LMFDB - Embedded newform 756.2.bm.a.17.4

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			17.4
Root			$1.68124 + 0.416458i$ of defining polynomial
Character	$\chi$	$=$	756.17
Dual form			756.2.bm.a.89.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.699656 q^{5} +(-0.461278 + 2.60523i) q^{7} +O(q^{10})$	$q-0.699656 q^{5} +(-0.461278 + 2.60523i) q^{7} +0.265217i q^{11} +(-1.13823 - 0.657156i) q^{13} +(-1.86392 + 3.22840i) q^{17} +(-0.382449 + 0.220807i) q^{19} +4.96463i q^{23} -4.51048 q^{25} +(0.273287 - 0.157782i) q^{29} +(-4.85521 + 2.80316i) q^{31} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(3.50285 - 6.06712i) q^{47} +(-6.57445 - 2.40347i) q^{49} +(8.51919 + 4.91856i) q^{53} -0.185561i q^{55} +(6.73182 + 11.6598i) q^{59} +(-4.89484 - 2.82604i) q^{61} +(0.796368 + 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(-0.690951 - 0.122339i) q^{77} +(-0.698360 + 1.20959i) q^{79} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(5.59261 + 9.68668i) q^{89} +(2.23708 - 2.66221i) q^{91} +(0.267582 - 0.154489i) q^{95} +(9.18225 - 5.30138i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7}+O(q^{10}) $ 16 * q - q^7	$ 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.699656			−0.312896			−0.156448	−	0.987686i	$-0.550004\pi$
$5$	−0.699656			−0.312896			−0.156448	+	0.987686i	$0.550004\pi$
$6$		0			0
$7$	−0.461278	+	2.60523i	−0.174347	+	0.984684i
$7$	−0.461278	+	2.60523i	−0.174347	+	0.984684i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			0.265217i			0.0799659i	0.999200	+	0.0399829i	$0.0127304\pi$
$11$			0.265217i			0.0799659i	−0.999200	+	0.0399829i	$0.987270\pi$
$12$		0			0
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	0.333781	−	0.942651i	$-0.391675\pi$
$13$	−1.13823	−	0.657156i	−0.315688	−	0.182262i	−0.649469	+	0.760388i	$0.725009\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.86392	+	3.22840i	−0.452067	+	0.783003i	−0.998514	−	0.0544906i	$-0.982646\pi$
$17$	−1.86392	+	3.22840i	−0.452067	+	0.783003i	0.546447	+	0.837493i	$0.315980\pi$
$18$		0			0
$19$	−0.382449	+	0.220807i	−0.0877398	+	0.0506566i	−0.543228	−	0.839585i	$-0.682798\pi$
$19$	−0.382449	+	0.220807i	−0.0877398	+	0.0506566i	0.455488	+	0.890242i	$0.349465\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			4.96463i			1.03520i	0.855624	+	0.517598i	$0.173174\pi$
$23$			4.96463i			1.03520i	−0.855624	+	0.517598i	$0.826826\pi$
$24$		0			0
$25$	−4.51048			−0.902096
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.273287	−	0.157782i	0.0507480	−	0.0292994i	−0.474411	−	0.880303i	$-0.657339\pi$
$29$	0.273287	−	0.157782i	0.0507480	−	0.0292994i	0.525159	+	0.851004i	$0.324006\pi$
$30$		0			0
$31$	−4.85521	+	2.80316i	−0.872022	+	0.503462i	−0.868020	−	0.496530i	$-0.834607\pi$
$31$	−4.85521	+	2.80316i	−0.872022	+	0.503462i	−0.00400255	+	0.999992i	$0.501274\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.322736	−	1.82276i	0.0545523	−	0.308103i
$36$		0			0
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	0.835719	−	0.549157i	$-0.185051\pi$
$37$	−0.351124	−	0.608164i	−0.0577244	−	0.0999816i	−0.893444	+	0.449175i	$0.851718\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.39354	+	9.34189i	−0.842330	+	1.45896i	0.0455900	+	0.998960i	$0.485483\pi$
$41$	−5.39354	+	9.34189i	−0.842330	+	1.45896i	−0.887920	+	0.459998i	$0.847850\pi$
$42$		0			0
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	0.996663	+	0.0816240i	$0.0260106\pi$
$43$	3.73131	+	6.46283i	0.569020	+	0.985572i	−0.427643	+	0.903948i	$0.640656\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	−0.488976	−	0.872297i	$-0.662630\pi$
$47$	3.50285	−	6.06712i	0.510943	−	0.884980i	0.999920	−	0.0126827i	$-0.00403713\pi$
$48$		0			0
$49$	−6.57445	−	2.40347i	−0.939207	−	0.343353i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.953727	−	0.300672i	$-0.0972111\pi$
$53$	8.51919	+	4.91856i	1.17020	+	0.675616i	0.216474	+	0.976288i	$0.430544\pi$
$54$		0			0
$55$		−	0.185561i		−	0.0250210i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.855256	+	0.518206i	$0.173400\pi$
$59$	6.73182	+	11.6598i	0.876408	+	1.51798i	0.0211522	+	0.999776i	$0.493267\pi$
$60$		0			0
$61$	−4.89484	−	2.82604i	−0.626720	−	0.361837i	0.152761	−	0.988263i	$-0.451184\pi$
$61$	−4.89484	−	2.82604i	−0.626720	−	0.361837i	−0.779481	+	0.626426i	$0.784517\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.796368	+	0.459783i	0.0987773	+	0.0570291i
$66$		0			0
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	0.988439	−	0.151616i	$-0.0484477\pi$
$67$	2.97060	+	5.14523i	0.362916	+	0.628590i	−0.625523	+	0.780206i	$0.715114\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	13.4323i		−	1.59412i	−0.603900	−	0.797060i	$-0.706387\pi$
$71$		−	13.4323i		−	1.59412i	0.603900	−	0.797060i	$-0.293613\pi$
$72$		0			0
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	0.0566194	−	0.998396i	$-0.481968\pi$
$73$	−6.66182	−	3.84620i	−0.779707	−	0.450164i	−0.836326	+	0.548232i	$0.815301\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.690951	−	0.122339i	−0.0787412	−	0.0139418i
$78$		0			0
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	−0.902634	−	0.430409i	$-0.858369\pi$
$79$	−0.698360	+	1.20959i	−0.0785716	+	0.136090i	0.824062	+	0.566499i	$0.191703\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	0.585990	−	0.810318i	$-0.300706\pi$
$83$	−3.72399	−	6.45014i	−0.408761	−	0.707995i	−0.994751	+	0.102323i	$0.967372\pi$
$84$		0			0
$85$	1.30410	−	2.25877i	0.141450	−	0.244998i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	0.993851	+	0.110724i	$0.0353168\pi$
$89$	5.59261	+	9.68668i	0.592815	+	1.02679i	−0.401036	+	0.916062i	$0.631350\pi$
$90$		0			0
$91$	2.23708	−	2.66221i	0.234510	−	0.279076i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.267582	−	0.154489i	0.0274534	−	0.0158502i
$96$		0			0
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.0447729	−	0.998997i	$-0.485744\pi$
