LMFDB - Embedded newform 2166.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2166,4,Mod(1,2166)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2166, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2166.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2166 = 2 \cdot 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2166.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:	$127.798137072$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2166.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.00000 q^{5} -6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -7.00000 q^{5} -6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -14.0000 q^{10} -49.0000 q^{11} -12.0000 q^{12} -14.0000 q^{13} -30.0000 q^{14} +21.0000 q^{15} +16.0000 q^{16} -33.0000 q^{17} +18.0000 q^{18} -28.0000 q^{20} +45.0000 q^{21} -98.0000 q^{22} -148.000 q^{23} -24.0000 q^{24} -76.0000 q^{25} -28.0000 q^{26} -27.0000 q^{27} -60.0000 q^{28} +278.000 q^{29} +42.0000 q^{30} -94.0000 q^{31} +32.0000 q^{32} +147.000 q^{33} -66.0000 q^{34} +105.000 q^{35} +36.0000 q^{36} -160.000 q^{37} +42.0000 q^{39} -56.0000 q^{40} -400.000 q^{41} +90.0000 q^{42} +73.0000 q^{43} -196.000 q^{44} -63.0000 q^{45} -296.000 q^{46} +173.000 q^{47} -48.0000 q^{48} -118.000 q^{49} -152.000 q^{50} +99.0000 q^{51} -56.0000 q^{52} -170.000 q^{53} -54.0000 q^{54} +343.000 q^{55} -120.000 q^{56} +556.000 q^{58} +12.0000 q^{59} +84.0000 q^{60} +419.000 q^{61} -188.000 q^{62} -135.000 q^{63} +64.0000 q^{64} +98.0000 q^{65} +294.000 q^{66} -444.000 q^{67} -132.000 q^{68} +444.000 q^{69} +210.000 q^{70} +952.000 q^{71} +72.0000 q^{72} -27.0000 q^{73} -320.000 q^{74} +228.000 q^{75} +735.000 q^{77} +84.0000 q^{78} +556.000 q^{79} -112.000 q^{80} +81.0000 q^{81} -800.000 q^{82} -276.000 q^{83} +180.000 q^{84} +231.000 q^{85} +146.000 q^{86} -834.000 q^{87} -392.000 q^{88} -1386.00 q^{89} -126.000 q^{90} +210.000 q^{91} -592.000 q^{92} +282.000 q^{93} +346.000 q^{94} -96.0000 q^{96} -130.000 q^{97} -236.000 q^{98} -441.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−7.00000	−0.626099	−0.313050	−	0.949737i	$-0.601351\pi$
$5$	−7.00000	−0.626099	−0.313050	+	0.949737i	$0.601351\pi$
$6$	−6.00000	−0.408248
$7$	−15.0000	−0.809924	−0.404962	−	0.914334i	$-0.632715\pi$
$7$	−15.0000	−0.809924	−0.404962	+	0.914334i	$0.632715\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−14.0000	−0.442719
$11$	−49.0000	−1.34310	−0.671548	−	0.740961i	$-0.734370\pi$
$11$	−49.0000	−1.34310	−0.671548	+	0.740961i	$0.734370\pi$
$12$	−12.0000	−0.288675
$13$	−14.0000	−0.298685	−0.149342	−	0.988786i	$-0.547716\pi$
$13$	−14.0000	−0.298685	−0.149342	+	0.988786i	$0.547716\pi$
$14$	−30.0000	−0.572703
$15$	21.0000	0.361478
$16$	16.0000	0.250000
$17$	−33.0000	−0.470804	−0.235402	−	0.971898i	$-0.575641\pi$
$17$	−33.0000	−0.470804	−0.235402	+	0.971898i	$0.575641\pi$
$18$	18.0000	0.235702
$19$	0	0
$19$	0	0
$20$	−28.0000	−0.313050
$21$	45.0000	0.467610
$22$	−98.0000	−0.949712
$23$	−148.000	−1.34174	−0.670872	−	0.741573i	$-0.734080\pi$
$23$	−148.000	−1.34174	−0.670872	+	0.741573i	$0.734080\pi$
$24$	−24.0000	−0.204124
$25$	−76.0000	−0.608000
$26$	−28.0000	−0.211202
$27$	−27.0000	−0.192450
$28$	−60.0000	−0.404962
$29$	278.000	1.78011	0.890057	−	0.455849i	$-0.150664\pi$
$29$	278.000	1.78011	0.890057	+	0.455849i	$0.150664\pi$
$30$	42.0000	0.255604
$31$	−94.0000	−0.544610	−0.272305	−	0.962211i	$-0.587786\pi$
$31$	−94.0000	−0.544610	−0.272305	+	0.962211i	$0.587786\pi$
$32$	32.0000	0.176777
$33$	147.000	0.775437
$34$	−66.0000	−0.332909
$35$	105.000	0.507093
$36$	36.0000	0.166667
$37$	−160.000	−0.710915	−0.355457	−	0.934693i	$-0.615675\pi$
$37$	−160.000	−0.710915	−0.355457	+	0.934693i	$0.615675\pi$
$38$	0	0
$39$	42.0000	0.172446
$40$	−56.0000	−0.221359
$41$	−400.000	−1.52365	−0.761823	−	0.647785i	$-0.775696\pi$
$41$	−400.000	−1.52365	−0.761823	+	0.647785i	$0.775696\pi$
$42$	90.0000	0.330650
$43$	73.0000	0.258893	0.129446	−	0.991586i	$-0.458680\pi$
$43$	73.0000	0.258893	0.129446	+	0.991586i	$0.458680\pi$
$44$	−196.000	−0.671548
$45$	−63.0000	−0.208700
$46$	−296.000	−0.948757
$47$	173.000	0.536907	0.268454	−	0.963293i	$-0.413487\pi$
$47$	173.000	0.536907	0.268454	+	0.963293i	$0.413487\pi$
$48$	−48.0000	−0.144338
$49$	−118.000	−0.344023
$50$	−152.000	−0.429921
$51$	99.0000	0.271819
$52$	−56.0000	−0.149342
$53$	−170.000	−0.440590	−0.220295	−	0.975433i	$-0.570702\pi$
$53$	−170.000	−0.440590	−0.220295	+	0.975433i	$0.570702\pi$
$54$	−54.0000	−0.136083
$55$	343.000	0.840911
$56$	−120.000	−0.286351
$57$	0	0
$58$	556.000	1.25873
$59$	12.0000	0.0264791	0.0132396	−	0.999912i	$-0.495786\pi$
$59$	12.0000	0.0264791	0.0132396	+	0.999912i	$0.495786\pi$
$60$	84.0000	0.180739
$61$	419.000	0.879466	0.439733	−	0.898128i	$-0.355073\pi$
$61$	419.000	0.879466	0.439733	+	0.898128i	$0.355073\pi$
$62$	−188.000	−0.385097
$63$	−135.000	−0.269975
$64$	64.0000	0.125000
$65$	98.0000	0.187006
$66$	294.000	0.548317
$67$	−444.000	−0.809600	−0.404800	−	0.914405i	$-0.632659\pi$
$67$	−444.000	−0.809600	−0.404800	+	0.914405i	$0.632659\pi$
$68$	−132.000	−0.235402
$69$	444.000	0.774657
$70$	210.000	0.358569
$71$	952.000	1.59129	0.795645	−	0.605763i	$-0.207132\pi$
$71$	952.000	1.59129	0.795645	+	0.605763i	$0.207132\pi$
