LMFDB - Embedded newform 23.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,4,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	23.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:	$1.35704393013$
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	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-2.00000 q^{2} -5.00000 q^{3} -4.00000 q^{4} -6.00000 q^{5} +10.0000 q^{6} -8.00000 q^{7} +24.0000 q^{8} -2.00000 q^{9} +O(q^{10})$

\(q-2.00000 q^{2} -5.00000 q^{3} -4.00000 q^{4} -6.00000 q^{5} +10.0000 q^{6} -8.00000 q^{7} +24.0000 q^{8} -2.00000 q^{9} +12.0000 q^{10} +34.0000 q^{11} +20.0000 q^{12} -57.0000 q^{13} +16.0000 q^{14} +30.0000 q^{15} -16.0000 q^{16} -80.0000 q^{17} +4.00000 q^{18} -70.0000 q^{19} +24.0000 q^{20} +40.0000 q^{21} -68.0000 q^{22} +23.0000 q^{23} -120.000 q^{24} -89.0000 q^{25} +114.000 q^{26} +145.000 q^{27} +32.0000 q^{28} +245.000 q^{29} -60.0000 q^{30} +103.000 q^{31} -160.000 q^{32} -170.000 q^{33} +160.000 q^{34} +48.0000 q^{35} +8.00000 q^{36} -298.000 q^{37} +140.000 q^{38} +285.000 q^{39} -144.000 q^{40} +95.0000 q^{41} -80.0000 q^{42} +88.0000 q^{43} -136.000 q^{44} +12.0000 q^{45} -46.0000 q^{46} -357.000 q^{47} +80.0000 q^{48} -279.000 q^{49} +178.000 q^{50} +400.000 q^{51} +228.000 q^{52} -414.000 q^{53} -290.000 q^{54} -204.000 q^{55} -192.000 q^{56} +350.000 q^{57} -490.000 q^{58} -408.000 q^{59} -120.000 q^{60} +822.000 q^{61} -206.000 q^{62} +16.0000 q^{63} +448.000 q^{64} +342.000 q^{65} +340.000 q^{66} +926.000 q^{67} +320.000 q^{68} -115.000 q^{69} -96.0000 q^{70} +335.000 q^{71} -48.0000 q^{72} -899.000 q^{73} +596.000 q^{74} +445.000 q^{75} +280.000 q^{76} -272.000 q^{77} -570.000 q^{78} -1322.00 q^{79} +96.0000 q^{80} -671.000 q^{81} -190.000 q^{82} -36.0000 q^{83} -160.000 q^{84} +480.000 q^{85} -176.000 q^{86} -1225.00 q^{87} +816.000 q^{88} -460.000 q^{89} -24.0000 q^{90} +456.000 q^{91} -92.0000 q^{92} -515.000 q^{93} +714.000 q^{94} +420.000 q^{95} +800.000 q^{96} -964.000 q^{97} +558.000 q^{98} -68.0000 q^{99} +O(q^{100})\)

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−2.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	−5.00000	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$3$	−5.00000	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$4$	−4.00000	−0.500000
$5$	−6.00000	−0.536656	−0.268328	−	0.963328i	$-0.586471\pi$
$5$	−6.00000	−0.536656	−0.268328	+	0.963328i	$0.586471\pi$
$6$	10.0000	0.680414
$7$	−8.00000	−0.431959	−0.215980	−	0.976398i	$-0.569295\pi$
$7$	−8.00000	−0.431959	−0.215980	+	0.976398i	$0.569295\pi$
$8$	24.0000	1.06066
$9$	−2.00000	−0.0740741
$10$	12.0000	0.379473
$11$	34.0000	0.931944	0.465972	−	0.884799i	$-0.345705\pi$
$11$	34.0000	0.931944	0.465972	+	0.884799i	$0.345705\pi$
$12$	20.0000	0.481125
$13$	−57.0000	−1.21607	−0.608037	−	0.793909i	$-0.708043\pi$
$13$	−57.0000	−1.21607	−0.608037	+	0.793909i	$0.708043\pi$
$14$	16.0000	0.305441
$15$	30.0000	0.516398
$16$	−16.0000	−0.250000
$17$	−80.0000	−1.14134	−0.570672	−	0.821178i	$-0.693317\pi$
$17$	−80.0000	−1.14134	−0.570672	+	0.821178i	$0.693317\pi$
$18$	4.00000	0.0523783
$19$	−70.0000	−0.845216	−0.422608	−	0.906313i	$-0.638885\pi$
$19$	−70.0000	−0.845216	−0.422608	+	0.906313i	$0.638885\pi$
$20$	24.0000	0.268328
$21$	40.0000	0.415653
$22$	−68.0000	−0.658984
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−120.000	−1.02062
$25$	−89.0000	−0.712000
$26$	114.000	0.859894
$27$	145.000	1.03353
$28$	32.0000	0.215980
$29$	245.000	1.56881	0.784403	−	0.620252i	$-0.212970\pi$
$29$	245.000	1.56881	0.784403	+	0.620252i	$0.212970\pi$
$30$	−60.0000	−0.365148
$31$	103.000	0.596753	0.298377	−	0.954448i	$-0.403555\pi$
$31$	103.000	0.596753	0.298377	+	0.954448i	$0.403555\pi$
$32$	−160.000	−0.883883
$33$	−170.000	−0.896764
$34$	160.000	0.807052
$35$	48.0000	0.231814
$36$	8.00000	0.0370370
$37$	−298.000	−1.32408	−0.662039	−	0.749469i	$-0.730309\pi$
$37$	−298.000	−1.32408	−0.662039	+	0.749469i	$0.730309\pi$
$38$	140.000	0.597658
$39$	285.000	1.17017
$40$	−144.000	−0.569210
$41$	95.0000	0.361866	0.180933	−	0.983495i	$-0.442088\pi$
$41$	95.0000	0.361866	0.180933	+	0.983495i	$0.442088\pi$
$42$	−80.0000	−0.293911
$43$	88.0000	0.312090	0.156045	−	0.987750i	$-0.450125\pi$
$43$	88.0000	0.312090	0.156045	+	0.987750i	$0.450125\pi$
$44$	−136.000	−0.465972
$45$	12.0000	0.0397523
$46$	−46.0000	−0.147442
$47$	−357.000	−1.10795	−0.553977	−	0.832532i	$-0.686890\pi$
$47$	−357.000	−1.10795	−0.553977	+	0.832532i	$0.686890\pi$
$48$	80.0000	0.240563
$49$	−279.000	−0.813411
$50$	178.000	0.503460
$51$	400.000	1.09826
$52$	228.000	0.608037
$53$	−414.000	−1.07297	−0.536484	−	0.843911i	$-0.680248\pi$
$53$	−414.000	−1.07297	−0.536484	+	0.843911i	$0.680248\pi$
$54$	−290.000	−0.730815
$55$	−204.000	−0.500134
$56$	−192.000	−0.458162
$57$	350.000	0.813309
$58$	−490.000	−1.10931
$59$	−408.000	−0.900289	−0.450145	−	0.892956i	$-0.648628\pi$
$59$	−408.000	−0.900289	−0.450145	+	0.892956i	$0.648628\pi$
$60$	−120.000	−0.258199
$61$	822.000	1.72535	0.862675	−	0.505759i	$-0.168788\pi$
$61$	822.000	1.72535	0.862675	+	0.505759i	$0.168788\pi$
$62$	−206.000	−0.421968
$63$	16.0000	0.0319970
$64$	448.000	0.875000
$65$	342.000	0.652614
$66$	340.000	0.634108
$67$	926.000	1.68849	0.844246	−	0.535957i	$-0.180049\pi$
$67$	926.000	1.68849	0.844246	+	0.535957i	$0.180049\pi$
$68$	320.000	0.570672
$69$	−115.000	−0.200643
$70$	−96.0000	−0.163917
