LMFDB - Embedded newform 7220.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7220,2,Mod(1,7220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7220, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7220.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7220 = 2^{2} \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7220.a (trivial)

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:	yes
Analytic conductor:	$57.6519902594$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 380)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	7220.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} -1.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} -1.00000 q^{5} -4.00000 q^{7} +1.00000 q^{9} -3.00000 q^{11} -6.00000 q^{13} +2.00000 q^{15} +2.00000 q^{17} +8.00000 q^{21} +4.00000 q^{23} +1.00000 q^{25} +4.00000 q^{27} -1.00000 q^{29} +5.00000 q^{31} +6.00000 q^{33} +4.00000 q^{35} +4.00000 q^{37} +12.0000 q^{39} -2.00000 q^{41} -1.00000 q^{45} +6.00000 q^{47} +9.00000 q^{49} -4.00000 q^{51} +6.00000 q^{53} +3.00000 q^{55} +1.00000 q^{59} -7.00000 q^{61} -4.00000 q^{63} +6.00000 q^{65} +14.0000 q^{67} -8.00000 q^{69} -15.0000 q^{71} +12.0000 q^{73} -2.00000 q^{75} +12.0000 q^{77} +1.00000 q^{79} -11.0000 q^{81} +16.0000 q^{83} -2.00000 q^{85} +2.00000 q^{87} -17.0000 q^{89} +24.0000 q^{91} -10.0000 q^{93} -12.0000 q^{97} -3.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

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
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	0	0
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	0	0
$9$	1.00000	0.333333
$10$	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
$13$	−6.00000	−1.66410	−0.832050	−	0.554700i	$-0.812833\pi$
$13$	−6.00000	−1.66410	−0.832050	+	0.554700i	$0.812833\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	0	0
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	0	0
$19$	0	0
$19$	0	0
$20$	0	0
$21$	8.00000	1.74574
$22$	0	0
$23$	4.00000	0.834058	0.417029	−	0.908893i	$-0.363071\pi$
$23$	4.00000	0.834058	0.417029	+	0.908893i	$0.363071\pi$
$24$	0	0
$25$	1.00000	0.200000
$26$	0	0
$27$	4.00000	0.769800
$28$	0	0
$29$	−1.00000	−0.185695	−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000	−0.185695	−0.0928477	+	0.995680i	$0.529597\pi$
$30$	0	0
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	0	0
$33$	6.00000	1.04447
$34$	0	0
$35$	4.00000	0.676123
$36$	0	0
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	0	0
$39$	12.0000	1.92154
$40$	0	0
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	0	0
$43$	0	0		−	1.00000i	$-0.5\pi$
$43$	0	0			1.00000i	$0.5\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0	0
$47$	6.00000	0.875190	0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000	0.875190	0.437595	+	0.899172i	$0.355830\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	0	0
$51$	−4.00000	−0.560112
$52$	0	0
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	0	0
$55$	3.00000	0.404520
$56$	0	0
$57$	0	0
$58$	0	0
$59$	1.00000	0.130189	0.0650945	−	0.997879i	$-0.479265\pi$
$59$	1.00000	0.130189	0.0650945	+	0.997879i	$0.479265\pi$
$60$	0	0
$61$	−7.00000	−0.896258	−0.448129	−	0.893969i	$-0.647910\pi$
$61$	−7.00000	−0.896258	−0.448129	+	0.893969i	$0.647910\pi$
$62$	0	0
$63$	−4.00000	−0.503953
$64$	0	0
$65$	6.00000	0.744208
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	0	0
$69$	−8.00000	−0.963087
$70$	0	0
$71$	−15.0000	−1.78017	−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000	−1.78017	−0.890086	+	0.455792i	$0.849356\pi$
$72$	0	0
$73$	12.0000	1.40449	0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000	1.40449	0.702247	+	0.711934i	$0.252180\pi$
$74$	0	0
$75$	−2.00000	−0.230940
$76$	0	0
$77$	12.0000	1.36753
$78$	0	0
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	−11.0000	−1.22222
$82$	0	0
$83$	16.0000	1.75623	0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000	1.75623	0.878114	+	0.478451i	$0.158802\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	0	0
$87$	2.00000	0.214423
$88$	0	0
$89$	−17.0000	−1.80200	−0.900998	−	0.433823i	$-0.857164\pi$
