LMFDB - Embedded newform 2268.2.t.b.2105.6

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			2105.6
Root			$-1.61108 + 0.635951i$ of defining polynomial
Character	$\chi$	$=$	2268.2105
Dual form			2268.2.t.b.1781.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09150 - 1.89054i) q^{5} +(-1.38614 - 2.25358i) q^{7} +O(q^{10})$	$q+(1.09150 - 1.89054i) q^{5} +(-1.38614 - 2.25358i) q^{7} +(1.26889 - 0.732592i) q^{11} -3.38041i q^{13} +(1.32136 + 2.28866i) q^{17} +(6.87816 + 3.97111i) q^{19} +(3.47245 + 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} -7.75105i q^{29} +(-0.612252 + 0.353484i) q^{31} +(-5.77345 + 0.160752i) q^{35} +(1.41738 - 2.45498i) q^{37} -7.48345 q^{41} +2.54224 q^{43} +(6.27538 - 10.8693i) q^{47} +(-3.15726 + 6.24754i) q^{49} +(-2.41675 + 1.39531i) q^{53} -3.19850i q^{55} +(-6.71650 - 11.6333i) q^{59} +(-6.75061 - 3.89747i) q^{61} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} -11.6854i q^{71} +(-3.95924 + 2.28587i) q^{73} +(-3.40980 - 1.84407i) q^{77} +(-4.69189 + 8.12659i) q^{79} -3.41695 q^{83} +5.76905 q^{85} +(4.61937 - 8.00099i) q^{89} +(-7.61803 + 4.68571i) q^{91} +(15.0150 - 8.66894i) q^{95} +7.37154i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	−0.511773	−	0.859121i	$-0.671011\pi$
$5$	1.09150	−	1.89054i	0.488134	−	0.845473i	0.999907	+	0.0136476i	$0.00434429\pi$
$6$		0			0
$7$	−1.38614	−	2.25358i	−0.523910	−	0.851774i
$7$	−1.38614	−	2.25358i	−0.523910	−	0.851774i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.26889	−	0.732592i	0.382584	−	0.220885i	−0.296358	−	0.955077i	$-0.595772\pi$
$11$	1.26889	−	0.732592i	0.382584	−	0.220885i	0.678942	+	0.734192i	$0.262439\pi$
$12$		0			0
$13$		−	3.38041i		−	0.937557i	−0.883316	−	0.468779i	$-0.844694\pi$
$13$		−	3.38041i		−	0.937557i	0.883316	−	0.468779i	$-0.155306\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.32136	+	2.28866i	0.320476	+	0.555081i	0.980586	−	0.196088i	$-0.0628238\pi$
$17$	1.32136	+	2.28866i	0.320476	+	0.555081i	−0.660110	+	0.751169i	$0.729491\pi$
$18$		0			0
$19$	6.87816	+	3.97111i	1.57796	+	0.911034i	0.995144	+	0.0984279i	$0.0313814\pi$
$19$	6.87816	+	3.97111i	1.57796	+	0.911034i	0.582813	+	0.812606i	$0.301952\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.47245	+	2.00482i	0.724056	+	0.418034i	0.816244	−	0.577708i	$-0.196053\pi$
$23$	3.47245	+	2.00482i	0.724056	+	0.418034i	−0.0921879	+	0.995742i	$0.529386\pi$
$24$		0			0
$25$	0.117249	+	0.203081i	0.0234498	+	0.0406163i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	7.75105i		−	1.43933i	−0.694319	−	0.719667i	$-0.744294\pi$
$29$		−	7.75105i		−	1.43933i	0.694319	−	0.719667i	$-0.255706\pi$
$30$		0			0
$31$	−0.612252	+	0.353484i	−0.109964	+	0.0634876i	−0.553973	−	0.832534i	$-0.686889\pi$
$31$	−0.612252	+	0.353484i	−0.109964	+	0.0634876i	0.444009	+	0.896022i	$0.353556\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.77345	+	0.160752i	−0.975890	+	0.0271721i
$36$		0			0
$37$	1.41738	−	2.45498i	0.233016	−	0.403596i	−0.725678	−	0.688034i	$-0.758474\pi$
$37$	1.41738	−	2.45498i	0.233016	−	0.403596i	0.958694	+	0.284438i	$0.0918071\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.48345			−1.16872			−0.584360	−	0.811495i	$-0.698654\pi$
$41$	−7.48345			−1.16872			−0.584360	+	0.811495i	$0.698654\pi$
$42$		0			0
$43$	2.54224			0.387688			0.193844	−	0.981032i	$-0.437904\pi$
$43$	2.54224			0.387688			0.193844	+	0.981032i	$0.437904\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.27538	−	10.8693i	0.915358	−	1.58545i	0.108983	−	0.994044i	$-0.465241\pi$
$47$	6.27538	−	10.8693i	0.915358	−	1.58545i	0.806376	−	0.591403i	$-0.201426\pi$
$48$		0			0
$49$	−3.15726	+	6.24754i	−0.451036	+	0.892506i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.41675	+	1.39531i	−0.331966	+	0.191661i	−0.656714	−	0.754140i	$-0.728054\pi$
$53$	−2.41675	+	1.39531i	−0.331966	+	0.191661i	0.324748	+	0.945801i	$0.394721\pi$
$54$		0			0
$55$		−	3.19850i		−	0.431286i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.71650	−	11.6333i	−0.874414	−	1.51453i	−0.857385	−	0.514675i	$-0.827913\pi$
$59$	−6.71650	−	11.6333i	−0.874414	−	1.51453i	−0.0170287	−	0.999855i	$-0.505421\pi$
$60$		0			0
$61$	−6.75061	−	3.89747i	−0.864327	−	0.499020i	0.00113176	−	0.999999i	$-0.499640\pi$
$61$	−6.75061	−	3.89747i	−0.864327	−	0.499020i	−0.865459	+	0.500980i	$0.832973\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.39079	−	3.68972i	−0.792680	−	0.457654i
$66$		0			0
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	0.630649	−	0.776068i	$-0.282789\pi$
$67$	−2.92029	−	5.05809i	−0.356770	−	0.617945i	−0.987419	+	0.158124i	$0.949455\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.6854i		−	1.38680i	−0.720554	−	0.693398i	$-0.756113\pi$
$71$		−	11.6854i		−	1.38680i	0.720554	−	0.693398i	$-0.243887\pi$
$72$		0			0
$73$	−3.95924	+	2.28587i	−0.463394	+	0.267541i	−0.713470	−	0.700685i	$-0.752878\pi$
$73$	−3.95924	+	2.28587i	−0.463394	+	0.267541i	0.250076	+	0.968226i	$0.419544\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.40980	−	1.84407i	−0.388583	−	0.210151i
$78$		0			0
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	0.471593	+	0.881816i	$0.343679\pi$
$79$	−4.69189	+	8.12659i	−0.527879	+	0.914312i	−0.999472	+	0.0324963i	$0.989654\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.41695			−0.375059			−0.187529	−	0.982259i	$-0.560048\pi$
$83$	−3.41695			−0.375059			−0.187529	+	0.982259i	$0.560048\pi$
$84$		0			0
$85$	5.76905			0.625741
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.61937	−	8.00099i	0.489653	−	0.848103i	−0.510276	−	0.860010i	$-0.670457\pi$
$89$	4.61937	−	8.00099i	0.489653	−	0.848103i	0.999929	+	0.0119070i	$0.00379021\pi$
$90$		0			0
$91$	−7.61803	+	4.68571i	−0.798586	+	0.491196i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.0150	−	8.66894i	1.54051	−	0.889414i
$96$		0			0
