LMFDB - Embedded newform 950.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,4,Mod(1,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("950.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	950.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:	$56.0518145055$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	950.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} -4.00000 q^{6} +12.0000 q^{7} +8.00000 q^{8} -23.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -2.00000 q^{3} +4.00000 q^{4} -4.00000 q^{6} +12.0000 q^{7} +8.00000 q^{8} -23.0000 q^{9} -20.0000 q^{11} -8.00000 q^{12} +4.00000 q^{13} +24.0000 q^{14} +16.0000 q^{16} +34.0000 q^{17} -46.0000 q^{18} -19.0000 q^{19} -24.0000 q^{21} -40.0000 q^{22} -40.0000 q^{23} -16.0000 q^{24} +8.00000 q^{26} +100.000 q^{27} +48.0000 q^{28} -150.000 q^{29} -200.000 q^{31} +32.0000 q^{32} +40.0000 q^{33} +68.0000 q^{34} -92.0000 q^{36} +156.000 q^{37} -38.0000 q^{38} -8.00000 q^{39} -218.000 q^{41} -48.0000 q^{42} -248.000 q^{43} -80.0000 q^{44} -80.0000 q^{46} +180.000 q^{47} -32.0000 q^{48} -199.000 q^{49} -68.0000 q^{51} +16.0000 q^{52} -72.0000 q^{53} +200.000 q^{54} +96.0000 q^{56} +38.0000 q^{57} -300.000 q^{58} -48.0000 q^{59} -134.000 q^{61} -400.000 q^{62} -276.000 q^{63} +64.0000 q^{64} +80.0000 q^{66} -334.000 q^{67} +136.000 q^{68} +80.0000 q^{69} -520.000 q^{71} -184.000 q^{72} -438.000 q^{73} +312.000 q^{74} -76.0000 q^{76} -240.000 q^{77} -16.0000 q^{78} +980.000 q^{79} +421.000 q^{81} -436.000 q^{82} +156.000 q^{83} -96.0000 q^{84} -496.000 q^{86} +300.000 q^{87} -160.000 q^{88} +670.000 q^{89} +48.0000 q^{91} -160.000 q^{92} +400.000 q^{93} +360.000 q^{94} -64.0000 q^{96} -1124.00 q^{97} -398.000 q^{98} +460.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	−4.00000	−0.272166
$7$	12.0000	0.647939	0.323970	−	0.946068i	$-0.394982\pi$
$7$	12.0000	0.647939	0.323970	+	0.946068i	$0.394982\pi$
$8$	8.00000	0.353553
$9$	−23.0000	−0.851852
$10$	0	0
$11$	−20.0000	−0.548202	−0.274101	−	0.961701i	$-0.588380\pi$
$11$	−20.0000	−0.548202	−0.274101	+	0.961701i	$0.588380\pi$
$12$	−8.00000	−0.192450
$13$	4.00000	0.0853385	0.0426692	−	0.999089i	$-0.486414\pi$
$13$	4.00000	0.0853385	0.0426692	+	0.999089i	$0.486414\pi$
$14$	24.0000	0.458162
$15$	0	0
$16$	16.0000	0.250000
$17$	34.0000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	34.0000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	−46.0000	−0.602350
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	0	0
$21$	−24.0000	−0.249392
$22$	−40.0000	−0.387638
$23$	−40.0000	−0.362634	−0.181317	−	0.983425i	$-0.558036\pi$
$23$	−40.0000	−0.362634	−0.181317	+	0.983425i	$0.558036\pi$
$24$	−16.0000	−0.136083
$25$	0	0
$26$	8.00000	0.0603434
$27$	100.000	0.712778
$28$	48.0000	0.323970
$29$	−150.000	−0.960493	−0.480247	−	0.877134i	$-0.659453\pi$
$29$	−150.000	−0.960493	−0.480247	+	0.877134i	$0.659453\pi$
$30$	0	0
$31$	−200.000	−1.15874	−0.579372	−	0.815063i	$-0.696702\pi$
$31$	−200.000	−1.15874	−0.579372	+	0.815063i	$0.696702\pi$
$32$	32.0000	0.176777
$33$	40.0000	0.211003
$34$	68.0000	0.342997
$35$	0	0
$36$	−92.0000	−0.425926
$37$	156.000	0.693142	0.346571	−	0.938024i	$-0.387346\pi$
$37$	156.000	0.693142	0.346571	+	0.938024i	$0.387346\pi$
$38$	−38.0000	−0.162221
$39$	−8.00000	−0.0328468
$40$	0	0
$41$	−218.000	−0.830387	−0.415194	−	0.909733i	$-0.636286\pi$
$41$	−218.000	−0.830387	−0.415194	+	0.909733i	$0.636286\pi$
$42$	−48.0000	−0.176347
$43$	−248.000	−0.879527	−0.439763	−	0.898114i	$-0.644938\pi$
$43$	−248.000	−0.879527	−0.439763	+	0.898114i	$0.644938\pi$
$44$	−80.0000	−0.274101
$45$	0	0
$46$	−80.0000	−0.256421
$47$	180.000	0.558632	0.279316	−	0.960199i	$-0.409892\pi$
$47$	180.000	0.558632	0.279316	+	0.960199i	$0.409892\pi$
$48$	−32.0000	−0.0962250
$49$	−199.000	−0.580175
$50$	0	0
$51$	−68.0000	−0.186704
$52$	16.0000	0.0426692
$53$	−72.0000	−0.186603	−0.0933015	−	0.995638i	$-0.529742\pi$
$53$	−72.0000	−0.186603	−0.0933015	+	0.995638i	$0.529742\pi$
$54$	200.000	0.504010
$55$	0	0
$56$	96.0000	0.229081
$57$	38.0000	0.0883022
$58$	−300.000	−0.679171
$59$	−48.0000	−0.105916	−0.0529582	−	0.998597i	$-0.516865\pi$
$59$	−48.0000	−0.105916	−0.0529582	+	0.998597i	$0.516865\pi$
$60$	0	0
$61$	−134.000	−0.281261	−0.140631	−	0.990062i	$-0.544913\pi$
$61$	−134.000	−0.281261	−0.140631	+	0.990062i	$0.544913\pi$
$62$	−400.000	−0.819356
$63$	−276.000	−0.551948
$64$	64.0000	0.125000
$65$	0	0
$66$	80.0000	0.149202
$67$	−334.000	−0.609024	−0.304512	−	0.952509i	$-0.598493\pi$
$67$	−334.000	−0.609024	−0.304512	+	0.952509i	$0.598493\pi$
$68$	136.000	0.242536
$69$	80.0000	0.139578
$70$	0	0
$71$	−520.000	−0.869192	−0.434596	−	0.900625i	$-0.643109\pi$
$71$	−520.000	−0.869192	−0.434596	+	0.900625i	$0.643109\pi$
$72$	−184.000	−0.301175
$73$	−438.000	−0.702247	−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−438.000	−0.702247	−0.351123	+	0.936329i	$0.614200\pi$
$74$	312.000	0.490125
$75$	0	0
$76$	−76.0000	−0.114708
