LMFDB - Embedded newform 46.14.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [46,14,Mod(1,46)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(46, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("46.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	46.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$49.3262273179$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 3257825x^{3} + 1372618617x^{2} + 279354108456x - 130815431589168 $ x^5 - x^4 - 3257825x^3 + 1372618617x^2 + 279354108456*x - 130815431589168
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 59 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$344.754$ of defining polynomial
Character	$\chi$	$=$	46.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-64.0000 q^{2} -1136.86 q^{3} +4096.00 q^{4} +57154.9 q^{5} +72759.2 q^{6} -17496.6 q^{7} -262144. q^{8} -301866. q^{9} -3.65791e6 q^{10} -1.74001e6 q^{11} -4.65659e6 q^{12} -1.27270e7 q^{13} +1.11978e6 q^{14} -6.49773e7 q^{15} +1.67772e7 q^{16} -2.14428e7 q^{17} +1.93194e7 q^{18} +2.97391e8 q^{19} +2.34107e8 q^{20} +1.98912e7 q^{21} +1.11361e8 q^{22} -1.48036e8 q^{23} +2.98022e8 q^{24} +2.04598e9 q^{25} +8.14529e8 q^{26} +2.15571e9 q^{27} -7.16660e7 q^{28} -2.80489e9 q^{29} +4.15855e9 q^{30} -4.74049e9 q^{31} -1.07374e9 q^{32} +1.97815e9 q^{33} +1.37234e9 q^{34} -1.00002e9 q^{35} -1.23644e9 q^{36} -5.60057e9 q^{37} -1.90330e10 q^{38} +1.44689e10 q^{39} -1.49828e10 q^{40} +2.44261e10 q^{41} -1.27304e9 q^{42} -7.21699e9 q^{43} -7.12709e9 q^{44} -1.72531e10 q^{45} +9.47430e9 q^{46} +4.52310e10 q^{47} -1.90734e10 q^{48} -9.65829e10 q^{49} -1.30943e11 q^{50} +2.43776e10 q^{51} -5.21299e10 q^{52} +2.28723e11 q^{53} -1.37965e11 q^{54} -9.94502e10 q^{55} +4.58663e9 q^{56} -3.38093e11 q^{57} +1.79513e11 q^{58} -1.38353e11 q^{59} -2.66147e11 q^{60} -3.19994e11 q^{61} +3.03391e11 q^{62} +5.28163e9 q^{63} +6.87195e10 q^{64} -7.27412e11 q^{65} -1.26602e11 q^{66} -1.05428e12 q^{67} -8.78299e10 q^{68} +1.68296e11 q^{69} +6.40010e10 q^{70} -5.18621e11 q^{71} +7.91324e10 q^{72} -1.45135e12 q^{73} +3.58437e11 q^{74} -2.32600e12 q^{75} +1.21812e12 q^{76} +3.04443e10 q^{77} -9.26008e11 q^{78} +9.39381e11 q^{79} +9.58900e11 q^{80} -1.96947e12 q^{81} -1.56327e12 q^{82} +2.50413e11 q^{83} +8.14744e10 q^{84} -1.22556e12 q^{85} +4.61888e11 q^{86} +3.18878e12 q^{87} +4.56134e11 q^{88} -8.60893e12 q^{89} +1.10420e12 q^{90} +2.22679e11 q^{91} -6.06355e11 q^{92} +5.38928e12 q^{93} -2.89479e12 q^{94} +1.69974e13 q^{95} +1.22070e12 q^{96} +4.41773e12 q^{97} +6.18130e12 q^{98} +5.25251e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 320 q^{2} + 690 q^{3} + 20480 q^{4} - 71798 q^{5} - 44160 q^{6} + 31366 q^{7} - 1310720 q^{8} + 3522701 q^{9} + 4595072 q^{10} - 7592076 q^{11} + 2826240 q^{12} + 28315858 q^{13} - 2007424 q^{14}+ \cdots - 14853301668582 q^{99}+O(q^{100}) $ 5 * q - 320 * q^2 + 690 * q^3 + 20480 * q^4 - 71798 * q^5 - 44160 * q^6 + 31366 * q^7 - 1310720 * q^8 + 3522701 * q^9 + 4595072 * q^10 - 7592076 * q^11 + 2826240 * q^12 + 28315858 * q^13 - 2007424 * q^14 - 86510134 * q^15 + 83886080 * q^16 - 148779352 * q^17 - 225452864 * q^18 + 208568226 * q^19 - 294084608 * q^20 - 376070558 * q^21 + 485892864 * q^22 - 740179445 * q^23 - 180879360 * q^24 + 4178813107 * q^25 - 1812214912 * q^26 + 6759494334 * q^27 + 128475136 * q^28 - 2797854522 * q^29 + 5536648576 * q^30 + 10251920410 * q^31 - 5368709120 * q^32 + 16966481802 * q^33 + 9521878528 * q^34 + 20954998696 * q^35 + 14428983296 * q^36 + 15840804470 * q^37 - 13348366464 * q^38 + 34201839550 * q^39 + 18821414912 * q^40 - 63837021618 * q^41 + 24068515712 * q^42 - 100763331186 * q^43 - 31097143296 * q^44 - 277396545728 * q^45 + 47371484480 * q^46 - 174976267710 * q^47 + 11576279040 * q^48 - 219104642047 * q^49 - 267444038848 * q^50 + 111262053138 * q^51 + 115981754368 * q^52 + 89802813568 * q^53 - 432607637376 * q^54 + 103862253116 * q^55 - 8222408704 * q^56 - 1409625112972 * q^57 + 179062689408 * q^58 - 1238416781664 * q^59 - 354345508864 * q^60 - 1267556050856 * q^61 - 656122906240 * q^62 - 1901815038072 * q^63 + 343597383680 * q^64 - 2745162221118 * q^65 - 1085854835328 * q^66 - 1575419391340 * q^67 - 609400225792 * q^68 - 102144763410 * q^69 - 1341119916544 * q^70 - 1683993935490 * q^71 - 923454930944 * q^72 - 1127194561170 * q^73 - 1013811486080 * q^74 - 7122659318494 * q^75 + 854295453696 * q^76 - 44261676728 * q^77 - 2188917731200 * q^78 - 1151083218244 * q^79 - 1204570554368 * q^80 + 2254336417973 * q^81 + 4085569383552 * q^82 - 846457405404 * q^83 - 1540385005568 * q^84 + 7375916269256 * q^85 + 6448853195904 * q^86 - 2306908932150 * q^87 + 1990217170944 * q^88 - 11559404717682 * q^89 + 17753378926592 * q^90 - 8233703279434 * q^91 - 3031775006720 * q^92 - 1468162531188 * q^93 + 11198481133440 * q^94 + 11131929151492 * q^95 - 740881858560 * q^96 - 2048127950232 * q^97 + 14022697091008 * q^98 - 14853301668582 * 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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	−1136.86	−0.900368	−0.450184	−	0.892936i	$-0.648642\pi$
$3$	−1136.86	−0.900368	−0.450184	+	0.892936i	$0.648642\pi$
$4$	4096.00	0.500000
$5$	57154.9	1.63587	0.817935	−	0.575311i	$-0.195119\pi$
$5$	57154.9	1.63587	0.817935	+	0.575311i	$0.195119\pi$
$6$	72759.2	0.636656
$7$	−17496.6	−0.0562103	−0.0281052	−	0.999605i	$-0.508947\pi$
$7$	−17496.6	−0.0562103	−0.0281052	+	0.999605i	$0.508947\pi$
$8$	−262144.	−0.353553
$9$	−301866.	−0.189338
$10$	−3.65791e6	−1.15673
$11$	−1.74001e6	−0.296142	−0.148071	−	0.988977i	$-0.547306\pi$
$11$	−1.74001e6	−0.296142	−0.148071	+	0.988977i	$0.547306\pi$
$12$	−4.65659e6	−0.450184
$13$	−1.27270e7	−0.731299	−0.365649	−	0.930753i	$-0.619153\pi$
$13$	−1.27270e7	−0.731299	−0.365649	+	0.930753i	$0.619153\pi$
$14$	1.11978e6	0.0397467
$15$	−6.49773e7	−1.47288
$16$	1.67772e7	0.250000
$17$	−2.14428e7	−0.215459	−0.107729	−	0.994180i	$-0.534358\pi$
$17$	−2.14428e7	−0.215459	−0.107729	+	0.994180i	$0.534358\pi$
$18$	1.93194e7	0.133882
$19$	2.97391e8	1.45021	0.725103	−	0.688640i	$-0.241792\pi$
$19$	2.97391e8	1.45021	0.725103	+	0.688640i	$0.241792\pi$
$20$	2.34107e8	0.817935
$21$	1.98912e7	0.0506100
$22$	1.11361e8	0.209404
$23$	−1.48036e8	−0.208514
$23$	−1.48036e8	−0.208514
$24$	2.98022e8	0.318328
$25$	2.04598e9	1.67607
$26$	8.14529e8	0.517106
$27$	2.15571e9	1.07084
$28$	−7.16660e7	−0.0281052
$29$	−2.80489e9	−0.875648	−0.437824	−	0.899061i	$-0.644251\pi$
$29$	−2.80489e9	−0.875648	−0.437824	+	0.899061i	$0.644251\pi$
$30$	4.15855e9	1.04149
$31$	−4.74049e9	−0.959338	−0.479669	−	0.877449i	$-0.659243\pi$
$31$	−4.74049e9	−0.959338	−0.479669	+	0.877449i	$0.659243\pi$
