LMFDB - Embedded newform 4730.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
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	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

$q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{8} -3.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -2.00000 q^{13} +1.00000 q^{16} +2.00000 q^{17} -3.00000 q^{18} +8.00000 q^{19} +1.00000 q^{20} -1.00000 q^{22} +4.00000 q^{23} +1.00000 q^{25} -2.00000 q^{26} +6.00000 q^{29} +1.00000 q^{32} +2.00000 q^{34} -3.00000 q^{36} -10.0000 q^{37} +8.00000 q^{38} +1.00000 q^{40} -6.00000 q^{41} +1.00000 q^{43} -1.00000 q^{44} -3.00000 q^{45} +4.00000 q^{46} +4.00000 q^{47} -7.00000 q^{49} +1.00000 q^{50} -2.00000 q^{52} +10.0000 q^{53} -1.00000 q^{55} +6.00000 q^{58} +12.0000 q^{59} -2.00000 q^{61} +1.00000 q^{64} -2.00000 q^{65} +12.0000 q^{67} +2.00000 q^{68} -3.00000 q^{72} +2.00000 q^{73} -10.0000 q^{74} +8.00000 q^{76} +4.00000 q^{79} +1.00000 q^{80} +9.00000 q^{81} -6.00000 q^{82} -4.00000 q^{83} +2.00000 q^{85} +1.00000 q^{86} -1.00000 q^{88} -14.0000 q^{89} -3.00000 q^{90} +4.00000 q^{92} +4.00000 q^{94} +8.00000 q^{95} +10.0000 q^{97} -7.00000 q^{98} +3.00000 q^{99} +O(q^{100})$

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0	0		−	1.00000i	$-0.5\pi$
$3$	0	0			1.00000i	$0.5\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0	0
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	1.00000	0.353553
$9$	−3.00000	−1.00000
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0	0
$13$	−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
$15$	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	$0.422021\pi$
$18$	−3.00000	−0.707107
$19$	8.00000	1.83533	0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000	1.83533	0.917663	+	0.397360i	$0.130073\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	−1.00000	−0.213201
$23$	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
$26$	−2.00000	−0.392232
$27$	0	0
$28$	0	0
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0	0
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.00000	0.342997
$35$	0	0
$36$	−3.00000	−0.500000
$37$	−10.0000	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$38$	8.00000	1.29777
$39$	0	0
$40$	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
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−3.00000	−0.447214
$46$	4.00000	0.589768
$47$	4.00000	0.583460	0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000	0.583460	0.291730	+	0.956501i	$0.405769\pi$
$48$	0	0
$49$	−7.00000	−1.00000
$50$	1.00000	0.141421
$51$	0	0
$52$	−2.00000	−0.277350
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	0	0
$55$	−1.00000	−0.134840
$56$	0	0
$57$	0	0
$58$	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	$0.214642\pi$
$60$	0	0
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	0	0
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	0	0
$67$	12.0000	1.46603	0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000	1.46603	0.733017	+	0.680211i	$0.238112\pi$
$68$	2.00000	0.242536
$69$	0	0
$70$	0	0
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−3.00000	−0.353553
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−10.0000	−1.16248
$75$	0	0
$76$	8.00000	0.917663
$77$	0	0
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	1.00000	0.111803
$81$	9.00000	1.00000
$82$	−6.00000	−0.662589
$83$	−4.00000	−0.439057	−0.219529	−	0.975606i	$-0.570452\pi$
$83$	−4.00000	−0.439057	−0.219529	+	0.975606i	$0.570452\pi$
$84$	0	0
$85$	2.00000	0.216930
$86$	1.00000	0.107833
$87$	0	0
$88$	−1.00000	−0.106600
$89$	−14.0000	−1.48400	−0.741999	−	0.670402i	$-0.766122\pi$
$89$	−14.0000	−1.48400	−0.741999	+	0.670402i	$0.766122\pi$
$90$	−3.00000	−0.316228
$91$	0	0
$92$	4.00000	0.417029
$93$	0	0
$94$	4.00000	0.412568
$95$	8.00000	0.820783
$96$	0	0
$97$	10.0000	1.01535	0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000	1.01535	0.507673	+	0.861550i	$0.330506\pi$
$98$	−7.00000	−0.707107
$99$	3.00000	0.301511
$100$	1.00000	0.100000
$101$	18.0000	1.79107	0.895533	−	0.444994i	$-0.146794\pi$
$101$	18.0000	1.79107	0.895533	+	0.444994i	$0.146794\pi$
