LMFDB - Embedded newform 756.2.w.a.341.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(341,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 5]))

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

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

chi := DirichletCharacter("756.341");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.8
Root			$-0.544978 + 1.64408i$ of defining polynomial
Character	$\chi$	$=$	756.341
Dual form			756.2.w.a.521.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95741 + 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +O(q^{10})$	$q+(1.95741 + 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(3.19958 + 1.84728i) q^{11} +(0.480242 + 0.277268i) q^{13} +(-2.91916 - 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(1.96965 - 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(-3.53638 + 2.04173i) q^{29} +8.08443i q^{31} +(9.85583 - 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(-3.59234 + 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +2.82833 q^{47} +(-6.38563 - 2.86770i) q^{49} +(0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +8.91313 q^{59} +6.96680i q^{61} +2.17091i q^{65} +1.17480 q^{67} -6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(6.55234 - 7.25364i) q^{77} -3.94747 q^{79} +(-3.84674 - 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(2.71300 - 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +20.9041i q^{95} +(13.9874 - 8.07563i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85} - 21 q^{89} + 9 q^{91} - 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.95741	+	3.39033i	0.875381	+	1.51620i	0.856357	+	0.516385i	$0.172722\pi$
$5$	1.95741	+	3.39033i	0.875381	+	1.51620i	0.0190238	+	0.999819i	$0.493944\pi$
$6$		0			0
$7$	0.554241	−	2.58705i	0.209483	−	0.977812i
$7$	0.554241	−	2.58705i	0.209483	−	0.977812i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.19958	+	1.84728i	0.964710	+	0.556976i	0.897620	−	0.440771i	$-0.145295\pi$
$11$	3.19958	+	1.84728i	0.964710	+	0.556976i	0.0670908	+	0.997747i	$0.478628\pi$
$12$		0			0
$13$	0.480242	+	0.277268i	0.133195	+	0.0769002i	0.565117	−	0.825011i	$-0.308831\pi$
$13$	0.480242	+	0.277268i	0.133195	+	0.0769002i	−0.431922	+	0.901911i	$0.642164\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.91916	−	5.05613i	−0.708000	−	1.22629i	−0.965598	−	0.260040i	$-0.916264\pi$
$17$	−2.91916	−	5.05613i	−0.708000	−	1.22629i	0.257598	−	0.966252i	$-0.417069\pi$
$18$		0			0
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.925680	−	0.378307i	$-0.123494\pi$
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.135216	+	0.990816i	$0.456827\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.96965	−	1.13718i	0.410700	−	0.237118i	−0.280390	−	0.959886i	$-0.590464\pi$
$23$	1.96965	−	1.13718i	0.410700	−	0.237118i	0.691090	+	0.722768i	$0.257131\pi$
$24$		0			0
$25$	−5.16291	+	8.94242i	−1.03258	+	1.78848i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.53638	+	2.04173i	−0.656690	+	0.379140i	−0.791014	−	0.611797i	$-0.790447\pi$
$29$	−3.53638	+	2.04173i	−0.656690	+	0.379140i	0.134325	+	0.990937i	$0.457113\pi$
$30$		0			0
$31$			8.08443i			1.45201i	0.687691	+	0.726004i	$0.258624\pi$
$31$			8.08443i			1.45201i	−0.687691	+	0.726004i	$0.741376\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.85583	−	3.18485i	1.66594	−	0.538338i
$36$		0			0
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	−0.344322	−	0.938852i	$-0.611891\pi$
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	0.985230	−	0.171235i	$-0.0547756\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.59234	+	6.22212i	−0.561030	+	0.971732i	0.436377	+	0.899764i	$0.356261\pi$
$41$	−3.59234	+	6.22212i	−0.561030	+	0.971732i	−0.997407	+	0.0719684i	$0.977072\pi$
$42$		0			0
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	0.802789	−	0.596264i	$-0.203349\pi$
$43$	−0.754009	−	1.30598i	−0.114985	−	0.199160i	−0.917774	+	0.397103i	$0.870015\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.82833			0.412554			0.206277	−	0.978494i	$-0.433865\pi$
$47$	2.82833			0.412554			0.206277	+	0.978494i	$0.433865\pi$
$48$		0			0
$49$	−6.38563	−	2.86770i	−0.912233	−	0.409671i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	−0.497143	−	0.867669i	$-0.665617\pi$
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	0.502852	+	0.864373i	$0.332284\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.91313			1.16039			0.580195	−	0.814477i	$-0.302976\pi$
$59$	8.91313			1.16039			0.580195	+	0.814477i	$0.302976\pi$
$60$		0			0
$61$			6.96680i			0.892008i	0.895031	+	0.446004i	$0.147153\pi$
$61$			6.96680i			0.892008i	−0.895031	+	0.446004i	$0.852847\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			2.17091i			0.269268i
$66$		0			0
$67$	1.17480			0.143525			0.0717626	−	0.997422i	$-0.477138\pi$
$67$	1.17480			0.143525			0.0717626	+	0.997422i	$0.477138\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	6.71061i		−	0.796403i	−0.917298	−	0.398202i	$-0.869634\pi$
$71$		−	6.71061i		−	0.796403i	0.917298	−	0.398202i	$-0.130366\pi$
$72$		0			0
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	−0.691990	−	0.721907i	$-0.743266\pi$
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	0.279195	+	0.960234i	$0.409932\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.55234	−	7.25364i	0.746709	−	0.826628i
$78$		0			0
$79$	−3.94747			−0.444125			−0.222063	−	0.975032i	$-0.571279\pi$
$79$	−3.94747			−0.444125			−0.222063	+	0.975032i	$0.571279\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.84674	−	6.66275i	−0.422235	−	0.731332i	0.573923	−	0.818909i	$-0.305421\pi$
$83$	−3.84674	−	6.66275i	−0.422235	−	0.731332i	−0.996158	+	0.0875774i	$0.972087\pi$
$84$		0			0
$85$	11.4280	−	19.7938i	1.23954	−	2.14694i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.71300	−	4.69905i	0.287577	−	0.498099i	−0.685654	−	0.727928i	$-0.740483\pi$
$89$	2.71300	−	4.69905i	0.287577	−	0.498099i	0.973231	+	0.229829i	$0.0738168\pi$
