LMFDB - Embedded newform 2240.2.bd.a.561.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (of order $4$, 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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.17
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25769 - 1.25769i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.163545i q^{9} +O(q^{10})$	\(q+(1.25769 - 1.25769i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.163545i q^{9} +(0.651231 + 0.651231i) q^{11} +(1.11286 - 1.11286i) q^{13} +1.77864 q^{15} -0.603016 q^{17} +(0.0481428 - 0.0481428i) q^{19} +(-1.25769 - 1.25769i) q^{21} -3.32354i q^{23} +1.00000i q^{25} +(3.56737 + 3.56737i) q^{27} +(4.73058 - 4.73058i) q^{29} +6.15445 q^{31} +1.63809 q^{33} +(0.707107 - 0.707107i) q^{35} +(3.26170 + 3.26170i) q^{37} -2.79926i q^{39} -5.83711i q^{41} +(-6.87578 - 6.87578i) q^{43} +(0.115644 - 0.115644i) q^{45} +5.47252 q^{47} -1.00000 q^{49} +(-0.758405 + 0.758405i) q^{51} +(8.02895 + 8.02895i) q^{53} +0.920980i q^{55} -0.121097i q^{57} +(-3.27037 - 3.27037i) q^{59} +(8.00019 - 8.00019i) q^{61} -0.163545 q^{63} +1.57382 q^{65} +(0.200912 - 0.200912i) q^{67} +(-4.17996 - 4.17996i) q^{69} -1.91971i q^{71} +7.86605i q^{73} +(1.25769 + 1.25769i) q^{75} +(0.651231 - 0.651231i) q^{77} -1.51045 q^{79} +9.46389 q^{81} +(-11.4075 + 11.4075i) q^{83} +(-0.426397 - 0.426397i) q^{85} -11.8992i q^{87} +1.79530i q^{89} +(-1.11286 - 1.11286i) q^{91} +(7.74036 - 7.74036i) q^{93} +0.0680842 q^{95} +4.28142 q^{97} +(0.106506 - 0.106506i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	1.25769	−	1.25769i	0.726125	−	0.726125i	−0.243720	−	0.969846i	$-0.578368\pi$
$3$	1.25769	−	1.25769i	0.726125	−	0.726125i	0.969846	+	0.243720i	$0.0783679\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	0.163545i		−	0.0545152i
$10$		0			0
$11$	0.651231	+	0.651231i	0.196354	+	0.196354i	0.798435	−	0.602081i	$-0.205662\pi$
$11$	0.651231	+	0.651231i	0.196354	+	0.196354i	−0.602081	+	0.798435i	$0.705662\pi$
$12$		0			0
$13$	1.11286	−	1.11286i	0.308652	−	0.308652i	−0.535734	−	0.844387i	$-0.679965\pi$
$13$	1.11286	−	1.11286i	0.308652	−	0.308652i	0.844387	+	0.535734i	$0.179965\pi$
$14$		0			0
$15$	1.77864			0.459242
$16$		0			0
$17$	−0.603016			−0.146253			−0.0731265	−	0.997323i	$-0.523298\pi$
$17$	−0.603016			−0.146253			−0.0731265	+	0.997323i	$0.523298\pi$
$18$		0			0
$19$	0.0481428	−	0.0481428i	0.0110447	−	0.0110447i	−0.701563	−	0.712608i	$-0.747514\pi$
$19$	0.0481428	−	0.0481428i	0.0110447	−	0.0110447i	0.712608	+	0.701563i	$0.247514\pi$
$20$		0			0
$21$	−1.25769	−	1.25769i	−0.274449	−	0.274449i
$22$		0			0
$23$		−	3.32354i		−	0.693005i	−0.938049	−	0.346503i	$-0.887369\pi$
$23$		−	3.32354i		−	0.693005i	0.938049	−	0.346503i	$-0.112631\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	3.56737	+	3.56737i	0.686540	+	0.686540i
$28$		0			0
$29$	4.73058	−	4.73058i	0.878446	−	0.878446i	−0.114928	−	0.993374i	$-0.536664\pi$
$29$	4.73058	−	4.73058i	0.878446	−	0.878446i	0.993374	+	0.114928i	$0.0366636\pi$
$30$		0			0
$31$	6.15445			1.10537			0.552686	−	0.833390i	$-0.313603\pi$
$31$	6.15445			1.10537			0.552686	+	0.833390i	$0.313603\pi$
$32$		0			0
$33$	1.63809			0.285155
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	3.26170	+	3.26170i	0.536220	+	0.536220i	0.922417	−	0.386196i	$-0.126211\pi$
$37$	3.26170	+	3.26170i	0.536220	+	0.536220i	−0.386196	+	0.922417i	$0.626211\pi$
$38$		0			0
$39$		−	2.79926i		−	0.448240i
$40$		0			0
$41$		−	5.83711i		−	0.911604i	−0.890081	−	0.455802i	$-0.849353\pi$
$41$		−	5.83711i		−	0.911604i	0.890081	−	0.455802i	$-0.150647\pi$
$42$		0			0
$43$	−6.87578	−	6.87578i	−1.04855	−	1.04855i	−0.998760	−	0.0497874i	$-0.984146\pi$
$43$	−6.87578	−	6.87578i	−1.04855	−	1.04855i	−0.0497874	−	0.998760i	$-0.515854\pi$
$44$		0			0
$45$	0.115644	−	0.115644i	0.0172392	−	0.0172392i
$46$		0			0
$47$	5.47252			0.798249			0.399125	−	0.916897i	$-0.369314\pi$
$47$	5.47252			0.798249			0.399125	+	0.916897i	$0.369314\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−0.758405	+	0.758405i	−0.106198	+	0.106198i
$52$		0			0
$53$	8.02895	+	8.02895i	1.10286	+	1.10286i	0.994064	+	0.108797i	$0.0346999\pi$
$53$	8.02895	+	8.02895i	1.10286	+	1.10286i	0.108797	+	0.994064i	$0.465300\pi$
$54$		0			0
$55$			0.920980i			0.124185i
$56$		0			0
$57$		−	0.121097i		−	0.0160397i
$58$		0			0
$59$	−3.27037	−	3.27037i	−0.425766	−	0.425766i	0.461417	−	0.887183i	$-0.347341\pi$
$59$	−3.27037	−	3.27037i	−0.425766	−	0.425766i	−0.887183	+	0.461417i	$0.847341\pi$
$60$		0			0
$61$	8.00019	−	8.00019i	1.02432	−	1.02432i	0.0246228	−	0.999697i	$-0.492162\pi$
$61$	8.00019	−	8.00019i	1.02432	−	1.02432i	0.999697	−	0.0246228i	$-0.00783847\pi$
$62$		0			0
$63$	−0.163545			−0.0206048
$64$		0			0
$65$	1.57382			0.195209
$66$		0			0
$67$	0.200912	−	0.200912i	0.0245453	−	0.0245453i	−0.694728	−	0.719273i	$-0.744475\pi$
$67$	0.200912	−	0.200912i	0.0245453	−	0.0245453i	0.719273	+	0.694728i	$0.244475\pi$
$68$		0			0
$69$	−4.17996	−	4.17996i	−0.503208	−	0.503208i
$70$		0			0
$71$		−	1.91971i		−	0.227828i	−0.993491	−	0.113914i	$-0.963661\pi$
$71$		−	1.91971i		−	0.227828i	0.993491	−	0.113914i	$-0.0363388\pi$
$72$		0			0
$73$			7.86605i			0.920652i	0.887750	+	0.460326i	$0.152267\pi$
$73$			7.86605i			0.920652i	−0.887750	+	0.460326i	$0.847733\pi$
$74$		0			0
$75$	1.25769	+	1.25769i	0.145225	+	0.145225i
$76$		0			0
$77$	0.651231	−	0.651231i	0.0742147	−	0.0742147i
$78$		0			0
$79$	−1.51045			−0.169939			−0.0849696	−	0.996384i	$-0.527079\pi$
$79$	−1.51045			−0.169939			−0.0849696	+	0.996384i	$0.527079\pi$
$80$		0			0
$81$	9.46389			1.05154
$82$		0			0
$83$	−11.4075	+	11.4075i	−1.25214	+	1.25214i	−0.297376	+	0.954760i	$0.596112\pi$
$83$	−11.4075	+	11.4075i	−1.25214	+	1.25214i	−0.954760	+	0.297376i	$0.903888\pi$
$84$		0			0
$85$	−0.426397	−	0.426397i	−0.0462492	−	0.0462492i
$86$		0			0
$87$		−	11.8992i		−	1.27572i
$88$		0			0
$89$			1.79530i			0.190301i	0.995463	+	0.0951507i	$0.0303333\pi$
