LMFDB - Embedded newform 1890.4.a.g.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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} +7.00000 q^{7} -8.00000 q^{8} -10.0000 q^{10} +18.0000 q^{11} +35.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +57.0000 q^{17} +104.000 q^{19} +20.0000 q^{20} -36.0000 q^{22} +171.000 q^{23} +25.0000 q^{25} -70.0000 q^{26} +28.0000 q^{28} +165.000 q^{29} -313.000 q^{31} -32.0000 q^{32} -114.000 q^{34} +35.0000 q^{35} +128.000 q^{37} -208.000 q^{38} -40.0000 q^{40} +114.000 q^{41} +47.0000 q^{43} +72.0000 q^{44} -342.000 q^{46} -174.000 q^{47} +49.0000 q^{49} -50.0000 q^{50} +140.000 q^{52} -291.000 q^{53} +90.0000 q^{55} -56.0000 q^{56} -330.000 q^{58} -21.0000 q^{59} +86.0000 q^{61} +626.000 q^{62} +64.0000 q^{64} +175.000 q^{65} +1067.00 q^{67} +228.000 q^{68} -70.0000 q^{70} +135.000 q^{71} -1066.00 q^{73} -256.000 q^{74} +416.000 q^{76} +126.000 q^{77} -220.000 q^{79} +80.0000 q^{80} -228.000 q^{82} +1020.00 q^{83} +285.000 q^{85} -94.0000 q^{86} -144.000 q^{88} +51.0000 q^{89} +245.000 q^{91} +684.000 q^{92} +348.000 q^{94} +520.000 q^{95} -1846.00 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
$11$	18.0000	0.493382	0.246691	−	0.969094i	$-0.420657\pi$
$11$	18.0000	0.493382	0.246691	+	0.969094i	$0.420657\pi$
$12$	0	0
$13$	35.0000	0.746712	0.373356	−	0.927688i	$-0.378207\pi$
$13$	35.0000	0.746712	0.373356	+	0.927688i	$0.378207\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	57.0000	0.813208	0.406604	−	0.913605i	$-0.366713\pi$
$17$	57.0000	0.813208	0.406604	+	0.913605i	$0.366713\pi$
$18$	0	0
$19$	104.000	1.25575	0.627875	−	0.778314i	$-0.283925\pi$
$19$	104.000	1.25575	0.627875	+	0.778314i	$0.283925\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−36.0000	−0.348874
$23$	171.000	1.55026	0.775130	−	0.631802i	$-0.217684\pi$
$23$	171.000	1.55026	0.775130	+	0.631802i	$0.217684\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	−70.0000	−0.528005
$27$	0	0
$28$	28.0000	0.188982
$29$	165.000	1.05654	0.528271	−	0.849076i	$-0.322840\pi$
$29$	165.000	1.05654	0.528271	+	0.849076i	$0.322840\pi$
$30$	0	0
$31$	−313.000	−1.81343	−0.906717	−	0.421739i	$-0.861420\pi$
$31$	−313.000	−1.81343	−0.906717	+	0.421739i	$0.861420\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−114.000	−0.575025
$35$	35.0000	0.169031
$36$	0	0
$37$	128.000	0.568732	0.284366	−	0.958716i	$-0.408217\pi$
$37$	128.000	0.568732	0.284366	+	0.958716i	$0.408217\pi$
$38$	−208.000	−0.887949
$39$	0	0
$40$	−40.0000	−0.158114
$41$	114.000	0.434239	0.217120	−	0.976145i	$-0.430334\pi$
$41$	114.000	0.434239	0.217120	+	0.976145i	$0.430334\pi$
$42$	0	0
$43$	47.0000	0.166684	0.0833422	−	0.996521i	$-0.473441\pi$
$43$	47.0000	0.166684	0.0833422	+	0.996521i	$0.473441\pi$
$44$	72.0000	0.246691
$45$	0	0
$46$	−342.000	−1.09620
$47$	−174.000	−0.540011	−0.270005	−	0.962859i	$-0.587025\pi$
$47$	−174.000	−0.540011	−0.270005	+	0.962859i	$0.587025\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	0	0
$52$	140.000	0.373356
$53$	−291.000	−0.754187	−0.377094	−	0.926175i	$-0.623077\pi$
$53$	−291.000	−0.754187	−0.377094	+	0.926175i	$0.623077\pi$
$54$	0	0
$55$	90.0000	0.220647
$56$	−56.0000	−0.133631
$57$	0	0
$58$	−330.000	−0.747088
$59$	−21.0000	−0.0463384	−0.0231692	−	0.999732i	$-0.507376\pi$
$59$	−21.0000	−0.0463384	−0.0231692	+	0.999732i	$0.507376\pi$
$60$	0	0
$61$	86.0000	0.180511	0.0902555	−	0.995919i	$-0.471232\pi$
$61$	86.0000	0.180511	0.0902555	+	0.995919i	$0.471232\pi$
$62$	626.000	1.28229
$63$	0	0
$64$	64.0000	0.125000
$65$	175.000	0.333940
$66$	0	0
$67$	1067.00	1.94559	0.972797	−	0.231659i	$-0.0744154\pi$
$67$	1067.00	1.94559	0.972797	+	0.231659i	$0.0744154\pi$
$68$	228.000	0.406604
$69$	0	0
$70$	−70.0000	−0.119523
$71$	135.000	0.225656	0.112828	−	0.993615i	$-0.464009\pi$
$71$	135.000	0.225656	0.112828	+	0.993615i	$0.464009\pi$
$72$	0	0
$73$	−1066.00	−1.70912	−0.854561	−	0.519352i	$-0.826174\pi$
$73$	−1066.00	−1.70912	−0.854561	+	0.519352i	$0.826174\pi$
$74$	−256.000	−0.402154
$75$	0	0
$76$	416.000	0.627875
$77$	126.000	0.186481
$78$	0	0
$79$	−220.000	−0.313316	−0.156658	−	0.987653i	$-0.550072\pi$
$79$	−220.000	−0.313316	−0.156658	+	0.987653i	$0.550072\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	−228.000	−0.307054
$83$	1020.00	1.34891	0.674455	−	0.738316i	$-0.264379\pi$
$83$	1020.00	1.34891	0.674455	+	0.738316i	$0.264379\pi$
$84$	0	0
$85$	285.000	0.363678
$86$	−94.0000	−0.117864
$87$	0	0
$88$	−144.000	−0.174437
$89$	51.0000	0.0607415	0.0303707	−	0.999539i	$-0.490331\pi$
$89$	51.0000	0.0607415	0.0303707	+	0.999539i	$0.490331\pi$
