Properties

Label 1.48.a.a.1.4
Level $1$
Weight $48$
Character 1.1
Self dual yes
Analytic conductor $13.991$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 48 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(13.9907662655\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Defining polynomial: \(x^{4} - x^{3} - 832803191366 x^{2} + 3710135215485780 x + 13175318942671469337000\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{7}\cdot 5^{3}\cdot 7^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(901372.\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} +O(q^{10})\) \(q+2.30793e7 q^{2} +1.28510e11 q^{3} +3.91917e14 q^{4} -1.15086e16 q^{5} +2.96592e18 q^{6} +1.54211e19 q^{7} +5.79706e21 q^{8} -1.00741e22 q^{9} -2.65611e23 q^{10} -3.19474e24 q^{11} +5.03652e25 q^{12} +1.57743e25 q^{13} +3.55908e26 q^{14} -1.47897e27 q^{15} +7.86346e28 q^{16} -3.42618e28 q^{17} -2.32503e29 q^{18} +1.00019e30 q^{19} -4.51042e30 q^{20} +1.98176e30 q^{21} -7.37325e31 q^{22} +5.17765e31 q^{23} +7.44978e32 q^{24} -5.78095e32 q^{25} +3.64060e32 q^{26} -4.71154e33 q^{27} +6.04378e33 q^{28} -6.90432e33 q^{29} -3.41336e34 q^{30} -1.79630e35 q^{31} +9.98970e35 q^{32} -4.10556e35 q^{33} -7.90739e35 q^{34} -1.77475e35 q^{35} -3.94820e36 q^{36} -2.68894e36 q^{37} +2.30836e37 q^{38} +2.02715e36 q^{39} -6.67160e37 q^{40} +1.17249e38 q^{41} +4.57376e37 q^{42} +1.58085e38 q^{43} -1.25208e39 q^{44} +1.15938e38 q^{45} +1.19497e39 q^{46} -1.34555e39 q^{47} +1.01053e40 q^{48} -5.00553e39 q^{49} -1.33420e40 q^{50} -4.40298e39 q^{51} +6.18221e39 q^{52} +4.68526e40 q^{53} -1.08739e41 q^{54} +3.67670e40 q^{55} +8.93968e40 q^{56} +1.28534e41 q^{57} -1.59347e41 q^{58} +3.84916e41 q^{59} -5.79633e41 q^{60} +4.37844e41 q^{61} -4.14573e42 q^{62} -1.55353e41 q^{63} +1.19887e43 q^{64} -1.81540e41 q^{65} -9.47534e42 q^{66} +4.64892e42 q^{67} -1.34278e43 q^{68} +6.65378e42 q^{69} -4.09600e42 q^{70} +1.91856e43 q^{71} -5.83999e43 q^{72} +8.25143e43 q^{73} -6.20589e43 q^{74} -7.42908e43 q^{75} +3.91990e44 q^{76} -4.92663e43 q^{77} +4.67852e43 q^{78} -5.45765e44 q^{79} -9.04975e44 q^{80} -3.37621e44 q^{81} +2.70603e45 q^{82} -1.02727e45 q^{83} +7.76685e44 q^{84} +3.94306e44 q^{85} +3.64849e45 q^{86} -8.87272e44 q^{87} -1.85201e46 q^{88} +1.06667e46 q^{89} +2.67578e45 q^{90} +2.43256e44 q^{91} +2.02921e46 q^{92} -2.30842e46 q^{93} -3.10543e46 q^{94} -1.15107e46 q^{95} +1.28377e47 q^{96} +3.72976e46 q^{97} -1.15524e47 q^{98} +3.21841e46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + 2392716988073784337920q^{8} - 17071972417358142200172q^{9} + O(q^{10}) \) \( 4q + 5785560q^{2} + 38461494960q^{3} + 404807499161152q^{4} - 31114680242272200q^{5} + 2130087053081157408q^{6} - 39169218725888423200q^{7} + \)\(23\!\cdots\!20\)\(q^{8} - \)\(17\!\cdots\!72\)\(q^{9} + \)\(16\!\cdots\!00\)\(q^{10} - \)\(19\!\cdots\!12\)\(q^{11} + \)\(50\!\cdots\!20\)\(q^{12} + \)\(12\!\cdots\!20\)\(q^{13} + \)\(34\!\cdots\!04\)\(q^{14} + \)\(12\!\cdots\!00\)\(q^{15} + \)\(12\!\cdots\!84\)\(q^{16} + \)\(21\!\cdots\!80\)\(q^{17} + \)\(40\!\cdots\!60\)\(q^{18} - \)\(10\!\cdots\!40\)\(q^{19} - \)\(15\!\cdots\!00\)\(q^{20} - \)\(26\!\cdots\!12\)\(q^{21} - \)\(79\!\cdots\!80\)\(q^{22} + \)\(13\!\cdots\!80\)\(q^{23} + \)\(11\!\cdots\!80\)\(q^{24} + \)\(10\!\cdots\!00\)\(q^{25} + \)\(22\!\cdots\!88\)\(q^{26} - \)\(73\!\cdots\!20\)\(q^{27} - \)\(36\!\cdots\!80\)\(q^{28} - \)\(22\!\cdots\!60\)\(q^{29} - \)\(25\!\cdots\!00\)\(q^{30} + \)\(75\!\cdots\!48\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(26\!\cdots\!20\)\(q^{33} - \)\(12\!\cdots\!16\)\(q^{34} - \)\(13\!\cdots\!00\)\(q^{35} - \)\(13\!\cdots\!36\)\(q^{36} - \)\(11\!\cdots\!60\)\(q^{37} + \)\(29\!\cdots\!80\)\(q^{38} + \)\(39\!\cdots\!36\)\(q^{39} + \)\(70\!\cdots\!00\)\(q^{40} + \)\(13\!\cdots\!28\)\(q^{41} - \)\(10\!\cdots\!20\)\(q^{42} - \)\(44\!\cdots\!00\)\(q^{43} - \)\(15\!\cdots\!56\)\(q^{44} + \)\(86\!\cdots\!00\)\(q^{45} + \)\(12\!\cdots\!68\)\(q^{46} + \)\(20\!\cdots\!20\)\(q^{47} + \)\(10\!\cdots\!80\)\(q^{48} + \)\(91\!\cdots\!72\)\(q^{49} - \)\(19\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!52\)\(q^{51} - \)\(55\!\cdots\!00\)\(q^{52} + \)\(29\!\cdots\!60\)\(q^{53} - \)\(11\!\cdots\!40\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} + \)\(27\!\cdots\!40\)\(q^{56} + \)\(55\!\cdots\!60\)\(q^{57} - \)\(73\!\cdots\!80\)\(q^{58} + \)\(47\!\cdots\!80\)\(q^{59} - \)\(21\!\cdots\!00\)\(q^{60} + \)\(62\!\cdots\!88\)\(q^{61} - \)\(68\!\cdots\!80\)\(q^{62} + \)\(58\!\cdots\!40\)\(q^{63} + \)\(55\!\cdots\!72\)\(q^{64} + \)\(12\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!24\)\(q^{66} + \)\(18\!\cdots\!80\)\(q^{67} - \)\(27\!\cdots\!40\)\(q^{68} - \)\(20\!\cdots\!04\)\(q^{69} - \)\(97\!\cdots\!00\)\(q^{70} + \)\(22\!\cdots\!68\)\(q^{71} - \)\(17\!\cdots\!60\)\(q^{72} + \)\(10\!\cdots\!80\)\(q^{73} + \)\(18\!\cdots\!44\)\(q^{74} + \)\(32\!\cdots\!00\)\(q^{75} + \)\(35\!\cdots\!80\)\(q^{76} - \)\(26\!\cdots\!00\)\(q^{77} - \)\(49\!\cdots\!00\)\(q^{78} - \)\(13\!\cdots\!60\)\(q^{79} - \)\(94\!\cdots\!00\)\(q^{80} - \)\(10\!\cdots\!16\)\(q^{81} + \)\(38\!\cdots\!20\)\(q^{82} - \)\(14\!\cdots\!60\)\(q^{83} + \)\(52\!\cdots\!44\)\(q^{84} - \)\(10\!\cdots\!00\)\(q^{85} + \)\(95\!\cdots\!28\)\(q^{86} - \)\(43\!\cdots\!60\)\(q^{87} - \)\(15\!\cdots\!60\)\(q^{88} - \)\(79\!\cdots\!80\)\(q^{89} - \)\(16\!\cdots\!00\)\(q^{90} + \)\(53\!\cdots\!68\)\(q^{91} + \)\(13\!\cdots\!80\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} + \)\(34\!\cdots\!24\)\(q^{94} + \)\(75\!\cdots\!00\)\(q^{95} + \)\(64\!\cdots\!28\)\(q^{96} + \)\(95\!\cdots\!20\)\(q^{97} - \)\(29\!\cdots\!20\)\(q^{98} + \)\(53\!\cdots\!16\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30793e7 1.94544 0.972720 0.231981i \(-0.0745207\pi\)
0.972720 + 0.231981i \(0.0745207\pi\)
\(3\) 1.28510e11 0.788109 0.394055 0.919087i \(-0.371072\pi\)
0.394055 + 0.919087i \(0.371072\pi\)
