LMFDB - Embedded newform 2240.2.e.a.2239.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(2239,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))

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

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

chi := DirichletCharacter("2240.2239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.e (of order $2$, degree $1$, 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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 9 $ x^4 + 4*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			2239.4
Root			$-0.707107 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	2240.2239
Dual form			2240.2.e.a.2239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.16228i q^{3} +2.23607i q^{5} +(2.12132 + 1.58114i) q^{7} -7.00000 q^{9} +O(q^{10})$	$q+3.16228i q^{3} +2.23607i q^{5} +(2.12132 + 1.58114i) q^{7} -7.00000 q^{9} -7.07107 q^{15} +(-5.00000 + 6.70820i) q^{21} +1.41421 q^{23} -5.00000 q^{25} -12.6491i q^{27} -6.00000 q^{29} +(-3.53553 + 4.74342i) q^{35} +4.47214i q^{41} -12.7279 q^{43} -15.6525i q^{45} -9.48683i q^{47} +(2.00000 + 6.70820i) q^{49} +13.4164i q^{61} +(-14.8492 - 11.0680i) q^{63} +4.24264 q^{67} +4.47214i q^{69} -15.8114i q^{75} +19.0000 q^{81} -9.48683i q^{83} -18.9737i q^{87} +17.8885i q^{89} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 28 q^{9}+O(q^{10}) $ 4 * q - 28 * q^9	$ 4 q - 28 q^{9} - 20 q^{21} - 20 q^{25} - 24 q^{29} + 8 q^{49} + 76 q^{81}+O(q^{100}) $ 4 * q - 28 * q^9 - 20 * q^21 - 20 * q^25 - 24 * q^29 + 8 * q^49 + 76 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$-1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$			3.16228i			1.82574i	0.408248	+	0.912871i	$0.366140\pi$
$3$			3.16228i			1.82574i	−0.408248	+	0.912871i	$0.633860\pi$
$4$		0			0
$5$			2.23607i			1.00000i
$5$			2.23607i			1.00000i
$6$		0			0
$7$	2.12132	+	1.58114i	0.801784	+	0.597614i
$7$	2.12132	+	1.58114i	0.801784	+	0.597614i
$8$		0			0
$9$	−7.00000			−2.33333
$10$		0			0
$11$		0			0		1.00000			$0$
$11$		0			0		−1.00000			$\pi$
$12$		0			0
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	−7.07107			−1.82574
$16$		0			0
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$		0			0
$21$	−5.00000	+	6.70820i	−1.09109	+	1.46385i
$22$		0			0
$23$	1.41421			0.294884			0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421			0.294884			0.147442	+	0.989071i	$0.452896\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$		0			0
$27$		−	12.6491i		−	2.43432i
$28$		0			0
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.53553	+	4.74342i	−0.597614	+	0.801784i
$36$		0			0
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			4.47214i			0.698430i	0.937043	+	0.349215i	$0.113552\pi$
$41$			4.47214i			0.698430i	−0.937043	+	0.349215i	$0.886448\pi$
$42$		0			0
$43$	−12.7279			−1.94099			−0.970495	−	0.241121i	$-0.922485\pi$
$43$	−12.7279			−1.94099			−0.970495	+	0.241121i	$0.922485\pi$
$44$		0			0
$45$		−	15.6525i		−	2.33333i
$46$		0			0
$47$		−	9.48683i		−	1.38380i	−0.721995	−	0.691898i	$-0.756775\pi$
$47$		−	9.48683i		−	1.38380i	0.721995	−	0.691898i	$-0.243225\pi$
$48$		0			0
$49$	2.00000	+	6.70820i	0.285714	+	0.958315i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$			13.4164i			1.71780i	0.512148	+	0.858898i	$0.328850\pi$
$61$			13.4164i			1.71780i	−0.512148	+	0.858898i	$0.671150\pi$