$89$			1.79530i			0.190301i	−0.995463	+	0.0951507i	$0.969667\pi$
$90$		0			0
$91$	−1.11286	−	1.11286i	−0.116660	−	0.116660i
$92$		0			0
$93$	7.74036	−	7.74036i	0.802638	−	0.802638i
$94$		0			0
$95$	0.0680842			0.00698529
$96$		0			0
$97$	4.28142			0.434712			0.217356	−	0.976092i	$-0.430257\pi$
$97$	4.28142			0.434712			0.217356	+	0.976092i	$0.430257\pi$
$98$		0			0
$99$	0.106506	−	0.106506i	0.0107043	−	0.0107043i
$100$		0			0
$101$	1.91367	+	1.91367i	0.190417	+	0.190417i	0.795876	−	0.605459i	$-0.207011\pi$
$101$	1.91367	+	1.91367i	0.190417	+	0.190417i	−0.605459	+	0.795876i	$0.707011\pi$
$102$		0			0
$103$		−	13.2595i		−	1.30650i	−0.757143	−	0.653249i	$-0.773406\pi$
$103$		−	13.2595i		−	1.30650i	0.757143	−	0.653249i	$-0.226594\pi$
$104$		0			0
$105$		−	1.77864i		−	0.173577i
$106$		0			0
$107$	−1.20430	−	1.20430i	−0.116424	−	0.116424i	0.646495	−	0.762918i	$-0.276234\pi$
$107$	−1.20430	−	1.20430i	−0.116424	−	0.116424i	−0.762918	+	0.646495i	$0.776234\pi$
$108$		0			0
$109$	3.16834	−	3.16834i	0.303472	−	0.303472i	−0.538898	−	0.842371i	$-0.681159\pi$
$109$	3.16834	−	3.16834i	0.303472	−	0.303472i	0.842371	+	0.538898i	$0.181159\pi$
$110$		0			0
$111$	8.20438			0.778726
$112$		0			0
$113$	11.7295			1.10341			0.551707	−	0.834038i	$-0.313977\pi$
$113$	11.7295			1.10341			0.551707	+	0.834038i	$0.313977\pi$
$114$		0			0
$115$	2.35010	−	2.35010i	0.219147	−	0.219147i
$116$		0			0
$117$	−0.182003	−	0.182003i	−0.0168262	−	0.0168262i
$118$		0			0
$119$			0.603016i			0.0552784i
$120$		0			0
$121$		−	10.1518i		−	0.922890i
$122$		0			0
$123$	−7.34125	−	7.34125i	−0.661938	−	0.661938i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	0.429799			0.0381385			0.0190692	−	0.999818i	$-0.493930\pi$
$127$	0.429799			0.0381385			0.0190692	+	0.999818i	$0.493930\pi$
$128$		0			0
$129$	−17.2951			−1.52275
$130$		0			0
$131$	−10.1923	+	10.1923i	−0.890502	+	0.890502i	−0.994570	−	0.104068i	$-0.966814\pi$
$131$	−10.1923	+	10.1923i	−0.890502	+	0.890502i	0.104068	+	0.994570i	$0.466814\pi$
$132$		0			0
$133$	−0.0481428	−	0.0481428i	−0.00417451	−	0.00417451i
$134$		0			0
$135$			5.04502i			0.434206i
$136$		0			0
$137$			8.88755i			0.759315i	0.925127	+	0.379657i	$0.123958\pi$
$137$			8.88755i			0.759315i	−0.925127	+	0.379657i	$0.876042\pi$
$138$		0			0
$139$	−5.64555	−	5.64555i	−0.478849	−	0.478849i	0.425914	−	0.904764i	$-0.359953\pi$
$139$	−5.64555	−	5.64555i	−0.478849	−	0.478849i	−0.904764	+	0.425914i	$0.859953\pi$
$140$		0			0
$141$	6.88271	−	6.88271i	0.579629	−	0.579629i
$142$		0			0
$143$	1.44946			0.121210
$144$		0			0
$145$	6.69005			0.555578
$146$		0			0
$147$	−1.25769	+	1.25769i	−0.103732	+	0.103732i
$148$		0			0
$149$	−14.7096	−	14.7096i	−1.20506	−	1.20506i	−0.972607	−	0.232454i	$-0.925324\pi$
$149$	−14.7096	−	14.7096i	−1.20506	−	1.20506i	−0.232454	−	0.972607i	$-0.574676\pi$
$150$		0			0
$151$			8.49500i			0.691313i	0.938361	+	0.345657i	$0.112344\pi$
$151$			8.49500i			0.691313i	−0.938361	+	0.345657i	$0.887656\pi$
$152$		0			0
$153$			0.0986206i			0.00797300i
$154$		0			0
$155$	4.35185	+	4.35185i	0.349549	+	0.349549i
$156$		0			0
$157$	−8.79716	+	8.79716i	−0.702090	+	0.702090i	−0.964859	−	0.262769i	$-0.915364\pi$
$157$	−8.79716	+	8.79716i	−0.702090	+	0.702090i	0.262769	+	0.964859i	$0.415364\pi$
$158$		0			0
$159$	20.1958			1.60163
$160$		0			0
$161$	−3.32354			−0.261931
$162$		0			0
$163$	−3.53993	+	3.53993i	−0.277269	+	0.277269i	−0.832018	−	0.554749i	$-0.812814\pi$
$163$	−3.53993	+	3.53993i	−0.277269	+	0.277269i	0.554749	+	0.832018i	$0.312814\pi$
$164$		0			0
$165$	1.15830	+	1.15830i	0.0901738	+	0.0901738i
$166$		0			0
$167$			17.1739i			1.32896i	0.747307	+	0.664479i	$0.231347\pi$
$167$			17.1739i			1.32896i	−0.747307	+	0.664479i	$0.768653\pi$
$168$		0			0
$169$			10.5231i			0.809468i
$170$		0			0
$171$	−0.00787353	−	0.00787353i	−0.000602104	−	0.000602104i
$172$		0			0
$173$	−11.0510	+	11.0510i	−0.840190	+	0.840190i	−0.988883	−	0.148694i	$-0.952493\pi$
$173$	−11.0510	+	11.0510i	−0.840190	+	0.840190i	0.148694	+	0.988883i	$0.452493\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−8.22620			−0.618319
$178$		0			0
$179$	1.10235	−	1.10235i	0.0823932	−	0.0823932i	−0.664709	−	0.747102i	$-0.731444\pi$
$179$	1.10235	−	1.10235i	0.0823932	−	0.0823932i	0.747102	+	0.664709i	$0.231444\pi$
$180$		0			0
$181$	−3.60640	−	3.60640i	−0.268062	−	0.268062i	0.560257	−	0.828319i	$-0.310702\pi$
$181$	−3.60640	−	3.60640i	−0.268062	−	0.268062i	−0.828319	+	0.560257i	$0.810702\pi$
$182$		0			0
$183$		−	20.1235i		−	1.48757i
$184$		0			0
$185$			4.61274i			0.339135i
$186$		0			0
$187$	−0.392703	−	0.392703i	−0.0287173	−	0.0287173i
$188$		0			0
$189$	3.56737	−	3.56737i	0.259488	−	0.259488i
$190$		0			0
$191$	17.1989			1.24447			0.622233	−	0.782832i	$-0.286225\pi$
$191$	17.1989			1.24447			0.622233	+	0.782832i	$0.286225\pi$
$192$		0			0
$193$	−6.12727			−0.441051			−0.220525	−	0.975381i	$-0.570777\pi$
$193$	−6.12727			−0.441051			−0.220525	+	0.975381i	$0.570777\pi$
$194$		0			0
$195$	1.97938	−	1.97938i	0.141746	−	0.141746i
$196$		0			0
$197$	−16.2447	−	16.2447i	−1.15739	−	1.15739i	−0.985035	−	0.172352i	$-0.944863\pi$
$197$	−16.2447	−	16.2447i	−1.15739	−	1.15739i	−0.172352	−	0.985035i	$-0.555137\pi$
$198$		0			0
$199$		−	4.47826i		−	0.317455i	−0.987322	−	0.158728i	$-0.949261\pi$
$199$		−	4.47826i		−	0.317455i	0.987322	−	0.158728i	$-0.0507392\pi$
$200$		0			0
$201$		−	0.505368i		−	0.0356459i
$202$		0			0
$203$	−4.73058	−	4.73058i	−0.332022	−	0.332022i
$204$		0			0
$205$	4.12746	−	4.12746i	0.288274	−	0.288274i
$206$		0			0
$207$	−0.543549			−0.0377793
$208$		0			0
$209$	0.0627042			0.00433734
$210$		0			0
$211$	6.10477	−	6.10477i	0.420270	−	0.420270i	−0.465027	−	0.885297i	$-0.653955\pi$
$211$	6.10477	−	6.10477i	0.420270	−	0.420270i	0.885297	+	0.465027i	$0.153955\pi$
$212$		0			0
$213$	−2.41439	−	2.41439i	−0.165431	−	0.165431i
$214$		0			0
$215$		−	9.72383i		−	0.663159i
$216$		0			0
