LMFDB - Embedded newform 756.2.w.a.341.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(341,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.341"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

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

Embedding invariants

Embedding label			341.1
Root			$-0.213160 - 1.71888i$ of defining polynomial
Character	$\chi$	$=$	756.341
Dual form			756.2.w.a.521.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43402 - 2.48379i) q^{5} +(2.56899 - 0.632668i) q^{7} +(2.34941 + 1.35643i) q^{11} +(-3.18987 - 1.84167i) q^{13} +(-3.22192 - 5.58052i) q^{17} +(2.73867 + 1.58117i) q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(2.48332 - 1.43375i) q^{29} -9.54636i q^{31} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(0.794538 - 1.37618i) q^{41} +(-4.67828 - 8.10302i) q^{43} -11.3074 q^{47} +(6.19946 - 3.25064i) q^{49} +(-2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +8.67361 q^{59} -0.654617i q^{61} +10.5640i q^{65} +7.72292 q^{67} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(6.89378 + 1.99827i) q^{77} +5.19132 q^{79} +(7.92948 + 13.7343i) q^{83} +(-9.24057 + 16.0051i) q^{85} +(-3.14826 + 5.45295i) q^{89} +(-9.35993 - 2.71312i) q^{91} -9.06971i q^{95} +(-13.2065 + 7.62477i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85}+ \cdots - 3 q^{97}+O(q^{100}) $ 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	−0.985140	−	0.171753i	$-0.945057\pi$
$5$	−1.43402	−	2.48379i	−0.641312	−	1.11079i	0.343828	−	0.939033i	$-0.388276\pi$
$6$		0			0
$7$	2.56899	−	0.632668i	0.970989	−	0.239126i
$7$	2.56899	−	0.632668i	0.970989	−	0.239126i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.34941	+	1.35643i	0.708373	+	0.408979i	0.810458	−	0.585797i	$-0.199218\pi$
$11$	2.34941	+	1.35643i	0.708373	+	0.408979i	−0.102086	+	0.994776i	$0.532552\pi$
$12$		0			0
$13$	−3.18987	−	1.84167i	−0.884712	−	0.510789i	−0.0125026	−	0.999922i	$-0.503980\pi$
$13$	−3.18987	−	1.84167i	−0.884712	−	0.510789i	−0.872209	+	0.489133i	$0.837313\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.22192	−	5.58052i	−0.781429	−	1.35348i	−0.931109	−	0.364741i	$-0.881158\pi$
$17$	−3.22192	−	5.58052i	−0.781429	−	1.35348i	0.149680	−	0.988735i	$-0.452176\pi$
$18$		0			0
$19$	2.73867	+	1.58117i	0.628294	+	0.362746i	0.780091	−	0.625666i	$-0.215173\pi$
$19$	2.73867	+	1.58117i	0.628294	+	0.362746i	−0.151797	+	0.988412i	$0.548506\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.59068	+	1.49573i	−0.540195	+	0.311882i	−0.745158	−	0.666888i	$-0.767626\pi$
$23$	−2.59068	+	1.49573i	−0.540195	+	0.311882i	0.204963	+	0.978770i	$0.434293\pi$
$24$		0			0
$25$	−1.61282	+	2.79348i	−0.322563	+	0.558696i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.48332	−	1.43375i	0.461142	−	0.266240i	−0.251383	−	0.967888i	$-0.580885\pi$
$29$	2.48332	−	1.43375i	0.461142	−	0.266240i	0.712524	+	0.701648i	$0.247552\pi$
$30$		0			0
$31$		−	9.54636i		−	1.71458i	−0.514836	−	0.857289i	$-0.672147\pi$
$31$		−	9.54636i		−	1.71458i	0.514836	−	0.857289i	$-0.327853\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.25540	−	5.47359i	−0.888325	−	0.925205i
$36$		0			0
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	−0.971515	−	0.236977i	$-0.923843\pi$
$37$	−1.70640	+	2.95556i	−0.280530	+	0.485892i	0.690986	+	0.722868i	$0.257177\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.794538	−	1.37618i	0.124086	−	0.214923i	−0.797289	−	0.603597i	$-0.793733\pi$
$41$	0.794538	−	1.37618i	0.124086	−	0.214923i	0.921375	+	0.388674i	$0.127067\pi$
$42$		0			0
$43$	−4.67828	−	8.10302i	−0.713431	−	1.23570i	−0.963562	−	0.267487i	$-0.913807\pi$
$43$	−4.67828	−	8.10302i	−0.713431	−	1.23570i	0.250131	−	0.968212i	$-0.419526\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−11.3074			−1.64936			−0.824680	−	0.565599i	$-0.808645\pi$
$47$	−11.3074			−1.64936			−0.824680	+	0.565599i	$0.808645\pi$
$48$		0			0
$49$	6.19946	−	3.25064i	0.885637	−	0.464378i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.16419	+	1.24950i	−0.297275	+	0.171632i	−0.641218	−	0.767359i	$-0.721571\pi$
$53$	−2.16419	+	1.24950i	−0.297275	+	0.171632i	0.343943	+	0.938990i	$0.388237\pi$
$54$		0			0
$55$		−	7.78058i		−	1.04913i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.67361			1.12921			0.564604	−	0.825362i	$-0.309029\pi$
$59$	8.67361			1.12921			0.564604	+	0.825362i	$0.309029\pi$
$60$		0			0
$61$		−	0.654617i		−	0.0838151i	−0.999121	−	0.0419075i	$-0.986657\pi$
$61$		−	0.654617i		−	0.0838151i	0.999121	−	0.0419075i	$-0.0133435\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			10.5640i			1.31030i
$66$		0			0
$67$	7.72292			0.943505			0.471752	−	0.881731i	$-0.343622\pi$
$67$	7.72292			0.943505			0.471752	+	0.881731i	$0.343622\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	7.86582i		−	0.933501i	−0.884389	−	0.466750i	$-0.845425\pi$
$71$		−	7.86582i		−	0.933501i	0.884389	−	0.466750i	$-0.154575\pi$
$72$		0			0
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.316667	−	0.948537i	$-0.397436\pi$
$73$	11.0769	−	6.39527i	1.29646	−	0.748510i	0.979790	+	0.200027i	$0.0641028\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.89378	+	1.99827i	0.785619	+	0.227724i
$78$		0			0
$79$	5.19132			0.584069			0.292034	−	0.956408i	$-0.405668\pi$
$79$	5.19132			0.584069			0.292034	+	0.956408i	$0.405668\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.92948	+	13.7343i	0.870373	+	1.50753i	0.861611	+	0.507569i	$0.169456\pi$
$83$	7.92948	+	13.7343i	0.870373	+	1.50753i	0.00876173	+	0.999962i	$0.497211\pi$
$84$		0			0
$85$	−9.24057	+	16.0051i	−1.00228	+	1.73600i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.14826	+	5.45295i	−0.333715	+	0.578012i	−0.983237	−	0.182331i	$-0.941636\pi$
$89$	−3.14826	+	5.45295i	−0.333715	+	0.578012i	0.649522	+	0.760343i	$0.274969\pi$
$90$		0			0
$91$	−9.35993	−	2.71312i	−0.981188	−	0.284412i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	9.06971i		−	0.930533i
