LMFDB - Embedded newform 1472.2.i.b.367.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1472,2,Mod(367,1472)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1472, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

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

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

chi := DirichletCharacter("1472.367");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1472 = 2^{6} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1472.i (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:	$11.7539791775$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			367.19
Character	$\chi$	$=$	1472.367
Dual form			1472.2.i.b.1103.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.112079 + 0.112079i) q^{3} +(-0.729430 - 0.729430i) q^{5} +4.66292i q^{7} +2.97488i q^{9} +(-0.0862197 + 0.0862197i) q^{11} +(-2.61277 - 2.61277i) q^{13} +0.163507 q^{15} +5.76731i q^{17} +(-3.43632 - 3.43632i) q^{19} +(-0.522614 - 0.522614i) q^{21} +(-3.88991 - 2.80511i) q^{23} -3.93586i q^{25} +(-0.669656 - 0.669656i) q^{27} +(-2.45601 - 2.45601i) q^{29} -4.03274i q^{31} -0.0193268i q^{33} +(3.40127 - 3.40127i) q^{35} +(3.28834 + 3.28834i) q^{37} +0.585671 q^{39} +3.98919i q^{41} +(0.534248 - 0.534248i) q^{43} +(2.16996 - 2.16996i) q^{45} -9.59198i q^{47} -14.7428 q^{49} +(-0.646392 - 0.646392i) q^{51} +(-5.60120 - 5.60120i) q^{53} +0.125782 q^{55} +0.770276 q^{57} +(1.63442 + 1.63442i) q^{59} +(-6.05032 + 6.05032i) q^{61} -13.8716 q^{63} +3.81166i q^{65} +(8.02993 + 8.02993i) q^{67} +(0.750369 - 0.121582i) q^{69} -4.98117 q^{71} -3.45530i q^{73} +(0.441127 + 0.441127i) q^{75} +(-0.402035 - 0.402035i) q^{77} -4.58624 q^{79} -8.77452 q^{81} +(-5.44851 - 5.44851i) q^{83} +(4.20685 - 4.20685i) q^{85} +0.550533 q^{87} +4.66835 q^{89} +(12.1831 - 12.1831i) q^{91} +(0.451984 + 0.451984i) q^{93} +5.01311i q^{95} +7.07523i q^{97} +(-0.256493 - 0.256493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} - 4 q^{13} - 4 q^{23} - 44 q^{27} - 20 q^{29} - 16 q^{35} + 128 q^{39} - 160 q^{49} + 8 q^{55} - 80 q^{59} - 24 q^{69} + 8 q^{71} + 12 q^{75} + 40 q^{77} + 40 q^{81} - 16 q^{85} + 8 q^{87}+ \cdots - 28 q^{93}+O(q^{100}) $ 80 * q + 4 * q^3 - 4 * q^13 - 4 * q^23 - 44 * q^27 - 20 * q^29 - 16 * q^35 + 128 * q^39 - 160 * q^49 + 8 * q^55 - 80 * q^59 - 24 * q^69 + 8 * q^71 + 12 * q^75 + 40 * q^77 + 40 * q^81 - 16 * q^85 + 8 * q^87 - 28 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1472\mathbb{Z}\right)^\times$.

$n$	$645$	$833$	$1151$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.112079	+	0.112079i	−0.0647087	+	0.0647087i	−0.738721	−	0.674012i	$-0.764570\pi$
$3$	−0.112079	+	0.112079i	−0.0647087	+	0.0647087i	0.674012	+	0.738721i	$0.264570\pi$
$4$		0			0
$5$	−0.729430	−	0.729430i	−0.326211	−	0.326211i	0.524933	−	0.851144i	$-0.324090\pi$
$5$	−0.729430	−	0.729430i	−0.326211	−	0.326211i	−0.851144	+	0.524933i	$0.824090\pi$
$6$		0			0
$7$			4.66292i			1.76242i	0.472727	+	0.881209i	$0.343270\pi$
$7$			4.66292i			1.76242i	−0.472727	+	0.881209i	$0.656730\pi$
$8$		0			0
$9$			2.97488i			0.991626i
$10$		0			0
$11$	−0.0862197	+	0.0862197i	−0.0259962	+	0.0259962i	−0.719985	−	0.693989i	$-0.755852\pi$
$11$	−0.0862197	+	0.0862197i	−0.0259962	+	0.0259962i	0.693989	+	0.719985i	$0.255852\pi$
$12$		0			0
$13$	−2.61277	−	2.61277i	−0.724652	−	0.724652i	0.244897	−	0.969549i	$-0.421246\pi$
$13$	−2.61277	−	2.61277i	−0.724652	−	0.724652i	−0.969549	+	0.244897i	$0.921246\pi$
$14$		0			0
$15$	0.163507			0.0422174
$16$		0			0
$17$			5.76731i			1.39878i	0.714741	+	0.699389i	$0.246544\pi$
$17$			5.76731i			1.39878i	−0.714741	+	0.699389i	$0.753456\pi$
$18$		0			0
$19$	−3.43632	−	3.43632i	−0.788346	−	0.788346i	0.192877	−	0.981223i	$-0.438218\pi$
$19$	−3.43632	−	3.43632i	−0.788346	−	0.788346i	−0.981223	+	0.192877i	$0.938218\pi$
$20$		0			0
$21$	−0.522614	−	0.522614i	−0.114044	−	0.114044i
$22$		0			0
$23$	−3.88991	−	2.80511i	−0.811101	−	0.584906i
$23$	−3.88991	−	2.80511i	−0.811101	−	0.584906i
$24$		0			0
$25$		−	3.93586i		−	0.787173i
$26$		0			0
$27$	−0.669656	−	0.669656i	−0.128875	−	0.128875i
$28$		0			0
$29$	−2.45601	−	2.45601i	−0.456069	−	0.456069i	0.441293	−	0.897363i	$-0.354520\pi$
$29$	−2.45601	−	2.45601i	−0.456069	−	0.456069i	−0.897363	+	0.441293i	$0.854520\pi$
$30$		0			0
$31$		−	4.03274i		−	0.724301i	−0.932120	−	0.362151i	$-0.882043\pi$
$31$		−	4.03274i		−	0.724301i	0.932120	−	0.362151i	$-0.117957\pi$
$32$		0			0
$33$		−	0.0193268i		−	0.00336436i
$34$		0			0
$35$	3.40127	−	3.40127i	0.574920	−	0.574920i
$36$		0			0
$37$	3.28834	+	3.28834i	0.540600	+	0.540600i	0.923705	−	0.383105i	$-0.125145\pi$
$37$	3.28834	+	3.28834i	0.540600	+	0.540600i	−0.383105	+	0.923705i	$0.625145\pi$
$38$		0			0
$39$	0.585671			0.0937825
$40$		0			0
$41$			3.98919i			0.623007i	0.950245	+	0.311504i	$0.100833\pi$
$41$			3.98919i			0.623007i	−0.950245	+	0.311504i	$0.899167\pi$
$42$		0			0
$43$	0.534248	−	0.534248i	0.0814721	−	0.0814721i	−0.665196	−	0.746668i	$-0.731652\pi$
$43$	0.534248	−	0.534248i	0.0814721	−	0.0814721i	0.746668	+	0.665196i	$0.231652\pi$
$44$		0			0
$45$	2.16996	−	2.16996i	0.323479	−	0.323479i
$46$		0			0
$47$		−	9.59198i		−	1.39913i	−0.714567	−	0.699567i	$-0.753376\pi$
$47$		−	9.59198i		−	1.39913i	0.714567	−	0.699567i	$-0.246624\pi$
$48$		0			0
$49$	−14.7428			−2.10611
$50$		0			0
$51$	−0.646392	−	0.646392i	−0.0905130	−	0.0905130i
$52$		0			0
$53$	−5.60120	−	5.60120i	−0.769384	−	0.769384i	0.208614	−	0.977998i	$-0.433105\pi$
$53$	−5.60120	−	5.60120i	−0.769384	−	0.769384i	−0.977998	+	0.208614i	$0.933105\pi$
$54$		0			0
$55$	0.125782			0.0169605
$56$		0			0
$57$	0.770276			0.102026
$58$		0			0
$59$	1.63442	+	1.63442i	0.212783	+	0.212783i	0.805449	−	0.592666i	$-0.201924\pi$
$59$	1.63442	+	1.63442i	0.212783	+	0.212783i	−0.592666	+	0.805449i	$0.701924\pi$
$60$		0			0
$61$	−6.05032	+	6.05032i	−0.774664	+	0.774664i	−0.978918	−	0.204254i	$-0.934523\pi$
$61$	−6.05032	+	6.05032i	−0.774664	+	0.774664i	0.204254	+	0.978918i	$0.434523\pi$
$62$		0			0
$63$	−13.8716			−1.74766
$64$		0			0
$65$			3.81166i			0.472779i
$66$		0			0
$67$	8.02993	+	8.02993i	0.981012	+	0.981012i	0.999823	−	0.0188107i	$-0.00598797\pi$
$67$	8.02993	+	8.02993i	0.981012	+	0.981012i	−0.0188107	+	0.999823i	$0.505988\pi$