$217$		−	6.15445i		−	0.417791i
$218$		0			0
$219$	9.89302	+	9.89302i	0.668508	+	0.668508i
$220$		0			0
$221$	−0.671074	+	0.671074i	−0.0451413	+	0.0451413i
$222$		0			0
$223$	14.9388			1.00038			0.500188	−	0.865917i	$-0.333264\pi$
$223$	14.9388			1.00038			0.500188	+	0.865917i	$0.333264\pi$
$224$		0			0
$225$	0.163545			0.0109030
$226$		0			0
$227$	−0.226203	+	0.226203i	−0.0150136	+	0.0150136i	−0.714574	−	0.699560i	$-0.753379\pi$
$227$	−0.226203	+	0.226203i	−0.0150136	+	0.0150136i	0.699560	+	0.714574i	$0.253379\pi$
$228$		0			0
$229$	−17.7070	−	17.7070i	−1.17011	−	1.17011i	−0.982183	−	0.187929i	$-0.939823\pi$
$229$	−17.7070	−	17.7070i	−1.17011	−	1.17011i	−0.187929	−	0.982183i	$-0.560177\pi$
$230$		0			0
$231$		−	1.63809i		−	0.107778i
$232$		0			0
$233$		−	20.3846i		−	1.33544i	−0.744412	−	0.667720i	$-0.767270\pi$
$233$		−	20.3846i		−	1.33544i	0.744412	−	0.667720i	$-0.232730\pi$
$234$		0			0
$235$	3.86966	+	3.86966i	0.252429	+	0.252429i
$236$		0			0
$237$	−1.89967	+	1.89967i	−0.123397	+	0.123397i
$238$		0			0
$239$	−27.5857			−1.78437			−0.892184	−	0.451673i	$-0.850828\pi$
$239$	−27.5857			−1.78437			−0.892184	+	0.451673i	$0.850828\pi$
$240$		0			0
$241$	2.38105			0.153377			0.0766885	−	0.997055i	$-0.475565\pi$
$241$	2.38105			0.153377			0.0766885	+	0.997055i	$0.475565\pi$
$242$		0			0
$243$	1.20049	−	1.20049i	0.0770117	−	0.0770117i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	0.107152i		−	0.00681795i
$248$		0			0
$249$			28.6941i			1.81842i
$250$		0			0
$251$	9.49501	+	9.49501i	0.599320	+	0.599320i	0.940132	−	0.340812i	$-0.110702\pi$
$251$	9.49501	+	9.49501i	0.599320	+	0.599320i	−0.340812	+	0.940132i	$0.610702\pi$
$252$		0			0
$253$	2.16439	−	2.16439i	0.136074	−	0.136074i
$254$		0			0
$255$	−1.07255			−0.0671655
$256$		0			0
$257$	17.5034			1.09183			0.545915	−	0.837841i	$-0.316182\pi$
$257$	17.5034			1.09183			0.545915	+	0.837841i	$0.316182\pi$
$258$		0			0
$259$	3.26170	−	3.26170i	0.202672	−	0.202672i
$260$		0			0
$261$	−0.773665	−	0.773665i	−0.0478886	−	0.0478886i
$262$		0			0
$263$			29.3793i			1.81160i	0.423703	+	0.905801i	$0.360730\pi$
$263$			29.3793i			1.81160i	−0.423703	+	0.905801i	$0.639270\pi$
$264$		0			0
$265$			11.3547i			0.697511i
$266$		0			0
$267$	2.25792	+	2.25792i	0.138183	+	0.138183i
$268$		0			0
$269$	10.4537	−	10.4537i	0.637372	−	0.637372i	−0.312534	−	0.949906i	$-0.601178\pi$
$269$	10.4537	−	10.4537i	0.637372	−	0.637372i	0.949906	+	0.312534i	$0.101178\pi$
$270$		0			0
$271$	20.1834			1.22605			0.613027	−	0.790062i	$-0.289952\pi$
$271$	20.1834			1.22605			0.613027	+	0.790062i	$0.289952\pi$
$272$		0			0
$273$	−2.79926			−0.169419
$274$		0			0
$275$	−0.651231	+	0.651231i	−0.0392707	+	0.0392707i
$276$		0			0
$277$	0.340772	+	0.340772i	0.0204750	+	0.0204750i	0.717270	−	0.696795i	$-0.245391\pi$
$277$	0.340772	+	0.340772i	0.0204750	+	0.0204750i	−0.696795	+	0.717270i	$0.745391\pi$
$278$		0			0
$279$		−	1.00653i		−	0.0602595i
$280$		0			0
$281$			11.4612i			0.683719i	0.939751	+	0.341860i	$0.111057\pi$
$281$			11.4612i			0.683719i	−0.939751	+	0.341860i	$0.888943\pi$
$282$		0			0
$283$	−17.5855	−	17.5855i	−1.04535	−	1.04535i	−0.998922	−	0.0464283i	$-0.985216\pi$
$283$	−17.5855	−	17.5855i	−1.04535	−	1.04535i	−0.0464283	−	0.998922i	$-0.514784\pi$
$284$		0			0
$285$	0.0856285	−	0.0856285i	0.00507219	−	0.00507219i
$286$		0			0
$287$	−5.83711			−0.344554
$288$		0			0
$289$	−16.6364			−0.978610
$290$		0			0
$291$	5.38468	−	5.38468i	0.315656	−	0.315656i
$292$		0			0
$293$	−10.0898	−	10.0898i	−0.589455	−	0.589455i	0.348029	−	0.937484i	$-0.386851\pi$
$293$	−10.0898	−	10.0898i	−0.589455	−	0.589455i	−0.937484	+	0.348029i	$0.886851\pi$
$294$		0			0
$295$		−	4.62501i		−	0.269278i
$296$		0			0
$297$			4.64636i			0.269609i
$298$		0			0
$299$	−3.69864	−	3.69864i	−0.213898	−	0.213898i
$300$		0			0
$301$	−6.87578	+	6.87578i	−0.396314	+	0.396314i
$302$		0			0
$303$	4.81358			0.276533
$304$		0			0
$305$	11.3140			0.647837
$306$		0			0
$307$	−18.8661	+	18.8661i	−1.07675	+	1.07675i	−0.0799466	+	0.996799i	$0.525475\pi$
$307$	−18.8661	+	18.8661i	−1.07675	+	1.07675i	−0.996799	+	0.0799466i	$0.974525\pi$
$308$		0			0
$309$	−16.6763	−	16.6763i	−0.948680	−	0.948680i
$310$		0			0
$311$			0.0904960i			0.00513156i	0.999997	+	0.00256578i	$0.000816714\pi$
$311$			0.0904960i			0.00513156i	−0.999997	+	0.00256578i	$0.999183\pi$
$312$		0			0
$313$			26.3979i			1.49210i	0.665892	+	0.746048i	$0.268051\pi$
$313$			26.3979i			1.49210i	−0.665892	+	0.746048i	$0.731949\pi$
$314$		0			0
$315$	−0.115644	−	0.115644i	−0.00651581	−	0.00651581i
$316$		0			0
$317$	2.76566	−	2.76566i	0.155335	−	0.155335i	−0.625161	−	0.780496i	$-0.714967\pi$
$317$	2.76566	−	2.76566i	0.155335	−	0.155335i	0.780496	+	0.625161i	$0.214967\pi$
$318$		0			0
$319$	6.16140			0.344972
$320$		0			0
$321$	−3.02925			−0.169076
$322$		0			0
$323$	−0.0290309	+	0.0290309i	−0.00161532	+	0.00161532i
$324$		0			0
$325$	1.11286	+	1.11286i	0.0617305	+	0.0617305i
$326$		0			0
$327$		−	7.96956i		−	0.440718i
$328$		0			0
$329$		−	5.47252i		−	0.301710i
$330$		0			0
$331$	−7.19158	−	7.19158i	−0.395285	−	0.395285i	0.481281	−	0.876566i	$-0.340172\pi$
$331$	−7.19158	−	7.19158i	−0.395285	−	0.395285i	−0.876566	+	0.481281i	$0.840172\pi$
$332$		0			0
$333$	0.533436	−	0.533436i	0.0292321	−	0.0292321i
$334$		0			0
$335$	0.284132			0.0155238
$336$		0			0
$337$	−0.126565			−0.00689444			−0.00344722	−	0.999994i	$-0.501097\pi$
$337$	−0.126565			−0.00689444			−0.00344722	+	0.999994i	$0.501097\pi$
$338$		0			0
$339$	14.7520	−	14.7520i	0.801217	−	0.801217i
$340$		0			0
$341$	4.00797	+	4.00797i	0.217044	+	0.217044i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	5.91136i		−	0.318257i
$346$		0			0
$347$	25.0440	+	25.0440i	1.34443	+	1.34443i	0.891589	+	0.452846i	$0.149591\pi$
$347$	25.0440	+	25.0440i	1.34443	+	1.34443i	0.452846	+	0.891589i	$0.350409\pi$
$348$		0			0
$349$	−3.85172	+	3.85172i	−0.206178	+	0.206178i	−0.802641	−	0.596463i	$-0.796572\pi$
