LMFDB - Embedded newform 784.4.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,4,Mod(1,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("784.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	784.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:	$46.2574974445$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	784.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-1.00000 q^{3} -7.00000 q^{5} -26.0000 q^{9} +O(q^{10})$

$q-1.00000 q^{3} -7.00000 q^{5} -26.0000 q^{9} -35.0000 q^{11} -66.0000 q^{13} +7.00000 q^{15} -59.0000 q^{17} +137.000 q^{19} +7.00000 q^{23} -76.0000 q^{25} +53.0000 q^{27} +106.000 q^{29} +75.0000 q^{31} +35.0000 q^{33} +11.0000 q^{37} +66.0000 q^{39} +498.000 q^{41} -260.000 q^{43} +182.000 q^{45} -171.000 q^{47} +59.0000 q^{51} -417.000 q^{53} +245.000 q^{55} -137.000 q^{57} -17.0000 q^{59} -51.0000 q^{61} +462.000 q^{65} -439.000 q^{67} -7.00000 q^{69} +784.000 q^{71} -295.000 q^{73} +76.0000 q^{75} +495.000 q^{79} +649.000 q^{81} +932.000 q^{83} +413.000 q^{85} -106.000 q^{87} +873.000 q^{89} -75.0000 q^{93} -959.000 q^{95} +290.000 q^{97} +910.000 q^{99} +O(q^{100})$

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
$3$	−1.00000	−0.192450	−0.0962250	−	0.995360i	$-0.530677\pi$
$3$	−1.00000	−0.192450	−0.0962250	+	0.995360i	$0.530677\pi$
$4$	0	0
$5$	−7.00000	−0.626099	−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000	−0.626099	−0.313050	+	0.949737i	$0.601351\pi$
$6$	0	0
$7$	0	0
$7$	0	0
$8$	0	0
$9$	−26.0000	−0.962963
$10$	0	0
$11$	−35.0000	−0.959354	−0.479677	−	0.877445i	$-0.659246\pi$
$11$	−35.0000	−0.959354	−0.479677	+	0.877445i	$0.659246\pi$
$12$	0	0
$13$	−66.0000	−1.40809	−0.704043	−	0.710158i	$-0.748624\pi$
$13$	−66.0000	−1.40809	−0.704043	+	0.710158i	$0.748624\pi$
$14$	0	0
$15$	7.00000	0.120493
$16$	0	0
$17$	−59.0000	−0.841741	−0.420871	−	0.907121i	$-0.638275\pi$
$17$	−59.0000	−0.841741	−0.420871	+	0.907121i	$0.638275\pi$
$18$	0	0
$19$	137.000	1.65421	0.827104	−	0.562049i	$-0.189987\pi$
$19$	137.000	1.65421	0.827104	+	0.562049i	$0.189987\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	7.00000	0.0634609	0.0317305	−	0.999496i	$-0.489898\pi$
$23$	7.00000	0.0634609	0.0317305	+	0.999496i	$0.489898\pi$
$24$	0	0
$25$	−76.0000	−0.608000
$26$	0	0
$27$	53.0000	0.377772
$28$	0	0
$29$	106.000	0.678748	0.339374	−	0.940651i	$-0.389785\pi$
$29$	106.000	0.678748	0.339374	+	0.940651i	$0.389785\pi$
$30$	0	0
$31$	75.0000	0.434529	0.217264	−	0.976113i	$-0.430287\pi$
$31$	75.0000	0.434529	0.217264	+	0.976113i	$0.430287\pi$
$32$	0	0
$33$	35.0000	0.184628
$34$	0	0
$35$	0	0
$36$	0	0
$37$	11.0000	0.0488754	0.0244377	−	0.999701i	$-0.492220\pi$
$37$	11.0000	0.0488754	0.0244377	+	0.999701i	$0.492220\pi$
$38$	0	0
$39$	66.0000	0.270986
$40$	0	0
$41$	498.000	1.89694	0.948470	−	0.316867i	$-0.102631\pi$
$41$	498.000	1.89694	0.948470	+	0.316867i	$0.102631\pi$
$42$	0	0
$43$	−260.000	−0.922084	−0.461042	−	0.887378i	$-0.652524\pi$
$43$	−260.000	−0.922084	−0.461042	+	0.887378i	$0.652524\pi$
$44$	0	0
$45$	182.000	0.602910
$46$	0	0
$47$	−171.000	−0.530700	−0.265350	−	0.964152i	$-0.585488\pi$
$47$	−171.000	−0.530700	−0.265350	+	0.964152i	$0.585488\pi$
$48$	0	0
$49$	0	0
$50$	0	0
$51$	59.0000	0.161993
$52$	0	0
$53$	−417.000	−1.08074	−0.540371	−	0.841427i	$-0.681716\pi$
$53$	−417.000	−1.08074	−0.540371	+	0.841427i	$0.681716\pi$
$54$	0	0
$55$	245.000	0.600651
$56$	0	0
$57$	−137.000	−0.318353
$58$	0	0
$59$	−17.0000	−0.0375121	−0.0187560	−	0.999824i	$-0.505971\pi$
$59$	−17.0000	−0.0375121	−0.0187560	+	0.999824i	$0.505971\pi$
$60$	0	0
$61$	−51.0000	−0.107047	−0.0535236	−	0.998567i	$-0.517045\pi$
$61$	−51.0000	−0.107047	−0.0535236	+	0.998567i	$0.517045\pi$
$62$	0	0
$63$	0	0
$64$	0	0
$65$	462.000	0.881601
$66$	0	0
$67$	−439.000	−0.800483	−0.400242	−	0.916410i	$-0.631074\pi$
$67$	−439.000	−0.800483	−0.400242	+	0.916410i	$0.631074\pi$
$68$	0	0
$69$	−7.00000	−0.0122131
$70$	0	0
$71$	784.000	1.31047	0.655237	−	0.755423i	$-0.272569\pi$
$71$	784.000	1.31047	0.655237	+	0.755423i	$0.272569\pi$
$72$	0	0
$73$	−295.000	−0.472974	−0.236487	−	0.971635i	$-0.575996\pi$
$73$	−295.000	−0.472974	−0.236487	+	0.971635i	$0.575996\pi$
$74$	0	0
$75$	76.0000	0.117010
$76$	0	0
$77$	0	0
$78$	0	0
$79$	495.000	0.704960	0.352480	−	0.935819i	$-0.385338\pi$
$79$	495.000	0.704960	0.352480	+	0.935819i	$0.385338\pi$
$80$	0	0
$81$	649.000	0.890261
$82$	0	0
$83$	932.000	1.23253	0.616267	−	0.787537i	$-0.288644\pi$
