LMFDB - Embedded newform 462.2.g.b.419.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.4
Root			$1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.b.419.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(1.22474 + 1.22474i) q^{6} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(1.22474 + 1.22474i) q^{6} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} -3.00000i q^{9} +2.44949i q^{10} -1.00000i q^{11} +(-1.22474 + 1.22474i) q^{12} -2.44949i q^{13} +(2.44949 - 1.00000i) q^{14} +(3.00000 - 3.00000i) q^{15} +1.00000 q^{16} +3.00000 q^{18} +7.34847i q^{19} -2.44949 q^{20} +(-4.22474 - 1.77526i) q^{21} +1.00000 q^{22} -6.00000i q^{23} +(-1.22474 - 1.22474i) q^{24} +1.00000 q^{25} +2.44949 q^{26} +(-3.67423 - 3.67423i) q^{27} +(1.00000 + 2.44949i) q^{28} +6.00000i q^{29} +(3.00000 + 3.00000i) q^{30} +4.89898i q^{31} +1.00000i q^{32} +(-1.22474 - 1.22474i) q^{33} +(-2.44949 - 6.00000i) q^{35} +3.00000i q^{36} +10.0000 q^{37} -7.34847 q^{38} +(-3.00000 - 3.00000i) q^{39} -2.44949i q^{40} +9.79796 q^{41} +(1.77526 - 4.22474i) q^{42} -8.00000 q^{43} +1.00000i q^{44} -7.34847i q^{45} +6.00000 q^{46} +9.79796 q^{47} +(1.22474 - 1.22474i) q^{48} +(-5.00000 + 4.89898i) q^{49} +1.00000i q^{50} +2.44949i q^{52} +6.00000i q^{53} +(3.67423 - 3.67423i) q^{54} -2.44949i q^{55} +(-2.44949 + 1.00000i) q^{56} +(9.00000 + 9.00000i) q^{57} -6.00000 q^{58} -2.44949 q^{59} +(-3.00000 + 3.00000i) q^{60} +7.34847i q^{61} -4.89898 q^{62} +(-7.34847 + 3.00000i) q^{63} -1.00000 q^{64} -6.00000i q^{65} +(1.22474 - 1.22474i) q^{66} -4.00000 q^{67} +(-7.34847 - 7.34847i) q^{69} +(6.00000 - 2.44949i) q^{70} -3.00000 q^{72} +4.89898i q^{73} +10.0000i q^{74} +(1.22474 - 1.22474i) q^{75} -7.34847i q^{76} +(-2.44949 + 1.00000i) q^{77} +(3.00000 - 3.00000i) q^{78} -10.0000 q^{79} +2.44949 q^{80} -9.00000 q^{81} +9.79796i q^{82} -2.44949 q^{83} +(4.22474 + 1.77526i) q^{84} -8.00000i q^{86} +(7.34847 + 7.34847i) q^{87} -1.00000 q^{88} +9.79796 q^{89} +7.34847 q^{90} +(-6.00000 + 2.44949i) q^{91} +6.00000i q^{92} +(6.00000 + 6.00000i) q^{93} +9.79796i q^{94} +18.0000i q^{95} +(1.22474 + 1.22474i) q^{96} -4.89898i q^{97} +(-4.89898 - 5.00000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^4 - 4 * q^7	$ 4 q - 4 q^{4} - 4 q^{7} + 12 q^{15} + 4 q^{16} + 12 q^{18} - 12 q^{21} + 4 q^{22} + 4 q^{25} + 4 q^{28} + 12 q^{30} + 40 q^{37} - 12 q^{39} + 12 q^{42} - 32 q^{43} + 24 q^{46} - 20 q^{49} + 36 q^{57} - 24 q^{58} - 12 q^{60} - 4 q^{64} - 16 q^{67} + 24 q^{70} - 12 q^{72} + 12 q^{78} - 40 q^{79} - 36 q^{81} + 12 q^{84} - 4 q^{88} - 24 q^{91} + 24 q^{93} - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 - 4 * q^7 + 12 * q^15 + 4 * q^16 + 12 * q^18 - 12 * q^21 + 4 * q^22 + 4 * q^25 + 4 * q^28 + 12 * q^30 + 40 * q^37 - 12 * q^39 + 12 * q^42 - 32 * q^43 + 24 * q^46 - 20 * q^49 + 36 * q^57 - 24 * q^58 - 12 * q^60 - 4 * q^64 - 16 * q^67 + 24 * q^70 - 12 * q^72 + 12 * q^78 - 40 * q^79 - 36 * q^81 + 12 * q^84 - 4 * q^88 - 24 * q^91 + 24 * q^93 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$3$	1.22474	−	1.22474i	0.707107	−	0.707107i
$4$	−1.00000			−0.500000
$5$	2.44949			1.09545			0.547723	−	0.836660i	$-0.315495\pi$
$5$	2.44949			1.09545			0.547723	+	0.836660i	$0.315495\pi$
$6$	1.22474	+	1.22474i	0.500000	+	0.500000i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$7$	−1.00000	−	2.44949i	−0.377964	−	0.925820i
$8$		−	1.00000i		−	0.353553i
$9$		−	3.00000i		−	1.00000i
$10$			2.44949i			0.774597i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−1.22474	+	1.22474i	−0.353553	+	0.353553i
$13$		−	2.44949i		−	0.679366i	−0.940540	−	0.339683i	$-0.889680\pi$
$13$		−	2.44949i		−	0.679366i	0.940540	−	0.339683i	$-0.110320\pi$
$14$	2.44949	−	1.00000i	0.654654	−	0.267261i
$15$	3.00000	−	3.00000i	0.774597	−	0.774597i
$16$	1.00000			0.250000
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	3.00000			0.707107
$19$			7.34847i			1.68585i	0.538028	+	0.842927i	$0.319170\pi$
$19$			7.34847i			1.68585i	−0.538028	+	0.842927i	$0.680830\pi$
$20$	−2.44949			−0.547723
$21$	−4.22474	−	1.77526i	−0.921915	−	0.387392i
$22$	1.00000			0.213201
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$	−1.22474	−	1.22474i	−0.250000	−	0.250000i
$25$	1.00000			0.200000
$26$	2.44949			0.480384
$27$	−3.67423	−	3.67423i	−0.707107	−	0.707107i
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$	3.00000	+	3.00000i	0.547723	+	0.547723i
$31$			4.89898i			0.879883i	0.898027	+	0.439941i	$0.145001\pi$
$31$			4.89898i			0.879883i	−0.898027	+	0.439941i	$0.854999\pi$
$32$			1.00000i			0.176777i
$33$	−1.22474	−	1.22474i	−0.213201	−	0.213201i
$34$		0			0
$35$	−2.44949	−	6.00000i	−0.414039	−	1.01419i
$36$			3.00000i			0.500000i
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$	−7.34847			−1.19208
$39$	−3.00000	−	3.00000i	−0.480384	−	0.480384i
$40$		−	2.44949i		−	0.387298i
$41$	9.79796			1.53018			0.765092	−	0.643921i	$-0.222693\pi$
$41$	9.79796			1.53018			0.765092	+	0.643921i	$0.222693\pi$
$42$	1.77526	−	4.22474i	0.273928	−	0.651892i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$			1.00000i			0.150756i
$45$		−	7.34847i		−	1.09545i
$46$	6.00000			0.884652
$47$	9.79796			1.42918			0.714590	−	0.699544i	$-0.246613\pi$
$47$	9.79796			1.42918			0.714590	+	0.699544i	$0.246613\pi$
$48$	1.22474	−	1.22474i	0.176777	−	0.176777i
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$			1.00000i			0.141421i
$51$		0			0
$52$			2.44949i			0.339683i
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$	3.67423	−	3.67423i	0.500000	−	0.500000i
$55$		−	2.44949i		−	0.330289i
$56$	−2.44949	+	1.00000i	−0.327327	+	0.133631i
$57$	9.00000	+	9.00000i	1.19208	+	1.19208i
$58$	−6.00000			−0.787839
$59$	−2.44949			−0.318896			−0.159448	−	0.987206i	$-0.550971\pi$
$59$	−2.44949			−0.318896			−0.159448	+	0.987206i	$0.550971\pi$
$60$	−3.00000	+	3.00000i	−0.387298	+	0.387298i
$61$			7.34847i			0.940875i	0.882433	+	0.470438i	$0.155904\pi$
$61$			7.34847i			0.940875i	−0.882433	+	0.470438i	$0.844096\pi$
$62$	−4.89898			−0.622171
$63$	−7.34847	+	3.00000i	−0.925820	+	0.377964i
$64$	−1.00000			−0.125000
$65$		−	6.00000i		−	0.744208i
$66$	1.22474	−	1.22474i	0.150756	−	0.150756i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	−7.34847	−	7.34847i	−0.884652	−	0.884652i
$70$	6.00000	−	2.44949i	0.717137	−	0.292770i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−3.00000			−0.353553
$73$			4.89898i			0.573382i	0.958023	+	0.286691i	$0.0925553\pi$
$73$			4.89898i			0.573382i	−0.958023	+	0.286691i	$0.907445\pi$
$74$			10.0000i			1.16248i
$75$	1.22474	−	1.22474i	0.141421	−	0.141421i
$76$		−	7.34847i		−	0.842927i
