LMFDB - Embedded newform 1225.2.a.f.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1225,2,Mod(1,1225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1225, 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("1225.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1225 = 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1225.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:	$9.78167424761$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1225.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000 q^{8} -2.00000 q^{9} +O(q^{10})$

$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000 q^{6} -3.00000 q^{8} -2.00000 q^{9} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{16} +2.00000 q^{17} -2.00000 q^{18} +6.00000 q^{19} -3.00000 q^{23} +3.00000 q^{24} +2.00000 q^{26} +5.00000 q^{27} +7.00000 q^{29} +2.00000 q^{31} +5.00000 q^{32} +2.00000 q^{34} +2.00000 q^{36} -8.00000 q^{37} +6.00000 q^{38} -2.00000 q^{39} +5.00000 q^{41} +7.00000 q^{43} -3.00000 q^{46} +1.00000 q^{48} -2.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} +5.00000 q^{54} -6.00000 q^{57} +7.00000 q^{58} +10.0000 q^{59} +7.00000 q^{61} +2.00000 q^{62} +7.00000 q^{64} -5.00000 q^{67} -2.00000 q^{68} +3.00000 q^{69} -2.00000 q^{71} +6.00000 q^{72} -6.00000 q^{73} -8.00000 q^{74} -6.00000 q^{76} -2.00000 q^{78} -2.00000 q^{79} +1.00000 q^{81} +5.00000 q^{82} -11.0000 q^{83} +7.00000 q^{86} -7.00000 q^{87} +9.00000 q^{89} +3.00000 q^{92} -2.00000 q^{93} -5.00000 q^{96} -16.0000 q^{97} +O(q^{100})$

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	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350	−0.288675	−	0.957427i	$-0.593215\pi$
$3$	−1.00000	−0.577350	−0.288675	+	0.957427i	$0.593215\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−3.00000	−1.06066
$9$	−2.00000	−0.666667
$10$	0	0
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	1.00000	0.288675
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	0	0
$15$	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	$0.422021\pi$
$18$	−2.00000	−0.471405
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	0	0
$21$	0	0
$22$	0	0
$23$	−3.00000	−0.625543	−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000	−0.625543	−0.312772	+	0.949828i	$0.601257\pi$
$24$	3.00000	0.612372
$25$	0	0
$26$	2.00000	0.392232
$27$	5.00000	0.962250
$28$	0	0
$29$	7.00000	1.29987	0.649934	−	0.759991i	$-0.274797\pi$
$29$	7.00000	1.29987	0.649934	+	0.759991i	$0.274797\pi$
$30$	0	0
$31$	2.00000	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	2.00000	0.333333
$37$	−8.00000	−1.31519	−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000	−1.31519	−0.657596	+	0.753371i	$0.728427\pi$
$38$	6.00000	0.973329
$39$	−2.00000	−0.320256
$40$	0	0
$41$	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
$43$	7.00000	1.06749	0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000	1.06749	0.533745	+	0.845645i	$0.320784\pi$
$44$	0	0
$45$	0	0
$46$	−3.00000	−0.442326
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	0	0
$51$	−2.00000	−0.280056
$52$	−2.00000	−0.277350
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	5.00000	0.680414
$55$	0	0
$56$	0	0
$57$	−6.00000	−0.794719
$58$	7.00000	0.919145
$59$	10.0000	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	7.00000	0.896258	0.448129	−	0.893969i	$-0.352090\pi$
$61$	7.00000	0.896258	0.448129	+	0.893969i	$0.352090\pi$
$62$	2.00000	0.254000
$63$	0	0
$64$	7.00000	0.875000
$65$	0	0
$66$	0	0
$67$	−5.00000	−0.610847	−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000	−0.610847	−0.305424	+	0.952217i	$0.598798\pi$
$68$	−2.00000	−0.242536
$69$	3.00000	0.361158
$70$	0	0
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	6.00000	0.707107
$73$	−6.00000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	−8.00000	−0.929981
$75$	0	0
$76$	−6.00000	−0.688247
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	5.00000	0.552158
$83$	−11.0000	−1.20741	−0.603703	−	0.797209i	$-0.706309\pi$
$83$	−11.0000	−1.20741	−0.603703	+	0.797209i	$0.706309\pi$
$84$	0	0
$85$	0	0
$86$	7.00000	0.754829
$87$	−7.00000	−0.750479
$88$	0	0
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	0	0
$92$	3.00000	0.312772
$93$	−2.00000	−0.207390
$94$	0	0
$95$	0	0
$96$	−5.00000	−0.510310
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	0	0
$99$	0	0
$100$	0	0
$101$	9.00000	0.895533	0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000	0.895533	0.447767	+	0.894150i	$0.352219\pi$
$102$	−2.00000	−0.198030
