LMFDB - Embedded newform 49.20.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,20,Mod(1,49)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(49, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	49.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:	$112.120181313$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+456.000 q^{2} -50652.0 q^{3} -316352. q^{4} +2.37741e6 q^{5} -2.30973e7 q^{6} -3.83332e8 q^{8} +1.40336e9 q^{9} +O(q^{10})$

\(q+456.000 q^{2} -50652.0 q^{3} -316352. q^{4} +2.37741e6 q^{5} -2.30973e7 q^{6} -3.83332e8 q^{8} +1.40336e9 q^{9} +1.08410e9 q^{10} -1.62121e7 q^{11} +1.60239e10 q^{12} -5.04216e10 q^{13} -1.20421e11 q^{15} -8.93976e9 q^{16} -2.25070e11 q^{17} +6.39934e11 q^{18} +1.71028e12 q^{19} -7.52098e11 q^{20} -7.39272e9 q^{22} +1.40365e13 q^{23} +1.94165e13 q^{24} -1.34214e13 q^{25} -2.29923e13 q^{26} -1.22123e13 q^{27} +1.13784e12 q^{29} -5.49118e13 q^{30} +1.04627e14 q^{31} +1.96900e14 q^{32} +8.21176e11 q^{33} -1.02632e14 q^{34} -4.43957e14 q^{36} -1.69392e14 q^{37} +7.79887e14 q^{38} +2.55396e15 q^{39} -9.11337e14 q^{40} +3.30998e15 q^{41} +1.12791e15 q^{43} +5.12873e12 q^{44} +3.33637e15 q^{45} +6.40066e15 q^{46} -3.49869e15 q^{47} +4.52817e14 q^{48} -6.12016e15 q^{50} +1.14003e16 q^{51} +1.59510e16 q^{52} +2.99563e16 q^{53} -5.56881e15 q^{54} -3.85428e13 q^{55} -8.66290e16 q^{57} +5.18853e14 q^{58} -5.83914e16 q^{59} +3.80953e16 q^{60} -2.33737e16 q^{61} +4.77099e16 q^{62} +9.44733e16 q^{64} -1.19873e17 q^{65} +3.74456e14 q^{66} -2.05103e17 q^{67} +7.12014e16 q^{68} -7.10979e17 q^{69} -1.77902e17 q^{71} -5.37954e17 q^{72} -2.99854e17 q^{73} -7.72429e16 q^{74} +6.79821e17 q^{75} -5.41050e17 q^{76} +1.16460e18 q^{78} -9.22271e16 q^{79} -2.12535e16 q^{80} -1.01250e18 q^{81} +1.50935e18 q^{82} -1.20854e18 q^{83} -5.35084e17 q^{85} +5.14329e17 q^{86} -5.76336e16 q^{87} +6.21462e15 q^{88} -4.37120e18 q^{89} +1.52139e18 q^{90} -4.44049e18 q^{92} -5.29956e18 q^{93} -1.59540e18 q^{94} +4.06603e18 q^{95} -9.97337e18 q^{96} +6.35013e17 q^{97} -2.27515e16 q^{99} +O(q^{100})\)

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 $

$2$	456.000	0.629767	0.314883	−	0.949130i	$-0.398035\pi$
$2$	456.000	0.629767	0.314883	+	0.949130i	$0.398035\pi$
$3$	−50652.0	−1.48575	−0.742873	−	0.669432i	$-0.766537\pi$
$3$	−50652.0	−1.48575	−0.742873	+	0.669432i	$0.766537\pi$
$4$	−316352.	−0.603394
$5$	2.37741e6	0.544364	0.272182	−	0.962246i	$-0.412255\pi$
$5$	2.37741e6	0.544364	0.272182	+	0.962246i	$0.412255\pi$
$6$	−2.30973e7	−0.935674
$7$	0	0
$7$	0	0
$8$	−3.83332e8	−1.00976
$9$	1.40336e9	1.20744
$10$	1.08410e9	0.342822
$11$	−1.62121e7	−0.00207305	−0.00103652	−	0.999999i	$-0.500330\pi$
$11$	−1.62121e7	−0.00207305	−0.00103652	+	0.999999i	$0.500330\pi$
$12$	1.60239e10	0.896490
$13$	−5.04216e10	−1.31873	−0.659364	−	0.751824i	$-0.729174\pi$
$13$	−5.04216e10	−1.31873	−0.659364	+	0.751824i	$0.729174\pi$
$14$	0	0
$15$	−1.20421e11	−0.808786
$16$	−8.93976e9	−0.0325227
$17$	−2.25070e11	−0.460313	−0.230156	−	0.973154i	$-0.573924\pi$
$17$	−2.25070e11	−0.460313	−0.230156	+	0.973154i	$0.573924\pi$
$18$	6.39934e11	0.760407
$19$	1.71028e12	1.21593	0.607964	−	0.793965i	$-0.291987\pi$
$19$	1.71028e12	1.21593	0.607964	+	0.793965i	$0.291987\pi$
$20$	−7.52098e11	−0.328465
$21$	0	0
$22$	−7.39272e9	−0.00130554
$23$	1.40365e13	1.62497	0.812485	−	0.582982i	$-0.198114\pi$
$23$	1.40365e13	1.62497	0.812485	+	0.582982i	$0.198114\pi$
$24$	1.94165e13	1.50025
$25$	−1.34214e13	−0.703668
$26$	−2.29923e13	−0.830491
$27$	−1.22123e13	−0.308207
$28$	0	0
$29$	1.13784e12	0.0145646	0.00728230	−	0.999973i	$-0.497682\pi$
$29$	1.13784e12	0.0145646	0.00728230	+	0.999973i	$0.497682\pi$
$30$	−5.49118e13	−0.509347
$31$	1.04627e14	0.710734	0.355367	−	0.934727i	$-0.384356\pi$
$31$	1.04627e14	0.710734	0.355367	+	0.934727i	$0.384356\pi$
$32$	1.96900e14	0.989283
$33$	8.21176e11	0.00308002
$34$	−1.02632e14	−0.289890
$35$	0	0
$36$	−4.43957e14	−0.728563
$37$	−1.69392e14	−0.214278	−0.107139	−	0.994244i	$-0.534169\pi$
$37$	−1.69392e14	−0.214278	−0.107139	+	0.994244i	$0.534169\pi$
$38$	7.79887e14	0.765751
$39$	2.55396e15	1.95929
$40$	−9.11337e14	−0.549679
$41$	3.30998e15	1.57899	0.789495	−	0.613757i	$-0.210343\pi$
$41$	3.30998e15	1.57899	0.789495	+	0.613757i	$0.210343\pi$
$42$	0	0
$43$	1.12791e15	0.342236	0.171118	−	0.985251i	$-0.445262\pi$
$43$	1.12791e15	0.342236	0.171118	+	0.985251i	$0.445262\pi$
$44$	5.12873e12	0.00125086
$45$	3.33637e15	0.657288
$46$	6.40066e15	1.02335
$47$	−3.49869e15	−0.456012	−0.228006	−	0.973660i	$-0.573221\pi$
$47$	−3.49869e15	−0.456012	−0.228006	+	0.973660i	$0.573221\pi$
$48$	4.52817e14	0.0483204
$49$	0	0
$50$	−6.12016e15	−0.443147
$51$	1.14003e16	0.683908
$52$	1.59510e16	0.795711
$53$	2.99563e16	1.24700	0.623501	−	0.781822i	$-0.285710\pi$
$53$	2.99563e16	1.24700	0.623501	+	0.781822i	$0.285710\pi$
$54$	−5.56881e15	−0.194098
$55$	−3.85428e13	−0.00112849
$56$	0	0
$57$	−8.66290e16	−1.80656
$58$	5.18853e14	0.00917230
$59$	−5.83914e16	−0.877515	−0.438758	−	0.898605i	$-0.644581\pi$
$59$	−5.83914e16	−0.877515	−0.438758	+	0.898605i	$0.644581\pi$
$60$	3.80953e16	0.488016
$61$	−2.33737e16	−0.255914	−0.127957	−	0.991780i	$-0.540842\pi$
$61$	−2.33737e16	−0.255914	−0.127957	+	0.991780i	$0.540842\pi$
$62$	4.77099e16	0.447597
$63$	0	0
$64$	9.44733e16	0.655540
$65$	−1.19873e17	−0.717867
$66$	3.74456e14	0.00193970
$67$	−2.05103e17	−0.921002	−0.460501	−	0.887659i	$-0.652330\pi$
$67$	−2.05103e17	−0.921002	−0.460501	+	0.887659i	$0.652330\pi$
$68$	7.12014e16	0.277750
$69$	−7.10979e17	−2.41429
$70$	0	0
