LMFDB - Embedded newform 49.24.a.g.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,24,Mod(1,49)] 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("49.1"); S:= CuspForms(chi, 24); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 24, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	49.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,-966,177148] 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:	$164.249978299$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 7 x^{13} - 21591353 x^{12} - 1736098763 x^{11} + 177925612890704 x^{10} + \cdots - 50\!\cdots\!18 $ x^14 - 7x^13 - 21591353x^12 - 1736098763x^11 + 177925612890704x^10 + 22440638605479136x^9 - 708837141279167425756x^8 - 93001068632447634048566x^7 + 1424565171490650325343339825x^6 + 138068341594650942193443298553x^5 - 1378620080712404619433990278685577x^4 - 54896928867175489851543883496924335x^3 + 543960992554124581410981342517061510574x^2 - 22214950574912968179617333346997657789218*x - 50990028542728296688623812565804153999177618
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{49}\cdot 3^{13}\cdot 5^{3}\cdot 7^{23} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1291.79$ of defining polynomial
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)

$f(q)$	$=$	\(q+2513.58 q^{2} +385363. q^{3} -2.07052e6 q^{4} +7.20022e7 q^{5} +9.68640e8 q^{6} -2.62899e10 q^{8} +5.43613e10 q^{9} +1.80983e11 q^{10} +9.26541e11 q^{11} -7.97903e11 q^{12} +5.15744e12 q^{13} +2.77470e13 q^{15} -4.87129e13 q^{16} +2.45074e13 q^{17} +1.36641e14 q^{18} +5.32381e14 q^{19} -1.49082e14 q^{20} +2.32894e15 q^{22} +1.17451e15 q^{23} -1.01311e16 q^{24} -6.73661e15 q^{25} +1.29636e16 q^{26} -1.53305e16 q^{27} +6.90610e16 q^{29} +6.97442e16 q^{30} -2.78413e17 q^{31} +9.80917e16 q^{32} +3.57054e17 q^{33} +6.16013e16 q^{34} -1.12556e17 q^{36} +1.43959e18 q^{37} +1.33818e18 q^{38} +1.98749e18 q^{39} -1.89293e18 q^{40} +1.70772e18 q^{41} +6.33058e18 q^{43} -1.91842e18 q^{44} +3.91413e18 q^{45} +2.95223e18 q^{46} -1.35510e19 q^{47} -1.87721e19 q^{48} -1.69330e19 q^{50} +9.44424e18 q^{51} -1.06786e19 q^{52} -7.01597e19 q^{53} -3.85343e19 q^{54} +6.67130e19 q^{55} +2.05160e20 q^{57} +1.73590e20 q^{58} +2.39631e20 q^{59} -5.74508e19 q^{60} +1.37828e20 q^{61} -6.99813e20 q^{62} +6.55194e20 q^{64} +3.71347e20 q^{65} +8.97485e20 q^{66} +6.78764e20 q^{67} -5.07431e19 q^{68} +4.52614e20 q^{69} +2.14404e21 q^{71} -1.42915e21 q^{72} +3.07547e21 q^{73} +3.61853e21 q^{74} -2.59604e21 q^{75} -1.10231e21 q^{76} +4.99571e21 q^{78} +6.81725e21 q^{79} -3.50743e21 q^{80} -1.10255e22 q^{81} +4.29249e21 q^{82} +8.36785e21 q^{83} +1.76459e21 q^{85} +1.59124e22 q^{86} +2.66135e22 q^{87} -2.43586e22 q^{88} +3.41597e22 q^{89} +9.83849e21 q^{90} -2.43186e21 q^{92} -1.07290e23 q^{93} -3.40615e22 q^{94} +3.83326e22 q^{95} +3.78009e22 q^{96} -1.21614e22 q^{97} +5.03680e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 966 q^{2} + 177148 q^{3} + 55357148 q^{4} + 74771022 q^{5} + 1504608254 q^{6} + 25222400616 q^{8} + 336909608980 q^{9} + 334296297894 q^{10} - 1355476566108 q^{11} + 4984668058916 q^{12} - 427040218556 q^{13}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) $ 14 * q - 966 * q^2 + 177148 * q^3 + 55357148 * q^4 + 74771022 * q^5 + 1504608254 * q^6 + 25222400616 * q^8 + 336909608980 * q^9 + 334296297894 * q^10 - 1355476566108 * q^11 + 4984668058916 * q^12 - 427040218556 * q^13 + 38670810653944 * q^15 + 160538324156336 * q^16 + 130193896130514 * q^17 - 110632655983108 * q^18 + 214771980430396 * q^19 - 48219439281468 * q^20 + 7534772282877126 * q^22 - 6685548913560552 * q^23 + 31330599354826008 * q^24 + 9156874000789424 * q^25 + 48260478025970868 * q^26 + 8477622198540028 * q^27 - 115398975455444604 * q^29 - 4149727265170942 * q^30 - 94821366637509632 * q^31 + 989053585410677472 * q^32 - 471925265098792298 * q^33 + 204665719203916350 * q^34 + 161548642910645480 * q^36 - 228196281955951106 * q^37 - 846979764807573006 * q^38 + 4289472930557071768 * q^39 + 10645750240235319192 * q^40 + 12663069502432601532 * q^41 - 427239519112420616 * q^43 - 11572396920387558444 * q^44 + 9362992784223924004 * q^45 + 33418566325741763586 * q^46 + 61615364375433533424 * q^47 + 158511629928130898960 * q^48 - 93272670392614362552 * q^50 - 84287583500847206172 * q^51 + 90603352071153943672 * q^52 + 282093764343878671758 * q^53 - 13895299932605385046 * q^54 + 237446342744567832720 * q^55 - 425457361374285462782 * q^57 - 339998979132364080060 * q^58 + 283820607003252730116 * q^59 + 701673169918628967164 * q^60 + 870322613357668504870 * q^61 + 282243301452069984966 * q^62 + 2124141067160402139584 * q^64 - 384582138286683330588 * q^65 + 157008004213679191250 * q^66 - 1414046473258733295716 * q^67 - 435228382363177447884 * q^68 - 2663127352907733668682 * q^69 + 213218335956247656048 * q^71 + 10118884230376615693104 * q^72 - 5942494661268692359862 * q^73 - 13389833203328450370642 * q^74 - 14120811240771906960232 * q^75 - 22920526497794398939844 * q^76 + 7201287217205176160828 * q^78 + 3444345943288433723680 * q^79 + 8255607259451726029008 * q^80 - 2565358457232096585122 * q^81 - 34656759475287179918772 * q^82 + 6085375799043077804904 * q^83 - 7680353239558358537262 * q^85 - 743687862046869712056 * q^86 + 7978312766181293835640 * q^87 + 2867657955669848060664 * q^88 + 68609868120257601678426 * q^89 + 17331740036513596551428 * q^90 - 7750847835981686889348 * q^92 - 50628291689744906093838 * q^93 - 18415808745499513811142 * q^94 + 113148862333982926479168 * q^95 + 150237583048546245409696 * q^96 + 230188776588461622952972 * q^97 - 234139240054754764282784 * q^99

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 $

$2$	2513.58	0.867856	0.433928	−	0.900948i	$-0.357127\pi$
$2$	2513.58	0.867856	0.433928	+	0.900948i	$0.357127\pi$
$3$	385363.	1.25596	0.627979	−	0.778230i	$-0.283882\pi$
$3$	385363.	1.25596	0.627979	+	0.778230i	$0.283882\pi$
$4$	−2.07052e6	−0.246826
$5$	7.20022e7	0.659464	0.329732	−	0.944075i	$-0.393042\pi$
$5$	7.20022e7	0.659464	0.329732	+	0.944075i	$0.393042\pi$
$6$	9.68640e8	1.08999
$7$	0	0
$7$	0	0
$8$	−2.62899e10	−1.08207
$9$	5.43613e10	0.577432
$10$	1.80983e11	0.572320
$11$	9.26541e11	0.979149	0.489575	−	0.871961i	$-0.337152\pi$
$11$	9.26541e11	0.979149	0.489575	+	0.871961i	$0.337152\pi$
$12$	−7.97903e11	−0.310003
$13$	5.15744e12	0.798153	0.399076	−	0.916918i	$-0.369331\pi$
$13$	5.15744e12	0.798153	0.399076	+	0.916918i	$0.369331\pi$
$14$	0	0