$103$	7.00000	0.689730	0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000	0.689730	0.344865	+	0.938652i	$0.387925\pi$
$104$	−6.00000	−0.588348
$105$	0	0
$106$	6.00000	0.582772
$107$	11.0000	1.06341	0.531705	−	0.846930i	$-0.321551\pi$
$107$	11.0000	1.06341	0.531705	+	0.846930i	$0.321551\pi$
$108$	−5.00000	−0.481125
$109$	5.00000	0.478913	0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000	0.478913	0.239457	+	0.970907i	$0.423031\pi$
$110$	0	0
$111$	8.00000	0.759326
$112$	0	0
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−6.00000	−0.561951
$115$	0	0
$116$	−7.00000	−0.649934
$117$	−4.00000	−0.369800
$118$	10.0000	0.920575
$119$	0	0
$120$	0	0
$121$	−11.0000	−1.00000
$122$	7.00000	0.633750
$123$	−5.00000	−0.450835
$124$	−2.00000	−0.179605
$125$	0	0
$126$	0	0
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	−3.00000	−0.265165
$129$	−7.00000	−0.616316
$130$	0	0
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	0	0
$133$	0	0
$134$	−5.00000	−0.431934
$135$	0	0
$136$	−6.00000	−0.514496
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	3.00000	0.255377
$139$	8.00000	0.678551	0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000	0.678551	0.339276	+	0.940687i	$0.389818\pi$
$140$	0	0
$141$	0	0
$142$	−2.00000	−0.167836
$143$	0	0
$144$	2.00000	0.166667
$145$	0	0
$146$	−6.00000	−0.496564
$147$	0	0
$148$	8.00000	0.657596
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	0	0
$151$	14.0000	1.13930	0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000	1.13930	0.569652	+	0.821886i	$0.307078\pi$
$152$	−18.0000	−1.45999
$153$	−4.00000	−0.323381
$154$	0	0
$155$	0	0
$156$	2.00000	0.160128
$157$	12.0000	0.957704	0.478852	−	0.877896i	$-0.341053\pi$
$157$	12.0000	0.957704	0.478852	+	0.877896i	$0.341053\pi$
$158$	−2.00000	−0.159111
$159$	−6.00000	−0.475831
$160$	0	0
$161$	0	0
$162$	1.00000	0.0785674
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	−5.00000	−0.390434
$165$	0	0
$166$	−11.0000	−0.853766
$167$	−3.00000	−0.232147	−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000	−0.232147	−0.116073	+	0.993241i	$0.537031\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	0	0
$171$	−12.0000	−0.917663
$172$	−7.00000	−0.533745
$173$	−12.0000	−0.912343	−0.456172	−	0.889892i	$-0.650780\pi$
$173$	−12.0000	−0.912343	−0.456172	+	0.889892i	$0.650780\pi$
$174$	−7.00000	−0.530669
$175$	0	0
$176$	0	0
$177$	−10.0000	−0.751646
$178$	9.00000	0.674579
$179$	−2.00000	−0.149487	−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000	−0.149487	−0.0747435	+	0.997203i	$0.523814\pi$
$180$	0	0
$181$	−3.00000	−0.222988	−0.111494	−	0.993765i	$-0.535564\pi$
$181$	−3.00000	−0.222988	−0.111494	+	0.993765i	$0.535564\pi$
$182$	0	0
$183$	−7.00000	−0.517455
$184$	9.00000	0.663489
$185$	0	0
$186$	−2.00000	−0.146647
$187$	0	0
$188$	0	0
$189$	0	0
$190$	0	0
$191$	12.0000	0.868290	0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000	0.868290	0.434145	+	0.900843i	$0.357051\pi$
$192$	−7.00000	−0.505181
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−16.0000	−1.14873
$195$	0	0
$196$	0	0
$197$	−8.00000	−0.569976	−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000	−0.569976	−0.284988	+	0.958531i	$0.591990\pi$
$198$	0	0
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	0	0
$201$	5.00000	0.352673
$202$	9.00000	0.633238
$203$	0	0
$204$	2.00000	0.140028
$205$	0	0
$206$	7.00000	0.487713
$207$	6.00000	0.417029
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	−10.0000	−0.688428	−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000	−0.688428	−0.344214	+	0.938891i	$0.611855\pi$
$212$	−6.00000	−0.412082
$213$	2.00000	0.137038
$214$	11.0000	0.751945
$215$	0	0
$216$	−15.0000	−1.02062
$217$	0	0
$218$	5.00000	0.338643
$219$	6.00000	0.405442
$220$	0	0
$221$	4.00000	0.269069
$222$	8.00000	0.536925
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	0	0
$226$	−6.00000	−0.399114
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	6.00000	0.397360
$229$	−22.0000	−1.45380	−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000	−1.45380	−0.726900	+	0.686743i	$0.759040\pi$
$230$	0	0
$231$	0	0
$232$	−21.0000	−1.37872
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−4.00000	−0.261488
$235$	0	0
$236$	−10.0000	−0.650945
$237$	2.00000	0.129914
$238$	0	0
$239$	−18.0000	−1.16432	−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000	−1.16432	−0.582162	+	0.813073i	$0.697793\pi$
$240$	0	0
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−11.0000	−0.707107
$243$	−16.0000	−1.02640
$244$	−7.00000	−0.448129
$245$	0	0
$246$	−5.00000	−0.318788