$71$	335.000	0.559960	0.279980	−	0.960006i	$-0.409672\pi$
$71$	335.000	0.559960	0.279980	+	0.960006i	$0.409672\pi$
$72$	−48.0000	−0.0785674
$73$	−899.000	−1.44137	−0.720685	−	0.693263i	$-0.756173\pi$
$73$	−899.000	−1.44137	−0.720685	+	0.693263i	$0.756173\pi$
$74$	596.000	0.936265
$75$	445.000	0.685122
$76$	280.000	0.422608
$77$	−272.000	−0.402562
$78$	−570.000	−0.827433
$79$	−1322.00	−1.88274	−0.941371	−	0.337373i	$-0.890462\pi$
$79$	−1322.00	−1.88274	−0.941371	+	0.337373i	$0.890462\pi$
$80$	96.0000	0.134164
$81$	−671.000	−0.920439
$82$	−190.000	−0.255878
$83$	−36.0000	−0.0476086	−0.0238043	−	0.999717i	$-0.507578\pi$
$83$	−36.0000	−0.0476086	−0.0238043	+	0.999717i	$0.507578\pi$
$84$	−160.000	−0.207827
$85$	480.000	0.612510
$86$	−176.000	−0.220681
$87$	−1225.00	−1.50958
$88$	816.000	0.988476
$89$	−460.000	−0.547864	−0.273932	−	0.961749i	$-0.588324\pi$
$89$	−460.000	−0.547864	−0.273932	+	0.961749i	$0.588324\pi$
$90$	−24.0000	−0.0281091
$91$	456.000	0.525294
$92$	−92.0000	−0.104257
$93$	−515.000	−0.574226
$94$	714.000	0.783441
$95$	420.000	0.453590
$96$	800.000	0.850517
$97$	−964.000	−1.00907	−0.504533	−	0.863393i	$-0.668335\pi$
$97$	−964.000	−1.00907	−0.504533	+	0.863393i	$0.668335\pi$
$98$	558.000	0.575168
$99$	−68.0000	−0.0690329
$100$	356.000	0.356000
$101$	−310.000	−0.305407	−0.152704	−	0.988272i	$-0.548798\pi$
$101$	−310.000	−0.305407	−0.152704	+	0.988272i	$0.548798\pi$
$102$	−800.000	−0.776586
$103$	1044.00	0.998722	0.499361	−	0.866394i	$-0.333568\pi$
$103$	1044.00	0.998722	0.499361	+	0.866394i	$0.333568\pi$
$104$	−1368.00	−1.28984
$105$	−240.000	−0.223063
$106$	828.000	0.758703
$107$	414.000	0.374046	0.187023	−	0.982356i	$-0.440116\pi$
$107$	414.000	0.374046	0.187023	+	0.982356i	$0.440116\pi$
$108$	−580.000	−0.516764
$109$	704.000	0.618633	0.309316	−	0.950959i	$-0.399900\pi$
$109$	704.000	0.618633	0.309316	+	0.950959i	$0.399900\pi$
$110$	408.000	0.353648
$111$	1490.00	1.27409
$112$	128.000	0.107990
$113$	952.000	0.792537	0.396268	−	0.918135i	$-0.370305\pi$
$113$	952.000	0.792537	0.396268	+	0.918135i	$0.370305\pi$
$114$	−700.000	−0.575097
$115$	−138.000	−0.111901
$116$	−980.000	−0.784403
$117$	114.000	0.0900795
$118$	816.000	0.636601
$119$	640.000	0.493014
$120$	720.000	0.547723
$121$	−175.000	−0.131480
$122$	−1644.00	−1.22001
$123$	−475.000	−0.348206
$124$	−412.000	−0.298377
$125$	1284.00	0.918756
$126$	−32.0000	−0.0226253
$127$	261.000	0.182362	0.0911811	−	0.995834i	$-0.470936\pi$
$127$	261.000	0.182362	0.0911811	+	0.995834i	$0.470936\pi$
$128$	384.000	0.265165
$129$	−440.000	−0.300309
$130$	−684.000	−0.461467
$131$	−1441.00	−0.961074	−0.480537	−	0.876974i	$-0.659558\pi$
$131$	−1441.00	−0.961074	−0.480537	+	0.876974i	$0.659558\pi$
$132$	680.000	0.448382
$133$	560.000	0.365099
$134$	−1852.00	−1.19394
$135$	−870.000	−0.554649
$136$	−1920.00	−1.21058
$137$	1556.00	0.970351	0.485175	−	0.874417i	$-0.338756\pi$
$137$	1556.00	0.970351	0.485175	+	0.874417i	$0.338756\pi$
$138$	230.000	0.141876
$139$	25.0000	0.0152552	0.00762760	−	0.999971i	$-0.497572\pi$
$139$	25.0000	0.0152552	0.00762760	+	0.999971i	$0.497572\pi$
$140$	−192.000	−0.115907
$141$	1785.00	1.06613
$142$	−670.000	−0.395952
$143$	−1938.00	−1.13331
$144$	32.0000	0.0185185
$145$	−1470.00	−0.841909
$146$	1798.00	1.01920
$147$	1395.00	0.782705
$148$	1192.00	0.662039
$149$	822.000	0.451952	0.225976	−	0.974133i	$-0.427443\pi$
$149$	822.000	0.451952	0.225976	+	0.974133i	$0.427443\pi$
$150$	−890.000	−0.484455
$151$	−1489.00	−0.802471	−0.401235	−	0.915975i	$-0.631419\pi$
$151$	−1489.00	−0.802471	−0.401235	+	0.915975i	$0.631419\pi$
$152$	−1680.00	−0.896487
$153$	160.000	0.0845440
$154$	544.000	0.284654
$155$	−618.000	−0.320251
$156$	−1140.00	−0.585084
$157$	−632.000	−0.321268	−0.160634	−	0.987014i	$-0.551354\pi$
$157$	−632.000	−0.321268	−0.160634	+	0.987014i	$0.551354\pi$
$158$	2644.00	1.33130
$159$	2070.00	1.03246
$160$	960.000	0.474342
$161$	−184.000	−0.0900698
$162$	1342.00	0.650849
$163$	−3043.00	−1.46225	−0.731123	−	0.682245i	$-0.761004\pi$
$163$	−3043.00	−1.46225	−0.731123	+	0.682245i	$0.761004\pi$
$164$	−380.000	−0.180933
$165$	1020.00	0.481254
$166$	72.0000	0.0336644
$167$	−2224.00	−1.03053	−0.515264	−	0.857031i	$-0.672306\pi$
$167$	−2224.00	−1.03053	−0.515264	+	0.857031i	$0.672306\pi$
$168$	960.000	0.440867
$169$	1052.00	0.478835
$170$	−960.000	−0.433110
$171$	140.000	0.0626086
$172$	−352.000	−0.156045
$173$	3230.00	1.41949	0.709747	−	0.704457i	$-0.248809\pi$
$173$	3230.00	1.41949	0.709747	+	0.704457i	$0.248809\pi$
$174$	2450.00	1.06744
$175$	712.000	0.307555
$176$	−544.000	−0.232986
$177$	2040.00	0.866304
$178$	920.000	0.387398
$179$	369.000	0.154080	0.0770401	−	0.997028i	$-0.475453\pi$
$179$	369.000	0.154080	0.0770401	+	0.997028i	$0.475453\pi$
$180$	−48.0000	−0.0198762
$181$	−1370.00	−0.562604	−0.281302	−	0.959619i	$-0.590766\pi$
$181$	−1370.00	−0.562604	−0.281302	+	0.959619i	$0.590766\pi$
$182$	−912.000	−0.371439
$183$	−4110.00	−1.66022
$184$	552.000	0.221163
$185$	1788.00	0.710575
$186$	1030.00	0.406039
$187$	−2720.00	−1.06367
$188$	1428.00	0.553977
$189$	−1160.00	−0.446442
$190$	−840.000	−0.320737
$191$	4410.00	1.67066	0.835331	−	0.549747i	$-0.185276\pi$
$191$	4410.00	1.67066	0.835331	+	0.549747i	$0.185276\pi$
$192$	−2240.00	−0.841969
$193$	−135.000	−0.0503498	−0.0251749	−	0.999683i	$-0.508014\pi$
$193$	−135.000	−0.0503498	−0.0251749	+	0.999683i	$0.508014\pi$
$194$	1928.00	0.713517
