LMFDB - Embedded newform 49.24.a.d.1.4

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 = [6,-2115,-129352] 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:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3 x^{5} - 27997302 x^{4} - 8334207232 x^{3} + 155343730039680 x^{2} + \cdots - 52\!\cdots\!92 $ x^6 - 3x^5 - 27997302x^4 - 8334207232x^3 + 155343730039680x^2 + 112911634264375296*x - 52432637519673556992
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{4}\cdot 5\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1242.12$ 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)

$f(q)$	$=$	\(q+890.125 q^{2} +64762.8 q^{3} -7.59629e6 q^{4} -1.51631e8 q^{5} +5.76470e7 q^{6} -1.42285e10 q^{8} -8.99490e10 q^{9} -1.34970e11 q^{10} +1.07109e12 q^{11} -4.91957e11 q^{12} +2.28738e12 q^{13} -9.82003e12 q^{15} +5.10571e13 q^{16} -1.43774e14 q^{17} -8.00658e13 q^{18} -2.49170e14 q^{19} +1.15183e15 q^{20} +9.53407e14 q^{22} +5.64345e15 q^{23} -9.21481e14 q^{24} +1.10709e16 q^{25} +2.03605e15 q^{26} -1.19223e16 q^{27} +9.30270e16 q^{29} -8.74105e15 q^{30} -1.39574e17 q^{31} +1.64805e17 q^{32} +6.93670e16 q^{33} -1.27976e17 q^{34} +6.83278e17 q^{36} -8.48399e17 q^{37} -2.21793e17 q^{38} +1.48137e17 q^{39} +2.15748e18 q^{40} +4.30314e18 q^{41} +1.11166e19 q^{43} -8.13633e18 q^{44} +1.36390e19 q^{45} +5.02338e18 q^{46} +2.03654e19 q^{47} +3.30660e18 q^{48} +9.85450e18 q^{50} -9.31118e18 q^{51} -1.73756e19 q^{52} +2.85416e19 q^{53} -1.06124e19 q^{54} -1.62411e20 q^{55} -1.61370e19 q^{57} +8.28056e19 q^{58} +2.78122e20 q^{59} +7.45957e19 q^{60} -4.38464e20 q^{61} -1.24239e20 q^{62} -2.81601e20 q^{64} -3.46837e20 q^{65} +6.17453e19 q^{66} -1.17983e21 q^{67} +1.09215e21 q^{68} +3.65486e20 q^{69} -8.77727e20 q^{71} +1.27984e21 q^{72} -3.16262e21 q^{73} -7.55181e20 q^{74} +7.16984e20 q^{75} +1.89277e21 q^{76} +1.31860e20 q^{78} -5.58011e21 q^{79} -7.74182e21 q^{80} +7.69596e21 q^{81} +3.83033e21 q^{82} -8.16381e21 q^{83} +2.18005e22 q^{85} +9.89512e21 q^{86} +6.02469e21 q^{87} -1.52401e22 q^{88} -1.74656e22 q^{89} +1.21404e22 q^{90} -4.28693e22 q^{92} -9.03922e21 q^{93} +1.81277e22 q^{94} +3.77819e22 q^{95} +1.06732e22 q^{96} -8.64253e22 q^{97} -9.63437e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2115 q^{2} - 129352 q^{3} + 6408501 q^{4} - 71437860 q^{5} - 3587653778 q^{6} - 49163897313 q^{8} + 379016247310 q^{9} + 181303960020 q^{10} - 1168850705976 q^{11} + 4703061003298 q^{12} - 11000714535636 q^{13}+ \cdots - 90\!\cdots\!04 q^{99}+O(q^{100}) $ 6 * q - 2115 * q^2 - 129352 * q^3 + 6408501 * q^4 - 71437860 * q^5 - 3587653778 * q^6 - 49163897313 * q^8 + 379016247310 * q^9 + 181303960020 * q^10 - 1168850705976 * q^11 + 4703061003298 * q^12 - 11000714535636 * q^13 - 47642583586400 * q^15 + 18002647337265 * q^16 + 131037332534676 * q^17 + 529552005104765 * q^18 + 465517985994456 * q^19 - 4943391871987800 * q^20 + 897855714076560 * q^22 + 7117263515782944 * q^23 - 33845264505914994 * q^24 + 59193078584081850 * q^25 + 14028640730008128 * q^26 - 133885130285006704 * q^27 + 262229251160335716 * q^29 + 865723792547512160 * q^30 - 62353891866345792 * q^31 + 60817903285433751 * q^32 - 656783103747874240 * q^33 - 547282704180314454 * q^34 + 2621034627679676861 * q^36 + 1939218016676008788 * q^37 + 3706293351149576370 * q^38 - 5440924440539077952 * q^39 + 9081341251088376000 * q^40 + 4731954216272399844 * q^41 - 24014219944449751704 * q^43 - 35009940957233293512 * q^44 - 3889099587334138420 * q^45 - 10024371971526875280 * q^46 + 16003565954092252224 * q^47 + 39357800694088338754 * q^48 - 35480060910606427425 * q^50 + 14150130737580870000 * q^51 - 145479234260898246660 * q^52 + 202556458664680403988 * q^53 - 332296415548302297788 * q^54 + 113721680610730698480 * q^55 + 483285990792481439152 * q^57 + 369031442265302613858 * q^58 - 410642445729067981848 * q^59 - 252127772417738489440 * q^60 - 323143816367671678740 * q^61 - 1415366445023186971716 * q^62 - 1111603155968170329615 * q^64 + 943372699520900652360 * q^65 + 3725312806903508474032 * q^66 - 579655126533238145448 * q^67 + 4217438616148514842722 * q^68 + 2487561554615627392320 * q^69 - 4214729769305546523888 * q^71 - 4997204873186276234745 * q^72 + 1754672903937008125764 * q^73 - 2545731661343127113286 * q^74 + 1081682226208732479400 * q^75 + 15054272754186740412366 * q^76 + 22528837564350510851192 * q^78 + 11526574620963653844480 * q^79 - 5407655723279367022800 * q^80 + 22052505466676180451910 * q^81 - 35925451975152054439782 * q^82 - 31653105166748099990088 * q^83 - 8683324350419512060440 * q^85 - 37145551308674423554872 * q^86 - 87814884336214862913616 * q^87 + 18253569093995420090808 * q^88 - 54130449609585297492156 * q^89 + 11101634800321218680740 * q^90 + 18734804418795932525328 * q^92 + 85314604106878433682720 * q^93 + 284937906702848285268180 * q^94 - 157825746495468308410560 * q^95 + 327539108386580666719598 * q^96 + 41184441040066248030036 * q^97 - 90199089796280394452504 * 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 $

$2$	890.125	0.307331	0.153665	−	0.988123i	$-0.450892\pi$
$2$	890.125	0.307331	0.153665	+	0.988123i	$0.450892\pi$
$3$	64762.8	0.211072	0.105536	−	0.994415i	$-0.466344\pi$
$3$	64762.8	0.211072	0.105536	+	0.994415i	$0.466344\pi$
$4$	−7.59629e6	−0.905548
$5$	−1.51631e8	−1.38878	−0.694388	−	0.719601i	$-0.744325\pi$
$5$	−1.51631e8	−1.38878	−0.694388	+	0.719601i	$0.744325\pi$
$6$	5.76470e7	0.0648690
$7$	0	0
$7$	0	0
$8$	−1.42285e10	−0.585633
$9$	−8.99490e10	−0.955448
$10$	−1.34970e11	−0.426813
$11$	1.07109e12	1.13191	0.565954	−	0.824436i	$-0.308508\pi$
$11$	1.07109e12	1.13191	0.565954	+	0.824436i	$0.308508\pi$
$12$	−4.91957e11	−0.191136
$13$	2.28738e12	0.353989	0.176994	−	0.984212i	$-0.443363\pi$
$13$	2.28738e12	0.353989	0.176994	+	0.984212i	$0.443363\pi$
$14$	0	0
$15$	−9.82003e12	−0.293132
$16$	5.10571e13	0.725565
$17$	−1.43774e14	−1.01746	−0.508729	−	0.860927i	$-0.669885\pi$
$17$	−1.43774e14	−1.01746	−0.508729	+	0.860927i	$0.669885\pi$
$18$	−8.00658e13	−0.293639
$19$	−2.49170e14	−0.490716	−0.245358	−	0.969433i	$-0.578905\pi$
$19$	−2.49170e14	−0.490716	−0.245358	+	0.969433i	$0.578905\pi$
$20$	1.15183e15	1.25760
$21$	0	0
$22$	9.53407e14	0.347870
$23$	5.64345e15	1.23502	0.617511	−	0.786562i	$-0.288141\pi$
$23$	5.64345e15	1.23502	0.617511	+	0.786562i	$0.288141\pi$
$24$	−9.21481e14	−0.123611
$25$	1.10709e16	0.928696
