LMFDB - Embedded newform 6014.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} +1.00000 q^{4} +2.00000 q^{5} -4.00000 q^{7} +1.00000 q^{8} -3.00000 q^{9} +2.00000 q^{10} +2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} -2.00000 q^{17} -3.00000 q^{18} +4.00000 q^{19} +2.00000 q^{20} -1.00000 q^{25} +2.00000 q^{26} -4.00000 q^{28} +2.00000 q^{29} -1.00000 q^{31} +1.00000 q^{32} -2.00000 q^{34} -8.00000 q^{35} -3.00000 q^{36} -6.00000 q^{37} +4.00000 q^{38} +2.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -6.00000 q^{45} +9.00000 q^{49} -1.00000 q^{50} +2.00000 q^{52} -14.0000 q^{53} -4.00000 q^{56} +2.00000 q^{58} -4.00000 q^{59} +2.00000 q^{61} -1.00000 q^{62} +12.0000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +12.0000 q^{67} -2.00000 q^{68} -8.00000 q^{70} -12.0000 q^{71} -3.00000 q^{72} +2.00000 q^{73} -6.00000 q^{74} +4.00000 q^{76} -16.0000 q^{79} +2.00000 q^{80} +9.00000 q^{81} +2.00000 q^{82} +4.00000 q^{83} -4.00000 q^{85} -8.00000 q^{86} -6.00000 q^{89} -6.00000 q^{90} -8.00000 q^{91} +8.00000 q^{95} +1.00000 q^{97} +9.00000 q^{98} +O(q^{100})$

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	0	0
$7$	−4.00000	−1.51186	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000	−1.51186	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	2.00000	0.632456
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	0	0
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−4.00000	−1.06904
$15$	0	0
$16$	1.00000	0.250000
$17$	−2.00000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	−3.00000	−0.707107
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	2.00000	0.447214
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	0	0
$25$	−1.00000	−0.200000
$26$	2.00000	0.392232
$27$	0	0
$28$	−4.00000	−0.755929
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	0	0
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−8.00000	−1.35225
$36$	−3.00000	−0.500000
$37$	−6.00000	−0.986394	−0.493197	−	0.869918i	$-0.664172\pi$
$37$	−6.00000	−0.986394	−0.493197	+	0.869918i	$0.664172\pi$
$38$	4.00000	0.648886
$39$	0	0
$40$	2.00000	0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	0	0
$45$	−6.00000	−0.894427
$46$	0	0
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	0	0
$49$	9.00000	1.28571
$50$	−1.00000	−0.141421
$51$	0	0
$52$	2.00000	0.277350
$53$	−14.0000	−1.92305	−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000	−1.92305	−0.961524	+	0.274721i	$0.911414\pi$
$54$	0	0
$55$	0	0
$56$	−4.00000	−0.534522
$57$	0	0
$58$	2.00000	0.262613
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	0	0
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−1.00000	−0.127000
$63$	12.0000	1.51186
$64$	1.00000	0.125000
$65$	4.00000	0.496139
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	−8.00000	−0.956183
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	−3.00000	−0.353553
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−6.00000	−0.697486
$75$	0	0
$76$	4.00000	0.458831
$77$	0	0
$78$	0	0
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	2.00000	0.223607
$81$	9.00000	1.00000
$82$	2.00000	0.220863
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	0	0
$85$	−4.00000	−0.433861
$86$	−8.00000	−0.862662
$87$	0	0
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	−6.00000	−0.632456
$91$	−8.00000	−0.838628
$92$	0	0
$93$	0	0
$94$	0	0
$95$	8.00000	0.820783
$96$	0	0
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	9.00000	0.909137
$99$	0	0
$100$	−1.00000	−0.100000
$101$	14.0000	1.39305	0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000	1.39305	0.696526	+	0.717532i	$0.254728\pi$
$102$	0	0
$103$	−16.0000	−1.57653	−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000	−1.57653	−0.788263	+	0.615338i	$0.789020\pi$
$104$	2.00000	0.196116
$105$	0	0
$106$	−14.0000	−1.35980
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	0	0
$109$	−18.0000	−1.72409	−0.862044	−	0.506834i	$-0.830816\pi$