$77$	−240.000	−0.355202
$78$	−16.0000	−0.0232262
$79$	980.000	1.39568	0.697839	−	0.716254i	$-0.254145\pi$
$79$	980.000	1.39568	0.697839	+	0.716254i	$0.254145\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	−436.000	−0.587173
$83$	156.000	0.206304	0.103152	−	0.994666i	$-0.467107\pi$
$83$	156.000	0.206304	0.103152	+	0.994666i	$0.467107\pi$
$84$	−96.0000	−0.124696
$85$	0	0
$86$	−496.000	−0.621919
$87$	300.000	0.369694
$88$	−160.000	−0.193819
$89$	670.000	0.797976	0.398988	−	0.916956i	$-0.369362\pi$
$89$	670.000	0.797976	0.398988	+	0.916956i	$0.369362\pi$
$90$	0	0
$91$	48.0000	0.0552941
$92$	−160.000	−0.181317
$93$	400.000	0.446001
$94$	360.000	0.395012
$95$	0	0
$96$	−64.0000	−0.0680414
$97$	−1124.00	−1.17655	−0.588273	−	0.808663i	$-0.700192\pi$
$97$	−1124.00	−1.17655	−0.588273	+	0.808663i	$0.700192\pi$
$98$	−398.000	−0.410246
$99$	460.000	0.466987
$100$	0	0
$101$	−1454.00	−1.43246	−0.716230	−	0.697865i	$-0.754134\pi$
$101$	−1454.00	−1.43246	−0.716230	+	0.697865i	$0.754134\pi$
$102$	−136.000	−0.132020
$103$	−1370.00	−1.31058	−0.655292	−	0.755376i	$-0.727454\pi$
$103$	−1370.00	−1.31058	−0.655292	+	0.755376i	$0.727454\pi$
$104$	32.0000	0.0301717
$105$	0	0
$106$	−144.000	−0.131948
$107$	−338.000	−0.305380	−0.152690	−	0.988274i	$-0.548794\pi$
$107$	−338.000	−0.305380	−0.152690	+	0.988274i	$0.548794\pi$
$108$	400.000	0.356389
$109$	102.000	0.0896315	0.0448157	−	0.998995i	$-0.485730\pi$
$109$	102.000	0.0896315	0.0448157	+	0.998995i	$0.485730\pi$
$110$	0	0
$111$	−312.000	−0.266790
$112$	192.000	0.161985
$113$	−4.00000	−0.00332999	−0.00166499	−	0.999999i	$-0.500530\pi$
$113$	−4.00000	−0.00332999	−0.00166499	+	0.999999i	$0.500530\pi$
$114$	76.0000	0.0624391
$115$	0	0
$116$	−600.000	−0.480247
$117$	−92.0000	−0.0726958
$118$	−96.0000	−0.0748942
$119$	408.000	0.314297
$120$	0	0
$121$	−931.000	−0.699474
$122$	−268.000	−0.198882
$123$	436.000	0.319616
$124$	−800.000	−0.579372
$125$	0	0
$126$	−552.000	−0.390286
$127$	−1358.00	−0.948843	−0.474421	−	0.880298i	$-0.657343\pi$
$127$	−1358.00	−0.948843	−0.474421	+	0.880298i	$0.657343\pi$
$128$	128.000	0.0883883
$129$	496.000	0.338530
$130$	0	0
$131$	−2700.00	−1.80076	−0.900382	−	0.435100i	$-0.856713\pi$
$131$	−2700.00	−1.80076	−0.900382	+	0.435100i	$0.856713\pi$
$132$	160.000	0.105502
$133$	−228.000	−0.148647
$134$	−668.000	−0.430645
$135$	0	0
$136$	272.000	0.171499
$137$	866.000	0.540054	0.270027	−	0.962853i	$-0.412967\pi$
$137$	866.000	0.540054	0.270027	+	0.962853i	$0.412967\pi$
$138$	160.000	0.0986964
$139$	148.000	0.0903108	0.0451554	−	0.998980i	$-0.485622\pi$
$139$	148.000	0.0903108	0.0451554	+	0.998980i	$0.485622\pi$
$140$	0	0
$141$	−360.000	−0.215018
$142$	−1040.00	−0.614612
$143$	−80.0000	−0.0467828
$144$	−368.000	−0.212963
$145$	0	0
$146$	−876.000	−0.496564
$147$	398.000	0.223309
$148$	624.000	0.346571
$149$	−2094.00	−1.15132	−0.575662	−	0.817688i	$-0.695255\pi$
$149$	−2094.00	−1.15132	−0.575662	+	0.817688i	$0.695255\pi$
$150$	0	0
$151$	444.000	0.239286	0.119643	−	0.992817i	$-0.461825\pi$
$151$	444.000	0.239286	0.119643	+	0.992817i	$0.461825\pi$
$152$	−152.000	−0.0811107
$153$	−782.000	−0.413209
$154$	−480.000	−0.251166
$155$	0	0
$156$	−32.0000	−0.0164234
$157$	−1546.00	−0.785887	−0.392943	−	0.919563i	$-0.628543\pi$
$157$	−1546.00	−0.785887	−0.392943	+	0.919563i	$0.628543\pi$
$158$	1960.00	0.986894
$159$	144.000	0.0718235
$160$	0	0
$161$	−480.000	−0.234965
$162$	842.000	0.408357
$163$	−176.000	−0.0845729	−0.0422865	−	0.999106i	$-0.513464\pi$
$163$	−176.000	−0.0845729	−0.0422865	+	0.999106i	$0.513464\pi$
$164$	−872.000	−0.415194
$165$	0	0
$166$	312.000	0.145879
$167$	−858.000	−0.397569	−0.198785	−	0.980043i	$-0.563699\pi$
$167$	−858.000	−0.397569	−0.198785	+	0.980043i	$0.563699\pi$
$168$	−192.000	−0.0881733
$169$	−2181.00	−0.992717
$170$	0	0
$171$	437.000	0.195428
$172$	−992.000	−0.439763
$173$	1312.00	0.576587	0.288293	−	0.957542i	$-0.406912\pi$
$173$	1312.00	0.576587	0.288293	+	0.957542i	$0.406912\pi$
$174$	600.000	0.261413
$175$	0	0
$176$	−320.000	−0.137051
$177$	96.0000	0.0407672
$178$	1340.00	0.564254
$179$	3416.00	1.42639	0.713195	−	0.700966i	$-0.247247\pi$
$179$	3416.00	1.42639	0.713195	+	0.700966i	$0.247247\pi$
$180$	0	0
$181$	1230.00	0.505111	0.252556	−	0.967582i	$-0.418729\pi$
$181$	1230.00	0.505111	0.252556	+	0.967582i	$0.418729\pi$
$182$	96.0000	0.0390989
$183$	268.000	0.108258
$184$	−320.000	−0.128210
$185$	0	0
$186$	800.000	0.315370
$187$	−680.000	−0.265917
$188$	720.000	0.279316
$189$	1200.00	0.461837
$190$	0	0
$191$	1928.00	0.730394	0.365197	−	0.930930i	$-0.381002\pi$
$191$	1928.00	0.730394	0.365197	+	0.930930i	$0.381002\pi$
$192$	−128.000	−0.0481125
$193$	1036.00	0.386388	0.193194	−	0.981161i	$-0.438115\pi$
$193$	1036.00	0.386388	0.193194	+	0.981161i	$0.438115\pi$
$194$	−2248.00	−0.831943
$195$	0	0
$196$	−796.000	−0.290087
$197$	1810.00	0.654605	0.327302	−	0.944920i	$-0.393860\pi$
$197$	1810.00	0.654605	0.327302	+	0.944920i	$0.393860\pi$
$198$	920.000	0.330210
