LMFDB - Embedded newform 1568.2.q.c.1391.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1568,2,Mod(815,1568)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1568, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1568.815"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1568 = 2^{5} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1568.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,4,0,-8,0,0,0,0,0,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(23)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.5205430369$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 392)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1391.3
Root			$1.60021 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1568.1391
Dual form			1568.2.q.c.815.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.937379 - 0.541196i) q^{3} +(0.662827 - 1.14805i) q^{5} +(-0.914214 + 1.58346i) q^{9} +(-1.00000 - 1.73205i) q^{11} -5.85172 q^{13} -1.43488i q^{15} +(-3.86324 + 2.23044i) q^{17} +(-3.58869 - 2.07193i) q^{19} +(-7.24264 - 4.18154i) q^{23} +(1.62132 + 2.80821i) q^{25} +5.22625i q^{27} +4.47871i q^{29} +(-3.20041 - 5.54328i) q^{31} +(-1.87476 - 1.08239i) q^{33} +(-2.12132 - 1.22474i) q^{37} +(-5.48528 + 3.16693i) q^{39} -0.317025i q^{41} +3.17157 q^{43} +(1.21193 + 2.09913i) q^{45} +(6.40083 - 11.0866i) q^{47} +(-2.41421 + 4.18154i) q^{51} +(-3.00000 + 1.73205i) q^{53} -2.65131 q^{55} -4.48528 q^{57} +(0.937379 - 0.541196i) q^{59} +(4.80062 - 8.31492i) q^{61} +(-3.87868 + 6.71807i) q^{65} +(6.00000 + 10.3923i) q^{67} -9.05213 q^{69} +(6.12627 - 3.53701i) q^{73} +(3.03958 + 1.75490i) q^{75} +(-1.75736 - 1.01461i) q^{79} +(0.0857864 + 0.148586i) q^{81} +5.67459i q^{83} +5.91359i q^{85} +(2.42386 + 4.19825i) q^{87} +(-11.0406 - 6.37430i) q^{89} +(-6.00000 - 3.46410i) q^{93} +(-4.75736 + 2.74666i) q^{95} +9.23880i q^{97} +3.65685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9} - 8 q^{11} - 24 q^{23} - 4 q^{25} + 24 q^{39} + 48 q^{43} - 8 q^{51} - 24 q^{53} + 32 q^{57} - 48 q^{65} + 48 q^{67} - 48 q^{79} + 12 q^{81} - 48 q^{93} - 72 q^{95} - 16 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 - 8 * q^11 - 24 * q^23 - 4 * q^25 + 24 * q^39 + 48 * q^43 - 8 * q^51 - 24 * q^53 + 32 * q^57 - 48 * q^65 + 48 * q^67 - 48 * q^79 + 12 * q^81 - 48 * q^93 - 72 * q^95 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times$.

$n$	$197$	$1471$	$1473$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.937379	−	0.541196i	0.541196	−	0.312460i	−0.204367	−	0.978894i	$-0.565514\pi$
$3$	0.937379	−	0.541196i	0.541196	−	0.312460i	0.745564	+	0.666435i	$0.232180\pi$
$4$		0			0
$5$	0.662827	−	1.14805i	0.296425	−	0.513424i	−0.678890	−	0.734240i	$-0.737539\pi$
$5$	0.662827	−	1.14805i	0.296425	−	0.513424i	0.975315	+	0.220816i	$0.0708721\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.914214	+	1.58346i	−0.304738	+	0.527821i
$10$		0			0
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−5.85172			−1.62298			−0.811488	−	0.584369i	$-0.801342\pi$
$13$	−5.85172			−1.62298			−0.811488	+	0.584369i	$0.801342\pi$
$14$		0			0
$15$		−	1.43488i		−	0.370484i
$16$		0			0
$17$	−3.86324	+	2.23044i	−0.936973	+	0.540962i	−0.889010	−	0.457887i	$-0.848606\pi$
$17$	−3.86324	+	2.23044i	−0.936973	+	0.540962i	−0.0479630	+	0.998849i	$0.515273\pi$
$18$		0			0
$19$	−3.58869	−	2.07193i	−0.823301	−	0.475333i	0.0282522	−	0.999601i	$-0.491006\pi$
$19$	−3.58869	−	2.07193i	−0.823301	−	0.475333i	−0.851554	+	0.524268i	$0.824339\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.24264	−	4.18154i	−1.51019	−	0.871911i	−0.999929	−	0.0118947i	$-0.996214\pi$
$23$	−7.24264	−	4.18154i	−1.51019	−	0.871911i	−0.510266	−	0.860017i	$-0.670453\pi$
$24$		0			0
$25$	1.62132	+	2.80821i	0.324264	+	0.561642i
$26$		0			0
$27$			5.22625i			1.00579i
$28$		0			0
$29$			4.47871i			0.831676i	0.909439	+	0.415838i	$0.136512\pi$
$29$			4.47871i			0.831676i	−0.909439	+	0.415838i	$0.863488\pi$
$30$		0			0
$31$	−3.20041	−	5.54328i	−0.574811	−	0.995602i	−0.996062	−	0.0886579i	$-0.971742\pi$
$31$	−3.20041	−	5.54328i	−0.574811	−	0.995602i	0.421251	−	0.906944i	$-0.361591\pi$
$32$		0			0
$33$	−1.87476	−	1.08239i	−0.326354	−	0.188420i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.12132	−	1.22474i	−0.348743	−	0.201347i	0.315389	−	0.948963i	$-0.397865\pi$
$37$	−2.12132	−	1.22474i	−0.348743	−	0.201347i	−0.664131	+	0.747616i	$0.731198\pi$
$38$		0			0
$39$	−5.48528	+	3.16693i	−0.878348	+	0.507114i
$40$		0			0
$41$		−	0.317025i		−	0.0495110i	−0.999694	−	0.0247555i	$-0.992119\pi$
$41$		−	0.317025i		−	0.0495110i	0.999694	−	0.0247555i	$-0.00788073\pi$
$42$		0			0
$43$	3.17157			0.483660			0.241830	−	0.970319i	$-0.422252\pi$
$43$	3.17157			0.483660			0.241830	+	0.970319i	$0.422252\pi$
$44$		0			0
$45$	1.21193	+	2.09913i	0.180664	+	0.312919i
$46$		0			0
$47$	6.40083	−	11.0866i	0.933656	−	1.61714i	0.156644	−	0.987655i	$-0.449933\pi$
$47$	6.40083	−	11.0866i	0.933656	−	1.61714i	0.777013	−	0.629485i	$-0.216734\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−2.41421	+	4.18154i	−0.338058	+	0.585533i
$52$		0			0
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	−0.691684	−	0.722200i	$-0.743131\pi$
$53$	−3.00000	+	1.73205i	−0.412082	+	0.237915i	0.279602	+	0.960116i	$0.409797\pi$
$54$		0			0
$55$	−2.65131			−0.357502
$56$		0			0
$57$	−4.48528			−0.594090
$58$		0			0
$59$	0.937379	−	0.541196i	0.122036	−	0.0704577i	−0.437739	−	0.899102i	$-0.644221\pi$
$59$	0.937379	−	0.541196i	0.122036	−	0.0704577i	0.559776	+	0.828644i	$0.310887\pi$
$60$		0			0
$61$	4.80062	−	8.31492i	0.614656	−	1.06462i	−0.375788	−	0.926705i	$-0.622628\pi$
$61$	4.80062	−	8.31492i	0.614656	−	1.06462i	0.990445	−	0.137910i	$-0.0440386\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.87868	+	6.71807i	−0.481091	+	0.833274i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$		0			0
$69$	−9.05213			−1.08975
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$	6.12627	−	3.53701i	0.717026	−	0.413975i	−0.0966311	−	0.995320i	$-0.530807\pi$
$73$	6.12627	−	3.53701i	0.717026	−	0.413975i	0.813657	+	0.581345i	$0.197473\pi$
$74$		0			0
$75$	3.03958	+	1.75490i	0.350981	+	0.202639i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−1.75736	−	1.01461i	−0.197718	−	0.114153i	0.397872	−	0.917441i	$-0.369749\pi$