$62$		0			0
$63$	−14.8492	−	11.0680i	−1.87083	−	1.39443i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	4.24264			0.518321			0.259161	−	0.965834i	$-0.416554\pi$
$67$	4.24264			0.518321			0.259161	+	0.965834i	$0.416554\pi$
$68$		0			0
$69$			4.47214i			0.538382i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$		0			0
$75$		−	15.8114i		−	1.82574i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	19.0000			2.11111
$82$		0			0
$83$		−	9.48683i		−	1.04132i	−0.853766	−	0.520658i	$-0.825687\pi$
$83$		−	9.48683i		−	1.04132i	0.853766	−	0.520658i	$-0.174313\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	18.9737i		−	2.03419i
$88$		0			0
$89$			17.8885i			1.89618i	0.317999	+	0.948091i	$0.396989\pi$
$89$			17.8885i			1.89618i	−0.317999	+	0.948091i	$0.603011\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	8.94427i		−	0.889988i	−0.895533	−	0.444994i	$-0.853206\pi$
$101$		−	8.94427i		−	0.889988i	0.895533	−	0.444994i	$-0.146794\pi$
$102$		0			0
$103$			15.8114i			1.55794i	0.627060	+	0.778971i	$0.284258\pi$
$103$			15.8114i			1.55794i	−0.627060	+	0.778971i	$0.715742\pi$
$104$		0			0
$105$	−15.0000	−	11.1803i	−1.46385	−	1.09109i
$106$		0			0
$107$	18.3848			1.77732			0.888662	−	0.458563i	$-0.151636\pi$
$107$	18.3848			1.77732			0.888662	+	0.458563i	$0.151636\pi$
$108$		0			0
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$			3.16228i			0.294884i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	11.0000			1.00000
$122$		0			0
$123$	−14.1421			−1.27515
$124$		0			0
$125$		−	11.1803i		−	1.00000i
$126$		0			0
$127$	4.24264			0.376473			0.188237	−	0.982124i	$-0.439723\pi$
$127$	4.24264			0.376473			0.188237	+	0.982124i	$0.439723\pi$
$128$		0			0
$129$		−	40.2492i		−	3.54375i
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	28.2843			2.43432
$136$		0			0
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	30.0000			2.52646
$142$		0			0
$143$		0			0
$144$		0			0
$145$		−	13.4164i		−	1.11417i
$146$		0			0
$147$	−21.2132	+	6.32456i	−1.74964	+	0.521641i
$148$		0			0
$149$	−24.0000			−1.96616			−0.983078	−	0.183186i	$-0.941359\pi$
$149$	−24.0000			−1.96616			−0.983078	+	0.183186i	$0.941359\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.00000	+	2.23607i	0.236433	+	0.176227i
$162$		0			0
$163$	12.7279			0.996928			0.498464	−	0.866910i	$-0.333898\pi$
$163$	12.7279			0.996928			0.498464	+	0.866910i	$0.333898\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			9.48683i			0.734113i	0.930199	+	0.367057i	$0.119634\pi$
$167$			9.48683i			0.734113i	−0.930199	+	0.367057i	$0.880366\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$	−10.6066	−	7.90569i	−0.801784	−	0.597614i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$		0			0
$181$			26.8328i			1.99447i	0.0743294	+	0.997234i	$0.476318\pi$
$181$			26.8328i			1.99447i	−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−42.4264			−3.13625
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	20.0000	−	26.8328i	1.45479	−	1.95180i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$		0			0
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$		0			0
$201$			13.4164i			0.946320i
$202$		0			0
$203$	−12.7279	−	9.48683i	−0.893325	−	0.665845i
$204$		0			0
$205$	−10.0000			−0.698430
$206$		0			0
$207$	−9.89949			−0.688062
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		1.00000			$0$