$96$		0			0
$97$	−13.2065	+	7.62477i	−1.34092	+	0.774178i	−0.986942	−	0.161077i	$-0.948503\pi$
$97$	−13.2065	+	7.62477i	−1.34092	+	0.774178i	−0.353974	+	0.935255i	$0.615170\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	−0.766086	−	0.642739i	$-0.777798\pi$
$101$	1.74451	−	3.02158i	0.173585	−	0.300658i	0.939671	+	0.342080i	$0.111131\pi$
$102$		0			0
$103$	−2.89161	+	1.66947i	−0.284919	+	0.164498i	−0.635648	−	0.771979i	$-0.719267\pi$
$103$	−2.89161	+	1.66947i	−0.284919	+	0.164498i	0.350729	+	0.936477i	$0.385934\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	0.642640	−	0.766168i	$-0.277839\pi$
$107$	3.10776	+	1.79427i	0.300439	+	0.173458i	−0.342201	+	0.939627i	$0.611172\pi$
$108$		0			0
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	0.980462	+	0.196710i	$0.0630258\pi$
$109$	6.89673	+	11.9455i	0.660587	+	1.14417i	−0.319875	+	0.947460i	$0.603641\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	5.28607	+	3.05191i	0.497271	+	0.287100i	0.727586	−	0.686016i	$-0.240642\pi$
$113$	5.28607	+	3.05191i	0.497271	+	0.287100i	−0.230315	+	0.973116i	$0.573976\pi$
$114$		0			0
$115$	7.43018	+	4.28981i	0.692867	+	0.400027i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.8077	−	12.2979i	−1.08241	−	1.12735i
$120$		0			0
$121$	−1.82019	−	3.15267i	−0.165472	−	0.286606i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.08895			−0.455170
$126$		0			0
$127$	−13.3819			−1.18745			−0.593727	−	0.804666i	$-0.702344\pi$
$127$	−13.3819			−1.18745			−0.593727	+	0.804666i	$0.702344\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	0.882517	−	0.470280i	$-0.155847\pi$
$131$	0.388964	+	0.673705i	0.0339839	+	0.0588619i	−0.848533	+	0.529142i	$0.822514\pi$
$132$		0			0
$133$	8.03598	+	2.32935i	0.696808	+	0.201980i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	14.3082	+	8.26083i	1.22243	+	0.705771i	0.965435	−	0.260642i	$-0.0839343\pi$
$137$	14.3082	+	8.26083i	1.22243	+	0.705771i	0.256995	+	0.966413i	$0.417268\pi$
$138$		0			0
$139$	9.91826	+	5.72631i	0.841256	+	0.485699i	0.857691	−	0.514165i	$-0.171898\pi$
$139$	9.91826	+	5.72631i	0.841256	+	0.485699i	−0.0164348	+	0.999865i	$0.505232\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.99620	−	8.65368i	−0.417804	−	0.723657i
$144$		0			0
$145$	−7.12226	−	4.11204i	−0.591472	−	0.341486i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.24781	−	2.45247i	0.347994	−	0.200914i	−0.315807	−	0.948823i	$-0.602275\pi$
$149$	4.24781	−	2.45247i	0.347994	−	0.200914i	0.663801	+	0.747909i	$0.268942\pi$
$150$		0			0
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	−0.993852	−	0.110712i	$-0.964687\pi$
$151$	−4.92814	+	8.53579i	−0.401047	+	0.694633i	0.592806	+	0.805345i	$0.298020\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−23.7112	+	13.6897i	−1.90453	+	1.09958i
$156$		0			0
$157$			15.4169i			1.23040i	0.788371	+	0.615200i	$0.210925\pi$
$157$			15.4169i			1.23040i	−0.788371	+	0.615200i	$0.789075\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.70915	+	5.48157i	−0.449944	+	0.432008i
$162$		0			0
$163$	−5.72053	+	9.90825i	−0.448066	+	0.776074i	−0.998260	−	0.0589632i	$-0.981221\pi$
$163$	−5.72053	+	9.90825i	−0.448066	+	0.776074i	0.550194	+	0.835037i	$0.314554\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.49103	−	11.2428i	0.502291	−	0.869993i	−0.497706	−	0.867346i	$-0.665824\pi$
$167$	6.49103	−	11.2428i	0.502291	−	0.869993i	0.999996	−	0.00264735i	$-0.000842678\pi$
$168$		0			0
$169$	0.283528	+	0.491084i	0.0218098	+	0.0377757i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	19.5997			1.49014			0.745068	−	0.666988i	$-0.232417\pi$
$173$	19.5997			1.49014			0.745068	+	0.666988i	$0.232417\pi$
$174$		0			0
$175$	−2.37597	+	8.19681i	−0.179606	+	0.619620i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	16.2630	−	9.38942i	1.21555	−	0.701799i	0.251588	−	0.967835i	$-0.419047\pi$
$179$	16.2630	−	9.38942i	1.21555	−	0.701799i	0.963963	+	0.266036i	$0.0857140\pi$
$180$		0			0
$181$			4.47775i			0.332829i	0.986056	+	0.166414i	$0.0532190\pi$
$181$			4.47775i			0.332829i	−0.986056	+	0.166414i	$0.946781\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	9.78801			0.719629
$186$		0			0
$187$		−	17.4812i		−	1.27835i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	6.81331i		−	0.492994i	−0.969144	−	0.246497i	$-0.920720\pi$
$191$		−	6.81331i		−	0.492994i	0.969144	−	0.246497i	$-0.0792795\pi$
$192$		0			0
$193$	−15.9539			−1.14839			−0.574193	−	0.818720i	$-0.694684\pi$
$193$	−15.9539			−1.14839			−0.574193	+	0.818720i	$0.694684\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			25.9511i			1.84894i	0.381254	+	0.924470i	$0.375492\pi$
$197$			25.9511i			1.84894i	−0.381254	+	0.924470i	$0.624508\pi$
$198$		0			0
$199$	2.75706	−	1.59179i	0.195443	−	0.112839i	−0.399085	−	0.916914i	$-0.630672\pi$
$199$	2.75706	−	1.59179i	0.195443	−	0.112839i	0.594528	+	0.804075i	$0.297339\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.47256	−	5.25441i	0.384098	−	0.368787i
$204$		0			0
$205$	−4.55752			−0.318311
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.28950	+	7.42963i	0.296711	+	0.513918i
$210$		0			0
$211$	−0.0552411	+	0.0956804i	−0.00380295	+	0.00658691i	−0.867921	−	0.496703i	$-0.834544\pi$
$211$	−0.0552411	+	0.0956804i	−0.00380295	+	0.00658691i	0.864118	+	0.503290i	$0.167877\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−13.4175	+	23.2397i	−0.915064	+	1.58494i
$216$		0			0
$217$	−6.03968	−	24.5245i	−0.410000	−	1.66483i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			23.7349i			1.59658i
$222$		0			0
$223$	11.3064	−	6.52775i	0.757132	−	0.437130i	−0.0711331	−	0.997467i	$-0.522661\pi$
$223$	11.3064	−	6.52775i	0.757132	−	0.437130i	0.828265	+	0.560336i	$0.189328\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	−0.977829	−	0.209406i	$-0.932847\pi$
$227$	−4.63392	+	8.02618i	−0.307564	+	0.532716i	0.670265	+	0.742122i	$0.266180\pi$
$228$		0			0