$79$	−1.75736	−	1.01461i	−0.197718	−	0.114153i	−0.595591	+	0.803288i	$0.703082\pi$
$80$		0			0
$81$	0.0857864	+	0.148586i	0.00953183	+	0.0165096i
$82$		0			0
$83$			5.67459i			0.622868i	0.950268	+	0.311434i	$0.100809\pi$
$83$			5.67459i			0.622868i	−0.950268	+	0.311434i	$0.899191\pi$
$84$		0			0
$85$			5.91359i			0.641419i
$86$		0			0
$87$	2.42386	+	4.19825i	0.259865	+	0.450100i
$88$		0			0
$89$	−11.0406	−	6.37430i	−1.17030	−	0.675675i	−0.216551	−	0.976271i	$-0.569481\pi$
$89$	−11.0406	−	6.37430i	−1.17030	−	0.675675i	−0.953751	+	0.300597i	$0.902814\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.00000	−	3.46410i	−0.622171	−	0.359211i
$94$		0			0
$95$	−4.75736	+	2.74666i	−0.488095	+	0.281802i
$96$		0			0
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$	3.65685			0.367528
$100$		0			0
$101$	0.274552	+	0.475538i	0.0273189	+	0.0473178i	0.879362	−	0.476154i	$-0.157970\pi$
$101$	0.274552	+	0.475538i	0.0273189	+	0.0473178i	−0.852043	+	0.523472i	$0.824636\pi$
$102$		0			0
$103$	0.549104	−	0.951076i	0.0541048	−	0.0937123i	−0.837704	−	0.546124i	$-0.816103\pi$
$103$	0.549104	−	0.951076i	0.0541048	−	0.0937123i	0.891809	+	0.452411i	$0.149436\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.24264	−	7.34847i	0.410152	−	0.710403i	−0.584754	−	0.811210i	$-0.698809\pi$
$107$	4.24264	−	7.34847i	0.410152	−	0.710403i	0.994906	+	0.100807i	$0.0321425\pi$
$108$		0			0
$109$	−12.3640	+	7.13834i	−1.18425	+	0.683729i	−0.956995	−	0.290106i	$-0.906309\pi$
$109$	−12.3640	+	7.13834i	−1.18425	+	0.683729i	−0.227258	+	0.973835i	$0.572976\pi$
$110$		0			0
$111$	−2.65131			−0.251651
$112$		0			0
$113$	0.485281			0.0456514			0.0228257	−	0.999739i	$-0.492734\pi$
$113$	0.485281			0.0456514			0.0228257	+	0.999739i	$0.492734\pi$
$114$		0			0
$115$	−9.60124	+	5.54328i	−0.895320	+	0.516913i
$116$		0			0
$117$	5.34972	−	9.26599i	0.494582	−	0.856641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$		0			0
$123$	−0.171573	−	0.297173i	−0.0154702	−	0.0267952i
$124$		0			0
$125$	10.9269			0.977331
$126$		0			0
$127$			15.2913i			1.35688i	0.734655	+	0.678441i	$0.237344\pi$
$127$			15.2913i			1.35688i	−0.734655	+	0.678441i	$0.762656\pi$
$128$		0			0
$129$	2.97297	−	1.71644i	0.261755	−	0.151124i
$130$		0			0
$131$	−11.8643	−	6.84984i	−1.03659	−	0.598473i	−0.117722	−	0.993047i	$-0.537559\pi$
$131$	−11.8643	−	6.84984i	−1.03659	−	0.598473i	−0.918864	+	0.394573i	$0.870892\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.00000	+	3.46410i	0.516398	+	0.298142i
$136$		0			0
$137$	4.12132	+	7.13834i	0.352108	+	0.609869i	0.986619	−	0.163045i	$-0.0521316\pi$
$137$	4.12132	+	7.13834i	0.352108	+	0.609869i	−0.634510	+	0.772914i	$0.718798\pi$
$138$		0			0
$139$		−	17.3952i		−	1.47544i	−0.675106	−	0.737721i	$-0.735902\pi$
$139$		−	17.3952i		−	1.47544i	0.675106	−	0.737721i	$-0.264098\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	5.85172	+	10.1355i	0.489346	+	0.847571i
$144$		0			0
$145$	5.14179	+	2.96861i	0.427002	+	0.246530i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.514719	−	0.297173i	−0.0421674	−	0.0243454i	0.478768	−	0.877941i	$-0.341083\pi$
$149$	−0.514719	−	0.297173i	−0.0421674	−	0.0243454i	−0.520936	+	0.853596i	$0.674417\pi$
$150$		0			0
$151$	−4.75736	+	2.74666i	−0.387148	+	0.223520i	−0.680924	−	0.732354i	$-0.738422\pi$
$151$	−4.75736	+	2.74666i	−0.387148	+	0.223520i	0.293775	+	0.955874i	$0.405088\pi$
$152$		0			0
$153$		−	8.15640i		−	0.659406i
$154$		0			0
$155$	−8.48528			−0.681554
$156$		0			0
$157$	−6.28710	−	10.8896i	−0.501765	−	0.869083i	−0.999998	−	0.00203967i	$-0.999351\pi$
$157$	−6.28710	−	10.8896i	−0.501765	−	0.869083i	0.498233	−	0.867043i	$-0.333983\pi$
$158$		0			0
$159$	−1.87476	+	3.24718i	−0.148678	+	0.257518i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.0711	+	17.4436i	−0.788827	+	1.36629i	0.137859	+	0.990452i	$0.455978\pi$
$163$	−10.0711	+	17.4436i	−0.788827	+	1.36629i	−0.926686	+	0.375836i	$0.877355\pi$
$164$		0			0
$165$	−2.48528	+	1.43488i	−0.193479	+	0.111705i
$166$		0			0
$167$	−16.5512			−1.28077			−0.640384	−	0.768055i	$-0.721225\pi$
$167$	−16.5512			−1.28077			−0.640384	+	0.768055i	$0.721225\pi$
$168$		0			0
$169$	21.2426			1.63405
$170$		0			0
$171$	6.56165	−	3.78837i	0.501782	−	0.289704i
$172$		0			0
$173$	−5.18889	+	8.98743i	−0.394504	+	0.683302i	−0.993038	−	0.117796i	$-0.962417\pi$
$173$	−5.18889	+	8.98743i	−0.394504	+	0.683302i	0.598533	+	0.801098i	$0.295750\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.585786	−	1.01461i	0.0440304	−	0.0762629i
$178$		0			0
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	0.792846	−	0.609421i	$-0.208598\pi$
$179$	−1.75736	−	3.04384i	−0.131351	−	0.227507i	−0.924198	+	0.381914i	$0.875265\pi$
$180$		0			0
$181$	14.1273			1.05007			0.525037	−	0.851079i	$-0.324051\pi$
$181$	14.1273			1.05007			0.525037	+	0.851079i	$0.324051\pi$
$182$		0			0
$183$		−	10.3923i		−	0.768221i
$184$		0			0
$185$	−2.81214	+	1.62359i	−0.206752	+	0.119369i
$186$		0			0
$187$	7.72648	+	4.46088i	0.565016	+	0.326212i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.75736	−	1.01461i	−0.127158	−	0.0734147i	0.435072	−	0.900396i	$-0.356723\pi$
$191$	−1.75736	−	1.01461i	−0.127158	−	0.0734147i	−0.562230	+	0.826981i	$0.690056\pi$
$192$		0			0
$193$	−7.07107	−	12.2474i	−0.508987	−	0.881591i	−0.999946	−	0.0104081i	$-0.996687\pi$
$193$	−7.07107	−	12.2474i	−0.508987	−	0.881591i	0.490959	−	0.871183i	$-0.336646\pi$
$194$		0			0
$195$			8.39651i			0.601286i
$196$		0			0
$197$		−	12.6677i		−	0.902537i	−0.892388	−	0.451269i	$-0.850972\pi$
$197$		−	12.6677i		−	0.902537i	0.892388	−	0.451269i	$-0.149028\pi$
$198$		0			0
$199$	−3.20041	−	5.54328i	−0.226871	−	0.392953i	0.730008	−	0.683439i	$-0.239516\pi$
$199$	−3.20041	−	5.54328i	−0.226871	−	0.392953i	−0.956879	+	0.290486i	$0.906183\pi$
$200$		0			0
$201$	11.2485	+	6.49435i	0.793412	+	0.458076i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.363961	−	0.210133i	−0.0254201	−	0.0146763i
$206$		0			0
$207$	13.2426	−	7.64564i	0.920427	−	0.531409i
$208$		0			0
$209$			8.28772i			0.573274i
$210$		0			0
$211$	−3.51472			−0.241963			−0.120982	−	0.992655i	$-0.538604\pi$
