LMFDB - Embedded newform 2268.2.t.a.2105.8

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			2105.8
Root			$-0.544978 - 1.64408i$ of defining polynomial
Character	$\chi$	$=$	2268.2105
Dual form			2268.2.t.a.1781.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95741 - 3.39033i) q^{5} +(1.96333 + 1.77351i) q^{7} +O(q^{10})$	$q+(1.95741 - 3.39033i) q^{5} +(1.96333 + 1.77351i) q^{7} +(-3.19958 + 1.84728i) q^{11} -0.554535i q^{13} +(-2.91916 - 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(-1.96965 - 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} -4.08346i q^{29} +(7.00132 - 4.04222i) q^{31} +(9.85583 - 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +7.18469 q^{41} +1.50802 q^{43} +(-1.41416 + 2.44940i) q^{47} +(0.709320 + 6.96397i) q^{49} +(0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +(-4.45656 - 7.71900i) q^{59} +(-6.03343 - 3.48340i) q^{61} +(-1.88006 - 1.08545i) q^{65} +(-0.587402 - 1.01741i) q^{67} -6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-9.55800 - 2.04768i) q^{77} +(1.97374 - 3.41861i) q^{79} +7.69348 q^{83} -22.8560 q^{85} +(2.71300 - 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(18.1035 - 10.4520i) q^{95} +16.1513i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.95741	−	3.39033i	0.875381	−	1.51620i	0.0190238	−	0.999819i	$-0.493944\pi$
$5$	1.95741	−	3.39033i	0.875381	−	1.51620i	0.856357	−	0.516385i	$-0.172722\pi$
$6$		0			0
$7$	1.96333	+	1.77351i	0.742069	+	0.670324i
$7$	1.96333	+	1.77351i	0.742069	+	0.670324i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.19958	+	1.84728i	−0.964710	+	0.556976i	−0.897620	−	0.440771i	$-0.854705\pi$
$11$	−3.19958	+	1.84728i	−0.964710	+	0.556976i	−0.0670908	+	0.997747i	$0.521372\pi$
$12$		0			0
$13$		−	0.554535i		−	0.153800i	−0.997039	−	0.0769002i	$-0.975498\pi$
$13$		−	0.554535i		−	0.153800i	0.997039	−	0.0769002i	$-0.0245023\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.91916	−	5.05613i	−0.708000	−	1.22629i	−0.965598	−	0.260040i	$-0.916264\pi$
$17$	−2.91916	−	5.05613i	−0.708000	−	1.22629i	0.257598	−	0.966252i	$-0.417069\pi$
$18$		0			0
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.925680	−	0.378307i	$-0.123494\pi$
$19$	4.62434	+	2.66986i	1.06090	+	0.612509i	0.135216	+	0.990816i	$0.456827\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.96965	−	1.13718i	−0.410700	−	0.237118i	0.280390	−	0.959886i	$-0.409536\pi$
$23$	−1.96965	−	1.13718i	−0.410700	−	0.237118i	−0.691090	+	0.722768i	$0.742869\pi$
$24$		0			0
$25$	−5.16291	−	8.94242i	−1.03258	−	1.78848i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	4.08346i		−	0.758280i	−0.925339	−	0.379140i	$-0.876220\pi$
$29$		−	4.08346i		−	0.758280i	0.925339	−	0.379140i	$-0.123780\pi$
$30$		0			0
$31$	7.00132	−	4.04222i	1.25748	−	0.726004i	0.284892	−	0.958560i	$-0.408042\pi$
$31$	7.00132	−	4.04222i	1.25748	−	0.726004i	0.972583	+	0.232556i	$0.0747089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	9.85583	−	3.18485i	1.66594	−	0.538338i
$36$		0			0
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	−0.344322	−	0.938852i	$-0.611891\pi$
$37$	3.89849	−	6.75239i	0.640909	−	1.11009i	0.985230	−	0.171235i	$-0.0547756\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.18469			1.12206			0.561030	−	0.827796i	$-0.310405\pi$
$41$	7.18469			1.12206			0.561030	+	0.827796i	$0.310405\pi$
$42$		0			0
$43$	1.50802			0.229971			0.114985	−	0.993367i	$-0.463318\pi$
$43$	1.50802			0.229971			0.114985	+	0.993367i	$0.463318\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.41416	+	2.44940i	−0.206277	+	0.357282i	−0.950539	−	0.310606i	$-0.899468\pi$
$47$	−1.41416	+	2.44940i	−0.206277	+	0.357282i	0.744262	+	0.667888i	$0.232801\pi$
$48$		0			0
$49$	0.709320	+	6.96397i	0.101331	+	0.994853i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	−0.497143	−	0.867669i	$-0.665617\pi$
$53$	0.0415658	−	0.0239980i	0.00570950	−	0.00329638i	0.502852	+	0.864373i	$0.332284\pi$
$54$		0			0
$55$			14.4635i			1.95026i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.45656	−	7.71900i	−0.580195	−	1.00493i	−0.995456	−	0.0952251i	$-0.969643\pi$
$59$	−4.45656	−	7.71900i	−0.580195	−	1.00493i	0.415261	−	0.909703i	$-0.363690\pi$
$60$		0			0
$61$	−6.03343	−	3.48340i	−0.772501	−	0.446004i	0.0612648	−	0.998122i	$-0.480487\pi$
$61$	−6.03343	−	3.48340i	−0.772501	−	0.446004i	−0.833766	+	0.552118i	$0.813820\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.88006	−	1.08545i	−0.233193	−	0.134634i
$66$		0			0
$67$	−0.587402	−	1.01741i	−0.0717626	−	0.124296i	0.827911	−	0.560859i	$-0.189529\pi$
$67$	−0.587402	−	1.01741i	−0.0717626	−	0.124296i	−0.899674	+	0.436563i	$0.856196\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	6.71061i		−	0.796403i	−0.917298	−	0.398202i	$-0.869634\pi$
$71$		−	6.71061i		−	0.796403i	0.917298	−	0.398202i	$-0.130366\pi$
$72$		0			0
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	−0.691990	−	0.721907i	$-0.743266\pi$
$73$	−3.52692	+	2.03627i	−0.412795	+	0.238327i	0.279195	+	0.960234i	$0.409932\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.55800	−	2.04768i	−1.08924	−	0.233354i
$78$		0			0
$79$	1.97374	−	3.41861i	0.222063	−	0.384624i	−0.733371	−	0.679828i	$-0.762054\pi$
$79$	1.97374	−	3.41861i	0.222063	−	0.384624i	0.955434	+	0.295204i	$0.0953877\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.69348			0.844469			0.422235	−	0.906487i	$-0.361246\pi$
$83$	7.69348			0.844469			0.422235	+	0.906487i	$0.361246\pi$
$84$		0			0
$85$	−22.8560			−2.47908
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.71300	−	4.69905i	0.287577	−	0.498099i	−0.685654	−	0.727928i	$-0.740483\pi$
$89$	2.71300	−	4.69905i	0.287577	−	0.498099i	0.973231	+	0.229829i	$0.0738168\pi$
$90$		0			0
$91$	0.983474	−	1.08874i	0.103096	−	0.114130i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	18.1035	−	10.4520i	1.85738	−	1.07236i
$96$		0			0
$97$			16.1513i			1.63991i	0.572426	+	0.819956i	$0.306002\pi$
