LMFDB - Embedded newform 756.2.bm.a.17.7

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			17.7
Root			$1.68042 - 0.419752i$ of defining polynomial
Character	$\chi$	$=$	756.17
Dual form			756.2.bm.a.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.96988 q^{5} +(2.38485 + 1.14563i) q^{7} -4.72811i q^{11} +(3.54045 + 2.04408i) q^{13} +(-0.835278 + 1.44674i) q^{17} +(-4.25377 + 2.45592i) q^{19} -4.91090i q^{23} +3.82018 q^{25} +(-0.238557 + 0.137731i) q^{29} +(-1.38847 + 0.801636i) q^{31} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +(5.49885 - 9.52430i) q^{47} +(4.37505 + 5.46433i) q^{49} +(0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +(-1.37428 - 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(10.5147 + 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(5.41668 - 11.2759i) q^{77} +(6.15163 - 10.6549i) q^{79} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(4.60872 + 7.98254i) q^{89} +(6.10169 + 8.93089i) q^{91} +(-12.6332 + 7.29377i) q^{95} +(-7.00772 + 4.04591i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

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

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
$5$	2.96988			1.32817			0.664085	−	0.747657i	$-0.268821\pi$
$5$	2.96988			1.32817			0.664085	+	0.747657i	$0.268821\pi$
$6$		0			0
$7$	2.38485	+	1.14563i	0.901390	+	0.433009i
$7$	2.38485	+	1.14563i	0.901390	+	0.433009i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	4.72811i		−	1.42558i	−0.701378	−	0.712790i	$-0.747431\pi$
$11$		−	4.72811i		−	1.42558i	0.701378	−	0.712790i	$-0.252569\pi$
$12$		0			0
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.902857	−	0.429942i	$-0.141466\pi$
$13$	3.54045	+	2.04408i	0.981945	+	0.566926i	0.0790880	+	0.996868i	$0.474799\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.835278	+	1.44674i	−0.202585	+	0.350887i	−0.949360	−	0.314189i	$-0.898267\pi$
$17$	−0.835278	+	1.44674i	−0.202585	+	0.350887i	0.746776	+	0.665076i	$0.231601\pi$
$18$		0			0
$19$	−4.25377	+	2.45592i	−0.975882	+	0.563426i	−0.901024	−	0.433768i	$-0.857184\pi$
$19$	−4.25377	+	2.45592i	−0.975882	+	0.563426i	−0.0748577	+	0.997194i	$0.523850\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	4.91090i		−	1.02399i	−0.858987	−	0.511997i	$-0.828906\pi$
$23$		−	4.91090i		−	1.02399i	0.858987	−	0.511997i	$-0.171094\pi$
$24$		0			0
$25$	3.82018			0.764036
$26$		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
$31$	−1.38847	+	0.801636i	−0.249377	+	0.143978i	−0.619479	−	0.785013i	$-0.712656\pi$
$31$	−1.38847	+	0.801636i	−0.249377	+	0.143978i	0.370102	+	0.928991i	$0.379323\pi$
$32$		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	0.692171	−	0.721733i	$-0.256654\pi$
$37$	−1.69681	−	2.93896i	−0.278954	−	0.483162i	−0.971125	+	0.238571i	$0.923321\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	0.442468	+	0.896784i	$0.354103\pi$
$41$	−3.55632	+	6.15972i	−0.555404	+	0.961987i	−0.997872	+	0.0652031i	$0.979230\pi$
$42$		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
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	−0.116148	−	0.993232i	$-0.537055\pi$
$47$	5.49885	−	9.52430i	0.802090	−	1.38926i	0.918238	−	0.396029i	$-0.129612\pi$
$48$		0			0
$49$	4.37505	+	5.46433i	0.625007	+	0.780619i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.707381	+	0.408407i	0.0971663	+	0.0560990i	0.547796	−	0.836612i	$-0.315467\pi$
$53$	0.707381	+	0.408407i	0.0971663	+	0.0560990i	−0.450629	+	0.892711i	$0.648800\pi$
$54$		0			0
$55$		−	14.0419i		−	1.89341i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	0.762594	−	0.646878i	$-0.223926\pi$
$59$	−1.37428	−	2.38032i	−0.178916	−	0.309891i	−0.941509	+	0.336986i	$0.890592\pi$
$60$		0			0
$61$	−6.23807	−	3.60155i	−0.798703	−	0.461131i	0.0443147	−	0.999018i	$-0.485890\pi$
$61$	−6.23807	−	3.60155i	−0.798703	−	0.461131i	−0.843017	+	0.537886i	$0.819223\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.5147	+	6.07067i	1.30419	+	0.752974i
$66$		0			0
$67$	−5.80513	−	10.0548i	−0.709210	−	1.22839i	−0.965151	−	0.261695i	$-0.915719\pi$
$67$	−5.80513	−	10.0548i	−0.709210	−	1.22839i	0.255941	−	0.966692i	$-0.417615\pi$
$68$		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	0.991962	+	0.126539i	$0.0403870\pi$
$73$	13.6493	+	7.88042i	1.59753	+	0.922334i	0.605567	+	0.795794i	$0.292946\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	5.41668	−	11.2759i	0.617288	−	1.28500i
$78$		0			0
$79$	6.15163	−	10.6549i	0.692112	−	1.19877i	−0.279032	−	0.960282i	$-0.590014\pi$
$79$	6.15163	−	10.6549i	0.692112	−	1.19877i	0.971145	−	0.238492i	$-0.0766530\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	0.554515	−	0.832174i	$-0.312904\pi$