$247$	12.0000	0.763542
$248$	−6.00000	−0.381000
$249$	11.0000	0.697097
$250$	0	0
$251$	30.0000	1.89358	0.946792	−	0.321847i	$-0.104304\pi$
$251$	30.0000	1.89358	0.946792	+	0.321847i	$0.104304\pi$
$252$	0	0
$253$	0	0
$254$	16.0000	1.00393
$255$	0	0
$256$	−17.0000	−1.06250
$257$	20.0000	1.24757	0.623783	−	0.781598i	$-0.285595\pi$
$257$	20.0000	1.24757	0.623783	+	0.781598i	$0.285595\pi$
$258$	−7.00000	−0.435801
$259$	0	0
$260$	0	0
$261$	−14.0000	−0.866578
$262$	4.00000	0.247121
$263$	−9.00000	−0.554964	−0.277482	−	0.960731i	$-0.589500\pi$
$263$	−9.00000	−0.554964	−0.277482	+	0.960731i	$0.589500\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−9.00000	−0.550791
$268$	5.00000	0.305424
$269$	−11.0000	−0.670682	−0.335341	−	0.942097i	$-0.608852\pi$
$269$	−11.0000	−0.670682	−0.335341	+	0.942097i	$0.608852\pi$
$270$	0	0
$271$	−2.00000	−0.121491	−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000	−0.121491	−0.0607457	+	0.998153i	$0.519348\pi$
$272$	−2.00000	−0.121268
$273$	0	0
$274$	0	0
$275$	0	0
$276$	−3.00000	−0.180579
$277$	10.0000	0.600842	0.300421	−	0.953807i	$-0.402873\pi$
$277$	10.0000	0.600842	0.300421	+	0.953807i	$0.402873\pi$
$278$	8.00000	0.479808
$279$	−4.00000	−0.239474
$280$	0	0
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	0	0
$283$	16.0000	0.951101	0.475551	−	0.879688i	$-0.342249\pi$
$283$	16.0000	0.951101	0.475551	+	0.879688i	$0.342249\pi$
$284$	2.00000	0.118678
$285$	0	0
$286$	0	0
$287$	0	0
$288$	−10.0000	−0.589256
$289$	−13.0000	−0.764706
$290$	0	0
$291$	16.0000	0.937937
$292$	6.00000	0.351123
$293$	24.0000	1.40209	0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000	1.40209	0.701047	+	0.713115i	$0.252716\pi$
$294$	0	0
$295$	0	0
$296$	24.0000	1.39497
$297$	0	0
$298$	1.00000	0.0579284
$299$	−6.00000	−0.346989
$300$	0	0
$301$	0	0
$302$	14.0000	0.805609
$303$	−9.00000	−0.517036
$304$	−6.00000	−0.344124
$305$	0	0
$306$	−4.00000	−0.228665
$307$	23.0000	1.31268	0.656340	−	0.754466i	$-0.272104\pi$
$307$	23.0000	1.31268	0.656340	+	0.754466i	$0.272104\pi$
$308$	0	0
$309$	−7.00000	−0.398216
$310$	0	0
$311$	30.0000	1.70114	0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000	1.70114	0.850572	+	0.525859i	$0.176256\pi$
$312$	6.00000	0.339683
$313$	24.0000	1.35656	0.678280	−	0.734803i	$-0.262726\pi$
$313$	24.0000	1.35656	0.678280	+	0.734803i	$0.262726\pi$
$314$	12.0000	0.677199
$315$	0	0
$316$	2.00000	0.112509
$317$	−6.00000	−0.336994	−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000	−0.336994	−0.168497	+	0.985702i	$0.553891\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	0	0
$321$	−11.0000	−0.613960
$322$	0	0
$323$	12.0000	0.667698
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	−4.00000	−0.221540
$327$	−5.00000	−0.276501
$328$	−15.0000	−0.828236
$329$	0	0
$330$	0	0
$331$	6.00000	0.329790	0.164895	−	0.986311i	$-0.447272\pi$
$331$	6.00000	0.329790	0.164895	+	0.986311i	$0.447272\pi$
$332$	11.0000	0.603703
$333$	16.0000	0.876795
$334$	−3.00000	−0.164153
$335$	0	0
$336$	0	0
$337$	18.0000	0.980522	0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000	0.980522	0.490261	+	0.871576i	$0.336901\pi$
$338$	−9.00000	−0.489535
$339$	6.00000	0.325875
$340$	0	0
$341$	0	0
$342$	−12.0000	−0.648886
$343$	0	0
$344$	−21.0000	−1.13224
$345$	0	0
$346$	−12.0000	−0.645124
$347$	15.0000	0.805242	0.402621	−	0.915367i	$-0.368099\pi$
$347$	15.0000	0.805242	0.402621	+	0.915367i	$0.368099\pi$
$348$	7.00000	0.375239
$349$	−17.0000	−0.909989	−0.454995	−	0.890494i	$-0.650359\pi$
$349$	−17.0000	−0.909989	−0.454995	+	0.890494i	$0.650359\pi$
$350$	0	0
$351$	10.0000	0.533761
$352$	0	0
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	−10.0000	−0.531494
$355$	0	0
$356$	−9.00000	−0.476999
$357$	0	0
$358$	−2.00000	−0.105703
$359$	10.0000	0.527780	0.263890	−	0.964553i	$-0.414994\pi$
$359$	10.0000	0.527780	0.263890	+	0.964553i	$0.414994\pi$
$360$	0	0
$361$	17.0000	0.894737
$362$	−3.00000	−0.157676
$363$	11.0000	0.577350
$364$	0	0
$365$	0	0
$366$	−7.00000	−0.365896
$367$	27.0000	1.40939	0.704694	−	0.709511i	$-0.251084\pi$
$367$	27.0000	1.40939	0.704694	+	0.709511i	$0.251084\pi$
$368$	3.00000	0.156386
$369$	−10.0000	−0.520579
$370$	0	0
$371$	0	0
$372$	2.00000	0.103695
$373$	−24.0000	−1.24267	−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000	−1.24267	−0.621336	+	0.783544i	$0.713410\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	14.0000	0.721037
$378$	0	0
$379$	−10.0000	−0.513665	−0.256833	−	0.966456i	$-0.582679\pi$
$379$	−10.0000	−0.513665	−0.256833	+	0.966456i	$0.582679\pi$
