LMFDB - Embedded newform 1890.4.a.a.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)

$f(q)$

$=$

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

\(q-2.00000 q^{2} +4.00000 q^{4} -5.00000 q^{5} -7.00000 q^{7} -8.00000 q^{8} +10.0000 q^{10} -28.0000 q^{11} -44.0000 q^{13} +14.0000 q^{14} +16.0000 q^{16} +47.0000 q^{17} -95.0000 q^{19} -20.0000 q^{20} +56.0000 q^{22} -131.000 q^{23} +25.0000 q^{25} +88.0000 q^{26} -28.0000 q^{28} +22.0000 q^{29} -171.000 q^{31} -32.0000 q^{32} -94.0000 q^{34} +35.0000 q^{35} -48.0000 q^{37} +190.000 q^{38} +40.0000 q^{40} +30.0000 q^{41} -262.000 q^{43} -112.000 q^{44} +262.000 q^{46} +360.000 q^{47} +49.0000 q^{49} -50.0000 q^{50} -176.000 q^{52} -343.000 q^{53} +140.000 q^{55} +56.0000 q^{56} -44.0000 q^{58} -150.000 q^{59} -685.000 q^{61} +342.000 q^{62} +64.0000 q^{64} +220.000 q^{65} +114.000 q^{67} +188.000 q^{68} -70.0000 q^{70} +370.000 q^{71} -1070.00 q^{73} +96.0000 q^{74} -380.000 q^{76} +196.000 q^{77} +841.000 q^{79} -80.0000 q^{80} -60.0000 q^{82} +1077.00 q^{83} -235.000 q^{85} +524.000 q^{86} +224.000 q^{88} -404.000 q^{89} +308.000 q^{91} -524.000 q^{92} -720.000 q^{94} +475.000 q^{95} +914.000 q^{97} -98.0000 q^{98} +O(q^{100})\)

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
$11$	−28.0000	−0.767483	−0.383742	−	0.923440i	$-0.625365\pi$
$11$	−28.0000	−0.767483	−0.383742	+	0.923440i	$0.625365\pi$
$12$	0	0
$13$	−44.0000	−0.938723	−0.469362	−	0.883006i	$-0.655516\pi$
$13$	−44.0000	−0.938723	−0.469362	+	0.883006i	$0.655516\pi$
$14$	14.0000	0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	47.0000	0.670540	0.335270	−	0.942122i	$-0.391173\pi$
$17$	47.0000	0.670540	0.335270	+	0.942122i	$0.391173\pi$
$18$	0	0
$19$	−95.0000	−1.14708	−0.573539	−	0.819178i	$-0.694430\pi$
$19$	−95.0000	−1.14708	−0.573539	+	0.819178i	$0.694430\pi$
$20$	−20.0000	−0.223607
$21$	0	0
$22$	56.0000	0.542693
$23$	−131.000	−1.18763	−0.593813	−	0.804603i	$-0.702378\pi$
$23$	−131.000	−1.18763	−0.593813	+	0.804603i	$0.702378\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	88.0000	0.663778
$27$	0	0
$28$	−28.0000	−0.188982
$29$	22.0000	0.140872	0.0704362	−	0.997516i	$-0.477561\pi$
$29$	22.0000	0.140872	0.0704362	+	0.997516i	$0.477561\pi$
$30$	0	0
$31$	−171.000	−0.990726	−0.495363	−	0.868686i	$-0.664965\pi$
$31$	−171.000	−0.990726	−0.495363	+	0.868686i	$0.664965\pi$
$32$	−32.0000	−0.176777
$33$	0	0
$34$	−94.0000	−0.474143
$35$	35.0000	0.169031
$36$	0	0
$37$	−48.0000	−0.213274	−0.106637	−	0.994298i	$-0.534008\pi$
$37$	−48.0000	−0.213274	−0.106637	+	0.994298i	$0.534008\pi$
$38$	190.000	0.811107
$39$	0	0
$40$	40.0000	0.158114
$41$	30.0000	0.114273	0.0571367	−	0.998366i	$-0.481803\pi$
$41$	30.0000	0.114273	0.0571367	+	0.998366i	$0.481803\pi$
$42$	0	0
$43$	−262.000	−0.929177	−0.464589	−	0.885527i	$-0.653798\pi$
$43$	−262.000	−0.929177	−0.464589	+	0.885527i	$0.653798\pi$
$44$	−112.000	−0.383742
$45$	0	0
$46$	262.000	0.839778
$47$	360.000	1.11726	0.558632	−	0.829416i	$-0.311326\pi$
$47$	360.000	1.11726	0.558632	+	0.829416i	$0.311326\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	−50.0000	−0.141421
$51$	0	0
$52$	−176.000	−0.469362
$53$	−343.000	−0.888956	−0.444478	−	0.895790i	$-0.646611\pi$
$53$	−343.000	−0.888956	−0.444478	+	0.895790i	$0.646611\pi$
$54$	0	0
$55$	140.000	0.343229
$56$	56.0000	0.133631
$57$	0	0
$58$	−44.0000	−0.0996118
$59$	−150.000	−0.330989	−0.165494	−	0.986211i	$-0.552922\pi$
$59$	−150.000	−0.330989	−0.165494	+	0.986211i	$0.552922\pi$
$60$	0	0
$61$	−685.000	−1.43779	−0.718896	−	0.695118i	$-0.755352\pi$
$61$	−685.000	−1.43779	−0.718896	+	0.695118i	$0.755352\pi$
$62$	342.000	0.700549
$63$	0	0
$64$	64.0000	0.125000
$65$	220.000	0.419810
$66$	0	0
$67$	114.000	0.207870	0.103935	−	0.994584i	$-0.466857\pi$
$67$	114.000	0.207870	0.103935	+	0.994584i	$0.466857\pi$
$68$	188.000	0.335270
$69$	0	0
$70$	−70.0000	−0.119523
$71$	370.000	0.618464	0.309232	−	0.950987i	$-0.399928\pi$
$71$	370.000	0.618464	0.309232	+	0.950987i	$0.399928\pi$
$72$	0	0
$73$	−1070.00	−1.71553	−0.857767	−	0.514038i	$-0.828149\pi$
$73$	−1070.00	−1.71553	−0.857767	+	0.514038i	$0.828149\pi$
$74$	96.0000	0.150808
$75$	0	0
$76$	−380.000	−0.573539
$77$	196.000	0.290081
$78$	0	0
$79$	841.000	1.19772	0.598860	−	0.800854i	$-0.295621\pi$
$79$	841.000	1.19772	0.598860	+	0.800854i	$0.295621\pi$
$80$	−80.0000	−0.111803
$81$	0	0
$82$	−60.0000	−0.0808036
$83$	1077.00	1.42429	0.712145	−	0.702032i	$-0.247724\pi$
$83$	1077.00	1.42429	0.712145	+	0.702032i	$0.247724\pi$
$84$	0	0
$85$	−235.000	−0.299874
$86$	524.000	0.657028
$87$	0	0
$88$	224.000	0.271346