$211$		0			0		−1.00000			$\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	28.4605i		−	1.94099i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$			3.16228i			0.211762i	0.994379	+	0.105881i	$0.0337662\pi$
$223$			3.16228i			0.211762i	−0.994379	+	0.105881i	$0.966234\pi$
$224$		0			0
$225$	35.0000			2.33333
$226$		0			0
$227$		−	28.4605i		−	1.88899i	−0.328526	−	0.944495i	$-0.606552\pi$
$227$		−	28.4605i		−	1.88899i	0.328526	−	0.944495i	$-0.393448\pi$
$228$		0			0
$229$		−	26.8328i		−	1.77316i	−0.462573	−	0.886581i	$-0.653074\pi$
$229$		−	26.8328i		−	1.77316i	0.462573	−	0.886581i	$-0.346926\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$	21.2132			1.38380
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$			13.4164i			0.864227i	0.901819	+	0.432113i	$0.142232\pi$
$241$			13.4164i			0.864227i	−0.901819	+	0.432113i	$0.857768\pi$
$242$		0			0
$243$			22.1359i			1.42002i
$244$		0			0
$245$	−15.0000	+	4.47214i	−0.958315	+	0.285714i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	30.0000			1.90117
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	42.0000			2.59973
$262$		0			0
$263$	15.5563			0.959246			0.479623	−	0.877475i	$-0.340774\pi$
$263$	15.5563			0.959246			0.479623	+	0.877475i	$0.340774\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−56.5685			−3.46194
$268$		0			0
$269$			22.3607i			1.36335i	0.731653	+	0.681677i	$0.238749\pi$
$269$			22.3607i			1.36335i	−0.731653	+	0.681677i	$0.761251\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		1.00000			$0$
$277$		0			0		−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$		0			0
$283$			15.8114i			0.939889i	0.882696	+	0.469945i	$0.155726\pi$
$283$			15.8114i			0.939889i	−0.882696	+	0.469945i	$0.844274\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.07107	+	9.48683i	−0.417392	+	0.559990i
$288$		0			0
$289$	−17.0000			−1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−27.0000	−	20.1246i	−1.55625	−	1.15996i
$302$		0			0
$303$	28.2843			1.62489
$304$		0			0
$305$	−30.0000			−1.71780
$306$		0			0
$307$			34.7851i			1.98529i	0.121070	+	0.992644i	$0.461367\pi$
$307$			34.7851i			1.98529i	−0.121070	+	0.992644i	$0.538633\pi$
$308$		0			0
$309$	−50.0000			−2.84440
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$		0			0
$315$	24.7487	−	33.2039i	1.39443	−	1.87083i
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			58.1378i			3.24493i
$322$		0			0
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$			50.5964i			2.79799i
$328$		0			0
$329$	15.0000	−	20.1246i	0.826977	−	1.10951i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			9.48683i			0.518321i
$336$		0			0
$337$		0			0		1.00000			$0$
$337$		0			0		−1.00000			$\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−6.36396	+	17.3925i	−0.343622	+	0.939108i
$344$		0			0
$345$	−10.0000			−0.538382
$346$		0			0
$347$	24.0416			1.29062			0.645311	−	0.763920i	$-0.276728\pi$
$347$	24.0416			1.29062			0.645311	+	0.763920i	$0.276728\pi$
$348$		0			0
$349$			26.8328i			1.43633i	0.695874	+	0.718164i	$0.255017\pi$
$349$			26.8328i			1.43633i	−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$		0			0
$363$			34.7851i			1.82574i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		−	3.16228i		−	0.165070i	−0.996588	−	0.0825348i	$-0.973698\pi$
$367$		−	3.16228i		−	0.165070i	0.996588	−	0.0825348i	$-0.0263016\pi$
