LMFDB - Embedded newform 114.4.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(1,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, 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("114.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.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:	$6.72621774065$
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	$\chi$	$=$	114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -11.0000 q^{5} -6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$

\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -11.0000 q^{5} -6.00000 q^{6} -15.0000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -22.0000 q^{10} -29.0000 q^{11} -12.0000 q^{12} -82.0000 q^{13} -30.0000 q^{14} +33.0000 q^{15} +16.0000 q^{16} +27.0000 q^{17} +18.0000 q^{18} -19.0000 q^{19} -44.0000 q^{20} +45.0000 q^{21} -58.0000 q^{22} +100.000 q^{23} -24.0000 q^{24} -4.00000 q^{25} -164.000 q^{26} -27.0000 q^{27} -60.0000 q^{28} -118.000 q^{29} +66.0000 q^{30} +70.0000 q^{31} +32.0000 q^{32} +87.0000 q^{33} +54.0000 q^{34} +165.000 q^{35} +36.0000 q^{36} +232.000 q^{37} -38.0000 q^{38} +246.000 q^{39} -88.0000 q^{40} +8.00000 q^{41} +90.0000 q^{42} -287.000 q^{43} -116.000 q^{44} -99.0000 q^{45} +200.000 q^{46} +385.000 q^{47} -48.0000 q^{48} -118.000 q^{49} -8.00000 q^{50} -81.0000 q^{51} -328.000 q^{52} +538.000 q^{53} -54.0000 q^{54} +319.000 q^{55} -120.000 q^{56} +57.0000 q^{57} -236.000 q^{58} -300.000 q^{59} +132.000 q^{60} -901.000 q^{61} +140.000 q^{62} -135.000 q^{63} +64.0000 q^{64} +902.000 q^{65} +174.000 q^{66} +132.000 q^{67} +108.000 q^{68} -300.000 q^{69} +330.000 q^{70} +472.000 q^{71} +72.0000 q^{72} -1131.00 q^{73} +464.000 q^{74} +12.0000 q^{75} -76.0000 q^{76} +435.000 q^{77} +492.000 q^{78} -52.0000 q^{79} -176.000 q^{80} +81.0000 q^{81} +16.0000 q^{82} +276.000 q^{83} +180.000 q^{84} -297.000 q^{85} -574.000 q^{86} +354.000 q^{87} -232.000 q^{88} -1302.00 q^{89} -198.000 q^{90} +1230.00 q^{91} +400.000 q^{92} -210.000 q^{93} +770.000 q^{94} +209.000 q^{95} -96.0000 q^{96} -1310.00 q^{97} -236.000 q^{98} -261.000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−11.0000	−0.983870	−0.491935	−	0.870632i	$-0.663710\pi$
$5$	−11.0000	−0.983870	−0.491935	+	0.870632i	$0.663710\pi$
$6$	−6.00000	−0.408248
$7$	−15.0000	−0.809924	−0.404962	−	0.914334i	$-0.632715\pi$
$7$	−15.0000	−0.809924	−0.404962	+	0.914334i	$0.632715\pi$
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−22.0000	−0.695701
$11$	−29.0000	−0.794894	−0.397447	−	0.917625i	$-0.630104\pi$
$11$	−29.0000	−0.794894	−0.397447	+	0.917625i	$0.630104\pi$
$12$	−12.0000	−0.288675
$13$	−82.0000	−1.74944	−0.874720	−	0.484629i	$-0.838954\pi$
$13$	−82.0000	−1.74944	−0.874720	+	0.484629i	$0.838954\pi$
$14$	−30.0000	−0.572703
$15$	33.0000	0.568038
$16$	16.0000	0.250000
$17$	27.0000	0.385204	0.192602	−	0.981277i	$-0.438307\pi$
$17$	27.0000	0.385204	0.192602	+	0.981277i	$0.438307\pi$
$18$	18.0000	0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−44.0000	−0.491935
$21$	45.0000	0.467610
$22$	−58.0000	−0.562075
$23$	100.000	0.906584	0.453292	−	0.891362i	$-0.350249\pi$
$23$	100.000	0.906584	0.453292	+	0.891362i	$0.350249\pi$
$24$	−24.0000	−0.204124
$25$	−4.00000	−0.0320000
$26$	−164.000	−1.23704
$27$	−27.0000	−0.192450
$28$	−60.0000	−0.404962
$29$	−118.000	−0.755588	−0.377794	−	0.925890i	$-0.623317\pi$
$29$	−118.000	−0.755588	−0.377794	+	0.925890i	$0.623317\pi$
$30$	66.0000	0.401663
$31$	70.0000	0.405560	0.202780	−	0.979224i	$-0.435002\pi$
$31$	70.0000	0.405560	0.202780	+	0.979224i	$0.435002\pi$
$32$	32.0000	0.176777
$33$	87.0000	0.458932
$34$	54.0000	0.272380
$35$	165.000	0.796860
$36$	36.0000	0.166667
$37$	232.000	1.03083	0.515413	−	0.856942i	$-0.327639\pi$
$37$	232.000	1.03083	0.515413	+	0.856942i	$0.327639\pi$
$38$	−38.0000	−0.162221
$39$	246.000	1.01004
$40$	−88.0000	−0.347851
$41$	8.00000	0.0304729	0.0152365	−	0.999884i	$-0.495150\pi$
$41$	8.00000	0.0304729	0.0152365	+	0.999884i	$0.495150\pi$
$42$	90.0000	0.330650
$43$	−287.000	−1.01784	−0.508920	−	0.860814i	$-0.669955\pi$
$43$	−287.000	−1.01784	−0.508920	+	0.860814i	$0.669955\pi$
$44$	−116.000	−0.397447
$45$	−99.0000	−0.327957
$46$	200.000	0.641052
$47$	385.000	1.19485	0.597426	−	0.801924i	$-0.296190\pi$
$47$	385.000	1.19485	0.597426	+	0.801924i	$0.296190\pi$
$48$	−48.0000	−0.144338
$49$	−118.000	−0.344023
$50$	−8.00000	−0.0226274
$51$	−81.0000	−0.222397
$52$	−328.000	−0.874720
$53$	538.000	1.39434	0.697170	−	0.716906i	$-0.254442\pi$
$53$	538.000	1.39434	0.697170	+	0.716906i	$0.254442\pi$
$54$	−54.0000	−0.136083
$55$	319.000	0.782072
$56$	−120.000	−0.286351
$57$	57.0000	0.132453
$58$	−236.000	−0.534281
$59$	−300.000	−0.661978	−0.330989	−	0.943635i	$-0.607382\pi$
$59$	−300.000	−0.661978	−0.330989	+	0.943635i	$0.607382\pi$
$60$	132.000	0.284019
$61$	−901.000	−1.89117	−0.945584	−	0.325379i	$-0.894508\pi$
$61$	−901.000	−1.89117	−0.945584	+	0.325379i	$0.894508\pi$
$62$	140.000	0.286774
$63$	−135.000	−0.269975
$64$	64.0000	0.125000
$65$	902.000	1.72122
$66$	174.000	0.324514
$67$	132.000	0.240692	0.120346	−	0.992732i	$-0.461600\pi$
$67$	132.000	0.240692	0.120346	+	0.992732i	$0.461600\pi$
$68$	108.000	0.192602
$69$	−300.000	−0.523417
$70$	330.000	0.563465
$71$	472.000	0.788959	0.394480	−	0.918905i	$-0.370925\pi$
$71$	472.000	0.788959	0.394480	+	0.918905i	$0.370925\pi$
