LMFDB - Embedded newform 756.2.w.a.341.7

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			341.7
Root			$1.68042 + 0.419752i$ of defining polynomial
Character	$\chi$	$=$	756.341
Dual form			756.2.w.a.521.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.48494 + 2.57199i) q^{5} +(-0.200279 + 2.63816i) q^{7} +O(q^{10})$	$q+(1.48494 + 2.57199i) q^{5} +(-0.200279 + 2.63816i) q^{7} +(4.09466 + 2.36406i) q^{11} +(-3.54045 - 2.04408i) q^{13} +(0.835278 + 1.44674i) q^{17} +(-4.25377 - 2.45592i) q^{19} +(-4.25297 + 2.45545i) q^{23} +(-1.91009 + 3.30837i) q^{25} +(-0.238557 + 0.137731i) q^{29} +1.60327i q^{31} +(-7.08273 + 3.40239i) q^{35} +(-1.69681 + 2.93896i) q^{37} +(3.55632 - 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +10.9977 q^{47} +(-6.91978 - 1.05674i) q^{49} +(-0.707381 + 0.408407i) q^{53} +14.0419i q^{55} -2.74856 q^{59} -7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +10.4406i q^{71} +(13.6493 - 7.88042i) q^{73} +(-7.05683 + 10.3289i) q^{77} -12.3033 q^{79} +(4.03981 + 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(-4.60872 + 7.98254i) q^{89} +(6.10169 - 8.93089i) q^{91} -14.5875i q^{95} +(7.00772 - 4.04591i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.48494	+	2.57199i	0.664085	+	1.15023i	0.979532	+	0.201286i	$0.0645121\pi$
$5$	1.48494	+	2.57199i	0.664085	+	1.15023i	−0.315447	+	0.948943i	$0.602155\pi$
$6$		0			0
$7$	−0.200279	+	2.63816i	−0.0756984	+	0.997131i
$7$	−0.200279	+	2.63816i	−0.0756984	+	0.997131i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	4.09466	+	2.36406i	1.23459	+	0.712790i	0.967983	−	0.251016i	$-0.0807648\pi$
$11$	4.09466	+	2.36406i	1.23459	+	0.712790i	0.266605	+	0.963806i	$0.414098\pi$
$12$		0			0
$13$	−3.54045	−	2.04408i	−0.981945	−	0.566926i	−0.0790880	−	0.996868i	$-0.525201\pi$
$13$	−3.54045	−	2.04408i	−0.981945	−	0.566926i	−0.902857	+	0.429942i	$0.858534\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.835278	+	1.44674i	0.202585	+	0.350887i	0.949360	−	0.314189i	$-0.101733\pi$
$17$	0.835278	+	1.44674i	0.202585	+	0.350887i	−0.746776	+	0.665076i	$0.768399\pi$
$18$		0			0
$19$	−4.25377	−	2.45592i	−0.975882	−	0.563426i	−0.0748577	−	0.997194i	$-0.523850\pi$
$19$	−4.25377	−	2.45592i	−0.975882	−	0.563426i	−0.901024	+	0.433768i	$0.857184\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.25297	+	2.45545i	−0.886805	+	0.511997i	−0.872896	−	0.487906i	$-0.837761\pi$
$23$	−4.25297	+	2.45545i	−0.886805	+	0.511997i	−0.0139086	+	0.999903i	$0.504427\pi$
$24$		0			0
$25$	−1.91009	+	3.30837i	−0.382018	+	0.661675i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.238557	+	0.137731i	−0.0442989	+	0.0255760i	−0.521986	−	0.852954i	$-0.674809\pi$
$29$	−0.238557	+	0.137731i	−0.0442989	+	0.0255760i	0.477687	+	0.878530i	$0.341475\pi$
$30$		0			0
$31$			1.60327i			0.287956i	0.989581	+	0.143978i	$0.0459895\pi$
$31$			1.60327i			0.287956i	−0.989581	+	0.143978i	$0.954011\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−7.08273	+	3.40239i	−1.19720	+	0.575109i
$36$		0			0
$37$	−1.69681	+	2.93896i	−0.278954	+	0.483162i	−0.971125	−	0.238571i	$-0.923321\pi$
$37$	−1.69681	+	2.93896i	−0.278954	+	0.483162i	0.692171	+	0.721733i	$0.256654\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.55632	−	6.15972i	0.555404	−	0.961987i	−0.442468	−	0.896784i	$-0.645897\pi$
$41$	3.55632	−	6.15972i	0.555404	−	0.961987i	0.997872	−	0.0652031i	$-0.0207695\pi$
$42$		0			0
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	0.921265	+	0.388936i	$0.127157\pi$
$43$	5.22930	+	9.05742i	0.797461	+	1.38124i	−0.123804	+	0.992307i	$0.539509\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.9977			1.60418			0.802090	−	0.597203i	$-0.203721\pi$
$47$	10.9977			1.60418			0.802090	+	0.597203i	$0.203721\pi$
$48$		0			0
$49$	−6.91978	−	1.05674i	−0.988540	−	0.150962i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.707381	+	0.408407i	−0.0971663	+	0.0560990i	−0.547796	−	0.836612i	$-0.684533\pi$
$53$	−0.707381	+	0.408407i	−0.0971663	+	0.0560990i	0.450629	+	0.892711i	$0.351200\pi$
$54$		0			0
$55$			14.0419i			1.89341i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.74856			−0.357832			−0.178916	−	0.983864i	$-0.557259\pi$
$59$	−2.74856			−0.357832			−0.178916	+	0.983864i	$0.557259\pi$
$60$		0			0
$61$		−	7.20310i		−	0.922262i	−0.887332	−	0.461131i	$-0.847444\pi$
$61$		−	7.20310i		−	0.922262i	0.887332	−	0.461131i	$-0.152556\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	12.1413i		−	1.50595i
$66$		0			0
$67$	11.6103			1.41842			0.709210	−	0.704998i	$-0.249052\pi$
$67$	11.6103			1.41842			0.709210	+	0.704998i	$0.249052\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			10.4406i			1.23907i	0.784968	+	0.619537i	$0.212680\pi$
$71$			10.4406i			1.23907i	−0.784968	+	0.619537i	$0.787320\pi$
$72$		0			0
$73$	13.6493	−	7.88042i	1.59753	−	0.922334i	0.605567	−	0.795794i	$-0.292946\pi$
$73$	13.6493	−	7.88042i	1.59753	−	0.922334i	0.991962	−	0.126539i	$-0.0403870\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.05683	+	10.3289i	−0.804201	+	1.17709i
$78$		0			0
$79$	−12.3033			−1.38422			−0.692112	−	0.721790i	$-0.743320\pi$
$79$	−12.3033			−1.38422			−0.692112	+	0.721790i	$0.743320\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.03981	+	6.99715i	0.443426	+	0.768037i	0.997941	−	0.0641368i	$-0.0204294\pi$
$83$	4.03981	+	6.99715i	0.443426	+	0.768037i	−0.554515	+	0.832174i	$0.687096\pi$
$84$		0			0
$85$	−2.48067	+	4.29665i	−0.269067	+	0.466037i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.60872	+	7.98254i	−0.488523	+	0.846147i	−0.999913	−	0.0132019i	$-0.995798\pi$
$89$	−4.60872	+	7.98254i	−0.488523	+	0.846147i	0.511390	+	0.859349i	$0.329131\pi$
$90$		0			0
$91$	6.10169	−	8.93089i	0.639631	−	0.936212i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	14.5875i		−	1.49665i
$96$		0			0
$97$	7.00772	−	4.04591i	0.711527	−	0.410800i	−0.100099	−	0.994977i	$-0.531916\pi$