$109$	−18.0000	−1.72409	−0.862044	+	0.506834i	$0.830816\pi$
$110$	0	0
$111$	0	0
$112$	−4.00000	−0.377964
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	0	0
$115$	0	0
$116$	2.00000	0.185695
$117$	−6.00000	−0.554700
$118$	−4.00000	−0.368230
$119$	8.00000	0.733359
$120$	0	0
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	0	0
$124$	−1.00000	−0.0898027
$125$	−12.0000	−1.07331
$126$	12.0000	1.06904
$127$	−8.00000	−0.709885	−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000	−0.709885	−0.354943	+	0.934888i	$0.615500\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	4.00000	0.350823
$131$	−12.0000	−1.04844	−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000	−1.04844	−0.524222	+	0.851581i	$0.675644\pi$
$132$	0	0
$133$	−16.0000	−1.38738
$134$	12.0000	1.03664
$135$	0	0
$136$	−2.00000	−0.171499
$137$	−10.0000	−0.854358	−0.427179	−	0.904167i	$-0.640493\pi$
$137$	−10.0000	−0.854358	−0.427179	+	0.904167i	$0.640493\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−8.00000	−0.676123
$141$	0	0
$142$	−12.0000	−1.00702
$143$	0	0
$144$	−3.00000	−0.250000
$145$	4.00000	0.332182
$146$	2.00000	0.165521
$147$	0	0
$148$	−6.00000	−0.493197
$149$	−14.0000	−1.14692	−0.573462	−	0.819232i	$-0.694400\pi$
$149$	−14.0000	−1.14692	−0.573462	+	0.819232i	$0.694400\pi$
$150$	0	0
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	4.00000	0.324443
$153$	6.00000	0.485071
$154$	0	0
$155$	−2.00000	−0.160644
$156$	0	0
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	−16.0000	−1.27289
$159$	0	0
$160$	2.00000	0.158114
$161$	0	0
$162$	9.00000	0.707107
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	2.00000	0.156174
$165$	0	0
$166$	4.00000	0.310460
$167$	−16.0000	−1.23812	−0.619059	−	0.785345i	$-0.712486\pi$
$167$	−16.0000	−1.23812	−0.619059	+	0.785345i	$0.712486\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	−4.00000	−0.306786
$171$	−12.0000	−0.917663
$172$	−8.00000	−0.609994
$173$	−6.00000	−0.456172	−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000	−0.456172	−0.228086	+	0.973641i	$0.573247\pi$
$174$	0	0
$175$	4.00000	0.302372
$176$	0	0
$177$	0	0
$178$	−6.00000	−0.449719
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−6.00000	−0.447214
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	−8.00000	−0.592999
$183$	0	0
$184$	0	0
$185$	−12.0000	−0.882258
$186$	0	0
$187$	0	0
$188$	0	0
$189$	0	0
$190$	8.00000	0.580381
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	0	0
$193$	18.0000	1.29567	0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000	1.29567	0.647834	+	0.761781i	$0.275675\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	9.00000	0.642857
$197$	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
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	0	0
$202$	14.0000	0.985037
$203$	−8.00000	−0.561490
$204$	0	0
$205$	4.00000	0.279372
$206$	−16.0000	−1.11477
$207$	0	0
$208$	2.00000	0.138675
$209$	0	0
$210$	0	0
$211$	−20.0000	−1.37686	−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000	−1.37686	−0.688428	+	0.725304i	$0.741699\pi$
$212$	−14.0000	−0.961524
$213$	0	0
$214$	−4.00000	−0.273434
$215$	−16.0000	−1.09119
$216$	0	0
$217$	4.00000	0.271538
$218$	−18.0000	−1.21911
$219$	0	0
$220$	0	0
$221$	−4.00000	−0.269069
$222$	0	0
$223$	24.0000	1.60716	0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000	1.60716	0.803579	+	0.595198i	$0.202926\pi$
$224$	−4.00000	−0.267261
$225$	3.00000	0.200000
$226$	18.0000	1.19734
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	0	0
$229$	18.0000	1.18947	0.594737	−	0.803921i	$-0.297256\pi$
$229$	18.0000	1.18947	0.594737	+	0.803921i	$0.297256\pi$
$230$	0	0
$231$	0	0
$232$	2.00000	0.131306
$233$	2.00000	0.131024	0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000	0.131024	0.0655122	+	0.997852i	$0.479132\pi$
$234$	−6.00000	−0.392232
$235$	0	0
$236$	−4.00000	−0.260378
$237$	0	0
$238$	8.00000	0.518563
