.408829	+	0.0542529i
$795$	0.915320	−	1.18596i	0.0324630	−	0.0420618i
$796$	−8.54162	−	31.6164i	−0.302750	−	1.12061i
$797$	−32.5582	+	32.5582i	−1.15327	+	1.15327i	−0.167376	+	0.985893i	$0.553529\pi$
$797$	−32.5582	+	32.5582i	−1.15327	+	1.15327i	−0.985893	+	0.167376i	$0.946471\pi$
$798$	9.92841	+	15.1132i	0.351462	+	0.535000i
$799$	40.4059			1.42946
$800$	26.6820	+	3.37268i	0.943352	+	0.119242i
$801$	8.52759	−	31.1257i	0.301307	−	1.09977i
$802$	37.2625	+	28.5314i	1.31578	+	1.00748i
$803$	−4.39389	−	16.3982i	−0.155057	−	0.578681i
$804$	40.7825	−	16.8573i	1.43829	−	0.594512i
$805$	−4.44915	−	3.94958i	−0.156812	−	0.139204i
$806$	−0.885264	−	0.365618i	−0.0311821	−	0.0128783i
$807$	27.4700	−	20.9563i	0.966990	−	0.737696i
$808$	0.630861	−	0.827449i	0.0221936	−	0.0291096i
$809$	14.9133	+	25.8307i	0.524325	+	0.908158i	0.999599	+	0.0283202i	$0.00901580\pi$
$809$	14.9133	+	25.8307i	0.524325	+	0.908158i	−0.475273	+	0.879838i	$0.657651\pi$
$810$	5.04422	−	3.78953i	0.177236	−	0.133151i
$811$	−4.30849	+	4.30849i	−0.151291	+	0.151291i	−0.778695	−	0.627403i	$-0.784118\pi$
$811$	−4.30849	+	4.30849i	−0.151291	+	0.151291i	0.627403	+	0.778695i	$0.284118\pi$
$812$	−11.6947	+	0.719859i	−0.410404	+	0.0252621i
$813$	−41.6633	+	17.1207i	−1.46120	+	0.600450i
$814$	3.21918	+	0.420431i	0.112832	+	0.0147361i
$815$	−2.54347	−	4.40542i	−0.0890939	−	0.154315i
$816$	17.5262	+	13.4114i	0.613538	+	0.469494i
$817$	17.7815	+	10.2661i	0.622094	+	0.359166i
$818$	−9.51235	−	22.8979i	−0.332592	−	0.800608i
$819$	2.98345	+	4.57966i	0.104250	+	0.160026i
$820$	−0.00589331	−	2.85318i	−0.000205803	−	0.0996375i
$821$	3.01464	+	11.2508i	0.105212	+	0.392655i	0.998369	−	0.0570892i	$-0.0181819\pi$
$821$	3.01464	+	11.2508i	0.105212	+	0.392655i	−0.893158	+	0.449744i	$0.851515\pi$
$822$	−27.8821	−	7.52398i	−0.972499	−	0.262429i
$823$	−21.9180	+	12.6544i	−0.764013	+	0.441103i	−0.830735	−	0.556669i	$-0.812079\pi$
$823$	−21.9180	+	12.6544i	−0.764013	+	0.441103i	0.0667219	+	0.997772i	$0.478746\pi$
$824$	−13.7623	+	10.6281i	−0.479433	+	0.370247i
$825$	4.76554	−	11.4144i	0.165915	−	0.397397i
$826$	−32.4624	−	37.3922i	−1.12951	−	1.30104i
$827$	12.8188	−	12.8188i	0.445752	−	0.445752i	−0.448187	−	0.893940i	$-0.647930\pi$
$827$	12.8188	−	12.8188i	0.445752	−	0.445752i	0.893940	+	0.448187i	$0.147930\pi$
$828$	−23.5232	−	13.6926i	−0.817487	−	0.475849i
$829$	0.389278	−	1.45280i	0.0135202	−	0.0504580i	−0.958836	−	0.283960i	$-0.908352\pi$
$829$	0.389278	−	1.45280i	0.0135202	−	0.0504580i	0.972356	+	0.233502i	$0.0750185\pi$
$830$	2.98201	−	3.89455i	0.103507	−	0.135182i
$831$	32.4292	+	42.5090i	1.12496	+	1.47462i
$832$	−0.0341362	−	5.50884i	−0.00118346	−	0.190985i
