LMFDB - Embedded newform 49.26.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [49,26,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, 26, names="a")

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

chi := DirichletCharacter("49.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 26 $
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:	$194.038422177$
Analytic rank:	$0$
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)

$f(q)$

$=$

$q-48.0000 q^{2} +195804. q^{3} -3.35521e7 q^{4} +7.41990e8 q^{5} -9.39859e6 q^{6} +3.22111e9 q^{8} -8.08949e11 q^{9} +O(q^{10})$

\(q-48.0000 q^{2} +195804. q^{3} -3.35521e7 q^{4} +7.41990e8 q^{5} -9.39859e6 q^{6} +3.22111e9 q^{8} -8.08949e11 q^{9} -3.56155e10 q^{10} +8.41952e12 q^{11} -6.56964e12 q^{12} +8.16510e13 q^{13} +1.45285e14 q^{15} +1.12567e15 q^{16} +2.51990e15 q^{17} +3.88296e13 q^{18} +6.08206e15 q^{19} -2.48953e16 q^{20} -4.04137e14 q^{22} -9.49953e16 q^{23} +6.30707e14 q^{24} +2.52526e17 q^{25} -3.91925e15 q^{26} -3.24298e17 q^{27} -2.71247e17 q^{29} -6.97366e15 q^{30} -4.29167e18 q^{31} -1.62115e17 q^{32} +1.64857e18 q^{33} -1.20955e17 q^{34} +2.71420e19 q^{36} +2.03015e19 q^{37} -2.91939e17 q^{38} +1.59876e19 q^{39} +2.39003e18 q^{40} +1.83744e20 q^{41} +3.00902e20 q^{43} -2.82493e20 q^{44} -6.00232e20 q^{45} +4.55977e18 q^{46} +9.24361e20 q^{47} +2.20410e20 q^{48} -1.21212e19 q^{50} +4.93407e20 q^{51} -2.73957e21 q^{52} -9.90292e20 q^{53} +1.55663e19 q^{54} +6.24719e21 q^{55} +1.19089e21 q^{57} +1.30199e19 q^{58} -1.30526e22 q^{59} -4.87461e21 q^{60} -9.01545e21 q^{61} +2.06000e20 q^{62} -3.77634e22 q^{64} +6.05842e22 q^{65} -7.91316e19 q^{66} -2.66891e22 q^{67} -8.45480e22 q^{68} -1.86005e22 q^{69} -1.92391e23 q^{71} -2.60572e21 q^{72} -4.24046e22 q^{73} -9.74471e20 q^{74} +4.94455e22 q^{75} -2.04066e23 q^{76} -7.67405e20 q^{78} -2.71681e23 q^{79} +8.35234e23 q^{80} +6.21915e23 q^{81} -8.81972e21 q^{82} +9.31454e23 q^{83} +1.86974e24 q^{85} -1.44433e22 q^{86} -5.31112e22 q^{87} +2.71202e22 q^{88} +1.76364e24 q^{89} +2.88111e22 q^{90} +3.18729e24 q^{92} -8.40325e23 q^{93} -4.43693e22 q^{94} +4.51282e24 q^{95} -3.17427e22 q^{96} -2.82924e24 q^{97} -6.81096e24 q^{99} +O(q^{100})\)

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 $

$2$	−48.0000	−0.00828641	−0.00414320	−	0.999991i	$-0.501319\pi$
$2$	−48.0000	−0.00828641	−0.00414320	+	0.999991i	$0.501319\pi$
$3$	195804.	0.212719	0.106359	−	0.994328i	$-0.466081\pi$
$3$	195804.	0.212719	0.106359	+	0.994328i	$0.466081\pi$
$4$	−3.35521e7	−0.999931
$5$	7.41990e8	1.35917	0.679584	−	0.733598i	$-0.262160\pi$
$5$	7.41990e8	1.35917	0.679584	+	0.733598i	$0.262160\pi$
$6$	−9.39859e6	−0.00176267
$7$	0	0
$7$	0	0
$8$	3.22111e9	0.0165722
$9$	−8.08949e11	−0.954751
$10$	−3.56155e10	−0.0112626
$11$	8.41952e12	0.808870	0.404435	−	0.914567i	$-0.367468\pi$
$11$	8.41952e12	0.808870	0.404435	+	0.914567i	$0.367468\pi$
$12$	−6.56964e12	−0.212704
$13$	8.16510e13	0.972008	0.486004	−	0.873957i	$-0.338454\pi$
$13$	8.16510e13	0.972008	0.486004	+	0.873957i	$0.338454\pi$
$14$	0	0
$15$	1.45285e14	0.289120
$16$	1.12567e15	0.999794
$17$	2.51990e15	1.04899	0.524496	−	0.851413i	$-0.324254\pi$
$17$	2.51990e15	1.04899	0.524496	+	0.851413i	$0.324254\pi$
$18$	3.88296e13	0.00791145
$19$	6.08206e15	0.630421	0.315210	−	0.949022i	$-0.397925\pi$
$19$	6.08206e15	0.630421	0.315210	+	0.949022i	$0.397925\pi$
$20$	−2.48953e16	−1.35907
$21$	0	0
$22$	−4.04137e14	−0.00670262
$23$	−9.49953e16	−0.903866	−0.451933	−	0.892052i	$-0.649265\pi$
$23$	−9.49953e16	−0.903866	−0.451933	+	0.892052i	$0.649265\pi$
$24$	6.30707e14	0.00352523
$25$	2.52526e17	0.847336
$26$	−3.91925e15	−0.00805445
$27$	−3.24298e17	−0.415812
$28$	0	0
$29$	−2.71247e17	−0.142361	−0.0711803	−	0.997463i	$-0.522677\pi$
$29$	−2.71247e17	−0.142361	−0.0711803	+	0.997463i	$0.522677\pi$
$30$	−6.97366e15	−0.00239577
$31$	−4.29167e18	−0.978599	−0.489299	−	0.872116i	$-0.662747\pi$
$31$	−4.29167e18	−0.978599	−0.489299	+	0.872116i	$0.662747\pi$
$32$	−1.62115e17	−0.0248569
$33$	1.64857e18	0.172062
$34$	−1.20955e17	−0.00869237
$35$	0	0
$36$	2.71420e19	0.954685
$37$	2.03015e19	0.506998	0.253499	−	0.967336i	$-0.418419\pi$
$37$	2.03015e19	0.506998	0.253499	+	0.967336i	$0.418419\pi$
$38$	−2.91939e17	−0.00522392
$39$	1.59876e19	0.206764
$40$	2.39003e18	0.0225245
$41$	1.83744e20	1.27179	0.635895	−	0.771775i	$-0.280631\pi$
$41$	1.83744e20	1.27179	0.635895	+	0.771775i	$0.280631\pi$
$42$	0	0
$43$	3.00902e20	1.14834	0.574168	−	0.818737i	$-0.305326\pi$
$43$	3.00902e20	1.14834	0.574168	+	0.818737i	$0.305326\pi$
$44$	−2.82493e20	−0.808814
$45$	−6.00232e20	−1.29767
$46$	4.55977e18	0.00748980
$47$	9.24361e20	1.16043	0.580214	−	0.814464i	$-0.302969\pi$
$47$	9.24361e20	1.16043	0.580214	+	0.814464i	$0.302969\pi$
$48$	2.20410e20	0.212675
$49$	0	0
$50$	−1.21212e19	−0.00702137
$51$	4.93407e20	0.223140
$52$	−2.73957e21	−0.971941
$53$	−9.90292e20	−0.276895	−0.138447	−	0.990370i	$-0.544211\pi$
$53$	−9.90292e20	−0.276895	−0.138447	+	0.990370i	$0.544211\pi$
$54$	1.55663e19	0.00344559
$55$	6.24719e21	1.09939
$56$	0	0
$57$	1.19089e21	0.134102
$58$	1.30199e19	0.00117966
$59$	−1.30526e22	−0.955093	−0.477547	−	0.878606i	$-0.658474\pi$
$59$	−1.30526e22	−0.955093	−0.477547	+	0.878606i	$0.658474\pi$
$60$	−4.87461e21	−0.289101
$61$	−9.01545e21	−0.434875	−0.217438	−	0.976074i	$-0.569770\pi$
$61$	−9.01545e21	−0.434875	−0.217438	+	0.976074i	$0.569770\pi$
$62$	2.06000e20	0.00810907
$63$	0	0
$64$	−3.77634e22	−0.999588
$65$	6.05842e22	1.32112
$66$	−7.91316e19	−0.00142577
$67$	−2.66891e22	−0.398473	−0.199236	−	0.979951i	$-0.563846\pi$