$229$	11.6204	−	6.70902i	0.767895	−	0.443344i	−0.0642281	−	0.997935i	$-0.520459\pi$
$229$	11.6204	−	6.70902i	0.767895	−	0.443344i	0.832123	+	0.554591i	$0.187125\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	18.3415	+	10.5895i	1.20159	+	0.693738i	0.960909	−	0.276866i	$-0.0892958\pi$
$233$	18.3415	+	10.5895i	1.20159	+	0.693738i	0.240681	+	0.970604i	$0.422629\pi$
$234$		0			0
$235$	16.2151	+	28.0853i	1.05776	+	1.83209i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.73342	+	4.46489i	0.500233	+	0.288810i	0.728810	−	0.684716i	$-0.240074\pi$
$239$	7.73342	+	4.46489i	0.500233	+	0.288810i	−0.228577	+	0.973526i	$0.573407\pi$
$240$		0			0
$241$	15.9430	+	9.20469i	1.02698	+	0.592926i	0.916117	−	0.400910i	$-0.131306\pi$
$241$	15.9430	+	9.20469i	1.02698	+	0.592926i	0.110860	+	0.993836i	$0.464639\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−16.9641	−	10.7367i	−1.08379	−	0.685942i
$246$		0			0
$247$	−5.82401	−	10.0875i	−0.370573	−	0.641851i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.33194			0.399669			0.199834	−	0.979830i	$-0.435960\pi$
$251$	6.33194			0.399669			0.199834	+	0.979830i	$0.435960\pi$
$252$		0			0
$253$	−8.11542			−0.510212
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	−0.999918	−	0.0128120i	$-0.995922\pi$
$257$	−8.19283	−	14.1904i	−0.511054	−	0.885172i	0.488863	−	0.872360i	$-0.337412\pi$
$258$		0			0
$259$	−2.51383	+	8.67241i	−0.156202	+	0.538877i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.4663	+	6.04270i	0.645377	+	0.372609i	0.786683	−	0.617357i	$-0.211797\pi$
$263$	10.4663	+	6.04270i	0.645377	+	0.372609i	−0.141306	+	0.989966i	$0.545130\pi$
$264$		0			0
$265$	6.20698	+	3.58360i	0.381292	+	0.220139i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.6652	−	21.9368i	−0.772212	−	1.33751i	−0.936348	−	0.351072i	$-0.885817\pi$
$269$	−12.6652	−	21.9368i	−0.772212	−	1.33751i	0.164136	−	0.986438i	$-0.447516\pi$
$270$		0			0
$271$	−0.195591	−	0.112924i	−0.0118813	−	0.00685967i	0.494048	−	0.869435i	$-0.335517\pi$
$271$	−0.195591	−	0.112924i	−0.0118813	−	0.00685967i	−0.505929	+	0.862575i	$0.668850\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.57832	+	4.37534i	−0.456990	+	0.263843i
$276$		0			0
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	−0.376702	−	0.926335i	$-0.622942\pi$
$277$	10.2170	−	17.6963i	0.613878	−	1.06327i	0.990580	−	0.136934i	$-0.0437248\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−8.96635	+	5.17672i	−0.534887	+	0.308817i	−0.743004	−	0.669287i	$-0.766600\pi$
$281$	−8.96635	+	5.17672i	−0.534887	+	0.308817i	0.208117	+	0.978104i	$0.433267\pi$
$282$		0			0
$283$		−	13.7157i		−	0.815311i	−0.913136	−	0.407656i	$-0.866346\pi$
$283$		−	13.7157i		−	0.815311i	0.913136	−	0.407656i	$-0.133654\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.17050	−	4.03808i	0.0690923	−	0.238360i
$288$		0			0
$289$	−12.2615	+	21.2375i	−0.721264	+	1.24927i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.21527	+	7.30105i	−0.246258	+	0.426532i	−0.962485	−	0.271336i	$-0.912535\pi$
$293$	−4.21527	+	7.30105i	−0.246258	+	0.426532i	0.716226	+	0.697868i	$0.245868\pi$
$294$		0			0
$295$	−12.4381	−	21.5434i	−0.724175	−	1.25431i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.0186			0.637222
$300$		0			0
$301$	−17.1450	−	17.8568i	−0.988221	−	1.02925i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.62593	+	0.938732i	−0.0931006	+	0.0537516i
$306$		0			0
$307$		−	5.34345i		−	0.304967i	−0.988306	−	0.152484i	$-0.951273\pi$
$307$		−	5.34345i		−	0.304967i	0.988306	−	0.152484i	$-0.0487271\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.41734			0.534008			0.267004	−	0.963695i	$-0.413966\pi$
$311$	9.41734			0.534008			0.267004	+	0.963695i	$0.413966\pi$
$312$		0			0
$313$			16.5523i			0.935590i	0.883837	+	0.467795i	$0.154951\pi$
$313$			16.5523i			0.935590i	−0.883837	+	0.467795i	$0.845049\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	26.5264i		−	1.48987i	−0.667138	−	0.744934i	$-0.732481\pi$
$317$		−	26.5264i		−	1.48987i	0.667138	−	0.744934i	$-0.267519\pi$
$318$		0			0
$319$	7.77911			0.435547
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	20.3776i		−	1.13384i
$324$		0			0
$325$	10.2894	−	5.94056i	0.570751	−	0.329523i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−29.0488	+	7.15386i	−1.60151	+	0.394405i
$330$		0			0
$331$	−17.6400			−0.969582			−0.484791	−	0.874630i	$-0.661104\pi$
$331$	−17.6400			−0.969582			−0.484791	+	0.874630i	$0.661104\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0748	−	19.1821i	−0.605081	−	1.04803i
$336$		0			0
$337$	7.31169	−	12.6642i	0.398293	−	0.689864i	−0.595222	−	0.803561i	$-0.702936\pi$
$337$	7.31169	−	12.6642i	0.398293	−	0.689864i	0.993515	+	0.113697i	$0.0362694\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.9490	−	22.4283i	0.701226	−	1.21456i
$342$		0			0
$343$	13.8698	−	12.2731i	0.748899	−	0.662684i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	1.21893i		−	0.0654358i	−0.999465	−	0.0327179i	$-0.989584\pi$
$347$		−	1.21893i		−	0.0654358i	0.999465	−	0.0327179i	$-0.0104163\pi$
$348$		0			0
$349$	−10.6857	+	6.16942i	−0.571995	+	0.330241i	−0.757946	−	0.652318i	$-0.773797\pi$
$349$	−10.6857	+	6.16942i	−0.571995	+	0.330241i	0.185951	+	0.982559i	$0.440463\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	−0.400402	−	0.916339i	$-0.631130\pi$
$353$	11.1484	−	19.3097i	0.593372	−	1.02775i	0.993774	−	0.111411i	$-0.0355370\pi$
$354$		0			0
$355$	−19.5371	+	11.2797i	−1.03692	+	0.598666i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−10.4819	−	6.05173i	−0.553214	−	0.319398i	0.197204	−	0.980363i	$-0.436814\pi$
$359$	−10.4819	−	6.05173i	−0.553214	−	0.319398i	−0.750417	+	0.660965i	$0.770147\pi$
$360$		0			0
$361$	−4.49979	−	7.79387i	−0.236831	−	0.410204i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−31.7691	−	18.3419i	−1.66287	−	0.960058i
$366$		0			0
$367$	12.7544	+	7.36375i	0.665774	+	0.384385i	0.794473	−	0.607299i	$-0.207747\pi$
