LMFDB - Embedded newform 2940.2.x.c.97.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2940,2,Mod(97,2940)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2940, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("2940.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.x (of order $4$, degree $2$, 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:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.15
Character	$\chi$	$=$	2940.97
Dual form			2940.2.x.c.1273.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-1.89349 + 1.18941i) q^{5} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{3} +(-1.89349 + 1.18941i) q^{5} +1.00000i q^{9} -2.43113 q^{11} +(-0.728866 - 0.728866i) q^{13} +(-2.17994 - 0.497865i) q^{15} +(5.36998 - 5.36998i) q^{17} -3.69931 q^{19} +(2.07634 - 2.07634i) q^{23} +(2.17063 - 4.50426i) q^{25} +(-0.707107 + 0.707107i) q^{27} -1.99120i q^{29} +6.95433i q^{31} +(-1.71907 - 1.71907i) q^{33} +(-6.01796 - 6.01796i) q^{37} -1.03077i q^{39} +1.08701i q^{41} +(5.91785 - 5.91785i) q^{43} +(-1.18941 - 1.89349i) q^{45} +(-3.52179 + 3.52179i) q^{47} +7.59429 q^{51} +(4.80937 - 4.80937i) q^{53} +(4.60332 - 2.89160i) q^{55} +(-2.61580 - 2.61580i) q^{57} +2.78807 q^{59} -0.251233i q^{61} +(2.24702 + 0.513185i) q^{65} +(-5.70338 - 5.70338i) q^{67} +2.93639 q^{69} +14.5737 q^{71} +(4.73234 + 4.73234i) q^{73} +(4.71986 - 1.65013i) q^{75} -11.0211i q^{79} -1.00000 q^{81} +(9.90994 + 9.90994i) q^{83} +(-3.78093 + 16.5551i) q^{85} +(1.40799 - 1.40799i) q^{87} +11.6294 q^{89} +(-4.91745 + 4.91745i) q^{93} +(7.00461 - 4.39997i) q^{95} +(10.8833 - 10.8833i) q^{97} -2.43113i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 16 q^{11} + 8 q^{15} - 32 q^{23} + 8 q^{25} - 40 q^{37} - 24 q^{43} + 16 q^{51} - 80 q^{53} - 16 q^{57} + 104 q^{65} - 16 q^{71} - 32 q^{81} - 8 q^{85} - 16 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q - 16 * q^11 + 8 * q^15 - 32 * q^23 + 8 * q^25 - 40 * q^37 - 24 * q^43 + 16 * q^51 - 80 * q^53 - 16 * q^57 + 104 * q^65 - 16 * q^71 - 32 * q^81 - 8 * q^85 - 16 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$1$

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
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−1.89349	+	1.18941i	−0.846796	+	0.531918i
$5$	−1.89349	+	1.18941i	−0.846796	+	0.531918i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.43113			−0.733013			−0.366506	−	0.930416i	$-0.619446\pi$
$11$	−2.43113			−0.733013			−0.366506	+	0.930416i	$0.619446\pi$
$12$		0			0
$13$	−0.728866	−	0.728866i	−0.202151	−	0.202151i	0.598770	−	0.800921i	$-0.295656\pi$
$13$	−0.728866	−	0.728866i	−0.202151	−	0.202151i	−0.800921	+	0.598770i	$0.795656\pi$
$14$		0			0
$15$	−2.17994	−	0.497865i	−0.562858	−	0.128548i
$16$		0			0
$17$	5.36998	−	5.36998i	1.30241	−	1.30241i	0.375648	−	0.926762i	$-0.377420\pi$
$17$	5.36998	−	5.36998i	1.30241	−	1.30241i	0.926762	−	0.375648i	$-0.122580\pi$
$18$		0			0
$19$	−3.69931			−0.848679			−0.424339	−	0.905503i	$-0.639494\pi$
$19$	−3.69931			−0.848679			−0.424339	+	0.905503i	$0.639494\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.07634	−	2.07634i	0.432948	−	0.432948i	−0.456682	−	0.889630i	$-0.650962\pi$
$23$	2.07634	−	2.07634i	0.432948	−	0.432948i	0.889630	+	0.456682i	$0.150962\pi$
$24$		0			0
$25$	2.17063	−	4.50426i	0.434126	−	0.900852i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$		−	1.99120i		−	0.369757i	−0.982761	−	0.184878i	$-0.940811\pi$
$29$		−	1.99120i		−	0.369757i	0.982761	−	0.184878i	$-0.0591891\pi$
$30$		0			0
$31$			6.95433i			1.24903i	0.781011	+	0.624517i	$0.214704\pi$
$31$			6.95433i			1.24903i	−0.781011	+	0.624517i	$0.785296\pi$
$32$		0			0
$33$	−1.71907	−	1.71907i	−0.299251	−	0.299251i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−6.01796	−	6.01796i	−0.989346	−	0.989346i	0.0105978	−	0.999944i	$-0.496627\pi$
$37$	−6.01796	−	6.01796i	−0.989346	−	0.989346i	−0.999944	+	0.0105978i	$0.996627\pi$
$38$		0			0
$39$		−	1.03077i		−	0.165056i
$40$		0			0
$41$			1.08701i			0.169762i	0.996391	+	0.0848810i	$0.0270510\pi$
$41$			1.08701i			0.169762i	−0.996391	+	0.0848810i	$0.972949\pi$
$42$		0			0
$43$	5.91785	−	5.91785i	0.902464	−	0.902464i	−0.0931848	−	0.995649i	$-0.529705\pi$
$43$	5.91785	−	5.91785i	0.902464	−	0.902464i	0.995649	+	0.0931848i	$0.0297048\pi$
$44$		0			0
$45$	−1.18941	−	1.89349i	−0.177306	−	0.282265i
$46$		0			0
$47$	−3.52179	+	3.52179i	−0.513706	+	0.513706i	−0.915660	−	0.401954i	$-0.868331\pi$
$47$	−3.52179	+	3.52179i	−0.513706	+	0.513706i	0.401954	+	0.915660i	$0.368331\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	7.59429			1.06341
$52$		0			0
$53$	4.80937	−	4.80937i	0.660617	−	0.660617i	−0.294908	−	0.955526i	$-0.595289\pi$
$53$	4.80937	−	4.80937i	0.660617	−	0.660617i	0.955526	+	0.294908i	$0.0952891\pi$
$54$		0			0
$55$	4.60332	−	2.89160i	0.620712	−	0.389903i
$56$		0			0
$57$	−2.61580	−	2.61580i	−0.346472	−	0.346472i
$58$		0			0
$59$	2.78807			0.362976			0.181488	−	0.983393i	$-0.441909\pi$
$59$	2.78807			0.362976			0.181488	+	0.983393i	$0.441909\pi$
$60$		0			0
$61$		−	0.251233i		−	0.0321670i	−0.999871	−	0.0160835i	$-0.994880\pi$
$61$		−	0.251233i		−	0.0321670i	0.999871	−	0.0160835i	$-0.00511976\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.24702	+	0.513185i	0.278709	+	0.0636528i
$66$		0			0
$67$	−5.70338	−	5.70338i	−0.696779	−	0.696779i	0.266935	−	0.963714i	$-0.413989\pi$
$67$	−5.70338	−	5.70338i	−0.696779	−	0.696779i	−0.963714	+	0.266935i	$0.913989\pi$
$68$		0			0
$69$	2.93639			0.353500
$70$		0			0
$71$	14.5737			1.72958			0.864790	−	0.502133i	$-0.167451\pi$
$71$	14.5737			1.72958			0.864790	+	0.502133i	$0.167451\pi$
$72$		0			0
$73$	4.73234	+	4.73234i	0.553879	+	0.553879i	0.927558	−	0.373679i	$-0.121904\pi$
$73$	4.73234	+	4.73234i	0.553879	+	0.553879i	−0.373679	+	0.927558i	$0.621904\pi$
$74$		0			0
$75$	4.71986	−	1.65013i	0.545003	−	0.190540i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		−	11.0211i		−	1.23997i	−0.784612	−	0.619987i	$-0.787138\pi$
