LMFDB - Embedded newform 3024.2.t.f.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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	3024.289
Dual form			3024.2.t.f.1873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})$	$q+3.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -3.00000 q^{11} +(-2.50000 - 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} -3.00000 q^{23} +4.00000 q^{25} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(1.50000 - 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-7.50000 - 12.9904i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-5.50000 - 9.52628i) q^{73} +(-1.50000 + 7.79423i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(7.50000 - 12.9904i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(7.50000 - 12.9904i) q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 6 q^{5} + q^{7}+O(q^{10}) $ 2 * q + 6 * q^5 + q^7	$ 2 q + 6 q^{5} + q^{7} - 6 q^{11} - 5 q^{13} + 3 q^{17} + 5 q^{19} - 6 q^{23} + 8 q^{25} - 3 q^{29} - 4 q^{31} + 3 q^{35} + 7 q^{37} - 9 q^{41} + 11 q^{43} - 13 q^{49} - 3 q^{53} - 18 q^{55} - 12 q^{59} - 2 q^{61} - 15 q^{65} - 4 q^{67} - 11 q^{73} - 3 q^{77} + 8 q^{79} - 3 q^{83} + 9 q^{85} + 15 q^{89} - 25 q^{91} + 15 q^{95} + q^{97}+O(q^{100}) $ 2 * q + 6 * q^5 + q^7 - 6 * q^11 - 5 * q^13 + 3 * q^17 + 5 * q^19 - 6 * q^23 + 8 * q^25 - 3 * q^29 - 4 * q^31 + 3 * q^35 + 7 * q^37 - 9 * q^41 + 11 * q^43 - 13 * q^49 - 3 * q^53 - 18 * q^55 - 12 * q^59 - 2 * q^61 - 15 * q^65 - 4 * q^67 - 11 * q^73 - 3 * q^77 + 8 * q^79 - 3 * q^83 + 9 * q^85 + 15 * q^89 - 25 * q^91 + 15 * q^95 + 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
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		0			0
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.50000	−	7.79423i	0.253546	−	1.31747i
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	−0.0522047	−	0.998636i	$-0.516625\pi$
$43$	5.50000	−	9.52628i	0.838742	−	1.45274i	0.890947	−	0.454108i	$-0.150042\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	0.744423	−	0.667708i	$-0.232725\pi$
$53$	−1.50000	−	2.59808i	−0.206041	−	0.356873i	−0.950464	+	0.310835i	$0.899391\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.50000	−	12.9904i	−0.930261	−	1.61126i
$66$		0			0
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.50000	+	7.79423i	−0.170941	+	0.888235i
$78$		0			0
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	−0.936530	−	0.350588i	$-0.885982\pi$
$83$	−1.50000	+	2.59808i	−0.164646	+	0.285176i	0.771883	+	0.635764i	$0.219315\pi$
$84$		0			0
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	−0.127842	−	0.991795i	$-0.540805\pi$
$89$	7.50000	−	12.9904i	0.794998	−	1.37698i	0.922840	−	0.385183i	$-0.125862\pi$
$90$		0			0
$91$	−12.5000	+	4.33013i	−1.31036	+	0.453921i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.50000	−	12.9904i	0.769484	−	1.33278i
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.00000			0.298511			0.149256	−	0.988799i	$-0.452312\pi$
$101$	3.00000			0.298511			0.149256	+	0.988799i	$0.452312\pi$
$102$		0			0
$103$	−5.00000			−0.492665			−0.246332	−	0.969185i	$-0.579225\pi$
$103$	−5.00000			−0.492665			−0.246332	+	0.969185i	$0.579225\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$		0			0
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	0.983531	−	0.180741i	$-0.0578495\pi$
$109$	3.50000	+	6.06218i	0.335239	+	0.580651i	−0.648292	+	0.761392i	$0.724516\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	−9.00000			−0.839254
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.50000	−	2.59808i	0.687524	−	0.238165i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.00000			−0.268328
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	−10.0000	−	8.66025i	−0.867110	−	0.750939i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.00000			−0.256307			−0.128154	−	0.991754i	$-0.540905\pi$
$137$	−3.00000			−0.256307			−0.128154	+	0.991754i	$0.540905\pi$
$138$		0			0