$67$	−2.66891e22	−0.398473	−0.199236	+	0.979951i	$0.563846\pi$
$68$	−8.45480e22	−1.04892
$69$	−1.86005e22	−0.192269
$70$	0	0
$71$	−1.92391e23	−1.39141	−0.695704	−	0.718329i	$-0.744907\pi$
$71$	−1.92391e23	−1.39141	−0.695704	+	0.718329i	$0.744907\pi$
$72$	−2.60572e21	−0.0158224
$73$	−4.24046e22	−0.216709	−0.108355	−	0.994112i	$-0.534558\pi$
$73$	−4.24046e22	−0.216709	−0.108355	+	0.994112i	$0.534558\pi$
$74$	−9.74471e20	−0.00420119
$75$	4.94455e22	0.180244
$76$	−2.04066e23	−0.630377
$77$	0	0
$78$	−7.67405e20	−0.00171333
$79$	−2.71681e23	−0.517274	−0.258637	−	0.965975i	$-0.583273\pi$
$79$	−2.71681e23	−0.517274	−0.258637	+	0.965975i	$0.583273\pi$
$80$	8.35234e23	1.35889
$81$	6.21915e23	0.866300
$82$	−8.81972e21	−0.0105386
$83$	9.31454e23	0.956501	0.478251	−	0.878223i	$-0.341271\pi$
$83$	9.31454e23	0.956501	0.478251	+	0.878223i	$0.341271\pi$
$84$	0	0
$85$	1.86974e24	1.42575
$86$	−1.44433e22	−0.00951558
$87$	−5.31112e22	−0.0302828
$88$	2.71202e22	0.0134048
$89$	1.76364e24	0.756892	0.378446	−	0.925623i	$-0.376459\pi$
$89$	1.76364e24	0.756892	0.378446	+	0.925623i	$0.376459\pi$
$90$	2.88111e22	0.0107530
$91$	0	0
$92$	3.18729e24	0.903804
$93$	−8.40325e23	−0.208166
$94$	−4.43693e22	−0.00961578
$95$	4.51282e24	0.856847
$96$	−3.17427e22	−0.00528754
$97$	−2.82924e24	−0.414022	−0.207011	−	0.978339i	$-0.566374\pi$
$97$	−2.82924e24	−0.414022	−0.207011	+	0.978339i	$0.566374\pi$
$98$	0	0
$99$	−6.81096e24	−0.772269
$100$	−8.47278e24	−0.847278
$101$	−1.86342e24	−0.164549	−0.0822744	−	0.996610i	$-0.526218\pi$
$101$	−1.86342e24	−0.164549	−0.0822744	+	0.996610i	$0.526218\pi$
$102$	−2.36835e22	−0.00184903
$103$	−4.85812e24	−0.335740	−0.167870	−	0.985809i	$-0.553689\pi$
$103$	−4.85812e24	−0.335740	−0.167870	+	0.985809i	$0.553689\pi$
$104$	2.63007e23	0.0161084
$105$	0	0
$106$	4.75340e22	0.00229446
$107$	3.58304e25	1.53799	0.768997	−	0.639252i	$-0.220756\pi$
$107$	3.58304e25	1.53799	0.768997	+	0.639252i	$0.220756\pi$
$108$	1.08809e25	0.415784
$109$	−4.77795e25	−1.62709	−0.813543	−	0.581505i	$-0.802464\pi$
$109$	−4.77795e25	−1.62709	−0.813543	+	0.581505i	$0.802464\pi$
$110$	−2.99865e23	−0.00910999
$111$	3.97511e24	0.107848
$112$	0	0
$113$	−7.46476e25	−1.62008	−0.810038	−	0.586378i	$-0.800553\pi$
$113$	−7.46476e25	−1.62008	−0.810038	+	0.586378i	$0.800553\pi$
$114$	−5.71628e22	−0.00111123
$115$	−7.04855e25	−1.22851
$116$	9.10091e24	0.142351
$117$	−6.60516e25	−0.928025
$118$	6.26523e23	0.00791429
$119$	0	0
$120$	4.67978e23	0.00479137
$121$	−3.74588e25	−0.345730
$122$	4.32742e23	0.00360355
$123$	3.59779e25	0.270534
$124$	1.43995e26	0.978532
$125$	−3.37587e25	−0.207496
$126$	0	0
$127$	3.35905e26	1.69305	0.846524	−	0.532350i	$-0.178691\pi$
$127$	3.35905e26	1.69305	0.846524	+	0.532350i	$0.178691\pi$
$128$	7.25231e24	0.0331399
$129$	5.89178e25	0.244273
$130$	−2.90804e24	−0.0109474
$131$	1.74971e26	0.598513	0.299257	−	0.954173i	$-0.403261\pi$
$131$	1.74971e26	0.598513	0.299257	+	0.954173i	$0.403261\pi$
$132$	−5.53132e25	−0.172050
$133$	0	0
$134$	1.28108e24	0.00330191
$135$	−2.40626e26	−0.565158
$136$	8.11689e24	0.0173841
$137$	6.18313e26	1.20837	0.604187	−	0.796843i	$-0.293498\pi$
$137$	6.18313e26	1.20837	0.604187	+	0.796843i	$0.293498\pi$
$138$	8.92822e23	0.00159322
$139$	4.84462e26	0.789905	0.394952	−	0.918702i	$-0.370761\pi$
$139$	4.84462e26	0.789905	0.394952	+	0.918702i	$0.370761\pi$
$140$	0	0
$141$	1.80994e26	0.246845
$142$	9.23474e24	0.0115298
$143$	6.87462e26	0.786228
$144$	−9.10608e26	−0.954554
$145$	−2.01262e26	−0.193492
$146$	2.03542e24	0.00179574
$147$	0	0
$148$	−6.81158e26	−0.506963
$149$	9.05569e26	0.619574	0.309787	−	0.950806i	$-0.399742\pi$
$149$	9.05569e26	0.619574	0.309787	+	0.950806i	$0.399742\pi$
$150$	−2.37339e24	−0.00149358
$151$	1.16190e27	0.672907	0.336454	−	0.941700i	$-0.390772\pi$
$151$	1.16190e27	0.672907	0.336454	+	0.941700i	$0.390772\pi$
$152$	1.95910e25	0.0104475
$153$	−2.03847e27	−1.00152
$154$	0	0
$155$	−3.18437e27	−1.33008
$156$	−5.36418e26	−0.206750
$157$	3.41505e26	0.121521	0.0607605	−	0.998152i	$-0.480647\pi$
$157$	3.41505e26	0.121521	0.0607605	+	0.998152i	$0.480647\pi$
$158$	1.30407e25	0.00428634
$159$	−1.93903e26	−0.0589008
$160$	−1.20287e26	−0.0337847
$161$	0	0
$162$	−2.98519e25	−0.00717851
$163$	4.63202e27	1.03140	0.515698	−	0.856771i	$-0.327533\pi$
$163$	4.63202e27	1.03140	0.515698	+	0.856771i	$0.327533\pi$
$164$	−6.16501e27	−1.27170
$165$	1.22323e27	0.233861
$166$	−4.47098e25	−0.00792596
$167$	8.26470e27	1.35916	0.679581	−	0.733600i	$-0.262162\pi$
$167$	8.26470e27	1.35916	0.679581	+	0.733600i	$0.262162\pi$
$168$	0	0
$169$	−3.89517e26	−0.0552004
$170$	−8.97475e25	−0.0118144
$171$	−4.92008e27	−0.601895
$172$	−1.00959e28	−1.14826
$173$	6.02602e27	0.637462	0.318731	−	0.947845i	$-0.396743\pi$
$173$	6.02602e27	0.637462	0.318731	+	0.947845i	$0.396743\pi$
$174$	2.54934e24	0.000250935 0
$175$	0	0
$176$	9.47758e27	0.808703
$177$	−2.55575e27	−0.203166
$178$	−8.46545e25	−0.00627191
$179$	2.41023e28	1.66493	0.832463	−	0.554081i	$-0.186930\pi$
$179$	2.41023e28	1.66493	0.832463	+	0.554081i	$0.186930\pi$
$180$	2.01391e28	1.29758
$181$	8.19193e27	0.492498	0.246249	−	0.969207i	$-0.420802\pi$
$181$	8.19193e27	0.492498	0.246249	+	0.969207i	$0.420802\pi$
$182$	0	0
$183$	−1.76526e27	−0.0925061
$184$	−3.05991e26	−0.0149791
$185$	1.50635e28	0.689095
$186$	4.03356e25	0.00172495
$187$	2.12163e28	0.848497
$188$	−3.10143e28	−1.16035
$189$	0	0
$190$	−2.16616e26	−0.00710018
$191$	5.50602e27	0.169013	0.0845066	−	0.996423i	$-0.473069\pi$
$191$	5.50602e27	0.169013	0.0845066	+	0.996423i	$0.473069\pi$
$192$	−7.39422e27	−0.212631
$193$	2.08716e28	0.562457	0.281228	−	0.959641i	$-0.409258\pi$
