LMFDB - Embedded newform 1890.4.a.i.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:	$1$
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)

$f(q)$

$=$

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

\(q+2.00000 q^{2} +4.00000 q^{4} +5.00000 q^{5} -7.00000 q^{7} +8.00000 q^{8} +10.0000 q^{10} -37.0000 q^{11} +73.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} -60.0000 q^{17} +9.00000 q^{19} +20.0000 q^{20} -74.0000 q^{22} -194.000 q^{23} +25.0000 q^{25} +146.000 q^{26} -28.0000 q^{28} -74.0000 q^{29} +76.0000 q^{31} +32.0000 q^{32} -120.000 q^{34} -35.0000 q^{35} -178.000 q^{37} +18.0000 q^{38} +40.0000 q^{40} -251.000 q^{41} +11.0000 q^{43} -148.000 q^{44} -388.000 q^{46} +199.000 q^{47} +49.0000 q^{49} +50.0000 q^{50} +292.000 q^{52} +109.000 q^{53} -185.000 q^{55} -56.0000 q^{56} -148.000 q^{58} +358.000 q^{59} -672.000 q^{61} +152.000 q^{62} +64.0000 q^{64} +365.000 q^{65} -1017.00 q^{67} -240.000 q^{68} -70.0000 q^{70} -552.000 q^{71} +165.000 q^{73} -356.000 q^{74} +36.0000 q^{76} +259.000 q^{77} +880.000 q^{79} +80.0000 q^{80} -502.000 q^{82} +431.000 q^{83} -300.000 q^{85} +22.0000 q^{86} -296.000 q^{88} -1039.00 q^{89} -511.000 q^{91} -776.000 q^{92} +398.000 q^{94} +45.0000 q^{95} +446.000 q^{97} +98.0000 q^{98} +O(q^{100})\)

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
$11$	−37.0000	−1.01417	−0.507087	−	0.861895i	$-0.669278\pi$
$11$	−37.0000	−1.01417	−0.507087	+	0.861895i	$0.669278\pi$
$12$	0	0
$13$	73.0000	1.55743	0.778714	−	0.627379i	$-0.215872\pi$
$13$	73.0000	1.55743	0.778714	+	0.627379i	$0.215872\pi$
$14$	−14.0000	−0.267261
$15$	0	0
$16$	16.0000	0.250000
$17$	−60.0000	−0.856008	−0.428004	−	0.903777i	$-0.640783\pi$
$17$	−60.0000	−0.856008	−0.428004	+	0.903777i	$0.640783\pi$
$18$	0	0
$19$	9.00000	0.108671	0.0543353	−	0.998523i	$-0.482696\pi$
$19$	9.00000	0.108671	0.0543353	+	0.998523i	$0.482696\pi$
$20$	20.0000	0.223607
$21$	0	0
$22$	−74.0000	−0.717130
$23$	−194.000	−1.75877	−0.879387	−	0.476108i	$-0.842047\pi$
$23$	−194.000	−1.75877	−0.879387	+	0.476108i	$0.842047\pi$
$24$	0	0
$25$	25.0000	0.200000
$26$	146.000	1.10127
$27$	0	0
$28$	−28.0000	−0.188982
$29$	−74.0000	−0.473843	−0.236922	−	0.971529i	$-0.576138\pi$
$29$	−74.0000	−0.473843	−0.236922	+	0.971529i	$0.576138\pi$
$30$	0	0
$31$	76.0000	0.440323	0.220161	−	0.975463i	$-0.429342\pi$
$31$	76.0000	0.440323	0.220161	+	0.975463i	$0.429342\pi$
$32$	32.0000	0.176777
$33$	0	0
$34$	−120.000	−0.605289
$35$	−35.0000	−0.169031
$36$	0	0
$37$	−178.000	−0.790892	−0.395446	−	0.918489i	$-0.629410\pi$
$37$	−178.000	−0.790892	−0.395446	+	0.918489i	$0.629410\pi$
$38$	18.0000	0.0768417
$39$	0	0
$40$	40.0000	0.158114
$41$	−251.000	−0.956088	−0.478044	−	0.878336i	$-0.658654\pi$
$41$	−251.000	−0.956088	−0.478044	+	0.878336i	$0.658654\pi$
$42$	0	0
$43$	11.0000	0.0390113	0.0195056	−	0.999810i	$-0.493791\pi$
$43$	11.0000	0.0390113	0.0195056	+	0.999810i	$0.493791\pi$
$44$	−148.000	−0.507087
$45$	0	0
$46$	−388.000	−1.24364
$47$	199.000	0.617599	0.308799	−	0.951127i	$-0.400073\pi$
$47$	199.000	0.617599	0.308799	+	0.951127i	$0.400073\pi$
$48$	0	0
$49$	49.0000	0.142857
$50$	50.0000	0.141421
$51$	0	0
$52$	292.000	0.778714
$53$	109.000	0.282496	0.141248	−	0.989974i	$-0.454888\pi$
$53$	109.000	0.282496	0.141248	+	0.989974i	$0.454888\pi$
$54$	0	0
$55$	−185.000	−0.453553
$56$	−56.0000	−0.133631
$57$	0	0
$58$	−148.000	−0.335058
$59$	358.000	0.789960	0.394980	−	0.918690i	$-0.370752\pi$
$59$	358.000	0.789960	0.394980	+	0.918690i	$0.370752\pi$
$60$	0	0
$61$	−672.000	−1.41050	−0.705252	−	0.708956i	$-0.749166\pi$
$61$	−672.000	−1.41050	−0.705252	+	0.708956i	$0.749166\pi$
$62$	152.000	0.311355
$63$	0	0
$64$	64.0000	0.125000
$65$	365.000	0.696503
$66$	0	0
$67$	−1017.00	−1.85442	−0.927211	−	0.374538i	$-0.877801\pi$
$67$	−1017.00	−1.85442	−0.927211	+	0.374538i	$0.877801\pi$
$68$	−240.000	−0.428004
$69$	0	0
$70$	−70.0000	−0.119523
$71$	−552.000	−0.922681	−0.461340	−	0.887223i	$-0.652631\pi$
$71$	−552.000	−0.922681	−0.461340	+	0.887223i	$0.652631\pi$
$72$	0	0
$73$	165.000	0.264545	0.132273	−	0.991213i	$-0.457773\pi$
$73$	165.000	0.264545	0.132273	+	0.991213i	$0.457773\pi$
$74$	−356.000	−0.559245
$75$	0	0
$76$	36.0000	0.0543353
$77$	259.000	0.383322
$78$	0	0
$79$	880.000	1.25326	0.626631	−	0.779316i	$-0.284433\pi$
$79$	880.000	1.25326	0.626631	+	0.779316i	$0.284433\pi$
$80$	80.0000	0.111803
$81$	0	0
$82$	−502.000	−0.676056
$83$	431.000	0.569981	0.284990	−	0.958530i	$-0.408010\pi$
$83$	431.000	0.569981	0.284990	+	0.958530i	$0.408010\pi$
$84$	0	0
$85$	−300.000	−0.382818
$86$	22.0000	0.0275851
