LMFDB - Embedded newform 9801.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9801,2,Mod(1,9801)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9801, 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("9801.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9801 = 3^{4} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9801.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:	$78.2613790211$
Analytic rank:	$0$
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	$\chi$	$=$	9801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q-1.00000 q^{2} -1.00000 q^{4} +2.00000 q^{5} -2.00000 q^{7} +3.00000 q^{8} -2.00000 q^{10} +1.00000 q^{13} +2.00000 q^{14} -1.00000 q^{16} +2.00000 q^{17} -2.00000 q^{20} +4.00000 q^{23} -1.00000 q^{25} -1.00000 q^{26} +2.00000 q^{28} +3.00000 q^{29} -8.00000 q^{31} -5.00000 q^{32} -2.00000 q^{34} -4.00000 q^{35} +9.00000 q^{37} +6.00000 q^{40} +5.00000 q^{41} -6.00000 q^{43} -4.00000 q^{46} +10.0000 q^{47} -3.00000 q^{49} +1.00000 q^{50} -1.00000 q^{52} +3.00000 q^{53} -6.00000 q^{56} -3.00000 q^{58} -2.00000 q^{59} -15.0000 q^{61} +8.00000 q^{62} +7.00000 q^{64} +2.00000 q^{65} +14.0000 q^{67} -2.00000 q^{68} +4.00000 q^{70} +6.00000 q^{71} +7.00000 q^{73} -9.00000 q^{74} -4.00000 q^{79} -2.00000 q^{80} -5.00000 q^{82} +6.00000 q^{83} +4.00000 q^{85} +6.00000 q^{86} -6.00000 q^{89} -2.00000 q^{91} -4.00000 q^{92} -10.0000 q^{94} -1.00000 q^{97} +3.00000 q^{98} +O(q^{100})$

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0	0
$3$	0	0
$4$	−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
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	3.00000	1.06066
$9$	0	0
$10$	−2.00000	−0.632456
$11$	0	0
$11$	0	0
$12$	0	0
$13$	1.00000	0.277350	0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000	0.277350	0.138675	+	0.990338i	$0.455716\pi$
$14$	2.00000	0.534522
$15$	0	0
$16$	−1.00000	−0.250000
$17$	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		−	1.00000i	$-0.5\pi$
$19$	0	0			1.00000i	$0.5\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	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
$26$	−1.00000	−0.196116
$27$	0	0
$28$	2.00000	0.377964
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	0	0
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	−2.00000	−0.342997
$35$	−4.00000	−0.676123
$36$	0	0
$37$	9.00000	1.47959	0.739795	−	0.672832i	$-0.234922\pi$
$37$	9.00000	1.47959	0.739795	+	0.672832i	$0.234922\pi$
$38$	0	0
$39$	0	0
$40$	6.00000	0.948683
$41$	5.00000	0.780869	0.390434	−	0.920631i	$-0.372325\pi$
$41$	5.00000	0.780869	0.390434	+	0.920631i	$0.372325\pi$
$42$	0	0
$43$	−6.00000	−0.914991	−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000	−0.914991	−0.457496	+	0.889212i	$0.651253\pi$
$44$	0	0
$45$	0	0
$46$	−4.00000	−0.589768
$47$	10.0000	1.45865	0.729325	−	0.684167i	$-0.239834\pi$
$47$	10.0000	1.45865	0.729325	+	0.684167i	$0.239834\pi$
$48$	0	0
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	0	0
$52$	−1.00000	−0.138675
$53$	3.00000	0.412082	0.206041	−	0.978543i	$-0.433942\pi$
$53$	3.00000	0.412082	0.206041	+	0.978543i	$0.433942\pi$
$54$	0	0
$55$	0	0
$56$	−6.00000	−0.801784
$57$	0	0
$58$	−3.00000	−0.393919
$59$	−2.00000	−0.260378	−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000	−0.260378	−0.130189	+	0.991489i	$0.541558\pi$
$60$	0	0
$61$	−15.0000	−1.92055	−0.960277	−	0.279050i	$-0.909981\pi$
$61$	−15.0000	−1.92055	−0.960277	+	0.279050i	$0.909981\pi$
$62$	8.00000	1.01600
$63$	0	0
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	0	0
$67$	14.0000	1.71037	0.855186	−	0.518321i	$-0.173443\pi$
$67$	14.0000	1.71037	0.855186	+	0.518321i	$0.173443\pi$
$68$	−2.00000	−0.242536
$69$	0	0
$70$	4.00000	0.478091
$71$	6.00000	0.712069	0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000	0.712069	0.356034	+	0.934473i	$0.384129\pi$
$72$	0	0
$73$	7.00000	0.819288	0.409644	−	0.912245i	$-0.365653\pi$
$73$	7.00000	0.819288	0.409644	+	0.912245i	$0.365653\pi$
$74$	−9.00000	−1.04623
$75$	0	0
$76$	0	0
$77$	0	0
$78$	0	0
$79$	−4.00000	−0.450035	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000	−0.450035	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−2.00000	−0.223607
$81$	0	0
$82$	−5.00000	−0.552158
