LMFDB - Embedded newform 2268.2.t.b.1781.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, degree $2$, 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:	$18.1100711784$
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			1781.8
Root			$-0.213160 + 1.71888i$ of defining polynomial
Character	$\chi$	$=$	2268.1781
Dual form			2268.2.t.b.2105.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43402 + 2.48379i) q^{5} +(-0.736590 - 2.54115i) q^{7} +O(q^{10})$	$q+(1.43402 + 2.48379i) q^{5} +(-0.736590 - 2.54115i) q^{7} +(2.34941 + 1.35643i) q^{11} -3.68335i q^{13} +(3.22192 - 5.58052i) q^{17} +(2.73867 - 1.58117i) q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +2.86749i q^{29} +(-8.26739 - 4.77318i) q^{31} +(5.25540 - 5.47359i) q^{35} +(-1.70640 - 2.95556i) q^{37} +1.58908 q^{41} +9.35656 q^{43} +(-5.65372 - 9.79254i) q^{47} +(-5.91487 + 3.74357i) q^{49} +(2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(4.33680 - 7.51156i) q^{59} +(0.566915 - 0.327308i) q^{61} +(9.14867 - 5.28199i) q^{65} +(-3.86146 + 6.68825i) q^{67} -7.86582i q^{71} +(11.0769 + 6.39527i) q^{73} +(1.71634 - 6.96932i) q^{77} +(-2.59566 - 4.49581i) q^{79} +15.8590 q^{83} +18.4811 q^{85} +(3.14826 + 5.45295i) q^{89} +(-9.35993 + 2.71312i) q^{91} +(7.85460 + 4.53486i) q^{95} +15.2495i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^7	$ 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) $ 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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	$0.0549431\pi$
$5$	1.43402	+	2.48379i	0.641312	+	1.11079i	−0.343828	+	0.939033i	$0.611724\pi$
$6$		0			0
$7$	−0.736590	−	2.54115i	−0.278405	−	0.960464i
$7$	−0.736590	−	2.54115i	−0.278405	−	0.960464i
$8$		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
$13$		−	3.68335i		−	1.02158i	−0.859706	−	0.510789i	$-0.829354\pi$
$13$		−	3.68335i		−	1.02158i	0.859706	−	0.510789i	$-0.170646\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.22192	−	5.58052i	0.781429	−	1.35348i	−0.149680	−	0.988735i	$-0.547824\pi$
$17$	3.22192	−	5.58052i	0.781429	−	1.35348i	0.931109	−	0.364741i	$-0.118842\pi$
$18$		0			0
$19$	2.73867	−	1.58117i	0.628294	−	0.362746i	−0.151797	−	0.988412i	$-0.548506\pi$
$19$	2.73867	−	1.58117i	0.628294	−	0.362746i	0.780091	+	0.625666i	$0.215173\pi$
$20$		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
$29$			2.86749i			0.532480i	0.963907	+	0.266240i	$0.0857814\pi$
$29$			2.86749i			0.532480i	−0.963907	+	0.266240i	$0.914219\pi$
$30$		0			0
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.485016	−	0.874506i	$-0.661186\pi$
$31$	−8.26739	−	4.77318i	−1.48487	−	0.857289i	−0.999852	+	0.0172169i	$0.994519\pi$
$32$		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	0.690986	−	0.722868i	$-0.257177\pi$
$37$	−1.70640	−	2.95556i	−0.280530	−	0.485892i	−0.971515	+	0.236977i	$0.923843\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.58908			0.248172			0.124086	−	0.992271i	$-0.460400\pi$
$41$	1.58908			0.248172			0.124086	+	0.992271i	$0.460400\pi$
$42$		0			0
$43$	9.35656			1.42686			0.713431	−	0.700726i	$-0.247140\pi$
$43$	9.35656			1.42686			0.713431	+	0.700726i	$0.247140\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.65372	−	9.79254i	−0.824680	−	1.42839i	−0.902163	−	0.431394i	$-0.858022\pi$
$47$	−5.65372	−	9.79254i	−0.824680	−	1.42839i	0.0774831	−	0.996994i	$-0.475312\pi$
$48$		0			0
$49$	−5.91487	+	3.74357i	−0.844981	+	0.534796i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	0.641218	−	0.767359i	$-0.278429\pi$
$53$	2.16419	+	1.24950i	0.297275	+	0.171632i	−0.343943	+	0.938990i	$0.611763\pi$
$54$		0			0
$55$			7.78058i			1.04913i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.33680	−	7.51156i	0.564604	−	0.977922i	−0.432483	−	0.901642i	$-0.642362\pi$
$59$	4.33680	−	7.51156i	0.564604	−	0.977922i	0.997086	−	0.0762801i	$-0.0243043\pi$
$60$		0			0
$61$	0.566915	−	0.327308i	0.0725860	−	0.0419075i	−0.463268	−	0.886218i	$-0.653323\pi$
$61$	0.566915	−	0.327308i	0.0725860	−	0.0419075i	0.535854	+	0.844311i	$0.319990\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.14867	−	5.28199i	1.13475	−	0.655150i
$66$		0			0
$67$	−3.86146	+	6.68825i	−0.471752	+	0.817099i	−0.999478	−	0.0323159i	$-0.989712\pi$
$67$	−3.86146	+	6.68825i	−0.471752	+	0.817099i	0.527725	+	0.849415i	$0.323045\pi$
$68$		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	0.979790	−	0.200027i	$-0.0641028\pi$
$73$	11.0769	+	6.39527i	1.29646	+	0.748510i	0.316667	+	0.948537i	$0.397436\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.71634	−	6.96932i	0.195595	−	0.794228i
$78$		0			0
$79$	−2.59566	−	4.49581i	−0.292034	−	0.505819i	0.682256	−	0.731113i	$-0.260999\pi$
$79$	−2.59566	−	4.49581i	−0.292034	−	0.505819i	−0.974291	+	0.225295i	$0.927666\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	15.8590			1.74075			0.870373	−	0.492393i	$-0.163878\pi$