$199$	4248.00	1.51323	0.756615	−	0.653861i	$-0.226852\pi$
$199$	4248.00	1.51323	0.756615	+	0.653861i	$0.226852\pi$
$200$	0	0
$201$	668.000	0.234413
$202$	−2908.00	−1.01290
$203$	−1800.00	−0.622341
$204$	−272.000	−0.0933520
$205$	0	0
$206$	−2740.00	−0.926723
$207$	920.000	0.308910
$208$	64.0000	0.0213346
$209$	380.000	0.125766
$210$	0	0
$211$	−2680.00	−0.874402	−0.437201	−	0.899364i	$-0.644030\pi$
$211$	−2680.00	−0.874402	−0.437201	+	0.899364i	$0.644030\pi$
$212$	−288.000	−0.0933015
$213$	1040.00	0.334552
$214$	−676.000	−0.215936
$215$	0	0
$216$	800.000	0.252005
$217$	−2400.00	−0.750795
$218$	204.000	0.0633790
$219$	876.000	0.270295
$220$	0	0
$221$	136.000	0.0413952
$222$	−624.000	−0.188649
$223$	−3234.00	−0.971142	−0.485571	−	0.874197i	$-0.661388\pi$
$223$	−3234.00	−0.971142	−0.485571	+	0.874197i	$0.661388\pi$
$224$	384.000	0.114541
$225$	0	0
$226$	−8.00000	−0.00235466
$227$	−250.000	−0.0730973	−0.0365486	−	0.999332i	$-0.511636\pi$
$227$	−250.000	−0.0730973	−0.0365486	+	0.999332i	$0.511636\pi$
$228$	152.000	0.0441511
$229$	1538.00	0.443816	0.221908	−	0.975068i	$-0.428772\pi$
$229$	1538.00	0.443816	0.221908	+	0.975068i	$0.428772\pi$
$230$	0	0
$231$	480.000	0.136717
$232$	−1200.00	−0.339586
$233$	3222.00	0.905924	0.452962	−	0.891530i	$-0.350367\pi$
$233$	3222.00	0.905924	0.452962	+	0.891530i	$0.350367\pi$
$234$	−184.000	−0.0514037
$235$	0	0
$236$	−192.000	−0.0529582
$237$	−1960.00	−0.537197
$238$	816.000	0.222241
$239$	1032.00	0.279308	0.139654	−	0.990200i	$-0.455401\pi$
$239$	1032.00	0.279308	0.139654	+	0.990200i	$0.455401\pi$
$240$	0	0
$241$	−3898.00	−1.04188	−0.520938	−	0.853594i	$-0.674418\pi$
$241$	−3898.00	−1.04188	−0.520938	+	0.853594i	$0.674418\pi$
$242$	−1862.00	−0.494603
$243$	−3542.00	−0.935059
$244$	−536.000	−0.140631
$245$	0	0
$246$	872.000	0.226003
$247$	−76.0000	−0.0195780
$248$	−1600.00	−0.409678
$249$	−312.000	−0.0794064
$250$	0	0
$251$	4084.00	1.02701	0.513506	−	0.858086i	$-0.328347\pi$
$251$	4084.00	1.02701	0.513506	+	0.858086i	$0.328347\pi$
$252$	−1104.00	−0.275974
$253$	800.000	0.198797
$254$	−2716.00	−0.670933
$255$	0	0
$256$	256.000	0.0625000
$257$	6952.00	1.68737	0.843685	−	0.536839i	$-0.180382\pi$
$257$	6952.00	1.68737	0.843685	+	0.536839i	$0.180382\pi$
$258$	992.000	0.239377
$259$	1872.00	0.449114
$260$	0	0
$261$	3450.00	0.818198
$262$	−5400.00	−1.27333
$263$	904.000	0.211951	0.105975	−	0.994369i	$-0.466204\pi$
$263$	904.000	0.211951	0.105975	+	0.994369i	$0.466204\pi$
$264$	320.000	0.0746009
$265$	0	0
$266$	−456.000	−0.105110
$267$	−1340.00	−0.307141
$268$	−1336.00	−0.304512
$269$	−2210.00	−0.500915	−0.250457	−	0.968128i	$-0.580581\pi$
$269$	−2210.00	−0.500915	−0.250457	+	0.968128i	$0.580581\pi$
$270$	0	0
$271$	440.000	0.0986277	0.0493138	−	0.998783i	$-0.484297\pi$
$271$	440.000	0.0986277	0.0493138	+	0.998783i	$0.484297\pi$
$272$	544.000	0.121268
$273$	−96.0000	−0.0212827
$274$	1732.00	0.381876
$275$	0	0
$276$	320.000	0.0697889
$277$	8054.00	1.74700	0.873498	−	0.486828i	$-0.161846\pi$
$277$	8054.00	1.74700	0.873498	+	0.486828i	$0.161846\pi$
$278$	296.000	0.0638594
$279$	4600.00	0.987078
$280$	0	0
$281$	3894.00	0.826678	0.413339	−	0.910577i	$-0.364362\pi$
$281$	3894.00	0.826678	0.413339	+	0.910577i	$0.364362\pi$
$282$	−720.000	−0.152040
$283$	4108.00	0.862881	0.431440	−	0.902141i	$-0.358006\pi$
$283$	4108.00	0.862881	0.431440	+	0.902141i	$0.358006\pi$
$284$	−2080.00	−0.434596
$285$	0	0
$286$	−160.000	−0.0330804
$287$	−2616.00	−0.538040
$288$	−736.000	−0.150588
$289$	−3757.00	−0.764706
$290$	0	0
$291$	2248.00	0.452853
$292$	−1752.00	−0.351123
$293$	−3208.00	−0.639636	−0.319818	−	0.947479i	$-0.603622\pi$
$293$	−3208.00	−0.639636	−0.319818	+	0.947479i	$0.603622\pi$
$294$	796.000	0.157904
$295$	0	0
$296$	1248.00	0.245063
$297$	−2000.00	−0.390747
$298$	−4188.00	−0.814108
$299$	−160.000	−0.0309466
$300$	0	0
$301$	−2976.00	−0.569880
$302$	888.000	0.169201
$303$	2908.00	0.551354
$304$	−304.000	−0.0573539
$305$	0	0
$306$	−1564.00	−0.292183
$307$	6422.00	1.19389	0.596943	−	0.802284i	$-0.296382\pi$
$307$	6422.00	1.19389	0.596943	+	0.802284i	$0.296382\pi$
$308$	−960.000	−0.177601
$309$	2740.00	0.504444
$310$	0	0
$311$	−4432.00	−0.808089	−0.404044	−	0.914739i	$-0.632396\pi$
$311$	−4432.00	−0.808089	−0.404044	+	0.914739i	$0.632396\pi$
$312$	−64.0000	−0.0116131
$313$	−1698.00	−0.306635	−0.153317	−	0.988177i	$-0.548996\pi$
$313$	−1698.00	−0.306635	−0.153317	+	0.988177i	$0.548996\pi$
$314$	−3092.00	−0.555706
$315$	0	0
$316$	3920.00	0.697839
$317$	6884.00	1.21970	0.609849	−	0.792518i	$-0.291230\pi$
$317$	6884.00	1.21970	0.609849	+	0.792518i	$0.291230\pi$
$318$	288.000	0.0507869
$319$	3000.00	0.526545
$320$	0	0
$321$	676.000	0.117541
$322$	−960.000	−0.166145
$323$	−646.000	−0.111283
$324$	1684.00	0.288752
$325$	0	0
$326$	−352.000	−0.0598021
$327$	−204.000	−0.0344992
$328$	−1744.00	−0.293586
$329$	2160.00	0.361959
$330$	0	0
$331$	3448.00	0.572566	0.286283	−	0.958145i	$-0.407580\pi$
$331$	3448.00	0.572566	0.286283	+	0.958145i	$0.407580\pi$