$83$	−4.03981	−	6.99715i	−0.443426	−	0.768037i	−0.997941	+	0.0641368i	$0.979571\pi$
$84$		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	$-0.00420240\pi$
$89$	4.60872	+	7.98254i	0.488523	+	0.846147i	−0.511390	+	0.859349i	$0.670869\pi$
$90$		0			0
$91$	6.10169	+	8.93089i	0.639631	+	0.936212i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−12.6332	+	7.29377i	−1.29614	+	0.748325i
$96$		0			0
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	−0.811626	−	0.584177i	$-0.801417\pi$
$97$	−7.00772	+	4.04591i	−0.711527	+	0.410800i	0.100099	+	0.994977i	$0.468084\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.30730			0.727103			0.363552	−	0.931574i	$-0.381564\pi$
$101$	7.30730			0.727103			0.363552	+	0.931574i	$0.381564\pi$
$102$		0			0
$103$			7.02530i			0.692224i	0.938193	+	0.346112i	$0.112498\pi$
$103$			7.02530i			0.692224i	−0.938193	+	0.346112i	$0.887502\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.957257	−	0.289239i	$-0.906598\pi$
$107$	−12.2618	+	7.07938i	−1.18540	+	0.684389i	−0.228140	+	0.973628i	$0.573265\pi$
$108$		0			0
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	−0.968939	−	0.247300i	$-0.920457\pi$
$109$	−2.82203	+	4.88789i	−0.270301	+	0.468175i	0.698638	+	0.715476i	$0.253790\pi$
$110$		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
$115$		−	14.5848i		−	1.36004i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.64945	+	2.49335i	−0.334545	+	0.228565i
$120$		0			0
$121$	−11.3550			−1.03228
$122$		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
$131$	−13.4178			−1.17232			−0.586159	−	0.810196i	$-0.699361\pi$
$131$	−13.4178			−1.17232			−0.586159	+	0.810196i	$0.699361\pi$
$132$		0			0
$133$	−12.9582	+	0.983737i	−1.12362	+	0.0853008i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	9.00030i		−	0.768948i	−0.923136	−	0.384474i	$-0.874383\pi$
$137$		−	9.00030i		−	0.768948i	0.923136	−	0.384474i	$-0.125617\pi$
$138$		0			0
$139$	−1.54902	−	0.894326i	−0.131386	−	0.0758557i	0.432866	−	0.901458i	$-0.357502\pi$
$139$	−1.54902	−	0.894326i	−0.131386	−	0.0758557i	−0.564252	+	0.825602i	$0.690836\pi$
$140$		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
$149$			12.9072i			1.05740i	0.848810	+	0.528698i	$0.177320\pi$
$149$			12.9072i			1.05740i	−0.848810	+	0.528698i	$0.822680\pi$
$150$		0			0
$151$	−12.9673			−1.05526			−0.527631	−	0.849473i	$-0.676920\pi$
$151$	−12.9673			−1.05526			−0.527631	+	0.849473i	$0.676920\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.12360	+	2.38076i	−0.331216	+	0.191227i
$156$		0			0
$157$	14.8720	−	8.58638i	1.18692	−	0.685268i	0.229314	−	0.973353i	$-0.426352\pi$
$157$	14.8720	−	8.58638i	1.18692	−	0.685268i	0.957605	+	0.288085i	$0.0930185\pi$
$158$		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	0.947961	−	0.318387i	$-0.103141\pi$
$163$	2.53107	+	4.38394i	0.198249	+	0.343377i	−0.749712	+	0.661764i	$0.769808\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	−0.998293	−	0.0584072i	$-0.981398\pi$
$167$	−5.79673	+	10.0402i	−0.448564	+	0.776936i	0.549729	+	0.835343i	$0.314731\pi$
$168$		0			0
$169$	1.85653	+	3.21561i	0.142810	+	0.247354i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.13346	+	5.42730i	−0.238232	+	0.412630i	−0.960207	−	0.279289i	$-0.909901\pi$
$173$	−3.13346	+	5.42730i	−0.238232	+	0.412630i	0.721975	+	0.691919i	$0.243235\pi$
$174$		0			0
$175$	9.11057	+	4.37653i	0.688694	+	0.330834i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.0598395	−	0.998208i	$-0.519059\pi$
$179$	−12.7668	−	7.37089i	−0.954233	−	0.550927i	−0.894393	+	0.447281i	$0.852392\pi$
$180$		0			0
$181$			0.0833642i			0.00619641i	0.999995	+	0.00309821i	$0.000986191\pi$
$181$			0.0833642i			0.00619641i	−0.999995	+	0.00309821i	$0.999014\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.03932	−	8.72835i	−0.370498	−	0.641721i
$186$		0			0
$187$	6.84036	+	3.94929i	0.500217	+	0.288800i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.3672	−	7.71754i	−0.967214	−	0.558421i	−0.0688282	−	0.997629i	$-0.521926\pi$
$191$	−13.3672	−	7.71754i	−0.967214	−	0.558421i	−0.898386	+	0.439207i	$0.855259\pi$
$192$		0			0
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	−0.934339	−	0.356385i	$-0.884009\pi$
$193$	−10.7779	−	18.6678i	−0.775808	−	1.34374i	0.158532	−	0.987354i	$-0.449324\pi$
$194$		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	0.139468	−	0.990227i	$-0.455461\pi$
$199$	−9.14623	−	5.28058i	−0.648359	−	0.374330i	−0.787827	+	0.615896i	$0.788794\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.726712	+	0.0551692i	−0.0510052	+	0.00387212i
$204$		0			0
$205$	−10.5618	+	18.2936i	−0.737670	+	1.27768i
$206$		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