$368$		0			0
$369$		−	31.3050i		−	1.62967i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$		0			0
$375$	35.3553			1.82574
$376$		0			0
$377$		0			0
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$			13.4164i			0.687343i
$382$		0			0
$383$		−	28.4605i		−	1.45426i	−0.686498	−	0.727132i	$-0.740853\pi$
$383$		−	28.4605i		−	1.45426i	0.686498	−	0.727132i	$-0.259147\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	89.0955			4.52898
$388$		0			0
$389$	24.0000			1.21685			0.608424	−	0.793612i	$-0.291802\pi$
$389$	24.0000			1.21685			0.608424	+	0.793612i	$0.291802\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$			42.4853i			2.11111i
$406$		0			0
$407$		0			0
$408$		0			0
$409$			40.2492i			1.99020i	0.0988936	+	0.995098i	$0.468470\pi$
$409$			40.2492i			1.99020i	−0.0988936	+	0.995098i	$0.531530\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	21.2132			1.04132
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$		0			0
$423$			66.4078i			3.22886i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−21.2132	+	28.4605i	−1.02658	+	1.37730i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		0			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	42.4264			2.03419
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$	−14.0000	−	46.9574i	−0.666667	−	2.23607i
$442$		0			0
$443$	−41.0122			−1.94855			−0.974274	−	0.225367i	$-0.927642\pi$
$443$	−41.0122			−1.94855			−0.974274	+	0.225367i	$0.927642\pi$
$444$		0			0
$445$	−40.0000			−1.89618
$446$		0			0
$447$		−	75.8947i		−	3.58969i
$448$		0			0
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			8.94427i			0.416576i	0.978068	+	0.208288i	$0.0667892\pi$
$461$			8.94427i			0.416576i	−0.978068	+	0.208288i	$0.933211\pi$
$462$		0			0
$463$	12.7279			0.591517			0.295758	−	0.955263i	$-0.404428\pi$
$463$	12.7279			0.591517			0.295758	+	0.955263i	$0.404428\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			28.4605i			1.31699i	0.752583	+	0.658497i	$0.228808\pi$
$467$			28.4605i			1.31699i	−0.752583	+	0.658497i	$0.771192\pi$
$468$		0			0
$469$	9.00000	+	6.70820i	0.415581	+	0.309756i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−7.07107	+	9.48683i	−0.321745	+	0.431666i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	38.1838			1.73027			0.865136	−	0.501538i	$-0.167232\pi$
$487$	38.1838			1.73027			0.865136	+	0.501538i	$0.167232\pi$
$488$		0			0
$489$			40.2492i			1.82013i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−30.0000			−1.34030
$502$		0			0
$503$			9.48683i			0.422997i	0.977378	+	0.211498i	$0.0678343\pi$
$503$			9.48683i			0.422997i	−0.977378	+	0.211498i	$0.932166\pi$
$504$		0			0
$505$	20.0000			0.889988
$506$		0			0
$507$		−	41.1096i		−	1.82574i
$508$		0			0
$509$			44.7214i			1.98224i	0.132973	+	0.991120i	$0.457548\pi$
$509$			44.7214i			1.98224i	−0.132973	+	0.991120i	$0.542452\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−35.3553			−1.55794
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	17.8885i		−	0.783711i	−0.920027	−	0.391856i	$-0.871833\pi$
$521$		−	17.8885i		−	0.783711i	0.920027	−	0.391856i	$-0.128167\pi$
$522$		0			0
$523$		−	34.7851i		−	1.52104i	−0.649312	−	0.760522i	$-0.724943\pi$
$523$		−	34.7851i		−	1.52104i	0.649312	−	0.760522i	$-0.275057\pi$
$524$		0			0
$525$	25.0000	−	33.5410i	1.09109	−	1.46385i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−21.0000			−0.913043