$97$			16.1513i			1.63991i	−0.572426	+	0.819956i	$0.693998\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.811750	−	1.40599i	−0.0807722	−	0.139901i	0.822810	−	0.568317i	$-0.192405\pi$
$101$	−0.811750	−	1.40599i	−0.0807722	−	0.139901i	−0.903582	+	0.428416i	$0.859072\pi$
$102$		0			0
$103$	0.342653	+	0.197831i	0.0337626	+	0.0194929i	0.516786	−	0.856114i	$-0.327128\pi$
$103$	0.342653	+	0.197831i	0.0337626	+	0.0194929i	−0.483024	+	0.875607i	$0.660461\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	0.718101	−	0.695938i	$-0.245011\pi$
$107$	4.90777	+	2.83350i	0.474452	+	0.273925i	−0.243650	+	0.969863i	$0.578345\pi$
$108$		0			0
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	−0.983795	−	0.179294i	$-0.942619\pi$
$109$	−6.75667	−	11.7029i	−0.647171	−	1.12093i	0.336624	−	0.941639i	$-0.390715\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			1.31232i			0.123453i	0.998093	+	0.0617265i	$0.0196607\pi$
$113$			1.31232i			0.123453i	−0.998093	+	0.0617265i	$0.980339\pi$
$114$		0			0
$115$	−7.71082	+	4.45184i	−0.719038	+	0.415137i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.23583	−	15.1040i	0.296628	−	1.38458i
$120$		0			0
$121$	1.32489	−	2.29477i	0.120444	−	0.208615i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−20.8496			−1.86485
$126$		0			0
$127$	−17.3935			−1.54342			−0.771710	−	0.635975i	$-0.780598\pi$
$127$	−17.3935			−1.54342			−0.771710	+	0.635975i	$0.780598\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.45361	+	9.44593i	−0.476484	+	0.825295i	−0.999637	−	0.0269442i	$-0.991422\pi$
$131$	−5.45361	+	9.44593i	−0.476484	+	0.825295i	0.523153	+	0.852239i	$0.324756\pi$
$132$		0			0
$133$	4.34407	+	13.4431i	0.376679	+	1.16567i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.62547	−	4.40257i	0.651488	−	0.376137i	−0.137538	−	0.990496i	$-0.543919\pi$
$137$	7.62547	−	4.40257i	0.651488	−	0.376137i	0.789026	+	0.614360i	$0.210586\pi$
$138$		0			0
$139$			16.4374i			1.39420i	0.716974	+	0.697100i	$0.245527\pi$
$139$			16.4374i			1.39420i	−0.716974	+	0.697100i	$0.754473\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.02438	+	1.77428i	0.0856631	+	0.148373i
$144$		0			0
$145$	−13.8443	−	7.99301i	−1.14971	−	0.663783i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	12.5814	+	7.26390i	1.03071	+	0.595082i	0.917188	−	0.398454i	$-0.130453\pi$
$149$	12.5814	+	7.26390i	1.03071	+	0.595082i	0.113523	+	0.993535i	$0.463786\pi$
$150$		0			0
$151$	−2.80307	−	4.85505i	−0.228110	−	0.395099i	0.729138	−	0.684367i	$-0.239921\pi$
$151$	−2.80307	−	4.85505i	−0.228110	−	0.395099i	−0.957248	+	0.289268i	$0.906588\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	31.6491i		−	2.54212i
$156$		0			0
$157$	15.4411	−	8.91493i	1.23233	−	0.711489i	0.264819	−	0.964298i	$-0.414688\pi$
$157$	15.4411	−	8.91493i	1.23233	−	0.711489i	0.967516	+	0.252809i	$0.0813545\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.85027	−	5.72584i	−0.145822	−	0.451260i
$162$		0			0
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	−0.887737	−	0.460350i	$-0.847724\pi$
$163$	−0.576994	+	0.999383i	−0.0451937	+	0.0782777i	0.842544	+	0.538628i	$0.181057\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.9110			−1.38599			−0.692997	−	0.720940i	$-0.743710\pi$
$167$	−17.9110			−1.38599			−0.692997	+	0.720940i	$0.743710\pi$
$168$		0			0
$169$	12.6925			0.976345
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.74814	−	6.49197i	0.284966	−	0.493576i	−0.687635	−	0.726057i	$-0.741351\pi$
$173$	3.74814	−	6.49197i	0.284966	−	0.493576i	0.972601	+	0.232481i	$0.0746843\pi$
$174$		0			0
$175$	5.72299	−	26.7134i	0.432618	−	2.01934i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	−0.523153	−	0.852239i	$-0.675244\pi$
$179$	−0.624382	+	0.360487i	−0.0466685	+	0.0269441i	0.476484	+	0.879183i	$0.341911\pi$
$180$		0			0
$181$		−	5.07121i		−	0.376940i	−0.982079	−	0.188470i	$-0.939647\pi$
$181$		−	5.07121i		−	0.376940i	0.982079	−	0.188470i	$-0.0603529\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−15.2619	−	26.4344i	−1.12208	−	1.94350i
$186$		0			0
$187$	18.6802	+	10.7850i	1.36603	+	0.788678i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	11.0005	+	6.35111i	0.795965	+	0.459551i	0.842058	−	0.539387i	$-0.181344\pi$
$191$	11.0005	+	6.35111i	0.795965	+	0.459551i	−0.0460934	+	0.998937i	$0.514677\pi$
$192$		0			0
$193$	11.4076	+	19.7586i	0.821140	+	1.42226i	0.904834	+	0.425765i	$0.139995\pi$
$193$	11.4076	+	19.7586i	0.821140	+	1.42226i	−0.0836931	+	0.996492i	$0.526672\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	0.0311360i		−	0.00221835i	−0.999999	−	0.00110918i	$-0.999647\pi$
$197$		−	0.0311360i		−	0.00221835i	0.999999	−	0.00110918i	$-0.000353062\pi$
$198$		0			0
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.416146	−	0.909298i	$-0.363380\pi$
$199$	19.9144	−	11.4976i	1.41169	−	0.815042i	0.995548	+	0.0942556i	$0.0300471\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.24206	−	8.01718i	0.508293	−	0.562696i
$204$		0			0
$205$	14.0634	−	24.3585i	0.982229	−	1.70127i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−19.7279			−1.36461
$210$		0			0
$211$	−17.1168			−1.17837			−0.589185	−	0.807998i	$-0.700551\pi$
$211$	−17.1168			−1.17837			−0.589185	+	0.807998i	$0.700551\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.95181	−	5.11268i	0.201312	−	0.348682i
$216$		0			0
$217$	20.9148	+	4.48072i	1.41979	+	0.304171i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.80380	+	1.61878i	−0.188604	+	0.108891i
$222$		0			0
$223$			1.44603i			0.0968334i	0.998827	+	0.0484167i	$0.0154175\pi$
$223$			1.44603i			0.0968334i	−0.998827	+	0.0484167i	$0.984582\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.23596	+	3.87280i	0.148406	+	0.257047i	0.930639	−	0.365940i	$-0.119252\pi$
$227$	2.23596	+	3.87280i	0.148406	+	0.257047i	−0.782232	+	0.622987i	$0.785919\pi$
$228$		0			0