$193$	2.08716e28	0.562457	0.281228	+	0.959641i	$0.409258\pi$
$194$	1.35804e26	0.00343075
$195$	1.18626e28	0.281027
$196$	0	0
$197$	−5.99370e28	−1.24988	−0.624938	−	0.780674i	$-0.714876\pi$
$197$	−5.99370e28	−1.24988	−0.624938	+	0.780674i	$0.714876\pi$
$198$	3.26926e26	0.00639933
$199$	−2.24042e27	−0.0411782	−0.0205891	−	0.999788i	$-0.506554\pi$
$199$	−2.24042e27	−0.0411782	−0.0205891	+	0.999788i	$0.506554\pi$
$200$	8.13414e26	0.0140423
$201$	−5.22583e27	−0.0847626
$202$	8.94444e25	0.00136352
$203$	0	0
$204$	−1.65548e28	−0.223125
$205$	1.36336e29	1.72858
$206$	2.33190e26	0.00278208
$207$	7.68464e28	0.862967
$208$	9.19120e28	0.971808
$209$	5.12080e28	0.509928
$210$	0	0
$211$	−7.52475e28	−0.665214	−0.332607	−	0.943066i	$-0.607928\pi$
$211$	−7.52475e28	−0.665214	−0.332607	+	0.943066i	$0.607928\pi$
$212$	3.32264e28	0.276876
$213$	−3.76708e28	−0.295979
$214$	−1.71986e27	−0.0127444
$215$	2.23266e29	1.56078
$216$	−1.04460e27	−0.00689094
$217$	0	0
$218$	2.29342e27	0.0134827
$219$	−8.30299e27	−0.0460981
$220$	−2.09607e29	−1.09931
$221$	2.05752e29	1.01963
$222$	−1.90805e26	−0.000893673 0
$223$	3.16696e29	1.40227	0.701135	−	0.713029i	$-0.252677\pi$
$223$	3.16696e29	1.40227	0.701135	+	0.713029i	$0.252677\pi$
$224$	0	0
$225$	−2.04281e29	−0.808994
$226$	3.58308e27	0.0134246
$227$	−3.85094e29	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$227$	−3.85094e29	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$228$	−3.99569e28	−0.134093
$229$	5.68261e29	1.80553	0.902765	−	0.430134i	$-0.141534\pi$
$229$	5.68261e29	1.80553	0.902765	+	0.430134i	$0.141534\pi$
$230$	3.38331e27	0.0101799
$231$	0	0
$232$	−8.73718e26	−0.00235924
$233$	4.95586e29	1.26815	0.634075	−	0.773272i	$-0.281381\pi$
$233$	4.95586e29	1.26815	0.634075	+	0.773272i	$0.281381\pi$
$234$	3.17048e27	0.00769000
$235$	6.85867e29	1.57722
$236$	4.37941e29	0.955028
$237$	−5.31962e28	−0.110034
$238$	0	0
$239$	−1.44023e29	−0.268200	−0.134100	−	0.990968i	$-0.542814\pi$
$239$	−1.44023e29	−0.268200	−0.134100	+	0.990968i	$0.542814\pi$
$240$	1.63542e29	0.289061
$241$	3.19456e29	0.536041	0.268020	−	0.963413i	$-0.413631\pi$
$241$	3.19456e29	0.536041	0.268020	+	0.963413i	$0.413631\pi$
$242$	1.79802e27	0.00286486
$243$	3.96547e29	0.600090
$244$	3.02488e29	0.434845
$245$	0	0
$246$	−1.72694e27	−0.00224175
$247$	4.96606e29	0.612774
$248$	−1.38239e28	−0.0162176
$249$	1.82383e29	0.203466
$250$	1.62042e27	0.00171940
$251$	−6.21677e29	−0.627543	−0.313771	−	0.949499i	$-0.601593\pi$
$251$	−6.21677e29	−0.627543	−0.313771	+	0.949499i	$0.601593\pi$
$252$	0	0
$253$	−7.99814e29	−0.731110
$254$	−1.61234e28	−0.0140293
$255$	3.66103e29	0.303285
$256$	1.26678e30	0.999313
$257$	2.29446e30	1.72392	0.861960	−	0.506977i	$-0.169237\pi$
$257$	2.29446e30	1.72392	0.861960	+	0.506977i	$0.169237\pi$
$258$	−2.82805e27	−0.00202414
$259$	0	0
$260$	−2.03273e30	−1.32103
$261$	2.19425e29	0.135919
$262$	−8.39859e27	−0.00495952
$263$	7.73316e29	0.435422	0.217711	−	0.976013i	$-0.430141\pi$
$263$	7.73316e29	0.435422	0.217711	+	0.976013i	$0.430141\pi$
$264$	5.31025e27	0.00285145
$265$	−7.34787e29	−0.376347
$266$	0	0
$267$	3.45327e29	0.161005
$268$	8.95475e29	0.398445
$269$	−3.62259e30	−1.53856	−0.769282	−	0.638910i	$-0.779386\pi$
$269$	−3.62259e30	−1.53856	−0.769282	+	0.638910i	$0.779386\pi$
$270$	1.15500e28	0.00468313
$271$	3.62767e30	1.40447	0.702234	−	0.711946i	$-0.252186\pi$
$271$	3.62767e30	1.40447	0.702234	+	0.711946i	$0.252186\pi$
$272$	2.83657e30	1.04877
$273$	0	0
$274$	−2.96790e28	−0.0100131
$275$	2.12614e30	0.685384
$276$	6.24085e29	0.192256
$277$	−2.54808e30	−0.750266	−0.375133	−	0.926971i	$-0.622403\pi$
$277$	−2.54808e30	−0.750266	−0.375133	+	0.926971i	$0.622403\pi$
$278$	−2.32542e28	−0.00654547
$279$	3.47174e30	0.934318
$280$	0	0
$281$	3.59817e30	0.885631	0.442816	−	0.896613i	$-0.353980\pi$
$281$	3.59817e30	0.885631	0.442816	+	0.896613i	$0.353980\pi$
$282$	−8.68769e27	−0.00204546
$283$	−3.82265e30	−0.861061	−0.430530	−	0.902576i	$-0.641673\pi$
$283$	−3.82265e30	−0.861061	−0.430530	+	0.902576i	$0.641673\pi$
$284$	6.45511e30	1.39131
$285$	8.83629e29	0.182267
$286$	−3.29982e28	−0.00651500
$287$	0	0
$288$	1.31143e29	0.0237322
$289$	5.79269e29	0.100382
$290$	9.66060e27	0.00160335
$291$	−5.53977e29	−0.0880702
$292$	1.42276e30	0.216694
$293$	−1.30007e29	−0.0189723	−0.00948615	−	0.999955i	$-0.503020\pi$
$293$	−1.30007e29	−0.0189723	−0.00948615	+	0.999955i	$0.503020\pi$
$294$	0	0
$295$	−9.68487e30	−1.29813
$296$	6.53934e28	0.00840210
$297$	−2.73043e30	−0.336338
$298$	−4.34673e28	−0.00513404
$299$	−7.75646e30	−0.878565
$300$	−1.65900e30	−0.180232
$301$	0	0
$302$	−5.57710e28	−0.00557599
$303$	−3.64866e29	−0.0350026
$304$	6.84638e30	0.630291
$305$	−6.68937e30	−0.591068
$306$	9.78466e28	0.00829904
$307$	−1.43602e31	−1.16931	−0.584657	−	0.811281i	$-0.698771\pi$
$307$	−1.43602e31	−1.16931	−0.584657	+	0.811281i	$0.698771\pi$
$308$	0	0
$309$	−9.51239e29	−0.0714182
$310$	1.52850e29	0.0110216
$311$	2.24630e31	1.55584	0.777918	−	0.628366i	$-0.216276\pi$
$311$	2.24630e31	1.55584	0.777918	+	0.628366i	$0.216276\pi$
$312$	5.14979e28	0.00342655
$313$	1.37956e30	0.0881934	0.0440967	−	0.999027i	$-0.485959\pi$
$313$	1.37956e30	0.0881934	0.0440967	+	0.999027i	$0.485959\pi$
$314$	−1.63922e28	−0.00100697
$315$	0	0
$316$	9.11548e30	0.517239
$317$	−1.02787e31	−0.560655	−0.280327	−	0.959904i	$-0.590443\pi$
$317$	−1.02787e31	−0.560655	−0.280327	+	0.959904i	$0.590443\pi$
$318$	9.30735e27	0.000488076 0
$319$	−2.28377e30	−0.115151
$320$	−2.80200e31	−1.35861
$321$	7.01574e30	0.327160
$322$	0	0
$323$	1.53262e31	0.661306
$324$	−2.08666e31	−0.866240
