Properties

Label 1.46.a.a.1.1
Level $1$
Weight $46$
Character 1.1
Self dual yes
Analytic conductor $12.826$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 46 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.8255726074\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - x^{2} - 148878150 x + 389915850150\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{14}\cdot 3^{6}\cdot 5 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-13344.8\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} +O(q^{10})\) \(q-6.41537e6 q^{2} -1.72036e10 q^{3} +5.97255e12 q^{4} +2.46761e15 q^{5} +1.10367e17 q^{6} +1.29065e19 q^{7} +1.87405e20 q^{8} -2.65835e21 q^{9} -1.58306e22 q^{10} +7.78755e22 q^{11} -1.02749e23 q^{12} -1.84585e25 q^{13} -8.27997e25 q^{14} -4.24517e25 q^{15} -1.41241e27 q^{16} -2.82858e27 q^{17} +1.70543e28 q^{18} +8.52388e28 q^{19} +1.47379e28 q^{20} -2.22037e29 q^{21} -4.99600e29 q^{22} -2.09625e30 q^{23} -3.22403e30 q^{24} -2.23326e31 q^{25} +1.18418e32 q^{26} +9.65579e31 q^{27} +7.70845e31 q^{28} -1.33372e33 q^{29} +2.72343e32 q^{30} -9.42299e32 q^{31} +2.46741e33 q^{32} -1.33974e33 q^{33} +1.81464e34 q^{34} +3.18481e34 q^{35} -1.58771e34 q^{36} -8.78606e34 q^{37} -5.46838e35 q^{38} +3.17552e35 q^{39} +4.62441e35 q^{40} +2.03901e36 q^{41} +1.42445e36 q^{42} -6.02099e36 q^{43} +4.65116e35 q^{44} -6.55977e36 q^{45} +1.34482e37 q^{46} -4.75078e37 q^{47} +2.42985e37 q^{48} +5.95698e37 q^{49} +1.43272e38 q^{50} +4.86617e37 q^{51} -1.10244e38 q^{52} -7.36820e38 q^{53} -6.19454e38 q^{54} +1.92166e38 q^{55} +2.41873e39 q^{56} -1.46641e39 q^{57} +8.55629e39 q^{58} -9.51309e39 q^{59} -2.53545e38 q^{60} -1.95631e39 q^{61} +6.04519e39 q^{62} -3.43099e40 q^{63} +3.38654e40 q^{64} -4.55483e40 q^{65} +8.59491e39 q^{66} +2.10749e41 q^{67} -1.68938e40 q^{68} +3.60631e40 q^{69} -2.04317e41 q^{70} -5.43331e41 q^{71} -4.98187e41 q^{72} +8.99506e41 q^{73} +5.63658e41 q^{74} +3.84201e41 q^{75} +5.09093e41 q^{76} +1.00510e42 q^{77} -2.03721e42 q^{78} -7.61415e41 q^{79} -3.48528e42 q^{80} +6.19245e42 q^{81} -1.30810e43 q^{82} +6.62221e42 q^{83} -1.32613e42 q^{84} -6.97983e42 q^{85} +3.86268e43 q^{86} +2.29447e43 q^{87} +1.45942e43 q^{88} -6.63932e43 q^{89} +4.20833e43 q^{90} -2.38234e44 q^{91} -1.25200e43 q^{92} +1.62109e43 q^{93} +3.04780e44 q^{94} +2.10336e44 q^{95} -4.24483e43 q^{96} +1.95163e44 q^{97} -3.82162e44 q^{98} -2.07020e44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3814272q^{2} + 5359866876q^{3} - 1915164893184q^{4} - 912448458460350q^{5} - 84402581069044224q^{6} - 7619710926638056008q^{7} - 108947667758662287360q^{8} + 1158701600689591796919q^{9} + O(q^{10}) \) \( 3q + 3814272q^{2} + 5359866876q^{3} - 1915164893184q^{4} - 912448458460350q^{5} - 84402581069044224q^{6} - 7619710926638056008q^{7} - \)\(10\!\cdots\!60\)\(q^{8} + \)\(11\!\cdots\!19\)\(q^{9} + \)\(14\!\cdots\!00\)\(q^{10} - \)\(29\!\cdots\!44\)\(q^{11} - \)\(33\!\cdots\!48\)\(q^{12} - \)\(24\!\cdots\!54\)\(q^{13} - \)\(20\!\cdots\!48\)\(q^{14} - \)\(11\!\cdots\!00\)\(q^{15} - \)\(25\!\cdots\!32\)\(q^{16} + \)\(11\!\cdots\!82\)\(q^{17} + \)\(29\!\cdots\!76\)\(q^{18} + \)\(13\!\cdots\!80\)\(q^{19} + \)\(38\!\cdots\!00\)\(q^{20} + \)\(22\!\cdots\!96\)\(q^{21} - \)\(36\!\cdots\!56\)\(q^{22} - \)\(10\!\cdots\!84\)\(q^{23} - \)\(10\!\cdots\!60\)\(q^{24} + \)\(43\!\cdots\!25\)\(q^{25} + \)\(10\!\cdots\!16\)\(q^{26} + \)\(28\!\cdots\!40\)\(q^{27} + \)\(53\!\cdots\!84\)\(q^{28} - \)\(67\!\cdots\!30\)\(q^{29} - \)\(44\!\cdots\!00\)\(q^{30} - \)\(43\!\cdots\!44\)\(q^{31} + \)\(27\!\cdots\!72\)\(q^{32} + \)\(32\!\cdots\!52\)\(q^{33} + \)\(53\!\cdots\!32\)\(q^{34} + \)\(15\!\cdots\!00\)\(q^{35} - \)\(10\!\cdots\!32\)\(q^{36} - \)\(38\!\cdots\!38\)\(q^{37} - \)\(29\!\cdots\!40\)\(q^{38} - \)\(40\!\cdots\!32\)\(q^{39} + \)\(14\!\cdots\!00\)\(q^{40} + \)\(27\!\cdots\!06\)\(q^{41} + \)\(55\!\cdots\!24\)\(q^{42} + \)\(12\!\cdots\!56\)\(q^{43} - \)\(10\!\cdots\!68\)\(q^{44} - \)\(36\!\cdots\!50\)\(q^{45} - \)\(29\!\cdots\!44\)\(q^{46} - \)\(53\!\cdots\!48\)\(q^{47} + \)\(14\!\cdots\!16\)\(q^{48} + \)\(78\!\cdots\!71\)\(q^{49} + \)\(36\!\cdots\!00\)\(q^{50} - \)\(37\!\cdots\!64\)\(q^{51} + \)\(13\!\cdots\!92\)\(q^{52} - \)\(18\!\cdots\!74\)\(q^{53} + \)\(59\!\cdots\!80\)\(q^{54} - \)\(34\!\cdots\!00\)\(q^{55} + \)\(52\!\cdots\!80\)\(q^{56} + \)\(10\!\cdots\!80\)\(q^{57} + \)\(13\!\cdots\!40\)\(q^{58} - \)\(35\!\cdots\!60\)\(q^{59} + \)\(13\!\cdots\!00\)\(q^{60} - \)\(51\!\cdots\!94\)\(q^{61} - \)\(56\!\cdots\!56\)\(q^{62} - \)\(63\!\cdots\!64\)\(q^{63} + \)\(41\!\cdots\!36\)\(q^{64} + \)\(37\!\cdots\!00\)\(q^{65} + \)\(22\!\cdots\!52\)\(q^{66} + \)\(14\!\cdots\!32\)\(q^{67} + \)\(12\!\cdots\!64\)\(q^{68} - \)\(91\!\cdots\!12\)\(q^{69} - \)\(61\!\cdots\!00\)\(q^{70} - \)\(12\!\cdots\!44\)\(q^{71} - \)\(11\!\cdots\!80\)\(q^{72} + \)\(54\!\cdots\!66\)\(q^{73} - \)\(92\!\cdots\!08\)\(q^{74} + \)\(46\!\cdots\!00\)\(q^{75} - \)\(25\!\cdots\!40\)\(q^{76} + \)\(66\!\cdots\!84\)\(q^{77} - \)\(45\!\cdots\!88\)\(q^{78} + \)\(90\!\cdots\!20\)\(q^{79} - \)\(16\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!77\)\(q^{81} - \)\(70\!\cdots\!56\)\(q^{82} + \)\(14\!\cdots\!36\)\(q^{83} + \)\(28\!\cdots\!12\)\(q^{84} + \)\(38\!\cdots\!00\)\(q^{85} + \)\(49\!\cdots\!36\)\(q^{86} - \)\(19\!\cdots\!80\)\(q^{87} + \)\(52\!\cdots\!80\)\(q^{88} - \)\(15\!\cdots\!90\)\(q^{89} - \)\(34\!\cdots\!00\)\(q^{90} - \)\(20\!\cdots\!64\)\(q^{91} + \)\(31\!\cdots\!32\)\(q^{92} - \)\(19\!\cdots\!48\)\(q^{93} + \)\(38\!\cdots\!72\)\(q^{94} + \)\(11\!\cdots\!00\)\(q^{95} + \)\(97\!\cdots\!76\)\(q^{96} + \)\(37\!\cdots\!02\)\(q^{97} + \)\(19\!\cdots\!04\)\(q^{98} - \)\(52\!\cdots\!12\)\(q^{99} + O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.41537e6 −1.08155 −0.540775 0.841167i \(-0.681869\pi\)
−0.540775 + 0.841167i \(0.681869\pi\)
\(3\) −1.72036e10 −0.316512 −0.158256 0.987398i \(-0.550587\pi\)
−0.158256 + 0.987398i \(0.550587\pi\)