$97$	7.00772	−	4.04591i	0.711527	−	0.410800i	0.811626	+	0.584177i	$0.198583\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.65365	−	6.32831i	0.363552	−	0.629690i	−0.624991	−	0.780632i	$-0.714897\pi$
$101$	3.65365	−	6.32831i	0.363552	−	0.629690i	0.988543	+	0.150942i	$0.0482307\pi$
$102$		0			0
$103$	−6.08409	+	3.51265i	−0.599483	+	0.346112i	−0.768838	−	0.639443i	$-0.779165\pi$
$103$	−6.08409	+	3.51265i	−0.599483	+	0.346112i	0.169355	+	0.985555i	$0.445832\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.2618	+	7.07938i	1.18540	+	0.684389i	0.957257	−	0.289239i	$-0.0934022\pi$
$107$	12.2618	+	7.07938i	1.18540	+	0.684389i	0.228140	+	0.973628i	$0.426735\pi$
$108$		0			0
$109$	−2.82203	−	4.88789i	−0.270301	−	0.468175i	0.698638	−	0.715476i	$-0.253790\pi$
$109$	−2.82203	−	4.88789i	−0.270301	−	0.468175i	−0.968939	+	0.247300i	$0.920457\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.6411	−	6.72099i	−1.09510	−	0.632258i	−0.160172	−	0.987089i	$-0.551205\pi$
$113$	−11.6411	−	6.72099i	−1.09510	−	0.632258i	−0.934930	+	0.354831i	$0.884538\pi$
$114$		0			0
$115$	−12.6308	−	7.29239i	−1.17783	−	0.680019i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.98403	+	1.91384i	−0.365215	+	0.175442i
$120$		0			0
$121$	5.67752	+	9.83375i	0.516138	+	0.893977i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.50392			0.313400
$126$		0			0
$127$	−12.7730			−1.13342			−0.566712	−	0.823916i	$-0.691785\pi$
$127$	−12.7730			−1.13342			−0.566712	+	0.823916i	$0.691785\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.70890	−	11.6202i	−0.586159	−	1.01526i	−0.994730	−	0.102531i	$-0.967306\pi$
$131$	−6.70890	−	11.6202i	−0.586159	−	1.01526i	0.408570	−	0.912727i	$-0.366027\pi$
$132$		0			0
$133$	7.33104	−	10.7303i	0.635682	−	0.930432i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.79449	+	4.50015i	0.665928	+	0.384474i	0.794532	−	0.607222i	$-0.207716\pi$
$137$	7.79449	+	4.50015i	0.665928	+	0.384474i	−0.128604	+	0.991696i	$0.541050\pi$
$138$		0			0
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	0.564252	−	0.825602i	$-0.309164\pi$
$139$	1.54902	+	0.894326i	0.131386	+	0.0758557i	−0.432866	+	0.901458i	$0.642498\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.66464	−	16.7397i	−0.808198	−	1.39984i
$144$		0			0
$145$	−0.708485	−	0.409044i	−0.0588365	−	0.0339693i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.1779	−	6.45358i	0.915732	−	0.528698i	0.0334609	−	0.999440i	$-0.489347\pi$
$149$	11.1779	−	6.45358i	0.915732	−	0.528698i	0.882271	+	0.470742i	$0.156014\pi$
$150$		0			0
$151$	6.48364	−	11.2300i	0.527631	−	0.913884i	−0.471850	−	0.881679i	$-0.656414\pi$
$151$	6.48364	−	11.2300i	0.527631	−	0.913884i	0.999481	−	0.0322054i	$-0.0102531\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.12360	+	2.38076i	−0.331216	+	0.191227i
$156$		0			0
$157$		−	17.1728i		−	1.37054i	−0.728291	−	0.685268i	$-0.759685\pi$
$157$		−	17.1728i		−	1.37054i	0.728291	−	0.685268i	$-0.240315\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.62609	−	11.7118i	−0.443398	−	0.923017i
$162$		0			0
$163$	2.53107	−	4.38394i	0.198249	−	0.343377i	−0.749712	−	0.661764i	$-0.769808\pi$
$163$	2.53107	−	4.38394i	0.198249	−	0.343377i	0.947961	+	0.318387i	$0.103141\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.79673	−	10.0402i	0.448564	−	0.776936i	−0.549729	−	0.835343i	$-0.685269\pi$
$167$	5.79673	−	10.0402i	0.448564	−	0.776936i	0.998293	+	0.0584072i	$0.0186022\pi$
$168$		0			0
$169$	1.85653	+	3.21561i	0.142810	+	0.247354i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.26691			−0.476464			−0.238232	−	0.971208i	$-0.576568\pi$
$173$	−6.26691			−0.476464			−0.238232	+	0.971208i	$0.576568\pi$
$174$		0			0
$175$	−8.34547	−	5.70172i	−0.630858	−	0.431010i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.7668	−	7.37089i	0.954233	−	0.550927i	0.0598395	−	0.998208i	$-0.480941\pi$
$179$	12.7668	−	7.37089i	0.954233	−	0.550927i	0.894393	+	0.447281i	$0.147608\pi$
$180$		0			0
$181$		−	0.0833642i		−	0.00619641i	−0.999995	−	0.00309821i	$-0.999014\pi$
$181$		−	0.0833642i		−	0.00619641i	0.999995	−	0.00309821i	$-0.000986191\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.0786			−0.740996
$186$		0			0
$187$			7.89857i			0.577601i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			15.4351i			1.11684i	0.829558	+	0.558421i	$0.188593\pi$
$191$			15.4351i			1.11684i	−0.829558	+	0.558421i	$0.811407\pi$
$192$		0			0
$193$	21.5557			1.55162			0.775808	−	0.630969i	$-0.217343\pi$
$193$	21.5557			1.55162			0.775808	+	0.630969i	$0.217343\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			9.88306i			0.704139i	0.935974	+	0.352069i	$0.114522\pi$
$197$			9.88306i			0.704139i	−0.935974	+	0.352069i	$0.885478\pi$
$198$		0			0
$199$	−9.14623	+	5.28058i	−0.648359	+	0.374330i	−0.787827	−	0.615896i	$-0.788794\pi$
$199$	−9.14623	+	5.28058i	−0.648359	+	0.374330i	0.139468	+	0.990227i	$0.455461\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.315578	−	0.656936i	−0.0221492	−	0.0461079i
$204$		0			0
$205$	21.1237			1.47534
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−11.6118	−	20.1123i	−0.803208	−	1.39120i
$210$		0			0
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	−0.576951	−	0.816779i	$-0.695758\pi$
$211$	6.08453	−	10.5387i	0.418876	−	0.725514i	0.995827	+	0.0912645i	$0.0290909\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.5304	+	26.8994i	−1.05916	+	1.83453i
$216$		0			0
$217$	−4.22969	−	0.321102i	−0.287130	−	0.0217978i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	6.82950i		−	0.459402i
$222$		0			0
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	−0.475886	−	0.879507i	$-0.657873\pi$
$223$	0.714485	−	0.412508i	0.0478455	−	0.0276236i	0.523732	+	0.851883i	$0.324539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.166778	+	0.288869i	−0.0110695	+	0.0191729i	−0.871507	−	0.490383i	$-0.836857\pi$
$227$	−0.166778	+	0.288869i	−0.0110695	+	0.0191729i	0.860438	+	0.509556i	$0.170190\pi$
