LMFDB - Embedded newform 3024.2.t.i.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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$-0.335166 + 0.580525i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.i.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.42494 q^{5} +(-2.21529 - 1.44655i) q^{7} +O(q^{10})$	$q-1.42494 q^{5} +(-2.21529 - 1.44655i) q^{7} -4.93077 q^{11} +(-1.37730 - 2.38556i) q^{13} +(-0.559839 - 0.969670i) q^{17} +(2.00752 - 3.47713i) q^{19} +5.43661 q^{23} -2.96955 q^{25} +(-3.40555 + 5.89858i) q^{29} +(1.25292 - 2.17012i) q^{31} +(3.15664 + 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} +(-0.124384 - 0.215440i) q^{41} +(0.498313 - 0.863104i) q^{43} +(4.73790 + 8.20628i) q^{47} +(2.81498 + 6.40905i) q^{49} +(0.410229 + 0.710537i) q^{53} +7.02604 q^{55} +(3.29204 - 5.70197i) q^{59} +(-0.0376322 - 0.0651809i) q^{61} +(1.96257 + 3.39927i) q^{65} +(-6.29385 + 10.9013i) q^{67} +0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +(10.9231 + 7.13261i) q^{77} +(-0.922457 - 1.59774i) q^{79} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(-6.76292 + 11.7137i) q^{89} +(-0.399711 + 7.27703i) q^{91} +(-2.86059 + 4.95469i) q^{95} +(2.70160 - 4.67930i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 8 q^{5} + q^{7}+O(q^{10}) $ 10 * q + 8 * q^5 + q^7	$ 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) $ 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * 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
$5$	−1.42494			−0.637251			−0.318626	−	0.947881i	$-0.603221\pi$
$5$	−1.42494			−0.637251			−0.318626	+	0.947881i	$0.603221\pi$
$6$		0			0
$7$	−2.21529	−	1.44655i	−0.837299	−	0.546745i
$7$	−2.21529	−	1.44655i	−0.837299	−	0.546745i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.93077			−1.48668			−0.743342	−	0.668911i	$-0.766761\pi$
$11$	−4.93077			−1.48668			−0.743342	+	0.668911i	$0.766761\pi$
$12$		0			0
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	0.609352	−	0.792900i	$-0.291429\pi$
$13$	−1.37730	−	2.38556i	−0.381995	−	0.661635i	−0.991347	+	0.131265i	$0.958096\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	0.790115	−	0.612959i	$-0.210021\pi$
$17$	−0.559839	−	0.969670i	−0.135781	−	0.235180i	−0.925896	+	0.377780i	$0.876688\pi$
$18$		0			0
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	−0.538431	−	0.842669i	$-0.680983\pi$
$19$	2.00752	−	3.47713i	0.460557	−	0.797709i	0.998989	+	0.0449606i	$0.0143162\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.43661			1.13361			0.566806	−	0.823851i	$-0.308179\pi$
$23$	5.43661			1.13361			0.566806	+	0.823851i	$0.308179\pi$
$24$		0			0
$25$	−2.96955			−0.593911
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	0.354667	+	0.934993i	$0.384594\pi$
$29$	−3.40555	+	5.89858i	−0.632394	+	1.09534i	−0.987061	+	0.160346i	$0.948739\pi$
$30$		0			0
$31$	1.25292	−	2.17012i	0.225031	−	0.389765i	−0.731298	−	0.682058i	$-0.761085\pi$
$31$	1.25292	−	2.17012i	0.225031	−	0.389765i	0.956329	+	0.292294i	$0.0944184\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.15664	+	2.06124i	0.533570	+	0.348414i
$36$		0			0
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	−0.801765	−	0.597639i	$-0.796106\pi$
$37$	0.709787	−	1.22939i	0.116688	−	0.202110i	0.918453	+	0.395529i	$0.129439\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	0.856149	−	0.516729i	$-0.172850\pi$
$41$	−0.124384	−	0.215440i	−0.0194256	−	0.0336460i	−0.875575	+	0.483083i	$0.839517\pi$
$42$		0			0
$43$	0.498313	−	0.863104i	0.0759921	−	0.131622i	−0.825525	−	0.564365i	$-0.809121\pi$
$43$	0.498313	−	0.863104i	0.0759921	−	0.131622i	0.901517	+	0.432743i	$0.142454\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.73790	+	8.20628i	0.691093	+	1.19701i	0.971480	+	0.237122i	$0.0762040\pi$
$47$	4.73790	+	8.20628i	0.691093	+	1.19701i	−0.280387	+	0.959887i	$0.590463\pi$
$48$		0			0
$49$	2.81498	+	6.40905i	0.402140	+	0.915578i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	0.892824	−	0.450406i	$-0.148721\pi$
$53$	0.410229	+	0.710537i	0.0563493	+	0.0975998i	−0.836475	+	0.548005i	$0.815387\pi$
$54$		0			0
$55$	7.02604			0.947392
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	−0.568161	−	0.822917i	$-0.692345\pi$
$59$	3.29204	−	5.70197i	0.428586	−	0.742334i	0.996748	+	0.0805836i	$0.0256784\pi$
$60$		0			0
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	0.863606	−	0.504167i	$-0.168200\pi$
$61$	−0.0376322	−	0.0651809i	−0.00481831	−	0.00834556i	−0.868425	+	0.495821i	$0.834867\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.96257	+	3.39927i	0.243427	+	0.421628i
$66$		0			0
$67$	−6.29385	+	10.9013i	−0.768916	+	1.33180i	0.169235	+	0.985576i	$0.445870\pi$
$67$	−6.29385	+	10.9013i	−0.768916	+	1.33180i	−0.938151	+	0.346226i	$0.887463\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.0804951			0.00955301			0.00477651	−	0.999989i	$-0.498480\pi$
$71$	0.0804951			0.00955301			0.00477651	+	0.999989i	$0.498480\pi$
$72$		0			0
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	0.988416	+	0.151769i	$0.0484971\pi$
$73$	5.34551	+	9.25869i	0.625644	+	1.08365i	−0.362772	+	0.931878i	$0.618170\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.9231	+	7.13261i	1.24480	+	0.812837i
$78$		0			0
$79$	−0.922457	−	1.59774i	−0.103785	−	0.179760i	0.809456	−	0.587180i	$-0.199762\pi$
$79$	−0.922457	−	1.59774i	−0.103785	−	0.179760i	−0.913241	+	0.407420i	$0.866429\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	0.129088	+	0.991633i	$0.458795\pi$
$83$	−7.23583	+	12.5328i	−0.794236	+	1.37566i	−0.923323	+	0.384023i	$0.874538\pi$
$84$		0			0
$85$	0.797736	+	1.38172i	0.0865266	+	0.149868i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	0.245366	+	0.969430i	$0.421092\pi$
$89$	−6.76292	+	11.7137i	−0.716868	+	1.24165i	−0.962235	+	0.272222i	$0.912242\pi$
$90$		0			0
$91$	−0.399711	+	7.27703i	−0.0419011	+	0.762840i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.86059	+	4.95469i	−0.293491	+	0.508341i