$90$	0	0
$91$	245.000	0.282231
$92$	684.000	0.775130
$93$	0	0
$94$	348.000	0.381845
$95$	520.000	0.561588
$96$	0	0
$97$	−1846.00	−1.93230	−0.966149	−	0.257985i	$-0.916942\pi$
$97$	−1846.00	−1.93230	−0.966149	+	0.257985i	$0.916942\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	372.000	0.366489	0.183244	−	0.983067i	$-0.441340\pi$
$101$	372.000	0.366489	0.183244	+	0.983067i	$0.441340\pi$
$102$	0	0
$103$	−397.000	−0.379782	−0.189891	−	0.981805i	$-0.560814\pi$
$103$	−397.000	−0.379782	−0.189891	+	0.981805i	$0.560814\pi$
$104$	−280.000	−0.264002
$105$	0	0
$106$	582.000	0.533291
$107$	390.000	0.352362	0.176181	−	0.984358i	$-0.443626\pi$
$107$	390.000	0.352362	0.176181	+	0.984358i	$0.443626\pi$
$108$	0	0
$109$	410.000	0.360283	0.180142	−	0.983641i	$-0.442344\pi$
$109$	410.000	0.360283	0.180142	+	0.983641i	$0.442344\pi$
$110$	−180.000	−0.156021
$111$	0	0
$112$	112.000	0.0944911
$113$	1314.00	1.09390	0.546950	−	0.837165i	$-0.315789\pi$
$113$	1314.00	1.09390	0.546950	+	0.837165i	$0.315789\pi$
$114$	0	0
$115$	855.000	0.693297
$116$	660.000	0.528271
$117$	0	0
$118$	42.0000	0.0327662
$119$	399.000	0.307364
$120$	0	0
$121$	−1007.00	−0.756574
$122$	−172.000	−0.127641
$123$	0	0
$124$	−1252.00	−0.906717
$125$	125.000	0.0894427
$126$	0	0
$127$	−2404.00	−1.67969	−0.839845	−	0.542827i	$-0.817354\pi$
$127$	−2404.00	−1.67969	−0.839845	+	0.542827i	$0.817354\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−350.000	−0.236131
$131$	−951.000	−0.634269	−0.317135	−	0.948381i	$-0.602721\pi$
$131$	−951.000	−0.634269	−0.317135	+	0.948381i	$0.602721\pi$
$132$	0	0
$133$	728.000	0.474629
$134$	−2134.00	−1.37574
$135$	0	0
$136$	−456.000	−0.287512
$137$	−1734.00	−1.08135	−0.540677	−	0.841230i	$-0.681832\pi$
$137$	−1734.00	−1.08135	−0.540677	+	0.841230i	$0.681832\pi$
$138$	0	0
$139$	−124.000	−0.0756658	−0.0378329	−	0.999284i	$-0.512045\pi$
$139$	−124.000	−0.0756658	−0.0378329	+	0.999284i	$0.512045\pi$
$140$	140.000	0.0845154
$141$	0	0
$142$	−270.000	−0.159563
$143$	630.000	0.368414
$144$	0	0
$145$	825.000	0.472500
$146$	2132.00	1.20853
$147$	0	0
$148$	512.000	0.284366
$149$	2673.00	1.46967	0.734835	−	0.678246i	$-0.237260\pi$
$149$	2673.00	1.46967	0.734835	+	0.678246i	$0.237260\pi$
$150$	0	0
$151$	−1156.00	−0.623006	−0.311503	−	0.950245i	$-0.600832\pi$
$151$	−1156.00	−0.623006	−0.311503	+	0.950245i	$0.600832\pi$
$152$	−832.000	−0.443974
$153$	0	0
$154$	−252.000	−0.131862
$155$	−1565.00	−0.810992
$156$	0	0
$157$	1241.00	0.630844	0.315422	−	0.948951i	$-0.397854\pi$
$157$	1241.00	0.630844	0.315422	+	0.948951i	$0.397854\pi$
$158$	440.000	0.221548
$159$	0	0
$160$	−160.000	−0.0790569
$161$	1197.00	0.585943
$162$	0	0
$163$	−2041.00	−0.980757	−0.490379	−	0.871509i	$-0.663142\pi$
$163$	−2041.00	−0.980757	−0.490379	+	0.871509i	$0.663142\pi$
$164$	456.000	0.217120
$165$	0	0
$166$	−2040.00	−0.953824
$167$	−474.000	−0.219636	−0.109818	−	0.993952i	$-0.535027\pi$
$167$	−474.000	−0.219636	−0.109818	+	0.993952i	$0.535027\pi$
$168$	0	0
$169$	−972.000	−0.442421
$170$	−570.000	−0.257159
$171$	0	0
$172$	188.000	0.0833422
$173$	822.000	0.361246	0.180623	−	0.983552i	$-0.442189\pi$
$173$	822.000	0.361246	0.180623	+	0.983552i	$0.442189\pi$
$174$	0	0
$175$	175.000	0.0755929
$176$	288.000	0.123346
$177$	0	0
$178$	−102.000	−0.0429507
$179$	180.000	0.0751611	0.0375805	−	0.999294i	$-0.488035\pi$
$179$	180.000	0.0751611	0.0375805	+	0.999294i	$0.488035\pi$
$180$	0	0
$181$	3953.00	1.62334	0.811669	−	0.584118i	$-0.198559\pi$
$181$	3953.00	1.62334	0.811669	+	0.584118i	$0.198559\pi$
$182$	−490.000	−0.199567
$183$	0	0
$184$	−1368.00	−0.548099
$185$	640.000	0.254345
$186$	0	0
$187$	1026.00	0.401222
$188$	−696.000	−0.270005
$189$	0	0
$190$	−1040.00	−0.397103
$191$	3600.00	1.36381	0.681903	−	0.731443i	$-0.261153\pi$
$191$	3600.00	1.36381	0.681903	+	0.731443i	$0.261153\pi$
$192$	0	0
$193$	−385.000	−0.143590	−0.0717951	−	0.997419i	$-0.522873\pi$
$193$	−385.000	−0.143590	−0.0717951	+	0.997419i	$0.522873\pi$
$194$	3692.00	1.36634
$195$	0	0
$196$	196.000	0.0714286
$197$	−1530.00	−0.553340	−0.276670	−	0.960965i	$-0.589231\pi$
$197$	−1530.00	−0.553340	−0.276670	+	0.960965i	$0.589231\pi$
$198$	0	0
$199$	1193.00	0.424973	0.212486	−	0.977164i	$-0.431844\pi$
$199$	1193.00	0.424973	0.212486	+	0.977164i	$0.431844\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	−744.000	−0.259147
$203$	1155.00	0.399336
$204$	0	0
$205$	570.000	0.194198
$206$	794.000	0.268547
$207$	0	0
$208$	560.000	0.186678
$209$	1872.00	0.619564
$210$	0	0
$211$	−4999.00	−1.63102	−0.815510	−	0.578743i	$-0.803544\pi$
