LMFDB - Embedded newform 1470.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(1,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$

\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +6.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} -6.00000 q^{29} -1.00000 q^{30} +4.00000 q^{31} +1.00000 q^{32} +6.00000 q^{34} +1.00000 q^{36} +2.00000 q^{37} +4.00000 q^{38} +2.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} +8.00000 q^{43} +1.00000 q^{45} +12.0000 q^{47} -1.00000 q^{48} +1.00000 q^{50} -6.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} -1.00000 q^{54} -4.00000 q^{57} -6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} -2.00000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -2.00000 q^{65} +8.00000 q^{67} +6.00000 q^{68} +1.00000 q^{72} -14.0000 q^{73} +2.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +2.00000 q^{78} -16.0000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} -12.0000 q^{83} +6.00000 q^{85} +8.00000 q^{86} +6.00000 q^{87} -6.00000 q^{89} +1.00000 q^{90} -4.00000 q^{93} +12.0000 q^{94} +4.00000 q^{95} -1.00000 q^{96} -14.0000 q^{97} +O(q^{100})\)

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
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	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	$-0.589456\pi$
$13$	−2.00000	−0.554700	−0.277350	+	0.960769i	$0.589456\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	6.00000	1.45521	0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000	1.45521	0.727607	+	0.685994i	$0.240633\pi$
$18$	1.00000	0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	0	0
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−1.00000	−0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	4.00000	0.648886
$39$	2.00000	0.320256
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	0	0
$43$	8.00000	1.21999	0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000	1.21999	0.609994	+	0.792406i	$0.291172\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	0	0
$47$	12.0000	1.75038	0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000	1.75038	0.875190	+	0.483779i	$0.160736\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	1.00000	0.141421
$51$	−6.00000	−0.840168
$52$	−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	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	0	0
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	12.0000	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$59$	12.0000	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$60$	−1.00000	−0.129099
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	4.00000	0.508001
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	8.00000	0.977356	0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000	0.977356	0.488678	+	0.872464i	$0.337479\pi$
$68$	6.00000	0.727607
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	−14.0000	−1.63858	−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000	−1.63858	−0.819288	+	0.573382i	$0.805631\pi$
$74$	2.00000	0.232495
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	2.00000	0.226455
$79$	−16.0000	−1.80014	−0.900070	−	0.435745i	$-0.856485\pi$
$79$	−16.0000	−1.80014	−0.900070	+	0.435745i	$0.856485\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−6.00000	−0.662589
$83$	−12.0000	−1.31717	−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000	−1.31717	−0.658586	+	0.752506i	$0.728845\pi$
$84$	0	0
$85$	6.00000	0.650791
$86$	8.00000	0.862662
$87$	6.00000	0.643268
$88$	0	0
$89$	−6.00000	−0.635999	−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000	−0.635999	−0.317999	+	0.948091i	$0.603011\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	0	0
$93$	−4.00000	−0.414781
$94$	12.0000	1.23771
$95$	4.00000	0.410391
$96$	−1.00000	−0.102062
$97$	−14.0000	−1.42148	−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000	−1.42148	−0.710742	+	0.703452i	$0.751641\pi$
$98$	0	0
$99$	0	0
$100$	1.00000	0.100000
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	−6.00000	−0.594089
$103$	16.0000	1.57653	0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000	1.57653	0.788263	+	0.615338i	$0.210980\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	6.00000	0.582772
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	−0.0962250