$90$		0			0
$91$	0.983474	−	1.08874i	0.103096	−	0.114130i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			20.9041i			2.14471i
$96$		0			0
$97$	13.9874	−	8.07563i	1.42021	−	0.819956i	0.423890	−	0.905714i	$-0.360664\pi$
$97$	13.9874	−	8.07563i	1.42021	−	0.819956i	0.996316	+	0.0857571i	$0.0273309\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.811750	+	1.40599i	−0.0807722	+	0.139901i	−0.903582	−	0.428416i	$-0.859072\pi$
$101$	−0.811750	+	1.40599i	−0.0807722	+	0.139901i	0.822810	+	0.568317i	$0.192405\pi$
$102$		0			0
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	−0.516786	−	0.856114i	$-0.672872\pi$
$103$	−0.342653	+	0.197831i	−0.0337626	+	0.0194929i	0.483024	+	0.875607i	$0.339539\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	0.718101	−	0.695938i	$-0.245011\pi$
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	−0.243650	+	0.969863i	$0.578345\pi$
$108$		0			0
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	−0.983795	−	0.179294i	$-0.942619\pi$
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	0.336624	−	0.941639i	$-0.390715\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.13651	−	0.656162i	−0.106913	−	0.0617265i	0.445590	−	0.895237i	$-0.352994\pi$
$113$	−1.13651	−	0.656162i	−0.106913	−	0.0617265i	−0.552503	+	0.833511i	$0.686327\pi$
$114$		0			0
$115$	7.71082	+	4.45184i	0.719038	+	0.415137i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−14.6984	+	4.74969i	−1.34740	+	0.435403i
$120$		0			0
$121$	1.32489	+	2.29477i	0.120444	+	0.208615i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−20.8496			−1.86485
$126$		0			0
$127$	−17.3935			−1.54342			−0.771710	−	0.635975i	$-0.780598\pi$
$127$	−17.3935			−1.54342			−0.771710	+	0.635975i	$0.780598\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.45361	−	9.44593i	−0.476484	−	0.825295i	0.523153	−	0.852239i	$-0.324756\pi$
$131$	−5.45361	−	9.44593i	−0.476484	−	0.825295i	−0.999637	+	0.0269442i	$0.991422\pi$
$132$		0			0
$133$	9.47007	−	10.4836i	0.821159	−	0.909047i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.62547	−	4.40257i	−0.651488	−	0.376137i	0.137538	−	0.990496i	$-0.456081\pi$
$137$	−7.62547	−	4.40257i	−0.651488	−	0.376137i	−0.789026	+	0.614360i	$0.789414\pi$
$138$		0			0
$139$	−14.2352	−	8.21869i	−1.20741	−	0.697100i	−0.245220	−	0.969468i	$-0.578860\pi$
$139$	−14.2352	−	8.21869i	−1.20741	−	0.697100i	−0.962193	+	0.272367i	$0.912193\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.02438	+	1.77428i	0.0856631	+	0.148373i
$144$		0			0
$145$	−13.8443	−	7.99301i	−1.14971	−	0.663783i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−12.5814	+	7.26390i	−1.03071	+	0.595082i	−0.917188	−	0.398454i	$-0.869547\pi$
$149$	−12.5814	+	7.26390i	−1.03071	+	0.595082i	−0.113523	+	0.993535i	$0.536214\pi$
$150$		0			0
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	−0.957248	−	0.289268i	$-0.906588\pi$
$151$	−2.80307	+	4.85505i	−0.228110	+	0.395099i	0.729138	+	0.684367i	$0.239921\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−27.4089	+	15.8246i	−2.20154	+	1.27106i
$156$		0			0
$157$			17.8299i			1.42298i	0.702697	+	0.711489i	$0.251979\pi$
$157$			17.8299i			1.42298i	−0.702697	+	0.711489i	$0.748021\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.85027	−	5.72584i	−0.145822	−	0.451260i
$162$		0			0
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	−0.887737	−	0.460350i	$-0.847724\pi$
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	0.842544	+	0.538628i	$0.181057\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.95550	−	15.5114i	0.692997	−	1.20031i	−0.277854	−	0.960623i	$-0.589623\pi$
$167$	8.95550	−	15.5114i	0.692997	−	1.20031i	0.970851	−	0.239683i	$-0.0770435\pi$
$168$		0			0
$169$	−6.34625	−	10.9920i	−0.488173	−	0.845540i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.49629			−0.569932			−0.284966	−	0.958538i	$-0.591982\pi$
$173$	−7.49629			−0.569932			−0.284966	+	0.958538i	$0.591982\pi$
$174$		0			0
$175$	20.2730	+	18.3130i	1.53249	+	1.38433i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	−0.523153	−	0.852239i	$-0.675244\pi$
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	0.476484	+	0.879183i	$0.341911\pi$
$180$		0			0
$181$		−	5.07121i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$181$		−	5.07121i		−	0.376940i	0.982079	−	0.188470i	$-0.0603529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	30.5238			2.24416
$186$		0			0
$187$		−	21.5700i		−	1.57736i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	12.7022i		−	0.919101i	−0.888152	−	0.459551i	$-0.848011\pi$
$191$		−	12.7022i		−	0.919101i	0.888152	−	0.459551i	$-0.151989\pi$
$192$		0			0
$193$	−22.8153			−1.64228			−0.821140	−	0.570726i	$-0.806662\pi$
$193$	−22.8153			−1.64228			−0.821140	+	0.570726i	$0.806662\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	0.0311360i		−	0.00221835i	−0.999999	−	0.00110918i	$-0.999647\pi$
$197$		−	0.0311360i		−	0.00221835i	0.999999	−	0.00110918i	$-0.000353062\pi$
$198$		0			0
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.416146	−	0.909298i	$-0.363380\pi$
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.995548	+	0.0942556i	$0.0300471\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.32205	+	10.2804i	0.233162	+	0.721543i
$204$		0			0
$205$	−28.1268			−1.96446
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.86397	+	17.0849i	0.682305	+	1.18179i
$210$		0			0
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	−0.405154	−	0.914248i	$-0.632782\pi$
$211$	8.55841	−	14.8236i	0.589185	−	1.02050i	0.994339	−	0.106250i	$-0.0338845\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.95181	−	5.11268i	0.201312	−	0.348682i
$216$		0			0
$217$	20.9148	+	4.48072i	1.41979	+	0.304171i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	3.23755i		−	0.217781i
$222$		0			0
$223$	1.25230	−	0.723016i	0.0838602	−	0.0484167i	−0.457484	−	0.889218i	$-0.651249\pi$