\(4\) 3.91917e14 2.78474
\(5\) −1.15086e16 −0.431745 −0.215873 0.976422i \(-0.569260\pi\)
−0.215873 + 0.976422i \(0.569260\pi\)
\(6\) 2.96592e18 1.53322
\(7\) 1.54211e19 0.212966 0.106483 0.994315i \(-0.466041\pi\)
0.106483 + 0.994315i \(0.466041\pi\)
\(8\) 5.79706e21 3.47211
\(9\) −1.00741e22 −0.378884
\(10\) −2.65611e23 −0.839935
\(11\) −3.19474e24 −1.07574 −0.537871 0.843027i \(-0.680771\pi\)
−0.537871 + 0.843027i \(0.680771\pi\)
\(12\) 5.03652e25 2.19468
\(13\) 1.57743e25 0.104781 0.0523903 0.998627i \(-0.483316\pi\)
0.0523903 + 0.998627i \(0.483316\pi\)
\(14\) 3.55908e26 0.414313
\(15\) −1.47897e27 −0.340262
\(16\) 7.86346e28 3.97004
\(17\) −3.42618e28 −0.416160 −0.208080 0.978112i \(-0.566722\pi\)
−0.208080 + 0.978112i \(0.566722\pi\)
\(18\) −2.32503e29 −0.737096
\(19\) 1.00019e30 0.889961 0.444980 0.895540i \(-0.353211\pi\)
0.444980 + 0.895540i \(0.353211\pi\)
\(20\) −4.51042e30 −1.20230
\(21\) 1.98176e30 0.167841
\(22\) −7.37325e31 −2.09279
\(23\) 5.17765e31 0.517045 0.258522 0.966005i \(-0.416764\pi\)
0.258522 + 0.966005i \(0.416764\pi\)
\(24\) 7.44978e32 2.73640
\(25\) −5.78095e32 −0.813596
\(26\) 3.64060e32 0.203844
\(27\) −4.71154e33 −1.08671
\(28\) 6.04378e33 0.593055
\(29\) −6.90432e33 −0.297008 −0.148504 0.988912i \(-0.547446\pi\)
−0.148504 + 0.988912i \(0.547446\pi\)
\(30\) −3.41336e34 −0.661960
\(31\) −1.79630e35 −1.61205 −0.806025 0.591882i \(-0.798385\pi\)
−0.806025 + 0.591882i \(0.798385\pi\)
\(32\) 9.98970e35 4.25136
\(33\) −4.10556e35 −0.847802
\(34\) −7.90739e35 −0.809615
\(35\) −1.77475e35 −0.0919471
\(36\) −3.94820e36 −1.05509
\(37\) −2.68894e36 −0.377434 −0.188717 0.982032i \(-0.560433\pi\)
−0.188717 + 0.982032i \(0.560433\pi\)
\(38\) 2.30836e37 1.73137
\(39\) 2.02715e36 0.0825786
\(40\) −6.67160e37 −1.49906
\(41\) 1.17249e38 1.47465 0.737325 0.675538i \(-0.236088\pi\)
0.737325 + 0.675538i \(0.236088\pi\)
\(42\) 4.57376e37 0.326524
\(43\) 1.58085e38 0.649204 0.324602 0.945851i \(-0.394770\pi\)
0.324602 + 0.945851i \(0.394770\pi\)
\(44\) −1.25208e39 −2.99566
\(45\) 1.15938e38 0.163581
\(46\) 1.19497e39 1.00588
\(47\) −1.34555e39 −0.683282 −0.341641 0.939831i \(-0.610983\pi\)
−0.341641 + 0.939831i \(0.610983\pi\)
\(48\) 1.01053e40 3.12882
\(49\) −5.00553e39 −0.954645
\(50\) −1.33420e40 −1.58280
\(51\) −4.40298e39 −0.327980
\(52\) 6.18221e39 0.291787
\(53\) 4.68526e40 1.41335 0.706677 0.707536i \(-0.250193\pi\)
0.706677 + 0.707536i \(0.250193\pi\)
\(54\) −1.08739e41 −2.11413
\(55\) 3.67670e40 0.464446
\(56\) 8.93968e40 0.739440
\(57\) 1.28534e41 0.701387
\(58\) −1.59347e41 −0.577811
\(59\) 3.84916e41 0.933993 0.466997 0.884259i \(-0.345336\pi\)
0.466997 + 0.884259i \(0.345336\pi\)
\(60\) −5.79633e41 −0.947542
\(61\) 4.37844e41 0.485365 0.242683 0.970106i \(-0.421973\pi\)
0.242683 + 0.970106i \(0.421973\pi\)
\(62\) −4.14573e42 −3.13615
\(63\) −1.55353e41 −0.0806893
\(64\) 1.19887e43 4.30074
\(65\) −1.81540e41 −0.0452385
\(66\) −9.47534e42 −1.64935
\(67\) 4.64892e42 0.568321 0.284161 0.958777i \(-0.408285\pi\)
0.284161 + 0.958777i \(0.408285\pi\)
\(68\) −1.34278e43 −1.15890
\(69\) 6.65378e42 0.407488
\(70\) −4.09600e42 −0.178878
\(71\) 1.91856e43 0.600349 0.300175 0.953884i \(-0.402955\pi\)
0.300175 + 0.953884i \(0.402955\pi\)
\(72\) −5.83999e43 −1.31552
\(73\) 8.25143e43 1.34413 0.672066 0.740491i \(-0.265407\pi\)
0.672066 + 0.740491i \(0.265407\pi\)
\(74\) −6.20589e43 −0.734275
\(75\) −7.42908e43 −0.641203
\(76\) 3.91990e44 2.47831
\(77\) −4.92663e43 −0.229096
\(78\) 4.67852e43 0.160652
\(79\) −5.45765e44 −1.38921 −0.694607 0.719389i \(-0.744422\pi\)
−0.694607 + 0.719389i \(0.744422\pi\)
\(80\) −9.04975e44 −1.71404
\(81\) −3.37621e44 −0.477564
\(82\) 2.70603e45 2.86885
\(83\) −1.02727e45 −0.819125 −0.409563 0.912282i \(-0.634319\pi\)
−0.409563 + 0.912282i \(0.634319\pi\)
\(84\) 7.76685e44 0.467392
\(85\) 3.94306e44 0.179675
\(86\) 3.64849e45 1.26299
\(87\) −8.87272e44 −0.234075
\(88\) −1.85201e46 −3.73509
\(89\) 1.06667e46 1.64954 0.824771 0.565467i \(-0.191304\pi\)
0.824771 + 0.565467i \(0.191304\pi\)
\(90\) 2.67578e45 0.318237
\(91\) 2.43256e44 0.0223147
\(92\) 2.02921e46 1.43984
\(93\) −2.30842e46 −1.27047
\(94\) −3.10543e46 −1.32928
\(95\) −1.15107e46 −0.384236
\(96\) 1.28377e47 3.35054
\(97\) 3.72976e46 0.763037 0.381518 0.924361i \(-0.375401\pi\)
0.381518 + 0.924361i \(0.375401\pi\)
\(98\) −1.15524e47 −1.85721
\(99\) 3.21841e46 0.407581
\(100\) −2.26565e47 −2.26565
\(101\) 9.27720e46 0.734285 0.367142 0.930165i \(-0.380336\pi\)
0.367142 + 0.930165i \(0.380336\pi\)
\(102\) −1.01618e47 −0.638065
\(103\) 1.00960e47 0.504051 0.252026 0.967721i \(-0.418903\pi\)
0.252026 + 0.967721i \(0.418903\pi\)
\(104\) 9.14444e46 0.363809
\(105\) −2.28072e46 −0.0724643
\(106\) 1.08133e48 2.74960
\(107\) 1.99211e47 0.406252 0.203126 0.979153i \(-0.434890\pi\)
0.203126 + 0.979153i \(0.434890\pi\)
\(108\) −1.84653e48 −3.02621
\(109\) −6.24516e47 −0.824177 −0.412089 0.911144i \(-0.635201\pi\)
−0.412089 + 0.911144i \(0.635201\pi\)
\(110\) 8.48558e47 0.903553
\(111\) −3.45555e47 −0.297459
\(112\) 1.21263e48 0.845483
\(113\) −2.17631e48 −1.23134 −0.615669 0.788005i \(-0.711114\pi\)
−0.615669 + 0.788005i \(0.711114\pi\)
\(114\) 2.96647e48 1.36451
\(115\) −5.95875e47 −0.223232
\(116\) −2.70592e48 −0.827089
\(117\) −1.58911e47 −0.0396996
\(118\) 8.88360e48 1.81703
\(119\) −5.28354e47 −0.0886280
\(120\) −8.57366e48 −1.18143
\(121\) 1.38664e48 0.157220
\(122\) 1.01051e49 0.944249
\(123\) 1.50677e49 1.16219
\(124\) −7.04000e49 −4.48914
\(125\) 1.48304e49 0.783011
\(126\) −3.58544e48 −0.156976
\(127\) −1.42624e49 −0.518568 −0.259284 0.965801i \(-0.583487\pi\)
−0.259284 + 0.965801i \(0.583487\pi\)
\(128\) 1.36099e50 4.11547
\(129\) 2.03154e49 0.511644
\(130\) −4.18982e48 −0.0880088
\(131\) −7.28871e49 −1.27872 −0.639359 0.768908i \(-0.720800\pi\)
−0.639359 + 0.768908i \(0.720800\pi\)
\(132\) −1.60904e50 −2.36091
\(133\) 1.54239e49 0.189531
\(134\) 1.07294e50 1.10564