$68$		0			0
$69$	0.750369	−	0.121582i	0.0903338	−	0.0146368i
$70$		0			0
$71$	−4.98117			−0.591156			−0.295578	−	0.955319i	$-0.595512\pi$
$71$	−4.98117			−0.591156			−0.295578	+	0.955319i	$0.595512\pi$
$72$		0			0
$73$		−	3.45530i		−	0.404412i	−0.979343	−	0.202206i	$-0.935189\pi$
$73$		−	3.45530i		−	0.404412i	0.979343	−	0.202206i	$-0.0648111\pi$
$74$		0			0
$75$	0.441127	+	0.441127i	0.0509369	+	0.0509369i
$76$		0			0
$77$	−0.402035	−	0.402035i	−0.0458162	−	0.0458162i
$78$		0			0
$79$	−4.58624			−0.515992			−0.257996	−	0.966146i	$-0.583062\pi$
$79$	−4.58624			−0.515992			−0.257996	+	0.966146i	$0.583062\pi$
$80$		0			0
$81$	−8.77452			−0.974947
$82$		0			0
$83$	−5.44851	−	5.44851i	−0.598051	−	0.598051i	0.341742	−	0.939794i	$-0.388983\pi$
$83$	−5.44851	−	5.44851i	−0.598051	−	0.598051i	−0.939794	+	0.341742i	$0.888983\pi$
$84$		0			0
$85$	4.20685	−	4.20685i	0.456297	−	0.456297i
$86$		0			0
$87$	0.550533			0.0590233
$88$		0			0
$89$	4.66835			0.494845			0.247422	−	0.968908i	$-0.420417\pi$
$89$	4.66835			0.494845			0.247422	+	0.968908i	$0.420417\pi$
$90$		0			0
$91$	12.1831	−	12.1831i	1.27714	−	1.27714i
$92$		0			0
$93$	0.451984	+	0.451984i	0.0468686	+	0.0468686i
$94$		0			0
$95$			5.01311i			0.514334i
$96$		0			0
$97$			7.07523i			0.718381i	0.933264	+	0.359190i	$0.116947\pi$
$97$			7.07523i			0.718381i	−0.933264	+	0.359190i	$0.883053\pi$
$98$		0			0
$99$	−0.256493	−	0.256493i	−0.0257785	−	0.0257785i
$100$		0			0
$101$	−3.84196	+	3.84196i	−0.382290	+	0.382290i	−0.871927	−	0.489637i	$-0.837129\pi$
$101$	−3.84196	+	3.84196i	−0.382290	+	0.382290i	0.489637	+	0.871927i	$0.337129\pi$
$102$		0			0
$103$			16.9617i			1.67129i	0.549270	+	0.835645i	$0.314906\pi$
$103$			16.9617i			1.67129i	−0.549270	+	0.835645i	$0.685094\pi$
$104$		0			0
$105$			0.762420i			0.0744046i
$106$		0			0
$107$	−12.9924	+	12.9924i	−1.25602	+	1.25602i	−0.303049	+	0.952975i	$0.598005\pi$
$107$	−12.9924	+	12.9924i	−1.25602	+	1.25602i	−0.952975	+	0.303049i	$0.901995\pi$
$108$		0			0
$109$	−11.7010	+	11.7010i	−1.12075	+	1.12075i	−0.129124	+	0.991628i	$0.541216\pi$
$109$	−11.7010	+	11.7010i	−1.12075	+	1.12075i	−0.991628	+	0.129124i	$0.958784\pi$
$110$		0			0
$111$	−0.737106			−0.0699630
$112$		0			0
$113$		−	6.25567i		−	0.588484i	−0.955731	−	0.294242i	$-0.904933\pi$
$113$		−	6.25567i		−	0.588484i	0.955731	−	0.294242i	$-0.0950672\pi$
$114$		0			0
$115$	0.791282	+	4.88354i	0.0737875	+	0.455393i
$116$		0			0
$117$	7.77266	−	7.77266i	0.718583	−	0.718583i
$118$		0			0
$119$	−26.8925			−2.46523
$120$		0			0
$121$			10.9851i			0.998648i
$122$		0			0
$123$	−0.447104	−	0.447104i	−0.0403140	−	0.0403140i
$124$		0			0
$125$	−6.51809	+	6.51809i	−0.582995	+	0.582995i
$126$		0			0
$127$		−	7.81367i		−	0.693351i	−0.937985	−	0.346675i	$-0.887311\pi$
$127$		−	7.81367i		−	0.693351i	0.937985	−	0.346675i	$-0.112689\pi$
$128$		0			0
$129$			0.119756i			0.0105439i
$130$		0			0
$131$	6.26056	−	6.26056i	0.546988	−	0.546988i	−0.378581	−	0.925568i	$-0.623588\pi$
$131$	6.26056	−	6.26056i	0.546988	−	0.546988i	0.925568	+	0.378581i	$0.123588\pi$
$132$		0			0
$133$	16.0233	−	16.0233i	1.38939	−	1.38939i
$134$		0			0
$135$			0.976935i			0.0840812i
$136$		0			0
$137$	15.4838			1.32287			0.661433	−	0.750004i	$-0.269949\pi$
$137$	15.4838			1.32287			0.661433	+	0.750004i	$0.269949\pi$
$138$		0			0
$139$	12.8654	+	12.8654i	1.09123	+	1.09123i	0.995397	+	0.0958351i	$0.0305521\pi$
$139$	12.8654	+	12.8654i	1.09123	+	1.09123i	0.0958351	+	0.995397i	$0.469448\pi$
$140$		0			0
$141$	1.07506	+	1.07506i	0.0905361	+	0.0905361i
$142$		0			0
$143$	0.450544			0.0376764
$144$		0			0
$145$			3.58297i			0.297550i
$146$		0			0
$147$	1.65235	−	1.65235i	0.136284	−	0.136284i
$148$		0			0
$149$	−16.1858	−	16.1858i	−1.32600	−	1.32600i	−0.908831	−	0.417164i	$-0.863024\pi$
$149$	−16.1858	−	16.1858i	−1.32600	−	1.32600i	−0.417164	−	0.908831i	$-0.636976\pi$
$150$		0			0
$151$	−2.36178			−0.192199			−0.0960994	−	0.995372i	$-0.530637\pi$
$151$	−2.36178			−0.192199			−0.0960994	+	0.995372i	$0.530637\pi$
$152$		0			0
$153$	−17.1570			−1.38706
$154$		0			0
$155$	−2.94160	+	2.94160i	−0.236275	+	0.236275i
$156$		0			0
$157$	12.6451	−	12.6451i	1.00919	−	1.00919i	0.00923376	−	0.999957i	$-0.497061\pi$
$157$	12.6451	−	12.6451i	1.00919	−	1.00919i	0.999957	−	0.00923376i	$-0.00293924\pi$
$158$		0			0
$159$	1.25555			0.0995717
$160$		0			0
$161$	13.0800	−	18.1383i	1.03085	−	1.42950i
$162$		0			0
$163$	1.13524	−	1.13524i	0.0889192	−	0.0889192i	−0.661248	−	0.750167i	$-0.729973\pi$
$163$	1.13524	−	1.13524i	0.0889192	−	0.0889192i	0.750167	+	0.661248i	$0.229973\pi$
$164$		0			0
$165$	−0.0140975	+	0.0140975i	−0.00109749	+	0.00109749i
$166$		0			0
$167$	2.44254			0.189009			0.0945045	−	0.995524i	$-0.469873\pi$
$167$	2.44254			0.189009			0.0945045	+	0.995524i	$0.469873\pi$
$168$		0			0
$169$			0.653119i			0.0502399i
$170$		0			0
$171$	10.2226	−	10.2226i	0.781744	−	0.781744i
$172$		0			0
$173$	−9.91223	−	9.91223i	−0.753613	−	0.753613i	0.221539	−	0.975152i	$-0.428892\pi$
$173$	−9.91223	−	9.91223i	−0.753613	−	0.753613i	−0.975152	+	0.221539i	$0.928892\pi$
$174$		0			0
$175$	18.3526			1.38733
$176$		0			0
$177$	−0.366367			−0.0275378
$178$		0			0
$179$	−6.77114	+	6.77114i	−0.506099	+	0.506099i	−0.913327	−	0.407228i	$-0.866496\pi$
$179$	−6.77114	+	6.77114i	−0.506099	+	0.506099i	0.407228	+	0.913327i	$0.366496\pi$
$180$		0			0
$181$	6.83492	+	6.83492i	0.508035	+	0.508035i	0.913923	−	0.405888i	$-0.133038\pi$
$181$	6.83492	+	6.83492i	0.508035	+	0.508035i	−0.405888	+	0.913923i	$0.633038\pi$
$182$		0			0
$183$		−	1.35622i		−	0.100255i
$184$		0			0
$185$		−	4.79723i		−	0.352699i
$186$		0			0
$187$	−0.497255	−	0.497255i	−0.0363629	−	0.0363629i
$188$		0			0
$189$	3.12255	−	3.12255i	0.227132	−	0.227132i
$190$		0			0
$191$	−0.650657			−0.0470799			−0.0235399	−	0.999723i	$-0.507494\pi$
$191$	−0.650657			−0.0470799			−0.0235399	+	0.999723i	$0.507494\pi$
$192$		0			0
$193$	−6.25135			−0.449982			−0.224991	−	0.974361i	$-0.572235\pi$
$193$	−6.25135			−0.449982			−0.224991	+	0.974361i	$0.572235\pi$
$194$		0			0
$195$	−0.427206	−	0.427206i	−0.0305929	−	0.0305929i
$196$		0			0
$197$	4.26647	−	4.26647i	0.303973	−	0.303973i	−0.538593	−	0.842566i	$-0.681044\pi$