$97$			7.37154i			0.748467i	0.927335	+	0.374233i	$0.122094\pi$
$97$			7.37154i			0.748467i	−0.927335	+	0.374233i	$0.877906\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	0.993023	−	0.117920i	$-0.0376226\pi$
$101$	3.96357	+	6.86510i	0.394390	+	0.683103i	−0.598633	+	0.801023i	$0.704289\pi$
$102$		0			0
$103$	3.26825	+	1.88693i	0.322031	+	0.185924i	0.652297	−	0.757963i	$-0.273805\pi$
$103$	3.26825	+	1.88693i	0.322031	+	0.185924i	−0.330267	+	0.943888i	$0.607139\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.88241	−	3.97356i	−0.665347	−	0.384138i	0.128964	−	0.991649i	$-0.458835\pi$
$107$	−6.88241	−	3.97356i	−0.665347	−	0.384138i	−0.794311	+	0.607511i	$0.792168\pi$
$108$		0			0
$109$	0.505142	+	0.874932i	0.0483838	+	0.0838033i	0.889203	−	0.457513i	$-0.151260\pi$
$109$	0.505142	+	0.874932i	0.0483838	+	0.0838033i	−0.840819	+	0.541316i	$0.817926\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			12.1886i			1.14661i	0.819342	+	0.573304i	$0.194339\pi$
$113$			12.1886i			1.14661i	−0.819342	+	0.573304i	$0.805661\pi$
$114$		0			0
$115$	7.58037	−	4.37653i	0.706873	−	0.408113i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.32609	−	6.15017i	0.304902	−	0.563785i
$120$		0			0
$121$	−4.42662	+	7.66713i	−0.402420	+	0.697012i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.4269			1.02206
$126$		0			0
$127$	6.79350			0.602826			0.301413	−	0.953494i	$-0.402542\pi$
$127$	6.79350			0.602826			0.301413	+	0.953494i	$0.402542\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	−0.392761	−	0.919640i	$-0.628480\pi$
$131$	6.86790	−	11.8956i	0.600051	−	1.03932i	0.992813	−	0.119679i	$-0.0381865\pi$
$132$		0			0
$133$	−0.584850	−	21.0050i	−0.0507130	−	1.82136i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−17.4028	+	10.0475i	−1.48682	+	0.858416i	−0.999887	−	0.0150235i	$-0.995218\pi$
$137$	−17.4028	+	10.0475i	−1.48682	+	0.858416i	−0.486933	+	0.873439i	$0.661884\pi$
$138$		0			0
$139$		−	9.83116i		−	0.833868i	−0.908937	−	0.416934i	$-0.863105\pi$
$139$		−	9.83116i		−	0.833868i	0.908937	−	0.416934i	$-0.136895\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.47646	−	4.28936i	−0.207092	−	0.358694i
$144$		0			0
$145$	−14.6536	−	8.46029i	−1.21692	−	0.702589i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.3512	−	10.0177i	−1.42146	−	0.820682i	−0.425038	−	0.905175i	$-0.639739\pi$
$149$	−17.3512	−	10.0177i	−1.42146	−	0.820682i	−0.996424	+	0.0844939i	$0.973073\pi$
$150$		0			0
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.821353	+	0.570420i	$0.193220\pi$
$151$	11.1168	+	19.2549i	0.904675	+	1.56694i	0.0833218	+	0.996523i	$0.473447\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1.54331i			0.123962i
$156$		0			0
$157$	−6.95305	+	4.01435i	−0.554914	+	0.320380i	−0.751102	−	0.660187i	$-0.770477\pi$
$157$	−6.95305	+	4.01435i	−0.554914	+	0.320380i	0.196188	+	0.980566i	$0.437144\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−0.295263	−	10.6044i	−0.0232700	−	0.835744i
$162$		0			0
$163$	−6.22604	+	10.7838i	−0.487661	+	0.844654i	−0.999899	−	0.0141893i	$-0.995483\pi$
$163$	−6.22604	+	10.7838i	−0.487661	+	0.844654i	0.512238	+	0.858844i	$0.328817\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.7197			1.52596			0.762978	−	0.646425i	$-0.223737\pi$
$167$	19.7197			1.52596			0.762978	+	0.646425i	$0.223737\pi$
$168$		0			0
$169$	1.57282			0.120987
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.913733	+	1.58263i	−0.0694699	+	0.120325i	−0.898668	−	0.438629i	$-0.855464\pi$
$173$	−0.913733	+	1.58263i	−0.0694699	+	0.120325i	0.829198	+	0.558955i	$0.188797\pi$
$174$		0			0
$175$	0.295137	−	0.545728i	0.0223103	−	0.0412532i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	12.1182	−	6.99645i	0.905757	−	0.522939i	0.0266934	−	0.999644i	$-0.491502\pi$
$179$	12.1182	−	6.99645i	0.905757	−	0.522939i	0.879064	+	0.476705i	$0.158169\pi$
$180$		0			0
$181$		−	16.3594i		−	1.21599i	−0.793942	−	0.607994i	$-0.791975\pi$
$181$		−	16.3594i		−	1.21599i	0.793942	−	0.607994i	$-0.208025\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.09415	−	5.35923i	−0.227486	−	0.394018i
$186$		0			0
$187$	3.35330	+	1.93603i	0.245218	+	0.141577i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	0.00655557	−	0.999979i	$-0.497913\pi$
$191$	−11.8326	−	6.83153i	−0.856173	−	0.494312i	−0.862729	+	0.505667i	$0.831247\pi$
$192$		0			0
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	0.933987	−	0.357307i	$-0.116305\pi$
$193$	2.18885	+	3.79119i	0.157557	+	0.272896i	−0.776430	+	0.630203i	$0.782972\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.00603i			0.0716767i	0.999358	+	0.0358384i	$0.0114101\pi$
$197$			1.00603i			0.0716767i	−0.999358	+	0.0358384i	$0.988590\pi$
$198$		0			0
$199$	−5.67639	+	3.27726i	−0.402388	+	0.232319i	−0.687514	−	0.726171i	$-0.741298\pi$
$199$	−5.67639	+	3.27726i	−0.402388	+	0.232319i	0.285126	+	0.958490i	$0.407965\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.4676	+	10.7440i	−1.22599	+	0.754082i
$204$		0			0
$205$	−8.16820	+	14.1477i	−0.570492	+	0.988121i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.6368			0.804934
$210$		0			0
$211$	18.2240			1.25459			0.627297	−	0.778780i	$-0.284161\pi$
$211$	18.2240			1.25459			0.627297	+	0.778780i	$0.284161\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.77486	−	4.80620i	0.189244	−	0.327780i
$216$		0			0
$217$	1.64527	+	0.889784i	0.111688	+	0.0604024i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.73660	−	4.46673i	0.520420	−	0.300464i
$222$		0			0
$223$		−	10.0656i		−	0.674041i	−0.941497	−	0.337021i	$-0.890581\pi$
$223$		−	10.0656i		−	0.674041i	0.941497	−	0.337021i	$-0.109419\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	0.980618	+	0.195928i	$0.0627720\pi$
$227$	9.94372	+	17.2230i	0.659988	+	1.14313i	−0.320630	+	0.947204i	$0.603895\pi$
$228$		0			0