$109$	14.0000	1.34096	0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000	1.34096	0.670478	+	0.741929i	$0.266089\pi$
$110$	0	0
$111$	−2.00000	−0.189832
$112$	0	0
$113$	18.0000	1.69330	0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000	1.69330	0.846649	+	0.532152i	$0.178617\pi$
$114$	−4.00000	−0.374634
$115$	0	0
$116$	−6.00000	−0.557086
$117$	−2.00000	−0.184900
$118$	12.0000	1.10469
$119$	0	0
$120$	−1.00000	−0.0912871
$121$	−11.0000	−1.00000
$122$	−2.00000	−0.181071
$123$	6.00000	0.541002
$124$	4.00000	0.359211
$125$	1.00000	0.0894427
$126$	0	0
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	−8.00000	−0.704361
$130$	−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
$134$	8.00000	0.691095
$135$	−1.00000	−0.0860663
$136$	6.00000	0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	0	0
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	0	0
$141$	−12.0000	−1.01058
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	−6.00000	−0.498273
$146$	−14.0000	−1.15865
$147$	0	0
$148$	2.00000	0.164399
$149$	18.0000	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$150$	−1.00000	−0.0816497
$151$	−16.0000	−1.30206	−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000	−1.30206	−0.651031	+	0.759051i	$0.725663\pi$
$152$	4.00000	0.324443
$153$	6.00000	0.485071
$154$	0	0
$155$	4.00000	0.321288
$156$	2.00000	0.160128
$157$	−2.00000	−0.159617	−0.0798087	−	0.996810i	$-0.525431\pi$
$157$	−2.00000	−0.159617	−0.0798087	+	0.996810i	$0.525431\pi$
$158$	−16.0000	−1.27289
$159$	−6.00000	−0.475831
$160$	1.00000	0.0790569
$161$	0	0
$162$	1.00000	0.0785674
$163$	−16.0000	−1.25322	−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000	−1.25322	−0.626608	+	0.779334i	$0.715557\pi$
$164$	−6.00000	−0.468521
$165$	0	0
$166$	−12.0000	−0.931381
$167$	−12.0000	−0.928588	−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000	−0.928588	−0.464294	+	0.885681i	$0.653692\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	6.00000	0.460179
$171$	4.00000	0.305888
$172$	8.00000	0.609994
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	0	0
$177$	−12.0000	−0.901975
$178$	−6.00000	−0.449719
$179$	0	0		−	1.00000i	$-0.5\pi$
$179$	0	0			1.00000i	$0.5\pi$
$180$	1.00000	0.0745356
$181$	−2.00000	−0.148659	−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000	−0.148659	−0.0743294	+	0.997234i	$0.523682\pi$
$182$	0	0
$183$	2.00000	0.147844
$184$	0	0
$185$	2.00000	0.147043
$186$	−4.00000	−0.293294
$187$	0	0
$188$	12.0000	0.875190
$189$	0	0
$190$	4.00000	0.290191
$191$	0	0		−	1.00000i	$-0.5\pi$
$191$	0	0			1.00000i	$0.5\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−14.0000	−1.00514
$195$	2.00000	0.143223
$196$	0	0
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	0	0
$199$	4.00000	0.283552	0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000	0.283552	0.141776	+	0.989899i	$0.454719\pi$
$200$	1.00000	0.0707107
$201$	−8.00000	−0.564276
$202$	6.00000	0.422159
$203$	0	0
$204$	−6.00000	−0.420084
$205$	−6.00000	−0.419058
$206$	16.0000	1.11477
$207$	0	0
$208$	−2.00000	−0.138675
$209$	0	0
$210$	0	0
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	12.0000	0.820303
$215$	8.00000	0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	14.0000	0.948200
$219$	14.0000	0.946032
$220$	0	0
$221$	−12.0000	−0.807207
$222$	−2.00000	−0.134231
$223$	16.0000	1.07144	0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000	1.07144	0.535720	+	0.844396i	$0.320040\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	18.0000	1.19734
$227$	12.0000	0.796468	0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000	0.796468	0.398234	+	0.917284i	$0.369623\pi$
$228$	−4.00000	−0.264906
$229$	−2.00000	−0.132164	−0.0660819	−	0.997814i	$-0.521050\pi$
$229$	−2.00000	−0.132164	−0.0660819	+	0.997814i	$0.521050\pi$
$230$	0	0
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−6.00000	−0.393073	−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000	−0.393073	−0.196537	+	0.980497i	$0.562969\pi$
$234$	−2.00000	−0.130744
$235$	12.0000	0.782794
$236$	12.0000	0.781133
$237$	16.0000	1.03931
$238$	0	0
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	−26.0000	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$241$	−26.0000	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$242$	−11.0000	−0.707107
$243$	−1.00000	−0.0641500
