LMFDB - Embedded newform 1520.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,4,Mod(1,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("1520.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1520.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:	$89.6829032087$
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	$\chi$	$=$	1520.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{3} +5.00000 q^{5} +12.0000 q^{7} -23.0000 q^{9} +O(q^{10})$

$q-2.00000 q^{3} +5.00000 q^{5} +12.0000 q^{7} -23.0000 q^{9} +20.0000 q^{11} -4.00000 q^{13} -10.0000 q^{15} -34.0000 q^{17} +19.0000 q^{19} -24.0000 q^{21} -40.0000 q^{23} +25.0000 q^{25} +100.000 q^{27} -150.000 q^{29} +200.000 q^{31} -40.0000 q^{33} +60.0000 q^{35} -156.000 q^{37} +8.00000 q^{39} -218.000 q^{41} -248.000 q^{43} -115.000 q^{45} +180.000 q^{47} -199.000 q^{49} +68.0000 q^{51} +72.0000 q^{53} +100.000 q^{55} -38.0000 q^{57} +48.0000 q^{59} -134.000 q^{61} -276.000 q^{63} -20.0000 q^{65} -334.000 q^{67} +80.0000 q^{69} +520.000 q^{71} +438.000 q^{73} -50.0000 q^{75} +240.000 q^{77} -980.000 q^{79} +421.000 q^{81} +156.000 q^{83} -170.000 q^{85} +300.000 q^{87} +670.000 q^{89} -48.0000 q^{91} -400.000 q^{93} +95.0000 q^{95} +1124.00 q^{97} -460.000 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	−2.00000	−0.384900	−0.192450	−	0.981307i	$-0.561643\pi$
$3$	−2.00000	−0.384900	−0.192450	+	0.981307i	$0.561643\pi$
$4$	0	0
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	0	0
$7$	12.0000	0.647939	0.323970	−	0.946068i	$-0.394982\pi$
$7$	12.0000	0.647939	0.323970	+	0.946068i	$0.394982\pi$
$8$	0	0
$9$	−23.0000	−0.851852
$10$	0	0
$11$	20.0000	0.548202	0.274101	−	0.961701i	$-0.411620\pi$
$11$	20.0000	0.548202	0.274101	+	0.961701i	$0.411620\pi$
$12$	0	0
$13$	−4.00000	−0.0853385	−0.0426692	−	0.999089i	$-0.513586\pi$
$13$	−4.00000	−0.0853385	−0.0426692	+	0.999089i	$0.513586\pi$
$14$	0	0
$15$	−10.0000	−0.172133
$16$	0	0
$17$	−34.0000	−0.485071	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−34.0000	−0.485071	−0.242536	+	0.970143i	$0.577979\pi$
$18$	0	0
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	0	0
$21$	−24.0000	−0.249392
$22$	0	0
$23$	−40.0000	−0.362634	−0.181317	−	0.983425i	$-0.558036\pi$
$23$	−40.0000	−0.362634	−0.181317	+	0.983425i	$0.558036\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	0	0
$27$	100.000	0.712778
$28$	0	0
$29$	−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	$-0.303298\pi$
$31$	200.000	1.15874	0.579372	+	0.815063i	$0.303298\pi$
$32$	0	0
$33$	−40.0000	−0.211003
$34$	0	0
$35$	60.0000	0.289767
$36$	0	0
$37$	−156.000	−0.693142	−0.346571	−	0.938024i	$-0.612654\pi$
$37$	−156.000	−0.693142	−0.346571	+	0.938024i	$0.612654\pi$
$38$	0	0
$39$	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	$0.636286\pi$
$42$	0	0
$43$	−248.000	−0.879527	−0.439763	−	0.898114i	$-0.644938\pi$
$43$	−248.000	−0.879527	−0.439763	+	0.898114i	$0.644938\pi$
$44$	0	0
$45$	−115.000	−0.380960
$46$	0	0
$47$	180.000	0.558632	0.279316	−	0.960199i	$-0.409892\pi$
$47$	180.000	0.558632	0.279316	+	0.960199i	$0.409892\pi$
$48$	0	0
$49$	−199.000	−0.580175
$50$	0	0
$51$	68.0000	0.186704
$52$	0	0
$53$	72.0000	0.186603	0.0933015	−	0.995638i	$-0.470258\pi$
$53$	72.0000	0.186603	0.0933015	+	0.995638i	$0.470258\pi$
$54$	0	0
$55$	100.000	0.245164
$56$	0	0
$57$	−38.0000	−0.0883022
$58$	0	0
$59$	48.0000	0.105916	0.0529582	−	0.998597i	$-0.483135\pi$
$59$	48.0000	0.105916	0.0529582	+	0.998597i	$0.483135\pi$
$60$	0	0
$61$	−134.000	−0.281261	−0.140631	−	0.990062i	$-0.544913\pi$
$61$	−134.000	−0.281261	−0.140631	+	0.990062i	$0.544913\pi$
$62$	0	0
$63$	−276.000	−0.551948
$64$	0	0
$65$	−20.0000	−0.0381645
$66$	0	0
$67$	−334.000	−0.609024	−0.304512	−	0.952509i	$-0.598493\pi$
$67$	−334.000	−0.609024	−0.304512	+	0.952509i	$0.598493\pi$
$68$	0	0
$69$	80.0000	0.139578
$70$	0	0
$71$	520.000	0.869192	0.434596	−	0.900625i	$-0.356891\pi$
$71$	520.000	0.869192	0.434596	+	0.900625i	$0.356891\pi$
$72$	0	0
$73$	438.000	0.702247	0.351123	−	0.936329i	$-0.385800\pi$
$73$	438.000	0.702247	0.351123	+	0.936329i	$0.385800\pi$