$833$	8.78106	−	20.4957i	0.304246	−	0.710133i
$834$	−0.0158775	+	8.95626i	−0.000549794	+	0.310130i
$835$	1.50257	+	5.60768i	0.0519987	+	0.194062i
$836$	−8.10114	−	2.15277i	−0.280184	−	0.0744551i
$837$	5.07218	−	0.624382i	0.175320	−	0.0215818i
$838$	18.7140	−	14.3905i	0.646466	−	0.497112i
$839$			21.2284i			0.732886i	0.930440	+	0.366443i	$0.119425\pi$
$839$			21.2284i			0.732886i	−0.930440	+	0.366443i	$0.880575\pi$
$840$	2.03022	+	6.09567i	0.0700491	+	0.210321i
$841$		−	24.0970i		−	0.830931i
$842$	32.9582	+	42.8603i	1.13582	+	1.47706i
$843$	10.2371	−	13.2640i	0.352584	−	0.456837i
$844$	−20.6830	+	11.9984i	−0.711938	+	0.413001i
$845$	−1.60698	−	5.99735i	−0.0552819	−	0.206315i
$846$	49.6260	+	20.8225i	1.70618	+	0.715891i
$847$	−19.3122	+	12.7360i	−0.663576	+	0.437615i
$848$	4.95569	+	4.91491i	0.170179	+	0.168779i
$849$	−36.4651	+	27.8185i	−1.25148	+	0.954728i
$850$	17.0047	+	13.0203i	0.583257	+	0.446593i
$851$	1.79436	−	6.69664i	0.0615098	−	0.229558i
$852$	31.1330	−	23.8526i	1.06660	−	0.817176i
$853$	11.6339	−	11.6339i	0.398337	−	0.398337i	−0.479309	−	0.877646i	$-0.659113\pi$
$853$	11.6339	−	11.6339i	0.398337	−	0.398337i	0.877646	+	0.479309i	$0.159113\pi$
$854$	14.7243	−	42.6735i	0.503856	−	1.46026i
$855$	−2.91744	−	2.95036i	−0.0997743	−	0.100900i
$856$	6.64019	−	51.6739i	0.226957	−	1.76618i
$857$	−10.1671	+	5.86996i	−0.347301	+	0.200514i	−0.663496	−	0.748180i	$-0.730928\pi$
$857$	−10.1671	+	5.86996i	−0.347301	+	0.200514i	0.316195	+	0.948694i	$0.397595\pi$
$858$	−2.44617	−	0.660100i	−0.0835110	−	0.0225354i
$859$	−6.64138	−	24.7860i	−0.226601	−	0.845686i	−0.981757	−	0.190141i	$-0.939105\pi$
$859$	−6.64138	−	24.7860i	−0.226601	−	0.845686i	0.755156	−	0.655545i	$-0.227561\pi$
$860$	5.16916	+	5.14785i	0.176267	+	0.175540i
$861$	−11.8797	+	5.72836i	−0.404858	+	0.195222i
$862$	35.0353	−	14.5545i	1.19331	−	0.495729i
$863$	−25.9379	−	14.9752i	−0.882936	−	0.509763i	−0.0113106	−	0.999936i	$-0.503600\pi$
$863$	−25.9379	−	14.9752i	−0.882936	−	0.509763i	−0.871625	+	0.490173i	$0.836934\pi$
$864$	14.6141	+	25.5035i	0.497180	+	0.867647i
$865$	−6.41606	−	11.1129i	−0.218153	−	0.377852i
$866$	−1.19267	+	9.13212i	−0.0405287	+	0.310322i
$867$	−4.51189	−	10.9797i	−0.153232	−	0.372890i
$868$	−1.03557	+	5.10017i	−0.0351495	+	0.173111i
$869$	7.60837	−	7.60837i	0.258096	−	0.258096i
$870$	2.59816	−	0.691241i	0.0880859	−	0.0234353i
$871$	−4.38615	−	7.59704i	−0.148619	−	0.257416i
$872$	13.3671	+	10.1913i	0.452667	+	0.345121i
$873$	−13.0065	+	3.40699i	−0.440204	+	0.115309i
$874$	−6.83304	+	16.5447i	−0.231131	+	0.559633i
$875$	4.03878	+	12.1382i	0.136536	+	0.410346i
$876$	36.1601	+	15.0094i	1.22174	+	0.507119i
