LMFDB - Embedded newform 2240.2.n.j.1119.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(1119,2240)]

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, 1, 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("2240.1119");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.n (of order $2$, degree $1$, 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:	$16$
Coefficient field:	16.0.968265199641600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 9x^{14} + 44x^{12} + 261x^{10} + 1029x^{8} + 1044x^{6} + 704x^{4} + 576x^{2} + 256 $ x^16 + 9x^14 + 44x^12 + 261x^10 + 1029x^8 + 1044x^6 + 704x^4 + 576*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			1119.14
Root			$-0.676408 - 0.553538i$ of defining polynomial
Character	$\chi$	$=$	2240.1119
Dual form			2240.2.n.j.1119.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.40932 q^{3} -2.23607i q^{5} +2.64575i q^{7} +8.62348 q^{9} +O(q^{10})$	$q+3.40932 q^{3} -2.23607i q^{5} +2.64575i q^{7} +8.62348 q^{9} +5.55612 q^{11} -1.06281i q^{13} -7.62348i q^{15} -5.90512 q^{17} +9.02022i q^{21} -5.00000 q^{25} +19.1722 q^{27} -4.83619i q^{29} +18.9426 q^{33} +5.91608 q^{35} -3.62348i q^{39} -19.2827i q^{45} +13.6511i q^{47} -7.00000 q^{49} -20.1324 q^{51} -12.4239i q^{55} +22.8156i q^{63} -2.37652 q^{65} +12.0000i q^{71} -10.5830 q^{73} -17.0466 q^{75} +14.7001i q^{77} -14.8704i q^{79} +39.4939 q^{81} -8.94427 q^{83} +13.2042i q^{85} -16.4881i q^{87} +2.81194 q^{91} +3.45065 q^{97} +47.9130 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 56 q^{9}+O(q^{10}) $ 16 * q + 56 * q^9	$ 16 q + 56 q^{9} - 80 q^{25} - 112 q^{49} - 120 q^{65} + 304 q^{81}+O(q^{100}) $ 16 * q + 56 * q^9 - 80 * q^25 - 112 * q^49 - 120 * q^65 + 304 * 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
$3$	3.40932	1.96837	0.984186	−	0.177136i	$-0.0566831\pi$
$3$	3.40932	1.96837	0.984186	+	0.177136i	$0.0566831\pi$
$4$	0	0
$5$	− 2.23607i	− 1.00000i
$5$	− 2.23607i	− 1.00000i
$6$	0	0
$7$	2.64575i	1.00000i
$7$	2.64575i	1.00000i
$8$	0	0
$9$	8.62348	2.87449
$10$	0	0
$11$	5.55612	1.67523	0.837616	−	0.546259i	$-0.183949\pi$
$11$	5.55612	1.67523	0.837616	+	0.546259i	$0.183949\pi$
$12$	0	0
$13$	− 1.06281i	− 0.294772i	−0.989079	−	0.147386i	$-0.952914\pi$
$13$	− 1.06281i	− 0.294772i	0.989079	−	0.147386i	$-0.0470859\pi$
$14$	0	0
$15$	− 7.62348i	− 1.96837i
$16$	0	0
$17$	−5.90512	−1.43220	−0.716101	−	0.697997i	$-0.754075\pi$
$17$	−5.90512	−1.43220	−0.716101	+	0.697997i	$0.754075\pi$
$18$	0	0
$19$	0	0	1.00000			$0$
$19$	0	0	−1.00000			$\pi$
$20$	0	0
$21$	9.02022i	1.96837i
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−5.00000	−1.00000
$26$	0	0
$27$	19.1722	3.68970
$28$	0	0
$29$	− 4.83619i	− 0.898058i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	− 4.83619i	− 0.898058i	0.893517	−	0.449029i	$-0.148230\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	0	0
$33$	18.9426	3.29748
$34$	0	0
$35$	5.91608	1.00000
$36$	0	0
$37$	0	0		−	1.00000i	$-0.5\pi$
$37$	0	0			1.00000i	$0.5\pi$
$38$	0	0
$39$	− 3.62348i	− 0.580220i
$40$	0	0
$41$	0	0	1.00000			$0$
$41$	0	0	−1.00000			$\pi$
$42$	0	0
$43$	0	0	1.00000			$0$
$43$	0	0	−1.00000			$\pi$
$44$	0	0
$45$	− 19.2827i	− 2.87449i
$46$	0	0
$47$	13.6511i	1.99122i	0.0936230	+	0.995608i	$0.470155\pi$
$47$	13.6511i	1.99122i	−0.0936230	+	0.995608i	$0.529845\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	0	0
$51$	−20.1324	−2.81911
$52$	0	0
$53$	0	0		−	1.00000i	$-0.5\pi$
$53$	0	0			1.00000i	$0.5\pi$
$54$	0	0
$55$	− 12.4239i	− 1.67523i
$56$	0	0
$57$	0	0
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	0	0
$63$	22.8156i	2.87449i
$64$	0	0
$65$	−2.37652	−0.294772
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	0	0
