LMFDB - Embedded newform 1260.2.dq.c.73.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(73,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 9, 2]))

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

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

chi := DirichletCharacter("1260.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.dq (of order $12$, degree $4$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	1260.73
Dual form			1260.2.dq.c.397.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0833091 - 2.23452i) q^{5} +(-1.70817 + 2.02043i) q^{7} +O(q^{10})$	$q+(0.0833091 - 2.23452i) q^{5} +(-1.70817 + 2.02043i) q^{7} +(-1.21556 + 2.10542i) q^{11} +(-0.728866 + 0.728866i) q^{13} +(7.33552 - 1.96555i) q^{17} +(1.84965 + 3.20369i) q^{19} +(-0.759994 + 2.83634i) q^{23} +(-4.98612 - 0.372311i) q^{25} -1.99120i q^{29} +(6.02262 + 3.47716i) q^{31} +(4.37238 + 3.98525i) q^{35} +(8.22068 + 2.20273i) q^{37} +1.08701i q^{41} +(5.91785 + 5.91785i) q^{43} +(1.28906 - 4.81085i) q^{47} +(-1.16431 - 6.90249i) q^{49} +(6.56972 - 1.76035i) q^{53} +(4.60332 + 2.89160i) q^{55} +(1.39403 - 2.41454i) q^{59} +(0.217574 - 0.125616i) q^{61} +(1.56794 + 1.68938i) q^{65} +(-2.08758 - 7.79096i) q^{67} -14.5737 q^{71} +(1.73216 + 6.46450i) q^{73} +(-2.17747 - 6.05238i) q^{77} +(9.54459 - 5.51057i) q^{79} +(-9.90994 + 9.90994i) q^{83} +(-3.78093 - 16.5551i) q^{85} +(5.81468 + 10.0713i) q^{89} +(-0.227598 - 2.71765i) q^{91} +(7.31279 - 3.86618i) q^{95} +(10.8833 + 10.8833i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{5}+O(q^{10}) $ 32 * q + 12 * q^5	$ 32 q + 12 q^{5} - 8 q^{11} - 16 q^{23} - 4 q^{25} + 24 q^{31} - 20 q^{35} + 20 q^{37} - 24 q^{43} - 12 q^{47} - 40 q^{53} - 24 q^{61} + 52 q^{65} + 16 q^{71} - 60 q^{73} + 84 q^{77} - 8 q^{85} + 40 q^{91} + 36 q^{95}+O(q^{100}) $ 32 * q + 12 * q^5 - 8 * q^11 - 16 * q^23 - 4 * q^25 + 24 * q^31 - 20 * q^35 + 20 * q^37 - 24 * q^43 - 12 * q^47 - 40 * q^53 - 24 * q^61 + 52 * q^65 + 16 * q^71 - 60 * q^73 + 84 * q^77 - 8 * q^85 + 40 * q^91 + 36 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0833091	−	2.23452i	0.0372570	−	0.999306i
$5$	0.0833091	−	2.23452i	0.0372570	−	0.999306i
$6$		0			0
$7$	−1.70817	+	2.02043i	−0.645628	+	0.763652i
$7$	−1.70817	+	2.02043i	−0.645628	+	0.763652i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.21556	+	2.10542i	−0.366506	+	0.634808i	−0.989017	−	0.147804i	$-0.952780\pi$
$11$	−1.21556	+	2.10542i	−0.366506	+	0.634808i	0.622510	+	0.782612i	$0.286113\pi$
$12$		0			0
$13$	−0.728866	+	0.728866i	−0.202151	+	0.202151i	−0.800921	−	0.598770i	$-0.795656\pi$
$13$	−0.728866	+	0.728866i	−0.202151	+	0.202151i	0.598770	+	0.800921i	$0.295656\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.33552	−	1.96555i	1.77913	−	0.476715i	0.788702	−	0.614776i	$-0.210753\pi$
$17$	7.33552	−	1.96555i	1.77913	−	0.476715i	0.990424	+	0.138060i	$0.0440867\pi$
$18$		0			0
$19$	1.84965	+	3.20369i	0.424339	+	0.734977i	0.996358	−	0.0852629i	$-0.0271730\pi$
$19$	1.84965	+	3.20369i	0.424339	+	0.734977i	−0.572019	+	0.820240i	$0.693840\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.759994	+	2.83634i	−0.158470	+	0.591417i	0.840313	+	0.542101i	$0.182371\pi$
$23$	−0.759994	+	2.83634i	−0.158470	+	0.591417i	−0.998783	+	0.0493165i	$0.984296\pi$
$24$		0			0
$25$	−4.98612	−	0.372311i	−0.997224	−	0.0744622i
$26$		0			0
$27$		0			0
$28$		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
$31$	6.02262	+	3.47716i	1.08169	+	0.624517i	0.931353	−	0.364117i	$-0.118629\pi$
$31$	6.02262	+	3.47716i	1.08169	+	0.624517i	0.150342	+	0.988634i	$0.451963\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.37238	+	3.98525i	0.739068	+	0.673631i
$36$		0			0
$37$	8.22068	+	2.20273i	1.35147	+	0.362126i	0.860678	−	0.509150i	$-0.170040\pi$
$37$	8.22068	+	2.20273i	1.35147	+	0.362126i	0.490794	+	0.871276i	$0.336707\pi$
$38$		0			0
$39$		0			0
$40$		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	0.995649	−	0.0931848i	$-0.0297048\pi$
$43$	5.91785	+	5.91785i	0.902464	+	0.902464i	−0.0931848	+	0.995649i	$0.529705\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.28906	−	4.81085i	0.188029	−	0.701735i	−0.805932	−	0.592007i	$-0.798336\pi$
$47$	1.28906	−	4.81085i	0.188029	−	0.701735i	0.993962	−	0.109727i	$-0.0349978\pi$
$48$		0			0
$49$	−1.16431	−	6.90249i	−0.166329	−	0.986070i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.56972	−	1.76035i	0.902420	−	0.241803i	0.222365	−	0.974964i	$-0.428622\pi$
$53$	6.56972	−	1.76035i	0.902420	−	0.241803i	0.680055	+	0.733161i	$0.261956\pi$
$54$		0			0
$55$	4.60332	+	2.89160i	0.620712	+	0.389903i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.39403	−	2.41454i	0.181488	−	0.314346i	−0.760900	−	0.648870i	$-0.775242\pi$
$59$	1.39403	−	2.41454i	0.181488	−	0.314346i	0.942387	+	0.334523i	$0.108575\pi$
$60$		0			0
$61$	0.217574	−	0.125616i	0.0278575	−	0.0160835i	−0.486007	−	0.873955i	$-0.661547\pi$
$61$	0.217574	−	0.125616i	0.0278575	−	0.0160835i	0.513864	+	0.857872i	$0.328214\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.56794	+	1.68938i	0.194479	+	0.209542i
$66$		0			0
$67$	−2.08758	−	7.79096i	−0.255039	−	0.951818i	−0.968069	−	0.250684i	$-0.919344\pi$
$67$	−2.08758	−	7.79096i	−0.255039	−	0.951818i	0.713030	−	0.701133i	$-0.247322\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−14.5737			−1.72958			−0.864790	−	0.502133i	$-0.832549\pi$
$71$	−14.5737			−1.72958			−0.864790	+	0.502133i	$0.832549\pi$
$72$		0			0
$73$	1.73216	+	6.46450i	0.202734	+	0.756612i	0.990128	+	0.140163i	$0.0447627\pi$
$73$	1.73216	+	6.46450i	0.202734	+	0.756612i	−0.787395	+	0.616449i	$0.788571\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.17747	−	6.05238i	−0.248146	−	0.689733i
$78$		0			0
$79$	9.54459	−	5.51057i	1.07385	−	0.619987i	0.144619	−	0.989487i	$-0.453804\pi$
$79$	9.54459	−	5.51057i	1.07385	−	0.619987i	0.929231	+	0.369500i	$0.120471\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−9.90994	+	9.90994i	−1.08776	+	1.08776i	−0.0919976	+	0.995759i	$0.529325\pi$