$211$	−4999.00	−1.63102	−0.815510	+	0.578743i	$0.803544\pi$
$212$	−1164.00	−0.377094
$213$	0	0
$214$	−780.000	−0.249157
$215$	235.000	0.0745436
$216$	0	0
$217$	−2191.00	−0.685414
$218$	−820.000	−0.254759
$219$	0	0
$220$	360.000	0.110324
$221$	1995.00	0.607232
$222$	0	0
$223$	392.000	0.117714	0.0588571	−	0.998266i	$-0.481254\pi$
$223$	392.000	0.117714	0.0588571	+	0.998266i	$0.481254\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−2628.00	−0.773504
$227$	537.000	0.157013	0.0785065	−	0.996914i	$-0.474985\pi$
$227$	537.000	0.157013	0.0785065	+	0.996914i	$0.474985\pi$
$228$	0	0
$229$	−3178.00	−0.917066	−0.458533	−	0.888677i	$-0.651625\pi$
$229$	−3178.00	−0.917066	−0.458533	+	0.888677i	$0.651625\pi$
$230$	−1710.00	−0.490235
$231$	0	0
$232$	−1320.00	−0.373544
$233$	−6162.00	−1.73256	−0.866279	−	0.499560i	$-0.833495\pi$
$233$	−6162.00	−1.73256	−0.866279	+	0.499560i	$0.833495\pi$
$234$	0	0
$235$	−870.000	−0.241500
$236$	−84.0000	−0.0231692
$237$	0	0
$238$	−798.000	−0.217339
$239$	216.000	0.0584597	0.0292299	−	0.999573i	$-0.490695\pi$
$239$	216.000	0.0584597	0.0292299	+	0.999573i	$0.490695\pi$
$240$	0	0
$241$	3836.00	1.02530	0.512652	−	0.858596i	$-0.328663\pi$
$241$	3836.00	1.02530	0.512652	+	0.858596i	$0.328663\pi$
$242$	2014.00	0.534979
$243$	0	0
$244$	344.000	0.0902555
$245$	245.000	0.0638877
$246$	0	0
$247$	3640.00	0.937683
$248$	2504.00	0.641146
$249$	0	0
$250$	−250.000	−0.0632456
$251$	1272.00	0.319872	0.159936	−	0.987127i	$-0.448871\pi$
$251$	1272.00	0.319872	0.159936	+	0.987127i	$0.448871\pi$
$252$	0	0
$253$	3078.00	0.764870
$254$	4808.00	1.18772
$255$	0	0
$256$	256.000	0.0625000
$257$	5754.00	1.39659	0.698297	−	0.715808i	$-0.253941\pi$
$257$	5754.00	1.39659	0.698297	+	0.715808i	$0.253941\pi$
$258$	0	0
$259$	896.000	0.214960
$260$	700.000	0.166970
$261$	0	0
$262$	1902.00	0.448496
$263$	3501.00	0.820840	0.410420	−	0.911897i	$-0.365382\pi$
$263$	3501.00	0.820840	0.410420	+	0.911897i	$0.365382\pi$
$264$	0	0
$265$	−1455.00	−0.337283
$266$	−1456.00	−0.335613
$267$	0	0
$268$	4268.00	0.972797
$269$	−180.000	−0.0407985	−0.0203992	−	0.999792i	$-0.506494\pi$
$269$	−180.000	−0.0407985	−0.0203992	+	0.999792i	$0.506494\pi$
$270$	0	0
$271$	−3625.00	−0.812557	−0.406279	−	0.913749i	$-0.633174\pi$
$271$	−3625.00	−0.812557	−0.406279	+	0.913749i	$0.633174\pi$
$272$	912.000	0.203302
$273$	0	0
$274$	3468.00	0.764633
$275$	450.000	0.0986764
$276$	0	0
$277$	−3196.00	−0.693246	−0.346623	−	0.938005i	$-0.612672\pi$
$277$	−3196.00	−0.693246	−0.346623	+	0.938005i	$0.612672\pi$
$278$	248.000	0.0535038
$279$	0	0
$280$	−280.000	−0.0597614
$281$	9060.00	1.92340	0.961698	−	0.274111i	$-0.0883836\pi$
$281$	9060.00	1.92340	0.961698	+	0.274111i	$0.0883836\pi$
$282$	0	0
$283$	2078.00	0.436482	0.218241	−	0.975895i	$-0.429968\pi$
$283$	2078.00	0.436482	0.218241	+	0.975895i	$0.429968\pi$
$284$	540.000	0.112828
$285$	0	0
$286$	−1260.00	−0.260508
$287$	798.000	0.164127
$288$	0	0
$289$	−1664.00	−0.338693
$290$	−1650.00	−0.334108
$291$	0	0
$292$	−4264.00	−0.854561
$293$	−8322.00	−1.65931	−0.829653	−	0.558280i	$-0.811461\pi$
$293$	−8322.00	−1.65931	−0.829653	+	0.558280i	$0.811461\pi$
$294$	0	0
$295$	−105.000	−0.0207232
$296$	−1024.00	−0.201077
$297$	0	0
$298$	−5346.00	−1.03921
$299$	5985.00	1.15760
$300$	0	0
$301$	329.000	0.0630008
$302$	2312.00	0.440532
$303$	0	0
$304$	1664.00	0.313937
$305$	430.000	0.0807270
$306$	0	0
$307$	2360.00	0.438737	0.219369	−	0.975642i	$-0.429600\pi$
$307$	2360.00	0.438737	0.219369	+	0.975642i	$0.429600\pi$
$308$	504.000	0.0932405
$309$	0	0
$310$	3130.00	0.573458
$311$	−5598.00	−1.02069	−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−5598.00	−1.02069	−0.510343	+	0.859971i	$0.670482\pi$
$312$	0	0
$313$	5780.00	1.04379	0.521893	−	0.853011i	$-0.325226\pi$
$313$	5780.00	1.04379	0.521893	+	0.853011i	$0.325226\pi$
$314$	−2482.00	−0.446074
$315$	0	0
$316$	−880.000	−0.156658
$317$	10254.0	1.81679	0.908394	−	0.418114i	$-0.137309\pi$
$317$	10254.0	1.81679	0.908394	+	0.418114i	$0.137309\pi$
$318$	0	0
$319$	2970.00	0.521279
$320$	320.000	0.0559017
$321$	0	0
$322$	−2394.00	−0.414324
$323$	5928.00	1.02118
$324$	0	0
$325$	875.000	0.149342
$326$	4082.00	0.693500
$327$	0	0
$328$	−912.000	−0.153527
$329$	−1218.00	−0.204105
$330$	0	0
$331$	9215.00	1.53022	0.765109	−	0.643901i	$-0.222685\pi$
$331$	9215.00	1.53022	0.765109	+	0.643901i	$0.222685\pi$
$332$	4080.00	0.674455
$333$	0	0
$334$	948.000	0.155306
$335$	5335.00	0.870096
$336$	0	0
$337$	−7171.00	−1.15914	−0.579569	−	0.814923i	$-0.696779\pi$
$337$	−7171.00	−1.15914	−0.579569	+	0.814923i	$0.696779\pi$
$338$	1944.00	0.312839