$97$	9.18225	−	5.30138i	0.932316	−	0.538273i	0.887543	+	0.460724i	$0.152410\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−17.5071			−1.74203			−0.871013	−	0.491260i	$-0.836537\pi$
$101$	−17.5071			−1.74203			−0.871013	+	0.491260i	$0.836537\pi$
$102$		0			0
$103$		−	8.54219i		−	0.841687i	−0.907133	−	0.420844i	$-0.861734\pi$
$103$		−	8.54219i		−	0.841687i	0.907133	−	0.420844i	$-0.138266\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.00882940	−	0.999961i	$-0.497189\pi$
$107$	9.09489	−	5.25093i	0.879236	−	0.507627i	0.870406	+	0.492334i	$0.163856\pi$
$108$		0			0
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	0.292268	+	0.956337i	$0.405590\pi$
$109$	−7.12110	+	12.3341i	−0.682078	+	1.18139i	−0.974346	+	0.225057i	$0.927743\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.3783	−	7.72396i	−1.25852	−	0.726609i	−0.285737	−	0.958308i	$-0.592238\pi$
$113$	−13.3783	−	7.72396i	−1.25852	−	0.726609i	−0.972788	+	0.231699i	$0.925572\pi$
$114$		0			0
$115$		−	3.47353i		−	0.323908i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.55095	−	6.34513i	−0.692194	−	0.581657i
$120$		0			0
$121$	10.9297			0.993605
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.65406			0.595157
$126$		0			0
$127$	21.8304			1.93713			0.968566	−	0.248758i	$-0.0800225\pi$
$127$	21.8304			1.93713			0.968566	+	0.248758i	$0.0800225\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.20922			−0.455132			−0.227566	−	0.973763i	$-0.573077\pi$
$131$	−5.20922			−0.455132			−0.227566	+	0.973763i	$0.573077\pi$
$132$		0			0
$133$	−0.398838	−	1.09822i	−0.0345836	−	0.0952278i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	2.69725i		−	0.230442i	−0.993340	−	0.115221i	$-0.963242\pi$
$137$		−	2.69725i		−	0.230442i	0.993340	−	0.115221i	$-0.0367576\pi$
$138$		0			0
$139$	10.1448	+	5.85710i	0.860470	+	0.496793i	0.864170	−	0.503200i	$-0.167844\pi$
$139$	10.1448	+	5.85710i	0.860470	+	0.496793i	−0.00369951	+	0.999993i	$0.501178\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.174289	−	0.301877i	0.0145748	−	0.0252442i
$144$		0			0
$145$	−0.191206	+	0.110393i	−0.0158788	+	0.00916765i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	18.8280i		−	1.54245i	−0.636564	−	0.771224i	$-0.719645\pi$
$149$		−	18.8280i		−	1.54245i	0.636564	−	0.771224i	$-0.280355\pi$
$150$		0			0
$151$	10.0029			0.814021			0.407010	−	0.913424i	$-0.366571\pi$
$151$	10.0029			0.814021			0.407010	+	0.913424i	$0.366571\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	3.39698	−	1.96125i	0.272852	−	0.157531i
$156$		0			0
$157$	−0.218293	+	0.126032i	−0.0174217	+	0.0100584i	−0.508686	−	0.860952i	$-0.669868\pi$
$157$	−0.218293	+	0.126032i	−0.0174217	+	0.0100584i	0.491264	+	0.871011i	$0.336535\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−12.9340	−	2.29007i	−1.01934	−	0.180483i
$162$		0			0
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	0.983796	−	0.179289i	$-0.0573797\pi$
$163$	4.29780	+	7.44400i	0.336629	+	0.583059i	−0.647167	+	0.762348i	$0.724046\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	−0.766027	−	0.642808i	$-0.777769\pi$
$167$	2.24437	−	3.88736i	0.173674	−	0.300813i	0.939702	+	0.341995i	$0.111103\pi$
$168$		0			0
$169$	−5.63629	−	9.76234i	−0.433561	−	0.750949i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.56072	−	6.16736i	0.270717	−	0.468895i	−0.698329	−	0.715777i	$-0.746073\pi$
$173$	3.56072	−	6.16736i	0.270717	−	0.468895i	0.969046	+	0.246882i	$0.0794060\pi$
$174$		0			0
$175$	2.08059	−	11.7508i	0.157277	−	0.888280i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.975470	+	0.220134i	$0.0706494\pi$
$179$	22.1270	+	12.7750i	1.65385	+	0.954848i	0.678376	+	0.734715i	$0.262684\pi$
$180$		0			0
$181$		−	0.943175i		−	0.0701057i	−0.999385	−	0.0350528i	$-0.988840\pi$
$181$		−	0.943175i		−	0.0701057i	0.999385	−	0.0350528i	$-0.0111599\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.245666	+	0.425506i	0.0180617	+	0.0312838i
$186$		0			0
$187$	−0.856227	−	0.494343i	−0.0626135	−	0.0361499i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	0.590229	−	0.807236i	$-0.299037\pi$
$191$	2.57413	+	1.48617i	0.186258	+	0.107536i	−0.403972	+	0.914771i	$0.632371\pi$
$192$		0			0
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	0.978918	+	0.204254i	$0.0654769\pi$
$193$	9.25721	+	16.0340i	0.666348	+	1.15415i	−0.312570	+	0.949895i	$0.601190\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	14.1774i		−	1.01010i	−0.863091	−	0.505048i	$-0.831475\pi$
$197$		−	14.1774i		−	1.01010i	0.863091	−	0.505048i	$-0.168525\pi$
$198$		0			0
$199$	−20.5293	−	11.8526i	−1.45529	−	0.840209i	−0.456512	−	0.889717i	$-0.650901\pi$
$199$	−20.5293	−	11.8526i	−1.45529	−	0.840209i	−0.998774	+	0.0495081i	$0.984235\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.284998	+	0.784756i	0.0200029	+	0.0550790i
$204$		0			0
$205$	3.77362	−	6.53611i	0.263561	−	0.456502i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0585617	−	0.101432i	−0.00405080	−	0.00701619i
$210$		0			0
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	−0.742205	−	0.670173i	$-0.766220\pi$
$211$	3.04004	−	5.26550i	0.209285	−	0.362492i	0.951489	+	0.307681i	$0.0995531\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.61063	−	4.52175i	−0.178044	−	0.308381i
$216$		0			0
$217$	−5.06327	−	13.9420i	−0.343717	−	0.946444i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	4.24313	−	2.44977i	0.285424	−	0.164790i
$222$		0			0
$223$	−0.796137	+	0.459650i	−0.0533133	+	0.0307804i	−0.526420	−	0.850225i	$-0.676466\pi$
$223$	−0.796137	+	0.459650i	−0.0533133	+	0.0307804i	0.473106	+	0.881005i	$0.343133\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.0059			−0.664118			−0.332059	−	0.943259i	$-0.607743\pi$
$227$	−10.0059			−0.664118			−0.332059	+	0.943259i	$0.607743\pi$
$228$		0			0
$229$			2.75025i			0.181742i	0.995863	+	0.0908710i	$0.0289651\pi$