$96$		0			0
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	−0.695654	−	0.718377i	$-0.744885\pi$
$97$	2.70160	−	4.67930i	0.274306	−	0.475111i	0.969960	+	0.243266i	$0.0782187\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.13540			0.510991			0.255496	−	0.966810i	$-0.417761\pi$
$101$	5.13540			0.510991			0.255496	+	0.966810i	$0.417761\pi$
$102$		0			0
$103$	14.2112			1.40027			0.700137	−	0.714009i	$-0.253122\pi$
$103$	14.2112			1.40027			0.700137	+	0.714009i	$0.253122\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	−0.619333	−	0.785128i	$-0.712597\pi$
$107$	3.83015	−	6.63401i	0.370274	−	0.641334i	0.989608	+	0.143794i	$0.0459303\pi$
$108$		0			0
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	0.822476	−	0.568800i	$-0.192592\pi$
$109$	−0.849394	−	1.47119i	−0.0813572	−	0.140915i	−0.903833	+	0.427885i	$0.859259\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	0.879807	−	0.475331i	$-0.157672\pi$
$113$	0.300351	+	0.520224i	0.0282547	+	0.0489385i	−0.851552	+	0.524270i	$0.824338\pi$
$114$		0			0
$115$	−7.74683			−0.722395
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.162473	+	2.95793i	−0.0148939	+	0.271153i
$120$		0			0
$121$	13.3125			1.21023
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.3561			1.01572
$126$		0			0
$127$	−7.25977			−0.644200			−0.322100	−	0.946706i	$-0.604389\pi$
$127$	−7.25977			−0.644200			−0.322100	+	0.946706i	$0.604389\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−20.4530			−1.78698			−0.893492	−	0.449079i	$-0.851752\pi$
$131$	−20.4530			−1.78698			−0.893492	+	0.449079i	$0.851752\pi$
$132$		0			0
$133$	−9.47708	+	4.79886i	−0.821767	+	0.416114i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−12.2116			−1.04331			−0.521655	−	0.853157i	$-0.674685\pi$
$137$	−12.2116			−1.04331			−0.521655	+	0.853157i	$0.674685\pi$
$138$		0			0
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	0.913842	−	0.406071i	$-0.133101\pi$
$139$	1.24092	+	2.14933i	0.105253	+	0.182304i	−0.808588	+	0.588375i	$0.799768\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.79117	+	11.7626i	0.567906	+	0.983642i
$144$		0			0
$145$	4.85269	−	8.40511i	0.402994	−	0.698006i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.55593			0.700929			0.350465	−	0.936576i	$-0.386024\pi$
$149$	8.55593			0.700929			0.350465	+	0.936576i	$0.386024\pi$
$150$		0			0
$151$	17.6592			1.43709			0.718544	−	0.695482i	$-0.244809\pi$
$151$	17.6592			1.43709			0.718544	+	0.695482i	$0.244809\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.78533	+	3.09228i	−0.143401	+	0.248378i
$156$		0			0
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	−0.964146	−	0.265371i	$-0.914505\pi$
$157$	−3.16074	+	5.47457i	−0.252255	+	0.436918i	0.711891	+	0.702289i	$0.247839\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−12.0436	−	7.86433i	−0.949172	−	0.619796i
$162$		0			0
$163$	4.01134	−	6.94784i	0.314192	−	0.544197i	−0.665073	−	0.746778i	$-0.731600\pi$
$163$	4.01134	−	6.94784i	0.314192	−	0.544197i	0.979265	+	0.202581i	$0.0649331\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	0.904132	−	0.427253i	$-0.140518\pi$
$167$	1.06038	+	1.83663i	0.0820545	+	0.142123i	−0.822078	+	0.569375i	$0.807185\pi$
$168$		0			0
$169$	2.70608	−	4.68706i	0.208160	−	0.360543i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	−0.970110	−	0.242664i	$-0.921979\pi$
$173$	−9.14404	−	15.8379i	−0.695208	−	1.20414i	0.274902	−	0.961472i	$-0.411354\pi$
$174$		0			0
$175$	6.57841	+	4.29561i	0.497281	+	0.324718i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	0.972604	−	0.232468i	$-0.0746801\pi$
$179$	3.81276	+	6.60389i	0.284979	+	0.493598i	−0.687625	+	0.726066i	$0.741347\pi$
$180$		0			0
$181$	15.5305			1.15438			0.577188	−	0.816611i	$-0.304150\pi$
$181$	15.5305			1.15438			0.577188	+	0.816611i	$0.304150\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.01140	+	1.75180i	−0.0743597	+	0.128795i
$186$		0			0
$187$	2.76044	+	4.78122i	0.201863	+	0.349638i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	−0.999083	−	0.0428150i	$-0.986367\pi$
$191$	−7.41624	−	12.8453i	−0.536620	−	0.929454i	0.462463	−	0.886639i	$-0.346966\pi$
$192$		0			0
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	0.397078	+	0.917785i	$0.370024\pi$
$193$	−8.28387	+	14.3481i	−0.596286	+	1.03280i	−0.993364	+	0.115013i	$0.963309\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.03740			0.287653			0.143826	−	0.989603i	$-0.454059\pi$
$197$	4.03740			0.287653			0.143826	+	0.989603i	$0.454059\pi$
$198$		0			0
$199$	12.6407	+	21.8943i	0.896076	+	1.55205i	0.832468	+	0.554074i	$0.186927\pi$
$199$	12.6407	+	21.8943i	0.896076	+	1.55205i	0.0636081	+	0.997975i	$0.479739\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	16.0769	−	8.14075i	1.12837	−	0.571368i
$204$		0			0
$205$	0.177240	+	0.306988i	0.0123790	+	0.0214410i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−9.89864	+	17.1449i	−0.684703	+	1.18594i
$210$		0			0
$211$	3.76246	+	6.51678i	0.259019	+	0.448634i	0.965979	−	0.258619i	$-0.0832675\pi$
$211$	3.76246	+	6.51678i	0.259019	+	0.448634i	−0.706961	+	0.707253i	$0.749934\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.710065	+	1.22987i	−0.0484261	+	0.0838764i
$216$		0			0
$217$	−5.91476	+	2.99502i	−0.401520	+	0.203315i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.54214	+	2.67106i	−0.103735	+	0.179675i
$222$		0			0
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	−0.997276	−	0.0737638i	$-0.976499\pi$
$223$	−6.49230	+	11.2450i	−0.434757	+	0.753020i	0.562519	+	0.826784i	$0.309832\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−28.9665			−1.92257			−0.961286	−	0.275551i	$-0.911140\pi$
$227$	−28.9665			−1.92257			−0.961286	+	0.275551i	$0.911140\pi$
$228$		0			0
$229$	15.4358			1.02003			0.510013	−	0.860167i	$-0.329640\pi$
