LMFDB - Embedded newform 756.2.bm.a.89.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(17,756)]

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, 1]))

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

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

chi := DirichletCharacter("756.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bm (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:	$\Z[a_1, \ldots, a_{19}]$
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			89.8
Root			$-0.544978 + 1.64408i$ of defining polynomial
Character	$\chi$	$=$	756.89
Dual form			756.2.bm.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.91482 q^{5} +(-2.51757 + 0.813537i) q^{7} +O(q^{10})$	$q+3.91482 q^{5} +(-2.51757 + 0.813537i) q^{7} +3.69456i q^{11} +(-0.480242 + 0.277268i) q^{13} +(2.91916 + 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} -2.27435i q^{23} +10.3258 q^{25} +(-3.53638 - 2.04173i) q^{29} +(-7.00132 - 4.04222i) q^{31} +(-9.85583 + 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(1.41416 + 2.44940i) q^{47} +(5.67631 - 4.09627i) q^{49} +(-0.0415658 + 0.0239980i) q^{53} +14.4635i q^{55} +(4.45656 - 7.71900i) q^{59} +(6.03343 - 3.48340i) q^{61} +(-1.88006 + 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-3.00566 - 9.30131i) q^{77} +(1.97374 + 3.41861i) q^{79} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-2.71300 + 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(18.1035 + 10.4520i) q^{95} +(-13.9874 - 8.07563i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	3.91482			1.75076			0.875381	−	0.483434i	$-0.160611\pi$
$5$	3.91482			1.75076			0.875381	+	0.483434i	$0.160611\pi$
$6$		0			0
$7$	−2.51757	+	0.813537i	−0.951552	+	0.307488i
$7$	−2.51757	+	0.813537i	−0.951552	+	0.307488i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			3.69456i			1.11395i	0.830529	+	0.556976i	$0.188038\pi$
$11$			3.69456i			1.11395i	−0.830529	+	0.556976i	$0.811962\pi$
$12$		0			0
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	−0.565117	−	0.825011i	$-0.691169\pi$
$13$	−0.480242	+	0.277268i	−0.133195	+	0.0769002i	0.431922	+	0.901911i	$0.357836\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	0.965598	+	0.260040i	$0.0837356\pi$
$17$	2.91916	+	5.05613i	0.708000	+	1.22629i	−0.257598	+	0.966252i	$0.582931\pi$
$18$		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
$23$		−	2.27435i		−	0.474236i	−0.971481	−	0.237118i	$-0.923797\pi$
$23$		−	2.27435i		−	0.474236i	0.971481	−	0.237118i	$-0.0762027\pi$
$24$		0			0
$25$	10.3258			2.06516
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.53638	−	2.04173i	−0.656690	−	0.379140i	0.134325	−	0.990937i	$-0.457113\pi$
$29$	−3.53638	−	2.04173i	−0.656690	−	0.379140i	−0.791014	+	0.611797i	$0.790447\pi$
$30$		0			0
$31$	−7.00132	−	4.04222i	−1.25748	−	0.726004i	−0.284892	−	0.958560i	$-0.591958\pi$
$31$	−7.00132	−	4.04222i	−1.25748	−	0.726004i	−0.972583	+	0.232556i	$0.925291\pi$
$32$		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	0.997407	+	0.0719684i	$0.0229281\pi$
$41$	3.59234	+	6.22212i	0.561030	+	0.971732i	−0.436377	+	0.899764i	$0.643739\pi$
$42$		0			0
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	−0.917774	−	0.397103i	$-0.870015\pi$
$43$	−0.754009	+	1.30598i	−0.114985	+	0.199160i	0.802789	+	0.596264i	$0.203349\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.41416	+	2.44940i	0.206277	+	0.357282i	0.950539	−	0.310606i	$-0.100532\pi$
$47$	1.41416	+	2.44940i	0.206277	+	0.357282i	−0.744262	+	0.667888i	$0.767199\pi$
$48$		0			0
$49$	5.67631	−	4.09627i	0.810902	−	0.585182i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.0415658	+	0.0239980i	−0.00570950	+	0.00329638i	−0.502852	−	0.864373i	$-0.667716\pi$
$53$	−0.0415658	+	0.0239980i	−0.00570950	+	0.00329638i	0.497143	+	0.867669i	$0.334383\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.45656	−	7.71900i	0.580195	−	1.00493i	−0.415261	−	0.909703i	$-0.636310\pi$
$59$	4.45656	−	7.71900i	0.580195	−	1.00493i	0.995456	−	0.0952251i	$-0.0303571\pi$
$60$		0			0
$61$	6.03343	−	3.48340i	0.772501	−	0.446004i	−0.0612648	−	0.998122i	$-0.519513\pi$
$61$	6.03343	−	3.48340i	0.772501	−	0.446004i	0.833766	+	0.552118i	$0.186180\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.88006	+	1.08545i	−0.233193	+	0.134634i
$66$		0			0
$67$	−0.587402	+	1.01741i	−0.0717626	+	0.124296i	−0.899674	−	0.436563i	$-0.856196\pi$
$67$	−0.587402	+	1.01741i	−0.0717626	+	0.124296i	0.827911	+	0.560859i	$0.189529\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			6.71061i			0.796403i	0.917298	+	0.398202i	$0.130366\pi$
$71$			6.71061i			0.796403i	−0.917298	+	0.398202i	$0.869634\pi$