$72$	72.0000	0.117851
$73$	−27.0000	−0.0432892	−0.0216446	−	0.999766i	$-0.506890\pi$
$73$	−27.0000	−0.0432892	−0.0216446	+	0.999766i	$0.506890\pi$
$74$	−320.000	−0.502692
$75$	228.000	0.351029
$76$	0	0
$77$	735.000	1.08781
$78$	84.0000	0.121938
$79$	556.000	0.791834	0.395917	−	0.918286i	$-0.370427\pi$
$79$	556.000	0.791834	0.395917	+	0.918286i	$0.370427\pi$
$80$	−112.000	−0.156525
$81$	81.0000	0.111111
$82$	−800.000	−1.07738
$83$	−276.000	−0.364999	−0.182500	−	0.983206i	$-0.558419\pi$
$83$	−276.000	−0.364999	−0.182500	+	0.983206i	$0.558419\pi$
$84$	180.000	0.233805
$85$	231.000	0.294770
$86$	146.000	0.183065
$87$	−834.000	−1.02775
$88$	−392.000	−0.474856
$89$	−1386.00	−1.65074	−0.825369	−	0.564593i	$-0.809033\pi$
$89$	−1386.00	−1.65074	−0.825369	+	0.564593i	$0.809033\pi$
$90$	−126.000	−0.147573
$91$	210.000	0.241912
$92$	−592.000	−0.670872
$93$	282.000	0.314431
$94$	346.000	0.379651
$95$	0	0
$96$	−96.0000	−0.102062
$97$	−130.000	−0.136077	−0.0680387	−	0.997683i	$-0.521674\pi$
$97$	−130.000	−0.136077	−0.0680387	+	0.997683i	$0.521674\pi$
$98$	−236.000	−0.243261
$99$	−441.000	−0.447699
$100$	−304.000	−0.304000
$101$	−238.000	−0.234474	−0.117237	−	0.993104i	$-0.537404\pi$
$101$	−238.000	−0.234474	−0.117237	+	0.993104i	$0.537404\pi$
$102$	198.000	0.192205
$103$	1374.00	1.31441	0.657205	−	0.753712i	$-0.271739\pi$
$103$	1374.00	1.31441	0.657205	+	0.753712i	$0.271739\pi$
$104$	−112.000	−0.105601
$105$	−315.000	−0.292770
$106$	−340.000	−0.311545
$107$	−218.000	−0.196961	−0.0984806	−	0.995139i	$-0.531398\pi$
$107$	−218.000	−0.196961	−0.0984806	+	0.995139i	$0.531398\pi$
$108$	−108.000	−0.0962250
$109$	2184.00	1.91917	0.959584	−	0.281423i	$-0.0908065\pi$
$109$	2184.00	1.91917	0.959584	+	0.281423i	$0.0908065\pi$
$110$	686.000	0.594614
$111$	480.000	0.410447
$112$	−240.000	−0.202481
$113$	−1334.00	−1.11055	−0.555275	−	0.831667i	$-0.687387\pi$
$113$	−1334.00	−1.11055	−0.555275	+	0.831667i	$0.687387\pi$
$114$	0	0
$115$	1036.00	0.840065
$116$	1112.00	0.890057
$117$	−126.000	−0.0995616
$118$	24.0000	0.0187236
$119$	495.000	0.381316
$120$	168.000	0.127802
$121$	1070.00	0.803907
$122$	838.000	0.621877
$123$	1200.00	0.879678
$124$	−376.000	−0.272305
$125$	1407.00	1.00677
$126$	−270.000	−0.190901
$127$	666.000	0.465338	0.232669	−	0.972556i	$-0.425254\pi$
$127$	666.000	0.465338	0.232669	+	0.972556i	$0.425254\pi$
$128$	128.000	0.0883883
$129$	−219.000	−0.149472
$130$	196.000	0.132233
$131$	−303.000	−0.202086	−0.101043	−	0.994882i	$-0.532218\pi$
$131$	−303.000	−0.202086	−0.101043	+	0.994882i	$0.532218\pi$
$132$	588.000	0.387718
$133$	0	0
$134$	−888.000	−0.572474
$135$	189.000	0.120493
$136$	−264.000	−0.166455
$137$	583.000	0.363570	0.181785	−	0.983338i	$-0.441813\pi$
$137$	583.000	0.363570	0.181785	+	0.983338i	$0.441813\pi$
$138$	888.000	0.547765
$139$	−1467.00	−0.895175	−0.447587	−	0.894240i	$-0.647717\pi$
$139$	−1467.00	−0.895175	−0.447587	+	0.894240i	$0.647717\pi$
$140$	420.000	0.253546
$141$	−519.000	−0.309984
$142$	1904.00	1.12521
$143$	686.000	0.401162
$144$	144.000	0.0833333
$145$	−1946.00	−1.11453
$146$	−54.0000	−0.0306101
$147$	354.000	0.198622
$148$	−640.000	−0.355457
$149$	351.000	0.192987	0.0964934	−	0.995334i	$-0.469237\pi$
$149$	351.000	0.192987	0.0964934	+	0.995334i	$0.469237\pi$
$150$	456.000	0.248215
$151$	3100.00	1.67069	0.835346	−	0.549725i	$-0.185267\pi$
$151$	3100.00	1.67069	0.835346	+	0.549725i	$0.185267\pi$
$152$	0	0
$153$	−297.000	−0.156935
$154$	1470.00	0.769195
$155$	658.000	0.340980
$156$	168.000	0.0862229
$157$	−2474.00	−1.25762	−0.628811	−	0.777558i	$-0.716458\pi$
$157$	−2474.00	−1.25762	−0.628811	+	0.777558i	$0.716458\pi$
$158$	1112.00	0.559911
$159$	510.000	0.254375
$160$	−224.000	−0.110680
$161$	2220.00	1.08671
$162$	162.000	0.0785674
$163$	2360.00	1.13405	0.567023	−	0.823702i	$-0.308095\pi$
$163$	2360.00	1.13405	0.567023	+	0.823702i	$0.308095\pi$
$164$	−1600.00	−0.761823
$165$	−1029.00	−0.485500
$166$	−552.000	−0.258093
$167$	1110.00	0.514338	0.257169	−	0.966366i	$-0.417210\pi$
$167$	1110.00	0.514338	0.257169	+	0.966366i	$0.417210\pi$
$168$	360.000	0.165325
$169$	−2001.00	−0.910787
$170$	462.000	0.208434
$171$	0	0
$172$	292.000	0.129446
$173$	258.000	0.113384	0.0566918	−	0.998392i	$-0.481945\pi$
$173$	258.000	0.113384	0.0566918	+	0.998392i	$0.481945\pi$
$174$	−1668.00	−0.726728
$175$	1140.00	0.492434
$176$	−784.000	−0.335774
$177$	−36.0000	−0.0152877
$178$	−2772.00	−1.16725
$179$	3762.00	1.57087	0.785433	−	0.618946i	$-0.212440\pi$
$179$	3762.00	1.57087	0.785433	+	0.618946i	$0.212440\pi$
$180$	−252.000	−0.104350
$181$	−706.000	−0.289926	−0.144963	−	0.989437i	$-0.546306\pi$
$181$	−706.000	−0.289926	−0.144963	+	0.989437i	$0.546306\pi$
$182$	420.000	0.171058
$183$	−1257.00	−0.507760
$184$	−1184.00	−0.474378
$185$	1120.00	0.445103
$186$	564.000	0.222336
$187$	1617.00	0.632336
$188$	692.000	0.268454
$189$	405.000	0.155870
$190$	0	0
$191$	2659.00	1.00732	0.503661	−	0.863901i	$-0.331986\pi$
$191$	2659.00	1.00732	0.503661	+	0.863901i	$0.331986\pi$
$192$	−192.000	−0.0721688
$193$	−3648.00	−1.36056	−0.680282	−	0.732951i	$-0.738143\pi$
$193$	−3648.00	−1.36056	−0.680282	+	0.732951i	$0.738143\pi$
$194$	−260.000	−0.0962212
$195$	−294.000	−0.107968
$196$	−472.000	−0.172012
$197$	494.000	0.178660	0.0893301	−	0.996002i	$-0.471527\pi$