$69$	0	0
$70$	0	0
$71$	12.0000i	1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$	12.0000i	1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	0	0
$73$	−10.5830	−1.23865	−0.619324	−	0.785136i	$-0.712593\pi$
$73$	−10.5830	−1.23865	−0.619324	+	0.785136i	$0.712593\pi$
$74$	0	0
$75$	−17.0466	−1.96837
$76$	0	0
$77$	14.7001i	1.67523i
$78$	0	0
$79$	− 14.8704i	− 1.67305i	−0.547926	−	0.836527i	$-0.684582\pi$
$79$	− 14.8704i	− 1.67305i	0.547926	−	0.836527i	$-0.315418\pi$
$80$	0	0
$81$	39.4939	4.38821
$82$	0	0
$83$	−8.94427	−0.981761	−0.490881	−	0.871227i	$-0.663325\pi$
$83$	−8.94427	−0.981761	−0.490881	+	0.871227i	$0.663325\pi$
$84$	0	0
$85$	13.2042i	1.43220i
$86$	0	0
$87$	− 16.4881i	− 1.76771i
$88$	0	0
$89$	0	0	1.00000			$0$
$89$	0	0	−1.00000			$\pi$
$90$	0	0
$91$	2.81194	0.294772
$92$	0	0
$93$	0	0
$94$	0	0
$95$	0	0
$96$	0	0
$97$	3.45065	0.350361	0.175180	−	0.984536i	$-0.443949\pi$
$97$	3.45065	0.350361	0.175180	+	0.984536i	$0.443949\pi$
$98$	0	0
$99$	47.9130	4.81544
$100$	0	0
$101$	0	0		−	1.00000i	$-0.5\pi$
$101$	0	0			1.00000i	$0.5\pi$
$102$	0	0
$103$	− 16.1055i	− 1.58693i	−0.608618	−	0.793463i	$-0.708276\pi$
$103$	− 16.1055i	− 1.58693i	0.608618	−	0.793463i	$-0.291724\pi$
$104$	0	0
$105$	20.1698	1.96837
$106$	0	0
$107$	0	0	1.00000			$0$
$107$	0	0	−1.00000			$\pi$
$108$	0	0
$109$	− 0.652160i	− 0.0624656i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	− 0.652160i	− 0.0624656i	0.999512	−	0.0312328i	$-0.00994332\pi$
$110$	0	0
$111$	0	0
$112$	0	0
$113$	0	0	1.00000			$0$
$113$	0	0	−1.00000			$\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	− 9.16515i	− 0.847319i
$118$	0	0
$119$	− 15.6235i	− 1.43220i
$120$	0	0
$121$	19.8704	1.80640
$122$	0	0
$123$	0	0
$124$	0	0
$125$	11.1803i	1.00000i
$126$	0	0
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	− 42.8704i	− 3.68970i
$136$	0	0
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	0	0
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	46.5409i	3.91945i
$142$	0	0
$143$	− 5.90512i	− 0.493811i
$144$	0	0
$145$	−10.8140	−0.898058
$146$	0	0
$147$	−23.8653	−1.96837
$148$	0	0
$149$	− 23.6643i	− 1.93866i	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	− 23.6643i	− 1.93866i	0.245770	−	0.969328i	$-0.420959\pi$
$150$	0	0
$151$	− 6.87043i	− 0.559107i	−0.960130	−	0.279554i	$-0.909814\pi$
$151$	− 6.87043i	− 0.559107i	0.960130	−	0.279554i	$-0.0901865\pi$
$152$	0	0
$153$	−50.9226	−4.11685
$154$	0	0
$155$	0	0
$156$	0	0
$157$	13.4164i	1.07075i	0.844616	+	0.535373i	$0.179829\pi$
$157$	13.4164i	1.07075i	−0.844616	+	0.535373i	$0.820171\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	0	0
$162$	0	0
$163$	0	0	1.00000			$0$
$163$	0	0	−1.00000			$\pi$
$164$	0	0
$165$	− 42.3569i	− 3.29748i
$166$	0	0
$167$	− 17.3328i	− 1.34125i	−0.741796	−	0.670625i	$-0.766026\pi$
$167$	− 17.3328i	− 1.34125i	0.741796	−	0.670625i	$-0.233974\pi$
$168$	0	0
$169$	11.8704	0.913110
$170$	0	0
$171$	0	0
$172$	0	0
$173$	26.2118i	1.99284i	0.0845218	+	0.996422i	$0.473064\pi$
$173$	26.2118i	1.99284i	−0.0845218	+	0.996422i	$0.526936\pi$
$174$	0	0
$175$	− 13.2288i	− 1.00000i
$176$	0	0
$177$	0	0
$178$	0	0
$179$	−11.8322	−0.884377	−0.442189	−	0.896922i	$-0.645798\pi$
$179$	−11.8322	−0.884377	−0.442189	+	0.896922i	$0.645798\pi$
$180$	0	0
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	0	0
$183$	0	0
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−32.8095	−2.39927
$188$	0	0
$189$	50.7250i	3.68970i
$190$	0	0
$191$	8.37652i	0.606104i	0.952974	+	0.303052i	$0.0980056\pi$
$191$	8.37652i	0.606104i	−0.952974	+	0.303052i	$0.901994\pi$
$192$	0	0
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	0	0
$195$	−8.10234	−0.580220
$196$	0	0
$197$	0	0		−	1.00000i	$-0.5\pi$