$72$	72.0000	0.117851
$73$	−1131.00	−1.81334	−0.906668	−	0.421845i	$-0.861383\pi$
$73$	−1131.00	−1.81334	−0.906668	+	0.421845i	$0.861383\pi$
$74$	464.000	0.728904
$75$	12.0000	0.0184752
$76$	−76.0000	−0.114708
$77$	435.000	0.643803
$78$	492.000	0.714206
$79$	−52.0000	−0.0740564	−0.0370282	−	0.999314i	$-0.511789\pi$
$79$	−52.0000	−0.0740564	−0.0370282	+	0.999314i	$0.511789\pi$
$80$	−176.000	−0.245967
$81$	81.0000	0.111111
$82$	16.0000	0.0215476
$83$	276.000	0.364999	0.182500	−	0.983206i	$-0.441581\pi$
$83$	276.000	0.364999	0.182500	+	0.983206i	$0.441581\pi$
$84$	180.000	0.233805
$85$	−297.000	−0.378990
$86$	−574.000	−0.719721
$87$	354.000	0.436239
$88$	−232.000	−0.281037
$89$	−1302.00	−1.55069	−0.775347	−	0.631536i	$-0.782425\pi$
$89$	−1302.00	−1.55069	−0.775347	+	0.631536i	$0.782425\pi$
$90$	−198.000	−0.231900
$91$	1230.00	1.41691
$92$	400.000	0.453292
$93$	−210.000	−0.234150
$94$	770.000	0.844888
$95$	209.000	0.225715
$96$	−96.0000	−0.102062
$97$	−1310.00	−1.37124	−0.685620	−	0.727959i	$-0.740469\pi$
$97$	−1310.00	−1.37124	−0.685620	+	0.727959i	$0.740469\pi$
$98$	−236.000	−0.243261
$99$	−261.000	−0.264965
$100$	−16.0000	−0.0160000
$101$	−638.000	−0.628548	−0.314274	−	0.949332i	$-0.601761\pi$
$101$	−638.000	−0.628548	−0.314274	+	0.949332i	$0.601761\pi$
$102$	−162.000	−0.157259
$103$	786.000	0.751911	0.375956	−	0.926638i	$-0.377314\pi$
$103$	786.000	0.751911	0.375956	+	0.926638i	$0.377314\pi$
$104$	−656.000	−0.618520
$105$	−495.000	−0.460067
$106$	1076.00	0.985947
$107$	−1310.00	−1.18357	−0.591787	−	0.806094i	$-0.701577\pi$
$107$	−1310.00	−1.18357	−0.591787	+	0.806094i	$0.701577\pi$
$108$	−108.000	−0.0962250
$109$	−1296.00	−1.13885	−0.569423	−	0.822044i	$-0.692833\pi$
$109$	−1296.00	−1.13885	−0.569423	+	0.822044i	$0.692833\pi$
$110$	638.000	0.553008
$111$	−696.000	−0.595148
$112$	−240.000	−0.202481
$113$	−1130.00	−0.940721	−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−1130.00	−0.940721	−0.470360	+	0.882474i	$0.655876\pi$
$114$	114.000	0.0936586
$115$	−1100.00	−0.891961
$116$	−472.000	−0.377794
$117$	−738.000	−0.583146
$118$	−600.000	−0.468089
$119$	−405.000	−0.311986
$120$	264.000	0.200832
$121$	−490.000	−0.368144
$122$	−1802.00	−1.33726
$123$	−24.0000	−0.0175936
$124$	280.000	0.202780
$125$	1419.00	1.01535
$126$	−270.000	−0.190901
$127$	750.000	0.524029	0.262015	−	0.965064i	$-0.415613\pi$
$127$	750.000	0.524029	0.262015	+	0.965064i	$0.415613\pi$
$128$	128.000	0.0883883
$129$	861.000	0.587650
$130$	1804.00	1.21709
$131$	−1275.00	−0.850361	−0.425180	−	0.905109i	$-0.639789\pi$
$131$	−1275.00	−0.850361	−0.425180	+	0.905109i	$0.639789\pi$
$132$	348.000	0.229466
$133$	285.000	0.185809
$134$	264.000	0.170195
$135$	297.000	0.189346
$136$	216.000	0.136190
$137$	2123.00	1.32394	0.661971	−	0.749529i	$-0.269720\pi$
$137$	2123.00	1.32394	0.661971	+	0.749529i	$0.269720\pi$
$138$	−600.000	−0.370112
$139$	2277.00	1.38944	0.694722	−	0.719279i	$-0.255528\pi$
$139$	2277.00	1.38944	0.694722	+	0.719279i	$0.255528\pi$
$140$	660.000	0.398430
$141$	−1155.00	−0.689848
$142$	944.000	0.557878
$143$	2378.00	1.39062
$144$	144.000	0.0833333
$145$	1298.00	0.743400
$146$	−2262.00	−1.28222
$147$	354.000	0.198622
$148$	928.000	0.515413
$149$	2235.00	1.22885	0.614424	−	0.788976i	$-0.289388\pi$
$149$	2235.00	1.22885	0.614424	+	0.788976i	$0.289388\pi$
$150$	24.0000	0.0130639
$151$	−2764.00	−1.48961	−0.744805	−	0.667282i	$-0.767458\pi$
$151$	−2764.00	−1.48961	−0.744805	+	0.667282i	$0.767458\pi$
$152$	−152.000	−0.0811107
$153$	243.000	0.128401
$154$	870.000	0.455238
$155$	−770.000	−0.399019
$156$	984.000	0.505020
$157$	1702.00	0.865187	0.432594	−	0.901589i	$-0.357599\pi$
$157$	1702.00	0.865187	0.432594	+	0.901589i	$0.357599\pi$
$158$	−104.000	−0.0523658
$159$	−1614.00	−0.805022
$160$	−352.000	−0.173925
$161$	−1500.00	−0.734264
$162$	162.000	0.0785674
$163$	2840.00	1.36470	0.682350	−	0.731026i	$-0.260958\pi$
$163$	2840.00	1.36470	0.682350	+	0.731026i	$0.260958\pi$
$164$	32.0000	0.0152365
$165$	−957.000	−0.451529
$166$	552.000	0.258093
$167$	1194.00	0.553260	0.276630	−	0.960976i	$-0.410782\pi$
$167$	1194.00	0.553260	0.276630	+	0.960976i	$0.410782\pi$
$168$	360.000	0.165325
$169$	4527.00	2.06054
$170$	−594.000	−0.267987
$171$	−171.000	−0.0764719
$172$	−1148.00	−0.508920
$173$	−3786.00	−1.66384	−0.831920	−	0.554896i	$-0.812758\pi$
$173$	−3786.00	−1.66384	−0.831920	+	0.554896i	$0.812758\pi$
$174$	708.000	0.308467
$175$	60.0000	0.0259176
$176$	−464.000	−0.198723
$177$	900.000	0.382193
$178$	−2604.00	−1.09651
$179$	2094.00	0.874374	0.437187	−	0.899371i	$-0.355975\pi$
$179$	2094.00	0.874374	0.437187	+	0.899371i	$0.355975\pi$
$180$	−396.000	−0.163978
$181$	−350.000	−0.143731	−0.0718655	−	0.997414i	$-0.522895\pi$
$181$	−350.000	−0.143731	−0.0718655	+	0.997414i	$0.522895\pi$
$182$	2460.00	1.00191
$183$	2703.00	1.09187
$184$	800.000	0.320526
$185$	−2552.00	−1.01420
$186$	−420.000	−0.165569
$187$	−783.000	−0.306196
$188$	1540.00	0.597426
$189$	405.000	0.155870
$190$	418.000	0.159605
$191$	−1489.00	−0.564085	−0.282043	−	0.959402i	$-0.591012\pi$
$191$	−1489.00	−0.564085	−0.282043	+	0.959402i	$0.591012\pi$
$192$	−192.000	−0.0721688
$193$	600.000	0.223777	0.111888	−	0.993721i	$-0.464310\pi$
$193$	600.000	0.223777	0.111888	+	0.993721i	$0.464310\pi$
$194$	−2620.00	−0.969614
$195$	−2706.00	−0.993747
$196$	−472.000	−0.172012