$87$	0	0
$88$	−296.000	−0.358565
$89$	−1039.00	−1.23746	−0.618729	−	0.785604i	$-0.712352\pi$
$89$	−1039.00	−1.23746	−0.618729	+	0.785604i	$0.712352\pi$
$90$	0	0
$91$	−511.000	−0.588652
$92$	−776.000	−0.879387
$93$	0	0
$94$	398.000	0.436708
$95$	45.0000	0.0485990
$96$	0	0
$97$	446.000	0.466850	0.233425	−	0.972375i	$-0.425007\pi$
$97$	446.000	0.466850	0.233425	+	0.972375i	$0.425007\pi$
$98$	98.0000	0.101015
$99$	0	0
$100$	100.000	0.100000
$101$	−213.000	−0.209844	−0.104922	−	0.994480i	$-0.533459\pi$
$101$	−213.000	−0.209844	−0.104922	+	0.994480i	$0.533459\pi$
$102$	0	0
$103$	1700.00	1.62627	0.813136	−	0.582074i	$-0.197759\pi$
$103$	1700.00	1.62627	0.813136	+	0.582074i	$0.197759\pi$
$104$	584.000	0.550634
$105$	0	0
$106$	218.000	0.199755
$107$	−724.000	−0.654128	−0.327064	−	0.945002i	$-0.606059\pi$
$107$	−724.000	−0.654128	−0.327064	+	0.945002i	$0.606059\pi$
$108$	0	0
$109$	−2205.00	−1.93762	−0.968811	−	0.247803i	$-0.920292\pi$
$109$	−2205.00	−1.93762	−0.968811	+	0.247803i	$0.920292\pi$
$110$	−370.000	−0.320710
$111$	0	0
$112$	−112.000	−0.0944911
$113$	−1245.00	−1.03646	−0.518229	−	0.855242i	$-0.673408\pi$
$113$	−1245.00	−1.03646	−0.518229	+	0.855242i	$0.673408\pi$
$114$	0	0
$115$	−970.000	−0.786548
$116$	−296.000	−0.236922
$117$	0	0
$118$	716.000	0.558586
$119$	420.000	0.323541
$120$	0	0
$121$	38.0000	0.0285500
$122$	−1344.00	−0.997377
$123$	0	0
$124$	304.000	0.220161
$125$	125.000	0.0894427
$126$	0	0
$127$	−1091.00	−0.762288	−0.381144	−	0.924516i	$-0.624470\pi$
$127$	−1091.00	−0.762288	−0.381144	+	0.924516i	$0.624470\pi$
$128$	128.000	0.0883883
$129$	0	0
$130$	730.000	0.492502
$131$	664.000	0.442855	0.221427	−	0.975177i	$-0.428928\pi$
$131$	664.000	0.442855	0.221427	+	0.975177i	$0.428928\pi$
$132$	0	0
$133$	−63.0000	−0.0410736
$134$	−2034.00	−1.31127
$135$	0	0
$136$	−480.000	−0.302645
$137$	−2451.00	−1.52849	−0.764245	−	0.644926i	$-0.776888\pi$
$137$	−2451.00	−1.52849	−0.764245	+	0.644926i	$0.776888\pi$
$138$	0	0
$139$	−532.000	−0.324631	−0.162315	−	0.986739i	$-0.551896\pi$
$139$	−532.000	−0.324631	−0.162315	+	0.986739i	$0.551896\pi$
$140$	−140.000	−0.0845154
$141$	0	0
$142$	−1104.00	−0.652434
$143$	−2701.00	−1.57950
$144$	0	0
$145$	−370.000	−0.211909
$146$	330.000	0.187062
$147$	0	0
$148$	−712.000	−0.395446
$149$	−1410.00	−0.775246	−0.387623	−	0.921818i	$-0.626704\pi$
$149$	−1410.00	−0.775246	−0.387623	+	0.921818i	$0.626704\pi$
$150$	0	0
$151$	1602.00	0.863370	0.431685	−	0.902024i	$-0.357919\pi$
$151$	1602.00	0.863370	0.431685	+	0.902024i	$0.357919\pi$
$152$	72.0000	0.0384209
$153$	0	0
$154$	518.000	0.271050
$155$	380.000	0.196918
$156$	0	0
$157$	−1750.00	−0.889587	−0.444794	−	0.895633i	$-0.646723\pi$
$157$	−1750.00	−0.889587	−0.444794	+	0.895633i	$0.646723\pi$
$158$	1760.00	0.886190
$159$	0	0
$160$	160.000	0.0790569
$161$	1358.00	0.664754
$162$	0	0
$163$	1888.00	0.907237	0.453618	−	0.891196i	$-0.350133\pi$
$163$	1888.00	0.907237	0.453618	+	0.891196i	$0.350133\pi$
$164$	−1004.00	−0.478044
$165$	0	0
$166$	862.000	0.403037
$167$	−1956.00	−0.906346	−0.453173	−	0.891423i	$-0.649708\pi$
$167$	−1956.00	−0.906346	−0.453173	+	0.891423i	$0.649708\pi$
$168$	0	0
$169$	3132.00	1.42558
$170$	−600.000	−0.270694
$171$	0	0
$172$	44.0000	0.0195056
$173$	342.000	0.150299	0.0751496	−	0.997172i	$-0.476057\pi$
$173$	342.000	0.150299	0.0751496	+	0.997172i	$0.476057\pi$
$174$	0	0
$175$	−175.000	−0.0755929
$176$	−592.000	−0.253544
$177$	0	0
$178$	−2078.00	−0.875015
$179$	3497.00	1.46021	0.730106	−	0.683334i	$-0.239471\pi$
$179$	3497.00	1.46021	0.730106	+	0.683334i	$0.239471\pi$
$180$	0	0
$181$	−450.000	−0.184797	−0.0923984	−	0.995722i	$-0.529453\pi$
$181$	−450.000	−0.184797	−0.0923984	+	0.995722i	$0.529453\pi$
$182$	−1022.00	−0.416240
$183$	0	0
$184$	−1552.00	−0.621820
$185$	−890.000	−0.353698
$186$	0	0
$187$	2220.00	0.868142
$188$	796.000	0.308799
$189$	0	0
$190$	90.0000	0.0343647
$191$	4035.00	1.52860	0.764299	−	0.644862i	$-0.223085\pi$
$191$	4035.00	1.52860	0.764299	+	0.644862i	$0.223085\pi$
$192$	0	0
$193$	−4262.00	−1.58956	−0.794781	−	0.606896i	$-0.792414\pi$
$193$	−4262.00	−1.58956	−0.794781	+	0.606896i	$0.792414\pi$
$194$	892.000	0.330113
$195$	0	0
$196$	196.000	0.0714286
$197$	−1921.00	−0.694749	−0.347375	−	0.937726i	$-0.612927\pi$
$197$	−1921.00	−0.694749	−0.347375	+	0.937726i	$0.612927\pi$
$198$	0	0
$199$	375.000	0.133583	0.0667916	−	0.997767i	$-0.478724\pi$
$199$	375.000	0.133583	0.0667916	+	0.997767i	$0.478724\pi$
$200$	200.000	0.0707107
$201$	0	0
$202$	−426.000	−0.148382
$203$	518.000	0.179096
$204$	0	0
$205$	−1255.00	−0.427576
$206$	3400.00	1.14995
$207$	0	0
