LMFDB - Embedded newform 1216.2.i.k.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(577,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("1216.577");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.i (of order $3$, degree $2$, not 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:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			577.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1216.577
Dual form			1216.2.i.k.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32288 - 2.29129i) q^{3} +(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(-1.32288 - 2.29129i) q^{3} +(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} -4.64575 q^{11} +(1.00000 - 1.73205i) q^{13} +(-2.17712 + 3.77089i) q^{15} +(1.67712 + 4.02334i) q^{19} +(4.82288 + 8.35347i) q^{21} +(-0.822876 + 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} +2.64575 q^{27} +(0.822876 - 1.42526i) q^{29} +5.64575 q^{31} +(6.14575 + 10.6448i) q^{33} +(3.00000 + 5.19615i) q^{35} -0.354249 q^{37} -5.29150 q^{39} +(0.145751 + 0.252449i) q^{41} +(-5.64575 - 9.77873i) q^{43} +6.58301 q^{45} +(2.17712 - 3.77089i) q^{47} +6.29150 q^{49} +(-6.29150 + 10.8972i) q^{53} +(3.82288 + 6.62141i) q^{55} +(7.00000 - 9.16515i) q^{57} +(3.96863 + 6.87386i) q^{59} +(0.468627 - 0.811686i) q^{61} +(7.29150 - 12.6293i) q^{63} -3.29150 q^{65} +(-0.322876 + 0.559237i) q^{67} +4.35425 q^{69} +(-1.35425 - 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} -6.06275 q^{75} +16.9373 q^{77} +(-2.00000 - 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +7.93725 q^{83} -4.35425 q^{87} +(-3.64575 + 6.31463i) q^{91} +(-7.46863 - 12.9360i) q^{93} +(4.35425 - 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +(9.29150 - 16.0934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^9	$ 4 q + 2 q^{5} - 4 q^{7} - 8 q^{9} - 8 q^{11} + 4 q^{13} - 14 q^{15} + 12 q^{19} + 14 q^{21} + 2 q^{23} - 6 q^{25} - 2 q^{29} + 12 q^{31} + 14 q^{33} + 12 q^{35} - 12 q^{37} - 10 q^{41} - 12 q^{43} - 16 q^{45} + 14 q^{47} + 4 q^{49} - 4 q^{53} + 10 q^{55} + 28 q^{57} - 14 q^{61} + 8 q^{63} + 8 q^{65} + 4 q^{67} + 28 q^{69} - 16 q^{71} - 14 q^{73} - 56 q^{75} + 36 q^{77} - 8 q^{79} + 10 q^{81} - 28 q^{87} - 4 q^{91} - 14 q^{93} + 28 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^9 - 8 * q^11 + 4 * q^13 - 14 * q^15 + 12 * q^19 + 14 * q^21 + 2 * q^23 - 6 * q^25 - 2 * q^29 + 12 * q^31 + 14 * q^33 + 12 * q^35 - 12 * q^37 - 10 * q^41 - 12 * q^43 - 16 * q^45 + 14 * q^47 + 4 * q^49 - 4 * q^53 + 10 * q^55 + 28 * q^57 - 14 * q^61 + 8 * q^63 + 8 * q^65 + 4 * q^67 + 28 * q^69 - 16 * q^71 - 14 * q^73 - 56 * q^75 + 36 * q^77 - 8 * q^79 + 10 * q^81 - 28 * q^87 - 4 * q^91 - 14 * q^93 + 28 * q^95 + 18 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	−0.940898	−	0.338689i	$-0.890016\pi$
$3$	−1.32288	−	2.29129i	−0.763763	−	1.32288i	0.177136	−	0.984186i	$-0.443317\pi$
$4$		0			0
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	0.621252	−	0.783611i	$-0.286624\pi$
$5$	−0.822876	−	1.42526i	−0.368001	−	0.637397i	−0.989253	+	0.146214i	$0.953291\pi$
$6$		0			0
$7$	−3.64575			−1.37796			−0.688982	−	0.724778i	$-0.741942\pi$
$7$	−3.64575			−1.37796			−0.688982	+	0.724778i	$0.741942\pi$
$8$		0			0
$9$	−2.00000	+	3.46410i	−0.666667	+	1.15470i
$10$		0			0
$11$	−4.64575			−1.40075			−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575			−1.40075			−0.700373	+	0.713777i	$0.746983\pi$
$12$		0			0
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$		0			0
$15$	−2.17712	+	3.77089i	−0.562131	+	0.973640i
$16$		0			0
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$19$	1.67712	+	4.02334i	0.384759	+	0.923017i
$20$		0			0
$21$	4.82288	+	8.35347i	1.05244	+	1.82288i
$22$		0			0
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	−0.938973	−	0.343991i	$-0.888221\pi$
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	0.767391	+	0.641179i	$0.221554\pi$
$24$		0			0
$25$	1.14575	−	1.98450i	0.229150	−	0.396900i
$26$		0			0
$27$	2.64575			0.509175
$28$		0			0
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	−0.779453	−	0.626461i	$-0.784503\pi$
$29$	0.822876	−	1.42526i	0.152804	−	0.264665i	0.932257	+	0.361796i	$0.117836\pi$
$30$		0			0
$31$	5.64575			1.01401			0.507003	−	0.861944i	$-0.330753\pi$
$31$	5.64575			1.01401			0.507003	+	0.861944i	$0.330753\pi$
$32$		0			0
$33$	6.14575	+	10.6448i	1.06984	+	1.85301i
$34$		0			0
$35$	3.00000	+	5.19615i	0.507093	+	0.878310i
$36$		0			0
$37$	−0.354249			−0.0582381			−0.0291191	−	0.999576i	$-0.509270\pi$
$37$	−0.354249			−0.0582381			−0.0291191	+	0.999576i	$0.509270\pi$
$38$		0			0
$39$	−5.29150			−0.847319
$40$		0			0
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	0.877182	−	0.480158i	$-0.159421\pi$
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	−0.854420	+	0.519583i	$0.826087\pi$
$42$		0			0
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	−0.870995	−	0.491292i	$-0.836525\pi$
$43$	−5.64575	−	9.77873i	−0.860969	−	1.49124i	0.0100257	−	0.999950i	$-0.496809\pi$
$44$		0			0
$45$	6.58301			0.981336
$46$		0			0
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	−0.662413	−	0.749138i	$-0.730468\pi$
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	0.979980	+	0.199098i	$0.0638011\pi$
$48$		0			0
$49$	6.29150			0.898786
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	0.00363070	+	0.999993i	$0.498844\pi$
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$54$		0			0
$55$	3.82288	+	6.62141i	0.515476	+	0.892831i
$56$		0			0
$57$	7.00000	−	9.16515i	0.927173	−	1.21395i
$58$		0			0
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$		0			0
$61$	0.468627	−	0.811686i	0.0600015	−	0.103926i	−0.834464	−	0.551062i	$-0.814223\pi$
$61$	0.468627	−	0.811686i	0.0600015	−	0.103926i	0.894466	+	0.447136i	$0.147556\pi$
$62$		0			0
$63$	7.29150	−	12.6293i	0.918643	−	1.59114i
$64$		0			0
$65$	−3.29150			−0.408261
$66$		0			0
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	−0.885074	−	0.465450i	$-0.845892\pi$
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	0.845629	+	0.533772i	$0.179226\pi$
$68$		0			0
$69$	4.35425			0.524190
$70$		0			0
$71$	−1.35425	−	2.34563i	−0.160720	−	0.278375i	0.774407	−	0.632687i	$-0.218048\pi$
$71$	−1.35425	−	2.34563i	−0.160720	−	0.278375i	−0.935127	+	0.354313i	$0.884715\pi$
$72$		0			0