$83$	15.8590			1.74075			0.870373	+	0.492393i	$0.163878\pi$
$84$		0			0
$85$	18.4811			2.00456
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.14826	+	5.45295i	0.333715	+	0.578012i	0.983237	−	0.182331i	$-0.0583643\pi$
$89$	3.14826	+	5.45295i	0.333715	+	0.578012i	−0.649522	+	0.760343i	$0.725031\pi$
$90$		0			0
$91$	−9.35993	+	2.71312i	−0.981188	+	0.284412i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.85460	+	4.53486i	0.805865	+	0.465267i
$96$		0			0
$97$			15.2495i			1.54836i	0.632968	+	0.774178i	$0.281837\pi$
$97$			15.2495i			1.54836i	−0.632968	+	0.774178i	$0.718163\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.74451	+	3.02158i	−0.173585	+	0.300658i	−0.939671	−	0.342080i	$-0.888869\pi$
$101$	−1.74451	+	3.02158i	−0.173585	+	0.300658i	0.766086	+	0.642739i	$0.222202\pi$
$102$		0			0
$103$	2.89161	−	1.66947i	0.284919	−	0.164498i	−0.350729	−	0.936477i	$-0.614066\pi$
$103$	2.89161	−	1.66947i	0.284919	−	0.164498i	0.635648	+	0.771979i	$0.280733\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	−0.642640	−	0.766168i	$-0.722161\pi$
$107$	−3.10776	+	1.79427i	−0.300439	+	0.173458i	0.342201	+	0.939627i	$0.388828\pi$
$108$		0			0
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	−0.319875	−	0.947460i	$-0.603641\pi$
$109$	6.89673	−	11.9455i	0.660587	−	1.14417i	0.980462	−	0.196710i	$-0.0630258\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	6.10383i		−	0.574200i	−0.957901	−	0.287100i	$-0.907309\pi$
$113$		−	6.10383i		−	0.574200i	0.957901	−	0.287100i	$-0.0926911\pi$
$114$		0			0
$115$	−7.43018	−	4.28981i	−0.692867	−	0.400027i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−16.5542	−	4.07681i	−1.51752	−	0.373720i
$120$		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	0.848533	−	0.529142i	$-0.177486\pi$
$131$	−0.388964	−	0.673705i	−0.0339839	−	0.0588619i	−0.882517	+	0.470280i	$0.844153\pi$
$132$		0			0
$133$	−6.03527	−	5.79469i	−0.523324	−	0.502463i
$134$		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
$139$			11.4526i			0.971399i	0.874126	+	0.485699i	$0.161435\pi$
$139$			11.4526i			0.971399i	−0.874126	+	0.485699i	$0.838565\pi$
$140$		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
$155$		−	27.3793i		−	2.19916i
$156$		0			0
$157$	13.3514	+	7.70843i	1.06556	+	0.615200i	0.926964	−	0.375149i	$-0.122409\pi$
$157$	13.3514	+	7.70843i	1.06556	+	0.615200i	0.138593	+	0.990349i	$0.455742\pi$
$158$		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	0.550194	−	0.835037i	$-0.314554\pi$
$163$	−5.72053	−	9.90825i	−0.448066	−	0.776074i	−0.998260	+	0.0589632i	$0.981221\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.9821			1.00458			0.502291	−	0.864699i	$-0.332491\pi$
$167$	12.9821			1.00458			0.502291	+	0.864699i	$0.332491\pi$
$168$		0			0
$169$	−0.567055			−0.0436196
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.79984	+	16.9738i	0.745068	+	1.29050i	0.950163	+	0.311754i	$0.100916\pi$
$173$	9.79984	+	16.9738i	0.745068	+	1.29050i	−0.205095	+	0.978742i	$0.565750\pi$
$174$		0			0
$175$	8.28663	+	2.04075i	0.626410	+	0.154267i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.251588	−	0.967835i	$-0.580953\pi$
$179$	−16.2630	−	9.38942i	−1.21555	−	0.701799i	−0.963963	+	0.266036i	$0.914286\pi$
$180$		0			0
$181$		−	4.47775i		−	0.332829i	−0.986056	−	0.166414i	$-0.946781\pi$
$181$		−	4.47775i		−	0.332829i	0.986056	−	0.166414i	$-0.0532190\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.89400	−	8.47666i	0.359814	−	0.623217i
$186$		0			0
$187$	15.1392	−	8.74061i	1.10709	−	0.639177i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.90050	+	3.40665i	−0.426945	+	0.246497i	−0.698044	−	0.716055i	$-0.745946\pi$
$191$	−5.90050	+	3.40665i	−0.426945	+	0.246497i	0.271099	+	0.962551i	$0.412613\pi$
$192$		0			0
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	−0.421936	−	0.906626i	$-0.638649\pi$
$193$	7.97694	−	13.8165i	0.574193	−	0.994531i	0.996129	−	0.0879053i	$-0.0280173\pi$
$194$		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	0.594528	−	0.804075i	$-0.297339\pi$
$199$	2.75706	+	1.59179i	0.195443	+	0.112839i	−0.399085	+	0.916914i	$0.630672\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.28673	−	2.11217i	0.511428	−	0.148245i
$204$		0			0
$205$	2.27876	+	3.94693i	0.159156	+	0.275666i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.57900			0.593422
$210$		0			0
$211$	0.110482			0.00760591			0.00380295	−	0.999993i	$-0.498789\pi$
$211$	0.110482			0.00760591			0.00380295	+	0.999993i	$0.498789\pi$
$212$		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
$221$	−20.5550	−	11.8674i	−1.38268	−	0.798290i
$222$		0			0
$223$		−	13.0555i		−	0.874261i	−0.899398	−	0.437130i	$-0.855995\pi$
