LMFDB - Embedded newform 10.4.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,4,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, 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("10.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	10.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:	$0.590019100057$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -8.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -16.0000 q^{6} -4.00000 q^{7} +8.00000 q^{8} +37.0000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -8.00000 q^{3} +4.00000 q^{4} +5.00000 q^{5} -16.0000 q^{6} -4.00000 q^{7} +8.00000 q^{8} +37.0000 q^{9} +10.0000 q^{10} +12.0000 q^{11} -32.0000 q^{12} -58.0000 q^{13} -8.00000 q^{14} -40.0000 q^{15} +16.0000 q^{16} +66.0000 q^{17} +74.0000 q^{18} -100.000 q^{19} +20.0000 q^{20} +32.0000 q^{21} +24.0000 q^{22} +132.000 q^{23} -64.0000 q^{24} +25.0000 q^{25} -116.000 q^{26} -80.0000 q^{27} -16.0000 q^{28} -90.0000 q^{29} -80.0000 q^{30} +152.000 q^{31} +32.0000 q^{32} -96.0000 q^{33} +132.000 q^{34} -20.0000 q^{35} +148.000 q^{36} -34.0000 q^{37} -200.000 q^{38} +464.000 q^{39} +40.0000 q^{40} -438.000 q^{41} +64.0000 q^{42} +32.0000 q^{43} +48.0000 q^{44} +185.000 q^{45} +264.000 q^{46} -204.000 q^{47} -128.000 q^{48} -327.000 q^{49} +50.0000 q^{50} -528.000 q^{51} -232.000 q^{52} +222.000 q^{53} -160.000 q^{54} +60.0000 q^{55} -32.0000 q^{56} +800.000 q^{57} -180.000 q^{58} +420.000 q^{59} -160.000 q^{60} +902.000 q^{61} +304.000 q^{62} -148.000 q^{63} +64.0000 q^{64} -290.000 q^{65} -192.000 q^{66} -1024.00 q^{67} +264.000 q^{68} -1056.00 q^{69} -40.0000 q^{70} +432.000 q^{71} +296.000 q^{72} +362.000 q^{73} -68.0000 q^{74} -200.000 q^{75} -400.000 q^{76} -48.0000 q^{77} +928.000 q^{78} -160.000 q^{79} +80.0000 q^{80} -359.000 q^{81} -876.000 q^{82} +72.0000 q^{83} +128.000 q^{84} +330.000 q^{85} +64.0000 q^{86} +720.000 q^{87} +96.0000 q^{88} +810.000 q^{89} +370.000 q^{90} +232.000 q^{91} +528.000 q^{92} -1216.00 q^{93} -408.000 q^{94} -500.000 q^{95} -256.000 q^{96} +1106.00 q^{97} -654.000 q^{98} +444.000 q^{99} +O(q^{100})\)

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
$3$	−8.00000	−1.53960	−0.769800	−	0.638285i	$-0.779644\pi$
$3$	−8.00000	−1.53960	−0.769800	+	0.638285i	$0.779644\pi$
$4$	4.00000	0.500000
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	−16.0000	−1.08866
$7$	−4.00000	−0.215980	−0.107990	−	0.994152i	$-0.534441\pi$
$7$	−4.00000	−0.215980	−0.107990	+	0.994152i	$0.534441\pi$
$8$	8.00000	0.353553
$9$	37.0000	1.37037
$10$	10.0000	0.316228
$11$	12.0000	0.328921	0.164461	−	0.986384i	$-0.447412\pi$
$11$	12.0000	0.328921	0.164461	+	0.986384i	$0.447412\pi$
$12$	−32.0000	−0.769800
$13$	−58.0000	−1.23741	−0.618704	−	0.785624i	$-0.712342\pi$
$13$	−58.0000	−1.23741	−0.618704	+	0.785624i	$0.712342\pi$
$14$	−8.00000	−0.152721
$15$	−40.0000	−0.688530
$16$	16.0000	0.250000
$17$	66.0000	0.941609	0.470804	−	0.882238i	$-0.343964\pi$
$17$	66.0000	0.941609	0.470804	+	0.882238i	$0.343964\pi$
$18$	74.0000	0.968998
$19$	−100.000	−1.20745	−0.603726	−	0.797192i	$-0.706318\pi$
$19$	−100.000	−1.20745	−0.603726	+	0.797192i	$0.706318\pi$
$20$	20.0000	0.223607
$21$	32.0000	0.332522
$22$	24.0000	0.232583
$23$	132.000	1.19669	0.598346	−	0.801238i	$-0.295825\pi$
$23$	132.000	1.19669	0.598346	+	0.801238i	$0.295825\pi$
$24$	−64.0000	−0.544331
$25$	25.0000	0.200000
$26$	−116.000	−0.874980
$27$	−80.0000	−0.570222
$28$	−16.0000	−0.107990
$29$	−90.0000	−0.576296	−0.288148	−	0.957586i	$-0.593039\pi$
$29$	−90.0000	−0.576296	−0.288148	+	0.957586i	$0.593039\pi$
$30$	−80.0000	−0.486864
$31$	152.000	0.880645	0.440323	−	0.897840i	$-0.354864\pi$
$31$	152.000	0.880645	0.440323	+	0.897840i	$0.354864\pi$
$32$	32.0000	0.176777
$33$	−96.0000	−0.506408
$34$	132.000	0.665818
$35$	−20.0000	−0.0965891
$36$	148.000	0.685185
$37$	−34.0000	−0.151069	−0.0755347	−	0.997143i	$-0.524066\pi$
$37$	−34.0000	−0.151069	−0.0755347	+	0.997143i	$0.524066\pi$
$38$	−200.000	−0.853797
$39$	464.000	1.90511
$40$	40.0000	0.158114
$41$	−438.000	−1.66839	−0.834196	−	0.551467i	$-0.814068\pi$
$41$	−438.000	−1.66839	−0.834196	+	0.551467i	$0.814068\pi$
$42$	64.0000	0.235129
$43$	32.0000	0.113487	0.0567437	−	0.998389i	$-0.481928\pi$
$43$	32.0000	0.113487	0.0567437	+	0.998389i	$0.481928\pi$
$44$	48.0000	0.164461
$45$	185.000	0.612848
$46$	264.000	0.846189
$47$	−204.000	−0.633116	−0.316558	−	0.948573i	$-0.602527\pi$
$47$	−204.000	−0.633116	−0.316558	+	0.948573i	$0.602527\pi$
$48$	−128.000	−0.384900
$49$	−327.000	−0.953353
$50$	50.0000	0.141421
$51$	−528.000	−1.44970
$52$	−232.000	−0.618704
$53$	222.000	0.575359	0.287680	−	0.957727i	$-0.407116\pi$
$53$	222.000	0.575359	0.287680	+	0.957727i	$0.407116\pi$
$54$	−160.000	−0.403208
$55$	60.0000	0.147098
$56$	−32.0000	−0.0763604
$57$	800.000	1.85899
$58$	−180.000	−0.407503
$59$	420.000	0.926769	0.463384	−	0.886157i	$-0.346635\pi$
$59$	420.000	0.926769	0.463384	+	0.886157i	$0.346635\pi$
$60$	−160.000	−0.344265
$61$	902.000	1.89327	0.946633	−	0.322312i	$-0.104460\pi$
$61$	902.000	1.89327	0.946633	+	0.322312i	$0.104460\pi$
$62$	304.000	0.622710
$63$	−148.000	−0.295972
$64$	64.0000	0.125000
$65$	−290.000	−0.553386
$66$	−192.000	−0.358084
$67$	−1024.00	−1.86719	−0.933593	−	0.358334i	$-0.883345\pi$
$67$	−1024.00	−1.86719	−0.933593	+	0.358334i	$0.883345\pi$
$68$	264.000	0.470804
$69$	−1056.00	−1.84243
$70$	−40.0000	−0.0682988
$71$	432.000	0.722098	0.361049	−	0.932547i	$-0.382419\pi$
$71$	432.000	0.722098	0.361049	+	0.932547i	$0.382419\pi$
$72$	296.000	0.484499
