LMFDB - Embedded newform 690.3.k.b.553.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,3,Mod(277,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("690.277");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.k (of order $4$, degree $2$, 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:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			553.11
Character	$\chi$	$=$	690.553
Dual form			690.3.k.b.277.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.94131 + 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 - 8.62845i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.94131 + 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 - 8.62845i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(4.17750 - 5.70513i) q^{10} -9.96233 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-1.36926 - 1.36926i) q^{13} +17.2569i q^{14} +(6.98733 + 5.11637i) q^{15} -4.00000 q^{16} +(12.8665 - 12.8665i) q^{17} +(-3.00000 - 3.00000i) q^{18} -21.6135i q^{19} +(1.52763 + 9.88263i) q^{20} -21.1353 q^{21} +(9.96233 - 9.96233i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(23.8332 - 7.54851i) q^{25} +2.73852 q^{26} +(3.67423 - 3.67423i) q^{27} +(-17.2569 - 17.2569i) q^{28} +41.0639i q^{29} +(-12.1037 + 1.87096i) q^{30} +39.6561 q^{31} +(4.00000 - 4.00000i) q^{32} +(12.2013 + 12.2013i) q^{33} +25.7330i q^{34} +(-36.0453 + 49.2264i) q^{35} +6.00000 q^{36} +(-47.8886 + 47.8886i) q^{37} +(21.6135 + 21.6135i) q^{38} +3.35399i q^{39} +(-11.4103 - 8.35500i) q^{40} -46.0597 q^{41} +(21.1353 - 21.1353i) q^{42} +(-42.5076 - 42.5076i) q^{43} +19.9247i q^{44} +(-2.29145 - 14.8239i) q^{45} -6.78233 q^{46} +(4.44905 - 4.44905i) q^{47} +(4.89898 + 4.89898i) q^{48} -99.9003i q^{49} +(-16.2847 + 31.3817i) q^{50} -31.5164 q^{51} +(-2.73852 + 2.73852i) q^{52} +(-10.1671 - 10.1671i) q^{53} +7.34847i q^{54} +(49.2270 - 7.60939i) q^{55} +34.5138 q^{56} +(-26.4710 + 26.4710i) q^{57} +(-41.0639 - 41.0639i) q^{58} -83.8782i q^{59} +(10.2327 - 13.9747i) q^{60} -94.9681 q^{61} +(-39.6561 + 39.6561i) q^{62} +(25.8853 + 25.8853i) q^{63} +8.00000i q^{64} +(7.81181 + 5.72008i) q^{65} -24.4026 q^{66} +(-24.0838 + 24.0838i) q^{67} +(-25.7330 - 25.7330i) q^{68} -8.30662i q^{69} +(-13.1811 - 85.2718i) q^{70} -127.966 q^{71} +(-6.00000 + 6.00000i) q^{72} +(59.6158 + 59.6158i) q^{73} -95.7772i q^{74} +(-38.4346 - 19.9446i) q^{75} -43.2269 q^{76} +(-85.9595 + 85.9595i) q^{77} +(-3.35399 - 3.35399i) q^{78} -27.1346i q^{79} +(19.7653 - 3.05526i) q^{80} -9.00000 q^{81} +(46.0597 - 46.0597i) q^{82} +(-61.0630 - 61.0630i) q^{83} +42.2706i q^{84} +(-53.7498 + 73.4051i) q^{85} +85.0153 q^{86} +(50.2928 - 50.2928i) q^{87} +(-19.9247 - 19.9247i) q^{88} -84.3721i q^{89} +(17.1154 + 12.5325i) q^{90} -23.6292 q^{91} +(6.78233 - 6.78233i) q^{92} +(-48.5686 - 48.5686i) q^{93} +8.89810i q^{94} +(16.5087 + 106.799i) q^{95} -9.79796 q^{96} +(-111.709 + 111.709i) q^{97} +(99.9003 + 99.9003i) q^{98} -29.8870i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	$ 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) $ 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$2$	−1.00000	+	1.00000i	−0.500000	+	0.500000i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$3$	−1.22474	−	1.22474i	−0.408248	−	0.408248i
$4$		−	2.00000i		−	0.500000i
$5$	−4.94131	+	0.763816i	−0.988263	+	0.152763i
$5$	−4.94131	+	0.763816i	−0.988263	+	0.152763i
$6$	2.44949			0.408248
$7$	8.62845	−	8.62845i	1.23264	−	1.23264i	0.269688	−	0.962948i	$-0.413080\pi$
$7$	8.62845	−	8.62845i	1.23264	−	1.23264i	0.962948	−	0.269688i	$-0.0869205\pi$
$8$	2.00000	+	2.00000i	0.250000	+	0.250000i
$9$			3.00000i			0.333333i
$10$	4.17750	−	5.70513i	0.417750	−	0.570513i
$11$	−9.96233			−0.905667			−0.452833	−	0.891595i	$-0.649587\pi$
$11$	−9.96233			−0.905667			−0.452833	+	0.891595i	$0.649587\pi$
$12$	−2.44949	+	2.44949i	−0.204124	+	0.204124i
$13$	−1.36926	−	1.36926i	−0.105328	−	0.105328i	0.652479	−	0.757807i	$-0.273729\pi$
$13$	−1.36926	−	1.36926i	−0.105328	−	0.105328i	−0.757807	+	0.652479i	$0.773729\pi$
$14$			17.2569i			1.23264i
$15$	6.98733	+	5.11637i	0.465822	+	0.341091i
$16$	−4.00000			−0.250000
$17$	12.8665	−	12.8665i	0.756853	−	0.756853i	−0.218895	−	0.975748i	$-0.570245\pi$
$17$	12.8665	−	12.8665i	0.756853	−	0.756853i	0.975748	+	0.218895i	$0.0702452\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$		−	21.6135i		−	1.13755i	−0.822493	−	0.568776i	$-0.807417\pi$
$19$		−	21.6135i		−	1.13755i	0.822493	−	0.568776i	$-0.192583\pi$
$20$	1.52763	+	9.88263i	0.0763816	+	0.494131i
$21$	−21.1353			−1.00644
$22$	9.96233	−	9.96233i	0.452833	−	0.452833i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$23$	3.39116	+	3.39116i	0.147442	+	0.147442i
$24$		−	4.89898i		−	0.204124i
$25$	23.8332	−	7.54851i	0.953327	−	0.301940i
$26$	2.73852			0.105328
$27$	3.67423	−	3.67423i	0.136083	−	0.136083i
$28$	−17.2569	−	17.2569i	−0.616318	−	0.616318i
$29$			41.0639i			1.41600i	0.706214	+	0.707998i	$0.250402\pi$
$29$			41.0639i			1.41600i	−0.706214	+	0.707998i	$0.749598\pi$
$30$	−12.1037	+	1.87096i	−0.403457	+	0.0623653i
$31$	39.6561			1.27923			0.639614	−	0.768696i	$-0.279094\pi$
$31$	39.6561			1.27923			0.639614	+	0.768696i	$0.279094\pi$
$32$	4.00000	−	4.00000i	0.125000	−	0.125000i
$33$	12.2013	+	12.2013i	0.369737	+	0.369737i
$34$			25.7330i			0.756853i
$35$	−36.0453	+	49.2264i	−1.02987	+	1.40647i
$36$	6.00000			0.166667
$37$	−47.8886	+	47.8886i	−1.29429	+	1.29429i	−0.362178	+	0.932109i	$0.617967\pi$
$37$	−47.8886	+	47.8886i	−1.29429	+	1.29429i	−0.932109	+	0.362178i	$0.882033\pi$
$38$	21.6135	+	21.6135i	0.568776	+	0.568776i
$39$			3.35399i			0.0859997i
$40$	−11.4103	−	8.35500i	−0.285257	−	0.208875i
$41$	−46.0597			−1.12341			−0.561704	−	0.827338i	$-0.689854\pi$
$41$	−46.0597			−1.12341			−0.561704	+	0.827338i	$0.689854\pi$
$42$	21.1353	−	21.1353i	0.503221	−	0.503221i
$43$	−42.5076	−	42.5076i	−0.988550	−	0.988550i	0.0113855	−	0.999935i	$-0.496376\pi$
$43$	−42.5076	−	42.5076i	−0.988550	−	0.988550i	−0.999935	+	0.0113855i	$0.996376\pi$
$44$			19.9247i			0.452833i
$45$	−2.29145	−	14.8239i	−0.0509211	−	0.329421i
$46$	−6.78233			−0.147442
$47$	4.44905	−	4.44905i	0.0946607	−	0.0946607i	−0.658191	−	0.752851i	$-0.728678\pi$
$47$	4.44905	−	4.44905i	0.0946607	−	0.0946607i	0.752851	+	0.658191i	$0.228678\pi$
$48$	4.89898	+	4.89898i	0.102062	+	0.102062i
$49$		−	99.9003i		−	2.03878i
$50$	−16.2847	+	31.3817i	−0.325693	+	0.627634i
$51$	−31.5164			−0.617968
$52$	−2.73852	+	2.73852i	−0.0526638	+	0.0526638i
$53$	−10.1671	−	10.1671i	−0.191832	−	0.191832i	0.604655	−	0.796487i	$-0.293311\pi$
$53$	−10.1671	−	10.1671i	−0.191832	−	0.191832i	−0.796487	+	0.604655i	$0.793311\pi$
$54$			7.34847i			0.136083i
$55$	49.2270	−	7.60939i	0.895037	−	0.138353i
$56$	34.5138			0.616318
$57$	−26.4710	+	26.4710i	−0.464403	+	0.464403i
$58$	−41.0639	−	41.0639i	−0.707998	−	0.707998i
$59$		−	83.8782i		−	1.42166i	−0.703362	−	0.710832i	$-0.748319\pi$
$59$		−	83.8782i		−	1.42166i	0.703362	−	0.710832i	$-0.251681\pi$
$60$	10.2327	−	13.9747i	0.170546	−	0.232911i
$61$	−94.9681			−1.55685			−0.778427	−	0.627735i	$-0.783982\pi$
$61$	−94.9681			−1.55685			−0.778427	+	0.627735i	$0.783982\pi$
$62$	−39.6561	+	39.6561i	−0.639614	+	0.639614i
$63$	25.8853	+	25.8853i	0.410879	+	0.410879i
$64$			8.00000i			0.125000i
$65$	7.81181	+	5.72008i	0.120182	+	0.0880013i
$66$	−24.4026			−0.369737
$67$	−24.0838	+	24.0838i	−0.359460	+	0.359460i	−0.863614	−	0.504154i	$-0.831804\pi$
$67$	−24.0838	+	24.0838i	−0.359460	+	0.359460i	0.504154	+	0.863614i	$0.331804\pi$
$68$	−25.7330	−	25.7330i	−0.378427	−	0.378427i
$69$		−	8.30662i		−	0.120386i
$70$	−13.1811	−	85.2718i	−0.188301	−	1.21817i
$71$	−127.966			−1.80234			−0.901171	−	0.433464i	$-0.857291\pi$
$71$	−127.966			−1.80234			−0.901171	+	0.433464i	$0.857291\pi$
$72$	−6.00000	+	6.00000i	−0.0833333	+	0.0833333i
$73$	59.6158	+	59.6158i	0.816655	+	0.816655i	0.985622	−	0.168967i	$-0.0540432\pi$
$73$	59.6158	+	59.6158i	0.816655	+	0.816655i	−0.168967	+	0.985622i	$0.554043\pi$
$74$		−	95.7772i		−	1.29429i
$75$	−38.4346	−	19.9446i	−0.512461	−	0.265927i
$76$	−43.2269			−0.568776
$77$	−85.9595	+	85.9595i	−1.11636	+	1.11636i
$78$	−3.35399	−	3.35399i	−0.0429999	−	0.0429999i
$79$		−	27.1346i		−	0.343476i	−0.985143	−	0.171738i	$-0.945062\pi$