$244$	−2.00000	−0.128037
$245$	0	0
$246$	6.00000	0.382546
$247$	−8.00000	−0.509028
$248$	4.00000	0.254000
$249$	12.0000	0.760469
$250$	1.00000	0.0632456
$251$	−12.0000	−0.757433	−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000	−0.757433	−0.378717	+	0.925513i	$0.623635\pi$
$252$	0	0
$253$	0	0
$254$	8.00000	0.501965
$255$	−6.00000	−0.375735
$256$	1.00000	0.0625000
$257$	6.00000	0.374270	0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000	0.374270	0.187135	+	0.982334i	$0.440080\pi$
$258$	−8.00000	−0.498058
$259$	0	0
$260$	−2.00000	−0.124035
$261$	−6.00000	−0.371391
$262$	−12.0000	−0.741362
$263$	0	0		−	1.00000i	$-0.5\pi$
$263$	0	0			1.00000i	$0.5\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	0	0
$267$	6.00000	0.367194
$268$	8.00000	0.488678
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−1.00000	−0.0608581
$271$	−20.0000	−1.21491	−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000	−1.21491	−0.607457	+	0.794353i	$0.707810\pi$
$272$	6.00000	0.363803
$273$	0	0
$274$	−6.00000	−0.362473
$275$	0	0
$276$	0	0
$277$	−22.0000	−1.32185	−0.660926	−	0.750451i	$-0.729836\pi$
$277$	−22.0000	−1.32185	−0.660926	+	0.750451i	$0.729836\pi$
$278$	4.00000	0.239904
$279$	4.00000	0.239474
$280$	0	0
$281$	−30.0000	−1.78965	−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000	−1.78965	−0.894825	+	0.446417i	$0.852700\pi$
$282$	−12.0000	−0.714590
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	0	0
$285$	−4.00000	−0.236940
$286$	0	0
$287$	0	0
$288$	1.00000	0.0589256
$289$	19.0000	1.11765
$290$	−6.00000	−0.352332
$291$	14.0000	0.820695
$292$	−14.0000	−0.819288
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	0	0
$295$	12.0000	0.698667
$296$	2.00000	0.116248
$297$	0	0
$298$	18.0000	1.04271
$299$	0	0
$300$	−1.00000	−0.0577350
$301$	0	0
$302$	−16.0000	−0.920697
$303$	−6.00000	−0.344691
$304$	4.00000	0.229416
$305$	−2.00000	−0.114520
$306$	6.00000	0.342997
$307$	−20.0000	−1.14146	−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000	−1.14146	−0.570730	+	0.821138i	$0.693340\pi$
$308$	0	0
$309$	−16.0000	−0.910208
$310$	4.00000	0.227185
$311$	0	0		−	1.00000i	$-0.5\pi$
$311$	0	0			1.00000i	$0.5\pi$
$312$	2.00000	0.113228
$313$	10.0000	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$313$	10.0000	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$314$	−2.00000	−0.112867
$315$	0	0
$316$	−16.0000	−0.900070
$317$	30.0000	1.68497	0.842484	−	0.538721i	$-0.181092\pi$
$317$	30.0000	1.68497	0.842484	+	0.538721i	$0.181092\pi$
$318$	−6.00000	−0.336463
$319$	0	0
$320$	1.00000	0.0559017
$321$	−12.0000	−0.669775
$322$	0	0
$323$	24.0000	1.33540
$324$	1.00000	0.0555556
$325$	−2.00000	−0.110940
$326$	−16.0000	−0.886158
$327$	−14.0000	−0.774202
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	−12.0000	−0.658586
$333$	2.00000	0.109599
$334$	−12.0000	−0.656611
$335$	8.00000	0.437087
$336$	0	0
$337$	−22.0000	−1.19842	−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000	−1.19842	−0.599208	+	0.800593i	$0.704518\pi$
$338$	−9.00000	−0.489535
$339$	−18.0000	−0.977626
$340$	6.00000	0.325396
$341$	0	0
$342$	4.00000	0.216295
$343$	0	0
$344$	8.00000	0.431331
$345$	0	0
$346$	6.00000	0.322562
$347$	12.0000	0.644194	0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000	0.644194	0.322097	+	0.946707i	$0.395612\pi$
$348$	6.00000	0.321634
$349$	−26.0000	−1.39175	−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000	−1.39175	−0.695874	+	0.718164i	$0.744983\pi$
$350$	0	0
$351$	2.00000	0.106752
$352$	0	0
$353$	−18.0000	−0.958043	−0.479022	−	0.877803i	$-0.659008\pi$
$353$	−18.0000	−0.958043	−0.479022	+	0.877803i	$0.659008\pi$
$354$	−12.0000	−0.637793
$355$	0	0
$356$	−6.00000	−0.317999
$357$	0	0
$358$	0	0
$359$	0	0		−	1.00000i	$-0.5\pi$
$359$	0	0			1.00000i	$0.5\pi$
$360$	1.00000	0.0527046
$361$	−3.00000	−0.157895
$362$	−2.00000	−0.105118
$363$	11.0000	0.577350
$364$	0	0
$365$	−14.0000	−0.732793
$366$	2.00000	0.104542
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	2.00000	0.103975
$371$	0	0
$372$	−4.00000	−0.207390
$373$	26.0000	1.34623	0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000	1.34623	0.673114	+	0.739538i	$0.264956\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	12.0000	0.618853
$377$	12.0000	0.618031
$378$	0	0