$74$	0	0
$75$	−50.0000	−0.0769800
$76$	0	0
$77$	240.000	0.355202
$78$	0	0
$79$	−980.000	−1.39568	−0.697839	−	0.716254i	$-0.745855\pi$
$79$	−980.000	−1.39568	−0.697839	+	0.716254i	$0.745855\pi$
$80$	0	0
$81$	421.000	0.577503
$82$	0	0
$83$	156.000	0.206304	0.103152	−	0.994666i	$-0.467107\pi$
$83$	156.000	0.206304	0.103152	+	0.994666i	$0.467107\pi$
$84$	0	0
$85$	−170.000	−0.216930
$86$	0	0
$87$	300.000	0.369694
$88$	0	0
$89$	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
$92$	0	0
$93$	−400.000	−0.446001
$94$	0	0
$95$	95.0000	0.102598
$96$	0	0
$97$	1124.00	1.17655	0.588273	−	0.808663i	$-0.299808\pi$
$97$	1124.00	1.17655	0.588273	+	0.808663i	$0.299808\pi$
$98$	0	0
$99$	−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	$0.754134\pi$
$102$	0	0
$103$	−1370.00	−1.31058	−0.655292	−	0.755376i	$-0.727454\pi$
$103$	−1370.00	−1.31058	−0.655292	+	0.755376i	$0.727454\pi$
$104$	0	0
$105$	−120.000	−0.111531
$106$	0	0
$107$	−338.000	−0.305380	−0.152690	−	0.988274i	$-0.548794\pi$
$107$	−338.000	−0.305380	−0.152690	+	0.988274i	$0.548794\pi$
$108$	0	0
$109$	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
$112$	0	0
$113$	4.00000	0.00332999	0.00166499	−	0.999999i	$-0.499470\pi$
$113$	4.00000	0.00332999	0.00166499	+	0.999999i	$0.499470\pi$
$114$	0	0
$115$	−200.000	−0.162175
$116$	0	0
$117$	92.0000	0.0726958
$118$	0	0
$119$	−408.000	−0.314297
$120$	0	0
$121$	−931.000	−0.699474
$122$	0	0
$123$	436.000	0.319616
$124$	0	0
$125$	125.000	0.0894427
$126$	0	0
$127$	−1358.00	−0.948843	−0.474421	−	0.880298i	$-0.657343\pi$
$127$	−1358.00	−0.948843	−0.474421	+	0.880298i	$0.657343\pi$
$128$	0	0
$129$	496.000	0.338530
$130$	0	0
$131$	2700.00	1.80076	0.900382	−	0.435100i	$-0.143287\pi$
$131$	2700.00	1.80076	0.900382	+	0.435100i	$0.143287\pi$
$132$	0	0
$133$	228.000	0.148647
$134$	0	0
$135$	500.000	0.318764
$136$	0	0
$137$	−866.000	−0.540054	−0.270027	−	0.962853i	$-0.587033\pi$
$137$	−866.000	−0.540054	−0.270027	+	0.962853i	$0.587033\pi$
$138$	0	0
$139$	−148.000	−0.0903108	−0.0451554	−	0.998980i	$-0.514378\pi$
$139$	−148.000	−0.0903108	−0.0451554	+	0.998980i	$0.514378\pi$
$140$	0	0
$141$	−360.000	−0.215018
$142$	0	0
$143$	−80.0000	−0.0467828
$144$	0	0
$145$	−750.000	−0.429546
$146$	0	0
$147$	398.000	0.223309
$148$	0	0
$149$	−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	$-0.538175\pi$
$151$	−444.000	−0.239286	−0.119643	+	0.992817i	$0.538175\pi$
$152$	0	0
$153$	782.000	0.413209
$154$	0	0
$155$	1000.00	0.518206
$156$	0	0
$157$	1546.00	0.785887	0.392943	−	0.919563i	$-0.371457\pi$
$157$	1546.00	0.785887	0.392943	+	0.919563i	$0.371457\pi$
$158$	0	0
$159$	−144.000	−0.0718235
$160$	0	0
$161$	−480.000	−0.234965
$162$	0	0
$163$	−176.000	−0.0845729	−0.0422865	−	0.999106i	$-0.513464\pi$
$163$	−176.000	−0.0845729	−0.0422865	+	0.999106i	$0.513464\pi$
$164$	0	0
$165$	−200.000	−0.0943635
$166$	0	0
$167$	−858.000	−0.397569	−0.198785	−	0.980043i	$-0.563699\pi$
$167$	−858.000	−0.397569	−0.198785	+	0.980043i	$0.563699\pi$
$168$	0	0
$169$	−2181.00	−0.992717
$170$	0	0
$171$	−437.000	−0.195428
$172$	0	0
$173$	−1312.00	−0.576587	−0.288293	−	0.957542i	$-0.593088\pi$
$173$	−1312.00	−0.576587	−0.288293	+	0.957542i	$0.593088\pi$
$174$	0	0
$175$	300.000	0.129588
$176$	0	0
$177$	−96.0000	−0.0407672
$178$	0	0
$179$	−3416.00	−1.42639	−0.713195	−	0.700966i	$-0.752753\pi$
$179$	−3416.00	−1.42639	−0.713195	+	0.700966i	$0.752753\pi$
$180$	0	0
$181$	1230.00	0.505111	0.252556	−	0.967582i	$-0.418729\pi$
$181$	1230.00	0.505111	0.252556	+	0.967582i	$0.418729\pi$
$182$	0	0
$183$	268.000	0.108258
$184$	0	0
$185$	−780.000	−0.309982
$186$	0	0
$187$	−680.000	−0.265917
$188$	0	0
$189$	1200.00	0.461837
$190$	0	0
$191$	−1928.00	−0.730394	−0.365197	−	0.930930i	$-0.618998\pi$
$191$	−1928.00	−0.730394	−0.365197	+	0.930930i	$0.618998\pi$
$192$	0	0
$193$	−1036.00	−0.386388	−0.193194	−	0.981161i	$-0.561885\pi$
$193$	−1036.00	−0.386388	−0.193194	+	0.981161i	$0.561885\pi$
$194$	0	0
$195$	40.0000	0.0146895
$196$	0	0
$197$	−1810.00	−0.654605	−0.327302	−	0.944920i	$-0.606140\pi$