$223$		−	13.0555i		−	0.874261i	0.899398	−	0.437130i	$-0.144005\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.63392	−	8.02618i	0.307564	−	0.532716i	−0.670265	−	0.742122i	$-0.733820\pi$
$227$	4.63392	−	8.02618i	0.307564	−	0.532716i	0.977829	+	0.209406i	$0.0671529\pi$
$228$		0			0
$229$	−11.6204	+	6.70902i	−0.767895	+	0.443344i	−0.832123	−	0.554591i	$-0.812875\pi$
$229$	−11.6204	+	6.70902i	−0.767895	+	0.443344i	0.0642281	+	0.997935i	$0.479541\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.960909	−	0.276866i	$-0.910704\pi$
$233$	−18.3415	+	10.5895i	−1.20159	+	0.693738i	−0.240681	+	0.970604i	$0.577371\pi$
$234$		0			0
$235$	16.2151	−	28.0853i	1.05776	−	1.83209i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	8.92978i		−	0.577620i	−0.957386	−	0.288810i	$-0.906740\pi$
$239$		−	8.92978i		−	0.577620i	0.957386	−	0.288810i	$-0.0932595\pi$
$240$		0			0
$241$	−15.9430	−	9.20469i	−1.02698	−	0.592926i	−0.110860	−	0.993836i	$-0.535361\pi$
$241$	−15.9430	−	9.20469i	−1.02698	−	0.592926i	−0.916117	+	0.400910i	$0.868694\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−17.7803	−	9.32296i	−1.13594	−	0.595622i
$246$		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	$-0.564040\pi$
$251$	−6.33194			−0.399669			−0.199834	+	0.979830i	$0.564040\pi$
$252$		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	$0.00407829\pi$
$257$	8.19283	+	14.1904i	0.511054	+	0.885172i	−0.488863	+	0.872360i	$0.662588\pi$
$258$		0			0
$259$	−6.25361	+	6.51324i	−0.388580	+	0.404713i
$260$		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
$265$			7.16721i			0.440278i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.6652	−	21.9368i	0.772212	−	1.33751i	−0.164136	−	0.986438i	$-0.552484\pi$
$269$	12.6652	−	21.9368i	0.772212	−	1.33751i	0.936348	−	0.351072i	$-0.114183\pi$
$270$		0			0
$271$	−0.195591	+	0.112924i	−0.0118813	+	0.00685967i	−0.505929	−	0.862575i	$-0.668850\pi$
$271$	−0.195591	+	0.112924i	−0.0118813	+	0.00685967i	0.494048	+	0.869435i	$0.335517\pi$
$272$		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
$281$		−	10.3534i		−	0.617635i	−0.951121	−	0.308817i	$-0.900067\pi$
$281$		−	10.3534i		−	0.617635i	0.951121	−	0.308817i	$-0.0999332\pi$
$282$		0			0
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	0.103528	−	0.994627i	$-0.466987\pi$
$283$	−11.8781	−	6.85783i	−0.706080	−	0.407656i	−0.809608	+	0.586971i	$0.800320\pi$
$284$		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
$293$	−8.43053			−0.492517			−0.246258	−	0.969204i	$-0.579201\pi$
$293$	−8.43053			−0.492517			−0.246258	+	0.969204i	$0.579201\pi$
$294$		0			0
$295$	24.8762			1.44835
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.50930	+	9.54239i	0.318611	+	0.551851i
$300$		0			0
$301$	−6.89195	−	23.7764i	−0.397245	−	1.37045i
$302$		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	$0.0487271\pi$
$307$			5.34345i			0.304967i	−0.988306	+	0.152484i	$0.951273\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.70867	−	8.15565i	0.267004	−	0.462465i	−0.701083	−	0.713080i	$-0.747300\pi$
$311$	4.70867	−	8.15565i	0.267004	−	0.462465i	0.968087	+	0.250615i	$0.0806329\pi$
$312$		0			0
$313$	−14.3347	+	8.27614i	−0.810245	+	0.467795i	−0.847041	−	0.531528i	$-0.821618\pi$
$313$	−14.3347	+	8.27614i	−0.810245	+	0.467795i	0.0367961	+	0.999323i	$0.488285\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.9725	+	13.2632i	−1.29026	+	0.744934i	−0.978701	−	0.205291i	$-0.934186\pi$
$317$	−22.9725	+	13.2632i	−1.29026	+	0.744934i	−0.311563	+	0.950225i	$0.600853\pi$
$318$		0			0
$319$	−3.88956	+	6.73691i	−0.217773	+	0.377194i
$320$		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
$329$	−20.7198	+	21.5800i	−1.14232	+	1.18975i
$330$		0			0
$331$	8.82000	+	15.2767i	0.484791	+	0.839682i	0.999847	−	0.0174739i	$-0.00556238\pi$
$331$	8.82000	+	15.2767i	0.484791	+	0.839682i	−0.515056	+	0.857156i	$0.672229\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−22.1496			−1.21016
$336$		0			0
$337$	−14.6234			−0.796586			−0.398293	−	0.917258i	$-0.630397\pi$
$337$	−14.6234			−0.796586			−0.398293	+	0.917258i	$0.630397\pi$
$338$		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
$347$	1.05563	+	0.609467i	0.0566691	+	0.0327179i	0.528067	−	0.849203i	$-0.322917\pi$
$347$	1.05563	+	0.609467i	0.0566691	+	0.0327179i	−0.471398	+	0.881921i	$0.656250\pi$
$348$		0			0
$349$			12.3388i			0.660483i	0.943897	+	0.330241i	$0.107130\pi$
$349$			12.3388i			0.660483i	−0.943897	+	0.330241i	$0.892870\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.1484	+	19.3097i	−0.593372	+	1.02775i	0.400402	+	0.916339i	$0.368870\pi$
$353$	−11.1484	+	19.3097i	−0.593372	+	1.02775i	−0.993774	+	0.111411i	$0.964463\pi$
$354$		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	$-0.563186\pi$
$359$	10.4819	−	6.05173i	0.553214	−	0.319398i	0.750417	+	0.660965i	$0.229853\pi$
$360$		0			0