$211$	−3.51472			−0.241963			−0.120982	+	0.992655i	$0.538604\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.10220	−	3.64113i	0.143369	−	0.248323i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.82843	−	6.63103i	0.258701	−	0.448084i
$220$		0			0
$221$	22.6066	−	13.0519i	1.52068	−	0.877968i
$222$		0			0
$223$	4.84772			0.324628			0.162314	−	0.986739i	$-0.448104\pi$
$223$	4.84772			0.324628			0.162314	+	0.986739i	$0.448104\pi$
$224$		0			0
$225$	−5.92893			−0.395262
$226$		0			0
$227$	10.2170	−	5.89876i	0.678123	−	0.391515i	−0.121024	−	0.992650i	$-0.538618\pi$
$227$	10.2170	−	5.89876i	0.678123	−	0.391515i	0.799148	+	0.601135i	$0.205285\pi$
$228$		0			0
$229$	−7.61276	+	13.1857i	−0.503065	+	0.871334i	0.496929	+	0.867791i	$0.334461\pi$
$229$	−7.61276	+	13.1857i	−0.503065	+	0.871334i	−0.999994	+	0.00354289i	$0.998872\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.87868	−	10.1822i	0.385125	−	0.667056i	−0.606661	−	0.794960i	$-0.707492\pi$
$233$	5.87868	−	10.1822i	0.385125	−	0.667056i	0.991787	+	0.127904i	$0.0408250\pi$
$234$		0			0
$235$	−8.48528	−	14.6969i	−0.553519	−	0.958723i
$236$		0			0
$237$	−2.19642			−0.142673
$238$		0			0
$239$			6.33386i			0.409703i	0.978793	+	0.204852i	$0.0656712\pi$
$239$			6.33386i			0.409703i	−0.978793	+	0.204852i	$0.934329\pi$
$240$		0			0
$241$	−14.5627	+	8.40777i	−0.938065	+	0.541592i	−0.889353	−	0.457221i	$-0.848845\pi$
$241$	−14.5627	+	8.40777i	−0.938065	+	0.541592i	−0.0487118	+	0.998813i	$0.515512\pi$
$242$		0			0
$243$	−13.4174	−	7.74652i	−0.860725	−	0.496940i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	21.0000	+	12.1244i	1.33620	+	0.771454i
$248$		0			0
$249$	3.07107	+	5.31925i	0.194621	+	0.337093i
$250$		0			0
$251$		−	20.1940i		−	1.27464i	−0.770601	−	0.637318i	$-0.780044\pi$
$251$		−	20.1940i		−	1.27464i	0.770601	−	0.637318i	$-0.219956\pi$
$252$		0			0
$253$			16.7262i			1.05156i
$254$		0			0
$255$	3.20041	+	5.54328i	0.200418	+	0.347133i
$256$		0			0
$257$	−1.05110	−	0.606854i	−0.0655660	−	0.0378545i	0.466859	−	0.884332i	$-0.345386\pi$
$257$	−1.05110	−	0.606854i	−0.0655660	−	0.0378545i	−0.532425	+	0.846477i	$0.678719\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−7.09188	−	4.09450i	−0.438977	−	0.253443i
$262$		0			0
$263$	16.2426	−	9.37769i	1.00156	−	0.578253i	0.0928534	−	0.995680i	$-0.470401\pi$
$263$	16.2426	−	9.37769i	1.00156	−	0.578253i	0.908711	+	0.417426i	$0.137068\pi$
$264$		0			0
$265$			4.59220i			0.282097i
$266$		0			0
$267$	−13.7990			−0.844484
$268$		0			0
$269$	6.12627	+	10.6110i	0.373525	+	0.646965i	0.990105	−	0.140327i	$-0.0448155\pi$
$269$	6.12627	+	10.6110i	0.373525	+	0.646965i	−0.616580	+	0.787293i	$0.711482\pi$
$270$		0			0
$271$	−16.0021	+	27.7164i	−0.972056	+	1.68365i	−0.282730	+	0.959200i	$0.591240\pi$
$271$	−16.0021	+	27.7164i	−0.972056	+	1.68365i	−0.689326	+	0.724451i	$0.742093\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.24264	−	5.61642i	0.195539	−	0.338683i
$276$		0			0
$277$	2.48528	−	1.43488i	0.149326	−	0.0862135i	−0.423475	−	0.905908i	$-0.639190\pi$
$277$	2.48528	−	1.43488i	0.149326	−	0.0862135i	0.572801	+	0.819694i	$0.305857\pi$
$278$		0			0
$279$	11.7034			0.700667
$280$		0			0
$281$	−16.7279			−0.997904			−0.498952	−	0.866630i	$-0.666282\pi$
$281$	−16.7279			−0.997904			−0.498952	+	0.866630i	$0.666282\pi$
$282$		0			0
$283$	−13.1899	+	7.61521i	−0.784060	+	0.452677i	−0.837867	−	0.545874i	$-0.816198\pi$
$283$	−13.1899	+	7.61521i	−0.784060	+	0.452677i	0.0538074	+	0.998551i	$0.482864\pi$
$284$		0			0
$285$	−2.97297	+	5.14933i	−0.176103	+	0.305020i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	1.44975	−	2.51104i	0.0852793	−	0.147708i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$		0			0
$293$	5.85172			0.341861			0.170931	−	0.985283i	$-0.445323\pi$
$293$	5.85172			0.341861			0.170931	+	0.985283i	$0.445323\pi$
$294$		0			0
$295$		−	1.43488i		−	0.0835418i
$296$		0			0
$297$	9.05213	−	5.22625i	0.525258	−	0.303258i
$298$		0			0
$299$	42.3819	+	24.4692i	2.45101	+	1.41509i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.514719	+	0.297173i	0.0295698	+	0.0170721i
$304$		0			0
$305$	−6.36396	−	11.0227i	−0.364399	−	0.631158i
$306$		0			0
$307$			21.9874i			1.25489i	0.778662	+	0.627444i	$0.215899\pi$
$307$			21.9874i			1.25489i	−0.778662	+	0.627444i	$0.784101\pi$
$308$		0			0
$309$		−	1.18869i		−	0.0676223i
$310$		0			0
$311$	−5.62427	−	9.74153i	−0.318923	−	0.552391i	0.661340	−	0.750086i	$-0.269988\pi$
$311$	−5.62427	−	9.74153i	−0.318923	−	0.552391i	−0.980264	+	0.197695i	$0.936655\pi$
$312$		0			0
$313$	13.0762	+	7.54955i	0.739111	+	0.426726i	0.821746	−	0.569854i	$-0.193000\pi$
$313$	13.0762	+	7.54955i	0.739111	+	0.426726i	−0.0826352	+	0.996580i	$0.526334\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.4853	+	11.8272i	1.15057	+	0.664281i	0.949026	−	0.315199i	$-0.102071\pi$
$317$	20.4853	+	11.8272i	1.15057	+	0.664281i	0.201542	+	0.979480i	$0.435405\pi$
$318$		0			0
$319$	7.75736	−	4.47871i	0.434329	−	0.250760i
$320$		0			0
$321$		−	9.18440i		−	0.512623i
$322$		0			0
$323$	18.4853			1.02855
$324$		0			0
$325$	−9.48751	−	16.4329i	−0.526273	−	0.911531i
$326$		0			0
$327$	−7.72648	+	13.3827i	−0.427275	+	0.740063i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.58579	−	13.1390i	0.416953	−	0.722183i	−0.578679	−	0.815556i	$-0.696431\pi$
$331$	7.58579	−	13.1390i	0.416953	−	0.722183i	0.995631	+	0.0933726i	$0.0297648\pi$
$332$		0			0
$333$	3.87868	−	2.23936i	0.212550	−	0.122716i
$334$		0			0
$335$	15.9079			0.869139
$336$		0			0
$337$	−4.24264			−0.231111			−0.115556	−	0.993301i	$-0.536865\pi$
$337$	−4.24264			−0.231111			−0.115556	+	0.993301i	$0.536865\pi$
$338$		0			0
$339$	0.454893	−	0.262632i	0.0247064	−	0.0142642i
$340$		0			0
$341$	−6.40083	+	11.0866i	−0.346624	+	0.600371i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$		0			0
$347$	−13.4853	−	23.3572i	−0.723928	−	1.25388i	−0.959414	−	0.282002i	$-0.909002\pi$
$347$	−13.4853	−	23.3572i	−0.723928	−	1.25388i	0.235486	−	0.971878i	$-0.424332\pi$
$348$		0			0
$349$	−9.27958			−0.496725			−0.248362	−	0.968667i	$-0.579892\pi$
$349$	−9.27958			−0.496725			−0.248362	+	0.968667i	$0.579892\pi$
$350$		0			0
$351$		−	30.5826i		−	1.63238i
$352$		0			0