$197$	0	0			1.00000i	$0.5\pi$
$198$	0	0
$199$	0	0		−	1.00000i	$-0.5\pi$
$199$	0	0			1.00000i	$0.5\pi$
$200$	0	0
$201$	0	0
$202$	0	0
$203$	12.7954	0.898058
$204$	0	0
$205$	0	0
$206$	0	0
$207$	0	0
$208$	0	0
$209$	0	0
$210$	0	0
$211$	−11.0445	−0.760332	−0.380166	−	0.924918i	$-0.624133\pi$
$211$	−11.0445	−0.760332	−0.380166	+	0.924918i	$0.624133\pi$
$212$	0	0
$213$	40.9119i	2.80323i
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0	0
$218$	0	0
$219$	−36.0809	−2.43812
$220$	0	0
$221$	6.27604i	0.422172i
$222$	0	0
$223$	8.74216i	0.585418i	0.956202	+	0.292709i	$0.0945567\pi$
$223$	8.74216i	0.585418i	−0.956202	+	0.292709i	$0.905443\pi$
$224$	0	0
$225$	−43.1174	−2.87449
$226$	0	0
$227$	−7.66058	−0.508450	−0.254225	−	0.967145i	$-0.581820\pi$
$227$	−7.66058	−0.508450	−0.254225	+	0.967145i	$0.581820\pi$
$228$	0	0
$229$	0	0		−	1.00000i	$-0.5\pi$
$229$	0	0			1.00000i	$0.5\pi$
$230$	0	0
$231$	50.1174i	3.29748i
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	0	0
$235$	30.5248	1.99122
$236$	0	0
$237$	− 50.6981i	− 3.29319i
$238$	0	0
$239$	30.1174i	1.94813i	0.226266	+	0.974066i	$0.427348\pi$
$239$	30.1174i	1.94813i	−0.226266	+	0.974066i	$0.572652\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	0	0
$243$	77.1307	4.94794
$244$	0	0
$245$	15.6525i	1.00000i
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−30.4939	−1.93247
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	0	0
$253$	0	0
$254$	0	0
$255$	45.0175i	2.81911i
$256$	0	0
$257$	−31.7490	−1.98045	−0.990225	−	0.139482i	$-0.955456\pi$
$257$	−31.7490	−1.98045	−0.990225	+	0.139482i	$0.955456\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	− 41.7048i	− 2.58146i
$262$	0	0
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	0	0
$268$	0	0
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	0	0
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	0	0
$273$	9.58681	0.580220
$274$	0	0
$275$	−27.7806	−1.67523
$276$	0	0
$277$	0	0		−	1.00000i	$-0.5\pi$
$277$	0	0			1.00000i	$0.5\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	21.6235	1.28995	0.644974	−	0.764204i	$-0.276868\pi$
$281$	21.6235	1.28995	0.644974	+	0.764204i	$0.276868\pi$
$282$	0	0
$283$	−14.4792	−0.860700	−0.430350	−	0.902662i	$-0.641610\pi$
$283$	−14.4792	−0.860700	−0.430350	+	0.902662i	$0.641610\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	0	0
$288$	0	0
$289$	17.8704	1.05120
$290$	0	0
$291$	11.7644	0.689641
$292$	0	0
$293$	8.32322i	0.486248i	0.969995	+	0.243124i	$0.0781721\pi$
$293$	8.32322i	0.486248i	−0.969995	+	0.243124i	$0.921828\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	106.523	6.18110
$298$	0	0
$299$	0	0
$300$	0	0
$301$	0	0
$302$	0	0
$303$	0	0
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−26.4326	−1.50859	−0.754295	−	0.656535i	$-0.772021\pi$
$307$	−26.4326	−1.50859	−0.754295	+	0.656535i	$0.772021\pi$
$308$	0	0
$309$	− 54.9090i	− 3.12366i
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	−31.9801	−1.80762	−0.903810	−	0.427934i	$-0.859241\pi$
$313$	−31.9801	−1.80762	−0.903810	+	0.427934i	$0.859241\pi$
$314$	0	0
$315$	51.0172	2.87449
$316$	0	0
$317$	0	0		−	1.00000i	$-0.5\pi$
$317$	0	0			1.00000i	$0.5\pi$
$318$	0	0
$319$	− 26.8704i	− 1.50446i
$320$	0	0
$321$	0	0
$322$	0	0
$323$	0	0
$324$	0	0
$325$	5.31407i	0.294772i
$326$	0	0
$327$	− 2.22342i	− 0.122956i
$328$	0	0
$329$	−36.1174	−1.99122
$330$	0	0
$331$	−35.4965	−1.95106	−0.975531	−	0.219860i	$-0.929440\pi$
$331$	−35.4965	−1.95106	−0.975531	+	0.219860i	$0.929440\pi$
$332$	0	0
$333$	0	0
$334$	0	0
$335$	0	0
$336$	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
$343$	− 18.5203i	− 1.00000i
$344$	0	0
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0		−	1.00000i	$-0.5\pi$