$367$	12.7544	+	7.36375i	0.665774	+	0.384385i	−0.128700	+	0.991684i	$0.541080\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.76928	+	4.57917i	−0.247609	+	0.237739i
$372$		0			0
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	0.959336	−	0.282268i	$-0.0910867\pi$
$373$	4.54279	+	7.86834i	0.235217	+	0.407407i	−0.724119	+	0.689675i	$0.757753\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.5620			−0.543970
$378$		0			0
$379$	21.2298			1.09050			0.545250	−	0.838273i	$-0.316435\pi$
$379$	21.2298			1.09050			0.545250	+	0.838273i	$0.316435\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	0.767579	−	0.640954i	$-0.221461\pi$
$383$	−3.35227	−	5.80630i	−0.171293	−	0.296688i	−0.938872	+	0.344266i	$0.888128\pi$
$384$		0			0
$385$	−4.92253	−	19.9883i	−0.250875	−	1.01870i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.66661	+	3.84897i	0.338011	+	0.195151i	0.659392	−	0.751799i	$-0.270814\pi$
$389$	6.66661	+	3.84897i	0.338011	+	0.195151i	−0.321381	+	0.946950i	$0.604147\pi$
$390$		0			0
$391$	16.6939	+	9.63825i	0.844249	+	0.487427i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.44444	−	12.8942i	−0.374571	−	0.648775i
$396$		0			0
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	0.498925	−	0.866645i	$-0.333728\pi$
$397$	−0.0428112	−	0.0247170i	−0.00214863	−	0.00124051i	−0.501074	+	0.865404i	$0.667062\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.6039	+	10.1636i	−0.879096	+	0.507546i	−0.870360	−	0.492416i	$-0.836114\pi$
$401$	−17.6039	+	10.1636i	−0.879096	+	0.507546i	−0.00873572	+	0.999962i	$0.502781\pi$
$402$		0			0
$403$	−17.5813	+	30.4517i	−0.875786	+	1.51691i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−8.01803	+	4.62921i	−0.397439	+	0.229461i
$408$		0			0
$409$		−	13.9886i		−	0.691689i	−0.938292	−	0.345845i	$-0.887592\pi$
$409$		−	13.9886i		−	0.691689i	0.938292	−	0.345845i	$-0.112408\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	22.2824	−	5.48752i	1.09645	−	0.270023i
$414$		0			0
$415$	22.7420	−	39.3903i	1.11636	−	1.93360i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6718	+	18.4842i	−0.521353	+	0.903010i	0.478339	+	0.878176i	$0.341239\pi$
$419$	−10.6718	+	18.4842i	−0.521353	+	0.903010i	−0.999692	+	0.0248344i	$0.992094\pi$
$420$		0			0
$421$	3.97287	+	6.88121i	0.193626	+	0.335370i	0.946449	−	0.322853i	$-0.104642\pi$
$421$	3.97287	+	6.88121i	0.193626	+	0.335370i	−0.752823	+	0.658223i	$0.771309\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	20.7854			1.00824
$426$		0			0
$427$	−0.414155	−	1.68171i	−0.0200424	−	0.0813835i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	27.6515	−	15.9646i	1.33193	−	0.768989i	0.346333	−	0.938112i	$-0.387427\pi$
$431$	27.6515	−	15.9646i	1.33193	−	0.768989i	0.985595	+	0.169123i	$0.0540934\pi$
$432$		0			0
$433$			18.5300i			0.890493i	0.895408	+	0.445247i	$0.146884\pi$
$433$			18.5300i			0.890493i	−0.895408	+	0.445247i	$0.853116\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.46004			−0.452535
$438$		0			0
$439$			2.08211i			0.0993739i	0.998765	+	0.0496869i	$0.0158224\pi$
$439$			2.08211i			0.0993739i	−0.998765	+	0.0496869i	$0.984178\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			2.46985i			0.117346i	0.998277	+	0.0586731i	$0.0186870\pi$
$443$			2.46985i			0.117346i	−0.998277	+	0.0586731i	$0.981313\pi$
$444$		0			0
$445$	18.0587			0.856063
$446$		0			0
$447$		0			0
$448$		0			0
$449$			37.5094i			1.77018i	0.465424	+	0.885088i	$0.345902\pi$
$449$			37.5094i			1.77018i	−0.465424	+	0.885088i	$0.654098\pi$
$450$		0			0
$451$	3.73338	−	2.15547i	0.175798	−	0.101497i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.68349	+	27.1388i	0.313327	+	1.27229i
$456$		0			0
$457$	5.84690			0.273506			0.136753	−	0.990605i	$-0.456333\pi$
$457$	5.84690			0.273506			0.136753	+	0.990605i	$0.456333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.82830	−	6.63081i	−0.178302	−	0.308827i	0.762997	−	0.646402i	$-0.223727\pi$
$461$	−3.82830	−	6.63081i	−0.178302	−	0.308827i	−0.941299	+	0.337574i	$0.890394\pi$
$462$		0			0
$463$	4.89449	−	8.47751i	0.227466	−	0.393983i	−0.729590	−	0.683885i	$-0.760289\pi$
$463$	4.89449	−	8.47751i	0.227466	−	0.393983i	0.957057	+	0.289901i	$0.0936225\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.0806	+	24.3883i	−0.651572	+	1.12856i	0.331169	+	0.943571i	$0.392557\pi$
$467$	−14.0806	+	24.3883i	−0.651572	+	1.12856i	−0.982741	+	0.184985i	$0.940776\pi$
$468$		0			0
$469$	19.8401	−	4.88605i	0.916132	−	0.225617i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	25.3830i		−	1.16711i
$474$		0			0
$475$	−8.83394	+	5.10028i	−0.405329	+	0.234017i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	−0.299567	−	0.954075i	$-0.596842\pi$
$479$	14.8053	−	25.6435i	0.676470	−	1.17168i	0.976037	−	0.217605i	$-0.0698245\pi$
$480$		0			0
$481$	10.8864	−	6.28525i	0.496376	−	0.286583i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	37.8767	+	21.8681i	1.71989	+	0.992980i
$486$		0			0
$487$	−14.6701	−	25.4094i	−0.664767	−	1.15141i	−0.979348	−	0.202180i	$-0.935198\pi$
$487$	−14.6701	−	25.4094i	−0.664767	−	1.15141i	0.314582	−	0.949230i	$-0.398136\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.63745	+	4.98683i	0.389803	+	0.225053i	0.682075	−	0.731283i	$-0.261078\pi$
$491$	8.63745	+	4.98683i	0.389803	+	0.225053i	−0.292272	+	0.956335i	$0.594411\pi$
$492$		0			0
$493$	−16.0021	−	9.23883i	−0.720699	−	0.416096i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.97645	−	20.2072i	−0.223224	−	0.906419i
$498$		0			0
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	0.997583	−	0.0694898i	$-0.0221371\pi$
$499$	9.79784	+	16.9704i	0.438611	+	0.759697i	−0.558971	+	0.829187i	$0.688804\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−21.2907			−0.949304			−0.474652	−	0.880174i	$-0.657426\pi$
$503$	−21.2907			−0.949304			−0.474652	+	0.880174i	$0.657426\pi$
$504$		0			0
$505$	−10.0066			−0.445289