$89$	−17.0000	−1.80200	−0.900998	+	0.433823i	$0.857164\pi$
$90$	0	0
$91$	24.0000	2.51588
$92$	0	0
$93$	−10.0000	−1.03695
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−12.0000	−1.21842	−0.609208	−	0.793011i	$-0.708512\pi$
$97$	−12.0000	−1.21842	−0.609208	+	0.793011i	$0.708512\pi$
$98$	0	0
$99$	−3.00000	−0.301511
$100$	0	0
$101$	11.0000	1.09454	0.547270	−	0.836956i	$-0.315667\pi$
$101$	11.0000	1.09454	0.547270	+	0.836956i	$0.315667\pi$
$102$	0	0
$103$	0	0		−	1.00000i	$-0.5\pi$
$103$	0	0			1.00000i	$0.5\pi$
$104$	0	0
$105$	−8.00000	−0.780720
$106$	0	0
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	−7.00000	−0.670478	−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000	−0.670478	−0.335239	+	0.942133i	$0.608817\pi$
$110$	0	0
$111$	−8.00000	−0.759326
$112$	0	0
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	0	0
$115$	−4.00000	−0.373002
$116$	0	0
$117$	−6.00000	−0.554700
$118$	0	0
$119$	−8.00000	−0.733359
$120$	0	0
$121$	−2.00000	−0.181818
$122$	0	0
$123$	4.00000	0.360668
$124$	0	0
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	−18.0000	−1.59724	−0.798621	−	0.601834i	$-0.794437\pi$
$127$	−18.0000	−1.59724	−0.798621	+	0.601834i	$0.794437\pi$
$128$	0	0
$129$	0	0
$130$	0	0
$131$	−20.0000	−1.74741	−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000	−1.74741	−0.873704	+	0.486458i	$0.838289\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−4.00000	−0.344265
$136$	0	0
$137$	12.0000	1.02523	0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000	1.02523	0.512615	+	0.858619i	$0.328677\pi$
$138$	0	0
$139$	0	0		−	1.00000i	$-0.5\pi$
$139$	0	0			1.00000i	$0.5\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	0	0
$143$	18.0000	1.50524
$144$	0	0
$145$	1.00000	0.0830455
$146$	0	0
$147$	−18.0000	−1.48461
$148$	0	0
$149$	−17.0000	−1.39269	−0.696347	−	0.717705i	$-0.745193\pi$
$149$	−17.0000	−1.39269	−0.696347	+	0.717705i	$0.745193\pi$
$150$	0	0
$151$	−3.00000	−0.244137	−0.122068	−	0.992522i	$-0.538953\pi$
$151$	−3.00000	−0.244137	−0.122068	+	0.992522i	$0.538953\pi$
$152$	0	0
$153$	2.00000	0.161690
$154$	0	0
$155$	−5.00000	−0.401610
$156$	0	0
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	0	0
$159$	−12.0000	−0.951662
$160$	0	0
$161$	−16.0000	−1.26098
$162$	0	0
$163$	18.0000	1.40987	0.704934	−	0.709273i	$-0.250976\pi$
$163$	18.0000	1.40987	0.704934	+	0.709273i	$0.250976\pi$
$164$	0	0
$165$	−6.00000	−0.467099
$166$	0	0
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	23.0000	1.76923
$170$	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
$175$	−4.00000	−0.302372
$176$	0	0
$177$	−2.00000	−0.150329
$178$	0	0
$179$	15.0000	1.12115	0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000	1.12115	0.560576	+	0.828103i	$0.310580\pi$
$180$	0	0
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	14.0000	1.03491
$184$	0	0
$185$	−4.00000	−0.294086
$186$	0	0
$187$	−6.00000	−0.438763
$188$	0	0
$189$	−16.0000	−1.16383
$190$	0	0
$191$	−13.0000	−0.940647	−0.470323	−	0.882494i	$-0.655863\pi$
$191$	−13.0000	−0.940647	−0.470323	+	0.882494i	$0.655863\pi$
$192$	0	0
$193$	−16.0000	−1.15171	−0.575853	−	0.817554i	$-0.695330\pi$
$193$	−16.0000	−1.15171	−0.575853	+	0.817554i	$0.695330\pi$
$194$	0	0
$195$	−12.0000	−0.859338
$196$	0	0
$197$	2.00000	0.142494	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000	0.142494	0.0712470	+	0.997459i	$0.477302\pi$
$198$	0	0
$199$	23.0000	1.63043	0.815213	−	0.579161i	$-0.196620\pi$
$199$	23.0000	1.63043	0.815213	+	0.579161i	$0.196620\pi$
$200$	0	0
$201$	−28.0000	−1.97497
$202$	0	0
$203$	4.00000	0.280745
$204$	0	0
$205$	2.00000	0.139686
$206$	0	0
$207$	4.00000	0.278019
$208$	0	0
$209$	0	0
$210$	0	0
$211$	1.00000	0.0688428	0.0344214	−	0.999407i	$-0.489041\pi$
$211$	1.00000	0.0688428	0.0344214	+	0.999407i	$0.489041\pi$
$212$	0	0
$213$	30.0000	2.05557
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−20.0000	−1.35769
$218$	0	0
$219$	−24.0000	−1.62177
$220$	0	0
$221$	−12.0000	−0.807207
$222$	0	0
$223$	−8.00000	−0.535720	−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000	−0.535720	−0.267860	+	0.963458i	$0.586316\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	0	0