$197$	494.000	0.178660	0.0893301	+	0.996002i	$0.471527\pi$
$198$	−882.000	−0.316571
$199$	−3679.00	−1.31054	−0.655270	−	0.755395i	$-0.727445\pi$
$199$	−3679.00	−1.31054	−0.655270	+	0.755395i	$0.727445\pi$
$200$	−608.000	−0.214960
$201$	1332.00	0.467423
$202$	−476.000	−0.165798
$203$	−4170.00	−1.44176
$204$	396.000	0.135910
$205$	2800.00	0.953954
$206$	2748.00	0.929428
$207$	−1332.00	−0.447248
$208$	−224.000	−0.0746712
$209$	0	0
$210$	−630.000	−0.207020
$211$	−792.000	−0.258405	−0.129203	−	0.991618i	$-0.541242\pi$
$211$	−792.000	−0.258405	−0.129203	+	0.991618i	$0.541242\pi$
$212$	−680.000	−0.220295
$213$	−2856.00	−0.918732
$214$	−436.000	−0.139273
$215$	−511.000	−0.162093
$216$	−216.000	−0.0680414
$217$	1410.00	0.441092
$218$	4368.00	1.35706
$219$	81.0000	0.0249930
$220$	1372.00	0.420456
$221$	462.000	0.140622
$222$	960.000	0.290230
$223$	4636.00	1.39215	0.696075	−	0.717969i	$-0.254928\pi$
$223$	4636.00	1.39215	0.696075	+	0.717969i	$0.254928\pi$
$224$	−480.000	−0.143176
$225$	−684.000	−0.202667
$226$	−2668.00	−0.785278
$227$	6446.00	1.88474	0.942370	−	0.334572i	$-0.108592\pi$
$227$	6446.00	1.88474	0.942370	+	0.334572i	$0.108592\pi$
$228$	0	0
$229$	5765.00	1.66359	0.831795	−	0.555084i	$-0.187314\pi$
$229$	5765.00	1.66359	0.831795	+	0.555084i	$0.187314\pi$
$230$	2072.00	0.594016
$231$	−2205.00	−0.628045
$232$	2224.00	0.629365
$233$	−5847.00	−1.64399	−0.821995	−	0.569495i	$-0.807139\pi$
$233$	−5847.00	−1.64399	−0.821995	+	0.569495i	$0.807139\pi$
$234$	−252.000	−0.0704007
$235$	−1211.00	−0.336157
$236$	48.0000	0.0132396
$237$	−1668.00	−0.457166
$238$	990.000	0.269631
$239$	2823.00	0.764036	0.382018	−	0.924155i	$-0.375229\pi$
$239$	2823.00	0.764036	0.382018	+	0.924155i	$0.375229\pi$
$240$	336.000	0.0903696
$241$	6140.00	1.64113	0.820565	−	0.571554i	$-0.193659\pi$
$241$	6140.00	1.64113	0.820565	+	0.571554i	$0.193659\pi$
$242$	2140.00	0.568448
$243$	−243.000	−0.0641500
$244$	1676.00	0.439733
$245$	826.000	0.215393
$246$	2400.00	0.622026
$247$	0	0
$248$	−752.000	−0.192549
$249$	828.000	0.210732
$250$	2814.00	0.711892
$251$	−3103.00	−0.780317	−0.390159	−	0.920748i	$-0.627580\pi$
$251$	−3103.00	−0.780317	−0.390159	+	0.920748i	$0.627580\pi$
$252$	−540.000	−0.134987
$253$	7252.00	1.80209
$254$	1332.00	0.329044
$255$	−693.000	−0.170186
$256$	256.000	0.0625000
$257$	−2336.00	−0.566987	−0.283494	−	0.958974i	$-0.591493\pi$
$257$	−2336.00	−0.566987	−0.283494	+	0.958974i	$0.591493\pi$
$258$	−438.000	−0.105693
$259$	2400.00	0.575787
$260$	392.000	0.0935031
$261$	2502.00	0.593371
$262$	−606.000	−0.142896
$263$	−2739.00	−0.642182	−0.321091	−	0.947048i	$-0.604050\pi$
$263$	−2739.00	−0.642182	−0.321091	+	0.947048i	$0.604050\pi$
$264$	1176.00	0.274158
$265$	1190.00	0.275853
$266$	0	0
$267$	4158.00	0.953054
$268$	−1776.00	−0.404800
$269$	6486.00	1.47011	0.735053	−	0.678010i	$-0.237157\pi$
$269$	6486.00	1.47011	0.735053	+	0.678010i	$0.237157\pi$
$270$	378.000	0.0852013
$271$	−308.000	−0.0690394	−0.0345197	−	0.999404i	$-0.510990\pi$
$271$	−308.000	−0.0690394	−0.0345197	+	0.999404i	$0.510990\pi$
$272$	−528.000	−0.117701
$273$	−630.000	−0.139668
$274$	1166.00	0.257083
$275$	3724.00	0.816602
$276$	1776.00	0.387328
$277$	2977.00	0.645742	0.322871	−	0.946443i	$-0.395352\pi$
$277$	2977.00	0.645742	0.322871	+	0.946443i	$0.395352\pi$
$278$	−2934.00	−0.632984
$279$	−846.000	−0.181537
$280$	840.000	0.179284
$281$	−4570.00	−0.970190	−0.485095	−	0.874462i	$-0.661215\pi$
$281$	−4570.00	−0.970190	−0.485095	+	0.874462i	$0.661215\pi$
$282$	−1038.00	−0.219191
$283$	6429.00	1.35040	0.675202	−	0.737633i	$-0.264056\pi$
$283$	6429.00	1.35040	0.675202	+	0.737633i	$0.264056\pi$
$284$	3808.00	0.795645
$285$	0	0
$286$	1372.00	0.283665
$287$	6000.00	1.23404
$288$	288.000	0.0589256
$289$	−3824.00	−0.778343
$290$	−3892.00	−0.788090
$291$	390.000	0.0785643
$292$	−108.000	−0.0216446
$293$	−5724.00	−1.14130	−0.570648	−	0.821195i	$-0.693308\pi$
$293$	−5724.00	−1.14130	−0.570648	+	0.821195i	$0.693308\pi$
$294$	708.000	0.140447
$295$	−84.0000	−0.0165785
$296$	−1280.00	−0.251346
$297$	1323.00	0.258479
$298$	702.000	0.136462
$299$	2072.00	0.400759
$300$	912.000	0.175514
$301$	−1095.00	−0.209684
$302$	6200.00	1.18136
$303$	714.000	0.135374
$304$	0	0
$305$	−2933.00	−0.550633
$306$	−594.000	−0.110970
$307$	−8304.00	−1.54376	−0.771880	−	0.635768i	$-0.780683\pi$
$307$	−8304.00	−1.54376	−0.771880	+	0.635768i	$0.780683\pi$
$308$	2940.00	0.543903
$309$	−4122.00	−0.758875
$310$	1316.00	0.241109
$311$	−791.000	−0.144223	−0.0721117	−	0.997397i	$-0.522974\pi$
$311$	−791.000	−0.144223	−0.0721117	+	0.997397i	$0.522974\pi$
$312$	336.000	0.0609688
$313$	10166.0	1.83583	0.917917	−	0.396772i	$-0.129869\pi$
$313$	10166.0	1.83583	0.917917	+	0.396772i	$0.129869\pi$
$314$	−4948.00	−0.889273
$315$	945.000	0.169031
$316$	2224.00	0.395917
$317$	−6408.00	−1.13536	−0.567680	−	0.823249i	$-0.692159\pi$
$317$	−6408.00	−1.13536	−0.567680	+	0.823249i	$0.692159\pi$
$318$	1020.00	0.179870
$319$	−13622.0	−2.39086
$320$	−448.000	−0.0782624
$321$	654.000	0.113716
$322$	4440.00	0.768421
$323$	0	0
$324$	324.000	0.0555556
$325$	1064.00	0.181600
$326$	4720.00	0.801891
$327$	−6552.00	−1.10803
$328$	−3200.00	−0.538690
$329$	−2595.00	−0.434854
$330$	−2058.00	−0.343301