$83$	6.00000	0.658586	0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000	0.658586	0.329293	+	0.944228i	$0.393190\pi$
$84$	0	0
$85$	4.00000	0.433861
$86$	6.00000	0.646997
$87$	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	$0.603011\pi$
$90$	0	0
$91$	−2.00000	−0.209657
$92$	−4.00000	−0.417029
$93$	0	0
$94$	−10.0000	−1.03142
$95$	0	0
$96$	0	0
$97$	−1.00000	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$98$	3.00000	0.303046
$99$	0	0
$100$	1.00000	0.100000
$101$	−14.0000	−1.39305	−0.696526	−	0.717532i	$-0.745272\pi$
$101$	−14.0000	−1.39305	−0.696526	+	0.717532i	$0.745272\pi$
$102$	0	0
$103$	2.00000	0.197066	0.0985329	−	0.995134i	$-0.468585\pi$
$103$	2.00000	0.197066	0.0985329	+	0.995134i	$0.468585\pi$
$104$	3.00000	0.294174
$105$	0	0
$106$	−3.00000	−0.291386
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0	0
$109$	−11.0000	−1.05361	−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000	−1.05361	−0.526804	+	0.849987i	$0.676610\pi$
$110$	0	0
$111$	0	0
$112$	2.00000	0.188982
$113$	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
$115$	8.00000	0.746004
$116$	−3.00000	−0.278543
$117$	0	0
$118$	2.00000	0.184115
$119$	−4.00000	−0.366679
$120$	0	0
$121$	0	0
$122$	15.0000	1.35804
$123$	0	0
$124$	8.00000	0.718421
$125$	−12.0000	−1.07331
$126$	0	0
$127$	14.0000	1.24230	0.621150	−	0.783692i	$-0.286666\pi$
$127$	14.0000	1.24230	0.621150	+	0.783692i	$0.286666\pi$
$128$	3.00000	0.265165
$129$	0	0
$130$	−2.00000	−0.175412
$131$	−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
$133$	0	0
$134$	−14.0000	−1.20942
$135$	0	0
$136$	6.00000	0.514496
$137$	13.0000	1.11066	0.555332	−	0.831628i	$-0.312591\pi$
$137$	13.0000	1.11066	0.555332	+	0.831628i	$0.312591\pi$
$138$	0	0
$139$	−8.00000	−0.678551	−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000	−0.678551	−0.339276	+	0.940687i	$0.610182\pi$
$140$	4.00000	0.338062
$141$	0	0
$142$	−6.00000	−0.503509
$143$	0	0
$144$	0	0
$145$	6.00000	0.498273
$146$	−7.00000	−0.579324
$147$	0	0
$148$	−9.00000	−0.739795
$149$	−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
$151$	20.0000	1.62758	0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000	1.62758	0.813788	+	0.581161i	$0.197401\pi$
$152$	0	0
$153$	0	0
$154$	0	0
$155$	−16.0000	−1.28515
$156$	0	0
$157$	5.00000	0.399043	0.199522	−	0.979893i	$-0.436061\pi$
$157$	5.00000	0.399043	0.199522	+	0.979893i	$0.436061\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	−10.0000	−0.790569
$161$	−8.00000	−0.630488
$162$	0	0
$163$	4.00000	0.313304	0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000	0.313304	0.156652	+	0.987654i	$0.449930\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−6.00000	−0.465690
$167$	18.0000	1.39288	0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000	1.39288	0.696441	+	0.717614i	$0.254766\pi$
$168$	0	0
$169$	−12.0000	−0.923077
$170$	−4.00000	−0.306786
$171$	0	0
$172$	6.00000	0.457496
$173$	−9.00000	−0.684257	−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000	−0.684257	−0.342129	+	0.939653i	$0.611148\pi$
$174$	0	0
$175$	2.00000	0.151186
$176$	0	0
$177$	0	0
$178$	6.00000	0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	0	0
$181$	−11.0000	−0.817624	−0.408812	−	0.912619i	$-0.634057\pi$
$181$	−11.0000	−0.817624	−0.408812	+	0.912619i	$0.634057\pi$
$182$	2.00000	0.148250
$183$	0	0
$184$	12.0000	0.884652
$185$	18.0000	1.32339
$186$	0	0
$187$	0	0
$188$	−10.0000	−0.729325
$189$	0	0
$190$	0	0
$191$	−20.0000	−1.44715	−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000	−1.44715	−0.723575	+	0.690246i	$0.757502\pi$
$192$	0	0
$193$	−5.00000	−0.359908	−0.179954	−	0.983675i	$-0.557595\pi$
$193$	−5.00000	−0.359908	−0.179954	+	0.983675i	$0.557595\pi$
$194$	1.00000	0.0717958
$195$	0	0
$196$	3.00000	0.214286
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	0	0
$199$	18.0000	1.27599	0.637993	−	0.770042i	$-0.279765\pi$
$199$	18.0000	1.27599	0.637993	+	0.770042i	$0.279765\pi$
$200$	−3.00000	−0.212132
$201$	0	0
$202$	14.0000	0.985037
$203$	−6.00000	−0.421117
$204$	0	0
$205$	10.0000	0.698430
$206$	−2.00000	−0.139347
$207$	0	0
$208$	−1.00000	−0.0693375
$209$	0	0
$210$	0	0
$211$	6.00000	0.413057	0.206529	−	0.978441i	$-0.433783\pi$
$211$	6.00000	0.413057	0.206529	+	0.978441i	$0.433783\pi$