$349$	−3.85172	+	3.85172i	−0.206178	+	0.206178i	0.596463	+	0.802641i	$0.296572\pi$
$350$		0			0
$351$	7.93997			0.423804
$352$		0			0
$353$	−3.43843			−0.183009			−0.0915046	−	0.995805i	$-0.529168\pi$
$353$	−3.43843			−0.183009			−0.0915046	+	0.995805i	$0.529168\pi$
$354$		0			0
$355$	1.35744	−	1.35744i	0.0720454	−	0.0720454i
$356$		0			0
$357$	0.758405	+	0.758405i	0.0401390	+	0.0401390i
$358$		0			0
$359$			31.0991i			1.64135i	0.571396	+	0.820675i	$0.306402\pi$
$359$			31.0991i			1.64135i	−0.571396	+	0.820675i	$0.693598\pi$
$360$		0			0
$361$			18.9954i			0.999756i
$362$		0			0
$363$	−12.7678	−	12.7678i	−0.670134	−	0.670134i
$364$		0			0
$365$	−5.56214	+	5.56214i	−0.291136	+	0.291136i
$366$		0			0
$367$	−18.1151			−0.945599			−0.472799	−	0.881170i	$-0.656756\pi$
$367$	−18.1151			−0.945599			−0.472799	+	0.881170i	$0.656756\pi$
$368$		0			0
$369$	−0.954634			−0.0496962
$370$		0			0
$371$	8.02895	−	8.02895i	0.416842	−	0.416842i
$372$		0			0
$373$	16.0111	+	16.0111i	0.829022	+	0.829022i	0.987381	−	0.158360i	$-0.0506206\pi$
$373$	16.0111	+	16.0111i	0.829022	+	0.829022i	−0.158360	+	0.987381i	$0.550621\pi$
$374$		0			0
$375$			1.77864i			0.0918484i
$376$		0			0
$377$		−	10.5290i		−	0.542269i
$378$		0			0
$379$	−15.6288	−	15.6288i	−0.802798	−	0.802798i	0.180734	−	0.983532i	$-0.442153\pi$
$379$	−15.6288	−	15.6288i	−0.802798	−	0.802798i	−0.983532	+	0.180734i	$0.942153\pi$
$380$		0			0
$381$	0.540552	−	0.540552i	0.0276933	−	0.0276933i
$382$		0			0
$383$	18.0295			0.921264			0.460632	−	0.887591i	$-0.347623\pi$
$383$	18.0295			0.921264			0.460632	+	0.887591i	$0.347623\pi$
$384$		0			0
$385$	0.920980			0.0469375
$386$		0			0
$387$	−1.12450	+	1.12450i	−0.0571617	+	0.0571617i
$388$		0			0
$389$	4.59304	+	4.59304i	0.232876	+	0.232876i	0.813892	−	0.581016i	$-0.197345\pi$
$389$	4.59304	+	4.59304i	0.232876	+	0.232876i	−0.581016	+	0.813892i	$0.697345\pi$
$390$		0			0
$391$			2.00415i			0.101354i
$392$		0			0
$393$			25.6373i			1.29323i
$394$		0			0
$395$	−1.06805	−	1.06805i	−0.0537395	−	0.0537395i
$396$		0			0
$397$	−16.6604	+	16.6604i	−0.836163	+	0.836163i	−0.988351	−	0.152189i	$-0.951368\pi$
$397$	−16.6604	+	16.6604i	−0.836163	+	0.836163i	0.152189	+	0.988351i	$0.451368\pi$
$398$		0			0
$399$	−0.121097			−0.00606243
$400$		0			0
$401$	23.9835			1.19768			0.598839	−	0.800869i	$-0.295629\pi$
$401$	23.9835			1.19768			0.598839	+	0.800869i	$0.295629\pi$
$402$		0			0
$403$	6.84905	−	6.84905i	0.341175	−	0.341175i
$404$		0			0
$405$	6.69198	+	6.69198i	0.332527	+	0.332527i
$406$		0			0
$407$			4.24824i			0.210578i
$408$		0			0
$409$			19.8597i			0.982000i	0.871160	+	0.491000i	$0.163369\pi$
$409$			19.8597i			0.982000i	−0.871160	+	0.491000i	$0.836631\pi$
$410$		0			0
$411$	11.1777	+	11.1777i	0.551357	+	0.551357i
$412$		0			0
$413$	−3.27037	+	3.27037i	−0.160925	+	0.160925i
$414$		0			0
$415$	−16.1327			−0.791921
$416$		0			0
$417$	−14.2007			−0.695409
$418$		0			0
$419$	−5.63336	+	5.63336i	−0.275208	+	0.275208i	−0.831192	−	0.555985i	$-0.812341\pi$
$419$	−5.63336	+	5.63336i	−0.275208	+	0.275208i	0.555985	+	0.831192i	$0.312341\pi$
$420$		0			0
$421$	−14.3170	−	14.3170i	−0.697768	−	0.697768i	0.266161	−	0.963929i	$-0.414245\pi$
$421$	−14.3170	−	14.3170i	−0.697768	−	0.697768i	−0.963929	+	0.266161i	$0.914245\pi$
$422$		0			0
$423$		−	0.895006i		−	0.0435167i
$424$		0			0
$425$		−	0.603016i		−	0.0292506i
$426$		0			0
$427$	−8.00019	−	8.00019i	−0.387156	−	0.387156i
$428$		0			0
$429$	1.82297	−	1.82297i	0.0880136	−	0.0880136i
$430$		0			0
$431$	27.8850			1.34317			0.671585	−	0.740927i	$-0.265614\pi$
$431$	27.8850			1.34317			0.671585	+	0.740927i	$0.265614\pi$
$432$		0			0
$433$	−11.7286			−0.563640			−0.281820	−	0.959467i	$-0.590938\pi$
$433$	−11.7286			−0.563640			−0.281820	+	0.959467i	$0.590938\pi$
$434$		0			0
$435$	8.41398	−	8.41398i	0.403419	−	0.403419i
$436$		0			0
$437$	−0.160004	−	0.160004i	−0.00765404	−	0.00765404i
$438$		0			0
$439$			0.485358i			0.0231649i	0.999933	+	0.0115824i	$0.00368688\pi$
$439$			0.485358i			0.0231649i	−0.999933	+	0.0115824i	$0.996313\pi$
$440$		0			0
$441$			0.163545i			0.00778788i
$442$		0			0
$443$	3.09351	+	3.09351i	0.146977	+	0.146977i	0.776766	−	0.629789i	$-0.216859\pi$
$443$	3.09351	+	3.09351i	0.146977	+	0.146977i	−0.629789	+	0.776766i	$0.716859\pi$
$444$		0			0
$445$	−1.26947	+	1.26947i	−0.0601786	+	0.0601786i
$446$		0			0
$447$	−37.0002			−1.75005
$448$		0			0
$449$	20.5596			0.970268			0.485134	−	0.874440i	$-0.338771\pi$
$449$	20.5596			0.970268			0.485134	+	0.874440i	$0.338771\pi$
$450$		0			0
$451$	3.80131	−	3.80131i	0.178997	−	0.178997i
$452$		0			0
$453$	10.6840	+	10.6840i	0.501980	+	0.501980i
$454$		0			0
$455$		−	1.57382i		−	0.0737820i
$456$		0			0
$457$		−	31.1867i		−	1.45885i	−0.684060	−	0.729425i	$-0.739788\pi$
$457$		−	31.1867i		−	1.45885i	0.684060	−	0.729425i	$-0.260212\pi$
$458$		0			0
$459$	−2.15118	−	2.15118i	−0.100409	−	0.100409i
$460$		0			0
$461$	−9.42653	+	9.42653i	−0.439037	+	0.439037i	−0.891688	−	0.452651i	$-0.850478\pi$
$461$	−9.42653	+	9.42653i	−0.439037	+	0.439037i	0.452651	+	0.891688i	$0.350478\pi$
$462$		0			0
$463$	−15.1464			−0.703914			−0.351957	−	0.936016i	$-0.614484\pi$
$463$	−15.1464			−0.703914			−0.351957	+	0.936016i	$0.614484\pi$
$464$		0			0
$465$	10.9465			0.507633
$466$		0			0
$467$	−22.3279	+	22.3279i	−1.03321	+	1.03321i	−0.0337836	+	0.999429i	$0.510756\pi$
$467$	−22.3279	+	22.3279i	−1.03321	+	1.03321i	−0.999429	+	0.0337836i	$0.989244\pi$
$468$		0			0
$469$	−0.200912	−	0.200912i	−0.00927725	−	0.00927725i
$470$		0			0
$471$			22.1281i			1.01961i
$472$		0			0
$473$		−	8.95545i		−	0.411772i
$474$		0			0
$475$	0.0481428	+	0.0481428i	0.00220894	+	0.00220894i
$476$		0			0
$477$	1.31310	−	1.31310i	0.0601227	−	0.0601227i
$478$		0			0
$479$	−21.3820			−0.976970			−0.488485	−	0.872572i	$-0.662450\pi$
$479$	−21.3820			−0.976970			−0.488485	+	0.872572i	$0.662450\pi$
$480$		0			0
$481$	7.25964			0.331011