$223$	1.25230	−	0.723016i	0.0838602	−	0.0484167i	0.541344	+	0.840801i	$0.317916\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.23596	−	3.87280i	0.148406	−	0.257047i	−0.782232	−	0.622987i	$-0.785919\pi$
$227$	2.23596	−	3.87280i	0.148406	−	0.257047i	0.930639	+	0.365940i	$0.119252\pi$
$228$		0			0
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	−0.424134	−	0.905599i	$-0.639421\pi$
$229$	2.24072	−	1.29368i	0.148071	−	0.0854888i	0.572205	+	0.820111i	$0.306088\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.0830679	−	0.996544i	$-0.526472\pi$
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.904566	+	0.426333i	$0.859805\pi$
$234$		0			0
$235$	5.53620	+	9.58898i	0.361142	+	0.625516i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.23642	−	2.44590i	−0.274031	−	0.158212i	0.356687	−	0.934224i	$-0.383906\pi$
$239$	−4.23642	−	2.44590i	−0.274031	−	0.158212i	−0.630718	+	0.776012i	$0.717240\pi$
$240$		0			0
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	0.709378	−	0.704828i	$-0.248976\pi$
$241$	7.04282	+	4.06618i	0.453668	+	0.261925i	−0.255710	+	0.966754i	$0.582309\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.77686	−	27.2627i	−0.177407	−	1.74175i
$246$		0			0
$247$	1.48053	+	2.56436i	0.0942041	+	0.163166i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	25.9341			1.63694			0.818472	−	0.574546i	$-0.194821\pi$
$251$	25.9341			1.63694			0.818472	+	0.574546i	$0.194821\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.4115	−	26.6935i	−0.961344	−	1.66510i	−0.719131	−	0.694874i	$-0.755460\pi$
$257$	−15.4115	−	26.6935i	−0.961344	−	1.66510i	−0.242213	−	0.970223i	$-0.577873\pi$
$258$		0			0
$259$	−15.3081	−	13.8280i	−0.951196	−	0.859233i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	15.6625	+	9.04276i	0.965792	+	0.557600i	0.897951	−	0.440096i	$-0.145056\pi$
$263$	15.6625	+	9.04276i	0.965792	+	0.557600i	0.0678413	+	0.997696i	$0.478389\pi$
$264$		0			0
$265$	0.162723	+	0.0939479i	0.00999597	+	0.00577117i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.8203	+	18.7413i	0.659725	+	1.14268i	0.980687	+	0.195585i	$0.0626607\pi$
$269$	10.8203	+	18.7413i	0.659725	+	1.14268i	−0.320961	+	0.947092i	$0.604006\pi$
$270$		0			0
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	0.0757430	−	0.997127i	$-0.475867\pi$
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	−0.825666	+	0.564159i	$0.809200\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−33.0383	+	19.0747i	−1.99229	+	1.15025i
$276$		0			0
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	−0.967424	−	0.253160i	$-0.918530\pi$
$277$	−4.40164	+	7.62386i	−0.264469	+	0.458073i	0.702956	+	0.711234i	$0.251863\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.6889	−	9.63537i	0.995579	−	0.574798i	0.0886417	−	0.996064i	$-0.471747\pi$
$281$	16.6889	−	9.63537i	0.995579	−	0.574798i	0.906937	+	0.421266i	$0.138414\pi$
$282$		0			0
$283$			9.61660i			0.571647i	0.958282	+	0.285824i	$0.0922672\pi$
$283$			9.61660i			0.571647i	−0.958282	+	0.285824i	$0.907733\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.1059	+	12.7421i	0.832645	+	0.752144i
$288$		0			0
$289$	−8.54297	+	14.7969i	−0.502528	+	0.870404i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.22598	+	2.12346i	−0.0716225	+	0.124054i	−0.899613	−	0.436689i	$-0.856151\pi$
$293$	−1.22598	+	2.12346i	−0.0716225	+	0.124054i	0.827990	+	0.560743i	$0.189484\pi$
$294$		0			0
$295$	17.4467	+	30.2185i	1.01578	+	1.75939i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.26121			0.0729376
$300$		0			0
$301$	−3.79654	+	1.22683i	−0.218829	+	0.0707132i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−23.6198	+	13.6369i	−1.35247	+	0.780846i
$306$		0			0
$307$		−	10.6839i		−	0.609760i	−0.952391	−	0.304880i	$-0.901384\pi$
$307$		−	10.6839i		−	0.609760i	0.952391	−	0.304880i	$-0.0986163\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	20.7665			1.17756			0.588780	−	0.808293i	$-0.299608\pi$
$311$	20.7665			1.17756			0.588780	+	0.808293i	$0.299608\pi$
$312$		0			0
$313$			3.93117i			0.222203i	0.993809	+	0.111101i	$0.0354378\pi$
$313$			3.93117i			0.222203i	−0.993809	+	0.111101i	$0.964562\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			2.29057i			0.128651i	0.997929	+	0.0643256i	$0.0204896\pi$
$317$			2.29057i			0.128651i	−0.997929	+	0.0643256i	$0.979510\pi$
$318$		0			0
$319$	−15.0866			−0.844687
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	31.1750i		−	1.73462i
$324$		0			0
$325$	−4.95889	+	2.86302i	−0.275070	+	0.158812i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.56757	−	7.31702i	0.0864232	−	0.403400i
$330$		0			0
$331$	6.93577			0.381224			0.190612	−	0.981665i	$-0.438953\pi$
$331$	6.93577			0.381224			0.190612	+	0.981665i	$0.438953\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.29957	+	3.98298i	0.125639	+	0.217613i
$336$		0			0
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	0.476827	+	0.878997i	$0.341787\pi$
$337$	−9.59771	+	16.6237i	−0.522821	+	0.905552i	−0.999647	+	0.0265545i	$0.991546\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.9342	+	25.8668i	−0.808733	+	1.40077i
$342$		0			0
$343$	−10.9580	+	14.9305i	−0.591679	+	0.806174i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			8.49036i			0.455786i	0.973686	+	0.227893i	$0.0731837\pi$
$347$			8.49036i			0.455786i	−0.973686	+	0.227893i	$0.926816\pi$
$348$		0			0
$349$	−16.5478	+	9.55386i	−0.885782	+	0.511407i	−0.872560	−	0.488506i	$-0.837542\pi$
$349$	−16.5478	+	9.55386i	−0.885782	+	0.511407i	−0.0132216	+	0.999913i	$0.504209\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.82951	+	11.8291i	−0.363498	+	0.629597i	−0.988534	−	0.150999i	$-0.951751\pi$
$353$	−6.82951	+	11.8291i	−0.363498	+	0.629597i	0.625036	+	0.780596i	$0.285084\pi$
$354$		0			0
$355$	22.7512	−	13.1354i	1.20751	−	0.697156i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	0.838520	−	0.544870i	$-0.183421\pi$
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	−0.0526113	+	0.998615i	$0.516754\pi$
$360$		0			0