$212$	−3.00000	−0.206041
$213$	0	0
$214$	−6.00000	−0.410152
$215$	−12.0000	−0.818393
$216$	0	0
$217$	16.0000	1.08615
$218$	11.0000	0.745014
$219$	0	0
$220$	0	0
$221$	2.00000	0.134535
$222$	0	0
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	10.0000	0.668153
$225$	0	0
$226$	−18.0000	−1.19734
$227$	−24.0000	−1.59294	−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000	−1.59294	−0.796468	+	0.604681i	$0.793301\pi$
$228$	0	0
$229$	21.0000	1.38772	0.693860	−	0.720110i	$-0.255909\pi$
$229$	21.0000	1.38772	0.693860	+	0.720110i	$0.255909\pi$
$230$	−8.00000	−0.527504
$231$	0	0
$232$	9.00000	0.590879
$233$	6.00000	0.393073	0.196537	−	0.980497i	$-0.437031\pi$
$233$	6.00000	0.393073	0.196537	+	0.980497i	$0.437031\pi$
$234$	0	0
$235$	20.0000	1.30466
$236$	2.00000	0.130189
$237$	0	0
$238$	4.00000	0.259281
$239$	30.0000	1.94054	0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000	1.94054	0.970269	+	0.242028i	$0.0778125\pi$
$240$	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
$243$	0	0
$244$	15.0000	0.960277
$245$	−6.00000	−0.383326
$246$	0	0
$247$	0	0
$248$	−24.0000	−1.52400
$249$	0	0
$250$	12.0000	0.758947
$251$	−10.0000	−0.631194	−0.315597	−	0.948893i	$-0.602205\pi$
$251$	−10.0000	−0.631194	−0.315597	+	0.948893i	$0.602205\pi$
$252$	0	0
$253$	0	0
$254$	−14.0000	−0.878438
$255$	0	0
$256$	−17.0000	−1.06250
$257$	17.0000	1.06043	0.530215	−	0.847863i	$-0.322111\pi$
$257$	17.0000	1.06043	0.530215	+	0.847863i	$0.322111\pi$
$258$	0	0
$259$	−18.0000	−1.11847
$260$	−2.00000	−0.124035
$261$	0	0
$262$	12.0000	0.741362
$263$	22.0000	1.35658	0.678289	−	0.734795i	$-0.262722\pi$
$263$	22.0000	1.35658	0.678289	+	0.734795i	$0.262722\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	0	0
$267$	0	0
$268$	−14.0000	−0.855186
$269$	11.0000	0.670682	0.335341	−	0.942097i	$-0.391148\pi$
$269$	11.0000	0.670682	0.335341	+	0.942097i	$0.391148\pi$
$270$	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
$274$	−13.0000	−0.785359
$275$	0	0
$276$	0	0
$277$	−23.0000	−1.38194	−0.690968	−	0.722885i	$-0.742815\pi$
$277$	−23.0000	−1.38194	−0.690968	+	0.722885i	$0.742815\pi$
$278$	8.00000	0.479808
$279$	0	0
$280$	−12.0000	−0.717137
$281$	9.00000	0.536895	0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000	0.536895	0.268447	+	0.963294i	$0.413489\pi$
$282$	0	0
$283$	−2.00000	−0.118888	−0.0594438	−	0.998232i	$-0.518933\pi$
$283$	−2.00000	−0.118888	−0.0594438	+	0.998232i	$0.518933\pi$
$284$	−6.00000	−0.356034
$285$	0	0
$286$	0	0
$287$	−10.0000	−0.590281
$288$	0	0
$289$	−13.0000	−0.764706
$290$	−6.00000	−0.352332
$291$	0	0
$292$	−7.00000	−0.409644
$293$	−9.00000	−0.525786	−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000	−0.525786	−0.262893	+	0.964825i	$0.584677\pi$
$294$	0	0
$295$	−4.00000	−0.232889
$296$	27.0000	1.56934
$297$	0	0
$298$	17.0000	0.984784
$299$	4.00000	0.231326
$300$	0	0
$301$	12.0000	0.691669
$302$	−20.0000	−1.15087
$303$	0	0
$304$	0	0
$305$	−30.0000	−1.71780
$306$	0	0
$307$	20.0000	1.14146	0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000	1.14146	0.570730	+	0.821138i	$0.306660\pi$
$308$	0	0
$309$	0	0
$310$	16.0000	0.908739
$311$	24.0000	1.36092	0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000	1.36092	0.680458	+	0.732787i	$0.261781\pi$
$312$	0	0
$313$	14.0000	0.791327	0.395663	−	0.918396i	$-0.370515\pi$
$313$	14.0000	0.791327	0.395663	+	0.918396i	$0.370515\pi$
$314$	−5.00000	−0.282166
$315$	0	0
$316$	4.00000	0.225018
$317$	−25.0000	−1.40414	−0.702070	−	0.712108i	$-0.747741\pi$
$317$	−25.0000	−1.40414	−0.702070	+	0.712108i	$0.747741\pi$
$318$	0	0
$319$	0	0
$320$	14.0000	0.782624
$321$	0	0
$322$	8.00000	0.445823
$323$	0	0
$324$	0	0
$325$	−1.00000	−0.0554700
$326$	−4.00000	−0.221540
$327$	0	0
$328$	15.0000	0.828236
$329$	−20.0000	−1.10264
$330$	0	0
$331$	22.0000	1.20923	0.604615	−	0.796518i	$-0.293327\pi$
$331$	22.0000	1.20923	0.604615	+	0.796518i	$0.293327\pi$
$332$	−6.00000	−0.329293
$333$	0	0
$334$	−18.0000	−0.984916
$335$	28.0000	1.52980
$336$	0	0
$337$	−13.0000	−0.708155	−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000	−0.708155	−0.354078	+	0.935216i	$0.615205\pi$
$338$	12.0000	0.652714
$339$	0	0
$340$	−4.00000	−0.216930
$341$	0	0
$342$	0	0
