LMFDB - Embedded newform 1890.4.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,4,Mod(1,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1890.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1890.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:	$111.513609911$
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	$\chi$	$=$	1890.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +O(q^{10})$

\(q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} +10.0000 q^{10} -9.00000 q^{11} -19.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +108.000 q^{17} +11.0000 q^{19} -20.0000 q^{20} +18.0000 q^{22} +126.000 q^{23} +25.0000 q^{25} +38.0000 q^{26} +28.0000 q^{28} +66.0000 q^{29} -148.000 q^{31} -32.0000 q^{32} -216.000 q^{34} -35.0000 q^{35} -346.000 q^{37} -22.0000 q^{38} +40.0000 q^{40} +147.000 q^{41} -139.000 q^{43} -36.0000 q^{44} -252.000 q^{46} -201.000 q^{47} +49.0000 q^{49} -50.0000 q^{50} -76.0000 q^{52} -249.000 q^{53} +45.0000 q^{55} -56.0000 q^{56} -132.000 q^{58} +582.000 q^{59} +344.000 q^{61} +296.000 q^{62} +64.0000 q^{64} +95.0000 q^{65} +305.000 q^{67} +432.000 q^{68} +70.0000 q^{70} +912.000 q^{71} -151.000 q^{73} +692.000 q^{74} +44.0000 q^{76} -63.0000 q^{77} -832.000 q^{79} -80.0000 q^{80} -294.000 q^{82} -873.000 q^{83} -540.000 q^{85} +278.000 q^{86} +72.0000 q^{88} -609.000 q^{89} -133.000 q^{91} +504.000 q^{92} +402.000 q^{94} -55.0000 q^{95} +686.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
$3$	0	0
$3$	0	0
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	0	0
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	0	0
$10$	10.0000	0.316228
$11$	−9.00000	−0.246691	−0.123346	−	0.992364i	$-0.539362\pi$
$11$	−9.00000	−0.246691	−0.123346	+	0.992364i	$0.539362\pi$
$12$	0	0
$13$	−19.0000	−0.405358	−0.202679	−	0.979245i	$-0.564965\pi$
$13$	−19.0000	−0.405358	−0.202679	+	0.979245i	$0.564965\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	108.000	1.54081	0.770407	−	0.637552i	$-0.220053\pi$
$17$	108.000	1.54081	0.770407	+	0.637552i	$0.220053\pi$
$18$	0	0
$19$	11.0000	0.132820	0.0664098	−	0.997792i	$-0.478846\pi$
$19$	11.0000	0.132820	0.0664098	+	0.997792i	$0.478846\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	18.0000	0.174437
$23$	126.000	1.14230	0.571148	−	0.820847i	$-0.306498\pi$
$23$	126.000	1.14230	0.571148	+	0.820847i	$0.306498\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	38.0000	0.286631
$27$	0	0
$28$	28.0000	0.188982
$29$	66.0000	0.422617	0.211308	−	0.977419i	$-0.432228\pi$
$29$	66.0000	0.422617	0.211308	+	0.977419i	$0.432228\pi$
$30$	0	0
$31$	−148.000	−0.857470	−0.428735	−	0.903430i	$-0.641041\pi$
$31$	−148.000	−0.857470	−0.428735	+	0.903430i	$0.641041\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−216.000	−1.08952
$35$	−35.0000	−0.169031
$36$	0	0
$37$	−346.000	−1.53735	−0.768676	−	0.639638i	$-0.779084\pi$
$37$	−346.000	−1.53735	−0.768676	+	0.639638i	$0.779084\pi$
$38$	−22.0000	−0.0939177
$39$	0	0
$40$	40.0000	0.158114
$41$	147.000	0.559940	0.279970	−	0.960009i	$-0.409675\pi$
$41$	147.000	0.559940	0.279970	+	0.960009i	$0.409675\pi$
$42$	0	0
$43$	−139.000	−0.492960	−0.246480	−	0.969148i	$-0.579274\pi$
$43$	−139.000	−0.492960	−0.246480	+	0.969148i	$0.579274\pi$
$44$	−36.0000	−0.123346
$45$	0	0
$46$	−252.000	−0.807725
$47$	−201.000	−0.623806	−0.311903	−	0.950114i	$-0.600966\pi$
$47$	−201.000	−0.623806	−0.311903	+	0.950114i	$0.600966\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	0	0
$52$	−76.0000	−0.202679
$53$	−249.000	−0.645335	−0.322668	−	0.946512i	$-0.604580\pi$
$53$	−249.000	−0.645335	−0.322668	+	0.946512i	$0.604580\pi$
$54$	0	0
$55$	45.0000	0.110324
$56$	−56.0000	−0.133631
$57$	0	0
$58$	−132.000	−0.298835
$59$	582.000	1.28424	0.642118	−	0.766606i	$-0.278056\pi$
$59$	582.000	1.28424	0.642118	+	0.766606i	$0.278056\pi$
$60$	0	0
$61$	344.000	0.722044	0.361022	−	0.932557i	$-0.382428\pi$
$61$	344.000	0.722044	0.361022	+	0.932557i	$0.382428\pi$
$62$	296.000	0.606323
$63$	0	0
$64$	64.0000	0.125000
$65$	95.0000	0.181282
$66$	0	0
$67$	305.000	0.556144	0.278072	−	0.960560i	$-0.410305\pi$
$67$	305.000	0.556144	0.278072	+	0.960560i	$0.410305\pi$
$68$	432.000	0.770407
$69$	0	0
$70$	70.0000	0.119523
$71$	912.000	1.52443	0.762215	−	0.647324i	$-0.224112\pi$
$71$	912.000	1.52443	0.762215	+	0.647324i	$0.224112\pi$
$72$	0	0
$73$	−151.000	−0.242099	−0.121049	−	0.992646i	$-0.538626\pi$
$73$	−151.000	−0.242099	−0.121049	+	0.992646i	$0.538626\pi$
$74$	692.000	1.08707
$75$	0	0
$76$	44.0000	0.0664098
$77$	−63.0000	−0.0932405
$78$	0	0
$79$	−832.000	−1.18490	−0.592451	−	0.805606i	$-0.701840\pi$
$79$	−832.000	−1.18490	−0.592451	+	0.805606i	$0.701840\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	−294.000	−0.395937