$195$	−1710.00	−0.627978
$196$	1116.00	0.406706
$197$	1221.00	0.441587	0.220794	−	0.975321i	$-0.429135\pi$
$197$	1221.00	0.441587	0.220794	+	0.975321i	$0.429135\pi$
$198$	136.000	0.0488136
$199$	−1098.00	−0.391131	−0.195566	−	0.980691i	$-0.562654\pi$
$199$	−1098.00	−0.391131	−0.195566	+	0.980691i	$0.562654\pi$
$200$	−2136.00	−0.755190
$201$	−4630.00	−1.62475
$202$	620.000	0.215956
$203$	−1960.00	−0.677660
$204$	−1600.00	−0.549129
$205$	−570.000	−0.194198
$206$	−2088.00	−0.706203
$207$	−46.0000	−0.0154455
$208$	912.000	0.304018
$209$	−2380.00	−0.787694
$210$	480.000	0.157729
$211$	−3676.00	−1.19937	−0.599683	−	0.800238i	$-0.704707\pi$
$211$	−3676.00	−1.19937	−0.599683	+	0.800238i	$0.704707\pi$
$212$	1656.00	0.536484
$213$	−1675.00	−0.538822
$214$	−828.000	−0.264490
$215$	−528.000	−0.167485
$216$	3480.00	1.09622
$217$	−824.000	−0.257773
$218$	−1408.00	−0.437439
$219$	4495.00	1.38696
$220$	816.000	0.250067
$221$	4560.00	1.38796
$222$	−2980.00	−0.900921
$223$	1656.00	0.497282	0.248641	−	0.968596i	$-0.420016\pi$
$223$	1656.00	0.497282	0.248641	+	0.968596i	$0.420016\pi$
$224$	1280.00	0.381802
$225$	178.000	0.0527407
$226$	−1904.00	−0.560408
$227$	2940.00	0.859624	0.429812	−	0.902918i	$-0.358580\pi$
$227$	2940.00	0.859624	0.429812	+	0.902918i	$0.358580\pi$
$228$	−1400.00	−0.406655
$229$	3612.00	1.04230	0.521152	−	0.853464i	$-0.325502\pi$
$229$	3612.00	1.04230	0.521152	+	0.853464i	$0.325502\pi$
$230$	276.000	0.0791257
$231$	1360.00	0.387366
$232$	5880.00	1.66397
$233$	−4325.00	−1.21605	−0.608026	−	0.793917i	$-0.708038\pi$
$233$	−4325.00	−1.21605	−0.608026	+	0.793917i	$0.708038\pi$
$234$	−228.000	−0.0636958
$235$	2142.00	0.594590
$236$	1632.00	0.450145
$237$	6610.00	1.81167
$238$	−1280.00	−0.348614
$239$	2735.00	0.740219	0.370110	−	0.928988i	$-0.379320\pi$
$239$	2735.00	0.740219	0.370110	+	0.928988i	$0.379320\pi$
$240$	−480.000	−0.129099
$241$	−6710.00	−1.79348	−0.896741	−	0.442556i	$-0.854072\pi$
$241$	−6710.00	−1.79348	−0.896741	+	0.442556i	$0.854072\pi$
$242$	350.000	0.0929705
$243$	−560.000	−0.147835
$244$	−3288.00	−0.862675
$245$	1674.00	0.436522
$246$	950.000	0.246219
$247$	3990.00	1.02784
$248$	2472.00	0.632952
$249$	180.000	0.0458114
$250$	−2568.00	−0.649658
$251$	−6948.00	−1.74723	−0.873613	−	0.486621i	$-0.838229\pi$
$251$	−6948.00	−1.74723	−0.873613	+	0.486621i	$0.838229\pi$
$252$	−64.0000	−0.0159985
$253$	782.000	0.194324
$254$	−522.000	−0.128950
$255$	−2400.00	−0.589388
$256$	−4352.00	−1.06250
$257$	−4929.00	−1.19635	−0.598176	−	0.801365i	$-0.704108\pi$
$257$	−4929.00	−1.19635	−0.598176	+	0.801365i	$0.704108\pi$
$258$	880.000	0.212350
$259$	2384.00	0.571948
$260$	−1368.00	−0.326307
$261$	−490.000	−0.116208
$262$	2882.00	0.679582
$263$	6138.00	1.43911	0.719554	−	0.694437i	$-0.244346\pi$
$263$	6138.00	1.43911	0.719554	+	0.694437i	$0.244346\pi$
$264$	−4080.00	−0.951162
$265$	2484.00	0.575815
$266$	−1120.00	−0.258164
$267$	2300.00	0.527182
$268$	−3704.00	−0.844246
$269$	−2063.00	−0.467596	−0.233798	−	0.972285i	$-0.575115\pi$
$269$	−2063.00	−0.467596	−0.233798	+	0.972285i	$0.575115\pi$
$270$	1740.00	0.392196
$271$	−1064.00	−0.238500	−0.119250	−	0.992864i	$-0.538049\pi$
$271$	−1064.00	−0.238500	−0.119250	+	0.992864i	$0.538049\pi$
$272$	1280.00	0.285336
$273$	−2280.00	−0.505465
$274$	−3112.00	−0.686142
$275$	−3026.00	−0.663544
$276$	460.000	0.100322
$277$	5729.00	1.24268	0.621340	−	0.783541i	$-0.286589\pi$
$277$	5729.00	1.24268	0.621340	+	0.783541i	$0.286589\pi$
$278$	−50.0000	−0.0107871
$279$	−206.000	−0.0442039
$280$	1152.00	0.245876
$281$	−960.000	−0.203804	−0.101902	−	0.994794i	$-0.532493\pi$
$281$	−960.000	−0.203804	−0.101902	+	0.994794i	$0.532493\pi$
$282$	−3570.00	−0.753867
$283$	−114.000	−0.0239456	−0.0119728	−	0.999928i	$-0.503811\pi$
$283$	−114.000	−0.0239456	−0.0119728	+	0.999928i	$0.503811\pi$
$284$	−1340.00	−0.279980
$285$	−2100.00	−0.436468
$286$	3876.00	0.801373
$287$	−760.000	−0.156311
$288$	320.000	0.0654729
$289$	1487.00	0.302666
$290$	2940.00	0.595320
$291$	4820.00	0.970974
$292$	3596.00	0.720685
$293$	−7048.00	−1.40529	−0.702643	−	0.711543i	$-0.747997\pi$
$293$	−7048.00	−1.40529	−0.702643	+	0.711543i	$0.747997\pi$
$294$	−2790.00	−0.553456
$295$	2448.00	0.483146
$296$	−7152.00	−1.40440
$297$	4930.00	0.963191
$298$	−1644.00	−0.319578
$299$	−1311.00	−0.253569
$300$	−1780.00	−0.342561
$301$	−704.000	−0.134810
$302$	2978.00	0.567433
$303$	1550.00	0.293878
$304$	1120.00	0.211304
$305$	−4932.00	−0.925920
$306$	−320.000	−0.0597816
$307$	3872.00	0.719826	0.359913	−	0.932986i	$-0.382806\pi$
$307$	3872.00	0.719826	0.359913	+	0.932986i	$0.382806\pi$
$308$	1088.00	0.201281
$309$	−5220.00	−0.961021
$310$	1236.00	0.226452
$311$	−4977.00	−0.907459	−0.453730	−	0.891139i	$-0.649907\pi$
$311$	−4977.00	−0.907459	−0.453730	+	0.891139i	$0.649907\pi$
$312$	6840.00	1.24115
$313$	−2536.00	−0.457965	−0.228983	−	0.973430i	$-0.573540\pi$
$313$	−2536.00	−0.457965	−0.228983	+	0.973430i	$0.573540\pi$
$314$	1264.00	0.227171
$315$	−96.0000	−0.0171714
$316$	5288.00	0.941371
$317$	1434.00	0.254074	0.127037	−	0.991898i	$-0.459453\pi$
$317$	1434.00	0.254074	0.127037	+	0.991898i	$0.459453\pi$
$318$	−4140.00	−0.730062
$319$	8330.00	1.46204
$320$	−2688.00	−0.469574
$321$	−2070.00	−0.359926
$322$	368.000	0.0636889
$323$	5600.00	0.964682
$324$	2684.00	0.460219
$325$	5073.00	0.865844
$326$	6086.00	1.03396
$327$	−3520.00	−0.595280
$328$	2280.00	0.383817