$353$	17.8297	−	10.2940i	0.948980	−	0.547894i	0.0562161	−	0.998419i	$-0.482096\pi$
$353$	17.8297	−	10.2940i	0.948980	−	0.547894i	0.892764	+	0.450525i	$0.148763\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0000	−	8.66025i	−0.791670	−	0.457071i	0.0488803	−	0.998805i	$-0.484435\pi$
$359$	−15.0000	−	8.66025i	−0.791670	−	0.457071i	−0.840550	+	0.541734i	$0.817768\pi$
$360$		0			0
$361$	−0.914214	−	1.58346i	−0.0481165	−	0.0833402i
$362$		0			0
$363$		−	7.57675i		−	0.397676i
$364$		0			0
$365$		−	9.37769i		−	0.490851i
$366$		0			0
$367$	−11.4760	−	19.8770i	−0.599042	−	1.03757i	−0.992963	−	0.118427i	$-0.962215\pi$
$367$	−11.4760	−	19.8770i	−0.599042	−	1.03757i	0.393921	−	0.919144i	$-0.371118\pi$
$368$		0			0
$369$	0.501998	+	0.289829i	0.0261330	+	0.0150879i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	25.9706	+	14.9941i	1.34470	+	0.776366i	0.987494	−	0.157658i	$-0.0503944\pi$
$373$	25.9706	+	14.9941i	1.34470	+	0.776366i	0.357211	+	0.934024i	$0.383728\pi$
$374$		0			0
$375$	10.2426	−	5.91359i	0.528928	−	0.305377i
$376$		0			0
$377$		−	26.2082i		−	1.34979i
$378$		0			0
$379$	5.31371			0.272947			0.136473	−	0.990644i	$-0.456423\pi$
$379$	5.31371			0.272947			0.136473	+	0.990644i	$0.456423\pi$
$380$		0			0
$381$	8.27558	+	14.3337i	0.423971	+	0.734339i
$382$		0			0
$383$	6.40083	−	11.0866i	0.327067	−	0.566496i	−0.654862	−	0.755749i	$-0.727273\pi$
$383$	6.40083	−	11.0866i	0.327067	−	0.566496i	0.981928	+	0.189252i	$0.0606064\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.89949	+	5.02207i	−0.147390	+	0.255286i
$388$		0			0
$389$	32.8492	−	18.9655i	1.66552	−	0.961590i	0.695516	−	0.718510i	$-0.255176\pi$
$389$	32.8492	−	18.9655i	1.66552	−	0.961590i	0.970006	−	0.243080i	$-0.0781577\pi$
$390$		0			0
$391$	37.3067			1.88668
$392$		0			0
$393$	−14.8284			−0.747995
$394$		0			0
$395$	−2.32965	+	1.34502i	−0.117217	+	0.0676755i
$396$		0			0
$397$	−6.90282	+	11.9560i	−0.346443	+	0.600056i	−0.985615	−	0.169007i	$-0.945944\pi$
$397$	−6.90282	+	11.9560i	−0.346443	+	0.600056i	0.639172	+	0.769064i	$0.279277\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−8.12132	+	14.0665i	−0.405559	+	0.702449i	−0.994386	−	0.105810i	$-0.966257\pi$
$401$	−8.12132	+	14.0665i	−0.405559	+	0.702449i	0.588827	+	0.808259i	$0.299590\pi$
$402$		0			0
$403$	18.7279	+	32.4377i	0.932904	+	1.61584i
$404$		0			0
$405$	0.227446			0.0113019
$406$		0			0
$407$			4.89898i			0.242833i
$408$		0			0
$409$	−8.00103	+	4.61940i	−0.395626	+	0.228415i	−0.684595	−	0.728924i	$-0.740021\pi$
$409$	−8.00103	+	4.61940i	−0.395626	+	0.228415i	0.288969	+	0.957338i	$0.406687\pi$
$410$		0			0
$411$	7.72648	+	4.46088i	0.381119	+	0.220039i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	6.51472	+	3.76127i	0.319795	+	0.184634i
$416$		0			0
$417$	−9.41421	−	16.3059i	−0.461016	−	0.798503i
$418$		0			0
$419$			7.31411i			0.357318i	0.983911	+	0.178659i	$0.0571759\pi$
$419$			7.31411i			0.357318i	−0.983911	+	0.178659i	$0.942824\pi$
$420$		0			0
$421$			12.6677i			0.617387i	0.951162	+	0.308693i	$0.0998917\pi$
$421$			12.6677i			0.617387i	−0.951162	+	0.308693i	$0.900108\pi$
$422$		0			0
$423$	11.7034	+	20.2710i	0.569041	+	0.985608i
$424$		0			0
$425$	−12.5271	−	7.23252i	−0.607654	−	0.350829i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	10.9706	+	6.33386i	0.529664	+	0.305802i
$430$		0			0
$431$	−23.4853	+	13.5592i	−1.13125	+	0.653125i	−0.944248	−	0.329235i	$-0.893209\pi$
$431$	−23.4853	+	13.5592i	−1.13125	+	0.653125i	−0.186998	+	0.982360i	$0.559876\pi$
$432$		0			0
$433$		−	28.1647i		−	1.35351i	−0.736208	−	0.676755i	$-0.763386\pi$
$433$		−	28.1647i		−	1.35351i	0.736208	−	0.676755i	$-0.236614\pi$
$434$		0			0
$435$	6.42641			0.308123
$436$		0			0
$437$	17.3277	+	30.0125i	0.828897	+	1.43569i
$438$		0			0
$439$	−11.1543	+	19.3199i	−0.532368	+	0.922088i	0.466918	+	0.884300i	$0.345364\pi$
$439$	−11.1543	+	19.3199i	−0.532368	+	0.922088i	−0.999286	+	0.0377871i	$0.987969\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.1421	−	24.4949i	0.671913	−	1.16379i	−0.305448	−	0.952209i	$-0.598806\pi$
$443$	14.1421	−	24.4949i	0.671913	−	1.16379i	0.977361	−	0.211579i	$-0.0678605\pi$
$444$		0			0
$445$	−14.6360	+	8.45012i	−0.693815	+	0.400574i
$446$		0			0
$447$	−0.643315			−0.0304278
$448$		0			0
$449$	5.65685			0.266963			0.133482	−	0.991051i	$-0.457384\pi$
$449$	5.65685			0.266963			0.133482	+	0.991051i	$0.457384\pi$
$450$		0			0
$451$	−0.549104	+	0.317025i	−0.0258563	+	0.0149281i
$452$		0			0
$453$	−2.97297	+	5.14933i	−0.139682	+	0.241937i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	13.4142	−	23.2341i	0.627490	−	1.08685i	−0.360563	−	0.932735i	$-0.617415\pi$
$457$	13.4142	−	23.2341i	0.627490	−	1.08685i	0.988054	−	0.154111i	$-0.0492512\pi$
$458$		0			0
$459$	−11.6569	−	20.1903i	−0.544095	−	0.942401i
$460$		0			0
$461$	18.9750			0.883755			0.441878	−	0.897075i	$-0.354313\pi$
$461$	18.9750			0.883755			0.441878	+	0.897075i	$0.354313\pi$
$462$		0			0
$463$		−	8.95743i		−	0.416287i	−0.978098	−	0.208143i	$-0.933258\pi$
$463$		−	8.95743i		−	0.416287i	0.978098	−	0.208143i	$-0.0667421\pi$
$464$		0			0
$465$	−7.95393	+	4.59220i	−0.368854	+	0.212958i
$466$		0			0
$467$	−31.8433	−	18.3847i	−1.47353	−	0.850744i	−0.473976	−	0.880538i	$-0.657182\pi$
$467$	−31.8433	−	18.3847i	−1.47353	−	0.850744i	−0.999556	+	0.0297936i	$0.990515\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−11.7868	−	6.80511i	−0.543107	−	0.313563i
$472$		0			0
$473$	−3.17157	−	5.49333i	−0.145829	−	0.252583i
$474$		0			0
$475$		−	13.4370i		−	0.616534i
$476$		0			0
$477$		−	6.33386i		−	0.290007i
$478$		0			0
$479$	5.07517	+	8.79045i	0.231890	+	0.401646i	0.958364	−	0.285548i	$-0.0921756\pi$
$479$	5.07517	+	8.79045i	0.231890	+	0.401646i	−0.726474	+	0.687194i	$0.758842\pi$
$480$		0			0
$481$	12.4134	+	7.16687i	0.566001	+	0.326781i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	10.6066	+	6.12372i	0.481621	+	0.278064i
$486$		0			0
$487$	−12.5147	+	7.22538i	−0.567096	+	0.327413i	−0.755989	−	0.654585i	$-0.772844\pi$
$487$	−12.5147	+	7.22538i	−0.567096	+	0.327413i	0.188893	+	0.981998i	$0.439510\pi$
$488$		0			0
$489$			21.8017i			0.985907i
$490$		0			0
$491$	−7.79899			−0.351963			−0.175982	−	0.984393i	$-0.556310\pi$