$339$	0	0
$340$	1140.00	0.181839
$341$	−5634.00	−0.894716
$342$	0	0
$343$	343.000	0.0539949
$344$	−376.000	−0.0589319
$345$	0	0
$346$	−1644.00	−0.255439
$347$	3486.00	0.539303	0.269652	−	0.962958i	$-0.413091\pi$
$347$	3486.00	0.539303	0.269652	+	0.962958i	$0.413091\pi$
$348$	0	0
$349$	8939.00	1.37104	0.685521	−	0.728053i	$-0.259574\pi$
$349$	8939.00	1.37104	0.685521	+	0.728053i	$0.259574\pi$
$350$	−350.000	−0.0534522
$351$	0	0
$352$	−576.000	−0.0872185
$353$	−1773.00	−0.267329	−0.133665	−	0.991027i	$-0.542675\pi$
$353$	−1773.00	−0.267329	−0.133665	+	0.991027i	$0.542675\pi$
$354$	0	0
$355$	675.000	0.100916
$356$	204.000	0.0303707
$357$	0	0
$358$	−360.000	−0.0531469
$359$	6543.00	0.961912	0.480956	−	0.876745i	$-0.340290\pi$
$359$	6543.00	0.961912	0.480956	+	0.876745i	$0.340290\pi$
$360$	0	0
$361$	3957.00	0.576906
$362$	−7906.00	−1.14787
$363$	0	0
$364$	980.000	0.141115
$365$	−5330.00	−0.764342
$366$	0	0
$367$	13061.0	1.85771	0.928854	−	0.370447i	$-0.120795\pi$
$367$	13061.0	1.85771	0.928854	+	0.370447i	$0.120795\pi$
$368$	2736.00	0.387565
$369$	0	0
$370$	−1280.00	−0.179849
$371$	−2037.00	−0.285056
$372$	0	0
$373$	−220.000	−0.0305393	−0.0152697	−	0.999883i	$-0.504861\pi$
$373$	−220.000	−0.0305393	−0.0152697	+	0.999883i	$0.504861\pi$
$374$	−2052.00	−0.283707
$375$	0	0
$376$	1392.00	0.190923
$377$	5775.00	0.788933
$378$	0	0
$379$	13844.0	1.87630	0.938151	−	0.346226i	$-0.112537\pi$
$379$	13844.0	1.87630	0.938151	+	0.346226i	$0.112537\pi$
$380$	2080.00	0.280794
$381$	0	0
$382$	−7200.00	−0.964356
$383$	−10908.0	−1.45528	−0.727641	−	0.685958i	$-0.759383\pi$
$383$	−10908.0	−1.45528	−0.727641	+	0.685958i	$0.759383\pi$
$384$	0	0
$385$	630.000	0.0833968
$386$	770.000	0.101534
$387$	0	0
$388$	−7384.00	−0.966149
$389$	−3558.00	−0.463747	−0.231874	−	0.972746i	$-0.574486\pi$
$389$	−3558.00	−0.463747	−0.231874	+	0.972746i	$0.574486\pi$
$390$	0	0
$391$	9747.00	1.26068
$392$	−392.000	−0.0505076
$393$	0	0
$394$	3060.00	0.391270
$395$	−1100.00	−0.140119
$396$	0	0
$397$	9542.00	1.20630	0.603148	−	0.797630i	$-0.293913\pi$
$397$	9542.00	1.20630	0.603148	+	0.797630i	$0.293913\pi$
$398$	−2386.00	−0.300501
$399$	0	0
$400$	400.000	0.0500000
$401$	10314.0	1.28443	0.642215	−	0.766524i	$-0.278016\pi$
$401$	10314.0	1.28443	0.642215	+	0.766524i	$0.278016\pi$
$402$	0	0
$403$	−10955.0	−1.35411
$404$	1488.00	0.183244
$405$	0	0
$406$	−2310.00	−0.282373
$407$	2304.00	0.280602
$408$	0	0
$409$	−2194.00	−0.265248	−0.132624	−	0.991166i	$-0.542340\pi$
$409$	−2194.00	−0.265248	−0.132624	+	0.991166i	$0.542340\pi$
$410$	−1140.00	−0.137319
$411$	0	0
$412$	−1588.00	−0.189891
$413$	−147.000	−0.0175143
$414$	0	0
$415$	5100.00	0.603251
$416$	−1120.00	−0.132001
$417$	0	0
$418$	−3744.00	−0.438098
$419$	2931.00	0.341739	0.170870	−	0.985294i	$-0.445342\pi$
$419$	2931.00	0.341739	0.170870	+	0.985294i	$0.445342\pi$
$420$	0	0
$421$	5186.00	0.600357	0.300178	−	0.953883i	$-0.402954\pi$
$421$	5186.00	0.600357	0.300178	+	0.953883i	$0.402954\pi$
$422$	9998.00	1.15331
$423$	0	0
$424$	2328.00	0.266645
$425$	1425.00	0.162642
$426$	0	0
$427$	602.000	0.0682267
$428$	1560.00	0.176181
$429$	0	0
$430$	−470.000	−0.0527103
$431$	11904.0	1.33038	0.665192	−	0.746672i	$-0.268350\pi$
$431$	11904.0	1.33038	0.665192	+	0.746672i	$0.268350\pi$
$432$	0	0
$433$	−10780.0	−1.19643	−0.598214	−	0.801336i	$-0.704123\pi$
$433$	−10780.0	−1.19643	−0.598214	+	0.801336i	$0.704123\pi$
$434$	4382.00	0.484661
$435$	0	0
$436$	1640.00	0.180142
$437$	17784.0	1.94674
$438$	0	0
$439$	−7459.00	−0.810931	−0.405465	−	0.914110i	$-0.632891\pi$
$439$	−7459.00	−0.810931	−0.405465	+	0.914110i	$0.632891\pi$
$440$	−720.000	−0.0780106
$441$	0	0
$442$	−3990.00	−0.429378
$443$	3324.00	0.356497	0.178248	−	0.983986i	$-0.442957\pi$
$443$	3324.00	0.356497	0.178248	+	0.983986i	$0.442957\pi$
$444$	0	0
$445$	255.000	0.0271644
$446$	−784.000	−0.0832365
$447$	0	0
$448$	448.000	0.0472456
$449$	−14352.0	−1.50849	−0.754246	−	0.656592i	$-0.771997\pi$
$449$	−14352.0	−1.50849	−0.754246	+	0.656592i	$0.771997\pi$
$450$	0	0
$451$	2052.00	0.214246
$452$	5256.00	0.546950
$453$	0	0
$454$	−1074.00	−0.111025
$455$	1225.00	0.126217
$456$	0	0
$457$	−11839.0	−1.21183	−0.605914	−	0.795530i	$-0.707192\pi$
$457$	−11839.0	−1.21183	−0.605914	+	0.795530i	$0.707192\pi$
$458$	6356.00	0.648464
$459$	0	0
$460$	3420.00	0.346649
$461$	−7302.00	−0.737718	−0.368859	−	0.929485i	$-0.620251\pi$
$461$	−7302.00	−0.737718	−0.368859	+	0.929485i	$0.620251\pi$
$462$	0	0
$463$	9152.00	0.918638	0.459319	−	0.888271i	$-0.348093\pi$
$463$	9152.00	0.918638	0.459319	+	0.888271i	$0.348093\pi$