$26$	2.03605e15	0.108792
$27$	−1.19223e16	−0.412741
$28$	0	0
$29$	9.30270e16	1.41590	0.707949	−	0.706264i	$-0.249621\pi$
$29$	9.30270e16	1.41590	0.707949	+	0.706264i	$0.249621\pi$
$30$	−8.74105e15	−0.0900884
$31$	−1.39574e17	−0.986611	−0.493305	−	0.869856i	$-0.664211\pi$
$31$	−1.39574e17	−0.986611	−0.493305	+	0.869856i	$0.664211\pi$
$32$	1.64805e17	0.808622
$33$	6.93670e16	0.238915
$34$	−1.27976e17	−0.312696
$35$	0	0
$36$	6.83278e17	0.865204
$37$	−8.48399e17	−0.783936	−0.391968	−	0.919979i	$-0.628206\pi$
$37$	−8.48399e17	−0.783936	−0.391968	+	0.919979i	$0.628206\pi$
$38$	−2.21793e17	−0.150812
$39$	1.48137e17	0.0747172
$40$	2.15748e18	0.813313
$41$	4.30314e18	1.22115	0.610577	−	0.791957i	$-0.290937\pi$
$41$	4.30314e18	1.22115	0.610577	+	0.791957i	$0.290937\pi$
$42$	0	0
$43$	1.11166e19	1.82424	0.912122	−	0.409918i	$-0.134443\pi$
$43$	1.11166e19	1.82424	0.912122	+	0.409918i	$0.134443\pi$
$44$	−8.13633e18	−1.02500
$45$	1.36390e19	1.32690
$46$	5.02338e18	0.379560
$47$	2.03654e19	1.20162	0.600811	−	0.799391i	$-0.294845\pi$
$47$	2.03654e19	1.20162	0.600811	+	0.799391i	$0.294845\pi$
$48$	3.30660e18	0.153147
$49$	0	0
$50$	9.85450e18	0.285417
$51$	−9.31118e18	−0.214757
$52$	−1.73756e19	−0.320554
$53$	2.85416e19	0.422966	0.211483	−	0.977382i	$-0.432171\pi$
$53$	2.85416e19	0.422966	0.211483	+	0.977382i	$0.432171\pi$
$54$	−1.06124e19	−0.126848
$55$	−1.62411e20	−1.57197
$56$	0	0
$57$	−1.61370e19	−0.103577
$58$	8.28056e19	0.435149
$59$	2.78122e20	1.20071	0.600355	−	0.799734i	$-0.295026\pi$
$59$	2.78122e20	1.20071	0.600355	+	0.799734i	$0.295026\pi$
$60$	7.45957e19	0.265445
$61$	−4.38464e20	−1.29015	−0.645077	−	0.764118i	$-0.723175\pi$
$61$	−4.38464e20	−1.29015	−0.645077	+	0.764118i	$0.723175\pi$
$62$	−1.24239e20	−0.303216
$63$	0	0
$64$	−2.81601e20	−0.477051
$65$	−3.46837e20	−0.491611
$66$	6.17453e19	0.0734258
$67$	−1.17983e21	−1.18021	−0.590105	−	0.807327i	$-0.700913\pi$
$67$	−1.17983e21	−1.18021	−0.590105	+	0.807327i	$0.700913\pi$
$68$	1.09215e21	0.921357
$69$	3.65486e20	0.260679
$70$	0	0
$71$	−8.77727e20	−0.450701	−0.225350	−	0.974278i	$-0.572353\pi$
$71$	−8.77727e20	−0.450701	−0.225350	+	0.974278i	$0.572353\pi$
$72$	1.27984e21	0.559542
$73$	−3.16262e21	−1.17987	−0.589934	−	0.807451i	$-0.700846\pi$
$73$	−3.16262e21	−1.17987	−0.589934	+	0.807451i	$0.700846\pi$
$74$	−7.55181e20	−0.240928
$75$	7.16984e20	0.196022
$76$	1.89277e21	0.444367
$77$	0	0
$78$	1.31860e20	0.0229629
$79$	−5.58011e21	−0.839327	−0.419664	−	0.907680i	$-0.637852\pi$
$79$	−5.58011e21	−0.839327	−0.419664	+	0.907680i	$0.637852\pi$
$80$	−7.74182e21	−1.00765
$81$	7.69596e21	0.868330
$82$	3.83033e21	0.375298
$83$	−8.16381e21	−0.695817	−0.347908	−	0.937529i	$-0.613108\pi$
$83$	−8.16381e21	−0.695817	−0.347908	+	0.937529i	$0.613108\pi$
$84$	0	0
$85$	2.18005e22	1.41302
$86$	9.89512e21	0.560646
$87$	6.02469e21	0.298857
$88$	−1.52401e22	−0.662884
$89$	−1.74656e22	−0.667110	−0.333555	−	0.942731i	$-0.608248\pi$
$89$	−1.74656e22	−0.667110	−0.333555	+	0.942731i	$0.608248\pi$
$90$	1.21404e22	0.407798
$91$	0	0
$92$	−4.28693e22	−1.11837
$93$	−9.03922e21	−0.208246
$94$	1.81277e22	0.369295
$95$	3.77819e22	0.681494
$96$	1.06732e22	0.170678
$97$	−8.64253e22	−1.22678	−0.613389	−	0.789781i	$-0.710194\pi$
$97$	−8.64253e22	−1.22678	−0.613389	+	0.789781i	$0.710194\pi$
$98$	0	0
$99$	−9.63437e22	−1.08148
$100$	−8.40979e22	−0.840979
$101$	1.28361e23	1.14482	0.572409	−	0.819968i	$-0.306009\pi$
$101$	1.28361e23	1.14482	0.572409	+	0.819968i	$0.306009\pi$
$102$	−8.28812e21	−0.0660015
$103$	7.38101e22	0.525397	0.262698	−	0.964878i	$-0.415388\pi$
$103$	7.38101e22	0.525397	0.262698	+	0.964878i	$0.415388\pi$
$104$	−3.25461e22	−0.207308
$105$	0	0
$106$	2.54056e22	0.129990
$107$	1.73662e22	0.0797611	0.0398805	−	0.999204i	$-0.487302\pi$
$107$	1.73662e22	0.0797611	0.0398805	+	0.999204i	$0.487302\pi$
$108$	9.05654e22	0.373757
$109$	3.48819e23	1.29478	0.647389	−	0.762160i	$-0.275861\pi$
$109$	3.48819e23	1.29478	0.647389	+	0.762160i	$0.275861\pi$
$110$	−1.44566e23	−0.483114
$111$	−5.49447e22	−0.165467
$112$	0	0
$113$	4.30441e23	1.05563	0.527814	−	0.849360i	$-0.323012\pi$
$113$	4.30441e23	1.05563	0.527814	+	0.849360i	$0.323012\pi$
$114$	−1.43639e22	−0.0318322
$115$	−8.55720e23	−1.71517
$116$	−7.06660e23	−1.28216
$117$	−2.05747e23	−0.338218
$118$	2.47564e23	0.369015
$119$	0	0
$120$	1.39725e23	0.171668
$121$	2.51811e23	0.281218
$122$	−3.90288e23	−0.396504
$123$	2.78683e23	0.257752
$124$	1.06025e24	0.893423
$125$	1.28887e23	0.0990247
$126$	0	0
$127$	−1.15919e24	−0.742013	−0.371007	−	0.928630i	$-0.620987\pi$
$127$	−1.15919e24	−0.742013	−0.371007	+	0.928630i	$0.620987\pi$
$128$	−1.63314e24	−0.955234
$129$	7.19939e23	0.385047
$130$	−3.08728e23	−0.151087
$131$	−1.59910e24	−0.716566	−0.358283	−	0.933613i	$-0.616638\pi$
$131$	−1.59910e24	−0.716566	−0.358283	+	0.933613i	$0.616638\pi$
$132$	−5.26932e23	−0.216349
$133$	0	0
$134$	−1.05020e24	−0.362714
$135$	1.80779e24	0.573204
$136$	2.04569e24	0.595858
$137$	−2.70096e24	−0.723155	−0.361578	−	0.932342i	$-0.617762\pi$
$137$	−2.70096e24	−0.723155	−0.361578	+	0.932342i	$0.617762\pi$
$138$	3.25328e23	0.0801147
$139$	−1.71289e24	−0.388203	−0.194101	−	0.980981i	$-0.562179\pi$
$139$	−1.71289e24	−0.388203	−0.194101	+	0.980981i	$0.562179\pi$
$140$	0	0
$141$	1.31892e24	0.253629
$142$	−7.81286e23	−0.138514
$143$	2.45000e24	0.400683
$144$	−4.59253e24	−0.693240
$145$	−1.41057e25	−1.96636
$146$	−2.81512e24	−0.362610
$147$	0	0
$148$	6.44468e24	0.709891
$149$	−1.25752e24	−0.128196	−0.0640979	−	0.997944i	$-0.520417\pi$
$149$	−1.25752e24	−0.128196	−0.0640979	+	0.997944i	$0.520417\pi$
$150$	6.38205e23	0.0602436
$151$	9.98857e24	0.873511	0.436755	−	0.899580i	$-0.356128\pi$
$151$	9.98857e24	0.873511	0.436755	+	0.899580i	$0.356128\pi$
$152$	3.54533e24	0.287380
$153$	1.29323e25	0.972129
$154$	0	0
$155$	2.11637e25	1.37018
$156$	−1.12529e24	−0.0676600
$157$	2.08240e25	1.16337	0.581687	−	0.813413i	$-0.302393\pi$
$157$	2.08240e25	1.16337	0.581687	+	0.813413i	$0.302393\pi$
$158$	−4.96699e24	−0.257951
$159$	1.84843e24	0.0892764
$160$	−2.49895e25	−1.12299
$161$	0	0
$162$	6.85036e24	0.266865
$163$	−3.72893e25	−1.35340	−0.676701	−	0.736258i	$-0.736591\pi$
$163$	−3.72893e25	−1.35340	−0.676701	+	0.736258i	$0.736591\pi$
$164$	−3.26879e25	−1.10581
$165$	−1.05182e25	−0.331799
$166$	−7.26681e24	−0.213846
$167$	6.32711e25	1.73766	0.868832	−	0.495107i	$-0.164871\pi$
$167$	6.32711e25	1.73766	0.868832	+	0.495107i	$0.164871\pi$