$491$	−7.79899			−0.351963			−0.175982	+	0.984393i	$0.556310\pi$
$492$		0			0
$493$	−9.98951	−	17.3023i	−0.449905	−	0.779258i
$494$		0			0
$495$	2.42386	−	4.19825i	0.108945	−	0.188697i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	4.24264	−	7.34847i	0.189927	−	0.328963i	−0.755299	−	0.655380i	$-0.772508\pi$
$499$	4.24264	−	7.34847i	0.189927	−	0.328963i	0.945226	+	0.326418i	$0.105842\pi$
$500$		0			0
$501$	−15.5147	+	8.95743i	−0.693147	+	0.400188i
$502$		0			0
$503$	4.84772			0.216149			0.108075	−	0.994143i	$-0.465531\pi$
$503$	4.84772			0.216149			0.108075	+	0.994143i	$0.465531\pi$
$504$		0			0
$505$	0.727922			0.0323921
$506$		0			0
$507$	19.9124	−	11.4964i	0.884341	−	0.510575i
$508$		0			0
$509$	−1.05110	+	1.82056i	−0.0465893	+	0.0806950i	−0.888380	−	0.459110i	$-0.848169\pi$
$509$	−1.05110	+	1.82056i	−0.0465893	+	0.0806950i	0.841790	+	0.539805i	$0.181502\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	10.8284	−	18.7554i	0.478087	−	0.828071i
$514$		0			0
$515$	−0.727922	−	1.26080i	−0.0320761	−	0.0555574i
$516$		0			0
$517$	−25.6033			−1.12603
$518$		0			0
$519$			11.2328i			0.493067i
$520$		0			0
$521$	2.69841	−	1.55793i	0.118220	−	0.0682542i	−0.439724	−	0.898133i	$-0.644924\pi$
$521$	2.69841	−	1.55793i	0.118220	−	0.0682542i	0.557944	+	0.829879i	$0.311590\pi$
$522$		0			0
$523$	17.3943	+	10.0426i	0.760601	+	0.439133i	0.829512	−	0.558490i	$-0.188619\pi$
$523$	17.3943	+	10.0426i	0.760601	+	0.439133i	−0.0689104	+	0.997623i	$0.521952\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	24.7279	+	14.2767i	1.07717	+	0.621902i
$528$		0			0
$529$	23.4706	+	40.6522i	1.02046	+	1.76749i
$530$		0			0
$531$			1.97908i			0.0858846i
$532$		0			0
$533$			1.85514i			0.0803552i
$534$		0			0
$535$	−5.62427	−	9.74153i	−0.243159	−	0.421163i
$536$		0			0
$537$	−3.29462	−	1.90215i	−0.142174	−	0.0820839i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−22.4558	−	12.9649i	−0.965452	−	0.557404i	−0.0676054	−	0.997712i	$-0.521536\pi$
$541$	−22.4558	−	12.9649i	−0.965452	−	0.557404i	−0.897847	+	0.440308i	$0.854869\pi$
$542$		0			0
$543$	13.2426	−	7.64564i	0.568296	−	0.328106i
$544$		0			0
$545$			18.9259i			0.810698i
$546$		0			0
$547$	20.8284			0.890559			0.445280	−	0.895392i	$-0.353104\pi$
$547$	20.8284			0.890559			0.445280	+	0.895392i	$0.353104\pi$
$548$		0			0
$549$	8.77758	+	15.2032i	0.374618	+	0.648858i
$550$		0			0
$551$	9.27958	−	16.0727i	0.395323	−	0.684720i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.75736	+	3.04384i	−0.0745957	+	0.129204i
$556$		0			0
$557$	2.48528	−	1.43488i	0.105305	−	0.0607977i	−0.446423	−	0.894822i	$-0.647302\pi$
$557$	2.48528	−	1.43488i	0.105305	−	0.0607977i	0.551727	+	0.834024i	$0.313969\pi$
$558$		0			0
$559$	−18.5592			−0.784969
$560$		0			0
$561$	9.65685			0.407713
$562$		0			0
$563$	3.36124	−	1.94061i	0.141659	−	0.0817871i	−0.427495	−	0.904018i	$-0.640604\pi$
$563$	3.36124	−	1.94061i	0.141659	−	0.0817871i	0.569155	+	0.822231i	$0.307271\pi$
$564$		0			0
$565$	0.321658	−	0.557127i	0.0135322	−	0.0234385i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.9497	+	29.3578i	−0.710570	+	1.23074i	0.254073	+	0.967185i	$0.418230\pi$
$569$	−16.9497	+	29.3578i	−0.710570	+	1.23074i	−0.964643	+	0.263559i	$0.915104\pi$
$570$		0			0
$571$	−6.17157	−	10.6895i	−0.258272	−	0.447341i	0.707507	−	0.706706i	$-0.249820\pi$
$571$	−6.17157	−	10.6895i	−0.258272	−	0.447341i	−0.965779	+	0.259366i	$0.916487\pi$
$572$		0			0
$573$	−2.19642			−0.0917566
$574$		0			0
$575$		−	27.1185i		−	1.13092i
$576$		0			0
$577$	−17.9905	+	10.3868i	−0.748956	+	0.432410i	−0.825317	−	0.564670i	$-0.809003\pi$
$577$	−17.9905	+	10.3868i	−0.748956	+	0.432410i	0.0763605	+	0.997080i	$0.475670\pi$
$578$		0			0
$579$	−13.2565	−	7.65367i	−0.550923	−	0.318076i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	6.00000	+	3.46410i	0.248495	+	0.143468i
$584$		0			0
$585$	−7.09188	−	12.2835i	−0.293213	−	0.507860i
$586$		0			0
$587$		−	15.7557i		−	0.650306i	−0.945661	−	0.325153i	$-0.894584\pi$
$587$		−	15.7557i		−	0.650306i	0.945661	−	0.325153i	$-0.105416\pi$
$588$		0			0
$589$			26.5241i			1.09291i
$590$		0			0
$591$	−6.85572	−	11.8745i	−0.282007	−	0.488450i
$592$		0			0
$593$	3.08669	+	1.78210i	0.126755	+	0.0731821i	0.562037	−	0.827112i	$-0.310018\pi$
$593$	3.08669	+	1.78210i	0.126755	+	0.0731821i	−0.435282	+	0.900294i	$0.643351\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.00000	−	3.46410i	−0.245564	−	0.141776i
$598$		0			0
$599$	5.27208	−	3.04384i	0.215411	−	0.124368i	−0.388412	−	0.921486i	$-0.626976\pi$
$599$	5.27208	−	3.04384i	0.215411	−	0.124368i	0.603824	+	0.797118i	$0.293643\pi$
$600$		0			0
$601$		−	22.2275i		−	0.906679i	−0.891338	−	0.453339i	$-0.850233\pi$
$601$		−	22.2275i		−	0.906679i	0.891338	−	0.453339i	$-0.149767\pi$
$602$		0			0
$603$	−21.9411			−0.893512
$604$		0			0
$605$	−4.63979	−	8.03635i	−0.188634	−	0.326724i
$606$		0			0
$607$	−5.30262	+	9.18440i	−0.215227	+	0.372783i	−0.953343	−	0.301890i	$-0.902382\pi$
$607$	−5.30262	+	9.18440i	−0.215227	+	0.372783i	0.738116	+	0.674674i	$0.235716\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−37.4558	+	64.8754i	−1.51530	+	2.62458i
$612$		0			0
$613$	−23.3345	+	13.4722i	−0.942473	+	0.544137i	−0.890735	−	0.454524i	$-0.849809\pi$
$613$	−23.3345	+	13.4722i	−0.942473	+	0.544137i	−0.0517380	+	0.998661i	$0.516476\pi$
$614$		0			0
$615$	−0.454893			−0.0183430
$616$		0			0
$617$	33.2132			1.33711			0.668557	−	0.743661i	$-0.266912\pi$
$617$	33.2132			1.33711			0.668557	+	0.743661i	$0.266912\pi$
$618$		0			0
$619$	16.0687	−	9.27726i	0.645855	−	0.372884i	−0.141011	−	0.990008i	$-0.545035\pi$
$619$	16.0687	−	9.27726i	0.645855	−	0.372884i	0.786866	+	0.617124i	$0.211702\pi$
$620$		0			0
$621$	21.8538	−	37.8519i	0.876962	−	1.51894i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.863961	+	1.49642i	−0.0345584	+	0.0598570i
$626$		0			0
$627$	4.48528	+	7.76874i	0.179125	+	0.310253i
$628$		0			0
$629$	10.9269			0.435684
$630$		0			0
$631$			39.5400i			1.57406i	0.616913	+	0.787031i	$0.288383\pi$
$631$			39.5400i			1.57406i	−0.616913	+	0.787031i	$0.711617\pi$
$632$		0			0
$633$	−3.29462	+	1.90215i	−0.130950	+	0.0756038i
$634$		0			0