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	0.811695	−	0.584082i	$-0.198545\pi$
$73$	−0.854249	−	1.47960i	−0.0999822	−	0.173174i	−0.911677	+	0.410907i	$0.865212\pi$
$74$		0			0
$75$	−6.06275			−0.700066
$76$		0			0
$77$	16.9373			1.93018
$78$		0			0
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$		0			0
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$		0			0
$83$	7.93725			0.871227			0.435613	−	0.900134i	$-0.356531\pi$
$83$	7.93725			0.871227			0.435613	+	0.900134i	$0.356531\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−4.35425			−0.466824
$88$		0			0
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−3.64575	+	6.31463i	−0.382179	+	0.661953i
$92$		0			0
$93$	−7.46863	−	12.9360i	−0.774461	−	1.34141i
$94$		0			0
$95$	4.35425	−	5.70105i	0.446736	−	0.584915i
$96$		0			0
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	0.944674	−	0.328012i	$-0.106379\pi$
$97$	1.85425	+	3.21165i	0.188270	+	0.326094i	−0.756403	+	0.654106i	$0.773045\pi$
$98$		0			0
$99$	9.29150	−	16.0934i	0.933831	−	1.61744i
$100$		0			0
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	0.296411	+	0.955061i	$0.404210\pi$
$101$	−6.82288	+	11.8176i	−0.678902	+	1.17589i	−0.975312	+	0.220831i	$0.929123\pi$
$102$		0			0
$103$	13.2915			1.30965			0.654825	−	0.755780i	$-0.272742\pi$
$103$	13.2915			1.30965			0.654825	+	0.755780i	$0.272742\pi$
$104$		0			0
$105$	7.93725	−	13.7477i	0.774597	−	1.34164i
$106$		0			0
$107$	15.2915			1.47829			0.739143	−	0.673549i	$-0.235231\pi$
$107$	15.2915			1.47829			0.739143	+	0.673549i	$0.235231\pi$
$108$		0			0
$109$	7.29150	+	12.6293i	0.698399	+	1.20966i	0.969021	+	0.246977i	$0.0794373\pi$
$109$	7.29150	+	12.6293i	0.698399	+	1.20966i	−0.270622	+	0.962686i	$0.587229\pi$
$110$		0			0
$111$	0.468627	+	0.811686i	0.0444801	+	0.0770418i
$112$		0			0
$113$	−15.5830			−1.46593			−0.732963	−	0.680269i	$-0.761863\pi$
$113$	−15.5830			−1.46593			−0.732963	+	0.680269i	$0.761863\pi$
$114$		0			0
$115$	2.70850			0.252569
$116$		0			0
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	10.5830			0.962091
$122$		0			0
$123$	0.385622	−	0.667916i	0.0347703	−	0.0602240i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	0.404554	+	0.914514i	$0.367427\pi$
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	−0.994270	+	0.106903i	$0.965907\pi$
$128$		0			0
$129$	−14.9373	+	25.8721i	−1.31515	+	2.27791i
$130$		0			0
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	0.820604	−	0.571497i	$-0.193637\pi$
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	−0.905233	+	0.424915i	$0.860304\pi$
$132$		0			0
$133$	−6.11438	−	14.6681i	−0.530184	−	1.27188i
$134$		0			0
$135$	−2.17712	−	3.77089i	−0.187377	−	0.324547i
$136$		0			0
$137$	−7.79150	+	13.4953i	−0.665673	+	1.15298i	0.313429	+	0.949612i	$0.398522\pi$
$137$	−7.79150	+	13.4953i	−0.665673	+	1.15298i	−0.979102	+	0.203368i	$0.934811\pi$
$138$		0			0
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	0.134743	+	0.990881i	$0.456979\pi$
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	−0.925499	+	0.378749i	$0.876354\pi$
$140$		0			0
$141$	−11.5203			−0.970181
$142$		0			0
$143$	−4.64575	+	8.04668i	−0.388497	+	0.672897i
$144$		0			0
$145$	−2.70850			−0.224928
$146$		0			0
$147$	−8.32288	−	14.4156i	−0.686459	−	1.18898i
$148$		0			0
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	0.998256	−	0.0590292i	$-0.0188005\pi$
$149$	5.46863	+	9.47194i	0.448007	+	0.775972i	−0.550249	+	0.835001i	$0.685467\pi$
$150$		0			0
$151$	−12.9373			−1.05282			−0.526409	−	0.850231i	$-0.676462\pi$
$151$	−12.9373			−1.05282			−0.526409	+	0.850231i	$0.676462\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.64575	−	8.04668i	−0.373156	−	0.646325i
$156$		0			0
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	0.573857	−	0.818956i	$-0.305447\pi$
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	−0.996165	+	0.0874969i	$0.972113\pi$
$158$		0			0
$159$	33.2915			2.64019
$160$		0			0
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$		0			0
$163$	3.93725			0.308390			0.154195	−	0.988040i	$-0.450722\pi$
$163$	3.93725			0.308390			0.154195	+	0.988040i	$0.450722\pi$
$164$		0			0
$165$	10.1144	−	17.5186i	0.787403	−	1.36382i
$166$		0			0
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−17.2915	−	2.23695i	−1.32231	−	0.171064i
$172$		0			0
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	−4.17712	+	7.23499i	−0.315761	+	0.546914i
$176$		0			0
$177$	10.5000	−	18.1865i	0.789228	−	1.36698i
$178$		0			0
$179$	4.06275			0.303664			0.151832	−	0.988406i	$-0.451483\pi$
$179$	4.06275			0.303664			0.151832	+	0.988406i	$0.451483\pi$
$180$		0			0
$181$	11.1144	−	19.2507i	0.826125	−	1.43089i	−0.0749311	−	0.997189i	$-0.523874\pi$
$181$	11.1144	−	19.2507i	0.826125	−	1.43089i	0.901056	−	0.433702i	$-0.142793\pi$
$182$		0			0
$183$	−2.47974			−0.183308
$184$		0			0
$185$	0.291503	+	0.504897i	0.0214317	+	0.0371208i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−9.64575			−0.701625
$190$		0			0
$191$	−6.58301			−0.476330			−0.238165	−	0.971225i	$-0.576546\pi$
$191$	−6.58301			−0.476330			−0.238165	+	0.971225i	$0.576546\pi$
$192$		0			0
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	−0.999581	−	0.0289406i	$-0.990787\pi$
$193$	−7.29150	−	12.6293i	−0.524854	−	0.909074i	0.474727	−	0.880133i	$-0.342547\pi$
$194$		0			0
$195$	4.35425	+	7.54178i	0.311814	+	0.540078i
$196$		0			0
$197$	7.64575			0.544737			0.272369	−	0.962193i	$-0.412193\pi$
$197$	7.64575			0.544737			0.272369	+	0.962193i	$0.412193\pi$
$198$		0			0
$199$	−9.93725	+	17.2118i	−0.704433	+	1.22011i	0.262462	+	0.964942i	$0.415465\pi$
$199$	−9.93725	+	17.2118i	−0.704433	+	1.22011i	−0.966896	+	0.255172i	$0.917868\pi$
$200$		0			0
$201$	1.70850			0.120508
$202$		0			0
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$		0			0
$205$	0.239870	−	0.415468i	0.0167533	−	0.0290175i
$206$		0			0
$207$	−3.29150	−	5.70105i	−0.228775	−	0.396250i
$208$		0			0
$209$	−7.79150	−	18.6914i	−0.538950	−	1.29291i
$210$		0			0
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	0.998829	−	0.0483843i	$-0.0154072\pi$
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	−0.541316	+	0.840819i	$0.682074\pi$
$212$		0			0
$213$	−3.58301	+	6.20595i	−0.245503	+	0.425224i
$214$		0			0
$215$	−9.29150	+	16.0934i	−0.633675	+	1.09756i
$216$		0			0