$102$	0	0
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−2.00000	−0.196116
$105$	0	0
$106$	10.0000	0.971286
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	0	0
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−1.00000	−0.0953463
$111$	0	0
$112$	0	0
$113$	14.0000	1.31701	0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000	1.31701	0.658505	+	0.752577i	$0.271189\pi$
$114$	0	0
$115$	4.00000	0.373002
$116$	6.00000	0.557086
$117$	6.00000	0.554700
$118$	12.0000	1.10469
$119$	0	0
$120$	0	0
$121$	1.00000	0.0909091
$122$	−2.00000	−0.181071
$123$	0	0
$124$	0	0
$125$	1.00000	0.0894427
$126$	0	0
$127$	−16.0000	−1.41977	−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000	−1.41977	−0.709885	+	0.704317i	$0.751253\pi$
$128$	1.00000	0.0883883
$129$	0	0
$130$	−2.00000	−0.175412
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	0	0
$134$	12.0000	1.03664
$135$	0	0
$136$	2.00000	0.171499
$137$	22.0000	1.87959	0.939793	−	0.341743i	$-0.111017\pi$
$137$	22.0000	1.87959	0.939793	+	0.341743i	$0.111017\pi$
$138$	0	0
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	0	0
$141$	0	0
$142$	0	0
$143$	2.00000	0.167248
$144$	−3.00000	−0.250000
$145$	6.00000	0.498273
$146$	2.00000	0.165521
$147$	0	0
$148$	−10.0000	−0.821995
$149$	−18.0000	−1.47462	−0.737309	−	0.675556i	$-0.763904\pi$
$149$	−18.0000	−1.47462	−0.737309	+	0.675556i	$0.763904\pi$
$150$	0	0
$151$	16.0000	1.30206	0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000	1.30206	0.651031	+	0.759051i	$0.274337\pi$
$152$	8.00000	0.648886
$153$	−6.00000	−0.485071
$154$	0	0
$155$	0	0
$156$	0	0
$157$	6.00000	0.478852	0.239426	−	0.970915i	$-0.423041\pi$
$157$	6.00000	0.478852	0.239426	+	0.970915i	$0.423041\pi$
$158$	4.00000	0.318223
$159$	0	0
$160$	1.00000	0.0790569
$161$	0	0
$162$	9.00000	0.707107
$163$	−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
$166$	−4.00000	−0.310460
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	0	0
$169$	−9.00000	−0.692308
$170$	2.00000	0.153393
$171$	−24.0000	−1.83533
$172$	1.00000	0.0762493
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	0	0
$175$	0	0
$176$	−1.00000	−0.0753778
$177$	0	0
$178$	−14.0000	−1.04934
$179$	−12.0000	−0.896922	−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000	−0.896922	−0.448461	+	0.893802i	$0.648028\pi$
$180$	−3.00000	−0.223607
$181$	22.0000	1.63525	0.817624	−	0.575753i	$-0.195291\pi$
$181$	22.0000	1.63525	0.817624	+	0.575753i	$0.195291\pi$
$182$	0	0
$183$	0	0
$184$	4.00000	0.294884
$185$	−10.0000	−0.735215
$186$	0	0
$187$	−2.00000	−0.146254
$188$	4.00000	0.291730
$189$	0	0
$190$	8.00000	0.580381
$191$	8.00000	0.578860	0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000	0.578860	0.289430	+	0.957199i	$0.406534\pi$
$192$	0	0
$193$	−14.0000	−1.00774	−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000	−1.00774	−0.503871	+	0.863779i	$0.668091\pi$
$194$	10.0000	0.717958
$195$	0	0
$196$	−7.00000	−0.500000
$197$	−18.0000	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$198$	3.00000	0.213201
$199$	−8.00000	−0.567105	−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000	−0.567105	−0.283552	+	0.958957i	$0.591513\pi$
$200$	1.00000	0.0707107
$201$	0	0
$202$	18.0000	1.26648
$203$	0	0
$204$	0	0
$205$	−6.00000	−0.419058
$206$	4.00000	0.278693
$207$	−12.0000	−0.834058
$208$	−2.00000	−0.138675
$209$	−8.00000	−0.553372
$210$	0	0
$211$	0	0		−	1.00000i	$-0.5\pi$
$211$	0	0			1.00000i	$0.5\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	12.0000	0.820303
$215$	1.00000	0.0681994
$216$	0	0
$217$	0	0
$218$	2.00000	0.135457
$219$	0	0
$220$	−1.00000	−0.0674200
$221$	−4.00000	−0.269069
$222$	0	0
$223$	0	0		−	1.00000i	$-0.5\pi$
$223$	0	0			1.00000i	$0.5\pi$
$224$	0	0
$225$	−3.00000	−0.200000
$226$	14.0000	0.931266
$227$	−12.0000	−0.796468	−0.398234	−	0.917284i	$-0.630377\pi$
$227$	−12.0000	−0.796468	−0.398234	+	0.917284i	$0.630377\pi$
$228$	0	0
$229$	30.0000	1.98246	0.991228	−	0.132164i	$-0.0421925\pi$
$229$	30.0000	1.98246	0.991228	+	0.132164i	$0.0421925\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	6.00000	0.393919
$233$	−22.0000	−1.44127	−0.720634	−	0.693316i	$-0.756149\pi$