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$			41.1096i			1.77732i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$		0			0
$543$	−84.8528			−3.64138
$544$		0			0
$545$			35.7771i			1.53252i
$546$		0			0
$547$	46.6690			1.99542			0.997712	−	0.0676046i	$-0.0215356\pi$
$547$	46.6690			1.99542			0.997712	+	0.0676046i	$0.0215356\pi$
$548$		0			0
$549$		−	93.9149i		−	4.00819i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			47.4342i			1.99911i	0.0298010	+	0.999556i	$0.490513\pi$
$563$			47.4342i			1.99911i	−0.0298010	+	0.999556i	$0.509487\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	40.3051	+	30.0416i	1.69265	+	1.26163i
$568$		0			0
$569$	36.0000			1.50920			0.754599	−	0.656186i	$-0.227831\pi$
$569$	36.0000			1.50920			0.754599	+	0.656186i	$0.227831\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.07107			−0.294884
$576$		0			0
$577$		0			0			−	1.00000i	$-0.5\pi$
$577$		0			0				1.00000i	$0.5\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	15.0000	−	20.1246i	0.622305	−	0.834910i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	47.4342i		−	1.95782i	−0.204298	−	0.978909i	$-0.565491\pi$
$587$		−	47.4342i		−	1.95782i	0.204298	−	0.978909i	$-0.434509\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$		−	40.2492i		−	1.64180i	−0.571072	−	0.820900i	$-0.693472\pi$
$601$		−	40.2492i		−	1.64180i	0.571072	−	0.820900i	$-0.306528\pi$
$602$		0			0
$603$	−29.6985			−1.20942
$604$		0			0
$605$			24.5967i			1.00000i
$606$		0			0
$607$			15.8114i			0.641764i	0.947119	+	0.320882i	$0.103979\pi$
$607$			15.8114i			0.641764i	−0.947119	+	0.320882i	$0.896021\pi$
$608$		0			0
$609$	30.0000	−	40.2492i	1.21566	−	1.63098i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		−	31.6228i		−	1.27515i
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		−	17.8885i		−	0.717843i
$622$		0			0
$623$	−28.2843	+	37.9473i	−1.13319	+	1.52033i
$624$		0			0
$625$	25.0000			1.00000
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$			9.48683i			0.376473i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$		0			0
$643$			41.1096i			1.62120i	0.585597	+	0.810602i	$0.300860\pi$
$643$			41.1096i			1.62120i	−0.585597	+	0.810602i	$0.699140\pi$
$644$		0			0
$645$	90.0000			3.54375
$646$		0			0
$647$		−	47.4342i		−	1.86483i	−0.361390	−	0.932415i	$-0.617698\pi$
$647$		−	47.4342i		−	1.86483i	0.361390	−	0.932415i	$-0.382302\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		1.00000			$0$
$653$		0			0		−1.00000			$\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$		−	40.2492i		−	1.56551i	−0.622328	−	0.782757i	$-0.713813\pi$
$661$		−	40.2492i		−	1.56551i	0.622328	−	0.782757i	$-0.286187\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−8.48528			−0.328551
$668$		0			0
$669$	−10.0000			−0.386622
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$		0			0
$675$			63.2456i			2.43432i
$676$		0			0
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	90.0000			3.44881
$682$		0			0
$683$	43.8406			1.67751			0.838757	−	0.544505i	$-0.183283\pi$
$683$	43.8406			1.67751			0.838757	+	0.544505i	$0.183283\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	84.8528			3.23734
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$			67.0820i			2.52646i
$706$		0			0
$707$	14.1421	−	18.9737i	0.531870	−	0.713578i
$708$		0			0