$197$	4.26647	−	4.26647i	0.303973	−	0.303973i	0.842566	+	0.538593i	$0.181044\pi$
$198$		0			0
$199$		−	0.581169i		−	0.0411980i	−0.999788	−	0.0205990i	$-0.993443\pi$
$199$		−	0.581169i		−	0.0411980i	0.999788	−	0.0205990i	$-0.00655733\pi$
$200$		0			0
$201$	−1.79997			−0.126960
$202$		0			0
$203$	11.4522	−	11.4522i	0.803785	−	0.803785i
$204$		0			0
$205$	2.90984	−	2.90984i	0.203232	−	0.203232i
$206$		0			0
$207$	8.34485	−	11.5720i	0.580008	−	0.804309i
$208$		0			0
$209$	0.592557			0.0409880
$210$		0			0
$211$	−15.5560	+	15.5560i	−1.07092	+	1.07092i	−0.0736342	+	0.997285i	$0.523460\pi$
$211$	−15.5560	+	15.5560i	−1.07092	+	1.07092i	−0.997285	+	0.0736342i	$0.976540\pi$
$212$		0			0
$213$	0.558283	−	0.558283i	0.0382529	−	0.0382529i
$214$		0			0
$215$	−0.779393			−0.0531542
$216$		0			0
$217$	18.8043			1.27652
$218$		0			0
$219$	0.387265	+	0.387265i	0.0261690	+	0.0261690i
$220$		0			0
$221$	15.0686	−	15.0686i	1.01363	−	1.01363i
$222$		0			0
$223$			14.1397i			0.946867i	0.880830	+	0.473433i	$0.156986\pi$
$223$			14.1397i			0.946867i	−0.880830	+	0.473433i	$0.843014\pi$
$224$		0			0
$225$	11.7087			0.780581
$226$		0			0
$227$	−5.79847	−	5.79847i	−0.384858	−	0.384858i	0.487991	−	0.872849i	$-0.337730\pi$
$227$	−5.79847	−	5.79847i	−0.384858	−	0.384858i	−0.872849	+	0.487991i	$0.837730\pi$
$228$		0			0
$229$	−15.7777	−	15.7777i	−1.04262	−	1.04262i	−0.999050	−	0.0435711i	$-0.986126\pi$
$229$	−15.7777	−	15.7777i	−1.04262	−	1.04262i	−0.0435711	−	0.999050i	$-0.513874\pi$
$230$		0			0
$231$	0.0901192			0.00592941
$232$		0			0
$233$			20.5046i			1.34330i	0.740867	+	0.671652i	$0.234415\pi$
$233$			20.5046i			1.34330i	−0.740867	+	0.671652i	$0.765585\pi$
$234$		0			0
$235$	−6.99668	+	6.99668i	−0.456413	+	0.456413i
$236$		0			0
$237$	0.514020	−	0.514020i	0.0333892	−	0.0333892i
$238$		0			0
$239$		−	12.9301i		−	0.836379i	−0.908360	−	0.418189i	$-0.862665\pi$
$239$		−	12.9301i		−	0.836379i	0.908360	−	0.418189i	$-0.137335\pi$
$240$		0			0
$241$			23.0963i			1.48777i	0.668310	+	0.743883i	$0.267018\pi$
$241$			23.0963i			1.48777i	−0.668310	+	0.743883i	$0.732982\pi$
$242$		0			0
$243$	2.99241	−	2.99241i	0.191963	−	0.191963i
$244$		0			0
$245$	10.7538	+	10.7538i	0.687038	+	0.687038i
$246$		0			0
$247$			17.9566i			1.14255i
$248$		0			0
$249$	1.22132			0.0773982
$250$		0			0
$251$	−4.65540	+	4.65540i	−0.293846	+	0.293846i	−0.838598	−	0.544751i	$-0.816624\pi$
$251$	−4.65540	+	4.65540i	−0.293846	+	0.293846i	0.544751	+	0.838598i	$0.316624\pi$
$252$		0			0
$253$	0.577242	−	0.0935307i	0.0362909	−	0.00588023i
$254$		0			0
$255$			0.942996i			0.0590527i
$256$		0			0
$257$	19.0318			1.18717			0.593584	−	0.804772i	$-0.297712\pi$
$257$	19.0318			1.18717			0.593584	+	0.804772i	$0.297712\pi$
$258$		0			0
$259$	−15.3333	+	15.3333i	−0.952763	+	0.952763i
$260$		0			0
$261$	7.30632	−	7.30632i	0.452250	−	0.452250i
$262$		0			0
$263$			4.90893i			0.302698i	0.988480	+	0.151349i	$0.0483617\pi$
$263$			4.90893i			0.302698i	−0.988480	+	0.151349i	$0.951638\pi$
$264$		0			0
$265$			8.17137i			0.501963i
$266$		0			0
$267$	−0.523223	+	0.523223i	−0.0320207	+	0.0320207i
$268$		0			0
$269$	12.3824	+	12.3824i	0.754965	+	0.754965i	0.975401	−	0.220436i	$-0.0707481\pi$
$269$	12.3824	+	12.3824i	0.754965	+	0.754965i	−0.220436	+	0.975401i	$0.570748\pi$
$270$		0			0
$271$			28.5174i			1.73231i	0.499778	+	0.866153i	$0.333415\pi$
$271$			28.5174i			1.73231i	−0.499778	+	0.866153i	$0.666585\pi$
$272$		0			0
$273$			2.73094i			0.165284i
$274$		0			0
$275$	0.339349	+	0.339349i	0.0204635	+	0.0204635i
$276$		0			0
$277$	−18.1669	+	18.1669i	−1.09154	+	1.09154i	−0.0961780	+	0.995364i	$0.530662\pi$
$277$	−18.1669	+	18.1669i	−1.09154	+	1.09154i	−0.995364	+	0.0961780i	$0.969338\pi$
$278$		0			0
$279$	11.9969			0.718236
$280$		0			0
$281$	−21.1812			−1.26357			−0.631783	−	0.775146i	$-0.717676\pi$
$281$	−21.1812			−1.26357			−0.631783	+	0.775146i	$0.717676\pi$
$282$		0			0
$283$	22.3833	−	22.3833i	1.33055	−	1.33055i	0.425668	−	0.904879i	$-0.360039\pi$
$283$	22.3833	−	22.3833i	1.33055	−	1.33055i	0.904879	−	0.425668i	$-0.139961\pi$
$284$		0			0
$285$	−0.561863	−	0.561863i	−0.0332819	−	0.0332819i
$286$		0			0
$287$	−18.6013			−1.09800
$288$		0			0
$289$	−16.2618			−0.956578
$290$		0			0
$291$	−0.792983	−	0.792983i	−0.0464855	−	0.0464855i
$292$		0			0
$293$	−9.99382	−	9.99382i	−0.583845	−	0.583845i	0.352113	−	0.935958i	$-0.385463\pi$
$293$	−9.99382	−	9.99382i	−0.583845	−	0.583845i	−0.935958	+	0.352113i	$0.885463\pi$
$294$		0			0
$295$		−	2.38439i		−	0.138824i
$296$		0			0
$297$	0.115475			0.00670055
$298$		0			0
$299$	2.83432	+	17.4925i	0.163913	+	1.01162i
$300$		0			0
$301$	2.49116	+	2.49116i	0.143588	+	0.143588i
$302$		0			0
$303$		−	0.861205i		−	0.0494749i
$304$		0			0
$305$	8.82657			0.505408
$306$		0			0
$307$	13.1735	−	13.1735i	0.751852	−	0.751852i	−0.222973	−	0.974825i	$-0.571576\pi$
$307$	13.1735	−	13.1735i	0.751852	−	0.751852i	0.974825	+	0.222973i	$0.0715761\pi$
$308$		0			0
$309$	−1.90105	−	1.90105i	−0.108147	−	0.108147i
$310$		0			0
$311$	26.1707			1.48400			0.742002	−	0.670397i	$-0.233876\pi$
$311$	26.1707			1.48400			0.742002	+	0.670397i	$0.233876\pi$
$312$		0			0
$313$	−12.7752			−0.722095			−0.361047	−	0.932547i	$-0.617581\pi$
$313$	−12.7752			−0.722095			−0.361047	+	0.932547i	$0.617581\pi$
$314$		0			0
$315$	10.1184	+	10.1184i	0.570105	+	0.570105i
$316$		0			0
$317$	18.4396	+	18.4396i	1.03567	+	1.03567i	0.999340	+	0.0363306i	$0.0115669\pi$
$317$	18.4396	+	18.4396i	1.03567	+	1.03567i	0.0363306	+	0.999340i	$0.488433\pi$
$318$		0			0
$319$	0.423513			0.0237122
$320$		0			0
$321$		−	2.91235i		−	0.162551i
$322$		0			0
$323$	19.8183	−	19.8183i	1.10272	−	1.10272i
$324$		0			0
$325$	−10.2835	+	10.2835i	−0.570426	+	0.570426i
$326$		0			0
$327$		−	2.62287i		−	0.145045i
$328$		0			0
$329$	44.7266			2.46586
$330$		0			0
$331$	19.7807	+	19.7807i	1.08725	+	1.08725i	0.995811	+	0.0914354i	$0.0291455\pi$
$331$	19.7807	+	19.7807i	1.08725	+	1.08725i	0.0914354	+	0.995811i	$0.470855\pi$
$332$		0			0
$333$	−9.78241	+	9.78241i	−0.536073	+	0.536073i
$334$		0			0
$335$		−	11.7145i		−	0.640034i
$336$		0			0
$337$		−	8.23618i		−	0.448653i	−0.974514	−	0.224327i	$-0.927982\pi$
$337$		−	8.23618i		−	0.448653i	0.974514	−	0.224327i	$-0.0720182\pi$
$338$		0			0