$361$	−4.49979	+	7.79387i	−0.236831	+	0.410204i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			36.6838i			1.92012i
$366$		0			0
$367$	−12.7544	−	7.36375i	−0.665774	−	0.384385i	0.128700	−	0.991684i	$-0.458920\pi$
$367$	−12.7544	−	7.36375i	−0.665774	−	0.384385i	−0.794473	+	0.607299i	$0.792253\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.58103	−	6.41990i	0.0820832	−	0.333305i
$372$		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	0.938872	−	0.344266i	$-0.111872\pi$
$383$	3.35227	+	5.80630i	0.171293	+	0.296688i	−0.767579	+	0.640954i	$0.778539\pi$
$384$		0			0
$385$	19.7716	−	5.73110i	1.00765	−	0.292084i
$386$		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
$391$			19.2765i			0.974854i
$392$		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	−0.501074	−	0.865404i	$-0.667062\pi$
$397$	−0.0428112	+	0.0247170i	−0.00214863	+	0.00124051i	0.498925	+	0.866645i	$0.333728\pi$
$398$		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
$407$		−	9.25842i		−	0.458923i
$408$		0			0
$409$	−12.1144	−	6.99428i	−0.599021	−	0.345845i	0.169636	−	0.985507i	$-0.445741\pi$
$409$	−12.1144	−	6.99428i	−0.599021	−	0.345845i	−0.768656	+	0.639662i	$0.779074\pi$
$410$		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
$419$	−21.3437			−1.04271			−0.521353	−	0.853341i	$-0.674573\pi$
$419$	−21.3437			−1.04271			−0.521353	+	0.853341i	$0.674573\pi$
$420$		0			0
$421$	−7.94574			−0.387252			−0.193626	−	0.981075i	$-0.562025\pi$
$421$	−7.94574			−0.387252			−0.193626	+	0.981075i	$0.562025\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.3927	+	18.0007i	0.504121	+	0.873163i
$426$		0			0
$427$	−1.24932	−	1.19952i	−0.0604590	−	0.0580489i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.346333	−	0.938112i	$-0.612573\pi$
$431$	−27.6515	−	15.9646i	−1.33193	−	0.768989i	−0.985595	+	0.169123i	$0.945907\pi$
$432$		0			0
$433$		−	18.5300i		−	0.890493i	−0.895408	−	0.445247i	$-0.853116\pi$
$433$		−	18.5300i		−	0.890493i	0.895408	−	0.445247i	$-0.146884\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−4.73002	+	8.19263i	−0.226267	+	0.391907i
$438$		0			0
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	−0.542413	−	0.840112i	$-0.682489\pi$
$439$	−1.80316	+	1.04106i	−0.0860603	+	0.0496869i	0.456352	+	0.889799i	$0.349156\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	−0.448326	−	0.893870i	$-0.647980\pi$
$443$	2.13895	−	1.23493i	0.101625	−	0.0586731i	0.549951	+	0.835197i	$0.314646\pi$
$444$		0			0
$445$	−9.02933	+	15.6393i	−0.428031	+	0.741372i
$446$		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
$455$	−20.1611	−	19.3575i	−0.945169	−	0.907492i
$456$		0			0
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	0.789513	−	0.613734i	$-0.210333\pi$
$457$	−2.92345	−	5.06356i	−0.136753	−	0.236864i	−0.926266	+	0.376871i	$0.877000\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.65659			−0.356603			−0.178302	−	0.983976i	$-0.557060\pi$
$461$	−7.65659			−0.356603			−0.178302	+	0.983976i	$0.557060\pi$
$462$		0			0
$463$	−9.78899			−0.454933			−0.227466	−	0.973786i	$-0.573044\pi$
$463$	−9.78899			−0.454933			−0.227466	+	0.973786i	$0.573044\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.0806	+	24.3883i	0.651572	+	1.12856i	0.982741	+	0.184985i	$0.0592235\pi$
$467$	14.0806	+	24.3883i	0.651572	+	1.12856i	−0.331169	+	0.943571i	$0.607443\pi$
$468$		0			0
$469$	19.8401	+	4.88605i	0.916132	+	0.225617i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	21.9824	+	12.6915i	1.01075	+	0.583557i
$474$		0			0
$475$			10.2006i			0.468033i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−14.8053	+	25.6435i	−0.676470	+	1.17168i	0.299567	+	0.954075i	$0.403158\pi$
$479$	−14.8053	+	25.6435i	−0.676470	+	1.17168i	−0.976037	+	0.217605i	$0.930175\pi$
$480$		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	0.314582	+	0.949230i	$0.398136\pi$
$487$	−14.6701	+	25.4094i	−0.664767	+	1.15141i	−0.979348	+	0.202180i	$0.935198\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	9.97367i		−	0.450105i	−0.974347	−	0.225053i	$-0.927745\pi$
$491$		−	9.97367i		−	0.450105i	0.974347	−	0.225053i	$-0.0722554\pi$
$492$		0			0
$493$	16.0021	+	9.23883i	0.720699	+	0.416096i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−19.9882	+	5.79388i	−0.896594	+	0.259891i
$498$		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	$-0.342574\pi$
$503$	21.2907			0.949304			0.474652	+	0.880174i	$0.342574\pi$
$504$		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	$0.252122\pi$
$509$	21.8307	+	37.8119i	0.967630	+	1.67598i	0.265252	+	0.964179i	$0.414545\pi$
$510$		0			0
$511$	8.09217	−	32.8588i	0.357977	−	1.45359i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.29324	+	4.78810i	0.365444	+	0.210989i
$516$		0			0
$517$		−	30.6755i		−	1.34911i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.60043	−	4.50408i	0.113927	−	0.197327i	−0.803423	−	0.595408i	$-0.796990\pi$