$72$		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
$77$	−3.00566	−	9.30131i	−0.342527	−	1.05998i
$78$		0			0
$79$	1.97374	+	3.41861i	0.222063	+	0.384624i	0.955434	−	0.295204i	$-0.0953877\pi$
$79$	1.97374	+	3.41861i	0.222063	+	0.384624i	−0.733371	+	0.679828i	$0.762054\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	−0.573923	−	0.818909i	$-0.694579\pi$
$83$	3.84674	−	6.66275i	0.422235	−	0.731332i	0.996158	+	0.0875774i	$0.0279125\pi$
$84$		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	−0.973231	−	0.229829i	$-0.926183\pi$
$89$	−2.71300	+	4.69905i	−0.287577	+	0.498099i	0.685654	+	0.727928i	$0.259517\pi$
$90$		0			0
$91$	0.983474	−	1.08874i	0.103096	−	0.114130i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18.1035	+	10.4520i	1.85738	+	1.07236i
$96$		0			0
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.423890	−	0.905714i	$-0.639336\pi$
$97$	−13.9874	−	8.07563i	−1.42021	−	0.819956i	−0.996316	+	0.0857571i	$0.972669\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.62350			−0.161544			−0.0807722	−	0.996733i	$-0.525739\pi$
$101$	−1.62350			−0.161544			−0.0807722	+	0.996733i	$0.525739\pi$
$102$		0			0
$103$		−	0.395662i		−	0.0389857i	−0.999810	−	0.0194929i	$-0.993795\pi$
$103$		−	0.395662i		−	0.0389857i	0.999810	−	0.0194929i	$-0.00620517\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.90777	−	2.83350i	−0.474452	−	0.273925i	0.243650	−	0.969863i	$-0.421655\pi$
$107$	−4.90777	−	2.83350i	−0.474452	−	0.273925i	−0.718101	+	0.695938i	$0.754989\pi$
$108$		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	−0.552503	−	0.833511i	$-0.686327\pi$
$113$	−1.13651	+	0.656162i	−0.106913	+	0.0617265i	0.445590	+	0.895237i	$0.352994\pi$
$114$		0			0
$115$		−	8.90369i		−	0.830273i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.4625	−	10.3543i	−1.05077	−	0.949179i
$120$		0			0
$121$	−2.64977			−0.240888
$122$		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
$131$	−10.9072			−0.952968			−0.476484	−	0.879183i	$-0.658089\pi$
$131$	−10.9072			−0.952968			−0.476484	+	0.879183i	$0.658089\pi$
$132$		0			0
$133$	−13.8141	−	2.95950i	−1.19784	−	0.256621i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	8.80514i		−	0.752274i	−0.926564	−	0.376137i	$-0.877252\pi$
$137$		−	8.80514i		−	0.752274i	0.926564	−	0.376137i	$-0.122748\pi$
$138$		0			0
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.245220	−	0.969468i	$-0.421140\pi$
$139$	14.2352	−	8.21869i	1.20741	−	0.697100i	0.962193	+	0.272367i	$0.0878066\pi$
$140$		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
$149$			14.5278i			1.19016i	0.803665	+	0.595082i	$0.202880\pi$
$149$			14.5278i			1.19016i	−0.803665	+	0.595082i	$0.797120\pi$
$150$		0			0
$151$	5.60613			0.456221			0.228110	−	0.973635i	$-0.426745\pi$
$151$	5.60613			0.456221			0.228110	+	0.973635i	$0.426745\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−27.4089	−	15.8246i	−2.20154	−	1.27106i
$156$		0			0
$157$	−15.4411	−	8.91493i	−1.23233	−	0.711489i	−0.264819	−	0.964298i	$-0.585312\pi$
$157$	−15.4411	−	8.91493i	−1.23233	−	0.711489i	−0.967516	+	0.252809i	$0.918645\pi$
$158$		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	−0.970851	−	0.239683i	$-0.922957\pi$
$167$	−8.95550	−	15.5114i	−0.692997	−	1.20031i	0.277854	−	0.960623i	$-0.410377\pi$
$168$		0			0
$169$	−6.34625	+	10.9920i	−0.488173	+	0.845540i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.74814	−	6.49197i	−0.284966	−	0.493576i	0.687635	−	0.726057i	$-0.258649\pi$
$173$	−3.74814	−	6.49197i	−0.284966	−	0.493576i	−0.972601	+	0.232481i	$0.925316\pi$
$174$		0			0
$175$	−25.9960	+	8.40044i	−1.96511	+	0.635014i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.624382	−	0.360487i	0.0466685	−	0.0269441i	−0.476484	−	0.879183i	$-0.658089\pi$
$179$	0.624382	−	0.360487i	0.0466685	−	0.0269441i	0.523153	+	0.852239i	$0.324756\pi$
$180$		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
$185$	15.2619	−	26.4344i	1.12208	−	1.94350i
$186$		0			0
$187$	−18.6802	+	10.7850i	−1.36603	+	0.788678i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0005	−	6.35111i	0.795965	−	0.459551i	−0.0460934	−	0.998937i	$-0.514677\pi$
$191$	11.0005	−	6.35111i	0.795965	−	0.459551i	0.842058	+	0.539387i	$0.181344\pi$
$192$		0			0
$193$	11.4076	−	19.7586i	0.821140	−	1.42226i	−0.0836931	−	0.996492i	$-0.526672\pi$
$193$	11.4076	−	19.7586i	0.821140	−	1.42226i	0.904834	−	0.425765i	$-0.139995\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			0.0311360i			0.00221835i	0.999999	+	0.00110918i	$0.000353062\pi$
$197$			0.0311360i			0.00221835i	−0.999999	+	0.00110918i	$0.999647\pi$
$198$		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