$83$	−873.000	−1.15451	−0.577254	−	0.816564i	$-0.695876\pi$
$83$	−873.000	−1.15451	−0.577254	+	0.816564i	$0.695876\pi$
$84$	0	0
$85$	−540.000	−0.689073
$86$	278.000	0.348576
$87$	0	0
$88$	72.0000	0.0872185
$89$	−609.000	−0.725324	−0.362662	−	0.931921i	$-0.618132\pi$
$89$	−609.000	−0.725324	−0.362662	+	0.931921i	$0.618132\pi$
$90$	0	0
$91$	−133.000	−0.153211
$92$	504.000	0.571148
$93$	0	0
$94$	402.000	0.441097
$95$	−55.0000	−0.0593987
$96$	0	0
$97$	686.000	0.718070	0.359035	−	0.933324i	$-0.383106\pi$
$97$	686.000	0.718070	0.359035	+	0.933324i	$0.383106\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	165.000	0.162556	0.0812778	−	0.996691i	$-0.474100\pi$
$101$	165.000	0.162556	0.0812778	+	0.996691i	$0.474100\pi$
$102$	0	0
$103$	−4.00000	−0.00382652	−0.00191326	−	0.999998i	$-0.500609\pi$
$103$	−4.00000	−0.00382652	−0.00191326	+	0.999998i	$0.500609\pi$
$104$	152.000	0.143316
$105$	0	0
$106$	498.000	0.456321
$107$	444.000	0.401150	0.200575	−	0.979678i	$-0.435719\pi$
$107$	444.000	0.401150	0.200575	+	0.979678i	$0.435719\pi$
$108$	0	0
$109$	611.000	0.536910	0.268455	−	0.963292i	$-0.413487\pi$
$109$	611.000	0.536910	0.268455	+	0.963292i	$0.413487\pi$
$110$	−90.0000	−0.0780106
$111$	0	0
$112$	112.000	0.0944911
$113$	−351.000	−0.292206	−0.146103	−	0.989269i	$-0.546673\pi$
$113$	−351.000	−0.292206	−0.146103	+	0.989269i	$0.546673\pi$
$114$	0	0
$115$	−630.000	−0.510850
$116$	264.000	0.211308
$117$	0	0
$118$	−1164.00	−0.908092
$119$	756.000	0.582373
$120$	0	0
$121$	−1250.00	−0.939144
$122$	−688.000	−0.510562
$123$	0	0
$124$	−592.000	−0.428735
$125$	−125.000	−0.0894427
$126$	0	0
$127$	1739.00	1.21505	0.607525	−	0.794301i	$-0.292163\pi$
$127$	1739.00	1.21505	0.607525	+	0.794301i	$0.292163\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−190.000	−0.128185
$131$	408.000	0.272115	0.136058	−	0.990701i	$-0.456557\pi$
$131$	408.000	0.272115	0.136058	+	0.990701i	$0.456557\pi$
$132$	0	0
$133$	77.0000	0.0502011
$134$	−610.000	−0.393254
$135$	0	0
$136$	−864.000	−0.544760
$137$	1071.00	0.667896	0.333948	−	0.942592i	$-0.391619\pi$
$137$	1071.00	0.667896	0.333948	+	0.942592i	$0.391619\pi$
$138$	0	0
$139$	−2020.00	−1.23262	−0.616310	−	0.787504i	$-0.711373\pi$
$139$	−2020.00	−1.23262	−0.616310	+	0.787504i	$0.711373\pi$
$140$	−140.000	−0.0845154
$141$	0	0
$142$	−1824.00	−1.07793
$143$	171.000	0.0999982
$144$	0	0
$145$	−330.000	−0.189000
$146$	302.000	0.171190
$147$	0	0
$148$	−1384.00	−0.768676
$149$	−1206.00	−0.663083	−0.331542	−	0.943441i	$-0.607569\pi$
$149$	−1206.00	−0.663083	−0.331542	+	0.943441i	$0.607569\pi$
$150$	0	0
$151$	470.000	0.253298	0.126649	−	0.991948i	$-0.459578\pi$
$151$	470.000	0.253298	0.126649	+	0.991948i	$0.459578\pi$
$152$	−88.0000	−0.0469588
$153$	0	0
$154$	126.000	0.0659310
$155$	740.000	0.383472
$156$	0	0
$157$	2234.00	1.13562	0.567811	−	0.823159i	$-0.307790\pi$
$157$	2234.00	1.13562	0.567811	+	0.823159i	$0.307790\pi$
$158$	1664.00	0.837853
$159$	0	0
$160$	160.000	0.0790569
$161$	882.000	0.431747
$162$	0	0
$163$	608.000	0.292161	0.146080	−	0.989273i	$-0.453334\pi$
$163$	608.000	0.292161	0.146080	+	0.989273i	$0.453334\pi$
$164$	588.000	0.279970
$165$	0	0
$166$	1746.00	0.816361
$167$	1836.00	0.850742	0.425371	−	0.905019i	$-0.360144\pi$
$167$	1836.00	0.850742	0.425371	+	0.905019i	$0.360144\pi$
$168$	0	0
$169$	−1836.00	−0.835685
$170$	1080.00	0.487248
$171$	0	0
$172$	−556.000	−0.246480
$173$	1626.00	0.714581	0.357290	−	0.933993i	$-0.383701\pi$
$173$	1626.00	0.714581	0.357290	+	0.933993i	$0.383701\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	−144.000	−0.0616728
$177$	0	0
$178$	1218.00	0.512882
$179$	741.000	0.309413	0.154707	−	0.987960i	$-0.450557\pi$
$179$	741.000	0.309413	0.154707	+	0.987960i	$0.450557\pi$
$180$	0	0
$181$	−106.000	−0.0435299	−0.0217650	−	0.999763i	$-0.506929\pi$
$181$	−106.000	−0.0435299	−0.0217650	+	0.999763i	$0.506929\pi$
$182$	266.000	0.108336
$183$	0	0
$184$	−1008.00	−0.403863
$185$	1730.00	0.687525
$186$	0	0
$187$	−972.000	−0.380105
$188$	−804.000	−0.311903
$189$	0	0
$190$	110.000	0.0420013
$191$	−1233.00	−0.467103	−0.233552	−	0.972344i	$-0.575035\pi$
$191$	−1233.00	−0.467103	−0.233552	+	0.972344i	$0.575035\pi$
$192$	0	0
$193$	578.000	0.215572	0.107786	−	0.994174i	$-0.465624\pi$
$193$	578.000	0.215572	0.107786	+	0.994174i	$0.465624\pi$
$194$	−1372.00	−0.507752
$195$	0	0
$196$	196.000	0.0714286
$197$	2037.00	0.736702	0.368351	−	0.929687i	$-0.379923\pi$
$197$	2037.00	0.736702	0.368351	+	0.929687i	$0.379923\pi$
$198$	0	0
$199$	−67.0000	−0.0238669	−0.0119334	−	0.999929i	$-0.503799\pi$
$199$	−67.0000	−0.0238669	−0.0119334	+	0.999929i	$0.503799\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−330.000	−0.114944