$197$	−1810.00	−0.654605	−0.327302	+	0.944920i	$0.606140\pi$
$198$	0	0
$199$	−4248.00	−1.51323	−0.756615	−	0.653861i	$-0.773148\pi$
$199$	−4248.00	−1.51323	−0.756615	+	0.653861i	$0.773148\pi$
$200$	0	0
$201$	668.000	0.234413
$202$	0	0
$203$	−1800.00	−0.622341
$204$	0	0
$205$	−1090.00	−0.371360
$206$	0	0
$207$	920.000	0.308910
$208$	0	0
$209$	380.000	0.125766
$210$	0	0
$211$	2680.00	0.874402	0.437201	−	0.899364i	$-0.355970\pi$
$211$	2680.00	0.874402	0.437201	+	0.899364i	$0.355970\pi$
$212$	0	0
$213$	−1040.00	−0.334552
$214$	0	0
$215$	−1240.00	−0.393336
$216$	0	0
$217$	2400.00	0.750795
$218$	0	0
$219$	−876.000	−0.270295
$220$	0	0
$221$	136.000	0.0413952
$222$	0	0
$223$	−3234.00	−0.971142	−0.485571	−	0.874197i	$-0.661388\pi$
$223$	−3234.00	−0.971142	−0.485571	+	0.874197i	$0.661388\pi$
$224$	0	0
$225$	−575.000	−0.170370
$226$	0	0
$227$	−250.000	−0.0730973	−0.0365486	−	0.999332i	$-0.511636\pi$
$227$	−250.000	−0.0730973	−0.0365486	+	0.999332i	$0.511636\pi$
$228$	0	0
$229$	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
$232$	0	0
$233$	−3222.00	−0.905924	−0.452962	−	0.891530i	$-0.649633\pi$
$233$	−3222.00	−0.905924	−0.452962	+	0.891530i	$0.649633\pi$
$234$	0	0
$235$	900.000	0.249828
$236$	0	0
$237$	1960.00	0.537197
$238$	0	0
$239$	−1032.00	−0.279308	−0.139654	−	0.990200i	$-0.544599\pi$
$239$	−1032.00	−0.279308	−0.139654	+	0.990200i	$0.544599\pi$
$240$	0	0
$241$	−3898.00	−1.04188	−0.520938	−	0.853594i	$-0.674418\pi$
$241$	−3898.00	−1.04188	−0.520938	+	0.853594i	$0.674418\pi$
$242$	0	0
$243$	−3542.00	−0.935059
$244$	0	0
$245$	−995.000	−0.259462
$246$	0	0
$247$	−76.0000	−0.0195780
$248$	0	0
$249$	−312.000	−0.0794064
$250$	0	0
$251$	−4084.00	−1.02701	−0.513506	−	0.858086i	$-0.671653\pi$
$251$	−4084.00	−1.02701	−0.513506	+	0.858086i	$0.671653\pi$
$252$	0	0
$253$	−800.000	−0.198797
$254$	0	0
$255$	340.000	0.0834966
$256$	0	0
$257$	−6952.00	−1.68737	−0.843685	−	0.536839i	$-0.819618\pi$
$257$	−6952.00	−1.68737	−0.843685	+	0.536839i	$0.819618\pi$
$258$	0	0
$259$	−1872.00	−0.449114
$260$	0	0
$261$	3450.00	0.818198
$262$	0	0
$263$	904.000	0.211951	0.105975	−	0.994369i	$-0.466204\pi$
$263$	904.000	0.211951	0.105975	+	0.994369i	$0.466204\pi$
$264$	0	0
$265$	360.000	0.0834514
$266$	0	0
$267$	−1340.00	−0.307141
$268$	0	0
$269$	−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	$-0.515703\pi$
$271$	−440.000	−0.0986277	−0.0493138	+	0.998783i	$0.515703\pi$
$272$	0	0
$273$	96.0000	0.0212827
$274$	0	0
$275$	500.000	0.109640
$276$	0	0
$277$	−8054.00	−1.74700	−0.873498	−	0.486828i	$-0.838154\pi$
$277$	−8054.00	−1.74700	−0.873498	+	0.486828i	$0.838154\pi$
$278$	0	0
$279$	−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	$0.364362\pi$
$282$	0	0
$283$	4108.00	0.862881	0.431440	−	0.902141i	$-0.358006\pi$
$283$	4108.00	0.862881	0.431440	+	0.902141i	$0.358006\pi$
$284$	0	0
$285$	−190.000	−0.0394899
$286$	0	0
$287$	−2616.00	−0.538040
$288$	0	0
$289$	−3757.00	−0.764706
$290$	0	0
$291$	−2248.00	−0.452853
$292$	0	0
$293$	3208.00	0.639636	0.319818	−	0.947479i	$-0.396378\pi$
$293$	3208.00	0.639636	0.319818	+	0.947479i	$0.396378\pi$
$294$	0	0
$295$	240.000	0.0473673
$296$	0	0
$297$	2000.00	0.390747
$298$	0	0
$299$	160.000	0.0309466
$300$	0	0
$301$	−2976.00	−0.569880
$302$	0	0
$303$	2908.00	0.551354
$304$	0	0
$305$	−670.000	−0.125784
$306$	0	0
$307$	6422.00	1.19389	0.596943	−	0.802284i	$-0.296382\pi$
$307$	6422.00	1.19389	0.596943	+	0.802284i	$0.296382\pi$
$308$	0	0
$309$	2740.00	0.504444
$310$	0	0
$311$	4432.00	0.808089	0.404044	−	0.914739i	$-0.367604\pi$
$311$	4432.00	0.808089	0.404044	+	0.914739i	$0.367604\pi$
$312$	0	0
$313$	1698.00	0.306635	0.153317	−	0.988177i	$-0.451004\pi$
$313$	1698.00	0.306635	0.153317	+	0.988177i	$0.451004\pi$
$314$	0	0
$315$	−1380.00	−0.246839
$316$	0	0
$317$	−6884.00	−1.21970	−0.609849	−	0.792518i	$-0.708770\pi$
$317$	−6884.00	−1.21970	−0.609849	+	0.792518i	$0.708770\pi$
$318$	0	0
$319$	−3000.00	−0.526545
$320$	0	0
$321$	676.000	0.117541
$322$	0	0
$323$	−646.000	−0.111283
$324$	0	0
$325$	−100.000	−0.0170677
$326$	0	0
$327$	−204.000	−0.0344992
$328$	0	0
$329$	2160.00	0.361959