$71$	−1.77902e17	−0.460498	−0.230249	−	0.973132i	$-0.573954\pi$
$71$	−1.77902e17	−0.460498	−0.230249	+	0.973132i	$0.573954\pi$
$72$	−5.37954e17	−1.21923
$73$	−2.99854e17	−0.596132	−0.298066	−	0.954545i	$-0.596342\pi$
$73$	−2.99854e17	−0.596132	−0.298066	+	0.954545i	$0.596342\pi$
$74$	−7.72429e16	−0.134945
$75$	6.79821e17	1.04547
$76$	−5.41050e17	−0.733683
$77$	0	0
$78$	1.16460e18	1.23390
$79$	−9.22271e16	−0.0865767	−0.0432884	−	0.999063i	$-0.513783\pi$
$79$	−9.22271e16	−0.0865767	−0.0432884	+	0.999063i	$0.513783\pi$
$80$	−2.12535e16	−0.0177042
$81$	−1.01250e18	−0.749525
$82$	1.50935e18	0.994396
$83$	−1.20854e18	−0.709611	−0.354805	−	0.934940i	$-0.615453\pi$
$83$	−1.20854e18	−0.709611	−0.354805	+	0.934940i	$0.615453\pi$
$84$	0	0
$85$	−5.35084e17	−0.250578
$86$	5.14329e17	0.215529
$87$	−5.76336e16	−0.0216393
$88$	6.21462e15	0.00209329
$89$	−4.37120e18	−1.32250	−0.661250	−	0.750166i	$-0.729974\pi$
$89$	−4.37120e18	−1.32250	−0.661250	+	0.750166i	$0.729974\pi$
$90$	1.52139e18	0.413938
$91$	0	0
$92$	−4.44049e18	−0.980497
$93$	−5.29956e18	−1.05597
$94$	−1.59540e18	−0.287181
$95$	4.06603e18	0.661907
$96$	−9.97337e18	−1.46982
$97$	6.35013e17	0.0848108	0.0424054	−	0.999100i	$-0.486498\pi$
$97$	6.35013e17	0.0848108	0.0424054	+	0.999100i	$0.486498\pi$
$98$	0	0
$99$	−2.27515e16	−0.00250308
$100$	4.24589e18	0.424589
$101$	1.42252e19	1.29421	0.647105	−	0.762401i	$-0.275979\pi$
$101$	1.42252e19	1.29421	0.647105	+	0.762401i	$0.275979\pi$
$102$	5.19851e18	0.430703
$103$	−4.90729e18	−0.370586	−0.185293	−	0.982683i	$-0.559323\pi$
$103$	−4.90729e18	−0.370586	−0.185293	+	0.982683i	$0.559323\pi$
$104$	1.93282e19	1.33160
$105$	0	0
$106$	1.36601e19	0.785321
$107$	2.64625e19	1.39151	0.695753	−	0.718281i	$-0.255071\pi$
$107$	2.64625e19	1.39151	0.695753	+	0.718281i	$0.255071\pi$
$108$	3.86339e18	0.185970
$109$	−1.84178e19	−0.812242	−0.406121	−	0.913819i	$-0.633119\pi$
$109$	−1.84178e19	−0.812242	−0.406121	+	0.913819i	$0.633119\pi$
$110$	−1.75755e16	−0.000710686 0
$111$	8.58006e18	0.318363
$112$	0	0
$113$	2.57421e19	0.806118	0.403059	−	0.915174i	$-0.367947\pi$
$113$	2.57421e19	0.806118	0.403059	+	0.915174i	$0.367947\pi$
$114$	−3.95028e19	−1.13771
$115$	3.33706e19	0.884575
$116$	−3.59956e17	−0.00878818
$117$	−7.07599e19	−1.59229
$118$	−2.66265e19	−0.552630
$119$	0	0
$120$	4.61610e19	0.816683
$121$	−6.11588e19	−0.999996
$122$	−1.06584e19	−0.161166
$123$	−1.67657e20	−2.34598
$124$	−3.30989e19	−0.428852
$125$	−7.72537e19	−0.927415
$126$	0	0
$127$	8.80720e19	0.909290	0.454645	−	0.890673i	$-0.349766\pi$
$127$	8.80720e19	0.909290	0.454645	+	0.890673i	$0.349766\pi$
$128$	−6.01524e19	−0.576445
$129$	−5.71311e19	−0.508476
$130$	−5.46620e19	−0.452089
$131$	−7.19289e19	−0.553129	−0.276564	−	0.960995i	$-0.589196\pi$
$131$	−7.19289e19	−0.553129	−0.276564	+	0.960995i	$0.589196\pi$
$132$	−2.59781e17	−0.00185846
$133$	0	0
$134$	−9.35268e19	−0.580016
$135$	−2.90337e19	−0.167776
$136$	8.62765e19	0.464807
$137$	−2.95426e20	−1.48458	−0.742290	−	0.670079i	$-0.766260\pi$
$137$	−2.95426e20	−1.48458	−0.742290	+	0.670079i	$0.766260\pi$
$138$	−3.24206e20	−1.52044
$139$	−1.38478e20	−0.606375	−0.303187	−	0.952931i	$-0.598051\pi$
$139$	−1.38478e20	−0.606375	−0.303187	+	0.952931i	$0.598051\pi$
$140$	0	0
$141$	1.77216e20	0.677518
$142$	−8.11235e19	−0.290006
$143$	8.17441e17	0.00273378
$144$	−1.25457e19	−0.0392692
$145$	2.70510e18	0.00792843
$146$	−1.36733e20	−0.375424
$147$	0	0
$148$	5.35876e19	0.129294
$149$	−2.66021e20	−0.602070	−0.301035	−	0.953613i	$-0.597332\pi$
$149$	−2.66021e20	−0.602070	−0.301035	+	0.953613i	$0.597332\pi$
$150$	3.09998e20	0.658404
$151$	5.75578e20	1.14769	0.573844	−	0.818965i	$-0.305452\pi$
$151$	5.75578e20	1.14769	0.573844	+	0.818965i	$0.305452\pi$
$152$	−6.55604e20	−1.22780
$153$	−3.15855e20	−0.555801
$154$	0	0
$155$	2.48741e20	0.386898
$156$	−8.07949e20	−1.18223
$157$	1.07238e21	1.47673	0.738363	−	0.674403i	$-0.235599\pi$
$157$	1.07238e21	1.47673	0.738363	+	0.674403i	$0.235599\pi$
$158$	−4.20556e19	−0.0545232
$159$	−1.51735e21	−1.85273
$160$	4.68111e20	0.538529
$161$	0	0
$162$	−4.61699e20	−0.472026
$163$	−5.80765e20	−0.560039	−0.280019	−	0.959994i	$-0.590341\pi$
$163$	−5.80765e20	−0.560039	−0.280019	+	0.959994i	$0.590341\pi$
$164$	−1.04712e21	−0.952752
$165$	1.95227e18	0.00167665
$166$	−5.51096e20	−0.446889
$167$	−2.43392e20	−0.186423	−0.0932117	−	0.995646i	$-0.529713\pi$
$167$	−2.43392e20	−0.186423	−0.0932117	+	0.995646i	$0.529713\pi$
$168$	0	0
$169$	1.08042e21	0.739041
$170$	−2.43998e20	−0.157805
$171$	2.40014e21	1.46816
$172$	−3.56818e20	−0.206503
$173$	1.19350e21	0.653711	0.326855	−	0.945074i	$-0.394011\pi$
$173$	1.19350e21	0.653711	0.326855	+	0.945074i	$0.394011\pi$
$174$	−2.62809e19	−0.0136277
$175$	0	0
$176$	1.44932e17	6.74210e−5 0
$177$	2.95764e21	1.30377
$178$	−1.99327e21	−0.832867
$179$	−4.14664e21	−1.64283	−0.821415	−	0.570331i	$-0.806815\pi$
$179$	−4.14664e21	−1.64283	−0.821415	+	0.570331i	$0.806815\pi$
$180$	−1.05547e21	−0.396603
$181$	−3.32364e21	−1.18486	−0.592430	−	0.805622i	$-0.701831\pi$
$181$	−3.32364e21	−1.18486	−0.592430	+	0.805622i	$0.701831\pi$
$182$	0	0
$183$	1.18392e21	0.380223
$184$	−5.38065e21	−1.64084
$185$	−4.02715e20	−0.116645
$186$	−2.41660e21	−0.665015
$187$	3.64886e18	0.000954250 0
$188$	1.10682e21	0.275155
$189$	0	0
$190$	1.85411e21	0.416847
$191$	6.19380e21	1.32477	0.662384	−	0.749164i	$-0.269545\pi$
$191$	6.19380e21	1.32477	0.662384	+	0.749164i	$0.269545\pi$
$192$	−4.78526e21	−0.973966
$193$	−5.20697e21	−1.00877	−0.504383	−	0.863480i	$-0.668280\pi$
$193$	−5.20697e21	−1.00877	−0.504383	+	0.863480i	$0.668280\pi$