$329$	2856.00	0.478591
$330$	−2040.00	−0.340298
$331$	5469.00	0.908167	0.454084	−	0.890959i	$-0.349967\pi$
$331$	5469.00	0.908167	0.454084	+	0.890959i	$0.349967\pi$
$332$	144.000	0.0238043
$333$	596.000	0.0980799
$334$	4448.00	0.728694
$335$	−5556.00	−0.906139
$336$	−640.000	−0.103913
$337$	−7796.00	−1.26016	−0.630082	−	0.776529i	$-0.716979\pi$
$337$	−7796.00	−1.26016	−0.630082	+	0.776529i	$0.716979\pi$
$338$	−2104.00	−0.338587
$339$	−4760.00	−0.762619
$340$	−1920.00	−0.306255
$341$	3502.00	0.556141
$342$	−280.000	−0.0442710
$343$	4976.00	0.783320
$344$	2112.00	0.331022
$345$	690.000	0.107676
$346$	−6460.00	−1.00373
$347$	−10068.0	−1.55758	−0.778788	−	0.627288i	$-0.784165\pi$
$347$	−10068.0	−1.55758	−0.778788	+	0.627288i	$0.784165\pi$
$348$	4900.00	0.754792
$349$	−7495.00	−1.14956	−0.574782	−	0.818306i	$-0.694913\pi$
$349$	−7495.00	−1.14956	−0.574782	+	0.818306i	$0.694913\pi$
$350$	−1424.00	−0.217474
$351$	−8265.00	−1.25685
$352$	−5440.00	−0.823730
$353$	10617.0	1.60081	0.800405	−	0.599460i	$-0.204618\pi$
$353$	10617.0	1.60081	0.800405	+	0.599460i	$0.204618\pi$
$354$	−4080.00	−0.612569
$355$	−2010.00	−0.300506
$356$	1840.00	0.273932
$357$	−3200.00	−0.474403
$358$	−738.000	−0.108951
$359$	2522.00	0.370769	0.185384	−	0.982666i	$-0.440647\pi$
$359$	2522.00	0.370769	0.185384	+	0.982666i	$0.440647\pi$
$360$	288.000	0.0421637
$361$	−1959.00	−0.285610
$362$	2740.00	0.397821
$363$	875.000	0.126517
$364$	−1824.00	−0.262647
$365$	5394.00	0.773520
$366$	8220.00	1.17395
$367$	7204.00	1.02465	0.512324	−	0.858792i	$-0.328785\pi$
$367$	7204.00	1.02465	0.512324	+	0.858792i	$0.328785\pi$
$368$	−368.000	−0.0521286
$369$	−190.000	−0.0268049
$370$	−3576.00	−0.502452
$371$	3312.00	0.463478
$372$	2060.00	0.287113
$373$	−13310.0	−1.84763	−0.923815	−	0.382840i	$-0.874946\pi$
$373$	−13310.0	−1.84763	−0.923815	+	0.382840i	$0.874946\pi$
$374$	5440.00	0.752128
$375$	−6420.00	−0.884073
$376$	−8568.00	−1.17516
$377$	−13965.0	−1.90778
$378$	2320.00	0.315682
$379$	12952.0	1.75541	0.877704	−	0.479203i	$-0.159074\pi$
$379$	12952.0	1.75541	0.877704	+	0.479203i	$0.159074\pi$
$380$	−1680.00	−0.226795
$381$	−1305.00	−0.175478
$382$	−8820.00	−1.18134
$383$	−2812.00	−0.375161	−0.187580	−	0.982249i	$-0.560064\pi$
$383$	−2812.00	−0.375161	−0.187580	+	0.982249i	$0.560064\pi$
$384$	−1920.00	−0.255155
$385$	1632.00	0.216037
$386$	270.000	0.0356027
$387$	−176.000	−0.0231178
$388$	3856.00	0.504533
$389$	1264.00	0.164749	0.0823745	−	0.996601i	$-0.473750\pi$
$389$	1264.00	0.164749	0.0823745	+	0.996601i	$0.473750\pi$
$390$	3420.00	0.444047
$391$	−1840.00	−0.237987
$392$	−6696.00	−0.862753
$393$	7205.00	0.924794
$394$	−2442.00	−0.312249
$395$	7932.00	1.01039
$396$	272.000	0.0345165
$397$	7119.00	0.899981	0.449990	−	0.893033i	$-0.351427\pi$
$397$	7119.00	0.899981	0.449990	+	0.893033i	$0.351427\pi$
$398$	2196.00	0.276572
$399$	−2800.00	−0.351317
$400$	1424.00	0.178000
$401$	4262.00	0.530758	0.265379	−	0.964144i	$-0.414503\pi$
$401$	4262.00	0.530758	0.265379	+	0.964144i	$0.414503\pi$
$402$	9260.00	1.14887
$403$	−5871.00	−0.725696
$404$	1240.00	0.152704
$405$	4026.00	0.493959
$406$	3920.00	0.479178
$407$	−10132.0	−1.23397
$408$	9600.00	1.16488
$409$	229.000	0.0276854	0.0138427	−	0.999904i	$-0.495594\pi$
$409$	229.000	0.0276854	0.0138427	+	0.999904i	$0.495594\pi$
$410$	1140.00	0.137319
$411$	−7780.00	−0.933720
$412$	−4176.00	−0.499361
$413$	3264.00	0.388888
$414$	92.0000	0.0109216
$415$	216.000	0.0255495
$416$	9120.00	1.07487
$417$	−125.000	−0.0146793
$418$	4760.00	0.556984
$419$	15776.0	1.83940	0.919699	−	0.392623i	$-0.128432\pi$
$419$	15776.0	1.83940	0.919699	+	0.392623i	$0.128432\pi$
$420$	960.000	0.111531
$421$	−8728.00	−1.01040	−0.505198	−	0.863003i	$-0.668581\pi$
$421$	−8728.00	−1.01040	−0.505198	+	0.863003i	$0.668581\pi$
$422$	7352.00	0.848080
$423$	714.000	0.0820706
$424$	−9936.00	−1.13805
$425$	7120.00	0.812637
$426$	3350.00	0.381005
$427$	−6576.00	−0.745281
$428$	−1656.00	−0.187023
$429$	9690.00	1.09053
$430$	1056.00	0.118430
$431$	−2928.00	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$431$	−2928.00	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$432$	−2320.00	−0.258382
$433$	−5314.00	−0.589780	−0.294890	−	0.955531i	$-0.595283\pi$
$433$	−5314.00	−0.589780	−0.294890	+	0.955531i	$0.595283\pi$
$434$	1648.00	0.182273
$435$	7350.00	0.810128
$436$	−2816.00	−0.309316
$437$	−1610.00	−0.176240
$438$	−8990.00	−0.980728
$439$	2585.00	0.281037	0.140519	−	0.990078i	$-0.455123\pi$
$439$	2585.00	0.281037	0.140519	+	0.990078i	$0.455123\pi$
$440$	−4896.00	−0.530472
$441$	558.000	0.0602527
$442$	−9120.00	−0.981435
$443$	−2997.00	−0.321426	−0.160713	−	0.987001i	$-0.551379\pi$
$443$	−2997.00	−0.321426	−0.160713	+	0.987001i	$0.551379\pi$
$444$	−5960.00	−0.637047
$445$	2760.00	0.294015
$446$	−3312.00	−0.351632
$447$	−4110.00	−0.434891
$448$	−3584.00	−0.377964
$449$	−16562.0	−1.74078	−0.870389	−	0.492365i	$-0.836132\pi$
$449$	−16562.0	−1.74078	−0.870389	+	0.492365i	$0.836132\pi$
$450$	−356.000	−0.0372933
$451$	3230.00	0.337239
$452$	−3808.00	−0.396268
$453$	7445.00	0.772178
$454$	−5880.00	−0.607846
$455$	−2736.00	−0.281903
$456$	8400.00	0.862645
$457$	3924.00	0.401656	0.200828	−	0.979626i	$-0.435637\pi$
$457$	3924.00	0.401656	0.200828	+	0.979626i	$0.435637\pi$
$458$	−7224.00	−0.737020
$459$	−11600.0	−1.17961
$460$	552.000	0.0559503
$461$	−4543.00	−0.458977	−0.229489	−	0.973311i	$-0.573705\pi$