$89$	−404.000	−0.481168	−0.240584	−	0.970628i	$-0.577339\pi$
$89$	−404.000	−0.481168	−0.240584	+	0.970628i	$0.577339\pi$
$90$	0	0
$91$	308.000	0.354804
$92$	−524.000	−0.593813
$93$	0	0
$94$	−720.000	−0.790025
$95$	475.000	0.512989
$96$	0	0
$97$	914.000	0.956728	0.478364	−	0.878162i	$-0.341230\pi$
$97$	914.000	0.956728	0.478364	+	0.878162i	$0.341230\pi$
$98$	−98.0000	−0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	−138.000	−0.135956	−0.0679778	−	0.997687i	$-0.521655\pi$
$101$	−138.000	−0.135956	−0.0679778	+	0.997687i	$0.521655\pi$
$102$	0	0
$103$	166.000	0.158801	0.0794003	−	0.996843i	$-0.474699\pi$
$103$	166.000	0.158801	0.0794003	+	0.996843i	$0.474699\pi$
$104$	352.000	0.331889
$105$	0	0
$106$	686.000	0.628587
$107$	48.0000	0.0433676	0.0216838	−	0.999765i	$-0.493097\pi$
$107$	48.0000	0.0433676	0.0216838	+	0.999765i	$0.493097\pi$
$108$	0	0
$109$	−931.000	−0.818107	−0.409053	−	0.912510i	$-0.634141\pi$
$109$	−931.000	−0.818107	−0.409053	+	0.912510i	$0.634141\pi$
$110$	−280.000	−0.242700
$111$	0	0
$112$	−112.000	−0.0944911
$113$	−666.000	−0.554443	−0.277221	−	0.960806i	$-0.589414\pi$
$113$	−666.000	−0.554443	−0.277221	+	0.960806i	$0.589414\pi$
$114$	0	0
$115$	655.000	0.531122
$116$	88.0000	0.0704362
$117$	0	0
$118$	300.000	0.234044
$119$	−329.000	−0.253440
$120$	0	0
$121$	−547.000	−0.410969
$122$	1370.00	1.01667
$123$	0	0
$124$	−684.000	−0.495363
$125$	−125.000	−0.0894427
$126$	0	0
$127$	92.0000	0.0642809	0.0321405	−	0.999483i	$-0.489768\pi$
$127$	92.0000	0.0642809	0.0321405	+	0.999483i	$0.489768\pi$
$128$	−128.000	−0.0883883
$129$	0	0
$130$	−440.000	−0.296850
$131$	1052.00	0.701631	0.350816	−	0.936445i	$-0.385904\pi$
$131$	1052.00	0.701631	0.350816	+	0.936445i	$0.385904\pi$
$132$	0	0
$133$	665.000	0.433555
$134$	−228.000	−0.146987
$135$	0	0
$136$	−376.000	−0.237072
$137$	−929.000	−0.579342	−0.289671	−	0.957126i	$-0.593546\pi$
$137$	−929.000	−0.579342	−0.289671	+	0.957126i	$0.593546\pi$
$138$	0	0
$139$	−1312.00	−0.800593	−0.400296	−	0.916386i	$-0.631093\pi$
$139$	−1312.00	−0.800593	−0.400296	+	0.916386i	$0.631093\pi$
$140$	140.000	0.0845154
$141$	0	0
$142$	−740.000	−0.437320
$143$	1232.00	0.720455
$144$	0	0
$145$	−110.000	−0.0630000
$146$	2140.00	1.21307
$147$	0	0
$148$	−192.000	−0.106637
$149$	734.000	0.403568	0.201784	−	0.979430i	$-0.435326\pi$
$149$	734.000	0.403568	0.201784	+	0.979430i	$0.435326\pi$
$150$	0	0
$151$	−920.000	−0.495818	−0.247909	−	0.968783i	$-0.579743\pi$
$151$	−920.000	−0.495818	−0.247909	+	0.968783i	$0.579743\pi$
$152$	760.000	0.405554
$153$	0	0
$154$	−392.000	−0.205119
$155$	855.000	0.443066
$156$	0	0
$157$	1656.00	0.841804	0.420902	−	0.907106i	$-0.361714\pi$
$157$	1656.00	0.841804	0.420902	+	0.907106i	$0.361714\pi$
$158$	−1682.00	−0.846916
$159$	0	0
$160$	160.000	0.0790569
$161$	917.000	0.448880
$162$	0	0
$163$	−556.000	−0.267174	−0.133587	−	0.991037i	$-0.542649\pi$
$163$	−556.000	−0.267174	−0.133587	+	0.991037i	$0.542649\pi$
$164$	120.000	0.0571367
$165$	0	0
$166$	−2154.00	−1.00713
$167$	1111.00	0.514801	0.257400	−	0.966305i	$-0.417134\pi$
$167$	1111.00	0.514801	0.257400	+	0.966305i	$0.417134\pi$
$168$	0	0
$169$	−261.000	−0.118798
$170$	470.000	0.212043
$171$	0	0
$172$	−1048.00	−0.464589
$173$	1413.00	0.620973	0.310487	−	0.950578i	$-0.399508\pi$
$173$	1413.00	0.620973	0.310487	+	0.950578i	$0.399508\pi$
$174$	0	0
$175$	−175.000	−0.0755929
$176$	−448.000	−0.191871
$177$	0	0
$178$	808.000	0.340237
$179$	1300.00	0.542830	0.271415	−	0.962462i	$-0.412508\pi$
$179$	1300.00	0.542830	0.271415	+	0.962462i	$0.412508\pi$
$180$	0	0
$181$	−2361.00	−0.969568	−0.484784	−	0.874634i	$-0.661102\pi$
$181$	−2361.00	−0.969568	−0.484784	+	0.874634i	$0.661102\pi$
$182$	−616.000	−0.250884
$183$	0	0
$184$	1048.00	0.419889
$185$	240.000	0.0953792
$186$	0	0
$187$	−1316.00	−0.514628
$188$	1440.00	0.558632
$189$	0	0
$190$	−950.000	−0.362738
$191$	2660.00	1.00770	0.503850	−	0.863791i	$-0.331916\pi$
$191$	2660.00	1.00770	0.503850	+	0.863791i	$0.331916\pi$
$192$	0	0
$193$	2888.00	1.07711	0.538556	−	0.842589i	$-0.318970\pi$
$193$	2888.00	1.07711	0.538556	+	0.842589i	$0.318970\pi$
$194$	−1828.00	−0.676509
$195$	0	0
$196$	196.000	0.0714286
$197$	−705.000	−0.254970	−0.127485	−	0.991840i	$-0.540691\pi$
$197$	−705.000	−0.254970	−0.127485	+	0.991840i	$0.540691\pi$
$198$	0	0
$199$	−2472.00	−0.880580	−0.440290	−	0.897856i	$-0.645124\pi$
$199$	−2472.00	−0.880580	−0.440290	+	0.897856i	$0.645124\pi$
$200$	−200.000	−0.0707107
$201$	0	0
$202$	276.000	0.0961351
$203$	−154.000	−0.0532447
$204$	0	0
$205$	−150.000	−0.0511047
$206$	−332.000	−0.112289
$207$	0	0