$229$	−2.24072	−	1.29368i	−0.148071	−	0.0854888i	0.424134	−	0.905599i	$-0.360579\pi$
$229$	−2.24072	−	1.29368i	−0.148071	−	0.0854888i	−0.572205	+	0.820111i	$0.693912\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.0830679	−	0.996544i	$-0.526472\pi$
$233$	−15.0756	−	8.70389i	−0.987634	−	0.570211i	−0.904566	+	0.426333i	$0.859805\pi$
$234$		0			0
$235$	5.53620	+	9.58898i	0.361142	+	0.625516i
$236$		0			0
$237$		0			0
$238$		0			0
$239$			4.89179i			0.316424i	0.987405	+	0.158212i	$0.0505729\pi$
$239$			4.89179i			0.316424i	−0.987405	+	0.158212i	$0.949427\pi$
$240$		0			0
$241$	−7.04282	+	4.06618i	−0.453668	+	0.261925i	−0.709378	−	0.704828i	$-0.751024\pi$
$241$	−7.04282	+	4.06618i	−0.453668	+	0.261925i	0.255710	+	0.966754i	$0.417691\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	24.9986	+	11.2265i	1.59710	+	0.717236i
$246$		0			0
$247$	1.48053	−	2.56436i	0.0942041	−	0.163166i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	25.9341			1.63694			0.818472	−	0.574546i	$-0.194821\pi$
$251$	25.9341			1.63694			0.818472	+	0.574546i	$0.194821\pi$
$252$		0			0
$253$	8.40274			0.528276
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.4115	+	26.6935i	−0.961344	+	1.66510i	−0.242213	+	0.970223i	$0.577873\pi$
$257$	−15.4115	+	26.6935i	−0.961344	+	1.66510i	−0.719131	+	0.694874i	$0.755460\pi$
$258$		0			0
$259$	19.6295	−	6.34314i	1.21972	−	0.394144i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−15.6625	+	9.04276i	−0.965792	+	0.557600i	−0.897951	−	0.440096i	$-0.854944\pi$
$263$	−15.6625	+	9.04276i	−0.965792	+	0.557600i	−0.0678413	+	0.997696i	$0.521611\pi$
$264$		0			0
$265$		−	0.187896i		−	0.0115423i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.8203	+	18.7413i	0.659725	+	1.14268i	0.980687	+	0.195585i	$0.0626607\pi$
$269$	10.8203	+	18.7413i	0.659725	+	1.14268i	−0.320961	+	0.947092i	$0.604006\pi$
$270$		0			0
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	0.0757430	−	0.997127i	$-0.475867\pi$
$271$	−12.3453	−	7.12756i	−0.749923	−	0.432968i	−0.825666	+	0.564159i	$0.809200\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	33.0383	+	19.0747i	1.99229	+	1.15025i
$276$		0			0
$277$	−4.40164	−	7.62386i	−0.264469	−	0.458073i	0.702956	−	0.711234i	$-0.251863\pi$
$277$	−4.40164	−	7.62386i	−0.264469	−	0.458073i	−0.967424	+	0.253160i	$0.918530\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			19.2707i			1.14960i	0.818296	+	0.574798i	$0.194919\pi$
$281$			19.2707i			1.14960i	−0.818296	+	0.574798i	$0.805081\pi$
$282$		0			0
$283$	8.32822	−	4.80830i	0.495061	−	0.285824i	−0.231611	−	0.972809i	$-0.574399\pi$
$283$	8.32822	−	4.80830i	0.495061	−	0.285824i	0.726672	+	0.686985i	$0.241066\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.1059	+	12.7421i	0.832645	+	0.752144i
$288$		0			0
$289$	−8.54297	+	14.7969i	−0.502528	+	0.870404i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.45196			0.143245			0.0716225	−	0.997432i	$-0.477182\pi$
$293$	2.45196			0.143245			0.0716225	+	0.997432i	$0.477182\pi$
$294$		0			0
$295$	−34.8933			−2.03157
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.630605	+	1.09224i	−0.0364688	+	0.0631658i
$300$		0			0
$301$	2.96073	+	2.67449i	0.170654	+	0.154155i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−23.6198	+	13.6369i	−1.35247	+	0.780846i
$306$		0			0
$307$		−	10.6839i		−	0.609760i	−0.952391	−	0.304880i	$-0.901384\pi$
$307$		−	10.6839i		−	0.609760i	0.952391	−	0.304880i	$-0.0986163\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.3833	−	17.9843i	−0.588780	−	1.01980i	−0.994393	−	0.105752i	$-0.966275\pi$
$311$	−10.3833	−	17.9843i	−0.588780	−	1.01980i	0.405612	−	0.914045i	$-0.367058\pi$
$312$		0			0
$313$	−3.40449	−	1.96558i	−0.192433	−	0.111101i	0.400688	−	0.916215i	$-0.368771\pi$
$313$	−3.40449	−	1.96558i	−0.192433	−	0.111101i	−0.593121	+	0.805113i	$0.702104\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.98369	−	1.14528i	−0.111415	−	0.0643256i	0.443257	−	0.896395i	$-0.353823\pi$
$317$	−1.98369	−	1.14528i	−0.111415	−	0.0643256i	−0.554672	+	0.832069i	$0.687156\pi$
$318$		0			0
$319$	7.54330	+	13.0654i	0.422344	+	0.731521i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	31.1750i		−	1.73462i
$324$		0			0
$325$	−4.95889	+	2.86302i	−0.275070	+	0.158812i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.12051	+	2.30095i	−0.392567	+	0.126856i
$330$		0			0
$331$	−3.46788	+	6.00655i	−0.190612	+	0.330150i	−0.945453	−	0.325758i	$-0.894381\pi$
$331$	−3.46788	+	6.00655i	−0.190612	+	0.330150i	0.754841	+	0.655908i	$0.227714\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.59915			−0.251278
$336$		0			0
$337$	19.1954			1.04564			0.522821	−	0.852443i	$-0.324880\pi$
$337$	19.1954			1.04564			0.522821	+	0.852443i	$0.324880\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−14.9342	+	25.8668i	−0.808733	+	1.40077i
$342$		0			0
$343$	−10.9580	+	14.9305i	−0.591679	+	0.806174i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.35287	−	4.24518i	0.394723	−	0.227893i	−0.289482	−	0.957184i	$-0.593483\pi$
$347$	7.35287	−	4.24518i	0.394723	−	0.227893i	0.684204	+	0.729290i	$0.260150\pi$
$348$		0			0
$349$		−	19.1077i		−	1.02281i	−0.859339	−	0.511407i	$-0.829125\pi$
$349$		−	19.1077i		−	1.02281i	0.859339	−	0.511407i	$-0.170875\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.82951	−	11.8291i	−0.363498	−	0.629597i	0.625036	−	0.780596i	$-0.285084\pi$
$353$	−6.82951	−	11.8291i	−0.363498	−	0.629597i	−0.988534	+	0.150999i	$0.951751\pi$
$354$		0			0
$355$	−22.7512	−	13.1354i	−1.20751	−	0.697156i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	0.838520	−	0.544870i	$-0.183421\pi$
$359$	14.8909	+	8.59724i	0.785909	+	0.453745i	−0.0526113	+	0.998615i	$0.516754\pi$
$360$		0			0
$361$	4.75635	+	8.23824i	0.250334	+	0.433592i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			15.9432i			0.834507i
$366$		0			0
$367$	−14.6001	+	8.42936i	−0.762118	+	0.440009i	−0.830056	−	0.557680i	$-0.811691\pi$