$221$	−5.91452	+	3.41475i	−0.397854	+	0.229701i
$222$		0			0
$223$	−0.714485	+	0.412508i	−0.0478455	+	0.0276236i	−0.523732	−	0.851883i	$-0.675461\pi$
$223$	−0.714485	+	0.412508i	−0.0478455	+	0.0276236i	0.475886	+	0.879507i	$0.342127\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.333557			−0.0221390			−0.0110695	−	0.999939i	$-0.503524\pi$
$227$	−0.333557			−0.0221390			−0.0110695	+	0.999939i	$0.503524\pi$
$228$		0			0
$229$		−	14.4214i		−	0.952996i	−0.879176	−	0.476498i	$-0.841906\pi$
$229$		−	14.4214i		−	0.952996i	0.879176	−	0.476498i	$-0.158094\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.7953	+	7.38739i	−0.838250	+	0.483964i	−0.856669	−	0.515867i	$-0.827470\pi$
$233$	−12.7953	+	7.38739i	−0.838250	+	0.483964i	0.0184192	+	0.999830i	$0.494137\pi$
$234$		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
$241$			1.92021i			0.123692i	0.998086	+	0.0618458i	$0.0196987\pi$
$241$			1.92021i			0.123692i	−0.998086	+	0.0618458i	$0.980301\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.9934	+	16.2284i	0.830116	+	1.03680i
$246$		0			0
$247$	−20.0804			−1.27768
$248$		0			0
$249$		0			0
$250$		0			0
$251$	9.97663			0.629719			0.314860	−	0.949138i	$-0.398043\pi$
$251$	9.97663			0.629719			0.314860	+	0.949138i	$0.398043\pi$
$252$		0			0
$253$	−23.2193			−1.45978
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.0073			−0.936129			−0.468064	−	0.883694i	$-0.655048\pi$
$257$	−15.0073			−0.936129			−0.468064	+	0.883694i	$0.655048\pi$
$258$		0			0
$259$	−0.679670	−	8.95291i	−0.0422327	−	0.556306i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			7.05534i			0.435051i	0.976055	+	0.217525i	$0.0697985\pi$
$263$			7.05534i			0.435051i	−0.976055	+	0.217525i	$0.930202\pi$
$264$		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	0.0907911	−	0.995870i	$-0.471060\pi$
$269$	14.8898	−	25.7898i	0.907844	−	1.57243i	0.817053	−	0.576562i	$-0.195606\pi$
$270$		0			0
$271$	−2.41462	+	1.39408i	−0.146677	+	0.0846843i	−0.571543	−	0.820572i	$-0.693655\pi$
$271$	−2.41462	+	1.39408i	−0.146677	+	0.0846843i	0.424865	+	0.905257i	$0.360321\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	18.0622i		−	1.08919i
$276$		0			0
$277$	13.5815			0.816032			0.408016	−	0.912975i	$-0.366221\pi$
$277$	13.5815			0.816032			0.408016	+	0.912975i	$0.366221\pi$
$278$		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
$283$	17.6685	−	10.2009i	1.05029	−	0.606383i	0.127556	−	0.991831i	$-0.459287\pi$
$283$	17.6685	−	10.2009i	1.05029	−	0.606383i	0.922729	+	0.385449i	$0.125953\pi$
$284$		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	−0.615754	−	0.787939i	$-0.711148\pi$
$293$	6.41037	−	11.1031i	0.374498	−	0.648649i	0.990252	+	0.139289i	$0.0444818\pi$
$294$		0			0
$295$	−4.08144	−	7.06926i	−0.237631	−	0.411589i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.0383	−	17.3868i	0.580529	−	1.00551i
$300$		0			0
$301$	2.09464	+	27.5915i	0.120733	+	1.59035i
$302$		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	$0.0175773\pi$
$307$			1.93411i			0.110386i	−0.998476	+	0.0551928i	$0.982423\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	0.834889	−	0.550419i	$-0.185532\pi$
$311$	−1.04458	−	1.80926i	−0.0592326	−	0.102594i	−0.894121	+	0.447825i	$0.852199\pi$
$312$		0			0
$313$	19.4066	+	11.2044i	1.09692	+	0.633309i	0.935411	−	0.353562i	$-0.115030\pi$
$313$	19.4066	+	11.2044i	1.09692	+	0.633309i	0.161512	+	0.986871i	$0.448363\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.01788	+	1.74237i	0.169501	+	0.0978614i	0.582350	−	0.812938i	$-0.302133\pi$
$317$	3.01788	+	1.74237i	0.169501	+	0.0978614i	−0.412850	+	0.910799i	$0.635466\pi$
$318$		0			0
$319$	0.651207	+	1.12792i	0.0364606	+	0.0631516i
$320$		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
$329$	24.0253	−	16.4144i	1.32456	−	0.904954i
$330$		0			0
$331$	2.28857	−	3.96392i	0.125791	−	0.217877i	−0.796251	−	0.604967i	$-0.793186\pi$
$331$	2.28857	−	3.96392i	0.125791	−	0.217877i	0.922042	+	0.387090i	$0.126520\pi$
$332$		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
$347$	−17.0245	+	9.82911i	−0.913924	+	0.527654i	−0.881692	−	0.471826i	$-0.843595\pi$
$347$	−17.0245	+	9.82911i	−0.913924	+	0.527654i	−0.0322323	+	0.999480i	$0.510262\pi$
$348$		0			0
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	−0.255783	−	0.966734i	$-0.582333\pi$
$349$	8.47286	−	4.89181i	0.453542	−	0.261852i	0.709325	+	0.704882i	$0.249000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−25.0645			−1.33405			−0.667023	−	0.745037i	$-0.732432\pi$
$353$	−25.0645			−1.33405			−0.667023	+	0.745037i	$0.732432\pi$
$354$		0			0
$355$			31.0074i			1.64570i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	−0.698251	−	0.715853i	$-0.746038\pi$