$79$		−	27.1346i		−	0.343476i	0.985143	−	0.171738i	$-0.0549383\pi$
$80$	19.7653	−	3.05526i	0.247066	−	0.0381908i
$81$	−9.00000			−0.111111
$82$	46.0597	−	46.0597i	0.561704	−	0.561704i
$83$	−61.0630	−	61.0630i	−0.735698	−	0.735698i	0.236044	−	0.971742i	$-0.424149\pi$
$83$	−61.0630	−	61.0630i	−0.735698	−	0.735698i	−0.971742	+	0.236044i	$0.924149\pi$
$84$			42.2706i			0.503221i
$85$	−53.7498	+	73.4051i	−0.632351	+	0.863589i
$86$	85.0153			0.988550
$87$	50.2928	−	50.2928i	0.578078	−	0.578078i
$88$	−19.9247	−	19.9247i	−0.226417	−	0.226417i
$89$		−	84.3721i		−	0.948001i	−0.880524	−	0.474001i	$-0.842809\pi$
$89$		−	84.3721i		−	0.948001i	0.880524	−	0.474001i	$-0.157191\pi$
$90$	17.1154	+	12.5325i	0.190171	+	0.139250i
$91$	−23.6292			−0.259661
$92$	6.78233	−	6.78233i	0.0737210	−	0.0737210i
$93$	−48.5686	−	48.5686i	−0.522243	−	0.522243i
$94$			8.89810i			0.0946607i
$95$	16.5087	+	106.799i	0.173776	+	1.12420i
$96$	−9.79796			−0.102062
$97$	−111.709	+	111.709i	−1.15164	+	1.15164i	−0.165418	+	0.986223i	$0.552897\pi$
$97$	−111.709	+	111.709i	−1.15164	+	1.15164i	−0.986223	+	0.165418i	$0.947103\pi$
$98$	99.9003	+	99.9003i	1.01939	+	1.01939i
$99$		−	29.8870i		−	0.301889i
$100$	−15.0970	−	47.6663i	−0.150970	−	0.476663i
$101$	77.7181			0.769486			0.384743	−	0.923024i	$-0.374290\pi$
$101$	77.7181			0.769486			0.384743	+	0.923024i	$0.374290\pi$
$102$	31.5164	−	31.5164i	0.308984	−	0.308984i
$103$	42.3360	+	42.3360i	0.411029	+	0.411029i	0.882097	−	0.471068i	$-0.156131\pi$
$103$	42.3360	+	42.3360i	0.411029	+	0.411029i	−0.471068	+	0.882097i	$0.656131\pi$
$104$		−	5.47704i		−	0.0526638i
$105$	104.436	−	16.1435i	0.994630	−	0.153747i
$106$	20.3342			0.191832
$107$	−106.967	+	106.967i	−0.999693	+	0.999693i	−1.00000		0.000307102i	$-0.999902\pi$
$107$	−106.967	+	106.967i	−0.999693	+	0.999693i	0.000307102		1.00000i	$0.499902\pi$
$108$	−7.34847	−	7.34847i	−0.0680414	−	0.0680414i
$109$		−	36.5144i		−	0.334994i	−0.985873	−	0.167497i	$-0.946432\pi$
$109$		−	36.5144i		−	0.334994i	0.985873	−	0.167497i	$-0.0535685\pi$
$110$	−41.6176	+	56.8364i	−0.378342	+	0.516695i
$111$	117.303			1.05678
$112$	−34.5138	+	34.5138i	−0.308159	+	0.308159i
$113$	−10.6656	−	10.6656i	−0.0943859	−	0.0943859i	0.658337	−	0.752723i	$-0.271260\pi$
$113$	−10.6656	−	10.6656i	−0.0943859	−	0.0943859i	−0.752723	+	0.658337i	$0.771260\pi$
$114$		−	52.9420i		−	0.464403i
$115$	−19.3470	−	14.1666i	−0.168235	−	0.123188i
$116$	82.1278			0.707998
$117$	4.10778	−	4.10778i	0.0351092	−	0.0351092i
$118$	83.8782	+	83.8782i	0.710832	+	0.710832i
$119$		−	222.036i		−	1.86585i
$120$	3.74192	+	24.2074i	0.0311827	+	0.201728i
$121$	−21.7519			−0.179768
$122$	94.9681	−	94.9681i	0.778427	−	0.778427i
$123$	56.4114	+	56.4114i	0.458629	+	0.458629i
$124$		−	79.3121i		−	0.639614i
$125$	−112.002	+	55.5037i	−0.896012	+	0.444030i
$126$	−51.7707			−0.410879
$127$	121.366	−	121.366i	0.955634	−	0.955634i	−0.0434223	−	0.999057i	$-0.513826\pi$
$127$	121.366	−	121.366i	0.955634	−	0.955634i	0.999057	+	0.0434223i	$0.0138261\pi$
$128$	−8.00000	−	8.00000i	−0.0625000	−	0.0625000i
$129$			104.122i			0.807147i
$130$	−13.5319	+	2.09173i	−0.104091	+	0.0160902i
$131$	188.546			1.43928			0.719642	−	0.694345i	$-0.244306\pi$
$131$	188.546			1.43928			0.719642	+	0.694345i	$0.244306\pi$
$132$	24.4026	−	24.4026i	0.184868	−	0.184868i
$133$	−186.491	−	186.491i	−1.40219	−	1.40219i
$134$		−	48.1676i		−	0.359460i
$135$	−15.3491	+	20.9620i	−0.113697	+	0.155274i
$136$	51.4660			0.378427
$137$	−86.1083	+	86.1083i	−0.628528	+	0.628528i	−0.947698	−	0.319170i	$-0.896596\pi$
$137$	−86.1083	+	86.1083i	−0.628528	+	0.628528i	0.319170	+	0.947698i	$0.396596\pi$
$138$	8.30662	+	8.30662i	0.0601929	+	0.0601929i
$139$		−	145.443i		−	1.04636i	−0.852224	−	0.523178i	$-0.824746\pi$
$139$		−	145.443i		−	1.04636i	0.852224	−	0.523178i	$-0.175254\pi$
$140$	98.4528	+	72.0907i	0.703235	+	0.514933i
$141$	−10.8979			−0.0772901
$142$	127.966	−	127.966i	0.901171	−	0.901171i
$143$	13.6410	+	13.6410i	0.0953918	+	0.0953918i
$144$		−	12.0000i		−	0.0833333i
$145$	−31.3653	−	202.910i	−0.216312	−	1.39938i
$146$	−119.232			−0.816655
$147$	−122.352	+	122.352i	−0.832329	+	0.832329i
$148$	95.7772	+	95.7772i	0.647144	+	0.647144i
$149$			135.574i			0.909889i	0.890520	+	0.454945i	$0.150341\pi$
$149$			135.574i			0.909889i	−0.890520	+	0.454945i	$0.849659\pi$
$150$	58.3791	−	18.4900i	0.389194	−	0.123267i
$151$	−222.424			−1.47300			−0.736502	−	0.676435i	$-0.763524\pi$
$151$	−222.424			−1.47300			−0.736502	+	0.676435i	$0.763524\pi$
$152$	43.2269	−	43.2269i	0.284388	−	0.284388i
$153$	38.5995	+	38.5995i	0.252284	+	0.252284i
$154$		−	171.919i		−	1.11636i
$155$	−195.953	+	30.2899i	−1.26421	+	0.195419i
$156$	6.70798			0.0429999
$157$	−164.277	+	164.277i	−1.04635	+	1.04635i	−0.0474752	+	0.998872i	$0.515118\pi$
$157$	−164.277	+	164.277i	−1.04635	+	1.04635i	−0.998872	+	0.0474752i	$0.984882\pi$
$158$	27.1346	+	27.1346i	0.171738	+	0.171738i
$159$			24.9042i			0.156630i
$160$	−16.7100	+	22.8205i	−0.104437	+	0.142628i
$161$	58.5210			0.363484
$162$	9.00000	−	9.00000i	0.0555556	−	0.0555556i
$163$	50.5955	+	50.5955i	0.310402	+	0.310402i	0.845065	−	0.534663i	$-0.179562\pi$
$163$	50.5955	+	50.5955i	0.310402	+	0.310402i	−0.534663	+	0.845065i	$0.679562\pi$
$164$			92.1194i			0.561704i
$165$	−69.6101	−	50.9710i	−0.421879	−	0.308915i
$166$	122.126			0.735698
$167$	−129.032	+	129.032i	−0.772645	+	0.772645i	−0.978568	−	0.205923i	$-0.933980\pi$
$167$	−129.032	+	129.032i	−0.772645	+	0.772645i	0.205923	+	0.978568i	$0.433980\pi$
$168$	−42.2706	−	42.2706i	−0.251611	−	0.251611i
$169$		−	165.250i		−	0.977812i
$170$	−19.6553	−	127.155i	−0.115619	−	0.747970i
$171$	64.8404			0.379184
$172$	−85.0153	+	85.0153i	−0.494275	+	0.494275i
$173$	31.0922	+	31.0922i	0.179724	+	0.179724i	0.791235	−	0.611512i	$-0.209438\pi$
$173$	31.0922	+	31.0922i	0.179724	+	0.179724i	−0.611512	+	0.791235i	$0.709438\pi$
$174$			100.586i			0.578078i
$175$	140.511	−	270.775i	0.802922	−	1.54729i
$176$	39.8493			0.226417
$177$	−102.729	+	102.729i	−0.580392	+	0.580392i
$178$	84.3721	+	84.3721i	0.474001	+	0.474001i
$179$			66.4446i			0.371199i	0.982625	+	0.185599i	$0.0594227\pi$
$179$			66.4446i			0.371199i	−0.982625	+	0.185599i	$0.940577\pi$
$180$	−29.6479	+	4.58290i	−0.164710	+	0.0254605i
$181$	57.8597			0.319667			0.159833	−	0.987144i	$-0.448904\pi$
$181$	57.8597			0.319667			0.159833	+	0.987144i	$0.448904\pi$
$182$	23.6292	−	23.6292i	0.129831	−	0.129831i
$183$	116.312	+	116.312i	0.635583	+	0.635583i
$184$			13.5647i			0.0737210i
$185$	200.055	−	273.211i	1.08138	−	1.47682i
$186$	97.1371			0.522243
$187$	−128.180	+	128.180i	−0.685457	+	0.685457i
$188$	−8.89810	−	8.89810i	−0.0473303	−	0.0473303i
$189$		−	63.4059i		−	0.335481i
$190$	−123.308	−	90.2903i	−0.648988	−	0.475212i
$191$	5.50354			0.0288143			0.0144072	−	0.999896i	$-0.495414\pi$
$191$	5.50354			0.0288143			0.0144072	+	0.999896i	$0.495414\pi$
$192$	9.79796	−	9.79796i	0.0510310	−	0.0510310i
$193$	179.960	+	179.960i	0.932434	+	0.932434i	0.997858	−	0.0654238i	$-0.0208399\pi$
$193$	179.960	+	179.960i	0.932434	+	0.932434i	−0.0654238	+	0.997858i	$0.520840\pi$
$194$		−	223.419i		−	1.15164i
$195$	−2.56183	−	16.5731i	−0.0131376	−	0.0849903i
$196$	−199.801			−1.01939
$197$	145.865	−	145.865i	0.740432	−	0.740432i	−0.232229	−	0.972661i	$-0.574602\pi$
$197$	145.865	−	145.865i	0.740432	−	0.740432i	0.972661	+	0.232229i	$0.0746019\pi$
$198$	29.8870	+	29.8870i	0.150944	+	0.150944i
$199$			94.1556i			0.473144i	0.971614	+	0.236572i	$0.0760239\pi$
$199$			94.1556i			0.473144i	−0.971614	+	0.236572i	$0.923976\pi$
$200$	62.7634	+	32.5693i	0.313817	+	0.162847i
$201$	58.9930			0.293498
$202$	−77.7181	+	77.7181i	−0.384743	+	0.384743i
$203$	354.318	+	354.318i	1.74541	+	1.74541i
$204$			63.0328i			0.308984i
$205$	227.596	−	35.1811i	1.11022	−	0.171615i
$206$	−84.6721			−0.411029
$207$	−10.1735	+	10.1735i	−0.0491473	+	0.0491473i
$208$	5.47704	+	5.47704i	0.0263319	+	0.0263319i
$209$			215.321i			1.03024i
$210$	−88.2927	+	120.580i	−0.420441	+	0.574189i
$211$	−36.0474			−0.170841			−0.0854204	−	0.996345i	$-0.527223\pi$
$211$	−36.0474			−0.170841			−0.0854204	+	0.996345i	$0.527223\pi$
$212$	−20.3342	+	20.3342i	−0.0959159	+	0.0959159i
$213$	156.726	+	156.726i	0.735803	+	0.735803i
$214$		−	213.934i		−	0.999693i
