LMFDB - Embedded newform 1127.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1127,4,Mod(1,1127)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1127, 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("1127.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1127 = 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1127.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:	$66.4951525765$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	1127.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

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

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	$-0.340228\pi$
$3$	5.00000	0.962250	0.481125	+	0.876652i	$0.340228\pi$
$4$	−4.00000	−0.500000
$5$	6.00000	0.536656	0.268328	−	0.963328i	$-0.413529\pi$
$5$	6.00000	0.536656	0.268328	+	0.963328i	$0.413529\pi$
$6$	−10.0000	−0.680414
$7$	0	0
$7$	0	0
$8$	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	$-0.291957\pi$
$13$	57.0000	1.21607	0.608037	+	0.793909i	$0.291957\pi$
$14$	0	0
$15$	30.0000	0.516398
$16$	−16.0000	−0.250000
$17$	80.0000	1.14134	0.570672	−	0.821178i	$-0.306683\pi$
$17$	80.0000	1.14134	0.570672	+	0.821178i	$0.306683\pi$
$18$	4.00000	0.0523783
$19$	70.0000	0.845216	0.422608	−	0.906313i	$-0.361115\pi$
$19$	70.0000	0.845216	0.422608	+	0.906313i	$0.361115\pi$
$20$	−24.0000	−0.268328
$21$	0	0
$22$	−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
$28$	0	0
$29$	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	$-0.596445\pi$
$31$	−103.000	−0.596753	−0.298377	+	0.954448i	$0.596445\pi$
$32$	−160.000	−0.883883
$33$	170.000	0.896764
$34$	−160.000	−0.807052
$35$	0	0
$36$	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	$-0.557912\pi$
$41$	−95.0000	−0.361866	−0.180933	+	0.983495i	$0.557912\pi$
$42$	0	0
$43$	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	$-0.313110\pi$
$47$	357.000	1.10795	0.553977	+	0.832532i	$0.313110\pi$
$48$	−80.0000	−0.240563
$49$	0	0
$50$	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
$56$	0	0
$57$	350.000	0.813309
$58$	−490.000	−1.10931
$59$	408.000	0.900289	0.450145	−	0.892956i	$-0.351372\pi$
$59$	408.000	0.900289	0.450145	+	0.892956i	$0.351372\pi$
$60$	−120.000	−0.258199
$61$	−822.000	−1.72535	−0.862675	−	0.505759i	$-0.831212\pi$
$61$	−822.000	−1.72535	−0.862675	+	0.505759i	$0.831212\pi$
$62$	206.000	0.421968
$63$	0	0
$64$	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
$70$	0	0
$71$	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	$-0.243827\pi$
$73$	899.000	1.44137	0.720685	+	0.693263i	$0.243827\pi$
$74$	596.000	0.936265
$75$	−445.000	−0.685122
$76$	−280.000	−0.422608
$77$	0	0
$78$	−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	$-0.492422\pi$
$83$	36.0000	0.0476086	0.0238043	+	0.999717i	$0.492422\pi$
$84$	0	0
$85$	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	$-0.411676\pi$
$89$	460.000	0.547864	0.273932	+	0.961749i	$0.411676\pi$
$90$	24.0000	0.0281091
$91$	0	0
$92$	−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	$-0.331665\pi$
$97$	964.000	1.00907	0.504533	+	0.863393i	$0.331665\pi$
$98$	0	0
$99$	−68.0000	−0.0690329
$100$	356.000	0.356000
$101$	310.000	0.305407	0.152704	−	0.988272i	$-0.451202\pi$
$101$	310.000	0.305407	0.152704	+	0.988272i	$0.451202\pi$
$102$	−800.000	−0.776586
$103$	−1044.00	−0.998722	−0.499361	−	0.866394i	$-0.666432\pi$
$103$	−1044.00	−0.998722	−0.499361	+	0.866394i	$0.666432\pi$
$104$	1368.00	1.28984
$105$	0	0
$106$	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
$112$	0	0
$113$	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
$119$	0	0