$461$	−4543.00	−0.458977	−0.229489	+	0.973311i	$0.573705\pi$
$462$	−2720.00	−0.273909
$463$	9616.00	0.965213	0.482606	−	0.875837i	$-0.339690\pi$
$463$	9616.00	0.965213	0.482606	+	0.875837i	$0.339690\pi$
$464$	−3920.00	−0.392201
$465$	3090.00	0.308162
$466$	8650.00	0.859879
$467$	7826.00	0.775469	0.387735	−	0.921771i	$-0.373258\pi$
$467$	7826.00	0.775469	0.387735	+	0.921771i	$0.373258\pi$
$468$	−456.000	−0.0450398
$469$	−7408.00	−0.729360
$470$	−4284.00	−0.420439
$471$	3160.00	0.309140
$472$	−9792.00	−0.954901
$473$	2992.00	0.290851
$474$	−13220.0	−1.28104
$475$	6230.00	0.601794
$476$	−2560.00	−0.246507
$477$	828.000	0.0794791
$478$	−5470.00	−0.523414
$479$	11404.0	1.08781	0.543906	−	0.839146i	$-0.316945\pi$
$479$	11404.0	1.08781	0.543906	+	0.839146i	$0.316945\pi$
$480$	−4800.00	−0.456435
$481$	16986.0	1.61018
$482$	13420.0	1.26818
$483$	920.000	0.0866697
$484$	700.000	0.0657400
$485$	5784.00	0.541521
$486$	1120.00	0.104535
$487$	−9267.00	−0.862275	−0.431137	−	0.902286i	$-0.641888\pi$
$487$	−9267.00	−0.862275	−0.431137	+	0.902286i	$0.641888\pi$
$488$	19728.0	1.83001
$489$	15215.0	1.40705
$490$	−3348.00	−0.308668
$491$	−18191.0	−1.67199	−0.835996	−	0.548735i	$-0.815110\pi$
$491$	−18191.0	−1.67199	−0.835996	+	0.548735i	$0.815110\pi$
$492$	1900.00	0.174103
$493$	−19600.0	−1.79055
$494$	−7980.00	−0.726796
$495$	408.000	0.0370469
$496$	−1648.00	−0.149188
$497$	−2680.00	−0.241880
$498$	−360.000	−0.0323935
$499$	19315.0	1.73278	0.866391	−	0.499366i	$-0.166434\pi$
$499$	19315.0	1.73278	0.866391	+	0.499366i	$0.166434\pi$
$500$	−5136.00	−0.459378
$501$	11120.0	0.991627
$502$	13896.0	1.23548
$503$	8422.00	0.746557	0.373279	−	0.927719i	$-0.378234\pi$
$503$	8422.00	0.746557	0.373279	+	0.927719i	$0.378234\pi$
$504$	384.000	0.0339379
$505$	1860.00	0.163899
$506$	−1564.00	−0.137408
$507$	−5260.00	−0.460759
$508$	−1044.00	−0.0911811
$509$	−863.000	−0.0751509	−0.0375754	−	0.999294i	$-0.511963\pi$
$509$	−863.000	−0.0751509	−0.0375754	+	0.999294i	$0.511963\pi$
$510$	4800.00	0.416760
$511$	7192.00	0.622613
$512$	5632.00	0.486136
$513$	−10150.0	−0.873554
$514$	9858.00	0.845949
$515$	−6264.00	−0.535971
$516$	1760.00	0.150154
$517$	−12138.0	−1.03255
$518$	−4768.00	−0.404428
$519$	−16150.0	−1.36591
$520$	8208.00	0.692201
$521$	19260.0	1.61957	0.809785	−	0.586727i	$-0.199584\pi$
$521$	19260.0	1.61957	0.809785	+	0.586727i	$0.199584\pi$
$522$	980.000	0.0821713
$523$	−11740.0	−0.981557	−0.490779	−	0.871284i	$-0.663288\pi$
$523$	−11740.0	−0.981557	−0.490779	+	0.871284i	$0.663288\pi$
$524$	5764.00	0.480537
$525$	−3560.00	−0.295945
$526$	−12276.0	−1.01760
$527$	−8240.00	−0.681101
$528$	2720.00	0.224191
$529$	529.000	0.0434783
$530$	−4968.00	−0.407163
$531$	816.000	0.0666881
$532$	−2240.00	−0.182549
$533$	−5415.00	−0.440056
$534$	−4600.00	−0.372774
$535$	−2484.00	−0.200734
$536$	22224.0	1.79092
$537$	−1845.00	−0.148264
$538$	4126.00	0.330640
$539$	−9486.00	−0.758054
$540$	3480.00	0.277325
$541$	17741.0	1.40988	0.704940	−	0.709267i	$-0.250974\pi$
$541$	17741.0	1.40988	0.704940	+	0.709267i	$0.250974\pi$
$542$	2128.00	0.168645
$543$	6850.00	0.541366
$544$	12800.0	1.00882
$545$	−4224.00	−0.331993
$546$	4560.00	0.357418
$547$	−6571.00	−0.513630	−0.256815	−	0.966461i	$-0.582673\pi$
$547$	−6571.00	−0.513630	−0.256815	+	0.966461i	$0.582673\pi$
$548$	−6224.00	−0.485175
$549$	−1644.00	−0.127804
$550$	6052.00	0.469197
$551$	−17150.0	−1.32598
$552$	−2760.00	−0.212814
$553$	10576.0	0.813268
$554$	−11458.0	−0.878707
$555$	−8940.00	−0.683751
$556$	−100.000	−0.00762760
$557$	−1372.00	−0.104369	−0.0521845	−	0.998637i	$-0.516618\pi$
$557$	−1372.00	−0.104369	−0.0521845	+	0.998637i	$0.516618\pi$
$558$	412.000	0.0312569
$559$	−5016.00	−0.379524
$560$	−768.000	−0.0579534
$561$	13600.0	1.02352
$562$	1920.00	0.144111
$563$	4332.00	0.324284	0.162142	−	0.986767i	$-0.448160\pi$
$563$	4332.00	0.324284	0.162142	+	0.986767i	$0.448160\pi$
$564$	−7140.00	−0.533064
$565$	−5712.00	−0.425320
$566$	228.000	0.0169321
$567$	5368.00	0.397592
$568$	8040.00	0.593928
$569$	−3546.00	−0.261258	−0.130629	−	0.991431i	$-0.541700\pi$
$569$	−3546.00	−0.261258	−0.130629	+	0.991431i	$0.541700\pi$
$570$	4200.00	0.308629
$571$	−6160.00	−0.451468	−0.225734	−	0.974189i	$-0.572478\pi$
$571$	−6160.00	−0.451468	−0.225734	+	0.974189i	$0.572478\pi$
$572$	7752.00	0.566656
$573$	−22050.0	−1.60760
$574$	1520.00	0.110529
$575$	−2047.00	−0.148462
$576$	−896.000	−0.0648148
$577$	2953.00	0.213059	0.106529	−	0.994310i	$-0.466026\pi$
$577$	2953.00	0.213059	0.106529	+	0.994310i	$0.466026\pi$
$578$	−2974.00	−0.214017
$579$	675.000	0.0484491
$580$	5880.00	0.420955
$581$	288.000	0.0205650
$582$	−9640.00	−0.686582
$583$	−14076.0	−0.999946
$584$	−21576.0	−1.52880
$585$	−684.000	−0.0483417
$586$	14096.0	0.993687
$587$	−2949.00	−0.207356	−0.103678	−	0.994611i	$-0.533061\pi$
$587$	−2949.00	−0.207356	−0.103678	+	0.994611i	$0.533061\pi$
$588$	−5580.00	−0.391353
$589$	−7210.00	−0.504385
$590$	−4896.00	−0.341636
$591$	−6105.00	−0.424917
$592$	4768.00	0.331020
$593$	16390.0	1.13500	0.567501	−	0.823372i	$-0.307910\pi$
$593$	16390.0	1.13500	0.567501	+	0.823372i	$0.307910\pi$
$594$	−9860.00	−0.681079
$595$	−3840.00	−0.264579
$596$	−3288.00	−0.225976
$597$	5490.00	0.376366
$598$	2622.00	0.179300
$599$	−12920.0	−0.881297	−0.440648	−	0.897680i	$-0.645251\pi$
$599$	−12920.0	−0.881297	−0.440648	+	0.897680i	$0.645251\pi$
$600$	10680.0	0.726682