$79$		−	11.0211i		−	1.23997i	0.784612	−	0.619987i	$-0.212862\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	9.90994	+	9.90994i	1.08776	+	1.08776i	0.995759	+	0.0919976i	$0.0293252\pi$
$83$	9.90994	+	9.90994i	1.08776	+	1.08776i	0.0919976	+	0.995759i	$0.470675\pi$
$84$		0			0
$85$	−3.78093	+	16.5551i	−0.410100	+	1.79565i
$86$		0			0
$87$	1.40799	−	1.40799i	0.150953	−	0.150953i
$88$		0			0
$89$	11.6294			1.23271			0.616354	−	0.787469i	$-0.288609\pi$
$89$	11.6294			1.23271			0.616354	+	0.787469i	$0.288609\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.91745	+	4.91745i	−0.509916	+	0.509916i
$94$		0			0
$95$	7.00461	−	4.39997i	0.718658	−	0.451428i
$96$		0			0
$97$	10.8833	−	10.8833i	1.10503	−	1.10503i	0.111236	−	0.993794i	$-0.464519\pi$
$97$	10.8833	−	10.8833i	1.10503	−	1.10503i	0.993794	−	0.111236i	$-0.0354808\pi$
$98$		0			0
$99$		−	2.43113i		−	0.244338i
$100$		0			0
$101$			6.28914i			0.625792i	0.949787	+	0.312896i	$0.101299\pi$
$101$			6.28914i			0.625792i	−0.949787	+	0.312896i	$0.898701\pi$
$102$		0			0
$103$	−10.6690	−	10.6690i	−1.05125	−	1.05125i	−0.998614	−	0.0526312i	$-0.983239\pi$
$103$	−10.6690	−	10.6690i	−1.05125	−	1.05125i	−0.0526312	−	0.998614i	$-0.516761\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.3422	+	10.3422i	0.999820	+	0.999820i	1.00000		0.000179954i	$-5.72812e-5\pi$
$107$	10.3422	+	10.3422i	0.999820	+	0.999820i	−0.000179954		1.00000i	$0.500057\pi$
$108$		0			0
$109$		−	11.9587i		−	1.14544i	−0.819753	−	0.572718i	$-0.805889\pi$
$109$		−	11.9587i		−	1.14544i	0.819753	−	0.572718i	$-0.194111\pi$
$110$		0			0
$111$		−	8.51068i		−	0.807798i
$112$		0			0
$113$	−5.10715	+	5.10715i	−0.480441	+	0.480441i	−0.905272	−	0.424832i	$-0.860333\pi$
$113$	−5.10715	+	5.10715i	−0.480441	+	0.480441i	0.424832	+	0.905272i	$0.360333\pi$
$114$		0			0
$115$	−1.46193	+	6.40116i	−0.136325	+	0.596911i
$116$		0			0
$117$	0.728866	−	0.728866i	0.0673837	−	0.0673837i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.08961			−0.462692
$122$		0			0
$123$	−0.768630	+	0.768630i	−0.0693050	+	0.0693050i
$124$		0			0
$125$	1.24732	+	11.1105i	0.111564	+	0.993757i
$126$		0			0
$127$	−0.0263367	−	0.0263367i	−0.00233701	−	0.00233701i	0.705937	−	0.708274i	$-0.250526\pi$
$127$	−0.0263367	−	0.0263367i	−0.00233701	−	0.00233701i	−0.708274	+	0.705937i	$0.750526\pi$
$128$		0			0
$129$	8.36911			0.736859
$130$		0			0
$131$		−	9.91293i		−	0.866097i	−0.901371	−	0.433048i	$-0.857438\pi$
$131$		−	9.91293i		−	0.866097i	0.901371	−	0.433048i	$-0.142562\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.497865	−	2.17994i	0.0428494	−	0.187619i
$136$		0			0
$137$	10.1629	+	10.1629i	0.868273	+	0.868273i	0.992281	−	0.124008i	$-0.0395748\pi$
$137$	10.1629	+	10.1629i	0.868273	+	0.868273i	−0.124008	+	0.992281i	$0.539575\pi$
$138$		0			0
$139$	−11.0917			−0.940787			−0.470394	−	0.882457i	$-0.655888\pi$
$139$	−11.0917			−0.940787			−0.470394	+	0.882457i	$0.655888\pi$
$140$		0			0
$141$	−4.98056			−0.419439
$142$		0			0
$143$	1.77197	+	1.77197i	0.148179	+	0.148179i
$144$		0			0
$145$	2.36835	+	3.77033i	0.196680	+	0.313108i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	8.84884i		−	0.724925i	−0.931998	−	0.362463i	$-0.881936\pi$
$149$		−	8.84884i		−	0.724925i	0.931998	−	0.362463i	$-0.118064\pi$
$150$		0			0
$151$	1.80212			0.146655			0.0733274	−	0.997308i	$-0.476638\pi$
$151$	1.80212			0.146655			0.0733274	+	0.997308i	$0.476638\pi$
$152$		0			0
$153$	5.36998	+	5.36998i	0.434137	+	0.434137i
$154$		0			0
$155$	−8.27151	−	13.1680i	−0.664384	−	1.05768i
$156$		0			0
$157$	8.11343	−	8.11343i	0.647522	−	0.647522i	−0.304871	−	0.952394i	$-0.598613\pi$
$157$	8.11343	−	8.11343i	0.647522	−	0.647522i	0.952394	+	0.304871i	$0.0986134\pi$
$158$		0			0
$159$	6.80147			0.539392
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.222170	+	0.222170i	−0.0174017	+	0.0174017i	−0.715754	−	0.698352i	$-0.753917\pi$
$163$	−0.222170	+	0.222170i	−0.0174017	+	0.0174017i	0.698352	+	0.715754i	$0.253917\pi$
$164$		0			0
$165$	5.29971	+	1.21037i	0.412582	+	0.0942274i
$166$		0			0
$167$	2.10159	−	2.10159i	0.162626	−	0.162626i	−0.621103	−	0.783729i	$-0.713315\pi$
$167$	2.10159	−	2.10159i	0.162626	−	0.162626i	0.783729	+	0.621103i	$0.213315\pi$
$168$		0			0
$169$		−	11.9375i		−	0.918270i
$170$		0			0
$171$		−	3.69931i		−	0.282893i
$172$		0			0
$173$	−6.94511	−	6.94511i	−0.528027	−	0.528027i	0.391957	−	0.919984i	$-0.371798\pi$
$173$	−6.94511	−	6.94511i	−0.528027	−	0.528027i	−0.919984	+	0.391957i	$0.871798\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.97146	+	1.97146i	0.148184	+	0.148184i
$178$		0			0
$179$		−	18.3034i		−	1.36806i	−0.729454	−	0.684030i	$-0.760226\pi$
$179$		−	18.3034i		−	1.36806i	0.729454	−	0.684030i	$-0.239774\pi$
$180$		0			0
$181$			20.1817i			1.50009i	0.661387	+	0.750045i	$0.269968\pi$
$181$			20.1817i			1.50009i	−0.661387	+	0.750045i	$0.730032\pi$
$182$		0			0
$183$	0.177648	−	0.177648i	0.0131321	−	0.0131321i
$184$		0			0
$185$	18.5527	+	4.23717i	1.36403	+	0.311523i
$186$		0			0
$187$	−13.0551	+	13.0551i	−0.954684	+	0.954684i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.48294			0.179659			0.0898297	−	0.995957i	$-0.471368\pi$
$191$	2.48294			0.179659			0.0898297	+	0.995957i	$0.471368\pi$
$192$		0			0
$193$	9.39877	−	9.39877i	0.676538	−	0.676538i	−0.282677	−	0.959215i	$-0.591222\pi$
$193$	9.39877	−	9.39877i	0.676538	−	0.676538i	0.959215	+	0.282677i	$0.0912224\pi$
$194$		0			0
$195$	1.22601	+	1.95176i	0.0877961	+	0.139768i
$196$		0			0
$197$	−5.45204	−	5.45204i	−0.388442	−	0.388442i	0.485690	−	0.874131i	$-0.338569\pi$
$197$	−5.45204	−	5.45204i	−0.388442	−	0.388442i	−0.874131	+	0.485690i	$0.838569\pi$
$198$		0			0
$199$	12.6591			0.897378			0.448689	−	0.893688i	$-0.351891\pi$
$199$	12.6591			0.897378			0.448689	+	0.893688i	$0.351891\pi$
$200$		0			0
$201$		−	8.06580i		−	0.568918i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.29289	−	2.05824i	−0.0902995	−	0.143754i
$206$		0			0
$207$	2.07634	+	2.07634i	0.144316	+	0.144316i
$208$		0			0
$209$	8.99349			0.622093
$210$		0			0
$211$	−5.37636			−0.370124			−0.185062	−	0.982727i	$-0.559249\pi$
$211$	−5.37636			−0.370124			−0.185062	+	0.982727i	$0.559249\pi$