$217$	−20.5830			−1.39727
$218$		0			0
$219$	−2.26013	+	3.91466i	−0.152725	+	0.264528i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	−0.987579	−	0.157126i	$-0.949777\pi$
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	0.357714	−	0.933831i	$-0.383556\pi$
$224$		0			0
$225$	4.58301	+	7.93800i	0.305534	+	0.529200i
$226$		0			0
$227$	−7.35425			−0.488119			−0.244059	−	0.969760i	$-0.578479\pi$
$227$	−7.35425			−0.488119			−0.244059	+	0.969760i	$0.578479\pi$
$228$		0			0
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$		0			0
$231$	−22.4059	−	38.8081i	−1.47420	−	2.55339i
$232$		0			0
$233$	−9.43725	−	16.3458i	−0.618255	−	1.07085i	−0.989804	−	0.142436i	$-0.954507\pi$
$233$	−9.43725	−	16.3458i	−0.618255	−	1.07085i	0.371549	−	0.928413i	$-0.378827\pi$
$234$		0			0
$235$	−7.16601			−0.467459
$236$		0			0
$237$	−5.29150	+	9.16515i	−0.343720	+	0.595341i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	−0.717683	−	0.696370i	$-0.754797\pi$
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	0.961915	+	0.273347i	$0.0881308\pi$
$242$		0			0
$243$	10.5830	−	18.3303i	0.678900	−	1.17589i
$244$		0			0
$245$	−5.17712	−	8.96704i	−0.330754	−	0.572883i
$246$		0			0
$247$	8.64575	+	1.11847i	0.550116	+	0.0711668i
$248$		0			0
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$		0			0
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.126842	+	0.991923i	$0.540484\pi$
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.795610	+	0.605810i	$0.792849\pi$
$252$		0			0
$253$	3.82288	−	6.62141i	0.240342	−	0.416285i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.14575	+	10.6448i	−0.383361	+	0.664001i	−0.991540	−	0.129798i	$-0.958567\pi$
$257$	−6.14575	+	10.6448i	−0.383361	+	0.664001i	0.608179	+	0.793800i	$0.291900\pi$
$258$		0			0
$259$	1.29150			0.0802501
$260$		0			0
$261$	3.29150	+	5.70105i	0.203739	+	0.352886i
$262$		0			0
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	0.646697	−	0.762747i	$-0.276150\pi$
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	−0.983907	+	0.178682i	$0.942817\pi$
$264$		0			0
$265$	20.7085			1.27211
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	6.17712	+	10.6991i	0.375234	+	0.649924i	0.990362	−	0.138503i	$-0.0442292\pi$
$271$	6.17712	+	10.6991i	0.375234	+	0.649924i	−0.615128	+	0.788427i	$0.710896\pi$
$272$		0			0
$273$	19.2915			1.16757
$274$		0			0
$275$	−5.32288	+	9.21949i	−0.320981	+	0.555956i
$276$		0			0
$277$	27.5203			1.65353			0.826766	−	0.562546i	$-0.190178\pi$
$277$	27.5203			1.65353			0.826766	+	0.562546i	$0.190178\pi$
$278$		0			0
$279$	−11.2915	+	19.5575i	−0.676005	+	1.17087i
$280$		0			0
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	0.183857	+	0.982953i	$0.441142\pi$
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	−0.943191	+	0.332252i	$0.892192\pi$
$282$		0			0
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.812866	−	0.582451i	$-0.802094\pi$
$283$	−15.3229	−	26.5400i	−0.910850	−	1.57764i	−0.0979848	−	0.995188i	$-0.531240\pi$
$284$		0			0
$285$	−18.8229	−	2.43506i	−1.11497	−	0.144240i
$286$		0			0
$287$	−0.531373	−	0.920365i	−0.0313660	−	0.0543274i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	4.90588	−	8.49723i	0.287588	−	0.498117i
$292$		0			0
$293$	−28.9373			−1.69053			−0.845266	−	0.534345i	$-0.820558\pi$
$293$	−28.9373			−1.69053			−0.845266	+	0.534345i	$0.820558\pi$
$294$		0			0
$295$	6.53137	−	11.3127i	0.380271	−	0.658649i
$296$		0			0
$297$	−12.2915			−0.713225
$298$		0			0
$299$	1.64575	+	2.85052i	0.0951763	+	0.164850i
$300$		0			0
$301$	20.5830	+	35.6508i	1.18638	+	2.05488i
$302$		0			0
$303$	36.1033			2.07408
$304$		0			0
$305$	−1.54249			−0.0883225
$306$		0			0
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	0.856665	−	0.515874i	$-0.172533\pi$
$307$	−0.322876	−	0.559237i	−0.0184275	−	0.0319173i	−0.875092	+	0.483956i	$0.839199\pi$
$308$		0			0
$309$	−17.5830	−	30.4547i	−1.00026	−	1.73250i
$310$		0			0
$311$	−13.6458			−0.773780			−0.386890	−	0.922126i	$-0.626451\pi$
$311$	−13.6458			−0.773780			−0.386890	+	0.922126i	$0.626451\pi$
$312$		0			0
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	−0.963749	−	0.266812i	$-0.914030\pi$
$313$	−4.43725	+	7.68555i	−0.250808	+	0.434413i	0.712940	+	0.701225i	$0.247363\pi$
$314$		0			0
$315$	−24.0000			−1.35225
$316$		0			0
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$		0			0
$319$	−3.82288	+	6.62141i	−0.214040	+	0.370728i
$320$		0			0
$321$	−20.2288	−	35.0372i	−1.12906	−	1.95559i
$322$		0			0
$323$		0			0
$324$		0			0
$325$	−2.29150	−	3.96900i	−0.127110	−	0.220160i
$326$		0			0
$327$	19.2915	−	33.4139i	1.06682	−	1.84779i
$328$		0			0
$329$	−7.93725	+	13.7477i	−0.437595	+	0.757937i
$330$		0			0
$331$	19.8118			1.08895			0.544476	−	0.838776i	$-0.316728\pi$
$331$	19.8118			1.08895			0.544476	+	0.838776i	$0.316728\pi$
$332$		0			0
$333$	0.708497	−	1.22715i	0.0388254	−	0.0672476i
$334$		0			0
$335$	1.06275			0.0580640
$336$		0			0
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	0.967414	−	0.253202i	$-0.0814836\pi$
$337$	4.85425	+	8.40781i	0.264428	+	0.458002i	−0.702986	+	0.711204i	$0.748150\pi$
$338$		0			0
$339$	20.6144	+	35.7052i	1.11962	+	1.93924i
$340$		0			0
$341$	−26.2288			−1.42037
$342$		0			0
$343$	2.58301			0.139469
$344$		0			0
$345$	−3.58301	−	6.20595i	−0.192903	−	0.334117i
$346$		0			0
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	0.988830	+	0.149046i	$0.0476201\pi$
$347$	11.6144	+	20.1167i	0.623492	+	1.07992i	−0.365338	+	0.930875i	$0.619047\pi$
$348$		0			0
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$		0			0
$351$	2.64575	−	4.58258i	0.141220	−	0.244600i
$352$		0			0
$353$	12.8745			0.685241			0.342620	−	0.939474i	$-0.388686\pi$
$353$	12.8745			0.685241			0.342620	+	0.939474i	$0.388686\pi$
$354$		0			0
$355$	−2.22876	+	3.86032i	−0.118290	+	0.204884i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.46863	−	4.27579i	−0.130289	−	0.225667i	0.793499	−	0.608572i	$-0.208257\pi$
$359$	−2.46863	−	4.27579i	−0.130289	−	0.225667i	−0.923788	+	0.382904i	$0.874924\pi$
$360$		0			0
$361$	−13.3745	+	13.4953i	−0.703921	+	0.710278i
$362$		0			0
$363$	−14.0000	−	24.2487i	−0.734809	−	1.27273i
$364$		0			0
$365$	−1.40588	+	2.43506i	−0.0735872	+	0.127457i
$366$		0			0
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	−0.572718	−	0.819752i	$-0.694111\pi$