$203$	462.000	0.159734
$204$	0	0
$205$	−735.000	−0.250413
$206$	8.00000	0.00270576
$207$	0	0
$208$	−304.000	−0.101339
$209$	−99.0000	−0.0327654
$210$	0	0
$211$	−3550.00	−1.15826	−0.579128	−	0.815237i	$-0.696607\pi$
$211$	−3550.00	−1.15826	−0.579128	+	0.815237i	$0.696607\pi$
$212$	−996.000	−0.322668
$213$	0	0
$214$	−888.000	−0.283656
$215$	695.000	0.220459
$216$	0	0
$217$	−1036.00	−0.324093
$218$	−1222.00	−0.379653
$219$	0	0
$220$	180.000	0.0551618
$221$	−2052.00	−0.624581
$222$	0	0
$223$	1802.00	0.541125	0.270562	−	0.962702i	$-0.412790\pi$
$223$	1802.00	0.541125	0.270562	+	0.962702i	$0.412790\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	702.000	0.206621
$227$	−33.0000	−0.00964884	−0.00482442	−	0.999988i	$-0.501536\pi$
$227$	−33.0000	−0.00964884	−0.00482442	+	0.999988i	$0.501536\pi$
$228$	0	0
$229$	4310.00	1.24372	0.621862	−	0.783127i	$-0.286376\pi$
$229$	4310.00	1.24372	0.621862	+	0.783127i	$0.286376\pi$
$230$	1260.00	0.361226
$231$	0	0
$232$	−528.000	−0.149418
$233$	6837.00	1.92235	0.961173	−	0.275945i	$-0.0889909\pi$
$233$	6837.00	1.92235	0.961173	+	0.275945i	$0.0889909\pi$
$234$	0	0
$235$	1005.00	0.278974
$236$	2328.00	0.642118
$237$	0	0
$238$	−1512.00	−0.411800
$239$	5496.00	1.48748	0.743738	−	0.668471i	$-0.233051\pi$
$239$	5496.00	1.48748	0.743738	+	0.668471i	$0.233051\pi$
$240$	0	0
$241$	−184.000	−0.0491804	−0.0245902	−	0.999698i	$-0.507828\pi$
$241$	−184.000	−0.0491804	−0.0245902	+	0.999698i	$0.507828\pi$
$242$	2500.00	0.664075
$243$	0	0
$244$	1376.00	0.361022
$245$	−245.000	−0.0638877
$246$	0	0
$247$	−209.000	−0.0538395
$248$	1184.00	0.303162
$249$	0	0
$250$	250.000	0.0632456
$251$	−3990.00	−1.00337	−0.501686	−	0.865050i	$-0.667287\pi$
$251$	−3990.00	−1.00337	−0.501686	+	0.865050i	$0.667287\pi$
$252$	0	0
$253$	−1134.00	−0.281794
$254$	−3478.00	−0.859170
$255$	0	0
$256$	256.000	0.0625000
$257$	444.000	0.107766	0.0538832	−	0.998547i	$-0.482840\pi$
$257$	444.000	0.107766	0.0538832	+	0.998547i	$0.482840\pi$
$258$	0	0
$259$	−2422.00	−0.581065
$260$	380.000	0.0906408
$261$	0	0
$262$	−816.000	−0.192415
$263$	1812.00	0.424839	0.212420	−	0.977179i	$-0.431866\pi$
$263$	1812.00	0.424839	0.212420	+	0.977179i	$0.431866\pi$
$264$	0	0
$265$	1245.00	0.288603
$266$	−154.000	−0.0354975
$267$	0	0
$268$	1220.00	0.278072
$269$	1770.00	0.401185	0.200593	−	0.979675i	$-0.435713\pi$
$269$	1770.00	0.401185	0.200593	+	0.979675i	$0.435713\pi$
$270$	0	0
$271$	3671.00	0.822869	0.411434	−	0.911439i	$-0.365028\pi$
$271$	3671.00	0.822869	0.411434	+	0.911439i	$0.365028\pi$
$272$	1728.00	0.385204
$273$	0	0
$274$	−2142.00	−0.472274
$275$	−225.000	−0.0493382
$276$	0	0
$277$	170.000	0.0368748	0.0184374	−	0.999830i	$-0.494131\pi$
$277$	170.000	0.0368748	0.0184374	+	0.999830i	$0.494131\pi$
$278$	4040.00	0.871594
$279$	0	0
$280$	280.000	0.0597614
$281$	−5202.00	−1.10436	−0.552180	−	0.833725i	$-0.686204\pi$
$281$	−5202.00	−1.10436	−0.552180	+	0.833725i	$0.686204\pi$
$282$	0	0
$283$	98.0000	0.0205848	0.0102924	−	0.999947i	$-0.496724\pi$
$283$	98.0000	0.0205848	0.0102924	+	0.999947i	$0.496724\pi$
$284$	3648.00	0.762215
$285$	0	0
$286$	−342.000	−0.0707094
$287$	1029.00	0.211637
$288$	0	0
$289$	6751.00	1.37411
$290$	660.000	0.133643
$291$	0	0
$292$	−604.000	−0.121049
$293$	8502.00	1.69520	0.847598	−	0.530640i	$-0.178048\pi$
$293$	8502.00	1.69520	0.847598	+	0.530640i	$0.178048\pi$
$294$	0	0
$295$	−2910.00	−0.574328
$296$	2768.00	0.543536
$297$	0	0
$298$	2412.00	0.468870
$299$	−2394.00	−0.463039
$300$	0	0
$301$	−973.000	−0.186322
$302$	−940.000	−0.179109
$303$	0	0
$304$	176.000	0.0332049
$305$	−1720.00	−0.322908
$306$	0	0
$307$	68.0000	0.0126416	0.00632079	−	0.999980i	$-0.497988\pi$
$307$	68.0000	0.0126416	0.00632079	+	0.999980i	$0.497988\pi$
$308$	−252.000	−0.0466202
$309$	0	0
$310$	−1480.00	−0.271156
$311$	8238.00	1.50204	0.751019	−	0.660280i	$-0.229562\pi$
$311$	8238.00	1.50204	0.751019	+	0.660280i	$0.229562\pi$
$312$	0	0
$313$	−4057.00	−0.732636	−0.366318	−	0.930490i	$-0.619382\pi$
$313$	−4057.00	−0.732636	−0.366318	+	0.930490i	$0.619382\pi$
$314$	−4468.00	−0.803006
$315$	0	0
$316$	−3328.00	−0.592451
$317$	−4329.00	−0.767006	−0.383503	−	0.923540i	$-0.625282\pi$
$317$	−4329.00	−0.767006	−0.383503	+	0.923540i	$0.625282\pi$
$318$	0	0
$319$	−594.000	−0.104256
$320$	−320.000	−0.0559017
$321$	0	0
$322$	−1764.00	−0.305292
$323$	1188.00	0.204650
$324$	0	0
$325$	−475.000	−0.0810716
$326$	−1216.00	−0.206589
$327$	0	0
$328$	−1176.00	−0.197969
$329$	−1407.00	−0.235776
$330$	0	0
$331$	9002.00	1.49485	0.747424	−	0.664347i	$-0.231290\pi$
$331$	9002.00	1.49485	0.747424	+	0.664347i	$0.231290\pi$
$332$	−3492.00	−0.577254