$212$		0			0
$213$	10.3052	+	10.3052i	0.706098	+	0.706098i
$214$		0			0
$215$	−4.16668	+	18.2441i	−0.284165	+	1.24424i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			6.69254i			0.452240i
$220$		0			0
$221$	−7.82799			−0.526567
$222$		0			0
$223$	17.2847	+	17.2847i	1.15747	+	1.15747i	0.985018	+	0.172452i	$0.0551689\pi$
$223$	17.2847	+	17.2847i	1.15747	+	1.15747i	0.172452	+	0.985018i	$0.444831\pi$
$224$		0			0
$225$	4.50426	+	2.17063i	0.300284	+	0.144709i
$226$		0			0
$227$	1.33160	−	1.33160i	0.0883817	−	0.0883817i	−0.661534	−	0.749915i	$-0.730094\pi$
$227$	1.33160	−	1.33160i	0.0883817	−	0.0883817i	0.749915	+	0.661534i	$0.230094\pi$
$228$		0			0
$229$	−25.0767			−1.65711			−0.828557	−	0.559904i	$-0.810838\pi$
$229$	−25.0767			−1.65711			−0.828557	+	0.559904i	$0.810838\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.8613	+	15.8613i	−1.03911	+	1.03911i	−0.0399036	+	0.999204i	$0.512705\pi$
$233$	−15.8613	+	15.8613i	−1.03911	+	1.03911i	−0.999204	+	0.0399036i	$0.987295\pi$
$234$		0			0
$235$	2.47965	−	10.8573i	0.161754	−	0.708253i
$236$		0			0
$237$	7.79312	−	7.79312i	0.506218	−	0.506218i
$238$		0			0
$239$		−	6.38917i		−	0.413281i	−0.978417	−	0.206641i	$-0.933747\pi$
$239$		−	6.38917i		−	0.413281i	0.978417	−	0.206641i	$-0.0662531\pi$
$240$		0			0
$241$		−	18.6296i		−	1.20004i	−0.799986	−	0.600018i	$-0.795160\pi$
$241$		−	18.6296i		−	1.20004i	0.799986	−	0.600018i	$-0.204840\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.69630	+	2.69630i	0.171561	+	0.171561i
$248$		0			0
$249$			14.0148i			0.888150i
$250$		0			0
$251$		−	31.5776i		−	1.99316i	−0.0826181	−	0.996581i	$-0.526328\pi$
$251$		−	31.5776i		−	1.99316i	0.0826181	−	0.996581i	$-0.473672\pi$
$252$		0			0
$253$	−5.04786	+	5.04786i	−0.317356	+	0.317356i
$254$		0			0
$255$	−14.3797	+	9.03269i	−0.900494	+	0.565649i
$256$		0			0
$257$	13.1446	−	13.1446i	0.819938	−	0.819938i	−0.166161	−	0.986099i	$-0.553137\pi$
$257$	13.1446	−	13.1446i	0.819938	−	0.819938i	0.986099	+	0.166161i	$0.0531371\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	1.99120			0.123252
$262$		0			0
$263$	−4.04223	+	4.04223i	−0.249254	+	0.249254i	−0.820665	−	0.571410i	$-0.806397\pi$
$263$	−4.04223	+	4.04223i	−0.249254	+	0.249254i	0.571410	+	0.820665i	$0.306397\pi$
$264$		0			0
$265$	−3.38621	+	14.8268i	−0.208013	+	0.910802i
$266$		0			0
$267$	8.22319	+	8.22319i	0.503251	+	0.503251i
$268$		0			0
$269$	−2.44964			−0.149357			−0.0746785	−	0.997208i	$-0.523793\pi$
$269$	−2.44964			−0.149357			−0.0746785	+	0.997208i	$0.523793\pi$
$270$		0			0
$271$			25.3059i			1.53723i	0.639714	+	0.768613i	$0.279053\pi$
$271$			25.3059i			1.53723i	−0.639714	+	0.768613i	$0.720947\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−5.27708	+	10.9504i	−0.318220	+	0.660336i
$276$		0			0
$277$	−22.6131	−	22.6131i	−1.35869	−	1.35869i	−0.875536	−	0.483153i	$-0.839491\pi$
$277$	−22.6131	−	22.6131i	−1.35869	−	1.35869i	−0.483153	−	0.875536i	$-0.660509\pi$
$278$		0			0
$279$	−6.95433			−0.416345
$280$		0			0
$281$	12.3044			0.734020			0.367010	−	0.930217i	$-0.380382\pi$
$281$	12.3044			0.734020			0.367010	+	0.930217i	$0.380382\pi$
$282$		0			0
$283$	1.59825	+	1.59825i	0.0950059	+	0.0950059i	0.753012	−	0.658006i	$-0.228600\pi$
$283$	1.59825	+	1.59825i	0.0950059	+	0.0950059i	−0.658006	+	0.753012i	$0.728600\pi$
$284$		0			0
$285$	8.06426	+	1.84175i	0.477685	+	0.109096i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	40.6733i		−	2.39255i
$290$		0			0
$291$	15.3913			0.902253
$292$		0			0
$293$	−3.19458	−	3.19458i	−0.186629	−	0.186629i	0.607608	−	0.794237i	$-0.292129\pi$
$293$	−3.19458	−	3.19458i	−0.186629	−	0.186629i	−0.794237	+	0.607608i	$0.792129\pi$
$294$		0			0
$295$	−5.27919	+	3.31615i	−0.307366	+	0.193073i
$296$		0			0
$297$	1.71907	−	1.71907i	0.0997504	−	0.0997504i
$298$		0			0
$299$	−3.02675			−0.175042
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.44709	+	4.44709i	−0.255479	+	0.255479i
$304$		0			0
$305$	0.298817	+	0.475707i	0.0171102	+	0.0272389i
$306$		0			0
$307$	−5.74597	+	5.74597i	−0.327940	+	0.327940i	−0.851803	−	0.523863i	$-0.824490\pi$
$307$	−5.74597	+	5.74597i	−0.327940	+	0.327940i	0.523863	+	0.851803i	$0.324490\pi$
$308$		0			0
$309$		−	15.0882i		−	0.858338i
$310$		0			0
$311$			14.4613i			0.820024i	0.912080	+	0.410012i	$0.134475\pi$
$311$			14.4613i			0.820024i	−0.912080	+	0.410012i	$0.865525\pi$
$312$		0			0
$313$	0.835892	+	0.835892i	0.0472474	+	0.0472474i	0.730336	−	0.683088i	$-0.239364\pi$
$313$	0.835892	+	0.835892i	0.0472474	+	0.0472474i	−0.683088	+	0.730336i	$0.739364\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.25169	−	6.25169i	−0.351130	−	0.351130i	0.509400	−	0.860530i	$-0.329867\pi$
$317$	−6.25169	−	6.25169i	−0.351130	−	0.351130i	−0.860530	+	0.509400i	$0.829867\pi$
$318$		0			0
$319$			4.84087i			0.271037i
$320$		0			0
$321$			14.6261i			0.816350i
$322$		0			0
$323$	−19.8652	+	19.8652i	−1.10533	+	1.10533i
$324$		0			0
$325$	−4.86510	+	1.70091i	−0.269867	+	0.0943493i
$326$		0			0
$327$	8.45608	−	8.45608i	0.467622	−	0.467622i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	21.8608			1.20158			0.600789	−	0.799408i	$-0.294853\pi$
$331$	21.8608			1.20158			0.600789	+	0.799408i	$0.294853\pi$
$332$		0			0
$333$	6.01796	−	6.01796i	0.329782	−	0.329782i
$334$		0			0
$335$	17.5829	+	4.01568i	0.960659	+	0.219400i
$336$		0			0
$337$	18.0987	+	18.0987i	0.985900	+	0.985900i	0.999902	−	0.0140019i	$-0.00445708\pi$
$337$	18.0987	+	18.0987i	0.985900	+	0.985900i	−0.0140019	+	0.999902i	$0.504457\pi$
$338$		0			0
$339$	−7.22260			−0.392278
$340$		0			0
$341$		−	16.9069i		−	0.915558i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.56004	+	3.49256i	−0.299342	+	0.188033i
$346$		0			0
$347$	−2.96269	−	2.96269i	−0.159046	−	0.159046i	0.623098	−	0.782144i	$-0.285874\pi$
$347$	−2.96269	−	2.96269i	−0.159046	−	0.159046i	−0.782144	+	0.623098i	$0.785874\pi$
$348$		0			0
$349$	−33.8258			−1.81065			−0.905327	−	0.424715i	$-0.860374\pi$
$349$	−33.8258			−1.81065			−0.905327	+	0.424715i	$0.860374\pi$
$350$		0			0