$380$	0	0
$381$	−16.0000	−0.819705
$382$	12.0000	0.613973
$383$	5.00000	0.255488	0.127744	−	0.991807i	$-0.459226\pi$
$383$	5.00000	0.255488	0.127744	+	0.991807i	$0.459226\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−4.00000	−0.203595
$387$	−14.0000	−0.711660
$388$	16.0000	0.812277
$389$	14.0000	0.709828	0.354914	−	0.934899i	$-0.384510\pi$
$389$	14.0000	0.709828	0.354914	+	0.934899i	$0.384510\pi$
$390$	0	0
$391$	−6.00000	−0.303433
$392$	0	0
$393$	−4.00000	−0.201773
$394$	−8.00000	−0.403034
$395$	0	0
$396$	0	0
$397$	−16.0000	−0.803017	−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000	−0.803017	−0.401508	+	0.915855i	$0.631514\pi$
$398$	−4.00000	−0.200502
$399$	0	0
$400$	0	0
$401$	3.00000	0.149813	0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000	0.149813	0.0749064	+	0.997191i	$0.476134\pi$
$402$	5.00000	0.249377
$403$	4.00000	0.199254
$404$	−9.00000	−0.447767
$405$	0	0
$406$	0	0
$407$	0	0
$408$	6.00000	0.297044
$409$	−25.0000	−1.23617	−0.618085	−	0.786111i	$-0.712091\pi$
$409$	−25.0000	−1.23617	−0.618085	+	0.786111i	$0.712091\pi$
$410$	0	0
$411$	0	0
$412$	−7.00000	−0.344865
$413$	0	0
$414$	6.00000	0.294884
$415$	0	0
$416$	10.0000	0.490290
$417$	−8.00000	−0.391762
$418$	0	0
$419$	24.0000	1.17248	0.586238	−	0.810139i	$-0.300608\pi$
$419$	24.0000	1.17248	0.586238	+	0.810139i	$0.300608\pi$
$420$	0	0
$421$	15.0000	0.731055	0.365528	−	0.930800i	$-0.380889\pi$
$421$	15.0000	0.731055	0.365528	+	0.930800i	$0.380889\pi$
$422$	−10.0000	−0.486792
$423$	0	0
$424$	−18.0000	−0.874157
$425$	0	0
$426$	2.00000	0.0969003
$427$	0	0
$428$	−11.0000	−0.531705
$429$	0	0
$430$	0	0
$431$	−32.0000	−1.54139	−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000	−1.54139	−0.770693	+	0.637207i	$0.780090\pi$
$432$	−5.00000	−0.240563
$433$	−2.00000	−0.0961139	−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000	−0.0961139	−0.0480569	+	0.998845i	$0.515303\pi$
$434$	0	0
$435$	0	0
$436$	−5.00000	−0.239457
$437$	−18.0000	−0.861057
$438$	6.00000	0.286691
$439$	24.0000	1.14546	0.572729	−	0.819745i	$-0.305885\pi$
$439$	24.0000	1.14546	0.572729	+	0.819745i	$0.305885\pi$
$440$	0	0
$441$	0	0
$442$	4.00000	0.190261
$443$	31.0000	1.47285	0.736427	−	0.676517i	$-0.236511\pi$
$443$	31.0000	1.47285	0.736427	+	0.676517i	$0.236511\pi$
$444$	−8.00000	−0.379663
$445$	0	0
$446$	0	0
$447$	−1.00000	−0.0472984
$448$	0	0
$449$	31.0000	1.46298	0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000	1.46298	0.731490	+	0.681852i	$0.238825\pi$
$450$	0	0
$451$	0	0
$452$	6.00000	0.282216
$453$	−14.0000	−0.657777
$454$	−20.0000	−0.938647
$455$	0	0
$456$	18.0000	0.842927
$457$	32.0000	1.49690	0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000	1.49690	0.748448	+	0.663193i	$0.230799\pi$
$458$	−22.0000	−1.02799
$459$	10.0000	0.466760
$460$	0	0
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	3.00000	0.139422	0.0697109	−	0.997567i	$-0.477792\pi$
$463$	3.00000	0.139422	0.0697109	+	0.997567i	$0.477792\pi$
$464$	−7.00000	−0.324967
$465$	0	0
$466$	14.0000	0.648537
$467$	3.00000	0.138823	0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000	0.138823	0.0694117	+	0.997588i	$0.477888\pi$
$468$	4.00000	0.184900
$469$	0	0
$470$	0	0
$471$	−12.0000	−0.552931
$472$	−30.0000	−1.38086
$473$	0	0
$474$	2.00000	0.0918630
$475$	0	0
$476$	0	0
$477$	−12.0000	−0.549442
$478$	−18.0000	−0.823301
$479$	42.0000	1.91903	0.959514	−	0.281659i	$-0.0908848\pi$
$479$	42.0000	1.91903	0.959514	+	0.281659i	$0.0908848\pi$
$480$	0	0
$481$	−16.0000	−0.729537
$482$	−14.0000	−0.637683
$483$	0	0
$484$	11.0000	0.500000
$485$	0	0
$486$	−16.0000	−0.725775
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−21.0000	−0.950625
$489$	4.00000	0.180886
$490$	0	0
$491$	−26.0000	−1.17336	−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000	−1.17336	−0.586682	+	0.809818i	$0.699566\pi$
$492$	5.00000	0.225417
$493$	14.0000	0.630528
$494$	12.0000	0.539906
$495$	0	0
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	11.0000	0.492922
$499$	16.0000	0.716258	0.358129	−	0.933672i	$-0.383415\pi$
$499$	16.0000	0.716258	0.358129	+	0.933672i	$0.383415\pi$
$500$	0	0
$501$	3.00000	0.134030
$502$	30.0000	1.33897
$503$	−15.0000	−0.668817	−0.334408	−	0.942428i	$-0.608537\pi$
$503$	−15.0000	−0.668817	−0.334408	+	0.942428i	$0.608537\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	9.00000	0.399704
$508$	−16.0000	−0.709885
$509$	27.0000	1.19675	0.598377	−	0.801215i	$-0.295813\pi$
$509$	27.0000	1.19675	0.598377	+	0.801215i	$0.295813\pi$
$510$	0	0
$511$	0	0
$512$	−11.0000	−0.486136