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.702378	−	0.711804i	$-0.747878\pi$
$509$	−21.8307	−	37.8119i	−0.967630	−	1.67598i	−0.265252	−	0.964179i	$-0.585455\pi$
$510$		0			0
$511$	24.4105	−	23.4374i	1.07986	−	1.03681i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.29324	+	4.78810i	0.365444	+	0.210989i
$516$		0			0
$517$	−26.5658	−	15.3378i	−1.16836	−	0.674554i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.60043	−	4.50408i	−0.113927	−	0.197327i	0.803423	−	0.595408i	$-0.203010\pi$
$521$	−2.60043	−	4.50408i	−0.113927	−	0.197327i	−0.917350	+	0.398081i	$0.869676\pi$
$522$		0			0
$523$	−34.7043	−	20.0365i	−1.51751	−	0.876137i	−0.999788	−	0.0205902i	$-0.993445\pi$
$523$	−34.7043	−	20.0365i	−1.51751	−	0.876137i	−0.517726	−	0.855547i	$-0.673221\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−53.2737	+	30.7576i	−2.32064	+	1.33982i
$528$		0			0
$529$	−7.02557	+	12.1686i	−0.305460	+	0.529072i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.06895	+	2.92656i	−0.219561	+	0.126763i
$534$		0			0
$535$		−	10.2920i		−	0.444964i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	18.9743	+	0.772057i	0.817282	+	0.0332549i
$540$		0			0
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	−0.940911	−	0.338653i	$-0.890029\pi$
$541$	−4.12096	+	7.13771i	−0.177174	+	0.306874i	0.763738	+	0.645527i	$0.223362\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	19.7801	−	34.2601i	0.847285	−	1.46754i
$546$		0			0
$547$	−2.53756	−	4.39518i	−0.108498	−	0.187925i	0.806664	−	0.591011i	$-0.201271\pi$
$547$	−2.53756	−	4.39518i	−0.108498	−	0.187925i	−0.915162	+	0.403086i	$0.867938\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.06800			0.386310
$552$		0			0
$553$	13.3365	−	3.28438i	0.567124	−	0.139666i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−37.6102	+	21.7142i	−1.59359	+	0.920062i	−0.600910	+	0.799316i	$0.705195\pi$
$557$	−37.6102	+	21.7142i	−1.59359	+	0.920062i	−0.992684	+	0.120745i	$0.961472\pi$
$558$		0			0
$559$			34.4635i			1.45765i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.98237			0.420707			0.210353	−	0.977625i	$-0.432539\pi$
$563$	9.98237			0.420707			0.210353	+	0.977625i	$0.432539\pi$
$564$		0			0
$565$		−	17.5060i		−	0.736483i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	16.2348i		−	0.680598i	−0.940317	−	0.340299i	$-0.889472\pi$
$569$		−	16.2348i		−	0.680598i	0.940317	−	0.340299i	$-0.110528\pi$
$570$		0			0
$571$	−12.6206			−0.528154			−0.264077	−	0.964502i	$-0.585067\pi$
$571$	−12.6206			−0.528154			−0.264077	+	0.964502i	$0.585067\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	9.64936i		−	0.402406i
$576$		0			0
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	−0.584480	−	0.811408i	$-0.698702\pi$
$577$	−4.18012	+	2.41339i	−0.174020	+	0.100471i	0.410460	+	0.911879i	$0.365368\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	29.0600	+	30.2665i	1.20561	+	1.25567i
$582$		0			0
$583$	−6.77942			−0.280775
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.26032	−	9.11114i	−0.217117	−	0.376057i	0.736809	−	0.676101i	$-0.236332\pi$
$587$	−5.26032	−	9.11114i	−0.217117	−	0.376057i	−0.953925	+	0.300044i	$0.902999\pi$
$588$		0			0
$589$	15.0944	−	26.1443i	0.621955	−	1.07726i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.7342	+	25.5205i	−0.605063	+	1.04800i	0.386979	+	0.922089i	$0.373519\pi$
$593$	−14.7342	+	25.5205i	−0.605063	+	1.04800i	−0.992042	+	0.125911i	$0.959815\pi$
$594$		0			0
$595$	−13.6130	+	46.9633i	−0.558080	+	1.92531i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			8.21752i			0.335759i	0.985808	+	0.167879i	$0.0536919\pi$
$599$			8.21752i			0.335759i	−0.985808	+	0.167879i	$0.946308\pi$
$600$		0			0
$601$	32.7131	−	18.8869i	1.33439	−	0.770413i	0.348425	−	0.937337i	$-0.386717\pi$
$601$	32.7131	−	18.8869i	1.33439	−	0.770413i	0.985970	+	0.166924i	$0.0533833\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.22038	+	9.04197i	−0.212239	+	0.367608i
$606$		0			0
$607$	−30.8497	+	17.8111i	−1.25215	+	0.722929i	−0.971536	−	0.236892i	$-0.923871\pi$
$607$	−30.8497	+	17.8111i	−1.25215	+	0.722929i	−0.280613	+	0.959821i	$0.590538\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	36.0693	+	20.8246i	1.45921	+	0.842474i
$612$		0			0
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	0.999816	−	0.0191767i	$-0.00610451\pi$
$613$	11.9660	+	20.7256i	0.483301	+	0.837101i	−0.516516	+	0.856278i	$0.672771\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.98622	+	1.14675i	0.0799623	+	0.0461663i	0.539448	−	0.842019i	$-0.318633\pi$
$617$	1.98622	+	1.14675i	0.0799623	+	0.0461663i	−0.459486	+	0.888185i	$0.651966\pi$
$618$		0			0
$619$	−9.10806	−	5.25854i	−0.366084	−	0.211359i	0.305662	−	0.952140i	$-0.401122\pi$
$619$	−9.10806	−	5.25854i	−0.366084	−	0.211359i	−0.671746	+	0.740781i	$0.734455\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−4.63796	+	16.0004i	−0.185816	+	0.641043i
$624$		0			0
$625$	15.3617	+	26.6073i	0.614469	+	1.06429i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.9914			0.876856
$630$		0			0
$631$	−2.02836			−0.0807477			−0.0403739	−	0.999185i	$-0.512855\pi$
$631$	−2.02836			−0.0807477			−0.0403739	+	0.999185i	$0.512855\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	19.1899	+	33.2380i	0.761530	+	1.31901i
$636$		0			0
$637$	−25.7621	−	1.04825i	−1.02073	−	0.0415332i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.7778	−	6.22257i	−0.425698	−	0.245777i	0.271814	−	0.962350i	$-0.412376\pi$
$641$	−10.7778	−	6.22257i	−0.425698	−	0.245777i	−0.697512	+	0.716573i	$0.745710\pi$
$642$		0			0
$643$	−12.3358	−	7.12209i	−0.486477	−	0.280868i	0.236635	−	0.971599i	$-0.423956\pi$
$643$	−12.3358	−	7.12209i	−0.486477	−	0.280868i	−0.723112	+	0.690731i	$0.757289\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	0.993804	−	0.111143i	$-0.0354512\pi$
$647$	10.1910	+	17.6513i	0.400649	+	0.693945i	−0.593155	+	0.805088i	$0.702118\pi$
$648$		0			0