$361$	4.75635	+	8.23824i	0.250334	+	0.433592i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−13.8073	−	7.97162i	−0.722705	−	0.417254i
$366$		0			0
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	0.830056	−	0.557680i	$-0.188309\pi$
$367$	14.6001	+	8.42936i	0.762118	+	0.440009i	−0.0679376	+	0.997690i	$0.521642\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0390466	−	0.120833i	−0.00202720	−	0.00627335i
$372$		0			0
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	0.883683	−	0.468086i	$-0.155056\pi$
$373$	0.704288	+	1.21986i	0.0364667	+	0.0631621i	−0.847216	+	0.531248i	$0.821723\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.26442			−0.116624
$378$		0			0
$379$	−0.598572			−0.0307466			−0.0153733	−	0.999882i	$-0.504894\pi$
$379$	−0.598572			−0.0307466			−0.0153733	+	0.999882i	$0.504894\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.26039	+	7.37921i	0.217696	+	0.377060i	0.954103	−	0.299478i	$-0.0968127\pi$
$383$	4.26039	+	7.37921i	0.217696	+	0.377060i	−0.736407	+	0.676538i	$0.763479\pi$
$384$		0			0
$385$	37.4179	+	8.01628i	1.90699	+	0.408548i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	29.9624	+	17.2988i	1.51915	+	0.877084i	0.999746	+	0.0225587i	$0.00718126\pi$
$389$	29.9624	+	17.2988i	1.51915	+	0.877084i	0.519409	+	0.854526i	$0.326152\pi$
$390$		0			0
$391$	−11.4994	−	6.63920i	−0.581551	−	0.335759i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.72683	−	13.3833i	−0.388779	−	0.673385i
$396$		0			0
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.994712	−	0.102699i	$-0.0327478\pi$
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.408416	+	0.912796i	$0.366081\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.3473	+	6.55139i	−0.566659	+	0.327161i	−0.755814	−	0.654787i	$-0.772758\pi$
$401$	−11.3473	+	6.55139i	−0.566659	+	0.327161i	0.189155	+	0.981947i	$0.439425\pi$
$402$		0			0
$403$	−2.24155	+	3.88248i	−0.111660	+	0.193400i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.9471	−	14.4032i	1.23658	−	0.713941i
$408$		0			0
$409$		−	37.3538i		−	1.84703i	−0.383568	−	0.923513i	$-0.625305\pi$
$409$		−	37.3538i		−	1.84703i	0.383568	−	0.923513i	$-0.374695\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.94002	−	23.0587i	0.243082	−	1.13464i
$414$		0			0
$415$	15.0593	−	26.0835i	0.739232	−	1.28039i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.1954	+	24.5871i	−0.693490	+	1.20116i	0.277198	+	0.960813i	$0.410594\pi$
$419$	−14.1954	+	24.5871i	−0.693490	+	1.20116i	−0.970687	+	0.240346i	$0.922739\pi$
$420$		0			0
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	−0.885707	−	0.464245i	$-0.846326\pi$
$421$	−17.3359	−	30.0267i	−0.844901	−	1.46341i	0.0408054	−	0.999167i	$-0.487008\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	60.2854			2.92427
$426$		0			0
$427$	18.0235	+	3.86129i	0.872216	+	0.186861i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	−0.782713	−	0.622383i	$-0.786165\pi$
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	0.147643	+	0.989041i	$0.452831\pi$
$432$		0			0
$433$			3.97041i			0.190806i	0.995439	+	0.0954028i	$0.0304139\pi$
$433$			3.97041i			0.190806i	−0.995439	+	0.0954028i	$0.969586\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.1444			0.580947
$438$		0			0
$439$			9.49060i			0.452962i	0.974016	+	0.226481i	$0.0727221\pi$
$439$			9.49060i			0.452962i	−0.974016	+	0.226481i	$0.927278\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	32.7883i		−	1.55782i	−0.627135	−	0.778910i	$-0.715773\pi$
$443$		−	32.7883i		−	1.55782i	0.627135	−	0.778910i	$-0.284227\pi$
$444$		0			0
$445$	21.2418			1.00696
$446$		0			0
$447$		0			0
$448$		0			0
$449$			0.658896i			0.0310952i	0.999879	+	0.0155476i	$0.00494916\pi$
$449$			0.658896i			0.0310952i	−0.999879	+	0.0155476i	$0.995051\pi$
$450$		0			0
$451$	−22.9880	+	13.2721i	−1.08246	+	0.624960i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.61624	+	1.20321i	0.263293	+	0.0564071i
$456$		0			0
$457$	15.8903			0.743316			0.371658	−	0.928370i	$-0.378789\pi$
$457$	15.8903			0.743316			0.371658	+	0.928370i	$0.378789\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	9.81626	+	17.0023i	0.457189	+	0.791874i	0.998811	−	0.0487477i	$-0.0155230\pi$
$461$	9.81626	+	17.0023i	0.457189	+	0.791874i	−0.541622	+	0.840622i	$0.682190\pi$
$462$		0			0
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	−0.851743	−	0.523960i	$-0.824454\pi$
$463$	0.600159	−	1.03951i	0.0278918	−	0.0483099i	0.879634	+	0.475651i	$0.157787\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.2809	+	33.3955i	−0.892213	+	1.54536i	−0.0549972	+	0.998487i	$0.517515\pi$
$467$	−19.2809	+	33.3955i	−0.892213	+	1.54536i	−0.837216	+	0.546872i	$0.815818\pi$
$468$		0			0
$469$	0.651124	−	3.03927i	0.0300661	−	0.140341i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	5.57146i		−	0.256176i
$474$		0			0
$475$	−47.7501	+	27.5685i	−2.19093	+	1.26493i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.61289	−	6.25771i	0.165077	−	0.285922i	−0.771606	−	0.636101i	$-0.780546\pi$
$479$	3.61289	−	6.25771i	0.165077	−	0.285922i	0.936683	+	0.350179i	$0.113879\pi$
$480$		0			0
$481$	3.74444	−	2.16185i	0.170732	−	0.0985720i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	54.7582	+	31.6147i	2.48644	+	1.43555i
$486$		0			0
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	0.954845	−	0.297104i	$-0.0960207\pi$
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	−0.734722	+	0.678368i	$0.762687\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.2480	−	9.95814i	−0.778392	−	0.449405i	0.0574682	−	0.998347i	$-0.481697\pi$
$491$	−17.2480	−	9.95814i	−0.778392	−	0.449405i	−0.835860	+	0.548943i	$0.815031\pi$
$492$		0			0
$493$	20.6465	+	11.9203i	0.929872	+	0.536862i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−17.3607	−	3.71930i	−0.778733	−	0.166833i
$498$		0			0
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	−0.937770	−	0.347258i	$-0.887113\pi$