$333$	0	0
$334$	−3672.00	−0.601566
$335$	−1525.00	−0.248715
$336$	0	0
$337$	10208.0	1.65005	0.825023	−	0.565100i	$-0.191162\pi$
$337$	10208.0	1.65005	0.825023	+	0.565100i	$0.191162\pi$
$338$	3672.00	0.590919
$339$	0	0
$340$	−2160.00	−0.344537
$341$	1332.00	0.211530
$342$	0	0
$343$	343.000	0.0539949
$344$	1112.00	0.174288
$345$	0	0
$346$	−3252.00	−0.505285
$347$	2802.00	0.433485	0.216742	−	0.976229i	$-0.430457\pi$
$347$	2802.00	0.433485	0.216742	+	0.976229i	$0.430457\pi$
$348$	0	0
$349$	−5914.00	−0.907075	−0.453537	−	0.891237i	$-0.649838\pi$
$349$	−5914.00	−0.907075	−0.453537	+	0.891237i	$0.649838\pi$
$350$	−350.000	−0.0534522
$351$	0	0
$352$	288.000	0.0436092
$353$	6372.00	0.960757	0.480379	−	0.877061i	$-0.340499\pi$
$353$	6372.00	0.960757	0.480379	+	0.877061i	$0.340499\pi$
$354$	0	0
$355$	−4560.00	−0.681746
$356$	−2436.00	−0.362662
$357$	0	0
$358$	−1482.00	−0.218788
$359$	11373.0	1.67199	0.835994	−	0.548738i	$-0.184892\pi$
$359$	11373.0	1.67199	0.835994	+	0.548738i	$0.184892\pi$
$360$	0	0
$361$	−6738.00	−0.982359
$362$	212.000	0.0307803
$363$	0	0
$364$	−532.000	−0.0766054
$365$	755.000	0.108270
$366$	0	0
$367$	−1438.00	−0.204531	−0.102266	−	0.994757i	$-0.532609\pi$
$367$	−1438.00	−0.204531	−0.102266	+	0.994757i	$0.532609\pi$
$368$	2016.00	0.285574
$369$	0	0
$370$	−3460.00	−0.486154
$371$	−1743.00	−0.243914
$372$	0	0
$373$	12656.0	1.75684	0.878422	−	0.477886i	$-0.158597\pi$
$373$	12656.0	1.75684	0.878422	+	0.477886i	$0.158597\pi$
$374$	1944.00	0.268775
$375$	0	0
$376$	1608.00	0.220549
$377$	−1254.00	−0.171311
$378$	0	0
$379$	260.000	0.0352383	0.0176191	−	0.999845i	$-0.494391\pi$
$379$	260.000	0.0352383	0.0176191	+	0.999845i	$0.494391\pi$
$380$	−220.000	−0.0296994
$381$	0	0
$382$	2466.00	0.330292
$383$	−8472.00	−1.13028	−0.565142	−	0.824993i	$-0.691179\pi$
$383$	−8472.00	−1.13028	−0.565142	+	0.824993i	$0.691179\pi$
$384$	0	0
$385$	315.000	0.0416984
$386$	−1156.00	−0.152432
$387$	0	0
$388$	2744.00	0.359035
$389$	2298.00	0.299520	0.149760	−	0.988722i	$-0.452150\pi$
$389$	2298.00	0.299520	0.149760	+	0.988722i	$0.452150\pi$
$390$	0	0
$391$	13608.0	1.76007
$392$	−392.000	−0.0505076
$393$	0	0
$394$	−4074.00	−0.520927
$395$	4160.00	0.529905
$396$	0	0
$397$	2966.00	0.374960	0.187480	−	0.982268i	$-0.439968\pi$
$397$	2966.00	0.374960	0.187480	+	0.982268i	$0.439968\pi$
$398$	134.000	0.0168764
$399$	0	0
$400$	400.000	0.0500000
$401$	12348.0	1.53773	0.768865	−	0.639411i	$-0.220822\pi$
$401$	12348.0	1.53773	0.768865	+	0.639411i	$0.220822\pi$
$402$	0	0
$403$	2812.00	0.347582
$404$	660.000	0.0812778
$405$	0	0
$406$	−924.000	−0.112949
$407$	3114.00	0.379251
$408$	0	0
$409$	10682.0	1.29142	0.645710	−	0.763583i	$-0.276561\pi$
$409$	10682.0	1.29142	0.645710	+	0.763583i	$0.276561\pi$
$410$	1470.00	0.177069
$411$	0	0
$412$	−16.0000	−0.00191326
$413$	4074.00	0.485396
$414$	0	0
$415$	4365.00	0.516312
$416$	608.000	0.0716578
$417$	0	0
$418$	198.000	0.0231687
$419$	−1446.00	−0.168596	−0.0842980	−	0.996441i	$-0.526865\pi$
$419$	−1446.00	−0.168596	−0.0842980	+	0.996441i	$0.526865\pi$
$420$	0	0
$421$	−3949.00	−0.457156	−0.228578	−	0.973526i	$-0.573408\pi$
$421$	−3949.00	−0.457156	−0.228578	+	0.973526i	$0.573408\pi$
$422$	7100.00	0.819011
$423$	0	0
$424$	1992.00	0.228161
$425$	2700.00	0.308163
$426$	0	0
$427$	2408.00	0.272907
$428$	1776.00	0.200575
$429$	0	0
$430$	−1390.00	−0.155888
$431$	−501.000	−0.0559915	−0.0279957	−	0.999608i	$-0.508912\pi$
$431$	−501.000	−0.0559915	−0.0279957	+	0.999608i	$0.508912\pi$
$432$	0	0
$433$	−157.000	−0.0174248	−0.00871240	−	0.999962i	$-0.502773\pi$
$433$	−157.000	−0.0174248	−0.00871240	+	0.999962i	$0.502773\pi$
$434$	2072.00	0.229169
$435$	0	0
$436$	2444.00	0.268455
$437$	1386.00	0.151719
$438$	0	0
$439$	−241.000	−0.0262011	−0.0131006	−	0.999914i	$-0.504170\pi$
$439$	−241.000	−0.0262011	−0.0131006	+	0.999914i	$0.504170\pi$
$440$	−360.000	−0.0390053
$441$	0	0
$442$	4104.00	0.441646
$443$	6552.00	0.702697	0.351349	−	0.936245i	$-0.385723\pi$
$443$	6552.00	0.702697	0.351349	+	0.936245i	$0.385723\pi$
$444$	0	0
$445$	3045.00	0.324375
$446$	−3604.00	−0.382633
$447$	0	0
$448$	448.000	0.0472456
$449$	17172.0	1.80489	0.902446	−	0.430802i	$-0.141769\pi$
$449$	17172.0	1.80489	0.902446	+	0.430802i	$0.141769\pi$
$450$	0	0
$451$	−1323.00	−0.138132
$452$	−1404.00	−0.146103
$453$	0	0
$454$	66.0000	0.00682276
$455$	665.000	0.0685180
$456$	0	0
$457$	2684.00	0.274731	0.137366	−	0.990520i	$-0.456136\pi$
$457$	2684.00	0.274731	0.137366	+	0.990520i	$0.456136\pi$
$458$	−8620.00	−0.879446
$459$	0	0
$460$	−2520.00	−0.255425
$461$	−5835.00	−0.589508	−0.294754	−	0.955573i	$-0.595238\pi$
$461$	−5835.00	−0.589508	−0.294754	+	0.955573i	$0.595238\pi$
$462$	0	0