$120$	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
$126$	0	0
$127$	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	$-0.340442\pi$
$131$	1441.00	0.961074	0.480537	+	0.876974i	$0.340442\pi$
$132$	−680.000	−0.448382
$133$	0	0
$134$	−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	$-0.502428\pi$
$139$	−25.0000	−0.0152552	−0.00762760	+	0.999971i	$0.502428\pi$
$140$	0	0
$141$	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
$147$	0	0
$148$	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
$154$	0	0
$155$	−618.000	−0.320251
$156$	−1140.00	−0.585084
$157$	632.000	0.321268	0.160634	−	0.987014i	$-0.448646\pi$
$157$	632.000	0.321268	0.160634	+	0.987014i	$0.448646\pi$
$158$	2644.00	1.33130
$159$	−2070.00	−1.03246
$160$	−960.000	−0.474342
$161$	0	0
$162$	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	$-0.327694\pi$
$167$	2224.00	1.03053	0.515264	+	0.857031i	$0.327694\pi$
$168$	0	0
$169$	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	$-0.751191\pi$
$173$	−3230.00	−1.41949	−0.709747	+	0.704457i	$0.751191\pi$
$174$	−2450.00	−1.06744
$175$	0	0
$176$	−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	$-0.409234\pi$
$181$	1370.00	0.562604	0.281302	+	0.959619i	$0.409234\pi$
$182$	0	0
$183$	−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
$189$	0	0
$190$	−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
$196$	0	0
$197$	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	$-0.437346\pi$
$199$	1098.00	0.391131	0.195566	+	0.980691i	$0.437346\pi$
$200$	−2136.00	−0.755190
$201$	4630.00	1.62475
$202$	−620.000	−0.215956
$203$	0	0
$204$	−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
$210$	0	0
$211$	−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
$217$	0	0
$218$	−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	$-0.579984\pi$
$223$	−1656.00	−0.497282	−0.248641	+	0.968596i	$0.579984\pi$
$224$	0	0
$225$	178.000	0.0527407
$226$	−1904.00	−0.560408
$227$	−2940.00	−0.859624	−0.429812	−	0.902918i	$-0.641420\pi$
$227$	−2940.00	−0.859624	−0.429812	+	0.902918i	$0.641420\pi$
$228$	−1400.00	−0.406655
$229$	−3612.00	−1.04230	−0.521152	−	0.853464i	$-0.674498\pi$
$229$	−3612.00	−1.04230	−0.521152	+	0.853464i	$0.674498\pi$
$230$	−276.000	−0.0791257
$231$	0	0
$232$	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
$238$	0	0
$239$	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	$-0.145928\pi$
$241$	6710.00	1.79348	0.896741	+	0.442556i	$0.145928\pi$
$242$	350.000	0.0929705
$243$	560.000	0.147835
$244$	3288.00	0.862675
$245$	0	0
$246$	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	$-0.161771\pi$
$251$	6948.00	1.74723	0.873613	+	0.486621i	$0.161771\pi$
$252$	0	0
$253$	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	$-0.295892\pi$
$257$	4929.00	1.19635	0.598176	+	0.801365i	$0.295892\pi$
$258$	−880.000	−0.212350
$259$	0	0
$260$	−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
$266$	0	0
$267$	2300.00	0.527182
$268$	−3704.00	−0.844246
$269$	2063.00	0.467596	0.233798	−	0.972285i	$-0.424885\pi$
$269$	2063.00	0.467596	0.233798	+	0.972285i	$0.424885\pi$
$270$	1740.00	0.392196
$271$	1064.00	0.238500	0.119250	−	0.992864i	$-0.461951\pi$
$271$	1064.00	0.238500	0.119250	+	0.992864i	$0.461951\pi$
$272$	−1280.00	−0.285336
$273$	0	0
$274$	−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
$280$	0	0
$281$	−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	$-0.496189\pi$
$283$	114.000	0.0239456	0.0119728	+	0.999928i	$0.496189\pi$
$284$	−1340.00	−0.279980
$285$	2100.00	0.436468
$286$	−3876.00	−0.801373
$287$	0	0
$288$	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	$-0.252003\pi$
