LMFDB - Embedded newform 3024.2.t.g.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(289,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 2]))

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

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

chi := DirichletCharacter("3024.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.224437i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.g.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.69963 q^{5} +(1.40545 + 2.24159i) q^{7} +O(q^{10})$	$q-3.69963 q^{5} +(1.40545 + 2.24159i) q^{7} -1.47710 q^{11} +(-1.34981 - 2.33795i) q^{13} +(-3.28799 - 5.69497i) q^{17} +(0.444368 - 0.769668i) q^{19} +6.28799 q^{23} +8.68725 q^{25} +(-1.25526 + 2.17417i) q^{29} +(3.40545 - 5.89841i) q^{31} +(-5.19963 - 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} +(2.05563 + 3.56046i) q^{41} +(-0.00618986 + 0.0107211i) q^{43} +(3.49381 + 6.05146i) q^{47} +(-3.04944 + 6.30087i) q^{49} +(1.60507 + 2.78007i) q^{53} +5.46472 q^{55} +(-3.45489 + 5.98404i) q^{59} +(2.86652 + 4.96497i) q^{61} +(4.99381 + 8.64953i) q^{65} +(-4.73236 + 8.19669i) q^{67} -5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} +(-2.07598 - 3.31105i) q^{77} +(5.72617 + 9.91802i) q^{79} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +(4.43818 - 7.68715i) q^{89} +(3.34362 - 6.31159i) q^{91} +(-1.64400 + 2.84748i) q^{95} +(-6.58836 + 11.4114i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 10 q^{5} + 2 q^{7}+O(q^{10}) $ 6 * q - 10 * q^5 + 2 * q^7	$ 6 q - 10 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} + 14 q^{23} + 4 q^{25} + 5 q^{29} + 14 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} + 3 q^{47} - 9 q^{53} - 14 q^{55} + 4 q^{59} + 4 q^{61} + 12 q^{65} - 5 q^{67} + 14 q^{71} - 25 q^{73} + 35 q^{77} - 7 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} + 2 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q - 10 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 + 14 * q^23 + 4 * q^25 + 5 * q^29 + 14 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 + 3 * q^47 - 9 * q^53 - 14 * q^55 + 4 * q^59 + 4 * q^61 + 12 * q^65 - 5 * q^67 + 14 * q^71 - 25 * q^73 + 35 * q^77 - 7 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 + 2 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−3.69963			−1.65452			−0.827262	−	0.561816i	$-0.810103\pi$
$5$	−3.69963			−1.65452			−0.827262	+	0.561816i	$0.810103\pi$
$6$		0			0
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$7$	1.40545	+	2.24159i	0.531209	+	0.847241i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.47710			−0.445362			−0.222681	−	0.974891i	$-0.571481\pi$
$11$	−1.47710			−0.445362			−0.222681	+	0.974891i	$0.571481\pi$
$12$		0			0
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	0.615862	−	0.787854i	$-0.288808\pi$
$13$	−1.34981	−	2.33795i	−0.374371	−	0.648430i	−0.990233	+	0.139425i	$0.955475\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.28799	−	5.69497i	−0.797455	−	1.38123i	−0.921268	−	0.388927i	$-0.872846\pi$
$17$	−3.28799	−	5.69497i	−0.797455	−	1.38123i	0.123813	−	0.992306i	$-0.460488\pi$
$18$		0			0
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	−0.810541	−	0.585682i	$-0.800827\pi$
$19$	0.444368	−	0.769668i	0.101945	−	0.176574i	0.912486	+	0.409108i	$0.134160\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.28799			1.31114			0.655568	−	0.755136i	$-0.272429\pi$
$23$	6.28799			1.31114			0.655568	+	0.755136i	$0.272429\pi$
$24$		0			0
$25$	8.68725			1.73745
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	−0.958718	−	0.284360i	$-0.908219\pi$
$29$	−1.25526	+	2.17417i	−0.233096	+	0.403734i	0.725622	+	0.688094i	$0.241552\pi$
$30$		0			0
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	−0.379329	−	0.925262i	$-0.623845\pi$
$31$	3.40545	−	5.89841i	0.611636	−	1.05938i	0.990965	−	0.134123i	$-0.0428217\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.19963	−	8.29305i	−0.878898	−	1.40178i
$36$		0			0
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	−0.957306	−	0.289075i	$-0.906652\pi$
$37$	−1.38874	+	2.40536i	−0.228307	+	0.395439i	0.729000	+	0.684514i	$0.239986\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	0.980702	−	0.195508i	$-0.0626357\pi$
$41$	2.05563	+	3.56046i	0.321036	+	0.556050i	−0.659666	+	0.751559i	$0.729302\pi$
$42$		0			0
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	−0.866497	−	0.499182i	$-0.833634\pi$
$43$	−0.00618986	+	0.0107211i	−0.000943944	+	0.00163496i	0.865553	+	0.500817i	$0.166967\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	0.999938	+	0.0111494i	$0.00354904\pi$
$47$	3.49381	+	6.05146i	0.509625	+	0.882696i	−0.490313	+	0.871546i	$0.663118\pi$
$48$		0			0
$49$	−3.04944	+	6.30087i	−0.435635	+	0.900124i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.60507	+	2.78007i	0.220474	+	0.381872i	0.954952	−	0.296760i	$-0.0959063\pi$
$53$	1.60507	+	2.78007i	0.220474	+	0.381872i	−0.734478	+	0.678632i	$0.762573\pi$
$54$		0			0
$55$	5.46472			0.736863
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	−0.998372	−	0.0570397i	$-0.981834\pi$
$59$	−3.45489	+	5.98404i	−0.449788	+	0.779056i	0.548584	+	0.836096i	$0.315167\pi$
$60$		0			0
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	0.989098	−	0.147257i	$-0.0470444\pi$
$61$	2.86652	+	4.96497i	0.367021	+	0.635699i	−0.622077	+	0.782956i	$0.713711\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.99381	+	8.64953i	0.619406	+	1.07284i
$66$		0			0
$67$	−4.73236	+	8.19669i	−0.578150	+	1.00138i	0.417542	+	0.908658i	$0.362892\pi$
$67$	−4.73236	+	8.19669i	−0.578150	+	1.00138i	−0.995692	+	0.0927271i	$0.970442\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.46472			−0.648543			−0.324271	−	0.945964i	$-0.605119\pi$
$71$	−5.46472			−0.648543			−0.324271	+	0.945964i	$0.605119\pi$
$72$		0			0
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	−0.966301	−	0.257414i	$-0.917130\pi$
$73$	−6.03273	−	10.4490i	−0.706078	−	1.22296i	0.260223	−	0.965548i	$-0.416204\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.07598	−	3.31105i	−0.236580	−	0.377329i