$228$		0			0
$229$	12.4893	−	7.21072i	0.825319	−	0.476498i	−0.0269285	−	0.999637i	$-0.508573\pi$
$229$	12.4893	−	7.21072i	0.825319	−	0.476498i	0.852247	+	0.523139i	$0.175239\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.7953	+	7.38739i	0.838250	+	0.483964i	0.856669	−	0.515867i	$-0.172530\pi$
$233$	12.7953	+	7.38739i	0.838250	+	0.483964i	−0.0184192	+	0.999830i	$0.505863\pi$
$234$		0			0
$235$	16.3309	+	28.2860i	1.06531	+	1.84518i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.998893	−	0.0470423i	$-0.0149795\pi$
$239$	22.5339	+	13.0100i	1.45760	+	0.841545i	0.458707	+	0.888588i	$0.348313\pi$
$240$		0			0
$241$	1.66295	+	0.960105i	0.107120	+	0.0618458i	0.552603	−	0.833445i	$-0.313635\pi$
$241$	1.66295	+	0.960105i	0.107120	+	0.0618458i	−0.445483	+	0.895290i	$0.646968\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.55753	−	19.3668i	−0.482833	−	1.23730i
$246$		0			0
$247$	10.0402	+	17.3901i	0.638841	+	1.10651i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−9.97663			−0.629719			−0.314860	−	0.949138i	$-0.601957\pi$
$251$	−9.97663			−0.629719			−0.314860	+	0.949138i	$0.601957\pi$
$252$		0			0
$253$	−23.2193			−1.45978
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.50364	−	12.9967i	−0.468064	−	0.810711i	0.531270	−	0.847203i	$-0.321715\pi$
$257$	−7.50364	−	12.9967i	−0.468064	−	0.810711i	−0.999334	+	0.0364915i	$0.988382\pi$
$258$		0			0
$259$	−7.41361	−	5.06506i	−0.460659	−	0.314728i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.11010	−	3.52767i	−0.376765	−	0.217525i	0.299645	−	0.954051i	$-0.403132\pi$
$263$	−6.11010	−	3.52767i	−0.376765	−	0.217525i	−0.676410	+	0.736525i	$0.736465\pi$
$264$		0			0
$265$	−2.10084	−	1.21292i	−0.129053	−	0.0745090i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.8898	−	25.7898i	−0.907844	−	1.57243i	−0.817053	−	0.576562i	$-0.804394\pi$
$269$	−14.8898	−	25.7898i	−0.907844	−	1.57243i	−0.0907911	−	0.995870i	$-0.528940\pi$
$270$		0			0
$271$	−2.41462	−	1.39408i	−0.146677	−	0.0846843i	0.424865	−	0.905257i	$-0.360321\pi$
$271$	−2.41462	−	1.39408i	−0.146677	−	0.0846843i	−0.571543	+	0.820572i	$0.693655\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−15.6424	+	9.03112i	−0.943270	+	0.544597i
$276$		0			0
$277$	−6.79074	+	11.7619i	−0.408016	+	0.706705i	−0.994667	−	0.103135i	$-0.967113\pi$
$277$	−6.79074	+	11.7619i	−0.408016	+	0.706705i	0.586651	+	0.809840i	$0.300446\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	3.95777	−	2.28502i	0.236101	−	0.136313i	−0.377283	−	0.926098i	$-0.623141\pi$
$281$	3.95777	−	2.28502i	0.236101	−	0.136313i	0.613383	+	0.789785i	$0.289808\pi$
$282$		0			0
$283$		−	20.4019i		−	1.21277i	−0.795173	−	0.606383i	$-0.792620\pi$
$283$		−	20.4019i		−	1.21277i	0.795173	−	0.606383i	$-0.207380\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	15.5381	+	10.6158i	0.917184	+	0.626631i
$288$		0			0
$289$	7.10462	−	12.3056i	0.417919	−	0.723857i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−6.41037	+	11.1031i	−0.374498	+	0.648649i	−0.990252	−	0.139289i	$-0.955518\pi$
$293$	−6.41037	+	11.1031i	−0.374498	+	0.648649i	0.615754	+	0.787939i	$0.288852\pi$
$294$		0			0
$295$	−4.08144	−	7.06926i	−0.237631	−	0.411589i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	20.0766			1.16106
$300$		0			0
$301$	−24.9422	+	11.9817i	−1.43765	+	0.690615i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	18.5263	−	10.6962i	1.06081	−	0.612461i
$306$		0			0
$307$		−	1.93411i		−	0.110386i	−0.998476	−	0.0551928i	$-0.982423\pi$
$307$		−	1.93411i		−	0.110386i	0.998476	−	0.0551928i	$-0.0175773\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−2.08916			−0.118465			−0.0592326	−	0.998244i	$-0.518865\pi$
$311$	−2.08916			−0.118465			−0.0592326	+	0.998244i	$0.518865\pi$
$312$		0			0
$313$			22.4088i			1.26662i	0.773899	+	0.633309i	$0.218304\pi$
$313$			22.4088i			1.26662i	−0.773899	+	0.633309i	$0.781696\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	3.48474i		−	0.195723i	−0.995200	−	0.0978614i	$-0.968800\pi$
$317$		−	3.48474i		−	0.195723i	0.995200	−	0.0978614i	$-0.0312002\pi$
$318$		0			0
$319$	−1.30241			−0.0729212
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	8.20549i		−	0.456565i
$324$		0			0
$325$	13.5252	−	7.80876i	0.750241	−	0.433152i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.20261	+	29.0137i	−0.121434	+	1.59958i
$330$		0			0
$331$	−4.57715			−0.251583			−0.125791	−	0.992057i	$-0.540147\pi$
$331$	−4.57715			−0.251583			−0.125791	+	0.992057i	$0.540147\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.2405	+	29.8615i	0.941951	+	1.63151i
$336$		0			0
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	0.117793	+	0.993038i	$0.462418\pi$
$337$	−14.7062	+	25.4720i	−0.801100	+	1.38755i	−0.918893	+	0.394508i	$0.870915\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.79023	+	6.56486i	−0.205252	+	0.355507i
$342$		0			0
$343$	4.17373	−	18.0438i	0.225360	−	0.974276i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	19.6582i		−	1.05531i	−0.849459	−	0.527654i	$-0.823072\pi$
$347$		−	19.6582i		−	1.05531i	0.849459	−	0.527654i	$-0.176928\pi$
$348$		0			0
$349$	−8.47286	+	4.89181i	−0.453542	+	0.261852i	−0.709325	−	0.704882i	$-0.751000\pi$
$349$	−8.47286	+	4.89181i	−0.453542	+	0.261852i	0.255783	+	0.966734i	$0.417667\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.5322	+	21.7065i	−0.667023	+	1.15532i	0.311709	+	0.950178i	$0.399099\pi$
$353$	−12.5322	+	21.7065i	−0.667023	+	1.15532i	−0.978733	+	0.205141i	$0.934235\pi$
$354$		0			0
$355$	−26.8532	+	15.5037i	−1.42522	+	0.822850i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.09861	+	4.67574i	0.427428	+	0.246776i	0.698251	−	0.715853i	$-0.253962\pi$
$359$	8.09861	+	4.67574i	0.427428	+	0.246776i	−0.270822	+	0.962629i	$0.587296\pi$
$360$		0			0
$361$	2.56305	+	4.43933i	0.134897	+	0.233649i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	40.5367	+	23.4039i	2.12179	+	1.22502i
$366$		0			0