$239$	−24.0000	−1.55243	−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000	−1.55243	−0.776215	+	0.630468i	$0.782863\pi$
$240$	0	0
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−11.0000	−0.707107
$243$	0	0
$244$	2.00000	0.128037
$245$	18.0000	1.14998
$246$	0	0
$247$	8.00000	0.509028
$248$	−1.00000	−0.0635001
$249$	0	0
$250$	−12.0000	−0.758947
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	12.0000	0.755929
$253$	0	0
$254$	−8.00000	−0.501965
$255$	0	0
$256$	1.00000	0.0625000
$257$	10.0000	0.623783	0.311891	−	0.950118i	$-0.399037\pi$
$257$	10.0000	0.623783	0.311891	+	0.950118i	$0.399037\pi$
$258$	0	0
$259$	24.0000	1.49129
$260$	4.00000	0.248069
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	−28.0000	−1.72003
$266$	−16.0000	−0.981023
$267$	0	0
$268$	12.0000	0.733017
$269$	−14.0000	−0.853595	−0.426798	−	0.904347i	$-0.640358\pi$
$269$	−14.0000	−0.853595	−0.426798	+	0.904347i	$0.640358\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	−10.0000	−0.604122
$275$	0	0
$276$	0	0
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	4.00000	0.239904
$279$	3.00000	0.179605
$280$	−8.00000	−0.478091
$281$	18.0000	1.07379	0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000	1.07379	0.536895	+	0.843649i	$0.319597\pi$
$282$	0	0
$283$	12.0000	0.713326	0.356663	−	0.934233i	$-0.383914\pi$
$283$	12.0000	0.713326	0.356663	+	0.934233i	$0.383914\pi$
$284$	−12.0000	−0.712069
$285$	0	0
$286$	0	0
$287$	−8.00000	−0.472225
$288$	−3.00000	−0.176777
$289$	−13.0000	−0.764706
$290$	4.00000	0.234888
$291$	0	0
$292$	2.00000	0.117041
$293$	30.0000	1.75262	0.876309	−	0.481749i	$-0.159998\pi$
$293$	30.0000	1.75262	0.876309	+	0.481749i	$0.159998\pi$
$294$	0	0
$295$	−8.00000	−0.465778
$296$	−6.00000	−0.348743
$297$	0	0
$298$	−14.0000	−0.810998
$299$	0	0
$300$	0	0
$301$	32.0000	1.84445
$302$	−16.0000	−0.920697
$303$	0	0
$304$	4.00000	0.229416
$305$	4.00000	0.229039
$306$	6.00000	0.342997
$307$	−28.0000	−1.59804	−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000	−1.59804	−0.799022	+	0.601302i	$0.794649\pi$
$308$	0	0
$309$	0	0
$310$	−2.00000	−0.113592
$311$	−12.0000	−0.680458	−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000	−0.680458	−0.340229	+	0.940343i	$0.610505\pi$
$312$	0	0
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	2.00000	0.112867
$315$	24.0000	1.35225
$316$	−16.0000	−0.900070
$317$	18.0000	1.01098	0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000	1.01098	0.505490	+	0.862832i	$0.331312\pi$
$318$	0	0
$319$	0	0
$320$	2.00000	0.111803
$321$	0	0
$322$	0	0
$323$	−8.00000	−0.445132
$324$	9.00000	0.500000
$325$	−2.00000	−0.110940
$326$	−4.00000	−0.221540
$327$	0	0
$328$	2.00000	0.110432
$329$	0	0
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	4.00000	0.219529
$333$	18.0000	0.986394
$334$	−16.0000	−0.875481
$335$	24.0000	1.31126
$336$	0	0
$337$	−10.0000	−0.544735	−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000	−0.544735	−0.272367	+	0.962193i	$0.587807\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	−4.00000	−0.216930
$341$	0	0
$342$	−12.0000	−0.648886
$343$	−8.00000	−0.431959
$344$	−8.00000	−0.431331
$345$	0	0
$346$	−6.00000	−0.322562
$347$	−12.0000	−0.644194	−0.322097	−	0.946707i	$-0.604388\pi$
$347$	−12.0000	−0.644194	−0.322097	+	0.946707i	$0.604388\pi$
$348$	0	0
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	4.00000	0.213809
$351$	0	0
$352$	0	0
$353$	−14.0000	−0.745145	−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000	−0.745145	−0.372572	+	0.928003i	$0.621524\pi$
$354$	0	0
$355$	−24.0000	−1.27379
$356$	−6.00000	−0.317999
$357$	0	0
$358$	20.0000	1.05703
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	−6.00000	−0.316228
$361$	−3.00000	−0.157895
$362$	10.0000	0.525588
$363$	0	0
$364$	−8.00000	−0.419314
$365$	4.00000	0.209370
$366$	0	0
$367$	32.0000	1.67039	0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000	1.67039	0.835193	+	0.549957i	$0.185356\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	−12.0000	−0.623850