$215$	242.512	+	177.576i	1.12796	+	0.825933i
$216$	14.6969			0.0680414
$217$	342.170	−	342.170i	1.57682	−	1.57682i
$218$	36.5144	+	36.5144i	0.167497	+	0.167497i
$219$		−	146.028i		−	0.666796i
$220$	−15.2188	−	98.4540i	−0.0691763	−	0.447518i
$221$	−35.2352			−0.159435
$222$	−117.303	+	117.303i	−0.528391	+	0.528391i
$223$	68.4373	+	68.4373i	0.306894	+	0.306894i	0.843703	−	0.536810i	$-0.180371\pi$
$223$	68.4373	+	68.4373i	0.306894	+	0.306894i	−0.536810	+	0.843703i	$0.680371\pi$
$224$		−	69.0276i		−	0.308159i
$225$	22.6455	+	71.4995i	0.100647	+	0.317776i
$226$	21.3312			0.0943859
$227$	−157.931	+	157.931i	−0.695732	+	0.695732i	−0.963487	−	0.267755i	$-0.913718\pi$
$227$	−157.931	+	157.931i	−0.695732	+	0.695732i	0.267755	+	0.963487i	$0.413718\pi$
$228$	52.9420	+	52.9420i	0.232202	+	0.232202i
$229$		−	278.744i		−	1.21722i	−0.793468	−	0.608612i	$-0.791726\pi$
$229$		−	278.744i		−	1.21722i	0.793468	−	0.608612i	$-0.208274\pi$
$230$	33.5136	−	5.18045i	0.145711	−	0.0225237i
$231$	210.557			0.911502
$232$	−82.1278	+	82.1278i	−0.353999	+	0.353999i
$233$	−263.213	−	263.213i	−1.12967	−	1.12967i	−0.990231	−	0.139438i	$-0.955470\pi$
$233$	−263.213	−	263.213i	−1.12967	−	1.12967i	−0.139438	−	0.990231i	$-0.544530\pi$
$234$			8.21556i			0.0351092i
$235$	−18.5859	+	25.3824i	−0.0790889	+	0.108010i
$236$	−167.756			−0.710832
$237$	−33.2330	+	33.2330i	−0.140224	+	0.140224i
$238$	222.036	+	222.036i	0.932924	+	0.932924i
$239$			47.8510i			0.200214i	0.994977	+	0.100107i	$0.0319184\pi$
$239$			47.8510i			0.200214i	−0.994977	+	0.100107i	$0.968082\pi$
$240$	−27.9493	−	20.4655i	−0.116455	−	0.0852728i
$241$	−91.5567			−0.379903			−0.189952	−	0.981793i	$-0.560833\pi$
$241$	−91.5567			−0.379903			−0.189952	+	0.981793i	$0.560833\pi$
$242$	21.7519	−	21.7519i	0.0898839	−	0.0898839i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$			189.936i			0.778427i
$245$	76.3054	+	493.639i	0.311451	+	2.01485i
$246$	−112.823			−0.458629
$247$	−29.5945	+	29.5945i	−0.119816	+	0.119816i
$248$	79.3121	+	79.3121i	0.319807	+	0.319807i
$249$			149.573i			0.600695i
$250$	56.4978	−	167.505i	0.225991	−	0.670021i
$251$	358.473			1.42818			0.714090	−	0.700054i	$-0.246841\pi$
$251$	358.473			1.42818			0.714090	+	0.700054i	$0.246841\pi$
$252$	51.7707	−	51.7707i	0.205439	−	0.205439i
$253$	−33.7839	−	33.7839i	−0.133533	−	0.133533i
$254$			242.731i			0.955634i
$255$	155.732	−	24.0727i	0.610715	−	0.0944028i
$256$	16.0000			0.0625000
$257$	45.2189	−	45.2189i	0.175949	−	0.175949i	−0.613638	−	0.789587i	$-0.710295\pi$
$257$	45.2189	−	45.2189i	0.175949	−	0.175949i	0.789587	+	0.613638i	$0.210295\pi$
$258$	−104.122	−	104.122i	−0.403574	−	0.403574i
$259$			826.409i			3.19077i
$260$	11.4402	−	15.6236i	0.0440006	−	0.0600908i
$261$	−123.192			−0.471999
$262$	−188.546	+	188.546i	−0.719642	+	0.719642i
$263$	7.35905	+	7.35905i	0.0279812	+	0.0279812i	0.720959	−	0.692978i	$-0.243702\pi$
$263$	7.35905	+	7.35905i	0.0279812	+	0.0279812i	−0.692978	+	0.720959i	$0.743702\pi$
$264$			48.8053i			0.184868i
$265$	58.0046	+	42.4730i	0.218885	+	0.160275i
$266$	372.982			1.40219
$267$	−103.334	+	103.334i	−0.387020	+	0.387020i
$268$	48.1676	+	48.1676i	0.179730	+	0.179730i
$269$		−	159.878i		−	0.594341i	−0.954824	−	0.297171i	$-0.903957\pi$
$269$		−	159.878i		−	0.594341i	0.954824	−	0.297171i	$-0.0960430\pi$
$270$	−5.61288	−	36.3111i	−0.0207884	−	0.134486i
$271$	211.259			0.779554			0.389777	−	0.920909i	$-0.372552\pi$
$271$	211.259			0.779554			0.389777	+	0.920909i	$0.372552\pi$
$272$	−51.4660	+	51.4660i	−0.189213	+	0.189213i
$273$	28.9397	+	28.9397i	0.106006	+	0.106006i
$274$		−	172.217i		−	0.628528i
$275$	−237.434	+	75.2008i	−0.863396	+	0.273457i
$276$	−16.6132			−0.0601929
$277$	219.374	−	219.374i	0.791962	−	0.791962i	−0.189851	−	0.981813i	$-0.560800\pi$
$277$	219.374	−	219.374i	0.791962	−	0.791962i	0.981813	+	0.189851i	$0.0608004\pi$
$278$	145.443	+	145.443i	0.523178	+	0.523178i
$279$			118.968i			0.426409i
$280$	−170.544	+	26.3622i	−0.609084	+	0.0941507i
$281$	168.520			0.599714			0.299857	−	0.953984i	$-0.403061\pi$
$281$	168.520			0.599714			0.299857	+	0.953984i	$0.403061\pi$
$282$	10.8979	−	10.8979i	0.0386450	−	0.0386450i
$283$	154.756	+	154.756i	0.546843	+	0.546843i	0.925526	−	0.378684i	$-0.123623\pi$
$283$	154.756	+	154.756i	0.546843	+	0.546843i	−0.378684	+	0.925526i	$0.623623\pi$
$284$			255.933i			0.901171i
$285$	110.583	−	151.020i	0.388009	−	0.529896i
$286$	−27.2821			−0.0953918
$287$	−397.424	+	397.424i	−1.38475	+	1.38475i
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$		−	42.0941i		−	0.145654i
$290$	234.275	+	171.544i	0.807844	+	0.591532i
$291$	273.631			0.940312
$292$	119.232	−	119.232i	0.408327	−	0.408327i
$293$	−312.900	−	312.900i	−1.06792	−	1.06792i	−0.997519	−	0.0703988i	$-0.977573\pi$
$293$	−312.900	−	312.900i	−1.06792	−	1.06792i	−0.0703988	−	0.997519i	$-0.522427\pi$
$294$		−	244.705i		−	0.832329i
$295$	64.0675	+	414.469i	0.217178	+	1.40498i
$296$	−191.554			−0.647144
$297$	−36.6040	+	36.6040i	−0.123246	+	0.123246i
$298$	−135.574	−	135.574i	−0.454945	−	0.454945i
$299$		−	9.28677i		−	0.0310594i
$300$	−39.8891	+	76.8691i	−0.132964	+	0.256230i
$301$	−733.550			−2.43704
$302$	222.424	−	222.424i	0.736502	−	0.736502i
$303$	−95.1848	−	95.1848i	−0.314141	−	0.314141i
$304$			86.4539i			0.284388i
$305$	469.267	−	72.5381i	1.53858	−	0.237830i
$306$	−77.1991			−0.252284
$307$	66.0310	−	66.0310i	0.215085	−	0.215085i	−0.591339	−	0.806423i	$-0.701400\pi$
$307$	66.0310	−	66.0310i	0.215085	−	0.215085i	0.806423	+	0.591339i	$0.201400\pi$
$308$	171.919	+	171.919i	0.558179	+	0.558179i
$309$		−	103.702i		−	0.335604i
$310$	165.663	−	226.243i	0.534397	−	0.729816i
$311$	−47.7193			−0.153438			−0.0767191	−	0.997053i	$-0.524444\pi$
$311$	−47.7193			−0.153438			−0.0767191	+	0.997053i	$0.524444\pi$
$312$	−6.70798	+	6.70798i	−0.0214999	+	0.0214999i
$313$	−342.502	−	342.502i	−1.09425	−	1.09425i	−0.995069	−	0.0991860i	$-0.968376\pi$
$313$	−342.502	−	342.502i	−1.09425	−	1.09425i	−0.0991860	−	0.995069i	$-0.531624\pi$
$314$		−	328.553i		−	1.04635i
$315$	−147.679	−	108.136i	−0.468823	−	0.343289i
$316$	−54.2693			−0.171738
$317$	265.894	−	265.894i	0.838783	−	0.838783i	−0.149916	−	0.988699i	$-0.547900\pi$
$317$	265.894	−	265.894i	0.838783	−	0.838783i	0.988699	+	0.149916i	$0.0479002\pi$
$318$	−24.9042	−	24.9042i	−0.0783150	−	0.0783150i
$319$		−	409.092i		−	1.28242i
$320$	−6.11053	−	39.5305i	−0.0190954	−	0.123533i
$321$	262.015			0.816246
$322$	−58.5210	+	58.5210i	−0.181742	+	0.181742i
$323$	−278.090	−	278.090i	−0.860960	−	0.860960i
$324$			18.0000i			0.0555556i
$325$	−42.9697	−	22.2979i	−0.132214	−	0.0686090i
$326$	−101.191			−0.310402
$327$	−44.7208	+	44.7208i	−0.136761	+	0.136761i
$328$	−92.1194	−	92.1194i	−0.280852	−	0.280852i
$329$		−	76.7768i		−	0.233364i
$330$	120.581	−	18.6391i	0.365397	−	0.0564822i
$331$	−49.2824			−0.148889			−0.0744447	−	0.997225i	$-0.523718\pi$
$331$	−49.2824			−0.148889			−0.0744447	+	0.997225i	$0.523718\pi$
$332$	−122.126	+	122.126i	−0.367849	+	0.367849i
$333$	−143.666	−	143.666i	−0.431429	−	0.431429i
$334$		−	258.064i		−	0.772645i
$335$	100.610	−	137.401i	0.300328	−	0.410153i
$336$	84.5412			0.251611
$337$	196.678	−	196.678i	0.583614	−	0.583614i	−0.352281	−	0.935894i	$-0.614594\pi$
$337$	196.678	−	196.678i	0.583614	−	0.583614i	0.935894	+	0.352281i	$0.114594\pi$
$338$	165.250	+	165.250i	0.488906	+	0.488906i
$339$			26.1253i			0.0770658i
$340$	146.810	+	107.500i	0.431795	+	0.316175i
$341$	−395.067			−1.15855
$342$	−64.8404	+	64.8404i	−0.189592	+	0.189592i
$343$	−439.190	−	439.190i	−1.28044	−	1.28044i
$344$		−	170.031i		−	0.494275i
$345$	6.34473	+	41.0456i	0.0183905	+	0.118973i
$346$	−62.1844			−0.179724
$347$	161.562	−	161.562i	0.465596	−	0.465596i	−0.434888	−	0.900484i	$-0.643212\pi$
$347$	161.562	−	161.562i	0.465596	−	0.465596i	0.900484	+	0.434888i	$0.143212\pi$
$348$	−100.586	−	100.586i	−0.289039	−	0.289039i
$349$		−	69.2537i		−	0.198435i	−0.995066	−	0.0992173i	$-0.968366\pi$
$349$		−	69.2537i		−	0.198435i	0.995066	−	0.0992173i	$-0.0316339\pi$
$350$	130.264	+	411.287i	0.372182	+	1.17510i
$351$	−10.0620			−0.0286666
$352$	−39.8493	+	39.8493i	−0.113208	+	0.113208i
$353$	187.924	+	187.924i	0.532363	+	0.532363i	0.921275	−	0.388912i	$-0.127149\pi$
$353$	187.924	+	187.924i	0.532363	+	0.532363i	−0.388912	+	0.921275i	$0.627149\pi$