$77$	−2.44949	+	1.00000i	−0.279145	+	0.113961i
$78$	3.00000	−	3.00000i	0.339683	−	0.339683i
$79$	−10.0000			−1.12509			−0.562544	−	0.826767i	$-0.690177\pi$
$79$	−10.0000			−1.12509			−0.562544	+	0.826767i	$0.690177\pi$
$80$	2.44949			0.273861
$81$	−9.00000			−1.00000
$82$			9.79796i			1.08200i
$83$	−2.44949			−0.268866			−0.134433	−	0.990923i	$-0.542921\pi$
$83$	−2.44949			−0.268866			−0.134433	+	0.990923i	$0.542921\pi$
$84$	4.22474	+	1.77526i	0.460957	+	0.193696i
$85$		0			0
$86$		−	8.00000i		−	0.862662i
$87$	7.34847	+	7.34847i	0.787839	+	0.787839i
$88$	−1.00000			−0.106600
$89$	9.79796			1.03858			0.519291	−	0.854598i	$-0.326196\pi$
$89$	9.79796			1.03858			0.519291	+	0.854598i	$0.326196\pi$
$90$	7.34847			0.774597
$91$	−6.00000	+	2.44949i	−0.628971	+	0.256776i
$92$			6.00000i			0.625543i
$93$	6.00000	+	6.00000i	0.622171	+	0.622171i
$94$			9.79796i			1.01058i
$95$			18.0000i			1.84676i
$96$	1.22474	+	1.22474i	0.125000	+	0.125000i
$97$		−	4.89898i		−	0.497416i	−0.968579	−	0.248708i	$-0.919994\pi$
$97$		−	4.89898i		−	0.497416i	0.968579	−	0.248708i	$-0.0800060\pi$
$98$	−4.89898	−	5.00000i	−0.494872	−	0.505076i
$99$	−3.00000			−0.301511
$100$	−1.00000			−0.100000
$101$	−2.44949			−0.243733			−0.121867	−	0.992546i	$-0.538888\pi$
$101$	−2.44949			−0.243733			−0.121867	+	0.992546i	$0.538888\pi$
$102$		0			0
$103$			4.89898i			0.482711i	0.970437	+	0.241355i	$0.0775919\pi$
$103$			4.89898i			0.482711i	−0.970437	+	0.241355i	$0.922408\pi$
$104$	−2.44949			−0.240192
$105$	−10.3485	−	4.34847i	−1.00991	−	0.424367i
$106$	−6.00000			−0.582772
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	3.67423	+	3.67423i	0.353553	+	0.353553i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$	2.44949			0.233550
$111$	12.2474	−	12.2474i	1.16248	−	1.16248i
$112$	−1.00000	−	2.44949i	−0.0944911	−	0.231455i
$113$		−	18.0000i		−	1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$		−	18.0000i		−	1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$	−9.00000	+	9.00000i	−0.842927	+	0.842927i
$115$		−	14.6969i		−	1.37050i
$116$		−	6.00000i		−	0.557086i
$117$	−7.34847			−0.679366
$118$		−	2.44949i		−	0.225494i
$119$		0			0
$120$	−3.00000	−	3.00000i	−0.273861	−	0.273861i
$121$	−1.00000			−0.0909091
$122$	−7.34847			−0.665299
$123$	12.0000	−	12.0000i	1.08200	−	1.08200i
$124$		−	4.89898i		−	0.439941i
$125$	−9.79796			−0.876356
$126$	−3.00000	−	7.34847i	−0.267261	−	0.654654i
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−9.79796	+	9.79796i	−0.862662	+	0.862662i
$130$	6.00000			0.526235
$131$	2.44949			0.214013			0.107006	−	0.994258i	$-0.465873\pi$
$131$	2.44949			0.214013			0.107006	+	0.994258i	$0.465873\pi$
$132$	1.22474	+	1.22474i	0.106600	+	0.106600i
$133$	18.0000	−	7.34847i	1.56080	−	0.637193i
$134$		−	4.00000i		−	0.345547i
$135$	−9.00000	−	9.00000i	−0.774597	−	0.774597i
$136$		0			0
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	7.34847	−	7.34847i	0.625543	−	0.625543i
$139$		−	12.2474i		−	1.03882i	−0.854527	−	0.519408i	$-0.826153\pi$
$139$		−	12.2474i		−	1.03882i	0.854527	−	0.519408i	$-0.173847\pi$
$140$	2.44949	+	6.00000i	0.207020	+	0.507093i
$141$	12.0000	−	12.0000i	1.01058	−	1.01058i
$142$		0			0
$143$	−2.44949			−0.204837
$144$		−	3.00000i		−	0.250000i
$145$			14.6969i			1.22051i
$146$	−4.89898			−0.405442
$147$	−0.123724	+	12.1237i	−0.0102046	+	0.999948i
$148$	−10.0000			−0.821995
$149$			18.0000i			1.47462i	0.675556	+	0.737309i	$0.263904\pi$
$149$			18.0000i			1.47462i	−0.675556	+	0.737309i	$0.736096\pi$
$150$	1.22474	+	1.22474i	0.100000	+	0.100000i
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	7.34847			0.596040
$153$		0			0
$154$	−1.00000	−	2.44949i	−0.0805823	−	0.197386i
$155$			12.0000i			0.963863i
$156$	3.00000	+	3.00000i	0.240192	+	0.240192i
$157$		−	12.2474i		−	0.977453i	−0.872437	−	0.488726i	$-0.837462\pi$
$157$		−	12.2474i		−	0.977453i	0.872437	−	0.488726i	$-0.162538\pi$
$158$		−	10.0000i		−	0.795557i
$159$	7.34847	+	7.34847i	0.582772	+	0.582772i
$160$			2.44949i			0.193649i
$161$	−14.6969	+	6.00000i	−1.15828	+	0.472866i
$162$		−	9.00000i		−	0.707107i
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−9.79796			−0.765092
$165$	−3.00000	−	3.00000i	−0.233550	−	0.233550i
$166$		−	2.44949i		−	0.190117i
$167$	−14.6969			−1.13728			−0.568642	−	0.822585i	$-0.692531\pi$
$167$	−14.6969			−1.13728			−0.568642	+	0.822585i	$0.692531\pi$
$168$	−1.77526	+	4.22474i	−0.136964	+	0.325946i
$169$	7.00000			0.538462
$170$		0			0
$171$	22.0454			1.68585
$172$	8.00000			0.609994
$173$	−2.44949			−0.186231			−0.0931156	−	0.995655i	$-0.529683\pi$
$173$	−2.44949			−0.186231			−0.0931156	+	0.995655i	$0.529683\pi$
$174$	−7.34847	+	7.34847i	−0.557086	+	0.557086i
$175$	−1.00000	−	2.44949i	−0.0755929	−	0.185164i
$176$		−	1.00000i		−	0.0753778i
$177$	−3.00000	+	3.00000i	−0.225494	+	0.225494i
$178$			9.79796i			0.734388i
$179$		−	24.0000i		−	1.79384i	−0.442189	−	0.896922i	$-0.645798\pi$
$179$		−	24.0000i		−	1.79384i	0.442189	−	0.896922i	$-0.354202\pi$
$180$			7.34847i			0.547723i
$181$			17.1464i			1.27448i	0.770664	+	0.637242i	$0.219925\pi$
$181$			17.1464i			1.27448i	−0.770664	+	0.637242i	$0.780075\pi$
$182$	−2.44949	−	6.00000i	−0.181568	−	0.444750i
$183$	9.00000	+	9.00000i	0.665299	+	0.665299i
$184$	−6.00000			−0.442326
$185$	24.4949			1.80090
$186$	−6.00000	+	6.00000i	−0.439941	+	0.439941i
$187$		0			0
$188$	−9.79796			−0.714590
$189$	−5.32577	+	12.6742i	−0.387392	+	0.921915i
$190$	−18.0000			−1.30586
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−1.22474	+	1.22474i	−0.0883883	+	0.0883883i
$193$	16.0000			1.15171			0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000			1.15171			0.575853	+	0.817554i	$0.304670\pi$
$194$	4.89898			0.351726
$195$	−7.34847	−	7.34847i	−0.526235	−	0.526235i
$196$	5.00000	−	4.89898i	0.357143	−	0.349927i
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$		−	3.00000i		−	0.213201i
$199$			14.6969i			1.04184i	0.853606	+	0.520919i	$0.174411\pi$
$199$			14.6969i			1.04184i	−0.853606	+	0.520919i	$0.825589\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	−4.89898	+	4.89898i	−0.345547	+	0.345547i
$202$		−	2.44949i		−	0.172345i
$203$	14.6969	−	6.00000i	1.03152	−	0.421117i
$204$		0			0
$205$	24.0000			1.67623
$206$	−4.89898			−0.341328
$207$	−18.0000			−1.25109
$208$		−	2.44949i		−	0.169842i
$209$	7.34847			0.508304
$210$	4.34847	−	10.3485i	0.300073	−	0.714112i
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$		−	6.00000i		−	0.412082i
$213$		0			0
$214$		0			0
$215$	−19.5959			−1.33643
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$	12.0000	−	4.89898i	0.814613	−	0.332564i
$218$		−	14.0000i		−	0.948200i