$229$	15.4358			1.02003			0.510013	+	0.860167i	$0.329640\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	−0.773568	−	0.633713i	$-0.781530\pi$
$233$	2.47324	−	4.28378i	0.162027	−	0.280640i	0.935596	+	0.353073i	$0.114863\pi$
$234$		0			0
$235$	−6.75121	−	11.6934i	−0.440400	−	0.762795i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.51732	+	11.2883i	0.421571	+	0.730182i	0.996093	−	0.0883069i	$-0.0281456\pi$
$239$	6.51732	+	11.2883i	0.421571	+	0.730182i	−0.574523	+	0.818489i	$0.694812\pi$
$240$		0			0
$241$	14.5825			0.939339			0.469670	−	0.882842i	$-0.344373\pi$
$241$	14.5825			0.939339			0.469670	+	0.882842i	$0.344373\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.01117	−	9.13249i	−0.256265	−	0.583453i
$246$		0			0
$247$	−11.0599			−0.703722
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−14.0715			−0.888187			−0.444094	−	0.895980i	$-0.646474\pi$
$251$	−14.0715			−0.888187			−0.444094	+	0.895980i	$0.646474\pi$
$252$		0			0
$253$	−26.8067			−1.68532
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.36215			0.521617			0.260808	−	0.965391i	$-0.416011\pi$
$257$	8.36215			0.521617			0.260808	+	0.965391i	$0.416011\pi$
$258$		0			0
$259$	−3.35075	+	1.69670i	−0.208206	+	0.105428i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.27066			0.201678			0.100839	−	0.994903i	$-0.467847\pi$
$263$	3.27066			0.201678			0.100839	+	0.994903i	$0.467847\pi$
$264$		0			0
$265$	−0.584551	−	1.01247i	−0.0359087	−	0.0621956i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	0.999375	−	0.0353420i	$-0.0112521\pi$
$269$	7.69349	+	13.3255i	0.469081	+	0.812471i	−0.530295	+	0.847813i	$0.677919\pi$
$270$		0			0
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	−0.962640	−	0.270783i	$-0.912717\pi$
$271$	−4.06308	+	7.03747i	−0.246815	+	0.427496i	0.715825	+	0.698279i	$0.246051\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	14.6422			0.882958
$276$		0			0
$277$	12.8457			0.771826			0.385913	−	0.922535i	$-0.373887\pi$
$277$	12.8457			0.771826			0.385913	+	0.922535i	$0.373887\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	−0.843620	−	0.536941i	$-0.819580\pi$
$281$	0.724081	−	1.25415i	0.0431951	−	0.0748161i	0.886815	+	0.462125i	$0.152913\pi$
$282$		0			0
$283$	−8.71926	+	15.1022i	−0.518306	+	0.897732i	0.481468	+	0.876464i	$0.340104\pi$
$283$	−8.71926	+	15.1022i	−0.518306	+	0.897732i	−0.999774	+	0.0212686i	$0.993229\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.0360979	+	0.657189i	−0.00213079	+	0.0387926i
$288$		0			0
$289$	7.87316	−	13.6367i	0.463127	−	0.802160i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	0.891118	−	0.453772i	$-0.149922\pi$
$293$	0.900048	+	1.55893i	0.0525814	+	0.0910736i	−0.838537	+	0.544845i	$0.816588\pi$
$294$		0			0
$295$	−4.69094	+	8.12495i	−0.273117	+	0.473053i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.48786	−	12.9693i	−0.433034	−	0.750037i
$300$		0			0
$301$	−2.35243	+	1.19119i	−0.135592	+	0.0686589i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.0536236	+	0.0928787i	0.00307048	+	0.00531822i
$306$		0			0
$307$	−1.06478			−0.0607699			−0.0303850	−	0.999538i	$-0.509673\pi$
$307$	−1.06478			−0.0607699			−0.0303850	+	0.999538i	$0.509673\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	−0.519751	−	0.854318i	$-0.673975\pi$
$311$	8.46463	−	14.6612i	0.479985	−	0.831359i	0.999736	+	0.0229591i	$0.00730874\pi$
$312$		0			0
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	0.958972	−	0.283502i	$-0.0914963\pi$
$313$	4.13928	+	7.16944i	0.233966	+	0.405241i	−0.725006	+	0.688743i	$0.758163\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.27371	+	5.67023i	0.183870	+	0.318472i	0.943195	−	0.332239i	$-0.107804\pi$
$317$	3.27371	+	5.67023i	0.183870	+	0.318472i	−0.759325	+	0.650711i	$0.774471\pi$
$318$		0			0
$319$	16.7920	−	29.0846i	0.940171	−	1.62842i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.49556			−0.250140
$324$		0			0
$325$	4.08997	+	7.08404i	0.226871	+	0.392952i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.37500	−	25.0329i	0.0758062	−	1.38011i
$330$		0			0
$331$	−13.3629	−	23.1453i	−0.734493	−	1.27218i	−0.954946	−	0.296781i	$-0.904087\pi$
$331$	−13.3629	−	23.1453i	−0.734493	−	1.27218i	0.220453	−	0.975398i	$-0.429246\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.96834	−	15.5336i	0.489993	−	0.848692i
$336$		0			0
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	0.706694	−	0.707520i	$-0.250186\pi$
$337$	−4.76164	−	8.24740i	−0.259383	−	0.449264i	−0.966077	+	0.258255i	$0.916853\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.17786	+	10.7004i	−0.334550	+	0.579457i
$342$		0			0
$343$	3.03502	−	18.2699i	0.163876	−	0.986481i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	−0.497979	−	0.867189i	$-0.665924\pi$
$347$	9.35156	−	16.1974i	0.502018	−	0.869521i	0.999997	−	0.00233189i	$-0.000742265\pi$
$348$		0			0
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	0.109893	+	0.993943i	$0.464949\pi$
$349$	−15.0542	+	26.0747i	−0.805834	+	1.39574i	−0.915727	+	0.401801i	$0.868384\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.25933			−0.333150			−0.166575	−	0.986029i	$-0.553271\pi$
$353$	−6.25933			−0.333150			−0.166575	+	0.986029i	$0.553271\pi$
$354$		0			0
$355$	−0.114700			−0.00608767
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	−0.968614	−	0.248571i	$-0.920039\pi$
$359$	−5.09755	+	8.82921i	−0.269038	+	0.465988i	0.699575	+	0.714559i	$0.253372\pi$
$360$		0			0
$361$	1.43970	+	2.49364i	0.0757739	+	0.131244i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.61701	−	13.1931i	−0.398693	−	0.690556i
$366$		0			0
$367$	28.6557			1.49581			0.747906	−	0.663804i	$-0.231059\pi$
$367$	28.6557			1.49581			0.747906	+	0.663804i	$0.231059\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.119054	−	2.16746i	0.00618097	−	0.112529i
$372$		0			0
$373$	−16.0734			−0.832249			−0.416124	−	0.909308i	$-0.636612\pi$