$229$	15.3854	+	8.88275i	1.01669	+	0.586988i	0.913145	−	0.407636i	$-0.133647\pi$
$229$	15.3854	+	8.88275i	1.01669	+	0.586988i	0.103549	+	0.994624i	$0.466980\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.9077	−	8.02962i	−0.911124	−	0.526038i	−0.0303317	−	0.999540i	$-0.509656\pi$
$233$	−13.9077	−	8.02962i	−0.911124	−	0.526038i	−0.880793	+	0.473502i	$0.842990\pi$
$234$		0			0
$235$	−13.6992	−	23.7277i	−0.893636	−	1.54782i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			8.21127i			0.531143i	0.964091	+	0.265572i	$0.0855607\pi$
$239$			8.21127i			0.531143i	−0.964091	+	0.265572i	$0.914439\pi$
$240$		0			0
$241$	24.6614	−	14.2382i	1.58858	−	0.917166i	0.595037	−	0.803698i	$-0.297137\pi$
$241$	24.6614	−	14.2382i	1.58858	−	0.917166i	0.993542	−	0.113468i	$-0.0361959\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.36505	+	12.7881i	0.534423	+	0.817002i
$246$		0			0
$247$	13.4240	−	23.2510i	0.854147	−	1.47943i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.656343			0.0414280			0.0207140	−	0.999785i	$-0.493406\pi$
$251$	0.656343			0.0414280			0.0207140	+	0.999785i	$0.493406\pi$
$252$		0			0
$253$	5.87486			0.369349
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	−0.960230	−	0.279211i	$-0.909927\pi$
$257$	−3.82042	+	6.61716i	−0.238311	+	0.412767i	0.721918	+	0.691978i	$0.243261\pi$
$258$		0			0
$259$	−7.49718	+	0.208747i	−0.465852	+	0.0129709i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	5.73888	−	3.31334i	0.353874	−	0.204310i	−0.312516	−	0.949913i	$-0.601172\pi$
$263$	5.73888	−	3.31334i	0.353874	−	0.204310i	0.666390	+	0.745603i	$0.267838\pi$
$264$		0			0
$265$			6.09194i			0.374225i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.38347	+	7.59239i	0.267265	+	0.462916i	0.968154	−	0.250354i	$-0.0805469\pi$
$269$	4.38347	+	7.59239i	0.267265	+	0.462916i	−0.700890	+	0.713270i	$0.747214\pi$
$270$		0			0
$271$	14.2608	+	8.23346i	0.866280	+	0.500147i	0.866110	−	0.499853i	$-0.166613\pi$
$271$	14.2608	+	8.23346i	0.866280	+	0.500147i	0.000169619		1.00000i	$0.499946\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.297551	+	0.171791i	0.0179430	+	0.0103594i
$276$		0			0
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	0.999212	+	0.0397001i	$0.0126402\pi$
$277$	8.88732	+	15.3933i	0.533987	+	0.924893i	−0.465225	+	0.885193i	$0.654026\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	16.1950i		−	0.966111i	−0.875590	−	0.483055i	$-0.839527\pi$
$281$		−	16.1950i		−	0.966111i	0.875590	−	0.483055i	$-0.160473\pi$
$282$		0			0
$283$	−24.5717	+	14.1865i	−1.46063	+	0.843298i	−0.999041	−	0.0437937i	$-0.986056\pi$
$283$	−24.5717	+	14.1865i	−1.46063	+	0.843298i	−0.461594	+	0.887091i	$0.652722\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.3731	+	16.8646i	0.612304	+	0.995484i
$288$		0			0
$289$	5.00804	−	8.67417i	0.294590	−	0.510246i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.76520			0.512068			0.256034	−	0.966668i	$-0.417584\pi$
$293$	8.76520			0.512068			0.256034	+	0.966668i	$0.417584\pi$
$294$		0			0
$295$	−29.3243			−1.70733
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.77711	−	11.7383i	0.391931	−	0.678844i
$300$		0			0
$301$	−3.52389	−	5.72914i	−0.203114	−	0.330222i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−14.7366	+	8.50818i	−0.843816	+	0.487177i
$306$		0			0
$307$			12.8497i			0.733372i	0.930345	+	0.366686i	$0.119508\pi$
$307$			12.8497i			0.733372i	−0.930345	+	0.366686i	$0.880492\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	0.944228	−	0.329291i	$-0.106810\pi$
$311$	3.29671	+	5.71007i	0.186939	+	0.323789i	−0.757289	+	0.653080i	$0.773477\pi$
$312$		0			0
$313$	2.95711	+	1.70729i	0.167146	+	0.0965018i	0.581239	−	0.813733i	$-0.302568\pi$
$313$	2.95711	+	1.70729i	0.167146	+	0.0965018i	−0.414093	+	0.910234i	$0.635901\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.997114	−	0.0759182i	$-0.975811\pi$
$317$	−27.8003	−	16.0505i	−1.56142	−	0.901485i	−0.564304	−	0.825567i	$-0.690855\pi$
$318$		0			0
$319$	−5.67836	−	9.83521i	−0.317927	−	0.550666i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			20.9890i			1.16786i
$324$		0			0
$325$	0.686498	−	0.396350i	0.0380801	−	0.0219855i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−33.1933	+	0.924216i	−1.83001	+	0.0509537i
$330$		0			0
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	−0.129824	−	0.991537i	$-0.541441\pi$
$331$	14.4416	−	25.0137i	0.793784	−	1.37487i	0.923608	−	0.383338i	$-0.125225\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.7500			−0.696608
$336$		0			0
$337$	−9.65137			−0.525743			−0.262872	−	0.964831i	$-0.584670\pi$
$337$	−9.65137			−0.525743			−0.262872	+	0.964831i	$0.584670\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.517919	+	0.897063i	−0.0280469	+	0.0485787i
$342$		0			0
$343$	18.4557	−	1.54481i	0.996515	−	0.0834117i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	−0.185283	−	0.982685i	$-0.559320\pi$
$347$	10.6758	−	6.16367i	0.573106	−	0.330883i	0.758389	+	0.651802i	$0.225987\pi$
$348$		0			0
$349$		−	11.8023i		−	0.631763i	−0.948799	−	0.315881i	$-0.897700\pi$
$349$		−	11.8023i		−	0.631763i	0.948799	−	0.315881i	$-0.102300\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	0.986461	−	0.163997i	$-0.0524386\pi$
$353$	6.59855	+	11.4290i	0.351205	+	0.608305i	−0.635256	+	0.772302i	$0.719105\pi$
$354$		0			0
$355$	−22.0916	−	12.7546i	−1.17250	−	0.676943i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.22483	−	3.01656i	−0.275756	−	0.159208i	0.355745	−	0.934583i	$-0.384227\pi$
$359$	−5.22483	−	3.01656i	−0.275756	−	0.159208i	−0.631501	+	0.775375i	$0.717561\pi$
$360$		0			0
$361$	22.0394	+	38.1733i	1.15997	+	2.00912i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			9.98012i			0.522384i
$366$		0			0
$367$	−14.8755	+	8.58836i	−0.776494	+	0.448309i	−0.835186	−	0.549967i	$-0.814640\pi$