$219$	6.00000	+	6.00000i	0.405442	+	0.405442i
$220$			2.44949i			0.165145i
$221$		0			0
$222$	12.2474	+	12.2474i	0.821995	+	0.821995i
$223$			9.79796i			0.656120i	0.944657	+	0.328060i	$0.106395\pi$
$223$			9.79796i			0.656120i	−0.944657	+	0.328060i	$0.893605\pi$
$224$	2.44949	−	1.00000i	0.163663	−	0.0668153i
$225$		−	3.00000i		−	0.200000i
$226$	18.0000			1.19734
$227$	17.1464			1.13805			0.569024	−	0.822321i	$-0.307321\pi$
$227$	17.1464			1.13805			0.569024	+	0.822321i	$0.307321\pi$
$228$	−9.00000	−	9.00000i	−0.596040	−	0.596040i
$229$		−	7.34847i		−	0.485601i	−0.970076	−	0.242800i	$-0.921934\pi$
$229$		−	7.34847i		−	0.485601i	0.970076	−	0.242800i	$-0.0780660\pi$
$230$	14.6969			0.969087
$231$	−1.77526	+	4.22474i	−0.116803	+	0.277968i
$232$	6.00000			0.393919
$233$			12.0000i			0.786146i	0.919507	+	0.393073i	$0.128588\pi$
$233$			12.0000i			0.786146i	−0.919507	+	0.393073i	$0.871412\pi$
$234$		−	7.34847i		−	0.480384i
$235$	24.0000			1.56559
$236$	2.44949			0.159448
$237$	−12.2474	+	12.2474i	−0.795557	+	0.795557i
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$	3.00000	−	3.00000i	0.193649	−	0.193649i
$241$		−	19.5959i		−	1.26228i	−0.775667	−	0.631142i	$-0.782587\pi$
$241$		−	19.5959i		−	1.26228i	0.775667	−	0.631142i	$-0.217413\pi$
$242$		−	1.00000i		−	0.0642824i
$243$	−11.0227	+	11.0227i	−0.707107	+	0.707107i
$244$		−	7.34847i		−	0.470438i
$245$	−12.2474	+	12.0000i	−0.782461	+	0.766652i
$246$	12.0000	+	12.0000i	0.765092	+	0.765092i
$247$	18.0000			1.14531
$248$	4.89898			0.311086
$249$	−3.00000	+	3.00000i	−0.190117	+	0.190117i
$250$		−	9.79796i		−	0.619677i
$251$	12.2474			0.773052			0.386526	−	0.922278i	$-0.373675\pi$
$251$	12.2474			0.773052			0.386526	+	0.922278i	$0.373675\pi$
$252$	7.34847	−	3.00000i	0.462910	−	0.188982i
$253$	−6.00000			−0.377217
$254$		−	16.0000i		−	1.00393i
$255$		0			0
$256$	1.00000			0.0625000
$257$	19.5959			1.22236			0.611180	−	0.791492i	$-0.290695\pi$
$257$	19.5959			1.22236			0.611180	+	0.791492i	$0.290695\pi$
$258$	−9.79796	−	9.79796i	−0.609994	−	0.609994i
$259$	−10.0000	−	24.4949i	−0.621370	−	1.52204i
$260$			6.00000i			0.372104i
$261$	18.0000			1.11417
$262$			2.44949i			0.151330i
$263$		−	24.0000i		−	1.47990i	−0.672660	−	0.739952i	$-0.734848\pi$
$263$		−	24.0000i		−	1.47990i	0.672660	−	0.739952i	$-0.265152\pi$
$264$	−1.22474	+	1.22474i	−0.0753778	+	0.0753778i
$265$			14.6969i			0.902826i
$266$	7.34847	+	18.0000i	0.450564	+	1.10365i
$267$	12.0000	−	12.0000i	0.734388	−	0.734388i
$268$	4.00000			0.244339
$269$	2.44949			0.149348			0.0746740	−	0.997208i	$-0.476208\pi$
$269$	2.44949			0.149348			0.0746740	+	0.997208i	$0.476208\pi$
$270$	9.00000	−	9.00000i	0.547723	−	0.547723i
$271$			4.89898i			0.297592i	0.988868	+	0.148796i	$0.0475397\pi$
$271$			4.89898i			0.297592i	−0.988868	+	0.148796i	$0.952460\pi$
$272$		0			0
$273$	−4.34847	+	10.3485i	−0.263181	+	0.626318i
$274$	−12.0000			−0.724947
$275$		−	1.00000i		−	0.0603023i
$276$	7.34847	+	7.34847i	0.442326	+	0.442326i
$277$	2.00000			0.120168			0.0600842	−	0.998193i	$-0.480863\pi$
$277$	2.00000			0.120168			0.0600842	+	0.998193i	$0.480863\pi$
$278$	12.2474			0.734553
$279$	14.6969			0.879883
$280$	−6.00000	+	2.44949i	−0.358569	+	0.146385i
$281$		−	12.0000i		−	0.715860i	−0.933748	−	0.357930i	$-0.883483\pi$
$281$		−	12.0000i		−	0.715860i	0.933748	−	0.357930i	$-0.116517\pi$
$282$	12.0000	+	12.0000i	0.714590	+	0.714590i
$283$		−	2.44949i		−	0.145607i	−0.997346	−	0.0728035i	$-0.976805\pi$
$283$		−	2.44949i		−	0.145607i	0.997346	−	0.0728035i	$-0.0231946\pi$
$284$		0			0
$285$	22.0454	+	22.0454i	1.30586	+	1.30586i
$286$		−	2.44949i		−	0.144841i
$287$	−9.79796	−	24.0000i	−0.578355	−	1.41668i
$288$	3.00000			0.176777
$289$	−17.0000			−1.00000
$290$	−14.6969			−0.863034
$291$	−6.00000	−	6.00000i	−0.351726	−	0.351726i
$292$		−	4.89898i		−	0.286691i
$293$	−17.1464			−1.00171			−0.500853	−	0.865533i	$-0.666980\pi$
$293$	−17.1464			−1.00171			−0.500853	+	0.865533i	$0.666980\pi$
$294$	−12.1237	−	0.123724i	−0.707070	−	0.00721575i
$295$	−6.00000			−0.349334
$296$		−	10.0000i		−	0.581238i
$297$	−3.67423	+	3.67423i	−0.213201	+	0.213201i
$298$	−18.0000			−1.04271
$299$	−14.6969			−0.849946
$300$	−1.22474	+	1.22474i	−0.0707107	+	0.0707107i
$301$	8.00000	+	19.5959i	0.461112	+	1.12949i
$302$			16.0000i			0.920697i
$303$	−3.00000	+	3.00000i	−0.172345	+	0.172345i
$304$			7.34847i			0.421464i
$305$			18.0000i			1.03068i
$306$		0			0
$307$		−	31.8434i		−	1.81740i	−0.417453	−	0.908698i	$-0.637077\pi$
$307$		−	31.8434i		−	1.81740i	0.417453	−	0.908698i	$-0.362923\pi$
$308$	2.44949	−	1.00000i	0.139573	−	0.0569803i
$309$	6.00000	+	6.00000i	0.341328	+	0.341328i
$310$	−12.0000			−0.681554
$311$	14.6969			0.833387			0.416693	−	0.909047i	$-0.363189\pi$
$311$	14.6969			0.833387			0.416693	+	0.909047i	$0.363189\pi$
$312$	−3.00000	+	3.00000i	−0.169842	+	0.169842i
$313$			4.89898i			0.276907i	0.990369	+	0.138453i	$0.0442131\pi$
$313$			4.89898i			0.276907i	−0.990369	+	0.138453i	$0.955787\pi$
$314$	12.2474			0.691164
$315$	−18.0000	+	7.34847i	−1.01419	+	0.414039i
$316$	10.0000			0.562544
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$	−7.34847	+	7.34847i	−0.412082	+	0.412082i
$319$	6.00000			0.335936
$320$	−2.44949			−0.136931
$321$		0			0
$322$	−6.00000	−	14.6969i	−0.334367	−	0.819028i
$323$		0			0
$324$	9.00000			0.500000
$325$		−	2.44949i		−	0.135873i
$326$		−	16.0000i		−	0.886158i
$327$	−17.1464	+	17.1464i	−0.948200	+	0.948200i
$328$		−	9.79796i		−	0.541002i
$329$	−9.79796	−	24.0000i	−0.540179	−	1.32316i
$330$	3.00000	−	3.00000i	0.165145	−	0.165145i
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	2.44949			0.134433
$333$		−	30.0000i		−	1.64399i
$334$		−	14.6969i		−	0.804181i
$335$	−9.79796			−0.535320
$336$	−4.22474	−	1.77526i	−0.230479	−	0.0968481i
$337$	−20.0000			−1.08947			−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000			−1.08947			−0.544735	+	0.838608i	$0.683370\pi$
$338$			7.00000i			0.380750i
$339$	−22.0454	−	22.0454i	−1.19734	−	1.19734i
$340$		0			0
$341$	4.89898			0.265295
$342$			22.0454i			1.19208i
$343$	17.0000	+	7.34847i	0.917914	+	0.396780i
$344$			8.00000i			0.431331i
$345$	−18.0000	−	18.0000i	−0.969087	−	0.969087i
$346$		−	2.44949i		−	0.131685i
$347$			12.0000i			0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$			12.0000i			0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$	−7.34847	−	7.34847i	−0.393919	−	0.393919i
$349$		−	7.34847i		−	0.393355i	−0.980468	−	0.196677i	$-0.936985\pi$
$349$		−	7.34847i		−	0.393355i	0.980468	−	0.196677i	$-0.0630151\pi$
$350$	2.44949	−	1.00000i	0.130931	−	0.0534522i
$351$	−9.00000	+	9.00000i	−0.480384	+	0.480384i