$373$	−16.0734			−0.832249			−0.416124	+	0.909308i	$0.636612\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.7619			0.966286
$378$		0			0
$379$	1.01893			0.0523388			0.0261694	−	0.999658i	$-0.491669\pi$
$379$	1.01893			0.0523388			0.0261694	+	0.999658i	$0.491669\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.5865			−0.592044			−0.296022	−	0.955181i	$-0.595660\pi$
$383$	−11.5865			−0.592044			−0.296022	+	0.955181i	$0.595660\pi$
$384$		0			0
$385$	−15.5647	−	10.1635i	−0.793250	−	0.517981i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.8135			−0.903181			−0.451590	−	0.892225i	$-0.649143\pi$
$389$	−17.8135			−0.903181			−0.451590	+	0.892225i	$0.649143\pi$
$390$		0			0
$391$	−3.04363	−	5.27172i	−0.153923	−	0.266602i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.31444	+	2.27668i	0.0661369	+	0.114552i
$396$		0			0
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	−0.982184	−	0.187921i	$-0.939825\pi$
$397$	−6.54229	+	11.3316i	−0.328348	+	0.568715i	0.653836	+	0.756636i	$0.273159\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.1033			−0.704285			−0.352143	−	0.935946i	$-0.614547\pi$
$401$	−14.1033			−0.704285			−0.352143	+	0.935946i	$0.614547\pi$
$402$		0			0
$403$	−6.90259			−0.343842
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.49980	+	6.06183i	−0.173479	+	0.300474i
$408$		0			0
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	−0.831461	−	0.555583i	$-0.812495\pi$
$409$	1.32300	−	2.29150i	0.0654179	−	0.113307i	0.896879	+	0.442275i	$0.145829\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.5410	+	7.86940i	−0.764722	+	0.387228i
$414$		0			0
$415$	10.3106	−	17.8585i	0.506128	−	0.876639i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	0.906700	+	0.421776i	$0.138593\pi$
$419$	16.7567	+	29.0235i	0.818619	+	1.41789i	−0.0880816	+	0.996113i	$0.528074\pi$
$420$		0			0
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	−0.918943	−	0.394390i	$-0.870956\pi$
$421$	−2.41950	+	4.19071i	−0.117919	+	0.204242i	0.801024	+	0.598633i	$0.204289\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.66247	+	2.87949i	0.0806418	+	0.139676i
$426$		0			0
$427$	−0.0109214	+	0.198831i	−0.000528522	+	0.00962212i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	0.880435	+	0.474166i	$0.157251\pi$
$431$	17.6643	+	30.5954i	0.850858	+	1.47373i	−0.0295774	+	0.999562i	$0.509416\pi$
$432$		0			0
$433$	5.47404			0.263066			0.131533	−	0.991312i	$-0.458010\pi$
$433$	5.47404			0.263066			0.131533	+	0.991312i	$0.458010\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.9141	−	18.9038i	0.522093	−	0.904292i
$438$		0			0
$439$	3.19906	+	5.54093i	0.152683	+	0.264454i	0.932213	−	0.361911i	$-0.117875\pi$
$439$	3.19906	+	5.54093i	0.152683	+	0.264454i	−0.779530	+	0.626365i	$0.784542\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	0.931861	−	0.362815i	$-0.118184\pi$
$443$	3.19341	+	5.53115i	0.151723	+	0.262793i	−0.780138	+	0.625608i	$0.784851\pi$
$444$		0			0
$445$	9.63674	−	16.6913i	0.456825	−	0.791245i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.7460			0.554327			0.277163	−	0.960823i	$-0.410606\pi$
$449$	11.7460			0.554327			0.277163	+	0.960823i	$0.410606\pi$
$450$		0			0
$451$	0.613311	+	1.06229i	0.0288797	+	0.0500210i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.569564	−	10.3693i	0.0267016	−	0.486121i
$456$		0			0
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	0.716334	−	0.697757i	$-0.245819\pi$
$457$	−5.26120	−	9.11266i	−0.246108	−	0.426272i	−0.962443	+	0.271485i	$0.912485\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	−0.771653	−	0.636044i	$-0.780570\pi$
$461$	3.54278	−	6.13627i	0.165004	−	0.285794i	0.936657	+	0.350249i	$0.113903\pi$
$462$		0			0
$463$	−16.3760	−	28.3641i	−0.761059	−	1.31819i	−0.942305	−	0.334755i	$-0.891346\pi$
$463$	−16.3760	−	28.3641i	−0.761059	−	1.31819i	0.181246	−	0.983438i	$-0.441987\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.96216	−	3.39856i	0.0907978	−	0.157266i	−0.817049	−	0.576568i	$-0.804392\pi$
$467$	1.96216	−	3.39856i	0.0907978	−	0.157266i	0.907847	+	0.419301i	$0.137725\pi$
$468$		0			0
$469$	29.7119	−	15.0450i	1.37197	−	0.694716i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.45707	+	4.25577i	−0.112976	+	0.195681i
$474$		0			0
$475$	−5.96145	+	10.3255i	−0.273530	+	0.473768i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	16.0865			0.735010			0.367505	−	0.930022i	$-0.380212\pi$
$479$	16.0865			0.735010			0.367505	+	0.930022i	$0.380212\pi$
$480$		0			0
$481$	−3.91036			−0.178297
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.84961	+	6.66771i	−0.174802	+	0.302765i
$486$		0			0
$487$	1.75172	+	3.03407i	0.0793781	+	0.137487i	0.902982	−	0.429679i	$-0.141373\pi$
$487$	1.75172	+	3.03407i	0.0793781	+	0.137487i	−0.823604	+	0.567166i	$0.808040\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−20.5546	−	35.6017i	−0.927618	−	1.60668i	−0.787296	−	0.616575i	$-0.788520\pi$
$491$	−20.5546	−	35.6017i	−0.927618	−	1.60668i	−0.140321	−	0.990106i	$-0.544814\pi$
$492$		0			0
$493$	7.62624			0.343468
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.178320	−	0.116440i	−0.00799873	−	0.00522306i
$498$		0			0
$499$	−11.8297			−0.529571			−0.264785	−	0.964307i	$-0.585301\pi$
$499$	−11.8297			−0.529571			−0.264785	+	0.964307i	$0.585301\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.8595			0.974665			0.487332	−	0.873217i	$-0.337970\pi$
$503$	21.8595			0.974665			0.487332	+	0.873217i	$0.337970\pi$
$504$		0			0
$505$	−7.31762			−0.325630
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.8966			−0.748930			−0.374465	−	0.927241i	$-0.622174\pi$
$509$	−16.8966			−0.748930			−0.374465	+	0.927241i	$0.622174\pi$
$510$		0			0
$511$	1.55134	−	28.2432i	0.0686271	−	1.24941i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−20.2501			−0.892326
$516$		0			0
$517$	−23.3615	−	40.4633i	−1.02744	−	1.77957i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	0.945082	+	0.326834i	$0.105982\pi$