$464$	2640.00	0.264136
$465$	0	0
$466$	12324.0	1.22510
$467$	−12948.0	−1.28300	−0.641501	−	0.767122i	$-0.721688\pi$
$467$	−12948.0	−1.28300	−0.641501	+	0.767122i	$0.721688\pi$
$468$	0	0
$469$	7469.00	0.735365
$470$	1740.00	0.170766
$471$	0	0
$472$	168.000	0.0163831
$473$	846.000	0.0822392
$474$	0	0
$475$	2600.00	0.251150
$476$	1596.00	0.153682
$477$	0	0
$478$	−432.000	−0.0413373
$479$	516.000	0.0492205	0.0246103	−	0.999697i	$-0.492166\pi$
$479$	516.000	0.0492205	0.0246103	+	0.999697i	$0.492166\pi$
$480$	0	0
$481$	4480.00	0.424679
$482$	−7672.00	−0.725000
$483$	0	0
$484$	−4028.00	−0.378287
$485$	−9230.00	−0.864150
$486$	0	0
$487$	−11626.0	−1.08177	−0.540887	−	0.841095i	$-0.681911\pi$
$487$	−11626.0	−1.08177	−0.540887	+	0.841095i	$0.681911\pi$
$488$	−688.000	−0.0638203
$489$	0	0
$490$	−490.000	−0.0451754
$491$	12444.0	1.14377	0.571884	−	0.820335i	$-0.306213\pi$
$491$	12444.0	1.14377	0.571884	+	0.820335i	$0.306213\pi$
$492$	0	0
$493$	9405.00	0.859188
$494$	−7280.00	−0.663042
$495$	0	0
$496$	−5008.00	−0.453359
$497$	945.000	0.0852898
$498$	0	0
$499$	1460.00	0.130979	0.0654896	−	0.997853i	$-0.479139\pi$
$499$	1460.00	0.130979	0.0654896	+	0.997853i	$0.479139\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	−2544.00	−0.226184
$503$	−11310.0	−1.00256	−0.501280	−	0.865285i	$-0.667137\pi$
$503$	−11310.0	−1.00256	−0.501280	+	0.865285i	$0.667137\pi$
$504$	0	0
$505$	1860.00	0.163899
$506$	−6156.00	−0.540845
$507$	0	0
$508$	−9616.00	−0.839845
$509$	1836.00	0.159881	0.0799403	−	0.996800i	$-0.474527\pi$
$509$	1836.00	0.159881	0.0799403	+	0.996800i	$0.474527\pi$
$510$	0	0
$511$	−7462.00	−0.645987
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−11508.0	−0.987541
$515$	−1985.00	−0.169844
$516$	0	0
$517$	−3132.00	−0.266432
$518$	−1792.00	−0.152000
$519$	0	0
$520$	−1400.00	−0.118066
$521$	6783.00	0.570381	0.285191	−	0.958471i	$-0.407943\pi$
$521$	6783.00	0.570381	0.285191	+	0.958471i	$0.407943\pi$
$522$	0	0
$523$	7112.00	0.594620	0.297310	−	0.954781i	$-0.403911\pi$
$523$	7112.00	0.594620	0.297310	+	0.954781i	$0.403911\pi$
$524$	−3804.00	−0.317135
$525$	0	0
$526$	−7002.00	−0.580421
$527$	−17841.0	−1.47470
$528$	0	0
$529$	17074.0	1.40330
$530$	2910.00	0.238495
$531$	0	0
$532$	2912.00	0.237314
$533$	3990.00	0.324252
$534$	0	0
$535$	1950.00	0.157581
$536$	−8536.00	−0.687871
$537$	0	0
$538$	360.000	0.0288489
$539$	882.000	0.0704832
$540$	0	0
$541$	3710.00	0.294834	0.147417	−	0.989074i	$-0.452904\pi$
$541$	3710.00	0.294834	0.147417	+	0.989074i	$0.452904\pi$
$542$	7250.00	0.574565
$543$	0	0
$544$	−1824.00	−0.143756
$545$	2050.00	0.161124
$546$	0	0
$547$	9884.00	0.772595	0.386297	−	0.922374i	$-0.373754\pi$
$547$	9884.00	0.772595	0.386297	+	0.922374i	$0.373754\pi$
$548$	−6936.00	−0.540677
$549$	0	0
$550$	−900.000	−0.0697748
$551$	17160.0	1.32675
$552$	0	0
$553$	−1540.00	−0.118422
$554$	6392.00	0.490199
$555$	0	0
$556$	−496.000	−0.0378329
$557$	−13029.0	−0.991125	−0.495562	−	0.868572i	$-0.665038\pi$
$557$	−13029.0	−0.991125	−0.495562	+	0.868572i	$0.665038\pi$
$558$	0	0
$559$	1645.00	0.124465
$560$	560.000	0.0422577
$561$	0	0
$562$	−18120.0	−1.36005
$563$	8217.00	0.615107	0.307554	−	0.951531i	$-0.400490\pi$
$563$	8217.00	0.615107	0.307554	+	0.951531i	$0.400490\pi$
$564$	0	0
$565$	6570.00	0.489207
$566$	−4156.00	−0.308639
$567$	0	0
$568$	−1080.00	−0.0797813
$569$	−2742.00	−0.202022	−0.101011	−	0.994885i	$-0.532208\pi$
$569$	−2742.00	−0.202022	−0.101011	+	0.994885i	$0.532208\pi$
$570$	0	0
$571$	−8089.00	−0.592844	−0.296422	−	0.955057i	$-0.595794\pi$
$571$	−8089.00	−0.592844	−0.296422	+	0.955057i	$0.595794\pi$
$572$	2520.00	0.184207
$573$	0	0
$574$	−1596.00	−0.116055
$575$	4275.00	0.310052
$576$	0	0
$577$	3764.00	0.271573	0.135786	−	0.990738i	$-0.456644\pi$
$577$	3764.00	0.271573	0.135786	+	0.990738i	$0.456644\pi$
$578$	3328.00	0.239492
$579$	0	0
$580$	3300.00	0.236250
$581$	7140.00	0.509840
$582$	0	0
$583$	−5238.00	−0.372103
$584$	8528.00	0.604266
$585$	0	0
$586$	16644.0	1.17331
$587$	9429.00	0.662992	0.331496	−	0.943457i	$-0.392447\pi$
$587$	9429.00	0.662992	0.331496	+	0.943457i	$0.392447\pi$
$588$	0	0
$589$	−32552.0	−2.27722
$590$	210.000	0.0146535
$591$	0	0
$592$	2048.00	0.142183
$593$	11238.0	0.778228	0.389114	−	0.921190i	$-0.372781\pi$
$593$	11238.0	0.778228	0.389114	+	0.921190i	$0.372781\pi$
$594$	0	0
$595$	1995.00	0.137457
$596$	10692.0	0.734835
$597$	0	0
$598$	−11970.0	−0.818545
$599$	14547.0	0.992278	0.496139	−	0.868243i	$-0.334751\pi$
$599$	14547.0	0.992278	0.496139	+	0.868243i	$0.334751\pi$
$600$	0	0
$601$	14072.0	0.955090	0.477545	−	0.878607i	$-0.341527\pi$