$359$	−8.09861	+	4.67574i	−0.427428	+	0.246776i	0.270822	+	0.962629i	$0.412704\pi$
$360$		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
$367$			21.8850i			1.14239i	0.820815	+	0.571194i	$0.193520\pi$
$367$			21.8850i			1.14239i	−0.820815	+	0.571194i	$0.806480\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.21912	+	1.78439i	0.0632934	+	0.0926409i
$372$		0			0
$373$	4.61644			0.239030			0.119515	−	0.992832i	$-0.461866\pi$
$373$	4.61644			0.239030			0.119515	+	0.992832i	$0.461866\pi$
$374$		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
$383$	21.9977			1.12403			0.562015	−	0.827127i	$-0.310026\pi$
$383$	21.9977			1.12403			0.562015	+	0.827127i	$0.310026\pi$
$384$		0			0
$385$	16.0869	−	33.4879i	0.819864	−	1.70670i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	9.82776i		−	0.498287i	−0.968467	−	0.249144i	$-0.919851\pi$
$389$		−	9.82776i		−	0.498287i	0.968467	−	0.249144i	$-0.0801491\pi$
$390$		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	−0.381369	−	0.924423i	$-0.624547\pi$
$397$	4.55324	−	2.62881i	0.228520	−	0.131936i	0.609889	+	0.792487i	$0.291214\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	17.0719i		−	0.852529i	−0.904598	−	0.426265i	$-0.859829\pi$
$401$		−	17.0719i		−	0.852529i	0.904598	−	0.426265i	$-0.140171\pi$
$402$		0			0
$403$	−6.55444			−0.326500
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−13.8957	+	8.02270i	−0.688786	+	0.397671i
$408$		0			0
$409$	16.9484	−	9.78516i	0.838044	−	0.483845i	−0.0185546	−	0.999828i	$-0.505906\pi$
$409$	16.9484	−	9.78516i	0.838044	−	0.483845i	0.856599	+	0.515983i	$0.172573\pi$
$410$		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	$-0.665361\pi$
$419$	10.3073	−	17.8529i	0.503547	−	0.872169i	0.999992	−	0.00410056i	$-0.00130525\pi$
$420$		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
$425$	−3.19091	+	5.52682i	−0.154782	+	0.268090i
$426$		0			0
$427$	−10.7508	−	15.7357i	−0.520268	−	0.761504i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	0.753931	−	0.656953i	$-0.228155\pi$
$431$	11.6666	+	6.73569i	0.561959	+	0.324447i	−0.191973	+	0.981400i	$0.561488\pi$
$432$		0			0
$433$			12.9356i			0.621646i	0.950468	+	0.310823i	$0.100605\pi$
$433$			12.9356i			0.621646i	−0.950468	+	0.310823i	$0.899395\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0608	+	20.8899i	0.576944	+	0.999297i
$438$		0			0
$439$	8.75023	+	5.05195i	0.417626	+	0.241116i	0.694061	−	0.719916i	$-0.255820\pi$
$439$	8.75023	+	5.05195i	0.417626	+	0.241116i	−0.276435	+	0.961033i	$0.589153\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	25.1220	+	14.5042i	1.19358	+	0.689115i	0.959117	−	0.283009i	$-0.0913326\pi$
$443$	25.1220	+	14.5042i	1.19358	+	0.689115i	0.234466	+	0.972124i	$0.424666\pi$
$444$		0			0
$445$	13.6873	+	23.7072i	0.648842	+	1.12383i
$446$		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
$455$	18.1213	+	26.5237i	0.849539	+	1.24345i
$456$		0			0
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	−0.655275	−	0.755391i	$-0.727447\pi$
$457$	6.98084	−	12.0912i	0.326550	−	0.565601i	0.981825	+	0.189789i	$0.0607805\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	−0.940793	−	0.338983i	$-0.889917\pi$
$461$	−16.4030	−	28.4108i	−0.763964	−	1.32322i	0.176829	−	0.984242i	$-0.443416\pi$
$462$		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	−0.999429	−	0.0337767i	$-0.989247\pi$
$467$	−11.4311	−	19.7992i	−0.528966	−	0.916196i	0.470463	−	0.882420i	$-0.344087\pi$
$468$		0			0
$469$	−2.32529	−	30.6297i	−0.107372	−	1.41435i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	42.8245	−	24.7247i	1.96907	−	1.13684i
$474$		0			0
$475$	−16.2502	+	9.38204i	−0.745609	+	0.430478i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.42425			−0.110767			−0.0553834	−	0.998465i	$-0.517638\pi$
$479$	−2.42425			−0.110767			−0.0553834	+	0.998465i	$0.517638\pi$
$480$		0			0
$481$		−	13.8737i		−	0.632584i
$482$		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	−0.723935	−	0.689868i	$-0.757668\pi$
$487$	5.19651	−	9.00061i	0.235476	−	0.407857i	0.959411	+	0.282012i	$0.0910017\pi$
$488$		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
$493$		−	0.460174i		−	0.0207252i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−11.9611	+	24.8993i	−0.536530	+	1.11689i
$498$		0			0
$499$	39.5603			1.77096			0.885481	−	0.464676i	$-0.153829\pi$
$499$	39.5603			1.77096			0.885481	+	0.464676i	$0.153829\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.5476			0.648645			0.324323	−	0.945947i	$-0.394864\pi$
$503$	14.5476			0.648645			0.324323	+	0.945947i	$0.394864\pi$
$504$		0			0
$505$	21.7018			0.965717
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−20.3916			−0.903841			−0.451921	−	0.892058i	$-0.649261\pi$