$371$	56.0000	2.90738
$372$	0	0
$373$	18.0000	0.932005	0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000	0.932005	0.466002	+	0.884783i	$0.345694\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	4.00000	0.206010
$378$	0	0
$379$	−36.0000	−1.84920	−0.924598	−	0.380945i	$-0.875599\pi$
$379$	−36.0000	−1.84920	−0.924598	+	0.380945i	$0.875599\pi$
$380$	8.00000	0.410391
$381$	0	0
$382$	0	0
$383$	−16.0000	−0.817562	−0.408781	−	0.912633i	$-0.634046\pi$
$383$	−16.0000	−0.817562	−0.408781	+	0.912633i	$0.634046\pi$
$384$	0	0
$385$	0	0
$386$	18.0000	0.916176
$387$	24.0000	1.21999
$388$	1.00000	0.0507673
$389$	18.0000	0.912636	0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000	0.912636	0.456318	+	0.889817i	$0.349168\pi$
$390$	0	0
$391$	0	0
$392$	9.00000	0.454569
$393$	0	0
$394$	2.00000	0.100759
$395$	−32.0000	−1.61009
$396$	0	0
$397$	22.0000	1.10415	0.552074	−	0.833795i	$-0.313837\pi$
$397$	22.0000	1.10415	0.552074	+	0.833795i	$0.313837\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−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
$403$	−2.00000	−0.0996271
$404$	14.0000	0.696526
$405$	18.0000	0.894427
$406$	−8.00000	−0.397033
$407$	0	0
$408$	0	0
$409$	−2.00000	−0.0988936	−0.0494468	−	0.998777i	$-0.515746\pi$
$409$	−2.00000	−0.0988936	−0.0494468	+	0.998777i	$0.515746\pi$
$410$	4.00000	0.197546
$411$	0	0
$412$	−16.0000	−0.788263
$413$	16.0000	0.787309
$414$	0	0
$415$	8.00000	0.392705
$416$	2.00000	0.0980581
$417$	0	0
$418$	0	0
$419$	−12.0000	−0.586238	−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000	−0.586238	−0.293119	+	0.956076i	$0.594693\pi$
$420$	0	0
$421$	−18.0000	−0.877266	−0.438633	−	0.898666i	$-0.644537\pi$
$421$	−18.0000	−0.877266	−0.438633	+	0.898666i	$0.644537\pi$
$422$	−20.0000	−0.973585
$423$	0	0
$424$	−14.0000	−0.679900
$425$	2.00000	0.0970143
$426$	0	0
$427$	−8.00000	−0.387147
$428$	−4.00000	−0.193347
$429$	0	0
$430$	−16.0000	−0.771589
$431$	0	0		−	1.00000i	$-0.5\pi$
$431$	0	0			1.00000i	$0.5\pi$
$432$	0	0
$433$	14.0000	0.672797	0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000	0.672797	0.336399	+	0.941720i	$0.390791\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	−18.0000	−0.862044
$437$	0	0
$438$	0	0
$439$	4.00000	0.190910	0.0954548	−	0.995434i	$-0.469569\pi$
$439$	4.00000	0.190910	0.0954548	+	0.995434i	$0.469569\pi$
$440$	0	0
$441$	−27.0000	−1.28571
$442$	−4.00000	−0.190261
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	−12.0000	−0.568855
$446$	24.0000	1.13643
$447$	0	0
$448$	−4.00000	−0.188982
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	3.00000	0.141421
$451$	0	0
$452$	18.0000	0.846649
$453$	0	0
$454$	12.0000	0.563188
$455$	−16.0000	−0.750092
$456$	0	0
$457$	−10.0000	−0.467780	−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000	−0.467780	−0.233890	+	0.972263i	$0.575146\pi$
$458$	18.0000	0.841085
$459$	0	0
$460$	0	0
$461$	2.00000	0.0931493	0.0465746	−	0.998915i	$-0.485169\pi$
$461$	2.00000	0.0931493	0.0465746	+	0.998915i	$0.485169\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	2.00000	0.0928477
$465$	0	0
$466$	2.00000	0.0926482
$467$	36.0000	1.66588	0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000	1.66588	0.832941	+	0.553362i	$0.186655\pi$
$468$	−6.00000	−0.277350
$469$	−48.0000	−2.21643
$470$	0	0
$471$	0	0
$472$	−4.00000	−0.184115
$473$	0	0
$474$	0	0
$475$	−4.00000	−0.183533
$476$	8.00000	0.366679
$477$	42.0000	1.92305
$478$	−24.0000	−1.09773
$479$	8.00000	0.365529	0.182765	−	0.983157i	$-0.441495\pi$
$479$	8.00000	0.365529	0.182765	+	0.983157i	$0.441495\pi$
$480$	0	0
$481$	−12.0000	−0.547153
$482$	10.0000	0.455488
$483$	0	0
$484$	−11.0000	−0.500000
$485$	2.00000	0.0908153
$486$	0	0
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	2.00000	0.0905357
$489$	0	0
$490$	18.0000	0.813157
$491$	−32.0000	−1.44414	−0.722070	−	0.691820i	$-0.756809\pi$
$491$	−32.0000	−1.44414	−0.722070	+	0.691820i	$0.756809\pi$
