Properties

Label 1.56.a.a.1.2
Level 1
Weight 56
Character 1.1
Self dual Yes
Analytic conductor 19.158
Analytic rank 0
Dimension 4
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 1 \)
Weight: \( k \) = \( 56 \)
Character orbit: \([\chi]\) = 1.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(19.1581467685\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{20}\cdot 3^{9}\cdot 5^{2}\cdot 7\cdot 11 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-972934.\)
Character \(\chi\) = 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} +O(q^{10})\) \(q+2.88052e7 q^{2} +1.23937e13 q^{3} -3.51991e16 q^{4} -1.26520e19 q^{5} +3.57004e20 q^{6} +2.79909e23 q^{7} -2.05173e24 q^{8} -2.08450e25 q^{9} -3.64445e26 q^{10} +4.43027e28 q^{11} -4.36247e29 q^{12} +1.55064e30 q^{13} +8.06283e30 q^{14} -1.56806e32 q^{15} +1.20908e33 q^{16} +8.73107e32 q^{17} -6.00444e32 q^{18} +1.64892e35 q^{19} +4.45340e35 q^{20} +3.46911e36 q^{21} +1.27615e36 q^{22} +5.17737e37 q^{23} -2.54286e37 q^{24} -1.17482e38 q^{25} +4.46665e37 q^{26} -2.42042e39 q^{27} -9.85253e39 q^{28} +1.58882e40 q^{29} -4.51682e39 q^{30} +5.89422e40 q^{31} +1.08749e41 q^{32} +5.49075e41 q^{33} +2.51500e40 q^{34} -3.54142e42 q^{35} +7.33724e41 q^{36} -1.50183e43 q^{37} +4.74974e42 q^{38} +1.92182e43 q^{39} +2.59586e43 q^{40} +2.49038e44 q^{41} +9.99285e43 q^{42} -2.64200e44 q^{43} -1.55941e45 q^{44} +2.63732e44 q^{45} +1.49135e45 q^{46} -1.75786e46 q^{47} +1.49850e46 q^{48} +4.81222e46 q^{49} -3.38408e45 q^{50} +1.08210e46 q^{51} -5.45811e46 q^{52} -7.37942e46 q^{53} -6.97207e46 q^{54} -5.60519e47 q^{55} -5.74298e47 q^{56} +2.04362e48 q^{57} +4.57662e47 q^{58} +2.54720e48 q^{59} +5.51942e48 q^{60} -1.07207e49 q^{61} +1.69784e48 q^{62} -5.83470e48 q^{63} -4.04291e49 q^{64} -1.96188e49 q^{65} +1.58162e49 q^{66} +1.06094e50 q^{67} -3.07325e49 q^{68} +6.41669e50 q^{69} -1.02011e50 q^{70} -1.17879e51 q^{71} +4.27683e49 q^{72} +2.92361e50 q^{73} -4.32604e50 q^{74} -1.45603e51 q^{75} -5.80404e51 q^{76} +1.24007e52 q^{77} +5.53584e50 q^{78} +2.26793e52 q^{79} -1.52973e52 q^{80} -2.63616e52 q^{81} +7.17360e51 q^{82} +3.10804e52 q^{83} -1.22109e53 q^{84} -1.10466e52 q^{85} -7.61035e51 q^{86} +1.96914e53 q^{87} -9.08973e52 q^{88} +4.89902e53 q^{89} +7.59684e51 q^{90} +4.34038e53 q^{91} -1.82239e54 q^{92} +7.30513e53 q^{93} -5.06356e53 q^{94} -2.08622e54 q^{95} +1.34781e54 q^{96} +4.57966e53 q^{97} +1.38617e54 q^{98} -9.23488e53 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 208622520q^{2} - 6821470691280q^{3} + 38727758778743872q^{4} + 14396937963387167160q^{5} + \)\(20\!