$521$	17.2466	+	29.8720i	0.755587	+	1.30872i	−0.189495	+	0.981882i	$0.560685\pi$
$522$		0			0
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	−0.886972	−	0.461823i	$-0.847195\pi$
$523$	−0.995615	+	1.72445i	−0.0435352	+	0.0754051i	0.843437	+	0.537229i	$0.180529\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.80573			−0.122220
$528$		0			0
$529$	6.55673			0.285075
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.342629	+	0.593452i	−0.0148409	+	0.0257052i
$534$		0			0
$535$	−5.45772	+	9.45305i	−0.235958	+	0.408691i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.8800	−	31.6016i	−0.597856	−	1.36118i
$540$		0			0
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	0.335810	+	0.941930i	$0.390990\pi$
$541$	−15.0681	+	26.0988i	−0.647830	+	1.12207i	−0.983640	+	0.180145i	$0.942343\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.21033	+	2.09636i	0.0518450	+	0.0897982i
$546$		0			0
$547$	−7.68070	+	13.3034i	−0.328403	+	0.568810i	−0.982195	−	0.187864i	$-0.939844\pi$
$547$	−7.68070	+	13.3034i	−0.328403	+	0.568810i	0.653792	+	0.756674i	$0.273177\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	13.6734	+	23.6831i	0.582508	+	1.00893i
$552$		0			0
$553$	−0.267709	+	4.87384i	−0.0113842	+	0.207257i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	0.999970	−	0.00777438i	$-0.00247469\pi$
$557$	11.6412	+	20.1631i	0.493252	+	0.854338i	−0.506718	+	0.862112i	$0.669141\pi$
$558$		0			0
$559$	−2.74531			−0.116114
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	−0.910053	−	0.414492i	$-0.863959\pi$
$563$	−2.27942	+	3.94808i	−0.0960663	+	0.166392i	0.813987	+	0.580883i	$0.197293\pi$
$564$		0			0
$565$	−0.427982	−	0.741286i	−0.0180053	−	0.0311861i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.09976	+	15.7612i	0.381482	+	0.660746i	0.991274	−	0.131815i	$-0.0420806\pi$
$569$	9.09976	+	15.7612i	0.381482	+	0.660746i	−0.609793	+	0.792561i	$0.708747\pi$
$570$		0			0
$571$	−8.52275	+	14.7618i	−0.356666	+	0.617763i	−0.987402	−	0.158234i	$-0.949420\pi$
$571$	−8.52275	+	14.7618i	−0.356666	+	0.617763i	0.630736	+	0.775998i	$0.282753\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−16.1443			−0.673264
$576$		0			0
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	0.722503	−	0.691368i	$-0.242992\pi$
$577$	−5.70473	−	9.88088i	−0.237491	−	0.411346i	−0.959994	+	0.280022i	$0.909658\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	34.1588	−	17.2968i	1.41715	−	0.717592i
$582$		0			0
$583$	−2.02275	−	3.50350i	−0.0837736	−	0.145100i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	−0.809190	−	0.587548i	$-0.800094\pi$
$587$	2.52544	−	4.37420i	0.104236	−	0.180543i	0.913426	+	0.407005i	$0.133427\pi$
$588$		0			0
$589$	−5.03052	−	8.71312i	−0.207279	−	0.359018i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	−0.584715	−	0.811239i	$-0.698794\pi$
$593$	9.98892	−	17.3013i	0.410196	−	0.710480i	0.994911	+	0.100759i	$0.0321271\pi$
$594$		0			0
$595$	0.231513	−	4.21487i	0.00949113	−	0.172793i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	−0.907406	−	0.420256i	$-0.861940\pi$
$599$	−2.19660	+	3.80463i	−0.0897508	+	0.155453i	0.817655	+	0.575709i	$0.195274\pi$
$600$		0			0
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	−0.503250	−	0.864141i	$-0.667862\pi$
$601$	12.1778	−	21.0926i	0.496743	−	0.860385i	0.999993	+	0.00375637i	$0.00119569\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−18.9695			−0.771221
$606$		0			0
$607$	−13.1256			−0.532752			−0.266376	−	0.963869i	$-0.585826\pi$
$607$	−13.1256			−0.532752			−0.266376	+	0.963869i	$0.585826\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.0510	−	22.6051i	0.527988	−	0.914502i
$612$		0			0
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.767960	−	0.640497i	$-0.778728\pi$
$613$	−23.2403	−	40.2534i	−0.938667	−	1.62582i	−0.170707	−	0.985322i	$-0.554605\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	−0.996416	−	0.0845873i	$-0.973043\pi$
$617$	−14.1948	−	24.5862i	−0.571463	−	0.989803i	0.424953	−	0.905215i	$-0.360291\pi$
$618$		0			0
$619$	−31.9212			−1.28302			−0.641511	−	0.767114i	$-0.721692\pi$
$619$	−31.9212			−1.28302			−0.641511	+	0.767114i	$0.721692\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	31.9263	−	16.1663i	1.27910	−	0.647691i
$624$		0			0
$625$	−1.33399			−0.0533594
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.58947			−0.0633762
$630$		0			0
$631$	−38.7184			−1.54135			−0.770677	−	0.637226i	$-0.780082\pi$
$631$	−38.7184			−1.54135			−0.770677	+	0.637226i	$0.780082\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	10.3447			0.410517
$636$		0			0
$637$	11.4121	−	15.5425i	0.452163	−	0.615816i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	40.4001			1.59571			0.797854	−	0.602851i	$-0.205968\pi$
$641$	40.4001			1.59571			0.797854	+	0.602851i	$0.205968\pi$
$642$		0			0
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	0.715400	−	0.698715i	$-0.246244\pi$
$643$	−6.27355	−	10.8661i	−0.247405	−	0.428517i	−0.962805	+	0.270198i	$0.912911\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	0.975209	+	0.221287i	$0.0710258\pi$
$647$	17.2774	+	29.9253i	0.679245	+	1.17649i	−0.295964	+	0.955199i	$0.595641\pi$
$648$		0			0
$649$	−16.2323	+	28.1151i	−0.637173	+	1.10362i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.2944			0.872446			0.436223	−	0.899839i	$-0.356316\pi$
$653$	22.2944			0.872446			0.436223	+	0.899839i	$0.356316\pi$
$654$		0			0
$655$	29.1442			1.13876
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.57493	−	6.19196i	0.139259	−	0.241204i	−0.787957	−	0.615730i	$-0.788861\pi$
$659$	3.57493	−	6.19196i	0.139259	−	0.241204i	0.927217	+	0.374526i	$0.122194\pi$
$660$		0			0
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	0.0600736	+	0.998194i	$0.480866\pi$
$661$	−21.4530	+	37.1577i	−0.834425	+	1.44527i	−0.894498	+	0.447072i	$0.852467\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	13.5043	−	6.83807i	0.523672	−	0.265169i