$83$	−9.90994	+	9.90994i	−1.08776	+	1.08776i	−0.995759	+	0.0919976i	$0.970675\pi$
$84$		0			0
$85$	−3.78093	−	16.5551i	−0.410100	−	1.79565i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.81468	+	10.0713i	0.616354	+	1.06756i	0.990145	+	0.140044i	$0.0447244\pi$
$89$	5.81468	+	10.0713i	0.616354	+	1.06756i	−0.373791	+	0.927513i	$0.621942\pi$
$90$		0			0
$91$	−0.227598	−	2.71765i	−0.0238587	−	0.284887i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.31279	−	3.86618i	0.750277	−	0.396662i
$96$		0			0
$97$	10.8833	+	10.8833i	1.10503	+	1.10503i	0.993794	+	0.111236i	$0.0354808\pi$
$97$	10.8833	+	10.8833i	1.10503	+	1.10503i	0.111236	+	0.993794i	$0.464519\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.44655	−	3.14457i	−0.541952	−	0.312896i	0.203918	−	0.978988i	$-0.434633\pi$
$101$	−5.44655	−	3.14457i	−0.541952	−	0.312896i	−0.745870	+	0.666092i	$0.767966\pi$
$102$		0			0
$103$	14.5741	+	3.90512i	1.43603	+	0.384782i	0.891141	−	0.453727i	$-0.149906\pi$
$103$	14.5741	+	3.90512i	1.43603	+	0.384782i	0.544887	+	0.838510i	$0.316573\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	14.1277	+	3.78551i	1.36578	+	0.365960i	0.865935	−	0.500156i	$-0.166724\pi$
$107$	14.1277	+	3.78551i	1.36578	+	0.365960i	0.499844	+	0.866115i	$0.333391\pi$
$108$		0			0
$109$	−10.3565	−	5.97935i	−0.991976	−	0.572718i	−0.0861118	−	0.996285i	$-0.527444\pi$
$109$	−10.3565	−	5.97935i	−0.991976	−	0.572718i	−0.905864	+	0.423568i	$0.860778\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.10715	+	5.10715i	0.480441	+	0.480441i	0.905272	−	0.424832i	$-0.139667\pi$
$113$	5.10715	+	5.10715i	0.480441	+	0.480441i	−0.424832	+	0.905272i	$0.639667\pi$
$114$		0			0
$115$	6.27453	+	1.93451i	0.585103	+	0.180394i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.55907	+	18.1784i	−0.784609	+	1.66641i
$120$		0			0
$121$	2.54481	+	4.40773i	0.231346	+	0.400703i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.24732	+	11.1105i	−0.111564	+	0.993757i
$126$		0			0
$127$	−0.0263367	+	0.0263367i	−0.00233701	+	0.00233701i	−0.708274	−	0.705937i	$-0.750526\pi$
$127$	−0.0263367	+	0.0263367i	−0.00233701	+	0.00233701i	0.705937	+	0.708274i	$0.250526\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.58485	+	4.95646i	−0.750062	+	0.433048i	−0.825716	−	0.564086i	$-0.809229\pi$
$131$	−8.58485	+	4.95646i	−0.750062	+	0.433048i	0.0756546	+	0.997134i	$0.475895\pi$
$132$		0			0
$133$	−9.63237	−	1.73535i	−0.835232	−	0.150474i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.71987	−	13.8828i	−0.317810	−	1.18608i	−0.921345	−	0.388747i	$-0.872908\pi$
$137$	−3.71987	−	13.8828i	−0.317810	−	1.18608i	0.603535	−	0.797337i	$-0.293759\pi$
$138$		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
$141$		0			0
$142$		0			0
$143$	−0.648585	−	2.42055i	−0.0542374	−	0.202417i
$144$		0			0
$145$	−4.44937	−	0.165885i	−0.369500	−	0.0137760i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.66332	+	4.42442i	−0.627804	+	0.362463i	−0.779901	−	0.625903i	$-0.784731\pi$
$149$	−7.66332	+	4.42442i	−0.627804	+	0.362463i	0.152097	+	0.988366i	$0.451397\pi$
$150$		0			0
$151$	−0.901062	+	1.56068i	−0.0733274	+	0.127007i	−0.900358	−	0.435151i	$-0.856695\pi$
$151$	−0.901062	+	1.56068i	−0.0733274	+	0.127007i	0.827030	+	0.562157i	$0.190028\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.27151	−	13.1680i	0.664384	−	1.05768i
$156$		0			0
$157$	−11.0832	+	2.96972i	−0.884532	+	0.237010i	−0.672361	−	0.740223i	$-0.734720\pi$
$157$	−11.0832	+	2.96972i	−0.884532	+	0.237010i	−0.212171	+	0.977233i	$0.568053\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.43243	−	6.38047i	−0.349325	−	0.502851i
$162$		0			0
$163$	−0.0813198	+	0.303489i	−0.00636946	+	0.0237711i	−0.969037	−	0.246914i	$-0.920584\pi$
$163$	−0.0813198	+	0.303489i	−0.00636946	+	0.0237711i	0.962668	+	0.270685i	$0.0872502\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.10159	−	2.10159i	−0.162626	−	0.162626i	0.621103	−	0.783729i	$-0.286685\pi$
$167$	−2.10159	−	2.10159i	−0.162626	−	0.162626i	−0.783729	+	0.621103i	$0.786685\pi$
$168$		0			0
$169$			11.9375i			0.918270i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.48720	−	2.54209i	−0.721298	−	0.193271i	−0.120547	−	0.992708i	$-0.538465\pi$
$173$	−9.48720	−	2.54209i	−0.721298	−	0.193271i	−0.600751	+	0.799436i	$0.705132\pi$
$174$		0			0
$175$	9.26937	−	9.43815i	0.700699	−	0.713457i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.8512	+	9.15169i	1.18477	+	0.684030i	0.957114	−	0.289711i	$-0.0935592\pi$
$179$	15.8512	+	9.15169i	1.18477	+	0.684030i	0.227660	+	0.973741i	$0.426893\pi$
$180$		0			0
$181$		−	20.1817i		−	1.50009i	−0.661387	−	0.750045i	$-0.730032\pi$
$181$		−	20.1817i		−	1.50009i	0.661387	−	0.750045i	$-0.269968\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.60688	−	18.1857i	0.412226	−	1.33704i
$186$		0			0
$187$	−4.77850	+	17.8336i	−0.349439	+	1.30412i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.24147	+	2.15029i	0.0898297	+	0.155590i	0.907439	−	0.420184i	$-0.138034\pi$
$191$	1.24147	+	2.15029i	0.0898297	+	0.155590i	−0.817609	+	0.575773i	$0.804701\pi$
$192$		0			0
$193$	−12.8390	+	3.44019i	−0.924169	+	0.247630i	−0.689366	−	0.724413i	$-0.742111\pi$
$193$	−12.8390	+	3.44019i	−0.924169	+	0.247630i	−0.234802	+	0.972043i	$0.575444\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.45204	−	5.45204i	0.388442	−	0.388442i	−0.485690	−	0.874131i	$-0.661431\pi$
$197$	5.45204	−	5.45204i	0.388442	−	0.388442i	0.874131	+	0.485690i	$0.161431\pi$
$198$		0			0
$199$	−6.32953	+	10.9631i	−0.448689	+	0.777152i	−0.998301	−	0.0582681i	$-0.981442\pi$
$199$	−6.32953	+	10.9631i	−0.448689	+	0.777152i	0.549612	+	0.835420i	$0.314776\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.02309	+	3.40131i	0.282366	+	0.238725i
$204$		0			0
$205$	2.42893	+	0.0905576i	0.169644	+	0.00632481i
$206$		0			0