\(4\) 5.97255e12 0.169750
\(5\) 2.46761e15 0.462862 0.231431 0.972851i \(-0.425659\pi\)
0.231431 + 0.972851i \(0.425659\pi\)
\(6\) 1.10367e17 0.342324
\(7\) 1.29065e19 1.24767 0.623837 0.781554i \(-0.285573\pi\)
0.623837 + 0.781554i \(0.285573\pi\)
\(8\) 1.87405e20 0.897957
\(9\) −2.65835e21 −0.899820
\(10\) −1.58306e22 −0.500608
\(11\) 7.78755e22 0.288447 0.144223 0.989545i \(-0.453932\pi\)
0.144223 + 0.989545i \(0.453932\pi\)
\(12\) −1.02749e23 −0.0537280
\(13\) −1.84585e25 −1.59393 −0.796967 0.604022i \(-0.793564\pi\)
−0.796967 + 0.604022i \(0.793564\pi\)
\(14\) −8.27997e25 −1.34942
\(15\) −4.24517e25 −0.146502
\(16\) −1.41241e27 −1.14094
\(17\) −2.82858e27 −0.584073 −0.292037 0.956407i \(-0.594333\pi\)
−0.292037 + 0.956407i \(0.594333\pi\)
\(18\) 1.70543e28 0.973200
\(19\) 8.52388e28 1.44106 0.720529 0.693425i \(-0.243899\pi\)
0.720529 + 0.693425i \(0.243899\pi\)
\(20\) 1.47379e28 0.0785709
\(21\) −2.22037e29 −0.394904
\(22\) −4.99600e29 −0.311970
\(23\) −2.09625e30 −0.481468 −0.240734 0.970591i \(-0.577388\pi\)
−0.240734 + 0.970591i \(0.577388\pi\)
\(24\) −3.22403e30 −0.284214
\(25\) −2.23326e31 −0.785759
\(26\) 1.18418e32 1.72392
\(27\) 9.65579e31 0.601316
\(28\) 7.70845e31 0.211793
\(29\) −1.33372e33 −1.66383 −0.831915 0.554903i \(-0.812755\pi\)
−0.831915 + 0.554903i \(0.812755\pi\)
\(30\) 2.72343e32 0.158449
\(31\) −9.42299e32 −0.262150 −0.131075 0.991372i \(-0.541843\pi\)
−0.131075 + 0.991372i \(0.541843\pi\)
\(32\) 2.46741e33 0.336022
\(33\) −1.33974e33 −0.0912969
\(34\) 1.81464e34 0.631704
\(35\) 3.18481e34 0.577501
\(36\) −1.58771e34 −0.152745
\(37\) −8.78606e34 −0.456305 −0.228153 0.973625i \(-0.573269\pi\)
−0.228153 + 0.973625i \(0.573269\pi\)
\(38\) −5.46838e35 −1.55858
\(39\) 3.17552e35 0.504500
\(40\) 4.62441e35 0.415630
\(41\) 2.03901e36 1.05144 0.525718 0.850659i \(-0.323797\pi\)
0.525718 + 0.850659i \(0.323797\pi\)
\(42\) 1.42445e36 0.427109
\(43\) −6.02099e36 −1.06323 −0.531615 0.846986i \(-0.678415\pi\)
−0.531615 + 0.846986i \(0.678415\pi\)
\(44\) 4.65116e35 0.0489639
\(45\) −6.55977e36 −0.416492
\(46\) 1.34482e37 0.520732
\(47\) −4.75078e37 −1.13387 −0.566935 0.823763i \(-0.691871\pi\)
−0.566935 + 0.823763i \(0.691871\pi\)
\(48\) 2.42985e37 0.361120
\(49\) 5.95698e37 0.556691
\(50\) 1.43272e38 0.849837
\(51\) 4.86617e37 0.184866
\(52\) −1.10244e38 −0.270571
\(53\) −7.36820e38 −1.17802 −0.589012 0.808124i \(-0.700483\pi\)
−0.589012 + 0.808124i \(0.700483\pi\)
\(54\) −6.19454e38 −0.650354
\(55\) 1.92166e38 0.133511
\(56\) 2.41873e39 1.12036
\(57\) −1.46641e39 −0.456112
\(58\) 8.55629e39 1.79951
\(59\) −9.51309e39 −1.36192 −0.680960 0.732321i \(-0.738437\pi\)
−0.680960 + 0.732321i \(0.738437\pi\)
\(60\) −2.53545e38 −0.0248687
\(61\) −1.95631e39 −0.132287 −0.0661433 0.997810i \(-0.521069\pi\)
−0.0661433 + 0.997810i \(0.521069\pi\)
\(62\) 6.04519e39 0.283529
\(63\) −3.43099e40 −1.12268
\(64\) 3.38654e40 0.777511
\(65\) −4.55483e40 −0.737772
\(66\) 8.59491e39 0.0987422
\(67\) 2.10749e41 1.72617 0.863083 0.505062i \(-0.168530\pi\)
0.863083 + 0.505062i \(0.168530\pi\)
\(68\) −1.68938e40 −0.0991466
\(69\) 3.60631e40 0.152391
\(70\) −2.04317e41 −0.624596
\(71\) −5.43331e41 −1.20712 −0.603561 0.797317i \(-0.706252\pi\)
−0.603561 + 0.797317i \(0.706252\pi\)
\(72\) −4.98187e41 −0.807999
\(73\) 8.99506e41 1.06965 0.534823 0.844964i \(-0.320378\pi\)
0.534823 + 0.844964i \(0.320378\pi\)
\(74\) 5.63658e41 0.493517
\(75\) 3.84201e41 0.248702
\(76\) 5.09093e41 0.244620
\(77\) 1.00510e42 0.359888
\(78\) −2.03721e42 −0.545642
\(79\) −7.61415e41 −0.153113 −0.0765565 0.997065i \(-0.524393\pi\)
−0.0765565 + 0.997065i \(0.524393\pi\)
\(80\) −3.48528e42 −0.528095
\(81\) 6.19245e42 0.709496
\(82\) −1.30810e43 −1.13718
\(83\) 6.62221e42 0.438274 0.219137 0.975694i \(-0.429676\pi\)
0.219137 + 0.975694i \(0.429676\pi\)
\(84\) −1.32613e42 −0.0670351
\(85\) −6.97983e42 −0.270345
\(86\) 3.86268e43 1.14994
\(87\) 2.29447e43 0.526623
\(88\) 1.45942e43 0.259013
\(89\) −6.63932e43 −0.913794 −0.456897 0.889520i \(-0.651039\pi\)
−0.456897 + 0.889520i \(0.651039\pi\)
\(90\) 4.20833e43 0.450457
\(91\) −2.38234e44 −1.98871
\(92\) −1.25200e43 −0.0817293
\(93\) 1.62109e43 0.0829738
\(94\) 3.04780e44 1.22634
\(95\) 2.10336e44 0.667011
\(96\) −4.24483e43 −0.106355
\(97\) 1.95163e44 0.387288 0.193644 0.981072i \(-0.437969\pi\)
0.193644 + 0.981072i \(0.437969\pi\)
\(98\) −3.82162e44 −0.602090
\(99\) −2.07020e44 −0.259550
\(100\) −1.33383e44 −0.133383
\(101\) −3.07178e44 −0.245561 −0.122780 0.992434i \(-0.539181\pi\)
−0.122780 + 0.992434i \(0.539181\pi\)
\(102\) −3.12182e44 −0.199942
\(103\) 1.90315e45 0.978666 0.489333 0.872097i \(-0.337240\pi\)
0.489333 + 0.872097i \(0.337240\pi\)
\(104\) −3.45920e45 −1.43128
\(105\) −5.47902e44 −0.182786
\(106\) 4.72697e45 1.27409
\(107\) 1.11782e45 0.243915 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(108\) 5.76697e44 0.102074
\(109\) 3.21871e45 0.463005 0.231502 0.972834i \(-0.425636\pi\)
0.231502 + 0.972834i \(0.425636\pi\)
\(110\) −1.23282e45 −0.144399
\(111\) 1.51152e45 0.144426
\(112\) −1.82292e46 −1.42352
\(113\) −1.15806e46 −0.740397 −0.370198 0.928953i \(-0.620710\pi\)
−0.370198 + 0.928953i \(0.620710\pi\)
\(114\) 9.40757e45 0.493308
\(115\) −5.17274e45 −0.222853
\(116\) −7.96570e45 −0.282435
\(117\) 4.90691e46 1.43425
\(118\) 6.10300e46 1.47298
\(119\) −3.65069e46 −0.728733
\(120\) −7.95565e45 −0.131552
\(121\) −6.68259e46 −0.916798
\(122\) 1.25504e46 0.143075
\(123\) −3.50783e46 −0.332792
\(124\) −5.62793e45 −0.0445001
\(125\) −1.25242e47 −0.826560
\(126\) 2.20110e47 1.21424
\(127\) 6.85398e46 0.316489 0.158245 0.987400i \(-0.449417\pi\)
0.158245 + 0.987400i \(0.449417\pi\)
\(128\) −3.04073e47 −1.17694
\(129\) 1.03583e47 0.336525
\(130\) 2.92209e47 0.797937
\(131\) −3.50099e46 −0.0804613 −0.0402306 0.999190i \(-0.512809\pi\)
−0.0402306 + 0.999190i \(0.512809\pi\)
\(132\) −8.00166e45 −0.0154977
\(133\) 1.10013e48 1.79797
\(134\) −1.35203e48 −1.86693
\(135\) 2.38267e47 0.278326