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	0.996285	+	0.0861125i	$0.0274444\pi$
$368$		0			0
$369$	−1.16601			−0.0607001
$370$		0			0
$371$	22.9373	−	39.7285i	1.19084	−	2.06260i
$372$		0			0
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$	15.8745	+	27.4955i	0.819756	+	1.41986i
$376$		0			0
$377$	−1.64575	−	2.85052i	−0.0847605	−	0.146810i
$378$		0			0
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$		0			0
$381$	35.1660			1.80161
$382$		0			0
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	0.927887	−	0.372861i	$-0.121623\pi$
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	−0.786851	+	0.617143i	$0.788290\pi$
$384$		0			0
$385$	−13.9373	−	24.1400i	−0.710308	−	1.23029i
$386$		0			0
$387$	45.1660			2.29592
$388$		0			0
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	−2.56275	+	4.43881i	−0.129273	+	0.223908i
$394$		0			0
$395$	−3.29150	+	5.70105i	−0.165613	+	0.286851i
$396$		0			0
$397$	10.5314	+	18.2409i	0.528554	+	0.915483i	0.999446	+	0.0332919i	$0.0105991\pi$
$397$	10.5314	+	18.2409i	0.528554	+	0.915483i	−0.470891	+	0.882191i	$0.656068\pi$
$398$		0			0
$399$	−25.5203	+	33.4139i	−1.27761	+	1.67279i
$400$		0			0
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	−0.972254	−	0.233928i	$-0.924842\pi$
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	0.283539	−	0.958961i	$-0.408491\pi$
$402$		0			0
$403$	5.64575	−	9.77873i	0.281235	−	0.487113i
$404$		0			0
$405$	4.11438	−	7.12631i	0.204445	−	0.354109i
$406$		0			0
$407$	1.64575			0.0815769
$408$		0			0
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	−0.756931	−	0.653495i	$-0.773302\pi$
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	0.944409	+	0.328774i	$0.106635\pi$
$410$		0			0
$411$	41.2288			2.03366
$412$		0			0
$413$	−14.4686	−	25.0604i	−0.711955	−	1.23314i
$414$		0			0
$415$	−6.53137	−	11.3127i	−0.320612	−	0.555317i
$416$		0			0
$417$	49.3320			2.41580
$418$		0			0
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	−12.4059	−	21.4876i	−0.604626	−	1.04724i	−0.992111	−	0.125366i	$-0.959989\pi$
$421$	−12.4059	−	21.4876i	−0.604626	−	1.04724i	0.387485	−	0.921876i	$-0.373344\pi$
$422$		0			0
$423$	8.70850	+	15.0836i	0.423422	+	0.733388i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.70850	+	2.95920i	−0.0826800	+	0.143206i
$428$		0			0
$429$	24.5830			1.18688
$430$		0			0
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	−0.306192	−	0.951970i	$-0.599055\pi$
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	0.977526	−	0.210815i	$-0.0676117\pi$
$432$		0			0
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	−0.996829	−	0.0795788i	$-0.974642\pi$
$433$	−8.93725	+	15.4798i	−0.429497	+	0.743911i	0.567332	+	0.823489i	$0.307976\pi$
$434$		0			0
$435$	3.58301	+	6.20595i	0.171792	+	0.297552i
$436$		0			0
$437$	−7.11438	−	0.920365i	−0.340327	−	0.0440270i
$438$		0			0
$439$	5.40588	+	9.36326i	0.258009	+	0.446884i	0.965708	−	0.259629i	$-0.0836004\pi$
$439$	5.40588	+	9.36326i	0.258009	+	0.446884i	−0.707700	+	0.706513i	$0.750267\pi$
$440$		0			0
$441$	−12.5830	+	21.7944i	−0.599191	+	1.03783i
$442$		0			0
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	−0.964322	−	0.264731i	$-0.914717\pi$
$443$	−5.32288	+	9.21949i	−0.252897	+	0.438031i	0.711425	+	0.702762i	$0.248050\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	14.4686	−	25.0604i	0.684343	−	1.18532i
$448$		0			0
$449$	−24.2915			−1.14639			−0.573193	−	0.819420i	$-0.694296\pi$
$449$	−24.2915			−1.14639			−0.573193	+	0.819420i	$0.694296\pi$
$450$		0			0
$451$	−0.677124	−	1.17281i	−0.0318845	−	0.0552256i
$452$		0			0
$453$	17.1144	+	29.6430i	0.804104	+	1.39275i
$454$		0			0
$455$	12.0000			0.562569
$456$		0			0
$457$	32.8745			1.53780			0.768902	−	0.639366i	$-0.220803\pi$
$457$	32.8745			1.53780			0.768902	+	0.639366i	$0.220803\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	0.998143	−	0.0609066i	$-0.0193992\pi$
$461$	9.58301	+	16.5983i	0.446325	+	0.773058i	−0.551818	+	0.833964i	$0.686066\pi$
$462$		0			0
$463$	38.4575			1.78727			0.893636	−	0.448792i	$-0.148146\pi$
$463$	38.4575			1.78727			0.893636	+	0.448792i	$0.148146\pi$
$464$		0			0
$465$	−12.2915	+	21.2895i	−0.570005	+	0.987277i
$466$		0			0
$467$	−19.3542			−0.895608			−0.447804	−	0.894132i	$-0.647794\pi$
$467$	−19.3542			−0.895608			−0.447804	+	0.894132i	$0.647794\pi$
$468$		0			0
$469$	1.17712	−	2.03884i	0.0543546	−	0.0941448i
$470$		0			0
$471$	−14.0000	+	24.2487i	−0.645086	+	1.11732i
$472$		0			0
$473$	26.2288	+	45.4295i	1.20600	+	2.08885i
$474$		0			0
$475$	9.90588	+	1.28149i	0.454513	+	0.0587989i
$476$		0			0
$477$	−25.1660	−	43.5888i	−1.15227	−	1.99579i
$478$		0			0
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	−0.780979	−	0.624557i	$-0.785280\pi$
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	0.931372	+	0.364069i	$0.118613\pi$
$480$		0			0
$481$	−0.354249	+	0.613577i	−0.0161523	+	0.0279767i
$482$		0			0
$483$	−15.8745			−0.722315
$484$		0			0
$485$	3.05163	−	5.28558i	0.138567	−	0.240006i
$486$		0			0
$487$	−4.22876			−0.191623			−0.0958116	−	0.995399i	$-0.530545\pi$
$487$	−4.22876			−0.191623			−0.0958116	+	0.995399i	$0.530545\pi$
$488$		0			0
$489$	−5.20850	−	9.02138i	−0.235536	−	0.407961i
$490$		0			0
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.843868	−	0.536550i	$-0.819727\pi$
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.0427320	−	0.999087i	$-0.513606\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−30.5830			−1.37460
$496$		0			0
$497$	4.93725	+	8.55157i	0.221466	+	0.383591i
$498$		0			0
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	0.914470	−	0.404653i	$-0.132608\pi$
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	−0.807675	+	0.589628i	$0.799274\pi$
$500$		0			0
$501$	31.7490			1.41844
$502$		0			0
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.102346	+	0.994749i	$0.532635\pi$
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.810305	+	0.586009i	$0.800698\pi$
$504$		0			0
$505$	22.4575			0.999346
$506$		0			0
$507$	11.9059	−	20.6216i	0.528759	−	0.915837i
$508$		0			0
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	0.263560	+	0.964643i	$0.415103\pi$
$509$	−15.8745	+	27.4955i	−0.703625	+	1.21871i	−0.967185	+	0.254072i	$0.918230\pi$
$510$		0			0
$511$	3.11438	+	5.39426i	0.137772	+	0.238628i