$332$	624.000	0.103152
$333$	−3588.00	−0.590454
$334$	−1716.00	−0.281124
$335$	0	0
$336$	−384.000	−0.0623480
$337$	6388.00	1.03257	0.516286	−	0.856416i	$-0.327314\pi$
$337$	6388.00	1.03257	0.516286	+	0.856416i	$0.327314\pi$
$338$	−4362.00	−0.701957
$339$	8.00000	0.00128171
$340$	0	0
$341$	4000.00	0.635226
$342$	874.000	0.138189
$343$	−6504.00	−1.02386
$344$	−1984.00	−0.310960
$345$	0	0
$346$	2624.00	0.407708
$347$	156.000	0.0241341	0.0120670	−	0.999927i	$-0.496159\pi$
$347$	156.000	0.0241341	0.0120670	+	0.999927i	$0.496159\pi$
$348$	1200.00	0.184847
$349$	4430.00	0.679463	0.339731	−	0.940523i	$-0.389664\pi$
$349$	4430.00	0.679463	0.339731	+	0.940523i	$0.389664\pi$
$350$	0	0
$351$	400.000	0.0608274
$352$	−640.000	−0.0969094
$353$	12034.0	1.81446	0.907231	−	0.420632i	$-0.138192\pi$
$353$	12034.0	1.81446	0.907231	+	0.420632i	$0.138192\pi$
$354$	192.000	0.0288268
$355$	0	0
$356$	2680.00	0.398988
$357$	−816.000	−0.120973
$358$	6832.00	1.00861
$359$	−8352.00	−1.22786	−0.613930	−	0.789361i	$-0.710412\pi$
$359$	−8352.00	−1.22786	−0.613930	+	0.789361i	$0.710412\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	2460.00	0.357168
$363$	1862.00	0.269228
$364$	192.000	0.0276471
$365$	0	0
$366$	536.000	0.0765496
$367$	2844.00	0.404511	0.202256	−	0.979333i	$-0.435173\pi$
$367$	2844.00	0.404511	0.202256	+	0.979333i	$0.435173\pi$
$368$	−640.000	−0.0906584
$369$	5014.00	0.707367
$370$	0	0
$371$	−864.000	−0.120907
$372$	1600.00	0.223000
$373$	−7064.00	−0.980590	−0.490295	−	0.871557i	$-0.663111\pi$
$373$	−7064.00	−0.980590	−0.490295	+	0.871557i	$0.663111\pi$
$374$	−1360.00	−0.188032
$375$	0	0
$376$	1440.00	0.197506
$377$	−600.000	−0.0819670
$378$	2400.00	0.326568
$379$	−6068.00	−0.822407	−0.411203	−	0.911544i	$-0.634891\pi$
$379$	−6068.00	−0.822407	−0.411203	+	0.911544i	$0.634891\pi$
$380$	0	0
$381$	2716.00	0.365210
$382$	3856.00	0.516466
$383$	6570.00	0.876531	0.438265	−	0.898846i	$-0.355593\pi$
$383$	6570.00	0.876531	0.438265	+	0.898846i	$0.355593\pi$
$384$	−256.000	−0.0340207
$385$	0	0
$386$	2072.00	0.273218
$387$	5704.00	0.749226
$388$	−4496.00	−0.588273
$389$	1886.00	0.245820	0.122910	−	0.992418i	$-0.460777\pi$
$389$	1886.00	0.245820	0.122910	+	0.992418i	$0.460777\pi$
$390$	0	0
$391$	−1360.00	−0.175903
$392$	−1592.00	−0.205123
$393$	5400.00	0.693114
$394$	3620.00	0.462876
$395$	0	0
$396$	1840.00	0.233494
$397$	11550.0	1.46015	0.730073	−	0.683369i	$-0.239486\pi$
$397$	11550.0	1.46015	0.730073	+	0.683369i	$0.239486\pi$
$398$	8496.00	1.07002
$399$	456.000	0.0572144
$400$	0	0
$401$	−8342.00	−1.03885	−0.519426	−	0.854515i	$-0.673854\pi$
$401$	−8342.00	−1.03885	−0.519426	+	0.854515i	$0.673854\pi$
$402$	1336.00	0.165755
$403$	−800.000	−0.0988855
$404$	−5816.00	−0.716230
$405$	0	0
$406$	−3600.00	−0.440062
$407$	−3120.00	−0.379982
$408$	−544.000	−0.0660098
$409$	−4926.00	−0.595538	−0.297769	−	0.954638i	$-0.596243\pi$
$409$	−4926.00	−0.595538	−0.297769	+	0.954638i	$0.596243\pi$
$410$	0	0
$411$	−1732.00	−0.207867
$412$	−5480.00	−0.655292
$413$	−576.000	−0.0686274
$414$	1840.00	0.218433
$415$	0	0
$416$	128.000	0.0150859
$417$	−296.000	−0.0347606
$418$	760.000	0.0889302
$419$	−4164.00	−0.485501	−0.242750	−	0.970089i	$-0.578050\pi$
$419$	−4164.00	−0.485501	−0.242750	+	0.970089i	$0.578050\pi$
$420$	0	0
$421$	3026.00	0.350305	0.175152	−	0.984541i	$-0.443958\pi$
$421$	3026.00	0.350305	0.175152	+	0.984541i	$0.443958\pi$
$422$	−5360.00	−0.618296
$423$	−4140.00	−0.475872
$424$	−576.000	−0.0659741
$425$	0	0
$426$	2080.00	0.236564
$427$	−1608.00	−0.182240
$428$	−1352.00	−0.152690
$429$	160.000	0.0180067
$430$	0	0
$431$	−10348.0	−1.15649	−0.578243	−	0.815864i	$-0.696262\pi$
$431$	−10348.0	−1.15649	−0.578243	+	0.815864i	$0.696262\pi$
$432$	1600.00	0.178195
$433$	3164.00	0.351160	0.175580	−	0.984465i	$-0.443820\pi$
$433$	3164.00	0.351160	0.175580	+	0.984465i	$0.443820\pi$
$434$	−4800.00	−0.530893
$435$	0	0
$436$	408.000	0.0448157
$437$	760.000	0.0831939
$438$	1752.00	0.191127
$439$	−17700.0	−1.92432	−0.962158	−	0.272491i	$-0.912152\pi$
$439$	−17700.0	−1.92432	−0.962158	+	0.272491i	$0.912152\pi$
$440$	0	0
$441$	4577.00	0.494223
$442$	272.000	0.0292709
$443$	−8572.00	−0.919341	−0.459670	−	0.888090i	$-0.652032\pi$
$443$	−8572.00	−0.919341	−0.459670	+	0.888090i	$0.652032\pi$
$444$	−1248.00	−0.133395
$445$	0	0
$446$	−6468.00	−0.686701
$447$	4188.00	0.443145
$448$	768.000	0.0809924
$449$	7866.00	0.826769	0.413385	−	0.910556i	$-0.364346\pi$
$449$	7866.00	0.826769	0.413385	+	0.910556i	$0.364346\pi$
$450$	0	0
$451$	4360.00	0.455220
$452$	−16.0000	−0.00166499
$453$	−888.000	−0.0921013
$454$	−500.000	−0.0516876
$455$	0	0
$456$	304.000	0.0312195
$457$	14982.0	1.53354	0.766771	−	0.641921i	$-0.221862\pi$
$457$	14982.0	1.53354	0.766771	+	0.641921i	$0.221862\pi$
$458$	3076.00	0.313825
$459$	3400.00	0.345748
$460$	0	0
$461$	7030.00	0.710238	0.355119	−	0.934821i	$-0.384440\pi$
$461$	7030.00	0.710238	0.355119	+	0.934821i	$0.384440\pi$
$462$	960.000	0.0966737