$349$	0	0			1.00000i	$0.5\pi$
$350$	0	0
$351$	− 20.3765i	− 1.08762i
$352$	0	0
$353$	13.2685	0.706212	0.353106	−	0.935583i	$-0.385126\pi$
$353$	13.2685	0.706212	0.353106	+	0.935583i	$0.385126\pi$
$354$	0	0
$355$	26.8328	1.42414
$356$	0	0
$357$	− 53.2655i	− 2.81911i
$358$	0	0
$359$	− 36.0000i	− 1.90001i	−0.312239	−	0.950004i	$-0.601079\pi$
$359$	− 36.0000i	− 1.90001i	0.312239	−	0.950004i	$-0.398921\pi$
$360$	0	0
$361$	19.0000	1.00000
$362$	0	0
$363$	67.7447	3.55567
$364$	0	0
$365$	23.6643i	1.23865i
$366$	0	0
$367$	19.7872i	1.03289i	0.856322	+	0.516443i	$0.172744\pi$
$367$	19.7872i	1.03289i	−0.856322	+	0.516443i	$0.827256\pi$
$368$	0	0
$369$	0	0
$370$	0	0
$371$	0	0
$372$	0	0
$373$	0	0		−	1.00000i	$-0.5\pi$
$373$	0	0			1.00000i	$0.5\pi$
$374$	0	0
$375$	38.1174i	1.96837i
$376$	0	0
$377$	−5.13997	−0.264722
$378$	0	0
$379$	35.4965	1.82333	0.911666	−	0.410932i	$-0.134797\pi$
$379$	35.4965	1.82333	0.911666	+	0.410932i	$0.134797\pi$
$380$	0	0
$381$	0	0
$382$	0	0
$383$	15.8745i	0.811149i	0.914062	+	0.405575i	$0.132929\pi$
$383$	15.8745i	0.811149i	−0.914062	+	0.405575i	$0.867071\pi$
$384$	0	0
$385$	32.8704	1.67523
$386$	0	0
$387$	0	0
$388$	0	0
$389$	36.7330i	1.86244i	0.364459	+	0.931219i	$0.381254\pi$
$389$	36.7330i	1.86244i	−0.364459	+	0.931219i	$0.618746\pi$
$390$	0	0
$391$	0	0
$392$	0	0
$393$	0	0
$394$	0	0
$395$	−33.2513	−1.67305
$396$	0	0
$397$	− 39.8490i	− 1.99997i	−0.00579782	−	0.999983i	$-0.501846\pi$
$397$	− 39.8490i	− 1.99997i	0.00579782	−	0.999983i	$-0.498154\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−12.1174	−0.605113	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	−12.1174	−0.605113	−0.302556	+	0.953131i	$0.597840\pi$
$402$	0	0
$403$	0	0
$404$	0	0
$405$	− 88.3110i	− 4.38821i
$406$	0	0
$407$	0	0
$408$	0	0
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	0	0
$415$	20.0000i	0.981761i
$416$	0	0
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	40.9171i	1.99418i	0.0762630	+	0.997088i	$0.475701\pi$
$421$	40.9171i	1.99418i	−0.0762630	+	0.997088i	$0.524299\pi$
$422$	0	0
$423$	117.720i	5.72373i
$424$	0	0
$425$	29.5256	1.43220
$426$	0	0
$427$	0	0
$428$	0	0
$429$	− 20.1324i	− 0.972004i
$430$	0	0
$431$	37.3643i	1.79978i	0.436121	+	0.899888i	$0.356352\pi$
$431$	37.3643i	1.79978i	−0.436121	+	0.899888i	$0.643648\pi$
$432$	0	0
$433$	10.5830	0.508587	0.254293	−	0.967127i	$-0.418157\pi$
$433$	10.5830	0.508587	0.254293	+	0.967127i	$0.418157\pi$
$434$	0	0
$435$	−36.8686	−1.76771
$436$	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
$441$	−60.3643	−2.87449
$442$	0	0
$443$	0	0	1.00000			$0$
$443$	0	0	−1.00000			$\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	− 80.6793i	− 3.81600i
$448$	0	0
$449$	−31.3643	−1.48017	−0.740087	−	0.672511i	$-0.765216\pi$
$449$	−31.3643	−1.48017	−0.740087	+	0.672511i	$0.765216\pi$
$450$	0	0
$451$	0	0
$452$	0	0
$453$	− 23.4235i	− 1.10053i
$454$	0	0
$455$	− 6.28769i	− 0.294772i
$456$	0	0
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	0	0
$459$	−113.214	−5.28439
$460$	0	0
$461$	0	0		−	1.00000i	$-0.5\pi$
$461$	0	0			1.00000i	$0.5\pi$
$462$	0	0
$463$	0	0		−	1.00000i	$-0.5\pi$
$463$	0	0			1.00000i	$0.5\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	28.1165	1.30108	0.650538	−	0.759473i	$-0.274543\pi$
$467$	28.1165	1.30108	0.650538	+	0.759473i	$0.274543\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	45.7409i	2.10763i
$472$	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
$483$	0	0
$484$	0	0
$485$	− 7.71590i	− 0.350361i
$486$	0	0
$487$	0	0		−	1.00000i	$-0.5\pi$
$487$	0	0			1.00000i	$0.5\pi$
$488$	0	0
$489$	0	0
$490$	0	0
$491$	13.7886	0.622273	0.311136	−	0.950365i	$-0.399290\pi$