$197$	−290.000	−0.104881	−0.0524407	−	0.998624i	$-0.516700\pi$
$197$	−290.000	−0.104881	−0.0524407	+	0.998624i	$0.516700\pi$
$198$	−522.000	−0.187358
$199$	4169.00	1.48509	0.742544	−	0.669797i	$-0.233619\pi$
$199$	4169.00	1.48509	0.742544	+	0.669797i	$0.233619\pi$
$200$	−32.0000	−0.0113137
$201$	−396.000	−0.138964
$202$	−1276.00	−0.444451
$203$	1770.00	0.611969
$204$	−324.000	−0.111199
$205$	−88.0000	−0.0299814
$206$	1572.00	0.531682
$207$	900.000	0.302195
$208$	−1312.00	−0.437360
$209$	551.000	0.182361
$210$	−990.000	−0.325317
$211$	−1368.00	−0.446337	−0.223168	−	0.974780i	$-0.571640\pi$
$211$	−1368.00	−0.446337	−0.223168	+	0.974780i	$0.571640\pi$
$212$	2152.00	0.697170
$213$	−1416.00	−0.455506
$214$	−2620.00	−0.836914
$215$	3157.00	1.00142
$216$	−216.000	−0.0680414
$217$	−1050.00	−0.328473
$218$	−2592.00	−0.805286
$219$	3393.00	1.04693
$220$	1276.00	0.391036
$221$	−2214.00	−0.673890
$222$	−1392.00	−0.420833
$223$	2540.00	0.762740	0.381370	−	0.924423i	$-0.375452\pi$
$223$	2540.00	0.762740	0.381370	+	0.924423i	$0.375452\pi$
$224$	−480.000	−0.143176
$225$	−36.0000	−0.0106667
$226$	−2260.00	−0.665190
$227$	−5974.00	−1.74673	−0.873366	−	0.487064i	$-0.838068\pi$
$227$	−5974.00	−1.74673	−0.873366	+	0.487064i	$0.838068\pi$
$228$	228.000	0.0662266
$229$	−355.000	−0.102441	−0.0512207	−	0.998687i	$-0.516311\pi$
$229$	−355.000	−0.102441	−0.0512207	+	0.998687i	$0.516311\pi$
$230$	−2200.00	−0.630712
$231$	−1305.00	−0.371700
$232$	−944.000	−0.267141
$233$	237.000	0.0666369	0.0333184	−	0.999445i	$-0.489392\pi$
$233$	237.000	0.0666369	0.0333184	+	0.999445i	$0.489392\pi$
$234$	−1476.00	−0.412347
$235$	−4235.00	−1.17558
$236$	−1200.00	−0.330989
$237$	156.000	0.0427565
$238$	−810.000	−0.220607
$239$	1635.00	0.442508	0.221254	−	0.975216i	$-0.428985\pi$
$239$	1635.00	0.442508	0.221254	+	0.975216i	$0.428985\pi$
$240$	528.000	0.142009
$241$	−164.000	−0.0438347	−0.0219174	−	0.999760i	$-0.506977\pi$
$241$	−164.000	−0.0438347	−0.0219174	+	0.999760i	$0.506977\pi$
$242$	−980.000	−0.260317
$243$	−243.000	−0.0641500
$244$	−3604.00	−0.945584
$245$	1298.00	0.338474
$246$	−48.0000	−0.0124405
$247$	1558.00	0.401349
$248$	560.000	0.143387
$249$	−828.000	−0.210732
$250$	2838.00	0.717964
$251$	−2099.00	−0.527839	−0.263920	−	0.964545i	$-0.585015\pi$
$251$	−2099.00	−0.527839	−0.263920	+	0.964545i	$0.585015\pi$
$252$	−540.000	−0.134987
$253$	−2900.00	−0.720638
$254$	1500.00	0.370545
$255$	891.000	0.218810
$256$	256.000	0.0625000
$257$	5536.00	1.34368	0.671841	−	0.740696i	$-0.265504\pi$
$257$	5536.00	1.34368	0.671841	+	0.740696i	$0.265504\pi$
$258$	1722.00	0.415531
$259$	−3480.00	−0.834891
$260$	3608.00	0.860610
$261$	−1062.00	−0.251863
$262$	−2550.00	−0.601296
$263$	2073.00	0.486033	0.243016	−	0.970022i	$-0.421863\pi$
$263$	2073.00	0.486033	0.243016	+	0.970022i	$0.421863\pi$
$264$	696.000	0.162257
$265$	−5918.00	−1.37185
$266$	570.000	0.131387
$267$	3906.00	0.895293
$268$	528.000	0.120346
$269$	1482.00	0.335908	0.167954	−	0.985795i	$-0.446284\pi$
$269$	1482.00	0.335908	0.167954	+	0.985795i	$0.446284\pi$
$270$	594.000	0.133888
$271$	−7268.00	−1.62915	−0.814575	−	0.580058i	$-0.803030\pi$
$271$	−7268.00	−1.62915	−0.814575	+	0.580058i	$0.803030\pi$
$272$	432.000	0.0963009
$273$	−3690.00	−0.818055
$274$	4246.00	0.936169
$275$	116.000	0.0254366
$276$	−1200.00	−0.261708
$277$	−4583.00	−0.994100	−0.497050	−	0.867722i	$-0.665584\pi$
$277$	−4583.00	−0.994100	−0.497050	+	0.867722i	$0.665584\pi$
$278$	4554.00	0.982485
$279$	630.000	0.135187
$280$	1320.00	0.281732
$281$	5762.00	1.22325	0.611623	−	0.791149i	$-0.290517\pi$
$281$	5762.00	1.22325	0.611623	+	0.791149i	$0.290517\pi$
$282$	−2310.00	−0.487796
$283$	3909.00	0.821081	0.410541	−	0.911842i	$-0.365340\pi$
$283$	3909.00	0.821081	0.410541	+	0.911842i	$0.365340\pi$
$284$	1888.00	0.394480
$285$	−627.000	−0.130317
$286$	4756.00	0.983315
$287$	−120.000	−0.0246808
$288$	288.000	0.0589256
$289$	−4184.00	−0.851618
$290$	2596.00	0.525663
$291$	3930.00	0.791686
$292$	−4524.00	−0.906668
$293$	−8148.00	−1.62461	−0.812306	−	0.583232i	$-0.801788\pi$
$293$	−8148.00	−1.62461	−0.812306	+	0.583232i	$0.801788\pi$
$294$	708.000	0.140447
$295$	3300.00	0.651300
$296$	1856.00	0.364452
$297$	783.000	0.152977
$298$	4470.00	0.868927
$299$	−8200.00	−1.58601
$300$	48.0000	0.00923760
$301$	4305.00	0.824372
$302$	−5528.00	−1.05331
$303$	1914.00	0.362892
$304$	−304.000	−0.0573539
$305$	9911.00	1.86066
$306$	486.000	0.0907934
$307$	600.000	0.111543	0.0557717	−	0.998444i	$-0.482238\pi$
$307$	600.000	0.111543	0.0557717	+	0.998444i	$0.482238\pi$
$308$	1740.00	0.321902
$309$	−2358.00	−0.434116
$310$	−1540.00	−0.282149
$311$	−4963.00	−0.904906	−0.452453	−	0.891788i	$-0.649451\pi$
$311$	−4963.00	−0.904906	−0.452453	+	0.891788i	$0.649451\pi$
$312$	1968.00	0.357103
$313$	5462.00	0.986359	0.493180	−	0.869927i	$-0.335835\pi$
$313$	5462.00	0.986359	0.493180	+	0.869927i	$0.335835\pi$
$314$	3404.00	0.611780
$315$	1485.00	0.265620
$316$	−208.000	−0.0370282
$317$	−984.000	−0.174344	−0.0871718	−	0.996193i	$-0.527783\pi$
$317$	−984.000	−0.174344	−0.0871718	+	0.996193i	$0.527783\pi$
$318$	−3228.00	−0.569237
$319$	3422.00	0.600612
$320$	−704.000	−0.122984
$321$	3930.00	0.683337
$322$	−3000.00	−0.519203
$323$	−513.000	−0.0883718
$324$	324.000	0.0555556
$325$	328.000	0.0559821
$326$	5680.00	0.964988
$327$	3888.00	0.657513