$709$	46.0000			1.72757			0.863783	−	0.503864i	$-0.168089\pi$
$709$	46.0000			1.72757			0.863783	+	0.503864i	$0.168089\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−25.0000	+	33.5410i	−0.931049	+	1.24913i
$722$		0			0
$723$	−42.4264			−1.57786
$724$		0			0
$725$	30.0000			1.11417
$726$		0			0
$727$			53.7587i			1.99380i	0.0786754	+	0.996900i	$0.474931\pi$
$727$			53.7587i			1.99380i	−0.0786754	+	0.996900i	$0.525069\pi$
$728$		0			0
$729$	−13.0000			−0.481481
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$		0			0
$735$	−14.1421	−	47.4342i	−0.521641	−	1.74964i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−26.8701			−0.985767			−0.492883	−	0.870095i	$-0.664057\pi$
$743$	−26.8701			−0.985767			−0.492883	+	0.870095i	$0.664057\pi$
$744$		0			0
$745$		−	53.6656i		−	1.96616i
$746$		0			0
$747$			66.4078i			2.42974i
$748$		0			0
$749$	39.0000	+	29.0689i	1.42503	+	1.06215i
$750$		0			0
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	35.7771i		−	1.29692i	−0.761249	−	0.648459i	$-0.775414\pi$
$761$		−	35.7771i		−	1.29692i	0.761249	−	0.648459i	$-0.224586\pi$
$762$		0			0
$763$	33.9411	+	25.2982i	1.22875	+	0.915857i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$			53.6656i			1.93523i	0.252426	+	0.967616i	$0.418771\pi$
$769$			53.6656i			1.93523i	−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$			75.8947i			2.71225i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		−	41.1096i		−	1.46540i	−0.680552	−	0.732700i	$-0.738260\pi$
$787$		−	41.1096i		−	1.46540i	0.680552	−	0.732700i	$-0.261740\pi$
$788$		0			0
$789$			49.1935i			1.75133i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		−	125.220i		−	4.42442i
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−5.00000	+	6.70820i	−0.176227	+	0.236433i
$806$		0			0
$807$	−70.7107			−2.48913
$808$		0			0
$809$	54.0000			1.89854			0.949269	−	0.314464i	$-0.101825\pi$
$809$	54.0000			1.89854			0.949269	+	0.314464i	$0.101825\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			28.4605i			0.996928i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	48.0000			1.67521			0.837606	−	0.546275i	$-0.183955\pi$
$821$	48.0000			1.67521			0.837606	+	0.546275i	$0.183955\pi$
$822$		0			0
$823$	55.1543			1.92256			0.961280	−	0.275575i	$-0.0888683\pi$
$823$	55.1543			1.92256			0.961280	+	0.275575i	$0.0888683\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.5269			−1.13107			−0.565536	−	0.824724i	$-0.691331\pi$
$827$	−32.5269			−1.13107			−0.565536	+	0.824724i	$0.691331\pi$
$828$		0			0
$829$		−	13.4164i		−	0.465971i	−0.972480	−	0.232986i	$-0.925151\pi$
$829$		−	13.4164i		−	0.465971i	0.972480	−	0.232986i	$-0.0748495\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−21.2132			−0.734113
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0			−	1.00000i	$-0.5\pi$
$839$		0			0				1.00000i	$0.5\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$		0			0
$843$		−	37.9473i		−	1.30698i
$844$		0			0
$845$		−	29.0689i		−	1.00000i
$846$		0			0
$847$	23.3345	+	17.3925i	0.801784	+	0.597614i
$848$		0			0
$849$	−50.0000			−1.71600
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$		0			0			−	1.00000i	$-0.5\pi$
$859$		0			0				1.00000i	$0.5\pi$
$860$		0			0
$861$	−30.0000	−	22.3607i	−1.02240	−	0.762050i
$862$		0			0
$863$	−57.9828			−1.97376			−0.986878	−	0.161468i	$-0.948377\pi$