$168$	0	0
$169$	−3.65218e25	−0.874692
$170$	1.94052e25	0.434265
$171$	2.24126e25	0.468854
$172$	−8.44445e25	−1.65194
$173$	−9.95491e25	−1.82183	−0.910914	−	0.412597i	$-0.864622\pi$
$173$	−9.95491e25	−1.82183	−0.910914	+	0.412597i	$0.864622\pi$
$174$	5.36272e24	0.0918479
$175$	0	0
$176$	5.46869e25	0.821273
$177$	1.80120e25	0.253436
$178$	−1.55465e25	−0.205023
$179$	−2.81958e25	−0.348638	−0.174319	−	0.984689i	$-0.555772\pi$
$179$	−2.81958e25	−0.348638	−0.174319	+	0.984689i	$0.555772\pi$
$180$	−1.03606e26	−1.20157
$181$	−1.49046e26	−1.62188	−0.810938	−	0.585132i	$-0.801043\pi$
$181$	−1.49046e26	−1.62188	−0.810938	+	0.585132i	$0.801043\pi$
$182$	0	0
$183$	−2.83962e25	−0.272316
$184$	−8.02981e25	−0.723270
$185$	1.28643e26	1.08871
$186$	−8.04603e24	−0.0640004
$187$	−1.53995e26	−1.15167
$188$	−1.54701e26	−1.08813
$189$	0	0
$190$	3.36306e25	0.209444
$191$	−1.42222e26	−0.833843	−0.416921	−	0.908943i	$-0.636891\pi$
$191$	−1.42222e26	−0.833843	−0.416921	+	0.908943i	$0.636891\pi$
$192$	−1.82373e25	−0.100692
$193$	−3.09575e25	−0.161011	−0.0805057	−	0.996754i	$-0.525654\pi$
$193$	−3.09575e25	−0.161011	−0.0805057	+	0.996754i	$0.525654\pi$
$194$	−7.69293e25	−0.377026
$195$	−2.24621e25	−0.103765
$196$	0	0
$197$	2.26722e26	0.931393	0.465697	−	0.884944i	$-0.345804\pi$
$197$	2.26722e26	0.931393	0.465697	+	0.884944i	$0.345804\pi$
$198$	−8.57579e25	−0.332372
$199$	2.38298e26	0.871586	0.435793	−	0.900047i	$-0.356468\pi$
$199$	2.38298e26	0.871586	0.435793	+	0.900047i	$0.356468\pi$
$200$	−1.57523e26	−0.543876
$201$	−7.64091e25	−0.249109
$202$	1.14257e26	0.351838
$203$	0	0
$204$	7.07304e25	0.194473
$205$	−6.52487e26	−1.69591
$206$	6.57002e25	0.161471
$207$	−5.07623e26	−1.18000
$208$	1.16787e26	0.256842
$209$	−2.66885e26	−0.555446
$210$	0	0
$211$	9.55207e26	1.78176	0.890880	−	0.454239i	$-0.150089\pi$
$211$	9.55207e26	1.78176	0.890880	+	0.454239i	$0.150089\pi$
$212$	−2.16810e26	−0.383016
$213$	−5.68440e25	−0.0951304
$214$	1.54581e25	0.0245130
$215$	−1.68561e27	−2.53347
$216$	1.69637e26	0.241715
$217$	0	0
$218$	3.10492e26	0.397925
$219$	−2.04820e26	−0.249038
$220$	1.23372e27	1.42349
$221$	−3.28865e26	−0.360169
$222$	−4.89077e25	−0.0508531
$223$	−4.99671e26	−0.493376	−0.246688	−	0.969095i	$-0.579342\pi$
$223$	−4.99671e26	−0.493376	−0.246688	+	0.969095i	$0.579342\pi$
$224$	0	0
$225$	−9.95818e26	−0.887322
$226$	3.83146e26	0.324427
$227$	−1.75238e27	−1.41037	−0.705183	−	0.709025i	$-0.749135\pi$
$227$	−1.75238e27	−1.41037	−0.705183	+	0.709025i	$0.749135\pi$
$228$	1.22581e26	0.0937935
$229$	−2.15445e27	−1.56757	−0.783787	−	0.621030i	$-0.786715\pi$
$229$	−2.15445e27	−1.56757	−0.783787	+	0.621030i	$0.786715\pi$
$230$	−7.61698e26	−0.527124
$231$	0	0
$232$	−1.32364e27	−0.829197
$233$	4.55206e26	0.271403	0.135702	−	0.990750i	$-0.456671\pi$
$233$	4.55206e26	0.271403	0.135702	+	0.990750i	$0.456671\pi$
$234$	−1.83141e26	−0.103945
$235$	−3.08802e27	−1.66878
$236$	−2.11270e27	−1.08730
$237$	−3.61384e26	−0.177159
$238$	0	0
$239$	1.28095e27	0.570108	0.285054	−	0.958512i	$-0.407989\pi$
$239$	1.28095e27	0.570108	0.285054	+	0.958512i	$0.407989\pi$
$240$	−5.01382e26	−0.212686
$241$	2.72097e27	1.10034	0.550170	−	0.835052i	$-0.314563\pi$
$241$	2.72097e27	1.10034	0.550170	+	0.835052i	$0.314563\pi$
$242$	2.24143e26	0.0864269
$243$	1.62082e27	0.596021
$244$	3.33070e27	1.16830
$245$	0	0
$246$	2.48063e26	0.0792151
$247$	−5.69947e26	−0.173708
$248$	1.98594e27	0.577792
$249$	−5.28711e26	−0.146868
$250$	1.14725e26	0.0304333
$251$	5.98415e26	0.151619	0.0758097	−	0.997122i	$-0.475846\pi$
$251$	5.98415e26	0.151619	0.0758097	+	0.997122i	$0.475846\pi$
$252$	0	0
$253$	6.04467e27	1.39793
$254$	−1.03182e27	−0.228043
$255$	1.41186e27	0.298250
$256$	9.08538e26	0.183478
$257$	8.42017e26	0.162588	0.0812942	−	0.996690i	$-0.474095\pi$
$257$	8.42017e26	0.162588	0.0812942	+	0.996690i	$0.474095\pi$
$258$	6.40836e26	0.118337
$259$	0	0
$260$	2.63467e27	0.445177
$261$	−8.36768e27	−1.35282
$262$	−1.42340e27	−0.220223
$263$	4.80396e27	0.711391	0.355696	−	0.934602i	$-0.384244\pi$
$263$	4.80396e27	0.711391	0.355696	+	0.934602i	$0.384244\pi$
$264$	−9.86992e26	−0.139916
$265$	−4.32778e27	−0.587405
$266$	0	0
$267$	−1.13112e27	−0.140808
$268$	8.96232e27	1.06874
$269$	−1.07995e28	−1.23382	−0.616910	−	0.787034i	$-0.711616\pi$
$269$	−1.07995e28	−1.23382	−0.616910	+	0.787034i	$0.711616\pi$
$270$	1.60916e27	0.176163
$271$	1.30317e28	1.36727	0.683635	−	0.729824i	$-0.260398\pi$
$271$	1.30317e28	1.36727	0.683635	+	0.729824i	$0.260398\pi$
$272$	−7.34066e27	−0.738232
$273$	0	0
$274$	−2.40419e27	−0.222248
$275$	1.18580e28	1.05120
$276$	−2.77634e27	−0.236057
$277$	−2.16382e25	−0.00176484	−0.000882418	−	1.00000i	$-0.500281\pi$
$277$	−2.16382e25	−0.00176484	−0.000882418		1.00000i	$0.500281\pi$
$278$	−1.52468e27	−0.119307
$279$	1.25546e28	0.942656
$280$	0	0
$281$	−1.54279e28	−1.06705	−0.533525	−	0.845784i	$-0.679133\pi$
$281$	−1.54279e28	−1.06705	−0.533525	+	0.845784i	$0.679133\pi$
$282$	1.17400e27	0.0779480
$283$	1.41163e28	0.899865	0.449932	−	0.893063i	$-0.351448\pi$
$283$	1.41163e28	0.899865	0.449932	+	0.893063i	$0.351448\pi$
$284$	6.66746e27	0.408131
$285$	2.44686e27	0.143845
$286$	2.18080e27	0.123142
$287$	0	0
$288$	−1.48240e28	−0.772596
$289$	7.03291e26	0.0352217
$290$	−1.25559e28	−0.604324
$291$	−5.59714e27	−0.258939
$292$	2.40241e28	1.06843
$293$	−1.36980e27	−0.0585704	−0.0292852	−	0.999571i	$-0.509323\pi$
$293$	−1.36980e27	−0.0585704	−0.0292852	+	0.999571i	$0.509323\pi$
$294$	0	0
$295$	−4.21719e28	−1.66752
$296$	1.20715e28	0.459099
$297$	−1.27699e28	−0.467185
$298$	−1.11935e27	−0.0393985
$299$	1.29087e28	0.437184
$300$	−5.44642e27	−0.177507
$301$	0	0
$302$	8.89107e27	0.268457
$303$	8.31301e27	0.241640
$304$	−1.27219e28	−0.356046
$305$	6.64846e28	1.79173
$306$	1.15114e28	0.298765
$307$	1.59921e28	0.399773	0.199886	−	0.979819i	$-0.435943\pi$
$307$	1.59921e28	0.399773	0.199886	+	0.979819i	$0.435943\pi$
$308$	0	0
$309$	4.78015e27	0.110897
$310$	1.88384e28	0.421099
$311$	−4.03507e28	−0.869175	−0.434587	−	0.900630i	$-0.643106\pi$
$311$	−4.03507e28	−0.869175	−0.434587	+	0.900630i	$0.643106\pi$
$312$	−2.10778e27	−0.0437569
$313$	8.30769e28	1.66234	0.831172	−	0.556016i	$-0.187671\pi$
$313$	8.30769e28	1.66234	0.831172	+	0.556016i	$0.187671\pi$
$314$	1.85360e28	0.357540
$315$	0	0
$316$	4.23881e28	0.760051
$317$	8.99748e27	0.155575	0.0777874	−	0.996970i	$-0.475214\pi$