$328$	64.0000	0.0107738
$329$	−5775.00	−0.967739
$330$	−1914.00	−0.319279
$331$	−2632.00	−0.437063	−0.218531	−	0.975830i	$-0.570127\pi$
$331$	−2632.00	−0.437063	−0.218531	+	0.975830i	$0.570127\pi$
$332$	1104.00	0.182500
$333$	2088.00	0.343609
$334$	2388.00	0.391214
$335$	−1452.00	−0.236810
$336$	720.000	0.116902
$337$	−11234.0	−1.81589	−0.907945	−	0.419089i	$-0.862349\pi$
$337$	−11234.0	−1.81589	−0.907945	+	0.419089i	$0.862349\pi$
$338$	9054.00	1.45702
$339$	3390.00	0.543125
$340$	−1188.00	−0.189495
$341$	−2030.00	−0.322377
$342$	−342.000	−0.0540738
$343$	6915.00	1.08856
$344$	−2296.00	−0.359861
$345$	3300.00	0.514974
$346$	−7572.00	−1.17651
$347$	−3211.00	−0.496759	−0.248380	−	0.968663i	$-0.579898\pi$
$347$	−3211.00	−0.496759	−0.248380	+	0.968663i	$0.579898\pi$
$348$	1416.00	0.218119
$349$	2341.00	0.359057	0.179528	−	0.983753i	$-0.442543\pi$
$349$	2341.00	0.359057	0.179528	+	0.983753i	$0.442543\pi$
$350$	120.000	0.0183265
$351$	2214.00	0.336680
$352$	−928.000	−0.140519
$353$	6366.00	0.959853	0.479926	−	0.877309i	$-0.340663\pi$
$353$	6366.00	0.959853	0.479926	+	0.877309i	$0.340663\pi$
$354$	1800.00	0.270251
$355$	−5192.00	−0.776233
$356$	−5208.00	−0.775347
$357$	1215.00	0.180125
$358$	4188.00	0.618276
$359$	−7989.00	−1.17449	−0.587247	−	0.809408i	$-0.699788\pi$
$359$	−7989.00	−1.17449	−0.587247	+	0.809408i	$0.699788\pi$
$360$	−792.000	−0.115950
$361$	361.000	0.0526316
$362$	−700.000	−0.101633
$363$	1470.00	0.212548
$364$	4920.00	0.708456
$365$	12441.0	1.78409
$366$	5406.00	0.772066
$367$	−10544.0	−1.49971	−0.749853	−	0.661604i	$-0.769876\pi$
$367$	−10544.0	−1.49971	−0.749853	+	0.661604i	$0.769876\pi$
$368$	1600.00	0.226646
$369$	72.0000	0.0101576
$370$	−5104.00	−0.717147
$371$	−8070.00	−1.12931
$372$	−840.000	−0.117075
$373$	7616.00	1.05722	0.528608	−	0.848866i	$-0.322714\pi$
$373$	7616.00	1.05722	0.528608	+	0.848866i	$0.322714\pi$
$374$	−1566.00	−0.216513
$375$	−4257.00	−0.586215
$376$	3080.00	0.422444
$377$	9676.00	1.32186
$378$	810.000	0.110217
$379$	5958.00	0.807498	0.403749	−	0.914870i	$-0.367707\pi$
$379$	5958.00	0.807498	0.403749	+	0.914870i	$0.367707\pi$
$380$	836.000	0.112858
$381$	−2250.00	−0.302549
$382$	−2978.00	−0.398868
$383$	−12382.0	−1.65193	−0.825967	−	0.563719i	$-0.809370\pi$
$383$	−12382.0	−1.65193	−0.825967	+	0.563719i	$0.809370\pi$
$384$	−384.000	−0.0510310
$385$	−4785.00	−0.633419
$386$	1200.00	0.158234
$387$	−2583.00	−0.339280
$388$	−5240.00	−0.685620
$389$	7989.00	1.04128	0.520641	−	0.853776i	$-0.325693\pi$
$389$	7989.00	1.04128	0.520641	+	0.853776i	$0.325693\pi$
$390$	−5412.00	−0.702685
$391$	2700.00	0.349220
$392$	−944.000	−0.121631
$393$	3825.00	0.490956
$394$	−580.000	−0.0741624
$395$	572.000	0.0728619
$396$	−1044.00	−0.132482
$397$	7061.00	0.892648	0.446324	−	0.894871i	$-0.352733\pi$
$397$	7061.00	0.892648	0.446324	+	0.894871i	$0.352733\pi$
$398$	8338.00	1.05012
$399$	−855.000	−0.107277
$400$	−64.0000	−0.00800000
$401$	−14512.0	−1.80722	−0.903609	−	0.428357i	$-0.859092\pi$
$401$	−14512.0	−1.80722	−0.903609	+	0.428357i	$0.859092\pi$
$402$	−792.000	−0.0982621
$403$	−5740.00	−0.709503
$404$	−2552.00	−0.314274
$405$	−891.000	−0.109319
$406$	3540.00	0.432727
$407$	−6728.00	−0.819397
$408$	−648.000	−0.0786294
$409$	12634.0	1.52741	0.763705	−	0.645565i	$-0.223378\pi$
$409$	12634.0	1.52741	0.763705	+	0.645565i	$0.223378\pi$
$410$	−176.000	−0.0212000
$411$	−6369.00	−0.764379
$412$	3144.00	0.375956
$413$	4500.00	0.536151
$414$	1800.00	0.213684
$415$	−3036.00	−0.359112
$416$	−2624.00	−0.309260
$417$	−6831.00	−0.802195
$418$	1102.00	0.128949
$419$	−8268.00	−0.964005	−0.482003	−	0.876170i	$-0.660090\pi$
$419$	−8268.00	−0.964005	−0.482003	+	0.876170i	$0.660090\pi$
$420$	−1980.00	−0.230034
$421$	−1534.00	−0.177583	−0.0887917	−	0.996050i	$-0.528301\pi$
$421$	−1534.00	−0.177583	−0.0887917	+	0.996050i	$0.528301\pi$
$422$	−2736.00	−0.315608
$423$	3465.00	0.398284
$424$	4304.00	0.492973
$425$	−108.000	−0.0123265
$426$	−2832.00	−0.322091
$427$	13515.0	1.53170
$428$	−5240.00	−0.591787
$429$	−7134.00	−0.802874
$430$	6314.00	0.708112
$431$	14358.0	1.60464	0.802321	−	0.596893i	$-0.203598\pi$
$431$	14358.0	1.60464	0.802321	+	0.596893i	$0.203598\pi$
$432$	−432.000	−0.0481125
$433$	−4534.00	−0.503210	−0.251605	−	0.967830i	$-0.580958\pi$
$433$	−4534.00	−0.503210	−0.251605	+	0.967830i	$0.580958\pi$
$434$	−2100.00	−0.232265
$435$	−3894.00	−0.429202
$436$	−5184.00	−0.569423
$437$	−1900.00	−0.207985
$438$	6786.00	0.740291
$439$	−12766.0	−1.38790	−0.693950	−	0.720023i	$-0.744131\pi$
$439$	−12766.0	−1.38790	−0.693950	+	0.720023i	$0.744131\pi$
$440$	2552.00	0.276504
$441$	−1062.00	−0.114674
$442$	−4428.00	−0.476512
$443$	−16711.0	−1.79224	−0.896121	−	0.443809i	$-0.853627\pi$
$443$	−16711.0	−1.79224	−0.896121	+	0.443809i	$0.853627\pi$
$444$	−2784.00	−0.297574
$445$	14322.0	1.52568
$446$	5080.00	0.539339
$447$	−6705.00	−0.709476
$448$	−960.000	−0.101240
$449$	3932.00	0.413280	0.206640	−	0.978417i	$-0.433747\pi$
$449$	3932.00	0.413280	0.206640	+	0.978417i	$0.433747\pi$
$450$	−72.0000	−0.00754247
$451$	−232.000	−0.0242227
$452$	−4520.00	−0.470360
$453$	8292.00	0.860027
$454$	−11948.0	−1.23513
$455$	−13530.0	−1.39406
$456$	456.000	0.0468293
$457$	4451.00	0.455600	0.227800	−	0.973708i	$-0.426847\pi$
$457$	4451.00	0.455600	0.227800	+	0.973708i	$0.426847\pi$
$458$	−710.000	−0.0724369
$459$	−729.000	−0.0741325