$15$	2.77470e13	0.828259
$16$	−4.87129e13	−0.692252
$17$	2.45074e13	0.173434	0.0867171	−	0.996233i	$-0.472362\pi$
$17$	2.45074e13	0.173434	0.0867171	+	0.996233i	$0.472362\pi$
$18$	1.36641e14	0.501128
$19$	5.32381e14	1.04847	0.524235	−	0.851573i	$-0.324351\pi$
$19$	5.32381e14	1.04847	0.524235	+	0.851573i	$0.324351\pi$
$20$	−1.49082e14	−0.162773
$21$	0	0
$22$	2.32894e15	0.849761
$23$	1.17451e15	0.257032	0.128516	−	0.991707i	$-0.458979\pi$
$23$	1.17451e15	0.257032	0.128516	+	0.991707i	$0.458979\pi$
$24$	−1.01311e16	−1.35903
$25$	−6.73661e15	−0.565108
$26$	1.29636e16	0.692682
$27$	−1.53305e16	−0.530728
$28$	0	0
$29$	6.90610e16	1.05113	0.525564	−	0.850754i	$-0.323854\pi$
$29$	6.90610e16	1.05113	0.525564	+	0.850754i	$0.323854\pi$
$30$	6.97442e16	0.718810
$31$	−2.78413e17	−1.96802	−0.984011	−	0.178109i	$-0.943002\pi$
$31$	−2.78413e17	−1.96802	−0.984011	+	0.178109i	$0.943002\pi$
$32$	9.80917e16	0.481291
$33$	3.57054e17	1.22977
$34$	6.16013e16	0.150516
$35$	0	0
$36$	−1.12556e17	−0.142525
$37$	1.43959e18	1.33021	0.665104	−	0.746750i	$-0.268387\pi$
$37$	1.43959e18	1.33021	0.665104	+	0.746750i	$0.268387\pi$
$38$	1.33818e18	0.909922
$39$	1.98749e18	1.00245
$40$	−1.89293e18	−0.713583
$41$	1.70772e18	0.484621	0.242311	−	0.970199i	$-0.422095\pi$
$41$	1.70772e18	0.484621	0.242311	+	0.970199i	$0.422095\pi$
$42$	0	0
$43$	6.33058e18	1.03886	0.519429	−	0.854513i	$-0.326145\pi$
$43$	6.33058e18	1.03886	0.519429	+	0.854513i	$0.326145\pi$
$44$	−1.91842e18	−0.241679
$45$	3.91413e18	0.380796
$46$	2.95223e18	0.223067
$47$	−1.35510e19	−0.799549	−0.399775	−	0.916613i	$-0.630912\pi$
$47$	−1.35510e19	−0.799549	−0.399775	+	0.916613i	$0.630912\pi$
$48$	−1.87721e19	−0.869439
$49$	0	0
$50$	−1.69330e19	−0.490432
$51$	9.44424e18	0.217826
$52$	−1.06786e19	−0.197005
$53$	−7.01597e19	−1.03972	−0.519859	−	0.854252i	$-0.674015\pi$
$53$	−7.01597e19	−1.03972	−0.519859	+	0.854252i	$0.674015\pi$
$54$	−3.85343e19	−0.460595
$55$	6.67130e19	0.645713
$56$	0	0
$57$	2.05160e20	1.31684
$58$	1.73590e20	0.912229
$59$	2.39631e20	1.03453	0.517267	−	0.855824i	$-0.326950\pi$
$59$	2.39631e20	1.03453	0.517267	+	0.855824i	$0.326950\pi$
$60$	−5.74508e19	−0.204436
$61$	1.37828e20	0.405551	0.202776	−	0.979225i	$-0.435004\pi$
$61$	1.37828e20	0.405551	0.202776	+	0.979225i	$0.435004\pi$
$62$	−6.99813e20	−1.70796
$63$	0	0
$64$	6.55194e20	1.10994
$65$	3.71347e20	0.526353
$66$	8.97485e20	1.06726
$67$	6.78764e20	0.678983	0.339491	−	0.940609i	$-0.389745\pi$
$67$	6.78764e20	0.678983	0.339491	+	0.940609i	$0.389745\pi$
$68$	−5.07431e19	−0.0428080
$69$	4.52614e20	0.322822
$70$	0	0
$71$	2.14404e21	1.10093	0.550467	−	0.834857i	$-0.314450\pi$
$71$	2.14404e21	1.10093	0.550467	+	0.834857i	$0.314450\pi$
$72$	−1.42915e21	−0.624819
$73$	3.07547e21	1.14736	0.573679	−	0.819080i	$-0.305516\pi$
$73$	3.07547e21	1.14736	0.573679	+	0.819080i	$0.305516\pi$
$74$	3.61853e21	1.15443
$75$	−2.59604e21	−0.709752
$76$	−1.10231e21	−0.258789
$77$	0	0
$78$	4.99571e21	0.869980
$79$	6.81725e21	1.02541	0.512705	−	0.858565i	$-0.328643\pi$
$79$	6.81725e21	1.02541	0.512705	+	0.858565i	$0.328643\pi$
$80$	−3.50743e21	−0.456515
$81$	−1.10255e22	−1.24400
$82$	4.29249e21	0.420581
$83$	8.36785e21	0.713208	0.356604	−	0.934256i	$-0.383935\pi$
$83$	8.36785e21	0.713208	0.356604	+	0.934256i	$0.383935\pi$
$84$	0	0
$85$	1.76459e21	0.114373
$86$	1.59124e22	0.901580
$87$	2.66135e22	1.32017
$88$	−2.43586e22	−1.05950
$89$	3.41597e22	1.30476	0.652378	−	0.757894i	$-0.273771\pi$
$89$	3.41597e22	1.30476	0.652378	+	0.757894i	$0.273771\pi$
$90$	9.83849e21	0.330476
$91$	0	0
$92$	−2.43186e21	−0.0634422
$93$	−1.07290e23	−2.47175
$94$	−3.40615e22	−0.693894
$95$	3.83326e22	0.691428
$96$	3.78009e22	0.604481
$97$	−1.21614e22	−0.172626	−0.0863131	−	0.996268i	$-0.527509\pi$
$97$	−1.21614e22	−0.172626	−0.0863131	+	0.996268i	$0.527509\pi$
$98$	0	0
$99$	5.03680e22	0.565392
$100$	1.39483e22	0.139483
$101$	1.89192e22	0.168736	0.0843680	−	0.996435i	$-0.473113\pi$
$101$	1.89192e22	0.168736	0.0843680	+	0.996435i	$0.473113\pi$
$102$	2.37388e22	0.189042
$103$	1.50443e23	1.07089	0.535445	−	0.844570i	$-0.320144\pi$
$103$	1.50443e23	1.07089	0.535445	+	0.844570i	$0.320144\pi$
$104$	−1.35588e23	−0.863653
$105$	0	0
$106$	−1.76352e23	−0.902325
$107$	−2.91039e23	−1.33671	−0.668357	−	0.743841i	$-0.733002\pi$
$107$	−2.91039e23	−1.33671	−0.668357	+	0.743841i	$0.733002\pi$
$108$	3.17421e22	0.130997
$109$	−4.92276e23	−1.82728	−0.913638	−	0.406529i	$-0.866739\pi$
$109$	−4.92276e23	−1.82728	−0.913638	+	0.406529i	$0.866739\pi$
$110$	1.67689e23	0.560386
$111$	5.54765e23	1.67069
$112$	0	0
$113$	4.47921e23	1.09850	0.549249	−	0.835659i	$-0.314914\pi$
$113$	4.47921e23	1.09850	0.549249	+	0.835659i	$0.314914\pi$
$114$	5.15686e23	1.14282
$115$	8.45675e22	0.169503
$116$	−1.42992e23	−0.259445
$117$	2.80365e23	0.460879
$118$	6.02331e23	0.897826
$119$	0	0
$120$	−7.29464e23	−0.896230
$121$	−3.69518e22	−0.0412671
$122$	3.46443e23	0.351960
$123$	6.58092e23	0.608664
$124$	5.76460e23	0.485758
$125$	−1.34338e24	−1.03213
$126$	0	0
$127$	2.53761e24	1.62436	0.812181	−	0.583406i	$-0.198280\pi$
$127$	2.53761e24	1.62436	0.812181	+	0.583406i	$0.198280\pi$
$128$	8.24031e23	0.481980
$129$	2.43957e24	1.30476
$130$	9.33411e23	0.456798
$131$	−3.99180e24	−1.78875	−0.894373	−	0.447322i	$-0.852378\pi$
$131$	−3.99180e24	−1.78875	−0.894373	+	0.447322i	$0.852378\pi$
$132$	−7.39290e23	−0.303539
$133$	0	0
$134$	1.70613e24	0.589259
$135$	−1.10383e24	−0.349996
$136$	−6.44296e23	−0.187667
$137$	1.97280e24	0.528199	0.264099	−	0.964495i	$-0.414925\pi$
$137$	1.97280e24	0.528199	0.264099	+	0.964495i	$0.414925\pi$
$138$	1.13768e24	0.280163
$139$	−2.25247e24	−0.510493	−0.255246	−	0.966876i	$-0.582157\pi$
$139$	−2.25247e24	−0.510493	−0.255246	+	0.966876i	$0.582157\pi$
$140$	0	0
$141$	−5.22204e24	−1.00420
$142$	5.38921e24	0.955453
$143$	4.77858e24	0.781510
$144$	−2.64810e24	−0.399728
$145$	4.97255e24	0.693181
$146$	7.73045e24	0.995742
$147$	0	0
$148$	−2.98071e24	−0.328330
$149$	1.21722e25	1.24088	0.620438	−	0.784256i	$-0.286955\pi$
$149$	1.21722e25	1.24088	0.620438	+	0.784256i	$0.286955\pi$
$150$	−6.52535e24	−0.615963
$151$	−1.79404e25	−1.56890	−0.784451	−	0.620190i	$-0.787055\pi$
$151$	−1.79404e25	−1.56890	−0.784451	+	0.620190i	$0.787055\pi$
$152$	−1.39962e25	−1.13451
$153$	1.33225e24	0.100146
$154$	0	0
$155$	−2.00463e25	−1.29784
$156$	−4.11514e24	−0.247430
$157$	−7.66380e24	−0.428152	−0.214076	−	0.976817i	$-0.568674\pi$
$157$	−7.66380e24	−0.428152	−0.214076	+	0.976817i	$0.568674\pi$