\cdots\!08\)\(q^{6} - \)\(20\!\cdots\!00\)\(q^{7} + \)\(45\!\cdots\!40\)\(q^{8} + \)\(47\!\cdots\!28\)\(q^{9} + O(q^{10}) \) \( 4q + 208622520q^{2} - 6821470691280q^{3} + 38727758778743872q^{4} + 14396937963387167160q^{5} + \)\(20\!\cdots\!08\)\(q^{6} - \)\(20\!\cdots\!00\)\(q^{7} + \)\(45\!\cdots\!40\)\(q^{8} + \)\(47\!\cdots\!28\)\(q^{9} + \)\(46\!\cdots\!60\)\(q^{10} + \)\(19\!\cdots\!08\)\(q^{11} + \)\(51\!\cdots\!40\)\(q^{12} - \)\(44\!\cdots\!60\)\(q^{13} - \)\(28\!\cdots\!56\)\(q^{14} + \)\(24\!\cdots\!20\)\(q^{15} + \)\(97\!\cdots\!04\)\(q^{16} + \)\(85\!\cdots\!60\)\(q^{17} + \)\(38\!\cdots\!20\)\(q^{18} + \)\(33\!\cdots\!00\)\(q^{19} + \)\(29\!\cdots\!80\)\(q^{20} + \)\(92\!\cdots\!08\)\(q^{21} + \)\(38\!\cdots\!40\)\(q^{22} + \)\(49\!\cdots\!60\)\(q^{23} + \)\(19\!\cdots\!00\)\(q^{24} + \)\(35\!\cdots\!00\)\(q^{25} - \)\(29\!\cdots\!92\)\(q^{26} - \)\(85\!\cdots\!40\)\(q^{27} - \)\(14\!\cdots\!60\)\(q^{28} - \)\(18\!\cdots\!00\)\(q^{29} + \)\(81\!\cdots\!20\)\(q^{30} + \)\(22\!\cdots\!08\)\(q^{31} + \)\(63\!\cdots\!20\)\(q^{32} + \)\(84\!\cdots\!40\)\(q^{33} + \)\(89\!\cdots\!44\)\(q^{34} - \)\(48\!\cdots\!40\)\(q^{35} - \)\(23\!\cdots\!96\)\(q^{36} - \)\(32\!\cdots\!20\)\(q^{37} - \)\(49\!\cdots\!40\)\(q^{38} + \)\(66\!\cdots\!56\)\(q^{39} + \)\(42\!\cdots\!00\)\(q^{40} + \)\(24\!\cdots\!08\)\(q^{41} + \)\(50\!\cdots\!60\)\(q^{42} - \)\(86\!\cdots\!00\)\(q^{43} - \)\(48\!\cdots\!56\)\(q^{44} - \)\(95\!\cdots\!80\)\(q^{45} - \)\(12\!\cdots\!92\)\(q^{46} + \)\(42\!\cdots\!40\)\(q^{47} + \)\(19\!\cdots\!60\)\(q^{48} + \)\(51\!\cdots\!72\)\(q^{49} + \)\(17\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!08\)\(q^{51} - \)\(26\!\cdots\!00\)\(q^{52} - \)\(48\!\cdots\!80\)\(q^{53} - \)\(13\!\cdots\!00\)\(q^{54} - \)\(12\!\cdots\!80\)\(q^{55} - \)\(29\!\cdots\!00\)\(q^{56} + \)\(16\!\cdots\!20\)\(q^{57} + \)\(60\!\cdots\!40\)\(q^{58} + \)\(81\!\cdots\!00\)\(q^{59} + \)\(10\!\cdots\!60\)\(q^{60} + \)\(70\!\cdots\!08\)\(q^{61} - \)\(30\!\cdots\!60\)\(q^{62} - \)\(71\!\cdots\!20\)\(q^{63} - \)\(98\!\cdots\!28\)\(q^{64} - \)\(96\!\cdots\!80\)\(q^{65} + \)\(64\!\cdots\!16\)\(q^{66} + \)\(41\!\cdots\!60\)\(q^{67} + \)\(62\!\cdots\!20\)\(q^{68} + \)\(51\!\cdots\!56\)\(q^{69} - \)\(47\!\cdots\!40\)\(q^{70} + \)\(99\!\cdots\!08\)\(q^{71} - \)\(43\!\cdots\!20\)\(q^{72} - \)\(89\!\cdots\!40\)\(q^{73} - \)\(79\!\cdots\!56\)\(q^{74} + \)\(52\!