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	4.00000	0.205196
$381$	−8.00000	−0.409852
$382$	0	0
$383$	36.0000	1.83951	0.919757	−	0.392488i	$-0.128386\pi$
$383$	36.0000	1.83951	0.919757	+	0.392488i	$0.128386\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−22.0000	−1.11977
$387$	8.00000	0.406663
$388$	−14.0000	−0.710742
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	2.00000	0.101274
$391$	0	0
$392$	0	0
$393$	12.0000	0.605320
$394$	−18.0000	−0.906827
$395$	−16.0000	−0.805047
$396$	0	0
$397$	−2.00000	−0.100377	−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000	−0.100377	−0.0501886	+	0.998740i	$0.515982\pi$
$398$	4.00000	0.200502
$399$	0	0
$400$	1.00000	0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	−8.00000	−0.399004
$403$	−8.00000	−0.398508
$404$	6.00000	0.298511
$405$	1.00000	0.0496904
$406$	0	0
$407$	0	0
$408$	−6.00000	−0.297044
$409$	22.0000	1.08783	0.543915	−	0.839140i	$-0.316941\pi$
$409$	22.0000	1.08783	0.543915	+	0.839140i	$0.316941\pi$
$410$	−6.00000	−0.296319
$411$	6.00000	0.295958
$412$	16.0000	0.788263
$413$	0	0
$414$	0	0
$415$	−12.0000	−0.589057
$416$	−2.00000	−0.0980581
$417$	−4.00000	−0.195881
$418$	0	0
$419$	12.0000	0.586238	0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000	0.586238	0.293119	+	0.956076i	$0.405307\pi$
$420$	0	0
$421$	−10.0000	−0.487370	−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000	−0.487370	−0.243685	+	0.969854i	$0.578356\pi$
$422$	−28.0000	−1.36302
$423$	12.0000	0.583460
$424$	6.00000	0.291386
$425$	6.00000	0.291043
$426$	0	0
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	8.00000	0.385794
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	−1.00000	−0.0481125
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	0	0
$435$	6.00000	0.287678
$436$	14.0000	0.670478
$437$	0	0
$438$	14.0000	0.668946
$439$	28.0000	1.33637	0.668184	−	0.743996i	$-0.267072\pi$
$439$	28.0000	1.33637	0.668184	+	0.743996i	$0.267072\pi$
$440$	0	0
$441$	0	0
$442$	−12.0000	−0.570782
$443$	12.0000	0.570137	0.285069	−	0.958507i	$-0.407984\pi$
$443$	12.0000	0.570137	0.285069	+	0.958507i	$0.407984\pi$
$444$	−2.00000	−0.0949158
$445$	−6.00000	−0.284427
$446$	16.0000	0.757622
$447$	−18.0000	−0.851371
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	18.0000	0.846649
$453$	16.0000	0.751746
$454$	12.0000	0.563188
$455$	0	0
$456$	−4.00000	−0.187317
$457$	2.00000	0.0935561	0.0467780	−	0.998905i	$-0.485105\pi$
$457$	2.00000	0.0935561	0.0467780	+	0.998905i	$0.485105\pi$
$458$	−2.00000	−0.0934539
$459$	−6.00000	−0.280056
$460$	0	0
$461$	30.0000	1.39724	0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000	1.39724	0.698620	+	0.715493i	$0.253798\pi$
$462$	0	0
$463$	−16.0000	−0.743583	−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000	−0.743583	−0.371792	+	0.928316i	$0.621256\pi$
$464$	−6.00000	−0.278543
$465$	−4.00000	−0.185496
$466$	−6.00000	−0.277945
$467$	−12.0000	−0.555294	−0.277647	−	0.960683i	$-0.589555\pi$
$467$	−12.0000	−0.555294	−0.277647	+	0.960683i	$0.589555\pi$
$468$	−2.00000	−0.0924500
$469$	0	0
$470$	12.0000	0.553519
$471$	2.00000	0.0921551
$472$	12.0000	0.552345
$473$	0	0
$474$	16.0000	0.734904
$475$	4.00000	0.183533
$476$	0	0
$477$	6.00000	0.274721
$478$	0	0
$479$	24.0000	1.09659	0.548294	−	0.836286i	$-0.315277\pi$
$479$	24.0000	1.09659	0.548294	+	0.836286i	$0.315277\pi$
$480$	−1.00000	−0.0456435
$481$	−4.00000	−0.182384
$482$	−26.0000	−1.18427
$483$	0	0
$484$	−11.0000	−0.500000
$485$	−14.0000	−0.635707
$486$	−1.00000	−0.0453609
$487$	−16.0000	−0.725029	−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000	−0.725029	−0.362515	+	0.931978i	$0.618082\pi$
$488$	−2.00000	−0.0905357
$489$	16.0000	0.723545
$490$	0	0
$491$	24.0000	1.08310	0.541552	−	0.840667i	$-0.317837\pi$
$491$	24.0000	1.08310	0.541552	+	0.840667i	$0.317837\pi$
$492$	6.00000	0.270501
$493$	−36.0000	−1.62136
$494$	−8.00000	−0.359937
$495$	0	0
$496$	4.00000	0.179605
$497$	0	0
$498$	12.0000	0.537733
$499$	−4.00000	−0.179065	−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000	−0.179065	−0.0895323	+	0.995984i	$0.528537\pi$
$500$	1.00000	0.0447214
$501$	12.0000	0.536120
$502$	−12.0000	−0.535586
$503$	−12.0000	−0.535054	−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000	−0.535054	−0.267527	+	0.963550i	$0.586206\pi$
$504$	0	0
$505$	6.00000	0.266996