$463$	11873.0	1.19176	0.595880	−	0.803073i	$-0.296803\pi$
$463$	11873.0	1.19176	0.595880	+	0.803073i	$0.296803\pi$
$464$	1056.00	0.105654
$465$	0	0
$466$	−13674.0	−1.35930
$467$	−492.000	−0.0487517	−0.0243759	−	0.999703i	$-0.507760\pi$
$467$	−492.000	−0.0487517	−0.0243759	+	0.999703i	$0.507760\pi$
$468$	0	0
$469$	2135.00	0.210203
$470$	−2010.00	−0.197265
$471$	0	0
$472$	−4656.00	−0.454046
$473$	1251.00	0.121609
$474$	0	0
$475$	275.000	0.0265639
$476$	3024.00	0.291187
$477$	0	0
$478$	−10992.0	−1.05180
$479$	−13176.0	−1.25684	−0.628420	−	0.777874i	$-0.716298\pi$
$479$	−13176.0	−1.25684	−0.628420	+	0.777874i	$0.716298\pi$
$480$	0	0
$481$	6574.00	0.623178
$482$	368.000	0.0347758
$483$	0	0
$484$	−5000.00	−0.469572
$485$	−3430.00	−0.321130
$486$	0	0
$487$	11531.0	1.07294	0.536468	−	0.843921i	$-0.319758\pi$
$487$	11531.0	1.07294	0.536468	+	0.843921i	$0.319758\pi$
$488$	−2752.00	−0.255281
$489$	0	0
$490$	490.000	0.0451754
$491$	−18708.0	−1.71951	−0.859756	−	0.510705i	$-0.829384\pi$
$491$	−18708.0	−1.71951	−0.859756	+	0.510705i	$0.829384\pi$
$492$	0	0
$493$	7128.00	0.651174
$494$	418.000	0.0380703
$495$	0	0
$496$	−2368.00	−0.214368
$497$	6384.00	0.576180
$498$	0	0
$499$	2654.00	0.238095	0.119047	−	0.992889i	$-0.462016\pi$
$499$	2654.00	0.238095	0.119047	+	0.992889i	$0.462016\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	7980.00	0.709492
$503$	14421.0	1.27833	0.639166	−	0.769069i	$-0.279280\pi$
$503$	14421.0	1.27833	0.639166	+	0.769069i	$0.279280\pi$
$504$	0	0
$505$	−825.000	−0.0726971
$506$	2268.00	0.199259
$507$	0	0
$508$	6956.00	0.607525
$509$	3894.00	0.339093	0.169547	−	0.985522i	$-0.445770\pi$
$509$	3894.00	0.339093	0.169547	+	0.985522i	$0.445770\pi$
$510$	0	0
$511$	−1057.00	−0.0915047
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−888.000	−0.0762023
$515$	20.0000	0.00171127
$516$	0	0
$517$	1809.00	0.153887
$518$	4844.00	0.410875
$519$	0	0
$520$	−760.000	−0.0640927
$521$	12987.0	1.09207	0.546037	−	0.837761i	$-0.316136\pi$
$521$	12987.0	1.09207	0.546037	+	0.837761i	$0.316136\pi$
$522$	0	0
$523$	13862.0	1.15897	0.579487	−	0.814982i	$-0.303253\pi$
$523$	13862.0	1.15897	0.579487	+	0.814982i	$0.303253\pi$
$524$	1632.00	0.136058
$525$	0	0
$526$	−3624.00	−0.300407
$527$	−15984.0	−1.32120
$528$	0	0
$529$	3709.00	0.304841
$530$	−2490.00	−0.204073
$531$	0	0
$532$	308.000	0.0251006
$533$	−2793.00	−0.226976
$534$	0	0
$535$	−2220.00	−0.179400
$536$	−2440.00	−0.196627
$537$	0	0
$538$	−3540.00	−0.283681
$539$	−441.000	−0.0352416
$540$	0	0
$541$	−19627.0	−1.55976	−0.779880	−	0.625929i	$-0.784720\pi$
$541$	−19627.0	−1.55976	−0.779880	+	0.625929i	$0.784720\pi$
$542$	−7342.00	−0.581856
$543$	0	0
$544$	−3456.00	−0.272380
$545$	−3055.00	−0.240113
$546$	0	0
$547$	−7480.00	−0.584683	−0.292342	−	0.956314i	$-0.594434\pi$
$547$	−7480.00	−0.584683	−0.292342	+	0.956314i	$0.594434\pi$
$548$	4284.00	0.333948
$549$	0	0
$550$	450.000	0.0348874
$551$	726.000	0.0561318
$552$	0	0
$553$	−5824.00	−0.447851
$554$	−340.000	−0.0260744
$555$	0	0
$556$	−8080.00	−0.616310
$557$	10746.0	0.817455	0.408728	−	0.912656i	$-0.365973\pi$
$557$	10746.0	0.817455	0.408728	+	0.912656i	$0.365973\pi$
$558$	0	0
$559$	2641.00	0.199825
$560$	−560.000	−0.0422577
$561$	0	0
$562$	10404.0	0.780901
$563$	−24513.0	−1.83499	−0.917495	−	0.397746i	$-0.869792\pi$
$563$	−24513.0	−1.83499	−0.917495	+	0.397746i	$0.869792\pi$
$564$	0	0
$565$	1755.00	0.130679
$566$	−196.000	−0.0145556
$567$	0	0
$568$	−7296.00	−0.538967
$569$	−2238.00	−0.164889	−0.0824445	−	0.996596i	$-0.526273\pi$
$569$	−2238.00	−0.164889	−0.0824445	+	0.996596i	$0.526273\pi$
$570$	0	0
$571$	11000.0	0.806192	0.403096	−	0.915158i	$-0.367934\pi$
$571$	11000.0	0.806192	0.403096	+	0.915158i	$0.367934\pi$
$572$	684.000	0.0499991
$573$	0	0
$574$	−2058.00	−0.149650
$575$	3150.00	0.228459
$576$	0	0
$577$	16499.0	1.19040	0.595201	−	0.803577i	$-0.297072\pi$
$577$	16499.0	1.19040	0.595201	+	0.803577i	$0.297072\pi$
$578$	−13502.0	−0.971642
$579$	0	0
$580$	−1320.00	−0.0945000
$581$	−6111.00	−0.436363
$582$	0	0
$583$	2241.00	0.159199
$584$	1208.00	0.0855949
$585$	0	0
$586$	−17004.0	−1.19868
$587$	−4788.00	−0.336664	−0.168332	−	0.985730i	$-0.553838\pi$
$587$	−4788.00	−0.336664	−0.168332	+	0.985730i	$0.553838\pi$
$588$	0	0
$589$	−1628.00	−0.113889
$590$	5820.00	0.406111
$591$	0	0
$592$	−5536.00	−0.384338
$593$	13740.0	0.951491	0.475746	−	0.879583i	$-0.342178\pi$
$593$	13740.0	0.951491	0.475746	+	0.879583i	$0.342178\pi$
$594$	0	0
$595$	−3780.00	−0.260445
$596$	−4824.00	−0.331542
$597$	0	0
$598$	4788.00	0.327418
$599$	5253.00	0.358317	0.179158	−	0.983820i	$-0.442663\pi$
$599$	5253.00	0.358317	0.179158	+	0.983820i	$0.442663\pi$
$600$	0	0