$367$	−14.6001	+	8.42936i	−0.762118	+	0.440009i	0.0679376	+	0.997690i	$0.478358\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.124168	+	0.0266014i	0.00644648	+	0.00138107i
$372$		0			0
$373$	0.704288	−	1.21986i	0.0364667	−	0.0631621i	−0.847216	−	0.531248i	$-0.821723\pi$
$373$	0.704288	−	1.21986i	0.0364667	−	0.0631621i	0.883683	+	0.468086i	$0.155056\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.26442			−0.116624
$378$		0			0
$379$	−0.598572			−0.0307466			−0.0153733	−	0.999882i	$-0.504894\pi$
$379$	−0.598572			−0.0307466			−0.0153733	+	0.999882i	$0.504894\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.26039	−	7.37921i	0.217696	−	0.377060i	−0.736407	−	0.676538i	$-0.763479\pi$
$383$	4.26039	−	7.37921i	0.217696	−	0.377060i	0.954103	+	0.299478i	$0.0968127\pi$
$384$		0			0
$385$	−25.6512	+	28.3967i	−1.30731	+	1.44723i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−29.9624	+	17.2988i	−1.51915	+	0.877084i	−0.519409	+	0.854526i	$0.673848\pi$
$389$	−29.9624	+	17.2988i	−1.51915	+	0.877084i	−0.999746	+	0.0225587i	$0.992819\pi$
$390$		0			0
$391$			13.2784i			0.671518i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.72683	−	13.3833i	−0.388779	−	0.673385i
$396$		0			0
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.994712	−	0.102699i	$-0.0327478\pi$
$397$	27.9571	+	16.1411i	1.40313	+	0.810097i	0.408416	+	0.912796i	$0.366081\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.3473	+	6.55139i	0.566659	+	0.327161i	0.755814	−	0.654787i	$-0.227242\pi$
$401$	11.3473	+	6.55139i	0.566659	+	0.327161i	−0.189155	+	0.981947i	$0.560575\pi$
$402$		0			0
$403$	−2.24155	−	3.88248i	−0.111660	−	0.193400i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			28.8064i			1.42788i
$408$		0			0
$409$	−32.3493	+	18.6769i	−1.59957	+	0.923513i	−0.608002	+	0.793936i	$0.708029\pi$
$409$	−32.3493	+	18.6769i	−1.59957	+	0.923513i	−0.991569	+	0.129577i	$0.958638\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.94002	−	23.0587i	0.243082	−	1.13464i
$414$		0			0
$415$	15.0593	−	26.0835i	0.739232	−	1.28039i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	28.3908			1.38698			0.693490	−	0.720467i	$-0.256072\pi$
$419$	28.3908			1.38698			0.693490	+	0.720467i	$0.256072\pi$
$420$		0			0
$421$	34.6719			1.68980			0.844901	−	0.534922i	$-0.179659\pi$
$421$	34.6719			1.68980			0.844901	+	0.534922i	$0.179659\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−30.1427	+	52.2087i	−1.46214	+	2.53249i
$426$		0			0
$427$	−5.66775	−	17.5394i	−0.274282	−	0.848792i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	−0.782713	−	0.622383i	$-0.786165\pi$
$431$	−13.1844	+	7.61200i	−0.635069	+	0.366657i	0.147643	+	0.989041i	$0.452831\pi$
$432$		0			0
$433$			3.97041i			0.190806i	0.995439	+	0.0954028i	$0.0304139\pi$
$433$			3.97041i			0.190806i	−0.995439	+	0.0954028i	$0.969586\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.07222	−	10.5174i	−0.290474	−	0.503115i
$438$		0			0
$439$	−8.21910	−	4.74530i	−0.392276	−	0.226481i	0.290870	−	0.956763i	$-0.406055\pi$
$439$	−8.21910	−	4.74530i	−0.392276	−	0.226481i	−0.683146	+	0.730282i	$0.739389\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.3955	+	16.3942i	1.34911	+	0.778910i	0.988124	−	0.153660i	$-0.0491060\pi$
$443$	28.3955	+	16.3942i	1.34911	+	0.778910i	0.360989	+	0.932570i	$0.382439\pi$
$444$		0			0
$445$	−10.6209	−	18.3960i	−0.503479	−	0.872052i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			0.658896i			0.0310952i	0.999879	+	0.0155476i	$0.00494916\pi$
$449$			0.658896i			0.0310952i	−0.999879	+	0.0155476i	$0.995051\pi$
$450$		0			0
$451$	−22.9880	+	13.2721i	−1.08246	+	0.624960i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.76611	−	5.46541i	−0.0827967	−	0.256222i
$456$		0			0
$457$	−7.94514	+	13.7614i	−0.371658	+	0.643730i	−0.989821	−	0.142320i	$-0.954544\pi$
$457$	−7.94514	+	13.7614i	−0.371658	+	0.643730i	0.618163	+	0.786050i	$0.287877\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.6325			−0.914378			−0.457189	−	0.889370i	$-0.651144\pi$
$461$	−19.6325			−0.914378			−0.457189	+	0.889370i	$0.651144\pi$
$462$		0			0
$463$	−1.20032			−0.0557835			−0.0278918	−	0.999611i	$-0.508879\pi$
$463$	−1.20032			−0.0557835			−0.0278918	+	0.999611i	$0.508879\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.2809	+	33.3955i	−0.892213	+	1.54536i	−0.0549972	+	0.998487i	$0.517515\pi$
$467$	−19.2809	+	33.3955i	−0.892213	+	1.54536i	−0.837216	+	0.546872i	$0.815818\pi$
$468$		0			0
$469$	0.651124	−	3.03927i	0.0300661	−	0.140341i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.82503	+	2.78573i	−0.221855	+	0.128088i
$474$		0			0
$475$		−	55.1371i		−	2.52986i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.61289	+	6.25771i	0.165077	+	0.285922i	0.936683	−	0.350179i	$-0.113879\pi$
$479$	3.61289	+	6.25771i	0.165077	+	0.285922i	−0.771606	+	0.636101i	$0.780546\pi$
$480$		0			0
$481$	−3.74444	−	2.16185i	−0.170732	−	0.0985720i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	54.7582	+	31.6147i	2.48644	+	1.43555i
$486$		0			0
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	0.954845	−	0.297104i	$-0.0960207\pi$
$487$	4.85770	+	8.41378i	0.220123	+	0.381265i	−0.734722	+	0.678368i	$0.762687\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			19.9163i			0.898809i	0.893328	+	0.449405i	$0.148364\pi$
$491$			19.9163i			0.898809i	−0.893328	+	0.449405i	$0.851636\pi$
$492$		0			0
$493$	−20.6465	+	11.9203i	−0.929872	+	0.536862i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.9013	−	13.1751i	0.533848	−	0.590986i
$498$		0			0
$499$	−17.1920	+	29.7774i	−0.769619	+	1.33302i	0.168150	+	0.985761i	$0.446221\pi$
$499$	−17.1920	+	29.7774i	−0.769619	+	1.33302i	−0.937770	+	0.347258i	$0.887113\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.22542			−0.0546388			−0.0273194	−	0.999627i	$-0.508697\pi$
$503$	−1.22542			−0.0546388			−0.0273194	+	0.999627i	$0.508697\pi$