$83$	932.000	1.23253	0.616267	+	0.787537i	$0.288644\pi$
$84$	0	0
$85$	413.000	0.527013
$86$	0	0
$87$	−106.000	−0.130625
$88$	0	0
$89$	873.000	1.03975	0.519875	−	0.854242i	$-0.325978\pi$
$89$	873.000	1.03975	0.519875	+	0.854242i	$0.325978\pi$
$90$	0	0
$91$	0	0
$92$	0	0
$93$	−75.0000	−0.0836251
$94$	0	0
$95$	−959.000	−1.03570
$96$	0	0
$97$	290.000	0.303557	0.151779	−	0.988415i	$-0.451500\pi$
$97$	290.000	0.303557	0.151779	+	0.988415i	$0.451500\pi$
$98$	0	0
$99$	910.000	0.923823
$100$	0	0
$101$	1085.00	1.06893	0.534463	−	0.845192i	$-0.320514\pi$
$101$	1085.00	1.06893	0.534463	+	0.845192i	$0.320514\pi$
$102$	0	0
$103$	1553.00	1.48565	0.742823	−	0.669487i	$-0.233486\pi$
$103$	1553.00	1.48565	0.742823	+	0.669487i	$0.233486\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−129.000	−0.116550	−0.0582752	−	0.998301i	$-0.518560\pi$
$107$	−129.000	−0.116550	−0.0582752	+	0.998301i	$0.518560\pi$
$108$	0	0
$109$	−965.000	−0.847984	−0.423992	−	0.905666i	$-0.639372\pi$
$109$	−965.000	−0.847984	−0.423992	+	0.905666i	$0.639372\pi$
$110$	0	0
$111$	−11.0000	−0.00940607
$112$	0	0
$113$	−50.0000	−0.0416248	−0.0208124	−	0.999783i	$-0.506625\pi$
$113$	−50.0000	−0.0416248	−0.0208124	+	0.999783i	$0.506625\pi$
$114$	0	0
$115$	−49.0000	−0.0397328
$116$	0	0
$117$	1716.00	1.35593
$118$	0	0
$119$	0	0
$120$	0	0
$121$	−106.000	−0.0796394
$122$	0	0
$123$	−498.000	−0.365066
$124$	0	0
$125$	1407.00	1.00677
$126$	0	0
$127$	−936.000	−0.653989	−0.326994	−	0.945026i	$-0.606036\pi$
$127$	−936.000	−0.653989	−0.326994	+	0.945026i	$0.606036\pi$
$128$	0	0
$129$	260.000	0.177455
$130$	0	0
$131$	−755.000	−0.503547	−0.251773	−	0.967786i	$-0.581014\pi$
$131$	−755.000	−0.503547	−0.251773	+	0.967786i	$0.581014\pi$
$132$	0	0
$133$	0	0
$134$	0	0
$135$	−371.000	−0.236523
$136$	0	0
$137$	−2357.00	−1.46987	−0.734935	−	0.678138i	$-0.762787\pi$
$137$	−2357.00	−1.46987	−0.734935	+	0.678138i	$0.762787\pi$
$138$	0	0
$139$	28.0000	0.0170858	0.00854291	−	0.999964i	$-0.497281\pi$
$139$	28.0000	0.0170858	0.00854291	+	0.999964i	$0.497281\pi$
$140$	0	0
$141$	171.000	0.102133
$142$	0	0
$143$	2310.00	1.35085
$144$	0	0
$145$	−742.000	−0.424964
$146$	0	0
$147$	0	0
$148$	0	0
$149$	2295.00	1.26184	0.630919	−	0.775849i	$-0.282678\pi$
$149$	2295.00	1.26184	0.630919	+	0.775849i	$0.282678\pi$
$150$	0	0
$151$	1109.00	0.597676	0.298838	−	0.954304i	$-0.403401\pi$
$151$	1109.00	0.597676	0.298838	+	0.954304i	$0.403401\pi$
$152$	0	0
$153$	1534.00	0.810566
$154$	0	0
$155$	−525.000	−0.272058
$156$	0	0
$157$	−1559.00	−0.792495	−0.396248	−	0.918144i	$-0.629688\pi$
$157$	−1559.00	−0.792495	−0.396248	+	0.918144i	$0.629688\pi$
$158$	0	0
$159$	417.000	0.207989
$160$	0	0
$161$	0	0
$162$	0	0
$163$	2251.00	1.08167	0.540834	−	0.841129i	$-0.318109\pi$
$163$	2251.00	1.08167	0.540834	+	0.841129i	$0.318109\pi$
$164$	0	0
$165$	−245.000	−0.115595
$166$	0	0
$167$	2788.00	1.29187	0.645934	−	0.763393i	$-0.276468\pi$
$167$	2788.00	1.29187	0.645934	+	0.763393i	$0.276468\pi$
$168$	0	0
$169$	2159.00	0.982704
$170$	0	0
$171$	−3562.00	−1.59294
$172$	0	0
$173$	−1579.00	−0.693926	−0.346963	−	0.937879i	$-0.612787\pi$
$173$	−1579.00	−0.693926	−0.346963	+	0.937879i	$0.612787\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	17.0000	0.00721920
$178$	0	0
$179$	−2451.00	−1.02344	−0.511722	−	0.859151i	$-0.670992\pi$
$179$	−2451.00	−1.02344	−0.511722	+	0.859151i	$0.670992\pi$
$180$	0	0
$181$	1170.00	0.480472	0.240236	−	0.970715i	$-0.422775\pi$
$181$	1170.00	0.480472	0.240236	+	0.970715i	$0.422775\pi$
$182$	0	0
$183$	51.0000	0.0206012
$184$	0	0
$185$	−77.0000	−0.0306008
$186$	0	0
$187$	2065.00	0.807528
$188$	0	0
$189$	0	0
$190$	0	0
$191$	1275.00	0.483014	0.241507	−	0.970399i	$-0.422358\pi$
$191$	1275.00	0.483014	0.241507	+	0.970399i	$0.422358\pi$
$192$	0	0
$193$	35.0000	0.0130537	0.00652683	−	0.999979i	$-0.497922\pi$
$193$	35.0000	0.0130537	0.00652683	+	0.999979i	$0.497922\pi$
$194$	0	0
$195$	−462.000	−0.169664
$196$	0	0
$197$	−2734.00	−0.988779	−0.494389	−	0.869241i	$-0.664608\pi$
$197$	−2734.00	−0.988779	−0.494389	+	0.869241i	$0.664608\pi$
$198$	0	0
$199$	2243.00	0.799005	0.399503	−	0.916732i	$-0.369183\pi$
$199$	2243.00	0.799005	0.399503	+	0.916732i	$0.369183\pi$
$200$	0	0
$201$	439.000	0.154053
$202$	0	0
$203$	0	0
$204$	0	0
$205$	−3486.00	−1.18767
$206$	0	0
$207$	−182.000	−0.0611105
$208$	0	0
$209$	−4795.00	−1.58697
$210$	0	0
$211$	−1172.00	−0.382388	−0.191194	−	0.981552i	$-0.561236\pi$
$211$	−1172.00	−0.382388	−0.191194	+	0.981552i	$0.561236\pi$