$601$	−13835.0	−0.939004	−0.469502	−	0.882931i	$-0.655567\pi$
$601$	−13835.0	−0.939004	−0.469502	+	0.882931i	$0.655567\pi$
$602$	1408.00	0.0953252
$603$	−1852.00	−0.125073
$604$	5956.00	0.401235
$605$	1050.00	0.0705596
$606$	−3100.00	−0.207803
$607$	6004.00	0.401474	0.200737	−	0.979645i	$-0.435666\pi$
$607$	6004.00	0.401474	0.200737	+	0.979645i	$0.435666\pi$
$608$	11200.0	0.747072
$609$	9800.00	0.652079
$610$	9864.00	0.654724
$611$	20349.0	1.34735
$612$	−640.000	−0.0422720
$613$	−16416.0	−1.08162	−0.540812	−	0.841143i	$-0.681883\pi$
$613$	−16416.0	−1.08162	−0.540812	+	0.841143i	$0.681883\pi$
$614$	−7744.00	−0.508994
$615$	2850.00	0.186867
$616$	−6528.00	−0.426982
$617$	3786.00	0.247032	0.123516	−	0.992343i	$-0.460583\pi$
$617$	3786.00	0.247032	0.123516	+	0.992343i	$0.460583\pi$
$618$	10440.0	0.679544
$619$	15824.0	1.02750	0.513748	−	0.857941i	$-0.328257\pi$
$619$	15824.0	1.02750	0.513748	+	0.857941i	$0.328257\pi$
$620$	2472.00	0.160126
$621$	3335.00	0.215506
$622$	9954.00	0.641670
$623$	3680.00	0.236655
$624$	−4560.00	−0.292542
$625$	3421.00	0.218944
$626$	5072.00	0.323830
$627$	11900.0	0.757959
$628$	2528.00	0.160634
$629$	23840.0	1.51123
$630$	192.000	0.0121420
$631$	17852.0	1.12627	0.563135	−	0.826365i	$-0.309595\pi$
$631$	17852.0	1.12627	0.563135	+	0.826365i	$0.309595\pi$
$632$	−31728.0	−1.99695
$633$	18380.0	1.15409
$634$	−2868.00	−0.179657
$635$	−1566.00	−0.0978658
$636$	−8280.00	−0.516232
$637$	15903.0	0.989168
$638$	−16660.0	−1.03382
$639$	−670.000	−0.0414785
$640$	−2304.00	−0.142302
$641$	10324.0	0.636152	0.318076	−	0.948065i	$-0.396963\pi$
$641$	10324.0	0.636152	0.318076	+	0.948065i	$0.396963\pi$
$642$	4140.00	0.254506
$643$	−14702.0	−0.901696	−0.450848	−	0.892601i	$-0.648878\pi$
$643$	−14702.0	−0.901696	−0.450848	+	0.892601i	$0.648878\pi$
$644$	736.000	0.0450349
$645$	2640.00	0.161163
$646$	−11200.0	−0.682133
$647$	11939.0	0.725457	0.362728	−	0.931895i	$-0.381845\pi$
$647$	11939.0	0.725457	0.362728	+	0.931895i	$0.381845\pi$
$648$	−16104.0	−0.976273
$649$	−13872.0	−0.839019
$650$	−10146.0	−0.612244
$651$	4120.00	0.248042
$652$	12172.0	0.731123
$653$	6159.00	0.369097	0.184548	−	0.982823i	$-0.440918\pi$
$653$	6159.00	0.369097	0.184548	+	0.982823i	$0.440918\pi$
$654$	7040.00	0.420926
$655$	8646.00	0.515767
$656$	−1520.00	−0.0904665
$657$	1798.00	0.106768
$658$	−5712.00	−0.338415
$659$	−21692.0	−1.28225	−0.641123	−	0.767438i	$-0.721531\pi$
$659$	−21692.0	−1.28225	−0.641123	+	0.767438i	$0.721531\pi$
$660$	−4080.00	−0.240627
$661$	16502.0	0.971034	0.485517	−	0.874227i	$-0.338631\pi$
$661$	16502.0	0.971034	0.485517	+	0.874227i	$0.338631\pi$
$662$	−10938.0	−0.642171
$663$	−22800.0	−1.33556
$664$	−864.000	−0.0504965
$665$	−3360.00	−0.195933
$666$	−1192.00	−0.0693529
$667$	5635.00	0.327119
$668$	8896.00	0.515264
$669$	−8280.00	−0.478510
$670$	11112.0	0.640737
$671$	27948.0	1.60793
$672$	−6400.00	−0.367389
$673$	−27733.0	−1.58845	−0.794226	−	0.607622i	$-0.792124\pi$
$673$	−27733.0	−1.58845	−0.794226	+	0.607622i	$0.792124\pi$
$674$	15592.0	0.891070
$675$	−12905.0	−0.735872
$676$	−4208.00	−0.239417
$677$	−8814.00	−0.500369	−0.250184	−	0.968198i	$-0.580491\pi$
$677$	−8814.00	−0.500369	−0.250184	+	0.968198i	$0.580491\pi$
$678$	9520.00	0.539253
$679$	7712.00	0.435875
$680$	11520.0	0.649664
$681$	−14700.0	−0.827174
$682$	−7004.00	−0.393251
$683$	−22999.0	−1.28848	−0.644240	−	0.764823i	$-0.722826\pi$
$683$	−22999.0	−1.28848	−0.644240	+	0.764823i	$0.722826\pi$
$684$	−560.000	−0.0313043
$685$	−9336.00	−0.520745
$686$	−9952.00	−0.553891
$687$	−18060.0	−1.00296
$688$	−1408.00	−0.0780225
$689$	23598.0	1.30481
$690$	−1380.00	−0.0761387
$691$	−12140.0	−0.668346	−0.334173	−	0.942512i	$-0.608457\pi$
$691$	−12140.0	−0.668346	−0.334173	+	0.942512i	$0.608457\pi$
$692$	−12920.0	−0.709747
$693$	544.000	0.0298194
$694$	20136.0	1.10137
$695$	−150.000	−0.00818680
$696$	−29400.0	−1.60116
$697$	−7600.00	−0.413014
$698$	14990.0	0.812865
$699$	21625.0	1.17015
$700$	−2848.00	−0.153778
$701$	−20024.0	−1.07888	−0.539441	−	0.842024i	$-0.681364\pi$
$701$	−20024.0	−1.07888	−0.539441	+	0.842024i	$0.681364\pi$
$702$	16530.0	0.888725
$703$	20860.0	1.11913
$704$	15232.0	0.815451
$705$	−10710.0	−0.572145
$706$	−21234.0	−1.13194
$707$	2480.00	0.131924
$708$	−8160.00	−0.433152
$709$	−4956.00	−0.262520	−0.131260	−	0.991348i	$-0.541902\pi$
$709$	−4956.00	−0.262520	−0.131260	+	0.991348i	$0.541902\pi$
$710$	4020.00	0.212490
$711$	2644.00	0.139462
$712$	−11040.0	−0.581098
$713$	2369.00	0.124432
$714$	6400.00	0.335454
$715$	11628.0	0.608199
$716$	−1476.00	−0.0770401
$717$	−13675.0	−0.712276
$718$	−5044.00	−0.262173
$719$	2760.00	0.143158	0.0715790	−	0.997435i	$-0.477196\pi$
$719$	2760.00	0.143158	0.0715790	+	0.997435i	$0.477196\pi$
$720$	−192.000	−0.00993808
$721$	−8352.00	−0.431407
$722$	3918.00	0.201957
$723$	33550.0	1.72578
$724$	5480.00	0.281302
$725$	−21805.0	−1.11699
$726$	−1750.00	−0.0894609
$727$	7746.00	0.395163	0.197581	−	0.980287i	$-0.436691\pi$
$727$	7746.00	0.395163	0.197581	+	0.980287i	$0.436691\pi$
$728$	10944.0	0.557159
$729$	20917.0	1.06269
$730$	−10788.0	−0.546961
$731$	−7040.00	−0.356202
$732$	16440.0	0.830109
$733$	−11976.0	−0.603470	−0.301735	−	0.953392i	$-0.597566\pi$
$733$	−11976.0	−0.603470	−0.301735	+	0.953392i	$0.597566\pi$
$734$	−14408.0	−0.724535
$735$	−8370.00	−0.420044
$736$	−3680.00	−0.184302
$737$	31484.0	1.57358
$738$	380.000	0.0189539