$367$	−14.8755	+	8.58836i	−0.776494	+	0.448309i	0.0586924	+	0.998276i	$0.481307\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.49439	+	3.51225i	0.337172	+	0.182347i
$372$		0			0
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	−0.920614	−	0.390475i	$-0.872311\pi$
$373$	−2.35902	+	4.08595i	−0.122146	+	0.211562i	0.798468	+	0.602037i	$0.205644\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−26.2017			−1.34946
$378$		0			0
$379$	9.34015			0.479771			0.239886	−	0.970801i	$-0.422890\pi$
$379$	9.34015			0.479771			0.239886	+	0.970801i	$0.422890\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	−0.783968	−	0.620802i	$-0.786807\pi$
$383$	2.85036	−	4.93696i	0.145646	−	0.252267i	0.929614	+	0.368535i	$0.120140\pi$
$384$		0			0
$385$	−7.20808	+	4.43356i	−0.367358	+	0.225955i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.63671	+	3.83171i	−0.336495	+	0.194275i	−0.658721	−	0.752387i	$-0.728902\pi$
$389$	−6.63671	+	3.83171i	−0.336495	+	0.194275i	0.322226	+	0.946663i	$0.395569\pi$
$390$		0			0
$391$			10.5963i			0.535879i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.2424	+	17.7404i	0.515351	+	0.892615i
$396$		0			0
$397$	−1.12810	−	0.651310i	−0.0566178	−	0.0326883i	0.471424	−	0.881907i	$-0.343740\pi$
$397$	−1.12810	−	0.651310i	−0.0566178	−	0.0326883i	−0.528042	+	0.849218i	$0.677074\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.18778	+	4.72722i	0.408878	+	0.236066i	0.690308	−	0.723516i	$-0.257475\pi$
$401$	8.18778	+	4.72722i	0.408878	+	0.236066i	−0.281429	+	0.959582i	$0.590809\pi$
$402$		0			0
$403$	1.19492	+	2.06966i	0.0595233	+	0.103097i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	4.15345i		−	0.205879i
$408$		0			0
$409$	16.5182	−	9.53678i	0.816771	−	0.471563i	−0.0325304	−	0.999471i	$-0.510357\pi$
$409$	16.5182	−	9.53678i	0.816771	−	0.471563i	0.849302	+	0.527908i	$0.177023\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−16.9067	+	31.2615i	−0.831922	+	1.53828i
$414$		0			0
$415$	−3.72961	+	6.45987i	−0.183079	+	0.317102i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.40005			0.410369			0.205185	−	0.978723i	$-0.434220\pi$
$419$	8.40005			0.410369			0.205185	+	0.978723i	$0.434220\pi$
$420$		0			0
$421$	−39.4355			−1.92197			−0.960985	−	0.276599i	$-0.910792\pi$
$421$	−39.4355			−1.92197			−0.960985	+	0.276599i	$0.910792\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.309855	+	0.536685i	−0.0150302	+	0.0260331i
$426$		0			0
$427$	0.574005	+	20.6155i	0.0277781	+	0.997652i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	10.3340	−	5.96634i	0.497772	−	0.287389i	−0.230021	−	0.973186i	$-0.573880\pi$
$431$	10.3340	−	5.96634i	0.497772	−	0.287389i	0.727793	+	0.685797i	$0.240546\pi$
$432$		0			0
$433$			12.2121i			0.586875i	0.955978	+	0.293437i	$0.0947992\pi$
$433$			12.2121i			0.586875i	−0.955978	+	0.293437i	$0.905201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.9227	+	27.5789i	0.761686	+	1.31928i
$438$		0			0
$439$	−14.4639	−	8.35076i	−0.690326	−	0.398560i	0.113408	−	0.993548i	$-0.463823\pi$
$439$	−14.4639	−	8.35076i	−0.690326	−	0.398560i	−0.803734	+	0.594989i	$0.797157\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.970453	−	0.241291i	$-0.0775708\pi$
$443$	26.2403	+	15.1499i	1.24672	+	0.719791i	0.276262	+	0.961082i	$0.410904\pi$
$444$		0			0
$445$	−10.0841	−	17.4662i	−0.478033	−	0.827977i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			30.1253i			1.42170i	0.703343	+	0.710851i	$0.251690\pi$
$449$			30.1253i			1.42170i	−0.703343	+	0.710851i	$0.748310\pi$
$450$		0			0
$451$	−9.49566	+	5.48232i	−0.447133	+	0.258152i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.543409	+	19.5166i	0.0254754	+	0.914953i
$456$		0			0
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	0.404067	+	0.914730i	$0.367596\pi$
$457$	−12.6159	+	21.8513i	−0.590146	+	1.02216i	−0.994212	+	0.107433i	$0.965737\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	24.6349			1.14736			0.573680	−	0.819079i	$-0.305515\pi$
$461$	24.6349			1.14736			0.573680	+	0.819079i	$0.305515\pi$
$462$		0			0
$463$	12.6643			0.588560			0.294280	−	0.955719i	$-0.404920\pi$
$463$	12.6643			0.588560			0.294280	+	0.955719i	$0.404920\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.4723	−	18.1385i	0.484599	−	0.839350i	−0.515245	−	0.857043i	$-0.672299\pi$
$467$	10.4723	−	18.1385i	0.484599	−	0.839350i	0.999843	+	0.0176932i	$0.00563223\pi$
$468$		0			0
$469$	−7.35090	+	13.5923i	−0.339433	+	0.627635i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.22581	−	1.86242i	0.148323	−	0.0856344i
$474$		0			0
$475$			1.86243i			0.0854543i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	0.958637	+	0.284630i	$0.0918707\pi$
$479$	15.8852	+	27.5141i	0.725816	+	1.25715i	−0.232822	+	0.972519i	$0.574796\pi$
$480$		0			0
$481$	−8.29884	−	4.79134i	−0.378394	−	0.218466i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.9362	+	8.04605i	0.632809	+	0.365352i
$486$		0			0
$487$	−17.7821	−	30.7995i	−0.805784	−	1.39566i	−0.915761	−	0.401724i	$-0.868411\pi$
$487$	−17.7821	−	30.7995i	−0.805784	−	1.39566i	0.109977	−	0.993934i	$-0.464922\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	3.18390i		−	0.143687i	−0.997416	−	0.0718437i	$-0.977112\pi$
$491$		−	3.18390i		−	0.143687i	0.997416	−	0.0718437i	$-0.0228883\pi$
$492$		0			0
$493$	17.7395	−	10.2419i	0.798947	−	0.461272i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−26.3339	+	16.1975i	−1.18124	+	0.726557i
$498$		0			0
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	0.244884	+	0.969552i	$0.421250\pi$
$499$	−16.0214	+	27.7498i	−0.717215	+	1.24225i	−0.962099	+	0.272700i	$0.912083\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.6608			0.519930			0.259965	−	0.965618i	$-0.416289\pi$
$503$	11.6608			0.519930			0.259965	+	0.965618i	$0.416289\pi$
$504$		0			0
$505$	17.3050			0.770061