$212$	0	0
$213$	−784.000	−0.252201
$214$	0	0
$215$	1820.00	0.577316
$216$	0	0
$217$	0	0
$218$	0	0
$219$	295.000	0.0910240
$220$	0	0
$221$	3894.00	1.18524
$222$	0	0
$223$	2024.00	0.607790	0.303895	−	0.952706i	$-0.401713\pi$
$223$	2024.00	0.607790	0.303895	+	0.952706i	$0.401713\pi$
$224$	0	0
$225$	1976.00	0.585481
$226$	0	0
$227$	2571.00	0.751732	0.375866	−	0.926674i	$-0.377345\pi$
$227$	2571.00	0.751732	0.375866	+	0.926674i	$0.377345\pi$
$228$	0	0
$229$	−895.000	−0.258268	−0.129134	−	0.991627i	$-0.541220\pi$
$229$	−895.000	−0.258268	−0.129134	+	0.991627i	$0.541220\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	1787.00	0.502447	0.251224	−	0.967929i	$-0.419167\pi$
$233$	1787.00	0.502447	0.251224	+	0.967929i	$0.419167\pi$
$234$	0	0
$235$	1197.00	0.332271
$236$	0	0
$237$	−495.000	−0.135670
$238$	0	0
$239$	5100.00	1.38030	0.690150	−	0.723667i	$-0.257545\pi$
$239$	5100.00	1.38030	0.690150	+	0.723667i	$0.257545\pi$
$240$	0	0
$241$	4177.00	1.11645	0.558225	−	0.829690i	$-0.311483\pi$
$241$	4177.00	1.11645	0.558225	+	0.829690i	$0.311483\pi$
$242$	0	0
$243$	−2080.00	−0.549103
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−9042.00	−2.32927
$248$	0	0
$249$	−932.000	−0.237201
$250$	0	0
$251$	−4680.00	−1.17689	−0.588444	−	0.808538i	$-0.700259\pi$
$251$	−4680.00	−1.17689	−0.588444	+	0.808538i	$0.700259\pi$
$252$	0	0
$253$	−245.000	−0.0608815
$254$	0	0
$255$	−413.000	−0.101424
$256$	0	0
$257$	1749.00	0.424512	0.212256	−	0.977214i	$-0.431919\pi$
$257$	1749.00	0.424512	0.212256	+	0.977214i	$0.431919\pi$
$258$	0	0
$259$	0	0
$260$	0	0
$261$	−2756.00	−0.653610
$262$	0	0
$263$	4473.00	1.04873	0.524367	−	0.851492i	$-0.324302\pi$
$263$	4473.00	1.04873	0.524367	+	0.851492i	$0.324302\pi$
$264$	0	0
$265$	2919.00	0.676652
$266$	0	0
$267$	−873.000	−0.200100
$268$	0	0
$269$	−1975.00	−0.447650	−0.223825	−	0.974629i	$-0.571854\pi$
$269$	−1975.00	−0.447650	−0.223825	+	0.974629i	$0.571854\pi$
$270$	0	0
$271$	−8439.00	−1.89163	−0.945817	−	0.324701i	$-0.894736\pi$
$271$	−8439.00	−1.89163	−0.945817	+	0.324701i	$0.894736\pi$
$272$	0	0
$273$	0	0
$274$	0	0
$275$	2660.00	0.583287
$276$	0	0
$277$	527.000	0.114312	0.0571559	−	0.998365i	$-0.481797\pi$
$277$	527.000	0.114312	0.0571559	+	0.998365i	$0.481797\pi$
$278$	0	0
$279$	−1950.00	−0.418435
$280$	0	0
$281$	−202.000	−0.0428837	−0.0214418	−	0.999770i	$-0.506826\pi$
$281$	−202.000	−0.0428837	−0.0214418	+	0.999770i	$0.506826\pi$
$282$	0	0
$283$	−7949.00	−1.66968	−0.834839	−	0.550494i	$-0.814439\pi$
$283$	−7949.00	−1.66968	−0.834839	+	0.550494i	$0.814439\pi$
$284$	0	0
$285$	959.000	0.199320
$286$	0	0
$287$	0	0
$288$	0	0
$289$	−1432.00	−0.291472
$290$	0	0
$291$	−290.000	−0.0584196
$292$	0	0
$293$	−318.000	−0.0634053	−0.0317027	−	0.999497i	$-0.510093\pi$
$293$	−318.000	−0.0634053	−0.0317027	+	0.999497i	$0.510093\pi$
$294$	0	0
$295$	119.000	0.0234863
$296$	0	0
$297$	−1855.00	−0.362418
$298$	0	0
$299$	−462.000	−0.0893584
$300$	0	0
$301$	0	0
$302$	0	0
$303$	−1085.00	−0.205715
$304$	0	0
$305$	357.000	0.0670222
$306$	0	0
$307$	−8132.00	−1.51178	−0.755892	−	0.654696i	$-0.772797\pi$
$307$	−8132.00	−1.51178	−0.755892	+	0.654696i	$0.772797\pi$
$308$	0	0
$309$	−1553.00	−0.285913
$310$	0	0
$311$	−929.000	−0.169385	−0.0846925	−	0.996407i	$-0.526991\pi$
$311$	−929.000	−0.169385	−0.0846925	+	0.996407i	$0.526991\pi$
$312$	0	0
$313$	209.000	0.0377424	0.0188712	−	0.999822i	$-0.493993\pi$
$313$	209.000	0.0377424	0.0188712	+	0.999822i	$0.493993\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	7131.00	1.26346	0.631730	−	0.775188i	$-0.282345\pi$
$317$	7131.00	1.26346	0.631730	+	0.775188i	$0.282345\pi$
$318$	0	0
$319$	−3710.00	−0.651160
$320$	0	0
$321$	129.000	0.0224301
$322$	0	0
$323$	−8083.00	−1.39242
$324$	0	0
$325$	5016.00	0.856116
$326$	0	0
$327$	965.000	0.163195
$328$	0	0
$329$	0	0
$330$	0	0
$331$	6571.00	1.09116	0.545581	−	0.838058i	$-0.316309\pi$
$331$	6571.00	1.09116	0.545581	+	0.838058i	$0.316309\pi$
$332$	0	0
$333$	−286.000	−0.0470652
$334$	0	0
$335$	3073.00	0.501182
$336$	0	0
$337$	−11466.0	−1.85339	−0.926696	−	0.375813i	$-0.877364\pi$
$337$	−11466.0	−1.85339	−0.926696	+	0.375813i	$0.877364\pi$
$338$	0	0
$339$	50.0000	0.00801070
$340$	0	0
$341$	−2625.00	−0.416867
$342$	0	0
$343$	0	0
$344$	0	0
$345$	49.0000	0.00764658
$346$	0	0
$347$	9777.00	1.51256	0.756278	−	0.654251i	$-0.227016\pi$
$347$	9777.00	1.51256	0.756278	+	0.654251i	$0.227016\pi$
$348$	0	0