$354$		−	205.459i		−	0.580392i
$355$	632.322	−	97.7427i	1.78119	−	0.275331i
$356$	−168.744			−0.474001
$357$	−271.937	+	271.937i	−0.761730	+	0.761730i
$358$	−66.4446	−	66.4446i	−0.185599	−	0.185599i
$359$		−	327.086i		−	0.911103i	−0.890209	−	0.455551i	$-0.849442\pi$
$359$		−	327.086i		−	0.911103i	0.890209	−	0.455551i	$-0.150558\pi$
$360$	25.0650	−	34.2308i	0.0696250	−	0.0950855i
$361$	−106.142			−0.294023
$362$	−57.8597	+	57.8597i	−0.159833	+	0.159833i
$363$	26.6405	+	26.6405i	0.0733899	+	0.0733899i
$364$			47.2584i			0.129831i
$365$	−340.116	−	249.045i	−0.931824	−	0.682315i
$366$	−232.623			−0.635583
$367$	−490.806	+	490.806i	−1.33735	+	1.33735i	−0.438724	+	0.898622i	$0.644569\pi$
$367$	−490.806	+	490.806i	−1.33735	+	1.33735i	−0.898622	+	0.438724i	$0.855431\pi$
$368$	−13.5647	−	13.5647i	−0.0368605	−	0.0368605i
$369$		−	138.179i		−	0.374469i
$370$	73.1562	+	473.265i	0.197719	+	1.27910i
$371$	−175.452			−0.472917
$372$	−97.1371	+	97.1371i	−0.261121	+	0.261121i
$373$	−21.0158	−	21.0158i	−0.0563427	−	0.0563427i	0.678374	−	0.734717i	$-0.262685\pi$
$373$	−21.0158	−	21.0158i	−0.0563427	−	0.0563427i	−0.734717	+	0.678374i	$0.762685\pi$
$374$		−	256.361i		−	0.685457i
$375$	205.151	+	69.1954i	0.547070	+	0.184521i
$376$	17.7962			0.0473303
$377$	56.2272	−	56.2272i	0.149144	−	0.149144i
$378$	63.4059	+	63.4059i	0.167740	+	0.167740i
$379$			310.295i			0.818720i	0.912373	+	0.409360i	$0.134248\pi$
$379$			310.295i			0.818720i	−0.912373	+	0.409360i	$0.865752\pi$
$380$	213.598	−	33.0174i	0.562100	−	0.0868880i
$381$	−297.284			−0.780272
$382$	−5.50354	+	5.50354i	−0.0144072	+	0.0144072i
$383$	246.947	+	246.947i	0.644769	+	0.644769i	0.951724	−	0.306955i	$-0.0993101\pi$
$383$	246.947	+	246.947i	0.644769	+	0.644769i	−0.306955	+	0.951724i	$0.599310\pi$
$384$			19.5959i			0.0510310i
$385$	359.096	−	490.410i	0.932716	−	1.27379i
$386$	−359.919			−0.932434
$387$	127.523	−	127.523i	0.329517	−	0.329517i
$388$	223.419	+	223.419i	0.575821	+	0.575821i
$389$		−	467.057i		−	1.20066i	−0.799752	−	0.600330i	$-0.795036\pi$
$389$		−	467.057i		−	1.20066i	0.799752	−	0.600330i	$-0.204964\pi$
$390$	19.1349	+	14.0113i	0.0490639	+	0.0359264i
$391$	87.2649			0.223184
$392$	199.801	−	199.801i	0.509695	−	0.509695i
$393$	−230.921	−	230.921i	−0.587586	−	0.587586i
$394$			291.730i			0.740432i
$395$	20.7259	+	134.081i	0.0524705	+	0.339445i
$396$	−59.7740			−0.150944
$397$	387.028	−	387.028i	0.974882	−	0.974882i	−0.0248106	−	0.999692i	$-0.507898\pi$
$397$	387.028	−	387.028i	0.974882	−	0.974882i	0.999692	+	0.0248106i	$0.00789828\pi$
$398$	−94.1556	−	94.1556i	−0.236572	−	0.236572i
$399$			456.807i			1.14488i
$400$	−95.3327	+	30.1940i	−0.238332	+	0.0754851i
$401$	−448.866			−1.11937			−0.559684	−	0.828706i	$-0.689077\pi$
$401$	−448.866			−1.11937			−0.559684	+	0.828706i	$0.689077\pi$
$402$	−58.9930	+	58.9930i	−0.146749	+	0.146749i
$403$	−54.2995	−	54.2995i	−0.134738	−	0.134738i
$404$		−	155.436i		−	0.384743i
$405$	44.4718	−	6.87434i	0.109807	−	0.0169737i
$406$	−708.635			−1.74541
$407$	477.082	−	477.082i	1.17219	−	1.17219i
$408$	−63.0328	−	63.0328i	−0.154492	−	0.154492i
$409$		−	335.091i		−	0.819293i	−0.912244	−	0.409647i	$-0.865652\pi$
$409$		−	335.091i		−	0.819293i	0.912244	−	0.409647i	$-0.134348\pi$
$410$	−192.414	+	262.777i	−0.469303	+	0.640919i
$411$	210.921			0.513191
$412$	84.6721	−	84.6721i	0.205515	−	0.205515i
$413$	−723.739	−	723.739i	−1.75239	−	1.75239i
$414$		−	20.3470i		−	0.0491473i
$415$	348.372	+	255.090i	0.839451	+	0.614676i
$416$	−10.9541			−0.0263319
$417$	−178.131	+	178.131i	−0.427173	+	0.427173i
$418$	−215.321	−	215.321i	−0.515121	−	0.515121i
$419$		−	235.423i		−	0.561869i	−0.959727	−	0.280934i	$-0.909356\pi$
$419$		−	235.423i		−	0.561869i	0.959727	−	0.280934i	$-0.0906444\pi$
$420$	−32.2870	−	208.872i	−0.0768737	−	0.497315i
$421$	−326.446			−0.775406			−0.387703	−	0.921784i	$-0.626731\pi$
$421$	−326.446			−0.775406			−0.387703	+	0.921784i	$0.626731\pi$
$422$	36.0474	−	36.0474i	0.0854204	−	0.0854204i
$423$	13.3472	+	13.3472i	0.0315536	+	0.0315536i
$424$		−	40.6683i		−	0.0959159i
$425$	209.527	−	403.773i	0.493004	−	0.950053i
$426$	−313.452			−0.735803
$427$	−819.427	+	819.427i	−1.91903	+	1.91903i
$428$	213.934	+	213.934i	0.499846	+	0.499846i
$429$		−	33.4136i		−	0.0778871i
$430$	−420.087	+	64.9360i	−0.976947	+	0.151014i
$431$	−307.959			−0.714523			−0.357262	−	0.934004i	$-0.616290\pi$
$431$	−307.959			−0.714523			−0.357262	+	0.934004i	$0.616290\pi$
$432$	−14.6969	+	14.6969i	−0.0340207	+	0.0340207i
$433$	393.236	+	393.236i	0.908166	+	0.908166i	0.996124	−	0.0879578i	$-0.0280341\pi$
$433$	393.236	+	393.236i	0.908166	+	0.908166i	−0.0879578	+	0.996124i	$0.528034\pi$
$434$			684.341i			1.57682i
$435$	−210.098	+	286.927i	−0.482984	+	0.659602i
$436$	−73.0287			−0.167497
$437$	73.2949	−	73.2949i	0.167723	−	0.167723i
$438$	146.028	+	146.028i	0.333398	+	0.333398i
$439$			330.522i			0.752897i	0.926438	+	0.376448i	$0.122855\pi$
$439$			330.522i			0.752897i	−0.926438	+	0.376448i	$0.877145\pi$
$440$	113.673	+	83.2353i	0.258347	+	0.189171i
$441$	299.701			0.679594
$442$	35.2352	−	35.2352i	0.0797176	−	0.0797176i
$443$	−116.455	−	116.455i	−0.262879	−	0.262879i	0.563344	−	0.826223i	$-0.309515\pi$
$443$	−116.455	−	116.455i	−0.262879	−	0.262879i	−0.826223	+	0.563344i	$0.809515\pi$
$444$		−	234.605i		−	0.528391i
$445$	64.4448	+	416.909i	0.144820	+	0.936874i
$446$	−136.875			−0.306894
$447$	166.043	−	166.043i	0.371461	−	0.371461i
$448$	69.0276	+	69.0276i	0.154079	+	0.154079i
$449$			149.486i			0.332930i	0.986047	+	0.166465i	$0.0532354\pi$
$449$			149.486i			0.332930i	−0.986047	+	0.166465i	$0.946765\pi$
$450$	−94.1450	−	48.8540i	−0.209211	−	0.108564i
$451$	458.862			1.01743
$452$	−21.3312	+	21.3312i	−0.0471929	+	0.0471929i
$453$	272.412	+	272.412i	0.601351	+	0.601351i
$454$		−	315.862i		−	0.695732i
$455$	116.759	−	18.0483i	0.256614	−	0.0396667i
$456$	−105.884			−0.232202
$457$	259.178	−	259.178i	0.567130	−	0.567130i	−0.364193	−	0.931323i	$-0.618655\pi$
$457$	259.178	−	259.178i	0.567130	−	0.567130i	0.931323	+	0.364193i	$0.118655\pi$
$458$	278.744	+	278.744i	0.608612	+	0.608612i
$459$		−	94.5491i		−	0.205989i
$460$	−28.3332	+	38.6941i	−0.0615939	+	0.0841176i
$461$	−804.421			−1.74495			−0.872474	−	0.488661i	$-0.837486\pi$
$461$	−804.421			−1.74495			−0.872474	+	0.488661i	$0.837486\pi$
$462$	−210.557	+	210.557i	−0.455751	+	0.455751i
$463$	284.414	+	284.414i	0.614284	+	0.614284i	0.944059	−	0.329775i	$-0.106973\pi$
$463$	284.414	+	284.414i	0.614284	+	0.614284i	−0.329775	+	0.944059i	$0.606973\pi$
$464$		−	164.256i		−	0.353999i
$465$	277.090	+	202.895i	0.595892	+	0.436333i
$466$	526.426			1.12967
$467$	542.008	−	542.008i	1.16062	−	1.16062i	0.176276	−	0.984341i	$-0.443595\pi$
$467$	542.008	−	542.008i	1.16062	−	1.16062i	0.984341	−	0.176276i	$-0.0564050\pi$
$468$	−8.21556	−	8.21556i	−0.0175546	−	0.0175546i
$469$			415.612i			0.886165i
$470$	−6.79651	−	43.9683i	−0.0144607	−	0.0935496i
$471$	402.394			0.854339
$472$	167.756	−	167.756i	0.355416	−	0.355416i
$473$	423.475	+	423.475i	0.895297	+	0.895297i
$474$		−	66.4660i		−	0.140224i
$475$	−163.149	−	515.118i	−0.343473	−	1.08446i
$476$	−444.072			−0.932924
$477$	30.5013	−	30.5013i	0.0639439	−	0.0639439i
$478$	−47.8510	−	47.8510i	−0.100107	−	0.100107i
$479$		−	419.970i		−	0.876764i	−0.898789	−	0.438382i	$-0.855552\pi$
$479$		−	419.970i		−	0.876764i	0.898789	−	0.438382i	$-0.144448\pi$
$480$	48.4148	−	7.48384i	0.100864	−	0.0155913i
$481$	131.144			0.272649
$482$	91.5567	−	91.5567i	0.189952	−	0.189952i
$483$	−71.6733	−	71.6733i	−0.148392	−	0.148392i
$484$			43.5038i			0.0898839i
$485$	466.665	−	637.316i	0.962196	−	1.31405i
$486$	−22.0454			−0.0453609
$487$	−463.650	+	463.650i	−0.952054	+	0.952054i	−0.998902	−	0.0468485i	$-0.985082\pi$
$487$	−463.650	+	463.650i	−0.952054	+	0.952054i	0.0468485	+	0.998902i	$0.485082\pi$
$488$	−189.936	−	189.936i	−0.389213	−	0.389213i
$489$		−	123.933i		−	0.253442i
$490$	−569.944	−	417.333i	−1.16315	−	0.851700i
$491$	−81.2134			−0.165404			−0.0827021	−	0.996574i	$-0.526355\pi$
$491$	−81.2134			−0.165404			−0.0827021	+	0.996574i	$0.526355\pi$
$492$	112.823	−	112.823i	0.229315	−	0.229315i
$493$	528.349	+	528.349i	1.07170	+	1.07170i
$494$		−	59.1889i		−	0.119816i