\(136\) −5.30088e47 −0.524472
\(137\) −1.53504e48 −1.28798 −0.643989 0.765035i \(-0.722722\pi\)
−0.643989 + 0.765035i \(0.722722\pi\)
\(138\) −2.31358e47 −0.164818
\(139\) 1.45287e48 0.879818 0.439909 0.898042i \(-0.355011\pi\)
0.439909 + 0.898042i \(0.355011\pi\)
\(140\) 1.90215e47 0.0980309
\(141\) 8.17304e47 0.358884
\(142\) 3.48566e48 1.30556
\(143\) −1.43746e48 −0.459765
\(144\) 3.75468e48 1.02664
\(145\) −3.29110e48 −0.770123
\(146\) −5.77066e48 −1.15688
\(147\) −1.02481e48 −0.176200
\(148\) −5.24752e47 −0.0774579
\(149\) 6.21806e47 0.0788794 0.0394397 0.999222i \(-0.487443\pi\)
0.0394397 + 0.999222i \(0.487443\pi\)
\(150\) −2.46479e48 −0.268984
\(151\) −5.84550e48 −0.549339 −0.274670 0.961539i \(-0.588568\pi\)
−0.274670 + 0.961539i \(0.588568\pi\)
\(152\) 1.59741e49 1.29401
\(153\) 7.51935e48 0.525561
\(154\) −6.44807e48 −0.389236
\(155\) −2.32523e48 −0.121339
\(156\) 1.89660e48 0.0856389
\(157\) 2.07022e48 0.0809607 0.0404804 0.999180i \(-0.487111\pi\)
0.0404804 + 0.999180i \(0.487111\pi\)
\(158\) 4.88476e48 0.165599
\(159\) 1.26759e49 0.372859
\(160\) 6.08861e48 0.155532
\(161\) −2.70552e49 −0.600715
\(162\) −3.97269e49 −0.767355
\(163\) −4.16253e49 −0.700062 −0.350031 0.936738i \(-0.613829\pi\)
−0.350031 + 0.936738i \(0.613829\pi\)
\(164\) 1.21781e49 0.178481
\(165\) −3.30595e48 −0.0422579
\(166\) −4.24839e49 −0.474015
\(167\) 1.93069e50 1.88188 0.940941 0.338570i \(-0.109943\pi\)
0.940941 + 0.338570i \(0.109943\pi\)
\(168\) −4.16108e49 −0.354607
\(169\) 2.06609e50 1.54063
\(170\) 4.47782e49 0.292392
\(171\) −2.26595e50 −1.29669
\(172\) −3.59607e49 −0.180484
\(173\) −8.78028e48 −0.0386786 −0.0193393 0.999813i \(-0.506156\pi\)
−0.0193393 + 0.999813i \(0.506156\pi\)
\(174\) −1.47199e50 −0.569569
\(175\) −2.88235e50 −0.980371
\(176\) −1.09992e50 −0.329099
\(177\) 1.63659e50 0.431064
\(178\) 4.25937e50 0.988314
\(179\) 3.03604e50 0.621032 0.310516 0.950568i \(-0.399498\pi\)
0.310516 + 0.950568i \(0.399498\pi\)
\(180\) −3.91786e49 −0.0706997
\(181\) −1.05625e51 −1.68268 −0.841338 0.540509i \(-0.818232\pi\)
−0.841338 + 0.540509i \(0.818232\pi\)
\(182\) 1.52836e51 2.15089
\(183\) 3.36555e49 0.0418703
\(184\) −3.92847e50 −0.432337
\(185\) −2.16806e50 −0.211206
\(186\) −1.03999e50 −0.0897403
\(187\) −2.20277e50 −0.168474
\(188\) −2.83743e50 −0.192475
\(189\) 1.24622e51 0.750247
\(190\) −1.34938e51 −0.721405
\(191\) −1.95146e51 −0.927060 −0.463530 0.886081i \(-0.653417\pi\)
−0.463530 + 0.886081i \(0.653417\pi\)
\(192\) −5.82606e50 −0.246092
\(193\) 2.53211e51 0.951574 0.475787 0.879561i \(-0.342163\pi\)
0.475787 + 0.879561i \(0.342163\pi\)
\(194\) −1.25205e51 −0.418872
\(195\) 7.83594e50 0.233514
\(196\) 3.55784e50 0.0944985
\(197\) 5.70705e51 1.35183 0.675914 0.736981i \(-0.263749\pi\)
0.675914 + 0.736981i \(0.263749\pi\)
\(198\) 1.32811e51 0.280716
\(199\) 2.85140e51 0.538102 0.269051 0.963126i \(-0.413290\pi\)
0.269051 + 0.963126i \(0.413290\pi\)
\(200\) −4.18523e51 −0.705577
\(201\) −3.62564e51 −0.546353
\(202\) 1.97066e51 0.265586
\(203\) −1.72136e52 −2.07592
\(204\) 2.90634e50 0.0313811
\(205\) 5.03149e51 0.486670
\(206\) −1.22094e52 −1.05848
\(207\) 5.57257e51 0.433235
\(208\) 2.60709e52 1.81858
\(209\) 6.63802e51 0.415668
\(210\) 3.51499e51 0.197692
\(211\) −1.00404e52 −0.507455 −0.253728 0.967276i \(-0.581657\pi\)
−0.253728 + 0.967276i \(0.581657\pi\)
\(212\) −4.40070e51 −0.199970
\(213\) 9.34723e51 0.382069
\(214\) −7.17125e51 −0.263806
\(215\) −1.48574e52 −0.492129
\(216\) 1.80954e52 0.539956
\(217\) −1.21617e52 −0.327078
\(218\) −2.06492e52 −0.500763
\(219\) −1.54747e52 −0.338556
\(220\) 1.14772e51 0.0226635
\(221\) 5.22112e52 0.930975
\(222\) −9.69694e51 −0.156204
\(223\) −1.08955e53 −1.58630 −0.793151 0.609025i \(-0.791561\pi\)
−0.793151 + 0.609025i \(0.791561\pi\)
\(224\) 3.18456e52 0.419246
\(225\) 5.93679e52 0.707041
\(226\) 7.42935e52 0.800776
\(227\) 8.59683e51 0.0838990 0.0419495 0.999120i \(-0.486643\pi\)
0.0419495 + 0.999120i \(0.486643\pi\)
\(228\) −8.75823e51 −0.0774252
\(229\) 8.54768e52 0.684779 0.342389 0.939558i \(-0.388764\pi\)
0.342389 + 0.939558i \(0.388764\pi\)
\(230\) 3.31850e52 0.241027
\(231\) −1.72913e52 −0.113909
\(232\) −2.49945e53 −1.49405
\(233\) 1.94501e53 1.05539 0.527695 0.849434i \(-0.323057\pi\)
0.527695 + 0.849434i \(0.323057\pi\)
\(234\) −3.14796e53 −1.55122
\(235\) −1.17231e53 −0.524825
\(236\) −5.68175e52 −0.231186
\(237\) 1.30991e52 0.0484621
\(238\) 2.34205e53 0.788161
\(239\) −4.67858e52 −0.143272 −0.0716360 0.997431i \(-0.522822\pi\)
−0.0716360 + 0.997431i \(0.522822\pi\)
\(240\) 5.99592e52 0.167149
\(241\) 5.41561e53 1.37488 0.687438 0.726243i \(-0.258735\pi\)
0.687438 + 0.726243i \(0.258735\pi\)
\(242\) 4.28713e53 0.991563
\(243\) −3.91795e53 −0.825881
\(244\) −1.16842e52 −0.0224557
\(245\) 1.46995e53 0.257671
\(246\) 2.25040e53 0.359932
\(247\) −1.57338e54 −2.29695
\(248\) −1.76591e53 −0.235400
\(249\) −1.13926e53 −0.138719
\(250\) 8.03473e53 0.893966
\(251\) 2.39905e53 0.243995 0.121997 0.992530i \(-0.461070\pi\)
0.121997 + 0.992530i \(0.461070\pi\)
\(252\) −2.04918e53 −0.190576
\(253\) −1.63247e53 −0.138878
\(254\) −4.39708e53 −0.342299
\(255\) 1.20078e53 0.0855676
\(256\) 7.59209e53 0.495407
\(257\) 1.10513e54 0.660569 0.330285 0.943881i \(-0.392855\pi\)
0.330285 + 0.943881i \(0.392855\pi\)
\(258\) −6.64520e53 −0.363969
\(259\) −1.13397e54 −0.569321
\(260\) −2.72040e53 −0.125237
\(261\) 3.54549e54 1.49715
\(262\) 2.24601e53 0.0870229
\(263\) 9.95471e53 0.354017 0.177009 0.984209i \(-0.443358\pi\)
0.177009 + 0.984209i \(0.443358\pi\)
\(264\) −2.51073e53 −0.0819807
\(265\) −1.81818e54 −0.545263
\(266\) −7.05775e54 −1.94460
\(267\) 1.14220e54 0.289227
\(268\) 1.25871e54 0.293017
\(269\) −1.90365e54 −0.407532 −0.203766 0.979020i \(-0.565318\pi\)
−0.203766 + 0.979020i \(0.565318\pi\)
\(270\) −1.52857e54 −0.301024
\(271\) −2.11803e54 −0.383815 −0.191908 0.981413i \(-0.561467\pi\)
−0.191908 + 0.981413i \(0.561467\pi\)