$158$	1.71357e25	0.889909
$159$	−2.70369e25	−1.30584
$160$	7.06282e24	0.317394
$161$	0	0
$162$	−2.77136e25	−1.07962
$163$	−4.65929e24	−0.169107	−0.0845536	−	0.996419i	$-0.526946\pi$
$163$	−4.65929e24	−0.169107	−0.0845536	+	0.996419i	$0.526946\pi$
$164$	−3.53587e24	−0.119617
$165$	2.57087e25	0.810989
$166$	2.10333e25	0.618962
$167$	1.36410e25	0.374634	0.187317	−	0.982300i	$-0.440021\pi$
$167$	1.36410e25	0.374634	0.187317	+	0.982300i	$0.440021\pi$
$168$	0	0
$169$	−1.51547e25	−0.362952
$170$	4.43543e24	0.0992597
$171$	2.89409e25	0.605421
$172$	−1.31076e25	−0.256417
$173$	8.71364e25	1.59467	0.797333	−	0.603540i	$-0.206244\pi$
$173$	8.71364e25	1.59467	0.797333	+	0.603540i	$0.206244\pi$
$174$	6.68953e25	1.14572
$175$	0	0
$176$	−4.51345e25	−0.677817
$177$	9.23448e25	1.29933
$178$	8.58632e25	1.13234
$179$	−8.05330e24	−0.0995781	−0.0497891	−	0.998760i	$-0.515855\pi$
$179$	−8.05330e24	−0.0995781	−0.0497891	+	0.998760i	$0.515855\pi$
$180$	−8.10431e24	−0.0939901
$181$	−5.91500e24	−0.0643652	−0.0321826	−	0.999482i	$-0.510246\pi$
$181$	−5.91500e24	−0.0643652	−0.0321826	+	0.999482i	$0.510246\pi$
$182$	0	0
$183$	5.31139e25	0.509356
$184$	−3.08778e25	−0.278126
$185$	1.03654e26	0.877224
$186$	−2.69682e26	−2.14513
$187$	2.27071e25	0.169818
$188$	2.80576e25	0.197349
$189$	0	0
$190$	9.63522e25	0.600060
$191$	2.80371e26	1.64380	0.821900	−	0.569632i	$-0.192914\pi$
$191$	2.80371e26	1.64380	0.821900	+	0.569632i	$0.192914\pi$
$192$	2.52488e26	1.39404
$193$	−5.04222e25	−0.262248	−0.131124	−	0.991366i	$-0.541859\pi$
$193$	−5.04222e25	−0.262248	−0.131124	+	0.991366i	$0.541859\pi$
$194$	−3.05685e25	−0.149815
$195$	1.43103e26	0.661077
$196$	0	0
$197$	2.81161e25	0.115503	0.0577514	−	0.998331i	$-0.481607\pi$
$197$	2.81161e25	0.115503	0.0577514	+	0.998331i	$0.481607\pi$
$198$	1.26604e26	0.490679
$199$	4.65599e26	1.70295	0.851474	−	0.524396i	$-0.175709\pi$
$199$	4.65599e26	1.70295	0.851474	+	0.524396i	$0.175709\pi$
$200$	1.77105e26	0.611483
$201$	2.61570e26	0.852774
$202$	4.75550e25	0.146439
$203$	0	0
$204$	−1.95545e25	−0.0537651
$205$	1.22960e26	0.319590
$206$	3.78151e26	0.929378
$207$	6.38481e25	0.148419
$208$	−2.51234e26	−0.552522
$209$	4.93273e26	1.02661
$210$	0	0
$211$	5.35197e26	0.998310	0.499155	−	0.866513i	$-0.333644\pi$
$211$	5.35197e26	0.998310	0.499155	+	0.866513i	$0.333644\pi$
$212$	1.45267e26	0.256629
$213$	8.26233e26	1.38273
$214$	−7.31551e26	−1.16007
$215$	4.55816e26	0.685090
$216$	4.03036e26	0.574282
$217$	0	0
$218$	−1.23738e27	−1.58581
$219$	1.18517e27	1.44103
$220$	−1.38131e26	−0.159379
$221$	1.26396e26	0.138427
$222$	1.39445e27	1.44992
$223$	1.49821e26	0.147934	0.0739669	−	0.997261i	$-0.476434\pi$
$223$	1.49821e26	0.147934	0.0739669	+	0.997261i	$0.476434\pi$
$224$	0	0
$225$	−3.66211e26	−0.326311
$226$	1.12588e27	0.953338
$227$	−7.45872e26	−0.600298	−0.300149	−	0.953892i	$-0.597036\pi$
$227$	−7.45872e26	−0.600298	−0.300149	+	0.953892i	$0.597036\pi$
$228$	−4.24788e26	−0.325029
$229$	−5.18314e26	−0.377124	−0.188562	−	0.982061i	$-0.560383\pi$
$229$	−5.18314e26	−0.377124	−0.188562	+	0.982061i	$0.560383\pi$
$230$	2.12567e26	0.147105
$231$	0	0
$232$	−1.81560e27	−1.13739
$233$	−2.55085e27	−1.52087	−0.760434	−	0.649415i	$-0.775014\pi$
$233$	−2.55085e27	−1.52087	−0.760434	+	0.649415i	$0.775014\pi$
$234$	7.04721e26	0.399977
$235$	−9.75700e26	−0.527274
$236$	−4.96161e26	−0.255349
$237$	2.62711e27	1.28787
$238$	0	0
$239$	−4.16431e27	−1.85339	−0.926696	−	0.375811i	$-0.877364\pi$
$239$	−4.16431e27	−1.85339	−0.926696	+	0.375811i	$0.877364\pi$
$240$	−1.35163e27	−0.573364
$241$	−2.81017e27	−1.13641	−0.568207	−	0.822886i	$-0.692363\pi$
$241$	−2.81017e27	−1.13641	−0.568207	+	0.822886i	$0.692363\pi$
$242$	−9.28814e25	−0.0358139
$243$	−2.80557e27	−1.03169
$244$	−2.85377e26	−0.100100
$245$	0	0
$246$	1.65417e27	0.528233
$247$	2.74573e27	0.836840
$248$	7.31944e27	2.12953
$249$	3.22466e27	0.895759
$250$	−3.37670e27	−0.895742
$251$	−5.49506e27	−1.39227	−0.696136	−	0.717909i	$-0.745099\pi$
$251$	−5.49506e27	−1.39227	−0.696136	+	0.717909i	$0.745099\pi$
$252$	0	0
$253$	1.08823e27	0.251673
$254$	6.37849e27	1.40971
$255$	6.80006e26	0.143648
$256$	−3.42490e27	−0.691653
$257$	5.83044e27	1.12582	0.562912	−	0.826517i	$-0.309681\pi$
$257$	5.83044e27	1.12582	0.562912	+	0.826517i	$0.309681\pi$
$258$	6.13206e27	1.13235
$259$	0	0
$260$	−7.68883e26	−0.129917
$261$	3.75425e27	0.606956
$262$	−1.00337e28	−1.55237
$263$	1.10681e28	1.63902	0.819509	−	0.573067i	$-0.194246\pi$
$263$	1.10681e28	1.63902	0.819509	+	0.573067i	$0.194246\pi$
$264$	−9.38691e27	−1.33069
$265$	−5.05165e27	−0.685656
$266$	0	0
$267$	1.31639e28	1.63872
$268$	−1.40540e27	−0.167590
$269$	1.58808e27	0.181435	0.0907177	−	0.995877i	$-0.471084\pi$
$269$	1.58808e27	0.181435	0.0907177	+	0.995877i	$0.471084\pi$
$270$	−2.77456e27	−0.303746
$271$	7.54776e27	0.791902	0.395951	−	0.918272i	$-0.370415\pi$
$271$	7.54776e27	0.791902	0.395951	+	0.918272i	$0.370415\pi$
$272$	−1.19383e27	−0.120060
$273$	0	0
$274$	4.95880e27	0.458401
$275$	−6.24175e27	−0.553325
$276$	−9.37147e26	−0.0796807
$277$	−7.14977e27	−0.583143	−0.291571	−	0.956549i	$-0.594178\pi$
$277$	−7.14977e27	−0.583143	−0.291571	+	0.956549i	$0.594178\pi$
$278$	−5.66177e27	−0.443034
$279$	−1.51349e28	−1.13640
$280$	0	0
$281$	−1.73530e27	−0.120019	−0.0600097	−	0.998198i	$-0.519113\pi$
$281$	−1.73530e27	−0.120019	−0.0600097	+	0.998198i	$0.519113\pi$
$282$	−1.31260e28	−0.871502
$283$	−4.93576e27	−0.314637	−0.157319	−	0.987548i	$-0.550285\pi$
$283$	−4.93576e27	−0.314637	−0.157319	+	0.987548i	$0.550285\pi$
$284$	−4.43928e27	−0.271739
$285$	1.47720e28	0.868406
$286$	1.20114e28	0.678239
$287$	0	0
$288$	5.33239e27	0.277913
$289$	−1.93670e28	−0.969921
$290$	1.24989e28	0.601582
$291$	−4.68653e27	−0.216811
$292$	−6.36784e27	−0.283197
$293$	−2.34613e28	−1.00317	−0.501586	−	0.865108i	$-0.667250\pi$
$293$	−2.34613e28	−1.00317	−0.501586	+	0.865108i	$0.667250\pi$
$294$	0	0
$295$	1.72540e28	0.682237
$296$	−3.78467e28	−1.43937
$297$	−1.42043e28	−0.519662
$298$	3.05959e28	1.07690
$299$	6.05748e27	0.205151
$300$	5.37516e27	0.175185
$301$	0	0
$302$	−4.50945e28	−1.36158
$303$	7.29077e27	0.211925
$304$	−2.59338e28	−0.725806
$305$	9.92395e27	0.267446
$306$	3.34873e27	0.0869127
$307$	3.49585e28	0.873900	0.436950	−	0.899486i	$-0.356059\pi$
$307$	3.49585e28	0.873900	0.436950	+	0.899486i	$0.356059\pi$
$308$	0	0
$309$	5.79752e28	1.34499
$310$	−5.03881e28	−1.12634
$311$	−8.86916e28	−1.91046	−0.955230	−	0.295864i	$-0.904392\pi$
