LMFDB - Embedded newform 98.10.a.b.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,16,-170] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$50.4735119441$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	98.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q+16.0000 q^{2} -170.000 q^{3} +256.000 q^{4} -544.000 q^{5} -2720.00 q^{6} +4096.00 q^{8} +9217.00 q^{9} -8704.00 q^{10} +48824.0 q^{11} -43520.0 q^{12} +15876.0 q^{13} +92480.0 q^{15} +65536.0 q^{16} +21418.0 q^{17} +147472. q^{18} +716410. q^{19} -139264. q^{20} +781184. q^{22} -2.47000e6 q^{23} -696320. q^{24} -1.65719e6 q^{25} +254016. q^{26} +1.77922e6 q^{27} +5.55683e6 q^{29} +1.47968e6 q^{30} -5.79935e6 q^{31} +1.04858e6 q^{32} -8.30008e6 q^{33} +342688. q^{34} +2.35955e6 q^{36} -3.89443e6 q^{37} +1.14626e7 q^{38} -2.69892e6 q^{39} -2.22822e6 q^{40} +6.36086e6 q^{41} -1.87013e7 q^{43} +1.24989e7 q^{44} -5.01405e6 q^{45} -3.95200e7 q^{46} -5.65391e7 q^{47} -1.11411e7 q^{48} -2.65150e7 q^{50} -3.64106e6 q^{51} +4.06426e6 q^{52} -5.98947e7 q^{53} +2.84675e7 q^{54} -2.65603e7 q^{55} -1.21790e8 q^{57} +8.89092e7 q^{58} -1.65630e8 q^{59} +2.36749e7 q^{60} -5.14190e7 q^{61} -9.27896e7 q^{62} +1.67772e7 q^{64} -8.63654e6 q^{65} -1.32801e8 q^{66} +9.35465e7 q^{67} +5.48301e6 q^{68} +4.19900e8 q^{69} -9.56335e7 q^{71} +3.77528e7 q^{72} -3.06496e8 q^{73} -6.23109e7 q^{74} +2.81722e8 q^{75} +1.83401e8 q^{76} -4.31827e7 q^{78} +4.96474e8 q^{79} -3.56516e7 q^{80} -4.83886e8 q^{81} +1.01774e8 q^{82} +3.71487e8 q^{83} -1.16514e7 q^{85} -2.99221e8 q^{86} -9.44660e8 q^{87} +1.99983e8 q^{88} +1.65483e8 q^{89} -8.02248e7 q^{90} -6.32320e8 q^{92} +9.85889e8 q^{93} -9.04625e8 q^{94} -3.89727e8 q^{95} -1.78258e8 q^{96} -7.58017e8 q^{97} +4.50011e8 q^{99} +O(q^{100})\)

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−170.000	−1.21172	−0.605861	−	0.795570i	$-0.707171\pi$
$3$	−170.000	−1.21172	−0.605861	+	0.795570i	$0.707171\pi$
$4$	256.000	0.500000
$5$	−544.000	−0.389255	−0.194627	−	0.980877i	$-0.562350\pi$
$5$	−544.000	−0.389255	−0.194627	+	0.980877i	$0.562350\pi$
$6$	−2720.00	−0.856817
$7$	0	0
$7$	0	0
$8$	4096.00	0.353553
$9$	9217.00	0.468272
$10$	−8704.00	−0.275245
$11$	48824.0	1.00546	0.502732	−	0.864442i	$-0.332328\pi$
$11$	48824.0	1.00546	0.502732	+	0.864442i	$0.332328\pi$
$12$	−43520.0	−0.605861
$13$	15876.0	0.154169	0.0770843	−	0.997025i	$-0.475439\pi$
$13$	15876.0	0.154169	0.0770843	+	0.997025i	$0.475439\pi$
$14$	0	0
$15$	92480.0	0.471669
$16$	65536.0	0.250000
$17$	21418.0	0.0621955	0.0310977	−	0.999516i	$-0.490100\pi$
$17$	21418.0	0.0621955	0.0310977	+	0.999516i	$0.490100\pi$
$18$	147472.	0.331118
$19$	716410.	1.26116	0.630580	−	0.776124i	$-0.282817\pi$
$19$	716410.	1.26116	0.630580	+	0.776124i	$0.282817\pi$
$20$	−139264.	−0.194627
$21$	0	0
$22$	781184.	0.710970
$23$	−2.47000e6	−1.84044	−0.920220	−	0.391401i	$-0.871990\pi$
$23$	−2.47000e6	−1.84044	−0.920220	+	0.391401i	$0.871990\pi$
$24$	−696320.	−0.428409
$25$	−1.65719e6	−0.848481
$26$	254016.	0.109014
$27$	1.77922e6	0.644307
$28$	0	0
$29$	5.55683e6	1.45893	0.729467	−	0.684016i	$-0.239768\pi$
$29$	5.55683e6	1.45893	0.729467	+	0.684016i	$0.239768\pi$
$30$	1.47968e6	0.333520
$31$	−5.79935e6	−1.12785	−0.563925	−	0.825826i	$-0.690709\pi$
$31$	−5.79935e6	−1.12785	−0.563925	+	0.825826i	$0.690709\pi$
$32$	1.04858e6	0.176777
$33$	−8.30008e6	−1.21834
$34$	342688.	0.0439788
$35$	0	0
$36$	2.35955e6	0.234136
$37$	−3.89443e6	−0.341614	−0.170807	−	0.985304i	$-0.554638\pi$
$37$	−3.89443e6	−0.341614	−0.170807	+	0.985304i	$0.554638\pi$
$38$	1.14626e7	0.891775
$39$	−2.69892e6	−0.186810
$40$	−2.22822e6	−0.137622
$41$	6.36086e6	0.351551	0.175776	−	0.984430i	$-0.443757\pi$
$41$	6.36086e6	0.351551	0.175776	+	0.984430i	$0.443757\pi$
$42$	0	0
$43$	−1.87013e7	−0.834187	−0.417094	−	0.908863i	$-0.636951\pi$
$43$	−1.87013e7	−0.834187	−0.417094	+	0.908863i	$0.636951\pi$
$44$	1.24989e7	0.502732
$45$	−5.01405e6	−0.182277
$46$	−3.95200e7	−1.30139
$47$	−5.65391e7	−1.69008	−0.845042	−	0.534700i	$-0.820425\pi$
$47$	−5.65391e7	−1.69008	−0.845042	+	0.534700i	$0.820425\pi$
$48$	−1.11411e7	−0.302931
$49$	0	0
$50$	−2.65150e7	−0.599967
$51$	−3.64106e6	−0.0753637
$52$	4.06426e6	0.0770843
$53$	−5.98947e7	−1.04267	−0.521335	−	0.853352i	$-0.674566\pi$
$53$	−5.98947e7	−1.04267	−0.521335	+	0.853352i	$0.674566\pi$
$54$	2.84675e7	0.455594
$55$	−2.65603e7	−0.391381
$56$	0	0
$57$	−1.21790e8	−1.52818
$58$	8.89092e7	1.03162
$59$	−1.65630e8	−1.77952	−0.889762	−	0.456424i	$-0.849130\pi$
$59$	−1.65630e8	−1.77952	−0.889762	+	0.456424i	$0.849130\pi$
$60$	2.36749e7	0.235834
$61$	−5.14190e7	−0.475488	−0.237744	−	0.971328i	$-0.576408\pi$
$61$	−5.14190e7	−0.475488	−0.237744	+	0.971328i	$0.576408\pi$
$62$	−9.27896e7	−0.797511
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−8.63654e6	−0.0600109
$66$	−1.32801e8	−0.861499
$67$	9.35465e7	0.567141	0.283570	−	0.958951i	$-0.408481\pi$
$67$	9.35465e7	0.567141	0.283570	+	0.958951i	$0.408481\pi$
$68$	5.48301e6	0.0310977
$69$	4.19900e8	2.23010
$70$	0	0
$71$	−9.56335e7	−0.446630	−0.223315	−	0.974746i	$-0.571688\pi$
$71$	−9.56335e7	−0.446630	−0.223315	+	0.974746i	$0.571688\pi$
$72$	3.77528e7	0.165559
$73$	−3.06496e8	−1.26320	−0.631601	−	0.775294i	$-0.717602\pi$
$73$	−3.06496e8	−1.26320	−0.631601	+	0.775294i	$0.717602\pi$
$74$	−6.23109e7	−0.241558
$75$	2.81722e8	1.02812
$76$	1.83401e8	0.630580
$77$	0	0
$78$	−4.31827e7	−0.132094
$79$	4.96474e8	1.43408	0.717042	−	0.697030i	$-0.245495\pi$