$351$	1.03077			0.0550186
$352$		0			0
$353$	−23.7852	−	23.7852i	−1.26596	−	1.26596i	−0.948158	−	0.317799i	$-0.897056\pi$
$353$	−23.7852	−	23.7852i	−1.26596	−	1.26596i	−0.317799	−	0.948158i	$-0.602944\pi$
$354$		0			0
$355$	−27.5952	+	17.3340i	−1.46460	+	0.919996i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	16.1863i		−	0.854278i	−0.904186	−	0.427139i	$-0.859522\pi$
$359$		−	16.1863i		−	0.854278i	0.904186	−	0.427139i	$-0.140478\pi$
$360$		0			0
$361$	−5.31514			−0.279744
$362$		0			0
$363$	−3.59890	−	3.59890i	−0.188893	−	0.188893i
$364$		0			0
$365$	−14.5893	−	3.33198i	−0.763640	−	0.174404i
$366$		0			0
$367$	−11.4414	+	11.4414i	−0.597238	+	0.597238i	−0.939577	−	0.342339i	$-0.888781\pi$
$367$	−11.4414	+	11.4414i	−0.597238	+	0.597238i	0.342339	+	0.939577i	$0.388781\pi$
$368$		0			0
$369$	−1.08701			−0.0565873
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.62964	+	2.62964i	−0.136158	+	0.136158i	−0.771901	−	0.635743i	$-0.780694\pi$
$373$	−2.62964	+	2.62964i	−0.136158	+	0.136158i	0.635743	+	0.771901i	$0.280694\pi$
$374$		0			0
$375$	−6.97435	+	8.73833i	−0.360154	+	0.451246i
$376$		0			0
$377$	−1.45132	+	1.45132i	−0.0747467	+	0.0747467i
$378$		0			0
$379$		−	0.149127i		−	0.00766015i	−0.999993	−	0.00383007i	$-0.998781\pi$
$379$		−	0.149127i		−	0.00766015i	0.999993	−	0.00383007i	$-0.00121915\pi$
$380$		0			0
$381$		−	0.0372458i		−	0.00190816i
$382$		0			0
$383$	24.5067	+	24.5067i	1.25223	+	1.25223i	0.954717	+	0.297515i	$0.0961578\pi$
$383$	24.5067	+	24.5067i	1.25223	+	1.25223i	0.297515	+	0.954717i	$0.403842\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.91785	+	5.91785i	0.300821	+	0.300821i
$388$		0			0
$389$			32.6948i			1.65769i	0.559475	+	0.828847i	$0.311003\pi$
$389$			32.6948i			1.65769i	−0.559475	+	0.828847i	$0.688997\pi$
$390$		0			0
$391$		−	22.2998i		−	1.12775i
$392$		0			0
$393$	7.00950	−	7.00950i	0.353582	−	0.353582i
$394$		0			0
$395$	13.1086	+	20.8684i	0.659565	+	1.05001i
$396$		0			0
$397$	12.9250	−	12.9250i	0.648687	−	0.648687i	−0.303989	−	0.952676i	$-0.598319\pi$
$397$	12.9250	−	12.9250i	0.648687	−	0.648687i	0.952676	+	0.303989i	$0.0983186\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.18176			0.0590144			0.0295072	−	0.999565i	$-0.490606\pi$
$401$	1.18176			0.0590144			0.0295072	+	0.999565i	$0.490606\pi$
$402$		0			0
$403$	5.06877	−	5.06877i	0.252493	−	0.252493i
$404$		0			0
$405$	1.89349	−	1.18941i	0.0940884	−	0.0591020i
$406$		0			0
$407$	14.6304	+	14.6304i	0.725203	+	0.725203i
$408$		0			0
$409$	−16.2247			−0.802260			−0.401130	−	0.916021i	$-0.631382\pi$
$409$	−16.2247			−0.802260			−0.401130	+	0.916021i	$0.631382\pi$
$410$		0			0
$411$			14.3725i			0.708942i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−30.5513	−	6.97746i	−1.49971	−	0.342510i
$416$		0			0
$417$	−7.84303	−	7.84303i	−0.384075	−	0.384075i
$418$		0			0
$419$	−15.4289			−0.753750			−0.376875	−	0.926264i	$-0.623001\pi$
$419$	−15.4289			−0.753750			−0.376875	+	0.926264i	$0.623001\pi$
$420$		0			0
$421$	26.6085			1.29682			0.648409	−	0.761292i	$-0.275435\pi$
$421$	26.6085			1.29682			0.648409	+	0.761292i	$0.275435\pi$
$422$		0			0
$423$	−3.52179	−	3.52179i	−0.171235	−	0.171235i
$424$		0			0
$425$	−12.5316	−	35.8440i	−0.607870	−	1.73869i
$426$		0			0
$427$		0			0
$428$		0			0
$429$			2.50594i			0.120988i
$430$		0			0
$431$	3.66608			0.176589			0.0882944	−	0.996094i	$-0.471858\pi$
$431$	3.66608			0.176589			0.0882944	+	0.996094i	$0.471858\pi$
$432$		0			0
$433$	−9.74318	−	9.74318i	−0.468227	−	0.468227i	0.433112	−	0.901340i	$-0.357415\pi$
$433$	−9.74318	−	9.74318i	−0.468227	−	0.468227i	−0.901340	+	0.433112i	$0.857415\pi$
$434$		0			0
$435$	−0.991349	+	4.34070i	−0.0475315	+	0.208120i
$436$		0			0
$437$	−7.68103	+	7.68103i	−0.367433	+	0.367433i
$438$		0			0
$439$	−6.01835			−0.287240			−0.143620	−	0.989633i	$-0.545874\pi$
$439$	−6.01835			−0.287240			−0.143620	+	0.989633i	$0.545874\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.3530	−	14.3530i	0.681930	−	0.681930i	−0.278505	−	0.960435i	$-0.589839\pi$
$443$	14.3530	−	14.3530i	0.681930	−	0.681930i	0.960435	+	0.278505i	$0.0898388\pi$
$444$		0			0
$445$	−22.0201	+	13.8320i	−1.04385	+	0.655700i
$446$		0			0
$447$	6.25708	−	6.25708i	0.295950	−	0.295950i
$448$		0			0
$449$		−	12.7251i		−	0.600534i	−0.953855	−	0.300267i	$-0.902924\pi$
$449$		−	12.7251i		−	0.600534i	0.953855	−	0.300267i	$-0.0970758\pi$
$450$		0			0
$451$		−	2.64265i		−	0.124438i
$452$		0			0
$453$	1.27429	+	1.27429i	0.0598715	+	0.0598715i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−22.0803	−	22.0803i	−1.03287	−	1.03287i	−0.999441	−	0.0334338i	$-0.989356\pi$
$457$	−22.0803	−	22.0803i	−1.03287	−	1.03287i	−0.0334338	−	0.999441i	$-0.510644\pi$
$458$		0			0
$459$			7.59429i			0.354471i
$460$		0			0
$461$		−	23.4059i		−	1.09012i	−0.838397	−	0.545060i	$-0.816507\pi$
$461$		−	23.4059i		−	1.09012i	0.838397	−	0.545060i	$-0.183493\pi$
$462$		0			0
$463$	−16.8382	+	16.8382i	−0.782539	+	0.782539i	−0.980259	−	0.197720i	$-0.936646\pi$
$463$	−16.8382	+	16.8382i	−0.782539	+	0.782539i	0.197720	+	0.980259i	$0.436646\pi$
$464$		0			0
$465$	3.46231	−	15.1600i	0.160561	−	0.703028i
$466$		0			0
$467$	27.5909	−	27.5909i	1.27675	−	1.27675i	0.334278	−	0.942475i	$-0.391508\pi$
$467$	27.5909	−	27.5909i	1.27675	−	1.27675i	0.942475	−	0.334278i	$-0.108492\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	11.4741			0.528700
$472$		0			0
$473$	−14.3871	+	14.3871i	−0.661518	+	0.661518i
$474$		0			0
$475$	−8.02982	+	16.6626i	−0.368433	+	0.764534i
$476$		0			0
$477$	4.80937	+	4.80937i	0.220206	+	0.220206i
$478$		0			0
$479$	−15.3217			−0.700066			−0.350033	−	0.936737i	$-0.613830\pi$
$479$	−15.3217			−0.700066			−0.350033	+	0.936737i	$0.613830\pi$
$480$		0			0
$481$			8.77257i			0.399995i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.66278	+	33.5520i	−0.347949	+	1.52352i
$486$		0			0
$487$	−11.8152	−	11.8152i	−0.535396	−	0.535396i	0.386777	−	0.922173i	$-0.373588\pi$
$487$	−11.8152	−	11.8152i	−0.535396	−	0.535396i	−0.922173	+	0.386777i	$0.873588\pi$
$488$		0			0
$489$	−0.314195			−0.0142084