$325$	2.06190e31	0.823617
$326$	−2.22337e29	−0.00854656
$327$	−9.35542e30	−0.346112
$328$	5.91861e29	0.0210764
$329$	0	0
$330$	−5.87148e28	−0.00193787
$331$	−5.75356e30	−0.182847	−0.0914233	−	0.995812i	$-0.529142\pi$
$331$	−5.75356e30	−0.182847	−0.0914233	+	0.995812i	$0.529142\pi$
$332$	−3.12523e31	−0.956435
$333$	−1.64229e31	−0.484057
$334$	−3.96706e29	−0.0112626
$335$	−1.98030e31	−0.541591
$336$	0	0
$337$	6.69268e31	1.69913	0.849564	−	0.527485i	$-0.176865\pi$
$337$	6.69268e31	1.69913	0.849564	+	0.527485i	$0.176865\pi$
$338$	1.86968e28	0.000457413 0
$339$	−1.46163e31	−0.344621
$340$	−6.27338e31	−1.42566
$341$	−3.61337e31	−0.791559
$342$	2.36164e29	0.00498754
$343$	0	0
$344$	9.69239e29	0.0190305
$345$	−1.38013e31	−0.261326
$346$	−2.89249e29	−0.00528227
$347$	9.41781e29	0.0165894	0.00829472	−	0.999966i	$-0.497360\pi$
$347$	9.41781e29	0.0165894	0.00829472	+	0.999966i	$0.497360\pi$
$348$	1.78200e30	0.0302807
$349$	3.39081e31	0.555886	0.277943	−	0.960598i	$-0.410347\pi$
$349$	3.39081e31	0.555886	0.277943	+	0.960598i	$0.410347\pi$
$350$	0	0
$351$	−2.64793e31	−0.404173
$352$	−1.36493e30	−0.0201060
$353$	−1.30313e31	−0.185269	−0.0926346	−	0.995700i	$-0.529529\pi$
$353$	−1.30313e31	−0.185269	−0.0926346	+	0.995700i	$0.529529\pi$
$354$	1.22676e29	0.00168352
$355$	−1.42752e32	−1.89116
$356$	−5.91737e31	−0.756840
$357$	0	0
$358$	−1.15691e30	−0.0137963
$359$	−1.30336e32	−1.50101	−0.750506	−	0.660864i	$-0.770190\pi$
$359$	−1.30336e32	−1.50101	−0.750506	+	0.660864i	$0.770190\pi$
$360$	−1.93342e30	−0.0215052
$361$	−5.60851e31	−0.602570
$362$	−3.93213e29	−0.00408104
$363$	−7.33459e30	−0.0735433
$364$	0	0
$365$	−3.14638e31	−0.294544
$366$	8.47325e28	0.000766543 0
$367$	2.06294e32	1.80369	0.901844	−	0.432061i	$-0.142214\pi$
$367$	2.06294e32	1.80369	0.901844	+	0.432061i	$0.142214\pi$
$368$	−1.06933e32	−0.903680
$369$	−1.48640e32	−1.21424
$370$	−7.23048e29	−0.00571012
$371$	0	0
$372$	2.81947e31	0.208152
$373$	2.46051e32	1.75657	0.878283	−	0.478142i	$-0.158689\pi$
$373$	2.46051e32	1.75657	0.878283	+	0.478142i	$0.158689\pi$
$374$	−1.01838e30	−0.00703099
$375$	−6.61009e30	−0.0441384
$376$	2.97747e30	0.0192309
$377$	−2.21476e31	−0.138376
$378$	0	0
$379$	7.12743e31	0.416815	0.208407	−	0.978042i	$-0.433172\pi$
$379$	7.12743e31	0.416815	0.208407	+	0.978042i	$0.433172\pi$
$380$	−1.51415e32	−0.856788
$381$	6.57715e31	0.360143
$382$	−2.64289e29	−0.00140051
$383$	−1.33051e32	−0.682393	−0.341196	−	0.939992i	$-0.610832\pi$
$383$	−1.33051e32	−0.682393	−0.341196	+	0.939992i	$0.610832\pi$
$384$	1.42003e30	0.00704949
$385$	0	0
$386$	−1.00184e30	−0.00466075
$387$	−2.43414e32	−1.09637
$388$	9.49271e31	0.413993
$389$	2.40509e32	1.01569	0.507844	−	0.861449i	$-0.330443\pi$
$389$	2.40509e32	1.01569	0.507844	+	0.861449i	$0.330443\pi$
$390$	−5.69407e29	−0.00232871
$391$	−2.39379e32	−0.948147
$392$	0	0
$393$	3.42599e31	0.127315
$394$	2.87698e30	0.0103570
$395$	−2.01585e32	−0.703062
$396$	2.28522e32	0.772216
$397$	4.12137e32	1.34946	0.674730	−	0.738065i	$-0.264260\pi$
$397$	4.12137e32	1.34946	0.674730	+	0.738065i	$0.264260\pi$
$398$	1.07540e29	0.000341219 0
$399$	0	0
$400$	2.84260e32	0.847161
$401$	−7.16647e31	−0.207014	−0.103507	−	0.994629i	$-0.533006\pi$
$401$	−7.16647e31	−0.207014	−0.103507	+	0.994629i	$0.533006\pi$
$402$	2.50840e29	0.000702377 0
$403$	−3.50419e32	−0.951206
$404$	6.25219e31	0.164537
$405$	4.61454e32	1.17745
$406$	0	0
$407$	1.70929e32	0.410095
$408$	1.58932e30	0.00369793
$409$	−1.34430e32	−0.303358	−0.151679	−	0.988430i	$-0.548468\pi$
$409$	−1.34430e32	−0.303358	−0.151679	+	0.988430i	$0.548468\pi$
$410$	−6.54415e30	−0.0143237
$411$	1.21068e32	0.257044
$412$	1.63000e32	0.335717
$413$	0	0
$414$	−3.68863e30	−0.00715089
$415$	6.91130e32	1.30004
$416$	−1.32368e31	−0.0241612
$417$	9.48596e31	0.168028
$418$	−2.45798e30	−0.00422547
$419$	1.71876e32	0.286774	0.143387	−	0.989667i	$-0.454201\pi$
$419$	1.71876e32	0.286774	0.143387	+	0.989667i	$0.454201\pi$
$420$	0	0
$421$	−8.27664e32	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$421$	−8.27664e32	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$422$	3.61188e30	0.00551223
$423$	−7.47761e32	−1.10792
$424$	−3.18984e30	−0.00458877
$425$	6.36340e32	0.888848
$426$	1.80820e30	0.00245260
$427$	0	0
$428$	−1.20219e33	−1.53789
$429$	1.34608e32	0.167245
$430$	−1.07168e31	−0.0129333
$431$	−7.83836e31	−0.0918881	−0.0459441	−	0.998944i	$-0.514630\pi$
$431$	−7.83836e31	−0.0918881	−0.0459441	+	0.998944i	$0.514630\pi$
$432$	−3.65052e32	−0.415727
$433$	−6.33273e32	−0.700635	−0.350318	−	0.936631i	$-0.613926\pi$
$433$	−6.33273e32	−0.700635	−0.350318	+	0.936631i	$0.613926\pi$
$434$	0	0
$435$	−3.94080e31	−0.0411594
$436$	1.60310e33	1.62697
$437$	−5.77767e32	−0.569816
$438$	3.98543e29	0.000381988 0
$439$	1.48299e33	1.38144	0.690718	−	0.723124i	$-0.257295\pi$
$439$	1.48299e33	1.38144	0.690718	+	0.723124i	$0.257295\pi$
$440$	2.01229e31	0.0182193
$441$	0	0
$442$	−9.87612e30	−0.00844905
$443$	−1.20901e33	−1.00551	−0.502753	−	0.864430i	$-0.667679\pi$
$443$	−1.20901e33	−1.00551	−0.502753	+	0.864430i	$0.667679\pi$
$444$	−1.33373e32	−0.107841
$445$	1.30860e33	1.02874
$446$	−1.52014e31	−0.0116198
$447$	1.77314e32	0.131795
$448$	0	0
$449$	−9.48861e32	−0.666996	−0.333498	−	0.942751i	$-0.608229\pi$
$449$	−9.48861e32	−0.666996	−0.333498	+	0.942751i	$0.608229\pi$
$450$	9.80547e30	0.00670366
$451$	1.54704e33	1.02871
$452$	2.50459e33	1.61996
$453$	2.27504e32	0.143140
$454$	1.84845e31	0.0113138
$455$	0	0
$456$	3.83600e30	0.00222238
$457$	1.90644e33	1.07466	0.537329	−	0.843373i	$-0.319433\pi$
$457$	1.90644e33	1.07466	0.537329	+	0.843373i	$0.319433\pi$