$317$	8.99748e27	0.155575	0.0777874	+	0.996970i	$0.475214\pi$
$318$	1.64534e27	0.0274374
$319$	9.96406e28	1.60267
$320$	4.26993e28	0.662516
$321$	1.12468e27	0.0168354
$322$	0	0
$323$	3.58241e28	0.499283
$324$	−5.84607e28	−0.786315
$325$	2.53234e28	0.328748
$326$	−3.31922e28	−0.415942
$327$	2.25905e28	0.273292
$328$	−6.12274e28	−0.715149
$329$	0	0
$330$	−9.36248e27	−0.101972
$331$	1.46834e29	1.54456	0.772280	−	0.635282i	$-0.219116\pi$
$331$	1.46834e29	1.54456	0.772280	+	0.635282i	$0.219116\pi$
$332$	6.20147e28	0.630096
$333$	7.63126e28	0.749010
$334$	5.63192e28	0.534038
$335$	1.78898e29	1.63904
$336$	0	0
$337$	−9.43637e28	−0.807349	−0.403674	−	0.914903i	$-0.632267\pi$
$337$	−9.43637e28	−0.807349	−0.403674	+	0.914903i	$0.632267\pi$
$338$	−3.25090e28	−0.268820
$339$	2.78765e28	0.222814
$340$	−1.65603e29	−1.27956
$341$	−1.49497e29	−1.11675
$342$	1.99500e28	0.144093
$343$	0	0
$344$	−1.58172e29	−1.06834
$345$	−5.54189e28	−0.362024
$346$	−8.86111e28	−0.559903
$347$	−1.03559e29	−0.632993	−0.316496	−	0.948594i	$-0.602506\pi$
$347$	−1.03559e29	−0.632993	−0.316496	+	0.948594i	$0.602506\pi$
$348$	−4.57653e28	−0.270629
$349$	−2.97469e29	−1.70196	−0.850980	−	0.525198i	$-0.823991\pi$
$349$	−2.97469e29	−1.70196	−0.850980	+	0.525198i	$0.823991\pi$
$350$	0	0
$351$	−2.72709e28	−0.146106
$352$	1.76521e29	0.915286
$353$	9.46025e27	0.0474781	0.0237391	−	0.999718i	$-0.492443\pi$
$353$	9.46025e27	0.0474781	0.0237391	+	0.999718i	$0.492443\pi$
$354$	1.60329e28	0.0778888
$355$	1.33090e29	0.625922
$356$	1.32673e29	0.604100
$357$	0	0
$358$	−2.50978e28	−0.107147
$359$	−1.61274e29	−0.666775	−0.333387	−	0.942790i	$-0.608192\pi$
$359$	−1.61274e29	−0.666775	−0.333387	+	0.942790i	$0.608192\pi$
$360$	−1.94063e29	−0.777079
$361$	−1.95744e29	−0.759198
$362$	−1.32670e29	−0.498452
$363$	1.63080e28	0.0593573
$364$	0	0
$365$	4.79550e29	1.63857
$366$	−2.52762e28	−0.0836909
$367$	1.76716e29	0.567042	0.283521	−	0.958966i	$-0.408497\pi$
$367$	1.76716e29	0.567042	0.283521	+	0.958966i	$0.408497\pi$
$368$	2.88138e29	0.896089
$369$	−3.87063e29	−1.16675
$370$	1.14509e29	0.334594
$371$	0	0
$372$	6.86645e28	0.188577
$373$	2.37051e29	0.631233	0.315616	−	0.948887i	$-0.397789\pi$
$373$	2.37051e29	0.631233	0.315616	+	0.948887i	$0.397789\pi$
$374$	−1.37075e29	−0.353944
$375$	8.34708e27	0.0209014
$376$	−2.89770e29	−0.703710
$377$	2.12788e29	0.501212
$378$	0	0
$379$	3.78863e29	0.839715	0.419857	−	0.907590i	$-0.362080\pi$
$379$	3.78863e29	0.839715	0.419857	+	0.907590i	$0.362080\pi$
$380$	−2.87002e29	−0.617125
$381$	−7.50724e28	−0.156618
$382$	−1.26596e29	−0.256266
$383$	3.44468e29	0.676648	0.338324	−	0.941030i	$-0.390140\pi$
$383$	3.44468e29	0.676648	0.338324	+	0.941030i	$0.390140\pi$
$384$	−1.05767e29	−0.201623
$385$	0	0
$386$	−2.75560e28	−0.0494837
$387$	−9.99923e29	−1.74297
$388$	6.56511e29	1.11091
$389$	−9.79654e29	−1.60936	−0.804679	−	0.593710i	$-0.797662\pi$
$389$	−9.79654e29	−1.60936	−0.804679	+	0.593710i	$0.797662\pi$
$390$	−1.99941e28	−0.0318903
$391$	−8.11380e29	−1.25658
$392$	0	0
$393$	−1.03562e29	−0.151247
$394$	2.01811e29	0.286246
$395$	8.46116e29	1.16564
$396$	7.31855e29	0.979333
$397$	−1.10909e30	−1.44171	−0.720854	−	0.693087i	$-0.756250\pi$
$397$	−1.10909e30	−1.44171	−0.720854	+	0.693087i	$0.756250\pi$
$398$	2.12115e29	0.267865
$399$	0	0
$400$	5.65249e29	0.673829
$401$	−1.45018e30	−1.67981	−0.839906	−	0.542731i	$-0.817390\pi$
$401$	−1.45018e30	−1.67981	−0.839906	+	0.542731i	$0.817390\pi$
$402$	−6.80136e28	−0.0765590
$403$	−3.19259e29	−0.349249
$404$	−9.75066e29	−1.03669
$405$	−1.16694e30	−1.20592
$406$	0	0
$407$	−9.08715e29	−0.887344
$408$	1.32485e29	0.125769
$409$	7.84921e29	0.724449	0.362225	−	0.932091i	$-0.382017\pi$
$409$	7.84921e29	0.724449	0.362225	+	0.932091i	$0.382017\pi$
$410$	−5.80795e29	−0.521205
$411$	−1.74922e29	−0.152638
$412$	−5.60682e29	−0.475772
$413$	0	0
$414$	−4.51848e29	−0.362650
$415$	1.23788e30	0.966333
$416$	3.76971e29	0.286243
$417$	−1.10931e29	−0.0819389
$418$	−2.37561e29	−0.170706
$419$	7.98737e29	0.558397	0.279198	−	0.960233i	$-0.409931\pi$
$419$	7.98737e29	0.558397	0.279198	+	0.960233i	$0.409931\pi$
$420$	0	0
$421$	1.80176e30	1.19248	0.596242	−	0.802805i	$-0.296660\pi$
$421$	1.80176e30	1.19248	0.596242	+	0.802805i	$0.296660\pi$
$422$	8.50253e29	0.547590
$423$	−1.83185e30	−1.14809
$424$	−4.06105e29	−0.247703
$425$	−1.59171e30	−0.944910
$426$	−5.05983e28	−0.0292365
$427$	0	0
$428$	−1.31918e29	−0.0722275
$429$	1.58669e29	0.0845731
$430$	−1.50040e30	−0.778612
$431$	−1.32586e30	−0.669897	−0.334949	−	0.942236i	$-0.608719\pi$
$431$	−1.32586e30	−0.669897	−0.334949	+	0.942236i	$0.608719\pi$
$432$	−6.08719e29	−0.299470
$433$	1.29410e29	0.0619948	0.0309974	−	0.999519i	$-0.490132\pi$
$433$	1.29410e29	0.0619948	0.0309974	+	0.999519i	$0.490132\pi$
$434$	0	0
$435$	−9.13527e29	−0.415045
$436$	−2.64973e30	−1.17248
$437$	−1.40618e30	−0.606045
$438$	−1.82315e29	−0.0765369
$439$	3.47403e30	1.42066	0.710332	−	0.703867i	$-0.248545\pi$
$439$	3.47403e30	1.42066	0.710332	+	0.703867i	$0.248545\pi$
$440$	2.31087e30	0.920596
$441$	0	0
$442$	−2.92731e29	−0.110691
$443$	−1.57809e29	−0.0581420	−0.0290710	−	0.999577i	$-0.509255\pi$
$443$	−1.57809e29	−0.0581420	−0.0290710	+	0.999577i	$0.509255\pi$
$444$	4.17376e29	0.149838
$445$	2.64831e30	0.926466
$446$	−4.44769e29	−0.151630
$447$	−8.14407e28	−0.0270586
$448$	0	0
$449$	4.63613e30	1.46327	0.731633	−	0.681699i	$-0.238759\pi$
$449$	4.63613e30	1.46327	0.731633	+	0.681699i	$0.238759\pi$
$450$	−8.86402e29	−0.272701
$451$	4.60906e30	1.38224
$452$	−3.26975e30	−0.955922
$453$	6.46888e29	0.184374
$454$	−1.55984e30	−0.433449
$455$	0	0
$456$	2.29606e29	0.0606579
$457$	1.44276e30	0.371671	0.185835	−	0.982581i	$-0.440501\pi$
$457$	1.44276e30	0.371671	0.185835	+	0.982581i	$0.440501\pi$
$458$	−1.91773e30	−0.481764
$459$	1.71412e30	0.419947
$460$	6.50030e30	1.55317
$461$	3.35071e30	0.780866	0.390433	−	0.920631i	$-0.372325\pi$
$461$	3.35071e30	0.780866	0.390433	+	0.920631i	$0.372325\pi$
$462$	0	0
$463$	−4.83600e30	−1.07227	−0.536136	−	0.844131i	$-0.680117\pi$
$463$	−4.83600e30	−1.07227	−0.536136	+	0.844131i	$0.680117\pi$
$464$	4.74969e30	1.02733
$465$	1.37062e30	0.289207
$466$	4.05190e29	0.0834105
$467$	−2.03898e30	−0.409514	−0.204757	−	0.978813i	$-0.565640\pi$
$467$	−2.03898e30	−0.409514	−0.204757	+	0.978813i	$0.565640\pi$
$468$	1.56292e30	0.306273
$469$	0	0
$470$	−2.74872e30	−0.512868
$471$	1.34862e30	0.245556