$227$	4.00000	0.265489	0.132745	−	0.991150i	$-0.457621\pi$
$227$	4.00000	0.265489	0.132745	+	0.991150i	$0.457621\pi$
$228$	0	0
$229$	21.0000	1.38772	0.693860	−	0.720110i	$-0.255909\pi$
$229$	21.0000	1.38772	0.693860	+	0.720110i	$0.255909\pi$
$230$	0	0
$231$	−24.0000	−1.57908
$232$	0	0
$233$	−10.0000	−0.655122	−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000	−0.655122	−0.327561	+	0.944830i	$0.606227\pi$
$234$	0	0
$235$	−6.00000	−0.391397
$236$	0	0
$237$	−2.00000	−0.129914
$238$	0	0
$239$	15.0000	0.970269	0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000	0.970269	0.485135	+	0.874439i	$0.338771\pi$
$240$	0	0
$241$	−5.00000	−0.322078	−0.161039	−	0.986948i	$-0.551485\pi$
$241$	−5.00000	−0.322078	−0.161039	+	0.986948i	$0.551485\pi$
$242$	0	0
$243$	10.0000	0.641500
$244$	0	0
$245$	−9.00000	−0.574989
$246$	0	0
$247$	0	0
$248$	0	0
$249$	−32.0000	−2.02792
$250$	0	0
$251$	31.0000	1.95670	0.978351	−	0.206951i	$-0.0663540\pi$
$251$	31.0000	1.95670	0.978351	+	0.206951i	$0.0663540\pi$
$252$	0	0
$253$	−12.0000	−0.754434
$254$	0	0
$255$	4.00000	0.250490
$256$	0	0
$257$	−18.0000	−1.12281	−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000	−1.12281	−0.561405	+	0.827541i	$0.689739\pi$
$258$	0	0
$259$	−16.0000	−0.994192
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	0	0
$263$	10.0000	0.616626	0.308313	−	0.951285i	$-0.400236\pi$
$263$	10.0000	0.616626	0.308313	+	0.951285i	$0.400236\pi$
$264$	0	0
$265$	−6.00000	−0.368577
$266$	0	0
$267$	34.0000	2.08077
$268$	0	0
$269$	1.00000	0.0609711	0.0304855	−	0.999535i	$-0.490295\pi$
$269$	1.00000	0.0609711	0.0304855	+	0.999535i	$0.490295\pi$
$270$	0	0
$271$	17.0000	1.03268	0.516338	−	0.856385i	$-0.327295\pi$
$271$	17.0000	1.03268	0.516338	+	0.856385i	$0.327295\pi$
$272$	0	0
$273$	−48.0000	−2.90509
$274$	0	0
$275$	−3.00000	−0.180907
$276$	0	0
$277$	16.0000	0.961347	0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000	0.961347	0.480673	+	0.876900i	$0.340392\pi$
$278$	0	0
$279$	5.00000	0.299342
$280$	0	0
$281$	26.0000	1.55103	0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000	1.55103	0.775515	+	0.631329i	$0.217490\pi$
$282$	0	0
$283$	−26.0000	−1.54554	−0.772770	−	0.634686i	$-0.781129\pi$
$283$	−26.0000	−1.54554	−0.772770	+	0.634686i	$0.781129\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	8.00000	0.472225
$288$	0	0
$289$	−13.0000	−0.764706
$290$	0	0
$291$	24.0000	1.40690
$292$	0	0
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	0	0
$295$	−1.00000	−0.0582223
$296$	0	0
$297$	−12.0000	−0.696311
$298$	0	0
$299$	−24.0000	−1.38796
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−22.0000	−1.26387
$304$	0	0
$305$	7.00000	0.400819
$306$	0	0
$307$	14.0000	0.799022	0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000	0.799022	0.399511	+	0.916728i	$0.369180\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	0	0
$313$	34.0000	1.92179	0.960897	−	0.276907i	$-0.0893093\pi$
$313$	34.0000	1.92179	0.960897	+	0.276907i	$0.0893093\pi$
$314$	0	0
$315$	4.00000	0.225374
$316$	0	0
$317$	12.0000	0.673987	0.336994	−	0.941507i	$-0.390590\pi$
$317$	12.0000	0.673987	0.336994	+	0.941507i	$0.390590\pi$
$318$	0	0
$319$	3.00000	0.167968
$320$	0	0
$321$	−24.0000	−1.33955
$322$	0	0
$323$	0	0
$324$	0	0
$325$	−6.00000	−0.332820
$326$	0	0
$327$	14.0000	0.774202
$328$	0	0
$329$	−24.0000	−1.32316
$330$	0	0
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	0	0
$333$	4.00000	0.219199
$334$	0	0
$335$	−14.0000	−0.764902
$336$	0	0
$337$	−4.00000	−0.217894	−0.108947	−	0.994048i	$-0.534748\pi$
$337$	−4.00000	−0.217894	−0.108947	+	0.994048i	$0.534748\pi$
$338$	0	0
$339$	28.0000	1.52075
$340$	0	0
$341$	−15.0000	−0.812296
$342$	0	0
$343$	−8.00000	−0.431959
$344$	0	0
$345$	8.00000	0.430706
$346$	0	0
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	0	0
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	0	0
$351$	−24.0000	−1.28103
$352$	0	0
$353$	−36.0000	−1.91609	−0.958043	−	0.286623i	$-0.907467\pi$
$353$	−36.0000	−1.91609	−0.958043	+	0.286623i	$0.907467\pi$