\cdots\!00\)\(q^{75} - \)\(60\!\cdots\!00\)\(q^{76} + \)\(14\!\cdots\!00\)\(q^{77} + \)\(39\!\cdots\!00\)\(q^{78} + \)\(48\!\cdots\!00\)\(q^{79} - \)\(35\!\cdots\!40\)\(q^{80} + \)\(62\!\cdots\!04\)\(q^{81} - \)\(16\!\cdots\!60\)\(q^{82} - \)\(71\!\cdots\!20\)\(q^{83} - \)\(31\!\cdots\!56\)\(q^{84} + \)\(24\!\cdots\!60\)\(q^{85} - \)\(39\!\cdots\!92\)\(q^{86} + \)\(79\!\cdots\!80\)\(q^{87} + \)\(26\!\cdots\!80\)\(q^{88} + \)\(15\!\cdots\!00\)\(q^{89} - \)\(12\!\cdots\!80\)\(q^{90} + \)\(16\!\cdots\!08\)\(q^{91} - \)\(27\!\cdots\!40\)\(q^{92} - \)\(11\!\cdots\!60\)\(q^{93} - \)\(40\!\cdots\!56\)\(q^{94} + \)\(90\!\cdots\!00\)\(q^{95} - \)\(54\!\cdots\!92\)\(q^{96} + \)\(51\!\cdots\!40\)\(q^{97} + \)\(43\!\cdots\!60\)\(q^{98} + \)\(79\!\cdots\!56\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.88052e7 0.151756 0.0758780 0.997117i \(-0.475824\pi\)
0.0758780 + 0.997117i \(0.475824\pi\)
\(3\) 1.23937e13 0.938355 0.469177 0.883104i \(-0.344550\pi\)
0.469177 + 0.883104i \(0.344550\pi\)
\(4\) −3.51991e16 −0.976970
\(5\) −1.26520e19 −0.759426 −0.379713 0.925104i \(-0.623977\pi\)
−0.379713 + 0.925104i \(0.623977\pi\)
\(6\) 3.57004e20 0.142401
\(7\) 2.79909e23 1.60998 0.804990 0.593288i \(-0.202171\pi\)
0.804990 + 0.593288i \(0.202171\pi\)
\(8\) −2.05173e24 −0.300017
\(9\) −2.08450e25 −0.119490
\(10\) −3.64445e26 −0.115247
\(11\) 4.43027e28 1.01890 0.509449 0.860501i \(-0.329849\pi\)
0.509449 + 0.860501i \(0.329849\pi\)
\(12\) −4.36247e29 −0.916745
\(13\) 1.55064e30 0.360636 0.180318 0.983608i \(-0.442287\pi\)
0.180318 + 0.983608i \(0.442287\pi\)
\(14\) 8.06283e30 0.244324
\(15\) −1.56806e32 −0.712611
\(16\) 1.20908e33 0.931441
\(17\) 8.73107e32 0.126976 0.0634881 0.997983i \(-0.479778\pi\)
0.0634881 + 0.997983i \(0.479778\pi\)
\(18\) −6.00444e32 −0.0181334
\(19\) 1.64892e35 1.12584 0.562918 0.826513i \(-0.309679\pi\)
0.562918 + 0.826513i \(0.309679\pi\)
\(20\) 4.45340e35 0.741936
\(21\) 3.46911e36 1.51073
\(22\) 1.27615e36 0.154624
\(23\) 5.17737e37 1.84754 0.923770 0.382948i \(-0.125091\pi\)
0.923770 + 0.382948i \(0.125091\pi\)
\(24\) −2.54286e37 −0.281523
\(25\) −1.17482e38 −0.423272
\(26\) 4.46665e37 0.0547287
\(27\) −2.42042e39 −1.05048
\(28\) −9.85253e39 −1.57290
\(29\) 1.58882e40 0.966338 0.483169 0.875527i \(-0.339486\pi\)
0.483169 + 0.875527i \(0.339486\pi\)
\(30\) −4.51682e39 −0.108143
\(31\) 5.89422e40 0.572770 0.286385 0.958115i \(-0.407546\pi\)
0.286385 + 0.958115i \(0.407546\pi\)
\(32\) 1.08749e41 0.441369
\(33\) 5.49075e41 0.956089