$233$	−22.0000	−1.44127	−0.720634	+	0.693316i	$0.756149\pi$
$234$	6.00000	0.392232
$235$	4.00000	0.260931
$236$	12.0000	0.781133
$237$	0	0
$238$	0	0
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	0	0
$241$	22.0000	1.41714	0.708572	−	0.705638i	$-0.249340\pi$
$241$	22.0000	1.41714	0.708572	+	0.705638i	$0.249340\pi$
$242$	1.00000	0.0642824
$243$	0	0
$244$	−2.00000	−0.128037
$245$	−7.00000	−0.447214
$246$	0	0
$247$	−16.0000	−1.01806
$248$	0	0
$249$	0	0
$250$	1.00000	0.0632456
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	0	0
$253$	−4.00000	−0.251478
$254$	−16.0000	−1.00393
$255$	0	0
$256$	1.00000	0.0625000
$257$	−26.0000	−1.62184	−0.810918	−	0.585160i	$-0.801032\pi$
$257$	−26.0000	−1.62184	−0.810918	+	0.585160i	$0.801032\pi$
$258$	0	0
$259$	0	0
$260$	−2.00000	−0.124035
$261$	−18.0000	−1.11417
$262$	0	0
$263$	−16.0000	−0.986602	−0.493301	−	0.869859i	$-0.664210\pi$
$263$	−16.0000	−0.986602	−0.493301	+	0.869859i	$0.664210\pi$
$264$	0	0
$265$	10.0000	0.614295
$266$	0	0
$267$	0	0
$268$	12.0000	0.733017
$269$	−2.00000	−0.121942	−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000	−0.121942	−0.0609711	+	0.998140i	$0.519420\pi$
$270$	0	0
$271$	−28.0000	−1.70088	−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000	−1.70088	−0.850439	+	0.526073i	$0.823664\pi$
$272$	2.00000	0.121268
$273$	0	0
$274$	22.0000	1.32907
$275$	−1.00000	−0.0603023
$276$	0	0
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−4.00000	−0.239904
$279$	0	0
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	0	0
$283$	4.00000	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$283$	4.00000	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$284$	0	0
$285$	0	0
$286$	2.00000	0.118262
$287$	0	0
$288$	−3.00000	−0.176777
$289$	−13.0000	−0.764706
$290$	6.00000	0.352332
$291$	0	0
$292$	2.00000	0.117041
$293$	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
$296$	−10.0000	−0.581238
$297$	0	0
$298$	−18.0000	−1.04271
$299$	−8.00000	−0.462652
$300$	0	0
$301$	0	0
$302$	16.0000	0.920697
$303$	0	0
$304$	8.00000	0.458831
$305$	−2.00000	−0.114520
$306$	−6.00000	−0.342997
$307$	28.0000	1.59804	0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000	1.59804	0.799022	+	0.601302i	$0.205351\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	−24.0000	−1.36092	−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000	−1.36092	−0.680458	+	0.732787i	$0.738219\pi$
$312$	0	0
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	6.00000	0.338600
$315$	0	0
$316$	4.00000	0.225018
$317$	2.00000	0.112331	0.0561656	−	0.998421i	$-0.482113\pi$
$317$	2.00000	0.112331	0.0561656	+	0.998421i	$0.482113\pi$
$318$	0	0
$319$	−6.00000	−0.335936
$320$	1.00000	0.0559017
$321$	0	0
$322$	0	0
$323$	16.0000	0.890264
$324$	9.00000	0.500000
$325$	−2.00000	−0.110940
$326$	−16.0000	−0.886158
$327$	0	0
$328$	−6.00000	−0.331295
$329$	0	0
$330$	0	0
$331$	4.00000	0.219860	0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000	0.219860	0.109930	+	0.993939i	$0.464937\pi$
$332$	−4.00000	−0.219529
$333$	30.0000	1.64399
$334$	−8.00000	−0.437741
$335$	12.0000	0.655630
$336$	0	0
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−9.00000	−0.489535
$339$	0	0
$340$	2.00000	0.108465
$341$	0	0
$342$	−24.0000	−1.29777
$343$	0	0
$344$	1.00000	0.0539164
$345$	0	0
$346$	6.00000	0.322562
$347$	28.0000	1.50312	0.751559	−	0.659665i	$-0.229302\pi$
$347$	28.0000	1.50312	0.751559	+	0.659665i	$0.229302\pi$
$348$	0	0
$349$	6.00000	0.321173	0.160586	−	0.987022i	$-0.448662\pi$
$349$	6.00000	0.321173	0.160586	+	0.987022i	$0.448662\pi$
$350$	0	0
$351$	0	0
$352$	−1.00000	−0.0533002
$353$	10.0000	0.532246	0.266123	−	0.963939i	$-0.414257\pi$
$353$	10.0000	0.532246	0.266123	+	0.963939i	$0.414257\pi$
$354$	0	0
$355$	0	0
$356$	−14.0000	−0.741999
$357$	0	0
$358$	−12.0000	−0.634220
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	−3.00000	−0.158114
$361$	45.0000	2.36842
$362$	22.0000	1.15629
$363$	0	0
$364$	0	0
$365$	2.00000	0.104685
$366$	0	0
$367$	−20.0000	−1.04399	−0.521996	−	0.852948i	$-0.674812\pi$
$367$	−20.0000	−1.04399	−0.521996	+	0.852948i	$0.674812\pi$
$368$	4.00000	0.208514