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.50000	+	12.9904i	0.627182	+	1.08631i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.00000			0.245770			0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000			0.245770			0.122885	+	0.992421i	$0.460785\pi$
$150$		0			0
$151$	−11.0000			−0.895167			−0.447584	−	0.894242i	$-0.647715\pi$
$151$	−11.0000			−0.895167			−0.447584	+	0.894242i	$0.647715\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.00000	+	10.3923i	−0.481932	+	0.834730i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		0			0
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	−0.313304	−	0.949653i	$-0.601436\pi$
$163$	8.50000	−	14.7224i	0.665771	−	1.15315i	0.979076	−	0.203497i	$-0.0652307\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	0.802135	−	0.597143i	$-0.203697\pi$
$167$	−1.50000	−	2.59808i	−0.116073	−	0.201045i	−0.918208	+	0.396098i	$0.870364\pi$
$168$		0			0
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	2.00000	−	10.3923i	0.151186	−	0.785584i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	0.804508	−	0.593942i	$-0.202429\pi$
$179$	−1.50000	−	2.59808i	−0.112115	−	0.194189i	−0.916623	+	0.399753i	$0.869096\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	10.5000	−	18.1865i	0.771975	−	1.33710i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$		0			0
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	0.714893	−	0.699234i	$-0.246476\pi$
$199$	−3.50000	−	6.06218i	−0.248108	−	0.429736i	−0.963001	+	0.269498i	$0.913142\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.00000	+	5.19615i	0.421117	+	0.364698i
$204$		0			0
$205$	−13.5000	−	23.3827i	−0.942881	−	1.63312i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−7.50000	+	12.9904i	−0.518786	+	0.898563i
$210$		0			0
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	16.5000	−	28.5788i	1.12529	−	1.94906i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.50000	−	12.9904i	0.504505	−	0.873828i
$222$		0			0
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	−0.427443	−	0.904042i	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.00000			0.597351			0.298675	−	0.954355i	$-0.403455\pi$
$227$	9.00000			0.597351			0.298675	+	0.954355i	$0.403455\pi$
$228$		0			0
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.0380310	−	0.999277i	$-0.487891\pi$
$233$	13.5000	−	23.3827i	0.884414	−	1.53185i	0.846383	−	0.532574i	$-0.178775\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.858623	−	0.512607i	$-0.828680\pi$
$239$	−13.5000	−	23.3827i	−0.873242	−	1.51250i	−0.0146191	−	0.999893i	$-0.504654\pi$
$240$		0			0
$241$	23.0000			1.48156			0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000			1.48156			0.740780	+	0.671748i	$0.234456\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−19.5000	−	7.79423i	−1.24581	−	0.497955i
$246$		0			0
$247$	−25.0000			−1.59071
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.0000			−0.935674			−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000			−0.935674			−0.467837	+	0.883815i	$0.654967\pi$
$258$		0			0
$259$	−14.0000	−	12.1244i	−0.869918	−	0.753371i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.00000			−0.554964			−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000			−0.554964			−0.277482	+	0.960731i	$0.589500\pi$
$264$		0			0
$265$	−4.50000	−	7.79423i	−0.276433	−	0.478796i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	0.985389	+	0.170321i	$0.0544803\pi$
$269$	10.5000	+	18.1865i	0.640196	+	1.10885i	−0.345192	+	0.938532i	$0.612186\pi$
$270$		0			0
$271$	−6.50000	+	11.2583i	−0.394847	+	0.683895i	−0.993082	−	0.117426i	$-0.962536\pi$
$271$	−6.50000	+	11.2583i	−0.394847	+	0.683895i	0.598235	+	0.801321i	$0.295869\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−12.0000			−0.723627
$276$		0			0
$277$	−7.00000			−0.420589			−0.210295	−	0.977638i	$-0.567442\pi$
$277$	−7.00000			−0.420589			−0.210295	+	0.977638i	$0.567442\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	−0.817810	−	0.575488i	$-0.804812\pi$
$281$	1.50000	−	2.59808i	0.0894825	−	0.154988i	0.907293	+	0.420500i	$0.138145\pi$
$282$		0			0
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	−0.722300	−	0.691580i	$-0.756915\pi$