$352$	1.00000			0.0533002
$353$	19.5959			1.04299			0.521493	−	0.853256i	$-0.325375\pi$
$353$	19.5959			1.04299			0.521493	+	0.853256i	$0.325375\pi$
$354$	−3.00000	−	3.00000i	−0.159448	−	0.159448i
$355$		0			0
$356$	−9.79796			−0.519291
$357$		0			0
$358$	24.0000			1.26844
$359$			18.0000i			0.950004i	0.879985	+	0.475002i	$0.157553\pi$
$359$			18.0000i			0.950004i	−0.879985	+	0.475002i	$0.842447\pi$
$360$	−7.34847			−0.387298
$361$	−35.0000			−1.84211
$362$	−17.1464			−0.901196
$363$	−1.22474	+	1.22474i	−0.0642824	+	0.0642824i
$364$	6.00000	−	2.44949i	0.314485	−	0.128388i
$365$			12.0000i			0.628109i
$366$	−9.00000	+	9.00000i	−0.470438	+	0.470438i
$367$		−	9.79796i		−	0.511449i	−0.966750	−	0.255725i	$-0.917686\pi$
$367$		−	9.79796i		−	0.511449i	0.966750	−	0.255725i	$-0.0823140\pi$
$368$		−	6.00000i		−	0.312772i
$369$		−	29.3939i		−	1.53018i
$370$			24.4949i			1.27343i
$371$	14.6969	−	6.00000i	0.763027	−	0.311504i
$372$	−6.00000	−	6.00000i	−0.311086	−	0.311086i
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$		0			0
$375$	−12.0000	+	12.0000i	−0.619677	+	0.619677i
$376$		−	9.79796i		−	0.505291i
$377$	14.6969			0.756931
$378$	−12.6742	−	5.32577i	−0.651892	−	0.273928i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		−	18.0000i		−	0.923381i
$381$	−19.5959	+	19.5959i	−1.00393	+	1.00393i
$382$		0			0
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$	−1.22474	−	1.22474i	−0.0625000	−	0.0625000i
$385$	−6.00000	+	2.44949i	−0.305788	+	0.124838i
$386$			16.0000i			0.814379i
$387$			24.0000i			1.21999i
$388$			4.89898i			0.248708i
$389$			30.0000i			1.52106i	0.649303	+	0.760530i	$0.275061\pi$
$389$			30.0000i			1.52106i	−0.649303	+	0.760530i	$0.724939\pi$
$390$	7.34847	−	7.34847i	0.372104	−	0.372104i
$391$		0			0
$392$	4.89898	+	5.00000i	0.247436	+	0.252538i
$393$	3.00000	−	3.00000i	0.151330	−	0.151330i
$394$	−6.00000			−0.302276
$395$	−24.4949			−1.23247
$396$	3.00000			0.150756
$397$			26.9444i			1.35230i	0.736764	+	0.676150i	$0.236353\pi$
$397$			26.9444i			1.35230i	−0.736764	+	0.676150i	$0.763647\pi$
$398$	−14.6969			−0.736691
$399$	13.0454	−	31.0454i	0.653087	−	1.55421i
$400$	1.00000			0.0500000
$401$		−	18.0000i		−	0.898877i	−0.893311	−	0.449439i	$-0.851624\pi$
$401$		−	18.0000i		−	0.898877i	0.893311	−	0.449439i	$-0.148376\pi$
$402$	−4.89898	−	4.89898i	−0.244339	−	0.244339i
$403$	12.0000			0.597763
$404$	2.44949			0.121867
$405$	−22.0454			−1.09545
$406$	6.00000	+	14.6969i	0.297775	+	0.729397i
$407$		−	10.0000i		−	0.495682i
$408$		0			0
$409$		−	29.3939i		−	1.45343i	−0.686937	−	0.726717i	$-0.741045\pi$
$409$		−	29.3939i		−	1.45343i	0.686937	−	0.726717i	$-0.258955\pi$
$410$			24.0000i			1.18528i
$411$	14.6969	+	14.6969i	0.724947	+	0.724947i
$412$		−	4.89898i		−	0.241355i
$413$	2.44949	+	6.00000i	0.120532	+	0.295241i
$414$		−	18.0000i		−	0.884652i
$415$	−6.00000			−0.294528
$416$	2.44949			0.120096
$417$	−15.0000	−	15.0000i	−0.734553	−	0.734553i
$418$			7.34847i			0.359425i
$419$	−26.9444			−1.31632			−0.658160	−	0.752878i	$-0.728665\pi$
$419$	−26.9444			−1.31632			−0.658160	+	0.752878i	$0.728665\pi$
$420$	10.3485	+	4.34847i	0.504954	+	0.212184i
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$			16.0000i			0.778868i
$423$		−	29.3939i		−	1.42918i
$424$	6.00000			0.291386
$425$		0			0
$426$		0			0
$427$	18.0000	−	7.34847i	0.871081	−	0.355617i
$428$		0			0
$429$	−3.00000	+	3.00000i	−0.144841	+	0.144841i
$430$		−	19.5959i		−	0.944999i
$431$		−	18.0000i		−	0.867029i	−0.901146	−	0.433515i	$-0.857273\pi$
$431$		−	18.0000i		−	0.867029i	0.901146	−	0.433515i	$-0.142727\pi$
$432$	−3.67423	−	3.67423i	−0.176777	−	0.176777i
$433$		−	4.89898i		−	0.235430i	−0.993047	−	0.117715i	$-0.962443\pi$
$433$		−	4.89898i		−	0.235430i	0.993047	−	0.117715i	$-0.0375569\pi$
$434$	4.89898	+	12.0000i	0.235159	+	0.576018i
$435$	18.0000	+	18.0000i	0.863034	+	0.863034i
$436$	14.0000			0.670478
$437$	44.0908			2.10915
$438$	−6.00000	+	6.00000i	−0.286691	+	0.286691i
$439$		−	24.4949i		−	1.16908i	−0.811366	−	0.584539i	$-0.801275\pi$
$439$		−	24.4949i		−	1.16908i	0.811366	−	0.584539i	$-0.198725\pi$
$440$	−2.44949			−0.116775
$441$	14.6969	+	15.0000i	0.699854	+	0.714286i
$442$		0			0
$443$			12.0000i			0.570137i	0.958507	+	0.285069i	$0.0920164\pi$
$443$			12.0000i			0.570137i	−0.958507	+	0.285069i	$0.907984\pi$
$444$	−12.2474	+	12.2474i	−0.581238	+	0.581238i
$445$	24.0000			1.13771
$446$	−9.79796			−0.463947
$447$	22.0454	+	22.0454i	1.04271	+	1.04271i
$448$	1.00000	+	2.44949i	0.0472456	+	0.115728i
$449$			12.0000i			0.566315i	0.959073	+	0.283158i	$0.0913819\pi$
$449$			12.0000i			0.566315i	−0.959073	+	0.283158i	$0.908618\pi$
$450$	3.00000			0.141421
$451$		−	9.79796i		−	0.461368i
$452$			18.0000i			0.846649i
$453$	19.5959	−	19.5959i	0.920697	−	0.920697i
$454$			17.1464i			0.804722i
$455$	−14.6969	+	6.00000i	−0.689003	+	0.281284i
$456$	9.00000	−	9.00000i	0.421464	−	0.421464i
$457$	−32.0000			−1.49690			−0.748448	−	0.663193i	$-0.769201\pi$
$457$	−32.0000			−1.49690			−0.748448	+	0.663193i	$0.769201\pi$
$458$	7.34847			0.343371
$459$		0			0
$460$			14.6969i			0.685248i
$461$	22.0454			1.02676			0.513378	−	0.858162i	$-0.328394\pi$
$461$	22.0454			1.02676			0.513378	+	0.858162i	$0.328394\pi$
$462$	−4.22474	−	1.77526i	−0.196553	−	0.0825923i
$463$	−22.0000			−1.02243			−0.511213	−	0.859454i	$-0.670804\pi$
$463$	−22.0000			−1.02243			−0.511213	+	0.859454i	$0.670804\pi$
$464$			6.00000i			0.278543i
$465$	14.6969	+	14.6969i	0.681554	+	0.681554i
$466$	−12.0000			−0.555889
$467$	−7.34847			−0.340047			−0.170023	−	0.985440i	$-0.554384\pi$
$467$	−7.34847			−0.340047			−0.170023	+	0.985440i	$0.554384\pi$
$468$	7.34847			0.339683
$469$	4.00000	+	9.79796i	0.184703	+	0.452428i
$470$			24.0000i			1.10704i
$471$	−15.0000	−	15.0000i	−0.691164	−	0.691164i
$472$			2.44949i			0.112747i
$473$			8.00000i			0.367840i
$474$	−12.2474	−	12.2474i	−0.562544	−	0.562544i
$475$			7.34847i			0.337171i
$476$		0			0
$477$	18.0000			0.824163
$478$	6.00000			0.274434
$479$	4.89898			0.223840			0.111920	−	0.993717i	$-0.464300\pi$
$479$	4.89898			0.223840			0.111920	+	0.993717i	$0.464300\pi$
$480$	3.00000	+	3.00000i	0.136931	+	0.136931i
$481$		−	24.4949i		−	1.11687i
$482$	19.5959			0.892570
$483$	−10.6515	+	25.3485i	−0.484661	+	1.15340i
$484$	1.00000			0.0454545
$485$		−	12.0000i		−	0.544892i
$486$	−11.0227	−	11.0227i	−0.500000	−	0.500000i
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	7.34847			0.332650
$489$	−19.5959	+	19.5959i	−0.886158	+	0.886158i
$490$	−12.0000	−	12.2474i	−0.542105	−	0.553283i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	−12.0000	+	12.0000i	−0.541002	+	0.541002i