$635$	17.5552	+	10.1355i	0.696655	+	0.402214i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.5355	+	26.9083i	0.613617	+	1.06282i	0.990626	+	0.136606i	$0.0436193\pi$
$641$	15.5355	+	26.9083i	0.613617	+	1.06282i	−0.377009	+	0.926210i	$0.623047\pi$
$642$		0			0
$643$			30.3839i			1.19822i	0.800665	+	0.599112i	$0.204480\pi$
$643$			30.3839i			1.19822i	−0.800665	+	0.599112i	$0.795520\pi$
$644$		0			0
$645$		−	4.55082i		−	0.179188i
$646$		0			0
$647$	5.07517	+	8.79045i	0.199526	+	0.345588i	0.948375	−	0.317152i	$-0.102727\pi$
$647$	5.07517	+	8.79045i	0.199526	+	0.345588i	−0.748849	+	0.662741i	$0.769393\pi$
$648$		0			0
$649$	−1.87476	−	1.08239i	−0.0735907	−	0.0424876i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−17.6360	−	10.1822i	−0.690152	−	0.398459i	0.113517	−	0.993536i	$-0.463788\pi$
$653$	−17.6360	−	10.1822i	−0.690152	−	0.398459i	−0.803669	+	0.595077i	$0.797122\pi$
$654$		0			0
$655$	−15.7279	+	9.08052i	−0.614541	+	0.354805i
$656$		0			0
$657$			12.9343i			0.504616i
$658$		0			0
$659$	−42.4853			−1.65499			−0.827496	−	0.561472i	$-0.810235\pi$
$659$	−42.4853			−1.65499			−0.827496	+	0.561472i	$0.810235\pi$
$660$		0			0
$661$	−15.5667	−	26.9623i	−0.605474	−	1.04871i	−0.991976	−	0.126423i	$-0.959650\pi$
$661$	−15.5667	−	26.9623i	−0.605474	−	1.04871i	0.386503	−	0.922288i	$-0.373683\pi$
$662$		0			0
$663$	14.1273	−	24.4692i	0.548659	−	0.950305i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	18.7279	−	32.4377i	0.725148	−	1.25599i
$668$		0			0
$669$	4.54416	−	2.62357i	0.175687	−	0.101433i
$670$		0			0
$671$	−19.2025			−0.741303
$672$		0			0
$673$	−6.38478			−0.246115			−0.123058	−	0.992400i	$-0.539270\pi$
$673$	−6.38478			−0.246115			−0.123058	+	0.992400i	$0.539270\pi$
$674$		0			0
$675$	−14.6764	+	8.47343i	−0.564895	+	0.326142i
$676$		0			0
$677$	14.7901	−	25.6173i	0.568431	−	0.984551i	−0.428290	−	0.903641i	$-0.640884\pi$
$677$	14.7901	−	25.6173i	0.568431	−	0.984551i	0.996721	−	0.0809101i	$-0.0257827\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	6.38478	−	11.0588i	0.244665	−	0.423772i
$682$		0			0
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	0.969007	−	0.247033i	$-0.0794555\pi$
$683$	7.07107	+	12.2474i	0.270567	+	0.468636i	−0.698440	+	0.715668i	$0.746122\pi$
$684$		0			0
$685$	10.9269			0.417495
$686$		0			0
$687$			16.4800i			0.628750i
$688$		0			0
$689$	17.5552	−	10.1355i	0.668798	−	0.386131i
$690$		0			0
$691$	−35.2712	−	20.3638i	−1.34178	−	0.774676i	−0.354710	−	0.934976i	$-0.615420\pi$
$691$	−35.2712	−	20.3638i	−1.34178	−	0.774676i	−0.987068	+	0.160301i	$0.948754\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.9706	−	11.5300i	−0.757527	−	0.437358i
$696$		0			0
$697$	0.707107	+	1.22474i	0.0267836	+	0.0463905i
$698$		0			0
$699$		−	12.7261i		−	0.481344i
$700$		0			0
$701$		−	47.7290i		−	1.80270i	−0.433092	−	0.901350i	$-0.642578\pi$
$701$		−	47.7290i		−	1.80270i	0.433092	−	0.901350i	$-0.357422\pi$
$702$		0			0
$703$	5.07517	+	8.79045i	0.191414	+	0.331538i
$704$		0			0
$705$	−15.9079	−	9.18440i	−0.599124	−	0.345905i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−31.8198	−	18.3712i	−1.19502	−	0.689944i	−0.235578	−	0.971856i	$-0.575698\pi$
$709$	−31.8198	−	18.3712i	−1.19502	−	0.689944i	−0.959440	+	0.281912i	$0.909031\pi$
$710$		0			0
$711$	3.21320	−	1.85514i	0.120505	−	0.0695733i
$712$		0			0
$713$			53.5306i			2.00474i
$714$		0			0
$715$	15.5147			0.580218
$716$		0			0
$717$	3.42786	+	5.93723i	0.128016	+	0.221730i
$718$		0			0
$719$	9.82868	−	17.0238i	0.366548	−	0.634880i	−0.622475	−	0.782639i	$-0.713873\pi$
$719$	9.82868	−	17.0238i	0.366548	−	0.634880i	0.989023	+	0.147760i	$0.0472062\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−9.10051	+	15.7625i	−0.338451	+	0.586215i
$724$		0			0
$725$	−12.5772	+	7.26143i	−0.467104	+	0.269683i
$726$		0			0
$727$	−49.6535			−1.84155			−0.920773	−	0.390098i	$-0.872441\pi$
$727$	−49.6535			−1.84155			−0.920773	+	0.390098i	$0.872441\pi$
$728$		0			0
$729$	−17.2843			−0.640158
$730$		0			0
$731$	−12.2525	+	7.07401i	−0.453177	+	0.261642i
$732$		0			0
$733$	−13.4645	+	23.3212i	−0.497322	+	0.861387i	−0.999995	−	0.00308974i	$-0.999017\pi$
$733$	−13.4645	+	23.3212i	−0.497322	+	0.861387i	0.502673	+	0.864476i	$0.332350\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$		0			0
$739$	10.4142	+	18.0379i	0.383093	+	0.663537i	0.991503	−	0.130087i	$-0.0415255\pi$
$739$	10.4142	+	18.0379i	0.383093	+	0.663537i	−0.608410	+	0.793623i	$0.708192\pi$
$740$		0			0
$741$	26.2466			0.964194
$742$		0			0
$743$		−	6.33386i		−	0.232367i	−0.993228	−	0.116183i	$-0.962934\pi$
$743$		−	6.33386i		−	0.232367i	0.993228	−	0.116183i	$-0.0370660\pi$
$744$		0			0
$745$	−0.682339	+	0.393949i	−0.0249990	+	0.0144332i
$746$		0			0
$747$	−8.98552	−	5.18779i	−0.328763	−	0.189811i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−36.9411	−	21.3280i	−1.34800	−	0.778269i	−0.360035	−	0.932939i	$-0.617235\pi$
$751$	−36.9411	−	21.3280i	−1.34800	−	0.778269i	−0.987966	+	0.154670i	$0.950568\pi$
$752$		0			0
$753$	−10.9289	−	18.9295i	−0.398272	−	0.689828i
$754$		0			0
$755$			7.28225i			0.265028i
$756$		0			0
$757$		−	8.18900i		−	0.297634i	−0.988865	−	0.148817i	$-0.952453\pi$
$757$		−	8.18900i		−	0.297634i	0.988865	−	0.148817i	$-0.0475466\pi$
$758$		0			0
$759$	9.05213	+	15.6788i	0.328572	+	0.569103i
$760$		0			0
$761$	4.09069	+	2.36176i	0.148287	+	0.0856137i	0.572308	−	0.820039i	$-0.306048\pi$
$761$	4.09069	+	2.36176i	0.148287	+	0.0856137i	−0.424021	+	0.905653i	$0.639382\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−9.36396	−	5.40629i	−0.338555	−	0.195465i
$766$		0			0
$767$	−5.48528	+	3.16693i	−0.198062	+	0.114351i
$768$		0			0
$769$			19.1342i			0.689996i	0.938603	+	0.344998i	$0.112120\pi$
$769$			19.1342i			0.689996i	−0.938603	+	0.344998i	$0.887880\pi$
$770$		0			0
$771$	−1.31371			−0.0473121
$772$		0			0
$773$	−21.4184	−	37.0978i	−0.770366	−	1.33431i	−0.937362	−	0.348356i	$-0.886740\pi$
$773$	−21.4184	−	37.0978i	−0.770366	−	1.33431i	0.166996	−	0.985958i	$-0.446593\pi$
$774$		0			0
$775$	10.3778	−	17.9749i	0.372781	−	0.645676i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.656854	+	1.13770i	−0.0235342	+	0.0407625i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−23.4069			−0.836494
$784$		0			0