$504$		0			0
$505$	−6.35571			−0.282826
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.05078	+	8.74820i	−0.223872	+	0.387757i	−0.955980	−	0.293431i	$-0.905203\pi$
$509$	−5.05078	+	8.74820i	−0.223872	+	0.387757i	0.732109	+	0.681188i	$0.238536\pi$
$510$		0			0
$511$	−10.5358	−	2.25716i	−0.466078	−	0.0998511i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.34143	−	0.774473i	0.0591103	−	0.0341274i
$516$		0			0
$517$		−	10.4494i		−	0.459565i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−10.5390	−	18.2541i	−0.461723	−	0.799728i	0.537324	−	0.843376i	$-0.319435\pi$
$521$	−10.5390	−	18.2541i	−0.461723	−	0.799728i	−0.999047	+	0.0436480i	$0.986102\pi$
$522$		0			0
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	0.824451	−	0.565934i	$-0.191484\pi$
$523$	17.0733	+	9.85727i	0.746563	+	0.431028i	−0.0778877	+	0.996962i	$0.524818\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−40.8760	−	23.5997i	−1.78058	−	1.02802i
$528$		0			0
$529$	−8.91366	−	15.4389i	−0.387550	−	0.671257i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	3.98416i		−	0.172573i
$534$		0			0
$535$	19.2130	−	11.0926i	0.830652	−	0.479577i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.1339	−	20.9715i	−0.651864	−	0.903306i
$540$		0			0
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	−0.942438	−	0.334381i	$-0.891473\pi$
$541$	−4.22475	+	7.31748i	−0.181636	+	0.314603i	0.760802	+	0.648984i	$0.224806\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−52.9023			−2.26608
$546$		0			0
$547$	8.05778			0.344526			0.172263	−	0.985051i	$-0.444892\pi$
$547$	8.05778			0.344526			0.172263	+	0.985051i	$0.444892\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	10.9023	−	18.8833i	0.464453	−	0.804456i
$552$		0			0
$553$	9.93804	−	3.21142i	0.422608	−	0.136563i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	−0.0613279	−	0.998118i	$-0.519534\pi$
$557$	18.2294	−	10.5247i	0.772403	−	0.445947i	0.833731	+	0.552170i	$0.186200\pi$
$558$		0			0
$559$		−	0.836249i		−	0.0353696i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	20.6410	+	35.7513i	0.869916	+	1.50674i	0.862082	+	0.506769i	$0.169160\pi$
$563$	20.6410	+	35.7513i	0.869916	+	1.50674i	0.00783378	+	0.999969i	$0.497506\pi$
$564$		0			0
$565$	4.44922	+	2.56876i	0.187180	+	0.108068i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−31.2691	−	18.0532i	−1.31087	−	0.756829i	−0.328627	−	0.944460i	$-0.606586\pi$
$569$	−31.2691	−	18.0532i	−1.31087	−	0.756829i	−0.982240	+	0.187630i	$0.939919\pi$
$570$		0			0
$571$	9.62111	+	16.6642i	0.402631	+	0.697377i	0.994043	−	0.108993i	$-0.0347625\pi$
$571$	9.62111	+	16.6642i	0.402631	+	0.697377i	−0.591412	+	0.806370i	$0.701429\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			23.4846i			0.979375i
$576$		0			0
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.929406	−	0.369060i	$-0.879680\pi$
$577$	−25.8102	+	14.9015i	−1.07449	+	0.620359i	−0.145088	+	0.989419i	$0.546346\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.1048	+	13.6445i	0.626654	+	0.566068i
$582$		0			0
$583$	−0.0886621	+	0.153567i	−0.00367201	+	0.00636010i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.44436			0.389810			0.194905	−	0.980822i	$-0.437560\pi$
$587$	9.44436			0.389810			0.194905	+	0.980822i	$0.437560\pi$
$588$		0			0
$589$	43.1687			1.77873
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.4176	+	21.5079i	−0.509929	+	0.883223i	0.490005	+	0.871720i	$0.336995\pi$
$593$	−12.4176	+	21.5079i	−0.509929	+	0.883223i	−0.999934	+	0.0115033i	$0.996338\pi$
$594$		0			0
$595$	−44.8738	−	40.5353i	−1.83965	−	1.66179i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	10.3052	−	5.94974i	0.421061	−	0.243100i	−0.274470	−	0.961596i	$-0.588502\pi$
$599$	10.3052	−	5.94974i	0.421061	−	0.243100i	0.695531	+	0.718496i	$0.255169\pi$
$600$		0			0
$601$			25.5508i			1.04224i	0.853484	+	0.521118i	$0.174485\pi$
$601$			25.5508i			1.04224i	−0.853484	+	0.521118i	$0.825515\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−5.18669	−	8.98361i	−0.210869	−	0.365236i
$606$		0			0
$607$	19.5544	+	11.2897i	0.793687	+	0.458235i	0.841259	−	0.540632i	$-0.181815\pi$
$607$	19.5544	+	11.2897i	0.793687	+	0.458235i	−0.0475718	+	0.998868i	$0.515148\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.35828	+	0.784204i	0.0549502	+	0.0317255i
$612$		0			0
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	0.537414	−	0.843319i	$-0.319401\pi$
$613$	−11.4294	−	19.7963i	−0.461628	−	0.799564i	−0.999042	+	0.0437549i	$0.986068\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			2.06452i			0.0831143i	0.999136	+	0.0415572i	$0.0132319\pi$
$617$			2.06452i			0.0831143i	−0.999136	+	0.0415572i	$0.986768\pi$
$618$		0			0
$619$	28.2233	−	16.2947i	1.13439	−	0.654940i	0.189354	−	0.981909i	$-0.439361\pi$
$619$	28.2233	−	16.2947i	1.13439	−	0.654940i	0.945035	+	0.326969i	$0.106027\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.6603	−	4.41425i	0.547290	−	0.176853i
$624$		0			0
$625$	−14.9967	+	25.9751i	−0.599870	+	1.03901i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−45.5213			−1.81505
$630$		0			0
$631$	38.4706			1.53149			0.765744	−	0.643145i	$-0.222371\pi$
$631$	38.4706			1.53149			0.765744	+	0.643145i	$0.222371\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−34.0461	+	58.9696i	−1.35108	+	2.34014i
$636$		0			0
$637$	3.86177	−	0.393343i	0.153009	−	0.0155848i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	41.3645	−	23.8818i	1.63380	−	0.943274i	0.650892	−	0.759170i	$-0.274395\pi$
$641$	41.3645	−	23.8818i	1.63380	−	0.943274i	0.982907	−	0.184104i	$-0.0589384\pi$
$642$		0			0
$643$		−	33.7572i		−	1.33125i	−0.746285	−	0.665626i	$-0.768165\pi$
$643$		−	33.7572i		−	1.33125i	0.746285	−	0.665626i	$-0.231835\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.536008	−	0.928393i	−0.0210727	−	0.0364989i	0.855297	−	0.518138i	$-0.173375\pi$