$492$	0	0
$493$	−4.00000	−0.180151
$494$	8.00000	0.359937
$495$	0	0
$496$	−1.00000	−0.0449013
$497$	48.0000	2.15309
$498$	0	0
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	−12.0000	−0.536656
$501$	0	0
$502$	−12.0000	−0.535586
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	12.0000	0.534522
$505$	28.0000	1.24598
$506$	0	0
$507$	0	0
$508$	−8.00000	−0.354943
$509$	18.0000	0.797836	0.398918	−	0.916987i	$-0.369386\pi$
$509$	18.0000	0.797836	0.398918	+	0.916987i	$0.369386\pi$
$510$	0	0
$511$	−8.00000	−0.353899
$512$	1.00000	0.0441942
$513$	0	0
$514$	10.0000	0.441081
$515$	−32.0000	−1.41009
$516$	0	0
$517$	0	0
$518$	24.0000	1.05450
$519$	0	0
$520$	4.00000	0.175412
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	−6.00000	−0.262613
$523$	44.0000	1.92399	0.961993	−	0.273075i	$-0.0880406\pi$
$523$	44.0000	1.92399	0.961993	+	0.273075i	$0.0880406\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	0	0
$527$	2.00000	0.0871214
$528$	0	0
$529$	−23.0000	−1.00000
$530$	−28.0000	−1.21624
$531$	12.0000	0.520756
$532$	−16.0000	−0.693688
$533$	4.00000	0.173259
$534$	0	0
$535$	−8.00000	−0.345870
$536$	12.0000	0.518321
$537$	0	0
$538$	−14.0000	−0.603583
$539$	0	0
$540$	0	0
$541$	34.0000	1.46177	0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000	1.46177	0.730887	+	0.682498i	$0.239107\pi$
$542$	8.00000	0.343629
$543$	0	0
$544$	−2.00000	−0.0857493
$545$	−36.0000	−1.54207
$546$	0	0
$547$	28.0000	1.19719	0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000	1.19719	0.598597	+	0.801050i	$0.295725\pi$
$548$	−10.0000	−0.427179
$549$	−6.00000	−0.256074
$550$	0	0
$551$	8.00000	0.340811
$552$	0	0
$553$	64.0000	2.72156
$554$	10.0000	0.424859
$555$	0	0
$556$	4.00000	0.169638
$557$	−22.0000	−0.932170	−0.466085	−	0.884740i	$-0.654336\pi$
$557$	−22.0000	−0.932170	−0.466085	+	0.884740i	$0.654336\pi$
$558$	3.00000	0.127000
$559$	−16.0000	−0.676728
$560$	−8.00000	−0.338062
$561$	0	0
$562$	18.0000	0.759284
$563$	12.0000	0.505740	0.252870	−	0.967500i	$-0.418626\pi$
$563$	12.0000	0.505740	0.252870	+	0.967500i	$0.418626\pi$
$564$	0	0
$565$	36.0000	1.51453
$566$	12.0000	0.504398
$567$	−36.0000	−1.51186
$568$	−12.0000	−0.503509
$569$	−26.0000	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$569$	−26.0000	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$570$	0	0
$571$	16.0000	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$572$	0	0
$573$	0	0
$574$	−8.00000	−0.333914
$575$	0	0
$576$	−3.00000	−0.125000
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	4.00000	0.166091
$581$	−16.0000	−0.663792
$582$	0	0
$583$	0	0
$584$	2.00000	0.0827606
$585$	−12.0000	−0.496139
$586$	30.0000	1.23929
$587$	20.0000	0.825488	0.412744	−	0.910847i	$-0.364570\pi$
$587$	20.0000	0.825488	0.412744	+	0.910847i	$0.364570\pi$
$588$	0	0
$589$	−4.00000	−0.164817
$590$	−8.00000	−0.329355
$591$	0	0
$592$	−6.00000	−0.246598
$593$	34.0000	1.39621	0.698106	−	0.715994i	$-0.254026\pi$
$593$	34.0000	1.39621	0.698106	+	0.715994i	$0.254026\pi$
$594$	0	0
$595$	16.0000	0.655936
$596$	−14.0000	−0.573462
$597$	0	0
$598$	0	0
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	0	0
$601$	30.0000	1.22373	0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000	1.22373	0.611863	+	0.790964i	$0.290420\pi$
$602$	32.0000	1.30422
$603$	−36.0000	−1.46603
$604$	−16.0000	−0.651031
$605$	−22.0000	−0.894427
$606$	0	0
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	4.00000	0.161955
$611$	0	0
$612$	6.00000	0.242536
$613$	26.0000	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$613$	26.0000	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$614$	−28.0000	−1.12999
$615$	0	0
$616$	0	0
$617$	−38.0000	−1.52982	−0.764911	−	0.644136i	$-0.777217\pi$
$617$	−38.0000	−1.52982	−0.764911	+	0.644136i	$0.777217\pi$
$618$	0	0
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	−2.00000	−0.0803219
$621$	0	0
$622$	−12.0000	−0.481156
$623$	24.0000	0.961540