$512$		0			0
$513$	4.43725	+	10.6448i	0.195910	+	0.469977i
$514$		0			0
$515$	−10.9373	−	18.9439i	−0.481953	−	0.834767i
$516$		0			0
$517$	−10.1144	+	17.5186i	−0.444830	+	0.770468i
$518$		0			0
$519$	−7.93725	+	13.7477i	−0.348407	+	0.603458i
$520$		0			0
$521$	−11.7085			−0.512959			−0.256479	−	0.966550i	$-0.582563\pi$
$521$	−11.7085			−0.512959			−0.256479	+	0.966550i	$0.582563\pi$
$522$		0			0
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	−0.844806	−	0.535072i	$-0.820284\pi$
$523$	0.937254	−	1.62337i	0.0409833	−	0.0709851i	0.885789	+	0.464087i	$0.153618\pi$
$524$		0			0
$525$	22.1033			0.964666
$526$		0			0
$527$		0			0
$528$		0			0
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$		0			0
$531$	−31.7490			−1.37779
$532$		0			0
$533$	0.583005			0.0252528
$534$		0			0
$535$	−12.5830	−	21.7944i	−0.544011	−	0.942254i
$536$		0			0
$537$	−5.37451	−	9.30892i	−0.231927	−	0.401710i
$538$		0			0
$539$	−29.2288			−1.25897
$540$		0			0
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	−0.767136	−	0.641484i	$-0.778319\pi$
$541$	4.00000	−	6.92820i	0.171973	−	0.297867i	0.939110	+	0.343617i	$0.111652\pi$
$542$		0			0
$543$	−58.8118			−2.52385
$544$		0			0
$545$	12.0000	−	20.7846i	0.514024	−	0.890315i
$546$		0			0
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	−0.961112	−	0.276159i	$-0.910938\pi$
$547$	−5.64575	+	9.77873i	−0.241395	+	0.418108i	0.719717	+	0.694268i	$0.244272\pi$
$548$		0			0
$549$	1.87451	+	3.24674i	0.0800020	+	0.138568i
$550$		0			0
$551$	7.11438	+	0.920365i	0.303083	+	0.0392089i
$552$		0			0
$553$	7.29150	+	12.6293i	0.310066	+	0.537050i
$554$		0			0
$555$	0.771243	−	1.33583i	0.0327375	−	0.0567029i
$556$		0			0
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	−0.917685	−	0.397309i	$-0.869944\pi$
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	0.802922	+	0.596084i	$0.203277\pi$
$558$		0			0
$559$	−22.5830			−0.955159
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.0627			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$563$	10.0627			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$564$		0			0
$565$	12.8229	+	22.2099i	0.539462	+	0.934376i
$566$		0			0
$567$	−9.11438	−	15.7866i	−0.382768	−	0.662973i
$568$		0			0
$569$	6.58301			0.275974			0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301			0.275974			0.137987	+	0.990434i	$0.455937\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$		0			0
$573$	8.70850	+	15.0836i	0.363803	+	0.630125i
$574$		0			0
$575$	1.88562	+	3.26599i	0.0786359	+	0.136201i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$		0			0
$579$	−19.2915	+	33.4139i	−0.801727	+	1.38863i
$580$		0			0
$581$	−28.9373			−1.20052
$582$		0			0
$583$	29.2288	−	50.6257i	1.21053	−	2.09670i
$584$		0			0
$585$	6.58301	−	11.4021i	0.272174	−	0.471419i
$586$		0			0
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	0.974167	−	0.225828i	$-0.0725088\pi$
$587$	7.06275	+	12.2330i	0.291511	+	0.504911i	−0.682656	+	0.730739i	$0.739175\pi$
$588$		0			0
$589$	9.46863	+	22.7148i	0.390148	+	0.935946i
$590$		0			0
$591$	−10.1144	−	17.5186i	−0.416050	−	0.720620i
$592$		0			0
$593$	−14.8542	+	25.7283i	−0.609991	+	1.05654i	0.381250	+	0.924472i	$0.375494\pi$
$593$	−14.8542	+	25.7283i	−0.609991	+	1.05654i	−0.991241	+	0.132063i	$0.957840\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	52.5830			2.15208
$598$		0			0
$599$	−8.46863	+	14.6681i	−0.346019	+	0.599322i	−0.985538	−	0.169453i	$-0.945800\pi$
$599$	−8.46863	+	14.6681i	−0.346019	+	0.599322i	0.639520	+	0.768775i	$0.279133\pi$
$600$		0			0
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$		0			0
$603$	−1.29150	−	2.23695i	−0.0525941	−	0.0910956i
$604$		0			0
$605$	−8.70850	−	15.0836i	−0.354051	−	0.613234i
$606$		0			0
$607$	−6.93725			−0.281574			−0.140787	−	0.990040i	$-0.544963\pi$
$607$	−6.93725			−0.281574			−0.140787	+	0.990040i	$0.544963\pi$
$608$		0			0
$609$	15.8745			0.643268
$610$		0			0
$611$	−4.35425	−	7.54178i	−0.176154	−	0.305108i
$612$		0			0
$613$	3.70850	+	6.42331i	0.149785	+	0.259435i	0.931148	−	0.364642i	$-0.118809\pi$
$613$	3.70850	+	6.42331i	0.149785	+	0.259435i	−0.781363	+	0.624077i	$0.785475\pi$
$614$		0			0
$615$	−1.26927			−0.0511821
$616$		0			0
$617$	15.4373	−	26.7381i	0.621480	−	1.07644i	−0.367730	−	0.929933i	$-0.619865\pi$
$617$	15.4373	−	26.7381i	0.621480	−	1.07644i	0.989210	−	0.146503i	$-0.0468018\pi$
$618$		0			0
$619$	−8.45751			−0.339936			−0.169968	−	0.985450i	$-0.554366\pi$
$619$	−8.45751			−0.339936			−0.169968	+	0.985450i	$0.554366\pi$
$620$		0			0
$621$	−2.17712	+	3.77089i	−0.0873650	+	0.151321i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.14575	+	7.18065i	0.165830	+	0.287226i
$626$		0			0
$627$	−32.5203	+	42.5790i	−1.29873	+	1.70044i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−12.4059	+	21.4876i	−0.493870	+	0.855408i	−0.999975	−	0.00706354i	$-0.997752\pi$
$631$	−12.4059	+	21.4876i	−0.493870	+	0.855408i	0.506105	+	0.862472i	$0.331085\pi$
$632$		0			0
$633$	17.5830	−	30.4547i	0.698862	−	1.21046i
$634$		0			0
$635$	21.8745			0.868063
$636$		0			0
$637$	6.29150	−	10.8972i	0.249278	−	0.431763i
$638$		0			0
$639$	10.8340			0.428586
$640$		0			0
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	0.710437	−	0.703761i	$-0.248497\pi$
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	−0.964693	+	0.263376i	$0.915164\pi$
$642$		0			0
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	0.923122	−	0.384508i	$-0.125629\pi$
$643$	3.26013	+	5.64671i	0.128567	+	0.222685i	−0.794555	+	0.607193i	$0.792296\pi$
$644$		0			0
$645$	49.1660			1.93591
$646$		0			0
$647$	22.4575			0.882896			0.441448	−	0.897287i	$-0.354465\pi$
$647$	22.4575			0.882896			0.441448	+	0.897287i	$0.354465\pi$
$648$		0			0
$649$	−18.4373	−	31.9343i	−0.723726	−	1.25353i
$650$		0			0
$651$	27.2288	+	47.1616i	1.06718	+	1.84841i
$652$		0			0
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$		0			0
$655$	−1.59412	+	2.76110i	−0.0622874	+	0.107885i
$656$		0			0
$657$	6.83399			0.266619
$658$		0			0
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	−0.626335	−	0.779554i	$-0.715446\pi$
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	0.988281	+	0.152646i	$0.0487793\pi$
$660$		0			0
$661$	8.11438	−	14.0545i	0.315613	−	0.546657i	−0.663955	−	0.747773i	$-0.731123\pi$