$283$	4.00000	−	6.92820i	0.237775	−	0.411839i	0.960076	+	0.279741i	$0.0902485\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−22.5000	+	7.79423i	−1.32813	+	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	−0.926777	−	0.375613i	$-0.877432\pi$
$293$	−13.5000	−	23.3827i	−0.788678	−	1.36603i	0.138098	−	0.990419i	$-0.455901\pi$
$294$		0			0
$295$	−18.0000	+	31.1769i	−1.04800	+	1.81519i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.50000	+	12.9904i	0.433736	+	0.751253i
$300$		0			0
$301$	−22.0000	−	19.0526i	−1.26806	−	1.09817i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	0.887788	+	0.460252i	$0.152241\pi$
$317$	15.0000	+	25.9808i	0.842484	+	1.45922i	−0.0453045	+	0.998973i	$0.514426\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	0.974701	+	0.223513i	$0.0717525\pi$
$337$	12.5000	+	21.6506i	0.680918	+	1.17939i	−0.293783	+	0.955872i	$0.594914\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.00000			0.479022			0.239511	−	0.970894i	$-0.423013\pi$
$353$	9.00000			0.479022			0.239511	+	0.970894i	$0.423013\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	−0.993207	−	0.116358i	$-0.962878\pi$
$359$	−7.50000	+	12.9904i	−0.395835	+	0.685606i	0.597372	+	0.801964i	$0.296211\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−16.5000	−	28.5788i	−0.863649	−	1.49588i
$366$		0			0
$367$	1.00000			0.0521996			0.0260998	−	0.999659i	$-0.491691\pi$
$367$	1.00000			0.0521996			0.0260998	+	0.999659i	$0.491691\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−7.50000	+	2.59808i	−0.389381	+	0.134885i
$372$		0			0
$373$	17.0000			0.880227			0.440113	−	0.897942i	$-0.354938\pi$
$373$	17.0000			0.880227			0.440113	+	0.897942i	$0.354938\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0000			0.772539
$378$		0			0
$379$	16.0000			0.821865			0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000			0.821865			0.410932	+	0.911666i	$0.365203\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.0000			−0.766464			−0.383232	−	0.923652i	$-0.625189\pi$
$383$	−15.0000			−0.766464			−0.383232	+	0.923652i	$0.625189\pi$
$384$		0			0
$385$	−4.50000	+	23.3827i	−0.229341	+	1.19169i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.00000			−0.456318			−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000			−0.456318			−0.228159	+	0.973624i	$0.573271\pi$
$390$		0			0
$391$	−4.50000	−	7.79423i	−0.227575	−	0.394171i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$		0			0
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	0.230105	+	0.973166i	$0.426093\pi$
$397$	−14.5000	+	25.1147i	−0.727734	+	1.26047i	−0.957839	+	0.287307i	$0.907240\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−27.0000			−1.34832			−0.674158	−	0.738587i	$-0.735493\pi$
$401$	−27.0000			−1.34832			−0.674158	+	0.738587i	$0.735493\pi$
$402$		0			0
$403$	20.0000			0.996271
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$		0			0
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	−0.454759	−	0.890614i	$-0.650275\pi$
$409$	11.0000	−	19.0526i	0.543915	−	0.942088i	0.998674	−	0.0514740i	$-0.0163919\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$		0			0
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	0.900337	−	0.435194i	$-0.143320\pi$
$419$	1.50000	+	2.59808i	0.0732798	+	0.126924i	−0.827057	+	0.562118i	$0.809987\pi$
$420$		0			0
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	−0.189740	−	0.981834i	$-0.560764\pi$
$421$	15.5000	−	26.8468i	0.755424	−	1.30843i	0.945163	−	0.326598i	$-0.105902\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	−5.00000	+	1.73205i	−0.241967	+	0.0838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	0.899888	−	0.436121i	$-0.143648\pi$
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	−0.827636	+	0.561266i	$0.810315\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.50000	+	12.9904i	−0.358774	+	0.621414i
$438$		0			0
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	0.945552	−	0.325471i	$-0.105523\pi$