$460$	−4400.00	−0.445981
$461$	9619.00	0.971804	0.485902	−	0.874013i	$-0.338491\pi$
$461$	9619.00	0.971804	0.485902	+	0.874013i	$0.338491\pi$
$462$	−2610.00	−0.262832
$463$	16603.0	1.66654	0.833269	−	0.552868i	$-0.186467\pi$
$463$	16603.0	1.66654	0.833269	+	0.552868i	$0.186467\pi$
$464$	−1888.00	−0.188897
$465$	2310.00	0.230374
$466$	474.000	0.0471194
$467$	12857.0	1.27399	0.636993	−	0.770870i	$-0.280178\pi$
$467$	12857.0	1.27399	0.636993	+	0.770870i	$0.280178\pi$
$468$	−2952.00	−0.291573
$469$	−1980.00	−0.194942
$470$	−8470.00	−0.831260
$471$	−5106.00	−0.499516
$472$	−2400.00	−0.234044
$473$	8323.00	0.809074
$474$	312.000	0.0302334
$475$	76.0000	0.00734130
$476$	−1620.00	−0.155993
$477$	4842.00	0.464780
$478$	3270.00	0.312900
$479$	11072.0	1.05614	0.528072	−	0.849200i	$-0.322915\pi$
$479$	11072.0	1.05614	0.528072	+	0.849200i	$0.322915\pi$
$480$	1056.00	0.100416
$481$	−19024.0	−1.80337
$482$	−328.000	−0.0309958
$483$	4500.00	0.423928
$484$	−1960.00	−0.184072
$485$	14410.0	1.34912
$486$	−486.000	−0.0453609
$487$	11284.0	1.04995	0.524976	−	0.851117i	$-0.324074\pi$
$487$	11284.0	1.04995	0.524976	+	0.851117i	$0.324074\pi$
$488$	−7208.00	−0.668629
$489$	−8520.00	−0.787909
$490$	2596.00	0.239337
$491$	−11984.0	−1.10149	−0.550744	−	0.834674i	$-0.685656\pi$
$491$	−11984.0	−1.10149	−0.550744	+	0.834674i	$0.685656\pi$
$492$	−96.0000	−0.00879678
$493$	−3186.00	−0.291055
$494$	3116.00	0.283796
$495$	2871.00	0.260691
$496$	1120.00	0.101390
$497$	−7080.00	−0.638997
$498$	−1656.00	−0.149010
$499$	−18701.0	−1.67770	−0.838849	−	0.544364i	$-0.816771\pi$
$499$	−18701.0	−1.67770	−0.838849	+	0.544364i	$0.816771\pi$
$500$	5676.00	0.507677
$501$	−3582.00	−0.319425
$502$	−4198.00	−0.373239
$503$	21888.0	1.94023	0.970117	−	0.242638i	$-0.0780126\pi$
$503$	21888.0	1.94023	0.970117	+	0.242638i	$0.0780126\pi$
$504$	−1080.00	−0.0954504
$505$	7018.00	0.618410
$506$	−5800.00	−0.509568
$507$	−13581.0	−1.18965
$508$	3000.00	0.262015
$509$	−14238.0	−1.23986	−0.619930	−	0.784657i	$-0.712839\pi$
$509$	−14238.0	−1.23986	−0.619930	+	0.784657i	$0.712839\pi$
$510$	1782.00	0.154722
$511$	16965.0	1.46866
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	11072.0	0.950126
$515$	−8646.00	−0.739783
$516$	3444.00	0.293825
$517$	−11165.0	−0.949780
$518$	−6960.00	−0.590357
$519$	11358.0	0.960618
$520$	7216.00	0.608543
$521$	−12992.0	−1.09249	−0.546247	−	0.837624i	$-0.683944\pi$
$521$	−12992.0	−1.09249	−0.546247	+	0.837624i	$0.683944\pi$
$522$	−2124.00	−0.178094
$523$	−9070.00	−0.758324	−0.379162	−	0.925330i	$-0.623788\pi$
$523$	−9070.00	−0.758324	−0.379162	+	0.925330i	$0.623788\pi$
$524$	−5100.00	−0.425180
$525$	−180.000	−0.0149635
$526$	4146.00	0.343677
$527$	1890.00	0.156223
$528$	1392.00	0.114733
$529$	−2167.00	−0.178105
$530$	−11836.0	−0.970043
$531$	−2700.00	−0.220659
$532$	1140.00	0.0929046
$533$	−656.000	−0.0533105
$534$	7812.00	0.633068
$535$	14410.0	1.16448
$536$	1056.00	0.0850975
$537$	−6282.00	−0.504820
$538$	2964.00	0.237523
$539$	3422.00	0.273462
$540$	1188.00	0.0946729
$541$	−2473.00	−0.196530	−0.0982649	−	0.995160i	$-0.531329\pi$
$541$	−2473.00	−0.196530	−0.0982649	+	0.995160i	$0.531329\pi$
$542$	−14536.0	−1.15198
$543$	1050.00	0.0829831
$544$	864.000	0.0680950
$545$	14256.0	1.12048
$546$	−7380.00	−0.578452
$547$	−11282.0	−0.881871	−0.440936	−	0.897539i	$-0.645353\pi$
$547$	−11282.0	−0.881871	−0.440936	+	0.897539i	$0.645353\pi$
$548$	8492.00	0.661971
$549$	−8109.00	−0.630389
$550$	232.000	0.0179864
$551$	2242.00	0.173344
$552$	−2400.00	−0.185056
$553$	780.000	0.0599801
$554$	−9166.00	−0.702935
$555$	7656.00	0.585548
$556$	9108.00	0.694722
$557$	23975.0	1.82379	0.911897	−	0.410419i	$-0.134618\pi$
$557$	23975.0	1.82379	0.911897	+	0.410419i	$0.134618\pi$
$558$	1260.00	0.0955915
$559$	23534.0	1.78065
$560$	2640.00	0.199215
$561$	2349.00	0.176782
$562$	11524.0	0.864965
$563$	17892.0	1.33936	0.669678	−	0.742651i	$-0.266432\pi$
$563$	17892.0	1.33936	0.669678	+	0.742651i	$0.266432\pi$
$564$	−4620.00	−0.344924
$565$	12430.0	0.925547
$566$	7818.00	0.580592
$567$	−1215.00	−0.0899915
$568$	3776.00	0.278939
$569$	10778.0	0.794090	0.397045	−	0.917799i	$-0.370036\pi$
$569$	10778.0	0.794090	0.397045	+	0.917799i	$0.370036\pi$
$570$	−1254.00	−0.0921479
$571$	8984.00	0.658439	0.329220	−	0.944253i	$-0.393214\pi$
$571$	8984.00	0.658439	0.329220	+	0.944253i	$0.393214\pi$
$572$	9512.00	0.695309
$573$	4467.00	0.325675
$574$	−240.000	−0.0174519
$575$	−400.000	−0.0290107
$576$	576.000	0.0416667
$577$	9539.00	0.688239	0.344119	−	0.938926i	$-0.388178\pi$
$577$	9539.00	0.688239	0.344119	+	0.938926i	$0.388178\pi$
$578$	−8368.00	−0.602185
$579$	−1800.00	−0.129198
$580$	5192.00	0.371700
$581$	−4140.00	−0.295622
$582$	7860.00	0.559807
$583$	−15602.0	−1.10835
$584$	−9048.00	−0.641111
$585$	8118.00	0.573740
$586$	−16296.0	−1.14877
$587$	21789.0	1.53208	0.766038	−	0.642796i	$-0.222226\pi$
$587$	21789.0	1.53208	0.766038	+	0.642796i	$0.222226\pi$
$588$	1416.00	0.0993110
$589$	−1330.00	−0.0930419
$590$	6600.00	0.460538
$591$	870.000	0.0605533
$592$	3712.00	0.257707
$593$	5474.00	0.379073	0.189536	−	0.981874i	$-0.439301\pi$
$593$	5474.00	0.379073	0.189536	+	0.981874i	$0.439301\pi$
$594$	1566.00	0.108171
$595$	4455.00	0.306953
$596$	8940.00	0.614424
$597$	−12507.0	−0.857416
$598$	−16400.0	−1.12148
$599$	−17748.0	−1.21062	−0.605312	−	0.795988i	$-0.706952\pi$