\(34\) 2.51500e40 0.0192694
\(35\) −3.54142e42 −1.22266
\(36\) 7.33724e41 0.116738
\(37\) −1.50183e43 −1.12479 −0.562396 0.826868i \(-0.690120\pi\)
−0.562396 + 0.826868i \(0.690120\pi\)
\(38\) 4.74974e42 0.170853
\(39\) 1.92182e43 0.338404
\(40\) 2.59586e43 0.227841
\(41\) 2.49038e44 1.10843 0.554217 0.832372i \(-0.313018\pi\)
0.554217 + 0.832372i \(0.313018\pi\)
\(42\) 9.99285e43 0.229263
\(43\) −2.64200e44 −0.317359 −0.158680 0.987330i \(-0.550724\pi\)
−0.158680 + 0.987330i \(0.550724\pi\)
\(44\) −1.55941e45 −0.995434
\(45\) 2.63732e44 0.0907440
\(46\) 1.49135e45 0.280375
\(47\) −1.75786e46 −1.82934 −0.914669 0.404204i \(-0.867549\pi\)
−0.914669 + 0.404204i \(0.867549\pi\)
\(48\) 1.49850e46 0.874022
\(49\) 4.81222e46 1.59204
\(50\) −3.38408e45 −0.0642341
\(51\) 1.08210e46 0.119149
\(52\) −5.45811e46 −0.352330
\(53\) −7.37942e46 −0.282121 −0.141061 0.990001i \(-0.545051\pi\)
−0.141061 + 0.990001i \(0.545051\pi\)
\(54\) −6.97207e46 −0.159417
\(55\) −5.60519e47 −0.773778
\(56\) −5.74298e47 −0.483022
\(57\) 2.04362e48 1.05643
\(58\) 4.57662e47 0.146648
\(59\) 2.54720e48 0.510073 0.255036 0.966931i \(-0.417913\pi\)
0.255036 + 0.966931i \(0.417913\pi\)
\(60\) 5.51942e48 0.696200
\(61\) −1.07207e49 −0.858325 −0.429162 0.903227i \(-0.641191\pi\)
−0.429162 + 0.903227i \(0.641191\pi\)
\(62\) 1.69784e48 0.0869213
\(63\) −5.83470e48 −0.192377
\(64\) −4.04291e49 −0.864460
\(65\) −1.96188e49 −0.273876
\(66\) 1.58162e49 0.145092
\(67\) 1.06094e50 0.643627 0.321814 0.946803i \(-0.395708\pi\)
0.321814 + 0.946803i \(0.395708\pi\)
\(68\) −3.07325e49 −0.124052
\(69\) 6.41669e50 1.73365
\(70\) −1.02011e50 −0.185546
\(71\) −1.17879e51 −1.45156 −0.725778 0.687929i \(-0.758520\pi\)
−0.725778 + 0.687929i \(0.758520\pi\)
\(72\) 4.27683e49 0.0358491
\(73\) 2.92361e50 0.167703 0.0838516 0.996478i \(-0.473278\pi\)
0.0838516 + 0.996478i \(0.473278\pi\)
\(74\) −4.32604e50 −0.170694
\(75\) −1.45603e51 −0.397180
\(76\) −5.80404e51 −1.09991
\(77\) 1.24007e52 1.64041
\(78\) 5.53584e50 0.0513549
\(79\) 2.26793e52 1.48212 0.741062 0.671436i \(-0.234322\pi\)
0.741062 + 0.671436i \(0.234322\pi\)
\(80\) −1.52973e52 −0.707360
\(81\) −2.63616e52 −0.866232
\(82\) 7.17360e51 0.168212
\(83\) 3.10804e52 0.522203 0.261101 0.965311i \(-0.415914\pi\)
0.261101 + 0.965311i \(0.415914\pi\)
\(84\) −1.22109e53 −1.47594
\(85\) −1.10466e52 −0.0964290
\(86\) −7.61035e51 −0.0481612
\(87\) 1.96914e53 0.906768
\(88\) −9.08973e52 −0.305687
\(89\) 4.89902e53 1.20749 0.603745 0.797177i \(-0.293674\pi\)