\(135\) 5.42232e49 0.469182
\(136\) −1.98618e50 −1.44495
\(137\) 2.99893e49 0.183668 0.0918338 0.995774i \(-0.470727\pi\)
0.0918338 + 0.995774i \(0.470727\pi\)
\(138\) 1.53565e50 0.792743
\(139\) 1.25821e50 0.548159 0.274079 0.961707i \(-0.411627\pi\)
0.274079 + 0.961707i \(0.411627\pi\)
\(140\) −6.95555e49 −0.256049
\(141\) −1.72916e50 −0.538501
\(142\) 4.42790e50 1.16794
\(143\) −5.03948e49 −0.112717
\(144\) −7.92171e50 −1.50418
\(145\) 7.94590e49 0.128232
\(146\) 1.90437e51 2.61493
\(147\) −6.43259e50 −0.752365
\(148\) −1.05384e51 −1.05106
\(149\) −1.60599e51 −1.36730 −0.683652 0.729809i \(-0.739609\pi\)
−0.683652 + 0.729809i \(0.739609\pi\)
\(150\) −1.71458e51 −1.24742
\(151\) 2.76267e49 0.0171938 0.00859689 0.999963i \(-0.497263\pi\)
0.00859689 + 0.999963i \(0.497263\pi\)
\(152\) 5.79813e51 3.09004
\(153\) 3.45156e50 0.157676
\(154\) −1.13703e51 −0.445693
\(155\) 2.06729e51 0.695995
\(156\) 7.94474e50 0.229960
\(157\) 3.26071e51 0.812214 0.406107 0.913825i \(-0.366886\pi\)
0.406107 + 0.913825i \(0.366886\pi\)
\(158\) −1.25959e52 −2.70263
\(159\) 6.02102e51 1.11388
\(160\) −1.14968e52 −1.83551
\(161\) 7.98448e50 0.110113
\(162\) −7.79206e51 −0.929072
\(163\) −1.71469e51 −0.176920 −0.0884602 0.996080i \(-0.528195\pi\)
−0.0884602 + 0.996080i \(0.528195\pi\)
\(164\) 4.59520e52 4.10652
\(165\) 4.72492e51 0.366034
\(166\) −2.37087e52 −1.59356
\(167\) −1.35054e52 −0.788264 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(168\) 1.14884e52 0.582760
\(169\) −2.24152e52 −0.989021
\(170\) 9.10030e51 0.349548
\(171\) −1.00759e52 −0.337192
\(172\) 6.19562e52 1.80787
\(173\) 9.07124e51 0.230985 0.115492 0.993308i \(-0.463155\pi\)
0.115492 + 0.993308i \(0.463155\pi\)
\(174\) −2.04776e52 −0.455378
\(175\) −8.91484e51 −0.173268
\(176\) −2.51218e53 −4.27073
\(177\) 4.94655e52 0.736089
\(178\) 2.46179e53 3.20908
\(179\) −2.83103e52 −0.323518 −0.161759 0.986830i \(-0.551717\pi\)
−0.161759 + 0.986830i \(0.551717\pi\)
\(180\) 4.54383e52 0.455531
\(181\) −7.28434e52 −0.641127 −0.320563 0.947227i \(-0.603872\pi\)
−0.320563 + 0.947227i \(0.603872\pi\)
\(182\) 5.61418e51 0.0434119
\(183\) 5.62672e52 0.382521
\(184\) 3.00151e53 1.79523
\(185\) 3.09460e52 0.162955
\(186\) −5.32767e53 −2.47163
\(187\) 1.09458e53 0.447681
\(188\) −5.27344e53 −1.90276
\(189\) −7.26569e52 −0.231433
\(190\) −2.65660e53 −0.747509
\(191\) 2.15414e53 0.535785 0.267893 0.963449i \(-0.413673\pi\)
0.267893 + 0.963449i \(0.413673\pi\)
\(192\) 1.54067e54 3.38945
\(193\) −4.58281e53 −0.892351 −0.446175 0.894946i \(-0.647214\pi\)
−0.446175 + 0.894946i \(0.647214\pi\)
\(194\) 8.60804e53 1.48444
\(195\) −2.33296e52 −0.0356529
\(196\) −1.96175e54 −2.65844
\(197\) 2.29005e53 0.275353 0.137676 0.990477i \(-0.456037\pi\)
0.137676 + 0.990477i \(0.456037\pi\)
\(198\) 7.42786e53 0.792924
\(199\) 1.26295e54 1.19767 0.598835 0.800872i \(-0.295630\pi\)
0.598835 + 0.800872i \(0.295630\pi\)
\(200\) −3.35125e54 −2.82489
\(201\) 5.97431e53 0.447899
\(202\) 2.14111e54 1.42851
\(203\) −1.06472e53 −0.0632525
\(204\) −1.72560e54 −0.913339
\(205\) −1.34937e54 −0.636673
\(206\) 2.33009e54 0.980602
\(207\) −5.21599e53 −0.195900
\(208\) 1.24040e54 0.415983
\(209\) −3.19534e54 −0.957368
\(210\) −5.26376e53 −0.140975
\(211\) −4.97549e54 −1.19178 −0.595892 0.803064i \(-0.703201\pi\)
−0.595892 + 0.803064i \(0.703201\pi\)
\(212\) 1.83624e55 3.93582
\(213\) 2.46554e54 0.473141
\(214\) 4.59766e54 0.790339
\(215\) −1.81934e54 −0.280291
\(216\) −2.73130e55 −3.77318
\(217\) −2.77008e54 −0.343312
\(218\) −1.44134e55 −1.60339
\(219\) 1.06039e55 1.05932
\(220\) 1.44096e55 1.29336
\(221\) −5.40455e53 −0.0436055
\(222\) −7.97518e54 −0.578689
\(223\) 2.79892e55 1.82737 0.913686 0.406421i \(-0.133223\pi\)
0.913686 + 0.406421i \(0.133223\pi\)
\(224\) 1.54052e55 0.905396
\(225\) 5.82376e54 0.308258
\(226\) −5.02277e55 −2.39549
\(227\) 1.40478e55 0.603949 0.301974 0.953316i \(-0.402354\pi\)
0.301974 + 0.953316i \(0.402354\pi\)
\(228\) 5.03745e55 1.95318
\(229\) −4.09641e55 −1.43308 −0.716539 0.697547i \(-0.754275\pi\)
−0.716539 + 0.697547i \(0.754275\pi\)
\(230\) −1.37524e55 −0.434284
\(231\) −6.33120e54 −0.180553
\(232\) −4.00247e55 −1.03124
\(233\) −1.21897e55 −0.283876 −0.141938 0.989876i \(-0.545333\pi\)
−0.141938 + 0.989876i \(0.545333\pi\)
\(234\) −3.66756e54 −0.0772333
\(235\) 1.54854e55 0.295004
\(236\) 1.50855e56 2.60093
\(237\) −7.01362e55 −1.09485
\(238\) −1.21940e55 −0.172421
\(239\) 6.34948e55 0.813556 0.406778 0.913527i \(-0.366652\pi\)
0.406778 + 0.913527i \(0.366652\pi\)
\(240\) −1.16298e56 −1.35085
\(241\) −1.11357e56 −1.17305 −0.586525 0.809931i \(-0.699504\pi\)
−0.586525 + 0.809931i \(0.699504\pi\)
\(242\) 3.20027e55 0.305862
\(243\) 8.18866e55 0.710339
\(244\) 1.71599e56 1.35162
\(245\) 5.76066e55 0.412164
\(246\) 3.47751e56 2.26096
\(247\) 1.57772e55 0.0932506
\(248\) −1.04132e57 −5.59721
\(249\) −1.32014e56 −0.645560
\(250\) 3.42276e56 1.52330
\(251\) 1.81960e56 0.737299 0.368649 0.929569i \(-0.379820\pi\)
0.368649 + 0.929569i \(0.379820\pi\)
\(252\) −6.08854e55 −0.224699
\(253\) −1.65413e56 −0.556207
\(254\) −3.29167e56 −1.00884
\(255\) 5.06721e55 0.141604
\(256\) 1.45380e57 3.70566
\(257\) −3.46416e56 −0.805694 −0.402847 0.915267i \(-0.631979\pi\)
−0.402847 + 0.915267i \(0.631979\pi\)
\(258\) 4.68866e56 0.995373
\(259\) −4.14663e55 −0.0803806
\(260\) −7.11486e55 −0.125977
\(261\) 6.95545e55 0.112531
\(262\) −1.68218e57 −2.48767
\(263\) 1.25535e57 1.69748 0.848738 0.528814i \(-0.177363\pi\)
0.848738 + 0.528814i \(0.177363\pi\)
\(264\) −2.38001e57 −2.94366
\(265\) −5.39208e56 −0.610209
\(266\) 3.55974e56 0.368722
\(267\) 1.37077e57 1.30002
\(268\) 1.82199e57 1.58263
\(269\) −2.60597e55 −0.0207391 −0.0103696 0.999946i \(-0.503301\pi\)
−0.0103696 + 0.999946i \(0.503301\pi\)
\(270\) 1.25143e57 0.912766
\(271\) −1.42492e57 −0.952822 −0.476411 0.879223i \(-0.658063\pi\)
−0.476411 + 0.879223i \(0.658063\pi\)