$354$	0	0
$355$	15.0000	0.796117
$356$	0	0
$357$	16.0000	0.846810
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	0	0
$361$	0	0
$362$	0	0
$363$	4.00000	0.209946
$364$	0	0
$365$	−12.0000	−0.628109
$366$	0	0
$367$	−28.0000	−1.46159	−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000	−1.46159	−0.730794	+	0.682598i	$0.760850\pi$
$368$	0	0
$369$	−2.00000	−0.104116
$370$	0	0
$371$	−24.0000	−1.24602
$372$	0	0
$373$	12.0000	0.621336	0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000	0.621336	0.310668	+	0.950518i	$0.399447\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	0	0
$377$	6.00000	0.309016
$378$	0	0
$379$	19.0000	0.975964	0.487982	−	0.872854i	$-0.337733\pi$
$379$	19.0000	0.975964	0.487982	+	0.872854i	$0.337733\pi$
$380$	0	0
$381$	36.0000	1.84434
$382$	0	0
$383$	18.0000	0.919757	0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000	0.919757	0.459879	+	0.887982i	$0.347893\pi$
$384$	0	0
$385$	−12.0000	−0.611577
$386$	0	0
$387$	0	0
$388$	0	0
$389$	−21.0000	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$389$	−21.0000	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	0	0
$393$	40.0000	2.01773
$394$	0	0
$395$	−1.00000	−0.0503155
$396$	0	0
$397$	−8.00000	−0.401508	−0.200754	−	0.979642i	$-0.564339\pi$
$397$	−8.00000	−0.401508	−0.200754	+	0.979642i	$0.564339\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−15.0000	−0.749064	−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000	−0.749064	−0.374532	+	0.927214i	$0.622197\pi$
$402$	0	0
$403$	−30.0000	−1.49441
$404$	0	0
$405$	11.0000	0.546594
$406$	0	0
$407$	−12.0000	−0.594818
$408$	0	0
$409$	1.00000	0.0494468	0.0247234	−	0.999694i	$-0.492129\pi$
$409$	1.00000	0.0494468	0.0247234	+	0.999694i	$0.492129\pi$
$410$	0	0
$411$	−24.0000	−1.18383
$412$	0	0
$413$	−4.00000	−0.196827
$414$	0	0
$415$	−16.0000	−0.785409
$416$	0	0
$417$	0	0
$418$	0	0
$419$	−5.00000	−0.244266	−0.122133	−	0.992514i	$-0.538973\pi$
$419$	−5.00000	−0.244266	−0.122133	+	0.992514i	$0.538973\pi$
$420$	0	0
$421$	−25.0000	−1.21843	−0.609213	−	0.793007i	$-0.708514\pi$
$421$	−25.0000	−1.21843	−0.609213	+	0.793007i	$0.708514\pi$
$422$	0	0
$423$	6.00000	0.291730
$424$	0	0
$425$	2.00000	0.0970143
$426$	0	0
$427$	28.0000	1.35501
$428$	0	0
$429$	−36.0000	−1.73810
$430$	0	0
$431$	−27.0000	−1.30054	−0.650272	−	0.759701i	$-0.725345\pi$
$431$	−27.0000	−1.30054	−0.650272	+	0.759701i	$0.725345\pi$
$432$	0	0
$433$	0	0		−	1.00000i	$-0.5\pi$
$433$	0	0			1.00000i	$0.5\pi$
$434$	0	0
$435$	−2.00000	−0.0958927
$436$	0	0
$437$	0	0
$438$	0	0
$439$	−1.00000	−0.0477274	−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000	−0.0477274	−0.0238637	+	0.999715i	$0.507597\pi$
$440$	0	0
$441$	9.00000	0.428571
$442$	0	0
$443$	−12.0000	−0.570137	−0.285069	−	0.958507i	$-0.592016\pi$
$443$	−12.0000	−0.570137	−0.285069	+	0.958507i	$0.592016\pi$
$444$	0	0
$445$	17.0000	0.805877
$446$	0	0
$447$	34.0000	1.60814
$448$	0	0
$449$	1.00000	0.0471929	0.0235965	−	0.999722i	$-0.492488\pi$
$449$	1.00000	0.0471929	0.0235965	+	0.999722i	$0.492488\pi$
$450$	0	0
$451$	6.00000	0.282529
$452$	0	0
$453$	6.00000	0.281905
$454$	0	0
$455$	−24.0000	−1.12514
$456$	0	0
$457$	−2.00000	−0.0935561	−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000	−0.0935561	−0.0467780	+	0.998905i	$0.514895\pi$
$458$	0	0
$459$	8.00000	0.373408
$460$	0	0
$461$	35.0000	1.63011	0.815056	−	0.579382i	$-0.196706\pi$
$461$	35.0000	1.63011	0.815056	+	0.579382i	$0.196706\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	0	0
$465$	10.0000	0.463739
$466$	0	0
$467$	−20.0000	−0.925490	−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000	−0.925490	−0.462745	+	0.886492i	$0.653135\pi$
$468$	0	0
$469$	−56.0000	−2.58584
$470$	0	0
$471$	−36.0000	−1.65879
$472$	0	0
$473$	0	0
$474$	0	0
$475$	0	0
$476$	0	0
$477$	6.00000	0.274721
$478$	0	0
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	0	0
$481$	−24.0000	−1.09431
$482$	0	0
$483$	32.0000	1.45605
$484$	0	0
$485$	12.0000	0.544892
$486$	0	0
$487$	−34.0000	−1.54069	−0.770344	−	0.637629i	$-0.779915\pi$