$229$			2.75025i			0.181742i	−0.995863	+	0.0908710i	$0.971035\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	−0.670803	−	0.741636i	$-0.734050\pi$
$233$	−5.55513	+	3.20725i	−0.363928	+	0.210114i	0.306874	+	0.951750i	$0.400717\pi$
$234$		0			0
$235$	−2.45079	+	4.24489i	−0.159872	+	0.276906i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	0.821804	−	0.569770i	$-0.192968\pi$
$239$	11.4288	+	6.59844i	0.739270	+	0.426818i	−0.0825337	+	0.996588i	$0.526301\pi$
$240$		0			0
$241$		−	2.54868i		−	0.164175i	−0.996625	−	0.0820874i	$-0.973841\pi$
$241$		−	2.54868i		−	0.164175i	0.996625	−	0.0820874i	$-0.0261587\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	4.59985	+	1.68160i	0.293874	+	0.107434i
$246$		0			0
$247$	0.580418			0.0369311
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.7893			1.18597			0.592986	−	0.805213i	$-0.297949\pi$
$251$	18.7893			1.18597			0.592986	+	0.805213i	$0.297949\pi$
$252$		0			0
$253$	−1.31670			−0.0827804
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.3945			−0.897907			−0.448953	−	0.893555i	$-0.648203\pi$
$257$	−14.3945			−0.897907			−0.448953	+	0.893555i	$0.648203\pi$
$258$		0			0
$259$	1.74637	−	0.634226i	0.108514	−	0.0394089i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			7.84976i			0.484037i	0.970272	+	0.242019i	$0.0778095\pi$
$263$			7.84976i			0.484037i	−0.970272	+	0.242019i	$0.922190\pi$
$264$		0			0
$265$	−5.96050	−	3.44130i	−0.366151	−	0.211397i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.72267	+	13.3760i	−0.470859	+	0.815552i	−0.999444	−	0.0333281i	$-0.989389\pi$
$269$	−7.72267	+	13.3760i	−0.470859	+	0.815552i	0.528585	+	0.848880i	$0.322723\pi$
$270$		0			0
$271$	10.9476	−	6.32057i	0.665016	−	0.383947i	−0.129169	−	0.991623i	$-0.541231\pi$
$271$	10.9476	−	6.32057i	0.665016	−	0.383947i	0.794186	+	0.607675i	$0.207898\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	1.19626i		−	0.0721369i
$276$		0			0
$277$	−11.8906			−0.714439			−0.357219	−	0.934021i	$-0.616275\pi$
$277$	−11.8906			−0.714439			−0.357219	+	0.934021i	$0.616275\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.75411	−	1.59009i	0.164297	−	0.0948568i	−0.415597	−	0.909549i	$-0.636427\pi$
$281$	2.75411	−	1.59009i	0.164297	−	0.0948568i	0.579894	+	0.814692i	$0.303094\pi$
$282$		0			0
$283$	−16.0195	+	9.24889i	−0.952263	+	0.549789i	−0.893783	−	0.448499i	$-0.851959\pi$
$283$	−16.0195	+	9.24889i	−0.952263	+	0.549789i	−0.0584799	+	0.998289i	$0.518625\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−21.8499	−	18.3606i	−1.28976	−	1.08379i
$288$		0			0
$289$	1.55161	+	2.68746i	0.0912711	+	0.158086i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.42975	+	2.47639i	−0.0835266	+	0.144672i	−0.904762	−	0.425917i	$-0.859952\pi$
$293$	−1.42975	+	2.47639i	−0.0835266	+	0.144672i	0.821236	+	0.570589i	$0.193285\pi$
$294$		0			0
$295$	−4.70995	−	8.15788i	−0.274224	−	0.474970i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.26254	−	5.65088i	0.188677	−	0.326799i
$300$		0			0
$301$	−18.5583	+	6.73977i	−1.06968	+	0.388474i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	3.42470	+	1.97725i	0.196098	+	0.113217i
$306$		0			0
$307$			21.6746i			1.23704i	0.785771	+	0.618518i	$0.212266\pi$
$307$			21.6746i			1.23704i	−0.785771	+	0.618518i	$0.787734\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	0.977411	+	0.211348i	$0.0677852\pi$
$311$	11.8462	+	20.5183i	0.671738	+	1.16348i	−0.305673	+	0.952136i	$0.598881\pi$
$312$		0			0
$313$	23.6283	+	13.6418i	1.33555	+	0.771081i	0.986144	−	0.165890i	$-0.0530496\pi$
$313$	23.6283	+	13.6418i	1.33555	+	0.771081i	0.349407	+	0.936971i	$0.386383\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	21.2647	+	12.2772i	1.19435	+	0.689556i	0.959289	−	0.282426i	$-0.0911391\pi$
$317$	21.2647	+	12.2772i	1.19435	+	0.689556i	0.235057	+	0.971982i	$0.424472\pi$
$318$		0			0
$319$	0.0418465	+	0.0724802i	0.00234295	+	0.00405811i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.64626i		−	0.0916006i
$324$		0			0
$325$	5.13396	+	2.96409i	0.284781	+	0.164418i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	14.1904	+	11.9244i	0.782344	+	0.657411i
$330$		0			0
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	−0.998274	−	0.0587215i	$-0.981298\pi$
$331$	−8.15579	+	14.1262i	−0.448283	+	0.776449i	0.549991	+	0.835170i	$0.314631\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.07840	−	3.59989i	−0.113555	−	0.196683i
$336$		0			0
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	−0.206663	−	0.978412i	$-0.566261\pi$
$337$	13.6580	−	23.6563i	0.743998	−	1.28864i	0.950661	−	0.310230i	$-0.100406\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.743445	−	1.28768i	−0.0402598	−	0.0697320i
$342$		0			0
$343$	9.29424	−	16.0193i	0.501842	−	0.864960i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	−0.348597	−	0.937273i	$-0.613342\pi$
$347$	5.37986	−	3.10606i	0.288806	−	0.166742i	0.637403	+	0.770530i	$0.280009\pi$
$348$		0			0
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.983671	−	0.179977i	$-0.942398\pi$
$349$	−24.6529	+	14.2334i	−1.31964	+	0.761896i	−0.335971	+	0.941872i	$0.609064\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.98691			−0.158977			−0.0794887	−	0.996836i	$-0.525329\pi$
$353$	−2.98691			−0.158977			−0.0794887	+	0.996836i	$0.525329\pi$
$354$		0			0
$355$			9.39798i			0.498793i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.994777	−	0.102070i	$-0.967454\pi$
$359$	−26.5977	+	15.3562i	−1.40377	+	0.810468i	−0.408994	+	0.912537i	$0.634120\pi$
$360$		0			0
$361$	−9.40249	+	16.2856i	−0.494868	+	0.857136i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	4.66098	+	2.69102i	0.243967	+	0.140854i
$366$		0			0
$367$			19.0384i			0.993794i	0.867809	+	0.496897i	$0.165527\pi$
$367$			19.0384i			0.993794i	−0.867809	+	0.496897i	$0.834473\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−16.7437	+	19.9256i	−0.869289	+	1.03449i