$785$	−16.6690			−0.594944
$786$		0			0
$787$	−40.4405	+	23.3484i	−1.44155	+	0.832279i	−0.997953	−	0.0639477i	$-0.979631\pi$
$787$	−40.4405	+	23.3484i	−1.44155	+	0.832279i	−0.443596	+	0.896227i	$0.646298\pi$
$788$		0			0
$789$	10.1503	−	17.5809i	0.361362	−	0.625897i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−28.0919	+	48.6566i	−0.997572	+	1.72785i
$794$		0			0
$795$	2.48528	+	4.30463i	0.0881438	+	0.152670i
$796$		0			0
$797$	−50.6575			−1.79438			−0.897190	−	0.441644i	$-0.854395\pi$
$797$	−50.6575			−1.79438			−0.897190	+	0.441644i	$0.854395\pi$
$798$		0			0
$799$			57.1067i			2.02029i
$800$		0			0
$801$	20.1870	−	11.6549i	0.713271	−	0.411807i
$802$		0			0
$803$	−12.2525	−	7.07401i	−0.432383	−	0.249636i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.4853	+	6.63103i	0.404301	+	0.233423i
$808$		0			0
$809$	−17.7279	−	30.7057i	−0.623281	−	1.07955i	−0.988871	−	0.148778i	$-0.952466\pi$
$809$	−17.7279	−	30.7057i	−0.623281	−	1.07955i	0.365590	−	0.930776i	$-0.380867\pi$
$810$		0			0
$811$			9.63274i			0.338251i	0.985594	+	0.169126i	$0.0540944\pi$
$811$			9.63274i			0.338251i	−0.985594	+	0.169126i	$0.945906\pi$
$812$		0			0
$813$			34.6410i			1.21491i
$814$		0			0
$815$	13.3508	+	23.1242i	0.467657	+	0.810005i
$816$		0			0
$817$	−11.3818	−	6.57128i	−0.398198	−	0.229900i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−32.4853	−	18.7554i	−1.13374	−	0.654567i	−0.188870	−	0.982002i	$-0.560483\pi$
$821$	−32.4853	−	18.7554i	−1.13374	−	0.654567i	−0.944874	+	0.327435i	$0.893816\pi$
$822$		0			0
$823$	−18.0000	+	10.3923i	−0.627441	+	0.362253i	−0.779760	−	0.626078i	$-0.784659\pi$
$823$	−18.0000	+	10.3923i	−0.627441	+	0.362253i	0.152320	+	0.988331i	$0.451326\pi$
$824$		0			0
$825$		−	7.01962i		−	0.244392i
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−2.14931	−	3.72271i	−0.0746486	−	0.129295i	0.826285	−	0.563253i	$-0.190450\pi$
$829$	−2.14931	−	3.72271i	−0.0746486	−	0.129295i	−0.900933	+	0.433957i	$0.857117\pi$
$830$		0			0
$831$	1.55310	−	2.69005i	0.0538765	−	0.0933168i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−10.9706	+	19.0016i	−0.379652	+	0.657577i
$836$		0			0
$837$	28.9706	−	16.7262i	1.00137	−	0.578141i
$838$		0			0
$839$	−35.1103			−1.21214			−0.606072	−	0.795410i	$-0.707255\pi$
$839$	−35.1103			−1.21214			−0.606072	+	0.795410i	$0.707255\pi$
$840$		0			0
$841$	8.94113			0.308315
$842$		0			0
$843$	−15.6804	+	9.05309i	−0.540062	+	0.311805i
$844$		0			0
$845$	14.0802	−	24.3876i	0.484374	−	0.838960i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−8.24264	+	14.2767i	−0.282887	+	0.489974i
$850$		0			0
$851$	10.2426	+	17.7408i	0.351113	+	0.608146i
$852$		0			0
$853$	−20.9830			−0.718445			−0.359223	−	0.933252i	$-0.616958\pi$
$853$	−20.9830			−0.718445			−0.359223	+	0.933252i	$0.616958\pi$
$854$		0			0
$855$		−	10.0441i		−	0.343503i
$856$		0			0
$857$	−4.86724	+	2.81010i	−0.166262	+	0.0959912i	−0.580822	−	0.814031i	$-0.697269\pi$
$857$	−4.86724	+	2.81010i	−0.166262	+	0.0959912i	0.414560	+	0.910022i	$0.363935\pi$
$858$		0			0
$859$	29.0978	+	16.7996i	0.992803	+	0.573195i	0.906111	−	0.423040i	$-0.139037\pi$
$859$	29.0978	+	16.7996i	0.992803	+	0.573195i	0.0866923	+	0.996235i	$0.472370\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−20.4853	−	11.8272i	−0.697327	−	0.402602i	0.109024	−	0.994039i	$-0.465227\pi$
$863$	−20.4853	−	11.8272i	−0.697327	−	0.402602i	−0.806351	+	0.591437i	$0.798561\pi$
$864$		0			0
$865$	6.87868	+	11.9142i	0.233882	+	0.405096i
$866$		0			0
$867$		−	3.13839i		−	0.106585i
$868$		0			0
$869$			4.05845i			0.137673i
$870$		0			0
$871$	−35.1103	−	60.8129i	−1.18967	−	2.06057i
$872$		0			0
$873$	−14.6293	−	8.44623i	−0.495127	−	0.285862i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.1213	+	18.5453i	1.08466	+	0.626229i	0.932150	−	0.362073i	$-0.117931\pi$
$877$	32.1213	+	18.5453i	1.08466	+	0.626229i	0.152510	+	0.988302i	$0.451264\pi$
$878$		0			0
$879$	5.48528	−	3.16693i	0.185014	−	0.106818i
$880$		0			0
$881$		−	36.0810i		−	1.21560i	−0.794090	−	0.607800i	$-0.792052\pi$
$881$		−	36.0810i		−	1.21560i	0.794090	−	0.607800i	$-0.207948\pi$
$882$		0			0
$883$	46.4264			1.56237			0.781186	−	0.624298i	$-0.214615\pi$
$883$	46.4264			1.56237			0.781186	+	0.624298i	$0.214615\pi$
$884$		0			0
$885$	−0.776550	−	1.34502i	−0.0261035	−	0.0452125i
$886$		0			0
$887$	2.97297	−	5.14933i	0.0998224	−	0.172898i	−0.811789	−	0.583951i	$-0.801506\pi$
$887$	2.97297	−	5.14933i	0.0998224	−	0.172898i	0.911611	+	0.411054i	$0.134839\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.171573	−	0.297173i	0.00574791	−	0.00995567i
$892$		0			0
$893$	−45.9411	+	26.5241i	−1.53736	+	0.887596i
$894$		0			0
$895$	−4.65930			−0.155743
$896$		0			0
$897$	52.9706			1.76864
$898$		0			0
$899$	24.8268	−	14.3337i	0.828018	−	0.478057i
$900$		0			0
$901$	7.72648	−	13.3827i	0.257406	−	0.445841i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.36396	−	16.2189i	0.311269	−	0.539133i
$906$		0			0
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	0.702094	−	0.712084i	$-0.252248\pi$
$907$	−8.00000	−	13.8564i	−0.265636	−	0.460094i	−0.967730	+	0.251990i	$0.918915\pi$
$908$		0			0
$909$	−1.00400			−0.0333005
$910$		0			0
$911$		−	15.2913i		−	0.506623i	−0.967385	−	0.253311i	$-0.918480\pi$
$911$		−	15.2913i		−	0.506623i	0.967385	−	0.253311i	$-0.0815197\pi$
$912$		0			0
$913$	9.82868	−	5.67459i	0.325282	−	0.187802i
$914$		0			0
$915$	−11.9309	−	6.88830i	−0.394423	−	0.227720i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	32.4853	+	18.7554i	1.07159	+	0.618683i	0.928616	−	0.371043i	$-0.121000\pi$
$919$	32.4853	+	18.7554i	1.07159	+	0.618683i	0.142975	+	0.989726i	$0.454333\pi$
$920$		0			0
$921$	11.8995	+	20.6105i	0.392102	+	0.679140i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		−	7.94282i		−	0.261158i
$926$		0			0
$927$	1.00400	+	1.73897i	0.0329756	+	0.0571154i
$928$		0			0
$929$	−19.3162	−	11.1522i	−0.633744	−	0.365892i	0.148457	−	0.988919i	$-0.452569\pi$
$929$	−19.3162	−	11.1522i	−0.633744	−	0.365892i	−0.782201	+	0.623027i	$0.785903\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−10.5442	−	6.08767i	−0.345200	−	0.199301i
$934$		0			0
$935$	10.2426	−	5.91359i	0.334970	−	0.193395i
$936$		0			0