$330$	0	0
$331$	−3448.00	−0.572566	−0.286283	−	0.958145i	$-0.592420\pi$
$331$	−3448.00	−0.572566	−0.286283	+	0.958145i	$0.592420\pi$
$332$	0	0
$333$	3588.00	0.590454
$334$	0	0
$335$	−1670.00	−0.272364
$336$	0	0
$337$	−6388.00	−1.03257	−0.516286	−	0.856416i	$-0.672686\pi$
$337$	−6388.00	−1.03257	−0.516286	+	0.856416i	$0.672686\pi$
$338$	0	0
$339$	−8.00000	−0.00128171
$340$	0	0
$341$	4000.00	0.635226
$342$	0	0
$343$	−6504.00	−1.02386
$344$	0	0
$345$	400.000	0.0624211
$346$	0	0
$347$	156.000	0.0241341	0.0120670	−	0.999927i	$-0.496159\pi$
$347$	156.000	0.0241341	0.0120670	+	0.999927i	$0.496159\pi$
$348$	0	0
$349$	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
$352$	0	0
$353$	−12034.0	−1.81446	−0.907231	−	0.420632i	$-0.861808\pi$
$353$	−12034.0	−1.81446	−0.907231	+	0.420632i	$0.861808\pi$
$354$	0	0
$355$	2600.00	0.388715
$356$	0	0
$357$	816.000	0.120973
$358$	0	0
$359$	8352.00	1.22786	0.613930	−	0.789361i	$-0.289588\pi$
$359$	8352.00	1.22786	0.613930	+	0.789361i	$0.289588\pi$
$360$	0	0
$361$	361.000	0.0526316
$362$	0	0
$363$	1862.00	0.269228
$364$	0	0
$365$	2190.00	0.314054
$366$	0	0
$367$	2844.00	0.404511	0.202256	−	0.979333i	$-0.435173\pi$
$367$	2844.00	0.404511	0.202256	+	0.979333i	$0.435173\pi$
$368$	0	0
$369$	5014.00	0.707367
$370$	0	0
$371$	864.000	0.120907
$372$	0	0
$373$	7064.00	0.980590	0.490295	−	0.871557i	$-0.336889\pi$
$373$	7064.00	0.980590	0.490295	+	0.871557i	$0.336889\pi$
$374$	0	0
$375$	−250.000	−0.0344265
$376$	0	0
$377$	600.000	0.0819670
$378$	0	0
$379$	6068.00	0.822407	0.411203	−	0.911544i	$-0.365109\pi$
$379$	6068.00	0.822407	0.411203	+	0.911544i	$0.365109\pi$
$380$	0	0
$381$	2716.00	0.365210
$382$	0	0
$383$	6570.00	0.876531	0.438265	−	0.898846i	$-0.355593\pi$
$383$	6570.00	0.876531	0.438265	+	0.898846i	$0.355593\pi$
$384$	0	0
$385$	1200.00	0.158851
$386$	0	0
$387$	5704.00	0.749226
$388$	0	0
$389$	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
$392$	0	0
$393$	−5400.00	−0.693114
$394$	0	0
$395$	−4900.00	−0.624166
$396$	0	0
$397$	−11550.0	−1.46015	−0.730073	−	0.683369i	$-0.760514\pi$
$397$	−11550.0	−1.46015	−0.730073	+	0.683369i	$0.760514\pi$
$398$	0	0
$399$	−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	$0.673854\pi$
$402$	0	0
$403$	−800.000	−0.0988855
$404$	0	0
$405$	2105.00	0.258267
$406$	0	0
$407$	−3120.00	−0.379982
$408$	0	0
$409$	−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
$412$	0	0
$413$	576.000	0.0686274
$414$	0	0
$415$	780.000	0.0922619
$416$	0	0
$417$	296.000	0.0347606
$418$	0	0
$419$	4164.00	0.485501	0.242750	−	0.970089i	$-0.421950\pi$
$419$	4164.00	0.485501	0.242750	+	0.970089i	$0.421950\pi$
$420$	0	0
$421$	3026.00	0.350305	0.175152	−	0.984541i	$-0.443958\pi$
$421$	3026.00	0.350305	0.175152	+	0.984541i	$0.443958\pi$
$422$	0	0
$423$	−4140.00	−0.475872
$424$	0	0
$425$	−850.000	−0.0970143
$426$	0	0
$427$	−1608.00	−0.182240
$428$	0	0
$429$	160.000	0.0180067
$430$	0	0
$431$	10348.0	1.15649	0.578243	−	0.815864i	$-0.303738\pi$
$431$	10348.0	1.15649	0.578243	+	0.815864i	$0.303738\pi$
$432$	0	0
$433$	−3164.00	−0.351160	−0.175580	−	0.984465i	$-0.556180\pi$
$433$	−3164.00	−0.351160	−0.175580	+	0.984465i	$0.556180\pi$
$434$	0	0
$435$	1500.00	0.165332
$436$	0	0
$437$	−760.000	−0.0831939
$438$	0	0
$439$	17700.0	1.92432	0.962158	−	0.272491i	$-0.0878476\pi$
$439$	17700.0	1.92432	0.962158	+	0.272491i	$0.0878476\pi$
$440$	0	0
$441$	4577.00	0.494223
$442$	0	0
$443$	−8572.00	−0.919341	−0.459670	−	0.888090i	$-0.652032\pi$
$443$	−8572.00	−0.919341	−0.459670	+	0.888090i	$0.652032\pi$
$444$	0	0
$445$	3350.00	0.356866
$446$	0	0
$447$	4188.00	0.443145
$448$	0	0
$449$	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
$452$	0	0
$453$	888.000	0.0921013
$454$	0	0
$455$	−240.000	−0.0247283
$456$	0	0
$457$	−14982.0	−1.53354	−0.766771	−	0.641921i	$-0.778138\pi$
$457$	−14982.0	−1.53354	−0.766771	+	0.641921i	$0.778138\pi$
$458$	0	0
$459$	−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	$0.384440\pi$
$462$	0	0
$463$	−4448.00	−0.446471	−0.223236	−	0.974765i	$-0.571662\pi$
$463$	−4448.00	−0.446471	−0.223236	+	0.974765i	$0.571662\pi$