$293$	7048.00	1.40529	0.702643	+	0.711543i	$0.252003\pi$
$294$	0	0
$295$	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
$301$	0	0
$302$	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	$-0.617194\pi$
$307$	−3872.00	−0.719826	−0.359913	+	0.932986i	$0.617194\pi$
$308$	0	0
$309$	−5220.00	−0.961021
$310$	1236.00	0.226452
$311$	4977.00	0.907459	0.453730	−	0.891139i	$-0.350093\pi$
$311$	4977.00	0.907459	0.453730	+	0.891139i	$0.350093\pi$
$312$	6840.00	1.24115
$313$	2536.00	0.457965	0.228983	−	0.973430i	$-0.426460\pi$
$313$	2536.00	0.457965	0.228983	+	0.973430i	$0.426460\pi$
$314$	−1264.00	−0.227171
$315$	0	0
$316$	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
$322$	0	0
$323$	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
$329$	0	0
$330$	−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
$336$	0	0
$337$	−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
$343$	0	0
$344$	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	$-0.305087\pi$
$349$	7495.00	1.14956	0.574782	+	0.818306i	$0.305087\pi$
$350$	0	0
$351$	−8265.00	−1.25685
$352$	−5440.00	−0.823730
$353$	−10617.0	−1.60081	−0.800405	−	0.599460i	$-0.795382\pi$
$353$	−10617.0	−1.60081	−0.800405	+	0.599460i	$0.795382\pi$
$354$	−4080.00	−0.612569
$355$	2010.00	0.300506
$356$	−1840.00	−0.273932
$357$	0	0
$358$	−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
$364$	0	0
$365$	5394.00	0.773520
$366$	8220.00	1.17395
$367$	−7204.00	−1.02465	−0.512324	−	0.858792i	$-0.671215\pi$
$367$	−7204.00	−1.02465	−0.512324	+	0.858792i	$0.671215\pi$
$368$	−368.000	−0.0521286
$369$	190.000	0.0268049
$370$	3576.00	0.502452
$371$	0	0
$372$	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
$378$	0	0
$379$	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	$-0.439936\pi$
$383$	2812.00	0.375161	0.187580	+	0.982249i	$0.439936\pi$
$384$	1920.00	0.255155
$385$	0	0
$386$	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
$392$	0	0
$393$	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	$-0.648573\pi$
$397$	−7119.00	−0.899981	−0.449990	+	0.893033i	$0.648573\pi$
$398$	−2196.00	−0.276572
$399$	0	0
$400$	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
$406$	0	0
$407$	−10132.0	−1.23397
$408$	9600.00	1.16488
$409$	−229.000	−0.0276854	−0.0138427	−	0.999904i	$-0.504406\pi$
$409$	−229.000	−0.0276854	−0.0138427	+	0.999904i	$0.504406\pi$
$410$	1140.00	0.137319
$411$	7780.00	0.933720
$412$	4176.00	0.499361
$413$	0	0
$414$	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	$-0.871568\pi$
$419$	−15776.0	−1.83940	−0.919699	+	0.392623i	$0.871568\pi$
$420$	0	0
$421$	−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
$427$	0	0
$428$	−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	$-0.404717\pi$
$433$	5314.00	0.589780	0.294890	+	0.955531i	$0.404717\pi$
$434$	0	0
$435$	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	$-0.544877\pi$
$439$	−2585.00	−0.281037	−0.140519	+	0.990078i	$0.544877\pi$
$440$	4896.00	0.530472
$441$	0	0
$442$	−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
$448$	0	0
$449$	−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
$455$	0	0
$456$	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	$-0.426295\pi$
$461$	4543.00	0.458977	0.229489	+	0.973311i	$0.426295\pi$
$462$	0	0
$463$	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	$-0.626742\pi$
$467$	−7826.00	−0.775469	−0.387735	+	0.921771i	$0.626742\pi$
$468$	456.000	0.0450398
$469$	0	0
$470$	−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
$476$	0	0
$477$	828.000	0.0794791
$478$	−5470.00	−0.523414