$647$	−0.536008	−	0.928393i	−0.0210727	−	0.0364989i	−0.876369	+	0.481640i	$0.840041\pi$
$648$		0			0
$649$	28.5183	+	16.4650i	1.11944	+	0.646309i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.8503	+	16.6567i	1.12900	+	0.651828i	0.943683	−	0.330851i	$-0.107336\pi$
$653$	28.8503	+	16.6567i	1.12900	+	0.651828i	0.185317	+	0.982679i	$0.440669\pi$
$654$		0			0
$655$	21.3499	+	36.9791i	0.834210	+	1.44489i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			9.72130i			0.378688i	0.981911	+	0.189344i	$0.0606362\pi$
$659$			9.72130i			0.378688i	−0.981911	+	0.189344i	$0.939364\pi$
$660$		0			0
$661$	14.7856	−	8.53647i	0.575093	−	0.332030i	−0.184088	−	0.982910i	$-0.558933\pi$
$661$	14.7856	−	8.53647i	0.575093	−	0.332030i	0.759181	+	0.650880i	$0.225600\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	54.0799	+	11.5859i	2.09713	+	0.449282i
$666$		0			0
$667$	−4.64362	+	8.04298i	−0.179802	+	0.311426i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	25.7393			0.993653
$672$		0			0
$673$	36.6719			1.41360			0.706798	−	0.707415i	$-0.250139\pi$
$673$	36.6719			1.41360			0.706798	+	0.707415i	$0.250139\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−20.1769	+	34.9474i	−0.775461	+	1.34314i	0.159073	+	0.987267i	$0.449149\pi$
$677$	−20.1769	+	34.9474i	−0.775461	+	1.34314i	−0.934535	+	0.355872i	$0.884184\pi$
$678$		0			0
$679$	−28.6444	+	31.7103i	−1.09927	+	1.21693i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	−0.649236	−	0.760587i	$-0.724911\pi$
$683$	−8.23662	+	4.75541i	−0.315165	+	0.181961i	0.334070	+	0.942548i	$0.391578\pi$
$684$		0			0
$685$		−	34.4705i		−	1.31705i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0133077	−	0.0230497i	−0.000506985	−	0.000878123i
$690$		0			0
$691$	6.67519	+	3.85392i	0.253936	+	0.146610i	0.621565	−	0.783362i	$-0.286497\pi$
$691$	6.67519	+	3.85392i	0.253936	+	0.146610i	−0.367629	+	0.929972i	$0.619830\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	55.7282	+	32.1747i	2.11389	+	1.22046i
$696$		0			0
$697$	−20.9732	−	36.3267i	−0.794418	−	1.37597i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			15.6388i			0.590671i	0.955394	+	0.295336i	$0.0954314\pi$
$701$			15.6388i			0.590671i	−0.955394	+	0.295336i	$0.904569\pi$
$702$		0			0
$703$	36.0559	−	20.8169i	1.35988	−	0.785124i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.899810	−	4.20007i	0.0338408	−	0.157960i
$708$		0			0
$709$	−6.72025	+	11.6398i	−0.252384	+	0.437142i	−0.964182	−	0.265242i	$-0.914548\pi$
$709$	−6.72025	+	11.6398i	−0.252384	+	0.437142i	0.711797	+	0.702385i	$0.247881\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−18.3869			−0.688593
$714$		0			0
$715$	8.02054			0.299951
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−20.0309	+	34.6946i	−0.747027	+	1.29389i	0.202214	+	0.979341i	$0.435186\pi$
$719$	−20.0309	+	34.6946i	−0.747027	+	1.29389i	−0.949242	+	0.314548i	$0.898147\pi$
$720$		0			0
$721$	0.321886	+	0.996107i	0.0119877	+	0.0370970i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−36.5161	+	21.0826i	−1.35617	+	0.782986i
$726$		0			0
$727$			49.8936i			1.85045i	0.379418	+	0.925225i	$0.376124\pi$
$727$			49.8936i			1.85045i	−0.379418	+	0.925225i	$0.623876\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.40214	−	7.62473i	−0.162819	−	0.282011i
$732$		0			0
$733$	9.91430	+	5.72402i	0.366193	+	0.211422i	0.671794	−	0.740738i	$-0.265524\pi$
$733$	9.91430	+	5.72402i	0.366193	+	0.211422i	−0.305601	+	0.952160i	$0.598857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.75888	+	2.17019i	0.138460	+	0.0799400i
$738$		0			0
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	0.936362	−	0.351036i	$-0.114170\pi$
$739$	4.46303	+	7.73020i	0.164175	+	0.284360i	−0.772187	+	0.635396i	$0.780837\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	52.9570i		−	1.94281i	−0.237438	−	0.971403i	$-0.576308\pi$
$743$		−	52.9570i		−	1.94281i	0.237438	−	0.971403i	$-0.423692\pi$
$744$		0			0
$745$	49.2541	−	28.4369i	1.80453	−	1.04185i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.61032	+	14.2671i	0.168457	+	0.521307i
$750$		0			0
$751$	13.2326	−	22.9195i	0.482865	−	0.836346i	−0.516942	−	0.856021i	$-0.672930\pi$
$751$	13.2326	−	22.9195i	0.482865	−	0.836346i	0.999806	+	0.0196744i	$0.00626295\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−21.9470			−0.798733
$756$		0			0
$757$	8.46749			0.307756			0.153878	−	0.988090i	$-0.450824\pi$
$757$	8.46749			0.307756			0.153878	+	0.988090i	$0.450824\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	26.9968	−	46.7599i	0.978635	−	1.69505i	0.311258	−	0.950325i	$-0.399250\pi$
$761$	26.9968	−	46.7599i	0.978635	−	1.69505i	0.667377	−	0.744720i	$-0.267417\pi$
$762$		0			0
$763$	7.48964	−	34.9596i	0.271143	−	1.26562i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.28046	+	2.47132i	−0.154558	+	0.0892343i
$768$		0			0
$769$		−	34.8618i		−	1.25715i	−0.777749	−	0.628575i	$-0.783639\pi$
$769$		−	34.8618i		−	1.25715i	0.777749	−	0.628575i	$-0.216361\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.06375	+	1.84246i	0.0382603	+	0.0662688i	0.884521	−	0.466499i	$-0.154485\pi$
$773$	1.06375	+	1.84246i	0.0382603	+	0.0662688i	−0.846261	+	0.532768i	$0.821152\pi$
$774$		0			0
$775$	−72.2944	−	41.7392i	−2.59689	−	1.49932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	33.2244	+	19.1821i	1.19039	+	0.687272i
$780$		0			0
$781$	12.3964	+	21.4712i	0.443577	+	0.768298i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	69.8007i		−	2.49129i
$786$		0			0
$787$	−24.5457	+	14.1715i	−0.874959	+	0.505158i	−0.868993	−	0.494824i	$-0.835232\pi$
$787$	−24.5457	+	14.1715i	−0.874959	+	0.505158i	−0.00596615	+	0.999982i	$0.501899\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.32742	+	2.57652i	−0.0827535	+	0.0916106i
$792$		0			0
$793$	−1.93167	+	3.34575i	−0.0685956	+	0.118811i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−37.8246			−1.33981			−0.669907	−	0.742445i	$-0.733666\pi$