$464$	0	0
$465$	−2000.00	−0.199458
$466$	0	0
$467$	13996.0	1.38685	0.693424	−	0.720530i	$-0.256101\pi$
$467$	13996.0	1.38685	0.693424	+	0.720530i	$0.256101\pi$
$468$	0	0
$469$	−4008.00	−0.394610
$470$	0	0
$471$	−3092.00	−0.302488
$472$	0	0
$473$	−4960.00	−0.482159
$474$	0	0
$475$	475.000	0.0458831
$476$	0	0
$477$	−1656.00	−0.158958
$478$	0	0
$479$	5056.00	0.482285	0.241143	−	0.970490i	$-0.422478\pi$
$479$	5056.00	0.482285	0.241143	+	0.970490i	$0.422478\pi$
$480$	0	0
$481$	624.000	0.0591517
$482$	0	0
$483$	960.000	0.0904379
$484$	0	0
$485$	5620.00	0.526167
$486$	0	0
$487$	−13786.0	−1.28276	−0.641379	−	0.767224i	$-0.721637\pi$
$487$	−13786.0	−1.28276	−0.641379	+	0.767224i	$0.721637\pi$
$488$	0	0
$489$	352.000	0.0325521
$490$	0	0
$491$	−4404.00	−0.404786	−0.202393	−	0.979304i	$-0.564872\pi$
$491$	−4404.00	−0.404786	−0.202393	+	0.979304i	$0.564872\pi$
$492$	0	0
$493$	5100.00	0.465908
$494$	0	0
$495$	−2300.00	−0.208843
$496$	0	0
$497$	6240.00	0.563184
$498$	0	0
$499$	−1668.00	−0.149639	−0.0748196	−	0.997197i	$-0.523838\pi$
$499$	−1668.00	−0.149639	−0.0748196	+	0.997197i	$0.523838\pi$
$500$	0	0
$501$	1716.00	0.153024
$502$	0	0
$503$	−12984.0	−1.15095	−0.575475	−	0.817819i	$-0.695183\pi$
$503$	−12984.0	−1.15095	−0.575475	+	0.817819i	$0.695183\pi$
$504$	0	0
$505$	−7270.00	−0.640615
$506$	0	0
$507$	4362.00	0.382097
$508$	0	0
$509$	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
$512$	0	0
$513$	1900.00	0.163523
$514$	0	0
$515$	−6850.00	−0.586111
$516$	0	0
$517$	3600.00	0.306243
$518$	0	0
$519$	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	$0.103828\pi$
$522$	0	0
$523$	−21958.0	−1.83586	−0.917931	−	0.396739i	$-0.870142\pi$
$523$	−21958.0	−1.83586	−0.917931	+	0.396739i	$0.870142\pi$
$524$	0	0
$525$	−600.000	−0.0498784
$526$	0	0
$527$	−6800.00	−0.562073
$528$	0	0
$529$	−10567.0	−0.868497
$530$	0	0
$531$	−1104.00	−0.0902251
$532$	0	0
$533$	872.000	0.0708640
$534$	0	0
$535$	−1690.00	−0.136570
$536$	0	0
$537$	6832.00	0.549018
$538$	0	0
$539$	−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	$0.358789\pi$
$542$	0	0
$543$	−2460.00	−0.194418
$544$	0	0
$545$	510.000	0.0400844
$546$	0	0
$547$	10150.0	0.793387	0.396693	−	0.917951i	$-0.370158\pi$
$547$	10150.0	0.793387	0.396693	+	0.917951i	$0.370158\pi$
$548$	0	0
$549$	3082.00	0.239593
$550$	0	0
$551$	−2850.00	−0.220352
$552$	0	0
$553$	−11760.0	−0.904315
$554$	0	0
$555$	1560.00	0.119312
$556$	0	0
$557$	25026.0	1.90374	0.951872	−	0.306495i	$-0.0991563\pi$
$557$	25026.0	1.90374	0.951872	+	0.306495i	$0.0991563\pi$
$558$	0	0
$559$	992.000	0.0750575
$560$	0	0
$561$	1360.00	0.102352
$562$	0	0
$563$	−6718.00	−0.502895	−0.251448	−	0.967871i	$-0.580907\pi$
$563$	−6718.00	−0.502895	−0.251448	+	0.967871i	$0.580907\pi$
$564$	0	0
$565$	20.0000	0.00148921
$566$	0	0
$567$	5052.00	0.374187
$568$	0	0
$569$	−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	$-0.487166\pi$
$571$	1100.00	0.0806192	0.0403096	+	0.999187i	$0.487166\pi$
$572$	0	0
$573$	3856.00	0.281129
$574$	0	0
$575$	−1000.00	−0.0725268
$576$	0	0
$577$	7458.00	0.538095	0.269047	−	0.963127i	$-0.413291\pi$
$577$	7458.00	0.538095	0.269047	+	0.963127i	$0.413291\pi$
$578$	0	0
$579$	2072.00	0.148721
$580$	0	0
$581$	1872.00	0.133672
$582$	0	0
$583$	1440.00	0.102296
$584$	0	0
$585$	460.000	0.0325105
$586$	0	0
$587$	14140.0	0.994242	0.497121	−	0.867681i	$-0.334390\pi$
$587$	14140.0	0.994242	0.497121	+	0.867681i	$0.334390\pi$
$588$	0	0
$589$	3800.00	0.265834
$590$	0	0
$591$	3620.00	0.251958
$592$	0	0
$593$	−9302.00	−0.644161	−0.322080	−	0.946712i	$-0.604382\pi$
$593$	−9302.00	−0.644161	−0.322080	+	0.946712i	$0.604382\pi$
$594$	0	0
$595$	−2040.00	−0.140558
$596$	0	0
$597$	8496.00	0.582442
$598$	0	0
$599$	−3460.00	−0.236013	−0.118006	−	0.993013i	$-0.537650\pi$
$599$	−3460.00	−0.236013	−0.118006	+	0.993013i	$0.537650\pi$
$600$	0	0
$601$	27910.0	1.89430	0.947149	−	0.320795i	$-0.103950\pi$
$601$	27910.0	1.89430	0.947149	+	0.320795i	$0.103950\pi$
$602$	0	0
$603$	7682.00	0.518798
$604$	0	0
$605$	−4655.00	−0.312814
$606$	0	0