\(272\) 3.99511e54 0.666390
\(273\) 4.09847e54 0.629452
\(274\) 9.84787e54 1.39301
\(275\) −1.73916e54 −0.226650
\(276\) 2.15389e53 0.0258683
\(277\) 7.86883e54 0.871195 0.435598 0.900141i \(-0.356537\pi\)
0.435598 + 0.900141i \(0.356537\pi\)
\(278\) −9.32067e54 −0.951567
\(279\) 2.50496e54 0.235888
\(280\) 5.96848e54 0.518571
\(281\) −2.25442e55 −1.80777 −0.903883 0.427781i \(-0.859296\pi\)
−0.903883 + 0.427781i \(0.859296\pi\)
\(282\) −5.24330e54 −0.388150
\(283\) −5.22384e54 −0.357104 −0.178552 0.983930i \(-0.557141\pi\)
−0.178552 + 0.983930i \(0.557141\pi\)
\(284\) −3.24507e54 −0.204909
\(285\) −3.61854e54 −0.211117
\(286\) 9.22186e54 0.497259
\(287\) 2.63164e55 1.31185
\(288\) −6.55924e54 −0.302359
\(289\) −1.54523e55 −0.658858
\(290\) 2.11136e55 0.832927
\(291\) −3.35751e54 −0.122582
\(292\) 5.37235e54 0.181573
\(293\) 1.63631e55 0.512088 0.256044 0.966665i \(-0.417581\pi\)
0.256044 + 0.966665i \(0.417581\pi\)
\(294\) 6.57456e54 0.190569
\(295\) −2.34746e55 −0.630381
\(296\) −1.64655e55 −0.409742
\(297\) 7.51950e54 0.173448
\(298\) −3.98911e54 −0.0853121
\(299\) 3.86936e55 0.767428
\(300\) 2.29466e54 0.0422173
\(301\) −7.77096e55 −1.32657
\(302\) 3.75010e55 0.594138
\(303\) 5.28456e54 0.0777230
\(304\) −1.20392e56 −1.64415
\(305\) −4.82741e54 −0.0612305
\(306\) −4.82394e55 −0.568420
\(307\) 1.67269e56 1.83148 0.915741 0.401768i \(-0.131604\pi\)
0.915741 + 0.401768i \(0.131604\pi\)
\(308\) 6.00300e54 0.0610910
\(309\) −3.27409e55 −0.309760
\(310\) 1.49172e55 0.131235
\(311\) 2.38430e56 1.95097 0.975487 0.220058i \(-0.0706246\pi\)
0.975487 + 0.220058i \(0.0706246\pi\)
\(312\) 5.95107e55 0.453019
\(313\) −7.01155e55 −0.496668 −0.248334 0.968674i \(-0.579883\pi\)
−0.248334 + 0.968674i \(0.579883\pi\)
\(314\) −1.32812e55 −0.0875631
\(315\) −8.46634e55 −0.519647
\(316\) −4.54759e54 −0.0259910
\(317\) −2.68335e56 −1.42838 −0.714191 0.699951i \(-0.753205\pi\)
−0.714191 + 0.699951i \(0.753205\pi\)
\(318\) −8.13208e55 −0.403266
\(319\) −1.03864e56 −0.479926
\(320\) 8.35666e55 0.359880
\(321\) −1.92306e55 −0.0772021
\(322\) 1.73569e56 0.649704
\(323\) −2.41105e56 −0.841683
\(324\) 3.69848e55 0.120437
\(325\) 4.12226e56 1.25245
\(326\) 2.67042e56 0.757152
\(327\) −5.53733e55 −0.146547
\(328\) 3.82120e56 0.944144
\(329\) −6.13157e56 −1.41470
\(330\) 2.12089e55 0.0457040
\(331\) 1.90982e56 0.384470 0.192235 0.981349i \(-0.438426\pi\)
0.192235 + 0.981349i \(0.438426\pi\)
\(332\) 3.95515e55 0.0743971
\(333\) 2.33564e56 0.410593
\(334\) −1.23861e57 −2.03535
\(335\) 5.20047e56 0.798977
\(336\) 3.13608e56 0.450560
\(337\) 2.57253e56 0.345691 0.172845 0.984949i \(-0.444704\pi\)
0.172845 + 0.984949i \(0.444704\pi\)
\(338\) −1.32547e57 −1.66627
\(339\) 1.99227e56 0.234345
\(340\) −4.16874e55 −0.0458912
\(341\) −7.33820e55 −0.0756164
\(342\) 1.45369e57 1.40244
\(343\) −6.12245e56 −0.553105
\(344\) −1.12836e57 −0.954735
\(345\) 8.89896e55 0.0705358
\(346\) 5.63287e55 0.0418329
\(347\) 1.10908e57 0.771878 0.385939 0.922524i \(-0.373877\pi\)
0.385939 + 0.922524i \(0.373877\pi\)
\(348\) 1.37039e56 0.0893943
\(349\) 1.91424e57 1.17064 0.585321 0.810802i \(-0.300968\pi\)
0.585321 + 0.810802i \(0.300968\pi\)
\(350\) 1.84913e57 1.06032
\(351\) −1.78231e57 −0.958459
\(352\) 1.92151e56 0.0969243
\(353\) −1.00890e57 −0.477437 −0.238719 0.971089i \(-0.576727\pi\)
−0.238719 + 0.971089i \(0.576727\pi\)
\(354\) −1.04993e57 −0.466217
\(355\) −1.34073e57 −0.558731
\(356\) −3.96537e56 −0.155117
\(357\) 6.28050e56 0.230653
\(358\) −1.94773e57 −0.671677
\(359\) −5.19166e57 −1.68144 −0.840720 0.541470i \(-0.817868\pi\)
−0.840720 + 0.541470i \(0.817868\pi\)
\(360\) −1.22933e57 −0.373992
\(361\) 3.76691e57 1.07665
\(362\) 6.77626e57 1.81990
\(363\) 1.14964e57 0.290178
\(364\) −1.42286e57 −0.337584
\(365\) 2.21963e57 0.495098
\(366\) −2.15912e56 −0.0452849
\(367\) 5.07031e57 1.00011 0.500056 0.865993i \(-0.333313\pi\)
0.500056 + 0.865993i \(0.333313\pi\)
\(368\) 2.96077e57 0.549324
\(369\) −5.42041e57 −0.946103
\(370\) 1.39089e57 0.228430
\(371\) −9.50974e57 −1.46979
\(372\) 9.68205e55 0.0140848
\(373\) −5.35043e57 −0.732723 −0.366362 0.930473i \(-0.619397\pi\)
−0.366362 + 0.930473i \(0.619397\pi\)
\(374\) 1.41316e57 0.182213
\(375\) 2.15461e57 0.261616
\(376\) −8.90317e57 −1.01817
\(377\) 2.46184e58 2.65204
\(378\) −7.99496e57 −0.811430
\(379\) −1.65597e58 −1.58369 −0.791846 0.610720i \(-0.790880\pi\)
−0.791846 + 0.610720i \(0.790880\pi\)
\(380\) 1.25624e57 0.113225
\(381\) −1.17913e57 −0.100173
\(382\) 1.25193e58 1.00266
\(383\) 4.08813e56 0.0308711 0.0154356 0.999881i \(-0.495087\pi\)
0.0154356 + 0.999881i \(0.495087\pi\)
\(384\) 5.23115e57 0.372515
\(385\) 2.48019e57 0.166578
\(386\) −1.62444e58 −1.02917
\(387\) 1.60059e58 0.956716
\(388\) 1.16562e57 0.0657423
\(389\) 8.62061e57 0.458851 0.229426 0.973326i \(-0.426315\pi\)
0.229426 + 0.973326i \(0.426315\pi\)
\(390\) −5.02705e57 −0.252557
\(391\) 5.92941e57 0.281213
\(392\) 1.11637e58 0.499885
\(393\) 6.02296e56 0.0254670
\(394\) −3.66128e58 −1.46207
\(395\) −1.87888e57 −0.0708702
\(396\) −1.23644e57 −0.0440587
\(397\) −9.58101e57 −0.322571 −0.161285 0.986908i \(-0.551564\pi\)
−0.161285 + 0.986908i \(0.551564\pi\)
\(398\) −1.82928e58 −0.581984
\(399\) −1.89262e58 −0.569080
\(400\) 3.15428e58 0.896500
\(401\) −3.87566e58 −1.04135 −0.520676 0.853755i \(-0.674320\pi\)
−0.520676 + 0.853755i \(0.674320\pi\)
\(402\) 2.32598e58 0.590908
\(403\) 1.73934e58 0.417850
\(404\) −1.83464e57 −0.0416840
\(405\) 1.52806e58 0.328399
\(406\) 1.10431e59 2.24521
\(407\) −6.84219e57 −0.131620
\(408\) 9.11941e57 0.166002
\(409\) −2.12182e58 −0.365539 −0.182769 0.983156i \(-0.558506\pi\)
−0.182769 + 0.983156i \(0.558506\pi\)
\(410\) −3.22788e58 −0.526358
\(411\) 2.64083e58 0.407661
\(412\) 1.13666e58 0.166129
\(413\) −1.22780e59 −1.69923
\(414\) −3.57501e58 −0.468565
\(415\) 1.63410e58 0.202860
\(416\) −4.55447e58 −0.535596
\(417\) −2.49945e58 −0.278473
\(418\) −4.25853e58 −0.449566