$482$		0			0
$483$	−4.17996	+	4.17996i	−0.190195	+	0.190195i
$484$		0			0
$485$	3.02742	+	3.02742i	0.137468	+	0.137468i
$486$		0			0
$487$			10.1750i			0.461075i	0.973063	+	0.230538i	$0.0740485\pi$
$487$			10.1750i			0.461075i	−0.973063	+	0.230538i	$0.925952\pi$
$488$		0			0
$489$			8.90425i			0.402664i
$490$		0			0
$491$	11.1601	+	11.1601i	0.503648	+	0.503648i	0.912569	−	0.408922i	$-0.134095\pi$
$491$	11.1601	+	11.1601i	0.503648	+	0.503648i	−0.408922	+	0.912569i	$0.634095\pi$
$492$		0			0
$493$	−2.85262	+	2.85262i	−0.128475	+	0.128475i
$494$		0			0
$495$	0.150622			0.00676996
$496$		0			0
$497$	−1.91971			−0.0861108
$498$		0			0
$499$	−24.2041	+	24.2041i	−1.08353	+	1.08353i	−0.0873482	+	0.996178i	$0.527839\pi$
$499$	−24.2041	+	24.2041i	−1.08353	+	1.08353i	−0.996178	+	0.0873482i	$0.972161\pi$
$500$		0			0
$501$	21.5994	+	21.5994i	0.964990	+	0.964990i
$502$		0			0
$503$		−	11.0233i		−	0.491503i	−0.969333	−	0.245751i	$-0.920965\pi$
$503$		−	11.0233i		−	0.491503i	0.969333	−	0.245751i	$-0.0790346\pi$
$504$		0			0
$505$			2.70634i			0.120430i
$506$		0			0
$507$	13.2347	+	13.2347i	0.587775	+	0.587775i
$508$		0			0
$509$	3.80620	−	3.80620i	0.168707	−	0.168707i	−0.617704	−	0.786411i	$-0.711937\pi$
$509$	3.80620	−	3.80620i	0.168707	−	0.168707i	0.786411	+	0.617704i	$0.211937\pi$
$510$		0			0
$511$	7.86605			0.347974
$512$		0			0
$513$	0.343486			0.0151653
$514$		0			0
$515$	9.37588	−	9.37588i	0.413151	−	0.413151i
$516$		0			0
$517$	3.56388	+	3.56388i	0.156739	+	0.156739i
$518$		0			0
$519$			27.7973i			1.22017i
$520$		0			0
$521$		−	8.86849i		−	0.388536i	−0.980949	−	0.194268i	$-0.937767\pi$
$521$		−	8.86849i		−	0.388536i	0.980949	−	0.194268i	$-0.0622331\pi$
$522$		0			0
$523$	−10.6892	−	10.6892i	−0.467407	−	0.467407i	0.433666	−	0.901074i	$-0.357220\pi$
$523$	−10.6892	−	10.6892i	−0.467407	−	0.467407i	−0.901074	+	0.433666i	$0.857220\pi$
$524$		0			0
$525$	1.25769	−	1.25769i	0.0548899	−	0.0548899i
$526$		0			0
$527$	−3.71123			−0.161664
$528$		0			0
$529$	11.9541			0.519744
$530$		0			0
$531$	−0.534855	+	0.534855i	−0.0232107	+	0.0232107i
$532$		0			0
$533$	−6.49590	−	6.49590i	−0.281369	−	0.281369i
$534$		0			0
$535$		−	1.70313i		−	0.0736328i
$536$		0			0
$537$		−	2.77281i		−	0.119656i
$538$		0			0
$539$	−0.651231	−	0.651231i	−0.0280505	−	0.0280505i
$540$		0			0
$541$	22.0050	−	22.0050i	0.946069	−	0.946069i	−0.0525493	−	0.998618i	$-0.516735\pi$
$541$	22.0050	−	22.0050i	0.946069	−	0.946069i	0.998618	+	0.0525493i	$0.0167347\pi$
$542$		0			0
$543$	−9.07145			−0.389293
$544$		0			0
$545$	4.48072			0.191933
$546$		0			0
$547$	7.10045	−	7.10045i	0.303593	−	0.303593i	−0.538825	−	0.842418i	$-0.681131\pi$
$547$	7.10045	−	7.10045i	0.303593	−	0.303593i	0.842418	+	0.538825i	$0.181131\pi$
$548$		0			0
$549$	−1.30840	−	1.30840i	−0.0558409	−	0.0558409i
$550$		0			0
$551$		−	0.455486i		−	0.0194044i
$552$		0			0
$553$			1.51045i			0.0642309i
$554$		0			0
$555$	5.80138	+	5.80138i	0.246255	+	0.246255i
$556$		0			0
$557$	−30.6211	+	30.6211i	−1.29746	+	1.29746i	−0.367392	+	0.930066i	$0.619749\pi$
$557$	−30.6211	+	30.6211i	−1.29746	+	1.29746i	−0.930066	+	0.367392i	$0.880251\pi$
$558$		0			0
$559$	−15.3036			−0.647273
$560$		0			0
$561$	−0.987794			−0.0417047
$562$		0			0
$563$	−31.3046	+	31.3046i	−1.31933	+	1.31933i	−0.405024	+	0.914306i	$0.632737\pi$
$563$	−31.3046	+	31.3046i	−1.31933	+	1.31933i	−0.914306	+	0.405024i	$0.867263\pi$
$564$		0			0
$565$	8.29398	+	8.29398i	0.348930	+	0.348930i
$566$		0			0
$567$		−	9.46389i		−	0.397446i
$568$		0			0
$569$			25.3468i			1.06260i	0.847185	+	0.531298i	$0.178295\pi$
$569$			25.3468i			1.06260i	−0.847185	+	0.531298i	$0.821705\pi$
$570$		0			0
$571$	6.57745	+	6.57745i	0.275258	+	0.275258i	0.831213	−	0.555955i	$-0.187647\pi$
$571$	6.57745	+	6.57745i	0.275258	+	0.275258i	−0.555955	+	0.831213i	$0.687647\pi$
$572$		0			0
$573$	21.6308	−	21.6308i	0.903638	−	0.903638i
$574$		0			0
$575$	3.32354			0.138601
$576$		0			0
$577$	−33.7316			−1.40427			−0.702133	−	0.712046i	$-0.747769\pi$
$577$	−33.7316			−1.40427			−0.702133	+	0.712046i	$0.747769\pi$
$578$		0			0
$579$	−7.70618	+	7.70618i	−0.320258	+	0.320258i
$580$		0			0
$581$	11.4075	+	11.4075i	0.473263	+	0.473263i
$582$		0			0
$583$			10.4574i			0.433102i
$584$		0			0
$585$		−	0.257392i		−	0.0106418i
$586$		0			0
$587$	−11.1272	−	11.1272i	−0.459270	−	0.459270i	0.439146	−	0.898416i	$-0.355281\pi$
$587$	−11.1272	−	11.1272i	−0.459270	−	0.459270i	−0.898416	+	0.439146i	$0.855281\pi$
$588$		0			0
$589$	0.296292	−	0.296292i	0.0122085	−	0.0122085i
$590$		0			0
$591$	−40.8615			−1.68082
$592$		0			0
$593$	−18.3956			−0.755418			−0.377709	−	0.925924i	$-0.623288\pi$
$593$	−18.3956			−0.755418			−0.377709	+	0.925924i	$0.623288\pi$
$594$		0			0
$595$	−0.426397	+	0.426397i	−0.0174806	+	0.0174806i
$596$		0			0
$597$	−5.63224	−	5.63224i	−0.230512	−	0.230512i
$598$		0			0
$599$			3.74093i			0.152850i	0.997075	+	0.0764250i	$0.0243506\pi$
$599$			3.74093i			0.152850i	−0.997075	+	0.0764250i	$0.975649\pi$
$600$		0			0
$601$		−	25.1470i		−	1.02577i	−0.858458	−	0.512883i	$-0.828577\pi$
$601$		−	25.1470i		−	1.02577i	0.858458	−	0.512883i	$-0.171423\pi$
$602$		0			0
$603$	−0.0328582	−	0.0328582i	−0.00133809	−	0.00133809i
$604$		0			0
$605$	7.17840	−	7.17840i	0.291844	−	0.291844i
$606$		0			0
$607$	−20.3554			−0.826199			−0.413099	−	0.910686i	$-0.635554\pi$
$607$	−20.3554			−0.826199			−0.413099	+	0.910686i	$0.635554\pi$
$608$		0			0
$609$	−11.8992			−0.482178
$610$		0			0
$611$	6.09016	−	6.09016i	0.246382	−	0.246382i
$612$		0			0
$613$	15.1285	+	15.1285i	0.611033	+	0.611033i	0.943215	−	0.332182i	$-0.107785\pi$
$613$	15.1285	+	15.1285i	0.611033	+	0.611033i	−0.332182	+	0.943215i	$0.607785\pi$
$614$		0			0
$615$		−	10.3821i		−	0.418647i
$616$		0			0
$617$		−	34.6485i		−	1.39489i	−0.716636	−	0.697447i	$-0.754319\pi$
$617$		−	34.6485i		−	1.39489i	0.716636	−	0.697447i	$-0.245681\pi$
$618$		0			0