$463$	−4448.00	−0.446471	−0.223236	−	0.974765i	$-0.571662\pi$
$463$	−4448.00	−0.446471	−0.223236	+	0.974765i	$0.571662\pi$
$464$	−2400.00	−0.240123
$465$	0	0
$466$	6444.00	0.640585
$467$	13996.0	1.38685	0.693424	−	0.720530i	$-0.256101\pi$
$467$	13996.0	1.38685	0.693424	+	0.720530i	$0.256101\pi$
$468$	−368.000	−0.0363479
$469$	−4008.00	−0.394610
$470$	0	0
$471$	3092.00	0.302488
$472$	−384.000	−0.0374471
$473$	4960.00	0.482159
$474$	−3920.00	−0.379856
$475$	0	0
$476$	1632.00	0.157148
$477$	1656.00	0.158958
$478$	2064.00	0.197500
$479$	−5056.00	−0.482285	−0.241143	−	0.970490i	$-0.577522\pi$
$479$	−5056.00	−0.482285	−0.241143	+	0.970490i	$0.577522\pi$
$480$	0	0
$481$	624.000	0.0591517
$482$	−7796.00	−0.736718
$483$	960.000	0.0904379
$484$	−3724.00	−0.349737
$485$	0	0
$486$	−7084.00	−0.661187
$487$	−13786.0	−1.28276	−0.641379	−	0.767224i	$-0.721637\pi$
$487$	−13786.0	−1.28276	−0.641379	+	0.767224i	$0.721637\pi$
$488$	−1072.00	−0.0994409
$489$	352.000	0.0325521
$490$	0	0
$491$	4404.00	0.404786	0.202393	−	0.979304i	$-0.435128\pi$
$491$	4404.00	0.404786	0.202393	+	0.979304i	$0.435128\pi$
$492$	1744.00	0.159808
$493$	−5100.00	−0.465908
$494$	−152.000	−0.0138437
$495$	0	0
$496$	−3200.00	−0.289686
$497$	−6240.00	−0.563184
$498$	−624.000	−0.0561488
$499$	1668.00	0.149639	0.0748196	−	0.997197i	$-0.476162\pi$
$499$	1668.00	0.149639	0.0748196	+	0.997197i	$0.476162\pi$
$500$	0	0
$501$	1716.00	0.153024
$502$	8168.00	0.726207
$503$	−12984.0	−1.15095	−0.575475	−	0.817819i	$-0.695183\pi$
$503$	−12984.0	−1.15095	−0.575475	+	0.817819i	$0.695183\pi$
$504$	−2208.00	−0.195143
$505$	0	0
$506$	1600.00	0.140571
$507$	4362.00	0.382097
$508$	−5432.00	−0.474421
$509$	6762.00	0.588842	0.294421	−	0.955676i	$-0.404873\pi$
$509$	6762.00	0.588842	0.294421	+	0.955676i	$0.404873\pi$
$510$	0	0
$511$	−5256.00	−0.455013
$512$	512.000	0.0441942
$513$	−1900.00	−0.163523
$514$	13904.0	1.19315
$515$	0	0
$516$	1984.00	0.169265
$517$	−3600.00	−0.306243
$518$	3744.00	0.317571
$519$	−2624.00	−0.221928
$520$	0	0
$521$	22530.0	1.89454	0.947272	−	0.320431i	$-0.103828\pi$
$521$	22530.0	1.89454	0.947272	+	0.320431i	$0.103828\pi$
$522$	6900.00	0.578553
$523$	−21958.0	−1.83586	−0.917931	−	0.396739i	$-0.870142\pi$
$523$	−21958.0	−1.83586	−0.917931	+	0.396739i	$0.870142\pi$
$524$	−10800.0	−0.900382
$525$	0	0
$526$	1808.00	0.149872
$527$	−6800.00	−0.562073
$528$	640.000	0.0527508
$529$	−10567.0	−0.868497
$530$	0	0
$531$	1104.00	0.0902251
$532$	−912.000	−0.0743237
$533$	−872.000	−0.0708640
$534$	−2680.00	−0.217182
$535$	0	0
$536$	−2672.00	−0.215322
$537$	−6832.00	−0.549018
$538$	−4420.00	−0.354200
$539$	3980.00	0.318053
$540$	0	0
$541$	10802.0	0.858437	0.429218	−	0.903201i	$-0.358789\pi$
$541$	10802.0	0.858437	0.429218	+	0.903201i	$0.358789\pi$
$542$	880.000	0.0697403
$543$	−2460.00	−0.194418
$544$	1088.00	0.0857493
$545$	0	0
$546$	−192.000	−0.0150492
$547$	10150.0	0.793387	0.396693	−	0.917951i	$-0.370158\pi$
$547$	10150.0	0.793387	0.396693	+	0.917951i	$0.370158\pi$
$548$	3464.00	0.270027
$549$	3082.00	0.239593
$550$	0	0
$551$	2850.00	0.220352
$552$	640.000	0.0493482
$553$	11760.0	0.904315
$554$	16108.0	1.23531
$555$	0	0
$556$	592.000	0.0451554
$557$	−25026.0	−1.90374	−0.951872	−	0.306495i	$-0.900844\pi$
$557$	−25026.0	−1.90374	−0.951872	+	0.306495i	$0.900844\pi$
$558$	9200.00	0.697970
$559$	−992.000	−0.0750575
$560$	0	0
$561$	1360.00	0.102352
$562$	7788.00	0.584550
$563$	−6718.00	−0.502895	−0.251448	−	0.967871i	$-0.580907\pi$
$563$	−6718.00	−0.502895	−0.251448	+	0.967871i	$0.580907\pi$
$564$	−1440.00	−0.107509
$565$	0	0
$566$	8216.00	0.610149
$567$	5052.00	0.374187
$568$	−4160.00	−0.307306
$569$	−8102.00	−0.596931	−0.298465	−	0.954420i	$-0.596475\pi$
$569$	−8102.00	−0.596931	−0.298465	+	0.954420i	$0.596475\pi$
$570$	0	0
$571$	−1100.00	−0.0806192	−0.0403096	−	0.999187i	$-0.512834\pi$
$571$	−1100.00	−0.0806192	−0.0403096	+	0.999187i	$0.512834\pi$
$572$	−320.000	−0.0233914
$573$	−3856.00	−0.281129
$574$	−5232.00	−0.380452
$575$	0	0
$576$	−1472.00	−0.106481
$577$	−7458.00	−0.538095	−0.269047	−	0.963127i	$-0.586709\pi$
$577$	−7458.00	−0.538095	−0.269047	+	0.963127i	$0.586709\pi$
$578$	−7514.00	−0.540729
$579$	−2072.00	−0.148721
$580$	0	0
$581$	1872.00	0.133672
$582$	4496.00	0.320215
$583$	1440.00	0.102296
$584$	−3504.00	−0.248282
$585$	0	0
$586$	−6416.00	−0.452291
$587$	14140.0	0.994242	0.497121	−	0.867681i	$-0.334390\pi$
$587$	14140.0	0.994242	0.497121	+	0.867681i	$0.334390\pi$
$588$	1592.00	0.111655
$589$	3800.00	0.265834
$590$	0	0
$591$	−3620.00	−0.251958
$592$	2496.00	0.173285
$593$	9302.00	0.644161	0.322080	−	0.946712i	$-0.395618\pi$
$593$	9302.00	0.644161	0.322080	+	0.946712i	$0.395618\pi$
$594$	−4000.00	−0.276300
$595$	0	0
$596$	−8376.00	−0.575662
$597$	−8496.00	−0.582442
$598$	−320.000	−0.0218826
$599$	3460.00	0.236013	0.118006	−	0.993013i	$-0.462350\pi$
$599$	3460.00	0.236013	0.118006	+	0.993013i	$0.462350\pi$
$600$	0	0
$601$	27910.0	1.89430	0.947149	−	0.320795i	$-0.103950\pi$