$73$	362.000	0.580396	0.290198	−	0.956967i	$-0.406279\pi$
$73$	362.000	0.580396	0.290198	+	0.956967i	$0.406279\pi$
$74$	−68.0000	−0.106822
$75$	−200.000	−0.307920
$76$	−400.000	−0.603726
$77$	−48.0000	−0.0710404
$78$	928.000	1.34712
$79$	−160.000	−0.227866	−0.113933	−	0.993488i	$-0.536345\pi$
$79$	−160.000	−0.227866	−0.113933	+	0.993488i	$0.536345\pi$
$80$	80.0000	0.111803
$81$	−359.000	−0.492455
$82$	−876.000	−1.17973
$83$	72.0000	0.0952172	0.0476086	−	0.998866i	$-0.484840\pi$
$83$	72.0000	0.0952172	0.0476086	+	0.998866i	$0.484840\pi$
$84$	128.000	0.166261
$85$	330.000	0.421100
$86$	64.0000	0.0802476
$87$	720.000	0.887266
$88$	96.0000	0.116291
$89$	810.000	0.964717	0.482359	−	0.875974i	$-0.339780\pi$
$89$	810.000	0.964717	0.482359	+	0.875974i	$0.339780\pi$
$90$	370.000	0.433349
$91$	232.000	0.267255
$92$	528.000	0.598346
$93$	−1216.00	−1.35584
$94$	−408.000	−0.447681
$95$	−500.000	−0.539989
$96$	−256.000	−0.272166
$97$	1106.00	1.15770	0.578852	−	0.815433i	$-0.303501\pi$
$97$	1106.00	1.15770	0.578852	+	0.815433i	$0.303501\pi$
$98$	−654.000	−0.674122
$99$	444.000	0.450744
$100$	100.000	0.100000
$101$	−258.000	−0.254178	−0.127089	−	0.991891i	$-0.540563\pi$
$101$	−258.000	−0.254178	−0.127089	+	0.991891i	$0.540563\pi$
$102$	−1056.00	−1.02509
$103$	−988.000	−0.945151	−0.472575	−	0.881290i	$-0.656676\pi$
$103$	−988.000	−0.945151	−0.472575	+	0.881290i	$0.656676\pi$
$104$	−464.000	−0.437490
$105$	160.000	0.148709
$106$	444.000	0.406840
$107$	−24.0000	−0.0216838	−0.0108419	−	0.999941i	$-0.503451\pi$
$107$	−24.0000	−0.0216838	−0.0108419	+	0.999941i	$0.503451\pi$
$108$	−320.000	−0.285111
$109$	950.000	0.834803	0.417401	−	0.908722i	$-0.362941\pi$
$109$	950.000	0.834803	0.417401	+	0.908722i	$0.362941\pi$
$110$	120.000	0.104014
$111$	272.000	0.232586
$112$	−64.0000	−0.0539949
$113$	−1038.00	−0.864131	−0.432066	−	0.901842i	$-0.642215\pi$
$113$	−1038.00	−0.864131	−0.432066	+	0.901842i	$0.642215\pi$
$114$	1600.00	1.31451
$115$	660.000	0.535177
$116$	−360.000	−0.288148
$117$	−2146.00	−1.69571
$118$	840.000	0.655324
$119$	−264.000	−0.203368
$120$	−320.000	−0.243432
$121$	−1187.00	−0.891811
$122$	1804.00	1.33874
$123$	3504.00	2.56866
$124$	608.000	0.440323
$125$	125.000	0.0894427
$126$	−296.000	−0.209284
$127$	−124.000	−0.0866395	−0.0433198	−	0.999061i	$-0.513793\pi$
$127$	−124.000	−0.0866395	−0.0433198	+	0.999061i	$0.513793\pi$
$128$	128.000	0.0883883
$129$	−256.000	−0.174725
$130$	−580.000	−0.391303
$131$	132.000	0.0880374	0.0440187	−	0.999031i	$-0.485984\pi$
$131$	132.000	0.0880374	0.0440187	+	0.999031i	$0.485984\pi$
$132$	−384.000	−0.253204
$133$	400.000	0.260785
$134$	−2048.00	−1.32030
$135$	−400.000	−0.255011
$136$	528.000	0.332909
$137$	−1254.00	−0.782018	−0.391009	−	0.920387i	$-0.627874\pi$
$137$	−1254.00	−0.782018	−0.391009	+	0.920387i	$0.627874\pi$
$138$	−2112.00	−1.30279
$139$	−2860.00	−1.74519	−0.872597	−	0.488440i	$-0.837566\pi$
$139$	−2860.00	−1.74519	−0.872597	+	0.488440i	$0.837566\pi$
$140$	−80.0000	−0.0482945
$141$	1632.00	0.974746
$142$	864.000	0.510600
$143$	−696.000	−0.407010
$144$	592.000	0.342593
$145$	−450.000	−0.257727
$146$	724.000	0.410402
$147$	2616.00	1.46778
$148$	−136.000	−0.0755347
$149$	750.000	0.412365	0.206183	−	0.978514i	$-0.433896\pi$
$149$	750.000	0.412365	0.206183	+	0.978514i	$0.433896\pi$
$150$	−400.000	−0.217732
$151$	−448.000	−0.241442	−0.120721	−	0.992686i	$-0.538521\pi$
$151$	−448.000	−0.241442	−0.120721	+	0.992686i	$0.538521\pi$
$152$	−800.000	−0.426898
$153$	2442.00	1.29035
$154$	−96.0000	−0.0502331
$155$	760.000	0.393837
$156$	1856.00	0.952557
$157$	2246.00	1.14172	0.570861	−	0.821047i	$-0.306610\pi$
$157$	2246.00	1.14172	0.570861	+	0.821047i	$0.306610\pi$
$158$	−320.000	−0.161126
$159$	−1776.00	−0.885824
$160$	160.000	0.0790569
$161$	−528.000	−0.258461
$162$	−718.000	−0.348219
$163$	−568.000	−0.272940	−0.136470	−	0.990644i	$-0.543576\pi$
$163$	−568.000	−0.272940	−0.136470	+	0.990644i	$0.543576\pi$
$164$	−1752.00	−0.834196
$165$	−480.000	−0.226472
$166$	144.000	0.0673287
$167$	−1524.00	−0.706172	−0.353086	−	0.935591i	$-0.614868\pi$
$167$	−1524.00	−0.706172	−0.353086	+	0.935591i	$0.614868\pi$
$168$	256.000	0.117564
$169$	1167.00	0.531179
$170$	660.000	0.297763
$171$	−3700.00	−1.65466
$172$	128.000	0.0567437
$173$	3702.00	1.62692	0.813462	−	0.581618i	$-0.197580\pi$
$173$	3702.00	1.62692	0.813462	+	0.581618i	$0.197580\pi$
$174$	1440.00	0.627391
$175$	−100.000	−0.0431959
$176$	192.000	0.0822304
$177$	−3360.00	−1.42685
$178$	1620.00	0.682158
$179$	3180.00	1.32785	0.663923	−	0.747801i	$-0.268890\pi$
$179$	3180.00	1.32785	0.663923	+	0.747801i	$0.268890\pi$
$180$	740.000	0.306424
$181$	−2098.00	−0.861564	−0.430782	−	0.902456i	$-0.641762\pi$
$181$	−2098.00	−0.861564	−0.430782	+	0.902456i	$0.641762\pi$
$182$	464.000	0.188978
$183$	−7216.00	−2.91487
$184$	1056.00	0.423094
$185$	−170.000	−0.0675603
$186$	−2432.00	−0.958725
$187$	792.000	0.309715
$188$	−816.000	−0.316558
$189$	320.000	0.123156
$190$	−1000.00	−0.381830
$191$	4392.00	1.66384	0.831921	−	0.554894i	$-0.187241\pi$
$191$	4392.00	1.66384	0.831921	+	0.554894i	$0.187241\pi$
$192$	−512.000	−0.192450
$193$	−2158.00	−0.804851	−0.402425	−	0.915453i	$-0.631833\pi$
$193$	−2158.00	−0.804851	−0.402425	+	0.915453i	$0.631833\pi$
$194$	2212.00	0.818620
$195$	2320.00	0.851993
$196$	−1308.00	−0.476676
$197$	−1074.00	−0.388423	−0.194212	−	0.980960i	$-0.562215\pi$
$197$	−1074.00	−0.388423	−0.194212	+	0.980960i	$0.562215\pi$
$198$	888.000	0.318724
$199$	2840.00	1.01167	0.505835	−	0.862630i	$-0.331185\pi$
$199$	2840.00	1.01167	0.505835	+	0.862630i	$0.331185\pi$