$343$	20.0000	1.07990
$344$	−18.0000	−0.970495
$345$	0	0
$346$	9.00000	0.483843
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	0	0
$349$	21.0000	1.12410	0.562052	−	0.827102i	$-0.310012\pi$
$349$	21.0000	1.12410	0.562052	+	0.827102i	$0.310012\pi$
$350$	−2.00000	−0.106904
$351$	0	0
$352$	0	0
$353$	−27.0000	−1.43706	−0.718532	−	0.695493i	$-0.755186\pi$
$353$	−27.0000	−1.43706	−0.718532	+	0.695493i	$0.755186\pi$
$354$	0	0
$355$	12.0000	0.636894
$356$	6.00000	0.317999
$357$	0	0
$358$	0	0
$359$	−4.00000	−0.211112	−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000	−0.211112	−0.105556	+	0.994413i	$0.533662\pi$
$360$	0	0
$361$	−19.0000	−1.00000
$362$	11.0000	0.578147
$363$	0	0
$364$	2.00000	0.104828
$365$	14.0000	0.732793
$366$	0	0
$367$	10.0000	0.521996	0.260998	−	0.965339i	$-0.415948\pi$
$367$	10.0000	0.521996	0.260998	+	0.965339i	$0.415948\pi$
$368$	−4.00000	−0.208514
$369$	0	0
$370$	−18.0000	−0.935775
$371$	−6.00000	−0.311504
$372$	0	0
$373$	−26.0000	−1.34623	−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000	−1.34623	−0.673114	+	0.739538i	$0.735044\pi$
$374$	0	0
$375$	0	0
$376$	30.0000	1.54713
$377$	3.00000	0.154508
$378$	0	0
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	0	0
$381$	0	0
$382$	20.0000	1.02329
$383$	−2.00000	−0.102195	−0.0510976	−	0.998694i	$-0.516272\pi$
$383$	−2.00000	−0.102195	−0.0510976	+	0.998694i	$0.516272\pi$
$384$	0	0
$385$	0	0
$386$	5.00000	0.254493
$387$	0	0
$388$	1.00000	0.0507673
$389$	−9.00000	−0.456318	−0.228159	−	0.973624i	$-0.573271\pi$
$389$	−9.00000	−0.456318	−0.228159	+	0.973624i	$0.573271\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	−9.00000	−0.454569
$393$	0	0
$394$	22.0000	1.10834
$395$	−8.00000	−0.402524
$396$	0	0
$397$	25.0000	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$398$	−18.0000	−0.902258
$399$	0	0
$400$	1.00000	0.0500000
$401$	13.0000	0.649189	0.324595	−	0.945853i	$-0.394772\pi$
$401$	13.0000	0.649189	0.324595	+	0.945853i	$0.394772\pi$
$402$	0	0
$403$	−8.00000	−0.398508
$404$	14.0000	0.696526
$405$	0	0
$406$	6.00000	0.297775
$407$	0	0
$408$	0	0
$409$	6.00000	0.296681	0.148340	−	0.988936i	$-0.452607\pi$
$409$	6.00000	0.296681	0.148340	+	0.988936i	$0.452607\pi$
$410$	−10.0000	−0.493865
$411$	0	0
$412$	−2.00000	−0.0985329
$413$	4.00000	0.196827
$414$	0	0
$415$	12.0000	0.589057
$416$	−5.00000	−0.245145
$417$	0	0
$418$	0	0
$419$	34.0000	1.66101	0.830504	−	0.557012i	$-0.188052\pi$
$419$	34.0000	1.66101	0.830504	+	0.557012i	$0.188052\pi$
$420$	0	0
$421$	1.00000	0.0487370	0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000	0.0487370	0.0243685	+	0.999703i	$0.492242\pi$
$422$	−6.00000	−0.292075
$423$	0	0
$424$	9.00000	0.437079
$425$	−2.00000	−0.0970143
$426$	0	0
$427$	30.0000	1.45180
$428$	−6.00000	−0.290021
$429$	0	0
$430$	12.0000	0.578691
$431$	18.0000	0.867029	0.433515	−	0.901146i	$-0.357273\pi$
$431$	18.0000	0.867029	0.433515	+	0.901146i	$0.357273\pi$
$432$	0	0
$433$	22.0000	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$433$	22.0000	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$434$	−16.0000	−0.768025
$435$	0	0
$436$	11.0000	0.526804
$437$	0	0
$438$	0	0
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	0	0
$442$	−2.00000	−0.0951303
$443$	2.00000	0.0950229	0.0475114	−	0.998871i	$-0.484871\pi$
$443$	2.00000	0.0950229	0.0475114	+	0.998871i	$0.484871\pi$
$444$	0	0
$445$	−12.0000	−0.568855
$446$	−16.0000	−0.757622
$447$	0	0
$448$	−14.0000	−0.661438
$449$	−11.0000	−0.519122	−0.259561	−	0.965727i	$-0.583578\pi$
$449$	−11.0000	−0.519122	−0.259561	+	0.965727i	$0.583578\pi$
$450$	0	0
$451$	0	0
$452$	−18.0000	−0.846649
$453$	0	0
$454$	24.0000	1.12638
$455$	−4.00000	−0.187523
$456$	0	0
$457$	−9.00000	−0.421002	−0.210501	−	0.977594i	$-0.567510\pi$
$457$	−9.00000	−0.421002	−0.210501	+	0.977594i	$0.567510\pi$
$458$	−21.0000	−0.981266
$459$	0	0
$460$	−8.00000	−0.373002
$461$	39.0000	1.81641	0.908206	−	0.418524i	$-0.137453\pi$
$461$	39.0000	1.81641	0.908206	+	0.418524i	$0.137453\pi$
$462$	0	0
$463$	40.0000	1.85896	0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000	1.85896	0.929479	+	0.368875i	$0.120257\pi$
$464$	−3.00000	−0.139272
$465$	0	0
$466$	−6.00000	−0.277945
$467$	0	0		−	1.00000i	$-0.5\pi$