$207$		0			0
$208$		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
$213$		0			0
$214$		0			0
$215$	13.7165	−	12.7305i	0.935460	−	0.868214i
$216$		0			0
$217$	−17.3130	+	6.22872i	−1.17529	+	0.422833i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−3.91399	+	6.77924i	−0.263284	+	0.456021i
$222$		0			0
$223$	17.2847	−	17.2847i	1.15747	−	1.15747i	0.172452	−	0.985018i	$-0.444831\pi$
$223$	17.2847	−	17.2847i	1.15747	−	1.15747i	0.985018	−	0.172452i	$-0.0551689\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.81901	−	0.487401i	0.120732	−	0.0323499i	−0.197947	−	0.980213i	$-0.563427\pi$
$227$	1.81901	−	0.487401i	0.120732	−	0.0323499i	0.318679	+	0.947863i	$0.396761\pi$
$228$		0			0
$229$	12.5383	+	21.7171i	0.828557	+	1.43510i	0.899170	+	0.437600i	$0.144171\pi$
$229$	12.5383	+	21.7171i	0.828557	+	1.43510i	−0.0706123	+	0.997504i	$0.522495\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.80563	−	21.6669i	0.380340	−	1.41945i	−0.465044	−	0.885287i	$-0.653962\pi$
$233$	5.80563	−	21.6669i	0.380340	−	1.41945i	0.845384	−	0.534159i	$-0.179372\pi$
$234$		0			0
$235$	−10.6425	−	3.28122i	−0.694242	−	0.214043i
$236$		0			0
$237$		0			0
$238$		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
$241$	−16.1337	−	9.31479i	−1.03926	−	0.600018i	−0.119638	−	0.992818i	$-0.538173\pi$
$241$	−16.1337	−	9.31479i	−1.03926	−	0.600018i	−0.919624	+	0.392799i	$0.871507\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−15.5207	+	2.02662i	−0.991583	+	0.129476i
$246$		0			0
$247$	−3.68321	−	0.986914i	−0.234357	−	0.0627958i
$248$		0			0
$249$		0			0
$250$		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
$255$		0			0
$256$		0			0
$257$	−4.81126	+	17.9559i	−0.300118	+	1.12006i	0.636949	+	0.770906i	$0.280196\pi$
$257$	−4.81126	+	17.9559i	−0.300118	+	1.12006i	−0.937067	+	0.349150i	$0.886470\pi$
$258$		0			0
$259$	−18.4928	+	12.8467i	−1.14909	+	0.798256i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.52178	+	1.47956i	−0.340488	+	0.0912334i	−0.425011	−	0.905188i	$-0.639730\pi$
$263$	−5.52178	+	1.47956i	−0.340488	+	0.0912334i	0.0845235	+	0.996421i	$0.473063\pi$
$264$		0			0
$265$	−3.38621	−	14.8268i	−0.208013	−	0.910802i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.22482	+	2.12145i	−0.0746785	+	0.129347i	−0.900946	−	0.433930i	$-0.857126\pi$
$269$	−1.22482	+	2.12145i	−0.0746785	+	0.129347i	0.826268	+	0.563277i	$0.190460\pi$
$270$		0			0
$271$	−21.9156	+	12.6530i	−1.33128	+	0.768613i	−0.985495	−	0.169702i	$-0.945720\pi$
$271$	−21.9156	+	12.6530i	−1.33128	+	0.768613i	−0.345782	+	0.938315i	$0.612386\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.84482	−	10.0453i	0.412758	−	0.605755i
$276$		0			0
$277$	−8.27697	−	30.8901i	−0.497315	−	1.85600i	−0.516660	−	0.856191i	$-0.672825\pi$
$277$	−8.27697	−	30.8901i	−0.497315	−	1.85600i	0.0193451	−	0.999813i	$-0.493842\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.3044			−0.734020			−0.367010	−	0.930217i	$-0.619618\pi$
$281$	−12.3044			−0.734020			−0.367010	+	0.930217i	$0.619618\pi$
$282$		0			0
$283$	0.584999	+	2.18325i	0.0347746	+	0.129780i	0.981131	−	0.193344i	$-0.0619334\pi$
$283$	0.584999	+	2.18325i	0.0347746	+	0.129780i	−0.946356	+	0.323125i	$0.895267\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.19623	−	1.85679i	−0.129639	−	0.109603i
$288$		0			0
$289$	35.2241	−	20.3366i	2.07201	−	1.19627i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.19458	−	3.19458i	0.186629	−	0.186629i	−0.607608	−	0.794237i	$-0.707871\pi$
$293$	3.19458	−	3.19458i	0.186629	−	0.186629i	0.794237	+	0.607608i	$0.207871\pi$
$294$		0			0
$295$	−5.27919	−	3.31615i	−0.307366	−	0.193073i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.51338	−	2.62124i	−0.0875208	−	0.151590i
$300$		0			0
$301$	−22.0653	+	1.84793i	−1.27182	+	0.106513i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.262566	−	0.496637i	−0.0150345	−	0.0284373i
$306$		0			0
$307$	−5.74597	−	5.74597i	−0.327940	−	0.327940i	0.523863	−	0.851803i	$-0.324490\pi$
$307$	−5.74597	−	5.74597i	−0.327940	−	0.327940i	−0.851803	+	0.523863i	$0.824490\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−12.5238	−	7.23064i	−0.710161	−	0.410012i	0.100959	−	0.994891i	$-0.467809\pi$
$311$	−12.5238	−	7.23064i	−0.710161	−	0.410012i	−0.811121	+	0.584879i	$0.801142\pi$
$312$		0			0
$313$	−1.14185	−	0.305958i	−0.0645412	−	0.0172938i	0.226404	−	0.974033i	$-0.427303\pi$
$313$	−1.14185	−	0.305958i	−0.0645412	−	0.0172938i	−0.290945	+	0.956740i	$0.593970\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.53996	−	2.28828i	−0.479652	−	0.128522i	0.0108885	−	0.999941i	$-0.496534\pi$
$317$	−8.53996	−	2.28828i	−0.479652	−	0.128522i	−0.490541	+	0.871418i	$0.663201\pi$
$318$		0			0
$319$	4.19231	+	2.42043i	0.234725	+	0.135518i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	19.8652	+	19.8652i	1.10533	+	1.10533i
$324$		0			0
$325$	3.90558	−	3.36285i	0.216642	−	0.186537i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	7.51807	+	10.8222i	0.414484	+	0.596649i
$330$		0			0
$331$	−10.9304	−	18.9320i	−0.600789	−	1.04060i	−0.992702	−	0.120595i	$-0.961520\pi$
$331$	−10.9304	−	18.9320i	−0.600789	−	1.04060i	0.391913	−	0.920002i	$-0.371814\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−17.5829	+	4.01568i	−0.960659	+	0.219400i
$336$		0			0
$337$	18.0987	−	18.0987i	0.985900	−	0.985900i	−0.0140019	−	0.999902i	$-0.504457\pi$
$337$	18.0987	−	18.0987i	0.985900	−	0.985900i	0.999902	+	0.0140019i	$0.00445708\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.6418	+	8.45343i	−0.792896	+	0.457779i
$342$		0			0
$343$	15.9349	+	9.43823i	0.860402	+	0.509617i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.08442	+	4.04711i	0.0582148	+	0.217261i	0.988905	−	0.148547i	$-0.0474596\pi$
$347$	1.08442	+	4.04711i	0.0582148	+	0.217261i	−0.930691	+	0.365807i	$0.880793\pi$
$348$		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
$351$		0			0
$352$		0			0