$369$	18.0000	0.937043
$370$	−10.0000	−0.519875
$371$	0	0
$372$	0	0
$373$	−10.0000	−0.517780	−0.258890	−	0.965907i	$-0.583357\pi$
$373$	−10.0000	−0.517780	−0.258890	+	0.965907i	$0.583357\pi$
$374$	−2.00000	−0.103418
$375$	0	0
$376$	4.00000	0.206284
$377$	−12.0000	−0.618031
$378$	0	0
$379$	−28.0000	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$380$	8.00000	0.410391
$381$	0	0
$382$	8.00000	0.409316
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	0	0
$385$	0	0
$386$	−14.0000	−0.712581
$387$	−3.00000	−0.152499
$388$	10.0000	0.507673
$389$	−10.0000	−0.507020	−0.253510	−	0.967333i	$-0.581585\pi$
$389$	−10.0000	−0.507020	−0.253510	+	0.967333i	$0.581585\pi$
$390$	0	0
$391$	8.00000	0.404577
$392$	−7.00000	−0.353553
$393$	0	0
$394$	−18.0000	−0.906827
$395$	4.00000	0.201262
$396$	3.00000	0.150756
$397$	−22.0000	−1.10415	−0.552074	−	0.833795i	$-0.686163\pi$
$397$	−22.0000	−1.10415	−0.552074	+	0.833795i	$0.686163\pi$
$398$	−8.00000	−0.401004
$399$	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	$0.351624\pi$
$402$	0	0
$403$	0	0
$404$	18.0000	0.895533
$405$	9.00000	0.447214
$406$	0	0
$407$	10.0000	0.495682
$408$	0	0
$409$	−10.0000	−0.494468	−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000	−0.494468	−0.247234	+	0.968956i	$0.579522\pi$
$410$	−6.00000	−0.296319
$411$	0	0
$412$	4.00000	0.197066
$413$	0	0
$414$	−12.0000	−0.589768
$415$	−4.00000	−0.196352
$416$	−2.00000	−0.0980581
$417$	0	0
$418$	−8.00000	−0.391293
$419$	−28.0000	−1.36789	−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000	−1.36789	−0.683945	+	0.729534i	$0.739737\pi$
$420$	0	0
$421$	−26.0000	−1.26716	−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000	−1.26716	−0.633581	+	0.773676i	$0.718416\pi$
$422$	0	0
$423$	−12.0000	−0.583460
$424$	10.0000	0.485643
$425$	2.00000	0.0970143
$426$	0	0
$427$	0	0
$428$	12.0000	0.580042
$429$	0	0
$430$	1.00000	0.0482243
$431$	28.0000	1.34871	0.674356	−	0.738406i	$-0.264421\pi$
$431$	28.0000	1.34871	0.674356	+	0.738406i	$0.264421\pi$
$432$	0	0
$433$	38.0000	1.82616	0.913082	−	0.407777i	$-0.133696\pi$
$433$	38.0000	1.82616	0.913082	+	0.407777i	$0.133696\pi$
$434$	0	0
$435$	0	0
$436$	2.00000	0.0957826
$437$	32.0000	1.53077
$438$	0	0
$439$	20.0000	0.954548	0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000	0.954548	0.477274	+	0.878755i	$0.341625\pi$
$440$	−1.00000	−0.0476731
$441$	21.0000	1.00000
$442$	−4.00000	−0.190261
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0	0
$445$	−14.0000	−0.663664
$446$	0	0
$447$	0	0
$448$	0	0
$449$	2.00000	0.0943858	0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000	0.0943858	0.0471929	+	0.998886i	$0.484972\pi$
$450$	−3.00000	−0.141421
$451$	6.00000	0.282529
$452$	14.0000	0.658505
$453$	0	0
$454$	−12.0000	−0.563188
$455$	0	0
$456$	0	0
$457$	10.0000	0.467780	0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000	0.467780	0.233890	+	0.972263i	$0.424854\pi$
$458$	30.0000	1.40181
$459$	0	0
$460$	4.00000	0.186501
$461$	−30.0000	−1.39724	−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000	−1.39724	−0.698620	+	0.715493i	$0.746202\pi$
$462$	0	0
$463$	−8.00000	−0.371792	−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000	−0.371792	−0.185896	+	0.982569i	$0.559519\pi$
$464$	6.00000	0.278543
$465$	0	0
$466$	−22.0000	−1.01913
$467$	8.00000	0.370196	0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000	0.370196	0.185098	+	0.982720i	$0.440740\pi$
$468$	6.00000	0.277350
$469$	0	0
$470$	4.00000	0.184506
$471$	0	0
$472$	12.0000	0.552345
$473$	−1.00000	−0.0459800
$474$	0	0
$475$	8.00000	0.367065
$476$	0	0
$477$	−30.0000	−1.37361
$478$	12.0000	0.548867
$479$	−28.0000	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$479$	−28.0000	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$480$	0	0
$481$	20.0000	0.911922
$482$	22.0000	1.00207
$483$	0	0
$484$	1.00000	0.0454545
$485$	10.0000	0.454077
$486$	0	0
$487$	−20.0000	−0.906287	−0.453143	−	0.891438i	$-0.649697\pi$
$487$	−20.0000	−0.906287	−0.453143	+	0.891438i	$0.649697\pi$
$488$	−2.00000	−0.0905357
$489$	0	0
$490$	−7.00000	−0.316228
$491$	−16.0000	−0.722070	−0.361035	−	0.932552i	$-0.617576\pi$