$311$	−8.86916e28	−1.91046	−0.955230	+	0.295864i	$0.904392\pi$
$312$	−5.22508e28	−1.08471
$313$	5.87749e28	1.17607	0.588033	−	0.808837i	$-0.299902\pi$
$313$	5.87749e28	1.17607	0.588033	+	0.808837i	$0.299902\pi$
$314$	−1.92636e28	−0.371575
$315$	0	0
$316$	−1.41153e28	−0.253098
$317$	1.10922e28	0.191795	0.0958974	−	0.995391i	$-0.469428\pi$
$317$	1.10922e28	0.191795	0.0958974	+	0.995391i	$0.469428\pi$
$318$	−6.79595e28	−1.13328
$319$	6.39879e28	1.02921
$320$	4.71755e28	0.731967
$321$	−1.12156e29	−1.67886
$322$	0	0
$323$	1.30473e28	0.181841
$324$	2.28286e28	0.307052
$325$	−3.47437e28	−0.451042
$326$	−1.17115e28	−0.146761
$327$	−1.89705e29	−2.29498
$328$	−4.48957e28	−0.524392
$329$	0	0
$330$	6.46209e28	0.703822
$331$	−4.08718e28	−0.429934	−0.214967	−	0.976621i	$-0.568964\pi$
$331$	−4.08718e28	−0.429934	−0.214967	+	0.976621i	$0.568964\pi$
$332$	−1.73258e28	−0.176038
$333$	7.82581e28	0.768105
$334$	3.42878e28	0.325129
$335$	4.88725e28	0.447764
$336$	0	0
$337$	4.89238e28	0.418578	0.209289	−	0.977854i	$-0.432885\pi$
$337$	4.89238e28	0.418578	0.209289	+	0.977854i	$0.432885\pi$
$338$	−3.80925e28	−0.314990
$339$	1.72612e29	1.37967
$340$	−3.65362e27	−0.0282303
$341$	−2.57961e29	−1.92699
$342$	7.27454e28	0.525418
$343$	0	0
$344$	−1.66430e29	−1.12411
$345$	3.25892e28	0.212889
$346$	2.19024e29	1.38394
$347$	−1.31576e29	−0.804244	−0.402122	−	0.915586i	$-0.631727\pi$
$347$	−1.31576e29	−0.804244	−0.402122	+	0.915586i	$0.631727\pi$
$348$	−5.51040e28	−0.325853
$349$	−1.32383e29	−0.757426	−0.378713	−	0.925514i	$-0.623633\pi$
$349$	−1.32383e29	−0.757426	−0.378713	+	0.925514i	$0.623633\pi$
$350$	0	0
$351$	−7.90660e28	−0.423602
$352$	9.08860e28	0.471255
$353$	−1.57619e29	−0.791040	−0.395520	−	0.918457i	$-0.629436\pi$
$353$	−1.57619e29	−0.791040	−0.395520	+	0.918457i	$0.629436\pi$
$354$	2.32116e29	1.12763
$355$	1.54376e29	0.726026
$356$	−7.07285e28	−0.322047
$357$	0	0
$358$	−2.02426e28	−0.0864195
$359$	1.73990e29	0.719347	0.359674	−	0.933078i	$-0.382888\pi$
$359$	1.73990e29	0.719347	0.359674	+	0.933078i	$0.382888\pi$
$360$	−1.02902e29	−0.412046
$361$	2.56002e28	0.0992913
$362$	−1.48678e28	−0.0558598
$363$	−1.42399e28	−0.0518298
$364$	0	0
$365$	2.21441e29	0.756641
$366$	1.33506e29	0.442047
$367$	−3.22943e29	−1.03625	−0.518127	−	0.855304i	$-0.673370\pi$
$367$	−3.22943e29	−1.03625	−0.518127	+	0.855304i	$0.673370\pi$
$368$	−5.72139e28	−0.177931
$369$	9.28339e28	0.279836
$370$	2.60542e29	0.761305
$371$	0	0
$372$	2.22146e29	0.610092
$373$	1.17082e28	0.0311773	0.0155887	−	0.999878i	$-0.495038\pi$
$373$	1.17082e28	0.0311773	0.0155887	+	0.999878i	$0.495038\pi$
$374$	5.70761e28	0.147377
$375$	−5.17690e29	−1.29631
$376$	3.56253e29	0.865165
$377$	3.56178e29	0.838961
$378$	0	0
$379$	−5.49051e29	−1.21692	−0.608460	−	0.793585i	$-0.708212\pi$
$379$	−5.49051e29	−1.21692	−0.608460	+	0.793585i	$0.708212\pi$
$380$	−7.93686e28	−0.170662
$381$	9.77902e29	2.04013
$382$	7.04734e29	1.42658
$383$	5.92667e28	0.116419	0.0582096	−	0.998304i	$-0.481461\pi$
$383$	5.92667e28	0.116419	0.0582096	+	0.998304i	$0.481461\pi$
$384$	3.17551e29	0.605347
$385$	0	0
$386$	−1.26740e29	−0.227594
$387$	3.44139e29	0.599871
$388$	2.51804e28	0.0426086
$389$	−7.31576e29	−1.20182	−0.600909	−	0.799317i	$-0.705195\pi$
$389$	−7.31576e29	−1.20182	−0.600909	+	0.799317i	$0.705195\pi$
$390$	3.59702e29	0.573720
$391$	2.87843e28	0.0445782
$392$	0	0
$393$	−1.53829e30	−2.24659
$394$	7.06720e28	0.100240
$395$	4.90857e29	0.676221
$396$	−1.04288e29	−0.139553
$397$	−2.05473e29	−0.267094	−0.133547	−	0.991042i	$-0.542637\pi$
$397$	−2.05473e29	−0.267094	−0.133547	+	0.991042i	$0.542637\pi$
$398$	1.17032e30	1.47791
$399$	0	0
$400$	3.28160e29	0.391197
$401$	−3.15365e29	−0.365303	−0.182652	−	0.983178i	$-0.558468\pi$
$401$	−3.15365e29	−0.365303	−0.182652	+	0.983178i	$0.558468\pi$
$402$	6.57478e29	0.740085
$403$	−1.43590e30	−1.57078
$404$	−3.91727e28	−0.0416484
$405$	−7.93863e29	−0.820376
$406$	0	0
$407$	1.33384e30	1.30247
$408$	−2.48288e29	−0.235702
$409$	9.57915e29	0.884115	0.442058	−	0.896987i	$-0.354249\pi$
$409$	9.57915e29	0.884115	0.442058	+	0.896987i	$0.354249\pi$
$410$	3.09069e29	0.277358
$411$	7.60245e29	0.663396
$412$	−3.11496e29	−0.264323
$413$	0	0
$414$	1.60487e29	0.128806
$415$	6.02504e29	0.470334
$416$	5.05902e29	0.384143
$417$	−8.68020e29	−0.641158
$418$	1.23988e30	0.890949
$419$	5.13468e29	0.358965	0.179483	−	0.983761i	$-0.442558\pi$
$419$	5.13468e29	0.358965	0.179483	+	0.983761i	$0.442558\pi$
$420$	0	0
$421$	2.43397e28	0.0161091	0.00805456	−	0.999968i	$-0.497436\pi$
$421$	2.43397e28	0.0161091	0.00805456	+	0.999968i	$0.497436\pi$
$422$	1.34526e30	0.866390
$423$	−7.36649e29	−0.461686
$424$	1.84449e30	1.12504
$425$	−1.65097e29	−0.0980090
$426$	2.07680e30	1.20001
$427$	0	0
$428$	6.02604e29	0.329935
$429$	1.84149e30	0.981545
$430$	1.14573e30	0.594559
$431$	−1.45777e30	−0.736549	−0.368274	−	0.929717i	$-0.620051\pi$
$431$	−1.45777e30	−0.736549	−0.368274	+	0.929717i	$0.620051\pi$
$432$	7.46790e29	0.367397
$433$	−2.75821e30	−1.32135	−0.660673	−	0.750673i	$-0.729729\pi$
$433$	−2.75821e30	−1.32135	−0.660673	+	0.750673i	$0.729729\pi$
$434$	0	0
$435$	1.91623e30	0.870607
$436$	1.01927e30	0.451018
$437$	6.25289e29	0.269491
$438$	2.97903e30	1.25061
$439$	−3.44878e30	−1.41034	−0.705170	−	0.709038i	$-0.749129\pi$
$439$	−3.44878e30	−1.41034	−0.705170	+	0.709038i	$0.749129\pi$
$440$	−1.75388e30	−0.698704
$441$	0	0
$442$	3.17705e29	0.120135
$443$	−1.57805e30	−0.581403	−0.290702	−	0.956814i	$-0.593889\pi$
$443$	−1.57805e30	−0.581403	−0.290702	+	0.956814i	$0.593889\pi$
$444$	−1.14865e30	−0.412368
$445$	2.45958e30	0.860439
$446$	3.76588e29	0.128385
$447$	4.69072e30	1.55849
$448$	0	0
$449$	−3.99683e30	−1.26149	−0.630743	−	0.775992i	$-0.717250\pi$
$449$	−3.99683e30	−1.26149	−0.630743	+	0.775992i	$0.717250\pi$
$450$	−9.20500e29	−0.283191
$451$	1.58227e30	0.474516
$452$	−9.27430e29	−0.271137
$453$	−6.91354e30	−1.97048
$454$	−1.87481e30	−0.520973
$455$	0	0
$456$	−5.39363e30	−1.42490
$457$	1.64681e30	0.424235	0.212118	−	0.977244i	$-0.431964\pi$
$457$	1.64681e30	0.424235	0.212118	+	0.977244i	$0.431964\pi$
$458$	−1.30282e30	−0.327290
$459$	−3.75709e29	−0.0920463
$460$	−1.75099e29	−0.0418378
$461$	−2.18794e30	−0.509888	−0.254944	−	0.966956i	$-0.582057\pi$
$461$	−2.18794e30	−0.509888	−0.254944	+	0.966956i	$0.582057\pi$
$462$	0	0
$463$	5.94749e30	1.31872	0.659360	−	0.751827i	$-0.270827\pi$
$463$	5.94749e30	1.31872	0.659360	+	0.751827i	$0.270827\pi$
$464$	−3.36416e30	−0.727645
$465$	−7.72512e30	−1.63003