$601$	−28504.0	−1.93461	−0.967306	−	0.253610i	$-0.918382\pi$
$601$	−28504.0	−1.93461	−0.967306	+	0.253610i	$0.918382\pi$
$602$	1946.00	0.131749
$603$	0	0
$604$	1880.00	0.126649
$605$	6250.00	0.419998
$606$	0	0
$607$	4466.00	0.298632	0.149316	−	0.988790i	$-0.452293\pi$
$607$	4466.00	0.298632	0.149316	+	0.988790i	$0.452293\pi$
$608$	−352.000	−0.0234794
$609$	0	0
$610$	3440.00	0.228330
$611$	3819.00	0.252864
$612$	0	0
$613$	2132.00	0.140474	0.0702371	−	0.997530i	$-0.477624\pi$
$613$	2132.00	0.140474	0.0702371	+	0.997530i	$0.477624\pi$
$614$	−136.000	−0.00893895
$615$	0	0
$616$	504.000	0.0329655
$617$	−486.000	−0.0317109	−0.0158554	−	0.999874i	$-0.505047\pi$
$617$	−486.000	−0.0317109	−0.0158554	+	0.999874i	$0.505047\pi$
$618$	0	0
$619$	9605.00	0.623679	0.311840	−	0.950135i	$-0.399055\pi$
$619$	9605.00	0.623679	0.311840	+	0.950135i	$0.399055\pi$
$620$	2960.00	0.191736
$621$	0	0
$622$	−16476.0	−1.06210
$623$	−4263.00	−0.274147
$624$	0	0
$625$	625.000	0.0400000
$626$	8114.00	0.518052
$627$	0	0
$628$	8936.00	0.567811
$629$	−37368.0	−2.36878
$630$	0	0
$631$	15638.0	0.986591	0.493296	−	0.869862i	$-0.335792\pi$
$631$	15638.0	0.986591	0.493296	+	0.869862i	$0.335792\pi$
$632$	6656.00	0.418926
$633$	0	0
$634$	8658.00	0.542355
$635$	−8695.00	−0.543387
$636$	0	0
$637$	−931.000	−0.0579083
$638$	1188.00	0.0737200
$639$	0	0
$640$	640.000	0.0395285
$641$	−18096.0	−1.11505	−0.557527	−	0.830159i	$-0.688250\pi$
$641$	−18096.0	−1.11505	−0.557527	+	0.830159i	$0.688250\pi$
$642$	0	0
$643$	13340.0	0.818162	0.409081	−	0.912498i	$-0.365849\pi$
$643$	13340.0	0.818162	0.409081	+	0.912498i	$0.365849\pi$
$644$	3528.00	0.215874
$645$	0	0
$646$	−2376.00	−0.144710
$647$	−18177.0	−1.10450	−0.552250	−	0.833679i	$-0.686231\pi$
$647$	−18177.0	−1.10450	−0.552250	+	0.833679i	$0.686231\pi$
$648$	0	0
$649$	−5238.00	−0.316810
$650$	950.000	0.0573263
$651$	0	0
$652$	2432.00	0.146080
$653$	3006.00	0.180144	0.0900719	−	0.995935i	$-0.471290\pi$
$653$	3006.00	0.180144	0.0900719	+	0.995935i	$0.471290\pi$
$654$	0	0
$655$	−2040.00	−0.121694
$656$	2352.00	0.139985
$657$	0	0
$658$	2814.00	0.166719
$659$	−5856.00	−0.346157	−0.173078	−	0.984908i	$-0.555371\pi$
$659$	−5856.00	−0.346157	−0.173078	+	0.984908i	$0.555371\pi$
$660$	0	0
$661$	21890.0	1.28808	0.644041	−	0.764991i	$-0.277257\pi$
$661$	21890.0	1.28808	0.644041	+	0.764991i	$0.277257\pi$
$662$	−18004.0	−1.05702
$663$	0	0
$664$	6984.00	0.408180
$665$	−385.000	−0.0224506
$666$	0	0
$667$	8316.00	0.482754
$668$	7344.00	0.425371
$669$	0	0
$670$	3050.00	0.175868
$671$	−3096.00	−0.178122
$672$	0	0
$673$	−25756.0	−1.47522	−0.737608	−	0.675229i	$-0.764045\pi$
$673$	−25756.0	−1.47522	−0.737608	+	0.675229i	$0.764045\pi$
$674$	−20416.0	−1.16676
$675$	0	0
$676$	−7344.00	−0.417843
$677$	−15570.0	−0.883905	−0.441953	−	0.897038i	$-0.645714\pi$
$677$	−15570.0	−0.883905	−0.441953	+	0.897038i	$0.645714\pi$
$678$	0	0
$679$	4802.00	0.271405
$680$	4320.00	0.243624
$681$	0	0
$682$	−2664.00	−0.149575
$683$	12762.0	0.714970	0.357485	−	0.933919i	$-0.383634\pi$
$683$	12762.0	0.714970	0.357485	+	0.933919i	$0.383634\pi$
$684$	0	0
$685$	−5355.00	−0.298692
$686$	−686.000	−0.0381802
$687$	0	0
$688$	−2224.00	−0.123240
$689$	4731.00	0.261592
$690$	0	0
$691$	−14965.0	−0.823872	−0.411936	−	0.911213i	$-0.635147\pi$
$691$	−14965.0	−0.823872	−0.411936	+	0.911213i	$0.635147\pi$
$692$	6504.00	0.357290
$693$	0	0
$694$	−5604.00	−0.306520
$695$	10100.0	0.551244
$696$	0	0
$697$	15876.0	0.862764
$698$	11828.0	0.641399
$699$	0	0
$700$	700.000	0.0377964
$701$	−28812.0	−1.55237	−0.776187	−	0.630503i	$-0.782849\pi$
$701$	−28812.0	−1.55237	−0.776187	+	0.630503i	$0.782849\pi$
$702$	0	0
$703$	−3806.00	−0.204191
$704$	−576.000	−0.0308364
$705$	0	0
$706$	−12744.0	−0.679358
$707$	1155.00	0.0614402
$708$	0	0
$709$	18821.0	0.996950	0.498475	−	0.866904i	$-0.333894\pi$
$709$	18821.0	0.996950	0.498475	+	0.866904i	$0.333894\pi$
$710$	9120.00	0.482067
$711$	0	0
$712$	4872.00	0.256441
$713$	−18648.0	−0.979485
$714$	0	0
$715$	−855.000	−0.0447205
$716$	2964.00	0.154707
$717$	0	0
$718$	−22746.0	−1.18227
$719$	−19116.0	−0.991525	−0.495763	−	0.868458i	$-0.665111\pi$
$719$	−19116.0	−0.991525	−0.495763	+	0.868458i	$0.665111\pi$
$720$	0	0
$721$	−28.0000	−0.00144629
$722$	13476.0	0.694633
$723$	0	0
$724$	−424.000	−0.0217650
$725$	1650.00	0.0845234
$726$	0	0
$727$	6452.00	0.329149	0.164575	−	0.986365i	$-0.447375\pi$
$727$	6452.00	0.329149	0.164575	+	0.986365i	$0.447375\pi$
$728$	1064.00	0.0541682
$729$	0	0
$730$	−1510.00	−0.0765584
$731$	−15012.0	−0.759561
$732$	0	0
$733$	23717.0	1.19510	0.597549	−	0.801832i	$-0.296141\pi$
$733$	23717.0	1.19510	0.597549	+	0.801832i	$0.296141\pi$
$734$	2876.00	0.144625
$735$	0	0