$439$	4.00000	+	6.92820i	0.190910	+	0.330665i	−0.754642	+	0.656136i	$0.772190\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	22.5000	−	38.9711i	1.06660	−	1.84741i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	13.5000	+	23.3827i	0.635690	+	1.10105i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−37.5000	+	12.9904i	−1.75803	+	0.608998i
$456$		0			0
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	0.922695	+	0.385530i	$0.125981\pi$
$457$	17.0000	+	29.4449i	0.795226	+	1.37737i	−0.127469	+	0.991843i	$0.540685\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	0.910546	+	0.413407i	$0.135661\pi$
$463$	17.5000	+	30.3109i	0.813294	+	1.40867i	−0.0972525	+	0.995260i	$0.531005\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	−0.829231	−	0.558906i	$-0.811221\pi$
$467$	1.50000	−	2.59808i	0.0694117	−	0.120225i	0.898642	+	0.438682i	$0.144554\pi$
$468$		0			0
$469$	8.00000	+	6.92820i	0.369406	+	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−16.5000	+	28.5788i	−0.758671	+	1.31406i
$474$		0			0
$475$	10.0000	−	17.3205i	0.458831	−	0.794719i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.00000			−0.411220			−0.205610	−	0.978634i	$-0.565918\pi$
$479$	−9.00000			−0.411220			−0.205610	+	0.978634i	$0.565918\pi$
$480$		0			0
$481$	−35.0000			−1.59586
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.50000	−	2.59808i	0.0681115	−	0.117973i
$486$		0			0
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	−0.967632	−	0.252367i	$-0.918791\pi$
$487$	−15.5000	−	26.8468i	−0.702372	−	1.21654i	0.265260	−	0.964177i	$-0.414542\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.851314	+	0.524656i	$0.175806\pi$
$491$	19.5000	+	33.7750i	0.880023	+	1.52424i	0.0287085	+	0.999588i	$0.490861\pi$
$492$		0			0
$493$	−9.00000			−0.405340
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−11.0000			−0.492428			−0.246214	−	0.969216i	$-0.579187\pi$
$499$	−11.0000			−0.492428			−0.246214	+	0.969216i	$0.579187\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$		0			0
$507$		0			0
$508$		0			0
$509$	27.0000			1.19675			0.598377	−	0.801215i	$-0.295813\pi$
$509$	27.0000			1.19675			0.598377	+	0.801215i	$0.295813\pi$
$510$		0			0
$511$	−27.5000	+	9.52628i	−1.21653	+	0.421418i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−15.0000			−0.660979
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	−0.932345	−	0.361569i	$-0.882241\pi$
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	0.779301	+	0.626650i	$0.215574\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−14.0000			−0.608696
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−22.5000	+	38.9711i	−0.974583	+	1.68803i
$534$		0			0
$535$	22.5000	−	38.9711i	0.972760	−	1.68487i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.5000	+	7.79423i	0.839924	+	0.335721i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	10.5000	+	18.1865i	0.449771	+	0.779026i
$546$		0			0
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	−0.724157	−	0.689635i	$-0.757771\pi$
$547$	5.50000	−	9.52628i	0.235163	−	0.407314i	0.959320	+	0.282321i	$0.0911043\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.50000	+	12.9904i	0.319511	+	0.553409i
$552$		0			0
$553$	20.0000	−	6.92820i	0.850487	−	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$		0			0
$559$	−55.0000			−2.32625
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$		0			0
$565$	22.5000	+	38.9711i	0.946582	+	1.63953i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$		0			0
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	−0.577301	−	0.816532i	$-0.695894\pi$
$571$	10.0000	−	17.3205i	0.418487	−	0.724841i	0.995788	+	0.0916910i	$0.0292272\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.00000	+	5.19615i	0.248922	+	0.215573i
$582$		0			0
$583$	4.50000	+	7.79423i	0.186371	+	0.322804i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	−0.293640	−	0.955916i	$-0.594867\pi$
$587$	16.5000	−	28.5788i	0.681028	−	1.17957i	0.974668	−	0.223659i	$-0.0718001\pi$
$588$		0			0