$499$	−17.1920	−	29.7774i	−0.769619	−	1.33302i	0.168150	−	0.985761i	$-0.446221\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.22542			−0.0546388			−0.0273194	−	0.999627i	$-0.508697\pi$
$503$	−1.22542			−0.0546388			−0.0273194	+	0.999627i	$0.508697\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.05078	−	8.74820i	−0.223872	−	0.387757i	0.732109	−	0.681188i	$-0.238536\pi$
$509$	−5.05078	−	8.74820i	−0.223872	−	0.387757i	−0.955980	+	0.293431i	$0.905203\pi$
$510$		0			0
$511$	3.31316	+	10.2529i	0.146565	+	0.453561i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.34143	−	0.774473i	−0.0591103	−	0.0341274i
$516$		0			0
$517$	9.04947	+	5.22471i	0.397995	+	0.229783i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.5390	−	18.2541i	−0.461723	−	0.799728i	0.537324	−	0.843376i	$-0.319435\pi$
$521$	−10.5390	−	18.2541i	−0.461723	−	0.799728i	−0.999047	+	0.0436480i	$0.986102\pi$
$522$		0			0
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	0.824451	−	0.565934i	$-0.191484\pi$
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	−0.0778877	+	0.996962i	$0.524818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	40.8760	−	23.5997i	1.78058	−	1.02802i
$528$		0			0
$529$	−8.91366	+	15.4389i	−0.387550	+	0.671257i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.45039	+	1.99208i	−0.149453	+	0.0862866i
$534$		0			0
$535$			22.1853i			0.959154i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.1339	−	20.9715i	−0.651864	−	0.903306i
$540$		0			0
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	−0.942438	−	0.334381i	$-0.891473\pi$
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	0.760802	+	0.648984i	$0.224806\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	26.4511	−	45.8147i	1.13304	−	1.96249i
$546$		0			0
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	0.766948	−	0.641709i	$-0.221774\pi$
$547$	−4.02889	−	6.97824i	−0.172263	−	0.298368i	−0.939211	+	0.343342i	$0.888441\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.8046			−0.928906
$552$		0			0
$553$	−2.18785	+	10.2123i	−0.0930369	+	0.434271i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	−0.0613279	−	0.998118i	$-0.519534\pi$
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	0.833731	+	0.552170i	$0.186200\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−41.2821			−1.73983			−0.869916	−	0.493200i	$-0.835827\pi$
$563$	−41.2821			−1.73983			−0.869916	+	0.493200i	$0.835827\pi$
$564$		0			0
$565$		−	5.13751i		−	0.216137i
$566$		0			0
$567$		0			0
$568$		0			0
$569$			36.1064i			1.51366i	0.653612	+	0.756829i	$0.273253\pi$
$569$			36.1064i			1.51366i	−0.653612	+	0.756829i	$0.726747\pi$
$570$		0			0
$571$	−19.2422			−0.805262			−0.402631	−	0.915362i	$-0.631904\pi$
$571$	−19.2422			−0.805262			−0.402631	+	0.915362i	$0.631904\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			23.4846i			0.979375i
$576$		0			0
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.929406	−	0.369060i	$-0.879680\pi$
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.145088	+	0.989419i	$0.546346\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.3689	+	6.25893i	−0.803556	+	0.259664i
$582$		0			0
$583$	0.177324			0.00734402
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.72218	−	8.17905i	−0.194905	−	0.337586i	0.751964	−	0.659204i	$-0.229107\pi$
$587$	−4.72218	−	8.17905i	−0.194905	−	0.337586i	−0.946869	+	0.321618i	$0.895773\pi$
$588$		0			0
$589$	−21.5843	+	37.3852i	−0.889367	+	1.54043i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.4176	+	21.5079i	−0.509929	+	0.883223i	0.490005	+	0.871720i	$0.336995\pi$
$593$	−12.4176	+	21.5079i	−0.509929	+	0.883223i	−0.999934	+	0.0115033i	$0.996338\pi$
$594$		0			0
$595$	−44.8738	−	40.5353i	−1.83965	−	1.66179i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			11.8995i			0.486199i	0.970001	+	0.243100i	$0.0781642\pi$
$599$			11.8995i			0.486199i	−0.970001	+	0.243100i	$0.921836\pi$
$600$		0			0
$601$	22.1276	−	12.7754i	0.902604	−	0.521118i	0.0245596	−	0.999698i	$-0.492182\pi$
$601$	22.1276	−	12.7754i	0.902604	−	0.521118i	0.878044	+	0.478580i	$0.158848\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.18669	+	8.98361i	−0.210869	+	0.365236i
$606$		0			0
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	−0.841259	−	0.540632i	$-0.818185\pi$
$607$	−19.5544	+	11.2897i	−0.793687	+	0.458235i	0.0475718	+	0.998868i	$0.484852\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.35828	+	0.784204i	0.0549502	+	0.0317255i
$612$		0			0
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	0.537414	−	0.843319i	$-0.319401\pi$
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	−0.999042	+	0.0437549i	$0.986068\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.78792	−	1.03226i	−0.0719791	−	0.0415572i	0.463578	−	0.886056i	$-0.346565\pi$
$617$	−1.78792	−	1.03226i	−0.0719791	−	0.0415572i	−0.535558	+	0.844499i	$0.679899\pi$
$618$		0			0
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.189354	−	0.981909i	$-0.560639\pi$
$619$	−28.2233	−	16.2947i	−1.13439	−	0.654940i	−0.945035	+	0.326969i	$0.893973\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−10.6530	−	9.62307i	−0.426804	−	0.385540i
$624$		0			0
$625$	−14.9967	−	25.9751i	−0.599870	−	1.03901i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.5213			−1.81505
$630$		0			0
$631$	38.4706			1.53149			0.765744	−	0.643145i	$-0.222371\pi$
$631$	38.4706			1.53149			0.765744	+	0.643145i	$0.222371\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−34.0461	−	58.9696i	−1.35108	−	2.34014i
$636$		0			0
$637$	−2.27153	−	3.14772i	−0.0900012	−	0.124717i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−41.3645	−	23.8818i	−1.63380	−	0.943274i	−0.982907	−	0.184104i	$-0.941062\pi$
$641$	−41.3645	−	23.8818i	−1.63380	−	0.943274i	−0.650892	−	0.759170i	$-0.725605\pi$
$642$		0			0
$643$	29.2346	+	16.8786i	1.15290	+	0.665626i	0.949592	−	0.313489i	$-0.101498\pi$