$666$		0			0
$667$	−18.5146	+	32.0683i	−0.716889	+	1.24169i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.185556	+	0.321392i	0.00716331	+	0.0124072i
$672$		0			0
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	0.232944	+	0.972490i	$0.425164\pi$
$673$	−18.8270	+	32.6094i	−0.725729	+	1.25700i	−0.958673	+	0.284510i	$0.908169\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	−0.999971	−	0.00761453i	$-0.997576\pi$
$677$	−13.1808	−	22.8298i	−0.506580	−	0.877422i	0.493391	−	0.869808i	$-0.335757\pi$
$678$		0			0
$679$	−12.7537	+	6.45800i	−0.489440	+	0.247835i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	0.901183	−	0.433439i	$-0.142700\pi$
$683$	1.96588	+	3.40500i	0.0752222	+	0.130289i	−0.825961	+	0.563728i	$0.809367\pi$
$684$		0			0
$685$	17.4008			0.664850
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.13002	−	1.95725i	0.0430503	−	0.0745653i
$690$		0			0
$691$	9.95052	+	17.2348i	0.378536	+	0.655643i	0.990849	−	0.134972i	$-0.0430944\pi$
$691$	9.95052	+	17.2348i	0.378536	+	0.655643i	−0.612314	+	0.790615i	$0.709761\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.76823	−	3.06266i	−0.0670727	−	0.116173i
$696$		0			0
$697$	−0.139270	+	0.241223i	−0.00527524	+	0.00913699i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−43.7908			−1.65396			−0.826979	−	0.562234i	$-0.809942\pi$
$701$	−43.7908			−1.65396			−0.826979	+	0.562234i	$0.809942\pi$
$702$		0			0
$703$	−2.84983	−	4.93604i	−0.107483	−	0.186166i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−11.3764	−	7.42861i	−0.427853	−	0.279382i
$708$		0			0
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	−0.891449	−	0.453121i	$-0.850310\pi$
$709$	−22.3172	−	38.6545i	−0.838139	−	1.45170i	0.0533097	−	0.998578i	$-0.483023\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.81163	−	11.7981i	0.255097	−	0.441842i
$714$		0			0
$715$	−9.67699	−	16.7610i	−0.361899	−	0.626827i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.5096	+	33.7917i	−0.727586	+	1.26022i	0.230315	+	0.973116i	$0.426024\pi$
$719$	−19.5096	+	33.7917i	−0.727586	+	1.26022i	−0.957901	+	0.287100i	$0.907309\pi$
$720$		0			0
$721$	−31.4819	−	20.5572i	−1.17245	−	0.765592i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.1130	−	17.5162i	0.375586	−	0.650534i
$726$		0			0
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	−0.578242	−	0.815865i	$-0.696261\pi$
$727$	11.2554	−	19.4949i	0.417439	−	0.723025i	0.995681	+	0.0928402i	$0.0295946\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.11590			−0.0412731
$732$		0			0
$733$	−0.897039			−0.0331329			−0.0165664	−	0.999863i	$-0.505274\pi$
$733$	−0.897039			−0.0331329			−0.0165664	+	0.999863i	$0.505274\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	31.0335	−	53.7517i	1.14314	−	1.97997i
$738$		0			0
$739$	−1.79032	−	3.10092i	−0.0658578	−	0.114069i	0.831216	−	0.555949i	$-0.187645\pi$
$739$	−1.79032	−	3.10092i	−0.0658578	−	0.114069i	−0.897074	+	0.441880i	$0.854312\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.7964	−	42.9486i	−0.909691	−	1.57563i	−0.814493	−	0.580173i	$-0.802985\pi$
$743$	−24.7964	−	42.9486i	−0.909691	−	1.57563i	−0.0951977	−	0.995458i	$-0.530348\pi$
$744$		0			0
$745$	−12.1917			−0.446668
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−18.0813	+	9.15573i	−0.660676	+	0.334543i
$750$		0			0
$751$	42.9030			1.56555			0.782776	−	0.622304i	$-0.213803\pi$
$751$	42.9030			1.56555			0.782776	+	0.622304i	$0.213803\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−25.1633			−0.915786
$756$		0			0
$757$	13.8029			0.501677			0.250838	−	0.968029i	$-0.419294\pi$
$757$	13.8029			0.501677			0.250838	+	0.968029i	$0.419294\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−40.7197			−1.47609			−0.738044	−	0.674752i	$-0.764251\pi$
$761$	−40.7197			−1.47609			−0.738044	+	0.674752i	$0.764251\pi$
$762$		0			0
$763$	−0.246505	+	4.48781i	−0.00892410	+	0.162470i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−18.1365			−0.654871
$768$		0			0
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	0.948850	−	0.315728i	$-0.102249\pi$
$769$	5.57381	+	9.65413i	0.200997	+	0.348137i	−0.747853	+	0.663864i	$0.768915\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	0.874229	−	0.485514i	$-0.161368\pi$
$773$	0.462831	+	0.801647i	0.0166469	+	0.0288332i	−0.857582	+	0.514347i	$0.828034\pi$
$774$		0			0
$775$	−3.72061	+	6.44428i	−0.133648	+	0.231485i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.998817			−0.0357863
$780$		0			0
$781$	−0.396903			−0.0142023
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.50386	−	7.80092i	0.160750	−	0.278427i
$786$		0			0
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	−0.584571	−	0.811343i	$-0.698737\pi$
$787$	11.5120	−	19.9393i	0.410358	−	0.710761i	0.994929	+	0.100582i	$0.0320704\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.0871659	−	1.58692i	0.00309926	−	0.0564243i
$792$		0			0
$793$	−0.103662	+	0.179548i	−0.00368114	+	0.00637593i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	0.590606	−	0.806960i	$-0.298889\pi$
$797$	−11.3925	−	19.7325i	−0.403544	−	0.698960i	−0.994151	+	0.108000i	$0.965555\pi$
$798$		0			0
$799$	5.30492	−	9.18839i	0.187675	−	0.325062i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−26.3575	−	45.6525i	−0.930135	−	1.61104i
$804$		0			0
$805$	17.1614	+	11.2062i	0.604861	+	0.394966i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	0.722938	−	0.690913i	$-0.242791\pi$
$809$	−6.73753	−	11.6697i	−0.236879	−	0.410286i	−0.959817	+	0.280627i	$0.909458\pi$
$810$		0			0
$811$	30.7348			1.07924			0.539622	−	0.841907i	$-0.318567\pi$
$811$	30.7348			1.07924			0.539622	+	0.841907i	$0.318567\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.71590	+	9.90023i	−0.200219	+	0.346790i
$816$		0			0