$493$		0			0
$494$			18.0000i			0.809858i
$495$	−7.34847			−0.330289
$496$			4.89898i			0.219971i
$497$		0			0
$498$	−3.00000	−	3.00000i	−0.134433	−	0.134433i
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$	9.79796			0.438178
$501$	−18.0000	+	18.0000i	−0.804181	+	0.804181i
$502$			12.2474i			0.546630i
$503$	19.5959			0.873739			0.436869	−	0.899525i	$-0.356087\pi$
$503$	19.5959			0.873739			0.436869	+	0.899525i	$0.356087\pi$
$504$	3.00000	+	7.34847i	0.133631	+	0.327327i
$505$	−6.00000			−0.266996
$506$		−	6.00000i		−	0.266733i
$507$	8.57321	−	8.57321i	0.380750	−	0.380750i
$508$	16.0000			0.709885
$509$	−17.1464			−0.760002			−0.380001	−	0.924986i	$-0.624076\pi$
$509$	−17.1464			−0.760002			−0.380001	+	0.924986i	$0.624076\pi$
$510$		0			0
$511$	12.0000	−	4.89898i	0.530849	−	0.216718i
$512$			1.00000i			0.0441942i
$513$	27.0000	−	27.0000i	1.19208	−	1.19208i
$514$			19.5959i			0.864339i
$515$			12.0000i			0.528783i
$516$	9.79796	−	9.79796i	0.431331	−	0.431331i
$517$		−	9.79796i		−	0.430914i
$518$	24.4949	−	10.0000i	1.07624	−	0.439375i
$519$	−3.00000	+	3.00000i	−0.131685	+	0.131685i
$520$	−6.00000			−0.263117
$521$	−44.0908			−1.93165			−0.965827	−	0.259188i	$-0.916545\pi$
$521$	−44.0908			−1.93165			−0.965827	+	0.259188i	$0.916545\pi$
$522$			18.0000i			0.787839i
$523$			22.0454i			0.963978i	0.876177	+	0.481989i	$0.160086\pi$
$523$			22.0454i			0.963978i	−0.876177	+	0.481989i	$0.839914\pi$
$524$	−2.44949			−0.107006
$525$	−4.22474	−	1.77526i	−0.184383	−	0.0774785i
$526$	24.0000			1.04645
$527$		0			0
$528$	−1.22474	−	1.22474i	−0.0533002	−	0.0533002i
$529$	−13.0000			−0.565217
$530$	−14.6969			−0.638394
$531$			7.34847i			0.318896i
$532$	−18.0000	+	7.34847i	−0.780399	+	0.318597i
$533$		−	24.0000i		−	1.03956i
$534$	12.0000	+	12.0000i	0.519291	+	0.519291i
$535$		0			0
$536$			4.00000i			0.172774i
$537$	−29.3939	−	29.3939i	−1.26844	−	1.26844i
$538$			2.44949i			0.105605i
$539$	4.89898	+	5.00000i	0.211014	+	0.215365i
$540$	9.00000	+	9.00000i	0.387298	+	0.387298i
$541$	−34.0000			−1.46177			−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000			−1.46177			−0.730887	+	0.682498i	$0.760893\pi$
$542$	−4.89898			−0.210429
$543$	21.0000	+	21.0000i	0.901196	+	0.901196i
$544$		0			0
$545$	−34.2929			−1.46894
$546$	−10.3485	−	4.34847i	−0.442874	−	0.186097i
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$		−	12.0000i		−	0.512615i
$549$	22.0454			0.940875
$550$	1.00000			0.0426401
$551$	−44.0908			−1.87833
$552$	−7.34847	+	7.34847i	−0.312772	+	0.312772i
$553$	10.0000	+	24.4949i	0.425243	+	1.04163i
$554$			2.00000i			0.0849719i
$555$	30.0000	−	30.0000i	1.27343	−	1.27343i
$556$			12.2474i			0.519408i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$			14.6969i			0.622171i
$559$			19.5959i			0.828819i
$560$	−2.44949	−	6.00000i	−0.103510	−	0.253546i
$561$		0			0
$562$	12.0000			0.506189
$563$	−17.1464			−0.722636			−0.361318	−	0.932443i	$-0.617673\pi$
$563$	−17.1464			−0.722636			−0.361318	+	0.932443i	$0.617673\pi$
$564$	−12.0000	+	12.0000i	−0.505291	+	0.505291i
$565$		−	44.0908i		−	1.85491i
$566$	2.44949			0.102960
$567$	9.00000	+	22.0454i	0.377964	+	0.925820i
$568$		0			0
$569$		−	6.00000i		−	0.251533i	−0.992060	−	0.125767i	$-0.959861\pi$
$569$		−	6.00000i		−	0.251533i	0.992060	−	0.125767i	$-0.0401390\pi$
$570$	−22.0454	+	22.0454i	−0.923381	+	0.923381i
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	2.44949			0.102418
$573$		0			0
$574$	24.0000	−	9.79796i	1.00174	−	0.408959i
$575$		−	6.00000i		−	0.250217i
$576$			3.00000i			0.125000i
$577$		−	29.3939i		−	1.22368i	−0.790980	−	0.611842i	$-0.790429\pi$
$577$		−	29.3939i		−	1.22368i	0.790980	−	0.611842i	$-0.209571\pi$
$578$		−	17.0000i		−	0.707107i
$579$	19.5959	−	19.5959i	0.814379	−	0.814379i
$580$		−	14.6969i		−	0.610257i
$581$	2.44949	+	6.00000i	0.101622	+	0.248922i
$582$	6.00000	−	6.00000i	0.248708	−	0.248708i
$583$	6.00000			0.248495
$584$	4.89898			0.202721
$585$	−18.0000			−0.744208
$586$		−	17.1464i		−	0.708312i
$587$	41.6413			1.71872			0.859361	−	0.511370i	$-0.170862\pi$
$587$	41.6413			1.71872			0.859361	+	0.511370i	$0.170862\pi$
$588$	0.123724	−	12.1237i	0.00510231	−	0.499974i
$589$	−36.0000			−1.48335
$590$		−	6.00000i		−	0.247016i
$591$	7.34847	+	7.34847i	0.302276	+	0.302276i
$592$	10.0000			0.410997
$593$	−24.4949			−1.00588			−0.502942	−	0.864320i	$-0.667749\pi$
$593$	−24.4949			−1.00588			−0.502942	+	0.864320i	$0.667749\pi$
$594$	−3.67423	−	3.67423i	−0.150756	−	0.150756i
$595$		0			0
$596$		−	18.0000i		−	0.737309i
$597$	18.0000	+	18.0000i	0.736691	+	0.736691i
$598$		−	14.6969i		−	0.601003i
$599$			24.0000i			0.980613i	0.871550	+	0.490307i	$0.163115\pi$
$599$			24.0000i			0.980613i	−0.871550	+	0.490307i	$0.836885\pi$
$600$	−1.22474	−	1.22474i	−0.0500000	−	0.0500000i
$601$		−	4.89898i		−	0.199834i	−0.994996	−	0.0999168i	$-0.968142\pi$
$601$		−	4.89898i		−	0.199834i	0.994996	−	0.0999168i	$-0.0318577\pi$
$602$	−19.5959	+	8.00000i	−0.798670	+	0.326056i
$603$			12.0000i			0.488678i
$604$	−16.0000			−0.651031
$605$	−2.44949			−0.0995859
$606$	−3.00000	−	3.00000i	−0.121867	−	0.121867i
$607$			34.2929i			1.39190i	0.718088	+	0.695952i	$0.245017\pi$
$607$			34.2929i			1.39190i	−0.718088	+	0.695952i	$0.754983\pi$
$608$	−7.34847			−0.298020
$609$	10.6515	−	25.3485i	0.431622	−	1.02717i
$610$	−18.0000			−0.728799
$611$		−	24.0000i		−	0.970936i
$612$		0			0
$613$	2.00000			0.0807792			0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000			0.0807792			0.0403896	+	0.999184i	$0.487140\pi$
$614$	31.8434			1.28509
$615$	29.3939	−	29.3939i	1.18528	−	1.18528i
$616$	1.00000	+	2.44949i	0.0402911	+	0.0986928i
$617$		−	30.0000i		−	1.20775i	−0.797077	−	0.603877i	$-0.793622\pi$
$617$		−	30.0000i		−	1.20775i	0.797077	−	0.603877i	$-0.206378\pi$
$618$	−6.00000	+	6.00000i	−0.241355	+	0.241355i
$619$			26.9444i			1.08299i	0.840705	+	0.541493i	$0.182141\pi$
$619$			26.9444i			1.08299i	−0.840705	+	0.541493i	$0.817859\pi$
$620$		−	12.0000i		−	0.481932i
$621$	−22.0454	+	22.0454i	−0.884652	+	0.884652i
$622$			14.6969i			0.589294i
$623$	−9.79796	−	24.0000i	−0.392547	−	0.961540i
$624$	−3.00000	−	3.00000i	−0.120096	−	0.120096i
$625$	−29.0000			−1.16000
$626$	−4.89898			−0.195803
$627$	9.00000	−	9.00000i	0.359425	−	0.359425i
$628$			12.2474i			0.488726i
$629$		0			0
$630$	−7.34847	−	18.0000i	−0.292770	−	0.717137i
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$			10.0000i			0.397779i
$633$	19.5959	−	19.5959i	0.778868	−	0.778868i
$634$	−6.00000			−0.238290
$635$	−39.1918			−1.55528
$636$	−7.34847	−	7.34847i	−0.291386	−	0.291386i
$637$	12.0000	+	12.2474i	0.475457	+	0.485262i