$877$	−8.73633	−	32.6044i	−0.295005	−	1.10097i	−0.941214	−	0.337812i	$-0.890313\pi$
$877$	−8.73633	−	32.6044i	−0.295005	−	1.10097i	0.646209	−	0.763161i	$-0.276354\pi$
$878$	18.5709	−	24.2538i	0.626736	−	0.818527i
$879$	11.8258	−	1.52316i	0.398875	−	0.0513749i
$880$	−2.58540	−	1.47847i	−0.0871538	−	0.0498393i
$881$	−13.3633			−0.450221			−0.225110	−	0.974333i	$-0.572274\pi$
$881$	−13.3633			−0.450221			−0.225110	+	0.974333i	$0.572274\pi$
$882$	21.3468	−	20.6473i	0.718785	−	0.695232i
$883$	−14.4528	+	14.4528i	−0.486374	+	0.486374i	−0.907160	−	0.420786i	$-0.861754\pi$
$883$	−14.4528	+	14.4528i	−0.486374	+	0.486374i	0.420786	+	0.907160i	$0.361754\pi$
$884$	2.18564	−	3.80377i	0.0735112	−	0.127935i
$885$	8.99485	+	6.94217i	0.302359	+	0.233359i
$886$	−2.68211	−	20.2114i	−0.0901074	−	0.679014i
$887$	−0.640290	−	0.369671i	−0.0214988	−	0.0124124i	0.489212	−	0.872165i	$-0.337284\pi$
$887$	−0.640290	−	0.369671i	−0.0214988	−	0.0124124i	−0.510711	+	0.859753i	$0.670618\pi$
$888$	−5.29261	+	5.29571i	−0.177608	+	0.177712i
$889$	16.0065	−	31.9698i	0.536839	−	1.07223i
$890$	−6.97012	−	2.87869i	−0.233639	−	0.0964939i
$891$	13.0966	−	3.35217i	0.438753	−	0.112302i
$892$	8.83800	−	33.2585i	0.295918	−	1.11358i
$893$	9.16051	−	34.1875i	0.306545	−	1.14404i
$894$	−38.4349	−	22.2813i	−1.28545	−	0.745199i
$895$			3.02313i			0.101052i
$896$	−29.3511	+	5.87464i	−0.980552	+	0.196258i
$897$	−2.08457	+	4.99292i	−0.0696016	+	0.166709i
$898$	3.17048	−	24.2759i	0.105800	−	0.810097i
$899$	2.10355	+	0.563646i	0.0701575	+	0.0187986i
$900$	14.1752	+	24.7544i	0.472507	+	0.825148i
$901$	1.43856	+	5.36876i	0.0479252	+	0.178859i
$902$	2.33377	−	5.65071i	0.0777060	−	0.188148i
$903$	11.1215	−	31.8350i	0.370100	−	1.05940i
$904$	8.87919	−	21.6255i	0.295318	−	0.719255i
$905$	−1.46683	+	2.54063i	−0.0487592	+	0.0844534i
$906$	−8.12230	+	30.0993i	−0.269845	+	0.999983i
$907$	2.67004	−	9.96471i	0.0886571	−	0.330873i	−0.907324	−	0.420431i	$-0.861879\pi$
$907$	2.67004	−	9.96471i	0.0886571	−	0.330873i	0.995982	+	0.0895583i	$0.0285455\pi$
$908$	−31.6517	−	18.1871i	−1.05040	−	0.603559i
$909$	1.10361	+	0.00619250i	0.0366044	+	0.000205392i
$910$	1.14828	−	0.559141i	0.0380652	−	0.0185353i
$911$			12.3633i			0.409613i	0.978802	+	0.204807i	$0.0656566\pi$
$911$			12.3633i			0.409613i	−0.978802	+	0.204807i	$0.934343\pi$
$912$	15.3208	−	11.7884i	0.507322	−	0.390352i
$913$	9.10225	−	5.25519i	0.301240	−	0.173921i
$914$	−4.05606	−	3.10568i	−0.134163	−	0.102727i
$915$	−1.38084	+	10.2659i	−0.0456492	+	0.339380i
$916$	0.0272941	+	13.2141i	0.000901821	+	0.436608i
$917$	−31.8580	−	6.53719i	−1.05205	−	0.215877i
$918$	−0.172836	+	23.4069i	−0.00570445	+	0.772542i