$495$	22.8282	+	147.681i	0.0461175	+	0.298346i
$496$	−158.624			−0.319807
$497$	−1104.15	+	1104.15i	−2.22163	+	2.22163i
$498$	−149.573	−	149.573i	−0.300348	−	0.300348i
$499$		−	486.389i		−	0.974727i	−0.873199	−	0.487364i	$-0.837959\pi$
$499$		−	486.389i		−	0.974727i	0.873199	−	0.487364i	$-0.162041\pi$
$500$	111.007	+	224.003i	0.222015	+	0.448006i
$501$	316.062			0.630862
$502$	−358.473	+	358.473i	−0.714090	+	0.714090i
$503$	−243.288	−	243.288i	−0.483674	−	0.483674i	0.422629	−	0.906303i	$-0.361107\pi$
$503$	−243.288	−	243.288i	−0.483674	−	0.483674i	−0.906303	+	0.422629i	$0.861107\pi$
$504$			103.541i			0.205439i
$505$	−384.029	+	59.3623i	−0.760454	+	0.117549i
$506$	67.5678			0.133533
$507$	−202.389	+	202.389i	−0.399190	+	0.399190i
$508$	−242.731	−	242.731i	−0.477817	−	0.477817i
$509$			224.497i			0.441056i	0.975381	+	0.220528i	$0.0707780\pi$
$509$			224.497i			0.441056i	−0.975381	+	0.220528i	$0.929222\pi$
$510$	−131.660	+	179.805i	−0.258156	+	0.352559i
$511$	1028.78			2.01327
$512$	−16.0000	+	16.0000i	−0.0312500	+	0.0312500i
$513$	−79.4130	−	79.4130i	−0.154801	−	0.154801i
$514$			90.4377i			0.175949i
$515$	−241.533	−	176.859i	−0.468995	−	0.343415i
$516$	208.244			0.403574
$517$	−44.3229	+	44.3229i	−0.0857310	+	0.0857310i
$518$	−826.409	−	826.409i	−1.59538	−	1.59538i
$519$		−	76.1600i		−	0.146744i
$520$	4.18345	+	27.0638i	0.00804510	+	0.0520457i
$521$	−581.302			−1.11574			−0.557872	−	0.829927i	$-0.688382\pi$
$521$	−581.302			−1.11574			−0.557872	+	0.829927i	$0.688382\pi$
$522$	123.192	−	123.192i	0.235999	−	0.235999i
$523$	−573.621	−	573.621i	−1.09679	−	1.09679i	−0.994784	−	0.102005i	$-0.967474\pi$
$523$	−573.621	−	573.621i	−1.09679	−	1.09679i	−0.102005	−	0.994784i	$-0.532526\pi$
$524$		−	377.093i		−	0.719642i
$525$	−503.721	+	159.540i	−0.959469	+	0.303886i
$526$	−14.7181			−0.0279812
$527$	510.235	−	510.235i	0.968188	−	0.968188i
$528$	−48.8053	−	48.8053i	−0.0924342	−	0.0924342i
$529$			23.0000i			0.0434783i
$530$	−100.478	+	15.5316i	−0.189580	+	0.0293048i
$531$	251.635			0.473888
$532$	−372.982	+	372.982i	−0.701093	+	0.701093i
$533$	63.0677	+	63.0677i	0.118326	+	0.118326i
$534$		−	206.669i		−	0.387020i
$535$	446.855	−	610.261i	0.835243	−	1.14068i
$536$	−96.3352			−0.179730
$537$	81.3777	−	81.3777i	0.151541	−	0.151541i
$538$	159.878	+	159.878i	0.297171	+	0.297171i
$539$			995.240i			1.84646i
$540$	41.9240	+	30.6982i	0.0776370	+	0.0568486i
$541$	582.198			1.07615			0.538075	−	0.842897i	$-0.319152\pi$
$541$	582.198			1.07615			0.538075	+	0.842897i	$0.319152\pi$
$542$	−211.259	+	211.259i	−0.389777	+	0.389777i
$543$	−70.8634	−	70.8634i	−0.130503	−	0.130503i
$544$		−	102.932i		−	0.189213i
$545$	27.8902	+	180.429i	0.0511748	+	0.331062i
$546$	−57.8794			−0.106006
$547$	−242.902	+	242.902i	−0.444063	+	0.444063i	−0.893375	−	0.449312i	$-0.851669\pi$
$547$	−242.902	+	242.902i	−0.444063	+	0.444063i	0.449312	+	0.893375i	$0.351669\pi$
$548$	172.217	+	172.217i	0.314264	+	0.314264i
$549$		−	284.904i		−	0.518951i
$550$	162.233	−	312.635i	0.294970	−	0.568427i
$551$	887.533			1.61077
$552$	16.6132	−	16.6132i	0.0300965	−	0.0300965i
$553$	−234.130	−	234.130i	−0.423381	−	0.423381i
$554$			438.747i			0.791962i
$555$	−579.629	+	89.5977i	−1.04438	+	0.161437i
$556$	−290.887			−0.523178
$557$	269.139	−	269.139i	0.483194	−	0.483194i	−0.422956	−	0.906150i	$-0.639007\pi$
$557$	269.139	−	269.139i	0.483194	−	0.483194i	0.906150	+	0.422956i	$0.139007\pi$
$558$	−118.968	−	118.968i	−0.213205	−	0.213205i
$559$			116.408i			0.208243i
$560$	144.181	−	196.906i	0.257467	−	0.351617i
$561$	313.977			0.559673
$562$	−168.520	+	168.520i	−0.299857	+	0.299857i
$563$	−695.370	−	695.370i	−1.23511	−	1.23511i	−0.961974	−	0.273141i	$-0.911938\pi$
$563$	−695.370	−	695.370i	−1.23511	−	1.23511i	−0.273141	−	0.961974i	$-0.588062\pi$
$564$			21.7958i			0.0386450i
$565$	60.8487	+	44.5555i	0.107697	+	0.0788594i
$566$	−309.513			−0.546843
$567$	−77.6560	+	77.6560i	−0.136960	+	0.136960i
$568$	−255.933	−	255.933i	−0.450585	−	0.450585i
$569$			132.973i			0.233696i	0.993150	+	0.116848i	$0.0372790\pi$
$569$			132.973i			0.233696i	−0.993150	+	0.116848i	$0.962721\pi$
$570$	40.4379	+	261.603i	0.0709437	+	0.458953i
$571$	331.378			0.580347			0.290174	−	0.956974i	$-0.406287\pi$
$571$	331.378			0.580347			0.290174	+	0.956974i	$0.406287\pi$
$572$	27.2821	−	27.2821i	0.0476959	−	0.0476959i
$573$	−6.74043	−	6.74043i	−0.0117634	−	0.0117634i
$574$		−	794.848i		−	1.38475i
$575$	106.420	+	55.2240i	0.185079	+	0.0960417i
$576$	−24.0000			−0.0416667
$577$	342.624	−	342.624i	0.593803	−	0.593803i	−0.344854	−	0.938656i	$-0.612072\pi$
$577$	342.624	−	342.624i	0.593803	−	0.593803i	0.938656	+	0.344854i	$0.112072\pi$
$578$	42.0941	+	42.0941i	0.0728271	+	0.0728271i
$579$		−	440.809i		−	0.761329i
$580$	−405.819	+	62.7305i	−0.699688	+	0.108156i
$581$	−1053.76			−1.81370
$582$	−273.631	+	273.631i	−0.470156	+	0.470156i
$583$	101.288	+	101.288i	0.173736	+	0.173736i
$584$			238.463i			0.408327i
$585$	−17.1602	+	23.4354i	−0.0293338	+	0.0400605i
$586$	625.800			1.06792
$587$	−761.501	+	761.501i	−1.29728	+	1.29728i	−0.367091	+	0.930185i	$0.619646\pi$
$587$	−761.501	+	761.501i	−1.29728	+	1.29728i	−0.930185	+	0.367091i	$0.880354\pi$
$588$	244.705	+	244.705i	0.416164	+	0.416164i
$589$		−	857.105i		−	1.45519i
$590$	−478.536	−	350.401i	−0.811078	−	0.593900i
$591$	−357.295			−0.604560
$592$	191.554	−	191.554i	0.323572	−	0.323572i
$593$	9.06060	+	9.06060i	0.0152793	+	0.0152793i	0.714705	−	0.699426i	$-0.246561\pi$
$593$	9.06060	+	9.06060i	0.0152793	+	0.0152793i	−0.699426	+	0.714705i	$0.746561\pi$
$594$		−	73.2079i		−	0.123246i
$595$	169.595	+	1097.15i	0.285033	+	1.84395i
$596$	271.147			0.454945
$597$	115.317	−	115.317i	0.193160	−	0.193160i
$598$	9.28677	+	9.28677i	0.0155297	+	0.0155297i
$599$		−	730.067i		−	1.21881i	−0.792859	−	0.609405i	$-0.791408\pi$
$599$		−	730.067i		−	1.21881i	0.792859	−	0.609405i	$-0.208592\pi$
$600$	−36.9800	−	116.758i	−0.0616333	−	0.194597i
$601$	−1150.36			−1.91407			−0.957036	−	0.289969i	$-0.906355\pi$
$601$	−1150.36			−1.91407			−0.957036	+	0.289969i	$0.906355\pi$
$602$	733.550	−	733.550i	1.21852	−	1.21852i
$603$	−72.2514	−	72.2514i	−0.119820	−	0.119820i
$604$			444.847i			0.736502i
$605$	107.483	−	16.6144i	0.177658	−	0.0274619i
$606$	190.370			0.314141
$607$	−121.692	+	121.692i	−0.200481	+	0.200481i	−0.800206	−	0.599725i	$-0.795277\pi$
$607$	−121.692	+	121.692i	−0.200481	+	0.200481i	0.599725	+	0.800206i	$0.295277\pi$
$608$	−86.4539	−	86.4539i	−0.142194	−	0.142194i
$609$		−	867.898i		−	1.42512i
$610$	−396.729	+	541.805i	−0.650375	+	0.888205i
$611$	−12.1838			−0.0199408
$612$	77.1991	−	77.1991i	0.126142	−	0.126142i
$613$	624.795	+	624.795i	1.01924	+	1.01924i	0.999811	+	0.0194306i	$0.00618533\pi$
$613$	624.795	+	624.795i	1.01924	+	1.01924i	0.0194306	+	0.999811i	$0.493815\pi$
$614$			132.062i			0.215085i
$615$	−321.834	−	235.659i	−0.523308	−	0.383185i
$616$	−343.838			−0.558179
$617$	−136.943	+	136.943i	−0.221951	+	0.221951i	−0.809319	−	0.587369i	$-0.800164\pi$
$617$	−136.943	+	136.943i	−0.221951	+	0.221951i	0.587369	+	0.809319i	$0.300164\pi$
$618$	103.702	+	103.702i	0.167802	+	0.167802i
$619$			57.3312i			0.0926191i	0.998927	+	0.0463095i	$0.0147461\pi$
$619$			57.3312i			0.0926191i	−0.998927	+	0.0463095i	$0.985254\pi$
$620$	60.5799	+	391.906i	0.0977094	+	0.632107i
$621$	24.9199			0.0401286
$622$	47.7193	−	47.7193i	0.0767191	−	0.0767191i
$623$	−728.000	−	728.000i	−1.16854	−	1.16854i
$624$		−	13.4160i		−	0.0214999i
$625$	511.040	−	359.810i	0.817664	−	0.575696i
$626$	685.004			1.09425
$627$	263.713	−	263.713i	0.420595	−	0.420595i
$628$	328.553	+	328.553i	0.523174	+	0.523174i
$629$			1232.32i			1.95917i
$630$	255.815	−	39.5433i	0.406056	−	0.0627671i
$631$	−148.750			−0.235737			−0.117868	−	0.993029i	$-0.537606\pi$
$631$	−148.750			−0.235737			−0.117868	+	0.993029i	$0.537606\pi$
$632$	54.2693	−	54.2693i	0.0858691	−	0.0858691i
$633$	44.1489	+	44.1489i	0.0697454	+	0.0697454i
$634$			531.789i			0.838783i
$635$	−507.004	+	692.406i	−0.798432	+	1.09040i
$636$	49.8083			0.0783150
$637$	−136.789	+	136.789i	−0.214740	+	0.214740i
$638$	409.092	+	409.092i	0.641210	+	0.641210i
$639$		−	383.899i		−	0.600781i
$640$	45.6410	+	33.4200i	0.0713141	+	0.0522187i
$641$	−891.369			−1.39059			−0.695296	−	0.718724i	$-0.744727\pi$