$203$	10.5641	+	2.26322i	0.741455	+	0.158847i
$204$		0			0
$205$	14.0634	+	24.3585i	0.982229	+	1.70127i
$206$		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	0.994339	+	0.106250i	$0.0338845\pi$
$211$	8.55841	+	14.8236i	0.589185	+	1.02050i	−0.405154	+	0.914248i	$0.632782\pi$
$212$		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
$221$	−2.80380	−	1.61878i	−0.188604	−	0.108891i
$222$		0			0
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	0.457484	−	0.889218i	$-0.348751\pi$
$223$	−1.25230	−	0.723016i	−0.0838602	−	0.0484167i	−0.541344	+	0.840801i	$0.682084\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.47193			0.296812			0.148406	−	0.988926i	$-0.452586\pi$
$227$	4.47193			0.296812			0.148406	+	0.988926i	$0.452586\pi$
$228$		0			0
$229$			2.58736i			0.170978i	0.996339	+	0.0854888i	$0.0272452\pi$
$229$			2.58736i			0.170978i	−0.996339	+	0.0854888i	$0.972755\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	15.0756	+	8.70389i	0.987634	+	0.570211i	0.904566	−	0.426333i	$-0.140195\pi$
$233$	15.0756	+	8.70389i	0.987634	+	0.570211i	0.0830679	+	0.996544i	$0.473528\pi$
$234$		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	−0.630718	−	0.776012i	$-0.717240\pi$
$239$	−4.23642	+	2.44590i	−0.274031	+	0.158212i	0.356687	+	0.934224i	$0.383906\pi$
$240$		0			0
$241$		−	8.13235i		−	0.523851i	−0.965088	−	0.261925i	$-0.915643\pi$
$241$		−	8.13235i		−	0.523851i	0.965088	−	0.261925i	$-0.0843574\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	22.2218	−	16.0362i	1.41970	−	1.02451i
$246$		0			0
$247$	−2.96107			−0.188408
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−25.9341			−1.63694			−0.818472	−	0.574546i	$-0.805179\pi$
$251$	−25.9341			−1.63694			−0.818472	+	0.574546i	$0.805179\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−30.8230			−1.92269			−0.961344	−	0.275349i	$-0.911207\pi$
$257$	−30.8230			−1.92269			−0.961344	+	0.275349i	$0.911207\pi$
$258$		0			0
$259$	−4.32141	+	20.1712i	−0.268519	+	1.25338i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			18.0855i			1.11520i	0.830110	+	0.557600i	$0.188278\pi$
$263$			18.0855i			1.11520i	−0.830110	+	0.557600i	$0.811722\pi$
$264$		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	$-0.937339\pi$
$269$	−10.8203	−	18.7413i	−0.659725	−	1.14268i	0.320961	−	0.947092i	$-0.395994\pi$
$270$		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
$275$			38.1494i			2.30049i
$276$		0			0
$277$	8.80327			0.528937			0.264469	−	0.964394i	$-0.414803\pi$
$277$	8.80327			0.528937			0.264469	+	0.964394i	$0.414803\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	16.6889	+	9.63537i	0.995579	+	0.574798i	0.906937	−	0.421266i	$-0.138414\pi$
$281$	16.6889	+	9.63537i	0.995579	+	0.574798i	0.0886417	+	0.996064i	$0.471747\pi$
$282$		0			0
$283$	−8.32822	−	4.80830i	−0.495061	−	0.285824i	0.231611	−	0.972809i	$-0.425601\pi$
$283$	−8.32822	−	4.80830i	−0.495061	−	0.285824i	−0.726672	+	0.686985i	$0.758934\pi$
$284$		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	$-0.143849\pi$
$293$	1.22598	+	2.12346i	0.0716225	+	0.124054i	−0.827990	+	0.560743i	$0.810516\pi$
$294$		0			0
$295$	17.4467	−	30.2185i	1.01578	−	1.75939i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.630605	+	1.09224i	0.0364688	+	0.0631658i
$300$		0			0
$301$	0.835805	−	3.90131i	0.0481750	−	0.224868i
$302$		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
$311$	10.3833	−	17.9843i	0.588780	−	1.01980i	−0.405612	−	0.914045i	$-0.632942\pi$
$311$	10.3833	−	17.9843i	0.588780	−	1.01980i	0.994393	−	0.105752i	$-0.0337250\pi$
$312$		0			0
$313$	3.40449	−	1.96558i	0.192433	−	0.111101i	−0.400688	−	0.916215i	$-0.631229\pi$
$313$	3.40449	−	1.96558i	0.192433	−	0.111101i	0.593121	+	0.805113i	$0.297896\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.98369	+	1.14528i	−0.111415	+	0.0643256i	−0.554672	−	0.832069i	$-0.687156\pi$
$317$	−1.98369	+	1.14528i	−0.111415	+	0.0643256i	0.443257	+	0.896395i	$0.353823\pi$
$318$		0			0
$319$	7.54330	−	13.0654i	0.422344	−	0.731521i
$320$		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
$329$	−5.55294	−	5.01607i	−0.306143	−	0.276545i
$330$		0			0
$331$	−3.46788	−	6.00655i	−0.190612	−	0.330150i	0.754841	−	0.655908i	$-0.227714\pi$
$331$	−3.46788	−	6.00655i	−0.190612	−	0.330150i	−0.945453	+	0.325758i	$0.894381\pi$
$332$		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	−0.999647	−	0.0265545i	$-0.991546\pi$
$337$	−9.59771	−	16.6237i	−0.522821	−	0.905552i	0.476827	−	0.878997i	$-0.341787\pi$
$338$		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
$347$	7.35287	+	4.24518i	0.394723	+	0.227893i	0.684204	−	0.729290i	$-0.260150\pi$