$200$	200.000	0.0707107
$201$	8192.00	2.87472
$202$	−516.000	−0.179731
$203$	360.000	0.124468
$204$	−2112.00	−0.724851
$205$	−2190.00	−0.746128
$206$	−1976.00	−0.668323
$207$	4884.00	1.63991
$208$	−928.000	−0.309352
$209$	−1200.00	−0.397157
$210$	320.000	0.105153
$211$	−2668.00	−0.870487	−0.435243	−	0.900313i	$-0.643338\pi$
$211$	−2668.00	−0.870487	−0.435243	+	0.900313i	$0.643338\pi$
$212$	888.000	0.287680
$213$	−3456.00	−1.11174
$214$	−48.0000	−0.0153328
$215$	160.000	0.0507531
$216$	−640.000	−0.201604
$217$	−608.000	−0.190202
$218$	1900.00	0.590295
$219$	−2896.00	−0.893578
$220$	240.000	0.0735491
$221$	−3828.00	−1.16515
$222$	544.000	0.164463
$223$	1772.00	0.532116	0.266058	−	0.963957i	$-0.414279\pi$
$223$	1772.00	0.532116	0.266058	+	0.963957i	$0.414279\pi$
$224$	−128.000	−0.0381802
$225$	925.000	0.274074
$226$	−2076.00	−0.611033
$227$	−2784.00	−0.814011	−0.407006	−	0.913426i	$-0.633427\pi$
$227$	−2784.00	−0.814011	−0.407006	+	0.913426i	$0.633427\pi$
$228$	3200.00	0.929496
$229$	350.000	0.100998	0.0504992	−	0.998724i	$-0.483919\pi$
$229$	350.000	0.100998	0.0504992	+	0.998724i	$0.483919\pi$
$230$	1320.00	0.378427
$231$	384.000	0.109374
$232$	−720.000	−0.203751
$233$	1962.00	0.551652	0.275826	−	0.961208i	$-0.411049\pi$
$233$	1962.00	0.551652	0.275826	+	0.961208i	$0.411049\pi$
$234$	−4292.00	−1.19905
$235$	−1020.00	−0.283138
$236$	1680.00	0.463384
$237$	1280.00	0.350823
$238$	−528.000	−0.143803
$239$	−4320.00	−1.16919	−0.584597	−	0.811324i	$-0.698748\pi$
$239$	−4320.00	−1.16919	−0.584597	+	0.811324i	$0.698748\pi$
$240$	−640.000	−0.172133
$241$	−478.000	−0.127762	−0.0638811	−	0.997958i	$-0.520348\pi$
$241$	−478.000	−0.127762	−0.0638811	+	0.997958i	$0.520348\pi$
$242$	−2374.00	−0.630605
$243$	5032.00	1.32841
$244$	3608.00	0.946633
$245$	−1635.00	−0.426352
$246$	7008.00	1.81632
$247$	5800.00	1.49411
$248$	1216.00	0.311355
$249$	−576.000	−0.146596
$250$	250.000	0.0632456
$251$	2652.00	0.666903	0.333452	−	0.942767i	$-0.391787\pi$
$251$	2652.00	0.666903	0.333452	+	0.942767i	$0.391787\pi$
$252$	−592.000	−0.147986
$253$	1584.00	0.393617
$254$	−248.000	−0.0612634
$255$	−2640.00	−0.648326
$256$	256.000	0.0625000
$257$	−2334.00	−0.566502	−0.283251	−	0.959046i	$-0.591413\pi$
$257$	−2334.00	−0.566502	−0.283251	+	0.959046i	$0.591413\pi$
$258$	−512.000	−0.123549
$259$	136.000	0.0326279
$260$	−1160.00	−0.276693
$261$	−3330.00	−0.789739
$262$	264.000	0.0622518
$263$	−3948.00	−0.925643	−0.462822	−	0.886451i	$-0.653163\pi$
$263$	−3948.00	−0.925643	−0.462822	+	0.886451i	$0.653163\pi$
$264$	−768.000	−0.179042
$265$	1110.00	0.257309
$266$	800.000	0.184403
$267$	−6480.00	−1.48528
$268$	−4096.00	−0.933593
$269$	1590.00	0.360387	0.180193	−	0.983631i	$-0.442328\pi$
$269$	1590.00	0.360387	0.180193	+	0.983631i	$0.442328\pi$
$270$	−800.000	−0.180320
$271$	4952.00	1.11001	0.555005	−	0.831847i	$-0.312716\pi$
$271$	4952.00	1.11001	0.555005	+	0.831847i	$0.312716\pi$
$272$	1056.00	0.235402
$273$	−1856.00	−0.411466
$274$	−2508.00	−0.552970
$275$	300.000	0.0657843
$276$	−4224.00	−0.921213
$277$	1646.00	0.357034	0.178517	−	0.983937i	$-0.442870\pi$
$277$	1646.00	0.357034	0.178517	+	0.983937i	$0.442870\pi$
$278$	−5720.00	−1.23404
$279$	5624.00	1.20681
$280$	−160.000	−0.0341494
$281$	−1158.00	−0.245838	−0.122919	−	0.992417i	$-0.539226\pi$
$281$	−1158.00	−0.245838	−0.122919	+	0.992417i	$0.539226\pi$
$282$	3264.00	0.689250
$283$	6992.00	1.46866	0.734331	−	0.678792i	$-0.237496\pi$
$283$	6992.00	1.46866	0.734331	+	0.678792i	$0.237496\pi$
$284$	1728.00	0.361049
$285$	4000.00	0.831367
$286$	−1392.00	−0.287800
$287$	1752.00	0.360339
$288$	1184.00	0.242250
$289$	−557.000	−0.113373
$290$	−900.000	−0.182241
$291$	−8848.00	−1.78240
$292$	1448.00	0.290198
$293$	−258.000	−0.0514421	−0.0257210	−	0.999669i	$-0.508188\pi$
$293$	−258.000	−0.0514421	−0.0257210	+	0.999669i	$0.508188\pi$
$294$	5232.00	1.03788
$295$	2100.00	0.414463
$296$	−272.000	−0.0534111
$297$	−960.000	−0.187558
$298$	1500.00	0.291586
$299$	−7656.00	−1.48080
$300$	−800.000	−0.153960
$301$	−128.000	−0.0245110
$302$	−896.000	−0.170725
$303$	2064.00	0.391332
$304$	−1600.00	−0.301863
$305$	4510.00	0.846695
$306$	4884.00	0.912417
$307$	−8944.00	−1.66274	−0.831370	−	0.555720i	$-0.812443\pi$
$307$	−8944.00	−1.66274	−0.831370	+	0.555720i	$0.812443\pi$
$308$	−192.000	−0.0355202
$309$	7904.00	1.45515
$310$	1520.00	0.278485
$311$	1392.00	0.253804	0.126902	−	0.991915i	$-0.459497\pi$
$311$	1392.00	0.253804	0.126902	+	0.991915i	$0.459497\pi$
$312$	3712.00	0.673560
$313$	−5878.00	−1.06148	−0.530742	−	0.847534i	$-0.678087\pi$
$313$	−5878.00	−1.06148	−0.530742	+	0.847534i	$0.678087\pi$
$314$	4492.00	0.807319
$315$	−740.000	−0.132363
$316$	−640.000	−0.113933
$317$	10326.0	1.82955	0.914773	−	0.403969i	$-0.132370\pi$
$317$	10326.0	1.82955	0.914773	+	0.403969i	$0.132370\pi$
$318$	−3552.00	−0.626372
$319$	−1080.00	−0.189556
$320$	320.000	0.0559017
$321$	192.000	0.0333844
$322$	−1056.00	−0.182760
$323$	−6600.00	−1.13695
$324$	−1436.00	−0.246228
$325$	−1450.00	−0.247482
$326$	−1136.00	−0.192998
$327$	−7600.00	−1.28526
$328$	−3504.00	−0.589866
$329$	816.000	0.136740
$330$	−960.000	−0.160140
$331$	−4228.00	−0.702090	−0.351045	−	0.936359i	$-0.614174\pi$
$331$	−4228.00	−0.702090	−0.351045	+	0.936359i	$0.614174\pi$
$332$	288.000	0.0476086
$333$	−1258.00	−0.207021
$334$	−3048.00	−0.499339
$335$	−5120.00	−0.835031
$336$	512.000	0.0831306
$337$	1106.00	0.178776	0.0893882	−	0.995997i	$-0.471509\pi$
$337$	1106.00	0.178776	0.0893882	+	0.995997i	$0.471509\pi$
$338$	2334.00	0.375600
$339$	8304.00	1.33042
$340$	1320.00	0.210550
$341$	1824.00	0.289663