$194$	2.89566e20	0.0534111
$195$	6.07180e21	1.06657
$196$	0	0
$197$	2.42384e21	0.386433	0.193216	−	0.981156i	$-0.438108\pi$
$197$	2.42384e21	0.386433	0.193216	+	0.981156i	$0.438108\pi$
$198$	−1.03747e19	−0.00157636
$199$	1.05907e21	0.153399	0.0766993	−	0.997054i	$-0.475562\pi$
$199$	1.05907e21	0.153399	0.0766993	+	0.997054i	$0.475562\pi$
$200$	5.14485e21	0.710539
$201$	1.03889e22	1.36837
$202$	6.48668e21	0.815051
$203$	0	0
$204$	−3.60649e21	−0.412666
$205$	7.86919e21	0.859545
$206$	−2.23773e21	−0.233383
$207$	1.96984e22	1.96206
$208$	4.50757e20	0.0428885
$209$	−2.77272e19	−0.00252067
$210$	0	0
$211$	−1.32424e22	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$211$	−1.32424e22	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$212$	−9.47673e21	−0.752433
$213$	9.01111e21	0.684183
$214$	1.20669e22	0.876325
$215$	2.68151e21	0.186301
$216$	4.68137e21	0.311216
$217$	0	0
$218$	−8.39851e21	−0.511523
$219$	1.51882e22	0.885701
$220$	1.21931e19	0.000680924 0
$221$	1.13484e22	0.607027
$222$	3.91251e21	0.200494
$223$	−2.00921e22	−0.986575	−0.493287	−	0.869866i	$-0.664205\pi$
$223$	−2.00921e22	−0.986575	−0.493287	+	0.869866i	$0.664205\pi$
$224$	0	0
$225$	−1.88351e22	−0.849639
$226$	1.17384e22	0.507667
$227$	2.03494e22	0.843929	0.421965	−	0.906612i	$-0.361341\pi$
$227$	2.03494e22	0.843929	0.421965	+	0.906612i	$0.361341\pi$
$228$	2.74053e22	1.09007
$229$	3.99900e22	1.52586	0.762930	−	0.646481i	$-0.223760\pi$
$229$	3.99900e22	1.52586	0.762930	+	0.646481i	$0.223760\pi$
$230$	1.52170e22	0.557076
$231$	0	0
$232$	−4.36168e20	−0.0147068
$233$	2.42170e22	0.783862	0.391931	−	0.919995i	$-0.371807\pi$
$233$	2.42170e22	0.783862	0.391931	+	0.919995i	$0.371807\pi$
$234$	−3.22665e22	−1.00277
$235$	−8.31783e21	−0.248236
$236$	1.84722e22	0.529487
$237$	4.67149e21	0.128631
$238$	0	0
$239$	2.62411e22	0.667116	0.333558	−	0.942730i	$-0.391751\pi$
$239$	2.62411e22	0.667116	0.333558	+	0.942730i	$0.391751\pi$
$240$	1.07653e21	0.0263039
$241$	−7.36445e22	−1.72973	−0.864865	−	0.502004i	$-0.832596\pi$
$241$	−7.36445e22	−1.72973	−0.864865	+	0.502004i	$0.832596\pi$
$242$	−2.78884e22	−0.629764
$243$	6.54789e22	1.42181
$244$	7.39431e21	0.154417
$245$	0	0
$246$	−7.64518e22	−1.47742
$247$	−8.62350e22	−1.60348
$248$	−4.01068e22	−0.717674
$249$	6.12151e22	1.05430
$250$	−3.52277e22	−0.584055
$251$	−7.29309e22	−1.16416	−0.582078	−	0.813133i	$-0.697760\pi$
$251$	−7.29309e22	−1.16416	−0.582078	+	0.813133i	$0.697760\pi$
$252$	0	0
$253$	−2.27562e20	−0.00336864
$254$	4.01608e22	0.572641
$255$	2.71031e22	0.372295
$256$	−7.69607e22	−1.01857
$257$	6.38120e22	0.813838	0.406919	−	0.913464i	$-0.366603\pi$
$257$	6.38120e22	0.813838	0.406919	+	0.913464i	$0.366603\pi$
$258$	−2.60518e22	−0.320221
$259$	0	0
$260$	3.79220e22	0.433156
$261$	1.59680e21	0.0175859
$262$	−3.27996e22	−0.348342
$263$	−1.35820e23	−1.39118	−0.695590	−	0.718439i	$-0.744857\pi$
$263$	−1.35820e23	−1.39118	−0.695590	+	0.718439i	$0.744857\pi$
$264$	−3.14783e20	−0.00311010
$265$	7.12184e22	0.678823
$266$	0	0
$267$	2.21410e23	1.96490
$268$	6.48846e22	0.555726
$269$	1.33672e23	1.10508	0.552540	−	0.833486i	$-0.313659\pi$
$269$	1.33672e23	1.10508	0.552540	+	0.833486i	$0.313659\pi$
$270$	−1.32393e22	−0.105660
$271$	−2.00548e23	−1.54529	−0.772643	−	0.634840i	$-0.781066\pi$
$271$	−2.00548e23	−1.54529	−0.772643	+	0.634840i	$0.781066\pi$
$272$	2.01207e21	0.0149706
$273$	0	0
$274$	−1.34714e23	−0.934939
$275$	2.17589e20	0.00145874
$276$	2.24919e23	1.45677
$277$	2.00223e23	1.25301	0.626507	−	0.779416i	$-0.284484\pi$
$277$	2.00223e23	1.25301	0.626507	+	0.779416i	$0.284484\pi$
$278$	−6.31461e22	−0.381875
$279$	1.46830e23	0.858170
$280$	0	0
$281$	−1.19239e23	−0.651194	−0.325597	−	0.945509i	$-0.605565\pi$
$281$	−1.19239e23	−0.651194	−0.325597	+	0.945509i	$0.605565\pi$
$282$	8.08104e22	0.426679
$283$	3.46108e21	0.0176702	0.00883509	−	0.999961i	$-0.497188\pi$
$283$	3.46108e21	0.0176702	0.00883509	+	0.999961i	$0.497188\pi$
$284$	5.62798e22	0.277861
$285$	−2.05953e23	−0.983425
$286$	3.72753e20	0.00172165
$287$	0	0
$288$	2.76322e23	1.19450
$289$	−1.88416e23	−0.788112
$290$	1.23353e21	0.00499307
$291$	−3.21647e22	−0.126007
$292$	9.48593e22	0.359702
$293$	2.13236e23	0.782739	0.391370	−	0.920234i	$-0.372001\pi$
$293$	2.13236e23	0.782739	0.391370	+	0.920234i	$0.372001\pi$
$294$	0	0
$295$	−1.38820e23	−0.477687
$296$	6.49335e22	0.216370
$297$	1.97987e20	0.000638927 0
$298$	−1.21306e23	−0.379164
$299$	−7.07745e23	−2.14289
$300$	−2.15063e23	−0.630831
$301$	0	0
$302$	2.62464e23	0.722776
$303$	−7.20534e23	−1.92287
$304$	−1.52895e22	−0.0395452
$305$	−5.55688e22	−0.139310
$306$	−1.44030e23	−0.350025
$307$	−1.91887e23	−0.452097	−0.226048	−	0.974116i	$-0.572581\pi$
$307$	−1.91887e23	−0.452097	−0.226048	+	0.974116i	$0.572581\pi$
$308$	0	0
$309$	2.48564e23	0.550596
$310$	1.13426e23	0.243655
$311$	1.54522e23	0.321933	0.160967	−	0.986960i	$-0.448539\pi$
$311$	1.54522e23	0.321933	0.160967	+	0.986960i	$0.448539\pi$
$312$	−9.79013e23	−1.97843
$313$	−2.87408e23	−0.563413	−0.281707	−	0.959501i	$-0.590900\pi$
$313$	−2.87408e23	−0.563413	−0.281707	+	0.959501i	$0.590900\pi$
$314$	4.89003e23	0.929994
$315$	0	0
$316$	2.91762e22	0.0522398
$317$	2.63533e22	0.0457901	0.0228950	−	0.999738i	$-0.492712\pi$
$317$	2.63533e22	0.0457901	0.0228950	+	0.999738i	$0.492712\pi$
$318$	−6.91910e23	−1.16679
$319$	−1.84467e19	−3.01931e−5 0
$320$	2.24602e23	0.356852
$321$	−1.34038e24	−2.06743
$322$	0	0
$323$	−3.84933e23	−0.559707
$324$	3.20306e23	0.452259
$325$	6.76729e23	0.927946
$326$	−2.64829e23	−0.352694
$327$	9.32897e23	1.20679
$328$	−1.26882e24	−1.59441