$472$	−3.95728e30	−0.703175
$473$	1.19069e31	2.06488
$474$	−3.21676e29	−0.0544463
$475$	−2.75855e30	−0.455726
$476$	0	0
$477$	−2.56728e30	−0.404122
$478$	1.14021e30	0.175212
$479$	6.03133e30	0.904804	0.452402	−	0.891814i	$-0.350567\pi$
$479$	6.03133e30	0.904804	0.452402	+	0.891814i	$0.350567\pi$
$480$	−1.61839e30	−0.237033
$481$	−1.94061e30	−0.277505
$482$	2.42200e30	0.338168
$483$	0	0
$484$	−1.91283e30	−0.254656
$485$	1.31047e31	1.70372
$486$	1.44273e30	0.183176
$487$	2.14394e30	0.265845	0.132923	−	0.991126i	$-0.457564\pi$
$487$	2.14394e30	0.265845	0.132923	+	0.991126i	$0.457564\pi$
$488$	6.23871e30	0.755557
$489$	−2.41496e30	−0.285666
$490$	0	0
$491$	1.03750e30	0.117099	0.0585494	−	0.998285i	$-0.481352\pi$
$491$	1.03750e30	0.117099	0.0585494	+	0.998285i	$0.481352\pi$
$492$	−2.11696e30	−0.233407
$493$	−1.33748e31	−1.44062
$494$	−5.07324e29	−0.0533858
$495$	1.46087e31	1.50193
$496$	−7.12625e30	−0.715850
$497$	0	0
$498$	−4.70619e29	−0.0451369
$499$	−1.61562e31	−1.51420	−0.757098	−	0.653301i	$-0.773383\pi$
$499$	−1.61562e31	−1.51420	−0.757098	+	0.653301i	$0.773383\pi$
$500$	−9.79062e29	−0.0896716
$501$	4.09761e30	0.366773
$502$	5.32664e29	0.0465973
$503$	7.76157e30	0.663618	0.331809	−	0.943347i	$-0.392341\pi$
$503$	7.76157e30	0.663618	0.331809	+	0.943347i	$0.392341\pi$
$504$	0	0
$505$	−1.94634e31	−1.58990
$506$	5.38051e30	0.429628
$507$	−2.36525e30	−0.184623
$508$	8.80553e30	0.671928
$509$	1.72478e31	1.28671	0.643354	−	0.765569i	$-0.277542\pi$
$509$	1.72478e31	1.28671	0.643354	+	0.765569i	$0.277542\pi$
$510$	1.25673e30	0.0916612
$511$	0	0
$512$	1.45085e31	1.01162
$513$	2.97069e30	0.202539
$514$	7.49500e29	0.0499684
$515$	−1.11919e31	−0.729658
$516$	−5.46887e30	−0.348679
$517$	2.18133e31	1.36013
$518$	0	0
$519$	−6.44708e30	−0.384537
$520$	4.93498e30	0.287904
$521$	−2.72128e31	−1.55288	−0.776442	−	0.630189i	$-0.782977\pi$
$521$	−2.72128e31	−1.55288	−0.776442	+	0.630189i	$0.782977\pi$
$522$	−7.44828e30	−0.415762
$523$	1.50504e31	0.821823	0.410911	−	0.911675i	$-0.365211\pi$
$523$	1.50504e31	0.821823	0.410911	+	0.911675i	$0.365211\pi$
$524$	1.21472e31	0.648885
$525$	0	0
$526$	4.27613e30	0.218632
$527$	2.00671e31	1.00384
$528$	3.54168e30	0.173348
$529$	1.09681e31	0.525280
$530$	−3.85226e30	−0.180527
$531$	−2.50168e31	−1.14722
$532$	0	0
$533$	9.84290e30	0.432275
$534$	−1.00684e30	−0.0432748
$535$	−2.63325e30	−0.110770
$536$	1.67873e31	0.691170
$537$	−1.82604e30	−0.0735879
$538$	−9.61289e30	−0.379191
$539$	0	0
$540$	−1.37325e31	−0.519064
$541$	−4.59192e31	−1.69913	−0.849563	−	0.527486i	$-0.823135\pi$
$541$	−4.59192e31	−1.69913	−0.849563	+	0.527486i	$0.823135\pi$
$542$	1.15998e31	0.420204
$543$	−9.65265e30	−0.342333
$544$	−2.36946e31	−0.822739
$545$	−5.28916e31	−1.79816
$546$	0	0
$547$	5.24770e30	0.171047	0.0855234	−	0.996336i	$-0.472744\pi$
$547$	5.24770e30	0.171047	0.0855234	+	0.996336i	$0.472744\pi$
$548$	2.05173e31	0.654852
$549$	3.94394e31	1.23267
$550$	1.05551e31	0.323066
$551$	−2.31796e31	−0.694804
$552$	−5.20033e30	−0.152662
$553$	0	0
$554$	−1.92607e28	−0.000542389 0
$555$	8.33130e30	0.229797
$556$	1.30116e31	0.351536
$557$	−2.34913e31	−0.621689	−0.310844	−	0.950461i	$-0.600612\pi$
$557$	−2.34913e31	−0.621689	−0.310844	+	0.950461i	$0.600612\pi$
$558$	1.11751e31	0.289707
$559$	2.54278e31	0.645762
$560$	0	0
$561$	−9.97315e30	−0.243086
$562$	−1.37328e31	−0.327937
$563$	5.53528e31	1.29507	0.647534	−	0.762036i	$-0.275800\pi$
$563$	5.53528e31	1.29507	0.647534	+	0.762036i	$0.275800\pi$
$564$	−1.00189e31	−0.229673
$565$	−6.52680e31	−1.46603
$566$	1.25653e31	0.276556
$567$	0	0
$568$	1.24888e31	0.263945
$569$	−7.33365e31	−1.51890	−0.759450	−	0.650566i	$-0.774532\pi$
$569$	−7.33365e31	−1.51890	−0.759450	+	0.650566i	$0.774532\pi$
$570$	2.17801e30	0.0442078
$571$	−6.80577e31	−1.35382	−0.676912	−	0.736064i	$-0.736682\pi$
$571$	−6.80577e31	−1.35382	−0.676912	+	0.736064i	$0.736682\pi$
$572$	−1.86109e31	−0.362838
$573$	−9.21072e30	−0.176001
$574$	0	0
$575$	6.24782e31	1.14696
$576$	2.53297e31	0.455797
$577$	−9.84369e31	−1.73634	−0.868172	−	0.496263i	$-0.834705\pi$
$577$	−9.84369e31	−1.73634	−0.868172	+	0.496263i	$0.834705\pi$
$578$	6.26017e29	0.0108247
$579$	−2.00489e30	−0.0339850
$580$	1.07151e32	1.78064
$581$	0	0
$582$	−4.98216e30	−0.0795798
$583$	3.05707e31	0.478759
$584$	4.49995e31	0.690971
$585$	3.11976e31	0.469709
$586$	−1.21929e30	−0.0180005
$587$	−1.12149e30	−0.0162352	−0.00811762	−	0.999967i	$-0.502584\pi$
$587$	−1.12149e30	−0.0162352	−0.00811762	+	0.999967i	$0.502584\pi$
$588$	0	0
$589$	3.47778e31	0.484146
$590$	−3.75382e31	−0.512479
$591$	1.46832e31	0.196591
$592$	−4.33168e31	−0.568796
$593$	−5.28192e31	−0.680242	−0.340121	−	0.940382i	$-0.610468\pi$
$593$	−5.28192e31	−0.680242	−0.340121	+	0.940382i	$0.610468\pi$
$594$	−1.13668e31	−0.143580
$595$	0	0
$596$	9.55250e30	0.116087
$597$	1.54329e31	0.183968
$598$	1.14904e31	0.134360
$599$	−5.09045e31	−0.583912	−0.291956	−	0.956432i	$-0.594306\pi$
$599$	−5.09045e31	−0.583912	−0.291956	+	0.956432i	$0.594306\pi$
$600$	−1.02016e31	−0.114797
$601$	−8.48335e31	−0.936507	−0.468254	−	0.883594i	$-0.655117\pi$
$601$	−8.48335e31	−0.936507	−0.468254	+	0.883594i	$0.655117\pi$
$602$	0	0
$603$	1.06124e32	1.12763
$604$	−7.58760e31	−0.791006
$605$	−3.81823e31	−0.390548
$606$	7.39961e30	0.0742632
$607$	−1.18404e32	−1.16600	−0.582998	−	0.812473i	$-0.698121\pi$
$607$	−1.18404e32	−1.16600	−0.582998	+	0.812473i	$0.698121\pi$
$608$	−4.10645e31	−0.396803
$609$	0	0
$610$	5.91796e31	0.550654
$611$	4.65834e31	0.425361
$612$	−9.82374e31	−0.880309
$613$	3.60490e31	0.317028	0.158514	−	0.987357i	$-0.449330\pi$
$613$	3.60490e31	0.317028	0.158514	+	0.987357i	$0.449330\pi$
$614$	1.42349e31	0.122862
$615$	−4.22569e31	−0.357960
$616$	0	0
$617$	−1.96078e32	−1.60011	−0.800053	−	0.599929i	$-0.795196\pi$
$617$	−1.96078e32	−1.60011	−0.800053	+	0.599929i	$0.795196\pi$
$618$	4.25493e30	0.0340820
$619$	5.83396e31	0.458692	0.229346	−	0.973345i	$-0.426341\pi$
$619$	5.83396e31	0.458692	0.229346	+	0.973345i	$0.426341\pi$
$620$	−1.60766e32	−1.24076
$621$	−6.72831e31	−0.509744
$622$	−3.59172e31	−0.267124
$623$	0	0
$624$	7.56345e30	0.0542122
$625$	−1.51519e32	−1.06622
$626$	7.39488e31	0.510889
$627$	−1.72842e31	−0.117239
$628$	−1.58185e32	−1.05349
$629$	1.21977e32	0.797622
$630$	0	0
$631$	−1.52200e32	−0.959571	−0.479785	−	0.877386i	$-0.659285\pi$
$631$	−1.52200e32	−0.959571	−0.479785	+	0.877386i	$0.659285\pi$