$349$	−11914.0	−1.82734	−0.913670	−	0.406456i	$-0.866764\pi$
$349$	−11914.0	−1.82734	−0.913670	+	0.406456i	$0.866764\pi$
$350$	0	0
$351$	−3498.00	−0.531936
$352$	0	0
$353$	−9123.00	−1.37555	−0.687774	−	0.725925i	$-0.741412\pi$
$353$	−9123.00	−1.37555	−0.687774	+	0.725925i	$0.741412\pi$
$354$	0	0
$355$	−5488.00	−0.820487
$356$	0	0
$357$	0	0
$358$	0	0
$359$	−8149.00	−1.19802	−0.599008	−	0.800743i	$-0.704438\pi$
$359$	−8149.00	−1.19802	−0.599008	+	0.800743i	$0.704438\pi$
$360$	0	0
$361$	11910.0	1.73640
$362$	0	0
$363$	106.000	0.0153266
$364$	0	0
$365$	2065.00	0.296129
$366$	0	0
$367$	9671.00	1.37554	0.687769	−	0.725930i	$-0.258590\pi$
$367$	9671.00	1.37554	0.687769	+	0.725930i	$0.258590\pi$
$368$	0	0
$369$	−12948.0	−1.82668
$370$	0	0
$371$	0	0
$372$	0	0
$373$	−4109.00	−0.570391	−0.285196	−	0.958469i	$-0.592059\pi$
$373$	−4109.00	−0.570391	−0.285196	+	0.958469i	$0.592059\pi$
$374$	0	0
$375$	−1407.00	−0.193752
$376$	0	0
$377$	−6996.00	−0.955736
$378$	0	0
$379$	3488.00	0.472735	0.236367	−	0.971664i	$-0.424043\pi$
$379$	3488.00	0.472735	0.236367	+	0.971664i	$0.424043\pi$
$380$	0	0
$381$	936.000	0.125860
$382$	0	0
$383$	8717.00	1.16297	0.581485	−	0.813557i	$-0.302472\pi$
$383$	8717.00	1.16297	0.581485	+	0.813557i	$0.302472\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	6760.00	0.887933
$388$	0	0
$389$	163.000	0.0212453	0.0106227	−	0.999944i	$-0.496619\pi$
$389$	163.000	0.0212453	0.0106227	+	0.999944i	$0.496619\pi$
$390$	0	0
$391$	−413.000	−0.0534177
$392$	0	0
$393$	755.000	0.0969077
$394$	0	0
$395$	−3465.00	−0.441375
$396$	0	0
$397$	−999.000	−0.126293	−0.0631466	−	0.998004i	$-0.520114\pi$
$397$	−999.000	−0.126293	−0.0631466	+	0.998004i	$0.520114\pi$
$398$	0	0
$399$	0	0
$400$	0	0
$401$	−14757.0	−1.83773	−0.918865	−	0.394573i	$-0.870893\pi$
$401$	−14757.0	−1.83773	−0.918865	+	0.394573i	$0.870893\pi$
$402$	0	0
$403$	−4950.00	−0.611854
$404$	0	0
$405$	−4543.00	−0.557391
$406$	0	0
$407$	−385.000	−0.0468888
$408$	0	0
$409$	133.000	0.0160793	0.00803964	−	0.999968i	$-0.497441\pi$
$409$	133.000	0.0160793	0.00803964	+	0.999968i	$0.497441\pi$
$410$	0	0
$411$	2357.00	0.282876
$412$	0	0
$413$	0	0
$414$	0	0
$415$	−6524.00	−0.771688
$416$	0	0
$417$	−28.0000	−0.00328817
$418$	0	0
$419$	−6420.00	−0.748538	−0.374269	−	0.927320i	$-0.622106\pi$
$419$	−6420.00	−0.748538	−0.374269	+	0.927320i	$0.622106\pi$
$420$	0	0
$421$	10266.0	1.18844	0.594221	−	0.804302i	$-0.297460\pi$
$421$	10266.0	1.18844	0.594221	+	0.804302i	$0.297460\pi$
$422$	0	0
$423$	4446.00	0.511045
$424$	0	0
$425$	4484.00	0.511779
$426$	0	0
$427$	0	0
$428$	0	0
$429$	−2310.00	−0.259972
$430$	0	0
$431$	15213.0	1.70020	0.850098	−	0.526625i	$-0.176543\pi$
$431$	15213.0	1.70020	0.850098	+	0.526625i	$0.176543\pi$
$432$	0	0
$433$	1378.00	0.152939	0.0764693	−	0.997072i	$-0.475635\pi$
$433$	1378.00	0.152939	0.0764693	+	0.997072i	$0.475635\pi$
$434$	0	0
$435$	742.000	0.0817843
$436$	0	0
$437$	959.000	0.104978
$438$	0	0
$439$	−2763.00	−0.300389	−0.150195	−	0.988656i	$-0.547990\pi$
$439$	−2763.00	−0.300389	−0.150195	+	0.988656i	$0.547990\pi$
$440$	0	0
$441$	0	0
$442$	0	0
$443$	−5849.00	−0.627301	−0.313651	−	0.949538i	$-0.601552\pi$
$443$	−5849.00	−0.627301	−0.313651	+	0.949538i	$0.601552\pi$
$444$	0	0
$445$	−6111.00	−0.650987
$446$	0	0
$447$	−2295.00	−0.242841
$448$	0	0
$449$	4582.00	0.481599	0.240799	−	0.970575i	$-0.422590\pi$
$449$	4582.00	0.481599	0.240799	+	0.970575i	$0.422590\pi$
$450$	0	0
$451$	−17430.0	−1.81984
$452$	0	0
$453$	−1109.00	−0.115023
$454$	0	0
$455$	0	0
$456$	0	0
$457$	11551.0	1.18235	0.591174	−	0.806544i	$-0.298665\pi$
$457$	11551.0	1.18235	0.591174	+	0.806544i	$0.298665\pi$
$458$	0	0
$459$	−3127.00	−0.317987
$460$	0	0
$461$	9494.00	0.959175	0.479587	−	0.877494i	$-0.340786\pi$
$461$	9494.00	0.959175	0.479587	+	0.877494i	$0.340786\pi$
$462$	0	0
$463$	10160.0	1.01982	0.509908	−	0.860229i	$-0.329679\pi$
$463$	10160.0	1.01982	0.509908	+	0.860229i	$0.329679\pi$
$464$	0	0
$465$	525.000	0.0523576
$466$	0	0
$467$	−1307.00	−0.129509	−0.0647545	−	0.997901i	$-0.520626\pi$
$467$	−1307.00	−0.129509	−0.0647545	+	0.997901i	$0.520626\pi$
$468$	0	0
$469$	0	0
$470$	0	0
$471$	1559.00	0.152516
$472$	0	0
$473$	9100.00	0.884606
$474$	0	0
$475$	−10412.0	−1.00576
$476$	0	0
$477$	10842.0	1.04072
$478$	0	0
$479$	18287.0	1.74437	0.872186	−	0.489174i	$-0.162702\pi$
$479$	18287.0	1.74437	0.872186	+	0.489174i	$0.162702\pi$
$480$	0	0
$481$	−726.000	−0.0688207
$482$	0	0
$483$	0	0
$484$	0	0
$485$	−2030.00	−0.190057
$486$	0	0