$661$	8.11438	−	14.0545i	0.315613	−	0.546657i	0.979568	+	0.201115i	$0.0644566\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.8745	+	20.7846i	−0.615587	+	0.805993i
$666$		0			0
$667$	1.35425	+	2.34563i	0.0524367	+	0.0908231i
$668$		0			0
$669$	−24.8856	+	43.1032i	−0.962134	+	1.66646i
$670$		0			0
$671$	−2.17712	+	3.77089i	−0.0840470	+	0.145574i
$672$		0			0
$673$	−13.8745			−0.534823			−0.267411	−	0.963582i	$-0.586168\pi$
$673$	−13.8745			−0.534823			−0.267411	+	0.963582i	$0.586168\pi$
$674$		0			0
$675$	3.03137	−	5.25049i	0.116678	−	0.202092i
$676$		0			0
$677$	11.4170			0.438791			0.219395	−	0.975636i	$-0.429592\pi$
$677$	11.4170			0.438791			0.219395	+	0.975636i	$0.429592\pi$
$678$		0			0
$679$	−6.76013	−	11.7089i	−0.259430	−	0.449346i
$680$		0			0
$681$	9.72876	+	16.8507i	0.372807	+	0.645720i
$682$		0			0
$683$	−5.41699			−0.207276			−0.103638	−	0.994615i	$-0.533048\pi$
$683$	−5.41699			−0.207276			−0.103638	+	0.994615i	$0.533048\pi$
$684$		0			0
$685$	25.6458			0.979874
$686$		0			0
$687$	26.4575	+	45.8258i	1.00942	+	1.74836i
$688$		0			0
$689$	12.5830	+	21.7944i	0.479374	+	0.830301i
$690$		0			0
$691$	2.58301			0.0982622			0.0491311	−	0.998792i	$-0.484355\pi$
$691$	2.58301			0.0982622			0.0491311	+	0.998792i	$0.484355\pi$
$692$		0			0
$693$	−33.8745	+	58.6724i	−1.28679	+	2.22878i
$694$		0			0
$695$	30.6863			1.16400
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−24.9686	+	43.2469i	−0.944400	+	1.63575i
$700$		0			0
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	0.947077	−	0.321008i	$-0.104022\pi$
$701$	5.17712	+	8.96704i	0.195537	+	0.338681i	−0.751539	+	0.659688i	$0.770688\pi$
$702$		0			0
$703$	−0.594119	−	1.42526i	−0.0224076	−	0.0537548i
$704$		0			0
$705$	9.47974	+	16.4194i	0.357028	+	0.618390i
$706$		0			0
$707$	24.8745	−	43.0839i	0.935502	−	1.62034i
$708$		0			0
$709$	1.82288	−	3.15731i	0.0684595	−	0.118575i	−0.829764	−	0.558115i	$-0.811525\pi$
$709$	1.82288	−	3.15731i	0.0684595	−	0.118575i	0.898223	+	0.439539i	$0.144858\pi$
$710$		0			0
$711$	16.0000			0.600047
$712$		0			0
$713$	−4.64575	+	8.04668i	−0.173985	+	0.301350i
$714$		0			0
$715$	15.2915			0.571870
$716$		0			0
$717$	−15.8745	−	27.4955i	−0.592844	−	1.02684i
$718$		0			0
$719$	1.35425	+	2.34563i	0.0505050	+	0.0874771i	0.890173	−	0.455623i	$-0.150584\pi$
$719$	1.35425	+	2.34563i	0.0505050	+	0.0874771i	−0.839668	+	0.543100i	$0.817250\pi$
$720$		0			0
$721$	−48.4575			−1.80465
$722$		0			0
$723$	−20.0627			−0.746142
$724$		0			0
$725$	−1.88562	−	3.26599i	−0.0700302	−	0.121296i
$726$		0			0
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	0.878865	−	0.477071i	$-0.158302\pi$
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	−0.852588	+	0.522584i	$0.824968\pi$
$728$		0			0
$729$	−41.0000			−1.51852
$730$		0			0
$731$		0			0
$732$		0			0
$733$	16.1033			0.594788			0.297394	−	0.954755i	$-0.403883\pi$
$733$	16.1033			0.594788			0.297394	+	0.954755i	$0.403883\pi$
$734$		0			0
$735$	−13.6974	+	23.7246i	−0.505236	+	0.875094i
$736$		0			0
$737$	1.50000	−	2.59808i	0.0552532	−	0.0957014i
$738$		0			0
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	0.989133	+	0.147024i	$0.0469694\pi$
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	−0.367240	+	0.930126i	$0.619697\pi$
$740$		0			0
$741$	−8.87451	−	21.2895i	−0.326013	−	0.782090i
$742$		0			0
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.860263	−	0.509850i	$-0.829701\pi$
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.0114112	−	0.999935i	$-0.503632\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		0			0
$747$	−15.8745	+	27.4955i	−0.580818	+	1.00601i
$748$		0			0
$749$	−55.7490			−2.03702
$750$		0			0
$751$	−3.93725	+	6.81952i	−0.143672	+	0.248848i	−0.928877	−	0.370389i	$-0.879225\pi$
$751$	−3.93725	+	6.81952i	−0.143672	+	0.248848i	0.785204	+	0.619237i	$0.212558\pi$
$752$		0			0
$753$	77.3320			2.81814
$754$		0			0
$755$	10.6458	+	18.4390i	0.387439	+	0.671063i
$756$		0			0
$757$	−2.29150	−	3.96900i	−0.0832861	−	0.144256i	0.821374	−	0.570391i	$-0.193208\pi$
$757$	−2.29150	−	3.96900i	−0.0832861	−	0.144256i	−0.904660	+	0.426135i	$0.859875\pi$
$758$		0			0
$759$	−20.2288			−0.734257
$760$		0			0
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$		0			0
$763$	−26.5830	−	46.0431i	−0.962369	−	1.66687i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.8745			0.573195
$768$		0			0
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	0.349911	+	0.936783i	$0.386212\pi$
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	−0.986233	+	0.165359i	$0.947122\pi$
$770$		0			0
$771$	32.5203			1.17119
$772$		0			0
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	−0.907000	−	0.421130i	$-0.861633\pi$
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	0.818210	+	0.574920i	$0.194967\pi$
$774$		0			0
$775$	6.46863	−	11.2040i	0.232360	−	0.402459i
$776$		0			0
$777$	−1.70850	−	2.95920i	−0.0612920	−	0.106161i
$778$		0			0
$779$	−0.771243	+	1.00979i	−0.0276327	+	0.0361796i
$780$		0			0
$781$	6.29150	+	10.8972i	0.225128	+	0.389933i
$782$		0			0
$783$	2.17712	−	3.77089i	0.0778041	−	0.134761i
$784$		0			0
$785$	−8.70850	+	15.0836i	−0.310820	+	0.538355i
$786$		0			0
$787$	−42.5203			−1.51568			−0.757842	−	0.652438i	$-0.773746\pi$
$787$	−42.5203			−1.51568			−0.757842	+	0.652438i	$0.773746\pi$
$788$		0			0
$789$	−14.4686	+	25.0604i	−0.515097	+	0.892174i
$790$		0			0
$791$	56.8118			2.01999
$792$		0			0
$793$	−0.937254	−	1.62337i	−0.0332829	−	0.0576476i
$794$		0			0
$795$	−27.3948	−	47.4491i	−0.971592	−	1.68285i
$796$		0			0
$797$	44.8118			1.58731			0.793657	−	0.608365i	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.96863	+	6.87386i	0.140050	+	0.242573i
$804$		0			0
$805$	−9.87451			−0.348031
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$		0			0
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	−0.448919	−	0.893572i	$-0.648191\pi$
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	0.998316	−	0.0580106i	$-0.0184757\pi$
$812$		0			0
$813$	16.3431	−	28.3071i	0.573179	−	0.992775i
$814$		0			0
$815$	−3.23987	−	5.61162i	−0.113488	−	0.196566i
$816$		0			0
$817$	29.8745	−	39.1149i	1.04518	−	1.36846i
$818$		0			0
$819$	−14.5830	−	25.2585i	−0.509571	−	0.882604i
$820$		0			0
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	0.442324	+	0.896855i	$0.354154\pi$