$347$	7.35287	+	4.24518i	0.394723	+	0.227893i	−0.289482	+	0.957184i	$0.593483\pi$
$348$		0			0
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.872560	−	0.488506i	$-0.162458\pi$
$349$	16.5478	+	9.55386i	0.885782	+	0.511407i	0.0132216	+	0.999913i	$0.495791\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−13.6590			−0.726996			−0.363498	−	0.931595i	$-0.618418\pi$
$353$	−13.6590			−0.726996			−0.363498	+	0.931595i	$0.618418\pi$
$354$		0			0
$355$			26.2708i			1.39431i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−14.8909	−	8.59724i	−0.785909	−	0.453745i	0.0526113	−	0.998615i	$-0.483246\pi$
$359$	−14.8909	−	8.59724i	−0.785909	−	0.453745i	−0.838520	+	0.544870i	$0.816579\pi$
$360$		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
$367$		−	16.8587i		−	0.880018i	−0.897993	−	0.440009i	$-0.854975\pi$
$367$		−	16.8587i		−	0.880018i	0.897993	−	0.440009i	$-0.145025\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.0851215	−	0.0942320i	0.00441929	−	0.00489228i
$372$		0			0
$373$	−1.40858			−0.0729333			−0.0364667	−	0.999335i	$-0.511610\pi$
$373$	−1.40858			−0.0729333			−0.0364667	+	0.999335i	$0.511610\pi$
$374$		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
$383$	8.52077			0.435391			0.217696	−	0.976017i	$-0.430146\pi$
$383$	8.52077			0.435391			0.217696	+	0.976017i	$0.430146\pi$
$384$		0			0
$385$	−11.7666	−	36.4130i	−0.599683	−	1.85578i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			34.5976i			1.75417i	0.480336	+	0.877084i	$0.340515\pi$
$389$			34.5976i			1.75417i	−0.480336	+	0.877084i	$0.659485\pi$
$390$		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
$401$			13.1028i			0.654321i	0.944969	+	0.327161i	$0.106092\pi$
$401$			13.1028i			0.654321i	−0.944969	+	0.327161i	$0.893908\pi$
$402$		0			0
$403$	4.48310			0.223319
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.9471	+	14.4032i	1.23658	+	0.713941i
$408$		0			0
$409$	32.3493	+	18.6769i	1.59957	+	0.923513i	0.991569	+	0.129577i	$0.0413620\pi$
$409$	32.3493	+	18.6769i	1.59957	+	0.923513i	0.608002	+	0.793936i	$0.291971\pi$
$410$		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	0.970687	+	0.240346i	$0.0772610\pi$
$419$	14.1954	+	24.5871i	0.693490	+	1.20116i	−0.277198	+	0.960813i	$0.589406\pi$
$420$		0			0
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	0.0408054	+	0.999167i	$0.487008\pi$
$421$	−17.3359	+	30.0267i	−0.844901	+	1.46341i	−0.885707	+	0.464245i	$0.846326\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	30.1427	+	52.2087i	1.46214	+	2.53249i
$426$		0			0
$427$	−12.3557	+	13.6781i	−0.597934	+	0.661931i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	13.1844	−	7.61200i	0.635069	−	0.366657i	−0.147643	−	0.989041i	$-0.547169\pi$
$431$	13.1844	−	7.61200i	0.635069	−	0.366657i	0.782713	+	0.622383i	$0.213835\pi$
$432$		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
$437$	6.07222	−	10.5174i	0.290474	−	0.503115i
$438$		0			0
$439$	8.21910	−	4.74530i	0.392276	−	0.226481i	−0.290870	−	0.956763i	$-0.593945\pi$
$439$	8.21910	−	4.74530i	0.392276	−	0.226481i	0.683146	+	0.730282i	$0.260611\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.3955	−	16.3942i	1.34911	−	0.778910i	0.360989	−	0.932570i	$-0.382439\pi$
$443$	28.3955	−	16.3942i	1.34911	−	0.778910i	0.988124	+	0.153660i	$0.0491060\pi$
$444$		0			0
$445$	−10.6209	+	18.3960i	−0.503479	+	0.872052i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	0.658896i		−	0.0310952i	−0.999879	−	0.0155476i	$-0.995051\pi$
$449$		−	0.658896i		−	0.0310952i	0.999879	−	0.0155476i	$-0.00494916\pi$
$450$		0			0
$451$	−22.9880	+	13.2721i	−1.08246	+	0.624960i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.85013	−	4.26220i	0.180497	−	0.199815i
$456$		0			0
$457$	−7.94514	−	13.7614i	−0.371658	−	0.643730i	0.618163	−	0.786050i	$-0.287877\pi$
$457$	−7.94514	−	13.7614i	−0.371658	−	0.643730i	−0.989821	+	0.142320i	$0.954544\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	−0.998811	−	0.0487477i	$-0.984477\pi$
$461$	−9.81626	+	17.0023i	−0.457189	+	0.791874i	0.541622	+	0.840622i	$0.317810\pi$
$462$		0			0
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	0.879634	−	0.475651i	$-0.157787\pi$
$463$	0.600159	+	1.03951i	0.0278918	+	0.0483099i	−0.851743	+	0.523960i	$0.824454\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.0549972	−	0.998487i	$-0.482485\pi$
$467$	19.2809	−	33.3955i	0.892213	−	1.54536i	0.837216	−	0.546872i	$-0.184182\pi$
$468$		0			0
$469$	0.651124	−	3.03927i	0.0300661	−	0.140341i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.82503	−	2.78573i	−0.221855	−	0.128088i
$474$		0			0