$601$	27910.0	1.89430	0.947149	+	0.320795i	$0.103950\pi$
$602$	−5952.00	−0.402966
$603$	7682.00	0.518798
$604$	1776.00	0.119643
$605$	0	0
$606$	5816.00	0.389866
$607$	13646.0	0.912478	0.456239	−	0.889857i	$-0.349196\pi$
$607$	13646.0	0.912478	0.456239	+	0.889857i	$0.349196\pi$
$608$	−608.000	−0.0405554
$609$	3600.00	0.239539
$610$	0	0
$611$	720.000	0.0476728
$612$	−3128.00	−0.206604
$613$	−12802.0	−0.843504	−0.421752	−	0.906711i	$-0.638585\pi$
$613$	−12802.0	−0.843504	−0.421752	+	0.906711i	$0.638585\pi$
$614$	12844.0	0.844205
$615$	0	0
$616$	−1920.00	−0.125583
$617$	−5806.00	−0.378834	−0.189417	−	0.981897i	$-0.560660\pi$
$617$	−5806.00	−0.378834	−0.189417	+	0.981897i	$0.560660\pi$
$618$	5480.00	0.356696
$619$	18868.0	1.22515	0.612576	−	0.790412i	$-0.290133\pi$
$619$	18868.0	1.22515	0.612576	+	0.790412i	$0.290133\pi$
$620$	0	0
$621$	−4000.00	−0.258477
$622$	−8864.00	−0.571405
$623$	8040.00	0.517040
$624$	−128.000	−0.00821170
$625$	0	0
$626$	−3396.00	−0.216823
$627$	−760.000	−0.0484075
$628$	−6184.00	−0.392943
$629$	5304.00	0.336223
$630$	0	0
$631$	−11960.0	−0.754548	−0.377274	−	0.926102i	$-0.623139\pi$
$631$	−11960.0	−0.754548	−0.377274	+	0.926102i	$0.623139\pi$
$632$	7840.00	0.493447
$633$	5360.00	0.336557
$634$	13768.0	0.862456
$635$	0	0
$636$	576.000	0.0359118
$637$	−796.000	−0.0495113
$638$	6000.00	0.372323
$639$	11960.0	0.740423
$640$	0	0
$641$	17478.0	1.07697	0.538486	−	0.842634i	$-0.318996\pi$
$641$	17478.0	1.07697	0.538486	+	0.842634i	$0.318996\pi$
$642$	1352.00	0.0831140
$643$	12556.0	0.770078	0.385039	−	0.922900i	$-0.374188\pi$
$643$	12556.0	0.770078	0.385039	+	0.922900i	$0.374188\pi$
$644$	−1920.00	−0.117482
$645$	0	0
$646$	−1292.00	−0.0786889
$647$	−14712.0	−0.893954	−0.446977	−	0.894545i	$-0.647499\pi$
$647$	−14712.0	−0.893954	−0.446977	+	0.894545i	$0.647499\pi$
$648$	3368.00	0.204178
$649$	960.000	0.0580636
$650$	0	0
$651$	4800.00	0.288981
$652$	−704.000	−0.0422865
$653$	7926.00	0.474990	0.237495	−	0.971389i	$-0.423674\pi$
$653$	7926.00	0.474990	0.237495	+	0.971389i	$0.423674\pi$
$654$	−408.000	−0.0243946
$655$	0	0
$656$	−3488.00	−0.207597
$657$	10074.0	0.598210
$658$	4320.00	0.255944
$659$	1560.00	0.0922139	0.0461070	−	0.998937i	$-0.485318\pi$
$659$	1560.00	0.0922139	0.0461070	+	0.998937i	$0.485318\pi$
$660$	0	0
$661$	3202.00	0.188417	0.0942083	−	0.995553i	$-0.469968\pi$
$661$	3202.00	0.188417	0.0942083	+	0.995553i	$0.469968\pi$
$662$	6896.00	0.404865
$663$	−272.000	−0.0159330
$664$	1248.00	0.0729394
$665$	0	0
$666$	−7176.00	−0.417514
$667$	6000.00	0.348307
$668$	−3432.00	−0.198785
$669$	6468.00	0.373793
$670$	0	0
$671$	2680.00	0.154188
$672$	−768.000	−0.0440867
$673$	24824.0	1.42183	0.710917	−	0.703275i	$-0.248280\pi$
$673$	24824.0	1.42183	0.710917	+	0.703275i	$0.248280\pi$
$674$	12776.0	0.730138
$675$	0	0
$676$	−8724.00	−0.496359
$677$	−25368.0	−1.44014	−0.720068	−	0.693904i	$-0.755889\pi$
$677$	−25368.0	−1.44014	−0.720068	+	0.693904i	$0.755889\pi$
$678$	16.0000	0.000906307 0
$679$	−13488.0	−0.762330
$680$	0	0
$681$	500.000	0.0281352
$682$	8000.00	0.449173
$683$	17202.0	0.963713	0.481857	−	0.876250i	$-0.339963\pi$
$683$	17202.0	0.963713	0.481857	+	0.876250i	$0.339963\pi$
$684$	1748.00	0.0977141
$685$	0	0
$686$	−13008.0	−0.723976
$687$	−3076.00	−0.170825
$688$	−3968.00	−0.219882
$689$	−288.000	−0.0159244
$690$	0	0
$691$	−32500.0	−1.78923	−0.894615	−	0.446837i	$-0.852550\pi$
$691$	−32500.0	−1.78923	−0.894615	+	0.446837i	$0.852550\pi$
$692$	5248.00	0.288293
$693$	5520.00	0.302579
$694$	312.000	0.0170654
$695$	0	0
$696$	2400.00	0.130707
$697$	−7412.00	−0.402797
$698$	8860.00	0.480453
$699$	−6444.00	−0.348690
$700$	0	0
$701$	−5766.00	−0.310669	−0.155334	−	0.987862i	$-0.549646\pi$
$701$	−5766.00	−0.310669	−0.155334	+	0.987862i	$0.549646\pi$
$702$	800.000	0.0430115
$703$	−2964.00	−0.159018
$704$	−1280.00	−0.0685253
$705$	0	0
$706$	24068.0	1.28302
$707$	−17448.0	−0.928147
$708$	384.000	0.0203836
$709$	−4906.00	−0.259871	−0.129936	−	0.991522i	$-0.541477\pi$
$709$	−4906.00	−0.259871	−0.129936	+	0.991522i	$0.541477\pi$
$710$	0	0
$711$	−22540.0	−1.18891
$712$	5360.00	0.282127
$713$	8000.00	0.420200
$714$	−1632.00	−0.0855407
$715$	0	0
$716$	13664.0	0.713195
$717$	−2064.00	−0.107506
$718$	−16704.0	−0.868228
$719$	−6704.00	−0.347729	−0.173864	−	0.984770i	$-0.555625\pi$
$719$	−6704.00	−0.347729	−0.173864	+	0.984770i	$0.555625\pi$
$720$	0	0
$721$	−16440.0	−0.849178
$722$	722.000	0.0372161
$723$	7796.00	0.401018
$724$	4920.00	0.252556
$725$	0	0
$726$	3724.00	0.190373
$727$	−9052.00	−0.461788	−0.230894	−	0.972979i	$-0.574165\pi$
$727$	−9052.00	−0.461788	−0.230894	+	0.972979i	$0.574165\pi$
$728$	384.000	0.0195494
$729$	−4283.00	−0.217599
$730$	0	0
$731$	−8432.00	−0.426633
$732$	1072.00	0.0541288
$733$	13058.0	0.657992	0.328996	−	0.944331i	$-0.393290\pi$
$733$	13058.0	0.657992	0.328996	+	0.944331i	$0.393290\pi$
$734$	5688.00	0.286033
$735$	0	0
$736$	−1280.00	−0.0641052
$737$	6680.00	0.333868