$78$		0			0
$79$	5.72617	+	9.91802i	0.644244	+	1.11586i	0.984475	+	0.175522i	$0.0561614\pi$
$79$	5.72617	+	9.91802i	0.644244	+	1.11586i	−0.340231	+	0.940342i	$0.610505\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	−0.716619	−	0.697465i	$-0.754311\pi$
$83$	2.23855	−	3.87728i	0.245713	−	0.425587i	0.962332	+	0.271878i	$0.0876447\pi$
$84$		0			0
$85$	12.1643	+	21.0693i	1.31941	+	2.28528i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.43818	−	7.68715i	0.470446	−	0.814836i	−0.528983	−	0.848633i	$-0.677426\pi$
$89$	4.43818	−	7.68715i	0.470446	−	0.814836i	0.999429	+	0.0337963i	$0.0107597\pi$
$90$		0			0
$91$	3.34362	−	6.31159i	0.350507	−	0.661634i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.64400	+	2.84748i	−0.168670	+	0.292146i
$96$		0			0
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	0.309252	+	0.950980i	$0.399921\pi$
$97$	−6.58836	+	11.4114i	−0.668947	+	1.15865i	−0.978199	+	0.207670i	$0.933412\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.25457			−0.522849			−0.261425	−	0.965224i	$-0.584192\pi$
$101$	−5.25457			−0.522849			−0.261425	+	0.965224i	$0.584192\pi$
$102$		0			0
$103$	−1.66621			−0.164176			−0.0820882	−	0.996625i	$-0.526159\pi$
$103$	−1.66621			−0.164176			−0.0820882	+	0.996625i	$0.526159\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	0.479370	+	0.877613i	$0.340865\pi$
$107$	−5.38255	+	9.32284i	−0.520350	+	0.901273i	−0.999720	+	0.0236602i	$0.992468\pi$
$108$		0			0
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	0.861462	−	0.507823i	$-0.169550\pi$
$109$	−0.0945538	−	0.163772i	−0.00905662	−	0.0156865i	−0.870518	+	0.492136i	$0.836216\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	0.985876	+	0.167478i	$0.0535624\pi$
$113$	6.78180	+	11.7464i	0.637978	+	1.10501i	−0.347897	+	0.937533i	$0.613104\pi$
$114$		0			0
$115$	−23.2632			−2.16931
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.14468	−	15.3743i	0.746622	−	1.40936i
$120$		0			0
$121$	−8.81818			−0.801652
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−13.6414			−1.22013
$126$		0			0
$127$	2.85669			0.253490			0.126745	−	0.991935i	$-0.459547\pi$
$127$	2.85669			0.253490			0.126745	+	0.991935i	$0.459547\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.155687			0.0136024			0.00680122	−	0.999977i	$-0.497835\pi$
$131$	0.155687			0.0136024			0.00680122	+	0.999977i	$0.497835\pi$
$132$		0			0
$133$	2.34981	−	0.0856364i	0.203755	−	0.00742562i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.41164			0.291476			0.145738	−	0.989323i	$-0.453444\pi$
$137$	3.41164			0.291476			0.145738	+	0.989323i	$0.453444\pi$
$138$		0			0
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	0.996259	+	0.0864229i	$0.0275436\pi$
$139$	6.75526	+	11.7005i	0.572974	+	0.992420i	−0.423285	+	0.905997i	$0.639123\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.99381	+	3.45338i	0.166731	+	0.288786i
$144$		0			0
$145$	4.64400	−	8.04364i	0.385663	−	0.667988i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−0.333792			−0.0273453			−0.0136727	−	0.999907i	$-0.504352\pi$
$149$	−0.333792			−0.0273453			−0.0136727	+	0.999907i	$0.504352\pi$
$150$		0			0
$151$	19.9098			1.62023			0.810117	−	0.586268i	$-0.199403\pi$
$151$	19.9098			1.62023			0.810117	+	0.586268i	$0.199403\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−12.5989	+	21.8219i	−1.01197	+	1.75278i
$156$		0			0
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	−0.693001	−	0.720936i	$-0.743712\pi$
$157$	3.48143	−	6.03001i	0.277848	−	0.481248i	0.970850	+	0.239689i	$0.0770454\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.83743	+	14.0951i	0.696487	+	1.11085i
$162$		0			0
$163$	−4.03706	+	6.99240i	−0.316207	+	0.547687i	−0.979693	−	0.200502i	$-0.935743\pi$
$163$	−4.03706	+	6.99240i	−0.316207	+	0.547687i	0.663486	+	0.748189i	$0.269076\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	0.945906	+	0.324440i	$0.105176\pi$
$167$	9.74288	+	16.8752i	0.753927	+	1.30584i	−0.191979	+	0.981399i	$0.561491\pi$
$168$		0			0
$169$	2.85600	−	4.94674i	0.219693	−	0.380519i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.2818	+	19.5407i	0.857740	+	1.48565i	0.874080	+	0.485782i	$0.161465\pi$
$173$	11.2818	+	19.5407i	0.857740	+	1.48565i	−0.0163405	+	0.999866i	$0.505202\pi$
$174$		0			0
$175$	12.2095	+	19.4732i	0.922948	+	1.47204i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	0.872195	−	0.489158i	$-0.162696\pi$
$179$	0.166896	+	0.289073i	0.0124744	+	0.0216063i	−0.859721	+	0.510764i	$0.829363\pi$
$180$		0			0
$181$	23.2422			1.72758			0.863789	−	0.503853i	$-0.168085\pi$
$181$	23.2422			1.72758			0.863789	+	0.503853i	$0.168085\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.13781	−	8.89894i	0.377739	−	0.654263i
$186$		0			0
$187$	4.85669	+	8.41204i	0.355157	+	0.615149i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	0.994167	+	0.107854i	$0.0343980\pi$
$191$	8.16071	+	14.1348i	0.590488	+	1.02276i	−0.403679	+	0.914901i	$0.632269\pi$
$192$		0			0
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	−0.484400	−	0.874846i	$-0.660962\pi$
$193$	7.16071	−	12.4027i	0.515439	−	0.892766i	0.999839	−	0.0179200i	$-0.00570443\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.42402			−0.172704			−0.0863520	−	0.996265i	$-0.527521\pi$
$197$	−2.42402			−0.172704			−0.0863520	+	0.996265i	$0.527521\pi$
$198$		0			0
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	0.953769	−	0.300541i	$-0.0971673\pi$
$199$	3.05563	+	5.29251i	0.216608	+	0.375176i	−0.737161	+	0.675717i	$0.763834\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.63781	+	0.241908i	−0.465883	+	0.0169786i
$204$		0			0
$205$	−7.60507	−	13.1724i	−0.531161	−	0.919999i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.656376	+	1.13688i	−0.0454025	+	0.0786394i
$210$		0			0
$211$	−5.72253	−	9.91171i	−0.393955	−	0.682350i	0.599012	−	0.800740i	$-0.295560\pi$
$211$	−5.72253	−	9.91171i	−0.393955	−	0.682350i	−0.992967	+	0.118390i	$0.962227\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0229002	−	0.0396643i	0.00156178	−	0.00270508i