\(272\) −2.69417e57 −1.65217
\(273\) 3.12608e55 0.0175864
\(274\) 6.92132e56 0.357314
\(275\) 1.84686e57 0.875219
\(276\) 2.60773e57 1.13475
\(277\) −3.96329e57 −1.58409 −0.792047 0.610461i \(-0.790984\pi\)
−0.792047 + 0.610461i \(0.790984\pi\)
\(278\) 2.90387e57 1.06641
\(279\) 1.80960e57 0.610779
\(280\) −1.02883e57 −0.319250
\(281\) −4.27684e57 −1.22046 −0.610231 0.792223i \(-0.708924\pi\)
−0.610231 + 0.792223i \(0.708924\pi\)
\(282\) −3.99078e57 −1.04762
\(283\) −9.57574e56 −0.231308 −0.115654 0.993290i \(-0.536896\pi\)
−0.115654 + 0.993290i \(0.536896\pi\)
\(284\) 7.51917e57 1.67182
\(285\) −1.47924e57 −0.302820
\(286\) −1.16308e57 −0.219284
\(287\) 1.80811e57 0.314050
\(288\) −1.00637e58 −1.61077
\(289\) −5.60409e57 −0.826811
\(290\) 1.83386e57 0.249467
\(291\) 4.79311e57 0.601357
\(292\) 3.23388e58 3.74306
\(293\) 1.40107e58 1.49648 0.748241 0.663427i \(-0.230899\pi\)
0.748241 + 0.663427i \(0.230899\pi\)
\(294\) −1.48460e58 −1.46368
\(295\) −4.42985e57 −0.403247
\(296\) −1.55880e58 −1.31049
\(297\) 1.50522e58 1.16902
\(298\) −3.70651e58 −2.66001
\(299\) 8.16736e56 0.0541762
\(300\) −2.91158e58 −1.78558
\(301\) 2.43784e57 0.138258
\(302\) 6.37606e56 0.0334495
\(303\) 1.19221e58 0.578697
\(304\) 7.86492e58 3.53318
\(305\) −5.03897e57 −0.209554
\(306\) 7.96596e57 0.306750
\(307\) −4.70339e58 −1.67749 −0.838743 0.544527i \(-0.816709\pi\)
−0.838743 + 0.544527i \(0.816709\pi\)
\(308\) −1.93083e58 −0.637974
\(309\) 1.29743e58 0.397248
\(310\) 4.77116e58 1.35402
\(311\) −2.66280e58 −0.700600 −0.350300 0.936638i \(-0.613920\pi\)
−0.350300 + 0.936638i \(0.613920\pi\)
\(312\) 1.17515e58 0.286721
\(313\) −5.63252e58 −1.27471 −0.637354 0.770571i \(-0.719971\pi\)
−0.637354 + 0.770571i \(0.719971\pi\)
\(314\) 7.52550e58 1.58012
\(315\) 1.78789e57 0.0348372
\(316\) −2.13895e59 −3.86860
\(317\) 9.99715e58 1.67874 0.839371 0.543560i \(-0.182924\pi\)
0.839371 + 0.543560i \(0.182924\pi\)
\(318\) 1.38961e59 2.16698
\(319\) 2.20575e58 0.319503
\(320\) −1.37973e59 −1.85682
\(321\) 2.56006e58 0.320171
\(322\) 1.84276e58 0.214218
\(323\) −3.42682e58 −0.370366
\(324\) −1.32319e59 −1.32989
\(325\) −9.11903e57 −0.0852491
\(326\) −3.95740e58 −0.344188
\(327\) −8.02563e58 −0.649542
\(328\) 6.79700e59 5.12014
\(329\) −2.07498e58 −0.145516
\(330\) 1.09048e59 0.712098
\(331\) −1.86524e58 −0.113443 −0.0567215 0.998390i \(-0.518065\pi\)
−0.0567215 + 0.998390i \(0.518065\pi\)
\(332\) −4.02606e59 −2.28105
\(333\) 2.70886e58 0.143004
\(334\) −3.11696e59 −1.53352
\(335\) −5.35025e58 −0.245370
\(336\) 1.55835e59 0.666333
\(337\) 2.11425e59 0.843050 0.421525 0.906817i \(-0.361495\pi\)
0.421525 + 0.906817i \(0.361495\pi\)
\(338\) −5.17328e59 −1.92408
\(339\) −2.79677e59 −0.970429
\(340\) 1.54535e59 0.500349
\(341\) 5.73871e59 1.73415
\(342\) −2.32546e59 −0.655986
\(343\) −1.58048e59 −0.416273
\(344\) 9.16427e59 2.25411
\(345\) −7.65757e58 −0.175931
\(346\) 2.09358e59 0.449367
\(347\) 1.60147e59 0.321200 0.160600 0.987020i \(-0.448657\pi\)
0.160600 + 0.987020i \(0.448657\pi\)
\(348\) −3.47737e59 −0.651837
\(349\) 8.79943e59 1.54190 0.770951 0.636894i \(-0.219781\pi\)
0.770951 + 0.636894i \(0.219781\pi\)
\(350\) −2.05748e59 −0.337083
\(351\) −7.43211e58 −0.113866
\(352\) −3.19145e60 −4.57337
\(353\) −9.28528e59 −1.24477 −0.622386 0.782711i \(-0.713836\pi\)
−0.622386 + 0.782711i \(0.713836\pi\)
\(354\) 1.14163e60 1.43202
\(355\) −2.20799e59 −0.259198
\(356\) 4.18045e60 4.59354
\(357\) −6.78986e58 −0.0698486
\(358\) −6.53382e59 −0.629385
\(359\) −1.74133e60 −1.57095 −0.785475 0.618893i \(-0.787581\pi\)
−0.785475 + 0.618893i \(0.787581\pi\)
\(360\) 6.72102e59 0.567971
\(361\) −2.62675e59 −0.207970
\(362\) −1.68118e60 −1.24727
\(363\) 1.78197e59 0.123906
\(364\) 9.53363e58 0.0621406
\(365\) −9.49624e59 −0.580323
\(366\) 1.29861e60 0.744171
\(367\) 2.18975e60 1.17691 0.588453 0.808531i \(-0.299737\pi\)
0.588453 + 0.808531i \(0.299737\pi\)
\(368\) 4.07142e60 2.05269
\(369\) −1.18118e60 −0.558721
\(370\) 7.14212e59 0.317020
\(371\) 7.22517e59 0.300996
\(372\) −9.04709e60 −3.53793
\(373\) 1.69293e60 0.621556 0.310778 0.950482i \(-0.399410\pi\)
0.310778 + 0.950482i \(0.399410\pi\)
\(374\) 2.52621e60 0.870937
\(375\) 1.90585e60 0.617099
\(376\) −7.80022e60 −2.37243
\(377\) −1.08911e59 −0.0311206
\(378\) −1.67687e60 −0.450238
\(379\) 4.02001e60 1.01439 0.507196 0.861831i \(-0.330682\pi\)
0.507196 + 0.861831i \(0.330682\pi\)
\(380\) −4.51126e60 −1.07000
\(381\) −1.83286e60 −0.408688
\(382\) 4.97162e60 1.04234
\(383\) 2.58725e60 0.510113 0.255057 0.966926i \(-0.417906\pi\)
0.255057 + 0.966926i \(0.417906\pi\)
\(384\) 1.74900e61 3.24344
\(385\) 5.66987e59 0.0989113
\(386\) −1.05768e61 −1.73602
\(387\) −1.59256e60 −0.245973
\(388\) 1.46176e61 2.12486
\(389\) −7.66990e60 −1.04948 −0.524740 0.851263i \(-0.675837\pi\)
−0.524740 + 0.851263i \(0.675837\pi\)
\(390\) −5.38432e59 −0.0693606
\(391\) −1.77396e60 −0.215174
\(392\) −2.90173e61 −3.31463
\(393\) −9.36670e60 −1.00777
\(394\) 5.28529e60 0.535683
\(395\) 6.28100e60 0.599787
\(396\) 1.26135e61 1.13501
\(397\) 2.69403e60 0.228468 0.114234 0.993454i \(-0.463559\pi\)
0.114234 + 0.993454i \(0.463559\pi\)
\(398\) 2.91479e61 2.33000
\(399\) 1.98212e60 0.149372
\(400\) −4.54583e61 −3.23001
\(401\) −8.61448e60 −0.577213 −0.288607 0.957448i \(-0.593192\pi\)
−0.288607 + 0.957448i \(0.593192\pi\)
\(402\) 1.37883e61 0.871362
\(403\) −2.83353e60 −0.168912
\(404\) 3.63589e61 2.04479
\(405\) 3.88554e60 0.206186
\(406\) −2.45730e60 −0.123054
\(407\) 8.59048e60 0.406021
\(408\) −2.55243e61 −1.13878
\(409\) −4.89023e60 −0.205983 −0.102992 0.994682i \(-0.532841\pi\)
−0.102992 + 0.994682i \(0.532841\pi\)
\(410\) −3.11426e61 −1.23861
\(411\) 3.85391e60 0.144750
\(412\) 3.95680e61 1.40365
\(413\) 5.93581e60 0.198909
\(414\) −1.20382e61 −0.381111
\(415\) 1.18225e61 0.353653
\(416\) 1.57580e61 0.445460
\(417\) 1.61693e61 0.432009
\(418\) −7.37462e61 −1.86250