$331$	−2576.00	−0.427764	−0.213882	−	0.976860i	$-0.568611\pi$
$331$	−2576.00	−0.427764	−0.213882	+	0.976860i	$0.568611\pi$
$332$	−1104.00	−0.182500
$333$	−1440.00	−0.236972
$334$	2220.00	0.363692
$335$	3108.00	0.506890
$336$	720.000	0.116902
$337$	7922.00	1.28053	0.640265	−	0.768154i	$-0.278824\pi$
$337$	7922.00	1.28053	0.640265	+	0.768154i	$0.278824\pi$
$338$	−4002.00	−0.644024
$339$	4002.00	0.641176
$340$	924.000	0.147385
$341$	4606.00	0.731463
$342$	0	0
$343$	6915.00	1.08856
$344$	584.000	0.0915325
$345$	−3108.00	−0.485012
$346$	516.000	0.0801744
$347$	2305.00	0.356596	0.178298	−	0.983977i	$-0.442941\pi$
$347$	2305.00	0.356596	0.178298	+	0.983977i	$0.442941\pi$
$348$	−3336.00	−0.513875
$349$	−4619.00	−0.708451	−0.354226	−	0.935160i	$-0.615255\pi$
$349$	−4619.00	−0.708451	−0.354226	+	0.935160i	$0.615255\pi$
$350$	2280.00	0.348203
$351$	378.000	0.0574819
$352$	−1568.00	−0.237428
$353$	12366.0	1.86452	0.932260	−	0.361788i	$-0.117834\pi$
$353$	12366.0	1.86452	0.932260	+	0.361788i	$0.117834\pi$
$354$	−72.0000	−0.0108100
$355$	−6664.00	−0.996305
$356$	−5544.00	−0.825369
$357$	−1485.00	−0.220153
$358$	7524.00	1.11077
$359$	−12417.0	−1.82547	−0.912736	−	0.408551i	$-0.866034\pi$
$359$	−12417.0	−1.82547	−0.912736	+	0.408551i	$0.866034\pi$
$360$	−504.000	−0.0737865
$361$	0	0
$362$	−1412.00	−0.205008
$363$	−3210.00	−0.464136
$364$	840.000	0.120956
$365$	189.000	0.0271033
$366$	−2514.00	−0.359041
$367$	5776.00	0.821539	0.410769	−	0.911739i	$-0.365260\pi$
$367$	5776.00	0.821539	0.410769	+	0.911739i	$0.365260\pi$
$368$	−2368.00	−0.335436
$369$	−3600.00	−0.507882
$370$	2240.00	0.314735
$371$	2550.00	0.356845
$372$	1128.00	0.157215
$373$	−3392.00	−0.470861	−0.235430	−	0.971891i	$-0.575650\pi$
$373$	−3392.00	−0.470861	−0.235430	+	0.971891i	$0.575650\pi$
$374$	3234.00	0.447129
$375$	−4221.00	−0.581257
$376$	1384.00	0.189825
$377$	−3892.00	−0.531693
$378$	810.000	0.110217
$379$	−5766.00	−0.781476	−0.390738	−	0.920502i	$-0.627780\pi$
$379$	−5766.00	−0.781476	−0.390738	+	0.920502i	$0.627780\pi$
$380$	0	0
$381$	−1998.00	−0.268663
$382$	5318.00	0.712284
$383$	−8482.00	−1.13162	−0.565809	−	0.824536i	$-0.691436\pi$
$383$	−8482.00	−1.13162	−0.565809	+	0.824536i	$0.691436\pi$
$384$	−384.000	−0.0510310
$385$	−5145.00	−0.681074
$386$	−7296.00	−0.962064
$387$	657.000	0.0862976
$388$	−520.000	−0.0680387
$389$	−1983.00	−0.258463	−0.129231	−	0.991614i	$-0.541251\pi$
$389$	−1983.00	−0.258463	−0.129231	+	0.991614i	$0.541251\pi$
$390$	−588.000	−0.0763450
$391$	4884.00	0.631699
$392$	−944.000	−0.121631
$393$	909.000	0.116674
$394$	988.000	0.126332
$395$	−3892.00	−0.495767
$396$	−1764.00	−0.223849
$397$	−4555.00	−0.575841	−0.287921	−	0.957654i	$-0.592964\pi$
$397$	−4555.00	−0.575841	−0.287921	+	0.957654i	$0.592964\pi$
$398$	−7358.00	−0.926691
$399$	0	0
$400$	−1216.00	−0.152000
$401$	11624.0	1.44757	0.723784	−	0.690026i	$-0.242401\pi$
$401$	11624.0	1.44757	0.723784	+	0.690026i	$0.242401\pi$
$402$	2664.00	0.330518
$403$	1316.00	0.162667
$404$	−952.000	−0.117237
$405$	−567.000	−0.0695666
$406$	−8340.00	−1.01948
$407$	7840.00	0.954826
$408$	792.000	0.0961026
$409$	12446.0	1.50468	0.752341	−	0.658774i	$-0.228925\pi$
$409$	12446.0	1.50468	0.752341	+	0.658774i	$0.228925\pi$
$410$	5600.00	0.674547
$411$	−1749.00	−0.209907
$412$	5496.00	0.657205
$413$	−180.000	−0.0214461
$414$	−2664.00	−0.316252
$415$	1932.00	0.228526
$416$	−448.000	−0.0528005
$417$	4401.00	0.516829
$418$	0	0
$419$	−468.000	−0.0545663	−0.0272832	−	0.999628i	$-0.508686\pi$
$419$	−468.000	−0.0545663	−0.0272832	+	0.999628i	$0.508686\pi$
$420$	−1260.00	−0.146385
$421$	7894.00	0.913848	0.456924	−	0.889506i	$-0.348951\pi$
$421$	7894.00	0.913848	0.456924	+	0.889506i	$0.348951\pi$
$422$	−1584.00	−0.182720
$423$	1557.00	0.178969
$424$	−1360.00	−0.155772
$425$	2508.00	0.286249
$426$	−5712.00	−0.649642
$427$	−6285.00	−0.712301
$428$	−872.000	−0.0984806
$429$	−2058.00	−0.231611
$430$	−1022.00	−0.114617
$431$	9234.00	1.03199	0.515993	−	0.856593i	$-0.327423\pi$
$431$	9234.00	1.03199	0.515993	+	0.856593i	$0.327423\pi$
$432$	−432.000	−0.0481125
$433$	−9842.00	−1.09232	−0.546162	−	0.837680i	$-0.683912\pi$
$433$	−9842.00	−1.09232	−0.546162	+	0.837680i	$0.683912\pi$
$434$	2820.00	0.311899
$435$	5838.00	0.643473
$436$	8736.00	0.959584
$437$	0	0
$438$	162.000	0.0176727
$439$	10966.0	1.19221	0.596103	−	0.802908i	$-0.296715\pi$
$439$	10966.0	1.19221	0.596103	+	0.802908i	$0.296715\pi$
$440$	2744.00	0.297307
$441$	−1062.00	−0.114674
$442$	924.000	0.0994348
$443$	−8795.00	−0.943257	−0.471629	−	0.881797i	$-0.656334\pi$
$443$	−8795.00	−0.943257	−0.471629	+	0.881797i	$0.656334\pi$
$444$	1920.00	0.205223
$445$	9702.00	1.03353
$446$	9272.00	0.984399
$447$	−1053.00	−0.111421
$448$	−960.000	−0.101240
$449$	−2476.00	−0.260244	−0.130122	−	0.991498i	$-0.541537\pi$
$449$	−2476.00	−0.260244	−0.130122	+	0.991498i	$0.541537\pi$
$450$	−1368.00	−0.143307
$451$	19600.0	2.04640
$452$	−5336.00	−0.555275
$453$	−9300.00	−0.964574
$454$	12892.0	1.33271
$455$	−1470.00	−0.151461
$456$	0	0
$457$	−13837.0	−1.41634	−0.708170	−	0.706042i	$-0.750479\pi$
$457$	−13837.0	−1.41634	−0.708170	+	0.706042i	$0.750479\pi$
$458$	11530.0	1.17634
$459$	891.000	0.0906064
$460$	4144.00	0.420033
$461$	407.000	0.0411190	0.0205595	−	0.999789i	$-0.493455\pi$