$643$	29.2346	+	16.8786i	1.15290	+	0.665626i	0.203306	+	0.979115i	$0.434831\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.536008	−	0.928393i	−0.0210727	−	0.0364989i	0.855297	−	0.518138i	$-0.173375\pi$
$647$	−0.536008	−	0.928393i	−0.0210727	−	0.0364989i	−0.876369	+	0.481640i	$0.840041\pi$
$648$		0			0
$649$	28.5183	+	16.4650i	1.11944	+	0.646309i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.8503	+	16.6567i	−1.12900	+	0.651828i	−0.943683	−	0.330851i	$-0.892664\pi$
$653$	−28.8503	+	16.6567i	−1.12900	+	0.651828i	−0.185317	+	0.982679i	$0.559331\pi$
$654$		0			0
$655$	21.3499	−	36.9791i	0.834210	−	1.44489i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.41890	−	4.86065i	0.327954	−	0.189344i	−0.326979	−	0.945032i	$-0.606031\pi$
$659$	8.41890	−	4.86065i	0.327954	−	0.189344i	0.654932	+	0.755688i	$0.272697\pi$
$660$		0			0
$661$			17.0729i			0.664060i	0.943269	+	0.332030i	$0.107734\pi$
$661$			17.0729i			0.664060i	−0.943269	+	0.332030i	$0.892266\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	54.0799	+	11.5859i	2.09713	+	0.449282i
$666$		0			0
$667$	−4.64362	+	8.04298i	−0.179802	+	0.311426i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−12.8696	+	22.2909i	−0.496827	+	0.860529i
$672$		0			0
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	−0.966039	−	0.258398i	$-0.916805\pi$
$673$	−18.3359	−	31.7588i	−0.706798	−	1.22421i	0.259240	−	0.965813i	$-0.416528\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	40.3538			1.55092			0.775461	−	0.631395i	$-0.217517\pi$
$677$	40.3538			1.55092			0.775461	+	0.631395i	$0.217517\pi$
$678$		0			0
$679$	−13.1397	−	40.6619i	−0.504254	−	1.56046i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	−0.649236	−	0.760587i	$-0.724911\pi$
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	0.334070	+	0.942548i	$0.391578\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.0266155			0.00101397
$690$		0			0
$691$		−	7.70784i		−	0.293220i	−0.989194	−	0.146610i	$-0.953164\pi$
$691$		−	7.70784i		−	0.293220i	0.989194	−	0.146610i	$-0.0468363\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	64.3494i		−	2.44091i
$696$		0			0
$697$	41.9465			1.58884
$698$		0			0
$699$		0			0
$700$		0			0
$701$			15.6388i			0.590671i	0.955394	+	0.295336i	$0.0954314\pi$
$701$			15.6388i			0.590671i	−0.955394	+	0.295336i	$0.904569\pi$
$702$		0			0
$703$	36.0559	−	20.8169i	1.35988	−	0.785124i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.18747	+	2.87930i	0.119877	+	0.108287i
$708$		0			0
$709$	13.4405			0.504769			0.252384	−	0.967627i	$-0.418785\pi$
$709$	13.4405			0.504769			0.252384	+	0.967627i	$0.418785\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.19343	+	15.9235i	0.344297	+	0.596339i
$714$		0			0
$715$	−4.01027	+	6.94599i	−0.149976	+	0.259765i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.0309	+	34.6946i	−0.747027	+	1.29389i	0.202214	+	0.979341i	$0.435186\pi$
$719$	−20.0309	+	34.6946i	−0.747027	+	1.29389i	−0.949242	+	0.314548i	$0.898147\pi$
$720$		0			0
$721$	0.321886	+	0.996107i	0.0119877	+	0.0370970i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	42.1651i		−	1.56597i
$726$		0			0
$727$	43.2091	−	24.9468i	1.60254	−	0.925225i	0.611560	−	0.791198i	$-0.290542\pi$
$727$	43.2091	−	24.9468i	1.60254	−	0.925225i	0.990978	−	0.134027i	$-0.0427910\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.40214	+	7.62473i	−0.162819	+	0.282011i
$732$		0			0
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	−0.671794	−	0.740738i	$-0.734476\pi$
$733$	−9.91430	+	5.72402i	−0.366193	+	0.211422i	0.305601	+	0.952160i	$0.401143\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.75888	+	2.17019i	0.138460	+	0.0799400i
$738$		0			0
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	0.936362	−	0.351036i	$-0.114170\pi$
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	−0.772187	+	0.635396i	$0.780837\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	45.8621	+	26.4785i	1.68252	+	0.971403i	0.959979	+	0.280074i	$0.0903589\pi$
$743$	45.8621	+	26.4785i	1.68252	+	0.971403i	0.722540	+	0.691329i	$0.242974\pi$
$744$		0			0
$745$	−49.2541	−	28.4369i	−1.80453	−	1.04185i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	10.0505	−	11.1262i	0.367237	−	0.406542i
$750$		0			0
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	0.999806	−	0.0196744i	$-0.00626295\pi$
$751$	13.2326	+	22.9195i	0.482865	+	0.836346i	−0.516942	+	0.856021i	$0.672930\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.9470			−0.798733
$756$		0			0
$757$	8.46749			0.307756			0.153878	−	0.988090i	$-0.450824\pi$
$757$	8.46749			0.307756			0.153878	+	0.988090i	$0.450824\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.9968	+	46.7599i	0.978635	+	1.69505i	0.667377	+	0.744720i	$0.267417\pi$
$761$	26.9968	+	46.7599i	0.978635	+	1.69505i	0.311258	+	0.950325i	$0.399250\pi$
$762$		0			0
$763$	−34.0208	+	10.9936i	−1.23163	+	0.397995i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.28046	+	2.47132i	0.154558	+	0.0892343i
$768$		0			0
$769$	30.1912	+	17.4309i	1.08872	+	0.628575i	0.933236	−	0.359263i	$-0.116972\pi$
$769$	30.1912	+	17.4309i	1.08872	+	0.628575i	0.155487	+	0.987838i	$0.450305\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.06375	+	1.84246i	0.0382603	+	0.0662688i	0.884521	−	0.466499i	$-0.154485\pi$
$773$	1.06375	+	1.84246i	0.0382603	+	0.0662688i	−0.846261	+	0.532768i	$0.821152\pi$
$774$		0			0
$775$	−72.2944	−	41.7392i	−2.59689	−	1.49932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−33.2244	+	19.1821i	−1.19039	+	0.687272i
$780$		0			0
$781$	12.3964	−	21.4712i	0.443577	−	0.768298i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−60.4492	+	34.9004i	−2.15752	+	1.24565i
$786$		0			0
$787$		−	28.3429i		−	1.01032i	−0.863027	−	0.505158i	$-0.831434\pi$
$787$		−	28.3429i		−	1.01032i	0.863027	−	0.505158i	$-0.168566\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.32742	+	2.57652i	−0.0827535	+	0.0916106i
$792$		0			0
$793$	−1.93167	+	3.34575i	−0.0685956	+	0.118811i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.9123	−	32.7570i	0.669907	−	1.16031i	−0.308022	−	0.951379i	$-0.599667\pi$