$467$	0	0			1.00000i	$0.5\pi$
$468$	0	0
$469$	−28.0000	−1.29292
$470$	−20.0000	−0.922531
$471$	0	0
$472$	−6.00000	−0.276172
$473$	0	0
$474$	0	0
$475$	0	0
$476$	4.00000	0.183340
$477$	0	0
$478$	−30.0000	−1.37217
$479$	4.00000	0.182765	0.0913823	−	0.995816i	$-0.470871\pi$
$479$	4.00000	0.182765	0.0913823	+	0.995816i	$0.470871\pi$
$480$	0	0
$481$	9.00000	0.410365
$482$	5.00000	0.227744
$483$	0	0
$484$	0	0
$485$	−2.00000	−0.0908153
$486$	0	0
$487$	−4.00000	−0.181257	−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000	−0.181257	−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−45.0000	−2.03705
$489$	0	0
$490$	6.00000	0.271052
$491$	26.0000	1.17336	0.586682	−	0.809818i	$-0.300434\pi$
$491$	26.0000	1.17336	0.586682	+	0.809818i	$0.300434\pi$
$492$	0	0
$493$	6.00000	0.270226
$494$	0	0
$495$	0	0
$496$	8.00000	0.359211
$497$	−12.0000	−0.538274
$498$	0	0
$499$	2.00000	0.0895323	0.0447661	−	0.998997i	$-0.485746\pi$
$499$	2.00000	0.0895323	0.0447661	+	0.998997i	$0.485746\pi$
$500$	12.0000	0.536656
$501$	0	0
$502$	10.0000	0.446322
$503$	−16.0000	−0.713405	−0.356702	−	0.934218i	$-0.616099\pi$
$503$	−16.0000	−0.713405	−0.356702	+	0.934218i	$0.616099\pi$
$504$	0	0
$505$	−28.0000	−1.24598
$506$	0	0
$507$	0	0
$508$	−14.0000	−0.621150
$509$	−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
$511$	−14.0000	−0.619324
$512$	11.0000	0.486136
$513$	0	0
$514$	−17.0000	−0.749838
$515$	4.00000	0.176261
$516$	0	0
$517$	0	0
$518$	18.0000	0.790875
$519$	0	0
$520$	6.00000	0.263117
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	0	0
$523$	−34.0000	−1.48672	−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000	−1.48672	−0.743358	+	0.668894i	$0.766768\pi$
$524$	12.0000	0.524222
$525$	0	0
$526$	−22.0000	−0.959246
$527$	−16.0000	−0.696971
$528$	0	0
$529$	−7.00000	−0.304348
$530$	−6.00000	−0.260623
$531$	0	0
$532$	0	0
$533$	5.00000	0.216574
$534$	0	0
$535$	12.0000	0.518805
$536$	42.0000	1.81412
$537$	0	0
$538$	−11.0000	−0.474244
$539$	0	0
$540$	0	0
$541$	25.0000	1.07483	0.537417	−	0.843317i	$-0.319400\pi$
$541$	25.0000	1.07483	0.537417	+	0.843317i	$0.319400\pi$
$542$	−8.00000	−0.343629
$543$	0	0
$544$	−10.0000	−0.428746
$545$	−22.0000	−0.942376
$546$	0	0
$547$	14.0000	0.598597	0.299298	−	0.954160i	$-0.403247\pi$
$547$	14.0000	0.598597	0.299298	+	0.954160i	$0.403247\pi$
$548$	−13.0000	−0.555332
$549$	0	0
$550$	0	0
$551$	0	0
$552$	0	0
$553$	8.00000	0.340195
$554$	23.0000	0.977176
$555$	0	0
$556$	8.00000	0.339276
$557$	11.0000	0.466085	0.233042	−	0.972467i	$-0.425132\pi$
$557$	11.0000	0.466085	0.233042	+	0.972467i	$0.425132\pi$
$558$	0	0
$559$	−6.00000	−0.253773
$560$	4.00000	0.169031
$561$	0	0
$562$	−9.00000	−0.379642
$563$	14.0000	0.590030	0.295015	−	0.955493i	$-0.404675\pi$
$563$	14.0000	0.590030	0.295015	+	0.955493i	$0.404675\pi$
$564$	0	0
$565$	36.0000	1.51453
$566$	2.00000	0.0840663
$567$	0	0
$568$	18.0000	0.755263
$569$	−15.0000	−0.628833	−0.314416	−	0.949285i	$-0.601809\pi$
$569$	−15.0000	−0.628833	−0.314416	+	0.949285i	$0.601809\pi$
$570$	0	0
$571$	2.00000	0.0836974	0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000	0.0836974	0.0418487	+	0.999124i	$0.486675\pi$
$572$	0	0
$573$	0	0
$574$	10.0000	0.417392
$575$	−4.00000	−0.166812
$576$	0	0
$577$	6.00000	0.249783	0.124892	−	0.992170i	$-0.460142\pi$
$577$	6.00000	0.249783	0.124892	+	0.992170i	$0.460142\pi$
$578$	13.0000	0.540729
$579$	0	0
$580$	−6.00000	−0.249136
$581$	−12.0000	−0.497844
$582$	0	0
$583$	0	0
$584$	21.0000	0.868986
$585$	0	0
$586$	9.00000	0.371787
$587$	44.0000	1.81607	0.908037	−	0.418890i	$-0.137581\pi$
$587$	44.0000	1.81607	0.908037	+	0.418890i	$0.137581\pi$
$588$	0	0
$589$	0	0
$590$	4.00000	0.164677
$591$	0	0
$592$	−9.00000	−0.369898
$593$	37.0000	1.51941	0.759704	−	0.650269i	$-0.225344\pi$
$593$	37.0000	1.51941	0.759704	+	0.650269i	$0.225344\pi$
$594$	0	0
$595$	−8.00000	−0.327968
$596$	17.0000	0.696347
$597$	0	0
$598$	−4.00000	−0.163572
$599$	−40.0000	−1.63436	−0.817178	−	0.576386i	$-0.804463\pi$
$599$	−40.0000	−1.63436	−0.817178	+	0.576386i	$0.804463\pi$
$600$	0	0
$601$	−34.0000	−1.38689	−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000	−1.38689	−0.693444	+	0.720510i	$0.743908\pi$
$602$	−12.0000	−0.489083
$603$	0	0
$604$	−20.0000	−0.813788