$461$	407.000	0.0411190	0.0205595	+	0.999789i	$0.493455\pi$
$462$	−4410.00	−0.444095
$463$	−17741.0	−1.78076	−0.890382	−	0.455213i	$-0.849563\pi$
$463$	−17741.0	−1.78076	−0.890382	+	0.455213i	$0.849563\pi$
$464$	4448.00	0.445028
$465$	−1974.00	−0.196865
$466$	−11694.0	−1.16248
$467$	16765.0	1.66122	0.830612	−	0.556851i	$-0.187991\pi$
$467$	16765.0	1.66122	0.830612	+	0.556851i	$0.187991\pi$
$468$	−504.000	−0.0497808
$469$	6660.00	0.655715
$470$	−2422.00	−0.237699
$471$	7422.00	0.726089
$472$	96.0000	0.00936178
$473$	−3577.00	−0.347718
$474$	−3336.00	−0.323265
$475$	0	0
$476$	1980.00	0.190658
$477$	−1530.00	−0.146863
$478$	5646.00	0.540255
$479$	−824.000	−0.0786003	−0.0393001	−	0.999227i	$-0.512513\pi$
$479$	−824.000	−0.0786003	−0.0393001	+	0.999227i	$0.512513\pi$
$480$	672.000	0.0639010
$481$	2240.00	0.212339
$482$	12280.0	1.16045
$483$	−6660.00	−0.627413
$484$	4280.00	0.401953
$485$	910.000	0.0851979
$486$	−486.000	−0.0453609
$487$	668.000	0.0621560	0.0310780	−	0.999517i	$-0.490106\pi$
$487$	668.000	0.0621560	0.0310780	+	0.999517i	$0.490106\pi$
$488$	3352.00	0.310938
$489$	−7080.00	−0.654742
$490$	1652.00	0.152306
$491$	15080.0	1.38605	0.693025	−	0.720913i	$-0.256277\pi$
$491$	15080.0	1.38605	0.693025	+	0.720913i	$0.256277\pi$
$492$	4800.00	0.439839
$493$	−9174.00	−0.838086
$494$	0	0
$495$	3087.00	0.280304
$496$	−1504.00	−0.136152
$497$	−14280.0	−1.28882
$498$	1656.00	0.149010
$499$	10915.0	0.979203	0.489602	−	0.871946i	$-0.337142\pi$
$499$	10915.0	0.979203	0.489602	+	0.871946i	$0.337142\pi$
$500$	5628.00	0.503384
$501$	−3330.00	−0.296953
$502$	−6206.00	−0.551768
$503$	−16728.0	−1.48283	−0.741416	−	0.671046i	$-0.765846\pi$
$503$	−16728.0	−1.48283	−0.741416	+	0.671046i	$0.765846\pi$
$504$	−1080.00	−0.0954504
$505$	1666.00	0.146804
$506$	14504.0	1.27427
$507$	6003.00	0.525843
$508$	2664.00	0.232669
$509$	−17754.0	−1.54604	−0.773018	−	0.634384i	$-0.781254\pi$
$509$	−17754.0	−1.54604	−0.773018	+	0.634384i	$0.781254\pi$
$510$	−1386.00	−0.120339
$511$	405.000	0.0350609
$512$	512.000	0.0441942
$513$	0	0
$514$	−4672.00	−0.400920
$515$	−9618.00	−0.822951
$516$	−876.000	−0.0747359
$517$	−8477.00	−0.721118
$518$	4800.00	0.407143
$519$	−774.000	−0.0654621
$520$	784.000	0.0661167
$521$	2584.00	0.217288	0.108644	−	0.994081i	$-0.465349\pi$
$521$	2584.00	0.217288	0.108644	+	0.994081i	$0.465349\pi$
$522$	5004.00	0.419577
$523$	2158.00	0.180426	0.0902130	−	0.995922i	$-0.471245\pi$
$523$	2158.00	0.180426	0.0902130	+	0.995922i	$0.471245\pi$
$524$	−1212.00	−0.101043
$525$	−3420.00	−0.284307
$526$	−5478.00	−0.454092
$527$	3102.00	0.256405
$528$	2352.00	0.193859
$529$	9737.00	0.800279
$530$	2380.00	0.195058
$531$	108.000	0.00882637
$532$	0	0
$533$	5600.00	0.455090
$534$	8316.00	0.673911
$535$	1526.00	0.123317
$536$	−3552.00	−0.286237
$537$	−11286.0	−0.906940
$538$	12972.0	1.03952
$539$	5782.00	0.462056
$540$	756.000	0.0602464
$541$	−14137.0	−1.12347	−0.561735	−	0.827317i	$-0.689866\pi$
$541$	−14137.0	−1.12347	−0.561735	+	0.827317i	$0.689866\pi$
$542$	−616.000	−0.0488182
$543$	2118.00	0.167389
$544$	−1056.00	−0.0832273
$545$	−15288.0	−1.20159
$546$	−1260.00	−0.0987601
$547$	−10222.0	−0.799015	−0.399507	−	0.916730i	$-0.630819\pi$
$547$	−10222.0	−0.799015	−0.399507	+	0.916730i	$0.630819\pi$
$548$	2332.00	0.181785
$549$	3771.00	0.293155
$550$	7448.00	0.577425
$551$	0	0
$552$	3552.00	0.273883
$553$	−8340.00	−0.641325
$554$	5954.00	0.456609
$555$	−3360.00	−0.256980
$556$	−5868.00	−0.447587
$557$	10387.0	0.790146	0.395073	−	0.918650i	$-0.370719\pi$
$557$	10387.0	0.790146	0.395073	+	0.918650i	$0.370719\pi$
$558$	−1692.00	−0.128366
$559$	−1022.00	−0.0773274
$560$	1680.00	0.126773
$561$	−4851.00	−0.365079
$562$	−9140.00	−0.686028
$563$	10404.0	0.778821	0.389411	−	0.921064i	$-0.372679\pi$
$563$	10404.0	0.778821	0.389411	+	0.921064i	$0.372679\pi$
$564$	−2076.00	−0.154992
$565$	9338.00	0.695314
$566$	12858.0	0.954880
$567$	−1215.00	−0.0899915
$568$	7616.00	0.562606
$569$	−4258.00	−0.313716	−0.156858	−	0.987621i	$-0.550137\pi$
$569$	−4258.00	−0.313716	−0.156858	+	0.987621i	$0.550137\pi$
$570$	0	0
$571$	6440.00	0.471989	0.235994	−	0.971754i	$-0.424165\pi$
$571$	6440.00	0.471989	0.235994	+	0.971754i	$0.424165\pi$
$572$	2744.00	0.200581
$573$	−7977.00	−0.581578
$574$	12000.0	0.872596
$575$	11248.0	0.815781
$576$	576.000	0.0416667
$577$	−14869.0	−1.07280	−0.536399	−	0.843964i	$-0.680216\pi$
$577$	−14869.0	−1.07280	−0.536399	+	0.843964i	$0.680216\pi$
$578$	−7648.00	−0.550372
$579$	10944.0	0.785522
$580$	−7784.00	−0.557264
$581$	4140.00	0.295622
$582$	780.000	0.0555533
$583$	8330.00	0.591755
$584$	−216.000	−0.0153050
$585$	882.000	0.0623354
$586$	−11448.0	−0.807018
$587$	1041.00	0.0731970	0.0365985	−	0.999330i	$-0.488348\pi$
$587$	1041.00	0.0731970	0.0365985	+	0.999330i	$0.488348\pi$
$588$	1416.00	0.0993110
$589$	0	0
$590$	−168.000	−0.0117228
$591$	−1482.00	−0.103149
$592$	−2560.00	−0.177729
$593$	−15662.0	−1.08459	−0.542294	−	0.840188i	$-0.682444\pi$
$593$	−15662.0	−1.08459	−0.542294	+	0.840188i	$0.682444\pi$
$594$	2646.00	0.182772
$595$	−3465.00	−0.238741
$596$	1404.00	0.0964934
$597$	11037.0	0.756640
$598$	4144.00	0.283379
$599$	−18900.0	−1.28920	−0.644602	−	0.764518i	$-0.722977\pi$
$599$	−18900.0	−1.28920	−0.644602	+	0.764518i	$0.722977\pi$