$491$	13.7886	0.622273	0.311136	+	0.950365i	$0.399290\pi$
$492$	0	0
$493$	28.5583i	1.28620i
$494$	0	0
$495$	− 107.137i	− 4.81544i
$496$	0	0
$497$	−31.7490	−1.42414
$498$	0	0
$499$	44.3812	1.98677	0.993387	−	0.114816i	$-0.0366277\pi$
$499$	44.3812	1.98677	0.993387	+	0.114816i	$0.0366277\pi$
$500$	0	0
$501$	− 59.0930i	− 2.64008i
$502$	0	0
$503$	− 21.0145i	− 0.936989i	−0.883466	−	0.468495i	$-0.844797\pi$
$503$	− 21.0145i	− 0.936989i	0.883466	−	0.468495i	$-0.155203\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	40.4701	1.79734
$508$	0	0
$509$	0	0		−	1.00000i	$-0.5\pi$
$509$	0	0			1.00000i	$0.5\pi$
$510$	0	0
$511$	− 28.0000i	− 1.23865i
$512$	0	0
$513$	0	0
$514$	0	0
$515$	−36.0131	−1.58693
$516$	0	0
$517$	75.8470i	3.33575i
$518$	0	0
$519$	89.3643i	3.92266i
$520$	0	0
$521$	0	0	1.00000			$0$
$521$	0	0	−1.00000			$\pi$
$522$	0	0
$523$	−26.8328	−1.17332	−0.586659	−	0.809834i	$-0.699557\pi$
$523$	−26.8328	−1.17332	−0.586659	+	0.809834i	$0.699557\pi$
$524$	0	0
$525$	− 45.1011i	− 1.96837i
$526$	0	0
$527$	0	0
$528$	0	0
$529$	−23.0000	−1.00000
$530$	0	0
$531$	0	0
$532$	0	0
$533$	0	0
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−40.3396	−1.74078
$538$	0	0
$539$	−38.8928	−1.67523
$540$	0	0
$541$	− 28.3650i	− 1.21951i	−0.792592	−	0.609753i	$-0.791269\pi$
$541$	− 28.3650i	− 1.21951i	0.792592	−	0.609753i	$-0.208731\pi$
$542$	0	0
$543$	0	0
$544$	0	0
$545$	−1.45827	−0.0624656
$546$	0	0
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	39.3434	1.67305
$554$	0	0
$555$	0	0
$556$	0	0
$557$	0	0		−	1.00000i	$-0.5\pi$
$557$	0	0			1.00000i	$0.5\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	−111.858	−4.72266
$562$	0	0
$563$	−44.7214	−1.88478	−0.942390	−	0.334515i	$-0.891427\pi$
$563$	−44.7214	−1.88478	−0.942390	+	0.334515i	$0.891427\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	104.491i	4.38821i
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	0	0
$571$	35.4965	1.48548	0.742741	−	0.669579i	$-0.233526\pi$
$571$	35.4965	1.48548	0.742741	+	0.669579i	$0.233526\pi$
$572$	0	0
$573$	28.5583i	1.19304i
$574$	0	0
$575$	0	0
$576$	0	0
$577$	46.2448	1.92519	0.962597	−	0.270936i	$-0.0873333\pi$
$577$	46.2448	1.92519	0.962597	+	0.270936i	$0.0873333\pi$
$578$	0	0
$579$	0	0
$580$	0	0
$581$	− 23.6643i	− 0.981761i
$582$	0	0
$583$	0	0
$584$	0	0
$585$	−20.4939	−0.847319
$586$	0	0
$587$	8.94427	0.369170	0.184585	−	0.982817i	$-0.440906\pi$
$587$	8.94427	0.369170	0.184585	+	0.982817i	$0.440906\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	0	0
$592$	0	0
$593$	−48.6992	−1.99984	−0.999919	−	0.0127518i	$-0.995941\pi$
$593$	−48.6992	−1.99984	−0.999919	+	0.0127518i	$0.995941\pi$
$594$	0	0
$595$	−34.9352	−1.43220
$596$	0	0
$597$	0	0
$598$	0	0
$599$	6.11738i	0.249949i	0.992160	+	0.124975i	$0.0398849\pi$
$599$	6.11738i	0.249949i	−0.992160	+	0.124975i	$0.960115\pi$
$600$	0	0
$601$	0	0	1.00000			$0$
$601$	0	0	−1.00000			$\pi$
$602$	0	0
$603$	0	0
$604$	0	0
$605$	− 44.4316i	− 1.80640i
$606$	0	0
$607$	5.06046i	0.205398i	0.994712	+	0.102699i	$0.0327478\pi$
$607$	5.06046i	0.205398i	−0.994712	+	0.102699i	$0.967252\pi$
$608$	0	0
$609$	43.6235	1.76771
$610$	0	0
$611$	14.5086	0.586954
$612$	0	0
$613$	0	0		−	1.00000i	$-0.5\pi$
$613$	0	0			1.00000i	$0.5\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	0	0	1.00000			$0$
$617$	0	0	−1.00000			$\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	0	0
$622$	0	0
$623$	0	0
$624$	0	0
$625$	25.0000	1.00000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	0	0
$630$	0	0
$631$	− 38.8704i	− 1.54741i	−0.633548	−	0.773704i	$-0.718402\pi$
$631$	− 38.8704i	− 1.54741i	0.633548	−	0.773704i	$-0.281598\pi$
$632$	0	0
$633$	−37.6541	−1.49662
$634$	0	0
$635$	0	0
$636$	0	0