$353$	8.70598	+	32.4911i	0.463372	+	1.72933i	0.662230	+	0.749301i	$0.269610\pi$
$353$	8.70598	+	32.4911i	0.463372	+	1.72933i	−0.198857	+	0.980028i	$0.563723\pi$
$354$		0			0
$355$	−1.21412	+	32.5652i	−0.0644389	+	1.72838i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.0177	+	8.09313i	−0.739826	+	0.427139i	−0.822006	−	0.569479i	$-0.807145\pi$
$359$	−14.0177	+	8.09313i	−0.739826	+	0.427139i	0.0821800	+	0.996618i	$0.473812\pi$
$360$		0			0
$361$	2.65757	−	4.60305i	0.139872	−	0.242266i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	14.5893	−	3.33198i	0.763640	−	0.174404i
$366$		0			0
$367$	15.6293	−	4.18786i	0.815842	−	0.218604i	0.173314	−	0.984867i	$-0.444552\pi$
$367$	15.6293	−	4.18786i	0.815842	−	0.218604i	0.642528	+	0.766262i	$0.277886\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.66553	+	16.2807i	−0.397974	+	0.845250i
$372$		0			0
$373$	−0.962517	+	3.59216i	−0.0498372	+	0.185995i	−0.986357	−	0.164619i	$-0.947360\pi$
$373$	−0.962517	+	3.59216i	−0.0498372	+	0.185995i	0.936520	+	0.350614i	$0.114027\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.45132	+	1.45132i	0.0747467	+	0.0747467i
$378$		0			0
$379$			0.149127i			0.00766015i	0.999993	+	0.00383007i	$0.00121915\pi$
$379$			0.149127i			0.00766015i	−0.999993	+	0.00383007i	$0.998781\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	33.4767	+	8.97006i	1.71058	+	0.458349i	0.975567	−	0.219703i	$-0.0705089\pi$
$383$	33.4767	+	8.97006i	1.71058	+	0.458349i	0.735014	+	0.678052i	$0.237176\pi$
$384$		0			0
$385$	−13.7055	+	4.36137i	−0.698499	+	0.222276i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−28.3146	−	16.3474i	−1.43561	−	0.828847i	−0.438065	−	0.898943i	$-0.644336\pi$
$389$	−28.3146	−	16.3474i	−1.43561	−	0.828847i	−0.997540	+	0.0700961i	$0.977669\pi$
$390$		0			0
$391$			22.2998i			1.12775i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.5183	−	21.7866i	−0.579549	−	1.09620i
$396$		0			0
$397$	4.73087	−	17.6559i	0.237436	−	0.886122i	−0.739600	−	0.673047i	$-0.764985\pi$
$397$	4.73087	−	17.6559i	0.237436	−	0.886122i	0.977036	−	0.213076i	$-0.0683481\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.590882	+	1.02344i	0.0295072	+	0.0511080i	0.880402	−	0.474228i	$-0.157273\pi$
$401$	0.590882	+	1.02344i	0.0295072	+	0.0511080i	−0.850895	+	0.525336i	$0.823940\pi$
$402$		0			0
$403$	−6.92407	+	1.85530i	−0.344913	+	0.0924190i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.6304	+	14.6304i	−0.725203	+	0.725203i
$408$		0			0
$409$	8.11235	−	14.0510i	0.401130	−	0.694777i	−0.592733	−	0.805399i	$-0.701951\pi$
$409$	8.11235	−	14.0510i	0.401130	−	0.694777i	0.993863	+	0.110622i	$0.0352843\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.49717	+	6.94100i	0.122878	+	0.341544i
$414$		0			0
$415$	21.3183	+	22.9695i	1.04648	+	1.12753i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.4289			0.753750			0.376875	−	0.926264i	$-0.376999\pi$
$419$	15.4289			0.753750			0.376875	+	0.926264i	$0.376999\pi$
$420$		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
$423$		0			0
$424$		0			0
$425$	−37.3076	+	7.06936i	−1.80968	+	0.342914i
$426$		0			0
$427$	−0.117854	+	0.654167i	−0.00570335	+	0.0316574i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.83304	−	3.17492i	0.0882944	−	0.152930i	−0.818496	−	0.574512i	$-0.805192\pi$
$431$	1.83304	−	3.17492i	0.0882944	−	0.152930i	0.906790	+	0.421582i	$0.138525\pi$
$432$		0			0
$433$	−9.74318	+	9.74318i	−0.468227	+	0.468227i	−0.901340	−	0.433112i	$-0.857415\pi$
$433$	−9.74318	+	9.74318i	−0.468227	+	0.468227i	0.433112	+	0.901340i	$0.357415\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.4925	+	2.81145i	−0.501923	+	0.134490i
$438$		0			0
$439$	3.00918	+	5.21204i	0.143620	+	0.248757i	0.928857	−	0.370438i	$-0.120792\pi$
$439$	3.00918	+	5.21204i	0.143620	+	0.248757i	−0.785237	+	0.619195i	$0.787459\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.25355	+	19.6065i	−0.249604	+	0.931534i	0.721410	+	0.692509i	$0.243495\pi$
$443$	−5.25355	+	19.6065i	−0.249604	+	0.931534i	−0.971013	+	0.239025i	$0.923172\pi$
$444$		0			0
$445$	22.9889	−	12.1540i	1.08978	−	0.576153i
$446$		0			0
$447$		0			0
$448$		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
$451$	−2.28861	−	1.32133i	−0.107766	−	0.0622189i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.09160	+	0.282166i	−0.285579	+	0.0132281i
$456$		0			0
$457$	30.1623	+	8.08197i	1.41093	+	0.378058i	0.882258	−	0.470766i	$-0.156022\pi$
$457$	30.1623	+	8.08197i	1.41093	+	0.378058i	0.528675	+	0.848824i	$0.322689\pi$
$458$		0			0
$459$		0			0
$460$		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	0.197720	−	0.980259i	$-0.436646\pi$
$463$	−16.8382	−	16.8382i	−0.782539	−	0.782539i	−0.980259	+	0.197720i	$0.936646\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.0990	+	37.6898i	−0.467324	+	1.74408i	0.181744	+	0.983346i	$0.441826\pi$
$467$	−10.0990	+	37.6898i	−0.467324	+	1.74408i	−0.649068	+	0.760730i	$0.724841\pi$
$468$		0			0
$469$	19.3071	+	9.09048i	0.891518	+	0.419759i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−19.6531	+	5.26603i	−0.903650	+	0.242132i
$474$		0			0
$475$	−8.02982	−	16.6626i	−0.368433	−	0.764534i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.66084	+	13.2690i	−0.350033	+	0.606275i	−0.986255	−	0.165231i	$-0.947163\pi$
$479$	−7.66084	+	13.2690i	−0.350033	+	0.606275i	0.636222	+	0.771506i	$0.280496\pi$
$480$		0			0
$481$	−7.59727	+	4.38628i	−0.346406	+	0.199997i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	25.2255	−	23.4122i	1.14543	−	1.06309i
$486$		0			0
$487$	−4.32465	−	16.1398i	−0.195968	−	0.731364i	−0.992014	−	0.126127i	$-0.959745\pi$
$487$	−4.32465	−	16.1398i	−0.195968	−	0.731364i	0.796046	−	0.605237i	$-0.206921\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.188878			−0.00852393			−0.00426196	−	0.999991i	$-0.501357\pi$
$491$	−0.188878			−0.00852393			−0.00426196	+	0.999991i	$0.501357\pi$
$492$		0			0