$607$	13646.0	0.912478	0.456239	−	0.889857i	$-0.349196\pi$
$607$	13646.0	0.912478	0.456239	+	0.889857i	$0.349196\pi$
$608$	0	0
$609$	3600.00	0.239539
$610$	0	0
$611$	−720.000	−0.0476728
$612$	0	0
$613$	12802.0	0.843504	0.421752	−	0.906711i	$-0.361415\pi$
$613$	12802.0	0.843504	0.421752	+	0.906711i	$0.361415\pi$
$614$	0	0
$615$	2180.00	0.142937
$616$	0	0
$617$	5806.00	0.378834	0.189417	−	0.981897i	$-0.439340\pi$
$617$	5806.00	0.378834	0.189417	+	0.981897i	$0.439340\pi$
$618$	0	0
$619$	−18868.0	−1.22515	−0.612576	−	0.790412i	$-0.709867\pi$
$619$	−18868.0	−1.22515	−0.612576	+	0.790412i	$0.709867\pi$
$620$	0	0
$621$	−4000.00	−0.258477
$622$	0	0
$623$	8040.00	0.517040
$624$	0	0
$625$	625.000	0.0400000
$626$	0	0
$627$	−760.000	−0.0484075
$628$	0	0
$629$	5304.00	0.336223
$630$	0	0
$631$	11960.0	0.754548	0.377274	−	0.926102i	$-0.376861\pi$
$631$	11960.0	0.754548	0.377274	+	0.926102i	$0.376861\pi$
$632$	0	0
$633$	−5360.00	−0.336557
$634$	0	0
$635$	−6790.00	−0.424335
$636$	0	0
$637$	796.000	0.0495113
$638$	0	0
$639$	−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	$0.318996\pi$
$642$	0	0
$643$	12556.0	0.770078	0.385039	−	0.922900i	$-0.374188\pi$
$643$	12556.0	0.770078	0.385039	+	0.922900i	$0.374188\pi$
$644$	0	0
$645$	2480.00	0.151395
$646$	0	0
$647$	−14712.0	−0.893954	−0.446977	−	0.894545i	$-0.647499\pi$
$647$	−14712.0	−0.893954	−0.446977	+	0.894545i	$0.647499\pi$
$648$	0	0
$649$	960.000	0.0580636
$650$	0	0
$651$	−4800.00	−0.288981
$652$	0	0
$653$	−7926.00	−0.474990	−0.237495	−	0.971389i	$-0.576326\pi$
$653$	−7926.00	−0.474990	−0.237495	+	0.971389i	$0.576326\pi$
$654$	0	0
$655$	13500.0	0.805326
$656$	0	0
$657$	−10074.0	−0.598210
$658$	0	0
$659$	−1560.00	−0.0922139	−0.0461070	−	0.998937i	$-0.514682\pi$
$659$	−1560.00	−0.0922139	−0.0461070	+	0.998937i	$0.514682\pi$
$660$	0	0
$661$	3202.00	0.188417	0.0942083	−	0.995553i	$-0.469968\pi$
$661$	3202.00	0.188417	0.0942083	+	0.995553i	$0.469968\pi$
$662$	0	0
$663$	−272.000	−0.0159330
$664$	0	0
$665$	1140.00	0.0664771
$666$	0	0
$667$	6000.00	0.348307
$668$	0	0
$669$	6468.00	0.373793
$670$	0	0
$671$	−2680.00	−0.154188
$672$	0	0
$673$	−24824.0	−1.42183	−0.710917	−	0.703275i	$-0.751720\pi$
$673$	−24824.0	−1.42183	−0.710917	+	0.703275i	$0.751720\pi$
$674$	0	0
$675$	2500.00	0.142556
$676$	0	0
$677$	25368.0	1.44014	0.720068	−	0.693904i	$-0.244111\pi$
$677$	25368.0	1.44014	0.720068	+	0.693904i	$0.244111\pi$
$678$	0	0
$679$	13488.0	0.762330
$680$	0	0
$681$	500.000	0.0281352
$682$	0	0
$683$	17202.0	0.963713	0.481857	−	0.876250i	$-0.339963\pi$
$683$	17202.0	0.963713	0.481857	+	0.876250i	$0.339963\pi$
$684$	0	0
$685$	−4330.00	−0.241519
$686$	0	0
$687$	−3076.00	−0.170825
$688$	0	0
$689$	−288.000	−0.0159244
$690$	0	0
$691$	32500.0	1.78923	0.894615	−	0.446837i	$-0.147450\pi$
$691$	32500.0	1.78923	0.894615	+	0.446837i	$0.147450\pi$
$692$	0	0
$693$	−5520.00	−0.302579
$694$	0	0
$695$	−740.000	−0.0403882
$696$	0	0
$697$	7412.00	0.402797
$698$	0	0
$699$	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	$0.549646\pi$
$702$	0	0
$703$	−2964.00	−0.159018
$704$	0	0
$705$	−1800.00	−0.0961588
$706$	0	0
$707$	−17448.0	−0.928147
$708$	0	0
$709$	−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
$712$	0	0
$713$	−8000.00	−0.420200
$714$	0	0
$715$	−400.000	−0.0209219
$716$	0	0
$717$	2064.00	0.107506
$718$	0	0
$719$	6704.00	0.347729	0.173864	−	0.984770i	$-0.444375\pi$
$719$	6704.00	0.347729	0.173864	+	0.984770i	$0.444375\pi$
$720$	0	0
$721$	−16440.0	−0.849178
$722$	0	0
$723$	7796.00	0.401018
$724$	0	0
$725$	−3750.00	−0.192099
$726$	0	0
$727$	−9052.00	−0.461788	−0.230894	−	0.972979i	$-0.574165\pi$
$727$	−9052.00	−0.461788	−0.230894	+	0.972979i	$0.574165\pi$
$728$	0	0
$729$	−4283.00	−0.217599
$730$	0	0
$731$	8432.00	0.426633
$732$	0	0
$733$	−13058.0	−0.657992	−0.328996	−	0.944331i	$-0.606710\pi$
$733$	−13058.0	−0.657992	−0.328996	+	0.944331i	$0.606710\pi$
$734$	0	0
$735$	1990.00	0.0998670
$736$	0	0
$737$	−6680.00	−0.333868
$738$	0	0
$739$	38540.0	1.91843	0.959213	−	0.282684i	$-0.0912249\pi$
$739$	38540.0	1.91843	0.959213	+	0.282684i	$0.0912249\pi$
$740$	0	0