$339$	0.701127	+	0.701127i	0.0380800	+	0.0380800i
$340$		0			0
$341$	0.347701	+	0.347701i	0.0188291	+	0.0188291i
$342$		0			0
$343$		−	36.1041i		−	1.94944i
$344$		0			0
$345$	−0.636027	−	0.458655i	−0.0342426	−	0.0246932i
$346$		0			0
$347$	−10.9221	−	10.9221i	−0.586328	−	0.586328i	0.350307	−	0.936635i	$-0.386077\pi$
$347$	−10.9221	−	10.9221i	−0.586328	−	0.586328i	−0.936635	+	0.350307i	$0.886077\pi$
$348$		0			0
$349$	−3.72241	−	3.72241i	−0.199256	−	0.199256i	0.600425	−	0.799681i	$-0.294998\pi$
$349$	−3.72241	−	3.72241i	−0.199256	−	0.199256i	−0.799681	+	0.600425i	$0.794998\pi$
$350$		0			0
$351$			3.49931i			0.186780i
$352$		0			0
$353$	−16.6757			−0.887556			−0.443778	−	0.896137i	$-0.646362\pi$
$353$	−16.6757			−0.887556			−0.443778	+	0.896137i	$0.646362\pi$
$354$		0			0
$355$	3.63341	+	3.63341i	0.192841	+	0.192841i
$356$		0			0
$357$	3.01407	−	3.01407i	0.159522	−	0.159522i
$358$		0			0
$359$		−	18.7425i		−	0.989192i	−0.869123	−	0.494596i	$-0.835316\pi$
$359$		−	18.7425i		−	0.989192i	0.869123	−	0.494596i	$-0.164684\pi$
$360$		0			0
$361$			4.61658i			0.242978i
$362$		0			0
$363$	−1.23120	−	1.23120i	−0.0646212	−	0.0646212i
$364$		0			0
$365$	−2.52040	+	2.52040i	−0.131924	+	0.131924i
$366$		0			0
$367$	−17.5288			−0.914994			−0.457497	−	0.889211i	$-0.651254\pi$
$367$	−17.5288			−0.914994			−0.457497	+	0.889211i	$0.651254\pi$
$368$		0			0
$369$	−11.8674			−0.617790
$370$		0			0
$371$	26.1179	−	26.1179i	1.35598	−	1.35598i
$372$		0			0
$373$	17.4147	+	17.4147i	0.901699	+	0.901699i	0.995583	−	0.0938840i	$-0.0299283\pi$
$373$	17.4147	+	17.4147i	0.901699	+	0.901699i	−0.0938840	+	0.995583i	$0.529928\pi$
$374$		0			0
$375$		−	1.46108i		−	0.0754497i
$376$		0			0
$377$			12.8340i			0.660983i
$378$		0			0
$379$	7.08012	−	7.08012i	0.363681	−	0.363681i	−0.501485	−	0.865166i	$-0.667213\pi$
$379$	7.08012	−	7.08012i	0.363681	−	0.363681i	0.865166	+	0.501485i	$0.167213\pi$
$380$		0			0
$381$	0.875746	+	0.875746i	0.0448658	+	0.0448658i
$382$		0			0
$383$	5.12232			0.261738			0.130869	−	0.991400i	$-0.458223\pi$
$383$	5.12232			0.261738			0.130869	+	0.991400i	$0.458223\pi$
$384$		0			0
$385$			0.586513i			0.0298915i
$386$		0			0
$387$	1.58932	+	1.58932i	0.0807898	+	0.0807898i
$388$		0			0
$389$	21.9017	+	21.9017i	1.11046	+	1.11046i	0.993088	+	0.117374i	$0.0374477\pi$
$389$	21.9017	+	21.9017i	1.11046	+	1.11046i	0.117374	+	0.993088i	$0.462552\pi$
$390$		0			0
$391$	16.1779	−	22.4343i	0.818153	−	1.13455i
$392$		0			0
$393$			1.40335i			0.0707897i
$394$		0			0
$395$	3.34534	+	3.34534i	0.168322	+	0.168322i
$396$		0			0
$397$	3.37089	+	3.37089i	0.169180	+	0.169180i	0.786619	−	0.617439i	$-0.211830\pi$
$397$	3.37089	+	3.37089i	0.169180	+	0.169180i	−0.617439	+	0.786619i	$0.711830\pi$
$398$		0			0
$399$			3.59174i			0.179812i
$400$		0			0
$401$			2.45224i			0.122459i	0.998124	+	0.0612295i	$0.0195022\pi$
$401$			2.45224i			0.122459i	−0.998124	+	0.0612295i	$0.980498\pi$
$402$		0			0
$403$	−10.5366	+	10.5366i	−0.524866	+	0.524866i
$404$		0			0
$405$	6.40040	+	6.40040i	0.318038	+	0.318038i
$406$		0			0
$407$	−0.567040			−0.0281071
$408$		0			0
$409$			0.828698i			0.0409765i	0.999790	+	0.0204882i	$0.00652206\pi$
$409$			0.828698i			0.0409765i	−0.999790	+	0.0204882i	$0.993478\pi$
$410$		0			0
$411$	−1.73540	+	1.73540i	−0.0856009	+	0.0856009i
$412$		0			0
$413$	−7.62116	+	7.62116i	−0.375013	+	0.375013i
$414$		0			0
$415$			7.94861i			0.390182i
$416$		0			0
$417$	−2.88388			−0.141224
$418$		0			0
$419$	−0.483571	−	0.483571i	−0.0236240	−	0.0236240i	0.695196	−	0.718820i	$-0.255318\pi$
$419$	−0.483571	−	0.483571i	−0.0236240	−	0.0236240i	−0.718820	+	0.695196i	$0.755318\pi$
$420$		0			0
$421$	−11.1496	−	11.1496i	−0.543397	−	0.543397i	0.381126	−	0.924523i	$-0.375536\pi$
$421$	−11.1496	−	11.1496i	−0.543397	−	0.543397i	−0.924523	+	0.381126i	$0.875536\pi$
$422$		0			0
$423$	28.5350			1.38742
$424$		0			0
$425$	22.6993			1.10108
$426$		0			0
$427$	−28.2122	−	28.2122i	−1.36528	−	1.36528i
$428$		0			0
$429$	−0.0504964	+	0.0504964i	−0.00243799	+	0.00243799i
$430$		0			0
$431$	−7.74410			−0.373020			−0.186510	−	0.982453i	$-0.559718\pi$
$431$	−7.74410			−0.373020			−0.186510	+	0.982453i	$0.559718\pi$
$432$		0			0
$433$		−	22.2803i		−	1.07072i	−0.844623	−	0.535362i	$-0.820175\pi$
$433$		−	22.2803i		−	1.07072i	0.844623	−	0.535362i	$-0.179825\pi$
$434$		0			0
$435$	−0.401575	−	0.401575i	−0.0192540	−	0.0192540i
$436$		0			0
$437$	3.72770	+	23.0062i	0.178320	+	1.10054i
$438$		0			0
$439$	−6.83055			−0.326004			−0.163002	−	0.986626i	$-0.552118\pi$
$439$	−6.83055			−0.326004			−0.163002	+	0.986626i	$0.552118\pi$
$440$		0			0
$441$		−	43.8580i		−	2.08848i
$442$		0			0
$443$	8.45559	+	8.45559i	0.401737	+	0.401737i	0.878845	−	0.477108i	$-0.158315\pi$
$443$	8.45559	+	8.45559i	0.401737	+	0.401737i	−0.477108	+	0.878845i	$0.658315\pi$
$444$		0			0
$445$	−3.40524	−	3.40524i	−0.161424	−	0.161424i
$446$		0			0
$447$	3.62817			0.171607
$448$		0			0
$449$	14.7606			0.696595			0.348298	−	0.937384i	$-0.386760\pi$
$449$	14.7606			0.696595			0.348298	+	0.937384i	$0.386760\pi$
$450$		0			0
$451$	−0.343947	−	0.343947i	−0.0161958	−	0.0161958i
$452$		0			0
$453$	0.264705	−	0.264705i	0.0124369	−	0.0124369i
$454$		0			0
$455$	−17.7735			−0.833233
$456$		0			0
$457$	−23.9129			−1.11860			−0.559299	−	0.828966i	$-0.688930\pi$
$457$	−23.9129			−1.11860			−0.559299	+	0.828966i	$0.688930\pi$
$458$		0			0
$459$	3.86211	−	3.86211i	0.180268	−	0.180268i
$460$		0			0
$461$	−9.09376	−	9.09376i	−0.423539	−	0.423539i	0.462882	−	0.886420i	$-0.346816\pi$
$461$	−9.09376	−	9.09376i	−0.423539	−	0.423539i	−0.886420	+	0.462882i	$0.846816\pi$
$462$		0			0
$463$			18.1484i			0.843428i	0.906729	+	0.421714i	$0.138571\pi$
$463$			18.1484i			0.843428i	−0.906729	+	0.421714i	$0.861429\pi$
$464$		0			0
$465$		−	0.659381i		−	0.0305781i
$466$		0			0
$467$	1.41183	+	1.41183i	0.0653319	+	0.0653319i	0.739018	−	0.673686i	$-0.235290\pi$
$467$	1.41183	+	1.41183i	0.0653319	+	0.0653319i	−0.673686	+	0.739018i	$0.735290\pi$
$468$		0			0
$469$	−37.4429	+	37.4429i	−1.72895	+	1.72895i
$470$		0			0
$471$			2.83450i			0.130607i
$472$		0			0
$473$			0.0921255i			0.00423593i
$474$		0			0
$475$	−13.5249	+	13.5249i	−0.620564	+	0.620564i
$476$		0			0
$477$	16.6629	−	16.6629i	0.762941	−	0.762941i