$736$	−4032.00	−0.201931
$737$	−2745.00	−0.137196
$738$	0	0
$739$	−19420.0	−0.966680	−0.483340	−	0.875433i	$-0.660576\pi$
$739$	−19420.0	−0.966680	−0.483340	+	0.875433i	$0.660576\pi$
$740$	6920.00	0.343763
$741$	0	0
$742$	3486.00	0.172473
$743$	35790.0	1.76717	0.883585	−	0.468270i	$-0.155123\pi$
$743$	35790.0	1.76717	0.883585	+	0.468270i	$0.155123\pi$
$744$	0	0
$745$	6030.00	0.296540
$746$	−25312.0	−1.24228
$747$	0	0
$748$	−3888.00	−0.190053
$749$	3108.00	0.151621
$750$	0	0
$751$	−8998.00	−0.437206	−0.218603	−	0.975814i	$-0.570150\pi$
$751$	−8998.00	−0.437206	−0.218603	+	0.975814i	$0.570150\pi$
$752$	−3216.00	−0.155951
$753$	0	0
$754$	2508.00	0.121135
$755$	−2350.00	−0.113278
$756$	0	0
$757$	−27232.0	−1.30748	−0.653741	−	0.756718i	$-0.726801\pi$
$757$	−27232.0	−1.30748	−0.653741	+	0.756718i	$0.726801\pi$
$758$	−520.000	−0.0249172
$759$	0	0
$760$	440.000	0.0210006
$761$	−20430.0	−0.973176	−0.486588	−	0.873632i	$-0.661759\pi$
$761$	−20430.0	−0.973176	−0.486588	+	0.873632i	$0.661759\pi$
$762$	0	0
$763$	4277.00	0.202933
$764$	−4932.00	−0.233552
$765$	0	0
$766$	16944.0	0.799232
$767$	−11058.0	−0.520575
$768$	0	0
$769$	−3796.00	−0.178007	−0.0890034	−	0.996031i	$-0.528368\pi$
$769$	−3796.00	−0.178007	−0.0890034	+	0.996031i	$0.528368\pi$
$770$	−630.000	−0.0294852
$771$	0	0
$772$	2312.00	0.107786
$773$	16134.0	0.750711	0.375356	−	0.926881i	$-0.377521\pi$
$773$	16134.0	0.750711	0.375356	+	0.926881i	$0.377521\pi$
$774$	0	0
$775$	−3700.00	−0.171494
$776$	−5488.00	−0.253876
$777$	0	0
$778$	−4596.00	−0.211793
$779$	1617.00	0.0743710
$780$	0	0
$781$	−8208.00	−0.376063
$782$	−27216.0	−1.24456
$783$	0	0
$784$	784.000	0.0357143
$785$	−11170.0	−0.507865
$786$	0	0
$787$	40448.0	1.83204	0.916020	−	0.401133i	$-0.131383\pi$
$787$	40448.0	1.83204	0.916020	+	0.401133i	$0.131383\pi$
$788$	8148.00	0.368351
$789$	0	0
$790$	−8320.00	−0.374699
$791$	−2457.00	−0.110444
$792$	0	0
$793$	−6536.00	−0.292686
$794$	−5932.00	−0.265137
$795$	0	0
$796$	−268.000	−0.0119334
$797$	−41364.0	−1.83838	−0.919189	−	0.393816i	$-0.871155\pi$
$797$	−41364.0	−1.83838	−0.919189	+	0.393816i	$0.871155\pi$
$798$	0	0
$799$	−21708.0	−0.961169
$800$	−800.000	−0.0353553
$801$	0	0
$802$	−24696.0	−1.08734
$803$	1359.00	0.0597236
$804$	0	0
$805$	−4410.00	−0.193083
$806$	−5624.00	−0.245778
$807$	0	0
$808$	−1320.00	−0.0574721
$809$	16770.0	0.728803	0.364402	−	0.931242i	$-0.381274\pi$
$809$	16770.0	0.728803	0.364402	+	0.931242i	$0.381274\pi$
$810$	0	0
$811$	−42685.0	−1.84818	−0.924089	−	0.382176i	$-0.875175\pi$
$811$	−42685.0	−1.84818	−0.924089	+	0.382176i	$0.875175\pi$
$812$	1848.00	0.0798671
$813$	0	0
$814$	−6228.00	−0.268171
$815$	−3040.00	−0.130658
$816$	0	0
$817$	−1529.00	−0.0654748
$818$	−21364.0	−0.913172
$819$	0	0
$820$	−2940.00	−0.125206
$821$	−5070.00	−0.215523	−0.107761	−	0.994177i	$-0.534368\pi$
$821$	−5070.00	−0.215523	−0.107761	+	0.994177i	$0.534368\pi$
$822$	0	0
$823$	−15187.0	−0.643239	−0.321619	−	0.946869i	$-0.604227\pi$
$823$	−15187.0	−0.643239	−0.321619	+	0.946869i	$0.604227\pi$
$824$	32.0000	0.00135288
$825$	0	0
$826$	−8148.00	−0.343227
$827$	−1236.00	−0.0519709	−0.0259854	−	0.999662i	$-0.508272\pi$
$827$	−1236.00	−0.0519709	−0.0259854	+	0.999662i	$0.508272\pi$
$828$	0	0
$829$	−4660.00	−0.195233	−0.0976167	−	0.995224i	$-0.531122\pi$
$829$	−4660.00	−0.195233	−0.0976167	+	0.995224i	$0.531122\pi$
$830$	−8730.00	−0.365088
$831$	0	0
$832$	−1216.00	−0.0506697
$833$	5292.00	0.220116
$834$	0	0
$835$	−9180.00	−0.380463
$836$	−396.000	−0.0163827
$837$	0	0
$838$	2892.00	0.119215
$839$	−114.000	−0.00469096	−0.00234548	−	0.999997i	$-0.500747\pi$
$839$	−114.000	−0.00469096	−0.00234548	+	0.999997i	$0.500747\pi$
$840$	0	0
$841$	−20033.0	−0.821395
$842$	7898.00	0.323258
$843$	0	0
$844$	−14200.0	−0.579128
$845$	9180.00	0.373730
$846$	0	0
$847$	−8750.00	−0.354963
$848$	−3984.00	−0.161334
$849$	0	0
$850$	−5400.00	−0.217904
$851$	−43596.0	−1.75611
$852$	0	0
$853$	−31498.0	−1.26433	−0.632164	−	0.774835i	$-0.717833\pi$
$853$	−31498.0	−1.26433	−0.632164	+	0.774835i	$0.717833\pi$
$854$	−4816.00	−0.192974
$855$	0	0
$856$	−3552.00	−0.141828
$857$	−25314.0	−1.00900	−0.504498	−	0.863413i	$-0.668322\pi$
$857$	−25314.0	−1.00900	−0.504498	+	0.863413i	$0.668322\pi$
$858$	0	0
$859$	26387.0	1.04809	0.524047	−	0.851689i	$-0.324422\pi$
$859$	26387.0	1.04809	0.524047	+	0.851689i	$0.324422\pi$
$860$	2780.00	0.110229
$861$	0	0
$862$	1002.00	0.0395919
$863$	26370.0	1.04015	0.520073	−	0.854122i	$-0.325905\pi$
$863$	26370.0	1.04015	0.520073	+	0.854122i	$0.325905\pi$
$864$	0	0
$865$	−8130.00	−0.319570
$866$	314.000	0.0123212
$867$	0	0
$868$	−4144.00	−0.162047
$869$	7488.00	0.292305
$870$	0	0
$871$	−5795.00	−0.225438