$487$	−34.0000	−1.54069	−0.770344	+	0.637629i	$0.779915\pi$
$488$	0	0
$489$	−36.0000	−1.62798
$490$	0	0
$491$	−25.0000	−1.12823	−0.564117	−	0.825695i	$-0.690783\pi$
$491$	−25.0000	−1.12823	−0.564117	+	0.825695i	$0.690783\pi$
$492$	0	0
$493$	−2.00000	−0.0900755
$494$	0	0
$495$	3.00000	0.134840
$496$	0	0
$497$	60.0000	2.69137
$498$	0	0
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	0	0
$501$	16.0000	0.714827
$502$	0	0
$503$	22.0000	0.980932	0.490466	−	0.871460i	$-0.336827\pi$
$503$	22.0000	0.980932	0.490466	+	0.871460i	$0.336827\pi$
$504$	0	0
$505$	−11.0000	−0.489494
$506$	0	0
$507$	−46.0000	−2.04293
$508$	0	0
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	−48.0000	−2.12339
$512$	0	0
$513$	0	0
$514$	0	0
$515$	0	0
$516$	0	0
$517$	−18.0000	−0.791639
$518$	0	0
$519$	0	0
$520$	0	0
$521$	45.0000	1.97149	0.985743	−	0.168259i	$-0.0538144\pi$
$521$	45.0000	1.97149	0.985743	+	0.168259i	$0.0538144\pi$
$522$	0	0
$523$	10.0000	0.437269	0.218635	−	0.975807i	$-0.429840\pi$
$523$	10.0000	0.437269	0.218635	+	0.975807i	$0.429840\pi$
$524$	0	0
$525$	8.00000	0.349149
$526$	0	0
$527$	10.0000	0.435607
$528$	0	0
$529$	−7.00000	−0.304348
$530$	0	0
$531$	1.00000	0.0433963
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	−12.0000	−0.518805
$536$	0	0
$537$	−30.0000	−1.29460
$538$	0	0
$539$	−27.0000	−1.16297
$540$	0	0
$541$	−25.0000	−1.07483	−0.537417	−	0.843317i	$-0.680600\pi$
$541$	−25.0000	−1.07483	−0.537417	+	0.843317i	$0.680600\pi$
$542$	0	0
$543$	4.00000	0.171656
$544$	0	0
$545$	7.00000	0.299847
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	0	0
$549$	−7.00000	−0.298753
$550$	0	0
$551$	0	0
$552$	0	0
$553$	−4.00000	−0.170097
$554$	0	0
$555$	8.00000	0.339581
$556$	0	0
$557$	−40.0000	−1.69485	−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000	−1.69485	−0.847427	+	0.530912i	$0.821850\pi$
$558$	0	0
$559$	0	0
$560$	0	0
$561$	12.0000	0.506640
$562$	0	0
$563$	−10.0000	−0.421450	−0.210725	−	0.977545i	$-0.567582\pi$
$563$	−10.0000	−0.421450	−0.210725	+	0.977545i	$0.567582\pi$
$564$	0	0
$565$	14.0000	0.588984
$566$	0	0
$567$	44.0000	1.84783
$568$	0	0
$569$	17.0000	0.712677	0.356339	−	0.934357i	$-0.384025\pi$
$569$	17.0000	0.712677	0.356339	+	0.934357i	$0.384025\pi$
$570$	0	0
$571$	−17.0000	−0.711428	−0.355714	−	0.934595i	$-0.615762\pi$
$571$	−17.0000	−0.711428	−0.355714	+	0.934595i	$0.615762\pi$
$572$	0	0
$573$	26.0000	1.08617
$574$	0	0
$575$	4.00000	0.166812
$576$	0	0
$577$	−20.0000	−0.832611	−0.416305	−	0.909225i	$-0.636675\pi$
$577$	−20.0000	−0.832611	−0.416305	+	0.909225i	$0.636675\pi$
$578$	0	0
$579$	32.0000	1.32987
$580$	0	0
$581$	−64.0000	−2.65517
$582$	0	0
$583$	−18.0000	−0.745484
$584$	0	0
$585$	6.00000	0.248069
$586$	0	0
$587$	−12.0000	−0.495293	−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000	−0.495293	−0.247647	+	0.968850i	$0.579657\pi$
$588$	0	0
$589$	0	0
$590$	0	0
$591$	−4.00000	−0.164538
$592$	0	0
$593$	−4.00000	−0.164260	−0.0821302	−	0.996622i	$-0.526172\pi$
$593$	−4.00000	−0.164260	−0.0821302	+	0.996622i	$0.526172\pi$
$594$	0	0
$595$	8.00000	0.327968
$596$	0	0
$597$	−46.0000	−1.88265
$598$	0	0
$599$	24.0000	0.980613	0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000	0.980613	0.490307	+	0.871550i	$0.336885\pi$
$600$	0	0
$601$	−17.0000	−0.693444	−0.346722	−	0.937968i	$-0.612705\pi$
$601$	−17.0000	−0.693444	−0.346722	+	0.937968i	$0.612705\pi$
$602$	0	0
$603$	14.0000	0.570124
$604$	0	0
$605$	2.00000	0.0813116
$606$	0	0
$607$	14.0000	0.568242	0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000	0.568242	0.284121	+	0.958788i	$0.408298\pi$
$608$	0	0
$609$	−8.00000	−0.324176
$610$	0	0
$611$	−36.0000	−1.45640
$612$	0	0
$613$	−22.0000	−0.888572	−0.444286	−	0.895885i	$-0.646543\pi$
$613$	−22.0000	−0.888572	−0.444286	+	0.895885i	$0.646543\pi$
$614$	0	0
$615$	−4.00000	−0.161296
$616$	0	0
$617$	−8.00000	−0.322068	−0.161034	−	0.986949i	$-0.551483\pi$
$617$	−8.00000	−0.322068	−0.161034	+	0.986949i	$0.551483\pi$
$618$	0	0
$619$	−20.0000	−0.803868	−0.401934	−	0.915669i	$-0.631662\pi$
$619$	−20.0000	−0.803868	−0.401934	+	0.915669i	$0.631662\pi$
$620$	0	0
$621$	16.0000	0.642058