$863$	−57.9828			−1.97376			−0.986878	+	0.161468i	$0.948377\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	53.7587i		−	1.82574i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	17.6777	−	23.7171i	0.597614	−	0.801784i
$876$		0			0
$877$		0			0		1.00000			$0$
$877$		0			0		−1.00000			$\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	58.1378i		−	1.95871i	−0.202145	−	0.979356i	$-0.564791\pi$
$881$		−	58.1378i		−	1.95871i	0.202145	−	0.979356i	$-0.435209\pi$
$882$		0			0
$883$	55.1543			1.85609			0.928045	−	0.372467i	$-0.121488\pi$
$883$	55.1543			1.85609			0.928045	+	0.372467i	$0.121488\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		−	28.4605i		−	0.955610i	−0.878466	−	0.477805i	$-0.841433\pi$
$887$		−	28.4605i		−	0.955610i	0.878466	−	0.477805i	$-0.158567\pi$
$888$		0			0
$889$	9.00000	+	6.70820i	0.301850	+	0.224986i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	63.6396	−	85.3815i	2.11779	−	2.84132i
$904$		0			0
$905$	−60.0000			−1.99447
$906$		0			0
$907$	4.24264			0.140875			0.0704373	−	0.997516i	$-0.477561\pi$
$907$	4.24264			0.140875			0.0704373	+	0.997516i	$0.477561\pi$
$908$		0			0
$909$			62.6099i			2.07664i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		−	94.8683i		−	3.13625i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−110.000			−3.62462
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		−	110.680i		−	3.63520i
$928$		0			0
$929$			49.1935i			1.61399i	0.590561	+	0.806993i	$0.298907\pi$
$929$			49.1935i			1.61399i	−0.590561	+	0.806993i	$0.701093\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	44.7214i		−	1.45787i	−0.684580	−	0.728937i	$-0.740015\pi$
$941$		−	44.7214i		−	1.45787i	0.684580	−	0.728937i	$-0.259985\pi$
$942$		0			0
$943$			6.32456i			0.205956i
$944$		0			0
$945$	60.0000	+	44.7214i	1.95180	+	1.45479i
$946$		0			0
$947$	−60.8112			−1.97610			−0.988049	−	0.154140i	$-0.950739\pi$
$947$	−60.8112			−1.97610			−0.988049	+	0.154140i	$0.950739\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		1.00000			$0$
$953$		0			0		−1.00000			$\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$		0			0
$963$	−128.693			−4.14709
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−46.6690			−1.50078			−0.750388	−	0.660998i	$-0.770133\pi$
$967$	−46.6690			−1.50078			−0.750388	+	0.660998i	$0.770133\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		1.00000			$0$
$977$		0			0		−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−112.000			−3.57588
$982$		0			0
$983$		−	47.4342i		−	1.51291i	−0.654043	−	0.756457i	$-0.726928\pi$
$983$		−	47.4342i		−	1.51291i	0.654043	−	0.756457i	$-0.273072\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	63.6396	+	47.4342i	2.02567	+	1.50985i
$988$		0			0
$989$	−18.0000			−0.572367
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0			−	1.00000i	$-0.5\pi$
$997$		0			0				1.00000i	$0.5\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.e.a.2239.4		4
4.3	odd	2	inner	2240.2.e.a.2239.2		4
5.4	even	2	inner	2240.2.e.a.2239.2		4
7.6	odd	2	inner	2240.2.e.a.2239.1		4
8.3	odd	2		140.2.c.a.139.4	yes	4
8.5	even	2		140.2.c.a.139.1	✓	4
20.19	odd	2	CM	2240.2.e.a.2239.4		4
28.27	even	2	inner	2240.2.e.a.2239.3		4
35.34	odd	2	inner	2240.2.e.a.2239.3		4
40.3	even	4		700.2.g.d.251.1		4
40.13	odd	4		700.2.g.d.251.4		4
40.19	odd	2		140.2.c.a.139.1	✓	4
40.27	even	4		700.2.g.d.251.4		4
40.29	even	2		140.2.c.a.139.4	yes	4