$641$	−891.369			−1.39059			−0.695296	+	0.718724i	$0.744727\pi$
$642$	−262.015	+	262.015i	−0.408123	+	0.408123i
$643$	518.375	+	518.375i	0.806182	+	0.806182i	0.984054	−	0.177872i	$-0.0569213\pi$
$643$	518.375	+	518.375i	0.806182	+	0.806182i	−0.177872	+	0.984054i	$0.556921\pi$
$644$		−	117.042i		−	0.181742i
$645$	−79.5301	−	514.500i	−0.123302	−	0.797674i
$646$	556.180			0.860960
$647$	716.167	−	716.167i	1.10690	−	1.10690i	0.113349	−	0.993555i	$-0.463842\pi$
$647$	716.167	−	716.167i	1.10690	−	1.10690i	0.993555	−	0.113349i	$-0.0361579\pi$
$648$	−18.0000	−	18.0000i	−0.0277778	−	0.0277778i
$649$			835.623i			1.28755i
$650$	65.2676	−	20.6717i	0.100412	−	0.0318027i
$651$	−838.143			−1.28747
$652$	101.191	−	101.191i	0.155201	−	0.155201i
$653$	3.21608	+	3.21608i	0.00492509	+	0.00492509i	0.709565	−	0.704640i	$-0.248891\pi$
$653$	3.21608	+	3.21608i	0.00492509	+	0.00492509i	−0.704640	+	0.709565i	$0.748891\pi$
$654$		−	89.4415i		−	0.136761i
$655$	−931.667	+	144.015i	−1.42239	+	0.219870i
$656$	184.239			0.280852
$657$	−178.847	+	178.847i	−0.272218	+	0.272218i
$658$	76.7768	+	76.7768i	0.116682	+	0.116682i
$659$			197.407i			0.299555i	0.988720	+	0.149778i	$0.0478558\pi$
$659$			197.407i			0.299555i	−0.988720	+	0.149778i	$0.952144\pi$
$660$	−101.942	+	139.220i	−0.154458	+	0.210940i
$661$	560.346			0.847725			0.423862	−	0.905727i	$-0.360674\pi$
$661$	560.346			0.847725			0.423862	+	0.905727i	$0.360674\pi$
$662$	49.2824	−	49.2824i	0.0744447	−	0.0744447i
$663$	43.1541	+	43.1541i	0.0650892	+	0.0650892i
$664$		−	244.252i		−	0.367849i
$665$	1063.95	+	779.065i	1.59993	+	1.17153i
$666$	287.332			0.431429
$667$	−139.254	+	139.254i	−0.208777	+	0.208777i
$668$	258.064	+	258.064i	0.386323	+	0.386323i
$669$		−	167.637i		−	0.250578i
$670$	36.7912	+	238.011i	0.0549122	+	0.355241i
$671$	946.104			1.40999
$672$	−84.5412	+	84.5412i	−0.125805	+	0.125805i
$673$	−947.596	−	947.596i	−1.40802	−	1.40802i	−0.770129	−	0.637889i	$-0.779808\pi$
$673$	−947.596	−	947.596i	−1.40802	−	1.40802i	−0.637889	−	0.770129i	$-0.720192\pi$
$674$			393.356i			0.583614i
$675$	59.8337	−	115.304i	0.0886425	−	0.170820i
$676$	−330.501			−0.488906
$677$	−121.113	+	121.113i	−0.178896	+	0.178896i	−0.790874	−	0.611978i	$-0.790374\pi$
$677$	−121.113	+	121.113i	−0.178896	+	0.178896i	0.611978	+	0.790874i	$0.290374\pi$
$678$	−26.1253	−	26.1253i	−0.0385329	−	0.0385329i
$679$			1927.76i			2.83911i
$680$	−254.310	+	39.3106i	−0.373985	+	0.0578097i
$681$	386.851			0.568063
$682$	395.067	−	395.067i	0.579277	−	0.579277i
$683$	446.080	+	446.080i	0.653119	+	0.653119i	0.953743	−	0.300624i	$-0.0971948\pi$
$683$	446.080	+	446.080i	0.653119	+	0.653119i	−0.300624	+	0.953743i	$0.597195\pi$
$684$		−	129.681i		−	0.189592i
$685$	359.717	−	491.259i	0.525135	−	0.717167i
$686$	878.380			1.28044
$687$	−341.391	+	341.391i	−0.496930	+	0.496930i
$688$	170.031	+	170.031i	0.247137	+	0.247137i
$689$			27.8428i			0.0404104i
$690$	−47.3904	−	34.7009i	−0.0686817	−	0.0502912i
$691$	−885.496			−1.28147			−0.640735	−	0.767762i	$-0.721370\pi$
$691$	−885.496			−1.28147			−0.640735	+	0.767762i	$0.721370\pi$
$692$	62.1844	−	62.1844i	0.0898619	−	0.0898619i
$693$	−257.878	−	257.878i	−0.372119	−	0.372119i
$694$			323.124i			0.465596i
$695$	111.092	+	718.682i	0.159845	+	1.03407i
$696$	201.171			0.289039
$697$	−592.628	+	592.628i	−0.850255	+	0.850255i
$698$	69.2537	+	69.2537i	0.0992173	+	0.0992173i
$699$			644.737i			0.922371i
$700$	−541.550	−	281.023i	−0.773643	−	0.401461i
$701$	1097.97			1.56628			0.783142	−	0.621843i	$-0.213616\pi$
$701$	1097.97			1.56628			0.783142	+	0.621843i	$0.213616\pi$
$702$	10.0620	−	10.0620i	0.0143333	−	0.0143333i
$703$	1035.04	+	1035.04i	1.47232	+	1.47232i
$704$		−	79.6987i		−	0.113208i
$705$	53.8500	−	8.32399i	0.0763829	−	0.0118071i
$706$	−375.848			−0.532363
$707$	670.586	−	670.586i	0.948496	−	0.948496i
$708$	205.459	+	205.459i	0.290196	+	0.290196i
$709$			567.023i			0.799750i	0.916570	+	0.399875i	$0.130946\pi$
$709$			567.023i			0.799750i	−0.916570	+	0.399875i	$0.869054\pi$
$710$	−534.579	+	730.064i	−0.752928	+	1.02826i
$711$	81.4039			0.114492
$712$	168.744	−	168.744i	0.237000	−	0.237000i
$713$	134.480	+	134.480i	0.188612	+	0.188612i
$714$		−	543.875i		−	0.761730i
$715$	−77.8238	−	56.9854i	−0.108845	−	0.0796998i
$716$	132.889			0.185599
$717$	58.6053	−	58.6053i	0.0817368	−	0.0817368i
$718$	327.086	+	327.086i	0.455551	+	0.455551i
$719$		−	1190.36i		−	1.65557i	−0.561045	−	0.827785i	$-0.689601\pi$
$719$		−	1190.36i		−	1.65557i	0.561045	−	0.827785i	$-0.310399\pi$
$720$	9.16579	+	59.2958i	0.0127303	+	0.0823552i
$721$	730.589			1.01330
$722$	106.142	−	106.142i	0.147011	−	0.147011i
$723$	112.134	+	112.134i	0.155095	+	0.155095i
$724$		−	115.719i		−	0.159833i
$725$	309.971	+	978.683i	0.427546	+	1.34991i
$726$	−53.2810			−0.0733899
$727$	100.239	−	100.239i	0.137881	−	0.137881i	−0.634798	−	0.772678i	$-0.718917\pi$
$727$	100.239	−	100.239i	0.137881	−	0.137881i	0.772678	+	0.634798i	$0.218917\pi$
$728$	−47.2584	−	47.2584i	−0.0649153	−	0.0649153i
$729$		−	27.0000i		−	0.0370370i
$730$	589.161	−	91.0710i	0.807069	−	0.124755i
$731$	−1093.85			−1.49637
$732$	232.623	−	232.623i	0.317791	−	0.317791i
$733$	272.933	+	272.933i	0.372350	+	0.372350i	0.868333	−	0.495982i	$-0.165192\pi$
$733$	272.933	+	272.933i	0.372350	+	0.372350i	−0.495982	+	0.868333i	$0.665192\pi$
$734$		−	981.612i		−	1.33735i
$735$	511.127	−	698.036i	0.695410	−	0.949709i
$736$	27.1293			0.0368605
$737$	239.931	−	239.931i	0.325551	−	0.325551i
$738$	138.179	+	138.179i	0.187235	+	0.187235i
$739$		−	1375.85i		−	1.86177i	−0.365313	−	0.930885i	$-0.619038\pi$
$739$		−	1375.85i		−	1.86177i	0.365313	−	0.930885i	$-0.380962\pi$
$740$	−546.422	−	400.109i	−0.738408	−	0.540688i
$741$	72.4913			0.0978291
$742$	175.452	−	175.452i	0.236459	−	0.236459i
$743$	−200.083	−	200.083i	−0.269291	−	0.269291i	0.559524	−	0.828814i	$-0.310984\pi$
$743$	−200.083	−	200.083i	−0.269291	−	0.269291i	−0.828814	+	0.559524i	$0.810984\pi$
$744$		−	194.274i		−	0.261121i
$745$	−103.553	−	669.911i	−0.138998	−	0.899210i
$746$	42.0317			0.0563427
$747$	183.189	−	183.189i	0.245233	−	0.245233i
$748$	256.361	+	256.361i	0.342729	+	0.342729i
$749$			1845.92i			2.46451i
$750$	−274.347	+	135.956i	−0.365795	+	0.181274i
$751$	46.1912			0.0615063			0.0307531	−	0.999527i	$-0.490209\pi$
$751$	46.1912			0.0615063			0.0307531	+	0.999527i	$0.490209\pi$
$752$	−17.7962	+	17.7962i	−0.0236652	+	0.0236652i
$753$	−439.038	−	439.038i	−0.583052	−	0.583052i
$754$			112.454i			0.149144i
$755$	1099.06	−	169.891i	1.45571	−	0.225021i
$756$	−126.812			−0.167740
$757$	−379.305	+	379.305i	−0.501063	+	0.501063i	−0.911768	−	0.410705i	$-0.865283\pi$
$757$	−379.305	+	379.305i	−0.501063	+	0.501063i	0.410705	+	0.911768i	$0.365283\pi$
$758$	−310.295	−	310.295i	−0.409360	−	0.409360i
$759$			82.7534i			0.109029i
$760$	−180.581	+	246.615i	−0.237606	+	0.324494i
$761$	−496.235			−0.652083			−0.326042	−	0.945355i	$-0.605715\pi$
$761$	−496.235			−0.652083			−0.326042	+	0.945355i	$0.605715\pi$
$762$	297.284	−	297.284i	0.390136	−	0.390136i
$763$	−315.062	−	315.062i	−0.412926	−	0.412926i
$764$		−	11.0071i		−	0.0144072i
$765$	−220.215	−	161.249i	−0.287863	−	0.210784i
$766$	−493.893			−0.644769
$767$	−114.851	+	114.851i	−0.149741	+	0.149741i
$768$	−19.5959	−	19.5959i	−0.0255155	−	0.0255155i
$769$			128.084i			0.166560i	0.996526	+	0.0832798i	$0.0265395\pi$
$769$			128.084i			0.166560i	−0.996526	+	0.0832798i	$0.973460\pi$
$770$	131.314	+	849.506i	0.170538	+	1.10325i
$771$	−110.763			−0.143662
$772$	359.919	−	359.919i	0.466217	−	0.466217i
$773$	−52.1777	−	52.1777i	−0.0675003	−	0.0675003i	0.672551	−	0.740051i	$-0.265199\pi$
$773$	−52.1777	−	52.1777i	−0.0675003	−	0.0675003i	−0.740051	+	0.672551i	$0.765199\pi$
$774$			255.046i			0.329517i
$775$	945.130	−	299.344i	1.21952	−	0.386250i
$776$	−446.837			−0.575821
$777$	1012.14	−	1012.14i	1.30263	−	1.30263i
$778$	467.057	+	467.057i	0.600330	+	0.600330i
$779$			995.510i			1.27793i
$780$	−33.1462	+	5.12366i	−0.0424952	+	0.00656879i
$781$	1274.84			1.63232
$782$	−87.2649	+	87.2649i	−0.111592	+	0.111592i
$783$	150.878	+	150.878i	0.192693	+	0.192693i
$784$			399.601i			0.509695i
$785$	686.265	−	937.219i	0.874223	−	1.19391i
$786$	461.842			0.587586