$79$	4.96474e8	1.43408	0.717042	+	0.697030i	$0.245495\pi$
$80$	−3.56516e7	−0.0973137
$81$	−4.83886e8	−1.24899
$82$	1.01774e8	0.248584
$83$	3.71487e8	0.859196	0.429598	−	0.903020i	$-0.358655\pi$
$83$	3.71487e8	0.859196	0.429598	+	0.903020i	$0.358655\pi$
$84$	0	0
$85$	−1.16514e7	−0.0242099
$86$	−2.99221e8	−0.589860
$87$	−9.44660e8	−1.76782
$88$	1.99983e8	0.355485
$89$	1.65483e8	0.279574	0.139787	−	0.990182i	$-0.455358\pi$
$89$	1.65483e8	0.279574	0.139787	+	0.990182i	$0.455358\pi$
$90$	−8.02248e7	−0.128889
$91$	0	0
$92$	−6.32320e8	−0.920220
$93$	9.85889e8	1.36664
$94$	−9.04625e8	−1.19507
$95$	−3.89727e8	−0.490913
$96$	−1.78258e8	−0.214204
$97$	−7.58017e8	−0.869373	−0.434686	−	0.900582i	$-0.643141\pi$
$97$	−7.58017e8	−0.869373	−0.434686	+	0.900582i	$0.643141\pi$
$98$	0	0
$99$	4.50011e8	0.470830
$100$	−4.24240e8	−0.424240
$101$	9.04212e8	0.864618	0.432309	−	0.901726i	$-0.357699\pi$
$101$	9.04212e8	0.864618	0.432309	+	0.901726i	$0.357699\pi$
$102$	−5.82570e7	−0.0532902
$103$	−1.98157e9	−1.73477	−0.867384	−	0.497639i	$-0.834200\pi$
$103$	−1.98157e9	−1.73477	−0.867384	+	0.497639i	$0.834200\pi$
$104$	6.50281e7	0.0545068
$105$	0	0
$106$	−9.58315e8	−0.737279
$107$	4.16379e8	0.307087	0.153544	−	0.988142i	$-0.450931\pi$
$107$	4.16379e8	0.307087	0.153544	+	0.988142i	$0.450931\pi$
$108$	4.55480e8	0.322153
$109$	−1.26921e9	−0.861220	−0.430610	−	0.902538i	$-0.641701\pi$
$109$	−1.26921e9	−0.861220	−0.430610	+	0.902538i	$0.641701\pi$
$110$	−4.24964e8	−0.276748
$111$	6.62053e8	0.413942
$112$	0	0
$113$	−2.83528e9	−1.63585	−0.817923	−	0.575328i	$-0.804874\pi$
$113$	−2.83528e9	−1.63585	−0.817923	+	0.575328i	$0.804874\pi$
$114$	−1.94864e9	−1.08058
$115$	1.34368e9	0.716400
$116$	1.42255e9	0.729467
$117$	1.46329e8	0.0721929
$118$	−2.65007e9	−1.25831
$119$	0	0
$120$	3.78798e8	0.166760
$121$	2.58353e7	0.0109567
$122$	−8.22704e8	−0.336221
$123$	−1.08135e9	−0.425982
$124$	−1.48463e9	−0.563925
$125$	1.96401e9	0.719530
$126$	0	0
$127$	5.44282e9	1.85655	0.928277	−	0.371889i	$-0.121290\pi$
$127$	5.44282e9	1.85655	0.928277	+	0.371889i	$0.121290\pi$
$128$	2.68435e8	0.0883883
$129$	3.17922e9	1.01080
$130$	−1.38185e8	−0.0424341
$131$	6.44057e8	0.191075	0.0955374	−	0.995426i	$-0.469543\pi$
$131$	6.44057e8	0.191075	0.0955374	+	0.995426i	$0.469543\pi$
$132$	−2.12482e9	−0.609171
$133$	0	0
$134$	1.49674e9	0.401029
$135$	−9.67896e8	−0.250799
$136$	8.77281e7	0.0219894
$137$	1.67376e9	0.405928	0.202964	−	0.979186i	$-0.434942\pi$
$137$	1.67376e9	0.405928	0.202964	+	0.979186i	$0.434942\pi$
$138$	6.71840e9	1.57692
$139$	4.17330e9	0.948229	0.474115	−	0.880463i	$-0.342768\pi$
$139$	4.17330e9	0.948229	0.474115	+	0.880463i	$0.342768\pi$
$140$	0	0
$141$	9.61164e9	2.04791
$142$	−1.53014e9	−0.315815
$143$	7.75130e8	0.155011
$144$	6.04045e8	0.117068
$145$	−3.02291e9	−0.567897
$146$	−4.90394e9	−0.893218
$147$	0	0
$148$	−9.96974e8	−0.170807
$149$	−4.64096e8	−0.0771382	−0.0385691	−	0.999256i	$-0.512280\pi$
$149$	−4.64096e8	−0.0771382	−0.0385691	+	0.999256i	$0.512280\pi$
$150$	4.50755e9	0.726993
$151$	7.31929e9	1.14571	0.572853	−	0.819658i	$-0.305837\pi$
$151$	7.31929e9	1.14571	0.572853	+	0.819658i	$0.305837\pi$
$152$	2.93442e9	0.445888
$153$	1.97410e8	0.0291244
$154$	0	0
$155$	3.15485e9	0.439021
$156$	−6.90924e8	−0.0934048
$157$	4.43050e9	0.581975	0.290987	−	0.956727i	$-0.406016\pi$
$157$	4.43050e9	0.581975	0.290987	+	0.956727i	$0.406016\pi$
$158$	7.94359e9	1.01405
$159$	1.01821e10	1.26343
$160$	−5.70425e8	−0.0688112
$161$	0	0
$162$	−7.74217e9	−0.883172
$163$	−1.33645e10	−1.48289	−0.741446	−	0.671013i	$-0.765860\pi$
$163$	−1.33645e10	−1.48289	−0.741446	+	0.671013i	$0.765860\pi$
$164$	1.62838e9	0.175776
$165$	4.51524e9	0.474246
$166$	5.94379e9	0.607543
$167$	1.24456e10	1.23821	0.619103	−	0.785310i	$-0.287496\pi$
$167$	1.24456e10	1.23821	0.619103	+	0.785310i	$0.287496\pi$
$168$	0	0
$169$	−1.03525e10	−0.976232
$170$	−1.86422e8	−0.0171190
$171$	6.60315e9	0.590566
$172$	−4.78753e9	−0.417094
$173$	−1.04544e10	−0.887345	−0.443672	−	0.896189i	$-0.646325\pi$
$173$	−1.04544e10	−0.887345	−0.443672	+	0.896189i	$0.646325\pi$
$174$	−1.51146e10	−1.25004
$175$	0	0
$176$	3.19973e9	0.251366
$177$	2.81570e10	2.15629
$178$	2.64772e9	0.197689
$179$	−4.04391e9	−0.294417	−0.147208	−	0.989105i	$-0.547029\pi$
$179$	−4.04391e9	−0.294417	−0.147208	+	0.989105i	$0.547029\pi$
$180$	−1.28360e9	−0.0911386
$181$	−1.24735e10	−0.863843	−0.431922	−	0.901911i	$-0.642164\pi$
$181$	−1.24735e10	−0.863843	−0.431922	+	0.901911i	$0.642164\pi$
$182$	0	0
$183$	8.74123e9	0.576160
$184$	−1.01171e10	−0.650694
$185$	2.11857e9	0.132975
$186$	1.57742e10	0.966362
$187$	1.04571e9	0.0625353
$188$	−1.44740e10	−0.845042
$189$	0	0
$190$	−6.23563e9	−0.347128
$191$	−3.81947e9	−0.207660	−0.103830	−	0.994595i	$-0.533110\pi$
$191$	−3.81947e9	−0.207660	−0.103830	+	0.994595i	$0.533110\pi$
$192$	−2.85213e9	−0.151465
$193$	−2.41193e10	−1.25129	−0.625644	−	0.780109i	$-0.715164\pi$
$193$	−2.41193e10	−1.25129	−0.625644	+	0.780109i	$0.715164\pi$
$194$	−1.21283e10	−0.614739
$195$	1.46821e9	0.0727165
$196$	0	0
$197$	−1.24798e10	−0.590351	−0.295176	−	0.955443i	$-0.595378\pi$
$197$	−1.24798e10	−0.590351	−0.295176	+	0.955443i	$0.595378\pi$
$198$	7.20017e9	0.332927
$199$	2.93127e9	0.132500	0.0662502	−	0.997803i	$-0.478896\pi$
$199$	2.93127e9	0.132500	0.0662502	+	0.997803i	$0.478896\pi$
$200$	−6.78785e9	−0.299983
$201$	−1.59029e10	−0.687218
$202$	1.44674e10	0.611377
$203$	0	0
$204$	−9.32111e8	−0.0376818
$205$	−3.46031e9	−0.136843