$521$	2.60043	−	4.50408i	0.113927	−	0.197327i	0.917350	+	0.398081i	$0.130324\pi$
$522$		0			0
$523$	−34.7043	+	20.0365i	−1.51751	+	0.876137i	−0.517726	+	0.855547i	$0.673221\pi$
$523$	−34.7043	+	20.0365i	−1.51751	+	0.876137i	−0.999788	+	0.0205902i	$0.993445\pi$
$524$		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
$533$		−	5.85312i		−	0.253527i
$534$		0			0
$535$	−8.91317	−	5.14602i	−0.385350	−	0.222482i
$536$		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	0.763738	−	0.645527i	$-0.223362\pi$
$541$	−4.12096	−	7.13771i	−0.177174	−	0.306874i	−0.940911	+	0.338653i	$0.890029\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	39.5601			1.69457
$546$		0			0
$547$	5.07512			0.216997			0.108498	−	0.994097i	$-0.465396\pi$
$547$	5.07512			0.216997			0.108498	+	0.994097i	$0.465396\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.53400	+	7.85312i	0.193155	+	0.334554i
$552$		0			0
$553$	−9.51259	+	9.90753i	−0.404517	+	0.421311i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.992684	+	0.120745i	$0.0385285\pi$
$557$	37.6102	+	21.7142i	1.59359	+	0.920062i	0.600910	+	0.799316i	$0.294805\pi$
$558$		0			0
$559$		−	34.4635i		−	1.45765i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.99118	−	8.64498i	0.210353	−	0.364343i	−0.741472	−	0.670984i	$-0.765872\pi$
$563$	4.99118	−	8.64498i	0.210353	−	0.364343i	0.951825	+	0.306641i	$0.0992052\pi$
$564$		0			0
$565$	15.1606	−	8.75300i	0.637813	−	0.368241i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−14.0597	+	8.11739i	−0.589415	+	0.340299i	−0.764866	−	0.644189i	$-0.777195\pi$
$569$	−14.0597	+	8.11739i	−0.589415	+	0.340299i	0.175451	+	0.984488i	$0.443862\pi$
$570$		0			0
$571$	6.31028	−	10.9297i	0.264077	−	0.457395i	−0.703244	−	0.710948i	$-0.748266\pi$
$571$	6.31028	−	10.9297i	0.264077	−	0.457395i	0.967321	+	0.253553i	$0.0815994\pi$
$572$		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	0.410460	−	0.911879i	$-0.365368\pi$
$577$	−4.18012	−	2.41339i	−0.174020	−	0.100471i	−0.584480	+	0.811408i	$0.698702\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−11.6815	−	40.2999i	−0.484632	−	1.67192i
$582$		0			0
$583$	3.38971	+	5.87115i	0.140387	+	0.243158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.5206			−0.434233			−0.217117	−	0.976146i	$-0.569665\pi$
$587$	−10.5206			−0.434233			−0.217117	+	0.976146i	$0.569665\pi$
$588$		0			0
$589$	−30.1889			−1.24391
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.7342	+	25.5205i	0.605063	+	1.04800i	0.992042	+	0.125911i	$0.0401853\pi$
$593$	14.7342	+	25.5205i	0.605063	+	1.04800i	−0.386979	+	0.922089i	$0.626481\pi$
$594$		0			0
$595$	−13.6130	−	46.9633i	−0.558080	−	1.92531i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−7.11658	−	4.10876i	−0.290776	−	0.167879i	0.347516	−	0.937674i	$-0.387025\pi$
$599$	−7.11658	−	4.10876i	−0.290776	−	0.167879i	−0.638292	+	0.769795i	$0.720359\pi$
$600$		0			0
$601$		−	37.7738i		−	1.54083i	−0.637545	−	0.770413i	$-0.720050\pi$
$601$		−	37.7738i		−	1.54083i	0.637545	−	0.770413i	$-0.279950\pi$
$602$		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	0.280613	−	0.959821i	$-0.409462\pi$
$607$	30.8497	−	17.8111i	1.25215	−	0.722929i	0.971536	+	0.236892i	$0.0761289\pi$
$608$		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	−0.516516	−	0.856278i	$-0.672771\pi$
$613$	11.9660	−	20.7256i	0.483301	−	0.837101i	0.999816	+	0.0191767i	$0.00610451\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	2.29349i		−	0.0923325i	−0.998934	−	0.0461663i	$-0.985300\pi$
$617$		−	2.29349i		−	0.0923325i	0.998934	−	0.0461663i	$-0.0147004\pi$
$618$		0			0
$619$	9.10806	+	5.25854i	0.366084	+	0.211359i	0.671746	−	0.740781i	$-0.265545\pi$
$619$	9.10806	+	5.25854i	0.366084	+	0.211359i	−0.305662	+	0.952140i	$0.598878\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	11.5378	−	12.0168i	0.462251	−	0.481443i
$624$		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
$637$	13.7889	+	21.7865i	0.546335	+	0.863214i
$638$		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
$643$		−	14.2442i		−	0.561735i	−0.959746	−	0.280868i	$-0.909378\pi$
$643$		−	14.2442i		−	0.561735i	0.959746	−	0.280868i	$-0.0906222\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.1910	+	17.6513i	−0.400649	+	0.693945i	−0.993804	−	0.111143i	$-0.964549\pi$
$647$	−10.1910	+	17.6513i	−0.400649	+	0.693945i	0.593155	+	0.805088i	$0.297882\pi$
$648$		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
$659$			19.3440i			0.753535i	0.926308	+	0.376768i	$0.122964\pi$
$659$			19.3440i			0.753535i	−0.926308	+	0.376768i	$0.877036\pi$
$660$		0			0
$661$	31.8948	+	18.4145i	1.24056	+	0.716240i	0.969209	−	0.246239i	$-0.0791949\pi$
$661$	31.8948	+	18.4145i	1.24056	+	0.716240i	0.271355	+	0.962479i	$0.412528\pi$