$509$	−20.3916			−0.903841			−0.451921	+	0.892058i	$0.649261\pi$
$510$		0			0
$511$	23.5235	+	34.4307i	1.04062	+	1.52313i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			20.8643i			0.919391i
$516$		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	$-0.943621\pi$
$521$	−7.75122	+	13.4255i	−0.339587	+	0.588182i	0.644768	+	0.764379i	$0.276954\pi$
$522$		0			0
$523$	9.35989	−	5.40394i	0.409280	−	0.236298i	−0.281201	−	0.959649i	$-0.590733\pi$
$523$	9.35989	−	5.40394i	0.409280	−	0.236298i	0.690480	+	0.723351i	$0.257399\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	2.67836i		−	0.116671i
$528$		0			0
$529$	−1.11695			−0.0485631
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−25.1819	+	14.5388i	−1.09075	+	0.629745i
$534$		0			0
$535$	−36.4162	+	21.0249i	−1.57441	+	0.908986i
$536$		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	0.612716	−	0.790303i	$-0.290077\pi$
$541$	−8.79357	−	15.2309i	−0.378065	−	0.654828i	−0.990781	+	0.135476i	$0.956744\pi$
$542$		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
$551$	0.676511	−	1.17175i	0.0288203	−	0.0499183i
$552$		0			0
$553$	26.8774	−	18.3629i	1.14294	−	0.780871i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−32.9159	−	19.0040i	−1.39469	−	0.805226i	−0.400863	−	0.916138i	$-0.631290\pi$
$557$	−32.9159	−	19.0040i	−1.39469	−	0.805226i	−0.993830	+	0.110912i	$0.964623\pi$
$558$		0			0
$559$			42.7565i			1.80841i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	0.990242	−	0.139360i	$-0.0445044\pi$
$563$	8.88438	+	15.3882i	0.374432	+	0.648535i	−0.615810	+	0.787895i	$0.711171\pi$
$564$		0			0
$565$	−34.5727	−	19.9605i	−1.45448	−	0.839746i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	33.7404	+	19.4801i	1.41447	+	0.816646i	0.995806	−	0.0914936i	$-0.0291641\pi$
$569$	33.7404	+	19.4801i	1.41447	+	0.816646i	0.418667	+	0.908140i	$0.362497\pi$
$570$		0			0
$571$	−8.45245	−	14.6401i	−0.353724	−	0.612668i	0.633175	−	0.774009i	$-0.281752\pi$
$571$	−8.45245	−	14.6401i	−0.353724	−	0.612668i	−0.986899	+	0.161341i	$0.948418\pi$
$572$		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	−0.941555	−	0.336858i	$-0.890636\pi$
$577$	−40.9329	−	23.6326i	−1.70406	−	0.983840i	−0.762506	−	0.646982i	$-0.776031\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.61818	−	21.3153i	−0.0671333	−	0.884308i
$582$		0			0
$583$	1.93099	−	3.34458i	0.0799736	−	0.138518i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	0.999742	−	0.0227138i	$-0.00723065\pi$
$587$	11.6343	+	20.1513i	0.480200	+	0.831731i	−0.519542	+	0.854445i	$0.673897\pi$
$588$		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	−0.940955	−	0.338530i	$-0.890070\pi$
$593$	−18.5962	−	32.2095i	−0.763654	−	1.32269i	0.177302	−	0.984157i	$-0.443263\pi$
$594$		0			0
$595$	−10.8384	+	7.40494i	−0.444332	+	0.303573i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−27.9591	+	16.1422i	−1.14238	+	0.659552i	−0.947018	−	0.321180i	$-0.895921\pi$
$599$	−27.9591	+	16.1422i	−1.14238	+	0.659552i	−0.195359	+	0.980732i	$0.562587\pi$
$600$		0			0
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	−0.167885	−	0.985807i	$-0.553694\pi$
$601$	14.7559	−	8.51933i	0.601906	−	0.347511i	0.769791	+	0.638296i	$0.220360\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−33.7231			−1.37104
$606$		0			0
$607$		−	9.75021i		−	0.395749i	−0.980227	−	0.197874i	$-0.936596\pi$
$607$		−	9.75021i		−	0.395749i	0.980227	−	0.197874i	$-0.0634038\pi$
$608$		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	−0.970690	−	0.240337i	$-0.922742\pi$
$613$	−6.86332	+	11.8876i	−0.277207	+	0.480136i	0.693483	+	0.720473i	$0.256075\pi$
$614$		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
$619$		−	17.3098i		−	0.695740i	−0.937543	−	0.347870i	$-0.886905\pi$
$619$		−	17.3098i		−	0.695740i	0.937543	−	0.347870i	$-0.113095\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.84606	+	24.3171i	0.0739608	+	0.974243i
$624$		0			0
$625$	−29.5071			−1.18028
$626$		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
$635$	−37.9344			−1.50538
$636$		0			0
$637$	4.32011	+	28.2892i	0.171169	+	1.12086i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	20.7601i		−	0.819976i	−0.912091	−	0.409988i	$-0.865533\pi$
$641$		−	20.7601i		−	0.819976i	0.912091	−	0.409988i	$-0.134467\pi$
$642$		0			0
$643$	17.2553	+	9.96236i	0.680483	+	0.392877i	0.800037	−	0.599950i	$-0.204813\pi$
$643$	17.2553	+	9.96236i	0.680483	+	0.392877i	−0.119554	+	0.992828i	$0.538146\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.7670	+	25.5772i	−0.580551	+	1.00554i	0.414863	+	0.909884i	$0.363830\pi$
$647$	−14.7670	+	25.5772i	−0.580551	+	1.00554i	−0.995414	+	0.0956605i	$0.969504\pi$