$491$	−16.0000	−0.722070	−0.361035	+	0.932552i	$0.617576\pi$
$492$	0	0
$493$	12.0000	0.540453
$494$	−16.0000	−0.719874
$495$	3.00000	0.134840
$496$	0	0
$497$	0	0
$498$	0	0
$499$	−36.0000	−1.61158	−0.805791	−	0.592200i	$-0.798259\pi$
$499$	−36.0000	−1.61158	−0.805791	+	0.592200i	$0.798259\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	12.0000	0.535586
$503$	−8.00000	−0.356702	−0.178351	−	0.983967i	$-0.557076\pi$
$503$	−8.00000	−0.356702	−0.178351	+	0.983967i	$0.557076\pi$
$504$	0	0
$505$	18.0000	0.800989
$506$	−4.00000	−0.177822
$507$	0	0
$508$	−16.0000	−0.709885
$509$	6.00000	0.265945	0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000	0.265945	0.132973	+	0.991120i	$0.457548\pi$
$510$	0	0
$511$	0	0
$512$	1.00000	0.0441942
$513$	0	0
$514$	−26.0000	−1.14681
$515$	4.00000	0.176261
$516$	0	0
$517$	−4.00000	−0.175920
$518$	0	0
$519$	0	0
$520$	−2.00000	−0.0877058
$521$	−30.0000	−1.31432	−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000	−1.31432	−0.657162	+	0.753749i	$0.728243\pi$
$522$	−18.0000	−0.787839
$523$	4.00000	0.174908	0.0874539	−	0.996169i	$-0.472127\pi$
$523$	4.00000	0.174908	0.0874539	+	0.996169i	$0.472127\pi$
$524$	0	0
$525$	0	0
$526$	−16.0000	−0.697633
$527$	0	0
$528$	0	0
$529$	−7.00000	−0.304348
$530$	10.0000	0.434372
$531$	−36.0000	−1.56227
$532$	0	0
$533$	12.0000	0.519778
$534$	0	0
$535$	12.0000	0.518805
$536$	12.0000	0.518321
$537$	0	0
$538$	−2.00000	−0.0862261
$539$	7.00000	0.301511
$540$	0	0
$541$	−6.00000	−0.257960	−0.128980	−	0.991647i	$-0.541170\pi$
$541$	−6.00000	−0.257960	−0.128980	+	0.991647i	$0.541170\pi$
$542$	−28.0000	−1.20270
$543$	0	0
$544$	2.00000	0.0857493
$545$	2.00000	0.0856706
$546$	0	0
$547$	−12.0000	−0.513083	−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000	−0.513083	−0.256541	+	0.966533i	$0.582583\pi$
$548$	22.0000	0.939793
$549$	6.00000	0.256074
$550$	−1.00000	−0.0426401
$551$	48.0000	2.04487
$552$	0	0
$553$	0	0
$554$	22.0000	0.934690
$555$	0	0
$556$	−4.00000	−0.169638
$557$	−10.0000	−0.423714	−0.211857	−	0.977301i	$-0.567951\pi$
$557$	−10.0000	−0.423714	−0.211857	+	0.977301i	$0.567951\pi$
$558$	0	0
$559$	−2.00000	−0.0845910
$560$	0	0
$561$	0	0
$562$	−6.00000	−0.253095
$563$	−4.00000	−0.168580	−0.0842900	−	0.996441i	$-0.526862\pi$
$563$	−4.00000	−0.168580	−0.0842900	+	0.996441i	$0.526862\pi$
$564$	0	0
$565$	14.0000	0.588984
$566$	4.00000	0.168133
$567$	0	0
$568$	0	0
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	0	0
$571$	−32.0000	−1.33916	−0.669579	−	0.742741i	$-0.733526\pi$
$571$	−32.0000	−1.33916	−0.669579	+	0.742741i	$0.733526\pi$
$572$	2.00000	0.0836242
$573$	0	0
$574$	0	0
$575$	4.00000	0.166812
$576$	−3.00000	−0.125000
$577$	−18.0000	−0.749350	−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000	−0.749350	−0.374675	+	0.927156i	$0.622246\pi$
$578$	−13.0000	−0.540729
$579$	0	0
$580$	6.00000	0.249136
$581$	0	0
$582$	0	0
$583$	−10.0000	−0.414158
$584$	2.00000	0.0827606
$585$	6.00000	0.248069
$586$	6.00000	0.247858
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	0	0
$590$	12.0000	0.494032
$591$	0	0
$592$	−10.0000	−0.410997
$593$	42.0000	1.72473	0.862367	−	0.506284i	$-0.168981\pi$
$593$	42.0000	1.72473	0.862367	+	0.506284i	$0.168981\pi$
$594$	0	0
$595$	0	0
$596$	−18.0000	−0.737309
$597$	0	0
$598$	−8.00000	−0.327144
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	6.00000	0.244745	0.122373	−	0.992484i	$-0.460950\pi$
$601$	6.00000	0.244745	0.122373	+	0.992484i	$0.460950\pi$
$602$	0	0
$603$	−36.0000	−1.46603
$604$	16.0000	0.651031
$605$	1.00000	0.0406558
$606$	0	0
$607$	0	0		−	1.00000i	$-0.5\pi$
$607$	0	0			1.00000i	$0.5\pi$
$608$	8.00000	0.324443
$609$	0	0
$610$	−2.00000	−0.0809776
$611$	−8.00000	−0.323645
$612$	−6.00000	−0.242536
$613$	−2.00000	−0.0807792	−0.0403896	−	0.999184i	$-0.512860\pi$
$613$	−2.00000	−0.0807792	−0.0403896	+	0.999184i	$0.512860\pi$
$614$	28.0000	1.12999
$615$	0	0
$616$	0	0
$617$	10.0000	0.402585	0.201292	−	0.979531i	$-0.435486\pi$
$617$	10.0000	0.402585	0.201292	+	0.979531i	$0.435486\pi$
$618$	0	0
$619$	−28.0000	−1.12542	−0.562708	−	0.826656i	$-0.690240\pi$
$619$	−28.0000	−1.12542	−0.562708	+	0.826656i	$0.690240\pi$