$487$	14953.0	1.39135	0.695673	−	0.718359i	$-0.255106\pi$
$487$	14953.0	1.39135	0.695673	+	0.718359i	$0.255106\pi$
$488$	0	0
$489$	−2251.00	−0.208167
$490$	0	0
$491$	−14352.0	−1.31914	−0.659569	−	0.751644i	$-0.729261\pi$
$491$	−14352.0	−1.31914	−0.659569	+	0.751644i	$0.729261\pi$
$492$	0	0
$493$	−6254.00	−0.571331
$494$	0	0
$495$	−6370.00	−0.578404
$496$	0	0
$497$	0	0
$498$	0	0
$499$	5531.00	0.496196	0.248098	−	0.968735i	$-0.420195\pi$
$499$	5531.00	0.496196	0.248098	+	0.968735i	$0.420195\pi$
$500$	0	0
$501$	−2788.00	−0.248620
$502$	0	0
$503$	8400.00	0.744607	0.372304	−	0.928111i	$-0.378568\pi$
$503$	8400.00	0.744607	0.372304	+	0.928111i	$0.378568\pi$
$504$	0	0
$505$	−7595.00	−0.669254
$506$	0	0
$507$	−2159.00	−0.189121
$508$	0	0
$509$	2385.00	0.207688	0.103844	−	0.994594i	$-0.466886\pi$
$509$	2385.00	0.207688	0.103844	+	0.994594i	$0.466886\pi$
$510$	0	0
$511$	0	0
$512$	0	0
$513$	7261.00	0.624914
$514$	0	0
$515$	−10871.0	−0.930162
$516$	0	0
$517$	5985.00	0.509130
$518$	0	0
$519$	1579.00	0.133546
$520$	0	0
$521$	9153.00	0.769674	0.384837	−	0.922985i	$-0.374258\pi$
$521$	9153.00	0.769674	0.384837	+	0.922985i	$0.374258\pi$
$522$	0	0
$523$	−13807.0	−1.15437	−0.577187	−	0.816612i	$-0.695850\pi$
$523$	−13807.0	−1.15437	−0.577187	+	0.816612i	$0.695850\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−4425.00	−0.365761
$528$	0	0
$529$	−12118.0	−0.995973
$530$	0	0
$531$	442.000	0.0361227
$532$	0	0
$533$	−32868.0	−2.67105
$534$	0	0
$535$	903.000	0.0729721
$536$	0	0
$537$	2451.00	0.196962
$538$	0	0
$539$	0	0
$540$	0	0
$541$	8175.00	0.649669	0.324834	−	0.945771i	$-0.394691\pi$
$541$	8175.00	0.649669	0.324834	+	0.945771i	$0.394691\pi$
$542$	0	0
$543$	−1170.00	−0.0924669
$544$	0	0
$545$	6755.00	0.530922
$546$	0	0
$547$	−4656.00	−0.363942	−0.181971	−	0.983304i	$-0.558248\pi$
$547$	−4656.00	−0.363942	−0.181971	+	0.983304i	$0.558248\pi$
$548$	0	0
$549$	1326.00	0.103083
$550$	0	0
$551$	14522.0	1.12279
$552$	0	0
$553$	0	0
$554$	0	0
$555$	77.0000	0.00588913
$556$	0	0
$557$	7003.00	0.532723	0.266361	−	0.963873i	$-0.414179\pi$
$557$	7003.00	0.532723	0.266361	+	0.963873i	$0.414179\pi$
$558$	0	0
$559$	17160.0	1.29837
$560$	0	0
$561$	−2065.00	−0.155409
$562$	0	0
$563$	−19753.0	−1.47867	−0.739334	−	0.673339i	$-0.764859\pi$
$563$	−19753.0	−1.47867	−0.739334	+	0.673339i	$0.764859\pi$
$564$	0	0
$565$	350.000	0.0260613
$566$	0	0
$567$	0	0
$568$	0	0
$569$	−6897.00	−0.508150	−0.254075	−	0.967185i	$-0.581771\pi$
$569$	−6897.00	−0.508150	−0.254075	+	0.967185i	$0.581771\pi$
$570$	0	0
$571$	−24915.0	−1.82603	−0.913013	−	0.407932i	$-0.866250\pi$
$571$	−24915.0	−1.82603	−0.913013	+	0.407932i	$0.866250\pi$
$572$	0	0
$573$	−1275.00	−0.0929562
$574$	0	0
$575$	−532.000	−0.0385842
$576$	0	0
$577$	−127.000	−0.00916305	−0.00458152	−	0.999990i	$-0.501458\pi$
$577$	−127.000	−0.00916305	−0.00458152	+	0.999990i	$0.501458\pi$
$578$	0	0
$579$	−35.0000	−0.00251218
$580$	0	0
$581$	0	0
$582$	0	0
$583$	14595.0	1.03681
$584$	0	0
$585$	−12012.0	−0.848949
$586$	0	0
$587$	9044.00	0.635921	0.317961	−	0.948104i	$-0.397002\pi$
$587$	9044.00	0.635921	0.317961	+	0.948104i	$0.397002\pi$
$588$	0	0
$589$	10275.0	0.718801
$590$	0	0
$591$	2734.00	0.190291
$592$	0	0
$593$	10701.0	0.741041	0.370521	−	0.928824i	$-0.379179\pi$
$593$	10701.0	0.741041	0.370521	+	0.928824i	$0.379179\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−2243.00	−0.153769
$598$	0	0
$599$	−20799.0	−1.41874	−0.709369	−	0.704837i	$-0.751020\pi$
$599$	−20799.0	−1.41874	−0.709369	+	0.704837i	$0.751020\pi$
$600$	0	0
$601$	1402.00	0.0951560	0.0475780	−	0.998868i	$-0.484850\pi$
$601$	1402.00	0.0951560	0.0475780	+	0.998868i	$0.484850\pi$
$602$	0	0
$603$	11414.0	0.770836
$604$	0	0
$605$	742.000	0.0498621
$606$	0	0
$607$	6525.00	0.436312	0.218156	−	0.975914i	$-0.429996\pi$
$607$	6525.00	0.436312	0.218156	+	0.975914i	$0.429996\pi$
$608$	0	0
$609$	0	0
$610$	0	0
$611$	11286.0	0.747271
$612$	0	0
$613$	15051.0	0.991687	0.495844	−	0.868412i	$-0.334859\pi$
$613$	15051.0	0.991687	0.495844	+	0.868412i	$0.334859\pi$
$614$	0	0
$615$	3486.00	0.228568
$616$	0	0
$617$	11150.0	0.727524	0.363762	−	0.931492i	$-0.381492\pi$
$617$	11150.0	0.727524	0.363762	+	0.931492i	$0.381492\pi$
$618$	0	0
$619$	3415.00	0.221745	0.110873	−	0.993835i	$-0.464635\pi$
$619$	3415.00	0.221745	0.110873	+	0.993835i	$0.464635\pi$
$620$	0	0
$621$	371.000	0.0239738
$622$	0	0
$623$	0	0
$624$	0	0
$625$	−349.000	−0.0223360
$626$	0	0
$627$	4795.00	0.305413