$605$	0	0
$606$	0	0
$607$	−22.0000	−0.892952	−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000	−0.892952	−0.446476	+	0.894795i	$0.647321\pi$
$608$	0	0
$609$	0	0
$610$	30.0000	1.21466
$611$	10.0000	0.404557
$612$	0	0
$613$	29.0000	1.17130	0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000	1.17130	0.585649	+	0.810564i	$0.300840\pi$
$614$	−20.0000	−0.807134
$615$	0	0
$616$	0	0
$617$	33.0000	1.32853	0.664265	−	0.747497i	$-0.268745\pi$
$617$	33.0000	1.32853	0.664265	+	0.747497i	$0.268745\pi$
$618$	0	0
$619$	−10.0000	−0.401934	−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000	−0.401934	−0.200967	+	0.979598i	$0.564408\pi$
$620$	16.0000	0.642575
$621$	0	0
$622$	−24.0000	−0.962312
$623$	12.0000	0.480770
$624$	0	0
$625$	−19.0000	−0.760000
$626$	−14.0000	−0.559553
$627$	0	0
$628$	−5.00000	−0.199522
$629$	18.0000	0.717707
$630$	0	0
$631$	−8.00000	−0.318475	−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000	−0.318475	−0.159237	+	0.987240i	$0.550904\pi$
$632$	−12.0000	−0.477334
$633$	0	0
$634$	25.0000	0.992877
$635$	28.0000	1.11115
$636$	0	0
$637$	−3.00000	−0.118864
$638$	0	0
$639$	0	0
$640$	6.00000	0.237171
$641$	33.0000	1.30342	0.651711	−	0.758468i	$-0.274052\pi$
$641$	33.0000	1.30342	0.651711	+	0.758468i	$0.274052\pi$
$642$	0	0
$643$	26.0000	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$644$	8.00000	0.315244
$645$	0	0
$646$	0	0
$647$	22.0000	0.864909	0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000	0.864909	0.432455	+	0.901656i	$0.357648\pi$
$648$	0	0
$649$	0	0
$650$	1.00000	0.0392232
$651$	0	0
$652$	−4.00000	−0.156652
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	0	0
$655$	−24.0000	−0.937758
$656$	−5.00000	−0.195217
$657$	0	0
$658$	20.0000	0.779681
$659$	−10.0000	−0.389545	−0.194772	−	0.980848i	$-0.562397\pi$
$659$	−10.0000	−0.389545	−0.194772	+	0.980848i	$0.562397\pi$
$660$	0	0
$661$	46.0000	1.78919	0.894596	−	0.446875i	$-0.147463\pi$
$661$	46.0000	1.78919	0.894596	+	0.446875i	$0.147463\pi$
$662$	−22.0000	−0.855054
$663$	0	0
$664$	18.0000	0.698535
$665$	0	0
$666$	0	0
$667$	12.0000	0.464642
$668$	−18.0000	−0.696441
$669$	0	0
$670$	−28.0000	−1.08173
$671$	0	0
$672$	0	0
$673$	11.0000	0.424019	0.212009	−	0.977268i	$-0.431999\pi$
$673$	11.0000	0.424019	0.212009	+	0.977268i	$0.431999\pi$
$674$	13.0000	0.500741
$675$	0	0
$676$	12.0000	0.461538
$677$	27.0000	1.03769	0.518847	−	0.854867i	$-0.326361\pi$
$677$	27.0000	1.03769	0.518847	+	0.854867i	$0.326361\pi$
$678$	0	0
$679$	2.00000	0.0767530
$680$	12.0000	0.460179
$681$	0	0
$682$	0	0
$683$	10.0000	0.382639	0.191320	−	0.981528i	$-0.438723\pi$
$683$	10.0000	0.382639	0.191320	+	0.981528i	$0.438723\pi$
$684$	0	0
$685$	26.0000	0.993409
$686$	−20.0000	−0.763604
$687$	0	0
$688$	6.00000	0.228748
$689$	3.00000	0.114291
$690$	0	0
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	9.00000	0.342129
$693$	0	0
$694$	28.0000	1.06287
$695$	−16.0000	−0.606915
$696$	0	0
$697$	10.0000	0.378777
$698$	−21.0000	−0.794862
$699$	0	0
$700$	−2.00000	−0.0755929
$701$	34.0000	1.28416	0.642081	−	0.766637i	$-0.278071\pi$
$701$	34.0000	1.28416	0.642081	+	0.766637i	$0.278071\pi$
$702$	0	0
$703$	0	0
$704$	0	0
$705$	0	0
$706$	27.0000	1.01616
$707$	28.0000	1.05305
$708$	0	0
$709$	−31.0000	−1.16423	−0.582115	−	0.813107i	$-0.697775\pi$
$709$	−31.0000	−1.16423	−0.582115	+	0.813107i	$0.697775\pi$
$710$	−12.0000	−0.450352
$711$	0	0
$712$	−18.0000	−0.674579
$713$	−32.0000	−1.19841
$714$	0	0
$715$	0	0
$716$	0	0
$717$	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	$0.647694\pi$
$720$	0	0
$721$	−4.00000	−0.148968
$722$	19.0000	0.707107
$723$	0	0
$724$	11.0000	0.408812
$725$	−3.00000	−0.111417
$726$	0	0
$727$	36.0000	1.33517	0.667583	−	0.744535i	$-0.267329\pi$
$727$	36.0000	1.33517	0.667583	+	0.744535i	$0.267329\pi$
$728$	−6.00000	−0.222375
$729$	0	0
$730$	−14.0000	−0.518163
$731$	−12.0000	−0.443836
$732$	0	0
$733$	−27.0000	−0.997268	−0.498634	−	0.866813i	$-0.666165\pi$
$733$	−27.0000	−0.997268	−0.498634	+	0.866813i	$0.666165\pi$
$734$	−10.0000	−0.369107
$735$	0	0
$736$	−20.0000	−0.737210
$737$	0	0
$738$	0	0
$739$	−4.00000	−0.147142	−0.0735712	−	0.997290i	$-0.523440\pi$
$739$	−4.00000	−0.147142	−0.0735712	+	0.997290i	$0.523440\pi$
$740$	−18.0000	−0.661693