$208$	−704.000	−0.234681
$209$	2660.00	0.880364
$210$	0	0
$211$	−2091.00	−0.682229	−0.341115	−	0.940022i	$-0.610804\pi$
$211$	−2091.00	−0.682229	−0.341115	+	0.940022i	$0.610804\pi$
$212$	−1372.00	−0.444478
$213$	0	0
$214$	−96.0000	−0.0306655
$215$	1310.00	0.415541
$216$	0	0
$217$	1197.00	0.374459
$218$	1862.00	0.578489
$219$	0	0
$220$	560.000	0.171615
$221$	−2068.00	−0.629451
$222$	0	0
$223$	1868.00	0.560944	0.280472	−	0.959862i	$-0.409509\pi$
$223$	1868.00	0.560944	0.280472	+	0.959862i	$0.409509\pi$
$224$	224.000	0.0668153
$225$	0	0
$226$	1332.00	0.392050
$227$	−4787.00	−1.39967	−0.699833	−	0.714306i	$-0.746742\pi$
$227$	−4787.00	−1.39967	−0.699833	+	0.714306i	$0.746742\pi$
$228$	0	0
$229$	−931.000	−0.268656	−0.134328	−	0.990937i	$-0.542888\pi$
$229$	−931.000	−0.268656	−0.134328	+	0.990937i	$0.542888\pi$
$230$	−1310.00	−0.375560
$231$	0	0
$232$	−176.000	−0.0498059
$233$	3686.00	1.03639	0.518193	−	0.855264i	$-0.326605\pi$
$233$	3686.00	1.03639	0.518193	+	0.855264i	$0.326605\pi$
$234$	0	0
$235$	−1800.00	−0.499656
$236$	−600.000	−0.165494
$237$	0	0
$238$	658.000	0.179209
$239$	3942.00	1.06689	0.533445	−	0.845835i	$-0.320897\pi$
$239$	3942.00	1.06689	0.533445	+	0.845835i	$0.320897\pi$
$240$	0	0
$241$	3709.00	0.991360	0.495680	−	0.868505i	$-0.334919\pi$
$241$	3709.00	0.991360	0.495680	+	0.868505i	$0.334919\pi$
$242$	1094.00	0.290599
$243$	0	0
$244$	−2740.00	−0.718896
$245$	−245.000	−0.0638877
$246$	0	0
$247$	4180.00	1.07679
$248$	1368.00	0.350275
$249$	0	0
$250$	250.000	0.0632456
$251$	−3570.00	−0.897755	−0.448877	−	0.893593i	$-0.648176\pi$
$251$	−3570.00	−0.897755	−0.448877	+	0.893593i	$0.648176\pi$
$252$	0	0
$253$	3668.00	0.911483
$254$	−184.000	−0.0454535
$255$	0	0
$256$	256.000	0.0625000
$257$	2617.00	0.635191	0.317595	−	0.948226i	$-0.397125\pi$
$257$	2617.00	0.635191	0.317595	+	0.948226i	$0.397125\pi$
$258$	0	0
$259$	336.000	0.0806101
$260$	880.000	0.209905
$261$	0	0
$262$	−2104.00	−0.496128
$263$	3512.00	0.823419	0.411710	−	0.911315i	$-0.364932\pi$
$263$	3512.00	0.823419	0.411710	+	0.911315i	$0.364932\pi$
$264$	0	0
$265$	1715.00	0.397553
$266$	−1330.00	−0.306570
$267$	0	0
$268$	456.000	0.103935
$269$	−1440.00	−0.326388	−0.163194	−	0.986594i	$-0.552180\pi$
$269$	−1440.00	−0.326388	−0.163194	+	0.986594i	$0.552180\pi$
$270$	0	0
$271$	5065.00	1.13534	0.567669	−	0.823257i	$-0.307845\pi$
$271$	5065.00	1.13534	0.567669	+	0.823257i	$0.307845\pi$
$272$	752.000	0.167635
$273$	0	0
$274$	1858.00	0.409657
$275$	−700.000	−0.153497
$276$	0	0
$277$	−3014.00	−0.653768	−0.326884	−	0.945064i	$-0.605999\pi$
$277$	−3014.00	−0.653768	−0.326884	+	0.945064i	$0.605999\pi$
$278$	2624.00	0.566105
$279$	0	0
$280$	−280.000	−0.0597614
$281$	462.000	0.0980805	0.0490402	−	0.998797i	$-0.484384\pi$
$281$	462.000	0.0980805	0.0490402	+	0.998797i	$0.484384\pi$
$282$	0	0
$283$	3694.00	0.775921	0.387960	−	0.921676i	$-0.373180\pi$
$283$	3694.00	0.775921	0.387960	+	0.921676i	$0.373180\pi$
$284$	1480.00	0.309232
$285$	0	0
$286$	−2464.00	−0.509438
$287$	−210.000	−0.0431913
$288$	0	0
$289$	−2704.00	−0.550377
$290$	220.000	0.0445477
$291$	0	0
$292$	−4280.00	−0.857767
$293$	3057.00	0.609528	0.304764	−	0.952428i	$-0.401422\pi$
$293$	3057.00	0.609528	0.304764	+	0.952428i	$0.401422\pi$
$294$	0	0
$295$	750.000	0.148023
$296$	384.000	0.0754039
$297$	0	0
$298$	−1468.00	−0.285366
$299$	5764.00	1.11485
$300$	0	0
$301$	1834.00	0.351196
$302$	1840.00	0.350596
$303$	0	0
$304$	−1520.00	−0.286770
$305$	3425.00	0.643000
$306$	0	0
$307$	−772.000	−0.143519	−0.0717596	−	0.997422i	$-0.522861\pi$
$307$	−772.000	−0.143519	−0.0717596	+	0.997422i	$0.522861\pi$
$308$	784.000	0.145041
$309$	0	0
$310$	−1710.00	−0.313295
$311$	−4676.00	−0.852578	−0.426289	−	0.904587i	$-0.640179\pi$
$311$	−4676.00	−0.852578	−0.426289	+	0.904587i	$0.640179\pi$
$312$	0	0
$313$	840.000	0.151692	0.0758460	−	0.997120i	$-0.475834\pi$
$313$	840.000	0.151692	0.0758460	+	0.997120i	$0.475834\pi$
$314$	−3312.00	−0.595245
$315$	0	0
$316$	3364.00	0.598860
$317$	8329.00	1.47572	0.737860	−	0.674954i	$-0.235836\pi$
$317$	8329.00	1.47572	0.737860	+	0.674954i	$0.235836\pi$
$318$	0	0
$319$	−616.000	−0.108117
$320$	−320.000	−0.0559017
$321$	0	0
$322$	−1834.00	−0.317406
$323$	−4465.00	−0.769162
$324$	0	0
$325$	−1100.00	−0.187745
$326$	1112.00	0.188920
$327$	0	0
$328$	−240.000	−0.0404018
$329$	−2520.00	−0.422286
$330$	0	0
$331$	−1212.00	−0.201261	−0.100631	−	0.994924i	$-0.532086\pi$
$331$	−1212.00	−0.201261	−0.100631	+	0.994924i	$0.532086\pi$
$332$	4308.00	0.712145
$333$	0	0
$334$	−2222.00	−0.364019
$335$	−570.000	−0.0929625
$336$	0	0