$458$	−2.72765e31	−0.0149614
$459$	−8.17199e32	−0.436183
$460$	2.36494e33	1.22842
$461$	4.56270e31	0.0230653	0.0115327	−	0.999933i	$-0.496329\pi$
$461$	4.56270e31	0.0230653	0.0115327	+	0.999933i	$0.496329\pi$
$462$	0	0
$463$	2.13521e33	1.02254	0.511269	−	0.859421i	$-0.329176\pi$
$463$	2.13521e33	1.02254	0.511269	+	0.859421i	$0.329176\pi$
$464$	−3.05334e32	−0.142331
$465$	−6.23513e32	−0.282933
$466$	−2.37882e31	−0.0105084
$467$	2.67225e33	1.14926	0.574628	−	0.818415i	$-0.305147\pi$
$467$	2.67225e33	1.14926	0.574628	+	0.818415i	$0.305147\pi$
$468$	2.21617e33	0.927962
$469$	0	0
$470$	−3.29216e31	−0.0130695
$471$	6.68680e31	0.0258498
$472$	−4.20438e31	−0.0158280
$473$	2.53345e33	0.928854
$474$	2.55342e30	0.000911786 0
$475$	1.53588e33	0.534178
$476$	0	0
$477$	8.01096e32	0.264366
$478$	6.91313e30	0.00222242
$479$	−1.97240e33	−0.617733	−0.308867	−	0.951105i	$-0.599950\pi$
$479$	−1.97240e33	−0.617733	−0.308867	+	0.951105i	$0.599950\pi$
$480$	−2.35528e31	−0.00718665
$481$	1.65764e33	0.492806
$482$	−1.53339e31	−0.00444185
$483$	0	0
$484$	1.25682e33	0.345706
$485$	−2.09927e33	−0.562725
$486$	−1.90343e31	−0.00497259
$487$	−3.96366e32	−0.100922	−0.0504608	−	0.998726i	$-0.516069\pi$
$487$	−3.96366e32	−0.100922	−0.0504608	+	0.998726i	$0.516069\pi$
$488$	−2.90398e31	−0.00720686
$489$	9.06968e32	0.219397
$490$	0	0
$491$	−7.22626e33	−1.66110	−0.830548	−	0.556947i	$-0.811973\pi$
$491$	−7.22626e33	−1.66110	−0.830548	+	0.556947i	$0.811973\pi$
$492$	−1.20713e33	−0.270515
$493$	−6.83515e32	−0.149335
$494$	−2.38371e31	−0.00507769
$495$	−5.05366e33	−1.04964
$496$	−4.83099e33	−0.978397
$497$	0	0
$498$	−8.75436e30	−0.00168600
$499$	8.19830e33	1.53981	0.769905	−	0.638159i	$-0.220304\pi$
$499$	8.19830e33	1.53981	0.769905	+	0.638159i	$0.220304\pi$
$500$	1.13268e33	0.207482
$501$	1.61826e33	0.289119
$502$	2.98405e31	0.00520008
$503$	−4.72562e33	−0.803265	−0.401633	−	0.915801i	$-0.631557\pi$
$503$	−4.72562e33	−0.803265	−0.401633	+	0.915801i	$0.631557\pi$
$504$	0	0
$505$	−1.38264e33	−0.223649
$506$	3.83911e31	0.00605827
$507$	−7.62689e31	−0.0117422
$508$	−1.12703e34	−1.69293
$509$	−1.96955e33	−0.288665	−0.144332	−	0.989529i	$-0.546103\pi$
$509$	−1.96955e33	−0.288665	−0.144332	+	0.989529i	$0.546103\pi$
$510$	−1.75729e31	−0.00251314
$511$	0	0
$512$	−3.04153e32	−0.0414207
$513$	−1.97240e33	−0.262137
$514$	−1.10134e32	−0.0142851
$515$	−3.60468e33	−0.456327
$516$	−1.97682e33	−0.244256
$517$	7.78267e33	0.938635
$518$	0	0
$519$	1.17992e33	0.135600
$520$	1.95149e32	0.0218940
$521$	−7.39782e33	−0.810274	−0.405137	−	0.914256i	$-0.632776\pi$
$521$	−7.39782e33	−0.810274	−0.405137	+	0.914256i	$0.632776\pi$
$522$	−1.05324e31	−0.00112628
$523$	−1.70332e34	−1.77838	−0.889191	−	0.457535i	$-0.848732\pi$
$523$	−1.70332e34	−1.77838	−0.889191	+	0.457535i	$0.848732\pi$
$524$	−5.87063e33	−0.598472
$525$	0	0
$526$	−3.71192e31	−0.00360808
$527$	−1.08146e34	−1.02654
$528$	1.85575e33	0.172026
$529$	−2.02166e33	−0.183026
$530$	3.52698e31	0.00311856
$531$	1.05589e34	0.911876
$532$	0	0
$533$	1.50029e34	1.23619
$534$	−1.65757e31	−0.00133415
$535$	2.65858e34	2.09039
$536$	−8.59686e31	−0.00660358
$537$	4.71932e33	0.354161
$538$	1.73884e32	0.0127492
$539$	0	0
$540$	8.07351e33	0.565120
$541$	−1.28681e34	−0.880134	−0.440067	−	0.897965i	$-0.645045\pi$
$541$	−1.28681e34	−0.880134	−0.440067	+	0.897965i	$0.645045\pi$
$542$	−1.74128e32	−0.0116380
$543$	1.60401e33	0.104764
$544$	−4.08513e32	−0.0260747
$545$	−3.54519e34	−2.21148
$546$	0	0
$547$	2.06624e34	1.23123	0.615616	−	0.788046i	$-0.288907\pi$
$547$	2.06624e34	1.23123	0.615616	+	0.788046i	$0.288907\pi$
$548$	−2.07457e34	−1.20829
$549$	7.29304e33	0.415197
$550$	−1.02055e32	−0.00567937
$551$	−1.64974e33	−0.0897471
$552$	−5.99142e31	−0.00318633
$553$	0	0
$554$	1.22308e32	0.00621701
$555$	2.94949e33	0.146583
$556$	−1.62547e34	−0.789851
$557$	−3.28751e33	−0.156198	−0.0780992	−	0.996946i	$-0.524885\pi$
$557$	−3.28751e33	−0.156198	−0.0780992	+	0.996946i	$0.524885\pi$
$558$	−1.66644e32	−0.00774214
$559$	2.45689e34	1.11619
$560$	0	0
$561$	4.15424e33	0.180491
$562$	−1.72712e32	−0.00733870
$563$	1.80804e34	0.751371	0.375685	−	0.926747i	$-0.377407\pi$
$563$	1.80804e34	0.751371	0.375685	+	0.926747i	$0.377407\pi$
$564$	−6.07272e33	−0.246828
$565$	−5.53878e34	−2.20195
$566$	1.83487e32	0.00713510
$567$	0	0
$568$	−6.19712e32	−0.0230587
$569$	−3.05967e33	−0.111371	−0.0556854	−	0.998448i	$-0.517734\pi$
$569$	−3.05967e33	−0.111371	−0.0556854	+	0.998448i	$0.517734\pi$
$570$	−4.24142e31	−0.00151034
$571$	−1.29884e34	−0.452486	−0.226243	−	0.974071i	$-0.572644\pi$
$571$	−1.29884e34	−0.452486	−0.226243	+	0.974071i	$0.572644\pi$
$572$	−2.30658e34	−0.786174
$573$	1.07810e33	0.0359523
$574$	0	0
$575$	−2.39888e34	−0.765878
$576$	3.05487e34	0.954357
$577$	7.31490e31	0.00223620	0.00111810	−	0.999999i	$-0.499644\pi$
$577$	7.31490e31	0.00223620	0.00111810	+	0.999999i	$0.499644\pi$
$578$	−2.78049e31	−0.000831808 0
$579$	4.08674e33	0.119645
$580$	6.75278e33	0.193479
$581$	0	0
$582$	2.65909e31	0.000729786 0
$583$	−8.33778e33	−0.223972
$584$	−1.36590e32	−0.00359136
$585$	−4.90096e34	−1.26134
$586$	6.24031e30	0.000157212 0
$587$	−5.16226e34	−1.27310	−0.636551	−	0.771234i	$-0.719640\pi$
$587$	−5.16226e34	−1.27310	−0.636551	+	0.771234i	$0.719640\pi$
$588$	0	0
$589$	−2.61022e34	−0.616929
$590$	4.64874e32	0.0107568
$591$	−1.17359e34	−0.265872
$592$	2.28527e34	0.506894
$593$	−2.40705e34	−0.522758	−0.261379	−	0.965236i	$-0.584177\pi$
$593$	−2.40705e34	−0.522758	−0.261379	+	0.965236i	$0.584177\pi$
$594$	1.31061e32	0.00278703
$595$	0	0
$596$	−3.03838e34	−0.619531
$597$	−4.38684e32	−0.00875937