$206$	−3.17051e10	−1.22667
$207$	−2.27660e10	−0.861827
$208$	1.04045e9	0.0385422
$209$	3.49780e10	1.26805
$210$	0	0
$211$	3.36978e10	1.17039	0.585195	−	0.810892i	$-0.301018\pi$
$211$	3.36978e10	1.17039	0.585195	+	0.810892i	$0.301018\pi$
$212$	−1.53330e10	−0.521335
$213$	1.62577e10	0.541191
$214$	6.66206e9	0.217143
$215$	1.01735e10	0.324711
$216$	7.28769e9	0.227797
$217$	0	0
$218$	−2.03073e10	−0.608974
$219$	5.21044e10	1.53065
$220$	−6.79943e9	−0.195691
$221$	3.40032e8	0.00958859
$222$	1.05928e10	0.292701
$223$	3.87208e10	1.04851	0.524255	−	0.851561i	$-0.324344\pi$
$223$	3.87208e10	1.04851	0.524255	+	0.851561i	$0.324344\pi$
$224$	0	0
$225$	−1.52743e10	−0.397320
$226$	−4.53644e10	−1.15672
$227$	−7.69011e10	−1.92228	−0.961139	−	0.276063i	$-0.910970\pi$
$227$	−7.69011e10	−1.92228	−0.961139	+	0.276063i	$0.910970\pi$
$228$	−3.11782e10	−0.764089
$229$	−4.35114e10	−1.04555	−0.522773	−	0.852472i	$-0.675103\pi$
$229$	−4.35114e10	−1.04555	−0.522773	+	0.852472i	$0.675103\pi$
$230$	2.14989e10	0.506571
$231$	0	0
$232$	2.27608e10	0.515811
$233$	−2.07043e10	−0.460213	−0.230107	−	0.973165i	$-0.573907\pi$
$233$	−2.07043e10	−0.460213	−0.230107	+	0.973165i	$0.573907\pi$
$234$	2.34127e9	0.0510481
$235$	3.07573e10	0.657873
$236$	−4.24012e10	−0.889762
$237$	−8.44006e10	−1.73771
$238$	0	0
$239$	2.16220e10	0.428653	0.214326	−	0.976762i	$-0.431244\pi$
$239$	2.16220e10	0.428653	0.214326	+	0.976762i	$0.431244\pi$
$240$	6.06077e9	0.117917
$241$	−6.77789e10	−1.29425	−0.647124	−	0.762385i	$-0.724029\pi$
$241$	−6.77789e10	−1.29425	−0.647124	+	0.762385i	$0.724029\pi$
$242$	4.13365e8	0.00774754
$243$	4.72402e10	0.869127
$244$	−1.31633e10	−0.237744
$245$	0	0
$246$	−1.73015e10	−0.301215
$247$	1.13737e10	0.194431
$248$	−2.37541e10	−0.398755
$249$	−6.31528e10	−1.04111
$250$	3.14242e10	0.508784
$251$	−4.87895e9	−0.0775881	−0.0387940	−	0.999247i	$-0.512352\pi$
$251$	−4.87895e9	−0.0775881	−0.0387940	+	0.999247i	$0.512352\pi$
$252$	0	0
$253$	−1.20595e11	−1.85050
$254$	8.70852e10	1.31278
$255$	1.98074e9	0.0293357
$256$	4.29497e9	0.0625000
$257$	2.75029e10	0.393259	0.196630	−	0.980478i	$-0.437000\pi$
$257$	2.75029e10	0.393259	0.196630	+	0.980478i	$0.437000\pi$
$258$	5.08675e10	0.714746
$259$	0	0
$260$	−2.21096e9	−0.0300054
$261$	5.12173e10	0.683178
$262$	1.03049e10	0.135110
$263$	−2.22595e10	−0.286889	−0.143445	−	0.989658i	$-0.545818\pi$
$263$	−2.22595e10	−0.286889	−0.143445	+	0.989658i	$0.545818\pi$
$264$	−3.39971e10	−0.430749
$265$	3.25827e10	0.405864
$266$	0	0
$267$	−2.81320e10	−0.338766
$268$	2.39479e10	0.283570
$269$	−1.73017e10	−0.201466	−0.100733	−	0.994913i	$-0.532119\pi$
$269$	−1.73017e10	−0.201466	−0.100733	+	0.994913i	$0.532119\pi$
$270$	−1.54863e10	−0.177342
$271$	−4.81901e10	−0.542745	−0.271372	−	0.962474i	$-0.587477\pi$
$271$	−4.81901e10	−0.542745	−0.271372	+	0.962474i	$0.587477\pi$
$272$	1.40365e9	0.0155489
$273$	0	0
$274$	2.67801e10	0.287035
$275$	−8.09106e10	−0.853116
$276$	1.07494e11	1.11505
$277$	8.03834e10	0.820365	0.410183	−	0.912003i	$-0.365465\pi$
$277$	8.03834e10	0.820365	0.410183	+	0.912003i	$0.365465\pi$
$278$	6.67728e10	0.670499
$279$	−5.34526e10	−0.528141
$280$	0	0
$281$	−1.95595e11	−1.87146	−0.935729	−	0.352719i	$-0.885257\pi$
$281$	−1.95595e11	−1.87146	−0.935729	+	0.352719i	$0.885257\pi$
$282$	1.53786e11	1.44809
$283$	6.02802e10	0.558645	0.279322	−	0.960197i	$-0.409890\pi$
$283$	6.02802e10	0.558645	0.279322	+	0.960197i	$0.409890\pi$
$284$	−2.44822e10	−0.223315
$285$	6.62536e10	0.594850
$286$	1.24021e10	0.109609
$287$	0	0
$288$	9.66472e9	0.0827796
$289$	−1.18129e11	−0.996132
$290$	−4.83666e10	−0.401564
$291$	1.28863e11	1.05344
$292$	−7.84631e10	−0.631601
$293$	4.86743e10	0.385830	0.192915	−	0.981216i	$-0.438206\pi$
$293$	4.86743e10	0.385830	0.192915	+	0.981216i	$0.438206\pi$
$294$	0	0
$295$	9.01025e10	0.692688
$296$	−1.59516e10	−0.120779
$297$	8.68686e10	0.647827
$298$	−7.42553e9	−0.0545449
$299$	−3.92137e10	−0.283738
$300$	7.21209e10	0.514062
$301$	0	0
$302$	1.17109e11	0.810136
$303$	−1.53716e11	−1.04768
$304$	4.69506e10	0.315290
$305$	2.79719e10	0.185086
$306$	3.15856e9	0.0205941
$307$	−2.75178e11	−1.76804	−0.884018	−	0.467453i	$-0.845172\pi$
$307$	−2.75178e11	−1.76804	−0.884018	+	0.467453i	$0.845172\pi$
$308$	0	0
$309$	3.36867e11	2.10206
$310$	5.04775e10	0.310435
$311$	−1.12322e11	−0.680835	−0.340418	−	0.940274i	$-0.610568\pi$
$311$	−1.12322e11	−0.680835	−0.340418	+	0.940274i	$0.610568\pi$
$312$	−1.10548e10	−0.0660472
$313$	1.06140e11	0.625069	0.312535	−	0.949906i	$-0.398822\pi$
$313$	1.06140e11	0.625069	0.312535	+	0.949906i	$0.398822\pi$
$314$	7.08880e10	0.411518
$315$	0	0
$316$	1.27097e11	0.717042
$317$	2.31358e9	0.0128682	0.00643409	−	0.999979i	$-0.497952\pi$
$317$	2.31358e9	0.0128682	0.00643409	+	0.999979i	$0.497952\pi$
$318$	1.62914e11	0.893378
$319$	2.71306e11	1.46691
$320$	−9.12681e9	−0.0486568
$321$	−7.07844e10	−0.372105
$322$	0	0
$323$	1.53441e10	0.0784385
$324$	−1.23875e11	−0.624497
$325$	−2.63095e10	−0.130809
$326$	−2.13832e11	−1.04856
$327$	2.15766e11	1.04356
$328$	2.60541e10	0.124292
$329$	0	0
$330$	7.22439e10	0.335342
$331$	−2.16185e11	−0.989921	−0.494960	−	0.868916i	$-0.664817\pi$
$331$	−2.16185e11	−0.989921	−0.494960	+	0.868916i	$0.664817\pi$
$332$	9.51007e10	0.429598
$333$	−3.58950e10	−0.159968
$334$	1.99130e11	0.875544
$335$	−5.08893e10	−0.220762
$336$	0	0
$337$	5.00291e10	0.211294	0.105647	−	0.994404i	$-0.466309\pi$
$337$	5.00291e10	0.211294	0.105647	+	0.994404i	$0.466309\pi$
$338$	−1.65639e11	−0.690300