$589$	10.0000	+	17.3205i	0.412043	+	0.713679i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	22.5000	−	7.79423i	0.922410	−	0.319532i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.00000			−0.243935
$606$		0			0
$607$	43.0000			1.74532			0.872658	−	0.488332i	$-0.162394\pi$
$607$	43.0000			1.74532			0.872658	+	0.488332i	$0.162394\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	0.988339	+	0.152270i	$0.0486583\pi$
$613$	15.5000	+	26.8468i	0.626039	+	1.08433i	−0.362300	+	0.932062i	$0.618008\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$		0			0
$619$	19.0000			0.763674			0.381837	−	0.924230i	$-0.375291\pi$
$619$	19.0000			0.763674			0.381837	+	0.924230i	$0.375291\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−30.0000	−	25.9808i	−1.20192	−	1.04090i
$624$		0			0
$625$	−29.0000			−1.16000
$626$		0			0
$627$		0			0
$628$		0			0
$629$	21.0000			0.837325
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	48.0000			1.90482
$636$		0			0
$637$	5.00000	+	34.6410i	0.198107	+	1.37253i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	45.0000			1.77739			0.888697	−	0.458496i	$-0.151612\pi$
$641$	45.0000			1.77739			0.888697	+	0.458496i	$0.151612\pi$
$642$		0			0
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	0.996379	+	0.0850262i	$0.0270974\pi$
$643$	14.5000	+	25.1147i	0.571824	+	0.990429i	−0.424555	+	0.905402i	$0.639569\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	0.894004	−	0.448059i	$-0.147885\pi$
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	−0.835033	+	0.550200i	$0.814551\pi$
$648$		0			0
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.00000			−0.352197			−0.176099	−	0.984373i	$-0.556348\pi$
$653$	−9.00000			−0.352197			−0.176099	+	0.984373i	$0.556348\pi$
$654$		0			0
$655$	9.00000			0.351659
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	0.183436	+	0.983032i	$0.441278\pi$
$659$	−19.5000	+	33.7750i	−0.759612	+	1.31569i	−0.943049	+	0.332655i	$0.892055\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−30.0000	−	25.9808i	−1.16335	−	1.00749i
$666$		0			0
$667$	4.50000	−	7.79423i	0.174241	−	0.301794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$		0			0
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	−2.00000	−	1.73205i	−0.0767530	−	0.0664700i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	0.987275	+	0.159022i	$0.0508342\pi$
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	−0.355920	+	0.934516i	$0.615832\pi$
$684$		0			0
$685$	−9.00000			−0.343872
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.50000	+	12.9904i	−0.285727	+	0.494894i
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.50000	+	12.9904i	0.284491	+	0.492753i
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−6.00000			−0.226617			−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000			−0.226617			−0.113308	+	0.993560i	$0.536145\pi$
$702$		0			0
$703$	−17.5000	−	30.3109i	−0.660025	−	1.14320i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.50000	−	7.79423i	0.0564133	−	0.293132i
$708$		0			0
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	22.5000	+	38.9711i	0.841452	+	1.45744i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.5000	+	33.7750i	−0.727227	+	1.25959i	0.230823	+	0.972996i	$0.425858\pi$
$719$	−19.5000	+	33.7750i	−0.727227	+	1.25959i	−0.958051	+	0.286599i	$0.907475\pi$
$720$		0			0
$721$	−2.50000	+	12.9904i	−0.0931049	+	0.483787i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.00000	+	10.3923i	−0.222834	+	0.385961i
$726$		0			0
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	−0.815935	−	0.578144i	$-0.803777\pi$
$727$	2.50000	−	4.33013i	0.0927199	−	0.160596i	0.908655	+	0.417548i	$0.137111\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	33.0000			1.22055
$732$		0			0
$733$	41.0000			1.51437			0.757185	−	0.653201i	$-0.226574\pi$
$733$	41.0000			1.51437			0.757185	+	0.653201i	$0.226574\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	0.867581	+	0.497296i	$0.165674\pi$
$739$	23.5000	+	40.7032i	0.864461	+	1.49729i	−0.00311943	+	0.999995i	$0.500993\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	0.837198	−	0.546899i	$-0.184192\pi$