\(419\) 7.28603e58 0.728913 0.364456 0.931220i \(-0.381255\pi\)
0.364456 + 0.931220i \(0.381255\pi\)
\(420\) −3.27237e57 −0.0310280
\(421\) 6.69387e58 0.601631 0.300815 0.953682i \(-0.402741\pi\)
0.300815 + 0.953682i \(0.402741\pi\)
\(422\) 6.44132e58 0.548838
\(423\) 1.26292e59 1.02028
\(424\) −1.38083e59 −1.05781
\(425\) 6.31695e58 0.458941
\(426\) −5.99659e58 −0.413227
\(427\) −2.52490e58 −0.165051
\(428\) 6.67627e57 0.0414046
\(429\) 2.47295e58 0.145521
\(430\) 9.53160e58 0.532262
\(431\) 1.33907e59 0.709684 0.354842 0.934926i \(-0.384535\pi\)
0.354842 + 0.934926i \(0.384535\pi\)
\(432\) −1.36379e59 −0.686063
\(433\) −1.66678e59 −0.795976 −0.397988 0.917391i \(-0.630292\pi\)
−0.397988 + 0.917391i \(0.630292\pi\)
\(434\) 7.80220e58 0.353751
\(435\) 5.66186e58 0.243754
\(436\) 1.92239e58 0.0785952
\(437\) −1.78682e59 −0.693823
\(438\) 9.92761e58 0.366165
\(439\) −1.80307e59 −0.631774 −0.315887 0.948797i \(-0.602302\pi\)
−0.315887 + 0.948797i \(0.602302\pi\)
\(440\) 3.60129e58 0.119887
\(441\) −1.58357e59 −0.500922
\(442\) −3.34954e59 −1.00690
\(443\) 1.21940e59 0.348388 0.174194 0.984711i \(-0.444268\pi\)
0.174194 + 0.984711i \(0.444268\pi\)
\(444\) 9.02762e57 0.0245164
\(445\) −1.63833e59 −0.422961
\(446\) 6.98983e59 1.71566
\(447\) −1.06973e58 −0.0249663
\(448\) 4.37082e59 0.970081
\(449\) 4.77895e59 1.00877 0.504383 0.863480i \(-0.331720\pi\)
0.504383 + 0.863480i \(0.331720\pi\)
\(450\) −3.80867e59 −0.764701
\(451\) 1.58789e59 0.303283
\(452\) −6.91655e58 −0.125682
\(453\) 1.00564e59 0.173873
\(454\) −5.51518e58 −0.0907410
\(455\) −5.87868e59 −0.920499
\(456\) −2.74812e59 −0.409569
\(457\) 2.48102e59 0.351978 0.175989 0.984392i \(-0.443688\pi\)
0.175989 + 0.984392i \(0.443688\pi\)
\(458\) −5.48365e59 −0.740622
\(459\) −2.73121e59 −0.351213
\(460\) −3.08944e58 −0.0378294
\(461\) −1.59001e60 −1.85408 −0.927040 0.374962i \(-0.877656\pi\)
−0.927040 + 0.374962i \(0.877656\pi\)
\(462\) 1.10930e59 0.123198
\(463\) 9.67043e59 1.02300 0.511498 0.859285i \(-0.329091\pi\)
0.511498 + 0.859285i \(0.329091\pi\)
\(464\) 1.88375e60 1.89832
\(465\) 4.00022e58 0.0384054
\(466\) −1.24779e60 −1.14146
\(467\) −1.81440e59 −0.158162 −0.0790812 0.996868i \(-0.525199\pi\)
−0.0790812 + 0.996868i \(0.525199\pi\)
\(468\) 2.93068e59 0.243465
\(469\) 2.72002e60 2.15369
\(470\) 7.52078e59 0.567624
\(471\) −3.56152e58 −0.0256251
\(472\) −1.78280e60 −1.22294
\(473\) −4.68887e59 −0.306685
\(474\) −8.40353e58 −0.0524142
\(475\) −1.90360e60 −1.13232
\(476\) −2.18040e59 −0.123703
\(477\) 1.95872e60 1.06001
\(478\) 3.00148e59 0.154956
\(479\) −1.15748e60 −0.570117 −0.285059 0.958510i \(-0.592013\pi\)
−0.285059 + 0.958510i \(0.592013\pi\)
\(480\) −1.04746e59 −0.0492277
\(481\) 1.62177e60 0.727321
\(482\) −3.47431e60 −1.48700
\(483\) 4.65446e59 0.190134
\(484\) −3.99121e59 −0.155627
\(485\) 4.81587e59 0.179261
\(486\) 2.51351e60 0.893231
\(487\) −1.82685e60 −0.619871 −0.309935 0.950758i \(-0.600307\pi\)
−0.309935 + 0.950758i \(0.600307\pi\)
\(488\) −3.66621e59 −0.118788
\(489\) 7.16104e59 0.221578
\(490\) −9.43028e59 −0.278684
\(491\) −2.65564e60 −0.749609 −0.374805 0.927104i \(-0.622290\pi\)
−0.374805 + 0.927104i \(0.622290\pi\)
\(492\) −2.09507e59 −0.0564916
\(493\) 3.77252e60 0.971799
\(494\) 1.00938e61 2.48427
\(495\) −5.10846e59 −0.120136
\(496\) 1.33091e60 0.299096
\(497\) −7.01248e60 −1.50610
\(498\) 7.30875e59 0.150032
\(499\) 2.18380e60 0.428500 0.214250 0.976779i \(-0.431269\pi\)
0.214250 + 0.976779i \(0.431269\pi\)
\(500\) −7.48014e59 −0.140309
\(501\) −3.32148e60 −0.595639
\(502\) −1.53908e60 −0.263893
\(503\) −4.41130e60 −0.723247 −0.361624 0.932324i \(-0.617777\pi\)
−0.361624 + 0.932324i \(0.617777\pi\)
\(504\) −6.42983e60 −1.00812
\(505\) −7.57995e59 −0.113661
\(506\) 1.04729e60 0.150203
\(507\) −3.55441e60 −0.487628
\(508\) 4.09357e59 0.0537241
\(509\) 3.40004e60 0.426908 0.213454 0.976953i \(-0.431529\pi\)
0.213454 + 0.976953i \(0.431529\pi\)
\(510\) −7.70344e59 −0.0925457
\(511\) 1.16094e61 1.33457
\(512\) 5.82802e60 0.641131
\(513\) 8.23048e60 0.866532
\(514\) −7.08982e60 −0.714439
\(515\) 4.69622e60 0.452987
\(516\) 6.18652e59 0.0571253
\(517\) −3.69969e60 −0.327061
\(518\) 7.27483e60 0.615749
\(519\) 1.51052e59 0.0122423
\(520\) −8.53596e60 −0.662487
\(521\) 7.11610e60 0.528924 0.264462 0.964396i \(-0.414806\pi\)
0.264462 + 0.964396i \(0.414806\pi\)
\(522\) −2.27456e61 −1.61924
\(523\) −6.62508e60 −0.451755 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(524\) −2.09099e59 −0.0136583
\(525\) 4.95867e60 0.310300
\(526\) −6.38631e60 −0.382887
\(527\) 2.66536e60 0.153115
\(528\) 1.89226e60 0.104164
\(529\) −1.45620e61 −0.768189
\(530\) 1.16643e61 0.589729
\(531\) 2.52891e61 1.22548
\(532\) 6.57059e60 0.305206
\(533\) −3.76371e61 −1.67592
\(534\) −7.32763e60 −0.312814
\(535\) 2.75836e60 0.112899
\(536\) 3.94953e61 1.55002
\(537\) −5.22307e60 −0.196564
\(538\) 1.22126e61 0.440766
\(539\) 4.63903e60 0.160576
\(540\) 1.42306e60 0.0472460
\(541\) −3.34138e61 −1.06411 −0.532056 0.846709i \(-0.678581\pi\)
−0.532056 + 0.846709i \(0.678581\pi\)
\(542\) 1.35879e61 0.415116
\(543\) 1.81713e61 0.532588
\(544\) −6.97927e60 −0.196261
\(545\) 7.94252e60 0.214307
\(546\) −2.62932e61 −0.680783
\(547\) 3.86064e61 0.959277 0.479638 0.877466i \(-0.340768\pi\)
0.479638 + 0.877466i \(0.340768\pi\)
\(548\) −9.16813e60 −0.218634
\(549\) 5.20055e60 0.119034
\(550\) 1.11574e61 0.245133
\(551\) −1.13684e62 −2.39767
\(552\) 6.75838e60 0.136840
\(553\) −9.82717e60 −0.191035
\(554\) −5.04815e61 −0.942241
\(555\) 3.72984e60 0.0668494
\(556\) 8.67733e60 0.149349
\(557\) 5.55735e61 0.918598 0.459299 0.888282i \(-0.348101\pi\)
0.459299 + 0.888282i \(0.348101\pi\)
\(558\) −1.60702e61 −0.255125
\(559\) 1.11138e62 1.69472
\(560\) −4.49826e61 −0.658891
\(561\) 3.78955e60 0.0533241
\(562\) 1.44629e62 1.95519
\(563\) −1.22198e61 −0.158718 −0.0793589 0.996846i \(-0.525287\pi\)
−0.0793589 + 0.996846i \(0.525287\pi\)
\(564\) 4.88139e60 0.0609206