$513$	30.0000	1.32453
$514$	20.0000	0.882162
$515$	0	0
$516$	7.00000	0.308158
$517$	0	0
$518$	0	0
$519$	12.0000	0.526742
$520$	0	0
$521$	14.0000	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$521$	14.0000	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$522$	−14.0000	−0.612763
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	−4.00000	−0.174741
$525$	0	0
$526$	−9.00000	−0.392419
$527$	4.00000	0.174243
$528$	0	0
$529$	−14.0000	−0.608696
$530$	0	0
$531$	−20.0000	−0.867926
$532$	0	0
$533$	10.0000	0.433148
$534$	−9.00000	−0.389468
$535$	0	0
$536$	15.0000	0.647901
$537$	2.00000	0.0863064
$538$	−11.0000	−0.474244
$539$	0	0
$540$	0	0
$541$	−3.00000	−0.128980	−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000	−0.128980	−0.0644900	+	0.997918i	$0.520542\pi$
$542$	−2.00000	−0.0859074
$543$	3.00000	0.128742
$544$	10.0000	0.428746
$545$	0	0
$546$	0	0
$547$	−17.0000	−0.726868	−0.363434	−	0.931620i	$-0.618396\pi$
$547$	−17.0000	−0.726868	−0.363434	+	0.931620i	$0.618396\pi$
$548$	0	0
$549$	−14.0000	−0.597505
$550$	0	0
$551$	42.0000	1.78926
$552$	−9.00000	−0.383065
$553$	0	0
$554$	10.0000	0.424859
$555$	0	0
$556$	−8.00000	−0.339276
$557$	−44.0000	−1.86434	−0.932170	−	0.362021i	$-0.882087\pi$
$557$	−44.0000	−1.86434	−0.932170	+	0.362021i	$0.882087\pi$
$558$	−4.00000	−0.169334
$559$	14.0000	0.592137
$560$	0	0
$561$	0	0
$562$	−14.0000	−0.590554
$563$	33.0000	1.39078	0.695392	−	0.718631i	$-0.255231\pi$
$563$	33.0000	1.39078	0.695392	+	0.718631i	$0.255231\pi$
$564$	0	0
$565$	0	0
$566$	16.0000	0.672530
$567$	0	0
$568$	6.00000	0.251754
$569$	−18.0000	−0.754599	−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000	−0.754599	−0.377300	+	0.926091i	$0.623147\pi$
$570$	0	0
$571$	−18.0000	−0.753277	−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000	−0.753277	−0.376638	+	0.926360i	$0.622920\pi$
$572$	0	0
$573$	−12.0000	−0.501307
$574$	0	0
$575$	0	0
$576$	−14.0000	−0.583333
$577$	−32.0000	−1.33218	−0.666089	−	0.745873i	$-0.732033\pi$
$577$	−32.0000	−1.33218	−0.666089	+	0.745873i	$0.732033\pi$
$578$	−13.0000	−0.540729
$579$	4.00000	0.166234
$580$	0	0
$581$	0	0
$582$	16.0000	0.663221
$583$	0	0
$584$	18.0000	0.744845
$585$	0	0
$586$	24.0000	0.991431
$587$	−36.0000	−1.48588	−0.742940	−	0.669359i	$-0.766569\pi$
$587$	−36.0000	−1.48588	−0.742940	+	0.669359i	$0.766569\pi$
$588$	0	0
$589$	12.0000	0.494451
$590$	0	0
$591$	8.00000	0.329076
$592$	8.00000	0.328798
$593$	22.0000	0.903432	0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000	0.903432	0.451716	+	0.892162i	$0.350812\pi$
$594$	0	0
$595$	0	0
$596$	−1.00000	−0.0409616
$597$	4.00000	0.163709
$598$	−6.00000	−0.245358
$599$	−44.0000	−1.79779	−0.898896	−	0.438163i	$-0.855629\pi$
$599$	−44.0000	−1.79779	−0.898896	+	0.438163i	$0.855629\pi$
$600$	0	0
$601$	10.0000	0.407909	0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000	0.407909	0.203954	+	0.978980i	$0.434621\pi$
$602$	0	0
$603$	10.0000	0.407231
$604$	−14.0000	−0.569652
$605$	0	0
$606$	−9.00000	−0.365600
$607$	−33.0000	−1.33943	−0.669714	−	0.742619i	$-0.733583\pi$
$607$	−33.0000	−1.33943	−0.669714	+	0.742619i	$0.733583\pi$
$608$	30.0000	1.21666
$609$	0	0
$610$	0	0
$611$	0	0
$612$	4.00000	0.161690
$613$	−34.0000	−1.37325	−0.686624	−	0.727013i	$-0.740908\pi$
$613$	−34.0000	−1.37325	−0.686624	+	0.727013i	$0.740908\pi$
$614$	23.0000	0.928204
$615$	0	0
$616$	0	0
$617$	−4.00000	−0.161034	−0.0805170	−	0.996753i	$-0.525657\pi$
$617$	−4.00000	−0.161034	−0.0805170	+	0.996753i	$0.525657\pi$
$618$	−7.00000	−0.281581
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	−15.0000	−0.601929
$622$	30.0000	1.20289
$623$	0	0
$624$	2.00000	0.0800641
$625$	0	0
$626$	24.0000	0.959233
$627$	0	0
$628$	−12.0000	−0.478852
$629$	−16.0000	−0.637962
$630$	0	0
$631$	40.0000	1.59237	0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000	1.59237	0.796187	+	0.605050i	$0.206847\pi$
$632$	6.00000	0.238667
$633$	10.0000	0.397464
$634$	−6.00000	−0.238290
$635$	0	0
$636$	6.00000	0.237915
$637$	0	0
$638$	0	0
$639$	4.00000	0.158238
$640$	0	0
$641$	−11.0000	−0.434474	−0.217237	−	0.976119i	$-0.569704\pi$
$641$	−11.0000	−0.434474	−0.217237	+	0.976119i	$0.569704\pi$
$642$	−11.0000	−0.434135
$643$	−4.00000	−0.157745	−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000	−0.157745	−0.0788723	+	0.996885i	$0.525132\pi$
$644$	0	0
$645$	0	0
$646$	12.0000	0.472134
$647$	47.0000	1.84776	0.923880	−	0.382682i	$-0.124999\pi$
$647$	47.0000	1.84776	0.923880	+	0.382682i	$0.124999\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	0	0