$738$	10028.0	0.500184
$739$	−38540.0	−1.91843	−0.959213	−	0.282684i	$-0.908775\pi$
$739$	−38540.0	−1.91843	−0.959213	+	0.282684i	$0.908775\pi$
$740$	0	0
$741$	152.000	0.00753557
$742$	−1728.00	−0.0854944
$743$	19778.0	0.976560	0.488280	−	0.872687i	$-0.337624\pi$
$743$	19778.0	0.976560	0.488280	+	0.872687i	$0.337624\pi$
$744$	3200.00	0.157685
$745$	0	0
$746$	−14128.0	−0.693382
$747$	−3588.00	−0.175740
$748$	−2720.00	−0.132959
$749$	−4056.00	−0.197868
$750$	0	0
$751$	1316.00	0.0639434	0.0319717	−	0.999489i	$-0.489821\pi$
$751$	1316.00	0.0639434	0.0319717	+	0.999489i	$0.489821\pi$
$752$	2880.00	0.139658
$753$	−8168.00	−0.395297
$754$	−1200.00	−0.0579594
$755$	0	0
$756$	4800.00	0.230918
$757$	18346.0	0.880841	0.440421	−	0.897792i	$-0.354829\pi$
$757$	18346.0	0.880841	0.440421	+	0.897792i	$0.354829\pi$
$758$	−12136.0	−0.581530
$759$	−1600.00	−0.0765169
$760$	0	0
$761$	−41370.0	−1.97065	−0.985323	−	0.170701i	$-0.945397\pi$
$761$	−41370.0	−1.97065	−0.985323	+	0.170701i	$0.945397\pi$
$762$	5432.00	0.258242
$763$	1224.00	0.0580757
$764$	7712.00	0.365197
$765$	0	0
$766$	13140.0	0.619801
$767$	−192.000	−0.00903875
$768$	−512.000	−0.0240563
$769$	−30514.0	−1.43090	−0.715451	−	0.698663i	$-0.753779\pi$
$769$	−30514.0	−1.43090	−0.715451	+	0.698663i	$0.753779\pi$
$770$	0	0
$771$	−13904.0	−0.649469
$772$	4144.00	0.193194
$773$	4740.00	0.220551	0.110276	−	0.993901i	$-0.464827\pi$
$773$	4740.00	0.220551	0.110276	+	0.993901i	$0.464827\pi$
$774$	11408.0	0.529783
$775$	0	0
$776$	−8992.00	−0.415972
$777$	−3744.00	−0.172864
$778$	3772.00	0.173821
$779$	4142.00	0.190504
$780$	0	0
$781$	10400.0	0.476493
$782$	−2720.00	−0.124382
$783$	−15000.0	−0.684618
$784$	−3184.00	−0.145044
$785$	0	0
$786$	10800.0	0.490106
$787$	3358.00	0.152096	0.0760481	−	0.997104i	$-0.475770\pi$
$787$	3358.00	0.152096	0.0760481	+	0.997104i	$0.475770\pi$
$788$	7240.00	0.327302
$789$	−1808.00	−0.0815799
$790$	0	0
$791$	−48.0000	−0.00215763
$792$	3680.00	0.165105
$793$	−536.000	−0.0240024
$794$	23100.0	1.03248
$795$	0	0
$796$	16992.0	0.756615
$797$	−37680.0	−1.67465	−0.837324	−	0.546707i	$-0.815881\pi$
$797$	−37680.0	−1.67465	−0.837324	+	0.546707i	$0.815881\pi$
$798$	912.000	0.0404567
$799$	6120.00	0.270976
$800$	0	0
$801$	−15410.0	−0.679757
$802$	−16684.0	−0.734579
$803$	8760.00	0.384973
$804$	2672.00	0.117207
$805$	0	0
$806$	−1600.00	−0.0699226
$807$	4420.00	0.192802
$808$	−11632.0	−0.506451
$809$	33034.0	1.43562	0.717808	−	0.696241i	$-0.245145\pi$
$809$	33034.0	1.43562	0.717808	+	0.696241i	$0.245145\pi$
$810$	0	0
$811$	−11564.0	−0.500699	−0.250350	−	0.968156i	$-0.580546\pi$
$811$	−11564.0	−0.500699	−0.250350	+	0.968156i	$0.580546\pi$
$812$	−7200.00	−0.311171
$813$	−880.000	−0.0379618
$814$	−6240.00	−0.268688
$815$	0	0
$816$	−1088.00	−0.0466760
$817$	4712.00	0.201777
$818$	−9852.00	−0.421109
$819$	−1104.00	−0.0471024
$820$	0	0
$821$	−3706.00	−0.157540	−0.0787700	−	0.996893i	$-0.525099\pi$
$821$	−3706.00	−0.157540	−0.0787700	+	0.996893i	$0.525099\pi$
$822$	−3464.00	−0.146984
$823$	−45692.0	−1.93526	−0.967632	−	0.252364i	$-0.918792\pi$
$823$	−45692.0	−1.93526	−0.967632	+	0.252364i	$0.918792\pi$
$824$	−10960.0	−0.463361
$825$	0	0
$826$	−1152.00	−0.0485269
$827$	−1302.00	−0.0547460	−0.0273730	−	0.999625i	$-0.508714\pi$
$827$	−1302.00	−0.0547460	−0.0273730	+	0.999625i	$0.508714\pi$
$828$	3680.00	0.154455
$829$	36526.0	1.53028	0.765139	−	0.643865i	$-0.222670\pi$
$829$	36526.0	1.53028	0.765139	+	0.643865i	$0.222670\pi$
$830$	0	0
$831$	−16108.0	−0.672419
$832$	256.000	0.0106673
$833$	−6766.00	−0.281426
$834$	−592.000	−0.0245795
$835$	0	0
$836$	1520.00	0.0628831
$837$	−20000.0	−0.825927
$838$	−8328.00	−0.343301
$839$	4668.00	0.192083	0.0960413	−	0.995377i	$-0.469382\pi$
$839$	4668.00	0.192083	0.0960413	+	0.995377i	$0.469382\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	6052.00	0.247703
$843$	−7788.00	−0.318189
$844$	−10720.0	−0.437201
$845$	0	0
$846$	−8280.00	−0.336492
$847$	−11172.0	−0.453217
$848$	−1152.00	−0.0466508
$849$	−8216.00	−0.332123
$850$	0	0
$851$	−6240.00	−0.251357
$852$	4160.00	0.167276
$853$	−6302.00	−0.252962	−0.126481	−	0.991969i	$-0.540368\pi$
$853$	−6302.00	−0.252962	−0.126481	+	0.991969i	$0.540368\pi$
$854$	−3216.00	−0.128863
$855$	0	0
$856$	−2704.00	−0.107968
$857$	−38288.0	−1.52613	−0.763065	−	0.646322i	$-0.776306\pi$
$857$	−38288.0	−1.52613	−0.763065	+	0.646322i	$0.776306\pi$
$858$	320.000	0.0127327
$859$	−3756.00	−0.149189	−0.0745943	−	0.997214i	$-0.523766\pi$
$859$	−3756.00	−0.149189	−0.0745943	+	0.997214i	$0.523766\pi$
$860$	0	0
$861$	5232.00	0.207092
$862$	−20696.0	−0.817759
$863$	−28862.0	−1.13844	−0.569220	−	0.822185i	$-0.692755\pi$
$863$	−28862.0	−1.13844	−0.569220	+	0.822185i	$0.692755\pi$
$864$	3200.00	0.126003
$865$	0	0
$866$	6328.00	0.248307
$867$	7514.00	0.294335
$868$	−9600.00	−0.375398
$869$	−19600.0	−0.765114
$870$	0	0
$871$	−1336.00	−0.0519732
$872$	816.000	0.0316895
$873$	25852.0	1.00224
$874$	1520.00	0.0588270
$875$	0	0
$876$	3504.00	0.135147