\(419\) −4.08353e60 −0.0975003 −0.0487501 0.998811i \(-0.515524\pi\)
−0.0487501 + 0.998811i \(0.515524\pi\)
\(420\) −8.93855e60 −0.201794
\(421\) −8.09919e61 −1.72907 −0.864534 0.502574i \(-0.832386\pi\)
−0.864534 + 0.502574i \(0.832386\pi\)
\(422\) −1.14831e62 −2.31855
\(423\) 1.35551e61 0.258884
\(424\) 2.71607e62 4.90731
\(425\) 1.98066e61 0.338586
\(426\) 5.69029e61 0.920468
\(427\) 6.75202e60 0.103366
\(428\) 7.80744e61 1.13131
\(429\) −6.47622e60 −0.0888332
\(430\) −4.19890e61 −0.545289
\(431\) 5.41910e61 0.666364 0.333182 0.942863i \(-0.391878\pi\)
0.333182 + 0.942863i \(0.391878\pi\)
\(432\) −3.70490e62 −4.31428
\(433\) 1.10085e62 1.21412 0.607060 0.794656i \(-0.292349\pi\)
0.607060 + 0.794656i \(0.292349\pi\)
\(434\) −6.39316e61 −0.667893
\(435\) 1.02113e61 0.101061
\(436\) −2.44758e62 −2.29512
\(437\) 5.17861e61 0.460150
\(438\) 2.44731e62 2.06085
\(439\) −1.32013e62 −1.05366 −0.526832 0.849969i \(-0.676620\pi\)
−0.526832 + 0.849969i \(0.676620\pi\)
\(440\) 2.13141e62 1.61261
\(441\) 5.04260e61 0.361699
\(442\) −1.24733e61 −0.0848320
\(443\) −8.89175e61 −0.573455 −0.286728 0.958012i \(-0.592567\pi\)
−0.286728 + 0.958012i \(0.592567\pi\)
\(444\) −1.35429e62 −0.828346
\(445\) −1.22758e62 −0.712181
\(446\) 6.45973e62 3.55504
\(447\) −2.06385e62 −1.07758
\(448\) 1.84879e62 0.915911
\(449\) 9.45855e61 0.444668 0.222334 0.974971i \(-0.428633\pi\)
0.222334 + 0.974971i \(0.428633\pi\)
\(450\) 1.34408e62 0.599698
\(451\) −3.74581e62 −1.58634
\(452\) −8.52933e62 −3.42896
\(453\) 3.55030e60 0.0135506
\(454\) 3.24213e62 1.17495
\(455\) −2.79954e60 −0.00963426
\(456\) 7.45116e62 2.43529
\(457\) 3.37293e62 1.04707 0.523536 0.852003i \(-0.324612\pi\)
0.523536 + 0.852003i \(0.324612\pi\)
\(458\) −9.45424e62 −2.78797
\(459\) 1.61426e62 0.452246
\(460\) −2.33534e62 −0.621642
\(461\) 4.97092e62 1.25738 0.628688 0.777658i \(-0.283592\pi\)
0.628688 + 0.777658i \(0.283592\pi\)
\(462\) −1.46120e62 −0.351255
\(463\) −4.42973e62 −1.01210 −0.506051 0.862504i \(-0.668895\pi\)
−0.506051 + 0.862504i \(0.668895\pi\)
\(464\) −5.42918e62 −1.17913
\(465\) 2.65667e62 0.548520
\(466\) −2.81330e62 −0.552264
\(467\) 7.17000e62 1.33836 0.669179 0.743101i \(-0.266646\pi\)
0.669179 + 0.743101i \(0.266646\pi\)
\(468\) −6.22800e61 −0.110553
\(469\) 7.16912e61 0.121033
\(470\) 3.57392e62 0.573912
\(471\) 4.19033e62 0.640114
\(472\) 2.23138e63 3.24292
\(473\) −5.05040e62 −0.698376
\(474\) −1.61869e63 −2.12997
\(475\) −5.78202e62 −0.724069
\(476\) −2.07071e62 −0.246806
\(477\) −4.71996e62 −0.535497
\(478\) 1.46542e63 1.58273
\(479\) −1.03149e62 −0.106067 −0.0530337 0.998593i \(-0.516889\pi\)
−0.0530337 + 0.998593i \(0.516889\pi\)
\(480\) −1.47744e63 −1.44658
\(481\) −4.24161e61 −0.0395477
\(482\) −2.57004e63 −2.28210
\(483\) 1.02608e62 0.0867811
\(484\) 5.43448e62 0.437816
\(485\) −4.29244e62 −0.329438
\(486\) 1.88989e63 1.38192
\(487\) −2.41720e61 −0.0168415 −0.00842076 0.999965i \(-0.502680\pi\)
−0.00842076 + 0.999965i \(0.502680\pi\)
\(488\) 2.53821e63 1.68524
\(489\) −2.20355e62 −0.139433
\(490\) 1.32952e63 0.801840
\(491\) −1.48334e63 −0.852760 −0.426380 0.904544i \(-0.640211\pi\)
−0.426380 + 0.904544i \(0.640211\pi\)
\(492\) 5.90528e63 3.23639
\(493\) 2.36554e62 0.123603
\(494\) 3.64127e62 0.181414
\(495\) −3.70394e62 −0.175971
\(496\) −1.41251e64 −6.39989
\(497\) 2.95862e62 0.127854
\(498\) −3.04680e63 −1.25590
\(499\) 3.58476e63 1.40960 0.704802 0.709404i \(-0.251036\pi\)
0.704802 + 0.709404i \(0.251036\pi\)
\(500\) 5.81230e63 2.18048
\(501\) −1.73558e63 −0.621238
\(502\) 4.19951e63 1.43437
\(503\) 3.59373e63 1.17138 0.585691 0.810535i \(-0.300823\pi\)
0.585691 + 0.810535i \(0.300823\pi\)
\(504\) −9.00589e62 −0.280162
\(505\) −1.06768e63 −0.317024
\(506\) −3.81761e63 −1.08207
\(507\) −2.88057e63 −0.779457
\(508\) −5.58969e63 −1.44408
\(509\) 1.51124e63 0.372790 0.186395 0.982475i \(-0.440320\pi\)
0.186395 + 0.982475i \(0.440320\pi\)
\(510\) 1.16948e63 0.275482
\(511\) 1.27246e63 0.286255
\(512\) 1.43986e64 3.09368
\(513\) −4.71241e63 −0.967130
\(514\) −7.99505e63 −1.56743
\(515\) −1.16191e63 −0.217622
\(516\) 7.96197e63 1.42480
\(517\) 4.29868e63 0.735034
\(518\) −9.57015e62 −0.156376
\(519\) 1.16574e63 0.182041
\(520\) −1.05240e63 −0.157073
\(521\) −5.89563e63 −0.841093 −0.420546 0.907271i \(-0.638162\pi\)
−0.420546 + 0.907271i \(0.638162\pi\)
\(522\) 1.60527e63 0.218923
\(523\) 1.19071e64 1.55245 0.776224 0.630457i \(-0.217132\pi\)
0.776224 + 0.630457i \(0.217132\pi\)
\(524\) −2.85657e64 −3.56090
\(525\) −1.14564e63 −0.136554
\(526\) 2.89725e64 3.30234
\(527\) 6.15444e63 0.670871
\(528\) −3.22839e64 −3.36580
\(529\) −7.34706e63 −0.732665
\(530\) −1.24446e64 −1.18712
\(531\) −3.87767e63 −0.353875
\(532\) 6.04490e63 0.527796
\(533\) 1.84952e63 0.154515
\(534\) 3.16364e64 2.52911
\(535\) −2.29264e63 −0.175397
\(536\) 2.69500e64 1.97327
\(537\) −3.63815e63 −0.254968
\(538\) −6.01439e62 −0.0403467
\(539\) 1.59914e64 1.02695
\(540\) 2.12510e64 1.30655
\(541\) −1.24707e64 −0.734101 −0.367051 0.930201i \(-0.619632\pi\)
−0.367051 + 0.930201i \(0.619632\pi\)
\(542\) −3.28861e64 −1.85366
\(543\) −9.36109e63 −0.505278
\(544\) −3.42265e64 −1.76925
\(545\) 7.18730e63 0.355835
\(546\) 7.21477e62 0.0342134
\(547\) −3.38744e64 −1.53876 −0.769378 0.638794i \(-0.779434\pi\)
−0.769378 + 0.638794i \(0.779434\pi\)
\(548\) 1.17533e64 0.511467
\(549\) −4.41087e63 −0.183897
\(550\) 4.26244e64 1.70269
\(551\) −6.90560e63 −0.264325
\(552\) 3.85723e64 1.41484
\(553\) −8.41628e63 −0.295856
\(554\) −9.14699e64 −3.08176
\(555\) 3.97686e63 0.128427
\(556\) 4.93115e64 1.52648
\(557\) 4.80284e64 1.42528 0.712641 0.701528i \(-0.247499\pi\)
0.712641 + 0.701528i \(0.247499\pi\)
\(558\) 4.17644e64 1.18823
\(559\) 2.49367e63 0.0680240
\(560\) −1.39557e64 −0.365033
\(561\) 1.40664e64 0.352822
\(562\) −9.87066e64 −2.37434
\(563\) 3.05103e64 0.703882 0.351941 0.936022i \(-0.385522\pi\)
0.351941 + 0.936022i \(0.385522\pi\)
\(564\) −6.77688e64 −1.49958