$490$		0			0
$491$	0.188878			0.00852393			0.00426196	−	0.999991i	$-0.498643\pi$
$491$	0.188878			0.00852393			0.00426196	+	0.999991i	$0.498643\pi$
$492$		0			0
$493$	−10.6927	−	10.6927i	−0.481575	−	0.481575i
$494$		0			0
$495$	2.89160	+	4.60332i	0.129968	+	0.206904i
$496$		0			0
$497$		0			0
$498$		0			0
$499$			14.0192i			0.627585i	0.949492	+	0.313792i	$0.101600\pi$
$499$			14.0192i			0.627585i	−0.949492	+	0.313792i	$0.898400\pi$
$500$		0			0
$501$	2.97209			0.132783
$502$		0			0
$503$	−20.0052	−	20.0052i	−0.891989	−	0.891989i	0.102721	−	0.994710i	$-0.467245\pi$
$503$	−20.0052	−	20.0052i	−0.891989	−	0.891989i	−0.994710	+	0.102721i	$0.967245\pi$
$504$		0			0
$505$	−7.48033	−	11.9084i	−0.332870	−	0.529918i
$506$		0			0
$507$	8.44109	−	8.44109i	0.374882	−	0.374882i
$508$		0			0
$509$	13.1673			0.583630			0.291815	−	0.956475i	$-0.405741\pi$
$509$	13.1673			0.583630			0.291815	+	0.956475i	$0.405741\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	2.61580	−	2.61580i	0.115491	−	0.115491i
$514$		0			0
$515$	32.8914	+	7.51189i	1.44937	+	0.331013i
$516$		0			0
$517$	8.56192	−	8.56192i	0.376553	−	0.376553i
$518$		0			0
$519$		−	9.82187i		−	0.431132i
$520$		0			0
$521$		−	26.1257i		−	1.14459i	−0.820049	−	0.572294i	$-0.806054\pi$
$521$		−	26.1257i		−	1.14459i	0.820049	−	0.572294i	$-0.193946\pi$
$522$		0			0
$523$	4.05244	+	4.05244i	0.177201	+	0.177201i	0.790134	−	0.612934i	$-0.210011\pi$
$523$	4.05244	+	4.05244i	0.177201	+	0.177201i	−0.612934	+	0.790134i	$0.710011\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	37.3446	+	37.3446i	1.62675	+	1.62675i
$528$		0			0
$529$			14.3776i			0.625113i
$530$		0			0
$531$			2.78807i			0.120992i
$532$		0			0
$533$	0.792283	−	0.792283i	0.0343176	−	0.0343176i
$534$		0			0
$535$	−31.8840	−	7.28182i	−1.37847	−	0.314821i
$536$		0			0
$537$	12.9424	−	12.9424i	0.558508	−	0.558508i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	28.2587			1.21494			0.607468	−	0.794344i	$-0.292185\pi$
$541$	28.2587			1.21494			0.607468	+	0.794344i	$0.292185\pi$
$542$		0			0
$543$	−14.2706	+	14.2706i	−0.612409	+	0.612409i
$544$		0			0
$545$	14.2237	+	22.6437i	0.609278	+	0.969950i
$546$		0			0
$547$	20.0515	+	20.0515i	0.857341	+	0.857341i	0.991024	−	0.133683i	$-0.0426804\pi$
$547$	20.0515	+	20.0515i	0.857341	+	0.857341i	−0.133683	+	0.991024i	$0.542680\pi$
$548$		0			0
$549$	0.251233			0.0107223
$550$		0			0
$551$			7.36606i			0.313805i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	10.1226	+	16.1149i	0.429682	+	0.684040i
$556$		0			0
$557$	15.6624	+	15.6624i	0.663636	+	0.663636i	0.956235	−	0.292599i	$-0.0945200\pi$
$557$	15.6624	+	15.6624i	0.663636	+	0.663636i	−0.292599	+	0.956235i	$0.594520\pi$
$558$		0			0
$559$	−8.62664			−0.364868
$560$		0			0
$561$	−18.4627			−0.779496
$562$		0			0
$563$	−0.922994	−	0.922994i	−0.0388996	−	0.0388996i	0.687389	−	0.726289i	$-0.258757\pi$
$563$	−0.922994	−	0.922994i	−0.0388996	−	0.0388996i	−0.726289	+	0.687389i	$0.758757\pi$
$564$		0			0
$565$	3.59588	−	15.7448i	0.151280	−	0.662390i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			0.493056i			0.0206700i	0.999947	+	0.0103350i	$0.00328979\pi$
$569$			0.493056i			0.0206700i	−0.999947	+	0.0103350i	$0.996710\pi$
$570$		0			0
$571$	3.59791			0.150568			0.0752839	−	0.997162i	$-0.476014\pi$
$571$	3.59791			0.150568			0.0752839	+	0.997162i	$0.476014\pi$
$572$		0			0
$573$	1.75571	+	1.75571i	0.0733456	+	0.0733456i
$574$		0			0
$575$	−4.84542	−	13.8594i	−0.202068	−	0.577975i
$576$		0			0
$577$	8.95360	−	8.95360i	0.372743	−	0.372743i	−0.495732	−	0.868475i	$-0.665100\pi$
$577$	8.95360	−	8.95360i	0.372743	−	0.372743i	0.868475	+	0.495732i	$0.165100\pi$
$578$		0			0
$579$	13.2919			0.552391
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−11.6922	+	11.6922i	−0.484241	+	0.484241i
$584$		0			0
$585$	−0.513185	+	2.24702i	−0.0212176	+	0.0929028i
$586$		0			0
$587$	2.84683	−	2.84683i	0.117501	−	0.117501i	−0.645911	−	0.763413i	$-0.723522\pi$
$587$	2.84683	−	2.84683i	0.117501	−	0.117501i	0.763413	+	0.645911i	$0.223522\pi$
$588$		0			0
$589$		−	25.7262i		−	1.06003i
$590$		0			0
$591$		−	7.71035i		−	0.317161i
$592$		0			0
$593$	22.5095	+	22.5095i	0.924352	+	0.924352i	0.997333	−	0.0729810i	$-0.0232512\pi$
$593$	22.5095	+	22.5095i	0.924352	+	0.924352i	−0.0729810	+	0.997333i	$0.523251\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	8.95131	+	8.95131i	0.366353	+	0.366353i
$598$		0			0
$599$			38.4832i			1.57238i	0.617984	+	0.786191i	$0.287950\pi$
$599$			38.4832i			1.57238i	−0.617984	+	0.786191i	$0.712050\pi$
$600$		0			0
$601$		−	45.6842i		−	1.86350i	−0.363102	−	0.931750i	$-0.618282\pi$
$601$		−	45.6842i		−	1.86350i	0.363102	−	0.931750i	$-0.381718\pi$
$602$		0			0
$603$	5.70338	−	5.70338i	0.232260	−	0.232260i
$604$		0			0
$605$	9.63714	−	6.05361i	0.391806	−	0.246114i
$606$		0			0
$607$	−17.5458	+	17.5458i	−0.712162	+	0.712162i	−0.966987	−	0.254825i	$-0.917982\pi$
$607$	−17.5458	+	17.5458i	−0.712162	+	0.712162i	0.254825	+	0.966987i	$0.417982\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.13382			0.207692
$612$		0			0
$613$	0.782557	−	0.782557i	0.0316072	−	0.0316072i	−0.691127	−	0.722734i	$-0.742885\pi$
$613$	0.782557	−	0.782557i	0.0316072	−	0.0316072i	0.722734	+	0.691127i	$0.242885\pi$
$614$		0			0
$615$	0.541183	−	2.36961i	0.0218226	−	0.0955518i
$616$		0			0
$617$	−0.353089	−	0.353089i	−0.0142148	−	0.0142148i	0.699964	−	0.714178i	$-0.253200\pi$
$617$	−0.353089	−	0.353089i	−0.0142148	−	0.0142148i	−0.714178	+	0.699964i	$0.753200\pi$
$618$		0			0
$619$	−23.2134			−0.933026			−0.466513	−	0.884514i	$-0.654490\pi$
$619$	−23.2134			−0.933026			−0.466513	+	0.884514i	$0.654490\pi$
$620$		0			0
$621$			2.93639i			0.117833i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−15.5767	−	19.5542i	−0.623070	−	0.782166i
$626$		0			0
$627$	6.35936	+	6.35936i	0.253968	+	0.253968i
$628$		0			0
$629$	−64.6326			−2.57707
$630$		0			0
$631$	18.8761			0.751445			0.375723	−	0.926732i	$-0.377395\pi$
$631$	18.8761			0.751445			0.375723	+	0.926732i	$0.377395\pi$
$632$		0			0