$662$		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
$671$	1.77588			0.0685572
$672$		0			0
$673$	−17.5841			−0.677816			−0.338908	−	0.940819i	$-0.610058\pi$
$673$	−17.5841			−0.677816			−0.338908	+	0.940819i	$0.610058\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.4146	−	35.3590i	−0.784595	−	1.35896i	−0.929241	−	0.369475i	$-0.879538\pi$
$677$	−20.4146	−	35.3590i	−0.784595	−	1.35896i	0.144646	−	0.989484i	$-0.453796\pi$
$678$		0			0
$679$	38.7514	−	11.2327i	1.48714	−	0.431070i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	0.327148	−	0.944973i	$-0.393912\pi$
$683$	−8.56287	−	4.94377i	−0.327649	−	0.189168i	−0.654797	+	0.755805i	$0.727246\pi$
$684$		0			0
$685$			47.3847i			1.81048i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.60233	−	7.97148i	0.175335	−	0.303689i
$690$		0			0
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.998023	−	0.0628444i	$-0.979983\pi$
$691$	−37.9217	+	21.8941i	−1.44261	+	0.832891i	−0.444587	+	0.895736i	$0.646649\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−28.4459	+	16.4233i	−1.07902	+	0.622970i
$696$		0			0
$697$	5.11987	−	8.86787i	0.193929	−	0.335894i
$698$		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
$707$	8.96327	+	2.20739i	0.337099	+	0.0830175i
$708$		0			0
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.847342	−	0.531048i	$-0.821799\pi$
$709$	−23.5269	−	40.7498i	−0.883572	−	1.53039i	−0.0362296	−	0.999343i	$-0.511535\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	28.5576			1.06949
$714$		0			0
$715$	28.6586			1.07177
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.909148	+	1.57469i	0.0339055	+	0.0587261i	0.882480	−	0.470349i	$-0.155872\pi$
$719$	0.909148	+	1.57469i	0.0339055	+	0.0587261i	−0.848575	+	0.529076i	$0.822539\pi$
$720$		0			0
$721$	−6.37230	−	6.11829i	−0.237317	−	0.227857i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.01029	−	4.62474i	−0.297495	−	0.171759i
$726$		0			0
$727$		−	25.1556i		−	0.932970i	−0.884529	−	0.466485i	$-0.845520\pi$
$727$		−	25.1556i		−	0.932970i	0.884529	−	0.466485i	$-0.154480\pi$
$728$		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	−0.427299	−	0.904110i	$-0.640535\pi$
$733$	3.84543	−	2.22016i	0.142034	−	0.0820034i	0.569333	+	0.822107i	$0.307201\pi$
$734$		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	−0.982549	−	0.186004i	$-0.940446\pi$
$739$	−8.97608	+	15.5470i	−0.330191	+	0.571907i	0.652358	+	0.757911i	$0.273780\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	36.2244i		−	1.32894i	−0.747313	−	0.664472i	$-0.768657\pi$
$743$		−	36.2244i		−	1.32894i	0.747313	−	0.664472i	$-0.231343\pi$
$744$		0			0
$745$	12.1829	+	7.03378i	0.446345	+	0.257698i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	6.84864	+	6.57564i	0.250244	+	0.240269i
$750$		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	$0.0111208\pi$
$761$	14.6192	+	25.3212i	0.529945	+	0.917892i	−0.469445	+	0.882962i	$0.655546\pi$
$762$		0			0
$763$	−35.4353	−	8.72668i	−1.28284	−	0.315927i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−27.6677	−	15.9740i	−0.999023	−	0.576786i
$768$		0			0
$769$		−	5.25030i		−	0.189331i	−0.995509	−	0.0946653i	$-0.969822\pi$
$769$		−	5.25030i		−	0.189331i	0.995509	−	0.0946653i	$-0.0301781\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−15.6829	+	27.1635i	−0.564073	+	0.977003i	0.433062	+	0.901364i	$0.357433\pi$
$773$	−15.6829	+	27.1635i	−0.564073	+	0.977003i	−0.997135	+	0.0756393i	$0.975900\pi$
$774$		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
$785$			44.2161i			1.57814i
$786$		0			0
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	0.528128	−	0.849165i	$-0.322894\pi$
$787$	1.59324	+	0.919855i	0.0567927	+	0.0327893i	−0.471335	+	0.881954i	$0.656228\pi$
$788$		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
$797$	12.7932			0.453158			0.226579	−	0.973993i	$-0.427246\pi$
$797$	12.7932			0.453158			0.226579	+	0.973993i	$0.427246\pi$
$798$		0			0
$799$	−72.8633			−2.57772
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.3495	+	30.0502i	0.612250	+	1.06045i
$804$		0			0
$805$	−5.42806	+	22.0410i	−0.191314	+	0.776844i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	0.709645	−	0.704559i	$-0.248855\pi$
$809$	12.9217	+	7.46032i	0.454301	+	0.262291i	−0.255344	+	0.966850i	$0.582189\pi$
$810$		0			0
$811$		−	37.5478i		−	1.31848i	−0.751933	−	0.659240i	$-0.770878\pi$
$811$		−	37.5478i		−	1.31848i	0.751933	−	0.659240i	$-0.229122\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.4067	−	28.4172i	0.574701	−	0.995411i
$816$		0			0
$817$	25.6245	−	14.7943i	0.896489	−	0.517588i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.88164	+	1.66371i	−0.100570	+	0.0580640i	−0.549441	−	0.835532i	$-0.685159\pi$
$821$	−2.88164	+	1.66371i	−0.100570	+	0.0580640i	0.448872	+	0.893596i	$0.351826\pi$
$822$		0			0