$32$	−1.07374e9	−0.176777
$33$	1.97815e9	0.266637
$34$	1.37234e9	0.152352
$35$	−1.00002e9	−0.0919527
$36$	−1.23644e9	−0.0946690
$37$	−5.60057e9	−0.358857	−0.179428	−	0.983771i	$-0.557425\pi$
$37$	−5.60057e9	−0.358857	−0.179428	+	0.983771i	$0.557425\pi$
$38$	−1.90330e10	−1.02545
$39$	1.44689e10	0.658438
$40$	−1.49828e10	−0.578367
$41$	2.44261e10	0.803080	0.401540	−	0.915842i	$-0.368475\pi$
$41$	2.44261e10	0.803080	0.401540	+	0.915842i	$0.368475\pi$
$42$	−1.27304e9	−0.0357866
$43$	−7.21699e9	−0.174105	−0.0870525	−	0.996204i	$-0.527745\pi$
$43$	−7.21699e9	−0.174105	−0.0870525	+	0.996204i	$0.527745\pi$
$44$	−7.12709e9	−0.148071
$45$	−1.72531e10	−0.309732
$46$	9.47430e9	0.147442
$47$	4.52310e10	0.612069	0.306035	−	0.952020i	$-0.400998\pi$
$47$	4.52310e10	0.612069	0.306035	+	0.952020i	$0.400998\pi$
$48$	−1.90734e10	−0.225092
$49$	−9.65829e10	−0.996840
$50$	−1.30943e11	−1.18516
$51$	2.43776e10	0.193992
$52$	−5.21299e10	−0.365649
$53$	2.28723e11	1.41748	0.708740	−	0.705470i	$-0.249264\pi$
$53$	2.28723e11	1.41748	0.708740	+	0.705470i	$0.249264\pi$
$54$	−1.37965e11	−0.757199
$55$	−9.94502e10	−0.484449
$56$	4.58663e9	0.0198734
$57$	−3.38093e11	−1.30572
$58$	1.79513e11	0.619177
$59$	−1.38353e11	−0.427021	−0.213511	−	0.976941i	$-0.568490\pi$
$59$	−1.38353e11	−0.427021	−0.213511	+	0.976941i	$0.568490\pi$
$60$	−2.66147e11	−0.736442
$61$	−3.19994e11	−0.795238	−0.397619	−	0.917551i	$-0.630163\pi$
$61$	−3.19994e11	−0.795238	−0.397619	+	0.917551i	$0.630163\pi$
$62$	3.03391e11	0.678355
$63$	5.28163e9	0.0106428
$64$	6.87195e10	0.125000
$65$	−7.27412e11	−1.19631
$66$	−1.26602e11	−0.188541
$67$	−1.05428e12	−1.42386	−0.711932	−	0.702249i	$-0.752180\pi$
$67$	−1.05428e12	−1.42386	−0.711932	+	0.702249i	$0.752180\pi$
$68$	−8.78299e10	−0.107729
$69$	1.68296e11	0.187740
$70$	6.40010e10	0.0650204
$71$	−5.18621e11	−0.480475	−0.240238	−	0.970714i	$-0.577225\pi$
$71$	−5.18621e11	−0.480475	−0.240238	+	0.970714i	$0.577225\pi$
$72$	7.91324e10	0.0669411
$73$	−1.45135e12	−1.12247	−0.561235	−	0.827656i	$-0.689674\pi$
$73$	−1.45135e12	−1.12247	−0.561235	+	0.827656i	$0.689674\pi$
$74$	3.58437e11	0.253750
$75$	−2.32600e12	−1.50908
$76$	1.21812e12	0.725103
$77$	3.04443e10	0.0166462
$78$	−9.26008e11	−0.465586
$79$	9.39381e11	0.434776	0.217388	−	0.976085i	$-0.430246\pi$
$79$	9.39381e11	0.434776	0.217388	+	0.976085i	$0.430246\pi$
$80$	9.58900e11	0.408967
$81$	−1.96947e12	−0.774813
$82$	−1.56327e12	−0.567863
$83$	2.50413e11	0.0840715	0.0420357	−	0.999116i	$-0.486616\pi$
$83$	2.50413e11	0.0840715	0.0420357	+	0.999116i	$0.486616\pi$
$84$	8.14744e10	0.0253050
$85$	−1.22556e12	−0.352463
$86$	4.61888e11	0.123111
$87$	3.18878e12	0.788405
$88$	4.56134e11	0.104702
$89$	−8.60893e12	−1.83617	−0.918087	−	0.396378i	$-0.870267\pi$
$89$	−8.60893e12	−1.83617	−0.918087	+	0.396378i	$0.870267\pi$
$90$	1.10420e12	0.219014
$91$	2.22679e11	0.0411065
$92$	−6.06355e11	−0.104257
$93$	5.38928e12	0.863757
$94$	−2.89479e12	−0.432798
$95$	1.69974e13	2.37235
$96$	1.22070e12	0.159164
$97$	4.41773e12	0.538497	0.269248	−	0.963071i	$-0.413225\pi$
$97$	4.41773e12	0.538497	0.269248	+	0.963071i	$0.413225\pi$
$98$	6.18130e12	0.704873
$99$	5.25251e11	0.0560709
$100$	8.38034e12	0.838034
$101$	−1.40297e13	−1.31510	−0.657551	−	0.753410i	$-0.728408\pi$
$101$	−1.40297e13	−1.31510	−0.657551	+	0.753410i	$0.728408\pi$
$102$	−1.56016e12	−0.137173
$103$	9.82884e12	0.811074	0.405537	−	0.914079i	$-0.367085\pi$
$103$	9.82884e12	0.811074	0.405537	+	0.914079i	$0.367085\pi$
$104$	3.33631e12	0.258553
$105$	1.13688e12	0.0827913
$106$	−1.46383e13	−1.00231
$107$	−7.74315e12	−0.498796	−0.249398	−	0.968401i	$-0.580233\pi$
$107$	−7.74315e12	−0.498796	−0.249398	+	0.968401i	$0.580233\pi$
$108$	8.82977e12	0.535421
$109$	−2.67925e13	−1.53017	−0.765086	−	0.643928i	$-0.777304\pi$
$109$	−2.67925e13	−1.53017	−0.765086	+	0.643928i	$0.777304\pi$
$110$	6.36482e12	0.342557
$111$	6.36708e12	0.323103
$112$	−2.93544e11	−0.0140526
$113$	−1.02428e12	−0.0462817	−0.0231409	−	0.999732i	$-0.507367\pi$
$113$	−1.02428e12	−0.0462817	−0.0231409	+	0.999732i	$0.507367\pi$
$114$	2.16380e13	0.923283
$115$	−8.46098e12	−0.341102
$116$	−1.14888e13	−0.437824
$117$	3.84185e12	0.138463
$118$	8.85457e12	0.301950
$119$	3.75177e11	0.0121110
$120$	1.70334e13	0.520743
$121$	−3.14951e13	−0.912300
$122$	2.04796e13	0.562318
$123$	−2.77691e13	−0.723067
$124$	−1.94170e13	−0.479669
$125$	4.71687e13	1.10596
$126$	−3.38024e11	−0.00752556
$127$	−2.21377e13	−0.468175	−0.234087	−	0.972216i	$-0.575210\pi$
$127$	−2.21377e13	−0.468175	−0.234087	+	0.972216i	$0.575210\pi$
$128$	−4.39805e12	−0.0883883
$129$	8.20473e12	0.156759
$130$	4.65543e13	0.845918
$131$	5.14353e13	0.889197	0.444599	−	0.895730i	$-0.353346\pi$
$131$	5.14353e13	0.889197	0.444599	+	0.895730i	$0.353346\pi$
$132$	8.10252e12	0.133318
$133$	−5.20333e12	−0.0815166
$134$	6.74737e13	1.00682
$135$	1.23209e14	1.75176
$136$	5.62111e12	0.0761762
$137$	−5.07666e12	−0.0655985	−0.0327993	−	0.999462i	$-0.510442\pi$
$137$	−5.07666e12	−0.0655985	−0.0327993	+	0.999462i	$0.510442\pi$
$138$	−1.07710e13	−0.132752
$139$	9.37600e13	1.10261	0.551304	−	0.834304i	$-0.314130\pi$
$139$	9.37600e13	1.10261	0.551304	+	0.834304i	$0.314130\pi$
$140$	−4.09607e12	−0.0459764
$141$	−5.14215e13	−0.551087
$142$	3.31917e13	0.339747
$143$	2.21452e13	0.216568
$144$	−5.06447e12	−0.0473345
$145$	−1.60313e14	−1.43245
$146$	9.28867e13	0.793707
$147$	1.09801e14	0.897523
$148$	−2.29399e13	−0.179428
$149$	−2.12749e14	−1.59278	−0.796391	−	0.604782i	$-0.793260\pi$
$149$	−2.12749e14	−1.59278	−0.796391	+	0.604782i	$0.793260\pi$
$150$	1.48864e14	1.06708
$151$	1.25527e14	0.861764	0.430882	−	0.902408i	$-0.358202\pi$
$151$	1.25527e14	0.861764	0.430882	+	0.902408i	$0.358202\pi$
$152$	−7.79594e13	−0.512726
$153$	6.47287e12	0.0407946
$154$	−1.94843e12	−0.0117707
$155$	−2.70942e14	−1.56935
$156$	5.92645e13	0.329219
$157$	−2.11221e14	−1.12562	−0.562808	−	0.826588i	$-0.690279\pi$
$157$	−2.11221e14	−1.12562	−0.562808	+	0.826588i	$0.690279\pi$
$158$	−6.01204e13	−0.307433
$159$	−2.60027e14	−1.27625
$160$	−6.13696e13	−0.289184
$161$	2.59012e12	0.0117207
$162$	1.26046e14	0.547876
$163$	−4.59744e14	−1.91998	−0.959990	−	0.280035i	$-0.909654\pi$
$163$	−4.59744e14	−1.91998	−0.959990	+	0.280035i	$0.909654\pi$
$164$	1.00049e14	0.401540
$165$	1.13061e14	0.436183
$166$	−1.60264e13	−0.0594475
$167$	−1.75187e14	−0.624949	−0.312475	−	0.949926i	$-0.601158\pi$
$167$	−1.75187e14	−0.624949	−0.312475	+	0.949926i	$0.601158\pi$
$168$	−5.21436e12	−0.0178933
$169$	−1.40898e14	−0.465202
$170$	7.84361e13	0.249229
$171$	−8.97724e13	−0.274579
$172$	−2.95608e13	−0.0870525
$173$	−1.33159e14	−0.377634	−0.188817	−	0.982012i	$-0.560465\pi$