$598$	3.72310e32	0.00728015
$599$	−8.30672e33	−0.159072	−0.0795361	−	0.996832i	$-0.525344\pi$
$599$	−8.30672e33	−0.159072	−0.0795361	+	0.996832i	$0.525344\pi$
$600$	1.59270e32	0.00298705
$601$	3.00405e34	0.551792	0.275896	−	0.961187i	$-0.411025\pi$
$601$	3.00405e34	0.551792	0.275896	+	0.961187i	$0.411025\pi$
$602$	0	0
$603$	2.15901e34	0.380442
$604$	−3.89841e34	−0.672861
$605$	−2.77941e34	−0.469905
$606$	1.75136e31	0.000290046 0
$607$	1.00963e35	1.63796	0.818978	−	0.573825i	$-0.194541\pi$
$607$	1.00963e35	1.63796	0.818978	+	0.573825i	$0.194541\pi$
$608$	−9.85991e32	−0.0156703
$609$	0	0
$610$	3.21090e32	0.00489783
$611$	7.54750e34	1.12795
$612$	6.83951e34	1.00146
$613$	−1.02453e33	−0.0146983	−0.00734915	−	0.999973i	$-0.502339\pi$
$613$	−1.02453e33	−0.0146983	−0.00734915	+	0.999973i	$0.502339\pi$
$614$	6.89290e32	0.00968941
$615$	2.66952e34	0.367701
$616$	0	0
$617$	4.53271e34	0.599505	0.299753	−	0.954017i	$-0.403096\pi$
$617$	4.53271e34	0.599505	0.299753	+	0.954017i	$0.403096\pi$
$618$	4.56595e31	0.000591800 0
$619$	−1.24784e35	−1.58499	−0.792496	−	0.609878i	$-0.791219\pi$
$619$	−1.24784e35	−1.58499	−0.792496	+	0.609878i	$0.791219\pi$
$620$	1.06842e35	1.32999
$621$	3.08068e34	0.375839
$622$	−1.07823e33	−0.0128923
$623$	0	0
$624$	1.79967e34	0.206722
$625$	−1.00307e35	−1.12936
$626$	−6.62189e31	−0.000730807 0
$627$	1.00267e34	0.108471
$628$	−1.14582e34	−0.121513
$629$	5.11577e34	0.531836
$630$	0	0
$631$	4.83338e34	0.482930	0.241465	−	0.970410i	$-0.422372\pi$
$631$	4.83338e34	0.482930	0.241465	+	0.970410i	$0.422372\pi$
$632$	−8.75116e32	−0.00857239
$633$	−1.47338e34	−0.141503
$634$	4.93375e32	0.00464581
$635$	2.49238e35	2.30114
$636$	6.50586e33	0.0588967
$637$	0	0
$638$	1.09621e32	0.000954190 0
$639$	1.55634e35	1.32845
$640$	5.38114e33	0.0450427
$641$	8.30494e34	0.681728	0.340864	−	0.940113i	$-0.389280\pi$
$641$	8.30494e34	0.681728	0.340864	+	0.940113i	$0.389280\pi$
$642$	−3.36756e32	−0.00271098
$643$	−5.25724e34	−0.415069	−0.207535	−	0.978228i	$-0.566544\pi$
$643$	−5.25724e34	−0.415069	−0.207535	+	0.978228i	$0.566544\pi$
$644$	0	0
$645$	4.37164e34	0.332008
$646$	−7.35656e32	−0.00547985
$647$	2.03021e35	1.48333	0.741665	−	0.670770i	$-0.234036\pi$
$647$	2.03021e35	1.48333	0.741665	+	0.670770i	$0.234036\pi$
$648$	2.00326e33	0.0143565
$649$	−1.09896e35	−0.772546
$650$	−9.89711e32	−0.00682483
$651$	0	0
$652$	−1.55414e35	−1.03132
$653$	1.67657e35	1.09146	0.545728	−	0.837962i	$-0.316253\pi$
$653$	1.67657e35	1.09146	0.545728	+	0.837962i	$0.316253\pi$
$654$	4.49060e32	0.00286802
$655$	1.29826e35	0.813479
$656$	2.06835e35	1.27153
$657$	3.43032e34	0.206903
$658$	0	0
$659$	−2.92521e35	−1.69859	−0.849296	−	0.527917i	$-0.822973\pi$
$659$	−2.92521e35	−1.69859	−0.849296	+	0.527917i	$0.822973\pi$
$660$	−4.10418e34	−0.233845
$661$	−8.30227e34	−0.464172	−0.232086	−	0.972695i	$-0.574555\pi$
$661$	−8.30227e34	−0.464172	−0.232086	+	0.972695i	$0.574555\pi$
$662$	2.76171e32	0.00151514
$663$	4.02872e34	0.216894
$664$	3.00032e33	0.0158514
$665$	0	0
$666$	7.88298e32	0.00401109
$667$	2.57672e34	0.128675
$668$	−2.77298e35	−1.35907
$669$	6.20103e34	0.298289
$670$	9.50545e32	0.00448784
$671$	−7.59057e34	−0.351757
$672$	0	0
$673$	−3.23598e35	−1.44483	−0.722417	−	0.691458i	$-0.756969\pi$
$673$	−3.23598e35	−1.44483	−0.722417	+	0.691458i	$0.756969\pi$
$674$	−3.21249e33	−0.0140797
$675$	−8.18936e34	−0.352333
$676$	1.30691e34	0.0551966
$677$	−7.76333e34	−0.321877	−0.160938	−	0.986964i	$-0.551452\pi$
$677$	−7.76333e34	−0.321877	−0.160938	+	0.986964i	$0.551452\pi$
$678$	7.01582e32	0.00285567
$679$	0	0
$680$	6.02265e33	0.0236280
$681$	−7.54029e34	−0.290435
$682$	1.73442e33	0.00655918
$683$	−2.49909e35	−0.927945	−0.463973	−	0.885850i	$-0.653576\pi$
$683$	−2.49909e35	−0.927945	−0.463973	+	0.885850i	$0.653576\pi$
$684$	1.65079e35	0.601853
$685$	4.58782e35	1.64238
$686$	0	0
$687$	1.11268e35	0.384070
$688$	3.38716e35	1.14810
$689$	−8.08584e34	−0.269144
$690$	6.62465e32	0.00216545
$691$	8.56964e34	0.275098	0.137549	−	0.990495i	$-0.456078\pi$
$691$	8.56964e34	0.275098	0.137549	+	0.990495i	$0.456078\pi$
$692$	−2.02186e35	−0.637419
$693$	0	0
$694$	−4.52055e31	−0.000137467 0
$695$	3.59466e35	1.07361
$696$	−1.71077e32	−0.000501854 0
$697$	4.63017e35	1.33410
$698$	−1.62759e33	−0.00460630
$699$	9.70378e34	0.269759
$700$	0	0
$701$	4.53464e35	1.21637	0.608187	−	0.793793i	$-0.291897\pi$
$701$	4.53464e35	1.21637	0.608187	+	0.793793i	$0.291897\pi$
$702$	1.27101e33	0.00334914
$703$	1.23475e35	0.319622
$704$	−3.17949e35	−0.808536
$705$	1.34295e35	0.335504
$706$	6.25502e32	0.00153522
$707$	0	0
$708$	8.57507e34	0.203152
$709$	−4.93254e35	−1.14813	−0.574067	−	0.818808i	$-0.694635\pi$
$709$	−4.93254e35	−1.14813	−0.574067	+	0.818808i	$0.694635\pi$
$710$	6.85209e33	0.0156709
$711$	2.19776e35	0.493868
$712$	5.68087e33	0.0125434
$713$	4.07688e35	0.884522
$714$	0	0
$715$	5.10090e35	1.06862
$716$	−8.08682e35	−1.66481
$717$	−2.82004e34	−0.0570513
$718$	6.25613e33	0.0124380
$719$	−2.13499e35	−0.417142	−0.208571	−	0.978007i	$-0.566881\pi$
$719$	−2.13499e35	−0.417142	−0.208571	+	0.978007i	$0.566881\pi$
$720$	−6.75662e35	−1.29740
$721$	0	0
$722$	2.69208e33	0.00499314
$723$	6.25508e34	0.114026
$724$	−2.74857e35	−0.492464
$725$	−6.84968e34	−0.120627
$726$	3.52060e32	0.000609409 0
$727$	−5.12190e35	−0.871467	−0.435734	−	0.900076i	$-0.643511\pi$
$727$	−5.12190e35	−0.871467	−0.435734	+	0.900076i	$0.643511\pi$
$728$	0	0
$729$	−4.49296e35	−0.738649
$730$	1.51026e33	0.00244071
$731$	7.58243e35	1.20459
$732$	5.92283e34	0.0924998
$733$	−1.77366e35	−0.272315	−0.136157	−	0.990687i	$-0.543475\pi$