$342$	−7400.00	−1.17002
$343$	2680.00	0.421885
$344$	256.000	0.0401238
$345$	−5280.00	−0.823958
$346$	7404.00	1.15041
$347$	9336.00	1.44433	0.722165	−	0.691720i	$-0.243147\pi$
$347$	9336.00	1.44433	0.722165	+	0.691720i	$0.243147\pi$
$348$	2880.00	0.443633
$349$	−11770.0	−1.80525	−0.902627	−	0.430424i	$-0.858364\pi$
$349$	−11770.0	−1.80525	−0.902627	+	0.430424i	$0.858364\pi$
$350$	−200.000	−0.0305441
$351$	4640.00	0.705598
$352$	384.000	0.0581456
$353$	8322.00	1.25477	0.627387	−	0.778707i	$-0.284124\pi$
$353$	8322.00	1.25477	0.627387	+	0.778707i	$0.284124\pi$
$354$	−6720.00	−1.00894
$355$	2160.00	0.322932
$356$	3240.00	0.482359
$357$	2112.00	0.313106
$358$	6360.00	0.938929
$359$	10680.0	1.57011	0.785054	−	0.619427i	$-0.212635\pi$
$359$	10680.0	1.57011	0.785054	+	0.619427i	$0.212635\pi$
$360$	1480.00	0.216675
$361$	3141.00	0.457938
$362$	−4196.00	−0.609218
$363$	9496.00	1.37303
$364$	928.000	0.133628
$365$	1810.00	0.259561
$366$	−14432.0	−2.06113
$367$	−5884.00	−0.836900	−0.418450	−	0.908240i	$-0.637426\pi$
$367$	−5884.00	−0.836900	−0.418450	+	0.908240i	$0.637426\pi$
$368$	2112.00	0.299173
$369$	−16206.0	−2.28632
$370$	−340.000	−0.0477723
$371$	−888.000	−0.124266
$372$	−4864.00	−0.677921
$373$	−2098.00	−0.291234	−0.145617	−	0.989341i	$-0.546517\pi$
$373$	−2098.00	−0.291234	−0.145617	+	0.989341i	$0.546517\pi$
$374$	1584.00	0.219002
$375$	−1000.00	−0.137706
$376$	−1632.00	−0.223840
$377$	5220.00	0.713113
$378$	640.000	0.0870848
$379$	3860.00	0.523153	0.261576	−	0.965183i	$-0.415758\pi$
$379$	3860.00	0.523153	0.261576	+	0.965183i	$0.415758\pi$
$380$	−2000.00	−0.269994
$381$	992.000	0.133390
$382$	8784.00	1.17651
$383$	−9588.00	−1.27917	−0.639587	−	0.768718i	$-0.720895\pi$
$383$	−9588.00	−1.27917	−0.639587	+	0.768718i	$0.720895\pi$
$384$	−1024.00	−0.136083
$385$	−240.000	−0.0317702
$386$	−4316.00	−0.569116
$387$	1184.00	0.155520
$388$	4424.00	0.578852
$389$	−13410.0	−1.74785	−0.873925	−	0.486060i	$-0.838434\pi$
$389$	−13410.0	−1.74785	−0.873925	+	0.486060i	$0.838434\pi$
$390$	4640.00	0.602450
$391$	8712.00	1.12682
$392$	−2616.00	−0.337061
$393$	−1056.00	−0.135542
$394$	−2148.00	−0.274657
$395$	−800.000	−0.101905
$396$	1776.00	0.225372
$397$	−13114.0	−1.65787	−0.828933	−	0.559348i	$-0.811052\pi$
$397$	−13114.0	−1.65787	−0.828933	+	0.559348i	$0.811052\pi$
$398$	5680.00	0.715358
$399$	−3200.00	−0.401505
$400$	400.000	0.0500000
$401$	−5838.00	−0.727022	−0.363511	−	0.931590i	$-0.618422\pi$
$401$	−5838.00	−0.727022	−0.363511	+	0.931590i	$0.618422\pi$
$402$	16384.0	2.03274
$403$	−8816.00	−1.08972
$404$	−1032.00	−0.127089
$405$	−1795.00	−0.220233
$406$	720.000	0.0880123
$407$	−408.000	−0.0496899
$408$	−4224.00	−0.512547
$409$	9530.00	1.15215	0.576074	−	0.817398i	$-0.304584\pi$
$409$	9530.00	1.15215	0.576074	+	0.817398i	$0.304584\pi$
$410$	−4380.00	−0.527592
$411$	10032.0	1.20400
$412$	−3952.00	−0.472575
$413$	−1680.00	−0.200163
$414$	9768.00	1.15959
$415$	360.000	0.0425824
$416$	−1856.00	−0.218745
$417$	22880.0	2.68690
$418$	−2400.00	−0.280832
$419$	7260.00	0.846478	0.423239	−	0.906018i	$-0.360893\pi$
$419$	7260.00	0.846478	0.423239	+	0.906018i	$0.360893\pi$
$420$	640.000	0.0743543
$421$	12062.0	1.39636	0.698178	−	0.715924i	$-0.253994\pi$
$421$	12062.0	1.39636	0.698178	+	0.715924i	$0.253994\pi$
$422$	−5336.00	−0.615527
$423$	−7548.00	−0.867604
$424$	1776.00	0.203420
$425$	1650.00	0.188322
$426$	−6912.00	−0.786121
$427$	−3608.00	−0.408907
$428$	−96.0000	−0.0108419
$429$	5568.00	0.626633
$430$	320.000	0.0358878
$431$	−13608.0	−1.52082	−0.760411	−	0.649442i	$-0.775002\pi$
$431$	−13608.0	−1.52082	−0.760411	+	0.649442i	$0.775002\pi$
$432$	−1280.00	−0.142556
$433$	−3838.00	−0.425964	−0.212982	−	0.977056i	$-0.568318\pi$
$433$	−3838.00	−0.425964	−0.212982	+	0.977056i	$0.568318\pi$
$434$	−1216.00	−0.134493
$435$	3600.00	0.396797
$436$	3800.00	0.417401
$437$	−13200.0	−1.44495
$438$	−5792.00	−0.631855
$439$	7400.00	0.804516	0.402258	−	0.915526i	$-0.368225\pi$
$439$	7400.00	0.804516	0.402258	+	0.915526i	$0.368225\pi$
$440$	480.000	0.0520071
$441$	−12099.0	−1.30645
$442$	−7656.00	−0.823889
$443$	8352.00	0.895746	0.447873	−	0.894097i	$-0.352182\pi$
$443$	8352.00	0.895746	0.447873	+	0.894097i	$0.352182\pi$
$444$	1088.00	0.116293
$445$	4050.00	0.431435
$446$	3544.00	0.376263
$447$	−6000.00	−0.634878
$448$	−256.000	−0.0269975
$449$	10770.0	1.13200	0.566000	−	0.824405i	$-0.308490\pi$
$449$	10770.0	1.13200	0.566000	+	0.824405i	$0.308490\pi$
$450$	1850.00	0.193800
$451$	−5256.00	−0.548770
$452$	−4152.00	−0.432066
$453$	3584.00	0.371724
$454$	−5568.00	−0.575593
$455$	1160.00	0.119520
$456$	6400.00	0.657253
$457$	−6694.00	−0.685191	−0.342595	−	0.939483i	$-0.611306\pi$
$457$	−6694.00	−0.685191	−0.342595	+	0.939483i	$0.611306\pi$
$458$	700.000	0.0714167
$459$	−5280.00	−0.536927
$460$	2640.00	0.267588
$461$	−3018.00	−0.304907	−0.152454	−	0.988311i	$-0.548717\pi$
$461$	−3018.00	−0.304907	−0.152454	+	0.988311i	$0.548717\pi$
$462$	768.000	0.0773389
$463$	14492.0	1.45464	0.727322	−	0.686296i	$-0.240765\pi$
$463$	14492.0	1.45464	0.727322	+	0.686296i	$0.240765\pi$
$464$	−1440.00	−0.144074
$465$	−6080.00	−0.606351
$466$	3924.00	0.390077
$467$	7776.00	0.770515	0.385257	−	0.922809i	$-0.374113\pi$
$467$	7776.00	0.770515	0.385257	+	0.922809i	$0.374113\pi$
$468$	−8584.00	−0.847854
$469$	4096.00	0.403274
$470$	−2040.00	−0.200209
$471$	−17968.0	−1.75780
$472$	3360.00	0.327662
$473$	384.000	0.0373284
$474$	2560.00	0.248069
$475$	−2500.00	−0.241490
$476$	−1056.00	−0.101684
$477$	8214.00	0.788455
$478$	−8640.00	−0.826746