$506$	0	0
$507$	9.00000	0.399704
$508$	8.00000	0.354943
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	−6.00000	−0.265684
$511$	0	0
$512$	1.00000	0.0441942
$513$	−4.00000	−0.176604
$514$	6.00000	0.264649
$515$	16.0000	0.705044
$516$	−8.00000	−0.352180
$517$	0	0
$518$	0	0
$519$	−6.00000	−0.263371
$520$	−2.00000	−0.0877058
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	−6.00000	−0.262613
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−12.0000	−0.524222
$525$	0	0
$526$	0	0
$527$	24.0000	1.04546
$528$	0	0
$529$	−23.0000	−1.00000
$530$	6.00000	0.260623
$531$	12.0000	0.520756
$532$	0	0
$533$	12.0000	0.519778
$534$	6.00000	0.259645
$535$	12.0000	0.518805
$536$	8.00000	0.345547
$537$	0	0
$538$	−18.0000	−0.776035
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	38.0000	1.63375	0.816874	−	0.576816i	$-0.195705\pi$
$541$	38.0000	1.63375	0.816874	+	0.576816i	$0.195705\pi$
$542$	−20.0000	−0.859074
$543$	2.00000	0.0858282
$544$	6.00000	0.257248
$545$	14.0000	0.599694
$546$	0	0
$547$	8.00000	0.342055	0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000	0.342055	0.171028	+	0.985266i	$0.445291\pi$
$548$	−6.00000	−0.256307
$549$	−2.00000	−0.0853579
$550$	0	0
$551$	−24.0000	−1.02243
$552$	0	0
$553$	0	0
$554$	−22.0000	−0.934690
$555$	−2.00000	−0.0848953
$556$	4.00000	0.169638
$557$	30.0000	1.27114	0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000	1.27114	0.635570	+	0.772043i	$0.280765\pi$
$558$	4.00000	0.169334
$559$	−16.0000	−0.676728
$560$	0	0
$561$	0	0
$562$	−30.0000	−1.26547
$563$	36.0000	1.51722	0.758610	−	0.651546i	$-0.225879\pi$
$563$	36.0000	1.51722	0.758610	+	0.651546i	$0.225879\pi$
$564$	−12.0000	−0.505291
$565$	18.0000	0.757266
$566$	−20.0000	−0.840663
$567$	0	0
$568$	0	0
$569$	−6.00000	−0.251533	−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000	−0.251533	−0.125767	+	0.992060i	$0.540139\pi$
$570$	−4.00000	−0.167542
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	0	0
$573$	0	0
$574$	0	0
$575$	0	0
$576$	1.00000	0.0416667
$577$	34.0000	1.41544	0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000	1.41544	0.707719	+	0.706494i	$0.249724\pi$
$578$	19.0000	0.790296
$579$	22.0000	0.914289
$580$	−6.00000	−0.249136
$581$	0	0
$582$	14.0000	0.580319
$583$	0	0
$584$	−14.0000	−0.579324
$585$	−2.00000	−0.0826898
$586$	6.00000	0.247858
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	0	0
$589$	16.0000	0.659269
$590$	12.0000	0.494032
$591$	18.0000	0.740421
$592$	2.00000	0.0821995
$593$	−42.0000	−1.72473	−0.862367	−	0.506284i	$-0.831019\pi$
$593$	−42.0000	−1.72473	−0.862367	+	0.506284i	$0.831019\pi$
$594$	0	0
$595$	0	0
$596$	18.0000	0.737309
$597$	−4.00000	−0.163709
$598$	0	0
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	−1.00000	−0.0408248
$601$	−2.00000	−0.0815817	−0.0407909	−	0.999168i	$-0.512988\pi$
$601$	−2.00000	−0.0815817	−0.0407909	+	0.999168i	$0.512988\pi$
$602$	0	0
$603$	8.00000	0.325785
$604$	−16.0000	−0.651031
$605$	−11.0000	−0.447214
$606$	−6.00000	−0.243733
$607$	−32.0000	−1.29884	−0.649420	−	0.760430i	$-0.724988\pi$
$607$	−32.0000	−1.29884	−0.649420	+	0.760430i	$0.724988\pi$
$608$	4.00000	0.162221
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	−24.0000	−0.970936
$612$	6.00000	0.242536
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	−20.0000	−0.807134
$615$	6.00000	0.241943
$616$	0	0
$617$	42.0000	1.69086	0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000	1.69086	0.845428	+	0.534089i	$0.179345\pi$
$618$	−16.0000	−0.643614
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	0	0
$623$	0	0
$624$	2.00000	0.0800641
$625$	1.00000	0.0400000
$626$	10.0000	0.399680
$627$	0	0
$628$	−2.00000	−0.0798087
$629$	12.0000	0.478471
$630$	0	0
$631$	−16.0000	−0.636950	−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000	−0.636950	−0.318475	+	0.947931i	$0.603171\pi$
$632$	−16.0000	−0.636446
$633$	28.0000	1.11290
$634$	30.0000	1.19145
$635$	8.00000	0.317470
$636$	−6.00000	−0.237915
$637$	0	0
$638$	0	0
$639$	0	0
$640$	1.00000	0.0395285
$641$	18.0000	0.710957	0.355479	−	0.934684i	$-0.384318\pi$
$641$	18.0000	0.710957	0.355479	+	0.934684i	$0.384318\pi$
$642$	−12.0000	−0.473602
$643$	4.00000	0.157745	0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000	0.157745	0.0788723	+	0.996885i	$0.474868\pi$
$644$	0	0