0.603745 + 0.797177i \(0.293674\pi\)
\(90\) 7.59684e51 0.0137710
\(91\) 4.34038e53 0.580616
\(92\) −1.82239e54 −1.80499
\(93\) 7.30513e53 0.537461
\(94\) −5.06356e53 −0.277613
\(95\) −2.08622e54 −0.854989
\(96\) 1.34781e54 0.414161
\(97\) 4.57966e53 0.105830 0.0529152 0.998599i \(-0.483149\pi\)
0.0529152 + 0.998599i \(0.483149\pi\)
\(98\) 1.38617e54 0.241601
\(99\) −9.23488e53 −0.121749
\(100\) 4.13524e54 0.413524
\(101\) 1.50130e55 1.14191 0.570953 0.820983i \(-0.306574\pi\)
0.570953 + 0.820983i \(0.306574\pi\)
\(102\) 3.11702e53 0.0180815
\(103\) −1.70225e55 −0.755090 −0.377545 0.925991i \(-0.623232\pi\)
−0.377545 + 0.925991i \(0.623232\pi\)
\(104\) −3.18150e54 −0.108197
\(105\) −4.38913e55 −1.14729
\(106\) −2.12566e54 −0.0428136
\(107\) −2.90724e55 −0.452300 −0.226150 0.974092i \(-0.572614\pi\)
−0.226150 + 0.974092i \(0.572614\pi\)
\(108\) 8.51965e55 1.02629
\(109\) 5.37285e55 0.502315 0.251157 0.967946i \(-0.419189\pi\)
0.251157 + 0.967946i \(0.419189\pi\)
\(110\) −1.61459e55 −0.117426
\(111\) −1.86132e56 −1.05545
\(112\) 3.38432e56 1.49960
\(113\) 2.45020e56 0.850247 0.425123 0.905135i \(-0.360231\pi\)
0.425123 + 0.905135i \(0.360231\pi\)
\(114\) 5.88670e55 0.160320
\(115\) −6.55043e56 −1.40307
\(116\) −5.59249e56 −0.944083
\(117\) −3.23231e55 −0.0430925
\(118\) 7.33725e55 0.0774066
\(119\) 2.44390e56 0.204429
\(120\) 3.21724e56 0.213796
\(121\) 7.21357e55 0.0381551
\(122\) −3.08811e56 −0.130256
\(123\) 3.08651e57 1.04010
\(124\) −2.07471e57 −0.559579
\(125\) 4.99803e57 1.08087
\(126\) −1.68070e56 −0.0291944
\(127\) −5.35925e57 −0.749035 −0.374517 0.927220i \(-0.622192\pi\)
−0.374517 + 0.927220i \(0.622192\pi\)
\(128\) −5.08267e57 −0.572556
\(129\) −3.27443e57 −0.297796
\(130\) −5.65122e56 −0.0415624
\(131\) −5.72408e57 −0.340993 −0.170496 0.985358i \(-0.554537\pi\)
−0.170496 + 0.985358i \(0.554537\pi\)
\(132\) −1.93269e58 −0.934070
\(133\) 4.61547e58 1.81257
\(134\) 3.05606e57 0.0976744
\(135\) 3.06233e58 0.797761
\(136\) −1.79138e57 −0.0380950
\(137\) −3.04892e58 −0.530067 −0.265033 0.964239i \(-0.585383\pi\)
−0.265033 + 0.964239i \(0.585383\pi\)
\(138\) 1.84834e58 0.263092
\(139\) −5.38797e58 −0.628809 −0.314404 0.949289i \(-0.601805\pi\)
−0.314404 + 0.949289i \(0.601805\pi\)
\(140\) 1.24655e59 1.19450
\(141\) −2.17865e59 −1.71657
\(142\) −3.39554e58 −0.220282
\(143\) 6.86975e58 0.367451
\(144\) −2.52032e58 −0.111298
\(145\) −2.01018e59 −0.733862
\(146\) 8.42153e57 0.0254500
\(147\) 5.96413e59 1.49390
\(148\) 5.28629e59 1.09889