$733$	−1.77366e35	−0.272315	−0.136157	+	0.990687i	$0.543475\pi$
$734$	−9.90213e33	−0.0149461
$735$	0	0
$736$	1.54001e34	0.0224674
$737$	−2.24709e35	−0.322312
$738$	7.13471e33	0.0100617
$739$	−1.13535e36	−1.57425	−0.787124	−	0.616794i	$-0.788431\pi$
$739$	−1.13535e36	−1.57425	−0.787124	+	0.616794i	$0.788431\pi$
$740$	−5.05412e35	−0.689048
$741$	9.72375e34	0.130349
$742$	0	0
$743$	4.03749e34	0.0523301	0.0261651	−	0.999658i	$-0.491670\pi$
$743$	4.03749e34	0.0523301	0.0261651	+	0.999658i	$0.491670\pi$
$744$	−2.70678e33	−0.00344978
$745$	6.71923e35	0.842104
$746$	−1.18104e34	−0.0145556
$747$	−7.53500e35	−0.913220
$748$	−7.11853e35	−0.848439
$749$	0	0
$750$	3.17284e32	0.000365749 0
$751$	7.72405e35	0.875681	0.437840	−	0.899053i	$-0.355744\pi$
$751$	7.72405e35	0.875681	0.437840	+	0.899053i	$0.355744\pi$
$752$	1.04052e36	1.16019
$753$	−1.21727e35	−0.133490
$754$	1.06308e33	0.00114664
$755$	8.62115e35	0.914594
$756$	0	0
$757$	3.31585e35	0.340327	0.170163	−	0.985416i	$-0.445570\pi$
$757$	3.31585e35	0.340327	0.170163	+	0.985416i	$0.445570\pi$
$758$	−3.42117e33	−0.00345390
$759$	−1.56607e35	−0.155521
$760$	1.45363e34	0.0141999
$761$	−2.02230e36	−1.94329	−0.971646	−	0.236440i	$-0.924019\pi$
$761$	−2.02230e36	−1.94329	−0.971646	+	0.236440i	$0.924019\pi$
$762$	−3.15703e33	−0.00298429
$763$	0	0
$764$	−1.84739e35	−0.169002
$765$	−1.51253e36	−1.36124
$766$	6.38646e33	0.00565458
$767$	−1.06576e36	−0.928358
$768$	2.48041e35	0.212573
$769$	−7.71193e35	−0.650255	−0.325128	−	0.945670i	$-0.605407\pi$
$769$	−7.71193e35	−0.650255	−0.325128	+	0.945670i	$0.605407\pi$
$770$	0	0
$771$	4.49265e35	0.366710
$772$	−7.00286e35	−0.562418
$773$	−1.96060e36	−1.54934	−0.774668	−	0.632368i	$-0.782083\pi$
$773$	−1.96060e36	−1.54934	−0.774668	+	0.632368i	$0.782083\pi$
$774$	1.16839e34	0.00908501
$775$	−1.08376e36	−0.829202
$776$	−9.11331e33	−0.00686127
$777$	0	0
$778$	−1.15444e34	−0.00841641
$779$	1.11754e36	0.801763
$780$	−3.98017e35	−0.281008
$781$	−1.61983e36	−1.12547
$782$	1.14902e34	0.00785674
$783$	8.79649e34	0.0591953
$784$	0	0
$785$	2.53393e35	0.165167
$786$	−1.64448e33	−0.00105498
$787$	8.92654e35	0.563637	0.281818	−	0.959468i	$-0.409062\pi$
$787$	8.92654e35	0.563637	0.281818	+	0.959468i	$0.409062\pi$
$788$	2.01101e36	1.24979
$789$	1.51418e35	0.0926224
$790$	9.67606e33	0.00582586
$791$	0	0
$792$	−2.19389e34	−0.0127982
$793$	−7.36121e35	−0.422702
$794$	−1.97826e34	−0.0111822
$795$	−1.43874e35	−0.0800560
$796$	7.51710e34	0.0411753
$797$	2.35494e36	1.26984	0.634921	−	0.772577i	$-0.281032\pi$
$797$	2.35494e36	1.26984	0.634921	+	0.772577i	$0.281032\pi$
$798$	0	0
$799$	2.32930e36	1.21728
$800$	−4.09381e34	−0.0210622
$801$	−1.42669e36	−0.722643
$802$	3.43990e33	0.00171541
$803$	−3.57026e35	−0.175289
$804$	1.75338e35	0.0847568
$805$	0	0
$806$	1.68201e34	0.00788208
$807$	−7.09317e35	−0.327281
$808$	−6.00231e33	−0.00272694
$809$	−1.29617e36	−0.579834	−0.289917	−	0.957052i	$-0.593628\pi$
$809$	−1.29617e36	−0.579834	−0.289917	+	0.957052i	$0.593628\pi$
$810$	−2.21498e34	−0.00975680
$811$	−2.63606e36	−1.14339	−0.571695	−	0.820467i	$-0.693714\pi$
$811$	−2.63606e36	−1.14339	−0.571695	+	0.820467i	$0.693714\pi$
$812$	0	0
$813$	7.10313e35	0.298757
$814$	−8.20458e33	−0.00339822
$815$	3.43691e36	1.40184
$816$	5.55412e35	0.223094
$817$	1.83010e36	0.723935
$818$	6.45265e33	0.00251375
$819$	0	0
$820$	−4.57438e36	−1.72846
$821$	−5.92271e35	−0.220410	−0.110205	−	0.993909i	$-0.535151\pi$
$821$	−5.92271e35	−0.220410	−0.110205	+	0.993909i	$0.535151\pi$
$822$	−5.81127e33	−0.00212997
$823$	4.76928e35	0.172169	0.0860845	−	0.996288i	$-0.472564\pi$
$823$	4.76928e35	0.172169	0.0860845	+	0.996288i	$0.472564\pi$
$824$	−1.56486e34	−0.00556396
$825$	4.16308e35	0.145794
$826$	0	0
$827$	4.17794e36	1.41953	0.709763	−	0.704440i	$-0.248802\pi$
$827$	4.17794e36	1.41953	0.709763	+	0.704440i	$0.248802\pi$
$828$	−2.57836e36	−0.862908
$829$	3.18023e36	1.04840	0.524199	−	0.851596i	$-0.324365\pi$
$829$	3.18023e36	1.04840	0.524199	+	0.851596i	$0.324365\pi$
$830$	−3.31742e34	−0.0107727
$831$	−4.98924e35	−0.159596
$832$	−3.08342e36	−0.971608
$833$	0	0
$834$	−4.55326e33	−0.00139235
$835$	6.13232e36	1.84733
$836$	−1.71814e36	−0.509893
$837$	1.39178e36	0.406913
$838$	−8.25006e33	−0.00237633
$839$	3.57270e36	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$839$	3.57270e36	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$840$	0	0
$841$	−3.55679e36	−0.979733
$842$	3.97279e34	0.0107819
$843$	7.04537e35	0.188390
$844$	2.52471e36	0.665168
$845$	−2.89018e35	−0.0750266
$846$	3.58925e34	0.00918068
$847$	0	0
$848$	−1.11474e36	−0.276838
$849$	−7.48489e35	−0.183164
$850$	−3.05443e34	−0.00736535
$851$	−1.92855e36	−0.458258
$852$	1.26394e36	0.295958
$853$	1.75466e36	0.404884	0.202442	−	0.979294i	$-0.435112\pi$
$853$	1.75466e36	0.404884	0.202442	+	0.979294i	$0.435112\pi$
$854$	0	0
$855$	−3.65065e36	−0.818075
$856$	1.15414e35	0.0254880
$857$	−7.10324e36	−1.54595	−0.772976	−	0.634435i	$-0.781233\pi$
$857$	−7.10324e36	−1.54595	−0.772976	+	0.634435i	$0.781233\pi$
$858$	−6.46118e33	−0.00138586
$859$	7.56695e36	1.59958	0.799791	−	0.600279i	$-0.204944\pi$
$859$	7.56695e36	1.59958	0.799791	+	0.600279i	$0.204944\pi$
$860$	−7.49105e36	−1.56067
$861$	0	0
$862$	3.76241e33	0.000761423 0
$863$	5.72195e36	1.14132	0.570662	−	0.821185i	$-0.306687\pi$
$863$	5.72195e36	1.14132	0.570662	+	0.821185i	$0.306687\pi$
$864$	5.25735e34	0.0103358
$865$	4.47125e36	0.866418
$866$	3.03971e34	0.00580575
$867$	1.13423e35	0.0213532
$868$	0	0
$869$	−2.28742e36	−0.418407
$870$	1.89158e33	0.000341063 0
$871$	−2.17919e36	−0.387318
$872$	−1.53903e35	−0.0269645
$873$	2.28871e36	0.395288