$173$	−1.33159e14	−0.377634	−0.188817	+	0.982012i	$0.560465\pi$
$174$	−2.04082e14	−0.557487
$175$	−3.57977e13	−0.0942123
$176$	−2.91926e13	−0.0740355
$177$	1.57288e14	0.384476
$178$	5.50971e14	1.29837
$179$	−3.38015e14	−0.768054	−0.384027	−	0.923322i	$-0.625463\pi$
$179$	−3.38015e14	−0.768054	−0.384027	+	0.923322i	$0.625463\pi$
$180$	−7.06688e13	−0.154866
$181$	1.87870e14	0.397142	0.198571	−	0.980086i	$-0.436370\pi$
$181$	1.87870e14	0.397142	0.198571	+	0.980086i	$0.436370\pi$
$182$	−1.42515e13	−0.0290667
$183$	3.63789e14	0.716007
$184$	3.88067e13	0.0737210
$185$	−3.20100e14	−0.587043
$186$	−3.44914e14	−0.610769
$187$	3.73108e13	0.0638064
$188$	1.85266e14	0.306035
$189$	−3.77175e13	−0.0601924
$190$	−1.08783e15	−1.67750
$191$	−9.91840e14	−1.47817	−0.739085	−	0.673612i	$-0.764742\pi$
$191$	−9.91840e14	−1.47817	−0.739085	+	0.673612i	$0.764742\pi$
$192$	−7.81246e13	−0.112546
$193$	−2.96328e14	−0.412715	−0.206358	−	0.978477i	$-0.566161\pi$
$193$	−2.96328e14	−0.412715	−0.206358	+	0.978477i	$0.566161\pi$
$194$	−2.82735e14	−0.380775
$195$	8.26967e14	1.07712
$196$	−3.95603e14	−0.498420
$197$	−7.90112e13	−0.0963071	−0.0481535	−	0.998840i	$-0.515334\pi$
$197$	−7.90112e13	−0.0963071	−0.0481535	+	0.998840i	$0.515334\pi$
$198$	−3.36160e13	−0.0396481
$199$	1.06708e15	1.21801	0.609005	−	0.793166i	$-0.291569\pi$
$199$	1.06708e15	1.21801	0.609005	+	0.793166i	$0.291569\pi$
$200$	−5.36342e14	−0.592579
$201$	1.19857e15	1.28200
$202$	8.97901e14	0.929918
$203$	4.90761e13	0.0492205
$204$	9.98505e13	0.0969961
$205$	1.39607e15	1.31373
$206$	−6.29046e14	−0.573516
$207$	4.46870e13	0.0394797
$208$	−2.13524e14	−0.182825
$209$	−5.17465e14	−0.429467
$210$	−7.27604e13	−0.0585423
$211$	1.99691e15	1.55784	0.778921	−	0.627122i	$-0.215767\pi$
$211$	1.99691e15	1.55784	0.778921	+	0.627122i	$0.215767\pi$
$212$	9.36849e14	0.708740
$213$	5.89601e14	0.432604
$214$	4.95561e14	0.352702
$215$	−4.12487e14	−0.284813
$216$	−5.65106e14	−0.378600
$217$	8.29423e13	0.0539247
$218$	1.71472e15	1.08200
$219$	1.64999e15	1.01064
$220$	−4.07348e14	−0.242225
$221$	2.72903e14	0.157565
$222$	−4.07493e14	−0.228468
$223$	2.10122e15	1.14417	0.572085	−	0.820194i	$-0.306135\pi$
$223$	2.10122e15	1.14417	0.572085	+	0.820194i	$0.306135\pi$
$224$	1.87868e13	0.00993668
$225$	−6.17612e14	−0.317343
$226$	6.55541e13	0.0327261
$227$	−3.40833e14	−0.165338	−0.0826692	−	0.996577i	$-0.526344\pi$
$227$	−3.40833e14	−0.165338	−0.0826692	+	0.996577i	$0.526344\pi$
$228$	−1.38483e15	−0.652860
$229$	2.24733e15	1.02976	0.514881	−	0.857261i	$-0.327836\pi$
$229$	2.24733e15	1.02976	0.514881	+	0.857261i	$0.327836\pi$
$230$	5.41503e14	0.241196
$231$	−3.46110e13	−0.0149877
$232$	7.35286e14	0.309588
$233$	−1.93897e15	−0.793887	−0.396943	−	0.917843i	$-0.629929\pi$
$233$	−1.93897e15	−0.793887	−0.396943	+	0.917843i	$0.629929\pi$
$234$	−2.45879e14	−0.0979079
$235$	2.58518e15	1.00127
$236$	−5.66693e14	−0.213511
$237$	−1.06795e15	−0.391458
$238$	−2.40113e13	−0.00856378
$239$	−2.30487e15	−0.799945	−0.399972	−	0.916527i	$-0.630980\pi$
$239$	−2.30487e15	−0.799945	−0.399972	+	0.916527i	$0.630980\pi$
$240$	−1.09014e15	−0.368221
$241$	−8.88360e14	−0.292064	−0.146032	−	0.989280i	$-0.546650\pi$
$241$	−8.88360e14	−0.292064	−0.146032	+	0.989280i	$0.546650\pi$
$242$	2.01568e15	0.645094
$243$	−1.19787e15	−0.373225
$244$	−1.31069e15	−0.397619
$245$	−5.52019e15	−1.63070
$246$	1.77722e15	0.511285
$247$	−3.78491e15	−1.06053
$248$	1.24269e15	0.339177
$249$	−2.84685e14	−0.0756952
$250$	−3.01880e15	−0.782031
$251$	2.48749e15	0.627887	0.313944	−	0.949442i	$-0.398350\pi$
$251$	2.48749e15	0.627887	0.313944	+	0.949442i	$0.398350\pi$
$252$	2.16335e13	0.00532138
$253$	2.57584e14	0.0617498
$254$	1.41681e15	0.331050
$255$	1.39330e15	0.317346
$256$	2.81475e14	0.0625000
$257$	7.12685e15	1.54288	0.771440	−	0.636302i	$-0.219537\pi$
$257$	7.12685e15	1.54288	0.771440	+	0.636302i	$0.219537\pi$
$258$	−5.25103e14	−0.110845
$259$	9.79909e13	0.0201715
$260$	−2.97948e15	−0.598155
$261$	8.46702e14	0.165793
$262$	−3.29186e15	−0.628757
$263$	8.32021e15	1.55032	0.775161	−	0.631764i	$-0.217669\pi$
$263$	8.32021e15	1.55032	0.775161	+	0.631764i	$0.217669\pi$
$264$	−5.18561e14	−0.0942703
$265$	1.30726e16	2.31881
$266$	3.33013e14	0.0576409
$267$	9.78717e15	1.65323
$268$	−4.31832e15	−0.711932
$269$	−9.84809e15	−1.58475	−0.792377	−	0.610031i	$-0.791157\pi$
$269$	−9.84809e15	−1.58475	−0.792377	+	0.610031i	$0.791157\pi$
$270$	−7.88539e15	−1.23868
$271$	−6.38864e15	−0.979734	−0.489867	−	0.871797i	$-0.662955\pi$
$271$	−6.38864e15	−0.979734	−0.489867	+	0.871797i	$0.662955\pi$
$272$	−3.59751e14	−0.0538647
$273$	−2.53156e14	−0.0370110
$274$	3.24906e14	0.0463852
$275$	−3.56003e15	−0.496354
$276$	6.89342e14	0.0938698
$277$	6.54312e15	0.870295	0.435147	−	0.900359i	$-0.356696\pi$
$277$	6.54312e15	0.870295	0.435147	+	0.900359i	$0.356696\pi$
$278$	−6.00064e15	−0.779662
$279$	1.43099e15	0.181639
$280$	2.62148e14	0.0325102
$281$	4.45548e15	0.539887	0.269944	−	0.962876i	$-0.412995\pi$
$281$	4.45548e15	0.539887	0.269944	+	0.962876i	$0.412995\pi$
$282$	3.29098e15	0.389678
$283$	−1.12396e16	−1.30058	−0.650290	−	0.759686i	$-0.725353\pi$
$283$	−1.12396e16	−1.30058	−0.650290	+	0.759686i	$0.725353\pi$
$284$	−2.12427e15	−0.240238
$285$	−1.93237e16	−2.13599
$286$	−1.41729e15	−0.153137
$287$	−4.27373e14	−0.0451414
$288$	3.24126e14	0.0334706
$289$	−9.44478e15	−0.953577
$290$	1.02601e16	1.01289
$291$	−5.02235e15	−0.484845
$292$	−5.94475e15	−0.561235
$293$	−4.81587e15	−0.444667	−0.222334	−	0.974971i	$-0.571367\pi$
$293$	−4.81587e15	−0.444667	−0.222334	+	0.974971i	$0.571367\pi$
$294$	−7.02729e15	−0.634644
$295$	−7.90754e15	−0.698551
$296$	1.46816e15	0.126875
$297$	−3.75096e15	−0.317121
$298$	1.36159e16	1.12627
$299$	1.88406e15	0.152486
$300$	−9.52730e15	−0.754539
$301$	1.26273e14	0.00978650
$302$	−8.03376e15	−0.609360
$303$	1.59498e16	1.18408
$304$	4.98940e15	0.362552
$305$	−1.82892e16	−1.30091
$306$	−4.14263e14	−0.0288461
$307$	5.31598e15	0.362397	0.181198	−	0.983447i	$-0.442002\pi$
$307$	5.31598e15	0.362397	0.181198	+	0.983447i	$0.442002\pi$
$308$	1.24700e14	0.00832312
$309$	−1.11740e16	−0.730265
$310$	1.73403e16	1.10970
$311$	1.45040e15	0.0908960	0.0454480	−	0.998967i	$-0.485528\pi$
$311$	1.45040e15	0.0908960	0.0454480	+	0.998967i	$0.485528\pi$
$312$	−3.79293e15	−0.232793
$313$	1.18950e16	0.715031	0.357516	−	0.933907i	$-0.383624\pi$
$313$	1.18950e16	0.715031	0.357516	+	0.933907i	$0.383624\pi$
$314$	1.35182e16	0.795930
$315$	3.01871e14	0.0174102
$316$	3.84771e15	0.217388
$317$	1.13995e16	0.630959	0.315480	−	0.948932i	$-0.397835\pi$
$317$	1.13995e16	0.630959	0.315480	+	0.948932i	$0.397835\pi$
$318$	1.66417e16	0.902447
$319$	4.88055e15	0.259316