$208$	1168.00	0.389357
$209$	−333.000	−0.110211
$210$	0	0
$211$	2342.00	0.764123	0.382061	−	0.924137i	$-0.375214\pi$
$211$	2342.00	0.764123	0.382061	+	0.924137i	$0.375214\pi$
$212$	436.000	0.141248
$213$	0	0
$214$	−1448.00	−0.462539
$215$	55.0000	0.0174464
$216$	0	0
$217$	−532.000	−0.166426
$218$	−4410.00	−1.37010
$219$	0	0
$220$	−740.000	−0.226776
$221$	−4380.00	−1.33317
$222$	0	0
$223$	1686.00	0.506291	0.253146	−	0.967428i	$-0.418535\pi$
$223$	1686.00	0.506291	0.253146	+	0.967428i	$0.418535\pi$
$224$	−224.000	−0.0668153
$225$	0	0
$226$	−2490.00	−0.732886
$227$	−4729.00	−1.38271	−0.691354	−	0.722516i	$-0.742986\pi$
$227$	−4729.00	−1.38271	−0.691354	+	0.722516i	$0.742986\pi$
$228$	0	0
$229$	−2842.00	−0.820108	−0.410054	−	0.912061i	$-0.634490\pi$
$229$	−2842.00	−0.820108	−0.410054	+	0.912061i	$0.634490\pi$
$230$	−1940.00	−0.556173
$231$	0	0
$232$	−592.000	−0.167529
$233$	−1593.00	−0.447901	−0.223950	−	0.974601i	$-0.571895\pi$
$233$	−1593.00	−0.447901	−0.223950	+	0.974601i	$0.571895\pi$
$234$	0	0
$235$	995.000	0.276198
$236$	1432.00	0.394980
$237$	0	0
$238$	840.000	0.228778
$239$	4560.00	1.23415	0.617075	−	0.786904i	$-0.288317\pi$
$239$	4560.00	1.23415	0.617075	+	0.786904i	$0.288317\pi$
$240$	0	0
$241$	−6704.00	−1.79188	−0.895939	−	0.444177i	$-0.853496\pi$
$241$	−6704.00	−1.79188	−0.895939	+	0.444177i	$0.853496\pi$
$242$	76.0000	0.0201879
$243$	0	0
$244$	−2688.00	−0.705252
$245$	245.000	0.0638877
$246$	0	0
$247$	657.000	0.169247
$248$	608.000	0.155678
$249$	0	0
$250$	250.000	0.0632456
$251$	34.0000	0.00855004	0.00427502	−	0.999991i	$-0.498639\pi$
$251$	34.0000	0.00855004	0.00427502	+	0.999991i	$0.498639\pi$
$252$	0	0
$253$	7178.00	1.78370
$254$	−2182.00	−0.539019
$255$	0	0
$256$	256.000	0.0625000
$257$	4156.00	1.00873	0.504366	−	0.863490i	$-0.331726\pi$
$257$	4156.00	1.00873	0.504366	+	0.863490i	$0.331726\pi$
$258$	0	0
$259$	1246.00	0.298929
$260$	1460.00	0.348251
$261$	0	0
$262$	1328.00	0.313145
$263$	−7308.00	−1.71342	−0.856712	−	0.515795i	$-0.827497\pi$
$263$	−7308.00	−1.71342	−0.856712	+	0.515795i	$0.827497\pi$
$264$	0	0
$265$	545.000	0.126336
$266$	−126.000	−0.0290434
$267$	0	0
$268$	−4068.00	−0.927211
$269$	5366.00	1.21625	0.608124	−	0.793842i	$-0.291922\pi$
$269$	5366.00	1.21625	0.608124	+	0.793842i	$0.291922\pi$
$270$	0	0
$271$	−2683.00	−0.601405	−0.300702	−	0.953718i	$-0.597221\pi$
$271$	−2683.00	−0.601405	−0.300702	+	0.953718i	$0.597221\pi$
$272$	−960.000	−0.214002
$273$	0	0
$274$	−4902.00	−1.08081
$275$	−925.000	−0.202835
$276$	0	0
$277$	5930.00	1.28628	0.643139	−	0.765749i	$-0.277632\pi$
$277$	5930.00	1.28628	0.643139	+	0.765749i	$0.277632\pi$
$278$	−1064.00	−0.229548
$279$	0	0
$280$	−280.000	−0.0597614
$281$	−6598.00	−1.40072	−0.700362	−	0.713787i	$-0.746978\pi$
$281$	−6598.00	−1.40072	−0.700362	+	0.713787i	$0.746978\pi$
$282$	0	0
$283$	2758.00	0.579315	0.289657	−	0.957130i	$-0.406459\pi$
$283$	2758.00	0.579315	0.289657	+	0.957130i	$0.406459\pi$
$284$	−2208.00	−0.461340
$285$	0	0
$286$	−5402.00	−1.11688
$287$	1757.00	0.361367
$288$	0	0
$289$	−1313.00	−0.267250
$290$	−740.000	−0.149842
$291$	0	0
$292$	660.000	0.132273
$293$	−4422.00	−0.881693	−0.440846	−	0.897583i	$-0.645322\pi$
$293$	−4422.00	−0.881693	−0.440846	+	0.897583i	$0.645322\pi$
$294$	0	0
$295$	1790.00	0.353281
$296$	−1424.00	−0.279623
$297$	0	0
$298$	−2820.00	−0.548182
$299$	−14162.0	−2.73916
$300$	0	0
$301$	−77.0000	−0.0147449
$302$	3204.00	0.610495
$303$	0	0
$304$	144.000	0.0271677
$305$	−3360.00	−0.630797
$306$	0	0
$307$	2036.00	0.378504	0.189252	−	0.981929i	$-0.439394\pi$
$307$	2036.00	0.378504	0.189252	+	0.981929i	$0.439394\pi$
$308$	1036.00	0.191661
$309$	0	0
$310$	760.000	0.139242
$311$	−3618.00	−0.659672	−0.329836	−	0.944038i	$-0.606993\pi$
$311$	−3618.00	−0.659672	−0.329836	+	0.944038i	$0.606993\pi$
$312$	0	0
$313$	4467.00	0.806677	0.403338	−	0.915051i	$-0.367850\pi$
$313$	4467.00	0.806677	0.403338	+	0.915051i	$0.367850\pi$
$314$	−3500.00	−0.629033
$315$	0	0
$316$	3520.00	0.626631
$317$	1005.00	0.178064	0.0890322	−	0.996029i	$-0.471623\pi$
$317$	1005.00	0.178064	0.0890322	+	0.996029i	$0.471623\pi$
$318$	0	0
$319$	2738.00	0.480560
$320$	320.000	0.0559017
$321$	0	0
$322$	2716.00	0.470052
$323$	−540.000	−0.0930229
$324$	0	0
$325$	1825.00	0.311485
$326$	3776.00	0.641513
$327$	0	0
$328$	−2008.00	−0.338028
$329$	−1393.00	−0.233430
$330$	0	0
$331$	5990.00	0.994683	0.497342	−	0.867555i	$-0.334310\pi$
$331$	5990.00	0.994683	0.497342	+	0.867555i	$0.334310\pi$
$332$	1724.00	0.284990
$333$	0	0
$334$	−3912.00	−0.640884
$335$	−5085.00	−0.829323
$336$	0	0
$337$	4944.00	0.799160	0.399580	−	0.916698i	$-0.369156\pi$