$637$	7.43970i	0.294772i
$638$	0	0
$639$	103.482i	4.09367i
$640$	0	0
$641$	−18.0000	−0.710957	−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000	−0.710957	−0.355479	+	0.934684i	$0.615682\pi$
$642$	0	0
$643$	46.8886	1.84910	0.924552	−	0.381055i	$-0.124439\pi$
$643$	46.8886	1.84910	0.924552	+	0.381055i	$0.124439\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	− 47.6235i	− 1.87227i	−0.351636	−	0.936137i	$-0.614374\pi$
$647$	− 47.6235i	− 1.87227i	0.351636	−	0.936137i	$-0.385626\pi$
$648$	0	0
$649$	0	0
$650$	0	0
$651$	0	0
$652$	0	0
$653$	0	0		−	1.00000i	$-0.5\pi$
$653$	0	0			1.00000i	$0.5\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	−91.2623	−3.56048
$658$	0	0
$659$	47.1253	1.83574	0.917871	−	0.396878i	$-0.129907\pi$
$659$	47.1253	1.83574	0.917871	+	0.396878i	$0.129907\pi$
$660$	0	0
$661$	0	0		−	1.00000i	$-0.5\pi$
$661$	0	0			1.00000i	$0.5\pi$
$662$	0	0
$663$	21.3971i	0.830993i
$664$	0	0
$665$	0	0
$666$	0	0
$667$	0	0
$668$	0	0
$669$	29.8048i	1.15232i
$670$	0	0
$671$	0	0
$672$	0	0
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	0	0
$675$	−95.8612	−3.68970
$676$	0	0
$677$	32.5886i	1.25248i	0.779629	+	0.626242i	$0.215408\pi$
$677$	32.5886i	1.25248i	−0.779629	+	0.626242i	$0.784592\pi$
$678$	0	0
$679$	9.12957i	0.350361i
$680$	0	0
$681$	−26.1174	−1.00082
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	0	0
$688$	0	0
$689$	0	0
$690$	0	0
$691$	0	0	1.00000			$0$
$691$	0	0	−1.00000			$\pi$
$692$	0	0
$693$	126.766i	4.81544i
$694$	0	0
$695$	0	0
$696$	0	0
$697$	0	0
$698$	0	0
$699$	0	0
$700$	0	0
$701$	− 49.2851i	− 1.86147i	−0.365690	−	0.930737i	$-0.619167\pi$
$701$	− 49.2851i	− 1.86147i	0.365690	−	0.930737i	$-0.380833\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	104.069	3.91945
$706$	0	0
$707$	0	0
$708$	0	0
$709$	25.7563i	0.967299i	0.875262	+	0.483650i	$0.160689\pi$
$709$	25.7563i	0.967299i	−0.875262	+	0.483650i	$0.839311\pi$
$710$	0	0
$711$	− 128.235i	− 4.80918i
$712$	0	0
$713$	0	0
$714$	0	0
$715$	−13.2042	−0.493811
$716$	0	0
$717$	102.680i	3.83465i
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	0	0
$721$	42.6113	1.58693
$722$	0	0
$723$	0	0
$724$	0	0
$725$	24.1809i	0.898058i
$726$	0	0
$727$	− 5.29150i	− 0.196251i	−0.995174	−	0.0981255i	$-0.968715\pi$
$727$	− 5.29150i	− 0.196251i	0.995174	−	0.0981255i	$-0.0312847\pi$
$728$	0	0
$729$	144.482	5.35117
$730$	0	0
$731$	0	0
$732$	0	0
$733$	33.4722i	1.23632i	0.786051	+	0.618161i	$0.212122\pi$
$733$	33.4722i	1.23632i	−0.786051	+	0.618161i	$0.787878\pi$
$734$	0	0
$735$	53.3643i	1.96837i
$736$	0	0
$737$	0	0
$738$	0	0
$739$	36.1486	1.32975	0.664875	−	0.746955i	$-0.268485\pi$
$739$	36.1486	1.32975	0.664875	+	0.746955i	$0.268485\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	0	0		−	1.00000i	$-0.5\pi$
$743$	0	0			1.00000i	$0.5\pi$
$744$	0	0
$745$	−52.9150	−1.93866
$746$	0	0
$747$	−77.1307	−2.82207
$748$	0	0
$749$	0	0
$750$	0	0
$751$	− 52.6113i	− 1.91981i	−0.280321	−	0.959906i	$-0.590441\pi$
$751$	− 52.6113i	− 1.91981i	0.280321	−	0.959906i	$-0.409559\pi$
$752$	0	0
$753$	0	0
$754$	0	0
$755$	−15.3627	−0.559107
$756$	0	0
$757$	0	0		−	1.00000i	$-0.5\pi$
$757$	0	0			1.00000i	$0.5\pi$
$758$	0	0
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	0	0
$763$	1.72545	0.0624656
$764$	0	0
$765$	113.866i	4.11685i
$766$	0	0
$767$	0	0
$768$	0	0
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	−108.243	−3.89826
$772$	0	0
$773$	− 49.2351i	− 1.77086i	−0.464770	−	0.885431i	$-0.653863\pi$
$773$	− 49.2351i	− 1.77086i	0.464770	−	0.885431i	$-0.346137\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	0	0
$778$	0	0
$779$	0	0
$780$	0	0
$781$	66.6734i	2.38576i
$782$	0	0
$783$	− 92.7206i	− 3.31356i
$784$	0	0
$785$	30.0000	1.07075