\(565\) 2.50463e64 0.531624
\(566\) −2.21002e64 −0.449997
\(567\) −5.20647e63 −0.101705
\(568\) 1.11220e65 2.08448
\(569\) 7.49437e64 1.34771 0.673856 0.738863i \(-0.264637\pi\)
0.673856 + 0.738863i \(0.264637\pi\)
\(570\) −3.41399e64 −0.589119
\(571\) −5.47320e64 −0.906344 −0.453172 0.891423i \(-0.649708\pi\)
−0.453172 + 0.891423i \(0.649708\pi\)
\(572\) −1.97506e64 −0.313887
\(573\) 2.76828e64 0.422257
\(574\) 4.17299e64 0.610967
\(575\) −2.99317e64 −0.420666
\(576\) −1.20775e65 −1.62948
\(577\) −4.19523e63 −0.0543406 −0.0271703 0.999631i \(-0.508650\pi\)
−0.0271703 + 0.999631i \(0.508650\pi\)
\(578\) −1.29339e65 −1.60851
\(579\) −5.88936e64 −0.703270
\(580\) 3.11414e64 0.357092
\(581\) −1.58416e64 −0.174446
\(582\) 1.10622e65 1.16990
\(583\) −1.49682e65 −1.52040
\(584\) 4.78340e65 4.66697
\(585\) 1.82884e63 0.0171401
\(586\) 3.23358e65 2.91132
\(587\) 3.17978e64 0.275043 0.137522 0.990499i \(-0.456086\pi\)
0.137522 + 0.990499i \(0.456086\pi\)
\(588\) −2.52104e65 −2.09514
\(589\) −1.79663e65 −1.43466
\(590\) −1.02238e65 −0.784493
\(591\) 2.94294e64 0.217008
\(592\) −2.11444e65 −1.49843
\(593\) 4.66511e64 0.317744 0.158872 0.987299i \(-0.449214\pi\)
0.158872 + 0.987299i \(0.449214\pi\)
\(594\) 3.47393e65 2.27426
\(595\) 6.08061e63 0.0382647
\(596\) −6.29414e65 −3.80758
\(597\) 1.62301e65 0.943896
\(598\) 1.88497e64 0.105397
\(599\) 2.50137e65 1.34477 0.672384 0.740202i \(-0.265270\pi\)
0.672384 + 0.740202i \(0.265270\pi\)
\(600\) −4.30668e65 −2.22632
\(601\) 4.33262e64 0.215377 0.107689 0.994185i \(-0.465655\pi\)
0.107689 + 0.994185i \(0.465655\pi\)
\(602\) 5.62636e64 0.268974
\(603\) −4.68335e64 −0.215328
\(604\) 1.08274e64 0.0478802
\(605\) −1.59583e64 −0.0678789
\(606\) 2.75154e65 1.12582
\(607\) −2.09462e64 −0.0824464 −0.0412232 0.999150i \(-0.513125\pi\)
−0.0412232 + 0.999150i \(0.513125\pi\)
\(608\) 9.99156e65 3.78355
\(609\) −1.36827e64 −0.0498499
\(610\) −1.16296e65 −0.407675
\(611\) −2.12251e64 −0.0715946
\(612\) 1.35273e65 0.439088
\(613\) −4.02606e65 −1.25765 −0.628824 0.777548i \(-0.716463\pi\)
−0.628824 + 0.777548i \(0.716463\pi\)
\(614\) −1.08551e66 −3.26345
\(615\) −1.73408e65 −0.501768
\(616\) −2.85600e65 −0.795447
\(617\) 4.25894e65 1.14183 0.570914 0.821010i \(-0.306589\pi\)
0.570914 + 0.821010i \(0.306589\pi\)
\(618\) 2.99439e65 0.772821
\(619\) 3.05847e65 0.759931 0.379965 0.925001i \(-0.375936\pi\)
0.379965 + 0.925001i \(0.375936\pi\)
\(620\) 8.10206e65 1.93816
\(621\) −2.43947e65 −0.561878
\(622\) −6.14557e65 −1.36298
\(623\) 1.64491e65 0.351296
\(624\) 1.59404e65 0.327840
\(625\) 2.40084e65 0.475535
\(626\) −1.29995e66 −2.47987
\(627\) −4.10632e65 −0.754511
\(628\) 1.27793e66 2.26181
\(629\) 9.21280e64 0.157073
\(630\) 4.12634e64 0.0677738
\(631\) 6.21302e65 0.983134 0.491567 0.870840i \(-0.336424\pi\)
0.491567 + 0.870840i \(0.336424\pi\)
\(632\) −3.16383e66 −4.82350
\(633\) −6.39398e65 −0.939257
\(634\) 2.30727e66 3.26589
\(635\) 1.64141e65 0.223889
\(636\) 2.35974e66 3.10186
\(637\) −7.89586e64 −0.100028
\(638\) 5.09072e65 0.621575
\(639\) −1.93277e65 −0.227463
\(640\) −1.56631e66 −1.77683
\(641\) −6.05212e65 −0.661826 −0.330913 0.943661i \(-0.607357\pi\)
−0.330913 + 0.943661i \(0.607357\pi\)
\(642\) 5.90844e65 0.622873
\(643\) 8.65041e65 0.879183 0.439591 0.898198i \(-0.355123\pi\)
0.439591 + 0.898198i \(0.355123\pi\)
\(644\) 3.12926e65 0.306636
\(645\) −2.33802e65 −0.220900
\(646\) −7.90886e65 −0.720526
\(647\) 2.75625e65 0.242141 0.121070 0.992644i \(-0.461367\pi\)
0.121070 + 0.992644i \(0.461367\pi\)
\(648\) −1.95721e66 −1.65815
\(649\) −1.22971e66 −1.00474
\(650\) −2.10461e65 −0.165847
\(651\) −3.55982e65 −0.270567
\(652\) −6.72018e65 −0.492677
\(653\) −1.27020e66 −0.898282 −0.449141 0.893461i \(-0.648270\pi\)
−0.449141 + 0.893461i \(0.648270\pi\)
\(654\) −1.85226e66 −1.26365
\(655\) 8.38828e65 0.552081
\(656\) 9.21985e66 5.85441
\(657\) −8.31254e65 −0.509270
\(658\) −4.78891e65 −0.283092
\(659\) 1.08832e66 0.620794 0.310397 0.950607i \(-0.399538\pi\)
0.310397 + 0.950607i \(0.399538\pi\)
\(660\) 1.85178e66 1.01931
\(661\) 1.19166e66 0.633020 0.316510 0.948589i \(-0.397489\pi\)
0.316510 + 0.948589i \(0.397489\pi\)
\(662\) −4.30485e65 −0.220697
\(663\) −6.94538e64 −0.0343659
\(664\) −5.95515e66 −2.84409
\(665\) −1.77508e65 −0.0818293
\(666\) 6.25186e65 0.278205
\(667\) −3.57481e65 −0.153566
\(668\) −5.29301e66 −2.19511
\(669\) 3.59689e66 1.44017
\(670\) −1.23480e66 −0.477353
\(671\) −1.39880e66 −0.522127
\(672\) 1.97972e66 0.713551
\(673\) 2.35019e66 0.817993 0.408997 0.912536i \(-0.365879\pi\)
0.408997 + 0.912536i \(0.365879\pi\)
\(674\) 4.87954e66 1.64010
\(675\) 2.72371e66 0.884144
\(676\) −8.78491e66 −2.75417
\(677\) −1.35609e66 −0.410633 −0.205316 0.978696i \(-0.565822\pi\)
−0.205316 + 0.978696i \(0.565822\pi\)
\(678\) −6.45475e66 −1.88791
\(679\) 5.75169e65 0.162501
\(680\) 2.28581e66 0.623851
\(681\) 1.80528e66 0.475978
\(682\) 1.32446e67 3.37368
\(683\) −2.30165e66 −0.566438 −0.283219 0.959055i \(-0.591402\pi\)
−0.283219 + 0.959055i \(0.591402\pi\)
\(684\) −3.94893e66 −0.938991
\(685\) −3.45135e65 −0.0792976
\(686\) −3.64765e66 −0.809835
\(687\) −5.26429e66 −1.12942
\(688\) 1.24309e67 2.57736
\(689\) 7.39066e65 0.148092
\(690\) −1.76731e66 −0.342263
\(691\) −8.06352e66 −1.50935 −0.754676 0.656098i \(-0.772206\pi\)
−0.754676 + 0.656098i \(0.772206\pi\)
\(692\) 3.55517e66 0.643232
\(693\) 4.96312e65 0.0868009
\(694\) 3.69608e66 0.624876
\(695\) −1.44803e66 −0.236665
\(696\) −5.14356e66 −0.812731
\(697\) −4.01717e66 −0.613691
\(698\) 2.03085e67 2.99968
\(699\) −1.56649e66 −0.223725
\(700\) −3.49388e66 −0.482507
\(701\) 5.85991e66 0.782560 0.391280 0.920272i \(-0.372032\pi\)
0.391280 + 0.920272i \(0.372032\pi\)
\(702\) −1.71528e66 −0.221520
\(703\) −2.68944e66 −0.335901
\(704\) −3.83009e67 −4.62648
\(705\) 1.99002e66 0.232495
\(706\) −2.14298e67 −2.42163
\(707\) 1.43064e66 0.156378
\(708\) 1.93864e67 2.04982