$624$	0	0
$625$	−19.0000	−0.760000
$626$	10.0000	0.399680
$627$	0	0
$628$	2.00000	0.0798087
$629$	12.0000	0.478471
$630$	24.0000	0.956183
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	−16.0000	−0.636446
$633$	0	0
$634$	18.0000	0.714871
$635$	−16.0000	−0.634941
$636$	0	0
$637$	18.0000	0.713186
$638$	0	0
$639$	36.0000	1.42414
$640$	2.00000	0.0790569
$641$	6.00000	0.236986	0.118493	−	0.992955i	$-0.462194\pi$
$641$	6.00000	0.236986	0.118493	+	0.992955i	$0.462194\pi$
$642$	0	0
$643$	−16.0000	−0.630978	−0.315489	−	0.948929i	$-0.602169\pi$
$643$	−16.0000	−0.630978	−0.315489	+	0.948929i	$0.602169\pi$
$644$	0	0
$645$	0	0
$646$	−8.00000	−0.314756
$647$	−48.0000	−1.88707	−0.943537	−	0.331266i	$-0.892524\pi$
$647$	−48.0000	−1.88707	−0.943537	+	0.331266i	$0.892524\pi$
$648$	9.00000	0.353553
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−4.00000	−0.156652
$653$	50.0000	1.95665	0.978326	−	0.207072i	$-0.0663936\pi$
$653$	50.0000	1.95665	0.978326	+	0.207072i	$0.0663936\pi$
$654$	0	0
$655$	−24.0000	−0.937758
$656$	2.00000	0.0780869
$657$	−6.00000	−0.234082
$658$	0	0
$659$	−12.0000	−0.467454	−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000	−0.467454	−0.233727	+	0.972302i	$0.575092\pi$
$660$	0	0
$661$	38.0000	1.47803	0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000	1.47803	0.739014	+	0.673690i	$0.235292\pi$
$662$	−4.00000	−0.155464
$663$	0	0
$664$	4.00000	0.155230
$665$	−32.0000	−1.24091
$666$	18.0000	0.697486
$667$	0	0
$668$	−16.0000	−0.619059
$669$	0	0
$670$	24.0000	0.927201
$671$	0	0
$672$	0	0
$673$	26.0000	1.00223	0.501113	−	0.865382i	$-0.332924\pi$
$673$	26.0000	1.00223	0.501113	+	0.865382i	$0.332924\pi$
$674$	−10.0000	−0.385186
$675$	0	0
$676$	−9.00000	−0.346154
$677$	−30.0000	−1.15299	−0.576497	−	0.817099i	$-0.695581\pi$
$677$	−30.0000	−1.15299	−0.576497	+	0.817099i	$0.695581\pi$
$678$	0	0
$679$	−4.00000	−0.153506
$680$	−4.00000	−0.153393
$681$	0	0
$682$	0	0
$683$	−4.00000	−0.153056	−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000	−0.153056	−0.0765279	+	0.997067i	$0.524383\pi$
$684$	−12.0000	−0.458831
$685$	−20.0000	−0.764161
$686$	−8.00000	−0.305441
$687$	0	0
$688$	−8.00000	−0.304997
$689$	−28.0000	−1.06672
$690$	0	0
$691$	−44.0000	−1.67384	−0.836919	−	0.547326i	$-0.815646\pi$
$691$	−44.0000	−1.67384	−0.836919	+	0.547326i	$0.815646\pi$
$692$	−6.00000	−0.228086
$693$	0	0
$694$	−12.0000	−0.455514
$695$	8.00000	0.303457
$696$	0	0
$697$	−4.00000	−0.151511
$698$	2.00000	0.0757011
$699$	0	0
$700$	4.00000	0.151186
$701$	−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
$703$	−24.0000	−0.905177
$704$	0	0
$705$	0	0
$706$	−14.0000	−0.526897
$707$	−56.0000	−2.10610
$708$	0	0
$709$	−6.00000	−0.225335	−0.112667	−	0.993633i	$-0.535939\pi$
$709$	−6.00000	−0.225335	−0.112667	+	0.993633i	$0.535939\pi$
$710$	−24.0000	−0.900704
$711$	48.0000	1.80014
$712$	−6.00000	−0.224860
$713$	0	0
$714$	0	0
$715$	0	0
$716$	20.0000	0.747435
$717$	0	0
$718$	−4.00000	−0.149279
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−6.00000	−0.223607
$721$	64.0000	2.38348
$722$	−3.00000	−0.111648
$723$	0	0
$724$	10.0000	0.371647
$725$	−2.00000	−0.0742781
$726$	0	0
$727$	−48.0000	−1.78022	−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000	−1.78022	−0.890111	+	0.455744i	$0.849373\pi$
$728$	−8.00000	−0.296500
$729$	−27.0000	−1.00000
$730$	4.00000	0.148047
$731$	16.0000	0.591781
$732$	0	0
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	32.0000	1.18114
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−6.00000	−0.220863
$739$	−28.0000	−1.03000	−0.514998	−	0.857191i	$-0.672207\pi$
$739$	−28.0000	−1.03000	−0.514998	+	0.857191i	$0.672207\pi$
$740$	−12.0000	−0.441129
$741$	0	0
$742$	56.0000	2.05582
$743$	16.0000	0.586983	0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000	0.586983	0.293492	+	0.955962i	$0.405183\pi$
$744$	0	0
$745$	−28.0000	−1.02584
$746$	18.0000	0.659027
$747$	−12.0000	−0.439057
$748$	0	0