$601$	14072.0	0.955090	0.477545	+	0.878607i	$0.341527\pi$
$602$	−658.000	−0.0445483
$603$	0	0
$604$	−4624.00	−0.311503
$605$	−5035.00	−0.338350
$606$	0	0
$607$	−14083.0	−0.941699	−0.470850	−	0.882214i	$-0.656053\pi$
$607$	−14083.0	−0.941699	−0.470850	+	0.882214i	$0.656053\pi$
$608$	−3328.00	−0.221987
$609$	0	0
$610$	−860.000	−0.0570826
$611$	−6090.00	−0.403232
$612$	0	0
$613$	7652.00	0.504178	0.252089	−	0.967704i	$-0.418882\pi$
$613$	7652.00	0.504178	0.252089	+	0.967704i	$0.418882\pi$
$614$	−4720.00	−0.310234
$615$	0	0
$616$	−1008.00	−0.0659310
$617$	−5466.00	−0.356650	−0.178325	−	0.983972i	$-0.557068\pi$
$617$	−5466.00	−0.356650	−0.178325	+	0.983972i	$0.557068\pi$
$618$	0	0
$619$	14258.0	0.925812	0.462906	−	0.886407i	$-0.346807\pi$
$619$	14258.0	0.925812	0.462906	+	0.886407i	$0.346807\pi$
$620$	−6260.00	−0.405496
$621$	0	0
$622$	11196.0	0.721734
$623$	357.000	0.0229581
$624$	0	0
$625$	625.000	0.0400000
$626$	−11560.0	−0.738068
$627$	0	0
$628$	4964.00	0.315422
$629$	7296.00	0.462497
$630$	0	0
$631$	14420.0	0.909748	0.454874	−	0.890556i	$-0.349684\pi$
$631$	14420.0	0.909748	0.454874	+	0.890556i	$0.349684\pi$
$632$	1760.00	0.110774
$633$	0	0
$634$	−20508.0	−1.28466
$635$	−12020.0	−0.751180
$636$	0	0
$637$	1715.00	0.106673
$638$	−5940.00	−0.368600
$639$	0	0
$640$	−640.000	−0.0395285
$641$	−3906.00	−0.240683	−0.120341	−	0.992733i	$-0.538399\pi$
$641$	−3906.00	−0.240683	−0.120341	+	0.992733i	$0.538399\pi$
$642$	0	0
$643$	−19150.0	−1.17450	−0.587249	−	0.809406i	$-0.699789\pi$
$643$	−19150.0	−1.17450	−0.587249	+	0.809406i	$0.699789\pi$
$644$	4788.00	0.292971
$645$	0	0
$646$	−11856.0	−0.722087
$647$	−17346.0	−1.05401	−0.527003	−	0.849864i	$-0.676684\pi$
$647$	−17346.0	−1.05401	−0.527003	+	0.849864i	$0.676684\pi$
$648$	0	0
$649$	−378.000	−0.0228626
$650$	−1750.00	−0.105601
$651$	0	0
$652$	−8164.00	−0.490379
$653$	−15315.0	−0.917798	−0.458899	−	0.888488i	$-0.651756\pi$
$653$	−15315.0	−0.917798	−0.458899	+	0.888488i	$0.651756\pi$
$654$	0	0
$655$	−4755.00	−0.283654
$656$	1824.00	0.108560
$657$	0	0
$658$	2436.00	0.144324
$659$	−26622.0	−1.57367	−0.786833	−	0.617166i	$-0.788281\pi$
$659$	−26622.0	−1.57367	−0.786833	+	0.617166i	$0.788281\pi$
$660$	0	0
$661$	17798.0	1.04729	0.523647	−	0.851935i	$-0.324571\pi$
$661$	17798.0	1.04729	0.523647	+	0.851935i	$0.324571\pi$
$662$	−18430.0	−1.08203
$663$	0	0
$664$	−8160.00	−0.476912
$665$	3640.00	0.212260
$666$	0	0
$667$	28215.0	1.63791
$668$	−1896.00	−0.109818
$669$	0	0
$670$	−10670.0	−0.615251
$671$	1548.00	0.0890609
$672$	0	0
$673$	9953.00	0.570074	0.285037	−	0.958516i	$-0.407994\pi$
$673$	9953.00	0.570074	0.285037	+	0.958516i	$0.407994\pi$
$674$	14342.0	0.819634
$675$	0	0
$676$	−3888.00	−0.221211
$677$	22272.0	1.26438	0.632188	−	0.774815i	$-0.282157\pi$
$677$	22272.0	1.26438	0.632188	+	0.774815i	$0.282157\pi$
$678$	0	0
$679$	−12922.0	−0.730340
$680$	−2280.00	−0.128579
$681$	0	0
$682$	11268.0	0.632660
$683$	−15930.0	−0.892452	−0.446226	−	0.894920i	$-0.647232\pi$
$683$	−15930.0	−0.892452	−0.446226	+	0.894920i	$0.647232\pi$
$684$	0	0
$685$	−8670.00	−0.483597
$686$	−686.000	−0.0381802
$687$	0	0
$688$	752.000	0.0416711
$689$	−10185.0	−0.563161
$690$	0	0
$691$	15080.0	0.830203	0.415101	−	0.909775i	$-0.363746\pi$
$691$	15080.0	0.830203	0.415101	+	0.909775i	$0.363746\pi$
$692$	3288.00	0.180623
$693$	0	0
$694$	−6972.00	−0.381345
$695$	−620.000	−0.0338388
$696$	0	0
$697$	6498.00	0.353127
$698$	−17878.0	−0.969473
$699$	0	0
$700$	700.000	0.0377964
$701$	−6630.00	−0.357221	−0.178610	−	0.983920i	$-0.557160\pi$
$701$	−6630.00	−0.357221	−0.178610	+	0.983920i	$0.557160\pi$
$702$	0	0
$703$	13312.0	0.714184
$704$	1152.00	0.0616728
$705$	0	0
$706$	3546.00	0.189030
$707$	2604.00	0.138520
$708$	0	0
$709$	18278.0	0.968187	0.484094	−	0.875016i	$-0.339149\pi$
$709$	18278.0	0.968187	0.484094	+	0.875016i	$0.339149\pi$
$710$	−1350.00	−0.0713586
$711$	0	0
$712$	−408.000	−0.0214753
$713$	−53523.0	−2.81129
$714$	0	0
$715$	3150.00	0.164760
$716$	720.000	0.0375805
$717$	0	0
$718$	−13086.0	−0.680174
$719$	−26046.0	−1.35098	−0.675488	−	0.737371i	$-0.736067\pi$
$719$	−26046.0	−1.35098	−0.675488	+	0.737371i	$0.736067\pi$
$720$	0	0
$721$	−2779.00	−0.143544
$722$	−7914.00	−0.407934
$723$	0	0
$724$	15812.0	0.811669
$725$	4125.00	0.211308
$726$	0	0
$727$	5681.00	0.289817	0.144908	−	0.989445i	$-0.453711\pi$
$727$	5681.00	0.289817	0.144908	+	0.989445i	$0.453711\pi$
$728$	−1960.00	−0.0997836
$729$	0	0
$730$	10660.0	0.540472
$731$	2679.00	0.135549
$732$	0	0
$733$	8873.00	0.447110	0.223555	−	0.974691i	$-0.428234\pi$