$619$	−17.6878	−	17.6878i	−0.710932	−	0.710932i	0.255798	−	0.966730i	$-0.417662\pi$
$619$	−17.6878	−	17.6878i	−0.710932	−	0.710932i	−0.966730	+	0.255798i	$0.917662\pi$
$620$		0			0
$621$	11.8563	−	11.8563i	0.475776	−	0.475776i
$622$		0			0
$623$	1.79530			0.0719272
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	0.0788621	−	0.0788621i	0.00314945	−	0.00314945i
$628$		0			0
$629$	−1.96686	−	1.96686i	−0.0784238	−	0.0784238i
$630$		0			0
$631$		−	15.3544i		−	0.611248i	−0.952152	−	0.305624i	$-0.901135\pi$
$631$		−	15.3544i		−	0.611248i	0.952152	−	0.305624i	$-0.0988650\pi$
$632$		0			0
$633$		−	15.3558i		−	0.610337i
$634$		0			0
$635$	0.303914	+	0.303914i	0.0120605	+	0.0120605i
$636$		0			0
$637$	−1.11286	+	1.11286i	−0.0440932	+	0.0440932i
$638$		0			0
$639$	−0.313960			−0.0124201
$640$		0			0
$641$	−12.4211			−0.490602			−0.245301	−	0.969447i	$-0.578887\pi$
$641$	−12.4211			−0.490602			−0.245301	+	0.969447i	$0.578887\pi$
$642$		0			0
$643$	4.58322	−	4.58322i	0.180744	−	0.180744i	−0.610936	−	0.791680i	$-0.709207\pi$
$643$	4.58322	−	4.58322i	0.180744	−	0.180744i	0.791680	+	0.610936i	$0.209207\pi$
$644$		0			0
$645$	−12.2295	−	12.2295i	−0.481537	−	0.481537i
$646$		0			0
$647$		−	3.25672i		−	0.128035i	−0.997949	−	0.0640174i	$-0.979609\pi$
$647$		−	3.25672i		−	0.128035i	0.997949	−	0.0640174i	$-0.0203913\pi$
$648$		0			0
$649$		−	4.25954i		−	0.167202i
$650$		0			0
$651$	−7.74036	−	7.74036i	−0.303368	−	0.303368i
$652$		0			0
$653$	−12.8699	+	12.8699i	−0.503636	+	0.503636i	−0.912566	−	0.408930i	$-0.865902\pi$
$653$	−12.8699	+	12.8699i	−0.503636	+	0.503636i	0.408930	+	0.912566i	$0.365902\pi$
$654$		0			0
$655$	−14.4140			−0.563203
$656$		0			0
$657$	1.28646			0.0501895
$658$		0			0
$659$	−33.4531	+	33.4531i	−1.30315	+	1.30315i	−0.376887	+	0.926259i	$0.623005\pi$
$659$	−33.4531	+	33.4531i	−1.30315	+	1.30315i	−0.926259	+	0.376887i	$0.876995\pi$
$660$		0			0
$661$	6.33269	+	6.33269i	0.246313	+	0.246313i	0.819456	−	0.573142i	$-0.194276\pi$
$661$	6.33269	+	6.33269i	0.246313	+	0.246313i	−0.573142	+	0.819456i	$0.694276\pi$
$662$		0			0
$663$			1.68800i			0.0655565i
$664$		0			0
$665$		−	0.0680842i		−	0.00264019i
$666$		0			0
$667$	−15.7222	−	15.7222i	−0.608768	−	0.608768i
$668$		0			0
$669$	18.7883	−	18.7883i	0.726399	−	0.726399i
$670$		0			0
$671$	10.4200			0.402258
$672$		0			0
$673$	−20.3771			−0.785481			−0.392740	−	0.919649i	$-0.628473\pi$
$673$	−20.3771			−0.785481			−0.392740	+	0.919649i	$0.628473\pi$
$674$		0			0
$675$	−3.56737	+	3.56737i	−0.137308	+	0.137308i
$676$		0			0
$677$	−5.97856	−	5.97856i	−0.229775	−	0.229775i	0.582824	−	0.812599i	$-0.301948\pi$
$677$	−5.97856	−	5.97856i	−0.229775	−	0.229775i	−0.812599	+	0.582824i	$0.801948\pi$
$678$		0			0
$679$		−	4.28142i		−	0.164306i
$680$		0			0
$681$			0.568985i			0.0218035i
$682$		0			0
$683$	32.5411	+	32.5411i	1.24515	+	1.24515i	0.957837	+	0.287312i	$0.0927617\pi$
$683$	32.5411	+	32.5411i	1.24515	+	1.24515i	0.287312	+	0.957837i	$0.407238\pi$
$684$		0			0
$685$	−6.28445	+	6.28445i	−0.240116	+	0.240116i
$686$		0			0
$687$	−44.5397			−1.69929
$688$		0			0
$689$	17.8702			0.680801
$690$		0			0
$691$	−31.9319	+	31.9319i	−1.21475	+	1.21475i	−0.245298	+	0.969448i	$0.578886\pi$
$691$	−31.9319	+	31.9319i	−1.21475	+	1.21475i	−0.969448	+	0.245298i	$0.921114\pi$
$692$		0			0
$693$	−0.106506	−	0.106506i	−0.00404583	−	0.00404583i
$694$		0			0
$695$		−	7.98401i		−	0.302851i
$696$		0			0
$697$			3.51987i			0.133325i
$698$		0			0
$699$	−25.6374	−	25.6374i	−0.969697	−	0.969697i
$700$		0			0
$701$	−1.20601	+	1.20601i	−0.0455503	+	0.0455503i	−0.729515	−	0.683965i	$-0.760254\pi$
$701$	−1.20601	+	1.20601i	−0.0455503	+	0.0455503i	0.683965	+	0.729515i	$0.260254\pi$
$702$		0			0
$703$	0.314055			0.0118448
$704$		0			0
$705$	9.73363			0.366590
$706$		0			0
$707$	1.91367	−	1.91367i	0.0719709	−	0.0719709i
$708$		0			0
$709$	33.1834	+	33.1834i	1.24623	+	1.24623i	0.957372	+	0.288856i	$0.0932750\pi$
$709$	33.1834	+	33.1834i	1.24623	+	1.24623i	0.288856	+	0.957372i	$0.406725\pi$
$710$		0			0
$711$			0.247028i			0.00926426i
$712$		0			0
$713$		−	20.4545i		−	0.766028i
$714$		0			0
$715$	1.02492	+	1.02492i	0.0383300	+	0.0383300i
$716$		0			0
$717$	−34.6941	+	34.6941i	−1.29567	+	1.29567i
$718$		0			0
$719$	34.7079			1.29439			0.647194	−	0.762326i	$-0.275943\pi$
$719$	34.7079			1.29439			0.647194	+	0.762326i	$0.275943\pi$
$720$		0			0
$721$	−13.2595			−0.493810
$722$		0			0
$723$	2.99461	−	2.99461i	0.111371	−	0.111371i
$724$		0			0
$725$	4.73058	+	4.73058i	0.175689	+	0.175689i
$726$		0			0
$727$		−	22.5592i		−	0.836673i	−0.908292	−	0.418337i	$-0.862613\pi$
$727$		−	22.5592i		−	0.836673i	0.908292	−	0.418337i	$-0.137387\pi$
$728$		0			0
$729$			25.3720i			0.939703i
$730$		0			0
$731$	4.14621	+	4.14621i	0.153353	+	0.153353i
$732$		0			0
$733$	−36.3696	+	36.3696i	−1.34334	+	1.34334i	−0.450633	+	0.892709i	$0.648802\pi$
$733$	−36.3696	+	36.3696i	−1.34334	+	1.34334i	−0.892709	+	0.450633i	$0.851198\pi$
$734$		0			0
$735$	−1.77864			−0.0656060
$736$		0			0
$737$	0.261680			0.00963912
$738$		0			0
$739$	28.6280	−	28.6280i	1.05310	−	1.05310i	0.0545872	−	0.998509i	$-0.482616\pi$
$739$	28.6280	−	28.6280i	1.05310	−	1.05310i	0.998509	−	0.0545872i	$-0.0173843\pi$
$740$		0			0
$741$	−0.134764	−	0.134764i	−0.00495068	−	0.00495068i
$742$		0			0
$743$			5.92667i			0.217429i	0.994073	+	0.108714i	$0.0346734\pi$
$743$			5.92667i			0.217429i	−0.994073	+	0.108714i	$0.965327\pi$
$744$		0			0
$745$		−	20.8026i		−	0.762148i
$746$		0			0
$747$	1.86565	+	1.86565i	0.0682604	+	0.0682604i
$748$		0			0
$749$	−1.20430	+	1.20430i	−0.0440040	+	0.0440040i
$750$		0			0
$751$	7.28601			0.265870			0.132935	−	0.991125i	$-0.457560\pi$
$751$	7.28601			0.265870			0.132935	+	0.991125i	$0.457560\pi$
$752$		0			0
$753$	23.8835			0.870362
$754$		0			0
$755$	−6.00687	+	6.00687i	−0.218613	+	0.218613i
$756$		0			0
$757$	−24.2438	−	24.2438i	−0.881155	−	0.881155i	0.112497	−	0.993652i	$-0.464115\pi$