$797$	18.9123	−	32.7570i	0.669907	−	1.16031i	0.977930	−	0.208935i	$-0.0669996\pi$
$798$		0			0
$799$	−8.25634	−	14.3004i	−0.292088	−	0.505912i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.0462			−0.530970
$804$		0			0
$805$	15.7908	−	17.4809i	0.556552	−	0.616120i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.992143	−	0.125109i	$-0.960072\pi$
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.387724	+	0.921776i	$0.626739\pi$
$810$		0			0
$811$		−	5.45145i		−	0.191426i	−0.995409	−	0.0957132i	$-0.969487\pi$
$811$		−	5.45145i		−	0.191426i	0.995409	−	0.0957132i	$-0.0305132\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−4.51766			−0.158247
$816$		0			0
$817$		−	8.05240i		−	0.281718i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	49.3196i		−	1.72127i	−0.509225	−	0.860634i	$-0.670068\pi$
$821$		−	49.3196i		−	1.72127i	0.509225	−	0.860634i	$-0.329932\pi$
$822$		0			0
$823$	−23.6992			−0.826101			−0.413050	−	0.910708i	$-0.635537\pi$
$823$	−23.6992			−0.826101			−0.413050	+	0.910708i	$0.635537\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	19.9706i		−	0.694445i	−0.937783	−	0.347222i	$-0.887125\pi$
$827$		−	19.9706i		−	0.694445i	0.937783	−	0.347222i	$-0.112875\pi$
$828$		0			0
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	−0.713936	−	0.700211i	$-0.753089\pi$
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	0.249433	+	0.968392i	$0.419756\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.14124	+	40.6579i	0.143485	+	1.40871i
$834$		0			0
$835$	70.1183			2.42654
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.53910	+	9.59401i	0.191231	+	0.331222i	0.945658	−	0.325162i	$-0.105419\pi$
$839$	5.53910	+	9.59401i	0.191231	+	0.331222i	−0.754427	+	0.656383i	$0.772085\pi$
$840$		0			0
$841$	−6.16267	+	10.6741i	−0.212506	+	0.368071i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.8444	−	43.0318i	0.854674	−	1.48034i
$846$		0			0
$847$	6.67098	−	2.15569i	0.229218	−	0.0740703i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	17.7331i		−	0.607883i
$852$		0			0
$853$	−42.1706	+	24.3472i	−1.44389	+	0.833633i	−0.998107	−	0.0615058i	$-0.980410\pi$
$853$	−42.1706	+	24.3472i	−1.44389	+	0.833633i	−0.445788	+	0.895139i	$0.647076\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.39130	+	14.5342i	−0.286641	+	0.496477i	−0.973006	−	0.230780i	$-0.925872\pi$
$857$	−8.39130	+	14.5342i	−0.286641	+	0.496477i	0.686365	+	0.727258i	$0.259205\pi$
$858$		0			0
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	−0.823058	−	0.567957i	$-0.807734\pi$
$859$	−21.7682	+	12.5679i	−0.742722	+	0.428811i	0.0803361	+	0.996768i	$0.474401\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	0.396685	−	0.917955i	$-0.370161\pi$
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	−0.596630	+	0.802516i	$0.703494\pi$
$864$		0			0
$865$	−14.6733	−	25.4149i	−0.498907	−	0.864133i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.6303	−	7.29209i	−0.428452	−	0.247367i
$870$		0			0
$871$	0.564190	+	0.325735i	0.0191168	+	0.0110371i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.5557	+	53.9390i	−0.390655	+	1.82347i
$876$		0			0
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	0.953278	+	0.302093i	$0.0976854\pi$
$877$	21.8630	+	37.8678i	0.738260	+	1.27870i	−0.215019	+	0.976610i	$0.568981\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	27.5307			0.927531			0.463766	−	0.885958i	$-0.346498\pi$
$881$	27.5307			0.927531			0.463766	+	0.885958i	$0.346498\pi$
$882$		0			0
$883$	5.56040			0.187122			0.0935612	−	0.995614i	$-0.470175\pi$
$883$	5.56040			0.187122			0.0935612	+	0.995614i	$0.470175\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.3092	−	21.3202i	−0.413303	−	0.715862i	0.581945	−	0.813228i	$-0.302292\pi$
$887$	−12.3092	−	21.3202i	−0.413303	−	0.715862i	−0.995249	+	0.0973655i	$0.968958\pi$
$888$		0			0
$889$	−9.64017	+	44.9977i	−0.323321	+	1.50917i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.0792	+	7.55125i	0.437677	+	0.252693i
$894$		0			0
$895$	−2.44434	−	1.41124i	−0.0817054	−	0.0471726i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.5062	−	28.5896i	−0.550514	−	0.953518i
$900$		0			0
$901$	−0.242674	−	0.140108i	−0.00808465	−	0.00466767i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	17.1931	−	9.92644i	0.571518	−	0.329966i
$906$		0			0
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	−0.770065	−	0.637966i	$-0.779776\pi$
$907$	5.04337	−	8.73537i	0.167462	−	0.290053i	0.937527	+	0.347913i	$0.113109\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.5808	+	13.6144i	−0.781267	+	0.451065i	−0.836879	−	0.547388i	$-0.815622\pi$
$911$	−23.5808	+	13.6144i	−0.781267	+	0.451065i	0.0556121	+	0.998452i	$0.482289\pi$
$912$		0			0
$913$		−	28.4240i		−	0.940698i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.4597	+	8.87343i	−0.906799	+	0.293026i
$918$		0			0
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	0.327183	+	0.944961i	$0.393901\pi$
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	−0.981952	+	0.189132i	$0.939433\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.86064	−	3.22272i	0.0612436	−	0.106077i
$924$		0			0
$925$	40.2552	+	69.7240i	1.32358	+	2.29251i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.284567			0.00933633			0.00466816	−	0.999989i	$-0.498514\pi$
$929$	0.284567			0.00933633			0.00466816	+	0.999989i	$0.498514\pi$
$930$		0			0
$931$	−21.8730	−	30.3100i	−0.716858	−	0.993369i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	73.1295	−	42.2214i	2.39159	−	1.38079i
$936$		0			0
$937$			21.7298i			0.709881i	0.934889	+	0.354940i	$0.115499\pi$
$937$			21.7298i			0.709881i	−0.934889	+	0.354940i	$0.884501\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.2848			0.367875			0.183938	−	0.982938i	$-0.441116\pi$
$941$	11.2848			0.367875			0.183938	+	0.982938i	$0.441116\pi$
$942$		0			0