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	−0.997861	+	0.0653641i	$0.979179\pi$
$824$		0			0
$825$	28.1660			0.980615
$826$		0			0
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.108928	−	0.994050i	$-0.465258\pi$
$827$	26.3229	−	45.5926i	0.915336	−	1.58541i	0.806408	−	0.591359i	$-0.201408\pi$
$828$		0			0
$829$	17.1660			0.596200			0.298100	−	0.954535i	$-0.403647\pi$
$829$	17.1660			0.596200			0.298100	+	0.954535i	$0.403647\pi$
$830$		0			0
$831$	−36.4059	−	63.0568i	−1.26291	−	2.18742i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	19.7490			0.683443
$836$		0			0
$837$	14.9373			0.516307
$838$		0			0
$839$	−20.7601	−	35.9576i	−0.716719	−	1.24139i	−0.962293	−	0.272016i	$-0.912310\pi$
$839$	−20.7601	−	35.9576i	−0.716719	−	1.24139i	0.245573	−	0.969378i	$-0.421024\pi$
$840$		0			0
$841$	13.1458	+	22.7691i	0.453302	+	0.785142i
$842$		0			0
$843$	67.3542			2.31980
$844$		0			0
$845$	7.40588	−	12.8274i	0.254770	−	0.441275i
$846$		0			0
$847$	−38.5830			−1.32573
$848$		0			0
$849$	−40.5405	+	70.2182i	−1.39135	+	2.40988i
$850$		0			0
$851$	0.291503	−	0.504897i	0.00999258	−	0.0173077i
$852$		0			0
$853$	4.29150	+	7.43310i	0.146938	+	0.254505i	0.930094	−	0.367321i	$-0.119725\pi$
$853$	4.29150	+	7.43310i	0.146938	+	0.254505i	−0.783156	+	0.621825i	$0.786391\pi$
$854$		0			0
$855$	11.0405	+	26.4857i	0.377578	+	0.905790i
$856$		0			0
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	0.629066	−	0.777352i	$-0.283437\pi$
$857$	−10.5000	−	18.1865i	−0.358673	−	0.621240i	−0.987739	+	0.156112i	$0.950104\pi$
$858$		0			0
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	−0.956523	−	0.291656i	$-0.905794\pi$
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	0.730843	+	0.682545i	$0.239127\pi$
$860$		0			0
$861$	−1.40588	+	2.43506i	−0.0479123	+	0.0829865i
$862$		0			0
$863$	31.0627			1.05739			0.528694	−	0.848812i	$-0.322682\pi$
$863$	31.0627			1.05739			0.528694	+	0.848812i	$0.322682\pi$
$864$		0			0
$865$	−4.93725	+	8.55157i	−0.167872	+	0.290762i
$866$		0			0
$867$	−44.9778			−1.52753
$868$		0			0
$869$	9.29150	+	16.0934i	0.315193	+	0.545930i
$870$		0			0
$871$	0.645751	+	1.11847i	0.0218804	+	0.0378980i
$872$		0			0
$873$	−14.8340			−0.502054
$874$		0			0
$875$	43.7490			1.47899
$876$		0			0
$877$	−20.8229	−	36.0663i	−0.703139	−	1.21787i	−0.967359	−	0.253409i	$-0.918448\pi$
$877$	−20.8229	−	36.0663i	−0.703139	−	1.21787i	0.264221	−	0.964462i	$-0.414885\pi$
$878$		0			0
$879$	38.2804	+	66.3036i	1.29117	+	2.23636i
$880$		0			0
$881$	−36.8745			−1.24233			−0.621167	−	0.783678i	$-0.713341\pi$
$881$	−36.8745			−1.24233			−0.621167	+	0.783678i	$0.713341\pi$
$882$		0			0
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	−0.521896	−	0.853009i	$-0.674775\pi$
$883$	14.1974	−	24.5906i	0.477780	−	0.827539i	0.999676	+	0.0254701i	$0.00810828\pi$
$884$		0			0
$885$	−34.5608			−1.16175
$886$		0			0
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	−0.974377	−	0.224919i	$-0.927788\pi$
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	0.681975	+	0.731376i	$0.261121\pi$
$888$		0			0
$889$	24.2288	−	41.9654i	0.812606	−	1.40748i
$890$		0			0
$891$	−11.6144	−	20.1167i	−0.389096	−	0.673935i
$892$		0			0
$893$	18.8229	+	2.43506i	0.629884	+	0.0814861i
$894$		0			0
$895$	−3.34313	−	5.79048i	−0.111749	−	0.193554i
$896$		0			0
$897$	4.35425	−	7.54178i	0.145384	−	0.251813i
$898$		0			0
$899$	4.64575	−	8.04668i	0.154944	−	0.268372i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	54.4575	−	94.3232i	1.81223	−	3.13888i
$904$		0			0
$905$	−36.5830			−1.21606
$906$		0			0
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	−0.979811	−	0.199927i	$-0.935929\pi$
$907$	−19.9686	−	34.5867i	−0.663047	−	1.14843i	0.316763	−	0.948505i	$-0.397404\pi$
$908$		0			0
$909$	−27.2915	−	47.2703i	−0.905202	−	1.56786i
$910$		0			0
$911$	−16.9373			−0.561156			−0.280578	−	0.959831i	$-0.590526\pi$
$911$	−16.9373			−0.561156			−0.280578	+	0.959831i	$0.590526\pi$
$912$		0			0
$913$	−36.8745			−1.22037
$914$		0			0
$915$	2.04052	+	3.53428i	0.0674575	+	0.116840i
$916$		0			0
$917$	3.53137	+	6.11652i	0.116616	+	0.201985i
$918$		0			0
$919$	19.8745			0.655600			0.327800	−	0.944747i	$-0.393693\pi$
$919$	19.8745			0.655600			0.327800	+	0.944747i	$0.393693\pi$
$920$		0			0
$921$	−0.854249	+	1.47960i	−0.0281485	+	0.0487545i
$922$		0			0
$923$	−5.41699			−0.178303
$924$		0			0
$925$	−0.405881	+	0.703006i	−0.0133453	+	0.0231147i
$926$		0			0
$927$	−26.5830	+	46.0431i	−0.873100	+	1.51225i
$928$		0			0
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	0.933859	−	0.357640i	$-0.116419\pi$
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	−0.776655	+	0.629926i	$0.783085\pi$
$930$		0			0
$931$	10.5516	+	25.3128i	0.345816	+	0.829595i
$932$		0			0
$933$	18.0516	+	31.2663i	0.590984	+	1.02361i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	−0.918334	−	0.395805i	$-0.870466\pi$
$937$	−3.56275	+	6.17086i	−0.116390	+	0.201593i	0.801945	+	0.597398i	$0.203799\pi$
$938$		0			0
$939$	23.4797			0.766232
$940$		0			0
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	−0.695594	−	0.718435i	$-0.744859\pi$
$941$	8.41699	−	14.5787i	0.274386	−	0.475251i	0.969980	+	0.243184i	$0.0781920\pi$
$942$		0			0
$943$	−0.479741			−0.0156225
$944$		0			0
$945$	7.93725	+	13.7477i	0.258199	+	0.447214i
$946$		0			0
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	0.922086	−	0.386985i	$-0.126483\pi$
$947$	3.87451	+	6.71084i	0.125905	+	0.218073i	−0.796182	+	0.605058i	$0.793150\pi$
$948$		0			0
$949$	−3.41699			−0.110920
$950$		0			0
$951$	15.8745			0.514766
$952$		0			0
$953$	6.72876	+	11.6545i	0.217966	+	0.377528i	0.954186	−	0.299214i	$-0.0967245\pi$
$953$	6.72876	+	11.6545i	0.217966	+	0.377528i	−0.736220	+	0.676742i	$0.763391\pi$
$954$		0			0
$955$	5.41699	+	9.38251i	0.175290	+	0.303611i
$956$		0			0
$957$	20.2288			0.653903
$958$		0			0
$959$	28.4059	−	49.2004i	0.917274	−	1.58876i
$960$		0			0
$961$	0.874508			0.0282099
$962$		0			0
$963$	−30.5830	+	52.9713i	−0.985524	+	1.70698i
$964$		0			0
$965$	−12.0000	+	20.7846i	−0.386294	+	0.669080i
$966$		0			0
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	0.739161	−	0.673529i	$-0.235222\pi$
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	−0.952874	+	0.303367i	$0.901889\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.859082	+	0.511838i	$0.171035\pi$