$372$		0			0
$373$	4.11738			0.213190			0.106595	−	0.994303i	$-0.466005\pi$
$373$	4.11738			0.213190			0.106595	+	0.994303i	$0.466005\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.414750			−0.0213607
$378$		0			0
$379$	−11.2436			−0.577546			−0.288773	−	0.957398i	$-0.593247\pi$
$379$	−11.2436			−0.577546			−0.288773	+	0.957398i	$0.593247\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−31.6093			−1.61516			−0.807580	−	0.589758i	$-0.799223\pi$
$383$	−31.6093			−1.61516			−0.807580	+	0.589758i	$0.799223\pi$
$384$		0			0
$385$	0.483428	+	0.0855949i	0.0246378	+	0.00436232i
$386$		0			0
$387$		0			0
$388$		0			0
$389$			21.2485i			1.07734i	0.842516	+	0.538672i	$0.181074\pi$
$389$			21.2485i			1.07734i	−0.842516	+	0.538672i	$0.818926\pi$
$390$		0			0
$391$	−16.0278	−	9.25367i	−0.810562	−	0.467978i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.488611	−	0.846300i	0.0245847	−	0.0425820i
$396$		0			0
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.119118	−	0.992880i	$-0.461993\pi$
$397$	20.6927	−	11.9469i	1.03854	−	0.599599i	0.919419	+	0.393281i	$0.128660\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$		−	25.4174i		−	1.26928i	−0.772806	−	0.634642i	$-0.781147\pi$
$401$		−	25.4174i		−	1.26928i	0.772806	−	0.634642i	$-0.218853\pi$
$402$		0			0
$403$	7.36845			0.367049
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.161295	−	0.0931240i	0.00799512	−	0.00461598i
$408$		0			0
$409$	−19.3831	+	11.1908i	−0.958433	+	0.553351i	−0.895690	−	0.444678i	$-0.853318\pi$
$409$	−19.3831	+	11.1908i	−0.958433	+	0.553351i	−0.0627424	+	0.998030i	$0.519985\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−33.4818	+	12.1595i	−1.64753	+	0.598330i
$414$		0			0
$415$	2.60551	+	4.51288i	0.127900	+	0.221528i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	−0.641159	−	0.767408i	$-0.721546\pi$
$419$	7.04181	−	12.1968i	0.344015	−	0.595851i	0.985174	+	0.171556i	$0.0548796\pi$
$420$		0			0
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	0.992924	−	0.118753i	$-0.0378896\pi$
$421$	8.07639	+	13.9887i	0.393619	+	0.681768i	−0.599305	+	0.800521i	$0.704556\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	8.40717	−	14.5617i	0.407808	−	0.706344i
$426$		0			0
$427$	9.62036	−	11.4486i	0.465562	−	0.554036i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	0.317497	−	0.948259i	$-0.397158\pi$
$431$	−7.16179	−	4.13486i	−0.344971	−	0.199169i	−0.662468	+	0.749090i	$0.730491\pi$
$432$		0			0
$433$		−	4.35102i		−	0.209097i	−0.994520	−	0.104548i	$-0.966660\pi$
$433$		−	4.35102i		−	0.209097i	0.994520	−	0.104548i	$-0.0333397\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.09622	−	1.89872i	−0.0524395	−	0.0908279i
$438$		0			0
$439$	−18.0200	−	10.4039i	−0.860048	−	0.496549i	0.00398054	−	0.999992i	$-0.498733\pi$
$439$	−18.0200	−	10.4039i	−0.860048	−	0.496549i	−0.864028	+	0.503443i	$0.832066\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.975544	−	0.219803i	$-0.0705414\pi$
$443$	26.7927	+	15.4688i	1.27296	+	0.734945i	0.297417	+	0.954748i	$0.403875\pi$
$444$		0			0
$445$	−3.91290	−	6.77734i	−0.185489	−	0.321277i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.9215i			0.987346i	0.869648	+	0.493673i	$0.164346\pi$
$449$			20.9215i			0.987346i	−0.869648	+	0.493673i	$0.835654\pi$
$450$		0			0
$451$	−2.47763	−	1.43046i	−0.116667	−	0.0673577i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.56519	+	1.86263i	−0.0733771	+	0.0873216i
$456$		0			0
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	−0.891681	−	0.452664i	$-0.850474\pi$
$457$	−1.15058	+	1.99286i	−0.0538217	+	0.0932218i	0.837859	+	0.545886i	$0.183807\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	8.92497	+	15.4585i	0.415677	+	0.719974i	0.995499	−	0.0947688i	$-0.0302112\pi$
$461$	8.92497	+	15.4585i	0.415677	+	0.719974i	−0.579822	+	0.814743i	$0.696878\pi$
$462$		0			0
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	−0.973813	−	0.227353i	$-0.926993\pi$
$463$	−6.24034	+	10.8086i	−0.290013	+	0.502318i	0.683799	+	0.729670i	$0.260326\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	0.804365	−	0.594136i	$-0.202506\pi$
$467$	−2.42799	−	4.20541i	−0.112354	−	0.194603i	−0.916719	+	0.399533i	$0.869172\pi$
$468$		0			0
$469$	−14.7748	+	5.36571i	−0.682236	+	0.247766i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.71405	+	0.989607i	−0.0788121	+	0.0455022i
$474$		0			0
$475$	1.72503	−	0.995945i	0.0791497	−	0.0456971i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.81084			−0.402577			−0.201289	−	0.979532i	$-0.564513\pi$
$479$	−8.81084			−0.402577			−0.201289	+	0.979532i	$0.564513\pi$
$480$		0			0
$481$			0.922973i			0.0420839i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−6.42441	+	3.70914i	−0.291718	+	0.168423i
$486$		0			0
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	−0.740857	−	0.671663i	$-0.765580\pi$
$487$	4.66185	−	8.07456i	0.211249	−	0.365893i	0.952106	+	0.305770i	$0.0989137\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.963811	−	0.266587i	$-0.0858960\pi$
$491$	26.9192	+	15.5418i	1.21485	+	0.701391i	0.251034	+	0.967978i	$0.419229\pi$
$492$		0			0
$493$			1.17637i			0.0529811i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	34.9942	+	6.19602i	1.56971	+	0.277930i
$498$		0			0
$499$	−22.3388			−1.00002			−0.500010	−	0.866020i	$-0.666670\pi$
$499$	−22.3388			−1.00002			−0.500010	+	0.866020i	$0.666670\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.2396			−0.545738			−0.272869	−	0.962051i	$-0.587973\pi$
$503$	−12.2396			−0.545738			−0.272869	+	0.962051i	$0.587973\pi$
$504$		0			0
$505$	12.2490			0.545072
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.1099			0.625411			0.312706	−	0.949850i	$-0.398765\pi$
$509$	14.1099			0.625411			0.312706	+	0.949850i	$0.398765\pi$
$510$		0			0