$633$	−3.80166	−	3.80166i	−0.151102	−	0.151102i
$634$		0			0
$635$	0.0811935	+	0.0185434i	0.00322207	+	0.000735871i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			14.5737i			0.576527i
$640$		0			0
$641$	−37.5350			−1.48254			−0.741271	−	0.671206i	$-0.765777\pi$
$641$	−37.5350			−1.48254			−0.741271	+	0.671206i	$0.765777\pi$
$642$		0			0
$643$	12.0570	+	12.0570i	0.475483	+	0.475483i	0.903684	−	0.428201i	$-0.140852\pi$
$643$	12.0570	+	12.0570i	0.475483	+	0.475483i	−0.428201	+	0.903684i	$0.640852\pi$
$644$		0			0
$645$	−15.8468	+	9.95426i	−0.623969	+	0.391949i
$646$		0			0
$647$	−13.1864	+	13.1864i	−0.518411	+	0.518411i	−0.917090	−	0.398679i	$-0.869469\pi$
$647$	−13.1864	+	13.1864i	−0.518411	+	0.518411i	0.398679	+	0.917090i	$0.369469\pi$
$648$		0			0
$649$	−6.77816			−0.266066
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−11.8735	+	11.8735i	−0.464647	+	0.464647i	−0.900175	−	0.435528i	$-0.856562\pi$
$653$	−11.8735	+	11.8735i	−0.464647	+	0.464647i	0.435528	+	0.900175i	$0.356562\pi$
$654$		0			0
$655$	11.7905	+	18.7701i	0.460693	+	0.733407i
$656$		0			0
$657$	−4.73234	+	4.73234i	−0.184626	+	0.184626i
$658$		0			0
$659$		−	47.4270i		−	1.84749i	−0.383005	−	0.923746i	$-0.625111\pi$
$659$		−	47.4270i		−	1.84749i	0.383005	−	0.923746i	$-0.374889\pi$
$660$		0			0
$661$			12.1884i			0.474072i	0.971501	+	0.237036i	$0.0761759\pi$
$661$			12.1884i			0.474072i	−0.971501	+	0.237036i	$0.923824\pi$
$662$		0			0
$663$	−5.53522	−	5.53522i	−0.214970	−	0.214970i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.13442	−	4.13442i	−0.160085	−	0.160085i
$668$		0			0
$669$			24.4443i			0.945070i
$670$		0			0
$671$			0.610779i			0.0235789i
$672$		0			0
$673$	1.19597	−	1.19597i	0.0461011	−	0.0461011i	−0.683680	−	0.729782i	$-0.739622\pi$
$673$	1.19597	−	1.19597i	0.0461011	−	0.0461011i	0.729782	+	0.683680i	$0.239622\pi$
$674$		0			0
$675$	1.65013	+	4.71986i	0.0635134	+	0.181668i
$676$		0			0
$677$	−6.69665	+	6.69665i	−0.257373	+	0.257373i	−0.823985	−	0.566612i	$-0.808254\pi$
$677$	−6.69665	+	6.69665i	−0.257373	+	0.257373i	0.566612	+	0.823985i	$0.308254\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.88317			0.0721633
$682$		0			0
$683$	−15.2123	+	15.2123i	−0.582082	+	0.582082i	−0.935475	−	0.353393i	$-0.885028\pi$
$683$	−15.2123	+	15.2123i	−0.582082	+	0.582082i	0.353393	+	0.935475i	$0.385028\pi$
$684$		0			0
$685$	−31.3311	−	7.15555i	−1.19710	−	0.273400i
$686$		0			0
$687$	−17.7319	−	17.7319i	−0.676514	−	0.676514i
$688$		0			0
$689$	−7.01077			−0.267089
$690$		0			0
$691$		−	6.26127i		−	0.238190i	−0.992883	−	0.119095i	$-0.962001\pi$
$691$		−	6.26127i		−	0.238190i	0.992883	−	0.119095i	$-0.0379993\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.0021	−	13.1926i	0.796655	−	0.500422i
$696$		0			0
$697$	5.83720	+	5.83720i	0.221100	+	0.221100i
$698$		0			0
$699$	−22.4312			−0.848427
$700$		0			0
$701$	−41.6155			−1.57180			−0.785899	−	0.618355i	$-0.787799\pi$
$701$	−41.6155			−1.57180			−0.785899	+	0.618355i	$0.787799\pi$
$702$		0			0
$703$	22.2623	+	22.2623i	0.839637	+	0.839637i
$704$		0			0
$705$	9.43065	−	5.92391i	0.355179	−	0.223107i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		−	0.322938i		−	0.0121282i	−0.999982	−	0.00606409i	$-0.998070\pi$
$709$		−	0.322938i		−	0.0121282i	0.999982	−	0.00606409i	$-0.00193027\pi$
$710$		0			0
$711$	11.0211			0.413325
$712$		0			0
$713$	14.4396	+	14.4396i	0.540766	+	0.540766i
$714$		0			0
$715$	−5.46279	−	1.24762i	−0.204297	−	0.0466583i
$716$		0			0
$717$	4.51783	−	4.51783i	0.168721	−	0.168721i
$718$		0			0
$719$	−20.2067			−0.753584			−0.376792	−	0.926298i	$-0.622973\pi$
$719$	−20.2067			−0.753584			−0.376792	+	0.926298i	$0.622973\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	13.1731	−	13.1731i	0.489913	−	0.489913i
$724$		0			0
$725$	−8.96889	−	4.32216i	−0.333096	−	0.160521i
$726$		0			0
$727$	−3.29844	+	3.29844i	−0.122332	+	0.122332i	−0.765622	−	0.643290i	$-0.777569\pi$
$727$	−3.29844	+	3.29844i	−0.122332	+	0.122332i	0.643290	+	0.765622i	$0.277569\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	63.5575i		−	2.35076i
$732$		0			0
$733$	−10.7393	−	10.7393i	−0.396663	−	0.396663i	0.480391	−	0.877054i	$-0.340495\pi$
$733$	−10.7393	−	10.7393i	−0.396663	−	0.396663i	−0.877054	+	0.480391i	$0.840495\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	13.8657	+	13.8657i	0.510748	+	0.510748i
$738$		0			0
$739$			18.0854i			0.665284i	0.943053	+	0.332642i	$0.107940\pi$
$739$			18.0854i			0.665284i	−0.943053	+	0.332642i	$0.892060\pi$
$740$		0			0
$741$			3.81314i			0.140079i
$742$		0			0
$743$	−4.73236	+	4.73236i	−0.173613	+	0.173613i	−0.788565	−	0.614952i	$-0.789176\pi$
$743$	−4.73236	+	4.73236i	−0.173613	+	0.173613i	0.614952	+	0.788565i	$0.289176\pi$
$744$		0			0
$745$	10.5249	+	16.7552i	0.385601	+	0.613864i
$746$		0			0
$747$	−9.90994	+	9.90994i	−0.362586	+	0.362586i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−45.2139			−1.64988			−0.824940	−	0.565220i	$-0.808791\pi$
$751$	−45.2139			−1.64988			−0.824940	+	0.565220i	$0.808791\pi$
$752$		0			0
$753$	22.3288	−	22.3288i	0.813705	−	0.813705i
$754$		0			0
$755$	−3.41231	+	2.14346i	−0.124187	+	0.0780083i
$756$		0			0
$757$	13.8934	+	13.8934i	0.504964	+	0.504964i	0.912976	−	0.408012i	$-0.133778\pi$
$757$	13.8934	+	13.8934i	0.504964	+	0.504964i	−0.408012	+	0.912976i	$0.633778\pi$
$758$		0			0
$759$	−7.13875			−0.259120
$760$		0			0
$761$			25.8668i			0.937670i	0.883286	+	0.468835i	$0.155326\pi$
$761$			25.8668i			0.937670i	−0.883286	+	0.468835i	$0.844674\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−16.5551	−	3.78093i	−0.598551	−	0.136700i
$766$		0			0
$767$	−2.03213	−	2.03213i	−0.0733759	−	0.0733759i
$768$		0			0
$769$	−3.97934			−0.143499			−0.0717493	−	0.997423i	$-0.522858\pi$
$769$	−3.97934			−0.143499			−0.0717493	+	0.997423i	$0.522858\pi$
$770$		0			0
$771$	18.5893			0.669476
$772$		0			0
$773$	−20.5814	−	20.5814i	−0.740262	−	0.740262i	0.232366	−	0.972628i	$-0.425353\pi$
$773$	−20.5814	−	20.5814i	−0.740262	−	0.740262i	−0.972628	+	0.232366i	$0.925353\pi$
$774$		0			0