$649$	20.3778	+	11.7651i	0.799899	+	0.461822i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.55335	+	4.36093i	−0.295585	+	0.170656i	−0.640458	−	0.767993i	$-0.721255\pi$
$653$	−7.55335	+	4.36093i	−0.295585	+	0.170656i	0.344873	+	0.938650i	$0.387922\pi$
$654$		0			0
$655$	1.11556	−	1.93221i	0.0435887	−	0.0754978i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	16.7524	−	9.67200i	0.652581	−	0.376768i	−0.136864	−	0.990590i	$-0.543702\pi$
$659$	16.7524	−	9.67200i	0.652581	−	0.376768i	0.789444	+	0.613822i	$0.210369\pi$
$660$		0			0
$661$			36.8289i			1.43248i	0.697854	+	0.716240i	$0.254138\pi$
$661$			36.8289i			1.43248i	−0.697854	+	0.716240i	$0.745862\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.73812	−	23.3000i	−0.222515	−	0.903537i
$666$		0			0
$667$	−4.28900	+	7.42877i	−0.166071	+	0.287643i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.887942	−	1.53796i	0.0342786	−	0.0593723i
$672$		0			0
$673$	8.79204	+	15.2283i	0.338908	+	0.587006i	0.984228	−	0.176907i	$-0.0566091\pi$
$673$	8.79204	+	15.2283i	0.338908	+	0.587006i	−0.645319	+	0.763913i	$0.723276\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−40.8291			−1.56919			−0.784595	−	0.620009i	$-0.787129\pi$
$677$	−40.8291			−1.56919			−0.784595	+	0.620009i	$0.787129\pi$
$678$		0			0
$679$	−29.1035	+	27.9433i	−1.11689	+	1.07237i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.56287	−	4.94377i	0.327649	−	0.189168i	−0.327148	−	0.944973i	$-0.606088\pi$
$683$	8.56287	−	4.94377i	0.327649	−	0.189168i	0.654797	+	0.755805i	$0.272754\pi$
$684$		0			0
$685$		−	47.3847i		−	1.81048i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.20467			0.350670
$690$		0			0
$691$			43.7882i			1.66578i	0.553436	+	0.832891i	$0.313316\pi$
$691$			43.7882i			1.66578i	−0.553436	+	0.832891i	$0.686684\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	32.8465i		−	1.24594i
$696$		0			0
$697$	−10.2397			−0.387858
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	29.6742i		−	1.12078i	−0.828229	−	0.560389i	$-0.810651\pi$
$701$		−	29.6742i		−	1.12078i	0.828229	−	0.560389i	$-0.189349\pi$
$702$		0			0
$703$	−9.34651	+	5.39621i	−0.352510	+	0.203522i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.56998	−	8.86612i	0.0966540	−	0.333445i
$708$		0			0
$709$	47.0538			1.76714			0.883572	−	0.468296i	$-0.155132\pi$
$709$	47.0538			1.76714			0.883572	+	0.468296i	$0.155132\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.2788	+	24.7316i	0.534745	+	0.926206i
$714$		0			0
$715$	−14.3293	+	24.8191i	−0.535885	+	0.928180i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.909148	+	1.57469i	−0.0339055	+	0.0587261i	−0.882480	−	0.470349i	$-0.844128\pi$
$719$	−0.909148	+	1.57469i	−0.0339055	+	0.0587261i	0.848575	+	0.529076i	$0.177461\pi$
$720$		0			0
$721$	−6.37230	+	6.11829i	−0.237317	+	0.227857i
$722$		0			0
$723$		0			0
$724$		0			0
$725$			9.24948i			0.343517i
$726$		0			0
$727$	21.7854	−	12.5778i	0.807976	−	0.466485i	−0.0382766	−	0.999267i	$-0.512187\pi$
$727$	21.7854	−	12.5778i	0.807976	−	0.466485i	0.846252	+	0.532782i	$0.178853\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−30.1460	+	52.2145i	−1.11499	+	1.93122i
$732$		0			0
$733$	−3.84543	+	2.22016i	−0.142034	+	0.0820034i	−0.569333	−	0.822107i	$-0.692799\pi$
$733$	−3.84543	+	2.22016i	−0.142034	+	0.0820034i	0.427299	+	0.904110i	$0.359465\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	18.1443	+	10.4756i	0.668353	+	0.385874i
$738$		0			0
$739$	−8.97608	−	15.5470i	−0.330191	−	0.571907i	0.652358	−	0.757911i	$-0.273780\pi$
$739$	−8.97608	−	15.5470i	−0.330191	−	0.571907i	−0.982549	+	0.186004i	$0.940446\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31.3712	+	18.1122i	1.15090	+	0.664472i	0.949106	−	0.314956i	$-0.101990\pi$
$743$	31.3712	+	18.1122i	1.15090	+	0.664472i	0.201793	+	0.979428i	$0.435323\pi$
$744$		0			0
$745$	−12.1829	−	7.03378i	−0.446345	−	0.257698i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.11899	+	2.64328i	0.333201	+	0.0965833i
$750$		0			0
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	0.735995	−	0.676986i	$-0.236714\pi$
$751$	−5.98210	−	10.3613i	−0.218290	−	0.378089i	−0.954285	+	0.298897i	$0.903381\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	28.2682			1.02878
$756$		0			0
$757$	−49.4440			−1.79707			−0.898537	−	0.438898i	$-0.855369\pi$
$757$	−49.4440			−1.79707			−0.898537	+	0.438898i	$0.855369\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	−0.999390	−	0.0349300i	$-0.988879\pi$
$761$	−14.6192	−	25.3212i	−0.529945	−	0.917892i	0.469445	−	0.882962i	$-0.344454\pi$
$762$		0			0
$763$	25.2752	+	26.3245i	0.915023	+	0.953012i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.6677	−	15.9740i	−0.999023	−	0.576786i
$768$		0			0
$769$	−4.54689	−	2.62515i	−0.163965	−	0.0946653i	0.415772	−	0.909469i	$-0.363511\pi$
$769$	−4.54689	−	2.62515i	−0.163965	−	0.0946653i	−0.579737	+	0.814804i	$0.696845\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	15.6829	+	27.1635i	0.564073	+	0.977003i	0.997135	+	0.0756393i	$0.0240997\pi$
$773$	15.6829	+	27.1635i	0.564073	+	0.977003i	−0.433062	+	0.901364i	$0.642567\pi$
$774$		0			0
$775$	26.6676	+	15.3965i	0.957927	+	0.553059i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.35195	−	2.51260i	0.155925	−	0.0900233i
$780$		0			0
$781$	10.6694	−	18.4800i	0.381782	−	0.661266i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	38.2923	−	22.1081i	1.36671	−	0.789071i
$786$		0			0
$787$			1.83971i			0.0655786i	0.999462	+	0.0327893i	$0.0104390\pi$
$787$			1.83971i			0.0655786i	−0.999462	+	0.0327893i	$0.989561\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.5107	+	4.49602i	0.551498	+	0.159860i
$792$		0			0
$793$	−1.20559	+	2.08814i	−0.0428118	+	0.0741522i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.39659	−	11.0792i	0.226579	−	0.392446i	−0.730213	−	0.683219i	$-0.760579\pi$
$797$	6.39659	−	11.0792i	0.226579	−	0.392446i	0.956792	+	0.290773i	$0.0939126\pi$