$638$			6.00000i			0.237542i
$639$		0			0
$640$		−	2.44949i		−	0.0968246i
$641$		−	30.0000i		−	1.18493i	−0.805597	−	0.592464i	$-0.798155\pi$
$641$		−	30.0000i		−	1.18493i	0.805597	−	0.592464i	$-0.201845\pi$
$642$		0			0
$643$			31.8434i			1.25578i	0.778302	+	0.627890i	$0.216081\pi$
$643$			31.8434i			1.25578i	−0.778302	+	0.627890i	$0.783919\pi$
$644$	14.6969	−	6.00000i	0.579141	−	0.236433i
$645$	−24.0000	+	24.0000i	−0.944999	+	0.944999i
$646$		0			0
$647$	−19.5959			−0.770395			−0.385198	−	0.922834i	$-0.625867\pi$
$647$	−19.5959			−0.770395			−0.385198	+	0.922834i	$0.625867\pi$
$648$			9.00000i			0.353553i
$649$			2.44949i			0.0961509i
$650$	2.44949			0.0960769
$651$	8.69694	−	20.6969i	0.340860	−	0.811177i
$652$	16.0000			0.626608
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	−17.1464	−	17.1464i	−0.670478	−	0.670478i
$655$	6.00000			0.234439
$656$	9.79796			0.382546
$657$	14.6969			0.573382
$658$	24.0000	−	9.79796i	0.935617	−	0.381964i
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$	3.00000	+	3.00000i	0.116775	+	0.116775i
$661$		−	12.2474i		−	0.476371i	−0.971220	−	0.238185i	$-0.923447\pi$
$661$		−	12.2474i		−	0.476371i	0.971220	−	0.238185i	$-0.0765525\pi$
$662$		−	20.0000i		−	0.777322i
$663$		0			0
$664$			2.44949i			0.0950586i
$665$	44.0908	−	18.0000i	1.70977	−	0.698010i
$666$	30.0000			1.16248
$667$	36.0000			1.39393
$668$	14.6969			0.568642
$669$	12.0000	+	12.0000i	0.463947	+	0.463947i
$670$		−	9.79796i		−	0.378528i
$671$	7.34847			0.283685
$672$	1.77526	−	4.22474i	0.0684820	−	0.162973i
$673$	10.0000			0.385472			0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000			0.385472			0.192736	+	0.981251i	$0.438264\pi$
$674$		−	20.0000i		−	0.770371i
$675$	−3.67423	−	3.67423i	−0.141421	−	0.141421i
$676$	−7.00000			−0.269231
$677$	12.2474			0.470708			0.235354	−	0.971910i	$-0.424375\pi$
$677$	12.2474			0.470708			0.235354	+	0.971910i	$0.424375\pi$
$678$	22.0454	−	22.0454i	0.846649	−	0.846649i
$679$	−12.0000	+	4.89898i	−0.460518	+	0.188006i
$680$		0			0
$681$	21.0000	−	21.0000i	0.804722	−	0.804722i
$682$			4.89898i			0.187592i
$683$			24.0000i			0.918334i	0.888350	+	0.459167i	$0.151852\pi$
$683$			24.0000i			0.918334i	−0.888350	+	0.459167i	$0.848148\pi$
$684$	−22.0454			−0.842927
$685$			29.3939i			1.12308i
$686$	−7.34847	+	17.0000i	−0.280566	+	0.649063i
$687$	−9.00000	−	9.00000i	−0.343371	−	0.343371i
$688$	−8.00000			−0.304997
$689$	14.6969			0.559909
$690$	18.0000	−	18.0000i	0.685248	−	0.685248i
$691$			12.2474i			0.465915i	0.972487	+	0.232957i	$0.0748403\pi$
$691$			12.2474i			0.465915i	−0.972487	+	0.232957i	$0.925160\pi$
$692$	2.44949			0.0931156
$693$	3.00000	+	7.34847i	0.113961	+	0.279145i
$694$	−12.0000			−0.455514
$695$		−	30.0000i		−	1.13796i
$696$	7.34847	−	7.34847i	0.278543	−	0.278543i
$697$		0			0
$698$	7.34847			0.278144
$699$	14.6969	+	14.6969i	0.555889	+	0.555889i
$700$	1.00000	+	2.44949i	0.0377964	+	0.0925820i
$701$			6.00000i			0.226617i	0.993560	+	0.113308i	$0.0361448\pi$
$701$			6.00000i			0.226617i	−0.993560	+	0.113308i	$0.963855\pi$
$702$	−9.00000	−	9.00000i	−0.339683	−	0.339683i
$703$			73.4847i			2.77153i
$704$			1.00000i			0.0376889i
$705$	29.3939	−	29.3939i	1.10704	−	1.10704i
$706$			19.5959i			0.737502i
$707$	2.44949	+	6.00000i	0.0921225	+	0.225653i
$708$	3.00000	−	3.00000i	0.112747	−	0.112747i
$709$	34.0000			1.27690			0.638448	−	0.769665i	$-0.279577\pi$
$709$	34.0000			1.27690			0.638448	+	0.769665i	$0.279577\pi$
$710$		0			0
$711$			30.0000i			1.12509i
$712$		−	9.79796i		−	0.367194i
$713$	29.3939			1.10081
$714$		0			0
$715$	−6.00000			−0.224387
$716$			24.0000i			0.896922i
$717$	−7.34847	−	7.34847i	−0.274434	−	0.274434i
$718$	−18.0000			−0.671754
$719$	−19.5959			−0.730804			−0.365402	−	0.930850i	$-0.619069\pi$
$719$	−19.5959			−0.730804			−0.365402	+	0.930850i	$0.619069\pi$
$720$		−	7.34847i		−	0.273861i
$721$	12.0000	−	4.89898i	0.446903	−	0.182448i
$722$		−	35.0000i		−	1.30257i
$723$	−24.0000	−	24.0000i	−0.892570	−	0.892570i
$724$		−	17.1464i		−	0.637242i
$725$			6.00000i			0.222834i
$726$	−1.22474	−	1.22474i	−0.0454545	−	0.0454545i
$727$		−	14.6969i		−	0.545079i	−0.962145	−	0.272540i	$-0.912136\pi$
$727$		−	14.6969i		−	0.545079i	0.962145	−	0.272540i	$-0.0878636\pi$
$728$	2.44949	+	6.00000i	0.0907841	+	0.222375i
$729$			27.0000i			1.00000i
$730$	−12.0000			−0.444140
$731$		0			0
$732$	−9.00000	−	9.00000i	−0.332650	−	0.332650i
$733$		−	36.7423i		−	1.35711i	−0.734550	−	0.678555i	$-0.762607\pi$
$733$		−	36.7423i		−	1.35711i	0.734550	−	0.678555i	$-0.237393\pi$
$734$	9.79796			0.361649
$735$	−0.303062	+	29.6969i	−0.0111786	+	1.09539i
$736$	6.00000			0.221163
$737$			4.00000i			0.147342i
$738$	29.3939			1.08200
$739$	−4.00000			−0.147142			−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000			−0.147142			−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−24.4949			−0.900450
$741$	22.0454	−	22.0454i	0.809858	−	0.809858i
$742$	6.00000	+	14.6969i	0.220267	+	0.539542i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$	6.00000	−	6.00000i	0.219971	−	0.219971i
$745$			44.0908i			1.61536i
$746$			26.0000i			0.951928i
$747$			7.34847i			0.268866i
$748$		0			0
$749$		0			0
$750$	−12.0000	−	12.0000i	−0.438178	−	0.438178i
$751$	40.0000			1.45962			0.729810	−	0.683650i	$-0.239608\pi$
$751$	40.0000			1.45962			0.729810	+	0.683650i	$0.239608\pi$
$752$	9.79796			0.357295
$753$	15.0000	−	15.0000i	0.546630	−	0.546630i
$754$			14.6969i			0.535231i
$755$	39.1918			1.42634
$756$	5.32577	−	12.6742i	0.193696	−	0.460957i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$		−	20.0000i		−	0.726433i
$759$	−7.34847	+	7.34847i	−0.266733	+	0.266733i
$760$	18.0000			0.652929
$761$	19.5959			0.710351			0.355176	−	0.934800i	$-0.384421\pi$
$761$	19.5959			0.710351			0.355176	+	0.934800i	$0.384421\pi$
$762$	−19.5959	−	19.5959i	−0.709885	−	0.709885i
$763$	14.0000	+	34.2929i	0.506834	+	1.24148i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			6.00000i			0.216647i
$768$	1.22474	−	1.22474i	0.0441942	−	0.0441942i
$769$		−	9.79796i		−	0.353323i	−0.984272	−	0.176662i	$-0.943470\pi$
$769$		−	9.79796i		−	0.353323i	0.984272	−	0.176662i	$-0.0565299\pi$
$770$	−2.44949	−	6.00000i	−0.0882735	−	0.216225i
$771$	24.0000	−	24.0000i	0.864339	−	0.864339i
$772$	−16.0000			−0.575853
$773$	22.0454			0.792918			0.396459	−	0.918052i	$-0.370239\pi$
$773$	22.0454			0.792918			0.396459	+	0.918052i	$0.370239\pi$
$774$	−24.0000			−0.862662
$775$			4.89898i			0.175977i
$776$	−4.89898			−0.175863
$777$	−42.2474	−	17.7526i	−1.51562	−	0.636869i
$778$	−30.0000			−1.07555
$779$			72.0000i			2.57967i
$780$	7.34847	+	7.34847i	0.263117	+	0.263117i