$775$	31.3241	+	15.0953i	1.12519	+	0.542238i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	4.02117i		−	0.144073i
$780$		0			0
$781$	−35.4306			−1.26781
$782$		0			0
$783$	1.40799	+	1.40799i	0.0503175	+	0.0503175i
$784$		0			0
$785$	−5.71256	+	25.0129i	−0.203890	+	0.892748i
$786$		0			0
$787$	−21.5064	+	21.5064i	−0.766621	+	0.766621i	−0.977510	−	0.210889i	$-0.932364\pi$
$787$	−21.5064	+	21.5064i	−0.766621	+	0.766621i	0.210889	+	0.977510i	$0.432364\pi$
$788$		0			0
$789$	−5.71657			−0.203515
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.183115	+	0.183115i	−0.00650260	+	0.00650260i
$794$		0			0
$795$	−12.8785	+	8.08971i	−0.456755	+	0.286912i
$796$		0			0
$797$	4.04054	−	4.04054i	0.143123	−	0.143123i	−0.631915	−	0.775038i	$-0.717731\pi$
$797$	4.04054	−	4.04054i	0.143123	−	0.143123i	0.775038	+	0.631915i	$0.217731\pi$
$798$		0			0
$799$			37.8238i			1.33811i
$800$		0			0
$801$			11.6294i			0.410903i
$802$		0			0
$803$	−11.5049	−	11.5049i	−0.406000	−	0.406000i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.73216	−	1.73216i	−0.0609748	−	0.0609748i
$808$		0			0
$809$		−	43.8195i		−	1.54061i	−0.637674	−	0.770306i	$-0.720103\pi$
$809$		−	43.8195i		−	1.54061i	0.637674	−	0.770306i	$-0.279897\pi$
$810$		0			0
$811$		−	1.74791i		−	0.0613774i	−0.999529	−	0.0306887i	$-0.990230\pi$
$811$		−	1.74791i		−	0.0613774i	0.999529	−	0.0306887i	$-0.00977005\pi$
$812$		0			0
$813$	−17.8940	+	17.8940i	−0.627570	+	0.627570i
$814$		0			0
$815$	0.156427	−	0.684927i	0.00547939	−	0.0239919i
$816$		0			0
$817$	−21.8919	+	21.8919i	−0.765902	+	0.765902i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−27.0420			−0.943772			−0.471886	−	0.881659i	$-0.656427\pi$
$821$	−27.0420			−0.943772			−0.471886	+	0.881659i	$0.656427\pi$
$822$		0			0
$823$	−1.83059	+	1.83059i	−0.0638104	+	0.0638104i	−0.738292	−	0.674481i	$-0.764367\pi$
$823$	−1.83059	+	1.83059i	−0.0638104	+	0.0638104i	0.674481	+	0.738292i	$0.264367\pi$
$824$		0			0
$825$	−11.4746	+	4.01167i	−0.399494	+	0.139668i
$826$		0			0
$827$	37.3013	+	37.3013i	1.29709	+	1.29709i	0.930305	+	0.366787i	$0.119542\pi$
$827$	37.3013	+	37.3013i	1.29709	+	1.29709i	0.366787	+	0.930305i	$0.380458\pi$
$828$		0			0
$829$	−38.1117			−1.32367			−0.661837	−	0.749648i	$-0.730223\pi$
$829$	−38.1117			−1.32367			−0.661837	+	0.749648i	$0.730223\pi$
$830$		0			0
$831$		−	31.9797i		−	1.10936i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−1.47970	+	6.47898i	−0.0512072	+	0.224214i
$836$		0			0
$837$	−4.91745	−	4.91745i	−0.169972	−	0.169972i
$838$		0			0
$839$	27.2101			0.939398			0.469699	−	0.882827i	$-0.344362\pi$
$839$	27.2101			0.939398			0.469699	+	0.882827i	$0.344362\pi$
$840$		0			0
$841$	25.0351			0.863280
$842$		0			0
$843$	8.70053	+	8.70053i	0.299662	+	0.299662i
$844$		0			0
$845$	14.1985	+	22.6036i	0.488445	+	0.777587i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			2.26026i			0.0775720i
$850$		0			0
$851$	−24.9907			−0.856670
$852$		0			0
$853$	−12.1745	−	12.1745i	−0.416848	−	0.416848i	0.467268	−	0.884116i	$-0.345238\pi$
$853$	−12.1745	−	12.1745i	−0.416848	−	0.416848i	−0.884116	+	0.467268i	$0.845238\pi$
$854$		0			0
$855$	4.39997	+	7.00461i	0.150476	+	0.239553i
$856$		0			0
$857$	−24.5841	+	24.5841i	−0.839776	+	0.839776i	−0.988829	−	0.149053i	$-0.952377\pi$
$857$	−24.5841	+	24.5841i	−0.839776	+	0.839776i	0.149053	+	0.988829i	$0.452377\pi$
$858$		0			0
$859$	33.5215			1.14374			0.571869	−	0.820345i	$-0.306219\pi$
$859$	33.5215			1.14374			0.571869	+	0.820345i	$0.306219\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−24.0314	+	24.0314i	−0.818037	+	0.818037i	−0.985823	−	0.167786i	$-0.946338\pi$
$863$	−24.0314	+	24.0314i	−0.818037	+	0.818037i	0.167786	+	0.985823i	$0.446338\pi$
$864$		0			0
$865$	21.4111	+	4.88996i	0.727998	+	0.166264i
$866$		0			0
$867$	28.7604	−	28.7604i	0.976753	−	0.976753i
$868$		0			0
$869$			26.7938i			0.908918i
$870$		0			0
$871$			8.31400i			0.281709i
$872$		0			0
$873$	10.8833	+	10.8833i	0.368343	+	0.368343i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	12.9523	+	12.9523i	0.437367	+	0.437367i	0.891125	−	0.453758i	$-0.149917\pi$
$877$	12.9523	+	12.9523i	0.437367	+	0.437367i	−0.453758	+	0.891125i	$0.649917\pi$
$878$		0			0
$879$		−	4.51782i		−	0.152382i
$880$		0			0
$881$			17.5109i			0.589956i	0.955504	+	0.294978i	$0.0953123\pi$
$881$			17.5109i			0.589956i	−0.955504	+	0.294978i	$0.904688\pi$
$882$		0			0
$883$	−33.5448	+	33.5448i	−1.12887	+	1.12887i	−0.138510	+	0.990361i	$0.544231\pi$
$883$	−33.5448	+	33.5448i	−1.12887	+	1.12887i	−0.990361	+	0.138510i	$0.955769\pi$
$884$		0			0
$885$	−6.07782	−	1.38808i	−0.204304	−	0.0466599i
$886$		0			0
$887$	−19.4004	+	19.4004i	−0.651402	+	0.651402i	−0.953331	−	0.301929i	$-0.902370\pi$
$887$	−19.4004	+	19.4004i	−0.651402	+	0.651402i	0.301929	+	0.953331i	$0.402370\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.43113			0.0814459
$892$		0			0
$893$	13.0282	−	13.0282i	0.435971	−	0.435971i
$894$		0			0
$895$	21.7702	+	34.6573i	0.727696	+	1.15847i
$896$		0			0
$897$	−2.14024	−	2.14024i	−0.0714604	−	0.0714604i
$898$		0			0
$899$	13.8475			0.461839
$900$		0			0
$901$		−	51.6524i		−	1.72079i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−24.0042	−	38.2138i	−0.797926	−	1.27027i
$906$		0			0
$907$	−2.26660	−	2.26660i	−0.0752611	−	0.0752611i	0.668474	−	0.743735i	$-0.266948\pi$
$907$	−2.26660	−	2.26660i	−0.0752611	−	0.0752611i	−0.743735	+	0.668474i	$0.766948\pi$
$908$		0			0
$909$	−6.28914			−0.208597
$910$		0			0
$911$	51.5087			1.70656			0.853279	−	0.521454i	$-0.174610\pi$
$911$	51.5087			1.70656			0.853279	+	0.521454i	$0.174610\pi$
$912$		0			0
$913$	−24.0923	−	24.0923i	−0.797340	−	0.797340i
$914$		0			0
$915$	−0.125080	+	0.547671i	−0.00413501	+	0.0181055i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		−	48.1725i		−	1.58906i	−0.607223	−	0.794531i	$-0.707717\pi$
$919$		−	48.1725i		−	1.58906i	0.607223	−	0.794531i	$-0.292283\pi$
$920$		0			0
$921$	−8.12602			−0.267762
$922$		0			0
$923$	−10.6223	−	10.6223i	−0.349637	−	0.349637i
$924$		0			0
$925$	−40.1692	+	14.0437i	−1.32076	+	0.461754i