$329$	0	0
$330$	8.90236e20	0.00105590
$331$	−1.05338e24	−1.21400	−0.606998	−	0.794703i	$-0.707626\pi$
$331$	−1.05338e24	−1.21400	−0.606998	+	0.794703i	$0.707626\pi$
$332$	3.82325e23	0.428175
$333$	−2.37719e23	−0.258728
$334$	−1.10987e23	−0.117403
$335$	−4.87613e23	−0.501360
$336$	0	0
$337$	6.76160e23	0.657000	0.328500	−	0.944504i	$-0.393457\pi$
$337$	6.76160e23	0.657000	0.328500	+	0.944504i	$0.393457\pi$
$338$	4.92671e23	0.465424
$339$	−1.30389e24	−1.19769
$340$	1.69275e23	0.151197
$341$	−1.69622e21	−0.00147338
$342$	1.09447e24	0.924600
$343$	0	0
$344$	−4.32365e23	−0.345578
$345$	−1.69029e24	−1.31425
$346$	5.44237e23	0.411685
$347$	1.06325e24	0.782535	0.391268	−	0.920277i	$-0.372037\pi$
$347$	1.06325e24	0.782535	0.391268	+	0.920277i	$0.372037\pi$
$348$	1.82325e22	0.0130570
$349$	7.14667e23	0.498037	0.249019	−	0.968499i	$-0.419892\pi$
$349$	7.14667e23	0.498037	0.249019	+	0.968499i	$0.419892\pi$
$350$	0	0
$351$	6.15764e23	0.406440
$352$	−3.19216e21	−0.00205083
$353$	5.07321e23	0.317266	0.158633	−	0.987338i	$-0.449291\pi$
$353$	5.07321e23	0.317266	0.158633	+	0.987338i	$0.449291\pi$
$354$	1.34868e24	0.821068
$355$	−4.22947e23	−0.250678
$356$	1.38284e24	0.797988
$357$	0	0
$358$	−1.89087e24	−1.03460
$359$	3.32006e24	1.76909	0.884544	−	0.466458i	$-0.154470\pi$
$359$	3.32006e24	1.76909	0.884544	+	0.466458i	$0.154470\pi$
$360$	−1.27894e24	−0.663706
$361$	9.46633e23	0.478479
$362$	−1.51558e24	−0.746186
$363$	3.09782e24	1.48574
$364$	0	0
$365$	−7.12875e23	−0.324512
$366$	5.39869e23	0.239452
$367$	2.24430e24	0.969958	0.484979	−	0.874526i	$-0.338827\pi$
$367$	2.24430e24	0.969958	0.484979	+	0.874526i	$0.338827\pi$
$368$	−1.25483e23	−0.0528484
$369$	4.64511e24	1.90654
$370$	−1.83638e23	−0.0734592
$371$	0	0
$372$	1.67653e24	0.637166
$373$	5.10606e24	1.89170	0.945850	−	0.324603i	$-0.105231\pi$
$373$	5.10606e24	1.89170	0.945850	+	0.324603i	$0.105231\pi$
$374$	1.66388e21	0.000600955 0
$375$	3.91305e24	1.37790
$376$	1.34116e24	0.460465
$377$	−5.73715e22	−0.0192067
$378$	0	0
$379$	−4.28975e24	−1.36571	−0.682857	−	0.730552i	$-0.739263\pi$
$379$	−4.28975e24	−1.36571	−0.682857	+	0.730552i	$0.739263\pi$
$380$	−1.28630e24	−0.399390
$381$	−4.46102e24	−1.35098
$382$	2.82437e24	0.834295
$383$	1.86803e24	0.538264	0.269132	−	0.963103i	$-0.413263\pi$
$383$	1.86803e24	0.538264	0.269132	+	0.963103i	$0.413263\pi$
$384$	3.04684e24	0.856451
$385$	0	0
$386$	−2.37438e24	−0.635288
$387$	1.58287e24	0.413230
$388$	−2.00888e23	−0.0511743
$389$	−6.47448e24	−1.60947	−0.804737	−	0.593632i	$-0.797694\pi$
$389$	−6.47448e24	−1.60947	−0.804737	+	0.593632i	$0.797694\pi$
$390$	2.76874e24	0.671689
$391$	−3.15920e24	−0.747995
$392$	0	0
$393$	3.64334e24	0.821809
$394$	1.10527e24	0.243363
$395$	−2.19262e23	−0.0471292
$396$	7.19748e21	0.00151034
$397$	−1.22760e24	−0.251505	−0.125752	−	0.992062i	$-0.540134\pi$
$397$	−1.22760e24	−0.251505	−0.125752	+	0.992062i	$0.540134\pi$
$398$	4.82937e23	0.0966054
$399$	0	0
$400$	1.19984e23	0.0228852
$401$	−5.17895e23	−0.0964651	−0.0482326	−	0.998836i	$-0.515359\pi$
$401$	−5.17895e23	−0.0964651	−0.0482326	+	0.998836i	$0.515359\pi$
$402$	4.73732e24	0.861757
$403$	−5.27546e24	−0.937264
$404$	−4.50017e24	−0.780918
$405$	−2.40712e24	−0.408014
$406$	0	0
$407$	2.74621e21	0.000444208 0
$408$	−4.37008e24	−0.690586
$409$	−2.81877e24	−0.435199	−0.217599	−	0.976038i	$-0.569823\pi$
$409$	−2.81877e24	−0.435199	−0.217599	+	0.976038i	$0.569823\pi$
$410$	3.58835e24	0.541313
$411$	1.49639e25	2.20571
$412$	1.55243e24	0.223609
$413$	0	0
$414$	8.98245e24	1.23564
$415$	−2.87320e24	−0.386286
$416$	−9.92800e24	−1.30459
$417$	7.01420e24	0.900919
$418$	−1.26436e22	−0.00158744
$419$	−8.65571e24	−1.06235	−0.531177	−	0.847261i	$-0.678250\pi$
$419$	−8.65571e24	−1.06235	−0.531177	+	0.847261i	$0.678250\pi$
$420$	0	0
$421$	−5.21652e24	−0.611929	−0.305964	−	0.952043i	$-0.598979\pi$
$421$	−5.21652e24	−0.611929	−0.305964	+	0.952043i	$0.598979\pi$
$422$	−6.03853e24	−0.692569
$423$	−4.90994e24	−0.550608
$424$	−1.14832e25	−1.25918
$425$	3.02076e24	0.323908
$426$	4.10907e24	0.430876
$427$	0	0
$428$	−8.37147e24	−0.839626
$429$	−4.14050e22	−0.00406171
$430$	1.22277e24	0.117326
$431$	1.04364e25	0.979526	0.489763	−	0.871856i	$-0.337083\pi$
$431$	1.04364e25	0.979526	0.489763	+	0.871856i	$0.337083\pi$
$432$	1.09175e23	0.0100237
$433$	−1.45110e25	−1.30335	−0.651675	−	0.758499i	$-0.725933\pi$
$433$	−1.45110e25	−1.30335	−0.651675	+	0.758499i	$0.725933\pi$
$434$	0	0
$435$	−1.37019e23	−0.0117796
$436$	5.82650e24	0.490102
$437$	2.40064e25	1.97585
$438$	6.92582e24	0.557785
$439$	−1.79857e25	−1.41747	−0.708735	−	0.705474i	$-0.750734\pi$
$439$	−1.79857e25	−1.41747	−0.708735	+	0.705474i	$0.750734\pi$
$440$	1.47747e22	0.00113951
$441$	0	0
$442$	5.17487e24	0.382286
$443$	8.73685e24	0.631712	0.315856	−	0.948807i	$-0.397708\pi$
$443$	8.73685e24	0.631712	0.315856	+	0.948807i	$0.397708\pi$
$444$	−2.71432e24	−0.192098
$445$	−1.03921e25	−0.719921
$446$	−9.16201e24	−0.621312
$447$	1.34745e25	0.894523
$448$	0	0
$449$	−1.60576e25	−1.02174	−0.510870	−	0.859658i	$-0.670677\pi$
$449$	−1.60576e25	−1.02174	−0.510870	+	0.859658i	$0.670677\pi$
$450$	−8.58881e24	−0.535075
$451$	−5.36618e22	−0.00327332
$452$	−8.14357e24	−0.486407
$453$	−2.91542e25	−1.70517
$454$	9.27933e24	0.531479
$455$	0	0
$456$	3.32077e25	1.82420
$457$	−2.67587e24	−0.143966	−0.0719831	−	0.997406i	$-0.522933\pi$
$457$	−2.67587e24	−0.143966	−0.0719831	+	0.997406i	$0.522933\pi$
$458$	1.82355e25	0.960936
$459$	2.74863e24	0.141871
$460$	−1.05569e25	−0.533747
$461$	−6.96807e24	−0.345107	−0.172553	−	0.985000i	$-0.555202\pi$