$817$	−2.00075	−	3.46540i	−0.0699974	−	0.121239i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−8.49319	−	14.7106i	−0.296414	−	0.513405i	0.678899	−	0.734232i	$-0.262458\pi$
$821$	−8.49319	−	14.7106i	−0.296414	−	0.513405i	−0.975313	+	0.220827i	$0.929124\pi$
$822$		0			0
$823$	−9.29157	+	16.0935i	−0.323884	+	0.560983i	−0.981286	−	0.192557i	$-0.938322\pi$
$823$	−9.29157	+	16.0935i	−0.323884	+	0.560983i	0.657402	+	0.753540i	$0.271655\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	14.5419			0.505670			0.252835	−	0.967509i	$-0.418637\pi$
$827$	14.5419			0.505670			0.252835	+	0.967509i	$0.418637\pi$
$828$		0			0
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	0.937104	−	0.349051i	$-0.113496\pi$
$829$	4.78717	+	8.29161i	0.166265	+	0.287980i	−0.770839	+	0.637030i	$0.780163\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.63872	−	6.31764i	0.160722	−	0.218893i
$834$		0			0
$835$	−1.51097	−	2.61708i	−0.0522894	−	0.0905678i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	−0.222664	−	0.974895i	$-0.571475\pi$
$839$	21.2303	−	36.7720i	0.732952	−	1.26951i	0.955616	−	0.294615i	$-0.0951913\pi$
$840$		0			0
$841$	−8.69551	−	15.0611i	−0.299845	−	0.519347i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.85599	+	6.67877i	−0.132650	+	0.229757i
$846$		0			0
$847$	−29.4911	−	19.2572i	−1.01332	−	0.661687i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.85883	−	6.68370i	0.132279	−	0.229114i
$852$		0			0
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	−0.717504	−	0.696555i	$-0.754715\pi$
$853$	7.14039	−	12.3675i	0.244482	−	0.423456i	0.961986	+	0.273099i	$0.0880486\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−34.7790			−1.18803			−0.594013	−	0.804455i	$-0.702457\pi$
$857$	−34.7790			−1.18803			−0.594013	+	0.804455i	$0.702457\pi$
$858$		0			0
$859$	12.6486			0.431564			0.215782	−	0.976442i	$-0.430770\pi$
$859$	12.6486			0.431564			0.215782	+	0.976442i	$0.430770\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	−0.547739	−	0.836649i	$-0.684511\pi$
$863$	13.2398	−	22.9321i	0.450690	−	0.780617i	0.998429	+	0.0560318i	$0.0178448\pi$
$864$		0			0
$865$	13.0297	+	22.5681i	0.443022	+	0.767337i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.54843	+	7.87811i	0.154295	+	0.267247i
$870$		0			0
$871$	34.6741			1.17489
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−25.1570	−	16.4272i	−0.850463	−	0.555341i
$876$		0			0
$877$	28.4534			0.960805			0.480402	−	0.877048i	$-0.340491\pi$
$877$	28.4534			0.960805			0.480402	+	0.877048i	$0.340491\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	20.3637			0.686071			0.343036	−	0.939322i	$-0.388545\pi$
$881$	20.3637			0.686071			0.343036	+	0.939322i	$0.388545\pi$
$882$		0			0
$883$	−49.1950			−1.65554			−0.827772	−	0.561065i	$-0.810392\pi$
$883$	−49.1950			−1.65554			−0.827772	+	0.561065i	$0.810392\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.21692			−0.141590			−0.0707952	−	0.997491i	$-0.522554\pi$
$887$	−4.21692			−0.141590			−0.0707952	+	0.997491i	$0.522554\pi$
$888$		0			0
$889$	16.0825	+	10.5016i	0.539388	+	0.352213i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	38.0457			1.27315
$894$		0			0
$895$	−5.43294	−	9.41013i	−0.181603	−	0.314546i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.53374	+	14.7809i	0.284616	+	0.492970i
$900$		0			0
$901$	0.459325	−	0.795574i	0.0153023	−	0.0265044i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−22.1301			−0.735628
$906$		0			0
$907$	−47.9851			−1.59332			−0.796659	−	0.604429i	$-0.793401\pi$
$907$	−47.9851			−1.59332			−0.796659	+	0.604429i	$0.793401\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.8667	+	22.2858i	−0.426294	+	0.738362i	−0.996540	−	0.0831113i	$-0.973514\pi$
$911$	−12.8667	+	22.2858i	−0.426294	+	0.738362i	0.570247	+	0.821474i	$0.306848\pi$
$912$		0			0
$913$	35.6782	−	61.7965i	1.18078	−	2.04517i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	45.3092	+	29.5863i	1.49624	+	0.977024i
$918$		0			0
$919$	−1.13478	+	1.96550i	−0.0374330	+	0.0648359i	−0.884135	−	0.467232i	$-0.845251\pi$
$919$	−1.13478	+	1.96550i	−0.0374330	+	0.0648359i	0.846702	+	0.532068i	$0.178585\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.110866	−	0.192026i	−0.00364920	−	0.00632060i
$924$		0			0
$925$	−2.10775	+	3.65073i	−0.0693024	+	0.120035i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	0.946785	+	0.321868i	$0.104311\pi$
$929$	22.9248	+	39.7069i	0.752138	+	1.30274i	−0.194647	+	0.980873i	$0.562356\pi$
$930$		0			0
$931$	27.9362	+	3.07824i	0.915573	+	0.100885i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.93346	−	6.81294i	−0.128638	−	0.222807i
$936$		0			0
$937$	−56.2075			−1.83622			−0.918110	−	0.396325i	$-0.870285\pi$
$937$	−56.2075			−1.83622			−0.918110	+	0.396325i	$0.870285\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	0.420983	+	0.907068i	$0.361685\pi$
$941$	−17.6402	+	30.5536i	−0.575053	+	0.996020i	−0.996036	+	0.0889519i	$0.971648\pi$
$942$		0			0
$943$	−0.676229	−	1.17126i	−0.0220210	−	0.0381415i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	0.902699	+	0.430272i	$0.141582\pi$
$947$	25.3565	+	43.9188i	0.823976	+	1.42717i	−0.0787236	+	0.996896i	$0.525084\pi$
$948$		0			0
$949$	14.7248	−	25.5040i	0.477986	−	0.827896i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−25.9988			−0.842184			−0.421092	−	0.907018i	$-0.638353\pi$
$953$	−25.9988			−0.842184			−0.421092	+	0.907018i	$0.638353\pi$
$954$		0			0
$955$	10.5677	+	18.3038i	0.341962	+	0.592296i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.0522	+	17.6647i	0.873562	+	0.570424i
$960$		0			0
$961$	12.3604	+	21.4088i	0.398722	+	0.690607i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	11.8040	−	20.4451i	0.379984	−	0.658152i
$966$		0			0
$967$	12.9810	+	22.4838i	0.417442	+	0.723031i	0.995681	−	0.0928360i	$-0.0295932\pi$
$967$	12.9810	+	22.4838i	0.417442	+	0.723031i	−0.578239	+	0.815867i	$0.696260\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.97206	+	6.87981i	−0.127469	+	0.220783i	−0.922696	−	0.385530i	$-0.874019\pi$