$797$	−37.8246			−1.33981			−0.669907	+	0.742445i	$0.733666\pi$
$798$		0			0
$799$	16.5127			0.584176
$800$		0			0
$801$		0			0
$802$		0			0
$803$	7.52311	−	13.0304i	0.265485	−	0.459833i
$804$		0			0
$805$	−23.0343	−	4.93479i	−0.811851	−	0.173928i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.992143	−	0.125109i	$-0.960072\pi$
$809$	−39.2475	+	22.6595i	−1.37987	+	0.796667i	−0.387724	+	0.921776i	$0.626739\pi$
$810$		0			0
$811$		−	5.45145i		−	0.191426i	−0.995409	−	0.0957132i	$-0.969487\pi$
$811$		−	5.45145i		−	0.191426i	0.995409	−	0.0957132i	$-0.0305132\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.25883	+	3.91241i	0.0791233	+	0.137046i
$816$		0			0
$817$	6.97359	+	4.02620i	0.243975	+	0.140859i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	42.7121	+	24.6598i	1.49066	+	0.860634i	0.999943	−	0.0106847i	$-0.00340111\pi$
$821$	42.7121	+	24.6598i	1.49066	+	0.860634i	0.490718	+	0.871318i	$0.336734\pi$
$822$		0			0
$823$	11.8496	+	20.5241i	0.413050	+	0.715424i	0.995222	−	0.0976419i	$-0.0311300\pi$
$823$	11.8496	+	20.5241i	0.413050	+	0.715424i	−0.582171	+	0.813066i	$0.697797\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	19.9706i		−	0.694445i	−0.937783	−	0.347222i	$-0.887125\pi$
$827$		−	19.9706i		−	0.694445i	0.937783	−	0.347222i	$-0.112875\pi$
$828$		0			0
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	−0.713936	−	0.700211i	$-0.753089\pi$
$829$	−13.3741	+	7.72155i	−0.464503	+	0.268181i	0.249433	+	0.968392i	$0.419756\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	33.1401	−	23.9153i	1.14824	−	0.828618i
$834$		0			0
$835$	−35.0592	+	60.7242i	−1.21327	+	2.10145i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.0782			−0.382462			−0.191231	−	0.981545i	$-0.561248\pi$
$839$	−11.0782			−0.382462			−0.191231	+	0.981545i	$0.561248\pi$
$840$		0			0
$841$	12.3253			0.425012
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.8444	−	43.0318i	0.854674	−	1.48034i
$846$		0			0
$847$	6.67098	−	2.15569i	0.229218	−	0.0740703i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−15.3573	+	8.86656i	−0.526442	+	0.303942i
$852$		0			0
$853$		−	48.6944i		−	1.66727i	−0.552319	−	0.833633i	$-0.686257\pi$
$853$		−	48.6944i		−	1.66727i	0.552319	−	0.833633i	$-0.313743\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.39130	−	14.5342i	−0.286641	−	0.496477i	0.686365	−	0.727258i	$-0.259205\pi$
$857$	−8.39130	−	14.5342i	−0.286641	−	0.496477i	−0.973006	+	0.230780i	$0.925872\pi$
$858$		0			0
$859$	21.7682	+	12.5679i	0.742722	+	0.428811i	0.823058	−	0.567957i	$-0.192266\pi$
$859$	21.7682	+	12.5679i	0.742722	+	0.428811i	−0.0803361	+	0.996768i	$0.525599\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	0.396685	−	0.917955i	$-0.370161\pi$
$863$	−5.87377	−	3.39122i	−0.199945	−	0.115438i	−0.596630	+	0.802516i	$0.703494\pi$
$864$		0			0
$865$	−14.6733	−	25.4149i	−0.498907	−	0.864133i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			14.5842i			0.494734i
$870$		0			0
$871$	−0.564190	+	0.325735i	−0.0191168	+	0.0110371i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−40.9347	−	36.9771i	−1.38385	−	1.25005i
$876$		0			0
$877$	21.8630	−	37.8678i	0.738260	−	1.27870i	−0.215019	−	0.976610i	$-0.568981\pi$
$877$	21.8630	−	37.8678i	0.738260	−	1.27870i	0.953278	−	0.302093i	$-0.0976854\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	27.5307			0.927531			0.463766	−	0.885958i	$-0.346498\pi$
$881$	27.5307			0.927531			0.463766	+	0.885958i	$0.346498\pi$
$882$		0			0
$883$	5.56040			0.187122			0.0935612	−	0.995614i	$-0.470175\pi$
$883$	5.56040			0.187122			0.0935612	+	0.995614i	$0.470175\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.3092	+	21.3202i	−0.413303	+	0.715862i	−0.995249	−	0.0973655i	$-0.968958\pi$
$887$	−12.3092	+	21.3202i	−0.413303	+	0.715862i	0.581945	+	0.813228i	$0.302292\pi$
$888$		0			0
$889$	−34.1491	−	30.8475i	−1.14532	−	1.03459i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.0792	+	7.55125i	−0.437677	+	0.252693i
$894$		0			0
$895$			2.82248i			0.0943452i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−16.5062	−	28.5896i	−0.550514	−	0.953518i
$900$		0			0
$901$	−0.242674	−	0.140108i	−0.00808465	−	0.00466767i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.1931	−	9.92644i	−0.571518	−	0.329966i
$906$		0			0
$907$	5.04337	+	8.73537i	0.167462	+	0.290053i	0.937527	−	0.347913i	$-0.113109\pi$
$907$	5.04337	+	8.73537i	0.167462	+	0.290053i	−0.770065	+	0.637966i	$0.779776\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	27.2288i		−	0.902130i	−0.892491	−	0.451065i	$-0.851044\pi$
$911$		−	27.2288i		−	0.902130i	0.892491	−	0.451065i	$-0.148956\pi$
$912$		0			0
$913$	−24.6159	+	14.2120i	−0.814668	+	0.470349i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.4597	+	8.87343i	−0.906799	+	0.293026i
$918$		0			0
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	0.327183	+	0.944961i	$0.393901\pi$
$919$	−19.8493	+	34.3800i	−0.654769	+	1.13409i	−0.981952	+	0.189132i	$0.939433\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.72127			−0.122487
$924$		0			0
$925$	−80.5103			−2.64716
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.142283	+	0.246442i	−0.00466816	+	0.00808550i	−0.868350	−	0.495952i	$-0.834819\pi$
$929$	−0.142283	+	0.246442i	−0.00466816	+	0.00808550i	0.863682	+	0.504037i	$0.168153\pi$
$930$		0			0
$931$	−15.3127	+	34.0976i	−0.501854	+	1.11750i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	73.1295	−	42.2214i	2.39159	−	1.38079i
$936$		0			0
$937$			21.7298i			0.709881i	0.934889	+	0.354940i	$0.115499\pi$
$937$			21.7298i			0.709881i	−0.934889	+	0.354940i	$0.884501\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.64242	−	9.77295i	−0.183938	−	0.318589i	0.759280	−	0.650764i	$-0.225551\pi$
$941$	−5.64242	−	9.77295i	−0.183938	−	0.318589i	−0.943218	+	0.332174i	$0.892218\pi$
$942$		0			0