$493$	−3.91380	−	14.6065i	−0.176269	−	0.657844i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	24.8944	−	29.4452i	1.11667	−	1.32080i
$498$		0			0
$499$	−12.1410	+	7.00959i	−0.543504	+	0.313792i	−0.746498	−	0.665388i	$-0.768266\pi$
$499$	−12.1410	+	7.00959i	−0.543504	+	0.313792i	0.202994	+	0.979180i	$0.434933\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	20.0052	−	20.0052i	0.891989	−	0.891989i	−0.102721	−	0.994710i	$-0.532755\pi$
$503$	20.0052	−	20.0052i	0.891989	−	0.891989i	0.994710	+	0.102721i	$0.0327549\pi$
$504$		0			0
$505$	−7.48033	+	11.9084i	−0.332870	+	0.529918i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.58364	+	11.4032i	0.291815	+	0.505438i	0.974239	−	0.225518i	$-0.0724076\pi$
$509$	6.58364	+	11.4032i	0.291815	+	0.505438i	−0.682424	+	0.730956i	$0.739074\pi$
$510$		0			0
$511$	−16.0199	−	7.54276i	−0.708679	−	0.333672i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.94019	−	32.2407i	0.438017	−	1.42069i
$516$		0			0
$517$	8.56192	+	8.56192i	0.376553	+	0.376553i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	22.6255	+	13.0628i	0.991242	+	0.572294i	0.905645	−	0.424036i	$-0.139387\pi$
$521$	22.6255	+	13.0628i	0.991242	+	0.572294i	0.0855965	+	0.996330i	$0.472720\pi$
$522$		0			0
$523$	−5.53573	−	1.48330i	−0.242061	−	0.0648600i	0.135749	−	0.990743i	$-0.456656\pi$
$523$	−5.53573	−	1.48330i	−0.242061	−	0.0648600i	−0.377810	+	0.925883i	$0.623323\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	51.0136	+	13.6691i	2.22219	+	0.595434i
$528$		0			0
$529$	12.4514	+	7.18880i	0.541364	+	0.312556i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.792283	−	0.792283i	−0.0343176	−	0.0343176i
$534$		0			0
$535$	9.63576	−	31.2533i	0.416590	−	1.35120i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.9479	+	5.93907i	0.686926	+	0.255814i
$540$		0			0
$541$	−14.1293	−	24.4727i	−0.607468	−	1.05217i	−0.991656	−	0.128910i	$-0.958852\pi$
$541$	−14.1293	−	24.4727i	−0.607468	−	1.05217i	0.384188	−	0.923255i	$-0.374481\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.2237	+	22.6437i	−0.609278	+	0.969950i
$546$		0			0
$547$	20.0515	−	20.0515i	0.857341	−	0.857341i	−0.133683	−	0.991024i	$-0.542680\pi$
$547$	20.0515	−	20.0515i	0.857341	−	0.857341i	0.991024	+	0.133683i	$0.0426804\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	6.37920	−	3.68303i	0.271763	−	0.156902i
$552$		0			0
$553$	−5.17004	+	28.6972i	−0.219853	+	1.22033i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.73283	−	21.3952i	−0.242908	−	0.906544i	−0.974423	−	0.224720i	$-0.927853\pi$
$557$	−5.73283	−	21.3952i	−0.242908	−	0.906544i	0.731516	−	0.681825i	$-0.238813\pi$
$558$		0			0
$559$	−8.62664			−0.364868
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.337839	+	1.26083i	0.0142382	+	0.0531378i	0.972679	−	0.232152i	$-0.0745768\pi$
$563$	0.337839	+	1.26083i	0.0142382	+	0.0531378i	−0.958441	+	0.285290i	$0.907910\pi$
$564$		0			0
$565$	11.8375	−	10.9865i	0.498007	−	0.462207i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.426999	−	0.246528i	0.0179007	−	0.0103350i	−0.491023	−	0.871147i	$-0.663377\pi$
$569$	0.426999	−	0.246528i	0.0179007	−	0.0103350i	0.508924	+	0.860812i	$0.330044\pi$
$570$		0			0
$571$	−1.79895	+	3.11588i	−0.0752839	+	0.130395i	−0.901210	−	0.433383i	$-0.857320\pi$
$571$	−1.79895	+	3.11588i	−0.0752839	+	0.130395i	0.825926	+	0.563779i	$0.190653\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.84542	−	13.8594i	0.202068	−	0.577975i
$576$		0			0
$577$	−12.2308	+	3.27724i	−0.509177	+	0.136433i	−0.504256	−	0.863554i	$-0.668233\pi$
$577$	−12.2308	+	3.27724i	−0.509177	+	0.136433i	−0.00492102	+	0.999988i	$0.501566\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.09451	−	36.9502i	−0.128382	−	1.53295i
$582$		0			0
$583$	−4.27964	+	15.9718i	−0.177245	+	0.661486i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.84683	−	2.84683i	−0.117501	−	0.117501i	0.645911	−	0.763413i	$-0.276478\pi$
$587$	−2.84683	−	2.84683i	−0.117501	−	0.117501i	−0.763413	+	0.645911i	$0.776478\pi$
$588$		0			0
$589$			25.7262i			1.06003i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	30.7485	+	8.23903i	1.26269	+	0.338336i	0.827226	−	0.561870i	$-0.189918\pi$
$593$	30.7485	+	8.23903i	1.26269	+	0.338336i	0.435463	+	0.900206i	$0.356585\pi$
$594$		0			0
$595$	39.9069	+	20.6398i	1.63603	+	0.846149i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−33.3274	−	19.2416i	−1.36172	−	0.786191i	−0.371869	−	0.928285i	$-0.621283\pi$
$599$	−33.3274	−	19.2416i	−1.36172	−	0.786191i	−0.989853	+	0.142095i	$0.954616\pi$
$600$		0			0
$601$			45.6842i			1.86350i	0.363102	+	0.931750i	$0.381718\pi$
$601$			45.6842i			1.86350i	−0.363102	+	0.931750i	$0.618282\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.0612	−	5.31920i	0.409044	−	0.216256i
$606$		0			0
$607$	−6.42220	+	23.9680i	−0.260669	+	0.972831i	0.704179	+	0.710023i	$0.251315\pi$
$607$	−6.42220	+	23.9680i	−0.260669	+	0.972831i	−0.964848	+	0.262808i	$0.915351\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.56691	+	4.44602i	0.103846	+	0.179867i
$612$		0			0
$613$	−1.06899	+	0.286436i	−0.0431762	+	0.0115690i	−0.280343	−	0.959900i	$-0.590448\pi$
$613$	−1.06899	+	0.286436i	−0.0431762	+	0.0115690i	0.237166	+	0.971469i	$0.423781\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.353089	−	0.353089i	0.0142148	−	0.0142148i	−0.699964	−	0.714178i	$-0.746800\pi$
$617$	0.353089	−	0.353089i	0.0142148	−	0.0142148i	0.714178	+	0.699964i	$0.246800\pi$
$618$		0			0
$619$	11.6067	−	20.1034i	0.466513	−	0.808024i	−0.532756	−	0.846269i	$-0.678844\pi$
$619$	11.6067	−	20.1034i	0.466513	−	0.808024i	0.999268	+	0.0382453i	$0.0121768\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−30.2809	−	5.45536i	−1.21318	−	0.218564i
$624$		0			0
$625$	24.7228	+	3.71277i	0.988911	+	0.148511i
$626$		0			0
$627$		0			0
$628$		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
$633$		0			0
$634$		0			0
$635$	0.0566558	+	0.0610440i	0.00224832	+	0.00242246i
$636$		0			0