$511$	13.0932	−	15.5814i	0.579209	−	0.689281i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			5.97659i			0.263360i
$516$		0			0
$517$	1.60910	+	0.929015i	0.0707682	+	0.0408580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.81632	−	4.87800i	0.123385	−	0.213709i	−0.797715	−	0.603034i	$-0.793958\pi$
$521$	2.81632	−	4.87800i	0.123385	−	0.213709i	0.921101	+	0.389325i	$0.127292\pi$
$522$		0			0
$523$	−33.2293	+	19.1849i	−1.45302	+	0.838899i	−0.998651	−	0.0519176i	$-0.983467\pi$
$523$	−33.2293	+	19.1849i	−1.45302	+	0.838899i	−0.454364	+	0.890816i	$0.650133\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	20.8995i		−	0.910395i
$528$		0			0
$529$	−1.64754			−0.0716321
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.2782	−	7.08880i	0.531826	−	0.307050i
$534$		0			0
$535$	−6.36329	+	3.67385i	−0.275109	+	0.158834i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.637441	−	1.74365i	0.0274565	−	0.0751045i
$540$		0			0
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	0.788555	−	0.614965i	$-0.210830\pi$
$541$	−3.21673	−	5.57154i	−0.138298	−	0.239539i	−0.926852	+	0.375426i	$0.877496\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.98232	−	8.62963i	0.213419	−	0.369653i
$546$		0			0
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	0.692020	−	0.721878i	$-0.256721\pi$
$547$	−6.52889	−	11.3084i	−0.279155	−	0.483511i	−0.971175	+	0.238368i	$0.923388\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.0696787	+	0.120687i	−0.00296841	+	0.00514144i
$552$		0			0
$553$	−2.82913	−	2.37735i	−0.120307	−	0.101095i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.150712	−	0.988578i	$-0.548157\pi$
$557$	−25.5409	−	14.7460i	−1.08220	−	0.624809i	−0.931489	+	0.363769i	$0.881490\pi$
$558$		0			0
$559$		−	9.80822i		−	0.414844i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	0.955311	−	0.295604i	$-0.0955209\pi$
$563$	5.25934	+	9.10944i	0.221655	+	0.383917i	−0.733656	+	0.679521i	$0.762188\pi$
$564$		0			0
$565$	9.36020	+	5.40411i	0.393787	+	0.227353i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	22.8054	+	13.1667i	0.956053	+	0.551977i	0.894956	−	0.446155i	$-0.147207\pi$
$569$	22.8054	+	13.1667i	0.956053	+	0.551977i	0.0610967	+	0.998132i	$0.480540\pi$
$570$		0			0
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.796463	+	0.604688i	$0.206702\pi$
$571$	22.0295	+	38.1562i	0.921906	+	1.59679i	0.125444	+	0.992101i	$0.459965\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	22.3929i		−	0.933847i
$576$		0			0
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	0.731170	−	0.682195i	$-0.238974\pi$
$577$	12.1535	+	7.01684i	0.505957	+	0.292115i	−0.225213	+	0.974310i	$0.572308\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.5219	−	6.72654i	0.768418	−	0.279064i
$582$		0			0
$583$	−1.30448	+	2.25943i	−0.0540262	+	0.0935762i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	0.895774	−	0.444509i	$-0.146622\pi$
$587$	1.52469	+	2.64085i	0.0629308	+	0.108999i	−0.832843	+	0.553509i	$0.813289\pi$
$588$		0			0
$589$	1.23791	−	2.14413i	0.0510073	−	0.0883473i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	0.998522	+	0.0543552i	$0.0173103\pi$
$593$	13.3041	+	23.0434i	0.546334	+	0.946278i	−0.452188	+	0.891923i	$0.649356\pi$
$594$		0			0
$595$	5.28306	+	4.43941i	0.216585	+	0.181998i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	−0.418993	−	0.907989i	$-0.637617\pi$
$599$	3.86333	−	2.23050i	0.157852	−	0.0911356i	0.576845	+	0.816854i	$0.304284\pi$
$600$		0			0
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	−0.603243	−	0.797557i	$-0.706125\pi$
$601$	−5.25019	+	3.03120i	−0.214160	+	0.123645i	0.389083	+	0.921203i	$0.372792\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.64700			−0.310895
$606$		0			0
$607$		−	45.3313i		−	1.83994i	−0.391986	−	0.919971i	$-0.628212\pi$
$607$		−	45.3313i		−	1.83994i	0.391986	−	0.919971i	$-0.371788\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.97409	+	4.60384i	−0.322597	+	0.186251i
$612$		0			0
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	−0.305781	−	0.952102i	$-0.598917\pi$
$613$	16.6294	−	28.8029i	0.671654	−	1.16334i	0.977435	−	0.211237i	$-0.0677492\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.3001	−	18.0711i	−1.26010	−	0.727516i	−0.287002	−	0.957930i	$-0.592659\pi$
$617$	−31.3001	−	18.0711i	−1.26010	−	0.727516i	−0.973093	+	0.230414i	$0.925992\pi$
$618$		0			0
$619$		−	26.4462i		−	1.06296i	−0.847069	−	0.531482i	$-0.821635\pi$
$619$		−	26.4462i		−	1.06296i	0.847069	−	0.531482i	$-0.178365\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−27.8158	+	10.1018i	−1.11442	+	0.404719i
$624$		0			0
$625$	17.8969			0.715874
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.61787			0.104381
$630$		0			0
$631$	−32.0484			−1.27583			−0.637914	−	0.770107i	$-0.720203\pi$
$631$	−32.0484			−1.27583			−0.637914	+	0.770107i	$0.720203\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−15.2737			−0.606120
$636$		0			0
$637$	5.90376	+	7.05613i	0.233916	+	0.279574i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	24.4154i		−	0.964351i	−0.876075	−	0.482176i	$-0.839847\pi$
$641$		−	24.4154i		−	0.964351i	0.876075	−	0.482176i	$-0.160153\pi$
$642$		0			0
$643$	31.9014	+	18.4183i	1.25807	+	0.726346i	0.972699	−	0.232071i	$-0.0745503\pi$
$643$	31.9014	+	18.4183i	1.25807	+	0.726346i	0.285370	+	0.958418i	$0.407884\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	−0.477389	−	0.878692i	$-0.658417\pi$
$647$	13.2847	−	23.0098i	0.522276	−	0.904608i	0.999664	−	0.0259155i	$-0.00825009\pi$
$648$		0			0
$649$	−3.09239	+	1.78539i	−0.121387	+	0.0700827i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	30.3418i		−	1.18737i	−0.804699	−	0.593683i	$-0.797673\pi$
$653$		−	30.3418i		−	1.18737i	0.804699	−	0.593683i	$-0.202327\pi$
$654$		0			0
$655$	3.64466			0.142409
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.604511	+	0.796597i	$0.706631\pi$