$466$	−6.41177e30	−1.31990
$467$	−2.10652e30	−0.423078	−0.211539	−	0.977370i	$-0.567848\pi$
$467$	−2.10652e30	−0.423078	−0.211539	+	0.977370i	$0.567848\pi$
$468$	−5.80503e29	−0.113757
$469$	0	0
$470$	−2.45250e30	−0.457598
$471$	−2.95334e30	−0.537742
$472$	−6.29986e30	−1.11943
$473$	5.86555e30	1.01720
$474$	6.60346e30	1.11769
$475$	−3.58644e30	−0.592499
$476$	0	0
$477$	−3.81397e30	−0.600366
$478$	−1.04673e31	−1.60848
$479$	−8.13298e30	−1.22009	−0.610044	−	0.792367i	$-0.708848\pi$
$479$	−8.13298e30	−1.22009	−0.610044	+	0.792367i	$0.708848\pi$
$480$	2.72175e30	0.398633
$481$	7.42462e30	1.06171
$482$	−7.06359e30	−0.986244
$483$	0	0
$484$	7.65096e28	0.0101858
$485$	−8.75644e29	−0.113841
$486$	−7.05203e30	−0.895359
$487$	−5.35921e30	−0.664534	−0.332267	−	0.943185i	$-0.607814\pi$
$487$	−5.35921e30	−0.664534	−0.332267	+	0.943185i	$0.607814\pi$
$488$	−3.62349e30	−0.438833
$489$	−1.79552e30	−0.212392
$490$	0	0
$491$	7.21743e30	0.814602	0.407301	−	0.913294i	$-0.366470\pi$
$491$	7.21743e30	0.814602	0.407301	+	0.913294i	$0.366470\pi$
$492$	−1.36259e30	−0.150234
$493$	1.69251e30	0.182302
$494$	6.90160e30	0.726257
$495$	3.62661e30	0.372856
$496$	1.35623e31	1.36237
$497$	0	0
$498$	8.10544e30	0.777390
$499$	−7.03081e29	−0.0658945	−0.0329472	−	0.999457i	$-0.510489\pi$
$499$	−7.03081e29	−0.0658945	−0.0329472	+	0.999457i	$0.510489\pi$
$500$	2.78151e30	0.254757
$501$	5.25674e30	0.470525
$502$	−1.38123e31	−1.20829
$503$	−1.27287e31	−1.08831	−0.544155	−	0.838984i	$-0.683150\pi$
$503$	−1.27287e31	−1.08831	−0.544155	+	0.838984i	$0.683150\pi$
$504$	0	0
$505$	1.36223e30	0.111275
$506$	2.73536e30	0.218416
$507$	−5.84005e30	−0.455853
$508$	−5.25419e30	−0.400934
$509$	8.95139e30	0.667784	0.333892	−	0.942611i	$-0.391638\pi$
$509$	8.95139e30	0.667784	0.333892	+	0.942611i	$0.391638\pi$
$510$	1.70925e30	0.124666
$511$	0	0
$512$	−1.55212e31	−1.08224
$513$	−8.16165e30	−0.556453
$514$	1.46553e31	0.977053
$515$	1.08323e31	0.706213
$516$	−5.05119e30	−0.322049
$517$	−1.25555e31	−0.782878
$518$	0	0
$519$	3.35791e31	2.00283
$520$	−9.76267e30	−0.569548
$521$	2.69654e31	1.53876	0.769382	−	0.638788i	$-0.220564\pi$
$521$	2.69654e31	1.53876	0.769382	+	0.638788i	$0.220564\pi$
$522$	9.43660e30	0.526750
$523$	1.66071e31	0.906825	0.453412	−	0.891301i	$-0.350206\pi$
$523$	1.66071e31	0.906825	0.453412	+	0.891301i	$0.350206\pi$
$524$	8.26511e30	0.441508
$525$	0	0
$526$	2.78207e31	1.42243
$527$	−6.82317e30	−0.341322
$528$	−1.73931e31	−0.851311
$529$	−1.95010e31	−0.933934
$530$	−1.26977e31	−0.595051
$531$	1.30266e31	0.597373
$532$	0	0
$533$	8.80747e30	0.386802
$534$	3.30885e31	1.42217
$535$	−2.09555e31	−0.881514
$536$	−1.78446e31	−0.734704
$537$	−3.10344e30	−0.125066
$538$	3.99177e30	0.157460
$539$	0	0
$540$	2.28550e30	0.0863879
$541$	−5.87543e30	−0.217406	−0.108703	−	0.994074i	$-0.534670\pi$
$541$	−5.87543e30	−0.217406	−0.108703	+	0.994074i	$0.534670\pi$
$542$	1.89719e31	0.687257
$543$	−2.27942e30	−0.0808401
$544$	2.40397e30	0.0834722
$545$	−3.54450e31	−1.20502
$546$	0	0
$547$	−4.88371e31	−1.59183	−0.795913	−	0.605411i	$-0.793009\pi$
$547$	−4.88371e31	−1.59183	−0.795913	+	0.605411i	$0.793009\pi$
$548$	−4.08474e30	−0.130373
$549$	7.49253e30	0.234178
$550$	−1.56891e31	−0.480206
$551$	3.67668e31	1.10208
$552$	−1.18991e31	−0.349314
$553$	0	0
$554$	−1.79715e31	−0.506084
$555$	3.99443e31	1.10176
$556$	4.66380e30	0.126003
$557$	7.07650e30	0.187277	0.0936383	−	0.995606i	$-0.470150\pi$
$557$	7.07650e30	0.187277	0.0936383	+	0.995606i	$0.470150\pi$
$558$	−3.80427e31	−0.986231
$559$	3.26496e31	0.829168
$560$	0	0
$561$	8.75047e30	0.213284
$562$	−4.36181e30	−0.104160
$563$	−1.45808e31	−0.341142	−0.170571	−	0.985345i	$-0.554561\pi$
$563$	−1.45808e31	−0.341142	−0.170571	+	0.985345i	$0.554561\pi$
$564$	1.08124e31	0.247862
$565$	3.22513e31	0.724419
$566$	−1.24064e31	−0.273060
$567$	0	0
$568$	−5.63665e31	−1.19128
$569$	−2.12452e31	−0.440018	−0.220009	−	0.975498i	$-0.570609\pi$
$569$	−2.12452e31	−0.440018	−0.220009	+	0.975498i	$0.570609\pi$
$570$	3.71305e31	0.753651
$571$	7.34941e31	1.46197	0.730983	−	0.682396i	$-0.239062\pi$
$571$	7.34941e31	1.46197	0.730983	+	0.682396i	$0.239062\pi$
$572$	−9.89417e30	−0.192897
$573$	1.08044e32	2.06455
$574$	0	0
$575$	−7.91223e30	−0.145251
$576$	3.56172e31	0.640917
$577$	5.51644e31	0.973054	0.486527	−	0.873666i	$-0.338264\pi$
$577$	5.51644e31	0.973054	0.486527	+	0.873666i	$0.338264\pi$
$578$	−4.86804e31	−0.841752
$579$	−1.94308e31	−0.329373
$580$	−1.02958e31	−0.171095
$581$	0	0
$582$	−1.17800e31	−0.188161
$583$	−6.50059e31	−1.01804
$584$	−8.08538e31	−1.24152
$585$	2.01869e31	0.303933
$586$	−5.89719e31	−0.870608
$587$	4.14937e30	0.0600681	0.0300340	−	0.999549i	$-0.490438\pi$
$587$	4.14937e30	0.0600681	0.0300340	+	0.999549i	$0.490438\pi$
$588$	0	0
$589$	−1.48222e32	−2.06341
$590$	4.33692e31	0.592084
$591$	1.08349e31	0.145067
$592$	−7.01267e31	−0.920839
$593$	−2.38093e31	−0.306632	−0.153316	−	0.988177i	$-0.548995\pi$
$593$	−2.38093e31	−0.306632	−0.153316	+	0.988177i	$0.548995\pi$
$594$	−3.57036e31	−0.450991
$595$	0	0
$596$	−2.52029e31	−0.306280
$597$	1.79424e32	2.13883
$598$	1.52260e31	0.178042
$599$	−5.95324e31	−0.682881	−0.341440	−	0.939903i	$-0.610915\pi$
$599$	−5.95324e31	−0.682881	−0.341440	+	0.939903i	$0.610915\pi$
$600$	6.82495e31	0.767998
$601$	1.13077e32	1.24830	0.624150	−	0.781304i	$-0.285445\pi$
$601$	1.13077e32	1.24830	0.624150	+	0.781304i	$0.285445\pi$
$602$	0	0
$603$	3.68985e31	0.392066
$604$	3.71459e31	0.387245
$605$	−2.66061e30	−0.0272142
$606$	1.83259e31	0.183921
$607$	−3.93266e31	−0.387272	−0.193636	−	0.981073i	$-0.562028\pi$
$607$	−3.93266e31	−0.387272	−0.193636	+	0.981073i	$0.562028\pi$
$608$	5.22222e31	0.504619
$609$	0	0
$610$	2.49446e31	0.232105
$611$	−6.98884e31	−0.638162
$612$	−2.75846e30	−0.0247187
$613$	−7.97272e31	−0.701150	−0.350575	−	0.936535i	$-0.614014\pi$
$613$	−7.97272e31	−0.701150	−0.350575	+	0.936535i	$0.614014\pi$
$614$	8.78710e31	0.758420
$615$	4.73841e31	0.401392
$616$	0	0
$617$	1.31619e32	1.07409	0.537044	−	0.843554i	$-0.319541\pi$
$617$	1.31619e32	1.07409	0.537044	+	0.843554i	$0.319541\pi$
$618$	1.45725e32	1.16726
$619$	1.94614e32	1.53014	0.765070	−	0.643947i	$-0.222704\pi$
$619$	1.94614e32	1.53014	0.765070	+	0.643947i	$0.222704\pi$
$620$	4.15064e31	0.320340
$621$	−1.80058e31	−0.136414
$622$	−2.22933e32	−1.65800
$623$	0	0
$624$	−9.68162e31	−0.693945
$625$	−1.64200e31	−0.115546
$626$	1.47735e32	1.02066
$627$	1.90089e32	1.28938
$628$	1.58681e31	0.105679
$629$	3.52807e31	0.230704