$741$	0	0
$742$	6.00000	0.220267
$743$	20.0000	0.733729	0.366864	−	0.930274i	$-0.380431\pi$
$743$	20.0000	0.733729	0.366864	+	0.930274i	$0.380431\pi$
$744$	0	0
$745$	−34.0000	−1.24566
$746$	26.0000	0.951928
$747$	0	0
$748$	0	0
$749$	−12.0000	−0.438470
$750$	0	0
$751$	28.0000	1.02173	0.510867	−	0.859660i	$-0.329324\pi$
$751$	28.0000	1.02173	0.510867	+	0.859660i	$0.329324\pi$
$752$	−10.0000	−0.364662
$753$	0	0
$754$	−3.00000	−0.109254
$755$	40.0000	1.45575
$756$	0	0
$757$	17.0000	0.617876	0.308938	−	0.951082i	$-0.400027\pi$
$757$	17.0000	0.617876	0.308938	+	0.951082i	$0.400027\pi$
$758$	−16.0000	−0.581146
$759$	0	0
$760$	0	0
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	0	0
$763$	22.0000	0.796453
$764$	20.0000	0.723575
$765$	0	0
$766$	2.00000	0.0722629
$767$	−2.00000	−0.0722158
$768$	0	0
$769$	47.0000	1.69486	0.847432	−	0.530904i	$-0.178148\pi$
$769$	47.0000	1.69486	0.847432	+	0.530904i	$0.178148\pi$
$770$	0	0
$771$	0	0
$772$	5.00000	0.179954
$773$	−9.00000	−0.323708	−0.161854	−	0.986815i	$-0.551747\pi$
$773$	−9.00000	−0.323708	−0.161854	+	0.986815i	$0.551747\pi$
$774$	0	0
$775$	8.00000	0.287368
$776$	−3.00000	−0.107694
$777$	0	0
$778$	9.00000	0.322666
$779$	0	0
$780$	0	0
$781$	0	0
$782$	−8.00000	−0.286079
$783$	0	0
$784$	3.00000	0.107143
$785$	10.0000	0.356915
$786$	0	0
$787$	−38.0000	−1.35455	−0.677277	−	0.735728i	$-0.736840\pi$
$787$	−38.0000	−1.35455	−0.677277	+	0.735728i	$0.736840\pi$
$788$	22.0000	0.783718
$789$	0	0
$790$	8.00000	0.284627
$791$	−36.0000	−1.28001
$792$	0	0
$793$	−15.0000	−0.532666
$794$	−25.0000	−0.887217
$795$	0	0
$796$	−18.0000	−0.637993
$797$	7.00000	0.247953	0.123976	−	0.992285i	$-0.460435\pi$
$797$	7.00000	0.247953	0.123976	+	0.992285i	$0.460435\pi$
$798$	0	0
$799$	20.0000	0.707549
$800$	5.00000	0.176777
$801$	0	0
$802$	−13.0000	−0.459046
$803$	0	0
$804$	0	0
$805$	−16.0000	−0.563926
$806$	8.00000	0.281788
$807$	0	0
$808$	−42.0000	−1.47755
$809$	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
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	6.00000	0.210559
$813$	0	0
$814$	0	0
$815$	8.00000	0.280228
$816$	0	0
$817$	0	0
$818$	−6.00000	−0.209785
$819$	0	0
$820$	−10.0000	−0.349215
$821$	−13.0000	−0.453703	−0.226852	−	0.973929i	$-0.572843\pi$
$821$	−13.0000	−0.453703	−0.226852	+	0.973929i	$0.572843\pi$
$822$	0	0
$823$	−12.0000	−0.418294	−0.209147	−	0.977884i	$-0.567069\pi$
$823$	−12.0000	−0.418294	−0.209147	+	0.977884i	$0.567069\pi$
$824$	6.00000	0.209020
$825$	0	0
$826$	−4.00000	−0.139178
$827$	22.0000	0.765015	0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000	0.765015	0.382507	+	0.923952i	$0.375061\pi$
$828$	0	0
$829$	25.0000	0.868286	0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000	0.868286	0.434143	+	0.900844i	$0.357051\pi$
$830$	−12.0000	−0.416526
$831$	0	0
$832$	7.00000	0.242681
$833$	−6.00000	−0.207888
$834$	0	0
$835$	36.0000	1.24583
$836$	0	0
$837$	0	0
$838$	−34.0000	−1.17451
$839$	−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
$841$	−20.0000	−0.689655
$842$	−1.00000	−0.0344623
$843$	0	0
$844$	−6.00000	−0.206529
$845$	−24.0000	−0.825625
$846$	0	0
$847$	0	0
$848$	−3.00000	−0.103020
$849$	0	0
$850$	2.00000	0.0685994
$851$	36.0000	1.23406
$852$	0	0
$853$	53.0000	1.81469	0.907343	−	0.420392i	$-0.138107\pi$
$853$	53.0000	1.81469	0.907343	+	0.420392i	$0.138107\pi$
$854$	−30.0000	−1.02658
$855$	0	0
$856$	18.0000	0.615227
$857$	25.0000	0.853984	0.426992	−	0.904255i	$-0.359573\pi$
$857$	25.0000	0.853984	0.426992	+	0.904255i	$0.359573\pi$
$858$	0	0
$859$	−18.0000	−0.614152	−0.307076	−	0.951685i	$-0.599351\pi$
$859$	−18.0000	−0.614152	−0.307076	+	0.951685i	$0.599351\pi$
$860$	12.0000	0.409197
$861$	0	0
$862$	−18.0000	−0.613082
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	0	0
$865$	−18.0000	−0.612018
$866$	−22.0000	−0.747590
$867$	0	0
$868$	−16.0000	−0.543075
$869$	0	0
$870$	0	0
$871$	14.0000	0.474372
$872$	−33.0000	−1.11752
$873$	0	0
$874$	0	0
$875$	24.0000	0.811348
$876$	0	0
$877$	−3.00000	−0.101303	−0.0506514	−	0.998716i	$-0.516130\pi$
$877$	−3.00000	−0.101303	−0.0506514	+	0.998716i	$0.516130\pi$
$878$	20.0000	0.674967
$879$	0	0
$880$	0	0
$881$	−23.0000	−0.774890	−0.387445	−	0.921893i	$-0.626642\pi$