$216$		0			0
$217$	18.0080	−	0.656281i	1.22246	−	0.0445513i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−8.87636	+	15.3743i	−0.597088	+	1.03419i
$222$		0			0
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	−0.719407	−	0.694589i	$-0.755586\pi$
$223$	3.61126	−	6.25489i	0.241828	−	0.418859i	0.961235	+	0.275730i	$0.0889196\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	13.6552			0.906328			0.453164	−	0.891427i	$-0.350295\pi$
$227$	13.6552			0.906328			0.453164	+	0.891427i	$0.350295\pi$
$228$		0			0
$229$	17.3745			1.14814			0.574070	−	0.818807i	$-0.305364\pi$
$229$	17.3745			1.14814			0.574070	+	0.818807i	$0.305364\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.62110	+	13.2001i	−0.499275	+	0.864769i	−1.00000		0.000837426i	$-0.999733\pi$
$233$	−7.62110	+	13.2001i	−0.499275	+	0.864769i	0.500725	+	0.865606i	$0.333067\pi$
$234$		0			0
$235$	−12.9258	−	22.3881i	−0.843186	−	1.46044i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	0.990749	+	0.135710i	$0.0433314\pi$
$239$	9.47524	+	16.4116i	0.612902	+	1.06158i	−0.377846	+	0.925868i	$0.623335\pi$
$240$		0			0
$241$	−24.5054			−1.57853			−0.789267	−	0.614051i	$-0.789539\pi$
$241$	−24.5054			−1.57853			−0.789267	+	0.614051i	$0.789539\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.2818	−	23.3109i	0.720768	−	1.48928i
$246$		0			0
$247$	−2.39926			−0.152661
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.1236			−0.765238			−0.382619	−	0.923906i	$-0.624978\pi$
$251$	−12.1236			−0.765238			−0.382619	+	0.923906i	$0.624978\pi$
$252$		0			0
$253$	−9.28799			−0.583931
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.20877			0.512049			0.256025	−	0.966670i	$-0.417587\pi$
$257$	8.20877			0.512049			0.256025	+	0.966670i	$0.417587\pi$
$258$		0			0
$259$	−7.34362	+	0.267630i	−0.456311	+	0.0166297i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.34617			−0.329659			−0.164830	−	0.986322i	$-0.552707\pi$
$263$	−5.34617			−0.329659			−0.164830	+	0.986322i	$0.552707\pi$
$264$		0			0
$265$	−5.93818	−	10.2852i	−0.364779	−	0.631816i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.24219	−	16.0079i	−0.563506	−	0.976022i	−0.997187	−	0.0749550i	$-0.976119\pi$
$269$	−9.24219	−	16.0079i	−0.563506	−	0.976022i	0.433681	−	0.901067i	$-0.357215\pi$
$270$		0			0
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	−0.732447	−	0.680824i	$-0.761622\pi$
$271$	3.67742	−	6.36947i	0.223387	−	0.386918i	0.955834	+	0.293906i	$0.0949552\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.8319			−0.773795
$276$		0			0
$277$	−9.09888			−0.546699			−0.273349	−	0.961915i	$-0.588132\pi$
$277$	−9.09888			−0.546699			−0.273349	+	0.961915i	$0.588132\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	−0.987658	−	0.156624i	$-0.949939\pi$
$281$	−6.00433	+	10.3998i	−0.358188	+	0.620400i	0.629470	+	0.777025i	$0.283272\pi$
$282$		0			0
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	−0.681861	−	0.731481i	$-0.738829\pi$
$283$	4.92147	−	8.52423i	0.292551	−	0.506713i	0.974412	+	0.224768i	$0.0721626\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−5.09201	+	9.61192i	−0.300572	+	0.567373i
$288$		0			0
$289$	−13.1218	+	22.7276i	−0.771870	+	1.33692i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	−0.988406	−	0.151832i	$-0.951483\pi$
$293$	−10.7101	−	18.5505i	−0.625694	−	1.08373i	0.362713	−	0.931901i	$-0.381851\pi$
$294$		0			0
$295$	12.7818	−	22.1387i	0.744185	−	1.28897i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.48762	−	14.7010i	−0.490852	−	0.850180i
$300$		0			0
$301$	−0.0327319	+	0.00119288i	−0.00188664	+	6.87564e-5i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.6051	−	18.3685i	−0.607245	−	1.05178i
$306$		0			0
$307$	5.68725			0.324588			0.162294	−	0.986742i	$-0.448111\pi$
$307$	5.68725			0.324588			0.162294	+	0.986742i	$0.448111\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	−0.650655	−	0.759373i	$-0.725506\pi$
$311$	5.86033	−	10.1504i	0.332309	−	0.575576i	0.982964	+	0.183797i	$0.0588390\pi$
$312$		0			0
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	0.944539	+	0.328398i	$0.106509\pi$
$313$	13.3869	+	23.1868i	0.756671	+	1.31059i	−0.187868	+	0.982194i	$0.560158\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.951246	+	1.64761i	0.0534273	+	0.0925388i	0.891502	−	0.453016i	$-0.149652\pi$
$317$	0.951246	+	1.64761i	0.0534273	+	0.0925388i	−0.838075	+	0.545555i	$0.816319\pi$
$318$		0			0
$319$	1.85414	−	3.21147i	0.103812	−	0.179808i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.84431			−0.325186
$324$		0			0
$325$	−11.7262	−	20.3103i	−0.650451	−	1.12661i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.65452	+	16.3367i	−0.477139	+	0.900670i
$330$		0			0
$331$	2.78366	+	4.82144i	0.153004	+	0.265010i	0.932330	−	0.361608i	$-0.117772\pi$
$331$	2.78366	+	4.82144i	0.153004	+	0.265010i	−0.779327	+	0.626618i	$0.784439\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.5080	−	30.3247i	0.956563	−	1.65682i
$336$		0			0
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.799585	−	0.600553i	$-0.794947\pi$
$337$	−16.8869	−	29.2489i	−0.919887	−	1.59329i	−0.120302	−	0.992737i	$-0.538386\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.03018	+	8.71253i	−0.272400	+	0.471810i
$342$		0			0
$343$	−18.4098	+	2.01993i	−0.994035	+	0.109066i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	−0.0923418	−	0.995727i	$-0.529435\pi$
$347$	15.2033	−	26.3328i	0.816154	−	1.41362i	0.908496	−	0.417893i	$-0.137231\pi$
$348$		0			0
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	−0.983889	−	0.178782i	$-0.942784\pi$
$349$	−6.29782	+	10.9082i	−0.337115	+	0.583900i	0.646774	+	0.762682i	$0.276118\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.53156			0.400865			0.200432	−	0.979708i	$-0.435765\pi$
$353$	7.53156			0.400865			0.200432	+	0.979708i	$0.435765\pi$
$354$		0			0
$355$	20.2174			1.07303
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	−0.942554	−	0.334053i	$-0.891584\pi$