\(565\) −2.85763e61 −0.342701
\(566\) 3.35128e61 0.386226
\(567\) 7.99227e61 0.885220
\(568\) −1.01823e62 −1.08394
\(569\) −1.79144e62 −1.83306 −0.916529 0.399967i \(-0.869022\pi\)
−0.916529 + 0.399967i \(0.869022\pi\)
\(570\) 2.32142e61 0.228334
\(571\) −4.92064e61 −0.465274 −0.232637 0.972564i \(-0.574735\pi\)
−0.232637 + 0.972564i \(0.574735\pi\)
\(572\) −8.58533e60 −0.0780452
\(573\) 3.35720e61 0.293426
\(574\) −1.68829e62 −1.41883
\(575\) 4.68148e61 0.378318
\(576\) −9.00260e61 −0.699620
\(577\) 1.61247e62 1.20513 0.602566 0.798069i \(-0.294145\pi\)
0.602566 + 0.798069i \(0.294145\pi\)
\(578\) 9.91323e61 0.712588
\(579\) −4.35613e61 −0.301185
\(580\) −1.96562e61 −0.130729
\(581\) 8.54693e61 0.546823
\(582\) 2.15397e61 0.132578
\(583\) −5.73802e61 −0.339797
\(584\) 1.68572e62 0.960495
\(585\) 1.21083e62 0.663862
\(586\) −1.04975e62 −0.553849
\(587\) −1.02006e62 −0.517925 −0.258962 0.965887i \(-0.583381\pi\)
−0.258962 + 0.965887i \(0.583381\pi\)
\(588\) −6.12076e60 −0.0299099
\(589\) −8.03204e61 −0.377774
\(590\) 1.50598e62 0.681788
\(591\) −9.81816e61 −0.427870
\(592\) 1.24095e62 0.520615
\(593\) 9.42772e61 0.380782 0.190391 0.981708i \(-0.439024\pi\)
0.190391 + 0.981708i \(0.439024\pi\)
\(594\) −4.82403e61 −0.187592
\(595\) −9.00849e61 −0.337303
\(596\) 3.71377e60 0.0133898
\(597\) −4.90543e61 −0.170316
\(598\) −2.48234e62 −0.830012
\(599\) −2.30170e62 −0.741217 −0.370609 0.928789i \(-0.620851\pi\)
−0.370609 + 0.928789i \(0.620851\pi\)
\(600\) 7.20010e61 0.223324
\(601\) 1.32397e62 0.395552 0.197776 0.980247i \(-0.436628\pi\)
0.197776 + 0.980247i \(0.436628\pi\)
\(602\) 4.98536e62 1.43475
\(603\) −5.60245e62 −1.55324
\(604\) −3.49126e61 −0.0932504
\(605\) −1.64900e62 −0.424351
\(606\) −3.39024e61 −0.0840613
\(607\) −1.86733e62 −0.446145 −0.223073 0.974802i \(-0.571609\pi\)
−0.223073 + 0.974802i \(0.571609\pi\)
\(608\) 2.10319e62 0.484227
\(609\) 2.96135e62 0.657053
\(610\) 3.09696e61 0.0662238
\(611\) 8.76921e62 1.80731
\(612\) 4.49097e61 0.0892141
\(613\) 7.96288e62 1.52479 0.762394 0.647113i \(-0.224024\pi\)
0.762394 + 0.647113i \(0.224024\pi\)
\(614\) −1.07309e63 −1.98084
\(615\) −8.65596e61 −0.154037
\(616\) 1.88360e62 0.323163
\(617\) −1.66014e62 −0.274617 −0.137309 0.990528i \(-0.543845\pi\)
−0.137309 + 0.990528i \(0.543845\pi\)
\(618\) 2.10045e62 0.335021
\(619\) 4.17933e62 0.642786 0.321393 0.946946i \(-0.395849\pi\)
0.321393 + 0.946946i \(0.395849\pi\)
\(620\) −1.38875e61 −0.0205974
\(621\) −2.02410e62 −0.289515
\(622\) −1.52961e63 −2.11008
\(623\) −8.56901e62 −1.14012
\(624\) −4.48513e62 −0.575602
\(625\) 3.25683e62 0.403176
\(626\) 4.49817e62 0.537171
\(627\) −1.14198e62 −0.131564
\(628\) 1.23645e61 0.0137431
\(629\) 2.48521e62 0.266516
\(630\) 5.43147e62 0.562024
\(631\) 4.78834e62 0.478106 0.239053 0.971007i \(-0.423163\pi\)
0.239053 + 0.971007i \(0.423163\pi\)
\(632\) −1.42693e62 −0.137489
\(633\) 1.72732e62 0.160616
\(634\) 1.72147e63 1.54487
\(635\) 1.69129e62 0.146491
\(636\) 7.57077e61 0.0632929
\(637\) −1.09957e63 −0.887330
\(638\) 6.66325e62 0.519064
\(639\) 1.44436e63 1.08619
\(640\) −7.50334e62 −0.544760
\(641\) −2.18288e63 −1.53011 −0.765056 0.643964i \(-0.777289\pi\)
−0.765056 + 0.643964i \(0.777289\pi\)
\(642\) 1.23371e62 0.0834979
\(643\) −1.90128e63 −1.24251 −0.621255 0.783609i \(-0.713377\pi\)
−0.621255 + 0.783609i \(0.713377\pi\)
\(644\) −1.61589e62 −0.101972
\(645\) 2.55601e62 0.155765
\(646\) 1.54677e63 0.910323
\(647\) 5.73318e62 0.325874 0.162937 0.986637i \(-0.447903\pi\)
0.162937 + 0.986637i \(0.447903\pi\)
\(648\) 1.16049e63 0.637097
\(649\) −7.40837e62 −0.392841
\(650\) −2.64458e63 −1.35459
\(651\) 2.09225e62 0.103524
\(652\) −2.48609e62 −0.118836
\(653\) 1.09427e63 0.505335 0.252667 0.967553i \(-0.418692\pi\)
0.252667 + 0.967553i \(0.418692\pi\)
\(654\) 3.55240e62 0.158498
\(655\) −8.63908e61 −0.0372425
\(656\) −2.87992e63 −1.19962
\(657\) −2.39120e63 −0.962488
\(658\) 3.93363e63 1.53007
\(659\) 3.42421e63 1.28718 0.643589 0.765372i \(-0.277445\pi\)
0.643589 + 0.765372i \(0.277445\pi\)
\(660\) −1.97450e61 −0.00717328
\(661\) 2.99634e61 0.0105210 0.00526051 0.999986i \(-0.498326\pi\)
0.00526051 + 0.999986i \(0.498326\pi\)
\(662\) −1.22522e63 −0.415823
\(663\) −8.98220e62 −0.294665
\(664\) 1.24103e63 0.393551
\(665\) 2.71470e63 0.832212
\(666\) −1.49840e63 −0.444077
\(667\) 2.79581e63 0.801081
\(668\) 1.15312e63 0.319450
\(669\) 1.87441e63 0.502084
\(670\) −3.33629e63 −0.864133
\(671\) −1.52349e62 −0.0381576
\(672\) −5.47858e62 −0.132696
\(673\) −5.41615e63 −1.26868 −0.634340 0.773054i \(-0.718728\pi\)
−0.634340 + 0.773054i \(0.718728\pi\)
\(674\) −1.65037e63 −0.373882
\(675\) −2.15639e63 −0.472490
\(676\) 1.23398e63 0.261522
\(677\) −4.55896e63 −0.934588 −0.467294 0.884102i \(-0.654771\pi\)
−0.467294 + 0.884102i \(0.654771\pi\)
\(678\) −1.27811e63 −0.253455
\(679\) 2.51887e63 0.483210
\(680\) −1.30805e63 −0.242758
\(681\) −1.47896e62 −0.0265551
\(682\) 4.70772e62 0.0817829
\(683\) 1.04266e64 1.75257 0.876287 0.481790i \(-0.160013\pi\)
0.876287 + 0.481790i \(0.160013\pi\)
\(684\) −1.35335e63 −0.220114
\(685\) −3.78789e63 −0.596156
\(686\) 3.92777e63 0.598210
\(687\) −1.47051e63 −0.216741
\(688\) 8.50410e63 1.21308
\(689\) 1.36006e64 1.87769
\(690\) −5.70901e62 −0.0762880
\(691\) −9.60653e63 −1.24254 −0.621270 0.783597i \(-0.713383\pi\)
−0.621270 + 0.783597i \(0.713383\pi\)
\(692\) −5.24407e61 −0.00656570
\(693\) −2.67190e63 −0.323834
\(694\) −7.11514e63 −0.834825
\(695\) 3.58511e63 0.407234
\(696\) 4.29994e63 0.472884
\(697\) −5.76750e63 −0.614116
\(698\) −1.22805e64 −1.26611
\(699\) −3.34611e63 −0.334044
\(700\) −1.72150e63 −0.166418
\(701\) −4.79975e63 −0.449327 −0.224664 0.974436i \(-0.572128\pi\)
−0.224664 + 0.974436i \(0.572128\pi\)
\(702\) 1.14342e64 1.03662
\(703\) −7.48914e63 −0.657562
\(704\) 2.63728e63 0.224270
\(705\) 2.01679e63 0.166114
\(706\) 6.47245e63 0.516372
\(707\) −3.96458e63 −0.306380
\(708\) 9.77464e62 0.0731732