$479$	−13680.0	−1.30492	−0.652458	−	0.757825i	$-0.726262\pi$
$479$	−13680.0	−1.30492	−0.652458	+	0.757825i	$0.726262\pi$
$480$	−1280.00	−0.121716
$481$	1972.00	0.186934
$482$	−956.000	−0.0903415
$483$	4224.00	0.397927
$484$	−4748.00	−0.445905
$485$	5530.00	0.517741
$486$	10064.0	0.939326
$487$	7916.00	0.736567	0.368284	−	0.929714i	$-0.379946\pi$
$487$	7916.00	0.736567	0.368284	+	0.929714i	$0.379946\pi$
$488$	7216.00	0.669371
$489$	4544.00	0.420218
$490$	−3270.00	−0.301477
$491$	13932.0	1.28053	0.640267	−	0.768152i	$-0.278824\pi$
$491$	13932.0	1.28053	0.640267	+	0.768152i	$0.278824\pi$
$492$	14016.0	1.28433
$493$	−5940.00	−0.542645
$494$	11600.0	1.05650
$495$	2220.00	0.201579
$496$	2432.00	0.220161
$497$	−1728.00	−0.155959
$498$	−1152.00	−0.103659
$499$	−8260.00	−0.741019	−0.370509	−	0.928829i	$-0.620817\pi$
$499$	−8260.00	−0.741019	−0.370509	+	0.928829i	$0.620817\pi$
$500$	500.000	0.0447214
$501$	12192.0	1.08722
$502$	5304.00	0.471572
$503$	−11148.0	−0.988200	−0.494100	−	0.869405i	$-0.664502\pi$
$503$	−11148.0	−0.988200	−0.494100	+	0.869405i	$0.664502\pi$
$504$	−1184.00	−0.104642
$505$	−1290.00	−0.113672
$506$	3168.00	0.278330
$507$	−9336.00	−0.817803
$508$	−496.000	−0.0433198
$509$	−9690.00	−0.843815	−0.421907	−	0.906639i	$-0.638639\pi$
$509$	−9690.00	−0.843815	−0.421907	+	0.906639i	$0.638639\pi$
$510$	−5280.00	−0.458436
$511$	−1448.00	−0.125354
$512$	512.000	0.0441942
$513$	8000.00	0.688516
$514$	−4668.00	−0.400577
$515$	−4940.00	−0.422684
$516$	−1024.00	−0.0873626
$517$	−2448.00	−0.208245
$518$	272.000	0.0230714
$519$	−29616.0	−2.50481
$520$	−2320.00	−0.195651
$521$	−16038.0	−1.34863	−0.674316	−	0.738443i	$-0.735562\pi$
$521$	−16038.0	−1.34863	−0.674316	+	0.738443i	$0.735562\pi$
$522$	−6660.00	−0.558430
$523$	992.000	0.0829391	0.0414695	−	0.999140i	$-0.486796\pi$
$523$	992.000	0.0829391	0.0414695	+	0.999140i	$0.486796\pi$
$524$	528.000	0.0440187
$525$	800.000	0.0665045
$526$	−7896.00	−0.654528
$527$	10032.0	0.829223
$528$	−1536.00	−0.126602
$529$	5257.00	0.432070
$530$	2220.00	0.181945
$531$	15540.0	1.27002
$532$	1600.00	0.130392
$533$	25404.0	2.06448
$534$	−12960.0	−1.05025
$535$	−120.000	−0.00969729
$536$	−8192.00	−0.660150
$537$	−25440.0	−2.04435
$538$	3180.00	0.254832
$539$	−3924.00	−0.313578
$540$	−1600.00	−0.127506
$541$	7142.00	0.567576	0.283788	−	0.958887i	$-0.408409\pi$
$541$	7142.00	0.567576	0.283788	+	0.958887i	$0.408409\pi$
$542$	9904.00	0.784895
$543$	16784.0	1.32646
$544$	2112.00	0.166455
$545$	4750.00	0.373335
$546$	−3712.00	−0.290950
$547$	7616.00	0.595314	0.297657	−	0.954673i	$-0.403795\pi$
$547$	7616.00	0.595314	0.297657	+	0.954673i	$0.403795\pi$
$548$	−5016.00	−0.391009
$549$	33374.0	2.59448
$550$	600.000	0.0465165
$551$	9000.00	0.695849
$552$	−8448.00	−0.651396
$553$	640.000	0.0492144
$554$	3292.00	0.252462
$555$	1360.00	0.104016
$556$	−11440.0	−0.872597
$557$	−10314.0	−0.784593	−0.392296	−	0.919839i	$-0.628319\pi$
$557$	−10314.0	−0.784593	−0.392296	+	0.919839i	$0.628319\pi$
$558$	11248.0	0.853344
$559$	−1856.00	−0.140430
$560$	−320.000	−0.0241473
$561$	−6336.00	−0.476838
$562$	−2316.00	−0.173834
$563$	−7128.00	−0.533587	−0.266793	−	0.963754i	$-0.585964\pi$
$563$	−7128.00	−0.533587	−0.266793	+	0.963754i	$0.585964\pi$
$564$	6528.00	0.487373
$565$	−5190.00	−0.386451
$566$	13984.0	1.03850
$567$	1436.00	0.106360
$568$	3456.00	0.255300
$569$	2010.00	0.148091	0.0740453	−	0.997255i	$-0.476409\pi$
$569$	2010.00	0.148091	0.0740453	+	0.997255i	$0.476409\pi$
$570$	8000.00	0.587865
$571$	−23188.0	−1.69945	−0.849726	−	0.527224i	$-0.823233\pi$
$571$	−23188.0	−1.69945	−0.849726	+	0.527224i	$0.823233\pi$
$572$	−2784.00	−0.203505
$573$	−35136.0	−2.56165
$574$	3504.00	0.254798
$575$	3300.00	0.239338
$576$	2368.00	0.171296
$577$	22466.0	1.62092	0.810461	−	0.585793i	$-0.199217\pi$
$577$	22466.0	1.62092	0.810461	+	0.585793i	$0.199217\pi$
$578$	−1114.00	−0.0801666
$579$	17264.0	1.23915
$580$	−1800.00	−0.128864
$581$	−288.000	−0.0205650
$582$	−17696.0	−1.26035
$583$	2664.00	0.189248
$584$	2896.00	0.205201
$585$	−10730.0	−0.758343
$586$	−516.000	−0.0363750
$587$	22776.0	1.60148	0.800738	−	0.599015i	$-0.204441\pi$
$587$	22776.0	1.60148	0.800738	+	0.599015i	$0.204441\pi$
$588$	10464.0	0.733891
$589$	−15200.0	−1.06334
$590$	4200.00	0.293070
$591$	8592.00	0.598016
$592$	−544.000	−0.0377673
$593$	−21198.0	−1.46796	−0.733978	−	0.679174i	$-0.762338\pi$
$593$	−21198.0	−1.46796	−0.733978	+	0.679174i	$0.762338\pi$
$594$	−1920.00	−0.132624
$595$	−1320.00	−0.0909491
$596$	3000.00	0.206183
$597$	−22720.0	−1.55757
$598$	−15312.0	−1.04708
$599$	15960.0	1.08866	0.544330	−	0.838871i	$-0.316784\pi$
$599$	15960.0	1.08866	0.544330	+	0.838871i	$0.316784\pi$
$600$	−1600.00	−0.108866
$601$	5882.00	0.399221	0.199610	−	0.979875i	$-0.436032\pi$
$601$	5882.00	0.399221	0.199610	+	0.979875i	$0.436032\pi$
$602$	−256.000	−0.0173319
$603$	−37888.0	−2.55874
$604$	−1792.00	−0.120721
$605$	−5935.00	−0.398830
$606$	4128.00	0.276714
$607$	8516.00	0.569446	0.284723	−	0.958610i	$-0.408098\pi$
$607$	8516.00	0.569446	0.284723	+	0.958610i	$0.408098\pi$
$608$	−3200.00	−0.213449
$609$	−2880.00	−0.191631
$610$	9020.00	0.598703
$611$	11832.0	0.783423
$612$	9768.00	0.645176
$613$	8462.00	0.557548	0.278774	−	0.960357i	$-0.410072\pi$
$613$	8462.00	0.557548	0.278774	+	0.960357i	$0.410072\pi$
$614$	−17888.0	−1.17573
$615$	17520.0	1.14874
$616$	−384.000	−0.0251166
$617$	−11094.0	−0.723870	−0.361935	−	0.932203i	$-0.617884\pi$
$617$	−11094.0	−0.723870	−0.361935	+	0.932203i	$0.617884\pi$
$618$	15808.0	1.02895
$619$	2180.00	0.141553	0.0707767	−	0.997492i	$-0.477452\pi$