$359$	−3.44801	+	5.97213i	−0.181979	+	0.315197i	0.760575	+	0.649250i	$0.224917\pi$
$360$		0			0
$361$	9.10507	+	15.7705i	0.479214	+	0.830024i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	22.3189	+	38.6574i	1.16822	+	2.02342i
$366$		0			0
$367$	−23.1236			−1.20704			−0.603522	−	0.797346i	$-0.706237\pi$
$367$	−23.1236			−1.20704			−0.603522	+	0.797346i	$0.706237\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.97593	+	7.50516i	−0.206420	+	0.389648i
$372$		0			0
$373$	29.1643			1.51007			0.755036	−	0.655683i	$-0.227619\pi$
$373$	29.1643			1.51007			0.755036	+	0.655683i	$0.227619\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.77747			0.349058
$378$		0			0
$379$	13.5622			0.696645			0.348322	−	0.937375i	$-0.386751\pi$
$379$	13.5622			0.696645			0.348322	+	0.937375i	$0.386751\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.83565			−0.144895			−0.0724475	−	0.997372i	$-0.523081\pi$
$383$	−2.83565			−0.144895			−0.0724475	+	0.997372i	$0.523081\pi$
$384$		0			0
$385$	7.68037	+	12.2497i	0.391428	+	0.624300i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	18.6080			0.943464			0.471732	−	0.881742i	$-0.343629\pi$
$389$	18.6080			0.943464			0.471732	+	0.881742i	$0.343629\pi$
$390$		0			0
$391$	−20.6749	−	35.8099i	−1.04557	−	1.81099i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−21.1847	−	36.6930i	−1.06592	−	1.84622i
$396$		0			0
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	0.483481	+	0.875355i	$0.339372\pi$
$397$	−10.2880	+	17.8193i	−0.516340	+	0.894326i	−0.999820	+	0.0189712i	$0.993961\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.75409			0.337283			0.168642	−	0.985677i	$-0.446062\pi$
$401$	6.75409			0.337283			0.168642	+	0.985677i	$0.446062\pi$
$402$		0			0
$403$	−18.3869			−0.915916
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.05130	−	3.55296i	0.101679	−	0.176114i
$408$		0			0
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	−0.990888	−	0.134691i	$-0.956996\pi$
$409$	−7.66071	+	13.2687i	−0.378798	+	0.656097i	0.612090	+	0.790788i	$0.290329\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−18.2694	+	0.665809i	−0.898980	+	0.0327623i
$414$		0			0
$415$	−8.28180	+	14.3445i	−0.406538	+	0.704144i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	0.740949	−	0.671561i	$-0.234376\pi$
$419$	−4.32141	−	7.48491i	−0.211115	−	0.365662i	−0.952064	+	0.305900i	$0.901043\pi$
$420$		0			0
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.0834618	−	0.996511i	$-0.473402\pi$
$421$	18.5636	−	32.1531i	0.904735	−	1.56705i	0.821273	−	0.570536i	$-0.193264\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−28.5636	−	49.4736i	−1.38554	−	2.39982i
$426$		0			0
$427$	−7.10067	+	13.4036i	−0.343625	+	0.648644i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	0.730002	−	0.683445i	$-0.239519\pi$
$431$	−4.71015	−	8.15822i	−0.226880	−	0.392967i	−0.956882	+	0.290478i	$0.906186\pi$
$432$		0			0
$433$	−0.208771			−0.0100329			−0.00501645	−	0.999987i	$-0.501597\pi$
$433$	−0.208771			−0.0100329			−0.00501645	+	0.999987i	$0.501597\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.79418	−	4.83967i	0.133664	−	0.231513i
$438$		0			0
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	0.722231	−	0.691652i	$-0.243117\pi$
$439$	−4.98398	−	8.63250i	−0.237872	−	0.412007i	−0.960104	+	0.279645i	$0.909783\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	0.990019	−	0.140935i	$-0.0450109\pi$
$443$	7.84981	+	13.5963i	0.372956	+	0.645979i	−0.617063	+	0.786914i	$0.711678\pi$
$444$		0			0
$445$	−16.4196	+	28.4396i	−0.778364	+	1.34817i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−33.6253			−1.58688			−0.793439	−	0.608650i	$-0.791712\pi$
$449$	−33.6253			−1.58688			−0.793439	+	0.608650i	$0.791712\pi$
$450$		0			0
$451$	−3.03637	−	5.25915i	−0.142977	−	0.247644i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−12.3702	+	23.3505i	−0.579922	+	1.09469i
$456$		0			0
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	−0.940239	−	0.340516i	$-0.889398\pi$
$457$	−16.3541	−	28.3262i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	−0.813742	−	0.581227i	$-0.802573\pi$
$461$	2.07165	−	3.58821i	0.0964865	−	0.167120i	0.910228	+	0.414107i	$0.135906\pi$
$462$		0			0
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	0.992136	−	0.125162i	$-0.0399451\pi$
$463$	8.34176	+	14.4484i	0.387675	+	0.671472i	−0.604462	+	0.796634i	$0.706612\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	−0.278918	−	0.960315i	$-0.589976\pi$
$467$	14.9585	−	25.9089i	0.692198	−	1.19892i	0.971116	−	0.238608i	$-0.0766909\pi$
$468$		0			0
$469$	−25.0247	+	0.911998i	−1.15553	+	0.0421121i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	0.00914304	−	0.0158362i	0.000420397	−	0.000728149i
$474$		0			0
$475$	3.86033	−	6.68630i	0.177124	−	0.306788i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.95930			−0.135214			−0.0676068	−	0.997712i	$-0.521536\pi$
$479$	−2.95930			−0.135214			−0.0676068	+	0.997712i	$0.521536\pi$
$480$		0			0
$481$	7.49814			0.341886
$482$		0			0
$483$		0			0
$484$		0			0
$485$	24.3745	−	42.2179i	1.10679	−	1.91701i
$486$		0			0
$487$	14.0309	+	24.3022i	0.635800	+	1.10124i	0.986345	+	0.164691i	$0.0526628\pi$
$487$	14.0309	+	24.3022i	0.635800	+	1.10124i	−0.350546	+	0.936546i	$0.614004\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	0.937282	+	0.348572i	$0.113333\pi$
$491$	17.0734	+	29.5721i	0.770513	+	1.33457i	−0.166769	+	0.985996i	$0.553333\pi$
$492$		0			0
$493$	16.5091			0.743534
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.68037	−	12.2497i	−0.344512	−	0.549472i
$498$		0			0
$499$	2.28071			0.102099			0.0510493	−	0.998696i	$-0.483743\pi$
$499$	2.28071			0.102099			0.0510493	+	0.998696i	$0.483743\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	13.9890			0.623739			0.311869	−	0.950125i	$-0.399045\pi$
$503$	13.9890			0.623739			0.311869	+	0.950125i	$0.399045\pi$
$504$		0			0
$505$	19.4400			0.865067