\(709\) 1.17722e67 1.20413 0.602064 0.798448i \(-0.294345\pi\)
0.602064 + 0.798448i \(0.294345\pi\)
\(710\) −5.09590e66 −0.504254
\(711\) 5.49808e66 0.526351
\(712\) 6.18352e67 5.72738
\(713\) −9.30059e66 −0.833502
\(714\) −1.56705e66 −0.135886
\(715\) 5.79974e65 0.0486649
\(716\) −1.10953e67 −0.900913
\(717\) 8.15970e66 0.641171
\(718\) −4.01888e67 −3.05619
\(719\) 1.34473e67 0.989709 0.494854 0.868976i \(-0.335221\pi\)
0.494854 + 0.868976i \(0.335221\pi\)
\(720\) 9.11678e66 0.649423
\(721\) 1.55691e66 0.107346
\(722\) −6.06236e66 −0.404593
\(723\) −1.43104e67 −0.924491
\(724\) −2.85486e67 −1.78537
\(725\) 3.99135e66 0.241644
\(726\) 4.11266e66 0.241053
\(727\) −6.52974e66 −0.370542 −0.185271 0.982687i \(-0.559316\pi\)
−0.185271 + 0.982687i \(0.559316\pi\)
\(728\) 1.41017e66 0.0774790
\(729\) 1.95002e67 1.03739
\(730\) −2.19167e67 −1.12898
\(731\) −5.41627e66 −0.270173
\(732\) 2.20521e67 1.06522
\(733\) −4.16163e67 −1.94679 −0.973397 0.229127i \(-0.926413\pi\)
−0.973397 + 0.229127i \(0.926413\pi\)
\(734\) 5.05379e67 2.28960
\(735\) 7.40301e66 0.324830
\(736\) 5.17232e67 2.19815
\(737\) −1.48521e67 −0.611367
\(738\) −2.72607e67 −1.08696
\(739\) 1.83231e67 0.707709 0.353854 0.935301i \(-0.384871\pi\)
0.353854 + 0.935301i \(0.384871\pi\)
\(740\) 1.21283e67 0.453788
\(741\) 2.02752e66 0.0734917
\(742\) 1.66752e67 0.585571
\(743\) −2.26817e67 −0.771681 −0.385840 0.922566i \(-0.626088\pi\)
−0.385840 + 0.922566i \(0.626088\pi\)
\(744\) −1.33820e68 −4.41121
\(745\) 1.84827e67 0.590327
\(746\) 3.90716e67 1.20920
\(747\) 1.03488e67 0.310353
\(748\) 4.28984e67 1.24668
\(749\) 3.07205e66 0.0865178
\(750\) 4.39858e67 1.20053
\(751\) 3.95970e67 1.04743 0.523713 0.851895i \(-0.324546\pi\)
0.523713 + 0.851895i \(0.324546\pi\)
\(752\) −1.05807e68 −2.71265
\(753\) 2.33836e67 0.581072
\(754\) −2.51358e66 −0.0605433
\(755\) −3.17945e65 −0.00742333
\(756\) −2.84755e67 −0.644479
\(757\) −3.90670e67 −0.857149 −0.428575 0.903506i \(-0.640984\pi\)
−0.428575 + 0.903506i \(0.640984\pi\)
\(758\) 9.27790e67 1.97344
\(759\) −2.12571e67 −0.438352
\(760\) −6.67284e67 −1.33411
\(761\) −8.64597e67 −1.67600 −0.838001 0.545669i \(-0.816276\pi\)
−0.838001 + 0.545669i \(0.816276\pi\)
\(762\) −4.23012e67 −0.795079
\(763\) −9.63069e66 −0.175522
\(764\) 8.44246e67 1.49202
\(765\) −3.97226e66 −0.0680760
\(766\) 5.97119e67 0.992395
\(767\) 6.07177e66 0.0978643
\(768\) 1.86828e68 2.92047
\(769\) 8.45845e67 1.28240 0.641198 0.767376i \(-0.278438\pi\)
0.641198 + 0.767376i \(0.278438\pi\)
\(770\) 1.30857e67 0.192426
\(771\) −4.45179e67 −0.634975
\(772\) −1.79608e68 −2.48496
\(773\) −9.32204e67 −1.25110 −0.625551 0.780183i \(-0.715126\pi\)
−0.625551 + 0.780183i \(0.715126\pi\)
\(774\) −3.67551e67 −0.478526
\(775\) 1.03843e68 1.31156
\(776\) 2.16217e68 2.64934
\(777\) −5.32883e66 −0.0633487
\(778\) −1.77016e68 −2.04170
\(779\) 1.17271e68 1.31238
\(780\) −9.14329e66 −0.0992840
\(781\) −6.12931e67 −0.645821
\(782\) −4.09417e67 −0.418607
\(783\) 3.25299e67 0.322762
\(784\) −3.93608e68 −3.78998
\(785\) −3.75262e67 −0.350670
\(786\) −2.16177e68 −1.96056
\(787\) 1.40543e68 1.23709 0.618547 0.785748i \(-0.287722\pi\)
0.618547 + 0.785748i \(0.287722\pi\)
\(788\) 8.97512e67 0.766786
\(789\) 1.61324e68 1.33780
\(790\) 1.44961e68 1.16685
\(791\) −3.35610e67 −0.262233
\(792\) 1.86573e68 1.41516
\(793\) 6.90668e66 0.0508568
\(794\) 6.21764e67 0.444471
\(795\) −6.92935e67 −0.480911
\(796\) 4.94970e68 3.33520
\(797\) −6.41377e67 −0.419607 −0.209804 0.977744i \(-0.567282\pi\)
−0.209804 + 0.977744i \(0.567282\pi\)
\(798\) 4.57461e67 0.290593
\(799\) 4.61009e67 0.284355
\(800\) −5.77500e68 −3.45889
\(801\) −1.07457e68 −0.624984
\(802\) −1.98816e68 −1.12293
\(803\) −2.63612e68 −1.44594
\(804\) 2.34144e68 1.24728
\(805\) −9.18902e66 −0.0475407
\(806\) −6.53959e67 −0.328607
\(807\) −3.34892e66 −0.0163447
\(808\) 5.37805e68 2.54951
\(809\) 7.54417e67 0.347393 0.173696 0.984799i \(-0.444429\pi\)
0.173696 + 0.984799i \(0.444429\pi\)
\(810\) 8.96757e67 0.401122
\(811\) −2.25843e68 −0.981332 −0.490666 0.871348i \(-0.663247\pi\)
−0.490666 + 0.871348i \(0.663247\pi\)
\(812\) −4.17282e67 −0.176142
\(813\) −1.83116e68 −0.750928
\(814\) 1.98262e68 0.789890
\(815\) 1.97337e67 0.0763845
\(816\) −3.46227e68 −1.30209
\(817\) 1.58114e68 0.577766
\(818\) −1.12863e68 −0.400728
\(819\) −2.45058e66 −0.00845467
\(820\) −5.28843e68 −1.77297
\(821\) 2.57889e68 0.840174 0.420087 0.907484i \(-0.362000\pi\)
0.420087 + 0.907484i \(0.362000\pi\)
\(822\) 8.89457e67 0.281603
\(823\) −8.83986e67 −0.271988 −0.135994 0.990710i \(-0.543423\pi\)
−0.135994 + 0.990710i \(0.543423\pi\)
\(824\) 5.85271e68 1.75012
\(825\) 2.37340e68 0.689768
\(826\) 1.36995e68 0.386965
\(827\) −2.82593e68 −0.775856 −0.387928 0.921690i \(-0.626809\pi\)
−0.387928 + 0.921690i \(0.626809\pi\)
\(828\) −2.04424e68 −0.545530
\(829\) 2.91606e68 0.756423 0.378211 0.925719i \(-0.376539\pi\)
0.378211 + 0.925719i \(0.376539\pi\)
\(830\) 2.72854e68 0.688012
\(831\) −5.09321e68 −1.24844
\(832\) 1.89113e68 0.450634
\(833\) 1.71499e68 0.397286
\(834\) 3.73175e68 0.840448
\(835\) 1.55429e68 0.340329
\(836\) −1.25231e69 −2.66602
\(837\) 8.46332e68 1.75183
\(838\) −9.42450e67 −0.189681
\(839\) 9.42111e68 1.84372 0.921862 0.387518i \(-0.126667\pi\)
0.921862 + 0.387518i \(0.126667\pi\)
\(840\) −1.32215e68 −0.251604
\(841\) −4.92719e68 −0.911786
\(842\) −1.86924e69 −3.36380
\(843\) −5.49616e68 −0.961858
\(844\) −1.94998e69 −3.31881
\(845\) 2.57968e68 0.427005
\(846\) 3.12843e68 0.503644
\(847\) 2.13835e67 0.0334825
\(848\) 3.68424e69 5.61106
\(849\) −1.23058e68 −0.182296
\(850\) 4.57122e68 0.658700
\(851\) −1.39224e68 −0.195150
\(852\) 9.66286e68 1.31757
\(853\) −1.22430e69 −1.62400 −0.811999 0.583659i \(-0.801620\pi\)
−0.811999 + 0.583659i \(0.801620\pi\)
\(854\) 1.55832e68 0.201093
\(855\) 1.15960e68 0.145581
\(856\) 1.15484e69 1.41055
\(857\) −4.45209e68 −0.529071 −0.264536 0.964376i \(-0.585219\pi\)