$337$	4944.00	0.799160	0.399580	+	0.916698i	$0.369156\pi$
$338$	6264.00	1.00804
$339$	0	0
$340$	−1200.00	−0.191409
$341$	−2812.00	−0.446564
$342$	0	0
$343$	−343.000	−0.0539949
$344$	88.0000	0.0137926
$345$	0	0
$346$	684.000	0.106278
$347$	10754.0	1.66370	0.831852	−	0.554998i	$-0.187281\pi$
$347$	10754.0	1.66370	0.831852	+	0.554998i	$0.187281\pi$
$348$	0	0
$349$	7830.00	1.20095	0.600473	−	0.799645i	$-0.294979\pi$
$349$	7830.00	1.20095	0.600473	+	0.799645i	$0.294979\pi$
$350$	−350.000	−0.0534522
$351$	0	0
$352$	−1184.00	−0.179282
$353$	−6012.00	−0.906477	−0.453239	−	0.891389i	$-0.649731\pi$
$353$	−6012.00	−0.906477	−0.453239	+	0.891389i	$0.649731\pi$
$354$	0	0
$355$	−2760.00	−0.412635
$356$	−4156.00	−0.618729
$357$	0	0
$358$	6994.00	1.03253
$359$	−5519.00	−0.811370	−0.405685	−	0.914013i	$-0.632967\pi$
$359$	−5519.00	−0.811370	−0.405685	+	0.914013i	$0.632967\pi$
$360$	0	0
$361$	−6778.00	−0.988191
$362$	−900.000	−0.130671
$363$	0	0
$364$	−2044.00	−0.294326
$365$	825.000	0.118308
$366$	0	0
$367$	−5810.00	−0.826375	−0.413187	−	0.910646i	$-0.635585\pi$
$367$	−5810.00	−0.826375	−0.413187	+	0.910646i	$0.635585\pi$
$368$	−3104.00	−0.439693
$369$	0	0
$370$	−1780.00	−0.250102
$371$	−763.000	−0.106774
$372$	0	0
$373$	−9768.00	−1.35595	−0.677973	−	0.735087i	$-0.737141\pi$
$373$	−9768.00	−1.35595	−0.677973	+	0.735087i	$0.737141\pi$
$374$	4440.00	0.613869
$375$	0	0
$376$	1592.00	0.218354
$377$	−5402.00	−0.737977
$378$	0	0
$379$	−8668.00	−1.17479	−0.587395	−	0.809301i	$-0.699846\pi$
$379$	−8668.00	−1.17479	−0.587395	+	0.809301i	$0.699846\pi$
$380$	180.000	0.0242995
$381$	0	0
$382$	8070.00	1.08088
$383$	−12280.0	−1.63833	−0.819163	−	0.573561i	$-0.805562\pi$
$383$	−12280.0	−1.63833	−0.819163	+	0.573561i	$0.805562\pi$
$384$	0	0
$385$	1295.00	0.171427
$386$	−8524.00	−1.12399
$387$	0	0
$388$	1784.00	0.233425
$389$	−578.000	−0.0753362	−0.0376681	−	0.999290i	$-0.511993\pi$
$389$	−578.000	−0.0753362	−0.0376681	+	0.999290i	$0.511993\pi$
$390$	0	0
$391$	11640.0	1.50552
$392$	392.000	0.0505076
$393$	0	0
$394$	−3842.00	−0.491262
$395$	4400.00	0.560476
$396$	0	0
$397$	10454.0	1.32159	0.660795	−	0.750566i	$-0.270219\pi$
$397$	10454.0	1.32159	0.660795	+	0.750566i	$0.270219\pi$
$398$	750.000	0.0944575
$399$	0	0
$400$	400.000	0.0500000
$401$	−10268.0	−1.27870	−0.639351	−	0.768915i	$-0.720797\pi$
$401$	−10268.0	−1.27870	−0.639351	+	0.768915i	$0.720797\pi$
$402$	0	0
$403$	5548.00	0.685771
$404$	−852.000	−0.104922
$405$	0	0
$406$	1036.00	0.126640
$407$	6586.00	0.802103
$408$	0	0
$409$	3794.00	0.458683	0.229341	−	0.973346i	$-0.426343\pi$
$409$	3794.00	0.458683	0.229341	+	0.973346i	$0.426343\pi$
$410$	−2510.00	−0.302342
$411$	0	0
$412$	6800.00	0.813136
$413$	−2506.00	−0.298577
$414$	0	0
$415$	2155.00	0.254903
$416$	2336.00	0.275317
$417$	0	0
$418$	−666.000	−0.0779309
$419$	−4478.00	−0.522111	−0.261056	−	0.965324i	$-0.584071\pi$
$419$	−4478.00	−0.522111	−0.261056	+	0.965324i	$0.584071\pi$
$420$	0	0
$421$	4363.00	0.505082	0.252541	−	0.967586i	$-0.418734\pi$
$421$	4363.00	0.505082	0.252541	+	0.967586i	$0.418734\pi$
$422$	4684.00	0.540316
$423$	0	0
$424$	872.000	0.0998775
$425$	−1500.00	−0.171202
$426$	0	0
$427$	4704.00	0.533121
$428$	−2896.00	−0.327064
$429$	0	0
$430$	110.000	0.0123364
$431$	3159.00	0.353048	0.176524	−	0.984296i	$-0.443515\pi$
$431$	3159.00	0.353048	0.176524	+	0.984296i	$0.443515\pi$
$432$	0	0
$433$	2671.00	0.296444	0.148222	−	0.988954i	$-0.452645\pi$
$433$	2671.00	0.296444	0.148222	+	0.988954i	$0.452645\pi$
$434$	−1064.00	−0.117681
$435$	0	0
$436$	−8820.00	−0.968811
$437$	−1746.00	−0.191127
$438$	0	0
$439$	−12475.0	−1.35626	−0.678131	−	0.734941i	$-0.737210\pi$
$439$	−12475.0	−1.35626	−0.678131	+	0.734941i	$0.737210\pi$
$440$	−1480.00	−0.160355
$441$	0	0
$442$	−8760.00	−0.942694
$443$	3520.00	0.377517	0.188759	−	0.982023i	$-0.439554\pi$
$443$	3520.00	0.377517	0.188759	+	0.982023i	$0.439554\pi$
$444$	0	0
$445$	−5195.00	−0.553408
$446$	3372.00	0.358002
$447$	0	0
$448$	−448.000	−0.0472456
$449$	12284.0	1.29113	0.645565	−	0.763705i	$-0.276622\pi$
$449$	12284.0	1.29113	0.645565	+	0.763705i	$0.276622\pi$
$450$	0	0
$451$	9287.00	0.969640
$452$	−4980.00	−0.518229
$453$	0	0
$454$	−9458.00	−0.977722
$455$	−2555.00	−0.263253
$456$	0	0
$457$	5052.00	0.517117	0.258559	−	0.965996i	$-0.416752\pi$
$457$	5052.00	0.517117	0.258559	+	0.965996i	$0.416752\pi$
$458$	−5684.00	−0.579904
$459$	0	0
$460$	−3880.00	−0.393274
$461$	−5805.00	−0.586477	−0.293238	−	0.956039i	$-0.594733\pi$
$461$	−5805.00	−0.586477	−0.293238	+	0.956039i	$0.594733\pi$
$462$	0	0