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−25.6181			−1.13550			−0.567750	−	0.823201i	$-0.692186\pi$
$509$	−25.6181			−1.13550			−0.567750	+	0.823201i	$0.692186\pi$
$510$		0			0
$511$	14.9437	−	28.2084i	0.661069	−	1.24787i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	6.16435			0.271634
$516$		0			0
$517$	−5.16071	−	8.93861i	−0.226968	−	0.393119i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.9127	+	36.2219i	0.916203	+	1.58691i	0.805130	+	0.593099i	$0.202096\pi$
$521$	20.9127	+	36.2219i	0.916203	+	1.58691i	0.111073	+	0.993812i	$0.464571\pi$
$522$		0			0
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	−0.985301	−	0.170827i	$-0.945356\pi$
$523$	−7.88323	+	13.6542i	−0.344710	+	0.597055i	0.640591	+	0.767882i	$0.278689\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−44.7883			−1.95101
$528$		0			0
$529$	16.5388			0.719080
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.54944	−	9.61192i	0.240373	−	0.416338i
$534$		0			0
$535$	19.9134	−	34.4911i	0.860932	−	1.49118i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.50433	−	9.30701i	0.194015	−	0.400881i
$540$		0			0
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.0887957	+	0.996050i	$0.528302\pi$
$541$	−21.0963	+	36.5399i	−0.907002	+	1.57097i	−0.818207	+	0.574924i	$0.805031\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.349814	+	0.605896i	0.0149844	+	0.0259537i
$546$		0			0
$547$	−20.3356	+	35.2222i	−0.869486	+	1.50599i	−0.00696400	+	0.999976i	$0.502217\pi$
$547$	−20.3356	+	35.2222i	−0.869486	+	1.50599i	−0.862522	+	0.506019i	$0.831117\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.11559	+	1.93227i	0.0475259	+	0.0823173i
$552$		0			0
$553$	−14.1843	+	26.7750i	−0.603178	+	1.13859i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.68794	−	11.5838i	−0.283377	−	0.490823i	0.688837	−	0.724916i	$-0.258121\pi$
$557$	−6.68794	−	11.5838i	−0.283377	−	0.490823i	−0.972214	+	0.234093i	$0.924788\pi$
$558$		0			0
$559$	0.0334206			0.00141354
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	−0.281355	−	0.959604i	$-0.590784\pi$
$563$	16.3807	−	28.3722i	0.690364	−	1.19574i	0.971719	−	0.236141i	$-0.0758828\pi$
$564$		0			0
$565$	−25.0901	−	43.4574i	−1.05555	−	1.82827i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.36398	−	14.4868i	−0.350636	−	0.607320i	0.635725	−	0.771916i	$-0.280701\pi$
$569$	−8.36398	−	14.4868i	−0.350636	−	0.607320i	−0.986361	+	0.164596i	$0.947368\pi$
$570$		0			0
$571$	−13.7367	+	23.7926i	−0.574863	+	0.995691i	0.421194	+	0.906971i	$0.361611\pi$
$571$	−13.7367	+	23.7926i	−0.574863	+	0.995691i	−0.996057	+	0.0887207i	$0.971722\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	54.6253			2.27803
$576$		0			0
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	0.894015	−	0.448037i	$-0.147877\pi$
$577$	1.41714	+	2.45455i	0.0589962	+	0.102184i	−0.835019	+	0.550221i	$0.814543\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	11.8374	−	0.431403i	0.491100	−	0.0178976i
$582$		0			0
$583$	−2.37085	−	4.10644i	−0.0981908	−	0.170071i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	−0.910404	−	0.413720i	$-0.864229\pi$
$587$	−2.34795	+	4.06678i	−0.0969105	+	0.167854i	0.813494	+	0.581573i	$0.197563\pi$
$588$		0			0
$589$	−3.02654	−	5.24212i	−0.124706	−	0.215998i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.636024	+	1.10163i	−0.0261184	+	0.0452383i	−0.878789	−	0.477210i	$-0.841648\pi$
$593$	−0.636024	+	1.10163i	−0.0261184	+	0.0452383i	0.852671	+	0.522449i	$0.174981\pi$
$594$		0			0
$595$	−30.1323	+	56.8792i	−1.23530	+	2.33182i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.0631320	+	0.998005i	$0.520109\pi$
$599$	−21.9258	+	37.9766i	−0.895864	+	1.55168i	−0.832732	+	0.553676i	$0.813224\pi$
$600$		0			0
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	−0.969874	−	0.243609i	$-0.921669\pi$
$601$	−6.71634	+	11.6330i	−0.273965	+	0.474522i	0.695908	+	0.718131i	$0.255002\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	32.6240			1.32635
$606$		0			0
$607$	4.58465			0.186085			0.0930425	−	0.995662i	$-0.470341\pi$
$607$	4.58465			0.186085			0.0930425	+	0.995662i	$0.470341\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	9.43199	−	16.3367i	0.381577	−	0.660911i
$612$		0			0
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	0.551695	−	0.834046i	$-0.313981\pi$
$613$	−11.0538	−	19.1457i	−0.446458	−	0.773287i	−0.998152	+	0.0607587i	$0.980648\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	0.719481	−	0.694513i	$-0.244380\pi$
$617$	−6.00433	−	10.3998i	−0.241725	−	0.418680i	−0.961206	+	0.275832i	$0.911047\pi$
$618$		0			0
$619$	17.5636			0.705941			0.352970	−	0.935634i	$-0.385172\pi$
$619$	17.5636			0.705941			0.352970	+	0.935634i	$0.385172\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	23.4691	−	0.855304i	0.940268	−	0.0342670i
$624$		0			0
$625$	7.03204			0.281282
$626$		0			0
$627$		0			0
$628$		0			0
$629$	18.2646			0.728258
$630$		0			0
$631$	44.9381			1.78896			0.894479	−	0.447110i	$-0.147547\pi$
$631$	44.9381			1.78896			0.894479	+	0.447110i	$0.147547\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−10.5687			−0.419406
$636$		0			0
$637$	18.8473	−	1.37556i	0.746756	−	0.0545018i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	28.9839			1.14480			0.572398	−	0.819976i	$-0.306013\pi$
$641$	28.9839			1.14480			0.572398	+	0.819976i	$0.306013\pi$
$642$		0			0
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	0.722258	−	0.691623i	$-0.243104\pi$
$643$	−6.03087	−	10.4458i	−0.237834	−	0.411941i	−0.960093	+	0.279682i	$0.909771\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	0.951423	+	0.307887i	$0.0996219\pi$
$647$	18.8825	+	32.7055i	0.742349	+	1.28579i	−0.209073	+	0.977900i	$0.567045\pi$
$648$		0			0
$649$	5.10322	−	8.83903i	0.200319	−	0.346962i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−37.4079			−1.46388			−0.731942	−	0.681366i	$-0.761386\pi$
$653$	−37.4079			−1.46388			−0.731942	+	0.681366i	$0.761386\pi$
$654$		0			0
$655$	−0.575984			−0.0225056
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	−0.413455	−	0.910524i	$-0.635678\pi$