$339$	4.81997e11	1.98219
$340$	−2.98276e9	−0.0121049
$341$	−2.83147e11	−1.13401
$342$	1.05650e11	0.417594
$343$	0	0
$344$	−7.66005e10	−0.294930
$345$	−2.28426e11	−0.868078
$346$	−1.67271e11	−0.627448
$347$	−1.84606e11	−0.683541	−0.341770	−	0.939784i	$-0.611026\pi$
$347$	−1.84606e11	−0.683541	−0.341770	+	0.939784i	$0.611026\pi$
$348$	−2.41833e11	−0.883912
$349$	−2.74666e11	−0.991039	−0.495520	−	0.868597i	$-0.665022\pi$
$349$	−2.74666e11	−0.991039	−0.495520	+	0.868597i	$0.665022\pi$
$350$	0	0
$351$	2.82469e10	0.0993319
$352$	5.11957e10	0.177743
$353$	1.58053e11	0.541774	0.270887	−	0.962611i	$-0.412683\pi$
$353$	1.58053e11	0.541774	0.270887	+	0.962611i	$0.412683\pi$
$354$	4.50513e11	1.52473
$355$	5.20246e10	0.173853
$356$	4.23635e10	0.139787
$357$	0	0
$358$	−6.47025e10	−0.208184
$359$	3.40759e11	1.08274	0.541368	−	0.840786i	$-0.317907\pi$
$359$	3.40759e11	1.08274	0.541368	+	0.840786i	$0.317907\pi$
$360$	−2.05375e10	−0.0644447
$361$	1.90556e11	0.590526
$362$	−1.99576e11	−0.610829
$363$	−4.39200e9	−0.0132765
$364$	0	0
$365$	1.66734e11	0.491707
$366$	1.39860e11	0.407406
$367$	6.10216e11	1.75584	0.877922	−	0.478803i	$-0.158929\pi$
$367$	6.10216e11	1.75584	0.877922	+	0.478803i	$0.158929\pi$
$368$	−1.61874e11	−0.460110
$369$	5.86280e10	0.164622
$370$	3.38971e10	0.0940275
$371$	0	0
$372$	2.52388e11	0.683321
$373$	4.34930e11	1.16340	0.581701	−	0.813402i	$-0.302387\pi$
$373$	4.34930e11	1.16340	0.581701	+	0.813402i	$0.302387\pi$
$374$	1.67314e10	0.0442191
$375$	−3.33882e11	−0.871871
$376$	−2.31584e11	−0.597535
$377$	8.82202e10	0.224922
$378$	0	0
$379$	−7.30677e11	−1.81907	−0.909534	−	0.415630i	$-0.863561\pi$
$379$	−7.30677e11	−1.81907	−0.909534	+	0.415630i	$0.863561\pi$
$380$	−9.97701e10	−0.245456
$381$	−9.25280e11	−2.24963
$382$	−6.11115e10	−0.146838
$383$	−2.11074e11	−0.501233	−0.250617	−	0.968086i	$-0.580633\pi$
$383$	−2.11074e11	−0.501233	−0.250617	+	0.968086i	$0.580633\pi$
$384$	−4.56340e10	−0.107102
$385$	0	0
$386$	−3.85909e11	−0.884794
$387$	−1.72370e11	−0.390627
$388$	−1.94052e11	−0.434686
$389$	7.21857e9	0.0159837	0.00799186	−	0.999968i	$-0.497456\pi$
$389$	7.21857e9	0.0159837	0.00799186	+	0.999968i	$0.497456\pi$
$390$	2.34914e10	0.0514184
$391$	−5.29025e10	−0.114467
$392$	0	0
$393$	−1.09490e11	−0.231530
$394$	−1.99677e11	−0.417441
$395$	−2.70082e11	−0.558224
$396$	1.15203e11	0.235415
$397$	6.99387e11	1.41306	0.706529	−	0.707684i	$-0.250260\pi$
$397$	6.99387e11	1.41306	0.706529	+	0.707684i	$0.250260\pi$
$398$	4.69004e10	0.0936920
$399$	0	0
$400$	−1.08606e11	−0.212120
$401$	6.40644e11	1.23728	0.618638	−	0.785676i	$-0.287685\pi$
$401$	6.40644e11	1.23728	0.618638	+	0.785676i	$0.287685\pi$
$402$	−2.54447e11	−0.485936
$403$	−9.20704e10	−0.173879
$404$	2.31478e11	0.432309
$405$	2.63234e11	0.486177
$406$	0	0
$407$	−1.90142e11	−0.343481
$408$	−1.49138e10	−0.0266451
$409$	1.31500e10	0.0232365	0.0116182	−	0.999933i	$-0.496302\pi$
$409$	1.31500e10	0.0232365	0.0116182	+	0.999933i	$0.496302\pi$
$410$	−5.53649e10	−0.0967625
$411$	−2.84538e11	−0.491873
$412$	−5.07281e11	−0.867384
$413$	0	0
$414$	−3.64256e11	−0.609404
$415$	−2.02089e11	−0.334446
$416$	1.66472e10	0.0272534
$417$	−7.09461e11	−1.14899
$418$	5.59648e11	0.896647
$419$	5.79915e11	0.919182	0.459591	−	0.888131i	$-0.347996\pi$
$419$	5.79915e11	0.919182	0.459591	+	0.888131i	$0.347996\pi$
$420$	0	0
$421$	1.66175e11	0.257808	0.128904	−	0.991657i	$-0.458854\pi$
$421$	1.66175e11	0.257808	0.128904	+	0.991657i	$0.458854\pi$
$422$	5.39165e11	0.827591
$423$	−5.21121e11	−0.791419
$424$	−2.45329e11	−0.368639
$425$	−3.54937e10	−0.0527717
$426$	2.60123e11	0.382680
$427$	0	0
$428$	1.06593e11	0.153544
$429$	−1.31772e11	−0.187830
$430$	1.62776e11	0.229606
$431$	7.57723e11	1.05770	0.528850	−	0.848715i	$-0.322623\pi$
$431$	7.57723e11	1.05770	0.528850	+	0.848715i	$0.322623\pi$
$432$	1.16603e11	0.161077
$433$	1.07485e12	1.46944	0.734719	−	0.678371i	$-0.237314\pi$
$433$	1.07485e12	1.46944	0.734719	+	0.678371i	$0.237314\pi$
$434$	0	0
$435$	5.13895e11	0.688134
$436$	−3.24918e11	−0.430610
$437$	−1.76953e12	−2.32109
$438$	8.33670e11	1.08233
$439$	−1.70418e11	−0.218991	−0.109496	−	0.993987i	$-0.534924\pi$
$439$	−1.70418e11	−0.218991	−0.109496	+	0.993987i	$0.534924\pi$
$440$	−1.08791e11	−0.138374
$441$	0	0
$442$	5.44051e9	0.00678016
$443$	1.22937e12	1.51658	0.758290	−	0.651918i	$-0.226035\pi$
$443$	1.22937e12	1.51658	0.758290	+	0.651918i	$0.226035\pi$
$444$	1.69486e11	0.206971
$445$	−9.00225e10	−0.108826
$446$	6.19533e11	0.741409
$447$	7.88963e10	0.0934701
$448$	0	0
$449$	−7.25792e10	−0.0842759	−0.0421380	−	0.999112i	$-0.513417\pi$
$449$	−7.25792e10	−0.0842759	−0.0421380	+	0.999112i	$0.513417\pi$
$450$	−2.44389e11	−0.280948
$451$	3.10563e11	0.353472
$452$	−7.25831e11	−0.817923
$453$	−1.24428e12	−1.38828
$454$	−1.23042e12	−1.35926
$455$	0	0
$456$	−4.98851e11	−0.540292
$457$	−6.64172e11	−0.712291	−0.356146	−	0.934431i	$-0.615909\pi$
$457$	−6.64172e11	−0.712291	−0.356146	+	0.934431i	$0.615909\pi$
$458$	−6.96183e11	−0.739313
$459$	3.81073e10	0.0400730
$460$	3.43982e11	0.358200
$461$	1.21501e12	1.25293	0.626463	−	0.779451i	$-0.284502\pi$
$461$	1.21501e12	1.25293	0.626463	+	0.779451i	$0.284502\pi$
$462$	0	0
$463$	2.93878e11	0.297202	0.148601	−	0.988897i	$-0.452523\pi$
$463$	2.93878e11	0.297202	0.148601	+	0.988897i	$0.452523\pi$
$464$	3.64172e11	0.364734
$465$	−5.36324e11	−0.531972
$466$	−3.31269e11	−0.325420
$467$	−4.73112e11	−0.460297	−0.230149	−	0.973155i	$-0.573921\pi$