$787$	433.630	−	433.630i	0.550991	−	0.550991i	−0.375736	−	0.926727i	$-0.622610\pi$
$787$	433.630	−	433.630i	0.550991	−	0.550991i	0.926727	+	0.375736i	$0.122610\pi$
$788$	−291.730	−	291.730i	−0.370216	−	0.370216i
$789$		−	18.0259i		−	0.0228465i
$790$	−154.807	−	113.355i	−0.195958	−	0.143487i
$791$	−184.055			−0.232687
$792$	59.7740	−	59.7740i	0.0754722	−	0.0754722i
$793$	130.036	+	130.036i	0.163980	+	0.163980i
$794$			774.056i			0.974882i
$795$	−19.0222	−	123.059i	−0.0239273	−	0.154792i
$796$	188.311			0.236572
$797$	−209.327	+	209.327i	−0.262643	+	0.262643i	−0.826127	−	0.563484i	$-0.809461\pi$
$797$	−209.327	+	209.327i	−0.262643	+	0.262643i	0.563484	+	0.826127i	$0.309461\pi$
$798$	−456.807	−	456.807i	−0.572440	−	0.572440i
$799$		−	114.487i		−	0.143288i
$800$	65.1386	−	125.527i	0.0814233	−	0.156908i
$801$	253.116			0.316000
$802$	448.866	−	448.866i	0.559684	−	0.559684i
$803$	−593.912	−	593.912i	−0.739617	−	0.739617i
$804$		−	117.986i		−	0.146749i
$805$	−289.171	+	44.6993i	−0.359218	+	0.0555270i
$806$	108.599			0.134738
$807$	−195.810	+	195.810i	−0.242639	+	0.242639i
$808$	155.436	+	155.436i	0.192371	+	0.192371i
$809$		−	1559.05i		−	1.92713i	−0.267469	−	0.963566i	$-0.586187\pi$
$809$		−	1559.05i		−	1.92713i	0.267469	−	0.963566i	$-0.413813\pi$
$810$	−37.5975	+	51.3462i	−0.0464166	+	0.0633903i
$811$	−203.515			−0.250943			−0.125471	−	0.992097i	$-0.540044\pi$
$811$	−203.515			−0.250943			−0.125471	+	0.992097i	$0.540044\pi$
$812$	708.635	−	708.635i	0.872704	−	0.872704i
$813$	−258.738	−	258.738i	−0.318251	−	0.318251i
$814$			954.165i			1.17219i
$815$	−288.654	−	211.362i	−0.354176	−	0.259340i
$816$	126.066			0.154492
$817$	−918.738	+	918.738i	−1.12453	+	1.12453i
$818$	335.091	+	335.091i	0.409647	+	0.409647i
$819$		−	70.8875i		−	0.0865538i
$820$	−70.3623	−	455.191i	−0.0858077	−	0.555111i
$821$	245.802			0.299393			0.149697	−	0.988732i	$-0.452170\pi$
$821$	245.802			0.299393			0.149697	+	0.988732i	$0.452170\pi$
$822$	−210.921	+	210.921i	−0.256595	+	0.256595i
$823$	725.015	+	725.015i	0.880942	+	0.880942i	0.993630	−	0.112688i	$-0.0359462\pi$
$823$	725.015	+	725.015i	0.880942	+	0.880942i	−0.112688	+	0.993630i	$0.535946\pi$
$824$			169.344i			0.205515i
$825$	382.898	+	198.694i	0.464119	+	0.240842i
$826$	1447.48			1.75239
$827$	40.3403	−	40.3403i	0.0487791	−	0.0487791i	−0.682296	−	0.731076i	$-0.739019\pi$
$827$	40.3403	−	40.3403i	0.0487791	−	0.0487791i	0.731076	+	0.682296i	$0.239019\pi$
$828$	20.3470	+	20.3470i	0.0245737	+	0.0245737i
$829$			112.945i			0.136243i	0.997677	+	0.0681213i	$0.0217005\pi$
$829$			112.945i			0.136243i	−0.997677	+	0.0681213i	$0.978300\pi$
$830$	−603.462	+	93.2817i	−0.727063	+	0.112388i
$831$	−537.353			−0.646635
$832$	10.9541	−	10.9541i	0.0131660	−	0.0131660i
$833$	−1285.37	−	1285.37i	−1.54306	−	1.54306i
$834$		−	356.262i		−	0.427173i
$835$	539.030	−	736.143i	0.645545	−	0.881608i
$836$	430.641			0.515121
$837$	145.706	−	145.706i	0.174081	−	0.174081i
$838$	235.423	+	235.423i	0.280934	+	0.280934i
$839$			1114.62i			1.32851i	0.747508	+	0.664253i	$0.231250\pi$
$839$			1114.62i			1.32851i	−0.747508	+	0.664253i	$0.768750\pi$
$840$	241.159	+	176.585i	0.287094	+	0.210221i
$841$	−845.243			−1.00505
$842$	326.446	−	326.446i	0.387703	−	0.387703i
$843$	−206.393	−	206.393i	−0.244832	−	0.244832i
$844$			72.0948i			0.0854204i
$845$	126.221	+	816.553i	0.149374	+	0.966335i
$846$	−26.6943			−0.0315536
$847$	−187.685	+	187.685i	−0.221588	+	0.221588i
$848$	40.6683	+	40.6683i	0.0479580	+	0.0479580i
$849$		−	379.074i		−	0.446495i
$850$	194.246	+	613.299i	0.228525	+	0.721529i
$851$	−324.796			−0.381664
$852$	313.452	−	313.452i	0.367902	−	0.367902i
$853$	968.069	+	968.069i	1.13490	+	1.13490i	0.989351	+	0.145547i	$0.0464943\pi$
$853$	968.069	+	968.069i	1.13490	+	1.13490i	0.145547	+	0.989351i	$0.453506\pi$
$854$		−	1638.85i		−	1.91903i
$855$	−320.397	+	49.5261i	−0.374733	+	0.0579253i
$856$	−427.869			−0.499846
$857$	−226.450	+	226.450i	−0.264235	+	0.264235i	−0.826772	−	0.562537i	$-0.809825\pi$
$857$	−226.450	+	226.450i	−0.264235	+	0.264235i	0.562537	+	0.826772i	$0.309825\pi$
$858$	33.4136	+	33.4136i	0.0389435	+	0.0389435i
$859$			130.650i			0.152096i	0.997104	+	0.0760478i	$0.0242301\pi$
$859$			130.650i			0.152096i	−0.997104	+	0.0760478i	$0.975770\pi$
$860$	355.151	−	485.023i	0.412966	−	0.563980i
$861$	973.486			1.13065
$862$	307.959	−	307.959i	0.357262	−	0.357262i
$863$	−433.283	−	433.283i	−0.502066	−	0.502066i	0.410014	−	0.912079i	$-0.365524\pi$
$863$	−433.283	−	433.283i	−0.502066	−	0.502066i	−0.912079	+	0.410014i	$0.865524\pi$
$864$		−	29.3939i		−	0.0340207i
$865$	−177.385	−	129.888i	−0.205069	−	0.150159i
$866$	−786.472			−0.908166
$867$	−51.5545	+	51.5545i	−0.0594631	+	0.0594631i
$868$	−684.341	−	684.341i	−0.788411	−	0.788411i
$869$			270.324i			0.311075i
$870$	−76.8289	−	497.025i	−0.0883090	−	0.571293i
$871$	65.9540			0.0757221
$872$	73.0287	−	73.0287i	0.0837485	−	0.0837485i
$873$	−335.128	−	335.128i	−0.383881	−	0.383881i
$874$			146.590i			0.167723i
$875$	−487.488	+	1445.31i	−0.557130	+	1.65178i
$876$	−292.057			−0.333398
$877$	1098.13	−	1098.13i	1.25215	−	1.25215i	0.297392	−	0.954755i	$-0.403883\pi$
$877$	1098.13	−	1098.13i	1.25215	−	1.25215i	0.954755	−	0.297392i	$-0.0961170\pi$
$878$	−330.522	−	330.522i	−0.376448	−	0.376448i
$879$			766.445i			0.871951i
$880$	−196.908	+	30.4376i	−0.223759	+	0.0345881i
$881$	−0.176371			−0.000200194			−0.000100097	−	1.00000i	$-0.500032\pi$
$881$	−0.176371			−0.000200194			−0.000100097		1.00000i	$0.500032\pi$
$882$	−299.701	+	299.701i	−0.339797	+	0.339797i
$883$	896.020	+	896.020i	1.01475	+	1.01475i	0.999890	+	0.0148558i	$0.00472891\pi$
$883$	896.020	+	896.020i	1.01475	+	1.01475i	0.0148558	+	0.999890i	$0.495271\pi$
$884$			70.4704i			0.0797176i
$885$	429.152	−	586.085i	0.484917	−	0.662242i
$886$	232.911			0.262879
$887$	358.656	−	358.656i	0.404348	−	0.404348i	−0.475414	−	0.879762i	$-0.657702\pi$
$887$	358.656	−	358.656i	0.404348	−	0.404348i	0.879762	+	0.475414i	$0.157702\pi$
$888$	234.605	+	234.605i	0.264195	+	0.264195i
$889$		−	2094.39i		−	2.35590i
$890$	−481.354	−	352.464i	−0.540847	−	0.396027i
$891$	89.6610			0.100630
$892$	136.875	−	136.875i	0.153447	−	0.153447i
$893$	−96.1594	−	96.1594i	−0.107681	−	0.107681i
$894$			332.086i			0.371461i
$895$	−50.7514	−	328.324i	−0.0567055	−	0.366842i
$896$	−138.055			−0.154079
$897$	−11.3739	+	11.3739i	−0.0126800	+	0.0126800i
$898$	−149.486	−	149.486i	−0.166465	−	0.166465i
$899$			1628.43i			1.81138i
$900$	142.999	−	45.2911i	0.158888	−	0.0503234i
$901$	−261.630			−0.290377
$902$	−458.862	+	458.862i	−0.508716	+	0.508716i
$903$	898.412	+	898.412i	0.994919	+	0.994919i
$904$		−	42.6624i		−	0.0471929i
$905$	−285.903	+	44.1942i	−0.315915	+	0.0488333i
$906$	−544.824			−0.601351
$907$	−81.2671	+	81.2671i	−0.0895999	+	0.0895999i	−0.750486	−	0.660886i	$-0.770181\pi$
$907$	−81.2671	+	81.2671i	−0.0895999	+	0.0895999i	0.660886	+	0.750486i	$0.270181\pi$
$908$	315.862	+	315.862i	0.347866	+	0.347866i
$909$			233.154i			0.256495i
$910$	−98.7109	+	134.808i	−0.108473	+	0.148140i
$911$	678.197			0.744453			0.372227	−	0.928142i	$-0.378594\pi$
$911$	678.197			0.744453			0.372227	+	0.928142i	$0.378594\pi$
$912$	105.884	−	105.884i	0.116101	−	0.116101i
$913$	608.330	+	608.330i	0.666297	+	0.666297i
$914$			518.357i			0.567130i
$915$	−663.573	−	485.892i	−0.725217	−	0.531029i
$916$	−557.489			−0.608612
$917$	1626.86	−	1626.86i	1.77411	−	1.77411i
$918$	94.5491	+	94.5491i	0.102995	+	0.102995i
$919$		−	1004.97i		−	1.09355i	−0.837281	−	0.546773i	$-0.815856\pi$
$919$		−	1004.97i		−	1.09355i	0.837281	−	0.546773i	$-0.184144\pi$
$920$	−10.3609	−	67.0272i	−0.0112619	−	0.0728557i
$921$	−161.742			−0.175616
$922$	804.421	−	804.421i	0.872474	−	0.872474i
$923$	175.219	+	175.219i	0.189837	+	0.189837i
$924$		−	421.114i		−	0.455751i
$925$	−779.850	+	1502.83i	−0.843081	+	1.62468i
$926$	−568.827			−0.614284
$927$	−127.008	+	127.008i	−0.137010	+	0.137010i
$928$	164.256	+	164.256i	0.177000	+	0.177000i
$929$			719.296i			0.774269i	0.922023	+	0.387134i	$0.126535\pi$
$929$			719.296i			0.774269i	−0.922023	+	0.387134i	$0.873465\pi$
$930$	−479.985	+	74.1949i	−0.516113	+	0.0797794i
$931$	−2159.19			−2.31922
$932$	−526.426	+	526.426i	−0.564834	+	0.564834i
$933$	58.4440	+	58.4440i	0.0626409	+	0.0626409i
$934$			1084.02i			1.16062i