$739$	15057.0	0.749500	0.374750	−	0.927126i	$-0.377728\pi$
$739$	15057.0	0.749500	0.374750	+	0.927126i	$0.377728\pi$
$740$	−7152.00	−0.355287
$741$	−19950.0	−0.989044
$742$	−6624.00	−0.327729
$743$	18532.0	0.915038	0.457519	−	0.889200i	$-0.348738\pi$
$743$	18532.0	0.915038	0.457519	+	0.889200i	$0.348738\pi$
$744$	−12360.0	−0.609059
$745$	−4932.00	−0.242543
$746$	26620.0	1.30647
$747$	72.0000	0.00352656
$748$	10880.0	0.531834
$749$	−3312.00	−0.161573
$750$	12840.0	0.625134
$751$	−192.000	−0.00932913	−0.00466457	−	0.999989i	$-0.501485\pi$
$751$	−192.000	−0.00932913	−0.00466457	+	0.999989i	$0.501485\pi$
$752$	5712.00	0.276988
$753$	34740.0	1.68127
$754$	27930.0	1.34901
$755$	8934.00	0.430651
$756$	4640.00	0.223221
$757$	−9830.00	−0.471965	−0.235982	−	0.971757i	$-0.575831\pi$
$757$	−9830.00	−0.471965	−0.235982	+	0.971757i	$0.575831\pi$
$758$	−25904.0	−1.24126
$759$	−3910.00	−0.186988
$760$	10080.0	0.481105
$761$	−30219.0	−1.43947	−0.719736	−	0.694248i	$-0.755737\pi$
$761$	−30219.0	−1.43947	−0.719736	+	0.694248i	$0.755737\pi$
$762$	2610.00	0.124082
$763$	−5632.00	−0.267224
$764$	−17640.0	−0.835331
$765$	−960.000	−0.0453711
$766$	5624.00	0.265279
$767$	23256.0	1.09482
$768$	21760.0	1.02239
$769$	1122.00	0.0526142	0.0263071	−	0.999654i	$-0.491625\pi$
$769$	1122.00	0.0526142	0.0263071	+	0.999654i	$0.491625\pi$
$770$	−3264.00	−0.152762
$771$	24645.0	1.15119
$772$	540.000	0.0251749
$773$	19300.0	0.898024	0.449012	−	0.893526i	$-0.351776\pi$
$773$	19300.0	0.898024	0.449012	+	0.893526i	$0.351776\pi$
$774$	352.000	0.0163467
$775$	−9167.00	−0.424888
$776$	−23136.0	−1.07028
$777$	−11920.0	−0.550357
$778$	−2528.00	−0.116495
$779$	−6650.00	−0.305855
$780$	6840.00	0.313989
$781$	11390.0	0.521852
$782$	3680.00	0.168282
$783$	35525.0	1.62140
$784$	4464.00	0.203353
$785$	3792.00	0.172411
$786$	−14410.0	−0.653928
$787$	−19396.0	−0.878517	−0.439258	−	0.898361i	$-0.644759\pi$
$787$	−19396.0	−0.878517	−0.439258	+	0.898361i	$0.644759\pi$
$788$	−4884.00	−0.220794
$789$	−30690.0	−1.38478
$790$	−15864.0	−0.714450
$791$	−7616.00	−0.342344
$792$	−1632.00	−0.0732204
$793$	−46854.0	−2.09815
$794$	−14238.0	−0.636383
$795$	−12420.0	−0.554078
$796$	4392.00	0.195566
$797$	−39034.0	−1.73482	−0.867412	−	0.497590i	$-0.834218\pi$
$797$	−39034.0	−1.73482	−0.867412	+	0.497590i	$0.834218\pi$
$798$	5600.00	0.248418
$799$	28560.0	1.26456
$800$	14240.0	0.629325
$801$	920.000	0.0405825
$802$	−8524.00	−0.375303
$803$	−30566.0	−1.34328
$804$	18520.0	0.812376
$805$	1104.00	0.0483365
$806$	11742.0	0.513144
$807$	10315.0	0.449944
$808$	−7440.00	−0.323934
$809$	−10310.0	−0.448060	−0.224030	−	0.974582i	$-0.571921\pi$
$809$	−10310.0	−0.448060	−0.224030	+	0.974582i	$0.571921\pi$
$810$	−8052.00	−0.349282
$811$	−40693.0	−1.76193	−0.880965	−	0.473182i	$-0.843105\pi$
$811$	−40693.0	−1.76193	−0.880965	+	0.473182i	$0.843105\pi$
$812$	7840.00	0.338830
$813$	5320.00	0.229496
$814$	20264.0	0.872546
$815$	18258.0	0.784724
$816$	−6400.00	−0.274565
$817$	−6160.00	−0.263784
$818$	−458.000	−0.0195765
$819$	−912.000	−0.0389107
$820$	2280.00	0.0970988
$821$	−13934.0	−0.592326	−0.296163	−	0.955137i	$-0.595707\pi$
$821$	−13934.0	−0.592326	−0.296163	+	0.955137i	$0.595707\pi$
$822$	15560.0	0.660240
$823$	6175.00	0.261539	0.130770	−	0.991413i	$-0.458255\pi$
$823$	6175.00	0.261539	0.130770	+	0.991413i	$0.458255\pi$
$824$	25056.0	1.05930
$825$	15130.0	0.638496
$826$	−6528.00	−0.274986
$827$	28664.0	1.20525	0.602627	−	0.798023i	$-0.294121\pi$
$827$	28664.0	1.20525	0.602627	+	0.798023i	$0.294121\pi$
$828$	184.000	0.00772276
$829$	−39590.0	−1.65865	−0.829323	−	0.558770i	$-0.811274\pi$
$829$	−39590.0	−1.65865	−0.829323	+	0.558770i	$0.811274\pi$
$830$	−432.000	−0.0180662
$831$	−28645.0	−1.19577
$832$	−25536.0	−1.06406
$833$	22320.0	0.928382
$834$	250.000	0.0103798
$835$	13344.0	0.553040
$836$	9520.00	0.393847
$837$	14935.0	0.616761
$838$	−31552.0	−1.30065
$839$	−14316.0	−0.589086	−0.294543	−	0.955638i	$-0.595167\pi$
$839$	−14316.0	−0.589086	−0.294543	+	0.955638i	$0.595167\pi$
$840$	−5760.00	−0.236594
$841$	35636.0	1.46115
$842$	17456.0	0.714458
$843$	4800.00	0.196110
$844$	14704.0	0.599683
$845$	−6312.00	−0.256970
$846$	−1428.00	−0.0580327
$847$	1400.00	0.0567941
$848$	6624.00	0.268242
$849$	570.000	0.0230416
$850$	−14240.0	−0.574621
$851$	−6854.00	−0.276089
$852$	6700.00	0.269411
$853$	28366.0	1.13861	0.569304	−	0.822127i	$-0.307213\pi$
$853$	28366.0	1.13861	0.569304	+	0.822127i	$0.307213\pi$
$854$	13152.0	0.526993
$855$	−840.000	−0.0335993
$856$	9936.00	0.396735
$857$	19283.0	0.768605	0.384303	−	0.923207i	$-0.374442\pi$
$857$	19283.0	0.768605	0.384303	+	0.923207i	$0.374442\pi$
$858$	−19380.0	−0.771122
$859$	−26101.0	−1.03673	−0.518367	−	0.855158i	$-0.673460\pi$
$859$	−26101.0	−1.03673	−0.518367	+	0.855158i	$0.673460\pi$
$860$	2112.00	0.0837426
$861$	3800.00	0.150411
$862$	5856.00	0.231388
$863$	973.000	0.0383793	0.0191896	−	0.999816i	$-0.493891\pi$
$863$	973.000	0.0383793	0.0191896	+	0.999816i	$0.493891\pi$
$864$	−23200.0	−0.913519
$865$	−19380.0	−0.761780
$866$	10628.0	0.417037
$867$	−7435.00	−0.291241
$868$	3296.00	0.128887
$869$	−44948.0	−1.75461
$870$	−14700.0	−0.572847
$871$	−52782.0	−2.05333
$872$	16896.0	0.656159
$873$	1928.00	0.0747456
$874$	3220.00	0.124620
$875$	−10272.0	−0.396865
$876$	−17980.0	−0.693479
$877$	5694.00	0.219239	0.109620	−	0.993974i	$-0.465037\pi$
$877$	5694.00	0.219239	0.109620	+	0.993974i	$0.465037\pi$