$467$	−4.73112e11	−0.460297	−0.230149	+	0.973155i	$0.573921\pi$
$468$	3.74602e10	0.0360964
$469$	0	0
$470$	4.92116e11	0.465187
$471$	−7.53185e11	−0.705192
$472$	−6.78419e11	−0.629157
$473$	−9.13072e11	−0.838745
$474$	−1.35041e12	−1.22875
$475$	−1.18723e12	−1.07007
$476$	0	0
$477$	−5.52049e11	−0.488253
$478$	3.45952e11	0.303103
$479$	2.05945e12	1.78748	0.893742	−	0.448582i	$-0.148071\pi$
$479$	2.05945e12	1.78748	0.893742	+	0.448582i	$0.148071\pi$
$480$	9.69723e10	0.0833801
$481$	−6.18280e10	−0.0526662
$482$	−1.08446e12	−0.915172
$483$	0	0
$484$	6.61383e9	0.00547834
$485$	4.12361e11	0.338407
$486$	7.55843e11	0.614566
$487$	−1.22247e12	−0.984821	−0.492411	−	0.870363i	$-0.663884\pi$
$487$	−1.22247e12	−0.984821	−0.492411	+	0.870363i	$0.663884\pi$
$488$	−2.10612e11	−0.168110
$489$	2.27197e12	1.79685
$490$	0	0
$491$	1.98225e11	0.153918	0.0769592	−	0.997034i	$-0.475479\pi$
$491$	1.98225e11	0.153918	0.0769592	+	0.997034i	$0.475479\pi$
$492$	−2.76825e11	−0.212991
$493$	1.19016e11	0.0907391
$494$	1.81980e11	0.137484
$495$	−2.44806e11	−0.183273
$496$	−3.80066e11	−0.281963
$497$	0	0
$498$	−1.01044e12	−0.736174
$499$	−3.00745e11	−0.217143	−0.108571	−	0.994089i	$-0.534628\pi$
$499$	−3.00745e11	−0.217143	−0.108571	+	0.994089i	$0.534628\pi$
$500$	5.02787e11	0.359765
$501$	−2.11576e12	−1.50036
$502$	−7.80633e10	−0.0548631
$503$	−3.30194e11	−0.229993	−0.114996	−	0.993366i	$-0.536686\pi$
$503$	−3.30194e11	−0.229993	−0.114996	+	0.993366i	$0.536686\pi$
$504$	0	0
$505$	−4.91891e11	−0.336556
$506$	−1.92952e12	−1.30850
$507$	1.75992e12	1.18292
$508$	1.39336e12	0.928277
$509$	6.32399e10	0.0417600	0.0208800	−	0.999782i	$-0.493353\pi$
$509$	6.32399e10	0.0417600	0.0208800	+	0.999782i	$0.493353\pi$
$510$	3.16918e10	0.0207434
$511$	0	0
$512$	6.87195e10	0.0441942
$513$	1.27465e12	0.812574
$514$	4.40046e11	0.278076
$515$	1.07797e12	0.675267
$516$	8.13880e11	0.505402
$517$	−2.76046e12	−1.69932
$518$	0	0
$519$	1.77725e12	1.07522
$520$	−3.53753e10	−0.0212170
$521$	1.88994e12	1.12377	0.561886	−	0.827215i	$-0.310076\pi$
$521$	1.88994e12	1.12377	0.561886	+	0.827215i	$0.310076\pi$
$522$	8.19476e11	0.483080
$523$	−8.95863e11	−0.523581	−0.261791	−	0.965125i	$-0.584313\pi$
$523$	−8.95863e11	−0.523581	−0.261791	+	0.965125i	$0.584313\pi$
$524$	1.64879e11	0.0955374
$525$	0	0
$526$	−3.56152e11	−0.202861
$527$	−1.24210e11	−0.0701472
$528$	−5.43954e11	−0.304586
$529$	4.29975e12	2.38722
$530$	5.21323e11	0.286989
$531$	−1.52661e12	−0.833302
$532$	0	0
$533$	1.00985e11	0.0541981
$534$	−4.50113e11	−0.239544
$535$	−2.26510e11	−0.119535
$536$	3.83166e11	0.200515
$537$	6.87464e11	0.356752
$538$	−2.76826e11	−0.142458
$539$	0	0
$540$	−2.47781e11	−0.125400
$541$	1.00221e12	0.503005	0.251502	−	0.967857i	$-0.419075\pi$
$541$	1.00221e12	0.503005	0.251502	+	0.967857i	$0.419075\pi$
$542$	−7.71041e11	−0.383778
$543$	2.12050e12	1.04674
$544$	2.24584e10	0.0109947
$545$	6.90450e11	0.335234
$546$	0	0
$547$	2.73436e12	1.30591	0.652955	−	0.757396i	$-0.273529\pi$
$547$	2.73436e12	1.30591	0.652955	+	0.757396i	$0.273529\pi$
$548$	4.28481e11	0.202964
$549$	−4.73929e11	−0.222658
$550$	−1.29457e12	−0.603244
$551$	3.98097e12	1.83995
$552$	1.71991e12	0.788461
$553$	0	0
$554$	1.28613e12	0.580086
$555$	−3.60157e11	−0.161129
$556$	1.06837e12	0.474115
$557$	−4.22359e12	−1.85923	−0.929614	−	0.368534i	$-0.879860\pi$
$557$	−4.22359e12	−1.85923	−0.929614	+	0.368534i	$0.879860\pi$
$558$	−8.55241e11	−0.373452
$559$	−2.96902e11	−0.128606
$560$	0	0
$561$	−1.77771e11	−0.0757754
$562$	−3.12953e12	−1.32332
$563$	3.08311e12	1.29330	0.646652	−	0.762785i	$-0.276169\pi$
$563$	3.08311e12	1.29330	0.646652	+	0.762785i	$0.276169\pi$
$564$	2.46058e12	1.02396
$565$	1.54239e12	0.636761
$566$	9.64483e11	0.395021
$567$	0	0
$568$	−3.91715e11	−0.157907
$569$	−2.74669e11	−0.109851	−0.0549256	−	0.998490i	$-0.517492\pi$
$569$	−2.74669e11	−0.109851	−0.0549256	+	0.998490i	$0.517492\pi$
$570$	1.06006e12	0.420623
$571$	2.82499e12	1.11213	0.556064	−	0.831140i	$-0.312311\pi$
$571$	2.82499e12	1.11213	0.556064	+	0.831140i	$0.312311\pi$
$572$	1.98433e11	0.0775055
$573$	6.49310e11	0.251626
$574$	0	0
$575$	4.09326e12	1.56158
$576$	1.54636e11	0.0585340
$577$	−3.76585e12	−1.41440	−0.707199	−	0.707014i	$-0.750042\pi$
$577$	−3.76585e12	−1.41440	−0.707199	+	0.707014i	$0.750042\pi$
$578$	−1.89007e12	−0.704371
$579$	4.10028e12	1.51621
$580$	−7.73866e11	−0.283949
$581$	0	0
$582$	2.06181e12	0.744894
$583$	−2.92430e12	−1.04837
$584$	−1.25541e12	−0.446609
$585$	−7.96030e10	−0.0281014
$586$	7.78789e11	0.272823
$587$	3.00831e12	1.04580	0.522902	−	0.852393i	$-0.324849\pi$
$587$	3.00831e12	1.04580	0.522902	+	0.852393i	$0.324849\pi$
$588$	0	0
$589$	−4.15471e12	−1.42240
$590$	1.44164e12	0.489805
$591$	2.12157e12	0.715342
$592$	−2.55225e11	−0.0854036
$593$	−3.64775e12	−1.21138	−0.605688	−	0.795703i	$-0.707102\pi$
$593$	−3.64775e12	−1.21138	−0.605688	+	0.795703i	$0.707102\pi$
$594$	1.38990e12	0.458083
$595$	0	0
$596$	−1.18809e11	−0.0385691
$597$	−4.98316e11	−0.160554
$598$	−6.27420e11	−0.200633
$599$	4.17778e12	1.32594	0.662972	−	0.748644i	$-0.269295\pi$
$599$	4.17778e12	1.32594	0.662972	+	0.748644i	$0.269295\pi$
$600$	1.15393e12	0.363497
$601$	−4.84445e12	−1.51464	−0.757321	−	0.653043i	$-0.773492\pi$
$601$	−4.84445e12	−1.51464	−0.757321	+	0.653043i	$0.773492\pi$
$602$	0	0
$603$	8.62218e11	0.265576
$604$	1.87374e12	0.572853
$605$	−1.40544e10	−0.00426494
$606$	−2.45946e12	−0.740819
$607$	1.58444e12	0.473726	0.236863	−	0.971543i	$-0.423881\pi$