\(709\) 9.62702e63 0.698155 0.349077 0.937094i \(-0.386495\pi\)
0.349077 + 0.937094i \(0.386495\pi\)
\(710\) 8.60126e63 0.604296
\(711\) 2.02411e63 0.137774
\(712\) −1.24424e64 −0.820547
\(713\) 1.97530e63 0.126217
\(714\) −4.02917e63 −0.249463
\(715\) −3.54710e63 −0.212808
\(716\) 1.81329e63 0.105420
\(717\) 8.04883e62 0.0453474
\(718\) 3.33064e64 1.81856
\(719\) −2.96105e64 −1.56692 −0.783459 0.621443i \(-0.786547\pi\)
−0.783459 + 0.621443i \(0.786547\pi\)
\(720\) 9.26508e63 0.475191
\(721\) 2.45629e64 1.22106
\(722\) −2.41661e64 −1.16445
\(723\) −9.31678e63 −0.435165
\(724\) −6.30853e63 −0.285635
\(725\) 2.97854e64 1.30737
\(726\) −7.37539e63 −0.313842
\(727\) 2.01758e64 0.832350 0.416175 0.909284i \(-0.363370\pi\)
0.416175 + 0.909284i \(0.363370\pi\)
\(728\) −4.46461e64 −1.78578
\(729\) −1.15542e64 −0.448095
\(730\) −1.42397e64 −0.535473
\(731\) 1.70308e64 0.621005
\(732\) 2.01009e62 0.00710750
\(733\) −2.30546e64 −0.790530 −0.395265 0.918567i \(-0.629347\pi\)
−0.395265 + 0.918567i \(0.629347\pi\)
\(734\) −3.25279e64 −1.08167
\(735\) −2.52884e63 −0.0815561
\(736\) −5.17232e63 −0.161784
\(737\) 1.64122e64 0.497907
\(738\) 3.47739e64 1.02326
\(739\) 4.27723e64 1.22085 0.610425 0.792074i \(-0.290999\pi\)
0.610425 + 0.792074i \(0.290999\pi\)
\(740\) −1.29488e63 −0.0358523
\(741\) 2.70677e64 0.727013
\(742\) 6.10084e64 1.58965
\(743\) −6.07984e64 −1.53689 −0.768447 0.639913i \(-0.778970\pi\)
−0.768447 + 0.639913i \(0.778970\pi\)
\(744\) 3.03800e63 0.0745069
\(745\) 1.53437e63 0.0365103
\(746\) 3.43250e64 0.792477
\(747\) −1.76041e64 −0.394368
\(748\) −1.31562e63 −0.0285985
\(749\) 1.44272e64 0.304327
\(750\) −1.38226e64 −0.282951
\(751\) −8.42750e64 −1.67417 −0.837086 0.547071i \(-0.815743\pi\)
−0.837086 + 0.547071i \(0.815743\pi\)
\(752\) 6.71004e64 1.29367
\(753\) −4.12723e63 −0.0772274
\(754\) −1.57936e65 −2.86831
\(755\) −1.44244e64 −0.254268
\(756\) 7.44312e63 0.127355
\(757\) −1.62790e64 −0.270377 −0.135189 0.990820i \(-0.543164\pi\)
−0.135189 + 0.990820i \(0.543164\pi\)
\(758\) 1.06237e65 1.71284
\(759\) 2.80843e63 0.0439565
\(760\) 3.94180e64 0.598947
\(761\) −1.06343e65 −1.56875 −0.784373 0.620289i \(-0.787015\pi\)
−0.784373 + 0.620289i \(0.787015\pi\)
\(762\) 7.56455e63 0.108342
\(763\) 4.15421e64 0.577679
\(764\) −1.16552e64 −0.157369
\(765\) 1.85548e64 0.243262
\(766\) −2.62269e63 −0.0333886
\(767\) 1.75597e65 2.17081
\(768\) −1.30611e64 −0.156802
\(769\) 3.91583e64 0.456542 0.228271 0.973598i \(-0.426693\pi\)
0.228271 + 0.973598i \(0.426693\pi\)
\(770\) −1.59113e64 −0.180163
\(771\) −1.90122e64 −0.209078
\(772\) 1.51231e64 0.161530
\(773\) −1.00996e65 −1.04777 −0.523885 0.851789i \(-0.675518\pi\)
−0.523885 + 0.851789i \(0.675518\pi\)
\(774\) −1.02684e65 −1.03474
\(775\) 2.10440e64 0.205987
\(776\) 3.65745e64 0.347768
\(777\) 1.95083e64 0.180197
\(778\) −5.53044e64 −0.496270
\(779\) 1.73803e65 1.51518
\(780\) 4.68006e63 0.0396390
\(781\) −4.23122e64 −0.348190
\(782\) −3.80394e64 −0.304145
\(783\) −1.28781e65 −1.00049
\(784\) −8.41370e64 −0.635149
\(785\) 5.10850e63 0.0374736
\(786\) −3.86395e63 −0.0275438
\(787\) 1.02621e65 0.710896 0.355448 0.934696i \(-0.384328\pi\)
0.355448 + 0.934696i \(0.384328\pi\)
\(788\) 3.40856e64 0.229473
\(789\) −1.71257e64 −0.112051
\(790\) 1.20537e64 0.0766496
\(791\) −1.49464e65 −0.923774
\(792\) −3.87966e64 −0.233065
\(793\) 3.61105e64 0.210856
\(794\) 6.14657e64 0.348876
\(795\) 3.12793e64 0.172582
\(796\) 1.70302e64 0.0913428
\(797\) −7.78531e64 −0.405942 −0.202971 0.979185i \(-0.565060\pi\)
−0.202971 + 0.979185i \(0.565060\pi\)
\(798\) 1.21418e65 0.615488
\(799\) 1.34379e65 0.662263
\(800\) −5.51038e64 −0.264032
\(801\) 1.76496e65 0.822250
\(802\) 2.48638e65 1.12627
\(803\) 7.00495e64 0.308536
\(804\) −2.16543e64 −0.0927435
\(805\) −6.67617e64 −0.278048
\(806\) −1.11585e65 −0.451926
\(807\) 3.27496e64 0.128989
\(808\) −5.75665e64 −0.220503
\(809\) −3.71145e65 −1.38262 −0.691308 0.722560i \(-0.742965\pi\)
−0.691308 + 0.722560i \(0.742965\pi\)
\(810\) −9.80304e64 −0.355180
\(811\) −1.97077e65 −0.694490 −0.347245 0.937774i \(-0.612883\pi\)
−0.347245 + 0.937774i \(0.612883\pi\)
\(812\) −1.02809e65 −0.352387
\(813\) 3.64376e64 0.121482
\(814\) 4.38952e64 0.142353
\(815\) −1.02715e65 −0.324032
\(816\) −6.87302e64 −0.210921
\(817\) −5.13222e65 −1.53218
\(818\) 1.36122e65 0.395349
\(819\) 6.33308e65 1.78948
\(820\) 3.00508e64 0.0826123
\(821\) 4.18847e65 1.12030 0.560150 0.828391i \(-0.310743\pi\)
0.560150 + 0.828391i \(0.310743\pi\)
\(822\) −1.69419e65 −0.440905
\(823\) −5.89925e64 −0.149383 −0.0746914 0.997207i \(-0.523797\pi\)
−0.0746914 + 0.997207i \(0.523797\pi\)
\(824\) 3.56658e65 0.878799
\(825\) 2.99198e64 0.0717374
\(826\) 7.87681e65 1.83780
\(827\) −4.27471e65 −0.970583 −0.485292 0.874352i \(-0.661287\pi\)
−0.485292 + 0.874352i \(0.661287\pi\)
\(828\) 3.32825e64 0.0735416
\(829\) 6.40554e64 0.137746 0.0688730 0.997625i \(-0.478060\pi\)
0.0688730 + 0.997625i \(0.478060\pi\)
\(830\) −1.04834e65 −0.219404
\(831\) −1.35372e65 −0.275744
\(832\) −6.25103e65 −1.23930
\(833\) −1.68498e65 −0.325149
\(834\) 1.60349e65 0.301183
\(835\) 4.76420e65 0.871052
\(836\) 3.96459e64 0.0705598
\(837\) −9.09863e64 −0.157635
\(838\) −4.67426e65 −0.788356
\(839\) −9.87581e65 −1.62154 −0.810772 0.585363i \(-0.800952\pi\)
−0.810772 + 0.585363i \(0.800952\pi\)
\(840\) −1.02679e65 −0.164134
\(841\) 1.13625e66 1.76833
\(842\) −4.29436e65 −0.650694
\(843\) 3.87840e65 0.572180
\(844\) −5.99671e64 −0.0861406
\(845\) 5.09830e65 0.713098
\(846\) −8.10211e65 −1.10348
\(847\) −8.62486e65 −1.14387
\(848\) 1.04069e66 1.34405
\(849\) 8.98687e64 0.113028
\(850\) −4.05256e65 −0.496367
\(851\) 1.84178e65 0.219696
\(852\) 5.58268e64 0.0648563
\(853\) 5.47101e65 0.619034 0.309517 0.950894i \(-0.399833\pi\)
0.309517 + 0.950894i \(0.399833\pi\)
\(854\) 1.61982e65 0.178511
\(855\) −5.59147e65 −0.600190
\(856\) 2.09485e65 0.219025
\(857\) 3.91129e65 0.398338 0.199169 0.979965i \(-0.436176\pi\)