$337$	−5976.00	−0.965975	−0.482987	−	0.875627i	$-0.660448\pi$
$337$	−5976.00	−0.965975	−0.482987	+	0.875627i	$0.660448\pi$
$338$	522.000	0.0840031
$339$	0	0
$340$	−940.000	−0.149937
$341$	4788.00	0.760366
$342$	0	0
$343$	−343.000	−0.0539949
$344$	2096.00	0.328514
$345$	0	0
$346$	−2826.00	−0.439095
$347$	6068.00	0.938753	0.469377	−	0.882998i	$-0.344479\pi$
$347$	6068.00	0.938753	0.469377	+	0.882998i	$0.344479\pi$
$348$	0	0
$349$	7739.00	1.18699	0.593495	−	0.804838i	$-0.297748\pi$
$349$	7739.00	1.18699	0.593495	+	0.804838i	$0.297748\pi$
$350$	350.000	0.0534522
$351$	0	0
$352$	896.000	0.135673
$353$	4582.00	0.690865	0.345432	−	0.938444i	$-0.387732\pi$
$353$	4582.00	0.690865	0.345432	+	0.938444i	$0.387732\pi$
$354$	0	0
$355$	−1850.00	−0.276585
$356$	−1616.00	−0.240584
$357$	0	0
$358$	−2600.00	−0.383839
$359$	−10146.0	−1.49160	−0.745801	−	0.666168i	$-0.767933\pi$
$359$	−10146.0	−1.49160	−0.745801	+	0.666168i	$0.767933\pi$
$360$	0	0
$361$	2166.00	0.315789
$362$	4722.00	0.685588
$363$	0	0
$364$	1232.00	0.177402
$365$	5350.00	0.767210
$366$	0	0
$367$	9244.00	1.31480	0.657402	−	0.753540i	$-0.271655\pi$
$367$	9244.00	1.31480	0.657402	+	0.753540i	$0.271655\pi$
$368$	−2096.00	−0.296906
$369$	0	0
$370$	−480.000	−0.0674433
$371$	2401.00	0.335994
$372$	0	0
$373$	−6232.00	−0.865096	−0.432548	−	0.901611i	$-0.642385\pi$
$373$	−6232.00	−0.865096	−0.432548	+	0.901611i	$0.642385\pi$
$374$	2632.00	0.363897
$375$	0	0
$376$	−2880.00	−0.395012
$377$	−968.000	−0.132240
$378$	0	0
$379$	13393.0	1.81518	0.907589	−	0.419860i	$-0.137921\pi$
$379$	13393.0	1.81518	0.907589	+	0.419860i	$0.137921\pi$
$380$	1900.00	0.256495
$381$	0	0
$382$	−5320.00	−0.712552
$383$	5923.00	0.790212	0.395106	−	0.918636i	$-0.370708\pi$
$383$	5923.00	0.790212	0.395106	+	0.918636i	$0.370708\pi$
$384$	0	0
$385$	−980.000	−0.129728
$386$	−5776.00	−0.761634
$387$	0	0
$388$	3656.00	0.478364
$389$	4192.00	0.546383	0.273191	−	0.961960i	$-0.411921\pi$
$389$	4192.00	0.546383	0.273191	+	0.961960i	$0.411921\pi$
$390$	0	0
$391$	−6157.00	−0.796350
$392$	−392.000	−0.0505076
$393$	0	0
$394$	1410.00	0.180291
$395$	−4205.00	−0.535637
$396$	0	0
$397$	8634.00	1.09151	0.545753	−	0.837946i	$-0.316244\pi$
$397$	8634.00	1.09151	0.545753	+	0.837946i	$0.316244\pi$
$398$	4944.00	0.622664
$399$	0	0
$400$	400.000	0.0500000
$401$	−10766.0	−1.34072	−0.670360	−	0.742036i	$-0.733860\pi$
$401$	−10766.0	−1.34072	−0.670360	+	0.742036i	$0.733860\pi$
$402$	0	0
$403$	7524.00	0.930018
$404$	−552.000	−0.0679778
$405$	0	0
$406$	308.000	0.0376497
$407$	1344.00	0.163685
$408$	0	0
$409$	−12365.0	−1.49489	−0.747445	−	0.664324i	$-0.768720\pi$
$409$	−12365.0	−1.49489	−0.747445	+	0.664324i	$0.768720\pi$
$410$	300.000	0.0361364
$411$	0	0
$412$	664.000	0.0794003
$413$	1050.00	0.125102
$414$	0	0
$415$	−5385.00	−0.636962
$416$	1408.00	0.165944
$417$	0	0
$418$	−5320.00	−0.622511
$419$	15164.0	1.76804	0.884021	−	0.467447i	$-0.154826\pi$
$419$	15164.0	1.76804	0.884021	+	0.467447i	$0.154826\pi$
$420$	0	0
$421$	619.000	0.0716585	0.0358292	−	0.999358i	$-0.488593\pi$
$421$	619.000	0.0716585	0.0358292	+	0.999358i	$0.488593\pi$
$422$	4182.00	0.482409
$423$	0	0
$424$	2744.00	0.314293
$425$	1175.00	0.134108
$426$	0	0
$427$	4795.00	0.543434
$428$	192.000	0.0216838
$429$	0	0
$430$	−2620.00	−0.293832
$431$	7956.00	0.889158	0.444579	−	0.895740i	$-0.353353\pi$
$431$	7956.00	0.889158	0.444579	+	0.895740i	$0.353353\pi$
$432$	0	0
$433$	16438.0	1.82439	0.912194	−	0.409759i	$-0.134387\pi$
$433$	16438.0	1.82439	0.912194	+	0.409759i	$0.134387\pi$
$434$	−2394.00	−0.264783
$435$	0	0
$436$	−3724.00	−0.409053
$437$	12445.0	1.36230
$438$	0	0
$439$	13057.0	1.41954	0.709768	−	0.704435i	$-0.248800\pi$
$439$	13057.0	1.41954	0.709768	+	0.704435i	$0.248800\pi$
$440$	−1120.00	−0.121350
$441$	0	0
$442$	4136.00	0.445089
$443$	−2025.00	−0.217180	−0.108590	−	0.994087i	$-0.534634\pi$
$443$	−2025.00	−0.217180	−0.108590	+	0.994087i	$0.534634\pi$
$444$	0	0
$445$	2020.00	0.215185
$446$	−3736.00	−0.396647
$447$	0	0
$448$	−448.000	−0.0472456
$449$	13196.0	1.38699	0.693494	−	0.720462i	$-0.256070\pi$
$449$	13196.0	1.38699	0.693494	+	0.720462i	$0.256070\pi$
$450$	0	0
$451$	−840.000	−0.0877030
$452$	−2664.00	−0.277221
$453$	0	0
$454$	9574.00	0.989714
$455$	−1540.00	−0.158673
$456$	0	0
$457$	15478.0	1.58431	0.792156	−	0.610319i	$-0.208959\pi$
$457$	15478.0	1.58431	0.792156	+	0.610319i	$0.208959\pi$
$458$	1862.00	0.189968
$459$	0	0
$460$	2620.00	0.265561
$461$	16478.0	1.66477	0.832383	−	0.554201i	$-0.186976\pi$
$461$	16478.0	1.66477	0.832383	+	0.554201i	$0.186976\pi$
$462$	0	0
$463$	5454.00	0.547449	0.273724	−	0.961808i	$-0.411744\pi$