$651$	0	0
$652$	4.00000	0.156652
$653$	−26.0000	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$653$	−26.0000	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$654$	−5.00000	−0.195515
$655$	0	0
$656$	−5.00000	−0.195217
$657$	12.0000	0.468165
$658$	0	0
$659$	6.00000	0.233727	0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000	0.233727	0.116863	+	0.993148i	$0.462716\pi$
$660$	0	0
$661$	−9.00000	−0.350059	−0.175030	−	0.984563i	$-0.556002\pi$
$661$	−9.00000	−0.350059	−0.175030	+	0.984563i	$0.556002\pi$
$662$	6.00000	0.233197
$663$	−4.00000	−0.155347
$664$	33.0000	1.28065
$665$	0	0
$666$	16.0000	0.619987
$667$	−21.0000	−0.813123
$668$	3.00000	0.116073
$669$	0	0
$670$	0	0
$671$	0	0
$672$	0	0
$673$	−36.0000	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$674$	18.0000	0.693334
$675$	0	0
$676$	9.00000	0.346154
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	6.00000	0.230429
$679$	0	0
$680$	0	0
$681$	20.0000	0.766402
$682$	0	0
$683$	35.0000	1.33924	0.669619	−	0.742705i	$-0.266457\pi$
$683$	35.0000	1.33924	0.669619	+	0.742705i	$0.266457\pi$
$684$	12.0000	0.458831
$685$	0	0
$686$	0	0
$687$	22.0000	0.839352
$688$	−7.00000	−0.266872
$689$	12.0000	0.457164
$690$	0	0
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	12.0000	0.456172
$693$	0	0
$694$	15.0000	0.569392
$695$	0	0
$696$	21.0000	0.796003
$697$	10.0000	0.378777
$698$	−17.0000	−0.643459
$699$	−14.0000	−0.529529
$700$	0	0
$701$	−1.00000	−0.0377695	−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000	−0.0377695	−0.0188847	+	0.999822i	$0.506012\pi$
$702$	10.0000	0.377426
$703$	−48.0000	−1.81035
$704$	0	0
$705$	0	0
$706$	−26.0000	−0.978523
$707$	0	0
$708$	10.0000	0.375823
$709$	−49.0000	−1.84023	−0.920117	−	0.391644i	$-0.871906\pi$
$709$	−49.0000	−1.84023	−0.920117	+	0.391644i	$0.871906\pi$
$710$	0	0
$711$	4.00000	0.150012
$712$	−27.0000	−1.01187
$713$	−6.00000	−0.224702
$714$	0	0
$715$	0	0
$716$	2.00000	0.0747435
$717$	18.0000	0.672222
$718$	10.0000	0.373197
$719$	36.0000	1.34257	0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000	1.34257	0.671287	+	0.741198i	$0.265742\pi$
$720$	0	0
$721$	0	0
$722$	17.0000	0.632674
$723$	14.0000	0.520666
$724$	3.00000	0.111494
$725$	0	0
$726$	11.0000	0.408248
$727$	−47.0000	−1.74313	−0.871567	−	0.490277i	$-0.836896\pi$
$727$	−47.0000	−1.74313	−0.871567	+	0.490277i	$0.836896\pi$
$728$	0	0
$729$	13.0000	0.481481
$730$	0	0
$731$	14.0000	0.517809
$732$	7.00000	0.258727
$733$	−16.0000	−0.590973	−0.295487	−	0.955347i	$-0.595482\pi$
$733$	−16.0000	−0.590973	−0.295487	+	0.955347i	$0.595482\pi$
$734$	27.0000	0.996588
$735$	0	0
$736$	−15.0000	−0.552907
$737$	0	0
$738$	−10.0000	−0.368105
$739$	16.0000	0.588570	0.294285	−	0.955718i	$-0.404919\pi$
$739$	16.0000	0.588570	0.294285	+	0.955718i	$0.404919\pi$
$740$	0	0
$741$	−12.0000	−0.440831
$742$	0	0
$743$	−49.0000	−1.79764	−0.898818	−	0.438322i	$-0.855573\pi$
$743$	−49.0000	−1.79764	−0.898818	+	0.438322i	$0.855573\pi$
$744$	6.00000	0.219971
$745$	0	0
$746$	−24.0000	−0.878702
$747$	22.0000	0.804938
$748$	0	0
$749$	0	0
$750$	0	0
$751$	−12.0000	−0.437886	−0.218943	−	0.975738i	$-0.570261\pi$
$751$	−12.0000	−0.437886	−0.218943	+	0.975738i	$0.570261\pi$
$752$	0	0
$753$	−30.0000	−1.09326
$754$	14.0000	0.509850
$755$	0	0
$756$	0	0
$757$	22.0000	0.799604	0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000	0.799604	0.399802	+	0.916602i	$0.369079\pi$
$758$	−10.0000	−0.363216
$759$	0	0
$760$	0	0
$761$	14.0000	0.507500	0.253750	−	0.967270i	$-0.418336\pi$
$761$	14.0000	0.507500	0.253750	+	0.967270i	$0.418336\pi$
$762$	−16.0000	−0.579619
$763$	0	0
$764$	−12.0000	−0.434145
$765$	0	0
$766$	5.00000	0.180657
$767$	20.0000	0.722158
$768$	17.0000	0.613435
$769$	−30.0000	−1.08183	−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000	−1.08183	−0.540914	+	0.841078i	$0.681921\pi$
$770$	0	0
$771$	−20.0000	−0.720282
$772$	4.00000	0.143963
$773$	18.0000	0.647415	0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000	0.647415	0.323708	+	0.946157i	$0.395071\pi$
$774$	−14.0000	−0.503220
$775$	0	0
$776$	48.0000	1.72310
$777$	0	0
$778$	14.0000	0.501924
$779$	30.0000	1.07486
$780$	0	0
$781$	0	0
$782$	−6.00000	−0.214560
$783$	35.0000	1.25080
$784$	0	0
$785$	0	0
$786$	−4.00000	−0.142675
$787$	−17.0000	−0.605985	−0.302992	−	0.952993i	$-0.597986\pi$
$787$	−17.0000	−0.605985	−0.302992	+	0.952993i	$0.597986\pi$
$788$	8.00000	0.284988
$789$	9.00000	0.320408
$790$	0	0
$791$	0	0
$792$	0	0
$793$	14.0000	0.497155
$794$	−16.0000	−0.567819
$795$	0	0
$796$	4.00000	0.141776