$659$	−40.9873	+	23.6640i	−1.59664	+	0.921820i	−0.992129	+	0.125223i	$0.960035\pi$
$660$		0			0
$661$	30.4187	−	17.5623i	1.18315	−	0.683092i	0.226409	−	0.974032i	$-0.427301\pi$
$661$	30.4187	−	17.5623i	1.18315	−	0.683092i	0.956741	+	0.290940i	$0.0939679\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.279049	+	0.768376i	0.0108211	+	0.0297963i
$666$		0			0
$667$	0.783329	+	1.35677i	0.0303306	+	0.0525342i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.749513	−	1.29819i	0.0289346	−	0.0501162i
$672$		0			0
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	0.812738	−	0.582629i	$-0.197976\pi$
$673$	−2.54758	−	4.41254i	−0.0982020	−	0.170091i	−0.910940	+	0.412538i	$0.864642\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.42072	−	14.5851i	0.323635	−	0.560551i	−0.657601	−	0.753367i	$-0.728429\pi$
$677$	8.42072	−	14.5851i	0.323635	−	0.560551i	0.981235	+	0.192815i	$0.0617618\pi$
$678$		0			0
$679$	9.57573	+	26.3673i	0.367483	+	1.01188i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	0.770169	−	0.637840i	$-0.220172\pi$
$683$	15.7555	+	9.09645i	0.602868	+	0.348066i	−0.167301	+	0.985906i	$0.553505\pi$
$684$		0			0
$685$			1.88715i			0.0721042i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.46452	−	11.1969i	−0.246279	−	0.426567i
$690$		0			0
$691$	−3.05405	−	1.76326i	−0.116182	−	0.0670775i	0.440783	−	0.897614i	$-0.354701\pi$
$691$	−3.05405	−	1.76326i	−0.116182	−	0.0670775i	−0.556965	+	0.830536i	$0.688034\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−7.09786	−	4.09795i	−0.269237	−	0.155444i
$696$		0			0
$697$	−20.1063	−	34.8251i	−0.761579	−	1.31909i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	13.3502i		−	0.504229i	−0.967697	−	0.252114i	$-0.918874\pi$
$701$		−	13.3502i		−	0.504229i	0.967697	−	0.252114i	$-0.0811259\pi$
$702$		0			0
$703$	0.268574	+	0.155061i	0.0101295	+	0.00584824i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.07566	−	45.6101i	0.303716	−	1.71535i
$708$		0			0
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	−0.129298	−	0.991606i	$-0.541273\pi$
$709$	21.1447	−	36.6237i	0.794107	−	1.37543i	0.923405	−	0.383827i	$-0.125394\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−13.9166	−	24.1043i	−0.521182	−	0.902715i
$714$		0			0
$715$	−0.121942	+	0.211210i	−0.00456038	+	0.00789881i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	0.996861	+	0.0791697i	$0.0252269\pi$
$719$	15.2035	+	26.3332i	0.566994	+	0.982062i	−0.429868	+	0.902892i	$0.641440\pi$
$720$		0			0
$721$	22.2544	+	3.94032i	0.828796	+	0.146745i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.23265	+	0.711673i	−0.0457796	+	0.0264309i
$726$		0			0
$727$	11.3671	−	6.56280i	0.421583	−	0.243401i	−0.274171	−	0.961681i	$-0.588404\pi$
$727$	11.3671	−	6.56280i	0.421583	−	0.243401i	0.695754	+	0.718280i	$0.255070\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−27.8195			−1.02894
$732$		0			0
$733$			37.7588i			1.39465i	0.716753	+	0.697327i	$0.245628\pi$
$733$			37.7588i			1.39465i	−0.716753	+	0.697327i	$0.754372\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.36460	+	0.787853i	−0.0502657	+	0.0290209i
$738$		0			0
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	−0.999802	−	0.0198820i	$-0.993671\pi$
$739$	−13.1215	+	22.7271i	−0.482683	+	0.836031i	0.517119	+	0.855913i	$0.327004\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	0.652393	−	0.757881i	$-0.273765\pi$
$743$	8.78379	+	5.07132i	0.322246	+	0.186049i	−0.330147	+	0.943929i	$0.607098\pi$
$744$		0			0
$745$			13.1731i			0.482625i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.48462	+	26.1164i	0.346561	+	0.954273i
$750$		0			0
$751$	7.90737			0.288544			0.144272	−	0.989538i	$-0.453916\pi$
$751$	7.90737			0.288544			0.144272	+	0.989538i	$0.453916\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.99855			−0.254703
$756$		0			0
$757$	29.8903			1.08638			0.543191	−	0.839609i	$-0.317216\pi$
$757$	29.8903			1.08638			0.543191	+	0.839609i	$0.317216\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.11374			0.221623			0.110811	−	0.993841i	$-0.464655\pi$
$761$	6.11374			0.221623			0.110811	+	0.993841i	$0.464655\pi$
$762$		0			0
$763$	−28.8484	−	24.2416i	−1.04438	−	0.877604i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	17.6954i		−	0.638944i
$768$		0			0
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	0.666159	−	0.745810i	$-0.267937\pi$
$769$	9.79863	+	5.65724i	0.353348	+	0.204005i	−0.312811	+	0.949815i	$0.601271\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	−0.280569	−	0.959834i	$-0.590523\pi$
$773$	19.2106	−	33.2737i	0.690956	−	1.19677i	0.971525	−	0.236937i	$-0.0761437\pi$
$774$		0			0
$775$	21.8994	−	12.6436i	0.786648	−	0.454172i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	4.76373i		−	0.170678i
$780$		0			0
$781$	3.56247			0.127475
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.152730	−	0.0881788i	0.00545117	−	0.00314723i
$786$		0			0
$787$	41.2747	−	23.8300i	1.47129	−	0.849447i	0.471806	−	0.881703i	$-0.343602\pi$
$787$	41.2747	−	23.8300i	1.47129	−	0.849447i	0.999480	+	0.0322557i	$0.0102691\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	26.2938	−	31.2906i	0.934900	−	1.11257i
$792$		0			0
$793$	3.71430	+	6.43335i	0.131898	+	0.228455i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.1359	+	26.2161i	−0.536139	+	0.928621i	0.462968	+	0.886375i	$0.346785\pi$
$797$	−15.1359	+	26.2161i	−0.536139	+	0.928621i	−0.999107	+	0.0422457i	$0.986549\pi$
$798$		0			0
$799$	13.0581	+	22.6172i	0.461961	+	0.800140i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.02008	−	1.76683i	0.0359978	−	0.0623500i
$804$		0			0
$805$	9.04935	+	1.60226i	0.318948	+	0.0564723i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	0.503851	−	0.863790i	$-0.331916\pi$
$809$	0.219373	+	0.126655i	0.00771273	+	0.00445295i	−0.496139	+	0.868243i	$0.665249\pi$
$810$		0			0