$622$	0	0
$623$	68.0000	2.72436
$624$	0	0
$625$	1.00000	0.0400000
$626$	0	0
$627$	0	0
$628$	0	0
$629$	8.00000	0.318981
$630$	0	0
$631$	−33.0000	−1.31371	−0.656855	−	0.754017i	$-0.728113\pi$
$631$	−33.0000	−1.31371	−0.656855	+	0.754017i	$0.728113\pi$
$632$	0	0
$633$	−2.00000	−0.0794929
$634$	0	0
$635$	18.0000	0.714308
$636$	0	0
$637$	−54.0000	−2.13956
$638$	0	0
$639$	−15.0000	−0.593391
$640$	0	0
$641$	−9.00000	−0.355479	−0.177739	−	0.984078i	$-0.556878\pi$
$641$	−9.00000	−0.355479	−0.177739	+	0.984078i	$0.556878\pi$
$642$	0	0
$643$	−2.00000	−0.0788723	−0.0394362	−	0.999222i	$-0.512556\pi$
$643$	−2.00000	−0.0788723	−0.0394362	+	0.999222i	$0.512556\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−30.0000	−1.17942	−0.589711	−	0.807614i	$-0.700758\pi$
$647$	−30.0000	−1.17942	−0.589711	+	0.807614i	$0.700758\pi$
$648$	0	0
$649$	−3.00000	−0.117760
$650$	0	0
$651$	40.0000	1.56772
$652$	0	0
$653$	12.0000	0.469596	0.234798	−	0.972044i	$-0.424557\pi$
$653$	12.0000	0.469596	0.234798	+	0.972044i	$0.424557\pi$
$654$	0	0
$655$	20.0000	0.781465
$656$	0	0
$657$	12.0000	0.468165
$658$	0	0
$659$	36.0000	1.40236	0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000	1.40236	0.701180	+	0.712984i	$0.252657\pi$
$660$	0	0
$661$	−41.0000	−1.59472	−0.797358	−	0.603507i	$-0.793769\pi$
$661$	−41.0000	−1.59472	−0.797358	+	0.603507i	$0.793769\pi$
$662$	0	0
$663$	24.0000	0.932083
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−4.00000	−0.154881
$668$	0	0
$669$	16.0000	0.618596
$670$	0	0
$671$	21.0000	0.810696
$672$	0	0
$673$	28.0000	1.07932	0.539660	−	0.841883i	$-0.318553\pi$
$673$	28.0000	1.07932	0.539660	+	0.841883i	$0.318553\pi$
$674$	0	0
$675$	4.00000	0.153960
$676$	0	0
$677$	32.0000	1.22986	0.614930	−	0.788582i	$-0.289184\pi$
$677$	32.0000	1.22986	0.614930	+	0.788582i	$0.289184\pi$
$678$	0	0
$679$	48.0000	1.84207
$680$	0	0
$681$	−8.00000	−0.306561
$682$	0	0
$683$	−6.00000	−0.229584	−0.114792	−	0.993390i	$-0.536620\pi$
$683$	−6.00000	−0.229584	−0.114792	+	0.993390i	$0.536620\pi$
$684$	0	0
$685$	−12.0000	−0.458496
$686$	0	0
$687$	−42.0000	−1.60240
$688$	0	0
$689$	−36.0000	−1.37149
$690$	0	0
$691$	37.0000	1.40755	0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000	1.40755	0.703773	+	0.710425i	$0.251497\pi$
$692$	0	0
$693$	12.0000	0.455842
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−4.00000	−0.151511
$698$	0	0
$699$	20.0000	0.756469
$700$	0	0
$701$	−42.0000	−1.58632	−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000	−1.58632	−0.793159	+	0.609015i	$0.791565\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	12.0000	0.451946
$706$	0	0
$707$	−44.0000	−1.65479
$708$	0	0
$709$	5.00000	0.187779	0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000	0.187779	0.0938895	+	0.995583i	$0.470070\pi$
$710$	0	0
$711$	1.00000	0.0375029
$712$	0	0
$713$	20.0000	0.749006
$714$	0	0
$715$	−18.0000	−0.673162
$716$	0	0
$717$	−30.0000	−1.12037
$718$	0	0
$719$	29.0000	1.08152	0.540759	−	0.841178i	$-0.318137\pi$
$719$	29.0000	1.08152	0.540759	+	0.841178i	$0.318137\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	10.0000	0.371904
$724$	0	0
$725$	−1.00000	−0.0371391
$726$	0	0
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	0	0
$732$	0	0
$733$	−12.0000	−0.443230	−0.221615	−	0.975134i	$-0.571133\pi$
$733$	−12.0000	−0.443230	−0.221615	+	0.975134i	$0.571133\pi$
$734$	0	0
$735$	18.0000	0.663940
$736$	0	0
$737$	−42.0000	−1.54709
$738$	0	0
$739$	−19.0000	−0.698926	−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000	−0.698926	−0.349463	+	0.936950i	$0.613636\pi$
$740$	0	0
$741$	0	0
$742$	0	0
$743$	−52.0000	−1.90769	−0.953847	−	0.300291i	$-0.902916\pi$
$743$	−52.0000	−1.90769	−0.953847	+	0.300291i	$0.902916\pi$
$744$	0	0
$745$	17.0000	0.622832
$746$	0	0
$747$	16.0000	0.585409
$748$	0	0
$749$	−48.0000	−1.75388
$750$	0	0
$751$	−19.0000	−0.693320	−0.346660	−	0.937991i	$-0.612684\pi$
$751$	−19.0000	−0.693320	−0.346660	+	0.937991i	$0.612684\pi$
$752$	0	0
$753$	−62.0000	−2.25941
$754$	0	0
$755$	3.00000	0.109181
$756$	0	0