$971$	−3.97206	+	6.87981i	−0.127469	+	0.220783i	0.795226	+	0.606313i	$0.207352\pi$
$972$		0			0
$973$	0.360130	−	6.55643i	0.0115452	−	0.210189i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−26.1274	+	45.2540i	−0.835889	+	1.44780i	0.0574149	+	0.998350i	$0.481714\pi$
$977$	−26.1274	+	45.2540i	−0.835889	+	1.44780i	−0.893304	+	0.449452i	$0.851619\pi$
$978$		0			0
$979$	33.3464	−	57.7577i	1.06576	−	1.84594i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−38.8379			−1.23874			−0.619369	−	0.785100i	$-0.712611\pi$
$983$	−38.8379			−1.23874			−0.619369	+	0.785100i	$0.712611\pi$
$984$		0			0
$985$	−5.75304			−0.183307
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.70914	−	4.69236i	0.0861455	−	0.149208i
$990$		0			0
$991$	15.4689	+	26.7929i	0.491385	+	0.851104i	0.999951	−	0.00991892i	$-0.00315734\pi$
$991$	15.4689	+	26.7929i	0.491385	+	0.851104i	−0.508565	+	0.861023i	$0.669824\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−18.0122	−	31.1981i	−0.571025	−	0.989045i
$996$		0			0
$997$	47.0670			1.49063			0.745313	−	0.666714i	$-0.232300\pi$
$997$	47.0670			1.49063			0.745313	+	0.666714i	$0.232300\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.i.289.1		10
3.2	odd	2		1008.2.t.i.961.4		10
4.3	odd	2		189.2.g.b.100.4		10
7.4	even	3		3024.2.q.i.2881.5		10
9.4	even	3		3024.2.q.i.2305.5		10
9.5	odd	6		1008.2.q.i.625.1		10
12.11	even	2		63.2.g.b.16.2	yes	10
21.11	odd	6		1008.2.q.i.529.1		10
28.3	even	6		1323.2.h.f.802.2		10
28.11	odd	6		189.2.h.b.46.2		10
28.19	even	6		1323.2.f.f.883.4		10
28.23	odd	6		1323.2.f.e.883.4		10
28.27	even	2		1323.2.g.f.667.4		10
36.7	odd	6		567.2.e.e.163.4		10
36.11	even	6		567.2.e.f.163.2		10
36.23	even	6		63.2.h.b.58.4	yes	10
36.31	odd	6		189.2.h.b.37.2		10
63.4	even	3	inner	3024.2.t.i.1873.1		10
63.32	odd	6		1008.2.t.i.193.4		10
84.11	even	6		63.2.h.b.25.4	yes	10
84.23	even	6		441.2.f.e.295.2		10
84.47	odd	6		441.2.f.f.295.2		10
84.59	odd	6		441.2.h.f.214.4		10
84.83	odd	2		441.2.g.f.79.2		10
252.11	even	6		567.2.e.f.487.2		10
252.23	even	6		441.2.f.e.148.2		10
252.31	even	6		1323.2.g.f.361.4		10
252.47	odd	6		3969.2.a.ba.1.4		5
252.59	odd	6		441.2.g.f.67.2		10
252.67	odd	6		189.2.g.b.172.4		10
252.79	odd	6		3969.2.a.bc.1.2		5
252.95	even	6		63.2.g.b.4.2	✓	10
252.103	even	6		1323.2.f.f.442.4		10
252.131	odd	6		441.2.f.f.148.2		10
252.139	even	6		1323.2.h.f.226.2		10
252.151	odd	6		567.2.e.e.487.4		10
252.167	odd	6		441.2.h.f.373.4		10
252.187	even	6		3969.2.a.bb.1.2		5
252.191	even	6		3969.2.a.z.1.4		5
252.247	odd	6		1323.2.f.e.442.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.2	✓	10	252.95	even	6
63.2.g.b.16.2	yes	10	12.11	even	2
63.2.h.b.25.4	yes	10	84.11	even	6
63.2.h.b.58.4	yes	10	36.23	even	6
189.2.g.b.100.4		10	4.3	odd	2
189.2.g.b.172.4		10	252.67	odd	6
189.2.h.b.37.2		10	36.31	odd	6
189.2.h.b.46.2		10	28.11	odd	6
441.2.f.e.148.2		10	252.23	even	6
441.2.f.e.295.2		10	84.23	even	6
441.2.f.f.148.2		10	252.131	odd	6
441.2.f.f.295.2		10	84.47	odd	6
441.2.g.f.67.2		10	252.59	odd	6
441.2.g.f.79.2		10	84.83	odd	2
441.2.h.f.214.4		10	84.59	odd	6
441.2.h.f.373.4		10	252.167	odd	6
567.2.e.e.163.4		10	36.7	odd	6
567.2.e.e.487.4		10	252.151	odd	6
567.2.e.f.163.2		10	36.11	even	6
567.2.e.f.487.2		10	252.11	even	6
1008.2.q.i.529.1		10	21.11	odd	6
1008.2.q.i.625.1		10	9.5	odd	6
1008.2.t.i.193.4		10	63.32	odd	6
1008.2.t.i.961.4		10	3.2	odd	2
1323.2.f.e.442.4		10	252.247	odd	6
1323.2.f.e.883.4		10	28.23	odd	6
1323.2.f.f.442.4		10	252.103	even	6
1323.2.f.f.883.4		10	28.19	even	6
1323.2.g.f.361.4		10	252.31	even	6
1323.2.g.f.667.4		10	28.27	even	2
1323.2.h.f.226.2		10	252.139	even	6
1323.2.h.f.802.2		10	28.3	even	6
3024.2.q.i.2305.5		10	9.4	even	3
3024.2.q.i.2881.5		10	7.4	even	3
3024.2.t.i.289.1		10	1.1	even	1	trivial
3024.2.t.i.1873.1		10	63.4	even	3	inner
3969.2.a.z.1.4		5	252.191	even	6
3969.2.a.ba.1.4		5	252.47	odd	6
3969.2.a.bb.1.2		5	252.187	even	6
3969.2.a.bc.1.2		5	252.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.42494 q^{5} +(-2.21529 - 1.44655i) q^{7} +O(q^{10})\)	\(q-1.42494 q^{5} +(-2.21529 - 1.44655i) q^{7} -4.93077 q^{11} +(-1.37730 - 2.38556i) q^{13} +(-0.559839 - 0.969670i) q^{17} +(2.00752 - 3.47713i) q^{19} +5.43661 q^{23} -2.96955 q^{25} +(-3.40555 + 5.89858i) q^{29} +(1.25292 - 2.17012i) q^{31} +(3.15664 + 2.06124i) q^{35} +(0.709787 - 1.22939i) q^{37} +(-0.124384 - 0.215440i) q^{41} +(0.498313 - 0.863104i) q^{43} +(4.73790 + 8.20628i) q^{47} +(2.81498 + 6.40905i) q^{49} +(0.410229 + 0.710537i) q^{53} +7.02604 q^{55} +(3.29204 - 5.70197i) q^{59} +(-0.0376322 - 0.0651809i) q^{61} +(1.96257 + 3.39927i) q^{65} +(-6.29385 + 10.9013i) q^{67} +0.0804951 q^{71} +(5.34551 + 9.25869i) q^{73} +(10.9231 + 7.13261i) q^{77} +(-0.922457 - 1.59774i) q^{79} +(-7.23583 + 12.5328i) q^{83} +(0.797736 + 1.38172i) q^{85} +(-6.76292 + 11.7137i) q^{89} +(-0.399711 + 7.27703i) q^{91} +(-2.86059 + 4.95469i) q^{95} +(2.70160 - 4.67930i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 8 q^{5} + q^{7}+O(q^{10}) \) 10 * q + 8 * q^5 + q^7	\( 10 q + 8 q^{5} + q^{7} - 8 q^{11} - 8 q^{13} - 12 q^{17} - q^{19} - 6 q^{23} + 2 q^{25} - 7 q^{29} + 3 q^{31} + 5 q^{35} - 5 q^{41} + 7 q^{43} + 27 q^{47} + 25 q^{49} + 21 q^{53} - 4 q^{55} + 30 q^{59} - 14 q^{61} + 11 q^{65} + 2 q^{67} - 6 q^{71} + 15 q^{73} + 31 q^{77} + 4 q^{79} + 9 q^{83} - 6 q^{85} - 28 q^{89} + 4 q^{91} - 14 q^{95} - 12 q^{97}+O(q^{100}) \) 10 * q + 8 * q^5 + q^7 - 8 * q^11 - 8 * q^13 - 12 * q^17 - q^19 - 6 * q^23 + 2 * q^25 - 7 * q^29 + 3 * q^31 + 5 * q^35 - 5 * q^41 + 7 * q^43 + 27 * q^47 + 25 * q^49 + 21 * q^53 - 4 * q^55 + 30 * q^59 - 14 * q^61 + 11 * q^65 + 2 * q^67 - 6 * q^71 + 15 * q^73 + 31 * q^77 + 4 * q^79 + 9 * q^83 - 6 * q^85 - 28 * q^89 + 4 * q^91 - 14 * q^95 - 12 * q^97

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