$619$	2180.00	0.141553	0.0707767	+	0.997492i	$0.477452\pi$
$620$	3040.00	0.196918
$621$	−10560.0	−0.682380
$622$	2784.00	0.179467
$623$	−3240.00	−0.208359
$624$	7424.00	0.476279
$625$	625.000	0.0400000
$626$	−11756.0	−0.750582
$627$	9600.00	0.611463
$628$	8984.00	0.570861
$629$	−2244.00	−0.142248
$630$	−1480.00	−0.0935946
$631$	−26848.0	−1.69382	−0.846911	−	0.531734i	$-0.821541\pi$
$631$	−26848.0	−1.69382	−0.846911	+	0.531734i	$0.821541\pi$
$632$	−1280.00	−0.0805628
$633$	21344.0	1.34020
$634$	20652.0	1.29368
$635$	−620.000	−0.0387464
$636$	−7104.00	−0.442912
$637$	18966.0	1.17969
$638$	−2160.00	−0.134036
$639$	15984.0	0.989542
$640$	640.000	0.0395285
$641$	26322.0	1.62193	0.810965	−	0.585095i	$-0.198943\pi$
$641$	26322.0	1.62193	0.810965	+	0.585095i	$0.198943\pi$
$642$	384.000	0.0236063
$643$	−10168.0	−0.623619	−0.311809	−	0.950145i	$-0.600935\pi$
$643$	−10168.0	−0.623619	−0.311809	+	0.950145i	$0.600935\pi$
$644$	−2112.00	−0.129231
$645$	−1280.00	−0.0781395
$646$	−13200.0	−0.803943
$647$	−23604.0	−1.43426	−0.717132	−	0.696937i	$-0.754546\pi$
$647$	−23604.0	−1.43426	−0.717132	+	0.696937i	$0.754546\pi$
$648$	−2872.00	−0.174109
$649$	5040.00	0.304834
$650$	−2900.00	−0.174996
$651$	4864.00	0.292834
$652$	−2272.00	−0.136470
$653$	16422.0	0.984139	0.492069	−	0.870556i	$-0.336241\pi$
$653$	16422.0	0.984139	0.492069	+	0.870556i	$0.336241\pi$
$654$	−15200.0	−0.908818
$655$	660.000	0.0393715
$656$	−7008.00	−0.417098
$657$	13394.0	0.795357
$658$	1632.00	0.0966899
$659$	−26100.0	−1.54281	−0.771405	−	0.636345i	$-0.780446\pi$
$659$	−26100.0	−1.54281	−0.771405	+	0.636345i	$0.780446\pi$
$660$	−1920.00	−0.113236
$661$	−3058.00	−0.179943	−0.0899716	−	0.995944i	$-0.528678\pi$
$661$	−3058.00	−0.179943	−0.0899716	+	0.995944i	$0.528678\pi$
$662$	−8456.00	−0.496453
$663$	30624.0	1.79387
$664$	576.000	0.0336644
$665$	2000.00	0.116627
$666$	−2516.00	−0.146386
$667$	−11880.0	−0.689648
$668$	−6096.00	−0.353086
$669$	−14176.0	−0.819246
$670$	−10240.0	−0.590456
$671$	10824.0	0.622736
$672$	1024.00	0.0587822
$673$	10802.0	0.618702	0.309351	−	0.950948i	$-0.399888\pi$
$673$	10802.0	0.618702	0.309351	+	0.950948i	$0.399888\pi$
$674$	2212.00	0.126414
$675$	−2000.00	−0.114044
$676$	4668.00	0.265589
$677$	−10674.0	−0.605960	−0.302980	−	0.952997i	$-0.597982\pi$
$677$	−10674.0	−0.605960	−0.302980	+	0.952997i	$0.597982\pi$
$678$	16608.0	0.940747
$679$	−4424.00	−0.250041
$680$	2640.00	0.148881
$681$	22272.0	1.25325
$682$	3648.00	0.204823
$683$	−28608.0	−1.60272	−0.801358	−	0.598185i	$-0.795889\pi$
$683$	−28608.0	−1.60272	−0.801358	+	0.598185i	$0.795889\pi$
$684$	−14800.0	−0.827328
$685$	−6270.00	−0.349729
$686$	5360.00	0.298317
$687$	−2800.00	−0.155497
$688$	512.000	0.0283718
$689$	−12876.0	−0.711954
$690$	−10560.0	−0.582627
$691$	−2428.00	−0.133669	−0.0668346	−	0.997764i	$-0.521290\pi$
$691$	−2428.00	−0.133669	−0.0668346	+	0.997764i	$0.521290\pi$
$692$	14808.0	0.813462
$693$	−1776.00	−0.0973516
$694$	18672.0	1.02130
$695$	−14300.0	−0.780475
$696$	5760.00	0.313696
$697$	−28908.0	−1.57097
$698$	−23540.0	−1.27651
$699$	−15696.0	−0.849324
$700$	−400.000	−0.0215980
$701$	−6618.00	−0.356574	−0.178287	−	0.983979i	$-0.557056\pi$
$701$	−6618.00	−0.356574	−0.178287	+	0.983979i	$0.557056\pi$
$702$	9280.00	0.498933
$703$	3400.00	0.182409
$704$	768.000	0.0411152
$705$	8160.00	0.435920
$706$	16644.0	0.887259
$707$	1032.00	0.0548972
$708$	−13440.0	−0.713427
$709$	20510.0	1.08642	0.543208	−	0.839598i	$-0.317209\pi$
$709$	20510.0	1.08642	0.543208	+	0.839598i	$0.317209\pi$
$710$	4320.00	0.228347
$711$	−5920.00	−0.312261
$712$	6480.00	0.341079
$713$	20064.0	1.05386
$714$	4224.00	0.221399
$715$	−3480.00	−0.182020
$716$	12720.0	0.663923
$717$	34560.0	1.80009
$718$	21360.0	1.11023
$719$	31680.0	1.64321	0.821603	−	0.570061i	$-0.193080\pi$
$719$	31680.0	1.64321	0.821603	+	0.570061i	$0.193080\pi$
$720$	2960.00	0.153212
$721$	3952.00	0.204133
$722$	6282.00	0.323811
$723$	3824.00	0.196703
$724$	−8392.00	−0.430782
$725$	−2250.00	−0.115259
$726$	18992.0	0.970880
$727$	13196.0	0.673195	0.336597	−	0.941649i	$-0.390724\pi$
$727$	13196.0	0.673195	0.336597	+	0.941649i	$0.390724\pi$
$728$	1856.00	0.0944889
$729$	−30563.0	−1.55276
$730$	3620.00	0.183537
$731$	2112.00	0.106861
$732$	−28864.0	−1.45744
$733$	8102.00	0.408259	0.204130	−	0.978944i	$-0.434564\pi$
$733$	8102.00	0.408259	0.204130	+	0.978944i	$0.434564\pi$
$734$	−11768.0	−0.591778
$735$	13080.0	0.656412
$736$	4224.00	0.211547
$737$	−12288.0	−0.614158
$738$	−32412.0	−1.61667
$739$	−12580.0	−0.626201	−0.313101	−	0.949720i	$-0.601368\pi$
$739$	−12580.0	−0.626201	−0.313101	+	0.949720i	$0.601368\pi$
$740$	−680.000	−0.0337801
$741$	−46400.0	−2.30033
$742$	−1776.00	−0.0878693
$743$	29892.0	1.47595	0.737975	−	0.674828i	$-0.235782\pi$
$743$	29892.0	1.47595	0.737975	+	0.674828i	$0.235782\pi$
$744$	−9728.00	−0.479363
$745$	3750.00	0.184415
$746$	−4196.00	−0.205934
$747$	2664.00	0.130483
$748$	3168.00	0.154858
$749$	96.0000	0.00468326
$750$	−2000.00	−0.0973729
$751$	−40408.0	−1.96339	−0.981697	−	0.190450i	$-0.939005\pi$
$751$	−40408.0	−1.96339	−0.981697	+	0.190450i	$0.939005\pi$
$752$	−3264.00	−0.158279
$753$	−21216.0	−1.02676
$754$	10440.0	0.504247
$755$	−2240.00	−0.107976
$756$	1280.00	0.0615782
$757$	32366.0	1.55398	0.776990	−	0.629513i	$-0.216746\pi$
$757$	32366.0	1.55398	0.776990	+	0.629513i	$0.216746\pi$
$758$	7720.00	0.369925
$759$	−12672.0	−0.606014
$760$	−4000.00	−0.190915
$761$	−17238.0	−0.821126	−0.410563	−	0.911832i	$-0.634668\pi$
$761$	−17238.0	−0.821126	−0.410563	+	0.911832i	$0.634668\pi$
$762$	1984.00	0.0943212
$763$	−3800.00	−0.180300