$320$	3.92766e15	0.204484
$321$	8.80289e15	0.449100
$322$	−1.65768e14	−0.00828776
$323$	−6.37692e15	−0.312460
$324$	−8.06695e15	−0.387407
$325$	−2.60392e16	−1.22571
$326$	2.94236e16	1.35763
$327$	3.04594e16	1.37772
$328$	−6.40315e15	−0.283931
$329$	−7.91389e14	−0.0344046
$330$	−7.23592e15	−0.308428
$331$	−2.32445e16	−0.971490	−0.485745	−	0.874101i	$-0.661452\pi$
$331$	−2.32445e16	−0.971490	−0.485745	+	0.874101i	$0.661452\pi$
$332$	1.02569e15	0.0420357
$333$	1.69062e15	0.0679452
$334$	1.12120e16	0.441906
$335$	−6.02571e16	−2.32925
$336$	3.33719e14	0.0126525
$337$	4.11640e16	1.53082	0.765409	−	0.643544i	$-0.222537\pi$
$337$	4.11640e16	1.53082	0.765409	+	0.643544i	$0.222537\pi$
$338$	9.01748e15	0.328947
$339$	1.16447e15	0.0416706
$340$	−5.01991e15	−0.176231
$341$	8.24850e15	0.284100
$342$	5.74543e15	0.194157
$343$	3.38510e15	0.112243
$344$	1.89189e15	0.0615554
$345$	9.61897e15	0.307117
$346$	8.52217e15	0.267027
$347$	−4.18381e16	−1.28656	−0.643281	−	0.765630i	$-0.722427\pi$
$347$	−4.18381e16	−1.28656	−0.643281	+	0.765630i	$0.722427\pi$
$348$	1.30612e16	0.394203
$349$	2.15279e16	0.637730	0.318865	−	0.947800i	$-0.396698\pi$
$349$	2.15279e16	0.637730	0.318865	+	0.947800i	$0.396698\pi$
$350$	2.29105e15	0.0666182
$351$	−2.74357e16	−0.783105
$352$	1.86832e15	0.0523510
$353$	−1.68814e15	−0.0464380	−0.0232190	−	0.999730i	$-0.507391\pi$
$353$	−1.68814e15	−0.0464380	−0.0232190	+	0.999730i	$0.507391\pi$
$354$	−1.00664e16	−0.271866
$355$	−2.96417e16	−0.785994
$356$	−3.52622e16	−0.918087
$357$	−4.26524e14	−0.0109044
$358$	2.16330e16	0.543096
$359$	5.30222e16	1.30720	0.653602	−	0.756838i	$-0.273257\pi$
$359$	5.30222e16	1.30720	0.653602	+	0.756838i	$0.273257\pi$
$360$	4.52280e15	0.109507
$361$	4.63886e16	1.10310
$362$	−1.20237e16	−0.280822
$363$	3.58056e16	0.821405
$364$	9.12095e14	0.0205533
$365$	−8.29521e16	−1.83621
$366$	−2.32825e16	−0.506293
$367$	−3.63750e15	−0.0777093	−0.0388547	−	0.999245i	$-0.512371\pi$
$367$	−3.63750e15	−0.0777093	−0.0388547	+	0.999245i	$0.512371\pi$
$368$	−2.48363e15	−0.0521286
$369$	−7.37340e15	−0.152054
$370$	2.04864e16	0.415102
$371$	−4.00187e15	−0.0796770
$372$	2.20745e16	0.431879
$373$	9.95279e16	1.91354	0.956770	−	0.290846i	$-0.0939368\pi$
$373$	9.95279e16	1.91354	0.956770	+	0.290846i	$0.0939368\pi$
$374$	−2.38789e15	−0.0451179
$375$	−5.36243e16	−0.995769
$376$	−1.18570e16	−0.216399
$377$	3.56979e16	0.640360
$378$	2.41392e15	0.0425624
$379$	3.26538e16	0.565951	0.282975	−	0.959127i	$-0.408679\pi$
$379$	3.26538e16	0.565951	0.282975	+	0.959127i	$0.408679\pi$
$380$	6.96213e16	1.18617
$381$	2.51675e16	0.421529
$382$	6.34777e16	1.04522
$383$	5.27891e16	0.854579	0.427290	−	0.904115i	$-0.359468\pi$
$383$	5.27891e16	0.854579	0.427290	+	0.904115i	$0.359468\pi$
$384$	4.99998e15	0.0795820
$385$	1.74004e15	0.0272311
$386$	1.89650e16	0.291834
$387$	2.17856e15	0.0329647
$388$	1.80950e16	0.269248
$389$	−6.87965e16	−1.00669	−0.503343	−	0.864087i	$-0.667897\pi$
$389$	−6.87965e16	−1.00669	−0.503343	+	0.864087i	$0.667897\pi$
$390$	−5.29259e16	−0.761638
$391$	3.17431e15	0.0449263
$392$	2.53186e16	0.352436
$393$	−5.84749e16	−0.800604
$394$	5.05672e15	0.0680994
$395$	5.36903e16	0.711237
$396$	2.15143e15	0.0280355
$397$	−5.36671e16	−0.687970	−0.343985	−	0.938975i	$-0.611777\pi$
$397$	−5.36671e16	−0.687970	−0.343985	+	0.938975i	$0.611777\pi$
$398$	−6.82929e16	−0.861263
$399$	5.91548e15	0.0733949
$400$	3.43259e16	0.419017
$401$	6.47016e16	0.777100	0.388550	−	0.921428i	$-0.372976\pi$
$401$	6.47016e16	0.777100	0.388550	+	0.921428i	$0.372976\pi$
$402$	−7.67084e16	−0.906511
$403$	6.03323e16	0.701563
$404$	−5.74657e16	−0.657551
$405$	−1.12565e17	−1.26749
$406$	−3.14087e15	−0.0348041
$407$	9.74506e15	0.106272
$408$	−6.39043e15	−0.0685866
$409$	−6.32594e16	−0.668226	−0.334113	−	0.942533i	$-0.608437\pi$
$409$	−6.32594e16	−0.668226	−0.334113	+	0.942533i	$0.608437\pi$
$410$	−8.93485e16	−0.928950
$411$	5.77146e15	0.0590628
$412$	4.02589e16	0.405537
$413$	2.42070e15	0.0240030
$414$	−2.85997e15	−0.0279164
$415$	1.43123e16	0.137530
$416$	1.36655e16	0.129277
$417$	−1.06592e17	−0.992753
$418$	3.31177e16	0.303679
$419$	4.26979e16	0.385492	0.192746	−	0.981249i	$-0.438261\pi$
$419$	4.26979e16	0.385492	0.192746	+	0.981249i	$0.438261\pi$
$420$	4.65666e15	0.0413956
$421$	−3.55599e16	−0.311262	−0.155631	−	0.987815i	$-0.549741\pi$
$421$	−3.55599e16	−0.311262	−0.155631	+	0.987815i	$0.549741\pi$
$422$	−1.27802e17	−1.10156
$423$	−1.36537e16	−0.115888
$424$	−5.99584e16	−0.501155
$425$	−4.38717e16	−0.361124
$426$	−3.77345e16	−0.305897
$427$	5.59879e15	0.0447006
$428$	−3.17159e16	−0.249398
$429$	−2.51760e16	−0.194991
$430$	2.63991e16	0.201393
$431$	−2.25887e17	−1.69742	−0.848709	−	0.528861i	$-0.822619\pi$
$431$	−2.25887e17	−1.69742	−0.848709	+	0.528861i	$0.822619\pi$
$432$	3.61668e16	0.267710
$433$	1.91523e17	1.39653	0.698264	−	0.715840i	$-0.253956\pi$
$433$	1.91523e17	1.39653	0.698264	+	0.715840i	$0.253956\pi$
$434$	−5.30831e15	−0.0381305
$435$	1.82254e17	1.28973
$436$	−1.09742e17	−0.765086
$437$	−4.40246e16	−0.302389
$438$	−1.05599e17	−0.714628
$439$	2.69279e17	1.79549	0.897744	−	0.440518i	$-0.145205\pi$
$439$	2.69279e17	1.79549	0.897744	+	0.440518i	$0.145205\pi$
$440$	2.60703e16	0.171279
$441$	2.91551e16	0.188740
$442$	−1.74658e16	−0.111415
$443$	−5.44255e16	−0.342120	−0.171060	−	0.985261i	$-0.554719\pi$
$443$	−5.44255e16	−0.342120	−0.171060	+	0.985261i	$0.554719\pi$
$444$	2.60796e16	0.161551
$445$	−4.92043e17	−3.00374
$446$	−1.34478e17	−0.809050
$447$	2.41866e17	1.43409
$448$	−1.20236e15	−0.00702629
$449$	−2.14513e17	−1.23553	−0.617763	−	0.786364i	$-0.711961\pi$
$449$	−2.14513e17	−1.23553	−0.617763	+	0.786364i	$0.711961\pi$
$450$	3.95272e16	0.224396
$451$	−4.25017e16	−0.237825
$452$	−4.19546e15	−0.0231409
$453$	−1.42707e17	−0.775905
$454$	2.18133e16	0.116912
$455$	1.27272e16	0.0672449
$456$	8.86291e16	0.461641
$457$	−2.97882e17	−1.52964	−0.764819	−	0.644245i	$-0.777172\pi$
$457$	−2.97882e17	−1.52964	−0.764819	+	0.644245i	$0.777172\pi$
$458$	−1.43829e17	−0.728152
$459$	−4.62245e16	−0.230722
$460$	−3.46562e16	−0.170551
$461$	−1.76100e17	−0.854485	−0.427243	−	0.904137i	$-0.640515\pi$
$461$	−1.76100e17	−0.854485	−0.427243	+	0.904137i	$0.640515\pi$
$462$	2.21510e15	0.0105979
$463$	1.93292e17	0.911880	0.455940	−	0.890010i	$-0.349303\pi$
$463$	1.93292e17	0.911880	0.455940	+	0.890010i	$0.349303\pi$
$464$	−4.70583e16	−0.218912
$465$	3.08024e17	1.41299
$466$	1.24094e17	0.561363
$467$	2.31596e17	1.03317	0.516585	−	0.856236i	$-0.327203\pi$
$467$	2.31596e17	1.03317	0.516585	+	0.856236i	$0.327203\pi$
$468$	1.57362e16	0.0692314
$469$	1.84462e16	0.0800358
$470$	−1.65451e17	−0.708001
$471$	2.40130e17	1.01347
$472$	3.62683e16	0.150975