$632$	7.93969e31	0.491538
$633$	6.18619e31	0.376080
$634$	8.00888e30	0.0478129
$635$	1.75769e32	1.03049
$636$	−1.40412e31	−0.0808440
$637$	0	0
$638$	8.86926e31	0.492549
$639$	7.89506e31	0.430621
$640$	2.47635e32	1.32661
$641$	1.75673e32	0.924354	0.462177	−	0.886788i	$-0.347068\pi$
$641$	1.75673e32	0.924354	0.462177	+	0.886788i	$0.347068\pi$
$642$	1.00111e30	0.00517402
$643$	−2.66226e32	−1.35153	−0.675764	−	0.737118i	$-0.736186\pi$
$643$	−2.66226e32	−1.35153	−0.675764	+	0.737118i	$0.736186\pi$
$644$	0	0
$645$	−1.09165e32	−0.534744
$646$	3.18880e31	0.153445
$647$	2.94266e30	0.0139104	0.00695521	−	0.999976i	$-0.497786\pi$
$647$	2.94266e30	0.0139104	0.00695521	+	0.999976i	$0.497786\pi$
$648$	−1.09502e32	−0.508523
$649$	2.97895e32	1.35909
$650$	2.25410e31	0.101034
$651$	0	0
$652$	2.83260e32	1.22557
$653$	−3.99686e32	−1.69909	−0.849547	−	0.527513i	$-0.823124\pi$
$653$	−3.99686e32	−1.69909	−0.849547	+	0.527513i	$0.823124\pi$
$654$	2.01084e31	0.0839910
$655$	2.42473e32	0.995149
$656$	2.19706e32	0.886027
$657$	2.84474e32	1.12730
$658$	0	0
$659$	−1.82318e32	−0.697667	−0.348833	−	0.937185i	$-0.613422\pi$
$659$	−1.82318e32	−0.697667	−0.348833	+	0.937185i	$0.613422\pi$
$660$	7.98990e31	0.300460
$661$	−2.68368e32	−0.991778	−0.495889	−	0.868386i	$-0.665158\pi$
$661$	−2.68368e32	−0.991778	−0.495889	+	0.868386i	$0.665158\pi$
$662$	1.30701e32	0.474691
$663$	−2.12982e31	−0.0760217
$664$	1.16159e32	0.407494
$665$	0	0
$666$	6.79278e31	0.230194
$667$	5.24993e32	1.74867
$668$	−4.80625e32	−1.57354
$669$	−3.23601e31	−0.104138
$670$	1.59242e32	0.503729
$671$	−4.69636e32	−1.46034
$672$	0	0
$673$	1.65242e32	0.496533	0.248266	−	0.968692i	$-0.420139\pi$
$673$	1.65242e32	0.496533	0.248266	+	0.968692i	$0.420139\pi$
$674$	−8.39955e31	−0.248123
$675$	−1.31991e32	−0.383311
$676$	2.77430e32	0.792075
$677$	1.18214e32	0.331818	0.165909	−	0.986141i	$-0.446944\pi$
$677$	1.18214e32	0.331818	0.165909	+	0.986141i	$0.446944\pi$
$678$	2.48136e31	0.0684776
$679$	0	0
$680$	−3.10189e32	−0.827512
$681$	−1.13489e32	−0.297689
$682$	−1.33071e32	−0.343213
$683$	4.55143e32	1.15428	0.577138	−	0.816646i	$-0.304169\pi$
$683$	4.55143e32	1.15428	0.577138	+	0.816646i	$0.304169\pi$
$684$	−1.70253e32	−0.424570
$685$	4.09548e32	1.00430
$686$	0	0
$687$	−1.39528e32	−0.330871
$688$	5.67579e32	1.32361
$689$	6.52854e31	0.149725
$690$	−4.93297e31	−0.111261
$691$	7.45692e32	1.65410	0.827051	−	0.562127i	$-0.190017\pi$
$691$	7.45692e32	1.65410	0.827051	+	0.562127i	$0.190017\pi$
$692$	7.56204e32	1.64975
$693$	0	0
$694$	−9.21804e31	−0.194538
$695$	2.59726e32	0.539126
$696$	−8.57226e31	−0.175021
$697$	−6.18678e32	−1.24247
$698$	−2.64785e32	−0.523065
$699$	2.94804e31	0.0572857
$700$	0	0
$701$	−4.19522e32	−0.788856	−0.394428	−	0.918927i	$-0.629057\pi$
$701$	−4.19522e32	−0.788856	−0.394428	+	0.918927i	$0.629057\pi$
$702$	−2.42745e31	−0.0449028
$703$	2.11396e32	0.384690
$704$	−3.01621e32	−0.539978
$705$	−1.99989e32	−0.352234
$706$	8.42080e30	0.0145915
$707$	0	0
$708$	−1.36824e32	−0.229499
$709$	−1.39513e31	−0.0230242	−0.0115121	−	0.999934i	$-0.503664\pi$
$709$	−1.39513e31	−0.0230242	−0.0115121	+	0.999934i	$0.503664\pi$
$710$	1.18467e32	0.192365
$711$	5.01925e32	0.801934
$712$	2.48510e32	0.390682
$713$	−7.87681e32	−1.21849
$714$	0	0
$715$	−3.71495e32	−0.556459
$716$	2.14184e32	0.315709
$717$	8.29580e31	0.120334
$718$	−1.43554e32	−0.204920
$719$	1.33967e33	1.88198	0.940989	−	0.338438i	$-0.109899\pi$
$719$	1.33967e33	1.88198	0.940989	+	0.338438i	$0.109899\pi$
$720$	6.96368e32	0.962754
$721$	0	0
$722$	−1.74236e32	−0.233325
$723$	1.76217e32	0.232251
$724$	1.13220e33	1.46869
$725$	1.02989e33	1.31494
$726$	1.45161e31	0.0182423
$727$	−8.66750e32	−1.07213	−0.536066	−	0.844176i	$-0.680090\pi$
$727$	−8.66750e32	−1.07213	−0.536066	+	0.844176i	$0.680090\pi$
$728$	0	0
$729$	−6.19553e32	−0.742527
$730$	4.26859e32	0.503584
$731$	−1.59827e33	−1.85609
$732$	2.15706e32	0.246595
$733$	−6.91088e32	−0.777745	−0.388873	−	0.921292i	$-0.627135\pi$
$733$	−6.91088e32	−0.777745	−0.388873	+	0.921292i	$0.627135\pi$
$734$	1.57299e32	0.174270
$735$	0	0
$736$	9.30069e32	0.998666
$737$	−1.26371e33	−1.33589
$738$	−3.44534e32	−0.358578
$739$	−8.60116e32	−0.881345	−0.440673	−	0.897668i	$-0.645260\pi$
$739$	−8.60116e32	−0.881345	−0.440673	+	0.897668i	$0.645260\pi$
$740$	−9.77212e32	−0.985879
$741$	−3.69114e31	−0.0366649
$742$	0	0
$743$	1.92705e33	1.85576	0.927878	−	0.372884i	$-0.121631\pi$
$743$	1.92705e33	1.85576	0.927878	+	0.372884i	$0.121631\pi$
$744$	1.28615e32	0.121956
$745$	1.90679e32	0.178035
$746$	2.11005e32	0.193997
$747$	7.34326e32	0.664817
$748$	1.16979e33	1.04289
$749$	0	0
$750$	7.42994e30	0.00642363
$751$	3.81351e32	0.324687	0.162344	−	0.986734i	$-0.448095\pi$
$751$	3.81351e32	0.324687	0.162344	+	0.986734i	$0.448095\pi$
$752$	1.03980e33	0.871854
$753$	3.87550e31	0.0320026
$754$	1.89408e32	0.154038
$755$	−1.51457e33	−1.21311
$756$	0	0
$757$	4.16996e32	0.323988	0.161994	−	0.986792i	$-0.448207\pi$
$757$	4.16996e32	0.323988	0.161994	+	0.986792i	$0.448207\pi$
$758$	3.37236e32	0.258070
$759$	3.91470e32	0.295065
$760$	−5.37581e32	−0.399106
$761$	−4.40419e32	−0.322064	−0.161032	−	0.986949i	$-0.551482\pi$
$761$	−4.40419e32	−0.322064	−0.161032	+	0.986949i	$0.551482\pi$
$762$	−6.68238e31	−0.0481336
$763$	0	0
$764$	1.08036e33	0.755085
$765$	−1.96093e33	−1.35007
$766$	3.06620e32	0.207955
$767$	6.36171e32	0.425038
$768$	5.88395e31	0.0387271
$769$	5.79153e32	0.375526	0.187763	−	0.982214i	$-0.439876\pi$
$769$	5.79153e32	0.375526	0.187763	+	0.982214i	$0.439876\pi$
$770$	0	0
$771$	5.45314e31	0.0343179
$772$	2.35162e32	0.145803
$773$	−1.64315e33	−1.00372	−0.501861	−	0.864948i	$-0.667351\pi$
$773$	−1.64315e33	−1.00372	−0.501861	+	0.864948i	$0.667351\pi$
$774$	−8.90056e32	−0.535669
$775$	−1.54522e33	−0.916262
$776$	1.22971e33	0.718442
$777$	0	0
$778$	−8.72015e32	−0.494605
$779$	−1.07221e33	−0.599240
$780$	1.70629e32	0.0939646
$781$	−9.40127e32	−0.510152
$782$	−7.22229e32	−0.386187
$783$	−1.10910e33	−0.584399
$784$	0	0
$785$	−3.15756e33	−1.61566
$786$	−9.21834e31	−0.0464829
$787$	7.89669e32	0.392406	0.196203	−	0.980563i	$-0.437139\pi$
$787$	7.89669e32	0.392406	0.196203	+	0.980563i	$0.437139\pi$
$788$	−1.72225e33	−0.843421
$789$	3.11118e32	0.150155
$790$	7.53149e32	0.358236
$791$	0	0
$792$	1.37083e33	0.633351
$793$	−1.00293e33	−0.456700
$794$	−9.87231e32	−0.443081
$795$	−2.80279e32	−0.123985
$796$	−1.81018e33	−0.789263