$645$	−8.00000	−0.315000
$646$	24.0000	0.944267
$647$	12.0000	0.471769	0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000	0.471769	0.235884	+	0.971781i	$0.424201\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−42.0000	−1.64359	−0.821794	−	0.569785i	$-0.807026\pi$
$653$	−42.0000	−1.64359	−0.821794	+	0.569785i	$0.807026\pi$
$654$	−14.0000	−0.547443
$655$	−12.0000	−0.468879
$656$	−6.00000	−0.234261
$657$	−14.0000	−0.546192
$658$	0	0
$659$	0	0		−	1.00000i	$-0.5\pi$
$659$	0	0			1.00000i	$0.5\pi$
$660$	0	0
$661$	−26.0000	−1.01128	−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000	−1.01128	−0.505641	+	0.862744i	$0.668744\pi$
$662$	−4.00000	−0.155464
$663$	12.0000	0.466041
$664$	−12.0000	−0.465690
$665$	0	0
$666$	2.00000	0.0774984
$667$	0	0
$668$	−12.0000	−0.464294
$669$	−16.0000	−0.618596
$670$	8.00000	0.309067
$671$	0	0
$672$	0	0
$673$	50.0000	1.92736	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000	1.92736	0.963679	+	0.267063i	$0.0860531\pi$
$674$	−22.0000	−0.847408
$675$	−1.00000	−0.0384900
$676$	−9.00000	−0.346154
$677$	30.0000	1.15299	0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000	1.15299	0.576497	+	0.817099i	$0.304419\pi$
$678$	−18.0000	−0.691286
$679$	0	0
$680$	6.00000	0.230089
$681$	−12.0000	−0.459841
$682$	0	0
$683$	36.0000	1.37750	0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000	1.37750	0.688751	+	0.724998i	$0.258159\pi$
$684$	4.00000	0.152944
$685$	−6.00000	−0.229248
$686$	0	0
$687$	2.00000	0.0763048
$688$	8.00000	0.304997
$689$	−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	$0.624220\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	12.0000	0.455514
$695$	4.00000	0.151729
$696$	6.00000	0.227429
$697$	−36.0000	−1.36360
$698$	−26.0000	−0.984115
$699$	6.00000	0.226941
$700$	0	0
$701$	−6.00000	−0.226617	−0.113308	−	0.993560i	$-0.536145\pi$
$701$	−6.00000	−0.226617	−0.113308	+	0.993560i	$0.536145\pi$
$702$	2.00000	0.0754851
$703$	8.00000	0.301726
$704$	0	0
$705$	−12.0000	−0.451946
$706$	−18.0000	−0.677439
$707$	0	0
$708$	−12.0000	−0.450988
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	0	0
$711$	−16.0000	−0.600047
$712$	−6.00000	−0.224860
$713$	0	0
$714$	0	0
$715$	0	0
$716$	0	0
$717$	0	0
$718$	0	0
$719$	0	0		−	1.00000i	$-0.5\pi$
$719$	0	0			1.00000i	$0.5\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	−3.00000	−0.111648
$723$	26.0000	0.966950
$724$	−2.00000	−0.0743294
$725$	−6.00000	−0.222834
$726$	11.0000	0.408248
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−14.0000	−0.518163
$731$	48.0000	1.77534
$732$	2.00000	0.0739221
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−8.00000	−0.295285
$735$	0	0
$736$	0	0
$737$	0	0
$738$	−6.00000	−0.220863
$739$	44.0000	1.61857	0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000	1.61857	0.809283	+	0.587419i	$0.199856\pi$
$740$	2.00000	0.0735215
$741$	8.00000	0.293887
$742$	0	0
$743$	−24.0000	−0.880475	−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000	−0.880475	−0.440237	+	0.897881i	$0.645106\pi$
$744$	−4.00000	−0.146647
$745$	18.0000	0.659469
$746$	26.0000	0.951928
$747$	−12.0000	−0.439057
$748$	0	0
$749$	0	0
$750$	−1.00000	−0.0365148
$751$	−40.0000	−1.45962	−0.729810	−	0.683650i	$-0.760392\pi$
$751$	−40.0000	−1.45962	−0.729810	+	0.683650i	$0.760392\pi$
$752$	12.0000	0.437595
$753$	12.0000	0.437304
$754$	12.0000	0.437014
$755$	−16.0000	−0.582300
$756$	0	0
$757$	−22.0000	−0.799604	−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000	−0.799604	−0.399802	+	0.916602i	$0.630921\pi$
$758$	20.0000	0.726433
$759$	0	0
$760$	4.00000	0.145095
$761$	−30.0000	−1.08750	−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000	−1.08750	−0.543750	+	0.839248i	$0.682996\pi$
$762$	−8.00000	−0.289809
$763$	0	0
$764$	0	0
$765$	6.00000	0.216930
$766$	36.0000	1.30073
$767$	−24.0000	−0.866590
$768$	−1.00000	−0.0360844
$769$	−50.0000	−1.80305	−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000	−1.80305	−0.901523	+	0.432731i	$0.857550\pi$
$770$	0	0
$771$	−6.00000	−0.216085
$772$	−22.0000	−0.791797
$773$	6.00000	0.215805	0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000	0.215805	0.107903	+	0.994161i	$0.465587\pi$
$774$	8.00000	0.287554
$775$	4.00000	0.143684
$776$	−14.0000	−0.502571
$777$	0	0
$778$	−30.0000	−1.07555
$779$	−24.0000	−0.859889