$628$	0	0
$629$	−649.000	−0.0411404
$630$	0	0
$631$	21184.0	1.33648	0.668242	−	0.743944i	$-0.267047\pi$
$631$	21184.0	1.33648	0.668242	+	0.743944i	$0.267047\pi$
$632$	0	0
$633$	1172.00	0.0735905
$634$	0	0
$635$	6552.00	0.409462
$636$	0	0
$637$	0	0
$638$	0	0
$639$	−20384.0	−1.26194
$640$	0	0
$641$	−10705.0	−0.659629	−0.329814	−	0.944046i	$-0.606986\pi$
$641$	−10705.0	−0.659629	−0.329814	+	0.944046i	$0.606986\pi$
$642$	0	0
$643$	6860.00	0.420734	0.210367	−	0.977622i	$-0.432534\pi$
$643$	6860.00	0.420734	0.210367	+	0.977622i	$0.432534\pi$
$644$	0	0
$645$	−1820.00	−0.111105
$646$	0	0
$647$	14463.0	0.878824	0.439412	−	0.898286i	$-0.355187\pi$
$647$	14463.0	0.878824	0.439412	+	0.898286i	$0.355187\pi$
$648$	0	0
$649$	595.000	0.0359874
$650$	0	0
$651$	0	0
$652$	0	0
$653$	5979.00	0.358310	0.179155	−	0.983821i	$-0.442664\pi$
$653$	5979.00	0.358310	0.179155	+	0.983821i	$0.442664\pi$
$654$	0	0
$655$	5285.00	0.315270
$656$	0	0
$657$	7670.00	0.455457
$658$	0	0
$659$	6940.00	0.410234	0.205117	−	0.978737i	$-0.434243\pi$
$659$	6940.00	0.410234	0.205117	+	0.978737i	$0.434243\pi$
$660$	0	0
$661$	−13399.0	−0.788443	−0.394221	−	0.919015i	$-0.628986\pi$
$661$	−13399.0	−0.788443	−0.394221	+	0.919015i	$0.628986\pi$
$662$	0	0
$663$	−3894.00	−0.228100
$664$	0	0
$665$	0	0
$666$	0	0
$667$	742.000	0.0430740
$668$	0	0
$669$	−2024.00	−0.116969
$670$	0	0
$671$	1785.00	0.102696
$672$	0	0
$673$	29510.0	1.69023	0.845117	−	0.534582i	$-0.179531\pi$
$673$	29510.0	1.69023	0.845117	+	0.534582i	$0.179531\pi$
$674$	0	0
$675$	−4028.00	−0.229686
$676$	0	0
$677$	26001.0	1.47607	0.738035	−	0.674762i	$-0.235754\pi$
$677$	26001.0	1.47607	0.738035	+	0.674762i	$0.235754\pi$
$678$	0	0
$679$	0	0
$680$	0	0
$681$	−2571.00	−0.144671
$682$	0	0
$683$	8805.00	0.493285	0.246643	−	0.969106i	$-0.420673\pi$
$683$	8805.00	0.493285	0.246643	+	0.969106i	$0.420673\pi$
$684$	0	0
$685$	16499.0	0.920284
$686$	0	0
$687$	895.000	0.0497036
$688$	0	0
$689$	27522.0	1.52178
$690$	0	0
$691$	28685.0	1.57920	0.789601	−	0.613620i	$-0.210287\pi$
$691$	28685.0	1.57920	0.789601	+	0.613620i	$0.210287\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	−196.000	−0.0106974
$696$	0	0
$697$	−29382.0	−1.59673
$698$	0	0
$699$	−1787.00	−0.0966961
$700$	0	0
$701$	−3146.00	−0.169505	−0.0847523	−	0.996402i	$-0.527010\pi$
$701$	−3146.00	−0.169505	−0.0847523	+	0.996402i	$0.527010\pi$
$702$	0	0
$703$	1507.00	0.0808500
$704$	0	0
$705$	−1197.00	−0.0639456
$706$	0	0
$707$	0	0
$708$	0	0
$709$	1259.00	0.0666893	0.0333447	−	0.999444i	$-0.489384\pi$
$709$	1259.00	0.0666893	0.0333447	+	0.999444i	$0.489384\pi$
$710$	0	0
$711$	−12870.0	−0.678851
$712$	0	0
$713$	525.000	0.0275756
$714$	0	0
$715$	−16170.0	−0.845767
$716$	0	0
$717$	−5100.00	−0.265639
$718$	0	0
$719$	16425.0	0.851946	0.425973	−	0.904736i	$-0.359932\pi$
$719$	16425.0	0.851946	0.425973	+	0.904736i	$0.359932\pi$
$720$	0	0
$721$	0	0
$722$	0	0
$723$	−4177.00	−0.214861
$724$	0	0
$725$	−8056.00	−0.412679
$726$	0	0
$727$	−6032.00	−0.307723	−0.153861	−	0.988092i	$-0.549171\pi$
$727$	−6032.00	−0.307723	−0.153861	+	0.988092i	$0.549171\pi$
$728$	0	0
$729$	−15443.0	−0.784586
$730$	0	0
$731$	15340.0	0.776156
$732$	0	0
$733$	−15243.0	−0.768094	−0.384047	−	0.923314i	$-0.625470\pi$
$733$	−15243.0	−0.768094	−0.384047	+	0.923314i	$0.625470\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	15365.0	0.767947
$738$	0	0
$739$	10053.0	0.500414	0.250207	−	0.968192i	$-0.419501\pi$
$739$	10053.0	0.500414	0.250207	+	0.968192i	$0.419501\pi$
$740$	0	0
$741$	9042.00	0.448267
$742$	0	0
$743$	−24384.0	−1.20399	−0.601993	−	0.798501i	$-0.705627\pi$
$743$	−24384.0	−1.20399	−0.601993	+	0.798501i	$0.705627\pi$
$744$	0	0
$745$	−16065.0	−0.790035
$746$	0	0
$747$	−24232.0	−1.18688
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−11589.0	−0.563101	−0.281550	−	0.959546i	$-0.590849\pi$
$751$	−11589.0	−0.563101	−0.281550	+	0.959546i	$0.590849\pi$
$752$	0	0
$753$	4680.00	0.226492
$754$	0	0
$755$	−7763.00	−0.374205
$756$	0	0
$757$	14562.0	0.699161	0.349581	−	0.936906i	$-0.386324\pi$
$757$	14562.0	0.699161	0.349581	+	0.936906i	$0.386324\pi$
$758$	0	0
$759$	245.000	0.0117166
$760$	0	0
$761$	22765.0	1.08440	0.542201	−	0.840249i	$-0.317591\pi$
$761$	22765.0	1.08440	0.542201	+	0.840249i	$0.317591\pi$
$762$	0	0
$763$	0	0
$764$	0	0
$765$	−10738.0	−0.507494
$766$	0	0
$767$	1122.00	0.0528202
$768$	0	0
$769$	−3766.00	−0.176600	−0.0883000	−	0.996094i	$-0.528143\pi$