$475$	47.7501	+	27.5685i	2.19093	+	1.26493i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	7.22578			0.330154			0.165077	−	0.986281i	$-0.447213\pi$
$479$	7.22578			0.330154			0.165077	+	0.986281i	$0.447213\pi$
$480$		0			0
$481$			4.32371i			0.197144i
$482$		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	−0.835860	−	0.548943i	$-0.815031\pi$
$491$	−17.2480	+	9.95814i	−0.778392	+	0.449405i	0.0574682	+	0.998347i	$0.481697\pi$
$492$		0			0
$493$		−	23.8405i		−	1.07372i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.45933	−	16.8944i	−0.244885	−	0.757819i
$498$		0			0
$499$	34.3840			1.53924			0.769619	−	0.638503i	$-0.220446\pi$
$499$	34.3840			1.53924			0.769619	+	0.638503i	$0.220446\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.22542			0.0546388			0.0273194	−	0.999627i	$-0.491303\pi$
$503$	1.22542			0.0546388			0.0273194	+	0.999627i	$0.491303\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.1016			−0.447744			−0.223872	−	0.974619i	$-0.571870\pi$
$509$	−10.1016			−0.447744			−0.223872	+	0.974619i	$0.571870\pi$
$510$		0			0
$511$	7.22268	−	7.99572i	0.319513	−	0.353710i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	1.54895i		−	0.0682547i
$516$		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	0.999047	−	0.0436480i	$-0.0138980\pi$
$521$	10.5390	+	18.2541i	0.461723	+	0.799728i	−0.537324	+	0.843376i	$0.680565\pi$
$522$		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
$527$		−	47.1995i		−	2.05604i
$528$		0			0
$529$	17.8273			0.775101
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.45039	−	1.99208i	−0.149453	−	0.0862866i
$534$		0			0
$535$	−19.2130	−	11.0926i	−0.830652	−	0.479577i
$536$		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	−0.939211	−	0.343342i	$-0.888441\pi$
$547$	−4.02889	+	6.97824i	−0.172263	+	0.298368i	0.766948	+	0.641709i	$0.221774\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−10.9023	−	18.8833i	−0.464453	−	0.804456i
$552$		0			0
$553$	−7.75019	−	7.00089i	−0.329572	−	0.297708i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.2294	+	10.5247i	−0.772403	+	0.445947i	−0.833731	−	0.552170i	$-0.813800\pi$
$557$	−18.2294	+	10.5247i	−0.772403	+	0.445947i	0.0613279	+	0.998118i	$0.480466\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−20.6410	+	35.7513i	−0.869916	+	1.50674i	−0.00783378	+	0.999969i	$0.502494\pi$
$563$	−20.6410	+	35.7513i	−0.869916	+	1.50674i	−0.862082	+	0.506769i	$0.830840\pi$
$564$		0			0
$565$	−4.44922	+	2.56876i	−0.187180	+	0.108068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−31.2691	+	18.0532i	−1.31087	+	0.756829i	−0.982240	−	0.187630i	$-0.939919\pi$
$569$	−31.2691	+	18.0532i	−1.31087	+	0.756829i	−0.328627	+	0.944460i	$0.606586\pi$
$570$		0			0
$571$	9.62111	−	16.6642i	0.402631	−	0.697377i	−0.591412	−	0.806370i	$-0.701429\pi$
$571$	9.62111	−	16.6642i	0.402631	−	0.697377i	0.994043	+	0.108993i	$0.0347625\pi$
$572$		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
$581$	−4.26404	+	19.9034i	−0.176902	+	0.825732i
$582$		0			0
$583$	−0.0886621	−	0.153567i	−0.00367201	−	0.00636010i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	−0.751964	−	0.659204i	$-0.770893\pi$
$587$	4.72218	−	8.17905i	0.194905	−	0.337586i	0.946869	+	0.321618i	$0.104227\pi$
$588$		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	$-0.663005\pi$
$593$	12.4176	−	21.5079i	0.509929	−	0.883223i	0.999934	−	0.0115033i	$-0.00366171\pi$
$594$		0			0
$595$	−44.8738	−	40.5353i	−1.83965	−	1.66179i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.3052	+	5.94974i	0.421061	+	0.243100i	0.695531	−	0.718496i	$-0.255169\pi$
$599$	10.3052	+	5.94974i	0.421061	+	0.243100i	−0.274470	+	0.961596i	$0.588502\pi$
$600$		0			0
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.0245596	−	0.999698i	$-0.507818\pi$
$601$	−22.1276	−	12.7754i	−0.902604	−	0.521118i	−0.878044	+	0.478580i	$0.841152\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−10.3734			−0.421738
$606$		0			0
$607$		−	22.5794i		−	0.916471i	−0.888831	−	0.458235i	$-0.848482\pi$
$607$		−	22.5794i		−	0.916471i	0.888831	−	0.458235i	$-0.151518\pi$
$608$		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	−0.535558	−	0.844499i	$-0.679899\pi$
$617$	−1.78792	+	1.03226i	−0.0719791	+	0.0415572i	0.463578	+	0.886056i	$0.346565\pi$
$618$		0			0
$619$			32.5894i			1.30988i	0.755681	+	0.654940i	$0.227306\pi$
$619$			32.5894i			1.30988i	−0.755681	+	0.654940i	$0.772694\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.00731	−	14.0373i	0.120485	−	0.562393i
$624$		0			0
$625$	29.9935			1.19974
$626$		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
$635$	−68.0923			−2.70216
$636$		0			0