$600$	1824.00	0.124107
$601$	−6100.00	−0.414017	−0.207008	−	0.978339i	$-0.566373\pi$
$601$	−6100.00	−0.414017	−0.207008	+	0.978339i	$0.566373\pi$
$602$	−2190.00	−0.148269
$603$	−3996.00	−0.269867
$604$	12400.0	0.835346
$605$	−7490.00	−0.503325
$606$	1428.00	0.0957237
$607$	5902.00	0.394654	0.197327	−	0.980338i	$-0.436774\pi$
$607$	5902.00	0.394654	0.197327	+	0.980338i	$0.436774\pi$
$608$	0	0
$609$	12510.0	0.832399
$610$	−5866.00	−0.389356
$611$	−2422.00	−0.160366
$612$	−1188.00	−0.0784674
$613$	15901.0	1.04769	0.523846	−	0.851813i	$-0.324497\pi$
$613$	15901.0	1.04769	0.523846	+	0.851813i	$0.324497\pi$
$614$	−16608.0	−1.09160
$615$	−8400.00	−0.550765
$616$	5880.00	0.384597
$617$	−30429.0	−1.98545	−0.992727	−	0.120385i	$-0.961587\pi$
$617$	−30429.0	−1.98545	−0.992727	+	0.120385i	$0.961587\pi$
$618$	−8244.00	−0.536606
$619$	−22484.0	−1.45995	−0.729974	−	0.683475i	$-0.760468\pi$
$619$	−22484.0	−1.45995	−0.729974	+	0.683475i	$0.760468\pi$
$620$	2632.00	0.170490
$621$	3996.00	0.258219
$622$	−1582.00	−0.101981
$623$	20790.0	1.33697
$624$	672.000	0.0431114
$625$	−349.000	−0.0223360
$626$	20332.0	1.29813
$627$	0	0
$628$	−9896.00	−0.628811
$629$	5280.00	0.334702
$630$	1890.00	0.119523
$631$	29885.0	1.88542	0.942712	−	0.333607i	$-0.108266\pi$
$631$	29885.0	1.88542	0.942712	+	0.333607i	$0.108266\pi$
$632$	4448.00	0.279956
$633$	2376.00	0.149190
$634$	−12816.0	−0.802821
$635$	−4662.00	−0.291348
$636$	2040.00	0.127188
$637$	1652.00	0.102755
$638$	−27244.0	−1.69060
$639$	8568.00	0.530430
$640$	−896.000	−0.0553399
$641$	−4038.00	−0.248817	−0.124408	−	0.992231i	$-0.539703\pi$
$641$	−4038.00	−0.248817	−0.124408	+	0.992231i	$0.539703\pi$
$642$	1308.00	0.0804091
$643$	19993.0	1.22620	0.613100	−	0.790005i	$-0.289922\pi$
$643$	19993.0	1.22620	0.613100	+	0.790005i	$0.289922\pi$
$644$	8880.00	0.543356
$645$	1533.00	0.0935842
$646$	0	0
$647$	−17077.0	−1.03766	−0.518830	−	0.854877i	$-0.673632\pi$
$647$	−17077.0	−1.03766	−0.518830	+	0.854877i	$0.673632\pi$
$648$	648.000	0.0392837
$649$	−588.000	−0.0355640
$650$	2128.00	0.128411
$651$	−4230.00	−0.254665
$652$	9440.00	0.567023
$653$	17631.0	1.05659	0.528296	−	0.849060i	$-0.322831\pi$
$653$	17631.0	1.05659	0.528296	+	0.849060i	$0.322831\pi$
$654$	−13104.0	−0.783497
$655$	2121.00	0.126526
$656$	−6400.00	−0.380912
$657$	−243.000	−0.0144297
$658$	−5190.00	−0.307488
$659$	−12014.0	−0.710165	−0.355083	−	0.934835i	$-0.615547\pi$
$659$	−12014.0	−0.710165	−0.355083	+	0.934835i	$0.615547\pi$
$660$	−4116.00	−0.242750
$661$	−10852.0	−0.638569	−0.319284	−	0.947659i	$-0.603442\pi$
$661$	−10852.0	−0.638569	−0.319284	+	0.947659i	$0.603442\pi$
$662$	−5152.00	−0.302475
$663$	−1386.00	−0.0811882
$664$	−2208.00	−0.129047
$665$	0	0
$666$	−2880.00	−0.167564
$667$	−41144.0	−2.38846
$668$	4440.00	0.257169
$669$	−13908.0	−0.803758
$670$	6216.00	0.358425
$671$	−20531.0	−1.18121
$672$	1440.00	0.0826625
$673$	1708.00	0.0978285	0.0489142	−	0.998803i	$-0.484424\pi$
$673$	1708.00	0.0978285	0.0489142	+	0.998803i	$0.484424\pi$
$674$	15844.0	0.905472
$675$	2052.00	0.117010
$676$	−8004.00	−0.455394
$677$	−17902.0	−1.01629	−0.508146	−	0.861271i	$-0.669669\pi$
$677$	−17902.0	−1.01629	−0.508146	+	0.861271i	$0.669669\pi$
$678$	8004.00	0.453380
$679$	1950.00	0.110212
$680$	1848.00	0.104217
$681$	−19338.0	−1.08816
$682$	9212.00	0.517222
$683$	−2938.00	−0.164597	−0.0822983	−	0.996608i	$-0.526226\pi$
$683$	−2938.00	−0.164597	−0.0822983	+	0.996608i	$0.526226\pi$
$684$	0	0
$685$	−4081.00	−0.227631
$686$	13830.0	0.769726
$687$	−17295.0	−0.960474
$688$	1168.00	0.0647232
$689$	2380.00	0.131598
$690$	−6216.00	−0.342955
$691$	519.000	0.0285726	0.0142863	−	0.999898i	$-0.495452\pi$
$691$	519.000	0.0285726	0.0142863	+	0.999898i	$0.495452\pi$
$692$	1032.00	0.0566918
$693$	6615.00	0.362602
$694$	4610.00	0.252152
$695$	10269.0	0.560468
$696$	−6672.00	−0.363364
$697$	13200.0	0.717340
$698$	−9238.00	−0.500951
$699$	17541.0	0.949158
$700$	4560.00	0.246217
$701$	−4942.00	−0.266272	−0.133136	−	0.991098i	$-0.542505\pi$
$701$	−4942.00	−0.266272	−0.133136	+	0.991098i	$0.542505\pi$
$702$	756.000	0.0406458
$703$	0	0
$704$	−3136.00	−0.167887
$705$	3633.00	0.194080
$706$	24732.0	1.31842
$707$	3570.00	0.189906
$708$	−144.000	−0.00764386
$709$	19302.0	1.02243	0.511214	−	0.859453i	$-0.329196\pi$
$709$	19302.0	1.02243	0.511214	+	0.859453i	$0.329196\pi$
$710$	−13328.0	−0.704494
$711$	5004.00	0.263945
$712$	−11088.0	−0.583624
$713$	13912.0	0.730727
$714$	−2970.00	−0.155672
$715$	−4802.00	−0.251167
$716$	15048.0	0.785433
$717$	−8469.00	−0.441117
$718$	−24834.0	−1.29080
$719$	−22973.0	−1.19158	−0.595792	−	0.803139i	$-0.703162\pi$
$719$	−22973.0	−1.19158	−0.595792	+	0.803139i	$0.703162\pi$
$720$	−1008.00	−0.0521749
$721$	−20610.0	−1.06457
$722$	0	0
$723$	−18420.0	−0.947506
$724$	−2824.00	−0.144963
$725$	−21128.0	−1.08231
$726$	−6420.00	−0.328194
$727$	−32429.0	−1.65437	−0.827184	−	0.561932i	$-0.810058\pi$
$727$	−32429.0	−1.65437	−0.827184	+	0.561932i	$0.810058\pi$
$728$	1680.00	0.0855288
$729$	729.000	0.0370370
$730$	378.000	0.0191649
$731$	−2409.00	−0.121888
$732$	−5028.00	−0.253880
$733$	2682.00	0.135146	0.0675729	−	0.997714i	$-0.478474\pi$
$733$	2682.00	0.135146	0.0675729	+	0.997714i	$0.478474\pi$
$734$	11552.0	0.580916