$769$	−3766.00	−0.176600	−0.0883000	+	0.996094i	$0.528143\pi$
$770$	0	0
$771$	−1749.00	−0.0816974
$772$	0	0
$773$	26861.0	1.24984	0.624918	−	0.780691i	$-0.285132\pi$
$773$	26861.0	1.24984	0.624918	+	0.780691i	$0.285132\pi$
$774$	0	0
$775$	−5700.00	−0.264194
$776$	0	0
$777$	0	0
$778$	0	0
$779$	68226.0	3.13793
$780$	0	0
$781$	−27440.0	−1.25721
$782$	0	0
$783$	5618.00	0.256412
$784$	0	0
$785$	10913.0	0.496180
$786$	0	0
$787$	−2097.00	−0.0949809	−0.0474905	−	0.998872i	$-0.515122\pi$
$787$	−2097.00	−0.0949809	−0.0474905	+	0.998872i	$0.515122\pi$
$788$	0	0
$789$	−4473.00	−0.201829
$790$	0	0
$791$	0	0
$792$	0	0
$793$	3366.00	0.150732
$794$	0	0
$795$	−2919.00	−0.130222
$796$	0	0
$797$	35334.0	1.57038	0.785191	−	0.619254i	$-0.212565\pi$
$797$	35334.0	1.57038	0.785191	+	0.619254i	$0.212565\pi$
$798$	0	0
$799$	10089.0	0.446712
$800$	0	0
$801$	−22698.0	−1.00124
$802$	0	0
$803$	10325.0	0.453750
$804$	0	0
$805$	0	0
$806$	0	0
$807$	1975.00	0.0861503
$808$	0	0
$809$	42535.0	1.84852	0.924259	−	0.381766i	$-0.124684\pi$
$809$	42535.0	1.84852	0.924259	+	0.381766i	$0.124684\pi$
$810$	0	0
$811$	30676.0	1.32821	0.664106	−	0.747638i	$-0.268812\pi$
$811$	30676.0	1.32821	0.664106	+	0.747638i	$0.268812\pi$
$812$	0	0
$813$	8439.00	0.364045
$814$	0	0
$815$	−15757.0	−0.677231
$816$	0	0
$817$	−35620.0	−1.52532
$818$	0	0
$819$	0	0
$820$	0	0
$821$	37343.0	1.58743	0.793715	−	0.608290i	$-0.208144\pi$
$821$	37343.0	1.58743	0.793715	+	0.608290i	$0.208144\pi$
$822$	0	0
$823$	−2815.00	−0.119228	−0.0596141	−	0.998222i	$-0.518987\pi$
$823$	−2815.00	−0.119228	−0.0596141	+	0.998222i	$0.518987\pi$
$824$	0	0
$825$	−2660.00	−0.112254
$826$	0	0
$827$	9276.00	0.390034	0.195017	−	0.980800i	$-0.437524\pi$
$827$	9276.00	0.390034	0.195017	+	0.980800i	$0.437524\pi$
$828$	0	0
$829$	−18571.0	−0.778043	−0.389021	−	0.921229i	$-0.627187\pi$
$829$	−18571.0	−0.778043	−0.389021	+	0.921229i	$0.627187\pi$
$830$	0	0
$831$	−527.000	−0.0219993
$832$	0	0
$833$	0	0
$834$	0	0
$835$	−19516.0	−0.808837
$836$	0	0
$837$	3975.00	0.164153
$838$	0	0
$839$	29048.0	1.19529	0.597645	−	0.801761i	$-0.296103\pi$
$839$	29048.0	1.19529	0.597645	+	0.801761i	$0.296103\pi$
$840$	0	0
$841$	−13153.0	−0.539301
$842$	0	0
$843$	202.000	0.00825297
$844$	0	0
$845$	−15113.0	−0.615270
$846$	0	0
$847$	0	0
$848$	0	0
$849$	7949.00	0.321330
$850$	0	0
$851$	77.0000	0.00310168
$852$	0	0
$853$	−32090.0	−1.28809	−0.644045	−	0.764988i	$-0.722745\pi$
$853$	−32090.0	−1.28809	−0.644045	+	0.764988i	$0.722745\pi$
$854$	0	0
$855$	24934.0	0.997339
$856$	0	0
$857$	24537.0	0.978026	0.489013	−	0.872277i	$-0.337357\pi$
$857$	24537.0	0.978026	0.489013	+	0.872277i	$0.337357\pi$
$858$	0	0
$859$	20825.0	0.827171	0.413585	−	0.910465i	$-0.364276\pi$
$859$	20825.0	0.827171	0.413585	+	0.910465i	$0.364276\pi$
$860$	0	0
$861$	0	0
$862$	0	0
$863$	22847.0	0.901183	0.450591	−	0.892730i	$-0.351213\pi$
$863$	22847.0	0.901183	0.450591	+	0.892730i	$0.351213\pi$
$864$	0	0
$865$	11053.0	0.434466
$866$	0	0
$867$	1432.00	0.0560937
$868$	0	0
$869$	−17325.0	−0.676307
$870$	0	0
$871$	28974.0	1.12715
$872$	0	0
$873$	−7540.00	−0.292314
$874$	0	0
$875$	0	0
$876$	0	0
$877$	−42737.0	−1.64553	−0.822763	−	0.568385i	$-0.807568\pi$
$877$	−42737.0	−1.64553	−0.822763	+	0.568385i	$0.807568\pi$
$878$	0	0
$879$	318.000	0.0122024
$880$	0	0
$881$	−6162.00	−0.235645	−0.117822	−	0.993035i	$-0.537591\pi$
$881$	−6162.00	−0.235645	−0.117822	+	0.993035i	$0.537591\pi$
$882$	0	0
$883$	−7748.00	−0.295290	−0.147645	−	0.989040i	$-0.547169\pi$
$883$	−7748.00	−0.295290	−0.147645	+	0.989040i	$0.547169\pi$
$884$	0	0
$885$	−119.000	−0.00451993
$886$	0	0
$887$	−25923.0	−0.981296	−0.490648	−	0.871358i	$-0.663240\pi$
$887$	−25923.0	−0.981296	−0.490648	+	0.871358i	$0.663240\pi$
$888$	0	0
$889$	0	0
$890$	0	0
$891$	−22715.0	−0.854075
$892$	0	0
$893$	−23427.0	−0.877889
$894$	0	0
$895$	17157.0	0.640777
$896$	0	0
$897$	462.000	0.0171970
$898$	0	0
$899$	7950.00	0.294936
$900$	0	0
$901$	24603.0	0.909706
$902$	0	0
$903$	0	0
$904$	0	0
$905$	−8190.00	−0.300823
$906$	0	0
$907$	−31935.0	−1.16911	−0.584556	−	0.811353i	$-0.698731\pi$
$907$	−31935.0	−1.16911	−0.584556	+	0.811353i	$0.698731\pi$
$908$	0	0
$909$	−28210.0	−1.02934
$910$	0	0
$911$	−3408.00	−0.123943	−0.0619715	−	0.998078i	$-0.519739\pi$
$911$	−3408.00	−0.123943	−0.0619715	+	0.998078i	$0.519739\pi$
$912$	0	0
$913$	−32620.0	−1.18244
$914$	0	0
$915$	−357.000	−0.0128984
$916$	0	0
$917$	0	0
$918$	0	0
$919$	−13909.0	−0.499255	−0.249628	−	0.968342i	$-0.580308\pi$