$479$	−11404.0	−1.08781	−0.543906	−	0.839146i	$-0.683055\pi$
$479$	−11404.0	−1.08781	−0.543906	+	0.839146i	$0.683055\pi$
$480$	−4800.00	−0.456435
$481$	−16986.0	−1.61018
$482$	−13420.0	−1.26818
$483$	0	0
$484$	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
$490$	0	0
$491$	−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
$497$	0	0
$498$	−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	$-0.621766\pi$
$503$	−8422.00	−0.746557	−0.373279	+	0.927719i	$0.621766\pi$
$504$	0	0
$505$	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	$-0.488037\pi$
$509$	863.000	0.0751509	0.0375754	+	0.999294i	$0.488037\pi$
$510$	−4800.00	−0.416760
$511$	0	0
$512$	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
$518$	0	0
$519$	−16150.0	−1.36591
$520$	8208.00	0.692201
$521$	−19260.0	−1.61957	−0.809785	−	0.586727i	$-0.800416\pi$
$521$	−19260.0	−1.61957	−0.809785	+	0.586727i	$0.800416\pi$
$522$	980.000	0.0821713
$523$	11740.0	0.981557	0.490779	−	0.871284i	$-0.336712\pi$
$523$	11740.0	0.981557	0.490779	+	0.871284i	$0.336712\pi$
$524$	−5764.00	−0.480537
$525$	0	0
$526$	−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
$532$	0	0
$533$	−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
$539$	0	0
$540$	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
$546$	0	0
$547$	−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
$553$	0	0
$554$	−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
$560$	0	0
$561$	13600.0	1.02352
$562$	1920.00	0.144111
$563$	−4332.00	−0.324284	−0.162142	−	0.986767i	$-0.551840\pi$
$563$	−4332.00	−0.324284	−0.162142	+	0.986767i	$0.551840\pi$
$564$	−7140.00	−0.533064
$565$	5712.00	0.425320
$566$	−228.000	−0.0169321
$567$	0	0
$568$	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
$574$	0	0
$575$	−2047.00	−0.148462
$576$	−896.000	−0.0648148
$577$	−2953.00	−0.213059	−0.106529	−	0.994310i	$-0.533974\pi$
$577$	−2953.00	−0.213059	−0.106529	+	0.994310i	$0.533974\pi$
$578$	−2974.00	−0.214017
$579$	−675.000	−0.0484491
$580$	−5880.00	−0.420955
$581$	0	0
$582$	−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	$-0.466939\pi$
$587$	2949.00	0.207356	0.103678	+	0.994611i	$0.466939\pi$
$588$	0	0
$589$	−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	$-0.692090\pi$
$593$	−16390.0	−1.13500	−0.567501	+	0.823372i	$0.692090\pi$
$594$	9860.00	0.681079
$595$	0	0
$596$	−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	$-0.344433\pi$
$601$	13835.0	0.939004	0.469502	+	0.882931i	$0.344433\pi$
$602$	0	0
$603$	−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	$-0.564334\pi$
$607$	−6004.00	−0.401474	−0.200737	+	0.979645i	$0.564334\pi$
$608$	−11200.0	−0.747072
$609$	0	0
$610$	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
$616$	0	0
$617$	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	$-0.671743\pi$
$619$	−15824.0	−1.02750	−0.513748	+	0.857941i	$0.671743\pi$
$620$	2472.00	0.160126
$621$	−3335.00	−0.215506
$622$	−9954.00	−0.641670
$623$	0	0
$624$	−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
$630$	0	0
$631$	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
$637$	0	0
$638$	−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	$-0.351122\pi$
$643$	14702.0	0.901696	0.450848	+	0.892601i	$0.351122\pi$
$644$	0	0
$645$	2640.00	0.161163
$646$	−11200.0	−0.682133
$647$	−11939.0	−0.725457	−0.362728	−	0.931895i	$-0.618155\pi$
$647$	−11939.0	−0.725457	−0.362728	+	0.931895i	$0.618155\pi$
$648$	−16104.0	−0.976273
$649$	13872.0	0.839019
$650$	10146.0	0.612244
$651$	0	0
$652$	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
$658$	0	0