$733$	8873.00	0.447110	0.223555	+	0.974691i	$0.428234\pi$
$734$	−26122.0	−1.31360
$735$	0	0
$736$	−5472.00	−0.274050
$737$	19206.0	0.959921
$738$	0	0
$739$	1664.00	0.0828298	0.0414149	−	0.999142i	$-0.486813\pi$
$739$	1664.00	0.0828298	0.0414149	+	0.999142i	$0.486813\pi$
$740$	2560.00	0.127172
$741$	0	0
$742$	4074.00	0.201565
$743$	−6369.00	−0.314476	−0.157238	−	0.987561i	$-0.550259\pi$
$743$	−6369.00	−0.314476	−0.157238	+	0.987561i	$0.550259\pi$
$744$	0	0
$745$	13365.0	0.657256
$746$	440.000	0.0215946
$747$	0	0
$748$	4104.00	0.200611
$749$	2730.00	0.133180
$750$	0	0
$751$	−10060.0	−0.488808	−0.244404	−	0.969674i	$-0.578592\pi$
$751$	−10060.0	−0.488808	−0.244404	+	0.969674i	$0.578592\pi$
$752$	−2784.00	−0.135003
$753$	0	0
$754$	−11550.0	−0.557860
$755$	−5780.00	−0.278617
$756$	0	0
$757$	−29272.0	−1.40543	−0.702714	−	0.711472i	$-0.748029\pi$
$757$	−29272.0	−1.40543	−0.702714	+	0.711472i	$0.748029\pi$
$758$	−27688.0	−1.32675
$759$	0	0
$760$	−4160.00	−0.198551
$761$	−31011.0	−1.47720	−0.738599	−	0.674145i	$-0.764512\pi$
$761$	−31011.0	−1.47720	−0.738599	+	0.674145i	$0.764512\pi$
$762$	0	0
$763$	2870.00	0.136174
$764$	14400.0	0.681903
$765$	0	0
$766$	21816.0	1.02904
$767$	−735.000	−0.0346014
$768$	0	0
$769$	−38554.0	−1.80792	−0.903962	−	0.427614i	$-0.859354\pi$
$769$	−38554.0	−1.80792	−0.903962	+	0.427614i	$0.859354\pi$
$770$	−1260.00	−0.0589705
$771$	0	0
$772$	−1540.00	−0.0717951
$773$	−30804.0	−1.43330	−0.716651	−	0.697432i	$-0.754326\pi$
$773$	−30804.0	−1.43330	−0.716651	+	0.697432i	$0.754326\pi$
$774$	0	0
$775$	−7825.00	−0.362687
$776$	14768.0	0.683170
$777$	0	0
$778$	7116.00	0.327919
$779$	11856.0	0.545296
$780$	0	0
$781$	2430.00	0.111334
$782$	−19494.0	−0.891437
$783$	0	0
$784$	784.000	0.0357143
$785$	6205.00	0.282122
$786$	0	0
$787$	−42106.0	−1.90714	−0.953568	−	0.301176i	$-0.902621\pi$
$787$	−42106.0	−1.90714	−0.953568	+	0.301176i	$0.902621\pi$
$788$	−6120.00	−0.276670
$789$	0	0
$790$	2200.00	0.0990791
$791$	9198.00	0.413455
$792$	0	0
$793$	3010.00	0.134790
$794$	−19084.0	−0.852980
$795$	0	0
$796$	4772.00	0.212486
$797$	−26034.0	−1.15705	−0.578527	−	0.815663i	$-0.696372\pi$
$797$	−26034.0	−1.15705	−0.578527	+	0.815663i	$0.696372\pi$
$798$	0	0
$799$	−9918.00	−0.439141
$800$	−800.000	−0.0353553
$801$	0	0
$802$	−20628.0	−0.908229
$803$	−19188.0	−0.843250
$804$	0	0
$805$	5985.00	0.262042
$806$	21910.0	0.957502
$807$	0	0
$808$	−2976.00	−0.129573
$809$	−24492.0	−1.06439	−0.532196	−	0.846621i	$-0.678633\pi$
$809$	−24492.0	−1.06439	−0.532196	+	0.846621i	$0.678633\pi$
$810$	0	0
$811$	26906.0	1.16498	0.582489	−	0.812838i	$-0.302079\pi$
$811$	26906.0	1.16498	0.582489	+	0.812838i	$0.302079\pi$
$812$	4620.00	0.199668
$813$	0	0
$814$	−4608.00	−0.198416
$815$	−10205.0	−0.438608
$816$	0	0
$817$	4888.00	0.209314
$818$	4388.00	0.187558
$819$	0	0
$820$	2280.00	0.0970988
$821$	11499.0	0.488816	0.244408	−	0.969672i	$-0.421406\pi$
$821$	11499.0	0.488816	0.244408	+	0.969672i	$0.421406\pi$
$822$	0	0
$823$	−27796.0	−1.17729	−0.588644	−	0.808393i	$-0.700338\pi$
$823$	−27796.0	−1.17729	−0.588644	+	0.808393i	$0.700338\pi$
$824$	3176.00	0.134273
$825$	0	0
$826$	294.000	0.0123845
$827$	22218.0	0.934215	0.467107	−	0.884201i	$-0.345296\pi$
$827$	22218.0	0.934215	0.467107	+	0.884201i	$0.345296\pi$
$828$	0	0
$829$	11042.0	0.462611	0.231305	−	0.972881i	$-0.425700\pi$
$829$	11042.0	0.462611	0.231305	+	0.972881i	$0.425700\pi$
$830$	−10200.0	−0.426563
$831$	0	0
$832$	2240.00	0.0933390
$833$	2793.00	0.116173
$834$	0	0
$835$	−2370.00	−0.0982242
$836$	7488.00	0.309782
$837$	0	0
$838$	−5862.00	−0.241646
$839$	1296.00	0.0533288	0.0266644	−	0.999644i	$-0.491511\pi$
$839$	1296.00	0.0533288	0.0266644	+	0.999644i	$0.491511\pi$
$840$	0	0
$841$	2836.00	0.116282
$842$	−10372.0	−0.424516
$843$	0	0
$844$	−19996.0	−0.815510
$845$	−4860.00	−0.197857
$846$	0	0
$847$	−7049.00	−0.285958
$848$	−4656.00	−0.188547
$849$	0	0
$850$	−2850.00	−0.115005
$851$	21888.0	0.881682
$852$	0	0
$853$	−29527.0	−1.18521	−0.592606	−	0.805493i	$-0.701901\pi$
$853$	−29527.0	−1.18521	−0.592606	+	0.805493i	$0.701901\pi$
$854$	−1204.00	−0.0482436
$855$	0	0
$856$	−3120.00	−0.124579
$857$	32139.0	1.28104	0.640518	−	0.767943i	$-0.278720\pi$
$857$	32139.0	1.28104	0.640518	+	0.767943i	$0.278720\pi$
$858$	0	0
$859$	1100.00	0.0436921	0.0218461	−	0.999761i	$-0.493046\pi$
$859$	1100.00	0.0436921	0.0218461	+	0.999761i	$0.493046\pi$
$860$	940.000	0.0372718
$861$	0	0
$862$	−23808.0	−0.940724
$863$	47409.0	1.87001	0.935006	−	0.354631i	$-0.115393\pi$
$863$	47409.0	1.87001	0.935006	+	0.354631i	$0.115393\pi$
$864$	0	0
$865$	4110.00	0.161554