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	0.397592	+	0.917562i	$0.369846\pi$
$509$	−13.4427	+	23.2834i	−0.595836	+	1.03202i	−0.993428	+	0.114457i	$0.963487\pi$
$510$		0			0
$511$	10.6394	+	5.75395i	0.470661	+	0.254540i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.13461	−	4.11917i	0.314388	−	0.181512i
$516$		0			0
$517$		−	18.3892i		−	0.808755i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.0385	+	29.5116i	0.746471	+	1.29293i	0.949504	+	0.313754i	$0.101587\pi$
$521$	17.0385	+	29.5116i	0.746471	+	1.29293i	−0.203033	+	0.979172i	$0.565080\pi$
$522$		0			0
$523$	4.71003	+	2.71933i	0.205955	+	0.118908i	0.599430	−	0.800427i	$-0.295394\pi$
$523$	4.71003	+	2.71933i	0.205955	+	0.118908i	−0.393475	+	0.919335i	$0.628727\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.61801	−	0.934157i	−0.0704815	−	0.0406925i
$528$		0			0
$529$	−3.46140	−	5.99532i	−0.150496	−	0.260666i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			25.2971i			1.09574i
$534$		0			0
$535$	−15.0243	+	8.67429i	−0.649558	+	0.375022i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.570698	+	10.2404i	0.0245817	+	0.441085i
$540$		0			0
$541$	11.8329	−	20.4952i	0.508737	−	0.881158i	−0.491212	−	0.871040i	$-0.663446\pi$
$541$	11.8329	−	20.4952i	0.508737	−	0.881158i	0.999949	−	0.0101183i	$-0.00322080\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.20545			0.0944713
$546$		0			0
$547$	24.1648			1.03321			0.516606	−	0.856223i	$-0.327195\pi$
$547$	24.1648			1.03321			0.516606	+	0.856223i	$0.327195\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	30.7803	−	53.3130i	1.31128	−	2.27121i
$552$		0			0
$553$	24.8175	−	0.691004i	1.05535	−	0.0293845i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.36315	+	4.25111i	−0.311987	+	0.180126i	−0.647815	−	0.761798i	$-0.724317\pi$
$557$	−7.36315	+	4.25111i	−0.311987	+	0.180126i	0.335829	+	0.941923i	$0.390984\pi$
$558$		0			0
$559$		−	8.59381i		−	0.363480i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.473776	−	0.820605i	−0.0199673	−	0.0345844i	0.855869	−	0.517192i	$-0.173023\pi$
$563$	−0.473776	−	0.820605i	−0.0199673	−	0.0345844i	−0.875836	+	0.482608i	$0.839690\pi$
$564$		0			0
$565$	23.0430	+	13.3039i	0.969427	+	0.559699i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	0.131175	−	0.991359i	$-0.458125\pi$
$569$	−15.7859	−	9.11401i	−0.661781	−	0.382079i	−0.792955	+	0.609280i	$0.791458\pi$
$570$		0			0
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	0.965211	−	0.261471i	$-0.0842077\pi$
$571$	6.12121	+	10.6023i	0.256165	+	0.443691i	−0.709046	+	0.705162i	$0.750874\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.940253i			0.0392112i
$576$		0			0
$577$	−10.2500	+	5.91784i	−0.426713	+	0.246363i	−0.697945	−	0.716151i	$-0.745902\pi$
$577$	−10.2500	+	5.91784i	−0.426713	+	0.246363i	0.271232	+	0.962514i	$0.412569\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.73636	+	7.70037i	0.196497	+	0.319465i
$582$		0			0
$583$	−2.04439	+	3.54098i	−0.0846699	+	0.146653i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−7.15361			−0.295261			−0.147631	−	0.989043i	$-0.547165\pi$
$587$	−7.15361			−0.295261			−0.147631	+	0.989043i	$0.547165\pi$
$588$		0			0
$589$	−5.61489			−0.231358
$590$		0			0
$591$		0			0
$592$		0			0
$593$	13.4811	−	23.3500i	0.553603	−	0.958869i	−0.444408	−	0.895825i	$-0.646586\pi$
$593$	13.4811	−	23.3500i	0.553603	−	0.958869i	0.998011	−	0.0630442i	$-0.0200809\pi$
$594$		0			0
$595$	−7.99668	−	13.0010i	−0.327832	−	0.532990i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.970532	−	0.240974i	$-0.922533\pi$
$599$	−30.5223	+	17.6221i	−1.24711	+	0.720018i	−0.276576	+	0.960992i	$0.589200\pi$
$600$		0			0
$601$			3.91750i			0.159798i	0.996803	+	0.0798991i	$0.0254598\pi$
$601$			3.91750i			0.159798i	−0.996803	+	0.0798991i	$0.974540\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.66332	+	16.7374i	0.392870	+	0.680470i
$606$		0			0
$607$	12.5377	+	7.23862i	0.508888	+	0.293807i	0.732376	−	0.680900i	$-0.238411\pi$
$607$	12.5377	+	7.23862i	0.508888	+	0.293807i	−0.223488	+	0.974707i	$0.571744\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−36.7426	−	21.2134i	−1.48645	−	0.858201i
$612$		0			0
$613$	−6.51761	−	11.2888i	−0.263244	−	0.455952i	0.703858	−	0.710341i	$-0.251459\pi$
$613$	−6.51761	−	11.2888i	−0.263244	−	0.455952i	−0.967102	+	0.254389i	$0.918126\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			3.63143i			0.146196i	0.997325	+	0.0730979i	$0.0232886\pi$
$617$			3.63143i			0.146196i	−0.997325	+	0.0730979i	$0.976711\pi$
$618$		0			0
$619$	14.2737	−	8.24091i	0.573708	−	0.331230i	−0.184921	−	0.982753i	$-0.559203\pi$
$619$	14.2737	−	8.24091i	0.573708	−	0.331230i	0.758629	+	0.651523i	$0.225870\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−24.4340	+	0.680325i	−0.978926	+	0.0272567i
$624$		0			0
$625$	11.8863	−	20.5876i	0.475450	−	0.823504i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	7.49147			0.298704
$630$		0			0
$631$	−34.8383			−1.38689			−0.693446	−	0.720508i	$-0.743909\pi$
$631$	−34.8383			−1.38689			−0.693446	+	0.720508i	$0.743909\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.41512	−	12.8434i	0.294260	−	0.509673i
$636$		0			0
$637$	21.1192	+	10.6728i	0.836775	+	0.422873i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−7.25538	+	4.18889i	−0.286570	+	0.165451i	−0.636394	−	0.771364i	$-0.719575\pi$
$641$	−7.25538	+	4.18889i	−0.286570	+	0.165451i	0.349824	+	0.936815i	$0.386241\pi$
$642$		0			0
$643$			20.7870i			0.819761i	0.912139	+	0.409881i	$0.134430\pi$
$643$			20.7870i			0.819761i	−0.912139	+	0.409881i	$0.865570\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.74770	+	8.22325i	0.186651	+	0.323289i	0.944132	−	0.329568i	$-0.106903\pi$
$647$	4.74770	+	8.22325i	0.186651	+	0.323289i	−0.757480	+	0.652858i	$0.773570\pi$
$648$		0			0