$630$	0	0
$631$	2.09276e32	1.31941	0.659707	−	0.751523i	$-0.270680\pi$
$631$	2.09276e32	1.31941	0.659707	+	0.751523i	$0.270680\pi$
$632$	−1.79225e32	−1.10956
$633$	2.06245e32	1.25384
$634$	2.78812e31	0.166450
$635$	1.82714e32	1.07121
$636$	5.59806e31	0.322315
$637$	0	0
$638$	1.60839e32	0.893208
$639$	1.16553e32	0.635715
$640$	5.93321e31	0.317848
$641$	−2.56078e32	−1.34743	−0.673714	−	0.738992i	$-0.735302\pi$
$641$	−2.56078e32	−1.34743	−0.673714	+	0.738992i	$0.735302\pi$
$642$	−2.81912e32	−1.45701
$643$	−1.90581e32	−0.967507	−0.483754	−	0.875204i	$-0.660727\pi$
$643$	−1.90581e32	−0.967507	−0.483754	+	0.875204i	$0.660727\pi$
$644$	0	0
$645$	1.75655e32	0.860444
$646$	3.27954e31	0.157812
$647$	−1.17375e32	−0.554851	−0.277426	−	0.960747i	$-0.589481\pi$
$647$	−1.17375e32	−0.554851	−0.277426	+	0.960747i	$0.589481\pi$
$648$	2.89860e32	1.34609
$649$	2.22028e32	1.01296
$650$	−8.73310e31	−0.391440
$651$	0	0
$652$	9.64717e30	0.0417400
$653$	−4.31869e32	−1.83591	−0.917954	−	0.396687i	$-0.870160\pi$
$653$	−4.31869e32	−1.83591	−0.917954	+	0.396687i	$0.870160\pi$
$654$	−4.76839e32	−1.99172
$655$	−2.87418e32	−1.17961
$656$	−8.31879e31	−0.335480
$657$	1.67187e32	0.662522
$658$	0	0
$659$	−4.05209e32	−1.55059	−0.775295	−	0.631600i	$-0.782399\pi$
$659$	−4.05209e32	−1.55059	−0.775295	+	0.631600i	$0.782399\pi$
$660$	−5.32305e31	−0.200173
$661$	−9.73763e31	−0.359862	−0.179931	−	0.983679i	$-0.557588\pi$
$661$	−9.73763e31	−0.359862	−0.179931	+	0.983679i	$0.557588\pi$
$662$	−1.02734e32	−0.373121
$663$	4.87081e31	0.173858
$664$	−2.19990e32	−0.771737
$665$	0	0
$666$	1.96708e32	0.666605
$667$	8.11130e31	0.270174
$668$	−2.82440e31	−0.0924693
$669$	5.77355e31	0.185799
$670$	1.22845e32	0.388595
$671$	1.27704e32	0.397095
$672$	0	0
$673$	−3.34090e31	−0.100390	−0.0501949	−	0.998739i	$-0.515984\pi$
$673$	−3.34090e31	−0.100390	−0.0501949	+	0.998739i	$0.515984\pi$
$674$	1.22974e32	0.363265
$675$	1.03275e32	0.299918
$676$	3.13781e31	0.0895859
$677$	−1.42876e32	−0.401042	−0.200521	−	0.979689i	$-0.564264\pi$
$677$	−1.42876e32	−0.401042	−0.200521	+	0.979689i	$0.564264\pi$
$678$	4.33874e32	1.19735
$679$	0	0
$680$	−4.63907e31	−0.123760
$681$	−2.87432e32	−0.753950
$682$	−6.48406e32	−1.67235
$683$	8.01003e31	0.203140	0.101570	−	0.994828i	$-0.467613\pi$
$683$	8.01003e31	0.203140	0.101570	+	0.994828i	$0.467613\pi$
$684$	−5.99229e31	−0.149433
$685$	1.42046e32	0.348328
$686$	0	0
$687$	−1.99739e32	−0.473653
$688$	−3.08381e32	−0.719152
$689$	−3.61845e32	−0.829853
$690$	8.19155e31	0.184757
$691$	6.06677e32	1.34574	0.672868	−	0.739762i	$-0.265062\pi$
$691$	6.06677e32	1.34574	0.672868	+	0.739762i	$0.265062\pi$
$692$	−1.80418e32	−0.393604
$693$	0	0
$694$	−3.30727e32	−0.697968
$695$	−1.62183e32	−0.336651
$696$	−6.99666e32	−1.42851
$697$	4.18518e31	0.0840498
$698$	−3.32756e32	−0.657337
$699$	−9.83003e32	−1.91015
$700$	0	0
$701$	5.03914e32	0.947544	0.473772	−	0.880648i	$-0.342892\pi$
$701$	5.03914e32	0.947544	0.473772	+	0.880648i	$0.342892\pi$
$702$	−1.98739e32	−0.367625
$703$	7.66412e32	1.39469
$704$	6.07065e32	1.08680
$705$	−3.75999e32	−0.662234
$706$	−3.96187e32	−0.686509
$707$	0	0
$708$	−1.91202e32	−0.320708
$709$	−1.95608e32	−0.322816	−0.161408	−	0.986888i	$-0.551603\pi$
$709$	−1.95608e32	−0.322816	−0.161408	+	0.986888i	$0.551603\pi$
$710$	3.88035e32	0.630086
$711$	3.70595e32	0.592105
$712$	−8.98055e32	−1.41183
$713$	−3.27000e32	−0.505845
$714$	0	0
$715$	3.44069e32	0.515378
$716$	1.66745e31	0.0245784
$717$	−1.60477e33	−2.32778
$718$	4.37338e32	0.624290
$719$	3.61354e32	0.507635	0.253817	−	0.967252i	$-0.418314\pi$
$719$	3.61354e32	0.507635	0.253817	+	0.967252i	$0.418314\pi$
$720$	−1.90669e32	−0.263606
$721$	0	0
$722$	6.43483e31	0.0861706
$723$	−1.08293e33	−1.42729
$724$	1.22472e31	0.0158870
$725$	−4.65237e32	−0.594001
$726$	−3.57930e31	−0.0449808
$727$	5.93026e32	0.733547	0.366773	−	0.930310i	$-0.380462\pi$
$727$	5.93026e32	0.733547	0.366773	+	0.930310i	$0.380462\pi$
$728$	0	0
$729$	−4.31845e31	−0.0517561
$730$	5.56610e32	0.656656
$731$	1.55146e32	0.180174
$732$	−1.09974e32	−0.125722
$733$	−1.20014e33	−1.35063	−0.675316	−	0.737529i	$-0.735993\pi$
$733$	−1.20014e33	−1.35063	−0.675316	+	0.737529i	$0.735993\pi$
$734$	−8.11743e32	−0.899319
$735$	0	0
$736$	1.15210e32	0.123707
$737$	6.28903e32	0.664825
$738$	2.33345e32	0.242857
$739$	1.98559e32	0.203460	0.101730	−	0.994812i	$-0.467562\pi$
$739$	1.98559e32	0.203460	0.101730	+	0.994812i	$0.467562\pi$
$740$	−2.14618e32	−0.216521
$741$	1.05810e33	1.05104
$742$	0	0
$743$	9.02149e32	0.868774	0.434387	−	0.900726i	$-0.356965\pi$
$743$	9.02149e32	0.868774	0.434387	+	0.900726i	$0.356965\pi$
$744$	2.82064e33	2.67460
$745$	8.76428e32	0.818312
$746$	2.94295e31	0.0270574
$747$	4.54887e32	0.411829
$748$	−4.70156e31	−0.0419154
$749$	0	0
$750$	−1.30126e33	−1.12501
$751$	3.97352e32	0.338311	0.169155	−	0.985589i	$-0.445896\pi$
$751$	3.97352e32	0.338311	0.169155	+	0.985589i	$0.445896\pi$
$752$	6.60107e32	0.553489
$753$	−2.11759e33	−1.74864
$754$	8.95282e32	0.728098
$755$	−1.29175e33	−1.03463
$756$	0	0
$757$	8.67116e32	0.673712	0.336856	−	0.941556i	$-0.390636\pi$
$757$	8.67116e32	0.673712	0.336856	+	0.941556i	$0.390636\pi$
$758$	−1.38008e33	−1.05611
$759$	4.19365e32	0.316091
$760$	−1.00776e33	−0.748171
$761$	2.16137e32	0.158054	0.0790272	−	0.996872i	$-0.474819\pi$
$761$	2.16137e32	0.158054	0.0790272	+	0.996872i	$0.474819\pi$
$762$	2.45803e33	1.77054
$763$	0	0
$764$	−5.80514e32	−0.405732
$765$	9.59252e31	0.0660429
$766$	1.48971e32	0.101035
$767$	1.23588e33	0.825716
$768$	−1.31983e33	−0.868688
$769$	7.41782e32	0.480976	0.240488	−	0.970652i	$-0.422693\pi$
$769$	7.41782e32	0.480976	0.240488	+	0.970652i	$0.422693\pi$
$770$	0	0
$771$	2.24684e33	1.41399
$772$	1.04400e32	0.0647296
$773$	8.03942e32	0.491090	0.245545	−	0.969385i	$-0.421033\pi$
$773$	8.03942e32	0.491090	0.245545	+	0.969385i	$0.421033\pi$
$774$	8.65020e32	0.520601
$775$	1.87556e33	1.11214
$776$	3.19720e32	0.186793
$777$	0	0
$778$	−1.83887e33	−1.04301
$779$	9.09158e32	0.508111
$780$	−2.96299e32	−0.163171
$781$	1.98654e33	1.07798
$782$	7.23515e31	0.0386874
$783$	−1.05874e33	−0.557863
$784$	0	0
$785$	−5.51811e32	−0.282351
$786$	−3.86662e33	−1.94972
$787$	2.14021e33	1.06352	0.531762	−	0.846894i	$-0.321530\pi$
$787$	2.14021e33	1.06352	0.531762	+	0.846894i	$0.321530\pi$
$788$	−5.82150e31	−0.0285091
$789$	4.26525e33	2.05854
$790$	1.23381e33	0.586862
$791$	0	0
$792$	−1.32417e33	−0.611791
$793$	7.10842e32	0.323692
$794$	−5.16473e32	−0.231799