$780$	2.00000	0.0716115
$781$	0	0
$782$	0	0
$783$	6.00000	0.214423
$784$	0	0
$785$	−2.00000	−0.0713831
$786$	12.0000	0.428026
$787$	28.0000	0.998092	0.499046	−	0.866575i	$-0.333684\pi$
$787$	28.0000	0.998092	0.499046	+	0.866575i	$0.333684\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	−16.0000	−0.569254
$791$	0	0
$792$	0	0
$793$	4.00000	0.142044
$794$	−2.00000	−0.0709773
$795$	−6.00000	−0.212798
$796$	4.00000	0.141776
$797$	6.00000	0.212531	0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000	0.212531	0.106265	+	0.994338i	$0.466111\pi$
$798$	0	0
$799$	72.0000	2.54718
$800$	1.00000	0.0353553
$801$	−6.00000	−0.212000
$802$	18.0000	0.635602
$803$	0	0
$804$	−8.00000	−0.282138
$805$	0	0
$806$	−8.00000	−0.281788
$807$	18.0000	0.633630
$808$	6.00000	0.211079
$809$	−30.0000	−1.05474	−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000	−1.05474	−0.527372	+	0.849635i	$0.676823\pi$
$810$	1.00000	0.0351364
$811$	4.00000	0.140459	0.0702295	−	0.997531i	$-0.477627\pi$
$811$	4.00000	0.140459	0.0702295	+	0.997531i	$0.477627\pi$
$812$	0	0
$813$	20.0000	0.701431
$814$	0	0
$815$	−16.0000	−0.560456
$816$	−6.00000	−0.210042
$817$	32.0000	1.11954
$818$	22.0000	0.769212
$819$	0	0
$820$	−6.00000	−0.209529
$821$	−30.0000	−1.04701	−0.523504	−	0.852023i	$-0.675375\pi$
$821$	−30.0000	−1.04701	−0.523504	+	0.852023i	$0.675375\pi$
$822$	6.00000	0.209274
$823$	8.00000	0.278862	0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000	0.278862	0.139431	+	0.990232i	$0.455473\pi$
$824$	16.0000	0.557386
$825$	0	0
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	0	0
$829$	46.0000	1.59765	0.798823	−	0.601566i	$-0.205456\pi$
$829$	46.0000	1.59765	0.798823	+	0.601566i	$0.205456\pi$
$830$	−12.0000	−0.416526
$831$	22.0000	0.763172
$832$	−2.00000	−0.0693375
$833$	0	0
$834$	−4.00000	−0.138509
$835$	−12.0000	−0.415277
$836$	0	0
$837$	−4.00000	−0.138260
$838$	12.0000	0.414533
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−10.0000	−0.344623
$843$	30.0000	1.03325
$844$	−28.0000	−0.963800
$845$	−9.00000	−0.309609
$846$	12.0000	0.412568
$847$	0	0
$848$	6.00000	0.206041
$849$	20.0000	0.686398
$850$	6.00000	0.205798
$851$	0	0
$852$	0	0
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	4.00000	0.136797
$856$	12.0000	0.410152
$857$	−18.0000	−0.614868	−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000	−0.614868	−0.307434	+	0.951569i	$0.599470\pi$
$858$	0	0
$859$	4.00000	0.136478	0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000	0.136478	0.0682391	+	0.997669i	$0.478262\pi$
$860$	8.00000	0.272798
$861$	0	0
$862$	24.0000	0.817443
$863$	−48.0000	−1.63394	−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000	−1.63394	−0.816970	+	0.576681i	$0.804348\pi$
$864$	−1.00000	−0.0340207
$865$	6.00000	0.204006
$866$	34.0000	1.15537
$867$	−19.0000	−0.645274
$868$	0	0
$869$	0	0
$870$	6.00000	0.203419
$871$	−16.0000	−0.542139
$872$	14.0000	0.474100
$873$	−14.0000	−0.473828
$874$	0	0
$875$	0	0
$876$	14.0000	0.473016
$877$	50.0000	1.68838	0.844190	−	0.536044i	$-0.180082\pi$
$877$	50.0000	1.68838	0.844190	+	0.536044i	$0.180082\pi$
$878$	28.0000	0.944954
$879$	−6.00000	−0.202375
$880$	0	0
$881$	42.0000	1.41502	0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000	1.41502	0.707508	+	0.706705i	$0.249819\pi$
$882$	0	0
$883$	−40.0000	−1.34611	−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000	−1.34611	−0.673054	+	0.739594i	$0.735018\pi$
$884$	−12.0000	−0.403604
$885$	−12.0000	−0.403376
$886$	12.0000	0.403148
$887$	12.0000	0.402921	0.201460	−	0.979497i	$-0.435431\pi$
$887$	12.0000	0.402921	0.201460	+	0.979497i	$0.435431\pi$
$888$	−2.00000	−0.0671156
$889$	0	0
$890$	−6.00000	−0.201120
$891$	0	0
$892$	16.0000	0.535720
$893$	48.0000	1.60626
$894$	−18.0000	−0.602010
$895$	0	0
$896$	0	0
$897$	0	0
$898$	−6.00000	−0.200223
$899$	−24.0000	−0.800445
$900$	1.00000	0.0333333
$901$	36.0000	1.19933
$902$	0	0
$903$	0	0
$904$	18.0000	0.598671
$905$	−2.00000	−0.0664822
$906$	16.0000	0.531564
$907$	−16.0000	−0.531271	−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000	−0.531271	−0.265636	+	0.964073i	$0.585582\pi$
$908$	12.0000	0.398234
$909$	6.00000	0.199007
$910$	0	0
$911$	0	0		−	1.00000i	$-0.5\pi$
$911$	0	0			1.00000i	$0.5\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	2.00000	0.0661541
$915$	2.00000	0.0661180