$743$	−1.50000	−	2.59808i	−0.0550297	−	0.0953142i	−0.892228	+	0.451585i	$0.850859\pi$
$744$		0			0
$745$	9.00000			0.329734
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−30.0000	−	25.9808i	−1.09618	−	0.949316i
$750$		0			0
$751$	−29.0000			−1.05823			−0.529113	−	0.848552i	$-0.677475\pi$
$751$	−29.0000			−1.05823			−0.529113	+	0.848552i	$0.677475\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−33.0000			−1.20099
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.00000			−0.108750			−0.0543750	−	0.998521i	$-0.517317\pi$
$761$	−3.00000			−0.108750			−0.0543750	+	0.998521i	$0.517317\pi$
$762$		0			0
$763$	17.5000	−	6.06218i	0.633543	−	0.219466i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	60.0000			2.16647
$768$		0			0
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	0.874900	−	0.484304i	$-0.160927\pi$
$769$	0.500000	+	0.866025i	0.0180305	+	0.0312297i	−0.856869	+	0.515534i	$0.827594\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	0.990721	−	0.135910i	$-0.0433959\pi$
$773$	10.5000	+	18.1865i	0.377659	+	0.654124i	−0.613062	+	0.790034i	$0.710063\pi$
$774$		0			0
$775$	−8.00000	+	13.8564i	−0.287368	+	0.497737i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−45.0000			−1.61229
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$		0			0
$787$	22.0000	−	38.1051i	0.784215	−	1.35830i	−0.145251	−	0.989395i	$-0.546399\pi$
$787$	22.0000	−	38.1051i	0.784215	−	1.35830i	0.929467	−	0.368906i	$-0.120268\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	37.5000	−	12.9904i	1.33335	−	0.461885i
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	0.521493	−	0.853256i	$-0.325375\pi$
$797$	−13.5000	−	23.3827i	−0.478195	−	0.828257i	−0.999687	+	0.0249984i	$0.992042\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	16.5000	+	28.5788i	0.582272	+	1.00853i
$804$		0			0
$805$	−4.50000	+	23.3827i	−0.158604	+	0.824131i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	0.973253	+	0.229736i	$0.0737862\pi$
$809$	19.5000	+	33.7750i	0.685583	+	1.18747i	−0.287670	+	0.957730i	$0.592880\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	25.5000	−	44.1673i	0.893226	−	1.54711i
$816$		0			0
$817$	−27.5000	−	47.6314i	−0.962103	−	1.66641i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$		0			0
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−24.0000			−0.834562			−0.417281	−	0.908778i	$-0.637017\pi$
$827$	−24.0000			−0.834562			−0.417281	+	0.908778i	$0.637017\pi$
$828$		0			0
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	−0.964107	−	0.265513i	$-0.914459\pi$
$829$	−20.5000	−	35.5070i	−0.711994	−	1.23321i	0.252113	−	0.967698i	$-0.418875\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.00000	−	20.7846i	−0.103944	−	0.720144i
$834$		0			0
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	−0.303773	−	0.952745i	$-0.598246\pi$
$839$	19.5000	−	33.7750i	0.673215	−	1.16604i	0.976987	−	0.213298i	$-0.0684204\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.5000	+	18.1865i	−0.359935	+	0.623426i
$852$		0			0
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	−0.974055	−	0.226313i	$-0.927333\pi$
$853$	−8.50000	+	14.7224i	−0.291034	+	0.504086i	0.683020	+	0.730400i	$0.260666\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	33.0000			1.12726			0.563629	−	0.826028i	$-0.309405\pi$
$857$	33.0000			1.12726			0.563629	+	0.826028i	$0.309405\pi$
$858$		0			0
$859$	−11.0000			−0.375315			−0.187658	−	0.982235i	$-0.560090\pi$
$859$	−11.0000			−0.375315			−0.187658	+	0.982235i	$0.560090\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.50000	+	12.9904i	−0.255303	+	0.442198i	−0.964978	−	0.262332i	$-0.915509\pi$
$863$	−7.50000	+	12.9904i	−0.255303	+	0.442198i	0.709675	+	0.704529i	$0.248842\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−12.0000	−	20.7846i	−0.407072	−	0.705070i
$870$		0			0
$871$	20.0000			0.677674
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.50000	+	7.79423i	−0.0507093	+	0.263493i
$876$		0			0