$781$		0			0
$782$		0			0
$783$	22.0454	−	22.0454i	0.787839	−	0.787839i
$784$	−5.00000	+	4.89898i	−0.178571	+	0.174964i
$785$		−	30.0000i		−	1.07075i
$786$	3.00000	+	3.00000i	0.107006	+	0.107006i
$787$		−	17.1464i		−	0.611204i	−0.952159	−	0.305602i	$-0.901142\pi$
$787$		−	17.1464i		−	0.611204i	0.952159	−	0.305602i	$-0.0988577\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−29.3939	−	29.3939i	−1.04645	−	1.04645i
$790$		−	24.4949i		−	0.871489i
$791$	−44.0908	+	18.0000i	−1.56769	+	0.640006i
$792$			3.00000i			0.106600i
$793$	18.0000			0.639199
$794$	−26.9444			−0.956221
$795$	18.0000	+	18.0000i	0.638394	+	0.638394i
$796$		−	14.6969i		−	0.520919i
$797$	−31.8434			−1.12795			−0.563975	−	0.825792i	$-0.690729\pi$
$797$	−31.8434			−1.12795			−0.563975	+	0.825792i	$0.690729\pi$
$798$	31.0454	+	13.0454i	1.09900	+	0.461802i
$799$		0			0
$800$			1.00000i			0.0353553i
$801$		−	29.3939i		−	1.03858i
$802$	18.0000			0.635602
$803$	4.89898			0.172881
$804$	4.89898	−	4.89898i	0.172774	−	0.172774i
$805$	−36.0000	+	14.6969i	−1.26883	+	0.517999i
$806$			12.0000i			0.422682i
$807$	3.00000	−	3.00000i	0.105605	−	0.105605i
$808$			2.44949i			0.0861727i
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		−	22.0454i		−	0.774597i
$811$			56.3383i			1.97830i	0.146896	+	0.989152i	$0.453072\pi$
$811$			56.3383i			1.97830i	−0.146896	+	0.989152i	$0.546928\pi$
$812$	−14.6969	+	6.00000i	−0.515761	+	0.210559i
$813$	6.00000	+	6.00000i	0.210429	+	0.210429i
$814$	10.0000			0.350500
$815$	−39.1918			−1.37283
$816$		0			0
$817$		−	58.7878i		−	2.05672i
$818$	29.3939			1.02773
$819$	7.34847	+	18.0000i	0.256776	+	0.628971i
$820$	−24.0000			−0.838116
$821$		−	6.00000i		−	0.209401i	−0.994504	−	0.104701i	$-0.966612\pi$
$821$		−	6.00000i		−	0.209401i	0.994504	−	0.104701i	$-0.0333885\pi$
$822$	−14.6969	+	14.6969i	−0.512615	+	0.512615i
$823$	2.00000			0.0697156			0.0348578	−	0.999392i	$-0.488902\pi$
$823$	2.00000			0.0697156			0.0348578	+	0.999392i	$0.488902\pi$
$824$	4.89898			0.170664
$825$	−1.22474	−	1.22474i	−0.0426401	−	0.0426401i
$826$	−6.00000	+	2.44949i	−0.208767	+	0.0852286i
$827$		−	12.0000i		−	0.417281i	−0.977992	−	0.208640i	$-0.933096\pi$
$827$		−	12.0000i		−	0.417281i	0.977992	−	0.208640i	$-0.0669038\pi$
$828$	18.0000			0.625543
$829$			51.4393i			1.78656i	0.449500	+	0.893280i	$0.351602\pi$
$829$			51.4393i			1.78656i	−0.449500	+	0.893280i	$0.648398\pi$
$830$		−	6.00000i		−	0.208263i
$831$	2.44949	−	2.44949i	0.0849719	−	0.0849719i
$832$			2.44949i			0.0849208i
$833$		0			0
$834$	15.0000	−	15.0000i	0.519408	−	0.519408i
$835$	−36.0000			−1.24583
$836$	−7.34847			−0.254152
$837$	18.0000	−	18.0000i	0.622171	−	0.622171i
$838$		−	26.9444i		−	0.930778i
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$	−4.34847	+	10.3485i	−0.150036	+	0.357056i
$841$	−7.00000			−0.241379
$842$		−	10.0000i		−	0.344623i
$843$	−14.6969	−	14.6969i	−0.506189	−	0.506189i
$844$	−16.0000			−0.550743
$845$	17.1464			0.589855
$846$	29.3939			1.01058
$847$	1.00000	+	2.44949i	0.0343604	+	0.0841655i
$848$			6.00000i			0.206041i
$849$	−3.00000	−	3.00000i	−0.102960	−	0.102960i
$850$		0			0
$851$		−	60.0000i		−	2.05677i
$852$		0			0
$853$			17.1464i			0.587083i	0.955946	+	0.293541i	$0.0948338\pi$
$853$			17.1464i			0.587083i	−0.955946	+	0.293541i	$0.905166\pi$
$854$	7.34847	+	18.0000i	0.251459	+	0.615947i
$855$	54.0000			1.84676
$856$		0			0
$857$	−48.9898			−1.67346			−0.836730	−	0.547616i	$-0.815535\pi$
$857$	−48.9898			−1.67346			−0.836730	+	0.547616i	$0.815535\pi$
$858$	−3.00000	−	3.00000i	−0.102418	−	0.102418i
$859$		−	22.0454i		−	0.752180i	−0.926583	−	0.376090i	$-0.877268\pi$
$859$		−	22.0454i		−	0.752180i	0.926583	−	0.376090i	$-0.122732\pi$
$860$	19.5959			0.668215
$861$	−41.3939	−	17.3939i	−1.41070	−	0.592782i
$862$	18.0000			0.613082
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	3.67423	−	3.67423i	0.125000	−	0.125000i
$865$	−6.00000			−0.204006
$866$	4.89898			0.166474
$867$	−20.8207	+	20.8207i	−0.707107	+	0.707107i
$868$	−12.0000	+	4.89898i	−0.407307	+	0.166282i
$869$			10.0000i			0.339227i
$870$	−18.0000	+	18.0000i	−0.610257	+	0.610257i
$871$			9.79796i			0.331991i
$872$			14.0000i			0.474100i
$873$	−14.6969			−0.497416
$874$			44.0908i			1.49139i
$875$	9.79796	+	24.0000i	0.331231	+	0.811348i
$876$	−6.00000	−	6.00000i	−0.202721	−	0.202721i
$877$	2.00000			0.0675352			0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000			0.0675352			0.0337676	+	0.999430i	$0.489249\pi$
$878$	24.4949			0.826663
$879$	−21.0000	+	21.0000i	−0.708312	+	0.708312i
$880$		−	2.44949i		−	0.0825723i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−15.0000	+	14.6969i	−0.505076	+	0.494872i
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$	−7.34847	+	7.34847i	−0.247016	+	0.247016i
$886$	−12.0000			−0.403148
$887$	−44.0908			−1.48042			−0.740212	−	0.672373i	$-0.765275\pi$
$887$	−44.0908			−1.48042			−0.740212	+	0.672373i	$0.765275\pi$
$888$	−12.2474	−	12.2474i	−0.410997	−	0.410997i
$889$	16.0000	+	39.1918i	0.536623	+	1.31445i
$890$			24.0000i			0.804482i
$891$			9.00000i			0.301511i
$892$		−	9.79796i		−	0.328060i
$893$			72.0000i			2.40939i
$894$	−22.0454	+	22.0454i	−0.737309	+	0.737309i
$895$		−	58.7878i		−	1.96506i
$896$	−2.44949	+	1.00000i	−0.0818317	+	0.0334077i
$897$	−18.0000	+	18.0000i	−0.601003	+	0.601003i
$898$	−12.0000			−0.400445
$899$	−29.3939			−0.980341
$900$			3.00000i			0.100000i
$901$		0			0
$902$	9.79796			0.326236
$903$	33.7980	+	14.2020i	1.12473	+	0.472614i
$904$	−18.0000			−0.598671
$905$			42.0000i			1.39613i
$906$	19.5959	+	19.5959i	0.651031	+	0.651031i
$907$	−32.0000			−1.06254			−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000			−1.06254			−0.531271	+	0.847202i	$0.678286\pi$
$908$	−17.1464			−0.569024
$909$			7.34847i			0.243733i
$910$	−6.00000	−	14.6969i	−0.198898	−	0.487199i
$911$			42.0000i			1.39152i	0.718273	+	0.695761i	$0.244933\pi$
$911$			42.0000i			1.39152i	−0.718273	+	0.695761i	$0.755067\pi$
$912$	9.00000	+	9.00000i	0.298020	+	0.298020i
$913$			2.44949i			0.0810663i
$914$		−	32.0000i		−	1.05847i
$915$	22.0454	+	22.0454i	0.728799	+	0.728799i
$916$			7.34847i			0.242800i
$917$	−2.44949	−	6.00000i	−0.0808893	−	0.198137i
$918$		0			0
$919$	34.0000			1.12156			0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000			1.12156			0.560778	+	0.827966i	$0.310502\pi$
$920$	−14.6969			−0.484544
$921$	−39.0000	−	39.0000i	−1.28509	−	1.28509i
$922$			22.0454i			0.726027i
$923$		0			0
$924$	1.77526	−	4.22474i	0.0584016	−	0.138984i
$925$	10.0000			0.328798
$926$		−	22.0000i		−	0.722965i
$927$	14.6969			0.482711
$928$	−6.00000			−0.196960