$811$		−	22.0629i		−	0.774735i	−0.921925	−	0.387367i	$-0.873385\pi$
$811$		−	22.0629i		−	0.774735i	0.921925	−	0.387367i	$-0.126615\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.00698	−	5.20824i	−0.105330	−	0.182437i
$816$		0			0
$817$	−2.85407	−	1.64780i	−0.0998514	−	0.0576492i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.2467	−	13.9988i	−0.846214	−	0.488562i	0.0131576	−	0.999913i	$-0.495812\pi$
$821$	−24.2467	−	13.9988i	−0.846214	−	0.488562i	−0.859372	+	0.511352i	$0.829145\pi$
$822$		0			0
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	−0.878289	−	0.478130i	$-0.841315\pi$
$823$	−24.4771	−	42.3955i	−0.853217	−	1.47782i	0.0250719	−	0.999686i	$-0.492019\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.641658i			0.0223126i	0.999938	+	0.0111563i	$0.00355124\pi$
$827$			0.641658i			0.0223126i	−0.999938	+	0.0111563i	$0.996449\pi$
$828$		0			0
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	0.656925	−	0.753956i	$-0.271857\pi$
$829$	9.57180	+	5.52628i	0.332442	+	0.191936i	−0.324483	+	0.945892i	$0.605190\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	20.0136	−	16.7451i	0.693430	−	0.580183i
$834$		0			0
$835$	−1.57029	+	2.71981i	−0.0543420	+	0.0941230i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	0.775115	−	0.631820i	$-0.217692\pi$
$839$	−4.62330	−	8.00780i	−0.159614	−	0.276460i	−0.934730	+	0.355360i	$0.884358\pi$
$840$		0			0
$841$	−14.4502	+	25.0285i	−0.498283	+	0.863052i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.94346	+	6.83028i	0.135659	+	0.234969i
$846$		0			0
$847$	−5.04161	+	28.4743i	−0.173232	+	0.978388i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.01931	−	1.74320i	0.103501	−	0.0597561i
$852$		0			0
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.220366	−	0.975417i	$-0.429275\pi$
$853$	34.3256	−	19.8179i	1.17529	−	0.678551i	0.954919	+	0.296866i	$0.0959414\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	23.8520			0.814770			0.407385	−	0.913256i	$-0.366441\pi$
$857$	23.8520			0.814770			0.407385	+	0.913256i	$0.366441\pi$
$858$		0			0
$859$			11.1138i			0.379197i	0.981862	+	0.189598i	$0.0607186\pi$
$859$			11.1138i			0.379197i	−0.981862	+	0.189598i	$0.939281\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.983731	−	0.179646i	$-0.942505\pi$
$863$	−38.7780	+	22.3885i	−1.32002	+	0.762113i	−0.336287	+	0.941759i	$0.609171\pi$
$864$		0			0
$865$	−2.49128	+	4.31503i	−0.0847061	+	0.146715i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.320805	−	0.185217i	−0.0108826	−	0.00628305i
$870$		0			0
$871$		−	7.80859i		−	0.264584i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.06937	+	17.3354i	−0.103764	+	0.586042i
$876$		0			0
$877$	3.68191			0.124329			0.0621647	−	0.998066i	$-0.480200\pi$
$877$	3.68191			0.124329			0.0621647	+	0.998066i	$0.480200\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	17.3992			0.586194			0.293097	−	0.956083i	$-0.405314\pi$
$881$	17.3992			0.586194			0.293097	+	0.956083i	$0.405314\pi$
$882$		0			0
$883$	−2.02834			−0.0682592			−0.0341296	−	0.999417i	$-0.510866\pi$
$883$	−2.02834			−0.0682592			−0.0341296	+	0.999417i	$0.510866\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−46.3780			−1.55722			−0.778610	−	0.627508i	$-0.784075\pi$
$887$	−46.3780			−1.55722			−0.778610	+	0.627508i	$0.784075\pi$
$888$		0			0
$889$	−10.0699	+	56.8731i	−0.337732	+	1.90746i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			3.09381i			0.103531i
$894$		0			0
$895$	−15.4812	−	8.93810i	−0.517481	−	0.298768i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.884576	+	1.53213i	−0.0295023	+	0.0510994i
$900$		0			0
$901$	−31.7582	+	18.3356i	−1.05802	+	0.610847i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			0.659898i			0.0219357i
$906$		0			0
$907$	16.0391			0.532571			0.266285	−	0.963894i	$-0.414204\pi$
$907$	16.0391			0.532571			0.266285	+	0.963894i	$0.414204\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	−0.764776	−	0.644296i	$-0.777150\pi$
$911$	−17.7833	+	10.2672i	−0.589187	+	0.340167i	0.175589	+	0.984464i	$0.443817\pi$
$912$		0			0
$913$	1.71069	−	0.987665i	0.0566154	−	0.0326869i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.40290	−	13.5712i	0.0793507	−	0.448161i
$918$		0			0
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	−0.994987	−	0.100001i	$-0.968115\pi$
$919$	−17.7069	−	30.6693i	−0.584097	−	1.01169i	0.410890	−	0.911685i	$-0.365218\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.82712	+	15.2890i	−0.290548	+	0.503244i
$924$		0			0
$925$	1.58374	+	2.74311i	0.0520730	+	0.0901930i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	19.8626	−	34.4030i	0.651670	−	1.12873i	−0.331048	−	0.943614i	$-0.607402\pi$
$929$	19.8626	−	34.4030i	0.651670	−	1.12873i	0.982718	−	0.185111i	$-0.0592646\pi$
$930$		0			0
$931$	3.04509	−	0.532479i	0.0997988	−	0.0174513i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.599064	+	0.345870i	0.0195915	+	0.0113112i
$936$		0			0
$937$		−	23.2142i		−	0.758376i	−0.925320	−	0.379188i	$-0.876203\pi$
$937$		−	23.2142i		−	0.758376i	0.925320	−	0.379188i	$-0.123797\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	17.9616	+	31.1104i	0.585531	+	1.01417i	0.994809	+	0.101760i	$0.0324474\pi$
$941$	17.9616	+	31.1104i	0.585531	+	1.01417i	−0.409278	+	0.912410i	$0.634219\pi$
$942$		0			0
$943$	−46.3790	−	26.7769i	−1.51031	−	0.871977i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.866955	−	0.498386i	$-0.166074\pi$
$947$	26.7365	+	15.4363i	0.868818	+	0.501612i	0.00186277	+	0.999998i	$0.499407\pi$
$948$		0			0
$949$	5.05511	+	8.75571i	0.164096	+	0.284222i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			30.4640i			0.986826i	0.869795	+	0.493413i	$0.164251\pi$
$953$			30.4640i			0.986826i	−0.869795	+	0.493413i	$0.835749\pi$
$954$		0			0
$955$	−1.80100	−	1.03981i	−0.0582791	−	0.0336475i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.02696	+	1.24418i	0.226912	+	0.0401768i