$764$	17568.0	0.831921
$765$	12210.0	0.577063
$766$	−19176.0	−0.904513
$767$	−24360.0	−1.14679
$768$	−2048.00	−0.0962250
$769$	10850.0	0.508792	0.254396	−	0.967100i	$-0.418123\pi$
$769$	10850.0	0.508792	0.254396	+	0.967100i	$0.418123\pi$
$770$	−480.000	−0.0224649
$771$	18672.0	0.872186
$772$	−8632.00	−0.402425
$773$	9102.00	0.423514	0.211757	−	0.977322i	$-0.432081\pi$
$773$	9102.00	0.423514	0.211757	+	0.977322i	$0.432081\pi$
$774$	2368.00	0.109969
$775$	3800.00	0.176129
$776$	8848.00	0.409310
$777$	−1088.00	−0.0502340
$778$	−26820.0	−1.23592
$779$	43800.0	2.01450
$780$	9280.00	0.425997
$781$	5184.00	0.237514
$782$	17424.0	0.796779
$783$	7200.00	0.328617
$784$	−5232.00	−0.238338
$785$	11230.0	0.510593
$786$	−2112.00	−0.0958429
$787$	−25504.0	−1.15517	−0.577585	−	0.816330i	$-0.696005\pi$
$787$	−25504.0	−1.15517	−0.577585	+	0.816330i	$0.696005\pi$
$788$	−4296.00	−0.194212
$789$	31584.0	1.42512
$790$	−1600.00	−0.0720575
$791$	4152.00	0.186635
$792$	3552.00	0.159362
$793$	−52316.0	−2.34274
$794$	−26228.0	−1.17229
$795$	−8880.00	−0.396152
$796$	11360.0	0.505835
$797$	14166.0	0.629593	0.314796	−	0.949159i	$-0.398064\pi$
$797$	14166.0	0.629593	0.314796	+	0.949159i	$0.398064\pi$
$798$	−6400.00	−0.283907
$799$	−13464.0	−0.596148
$800$	800.000	0.0353553
$801$	29970.0	1.32202
$802$	−11676.0	−0.514082
$803$	4344.00	0.190905
$804$	32768.0	1.43736
$805$	−2640.00	−0.115587
$806$	−17632.0	−0.770547
$807$	−12720.0	−0.554852
$808$	−2064.00	−0.0898654
$809$	33210.0	1.44327	0.721633	−	0.692276i	$-0.243392\pi$
$809$	33210.0	1.44327	0.721633	+	0.692276i	$0.243392\pi$
$810$	−3590.00	−0.155728
$811$	39212.0	1.69780	0.848902	−	0.528550i	$-0.177264\pi$
$811$	39212.0	1.69780	0.848902	+	0.528550i	$0.177264\pi$
$812$	1440.00	0.0622341
$813$	−39616.0	−1.70897
$814$	−816.000	−0.0351361
$815$	−2840.00	−0.122062
$816$	−8448.00	−0.362425
$817$	−3200.00	−0.137030
$818$	19060.0	0.814691
$819$	8584.00	0.366238
$820$	−8760.00	−0.373064
$821$	6222.00	0.264494	0.132247	−	0.991217i	$-0.457781\pi$
$821$	6222.00	0.264494	0.132247	+	0.991217i	$0.457781\pi$
$822$	20064.0	0.851353
$823$	31172.0	1.32028	0.660138	−	0.751144i	$-0.270498\pi$
$823$	31172.0	1.32028	0.660138	+	0.751144i	$0.270498\pi$
$824$	−7904.00	−0.334161
$825$	−2400.00	−0.101282
$826$	−3360.00	−0.141537
$827$	−264.000	−0.0111006	−0.00555029	−	0.999985i	$-0.501767\pi$
$827$	−264.000	−0.0111006	−0.00555029	+	0.999985i	$0.501767\pi$
$828$	19536.0	0.819955
$829$	−29050.0	−1.21707	−0.608533	−	0.793528i	$-0.708242\pi$
$829$	−29050.0	−1.21707	−0.608533	+	0.793528i	$0.708242\pi$
$830$	720.000	0.0301103
$831$	−13168.0	−0.549691
$832$	−3712.00	−0.154676
$833$	−21582.0	−0.897685
$834$	45760.0	1.89993
$835$	−7620.00	−0.315810
$836$	−4800.00	−0.198578
$837$	−12160.0	−0.502164
$838$	14520.0	0.598550
$839$	−21720.0	−0.893752	−0.446876	−	0.894596i	$-0.647463\pi$
$839$	−21720.0	−0.893752	−0.446876	+	0.894596i	$0.647463\pi$
$840$	1280.00	0.0525764
$841$	−16289.0	−0.667883
$842$	24124.0	0.987373
$843$	9264.00	0.378492
$844$	−10672.0	−0.435243
$845$	5835.00	0.237550
$846$	−15096.0	−0.613488
$847$	4748.00	0.192613
$848$	3552.00	0.143840
$849$	−55936.0	−2.26115
$850$	3300.00	0.133164
$851$	−4488.00	−0.180783
$852$	−13824.0	−0.555871
$853$	−6658.00	−0.267252	−0.133626	−	0.991032i	$-0.542662\pi$
$853$	−6658.00	−0.267252	−0.133626	+	0.991032i	$0.542662\pi$
$854$	−7216.00	−0.289141
$855$	−18500.0	−0.739984
$856$	−192.000	−0.00766638
$857$	−13974.0	−0.556993	−0.278496	−	0.960437i	$-0.589836\pi$
$857$	−13974.0	−0.556993	−0.278496	+	0.960437i	$0.589836\pi$
$858$	11136.0	0.443096
$859$	23780.0	0.944544	0.472272	−	0.881453i	$-0.343434\pi$
$859$	23780.0	0.944544	0.472272	+	0.881453i	$0.343434\pi$
$860$	640.000	0.0253765
$861$	−14016.0	−0.554778
$862$	−27216.0	−1.07538
$863$	−12228.0	−0.482324	−0.241162	−	0.970485i	$-0.577529\pi$
$863$	−12228.0	−0.482324	−0.241162	+	0.970485i	$0.577529\pi$
$864$	−2560.00	−0.100802
$865$	18510.0	0.727583
$866$	−7676.00	−0.301202
$867$	4456.00	0.174549
$868$	−2432.00	−0.0951008
$869$	−1920.00	−0.0749500
$870$	7200.00	0.280578
$871$	59392.0	2.31047
$872$	7600.00	0.295147
$873$	40922.0	1.58648
$874$	−26400.0	−1.02173
$875$	−500.000	−0.0193178
$876$	−11584.0	−0.446789
$877$	11606.0	0.446872	0.223436	−	0.974719i	$-0.428273\pi$
$877$	11606.0	0.446872	0.223436	+	0.974719i	$0.428273\pi$
$878$	14800.0	0.568879
$879$	2064.00	0.0792002
$880$	960.000	0.0367745
$881$	−32958.0	−1.26037	−0.630183	−	0.776446i	$-0.717020\pi$
$881$	−32958.0	−1.26037	−0.630183	+	0.776446i	$0.717020\pi$
$882$	−24198.0	−0.923797
$883$	8072.00	0.307638	0.153819	−	0.988099i	$-0.450843\pi$
$883$	8072.00	0.307638	0.153819	+	0.988099i	$0.450843\pi$
$884$	−15312.0	−0.582577
$885$	−16800.0	−0.638108
$886$	16704.0	0.633388
$887$	15756.0	0.596431	0.298216	−	0.954498i	$-0.403609\pi$
$887$	15756.0	0.596431	0.298216	+	0.954498i	$0.403609\pi$
$888$	2176.00	0.0822317
$889$	496.000	0.0187124
$890$	8100.00	0.305070
$891$	−4308.00	−0.161979
$892$	7088.00	0.266058
$893$	20400.0	0.764457
$894$	−12000.0	−0.448926
$895$	15900.0	0.593831
$896$	−512.000	−0.0190901
$897$	61248.0	2.27983
$898$	21540.0	0.800444
$899$	−13680.0	−0.507512
$900$	3700.00	0.137037
$901$	14652.0	0.541763
$902$	−10512.0	−0.388039
$903$	1024.00	0.0377371
$904$	−8304.00	−0.305517
$905$	−10490.0	−0.385303
$906$	7168.00	0.262849
$907$	18776.0	0.687372	0.343686	−	0.939085i	$-0.388324\pi$
$907$	18776.0	0.687372	0.343686	+	0.939085i	$0.388324\pi$
$908$	−11136.0	−0.407006
$909$	−9546.00	−0.348318
$910$	2320.00	0.0845135
$911$	−20568.0	−0.748022	−0.374011	−	0.927424i	$-0.622018\pi$