$797$	40.0000	1.41687	0.708436	−	0.705775i	$-0.249401\pi$
$797$	40.0000	1.41687	0.708436	+	0.705775i	$0.249401\pi$
$798$	0	0
$799$	0	0
$800$	0	0
$801$	−18.0000	−0.635999
$802$	3.00000	0.105934
$803$	0	0
$804$	−5.00000	−0.176336
$805$	0	0
$806$	4.00000	0.140894
$807$	11.0000	0.387218
$808$	−27.0000	−0.949857
$809$	9.00000	0.316423	0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000	0.316423	0.158212	+	0.987405i	$0.449427\pi$
$810$	0	0
$811$	−2.00000	−0.0702295	−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000	−0.0702295	−0.0351147	+	0.999383i	$0.511180\pi$
$812$	0	0
$813$	2.00000	0.0701431
$814$	0	0
$815$	0	0
$816$	2.00000	0.0700140
$817$	42.0000	1.46939
$818$	−25.0000	−0.874105
$819$	0	0
$820$	0	0
$821$	22.0000	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$821$	22.0000	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$822$	0	0
$823$	25.0000	0.871445	0.435723	−	0.900081i	$-0.356493\pi$
$823$	25.0000	0.871445	0.435723	+	0.900081i	$0.356493\pi$
$824$	−21.0000	−0.731570
$825$	0	0
$826$	0	0
$827$	−39.0000	−1.35616	−0.678081	−	0.734987i	$-0.737188\pi$
$827$	−39.0000	−1.35616	−0.678081	+	0.734987i	$0.737188\pi$
$828$	−6.00000	−0.208514
$829$	−30.0000	−1.04194	−0.520972	−	0.853574i	$-0.674430\pi$
$829$	−30.0000	−1.04194	−0.520972	+	0.853574i	$0.674430\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	14.0000	0.485363
$833$	0	0
$834$	−8.00000	−0.277017
$835$	0	0
$836$	0	0
$837$	10.0000	0.345651
$838$	24.0000	0.829066
$839$	48.0000	1.65714	0.828572	−	0.559883i	$-0.189154\pi$
$839$	48.0000	1.65714	0.828572	+	0.559883i	$0.189154\pi$
$840$	0	0
$841$	20.0000	0.689655
$842$	15.0000	0.516934
$843$	14.0000	0.482186
$844$	10.0000	0.344214
$845$	0	0
$846$	0	0
$847$	0	0
$848$	−6.00000	−0.206041
$849$	−16.0000	−0.549119
$850$	0	0
$851$	24.0000	0.822709
$852$	−2.00000	−0.0685189
$853$	−6.00000	−0.205436	−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000	−0.205436	−0.102718	+	0.994711i	$0.532754\pi$
$854$	0	0
$855$	0	0
$856$	−33.0000	−1.12792
$857$	−12.0000	−0.409912	−0.204956	−	0.978771i	$-0.565705\pi$
$857$	−12.0000	−0.409912	−0.204956	+	0.978771i	$0.565705\pi$
$858$	0	0
$859$	−32.0000	−1.09183	−0.545913	−	0.837842i	$-0.683817\pi$
$859$	−32.0000	−1.09183	−0.545913	+	0.837842i	$0.683817\pi$
$860$	0	0
$861$	0	0
$862$	−32.0000	−1.08992
$863$	−9.00000	−0.306364	−0.153182	−	0.988198i	$-0.548952\pi$
$863$	−9.00000	−0.306364	−0.153182	+	0.988198i	$0.548952\pi$
$864$	25.0000	0.850517
$865$	0	0
$866$	−2.00000	−0.0679628
$867$	13.0000	0.441503
$868$	0	0
$869$	0	0
$870$	0	0
$871$	−10.0000	−0.338837
$872$	−15.0000	−0.507964
$873$	32.0000	1.08304
$874$	−18.0000	−0.608859
$875$	0	0
$876$	−6.00000	−0.202721
$877$	−2.00000	−0.0675352	−0.0337676	−	0.999430i	$-0.510751\pi$
$877$	−2.00000	−0.0675352	−0.0337676	+	0.999430i	$0.510751\pi$
$878$	24.0000	0.809961
$879$	−24.0000	−0.809500
$880$	0	0
$881$	−43.0000	−1.44871	−0.724353	−	0.689429i	$-0.757862\pi$
$881$	−43.0000	−1.44871	−0.724353	+	0.689429i	$0.757862\pi$
$882$	0	0
$883$	36.0000	1.21150	0.605748	−	0.795656i	$-0.292874\pi$
$883$	36.0000	1.21150	0.605748	+	0.795656i	$0.292874\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	31.0000	1.04147
$887$	43.0000	1.44380	0.721899	−	0.691998i	$-0.243269\pi$
$887$	43.0000	1.44380	0.721899	+	0.691998i	$0.243269\pi$
$888$	−24.0000	−0.805387
$889$	0	0
$890$	0	0
$891$	0	0
$892$	0	0
$893$	0	0
$894$	−1.00000	−0.0334450
$895$	0	0
$896$	0	0
$897$	6.00000	0.200334
$898$	31.0000	1.03448
$899$	14.0000	0.466926
$900$	0	0
$901$	12.0000	0.399778
$902$	0	0
$903$	0	0
$904$	18.0000	0.598671
$905$	0	0
$906$	−14.0000	−0.465119
$907$	−19.0000	−0.630885	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	−19.0000	−0.630885	−0.315442	+	0.948945i	$0.602153\pi$
$908$	20.0000	0.663723
$909$	−18.0000	−0.597022
$910$	0	0
$911$	24.0000	0.795155	0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000	0.795155	0.397578	+	0.917568i	$0.369851\pi$
$912$	6.00000	0.198680
$913$	0	0
$914$	32.0000	1.05847
$915$	0	0
$916$	22.0000	0.726900
$917$	0	0
$918$	10.0000	0.330049
$919$	34.0000	1.12156	0.560778	−	0.827966i	$-0.310502\pi$
$919$	34.0000	1.12156	0.560778	+	0.827966i	$0.310502\pi$
$920$	0	0
$921$	−23.0000	−0.757876
$922$	18.0000	0.592798
$923$	−4.00000	−0.131662
$924$	0	0
$925$	0	0
$926$	3.00000	0.0985861
$927$	−14.0000	−0.459820
$928$	35.0000	1.14893
$929$	−29.0000	−0.951459	−0.475730	−	0.879592i	$-0.657816\pi$
$929$	−29.0000	−0.951459	−0.475730	+	0.879592i	$0.657816\pi$
$930$	0	0
$931$	0	0
$932$	−14.0000	−0.458585
$933$	−30.0000	−0.982156