$749$	16.0000	0.584627
$750$	0	0
$751$	−16.0000	−0.583848	−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000	−0.583848	−0.291924	+	0.956441i	$0.594295\pi$
$752$	0	0
$753$	0	0
$754$	4.00000	0.145671
$755$	−32.0000	−1.16460
$756$	0	0
$757$	10.0000	0.363456	0.181728	−	0.983349i	$-0.441831\pi$
$757$	10.0000	0.363456	0.181728	+	0.983349i	$0.441831\pi$
$758$	−36.0000	−1.30758
$759$	0	0
$760$	8.00000	0.290191
$761$	6.00000	0.217500	0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000	0.217500	0.108750	+	0.994069i	$0.465315\pi$
$762$	0	0
$763$	72.0000	2.60658
$764$	0	0
$765$	12.0000	0.433861
$766$	−16.0000	−0.578103
$767$	−8.00000	−0.288863
$768$	0	0
$769$	2.00000	0.0721218	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	2.00000	0.0721218	0.0360609	+	0.999350i	$0.488519\pi$
$770$	0	0
$771$	0	0
$772$	18.0000	0.647834
$773$	42.0000	1.51064	0.755318	−	0.655359i	$-0.227483\pi$
$773$	42.0000	1.51064	0.755318	+	0.655359i	$0.227483\pi$
$774$	24.0000	0.862662
$775$	1.00000	0.0359211
$776$	1.00000	0.0358979
$777$	0	0
$778$	18.0000	0.645331
$779$	8.00000	0.286630
$780$	0	0
$781$	0	0
$782$	0	0
$783$	0	0
$784$	9.00000	0.321429
$785$	4.00000	0.142766
$786$	0	0
$787$	−32.0000	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$787$	−32.0000	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$788$	2.00000	0.0712470
$789$	0	0
$790$	−32.0000	−1.13851
$791$	−72.0000	−2.56003
$792$	0	0
$793$	4.00000	0.142044
$794$	22.0000	0.780751
$795$	0	0
$796$	16.0000	0.567105
$797$	18.0000	0.637593	0.318796	−	0.947823i	$-0.396721\pi$
$797$	18.0000	0.637593	0.318796	+	0.947823i	$0.396721\pi$
$798$	0	0
$799$	0	0
$800$	−1.00000	−0.0353553
$801$	18.0000	0.635999
$802$	−18.0000	−0.635602
$803$	0	0
$804$	0	0
$805$	0	0
$806$	−2.00000	−0.0704470
$807$	0	0
$808$	14.0000	0.492518
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	18.0000	0.632456
$811$	52.0000	1.82597	0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000	1.82597	0.912983	+	0.407997i	$0.133772\pi$
$812$	−8.00000	−0.280745
$813$	0	0
$814$	0	0
$815$	−8.00000	−0.280228
$816$	0	0
$817$	−32.0000	−1.11954
$818$	−2.00000	−0.0699284
$819$	24.0000	0.838628
$820$	4.00000	0.139686
$821$	10.0000	0.349002	0.174501	−	0.984657i	$-0.444169\pi$
$821$	10.0000	0.349002	0.174501	+	0.984657i	$0.444169\pi$
$822$	0	0
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	−16.0000	−0.557386
$825$	0	0
$826$	16.0000	0.556711
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	34.0000	1.18087	0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000	1.18087	0.590434	+	0.807086i	$0.298956\pi$
$830$	8.00000	0.277684
$831$	0	0
$832$	2.00000	0.0693375
$833$	−18.0000	−0.623663
$834$	0	0
$835$	−32.0000	−1.10741
$836$	0	0
$837$	0	0
$838$	−12.0000	−0.414533
$839$	−28.0000	−0.966667	−0.483334	−	0.875436i	$-0.660574\pi$
$839$	−28.0000	−0.966667	−0.483334	+	0.875436i	$0.660574\pi$
$840$	0	0
$841$	−25.0000	−0.862069
$842$	−18.0000	−0.620321
$843$	0	0
$844$	−20.0000	−0.688428
$845$	−18.0000	−0.619219
$846$	0	0
$847$	44.0000	1.51186
$848$	−14.0000	−0.480762
$849$	0	0
$850$	2.00000	0.0685994
$851$	0	0
$852$	0	0
$853$	18.0000	0.616308	0.308154	−	0.951336i	$-0.400289\pi$
$853$	18.0000	0.616308	0.308154	+	0.951336i	$0.400289\pi$
$854$	−8.00000	−0.273754
$855$	−24.0000	−0.820783
$856$	−4.00000	−0.136717
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	20.0000	0.682391	0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000	0.682391	0.341196	+	0.939992i	$0.389168\pi$
$860$	−16.0000	−0.545595
$861$	0	0
$862$	0	0
$863$	−24.0000	−0.816970	−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000	−0.816970	−0.408485	+	0.912765i	$0.633943\pi$
$864$	0	0
$865$	−12.0000	−0.408012
$866$	14.0000	0.475739
$867$	0	0
$868$	4.00000	0.135769
$869$	0	0
$870$	0	0
$871$	24.0000	0.813209
$872$	−18.0000	−0.609557
$873$	−3.00000	−0.101535
$874$	0	0
$875$	48.0000	1.62270
$876$	0	0
$877$	22.0000	0.742887	0.371444	−	0.928456i	$-0.378863\pi$