$786$	0	0
$787$	22.1814	0.790681	0.395340	−	0.918535i	$-0.370627\pi$
$787$	22.1814	0.790681	0.395340	+	0.918535i	$0.370627\pi$
$788$	0	0
$789$	0	0
$790$	0	0
$791$	0	0
$792$	0	0
$793$	0	0
$794$	0	0
$795$	0	0
$796$	0	0
$797$	− 21.0770i	− 0.746585i	−0.927714	−	0.373293i	$-0.878229\pi$
$797$	− 21.0770i	− 0.746585i	0.927714	−	0.373293i	$-0.121771\pi$
$798$	0	0
$799$	− 80.6113i	− 2.85182i
$800$	0	0
$801$	0	0
$802$	0	0
$803$	−58.8004	−2.07502
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	0	0
$809$	−55.3643	−1.94651	−0.973253	−	0.229736i	$-0.926214\pi$
$809$	−55.3643	−1.94651	−0.973253	+	0.229736i	$0.926214\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	0	0
$817$	0	0
$818$	0	0
$819$	24.2487	0.847319
$820$	0	0
$821$	− 46.4054i	− 1.61956i	−0.586734	−	0.809780i	$-0.699586\pi$
$821$	− 46.4054i	− 1.61956i	0.586734	−	0.809780i	$-0.300414\pi$
$822$	0	0
$823$	0	0		−	1.00000i	$-0.5\pi$
$823$	0	0			1.00000i	$0.5\pi$
$824$	0	0
$825$	−94.7129	−3.29748
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	0	0
$829$	0	0		−	1.00000i	$-0.5\pi$
$829$	0	0			1.00000i	$0.5\pi$
$830$	0	0
$831$	0	0
$832$	0	0
$833$	41.3358	1.43220
$834$	0	0
$835$	−38.7573	−1.34125
$836$	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
$841$	5.61128	0.193492
$842$	0	0
$843$	73.7214	2.53910
$844$	0	0
$845$	− 26.5431i	− 0.913110i
$846$	0	0
$847$	52.5722i	1.80640i
$848$	0	0
$849$	−49.3643	−1.69418
$850$	0	0
$851$	0	0
$852$	0	0
$853$	− 40.2492i	− 1.37811i	−0.724710	−	0.689054i	$-0.758026\pi$
$853$	− 40.2492i	− 1.37811i	0.724710	−	0.689054i	$-0.241974\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	31.7490	1.08453	0.542263	−	0.840209i	$-0.317568\pi$
$857$	31.7490	1.08453	0.542263	+	0.840209i	$0.317568\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	0	0		−	1.00000i	$-0.5\pi$
$863$	0	0			1.00000i	$0.5\pi$
$864$	0	0
$865$	58.6113	1.99284
$866$	0	0
$867$	60.9260	2.06916
$868$	0	0
$869$	− 82.6218i	− 2.80275i
$870$	0	0
$871$	0	0
$872$	0	0
$873$	29.7566	1.00711
$874$	0	0
$875$	−29.5804	−1.00000
$876$	0	0
$877$	0	0		−	1.00000i	$-0.5\pi$
$877$	0	0			1.00000i	$0.5\pi$
$878$	0	0
$879$	28.3765i	0.957116i
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	0	0
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	47.6235i	1.59904i	0.600639	+	0.799521i	$0.294913\pi$
$887$	47.6235i	1.59904i	−0.600639	+	0.799521i	$0.705087\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	219.433	7.35127
$892$	0	0
$893$	0	0
$894$	0	0
$895$	26.4575i	0.884377i
$896$	0	0
$897$	0	0
$898$	0	0
$899$	0	0
$900$	0	0
$901$	0	0
$902$	0	0
$903$	0	0
$904$	0	0
$905$	0	0
$906$	0	0
$907$	0	0	1.00000			$0$
$907$	0	0	−1.00000			$\pi$
$908$	0	0
$909$	0	0
$910$	0	0
$911$	− 12.0000i	− 0.397578i	−0.980042	−	0.198789i	$-0.936299\pi$
$911$	− 12.0000i	− 0.397578i	0.980042	−	0.198789i	$-0.0637008\pi$
$912$	0	0
$913$	−49.6954	−1.64468
$914$	0	0
$915$	0	0
$916$	0	0
$917$	0	0
$918$	0	0
$919$	− 60.6113i	− 1.99938i	−0.0248659	−	0.999691i	$-0.507916\pi$
$919$	− 60.6113i	− 1.99938i	0.0248659	−	0.999691i	$-0.492084\pi$
$920$	0	0
$921$	−90.1174	−2.96947
$922$	0	0
$923$	12.7538	0.419795
$924$	0	0
$925$	0	0
$926$	0	0
$927$	− 138.886i	− 4.56161i
$928$	0	0
$929$	0	0	1.00000			$0$
$929$	0	0	−1.00000			$\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	73.3643i	2.39927i
$936$	0	0
$937$	24.6167	0.804191	0.402096	−	0.915598i	$-0.368282\pi$
$937$	24.6167	0.804191	0.402096	+	0.915598i	$0.368282\pi$
$938$	0	0
$939$	−109.030	−3.55807
$940$	0	0
$941$	0	0		−	1.00000i	$-0.5\pi$
$941$	0	0			1.00000i	$0.5\pi$
$942$	0	0
$943$	0	0
$944$	0	0
$945$	113.424	3.68970
$946$	0	0
$947$	0	0	1.00000			$0$
$947$	0	0	−1.00000			$\pi$
$948$	0	0
$949$	11.2478i	0.365118i