$461$	−6.96807e24	−0.345107	−0.172553	+	0.985000i	$0.555202\pi$
$462$	0	0
$463$	−2.49843e25	−1.18754	−0.593770	−	0.804635i	$-0.702361\pi$
$463$	−2.49843e25	−1.18754	−0.593770	+	0.804635i	$0.702361\pi$
$464$	−1.01720e22	−0.000473679 0
$465$	−1.25992e25	−0.574832
$466$	1.10430e25	0.493650
$467$	−1.94531e25	−0.852075	−0.426037	−	0.904706i	$-0.640091\pi$
$467$	−1.94531e25	−0.852075	−0.426037	+	0.904706i	$0.640091\pi$
$468$	2.23850e25	0.960776
$469$	0	0
$470$	−3.79293e24	−0.156331
$471$	−5.43180e25	−2.19404
$472$	2.23833e25	0.886084
$473$	−1.82859e22	−0.000709471 0
$474$	2.13020e24	0.0810076
$475$	−2.29543e25	−0.855610
$476$	0	0
$477$	4.20396e25	1.50568
$478$	1.19659e25	0.420128
$479$	−3.34153e25	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$479$	−3.34153e25	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$480$	−2.37108e25	−0.800118
$481$	8.54103e24	0.282574
$482$	−3.35819e25	−1.08933
$483$	0	0
$484$	1.93477e25	0.603391
$485$	1.50969e24	0.0461679
$486$	2.98584e25	0.895410
$487$	−4.86181e25	−1.42979	−0.714896	−	0.699231i	$-0.753526\pi$
$487$	−4.86181e25	−1.42979	−0.714896	+	0.699231i	$0.753526\pi$
$488$	8.95988e24	0.258413
$489$	2.94169e25	0.832075
$490$	0	0
$491$	9.86730e24	0.268488	0.134244	−	0.990948i	$-0.457139\pi$
$491$	9.86730e24	0.268488	0.134244	+	0.990948i	$0.457139\pi$
$492$	5.30387e25	1.41555
$493$	−2.56093e23	−0.00670427
$494$	−3.93232e25	−1.00982
$495$	−5.40896e22	−0.00136259
$496$	−9.35339e23	−0.0231150
$497$	0	0
$498$	2.79141e25	0.663964
$499$	−3.54150e25	−0.826481	−0.413240	−	0.910622i	$-0.635603\pi$
$499$	−3.54150e25	−0.826481	−0.413240	+	0.910622i	$0.635603\pi$
$500$	2.44394e25	0.559596
$501$	1.23283e25	0.276978
$502$	−3.32565e25	−0.733147
$503$	−1.47204e25	−0.318436	−0.159218	−	0.987243i	$-0.550897\pi$
$503$	−1.47204e25	−0.318436	−0.159218	+	0.987243i	$0.550897\pi$
$504$	0	0
$505$	3.38191e25	0.704521
$506$	−1.03768e23	−0.00212146
$507$	−5.47254e25	−1.09803
$508$	−2.78618e25	−0.548660
$509$	4.88290e25	0.943754	0.471877	−	0.881664i	$-0.343577\pi$
$509$	4.88290e25	0.943754	0.471877	+	0.881664i	$0.343577\pi$
$510$	1.23590e25	0.234459
$511$	0	0
$512$	−3.55692e24	−0.0650143
$513$	−2.08864e25	−0.374757
$514$	2.90983e25	0.512528
$515$	−1.16667e25	−0.201733
$516$	1.80735e25	0.306811
$517$	5.67212e22	0.000945334 0
$518$	0	0
$519$	−6.04533e25	−0.971248
$520$	4.59511e25	0.724876
$521$	−7.14445e25	−1.10665	−0.553325	−	0.832965i	$-0.686641\pi$
$521$	−7.14445e25	−1.10665	−0.553325	+	0.832965i	$0.686641\pi$
$522$	7.28139e23	0.0110750
$523$	−8.99895e25	−1.34408	−0.672041	−	0.740514i	$-0.734582\pi$
$523$	−8.99895e25	−1.34408	−0.672041	+	0.740514i	$0.734582\pi$
$524$	2.27548e25	0.333754
$525$	0	0
$526$	−6.19338e25	−0.876120
$527$	−2.35484e25	−0.327160
$528$	−7.34111e21	−0.000100170 0
$529$	1.22409e26	1.64053
$530$	3.24756e25	0.427500
$531$	−8.19444e25	−1.05955
$532$	0	0
$533$	−1.66895e26	−2.08226
$534$	1.00963e26	1.23743
$535$	6.29123e25	0.757486
$536$	7.86223e25	0.929995
$537$	2.10036e26	2.44083
$538$	6.09544e25	0.695943
$539$	0	0
$540$	9.18486e24	0.101235
$541$	−9.33602e25	−1.01109	−0.505543	−	0.862802i	$-0.668708\pi$
$541$	−9.33602e25	−1.01109	−0.505543	+	0.862802i	$0.668708\pi$
$542$	−9.14497e25	−0.973171
$543$	1.68349e26	1.76040
$544$	−4.43162e25	−0.455379
$545$	−4.37866e25	−0.442155
$546$	0	0
$547$	−2.74670e25	−0.267875	−0.133938	−	0.990990i	$-0.542762\pi$
$547$	−2.74670e25	−0.267875	−0.133938	+	0.990990i	$0.542762\pi$
$548$	9.34587e25	0.895786
$549$	−3.28018e25	−0.309001
$550$	9.92207e22	0.000918664 0
$551$	1.94602e24	0.0177095
$552$	2.72541e26	2.43787
$553$	0	0
$554$	9.13016e25	0.789106
$555$	2.03983e25	0.173305
$556$	4.38079e25	0.365882
$557$	1.42589e26	1.17074	0.585370	−	0.810766i	$-0.300949\pi$
$557$	1.42589e26	1.17074	0.585370	+	0.810766i	$0.300949\pi$
$558$	6.69543e25	0.540447
$559$	−5.68712e25	−0.451316
$560$	0	0
$561$	−1.84822e23	−0.00141777
$562$	−5.43732e25	−0.410100
$563$	1.72252e26	1.27742	0.638712	−	0.769446i	$-0.279467\pi$
$563$	1.72252e26	1.27742	0.638712	+	0.769446i	$0.279467\pi$
$564$	−5.60626e25	−0.408810
$565$	6.11995e25	0.438821
$566$	1.57825e24	0.0111281
$567$	0	0
$568$	6.81956e25	0.464994
$569$	5.24893e25	0.351969	0.175984	−	0.984393i	$-0.443689\pi$
$569$	5.24893e25	0.351969	0.175984	+	0.984393i	$0.443689\pi$
$570$	−9.39144e25	−0.619329
$571$	−3.21674e24	−0.0208628	−0.0104314	−	0.999946i	$-0.503320\pi$
$571$	−3.21674e24	−0.0208628	−0.0104314	+	0.999946i	$0.503320\pi$
$572$	−2.58599e23	−0.00164955
$573$	−3.13728e26	−1.96827
$574$	0	0
$575$	−1.88390e26	−1.14344
$576$	1.32580e26	0.791527
$577$	−1.17453e26	−0.689752	−0.344876	−	0.938648i	$-0.612079\pi$
$577$	−1.17453e26	−0.689752	−0.344876	+	0.938648i	$0.612079\pi$
$578$	−8.59176e25	−0.496327
$579$	2.63744e26	1.49877
$580$	−8.55764e23	−0.00478397
$581$	0	0
$582$	−1.46671e25	−0.0793553
$583$	−4.85655e23	−0.00258509
$584$	1.14943e26	0.601953
$585$	−1.68225e26	−0.866783
$586$	9.72354e25	0.492943
$587$	−1.86886e24	−0.00932213	−0.00466107	−	0.999989i	$-0.501484\pi$
$587$	−1.86886e24	−0.00932213	−0.00466107	+	0.999989i	$0.501484\pi$
$588$	0	0
$589$	1.78941e26	0.864201
$590$	−6.33021e25	−0.300832
$591$	−1.22772e26	−0.574141
$592$	1.51433e24	0.00696889
$593$	1.50165e26	0.680063	0.340032	−	0.940414i	$-0.389562\pi$
$593$	1.50165e26	0.680063	0.340032	+	0.940414i	$0.389562\pi$
$594$	9.02822e22	0.000402375 0
$595$	0	0
$596$	8.41563e25	0.363285
$597$	−5.36441e25	−0.227911
$598$	−3.22732e26	−1.34952
$599$	1.65804e26	0.682403	0.341201	−	0.939990i	$-0.389166\pi$
$599$	1.65804e26	0.682403	0.341201	+	0.939990i	$0.389166\pi$