$649$	−17.0450	−	9.84091i	−0.669073	−	0.386290i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.64747	+	3.83792i	0.260136	+	0.150189i	0.624396	−	0.781108i	$-0.285345\pi$
$653$	6.64747	+	3.83792i	0.260136	+	0.150189i	−0.364261	+	0.931297i	$0.618678\pi$
$654$		0			0
$655$	−14.9927	−	25.9680i	−0.585811	−	1.01465i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			43.9356i			1.71149i	0.517400	+	0.855743i	$0.326900\pi$
$659$			43.9356i			1.71149i	−0.517400	+	0.855743i	$0.673100\pi$
$660$		0			0
$661$	22.1649	−	12.7969i	0.862115	−	0.497742i	−0.00260513	−	0.999997i	$-0.500829\pi$
$661$	22.1649	−	12.7969i	0.862115	−	0.497742i	0.864720	+	0.502254i	$0.167496\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−40.3490	−	21.8213i	−1.56467	−	0.846193i
$666$		0			0
$667$	15.5395	−	26.9151i	0.601691	−	1.04216i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.4210			−0.440903
$672$		0			0
$673$	15.2934			0.589518			0.294759	−	0.955572i	$-0.404761\pi$
$673$	15.2934			0.589518			0.294759	+	0.955572i	$0.404761\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−22.6459	+	39.2238i	−0.870352	+	1.50749i	−0.00871898	+	0.999962i	$0.502775\pi$
$677$	−22.6459	+	39.2238i	−0.870352	+	1.50749i	−0.861633	+	0.507532i	$0.830558\pi$
$678$		0			0
$679$	16.6124	−	10.2180i	0.637524	−	0.392129i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	24.0891	−	13.9079i	0.921744	−	0.532169i	0.0375529	−	0.999295i	$-0.488044\pi$
$683$	24.0891	−	13.9079i	0.921744	−	0.532169i	0.884191	+	0.467126i	$0.154710\pi$
$684$		0			0
$685$			43.8674i			1.67609i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.71672	+	8.16961i	0.179693	+	0.311237i
$690$		0			0
$691$	−14.1115	−	8.14729i	−0.536828	−	0.309938i	0.206965	−	0.978348i	$-0.433641\pi$
$691$	−14.1115	−	8.14729i	−0.536828	−	0.309938i	−0.743792	+	0.668411i	$0.766975\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−18.5862	−	10.7307i	−0.705013	−	0.407040i
$696$		0			0
$697$	−9.88831	−	17.1271i	−0.374546	−	0.648733i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	0.393403i		−	0.0148586i	−0.999972	−	0.00742932i	$-0.997635\pi$
$701$		−	0.393403i		−	0.0148586i	0.999972	−	0.00742932i	$-0.00236485\pi$
$702$		0			0
$703$	19.4980	−	11.2572i	0.735379	−	0.424572i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.97702	−	18.4482i	0.375225	−	0.693816i
$708$		0			0
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	−0.377912	−	0.925841i	$-0.623358\pi$
$709$	16.3183	−	28.2641i	0.612846	−	1.06148i	0.990758	−	0.135639i	$-0.0433087\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.83469			−0.106160
$714$		0			0
$715$	−10.8122			−0.404355
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.106604	−	0.184643i	0.00397565	−	0.00688602i	−0.864031	−	0.503439i	$-0.832068\pi$
$719$	0.106604	−	0.184643i	0.00397565	−	0.00688602i	0.868006	+	0.496553i	$0.165401\pi$
$720$		0			0
$721$	−0.277900	−	9.98081i	−0.0103495	−	0.371705i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.57409	−	0.908804i	0.0584604	−	0.0337521i
$726$		0			0
$727$			36.7435i			1.36274i	0.731939	+	0.681370i	$0.238615\pi$
$727$			36.7435i			1.36274i	−0.731939	+	0.681370i	$0.761385\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.35920	+	5.81831i	0.124245	+	0.215198i
$732$		0			0
$733$	−9.41829	−	5.43765i	−0.347873	−	0.200844i	0.315875	−	0.948801i	$-0.397702\pi$
$733$	−9.41829	−	5.43765i	−0.347873	−	0.200844i	−0.663748	+	0.747956i	$0.731035\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.41104	−	4.27877i	−0.272989	−	0.157610i
$738$		0			0
$739$	6.91282	+	11.9734i	0.254292	+	0.440447i	0.964703	−	0.263340i	$-0.0848242\pi$
$739$	6.91282	+	11.9734i	0.254292	+	0.440447i	−0.710411	+	0.703787i	$0.751491\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			18.3310i			0.672501i	0.941773	+	0.336250i	$0.109159\pi$
$743$			18.3310i			0.672501i	−0.941773	+	0.336250i	$0.890841\pi$
$744$		0			0
$745$	−37.8776	+	21.8687i	−1.38773	+	0.801206i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.585212	+	21.0180i	0.0213832	+	0.767979i
$750$		0			0
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	−0.624748	−	0.780826i	$-0.714798\pi$
$751$	9.97084	−	17.2700i	0.363841	−	0.630191i	0.988589	+	0.150635i	$0.0481318\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	48.5362			1.76641
$756$		0			0
$757$	−46.9292			−1.70567			−0.852836	−	0.522178i	$-0.825119\pi$
$757$	−46.9292			−1.70567			−0.852836	+	0.522178i	$0.825119\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.277093	−	0.960843i	$-0.410629\pi$
$761$	26.7769	−	46.3789i	0.970661	−	1.68123i	0.693568	−	0.720391i	$-0.256038\pi$
$762$		0			0
$763$	1.27153	−	2.35115i	0.0460326	−	0.0851175i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−39.3254	+	22.7045i	−1.41996	+	0.819813i
$768$		0			0
$769$			40.1035i			1.44617i	0.690760	+	0.723085i	$0.257276\pi$
$769$			40.1035i			1.44617i	−0.690760	+	0.723085i	$0.742724\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−7.82375	−	13.5511i	−0.281401	−	0.487400i	0.690329	−	0.723495i	$-0.257466\pi$
$773$	−7.82375	−	13.5511i	−0.281401	−	0.487400i	−0.971730	+	0.236095i	$0.924132\pi$
$774$		0			0
$775$	−0.143572	−	0.0828913i	−0.00515726	−	0.00297755i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−51.4724	−	29.7176i	−1.84419	−	1.06474i
$780$		0			0
$781$	−8.56060	−	14.8274i	−0.306322	−	0.530566i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			17.5267i			0.625553i
$786$		0			0
$787$	39.9920	−	23.0894i	1.42556	−	0.823048i	0.428795	−	0.903402i	$-0.358938\pi$
$787$	39.9920	−	23.0894i	1.42556	−	0.823048i	0.996766	+	0.0803536i	$0.0256050\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	27.4680	−	16.8951i	0.976651	−	0.600720i
$792$		0			0
$793$	−13.1750	+	22.8198i	−0.467859	+	0.810356i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	33.8775			1.20000			0.600002	−	0.799998i	$-0.295166\pi$
$797$	33.8775			1.20000			0.600002	+	0.799998i	$0.295166\pi$