$607$	1.58444e12	0.473726	0.236863	+	0.971543i	$0.423881\pi$
$608$	7.51210e11	0.222944
$609$	0	0
$610$	4.47551e11	0.130876
$611$	−8.97614e11	−0.260558
$612$	5.05369e10	0.0145622
$613$	−2.79203e11	−0.0798635	−0.0399318	−	0.999202i	$-0.512714\pi$
$613$	−2.79203e11	−0.0798635	−0.0399318	+	0.999202i	$0.512714\pi$
$614$	−4.40285e12	−1.25019
$615$	5.88252e11	0.165816
$616$	0	0
$617$	−5.55576e12	−1.54333	−0.771667	−	0.636027i	$-0.780577\pi$
$617$	−5.55576e12	−1.54333	−0.771667	+	0.636027i	$0.780577\pi$
$618$	5.38986e12	1.48638
$619$	2.70437e12	0.740385	0.370192	−	0.928955i	$-0.379292\pi$
$619$	2.70437e12	0.740385	0.370192	+	0.928955i	$0.379292\pi$
$620$	8.07640e11	0.219511
$621$	−4.39467e12	−1.18581
$622$	−1.79715e12	−0.481423
$623$	0	0
$624$	−1.76876e11	−0.0467024
$625$	2.16828e12	0.568400
$626$	1.69823e12	0.441991
$627$	−5.94626e12	−1.53653
$628$	1.13421e12	0.290987
$629$	−8.34109e10	−0.0212469
$630$	0	0
$631$	−4.73158e12	−1.18816	−0.594078	−	0.804407i	$-0.702483\pi$
$631$	−4.73158e12	−1.18816	−0.594078	+	0.804407i	$0.702483\pi$
$632$	2.03356e12	0.507025
$633$	−5.72863e12	−1.41819
$634$	3.70172e10	0.00909918
$635$	−2.96090e12	−0.722672
$636$	2.60662e12	0.631713
$637$	0	0
$638$	4.34090e12	1.03726
$639$	−8.81454e11	−0.209144
$640$	−1.46029e11	−0.0344056
$641$	1.38865e12	0.324887	0.162444	−	0.986718i	$-0.448062\pi$
$641$	1.38865e12	0.324887	0.162444	+	0.986718i	$0.448062\pi$
$642$	−1.13255e12	−0.263118
$643$	−3.09398e12	−0.713786	−0.356893	−	0.934145i	$-0.616164\pi$
$643$	−3.09398e12	−0.713786	−0.356893	+	0.934145i	$0.616164\pi$
$644$	0	0
$645$	−1.72950e12	−0.393460
$646$	2.45505e11	0.0554644
$647$	−2.31453e12	−0.519270	−0.259635	−	0.965707i	$-0.583602\pi$
$647$	−2.31453e12	−0.519270	−0.259635	+	0.965707i	$0.583602\pi$
$648$	−1.98200e12	−0.441586
$649$	−8.08670e12	−1.78925
$650$	−4.20953e11	−0.0924960
$651$	0	0
$652$	−3.42132e12	−0.741446
$653$	−8.10575e11	−0.174455	−0.0872276	−	0.996188i	$-0.527801\pi$
$653$	−8.10575e11	−0.174455	−0.0872276	+	0.996188i	$0.527801\pi$
$654$	3.45225e12	0.737908
$655$	−3.50367e11	−0.0743768
$656$	4.16865e11	0.0878878
$657$	−2.82498e12	−0.591522
$658$	0	0
$659$	4.57355e11	0.0944645	0.0472323	−	0.998884i	$-0.484960\pi$
$659$	4.57355e11	0.0944645	0.0472323	+	0.998884i	$0.484960\pi$
$660$	1.15590e12	0.237123
$661$	−7.94557e12	−1.61889	−0.809447	−	0.587193i	$-0.800233\pi$
$661$	−7.94557e12	−1.61889	−0.809447	+	0.587193i	$0.800233\pi$
$662$	−3.45897e12	−0.699980
$663$	−5.78055e10	−0.0116187
$664$	1.52161e12	0.303772
$665$	0	0
$666$	−5.74319e11	−0.113115
$667$	−1.37254e13	−2.68508
$668$	3.18608e12	0.619103
$669$	−6.58254e12	−1.27050
$670$	−8.14229e11	−0.156102
$671$	−2.51048e12	−0.478086
$672$	0	0
$673$	−8.92805e12	−1.67760	−0.838801	−	0.544439i	$-0.816743\pi$
$673$	−8.92805e12	−1.67760	−0.838801	+	0.544439i	$0.816743\pi$
$674$	8.00465e11	0.149408
$675$	−2.94850e12	−0.546682
$676$	−2.65023e12	−0.488116
$677$	8.01730e12	1.46683	0.733414	−	0.679782i	$-0.237926\pi$
$677$	8.01730e12	1.46683	0.733414	+	0.679782i	$0.237926\pi$
$678$	7.71195e12	1.40162
$679$	0	0
$680$	−4.77241e10	−0.00855949
$681$	1.30732e13	2.32927
$682$	−4.53036e12	−0.801868
$683$	4.14724e12	0.729233	0.364617	−	0.931158i	$-0.381200\pi$
$683$	4.14724e12	0.729233	0.364617	+	0.931158i	$0.381200\pi$
$684$	1.69041e12	0.295283
$685$	−9.10523e11	−0.158010
$686$	0	0
$687$	7.39694e12	1.26691
$688$	−1.22561e12	−0.208547
$689$	−9.50888e11	−0.160747
$690$	−3.65481e12	−0.613824
$691$	6.05580e12	1.01046	0.505231	−	0.862984i	$-0.331407\pi$
$691$	6.05580e12	1.01046	0.505231	+	0.862984i	$0.331407\pi$
$692$	−2.67633e12	−0.443672
$693$	0	0
$694$	−2.95370e12	−0.483336
$695$	−2.27028e12	−0.369103
$696$	−3.86933e12	−0.625020
$697$	1.36237e11	0.0218649
$698$	−4.39466e12	−0.700771
$699$	3.51973e12	0.557651
$700$	0	0
$701$	1.88599e12	0.294990	0.147495	−	0.989063i	$-0.452879\pi$
$701$	1.88599e12	0.294990	0.147495	+	0.989063i	$0.452879\pi$
$702$	4.51950e11	0.0702383
$703$	−2.79001e12	−0.430831
$704$	8.19131e11	0.125683
$705$	−5.22873e12	−0.797160
$706$	2.52886e12	0.383092
$707$	0	0
$708$	7.20820e12	1.07815
$709$	−4.76210e12	−0.707767	−0.353884	−	0.935289i	$-0.615139\pi$
$709$	−4.76210e12	−0.707767	−0.353884	+	0.935289i	$0.615139\pi$
$710$	8.32394e11	0.122932
$711$	4.57600e12	0.671542
$712$	6.77817e11	0.0988444
$713$	1.43244e13	2.07574
$714$	0	0
$715$	−4.21671e11	−0.0603387
$716$	−1.03524e12	−0.147208
$717$	−3.67574e12	−0.519408
$718$	5.45215e12	0.765610
$719$	−5.34893e12	−0.746427	−0.373213	−	0.927746i	$-0.621744\pi$
$719$	−5.34893e12	−0.746427	−0.373213	+	0.927746i	$0.621744\pi$
$720$	−3.28601e11	−0.0455693
$721$	0	0
$722$	3.04889e12	0.417565
$723$	1.15224e13	1.56827
$724$	−3.19322e12	−0.431922
$725$	−9.20871e12	−1.23788
$726$	−7.02720e10	−0.00938788
$727$	−9.08222e12	−1.20583	−0.602917	−	0.797804i	$-0.705995\pi$
$727$	−9.08222e12	−1.20583	−0.602917	+	0.797804i	$0.705995\pi$
$728$	0	0
$729$	1.49349e12	0.195852
$730$	2.66774e12	0.347689
$731$	−4.00544e11	−0.0518827
$732$	2.23776e12	0.288080
$733$	1.20547e13	1.54237	0.771185	−	0.636611i	$-0.219664\pi$
$733$	1.20547e13	1.54237	0.771185	+	0.636611i	$0.219664\pi$
$734$	9.76345e12	1.24157
$735$	0	0
$736$	−2.58998e12	−0.325347
$737$	4.56731e12	0.570239
$738$	9.38048e11	0.116405
$739$	1.08128e13	1.33364	0.666822	−	0.745217i	$-0.267654\pi$
$739$	1.08128e13	1.33364	0.666822	+	0.745217i	$0.267654\pi$
$740$	5.42354e11	0.0664875
$741$	−1.93353e12	−0.235597
$742$	0	0
$743$	6.39433e12	0.769742	0.384871	−	0.922970i	$-0.374246\pi$