$757$	−24.2438	−	24.2438i	−0.881155	−	0.881155i	−0.993652	+	0.112497i	$0.964115\pi$
$758$		0			0
$759$		−	5.44425i		−	0.197614i
$760$		0			0
$761$			7.13566i			0.258668i	0.991601	+	0.129334i	$0.0412839\pi$
$761$			7.13566i			0.258668i	−0.991601	+	0.129334i	$0.958716\pi$
$762$		0			0
$763$	−3.16834	−	3.16834i	−0.114702	−	0.114702i
$764$		0			0
$765$	−0.0697353	+	0.0697353i	−0.00252128	+	0.00252128i
$766$		0			0
$767$	−7.27894			−0.262827
$768$		0			0
$769$	−41.9735			−1.51360			−0.756802	−	0.653645i	$-0.773239\pi$
$769$	−41.9735			−1.51360			−0.756802	+	0.653645i	$0.773239\pi$
$770$		0			0
$771$	22.0137	−	22.0137i	0.792805	−	0.792805i
$772$		0			0
$773$	−15.5336	−	15.5336i	−0.558705	−	0.558705i	0.370233	−	0.928939i	$-0.379278\pi$
$773$	−15.5336	−	15.5336i	−0.558705	−	0.558705i	−0.928939	+	0.370233i	$0.879278\pi$
$774$		0			0
$775$			6.15445i			0.221074i
$776$		0			0
$777$		−	8.20438i		−	0.294331i
$778$		0			0
$779$	−0.281015	−	0.281015i	−0.0100684	−	0.0100684i
$780$		0			0
$781$	1.25018	−	1.25018i	0.0447348	−	0.0447348i
$782$		0			0
$783$	33.7514			1.20618
$784$		0			0
$785$	−12.4411			−0.444041
$786$		0			0
$787$	36.4484	−	36.4484i	1.29924	−	1.29924i	0.370353	−	0.928891i	$-0.379237\pi$
$787$	36.4484	−	36.4484i	1.29924	−	1.29924i	0.928891	−	0.370353i	$-0.120763\pi$
$788$		0			0
$789$	36.9499	+	36.9499i	1.31545	+	1.31545i
$790$		0			0
$791$		−	11.7295i		−	0.417052i
$792$		0			0
$793$		−	17.8062i		−	0.632317i
$794$		0			0
$795$	14.2806	+	14.2806i	0.506480	+	0.506480i
$796$		0			0
$797$	−32.7530	+	32.7530i	−1.16017	+	1.16017i	−0.175732	+	0.984438i	$0.556229\pi$
$797$	−32.7530	+	32.7530i	−1.16017	+	1.16017i	−0.984438	+	0.175732i	$0.943771\pi$
$798$		0			0
$799$	−3.30002			−0.116746
$800$		0			0
$801$	0.293613			0.0103743
$802$		0			0
$803$	−5.12262	+	5.12262i	−0.180773	+	0.180773i
$804$		0			0
$805$	−2.35010	−	2.35010i	−0.0828300	−	0.0828300i
$806$		0			0
$807$		−	26.2949i		−	0.925624i
$808$		0			0
$809$		−	4.49260i		−	0.157951i	−0.996877	−	0.0789756i	$-0.974835\pi$
$809$		−	4.49260i		−	0.157951i	0.996877	−	0.0789756i	$-0.0251649\pi$
$810$		0			0
$811$	−3.24039	−	3.24039i	−0.113786	−	0.113786i	0.647922	−	0.761707i	$-0.275638\pi$
$811$	−3.24039	−	3.24039i	−0.113786	−	0.113786i	−0.761707	+	0.647922i	$0.775638\pi$
$812$		0			0
$813$	25.3844	−	25.3844i	0.890268	−	0.890268i
$814$		0			0
$815$	−5.00622			−0.175360
$816$		0			0
$817$	−0.662039			−0.0231618
$818$		0			0
$819$	−0.182003	+	0.182003i	−0.00635972	+	0.00635972i
$820$		0			0
$821$	36.5352	+	36.5352i	1.27509	+	1.27509i	0.943383	+	0.331706i	$0.107624\pi$
$821$	36.5352	+	36.5352i	1.27509	+	1.27509i	0.331706	+	0.943383i	$0.392376\pi$
$822$		0			0
$823$			24.0637i			0.838809i	0.907799	+	0.419404i	$0.137761\pi$
$823$			24.0637i			0.838809i	−0.907799	+	0.419404i	$0.862239\pi$
$824$		0			0
$825$			1.63809i			0.0570309i
$826$		0			0
$827$	27.2971	+	27.2971i	0.949213	+	0.949213i	0.998771	−	0.0495578i	$-0.0157812\pi$
$827$	27.2971	+	27.2971i	0.949213	+	0.949213i	−0.0495578	+	0.998771i	$0.515781\pi$
$828$		0			0
$829$	31.3499	−	31.3499i	1.08883	−	1.08883i	0.0931792	−	0.995649i	$-0.470297\pi$
$829$	31.3499	−	31.3499i	1.08883	−	1.08883i	0.995649	−	0.0931792i	$-0.0297029\pi$
$830$		0			0
$831$	0.857167			0.0297348
$832$		0			0
$833$	0.603016			0.0208933
$834$		0			0
$835$	−12.1438	+	12.1438i	−0.420254	+	0.420254i
$836$		0			0
$837$	21.9552	+	21.9552i	0.758882	+	0.758882i
$838$		0			0
$839$		−	34.6426i		−	1.19599i	−0.801498	−	0.597997i	$-0.795963\pi$
$839$		−	34.6426i		−	1.19599i	0.801498	−	0.597997i	$-0.204037\pi$
$840$		0			0
$841$		−	15.7567i		−	0.543336i
$842$		0			0
$843$	14.4146	+	14.4146i	0.496466	+	0.496466i
$844$		0			0
$845$	−7.44094	+	7.44094i	−0.255976	+	0.255976i
$846$		0			0
$847$	−10.1518			−0.348820
$848$		0			0
$849$	−44.2341			−1.51811
$850$		0			0
$851$	10.8404	−	10.8404i	0.371603	−	0.371603i
$852$		0			0
$853$	−17.6395	−	17.6395i	−0.603963	−	0.603963i	0.337399	−	0.941362i	$-0.390453\pi$
$853$	−17.6395	−	17.6395i	−0.603963	−	0.603963i	−0.941362	+	0.337399i	$0.890453\pi$
$854$		0			0
$855$		−	0.0111349i		−	0.000380804i
$856$		0			0
$857$		−	9.60441i		−	0.328080i	−0.986454	−	0.164040i	$-0.947547\pi$
$857$		−	9.60441i		−	0.328080i	0.986454	−	0.164040i	$-0.0524527\pi$
$858$		0			0
$859$	−12.1676	−	12.1676i	−0.415155	−	0.415155i	0.468375	−	0.883530i	$-0.344840\pi$
$859$	−12.1676	−	12.1676i	−0.415155	−	0.415155i	−0.883530	+	0.468375i	$0.844840\pi$
$860$		0			0
$861$	−7.34125	+	7.34125i	−0.250189	+	0.250189i
$862$		0			0
$863$	31.2901			1.06513			0.532564	−	0.846390i	$-0.321229\pi$
$863$	31.2901			1.06513			0.532564	+	0.846390i	$0.321229\pi$
$864$		0			0
$865$	−15.6284			−0.531383
$866$		0			0
$867$	−20.9233	+	20.9233i	−0.710593	+	0.710593i
$868$		0			0
$869$	−0.983654	−	0.983654i	−0.0333682	−	0.0333682i
$870$		0			0
$871$		−	0.447174i		−	0.0151519i
$872$		0			0
$873$		−	0.700207i		−	0.0236984i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	−25.0684	+	25.0684i	−0.846501	+	0.846501i	−0.989695	−	0.143194i	$-0.954263\pi$
$877$	−25.0684	+	25.0684i	−0.846501	+	0.846501i	0.143194	+	0.989695i	$0.454263\pi$
$878$		0			0
$879$	−25.3797			−0.856036
$880$		0			0
$881$	2.08150			0.0701277			0.0350638	−	0.999385i	$-0.488837\pi$
$881$	2.08150			0.0701277			0.0350638	+	0.999385i	$0.488837\pi$
$882$		0			0
$883$	17.8914	−	17.8914i	0.602094	−	0.602094i	−0.338774	−	0.940868i	$-0.610012\pi$
$883$	17.8914	−	17.8914i	0.602094	−	0.602094i	0.940868	+	0.338774i	$0.110012\pi$
$884$		0			0
$885$	−5.81680	−	5.81680i	−0.195530	−	0.195530i
$886$		0			0
$887$		−	52.0223i		−	1.74674i	−0.487060	−	0.873368i	$-0.661931\pi$
$887$		−	52.0223i		−	1.74674i	0.487060	−	0.873368i	$-0.338069\pi$
$888$		0			0
$889$		−	0.429799i		−	0.0144150i
$890$		0			0
$891$	6.16318	+	6.16318i	0.206474	+	0.206474i
$892$		0			0
$893$	0.263462	−	0.263462i	0.00881643	−	0.00881643i
$894$		0			0
$895$	1.55895			0.0521101
$896$		0			0
$897$	−9.30344			−0.310633
$898$		0			0