$620$	0	0
$621$	0	0
$622$	−24.0000	−0.962312
$623$	0	0
$624$	0	0
$625$	1.00000	0.0400000
$626$	−18.0000	−0.719425
$627$	0	0
$628$	6.00000	0.239426
$629$	−20.0000	−0.797452
$630$	0	0
$631$	8.00000	0.318475	0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000	0.318475	0.159237	+	0.987240i	$0.449096\pi$
$632$	4.00000	0.159111
$633$	0	0
$634$	2.00000	0.0794301
$635$	−16.0000	−0.634941
$636$	0	0
$637$	14.0000	0.554700
$638$	−6.00000	−0.237542
$639$	0	0
$640$	1.00000	0.0395285
$641$	−6.00000	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$641$	−6.00000	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$642$	0	0
$643$	20.0000	0.788723	0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000	0.788723	0.394362	+	0.918955i	$0.370966\pi$
$644$	0	0
$645$	0	0
$646$	16.0000	0.629512
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	9.00000	0.353553
$649$	−12.0000	−0.471041
$650$	−2.00000	−0.0784465
$651$	0	0
$652$	−16.0000	−0.626608
$653$	−10.0000	−0.391330	−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000	−0.391330	−0.195665	+	0.980671i	$0.562687\pi$
$654$	0	0
$655$	0	0
$656$	−6.00000	−0.234261
$657$	−6.00000	−0.234082
$658$	0	0
$659$	−20.0000	−0.779089	−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000	−0.779089	−0.389545	+	0.921008i	$0.627368\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	4.00000	0.155464
$663$	0	0
$664$	−4.00000	−0.155230
$665$	0	0
$666$	30.0000	1.16248
$667$	24.0000	0.929284
$668$	−8.00000	−0.309529
$669$	0	0
$670$	12.0000	0.463600
$671$	2.00000	0.0772091
$672$	0	0
$673$	10.0000	0.385472	0.192736	−	0.981251i	$-0.438264\pi$
$673$	10.0000	0.385472	0.192736	+	0.981251i	$0.438264\pi$
$674$	2.00000	0.0770371
$675$	0	0
$676$	−9.00000	−0.346154
$677$	6.00000	0.230599	0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000	0.230599	0.115299	+	0.993331i	$0.463217\pi$
$678$	0	0
$679$	0	0
$680$	2.00000	0.0766965
$681$	0	0
$682$	0	0
$683$	−36.0000	−1.37750	−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000	−1.37750	−0.688751	+	0.724998i	$0.741841\pi$
$684$	−24.0000	−0.917663
$685$	22.0000	0.840577
$686$	0	0
$687$	0	0
$688$	1.00000	0.0381246
$689$	−20.0000	−0.761939
$690$	0	0
$691$	12.0000	0.456502	0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000	0.456502	0.228251	+	0.973602i	$0.426699\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	28.0000	1.06287
$695$	−4.00000	−0.151729
$696$	0	0
$697$	−12.0000	−0.454532
$698$	6.00000	0.227103
$699$	0	0
$700$	0	0
$701$	−22.0000	−0.830929	−0.415464	−	0.909610i	$-0.636381\pi$
$701$	−22.0000	−0.830929	−0.415464	+	0.909610i	$0.636381\pi$
$702$	0	0
$703$	−80.0000	−3.01726
$704$	−1.00000	−0.0376889
$705$	0	0
$706$	10.0000	0.376355
$707$	0	0
$708$	0	0
$709$	−18.0000	−0.676004	−0.338002	−	0.941145i	$-0.609751\pi$
$709$	−18.0000	−0.676004	−0.338002	+	0.941145i	$0.609751\pi$
$710$	0	0
$711$	−12.0000	−0.450035
$712$	−14.0000	−0.524672
$713$	0	0
$714$	0	0
$715$	2.00000	0.0747958
$716$	−12.0000	−0.448461
$717$	0	0
$718$	12.0000	0.447836
$719$	−24.0000	−0.895049	−0.447524	−	0.894272i	$-0.647694\pi$
$719$	−24.0000	−0.895049	−0.447524	+	0.894272i	$0.647694\pi$
$720$	−3.00000	−0.111803
$721$	0	0
$722$	45.0000	1.67473
$723$	0	0
$724$	22.0000	0.817624
$725$	6.00000	0.222834
$726$	0	0
$727$	16.0000	0.593407	0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000	0.593407	0.296704	+	0.954970i	$0.404113\pi$
$728$	0	0
$729$	−27.0000	−1.00000
$730$	2.00000	0.0740233
$731$	2.00000	0.0739727
$732$	0	0
$733$	46.0000	1.69905	0.849524	−	0.527549i	$-0.176889\pi$
$733$	46.0000	1.69905	0.849524	+	0.527549i	$0.176889\pi$
$734$	−20.0000	−0.738213
$735$	0	0
$736$	4.00000	0.147442
$737$	−12.0000	−0.442026
$738$	18.0000	0.662589
$739$	−24.0000	−0.882854	−0.441427	−	0.897297i	$-0.645528\pi$
$739$	−24.0000	−0.882854	−0.441427	+	0.897297i	$0.645528\pi$
$740$	−10.0000	−0.367607
$741$	0	0
$742$	0	0
$743$	24.0000	0.880475	0.440237	−	0.897881i	$-0.354894\pi$
$743$	24.0000	0.880475	0.440237	+	0.897881i	$0.354894\pi$
$744$	0	0
$745$	−18.0000	−0.659469
$746$	−10.0000	−0.366126
$747$	12.0000	0.439057
$748$	−2.00000	−0.0731272
$749$	0	0
$750$	0	0