$877$	−43.0000			−1.45201			−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000			−1.45201			−0.726003	+	0.687691i	$0.758624\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	4.00000			0.134611			0.0673054	−	0.997732i	$-0.478560\pi$
$883$	4.00000			0.134611			0.0673054	+	0.997732i	$0.478560\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−39.0000			−1.30949			−0.654746	−	0.755849i	$-0.727224\pi$
$887$	−39.0000			−1.30949			−0.654746	+	0.755849i	$0.727224\pi$
$888$		0			0
$889$	8.00000	−	41.5692i	0.268311	−	1.39419i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−4.50000	−	7.79423i	−0.150418	−	0.260532i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$		0			0
$901$	4.50000	−	7.79423i	0.149917	−	0.259663i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−30.0000			−0.997234
$906$		0			0
$907$	−17.0000			−0.564476			−0.282238	−	0.959344i	$-0.591077\pi$
$907$	−17.0000			−0.564476			−0.282238	+	0.959344i	$0.591077\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	−0.930892	−	0.365295i	$-0.880968\pi$
$911$	−4.50000	+	7.79423i	−0.149092	+	0.258234i	0.781800	+	0.623529i	$0.214302\pi$
$912$		0			0
$913$	4.50000	−	7.79423i	0.148928	−	0.257951i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.50000	−	7.79423i	0.0495344	−	0.257388i
$918$		0			0
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	−0.874154	−	0.485648i	$-0.838584\pi$
$919$	−0.500000	+	0.866025i	−0.0164935	+	0.0285675i	0.857661	+	0.514216i	$0.171917\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	0.679770	−	0.733426i	$-0.262080\pi$
$929$	−9.00000	−	15.5885i	−0.295280	−	0.511441i	−0.975050	+	0.221985i	$0.928746\pi$
$930$		0			0
$931$	−27.5000	+	21.6506i	−0.901276	+	0.709571i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−13.5000	−	23.3827i	−0.441497	−	0.764696i
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.0290288	−	0.999579i	$-0.490759\pi$
$941$	27.0000	−	46.7654i	0.880175	−	1.52451i	0.851146	−	0.524929i	$-0.175908\pi$
$942$		0			0
$943$	13.5000	+	23.3827i	0.439620	+	0.761445i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	−27.5000	+	47.6314i	−0.892688	+	1.54618i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$	−18.0000	−	31.1769i	−0.582466	−	1.00886i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.50000	+	7.79423i	−0.0484375	+	0.251689i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$		0			0
$967$	−24.5000	−	42.4352i	−0.787867	−	1.36463i	−0.927271	−	0.374390i	$-0.877852\pi$
$967$	−24.5000	−	42.4352i	−0.787867	−	1.36463i	0.139404	−	0.990236i	$-0.455481\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	−0.563914	−	0.825833i	$-0.690705\pi$
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	0.997150	+	0.0754473i	$0.0240385\pi$
$972$		0			0
$973$	12.5000	−	4.33013i	0.400732	−	0.138817i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$		0			0
$979$	−22.5000	+	38.9711i	−0.719103	+	1.24552i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−21.0000			−0.669796			−0.334898	−	0.942254i	$-0.608702\pi$
$983$	−21.0000			−0.669796			−0.334898	+	0.942254i	$0.608702\pi$
$984$		0			0
$985$	18.0000			0.573528
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−16.5000	+	28.5788i	−0.524669	+	0.908754i
$990$		0			0
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	0.998991	−	0.0449040i	$-0.0142982\pi$
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	−0.538384	+	0.842700i	$0.680965\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.5000	−	18.1865i	−0.332872	−	0.576552i
$996$		0			0
$997$	41.0000			1.29848			0.649242	−	0.760582i	$-0.275086\pi$
$997$	41.0000			1.29848			0.649242	+	0.760582i	$0.275086\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.f.289.1		2
3.2	odd	2		1008.2.t.c.961.1		2
4.3	odd	2		378.2.h.b.289.1		2
7.4	even	3		3024.2.q.a.2881.1		2
9.4	even	3		3024.2.q.a.2305.1		2
9.5	odd	6		1008.2.q.e.625.1		2
12.11	even	2		126.2.h.a.79.1	yes	2
21.11	odd	6		1008.2.q.e.529.1		2
28.3	even	6		2646.2.e.e.2125.1		2
28.11	odd	6		378.2.e.a.235.1		2
28.19	even	6		2646.2.f.i.883.1		2
28.23	odd	6		2646.2.f.e.883.1		2
28.27	even	2		2646.2.h.f.667.1		2
36.7	odd	6		1134.2.g.f.163.1		2