$823$	−25.4654	+	44.1073i	−0.887667	+	1.53748i	−0.0450407	+	0.998985i	$0.514342\pi$
$823$	−25.4654	+	44.1073i	−0.887667	+	1.53748i	−0.842626	+	0.538499i	$0.818992\pi$
$824$		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	0.416986	−	0.908913i	$-0.363087\pi$
$829$	−4.65467	−	2.68737i	−0.161663	−	0.0933364i	−0.578649	+	0.815577i	$0.696420\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.83386	+	45.0695i	0.0635395	+	1.56157i
$834$		0			0
$835$	18.6165	+	32.2447i	0.644251	+	1.11588i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.7428			0.819692			0.409846	−	0.912155i	$-0.365582\pi$
$839$	23.7428			0.819692			0.409846	+	0.912155i	$0.365582\pi$
$840$		0			0
$841$	20.7775			0.716465
$842$		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
$851$	8.84146	+	5.10462i	0.303081	+	0.174984i
$852$		0			0
$853$			11.9869i			0.410424i	0.978718	+	0.205212i	$0.0657883\pi$
$853$			11.9869i			0.410424i	−0.978718	+	0.205212i	$0.934212\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.5318	−	47.6864i	0.940467	−	1.62894i	0.175884	−	0.984411i	$-0.443722\pi$
$857$	27.5318	−	47.6864i	0.940467	−	1.62894i	0.764583	−	0.644526i	$-0.222945\pi$
$858$		0			0
$859$	−33.8798	+	19.5605i	−1.15596	+	0.667395i	−0.950333	−	0.311235i	$-0.899258\pi$
$859$	−33.8798	+	19.5605i	−1.15596	+	0.667395i	−0.205630	+	0.978630i	$0.565924\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.349338	−	0.936997i	$-0.386407\pi$
$863$	39.2319	−	22.6506i	1.33547	−	0.771034i	0.986132	+	0.165963i	$0.0530733\pi$
$864$		0			0
$865$	−28.1063	+	48.6815i	−0.955643	+	1.65522i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	14.0833i		−	0.477744i
$870$		0			0
$871$	24.6351	+	14.2231i	0.834730	+	0.481931i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.74847	−	12.9318i	−0.126722	−	0.437174i
$876$		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	$-0.131454\pi$
$881$	54.3727			1.83186			0.915931	+	0.401336i	$0.131454\pi$
$882$		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	0.996800	−	0.0799384i	$-0.0254724\pi$
$887$	12.7818	+	22.1387i	0.429171	+	0.743346i	−0.567629	+	0.823285i	$0.692139\pi$
$888$		0			0
$889$	9.85700	+	34.0055i	0.330593	+	1.14051i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−30.9674	−	17.8790i	−1.03628	−	0.598298i
$894$		0			0
$895$		−	53.8584i		−	1.80029i
$896$		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
$911$		−	3.65193i		−	0.120994i	−0.998168	−	0.0604969i	$-0.980731\pi$
$911$		−	3.65193i		−	0.120994i	0.998168	−	0.0604969i	$-0.0192685\pi$
$912$		0			0
$913$	37.2591	+	21.5116i	1.23310	+	0.711929i
$914$		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	0.996154	+	0.0876145i	$0.0279244\pi$
$919$	17.3994	+	30.1367i	0.573954	+	0.994117i	−0.422201	+	0.906502i	$0.638742\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−28.9725			−0.953643
$924$		0			0
$925$	11.0084			0.361954
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.1736	+	43.6019i	0.825917	+	1.43053i	0.901216	+	0.433370i	$0.142676\pi$
$929$	25.1736	+	43.6019i	0.825917	+	1.43053i	−0.0752987	+	0.997161i	$0.523991\pi$
$930$		0			0
$931$	−10.2796	+	19.6048i	−0.336902	+	0.642522i
$932$		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	$-0.966240\pi$
$937$		−	6.48087i		−	0.211721i	0.994381	−	0.105860i	$-0.0337596\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.334024	+	0.578547i	−0.0108889	+	0.0188601i	−0.871418	−	0.490540i	$-0.836799\pi$
$941$	−0.334024	+	0.578547i	−0.0108889	+	0.0188601i	0.860530	+	0.509400i	$0.170133\pi$
$942$		0			0
$943$	−4.11679	+	2.37683i	−0.134061	+	0.0774003i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−50.7461	+	29.2983i	−1.64903	+	0.952067i	−0.671569	+	0.740942i	$0.734379\pi$
$947$	−50.7461	+	29.2983i	−1.64903	+	0.952067i	−0.977459	+	0.211125i	$0.932287\pi$
$948$		0			0
$949$	23.5560	−	40.8002i	0.764661	−	1.32443i
$950$		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
$959$	10.4527	−	42.4441i	0.337536	−	1.37059i
$960$		0			0
$961$	30.0665	+	52.0767i	0.969887	+	1.67989i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	45.7563			1.47295
$966$		0			0
$967$	−17.0278			−0.547577			−0.273788	−	0.961790i	$-0.588277\pi$
$967$	−17.0278			−0.547577			−0.273788	+	0.961790i	$0.588277\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.5651	+	23.4955i	0.435325	+	0.754006i	0.997322	−	0.0731339i	$-0.0233000\pi$
$971$	13.5651	+	23.4955i	0.435325	+	0.754006i	−0.561997	+	0.827139i	$0.689967\pi$
$972$		0			0
$973$	29.1028	−	8.43589i	0.932994	−	0.270442i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.49838	+	3.17449i	0.175909	+	0.101561i	0.585369	−	0.810767i	$-0.300950\pi$
$977$	5.49838	+	3.17449i	0.175909	+	0.101561i	−0.409460	+	0.912328i	$0.634283\pi$
$978$		0			0
$979$			17.0816i			0.545930i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.98300	−	17.2911i	0.318408	−	0.551499i	−0.661748	−	0.749727i	$-0.730185\pi$