$478$		0			0
$479$	32.6602			1.49228			0.746141	−	0.665788i	$-0.231904\pi$
$479$	32.6602			1.49228			0.746141	+	0.665788i	$0.231904\pi$
$480$		0			0
$481$		−	17.1834i		−	0.783493i
$482$		0			0
$483$	0.566929	+	3.49891i	0.0257962	+	0.159206i
$484$		0			0
$485$	5.16088	−	5.16088i	0.234344	−	0.234344i
$486$		0			0
$487$	−14.3434			−0.649959			−0.324980	−	0.945721i	$-0.605357\pi$
$487$	−14.3434			−0.649959			−0.324980	+	0.945721i	$0.605357\pi$
$488$		0			0
$489$			0.254473i			0.0115077i
$490$		0			0
$491$	−28.0783	−	28.0783i	−1.26715	−	1.26715i	−0.947552	−	0.319603i	$-0.896451\pi$
$491$	−28.0783	−	28.0783i	−1.26715	−	1.26715i	−0.319603	−	0.947552i	$-0.603549\pi$
$492$		0			0
$493$	14.1646	−	14.1646i	0.637940	−	0.637940i
$494$		0			0
$495$			0.374187i			0.0168185i
$496$		0			0
$497$		−	23.2268i		−	1.04186i
$498$		0			0
$499$	−3.12400	+	3.12400i	−0.139850	+	0.139850i	−0.773566	−	0.633716i	$-0.781529\pi$
$499$	−3.12400	+	3.12400i	−0.139850	+	0.139850i	0.633716	+	0.773566i	$0.281529\pi$
$500$		0			0
$501$	−0.273756	+	0.273756i	−0.0122305	+	0.0122305i
$502$		0			0
$503$			33.7783i			1.50610i	0.657963	+	0.753050i	$0.271418\pi$
$503$			33.7783i			1.50610i	−0.657963	+	0.753050i	$0.728582\pi$
$504$		0			0
$505$	5.60489			0.249414
$506$		0			0
$507$	−0.0732008	−	0.0732008i	−0.00325096	−	0.00325096i
$508$		0			0
$509$	14.3980	+	14.3980i	0.638182	+	0.638182i	0.950107	−	0.311925i	$-0.100974\pi$
$509$	14.3980	+	14.3980i	0.638182	+	0.638182i	−0.311925	+	0.950107i	$0.600974\pi$
$510$		0			0
$511$	16.1118			0.712743
$512$		0			0
$513$			4.60231i			0.203197i
$514$		0			0
$515$	12.3724	−	12.3724i	0.545193	−	0.545193i
$516$		0			0
$517$	0.827017	+	0.827017i	0.0363722	+	0.0363722i
$518$		0			0
$519$	2.22190			0.0975305
$520$		0			0
$521$	−13.2424			−0.580159			−0.290080	−	0.957003i	$-0.593682\pi$
$521$	−13.2424			−0.580159			−0.290080	+	0.957003i	$0.593682\pi$
$522$		0			0
$523$	9.72568	−	9.72568i	0.425274	−	0.425274i	−0.461741	−	0.887015i	$-0.652775\pi$
$523$	9.72568	−	9.72568i	0.425274	−	0.425274i	0.887015	+	0.461741i	$0.152775\pi$
$524$		0			0
$525$	−2.05694	+	2.05694i	−0.0897721	+	0.0897721i
$526$		0			0
$527$	23.2580			1.01314
$528$		0			0
$529$	7.26272	+	21.8232i	0.315771	+	0.948836i
$530$		0			0
$531$	−4.86219	+	4.86219i	−0.211001	+	0.211001i
$532$		0			0
$533$	10.4228	−	10.4228i	0.451463	−	0.451463i
$534$		0			0
$535$	18.9541			0.819458
$536$		0			0
$537$		−	1.51780i		−	0.0654980i
$538$		0			0
$539$	1.27112	−	1.27112i	0.0547510	−	0.0547510i
$540$		0			0
$541$	−10.0624	−	10.0624i	−0.432617	−	0.432617i	0.456901	−	0.889518i	$-0.348959\pi$
$541$	−10.0624	−	10.0624i	−0.432617	−	0.432617i	−0.889518	+	0.456901i	$0.848959\pi$
$542$		0			0
$543$	−1.53210			−0.0657486
$544$		0			0
$545$	17.0701			0.731203
$546$		0			0
$547$	−29.0873	+	29.0873i	−1.24369	+	1.24369i	−0.285224	+	0.958461i	$0.592068\pi$
$547$	−29.0873	+	29.0873i	−1.24369	+	1.24369i	−0.958461	+	0.285224i	$0.907932\pi$
$548$		0			0
$549$	−17.9990	−	17.9990i	−0.768177	−	0.768177i
$550$		0			0
$551$			16.8793i			0.719081i
$552$		0			0
$553$		−	21.3853i		−	0.909394i
$554$		0			0
$555$	0.537667	+	0.537667i	0.0228227	+	0.0228227i
$556$		0			0
$557$	−8.31217	+	8.31217i	−0.352198	+	0.352198i	−0.860927	−	0.508729i	$-0.830116\pi$
$557$	−8.31217	+	8.31217i	−0.352198	+	0.352198i	0.508729	+	0.860927i	$0.330116\pi$
$558$		0			0
$559$	−2.79173			−0.118078
$560$		0			0
$561$	0.111464			0.00470599
$562$		0			0
$563$	−17.3259	−	17.3259i	−0.730202	−	0.730202i	0.240458	−	0.970660i	$-0.422702\pi$
$563$	−17.3259	−	17.3259i	−0.730202	−	0.730202i	−0.970660	+	0.240458i	$0.922702\pi$
$564$		0			0
$565$	−4.56307	+	4.56307i	−0.191970	+	0.191970i
$566$		0			0
$567$		−	40.9149i		−	1.71826i
$568$		0			0
$569$	−23.2407			−0.974303			−0.487151	−	0.873318i	$-0.661964\pi$
$569$	−23.2407			−0.974303			−0.487151	+	0.873318i	$0.661964\pi$
$570$		0			0
$571$	−22.9827	+	22.9827i	−0.961797	+	0.961797i	−0.999297	−	0.0374999i	$-0.988061\pi$
$571$	−22.9827	+	22.9827i	−0.961797	+	0.961797i	0.0374999	+	0.999297i	$0.488061\pi$
$572$		0			0
$573$	0.0729248	−	0.0729248i	0.00304648	−	0.00304648i
$574$		0			0
$575$	−11.0405	+	15.3101i	−0.460422	+	0.638477i
$576$		0			0
$577$	3.22115			0.134098			0.0670491	−	0.997750i	$-0.478642\pi$
$577$	3.22115			0.134098			0.0670491	+	0.997750i	$0.478642\pi$
$578$		0			0
$579$	0.700643	−	0.700643i	0.0291177	−	0.0291177i
$580$		0			0
$581$	25.4059	−	25.4059i	1.05402	−	1.05402i
$582$		0			0
$583$	0.965868			0.0400022
$584$		0			0
$585$	−11.3392			−0.468819
$586$		0			0
$587$	−25.3561	−	25.3561i	−1.04656	−	1.04656i	−0.998862	−	0.0476943i	$-0.984813\pi$
$587$	−25.3561	−	25.3561i	−1.04656	−	1.04656i	−0.0476943	−	0.998862i	$-0.515187\pi$
$588$		0			0
$589$	−13.8578	+	13.8578i	−0.571000	+	0.571000i
$590$		0			0
$591$			0.956361i			0.0393394i
$592$		0			0
$593$	36.1550			1.48471			0.742354	−	0.670008i	$-0.233709\pi$
$593$	36.1550			1.48471			0.742354	+	0.670008i	$0.233709\pi$
$594$		0			0
$595$	19.6162	+	19.6162i	0.804185	+	0.804185i
$596$		0			0
$597$	0.0651367	+	0.0651367i	0.00266587	+	0.00266587i
$598$		0			0
$599$	−8.63739			−0.352914			−0.176457	−	0.984308i	$-0.556464\pi$
$599$	−8.63739			−0.352914			−0.176457	+	0.984308i	$0.556464\pi$
$600$		0			0
$601$		−	24.2862i		−	0.990655i	−0.868706	−	0.495328i	$-0.835048\pi$
$601$		−	24.2862i		−	0.990655i	0.868706	−	0.495328i	$-0.164952\pi$
$602$		0			0
$603$	−23.8881	+	23.8881i	−0.972797	+	0.972797i
$604$		0			0
$605$	8.01288	−	8.01288i	0.325770	−	0.325770i
$606$		0			0
$607$		−	31.3867i		−	1.27395i	−0.770886	−	0.636973i	$-0.780186\pi$
$607$		−	31.3867i		−	1.27395i	0.770886	−	0.636973i	$-0.219814\pi$
$608$		0			0
$609$			2.56709i			0.104024i
$610$		0			0
$611$	−25.0616	+	25.0616i	−1.01388	+	1.01388i
$612$		0			0
$613$	15.0139	+	15.0139i	0.606407	+	0.606407i	0.942005	−	0.335598i	$-0.108938\pi$
$613$	15.0139	+	15.0139i	0.606407	+	0.606407i	−0.335598	+	0.942005i	$0.608938\pi$
$614$		0			0
$615$			0.652262i			0.0263017i
$616$		0			0
$617$	−28.4260			−1.14439			−0.572194	−	0.820119i	$-0.693907\pi$
$617$	−28.4260			−1.14439			−0.572194	+	0.820119i	$0.693907\pi$
$618$		0			0
$619$	−29.8563	+	29.8563i	−1.20002	+	1.20002i	−0.225866	+	0.974158i	$0.572521\pi$