$797$	−3.81417e33	−1.63919	−0.819595	−	0.572943i	$-0.805802\pi$
$797$	−3.81417e33	−1.63919	−0.819595	+	0.572943i	$0.805802\pi$
$798$	0	0
$799$	−2.92801e33	−1.22260
$800$	1.82454e33	0.750964
$801$	1.57101e33	0.637389
$802$	−1.29084e33	−0.516258
$803$	−3.38746e33	−1.33550
$804$	5.80425e32	0.225581
$805$	0	0
$806$	−2.84181e32	−0.107335
$807$	−6.99405e32	−0.260425
$808$	−1.82639e33	−0.670444
$809$	1.17133e32	0.0423909	0.0211955	−	0.999775i	$-0.493253\pi$
$809$	1.17133e32	0.0423909	0.0211955	+	0.999775i	$0.493253\pi$
$810$	−1.03872e33	−0.370615
$811$	−2.96884e33	−1.04435	−0.522175	−	0.852838i	$-0.674879\pi$
$811$	−2.96884e33	−1.04435	−0.522175	+	0.852838i	$0.674879\pi$
$812$	0	0
$813$	8.43969e32	0.288593
$814$	−8.08870e32	−0.272708
$815$	5.65420e33	1.87957
$816$	−4.75402e32	−0.155820
$817$	−2.76992e33	−0.895186
$818$	6.98678e32	0.222645
$819$	0	0
$820$	4.95648e33	1.53573
$821$	−1.00945e33	−0.308418	−0.154209	−	0.988038i	$-0.549283\pi$
$821$	−1.00945e33	−0.308418	−0.154209	+	0.988038i	$0.549283\pi$
$822$	−1.55702e32	−0.0469103
$823$	2.59825e33	0.771940	0.385970	−	0.922511i	$-0.373867\pi$
$823$	2.59825e33	0.771940	0.385970	+	0.922511i	$0.373867\pi$
$824$	−1.05021e33	−0.307690
$825$	7.67957e32	0.221879
$826$	0	0
$827$	3.90779e33	1.09804	0.549020	−	0.835809i	$-0.315001\pi$
$827$	3.90779e33	1.09804	0.549020	+	0.835809i	$0.315001\pi$
$828$	3.85605e33	1.06855
$829$	−8.72376e32	−0.238411	−0.119206	−	0.992870i	$-0.538035\pi$
$829$	−8.72376e32	−0.238411	−0.119206	+	0.992870i	$0.538035\pi$
$830$	1.10187e33	0.296984
$831$	−1.40135e30	−0.000372508 0
$832$	−6.44128e32	−0.168871
$833$	0	0
$834$	−9.87428e31	−0.0251823
$835$	−9.59384e33	−2.41323
$836$	2.02733e33	0.502983
$837$	1.66405e33	0.407215
$838$	7.10976e32	0.171612
$839$	4.58873e33	1.09252	0.546261	−	0.837615i	$-0.316051\pi$
$839$	4.58873e33	1.09252	0.546261	+	0.837615i	$0.316051\pi$
$840$	0	0
$841$	4.33730e33	1.00477
$842$	1.60379e33	0.366487
$843$	−9.99156e32	−0.225225
$844$	−7.25603e33	−1.61347
$845$	5.53782e33	1.21475
$846$	−1.63057e33	−0.352842
$847$	0	0
$848$	1.45725e33	0.306889
$849$	9.14212e32	0.189937
$850$	−1.41682e33	−0.290400
$851$	−4.78790e33	−0.968178
$852$	4.31804e32	0.0861452
$853$	−5.41155e33	−1.06514	−0.532571	−	0.846385i	$-0.678774\pi$
$853$	−5.41155e33	−1.06514	−0.532571	+	0.846385i	$0.678774\pi$
$854$	0	0
$855$	−3.39844e33	−0.651132
$856$	−2.47096e32	−0.0467107
$857$	7.57182e32	0.141228	0.0706140	−	0.997504i	$-0.477504\pi$
$857$	7.57182e32	0.141228	0.0706140	+	0.997504i	$0.477504\pi$
$858$	1.41235e32	0.0259919
$859$	3.11427e33	0.565504	0.282752	−	0.959193i	$-0.408753\pi$
$859$	3.11427e33	0.565504	0.282752	+	0.959193i	$0.408753\pi$
$860$	1.28044e34	2.29417
$861$	0	0
$862$	−1.18018e33	−0.205880
$863$	4.25085e33	0.731731	0.365865	−	0.930668i	$-0.380773\pi$
$863$	4.25085e33	0.731731	0.365865	+	0.930668i	$0.380773\pi$
$864$	−1.96486e33	−0.333751
$865$	1.50947e34	2.53011
$866$	1.15191e32	0.0190529
$867$	4.55471e31	0.00743432
$868$	0	0
$869$	−5.97682e33	−0.950042
$870$	−8.13153e32	−0.127556
$871$	−2.69872e33	−0.417781
$872$	−4.96319e33	−0.758265
$873$	7.77386e33	1.17212
$874$	−1.25168e33	−0.186256
$875$	0	0
$876$	1.55587e33	0.225515
$877$	−1.78706e33	−0.255650	−0.127825	−	0.991797i	$-0.540800\pi$
$877$	−1.78706e33	−0.255650	−0.127825	+	0.991797i	$0.540800\pi$
$878$	3.09232e33	0.436614
$879$	−8.87119e31	−0.0123626
$880$	−8.29221e33	−1.14056
$881$	−7.17012e33	−0.973427	−0.486713	−	0.873562i	$-0.661804\pi$
$881$	−7.17012e33	−0.973427	−0.486713	+	0.873562i	$0.661804\pi$
$882$	0	0
$883$	−9.31409e33	−1.23195	−0.615974	−	0.787766i	$-0.711237\pi$
$883$	−9.31409e33	−1.23195	−0.615974	+	0.787766i	$0.711237\pi$
$884$	2.49815e33	0.326150
$885$	−2.73117e33	−0.351966
$886$	−1.40470e32	−0.0178688
$887$	−1.54894e33	−0.194497	−0.0972486	−	0.995260i	$-0.531004\pi$
$887$	−1.54894e33	−0.194497	−0.0972486	+	0.995260i	$0.531004\pi$
$888$	7.81784e32	0.0969031
$889$	0	0
$890$	2.35733e33	0.284731
$891$	8.24309e33	0.982871
$892$	3.79564e33	0.446776
$893$	−5.07446e33	−0.589655
$894$	−7.24924e31	−0.00831593
$895$	4.27535e33	0.484180
$896$	0	0
$897$	8.36005e32	0.0922775
$898$	4.12674e33	0.449706
$899$	−1.29842e34	−1.39694
$900$	7.56452e33	0.803512
$901$	−4.10353e33	−0.430350
$902$	4.10264e33	0.424804
$903$	0	0
$904$	−6.12455e33	−0.618211
$905$	2.26000e34	2.25242
$906$	5.75811e32	0.0566638
$907$	7.63345e32	0.0741715	0.0370857	−	0.999312i	$-0.488193\pi$
$907$	7.63345e32	0.0741715	0.0370857	+	0.999312i	$0.488193\pi$
$908$	1.33116e34	1.27715
$909$	−1.15459e34	−1.09382
$910$	0	0
$911$	−5.46652e33	−0.504952	−0.252476	−	0.967603i	$-0.581245\pi$
$911$	−5.46652e33	−0.504952	−0.252476	+	0.967603i	$0.581245\pi$
$912$	−8.23907e32	−0.0751515
$913$	−8.74421e33	−0.787601
$914$	1.28424e33	0.114226
$915$	4.30573e33	0.378185
$916$	1.63658e34	1.41951
$917$	0	0
$918$	1.52578e33	0.129063
$919$	−2.05334e34	−1.71527	−0.857636	−	0.514258i	$-0.828068\pi$
$919$	−2.05334e34	−1.71527	−0.857636	+	0.514258i	$0.828068\pi$
$920$	1.21757e34	1.00446
$921$	1.03569e33	0.0843809
$922$	2.98255e33	0.239984
$923$	−2.00769e33	−0.159543
$924$	0	0
$925$	−9.39256e33	−0.728038
$926$	−4.30465e33	−0.329542
$927$	−6.63914e33	−0.501990
$928$	1.53313e34	1.14493
$929$	2.41565e34	1.78178	0.890889	−	0.454221i	$-0.150082\pi$
$929$	2.41565e34	1.78178	0.890889	+	0.454221i	$0.150082\pi$
$930$	1.22003e33	0.0888822
$931$	0	0
$932$	−3.45787e33	−0.245768
$933$	−2.61323e33	−0.183459
$934$	−1.81495e33	−0.125856
$935$	2.33504e34	1.59941
$936$	2.92749e33	0.198072
$937$	−1.64580e34	−1.09994	−0.549972	−	0.835183i	$-0.685362\pi$
$937$	−1.64580e34	−1.09994	−0.549972	+	0.835183i	$0.685362\pi$
$938$	0	0
$939$	5.38030e33	0.350875
$940$	2.34575e34	1.51116
$941$	−1.62246e33	−0.103251	−0.0516254	−	0.998667i	$-0.516440\pi$
$941$	−1.62246e33	−0.103251	−0.0516254	+	0.998667i	$0.516440\pi$
$942$	1.20044e33	0.0754668
$943$	2.42845e34	1.50815
$944$	1.42001e34	0.871192
$945$	0	0
$946$	1.05986e34	0.634601
$947$	−2.60058e34	−1.53832	−0.769158	−	0.639059i	$-0.779324\pi$
$947$	−2.60058e34	−1.53832	−0.769158	+	0.639059i	$0.779324\pi$
$948$	2.74517e33	0.160426
$949$	−7.23411e33	−0.417660
$950$	−2.45545e33	−0.140059
$951$	5.82702e32	0.0328375
$952$	0	0
$953$	8.06981e33	0.443910	0.221955	−	0.975057i	$-0.428756\pi$
$953$	8.06981e33	0.443910	0.221955	+	0.975057i	$0.428756\pi$
$954$	−2.28520e33	−0.124199
$955$	2.15653e34	1.15802
$956$	−9.73047e33	−0.516260
$957$	6.45300e33	0.338279