$735$	−2478.00	−0.124357
$736$	−4736.00	−0.237189
$737$	21756.0	1.08737
$738$	−7200.00	−0.359127
$739$	−15835.0	−0.788227	−0.394114	−	0.919062i	$-0.628948\pi$
$739$	−15835.0	−0.788227	−0.394114	+	0.919062i	$0.628948\pi$
$740$	4480.00	0.222551
$741$	0	0
$742$	5100.00	0.252327
$743$	16876.0	0.833271	0.416636	−	0.909074i	$-0.363209\pi$
$743$	16876.0	0.833271	0.416636	+	0.909074i	$0.363209\pi$
$744$	2256.00	0.111168
$745$	−2457.00	−0.120829
$746$	−6784.00	−0.332949
$747$	−2484.00	−0.121666
$748$	6468.00	0.316168
$749$	3270.00	0.159524
$750$	−8442.00	−0.411011
$751$	35296.0	1.71501	0.857503	−	0.514479i	$-0.172015\pi$
$751$	35296.0	1.71501	0.857503	+	0.514479i	$0.172015\pi$
$752$	2768.00	0.134227
$753$	9309.00	0.450516
$754$	−7784.00	−0.375964
$755$	−21700.0	−1.04602
$756$	1620.00	0.0779350
$757$	18259.0	0.876664	0.438332	−	0.898813i	$-0.355569\pi$
$757$	18259.0	0.876664	0.438332	+	0.898813i	$0.355569\pi$
$758$	−11532.0	−0.552587
$759$	−21756.0	−1.04044
$760$	0	0
$761$	13455.0	0.640924	0.320462	−	0.947261i	$-0.396162\pi$
$761$	13455.0	0.640924	0.320462	+	0.947261i	$0.396162\pi$
$762$	−3996.00	−0.189973
$763$	−32760.0	−1.55438
$764$	10636.0	0.503661
$765$	2079.00	0.0982567
$766$	−16964.0	−0.800175
$767$	−168.000	−0.00790890
$768$	−768.000	−0.0360844
$769$	−16061.0	−0.753153	−0.376576	−	0.926386i	$-0.622899\pi$
$769$	−16061.0	−0.753153	−0.376576	+	0.926386i	$0.622899\pi$
$770$	−10290.0	−0.481592
$771$	7008.00	0.327350
$772$	−14592.0	−0.680282
$773$	−4680.00	−0.217759	−0.108880	−	0.994055i	$-0.534726\pi$
$773$	−4680.00	−0.217759	−0.108880	+	0.994055i	$0.534726\pi$
$774$	1314.00	0.0610216
$775$	7144.00	0.331123
$776$	−1040.00	−0.0481106
$777$	−7200.00	−0.332431
$778$	−3966.00	−0.182761
$779$	0	0
$780$	−1176.00	−0.0539840
$781$	−46648.0	−2.13726
$782$	9768.00	0.446679
$783$	−7506.00	−0.342583
$784$	−1888.00	−0.0860058
$785$	17318.0	0.787396
$786$	1818.00	0.0825012
$787$	37760.0	1.71029	0.855145	−	0.518388i	$-0.173468\pi$
$787$	37760.0	1.71029	0.855145	+	0.518388i	$0.173468\pi$
$788$	1976.00	0.0893301
$789$	8217.00	0.370764
$790$	−7784.00	−0.350560
$791$	20010.0	0.899461
$792$	−3528.00	−0.158285
$793$	−5866.00	−0.262683
$794$	−9110.00	−0.407181
$795$	−3570.00	−0.159264
$796$	−14716.0	−0.655270
$797$	−22008.0	−0.978122	−0.489061	−	0.872250i	$-0.662660\pi$
$797$	−22008.0	−0.978122	−0.489061	+	0.872250i	$0.662660\pi$
$798$	0	0
$799$	−5709.00	−0.252778
$800$	−2432.00	−0.107480
$801$	−12474.0	−0.550246
$802$	23248.0	1.02359
$803$	1323.00	0.0581415
$804$	5328.00	0.233712
$805$	−15540.0	−0.680389
$806$	2632.00	0.115023
$807$	−19458.0	−0.848766
$808$	−1904.00	−0.0828991
$809$	−12615.0	−0.548232	−0.274116	−	0.961697i	$-0.588385\pi$
$809$	−12615.0	−0.548232	−0.274116	+	0.961697i	$0.588385\pi$
$810$	−1134.00	−0.0491910
$811$	−45402.0	−1.96582	−0.982910	−	0.184087i	$-0.941067\pi$
$811$	−45402.0	−1.96582	−0.982910	+	0.184087i	$0.941067\pi$
$812$	−16680.0	−0.720878
$813$	924.000	0.0398599
$814$	15680.0	0.675164
$815$	−16520.0	−0.710025
$816$	1584.00	0.0679548
$817$	0	0
$818$	24892.0	1.06397
$819$	1890.00	0.0806373
$820$	11200.0	0.476977
$821$	1335.00	0.0567501	0.0283750	−	0.999597i	$-0.490967\pi$
$821$	1335.00	0.0567501	0.0283750	+	0.999597i	$0.490967\pi$
$822$	−3498.00	−0.148427
$823$	−559.000	−0.0236762	−0.0118381	−	0.999930i	$-0.503768\pi$
$823$	−559.000	−0.0236762	−0.0118381	+	0.999930i	$0.503768\pi$
$824$	10992.0	0.464714
$825$	−11172.0	−0.471466
$826$	−360.000	−0.0151647
$827$	−13856.0	−0.582612	−0.291306	−	0.956630i	$-0.594090\pi$
$827$	−13856.0	−0.582612	−0.291306	+	0.956630i	$0.594090\pi$
$828$	−5328.00	−0.223624
$829$	−18228.0	−0.763673	−0.381836	−	0.924230i	$-0.624708\pi$
$829$	−18228.0	−0.763673	−0.381836	+	0.924230i	$0.624708\pi$
$830$	3864.00	0.161592
$831$	−8931.00	−0.372819
$832$	−896.000	−0.0373356
$833$	3894.00	0.161968
$834$	8802.00	0.365454
$835$	−7770.00	−0.322026
$836$	0	0
$837$	2538.00	0.104810
$838$	−936.000	−0.0385842
$839$	13414.0	0.551970	0.275985	−	0.961162i	$-0.410996\pi$
$839$	13414.0	0.551970	0.275985	+	0.961162i	$0.410996\pi$
$840$	−2520.00	−0.103510
$841$	52895.0	2.16881
$842$	15788.0	0.646188
$843$	13710.0	0.560139
$844$	−3168.00	−0.129203
$845$	14007.0	0.570243
$846$	3114.00	0.126550
$847$	−16050.0	−0.651103
$848$	−2720.00	−0.110148
$849$	−19287.0	−0.779656
$850$	5016.00	0.202409
$851$	23680.0	0.953866
$852$	−11424.0	−0.459366
$853$	−44718.0	−1.79498	−0.897488	−	0.441038i	$-0.854610\pi$
$853$	−44718.0	−1.79498	−0.897488	+	0.441038i	$0.854610\pi$
$854$	−12570.0	−0.503673
$855$	0	0
$856$	−1744.00	−0.0696363
$857$	33924.0	1.35218	0.676092	−	0.736817i	$-0.263672\pi$
$857$	33924.0	1.35218	0.676092	+	0.736817i	$0.263672\pi$
$858$	−4116.00	−0.163774
$859$	−16427.0	−0.652482	−0.326241	−	0.945287i	$-0.605782\pi$
$859$	−16427.0	−0.652482	−0.326241	+	0.945287i	$0.605782\pi$
$860$	−2044.00	−0.0810463
$861$	−18000.0	−0.712472
$862$	18468.0	0.729725
$863$	−23292.0	−0.918736	−0.459368	−	0.888246i	$-0.651924\pi$
$863$	−23292.0	−0.918736	−0.459368	+	0.888246i	$0.651924\pi$
$864$	−864.000	−0.0340207
$865$	−1806.00	−0.0709894
$866$	−19684.0	−0.772390
$867$	11472.0	0.449377
$868$	5640.00	0.220546
$869$	−27244.0	−1.06351
$870$	11676.0	0.455004
$871$	6216.00	0.241815
$872$	17472.0	0.678528
$873$	−1170.00	−0.0453591