$599$	−17748.0	−1.21062	−0.605312	+	0.795988i	$0.706952\pi$
$600$	96.0000	0.00653197
$601$	−8972.00	−0.608944	−0.304472	−	0.952521i	$-0.598480\pi$
$601$	−8972.00	−0.608944	−0.304472	+	0.952521i	$0.598480\pi$
$602$	8610.00	0.582919
$603$	1188.00	0.0802307
$604$	−11056.0	−0.744805
$605$	5390.00	0.362206
$606$	3828.00	0.256604
$607$	−17710.0	−1.18423	−0.592114	−	0.805854i	$-0.701707\pi$
$607$	−17710.0	−1.18423	−0.592114	+	0.805854i	$0.701707\pi$
$608$	−608.000	−0.0405554
$609$	−5310.00	−0.353320
$610$	19822.0	1.31569
$611$	−31570.0	−2.09032
$612$	972.000	0.0642006
$613$	11557.0	0.761473	0.380736	−	0.924684i	$-0.375671\pi$
$613$	11557.0	0.761473	0.380736	+	0.924684i	$0.375671\pi$
$614$	1200.00	0.0788731
$615$	264.000	0.0173098
$616$	3480.00	0.227619
$617$	−4473.00	−0.291858	−0.145929	−	0.989295i	$-0.546617\pi$
$617$	−4473.00	−0.291858	−0.145929	+	0.989295i	$0.546617\pi$
$618$	−4716.00	−0.306967
$619$	1948.00	0.126489	0.0632445	−	0.997998i	$-0.479855\pi$
$619$	1948.00	0.126489	0.0632445	+	0.997998i	$0.479855\pi$
$620$	−3080.00	−0.199509
$621$	−2700.00	−0.174472
$622$	−9926.00	−0.639865
$623$	19530.0	1.25594
$624$	3936.00	0.252510
$625$	−15109.0	−0.966976
$626$	10924.0	0.697461
$627$	−1653.00	−0.105286
$628$	6808.00	0.432594
$629$	6264.00	0.397078
$630$	2970.00	0.187822
$631$	12653.0	0.798269	0.399135	−	0.916892i	$-0.369311\pi$
$631$	12653.0	0.798269	0.399135	+	0.916892i	$0.369311\pi$
$632$	−416.000	−0.0261829
$633$	4104.00	0.257693
$634$	−1968.00	−0.123280
$635$	−8250.00	−0.515577
$636$	−6456.00	−0.402511
$637$	9676.00	0.601848
$638$	6844.00	0.424697
$639$	4248.00	0.262986
$640$	−1408.00	−0.0869626
$641$	−11874.0	−0.731661	−0.365831	−	0.930681i	$-0.619215\pi$
$641$	−11874.0	−0.731661	−0.365831	+	0.930681i	$0.619215\pi$
$642$	7860.00	0.483192
$643$	−26783.0	−1.64264	−0.821321	−	0.570467i	$-0.806762\pi$
$643$	−26783.0	−1.64264	−0.821321	+	0.570467i	$0.806762\pi$
$644$	−6000.00	−0.367132
$645$	−9471.00	−0.578171
$646$	−1026.00	−0.0624883
$647$	−24593.0	−1.49436	−0.747180	−	0.664622i	$-0.768593\pi$
$647$	−24593.0	−1.49436	−0.747180	+	0.664622i	$0.768593\pi$
$648$	648.000	0.0392837
$649$	8700.00	0.526202
$650$	656.000	0.0395853
$651$	3150.00	0.189644
$652$	11360.0	0.682350
$653$	−3261.00	−0.195425	−0.0977127	−	0.995215i	$-0.531153\pi$
$653$	−3261.00	−0.195425	−0.0977127	+	0.995215i	$0.531153\pi$
$654$	7776.00	0.464932
$655$	14025.0	0.836644
$656$	128.000	0.00761823
$657$	−10179.0	−0.604445
$658$	−11550.0	−0.684295
$659$	−20714.0	−1.22444	−0.612218	−	0.790689i	$-0.709722\pi$
$659$	−20714.0	−1.22444	−0.612218	+	0.790689i	$0.709722\pi$
$660$	−3828.00	−0.225765
$661$	−30572.0	−1.79896	−0.899480	−	0.436961i	$-0.856055\pi$
$661$	−30572.0	−1.79896	−0.899480	+	0.436961i	$0.856055\pi$
$662$	−5264.00	−0.309050
$663$	6642.00	0.389071
$664$	2208.00	0.129047
$665$	−3135.00	−0.182812
$666$	4176.00	0.242968
$667$	−11800.0	−0.685004
$668$	4776.00	0.276630
$669$	−7620.00	−0.440368
$670$	−2904.00	−0.167450
$671$	26129.0	1.50328
$672$	1440.00	0.0826625
$673$	−9772.00	−0.559707	−0.279854	−	0.960043i	$-0.590286\pi$
$673$	−9772.00	−0.559707	−0.279854	+	0.960043i	$0.590286\pi$
$674$	−22468.0	−1.28403
$675$	108.000	0.00615840
$676$	18108.0	1.03027
$677$	12350.0	0.701106	0.350553	−	0.936543i	$-0.385994\pi$
$677$	12350.0	0.701106	0.350553	+	0.936543i	$0.385994\pi$
$678$	6780.00	0.384048
$679$	19650.0	1.11060
$680$	−2376.00	−0.133993
$681$	17922.0	1.00848
$682$	−4060.00	−0.227955
$683$	−8686.00	−0.486619	−0.243309	−	0.969949i	$-0.578233\pi$
$683$	−8686.00	−0.486619	−0.243309	+	0.969949i	$0.578233\pi$
$684$	−684.000	−0.0382360
$685$	−23353.0	−1.30259
$686$	13830.0	0.769726
$687$	1065.00	0.0591445
$688$	−4592.00	−0.254460
$689$	−44116.0	−2.43931
$690$	6600.00	0.364142
$691$	−22449.0	−1.23589	−0.617945	−	0.786221i	$-0.712035\pi$
$691$	−22449.0	−1.23589	−0.617945	+	0.786221i	$0.712035\pi$
$692$	−15144.0	−0.831920
$693$	3915.00	0.214601
$694$	−6422.00	−0.351262
$695$	−25047.0	−1.36703
$696$	2832.00	0.154234
$697$	216.000	0.0117383
$698$	4682.00	0.253892
$699$	−711.000	−0.0384728
$700$	240.000	0.0129588
$701$	−16430.0	−0.885239	−0.442619	−	0.896710i	$-0.645951\pi$
$701$	−16430.0	−0.885239	−0.442619	+	0.896710i	$0.645951\pi$
$702$	4428.00	0.238069
$703$	−4408.00	−0.236488
$704$	−1856.00	−0.0993617
$705$	12705.0	0.678721
$706$	12732.0	0.678718
$707$	9570.00	0.509076
$708$	3600.00	0.191096
$709$	−15882.0	−0.841271	−0.420635	−	0.907230i	$-0.638193\pi$
$709$	−15882.0	−0.841271	−0.420635	+	0.907230i	$0.638193\pi$
$710$	−10384.0	−0.548880
$711$	−468.000	−0.0246855
$712$	−10416.0	−0.548253
$713$	7000.00	0.367675
$714$	2430.00	0.127368
$715$	−26158.0	−1.36819
$716$	8376.00	0.437187
$717$	−4905.00	−0.255482
$718$	−15978.0	−0.830493
$719$	19079.0	0.989606	0.494803	−	0.869005i	$-0.335240\pi$
$719$	19079.0	0.989606	0.494803	+	0.869005i	$0.335240\pi$
$720$	−1584.00	−0.0819892
$721$	−11790.0	−0.608991
$722$	722.000	0.0372161
$723$	492.000	0.0253080
$724$	−1400.00	−0.0718655
$725$	472.000	0.0241788
$726$	2940.00	0.150294
$727$	17275.0	0.881285	0.440643	−	0.897683i	$-0.354751\pi$
$727$	17275.0	0.881285	0.440643	+	0.897683i	$0.354751\pi$
$728$	9840.00	0.500954
$729$	729.000	0.0370370
$730$	24882.0	1.26154
$731$	−7749.00	−0.392075
$732$	10812.0	0.545933
$733$	−26358.0	−1.32818	−0.664089	−	0.747653i	$-0.731181\pi$