$943$	−14.1513	−	8.17026i	−0.460830	−	0.266060i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−19.6701	−	11.3566i	−0.639194	−	0.369039i	0.145110	−	0.989416i	$-0.453646\pi$
$947$	−19.6701	−	11.3566i	−0.639194	−	0.369039i	−0.784304	+	0.620377i	$0.786980\pi$
$948$		0			0
$949$	1.12918	+	1.95580i	0.0366548	+	0.0634880i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			16.5638i			0.536554i	0.963342	+	0.268277i	$0.0864543\pi$
$953$			16.5638i			0.536554i	−0.963342	+	0.268277i	$0.913546\pi$
$954$		0			0
$955$	43.0648	−	24.8635i	1.39354	−	0.804563i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	22.7793	+	4.88017i	0.735582	+	0.157589i
$960$		0			0
$961$	17.1790	−	29.7550i	0.554162	−	0.959837i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	89.3178			2.87524
$966$		0			0
$967$	−16.7773			−0.539523			−0.269762	−	0.962927i	$-0.586945\pi$
$967$	−16.7773			−0.539523			−0.269762	+	0.962927i	$0.586945\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	15.6820	−	27.1620i	0.503259	−	0.871670i	−0.496734	−	0.867903i	$-0.665468\pi$
$971$	15.6820	−	27.1620i	0.503259	−	0.871670i	0.999993	−	0.00376705i	$-0.00119909\pi$
$972$		0			0
$973$	−29.1519	+	32.2720i	−0.934566	+	1.03459i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−49.0953	+	28.3452i	−1.57070	+	0.906843i	−0.574614	+	0.818424i	$0.694848\pi$
$977$	−49.0953	+	28.3452i	−1.57070	+	0.906843i	−0.996083	+	0.0884183i	$0.971819\pi$
$978$		0			0
$979$			20.0467i			0.640695i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.9204	−	34.5032i	−0.635362	−	1.10048i	−0.986438	−	0.164133i	$-0.947517\pi$
$983$	−19.9204	−	34.5032i	−0.635362	−	1.10048i	0.351076	−	0.936347i	$-0.385816\pi$
$984$		0			0
$985$	−0.105562	−	0.0609460i	−0.00336347	−	0.00194190i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.97026	−	1.71488i	−0.0944489	−	0.0545301i
$990$		0			0
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.590247	+	0.807223i	$0.299030\pi$
$991$	31.2975	+	54.2089i	0.994199	+	1.72200i	0.403952	+	0.914780i	$0.367636\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	90.0220i		−	2.85389i
$996$		0			0
$997$	−39.0613	+	22.5520i	−1.23708	+	0.714230i	−0.968497	−	0.249025i	$-0.919890\pi$
$997$	−39.0613	+	22.5520i	−1.23708	+	0.714230i	−0.268586	+	0.963256i	$0.586556\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.a.2105.8		16
3.2	odd	2		2268.2.t.b.2105.1		16
7.3	odd	6		2268.2.t.b.1781.1		16
9.2	odd	6		252.2.w.a.5.8	✓	16
9.4	even	3		252.2.bm.a.173.6	yes	16
9.5	odd	6		756.2.bm.a.89.8		16
9.7	even	3		756.2.w.a.341.8		16
21.17	even	6	inner	2268.2.t.a.1781.8		16
36.7	odd	6		3024.2.ca.d.2609.8		16
36.11	even	6		1008.2.ca.d.257.1		16
36.23	even	6		3024.2.df.d.1601.8		16
36.31	odd	6		1008.2.df.d.929.3		16
63.2	odd	6		1764.2.x.a.293.3		16
63.4	even	3		1764.2.w.b.1109.1		16
63.5	even	6		5292.2.x.a.4409.8		16
63.11	odd	6		1764.2.bm.a.1697.3		16
63.13	odd	6		1764.2.bm.a.1685.3		16
63.16	even	3		5292.2.x.a.881.8		16
63.20	even	6		1764.2.w.b.509.1		16
63.23	odd	6		5292.2.x.b.4409.1		16
63.25	even	3		5292.2.bm.a.2285.1		16
63.31	odd	6		252.2.w.a.101.8	yes	16
63.32	odd	6		5292.2.w.b.521.1		16
63.34	odd	6		5292.2.w.b.1097.1		16
63.38	even	6		252.2.bm.a.185.6	yes	16
63.40	odd	6		1764.2.x.a.1469.3		16
63.41	even	6		5292.2.bm.a.4625.1		16
63.47	even	6		1764.2.x.b.293.6		16
63.52	odd	6		756.2.bm.a.17.8		16
63.58	even	3		1764.2.x.b.1469.6		16
63.59	even	6		756.2.w.a.521.8		16
63.61	odd	6		5292.2.x.b.881.1		16
252.31	even	6		1008.2.ca.d.353.1		16
252.59	odd	6		3024.2.ca.d.2033.8		16
252.115	even	6		3024.2.df.d.17.8		16
252.227	odd	6		1008.2.df.d.689.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.8	✓	16	9.2	odd	6
252.2.w.a.101.8	yes	16	63.31	odd	6
252.2.bm.a.173.6	yes	16	9.4	even	3
252.2.bm.a.185.6	yes	16	63.38	even	6
756.2.w.a.341.8		16	9.7	even	3
756.2.w.a.521.8		16	63.59	even	6
756.2.bm.a.17.8		16	63.52	odd	6
756.2.bm.a.89.8		16	9.5	odd	6
1008.2.ca.d.257.1		16	36.11	even	6
1008.2.ca.d.353.1		16	252.31	even	6
1008.2.df.d.689.3		16	252.227	odd	6
1008.2.df.d.929.3		16	36.31	odd	6
1764.2.w.b.509.1		16	63.20	even	6
1764.2.w.b.1109.1		16	63.4	even	3
1764.2.x.a.293.3		16	63.2	odd	6
1764.2.x.a.1469.3		16	63.40	odd	6
1764.2.x.b.293.6		16	63.47	even	6
1764.2.x.b.1469.6		16	63.58	even	3
1764.2.bm.a.1685.3		16	63.13	odd	6
1764.2.bm.a.1697.3		16	63.11	odd	6
2268.2.t.a.1781.8		16	21.17	even	6	inner
2268.2.t.a.2105.8		16	1.1	even	1	trivial
2268.2.t.b.1781.1		16	7.3	odd	6
2268.2.t.b.2105.1		16	3.2	odd	2
3024.2.ca.d.2033.8		16	252.59	odd	6
3024.2.ca.d.2609.8		16	36.7	odd	6
3024.2.df.d.17.8		16	252.115	even	6
3024.2.df.d.1601.8		16	36.23	even	6
5292.2.w.b.521.1		16	63.32	odd	6
5292.2.w.b.1097.1		16	63.34	odd	6
5292.2.x.a.881.8		16	63.16	even	3
5292.2.x.a.4409.8		16	63.5	even	6
5292.2.x.b.881.1		16	63.61	odd	6
5292.2.x.b.4409.1		16	63.23	odd	6
5292.2.bm.a.2285.1		16	63.25	even	3
5292.2.bm.a.4625.1		16	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.95741 - 3.39033i) q^{5} +(1.96333 + 1.77351i) q^{7} +O(q^{10})\)	\(q+(1.95741 - 3.39033i) q^{5} +(1.96333 + 1.77351i) q^{7} +(-3.19958 + 1.84728i) q^{11} -0.554535i q^{13} +(-2.91916 - 5.05613i) q^{17} +(4.62434 + 2.66986i) q^{19} +(-1.96965 - 1.13718i) q^{23} +(-5.16291 - 8.94242i) q^{25} -4.08346i q^{29} +(7.00132 - 4.04222i) q^{31} +(9.85583 - 3.18485i) q^{35} +(3.89849 - 6.75239i) q^{37} +7.18469 q^{41} +1.50802 q^{43} +(-1.41416 + 2.44940i) q^{47} +(0.709320 + 6.96397i) q^{49} +(0.0415658 - 0.0239980i) q^{53} +14.4635i q^{55} +(-4.45656 - 7.71900i) q^{59} +(-6.03343 - 3.48340i) q^{61} +(-1.88006 - 1.08545i) q^{65} +(-0.587402 - 1.01741i) q^{67} -6.71061i q^{71} +(-3.52692 + 2.03627i) q^{73} +(-9.55800 - 2.04768i) q^{77} +(1.97374 - 3.41861i) q^{79} +7.69348 q^{83} -22.8560 q^{85} +(2.71300 - 4.69905i) q^{89} +(0.983474 - 1.08874i) q^{91} +(18.1035 - 10.4520i) q^{95} +16.1513i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 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