$463$	1463.00	0.146850	0.0734248	−	0.997301i	$-0.476607\pi$
$463$	1463.00	0.146850	0.0734248	+	0.997301i	$0.476607\pi$
$464$	−1184.00	−0.118461
$465$	0	0
$466$	−3186.00	−0.316714
$467$	1524.00	0.151011	0.0755057	−	0.997145i	$-0.475943\pi$
$467$	1524.00	0.151011	0.0755057	+	0.997145i	$0.475943\pi$
$468$	0	0
$469$	7119.00	0.700906
$470$	1990.00	0.195302
$471$	0	0
$472$	2864.00	0.279293
$473$	−407.000	−0.0395642
$474$	0	0
$475$	225.000	0.0217341
$476$	1680.00	0.161770
$477$	0	0
$478$	9120.00	0.872676
$479$	−2216.00	−0.211381	−0.105691	−	0.994399i	$-0.533705\pi$
$479$	−2216.00	−0.211381	−0.105691	+	0.994399i	$0.533705\pi$
$480$	0	0
$481$	−12994.0	−1.23176
$482$	−13408.0	−1.26705
$483$	0	0
$484$	152.000	0.0142750
$485$	2230.00	0.208782
$486$	0	0
$487$	−7219.00	−0.671713	−0.335856	−	0.941913i	$-0.609026\pi$
$487$	−7219.00	−0.671713	−0.335856	+	0.941913i	$0.609026\pi$
$488$	−5376.00	−0.498689
$489$	0	0
$490$	490.000	0.0451754
$491$	10628.0	0.976853	0.488427	−	0.872605i	$-0.337571\pi$
$491$	10628.0	0.976853	0.488427	+	0.872605i	$0.337571\pi$
$492$	0	0
$493$	4440.00	0.405614
$494$	1314.00	0.119675
$495$	0	0
$496$	1216.00	0.110081
$497$	3864.00	0.348741
$498$	0	0
$499$	13162.0	1.18079	0.590393	−	0.807116i	$-0.298973\pi$
$499$	13162.0	1.18079	0.590393	+	0.807116i	$0.298973\pi$
$500$	500.000	0.0447214
$501$	0	0
$502$	68.0000	0.00604579
$503$	13677.0	1.21238	0.606190	−	0.795320i	$-0.292697\pi$
$503$	13677.0	1.21238	0.606190	+	0.795320i	$0.292697\pi$
$504$	0	0
$505$	−1065.00	−0.0938453
$506$	14356.0	1.26127
$507$	0	0
$508$	−4364.00	−0.381144
$509$	−16534.0	−1.43980	−0.719898	−	0.694079i	$-0.755812\pi$
$509$	−16534.0	−1.43980	−0.719898	+	0.694079i	$0.755812\pi$
$510$	0	0
$511$	−1155.00	−0.0999886
$512$	512.000	0.0441942
$513$	0	0
$514$	8312.00	0.713281
$515$	8500.00	0.727291
$516$	0	0
$517$	−7363.00	−0.626353
$518$	2492.00	0.211375
$519$	0	0
$520$	2920.00	0.246251
$521$	14733.0	1.23890	0.619448	−	0.785038i	$-0.287357\pi$
$521$	14733.0	1.23890	0.619448	+	0.785038i	$0.287357\pi$
$522$	0	0
$523$	17162.0	1.43488	0.717440	−	0.696621i	$-0.245314\pi$
$523$	17162.0	1.43488	0.717440	+	0.696621i	$0.245314\pi$
$524$	2656.00	0.221427
$525$	0	0
$526$	−14616.0	−1.21157
$527$	−4560.00	−0.376920
$528$	0	0
$529$	25469.0	2.09329
$530$	1090.00	0.0893332
$531$	0	0
$532$	−252.000	−0.0205368
$533$	−18323.0	−1.48904
$534$	0	0
$535$	−3620.00	−0.292535
$536$	−8136.00	−0.655637
$537$	0	0
$538$	10732.0	0.860017
$539$	−1813.00	−0.144882
$540$	0	0
$541$	7757.00	0.616450	0.308225	−	0.951313i	$-0.400265\pi$
$541$	7757.00	0.616450	0.308225	+	0.951313i	$0.400265\pi$
$542$	−5366.00	−0.425257
$543$	0	0
$544$	−1920.00	−0.151322
$545$	−11025.0	−0.866530
$546$	0	0
$547$	13672.0	1.06869	0.534344	−	0.845267i	$-0.320559\pi$
$547$	13672.0	1.06869	0.534344	+	0.845267i	$0.320559\pi$
$548$	−9804.00	−0.764245
$549$	0	0
$550$	−1850.00	−0.143426
$551$	−666.000	−0.0514928
$552$	0	0
$553$	−6160.00	−0.473689
$554$	11860.0	0.909536
$555$	0	0
$556$	−2128.00	−0.162315
$557$	17478.0	1.32956	0.664782	−	0.747038i	$-0.268525\pi$
$557$	17478.0	1.32956	0.664782	+	0.747038i	$0.268525\pi$
$558$	0	0
$559$	803.000	0.0607572
$560$	−560.000	−0.0422577
$561$	0	0
$562$	−13196.0	−0.990462
$563$	9439.00	0.706583	0.353292	−	0.935513i	$-0.385062\pi$
$563$	9439.00	0.706583	0.353292	+	0.935513i	$0.385062\pi$
$564$	0	0
$565$	−6225.00	−0.463518
$566$	5516.00	0.409637
$567$	0	0
$568$	−4416.00	−0.326217
$569$	−7242.00	−0.533568	−0.266784	−	0.963756i	$-0.585961\pi$
$569$	−7242.00	−0.533568	−0.266784	+	0.963756i	$0.585961\pi$
$570$	0	0
$571$	−21608.0	−1.58365	−0.791827	−	0.610745i	$-0.790870\pi$
$571$	−21608.0	−1.58365	−0.791827	+	0.610745i	$0.790870\pi$
$572$	−10804.0	−0.789752
$573$	0	0
$574$	3514.00	0.255525
$575$	−4850.00	−0.351755
$576$	0	0
$577$	17311.0	1.24899	0.624494	−	0.781029i	$-0.285305\pi$
$577$	17311.0	1.24899	0.624494	+	0.781029i	$0.285305\pi$
$578$	−2626.00	−0.188974
$579$	0	0
$580$	−1480.00	−0.105955
$581$	−3017.00	−0.215432
$582$	0	0
$583$	−4033.00	−0.286501
$584$	1320.00	0.0935308
$585$	0	0
$586$	−8844.00	−0.623451
$587$	−8052.00	−0.566170	−0.283085	−	0.959095i	$-0.591358\pi$
$587$	−8052.00	−0.566170	−0.283085	+	0.959095i	$0.591358\pi$
$588$	0	0
$589$	684.000	0.0478501
$590$	3580.00	0.249807
$591$	0	0
$592$	−2848.00	−0.197723
$593$	6820.00	0.472283	0.236142	−	0.971719i	$-0.424117\pi$
$593$	6820.00	0.472283	0.236142	+	0.971719i	$0.424117\pi$
$594$	0	0
$595$	2100.00	0.144692
$596$	−5640.00	−0.387623
$597$	0	0
$598$	−28324.0	−1.93688
$599$	7001.00	0.477551	0.238776	−	0.971075i	$-0.423254\pi$
$599$	7001.00	0.477551	0.238776	+	0.971075i	$0.423254\pi$