$463$	5454.00	0.547449	0.273724	+	0.961808i	$0.411744\pi$
$464$	352.000	0.0352181
$465$	0	0
$466$	−7372.00	−0.732835
$467$	−8895.00	−0.881395	−0.440698	−	0.897656i	$-0.645269\pi$
$467$	−8895.00	−0.881395	−0.440698	+	0.897656i	$0.645269\pi$
$468$	0	0
$469$	−798.000	−0.0785676
$470$	3600.00	0.353310
$471$	0	0
$472$	1200.00	0.117022
$473$	7336.00	0.713128
$474$	0	0
$475$	−2375.00	−0.229416
$476$	−1316.00	−0.126720
$477$	0	0
$478$	−7884.00	−0.754405
$479$	13760.0	1.31255	0.656274	−	0.754523i	$-0.272132\pi$
$479$	13760.0	1.31255	0.656274	+	0.754523i	$0.272132\pi$
$480$	0	0
$481$	2112.00	0.200206
$482$	−7418.00	−0.700997
$483$	0	0
$484$	−2188.00	−0.205485
$485$	−4570.00	−0.427862
$486$	0	0
$487$	11332.0	1.05442	0.527209	−	0.849735i	$-0.323238\pi$
$487$	11332.0	1.05442	0.527209	+	0.849735i	$0.323238\pi$
$488$	5480.00	0.508336
$489$	0	0
$490$	490.000	0.0451754
$491$	8586.00	0.789167	0.394583	−	0.918860i	$-0.370889\pi$
$491$	8586.00	0.789167	0.394583	+	0.918860i	$0.370889\pi$
$492$	0	0
$493$	1034.00	0.0944605
$494$	−8360.00	−0.761405
$495$	0	0
$496$	−2736.00	−0.247682
$497$	−2590.00	−0.233757
$498$	0	0
$499$	−18129.0	−1.62638	−0.813192	−	0.581996i	$-0.802272\pi$
$499$	−18129.0	−1.62638	−0.813192	+	0.581996i	$0.802272\pi$
$500$	−500.000	−0.0447214
$501$	0	0
$502$	7140.00	0.634808
$503$	4315.00	0.382498	0.191249	−	0.981542i	$-0.438746\pi$
$503$	4315.00	0.382498	0.191249	+	0.981542i	$0.438746\pi$
$504$	0	0
$505$	690.000	0.0608012
$506$	−7336.00	−0.644516
$507$	0	0
$508$	368.000	0.0321405
$509$	−18384.0	−1.60090	−0.800448	−	0.599402i	$-0.795405\pi$
$509$	−18384.0	−1.60090	−0.800448	+	0.599402i	$0.795405\pi$
$510$	0	0
$511$	7490.00	0.648411
$512$	−512.000	−0.0441942
$513$	0	0
$514$	−5234.00	−0.449148
$515$	−830.000	−0.0710178
$516$	0	0
$517$	−10080.0	−0.857481
$518$	−672.000	−0.0570000
$519$	0	0
$520$	−1760.00	−0.148425
$521$	−9780.00	−0.822398	−0.411199	−	0.911546i	$-0.634890\pi$
$521$	−9780.00	−0.822398	−0.411199	+	0.911546i	$0.634890\pi$
$522$	0	0
$523$	−12998.0	−1.08674	−0.543368	−	0.839495i	$-0.682851\pi$
$523$	−12998.0	−1.08674	−0.543368	+	0.839495i	$0.682851\pi$
$524$	4208.00	0.350816
$525$	0	0
$526$	−7024.00	−0.582245
$527$	−8037.00	−0.664321
$528$	0	0
$529$	4994.00	0.410455
$530$	−3430.00	−0.281113
$531$	0	0
$532$	2660.00	0.216777
$533$	−1320.00	−0.107271
$534$	0	0
$535$	−240.000	−0.0193946
$536$	−912.000	−0.0734933
$537$	0	0
$538$	2880.00	0.230791
$539$	−1372.00	−0.109640
$540$	0	0
$541$	−1798.00	−0.142887	−0.0714437	−	0.997445i	$-0.522761\pi$
$541$	−1798.00	−0.142887	−0.0714437	+	0.997445i	$0.522761\pi$
$542$	−10130.0	−0.802806
$543$	0	0
$544$	−1504.00	−0.118536
$545$	4655.00	0.365868
$546$	0	0
$547$	23604.0	1.84504	0.922518	−	0.385955i	$-0.126128\pi$
$547$	23604.0	1.84504	0.922518	+	0.385955i	$0.126128\pi$
$548$	−3716.00	−0.289671
$549$	0	0
$550$	1400.00	0.108539
$551$	−2090.00	−0.161592
$552$	0	0
$553$	−5887.00	−0.452696
$554$	6028.00	0.462284
$555$	0	0
$556$	−5248.00	−0.400296
$557$	−13266.0	−1.00915	−0.504577	−	0.863367i	$-0.668351\pi$
$557$	−13266.0	−1.00915	−0.504577	+	0.863367i	$0.668351\pi$
$558$	0	0
$559$	11528.0	0.872241
$560$	560.000	0.0422577
$561$	0	0
$562$	−924.000	−0.0693534
$563$	−1288.00	−0.0964169	−0.0482085	−	0.998837i	$-0.515351\pi$
$563$	−1288.00	−0.0964169	−0.0482085	+	0.998837i	$0.515351\pi$
$564$	0	0
$565$	3330.00	0.247954
$566$	−7388.00	−0.548659
$567$	0	0
$568$	−2960.00	−0.218660
$569$	−8332.00	−0.613876	−0.306938	−	0.951729i	$-0.599304\pi$
$569$	−8332.00	−0.613876	−0.306938	+	0.951729i	$0.599304\pi$
$570$	0	0
$571$	7447.00	0.545792	0.272896	−	0.962044i	$-0.412019\pi$
$571$	7447.00	0.545792	0.272896	+	0.962044i	$0.412019\pi$
$572$	4928.00	0.360227
$573$	0	0
$574$	420.000	0.0305409
$575$	−3275.00	−0.237525
$576$	0	0
$577$	−19856.0	−1.43261	−0.716305	−	0.697787i	$-0.754168\pi$
$577$	−19856.0	−1.43261	−0.716305	+	0.697787i	$0.754168\pi$
$578$	5408.00	0.389175
$579$	0	0
$580$	−440.000	−0.0315000
$581$	−7539.00	−0.538331
$582$	0	0
$583$	9604.00	0.682259
$584$	8560.00	0.606533
$585$	0	0
$586$	−6114.00	−0.431002
$587$	−17961.0	−1.26291	−0.631456	−	0.775411i	$-0.717543\pi$
$587$	−17961.0	−1.26291	−0.631456	+	0.775411i	$0.717543\pi$
$588$	0	0
$589$	16245.0	1.13644
$590$	−1500.00	−0.104668
$591$	0	0
$592$	−768.000	−0.0533186
$593$	9573.00	0.662927	0.331464	−	0.943468i	$-0.392458\pi$
$593$	9573.00	0.662927	0.331464	+	0.943468i	$0.392458\pi$
$594$	0	0
$595$	1645.00	0.113342
$596$	2936.00	0.201784
$597$	0	0
$598$	−11528.0	−0.788319
$599$	−20040.0	−1.36697	−0.683483	−	0.729967i	$-0.739536\pi$