$619$	−29.8563	+	29.8563i	−1.20002	+	1.20002i	−0.974158	+	0.225866i	$0.927479\pi$
$620$		0			0
$621$	0.726440	+	4.48336i	0.0291510	+	0.179911i
$622$		0			0
$623$			21.7682i			0.872123i
$624$		0			0
$625$	−10.1703			−0.406814
$626$		0			0
$627$	−0.0664130	+	0.0664130i	−0.00265228	+	0.00265228i
$628$		0			0
$629$	−18.9649	+	18.9649i	−0.756179	+	0.756179i
$630$		0			0
$631$			29.1928i			1.16215i	0.813850	+	0.581074i	$0.197367\pi$
$631$			29.1928i			1.16215i	−0.813850	+	0.581074i	$0.802633\pi$
$632$		0			0
$633$		−	3.48699i		−	0.138596i
$634$		0			0
$635$	−5.69952	+	5.69952i	−0.226179	+	0.226179i
$636$		0			0
$637$	38.5195	+	38.5195i	1.52620	+	1.52620i
$638$		0			0
$639$		−	14.8184i		−	0.586205i
$640$		0			0
$641$		−	10.6551i		−	0.420853i	−0.977610	−	0.210426i	$-0.932515\pi$
$641$		−	10.6551i		−	0.420853i	0.977610	−	0.210426i	$-0.0674853\pi$
$642$		0			0
$643$	−10.4584	−	10.4584i	−0.412438	−	0.412438i	0.470149	−	0.882587i	$-0.344200\pi$
$643$	−10.4584	−	10.4584i	−0.412438	−	0.412438i	−0.882587	+	0.470149i	$0.844200\pi$
$644$		0			0
$645$	0.0873534	−	0.0873534i	0.00343954	−	0.00343954i
$646$		0			0
$647$	28.9293			1.13733			0.568663	−	0.822570i	$-0.307461\pi$
$647$	28.9293			1.13733			0.568663	+	0.822570i	$0.307461\pi$
$648$		0			0
$649$	−0.281838			−0.0110631
$650$		0			0
$651$	−2.10756	+	2.10756i	−0.0826020	+	0.0826020i
$652$		0			0
$653$	−32.2933	−	32.2933i	−1.26374	−	1.26374i	−0.949268	−	0.314468i	$-0.898174\pi$
$653$	−32.2933	−	32.2933i	−1.26374	−	1.26374i	−0.314468	−	0.949268i	$-0.601826\pi$
$654$		0			0
$655$	−9.13328			−0.356867
$656$		0			0
$657$	10.2791			0.401025
$658$		0			0
$659$	8.22302	+	8.22302i	0.320323	+	0.320323i	0.848891	−	0.528568i	$-0.177271\pi$
$659$	8.22302	+	8.22302i	0.320323	+	0.320323i	−0.528568	+	0.848891i	$0.677271\pi$
$660$		0			0
$661$	9.08644	+	9.08644i	0.353421	+	0.353421i	0.861381	−	0.507960i	$-0.169600\pi$
$661$	9.08644	+	9.08644i	0.353421	+	0.353421i	−0.507960	+	0.861381i	$0.669600\pi$
$662$		0			0
$663$			3.37775i			0.131181i
$664$		0			0
$665$	−23.3757			−0.906471
$666$		0			0
$667$	2.66427	+	16.4430i	0.103161	+	0.636676i
$668$		0			0
$669$	−1.58476	−	1.58476i	−0.0612705	−	0.0612705i
$670$		0			0
$671$		−	1.04331i		−	0.0402767i
$672$		0			0
$673$	44.5725			1.71814			0.859071	−	0.511857i	$-0.171042\pi$
$673$	44.5725			1.71814			0.859071	+	0.511857i	$0.171042\pi$
$674$		0			0
$675$	−2.63568	+	2.63568i	−0.101447	+	0.101447i
$676$		0			0
$677$	−16.5145	−	16.5145i	−0.634704	−	0.634704i	0.314540	−	0.949244i	$-0.398150\pi$
$677$	−16.5145	−	16.5145i	−0.634704	−	0.634704i	−0.949244	+	0.314540i	$0.898150\pi$
$678$		0			0
$679$	−32.9912			−1.26609
$680$		0			0
$681$	1.29977			0.0498073
$682$		0			0
$683$	4.58795	+	4.58795i	0.175553	+	0.175553i	0.789414	−	0.613861i	$-0.210384\pi$
$683$	4.58795	+	4.58795i	0.175553	+	0.175553i	−0.613861	+	0.789414i	$0.710384\pi$
$684$		0			0
$685$	−11.2943	−	11.2943i	−0.431533	−	0.431533i
$686$		0			0
$687$	3.53669			0.134933
$688$		0			0
$689$			29.2693i			1.11507i
$690$		0			0
$691$	−20.0384	+	20.0384i	−0.762298	+	0.762298i	−0.976737	−	0.214439i	$-0.931208\pi$
$691$	−20.0384	+	20.0384i	−0.762298	+	0.762298i	0.214439	+	0.976737i	$0.431208\pi$
$692$		0			0
$693$	1.19601	−	1.19601i	0.0454325	−	0.0454325i
$694$		0			0
$695$		−	18.7689i		−	0.711944i
$696$		0			0
$697$	−23.0069			−0.871449
$698$		0			0
$699$	−2.29813	−	2.29813i	−0.0869234	−	0.0869234i
$700$		0			0
$701$	−19.9864	+	19.9864i	−0.754876	+	0.754876i	−0.975385	−	0.220509i	$-0.929228\pi$
$701$	−19.9864	+	19.9864i	−0.754876	+	0.754876i	0.220509	+	0.975385i	$0.429228\pi$
$702$		0			0
$703$		−	22.5996i		−	0.852359i
$704$		0			0
$705$		−	1.56836i		−	0.0590677i
$706$		0			0
$707$	−17.9148	−	17.9148i	−0.673754	−	0.673754i
$708$		0			0
$709$	13.7084	+	13.7084i	0.514828	+	0.514828i	0.916002	−	0.401174i	$-0.131398\pi$
$709$	13.7084	+	13.7084i	0.514828	+	0.514828i	−0.401174	+	0.916002i	$0.631398\pi$
$710$		0			0
$711$		−	13.6435i		−	0.511671i
$712$		0			0
$713$	−11.3123	+	15.6870i	−0.423648	+	0.587482i
$714$		0			0
$715$	−0.328640	−	0.328640i	−0.0122905	−	0.0122905i
$716$		0			0
$717$	1.44919	+	1.44919i	0.0541210	+	0.0541210i
$718$		0			0
$719$			28.9170i			1.07842i	0.842171	+	0.539210i	$0.181277\pi$
$719$			28.9170i			1.07842i	−0.842171	+	0.539210i	$0.818723\pi$
$720$		0			0
$721$	−79.0912			−2.94551
$722$		0			0
$723$	−2.58861	−	2.58861i	−0.0962714	−	0.0962714i
$724$		0			0
$725$	−9.66652	+	9.66652i	−0.359005	+	0.359005i
$726$		0			0
$727$			24.6899i			0.915697i	0.889030	+	0.457848i	$0.151380\pi$
$727$			24.6899i			0.915697i	−0.889030	+	0.457848i	$0.848620\pi$
$728$		0			0
$729$		−	25.6528i		−	0.950104i
$730$		0			0
$731$	3.08117	+	3.08117i	0.113961	+	0.113961i
$732$		0			0
$733$	21.6796	−	21.6796i	0.800755	−	0.800755i	−0.182459	−	0.983214i	$-0.558406\pi$
$733$	21.6796	−	21.6796i	0.800755	−	0.800755i	0.983214	+	0.182459i	$0.0584055\pi$
$734$		0			0
$735$	−2.41055			−0.0889146
$736$		0			0
$737$	−1.38468			−0.0510052
$738$		0			0
$739$	25.0597	−	25.0597i	0.921836	−	0.921836i	−0.0753235	−	0.997159i	$-0.523999\pi$
$739$	25.0597	−	25.0597i	0.921836	−	0.921836i	0.997159	+	0.0753235i	$0.0239989\pi$
$740$		0			0
$741$	−2.01255	−	2.01255i	−0.0739330	−	0.0739330i
$742$		0			0
$743$			15.9690i			0.585846i	0.956136	+	0.292923i	$0.0946280\pi$
$743$			15.9690i			0.585846i	−0.956136	+	0.292923i	$0.905372\pi$
$744$		0			0
$745$			23.6129i			0.865108i
$746$		0			0
$747$	16.2086	−	16.2086i	0.593043	−	0.593043i
$748$		0			0
$749$	−60.5826	−	60.5826i	−2.21364	−	2.21364i
$750$		0			0
$751$	1.85434			0.0676657			0.0338328	−	0.999428i	$-0.489229\pi$
$751$	1.85434			0.0676657			0.0338328	+	0.999428i	$0.489229\pi$
$752$		0			0
$753$		−	1.04354i		−	0.0380288i
$754$		0			0
$755$	1.72275	+	1.72275i	0.0626973	+	0.0626973i
$756$		0			0
$757$	12.4486	+	12.4486i	0.452451	+	0.452451i	0.896167	−	0.443716i	$-0.146340\pi$
$757$	12.4486	+	12.4486i	0.452451	+	0.452451i	−0.443716	+	0.896167i	$0.646340\pi$
$758$		0			0
$759$	−0.0542137	+	0.0751794i	−0.00196783	+	0.00272884i
$760$		0			0
$761$		−	44.0882i		−	1.59819i	−0.601202	−	0.799097i	$-0.705311\pi$
$761$		−	44.0882i		−	1.59819i	0.601202	−	0.799097i	$-0.294689\pi$
$762$		0			0
$763$	−54.5608	−	54.5608i	−1.97523	−	1.97523i
$764$		0			0