$751$	0	0		−	1.00000i	$-0.5\pi$
$751$	0	0			1.00000i	$0.5\pi$
$752$	4.00000	0.145865
$753$	0	0
$754$	−12.0000	−0.437014
$755$	16.0000	0.582300
$756$	0	0
$757$	−10.0000	−0.363456	−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000	−0.363456	−0.181728	+	0.983349i	$0.558169\pi$
$758$	−28.0000	−1.01701
$759$	0	0
$760$	8.00000	0.290191
$761$	38.0000	1.37750	0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000	1.37750	0.688749	+	0.724999i	$0.258160\pi$
$762$	0	0
$763$	0	0
$764$	8.00000	0.289430
$765$	−6.00000	−0.216930
$766$	8.00000	0.289052
$767$	−24.0000	−0.866590
$768$	0	0
$769$	−6.00000	−0.216366	−0.108183	−	0.994131i	$-0.534503\pi$
$769$	−6.00000	−0.216366	−0.108183	+	0.994131i	$0.534503\pi$
$770$	0	0
$771$	0	0
$772$	−14.0000	−0.503871
$773$	14.0000	0.503545	0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000	0.503545	0.251773	+	0.967786i	$0.418987\pi$
$774$	−3.00000	−0.107833
$775$	0	0
$776$	10.0000	0.358979
$777$	0	0
$778$	−10.0000	−0.358517
$779$	−48.0000	−1.71978
$780$	0	0
$781$	0	0
$782$	8.00000	0.286079
$783$	0	0
$784$	−7.00000	−0.250000
$785$	6.00000	0.214149
$786$	0	0
$787$	−4.00000	−0.142585	−0.0712923	−	0.997455i	$-0.522712\pi$
$787$	−4.00000	−0.142585	−0.0712923	+	0.997455i	$0.522712\pi$
$788$	−18.0000	−0.641223
$789$	0	0
$790$	4.00000	0.142314
$791$	0	0
$792$	3.00000	0.106600
$793$	4.00000	0.142044
$794$	−22.0000	−0.780751
$795$	0	0
$796$	−8.00000	−0.283552
$797$	34.0000	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$797$	34.0000	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	1.00000	0.0353553
$801$	42.0000	1.48400
$802$	18.0000	0.635602
$803$	−2.00000	−0.0705785
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	18.0000	0.633238
$809$	−6.00000	−0.210949	−0.105474	−	0.994422i	$-0.533636\pi$
$809$	−6.00000	−0.210949	−0.105474	+	0.994422i	$0.533636\pi$
$810$	9.00000	0.316228
$811$	40.0000	1.40459	0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000	1.40459	0.702295	+	0.711886i	$0.252159\pi$
$812$	0	0
$813$	0	0
$814$	10.0000	0.350500
$815$	−16.0000	−0.560456
$816$	0	0
$817$	8.00000	0.279885
$818$	−10.0000	−0.349642
$819$	0	0
$820$	−6.00000	−0.209529
$821$	18.0000	0.628204	0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000	0.628204	0.314102	+	0.949389i	$0.398297\pi$
$822$	0	0
$823$	4.00000	0.139431	0.0697156	−	0.997567i	$-0.477791\pi$
$823$	4.00000	0.139431	0.0697156	+	0.997567i	$0.477791\pi$
$824$	4.00000	0.139347
$825$	0	0
$826$	0	0
$827$	44.0000	1.53003	0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000	1.53003	0.765015	+	0.644013i	$0.222732\pi$
$828$	−12.0000	−0.417029
$829$	−18.0000	−0.625166	−0.312583	−	0.949890i	$-0.601194\pi$
$829$	−18.0000	−0.625166	−0.312583	+	0.949890i	$0.601194\pi$
$830$	−4.00000	−0.138842
$831$	0	0
$832$	−2.00000	−0.0693375
$833$	−14.0000	−0.485071
$834$	0	0
$835$	−8.00000	−0.276851
$836$	−8.00000	−0.276686
$837$	0	0
$838$	−28.0000	−0.967244
$839$	−40.0000	−1.38095	−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000	−1.38095	−0.690477	+	0.723355i	$0.742599\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−26.0000	−0.896019
$843$	0	0
$844$	0	0
$845$	−9.00000	−0.309609
$846$	−12.0000	−0.412568
$847$	0	0
$848$	10.0000	0.343401
$849$	0	0
$850$	2.00000	0.0685994
$851$	−40.0000	−1.37118
$852$	0	0
$853$	−34.0000	−1.16414	−0.582069	−	0.813139i	$-0.697757\pi$
$853$	−34.0000	−1.16414	−0.582069	+	0.813139i	$0.697757\pi$
$854$	0	0
$855$	−24.0000	−0.820783
$856$	12.0000	0.410152
$857$	−38.0000	−1.29806	−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000	−1.29806	−0.649028	+	0.760765i	$0.724824\pi$
$858$	0	0
$859$	36.0000	1.22830	0.614152	−	0.789188i	$-0.289498\pi$
$859$	36.0000	1.22830	0.614152	+	0.789188i	$0.289498\pi$
$860$	1.00000	0.0340997
$861$	0	0
$862$	28.0000	0.953684
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	0	0
$865$	6.00000	0.204006
$866$	38.0000	1.29129
$867$	0	0
$868$	0	0
$869$	−4.00000	−0.135691
$870$	0	0
$871$	−24.0000	−0.813209
$872$	2.00000	0.0677285
$873$	−30.0000	−1.01535
$874$	32.0000	1.08242
$875$	0	0
$876$	0	0
$877$	38.0000	1.28317	0.641584	−	0.767052i	$-0.278277\pi$
$877$	38.0000	1.28317	0.641584	+	0.767052i	$0.278277\pi$