$757$	−14.0000	−0.508839	−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000	−0.508839	−0.254419	+	0.967094i	$0.581884\pi$
$758$	0	0
$759$	24.0000	0.871145
$760$	0	0
$761$	54.0000	1.95750	0.978749	−	0.205061i	$-0.0657392\pi$
$761$	54.0000	1.95750	0.978749	+	0.205061i	$0.0657392\pi$
$762$	0	0
$763$	28.0000	1.01367
$764$	0	0
$765$	−2.00000	−0.0723102
$766$	0	0
$767$	−6.00000	−0.216647
$768$	0	0
$769$	13.0000	0.468792	0.234396	−	0.972141i	$-0.424689\pi$
$769$	13.0000	0.468792	0.234396	+	0.972141i	$0.424689\pi$
$770$	0	0
$771$	36.0000	1.29651
$772$	0	0
$773$	54.0000	1.94225	0.971123	−	0.238581i	$-0.0766824\pi$
$773$	54.0000	1.94225	0.971123	+	0.238581i	$0.0766824\pi$
$774$	0	0
$775$	5.00000	0.179605
$776$	0	0
$777$	32.0000	1.14799
$778$	0	0
$779$	0	0
$780$	0	0
$781$	45.0000	1.61023
$782$	0	0
$783$	−4.00000	−0.142948
$784$	0	0
$785$	−18.0000	−0.642448
$786$	0	0
$787$	−38.0000	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$788$	0	0
$789$	−20.0000	−0.712019
$790$	0	0
$791$	56.0000	1.99113
$792$	0	0
$793$	42.0000	1.49146
$794$	0	0
$795$	12.0000	0.425596
$796$	0	0
$797$	22.0000	0.779280	0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000	0.779280	0.389640	+	0.920967i	$0.372599\pi$
$798$	0	0
$799$	12.0000	0.424529
$800$	0	0
$801$	−17.0000	−0.600665
$802$	0	0
$803$	−36.0000	−1.27041
$804$	0	0
$805$	16.0000	0.563926
$806$	0	0
$807$	−2.00000	−0.0704033
$808$	0	0
$809$	45.0000	1.58212	0.791058	−	0.611741i	$-0.209531\pi$
$809$	45.0000	1.58212	0.791058	+	0.611741i	$0.209531\pi$
$810$	0	0
$811$	13.0000	0.456492	0.228246	−	0.973604i	$-0.426701\pi$
$811$	13.0000	0.456492	0.228246	+	0.973604i	$0.426701\pi$
$812$	0	0
$813$	−34.0000	−1.19243
$814$	0	0
$815$	−18.0000	−0.630512
$816$	0	0
$817$	0	0
$818$	0	0
$819$	24.0000	0.838628
$820$	0	0
$821$	25.0000	0.872506	0.436253	−	0.899824i	$-0.356305\pi$
$821$	25.0000	0.872506	0.436253	+	0.899824i	$0.356305\pi$
$822$	0	0
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	0	0
$825$	6.00000	0.208893
$826$	0	0
$827$	18.0000	0.625921	0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000	0.625921	0.312961	+	0.949766i	$0.398679\pi$
$828$	0	0
$829$	30.0000	1.04194	0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000	1.04194	0.520972	+	0.853574i	$0.325570\pi$
$830$	0	0
$831$	−32.0000	−1.11007
$832$	0	0
$833$	18.0000	0.623663
$834$	0	0
$835$	8.00000	0.276851
$836$	0	0
$837$	20.0000	0.691301
$838$	0	0
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	0	0
$843$	−52.0000	−1.79098
$844$	0	0
$845$	−23.0000	−0.791224
$846$	0	0
$847$	8.00000	0.274883
$848$	0	0
$849$	52.0000	1.78464
$850$	0	0
$851$	16.0000	0.548473
$852$	0	0
$853$	38.0000	1.30110	0.650548	−	0.759465i	$-0.274539\pi$
$853$	38.0000	1.30110	0.650548	+	0.759465i	$0.274539\pi$
$854$	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
$859$	−1.00000	−0.0341196	−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000	−0.0341196	−0.0170598	+	0.999854i	$0.505431\pi$
$860$	0	0
$861$	−16.0000	−0.545279
$862$	0	0
$863$	18.0000	0.612727	0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000	0.612727	0.306364	+	0.951915i	$0.400888\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	26.0000	0.883006
$868$	0	0
$869$	−3.00000	−0.101768
$870$	0	0
$871$	−84.0000	−2.84623
$872$	0	0
$873$	−12.0000	−0.406138
$874$	0	0
$875$	4.00000	0.135225
$876$	0	0
$877$	−40.0000	−1.35070	−0.675352	−	0.737496i	$-0.736008\pi$
$877$	−40.0000	−1.35070	−0.675352	+	0.737496i	$0.736008\pi$
$878$	0	0
$879$	32.0000	1.07933
$880$	0	0
$881$	−7.00000	−0.235836	−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000	−0.235836	−0.117918	+	0.993023i	$0.537622\pi$
$882$	0	0
$883$	8.00000	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$884$	0	0
$885$	2.00000	0.0672293
$886$	0	0
$887$	−28.0000	−0.940148	−0.470074	−	0.882627i	$-0.655773\pi$
$887$	−28.0000	−0.940148	−0.470074	+	0.882627i	$0.655773\pi$
$888$	0	0
$889$	72.0000	2.41480
$890$	0	0
$891$	33.0000	1.10554
$892$	0	0
$893$	0	0
$894$	0	0
$895$	−15.0000	−0.501395
$896$	0	0
$897$	48.0000	1.60267
$898$	0	0
$899$	−5.00000	−0.166759
$900$	0	0
$901$	12.0000	0.399778
$902$	0	0
$903$	0	0
$904$	0	0