$367$	18.9530	+	10.9425i	0.989337	+	0.571194i	0.905076	−	0.425250i	$-0.139814\pi$
$367$	18.9530	+	10.9425i	0.989337	+	0.571194i	0.0842608	+	0.996444i	$0.473147\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.935769	−	1.94798i	−0.0485827	−	0.101134i
$372$		0			0
$373$	−2.30822	−	3.99795i	−0.119515	−	0.207006i	0.800061	−	0.599919i	$-0.204801\pi$
$373$	−2.30822	−	3.99795i	−0.119515	−	0.207006i	−0.919576	+	0.392913i	$0.871467\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.12613			0.0579988
$378$		0			0
$379$	−6.22396			−0.319703			−0.159852	−	0.987141i	$-0.551102\pi$
$379$	−6.22396			−0.319703			−0.159852	+	0.987141i	$0.551102\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.9989	+	19.0506i	0.562015	+	0.973439i	0.997321	+	0.0731560i	$0.0233071\pi$
$383$	10.9989	+	19.0506i	0.562015	+	0.973439i	−0.435305	+	0.900283i	$0.643360\pi$
$384$		0			0
$385$	−37.0448	−	2.81230i	−1.88798	−	0.143328i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.51109	+	4.91388i	0.431529	+	0.249144i	0.699998	−	0.714145i	$-0.253184\pi$
$389$	8.51109	+	4.91388i	0.431529	+	0.249144i	−0.268469	+	0.963288i	$0.586518\pi$
$390$		0			0
$391$	−7.10481	−	4.10197i	−0.359306	−	0.207445i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−18.2696	−	31.6439i	−0.919243	−	1.59218i
$396$		0			0
$397$	4.55324	+	2.62881i	0.228520	+	0.131936i	0.609889	−	0.792487i	$-0.291214\pi$
$397$	4.55324	+	2.62881i	0.228520	+	0.131936i	−0.381369	+	0.924423i	$0.624547\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.7847	+	8.53594i	−0.738312	+	0.426265i	−0.821455	−	0.570273i	$-0.806837\pi$
$401$	−14.7847	+	8.53594i	−0.738312	+	0.426265i	0.0831432	+	0.996538i	$0.473504\pi$
$402$		0			0
$403$	3.27722	−	5.67631i	0.163250	−	0.282757i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.8957	+	8.02270i	−0.688786	+	0.397671i
$408$		0			0
$409$		−	19.5703i		−	0.967690i	−0.875154	−	0.483845i	$-0.839240\pi$
$409$		−	19.5703i		−	0.967690i	0.875154	−	0.483845i	$-0.160760\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.550478	−	7.25114i	0.0270873	−	0.356805i
$414$		0			0
$415$	−11.9977	+	20.7807i	−0.588946	+	1.02008i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.3073	+	17.8529i	−0.503547	+	0.872169i	0.496445	+	0.868068i	$0.334639\pi$
$419$	−10.3073	+	17.8529i	−0.503547	+	0.872169i	−0.999992	+	0.00410056i	$0.998695\pi$
$420$		0			0
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	0.882688	−	0.469959i	$-0.155731\pi$
$421$	0.704748	+	1.22066i	0.0343473	+	0.0594913i	−0.848341	+	0.529451i	$0.822398\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.38182			−0.309564
$426$		0			0
$427$	19.0029	+	1.44263i	0.919616	+	0.0698137i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.6666	+	6.73569i	−0.561959	+	0.324447i	−0.753931	−	0.656953i	$-0.771845\pi$
$431$	−11.6666	+	6.73569i	−0.561959	+	0.324447i	0.191973	+	0.981400i	$0.438512\pi$
$432$		0			0
$433$		−	12.9356i		−	0.621646i	−0.950468	−	0.310823i	$-0.899395\pi$
$433$		−	12.9356i		−	0.621646i	0.950468	−	0.310823i	$-0.100605\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	24.1215			1.15389
$438$		0			0
$439$			10.1039i			0.482233i	0.970496	+	0.241116i	$0.0775135\pi$
$439$			10.1039i			0.482233i	−0.970496	+	0.241116i	$0.922486\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	29.0084i		−	1.37823i	−0.724652	−	0.689115i	$-0.757999\pi$
$443$		−	29.0084i		−	1.37823i	0.724652	−	0.689115i	$-0.242001\pi$
$444$		0			0
$445$	−27.3747			−1.29768
$446$		0			0
$447$		0			0
$448$		0			0
$449$			7.94881i			0.375127i	0.982252	+	0.187564i	$0.0600591\pi$
$449$			7.94881i			0.375127i	−0.982252	+	0.187564i	$0.939941\pi$
$450$		0			0
$451$	29.1239	−	16.8147i	1.37139	−	0.791772i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	32.0308	+	2.43166i	1.50163	+	0.113998i
$456$		0			0
$457$	−13.9617			−0.653100			−0.326550	−	0.945180i	$-0.605886\pi$
$457$	−13.9617			−0.653100			−0.326550	+	0.945180i	$0.605886\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	16.4030	+	28.4108i	0.763964	+	1.32322i	0.940793	+	0.338983i	$0.110083\pi$
$461$	16.4030	+	28.4108i	0.763964	+	1.32322i	−0.176829	+	0.984242i	$0.556584\pi$
$462$		0			0
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	0.339163	+	0.940727i	$0.389856\pi$
$463$	−13.8812	+	24.0429i	−0.645112	+	1.11737i	−0.984276	+	0.176640i	$0.943477\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.4311	−	19.7992i	0.528966	−	0.916196i	−0.470463	−	0.882420i	$-0.655913\pi$
$467$	11.4311	−	19.7992i	0.528966	−	0.916196i	0.999429	−	0.0337767i	$-0.0107535\pi$
$468$		0			0
$469$	−2.32529	+	30.6297i	−0.107372	+	1.41435i
$470$		0			0
$471$		0			0
$472$		0			0
$473$			49.4494i			2.27369i
$474$		0			0
$475$	16.2502	−	9.38204i	0.745609	−	0.430478i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.21212	+	2.09946i	−0.0553834	+	0.0959269i	−0.892388	−	0.451269i	$-0.850971\pi$
$479$	−1.21212	+	2.09946i	−0.0553834	+	0.0959269i	0.837004	+	0.547196i	$0.184305\pi$
$480$		0			0
$481$	12.0149	−	6.93683i	0.547834	−	0.316292i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	20.8121	+	12.0159i	0.945028	+	0.545612i
$486$		0			0
$487$	5.19651	+	9.00061i	0.235476	+	0.407857i	0.959411	−	0.282012i	$-0.0910017\pi$
$487$	5.19651	+	9.00061i	0.235476	+	0.407857i	−0.723935	+	0.689868i	$0.757668\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	0.564658	−	0.825325i	$-0.309008\pi$
$491$	2.93014	+	1.69172i	0.132235	+	0.0763462i	−0.432423	+	0.901671i	$0.642341\pi$
$492$		0			0
$493$	−0.398522	−	0.230087i	−0.0179485	−	0.0103626i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−27.5440	−	2.09104i	−1.23552	−	0.0937958i
$498$		0			0
$499$	−19.7801	−	34.2602i	−0.885481	−	1.53370i	−0.845162	−	0.534511i	$-0.820496\pi$
$499$	−19.7801	−	34.2602i	−0.885481	−	1.53370i	−0.0403188	−	0.999187i	$-0.512837\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−14.5476			−0.648645			−0.324323	−	0.945947i	$-0.605136\pi$