$473$	1.25577e16	0.0515598
$474$	6.83486e16	0.276803
$475$	6.08457e17	2.43065
$476$	1.53672e15	0.00605551
$477$	−6.90437e16	−0.268383
$478$	1.47512e17	0.565646
$479$	−3.50943e17	−1.32757	−0.663783	−	0.747925i	$-0.731050\pi$
$479$	−3.50943e17	−1.32757	−0.663783	+	0.747925i	$0.731050\pi$
$480$	6.97688e16	0.260372
$481$	7.12786e16	0.262432
$482$	5.68550e16	0.206520
$483$	−2.94461e15	−0.0105529
$484$	−1.29004e17	−0.456150
$485$	2.52495e17	0.880910
$486$	7.66640e16	0.263910
$487$	−1.51993e17	−0.516280	−0.258140	−	0.966107i	$-0.583110\pi$
$487$	−1.51993e17	−0.516280	−0.258140	+	0.966107i	$0.583110\pi$
$488$	8.38844e16	0.281159
$489$	5.22666e17	1.72869
$490$	3.53292e17	1.15308
$491$	4.84168e17	1.55943	0.779716	−	0.626134i	$-0.215364\pi$
$491$	4.84168e17	1.55943	0.779716	+	0.626134i	$0.215364\pi$
$492$	−1.13742e17	−0.361533
$493$	6.01449e16	0.188666
$494$	2.42234e17	0.749911
$495$	3.00207e16	0.0917247
$496$	−7.95322e16	−0.239835
$497$	9.07410e15	0.0270077
$498$	1.82198e16	0.0535246
$499$	−2.55875e17	−0.741951	−0.370975	−	0.928643i	$-0.620977\pi$
$499$	−2.55875e17	−0.741951	−0.370975	+	0.928643i	$0.620977\pi$
$500$	1.93203e17	0.552979
$501$	1.99164e17	0.562684
$502$	−1.59199e17	−0.443983
$503$	5.66711e17	1.56016	0.780081	−	0.625679i	$-0.215178\pi$
$503$	5.66711e17	1.56016	0.780081	+	0.625679i	$0.215178\pi$
$504$	−1.38455e15	−0.00376278
$505$	−8.01866e17	−2.15134
$506$	−1.64854e16	−0.0436637
$507$	1.60182e17	0.418853
$508$	−9.06760e16	−0.234087
$509$	−7.57570e17	−1.93089	−0.965444	−	0.260611i	$-0.916076\pi$
$509$	−7.57570e17	−1.93089	−0.965444	+	0.260611i	$0.916076\pi$
$510$	−8.91711e16	−0.224397
$511$	2.53938e16	0.0630944
$512$	−1.80144e16	−0.0441942
$513$	6.41089e17	1.55294
$514$	−4.56118e17	−1.09098
$515$	5.61767e17	1.32681
$516$	3.36066e16	0.0783793
$517$	−7.87026e16	−0.181259
$518$	−6.27142e15	−0.0142634
$519$	1.51383e17	0.340009
$520$	1.90687e17	0.422959
$521$	3.75972e17	0.823590	0.411795	−	0.911277i	$-0.364902\pi$
$521$	3.75972e17	0.823590	0.411795	+	0.911277i	$0.364902\pi$
$522$	−5.41889e16	−0.117234
$523$	3.34023e16	0.0713700	0.0356850	−	0.999363i	$-0.488639\pi$
$523$	3.34023e16	0.0713700	0.0356850	+	0.999363i	$0.488639\pi$
$524$	2.10679e17	0.444599
$525$	4.06971e16	0.0848257
$526$	−5.32493e17	−1.09624
$527$	1.01650e17	0.206698
$528$	3.31879e16	0.0666591
$529$	2.19146e16	0.0434783
$530$	−8.36649e17	−1.63965
$531$	4.17640e16	0.0808514
$532$	−2.13129e16	−0.0407583
$533$	−3.10871e17	−0.587291
$534$	−6.26379e17	−1.16901
$535$	−4.42559e17	−0.815965
$536$	2.76372e17	0.503412
$537$	3.84277e17	0.691531
$538$	6.30278e17	1.12059
$539$	1.68055e17	0.295206
$540$	5.04665e17	0.875878
$541$	−8.94028e17	−1.53309	−0.766547	−	0.642188i	$-0.778027\pi$
$541$	−8.94028e17	−1.53309	−0.766547	+	0.642188i	$0.778027\pi$
$542$	4.08873e17	0.692776
$543$	−2.13582e17	−0.357574
$544$	2.30241e16	0.0380881
$545$	−1.53132e18	−2.50316
$546$	1.62020e16	0.0261707
$547$	−4.75904e17	−0.759630	−0.379815	−	0.925062i	$-0.624012\pi$
$547$	−4.75904e17	−0.759630	−0.379815	+	0.925062i	$0.624012\pi$
$548$	−2.07940e16	−0.0327993
$549$	9.65952e16	0.150569
$550$	2.27842e17	0.350975
$551$	−8.34151e17	−1.26987
$552$	−4.41179e16	−0.0663760
$553$	−1.64360e16	−0.0244389
$554$	−4.18760e17	−0.615391
$555$	3.63910e17	0.528554
$556$	3.84041e17	0.551304
$557$	−3.86695e17	−0.548669	−0.274334	−	0.961634i	$-0.588458\pi$
$557$	−3.86695e17	−0.548669	−0.274334	+	0.961634i	$0.588458\pi$
$558$	−9.15835e16	−0.128438
$559$	9.18508e16	0.127323
$560$	−1.67775e16	−0.0229882
$561$	−4.24173e16	−0.0574492
$562$	−2.85150e17	−0.381758
$563$	3.97025e17	0.525428	0.262714	−	0.964874i	$-0.415382\pi$
$563$	3.97025e17	0.525428	0.262714	+	0.964874i	$0.415382\pi$
$564$	−2.10622e17	−0.275544
$565$	−5.85428e16	−0.0757109
$566$	7.19331e17	0.919649
$567$	3.44590e16	0.0435525
$568$	1.35953e17	0.169874
$569$	−5.77929e17	−0.713912	−0.356956	−	0.934121i	$-0.616185\pi$
$569$	−5.77929e17	−0.713912	−0.356956	+	0.934121i	$0.616185\pi$
$570$	1.23672e18	1.51037
$571$	−1.26045e18	−1.52192	−0.760960	−	0.648799i	$-0.775272\pi$
$571$	−1.26045e18	−1.52192	−0.760960	+	0.648799i	$0.775272\pi$
$572$	9.07066e16	0.108284
$573$	1.12759e18	1.33090
$574$	2.73519e16	0.0319198
$575$	−3.02879e17	−0.349484
$576$	−2.07441e16	−0.0236673
$577$	1.53617e18	1.73299	0.866497	−	0.499182i	$-0.166366\pi$
$577$	1.53617e18	1.73299	0.866497	+	0.499182i	$0.166366\pi$
$578$	6.04466e17	0.674281
$579$	3.36884e17	0.371595
$580$	−6.56644e17	−0.716223
$581$	−4.38137e15	−0.00472568
$582$	3.21431e17	0.342837
$583$	−3.97981e17	−0.419775
$584$	3.80464e17	0.396853
$585$	2.19581e17	0.226507
$586$	3.08216e17	0.314427
$587$	−1.20239e18	−1.21310	−0.606551	−	0.795044i	$-0.707448\pi$
$587$	−1.20239e18	−1.21310	−0.606551	+	0.795044i	$0.707448\pi$
$588$	4.49747e17	0.448761
$589$	−1.40978e18	−1.39124
$590$	5.06082e17	0.493950
$591$	8.98249e16	0.0867118
$592$	−9.39620e16	−0.0897142
$593$	−1.26501e18	−1.19464	−0.597320	−	0.802003i	$-0.703768\pi$
$593$	−1.26501e18	−1.19464	−0.597320	+	0.802003i	$0.703768\pi$
$594$	2.40061e17	0.224238
$595$	2.14432e16	0.0198120
$596$	−8.71419e17	−0.796391
$597$	−1.21312e18	−1.09666
$598$	−1.20580e17	−0.107824
$599$	−2.13762e18	−1.89085	−0.945425	−	0.325840i	$-0.894353\pi$
$599$	−2.13762e18	−1.89085	−0.945425	+	0.325840i	$0.894353\pi$
$600$	6.09747e17	0.533539
$601$	8.42319e17	0.729109	0.364554	−	0.931182i	$-0.381221\pi$
$601$	8.42319e17	0.729109	0.364554	+	0.931182i	$0.381221\pi$
$602$	−8.08146e15	−0.00692010
$603$	3.18250e17	0.269592
$604$	5.14160e17	0.430882
$605$	−1.80010e18	−1.49240
$606$	−1.02079e18	−0.837268
$607$	4.78264e17	0.388098	0.194049	−	0.980992i	$-0.437838\pi$
$607$	4.78264e17	0.388098	0.194049	+	0.980992i	$0.437838\pi$
$608$	−3.19322e17	−0.256363
$609$	−5.57928e16	−0.0443165
$610$	1.17051e18	0.919879
$611$	−5.75656e17	−0.447606
$612$	2.65129e16	0.0203973
$613$	2.50182e18	1.90442	0.952209	−	0.305446i	$-0.0988055\pi$
$613$	2.50182e18	1.90442	0.952209	+	0.305446i	$0.0988055\pi$
$614$	−3.40223e17	−0.256253
$615$	−1.58714e18	−1.18284
$616$	−7.98078e15	−0.00588533
$617$	1.28686e18	0.939026	0.469513	−	0.882926i	$-0.344430\pi$
$617$	1.28686e18	0.939026	0.469513	+	0.882926i	$0.344430\pi$
$618$	7.15139e17	0.516375
$619$	1.84952e18	1.32151	0.660756	−	0.750601i	$-0.270236\pi$
$619$	1.84952e18	1.32151	0.660756	+	0.750601i	$0.270236\pi$
$620$	−1.10978e18	−0.784676
$621$	−3.19122e17	−0.223286
$622$	−9.28255e16	−0.0642731
$623$	1.50627e17	0.103212
$624$	2.42747e17	0.164609
$625$	1.98388e17	0.133136
$626$	−7.61278e17	−0.505603
$627$	5.88286e17	0.386678
$628$	−8.65162e17	−0.562808
$629$	1.20092e17	0.0773189
$630$	−1.93197e16	−0.0123108
$631$	1.93407e18	1.21978	0.609889	−	0.792487i	$-0.291214\pi$