$600$	0	0
$601$	13840.0	0.939343	0.469672	−	0.882841i	$-0.344372\pi$
$601$	13840.0	0.939343	0.469672	+	0.882841i	$0.344372\pi$
$602$	−154.000	−0.0104262
$603$	0	0
$604$	6408.00	0.431685
$605$	190.000	0.0127679
$606$	0	0
$607$	−2986.00	−0.199667	−0.0998336	−	0.995004i	$-0.531831\pi$
$607$	−2986.00	−0.199667	−0.0998336	+	0.995004i	$0.531831\pi$
$608$	288.000	0.0192104
$609$	0	0
$610$	−6720.00	−0.446041
$611$	14527.0	0.961865
$612$	0	0
$613$	5692.00	0.375037	0.187519	−	0.982261i	$-0.439956\pi$
$613$	5692.00	0.375037	0.187519	+	0.982261i	$0.439956\pi$
$614$	4072.00	0.267643
$615$	0	0
$616$	2072.00	0.135525
$617$	14806.0	0.966073	0.483037	−	0.875600i	$-0.339534\pi$
$617$	14806.0	0.966073	0.483037	+	0.875600i	$0.339534\pi$
$618$	0	0
$619$	623.000	0.0404531	0.0202266	−	0.999795i	$-0.493561\pi$
$619$	623.000	0.0404531	0.0202266	+	0.999795i	$0.493561\pi$
$620$	1520.00	0.0984591
$621$	0	0
$622$	−7236.00	−0.466458
$623$	7273.00	0.467715
$624$	0	0
$625$	625.000	0.0400000
$626$	8934.00	0.570406
$627$	0	0
$628$	−7000.00	−0.444794
$629$	10680.0	0.677010
$630$	0	0
$631$	11026.0	0.695623	0.347812	−	0.937564i	$-0.386925\pi$
$631$	11026.0	0.695623	0.347812	+	0.937564i	$0.386925\pi$
$632$	7040.00	0.443095
$633$	0	0
$634$	2010.00	0.125911
$635$	−5455.00	−0.340906
$636$	0	0
$637$	3577.00	0.222490
$638$	5476.00	0.339807
$639$	0	0
$640$	640.000	0.0395285
$641$	−1752.00	−0.107956	−0.0539780	−	0.998542i	$-0.517190\pi$
$641$	−1752.00	−0.107956	−0.0539780	+	0.998542i	$0.517190\pi$
$642$	0	0
$643$	6284.00	0.385407	0.192704	−	0.981257i	$-0.438274\pi$
$643$	6284.00	0.385407	0.192704	+	0.981257i	$0.438274\pi$
$644$	5432.00	0.332377
$645$	0	0
$646$	−1080.00	−0.0657771
$647$	−25433.0	−1.54540	−0.772700	−	0.634771i	$-0.781095\pi$
$647$	−25433.0	−1.54540	−0.772700	+	0.634771i	$0.781095\pi$
$648$	0	0
$649$	−13246.0	−0.801157
$650$	3650.00	0.220254
$651$	0	0
$652$	7552.00	0.453618
$653$	16018.0	0.959928	0.479964	−	0.877288i	$-0.340650\pi$
$653$	16018.0	0.959928	0.479964	+	0.877288i	$0.340650\pi$
$654$	0	0
$655$	3320.00	0.198051
$656$	−4016.00	−0.239022
$657$	0	0
$658$	−2786.00	−0.165060
$659$	19896.0	1.17608	0.588041	−	0.808831i	$-0.299899\pi$
$659$	19896.0	1.17608	0.588041	+	0.808831i	$0.299899\pi$
$660$	0	0
$661$	−13926.0	−0.819453	−0.409727	−	0.912208i	$-0.634376\pi$
$661$	−13926.0	−0.819453	−0.409727	+	0.912208i	$0.634376\pi$
$662$	11980.0	0.703347
$663$	0	0
$664$	3448.00	0.201519
$665$	−315.000	−0.0183687
$666$	0	0
$667$	14356.0	0.833383
$668$	−7824.00	−0.453173
$669$	0	0
$670$	−10170.0	−0.586420
$671$	24864.0	1.43050
$672$	0	0
$673$	11068.0	0.633938	0.316969	−	0.948436i	$-0.397335\pi$
$673$	11068.0	0.633938	0.316969	+	0.948436i	$0.397335\pi$
$674$	9888.00	0.565091
$675$	0	0
$676$	12528.0	0.712790
$677$	16874.0	0.957933	0.478966	−	0.877833i	$-0.341012\pi$
$677$	16874.0	0.957933	0.478966	+	0.877833i	$0.341012\pi$
$678$	0	0
$679$	−3122.00	−0.176453
$680$	−2400.00	−0.135347
$681$	0	0
$682$	−5624.00	−0.315768
$683$	−26990.0	−1.51207	−0.756035	−	0.654531i	$-0.772866\pi$
$683$	−26990.0	−1.51207	−0.756035	+	0.654531i	$0.772866\pi$
$684$	0	0
$685$	−12255.0	−0.683561
$686$	−686.000	−0.0381802
$687$	0	0
$688$	176.000	0.00975282
$689$	7957.00	0.439967
$690$	0	0
$691$	21537.0	1.18568	0.592841	−	0.805320i	$-0.298006\pi$
$691$	21537.0	1.18568	0.592841	+	0.805320i	$0.298006\pi$
$692$	1368.00	0.0751496
$693$	0	0
$694$	21508.0	1.17642
$695$	−2660.00	−0.145179
$696$	0	0
$697$	15060.0	0.818419
$698$	15660.0	0.849197
$699$	0	0
$700$	−700.000	−0.0377964
$701$	24972.0	1.34548	0.672739	−	0.739880i	$-0.265118\pi$
$701$	24972.0	1.34548	0.672739	+	0.739880i	$0.265118\pi$
$702$	0	0
$703$	−1602.00	−0.0859468
$704$	−2368.00	−0.126772
$705$	0	0
$706$	−12024.0	−0.640976
$707$	1491.00	0.0793138
$708$	0	0
$709$	13949.0	0.738880	0.369440	−	0.929255i	$-0.379550\pi$
$709$	13949.0	0.738880	0.369440	+	0.929255i	$0.379550\pi$
$710$	−5520.00	−0.291777
$711$	0	0
$712$	−8312.00	−0.437508
$713$	−14744.0	−0.774428
$714$	0	0
$715$	−13505.0	−0.706375
$716$	13988.0	0.730106
$717$	0	0
$718$	−11038.0	−0.573725
$719$	4796.00	0.248763	0.124382	−	0.992234i	$-0.460305\pi$
$719$	4796.00	0.248763	0.124382	+	0.992234i	$0.460305\pi$
$720$	0	0
$721$	−11900.0	−0.614673
$722$	−13556.0	−0.698756
$723$	0	0
$724$	−1800.00	−0.0923984
$725$	−1850.00	−0.0947687
$726$	0	0
$727$	30812.0	1.57188	0.785938	−	0.618305i	$-0.212180\pi$
$727$	30812.0	1.57188	0.785938	+	0.618305i	$0.212180\pi$
$728$	−4088.00	−0.208120
$729$	0	0
$730$	1650.00	0.0836565
$731$	−660.000	−0.0333940
$732$	0	0
$733$	−5623.00	−0.283343	−0.141671	−	0.989914i	$-0.545248\pi$