$935$	535.474	−	731.286i	0.572699	−	0.782124i
$936$	16.4311			0.0175546
$937$	−73.5570	+	73.5570i	−0.0785027	+	0.0785027i	−0.745268	−	0.666765i	$-0.767678\pi$
$937$	−73.5570	+	73.5570i	−0.0785027	+	0.0785027i	0.666765	+	0.745268i	$0.267678\pi$
$938$	−415.612	−	415.612i	−0.443083	−	0.443083i
$939$			838.955i			0.893455i
$940$	50.7648	+	37.1718i	0.0540051	+	0.0395445i
$941$	647.565			0.688167			0.344084	−	0.938939i	$-0.388190\pi$
$941$	647.565			0.688167			0.344084	+	0.938939i	$0.388190\pi$
$942$	−402.394	+	402.394i	−0.427170	+	0.427170i
$943$	−156.196	−	156.196i	−0.165637	−	0.165637i
$944$			335.513i			0.355416i
$945$	48.4304	+	313.308i	0.0512491	+	0.331543i
$946$	−846.951			−0.895297
$947$	331.454	−	331.454i	0.350004	−	0.350004i	−0.510107	−	0.860111i	$-0.670394\pi$
$947$	331.454	−	331.454i	0.350004	−	0.350004i	0.860111	+	0.510107i	$0.170394\pi$
$948$	66.4660	+	66.4660i	0.0701118	+	0.0701118i
$949$		−	163.259i		−	0.172033i
$950$	678.267	+	351.968i	0.713965	+	0.370493i
$951$	−651.305			−0.684864
$952$	444.072	−	444.072i	0.466462	−	0.466462i
$953$	169.575	+	169.575i	0.177938	+	0.177938i	0.790457	−	0.612518i	$-0.209843\pi$
$953$	169.575	+	169.575i	0.177938	+	0.177938i	−0.612518	+	0.790457i	$0.709843\pi$
$954$			61.0025i			0.0639439i
$955$	−27.1947	+	4.20369i	−0.0284761	+	0.00440177i
$956$	95.7021			0.100107
$957$	−501.034	+	501.034i	−0.523546	+	0.523546i
$958$	419.970	+	419.970i	0.438382	+	0.438382i
$959$			1485.96i			1.54949i
$960$	−40.9310	+	55.8986i	−0.0426364	+	0.0582277i
$961$	611.603			0.636424
$962$	−131.144	+	131.144i	−0.136324	+	0.136324i
$963$	−320.901	−	320.901i	−0.333231	−	0.333231i
$964$			183.113i			0.189952i
$965$	−1026.69	−	751.781i	−1.06393	−	0.779048i
$966$	143.347			0.148392
$967$	−330.701	+	330.701i	−0.341986	+	0.341986i	−0.857114	−	0.515127i	$-0.827745\pi$
$967$	−330.701	+	330.701i	−0.341986	+	0.341986i	0.515127	+	0.857114i	$0.327745\pi$
$968$	−43.5038	−	43.5038i	−0.0449419	−	0.0449419i
$969$			681.178i			0.702971i
$970$	170.651	+	1103.98i	0.175928	+	1.13812i
$971$	1031.02			1.06181			0.530904	−	0.847432i	$-0.321853\pi$
$971$	1031.02			1.06181			0.530904	+	0.847432i	$0.321853\pi$
$972$	22.0454	−	22.0454i	0.0226805	−	0.0226805i
$973$	−1254.95	−	1254.95i	−1.28978	−	1.28978i
$974$		−	927.300i		−	0.952054i
$975$	25.3176	+	79.9362i	0.0259668	+	0.0819858i
$976$	379.872			0.389213
$977$	348.065	−	348.065i	0.356259	−	0.356259i	−0.506173	−	0.862432i	$-0.668940\pi$
$977$	348.065	−	348.065i	0.356259	−	0.356259i	0.862432	+	0.506173i	$0.168940\pi$
$978$	123.933	+	123.933i	0.126721	+	0.126721i
$979$			840.543i			0.858573i
$980$	987.277	−	152.611i	1.00743	−	0.155725i
$981$	109.543			0.111665
$982$	81.2134	−	81.2134i	0.0827021	−	0.0827021i
$983$	−358.451	−	358.451i	−0.364650	−	0.364650i	0.500872	−	0.865522i	$-0.333013\pi$
$983$	−358.451	−	358.451i	−0.364650	−	0.364650i	−0.865522	+	0.500872i	$0.833013\pi$
$984$			225.646i			0.229315i
$985$	−609.351	+	832.179i	−0.618631	+	0.844852i
$986$	−1056.70			−1.07170
$987$	−94.0320	+	94.0320i	−0.0952705	+	0.0952705i
$988$	59.1889	+	59.1889i	0.0599078	+	0.0599078i
$989$		−	288.301i		−	0.291507i
$990$	−170.509	−	124.853i	−0.172232	−	0.126114i
$991$	1743.30			1.75913			0.879565	−	0.475779i	$-0.157834\pi$
$991$	1743.30			1.75913			0.879565	+	0.475779i	$0.157834\pi$
$992$	158.624	−	158.624i	0.159903	−	0.159903i
$993$	60.3584	+	60.3584i	0.0607838	+	0.0607838i
$994$		−	2208.30i		−	2.22163i
$995$	−71.9175	−	465.252i	−0.0722789	−	0.467590i
$996$	299.146			0.300348
$997$	1281.65	−	1281.65i	1.28551	−	1.28551i	0.348021	−	0.937487i	$-0.386854\pi$
$997$	1281.65	−	1281.65i	1.28551	−	1.28551i	0.937487	−	0.348021i	$-0.113146\pi$
$998$	486.389	+	486.389i	0.487364	+	0.487364i
$999$			351.908i			0.352260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.3.k.b.553.11	yes	48
5.2	odd	4	inner	690.3.k.b.277.11	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.3.k.b.277.11	✓	48	5.2	odd	4	inner
690.3.k.b.553.11	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.94131 + 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 - 8.62845i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-1.22474 - 1.22474i) q^{3} -2.00000i q^{4} +(-4.94131 + 0.763816i) q^{5} +2.44949 q^{6} +(8.62845 - 8.62845i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000i q^{9} +(4.17750 - 5.70513i) q^{10} -9.96233 q^{11} +(-2.44949 + 2.44949i) q^{12} +(-1.36926 - 1.36926i) q^{13} +17.2569i q^{14} +(6.98733 + 5.11637i) q^{15} -4.00000 q^{16} +(12.8665 - 12.8665i) q^{17} +(-3.00000 - 3.00000i) q^{18} -21.6135i q^{19} +(1.52763 + 9.88263i) q^{20} -21.1353 q^{21} +(9.96233 - 9.96233i) q^{22} +(3.39116 + 3.39116i) q^{23} -4.89898i q^{24} +(23.8332 - 7.54851i) q^{25} +2.73852 q^{26} +(3.67423 - 3.67423i) q^{27} +(-17.2569 - 17.2569i) q^{28} +41.0639i q^{29} +(-12.1037 + 1.87096i) q^{30} +39.6561 q^{31} +(4.00000 - 4.00000i) q^{32} +(12.2013 + 12.2013i) q^{33} +25.7330i q^{34} +(-36.0453 + 49.2264i) q^{35} +6.00000 q^{36} +(-47.8886 + 47.8886i) q^{37} +(21.6135 + 21.6135i) q^{38} +3.35399i q^{39} +(-11.4103 - 8.35500i) q^{40} -46.0597 q^{41} +(21.1353 - 21.1353i) q^{42} +(-42.5076 - 42.5076i) q^{43} +19.9247i q^{44} +(-2.29145 - 14.8239i) q^{45} -6.78233 q^{46} +(4.44905 - 4.44905i) q^{47} +(4.89898 + 4.89898i) q^{48} -99.9003i q^{49} +(-16.2847 + 31.3817i) q^{50} -31.5164 q^{51} +(-2.73852 + 2.73852i) q^{52} +(-10.1671 - 10.1671i) q^{53} +7.34847i q^{54} +(49.2270 - 7.60939i) q^{55} +34.5138 q^{56} +(-26.4710 + 26.4710i) q^{57} +(-41.0639 - 41.0639i) q^{58} -83.8782i q^{59} +(10.2327 - 13.9747i) q^{60} -94.9681 q^{61} +(-39.6561 + 39.6561i) q^{62} +(25.8853 + 25.8853i) q^{63} +8.00000i q^{64} +(7.81181 + 5.72008i) q^{65} -24.4026 q^{66} +(-24.0838 + 24.0838i) q^{67} +(-25.7330 - 25.7330i) q^{68} -8.30662i q^{69} +(-13.1811 - 85.2718i) q^{70} -127.966 q^{71} +(-6.00000 + 6.00000i) q^{72} +(59.6158 + 59.6158i) q^{73} -95.7772i q^{74} +(-38.4346 - 19.9446i) q^{75} -43.2269 q^{76} +(-85.9595 + 85.9595i) q^{77} +(-3.35399 - 3.35399i) q^{78} -27.1346i q^{79} +(19.7653 - 3.05526i) q^{80} -9.00000 q^{81} +(46.0597 - 46.0597i) q^{82} +(-61.0630 - 61.0630i) q^{83} +42.2706i q^{84} +(-53.7498 + 73.4051i) q^{85} +85.0153 q^{86} +(50.2928 - 50.2928i) q^{87} +(-19.9247 - 19.9247i) q^{88} -84.3721i q^{89} +(17.1154 + 12.5325i) q^{90} -23.6292 q^{91} +(6.78233 - 6.78233i) q^{92} +(-48.5686 - 48.5686i) q^{93} +8.89810i q^{94} +(16.5087 + 106.799i) q^{95} -9.79796 q^{96} +(-111.709 + 111.709i) q^{97} +(99.9003 + 99.9003i) q^{98} -29.8870i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8}+O(q^{10}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8	\( 48 q - 48 q^{2} - 8 q^{5} - 8 q^{7} + 96 q^{8} + 8 q^{10} - 32 q^{11} - 24 q^{13} + 24 q^{15} - 192 q^{16} + 72 q^{17} - 144 q^{18} + 32 q^{22} + 24 q^{25} + 48 q^{26} + 16 q^{28} - 24 q^{30} + 24 q^{31} + 192 q^{32} - 24 q^{33} + 288 q^{36} - 128 q^{37} - 16 q^{38} - 16 q^{40} - 40 q^{41} + 48 q^{43} - 136 q^{47} - 80 q^{50} - 48 q^{52} + 144 q^{53} - 144 q^{55} - 32 q^{56} + 96 q^{57} + 8 q^{58} + 128 q^{61} - 24 q^{62} - 24 q^{63} + 184 q^{65} + 48 q^{66} - 144 q^{68} + 40 q^{70} - 40 q^{71} - 288 q^{72} + 40 q^{73} - 72 q^{75} + 32 q^{76} - 104 q^{77} + 96 q^{78} + 32 q^{80} - 432 q^{81} + 40 q^{82} - 88 q^{85} - 96 q^{86} + 120 q^{87} - 64 q^{88} + 24 q^{90} + 144 q^{91} - 96 q^{93} + 312 q^{95} + 480 q^{97} + 584 q^{98}+O(q^{100}) \) 48 * q - 48 * q^2 - 8 * q^5 - 8 * q^7 + 96 * q^8 + 8 * q^10 - 32 * q^11 - 24 * q^13 + 24 * q^15 - 192 * q^16 + 72 * q^17 - 144 * q^18 + 32 * q^22 + 24 * q^25 + 48 * q^26 + 16 * q^28 - 24 * q^30 + 24 * q^31 + 192 * q^32 - 24 * q^33 + 288 * q^36 - 128 * q^37 - 16 * q^38 - 16 * q^40 - 40 * q^41 + 48 * q^43 - 136 * q^47 - 80 * q^50 - 48 * q^52 + 144 * q^53 - 144 * q^55 - 32 * q^56 + 96 * q^57 + 8 * q^58 + 128 * q^61 - 24 * q^62 - 24 * q^63 + 184 * q^65 + 48 * q^66 - 144 * q^68 + 40 * q^70 - 40 * q^71 - 288 * q^72 + 40 * q^73 - 72 * q^75 + 32 * q^76 - 104 * q^77 + 96 * q^78 + 32 * q^80 - 432 * q^81 + 40 * q^82 - 88 * q^85 - 96 * q^86 + 120 * q^87 - 64 * q^88 + 24 * q^90 + 144 * q^91 - 96 * q^93 + 312 * q^95 + 480 * q^97 + 584 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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