$874$	0	0
$875$	−21105.0	−0.815405
$876$	324.000	0.0124965
$877$	43598.0	1.67868	0.839339	−	0.543609i	$-0.182943\pi$
$877$	43598.0	1.67868	0.839339	+	0.543609i	$0.182943\pi$
$878$	21932.0	0.843017
$879$	17172.0	0.658927
$880$	5488.00	0.210228
$881$	39123.0	1.49613	0.748063	−	0.663627i	$-0.230984\pi$
$881$	39123.0	1.49613	0.748063	+	0.663627i	$0.230984\pi$
$882$	−2124.00	−0.0810871
$883$	−4115.00	−0.156830	−0.0784149	−	0.996921i	$-0.524986\pi$
$883$	−4115.00	−0.156830	−0.0784149	+	0.996921i	$0.524986\pi$
$884$	1848.00	0.0703110
$885$	252.000	0.00957162
$886$	−17590.0	−0.666984
$887$	−13384.0	−0.506641	−0.253321	−	0.967382i	$-0.581523\pi$
$887$	−13384.0	−0.506641	−0.253321	+	0.967382i	$0.581523\pi$
$888$	3840.00	0.145115
$889$	−9990.00	−0.376888
$890$	19404.0	0.730813
$891$	−3969.00	−0.149233
$892$	18544.0	0.696075
$893$	0	0
$894$	−2106.00	−0.0787866
$895$	−26334.0	−0.983518
$896$	−1920.00	−0.0715878
$897$	−6216.00	−0.231378
$898$	−4952.00	−0.184020
$899$	−26132.0	−0.969467
$900$	−2736.00	−0.101333
$901$	5610.00	0.207432
$902$	39200.0	1.44703
$903$	3285.00	0.121061
$904$	−10672.0	−0.392639
$905$	4942.00	0.181522
$906$	−18600.0	−0.682057
$907$	36718.0	1.34421	0.672106	−	0.740454i	$-0.265390\pi$
$907$	36718.0	1.34421	0.672106	+	0.740454i	$0.265390\pi$
$908$	25784.0	0.942370
$909$	−2142.00	−0.0781580
$910$	−2940.00	−0.107099
$911$	−46614.0	−1.69527	−0.847635	−	0.530580i	$-0.821974\pi$
$911$	−46614.0	−1.69527	−0.847635	+	0.530580i	$0.821974\pi$
$912$	0	0
$913$	13524.0	0.490229
$914$	−27674.0	−1.00150
$915$	8799.00	0.317908
$916$	23060.0	0.831795
$917$	4545.00	0.163674
$918$	1782.00	0.0640684
$919$	11192.0	0.401730	0.200865	−	0.979619i	$-0.435625\pi$
$919$	11192.0	0.401730	0.200865	+	0.979619i	$0.435625\pi$
$920$	8288.00	0.297008
$921$	24912.0	0.891290
$922$	814.000	0.0290756
$923$	−13328.0	−0.475294
$924$	−8820.00	−0.314022
$925$	12160.0	0.432236
$926$	−35482.0	−1.25919
$927$	12366.0	0.438137
$928$	8896.00	0.314683
$929$	542.000	0.0191415	0.00957074	−	0.999954i	$-0.496953\pi$
$929$	542.000	0.0191415	0.00957074	+	0.999954i	$0.496953\pi$
$930$	−3948.00	−0.139204
$931$	0	0
$932$	−23388.0	−0.821995
$933$	2373.00	0.0832675
$934$	33530.0	1.17466
$935$	−11319.0	−0.395905
$936$	−1008.00	−0.0352003
$937$	39053.0	1.36159	0.680793	−	0.732476i	$-0.261635\pi$
$937$	39053.0	1.36159	0.680793	+	0.732476i	$0.261635\pi$
$938$	13320.0	0.463660
$939$	−30498.0	−1.05992
$940$	−4844.00	−0.168079
$941$	33398.0	1.15701	0.578504	−	0.815680i	$-0.303637\pi$
$941$	33398.0	1.15701	0.578504	+	0.815680i	$0.303637\pi$
$942$	14844.0	0.513422
$943$	59200.0	2.04434
$944$	192.000	0.00661978
$945$	−2835.00	−0.0975900
$946$	−7154.00	−0.245874
$947$	−54084.0	−1.85585	−0.927927	−	0.372762i	$-0.878411\pi$
$947$	−54084.0	−1.85585	−0.927927	+	0.372762i	$0.878411\pi$
$948$	−6672.00	−0.228583
$949$	378.000	0.0129298
$950$	0	0
$951$	19224.0	0.655500
$952$	3960.00	0.134815
$953$	30484.0	1.03617	0.518087	−	0.855328i	$-0.326644\pi$
$953$	30484.0	1.03617	0.518087	+	0.855328i	$0.326644\pi$
$954$	−3060.00	−0.103848
$955$	−18613.0	−0.630683
$956$	11292.0	0.382018
$957$	40866.0	1.38037
$958$	−1648.00	−0.0555788
$959$	−8745.00	−0.294464
$960$	1344.00	0.0451848
$961$	−20955.0	−0.703400
$962$	4480.00	0.150147
$963$	−1962.00	−0.0656538
$964$	24560.0	0.820565
$965$	25536.0	0.851848
$966$	−13320.0	−0.443648
$967$	13584.0	0.451739	0.225870	−	0.974158i	$-0.427478\pi$
$967$	13584.0	0.451739	0.225870	+	0.974158i	$0.427478\pi$
$968$	8560.00	0.284224
$969$	0	0
$970$	1820.00	0.0602440
$971$	−43892.0	−1.45063	−0.725315	−	0.688417i	$-0.758306\pi$
$971$	−43892.0	−1.45063	−0.725315	+	0.688417i	$0.758306\pi$
$972$	−972.000	−0.0320750
$973$	22005.0	0.725024
$974$	1336.00	0.0439509
$975$	−3192.00	−0.104847
$976$	6704.00	0.219867
$977$	−30542.0	−1.00013	−0.500064	−	0.865988i	$-0.666690\pi$
$977$	−30542.0	−1.00013	−0.500064	+	0.865988i	$0.666690\pi$
$978$	−14160.0	−0.462972
$979$	67914.0	2.21710
$980$	3304.00	0.107696
$981$	19656.0	0.639723
$982$	30160.0	0.980086
$983$	2868.00	0.0930570	0.0465285	−	0.998917i	$-0.485184\pi$
$983$	2868.00	0.0930570	0.0465285	+	0.998917i	$0.485184\pi$
$984$	9600.00	0.311013
$985$	−3458.00	−0.111859
$986$	−18348.0	−0.592616
$987$	7785.00	0.251063
$988$	0	0
$989$	−10804.0	−0.347368
$990$	6174.00	0.198205
$991$	23696.0	0.759564	0.379782	−	0.925076i	$-0.375999\pi$
$991$	23696.0	0.759564	0.379782	+	0.925076i	$0.375999\pi$
$992$	−3008.00	−0.0962743
$993$	7728.00	0.246969
$994$	−28560.0	−0.911336
$995$	25753.0	0.820528
$996$	3312.00	0.105366
$997$	−46811.0	−1.48698	−0.743490	−	0.668747i	$-0.766831\pi$
$997$	−46811.0	−1.48698	−0.743490	+	0.668747i	$0.766831\pi$
$998$	21830.0	0.692401
$999$	4320.00	0.136816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2166.4.a.d.1.1		1
19.18	odd	2		114.4.a.b.1.1	✓	1
57.56	even	2		342.4.a.c.1.1		1
76.75	even	2		912.4.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.a.b.1.1	✓	1	19.18	odd	2
342.4.a.c.1.1		1	57.56	even	2
912.4.a.b.1.1		1	76.75	even	2
2166.4.a.d.1.1		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:	\( N \)	\(=\)	\( 2166 = 2 \cdot 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2166.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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