$878$	20.0000	0.674967
$879$	0	0
$880$	−1.00000	−0.0337100
$881$	−46.0000	−1.54978	−0.774890	−	0.632096i	$-0.782195\pi$
$881$	−46.0000	−1.54978	−0.774890	+	0.632096i	$0.782195\pi$
$882$	21.0000	0.707107
$883$	−44.0000	−1.48072	−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000	−1.48072	−0.740359	+	0.672212i	$0.765344\pi$
$884$	−4.00000	−0.134535
$885$	0	0
$886$	−4.00000	−0.134383
$887$	−48.0000	−1.61168	−0.805841	−	0.592132i	$-0.798286\pi$
$887$	−48.0000	−1.61168	−0.805841	+	0.592132i	$0.798286\pi$
$888$	0	0
$889$	0	0
$890$	−14.0000	−0.469281
$891$	−9.00000	−0.301511
$892$	0	0
$893$	32.0000	1.07084
$894$	0	0
$895$	−12.0000	−0.401116
$896$	0	0
$897$	0	0
$898$	2.00000	0.0667409
$899$	0	0
$900$	−3.00000	−0.100000
$901$	20.0000	0.666297
$902$	6.00000	0.199778
$903$	0	0
$904$	14.0000	0.465633
$905$	22.0000	0.731305
$906$	0	0
$907$	36.0000	1.19536	0.597680	−	0.801735i	$-0.296089\pi$
$907$	36.0000	1.19536	0.597680	+	0.801735i	$0.296089\pi$
$908$	−12.0000	−0.398234
$909$	−54.0000	−1.79107
$910$	0	0
$911$	8.00000	0.265052	0.132526	−	0.991180i	$-0.457691\pi$
$911$	8.00000	0.265052	0.132526	+	0.991180i	$0.457691\pi$
$912$	0	0
$913$	4.00000	0.132381
$914$	10.0000	0.330771
$915$	0	0
$916$	30.0000	0.991228
$917$	0	0
$918$	0	0
$919$	12.0000	0.395843	0.197922	−	0.980218i	$-0.436581\pi$
$919$	12.0000	0.395843	0.197922	+	0.980218i	$0.436581\pi$
$920$	4.00000	0.131876
$921$	0	0
$922$	−30.0000	−0.987997
$923$	0	0
$924$	0	0
$925$	−10.0000	−0.328798
$926$	−8.00000	−0.262896
$927$	−12.0000	−0.394132
$928$	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	$0.846418\pi$
$930$	0	0
$931$	−56.0000	−1.83533
$932$	−22.0000	−0.720634
$933$	0	0
$934$	8.00000	0.261768
$935$	−2.00000	−0.0654070
$936$	6.00000	0.196116
$937$	−22.0000	−0.718709	−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000	−0.718709	−0.359354	+	0.933201i	$0.617003\pi$
$938$	0	0
$939$	0	0
$940$	4.00000	0.130466
$941$	−22.0000	−0.717180	−0.358590	−	0.933495i	$-0.616742\pi$
$941$	−22.0000	−0.717180	−0.358590	+	0.933495i	$0.616742\pi$
$942$	0	0
$943$	−24.0000	−0.781548
$944$	12.0000	0.390567
$945$	0	0
$946$	−1.00000	−0.0325128
$947$	12.0000	0.389948	0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000	0.389948	0.194974	+	0.980808i	$0.437538\pi$
$948$	0	0
$949$	−4.00000	−0.129845
$950$	8.00000	0.259554
$951$	0	0
$952$	0	0
$953$	26.0000	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$954$	−30.0000	−0.971286
$955$	8.00000	0.258874
$956$	12.0000	0.388108
$957$	0	0
$958$	−28.0000	−0.904639
$959$	0	0
$960$	0	0
$961$	−31.0000	−1.00000
$962$	20.0000	0.644826
$963$	−36.0000	−1.16008
$964$	22.0000	0.708572
$965$	−14.0000	−0.450676
$966$	0	0
$967$	32.0000	1.02905	0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000	1.02905	0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	10.0000	0.321081
$971$	−52.0000	−1.66876	−0.834380	−	0.551190i	$-0.814174\pi$
$971$	−52.0000	−1.66876	−0.834380	+	0.551190i	$0.814174\pi$
$972$	0	0
$973$	0	0
$974$	−20.0000	−0.640841
$975$	0	0
$976$	−2.00000	−0.0640184
$977$	26.0000	0.831814	0.415907	−	0.909407i	$-0.363464\pi$
$977$	26.0000	0.831814	0.415907	+	0.909407i	$0.363464\pi$
$978$	0	0
$979$	14.0000	0.447442
$980$	−7.00000	−0.223607
$981$	−6.00000	−0.191565
$982$	−16.0000	−0.510581
$983$	−56.0000	−1.78612	−0.893061	−	0.449935i	$-0.851447\pi$
$983$	−56.0000	−1.78612	−0.893061	+	0.449935i	$0.851447\pi$
$984$	0	0
$985$	−18.0000	−0.573528
$986$	12.0000	0.382158
$987$	0	0
$988$	−16.0000	−0.509028
$989$	4.00000	0.127193
$990$	3.00000	0.0953463
$991$	−8.00000	−0.254128	−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000	−0.254128	−0.127064	+	0.991894i	$0.540555\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	−8.00000	−0.253617
$996$	0	0
$997$	22.0000	0.696747	0.348373	−	0.937356i	$-0.386734\pi$
$997$	22.0000	0.696747	0.348373	+	0.937356i	$0.386734\pi$
$998$	−36.0000	−1.13956
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.g.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.g.1.1	✓	1	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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