$899$	29.1141	−	29.1141i	0.971009	−	0.971009i
$900$		0			0
$901$	−4.84159	−	4.84159i	−0.161297	−	0.161297i
$902$		0			0
$903$			17.2951i			0.575546i
$904$		0			0
$905$		−	5.10023i		−	0.169537i
$906$		0			0
$907$	−15.2655	−	15.2655i	−0.506884	−	0.506884i	0.406685	−	0.913568i	$-0.366685\pi$
$907$	−15.2655	−	15.2655i	−0.506884	−	0.506884i	−0.913568	+	0.406685i	$0.866685\pi$
$908$		0			0
$909$	0.312972	−	0.312972i	0.0103806	−	0.0103806i
$910$		0			0
$911$	−25.0817			−0.830992			−0.415496	−	0.909595i	$-0.636392\pi$
$911$	−25.0817			−0.830992			−0.415496	+	0.909595i	$0.636392\pi$
$912$		0			0
$913$	−14.8579			−0.491723
$914$		0			0
$915$	14.2294	−	14.2294i	0.470410	−	0.470410i
$916$		0			0
$917$	10.1923	+	10.1923i	0.336578	+	0.336578i
$918$		0			0
$919$			33.4635i			1.10386i	0.833891	+	0.551929i	$0.186108\pi$
$919$			33.4635i			1.10386i	−0.833891	+	0.551929i	$0.813892\pi$
$920$		0			0
$921$			47.4553i			1.56370i
$922$		0			0
$923$	−2.13637	−	2.13637i	−0.0703195	−	0.0703195i
$924$		0			0
$925$	−3.26170	+	3.26170i	−0.107244	+	0.107244i
$926$		0			0
$927$	−2.16853			−0.0712239
$928$		0			0
$929$	32.1012			1.05321			0.526604	−	0.850111i	$-0.323465\pi$
$929$	32.1012			1.05321			0.526604	+	0.850111i	$0.323465\pi$
$930$		0			0
$931$	−0.0481428	+	0.0481428i	−0.00157782	+	0.00157782i
$932$		0			0
$933$	0.113815	+	0.113815i	0.00372615	+	0.00372615i
$934$		0			0
$935$		−	0.555366i		−	0.0181624i
$936$		0			0
$937$		−	51.7263i		−	1.68983i	−0.534904	−	0.844913i	$-0.679652\pi$
$937$		−	51.7263i		−	1.68983i	0.534904	−	0.844913i	$-0.320348\pi$
$938$		0			0
$939$	33.2002	+	33.2002i	1.08345	+	1.08345i
$940$		0			0
$941$	28.8417	−	28.8417i	0.940213	−	0.940213i	−0.0580982	−	0.998311i	$-0.518504\pi$
$941$	28.8417	−	28.8417i	0.940213	−	0.940213i	0.998311	+	0.0580982i	$0.0185036\pi$
$942$		0			0
$943$	−19.3999			−0.631746
$944$		0			0
$945$	5.04502			0.164115
$946$		0			0
$947$	32.4926	−	32.4926i	1.05587	−	1.05587i	0.0575247	−	0.998344i	$-0.481679\pi$
$947$	32.4926	−	32.4926i	1.05587	−	1.05587i	0.998344	−	0.0575247i	$-0.0183208\pi$
$948$		0			0
$949$	8.75383	+	8.75383i	0.284161	+	0.284161i
$950$		0			0
$951$		−	6.95666i		−	0.225585i
$952$		0			0
$953$			56.0737i			1.81641i	0.418530	+	0.908203i	$0.362546\pi$
$953$			56.0737i			1.81641i	−0.418530	+	0.908203i	$0.637454\pi$
$954$		0			0
$955$	12.1614	+	12.1614i	0.393535	+	0.393535i
$956$		0			0
$957$	7.74911	−	7.74911i	0.250493	−	0.250493i
$958$		0			0
$959$	8.88755			0.286994
$960$		0			0
$961$	6.87720			0.221845
$962$		0			0
$963$	−0.196957	+	0.196957i	−0.00634685	+	0.00634685i
$964$		0			0
$965$	−4.33263	−	4.33263i	−0.139472	−	0.139472i
$966$		0			0
$967$		−	21.7506i		−	0.699453i	−0.936852	−	0.349726i	$-0.886275\pi$
$967$		−	21.7506i		−	0.699453i	0.936852	−	0.349726i	$-0.113725\pi$
$968$		0			0
$969$			0.0730234i			0.00234585i
$970$		0			0
$971$	9.05037	+	9.05037i	0.290440	+	0.290440i	0.837254	−	0.546814i	$-0.184160\pi$
$971$	9.05037	+	9.05037i	0.290440	+	0.290440i	−0.546814	+	0.837254i	$0.684160\pi$
$972$		0			0
$973$	−5.64555	+	5.64555i	−0.180988	+	0.180988i
$974$		0			0
$975$	2.79926			0.0896481
$976$		0			0
$977$	38.0834			1.21840			0.609198	−	0.793018i	$-0.291491\pi$
$977$	38.0834			1.21840			0.609198	+	0.793018i	$0.291491\pi$
$978$		0			0
$979$	−1.16916	+	1.16916i	−0.0373664	+	0.0373664i
$980$		0			0
$981$	−0.518169	−	0.518169i	−0.0165438	−	0.0165438i
$982$		0			0
$983$			33.0264i			1.05338i	0.850058	+	0.526690i	$0.176567\pi$
$983$			33.0264i			1.05338i	−0.850058	+	0.526690i	$0.823433\pi$
$984$		0			0
$985$		−	22.9735i		−	0.731996i
$986$		0			0
$987$	−6.88271	−	6.88271i	−0.219079	−	0.219079i
$988$		0			0
$989$	−22.8519	+	22.8519i	−0.726649	+	0.726649i
$990$		0			0
$991$	53.6439			1.70405			0.852027	−	0.523498i	$-0.175373\pi$
$991$	53.6439			1.70405			0.852027	+	0.523498i	$0.175373\pi$
$992$		0			0
$993$	−18.0895			−0.574053
$994$		0			0
$995$	3.16661	−	3.16661i	0.100388	−	0.100388i
$996$		0			0
$997$	−24.9318	−	24.9318i	−0.789597	−	0.789597i	0.191831	−	0.981428i	$-0.438557\pi$
$997$	−24.9318	−	24.9318i	−0.789597	−	0.789597i	−0.981428	+	0.191831i	$0.938557\pi$
$998$		0			0
$999$			23.2714i			0.736273i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.17		44
4.3	odd	2		560.2.bd.a.421.17	yes	44
16.3	odd	4		560.2.bd.a.141.17	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.17		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.17	✓	44	16.3	odd	4
560.2.bd.a.421.17	yes	44	4.3	odd	2
2240.2.bd.a.561.17		44	1.1	even	1	trivial
2240.2.bd.a.1681.17		44	16.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25769 - 1.25769i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.163545i q^{9} +O(q^{10})\)	\(q+(1.25769 - 1.25769i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.163545i q^{9} +(0.651231 + 0.651231i) q^{11} +(1.11286 - 1.11286i) q^{13} +1.77864 q^{15} -0.603016 q^{17} +(0.0481428 - 0.0481428i) q^{19} +(-1.25769 - 1.25769i) q^{21} -3.32354i q^{23} +1.00000i q^{25} +(3.56737 + 3.56737i) q^{27} +(4.73058 - 4.73058i) q^{29} +6.15445 q^{31} +1.63809 q^{33} +(0.707107 - 0.707107i) q^{35} +(3.26170 + 3.26170i) q^{37} -2.79926i q^{39} -5.83711i q^{41} +(-6.87578 - 6.87578i) q^{43} +(0.115644 - 0.115644i) q^{45} +5.47252 q^{47} -1.00000 q^{49} +(-0.758405 + 0.758405i) q^{51} +(8.02895 + 8.02895i) q^{53} +0.920980i q^{55} -0.121097i q^{57} +(-3.27037 - 3.27037i) q^{59} +(8.00019 - 8.00019i) q^{61} -0.163545 q^{63} +1.57382 q^{65} +(0.200912 - 0.200912i) q^{67} +(-4.17996 - 4.17996i) q^{69} -1.91971i q^{71} +7.86605i q^{73} +(1.25769 + 1.25769i) q^{75} +(0.651231 - 0.651231i) q^{77} -1.51045 q^{79} +9.46389 q^{81} +(-11.4075 + 11.4075i) q^{83} +(-0.426397 - 0.426397i) q^{85} -11.8992i q^{87} +1.79530i q^{89} +(-1.11286 - 1.11286i) q^{91} +(7.74036 - 7.74036i) q^{93} +0.0680842 q^{95} +4.28142 q^{97} +(0.106506 - 0.106506i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

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