$950$	0	0
$951$	0	0
$952$	0	0
$953$	0	0	1.00000			$0$
$953$	0	0	−1.00000			$\pi$
$954$	0	0
$955$	18.7305	0.606104
$956$	0	0
$957$	− 91.6099i	− 2.96133i
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	0	0
$963$	0	0
$964$	0	0
$965$	0	0
$966$	0	0
$967$	0	0		−	1.00000i	$-0.5\pi$
$967$	0	0			1.00000i	$0.5\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	0	0	1.00000			$0$
$971$	0	0	−1.00000			$\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	18.1174i	0.580220i
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	0	0
$979$	0	0
$980$	0	0
$981$	− 5.62388i	− 0.179557i
$982$	0	0
$983$	− 2.60600i	− 0.0831184i	−0.999136	−	0.0415592i	$-0.986767\pi$
$983$	− 2.60600i	− 0.0831184i	0.999136	−	0.0415592i	$-0.0132325\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	−123.136	−3.91945
$988$	0	0
$989$	0	0
$990$	0	0
$991$	52.0000i	1.65183i	0.563791	+	0.825917i	$0.309342\pi$
$991$	52.0000i	1.65183i	−0.563791	+	0.825917i	$0.690658\pi$
$992$	0	0
$993$	−121.019	−3.84042
$994$	0	0
$995$	0	0
$996$	0	0
$997$	− 46.2259i	− 1.46399i	−0.681310	−	0.731995i	$-0.738589\pi$
$997$	− 46.2259i	− 1.46399i	0.681310	−	0.731995i	$-0.261411\pi$
$998$	0	0
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.n.j.1119.14	yes	16
4.3	odd	2	inner	2240.2.n.j.1119.1	✓	16
5.4	even	2	inner	2240.2.n.j.1119.3	yes	16
7.6	odd	2	inner	2240.2.n.j.1119.3	yes	16
8.3	odd	2	inner	2240.2.n.j.1119.15	yes	16
8.5	even	2	inner	2240.2.n.j.1119.4	yes	16
20.19	odd	2	inner	2240.2.n.j.1119.16	yes	16
28.27	even	2	inner	2240.2.n.j.1119.16	yes	16
35.34	odd	2	CM	2240.2.n.j.1119.14	yes	16
40.19	odd	2	inner	2240.2.n.j.1119.2	yes	16
40.29	even	2	inner	2240.2.n.j.1119.13	yes	16
56.13	odd	2	inner	2240.2.n.j.1119.13	yes	16
56.27	even	2	inner	2240.2.n.j.1119.2	yes	16
140.139	even	2	inner	2240.2.n.j.1119.1	✓	16
280.69	odd	2	inner	2240.2.n.j.1119.4	yes	16
280.139	even	2	inner	2240.2.n.j.1119.15	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2240.2.n.j.1119.1	✓	16	4.3	odd	2	inner
2240.2.n.j.1119.1	✓	16	140.139	even	2	inner
2240.2.n.j.1119.2	yes	16	40.19	odd	2	inner
2240.2.n.j.1119.2	yes	16	56.27	even	2	inner
2240.2.n.j.1119.3	yes	16	5.4	even	2	inner
2240.2.n.j.1119.3	yes	16	7.6	odd	2	inner
2240.2.n.j.1119.4	yes	16	8.5	even	2	inner
2240.2.n.j.1119.4	yes	16	280.69	odd	2	inner
2240.2.n.j.1119.13	yes	16	40.29	even	2	inner
2240.2.n.j.1119.13	yes	16	56.13	odd	2	inner
2240.2.n.j.1119.14	yes	16	1.1	even	1	trivial
2240.2.n.j.1119.14	yes	16	35.34	odd	2	CM
2240.2.n.j.1119.15	yes	16	8.3	odd	2	inner
2240.2.n.j.1119.15	yes	16	280.139	even	2	inner
2240.2.n.j.1119.16	yes	16	20.19	odd	2	inner
2240.2.n.j.1119.16	yes	16	28.27	even	2	inner

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.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.40932 q^{3} -2.23607i q^{5} +2.64575i q^{7} +8.62348 q^{9} +O(q^{10})\)	\(q+3.40932 q^{3} -2.23607i q^{5} +2.64575i q^{7} +8.62348 q^{9} +5.55612 q^{11} -1.06281i q^{13} -7.62348i q^{15} -5.90512 q^{17} +9.02022i q^{21} -5.00000 q^{25} +19.1722 q^{27} -4.83619i q^{29} +18.9426 q^{33} +5.91608 q^{35} -3.62348i q^{39} -19.2827i q^{45} +13.6511i q^{47} -7.00000 q^{49} -20.1324 q^{51} -12.4239i q^{55} +22.8156i q^{63} -2.37652 q^{65} +12.0000i q^{71} -10.5830 q^{73} -17.0466 q^{75} +14.7001i q^{77} -14.8704i q^{79} +39.4939 q^{81} -8.94427 q^{83} +13.2042i q^{85} -16.4881i q^{87} +2.81194 q^{91} +3.45065 q^{97} +47.9130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 56 q^{9}+O(q^{10}) \) 16 * q + 56 * q^9	\( 16 q + 56 q^{9} - 80 q^{25} - 112 q^{49} - 120 q^{65} + 304 q^{81}+O(q^{100}) \) 16 * q + 56 * q^9 - 80 * q^25 - 112 * q^49 - 120 * q^65 + 304 * q^81

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more