$600$	−2.60597e26	−1.05568
$601$	2.54795e26	1.01598	0.507989	−	0.861364i	$-0.330389\pi$
$601$	2.54795e26	1.01598	0.507989	+	0.861364i	$0.330389\pi$
$602$	0	0
$603$	−2.87833e26	−1.11206
$604$	−1.82085e26	−0.692507
$605$	−1.45400e26	−0.544361
$606$	−3.28564e26	−1.21096
$607$	−3.14191e26	−1.13999	−0.569996	−	0.821648i	$-0.693055\pi$
$607$	−3.14191e26	−1.13999	−0.569996	+	0.821648i	$0.693055\pi$
$608$	3.36753e26	1.20290
$609$	0	0
$610$	−2.53394e25	−0.0877329
$611$	1.76410e26	0.601355
$612$	9.99214e25	0.335367
$613$	−3.91478e26	−1.29370	−0.646848	−	0.762619i	$-0.723913\pi$
$613$	−3.91478e26	−1.29370	−0.646848	+	0.762619i	$0.723913\pi$
$614$	−8.75005e25	−0.284715
$615$	−3.98590e26	−1.27707
$616$	0	0
$617$	4.86066e26	1.51003	0.755016	−	0.655706i	$-0.227629\pi$
$617$	4.86066e26	1.51003	0.755016	+	0.655706i	$0.227629\pi$
$618$	1.13345e26	0.346747
$619$	4.51098e26	1.35897	0.679485	−	0.733689i	$-0.262203\pi$
$619$	4.51098e26	1.35897	0.679485	+	0.733689i	$0.262203\pi$
$620$	−7.86897e25	−0.233452
$621$	−1.71418e26	−0.500827
$622$	7.04619e25	0.202743
$623$	0	0
$624$	−2.28318e25	−0.0637215
$625$	7.23294e25	0.198817
$626$	−1.31058e26	−0.354819
$627$	1.40444e24	0.00374508
$628$	−3.39248e26	−0.891047
$629$	3.81251e25	0.0986349
$630$	0	0
$631$	2.03805e26	0.511607	0.255803	−	0.966729i	$-0.417660\pi$
$631$	2.03805e26	0.511607	0.255803	+	0.966729i	$0.417660\pi$
$632$	3.53536e25	0.0874221
$633$	6.70753e26	1.63391
$634$	1.20171e25	0.0288371
$635$	2.09383e26	0.494985
$636$	4.80016e26	1.11793
$637$	0	0
$638$	−8.41170e21	−1.90146e−5 0
$639$	−2.49662e26	−0.556024
$640$	−1.43007e26	−0.313796
$641$	5.77927e26	1.24946	0.624729	−	0.780842i	$-0.285209\pi$
$641$	5.77927e26	1.24946	0.624729	+	0.780842i	$0.285209\pi$
$642$	−6.11213e26	−1.30200
$643$	−7.72049e26	−1.62047	−0.810235	−	0.586106i	$-0.800660\pi$
$643$	−7.72049e26	−1.62047	−0.810235	+	0.586106i	$0.800660\pi$
$644$	0	0
$645$	−1.35824e26	−0.276796
$646$	−1.75529e26	−0.352485
$647$	1.39226e24	0.00275504	0.00137752	−	0.999999i	$-0.499562\pi$
$647$	1.39226e24	0.00275504	0.00137752	+	0.999999i	$0.499562\pi$
$648$	3.88123e26	0.756844
$649$	9.46648e23	0.00181913
$650$	3.08588e26	0.584390
$651$	0	0
$652$	1.83726e26	0.337924
$653$	−6.19470e26	−1.12291	−0.561455	−	0.827507i	$-0.689758\pi$
$653$	−6.19470e26	−1.12291	−0.561455	+	0.827507i	$0.689758\pi$
$654$	4.25401e26	0.759994
$655$	−1.71004e26	−0.301103
$656$	−2.95905e25	−0.0513530
$657$	−4.20804e26	−0.719795
$658$	0	0
$659$	−7.96627e25	−0.132386	−0.0661932	−	0.997807i	$-0.521085\pi$
$659$	−7.96627e25	−0.132386	−0.0661932	+	0.997807i	$0.521085\pi$
$660$	−6.17605e23	−0.00101168
$661$	1.85436e26	0.299420	0.149710	−	0.988730i	$-0.452166\pi$
$661$	1.85436e26	0.299420	0.149710	+	0.988730i	$0.452166\pi$
$662$	−4.80339e26	−0.764535
$663$	−5.74819e26	−0.901888
$664$	4.63273e26	0.716540
$665$	0	0
$666$	−1.08400e26	−0.162938
$667$	1.59713e25	0.0236670
$668$	7.69977e25	0.112487
$669$	1.01771e27	1.46580
$670$	−2.22351e26	−0.315740
$671$	3.78937e23	0.000530521 0
$672$	0	0
$673$	5.91532e26	0.805073	0.402536	−	0.915404i	$-0.368129\pi$
$673$	5.91532e26	0.805073	0.402536	+	0.915404i	$0.368129\pi$
$674$	3.08329e26	0.413757
$675$	1.63906e26	0.216875
$676$	−3.41793e26	−0.445933
$677$	2.97418e26	0.382626	0.191313	−	0.981529i	$-0.438725\pi$
$677$	2.97418e26	0.382626	0.191313	+	0.981529i	$0.438725\pi$
$678$	−5.94573e26	−0.754264
$679$	0	0
$680$	2.05115e26	0.253024
$681$	−1.03074e27	−1.25387
$682$	−7.73477e23	−0.000927889 0
$683$	−1.25943e27	−1.48997	−0.744983	−	0.667084i	$-0.767542\pi$
$683$	−1.25943e27	−1.48997	−0.744983	+	0.667084i	$0.767542\pi$
$684$	−7.59290e26	−0.885880
$685$	−7.02349e26	−0.808151
$686$	0	0
$687$	−2.02558e27	−2.26704
$688$	−1.00833e25	−0.0111304
$689$	−1.51044e27	−1.64446
$690$	−7.70771e26	−0.827674
$691$	−3.19965e25	−0.0338891	−0.0169446	−	0.999856i	$-0.505394\pi$
$691$	−3.19965e25	−0.0338891	−0.0169446	+	0.999856i	$0.505394\pi$
$692$	−3.77567e26	−0.394445
$693$	0	0
$694$	4.84840e26	0.492815
$695$	−3.29220e26	−0.330088
$696$	2.20928e25	0.0218506
$697$	−7.44979e26	−0.726829
$698$	3.25888e26	0.313648
$699$	−1.22664e27	−1.16462
$700$	0	0
$701$	2.06463e27	1.90775	0.953874	−	0.300208i	$-0.0970562\pi$
$701$	2.06463e27	1.90775	0.953874	+	0.300208i	$0.0970562\pi$
$702$	2.80788e26	0.255963
$703$	−2.89708e26	−0.260546
$704$	−1.53161e24	−0.00135897
$705$	4.21315e26	0.368816
$706$	2.31338e26	0.199803
$707$	0	0
$708$	−9.35656e26	−0.786684
$709$	−1.44096e27	−1.19539	−0.597697	−	0.801722i	$-0.703918\pi$
$709$	−1.44096e27	−1.19539	−0.597697	+	0.801722i	$0.703918\pi$
$710$	−1.92864e26	−0.157869
$711$	−1.29428e26	−0.104536
$712$	1.67562e27	1.33541
$713$	1.46860e27	1.15492
$714$	0	0
$715$	1.94339e24	0.00148817
$716$	1.31180e27	0.991273
$717$	−1.32916e27	−0.991165
$718$	1.51395e27	1.11411
$719$	1.26393e27	0.917907	0.458953	−	0.888460i	$-0.348224\pi$
$719$	1.26393e27	0.917907	0.458953	+	0.888460i	$0.348224\pi$
$720$	−2.98264e25	−0.0213767
$721$	0	0
$722$	4.31665e26	0.301331
$723$	3.73024e27	2.56994
$724$	1.05144e27	0.714937
$725$	−1.52714e25	−0.0102486
$726$	1.41260e27	0.935670
$727$	−5.54468e26	−0.362493	−0.181246	−	0.983438i	$-0.558013\pi$
$727$	−5.54468e26	−0.362493	−0.181246	+	0.983438i	$0.558013\pi$
$728$	0	0
$729$	−2.13985e27	−1.36293
$730$	−3.25071e26	−0.204367
$731$	−2.53860e26	−0.157536
$732$	−3.74537e26	−0.229424
$733$	−8.06563e26	−0.487698	−0.243849	−	0.969813i	$-0.578410\pi$
$733$	−8.06563e26	−0.487698	−0.243849	+	0.969813i	$0.578410\pi$
$734$	1.02340e27	0.610848
$735$	0	0
$736$	2.76379e27	1.60755
$737$	3.32514e24	0.00190928
$738$	2.11817e27	1.20068