$919$	−21.4978	−	12.4118i	−0.709147	−	0.409426i	0.101598	−	0.994826i	$-0.467604\pi$
$919$	−21.4978	−	12.4118i	−0.709147	−	0.409426i	−0.810745	+	0.585399i	$0.800938\pi$
$920$	−3.85611	+	5.05775i	−0.127132	+	0.166749i
$921$	−16.6150	+	2.14001i	−0.547484	+	0.0705156i
$922$	17.4292	−	13.4025i	0.574000	−	0.441388i
$923$	−5.51290	−	5.51290i	−0.181459	−	0.181459i
$924$	−0.993498	+	13.7310i	−0.0326837	+	0.451717i
$925$	−5.13780	+	5.13780i	−0.168930	+	0.168930i
$926$	11.6230	+	1.51799i	0.381956	+	0.0498842i
$927$	−17.7877	−	4.87334i	−0.584225	−	0.160061i
$928$	1.69905	+	12.4101i	0.0557742	+	0.407380i
$929$	−20.1109	+	34.8331i	−0.659818	+	1.14284i	0.320845	+	0.947132i	$0.396033\pi$
$929$	−20.1109	+	34.8331i	−0.659818	+	1.14284i	−0.980663	+	0.195706i	$0.937300\pi$
$930$	0.00211699	−	1.19416i	6.94189e−5	−	0.0391581i
$931$	−15.3506	−	12.0763i	−0.503096	−	0.395784i
$932$	3.49980	−	3.51428i	0.114640	−	0.115114i
$933$	5.35436	−	39.8071i	0.175294	−	1.30323i
$934$	−0.419139	−	3.15847i	−0.0137146	−	0.103348i
$935$	−1.18586	−	2.05397i	−0.0387819	−	0.0671722i
$936$	4.64458	−	3.54541i	0.151813	−	0.115885i
$937$	−34.7658			−1.13575			−0.567875	−	0.823115i	$-0.692234\pi$
$937$	−34.7658			−1.13575			−0.567875	+	0.823115i	$0.692234\pi$
$938$	−35.9933	+	31.2479i	−1.17522	+	1.02028i
$939$	0.733520	+	1.78502i	0.0239375	+	0.0582520i
$940$	6.26526	−	10.9037i	0.204350	−	0.355639i
$941$	−24.7131	−	6.62185i	−0.805623	−	0.215866i	−0.167572	−	0.985860i	$-0.553593\pi$
$941$	−24.7131	−	6.62185i	−0.805623	−	0.215866i	−0.638051	+	0.769994i	$0.720259\pi$
$942$	−15.5979	−	27.1273i	−0.508207	−	0.883855i
$943$	−11.3065	−	6.52782i	−0.368191	−	0.212575i
$944$	−37.2768	+	37.5860i	−1.21326	+	1.22332i
$945$	−3.86750	+	5.61082i	−0.125810	+	0.182520i
$946$	5.99698	+	14.4358i	0.194979	+	0.469348i
$947$	0.433210	−	0.116078i	0.0140774	−	0.00377203i	−0.251773	−	0.967786i	$-0.581014\pi$
$947$	0.433210	−	0.116078i	0.0140774	−	0.00377203i	0.265851	+	0.964014i	$0.414347\pi$
$948$	3.22070	+	24.6043i	0.104604	+	0.799112i
$949$	2.01433	−	7.51759i	0.0653880	−	0.244031i
$950$	14.8717	−	11.4358i	0.482500	−	0.371028i
$951$	14.9398	−	35.7835i	0.484455	−	1.16036i
$952$	−22.5494	−	7.72850i	−0.730830	−	0.250482i
$953$	43.7385			1.41683			0.708414	−	0.705797i	$-0.249411\pi$
$953$	43.7385			1.41683			0.708414	+	0.705797i	$0.249411\pi$
$954$	−0.999880	+	7.33518i	−0.0323723	+	0.237485i
$955$	−6.32964	−	1.69602i	−0.204822	−	0.0548820i
$956$	−10.2314	+	38.5019i	−0.330906	+	1.24524i
$957$	5.70946	+	0.767966i	0.184561	+	0.0248248i
$958$	−3.83333	−	9.22751i	−0.123849	−	0.298127i
$959$	31.1383	−	1.85214i	1.00551	−	0.0598088i