$637$	5.87961	+	4.18237i	0.232959	+	0.165712i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.7675	+	32.5062i	−0.741271	+	1.28392i	0.210646	+	0.977562i	$0.432443\pi$
$641$	−18.7675	+	32.5062i	−0.741271	+	1.28392i	−0.951917	+	0.306356i	$0.900890\pi$
$642$		0			0
$643$	12.0570	−	12.0570i	0.475483	−	0.475483i	−0.428201	−	0.903684i	$-0.640852\pi$
$643$	12.0570	−	12.0570i	0.475483	−	0.475483i	0.903684	+	0.428201i	$0.140852\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.0130	+	4.82656i	−0.708163	+	0.189752i	−0.594884	−	0.803812i	$-0.702802\pi$
$647$	−18.0130	+	4.82656i	−0.708163	+	0.189752i	−0.113279	+	0.993563i	$0.536135\pi$
$648$		0			0
$649$	3.38908	+	5.87006i	0.133033	+	0.230420i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.34601	−	16.2195i	0.170073	−	0.634719i	−0.827266	−	0.561810i	$-0.810105\pi$
$653$	4.34601	−	16.2195i	0.170073	−	0.634719i	0.997339	−	0.0729090i	$-0.0232283\pi$
$654$		0			0
$655$	10.3601	+	19.5959i	0.404803	+	0.765675i
$656$		0			0
$657$		0			0
$658$		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
$661$	10.5554	+	6.09418i	0.410558	+	0.237036i	0.691030	−	0.722826i	$-0.257157\pi$
$661$	10.5554	+	6.09418i	0.410558	+	0.237036i	−0.280471	+	0.959862i	$0.590491\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.68014	+	21.3791i	−0.181488	+	0.829046i
$666$		0			0
$667$	5.64772	+	1.51330i	0.218681	+	0.0585953i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			0.610779i			0.0235789i
$672$		0			0
$673$	1.19597	+	1.19597i	0.0461011	+	0.0461011i	0.729782	−	0.683680i	$-0.239622\pi$
$673$	1.19597	+	1.19597i	0.0461011	+	0.0461011i	−0.683680	+	0.729782i	$0.739622\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.45115	−	9.14780i	0.0942052	−	0.351578i	−0.902693	−	0.430286i	$-0.858413\pi$
$677$	2.45115	−	9.14780i	0.0942052	−	0.351578i	0.996898	+	0.0787076i	$0.0250794\pi$
$678$		0			0
$679$	−40.5794	+	3.39845i	−1.55730	+	0.130420i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.7804	+	5.56809i	−0.795139	+	0.213057i	−0.633449	−	0.773785i	$-0.718361\pi$
$683$	−20.7804	+	5.56809i	−0.795139	+	0.213057i	−0.161690	+	0.986842i	$0.551695\pi$
$684$		0			0
$685$	−31.3311	+	7.15555i	−1.19710	+	0.273400i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.50538	+	6.07150i	−0.133544	+	0.231306i
$690$		0			0
$691$	5.42242	−	3.13064i	0.206279	−	0.119095i	−0.393302	−	0.919409i	$-0.628667\pi$
$691$	5.42242	−	3.13064i	0.206279	−	0.119095i	0.599581	+	0.800314i	$0.295334\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.924041	+	24.7846i	−0.0350509	+	0.940134i
$696$		0			0
$697$	2.13656	+	7.97377i	0.0809281	+	0.302028i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	41.6155			1.57180			0.785899	−	0.618355i	$-0.212201\pi$
$701$	41.6155			1.57180			0.785899	+	0.618355i	$0.212201\pi$
$702$		0			0
$703$	8.14855	+	30.4108i	0.307328	+	1.14697i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.6570	−	5.63294i	0.588843	−	0.211848i
$708$		0			0
$709$	0.279672	−	0.161469i	0.0105033	−	0.00606409i	−0.494739	−	0.869042i	$-0.664736\pi$
$709$	0.279672	−	0.161469i	0.0105033	−	0.00606409i	0.505242	+	0.862977i	$0.331403\pi$
$710$		0			0
$711$		0			0
$712$		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
$717$		0			0
$718$		0			0
$719$	−10.1034	−	17.4996i	−0.376792	−	0.652623i	0.613801	−	0.789460i	$-0.289640\pi$
$719$	−10.1034	−	17.4996i	−0.376792	−	0.652623i	−0.990594	+	0.136837i	$0.956306\pi$
$720$		0			0
$721$	−32.7851	+	22.7754i	−1.22098	+	0.848199i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.741346	+	9.92837i	−0.0275329	+	0.368730i
$726$		0			0
$727$	−3.29844	−	3.29844i	−0.122332	−	0.122332i	0.643290	−	0.765622i	$-0.277569\pi$
$727$	−3.29844	−	3.29844i	−0.122332	−	0.122332i	−0.765622	+	0.643290i	$0.777569\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	55.0424	+	31.7787i	2.03582	+	1.17538i
$732$		0			0
$733$	14.6701	+	3.93084i	0.541852	+	0.145189i	0.519356	−	0.854558i	$-0.326172\pi$
$733$	14.6701	+	3.93084i	0.541852	+	0.145189i	0.0224964	+	0.999747i	$0.492839\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.9408	+	5.07518i	0.697695	+	0.186947i
$738$		0			0
$739$	15.6624	+	9.04272i	0.576153	+	0.332642i	0.759603	−	0.650387i	$-0.225393\pi$
$739$	15.6624	+	9.04272i	0.576153	+	0.332642i	−0.183450	+	0.983029i	$0.558727\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.73236	+	4.73236i	0.173613	+	0.173613i	0.788565	−	0.614952i	$-0.210824\pi$
$743$	4.73236	+	4.73236i	0.173613	+	0.173613i	−0.614952	+	0.788565i	$0.710824\pi$
$744$		0			0
$745$	9.24801	+	17.4924i	0.338821	+	0.640872i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−31.7810	+	22.0778i	−1.16125	+	0.806707i
$750$		0			0
$751$	22.6070	+	39.1564i	0.824940	+	1.42884i	0.901965	+	0.431809i	$0.142124\pi$
$751$	22.6070	+	39.1564i	0.824940	+	1.42884i	−0.0770253	+	0.997029i	$0.524542\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.41231	+	2.14346i	0.124187	+	0.0780083i
$756$		0			0
$757$	13.8934	−	13.8934i	0.504964	−	0.504964i	−0.408012	−	0.912976i	$-0.633778\pi$
$757$	13.8934	−	13.8934i	0.504964	−	0.504964i	0.912976	+	0.408012i	$0.133778\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	22.4013	−	12.9334i	0.812046	−	0.468835i	−0.0356201	−	0.999365i	$-0.511341\pi$
$761$	22.4013	−	12.9334i	0.812046	−	0.468835i	0.847666	+	0.530531i	$0.178007\pi$
$762$		0			0
$763$	29.7716	−	10.7109i	1.07780	−	0.387762i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.743811	+	2.77594i	0.0268575	+	0.100233i
$768$		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
$771$		0			0
$772$		0			0
$773$	7.53332	+	28.1147i	0.270955	+	1.01122i	0.958504	+	0.285079i	$0.0920198\pi$
$773$	7.53332	+	28.1147i	0.270955	+	1.01122i	−0.687549	+	0.726138i	$0.741314\pi$
$774$		0			0
$775$	−28.7349	−	19.5798i	−1.03219	−	0.703328i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.48244	+	2.01059i	−0.124771	+	0.0720367i
$780$		0			0