$733$	−5623.00	−0.283343	−0.141671	+	0.989914i	$0.545248\pi$
$734$	−11620.0	−0.584335
$735$	0	0
$736$	−6208.00	−0.310910
$737$	37629.0	1.88071
$738$	0	0
$739$	38516.0	1.91723	0.958616	−	0.284703i	$-0.0918951\pi$
$739$	38516.0	1.91723	0.958616	+	0.284703i	$0.0918951\pi$
$740$	−3560.00	−0.176849
$741$	0	0
$742$	−1526.00	−0.0755003
$743$	−10994.0	−0.542841	−0.271420	−	0.962461i	$-0.587493\pi$
$743$	−10994.0	−0.542841	−0.271420	+	0.962461i	$0.587493\pi$
$744$	0	0
$745$	−7050.00	−0.346701
$746$	−19536.0	−0.958799
$747$	0	0
$748$	8880.00	0.434071
$749$	5068.00	0.247237
$750$	0	0
$751$	−24274.0	−1.17946	−0.589728	−	0.807602i	$-0.700765\pi$
$751$	−24274.0	−1.17946	−0.589728	+	0.807602i	$0.700765\pi$
$752$	3184.00	0.154400
$753$	0	0
$754$	−10804.0	−0.521828
$755$	8010.00	0.386111
$756$	0	0
$757$	20360.0	0.977539	0.488769	−	0.872413i	$-0.337446\pi$
$757$	20360.0	0.977539	0.488769	+	0.872413i	$0.337446\pi$
$758$	−17336.0	−0.830702
$759$	0	0
$760$	360.000	0.0171823
$761$	26094.0	1.24298	0.621489	−	0.783423i	$-0.286528\pi$
$761$	26094.0	1.24298	0.621489	+	0.783423i	$0.286528\pi$
$762$	0	0
$763$	15435.0	0.732352
$764$	16140.0	0.764299
$765$	0	0
$766$	−24560.0	−1.15847
$767$	26134.0	1.23031
$768$	0	0
$769$	−8564.00	−0.401594	−0.200797	−	0.979633i	$-0.564353\pi$
$769$	−8564.00	−0.401594	−0.200797	+	0.979633i	$0.564353\pi$
$770$	2590.00	0.121217
$771$	0	0
$772$	−17048.0	−0.794781
$773$	−4878.00	−0.226972	−0.113486	−	0.993540i	$-0.536202\pi$
$773$	−4878.00	−0.226972	−0.113486	+	0.993540i	$0.536202\pi$
$774$	0	0
$775$	1900.00	0.0880645
$776$	3568.00	0.165056
$777$	0	0
$778$	−1156.00	−0.0532707
$779$	−2259.00	−0.103899
$780$	0	0
$781$	20424.0	0.935760
$782$	23280.0	1.06457
$783$	0	0
$784$	784.000	0.0357143
$785$	−8750.00	−0.397836
$786$	0	0
$787$	−39944.0	−1.80921	−0.904606	−	0.426249i	$-0.859835\pi$
$787$	−39944.0	−1.80921	−0.904606	+	0.426249i	$0.859835\pi$
$788$	−7684.00	−0.347375
$789$	0	0
$790$	8800.00	0.396316
$791$	8715.00	0.391744
$792$	0	0
$793$	−49056.0	−2.19676
$794$	20908.0	0.934505
$795$	0	0
$796$	1500.00	0.0667916
$797$	−17604.0	−0.782391	−0.391196	−	0.920308i	$-0.627938\pi$
$797$	−17604.0	−0.782391	−0.391196	+	0.920308i	$0.627938\pi$
$798$	0	0
$799$	−11940.0	−0.528669
$800$	800.000	0.0353553
$801$	0	0
$802$	−20536.0	−0.904179
$803$	−6105.00	−0.268295
$804$	0	0
$805$	6790.00	0.297287
$806$	11096.0	0.484913
$807$	0	0
$808$	−1704.00	−0.0741912
$809$	−31242.0	−1.35774	−0.678869	−	0.734259i	$-0.737530\pi$
$809$	−31242.0	−1.35774	−0.678869	+	0.734259i	$0.737530\pi$
$810$	0	0
$811$	−18351.0	−0.794563	−0.397282	−	0.917697i	$-0.630046\pi$
$811$	−18351.0	−0.794563	−0.397282	+	0.917697i	$0.630046\pi$
$812$	2072.00	0.0895480
$813$	0	0
$814$	13172.0	0.567172
$815$	9440.00	0.405729
$816$	0	0
$817$	99.0000	0.00423938
$818$	7588.00	0.324338
$819$	0	0
$820$	−5020.00	−0.213788
$821$	39798.0	1.69179	0.845895	−	0.533349i	$-0.179067\pi$
$821$	39798.0	1.69179	0.845895	+	0.533349i	$0.179067\pi$
$822$	0	0
$823$	−6453.00	−0.273314	−0.136657	−	0.990618i	$-0.543636\pi$
$823$	−6453.00	−0.273314	−0.136657	+	0.990618i	$0.543636\pi$
$824$	13600.0	0.574974
$825$	0	0
$826$	−5012.00	−0.211126
$827$	9476.00	0.398444	0.199222	−	0.979954i	$-0.436159\pi$
$827$	9476.00	0.398444	0.199222	+	0.979954i	$0.436159\pi$
$828$	0	0
$829$	−40340.0	−1.69007	−0.845034	−	0.534713i	$-0.820420\pi$
$829$	−40340.0	−1.69007	−0.845034	+	0.534713i	$0.820420\pi$
$830$	4310.00	0.180244
$831$	0	0
$832$	4672.00	0.194678
$833$	−2940.00	−0.122287
$834$	0	0
$835$	−9780.00	−0.405330
$836$	−1332.00	−0.0551055
$837$	0	0
$838$	−8956.00	−0.369188
$839$	−28546.0	−1.17463	−0.587317	−	0.809357i	$-0.699816\pi$
$839$	−28546.0	−1.17463	−0.587317	+	0.809357i	$0.699816\pi$
$840$	0	0
$841$	−18913.0	−0.775473
$842$	8726.00	0.357147
$843$	0	0
$844$	9368.00	0.382061
$845$	15660.0	0.637539
$846$	0	0
$847$	−266.000	−0.0107909
$848$	1744.00	0.0706241
$849$	0	0
$850$	−3000.00	−0.121058
$851$	34532.0	1.39100
$852$	0	0
$853$	−12266.0	−0.492356	−0.246178	−	0.969225i	$-0.579175\pi$
$853$	−12266.0	−0.492356	−0.246178	+	0.969225i	$0.579175\pi$
$854$	9408.00	0.376973
$855$	0	0
$856$	−5792.00	−0.231269
$857$	29218.0	1.16461	0.582303	−	0.812972i	$-0.302152\pi$
$857$	29218.0	1.16461	0.582303	+	0.812972i	$0.302152\pi$
$858$	0	0
$859$	−16599.0	−0.659314	−0.329657	−	0.944101i	$-0.606933\pi$
$859$	−16599.0	−0.659314	−0.329657	+	0.944101i	$0.606933\pi$
$860$	220.000	0.00872318
$861$	0	0
$862$	6318.00	0.249643
$863$	22330.0	0.880790	0.440395	−	0.897804i	$-0.354838\pi$
$863$	22330.0	0.880790	0.440395	+	0.897804i	$0.354838\pi$
$864$	0	0
$865$	1710.00	0.0672159