$631$	1.93407e18	1.21978	0.609889	+	0.792487i	$0.291214\pi$
$632$	−2.46253e17	−0.153717
$633$	−2.27022e18	−1.40263
$634$	−7.29569e17	−0.446156
$635$	−1.26528e18	−0.765873
$636$	−1.06507e18	−0.638126
$637$	1.22921e18	0.728988
$638$	−3.12355e17	−0.183364
$639$	1.56554e17	0.0909722
$640$	−2.51370e17	−0.144592
$641$	−2.37208e18	−1.35068	−0.675338	−	0.737508i	$-0.736002\pi$
$641$	−2.37208e18	−1.35068	−0.675338	+	0.737508i	$0.736002\pi$
$642$	−5.63385e17	−0.317561
$643$	2.84643e18	1.58829	0.794143	−	0.607731i	$-0.207920\pi$
$643$	2.84643e18	1.58829	0.794143	+	0.607731i	$0.207920\pi$
$644$	1.06091e16	0.00586033
$645$	4.68941e17	0.256436
$646$	4.08123e17	0.220943
$647$	2.59575e18	1.39118	0.695591	−	0.718438i	$-0.255142\pi$
$647$	2.59575e18	1.39118	0.695591	+	0.718438i	$0.255142\pi$
$648$	5.16285e17	0.273938
$649$	2.40735e17	0.126459
$650$	1.66651e18	0.866705
$651$	−9.42940e16	−0.0485521
$652$	−1.88311e18	−0.959990
$653$	−2.46807e18	−1.24573	−0.622863	−	0.782331i	$-0.714031\pi$
$653$	−2.46807e18	−1.24573	−0.622863	+	0.782331i	$0.714031\pi$
$654$	−1.94940e18	−0.974194
$655$	2.93978e18	1.45461
$656$	4.09801e17	0.200770
$657$	4.38115e17	0.212526
$658$	5.06489e16	0.0243277
$659$	3.14017e18	1.49348	0.746739	−	0.665118i	$-0.231619\pi$
$659$	3.14017e18	1.49348	0.746739	+	0.665118i	$0.231619\pi$
$660$	4.63099e17	0.218091
$661$	2.32109e18	1.08239	0.541193	−	0.840898i	$-0.317973\pi$
$661$	2.32109e18	1.08239	0.541193	+	0.840898i	$0.317973\pi$
$662$	1.48765e18	0.686947
$663$	−3.10254e17	−0.141866
$664$	−6.56442e16	−0.0297237
$665$	−2.97396e17	−0.133350
$666$	−1.08200e17	−0.0480445
$667$	4.15225e17	0.182585
$668$	−7.17566e17	−0.312475
$669$	−2.38880e18	−1.03017
$670$	3.85645e18	1.64703
$671$	5.56793e17	0.235503
$672$	−2.13580e16	−0.00894666
$673$	−9.03436e17	−0.374800	−0.187400	−	0.982284i	$-0.560006\pi$
$673$	−9.03436e17	−0.374800	−0.187400	+	0.982284i	$0.560006\pi$
$674$	−2.63450e18	−1.08245
$675$	4.41054e18	1.79480
$676$	−5.77119e17	−0.232601
$677$	2.09829e18	0.837605	0.418802	−	0.908077i	$-0.362450\pi$
$677$	2.09829e18	0.837605	0.418802	+	0.908077i	$0.362450\pi$
$678$	−7.45260e16	−0.0294656
$679$	−7.72952e16	−0.0302691
$680$	3.21274e17	0.124614
$681$	3.87480e17	0.148865
$682$	−5.27904e17	−0.200889
$683$	−3.26593e18	−1.23104	−0.615520	−	0.788121i	$-0.711054\pi$
$683$	−3.26593e18	−1.23104	−0.615520	+	0.788121i	$0.711054\pi$
$684$	−3.67708e17	−0.137290
$685$	−2.90156e17	−0.107311
$686$	−2.16646e17	−0.0793678
$687$	−2.55491e18	−0.927165
$688$	−1.21081e17	−0.0435263
$689$	−2.91096e18	−1.03660
$690$	−6.15614e17	−0.217165
$691$	8.00812e17	0.279849	0.139924	−	0.990162i	$-0.455314\pi$
$691$	8.00812e17	0.279849	0.139924	+	0.990162i	$0.455314\pi$
$692$	−5.45419e17	−0.188817
$693$	−9.19009e15	−0.00315177
$694$	2.67764e18	0.909737
$695$	5.35884e18	1.80372
$696$	−8.35919e17	−0.278743
$697$	−5.23764e17	−0.173031
$698$	−1.37779e18	−0.450943
$699$	2.20435e18	0.714790
$700$	−1.46627e17	−0.0471062
$701$	3.02588e18	0.963129	0.481565	−	0.876411i	$-0.340069\pi$
$701$	3.02588e18	0.963129	0.481565	+	0.876411i	$0.340069\pi$
$702$	1.75589e18	0.553739
$703$	−1.66556e18	−0.520416
$704$	−1.19573e17	−0.0370177
$705$	−2.93899e18	−0.901507
$706$	1.08041e17	0.0328366
$707$	2.45472e17	0.0739223
$708$	6.44252e17	0.192238
$709$	8.12420e17	0.240204	0.120102	−	0.992762i	$-0.461678\pi$
$709$	8.12420e17	0.240204	0.120102	+	0.992762i	$0.461678\pi$
$710$	1.89707e18	0.555782
$711$	−2.83567e17	−0.0823197
$712$	2.25678e18	0.649186
$713$	7.01762e17	0.200036
$714$	2.72976e16	0.00771055
$715$	1.26571e18	0.354277
$716$	−1.38451e18	−0.384027
$717$	2.62032e18	0.720244
$718$	−3.39342e18	−0.924333
$719$	−5.84702e18	−1.57833	−0.789163	−	0.614184i	$-0.789485\pi$
$719$	−5.84702e18	−1.57833	−0.789163	+	0.614184i	$0.789485\pi$
$720$	−2.89459e17	−0.0774331
$721$	−1.71971e17	−0.0455907
$722$	−2.96887e18	−0.780009
$723$	1.00994e18	0.262965
$724$	7.69514e17	0.198571
$725$	−5.73876e18	−1.46765
$726$	−2.29156e18	−0.580821
$727$	3.07765e17	0.0773118	0.0386559	−	0.999253i	$-0.487692\pi$
$727$	3.07765e17	0.0773118	0.0386559	+	0.999253i	$0.487692\pi$
$728$	−5.83741e16	−0.0145334
$729$	4.50179e18	1.11085
$730$	5.30893e18	1.29840
$731$	1.54753e17	0.0375125
$732$	1.49008e18	0.358003
$733$	4.60541e18	1.09671	0.548356	−	0.836245i	$-0.315254\pi$
$733$	4.60541e18	1.09671	0.548356	+	0.836245i	$0.315254\pi$
$734$	2.32800e17	0.0549488
$735$	6.27569e18	1.46823
$736$	1.58952e17	0.0368605
$737$	1.83445e18	0.421666
$738$	4.71898e17	0.107518
$739$	−6.58034e17	−0.148614	−0.0743069	−	0.997235i	$-0.523674\pi$
$739$	−6.58034e17	−0.148614	−0.0743069	+	0.997235i	$0.523674\pi$
$740$	−1.31113e18	−0.293521
$741$	4.30292e18	0.954871
$742$	2.56120e17	0.0563401
$743$	−2.55703e18	−0.557581	−0.278791	−	0.960352i	$-0.589934\pi$
$743$	−2.55703e18	−0.557581	−0.278791	+	0.960352i	$0.589934\pi$
$744$	−1.41277e18	−0.305384
$745$	−1.21596e19	−2.60558
$746$	−6.36979e18	−1.35308
$747$	−7.55911e16	−0.0159179
$748$	1.52825e17	0.0319032
$749$	1.35479e17	0.0280375
$750$	3.43196e18	0.704115
$751$	−1.69390e18	−0.344531	−0.172266	−	0.985051i	$-0.555109\pi$
$751$	−1.69390e18	−0.344531	−0.172266	+	0.985051i	$0.555109\pi$
$752$	7.58851e17	0.153017
$753$	−2.82793e18	−0.565330
$754$	−2.28467e18	−0.452803
$755$	7.17451e18	1.40973
$756$	−1.54491e17	−0.0300962
$757$	2.09315e18	0.404276	0.202138	−	0.979357i	$-0.435211\pi$
$757$	2.09315e18	0.404276	0.202138	+	0.979357i	$0.435211\pi$
$758$	−2.08984e18	−0.400188
$759$	−2.92838e17	−0.0555976
$760$	−4.45576e18	−0.838752
$761$	−4.67350e18	−0.872253	−0.436126	−	0.899885i	$-0.643650\pi$
$761$	−4.67350e18	−0.872253	−0.436126	+	0.899885i	$0.643650\pi$
$762$	−1.61072e18	−0.298066
$763$	4.68777e17	0.0860115
$764$	−4.06258e18	−0.739085
$765$	3.69956e17	0.0667346
$766$	−3.37850e18	−0.604279
$767$	1.76082e18	0.312280
$768$	−3.19998e17	−0.0562730
$769$	−4.89213e18	−0.853055	−0.426527	−	0.904475i	$-0.640263\pi$
$769$	−4.89213e18	−0.853055	−0.426527	+	0.904475i	$0.640263\pi$
$770$	−1.11363e17	−0.0192553
$771$	−8.10225e18	−1.38916
$772$	−1.21376e18	−0.206358
$773$	6.87828e18	1.15961	0.579807	−	0.814754i	$-0.303128\pi$
$773$	6.87828e18	1.15961	0.579807	+	0.814754i	$0.303128\pi$
$774$	−1.39428e17	−0.0233096
$775$	−9.69895e18	−1.60792
$776$	−1.15808e18	−0.190387
$777$	−1.11402e17	−0.0181617
$778$	4.40298e18	0.711834
$779$	7.26410e18	1.16463
$780$	3.38726e18	0.538559
$781$	9.02407e17	0.142289
$782$	−2.03156e17	−0.0317677
$783$	−6.04653e18	−0.937680
$784$	−1.62039e18	−0.249210
$785$	−1.20723e19	−1.84136
$786$	3.74239e18	0.566113
$787$	6.31489e18	0.947392	0.473696	−	0.880688i	$-0.342920\pi$
$787$	6.31489e18	0.947392	0.473696	+	0.880688i	$0.342920\pi$