$765$	12.5148	+	12.5148i	0.452475	+	0.452475i
$766$		0			0
$767$		−	8.54071i		−	0.308387i
$768$		0			0
$769$			19.6450i			0.708418i	0.935166	+	0.354209i	$0.115250\pi$
$769$			19.6450i			0.708418i	−0.935166	+	0.354209i	$0.884750\pi$
$770$		0			0
$771$	−2.13306	+	2.13306i	−0.0768201	+	0.0768201i
$772$		0			0
$773$	0.407924	+	0.407924i	0.0146720	+	0.0146720i	0.714405	−	0.699733i	$-0.246698\pi$
$773$	0.407924	+	0.407924i	0.0146720	+	0.0146720i	−0.699733	+	0.714405i	$0.746698\pi$
$774$		0			0
$775$	−15.8723			−0.570150
$776$		0			0
$777$		−	3.43707i		−	0.123304i
$778$		0			0
$779$	13.7081	−	13.7081i	0.491145	−	0.491145i
$780$		0			0
$781$	0.429475	−	0.429475i	0.0153678	−	0.0153678i
$782$		0			0
$783$			3.28936i			0.117552i
$784$		0			0
$785$	−18.4475			−0.658418
$786$		0			0
$787$	14.0586	+	14.0586i	0.501134	+	0.501134i	0.911790	−	0.410656i	$-0.134700\pi$
$787$	14.0586	+	14.0586i	0.501134	+	0.501134i	−0.410656	+	0.911790i	$0.634700\pi$
$788$		0			0
$789$	−0.550187	−	0.550187i	−0.0195872	−	0.0195872i
$790$		0			0
$791$	29.1697			1.03715
$792$		0			0
$793$	31.6162			1.12272
$794$		0			0
$795$	−0.915836	−	0.915836i	−0.0324814	−	0.0324814i
$796$		0			0
$797$	13.2338	−	13.2338i	0.468764	−	0.468764i	−0.432750	−	0.901514i	$-0.642457\pi$
$797$	13.2338	−	13.2338i	0.468764	−	0.468764i	0.901514	+	0.432750i	$0.142457\pi$
$798$		0			0
$799$	55.3199			1.95708
$800$		0			0
$801$			13.8878i			0.490701i
$802$		0			0
$803$	0.297915	+	0.297915i	0.0105132	+	0.0105132i
$804$		0			0
$805$	−22.7716	+	3.68968i	−0.802592	+	0.130044i
$806$		0			0
$807$	−2.77560			−0.0977056
$808$		0			0
$809$		−	20.6778i		−	0.726992i	−0.931596	−	0.363496i	$-0.881583\pi$
$809$		−	20.6778i		−	0.726992i	0.931596	−	0.363496i	$-0.118417\pi$
$810$		0			0
$811$	−16.0486	−	16.0486i	−0.563543	−	0.563543i	0.366769	−	0.930312i	$-0.380464\pi$
$811$	−16.0486	−	16.0486i	−0.563543	−	0.563543i	−0.930312	+	0.366769i	$0.880464\pi$
$812$		0			0
$813$	−3.19619	−	3.19619i	−0.112095	−	0.112095i
$814$		0			0
$815$	−1.65616			−0.0580128
$816$		0			0
$817$	−3.67170			−0.128456
$818$		0			0
$819$	36.2433	+	36.2433i	1.26644	+	1.26644i
$820$		0			0
$821$	−16.6826	+	16.6826i	−0.582228	+	0.582228i	−0.935515	−	0.353287i	$-0.885064\pi$
$821$	−16.6826	+	16.6826i	−0.582228	+	0.582228i	0.353287	+	0.935515i	$0.385064\pi$
$822$		0			0
$823$	35.6183			1.24158			0.620788	−	0.783979i	$-0.286813\pi$
$823$	35.6183			1.24158			0.620788	+	0.783979i	$0.286813\pi$
$824$		0			0
$825$	−0.0760676			−0.00264833
$826$		0			0
$827$	−14.5778	+	14.5778i	−0.506921	+	0.506921i	−0.913580	−	0.406659i	$-0.866694\pi$
$827$	−14.5778	+	14.5778i	−0.506921	+	0.506921i	0.406659	+	0.913580i	$0.366694\pi$
$828$		0			0
$829$	20.5617	+	20.5617i	0.714137	+	0.714137i	0.967398	−	0.253261i	$-0.0815031\pi$
$829$	20.5617	+	20.5617i	0.714137	+	0.714137i	−0.253261	+	0.967398i	$0.581503\pi$
$830$		0			0
$831$		−	4.07224i		−	0.141264i
$832$		0			0
$833$		−	85.0263i		−	2.94599i
$834$		0			0
$835$	−1.78166	−	1.78166i	−0.0616568	−	0.0616568i
$836$		0			0
$837$	−2.70055	+	2.70055i	−0.0933446	+	0.0933446i
$838$		0			0
$839$		−	31.6104i		−	1.09131i	−0.838009	−	0.545656i	$-0.816281\pi$
$839$		−	31.6104i		−	1.09131i	0.838009	−	0.545656i	$-0.183719\pi$
$840$		0			0
$841$		−	16.9360i		−	0.584001i
$842$		0			0
$843$	2.37396	−	2.37396i	0.0817636	−	0.0817636i
$844$		0			0
$845$	0.476405	−	0.476405i	0.0163888	−	0.0163888i
$846$		0			0
$847$	−51.2228			−1.76004
$848$		0			0
$849$			5.01738i			0.172196i
$850$		0			0
$851$	−3.56718	−	22.0155i	−0.122281	−	0.754681i
$852$		0			0
$853$	−14.5005	+	14.5005i	−0.496486	+	0.496486i	−0.910342	−	0.413856i	$-0.864182\pi$
$853$	−14.5005	+	14.5005i	−0.496486	+	0.496486i	0.413856	+	0.910342i	$0.364182\pi$
$854$		0			0
$855$	−14.9134			−0.510027
$856$		0			0
$857$		−	14.0190i		−	0.478881i	−0.970911	−	0.239440i	$-0.923036\pi$
$857$		−	14.0190i		−	0.478881i	0.970911	−	0.239440i	$-0.0769640\pi$
$858$		0			0
$859$	−3.42733	−	3.42733i	−0.116939	−	0.116939i	0.646216	−	0.763155i	$-0.276351\pi$
$859$	−3.42733	−	3.42733i	−0.116939	−	0.116939i	−0.763155	+	0.646216i	$0.776351\pi$
$860$		0			0
$861$	2.08481	−	2.08481i	0.0710501	−	0.0710501i
$862$		0			0
$863$		−	3.52851i		−	0.120112i	−0.998195	−	0.0600559i	$-0.980872\pi$
$863$		−	3.52851i		−	0.120112i	0.998195	−	0.0600559i	$-0.0191279\pi$
$864$		0			0
$865$			14.4605i			0.491673i
$866$		0			0
$867$	1.82261	−	1.82261i	0.0618989	−	0.0618989i
$868$		0			0
$869$	0.395424	−	0.395424i	0.0134139	−	0.0134139i
$870$		0			0
$871$		−	41.9607i		−	1.42178i
$872$		0			0
$873$	−21.0479			−0.712365
$874$		0			0
$875$	−30.3933	−	30.3933i	−1.02748	−	1.02748i
$876$		0			0
$877$	27.5470	+	27.5470i	0.930196	+	0.930196i	0.997718	−	0.0675215i	$-0.0215091\pi$
$877$	27.5470	+	27.5470i	0.930196	+	0.930196i	−0.0675215	+	0.997718i	$0.521509\pi$
$878$		0			0
$879$	2.24019			0.0755597
$880$		0			0
$881$			29.3644i			0.989312i	0.869089	+	0.494656i	$0.164706\pi$
$881$			29.3644i			0.989312i	−0.869089	+	0.494656i	$0.835294\pi$
$882$		0			0
$883$	0.466491	−	0.466491i	0.0156987	−	0.0156987i	−0.699214	−	0.714913i	$-0.746466\pi$
$883$	0.466491	−	0.466491i	0.0156987	−	0.0156987i	0.714913	+	0.699214i	$0.246466\pi$
$884$		0			0
$885$	0.267239	+	0.267239i	0.00898314	+	0.00898314i
$886$		0			0
$887$	−8.47266			−0.284484			−0.142242	−	0.989832i	$-0.545431\pi$
$887$	−8.47266			−0.284484			−0.142242	+	0.989832i	$0.545431\pi$
$888$		0			0
$889$	36.4345			1.22197
$890$		0			0
$891$	0.756537	−	0.756537i	0.0253449	−	0.0253449i
$892$		0			0
$893$	−32.9611	+	32.9611i	−1.10300	+	1.10300i
$894$		0			0
$895$	9.87815			0.330190
$896$		0			0
$897$	−2.27821	−	1.64287i	−0.0760671	−	0.0548539i
$898$		0			0
$899$	−9.90444	+	9.90444i	−0.330332	+	0.330332i
$900$		0			0
$901$	32.3039	−	32.3039i	1.07620	−	1.07620i
$902$		0			0
$903$	−0.558411			−0.0185828
$904$		0			0
$905$		−	9.97118i		−	0.331453i
$906$		0			0
$907$	2.52164	−	2.52164i	0.0837298	−	0.0837298i	−0.664001	−	0.747731i	$-0.731143\pi$
$907$	2.52164	−	2.52164i	0.0837298	−	0.0837298i	0.747731	+	0.664001i	$0.231143\pi$
$908$		0			0
$909$	−11.4294	−	11.4294i	−0.379088	−	0.379088i
$910$		0			0
$911$	−48.5500			−1.60853			−0.804267	−	0.594268i	$-0.797442\pi$
$911$	−48.5500			−1.60853			−0.804267	+	0.594268i	$0.797442\pi$
$912$		0			0