$637$	−1.59024	+	3.54106i	−0.0630075	+	0.140302i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	47.7636i		−	1.88655i	−0.332014	−	0.943274i	$-0.607728\pi$
$641$		−	47.7636i		−	1.88655i	0.332014	−	0.943274i	$-0.392272\pi$
$642$		0			0
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.949592	−	0.313489i	$-0.898502\pi$
$643$	−29.2346	+	16.8786i	−1.15290	+	0.665626i	−0.203306	+	0.979115i	$0.565169\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.536008	+	0.928393i	0.0210727	+	0.0364989i	0.876369	−	0.481640i	$-0.159959\pi$
$647$	0.536008	+	0.928393i	0.0210727	+	0.0364989i	−0.855297	+	0.518138i	$0.826625\pi$
$648$		0			0
$649$	28.5183	+	16.4650i	1.11944	+	0.646309i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			33.3135i			1.30366i	0.758367	+	0.651828i	$0.225998\pi$
$653$			33.3135i			1.30366i	−0.758367	+	0.651828i	$0.774002\pi$
$654$		0			0
$655$	−42.6998			−1.66842
$656$		0			0
$657$		0			0
$658$		0			0
$659$	8.41890	+	4.86065i	0.327954	+	0.189344i	0.654932	−	0.755688i	$-0.272697\pi$
$659$	8.41890	+	4.86065i	0.327954	+	0.189344i	−0.326979	+	0.945032i	$0.606031\pi$
$660$		0			0
$661$	−14.7856	−	8.53647i	−0.575093	−	0.332030i	0.184088	−	0.982910i	$-0.441067\pi$
$661$	−14.7856	−	8.53647i	−0.575093	−	0.332030i	−0.759181	+	0.650880i	$0.774400\pi$
$662$		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	0.259240	+	0.965813i	$0.416528\pi$
$673$	−18.3359	+	31.7588i	−0.706798	+	1.22421i	−0.966039	+	0.258398i	$0.916805\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	20.1769	+	34.9474i	0.775461	+	1.34314i	0.934535	+	0.355872i	$0.115816\pi$
$677$	20.1769	+	34.9474i	0.775461	+	1.34314i	−0.159073	+	0.987267i	$0.550851\pi$
$678$		0			0
$679$	41.7841	+	8.95169i	1.60353	+	0.343534i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.23662	−	4.75541i	0.315165	−	0.181961i	−0.334070	−	0.942548i	$-0.608422\pi$
$683$	8.23662	−	4.75541i	0.315165	−	0.181961i	0.649236	+	0.760587i	$0.275089\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.0133077	−	0.0230497i	0.000506985	−	0.000878123i
$690$		0			0
$691$	−6.67519	+	3.85392i	−0.253936	+	0.146610i	−0.621565	−	0.783362i	$-0.713503\pi$
$691$	−6.67519	+	3.85392i	−0.253936	+	0.146610i	0.367629	+	0.929972i	$0.380170\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	55.7282	−	32.1747i	2.11389	−	1.22046i
$696$		0			0
$697$	−20.9732	+	36.3267i	−0.794418	+	1.37597i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	15.6388i		−	0.590671i	−0.955394	−	0.295336i	$-0.904569\pi$
$701$		−	15.6388i		−	0.590671i	0.955394	−	0.295336i	$-0.0954314\pi$
$702$		0			0
$703$	36.0559	−	20.8169i	1.35988	−	0.785124i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.08728	−	1.32078i	0.153718	−	0.0496730i
$708$		0			0
$709$	−6.72025	−	11.6398i	−0.252384	−	0.437142i	0.711797	−	0.702385i	$-0.247881\pi$
$709$	−6.72025	−	11.6398i	−0.252384	−	0.437142i	−0.964182	+	0.265242i	$0.914548\pi$
$710$		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	$-0.564814\pi$
$719$	20.0309	−	34.6946i	0.747027	−	1.29389i	0.949242	−	0.314548i	$-0.101853\pi$
$720$		0			0
$721$	0.321886	+	0.996107i	0.0119877	+	0.0370970i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−36.5161	−	21.0826i	−1.35617	−	0.782986i
$726$		0			0
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.990978	−	0.134027i	$-0.957209\pi$
$727$	−43.2091	−	24.9468i	−1.60254	−	0.925225i	−0.611560	−	0.791198i	$-0.709458\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.80428			−0.325638
$732$		0			0
$733$		−	11.4480i		−	0.422843i	−0.977395	−	0.211422i	$-0.932191\pi$
$733$		−	11.4480i		−	0.422843i	0.977395	−	0.211422i	$-0.0678093\pi$
$734$		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	0.722540	−	0.691329i	$-0.242974\pi$
$743$	45.8621	−	26.4785i	1.68252	−	0.971403i	0.959979	−	0.280074i	$-0.0903589\pi$
$744$		0			0
$745$			56.8737i			2.08369i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.6608	+	3.14088i	0.535694	+	0.114765i
$750$		0			0
$751$	−26.4652			−0.965729			−0.482865	−	0.875695i	$-0.660404\pi$
$751$	−26.4652			−0.965729			−0.482865	+	0.875695i	$0.660404\pi$
$752$		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
$761$	53.9937			1.95727			0.978635	−	0.205605i	$-0.0659162\pi$
$761$	53.9937			1.95727			0.978635	+	0.205605i	$0.0659162\pi$
$762$		0			0
$763$	26.5311	+	23.9660i	0.960491	+	0.867629i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			4.94264i			0.178469i
$768$		0			0
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.933236	−	0.359263i	$-0.883028\pi$
$769$	−30.1912	+	17.4309i	−1.08872	+	0.628575i	−0.155487	+	0.987838i	$0.549695\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.06375	−	1.84246i	−0.0382603	−	0.0662688i	0.846261	−	0.532768i	$-0.178848\pi$