$781$	17.7153	−	30.6838i	0.633903	−	1.09795i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.71256	+	25.0129i	0.203890	+	0.892748i
$786$		0			0
$787$	29.3783	−	7.87190i	1.04722	−	0.280603i	0.306120	−	0.951993i	$-0.400969\pi$
$787$	29.3783	−	7.87190i	1.04722	−	0.280603i	0.741104	+	0.671390i	$0.234302\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−19.0426	+	1.59477i	−0.677075	+	0.0567037i
$792$		0			0
$793$	−0.0670247	+	0.250140i	−0.00238012	+	0.00888272i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.04054	−	4.04054i	−0.143123	−	0.143123i	0.631915	−	0.775038i	$-0.282269\pi$
$797$	−4.04054	−	4.04054i	−0.143123	−	0.143123i	−0.775038	+	0.631915i	$0.782269\pi$
$798$		0			0
$799$		−	37.8238i		−	1.33811i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.7160	−	4.21110i	−0.554607	−	0.148606i
$804$		0			0
$805$	−14.6265	+	9.37279i	−0.515517	+	0.330347i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	37.9488	+	21.9098i	1.33421	+	0.770306i	0.985942	−	0.167089i	$-0.0534366\pi$
$809$	37.9488	+	21.9098i	1.33421	+	0.770306i	0.348268	+	0.937395i	$0.386770\pi$
$810$		0			0
$811$			1.74791i			0.0613774i	0.999529	+	0.0306887i	$0.00977005\pi$
$811$			1.74791i			0.0613774i	−0.999529	+	0.0306887i	$0.990230\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.671377	+	0.206994i	0.0235173	+	0.00725067i
$816$		0			0
$817$	−8.01301	+	29.9049i	−0.280340	+	1.04624i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−13.5210	−	23.4191i	−0.471886	−	0.817331i	0.527596	−	0.849495i	$-0.323093\pi$
$821$	−13.5210	−	23.4191i	−0.471886	−	0.817331i	−0.999483	+	0.0321643i	$0.989760\pi$
$822$		0			0
$823$	2.50063	−	0.670043i	0.0871667	−	0.0233562i	−0.214972	−	0.976620i	$-0.568966\pi$
$823$	2.50063	−	0.670043i	0.0871667	−	0.0233562i	0.302139	+	0.953264i	$0.402299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−37.3013	+	37.3013i	−1.29709	+	1.29709i	−0.366787	+	0.930305i	$0.619542\pi$
$827$	−37.3013	+	37.3013i	−1.29709	+	1.29709i	−0.930305	+	0.366787i	$0.880458\pi$
$828$		0			0
$829$	19.0559	−	33.0057i	0.661837	−	1.14634i	−0.318295	−	0.947992i	$-0.603110\pi$
$829$	19.0559	−	33.0057i	0.661837	−	1.14634i	0.980132	−	0.198344i	$-0.0635563\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−22.1080	−	48.3449i	−0.765996	−	1.67505i
$834$		0			0
$835$	−4.87111	+	4.52095i	−0.168572	+	0.156454i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−27.2101			−0.939398			−0.469699	−	0.882827i	$-0.655638\pi$
$839$	−27.2101			−0.939398			−0.469699	+	0.882827i	$0.655638\pi$
$840$		0			0
$841$	25.0351			0.863280
$842$		0			0
$843$		0			0
$844$		0			0
$845$	26.6745	+	0.994503i	0.917632	+	0.0342119i
$846$		0			0
$847$	−13.2525	−	2.38755i	−0.455361	−	0.0820372i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12.4953	+	21.6426i	−0.428335	+	0.741898i
$852$		0			0
$853$	−12.1745	+	12.1745i	−0.416848	+	0.416848i	−0.884116	−	0.467268i	$-0.845238\pi$
$853$	−12.1745	+	12.1745i	−0.416848	+	0.416848i	0.467268	+	0.884116i	$0.345238\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−33.5825	+	8.99840i	−1.14716	+	0.307379i	−0.781825	−	0.623498i	$-0.785711\pi$
$857$	−33.5825	+	8.99840i	−1.14716	+	0.307379i	−0.365331	+	0.930878i	$0.619044\pi$
$858$		0			0
$859$	−16.7607	−	29.0304i	−0.571869	−	0.990506i	−0.996374	−	0.0850805i	$-0.972885\pi$
$859$	−16.7607	−	29.0304i	−0.571869	−	0.990506i	0.424505	−	0.905426i	$-0.360448\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.79609	−	32.8275i	0.299422	−	1.11746i	−0.638219	−	0.769855i	$-0.720329\pi$
$863$	8.79609	−	32.8275i	0.299422	−	1.11746i	0.937641	−	0.347605i	$-0.113005\pi$
$864$		0			0
$865$	−6.47070	+	20.9875i	−0.220010	+	0.713597i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			26.7938i			0.908918i
$870$		0			0
$871$	7.20014	+	4.15700i	0.243967	+	0.140855i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−20.3175	−	21.4988i	−0.686856	−	0.726793i
$876$		0			0
$877$	−17.6931	−	4.74085i	−0.597454	−	0.160087i	−0.0525963	−	0.998616i	$-0.516750\pi$
$877$	−17.6931	−	4.74085i	−0.597454	−	0.160087i	−0.544858	+	0.838529i	$0.683416\pi$
$878$		0			0
$879$		0			0
$880$		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	−0.990361	−	0.138510i	$-0.955769\pi$
$883$	−33.5448	−	33.5448i	−1.12887	−	1.12887i	−0.138510	−	0.990361i	$-0.544231\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.10104	−	26.5015i	0.238430	−	0.889832i	−0.738143	−	0.674644i	$-0.764297\pi$
$887$	7.10104	−	26.5015i	0.238430	−	0.889832i	0.976573	−	0.215188i	$-0.0690363\pi$
$888$		0			0
$889$	−0.00822399	−	0.0981993i	−0.000275824	−	0.00329350i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.7968	−	4.76864i	0.595547	−	0.159576i
$894$		0			0
$895$	21.7702	−	34.6573i	0.727696	−	1.15847i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	6.92373	−	11.9923i	0.230919	−	0.399964i
$900$		0			0
$901$	44.7323	−	25.8262i	1.49025	−	0.860395i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−45.0962	−	1.68131i	−1.49905	−	0.0558888i
$906$		0			0
$907$	−0.829631	−	3.09623i	−0.0275475	−	0.102809i	0.950783	−	0.309857i	$-0.100281\pi$
$907$	−0.829631	−	3.09623i	−0.0275475	−	0.102809i	−0.978331	+	0.207048i	$0.933614\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−51.5087			−1.70656			−0.853279	−	0.521454i	$-0.825390\pi$
$911$	−51.5087			−1.70656			−0.853279	+	0.521454i	$0.825390\pi$
$912$		0			0
$913$	−8.81841	−	32.9107i	−0.291847	−	1.08919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	4.65018	−	25.8116i	0.153562	−	0.852374i
$918$		0			0
$919$	41.7186	−	24.0862i	1.37617	−	0.794531i	0.384473	−	0.923136i	$-0.374383\pi$
$919$	41.7186	−	24.0862i	1.37617	−	0.794531i	0.991696	+	0.128605i	$0.0410499\pi$
$920$		0			0
$921$		0			0
$922$		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
$927$		0			0
$928$		0			0
$929$	14.4707	+	25.0639i	0.474767	+	0.822321i	0.999582	−	0.0288955i	$-0.00919901\pi$
$929$	14.4707	+	25.0639i	0.474767	+	0.822321i	−0.524815	+	0.851216i	$0.675866\pi$
$930$		0			0