$741$	152.000	0.00753557
$742$	0	0
$743$	19778.0	0.976560	0.488280	−	0.872687i	$-0.337624\pi$
$743$	19778.0	0.976560	0.488280	+	0.872687i	$0.337624\pi$
$744$	0	0
$745$	−10470.0	−0.514887
$746$	0	0
$747$	−3588.00	−0.175740
$748$	0	0
$749$	−4056.00	−0.197868
$750$	0	0
$751$	−1316.00	−0.0639434	−0.0319717	−	0.999489i	$-0.510179\pi$
$751$	−1316.00	−0.0639434	−0.0319717	+	0.999489i	$0.510179\pi$
$752$	0	0
$753$	8168.00	0.395297
$754$	0	0
$755$	−2220.00	−0.107012
$756$	0	0
$757$	−18346.0	−0.880841	−0.440421	−	0.897792i	$-0.645171\pi$
$757$	−18346.0	−0.880841	−0.440421	+	0.897792i	$0.645171\pi$
$758$	0	0
$759$	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	$0.945397\pi$
$762$	0	0
$763$	1224.00	0.0580757
$764$	0	0
$765$	3910.00	0.184793
$766$	0	0
$767$	−192.000	−0.00903875
$768$	0	0
$769$	−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
$772$	0	0
$773$	−4740.00	−0.220551	−0.110276	−	0.993901i	$-0.535173\pi$
$773$	−4740.00	−0.220551	−0.110276	+	0.993901i	$0.535173\pi$
$774$	0	0
$775$	5000.00	0.231749
$776$	0	0
$777$	3744.00	0.172864
$778$	0	0
$779$	−4142.00	−0.190504
$780$	0	0
$781$	10400.0	0.476493
$782$	0	0
$783$	−15000.0	−0.684618
$784$	0	0
$785$	7730.00	0.351459
$786$	0	0
$787$	3358.00	0.152096	0.0760481	−	0.997104i	$-0.475770\pi$
$787$	3358.00	0.152096	0.0760481	+	0.997104i	$0.475770\pi$
$788$	0	0
$789$	−1808.00	−0.0815799
$790$	0	0
$791$	48.0000	0.00215763
$792$	0	0
$793$	536.000	0.0240024
$794$	0	0
$795$	−720.000	−0.0321205
$796$	0	0
$797$	37680.0	1.67465	0.837324	−	0.546707i	$-0.184119\pi$
$797$	37680.0	1.67465	0.837324	+	0.546707i	$0.184119\pi$
$798$	0	0
$799$	−6120.00	−0.270976
$800$	0	0
$801$	−15410.0	−0.679757
$802$	0	0
$803$	8760.00	0.384973
$804$	0	0
$805$	−2400.00	−0.105079
$806$	0	0
$807$	4420.00	0.192802
$808$	0	0
$809$	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	$-0.419454\pi$
$811$	11564.0	0.500699	0.250350	+	0.968156i	$0.419454\pi$
$812$	0	0
$813$	880.000	0.0379618
$814$	0	0
$815$	−880.000	−0.0378222
$816$	0	0
$817$	−4712.00	−0.201777
$818$	0	0
$819$	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	$0.525099\pi$
$822$	0	0
$823$	−45692.0	−1.93526	−0.967632	−	0.252364i	$-0.918792\pi$
$823$	−45692.0	−1.93526	−0.967632	+	0.252364i	$0.918792\pi$
$824$	0	0
$825$	−1000.00	−0.0422006
$826$	0	0
$827$	−1302.00	−0.0547460	−0.0273730	−	0.999625i	$-0.508714\pi$
$827$	−1302.00	−0.0547460	−0.0273730	+	0.999625i	$0.508714\pi$
$828$	0	0
$829$	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
$832$	0	0
$833$	6766.00	0.281426
$834$	0	0
$835$	−4290.00	−0.177798
$836$	0	0
$837$	20000.0	0.825927
$838$	0	0
$839$	−4668.00	−0.192083	−0.0960413	−	0.995377i	$-0.530618\pi$
$839$	−4668.00	−0.192083	−0.0960413	+	0.995377i	$0.530618\pi$
$840$	0	0
$841$	−1889.00	−0.0774530
$842$	0	0
$843$	−7788.00	−0.318189
$844$	0	0
$845$	−10905.0	−0.443957
$846$	0	0
$847$	−11172.0	−0.453217
$848$	0	0
$849$	−8216.00	−0.332123
$850$	0	0
$851$	6240.00	0.251357
$852$	0	0
$853$	6302.00	0.252962	0.126481	−	0.991969i	$-0.459632\pi$
$853$	6302.00	0.252962	0.126481	+	0.991969i	$0.459632\pi$
$854$	0	0
$855$	−2185.00	−0.0873982
$856$	0	0
$857$	38288.0	1.52613	0.763065	−	0.646322i	$-0.223694\pi$
$857$	38288.0	1.52613	0.763065	+	0.646322i	$0.223694\pi$
$858$	0	0
$859$	3756.00	0.149189	0.0745943	−	0.997214i	$-0.476234\pi$
$859$	3756.00	0.149189	0.0745943	+	0.997214i	$0.476234\pi$
$860$	0	0
$861$	5232.00	0.207092
$862$	0	0
$863$	−28862.0	−1.13844	−0.569220	−	0.822185i	$-0.692755\pi$
$863$	−28862.0	−1.13844	−0.569220	+	0.822185i	$0.692755\pi$
$864$	0	0
$865$	−6560.00	−0.257857
$866$	0	0
$867$	7514.00	0.294335
$868$	0	0
$869$	−19600.0	−0.765114
$870$	0	0
$871$	1336.00	0.0519732
$872$	0	0
$873$	−25852.0	−1.00224
$874$	0	0
$875$	1500.00	0.0579534
$876$	0	0
$877$	20360.0	0.783932	0.391966	−	0.919980i	$-0.371795\pi$
$877$	20360.0	0.783932	0.391966	+	0.919980i	$0.371795\pi$
$878$	0	0
$879$	−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	$0.466451\pi$
$882$	0	0
$883$	−27488.0	−1.04762	−0.523808	−	0.851836i	$-0.675489\pi$
$883$	−27488.0	−1.04762	−0.523808	+	0.851836i	$0.675489\pi$