$773$	−1.06375	−	1.84246i	−0.0382603	−	0.0662688i	−0.884521	+	0.466499i	$0.845515\pi$
$774$		0			0
$775$	−72.2944	−	41.7392i	−2.59689	−	1.49932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			38.3643i			1.37454i
$780$		0			0
$781$	−24.7928			−0.887155
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−60.4492	−	34.9004i	−2.15752	−	1.24565i
$786$		0			0
$787$	24.5457	+	14.1715i	0.874959	+	0.505158i	0.868993	−	0.494824i	$-0.164768\pi$
$787$	24.5457	+	14.1715i	0.874959	+	0.505158i	0.00596615	+	0.999982i	$0.498101\pi$
$788$		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	−0.977930	−	0.208935i	$-0.933000\pi$
$797$	−18.9123	−	32.7570i	−0.669907	−	1.16031i	0.308022	−	0.951379i	$-0.400333\pi$
$798$		0			0
$799$	−8.25634	+	14.3004i	−0.292088	+	0.505912i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.52311	−	13.0304i	−0.265485	−	0.459833i
$804$		0			0
$805$	7.24348	+	22.4157i	0.255299	+	0.790048i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	39.2475	−	22.6595i	1.37987	−	0.796667i	0.387724	−	0.921776i	$-0.373261\pi$
$809$	39.2475	−	22.6595i	1.37987	−	0.796667i	0.992143	+	0.125109i	$0.0399280\pi$
$810$		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
$815$	−2.25883	+	3.91241i	−0.0791233	+	0.137046i
$816$		0			0
$817$	−6.97359	+	4.02620i	−0.243975	+	0.140859i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.7121	−	24.6598i	1.49066	−	0.860634i	0.490718	−	0.871318i	$-0.336734\pi$
$821$	42.7121	−	24.6598i	1.49066	−	0.860634i	0.999943	+	0.0106847i	$0.00340111\pi$
$822$		0			0
$823$	11.8496	−	20.5241i	0.413050	−	0.715424i	−0.582171	−	0.813066i	$-0.697797\pi$
$823$	11.8496	−	20.5241i	0.413050	−	0.715424i	0.995222	+	0.0976419i	$0.0311300\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			19.9706i			0.694445i	0.937783	+	0.347222i	$0.112875\pi$
$827$			19.9706i			0.694445i	−0.937783	+	0.347222i	$0.887125\pi$
$828$		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
$833$	37.2814	+	16.7425i	1.29172	+	0.580094i
$834$		0			0
$835$	−35.0592	−	60.7242i	−1.21327	−	2.10145i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	−0.945658	−	0.325162i	$-0.894581\pi$
$839$	−5.53910	+	9.59401i	−0.191231	+	0.331222i	0.754427	+	0.656383i	$0.227915\pi$
$840$		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
$851$	−15.3573	−	8.86656i	−0.526442	−	0.303942i
$852$		0			0
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.998107	−	0.0615058i	$-0.0195903\pi$
$853$	42.1706	+	24.3472i	1.44389	+	0.833633i	0.445788	+	0.895139i	$0.352924\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−16.7826			−0.573283			−0.286641	−	0.958038i	$-0.592539\pi$
$857$	−16.7826			−0.573283			−0.286641	+	0.958038i	$0.592539\pi$
$858$		0			0
$859$		−	25.1358i		−	0.857622i	−0.903394	−	0.428811i	$-0.858933\pi$
$859$		−	25.1358i		−	0.857622i	0.903394	−	0.428811i	$-0.141067\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.87377	+	3.39122i	0.199945	+	0.115438i	0.596630	−	0.802516i	$-0.296506\pi$
$863$	5.87377	+	3.39122i	0.199945	+	0.115438i	−0.396685	+	0.917955i	$0.629839\pi$
$864$		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
$871$		−	0.651470i		−	0.0220742i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−52.4904	+	16.9620i	−1.77450	+	0.573419i
$876$		0			0
$877$	−43.7259			−1.47652			−0.738260	−	0.674517i	$-0.764352\pi$
$877$	−43.7259			−1.47652			−0.738260	+	0.674517i	$0.764352\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−27.5307			−0.927531			−0.463766	−	0.885958i	$-0.653502\pi$
$881$	−27.5307			−0.927531			−0.463766	+	0.885958i	$0.653502\pi$
$882$		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
$887$	−24.6185			−0.826607			−0.413303	−	0.910593i	$-0.635625\pi$
$887$	−24.6185			−0.826607			−0.413303	+	0.910593i	$0.635625\pi$
$888$		0			0
$889$	43.7892	−	14.1502i	1.46864	−	0.474583i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			15.1025i			0.505386i
$894$		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
$905$		−	19.8529i		−	0.659932i
$906$		0			0
$907$	−10.0867			−0.334925			−0.167462	−	0.985878i	$-0.553557\pi$
$907$	−10.0867			−0.334925			−0.167462	+	0.985878i	$0.553557\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.5808	−	13.6144i	−0.781267	−	0.451065i	0.0556121	−	0.998452i	$-0.482289\pi$
$911$	−23.5808	−	13.6144i	−0.781267	−	0.451065i	−0.836879	+	0.547388i	$0.815622\pi$
$912$		0			0
$913$	24.6159	+	14.2120i	0.814668	+	0.470349i
$914$		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
$929$	0.142283	+	0.246442i	0.00466816	+	0.00808550i	0.868350	−	0.495952i	$-0.165181\pi$