$798$		0			0
$799$	33.1680			1.17340
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.34922	+	5.80102i	−0.118191	+	0.204714i
$804$		0			0
$805$	−20.3703	−	11.0165i	−0.717958	−	0.388281i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−33.7873	+	19.5071i	−1.18790	+	0.685834i	−0.957829	−	0.287340i	$-0.907229\pi$
$809$	−33.7873	+	19.5071i	−1.18790	+	0.685834i	−0.230070	+	0.973174i	$0.573896\pi$
$810$		0			0
$811$		−	7.73397i		−	0.271577i	−0.990738	−	0.135788i	$-0.956643\pi$
$811$		−	7.73397i		−	0.271577i	0.990738	−	0.135788i	$-0.0433567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	13.5915	+	23.5411i	0.476088	+	0.824609i
$816$		0			0
$817$	17.4859	+	10.0955i	0.611755	+	0.353197i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	0.492238	−	0.870460i	$-0.336179\pi$
$821$	−0.443638	−	0.256134i	−0.0154831	−	0.00893915i	−0.507722	+	0.861521i	$0.669512\pi$
$822$		0			0
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	0.887606	+	0.460604i	$0.152367\pi$
$823$	24.1753	+	41.8728i	0.842698	+	1.45960i	−0.0449080	+	0.998991i	$0.514299\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	17.3086i		−	0.601879i	−0.953643	−	0.300940i	$-0.902700\pi$
$827$		−	17.3086i		−	0.601879i	0.953643	−	0.300940i	$-0.0973003\pi$
$828$		0			0
$829$	33.0205	−	19.0644i	1.14685	−	0.662134i	0.198733	−	0.980054i	$-0.436317\pi$
$829$	33.0205	−	19.0644i	1.14685	−	0.662134i	0.948118	+	0.317919i	$0.102984\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−18.4703	+	1.02935i	−0.639959	+	0.0356649i
$834$		0			0
$835$	21.5241	−	37.2808i	0.744871	−	1.29015i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	30.4052			1.04970			0.524852	−	0.851193i	$-0.324121\pi$
$839$	30.4052			1.04970			0.524852	+	0.851193i	$0.324121\pi$
$840$		0			0
$841$	−31.0789			−1.07168
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.71674	−	2.97348i	0.0590577	−	0.102291i
$846$		0			0
$847$	23.4144	−	0.651937i	0.804528	−	0.0224008i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	9.84358	−	5.68319i	0.337434	−	0.194817i
$852$		0			0
$853$			32.0017i			1.09572i	0.836571	+	0.547858i	$0.184557\pi$
$853$			32.0017i			1.09572i	−0.836571	+	0.547858i	$0.815443\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	−0.936889	−	0.349627i	$-0.886308\pi$
$857$	−22.5774	−	39.1053i	−0.771230	−	1.33581i	0.165659	−	0.986183i	$-0.447025\pi$
$858$		0			0
$859$	15.7911	+	9.11701i	0.538786	+	0.311068i	0.744587	−	0.667526i	$-0.232647\pi$
$859$	15.7911	+	9.11701i	0.538786	+	0.311068i	−0.205801	+	0.978594i	$0.565980\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−6.61966	−	3.82186i	−0.225336	−	0.130098i	0.383083	−	0.923714i	$-0.374862\pi$
$863$	−6.61966	−	3.82186i	−0.225336	−	0.130098i	−0.608419	+	0.793616i	$0.708196\pi$
$864$		0			0
$865$	1.99468	+	3.45489i	0.0678213	+	0.117470i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			13.7490i			0.466401i
$870$		0			0
$871$	−17.0984	+	9.87179i	−0.579358	+	0.334493i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.8393	−	25.7515i	−0.535465	−	0.870560i
$876$		0			0
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	−0.969035	−	0.246924i	$-0.920580\pi$
$877$	−8.01581	+	13.8838i	−0.270675	+	0.468822i	0.698360	+	0.715747i	$0.253913\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	24.7532			0.833958			0.416979	−	0.908916i	$-0.363089\pi$
$881$	24.7532			0.833958			0.416979	+	0.908916i	$0.363089\pi$
$882$		0			0
$883$	−11.6958			−0.393595			−0.196798	−	0.980444i	$-0.563054\pi$
$883$	−11.6958			−0.393595			−0.196798	+	0.980444i	$0.563054\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.132921	−	0.991127i	$-0.457564\pi$
$887$	27.5429	−	47.7058i	0.924801	−	1.60180i	0.791880	−	0.610676i	$-0.209102\pi$
$888$		0			0
$889$	−9.41671	−	15.3097i	−0.315826	−	0.513471i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	86.3261	−	49.8404i	2.88879	−	1.66785i
$894$		0			0
$895$		−	30.5465i		−	1.02106i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.73987	+	4.74560i	0.0913799	+	0.158275i
$900$		0			0
$901$	−6.38677	−	3.68741i	−0.212774	−	0.122845i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.9281	−	17.8563i	−1.02808	−	0.593565i
$906$		0			0
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	0.996839	−	0.0794540i	$-0.0253177\pi$
$907$	12.9383	+	22.4098i	0.429610	+	0.744107i	−0.567228	+	0.823560i	$0.691984\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	4.46068i		−	0.147789i	−0.997266	−	0.0738944i	$-0.976457\pi$
$911$		−	4.46068i		−	0.147789i	0.997266	−	0.0738944i	$-0.0235428\pi$
$912$		0			0
$913$	−4.33572	+	2.50323i	−0.143491	+	0.0828448i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−36.3274	+	1.01148i	−1.19964	+	0.0334020i
$918$		0			0
$919$	−21.2352	+	36.7805i	−0.700485	+	1.21328i	0.267811	+	0.963471i	$0.413700\pi$
$919$	−21.2352	+	36.7805i	−0.700485	+	1.21328i	−0.968296	+	0.249804i	$0.919634\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−39.5013			−1.30020
$924$		0			0
$925$	0.664747			0.0218567
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.72508	−	13.3802i	0.253452	−	0.438991i	−0.711022	−	0.703170i	$-0.751767\pi$
$929$	7.72508	−	13.3802i	0.253452	−	0.438991i	0.964474	+	0.264178i	$0.0851008\pi$
$930$		0			0
$931$	−46.5257	+	30.4338i	−1.52482	+	0.997426i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.32027	−	4.22636i	0.239398	−	0.138217i
$936$		0			0
$937$		−	46.1410i		−	1.50736i	−0.657241	−	0.753680i	$-0.728277\pi$
$937$		−	46.1410i		−	1.50736i	0.657241	−	0.753680i	$-0.271723\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	20.5052	+	35.5161i	0.668451	+	1.15779i	0.978337	+	0.207017i	$0.0663756\pi$
$941$	20.5052	+	35.5161i	0.668451	+	1.15779i	−0.309886	+	0.950774i	$0.600291\pi$
$942$		0			0
$943$	−25.9859	−	15.0030i	−0.846218	−	0.488564i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	0.355378	−	0.934723i	$-0.384352\pi$