$503$	−14.5476			−0.648645			−0.324323	+	0.945947i	$0.605136\pi$
$504$		0			0
$505$	21.7018			0.965717
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.1958	−	17.6596i	−0.451921	−	0.782750i	0.546585	−	0.837404i	$-0.315928\pi$
$509$	−10.1958	−	17.6596i	−0.451921	−	0.782750i	−0.998505	+	0.0546542i	$0.982594\pi$
$510$		0			0
$511$	18.0561	+	37.5873i	0.798757	+	1.66276i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−18.0690	−	10.4322i	−0.796216	−	0.459696i
$516$		0			0
$517$	45.0319	+	25.9992i	1.98050	+	1.14344i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	7.75122	+	13.4255i	0.339587	+	0.588182i	0.984355	−	0.176196i	$-0.0563793\pi$
$521$	7.75122	+	13.4255i	0.339587	+	0.588182i	−0.644768	+	0.764379i	$0.723046\pi$
$522$		0			0
$523$	9.35989	+	5.40394i	0.409280	+	0.236298i	0.690480	−	0.723351i	$-0.257399\pi$
$523$	9.35989	+	5.40394i	0.409280	+	0.236298i	−0.281201	+	0.959649i	$0.590733\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.31952	+	1.33918i	−0.101040	+	0.0583355i
$528$		0			0
$529$	0.558476	−	0.967309i	0.0242816	−	0.0420569i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.1819	+	14.5388i	−1.09075	+	0.629745i
$534$		0			0
$535$			42.0498i			1.81797i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−25.8360	−	20.6857i	−1.11283	−	0.890997i
$540$		0			0
$541$	−8.79357	+	15.2309i	−0.378065	+	0.654828i	−0.990781	−	0.135476i	$-0.956744\pi$
$541$	−8.79357	+	15.2309i	−0.378065	+	0.654828i	0.612716	+	0.790303i	$0.290077\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.38108	−	14.5165i	0.359006	−	0.621817i
$546$		0			0
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	0.717303	−	0.696762i	$-0.245377\pi$
$547$	−5.72451	−	9.91513i	−0.244762	−	0.423940i	−0.962065	+	0.272821i	$0.912043\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.35302			0.0576407
$552$		0			0
$553$	2.46408	−	32.4580i	0.104784	−	1.38025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	32.9159	−	19.0040i	1.39469	−	0.805226i	0.400863	−	0.916138i	$-0.368710\pi$
$557$	32.9159	−	19.0040i	1.39469	−	0.805226i	0.993830	+	0.110912i	$0.0353771\pi$
$558$		0			0
$559$		−	42.7565i		−	1.80841i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.7688			0.748864			0.374432	−	0.927254i	$-0.377838\pi$
$563$	17.7688			0.748864			0.374432	+	0.927254i	$0.377838\pi$
$564$		0			0
$565$		−	39.9211i		−	1.67949i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	38.9601i		−	1.63329i	−0.577139	−	0.816646i	$-0.695831\pi$
$569$		−	38.9601i		−	1.63329i	0.577139	−	0.816646i	$-0.304169\pi$
$570$		0			0
$571$	16.9049			0.707448			0.353724	−	0.935350i	$-0.384915\pi$
$571$	16.9049			0.707448			0.353724	+	0.935350i	$0.384915\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	18.7605i		−	0.782368i
$576$		0			0
$577$	−40.9329	+	23.6326i	−1.70406	+	0.983840i	−0.762506	+	0.646982i	$0.776031\pi$
$577$	−40.9329	+	23.6326i	−1.70406	+	0.983840i	−0.941555	+	0.336858i	$0.890636\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.2687	+	9.25628i	−0.799400	+	0.384015i
$582$		0			0
$583$	−3.86199			−0.159947
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.6343	−	20.1513i	−0.480200	−	0.831731i	0.519542	−	0.854445i	$-0.326103\pi$
$587$	−11.6343	−	20.1513i	−0.480200	−	0.831731i	−0.999742	+	0.0227138i	$0.992769\pi$
$588$		0			0
$589$	3.93750	−	6.81995i	0.162242	−	0.281011i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	18.5962	−	32.2095i	0.763654	−	1.32269i	−0.177302	−	0.984157i	$-0.556737\pi$
$593$	18.5962	−	32.2095i	0.763654	−	1.32269i	0.940955	−	0.338530i	$-0.109930\pi$
$594$		0			0
$595$	−10.8384	−	7.40494i	−0.444332	−	0.303573i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	32.2844i		−	1.31910i	−0.751659	−	0.659552i	$-0.770746\pi$
$599$		−	32.2844i		−	1.31910i	0.751659	−	0.659552i	$-0.229254\pi$
$600$		0			0
$601$	−14.7559	+	8.51933i	−0.601906	+	0.347511i	−0.769791	−	0.638296i	$-0.779640\pi$
$601$	−14.7559	+	8.51933i	−0.601906	+	0.347511i	0.167885	+	0.985807i	$0.446306\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−16.8615	+	29.2051i	−0.685519	+	1.18735i
$606$		0			0
$607$	8.44393	−	4.87510i	0.342728	−	0.197874i	−0.318749	−	0.947839i	$-0.603263\pi$
$607$	8.44393	−	4.87510i	0.342728	−	0.197874i	0.661478	+	0.749965i	$0.269930\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−38.9369	−	22.4802i	−1.57522	−	0.909452i
$612$		0			0
$613$	−6.86332	−	11.8876i	−0.277207	−	0.480136i	0.693483	−	0.720473i	$-0.256075\pi$
$613$	−6.86332	−	11.8876i	−0.277207	−	0.480136i	−0.970690	+	0.240337i	$0.922742\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.84301	+	1.64141i	0.114455	+	0.0660807i	0.556135	−	0.831092i	$-0.312284\pi$
$617$	2.84301	+	1.64141i	0.114455	+	0.0660807i	−0.441680	+	0.897173i	$0.645617\pi$
$618$		0			0
$619$	−14.9907	−	8.65490i	−0.602528	−	0.347870i	0.167507	−	0.985871i	$-0.446428\pi$
$619$	−14.9907	−	8.65490i	−0.602528	−	0.347870i	−0.770036	+	0.638001i	$0.779762\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−20.1362	−	13.7573i	−0.806739	−	0.551174i
$624$		0			0
$625$	14.7536	+	25.5539i	0.590142	+	1.02216i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.66923			−0.226047
$630$		0			0
$631$	−6.27821			−0.249932			−0.124966	−	0.992161i	$-0.539882\pi$
$631$	−6.27821			−0.249932			−0.124966	+	0.992161i	$0.539882\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−18.9672	−	32.8522i	−0.752691	−	1.30370i
$636$		0			0
$637$	22.3391	+	17.8859i	0.885107	+	0.708665i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	17.9788	+	10.3801i	0.710120	+	0.409988i	0.811105	−	0.584900i	$-0.198866\pi$
$641$	17.9788	+	10.3801i	0.710120	+	0.409988i	−0.100986	+	0.994888i	$0.532200\pi$
$642$		0			0
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	0.119554	−	0.992828i	$-0.461854\pi$
$643$	−17.2553	−	9.96236i	−0.680483	−	0.392877i	−0.800037	+	0.599950i	$0.795187\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.7670	+	25.5772i	0.580551	+	1.00554i	0.995414	+	0.0956605i	$0.0304963\pi$