$926$		0			0
$927$	10.6690	−	10.6690i	0.350415	−	0.350415i
$928$		0			0
$929$	28.9413			0.949534			0.474767	−	0.880112i	$-0.342532\pi$
$929$	28.9413			0.949534			0.474767	+	0.880112i	$0.342532\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−10.2257	+	10.2257i	−0.334773	+	0.334773i
$934$		0			0
$935$	9.19193	−	40.2476i	0.300608	−	1.31624i
$936$		0			0
$937$	9.57644	−	9.57644i	0.312849	−	0.312849i	−0.533164	−	0.846012i	$-0.678997\pi$
$937$	9.57644	−	9.57644i	0.312849	−	0.312849i	0.846012	+	0.533164i	$0.178997\pi$
$938$		0			0
$939$			1.18213i			0.0385774i
$940$		0			0
$941$			15.9827i			0.521021i	0.965471	+	0.260511i	$0.0838909\pi$
$941$			15.9827i			0.521021i	−0.965471	+	0.260511i	$0.916109\pi$
$942$		0			0
$943$	2.25700	+	2.25700i	0.0734980	+	0.0734980i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.83489	+	5.83489i	0.189608	+	0.189608i	0.795527	−	0.605918i	$-0.207194\pi$
$947$	5.83489	+	5.83489i	0.189608	+	0.189608i	−0.605918	+	0.795527i	$0.707194\pi$
$948$		0			0
$949$		−	6.89849i		−	0.223934i
$950$		0			0
$951$		−	8.84122i		−	0.286696i
$952$		0			0
$953$	25.2246	−	25.2246i	0.817104	−	0.817104i	−0.168584	−	0.985687i	$-0.553919\pi$
$953$	25.2246	−	25.2246i	0.817104	−	0.817104i	0.985687	+	0.168584i	$0.0539194\pi$
$954$		0			0
$955$	−4.70143	+	2.95322i	−0.152135	+	0.0955641i
$956$		0			0
$957$	−3.42301	+	3.42301i	−0.110650	+	0.110650i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−17.3626			−0.560085
$962$		0			0
$963$	−10.3422	+	10.3422i	−0.333273	+	0.333273i
$964$		0			0
$965$	−6.61755	+	28.9755i	−0.213027	+	0.932753i
$966$		0			0
$967$	−16.3072	−	16.3072i	−0.524405	−	0.524405i	0.394494	−	0.918899i	$-0.370920\pi$
$967$	−16.3072	−	16.3072i	−0.524405	−	0.524405i	−0.918899	+	0.394494i	$0.870920\pi$
$968$		0			0
$969$	−28.0936			−0.902497
$970$		0			0
$971$			4.39646i			0.141089i	0.997509	+	0.0705445i	$0.0224737\pi$
$971$			4.39646i			0.141089i	−0.997509	+	0.0705445i	$0.977526\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−4.64287	−	2.23742i	−0.148691	−	0.0716549i
$976$		0			0
$977$	29.0436	+	29.0436i	0.929188	+	0.929188i	0.997653	−	0.0684658i	$-0.0218104\pi$
$977$	29.0436	+	29.0436i	0.929188	+	0.929188i	−0.0684658	+	0.997653i	$0.521810\pi$
$978$		0			0
$979$	−28.2725			−0.903592
$980$		0			0
$981$	11.9587			0.381812
$982$		0			0
$983$	1.86456	+	1.86456i	0.0594704	+	0.0594704i	0.736216	−	0.676746i	$-0.236611\pi$
$983$	1.86456	+	1.86456i	0.0594704	+	0.0594704i	−0.676746	+	0.736216i	$0.736611\pi$
$984$		0			0
$985$	16.8081	+	3.83871i	0.535550	+	0.122311i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	24.5750i		−	0.781439i
$990$		0			0
$991$	−1.31673			−0.0418273			−0.0209136	−	0.999781i	$-0.506658\pi$
$991$	−1.31673			−0.0418273			−0.0209136	+	0.999781i	$0.506658\pi$
$992$		0			0
$993$	15.4579	+	15.4579i	0.490542	+	0.490542i
$994$		0			0
$995$	−23.9699	+	15.0568i	−0.759896	+	0.477332i
$996$		0			0
$997$	36.2398	−	36.2398i	1.14772	−	1.14772i	0.160726	−	0.986999i	$-0.448617\pi$
$997$	36.2398	−	36.2398i	1.14772	−	1.14772i	0.986999	−	0.160726i	$-0.0513834\pi$
$998$		0			0
$999$	8.51068			0.269266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.x.c.97.15		32
5.3	odd	4	inner	2940.2.x.c.1273.4		32
7.4	even	3		420.2.bo.a.397.7	yes	32
7.5	odd	6		420.2.bo.a.157.5	yes	32
7.6	odd	2	inner	2940.2.x.c.97.4		32
21.5	even	6		1260.2.dq.c.577.7		32
21.11	odd	6		1260.2.dq.c.397.4		32
35.4	even	6		2100.2.ce.e.1657.2		32
35.12	even	12		2100.2.ce.e.493.2		32
35.13	even	4	inner	2940.2.x.c.1273.15		32
35.18	odd	12		420.2.bo.a.313.5	yes	32
35.19	odd	6		2100.2.ce.e.157.4		32
35.32	odd	12		2100.2.ce.e.1993.4		32
35.33	even	12		420.2.bo.a.73.7	✓	32
105.53	even	12		1260.2.dq.c.1153.7		32
105.68	odd	12		1260.2.dq.c.73.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.7	✓	32	35.33	even	12
420.2.bo.a.157.5	yes	32	7.5	odd	6
420.2.bo.a.313.5	yes	32	35.18	odd	12
420.2.bo.a.397.7	yes	32	7.4	even	3
1260.2.dq.c.73.4		32	105.68	odd	12
1260.2.dq.c.397.4		32	21.11	odd	6
1260.2.dq.c.577.7		32	21.5	even	6
1260.2.dq.c.1153.7		32	105.53	even	12
2100.2.ce.e.157.4		32	35.19	odd	6
2100.2.ce.e.493.2		32	35.12	even	12
2100.2.ce.e.1657.2		32	35.4	even	6
2100.2.ce.e.1993.4		32	35.32	odd	12
2940.2.x.c.97.4		32	7.6	odd	2	inner
2940.2.x.c.97.15		32	1.1	even	1	trivial
2940.2.x.c.1273.4		32	5.3	odd	4	inner
2940.2.x.c.1273.15		32	35.13	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:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.89349 + 1.18941i) q^{5} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.89349 + 1.18941i) q^{5} +1.00000i q^{9} -2.43113 q^{11} +(-0.728866 - 0.728866i) q^{13} +(-2.17994 - 0.497865i) q^{15} +(5.36998 - 5.36998i) q^{17} -3.69931 q^{19} +(2.07634 - 2.07634i) q^{23} +(2.17063 - 4.50426i) q^{25} +(-0.707107 + 0.707107i) q^{27} -1.99120i q^{29} +6.95433i q^{31} +(-1.71907 - 1.71907i) q^{33} +(-6.01796 - 6.01796i) q^{37} -1.03077i q^{39} +1.08701i q^{41} +(5.91785 - 5.91785i) q^{43} +(-1.18941 - 1.89349i) q^{45} +(-3.52179 + 3.52179i) q^{47} +7.59429 q^{51} +(4.80937 - 4.80937i) q^{53} +(4.60332 - 2.89160i) q^{55} +(-2.61580 - 2.61580i) q^{57} +2.78807 q^{59} -0.251233i q^{61} +(2.24702 + 0.513185i) q^{65} +(-5.70338 - 5.70338i) q^{67} +2.93639 q^{69} +14.5737 q^{71} +(4.73234 + 4.73234i) q^{73} +(4.71986 - 1.65013i) q^{75} -11.0211i q^{79} -1.00000 q^{81} +(9.90994 + 9.90994i) q^{83} +(-3.78093 + 16.5551i) q^{85} +(1.40799 - 1.40799i) q^{87} +11.6294 q^{89} +(-4.91745 + 4.91745i) q^{93} +(7.00461 - 4.39997i) q^{95} +(10.8833 - 10.8833i) q^{97} -2.43113i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 16 q^{11} + 8 q^{15} - 32 q^{23} + 8 q^{25} - 40 q^{37} - 24 q^{43} + 16 q^{51} - 80 q^{53} - 16 q^{57} + 104 q^{65} - 16 q^{71} - 32 q^{81} - 8 q^{85} - 16 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q - 16 * q^11 + 8 * q^15 - 32 * q^23 + 8 * q^25 - 40 * q^37 - 24 * q^43 + 16 * q^51 - 80 * q^53 - 16 * q^57 + 104 * q^65 - 16 * q^71 - 32 * q^81 - 8 * q^85 - 16 * q^93 + 72 * q^95

Introduction

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