$960$	6.33669	−	2.64995i	0.204516	−	0.0855269i
$961$	−15.0164	+	26.0091i	−0.484399	+	0.839003i
$962$	1.18171	+	0.904819i	0.0380998	+	0.0291725i
$963$	48.0100	−	27.3606i	1.54710	−	0.881683i
$964$	−16.3352	+	4.41319i	−0.526121	+	0.142139i
$965$	6.98802	+	6.98802i	0.224952	+	0.224952i
$966$	28.7884	+	5.96050i	0.926250	+	0.191776i
$967$		−	14.8702i		−	0.478194i	−0.970996	−	0.239097i	$-0.923149\pi$
$967$		−	14.8702i		−	0.478194i	0.970996	−	0.239097i	$-0.0768515\pi$
$968$	15.1160	+	19.5737i	0.485846	+	0.629121i
$969$	15.2680	−	1.96651i	0.490480	−	0.0631735i
$970$	0.413301	+	3.11447i	0.0132703	+	0.0999997i
$971$	−5.74858	+	1.54033i	−0.184481	+	0.0494314i	−0.349877	−	0.936796i	$-0.613776\pi$
$971$	−5.74858	+	1.54033i	−0.184481	+	0.0494314i	0.165396	+	0.986227i	$0.447110\pi$
$972$	−12.2746	+	28.6589i	−0.393707	+	0.919236i
$973$	−3.05419	−	9.17910i	−0.0979130	−	0.294268i
$974$	−29.5486	+	12.2752i	−0.946799	+	0.393323i
$975$	4.50841	−	3.43937i	0.144385	−	0.110148i
$976$	−46.6660	−	12.2977i	−1.49374	−	0.393641i
$977$	32.2106	−	18.5968i	1.03051	−	0.594964i	0.113378	−	0.993552i	$-0.463833\pi$
$977$	32.2106	−	18.5968i	1.03051	−	0.594964i	0.917130	+	0.398588i	$0.130500\pi$
$978$	21.7474	+	12.6073i	0.695406	+	0.403138i
$979$	−11.4261	−	11.4261i	−0.365178	−	0.365178i
$980$	−4.16926	−	5.54761i	−0.133182	−	0.177212i
$981$	−0.100037	+	17.8283i	−0.00319395	+	0.569215i
$982$	−40.3006	+	30.9899i	−1.28604	+	0.988928i
$983$	21.4615	−	12.3908i	0.684515	−	0.395205i	−0.117039	−	0.993127i	$-0.537340\pi$
$983$	21.4615	−	12.3908i	0.684515	−	0.395205i	0.801554	+	0.597923i	$0.204007\pi$
$984$	7.05321	+	12.2083i	0.224848	+	0.389185i
$985$	−2.93399	+	5.08182i	−0.0934847	+	0.161920i
$986$	−3.80768	+	9.21946i	−0.121261	+	0.293608i
$987$	−57.9691	−	4.31470i	−1.84518	−	0.137338i
$988$	−2.72286	−	2.71163i	−0.0866257	−	0.0862686i
$989$	32.2441	−	8.63979i	1.02530	−	0.274729i
$990$	−0.397982	−	3.13378i	−0.0126487	−	0.0995979i
$991$	−2.66875	−	4.62241i	−0.0847757	−	0.146836i	0.820520	−	0.571618i	$-0.193684\pi$
$991$	−2.66875	−	4.62241i	−0.0847757	−	0.146836i	−0.905296	+	0.424782i	$0.860351\pi$
$992$	5.51965	+	0.697699i	0.175249	+	0.0221520i
$993$	17.8708	−	42.8038i	0.567112	−	1.35834i
$994$	−23.7113	+	35.1048i	−0.752078	+	1.11346i
$995$	−5.73951	−	5.73951i	−0.181955	−	0.181955i
$996$	−3.18159	+	24.0292i	−0.100813	+	0.761393i
$997$	−45.8634	−	12.2891i	−1.45251	−	0.389199i	−0.555613	−	0.831441i	$-0.687516\pi$
$997$	−45.8634	−	12.2891i	−1.45251	−	0.389199i	−0.896896	+	0.442242i	$0.854183\pi$
$998$	−2.52533	−	19.0299i	−0.0799378	−	0.602380i
$999$	−7.86430	−	1.10277i	−0.248815	−	0.0348900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bo.a.5.4	✓	240