$798$		0			0
$799$	36.4316	+	63.1015i	1.28886	+	2.23237i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	34.6990			1.22450
$804$		0			0
$805$	21.8021	+	6.31967i	0.768423	+	0.222739i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.9217	+	7.46032i	−0.454301	+	0.262291i	−0.709645	−	0.704559i	$-0.751145\pi$
$809$	−12.9217	+	7.46032i	−0.454301	+	0.262291i	0.255344	+	0.966850i	$0.417811\pi$
$810$		0			0
$811$			37.5478i			1.31848i	0.751933	+	0.659240i	$0.229122\pi$
$811$			37.5478i			1.31848i	−0.751933	+	0.659240i	$0.770878\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	32.8134			1.14940
$816$		0			0
$817$		−	29.5887i		−	1.03518i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	3.32743i		−	0.116128i	−0.998313	−	0.0580640i	$-0.981507\pi$
$821$		−	3.32743i		−	0.116128i	0.998313	−	0.0580640i	$-0.0184927\pi$
$822$		0			0
$823$	50.9307			1.77533			0.887667	−	0.460486i	$-0.152325\pi$
$823$	50.9307			1.77533			0.887667	+	0.460486i	$0.152325\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			16.9198i			0.588360i	0.955750	+	0.294180i	$0.0950465\pi$
$827$			16.9198i			0.588360i	−0.955750	+	0.294180i	$0.904954\pi$
$828$		0			0
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	−0.578649	−	0.815577i	$-0.696420\pi$
$829$	−4.65467	+	2.68737i	−0.161663	+	0.0933364i	0.416986	+	0.908913i	$0.363087\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−38.1144	−	24.1229i	−1.32059	−	0.835810i
$834$		0			0
$835$	−37.2330			−1.28850
$836$		0			0
$837$		0			0
$838$		0			0
$839$	11.8714	+	20.5618i	0.409846	+	0.709874i	0.994872	−	0.101140i	$-0.0322492\pi$
$839$	11.8714	+	20.5618i	0.409846	+	0.709874i	−0.585026	+	0.811014i	$0.698916\pi$
$840$		0			0
$841$	−10.3887	+	17.9938i	−0.358232	+	0.620477i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.813168	−	1.40845i	0.0279738	−	0.0484521i
$846$		0			0
$847$	−6.67066	−	6.94761i	−0.229207	−	0.238723i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	10.2092i		−	0.349968i
$852$		0			0
$853$	−10.3810	+	5.99345i	−0.355437	+	0.205212i	−0.667077	−	0.744988i	$-0.732455\pi$
$853$	−10.3810	+	5.99345i	−0.355437	+	0.205212i	0.311640	+	0.950200i	$0.399122\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.175884	+	0.984411i	$0.556278\pi$
$857$	−27.5318	+	47.6864i	−0.940467	+	1.62894i	−0.764583	+	0.644526i	$0.777055\pi$
$858$		0			0
$859$	33.8798	−	19.5605i	1.15596	−	0.667395i	0.205630	−	0.978630i	$-0.434076\pi$
$859$	33.8798	−	19.5605i	1.15596	−	0.667395i	0.950333	+	0.311235i	$0.100742\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.349338	−	0.936997i	$-0.613593\pi$
$863$	−39.2319	−	22.6506i	−1.33547	−	0.771034i	−0.986132	+	0.165963i	$0.946927\pi$
$864$		0			0
$865$	−28.1063	−	48.6815i	−0.955643	−	1.65522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.1965	+	7.04166i	0.413738	+	0.238872i
$870$		0			0
$871$	−24.6351	−	14.2231i	−0.834730	−	0.481931i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−13.0735	+	3.21962i	−0.441965	+	0.108843i
$876$		0			0
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	0.898236	−	0.439512i	$-0.144849\pi$
$877$	2.02825	+	3.51304i	0.0684893	+	0.118627i	−0.829747	+	0.558139i	$0.811515\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−54.3727			−1.83186			−0.915931	−	0.401336i	$-0.868546\pi$
$881$	−54.3727			−1.83186			−0.915931	+	0.401336i	$0.868546\pi$
$882$		0			0
$883$	23.1175			0.777965			0.388982	−	0.921245i	$-0.372827\pi$
$883$	23.1175			0.777965			0.388982	+	0.921245i	$0.372827\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	0.567629	−	0.823285i	$-0.307861\pi$
$887$	−12.7818	−	22.1387i	−0.429171	−	0.743346i	−0.996800	+	0.0799384i	$0.974528\pi$
$888$		0			0
$889$	−34.3781	+	8.46633i	−1.15301	+	0.283952i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−30.9674	−	17.8790i	−1.03628	−	0.598298i
$894$		0			0
$895$	−46.6428	−	26.9292i	−1.55910	−	0.900144i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−13.6871	−	23.7067i	−0.456489	−	0.790663i
$900$		0			0
$901$	13.9457	+	8.05155i	0.464598	+	0.268236i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	11.1218	−	6.42118i	0.369702	−	0.213447i
$906$		0			0
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	−0.375974	−	0.926630i	$-0.622692\pi$
$907$	18.5065	−	32.0542i	0.614498	−	1.06434i	0.990472	−	0.137712i	$-0.0439748\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−3.16266	+	1.82596i	−0.104784	+	0.0604969i	−0.551476	−	0.834191i	$-0.685935\pi$
$911$	−3.16266	+	1.82596i	−0.104784	+	0.0604969i	0.446692	+	0.894688i	$0.352602\pi$
$912$		0			0
$913$			43.0231i			1.42386i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.42548	+	1.48466i	0.0470734	+	0.0490278i
$918$		0			0
$919$	17.3994	−	30.1367i	0.573954	−	0.994117i	−0.422201	−	0.906502i	$-0.638742\pi$
$919$	17.3994	−	30.1367i	0.573954	−	0.994117i	0.996154	−	0.0876145i	$-0.0279244\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.4863	+	25.0910i	−0.476822	+	0.825879i
$924$		0			0
$925$	−5.50420	−	9.53356i	−0.180977	−	0.313461i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	50.3471			1.65183			0.825917	−	0.563791i	$-0.190658\pi$
$929$	50.3471			1.65183			0.825917	+	0.563791i	$0.190658\pi$
$930$		0			0
$931$	22.1181	+	0.899977i	0.724891	+	0.0294955i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−43.4197	+	25.0684i	−1.41998	+	0.819824i
$936$		0			0
$937$			6.48087i			0.211721i	0.994381	+	0.105860i	$0.0337596\pi$
$937$			6.48087i			0.211721i	−0.994381	+	0.105860i	$0.966240\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.668048			−0.0217777			−0.0108889	−	0.999941i	$-0.503466\pi$
$941$	−0.668048			−0.0217777			−0.0108889	+	0.999941i	$0.503466\pi$
$942$		0			0
$943$			4.75366i			0.154801i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	58.5966i		−	1.90413i	−0.305890	−	0.952067i	$-0.598954\pi$
$947$		−	58.5966i		−	1.90413i	0.305890	−	0.952067i	$-0.401046\pi$
$948$		0			0
$949$	−47.1120			−1.52932