$659$	14.9356	−	25.8693i	0.581810	−	1.00772i	0.995265	−	0.0971993i	$-0.0309884\pi$
$660$		0			0
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	−0.915391	−	0.402566i	$-0.868119\pi$
$661$	−2.80401	+	4.85669i	−0.109063	+	0.188904i	0.806328	+	0.591469i	$0.201452\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.69344	+	0.316823i	−0.337117	+	0.0122859i
$666$		0			0
$667$	−7.89307	+	13.6712i	−0.305621	+	0.529351i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.23414	−	7.33375i	−0.163457	−	0.283116i
$672$		0			0
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	−0.942575	−	0.333994i	$-0.891603\pi$
$673$	−4.72253	+	8.17966i	−0.182040	+	0.315303i	0.760535	+	0.649297i	$0.224937\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.53087	+	9.57975i	0.212569	+	0.368180i	0.952518	−	0.304483i	$-0.0984837\pi$
$677$	5.53087	+	9.57975i	0.212569	+	0.368180i	−0.739949	+	0.672663i	$0.765150\pi$
$678$		0			0
$679$	−34.8392	+	1.26968i	−1.33701	+	0.0487258i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	0.768996	−	0.639253i	$-0.220757\pi$
$683$	−4.41961	−	7.65499i	−0.169112	−	0.292910i	−0.938108	+	0.346343i	$0.887423\pi$
$684$		0			0
$685$	−12.6218			−0.482254
$686$		0			0
$687$		0			0
$688$		0			0
$689$	4.33310	−	7.50516i	0.165078	−	0.285924i
$690$		0			0
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	0.999643	−	0.0267023i	$-0.00850061\pi$
$691$	12.5309	+	21.7041i	0.476697	+	0.825663i	−0.522947	+	0.852365i	$0.675167\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−24.9920	−	43.2873i	−0.947999	−	1.64198i
$696$		0			0
$697$	13.5178	−	23.4135i	0.512023	−	0.886850i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	43.4858			1.64243			0.821217	−	0.570616i	$-0.193295\pi$
$701$	43.4858			1.64243			0.821217	+	0.570616i	$0.193295\pi$
$702$		0			0
$703$	1.23422	+	2.13773i	0.0465495	+	0.0806260i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.38502	−	11.7786i	−0.277742	−	0.442979i
$708$		0			0
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	0.996606	−	0.0823158i	$-0.0262316\pi$
$709$	11.3702	+	19.6937i	0.427016	+	0.739613i	−0.569591	+	0.821928i	$0.692898\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	21.4134	−	37.0891i	0.801939	−	1.38900i
$714$		0			0
$715$	−7.37636	−	12.7762i	−0.275860	−	0.477804i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	−0.730571	−	0.682836i	$-0.760746\pi$
$719$	6.06182	−	10.4994i	0.226068	−	0.391561i	0.956639	+	0.291275i	$0.0940796\pi$
$720$		0			0
$721$	−2.34176	−	3.73495i	−0.0872119	−	0.139097i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−10.9048	+	18.8876i	−0.404993	+	0.701468i
$726$		0			0
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	0.0189562	+	0.999820i	$0.493966\pi$
$727$	−23.0908	+	39.9945i	−0.856392	+	1.48331i	−0.875348	+	0.483494i	$0.839368\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.0814088			0.00301101
$732$		0			0
$733$	−36.0297			−1.33079			−0.665394	−	0.746493i	$-0.731736\pi$
$733$	−36.0297			−1.33079			−0.665394	+	0.746493i	$0.731736\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.99017	−	12.1073i	0.257486	−	0.445979i
$738$		0			0
$739$	−23.2119	−	40.2042i	−0.853865	−	1.47894i	−0.877694	−	0.479221i	$-0.840919\pi$
$739$	−23.2119	−	40.2042i	−0.853865	−	1.47894i	0.0238296	−	0.999716i	$-0.492414\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	0.876802	−	0.480852i	$-0.159673\pi$
$743$	0.598884	+	1.03730i	0.0219709	+	0.0380548i	−0.854831	+	0.518907i	$0.826339\pi$
$744$		0			0
$745$	1.23491			0.0452435
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−28.4629	+	1.03730i	−1.04001	+	0.0379021i
$750$		0			0
$751$	−48.1199			−1.75592			−0.877961	−	0.478733i	$-0.841096\pi$
$751$	−48.1199			−1.75592			−0.877961	+	0.478733i	$0.841096\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−73.6588			−2.68072
$756$		0			0
$757$	49.6006			1.80276			0.901382	−	0.433025i	$-0.142554\pi$
$757$	49.6006			1.80276			0.901382	+	0.433025i	$0.142554\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	37.5402			1.36083			0.680416	−	0.732826i	$-0.261799\pi$
$761$	37.5402			1.36083			0.680416	+	0.732826i	$0.261799\pi$
$762$		0			0
$763$	0.234219	−	0.442124i	0.00847931	−	0.0160060i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.6538			0.673551
$768$		0			0
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	0.514506	−	0.857486i	$-0.327975\pi$
$769$	−13.4592	−	23.3121i	−0.485352	−	0.840654i	−0.999858	+	0.0168324i	$0.994642\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−25.1130	−	43.4971i	−0.903254	−	1.56448i	−0.823245	−	0.567687i	$-0.807838\pi$
$773$	−25.1130	−	43.4971i	−0.903254	−	1.56448i	−0.0800089	−	0.996794i	$-0.525495\pi$
$774$		0			0
$775$	29.5840	−	51.2409i	1.06269	−	1.84063i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.65383			0.130912
$780$		0			0
$781$	8.07194			0.288837
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.8800	+	22.3088i	−0.459707	+	0.796236i
$786$		0			0
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	−0.880430	−	0.474176i	$-0.842746\pi$
$787$	−0.829462	+	1.43667i	−0.0295671	+	0.0512118i	0.850863	+	0.525387i	$0.176080\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.7992	+	31.7110i	−0.597311	+	1.12751i
$792$		0			0
$793$	7.73855	−	13.4036i	0.274804	−	0.475974i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	0.998642	+	0.0520981i	$0.0165908\pi$
$797$	15.3702	+	26.6219i	0.544439	+	0.942996i	−0.454203	+	0.890898i	$0.650076\pi$
$798$		0			0
$799$	22.9752	−	39.7943i	0.812806	−	1.40782i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.91095	+	15.4342i	0.314461	+	0.544662i
$804$		0			0
$805$	−32.6952	−	52.1466i	−1.15236	−	1.83793i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.44251	+	2.49850i	0.0507159	+	0.0878425i	0.890269	−	0.455435i	$-0.150516\pi$
$809$	1.44251	+	2.49850i	0.0507159	+	0.0878425i	−0.839553	+	0.543278i	$0.817183\pi$
$810$		0			0
$811$	−28.5461			−1.00239			−0.501195	−	0.865334i	$-0.667106\pi$