$648$		0			0
$649$	−11.2544	+	6.49774i	−0.441775	+	0.255059i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	15.9250i		−	0.623193i	−0.950215	−	0.311596i	$-0.899136\pi$
$653$		−	15.9250i		−	0.623193i	0.950215	−	0.311596i	$-0.100864\pi$
$654$		0			0
$655$	−39.8493			−1.55704
$656$		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
$661$	7.71194	−	4.45249i	0.299960	−	0.173182i	−0.342465	−	0.939531i	$-0.611262\pi$
$661$	7.71194	−	4.45249i	0.299960	−	0.173182i	0.642425	+	0.766349i	$0.277928\pi$
$662$		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
$677$	−4.46424	+	7.73229i	−0.171575	+	0.297176i	−0.938971	−	0.343997i	$-0.888219\pi$
$677$	−4.46424	+	7.73229i	−0.171575	+	0.297176i	0.767396	+	0.641174i	$0.221552\pi$
$678$		0			0
$679$	−21.3475	+	1.62062i	−0.819243	+	0.0621938i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.972035	−	0.234834i	$-0.0754547\pi$
$683$	32.7902	+	18.9314i	1.25468	+	0.724390i	0.282645	+	0.959225i	$0.408788\pi$
$684$		0			0
$685$		−	26.7298i		−	1.02129i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.66963	+	2.89189i	0.0636080	+	0.110172i
$690$		0			0
$691$	−4.94211	−	2.85333i	−0.188007	−	0.108546i	0.403042	−	0.915181i	$-0.367953\pi$
$691$	−4.94211	−	2.85333i	−0.188007	−	0.108546i	−0.591049	+	0.806636i	$0.701286\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.60039	−	2.65604i	−0.174503	−	0.100749i
$696$		0			0
$697$	−5.94103	−	10.2902i	−0.225032	−	0.389768i
$698$		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
$707$	17.4268	+	8.37148i	0.655403	+	0.314842i
$708$		0			0
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	−0.990830	−	0.135115i	$-0.956860\pi$
$709$	−10.0757	+	17.4517i	−0.378402	+	0.655412i	0.612428	+	0.790527i	$0.290193\pi$
$710$		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	0.735048	+	0.678015i	$0.237159\pi$
$719$	25.5996	+	44.3397i	0.954702	+	1.65359i	0.219654	+	0.975578i	$0.429507\pi$
$720$		0			0
$721$	−8.04842	+	16.7543i	−0.299739	+	0.623963i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.911330	+	0.526157i	−0.0338460	+	0.0195410i
$726$		0			0
$727$	−13.7848	+	7.95865i	−0.511249	+	0.295170i	−0.733347	−	0.679854i	$-0.762043\pi$
$727$	−13.7848	+	7.95865i	−0.511249	+	0.295170i	0.222098	+	0.975024i	$0.428710\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−17.4717			−0.646213
$732$		0			0
$733$		−	4.24025i		−	0.156617i	−0.996929	−	0.0783086i	$-0.975048\pi$
$733$		−	4.24025i		−	0.156617i	0.996929	−	0.0783086i	$-0.0249519\pi$
$734$		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	0.477933	+	0.878397i	$0.341386\pi$
$739$	−14.1835	+	24.5665i	−0.521747	+	0.903693i	−0.999680	+	0.0252966i	$0.991947\pi$
$740$		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
$745$			38.3327i			1.40440i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−37.3531	+	2.83570i	−1.36485	+	0.103614i
$750$		0			0
$751$	47.5460			1.73498			0.867490	−	0.497455i	$-0.165732\pi$
$751$	47.5460			1.73498			0.867490	+	0.497455i	$0.165732\pi$
$752$		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
$761$	8.24283			0.298802			0.149401	−	0.988777i	$-0.452265\pi$
$761$	8.24283			0.298802			0.149401	+	0.988777i	$0.452265\pi$
$762$		0			0
$763$	−12.3299	+	8.42390i	−0.446371	+	0.304966i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	11.2365i		−	0.405728i
$768$		0			0
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	0.818088	−	0.575094i	$-0.195034\pi$
$769$	20.2182	+	11.6730i	0.729086	+	0.420938i	−0.0890020	+	0.996031i	$0.528368\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	17.2201	−	29.8261i	0.619364	−	1.07277i	−0.370238	−	0.928937i	$-0.620724\pi$
$773$	17.2201	−	29.8261i	0.619364	−	1.07277i	0.989602	−	0.143833i	$-0.0459428\pi$
$774$		0			0
$775$	−5.30422	+	3.06240i	−0.190533	+	0.110004i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	34.9361i		−	1.25171i
$780$		0			0
$781$	49.3644			1.76640
$782$		0			0
$783$		0			0
$784$		0			0
$785$	44.1682	−	25.5005i	1.57643	−	0.910152i
$786$		0			0
$787$	−7.19975	+	4.15678i	−0.256643	+	0.148173i	−0.622802	−	0.782379i	$-0.714006\pi$
$787$	−7.19975	+	4.15678i	−0.256643	+	0.148173i	0.366159	+	0.930552i	$0.380673\pi$
$788$		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	−0.873472	−	0.486874i	$-0.838137\pi$
$797$	−0.426036	+	0.737916i	−0.0150910	+	0.0261383i	0.858381	+	0.513012i	$0.171470\pi$
$798$		0			0
$799$	9.18614	+	15.9109i	0.324982	+	0.562886i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	37.2595	−	64.5354i	1.31486	−	2.27740i
$804$		0			0
$805$	16.7088	−	34.7826i	0.588908	−	1.22592i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	31.5580	+	18.2200i	1.10952	+	0.640581i	0.938705	−	0.344722i	$-0.112027\pi$