−0.264536 + 0.964376i \(0.585219\pi\)
\(858\) −1.49467e68 −0.172820
\(859\) −2.77149e68 −0.311799 −0.155899 0.987773i \(-0.549828\pi\)
−0.155899 + 0.987773i \(0.549828\pi\)
\(860\) −7.13029e68 −0.780537
\(861\) 2.32359e68 0.247506
\(862\) 1.25069e69 1.29637
\(863\) 2.86475e68 0.288957 0.144479 0.989508i \(-0.453850\pi\)
0.144479 + 0.989508i \(0.453850\pi\)
\(864\) −4.70669e69 −4.62000
\(865\) −1.04397e68 −0.0997265
\(866\) 2.54068e69 2.36200
\(867\) −7.20180e68 −0.651617
\(868\) −1.08564e69 −0.956034
\(869\) 1.74358e69 1.49444
\(870\) 2.35669e68 0.196607
\(871\) 7.33333e67 0.0595490
\(872\) −3.62035e69 −2.86163
\(873\) −3.75739e68 −0.289102
\(874\) 1.19519e69 0.895194
\(875\) 2.28701e68 0.166755
\(876\) 4.15585e69 2.94994
\(877\) −6.75109e68 −0.466534 −0.233267 0.972413i \(-0.574942\pi\)
−0.233267 + 0.972413i \(0.574942\pi\)
\(878\) −3.04678e69 −2.04984
\(879\) 1.80052e69 1.17939
\(880\) 2.89116e69 1.84387
\(881\) −2.56812e67 −0.0159471 −0.00797354 0.999968i \(-0.502538\pi\)
−0.00797354 + 0.999968i \(0.502538\pi\)
\(882\) 1.16380e69 0.703665
\(883\) −1.81395e69 −1.06794 −0.533972 0.845502i \(-0.679301\pi\)
−0.533972 + 0.845502i \(0.679301\pi\)
\(884\) −2.11814e68 −0.121430
\(885\) −5.69278e68 −0.317803
\(886\) −2.05215e69 −1.11562
\(887\) 1.74355e68 0.0923059 0.0461529 0.998934i \(-0.485304\pi\)
0.0461529 + 0.998934i \(0.485304\pi\)
\(888\) −2.00320e69 −1.03281
\(889\) −2.19942e68 −0.110437
\(890\) −2.83318e69 −1.38551
\(891\) 1.07861e69 0.513735
\(892\) 1.09695e70 5.08875
\(893\) −1.34580e69 −0.608094
\(894\) −4.76322e69 −2.09638
\(895\) 3.25812e68 0.139677
\(896\) 2.09879e69 0.876455
\(897\) 1.04959e68 0.0426968
\(898\) 2.18297e69 0.865074
\(899\) 1.24022e69 0.478791
\(900\) 2.28243e69 0.858419
\(901\) −1.60526e69 −0.588182
\(902\) −8.64507e69 −3.08614
\(903\) 3.13286e68 0.108963
\(904\) −1.26162e70 −4.27533
\(905\) 8.38326e68 0.276803
\(906\) 8.19386e67 0.0263618
\(907\) −7.97555e68 −0.250028 −0.125014 0.992155i \(-0.539898\pi\)
−0.125014 + 0.992155i \(0.539898\pi\)
\(908\) 5.50557e69 1.68184
\(909\) −9.34591e68 −0.278208
\(910\) −6.46114e67 −0.0187429
\(911\) 6.39008e69 1.80644 0.903222 0.429173i \(-0.141195\pi\)
0.903222 + 0.429173i \(0.141195\pi\)
\(912\) 1.01072e70 2.78453
\(913\) 3.28187e69 0.881167
\(914\) 7.78449e69 2.03702
\(915\) −6.47557e68 −0.165151
\(916\) −1.60546e70 −3.99075
\(917\) −1.12400e69 −0.272324
\(918\) 3.72560e69 0.879818
\(919\) 3.86963e69 0.890747 0.445373 0.895345i \(-0.353071\pi\)
0.445373 + 0.895345i \(0.353071\pi\)
\(920\) −3.45432e69 −0.775084
\(921\) −6.04431e69 −1.32204
\(922\) 1.14725e70 2.44615
\(923\) 3.02639e68 0.0629050
\(924\) −2.48131e69 −0.502793
\(925\) 1.55446e69 0.307079
\(926\) −1.02235e70 −1.96898
\(927\) −1.01708e69 −0.190977
\(928\) −6.89721e69 −1.26269
\(929\) −4.53114e69 −0.808795 −0.404398 0.914583i \(-0.632519\pi\)
−0.404398 + 0.914583i \(0.632519\pi\)
\(930\) 6.13140e69 1.06711
\(931\) −5.00646e69 −0.849597
\(932\) −4.77735e69 −0.790520
\(933\) −3.42196e69 −0.552149
\(934\) 1.65479e70 2.60370
\(935\) −1.25971e69 −0.193284
\(936\) −9.21217e68 −0.137841
\(937\) 2.69082e69 0.392648 0.196324 0.980539i \(-0.437100\pi\)
0.196324 + 0.980539i \(0.437100\pi\)
\(938\) 1.65458e69 0.235463
\(939\) −7.23833e69 −1.00461
\(940\) 6.06899e69 0.821508
\(941\) −3.38983e69 −0.447530 −0.223765 0.974643i \(-0.571835\pi\)
−0.223765 + 0.974643i \(0.571835\pi\)
\(942\) 9.67100e69 1.24530
\(943\) 6.07075e69 0.762460
\(944\) 3.02677e70 3.70799
\(945\) 8.36179e68 0.0999199
\(946\) −1.16560e70 −1.35865
\(947\) −1.24658e70 −1.41742 −0.708708 0.705502i \(-0.750721\pi\)
−0.708708 + 0.705502i \(0.750721\pi\)
\(948\) −2.74876e70 −3.04888
\(949\) 1.30160e69 0.140839
\(950\) −1.33445e70 −1.40863
\(951\) 1.28473e70 1.32303
\(952\) −3.06290e69 −0.307726
\(953\) 1.47472e70 1.44553 0.722766 0.691093i \(-0.242870\pi\)
0.722766 + 0.691093i \(0.242870\pi\)
\(954\) −1.08934e70 −1.04178
\(955\) −2.47912e69 −0.231323
\(956\) 2.48847e70 2.26554
\(957\) 2.83461e69 0.251804
\(958\) −2.38062e69 −0.206348
\(959\) 4.62466e68 0.0391150
\(960\) −1.77309e70 −1.46338
\(961\) 1.98503e70 1.59871
\(962\) −9.78935e68 −0.0769378
\(963\) −2.00687e69 −0.153922
\(964\) −4.36427e70 −3.26664
\(965\) 5.27418e69 0.385268
\(966\) 2.36813e69 0.168827
\(967\) 9.72062e69 0.676351 0.338175 0.941083i \(-0.390190\pi\)
0.338175 + 0.941083i \(0.390190\pi\)
\(968\) 8.03843e69 0.545884
\(969\) −4.40379e69 −0.291889
\(970\) −9.90665e69 −0.640901
\(971\) −2.15826e70 −1.36286 −0.681431 0.731883i \(-0.738642\pi\)
−0.681431 + 0.731883i \(0.738642\pi\)
\(972\) 3.20928e70 1.97811
\(973\) 1.94030e69 0.116739
\(974\) −5.57872e68 −0.0327642
\(975\) −1.17188e69 −0.0671856
\(976\) 3.44297e70 1.92692
\(977\) −1.11352e69 −0.0608384 −0.0304192 0.999537i \(-0.509684\pi\)
−0.0304192 + 0.999537i \(0.509684\pi\)
\(978\) −5.08564e69 −0.271258
\(979\) −3.40772e70 −1.77448
\(980\) 2.25770e70 1.14777
\(981\) 6.29141e69 0.312267
\(982\) −3.42345e70 −1.65899
\(983\) −3.46672e69 −0.164025 −0.0820127 0.996631i \(-0.526135\pi\)
−0.0820127 + 0.996631i \(0.526135\pi\)
\(984\) 8.73481e70 4.03523
\(985\) −2.63553e69 −0.118882
\(986\) 5.45951e69 0.240462
\(987\) −2.66655e69 −0.114682
\(988\) 6.18336e69 0.259679
\(989\) 8.18507e69 0.335668
\(990\) −8.54843e69 −0.342341
\(991\) 1.50226e70 0.587510 0.293755 0.955881i \(-0.405095\pi\)
0.293755 + 0.955881i \(0.405095\pi\)
\(992\) −1.79445e71 −6.85341
\(993\) −2.39702e69 −0.0894055
\(994\) 6.82830e69 0.248732
\(995\) −1.45347e70 −0.517089
\(996\) −5.17387e70 −1.79772
\(997\) −9.94591e69 −0.337527 −0.168763 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(998\) 8.27338e70 2.74230
\(999\) 1.26690e70 0.410162
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 1.48.a.a.1.4 4
3.2 odd 2 9.48.a.c.1.1 4
4.3 odd 2 16.48.a.d.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.48.a.a.1.4 4 1.1 even 1 trivial
9.48.a.c.1.1 4 3.2 odd 2
16.48.a.d.1.2 4 4.3 odd 2