$931$	19.9599	−	16.4973i	0.654159	−	0.540677i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	39.4514	+	12.1633i	1.29020	+	0.397784i
$936$		0			0
$937$	9.57644	+	9.57644i	0.312849	+	0.312849i	0.846012	−	0.533164i	$-0.178997\pi$
$937$	9.57644	+	9.57644i	0.312849	+	0.312849i	−0.533164	+	0.846012i	$0.678997\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.8414	−	7.99136i	−0.451218	−	0.260511i	0.257127	−	0.966378i	$-0.417224\pi$
$941$	−13.8414	−	7.99136i	−0.451218	−	0.260511i	−0.708344	+	0.705867i	$0.750558\pi$
$942$		0			0
$943$	−3.08312	−	0.826119i	−0.100400	−	0.0269021i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.97060	+	2.13572i	0.259010	+	0.0694015i	0.385987	−	0.922504i	$-0.373861\pi$
$947$	7.97060	+	2.13572i	0.259010	+	0.0694015i	−0.126977	+	0.991906i	$0.540528\pi$
$948$		0			0
$949$	−5.97426	−	3.44924i	−0.193933	−	0.111967i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−25.2246	−	25.2246i	−0.817104	−	0.817104i	0.168584	−	0.985687i	$-0.446081\pi$
$953$	−25.2246	−	25.2246i	−0.817104	−	0.817104i	−0.985687	+	0.168584i	$0.946081\pi$
$954$		0			0
$955$	4.90828	−	2.59495i	0.158828	−	0.0839705i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	34.4034	+	16.1984i	1.11094	+	0.523072i
$960$		0			0
$961$	8.68132	+	15.0365i	0.280043	+	0.485048i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.61755	+	28.9755i	0.213027	+	0.932753i
$966$		0			0
$967$	−16.3072	+	16.3072i	−0.524405	+	0.524405i	−0.918899	−	0.394494i	$-0.870920\pi$
$967$	−16.3072	+	16.3072i	−0.524405	+	0.524405i	0.394494	+	0.918899i	$0.370920\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.80744	−	2.19823i	0.122187	−	0.0705445i	−0.437661	−	0.899140i	$-0.644193\pi$
$971$	3.80744	−	2.19823i	0.122187	−	0.0705445i	0.559848	+	0.828596i	$0.310860\pi$
$972$		0			0
$973$	18.9466	−	22.4101i	0.607399	−	0.718434i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.6307	−	39.6743i	−0.340106	−	1.26929i	−0.898226	−	0.439534i	$-0.855144\pi$
$977$	−10.6307	−	39.6743i	−0.340106	−	1.26929i	0.558120	−	0.829760i	$-0.311523\pi$
$978$		0			0
$979$	−28.2725			−0.903592
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−0.682478	−	2.54704i	−0.0217677	−	0.0812380i	0.954188	−	0.299209i	$-0.0967228\pi$
$983$	−0.682478	−	2.54704i	−0.0217677	−	0.0812380i	−0.975955	+	0.217971i	$0.930056\pi$
$984$		0			0
$985$	−11.7285	−	12.6369i	−0.373700	−	0.402644i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.2826	+	12.2875i	−0.676746	+	0.390720i
$990$		0			0
$991$	0.658365	−	1.14032i	0.0209136	−	0.0362235i	−0.855379	−	0.518002i	$-0.826676\pi$
$991$	0.658365	−	1.14032i	0.0209136	−	0.0362235i	0.876293	+	0.481779i	$0.160009\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	23.9699	+	15.0568i	0.759896	+	0.477332i
$996$		0			0
$997$	−49.5044	+	13.2647i	−1.56782	+	0.420096i	−0.935129	−	0.354307i	$-0.884717\pi$
$997$	−49.5044	+	13.2647i	−1.56782	+	0.420096i	−0.632692	+	0.774404i	$0.718050\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.dq.c.73.4		32
3.2	odd	2		420.2.bo.a.73.7	✓	32
5.2	odd	4	inner	1260.2.dq.c.577.7		32
7.5	odd	6	inner	1260.2.dq.c.1153.7		32
15.2	even	4		420.2.bo.a.157.5	yes	32
15.8	even	4		2100.2.ce.e.157.4		32
15.14	odd	2		2100.2.ce.e.493.2		32
21.5	even	6		420.2.bo.a.313.5	yes	32
21.11	odd	6		2940.2.x.c.1273.15		32
21.17	even	6		2940.2.x.c.1273.4		32
35.12	even	12	inner	1260.2.dq.c.397.4		32
105.17	odd	12		2940.2.x.c.97.15		32
105.32	even	12		2940.2.x.c.97.4		32
105.47	odd	12		420.2.bo.a.397.7	yes	32
105.68	odd	12		2100.2.ce.e.1657.2		32
105.89	even	6		2100.2.ce.e.1993.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bo.a.73.7	✓	32	3.2	odd	2
420.2.bo.a.157.5	yes	32	15.2	even	4
420.2.bo.a.313.5	yes	32	21.5	even	6
420.2.bo.a.397.7	yes	32	105.47	odd	12
1260.2.dq.c.73.4		32	1.1	even	1	trivial
1260.2.dq.c.397.4		32	35.12	even	12	inner
1260.2.dq.c.577.7		32	5.2	odd	4	inner
1260.2.dq.c.1153.7		32	7.5	odd	6	inner
2100.2.ce.e.157.4		32	15.8	even	4
2100.2.ce.e.493.2		32	15.14	odd	2
2100.2.ce.e.1657.2		32	105.68	odd	12
2100.2.ce.e.1993.4		32	105.89	even	6
2940.2.x.c.97.4		32	105.32	even	12
2940.2.x.c.97.15		32	105.17	odd	12
2940.2.x.c.1273.4		32	21.17	even	6
2940.2.x.c.1273.15		32	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.dq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0833091 - 2.23452i) q^{5} +(-1.70817 + 2.02043i) q^{7} +O(q^{10})\)	\(q+(0.0833091 - 2.23452i) q^{5} +(-1.70817 + 2.02043i) q^{7} +(-1.21556 + 2.10542i) q^{11} +(-0.728866 + 0.728866i) q^{13} +(7.33552 - 1.96555i) q^{17} +(1.84965 + 3.20369i) q^{19} +(-0.759994 + 2.83634i) q^{23} +(-4.98612 - 0.372311i) q^{25} -1.99120i q^{29} +(6.02262 + 3.47716i) q^{31} +(4.37238 + 3.98525i) q^{35} +(8.22068 + 2.20273i) q^{37} +1.08701i q^{41} +(5.91785 + 5.91785i) q^{43} +(1.28906 - 4.81085i) q^{47} +(-1.16431 - 6.90249i) q^{49} +(6.56972 - 1.76035i) q^{53} +(4.60332 + 2.89160i) q^{55} +(1.39403 - 2.41454i) q^{59} +(0.217574 - 0.125616i) q^{61} +(1.56794 + 1.68938i) q^{65} +(-2.08758 - 7.79096i) q^{67} -14.5737 q^{71} +(1.73216 + 6.46450i) q^{73} +(-2.17747 - 6.05238i) q^{77} +(9.54459 - 5.51057i) q^{79} +(-9.90994 + 9.90994i) q^{83} +(-3.78093 - 16.5551i) q^{85} +(5.81468 + 10.0713i) q^{89} +(-0.227598 - 2.71765i) q^{91} +(7.31279 - 3.86618i) q^{95} +(10.8833 + 10.8833i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{5}+O(q^{10}) \) 32 * q + 12 * q^5	\( 32 q + 12 q^{5} - 8 q^{11} - 16 q^{23} - 4 q^{25} + 24 q^{31} - 20 q^{35} + 20 q^{37} - 24 q^{43} - 12 q^{47} - 40 q^{53} - 24 q^{61} + 52 q^{65} + 16 q^{71} - 60 q^{73} + 84 q^{77} - 8 q^{85} + 40 q^{91} + 36 q^{95}+O(q^{100}) \) 32 * q + 12 * q^5 - 8 * q^11 - 16 * q^23 - 4 * q^25 + 24 * q^31 - 20 * q^35 + 20 * q^37 - 24 * q^43 - 12 * q^47 - 40 * q^53 - 24 * q^61 + 52 * q^65 + 16 * q^71 - 60 * q^73 + 84 * q^77 - 8 * q^85 + 40 * q^91 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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