$872$	−4888.00	−0.189826
$873$	0	0
$874$	−2772.00	−0.107282
$875$	−875.000	−0.0338062
$876$	0	0
$877$	−232.000	−0.00893282	−0.00446641	−	0.999990i	$-0.501422\pi$
$877$	−232.000	−0.00893282	−0.00446641	+	0.999990i	$0.501422\pi$
$878$	482.000	0.0185270
$879$	0	0
$880$	720.000	0.0275809
$881$	−37590.0	−1.43750	−0.718751	−	0.695268i	$-0.755286\pi$
$881$	−37590.0	−1.43750	−0.718751	+	0.695268i	$0.755286\pi$
$882$	0	0
$883$	15212.0	0.579756	0.289878	−	0.957064i	$-0.406385\pi$
$883$	15212.0	0.579756	0.289878	+	0.957064i	$0.406385\pi$
$884$	−8208.00	−0.312291
$885$	0	0
$886$	−13104.0	−0.496882
$887$	−34605.0	−1.30995	−0.654973	−	0.755652i	$-0.727320\pi$
$887$	−34605.0	−1.30995	−0.654973	+	0.755652i	$0.727320\pi$
$888$	0	0
$889$	12173.0	0.459246
$890$	−6090.00	−0.229368
$891$	0	0
$892$	7208.00	0.270562
$893$	−2211.00	−0.0828536
$894$	0	0
$895$	−3705.00	−0.138374
$896$	−896.000	−0.0334077
$897$	0	0
$898$	−34344.0	−1.27625
$899$	−9768.00	−0.362382
$900$	0	0
$901$	−26892.0	−0.994342
$902$	2646.00	0.0976742
$903$	0	0
$904$	2808.00	0.103310
$905$	530.000	0.0194672
$906$	0	0
$907$	4541.00	0.166242	0.0831210	−	0.996539i	$-0.473511\pi$
$907$	4541.00	0.166242	0.0831210	+	0.996539i	$0.473511\pi$
$908$	−132.000	−0.00482442
$909$	0	0
$910$	−1330.00	−0.0484495
$911$	51405.0	1.86951	0.934755	−	0.355293i	$-0.115619\pi$
$911$	51405.0	1.86951	0.934755	+	0.355293i	$0.115619\pi$
$912$	0	0
$913$	7857.00	0.284807
$914$	−5368.00	−0.194264
$915$	0	0
$916$	17240.0	0.621862
$917$	2856.00	0.102850
$918$	0	0
$919$	15800.0	0.567132	0.283566	−	0.958953i	$-0.408483\pi$
$919$	15800.0	0.567132	0.283566	+	0.958953i	$0.408483\pi$
$920$	5040.00	0.180613
$921$	0	0
$922$	11670.0	0.416845
$923$	−17328.0	−0.617939
$924$	0	0
$925$	−8650.00	−0.307471
$926$	−23746.0	−0.842702
$927$	0	0
$928$	−2112.00	−0.0747088
$929$	18741.0	0.661865	0.330932	−	0.943654i	$-0.392637\pi$
$929$	18741.0	0.661865	0.330932	+	0.943654i	$0.392637\pi$
$930$	0	0
$931$	539.000	0.0189742
$932$	27348.0	0.961173
$933$	0	0
$934$	984.000	0.0344727
$935$	4860.00	0.169988
$936$	0	0
$937$	44921.0	1.56617	0.783087	−	0.621912i	$-0.213644\pi$
$937$	44921.0	1.56617	0.783087	+	0.621912i	$0.213644\pi$
$938$	−4270.00	−0.148636
$939$	0	0
$940$	4020.00	0.139487
$941$	−12333.0	−0.427252	−0.213626	−	0.976915i	$-0.568527\pi$
$941$	−12333.0	−0.427252	−0.213626	+	0.976915i	$0.568527\pi$
$942$	0	0
$943$	18522.0	0.639618
$944$	9312.00	0.321059
$945$	0	0
$946$	−2502.00	−0.0859905
$947$	7716.00	0.264769	0.132385	−	0.991198i	$-0.457737\pi$
$947$	7716.00	0.264769	0.132385	+	0.991198i	$0.457737\pi$
$948$	0	0
$949$	2869.00	0.0981367
$950$	−550.000	−0.0187835
$951$	0	0
$952$	−6048.00	−0.205900
$953$	−12846.0	−0.436645	−0.218323	−	0.975877i	$-0.570058\pi$
$953$	−12846.0	−0.436645	−0.218323	+	0.975877i	$0.570058\pi$
$954$	0	0
$955$	6165.00	0.208895
$956$	21984.0	0.743738
$957$	0	0
$958$	26352.0	0.888721
$959$	7497.00	0.252441
$960$	0	0
$961$	−7887.00	−0.264744
$962$	−13148.0	−0.440653
$963$	0	0
$964$	−736.000	−0.0245902
$965$	−2890.00	−0.0964066
$966$	0	0
$967$	6341.00	0.210872	0.105436	−	0.994426i	$-0.466376\pi$
$967$	6341.00	0.210872	0.105436	+	0.994426i	$0.466376\pi$
$968$	10000.0	0.332037
$969$	0	0
$970$	6860.00	0.227074
$971$	14940.0	0.493767	0.246883	−	0.969045i	$-0.420594\pi$
$971$	14940.0	0.493767	0.246883	+	0.969045i	$0.420594\pi$
$972$	0	0
$973$	−14140.0	−0.465887
$974$	−23062.0	−0.758680
$975$	0	0
$976$	5504.00	0.180511
$977$	−19983.0	−0.654363	−0.327182	−	0.944961i	$-0.606099\pi$
$977$	−19983.0	−0.654363	−0.327182	+	0.944961i	$0.606099\pi$
$978$	0	0
$979$	5481.00	0.178931
$980$	−980.000	−0.0319438
$981$	0	0
$982$	37416.0	1.21588
$983$	4752.00	0.154186	0.0770932	−	0.997024i	$-0.475436\pi$
$983$	4752.00	0.154186	0.0770932	+	0.997024i	$0.475436\pi$
$984$	0	0
$985$	−10185.0	−0.329463
$986$	−14256.0	−0.460450
$987$	0	0
$988$	−836.000	−0.0269197
$989$	−17514.0	−0.563107
$990$	0	0
$991$	−39904.0	−1.27910	−0.639552	−	0.768748i	$-0.720880\pi$
$991$	−39904.0	−1.27910	−0.639552	+	0.768748i	$0.720880\pi$
$992$	4736.00	0.151581
$993$	0	0
$994$	−12768.0	−0.407421
$995$	335.000	0.0106736
$996$	0	0
$997$	6626.00	0.210479	0.105239	−	0.994447i	$-0.466439\pi$
$997$	6626.00	0.210479	0.105239	+	0.994447i	$0.466439\pi$
$998$	−5308.00	−0.168359
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.4.a.e.1.1	✓	1
3.2	odd	2		1890.4.a.m.1.1	yes	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.4.a.e.1.1	✓	1	1.1	even	1	trivial
1890.4.a.m.1.1	yes	1	3.2	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:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1890.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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