$929$	0.142283	+	0.246442i	0.00466816	+	0.00808550i	−0.863682	+	0.504037i	$0.831847\pi$
$930$		0			0
$931$	37.1857	−	3.78758i	1.21871	−	0.124133i
$932$		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
$941$	5.64242	−	9.77295i	0.183938	−	0.318589i	−0.759280	−	0.650764i	$-0.774449\pi$
$941$	5.64242	−	9.77295i	0.183938	−	0.318589i	0.943218	+	0.332174i	$0.107782\pi$
$942$		0			0
$943$	14.1513	−	8.17026i	0.460830	−	0.266060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.6701	+	11.3566i	−0.639194	+	0.369039i	−0.784304	−	0.620377i	$-0.786980\pi$
$947$	−19.6701	+	11.3566i	−0.639194	+	0.369039i	0.145110	+	0.989416i	$0.453646\pi$
$948$		0			0
$949$	1.12918	−	1.95580i	0.0366548	−	0.0634880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	16.5638i		−	0.536554i	−0.963342	−	0.268277i	$-0.913546\pi$
$953$		−	16.5638i		−	0.536554i	0.963342	−	0.268277i	$-0.0864543\pi$
$954$		0			0
$955$	43.0648	−	24.8635i	1.39354	−	0.804563i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.16331	+	22.1675i	0.231315	+	0.715827i
$960$		0			0
$961$	17.1790	+	29.7550i	0.554162	+	0.959837i
$962$		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	0.968800	−	0.247843i	$-0.0797218\pi$
$967$	8.38867	+	14.5296i	0.269762	+	0.467241i	−0.699039	+	0.715084i	$0.746388\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	0.496734	+	0.867903i	$0.334532\pi$
$971$	−15.6820	+	27.1620i	−0.503259	+	0.871670i	−0.999993	+	0.00376705i	$0.998801\pi$
$972$		0			0
$973$	−29.1519	+	32.2720i	−0.934566	+	1.03459i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−49.0953	−	28.3452i	−1.57070	−	0.906843i	−0.996083	−	0.0884183i	$-0.971819\pi$
$977$	−49.0953	−	28.3452i	−1.57070	−	0.906843i	−0.574614	−	0.818424i	$-0.694848\pi$
$978$		0			0
$979$	−17.3609	−	10.0233i	−0.554858	−	0.320347i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.8408			−1.27072			−0.635362	−	0.772214i	$-0.719149\pi$
$983$	−39.8408			−1.27072			−0.635362	+	0.772214i	$0.719149\pi$
$984$		0			0
$985$			0.121892i			0.00388380i
$986$		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
$997$		−	45.1041i		−	1.42846i	−0.699911	−	0.714230i	$-0.746777\pi$
$997$		−	45.1041i		−	1.42846i	0.699911	−	0.714230i	$-0.253223\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	9.4	even	3
252.2.w.a.101.8	yes	16	21.17	even	6
252.2.bm.a.173.6	yes	16	3.2	odd	2
252.2.bm.a.185.6	yes	16	63.31	odd	6
756.2.w.a.341.8		16	9.5	odd	6
756.2.w.a.521.8		16	7.3	odd	6
756.2.bm.a.17.8		16	63.59	even	6	inner
756.2.bm.a.89.8		16	1.1	even	1	trivial
1008.2.ca.d.257.1		16	36.31	odd	6
1008.2.ca.d.353.1		16	84.59	odd	6
1008.2.df.d.689.3		16	252.31	even	6
1008.2.df.d.929.3		16	12.11	even	2
1764.2.w.b.509.1		16	63.13	odd	6
1764.2.w.b.1109.1		16	21.11	odd	6
1764.2.x.a.293.3		16	63.58	even	3
1764.2.x.a.1469.3		16	21.5	even	6
1764.2.x.b.293.6		16	63.40	odd	6
1764.2.x.b.1469.6		16	21.2	odd	6
1764.2.bm.a.1685.3		16	21.20	even	2
1764.2.bm.a.1697.3		16	63.4	even	3
2268.2.t.a.1781.8		16	63.52	odd	6
2268.2.t.a.2105.8		16	9.2	odd	6
2268.2.t.b.1781.1		16	63.38	even	6
2268.2.t.b.2105.1		16	9.7	even	3
3024.2.ca.d.2033.8		16	28.3	even	6
3024.2.ca.d.2609.8		16	36.23	even	6
3024.2.df.d.17.8		16	252.59	odd	6
3024.2.df.d.1601.8		16	4.3	odd	2
5292.2.w.b.521.1		16	7.4	even	3
5292.2.w.b.1097.1		16	63.41	even	6
5292.2.x.a.881.8		16	63.23	odd	6
5292.2.x.a.4409.8		16	7.5	odd	6
5292.2.x.b.881.1		16	63.5	even	6
5292.2.x.b.4409.1		16	7.2	even	3
5292.2.bm.a.2285.1		16	63.32	odd	6
5292.2.bm.a.4625.1		16	7.6	odd	2

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.bm (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.91482 q^{5} +(-2.51757 + 0.813537i) q^{7} +O(q^{10})\)	\(q+3.91482 q^{5} +(-2.51757 + 0.813537i) q^{7} +3.69456i q^{11} +(-0.480242 + 0.277268i) q^{13} +(2.91916 + 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} -2.27435i q^{23} +10.3258 q^{25} +(-3.53638 - 2.04173i) q^{29} +(-7.00132 - 4.04222i) q^{31} +(-9.85583 + 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +(3.59234 + 6.22212i) q^{41} +(-0.754009 + 1.30598i) q^{43} +(1.41416 + 2.44940i) q^{47} +(5.67631 - 4.09627i) q^{49} +(-0.0415658 + 0.0239980i) q^{53} +14.4635i q^{55} +(4.45656 - 7.71900i) q^{59} +(6.03343 - 3.48340i) q^{61} +(-1.88006 + 1.08545i) q^{65} +(-0.587402 + 1.01741i) q^{67} +6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-3.00566 - 9.30131i) q^{77} +(1.97374 + 3.41861i) q^{79} +(3.84674 - 6.66275i) q^{83} +(11.4280 + 19.7938i) q^{85} +(-2.71300 + 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(18.1035 + 10.4520i) q^{95} +(-13.9874 - 8.07563i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

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