$743$	6.39433e12	0.769742	0.384871	+	0.922970i	$0.374246\pi$
$744$	4.03820e12	0.483181
$745$	2.52468e11	0.0300264
$746$	6.95889e12	0.822650
$747$	3.42400e12	0.402337
$748$	2.67702e11	0.0312676
$749$	0	0
$750$	−5.34211e12	−0.616506
$751$	−2.30580e12	−0.264510	−0.132255	−	0.991216i	$-0.542222\pi$
$751$	−2.30580e12	−0.264510	−0.132255	+	0.991216i	$0.542222\pi$
$752$	−3.70534e12	−0.422521
$753$	8.29422e11	0.0940152
$754$	1.41152e12	0.159044
$755$	−3.98170e12	−0.445971
$756$	0	0
$757$	−6.85316e12	−0.758507	−0.379253	−	0.925293i	$-0.623819\pi$
$757$	−6.85316e12	−0.758507	−0.379253	+	0.925293i	$0.623819\pi$
$758$	−1.16908e13	−1.28628
$759$	2.05012e13	2.24229
$760$	−1.59632e12	−0.173564
$761$	1.55520e12	0.168095	0.0840474	−	0.996462i	$-0.473215\pi$
$761$	1.55520e12	0.168095	0.0840474	+	0.996462i	$0.473215\pi$
$762$	−1.48045e13	−1.59073
$763$	0	0
$764$	−9.77784e11	−0.103830
$765$	−1.07391e11	−0.0113368
$766$	−3.37718e12	−0.354425
$767$	−2.62954e12	−0.274347
$768$	−7.30144e11	−0.0757327
$769$	1.31148e12	0.135236	0.0676179	−	0.997711i	$-0.478460\pi$
$769$	1.31148e12	0.135236	0.0676179	+	0.997711i	$0.478460\pi$
$770$	0	0
$771$	−4.67549e12	−0.476521
$772$	−6.17454e12	−0.625644
$773$	9.82010e12	0.989255	0.494627	−	0.869105i	$-0.335305\pi$
$773$	9.82010e12	0.989255	0.494627	+	0.869105i	$0.335305\pi$
$774$	−2.75792e12	−0.276215
$775$	9.61062e12	0.956959
$776$	−3.10484e12	−0.307370
$777$	0	0
$778$	1.15497e11	0.0113022
$779$	4.55698e12	0.443362
$780$	3.75862e11	0.0363583
$781$	−4.66921e12	−0.449070
$782$	−8.46439e11	−0.0809404
$783$	9.88682e12	0.940001
$784$	0	0
$785$	−2.41019e12	−0.226536
$786$	−1.75184e12	−0.163716
$787$	4.81658e12	0.447562	0.223781	−	0.974639i	$-0.428160\pi$
$787$	4.81658e12	0.447562	0.223781	+	0.974639i	$0.428160\pi$
$788$	−3.19484e12	−0.295176
$789$	3.78411e12	0.347630
$790$	−4.32131e12	−0.394724
$791$	0	0
$792$	1.84324e12	0.166464
$793$	−8.16328e11	−0.0733053
$794$	1.11902e13	0.999183
$795$	−5.53906e12	−0.491795
$796$	7.50406e11	0.0662502
$797$	−7.71344e12	−0.677151	−0.338575	−	0.940939i	$-0.609945\pi$
$797$	−7.71344e12	−0.677151	−0.338575	+	0.940939i	$0.609945\pi$
$798$	0	0
$799$	−1.21095e12	−0.105116
$800$	−1.73769e12	−0.149992
$801$	1.52525e12	0.130917
$802$	1.02503e13	0.874887
$803$	−1.49644e13	−1.27010
$804$	−4.07114e12	−0.343609
$805$	0	0
$806$	−1.47313e12	−0.122951
$807$	2.94128e12	0.244121
$808$	3.70365e12	0.305688
$809$	2.12869e13	1.74721	0.873604	−	0.486637i	$-0.161777\pi$
$809$	2.12869e13	1.74721	0.873604	+	0.486637i	$0.161777\pi$
$810$	4.21174e12	0.343779
$811$	−2.45053e13	−1.98914	−0.994570	−	0.104067i	$-0.966814\pi$
$811$	−2.45053e13	−1.98914	−0.994570	+	0.104067i	$0.966814\pi$
$812$	0	0
$813$	8.19231e12	0.657656
$814$	−3.04227e12	−0.242878
$815$	7.27030e12	0.577223
$816$	−2.38621e11	−0.0188409
$817$	−1.33978e13	−1.05204
$818$	2.10400e11	0.0164307
$819$	0	0
$820$	−8.85839e11	−0.0684214
$821$	−9.72826e12	−0.747293	−0.373646	−	0.927571i	$-0.621893\pi$
$821$	−9.72826e12	−0.747293	−0.373646	+	0.927571i	$0.621893\pi$
$822$	−4.55261e12	−0.347807
$823$	−8.28745e11	−0.0629683	−0.0314841	−	0.999504i	$-0.510023\pi$
$823$	−8.28745e11	−0.0629683	−0.0314841	+	0.999504i	$0.510023\pi$
$824$	−8.11650e12	−0.613333
$825$	1.37548e13	1.03374
$826$	0	0
$827$	2.42842e13	1.80530	0.902649	−	0.430376i	$-0.141619\pi$
$827$	2.42842e13	1.80530	0.902649	+	0.430376i	$0.141619\pi$
$828$	−5.82809e12	−0.430913
$829$	−1.95570e13	−1.43816	−0.719078	−	0.694929i	$-0.755436\pi$
$829$	−1.95570e13	−1.43816	−0.719078	+	0.694929i	$0.755436\pi$
$830$	−3.23342e12	−0.236489
$831$	−1.36652e13	−0.994055
$832$	2.66355e11	0.0192711
$833$	0	0
$834$	−1.13514e13	−0.812459
$835$	−6.77043e12	−0.481978
$836$	8.95437e12	0.634025
$837$	−1.03183e13	−0.726682
$838$	9.27865e12	0.649960
$839$	7.69577e12	0.536196	0.268098	−	0.963392i	$-0.413605\pi$
$839$	7.69577e12	0.536196	0.268098	+	0.963392i	$0.413605\pi$
$840$	0	0
$841$	1.63712e13	1.12849
$842$	2.65880e12	0.182298
$843$	3.32512e13	2.26769
$844$	8.62664e12	0.585195
$845$	5.63173e12	0.380003
$846$	−8.33793e12	−0.559618
$847$	0	0
$848$	−3.92526e12	−0.260667
$849$	−1.02476e13	−0.676923
$850$	−5.67899e11	−0.0373152
$851$	9.61924e12	0.628721
$852$	4.16197e12	0.270596
$853$	2.79895e12	0.181019	0.0905097	−	0.995896i	$-0.471150\pi$
$853$	2.79895e12	0.181019	0.0905097	+	0.995896i	$0.471150\pi$
$854$	0	0
$855$	−3.59211e12	−0.229881
$856$	1.70549e12	0.108572
$857$	5.56141e12	0.352185	0.176093	−	0.984374i	$-0.443654\pi$
$857$	5.56141e12	0.352185	0.176093	+	0.984374i	$0.443654\pi$
$858$	−2.10835e12	−0.132816
$859$	−3.51052e12	−0.219989	−0.109995	−	0.993932i	$-0.535083\pi$
$859$	−3.51052e12	−0.219989	−0.109995	+	0.993932i	$0.535083\pi$
$860$	2.60442e12	0.162356
$861$	0	0
$862$	1.21236e13	0.747908
$863$	1.43838e13	0.882721	0.441361	−	0.897330i	$-0.354496\pi$
$863$	1.43838e13	0.882721	0.441361	+	0.897330i	$0.354496\pi$
$864$	1.86565e12	0.113898
$865$	5.68720e12	0.345403
$866$	1.71976e13	1.03905
$867$	2.00820e13	1.20704
$868$	0	0
$869$	2.42399e13	1.44192
$870$	8.22232e12	0.486584
$871$	1.48514e12	0.0874353
$872$	−5.19868e12	−0.304487
$873$	−6.98664e12	−0.407103
$874$	−2.83125e13	−1.64126
$875$	0	0
$876$	1.33387e13	0.765325
$877$	−6.34278e12	−0.362061	−0.181030	−	0.983477i	$-0.557943\pi$
$877$	−6.34278e12	−0.362061	−0.181030	+	0.983477i	$0.557943\pi$
$878$	−2.72670e12	−0.154850
$879$	−8.27463e12	−0.467519
$880$	−1.74065e12	−0.0978453
$881$	2.89282e13	1.61782	0.808910	−	0.587933i	$-0.200058\pi$