$919$	−13909.0	−0.499255	−0.249628	+	0.968342i	$0.580308\pi$
$920$	0	0
$921$	8132.00	0.290943
$922$	0	0
$923$	−51744.0	−1.84526
$924$	0	0
$925$	−836.000	−0.0297162
$926$	0	0
$927$	−40378.0	−1.43062
$928$	0	0
$929$	24537.0	0.866559	0.433279	−	0.901260i	$-0.357356\pi$
$929$	24537.0	0.866559	0.433279	+	0.901260i	$0.357356\pi$
$930$	0	0
$931$	0	0
$932$	0	0
$933$	929.000	0.0325982
$934$	0	0
$935$	−14455.0	−0.505593
$936$	0	0
$937$	32758.0	1.14211	0.571055	−	0.820912i	$-0.306534\pi$
$937$	32758.0	1.14211	0.571055	+	0.820912i	$0.306534\pi$
$938$	0	0
$939$	−209.000	−0.00726353
$940$	0	0
$941$	38561.0	1.33587	0.667934	−	0.744220i	$-0.267179\pi$
$941$	38561.0	1.33587	0.667934	+	0.744220i	$0.267179\pi$
$942$	0	0
$943$	3486.00	0.120382
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−39661.0	−1.36094	−0.680470	−	0.732776i	$-0.738224\pi$
$947$	−39661.0	−1.36094	−0.680470	+	0.732776i	$0.738224\pi$
$948$	0	0
$949$	19470.0	0.665988
$950$	0	0
$951$	−7131.00	−0.243153
$952$	0	0
$953$	−46618.0	−1.58458	−0.792290	−	0.610144i	$-0.791111\pi$
$953$	−46618.0	−1.58458	−0.792290	+	0.610144i	$0.791111\pi$
$954$	0	0
$955$	−8925.00	−0.302415
$956$	0	0
$957$	3710.00	0.125316
$958$	0	0
$959$	0	0
$960$	0	0
$961$	−24166.0	−0.811185
$962$	0	0
$963$	3354.00	0.112234
$964$	0	0
$965$	−245.000	−0.00817288
$966$	0	0
$967$	−14816.0	−0.492710	−0.246355	−	0.969180i	$-0.579233\pi$
$967$	−14816.0	−0.492710	−0.246355	+	0.969180i	$0.579233\pi$
$968$	0	0
$969$	8083.00	0.267970
$970$	0	0
$971$	−16875.0	−0.557718	−0.278859	−	0.960332i	$-0.589956\pi$
$971$	−16875.0	−0.557718	−0.278859	+	0.960332i	$0.589956\pi$
$972$	0	0
$973$	0	0
$974$	0	0
$975$	−5016.00	−0.164760
$976$	0	0
$977$	−15837.0	−0.518598	−0.259299	−	0.965797i	$-0.583492\pi$
$977$	−15837.0	−0.518598	−0.259299	+	0.965797i	$0.583492\pi$
$978$	0	0
$979$	−30555.0	−0.997489
$980$	0	0
$981$	25090.0	0.816577
$982$	0	0
$983$	9915.00	0.321708	0.160854	−	0.986978i	$-0.448575\pi$
$983$	9915.00	0.321708	0.160854	+	0.986978i	$0.448575\pi$
$984$	0	0
$985$	19138.0	0.619073
$986$	0	0
$987$	0	0
$988$	0	0
$989$	−1820.00	−0.0585163
$990$	0	0
$991$	43681.0	1.40017	0.700087	−	0.714057i	$-0.253144\pi$
$991$	43681.0	1.40017	0.700087	+	0.714057i	$0.253144\pi$
$992$	0	0
$993$	−6571.00	−0.209994
$994$	0	0
$995$	−15701.0	−0.500256
$996$	0	0
$997$	47113.0	1.49657	0.748287	−	0.663375i	$-0.230877\pi$
$997$	47113.0	1.49657	0.748287	+	0.663375i	$0.230877\pi$
$998$	0	0
$999$	583.000	0.0184638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.4.a.j.1.1		1
4.3	odd	2		98.4.a.c.1.1		1
7.3	odd	6		112.4.i.b.65.1		2
7.5	odd	6		112.4.i.b.81.1		2
7.6	odd	2		784.4.a.l.1.1		1
12.11	even	2		882.4.a.p.1.1		1
20.19	odd	2		2450.4.a.bf.1.1		1
28.3	even	6		14.4.c.b.9.1	✓	2
28.11	odd	6		98.4.c.e.79.1		2
28.19	even	6		14.4.c.b.11.1	yes	2
28.23	odd	6		98.4.c.e.67.1		2
28.27	even	2		98.4.a.b.1.1		1
56.3	even	6		448.4.i.c.65.1		2
56.5	odd	6		448.4.i.d.193.1		2
56.19	even	6		448.4.i.c.193.1		2
56.45	odd	6		448.4.i.d.65.1		2
84.11	even	6		882.4.g.d.667.1		2
84.23	even	6		882.4.g.d.361.1		2
84.47	odd	6		126.4.g.c.109.1		2
84.59	odd	6		126.4.g.c.37.1		2
84.83	odd	2		882.4.a.k.1.1		1
140.3	odd	12		350.4.j.d.149.1		4
140.19	even	6		350.4.e.b.151.1		2
140.47	odd	12		350.4.j.d.249.1		4
140.59	even	6		350.4.e.b.51.1		2
140.87	odd	12		350.4.j.d.149.2		4
140.103	odd	12		350.4.j.d.249.2		4
140.139	even	2		2450.4.a.bh.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.4.c.b.9.1	✓	2	28.3	even	6
14.4.c.b.11.1	yes	2	28.19	even	6
98.4.a.b.1.1		1	28.27	even	2
98.4.a.c.1.1		1	4.3	odd	2
98.4.c.e.67.1		2	28.23	odd	6
98.4.c.e.79.1		2	28.11	odd	6
112.4.i.b.65.1		2	7.3	odd	6
112.4.i.b.81.1		2	7.5	odd	6
126.4.g.c.37.1		2	84.59	odd	6
126.4.g.c.109.1		2	84.47	odd	6
350.4.e.b.51.1		2	140.59	even	6
350.4.e.b.151.1		2	140.19	even	6
350.4.j.d.149.1		4	140.3	odd	12
350.4.j.d.149.2		4	140.87	odd	12
350.4.j.d.249.1		4	140.47	odd	12
350.4.j.d.249.2		4	140.103	odd	12
448.4.i.c.65.1		2	56.3	even	6
448.4.i.c.193.1		2	56.19	even	6
448.4.i.d.65.1		2	56.45	odd	6
448.4.i.d.193.1		2	56.5	odd	6
784.4.a.j.1.1		1	1.1	even	1	trivial
784.4.a.l.1.1		1	7.6	odd	2
882.4.a.k.1.1		1	84.83	odd	2
882.4.a.p.1.1		1	12.11	even	2
882.4.g.d.361.1		2	84.23	even	6
882.4.g.d.667.1		2	84.11	even	6
2450.4.a.bf.1.1		1	20.19	odd	2
2450.4.a.bh.1.1		1	140.139	even	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	784.a (trivial)

Introduction

L-functions

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