$659$	−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	$-0.661369\pi$
$661$	−16502.0	−0.971034	−0.485517	+	0.874227i	$0.661369\pi$
$662$	−10938.0	−0.642171
$663$	22800.0	1.33556
$664$	864.000	0.0504965
$665$	0	0
$666$	−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
$672$	0	0
$673$	−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	$-0.419509\pi$
$677$	8814.00	0.500369	0.250184	+	0.968198i	$0.419509\pi$
$678$	−9520.00	−0.539253
$679$	0	0
$680$	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
$686$	0	0
$687$	−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	$-0.391543\pi$
$691$	12140.0	0.668346	0.334173	+	0.942512i	$0.391543\pi$
$692$	12920.0	0.709747
$693$	0	0
$694$	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
$700$	0	0
$701$	−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
$707$	0	0
$708$	−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
$714$	0	0
$715$	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	$-0.522804\pi$
$719$	−2760.00	−0.143158	−0.0715790	+	0.997435i	$0.522804\pi$
$720$	192.000	0.00993808
$721$	0	0
$722$	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	$-0.563309\pi$
$727$	−7746.00	−0.395163	−0.197581	+	0.980287i	$0.563309\pi$
$728$	0	0
$729$	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	$-0.402434\pi$
$733$	11976.0	0.603470	0.301735	+	0.953392i	$0.402434\pi$
$734$	14408.0	0.724535
$735$	0	0
$736$	−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
$742$	0	0
$743$	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
$749$	0	0
$750$	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
$756$	0	0
$757$	−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	$-0.244263\pi$
$761$	30219.0	1.43947	0.719736	+	0.694248i	$0.244263\pi$
$762$	−2610.00	−0.124082
$763$	0	0
$764$	−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	$-0.508375\pi$
$769$	−1122.00	−0.0526142	−0.0263071	+	0.999654i	$0.508375\pi$
$770$	0	0
$771$	24645.0	1.15119
$772$	540.000	0.0251749
$773$	−19300.0	−0.898024	−0.449012	−	0.893526i	$-0.648224\pi$
$773$	−19300.0	−0.898024	−0.449012	+	0.893526i	$0.648224\pi$
$774$	352.000	0.0163467
$775$	9167.00	0.424888
$776$	23136.0	1.07028
$777$	0	0
$778$	−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
$784$	0	0
$785$	3792.00	0.172411
$786$	−14410.0	−0.653928
$787$	19396.0	0.878517	0.439258	−	0.898361i	$-0.355241\pi$
$787$	19396.0	0.878517	0.439258	+	0.898361i	$0.355241\pi$
$788$	−4884.00	−0.220794
$789$	30690.0	1.38478
$790$	15864.0	0.714450
$791$	0	0
$792$	−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	$-0.165782\pi$
$797$	39034.0	1.73482	0.867412	+	0.497590i	$0.165782\pi$
$798$	0	0
$799$	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
$805$	0	0
$806$	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	$-0.156895\pi$
$811$	40693.0	1.76193	0.880965	+	0.473182i	$0.156895\pi$
$812$	0	0
$813$	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
$819$	0	0
$820$	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
$826$	0	0
$827$	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	$-0.188726\pi$
$829$	39590.0	1.65865	0.829323	+	0.558770i	$0.188726\pi$
$830$	−432.000	−0.0180662
$831$	28645.0	1.19577
$832$	25536.0	1.06406
$833$	0	0
$834$	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	$-0.404833\pi$
$839$	14316.0	0.589086	0.294543	+	0.955638i	$0.404833\pi$
$840$	0	0
$841$	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
$847$	0	0
$848$	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	$-0.692787\pi$
$853$	−28366.0	−1.13861	−0.569304	+	0.822127i	$0.692787\pi$
$854$	0	0
$855$	−840.000	−0.0335993