$884$	0	0
$885$	−480.000	−0.0182317
$886$	0	0
$887$	17106.0	0.647535	0.323767	−	0.946137i	$-0.395050\pi$
$887$	17106.0	0.647535	0.323767	+	0.946137i	$0.395050\pi$
$888$	0	0
$889$	−16296.0	−0.614792
$890$	0	0
$891$	8420.00	0.316589
$892$	0	0
$893$	3420.00	0.128159
$894$	0	0
$895$	−17080.0	−0.637901
$896$	0	0
$897$	−320.000	−0.0119114
$898$	0	0
$899$	−30000.0	−1.11297
$900$	0	0
$901$	−2448.00	−0.0905158
$902$	0	0
$903$	5952.00	0.219347
$904$	0	0
$905$	6150.00	0.225893
$906$	0	0
$907$	−45970.0	−1.68292	−0.841460	−	0.540319i	$-0.818304\pi$
$907$	−45970.0	−1.68292	−0.841460	+	0.540319i	$0.818304\pi$
$908$	0	0
$909$	33442.0	1.22024
$910$	0	0
$911$	36732.0	1.33588	0.667939	−	0.744216i	$-0.267177\pi$
$911$	36732.0	1.33588	0.667939	+	0.744216i	$0.267177\pi$
$912$	0	0
$913$	3120.00	0.113096
$914$	0	0
$915$	1340.00	0.0484142
$916$	0	0
$917$	32400.0	1.16679
$918$	0	0
$919$	36496.0	1.31000	0.655001	−	0.755628i	$-0.272668\pi$
$919$	36496.0	1.31000	0.655001	+	0.755628i	$0.272668\pi$
$920$	0	0
$921$	−12844.0	−0.459527
$922$	0	0
$923$	−2080.00	−0.0741756
$924$	0	0
$925$	−3900.00	−0.138628
$926$	0	0
$927$	31510.0	1.11642
$928$	0	0
$929$	−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
$932$	0	0
$933$	−8864.00	−0.311034
$934$	0	0
$935$	−3400.00	−0.118922
$936$	0	0
$937$	574.000	0.0200126	0.0100063	−	0.999950i	$-0.496815\pi$
$937$	574.000	0.0200126	0.0100063	+	0.999950i	$0.496815\pi$
$938$	0	0
$939$	−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	$0.478381\pi$
$942$	0	0
$943$	8720.00	0.301126
$944$	0	0
$945$	6000.00	0.206540
$946$	0	0
$947$	−7324.00	−0.251318	−0.125659	−	0.992074i	$-0.540104\pi$
$947$	−7324.00	−0.251318	−0.125659	+	0.992074i	$0.540104\pi$
$948$	0	0
$949$	−1752.00	−0.0599287
$950$	0	0
$951$	13768.0	0.469462
$952$	0	0
$953$	−38928.0	−1.32319	−0.661596	−	0.749861i	$-0.730121\pi$
$953$	−38928.0	−1.32319	−0.661596	+	0.749861i	$0.730121\pi$
$954$	0	0
$955$	−9640.00	−0.326642
$956$	0	0
$957$	6000.00	0.202667
$958$	0	0
$959$	−10392.0	−0.349922
$960$	0	0
$961$	10209.0	0.342687
$962$	0	0
$963$	7774.00	0.260139
$964$	0	0
$965$	−5180.00	−0.172798
$966$	0	0
$967$	−1384.00	−0.0460253	−0.0230126	−	0.999735i	$-0.507326\pi$
$967$	−1384.00	−0.0460253	−0.0230126	+	0.999735i	$0.507326\pi$
$968$	0	0
$969$	1292.00	0.0428328
$970$	0	0
$971$	−6876.00	−0.227252	−0.113626	−	0.993524i	$-0.536247\pi$
$971$	−6876.00	−0.227252	−0.113626	+	0.993524i	$0.536247\pi$
$972$	0	0
$973$	−1776.00	−0.0585159
$974$	0	0
$975$	200.000	0.00656936
$976$	0	0
$977$	21104.0	0.691071	0.345536	−	0.938406i	$-0.387697\pi$
$977$	21104.0	0.691071	0.345536	+	0.938406i	$0.387697\pi$
$978$	0	0
$979$	13400.0	0.437452
$980$	0	0
$981$	−2346.00	−0.0763527
$982$	0	0
$983$	22594.0	0.733099	0.366550	−	0.930398i	$-0.380539\pi$
$983$	22594.0	0.733099	0.366550	+	0.930398i	$0.380539\pi$
$984$	0	0
$985$	−9050.00	−0.292748
$986$	0	0
$987$	−4320.00	−0.139318
$988$	0	0
$989$	9920.00	0.318946
$990$	0	0
$991$	−6124.00	−0.196302	−0.0981510	−	0.995172i	$-0.531293\pi$
$991$	−6124.00	−0.196302	−0.0981510	+	0.995172i	$0.531293\pi$
$992$	0	0
$993$	6896.00	0.220381
$994$	0	0
$995$	−21240.0	−0.676737
$996$	0	0
$997$	17258.0	0.548211	0.274105	−	0.961700i	$-0.411618\pi$
$997$	17258.0	0.548211	0.274105	+	0.961700i	$0.411618\pi$
$998$	0	0
$999$	−15600.0	−0.494056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.4.a.d.1.1		1
4.3	odd	2		190.4.a.b.1.1	✓	1
12.11	even	2		1710.4.a.g.1.1		1
20.3	even	4		950.4.b.b.799.2		2
20.7	even	4		950.4.b.b.799.1		2
20.19	odd	2		950.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.4.a.b.1.1	✓	1	4.3	odd	2
950.4.a.b.1.1		1	20.19	odd	2
950.4.b.b.799.1		2	20.7	even	4
950.4.b.b.799.2		2	20.3	even	4
1520.4.a.d.1.1		1	1.1	even	1	trivial
1710.4.a.g.1.1		1	12.11	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:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1520.a (trivial)

Introduction

L-functions

Modular forms

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Fields

Representations

Groups

Database

Properties

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