$874$	2.77328e34	0.00472173
$875$	0	0
$876$	2.78583e35	0.0460949
$877$	3.21926e36	0.525123	0.262561	−	0.964915i	$-0.415433\pi$
$877$	3.21926e36	0.525123	0.262561	+	0.964915i	$0.415433\pi$
$878$	−7.11834e34	−0.0114471
$879$	−2.54558e34	−0.00403576
$880$	7.03227e36	1.09916
$881$	1.04633e37	1.61238	0.806191	−	0.591655i	$-0.201525\pi$
$881$	1.04633e37	1.61238	0.806191	+	0.591655i	$0.201525\pi$
$882$	0	0
$883$	4.11745e36	0.616765	0.308382	−	0.951263i	$-0.400212\pi$
$883$	4.11745e36	0.616765	0.308382	+	0.951263i	$0.400212\pi$
$884$	−6.90343e36	−1.01956
$885$	−1.89634e36	−0.276137
$886$	5.80326e34	0.00833202
$887$	2.52904e36	0.358022	0.179011	−	0.983847i	$-0.442710\pi$
$887$	2.52904e36	0.358022	0.179011	+	0.983847i	$0.442710\pi$
$888$	1.28043e34	0.00178728
$889$	0	0
$890$	−6.28128e34	−0.00852458
$891$	5.23622e36	0.700723
$892$	−1.06258e37	−1.40217
$893$	5.62202e36	0.731558
$894$	−8.51107e33	−0.00109211
$895$	1.78836e37	2.26291
$896$	0	0
$897$	−1.51875e36	−0.186887
$898$	4.55453e34	0.00552700
$899$	1.16410e36	0.139314
$900$	6.85405e36	0.808939
$901$	−2.49544e36	−0.290460
$902$	−7.42578e34	−0.00852433
$903$	0	0
$904$	−2.40448e35	−0.0268483
$905$	6.07833e36	0.669387
$906$	−1.09202e34	−0.00118612
$907$	−4.93129e36	−0.528286	−0.264143	−	0.964484i	$-0.585089\pi$
$907$	−4.93129e36	−0.528286	−0.264143	+	0.964484i	$0.585089\pi$
$908$	1.29207e37	1.36525
$909$	1.50742e36	0.157103
$910$	0	0
$911$	−7.10548e36	−0.720466	−0.360233	−	0.932862i	$-0.617303\pi$
$911$	−7.10548e36	−0.720466	−0.360233	+	0.932862i	$0.617303\pi$
$912$	1.34055e36	0.134075
$913$	7.84240e36	0.773685
$914$	−9.15090e34	−0.00890505
$915$	−1.30981e36	−0.125731
$916$	−1.90664e37	−1.80541
$917$	0	0
$918$	3.92255e34	0.00361439
$919$	2.64155e36	0.240112	0.120056	−	0.992767i	$-0.461693\pi$
$919$	2.64155e36	0.240112	0.120056	+	0.992767i	$0.461693\pi$
$920$	−2.27042e35	−0.0203591
$921$	−2.81179e36	−0.248735
$922$	−2.19009e33	−0.000191129 0
$923$	−1.57089e37	−1.35246
$924$	0	0
$925$	5.12665e36	0.429597
$926$	−1.02490e35	−0.00847316
$927$	3.92997e36	0.320548
$928$	4.39731e34	0.00353865
$929$	−5.01934e36	−0.398520	−0.199260	−	0.979947i	$-0.563854\pi$
$929$	−5.01934e36	−0.398520	−0.199260	+	0.979947i	$0.563854\pi$
$930$	2.99286e34	0.00234450
$931$	0	0
$932$	−1.66280e37	−1.26806
$933$	4.39835e36	0.330955
$934$	−1.28268e35	−0.00952320
$935$	1.57423e37	1.15325
$936$	−2.12760e35	−0.0153795
$937$	1.70189e37	1.21391	0.606956	−	0.794735i	$-0.292390\pi$
$937$	1.70189e37	1.21391	0.606956	+	0.794735i	$0.292390\pi$
$938$	0	0
$939$	2.70123e35	0.0187604
$940$	−2.30123e37	−1.57711
$941$	1.51254e37	1.02291	0.511455	−	0.859310i	$-0.329107\pi$
$941$	1.51254e37	1.02291	0.511455	+	0.859310i	$0.329107\pi$
$942$	−3.20967e33	−0.000214202 0
$943$	−1.74548e37	−1.14953
$944$	−1.46929e37	−0.954897
$945$	0	0
$946$	−1.21605e35	−0.00769687
$947$	1.65329e36	0.103270	0.0516351	−	0.998666i	$-0.483557\pi$
$947$	1.65329e36	0.103270	0.0516351	+	0.998666i	$0.483557\pi$
$948$	1.78485e36	0.110026
$949$	−3.46238e36	−0.210643
$950$	−7.37220e34	−0.00442642
$951$	−2.01260e36	−0.119262
$952$	0	0
$953$	2.77784e37	1.60341	0.801706	−	0.597718i	$-0.203926\pi$
$953$	2.77784e37	1.60341	0.801706	+	0.597718i	$0.203926\pi$
$954$	−3.84526e34	−0.00219064
$955$	4.08541e36	0.229717
$956$	4.83229e36	0.268182
$957$	−4.47171e35	−0.0244948
$958$	9.46752e34	0.00511879
$959$	0	0
$960$	−5.48644e36	−0.289001
$961$	−8.14395e35	−0.0423441
$962$	−7.95666e34	−0.00408359
$963$	−2.89850e37	−1.46840
$964$	−1.07184e37	−0.536004
$965$	1.54865e37	0.764473
$966$	0	0
$967$	3.82441e36	0.183965	0.0919823	−	0.995761i	$-0.470680\pi$
$967$	3.82441e36	0.183965	0.0919823	+	0.995761i	$0.470680\pi$
$968$	−1.20659e35	−0.00572952
$969$	3.00093e36	0.140672
$970$	1.00765e35	0.00466297
$971$	1.67087e37	0.763311	0.381655	−	0.924305i	$-0.375354\pi$
$971$	1.67087e37	0.763311	0.381655	+	0.924305i	$0.375354\pi$
$972$	−1.33050e37	−0.600049
$973$	0	0
$974$	1.90256e34	0.000836277 0
$975$	4.03728e36	0.175199
$976$	−1.01484e37	−0.434786
$977$	−3.54376e37	−1.49893	−0.749466	−	0.662043i	$-0.769690\pi$
$977$	−3.54376e37	−1.49893	−0.749466	+	0.662043i	$0.769690\pi$
$978$	−4.35345e34	−0.00181802
$979$	1.48490e37	0.612227
$980$	0	0
$981$	3.86512e37	1.55346
$982$	3.46860e35	0.0137645
$983$	−2.26759e37	−0.888476	−0.444238	−	0.895909i	$-0.646525\pi$
$983$	−2.26759e37	−0.888476	−0.444238	+	0.895909i	$0.646525\pi$
$984$	1.15889e35	0.00448335
$985$	−4.44726e37	−1.69879
$986$	3.28087e34	0.00123745
$987$	0	0
$988$	−1.66622e37	−0.612732
$989$	−2.85843e37	−1.03794
$990$	2.42576e35	0.00869777
$991$	−1.82706e36	−0.0646891	−0.0323445	−	0.999477i	$-0.510297\pi$
$991$	−1.82706e36	−0.0646891	−0.0323445	+	0.999477i	$0.510297\pi$
$992$	6.95742e35	0.0243250
$993$	−1.12657e36	−0.0388949
$994$	0	0
$995$	−1.66237e36	−0.0559680
$996$	−6.11932e36	−0.203452
$997$	−2.34599e37	−0.770260	−0.385130	−	0.922862i	$-0.625843\pi$
$997$	−2.34599e37	−0.770260	−0.385130	+	0.922862i	$0.625843\pi$
$998$	−3.93518e35	−0.0127595
$999$	−6.58373e36	−0.210816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.26.a.a.1.1		1
7.6	odd	2		1.26.a.a.1.1	✓	1
21.20	even	2		9.26.a.a.1.1		1
28.27	even	2		16.26.a.b.1.1		1
35.13	even	4		25.26.b.a.24.2		2
35.27	even	4		25.26.b.a.24.1		2
35.34	odd	2		25.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.26.a.a.1.1	✓	1	7.6	odd	2
9.26.a.a.1.1		1	21.20	even	2
16.26.a.b.1.1		1	28.27	even	2
25.26.a.a.1.1		1	35.34	odd	2
25.26.b.a.24.1		2	35.27	even	4
25.26.b.a.24.2		2	35.13	even	4
49.26.a.a.1.1		1	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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