$877$	22.0000	0.742887	0.371444	+	0.928456i	$0.378863\pi$
$878$	4.00000	0.134993
$879$	0	0
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	−27.0000	−0.909137
$883$	−52.0000	−1.74994	−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000	−1.74994	−0.874970	+	0.484178i	$0.839119\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−4.00000	−0.134383
$887$	−36.0000	−1.20876	−0.604381	−	0.796696i	$-0.706579\pi$
$887$	−36.0000	−1.20876	−0.604381	+	0.796696i	$0.706579\pi$
$888$	0	0
$889$	32.0000	1.07325
$890$	−12.0000	−0.402241
$891$	0	0
$892$	24.0000	0.803579
$893$	0	0
$894$	0	0
$895$	40.0000	1.33705
$896$	−4.00000	−0.133631
$897$	0	0
$898$	18.0000	0.600668
$899$	−2.00000	−0.0667037
$900$	3.00000	0.100000
$901$	28.0000	0.932815
$902$	0	0
$903$	0	0
$904$	18.0000	0.598671
$905$	20.0000	0.664822
$906$	0	0
$907$	−12.0000	−0.398453	−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000	−0.398453	−0.199227	+	0.979953i	$0.563843\pi$
$908$	12.0000	0.398234
$909$	−42.0000	−1.39305
$910$	−16.0000	−0.530395
$911$	−48.0000	−1.59031	−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000	−1.59031	−0.795155	+	0.606406i	$0.792611\pi$
$912$	0	0
$913$	0	0
$914$	−10.0000	−0.330771
$915$	0	0
$916$	18.0000	0.594737
$917$	48.0000	1.58510
$918$	0	0
$919$	20.0000	0.659739	0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000	0.659739	0.329870	+	0.944027i	$0.392995\pi$
$920$	0	0
$921$	0	0
$922$	2.00000	0.0658665
$923$	−24.0000	−0.789970
$924$	0	0
$925$	6.00000	0.197279
$926$	−8.00000	−0.262896
$927$	48.0000	1.57653
$928$	2.00000	0.0656532
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	0	0
$931$	36.0000	1.17985
$932$	2.00000	0.0655122
$933$	0	0
$934$	36.0000	1.17796
$935$	0	0
$936$	−6.00000	−0.196116
$937$	−38.0000	−1.24141	−0.620703	−	0.784046i	$-0.713153\pi$
$937$	−38.0000	−1.24141	−0.620703	+	0.784046i	$0.713153\pi$
$938$	−48.0000	−1.56726
$939$	0	0
$940$	0	0
$941$	−30.0000	−0.977972	−0.488986	−	0.872292i	$-0.662633\pi$
$941$	−30.0000	−0.977972	−0.488986	+	0.872292i	$0.662633\pi$
$942$	0	0
$943$	0	0
$944$	−4.00000	−0.130189
$945$	0	0
$946$	0	0
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	0	0
$949$	4.00000	0.129845
$950$	−4.00000	−0.129777
$951$	0	0
$952$	8.00000	0.259281
$953$	−42.0000	−1.36051	−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000	−1.36051	−0.680257	+	0.732974i	$0.738132\pi$
$954$	42.0000	1.35980
$955$	0	0
$956$	−24.0000	−0.776215
$957$	0	0
$958$	8.00000	0.258468
$959$	40.0000	1.29167
$960$	0	0
$961$	1.00000	0.0322581
$962$	−12.0000	−0.386896
$963$	12.0000	0.386695
$964$	10.0000	0.322078
$965$	36.0000	1.15888
$966$	0	0
$967$	−40.0000	−1.28631	−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000	−1.28631	−0.643157	+	0.765735i	$0.722376\pi$
$968$	−11.0000	−0.353553
$969$	0	0
$970$	2.00000	0.0642161
$971$	28.0000	0.898563	0.449281	−	0.893390i	$-0.351680\pi$
$971$	28.0000	0.898563	0.449281	+	0.893390i	$0.351680\pi$
$972$	0	0
$973$	−16.0000	−0.512936
$974$	−8.00000	−0.256337
$975$	0	0
$976$	2.00000	0.0640184
$977$	10.0000	0.319928	0.159964	−	0.987123i	$-0.448862\pi$
$977$	10.0000	0.319928	0.159964	+	0.987123i	$0.448862\pi$
$978$	0	0
$979$	0	0
$980$	18.0000	0.574989
$981$	54.0000	1.72409
$982$	−32.0000	−1.02116
$983$	−24.0000	−0.765481	−0.382741	−	0.923856i	$-0.625020\pi$
$983$	−24.0000	−0.765481	−0.382741	+	0.923856i	$0.625020\pi$
$984$	0	0
$985$	4.00000	0.127451
$986$	−4.00000	−0.127386
$987$	0	0
$988$	8.00000	0.254514
$989$	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	$0.669710\pi$
$992$	−1.00000	−0.0317500
$993$	0	0
$994$	48.0000	1.52247
$995$	32.0000	1.01447
$996$	0	0
$997$	−18.0000	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$997$	−18.0000	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$998$	36.0000	1.13956
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.b.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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