$811$	−28.5461			−1.00239			−0.501195	+	0.865334i	$0.667106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	14.9356	−	25.8693i	0.523172	−	0.906161i
$816$		0			0
$817$	0.00550115	+	0.00952827i	0.000192461	+	0.000333352i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.98329	+	6.89926i	0.139018	+	0.240786i	0.927125	−	0.374752i	$-0.122272\pi$
$821$	3.98329	+	6.89926i	0.139018	+	0.240786i	−0.788107	+	0.615538i	$0.788939\pi$
$822$		0			0
$823$	20.2731	−	35.1140i	0.706675	−	1.22400i	−0.259409	−	0.965768i	$-0.583528\pi$
$823$	20.2731	−	35.1140i	0.706675	−	1.22400i	0.966084	−	0.258229i	$-0.0831388\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.22115			0.0424636			0.0212318	−	0.999775i	$-0.493241\pi$
$827$	1.22115			0.0424636			0.0212318	+	0.999775i	$0.493241\pi$
$828$		0			0
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	0.716603	−	0.697481i	$-0.245696\pi$
$829$	−7.07530	−	12.2548i	−0.245735	−	0.425626i	−0.962338	+	0.271856i	$0.912363\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	45.9098	−	3.35071i	1.59068	−	0.116095i
$834$		0			0
$835$	−36.0450	−	62.4318i	−1.24739	−	2.16054i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	−0.844642	−	0.535332i	$-0.820187\pi$
$839$	1.19599	−	2.07151i	0.0412900	−	0.0715164i	0.885932	+	0.463815i	$0.153520\pi$
$840$		0			0
$841$	11.3486	+	19.6564i	0.391333	+	0.677808i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−10.5662	+	18.3011i	−0.363487	+	0.629577i
$846$		0			0
$847$	−12.3935	−	19.7667i	−0.425845	−	0.679193i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−8.73236	+	15.1249i	−0.299341	+	0.518475i
$852$		0			0
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	−0.972744	−	0.231883i	$-0.925511\pi$
$853$	−8.33998	+	14.4453i	−0.285556	+	0.494597i	0.687188	+	0.726479i	$0.258845\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	13.8516			0.473162			0.236581	−	0.971612i	$-0.423973\pi$
$857$	13.8516			0.473162			0.236581	+	0.971612i	$0.423973\pi$
$858$		0			0
$859$	−48.4944			−1.65461			−0.827304	−	0.561754i	$-0.810127\pi$
$859$	−48.4944			−1.65461			−0.827304	+	0.561754i	$0.810127\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	−0.811130	−	0.584866i	$-0.801147\pi$
$863$	2.96541	−	5.13624i	0.100944	−	0.174840i	0.912074	+	0.410026i	$0.134480\pi$
$864$		0			0
$865$	−41.7385	−	72.2932i	−1.41915	−	2.45804i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−8.45813	−	14.6499i	−0.286922	−	0.496964i
$870$		0			0
$871$	25.5512			0.865770
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−19.1723	−	30.5785i	−0.648143	−	1.03374i
$876$		0			0
$877$	3.92944			0.132688			0.0663439	−	0.997797i	$-0.478867\pi$
$877$	3.92944			0.132688			0.0663439	+	0.997797i	$0.478867\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.6552			−1.26864			−0.634318	−	0.773072i	$-0.718719\pi$
$881$	−37.6552			−1.26864			−0.634318	+	0.773072i	$0.718719\pi$
$882$		0			0
$883$	53.2334			1.79145			0.895723	−	0.444613i	$-0.146659\pi$
$883$	53.2334			1.79145			0.895723	+	0.444613i	$0.146659\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−36.9876			−1.24192			−0.620961	−	0.783841i	$-0.713258\pi$
$887$	−36.9876			−1.24192			−0.620961	+	0.783841i	$0.713258\pi$
$888$		0			0
$889$	4.01493	+	6.40353i	0.134656	+	0.214768i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	6.21015			0.207815
$894$		0			0
$895$	−0.617454	−	1.06946i	−0.0206392	−	0.0357482i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.54944	+	14.8081i	0.285140	+	0.493877i
$900$		0			0
$901$	10.5549	−	18.2817i	0.351636	−	0.609052i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−85.9875			−2.85832
$906$		0			0
$907$	39.0159			1.29550			0.647752	−	0.761852i	$-0.275709\pi$
$907$	39.0159			1.29550			0.647752	+	0.761852i	$0.275709\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	−0.996363	−	0.0852158i	$-0.972842\pi$
$911$	−12.8090	+	22.1859i	−0.424382	+	0.735052i	0.571980	+	0.820267i	$0.306175\pi$
$912$		0			0
$913$	−3.30656	+	5.72713i	−0.109431	+	0.189540i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.218810	+	0.348986i	0.00722574	+	0.0115245i
$918$		0			0
$919$	−10.3367	+	17.9038i	−0.340978	+	0.590591i	−0.984615	−	0.174740i	$-0.944091\pi$
$919$	−10.3367	+	17.9038i	−0.340978	+	0.590591i	0.643637	+	0.765331i	$0.277425\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.37636	+	12.7762i	0.242796	+	0.420535i
$924$		0			0
$925$	−12.0643	+	20.8960i	−0.396672	+	0.687055i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.87017	−	3.23922i	−0.0613582	−	0.106275i	0.833715	−	0.552196i	$-0.186210\pi$
$929$	−1.87017	−	3.23922i	−0.0613582	−	0.106275i	−0.895073	+	0.445920i	$0.852877\pi$
$930$		0			0
$931$	3.49450	+	5.14696i	0.114528	+	0.168685i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−17.9680	−	31.1214i	−0.587615	−	1.01778i
$936$		0			0
$937$	−27.1345			−0.886445			−0.443223	−	0.896412i	$-0.646165\pi$
$937$	−27.1345			−0.886445			−0.443223	+	0.896412i	$0.646165\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	3.16435	−	5.48081i	0.103155	−	0.178669i	−0.809828	−	0.586667i	$-0.800440\pi$
$941$	3.16435	−	5.48081i	0.103155	−	0.178669i	0.912983	+	0.407998i	$0.133773\pi$
$942$		0			0
$943$	12.9258	+	22.3881i	0.420922	+	0.729058i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	−0.999955	−	0.00951587i	$-0.996971\pi$
$947$	−15.6396	−	27.0886i	−0.508218	−	0.880260i	0.491736	−	0.870744i	$-0.336362\pi$
$948$		0			0
$949$	−16.2861	+	28.2084i	−0.528670	+	0.915684i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.28937			−0.138946			−0.0694732	−	0.997584i	$-0.522132\pi$
$953$	−4.28937			−0.138946			−0.0694732	+	0.997584i	$0.522132\pi$
$954$		0			0
$955$	−30.1916	−	52.2933i	−0.976977	−	1.69217i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	4.79487	+	7.64749i	0.154834	+	0.246950i
$960$		0			0
$961$	−7.69413	−	13.3266i	−0.248198	−	0.429891i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−26.4920	+	45.8854i	−0.852806	+	1.47710i
$966$		0			0
$967$	7.59201	+	13.1497i	0.244142	+	0.422867i	0.961890	−	0.273436i	$-0.0881602\pi$