36.11	even	6		1134.2.g.d.163.1		2
36.23	even	6		126.2.e.b.121.1	yes	2
36.31	odd	6		378.2.e.a.37.1		2
63.4	even	3	inner	3024.2.t.f.1873.1		2
63.32	odd	6		1008.2.t.c.193.1		2
84.11	even	6		126.2.e.b.25.1	✓	2
84.23	even	6		882.2.f.e.295.1		2
84.47	odd	6		882.2.f.a.295.1		2
84.59	odd	6		882.2.e.h.655.1		2
84.83	odd	2		882.2.h.e.79.1		2
252.11	even	6		1134.2.g.d.487.1		2
252.23	even	6		882.2.f.e.589.1		2
252.31	even	6		2646.2.h.f.361.1		2
252.47	odd	6		7938.2.a.bd.1.1		1
252.59	odd	6		882.2.h.e.67.1		2
252.67	odd	6		378.2.h.b.361.1		2
252.79	odd	6		7938.2.a.o.1.1		1
252.95	even	6		126.2.h.a.67.1	yes	2
252.103	even	6		2646.2.f.i.1765.1		2
252.131	odd	6		882.2.f.a.589.1		2
252.139	even	6		2646.2.e.e.1549.1		2
252.151	odd	6		1134.2.g.f.487.1		2
252.167	odd	6		882.2.e.h.373.1		2
252.187	even	6		7938.2.a.c.1.1		1
252.191	even	6		7938.2.a.r.1.1		1
252.247	odd	6		2646.2.f.e.1765.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.b.25.1	✓	2	84.11	even	6
126.2.e.b.121.1	yes	2	36.23	even	6
126.2.h.a.67.1	yes	2	252.95	even	6
126.2.h.a.79.1	yes	2	12.11	even	2
378.2.e.a.37.1		2	36.31	odd	6
378.2.e.a.235.1		2	28.11	odd	6
378.2.h.b.289.1		2	4.3	odd	2
378.2.h.b.361.1		2	252.67	odd	6
882.2.e.h.373.1		2	252.167	odd	6
882.2.e.h.655.1		2	84.59	odd	6
882.2.f.a.295.1		2	84.47	odd	6
882.2.f.a.589.1		2	252.131	odd	6
882.2.f.e.295.1		2	84.23	even	6
882.2.f.e.589.1		2	252.23	even	6
882.2.h.e.67.1		2	252.59	odd	6
882.2.h.e.79.1		2	84.83	odd	2
1008.2.q.e.529.1		2	21.11	odd	6
1008.2.q.e.625.1		2	9.5	odd	6
1008.2.t.c.193.1		2	63.32	odd	6
1008.2.t.c.961.1		2	3.2	odd	2
1134.2.g.d.163.1		2	36.11	even	6
1134.2.g.d.487.1		2	252.11	even	6
1134.2.g.f.163.1		2	36.7	odd	6
1134.2.g.f.487.1		2	252.151	odd	6
2646.2.e.e.1549.1		2	252.139	even	6
2646.2.e.e.2125.1		2	28.3	even	6
2646.2.f.e.883.1		2	28.23	odd	6
2646.2.f.e.1765.1		2	252.247	odd	6
2646.2.f.i.883.1		2	28.19	even	6
2646.2.f.i.1765.1		2	252.103	even	6
2646.2.h.f.361.1		2	252.31	even	6
2646.2.h.f.667.1		2	28.27	even	2
3024.2.q.a.2305.1		2	9.4	even	3
3024.2.q.a.2881.1		2	7.4	even	3
3024.2.t.f.289.1		2	1.1	even	1	trivial
3024.2.t.f.1873.1		2	63.4	even	3	inner
7938.2.a.c.1.1		1	252.187	even	6
7938.2.a.o.1.1		1	252.79	odd	6
7938.2.a.r.1.1		1	252.191	even	6
7938.2.a.bd.1.1		1	252.47	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)

\(f(q)\)	\(=\)	\(q+3.00000 q^{5} +(0.500000 - 2.59808i) q^{7} +O(q^{10})\)	\(q+3.00000 q^{5} +(0.500000 - 2.59808i) q^{7} -3.00000 q^{11} +(-2.50000 - 4.33013i) q^{13} +(1.50000 + 2.59808i) q^{17} +(2.50000 - 4.33013i) q^{19} -3.00000 q^{23} +4.00000 q^{25} +(-1.50000 + 2.59808i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(1.50000 - 7.79423i) q^{35} +(3.50000 - 6.06218i) q^{37} +(-4.50000 - 7.79423i) q^{41} +(5.50000 - 9.52628i) q^{43} +(-6.50000 - 2.59808i) q^{49} +(-1.50000 - 2.59808i) q^{53} -9.00000 q^{55} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-7.50000 - 12.9904i) q^{65} +(-2.00000 + 3.46410i) q^{67} +(-5.50000 - 9.52628i) q^{73} +(-1.50000 + 7.79423i) q^{77} +(4.00000 + 6.92820i) q^{79} +(-1.50000 + 2.59808i) q^{83} +(4.50000 + 7.79423i) q^{85} +(7.50000 - 12.9904i) q^{89} +(-12.5000 + 4.33013i) q^{91} +(7.50000 - 12.9904i) q^{95} +(0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 6 q^{5} + q^{7}+O(q^{10}) \) 2 * q + 6 * q^5 + q^7	\( 2 q + 6 q^{5} + q^{7} - 6 q^{11} - 5 q^{13} + 3 q^{17} + 5 q^{19} - 6 q^{23} + 8 q^{25} - 3 q^{29} - 4 q^{31} + 3 q^{35} + 7 q^{37} - 9 q^{41} + 11 q^{43} - 13 q^{49} - 3 q^{53} - 18 q^{55} - 12 q^{59} - 2 q^{61} - 15 q^{65} - 4 q^{67} - 11 q^{73} - 3 q^{77} + 8 q^{79} - 3 q^{83} + 9 q^{85} + 15 q^{89} - 25 q^{91} + 15 q^{95} + q^{97}+O(q^{100}) \) 2 * q + 6 * q^5 + q^7 - 6 * q^11 - 5 * q^13 + 3 * q^17 + 5 * q^19 - 6 * q^23 + 8 * q^25 - 3 * q^29 - 4 * q^31 + 3 * q^35 + 7 * q^37 - 9 * q^41 + 11 * q^43 - 13 * q^49 - 3 * q^53 - 18 * q^55 - 12 * q^59 - 2 * q^61 - 15 * q^65 - 4 * q^67 - 11 * q^73 - 3 * q^77 + 8 * q^79 - 3 * q^83 + 9 * q^85 + 15 * q^89 - 25 * q^91 + 15 * q^95 + q^97

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