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.0137234	+	0.999906i	$0.495632\pi$
$972$		0			0
$973$	33.9889	−	58.8705i	1.08963	−	1.88730i
$974$		0			0
$975$	−6.06275	+	10.5010i	−0.194163	+	0.336301i
$976$		0			0
$977$	−7.45751			−0.238587			−0.119293	−	0.992859i	$-0.538063\pi$
$977$	−7.45751			−0.238587			−0.119293	+	0.992859i	$0.538063\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−58.3320			−1.86240
$982$		0			0
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	0.999973	+	0.00731102i	$0.00232719\pi$
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	−0.493655	+	0.869658i	$0.664339\pi$
$984$		0			0
$985$	−6.29150	−	10.8972i	−0.200464	−	0.347214i
$986$		0			0
$987$	42.0000			1.33687
$988$		0			0
$989$	18.5830			0.590905
$990$		0			0
$991$	−1.41699	−	2.45431i	−0.0450123	−	0.0779636i	0.842641	−	0.538475i	$-0.180999\pi$
$991$	−1.41699	−	2.45431i	−0.0450123	−	0.0779636i	−0.887654	+	0.460511i	$0.847666\pi$
$992$		0			0
$993$	−26.2085	−	45.3944i	−0.831702	−	1.44055i
$994$		0			0
$995$	32.7085			1.03693
$996$		0			0
$997$	8.11438	−	14.0545i	0.256985	−	0.445111i	−0.708448	−	0.705763i	$-0.750604\pi$
$997$	8.11438	−	14.0545i	0.256985	−	0.445111i	0.965433	+	0.260652i	$0.0839376\pi$
$998$		0			0
$999$	−0.937254			−0.0296534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.i.k.577.1		4
4.3	odd	2		1216.2.i.l.577.2		4
8.3	odd	2		38.2.c.b.7.1	✓	4
8.5	even	2		304.2.i.e.273.2		4
19.11	even	3	inner	1216.2.i.k.961.1		4
24.5	odd	2		2736.2.s.v.577.1		4
24.11	even	2		342.2.g.f.235.1		4
40.3	even	4		950.2.j.g.349.2		8
40.19	odd	2		950.2.e.k.501.2		4
40.27	even	4		950.2.j.g.349.3		8
76.11	odd	6		1216.2.i.l.961.2		4
152.3	even	18		722.2.e.o.595.2		12
152.11	odd	6		38.2.c.b.11.1	yes	4
152.27	even	6		722.2.c.j.429.2		4
152.35	odd	18		722.2.e.n.595.1		12
152.43	odd	18		722.2.e.n.99.2		12
152.45	even	6		5776.2.a.ba.1.1		2
152.51	even	18		722.2.e.o.423.1		12
152.59	even	18		722.2.e.o.389.1		12
152.67	even	18		722.2.e.o.415.2		12
152.69	odd	6		5776.2.a.z.1.2		2
152.75	even	2		722.2.c.j.653.2		4
152.83	odd	6		722.2.a.j.1.2		2
152.91	even	18		722.2.e.o.245.1		12
152.99	odd	18		722.2.e.n.245.2		12
152.107	even	6		722.2.a.g.1.1		2
152.123	odd	18		722.2.e.n.415.1		12
152.125	even	6		304.2.i.e.49.2		4
152.131	odd	18		722.2.e.n.389.2		12
152.139	odd	18		722.2.e.n.423.2		12
152.147	even	18		722.2.e.o.99.1		12
456.11	even	6		342.2.g.f.163.1		4
456.83	even	6		6498.2.a.ba.1.2		2
456.107	odd	6		6498.2.a.bg.1.2		2
456.125	odd	6		2736.2.s.v.1873.1		4
760.163	even	12		950.2.j.g.49.3		8
760.467	even	12		950.2.j.g.49.2		8
760.619	odd	6		950.2.e.k.201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	8.3	odd	2
38.2.c.b.11.1	yes	4	152.11	odd	6
304.2.i.e.49.2		4	152.125	even	6
304.2.i.e.273.2		4	8.5	even	2
342.2.g.f.163.1		4	456.11	even	6
342.2.g.f.235.1		4	24.11	even	2
722.2.a.g.1.1		2	152.107	even	6
722.2.a.j.1.2		2	152.83	odd	6
722.2.c.j.429.2		4	152.27	even	6
722.2.c.j.653.2		4	152.75	even	2
722.2.e.n.99.2		12	152.43	odd	18
722.2.e.n.245.2		12	152.99	odd	18
722.2.e.n.389.2		12	152.131	odd	18
722.2.e.n.415.1		12	152.123	odd	18
722.2.e.n.423.2		12	152.139	odd	18
722.2.e.n.595.1		12	152.35	odd	18
722.2.e.o.99.1		12	152.147	even	18
722.2.e.o.245.1		12	152.91	even	18
722.2.e.o.389.1		12	152.59	even	18
722.2.e.o.415.2		12	152.67	even	18
722.2.e.o.423.1		12	152.51	even	18
722.2.e.o.595.2		12	152.3	even	18
950.2.e.k.201.2		4	760.619	odd	6
950.2.e.k.501.2		4	40.19	odd	2
950.2.j.g.49.2		8	760.467	even	12
950.2.j.g.49.3		8	760.163	even	12
950.2.j.g.349.2		8	40.3	even	4
950.2.j.g.349.3		8	40.27	even	4
1216.2.i.k.577.1		4	1.1	even	1	trivial
1216.2.i.k.961.1		4	19.11	even	3	inner
1216.2.i.l.577.2		4	4.3	odd	2
1216.2.i.l.961.2		4	76.11	odd	6
2736.2.s.v.577.1		4	24.5	odd	2
2736.2.s.v.1873.1		4	456.125	odd	6
5776.2.a.z.1.2		2	152.69	odd	6
5776.2.a.ba.1.1		2	152.45	even	6
6498.2.a.ba.1.2		2	456.83	even	6
6498.2.a.bg.1.2		2	456.107	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 - 2.29129i) q^{3} +(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(-1.32288 - 2.29129i) q^{3} +(-0.822876 - 1.42526i) q^{5} -3.64575 q^{7} +(-2.00000 + 3.46410i) q^{9} -4.64575 q^{11} +(1.00000 - 1.73205i) q^{13} +(-2.17712 + 3.77089i) q^{15} +(1.67712 + 4.02334i) q^{19} +(4.82288 + 8.35347i) q^{21} +(-0.822876 + 1.42526i) q^{23} +(1.14575 - 1.98450i) q^{25} +2.64575 q^{27} +(0.822876 - 1.42526i) q^{29} +5.64575 q^{31} +(6.14575 + 10.6448i) q^{33} +(3.00000 + 5.19615i) q^{35} -0.354249 q^{37} -5.29150 q^{39} +(0.145751 + 0.252449i) q^{41} +(-5.64575 - 9.77873i) q^{43} +6.58301 q^{45} +(2.17712 - 3.77089i) q^{47} +6.29150 q^{49} +(-6.29150 + 10.8972i) q^{53} +(3.82288 + 6.62141i) q^{55} +(7.00000 - 9.16515i) q^{57} +(3.96863 + 6.87386i) q^{59} +(0.468627 - 0.811686i) q^{61} +(7.29150 - 12.6293i) q^{63} -3.29150 q^{65} +(-0.322876 + 0.559237i) q^{67} +4.35425 q^{69} +(-1.35425 - 2.34563i) q^{71} +(-0.854249 - 1.47960i) q^{73} -6.06275 q^{75} +16.9373 q^{77} +(-2.00000 - 3.46410i) q^{79} +(2.50000 + 4.33013i) q^{81} +7.93725 q^{83} -4.35425 q^{87} +(-3.64575 + 6.31463i) q^{91} +(-7.46863 - 12.9360i) q^{93} +(4.35425 - 5.70105i) q^{95} +(1.85425 + 3.21165i) q^{97} +(9.29150 - 16.0934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^9	\( 4 q + 2 q^{5} - 4 q^{7} - 8 q^{9} - 8 q^{11} + 4 q^{13} - 14 q^{15} + 12 q^{19} + 14 q^{21} + 2 q^{23} - 6 q^{25} - 2 q^{29} + 12 q^{31} + 14 q^{33} + 12 q^{35} - 12 q^{37} - 10 q^{41} - 12 q^{43} - 16 q^{45} + 14 q^{47} + 4 q^{49} - 4 q^{53} + 10 q^{55} + 28 q^{57} - 14 q^{61} + 8 q^{63} + 8 q^{65} + 4 q^{67} + 28 q^{69} - 16 q^{71} - 14 q^{73} - 56 q^{75} + 36 q^{77} - 8 q^{79} + 10 q^{81} - 28 q^{87} - 4 q^{91} - 14 q^{93} + 28 q^{95} + 18 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q + 2 * q^5 - 4 * q^7 - 8 * q^9 - 8 * q^11 + 4 * q^13 - 14 * q^15 + 12 * q^19 + 14 * q^21 + 2 * q^23 - 6 * q^25 - 2 * q^29 + 12 * q^31 + 14 * q^33 + 12 * q^35 - 12 * q^37 - 10 * q^41 - 12 * q^43 - 16 * q^45 + 14 * q^47 + 4 * q^49 - 4 * q^53 + 10 * q^55 + 28 * q^57 - 14 * q^61 + 8 * q^63 + 8 * q^65 + 4 * q^67 + 28 * q^69 - 16 * q^71 - 14 * q^73 - 56 * q^75 + 36 * q^77 - 8 * q^79 + 10 * q^81 - 28 * q^87 - 4 * q^91 - 14 * q^93 + 28 * q^95 + 18 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more