$911$	−20568.0	−0.748022	−0.374011	+	0.927424i	$0.622018\pi$
$912$	12800.0	0.464748
$913$	864.000	0.0313190
$914$	−13388.0	−0.484503
$915$	−36080.0	−1.30357
$916$	1400.00	0.0504992
$917$	−528.000	−0.0190143
$918$	−10560.0	−0.379664
$919$	−6280.00	−0.225417	−0.112708	−	0.993628i	$-0.535953\pi$
$919$	−6280.00	−0.225417	−0.112708	+	0.993628i	$0.535953\pi$
$920$	5280.00	0.189214
$921$	71552.0	2.55996
$922$	−6036.00	−0.215602
$923$	−25056.0	−0.893530
$924$	1536.00	0.0546869
$925$	−850.000	−0.0302139
$926$	28984.0	1.02859
$927$	−36556.0	−1.29521
$928$	−2880.00	−0.101876
$929$	−20430.0	−0.721514	−0.360757	−	0.932660i	$-0.617482\pi$
$929$	−20430.0	−0.721514	−0.360757	+	0.932660i	$0.617482\pi$
$930$	−12160.0	−0.428755
$931$	32700.0	1.15113
$932$	7848.00	0.275826
$933$	−11136.0	−0.390757
$934$	15552.0	0.544836
$935$	3960.00	0.138509
$936$	−17168.0	−0.599523
$937$	8906.00	0.310508	0.155254	−	0.987875i	$-0.450380\pi$
$937$	8906.00	0.310508	0.155254	+	0.987875i	$0.450380\pi$
$938$	8192.00	0.285158
$939$	47024.0	1.63426
$940$	−4080.00	−0.141569
$941$	−17418.0	−0.603412	−0.301706	−	0.953401i	$-0.597556\pi$
$941$	−17418.0	−0.603412	−0.301706	+	0.953401i	$0.597556\pi$
$942$	−35936.0	−1.24295
$943$	−57816.0	−1.99655
$944$	6720.00	0.231692
$945$	1600.00	0.0550773
$946$	768.000	0.0263952
$947$	−2544.00	−0.0872956	−0.0436478	−	0.999047i	$-0.513898\pi$
$947$	−2544.00	−0.0872956	−0.0436478	+	0.999047i	$0.513898\pi$
$948$	5120.00	0.175411
$949$	−20996.0	−0.718187
$950$	−5000.00	−0.170759
$951$	−82608.0	−2.81677
$952$	−2112.00	−0.0719016
$953$	15402.0	0.523525	0.261763	−	0.965132i	$-0.415696\pi$
$953$	15402.0	0.523525	0.261763	+	0.965132i	$0.415696\pi$
$954$	16428.0	0.557522
$955$	21960.0	0.744093
$956$	−17280.0	−0.584597
$957$	8640.00	0.291841
$958$	−27360.0	−0.922716
$959$	5016.00	0.168900
$960$	−2560.00	−0.0860663
$961$	−6687.00	−0.224464
$962$	3944.00	0.132183
$963$	−888.000	−0.0297148
$964$	−1912.00	−0.0638811
$965$	−10790.0	−0.359940
$966$	8448.00	0.281377
$967$	−49444.0	−1.64427	−0.822136	−	0.569291i	$-0.807218\pi$
$967$	−49444.0	−1.64427	−0.822136	+	0.569291i	$0.807218\pi$
$968$	−9496.00	−0.315303
$969$	52800.0	1.75044
$970$	11060.0	0.366098
$971$	−25188.0	−0.832463	−0.416231	−	0.909259i	$-0.636649\pi$
$971$	−25188.0	−0.832463	−0.416231	+	0.909259i	$0.636649\pi$
$972$	20128.0	0.664204
$973$	11440.0	0.376927
$974$	15832.0	0.520832
$975$	11600.0	0.381023
$976$	14432.0	0.473317
$977$	2946.00	0.0964697	0.0482348	−	0.998836i	$-0.484640\pi$
$977$	2946.00	0.0964697	0.0482348	+	0.998836i	$0.484640\pi$
$978$	9088.00	0.297139
$979$	9720.00	0.317316
$980$	−6540.00	−0.213176
$981$	35150.0	1.14399
$982$	27864.0	0.905475
$983$	15012.0	0.487089	0.243544	−	0.969890i	$-0.421690\pi$
$983$	15012.0	0.487089	0.243544	+	0.969890i	$0.421690\pi$
$984$	28032.0	0.908158
$985$	−5370.00	−0.173708
$986$	−11880.0	−0.383708
$987$	−6528.00	−0.210525
$988$	23200.0	0.747055
$989$	4224.00	0.135809
$990$	4440.00	0.142538
$991$	−5128.00	−0.164376	−0.0821878	−	0.996617i	$-0.526191\pi$
$991$	−5128.00	−0.164376	−0.0821878	+	0.996617i	$0.526191\pi$
$992$	4864.00	0.155678
$993$	33824.0	1.08094
$994$	−3456.00	−0.110279
$995$	14200.0	0.452432
$996$	−2304.00	−0.0732982
$997$	−49714.0	−1.57920	−0.789598	−	0.613625i	$-0.789711\pi$
$997$	−49714.0	−1.57920	−0.789598	+	0.613625i	$0.789711\pi$
$998$	−16520.0	−0.523979
$999$	2720.00	0.0861431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.4.a.a.1.1	✓	1
3.2	odd	2		90.4.a.a.1.1		1
4.3	odd	2		80.4.a.f.1.1		1
5.2	odd	4		50.4.b.a.49.2		2
5.3	odd	4		50.4.b.a.49.1		2
5.4	even	2		50.4.a.c.1.1		1
7.2	even	3		490.4.e.i.361.1		2
7.3	odd	6		490.4.e.a.471.1		2
7.4	even	3		490.4.e.i.471.1		2
7.5	odd	6		490.4.e.a.361.1		2
7.6	odd	2		490.4.a.o.1.1		1
8.3	odd	2		320.4.a.b.1.1		1
8.5	even	2		320.4.a.m.1.1		1
9.2	odd	6		810.4.e.w.271.1		2
9.4	even	3		810.4.e.c.541.1		2
9.5	odd	6		810.4.e.w.541.1		2
9.7	even	3		810.4.e.c.271.1		2
11.10	odd	2		1210.4.a.b.1.1		1
12.11	even	2		720.4.a.j.1.1		1
13.12	even	2		1690.4.a.a.1.1		1
15.2	even	4		450.4.c.d.199.1		2
15.8	even	4		450.4.c.d.199.2		2
15.14	odd	2		450.4.a.q.1.1		1
16.3	odd	4		1280.4.d.g.641.2		2
16.5	even	4		1280.4.d.j.641.2		2
16.11	odd	4		1280.4.d.g.641.1		2
16.13	even	4		1280.4.d.j.641.1		2
20.3	even	4		400.4.c.c.49.2		2
20.7	even	4		400.4.c.c.49.1		2
20.19	odd	2		400.4.a.b.1.1		1
35.34	odd	2		2450.4.a.b.1.1		1
40.19	odd	2		1600.4.a.bx.1.1		1
40.29	even	2		1600.4.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.4.a.a.1.1	✓	1	1.1	even	1	trivial
50.4.a.c.1.1		1	5.4	even	2
50.4.b.a.49.1		2	5.3	odd	4
50.4.b.a.49.2		2	5.2	odd	4
80.4.a.f.1.1		1	4.3	odd	2
90.4.a.a.1.1		1	3.2	odd	2
320.4.a.b.1.1		1	8.3	odd	2
320.4.a.m.1.1		1	8.5	even	2
400.4.a.b.1.1		1	20.19	odd	2
400.4.c.c.49.1		2	20.7	even	4
400.4.c.c.49.2		2	20.3	even	4
450.4.a.q.1.1		1	15.14	odd	2
450.4.c.d.199.1		2	15.2	even	4
450.4.c.d.199.2		2	15.8	even	4
490.4.a.o.1.1		1	7.6	odd	2
490.4.e.a.361.1		2	7.5	odd	6
490.4.e.a.471.1		2	7.3	odd	6
490.4.e.i.361.1		2	7.2	even	3
490.4.e.i.471.1		2	7.4	even	3
720.4.a.j.1.1		1	12.11	even	2
810.4.e.c.271.1		2	9.7	even	3
810.4.e.c.541.1		2	9.4	even	3
810.4.e.w.271.1		2	9.2	odd	6
810.4.e.w.541.1		2	9.5	odd	6
1210.4.a.b.1.1		1	11.10	odd	2
1280.4.d.g.641.1		2	16.11	odd	4
1280.4.d.g.641.2		2	16.3	odd	4
1280.4.d.j.641.1		2	16.13	even	4
1280.4.d.j.641.2		2	16.5	even	4
1600.4.a.d.1.1		1	40.29	even	2
1600.4.a.bx.1.1		1	40.19	odd	2
1690.4.a.a.1.1		1	13.12	even	2
2450.4.a.b.1.1		1	35.34	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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