$733$	−26358.0	−1.32818	−0.664089	+	0.747653i	$0.731181\pi$
$734$	−21088.0	−1.06045
$735$	−3894.00	−0.195418
$736$	3200.00	0.160263
$737$	−3828.00	−0.191325
$738$	144.000	0.00718254
$739$	−1675.00	−0.0833774	−0.0416887	−	0.999131i	$-0.513274\pi$
$739$	−1675.00	−0.0833774	−0.0416887	+	0.999131i	$0.513274\pi$
$740$	−10208.0	−0.507099
$741$	−4674.00	−0.231719
$742$	−16140.0	−0.798542
$743$	26428.0	1.30491	0.652456	−	0.757827i	$-0.273739\pi$
$743$	26428.0	1.30491	0.652456	+	0.757827i	$0.273739\pi$
$744$	−1680.00	−0.0827847
$745$	−24585.0	−1.20903
$746$	15232.0	0.747565
$747$	2484.00	0.121666
$748$	−3132.00	−0.153098
$749$	19650.0	0.958605
$750$	−8514.00	−0.414516
$751$	−21328.0	−1.03631	−0.518156	−	0.855286i	$-0.673381\pi$
$751$	−21328.0	−1.03631	−0.518156	+	0.855286i	$0.673381\pi$
$752$	6160.00	0.298713
$753$	6297.00	0.304748
$754$	19352.0	0.934693
$755$	30404.0	1.46558
$756$	1620.00	0.0779350
$757$	−16229.0	−0.779198	−0.389599	−	0.920985i	$-0.627386\pi$
$757$	−16229.0	−0.779198	−0.389599	+	0.920985i	$0.627386\pi$
$758$	11916.0	0.570988
$759$	8700.00	0.416061
$760$	1672.00	0.0798024
$761$	−4965.00	−0.236506	−0.118253	−	0.992983i	$-0.537729\pi$
$761$	−4965.00	−0.236506	−0.118253	+	0.992983i	$0.537729\pi$
$762$	−4500.00	−0.213934
$763$	19440.0	0.922379
$764$	−5956.00	−0.282043
$765$	−2673.00	−0.126330
$766$	−24764.0	−1.16809
$767$	24600.0	1.15809
$768$	−768.000	−0.0360844
$769$	35275.0	1.65416	0.827080	−	0.562084i	$-0.190000\pi$
$769$	35275.0	1.65416	0.827080	+	0.562084i	$0.190000\pi$
$770$	−9570.00	−0.447895
$771$	−16608.0	−0.775775
$772$	2400.00	0.111888
$773$	4776.00	0.222226	0.111113	−	0.993808i	$-0.464558\pi$
$773$	4776.00	0.222226	0.111113	+	0.993808i	$0.464558\pi$
$774$	−5166.00	−0.239907
$775$	−280.000	−0.0129779
$776$	−10480.0	−0.484807
$777$	10440.0	0.482024
$778$	15978.0	0.736297
$779$	−152.000	−0.00699097
$780$	−10824.0	−0.496874
$781$	−13688.0	−0.627138
$782$	5400.00	0.246936
$783$	3186.00	0.145413
$784$	−1888.00	−0.0860058
$785$	−18722.0	−0.851232
$786$	7650.00	0.347158
$787$	21136.0	0.957328	0.478664	−	0.877998i	$-0.341121\pi$
$787$	21136.0	0.957328	0.478664	+	0.877998i	$0.341121\pi$
$788$	−1160.00	−0.0524407
$789$	−6219.00	−0.280611
$790$	1144.00	0.0515211
$791$	16950.0	0.761912
$792$	−2088.00	−0.0936791
$793$	73882.0	3.30848
$794$	14122.0	0.631198
$795$	17754.0	0.792037
$796$	16676.0	0.742544
$797$	38256.0	1.70025	0.850124	−	0.526583i	$-0.176527\pi$
$797$	38256.0	1.70025	0.850124	+	0.526583i	$0.176527\pi$
$798$	−1710.00	−0.0758563
$799$	10395.0	0.460261
$800$	−128.000	−0.00565685
$801$	−11718.0	−0.516898
$802$	−29024.0	−1.27790
$803$	32799.0	1.44141
$804$	−1584.00	−0.0694818
$805$	16500.0	0.722421
$806$	−11480.0	−0.501694
$807$	−4446.00	−0.193936
$808$	−5104.00	−0.222225
$809$	6189.00	0.268966	0.134483	−	0.990916i	$-0.457063\pi$
$809$	6189.00	0.268966	0.134483	+	0.990916i	$0.457063\pi$
$810$	−1782.00	−0.0773001
$811$	−3030.00	−0.131193	−0.0655966	−	0.997846i	$-0.520895\pi$
$811$	−3030.00	−0.131193	−0.0655966	+	0.997846i	$0.520895\pi$
$812$	7080.00	0.305984
$813$	21804.0	0.940590
$814$	−13456.0	−0.579401
$815$	−31240.0	−1.34269
$816$	−1296.00	−0.0555994
$817$	5453.00	0.233508
$818$	25268.0	1.08004
$819$	11070.0	0.472304
$820$	−352.000	−0.0149907
$821$	38571.0	1.63963	0.819816	−	0.572628i	$-0.194076\pi$
$821$	38571.0	1.63963	0.819816	+	0.572628i	$0.194076\pi$
$822$	−12738.0	−0.540497
$823$	−14287.0	−0.605120	−0.302560	−	0.953130i	$-0.597841\pi$
$823$	−14287.0	−0.605120	−0.302560	+	0.953130i	$0.597841\pi$
$824$	6288.00	0.265841
$825$	−348.000	−0.0146858
$826$	9000.00	0.379116
$827$	23464.0	0.986606	0.493303	−	0.869858i	$-0.335789\pi$
$827$	23464.0	0.986606	0.493303	+	0.869858i	$0.335789\pi$
$828$	3600.00	0.151097
$829$	−38700.0	−1.62136	−0.810679	−	0.585490i	$-0.800902\pi$
$829$	−38700.0	−1.62136	−0.810679	+	0.585490i	$0.800902\pi$
$830$	−6072.00	−0.253930
$831$	13749.0	0.573944
$832$	−5248.00	−0.218680
$833$	−3186.00	−0.132519
$834$	−13662.0	−0.567238
$835$	−13134.0	−0.544336
$836$	2204.00	0.0911805
$837$	−1890.00	−0.0780501
$838$	−16536.0	−0.681655
$839$	−21758.0	−0.895315	−0.447658	−	0.894205i	$-0.647742\pi$
$839$	−21758.0	−0.895315	−0.447658	+	0.894205i	$0.647742\pi$
$840$	−3960.00	−0.162658
$841$	−10465.0	−0.429087
$842$	−3068.00	−0.125570
$843$	−17286.0	−0.706241
$844$	−5472.00	−0.223168
$845$	−49797.0	−2.02730
$846$	6930.00	0.281629
$847$	7350.00	0.298169
$848$	8608.00	0.348585
$849$	−11727.0	−0.474051
$850$	−216.000	−0.00871616
$851$	23200.0	0.934531
$852$	−5664.00	−0.227753
$853$	22770.0	0.913986	0.456993	−	0.889470i	$-0.348926\pi$
$853$	22770.0	0.913986	0.456993	+	0.889470i	$0.348926\pi$
$854$	27030.0	1.08308
$855$	1881.00	0.0752384
$856$	−10480.0	−0.418457
$857$	−38484.0	−1.53394	−0.766971	−	0.641682i	$-0.778237\pi$
$857$	−38484.0	−1.53394	−0.766971	+	0.641682i	$0.778237\pi$
$858$	−14268.0	−0.567717
$859$	23653.0	0.939499	0.469750	−	0.882800i	$-0.344344\pi$
$859$	23653.0	0.939499	0.469750	+	0.882800i	$0.344344\pi$
$860$	12628.0	0.500711
$861$	360.000	0.0142494
$862$	28716.0	1.13465
$863$	29988.0	1.18285	0.591427	−	0.806358i	$-0.298565\pi$
$863$	29988.0	1.18285	0.591427	+	0.806358i	$0.298565\pi$
$864$	−864.000	−0.0340207
$865$	41646.0	1.63700
$866$	−9068.00	−0.355824
$867$	12552.0	0.491682
$868$	−4200.00	−0.164237
$869$	1508.00	0.0588670
$870$	−7788.00	−0.303492
$871$	−10824.0	−0.421076