$947$	−8.50657	−	4.91127i	−0.276426	−	0.159595i	−0.631804	+	0.775128i	$0.717685\pi$
$948$		0			0
$949$	7.72718	+	13.3839i	0.250835	+	0.434459i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	17.0826i		−	0.553359i	−0.960962	−	0.276679i	$-0.910766\pi$
$953$		−	17.0826i		−	0.553359i	0.960962	−	0.276679i	$-0.0892340\pi$
$954$		0			0
$955$	−25.8305	+	14.9132i	−0.835855	+	0.482581i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	46.7655	+	25.2914i	1.51014	+	0.816701i
$960$		0			0
$961$	−15.2501	+	26.4139i	−0.491939	+	0.852063i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	9.55652			0.307635
$966$		0			0
$967$	−42.6481			−1.37147			−0.685735	−	0.727852i	$-0.740519\pi$
$967$	−42.6481			−1.37147			−0.685735	+	0.727852i	$0.740519\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.7562	−	20.3623i	0.377275	−	0.653459i	−0.613390	−	0.789780i	$-0.710195\pi$
$971$	11.7562	−	20.3623i	0.377275	−	0.653459i	0.990665	+	0.136321i	$0.0435280\pi$
$972$		0			0
$973$	−22.1553	+	13.6273i	−0.710267	+	0.436872i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.898015	−	0.439964i	$-0.854991\pi$
$977$	−30.1944	+	17.4327i	−0.966003	+	0.557722i	−0.0679878	+	0.997686i	$0.521658\pi$
$978$		0			0
$979$		−	13.5365i		−	0.432627i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	0.575587	−	0.817740i	$-0.304773\pi$
$983$	−13.1804	−	22.8292i	−0.420390	−	0.728137i	−0.995978	+	0.0896033i	$0.971440\pi$
$984$		0			0
$985$	1.90194	+	1.09808i	0.0606008	+	0.0349879i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.82780	+	5.09673i	0.280708	+	0.162067i
$990$		0			0
$991$	0.0805213	+	0.139467i	0.00255784	+	0.00443031i	0.867301	−	0.497783i	$-0.165852\pi$
$991$	0.0805213	+	0.139467i	0.00255784	+	0.00443031i	−0.864744	+	0.502214i	$0.832519\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			14.3085i			0.453611i
$996$		0			0
$997$	−14.5820	+	8.41890i	−0.461816	+	0.266629i	−0.712807	−	0.701360i	$-0.752577\pi$
$997$	−14.5820	+	8.41890i	−0.461816	+	0.266629i	0.250992	+	0.967989i	$0.419243\pi$
$998$		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.2105.6		16
3.2	odd	2		2268.2.t.a.2105.3		16
7.3	odd	6		2268.2.t.a.1781.3		16
9.2	odd	6		756.2.w.a.341.3		16
9.4	even	3		756.2.bm.a.89.3		16
9.5	odd	6		252.2.bm.a.173.4	yes	16
9.7	even	3		252.2.w.a.5.2	✓	16
21.17	even	6	inner	2268.2.t.b.1781.6		16
36.7	odd	6		1008.2.ca.d.257.7		16
36.11	even	6		3024.2.ca.d.2609.3		16
36.23	even	6		1008.2.df.d.929.5		16
36.31	odd	6		3024.2.df.d.1601.3		16
63.2	odd	6		5292.2.x.a.881.3		16
63.4	even	3		5292.2.w.b.521.6		16
63.5	even	6		1764.2.x.a.1469.7		16
63.11	odd	6		5292.2.bm.a.2285.6		16
63.13	odd	6		5292.2.bm.a.4625.6		16
63.16	even	3		1764.2.x.a.293.7		16
63.20	even	6		5292.2.w.b.1097.6		16
63.23	odd	6		1764.2.x.b.1469.2		16
63.25	even	3		1764.2.bm.a.1697.5		16
63.31	odd	6		756.2.w.a.521.3		16
63.32	odd	6		1764.2.w.b.1109.7		16
63.34	odd	6		1764.2.w.b.509.7		16
63.38	even	6		756.2.bm.a.17.3		16
63.40	odd	6		5292.2.x.a.4409.3		16
63.41	even	6		1764.2.bm.a.1685.5		16
63.47	even	6		5292.2.x.b.881.6		16
63.52	odd	6		252.2.bm.a.185.4	yes	16
63.58	even	3		5292.2.x.b.4409.6		16
63.59	even	6		252.2.w.a.101.2	yes	16
63.61	odd	6		1764.2.x.b.293.2		16
252.31	even	6		3024.2.ca.d.2033.3		16
252.59	odd	6		1008.2.ca.d.353.7		16
252.115	even	6		1008.2.df.d.689.5		16
252.227	odd	6		3024.2.df.d.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.2	✓	16	9.7	even	3
252.2.w.a.101.2	yes	16	63.59	even	6
252.2.bm.a.173.4	yes	16	9.5	odd	6
252.2.bm.a.185.4	yes	16	63.52	odd	6
756.2.w.a.341.3		16	9.2	odd	6
756.2.w.a.521.3		16	63.31	odd	6
756.2.bm.a.17.3		16	63.38	even	6
756.2.bm.a.89.3		16	9.4	even	3
1008.2.ca.d.257.7		16	36.7	odd	6
1008.2.ca.d.353.7		16	252.59	odd	6
1008.2.df.d.689.5		16	252.115	even	6
1008.2.df.d.929.5		16	36.23	even	6
1764.2.w.b.509.7		16	63.34	odd	6
1764.2.w.b.1109.7		16	63.32	odd	6
1764.2.x.a.293.7		16	63.16	even	3
1764.2.x.a.1469.7		16	63.5	even	6
1764.2.x.b.293.2		16	63.61	odd	6
1764.2.x.b.1469.2		16	63.23	odd	6
1764.2.bm.a.1685.5		16	63.41	even	6
1764.2.bm.a.1697.5		16	63.25	even	3
2268.2.t.a.1781.3		16	7.3	odd	6
2268.2.t.a.2105.3		16	3.2	odd	2
2268.2.t.b.1781.6		16	21.17	even	6	inner
2268.2.t.b.2105.6		16	1.1	even	1	trivial
3024.2.ca.d.2033.3		16	252.31	even	6
3024.2.ca.d.2609.3		16	36.11	even	6
3024.2.df.d.17.3		16	252.227	odd	6
3024.2.df.d.1601.3		16	36.31	odd	6
5292.2.w.b.521.6		16	63.4	even	3
5292.2.w.b.1097.6		16	63.20	even	6
5292.2.x.a.881.3		16	63.2	odd	6
5292.2.x.a.4409.3		16	63.40	odd	6
5292.2.x.b.881.6		16	63.47	even	6
5292.2.x.b.4409.6		16	63.58	even	3
5292.2.bm.a.2285.6		16	63.11	odd	6
5292.2.bm.a.4625.6		16	63.13	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)

\(f(q)\)	\(=\)	\(q+(1.09150 - 1.89054i) q^{5} +(-1.38614 - 2.25358i) q^{7} +O(q^{10})\)	\(q+(1.09150 - 1.89054i) q^{5} +(-1.38614 - 2.25358i) q^{7} +(1.26889 - 0.732592i) q^{11} -3.38041i q^{13} +(1.32136 + 2.28866i) q^{17} +(6.87816 + 3.97111i) q^{19} +(3.47245 + 2.00482i) q^{23} +(0.117249 + 0.203081i) q^{25} -7.75105i q^{29} +(-0.612252 + 0.353484i) q^{31} +(-5.77345 + 0.160752i) q^{35} +(1.41738 - 2.45498i) q^{37} -7.48345 q^{41} +2.54224 q^{43} +(6.27538 - 10.8693i) q^{47} +(-3.15726 + 6.24754i) q^{49} +(-2.41675 + 1.39531i) q^{53} -3.19850i q^{55} +(-6.71650 - 11.6333i) q^{59} +(-6.75061 - 3.89747i) q^{61} +(-6.39079 - 3.68972i) q^{65} +(-2.92029 - 5.05809i) q^{67} -11.6854i q^{71} +(-3.95924 + 2.28587i) q^{73} +(-3.40980 - 1.84407i) q^{77} +(-4.69189 + 8.12659i) q^{79} -3.41695 q^{83} +5.76905 q^{85} +(4.61937 - 8.00099i) q^{89} +(-7.61803 + 4.68571i) q^{91} +(15.0150 - 8.66894i) q^{95} +7.37154i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 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

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