$647$	14.7670	+	25.5772i	0.580551	+	1.00554i	−0.414863	+	0.909884i	$0.636170\pi$
$648$		0			0
$649$	−11.2544	−	6.49774i	−0.441775	−	0.255059i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−13.7914	+	7.96249i	−0.539701	+	0.311596i	−0.744958	−	0.667112i	$-0.767530\pi$
$653$	−13.7914	+	7.96249i	−0.539701	+	0.311596i	0.205257	+	0.978708i	$0.434197\pi$
$654$		0			0
$655$	19.9246	−	34.5105i	0.778520	−	1.34844i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	−0.553597	−	0.832785i	$-0.686745\pi$
$659$	−2.80283	+	1.61822i	−0.109183	+	0.0630368i	0.444414	+	0.895821i	$0.353412\pi$
$660$		0			0
$661$		−	8.90498i		−	0.346364i	−0.984890	−	0.173182i	$-0.944595\pi$
$661$		−	8.90498i		−	0.346364i	0.984890	−	0.173182i	$-0.0554048\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	38.4843	+	2.92158i	1.49236	+	0.113294i
$666$		0			0
$667$	0.676383	−	1.17153i	0.0261896	−	0.0453618i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	17.0285	−	29.4943i	0.657379	−	1.13861i
$672$		0			0
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	−0.999933	−	0.0116101i	$-0.996304\pi$
$673$	−13.2311	−	22.9169i	−0.510021	−	0.883382i	0.489912	−	0.871772i	$-0.337029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−8.92848			−0.343149			−0.171575	−	0.985171i	$-0.554886\pi$
$677$	−8.92848			−0.343149			−0.171575	+	0.985171i	$0.554886\pi$
$678$		0			0
$679$	9.27026	+	19.2978i	0.355760	+	0.740582i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.7902	+	18.9314i	−1.25468	+	0.724390i	−0.972035	−	0.234834i	$-0.924545\pi$
$683$	−32.7902	+	18.9314i	−1.25468	+	0.724390i	−0.282645	+	0.959225i	$0.591212\pi$
$684$		0			0
$685$			26.7298i			1.02129i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.33927			0.127216
$690$		0			0
$691$		−	5.70665i		−	0.217091i	−0.994091	−	0.108546i	$-0.965381\pi$
$691$		−	5.70665i		−	0.217091i	0.994091	−	0.108546i	$-0.0346194\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			5.31208i			0.201499i
$696$		0			0
$697$	11.8821			0.450065
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	8.19949i		−	0.309690i	−0.987939	−	0.154845i	$-0.950512\pi$
$701$		−	8.19949i		−	0.309690i	0.987939	−	0.154845i	$-0.0494879\pi$
$702$		0			0
$703$	14.4357	−	8.33444i	0.544452	−	0.314339i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.9633	+	10.9063i	0.600363	+	0.410175i
$708$		0			0
$709$	20.1515			0.756805			0.378402	−	0.925641i	$-0.376474\pi$
$709$	20.1515			0.756805			0.378402	+	0.925641i	$0.376474\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.93676	−	6.81866i	−0.147433	−	0.255361i
$714$		0			0
$715$	28.7028	−	49.7147i	1.07342	−	1.85923i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−25.5996	+	44.3397i	−0.954702	+	1.65359i	−0.219654	+	0.975578i	$0.570493\pi$
$719$	−25.5996	+	44.3397i	−0.954702	+	1.65359i	−0.735048	+	0.678015i	$0.762841\pi$
$720$		0			0
$721$	−8.04842	−	16.7543i	−0.299739	−	0.623963i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	1.05231i		−	0.0390820i
$726$		0			0
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	−0.222098	−	0.975024i	$-0.571290\pi$
$727$	13.7848	−	7.95865i	0.511249	−	0.295170i	0.733347	+	0.679854i	$0.237957\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.73584	+	15.1309i	−0.323107	+	0.559637i
$732$		0			0
$733$	3.67216	−	2.12012i	0.135634	−	0.0783086i	−0.430647	−	0.902520i	$-0.641715\pi$
$733$	3.67216	−	2.12012i	0.135634	−	0.0783086i	0.566282	+	0.824212i	$0.308381\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	47.5401	+	27.4473i	1.75116	+	1.01103i
$738$		0			0
$739$	−14.1835	−	24.5665i	−0.521747	−	0.903693i	−0.999680	−	0.0252966i	$-0.991947\pi$
$739$	−14.1835	−	24.5665i	−0.521747	−	0.903693i	0.477933	−	0.878397i	$-0.341386\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	0.0415945	−	0.999135i	$-0.486756\pi$
$743$	−21.8850	−	12.6353i	−0.802884	−	0.463545i	−0.844479	+	0.535589i	$0.820090\pi$
$744$		0			0
$745$	33.1971	+	19.1664i	1.21625	+	0.702201i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−21.1323	+	30.9309i	−0.772158	+	1.13019i
$750$		0			0
$751$	−23.7730	−	41.1761i	−0.867490	−	1.50254i	−0.864554	−	0.502540i	$-0.832399\pi$
$751$	−23.7730	−	41.1761i	−0.867490	−	1.50254i	−0.00293597	−	0.999996i	$-0.500935\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	38.5113			1.40157
$756$		0			0
$757$	37.3922			1.35904			0.679521	−	0.733656i	$-0.262188\pi$
$757$	37.3922			1.35904			0.679521	+	0.733656i	$0.262188\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.12142	+	7.13850i	0.149401	+	0.258770i	0.931006	−	0.365003i	$-0.118932\pi$
$761$	4.12142	+	7.13850i	0.149401	+	0.258770i	−0.781605	+	0.623774i	$0.785599\pi$
$762$		0			0
$763$	13.4602	−	6.46602i	0.487293	−	0.234086i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.73114	+	5.61827i	0.351371	+	0.202864i
$768$		0			0
$769$	−20.2182	−	11.6730i	−0.729086	−	0.420938i	0.0890020	−	0.996031i	$-0.471632\pi$
$769$	−20.2182	−	11.6730i	−0.729086	−	0.420938i	−0.818088	+	0.575094i	$0.804966\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.2201	−	29.8261i	−0.619364	−	1.07277i	−0.989602	−	0.143833i	$-0.954057\pi$
$773$	−17.2201	−	29.8261i	−0.619364	−	1.07277i	0.370238	−	0.928937i	$-0.379276\pi$
$774$		0			0
$775$	−5.30422	−	3.06240i	−0.190533	−	0.110004i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−30.2555	+	17.4680i	−1.08402	+	0.625857i
$780$		0			0
$781$	−24.6822	+	42.7508i	−0.883199	+	1.52975i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	44.1682	−	25.5005i	1.57643	−	0.910152i
$786$		0			0
$787$			8.31355i			0.296346i	0.988961	+	0.148173i	$0.0473393\pi$
$787$			8.31355i			0.296346i	−0.988961	+	0.148173i	$0.952661\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	20.0625	−	29.3650i	0.713341	−	1.04410i
$792$		0			0
$793$	−14.7237	+	25.5022i	−0.522854	+	0.905610i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.426036	−	0.737916i	0.0150910	−	0.0261383i	−0.858381	−	0.513012i	$-0.828530\pi$