$872$	−10368.0	−0.402643
$873$	−11790.0	−0.457080
$874$	−3800.00	−0.147067
$875$	−21285.0	−0.822359
$876$	13572.0	0.523465
$877$	−29726.0	−1.14456	−0.572278	−	0.820060i	$-0.693940\pi$
$877$	−29726.0	−1.14456	−0.572278	+	0.820060i	$0.693940\pi$
$878$	−25532.0	−0.981393
$879$	24444.0	0.937970
$880$	5104.00	0.195518
$881$	−28713.0	−1.09803	−0.549016	−	0.835812i	$-0.684997\pi$
$881$	−28713.0	−1.09803	−0.549016	+	0.835812i	$0.684997\pi$
$882$	−2124.00	−0.0810871
$883$	−2771.00	−0.105608	−0.0528038	−	0.998605i	$-0.516816\pi$
$883$	−2771.00	−0.105608	−0.0528038	+	0.998605i	$0.516816\pi$
$884$	−8856.00	−0.336945
$885$	−9900.00	−0.376028
$886$	−33422.0	−1.26731
$887$	23000.0	0.870648	0.435324	−	0.900274i	$-0.356634\pi$
$887$	23000.0	0.870648	0.435324	+	0.900274i	$0.356634\pi$
$888$	−5568.00	−0.210416
$889$	−11250.0	−0.424424
$890$	28644.0	1.07882
$891$	−2349.00	−0.0883215
$892$	10160.0	0.381370
$893$	−7315.00	−0.274118
$894$	−13410.0	−0.501675
$895$	−23034.0	−0.860270
$896$	−1920.00	−0.0715878
$897$	24600.0	0.915686
$898$	7864.00	0.292233
$899$	−8260.00	−0.306437
$900$	−144.000	−0.00533333
$901$	14526.0	0.537105
$902$	−464.000	−0.0171281
$903$	−12915.0	−0.475952
$904$	−9040.00	−0.332595
$905$	3850.00	0.141413
$906$	16584.0	0.608131
$907$	42074.0	1.54029	0.770146	−	0.637868i	$-0.220183\pi$
$907$	42074.0	1.54029	0.770146	+	0.637868i	$0.220183\pi$
$908$	−23896.0	−0.873366
$909$	−5742.00	−0.209516
$910$	−27060.0	−0.985748
$911$	6462.00	0.235012	0.117506	−	0.993072i	$-0.462510\pi$
$911$	6462.00	0.235012	0.117506	+	0.993072i	$0.462510\pi$
$912$	912.000	0.0331133
$913$	−8004.00	−0.290136
$914$	8902.00	0.322158
$915$	−29733.0	−1.07425
$916$	−1420.00	−0.0512207
$917$	19125.0	0.688728
$918$	−1458.00	−0.0524196
$919$	24776.0	0.889320	0.444660	−	0.895700i	$-0.353325\pi$
$919$	24776.0	0.889320	0.444660	+	0.895700i	$0.353325\pi$
$920$	−8800.00	−0.315356
$921$	−1800.00	−0.0643996
$922$	19238.0	0.687169
$923$	−38704.0	−1.38024
$924$	−5220.00	−0.185850
$925$	−928.000	−0.0329864
$926$	33206.0	1.17842
$927$	7074.00	0.250637
$928$	−3776.00	−0.133570
$929$	15022.0	0.530523	0.265261	−	0.964177i	$-0.414542\pi$
$929$	15022.0	0.530523	0.265261	+	0.964177i	$0.414542\pi$
$930$	4620.00	0.162899
$931$	2242.00	0.0789244
$932$	948.000	0.0333184
$933$	14889.0	0.522448
$934$	25714.0	0.900843
$935$	8613.00	0.301257
$936$	−5904.00	−0.206173
$937$	26285.0	0.916429	0.458214	−	0.888842i	$-0.348489\pi$
$937$	26285.0	0.916429	0.458214	+	0.888842i	$0.348489\pi$
$938$	−3960.00	−0.137845
$939$	−16386.0	−0.569475
$940$	−16940.0	−0.587789
$941$	−18622.0	−0.645122	−0.322561	−	0.946549i	$-0.604544\pi$
$941$	−18622.0	−0.645122	−0.322561	+	0.946549i	$0.604544\pi$
$942$	−10212.0	−0.353211
$943$	800.000	0.0276263
$944$	−4800.00	−0.165494
$945$	−4455.00	−0.153356
$946$	16646.0	0.572102
$947$	−3660.00	−0.125590	−0.0627952	−	0.998026i	$-0.520001\pi$
$947$	−3660.00	−0.125590	−0.0627952	+	0.998026i	$0.520001\pi$
$948$	624.000	0.0213782
$949$	92742.0	3.17232
$950$	152.000	0.00519109
$951$	2952.00	0.100657
$952$	−3240.00	−0.110304
$953$	−30044.0	−1.02122	−0.510609	−	0.859813i	$-0.670580\pi$
$953$	−30044.0	−1.02122	−0.510609	+	0.859813i	$0.670580\pi$
$954$	9684.00	0.328649
$955$	16379.0	0.554986
$956$	6540.00	0.221254
$957$	−10266.0	−0.346763
$958$	22144.0	0.746806
$959$	−31845.0	−1.07229
$960$	2112.00	0.0710047
$961$	−24891.0	−0.835521
$962$	−38048.0	−1.27517
$963$	−11790.0	−0.394525
$964$	−656.000	−0.0219174
$965$	−6600.00	−0.220167
$966$	9000.00	0.299762
$967$	−6288.00	−0.209109	−0.104555	−	0.994519i	$-0.533342\pi$
$967$	−6288.00	−0.209109	−0.104555	+	0.994519i	$0.533342\pi$
$968$	−3920.00	−0.130159
$969$	1539.00	0.0510215
$970$	28820.0	0.953974
$971$	39028.0	1.28987	0.644937	−	0.764236i	$-0.276883\pi$
$971$	39028.0	1.28987	0.644937	+	0.764236i	$0.276883\pi$
$972$	−972.000	−0.0320750
$973$	−34155.0	−1.12534
$974$	22568.0	0.742429
$975$	−984.000	−0.0323213
$976$	−14416.0	−0.472792
$977$	1678.00	0.0549478	0.0274739	−	0.999623i	$-0.491254\pi$
$977$	1678.00	0.0549478	0.0274739	+	0.999623i	$0.491254\pi$
$978$	−17040.0	−0.557136
$979$	37758.0	1.23264
$980$	5192.00	0.169237
$981$	−11664.0	−0.379616
$982$	−23968.0	−0.778869
$983$	−39972.0	−1.29696	−0.648479	−	0.761233i	$-0.724594\pi$
$983$	−39972.0	−1.29696	−0.648479	+	0.761233i	$0.724594\pi$
$984$	−192.000	−0.00622026
$985$	3190.00	0.103190
$986$	−6372.00	−0.205807
$987$	17325.0	0.558724
$988$	6232.00	0.200674
$989$	−28700.0	−0.922757
$990$	5742.00	0.184336
$991$	−23672.0	−0.758795	−0.379398	−	0.925234i	$-0.623869\pi$
$991$	−23672.0	−0.758795	−0.379398	+	0.925234i	$0.623869\pi$
$992$	2240.00	0.0716936
$993$	7896.00	0.252338
$994$	−14160.0	−0.451839
$995$	−45859.0	−1.46113
$996$	−3312.00	−0.105366
$997$	−36899.0	−1.17212	−0.586060	−	0.810268i	$-0.699322\pi$
$997$	−36899.0	−1.17212	−0.586060	+	0.810268i	$0.699322\pi$
$998$	−37402.0	−1.18631
$999$	−6264.00	−0.198383

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.a.d.1.1	✓	1
3.2	odd	2		342.4.a.a.1.1		1
4.3	odd	2		912.4.a.f.1.1		1
19.18	odd	2		2166.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.a.d.1.1	✓	1	1.1	even	1	trivial
342.4.a.a.1.1		1	3.2	odd	2
912.4.a.f.1.1		1	4.3	odd	2
2166.4.a.a.1.1		1	19.18	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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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