$929$	44.0908			1.44657			0.723286	−	0.690548i	$-0.242631\pi$
$929$	44.0908			1.44657			0.723286	+	0.690548i	$0.242631\pi$
$930$	−14.6969	+	14.6969i	−0.481932	+	0.481932i
$931$	−36.0000	−	36.7423i	−1.17985	−	1.20418i
$932$		−	12.0000i		−	0.393073i
$933$	18.0000	−	18.0000i	0.589294	−	0.589294i
$934$		−	7.34847i		−	0.240449i
$935$		0			0
$936$			7.34847i			0.240192i
$937$		−	24.4949i		−	0.800213i	−0.916469	−	0.400107i	$-0.868973\pi$
$937$		−	24.4949i		−	0.800213i	0.916469	−	0.400107i	$-0.131027\pi$
$938$	−9.79796	+	4.00000i	−0.319915	+	0.130605i
$939$	6.00000	+	6.00000i	0.195803	+	0.195803i
$940$	−24.0000			−0.782794
$941$	−26.9444			−0.878362			−0.439181	−	0.898399i	$-0.644731\pi$
$941$	−26.9444			−0.878362			−0.439181	+	0.898399i	$0.644731\pi$
$942$	15.0000	−	15.0000i	0.488726	−	0.488726i
$943$		−	58.7878i		−	1.91439i
$944$	−2.44949			−0.0797241
$945$	−13.0454	+	31.0454i	−0.424367	+	1.00991i
$946$	−8.00000			−0.260102
$947$			48.0000i			1.55979i	0.625910	+	0.779895i	$0.284728\pi$
$947$			48.0000i			1.55979i	−0.625910	+	0.779895i	$0.715272\pi$
$948$	12.2474	−	12.2474i	0.397779	−	0.397779i
$949$	12.0000			0.389536
$950$	−7.34847			−0.238416
$951$	7.34847	+	7.34847i	0.238290	+	0.238290i
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$			18.0000i			0.582772i
$955$		0			0
$956$			6.00000i			0.194054i
$957$	7.34847	−	7.34847i	0.237542	−	0.237542i
$958$			4.89898i			0.158279i
$959$	29.3939	−	12.0000i	0.949178	−	0.387500i
$960$	−3.00000	+	3.00000i	−0.0968246	+	0.0968246i
$961$	7.00000			0.225806
$962$	24.4949			0.789747
$963$		0			0
$964$			19.5959i			0.631142i
$965$	39.1918			1.26163
$966$	−25.3485	−	10.6515i	−0.815574	−	0.342707i
$967$	56.0000			1.80084			0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000			1.80084			0.900419	+	0.435023i	$0.143260\pi$
$968$			1.00000i			0.0321412i
$969$		0			0
$970$	12.0000			0.385297
$971$	−22.0454			−0.707471			−0.353735	−	0.935346i	$-0.615089\pi$
$971$	−22.0454			−0.707471			−0.353735	+	0.935346i	$0.615089\pi$
$972$	11.0227	−	11.0227i	0.353553	−	0.353553i
$973$	−30.0000	+	12.2474i	−0.961756	+	0.392635i
$974$			16.0000i			0.512673i
$975$	−3.00000	−	3.00000i	−0.0960769	−	0.0960769i
$976$			7.34847i			0.235219i
$977$		−	60.0000i		−	1.91957i	−0.280736	−	0.959785i	$-0.590579\pi$
$977$		−	60.0000i		−	1.91957i	0.280736	−	0.959785i	$-0.409421\pi$
$978$	−19.5959	−	19.5959i	−0.626608	−	0.626608i
$979$		−	9.79796i		−	0.313144i
$980$	12.2474	−	12.0000i	0.391230	−	0.383326i
$981$			42.0000i			1.34096i
$982$		0			0
$983$	39.1918			1.25003			0.625013	−	0.780615i	$-0.285094\pi$
$983$	39.1918			1.25003			0.625013	+	0.780615i	$0.285094\pi$
$984$	−12.0000	−	12.0000i	−0.382546	−	0.382546i
$985$			14.6969i			0.468283i
$986$		0			0
$987$	−41.3939	−	17.3939i	−1.31758	−	0.553653i
$988$	−18.0000			−0.572656
$989$			48.0000i			1.52631i
$990$		−	7.34847i		−	0.233550i
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	−4.89898			−0.155543
$993$	−24.4949	+	24.4949i	−0.777322	+	0.777322i
$994$		0			0
$995$			36.0000i			1.14128i
$996$	3.00000	−	3.00000i	0.0950586	−	0.0950586i
$997$		−	17.1464i		−	0.543033i	−0.962434	−	0.271516i	$-0.912475\pi$
$997$		−	17.1464i		−	0.543033i	0.962434	−	0.271516i	$-0.0875251\pi$
$998$		−	32.0000i		−	1.01294i
$999$	−36.7423	−	36.7423i	−1.16248	−	1.16248i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.g.b.419.4	yes	4
3.2	odd	2	inner	462.2.g.b.419.1	✓	4
7.6	odd	2	inner	462.2.g.b.419.3	yes	4
21.20	even	2	inner	462.2.g.b.419.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.b.419.1	✓	4	3.2	odd	2	inner
462.2.g.b.419.2	yes	4	21.20	even	2	inner
462.2.g.b.419.3	yes	4	7.6	odd	2	inner
462.2.g.b.419.4	yes	4	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(1.22474 + 1.22474i) q^{6} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.22474 - 1.22474i) q^{3} -1.00000 q^{4} +2.44949 q^{5} +(1.22474 + 1.22474i) q^{6} +(-1.00000 - 2.44949i) q^{7} -1.00000i q^{8} -3.00000i q^{9} +2.44949i q^{10} -1.00000i q^{11} +(-1.22474 + 1.22474i) q^{12} -2.44949i q^{13} +(2.44949 - 1.00000i) q^{14} +(3.00000 - 3.00000i) q^{15} +1.00000 q^{16} +3.00000 q^{18} +7.34847i q^{19} -2.44949 q^{20} +(-4.22474 - 1.77526i) q^{21} +1.00000 q^{22} -6.00000i q^{23} +(-1.22474 - 1.22474i) q^{24} +1.00000 q^{25} +2.44949 q^{26} +(-3.67423 - 3.67423i) q^{27} +(1.00000 + 2.44949i) q^{28} +6.00000i q^{29} +(3.00000 + 3.00000i) q^{30} +4.89898i q^{31} +1.00000i q^{32} +(-1.22474 - 1.22474i) q^{33} +(-2.44949 - 6.00000i) q^{35} +3.00000i q^{36} +10.0000 q^{37} -7.34847 q^{38} +(-3.00000 - 3.00000i) q^{39} -2.44949i q^{40} +9.79796 q^{41} +(1.77526 - 4.22474i) q^{42} -8.00000 q^{43} +1.00000i q^{44} -7.34847i q^{45} +6.00000 q^{46} +9.79796 q^{47} +(1.22474 - 1.22474i) q^{48} +(-5.00000 + 4.89898i) q^{49} +1.00000i q^{50} +2.44949i q^{52} +6.00000i q^{53} +(3.67423 - 3.67423i) q^{54} -2.44949i q^{55} +(-2.44949 + 1.00000i) q^{56} +(9.00000 + 9.00000i) q^{57} -6.00000 q^{58} -2.44949 q^{59} +(-3.00000 + 3.00000i) q^{60} +7.34847i q^{61} -4.89898 q^{62} +(-7.34847 + 3.00000i) q^{63} -1.00000 q^{64} -6.00000i q^{65} +(1.22474 - 1.22474i) q^{66} -4.00000 q^{67} +(-7.34847 - 7.34847i) q^{69} +(6.00000 - 2.44949i) q^{70} -3.00000 q^{72} +4.89898i q^{73} +10.0000i q^{74} +(1.22474 - 1.22474i) q^{75} -7.34847i q^{76} +(-2.44949 + 1.00000i) q^{77} +(3.00000 - 3.00000i) q^{78} -10.0000 q^{79} +2.44949 q^{80} -9.00000 q^{81} +9.79796i q^{82} -2.44949 q^{83} +(4.22474 + 1.77526i) q^{84} -8.00000i q^{86} +(7.34847 + 7.34847i) q^{87} -1.00000 q^{88} +9.79796 q^{89} +7.34847 q^{90} +(-6.00000 + 2.44949i) q^{91} +6.00000i q^{92} +(6.00000 + 6.00000i) q^{93} +9.79796i q^{94} +18.0000i q^{95} +(1.22474 + 1.22474i) q^{96} -4.89898i q^{97} +(-4.89898 - 5.00000i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^4 - 4 * q^7	\( 4 q - 4 q^{4} - 4 q^{7} + 12 q^{15} + 4 q^{16} + 12 q^{18} - 12 q^{21} + 4 q^{22} + 4 q^{25} + 4 q^{28} + 12 q^{30} + 40 q^{37} - 12 q^{39} + 12 q^{42} - 32 q^{43} + 24 q^{46} - 20 q^{49} + 36 q^{57} - 24 q^{58} - 12 q^{60} - 4 q^{64} - 16 q^{67} + 24 q^{70} - 12 q^{72} + 12 q^{78} - 40 q^{79} - 36 q^{81} + 12 q^{84} - 4 q^{88} - 24 q^{91} + 24 q^{93} - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 - 4 * q^7 + 12 * q^15 + 4 * q^16 + 12 * q^18 - 12 * q^21 + 4 * q^22 + 4 * q^25 + 4 * q^28 + 12 * q^30 + 40 * q^37 - 12 * q^39 + 12 * q^42 - 32 * q^43 + 24 * q^46 - 20 * q^49 + 36 * q^57 - 24 * q^58 - 12 * q^60 - 4 * q^64 - 16 * q^67 + 24 * q^70 - 12 * q^72 + 12 * q^78 - 40 * q^79 - 36 * q^81 + 12 * q^84 - 4 * q^88 - 24 * q^91 + 24 * q^93 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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