$797$	0.426036	−	0.737916i	0.0150910	−	0.0261383i	0.873472	+	0.486874i	$0.161863\pi$
$798$		0			0
$799$	9.18614	+	15.9109i	0.324982	+	0.562886i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	74.5190			2.62972
$804$		0			0
$805$	21.7682	−	31.8615i	0.767227	−	1.12297i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−31.5580	+	18.2200i	−1.10952	+	0.640581i	−0.938705	−	0.344722i	$-0.887973\pi$
$809$	−31.5580	+	18.2200i	−1.10952	+	0.640581i	−0.170814	+	0.985303i	$0.554640\pi$
$810$		0			0
$811$			1.08986i			0.0382702i	0.999817	+	0.0191351i	$0.00609126\pi$
$811$			1.08986i			0.0382702i	−0.999817	+	0.0191351i	$0.993909\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	15.0339			0.526616
$816$		0			0
$817$		−	51.3709i		−	1.79724i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	24.2196i		−	0.845270i	−0.906300	−	0.422635i	$-0.861105\pi$
$821$		−	24.2196i		−	0.845270i	0.906300	−	0.422635i	$-0.138895\pi$
$822$		0			0
$823$	5.71185			0.199102			0.0995512	−	0.995032i	$-0.468259\pi$
$823$	5.71185			0.199102			0.0995512	+	0.995032i	$0.468259\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	36.4579i		−	1.26777i	−0.773429	−	0.633883i	$-0.781460\pi$
$827$		−	36.4579i		−	1.26777i	0.773429	−	0.633883i	$-0.218540\pi$
$828$		0			0
$829$	−0.498269	+	0.287676i	−0.0173056	+	0.00999140i	−0.508628	−	0.860986i	$-0.669847\pi$
$829$	−0.498269	+	0.287676i	−0.0173056	+	0.00999140i	0.491322	+	0.870978i	$0.336514\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.25111	−	10.8938i	−0.147292	−	0.377448i
$834$		0			0
$835$	34.4312			1.19154
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−23.9341	−	41.4550i	−0.826295	−	1.43119i	−0.900925	−	0.433974i	$-0.857111\pi$
$839$	−23.9341	−	41.4550i	−0.826295	−	1.43119i	0.0746300	−	0.997211i	$-0.476222\pi$
$840$		0			0
$841$	−14.4621	+	25.0490i	−0.498692	+	0.863759i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.51368	+	9.54997i	−0.189676	+	0.328529i
$846$		0			0
$847$	−27.0801	+	13.0087i	−0.930483	+	0.446985i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	16.6657i		−	0.571294i
$852$		0			0
$853$	−40.5393	+	23.4054i	−1.38804	+	0.801385i	−0.993094	−	0.117320i	$-0.962570\pi$
$853$	−40.5393	+	23.4054i	−1.38804	+	0.801385i	−0.394945	+	0.918705i	$0.629236\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.78220	+	8.28302i	−0.163357	+	0.282943i	−0.936071	−	0.351812i	$-0.885566\pi$
$857$	−4.78220	+	8.28302i	−0.163357	+	0.282943i	0.772714	+	0.634755i	$0.218899\pi$
$858$		0			0
$859$	−4.68311	+	2.70379i	−0.159786	+	0.0922523i	−0.577761	−	0.816206i	$-0.696073\pi$
$859$	−4.68311	+	2.70379i	−0.159786	+	0.0922523i	0.417975	+	0.908459i	$0.362740\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	35.5402	+	20.5191i	1.20980	+	0.698480i	0.962716	−	0.270514i	$-0.0871936\pi$
$863$	35.5402	+	20.5191i	1.20980	+	0.698480i	0.247086	+	0.968994i	$0.420527\pi$
$864$		0			0
$865$	−9.30598	−	16.1184i	−0.316413	−	0.548043i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−50.3777	−	29.0856i	−1.70895	−	0.986661i
$870$		0			0
$871$	−41.1056	−	23.7323i	−1.39281	−	0.804139i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.701762	+	9.24390i	−0.0237239	+	0.312501i
$876$		0			0
$877$	7.32509	+	12.6874i	0.247351	+	0.428424i	0.962790	−	0.270251i	$-0.0871067\pi$
$877$	7.32509	+	12.6874i	0.247351	+	0.428424i	−0.715439	+	0.698675i	$0.753773\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−44.8295			−1.51034			−0.755172	−	0.655527i	$-0.772447\pi$
$881$	−44.8295			−1.51034			−0.755172	+	0.655527i	$0.772447\pi$
$882$		0			0
$883$	33.8527			1.13923			0.569617	−	0.821910i	$-0.307091\pi$
$883$	33.8527			1.13923			0.569617	+	0.821910i	$0.307091\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	13.3422	+	23.1093i	0.447987	+	0.775936i	0.998255	−	0.0590523i	$-0.0188079\pi$
$887$	13.3422	+	23.1093i	0.447987	+	0.775936i	−0.550268	+	0.834988i	$0.685475\pi$
$888$		0			0
$889$	2.55817	−	33.6973i	0.0857984	−	1.13017i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−46.7817	−	27.0094i	−1.56549	−	0.903837i
$894$		0			0
$895$	37.9157	+	21.8907i	1.26738	+	0.731724i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.220820	−	0.382472i	−0.00736476	−	0.0127561i
$900$		0			0
$901$	−1.18172	−	0.682266i	−0.0393688	−	0.0227296i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.214412	−	0.123791i	0.00712729	−	0.00411494i
$906$		0			0
$907$	7.97211	−	13.8081i	0.264710	−	0.458490i	−0.702778	−	0.711409i	$-0.748057\pi$
$907$	7.97211	−	13.8081i	0.264710	−	0.458490i	0.967487	+	0.252919i	$0.0813906\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.989050	−	0.147584i	$-0.952850\pi$
$911$	−40.9207	+	23.6256i	−1.35576	+	0.782750i	−0.366713	+	0.930334i	$0.619517\pi$
$912$		0			0
$913$			38.2013i			1.26428i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	31.9995	−	15.3719i	1.05672	−	0.507624i
$918$		0			0
$919$	14.8163	−	25.6625i	0.488743	−	0.846528i	−0.511173	−	0.859478i	$-0.670789\pi$
$919$	14.8163	−	25.6625i	0.488743	−	0.846528i	0.999916	+	0.0129500i	$0.00412223\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	21.3415	−	36.9645i	0.702463	−	1.21670i
$924$		0			0
$925$	−6.48212	−	11.2274i	−0.213131	−	0.369153i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−33.2372			−1.09048			−0.545238	−	0.838281i	$-0.683561\pi$
$929$	−33.2372			−1.09048			−0.545238	+	0.838281i	$0.683561\pi$
$930$		0			0
$931$	26.8399	+	21.4895i	0.879642	+	0.704290i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−20.3151	+	11.7289i	−0.664373	+	0.383576i
$936$		0			0
$937$			23.8190i			0.778134i	0.921209	+	0.389067i	$0.127203\pi$
$937$			23.8190i			0.778134i	−0.921209	+	0.389067i	$0.872797\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	54.2403			1.76818			0.884091	−	0.467315i	$-0.154779\pi$
$941$	54.2403			1.76818			0.884091	+	0.467315i	$0.154779\pi$
$942$		0			0