$809$	31.5580	+	18.2200i	1.10952	+	0.640581i	0.170814	+	0.985303i	$0.445360\pi$
$810$		0			0
$811$		−	1.08986i		−	0.0382702i	−0.999817	−	0.0191351i	$-0.993909\pi$
$811$		−	1.08986i		−	0.0382702i	0.999817	−	0.0191351i	$-0.00609126\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.51697	+	13.0198i	0.263308	+	0.456063i
$816$		0			0
$817$	−44.4885	−	25.6855i	−1.55646	−	0.898620i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.9748	+	12.1098i	0.732025	+	0.422635i	0.819163	−	0.573561i	$-0.194439\pi$
$821$	20.9748	+	12.1098i	0.732025	+	0.422635i	−0.0871374	+	0.996196i	$0.527772\pi$
$822$		0			0
$823$	−2.85592	−	4.94660i	−0.0995512	−	0.172428i	0.811948	−	0.583730i	$-0.198407\pi$
$823$	−2.85592	−	4.94660i	−0.0995512	−	0.172428i	−0.911499	+	0.411302i	$0.865074\pi$
$824$		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	0.491322	−	0.870978i	$-0.336514\pi$
$829$	−0.498269	−	0.287676i	−0.0173056	−	0.00999140i	−0.508628	+	0.860986i	$0.669847\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−11.5599	+	1.76534i	−0.400526	+	0.0611653i
$834$		0			0
$835$	−17.2156	+	29.8183i	−0.595770	+	1.03190i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	0.900925	+	0.433974i	$0.142889\pi$
$839$	23.9341	+	41.4550i	0.826295	+	1.43119i	−0.0746300	+	0.997211i	$0.523778\pi$
$840$		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
$851$	−14.4329	+	8.33286i	−0.494755	+	0.285647i
$852$		0			0
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.394945	−	0.918705i	$-0.370764\pi$
$853$	40.5393	−	23.4054i	1.38804	−	0.801385i	0.993094	+	0.117320i	$0.0374303\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.56441			−0.326714			−0.163357	−	0.986567i	$-0.552232\pi$
$857$	−9.56441			−0.326714			−0.163357	+	0.986567i	$0.552232\pi$
$858$		0			0
$859$			5.40759i			0.184505i	0.995736	+	0.0922523i	$0.0294066\pi$
$859$			5.40759i			0.184505i	−0.995736	+	0.0922523i	$0.970593\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.962716	−	0.270514i	$-0.912806\pi$
$863$	−35.5402	+	20.5191i	−1.20980	+	0.698480i	−0.247086	+	0.968994i	$0.579473\pi$
$864$		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
$871$		−	47.4646i		−	1.60828i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.35633	−	4.01421i	−0.282496	−	0.135705i
$876$		0			0
$877$	−14.6502			−0.494701			−0.247351	−	0.968926i	$-0.579560\pi$
$877$	−14.6502			−0.494701			−0.247351	+	0.968926i	$0.579560\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	44.8295			1.51034			0.755172	−	0.655527i	$-0.227553\pi$
$881$	44.8295			1.51034			0.755172	+	0.655527i	$0.227553\pi$
$882$		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
$887$	26.6844			0.895973			0.447987	−	0.894040i	$-0.352141\pi$
$887$	26.6844			0.895973			0.447987	+	0.894040i	$0.352141\pi$
$888$		0			0
$889$	−30.4618	−	14.6332i	−1.02166	−	0.490783i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			54.0189i			1.80767i
$894$		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
$905$			0.247582i			0.00822989i
$906$		0			0
$907$	−15.9442			−0.529419			−0.264710	−	0.964328i	$-0.585276\pi$
$907$	−15.9442			−0.529419			−0.264710	+	0.964328i	$0.585276\pi$
$908$		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
$913$	−33.0833	+	19.1007i	−1.09490	+	0.632140i
$914$		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	0.999916	−	0.0129500i	$-0.00412223\pi$
$919$	14.8163	+	25.6625i	0.488743	+	0.846528i	−0.511173	+	0.859478i	$0.670789\pi$
$920$		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
$929$	−16.6186	+	28.7842i	−0.545238	+	0.944380i	0.453354	+	0.891331i	$0.350227\pi$
$929$	−16.6186	+	28.7842i	−0.545238	+	0.944380i	−0.998592	+	0.0530496i	$0.983106\pi$
$930$		0			0
$931$	−32.0304	−	12.4993i	−1.04975	−	0.409647i
$932$		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	$-0.872797\pi$
$937$		−	23.8190i		−	0.778134i	0.921209	−	0.389067i	$-0.127203\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.1201	+	46.9734i	0.884091	+	1.53129i	0.846752	+	0.531988i	$0.178555\pi$
$941$	27.1201	+	46.9734i	0.884091	+	1.53129i	0.0373389	+	0.999303i	$0.488112\pi$
$942$		0			0
$943$	30.2498	+	17.4647i	0.985069	+	0.568730i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.2427	−	10.5324i	−0.592807	−	0.342257i	0.173399	−	0.984852i	$-0.444525\pi$
$947$	−18.2427	−	10.5324i	−0.592807	−	0.342257i	−0.766207	+	0.642594i	$0.777858\pi$
$948$		0			0
$949$	32.2164	+	55.8005i	1.04579	+	1.81136i
$950$		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
$959$	10.3110	−	21.4644i	0.332961	−	0.693122i
$960$		0			0
$961$	−14.2148	+	24.6207i	−0.458541	+	0.794216i
$962$		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	0.945443	+	0.325788i	$0.105629\pi$