$866$	5342.00	0.209617
$867$	0	0
$868$	−2128.00	−0.0832132
$869$	−32560.0	−1.27103
$870$	0	0
$871$	−74241.0	−2.88813
$872$	−17640.0	−0.685052
$873$	0	0
$874$	−3492.00	−0.135147
$875$	−875.000	−0.0338062
$876$	0	0
$877$	−30304.0	−1.16681	−0.583406	−	0.812181i	$-0.698280\pi$
$877$	−30304.0	−1.16681	−0.583406	+	0.812181i	$0.698280\pi$
$878$	−24950.0	−0.959022
$879$	0	0
$880$	−2960.00	−0.113388
$881$	−32618.0	−1.24736	−0.623682	−	0.781678i	$-0.714364\pi$
$881$	−32618.0	−1.24736	−0.623682	+	0.781678i	$0.714364\pi$
$882$	0	0
$883$	31908.0	1.21607	0.608035	−	0.793910i	$-0.291958\pi$
$883$	31908.0	1.21607	0.608035	+	0.793910i	$0.291958\pi$
$884$	−17520.0	−0.666585
$885$	0	0
$886$	7040.00	0.266945
$887$	−44461.0	−1.68304	−0.841519	−	0.540228i	$-0.818338\pi$
$887$	−44461.0	−1.68304	−0.841519	+	0.540228i	$0.818338\pi$
$888$	0	0
$889$	7637.00	0.288118
$890$	−10390.0	−0.391319
$891$	0	0
$892$	6744.00	0.253146
$893$	1791.00	0.0671148
$894$	0	0
$895$	17485.0	0.653027
$896$	−896.000	−0.0334077
$897$	0	0
$898$	24568.0	0.912967
$899$	−5624.00	−0.208644
$900$	0	0
$901$	−6540.00	−0.241819
$902$	18574.0	0.685639
$903$	0	0
$904$	−9960.00	−0.366443
$905$	−2250.00	−0.0826437
$906$	0	0
$907$	20027.0	0.733170	0.366585	−	0.930384i	$-0.380527\pi$
$907$	20027.0	0.733170	0.366585	+	0.930384i	$0.380527\pi$
$908$	−18916.0	−0.691354
$909$	0	0
$910$	−5110.00	−0.186148
$911$	−21551.0	−0.783772	−0.391886	−	0.920014i	$-0.628177\pi$
$911$	−21551.0	−0.783772	−0.391886	+	0.920014i	$0.628177\pi$
$912$	0	0
$913$	−15947.0	−0.578060
$914$	10104.0	0.365657
$915$	0	0
$916$	−11368.0	−0.410054
$917$	−4648.00	−0.167383
$918$	0	0
$919$	−34728.0	−1.24654	−0.623270	−	0.782006i	$-0.714196\pi$
$919$	−34728.0	−1.24654	−0.623270	+	0.782006i	$0.714196\pi$
$920$	−7760.00	−0.278087
$921$	0	0
$922$	−11610.0	−0.414702
$923$	−40296.0	−1.43701
$924$	0	0
$925$	−4450.00	−0.158178
$926$	2926.00	0.103838
$927$	0	0
$928$	−2368.00	−0.0837644
$929$	41499.0	1.46560	0.732798	−	0.680447i	$-0.238214\pi$
$929$	41499.0	1.46560	0.732798	+	0.680447i	$0.238214\pi$
$930$	0	0
$931$	441.000	0.0155244
$932$	−6372.00	−0.223950
$933$	0	0
$934$	3048.00	0.106781
$935$	11100.0	0.388245
$936$	0	0
$937$	24117.0	0.840841	0.420421	−	0.907329i	$-0.361883\pi$
$937$	24117.0	0.840841	0.420421	+	0.907329i	$0.361883\pi$
$938$	14238.0	0.495615
$939$	0	0
$940$	3980.00	0.138099
$941$	405.000	0.0140304	0.00701521	−	0.999975i	$-0.497767\pi$
$941$	405.000	0.0140304	0.00701521	+	0.999975i	$0.497767\pi$
$942$	0	0
$943$	48694.0	1.68154
$944$	5728.00	0.197490
$945$	0	0
$946$	−814.000	−0.0279761
$947$	37732.0	1.29475	0.647373	−	0.762173i	$-0.275867\pi$
$947$	37732.0	1.29475	0.647373	+	0.762173i	$0.275867\pi$
$948$	0	0
$949$	12045.0	0.412010
$950$	450.000	0.0153683
$951$	0	0
$952$	3360.00	0.114389
$953$	37102.0	1.26112	0.630562	−	0.776139i	$-0.282824\pi$
$953$	37102.0	1.26112	0.630562	+	0.776139i	$0.282824\pi$
$954$	0	0
$955$	20175.0	0.683610
$956$	18240.0	0.617075
$957$	0	0
$958$	−4432.00	−0.149469
$959$	17157.0	0.577715
$960$	0	0
$961$	−24015.0	−0.806116
$962$	−25988.0	−0.870984
$963$	0	0
$964$	−26816.0	−0.895939
$965$	−21310.0	−0.710874
$966$	0	0
$967$	6619.00	0.220117	0.110058	−	0.993925i	$-0.464896\pi$
$967$	6619.00	0.220117	0.110058	+	0.993925i	$0.464896\pi$
$968$	304.000	0.0100939
$969$	0	0
$970$	4460.00	0.147631
$971$	35028.0	1.15767	0.578837	−	0.815443i	$-0.303507\pi$
$971$	35028.0	1.15767	0.578837	+	0.815443i	$0.303507\pi$
$972$	0	0
$973$	3724.00	0.122699
$974$	−14438.0	−0.474973
$975$	0	0
$976$	−10752.0	−0.352626
$977$	22443.0	0.734918	0.367459	−	0.930040i	$-0.380228\pi$
$977$	22443.0	0.734918	0.367459	+	0.930040i	$0.380228\pi$
$978$	0	0
$979$	38443.0	1.25500
$980$	980.000	0.0319438
$981$	0	0
$982$	21256.0	0.690740
$983$	−15392.0	−0.499419	−0.249709	−	0.968321i	$-0.580335\pi$
$983$	−15392.0	−0.499419	−0.249709	+	0.968321i	$0.580335\pi$
$984$	0	0
$985$	−9605.00	−0.310701
$986$	8880.00	0.286812
$987$	0	0
$988$	2628.00	0.0846233
$989$	−2134.00	−0.0686120
$990$	0	0
$991$	−11288.0	−0.361832	−0.180916	−	0.983499i	$-0.557906\pi$
$991$	−11288.0	−0.361832	−0.180916	+	0.983499i	$0.557906\pi$
$992$	2432.00	0.0778388
$993$	0	0
$994$	7728.00	0.246597
$995$	1875.00	0.0597402
$996$	0	0
$997$	59906.0	1.90295	0.951475	−	0.307725i	$-0.0995676\pi$
$997$	59906.0	1.90295	0.951475	+	0.307725i	$0.0995676\pi$
$998$	26324.0	0.834942
$999$	0	0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1890.4.a.c.1.1	✓	1	3.2	odd	2
1890.4.a.i.1.1	yes	1	1.1	even	1	trivial

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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