$934$	3.00000	0.0981630
$935$	0	0
$936$	12.0000	0.392232
$937$	−8.00000	−0.261349	−0.130674	−	0.991425i	$-0.541714\pi$
$937$	−8.00000	−0.261349	−0.130674	+	0.991425i	$0.541714\pi$
$938$	0	0
$939$	−24.0000	−0.783210
$940$	0	0
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	−12.0000	−0.390981
$943$	−15.0000	−0.488467
$944$	−10.0000	−0.325472
$945$	0	0
$946$	0	0
$947$	−57.0000	−1.85225	−0.926126	−	0.377215i	$-0.876882\pi$
$947$	−57.0000	−1.85225	−0.926126	+	0.377215i	$0.876882\pi$
$948$	−2.00000	−0.0649570
$949$	−12.0000	−0.389536
$950$	0	0
$951$	6.00000	0.194563
$952$	0	0
$953$	60.0000	1.94359	0.971795	−	0.235826i	$-0.0757795\pi$
$953$	60.0000	1.94359	0.971795	+	0.235826i	$0.0757795\pi$
$954$	−12.0000	−0.388514
$955$	0	0
$956$	18.0000	0.582162
$957$	0	0
$958$	42.0000	1.35696
$959$	0	0
$960$	0	0
$961$	−27.0000	−0.870968
$962$	−16.0000	−0.515861
$963$	−22.0000	−0.708940
$964$	14.0000	0.450910
$965$	0	0
$966$	0	0
$967$	−13.0000	−0.418052	−0.209026	−	0.977910i	$-0.567029\pi$
$967$	−13.0000	−0.418052	−0.209026	+	0.977910i	$0.567029\pi$
$968$	33.0000	1.06066
$969$	−12.0000	−0.385496
$970$	0	0
$971$	−32.0000	−1.02693	−0.513464	−	0.858111i	$-0.671638\pi$
$971$	−32.0000	−1.02693	−0.513464	+	0.858111i	$0.671638\pi$
$972$	16.0000	0.513200
$973$	0	0
$974$	−12.0000	−0.384505
$975$	0	0
$976$	−7.00000	−0.224065
$977$	60.0000	1.91957	0.959785	−	0.280736i	$-0.0905785\pi$
$977$	60.0000	1.91957	0.959785	+	0.280736i	$0.0905785\pi$
$978$	4.00000	0.127906
$979$	0	0
$980$	0	0
$981$	−10.0000	−0.319275
$982$	−26.0000	−0.829693
$983$	3.00000	0.0956851	0.0478426	−	0.998855i	$-0.484765\pi$
$983$	3.00000	0.0956851	0.0478426	+	0.998855i	$0.484765\pi$
$984$	15.0000	0.478183
$985$	0	0
$986$	14.0000	0.445851
$987$	0	0
$988$	−12.0000	−0.381771
$989$	−21.0000	−0.667761
$990$	0	0
$991$	−50.0000	−1.58830	−0.794151	−	0.607720i	$-0.792084\pi$
$991$	−50.0000	−1.58830	−0.794151	+	0.607720i	$0.792084\pi$
$992$	10.0000	0.317500
$993$	−6.00000	−0.190404
$994$	0	0
$995$	0	0
$996$	−11.0000	−0.348548
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	16.0000	0.506471
$999$	−40.0000	−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1225.2.a.f.1.1		1
5.2	odd	4		245.2.b.c.99.2		2
5.3	odd	4		245.2.b.c.99.1		2
5.4	even	2		1225.2.a.d.1.1		1
7.2	even	3		175.2.e.a.151.1		2
7.4	even	3		175.2.e.a.51.1		2
7.6	odd	2		1225.2.a.g.1.1		1
15.2	even	4		2205.2.d.d.1324.1		2
15.8	even	4		2205.2.d.d.1324.2		2
35.2	odd	12		35.2.j.a.4.2	yes	4
35.3	even	12		245.2.j.c.79.2		4
35.4	even	6		175.2.e.b.51.1		2
35.9	even	6		175.2.e.b.151.1		2
35.12	even	12		245.2.j.c.214.2		4
35.13	even	4		245.2.b.b.99.1		2
35.17	even	12		245.2.j.c.79.1		4
35.18	odd	12		35.2.j.a.9.2	yes	4
35.23	odd	12		35.2.j.a.4.1	✓	4
35.27	even	4		245.2.b.b.99.2		2
35.32	odd	12		35.2.j.a.9.1	yes	4
35.33	even	12		245.2.j.c.214.1		4
35.34	odd	2		1225.2.a.b.1.1		1
105.2	even	12		315.2.bf.a.109.1		4
105.23	even	12		315.2.bf.a.109.2		4
105.32	even	12		315.2.bf.a.289.2		4
105.53	even	12		315.2.bf.a.289.1		4
105.62	odd	4		2205.2.d.e.1324.1		2
105.83	odd	4		2205.2.d.e.1324.2		2
140.23	even	12		560.2.bw.b.529.1		4
140.67	even	12		560.2.bw.b.289.1		4
140.107	even	12		560.2.bw.b.529.2		4
140.123	even	12		560.2.bw.b.289.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.j.a.4.1	✓	4	35.23	odd	12
35.2.j.a.4.2	yes	4	35.2	odd	12
35.2.j.a.9.1	yes	4	35.32	odd	12
35.2.j.a.9.2	yes	4	35.18	odd	12
175.2.e.a.51.1		2	7.4	even	3
175.2.e.a.151.1		2	7.2	even	3
175.2.e.b.51.1		2	35.4	even	6
175.2.e.b.151.1		2	35.9	even	6
245.2.b.b.99.1		2	35.13	even	4
245.2.b.b.99.2		2	35.27	even	4
245.2.b.c.99.1		2	5.3	odd	4
245.2.b.c.99.2		2	5.2	odd	4
245.2.j.c.79.1		4	35.17	even	12
245.2.j.c.79.2		4	35.3	even	12
245.2.j.c.214.1		4	35.33	even	12
245.2.j.c.214.2		4	35.12	even	12
315.2.bf.a.109.1		4	105.2	even	12
315.2.bf.a.109.2		4	105.23	even	12
315.2.bf.a.289.1		4	105.53	even	12
315.2.bf.a.289.2		4	105.32	even	12
560.2.bw.b.289.1		4	140.67	even	12
560.2.bw.b.289.2		4	140.123	even	12
560.2.bw.b.529.1		4	140.23	even	12
560.2.bw.b.529.2		4	140.107	even	12
1225.2.a.b.1.1		1	35.34	odd	2
1225.2.a.d.1.1		1	5.4	even	2
1225.2.a.f.1.1		1	1.1	even	1	trivial
1225.2.a.g.1.1		1	7.6	odd	2
2205.2.d.d.1324.1		2	15.2	even	4
2205.2.d.d.1324.2		2	15.8	even	4
2205.2.d.e.1324.1		2	105.62	odd	4
2205.2.d.e.1324.2		2	105.83	odd	4

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:	\( N \)	\(=\)	\( 1225 = 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1225.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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