$943$			16.3405i			0.532121i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			22.7131i			0.738077i	0.929414	+	0.369039i	$0.120313\pi$
$947$			22.7131i			0.738077i	−0.929414	+	0.369039i	$0.879687\pi$
$948$		0			0
$949$	−2.25836			−0.0733096
$950$		0			0
$951$		0			0
$952$		0			0
$953$			16.5638i			0.536554i	0.963342	+	0.268277i	$0.0864543\pi$
$953$			16.5638i			0.536554i	−0.963342	+	0.268277i	$0.913546\pi$
$954$		0			0
$955$	43.0648	−	24.8635i	1.39354	−	0.804563i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−15.6160	+	17.2874i	−0.504267	+	0.558239i
$960$		0			0
$961$	−34.3581			−1.10832
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−44.6589	−	77.3515i	−1.43762	−	2.49003i
$966$		0			0
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	−0.699039	−	0.715084i	$-0.746388\pi$
$967$	8.38867	−	14.5296i	0.269762	−	0.467241i	0.968800	+	0.247843i	$0.0797218\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.6820	−	27.1620i	0.503259	−	0.871670i	−0.496734	−	0.867903i	$-0.665468\pi$
$971$	15.6820	−	27.1620i	0.503259	−	0.871670i	0.999993	−	0.00376705i	$-0.00119909\pi$
$972$		0			0
$973$	−29.1519	+	32.2720i	−0.934566	+	1.03459i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	56.6904i		−	1.81369i	−0.421469	−	0.906843i	$-0.638485\pi$
$977$		−	56.6904i		−	1.81369i	0.421469	−	0.906843i	$-0.361515\pi$
$978$		0			0
$979$	17.3609	−	10.0233i	0.554858	−	0.320347i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.9204	+	34.5032i	−0.635362	+	1.10048i	0.351076	+	0.936347i	$0.385816\pi$
$983$	−19.9204	+	34.5032i	−0.635362	+	1.10048i	−0.986438	+	0.164133i	$0.947517\pi$
$984$		0			0
$985$	0.105562	−	0.0609460i	0.00336347	−	0.00194190i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.97026	−	1.71488i	−0.0944489	−	0.0545301i
$990$		0			0
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.590247	+	0.807223i	$0.299030\pi$
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.403952	+	0.914780i	$0.367636\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	77.9613	+	45.0110i	2.47154	+	1.42694i
$996$		0			0
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.968497	−	0.249025i	$-0.0801102\pi$
$997$	39.0613	+	22.5520i	1.23708	+	0.714230i	0.268586	+	0.963256i	$0.413444\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.w.a.341.8		16
3.2	odd	2		252.2.w.a.5.8	✓	16
4.3	odd	2		3024.2.ca.d.2609.8		16
7.2	even	3		5292.2.x.a.881.8		16
7.3	odd	6		756.2.bm.a.17.8		16
7.4	even	3		5292.2.bm.a.2285.1		16
7.5	odd	6		5292.2.x.b.881.1		16
7.6	odd	2		5292.2.w.b.1097.1		16
9.2	odd	6		756.2.bm.a.89.8		16
9.4	even	3		2268.2.t.a.2105.8		16
9.5	odd	6		2268.2.t.b.2105.1		16
9.7	even	3		252.2.bm.a.173.6	yes	16
12.11	even	2		1008.2.ca.d.257.1		16
21.2	odd	6		1764.2.x.a.293.3		16
21.5	even	6		1764.2.x.b.293.6		16
21.11	odd	6		1764.2.bm.a.1697.3		16
21.17	even	6		252.2.bm.a.185.6	yes	16
21.20	even	2		1764.2.w.b.509.1		16
28.3	even	6		3024.2.df.d.17.8		16
36.7	odd	6		1008.2.df.d.929.3		16
36.11	even	6		3024.2.df.d.1601.8		16
63.2	odd	6		5292.2.x.b.4409.1		16
63.11	odd	6		5292.2.w.b.521.1		16
63.16	even	3		1764.2.x.b.1469.6		16
63.20	even	6		5292.2.bm.a.4625.1		16
63.25	even	3		1764.2.w.b.1109.1		16
63.31	odd	6		2268.2.t.b.1781.1		16
63.34	odd	6		1764.2.bm.a.1685.3		16
63.38	even	6	inner	756.2.w.a.521.8		16
63.47	even	6		5292.2.x.a.4409.8		16
63.52	odd	6		252.2.w.a.101.8	yes	16
63.59	even	6		2268.2.t.a.1781.8		16
63.61	odd	6		1764.2.x.a.1469.3		16
84.59	odd	6		1008.2.df.d.689.3		16
252.115	even	6		1008.2.ca.d.353.1		16
252.227	odd	6		3024.2.ca.d.2033.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	3.2	odd	2
252.2.w.a.101.8	yes	16	63.52	odd	6
252.2.bm.a.173.6	yes	16	9.7	even	3
252.2.bm.a.185.6	yes	16	21.17	even	6
756.2.w.a.341.8		16	1.1	even	1	trivial
756.2.w.a.521.8		16	63.38	even	6	inner
756.2.bm.a.17.8		16	7.3	odd	6
756.2.bm.a.89.8		16	9.2	odd	6
1008.2.ca.d.257.1		16	12.11	even	2
1008.2.ca.d.353.1		16	252.115	even	6
1008.2.df.d.689.3		16	84.59	odd	6
1008.2.df.d.929.3		16	36.7	odd	6
1764.2.w.b.509.1		16	21.20	even	2
1764.2.w.b.1109.1		16	63.25	even	3
1764.2.x.a.293.3		16	21.2	odd	6
1764.2.x.a.1469.3		16	63.61	odd	6
1764.2.x.b.293.6		16	21.5	even	6
1764.2.x.b.1469.6		16	63.16	even	3
1764.2.bm.a.1685.3		16	63.34	odd	6
1764.2.bm.a.1697.3		16	21.11	odd	6
2268.2.t.a.1781.8		16	63.59	even	6
2268.2.t.a.2105.8		16	9.4	even	3
2268.2.t.b.1781.1		16	63.31	odd	6
2268.2.t.b.2105.1		16	9.5	odd	6
3024.2.ca.d.2033.8		16	252.227	odd	6
3024.2.ca.d.2609.8		16	4.3	odd	2
3024.2.df.d.17.8		16	28.3	even	6
3024.2.df.d.1601.8		16	36.11	even	6
5292.2.w.b.521.1		16	63.11	odd	6
5292.2.w.b.1097.1		16	7.6	odd	2
5292.2.x.a.881.8		16	7.2	even	3
5292.2.x.a.4409.8		16	63.47	even	6
5292.2.x.b.881.1		16	7.5	odd	6
5292.2.x.b.4409.1		16	63.2	odd	6
5292.2.bm.a.2285.1		16	7.4	even	3
5292.2.bm.a.4625.1		16	63.20	even	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.95741 + 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +O(q^{10})\)	\(q+(1.95741 + 3.39033i) q^{5} +(0.554241 - 2.58705i) q^{7} +(3.19958 + 1.84728i) q^{11} +(0.480242 + 0.277268i) q^{13} +(-2.91916 - 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(1.96965 - 1.13718i) q^{23} +(-5.16291 + 8.94242i) q^{25} +(-3.53638 + 2.04173i) q^{29} +8.08443i q^{31} +(9.85583 - 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(-3.59234 + 6.22212i) q^{41} +(-0.754009 - 1.30598i) q^{43} +2.82833 q^{47} +(-6.38563 - 2.86770i) q^{49} +(0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +8.91313 q^{59} +6.96680i q^{61} +2.17091i q^{65} +1.17480 q^{67} -6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(6.55234 - 7.25364i) q^{77} -3.94747 q^{79} +(-3.84674 - 6.66275i) q^{83} +(11.4280 - 19.7938i) q^{85} +(2.71300 - 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +20.9041i q^{95} +(13.9874 - 8.07563i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85} - 21 q^{89} + 9 q^{91} - 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

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