$943$			34.9295i			1.13746i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			21.0648i			0.684515i	0.939606	+	0.342257i	$0.111191\pi$
$947$			21.0648i			0.684515i	−0.939606	+	0.342257i	$0.888809\pi$
$948$		0			0
$949$	−64.4329			−2.09158
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	4.50028i		−	0.145778i	−0.997340	−	0.0728892i	$-0.976778\pi$
$953$		−	4.50028i		−	0.145778i	0.997340	−	0.0728892i	$-0.0232219\pi$
$954$		0			0
$955$	−39.6989	+	22.9201i	−1.28462	+	0.741679i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−13.4332	+	19.6618i	−0.433780	+	0.634913i
$960$		0			0
$961$	28.4295			0.917081
$962$		0			0
$963$		0			0
$964$		0			0
$965$	32.0090	+	55.4411i	1.03040	+	1.78471i
$966$		0			0
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	−0.986233	−	0.165359i	$-0.947122\pi$
$967$	−10.8811	+	18.8466i	−0.349912	+	0.606065i	0.636322	+	0.771424i	$0.280455\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.5222	+	40.7416i	−0.754862	+	1.30746i	0.190581	+	0.981671i	$0.438963\pi$
$971$	−23.5222	+	40.7416i	−0.754862	+	1.30746i	−0.945443	+	0.325788i	$0.894371\pi$
$972$		0			0
$973$	−2.66961	+	3.90744i	−0.0855838	+	0.125267i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			25.1455i			0.804475i	0.915535	+	0.402237i	$0.131767\pi$
$977$			25.1455i			0.804475i	−0.915535	+	0.402237i	$0.868233\pi$
$978$		0			0
$979$	−37.7423	+	21.7905i	−1.20625	+	0.696429i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	18.1071	−	31.3624i	0.577527	−	1.00031i	−0.418235	−	0.908339i	$-0.637351\pi$
$983$	18.1071	−	31.3624i	0.577527	−	1.00031i	0.995762	−	0.0919674i	$-0.0293156\pi$
$984$		0			0
$985$	−25.4191	+	14.6757i	−0.809921	+	0.467608i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−44.4801	−	25.6806i	−1.41438	−	0.816595i
$990$		0			0
$991$	−9.32769	−	16.1560i	−0.296304	−	0.513213i	0.678984	−	0.734153i	$-0.262421\pi$
$991$	−9.32769	−	16.1560i	−0.296304	−	0.513213i	−0.975287	+	0.220940i	$0.929087\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.1632	−	15.6827i	−0.861131	−	0.497174i
$996$		0			0
$997$	−15.1413	−	8.74181i	−0.479528	−	0.276856i	0.240691	−	0.970602i	$-0.422626\pi$
$997$	−15.1413	−	8.74181i	−0.479528	−	0.276856i	−0.720220	+	0.693746i	$0.755959\pi$
$998$		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.341.7		16
3.2	odd	2		252.2.w.a.5.3	✓	16
4.3	odd	2		3024.2.ca.d.2609.7		16
7.2	even	3		5292.2.x.a.881.7		16
7.3	odd	6		756.2.bm.a.17.7		16
7.4	even	3		5292.2.bm.a.2285.2		16
7.5	odd	6		5292.2.x.b.881.2		16
7.6	odd	2		5292.2.w.b.1097.2		16
9.2	odd	6		756.2.bm.a.89.7		16
9.4	even	3		2268.2.t.a.2105.7		16
9.5	odd	6		2268.2.t.b.2105.2		16
9.7	even	3		252.2.bm.a.173.1	yes	16
12.11	even	2		1008.2.ca.d.257.6		16
21.2	odd	6		1764.2.x.a.293.4		16
21.5	even	6		1764.2.x.b.293.5		16
21.11	odd	6		1764.2.bm.a.1697.8		16
21.17	even	6		252.2.bm.a.185.1	yes	16
21.20	even	2		1764.2.w.b.509.6		16
28.3	even	6		3024.2.df.d.17.7		16
36.7	odd	6		1008.2.df.d.929.8		16
36.11	even	6		3024.2.df.d.1601.7		16
63.2	odd	6		5292.2.x.b.4409.2		16
63.11	odd	6		5292.2.w.b.521.2		16
63.16	even	3		1764.2.x.b.1469.5		16
63.20	even	6		5292.2.bm.a.4625.2		16
63.25	even	3		1764.2.w.b.1109.6		16
63.31	odd	6		2268.2.t.b.1781.2		16
63.34	odd	6		1764.2.bm.a.1685.8		16
63.38	even	6	inner	756.2.w.a.521.7		16
63.47	even	6		5292.2.x.a.4409.7		16
63.52	odd	6		252.2.w.a.101.3	yes	16
63.59	even	6		2268.2.t.a.1781.7		16
63.61	odd	6		1764.2.x.a.1469.4		16
84.59	odd	6		1008.2.df.d.689.8		16
252.115	even	6		1008.2.ca.d.353.6		16
252.227	odd	6		3024.2.ca.d.2033.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	3.2	odd	2
252.2.w.a.101.3	yes	16	63.52	odd	6
252.2.bm.a.173.1	yes	16	9.7	even	3
252.2.bm.a.185.1	yes	16	21.17	even	6
756.2.w.a.341.7		16	1.1	even	1	trivial
756.2.w.a.521.7		16	63.38	even	6	inner
756.2.bm.a.17.7		16	7.3	odd	6
756.2.bm.a.89.7		16	9.2	odd	6
1008.2.ca.d.257.6		16	12.11	even	2
1008.2.ca.d.353.6		16	252.115	even	6
1008.2.df.d.689.8		16	84.59	odd	6
1008.2.df.d.929.8		16	36.7	odd	6
1764.2.w.b.509.6		16	21.20	even	2
1764.2.w.b.1109.6		16	63.25	even	3
1764.2.x.a.293.4		16	21.2	odd	6
1764.2.x.a.1469.4		16	63.61	odd	6
1764.2.x.b.293.5		16	21.5	even	6
1764.2.x.b.1469.5		16	63.16	even	3
1764.2.bm.a.1685.8		16	63.34	odd	6
1764.2.bm.a.1697.8		16	21.11	odd	6
2268.2.t.a.1781.7		16	63.59	even	6
2268.2.t.a.2105.7		16	9.4	even	3
2268.2.t.b.1781.2		16	63.31	odd	6
2268.2.t.b.2105.2		16	9.5	odd	6
3024.2.ca.d.2033.7		16	252.227	odd	6
3024.2.ca.d.2609.7		16	4.3	odd	2
3024.2.df.d.17.7		16	28.3	even	6
3024.2.df.d.1601.7		16	36.11	even	6
5292.2.w.b.521.2		16	63.11	odd	6
5292.2.w.b.1097.2		16	7.6	odd	2
5292.2.x.a.881.7		16	7.2	even	3
5292.2.x.a.4409.7		16	63.47	even	6
5292.2.x.b.881.2		16	7.5	odd	6
5292.2.x.b.4409.2		16	63.2	odd	6
5292.2.bm.a.2285.2		16	7.4	even	3
5292.2.bm.a.4625.2		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)

\(f(q)\)	\(=\)	\(q+(1.48494 + 2.57199i) q^{5} +(-0.200279 + 2.63816i) q^{7} +O(q^{10})\)	\(q+(1.48494 + 2.57199i) q^{5} +(-0.200279 + 2.63816i) q^{7} +(4.09466 + 2.36406i) q^{11} +(-3.54045 - 2.04408i) q^{13} +(0.835278 + 1.44674i) q^{17} +(-4.25377 - 2.45592i) q^{19} +(-4.25297 + 2.45545i) q^{23} +(-1.91009 + 3.30837i) q^{25} +(-0.238557 + 0.137731i) q^{29} +1.60327i q^{31} +(-7.08273 + 3.40239i) q^{35} +(-1.69681 + 2.93896i) q^{37} +(3.55632 - 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +10.9977 q^{47} +(-6.91978 - 1.05674i) q^{49} +(-0.707381 + 0.408407i) q^{53} +14.0419i q^{55} -2.74856 q^{59} -7.20310i q^{61} -12.1413i q^{65} +11.6103 q^{67} +10.4406i q^{71} +(13.6493 - 7.88042i) q^{73} +(-7.05683 + 10.3289i) q^{77} -12.3033 q^{79} +(4.03981 + 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(-4.60872 + 7.98254i) q^{89} +(6.10169 - 8.93089i) q^{91} -14.5875i q^{95} +(7.00772 - 4.04591i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 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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