$960$		0			0
$961$	0.215406	−	0.373095i	0.00694859	−	0.0120353i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.47686	−	11.2182i	−0.208497	−	0.361128i
$966$		0			0
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	−0.953995	−	0.299823i	$-0.903072\pi$
$967$	−6.75865	+	11.7063i	−0.217343	+	0.376450i	0.736652	+	0.676272i	$0.236406\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	0.999207	+	0.0398238i	$0.0126797\pi$
$971$	16.6428	+	28.8261i	0.534092	+	0.925074i	−0.465115	+	0.885250i	$0.653987\pi$
$972$		0			0
$973$	−19.9387	+	23.7278i	−0.639204	+	0.760677i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−38.9127	+	22.4662i	−1.24493	+	0.718758i	−0.970093	−	0.242734i	$-0.921956\pi$
$977$	−38.9127	+	22.4662i	−1.24493	+	0.718758i	−0.274833	+	0.961492i	$0.588623\pi$
$978$		0			0
$979$	−2.56907	+	1.48325i	−0.0821079	+	0.0474050i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	26.8949			0.857813			0.428907	−	0.903349i	$-0.358899\pi$
$983$	26.8949			0.857813			0.428907	+	0.903349i	$0.358899\pi$
$984$		0			0
$985$			9.91929i			0.316055i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−32.0855	+	18.5246i	−1.02026	+	0.589048i
$990$		0			0
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	−0.434346	−	0.900746i	$-0.643020\pi$
$991$	17.7201	−	30.6920i	0.562896	−	0.974965i	0.997242	−	0.0742186i	$-0.0236463\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	14.3635	+	8.29275i	0.455352	+	0.262898i
$996$		0			0
$997$		−	32.4953i		−	1.02914i	−0.857449	−	0.514568i	$-0.827952\pi$
$997$		−	32.4953i		−	1.02914i	0.857449	−	0.514568i	$-0.172048\pi$
$998$		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.17.4		16
3.2	odd	2		252.2.bm.a.185.8	yes	16
4.3	odd	2		3024.2.df.d.17.4		16
7.2	even	3		5292.2.w.b.1097.5		16
7.3	odd	6		5292.2.x.a.881.4		16
7.4	even	3		5292.2.x.b.881.5		16
7.5	odd	6		756.2.w.a.341.4		16
7.6	odd	2		5292.2.bm.a.2285.5		16
9.2	odd	6		756.2.w.a.521.4		16
9.4	even	3		2268.2.t.b.1781.5		16
9.5	odd	6		2268.2.t.a.1781.4		16
9.7	even	3		252.2.w.a.101.6	yes	16
12.11	even	2		1008.2.df.d.689.1		16
21.2	odd	6		1764.2.w.b.509.3		16
21.5	even	6		252.2.w.a.5.6	✓	16
21.11	odd	6		1764.2.x.b.293.3		16
21.17	even	6		1764.2.x.a.293.6		16
21.20	even	2		1764.2.bm.a.1697.1		16
28.19	even	6		3024.2.ca.d.2609.4		16
36.7	odd	6		1008.2.ca.d.353.3		16
36.11	even	6		3024.2.ca.d.2033.4		16
63.2	odd	6		5292.2.bm.a.4625.5		16
63.5	even	6		2268.2.t.b.2105.5		16
63.11	odd	6		5292.2.x.a.4409.4		16
63.16	even	3		1764.2.bm.a.1685.1		16
63.20	even	6		5292.2.w.b.521.5		16
63.25	even	3		1764.2.x.a.1469.6		16
63.34	odd	6		1764.2.w.b.1109.3		16
63.38	even	6		5292.2.x.b.4409.5		16
63.40	odd	6		2268.2.t.a.2105.4		16
63.47	even	6	inner	756.2.bm.a.89.4		16
63.52	odd	6		1764.2.x.b.1469.3		16
63.61	odd	6		252.2.bm.a.173.8	yes	16
84.47	odd	6		1008.2.ca.d.257.3		16
252.47	odd	6		3024.2.df.d.1601.4		16
252.187	even	6		1008.2.df.d.929.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.6	✓	16	21.5	even	6
252.2.w.a.101.6	yes	16	9.7	even	3
252.2.bm.a.173.8	yes	16	63.61	odd	6
252.2.bm.a.185.8	yes	16	3.2	odd	2
756.2.w.a.341.4		16	7.5	odd	6
756.2.w.a.521.4		16	9.2	odd	6
756.2.bm.a.17.4		16	1.1	even	1	trivial
756.2.bm.a.89.4		16	63.47	even	6	inner
1008.2.ca.d.257.3		16	84.47	odd	6
1008.2.ca.d.353.3		16	36.7	odd	6
1008.2.df.d.689.1		16	12.11	even	2
1008.2.df.d.929.1		16	252.187	even	6
1764.2.w.b.509.3		16	21.2	odd	6
1764.2.w.b.1109.3		16	63.34	odd	6
1764.2.x.a.293.6		16	21.17	even	6
1764.2.x.a.1469.6		16	63.25	even	3
1764.2.x.b.293.3		16	21.11	odd	6
1764.2.x.b.1469.3		16	63.52	odd	6
1764.2.bm.a.1685.1		16	63.16	even	3
1764.2.bm.a.1697.1		16	21.20	even	2
2268.2.t.a.1781.4		16	9.5	odd	6
2268.2.t.a.2105.4		16	63.40	odd	6
2268.2.t.b.1781.5		16	9.4	even	3
2268.2.t.b.2105.5		16	63.5	even	6
3024.2.ca.d.2033.4		16	36.11	even	6
3024.2.ca.d.2609.4		16	28.19	even	6
3024.2.df.d.17.4		16	4.3	odd	2
3024.2.df.d.1601.4		16	252.47	odd	6
5292.2.w.b.521.5		16	63.20	even	6
5292.2.w.b.1097.5		16	7.2	even	3
5292.2.x.a.881.4		16	7.3	odd	6
5292.2.x.a.4409.4		16	63.11	odd	6
5292.2.x.b.881.5		16	7.4	even	3
5292.2.x.b.4409.5		16	63.38	even	6
5292.2.bm.a.2285.5		16	7.6	odd	2
5292.2.bm.a.4625.5		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)

\(f(q)\)	\(=\)	\(q-0.699656 q^{5} +(-0.461278 + 2.60523i) q^{7} +O(q^{10})\)	\(q-0.699656 q^{5} +(-0.461278 + 2.60523i) q^{7} +0.265217i q^{11} +(-1.13823 - 0.657156i) q^{13} +(-1.86392 + 3.22840i) q^{17} +(-0.382449 + 0.220807i) q^{19} +4.96463i q^{23} -4.51048 q^{25} +(0.273287 - 0.157782i) q^{29} +(-4.85521 + 2.80316i) q^{31} +(0.322736 - 1.82276i) q^{35} +(-0.351124 - 0.608164i) q^{37} +(-5.39354 + 9.34189i) q^{41} +(3.73131 + 6.46283i) q^{43} +(3.50285 - 6.06712i) q^{47} +(-6.57445 - 2.40347i) q^{49} +(8.51919 + 4.91856i) q^{53} -0.185561i q^{55} +(6.73182 + 11.6598i) q^{59} +(-4.89484 - 2.82604i) q^{61} +(0.796368 + 0.459783i) q^{65} +(2.97060 + 5.14523i) q^{67} -13.4323i q^{71} +(-6.66182 - 3.84620i) q^{73} +(-0.690951 - 0.122339i) q^{77} +(-0.698360 + 1.20959i) q^{79} +(-3.72399 - 6.45014i) q^{83} +(1.30410 - 2.25877i) q^{85} +(5.59261 + 9.68668i) q^{89} +(2.23708 - 2.66221i) q^{91} +(0.267582 - 0.154489i) q^{95} +(9.18225 - 5.30138i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7}+O(q^{10}) \) 16 * q - q^7	\( 16 q - q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} + 6 q^{31} - 15 q^{35} + q^{37} - 6 q^{41} - 2 q^{43} + 18 q^{47} + 13 q^{49} + 15 q^{59} + 3 q^{61} + 39 q^{65} - 7 q^{67} + 45 q^{77} - q^{79} + 6 q^{85} + 21 q^{89} + 9 q^{91} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 + 6 * q^31 - 15 * q^35 + q^37 - 6 * q^41 - 2 * q^43 + 18 * q^47 + 13 * q^49 + 15 * q^59 + 3 * q^61 + 39 * q^65 - 7 * q^67 + 45 * q^77 - q^79 + 6 * q^85 + 21 * q^89 + 9 * q^91 - 6 * q^95 + 3 * q^97

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