$788$	−3.23630e17	−0.0481535
$789$	−9.45893e18	−1.39586
$790$	−3.43618e18	−0.502920
$791$	1.79214e16	0.00260151
$792$	−1.37691e17	−0.0198241
$793$	4.07256e18	0.581557
$794$	3.43469e18	0.486468
$795$	−1.48618e19	−2.08778
$796$	4.37075e18	0.609005
$797$	4.72048e16	0.00652390	0.00326195	−	0.999995i	$-0.498962\pi$
$797$	4.72048e16	0.00652390	0.00326195	+	0.999995i	$0.498962\pi$
$798$	−3.78591e17	−0.0518980
$799$	−9.69882e17	−0.131876
$800$	−2.19686e18	−0.296290
$801$	2.59874e18	0.347658
$802$	−4.14090e18	−0.549492
$803$	2.52537e18	0.332411
$804$	4.90933e18	0.641000
$805$	1.48038e17	0.0191735
$806$	−3.86126e18	−0.496080
$807$	1.11959e19	1.42686
$808$	3.67780e18	0.464959
$809$	7.73158e18	0.969623	0.484812	−	0.874619i	$-0.338888\pi$
$809$	7.73158e18	0.969623	0.484812	+	0.874619i	$0.338888\pi$
$810$	7.20416e18	0.896253
$811$	1.10174e19	1.35970	0.679849	−	0.733352i	$-0.262045\pi$
$811$	1.10174e19	1.35970	0.679849	+	0.733352i	$0.262045\pi$
$812$	2.01016e17	0.0246102
$813$	7.26301e18	0.882121
$814$	−6.23684e17	−0.0751460
$815$	−2.62766e19	−3.14084
$816$	4.08988e17	0.0484981
$817$	−2.14627e18	−0.252488
$818$	4.04860e18	0.472507
$819$	−6.72194e16	−0.00778303
$820$	5.71830e18	0.656867
$821$	4.99991e17	0.0569812	0.0284906	−	0.999594i	$-0.490930\pi$
$821$	4.99991e17	0.0569812	0.0284906	+	0.999594i	$0.490930\pi$
$822$	−3.69374e17	−0.0417637
$823$	−9.19701e18	−1.03169	−0.515843	−	0.856683i	$-0.672521\pi$
$823$	−9.19701e18	−1.03169	−0.515843	+	0.856683i	$0.672521\pi$
$824$	−2.57657e18	−0.286758
$825$	4.04727e18	0.446901
$826$	−1.54925e17	−0.0169727
$827$	1.31170e19	1.42577	0.712884	−	0.701282i	$-0.247388\pi$
$827$	1.31170e19	1.42577	0.712884	+	0.701282i	$0.247388\pi$
$828$	1.83038e17	0.0197399
$829$	1.85140e19	1.98106	0.990528	−	0.137311i	$-0.0438460\pi$
$829$	1.85140e19	1.98106	0.990528	+	0.137311i	$0.0438460\pi$
$830$	−9.15988e17	−0.0972483
$831$	−7.43863e18	−0.783585
$832$	−8.74594e17	−0.0914124
$833$	2.07101e18	0.214778
$834$	6.82190e18	0.701982
$835$	−1.00128e19	−1.02234
$836$	−2.11953e18	−0.214733
$837$	−1.02191e19	−1.02730
$838$	−2.73266e18	−0.272584
$839$	−7.02480e18	−0.695315	−0.347657	−	0.937622i	$-0.613023\pi$
$839$	−7.02480e18	−0.695315	−0.347657	+	0.937622i	$0.613023\pi$
$840$	−2.98027e17	−0.0292711
$841$	−2.39320e18	−0.233241
$842$	2.27583e18	0.220096
$843$	−5.06526e18	−0.486097
$844$	8.17936e18	0.778921
$845$	−8.05302e18	−0.761010
$846$	8.73838e17	0.0819452
$847$	5.51056e17	0.0512807
$848$	3.83733e18	0.354370
$849$	1.27778e19	1.17100
$850$	2.80779e18	0.255353
$851$	8.29085e17	0.0748268
$852$	2.41501e18	0.216302
$853$	−1.09706e17	−0.00975128	−0.00487564	−	0.999988i	$-0.501552\pi$
$853$	−1.09706e17	−0.00975128	−0.00487564	+	0.999988i	$0.501552\pi$
$854$	−3.58323e17	−0.0316081
$855$	−5.13093e18	−0.449176
$856$	2.02982e18	0.176351
$857$	8.54144e18	0.736471	0.368236	−	0.929733i	$-0.379962\pi$
$857$	8.54144e18	0.736471	0.368236	+	0.929733i	$0.379962\pi$
$858$	1.61127e18	0.137879
$859$	−8.52295e18	−0.723827	−0.361913	−	0.932212i	$-0.617876\pi$
$859$	−8.52295e18	−0.723827	−0.361913	+	0.932212i	$0.617876\pi$
$860$	−1.68955e18	−0.142407
$861$	4.85864e17	0.0406438
$862$	1.44568e19	1.20026
$863$	7.83483e18	0.645594	0.322797	−	0.946468i	$-0.395377\pi$
$863$	7.83483e18	0.645594	0.322797	+	0.946468i	$0.395377\pi$
$864$	−2.31467e18	−0.189300
$865$	−7.61069e18	−0.617759
$866$	−1.22575e19	−0.987495
$867$	1.07374e19	0.858570
$868$	3.39732e17	0.0269624
$869$	−1.63453e18	−0.128755
$870$	−1.16643e19	−0.911975
$871$	1.34178e19	1.04127
$872$	7.02348e18	0.540998
$873$	−1.33356e18	−0.101958
$874$	2.81757e18	0.213821
$875$	−8.25291e17	−0.0621663
$876$	6.75836e18	0.505318
$877$	1.84618e19	1.37018	0.685090	−	0.728459i	$-0.259763\pi$
$877$	1.84618e19	1.37018	0.685090	+	0.728459i	$0.259763\pi$
$878$	−1.72338e19	−1.26960
$879$	5.47498e18	0.400364
$880$	−1.66850e18	−0.121112
$881$	1.02853e19	0.741091	0.370546	−	0.928814i	$-0.379171\pi$
$881$	1.02853e19	0.741091	0.370546	+	0.928814i	$0.379171\pi$
$882$	−1.86593e18	−0.133459
$883$	−2.63873e19	−1.87348	−0.936742	−	0.350022i	$-0.886174\pi$
$883$	−2.63873e19	−1.87348	−0.936742	+	0.350022i	$0.886174\pi$
$884$	1.11781e18	0.0787824
$885$	8.98978e18	0.628953
$886$	3.48323e18	0.241915
$887$	3.43400e18	0.236754	0.118377	−	0.992969i	$-0.462231\pi$
$887$	3.43400e18	0.236754	0.118377	+	0.992969i	$0.462231\pi$
$888$	−1.66909e18	−0.114234
$889$	3.87334e17	0.0263163
$890$	3.14907e19	2.12397
$891$	3.42690e18	0.229455
$892$	8.60661e18	0.572085
$893$	1.34513e19	0.887627
$894$	−1.54794e19	−1.01405
$895$	−1.93192e19	−1.25644
$896$	7.69508e16	0.00496834
$897$	−2.14191e18	−0.137294
$898$	1.37288e19	0.873649
$899$	1.32966e19	0.840043
$900$	−2.52974e18	−0.158672
$901$	−4.90447e18	−0.305408
$902$	2.72011e18	0.168168
$903$	−1.43555e17	−0.00881145
$904$	2.68509e17	0.0163631
$905$	1.07377e19	0.649673
$906$	9.13328e18	0.548648
$907$	5.65800e18	0.337455	0.168727	−	0.985663i	$-0.446034\pi$
$907$	5.65800e18	0.337455	0.168727	+	0.985663i	$0.446034\pi$
$908$	−1.39605e18	−0.0826692
$909$	4.23509e18	0.248999
$910$	−8.14542e17	−0.0475493
$911$	−1.06394e19	−0.616665	−0.308333	−	0.951279i	$-0.599771\pi$
$911$	−1.06394e19	−0.616665	−0.308333	+	0.951279i	$0.599771\pi$
$912$	−5.67226e18	−0.326430
$913$	−4.35721e17	−0.0248971
$914$	1.90644e19	1.08162
$915$	2.07923e19	1.17129
$916$	9.20508e18	0.514881
$917$	−8.99943e17	−0.0499821
$918$	2.95837e18	0.163145
$919$	2.20655e19	1.20827	0.604134	−	0.796883i	$-0.293519\pi$
$919$	2.20655e19	1.20827	0.604134	+	0.796883i	$0.293519\pi$
$920$	2.21799e18	0.120598
$921$	−6.04354e18	−0.326290
$922$	1.12704e19	0.604212
$923$	6.60050e18	0.351371
$924$	−1.41767e17	−0.00749386
$925$	−1.14587e19	−0.601468
$926$	−1.23707e19	−0.644797
$927$	−2.96699e18	−0.153567
$928$	3.01173e18	0.154794
$929$	−2.05129e18	−0.104695	−0.0523474	−	0.998629i	$-0.516670\pi$
$929$	−2.05129e18	−0.104695	−0.0523474	+	0.998629i	$0.516670\pi$
$930$	−1.97135e19	−0.999138
$931$	−2.87229e19	−1.44562
$932$	−7.94204e18	−0.396943
$933$	−1.64890e18	−0.0818398
$934$	−1.48222e19	−0.730562
$935$	2.13250e18	0.104379
$936$	−1.00712e18	−0.0489540
$937$	1.60702e18	0.0775736	0.0387868	−	0.999248i	$-0.487651\pi$
$937$	1.60702e18	0.0775736	0.0387868	+	0.999248i	$0.487651\pi$
$938$	−1.18056e18	−0.0565939
$939$	−1.35229e19	−0.643791
$940$	1.05889e19	0.500633
$941$	−3.09526e19	−1.45333	−0.726665	−	0.686992i	$-0.758931\pi$
$941$	−3.09526e19	−1.45333	−0.726665	+	0.686992i	$0.758931\pi$
$942$	−1.53683e19	−0.716630
$943$	−3.61594e18	−0.167454
$944$	−2.32117e18	−0.106755
$945$	−2.15574e18	−0.0984668
$946$	−8.03690e17	−0.0364583
$947$	−3.93763e19	−1.77403	−0.887014	−	0.461743i	$-0.847224\pi$