$937$			51.4202i			1.67983i	0.542721	+	0.839913i	$0.317394\pi$
$937$			51.4202i			1.67983i	−0.542721	+	0.839913i	$0.682606\pi$
$938$		0			0
$939$	16.3431			0.533338
$940$		0			0
$941$	6.12627	+	10.6110i	0.199711	+	0.345909i	0.948435	−	0.316973i	$-0.102666\pi$
$941$	6.12627	+	10.6110i	0.199711	+	0.345909i	−0.748724	+	0.662882i	$0.769333\pi$
$942$		0			0
$943$	−1.32565	+	2.29610i	−0.0431692	+	0.0747713i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	0.272078	−	0.471253i	0.00884135	−	0.0153137i	−0.861571	−	0.507637i	$-0.830519\pi$
$947$	0.272078	−	0.471253i	0.00884135	−	0.0153137i	0.870412	+	0.492324i	$0.163852\pi$
$948$		0			0
$949$	−35.8492	+	20.6976i	−1.16372	+	0.671872i
$950$		0			0
$951$	25.6033			0.830244
$952$		0			0
$953$	−18.6863			−0.605308			−0.302654	−	0.953100i	$-0.597873\pi$
$953$	−18.6863			−0.605308			−0.302654	+	0.953100i	$0.597873\pi$
$954$		0			0
$955$	−2.32965	+	1.34502i	−0.0753857	+	0.0435240i
$956$		0			0
$957$	4.84772	−	8.39651i	0.156705	−	0.271420i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−4.98528	+	8.63476i	−0.160816	+	0.278541i
$962$		0			0
$963$	7.75736	+	13.4361i	0.249977	+	0.432974i
$964$		0			0
$965$	−18.7476			−0.603506
$966$		0			0
$967$		−	27.9590i		−	0.899101i	−0.893255	−	0.449550i	$-0.851584\pi$
$967$		−	27.9590i		−	0.899101i	0.893255	−	0.449550i	$-0.148416\pi$
$968$		0			0
$969$	17.3277	−	10.0042i	0.556646	−	0.321380i
$970$		0			0
$971$	−7.01655	−	4.05101i	−0.225172	−	0.130003i	0.383171	−	0.923677i	$-0.374832\pi$
$971$	−7.01655	−	4.05101i	−0.225172	−	0.130003i	−0.608343	+	0.793675i	$0.708165\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−17.7868	−	10.2692i	−0.569633	−	0.328878i
$976$		0			0
$977$	2.60660	+	4.51477i	0.0833926	+	0.144440i	0.904705	−	0.426038i	$-0.140091\pi$
$977$	2.60660	+	4.51477i	0.0833926	+	0.144440i	−0.821313	+	0.570478i	$0.806758\pi$
$978$		0			0
$979$			25.4972i			0.814894i
$980$		0			0
$981$		−	26.1039i		−	0.833432i
$982$		0			0
$983$	13.3508	+	23.1242i	0.425823	+	0.737547i	0.996497	−	0.0836298i	$-0.0266513\pi$
$983$	13.3508	+	23.1242i	0.425823	+	0.737547i	−0.570674	+	0.821177i	$0.693318\pi$
$984$		0			0
$985$	−14.5432	−	8.39651i	−0.463384	−	0.267535i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−22.9706	−	13.2621i	−0.730421	−	0.421709i
$990$		0			0
$991$	−39.9411	+	23.0600i	−1.26877	+	0.732526i	−0.974756	−	0.223275i	$-0.928325\pi$
$991$	−39.9411	+	23.0600i	−1.26877	+	0.732526i	−0.294016	+	0.955800i	$0.594992\pi$
$992$		0			0
$993$		−	16.4216i		−	0.521123i
$994$		0			0
$995$	−8.48528			−0.269002
$996$		0			0
$997$	16.1158	+	27.9134i	0.510392	+	0.884025i	0.999927	+	0.0120416i	$0.00383305\pi$
$997$	16.1158	+	27.9134i	0.510392	+	0.884025i	−0.489535	+	0.871983i	$0.662834\pi$
$998$		0			0
$999$	6.40083	−	11.0866i	0.202513	−	0.350763i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1568.2.q.c.1391.3		8
4.3	odd	2		392.2.m.c.19.1		8
7.2	even	3		1568.2.e.c.783.5		8
7.3	odd	6		1568.2.q.d.815.3		8
7.4	even	3		1568.2.q.d.815.2		8
7.5	odd	6		1568.2.e.c.783.4		8
7.6	odd	2	inner	1568.2.q.c.1391.2		8
8.3	odd	2		1568.2.q.d.1391.3		8
8.5	even	2		392.2.m.e.19.3		8
28.3	even	6		392.2.m.e.227.3		8
28.11	odd	6		392.2.m.e.227.4		8
28.19	even	6		392.2.e.c.195.4	yes	8
28.23	odd	6		392.2.e.c.195.3	yes	8
28.27	even	2		392.2.m.c.19.2		8
56.3	even	6	inner	1568.2.q.c.815.3		8
56.5	odd	6		392.2.e.c.195.2	yes	8
56.11	odd	6	inner	1568.2.q.c.815.2		8
56.13	odd	2		392.2.m.e.19.4		8
56.19	even	6		1568.2.e.c.783.3		8
56.27	even	2		1568.2.q.d.1391.2		8
56.37	even	6		392.2.e.c.195.1	✓	8
56.45	odd	6		392.2.m.c.227.1		8
56.51	odd	6		1568.2.e.c.783.6		8
56.53	even	6		392.2.m.c.227.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.c.195.1	✓	8	56.37	even	6
392.2.e.c.195.2	yes	8	56.5	odd	6
392.2.e.c.195.3	yes	8	28.23	odd	6
392.2.e.c.195.4	yes	8	28.19	even	6
392.2.m.c.19.1		8	4.3	odd	2
392.2.m.c.19.2		8	28.27	even	2
392.2.m.c.227.1		8	56.45	odd	6
392.2.m.c.227.2		8	56.53	even	6
392.2.m.e.19.3		8	8.5	even	2
392.2.m.e.19.4		8	56.13	odd	2
392.2.m.e.227.3		8	28.3	even	6
392.2.m.e.227.4		8	28.11	odd	6
1568.2.e.c.783.3		8	56.19	even	6
1568.2.e.c.783.4		8	7.5	odd	6
1568.2.e.c.783.5		8	7.2	even	3
1568.2.e.c.783.6		8	56.51	odd	6
1568.2.q.c.815.2		8	56.11	odd	6	inner
1568.2.q.c.815.3		8	56.3	even	6	inner
1568.2.q.c.1391.2		8	7.6	odd	2	inner
1568.2.q.c.1391.3		8	1.1	even	1	trivial
1568.2.q.d.815.2		8	7.4	even	3
1568.2.q.d.815.3		8	7.3	odd	6
1568.2.q.d.1391.2		8	56.27	even	2
1568.2.q.d.1391.3		8	8.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1568 = 2^{5} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1568.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.937379 - 0.541196i) q^{3} +(0.662827 - 1.14805i) q^{5} +(-0.914214 + 1.58346i) q^{9} +(-1.00000 - 1.73205i) q^{11} -5.85172 q^{13} -1.43488i q^{15} +(-3.86324 + 2.23044i) q^{17} +(-3.58869 - 2.07193i) q^{19} +(-7.24264 - 4.18154i) q^{23} +(1.62132 + 2.80821i) q^{25} +5.22625i q^{27} +4.47871i q^{29} +(-3.20041 - 5.54328i) q^{31} +(-1.87476 - 1.08239i) q^{33} +(-2.12132 - 1.22474i) q^{37} +(-5.48528 + 3.16693i) q^{39} -0.317025i q^{41} +3.17157 q^{43} +(1.21193 + 2.09913i) q^{45} +(6.40083 - 11.0866i) q^{47} +(-2.41421 + 4.18154i) q^{51} +(-3.00000 + 1.73205i) q^{53} -2.65131 q^{55} -4.48528 q^{57} +(0.937379 - 0.541196i) q^{59} +(4.80062 - 8.31492i) q^{61} +(-3.87868 + 6.71807i) q^{65} +(6.00000 + 10.3923i) q^{67} -9.05213 q^{69} +(6.12627 - 3.53701i) q^{73} +(3.03958 + 1.75490i) q^{75} +(-1.75736 - 1.01461i) q^{79} +(0.0857864 + 0.148586i) q^{81} +5.67459i q^{83} +5.91359i q^{85} +(2.42386 + 4.19825i) q^{87} +(-11.0406 - 6.37430i) q^{89} +(-6.00000 - 3.46410i) q^{93} +(-4.75736 + 2.74666i) q^{95} +9.23880i q^{97} +3.65685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9} - 8 q^{11} - 24 q^{23} - 4 q^{25} + 24 q^{39} + 48 q^{43} - 8 q^{51} - 24 q^{53} + 32 q^{57} - 48 q^{65} + 48 q^{67} - 48 q^{79} + 12 q^{81} - 48 q^{93} - 72 q^{95} - 16 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 - 8 * q^11 - 24 * q^23 - 4 * q^25 + 24 * q^39 + 48 * q^43 - 8 * q^51 - 24 * q^53 + 32 * q^57 - 48 * q^65 + 48 * q^67 - 48 * q^79 + 12 * q^81 - 48 * q^93 - 72 * q^95 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more