$877$	−20360.0	−0.783932	−0.391966	−	0.919980i	$-0.628205\pi$
$877$	−20360.0	−0.783932	−0.391966	+	0.919980i	$0.628205\pi$
$878$	−35400.0	−1.36070
$879$	6416.00	0.246196
$880$	0	0
$881$	5502.00	0.210405	0.105203	−	0.994451i	$-0.466451\pi$
$881$	5502.00	0.210405	0.105203	+	0.994451i	$0.466451\pi$
$882$	9154.00	0.349468
$883$	−27488.0	−1.04762	−0.523808	−	0.851836i	$-0.675489\pi$
$883$	−27488.0	−1.04762	−0.523808	+	0.851836i	$0.675489\pi$
$884$	544.000	0.0206976
$885$	0	0
$886$	−17144.0	−0.650072
$887$	17106.0	0.647535	0.323767	−	0.946137i	$-0.395050\pi$
$887$	17106.0	0.647535	0.323767	+	0.946137i	$0.395050\pi$
$888$	−2496.00	−0.0943246
$889$	−16296.0	−0.614792
$890$	0	0
$891$	−8420.00	−0.316589
$892$	−12936.0	−0.485571
$893$	−3420.00	−0.128159
$894$	8376.00	0.313350
$895$	0	0
$896$	1536.00	0.0572703
$897$	320.000	0.0119114
$898$	15732.0	0.584614
$899$	30000.0	1.11297
$900$	0	0
$901$	−2448.00	−0.0905158
$902$	8720.00	0.321889
$903$	5952.00	0.219347
$904$	−32.0000	−0.00117733
$905$	0	0
$906$	−1776.00	−0.0651254
$907$	−45970.0	−1.68292	−0.841460	−	0.540319i	$-0.818304\pi$
$907$	−45970.0	−1.68292	−0.841460	+	0.540319i	$0.818304\pi$
$908$	−1000.00	−0.0365486
$909$	33442.0	1.22024
$910$	0	0
$911$	−36732.0	−1.33588	−0.667939	−	0.744216i	$-0.732823\pi$
$911$	−36732.0	−1.33588	−0.667939	+	0.744216i	$0.732823\pi$
$912$	608.000	0.0220755
$913$	−3120.00	−0.113096
$914$	29964.0	1.08438
$915$	0	0
$916$	6152.00	0.221908
$917$	−32400.0	−1.16679
$918$	6800.00	0.244481
$919$	−36496.0	−1.31000	−0.655001	−	0.755628i	$-0.727332\pi$
$919$	−36496.0	−1.31000	−0.655001	+	0.755628i	$0.727332\pi$
$920$	0	0
$921$	−12844.0	−0.459527
$922$	14060.0	0.502214
$923$	−2080.00	−0.0741756
$924$	1920.00	0.0683586
$925$	0	0
$926$	−8896.00	−0.315703
$927$	31510.0	1.11642
$928$	−4800.00	−0.169793
$929$	−30366.0	−1.07242	−0.536209	−	0.844085i	$-0.680144\pi$
$929$	−30366.0	−1.07242	−0.536209	+	0.844085i	$0.680144\pi$
$930$	0	0
$931$	3781.00	0.133101
$932$	12888.0	0.452962
$933$	8864.00	0.311034
$934$	27992.0	0.980649
$935$	0	0
$936$	−736.000	−0.0257018
$937$	−574.000	−0.0200126	−0.0100063	−	0.999950i	$-0.503185\pi$
$937$	−574.000	−0.0200126	−0.0100063	+	0.999950i	$0.503185\pi$
$938$	−8016.00	−0.279032
$939$	3396.00	0.118024
$940$	0	0
$941$	3918.00	0.135731	0.0678656	−	0.997694i	$-0.478381\pi$
$941$	3918.00	0.135731	0.0678656	+	0.997694i	$0.478381\pi$
$942$	6184.00	0.213891
$943$	8720.00	0.301126
$944$	−768.000	−0.0264791
$945$	0	0
$946$	9920.00	0.340938
$947$	−7324.00	−0.251318	−0.125659	−	0.992074i	$-0.540104\pi$
$947$	−7324.00	−0.251318	−0.125659	+	0.992074i	$0.540104\pi$
$948$	−7840.00	−0.268598
$949$	−1752.00	−0.0599287
$950$	0	0
$951$	−13768.0	−0.469462
$952$	3264.00	0.111121
$953$	38928.0	1.32319	0.661596	−	0.749861i	$-0.269879\pi$
$953$	38928.0	1.32319	0.661596	+	0.749861i	$0.269879\pi$
$954$	3312.00	0.112400
$955$	0	0
$956$	4128.00	0.139654
$957$	−6000.00	−0.202667
$958$	−10112.0	−0.341027
$959$	10392.0	0.349922
$960$	0	0
$961$	10209.0	0.342687
$962$	1248.00	0.0418265
$963$	7774.00	0.260139
$964$	−15592.0	−0.520938
$965$	0	0
$966$	1920.00	0.0639493
$967$	−1384.00	−0.0460253	−0.0230126	−	0.999735i	$-0.507326\pi$
$967$	−1384.00	−0.0460253	−0.0230126	+	0.999735i	$0.507326\pi$
$968$	−7448.00	−0.247301
$969$	1292.00	0.0428328
$970$	0	0
$971$	6876.00	0.227252	0.113626	−	0.993524i	$-0.463753\pi$
$971$	6876.00	0.227252	0.113626	+	0.993524i	$0.463753\pi$
$972$	−14168.0	−0.467530
$973$	1776.00	0.0585159
$974$	−27572.0	−0.907047
$975$	0	0
$976$	−2144.00	−0.0703153
$977$	−21104.0	−0.691071	−0.345536	−	0.938406i	$-0.612303\pi$
$977$	−21104.0	−0.691071	−0.345536	+	0.938406i	$0.612303\pi$
$978$	704.000	0.0230178
$979$	−13400.0	−0.437452
$980$	0	0
$981$	−2346.00	−0.0763527
$982$	8808.00	0.286227
$983$	22594.0	0.733099	0.366550	−	0.930398i	$-0.380539\pi$
$983$	22594.0	0.733099	0.366550	+	0.930398i	$0.380539\pi$
$984$	3488.00	0.113001
$985$	0	0
$986$	−10200.0	−0.329446
$987$	−4320.00	−0.139318
$988$	−304.000	−0.00978900
$989$	9920.00	0.318946
$990$	0	0
$991$	6124.00	0.196302	0.0981510	−	0.995172i	$-0.468707\pi$
$991$	6124.00	0.196302	0.0981510	+	0.995172i	$0.468707\pi$
$992$	−6400.00	−0.204839
$993$	−6896.00	−0.220381
$994$	−12480.0	−0.398231
$995$	0	0
$996$	−1248.00	−0.0397032
$997$	−17258.0	−0.548211	−0.274105	−	0.961700i	$-0.588382\pi$
$997$	−17258.0	−0.548211	−0.274105	+	0.961700i	$0.588382\pi$
$998$	3336.00	0.105811
$999$	15600.0	0.494056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.4.a.b.1.1		1
5.2	odd	4		950.4.b.b.799.2		2
5.3	odd	4		950.4.b.b.799.1		2
5.4	even	2		190.4.a.b.1.1	✓	1
15.14	odd	2		1710.4.a.g.1.1		1
20.19	odd	2		1520.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.4.a.b.1.1	✓	1	5.4	even	2
950.4.a.b.1.1		1	1.1	even	1	trivial
950.4.b.b.799.1		2	5.3	odd	4
950.4.b.b.799.2		2	5.2	odd	4
1520.4.a.d.1.1		1	20.19	odd	2
1710.4.a.g.1.1		1	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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