0.199169 + 0.979965i \(0.436176\pi\)
\(858\) −1.58649e65 −0.157389
\(859\) 1.59577e66 1.54214 0.771072 0.636748i \(-0.219721\pi\)
0.771072 + 0.636748i \(0.219721\pi\)
\(860\) −8.87369e64 −0.0835390
\(861\) −4.52737e65 −0.415217
\(862\) −8.59063e65 −0.767559
\(863\) −1.43745e65 −0.125127 −0.0625633 0.998041i \(-0.519928\pi\)
−0.0625633 + 0.998041i \(0.519928\pi\)
\(864\) 2.38248e65 0.202055
\(865\) −2.16663e64 −0.0179029
\(866\) 1.06930e66 0.860888
\(867\) 2.65835e65 0.208537
\(868\) −7.26366e64 −0.0555216
\(869\) −5.92956e64 −0.0441649
\(870\) −3.63229e65 −0.263632
\(871\) −3.89011e66 −2.75140
\(872\) 6.03201e65 0.415758
\(873\) −5.18813e65 −0.348490
\(874\) 1.14631e66 0.750404
\(875\) −1.61643e66 −1.03128
\(876\) −9.24237e64 −0.0574699
\(877\) −9.07110e65 −0.549755 −0.274878 0.961479i \(-0.588637\pi\)
−0.274878 + 0.961479i \(0.588637\pi\)
\(878\) 1.15674e66 0.683295
\(879\) −2.81504e65 −0.162082
\(880\) −2.71418e65 −0.152327
\(881\) 2.58911e66 1.41642 0.708212 0.706000i \(-0.249502\pi\)
0.708212 + 0.706000i \(0.249502\pi\)
\(882\) 1.01592e66 0.541772
\(883\) 1.38977e66 0.722480 0.361240 0.932473i \(-0.382353\pi\)
0.361240 + 0.932473i \(0.382353\pi\)
\(884\) 3.11834e65 0.158033
\(885\) 4.03847e65 0.199523
\(886\) −7.82292e65 −0.376799
\(887\) 1.62550e66 0.763319 0.381660 0.924303i \(-0.375353\pi\)
0.381660 + 0.924303i \(0.375353\pi\)
\(888\) 2.83265e65 0.129689
\(889\) 8.84606e65 0.394875
\(890\) 1.05105e66 0.457453
\(891\) 4.82241e65 0.204652
\(892\) −6.50737e65 −0.269275
\(893\) −4.04951e66 −1.63397
\(894\) 6.86270e64 0.0270023
\(895\) 7.49176e65 0.287452
\(896\) −3.92451e66 −1.46844
\(897\) −6.65669e65 −0.242901
\(898\) −3.06587e66 −1.09103
\(899\) 1.25676e66 0.436173
\(900\) 3.54578e65 0.120020
\(901\) 2.08415e66 0.688052
\(902\) −1.01869e66 −0.328016
\(903\) 1.33688e66 0.419874
\(904\) −2.17025e66 −0.664844
\(905\) −2.60642e66 −0.778847
\(906\) −6.45152e65 −0.188052
\(907\) 6.17539e66 1.75590 0.877951 0.478751i \(-0.158910\pi\)
0.877951 + 0.478751i \(0.158910\pi\)
\(908\) 5.13451e64 0.0142419
\(909\) 8.16586e65 0.220960
\(910\) 3.77139e66 0.995566
\(911\) −2.64162e66 −0.680311 −0.340155 0.940369i \(-0.610480\pi\)
−0.340155 + 0.940369i \(0.610480\pi\)
\(912\) 2.07117e66 0.520395
\(913\) 5.15708e65 0.126419
\(914\) −1.59166e66 −0.380682
\(915\) 8.30487e64 0.0193802
\(916\) 5.10515e65 0.116241
\(917\) −4.51854e65 −0.100389
\(918\) 1.75217e66 0.379854
\(919\) −8.03936e66 −1.70068 −0.850340 0.526234i \(-0.823604\pi\)
−0.850340 + 0.526234i \(0.823604\pi\)
\(920\) −9.69394e65 −0.200113
\(921\) −2.87763e66 −0.579687
\(922\) 1.02005e67 2.00528
\(923\) 1.00291e67 1.92407
\(924\) −1.03273e65 −0.0193360
\(925\) 1.96216e66 0.358546
\(926\) −6.20394e66 −1.10642
\(927\) −5.05923e66 −0.880623
\(928\) −3.29083e66 −0.559083
\(929\) −6.85607e66 −1.13690 −0.568449 0.822718i \(-0.692457\pi\)
−0.568449 + 0.822718i \(0.692457\pi\)
\(930\) −2.56629e65 −0.0415374
\(931\) 5.07766e66 0.802225
\(932\) 1.16167e66 0.179153
\(933\) −4.10184e66 −0.617507
\(934\) 1.16400e66 0.171060
\(935\) −5.43558e65 −0.0779802
\(936\) 9.19577e66 1.28790
\(937\) −5.58369e66 −0.763450 −0.381725 0.924276i \(-0.624670\pi\)
−0.381725 + 0.924276i \(0.624670\pi\)
\(938\) −1.74500e67 −2.32933
\(939\) 1.20624e66 0.157202
\(940\) −7.00167e65 −0.0890891
\(941\) 8.59076e66 1.06725 0.533624 0.845722i \(-0.320830\pi\)
0.533624 + 0.845722i \(0.320830\pi\)
\(942\) 2.28485e65 0.0277148
\(943\) −4.27428e66 −0.506233
\(944\) 1.34364e67 1.55386
\(945\) 3.07519e66 0.347261
\(946\) 3.00808e66 0.331695
\(947\) 1.38497e67 1.49131 0.745654 0.666334i \(-0.232137\pi\)
0.745654 + 0.666334i \(0.232137\pi\)
\(948\) 7.82349e64 0.00822646
\(949\) −1.66035e67 −1.70495
\(950\) 1.22123e67 1.22466
\(951\) 4.61633e66 0.452101
\(952\) −6.84156e66 −0.654371
\(953\) 1.29710e67 1.21166 0.605831 0.795593i \(-0.292841\pi\)
0.605831 + 0.795593i \(0.292841\pi\)
\(954\) −1.25659e67 −1.14645
\(955\) −4.81543e66 −0.429101
\(956\) −2.79431e65 −0.0243205
\(957\) 1.78683e66 0.151903
\(958\) 7.42566e66 0.616610
\(959\) −1.98120e67 −1.60698
\(960\) −1.43764e66 −0.113907
\(961\) −1.20325e67 −0.931277
\(962\) −1.04043e67 −0.786634
\(963\) −2.97157e66 −0.219480
\(964\) 3.23450e66 0.233385
\(965\) 6.24825e66 0.440447
\(966\) −2.98601e66 −0.205639
\(967\) 2.84025e66 0.191100 0.0955502 0.995425i \(-0.469539\pi\)
0.0955502 + 0.995425i \(0.469539\pi\)
\(968\) −1.25235e67 −0.823245
\(969\) 4.14786e66 0.266403
\(970\) −3.08956e66 −0.193880
\(971\) 2.77039e67 1.69866 0.849332 0.527858i \(-0.177005\pi\)
0.849332 + 0.527858i \(0.177005\pi\)
\(972\) −2.34001e66 −0.140193
\(973\) 1.87514e67 1.09773
\(974\) 1.17199e67 0.670421
\(975\) −7.09176e66 −0.396415
\(976\) 2.76311e66 0.150930
\(977\) 1.30344e67 0.695766 0.347883 0.937538i \(-0.386901\pi\)
0.347883 + 0.937538i \(0.386901\pi\)
\(978\) −4.59407e66 −0.239648
\(979\) −5.17040e66 −0.263581
\(980\) 8.77936e65 0.0437398
\(981\) −8.55645e66 −0.416621
\(982\) 1.70369e67 0.810740
\(983\) −2.69857e67 −1.25510 −0.627551 0.778576i \(-0.715943\pi\)
−0.627551 + 0.778576i \(0.715943\pi\)
\(984\) −6.57383e66 −0.298833
\(985\) 1.40828e67 0.625710
\(986\) −2.42021e67 −1.05105
\(987\) 1.05485e67 0.447770
\(988\) −9.39709e66 −0.389908
\(989\) 1.26215e67 0.511911
\(990\) 3.27726e66 0.129933
\(991\) −3.22029e67 −1.24807 −0.624034 0.781397i \(-0.714507\pi\)
−0.624034 + 0.781397i \(0.714507\pi\)
\(992\) −2.32504e66 −0.0880882
\(993\) −3.28557e66 −0.121689
\(994\) 4.49876e67 1.62892
\(995\) 7.03615e66 0.249067
\(996\) −6.80427e65 −0.0235476
\(997\) −1.99799e67 −0.676009 −0.338005 0.941144i \(-0.609752\pi\)
−0.338005 + 0.941144i \(0.609752\pi\)
\(998\) −1.40099e67 −0.463444
\(999\) −8.48364e66 −0.274384
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.46.a.a.1.1 3
3.2 odd 2 9.46.a.b.1.3 3
4.3 odd 2 16.46.a.c.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.46.a.a.1.1 3 1.1 even 1 trivial
9.46.a.b.1.3 3 3.2 odd 2
16.46.a.c.1.2 3 4.3 odd 2