$905$	2.00000	0.0664822
$906$	0	0
$907$	−32.0000	−1.06254	−0.531271	−	0.847202i	$-0.678286\pi$
$907$	−32.0000	−1.06254	−0.531271	+	0.847202i	$0.678286\pi$
$908$	0	0
$909$	11.0000	0.364847
$910$	0	0
$911$	−7.00000	−0.231920	−0.115960	−	0.993254i	$-0.536994\pi$
$911$	−7.00000	−0.231920	−0.115960	+	0.993254i	$0.536994\pi$
$912$	0	0
$913$	−48.0000	−1.58857
$914$	0	0
$915$	−14.0000	−0.462826
$916$	0	0
$917$	80.0000	2.64183
$918$	0	0
$919$	8.00000	0.263896	0.131948	−	0.991257i	$-0.457877\pi$
$919$	8.00000	0.263896	0.131948	+	0.991257i	$0.457877\pi$
$920$	0	0
$921$	−28.0000	−0.922631
$922$	0	0
$923$	90.0000	2.96239
$924$	0	0
$925$	4.00000	0.131519
$926$	0	0
$927$	0	0
$928$	0	0
$929$	−21.0000	−0.688988	−0.344494	−	0.938789i	$-0.611949\pi$
$929$	−21.0000	−0.688988	−0.344494	+	0.938789i	$0.611949\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	0	0
$934$	0	0
$935$	6.00000	0.196221
$936$	0	0
$937$	2.00000	0.0653372	0.0326686	−	0.999466i	$-0.489599\pi$
$937$	2.00000	0.0653372	0.0326686	+	0.999466i	$0.489599\pi$
$938$	0	0
$939$	−68.0000	−2.21910
$940$	0	0
$941$	−35.0000	−1.14097	−0.570484	−	0.821309i	$-0.693244\pi$
$941$	−35.0000	−1.14097	−0.570484	+	0.821309i	$0.693244\pi$
$942$	0	0
$943$	−8.00000	−0.260516
$944$	0	0
$945$	16.0000	0.520480
$946$	0	0
$947$	−10.0000	−0.324956	−0.162478	−	0.986712i	$-0.551949\pi$
$947$	−10.0000	−0.324956	−0.162478	+	0.986712i	$0.551949\pi$
$948$	0	0
$949$	−72.0000	−2.33722
$950$	0	0
$951$	−24.0000	−0.778253
$952$	0	0
$953$	28.0000	0.907009	0.453504	−	0.891254i	$-0.350174\pi$
$953$	28.0000	0.907009	0.453504	+	0.891254i	$0.350174\pi$
$954$	0	0
$955$	13.0000	0.420670
$956$	0	0
$957$	−6.00000	−0.193952
$958$	0	0
$959$	−48.0000	−1.55000
$960$	0	0
$961$	−6.00000	−0.193548
$962$	0	0
$963$	12.0000	0.386695
$964$	0	0
$965$	16.0000	0.515058
$966$	0	0
$967$	−12.0000	−0.385894	−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000	−0.385894	−0.192947	+	0.981209i	$0.561805\pi$
$968$	0	0
$969$	0	0
$970$	0	0
$971$	−60.0000	−1.92549	−0.962746	−	0.270408i	$-0.912841\pi$
$971$	−60.0000	−1.92549	−0.962746	+	0.270408i	$0.912841\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	12.0000	0.384308
$976$	0	0
$977$	−12.0000	−0.383914	−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000	−0.383914	−0.191957	+	0.981403i	$0.561483\pi$
$978$	0	0
$979$	51.0000	1.62997
$980$	0	0
$981$	−7.00000	−0.223493
$982$	0	0
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	0	0
$985$	−2.00000	−0.0637253
$986$	0	0
$987$	48.0000	1.52786
$988$	0	0
$989$	0	0
$990$	0	0
$991$	−32.0000	−1.01651	−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000	−1.01651	−0.508257	+	0.861206i	$0.669710\pi$
$992$	0	0
$993$	−40.0000	−1.26936
$994$	0	0
$995$	−23.0000	−0.729149
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	0	0
$999$	16.0000	0.506218

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7220.2.a.a.1.1		1
19.8	odd	6		380.2.i.a.121.1	✓	2
19.12	odd	6		380.2.i.a.201.1	yes	2
19.18	odd	2		7220.2.a.e.1.1		1
57.8	even	6		3420.2.t.b.1261.1		2
57.50	even	6		3420.2.t.b.3241.1		2
76.27	even	6		1520.2.q.g.881.1		2
76.31	even	6		1520.2.q.g.961.1		2
95.8	even	12		1900.2.s.b.349.2		4
95.12	even	12		1900.2.s.b.49.2		4
95.27	even	12		1900.2.s.b.349.1		4
95.69	odd	6		1900.2.i.b.201.1		2
95.84	odd	6		1900.2.i.b.501.1		2
95.88	even	12		1900.2.s.b.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.a.121.1	✓	2	19.8	odd	6
380.2.i.a.201.1	yes	2	19.12	odd	6
1520.2.q.g.881.1		2	76.27	even	6
1520.2.q.g.961.1		2	76.31	even	6
1900.2.i.b.201.1		2	95.69	odd	6
1900.2.i.b.501.1		2	95.84	odd	6
1900.2.s.b.49.1		4	95.88	even	12
1900.2.s.b.49.2		4	95.12	even	12
1900.2.s.b.349.1		4	95.27	even	12
1900.2.s.b.349.2		4	95.8	even	12
3420.2.t.b.1261.1		2	57.8	even	6
3420.2.t.b.3241.1		2	57.50	even	6
7220.2.a.a.1.1		1	1.1	even	1	trivial
7220.2.a.e.1.1		1	19.18	odd	2

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:	\( N \)	\(=\)	\( 7220 = 2^{2} \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7220.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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