$967$	7.59201	+	13.1497i	0.244142	+	0.422867i	−0.717748	+	0.696303i	$0.754827\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	−0.838796	−	0.544445i	$-0.816740\pi$
$971$	1.62364	−	2.81223i	0.0521052	−	0.0902489i	0.890902	+	0.454196i	$0.150074\pi$
$972$		0			0
$973$	−16.7335	+	31.5869i	−0.536450	+	1.01263i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	7.77197	−	13.4614i	0.248647	−	0.430670i	−0.714503	−	0.699632i	$-0.753347\pi$
$977$	7.77197	−	13.4614i	0.248647	−	0.430670i	0.963151	+	0.268962i	$0.0866806\pi$
$978$		0			0
$979$	−6.55563	+	11.3547i	−0.209519	+	0.362897i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	12.3832			0.394961			0.197481	−	0.980307i	$-0.436724\pi$
$983$	12.3832			0.394961			0.197481	+	0.980307i	$0.436724\pi$
$984$		0			0
$985$	8.96796			0.285743
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.0389218	+	0.0674145i	−0.00123764	+	0.00214366i
$990$		0			0
$991$	3.32760	+	5.76358i	0.105705	+	0.183086i	0.914026	−	0.405656i	$-0.132957\pi$
$991$	3.32760	+	5.76358i	0.105705	+	0.183086i	−0.808321	+	0.588742i	$0.799623\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−11.3047	−	19.5803i	−0.358383	−	0.620738i
$996$		0			0
$997$	4.80208			0.152083			0.0760417	−	0.997105i	$-0.475772\pi$
$997$	4.80208			0.152083			0.0760417	+	0.997105i	$0.475772\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.g.289.1		6
3.2	odd	2		1008.2.t.g.961.3		6
4.3	odd	2		378.2.h.d.289.1		6
7.4	even	3		3024.2.q.h.2881.3		6
9.4	even	3		3024.2.q.h.2305.3		6
9.5	odd	6		1008.2.q.h.625.3		6
12.11	even	2		126.2.h.c.79.1	yes	6
21.11	odd	6		1008.2.q.h.529.3		6
28.3	even	6		2646.2.e.o.2125.1		6
28.11	odd	6		378.2.e.c.235.3		6
28.19	even	6		2646.2.f.n.883.1		6
28.23	odd	6		2646.2.f.o.883.3		6
28.27	even	2		2646.2.h.p.667.3		6
36.7	odd	6		1134.2.g.n.163.3		6
36.11	even	6		1134.2.g.k.163.1		6
36.23	even	6		126.2.e.d.121.1	yes	6
36.31	odd	6		378.2.e.c.37.3		6
63.4	even	3	inner	3024.2.t.g.1873.1		6
63.32	odd	6		1008.2.t.g.193.3		6
84.11	even	6		126.2.e.d.25.1	✓	6
84.23	even	6		882.2.f.l.295.3		6
84.47	odd	6		882.2.f.m.295.1		6
84.59	odd	6		882.2.e.p.655.3		6
84.83	odd	2		882.2.h.o.79.3		6
252.11	even	6		1134.2.g.k.487.1		6
252.23	even	6		882.2.f.l.589.3		6
252.31	even	6		2646.2.h.p.361.3		6
252.47	odd	6		7938.2.a.by.1.1		3
252.59	odd	6		882.2.h.o.67.3		6
252.67	odd	6		378.2.h.d.361.1		6
252.79	odd	6		7938.2.a.bu.1.1		3
252.95	even	6		126.2.h.c.67.1	yes	6
252.103	even	6		2646.2.f.n.1765.1		6
252.131	odd	6		882.2.f.m.589.1		6
252.139	even	6		2646.2.e.o.1549.1		6
252.151	odd	6		1134.2.g.n.487.3		6
252.167	odd	6		882.2.e.p.373.3		6
252.187	even	6		7938.2.a.bx.1.3		3
252.191	even	6		7938.2.a.cb.1.3		3
252.247	odd	6		2646.2.f.o.1765.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.d.25.1	✓	6	84.11	even	6
126.2.e.d.121.1	yes	6	36.23	even	6
126.2.h.c.67.1	yes	6	252.95	even	6
126.2.h.c.79.1	yes	6	12.11	even	2
378.2.e.c.37.3		6	36.31	odd	6
378.2.e.c.235.3		6	28.11	odd	6
378.2.h.d.289.1		6	4.3	odd	2
378.2.h.d.361.1		6	252.67	odd	6
882.2.e.p.373.3		6	252.167	odd	6
882.2.e.p.655.3		6	84.59	odd	6
882.2.f.l.295.3		6	84.23	even	6
882.2.f.l.589.3		6	252.23	even	6
882.2.f.m.295.1		6	84.47	odd	6
882.2.f.m.589.1		6	252.131	odd	6
882.2.h.o.67.3		6	252.59	odd	6
882.2.h.o.79.3		6	84.83	odd	2
1008.2.q.h.529.3		6	21.11	odd	6
1008.2.q.h.625.3		6	9.5	odd	6
1008.2.t.g.193.3		6	63.32	odd	6
1008.2.t.g.961.3		6	3.2	odd	2
1134.2.g.k.163.1		6	36.11	even	6
1134.2.g.k.487.1		6	252.11	even	6
1134.2.g.n.163.3		6	36.7	odd	6
1134.2.g.n.487.3		6	252.151	odd	6
2646.2.e.o.1549.1		6	252.139	even	6
2646.2.e.o.2125.1		6	28.3	even	6
2646.2.f.n.883.1		6	28.19	even	6
2646.2.f.n.1765.1		6	252.103	even	6
2646.2.f.o.883.3		6	28.23	odd	6
2646.2.f.o.1765.3		6	252.247	odd	6
2646.2.h.p.361.3		6	252.31	even	6
2646.2.h.p.667.3		6	28.27	even	2
3024.2.q.h.2305.3		6	9.4	even	3
3024.2.q.h.2881.3		6	7.4	even	3
3024.2.t.g.289.1		6	1.1	even	1	trivial
3024.2.t.g.1873.1		6	63.4	even	3	inner
7938.2.a.bu.1.1		3	252.79	odd	6
7938.2.a.bx.1.3		3	252.187	even	6
7938.2.a.by.1.1		3	252.47	odd	6
7938.2.a.cb.1.3		3	252.191	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-3.69963 q^{5} +(1.40545 + 2.24159i) q^{7} +O(q^{10})\)	\(q-3.69963 q^{5} +(1.40545 + 2.24159i) q^{7} -1.47710 q^{11} +(-1.34981 - 2.33795i) q^{13} +(-3.28799 - 5.69497i) q^{17} +(0.444368 - 0.769668i) q^{19} +6.28799 q^{23} +8.68725 q^{25} +(-1.25526 + 2.17417i) q^{29} +(3.40545 - 5.89841i) q^{31} +(-5.19963 - 8.29305i) q^{35} +(-1.38874 + 2.40536i) q^{37} +(2.05563 + 3.56046i) q^{41} +(-0.00618986 + 0.0107211i) q^{43} +(3.49381 + 6.05146i) q^{47} +(-3.04944 + 6.30087i) q^{49} +(1.60507 + 2.78007i) q^{53} +5.46472 q^{55} +(-3.45489 + 5.98404i) q^{59} +(2.86652 + 4.96497i) q^{61} +(4.99381 + 8.64953i) q^{65} +(-4.73236 + 8.19669i) q^{67} -5.46472 q^{71} +(-6.03273 - 10.4490i) q^{73} +(-2.07598 - 3.31105i) q^{77} +(5.72617 + 9.91802i) q^{79} +(2.23855 - 3.87728i) q^{83} +(12.1643 + 21.0693i) q^{85} +(4.43818 - 7.68715i) q^{89} +(3.34362 - 6.31159i) q^{91} +(-1.64400 + 2.84748i) q^{95} +(-6.58836 + 11.4114i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 10 q^{5} + 2 q^{7}+O(q^{10}) \) 6 * q - 10 * q^5 + 2 * q^7	\( 6 q - 10 q^{5} + 2 q^{7} + 2 q^{11} - 2 q^{13} + 4 q^{17} + 3 q^{19} + 14 q^{23} + 4 q^{25} + 5 q^{29} + 14 q^{31} - 19 q^{35} - 9 q^{37} + 12 q^{41} - 18 q^{43} + 3 q^{47} - 9 q^{53} - 14 q^{55} + 4 q^{59} + 4 q^{61} + 12 q^{65} - 5 q^{67} + 14 q^{71} - 25 q^{73} + 35 q^{77} - 7 q^{79} + 8 q^{83} + 14 q^{85} + 9 q^{89} - 4 q^{91} + 2 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q - 10 * q^5 + 2 * q^7 + 2 * q^11 - 2 * q^13 + 4 * q^17 + 3 * q^19 + 14 * q^23 + 4 * q^25 + 5 * q^29 + 14 * q^31 - 19 * q^35 - 9 * q^37 + 12 * q^41 - 18 * q^43 + 3 * q^47 - 9 * q^53 - 14 * q^55 + 4 * q^59 + 4 * q^61 + 12 * q^65 - 5 * q^67 + 14 * q^71 - 25 * q^73 + 35 * q^77 - 7 * q^79 + 8 * q^83 + 14 * q^85 + 9 * q^89 - 4 * q^91 + 2 * q^95 - 28 * q^97

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