$881$	2.89282e13	1.61782	0.808910	+	0.587933i	$0.200058\pi$
$882$	0	0
$883$	−7.17154e12	−0.396999	−0.198500	−	0.980101i	$-0.563607\pi$
$883$	−7.17154e12	−0.396999	−0.198500	+	0.980101i	$0.563607\pi$
$884$	8.70482e10	0.00479430
$885$	−1.53174e13	−0.839346
$886$	1.96699e13	1.07238
$887$	1.68020e13	0.911389	0.455695	−	0.890136i	$-0.349391\pi$
$887$	1.68020e13	0.911389	0.455695	+	0.890136i	$0.349391\pi$
$888$	2.71177e12	0.146351
$889$	0	0
$890$	−1.44036e12	−0.0769513
$891$	−2.36252e13	−1.25582
$892$	9.91254e12	0.524255
$893$	−4.05052e13	−2.13147
$894$	1.26234e12	0.0660933
$895$	2.19989e12	0.114603
$896$	0	0
$897$	6.66633e12	0.343812
$898$	−1.16127e12	−0.0595921
$899$	−3.22260e13	−1.64546
$900$	−3.91022e12	−0.198660
$901$	−1.28282e12	−0.0648493
$902$	4.96900e12	0.249942
$903$	0	0
$904$	−1.16133e13	−0.578359
$905$	6.78559e12	0.336255
$906$	−1.99085e13	−0.981660
$907$	−1.87924e13	−0.922038	−0.461019	−	0.887390i	$-0.652516\pi$
$907$	−1.87924e13	−0.922038	−0.461019	+	0.887390i	$0.652516\pi$
$908$	−1.96867e13	−0.961139
$909$	8.33412e12	0.404876
$910$	0	0
$911$	−3.39496e13	−1.63306	−0.816529	−	0.577304i	$-0.804105\pi$
$911$	−3.39496e13	−1.63306	−0.816529	+	0.577304i	$0.804105\pi$
$912$	−7.98161e12	−0.382044
$913$	1.81375e13	0.863890
$914$	−1.06267e13	−0.503666
$915$	−4.75523e12	−0.224273
$916$	−1.11389e13	−0.522773
$917$	0	0
$918$	6.09717e11	0.0283359
$919$	1.03287e13	0.477667	0.238833	−	0.971061i	$-0.423235\pi$
$919$	1.03287e13	0.477667	0.238833	+	0.971061i	$0.423235\pi$
$920$	5.50371e12	0.253286
$921$	4.67803e13	2.14237
$922$	1.94401e13	0.885952
$923$	−1.51828e12	−0.0688563
$924$	0	0
$925$	6.45381e12	0.289853
$926$	4.70205e12	0.210154
$927$	−1.82641e13	−0.812344
$928$	5.82675e12	0.257906
$929$	2.79767e13	1.23233	0.616163	−	0.787619i	$-0.288686\pi$
$929$	2.79767e13	1.23233	0.616163	+	0.787619i	$0.288686\pi$
$930$	−8.58118e12	−0.376161
$931$	0	0
$932$	−5.30030e12	−0.230107
$933$	1.90947e13	0.824984
$934$	−7.56980e12	−0.325479
$935$	−5.68868e11	−0.0243421
$936$	5.99364e11	0.0255240
$937$	−3.31649e13	−1.40556	−0.702782	−	0.711406i	$-0.748059\pi$
$937$	−3.31649e13	−1.40556	−0.702782	+	0.711406i	$0.748059\pi$
$938$	0	0
$939$	−1.80437e13	−0.757411
$940$	7.87386e12	0.328937
$941$	−3.19309e13	−1.32757	−0.663786	−	0.747923i	$-0.731051\pi$
$941$	−3.19309e13	−1.32757	−0.663786	+	0.747923i	$0.731051\pi$
$942$	−1.20510e13	−0.498646
$943$	−1.57113e13	−0.647009
$944$	−1.08547e13	−0.444881
$945$	0	0
$946$	−1.46092e13	−0.593082
$947$	3.56921e13	1.44210	0.721052	−	0.692881i	$-0.243659\pi$
$947$	3.56921e13	1.44210	0.721052	+	0.692881i	$0.243659\pi$
$948$	−2.16066e13	−0.868856
$949$	−4.86594e12	−0.194746
$950$	−1.89956e13	−0.756654
$951$	−3.93308e11	−0.0155927
$952$	0	0
$953$	−3.04923e13	−1.19749	−0.598745	−	0.800940i	$-0.704334\pi$
$953$	−3.04923e13	−1.19749	−0.598745	+	0.800940i	$0.704334\pi$
$954$	−8.83279e12	−0.345247
$955$	2.07779e12	0.0808327
$956$	5.53524e12	0.214326
$957$	−4.61221e13	−1.77748
$958$	3.29512e13	1.26394
$959$	0	0
$960$	1.55156e12	0.0589586
$961$	7.19282e12	0.272047
$962$	−9.89248e11	−0.0372406
$963$	3.83776e12	0.143800
$964$	−1.73514e13	−0.647124
$965$	1.31209e13	0.487069
$966$	0	0
$967$	−3.45533e13	−1.27078	−0.635389	−	0.772192i	$-0.719160\pi$
$967$	−3.45533e13	−1.27078	−0.635389	+	0.772192i	$0.719160\pi$
$968$	1.05821e11	0.00387377
$969$	−2.60849e12	−0.0950457
$970$	6.59778e12	0.239290
$971$	2.06708e13	0.746225	0.373112	−	0.927786i	$-0.378291\pi$
$971$	2.06708e13	0.746225	0.373112	+	0.927786i	$0.378291\pi$
$972$	1.20935e13	0.434563
$973$	0	0
$974$	−1.95595e13	−0.696374
$975$	4.47262e12	0.158504
$976$	−3.36980e12	−0.118872
$977$	1.78789e11	0.00627791	0.00313896	−	0.999995i	$-0.499001\pi$
$977$	1.78789e11	0.00627791	0.00313896	+	0.999995i	$0.499001\pi$
$978$	3.63515e13	1.27057
$979$	8.07952e12	0.281102
$980$	0	0
$981$	−1.16983e13	−0.403285
$982$	3.17159e12	0.108837
$983$	1.42657e13	0.487305	0.243652	−	0.969863i	$-0.421654\pi$
$983$	1.42657e13	0.487305	0.243652	+	0.969863i	$0.421654\pi$
$984$	−4.42919e12	−0.150608
$985$	6.78902e12	0.229797
$986$	1.90426e12	0.0641622
$987$	0	0
$988$	2.91167e12	0.0972157
$989$	4.61922e13	1.53527
$990$	−3.91689e12	−0.129594
$991$	−2.71296e13	−0.893537	−0.446768	−	0.894650i	$-0.647425\pi$
$991$	−2.71296e13	−0.893537	−0.446768	+	0.894650i	$0.647425\pi$
$992$	−6.08106e12	−0.199378
$993$	3.67515e13	1.19951
$994$	0	0
$995$	−1.59461e12	−0.0515764
$996$	−1.61671e13	−0.520554
$997$	3.86723e12	0.123957	0.0619787	−	0.998077i	$-0.480259\pi$
$997$	3.86723e12	0.123957	0.0619787	+	0.998077i	$0.480259\pi$
$998$	−4.81191e12	−0.153543
$999$	−6.92905e12	−0.220104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.b.1.1		1
7.2	even	3		98.10.c.d.67.1		2
7.3	odd	6		98.10.c.a.79.1		2
7.4	even	3		98.10.c.d.79.1		2
7.5	odd	6		98.10.c.a.67.1		2
7.6	odd	2		14.10.a.b.1.1	✓	1
21.20	even	2		126.10.a.a.1.1		1
28.27	even	2		112.10.a.a.1.1		1
35.13	even	4		350.10.c.d.99.1		2
35.27	even	4		350.10.c.d.99.2		2
35.34	odd	2		350.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.b.1.1	✓	1	7.6	odd	2
98.10.a.b.1.1		1	1.1	even	1	trivial
98.10.c.a.67.1		2	7.5	odd	6
98.10.c.a.79.1		2	7.3	odd	6
98.10.c.d.67.1		2	7.2	even	3
98.10.c.d.79.1		2	7.4	even	3
112.10.a.a.1.1		1	28.27	even	2
126.10.a.a.1.1		1	21.20	even	2
350.10.a.a.1.1		1	35.34	odd	2
350.10.c.d.99.1		2	35.13	even	4
350.10.c.d.99.2		2	35.27	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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