$795$	−1.94672e33	−0.861155
$796$	−9.64033e32	−0.420331
$797$	9.61312e31	0.0413136	0.0206568	−	0.999787i	$-0.493424\pi$
$797$	9.61312e31	0.0413136	0.0206568	+	0.999787i	$0.493424\pi$
$798$	0	0
$799$	−3.32099e32	−0.138669
$800$	−6.60805e32	−0.271981
$801$	1.85697e33	0.753408
$802$	−7.92696e32	−0.317031
$803$	2.84955e33	1.12344
$804$	−5.41588e32	−0.210487
$805$	0	0
$806$	−3.60925e33	−1.36321
$807$	6.11988e32	0.227875
$808$	−4.97384e32	−0.182583
$809$	−3.70647e33	−1.34138	−0.670691	−	0.741737i	$-0.734002\pi$
$809$	−3.70647e33	−1.34138	−0.670691	+	0.741737i	$0.734002\pi$
$810$	−1.99544e33	−0.711968
$811$	3.98885e33	1.40316	0.701580	−	0.712590i	$-0.252478\pi$
$811$	3.98885e33	1.40316	0.701580	+	0.712590i	$0.252478\pi$
$812$	0	0
$813$	2.90863e33	0.994596
$814$	3.35272e33	1.13036
$815$	−3.35479e32	−0.111520
$816$	−4.60056e32	−0.150790
$817$	3.37028e33	1.08921
$818$	2.40780e33	0.767285
$819$	0	0
$820$	−2.54591e32	−0.0788830
$821$	4.22086e33	1.28960	0.644799	−	0.764352i	$-0.276941\pi$
$821$	4.22086e33	1.28960	0.644799	+	0.764352i	$0.276941\pi$
$822$	1.91094e33	0.575732
$823$	−4.93005e33	−1.46471	−0.732357	−	0.680921i	$-0.761580\pi$
$823$	−4.93005e33	−1.46471	−0.732357	+	0.680921i	$0.761580\pi$
$824$	−3.95513e33	−1.15877
$825$	−2.40534e33	−0.694953
$826$	0	0
$827$	−6.03766e32	−0.169651	−0.0848253	−	0.996396i	$-0.527033\pi$
$827$	−6.03766e32	−0.169651	−0.0848253	+	0.996396i	$0.527033\pi$
$828$	−1.32199e32	−0.0366335
$829$	4.31323e33	1.17876	0.589381	−	0.807856i	$-0.299372\pi$
$829$	4.31323e33	1.17876	0.589381	+	0.807856i	$0.299372\pi$
$830$	1.51444e33	0.408183
$831$	−2.75526e33	−0.732403
$832$	3.37913e33	0.885904
$833$	0	0
$834$	−2.18184e33	−0.556433
$835$	9.82183e32	0.247058
$836$	−1.02133e33	−0.253393
$837$	4.26820e33	1.04448
$838$	1.29064e33	0.311530
$839$	−2.82182e33	−0.671842	−0.335921	−	0.941890i	$-0.609047\pi$
$839$	−2.82182e33	−0.671842	−0.335921	+	0.941890i	$0.609047\pi$
$840$	0	0
$841$	4.52701e32	0.104871
$842$	6.11799e31	0.0139804
$843$	−6.68720e32	−0.150739
$844$	−1.10814e33	−0.246409
$845$	−1.09117e33	−0.239354
$846$	−1.85163e33	−0.400677
$847$	0	0
$848$	3.41768e33	0.719746
$849$	−1.90206e33	−0.395171
$850$	−4.14984e32	−0.0850577
$851$	1.69082e33	0.341907
$852$	−1.71073e33	−0.341293
$853$	−8.25823e32	−0.162545	−0.0812724	−	0.996692i	$-0.525898\pi$
$853$	−8.25823e32	−0.162545	−0.0812724	+	0.996692i	$0.525898\pi$
$854$	0	0
$855$	2.08381e33	0.399253
$856$	7.65138e33	1.44641
$857$	−2.54873e33	−0.475383	−0.237692	−	0.971341i	$-0.576391\pi$
$857$	−2.54873e33	−0.475383	−0.237692	+	0.971341i	$0.576391\pi$
$858$	4.62873e33	0.851840
$859$	−4.42760e33	−0.803984	−0.401992	−	0.915643i	$-0.631682\pi$
$859$	−4.42760e33	−0.803984	−0.401992	+	0.915643i	$0.631682\pi$
$860$	−9.43778e32	−0.169098
$861$	0	0
$862$	−3.66423e33	−0.639218
$863$	−1.11946e34	−1.92701	−0.963505	−	0.267691i	$-0.913739\pi$
$863$	−1.11946e34	−1.92701	−0.963505	+	0.267691i	$0.913739\pi$
$864$	−1.50379e33	−0.255434
$865$	6.27402e33	1.05162
$866$	−6.93299e33	−1.14674
$867$	−7.46330e33	−1.21818
$868$	0	0
$869$	6.31646e33	1.00403
$870$	4.81661e33	0.755562
$871$	3.50069e33	0.541932
$872$	1.29419e34	1.97723
$873$	−6.61107e32	−0.0996800
$874$	1.57171e33	0.233879
$875$	0	0
$876$	−2.45393e33	−0.355684
$877$	6.04480e33	0.864742	0.432371	−	0.901696i	$-0.357677\pi$
$877$	6.04480e33	0.864742	0.432371	+	0.901696i	$0.357677\pi$
$878$	−8.66879e33	−1.22397
$879$	−9.04112e33	−1.25994
$880$	−3.24978e33	−0.446996
$881$	7.67902e33	1.04252	0.521258	−	0.853399i	$-0.325463\pi$
$881$	7.67902e33	1.04252	0.521258	+	0.853399i	$0.325463\pi$
$882$	0	0
$883$	−1.70686e33	−0.225762	−0.112881	−	0.993609i	$-0.536008\pi$
$883$	−1.70686e33	−0.225762	−0.112881	+	0.993609i	$0.536008\pi$
$884$	−2.61705e32	−0.0341673
$885$	6.64903e33	0.856862
$886$	−3.96655e33	−0.504574
$887$	6.39269e33	0.802716	0.401358	−	0.915921i	$-0.368538\pi$
$887$	6.39269e33	0.802716	0.401358	+	0.915921i	$0.368538\pi$
$888$	−1.45847e34	−1.80779
$889$	0	0
$890$	6.18234e33	0.746738
$891$	−1.02156e34	−1.21807
$892$	−3.10208e32	−0.0365138
$893$	−7.21429e33	−0.838304
$894$	1.17905e34	1.35254
$895$	−5.79855e32	−0.0656681
$896$	0	0
$897$	2.33433e33	0.257661
$898$	−1.00463e34	−1.09479
$899$	−1.92275e34	−2.06864
$900$	7.58248e32	0.0805420
$901$	−1.71943e33	−0.180322
$902$	3.97717e33	0.411812
$903$	0	0
$904$	−1.17758e34	−1.18865
$905$	−4.25893e32	−0.0424465
$906$	−1.73777e34	−1.71009
$907$	−1.60453e34	−1.55906	−0.779531	−	0.626363i	$-0.784543\pi$
$907$	−1.60453e34	−1.55906	−0.779531	+	0.626363i	$0.784543\pi$
$908$	1.54435e33	0.148169
$909$	1.02847e33	0.0974336
$910$	0	0
$911$	−2.12344e33	−0.196146	−0.0980730	−	0.995179i	$-0.531268\pi$
$911$	−2.12344e33	−0.196146	−0.0980730	+	0.995179i	$0.531268\pi$
$912$	−9.99393e33	−0.911582
$913$	7.75316e33	0.698337
$914$	4.13938e33	0.368175
$915$	3.82432e33	0.335901
$916$	1.07318e33	0.0930840
$917$	0	0
$918$	−9.44376e32	−0.0798829
$919$	−7.46924e33	−0.623947	−0.311974	−	0.950091i	$-0.600990\pi$
$919$	−7.46924e33	−0.623947	−0.311974	+	0.950091i	$0.600990\pi$
$920$	−2.22327e33	−0.183414
$921$	1.34717e34	1.09758
$922$	−5.49956e33	−0.442509
$923$	1.10578e34	0.878714
$924$	0	0
$925$	−9.69797e33	−0.751711
$926$	1.49495e34	1.14446
$927$	8.17829e33	0.618366
$928$	6.77431e33	0.505898
$929$	1.26293e33	0.0931533	0.0465767	−	0.998915i	$-0.485169\pi$
$929$	1.26293e33	0.0931533	0.0465767	+	0.998915i	$0.485169\pi$
$930$	−1.94177e34	−1.41463
$931$	0	0
$932$	5.28159e33	0.375389
$933$	−3.41784e34	−2.39946
$934$	−5.29490e33	−0.367171
$935$	1.63496e33	0.111989
$936$	−7.37077e33	−0.498701
$937$	7.33696e33	0.490355	0.245178	−	0.969478i	$-0.421154\pi$
$937$	7.33696e33	0.490355	0.245178	+	0.969478i	$0.421154\pi$
$938$	0	0
$939$	2.26496e34	1.47709
$940$	2.02021e33	0.130145
$941$	−2.33812e34	−1.48794	−0.743971	−	0.668212i	$-0.767060\pi$
$941$	−2.33812e34	−1.48794	−0.743971	+	0.668212i	$0.767060\pi$
$942$	−7.42347e33	−0.466682
$943$	2.00574e33	0.124563
$944$	−1.16731e34	−0.716157
$945$	0	0
$946$	1.47435e34	0.882781
$947$	−1.00540e34	−0.594724	−0.297362	−	0.954765i	$-0.596107\pi$
$947$	−1.00540e34	−0.594724	−0.297362	+	0.954765i	$0.596107\pi$
$948$	−5.43950e33	−0.317880
$949$	1.58616e34	0.915767
$950$	−9.01482e33	−0.514204
$951$	4.27453e33	0.240886
$952$	0	0
$953$	5.87817e33	0.323351	0.161675	−	0.986844i	$-0.448310\pi$
$953$	5.87817e33	0.323351	0.161675	+	0.986844i	$0.448310\pi$
$954$	−9.58673e33	−0.521032
$955$	2.01873e34	1.08403
$956$	8.62230e33	0.457465
$957$	2.46585e34	1.29265