40.37	odd	4		700.2.g.d.251.1		4
56.3	even	6		980.2.s.b.19.1		8
56.5	odd	6		980.2.s.b.619.3		8
56.11	odd	6		980.2.s.b.19.2		8
56.13	odd	2		140.2.c.a.139.2	yes	4
56.19	even	6		980.2.s.b.619.2		8
56.27	even	2		140.2.c.a.139.3	yes	4
56.37	even	6		980.2.s.b.619.4		8
56.45	odd	6		980.2.s.b.19.4		8
56.51	odd	6		980.2.s.b.619.1		8
56.53	even	6		980.2.s.b.19.3		8
140.139	even	2	inner	2240.2.e.a.2239.1		4
280.13	even	4		700.2.g.d.251.3		4
280.19	even	6		980.2.s.b.619.3		8
280.27	odd	4		700.2.g.d.251.3		4
280.59	even	6		980.2.s.b.19.4		8
280.69	odd	2		140.2.c.a.139.3	yes	4
280.83	odd	4		700.2.g.d.251.2		4
280.109	even	6		980.2.s.b.19.2		8
280.139	even	2		140.2.c.a.139.2	yes	4
280.149	even	6		980.2.s.b.619.1		8
280.179	odd	6		980.2.s.b.19.3		8
280.219	odd	6		980.2.s.b.619.4		8
280.229	odd	6		980.2.s.b.619.2		8
280.237	even	4		700.2.g.d.251.2		4
280.269	odd	6		980.2.s.b.19.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.c.a.139.1	✓	4	8.5	even	2
140.2.c.a.139.1	✓	4	40.19	odd	2
140.2.c.a.139.2	yes	4	56.13	odd	2
140.2.c.a.139.2	yes	4	280.139	even	2
140.2.c.a.139.3	yes	4	56.27	even	2
140.2.c.a.139.3	yes	4	280.69	odd	2
140.2.c.a.139.4	yes	4	8.3	odd	2
140.2.c.a.139.4	yes	4	40.29	even	2
700.2.g.d.251.1		4	40.3	even	4
700.2.g.d.251.1		4	40.37	odd	4
700.2.g.d.251.2		4	280.83	odd	4
700.2.g.d.251.2		4	280.237	even	4
700.2.g.d.251.3		4	280.13	even	4
700.2.g.d.251.3		4	280.27	odd	4
700.2.g.d.251.4		4	40.13	odd	4
700.2.g.d.251.4		4	40.27	even	4
980.2.s.b.19.1		8	56.3	even	6
980.2.s.b.19.1		8	280.269	odd	6
980.2.s.b.19.2		8	56.11	odd	6
980.2.s.b.19.2		8	280.109	even	6
980.2.s.b.19.3		8	56.53	even	6
980.2.s.b.19.3		8	280.179	odd	6
980.2.s.b.19.4		8	56.45	odd	6
980.2.s.b.19.4		8	280.59	even	6
980.2.s.b.619.1		8	56.51	odd	6
980.2.s.b.619.1		8	280.149	even	6
980.2.s.b.619.2		8	56.19	even	6
980.2.s.b.619.2		8	280.229	odd	6
980.2.s.b.619.3		8	56.5	odd	6
980.2.s.b.619.3		8	280.19	even	6
980.2.s.b.619.4		8	56.37	even	6
980.2.s.b.619.4		8	280.219	odd	6
2240.2.e.a.2239.1		4	7.6	odd	2	inner
2240.2.e.a.2239.1		4	140.139	even	2	inner
2240.2.e.a.2239.2		4	4.3	odd	2	inner
2240.2.e.a.2239.2		4	5.4	even	2	inner
2240.2.e.a.2239.3		4	28.27	even	2	inner
2240.2.e.a.2239.3		4	35.34	odd	2	inner
2240.2.e.a.2239.4		4	1.1	even	1	trivial
2240.2.e.a.2239.4		4	20.19	odd	2	CM

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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.e (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+3.16228i q^{3} +2.23607i q^{5} +(2.12132 + 1.58114i) q^{7} -7.00000 q^{9} +O(q^{10})\)	\(q+3.16228i q^{3} +2.23607i q^{5} +(2.12132 + 1.58114i) q^{7} -7.00000 q^{9} -7.07107 q^{15} +(-5.00000 + 6.70820i) q^{21} +1.41421 q^{23} -5.00000 q^{25} -12.6491i q^{27} -6.00000 q^{29} +(-3.53553 + 4.74342i) q^{35} +4.47214i q^{41} -12.7279 q^{43} -15.6525i q^{45} -9.48683i q^{47} +(2.00000 + 6.70820i) q^{49} +13.4164i q^{61} +(-14.8492 - 11.0680i) q^{63} +4.24264 q^{67} +4.47214i q^{69} -15.8114i q^{75} +19.0000 q^{81} -9.48683i q^{83} -18.9737i q^{87} +17.8885i q^{89} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 28 q^{9}+O(q^{10}) \) 4 * q - 28 * q^9	\( 4 q - 28 q^{9} - 20 q^{21} - 20 q^{25} - 24 q^{29} + 8 q^{49} + 76 q^{81}+O(q^{100}) \) 4 * q - 28 * q^9 - 20 * q^21 - 20 * q^25 - 24 * q^29 + 8 * q^49 + 76 * q^81

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