$599$	−20040.0	−1.36697	−0.683483	+	0.729967i	$0.739536\pi$
$600$	0	0
$601$	931.000	0.0631885	0.0315942	−	0.999501i	$-0.489942\pi$
$601$	931.000	0.0631885	0.0315942	+	0.999501i	$0.489942\pi$
$602$	−3668.00	−0.248333
$603$	0	0
$604$	−3680.00	−0.247909
$605$	2735.00	0.183791
$606$	0	0
$607$	4762.00	0.318424	0.159212	−	0.987244i	$-0.449105\pi$
$607$	4762.00	0.318424	0.159212	+	0.987244i	$0.449105\pi$
$608$	3040.00	0.202777
$609$	0	0
$610$	−6850.00	−0.454669
$611$	−15840.0	−1.04880
$612$	0	0
$613$	1662.00	0.109507	0.0547533	−	0.998500i	$-0.482563\pi$
$613$	1662.00	0.109507	0.0547533	+	0.998500i	$0.482563\pi$
$614$	1544.00	0.101483
$615$	0	0
$616$	−1568.00	−0.102559
$617$	−17575.0	−1.14675	−0.573373	−	0.819294i	$-0.694366\pi$
$617$	−17575.0	−1.14675	−0.573373	+	0.819294i	$0.694366\pi$
$618$	0	0
$619$	10412.0	0.676080	0.338040	−	0.941132i	$-0.390236\pi$
$619$	10412.0	0.676080	0.338040	+	0.941132i	$0.390236\pi$
$620$	3420.00	0.221533
$621$	0	0
$622$	9352.00	0.602863
$623$	2828.00	0.181864
$624$	0	0
$625$	625.000	0.0400000
$626$	−1680.00	−0.107262
$627$	0	0
$628$	6624.00	0.420902
$629$	−2256.00	−0.143009
$630$	0	0
$631$	19697.0	1.24267	0.621335	−	0.783545i	$-0.286590\pi$
$631$	19697.0	1.24267	0.621335	+	0.783545i	$0.286590\pi$
$632$	−6728.00	−0.423458
$633$	0	0
$634$	−16658.0	−1.04349
$635$	−460.000	−0.0287473
$636$	0	0
$637$	−2156.00	−0.134103
$638$	1232.00	0.0764504
$639$	0	0
$640$	640.000	0.0395285
$641$	−23234.0	−1.43165	−0.715825	−	0.698280i	$-0.753949\pi$
$641$	−23234.0	−1.43165	−0.715825	+	0.698280i	$0.753949\pi$
$642$	0	0
$643$	22118.0	1.35653	0.678265	−	0.734817i	$-0.262732\pi$
$643$	22118.0	1.35653	0.678265	+	0.734817i	$0.262732\pi$
$644$	3668.00	0.224440
$645$	0	0
$646$	8930.00	0.543879
$647$	−23421.0	−1.42314	−0.711572	−	0.702613i	$-0.752017\pi$
$647$	−23421.0	−1.42314	−0.711572	+	0.702613i	$0.752017\pi$
$648$	0	0
$649$	4200.00	0.254028
$650$	2200.00	0.132756
$651$	0	0
$652$	−2224.00	−0.133587
$653$	3521.00	0.211007	0.105503	−	0.994419i	$-0.466355\pi$
$653$	3521.00	0.211007	0.105503	+	0.994419i	$0.466355\pi$
$654$	0	0
$655$	−5260.00	−0.313779
$656$	480.000	0.0285684
$657$	0	0
$658$	5040.00	0.298601
$659$	−21456.0	−1.26830	−0.634148	−	0.773212i	$-0.718649\pi$
$659$	−21456.0	−1.26830	−0.634148	+	0.773212i	$0.718649\pi$
$660$	0	0
$661$	−26614.0	−1.56606	−0.783029	−	0.621985i	$-0.786327\pi$
$661$	−26614.0	−1.56606	−0.783029	+	0.621985i	$0.786327\pi$
$662$	2424.00	0.142313
$663$	0	0
$664$	−8616.00	−0.503563
$665$	−3325.00	−0.193892
$666$	0	0
$667$	−2882.00	−0.167304
$668$	4444.00	0.257400
$669$	0	0
$670$	1140.00	0.0657344
$671$	19180.0	1.10348
$672$	0	0
$673$	−13710.0	−0.785263	−0.392631	−	0.919696i	$-0.628435\pi$
$673$	−13710.0	−0.785263	−0.392631	+	0.919696i	$0.628435\pi$
$674$	11952.0	0.683047
$675$	0	0
$676$	−1044.00	−0.0593992
$677$	19474.0	1.10553	0.552767	−	0.833336i	$-0.313572\pi$
$677$	19474.0	1.10553	0.552767	+	0.833336i	$0.313572\pi$
$678$	0	0
$679$	−6398.00	−0.361609
$680$	1880.00	0.106022
$681$	0	0
$682$	−9576.00	−0.537660
$683$	−609.000	−0.0341182	−0.0170591	−	0.999854i	$-0.505430\pi$
$683$	−609.000	−0.0341182	−0.0170591	+	0.999854i	$0.505430\pi$
$684$	0	0
$685$	4645.00	0.259090
$686$	686.000	0.0381802
$687$	0	0
$688$	−4192.00	−0.232294
$689$	15092.0	0.834484
$690$	0	0
$691$	−12861.0	−0.708040	−0.354020	−	0.935238i	$-0.615185\pi$
$691$	−12861.0	−0.708040	−0.354020	+	0.935238i	$0.615185\pi$
$692$	5652.00	0.310487
$693$	0	0
$694$	−12136.0	−0.663799
$695$	6560.00	0.358036
$696$	0	0
$697$	1410.00	0.0766249
$698$	−15478.0	−0.839328
$699$	0	0
$700$	−700.000	−0.0377964
$701$	−9294.00	−0.500755	−0.250378	−	0.968148i	$-0.580555\pi$
$701$	−9294.00	−0.500755	−0.250378	+	0.968148i	$0.580555\pi$
$702$	0	0
$703$	4560.00	0.244642
$704$	−1792.00	−0.0959354
$705$	0	0
$706$	−9164.00	−0.488515
$707$	966.000	0.0513864
$708$	0	0
$709$	−7670.00	−0.406281	−0.203140	−	0.979150i	$-0.565115\pi$
$709$	−7670.00	−0.406281	−0.203140	+	0.979150i	$0.565115\pi$
$710$	3700.00	0.195575
$711$	0	0
$712$	3232.00	0.170118
$713$	22401.0	1.17661
$714$	0	0
$715$	−6160.00	−0.322197
$716$	5200.00	0.271415
$717$	0	0
$718$	20292.0	1.05472
$719$	−31030.0	−1.60949	−0.804745	−	0.593620i	$-0.797698\pi$
$719$	−31030.0	−1.60949	−0.804745	+	0.593620i	$0.797698\pi$
$720$	0	0
$721$	−1162.00	−0.0600210
$722$	−4332.00	−0.223297
$723$	0	0
$724$	−9444.00	−0.484784
$725$	550.000	0.0281745
$726$	0	0
$727$	26444.0	1.34904	0.674521	−	0.738256i	$-0.264350\pi$
$727$	26444.0	1.34904	0.674521	+	0.738256i	$0.264350\pi$
$728$	−2464.00	−0.125442
$729$	0	0
$730$	−10700.0	−0.542500
$731$	−12314.0	−0.623050
$732$	0	0