$913$	0.939537			0.0310942
$914$		0			0
$915$	−0.989271	+	0.989271i	−0.0327043	+	0.0327043i
$916$		0			0
$917$	29.1925	+	29.1925i	0.964021	+	0.964021i
$918$		0			0
$919$			20.0332i			0.660835i	0.943835	+	0.330417i	$0.107190\pi$
$919$			20.0332i			0.660835i	−0.943835	+	0.330417i	$0.892810\pi$
$920$		0			0
$921$			2.95294i			0.0973027i
$922$		0			0
$923$	13.0146	+	13.0146i	0.428382	+	0.428382i
$924$		0			0
$925$	12.9425	−	12.9425i	0.425546	−	0.425546i
$926$		0			0
$927$	−50.4591			−1.65729
$928$		0			0
$929$	20.6586			0.677787			0.338893	−	0.940825i	$-0.389947\pi$
$929$	20.6586			0.677787			0.338893	+	0.940825i	$0.389947\pi$
$930$		0			0
$931$	50.6610	+	50.6610i	1.66035	+	1.66035i
$932$		0			0
$933$	−2.93318	+	2.93318i	−0.0960280	+	0.0960280i
$934$		0			0
$935$			0.725426i			0.0237240i
$936$		0			0
$937$	35.7386			1.16753			0.583764	−	0.811923i	$-0.301579\pi$
$937$	35.7386			1.16753			0.583764	+	0.811923i	$0.301579\pi$
$938$		0			0
$939$	1.43182	−	1.43182i	0.0467258	−	0.0467258i
$940$		0			0
$941$	−12.8774	+	12.8774i	−0.419790	+	0.419790i	−0.885131	−	0.465341i	$-0.845932\pi$
$941$	−12.8774	+	12.8774i	−0.419790	+	0.419790i	0.465341	+	0.885131i	$0.345932\pi$
$942$		0			0
$943$	11.1901	−	15.5176i	0.364401	−	0.505322i
$944$		0			0
$945$	−4.55537			−0.148186
$946$		0			0
$947$	10.4161	−	10.4161i	0.338478	−	0.338478i	−0.517316	−	0.855794i	$-0.673069\pi$
$947$	10.4161	−	10.4161i	0.338478	−	0.338478i	0.855794	+	0.517316i	$0.173069\pi$
$948$		0			0
$949$	−9.02789	+	9.02789i	−0.293058	+	0.293058i
$950$		0			0
$951$	−4.13337			−0.134034
$952$		0			0
$953$	−9.70939			−0.314518			−0.157259	−	0.987557i	$-0.550266\pi$
$953$	−9.70939			−0.314518			−0.157259	+	0.987557i	$0.550266\pi$
$954$		0			0
$955$	0.474608	+	0.474608i	0.0153580	+	0.0153580i
$956$		0			0
$957$	−0.0474668	+	0.0474668i	−0.00153438	+	0.00153438i
$958$		0			0
$959$			72.1995i			2.33144i
$960$		0			0
$961$	14.7370			0.475388
$962$		0			0
$963$	−38.6508	−	38.6508i	−1.24551	−	1.24551i
$964$		0			0
$965$	4.55992	+	4.55992i	0.146789	+	0.146789i
$966$		0			0
$967$	−32.8882			−1.05761			−0.528807	−	0.848742i	$-0.677361\pi$
$967$	−32.8882			−1.05761			−0.528807	+	0.848742i	$0.677361\pi$
$968$		0			0
$969$			4.44242i			0.142711i
$970$		0			0
$971$	15.4559	−	15.4559i	0.496003	−	0.496003i	−0.414188	−	0.910191i	$-0.635934\pi$
$971$	15.4559	−	15.4559i	0.496003	−	0.496003i	0.910191	+	0.414188i	$0.135934\pi$
$972$		0			0
$973$	−59.9905	+	59.9905i	−1.92321	+	1.92321i
$974$		0			0
$975$		−	2.30512i		−	0.0738230i
$976$		0			0
$977$		−	45.9537i		−	1.47019i	−0.677965	−	0.735094i	$-0.737138\pi$
$977$		−	45.9537i		−	1.47019i	0.677965	−	0.735094i	$-0.262862\pi$
$978$		0			0
$979$	−0.402504	+	0.402504i	−0.0128641	+	0.0128641i
$980$		0			0
$981$	−34.8090	−	34.8090i	−1.11137	−	1.11137i
$982$		0			0
$983$		−	2.37627i		−	0.0757913i	−0.999282	−	0.0378956i	$-0.987935\pi$
$983$		−	2.37627i		−	0.0757913i	0.999282	−	0.0378956i	$-0.0120654\pi$
$984$		0			0
$985$	−6.22418			−0.198319
$986$		0			0
$987$	−5.01290	+	5.01290i	−0.159562	+	0.159562i
$988$		0			0
$989$	−3.57680	+	0.579550i	−0.113736	+	0.0184286i
$990$		0			0
$991$		−	22.4867i		−	0.714313i	−0.934045	−	0.357157i	$-0.883746\pi$
$991$		−	22.4867i		−	0.714313i	0.934045	−	0.357157i	$-0.116254\pi$
$992$		0			0
$993$	−4.43399			−0.140709
$994$		0			0
$995$	−0.423922	+	0.423922i	−0.0134392	+	0.0134392i
$996$		0			0
$997$	−19.5816	+	19.5816i	−0.620155	+	0.620155i	−0.945571	−	0.325416i	$-0.894496\pi$
$997$	−19.5816	+	19.5816i	−0.620155	+	0.620155i	0.325416	+	0.945571i	$0.394496\pi$
$998$		0			0
$999$		−	4.40412i		−	0.139340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1472.2.i.b.367.19		80
4.3	odd	2		368.2.i.b.275.39	yes	80
16.5	even	4		368.2.i.b.91.40	yes	80
16.11	odd	4	inner	1472.2.i.b.1103.20		80
23.22	odd	2	inner	1472.2.i.b.367.20		80
92.91	even	2		368.2.i.b.275.40	yes	80
368.91	even	4	inner	1472.2.i.b.1103.19		80
368.229	odd	4		368.2.i.b.91.39	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.i.b.91.39	✓	80	368.229	odd	4
368.2.i.b.91.40	yes	80	16.5	even	4
368.2.i.b.275.39	yes	80	4.3	odd	2
368.2.i.b.275.40	yes	80	92.91	even	2
1472.2.i.b.367.19		80	1.1	even	1	trivial
1472.2.i.b.367.20		80	23.22	odd	2	inner
1472.2.i.b.1103.19		80	368.91	even	4	inner
1472.2.i.b.1103.20		80	16.11	odd	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:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.i (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.112079 + 0.112079i) q^{3} +(-0.729430 - 0.729430i) q^{5} +4.66292i q^{7} +2.97488i q^{9} +(-0.0862197 + 0.0862197i) q^{11} +(-2.61277 - 2.61277i) q^{13} +0.163507 q^{15} +5.76731i q^{17} +(-3.43632 - 3.43632i) q^{19} +(-0.522614 - 0.522614i) q^{21} +(-3.88991 - 2.80511i) q^{23} -3.93586i q^{25} +(-0.669656 - 0.669656i) q^{27} +(-2.45601 - 2.45601i) q^{29} -4.03274i q^{31} -0.0193268i q^{33} +(3.40127 - 3.40127i) q^{35} +(3.28834 + 3.28834i) q^{37} +0.585671 q^{39} +3.98919i q^{41} +(0.534248 - 0.534248i) q^{43} +(2.16996 - 2.16996i) q^{45} -9.59198i q^{47} -14.7428 q^{49} +(-0.646392 - 0.646392i) q^{51} +(-5.60120 - 5.60120i) q^{53} +0.125782 q^{55} +0.770276 q^{57} +(1.63442 + 1.63442i) q^{59} +(-6.05032 + 6.05032i) q^{61} -13.8716 q^{63} +3.81166i q^{65} +(8.02993 + 8.02993i) q^{67} +(0.750369 - 0.121582i) q^{69} -4.98117 q^{71} -3.45530i q^{73} +(0.441127 + 0.441127i) q^{75} +(-0.402035 - 0.402035i) q^{77} -4.58624 q^{79} -8.77452 q^{81} +(-5.44851 - 5.44851i) q^{83} +(4.20685 - 4.20685i) q^{85} +0.550533 q^{87} +4.66835 q^{89} +(12.1831 - 12.1831i) q^{91} +(0.451984 + 0.451984i) q^{93} +5.01311i q^{95} +7.07523i q^{97} +(-0.256493 - 0.256493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} - 4 q^{13} - 4 q^{23} - 44 q^{27} - 20 q^{29} - 16 q^{35} + 128 q^{39} - 160 q^{49} + 8 q^{55} - 80 q^{59} - 24 q^{69} + 8 q^{71} + 12 q^{75} + 40 q^{77} + 40 q^{81} - 16 q^{85} + 8 q^{87}+ \cdots - 28 q^{93}+O(q^{100}) \) 80 * q + 4 * q^3 - 4 * q^13 - 4 * q^23 - 44 * q^27 - 20 * q^29 - 16 * q^35 + 128 * q^39 - 160 * q^49 + 8 * q^55 - 80 * q^59 - 24 * q^69 + 8 * q^71 + 12 * q^75 + 40 * q^77 + 40 * q^81 - 16 * q^85 + 8 * q^87 - 28 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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