$958$	5.36863e33	0.278074
$959$	0	0
$960$	2.76533e33	0.139839
$961$	−5.32336e32	−0.0265991
$962$	−1.72739e33	−0.0852857
$963$	−1.56207e33	−0.0762076
$964$	−2.06692e34	−0.996411
$965$	4.69410e33	0.223609
$966$	0	0
$967$	1.00931e34	0.469484	0.234742	−	0.972058i	$-0.424576\pi$
$967$	1.00931e34	0.469484	0.234742	+	0.972058i	$0.424576\pi$
$968$	−3.58290e33	−0.164691
$969$	2.32007e33	0.105385
$970$	1.16648e34	0.523605
$971$	−1.07287e34	−0.475910	−0.237955	−	0.971276i	$-0.576477\pi$
$971$	−1.07287e34	−0.475910	−0.237955	+	0.971276i	$0.576477\pi$
$972$	−1.23122e34	−0.539726
$973$	0	0
$974$	1.90837e33	0.0817024
$975$	1.64001e33	0.0693896
$976$	−2.23867e34	−0.936090
$977$	−3.65579e33	−0.151075	−0.0755377	−	0.997143i	$-0.524067\pi$
$977$	−3.65579e33	−0.151075	−0.0755377	+	0.997143i	$0.524067\pi$
$978$	−2.14962e33	−0.0877939
$979$	−1.87073e34	−0.755108
$980$	0	0
$981$	−3.13759e34	−1.23709
$982$	9.23507e32	0.0359880
$983$	−2.92597e34	−1.12695	−0.563475	−	0.826133i	$-0.690536\pi$
$983$	−2.92597e34	−1.12695	−0.563475	+	0.826133i	$0.690536\pi$
$984$	−3.96526e33	−0.150948
$985$	−3.43781e34	−1.29350
$986$	−1.19053e34	−0.442746
$987$	0	0
$988$	4.32948e33	0.157301
$989$	6.27358e34	2.25298
$990$	1.30035e34	0.461590
$991$	−4.79847e34	−1.68367	−0.841833	−	0.539739i	$-0.818523\pi$
$991$	−4.79847e34	−1.68367	−0.841833	+	0.539739i	$0.818523\pi$
$992$	−2.30025e34	−0.797795
$993$	9.50938e33	0.326014
$994$	0	0
$995$	−3.61333e34	−1.21044
$996$	4.01624e33	0.132996
$997$	2.15477e34	0.705355	0.352677	−	0.935745i	$-0.385271\pi$
$997$	2.15477e34	0.705355	0.352677	+	0.935745i	$0.385271\pi$
$998$	−1.43810e34	−0.465359
$999$	1.01149e34	0.323562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.24.a.d.1.4		6
7.6	odd	2		7.24.a.b.1.4	✓	6
21.20	even	2		63.24.a.e.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7.24.a.b.1.4	✓	6	7.6	odd	2
49.24.a.d.1.4		6	1.1	even	1	trivial
63.24.a.e.1.3		6	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+890.125 q^{2} +64762.8 q^{3} -7.59629e6 q^{4} -1.51631e8 q^{5} +5.76470e7 q^{6} -1.42285e10 q^{8} -8.99490e10 q^{9} -1.34970e11 q^{10} +1.07109e12 q^{11} -4.91957e11 q^{12} +2.28738e12 q^{13} -9.82003e12 q^{15} +5.10571e13 q^{16} -1.43774e14 q^{17} -8.00658e13 q^{18} -2.49170e14 q^{19} +1.15183e15 q^{20} +9.53407e14 q^{22} +5.64345e15 q^{23} -9.21481e14 q^{24} +1.10709e16 q^{25} +2.03605e15 q^{26} -1.19223e16 q^{27} +9.30270e16 q^{29} -8.74105e15 q^{30} -1.39574e17 q^{31} +1.64805e17 q^{32} +6.93670e16 q^{33} -1.27976e17 q^{34} +6.83278e17 q^{36} -8.48399e17 q^{37} -2.21793e17 q^{38} +1.48137e17 q^{39} +2.15748e18 q^{40} +4.30314e18 q^{41} +1.11166e19 q^{43} -8.13633e18 q^{44} +1.36390e19 q^{45} +5.02338e18 q^{46} +2.03654e19 q^{47} +3.30660e18 q^{48} +9.85450e18 q^{50} -9.31118e18 q^{51} -1.73756e19 q^{52} +2.85416e19 q^{53} -1.06124e19 q^{54} -1.62411e20 q^{55} -1.61370e19 q^{57} +8.28056e19 q^{58} +2.78122e20 q^{59} +7.45957e19 q^{60} -4.38464e20 q^{61} -1.24239e20 q^{62} -2.81601e20 q^{64} -3.46837e20 q^{65} +6.17453e19 q^{66} -1.17983e21 q^{67} +1.09215e21 q^{68} +3.65486e20 q^{69} -8.77727e20 q^{71} +1.27984e21 q^{72} -3.16262e21 q^{73} -7.55181e20 q^{74} +7.16984e20 q^{75} +1.89277e21 q^{76} +1.31860e20 q^{78} -5.58011e21 q^{79} -7.74182e21 q^{80} +7.69596e21 q^{81} +3.83033e21 q^{82} -8.16381e21 q^{83} +2.18005e22 q^{85} +9.89512e21 q^{86} +6.02469e21 q^{87} -1.52401e22 q^{88} -1.74656e22 q^{89} +1.21404e22 q^{90} -4.28693e22 q^{92} -9.03922e21 q^{93} +1.81277e22 q^{94} +3.77819e22 q^{95} +1.06732e22 q^{96} -8.64253e22 q^{97} -9.63437e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2115 q^{2} - 129352 q^{3} + 6408501 q^{4} - 71437860 q^{5} - 3587653778 q^{6} - 49163897313 q^{8} + 379016247310 q^{9} + 181303960020 q^{10} - 1168850705976 q^{11} + 4703061003298 q^{12} - 11000714535636 q^{13}+ \cdots - 90\!\cdots\!04 q^{99}+O(q^{100}) \) 6 * q - 2115 * q^2 - 129352 * q^3 + 6408501 * q^4 - 71437860 * q^5 - 3587653778 * q^6 - 49163897313 * q^8 + 379016247310 * q^9 + 181303960020 * q^10 - 1168850705976 * q^11 + 4703061003298 * q^12 - 11000714535636 * q^13 - 47642583586400 * q^15 + 18002647337265 * q^16 + 131037332534676 * q^17 + 529552005104765 * q^18 + 465517985994456 * q^19 - 4943391871987800 * q^20 + 897855714076560 * q^22 + 7117263515782944 * q^23 - 33845264505914994 * q^24 + 59193078584081850 * q^25 + 14028640730008128 * q^26 - 133885130285006704 * q^27 + 262229251160335716 * q^29 + 865723792547512160 * q^30 - 62353891866345792 * q^31 + 60817903285433751 * q^32 - 656783103747874240 * q^33 - 547282704180314454 * q^34 + 2621034627679676861 * q^36 + 1939218016676008788 * q^37 + 3706293351149576370 * q^38 - 5440924440539077952 * q^39 + 9081341251088376000 * q^40 + 4731954216272399844 * q^41 - 24014219944449751704 * q^43 - 35009940957233293512 * q^44 - 3889099587334138420 * q^45 - 10024371971526875280 * q^46 + 16003565954092252224 * q^47 + 39357800694088338754 * q^48 - 35480060910606427425 * q^50 + 14150130737580870000 * q^51 - 145479234260898246660 * q^52 + 202556458664680403988 * q^53 - 332296415548302297788 * q^54 + 113721680610730698480 * q^55 + 483285990792481439152 * q^57 + 369031442265302613858 * q^58 - 410642445729067981848 * q^59 - 252127772417738489440 * q^60 - 323143816367671678740 * q^61 - 1415366445023186971716 * q^62 - 1111603155968170329615 * q^64 + 943372699520900652360 * q^65 + 3725312806903508474032 * q^66 - 579655126533238145448 * q^67 + 4217438616148514842722 * q^68 + 2487561554615627392320 * q^69 - 4214729769305546523888 * q^71 - 4997204873186276234745 * q^72 + 1754672903937008125764 * q^73 - 2545731661343127113286 * q^74 + 1081682226208732479400 * q^75 + 15054272754186740412366 * q^76 + 22528837564350510851192 * q^78 + 11526574620963653844480 * q^79 - 5407655723279367022800 * q^80 + 22052505466676180451910 * q^81 - 35925451975152054439782 * q^82 - 31653105166748099990088 * q^83 - 8683324350419512060440 * q^85 - 37145551308674423554872 * q^86 - 87814884336214862913616 * q^87 + 18253569093995420090808 * q^88 - 54130449609585297492156 * q^89 + 11101634800321218680740 * q^90 + 18734804418795932525328 * q^92 + 85314604106878433682720 * q^93 + 284937906702848285268180 * q^94 - 157825746495468308410560 * q^95 + 327539108386580666719598 * q^96 + 41184441040066248030036 * q^97 - 90199089796280394452504 * q^99

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