$881$	−23.0000	−0.774890	−0.387445	+	0.921893i	$0.626642\pi$
$882$	0	0
$883$	46.0000	1.54802	0.774012	−	0.633171i	$-0.218247\pi$
$883$	46.0000	1.54802	0.774012	+	0.633171i	$0.218247\pi$
$884$	−2.00000	−0.0672673
$885$	0	0
$886$	−2.00000	−0.0671913
$887$	−8.00000	−0.268614	−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000	−0.268614	−0.134307	+	0.990940i	$0.542881\pi$
$888$	0	0
$889$	−28.0000	−0.939090
$890$	12.0000	0.402241
$891$	0	0
$892$	−16.0000	−0.535720
$893$	0	0
$894$	0	0
$895$	0	0
$896$	−6.00000	−0.200446
$897$	0	0
$898$	11.0000	0.367075
$899$	−24.0000	−0.800445
$900$	0	0
$901$	6.00000	0.199889
$902$	0	0
$903$	0	0
$904$	54.0000	1.79601
$905$	−22.0000	−0.731305
$906$	0	0
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	24.0000	0.796468
$909$	0	0
$910$	4.00000	0.132599
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	0	0
$913$	0	0
$914$	9.00000	0.297694
$915$	0	0
$916$	−21.0000	−0.693860
$917$	24.0000	0.792550
$918$	0	0
$919$	10.0000	0.329870	0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000	0.329870	0.164935	+	0.986304i	$0.447259\pi$
$920$	24.0000	0.791257
$921$	0	0
$922$	−39.0000	−1.28440
$923$	6.00000	0.197492
$924$	0	0
$925$	−9.00000	−0.295918
$926$	−40.0000	−1.31448
$927$	0	0
$928$	−15.0000	−0.492399
$929$	57.0000	1.87011	0.935055	−	0.354504i	$-0.115350\pi$
$929$	57.0000	1.87011	0.935055	+	0.354504i	$0.115350\pi$
$930$	0	0
$931$	0	0
$932$	−6.00000	−0.196537
$933$	0	0
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−37.0000	−1.20874	−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000	−1.20874	−0.604369	+	0.796705i	$0.706575\pi$
$938$	28.0000	0.914232
$939$	0	0
$940$	−20.0000	−0.652328
$941$	18.0000	0.586783	0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000	0.586783	0.293392	+	0.955992i	$0.405216\pi$
$942$	0	0
$943$	20.0000	0.651290
$944$	2.00000	0.0650945
$945$	0	0
$946$	0	0
$947$	−18.0000	−0.584921	−0.292461	−	0.956278i	$-0.594474\pi$
$947$	−18.0000	−0.584921	−0.292461	+	0.956278i	$0.594474\pi$
$948$	0	0
$949$	7.00000	0.227230
$950$	0	0
$951$	0	0
$952$	−12.0000	−0.388922
$953$	2.00000	0.0647864	0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000	0.0647864	0.0323932	+	0.999475i	$0.489687\pi$
$954$	0	0
$955$	−40.0000	−1.29437
$956$	−30.0000	−0.970269
$957$	0	0
$958$	−4.00000	−0.129234
$959$	−26.0000	−0.839584
$960$	0	0
$961$	33.0000	1.06452
$962$	−9.00000	−0.290172
$963$	0	0
$964$	5.00000	0.161039
$965$	−10.0000	−0.321911
$966$	0	0
$967$	4.00000	0.128631	0.0643157	−	0.997930i	$-0.479514\pi$
$967$	4.00000	0.128631	0.0643157	+	0.997930i	$0.479514\pi$
$968$	0	0
$969$	0	0
$970$	2.00000	0.0642161
$971$	16.0000	0.513464	0.256732	−	0.966483i	$-0.417354\pi$
$971$	16.0000	0.513464	0.256732	+	0.966483i	$0.417354\pi$
$972$	0	0
$973$	16.0000	0.512936
$974$	4.00000	0.128168
$975$	0	0
$976$	15.0000	0.480138
$977$	45.0000	1.43968	0.719839	−	0.694141i	$-0.244216\pi$
$977$	45.0000	1.43968	0.719839	+	0.694141i	$0.244216\pi$
$978$	0	0
$979$	0	0
$980$	6.00000	0.191663
$981$	0	0
$982$	−26.0000	−0.829693
$983$	60.0000	1.91370	0.956851	−	0.290578i	$-0.0938475\pi$
$983$	60.0000	1.91370	0.956851	+	0.290578i	$0.0938475\pi$
$984$	0	0
$985$	−44.0000	−1.40196
$986$	−6.00000	−0.191079
$987$	0	0
$988$	0	0
$989$	−24.0000	−0.763156
$990$	0	0
$991$	−62.0000	−1.96949	−0.984747	−	0.173990i	$-0.944334\pi$
$991$	−62.0000	−1.96949	−0.984747	+	0.173990i	$0.944334\pi$
$992$	40.0000	1.27000
$993$	0	0
$994$	12.0000	0.380617
$995$	36.0000	1.14128
$996$	0	0
$997$	−10.0000	−0.316703	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	−10.0000	−0.316703	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−2.00000	−0.0633089
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9801.2.a.e.1.1	yes	1
3.2	odd	2		9801.2.a.h.1.1	yes	1
11.10	odd	2		9801.2.a.k.1.1	yes	1
33.32	even	2		9801.2.a.b.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9801.2.a.b.1.1	✓	1	33.32	even	2
9801.2.a.e.1.1	yes	1	1.1	even	1	trivial
9801.2.a.h.1.1	yes	1	3.2	odd	2
9801.2.a.k.1.1	yes	1	11.10	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:	\( N \)	\(=\)	\( 9801 = 3^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9801.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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