$878$	−5170.00	−0.198723
$879$	35240.0	1.35224
$880$	3264.00	0.125033
$881$	45960.0	1.75758	0.878792	−	0.477205i	$-0.158350\pi$
$881$	45960.0	1.75758	0.878792	+	0.477205i	$0.158350\pi$
$882$	−1116.00	−0.0426051
$883$	17188.0	0.655065	0.327532	−	0.944840i	$-0.393783\pi$
$883$	17188.0	0.655065	0.327532	+	0.944840i	$0.393783\pi$
$884$	−18240.0	−0.693979
$885$	−12240.0	−0.464907
$886$	5994.00	0.227283
$887$	8451.00	0.319906	0.159953	−	0.987125i	$-0.448866\pi$
$887$	8451.00	0.319906	0.159953	+	0.987125i	$0.448866\pi$
$888$	35760.0	1.35138
$889$	−2088.00	−0.0787731
$890$	−5520.00	−0.207900
$891$	−22814.0	−0.857798
$892$	−6624.00	−0.248641
$893$	24990.0	0.936460
$894$	8220.00	0.307514
$895$	−2214.00	−0.0826881
$896$	−3072.00	−0.114541
$897$	6555.00	0.243997
$898$	33124.0	1.23092
$899$	25235.0	0.936190
$900$	−712.000	−0.0263704
$901$	33120.0	1.22463
$902$	−6460.00	−0.238464
$903$	3520.00	0.129721
$904$	22848.0	0.840612
$905$	8220.00	0.301925
$906$	−14890.0	−0.546012
$907$	32774.0	1.19983	0.599913	−	0.800065i	$-0.295202\pi$
$907$	32774.0	1.19983	0.599913	+	0.800065i	$0.295202\pi$
$908$	−11760.0	−0.429812
$909$	620.000	0.0226228
$910$	5472.00	0.199335
$911$	−23690.0	−0.861564	−0.430782	−	0.902456i	$-0.641762\pi$
$911$	−23690.0	−0.861564	−0.430782	+	0.902456i	$0.641762\pi$
$912$	−5600.00	−0.203327
$913$	−1224.00	−0.0443686
$914$	−7848.00	−0.284014
$915$	24660.0	0.890967
$916$	−14448.0	−0.521152
$917$	11528.0	0.415145
$918$	23200.0	0.834111
$919$	−30044.0	−1.07841	−0.539206	−	0.842174i	$-0.681275\pi$
$919$	−30044.0	−1.07841	−0.539206	+	0.842174i	$0.681275\pi$
$920$	−3312.00	−0.118688
$921$	−19360.0	−0.692653
$922$	9086.00	0.324546
$923$	−19095.0	−0.680953
$924$	−5440.00	−0.193683
$925$	26522.0	0.942744
$926$	−19232.0	−0.682508
$927$	−2088.00	−0.0739794
$928$	−39200.0	−1.38664
$929$	−39705.0	−1.40224	−0.701119	−	0.713044i	$-0.747316\pi$
$929$	−39705.0	−1.40224	−0.701119	+	0.713044i	$0.747316\pi$
$930$	−6180.00	−0.217903
$931$	19530.0	0.687508
$932$	17300.0	0.608026
$933$	24885.0	0.873203
$934$	−15652.0	−0.548339
$935$	16320.0	0.570825
$936$	2736.00	0.0955438
$937$	17422.0	0.607419	0.303710	−	0.952765i	$-0.401775\pi$
$937$	17422.0	0.607419	0.303710	+	0.952765i	$0.401775\pi$
$938$	14816.0	0.515735
$939$	12680.0	0.440677
$940$	−8568.00	−0.297295
$941$	−25292.0	−0.876191	−0.438095	−	0.898928i	$-0.644347\pi$
$941$	−25292.0	−0.876191	−0.438095	+	0.898928i	$0.644347\pi$
$942$	−6320.00	−0.218595
$943$	2185.00	0.0754543
$944$	6528.00	0.225072
$945$	6960.00	0.239586
$946$	−5984.00	−0.205662
$947$	33211.0	1.13961	0.569806	−	0.821779i	$-0.307018\pi$
$947$	33211.0	1.13961	0.569806	+	0.821779i	$0.307018\pi$
$948$	−26440.0	−0.905835
$949$	51243.0	1.75281
$950$	−12460.0	−0.425532
$951$	−7170.00	−0.244483
$952$	15360.0	0.522921
$953$	−14154.0	−0.481105	−0.240552	−	0.970636i	$-0.577329\pi$
$953$	−14154.0	−0.481105	−0.240552	+	0.970636i	$0.577329\pi$
$954$	−1656.00	−0.0562002
$955$	−26460.0	−0.896571
$956$	−10940.0	−0.370110
$957$	−41650.0	−1.40685
$958$	−22808.0	−0.769199
$959$	−12448.0	−0.419152
$960$	13440.0	0.451848
$961$	−19182.0	−0.643886
$962$	−33972.0	−1.13857
$963$	−828.000	−0.0277071
$964$	26840.0	0.896741
$965$	810.000	0.0270205
$966$	−1840.00	−0.0612847
$967$	−46343.0	−1.54115	−0.770574	−	0.637350i	$-0.780030\pi$
$967$	−46343.0	−1.54115	−0.770574	+	0.637350i	$0.780030\pi$
$968$	−4200.00	−0.139456
$969$	−28000.0	−0.928266
$970$	−11568.0	−0.382914
$971$	11710.0	0.387015	0.193508	−	0.981099i	$-0.438014\pi$
$971$	11710.0	0.387015	0.193508	+	0.981099i	$0.438014\pi$
$972$	2240.00	0.0739177
$973$	−200.000	−0.00658963
$974$	18534.0	0.609720
$975$	−25365.0	−0.833159
$976$	−13152.0	−0.431337
$977$	47854.0	1.56703	0.783513	−	0.621375i	$-0.213426\pi$
$977$	47854.0	1.56703	0.783513	+	0.621375i	$0.213426\pi$
$978$	−30430.0	−0.994933
$979$	−15640.0	−0.510579
$980$	−6696.00	−0.218261
$981$	−1408.00	−0.0458246
$982$	36382.0	1.18228
$983$	−22078.0	−0.716357	−0.358178	−	0.933653i	$-0.616602\pi$
$983$	−22078.0	−0.716357	−0.358178	+	0.933653i	$0.616602\pi$
$984$	−11400.0	−0.369328
$985$	−7326.00	−0.236980
$986$	39200.0	1.26611
$987$	−14280.0	−0.460524
$988$	−15960.0	−0.513922
$989$	2024.00	0.0650753
$990$	−816.000	−0.0261961
$991$	−4288.00	−0.137450	−0.0687249	−	0.997636i	$-0.521893\pi$
$991$	−4288.00	−0.137450	−0.0687249	+	0.997636i	$0.521893\pi$
$992$	−16480.0	−0.527460
$993$	−27345.0	−0.873885
$994$	5360.00	0.171035
$995$	6588.00	0.209903
$996$	−720.000	−0.0229057
$997$	28966.0	0.920123	0.460061	−	0.887887i	$-0.347827\pi$
$997$	28966.0	0.920123	0.460061	+	0.887887i	$0.347827\pi$
$998$	−38630.0	−1.22526
$999$	−43210.0	−1.36847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.4.a.a.1.1	✓	1
3.2	odd	2		207.4.a.a.1.1		1
4.3	odd	2		368.4.a.d.1.1		1
5.2	odd	4		575.4.b.b.24.1		2
5.3	odd	4		575.4.b.b.24.2		2
5.4	even	2		575.4.a.g.1.1		1
7.6	odd	2		1127.4.a.a.1.1		1
8.3	odd	2		1472.4.a.c.1.1		1
8.5	even	2		1472.4.a.h.1.1		1
23.22	odd	2		529.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.a.a.1.1	✓	1	1.1	even	1	trivial
207.4.a.a.1.1		1	3.2	odd	2
368.4.a.d.1.1		1	4.3	odd	2
529.4.a.a.1.1		1	23.22	odd	2
575.4.a.g.1.1		1	5.4	even	2
575.4.b.b.24.1		2	5.2	odd	4
575.4.b.b.24.2		2	5.3	odd	4
1127.4.a.a.1.1		1	7.6	odd	2
1472.4.a.c.1.1		1	8.3	odd	2
1472.4.a.h.1.1		1	8.5	even	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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