$983$	9.98300	−	17.2911i	0.318408	−	0.551499i	0.980156	+	0.198227i	$0.0635184\pi$
$984$		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	−0.746546	−	0.665333i	$-0.768289\pi$
$991$	6.38803	−	11.0644i	0.202922	−	0.351472i	0.949469	+	0.313861i	$0.101623\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			9.13061i			0.289460i
$996$		0			0
$997$	17.9846	+	10.3834i	0.569579	+	0.328847i	0.756981	−	0.653436i	$-0.226673\pi$
$997$	17.9846	+	10.3834i	0.569579	+	0.328847i	−0.187402	+	0.982283i	$0.560007\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.b.1781.8		16
3.2	odd	2		2268.2.t.a.1781.1		16
7.5	odd	6		2268.2.t.a.2105.1		16
9.2	odd	6		252.2.bm.a.185.2	yes	16
9.4	even	3		252.2.w.a.101.5	yes	16
9.5	odd	6		756.2.w.a.521.1		16
9.7	even	3		756.2.bm.a.17.1		16
21.5	even	6	inner	2268.2.t.b.2105.8		16
36.7	odd	6		3024.2.df.d.17.1		16
36.11	even	6		1008.2.df.d.689.7		16
36.23	even	6		3024.2.ca.d.2033.1		16
36.31	odd	6		1008.2.ca.d.353.4		16
63.2	odd	6		1764.2.w.b.509.4		16
63.4	even	3		1764.2.x.a.1469.1		16
63.5	even	6		756.2.bm.a.89.1		16
63.11	odd	6		1764.2.x.b.293.8		16
63.13	odd	6		1764.2.w.b.1109.4		16
63.16	even	3		5292.2.w.b.1097.8		16
63.20	even	6		1764.2.bm.a.1697.7		16
63.23	odd	6		5292.2.bm.a.4625.8		16
63.25	even	3		5292.2.x.b.881.8		16
63.31	odd	6		1764.2.x.b.1469.8		16
63.32	odd	6		5292.2.x.a.4409.1		16
63.34	odd	6		5292.2.bm.a.2285.8		16
63.38	even	6		1764.2.x.a.293.1		16
63.40	odd	6		252.2.bm.a.173.2	yes	16
63.41	even	6		5292.2.w.b.521.8		16
63.47	even	6		252.2.w.a.5.5	✓	16
63.52	odd	6		5292.2.x.a.881.1		16
63.58	even	3		1764.2.bm.a.1685.7		16
63.59	even	6		5292.2.x.b.4409.8		16
63.61	odd	6		756.2.w.a.341.1		16
252.47	odd	6		1008.2.ca.d.257.4		16
252.103	even	6		1008.2.df.d.929.7		16
252.131	odd	6		3024.2.df.d.1601.1		16
252.187	even	6		3024.2.ca.d.2609.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.5	✓	16	63.47	even	6
252.2.w.a.101.5	yes	16	9.4	even	3
252.2.bm.a.173.2	yes	16	63.40	odd	6
252.2.bm.a.185.2	yes	16	9.2	odd	6
756.2.w.a.341.1		16	63.61	odd	6
756.2.w.a.521.1		16	9.5	odd	6
756.2.bm.a.17.1		16	9.7	even	3
756.2.bm.a.89.1		16	63.5	even	6
1008.2.ca.d.257.4		16	252.47	odd	6
1008.2.ca.d.353.4		16	36.31	odd	6
1008.2.df.d.689.7		16	36.11	even	6
1008.2.df.d.929.7		16	252.103	even	6
1764.2.w.b.509.4		16	63.2	odd	6
1764.2.w.b.1109.4		16	63.13	odd	6
1764.2.x.a.293.1		16	63.38	even	6
1764.2.x.a.1469.1		16	63.4	even	3
1764.2.x.b.293.8		16	63.11	odd	6
1764.2.x.b.1469.8		16	63.31	odd	6
1764.2.bm.a.1685.7		16	63.58	even	3
1764.2.bm.a.1697.7		16	63.20	even	6
2268.2.t.a.1781.1		16	3.2	odd	2
2268.2.t.a.2105.1		16	7.5	odd	6
2268.2.t.b.1781.8		16	1.1	even	1	trivial
2268.2.t.b.2105.8		16	21.5	even	6	inner
3024.2.ca.d.2033.1		16	36.23	even	6
3024.2.ca.d.2609.1		16	252.187	even	6
3024.2.df.d.17.1		16	36.7	odd	6
3024.2.df.d.1601.1		16	252.131	odd	6
5292.2.w.b.521.8		16	63.41	even	6
5292.2.w.b.1097.8		16	63.16	even	3
5292.2.x.a.881.1		16	63.52	odd	6
5292.2.x.a.4409.1		16	63.32	odd	6
5292.2.x.b.881.8		16	63.25	even	3
5292.2.x.b.4409.8		16	63.59	even	6
5292.2.bm.a.2285.8		16	63.34	odd	6
5292.2.bm.a.4625.8		16	63.23	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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43402 + 2.48379i) q^{5} +(-0.736590 - 2.54115i) q^{7} +O(q^{10})\)	\(q+(1.43402 + 2.48379i) q^{5} +(-0.736590 - 2.54115i) q^{7} +(2.34941 + 1.35643i) q^{11} -3.68335i q^{13} +(3.22192 - 5.58052i) q^{17} +(2.73867 - 1.58117i) q^{19} +(-2.59068 + 1.49573i) q^{23} +(-1.61282 + 2.79348i) q^{25} +2.86749i q^{29} +(-8.26739 - 4.77318i) q^{31} +(5.25540 - 5.47359i) q^{35} +(-1.70640 - 2.95556i) q^{37} +1.58908 q^{41} +9.35656 q^{43} +(-5.65372 - 9.79254i) q^{47} +(-5.91487 + 3.74357i) q^{49} +(2.16419 + 1.24950i) q^{53} +7.78058i q^{55} +(4.33680 - 7.51156i) q^{59} +(0.566915 - 0.327308i) q^{61} +(9.14867 - 5.28199i) q^{65} +(-3.86146 + 6.68825i) q^{67} -7.86582i q^{71} +(11.0769 + 6.39527i) q^{73} +(1.71634 - 6.96932i) q^{77} +(-2.59566 - 4.49581i) q^{79} +15.8590 q^{83} +18.4811 q^{85} +(3.14826 + 5.45295i) q^{89} +(-9.35993 + 2.71312i) q^{91} +(7.85460 + 4.53486i) q^{95} +15.2495i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^7	\( 16 q + 2 q^{7} + 6 q^{11} + 9 q^{17} - 21 q^{23} - 8 q^{25} - 6 q^{31} - 15 q^{35} + q^{37} + 12 q^{41} + 4 q^{43} + 18 q^{47} - 8 q^{49} + 15 q^{59} - 3 q^{61} - 39 q^{65} - 7 q^{67} - 48 q^{77} - q^{79} - 12 q^{85} + 21 q^{89} + 9 q^{91} + 6 q^{95}+O(q^{100}) \) 16 * q + 2 * q^7 + 6 * q^11 + 9 * q^17 - 21 * q^23 - 8 * q^25 - 6 * q^31 - 15 * q^35 + q^37 + 12 * q^41 + 4 * q^43 + 18 * q^47 - 8 * q^49 + 15 * q^59 - 3 * q^61 - 39 * q^65 - 7 * q^67 - 48 * q^77 - q^79 - 12 * q^85 + 21 * q^89 + 9 * q^91 + 6 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more