$739$	6.63850e26	0.371490	0.185745	−	0.982598i	$-0.440530\pi$
$739$	6.63850e26	0.371490	0.185745	+	0.982598i	$0.440530\pi$
$740$	1.27400e26	0.0703829
$741$	4.36798e27	2.38236
$742$	0	0
$743$	−3.64095e27	−1.93562	−0.967811	−	0.251677i	$-0.919018\pi$
$743$	−3.64095e27	−1.93562	−0.967811	+	0.251677i	$0.919018\pi$
$744$	2.03149e27	1.06628
$745$	−6.32441e26	−0.327745
$746$	2.32837e27	1.19133
$747$	−1.69603e27	−0.856814
$748$	−1.15432e24	−0.000575788 0
$749$	0	0
$750$	1.78435e27	0.867758
$751$	−1.55458e27	−0.746505	−0.373253	−	0.927730i	$-0.621758\pi$
$751$	−1.55458e27	−0.746505	−0.373253	+	0.927730i	$0.621758\pi$
$752$	3.12775e25	0.0148307
$753$	3.69410e27	1.72964
$754$	−2.61614e25	−0.0120958
$755$	1.36839e27	0.624759
$756$	0	0
$757$	1.33406e27	0.593970	0.296985	−	0.954882i	$-0.404019\pi$
$757$	1.33406e27	0.593970	0.296985	+	0.954882i	$0.404019\pi$
$758$	−1.95613e27	−0.860081
$759$	1.15265e25	0.00500494
$760$	−1.55864e27	−0.668370
$761$	6.89829e25	0.0292137	0.0146069	−	0.999893i	$-0.495350\pi$
$761$	6.89829e25	0.0292137	0.0146069	+	0.999893i	$0.495350\pi$
$762$	−2.03423e27	−0.850799
$763$	0	0
$764$	−1.95942e27	−0.799357
$765$	−7.50917e26	−0.302558
$766$	8.51822e26	0.338981
$767$	2.94419e27	1.15720
$768$	3.89821e27	1.51333
$769$	8.09673e26	0.310463	0.155231	−	0.987878i	$-0.450388\pi$
$769$	8.09673e26	0.310463	0.155231	+	0.987878i	$0.450388\pi$
$770$	0	0
$771$	−3.23221e27	−1.20916
$772$	1.64724e27	0.608683
$773$	−1.00924e27	−0.368374	−0.184187	−	0.982891i	$-0.558965\pi$
$773$	−1.00924e27	−0.368374	−0.184187	+	0.982891i	$0.558965\pi$
$774$	7.21790e26	0.260239
$775$	−1.40424e27	−0.500121
$776$	−2.43421e26	−0.0856389
$777$	0	0
$778$	−2.95236e27	−1.01359
$779$	5.66100e27	1.91994
$780$	−1.92083e27	−0.643560
$781$	2.88417e24	0.000954633 0
$782$	−1.44060e27	−0.471062
$783$	−1.38956e25	−0.00448890
$784$	0	0
$785$	2.54948e27	0.803876
$786$	1.66136e27	0.517548
$787$	4.88307e27	1.50291	0.751456	−	0.659784i	$-0.229352\pi$
$787$	4.88307e27	1.50291	0.751456	+	0.659784i	$0.229352\pi$
$788$	−7.66785e26	−0.233171
$789$	6.87955e27	2.06694
$790$	−9.99833e25	−0.0296804
$791$	0	0
$792$	8.72137e24	0.00252752
$793$	1.17854e27	0.337480
$794$	−5.59784e26	−0.158389
$795$	−3.60735e27	−1.00856
$796$	−3.35040e26	−0.0925598
$797$	−1.18346e27	−0.323072	−0.161536	−	0.986867i	$-0.551645\pi$
$797$	−1.18346e27	−0.323072	−0.161536	+	0.986867i	$0.551645\pi$
$798$	0	0
$799$	7.87451e26	0.209908
$800$	−2.64267e27	−0.696127
$801$	−6.13438e27	−1.59684
$802$	−2.36160e26	−0.0607506
$803$	4.86126e24	0.00123581
$804$	−3.28653e27	−0.825669
$805$	0	0
$806$	−2.40561e27	−0.590258
$807$	−6.77075e27	−1.64187
$808$	−5.45297e27	−1.30685
$809$	−5.08495e27	−1.20441	−0.602207	−	0.798340i	$-0.705712\pi$
$809$	−5.08495e27	−1.20441	−0.602207	+	0.798340i	$0.705712\pi$
$810$	−1.09765e27	−0.256954
$811$	2.72133e25	0.00629627	0.00314813	−	0.999995i	$-0.498998\pi$
$811$	2.72133e25	0.00629627	0.00314813	+	0.999995i	$0.498998\pi$
$812$	0	0
$813$	1.01581e28	2.29590
$814$	1.25227e24	0.000279748 0
$815$	−1.38072e27	−0.304865
$816$	−1.01916e26	−0.0222425
$817$	1.92905e27	0.416134
$818$	−1.28536e27	−0.274074
$819$	0	0
$820$	−2.48943e27	−0.518644
$821$	−5.16381e26	−0.106343	−0.0531716	−	0.998585i	$-0.516933\pi$
$821$	−5.16381e26	−0.106343	−0.0531716	+	0.998585i	$0.516933\pi$
$822$	6.82355e27	1.38908
$823$	−1.97624e27	−0.397687	−0.198843	−	0.980031i	$-0.563718\pi$
$823$	−1.97624e27	−0.397687	−0.198843	+	0.980031i	$0.563718\pi$
$824$	1.88112e27	0.374204
$825$	−1.10213e25	−0.00216731
$826$	0	0
$827$	−1.16795e27	−0.224450	−0.112225	−	0.993683i	$-0.535798\pi$
$827$	−1.16795e27	−0.224450	−0.112225	+	0.993683i	$0.535798\pi$
$828$	−6.23162e27	−1.18389
$829$	−4.20809e27	−0.790345	−0.395173	−	0.918607i	$-0.629315\pi$
$829$	−4.20809e27	−0.790345	−0.395173	+	0.918607i	$0.629315\pi$
$830$	−1.31018e27	−0.243270
$831$	−1.01417e28	−1.86166
$832$	−4.76350e27	−0.864479
$833$	0	0
$834$	3.19848e27	0.567369
$835$	−5.78644e26	−0.101482
$836$	8.77156e24	0.00152096
$837$	−1.27774e27	−0.219053
$838$	−3.94700e27	−0.669036
$839$	−8.49254e27	−1.42331	−0.711654	−	0.702530i	$-0.752053\pi$
$839$	−8.49254e27	−1.42331	−0.711654	+	0.702530i	$0.752053\pi$
$840$	0	0
$841$	−6.10197e27	−0.999788
$842$	−2.37873e27	−0.385372
$843$	6.03972e27	0.967508
$844$	4.18926e27	0.663565
$845$	2.56860e27	0.402307
$846$	−2.23893e27	−0.346755
$847$	0	0
$848$	−2.67802e26	−0.0405558
$849$	−1.75311e26	−0.0262534
$850$	1.37747e27	0.203986
$851$	−2.37768e27	−0.348195
$852$	−2.85068e27	−0.412831
$853$	9.33345e27	1.33668	0.668338	−	0.743857i	$-0.267006\pi$
$853$	9.33345e27	1.33668	0.668338	+	0.743857i	$0.267006\pi$
$854$	0	0
$855$	5.70612e27	0.799214
$856$	−1.01439e28	−1.40509
$857$	1.11037e28	1.52108	0.760539	−	0.649292i	$-0.224935\pi$
$857$	1.11037e28	1.52108	0.760539	+	0.649292i	$0.224935\pi$
$858$	−1.88807e25	−0.00255793
$859$	−1.11478e28	−1.49367	−0.746834	−	0.665011i	$-0.768427\pi$
$859$	−1.11478e28	−1.49367	−0.746834	+	0.665011i	$0.768427\pi$
$860$	−8.48302e26	−0.112413
$861$	0	0
$862$	4.75899e27	0.616873
$863$	1.15445e28	1.48004	0.740021	−	0.672583i	$-0.234815\pi$
$863$	1.15445e28	1.48004	0.740021	+	0.672583i	$0.234815\pi$
$864$	−2.40460e27	−0.304903
$865$	2.83745e27	0.355856
$866$	−6.61699e27	−0.820806
$867$	9.54364e27	1.17093
$868$	0	0
$869$	1.49520e24	0.000179478 0
$870$	−6.24806e25	−0.00741843
$871$	1.03416e28	1.21455
$872$	7.06012e27	0.820173
$873$	8.91154e26	0.102404
$874$	1.09469e28	1.24432
$875$	0	0
$876$	−4.80482e27	−0.534426
$877$	1.55912e28	1.71547	0.857734	−	0.514094i	$-0.171872\pi$