$916$	−2.00000	−0.0660819
$917$	0	0
$918$	−6.00000	−0.198030
$919$	−16.0000	−0.527791	−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000	−0.527791	−0.263896	+	0.964551i	$0.585007\pi$
$920$	0	0
$921$	20.0000	0.659022
$922$	30.0000	0.987997
$923$	0	0
$924$	0	0
$925$	2.00000	0.0657596
$926$	−16.0000	−0.525793
$927$	16.0000	0.525509
$928$	−6.00000	−0.196960
$929$	−54.0000	−1.77168	−0.885841	−	0.463988i	$-0.846418\pi$
$929$	−54.0000	−1.77168	−0.885841	+	0.463988i	$0.846418\pi$
$930$	−4.00000	−0.131165
$931$	0	0
$932$	−6.00000	−0.196537
$933$	0	0
$934$	−12.0000	−0.392652
$935$	0	0
$936$	−2.00000	−0.0653720
$937$	34.0000	1.11073	0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000	1.11073	0.555366	+	0.831606i	$0.312578\pi$
$938$	0	0
$939$	−10.0000	−0.326338
$940$	12.0000	0.391397
$941$	−18.0000	−0.586783	−0.293392	−	0.955992i	$-0.594784\pi$
$941$	−18.0000	−0.586783	−0.293392	+	0.955992i	$0.594784\pi$
$942$	2.00000	0.0651635
$943$	0	0
$944$	12.0000	0.390567
$945$	0	0
$946$	0	0
$947$	−36.0000	−1.16984	−0.584921	−	0.811090i	$-0.698875\pi$
$947$	−36.0000	−1.16984	−0.584921	+	0.811090i	$0.698875\pi$
$948$	16.0000	0.519656
$949$	28.0000	0.908918
$950$	4.00000	0.129777
$951$	−30.0000	−0.972817
$952$	0	0
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	6.00000	0.194257
$955$	0	0
$956$	0	0
$957$	0	0
$958$	24.0000	0.775405
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	−4.00000	−0.128965
$963$	12.0000	0.386695
$964$	−26.0000	−0.837404
$965$	−22.0000	−0.708205
$966$	0	0
$967$	56.0000	1.80084	0.900419	−	0.435023i	$-0.143260\pi$
$967$	56.0000	1.80084	0.900419	+	0.435023i	$0.143260\pi$
$968$	−11.0000	−0.353553
$969$	−24.0000	−0.770991
$970$	−14.0000	−0.449513
$971$	−12.0000	−0.385098	−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000	−0.385098	−0.192549	+	0.981287i	$0.561675\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−16.0000	−0.512673
$975$	2.00000	0.0640513
$976$	−2.00000	−0.0640184
$977$	18.0000	0.575871	0.287936	−	0.957650i	$-0.407031\pi$
$977$	18.0000	0.575871	0.287936	+	0.957650i	$0.407031\pi$
$978$	16.0000	0.511624
$979$	0	0
$980$	0	0
$981$	14.0000	0.446986
$982$	24.0000	0.765871
$983$	36.0000	1.14822	0.574111	−	0.818778i	$-0.305348\pi$
$983$	36.0000	1.14822	0.574111	+	0.818778i	$0.305348\pi$
$984$	6.00000	0.191273
$985$	−18.0000	−0.573528
$986$	−36.0000	−1.14647
$987$	0	0
$988$	−8.00000	−0.254514
$989$	0	0
$990$	0	0
$991$	56.0000	1.77890	0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000	1.77890	0.889449	+	0.457034i	$0.151088\pi$
$992$	4.00000	0.127000
$993$	4.00000	0.126936
$994$	0	0
$995$	4.00000	0.126809
$996$	12.0000	0.380235
$997$	−26.0000	−0.823428	−0.411714	−	0.911313i	$-0.635070\pi$
$997$	−26.0000	−0.823428	−0.411714	+	0.911313i	$0.635070\pi$
$998$	−4.00000	−0.126618
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.a.m.1.1		1
3.2	odd	2		4410.2.a.f.1.1		1
5.4	even	2		7350.2.a.bd.1.1		1
7.2	even	3		1470.2.i.h.361.1		2
7.3	odd	6		1470.2.i.d.961.1		2
7.4	even	3		1470.2.i.h.961.1		2
7.5	odd	6		1470.2.i.d.361.1		2
7.6	odd	2		210.2.a.d.1.1	✓	1
21.20	even	2		630.2.a.f.1.1		1
28.27	even	2		1680.2.a.b.1.1		1
35.13	even	4		1050.2.g.h.799.1		2
35.27	even	4		1050.2.g.h.799.2		2
35.34	odd	2		1050.2.a.a.1.1		1
56.13	odd	2		6720.2.a.bb.1.1		1
56.27	even	2		6720.2.a.cc.1.1		1
84.83	odd	2		5040.2.a.ba.1.1		1
105.62	odd	4		3150.2.g.o.2899.1		2
105.83	odd	4		3150.2.g.o.2899.2		2
105.104	even	2		3150.2.a.ba.1.1		1
140.139	even	2		8400.2.a.cn.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.d.1.1	✓	1	7.6	odd	2
630.2.a.f.1.1		1	21.20	even	2
1050.2.a.a.1.1		1	35.34	odd	2
1050.2.g.h.799.1		2	35.13	even	4
1050.2.g.h.799.2		2	35.27	even	4
1470.2.a.m.1.1		1	1.1	even	1	trivial
1470.2.i.d.361.1		2	7.5	odd	6
1470.2.i.d.961.1		2	7.3	odd	6
1470.2.i.h.361.1		2	7.2	even	3
1470.2.i.h.961.1		2	7.4	even	3
1680.2.a.b.1.1		1	28.27	even	2
3150.2.a.ba.1.1		1	105.104	even	2
3150.2.g.o.2899.1		2	105.62	odd	4
3150.2.g.o.2899.2		2	105.83	odd	4
4410.2.a.f.1.1		1	3.2	odd	2
5040.2.a.ba.1.1		1	84.83	odd	2
6720.2.a.bb.1.1		1	56.13	odd	2
6720.2.a.cc.1.1		1	56.27	even	2
7350.2.a.bd.1.1		1	5.4	even	2
8400.2.a.cn.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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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