3.2	odd	2	inner	336.2.bo.a.5.57	yes	240
7.3	odd	6	inner	336.2.bo.a.101.44	yes	240
16.13	even	4	inner	336.2.bo.a.173.17	yes	240
21.17	even	6	inner	336.2.bo.a.101.17	yes	240
48.29	odd	4	inner	336.2.bo.a.173.44	yes	240
112.45	odd	12	inner	336.2.bo.a.269.57	yes	240
336.269	even	12	inner	336.2.bo.a.269.4	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bo.a.5.4	✓	240	1.1	even	1	trivial
336.2.bo.a.5.57	yes	240	3.2	odd	2	inner
336.2.bo.a.101.17	yes	240	21.17	even	6	inner
336.2.bo.a.101.44	yes	240	7.3	odd	6	inner
336.2.bo.a.173.17	yes	240	16.13	even	4	inner
336.2.bo.a.173.44	yes	240	48.29	odd	4	inner
336.2.bo.a.269.4	yes	240	336.269	even	12	inner
336.2.bo.a.269.57	yes	240	112.45	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40230 - 0.183144i) q^{2} +(1.05826 - 1.37116i) q^{3} +(1.93292 + 0.513647i) q^{4} +(0.478799 - 0.128294i) q^{5} +(-1.73512 + 1.72898i) q^{6} +(1.18449 - 2.36579i) q^{7} +(-2.61647 - 1.07429i) q^{8} +(-0.760185 - 2.90209i) q^{9} +O(q^{10})\)	\(q+(-1.40230 - 0.183144i) q^{2} +(1.05826 - 1.37116i) q^{3} +(1.93292 + 0.513647i) q^{4} +(0.478799 - 0.128294i) q^{5} +(-1.73512 + 1.72898i) q^{6} +(1.18449 - 2.36579i) q^{7} +(-2.61647 - 1.07429i) q^{8} +(-0.760185 - 2.90209i) q^{9} +(-0.694919 + 0.0922180i) q^{10} +(-1.45091 - 0.388770i) q^{11} +(2.74982 - 2.10678i) q^{12} +(-0.486926 - 0.486926i) q^{13} +(-2.09430 + 3.10063i) q^{14} +(0.330780 - 0.792280i) q^{15} +(3.47233 + 1.98567i) q^{16} +(1.59268 + 2.75860i) q^{17} +(0.534512 + 4.20884i) q^{18} +(2.69513 - 0.722159i) q^{19} +(0.991377 - 0.00204771i) q^{20} +(-1.99039 - 4.12775i) q^{21} +(1.96342 + 0.810899i) q^{22} +(2.26818 - 3.92860i) q^{23} +(-4.24192 + 2.45073i) q^{24} +(-4.11734 + 2.37715i) q^{25} +(0.593642 + 0.771997i) q^{26} +(-4.78371 - 2.02882i) q^{27} +(3.50471 - 3.96447i) q^{28} +(-1.56573 - 1.56573i) q^{29} +(-0.608956 + 1.05044i) q^{30} +(-0.851744 + 0.491755i) q^{31} +(-4.50561 - 3.42045i) q^{32} +(-2.06850 + 1.57802i) q^{33} +(-1.72820 - 4.16009i) q^{34} +(0.263618 - 1.28470i) q^{35} +(0.0212733 - 5.99996i) q^{36} +(1.47622 - 0.395551i) q^{37} +(-3.91166 + 0.519090i) q^{38} +(-1.18295 + 0.152363i) q^{39} +(-1.39059 - 0.178693i) q^{40} -2.87800i q^{41} +(2.03517 + 6.15289i) q^{42} +(5.20338 + 5.20338i) q^{43} +(-2.60480 - 1.49671i) q^{44} +(-0.736296 - 1.29199i) q^{45} +(-3.90017 + 5.09369i) q^{46} +(6.34245 - 10.9854i) q^{47} +(6.39731 - 2.65979i) q^{48} +(-4.19395 - 5.60453i) q^{49} +(6.20912 - 2.57942i) q^{50} +(5.46796 + 0.735483i) q^{51} +(-0.691080 - 1.19130i) q^{52} +(1.68545 + 0.451615i) q^{53} +(6.33666 + 3.72112i) q^{54} -0.744571 q^{55} +(-5.64074 + 