$733$	−37382.0	−1.88368	−0.941839	−	0.336065i	$-0.890904\pi$
$733$	−37382.0	−1.88368	−0.941839	+	0.336065i	$0.890904\pi$
$734$	−18488.0	−0.929706
$735$	0	0
$736$	4192.00	0.209945
$737$	−3192.00	−0.159537
$738$	0	0
$739$	−26263.0	−1.30731	−0.653654	−	0.756794i	$-0.726765\pi$
$739$	−26263.0	−1.30731	−0.653654	+	0.756794i	$0.726765\pi$
$740$	960.000	0.0476896
$741$	0	0
$742$	−4802.00	−0.237584
$743$	3792.00	0.187234	0.0936171	−	0.995608i	$-0.470157\pi$
$743$	3792.00	0.187234	0.0936171	+	0.995608i	$0.470157\pi$
$744$	0	0
$745$	−3670.00	−0.180481
$746$	12464.0	0.611715
$747$	0	0
$748$	−5264.00	−0.257314
$749$	−336.000	−0.0163914
$750$	0	0
$751$	−29123.0	−1.41506	−0.707532	−	0.706681i	$-0.750192\pi$
$751$	−29123.0	−1.41506	−0.707532	+	0.706681i	$0.750192\pi$
$752$	5760.00	0.279316
$753$	0	0
$754$	1936.00	0.0935079
$755$	4600.00	0.221737
$756$	0	0
$757$	21010.0	1.00875	0.504373	−	0.863486i	$-0.331723\pi$
$757$	21010.0	1.00875	0.504373	+	0.863486i	$0.331723\pi$
$758$	−26786.0	−1.28352
$759$	0	0
$760$	−3800.00	−0.181369
$761$	−13640.0	−0.649737	−0.324868	−	0.945759i	$-0.605320\pi$
$761$	−13640.0	−0.649737	−0.324868	+	0.945759i	$0.605320\pi$
$762$	0	0
$763$	6517.00	0.309215
$764$	10640.0	0.503850
$765$	0	0
$766$	−11846.0	−0.558764
$767$	6600.00	0.310707
$768$	0	0
$769$	523.000	0.0245252	0.0122626	−	0.999925i	$-0.496097\pi$
$769$	523.000	0.0245252	0.0122626	+	0.999925i	$0.496097\pi$
$770$	1960.00	0.0917318
$771$	0	0
$772$	11552.0	0.538556
$773$	−2753.00	−0.128096	−0.0640482	−	0.997947i	$-0.520401\pi$
$773$	−2753.00	−0.128096	−0.0640482	+	0.997947i	$0.520401\pi$
$774$	0	0
$775$	−4275.00	−0.198145
$776$	−7312.00	−0.338255
$777$	0	0
$778$	−8384.00	−0.386351
$779$	−2850.00	−0.131081
$780$	0	0
$781$	−10360.0	−0.474661
$782$	12314.0	0.563105
$783$	0	0
$784$	784.000	0.0357143
$785$	−8280.00	−0.376466
$786$	0	0
$787$	6596.00	0.298757	0.149379	−	0.988780i	$-0.452273\pi$
$787$	6596.00	0.298757	0.149379	+	0.988780i	$0.452273\pi$
$788$	−2820.00	−0.127485
$789$	0	0
$790$	8410.00	0.378752
$791$	4662.00	0.209560
$792$	0	0
$793$	30140.0	1.34969
$794$	−17268.0	−0.771812
$795$	0	0
$796$	−9888.00	−0.440290
$797$	−7395.00	−0.328663	−0.164331	−	0.986405i	$-0.552547\pi$
$797$	−7395.00	−0.328663	−0.164331	+	0.986405i	$0.552547\pi$
$798$	0	0
$799$	16920.0	0.749170
$800$	−800.000	−0.0353553
$801$	0	0
$802$	21532.0	0.948032
$803$	29960.0	1.31664
$804$	0	0
$805$	−4585.00	−0.200745
$806$	−15048.0	−0.657622
$807$	0	0
$808$	1104.00	0.0480676
$809$	−9526.00	−0.413988	−0.206994	−	0.978342i	$-0.566368\pi$
$809$	−9526.00	−0.413988	−0.206994	+	0.978342i	$0.566368\pi$
$810$	0	0
$811$	−7028.00	−0.304299	−0.152149	−	0.988357i	$-0.548620\pi$
$811$	−7028.00	−0.304299	−0.152149	+	0.988357i	$0.548620\pi$
$812$	−616.000	−0.0266224
$813$	0	0
$814$	−2688.00	−0.115742
$815$	2780.00	0.119484
$816$	0	0
$817$	24890.0	1.06584
$818$	24730.0	1.05705
$819$	0	0
$820$	−600.000	−0.0255523
$821$	−40058.0	−1.70284	−0.851421	−	0.524482i	$-0.824259\pi$
$821$	−40058.0	−1.70284	−0.851421	+	0.524482i	$0.824259\pi$
$822$	0	0
$823$	−26070.0	−1.10418	−0.552092	−	0.833783i	$-0.686170\pi$
$823$	−26070.0	−1.10418	−0.552092	+	0.833783i	$0.686170\pi$
$824$	−1328.00	−0.0561445
$825$	0	0
$826$	−2100.00	−0.0884605
$827$	−45863.0	−1.92843	−0.964216	−	0.265119i	$-0.914589\pi$
$827$	−45863.0	−1.92843	−0.964216	+	0.265119i	$0.914589\pi$
$828$	0	0
$829$	27702.0	1.16059	0.580296	−	0.814406i	$-0.302937\pi$
$829$	27702.0	1.16059	0.580296	+	0.814406i	$0.302937\pi$
$830$	10770.0	0.450400
$831$	0	0
$832$	−2816.00	−0.117340
$833$	2303.00	0.0957914
$834$	0	0
$835$	−5555.00	−0.230226
$836$	10640.0	0.440182
$837$	0	0
$838$	−30328.0	−1.25019
$839$	12530.0	0.515594	0.257797	−	0.966199i	$-0.417003\pi$
$839$	12530.0	0.515594	0.257797	+	0.966199i	$0.417003\pi$
$840$	0	0
$841$	−23905.0	−0.980155
$842$	−1238.00	−0.0506702
$843$	0	0
$844$	−8364.00	−0.341115
$845$	1305.00	0.0531282
$846$	0	0
$847$	3829.00	0.155332
$848$	−5488.00	−0.222239
$849$	0	0
$850$	−2350.00	−0.0948286
$851$	6288.00	0.253290
$852$	0	0
$853$	12148.0	0.487620	0.243810	−	0.969823i	$-0.421603\pi$
$853$	12148.0	0.487620	0.243810	+	0.969823i	$0.421603\pi$
$854$	−9590.00	−0.384266
$855$	0	0
$856$	−384.000	−0.0153328
$857$	1007.00	0.0401382	0.0200691	−	0.999799i	$-0.493611\pi$
$857$	1007.00	0.0401382	0.0200691	+	0.999799i	$0.493611\pi$
$858$	0	0
$859$	14887.0	0.591313	0.295657	−	0.955294i	$-0.404462\pi$
$859$	14887.0	0.591313	0.295657	+	0.955294i	$0.404462\pi$
$860$	5240.00	0.207770
$861$	0	0
$862$	−15912.0	−0.628730
$863$	2201.00	0.0868168	0.0434084	−	0.999057i	$-0.486178\pi$