$971$	23.5222	+	40.7416i	0.754862	+	1.30746i	−0.190581	+	0.981671i	$0.561037\pi$
$972$		0			0
$973$	−2.66961	−	3.90744i	−0.0855838	−	0.125267i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.7766	−	12.5727i	0.696695	−	0.402237i	−0.109420	−	0.993996i	$-0.534899\pi$
$977$	21.7766	−	12.5727i	0.696695	−	0.402237i	0.806115	+	0.591758i	$0.201566\pi$
$978$		0			0
$979$	37.7423	−	21.7905i	1.20625	−	0.696429i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	36.2142			1.15505			0.577527	−	0.816372i	$-0.304018\pi$
$983$	36.2142			1.15505			0.577527	+	0.816372i	$0.304018\pi$
$984$		0			0
$985$			29.3515i			0.935216i
$986$		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	−0.975287	−	0.220940i	$-0.929087\pi$
$991$	−9.32769	+	16.1560i	−0.296304	+	0.513213i	0.678984	+	0.734153i	$0.262421\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.1632	−	15.6827i	−0.861131	−	0.497174i
$996$		0			0
$997$		−	17.4836i		−	0.553712i	−0.960911	−	0.276856i	$-0.910708\pi$
$997$		−	17.4836i		−	0.553712i	0.960911	−	0.276856i	$-0.0892925\pi$
$998$		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.17.7		16
3.2	odd	2		252.2.bm.a.185.1	yes	16
4.3	odd	2		3024.2.df.d.17.7		16
7.2	even	3		5292.2.w.b.1097.2		16
7.3	odd	6		5292.2.x.a.881.7		16
7.4	even	3		5292.2.x.b.881.2		16
7.5	odd	6		756.2.w.a.341.7		16
7.6	odd	2		5292.2.bm.a.2285.2		16
9.2	odd	6		756.2.w.a.521.7		16
9.4	even	3		2268.2.t.b.1781.2		16
9.5	odd	6		2268.2.t.a.1781.7		16
9.7	even	3		252.2.w.a.101.3	yes	16
12.11	even	2		1008.2.df.d.689.8		16
21.2	odd	6		1764.2.w.b.509.6		16
21.5	even	6		252.2.w.a.5.3	✓	16
21.11	odd	6		1764.2.x.b.293.5		16
21.17	even	6		1764.2.x.a.293.4		16
21.20	even	2		1764.2.bm.a.1697.8		16
28.19	even	6		3024.2.ca.d.2609.7		16
36.7	odd	6		1008.2.ca.d.353.6		16
36.11	even	6		3024.2.ca.d.2033.7		16
63.2	odd	6		5292.2.bm.a.4625.2		16
63.5	even	6		2268.2.t.b.2105.2		16
63.11	odd	6		5292.2.x.a.4409.7		16
63.16	even	3		1764.2.bm.a.1685.8		16
63.20	even	6		5292.2.w.b.521.2		16
63.25	even	3		1764.2.x.a.1469.4		16
63.34	odd	6		1764.2.w.b.1109.6		16
63.38	even	6		5292.2.x.b.4409.2		16
63.40	odd	6		2268.2.t.a.2105.7		16
63.47	even	6	inner	756.2.bm.a.89.7		16
63.52	odd	6		1764.2.x.b.1469.5		16
63.61	odd	6		252.2.bm.a.173.1	yes	16
84.47	odd	6		1008.2.ca.d.257.6		16
252.47	odd	6		3024.2.df.d.1601.7		16
252.187	even	6		1008.2.df.d.929.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.3	✓	16	21.5	even	6
252.2.w.a.101.3	yes	16	9.7	even	3
252.2.bm.a.173.1	yes	16	63.61	odd	6
252.2.bm.a.185.1	yes	16	3.2	odd	2
756.2.w.a.341.7		16	7.5	odd	6
756.2.w.a.521.7		16	9.2	odd	6
756.2.bm.a.17.7		16	1.1	even	1	trivial
756.2.bm.a.89.7		16	63.47	even	6	inner
1008.2.ca.d.257.6		16	84.47	odd	6
1008.2.ca.d.353.6		16	36.7	odd	6
1008.2.df.d.689.8		16	12.11	even	2
1008.2.df.d.929.8		16	252.187	even	6
1764.2.w.b.509.6		16	21.2	odd	6
1764.2.w.b.1109.6		16	63.34	odd	6
1764.2.x.a.293.4		16	21.17	even	6
1764.2.x.a.1469.4		16	63.25	even	3
1764.2.x.b.293.5		16	21.11	odd	6
1764.2.x.b.1469.5		16	63.52	odd	6
1764.2.bm.a.1685.8		16	63.16	even	3
1764.2.bm.a.1697.8		16	21.20	even	2
2268.2.t.a.1781.7		16	9.5	odd	6
2268.2.t.a.2105.7		16	63.40	odd	6
2268.2.t.b.1781.2		16	9.4	even	3
2268.2.t.b.2105.2		16	63.5	even	6
3024.2.ca.d.2033.7		16	36.11	even	6
3024.2.ca.d.2609.7		16	28.19	even	6
3024.2.df.d.17.7		16	4.3	odd	2
3024.2.df.d.1601.7		16	252.47	odd	6
5292.2.w.b.521.2		16	63.20	even	6
5292.2.w.b.1097.2		16	7.2	even	3
5292.2.x.a.881.7		16	7.3	odd	6
5292.2.x.a.4409.7		16	63.11	odd	6
5292.2.x.b.881.2		16	7.4	even	3
5292.2.x.b.4409.2		16	63.38	even	6
5292.2.bm.a.2285.2		16	7.6	odd	2
5292.2.bm.a.4625.2		16	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.96988 q^{5} +(2.38485 + 1.14563i) q^{7} -4.72811i q^{11} +(3.54045 + 2.04408i) q^{13} +(-0.835278 + 1.44674i) q^{17} +(-4.25377 + 2.45592i) q^{19} -4.91090i q^{23} +3.82018 q^{25} +(-0.238557 + 0.137731i) q^{29} +(-1.38847 + 0.801636i) q^{31} +(7.08273 + 3.40239i) q^{35} +(-1.69681 - 2.93896i) q^{37} +(-3.55632 + 6.15972i) q^{41} +(5.22930 + 9.05742i) q^{43} +(5.49885 - 9.52430i) q^{47} +(4.37505 + 5.46433i) q^{49} +(0.707381 + 0.408407i) q^{53} -14.0419i q^{55} +(-1.37428 - 2.38032i) q^{59} +(-6.23807 - 3.60155i) q^{61} +(10.5147 + 6.07067i) q^{65} +(-5.80513 - 10.0548i) q^{67} +10.4406i q^{71} +(13.6493 + 7.88042i) q^{73} +(5.41668 - 11.2759i) q^{77} +(6.15163 - 10.6549i) q^{79} +(-4.03981 - 6.99715i) q^{83} +(-2.48067 + 4.29665i) q^{85} +(4.60872 + 7.98254i) q^{89} +(6.10169 + 8.93089i) q^{91} +(-12.6332 + 7.29377i) q^{95} +(-7.00772 + 4.04591i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79}+ \cdots + 3 q^{97}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more