4.91753i) q^{56} +(1.86194 - 4.45970i) q^{57} +(1.90887 + 2.48238i) q^{58} +(-3.42524 + 12.7832i) q^{59} +(1.04632 - 1.36151i) q^{60} +(-11.6537 + 3.12260i) q^{61} +(1.28447 - 0.533599i) q^{62} +(-7.76617 - 1.63906i) q^{63} +(5.69180 + 5.62169i) q^{64} +(-0.295610 - 0.170670i) q^{65} +(3.18967 - 1.83403i) q^{66} +(12.3049 + 3.29710i) q^{67} +(1.66157 + 6.15022i) q^{68} +(-2.98644 - 7.26751i) q^{69} +(-0.604958 + 1.75326i) q^{70} +11.3218 q^{71} +(-1.12869 + 8.40988i) q^{72} +(5.65102 + 9.78785i) q^{73} +(-2.14255 + 0.284323i) q^{74} +(-1.09774 + 8.16118i) q^{75} +(5.58040 - 0.0115264i) q^{76} +(-2.63834 + 2.97205i) q^{77} +(1.68676 + 0.00299026i) q^{78} +(-3.58163 + 6.20356i) q^{79} +(1.91730 + 0.505259i) q^{80} +(-7.84424 + 4.41225i) q^{81} +(-0.527088 + 4.03584i) q^{82} +(-4.94774 + 4.94774i) q^{83} +(-1.72706 - 9.00096i) q^{84} +(1.11649 + 1.11649i) q^{85} +(-6.34375 - 8.24968i) q^{86} +(-3.80381 + 0.489929i) q^{87} +(3.37860 + 2.57590i) q^{88} +(9.31634 + 5.37879i) q^{89} +(0.795892 + 1.94661i) q^{90} +(-1.72873 + 0.575206i) q^{91} +(6.40211 - 6.42861i) q^{92} +(-0.227087 + 1.68828i) q^{93} +(-10.9060 + 14.2434i) q^{94} +(1.19778 - 0.691538i) q^{95} +(-9.45810 + 2.55821i) q^{96} -4.48178i q^{97} +(4.85476 + 8.62736i) q^{98} +(-0.0252849 + 4.50620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 6 q^{3} - 4 q^{4}+O(q^{10}) \) 240 * q - 6 * q^3 - 4 * q^4	\( 240 q - 6 q^{3} - 4 q^{4} - 12 q^{10} - 6 q^{12} - 16 q^{15} - 20 q^{16} - 4 q^{18} - 12 q^{19} + 2 q^{21} - 40 q^{22} - 6 q^{24} - 12 q^{28} + 22 q^{30} - 24 q^{31} - 12 q^{33} - 64 q^{36} - 4 q^{37} + 48 q^{40} - 18 q^{42} - 16 q^{43} - 6 q^{45} + 12 q^{46} - 16 q^{49} - 10 q^{51} - 48 q^{52} - 90 q^{54} - 4 q^{58} - 18 q^{60} - 12 q^{61} - 36 q^{63} + 32 q^{64} - 66 q^{66} - 36 q^{67} - 76 q^{70} - 46 q^{72} + 24 q^{75} - 76 q^{78} - 8 q^{79} - 4 q^{81} + 72 q^{82} - 24 q^{84} + 24 q^{85} + 12 q^{88} - 88 q^{91} - 14 q^{93} + 24 q^{94} + 96 q^{96} + 28 q^{99}+O(q^{100}) \) 240 * q - 6 * q^3 - 4 * q^4 - 12 * q^10 - 6 * q^12 - 16 * q^15 - 20 * q^16 - 4 * q^18 - 12 * q^19 + 2 * q^21 - 40 * q^22 - 6 * q^24 - 12 * q^28 + 22 * q^30 - 24 * q^31 - 12 * q^33 - 64 * q^36 - 4 * q^37 + 48 * q^40 - 18 * q^42 - 16 * q^43 - 6 * q^45 + 12 * q^46 - 16 * q^49 - 10 * q^51 - 48 * q^52 - 90 * q^54 - 4 * q^58 - 18 * q^60 - 12 * q^61 - 36 * q^63 + 32 * q^64 - 66 * q^66 - 36 * q^67 - 76 * q^70 - 46 * q^72 + 24 * q^75 - 76 * q^78 - 8 * q^79 - 4 * q^81 + 72 * q^82 - 24 * q^84 + 24 * q^85 + 12 * q^88 - 88 * q^91 - 14 * q^93 + 24 * q^94 + 96 * q^96 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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