$877$	1.55912e28	1.71547	0.857734	+	0.514094i	$0.171872\pi$
$878$	−8.20147e27	−0.892676
$879$	−1.08008e28	−1.16295
$880$	3.44564e23	3.67015e−5 0
$881$	−3.35920e26	−0.0353969	−0.0176985	−	0.999843i	$-0.505634\pi$
$881$	−3.35920e26	−0.0353969	−0.0176985	+	0.999843i	$0.505634\pi$
$882$	0	0
$883$	−1.34374e26	−0.0138576	−0.00692882	−	0.999976i	$-0.502206\pi$
$883$	−1.34374e26	−0.0138576	−0.00692882	+	0.999976i	$0.502206\pi$
$884$	−3.59009e27	−0.366276
$885$	7.03153e27	0.709722
$886$	3.98400e27	0.397832
$887$	−9.23887e27	−0.912735	−0.456367	−	0.889791i	$-0.650850\pi$
$887$	−9.23887e27	−0.912735	−0.456367	+	0.889791i	$0.650850\pi$
$888$	−3.28901e27	−0.321471
$889$	0	0
$890$	−4.73881e27	−0.453382
$891$	1.64147e25	0.00155380
$892$	6.35619e27	0.595293
$893$	−5.98374e27	−0.554478
$894$	6.14437e27	0.563341
$895$	−9.85826e27	−0.894296
$896$	0	0
$897$	3.58487e28	3.18379
$898$	−7.32226e27	−0.643458
$899$	1.19048e26	0.0103516
$900$	5.95853e27	0.512667
$901$	−6.74227e27	−0.574011
$902$	−2.44698e25	−0.00206143
$903$	0	0
$904$	−9.86777e27	−0.813990
$905$	−7.90165e27	−0.644995
$906$	−1.32943e28	−1.07386
$907$	−1.80585e28	−1.44349	−0.721743	−	0.692161i	$-0.756659\pi$
$907$	−1.80585e28	−1.44349	−0.721743	+	0.692161i	$0.756659\pi$
$908$	−6.43758e27	−0.509222
$909$	1.99631e28	1.56268
$910$	0	0
$911$	−1.99304e28	−1.52789	−0.763943	−	0.645283i	$-0.776739\pi$
$911$	−1.99304e28	−1.52789	−0.763943	+	0.645283i	$0.776739\pi$
$912$	7.74443e26	0.0587541
$913$	1.95930e25	0.00147106
$914$	−1.22020e27	−0.0906651
$915$	2.81467e27	0.206980
$916$	−1.26509e28	−0.920694
$917$	0	0
$918$	1.25337e27	0.0893460
$919$	1.04320e28	0.735984	0.367992	−	0.929829i	$-0.380045\pi$
$919$	1.04320e28	0.735984	0.367992	+	0.929829i	$0.380045\pi$
$920$	−1.27920e28	−0.893212
$921$	9.71946e27	0.671701
$922$	−3.17744e27	−0.217337
$923$	8.97012e27	0.607271
$924$	0	0
$925$	2.27348e27	0.150781
$926$	−1.13929e28	−0.747874
$927$	−6.88672e27	−0.447461
$928$	2.24039e26	0.0144085
$929$	5.17736e27	0.329578	0.164789	−	0.986329i	$-0.447306\pi$
$929$	5.17736e27	0.329578	0.164789	+	0.986329i	$0.447306\pi$
$930$	−5.74525e27	−0.362010
$931$	0	0
$932$	−7.66111e27	−0.472977
$933$	−7.82683e27	−0.478311
$934$	−8.87060e27	−0.536609
$935$	8.67484e24	0.000519459 0
$936$	2.71245e28	1.60783
$937$	−9.33202e27	−0.547582	−0.273791	−	0.961789i	$-0.588278\pi$
$937$	−9.33202e27	−0.547582	−0.273791	+	0.961789i	$0.588278\pi$
$938$	0	0
$939$	1.45578e28	0.837089
$940$	2.63136e27	0.149784
$941$	−4.50115e27	−0.253642	−0.126821	−	0.991926i	$-0.540477\pi$
$941$	−4.50115e27	−0.253642	−0.126821	+	0.991926i	$0.540477\pi$
$942$	−2.47690e28	−1.38173
$943$	4.64607e28	2.56581
$944$	5.22005e26	0.0285391
$945$	0	0
$946$	−8.33835e24	−0.000446801 0
$947$	1.76126e28	0.934324	0.467162	−	0.884172i	$-0.345276\pi$
$947$	1.76126e28	0.934324	0.467162	+	0.884172i	$0.345276\pi$
$948$	−1.47783e27	−0.0776151
$949$	1.51191e28	0.786135
$950$	−1.04672e28	−0.538835
$951$	−1.33485e27	−0.0680325
$952$	0	0
$953$	5.93730e27	0.296624	0.148312	−	0.988941i	$-0.452616\pi$
$953$	5.93730e27	0.296624	0.148312	+	0.988941i	$0.452616\pi$
$954$	1.91700e28	0.948230
$955$	1.47252e28	0.721155
$956$	−8.30141e27	−0.402534
$957$	9.34363e23	4.48593e−5 0
$958$	−1.52374e28	−0.724333
$959$	0	0
$960$	−1.13765e28	−0.530192
$961$	−1.07239e28	−0.494857
$962$	3.89471e27	0.177956
$963$	3.71365e28	1.68016
$964$	2.32976e28	1.04371
$965$	−1.23791e28	−0.549136
$966$	0	0
$967$	−2.58489e28	−1.12432	−0.562160	−	0.827028i	$-0.690030\pi$
$967$	−2.58489e28	−1.12432	−0.562160	+	0.827028i	$0.690030\pi$
$968$	2.34441e28	1.00976
$969$	1.94976e28	0.831583
$970$	6.88417e26	0.0290750
$971$	−2.05732e28	−0.860438	−0.430219	−	0.902725i	$-0.641564\pi$
$971$	−2.05732e28	−0.860438	−0.430219	+	0.902725i	$0.641564\pi$
$972$	−2.07144e28	−0.857912
$973$	0	0
$974$	−2.21698e28	−0.900435
$975$	−3.42777e28	−1.37869
$976$	2.08955e26	0.00832300
$977$	−2.34524e28	−0.925099	−0.462550	−	0.886593i	$-0.653065\pi$
$977$	−2.34524e28	−0.925099	−0.462550	+	0.886593i	$0.653065\pi$
$978$	1.34141e28	0.524014
$979$	7.08664e25	0.00274160
$980$	0	0
$981$	−2.58468e28	−0.980736
$982$	4.49949e27	0.169085
$983$	−4.25526e28	−1.58368	−0.791840	−	0.610729i	$-0.790877\pi$
$983$	−4.25526e28	−1.58368	−0.791840	+	0.610729i	$0.790877\pi$
$984$	6.42684e28	2.36889
$985$	5.76245e27	0.210360
$986$	−1.16778e26	−0.00422213
$987$	0	0
$988$	2.72806e28	0.967527
$989$	1.58320e28	0.556123
$990$	−2.46649e25	−0.000858113 0
$991$	5.21472e28	1.79693	0.898466	−	0.439044i	$-0.144683\pi$
$991$	5.21472e28	1.79693	0.898466	+	0.439044i	$0.144683\pi$
$992$	2.06010e28	0.703117
$993$	5.33556e28	1.80369
$994$	0	0
$995$	2.51785e27	0.0835046
$996$	−1.93655e28	−0.636159
$997$	1.61541e27	0.0525629	0.0262815	−	0.999655i	$-0.491633\pi$
$997$	1.61541e27	0.0525629	0.0262815	+	0.999655i	$0.491633\pi$
$998$	−1.61493e28	−0.520490
$999$	2.06867e27	0.0660419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.20.a.b.1.1		1
7.6	odd	2		1.20.a.a.1.1	✓	1
21.20	even	2		9.20.a.a.1.1		1
28.27	even	2		16.20.a.a.1.1		1
35.13	even	4		25.20.b.a.24.1		2
35.27	even	4		25.20.b.a.24.2		2
35.34	odd	2		25.20.a.a.1.1		1
56.13	odd	2		64.20.a.b.1.1		1
56.27	even	2		64.20.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.20.a.a.1.1	✓	1	7.6	odd	2
9.20.a.a.1.1		1	21.20	even	2
16.20.a.a.1.1		1	28.27	even	2
25.20.a.a.1.1		1	35.34	odd	2
25.20.b.a.24.1		2	35.13	even	4
25.20.b.a.24.2		2	35.27	even	4
49.20.a.b.1.1		1	1.1	even	1	trivial
64.20.a.b.1.1		1	56.13	odd	2
64.20.a.h.1.1		1	56.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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