$863$	2201.00	0.0868168	0.0434084	+	0.999057i	$0.486178\pi$
$864$	0	0
$865$	−7065.00	−0.277708
$866$	−32876.0	−1.29004
$867$	0	0
$868$	4788.00	0.187230
$869$	−23548.0	−0.919230
$870$	0	0
$871$	−5016.00	−0.195133
$872$	7448.00	0.289244
$873$	0	0
$874$	−24890.0	−0.963292
$875$	875.000	0.0338062
$876$	0	0
$877$	−14236.0	−0.548136	−0.274068	−	0.961710i	$-0.588369\pi$
$877$	−14236.0	−0.548136	−0.274068	+	0.961710i	$0.588369\pi$
$878$	−26114.0	−1.00376
$879$	0	0
$880$	2240.00	0.0858073
$881$	4538.00	0.173540	0.0867702	−	0.996228i	$-0.472345\pi$
$881$	4538.00	0.173540	0.0867702	+	0.996228i	$0.472345\pi$
$882$	0	0
$883$	6974.00	0.265791	0.132896	−	0.991130i	$-0.457572\pi$
$883$	6974.00	0.265791	0.132896	+	0.991130i	$0.457572\pi$
$884$	−8272.00	−0.314726
$885$	0	0
$886$	4050.00	0.153569
$887$	−33097.0	−1.25286	−0.626431	−	0.779477i	$-0.715485\pi$
$887$	−33097.0	−1.25286	−0.626431	+	0.779477i	$0.715485\pi$
$888$	0	0
$889$	−644.000	−0.0242959
$890$	−4040.00	−0.152159
$891$	0	0
$892$	7472.00	0.280472
$893$	−34200.0	−1.28159
$894$	0	0
$895$	−6500.00	−0.242761
$896$	896.000	0.0334077
$897$	0	0
$898$	−26392.0	−0.980749
$899$	−3762.00	−0.139566
$900$	0	0
$901$	−16121.0	−0.596080
$902$	1680.00	0.0620154
$903$	0	0
$904$	5328.00	0.196025
$905$	11805.0	0.433604
$906$	0	0
$907$	31246.0	1.14389	0.571944	−	0.820293i	$-0.306189\pi$
$907$	31246.0	1.14389	0.571944	+	0.820293i	$0.306189\pi$
$908$	−19148.0	−0.699833
$909$	0	0
$910$	3080.00	0.112199
$911$	−16318.0	−0.593457	−0.296729	−	0.954962i	$-0.595896\pi$
$911$	−16318.0	−0.593457	−0.296729	+	0.954962i	$0.595896\pi$
$912$	0	0
$913$	−30156.0	−1.09312
$914$	−30956.0	−1.12028
$915$	0	0
$916$	−3724.00	−0.134328
$917$	−7364.00	−0.265192
$918$	0	0
$919$	30844.0	1.10713	0.553563	−	0.832807i	$-0.313268\pi$
$919$	30844.0	1.10713	0.553563	+	0.832807i	$0.313268\pi$
$920$	−5240.00	−0.187780
$921$	0	0
$922$	−32956.0	−1.17717
$923$	−16280.0	−0.580566
$924$	0	0
$925$	−1200.00	−0.0426549
$926$	−10908.0	−0.387105
$927$	0	0
$928$	−704.000	−0.0249029
$929$	23644.0	0.835021	0.417510	−	0.908672i	$-0.362903\pi$
$929$	23644.0	0.835021	0.417510	+	0.908672i	$0.362903\pi$
$930$	0	0
$931$	−4655.00	−0.163868
$932$	14744.0	0.518193
$933$	0	0
$934$	17790.0	0.623240
$935$	6580.00	0.230149
$936$	0	0
$937$	3304.00	0.115194	0.0575971	−	0.998340i	$-0.481656\pi$
$937$	3304.00	0.115194	0.0575971	+	0.998340i	$0.481656\pi$
$938$	1596.00	0.0555557
$939$	0	0
$940$	−7200.00	−0.249828
$941$	−29772.0	−1.03139	−0.515696	−	0.856772i	$-0.672467\pi$
$941$	−29772.0	−1.03139	−0.515696	+	0.856772i	$0.672467\pi$
$942$	0	0
$943$	−3930.00	−0.135714
$944$	−2400.00	−0.0827472
$945$	0	0
$946$	−14672.0	−0.504258
$947$	−42737.0	−1.46649	−0.733245	−	0.679965i	$-0.761995\pi$
$947$	−42737.0	−1.46649	−0.733245	+	0.679965i	$0.761995\pi$
$948$	0	0
$949$	47080.0	1.61041
$950$	4750.00	0.162221
$951$	0	0
$952$	2632.00	0.0896046
$953$	−16822.0	−0.571792	−0.285896	−	0.958261i	$-0.592291\pi$
$953$	−16822.0	−0.571792	−0.285896	+	0.958261i	$0.592291\pi$
$954$	0	0
$955$	−13300.0	−0.450657
$956$	15768.0	0.533445
$957$	0	0
$958$	−27520.0	−0.928112
$959$	6503.00	0.218971
$960$	0	0
$961$	−550.000	−0.0184620
$962$	−4224.00	−0.141567
$963$	0	0
$964$	14836.0	0.495680
$965$	−14440.0	−0.481700
$966$	0	0
$967$	−2156.00	−0.0716983	−0.0358492	−	0.999357i	$-0.511414\pi$
$967$	−2156.00	−0.0716983	−0.0358492	+	0.999357i	$0.511414\pi$
$968$	4376.00	0.145300
$969$	0	0
$970$	9140.00	0.302544
$971$	514.000	0.0169877	0.00849384	−	0.999964i	$-0.497296\pi$
$971$	514.000	0.0169877	0.00849384	+	0.999964i	$0.497296\pi$
$972$	0	0
$973$	9184.00	0.302596
$974$	−22664.0	−0.745587
$975$	0	0
$976$	−10960.0	−0.359448
$977$	34146.0	1.11814	0.559072	−	0.829119i	$-0.311157\pi$
$977$	34146.0	1.11814	0.559072	+	0.829119i	$0.311157\pi$
$978$	0	0
$979$	11312.0	0.369288
$980$	−980.000	−0.0319438
$981$	0	0
$982$	−17172.0	−0.558025
$983$	52923.0	1.71717	0.858587	−	0.512668i	$-0.171343\pi$
$983$	52923.0	1.71717	0.858587	+	0.512668i	$0.171343\pi$
$984$	0	0
$985$	3525.00	0.114026
$986$	−2068.00	−0.0667936
$987$	0	0
$988$	16720.0	0.538395
$989$	34322.0	1.10351
$990$	0	0
$991$	−95.0000	−0.00304518	−0.00152259	−	0.999999i	$-0.500485\pi$
$991$	−95.0000	−0.00304518	−0.00152259	+	0.999999i	$0.500485\pi$
$992$	5472.00	0.175137
$993$	0	0
$994$	5180.00	0.165291
$995$	12360.0	0.393807
$996$	0	0
$997$	−42326.0	−1.34451	−0.672256	−	0.740319i	$-0.734674\pi$
$997$	−42326.0	−1.34451	−0.672256	+	0.740319i	$0.734674\pi$
$998$	36258.0	1.15003
$999$	0	0

Twists

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

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