$856$	9936.00	0.396735
$857$	−19283.0	−0.768605	−0.384303	−	0.923207i	$-0.625558\pi$
$857$	−19283.0	−0.768605	−0.384303	+	0.923207i	$0.625558\pi$
$858$	−19380.0	−0.771122
$859$	26101.0	1.03673	0.518367	−	0.855158i	$-0.326540\pi$
$859$	26101.0	1.03673	0.518367	+	0.855158i	$0.326540\pi$
$860$	−2112.00	−0.0837426
$861$	0	0
$862$	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
$868$	0	0
$869$	−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
$875$	0	0
$876$	−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	$-0.841650\pi$
$881$	−45960.0	−1.75758	−0.878792	+	0.477205i	$0.841650\pi$
$882$	0	0
$883$	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	$-0.551134\pi$
$887$	−8451.00	−0.319906	−0.159953	+	0.987125i	$0.551134\pi$
$888$	−35760.0	−1.35138
$889$	0	0
$890$	−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
$896$	0	0
$897$	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
$903$	0	0
$904$	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
$910$	0	0
$911$	−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
$917$	0	0
$918$	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
$924$	0	0
$925$	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	$-0.252684\pi$
$929$	39705.0	1.40224	0.701119	+	0.713044i	$0.252684\pi$
$930$	6180.00	0.217903
$931$	0	0
$932$	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	$-0.598225\pi$
$937$	−17422.0	−0.607419	−0.303710	+	0.952765i	$0.598225\pi$
$938$	0	0
$939$	12680.0	0.440677
$940$	−8568.00	−0.297295
$941$	25292.0	0.876191	0.438095	−	0.898928i	$-0.355653\pi$
$941$	25292.0	0.876191	0.438095	+	0.898928i	$0.355653\pi$
$942$	−6320.00	−0.218595
$943$	−2185.00	−0.0754543
$944$	−6528.00	−0.225072
$945$	0	0
$946$	−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
$952$	0	0
$953$	−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
$959$	0	0
$960$	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
$966$	0	0
$967$	−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	$-0.561986\pi$
$971$	−11710.0	−0.387015	−0.193508	+	0.981099i	$0.561986\pi$
$972$	−2240.00	−0.0739177
$973$	0	0
$974$	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
$980$	0	0
$981$	−1408.00	−0.0458246
$982$	36382.0	1.18228
$983$	22078.0	0.716357	0.358178	−	0.933653i	$-0.383398\pi$
$983$	22078.0	0.716357	0.358178	+	0.933653i	$0.383398\pi$
$984$	−11400.0	−0.369328
$985$	7326.00	0.236980
$986$	−39200.0	−1.26611
$987$	0	0
$988$	−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
$994$	0	0
$995$	6588.00	0.209903
$996$	−720.000	−0.0229057
$997$	−28966.0	−0.920123	−0.460061	−	0.887887i	$-0.652173\pi$
$997$	−28966.0	−0.920123	−0.460061	+	0.887887i	$0.652173\pi$
$998$	−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	1127.4.a.a.1.1		1
7.6	odd	2		23.4.a.a.1.1	✓	1
21.20	even	2		207.4.a.a.1.1		1
28.27	even	2		368.4.a.d.1.1		1
35.13	even	4		575.4.b.b.24.2		2
35.27	even	4		575.4.b.b.24.1		2
35.34	odd	2		575.4.a.g.1.1		1
56.13	odd	2		1472.4.a.h.1.1		1
56.27	even	2		1472.4.a.c.1.1		1
161.160	even	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	7.6	odd	2
207.4.a.a.1.1		1	21.20	even	2
368.4.a.d.1.1		1	28.27	even	2
529.4.a.a.1.1		1	161.160	even	2
575.4.a.g.1.1		1	35.34	odd	2
575.4.b.b.24.1		2	35.27	even	4
575.4.b.b.24.2		2	35.13	even	4
1127.4.a.a.1.1		1	1.1	even	1	trivial
1472.4.a.c.1.1		1	56.27	even	2
1472.4.a.h.1.1		1	56.13	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1127 = 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1127.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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