$866$	21560.0	0.846003
$867$	0	0
$868$	−8764.00	−0.342707
$869$	−3960.00	−0.154584
$870$	0	0
$871$	37345.0	1.45280
$872$	−3280.00	−0.127379
$873$	0	0
$874$	−35568.0	−1.37655
$875$	875.000	0.0338062
$876$	0	0
$877$	−21328.0	−0.821203	−0.410602	−	0.911815i	$-0.634681\pi$
$877$	−21328.0	−0.821203	−0.410602	+	0.911815i	$0.634681\pi$
$878$	14918.0	0.573415
$879$	0	0
$880$	1440.00	0.0551618
$881$	−36015.0	−1.37727	−0.688636	−	0.725107i	$-0.741790\pi$
$881$	−36015.0	−1.37727	−0.688636	+	0.725107i	$0.741790\pi$
$882$	0	0
$883$	−28579.0	−1.08920	−0.544598	−	0.838697i	$-0.683318\pi$
$883$	−28579.0	−1.08920	−0.544598	+	0.838697i	$0.683318\pi$
$884$	7980.00	0.303616
$885$	0	0
$886$	−6648.00	−0.252081
$887$	36852.0	1.39500	0.697502	−	0.716583i	$-0.254295\pi$
$887$	36852.0	1.39500	0.697502	+	0.716583i	$0.254295\pi$
$888$	0	0
$889$	−16828.0	−0.634863
$890$	−510.000	−0.0192081
$891$	0	0
$892$	1568.00	0.0588571
$893$	−18096.0	−0.678118
$894$	0	0
$895$	900.000	0.0336131
$896$	−896.000	−0.0334077
$897$	0	0
$898$	28704.0	1.06666
$899$	−51645.0	−1.91597
$900$	0	0
$901$	−16587.0	−0.613311
$902$	−4104.00	−0.151495
$903$	0	0
$904$	−10512.0	−0.386752
$905$	19765.0	0.725979
$906$	0	0
$907$	5756.00	0.210722	0.105361	−	0.994434i	$-0.466400\pi$
$907$	5756.00	0.210722	0.105361	+	0.994434i	$0.466400\pi$
$908$	2148.00	0.0785065
$909$	0	0
$910$	−2450.00	−0.0892491
$911$	−25272.0	−0.919098	−0.459549	−	0.888152i	$-0.651989\pi$
$911$	−25272.0	−0.919098	−0.459549	+	0.888152i	$0.651989\pi$
$912$	0	0
$913$	18360.0	0.665528
$914$	23678.0	0.856891
$915$	0	0
$916$	−12712.0	−0.458533
$917$	−6657.00	−0.239731
$918$	0	0
$919$	35246.0	1.26513	0.632567	−	0.774506i	$-0.282001\pi$
$919$	35246.0	1.26513	0.632567	+	0.774506i	$0.282001\pi$
$920$	−6840.00	−0.245118
$921$	0	0
$922$	14604.0	0.521645
$923$	4725.00	0.168500
$924$	0	0
$925$	3200.00	0.113746
$926$	−18304.0	−0.649575
$927$	0	0
$928$	−5280.00	−0.186772
$929$	13050.0	0.460879	0.230440	−	0.973087i	$-0.425984\pi$
$929$	13050.0	0.460879	0.230440	+	0.973087i	$0.425984\pi$
$930$	0	0
$931$	5096.00	0.179393
$932$	−24648.0	−0.866279
$933$	0	0
$934$	25896.0	0.907219
$935$	5130.00	0.179432
$936$	0	0
$937$	−55834.0	−1.94666	−0.973328	−	0.229417i	$-0.926318\pi$
$937$	−55834.0	−1.94666	−0.973328	+	0.229417i	$0.926318\pi$
$938$	−14938.0	−0.519982
$939$	0	0
$940$	−3480.00	−0.120750
$941$	8622.00	0.298692	0.149346	−	0.988785i	$-0.452283\pi$
$941$	8622.00	0.298692	0.149346	+	0.988785i	$0.452283\pi$
$942$	0	0
$943$	19494.0	0.673183
$944$	−336.000	−0.0115846
$945$	0	0
$946$	−1692.00	−0.0581519
$947$	−1404.00	−0.0481773	−0.0240886	−	0.999710i	$-0.507668\pi$
$947$	−1404.00	−0.0481773	−0.0240886	+	0.999710i	$0.507668\pi$
$948$	0	0
$949$	−37310.0	−1.27622
$950$	−5200.00	−0.177590
$951$	0	0
$952$	−3192.00	−0.108669
$953$	−40056.0	−1.36153	−0.680767	−	0.732500i	$-0.738353\pi$
$953$	−40056.0	−1.36153	−0.680767	+	0.732500i	$0.738353\pi$
$954$	0	0
$955$	18000.0	0.609912
$956$	864.000	0.0292299
$957$	0	0
$958$	−1032.00	−0.0348042
$959$	−12138.0	−0.408714
$960$	0	0
$961$	68178.0	2.28854
$962$	−8960.00	−0.300293
$963$	0	0
$964$	15344.0	0.512652
$965$	−1925.00	−0.0642155
$966$	0	0
$967$	2888.00	0.0960412	0.0480206	−	0.998846i	$-0.484709\pi$
$967$	2888.00	0.0960412	0.0480206	+	0.998846i	$0.484709\pi$
$968$	8056.00	0.267489
$969$	0	0
$970$	18460.0	0.611046
$971$	14133.0	0.467095	0.233548	−	0.972345i	$-0.424967\pi$
$971$	14133.0	0.467095	0.233548	+	0.972345i	$0.424967\pi$
$972$	0	0
$973$	−868.000	−0.0285990
$974$	23252.0	0.764930
$975$	0	0
$976$	1376.00	0.0451278
$977$	−36846.0	−1.20656	−0.603279	−	0.797530i	$-0.706140\pi$
$977$	−36846.0	−1.20656	−0.603279	+	0.797530i	$0.706140\pi$
$978$	0	0
$979$	918.000	0.0299688
$980$	980.000	0.0319438
$981$	0	0
$982$	−24888.0	−0.808766
$983$	−53748.0	−1.74394	−0.871971	−	0.489558i	$-0.837158\pi$
$983$	−53748.0	−1.74394	−0.871971	+	0.489558i	$0.837158\pi$
$984$	0	0
$985$	−7650.00	−0.247461
$986$	−18810.0	−0.607538
$987$	0	0
$988$	14560.0	0.468841
$989$	8037.00	0.258404
$990$	0	0
$991$	26282.0	0.842457	0.421229	−	0.906954i	$-0.361599\pi$
$991$	26282.0	0.842457	0.421229	+	0.906954i	$0.361599\pi$
$992$	10016.0	0.320573
$993$	0	0
$994$	−1890.00	−0.0603090
$995$	5965.00	0.190053
$996$	0	0
$997$	−53053.0	−1.68526	−0.842631	−	0.538492i	$-0.818994\pi$
$997$	−53053.0	−1.68526	−0.842631	+	0.538492i	$0.818994\pi$
$998$	−2920.00	−0.0926162
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.4.a.g.1.1	✓	1	1.1	even	1	trivial
1890.4.a.h.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

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