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	48.3707i		−	1.56688i	−0.621467	−	0.783441i	$-0.713463\pi$
$953$		−	48.3707i		−	1.56688i	0.621467	−	0.783441i	$-0.286537\pi$
$954$		0			0
$955$	−16.9228	+	9.77041i	−0.547610	+	0.316163i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	41.9840	+	12.1697i	1.35573	+	0.392980i
$960$		0			0
$961$	−60.1330			−1.93977
$962$		0			0
$963$		0			0
$964$		0			0
$965$	22.8781	+	39.6261i	0.736474	+	1.27561i
$966$		0			0
$967$	8.51390	−	14.7465i	0.273788	−	0.474216i	−0.696040	−	0.718003i	$-0.745057\pi$
$967$	8.51390	−	14.7465i	0.273788	−	0.474216i	0.969829	+	0.243787i	$0.0783898\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	−0.997322	−	0.0731339i	$-0.976700\pi$
$971$	−13.5651	+	23.4955i	−0.435325	+	0.754006i	0.561997	+	0.827139i	$0.310033\pi$
$972$		0			0
$973$	29.1028	+	8.43589i	0.932994	+	0.270442i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	6.34898i		−	0.203122i	−0.994829	−	0.101561i	$-0.967616\pi$
$977$		−	6.34898i		−	0.203122i	0.994829	−	0.101561i	$-0.0323837\pi$
$978$		0			0
$979$	−14.7931	+	8.54080i	−0.472789	+	0.272965i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	−0.980156	−	0.198227i	$-0.936482\pi$
$983$	−9.98300	+	17.2911i	−0.318408	+	0.551499i	0.661748	+	0.749727i	$0.269815\pi$
$984$		0			0
$985$	64.4572	−	37.2144i	2.05378	−	1.18575i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.2399	+	13.9949i	0.770784	+	0.445012i
$990$		0			0
$991$	6.38803	+	11.0644i	0.202922	+	0.351472i	0.949469	−	0.313861i	$-0.101623\pi$
$991$	6.38803	+	11.0644i	0.202922	+	0.351472i	−0.746546	+	0.665333i	$0.768289\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.90734	−	4.56530i	−0.250679	−	0.144730i
$996$		0			0
$997$	−17.9846	−	10.3834i	−0.569579	−	0.328847i	0.187402	−	0.982283i	$-0.439993\pi$
$997$	−17.9846	−	10.3834i	−0.569579	−	0.328847i	−0.756981	+	0.653436i	$0.773327\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.w.a.341.1		16
3.2	odd	2		252.2.w.a.5.5	✓	16
4.3	odd	2		3024.2.ca.d.2609.1		16
7.2	even	3		5292.2.x.a.881.1		16
7.3	odd	6		756.2.bm.a.17.1		16
7.4	even	3		5292.2.bm.a.2285.8		16
7.5	odd	6		5292.2.x.b.881.8		16
7.6	odd	2		5292.2.w.b.1097.8		16
9.2	odd	6		756.2.bm.a.89.1		16
9.4	even	3		2268.2.t.a.2105.1		16
9.5	odd	6		2268.2.t.b.2105.8		16
9.7	even	3		252.2.bm.a.173.2	yes	16
12.11	even	2		1008.2.ca.d.257.4		16
21.2	odd	6		1764.2.x.a.293.1		16
21.5	even	6		1764.2.x.b.293.8		16
21.11	odd	6		1764.2.bm.a.1697.7		16
21.17	even	6		252.2.bm.a.185.2	yes	16
21.20	even	2		1764.2.w.b.509.4		16
28.3	even	6		3024.2.df.d.17.1		16
36.7	odd	6		1008.2.df.d.929.7		16
36.11	even	6		3024.2.df.d.1601.1		16
63.2	odd	6		5292.2.x.b.4409.8		16
63.11	odd	6		5292.2.w.b.521.8		16
63.16	even	3		1764.2.x.b.1469.8		16
63.20	even	6		5292.2.bm.a.4625.8		16
63.25	even	3		1764.2.w.b.1109.4		16
63.31	odd	6		2268.2.t.b.1781.8		16
63.34	odd	6		1764.2.bm.a.1685.7		16
63.38	even	6	inner	756.2.w.a.521.1		16
63.47	even	6		5292.2.x.a.4409.1		16
63.52	odd	6		252.2.w.a.101.5	yes	16
63.59	even	6		2268.2.t.a.1781.1		16
63.61	odd	6		1764.2.x.a.1469.1		16
84.59	odd	6		1008.2.df.d.689.7		16
252.115	even	6		1008.2.ca.d.353.4		16
252.227	odd	6		3024.2.ca.d.2033.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	3.2	odd	2
252.2.w.a.101.5	yes	16	63.52	odd	6
252.2.bm.a.173.2	yes	16	9.7	even	3
252.2.bm.a.185.2	yes	16	21.17	even	6
756.2.w.a.341.1		16	1.1	even	1	trivial
756.2.w.a.521.1		16	63.38	even	6	inner
756.2.bm.a.17.1		16	7.3	odd	6
756.2.bm.a.89.1		16	9.2	odd	6
1008.2.ca.d.257.4		16	12.11	even	2
1008.2.ca.d.353.4		16	252.115	even	6
1008.2.df.d.689.7		16	84.59	odd	6
1008.2.df.d.929.7		16	36.7	odd	6
1764.2.w.b.509.4		16	21.20	even	2
1764.2.w.b.1109.4		16	63.25	even	3
1764.2.x.a.293.1		16	21.2	odd	6
1764.2.x.a.1469.1		16	63.61	odd	6
1764.2.x.b.293.8		16	21.5	even	6
1764.2.x.b.1469.8		16	63.16	even	3
1764.2.bm.a.1685.7		16	63.34	odd	6
1764.2.bm.a.1697.7		16	21.11	odd	6
2268.2.t.a.1781.1		16	63.59	even	6
2268.2.t.a.2105.1		16	9.4	even	3
2268.2.t.b.1781.8		16	63.31	odd	6
2268.2.t.b.2105.8		16	9.5	odd	6
3024.2.ca.d.2033.1		16	252.227	odd	6
3024.2.ca.d.2609.1		16	4.3	odd	2
3024.2.df.d.17.1		16	28.3	even	6
3024.2.df.d.1601.1		16	36.11	even	6
5292.2.w.b.521.8		16	63.11	odd	6
5292.2.w.b.1097.8		16	7.6	odd	2
5292.2.x.a.881.1		16	7.2	even	3
5292.2.x.a.4409.1		16	63.47	even	6
5292.2.x.b.881.8		16	7.5	odd	6
5292.2.x.b.4409.8		16	63.2	odd	6
5292.2.bm.a.2285.8		16	7.4	even	3
5292.2.bm.a.4625.8		16	63.20	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.43402 - 2.48379i) q^{5} +(2.56899 - 0.632668i) q^{7} +(2.34941 + 1.35643i) q^{11} +(-3.18987 - 1.84167i) q^{13} +(-3.22192 - 5.58052i) q^{17} +(2.73867 + 1.58117i) q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +(2.48332 - 1.43375i) q^{29} -9.54636i q^{31} +(-5.25540 - 5.47359i) q^{35} +(-1.70640 + 2.95556i) q^{37} +(0.794538 - 1.37618i) q^{41} +(-4.67828 - 8.10302i) q^{43} -11.3074 q^{47} +(6.19946 - 3.25064i) q^{49} +(-2.16419 + 1.24950i) q^{53} -7.78058i q^{55} +8.67361 q^{59} -0.654617i q^{61} +10.5640i q^{65} +7.72292 q^{67} -7.86582i q^{71} +(11.0769 - 6.39527i) q^{73} +(6.89378 + 1.99827i) q^{77} +5.19132 q^{79} +(7.92948 + 13.7343i) q^{83} +(-9.24057 + 16.0051i) q^{85} +(-3.14826 + 5.45295i) q^{89} +(-9.35993 - 2.71312i) q^{91} -9.06971i q^{95} +(-13.2065 + 7.62477i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{7} + 6 q^{11} - 3 q^{13} - 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{29} + 15 q^{35} + q^{37} + 6 q^{41} - 2 q^{43} + 36 q^{47} - 5 q^{49} + 30 q^{59} + 14 q^{67} - 3 q^{77} + 2 q^{79} + 6 q^{85}+ \cdots - 3 q^{97}+O(q^{100}) \) 16 * q - q^7 + 6 * q^11 - 3 * q^13 - 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^29 + 15 * q^35 + q^37 + 6 * q^41 - 2 * q^43 + 36 * q^47 - 5 * q^49 + 30 * q^59 + 14 * q^67 - 3 * q^77 + 2 * q^79 + 6 * q^85 - 21 * q^89 + 9 * q^91 - 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more