$947$	−3.93763e19	−1.77403	−0.887014	+	0.461743i	$0.847224\pi$
$948$	−4.37431e18	−0.195729
$949$	1.84714e19	0.820861
$950$	−3.89413e19	−1.71873
$951$	−1.29597e19	−0.568095
$952$	−9.83503e16	−0.00428189
$953$	−2.24776e19	−0.971953	−0.485976	−	0.873972i	$-0.661536\pi$
$953$	−2.24776e19	−0.971953	−0.485976	+	0.873972i	$0.661536\pi$
$954$	4.41880e18	0.189775
$955$	−5.66885e19	−2.41809
$956$	−9.44075e18	−0.399972
$957$	−5.54852e18	−0.233480
$958$	2.24604e19	0.938731
$959$	8.88242e16	0.00368732
$960$	−4.46521e18	−0.184110
$961$	−1.94534e18	−0.0796697
$962$	−4.56183e18	−0.185567
$963$	2.33739e18	0.0944411
$964$	−3.63872e18	−0.146032
$965$	−1.69366e19	−0.675148
$966$	1.88455e17	0.00746203
$967$	−1.92950e19	−0.758880	−0.379440	−	0.925216i	$-0.623883\pi$
$967$	−1.92950e19	−0.758880	−0.379440	+	0.925216i	$0.623883\pi$
$968$	8.25624e18	0.322547
$969$	7.24968e18	0.281329
$970$	−1.61597e19	−0.622898
$971$	2.08769e19	0.799357	0.399678	−	0.916655i	$-0.369122\pi$
$971$	2.08769e19	0.799357	0.399678	+	0.916655i	$0.369122\pi$
$972$	−4.90650e18	−0.186612
$973$	−1.64048e18	−0.0619780
$974$	9.72756e18	0.365065
$975$	2.96030e19	1.10359
$976$	−5.36860e18	−0.198810
$977$	2.71300e19	0.998011	0.499005	−	0.866599i	$-0.333699\pi$
$977$	2.71300e19	0.998011	0.499005	+	0.866599i	$0.333699\pi$
$978$	−3.34506e19	−1.22237
$979$	1.49796e19	0.543768
$980$	−2.26107e19	−0.815350
$981$	8.08773e18	0.289720
$982$	−3.09867e19	−1.10268
$983$	−1.55300e19	−0.549000	−0.274500	−	0.961587i	$-0.588512\pi$
$983$	−1.55300e19	−0.549000	−0.274500	+	0.961587i	$0.588512\pi$
$984$	7.27950e18	0.255643
$985$	−4.51588e18	−0.157546
$986$	−3.84927e18	−0.133407
$987$	8.99701e17	0.0309768
$988$	−1.55030e19	−0.530267
$989$	1.06837e18	0.0363034
$990$	−1.92132e18	−0.0648592
$991$	−3.50778e19	−1.17640	−0.588198	−	0.808717i	$-0.700162\pi$
$991$	−3.50778e19	−1.17640	−0.588198	+	0.808717i	$0.700162\pi$
$992$	5.09006e18	0.169589
$993$	2.64258e19	0.874698
$994$	−5.80742e17	−0.0190973
$995$	6.09887e19	1.99250
$996$	−1.16607e18	−0.0378476
$997$	4.58430e19	1.47827	0.739136	−	0.673556i	$-0.235234\pi$
$997$	4.58430e19	1.47827	0.739136	+	0.673556i	$0.235234\pi$
$998$	1.63760e19	0.524638
$999$	−1.20732e19	−0.384279

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.14.a.a.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.14.a.a.1.2	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	46.a (trivial)

\(f(q)\)	\(=\)	\(q-64.0000 q^{2} -1136.86 q^{3} +4096.00 q^{4} +57154.9 q^{5} +72759.2 q^{6} -17496.6 q^{7} -262144. q^{8} -301866. q^{9} -3.65791e6 q^{10} -1.74001e6 q^{11} -4.65659e6 q^{12} -1.27270e7 q^{13} +1.11978e6 q^{14} -6.49773e7 q^{15} +1.67772e7 q^{16} -2.14428e7 q^{17} +1.93194e7 q^{18} +2.97391e8 q^{19} +2.34107e8 q^{20} +1.98912e7 q^{21} +1.11361e8 q^{22} -1.48036e8 q^{23} +2.98022e8 q^{24} +2.04598e9 q^{25} +8.14529e8 q^{26} +2.15571e9 q^{27} -7.16660e7 q^{28} -2.80489e9 q^{29} +4.15855e9 q^{30} -4.74049e9 q^{31} -1.07374e9 q^{32} +1.97815e9 q^{33} +1.37234e9 q^{34} -1.00002e9 q^{35} -1.23644e9 q^{36} -5.60057e9 q^{37} -1.90330e10 q^{38} +1.44689e10 q^{39} -1.49828e10 q^{40} +2.44261e10 q^{41} -1.27304e9 q^{42} -7.21699e9 q^{43} -7.12709e9 q^{44} -1.72531e10 q^{45} +9.47430e9 q^{46} +4.52310e10 q^{47} -1.90734e10 q^{48} -9.65829e10 q^{49} -1.30943e11 q^{50} +2.43776e10 q^{51} -5.21299e10 q^{52} +2.28723e11 q^{53} -1.37965e11 q^{54} -9.94502e10 q^{55} +4.58663e9 q^{56} -3.38093e11 q^{57} +1.79513e11 q^{58} -1.38353e11 q^{59} -2.66147e11 q^{60} -3.19994e11 q^{61} +3.03391e11 q^{62} +5.28163e9 q^{63} +6.87195e10 q^{64} -7.27412e11 q^{65} -1.26602e11 q^{66} -1.05428e12 q^{67} -8.78299e10 q^{68} +1.68296e11 q^{69} +6.40010e10 q^{70} -5.18621e11 q^{71} +7.91324e10 q^{72} -1.45135e12 q^{73} +3.58437e11 q^{74} -2.32600e12 q^{75} +1.21812e12 q^{76} +3.04443e10 q^{77} -9.26008e11 q^{78} +9.39381e11 q^{79} +9.58900e11 q^{80} -1.96947e12 q^{81} -1.56327e12 q^{82} +2.50413e11 q^{83} +8.14744e10 q^{84} -1.22556e12 q^{85} +4.61888e11 q^{86} +3.18878e12 q^{87} +4.56134e11 q^{88} -8.60893e12 q^{89} +1.10420e12 q^{90} +2.22679e11 q^{91} -6.06355e11 q^{92} +5.38928e12 q^{93} -2.89479e12 q^{94} +1.69974e13 q^{95} +1.22070e12 q^{96} +4.41773e12 q^{97} +6.18130e12 q^{98} +5.25251e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 320 q^{2} + 690 q^{3} + 20480 q^{4} - 71798 q^{5} - 44160 q^{6} + 31366 q^{7} - 1310720 q^{8} + 3522701 q^{9} + 4595072 q^{10} - 7592076 q^{11} + 2826240 q^{12} + 28315858 q^{13} - 2007424 q^{14}+ \cdots - 14853301668582 q^{99}+O(q^{100}) \) 5 * q - 320 * q^2 + 690 * q^3 + 20480 * q^4 - 71798 * q^5 - 44160 * q^6 + 31366 * q^7 - 1310720 * q^8 + 3522701 * q^9 + 4595072 * q^10 - 7592076 * q^11 + 2826240 * q^12 + 28315858 * q^13 - 2007424 * q^14 - 86510134 * q^15 + 83886080 * q^16 - 148779352 * q^17 - 225452864 * q^18 + 208568226 * q^19 - 294084608 * q^20 - 376070558 * q^21 + 485892864 * q^22 - 740179445 * q^23 - 180879360 * q^24 + 4178813107 * q^25 - 1812214912 * q^26 + 6759494334 * q^27 + 128475136 * q^28 - 2797854522 * q^29 + 5536648576 * q^30 + 10251920410 * q^31 - 5368709120 * q^32 + 16966481802 * q^33 + 9521878528 * q^34 + 20954998696 * q^35 + 14428983296 * q^36 + 15840804470 * q^37 - 13348366464 * q^38 + 34201839550 * q^39 + 18821414912 * q^40 - 63837021618 * q^41 + 24068515712 * q^42 - 100763331186 * q^43 - 31097143296 * q^44 - 277396545728 * q^45 + 47371484480 * q^46 - 174976267710 * q^47 + 11576279040 * q^48 - 219104642047 * q^49 - 267444038848 * q^50 + 111262053138 * q^51 + 115981754368 * q^52 + 89802813568 * q^53 - 432607637376 * q^54 + 103862253116 * q^55 - 8222408704 * q^56 - 1409625112972 * q^57 + 179062689408 * q^58 - 1238416781664 * q^59 - 354345508864 * q^60 - 1267556050856 * q^61 - 656122906240 * q^62 - 1901815038072 * q^63 + 343597383680 * q^64 - 2745162221118 * q^65 - 1085854835328 * q^66 - 1575419391340 * q^67 - 609400225792 * q^68 - 102144763410 * q^69 - 1341119916544 * q^70 - 1683993935490 * q^71 - 923454930944 * q^72 - 1127194561170 * q^73 - 1013811486080 * q^74 - 7122659318494 * q^75 + 854295453696 * q^76 - 44261676728 * q^77 - 2188917731200 * q^78 - 1151083218244 * q^79 - 1204570554368 * q^80 + 2254336417973 * q^81 + 4085569383552 * q^82 - 846457405404 * q^83 - 1540385005568 * q^84 + 7375916269256 * q^85 + 6448853195904 * q^86 - 2306908932150 * q^87 + 1990217170944 * q^88 - 11559404717682 * q^89 + 17753378926592 * q^90 - 8233703279434 * q^91 - 3031775006720 * q^92 - 1468162531188 * q^93 + 11198481133440 * q^94 + 11131929151492 * q^95 - 740881858560 * q^96 - 2048127950232 * q^97 + 14022697091008 * q^98 - 14853301668582 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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