$958$	−2.04429e34	−1.05886
$959$	0	0
$960$	1.81797e34	0.919320
$961$	5.75004e34	2.87311
$962$	1.86624e34	0.921411
$963$	−1.58213e34	−0.771861
$964$	5.81852e33	0.280496
$965$	−3.63051e33	−0.172943
$966$	0	0
$967$	2.63145e33	0.122402	0.0612012	−	0.998125i	$-0.480507\pi$
$967$	2.63145e33	0.122402	0.0612012	+	0.998125i	$0.480507\pi$
$968$	9.71459e32	0.0446537
$969$	5.02794e33	0.228384
$970$	−2.20100e33	−0.0987974
$971$	1.83507e34	0.814014	0.407007	−	0.913425i	$-0.366572\pi$
$971$	1.83507e34	0.814014	0.407007	+	0.913425i	$0.366572\pi$
$972$	5.80900e33	0.254648
$973$	0	0
$974$	−1.34708e34	−0.576720
$975$	−1.33889e34	−0.566490
$976$	−6.71402e33	−0.280743
$977$	−4.47994e33	−0.185133	−0.0925666	−	0.995706i	$-0.529507\pi$
$977$	−4.47994e33	−0.185133	−0.0925666	+	0.995706i	$0.529507\pi$
$978$	−4.51317e33	−0.184325
$979$	3.16504e34	1.27755
$980$	0	0
$981$	−2.67608e34	−1.05513
$982$	1.81416e34	0.706957
$983$	1.86230e34	0.717274	0.358637	−	0.933477i	$-0.383242\pi$
$983$	1.86230e34	0.717274	0.358637	+	0.933477i	$0.383242\pi$
$984$	−1.73011e34	−0.658614
$985$	2.02442e33	0.0761699
$986$	4.25425e33	0.158212
$987$	0	0
$988$	−5.68509e33	−0.206554
$989$	7.43535e33	0.267020
$990$	9.11577e33	0.323585
$991$	−1.44747e34	−0.507881	−0.253941	−	0.967220i	$-0.581727\pi$
$991$	−1.44747e34	−0.507881	−0.253941	+	0.967220i	$0.581727\pi$
$992$	−2.73100e34	−0.947190
$993$	−1.57505e34	−0.539979
$994$	0	0
$995$	3.35242e34	1.12303
$996$	−6.67673e33	−0.221096
$997$	−2.88400e33	−0.0944063	−0.0472032	−	0.998885i	$-0.515031\pi$
$997$	−2.88400e33	−0.0944063	−0.0472032	+	0.998885i	$0.515031\pi$
$998$	−1.76725e33	−0.0571869
$999$	−2.20696e34	−0.705979

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.g.1.10		14
7.2	even	3		7.24.c.a.4.5	yes	28
7.4	even	3		7.24.c.a.2.5	✓	28
7.6	odd	2		49.24.a.f.1.10		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.24.c.a.2.5	✓	28	7.4	even	3
7.24.c.a.4.5	yes	28	7.2	even	3
49.24.a.f.1.10		14	7.6	odd	2
49.24.a.g.1.10		14	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	49.a (trivial)

\(f(q)\)	\(=\)	\(q+2513.58 q^{2} +385363. q^{3} -2.07052e6 q^{4} +7.20022e7 q^{5} +9.68640e8 q^{6} -2.62899e10 q^{8} +5.43613e10 q^{9} +1.80983e11 q^{10} +9.26541e11 q^{11} -7.97903e11 q^{12} +5.15744e12 q^{13} +2.77470e13 q^{15} -4.87129e13 q^{16} +2.45074e13 q^{17} +1.36641e14 q^{18} +5.32381e14 q^{19} -1.49082e14 q^{20} +2.32894e15 q^{22} +1.17451e15 q^{23} -1.01311e16 q^{24} -6.73661e15 q^{25} +1.29636e16 q^{26} -1.53305e16 q^{27} +6.90610e16 q^{29} +6.97442e16 q^{30} -2.78413e17 q^{31} +9.80917e16 q^{32} +3.57054e17 q^{33} +6.16013e16 q^{34} -1.12556e17 q^{36} +1.43959e18 q^{37} +1.33818e18 q^{38} +1.98749e18 q^{39} -1.89293e18 q^{40} +1.70772e18 q^{41} +6.33058e18 q^{43} -1.91842e18 q^{44} +3.91413e18 q^{45} +2.95223e18 q^{46} -1.35510e19 q^{47} -1.87721e19 q^{48} -1.69330e19 q^{50} +9.44424e18 q^{51} -1.06786e19 q^{52} -7.01597e19 q^{53} -3.85343e19 q^{54} +6.67130e19 q^{55} +2.05160e20 q^{57} +1.73590e20 q^{58} +2.39631e20 q^{59} -5.74508e19 q^{60} +1.37828e20 q^{61} -6.99813e20 q^{62} +6.55194e20 q^{64} +3.71347e20 q^{65} +8.97485e20 q^{66} +6.78764e20 q^{67} -5.07431e19 q^{68} +4.52614e20 q^{69} +2.14404e21 q^{71} -1.42915e21 q^{72} +3.07547e21 q^{73} +3.61853e21 q^{74} -2.59604e21 q^{75} -1.10231e21 q^{76} +4.99571e21 q^{78} +6.81725e21 q^{79} -3.50743e21 q^{80} -1.10255e22 q^{81} +4.29249e21 q^{82} +8.36785e21 q^{83} +1.76459e21 q^{85} +1.59124e22 q^{86} +2.66135e22 q^{87} -2.43586e22 q^{88} +3.41597e22 q^{89} +9.83849e21 q^{90} -2.43186e21 q^{92} -1.07290e23 q^{93} -3.40615e22 q^{94} +3.83326e22 q^{95} +3.78009e22 q^{96} -1.21614e22 q^{97} +5.03680e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 966 q^{2} + 177148 q^{3} + 55357148 q^{4} + 74771022 q^{5} + 1504608254 q^{6} + 25222400616 q^{8} + 336909608980 q^{9} + 334296297894 q^{10} - 1355476566108 q^{11} + 4984668058916 q^{12} - 427040218556 q^{13}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) \) 14 * q - 966 * q^2 + 177148 * q^3 + 55357148 * q^4 + 74771022 * q^5 + 1504608254 * q^6 + 25222400616 * q^8 + 336909608980 * q^9 + 334296297894 * q^10 - 1355476566108 * q^11 + 4984668058916 * q^12 - 427040218556 * q^13 + 38670810653944 * q^15 + 160538324156336 * q^16 + 130193896130514 * q^17 - 110632655983108 * q^18 + 214771980430396 * q^19 - 48219439281468 * q^20 + 7534772282877126 * q^22 - 6685548913560552 * q^23 + 31330599354826008 * q^24 + 9156874000789424 * q^25 + 48260478025970868 * q^26 + 8477622198540028 * q^27 - 115398975455444604 * q^29 - 4149727265170942 * q^30 - 94821366637509632 * q^31 + 989053585410677472 * q^32 - 471925265098792298 * q^33 + 204665719203916350 * q^34 + 161548642910645480 * q^36 - 228196281955951106 * q^37 - 846979764807573006 * q^38 + 4289472930557071768 * q^39 + 10645750240235319192 * q^40 + 12663069502432601532 * q^41 - 427239519112420616 * q^43 - 11572396920387558444 * q^44 + 9362992784223924004 * q^45 + 33418566325741763586 * q^46 + 61615364375433533424 * q^47 + 158511629928130898960 * q^48 - 93272670392614362552 * q^50 - 84287583500847206172 * q^51 + 90603352071153943672 * q^52 + 282093764343878671758 * q^53 - 13895299932605385046 * q^54 + 237446342744567832720 * q^55 - 425457361374285462782 * q^57 - 339998979132364080060 * q^58 + 283820607003252730116 * q^59 + 701673169918628967164 * q^60 + 870322613357668504870 * q^61 + 282243301452069984966 * q^62 + 2124141067160402139584 * q^64 - 384582138286683330588 * q^65 + 157008004213679191250 * q^66 - 1414046473258733295716 * q^67 - 435228382363177447884 * q^68 - 2663127352907733668682 * q^69 + 213218335956247656048 * q^71 + 10118884230376615693104 * q^72 - 5942494661268692359862 * q^73 - 13389833203328450370642 * q^74 - 14120811240771906960232 * q^75 - 22920526497794398939844 * q^76 + 7201287217205176160828 * q^78 + 3444345943288433723680 * q^79 + 8255607259451726029008 * q^80 - 2565358457232096585122 * q^81 - 34656759475287179918772 * q^82 + 6085375799043077804904 * q^83 - 7680353239558358537262 * q^85 - 743687862046869712056 * q^86 + 7978312766181293835640 * q^87 + 2867657955669848060664 * q^88 + 68609868120257601678426 * q^89 + 17331740036513596551428 * q^90 - 7750847835981686889348 * q^92 - 50628291689744906093838 * q^93 - 18415808745499513811142 * q^94 + 113148862333982926479168 * q^95 + 150237583048546245409696 * q^96 + 230188776588461622952972 * q^97 - 234139240054754764282784 * q^99

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