\(149\) −2.75514e59 −0.475907 −0.237953 0.971277i \(-0.576477\pi\)
−0.237953 + 0.971277i \(0.576477\pi\)
\(150\) −4.19414e58 −0.0602744
\(151\) −3.94876e59 −0.472709 −0.236355 0.971667i \(-0.575953\pi\)
−0.236355 + 0.971667i \(0.575953\pi\)
\(152\) −3.38314e59 −0.337770
\(153\) −1.81999e58 −0.0151724
\(154\) 3.57205e59 0.248942
\(155\) −7.45739e59 −0.434976
\(156\) −6.76462e59 −0.330611
\(157\) −1.28546e60 −0.527009 −0.263505 0.964658i \(-0.584878\pi\)
−0.263505 + 0.964658i \(0.584878\pi\)
\(158\) 6.53282e59 0.224921
\(159\) −9.14584e59 −0.264730
\(160\) −1.37590e60 −0.335187
\(161\) 1.44919e61 2.97450
\(162\) −7.59352e59 −0.131456
\(163\) 8.10357e59 0.118445 0.0592226 0.998245i \(-0.481138\pi\)
0.0592226 + 0.998245i \(0.481138\pi\)
\(164\) −8.76591e60 −1.08291
\(165\) −6.94692e60 −0.726079
\(166\) 8.95277e59 0.0792474
\(167\) 8.63145e60 0.647710 0.323855 0.946107i \(-0.395021\pi\)
0.323855 + 0.946107i \(0.395021\pi\)
\(168\) −7.11769e60 −0.453246
\(169\) −1.60833e61 −0.869942
\(170\) −3.18199e59 −0.0146337
\(171\) −3.43717e60 −0.134526
\(172\) 9.29961e60 0.310050
\(173\) 2.85400e61 0.811307 0.405654 0.914027i \(-0.367044\pi\)
0.405654 + 0.914027i \(0.367044\pi\)
\(174\) 5.67214e60 0.137608
\(175\) −3.28842e61 −0.681460
\(176\) 5.35654e61 0.949044
\(177\) 3.15692e61 0.478629
\(178\) 1.41117e61 0.183244
\(179\) −4.09139e61 −0.455421 −0.227710 0.973729i \(-0.573124\pi\)
−0.227710 + 0.973729i \(0.573124\pi\)
\(180\) −9.28310e60 −0.0886542
\(181\) −1.09499e62 −0.897946 −0.448973 0.893545i \(-0.648210\pi\)
−0.448973 + 0.893545i \(0.648210\pi\)
\(182\) 1.25025e61 0.0881121
\(183\) −1.32869e62 −0.805413
\(184\) −1.06226e62 −0.554294
\(185\) 1.90012e62 0.854197
\(186\) 2.10426e61 0.0815630
\(187\) 3.86810e61 0.129376
\(188\) 6.18751e62 1.78721
\(189\) −6.77497e62 −1.69125
\(190\) −6.00940e61 −0.129750
\(191\) 9.82615e62 1.83639 0.918197 0.396125i \(-0.129645\pi\)
0.918197 + 0.396125i \(0.129645\pi\)
\(192\) −5.01067e62 −0.811170
\(193\) 3.58891e62 0.503659 0.251830 0.967772i \(-0.418968\pi\)
0.251830 + 0.967772i \(0.418968\pi\)
\(194\) 1.31918e61 0.0160604
\(195\) −2.43149e62 −0.256993
\(196\) −1.69386e63 −1.55537
\(197\) −1.12979e62 −0.0901937 −0.0450968 0.998983i \(-0.514360\pi\)
−0.0450968 + 0.998983i \(0.514360\pi\)
\(198\) −2.66013e61 −0.0184761
\(199\) −6.41270e62 −0.387776 −0.193888 0.981024i \(-0.562110\pi\)
−0.193888 + 0.981024i \(0.562110\pi\)
\(200\) 2.41041e62 0.126989
\(201\) 1.31490e63 0.603951
\(202\) 4.32453e62 0.173291
\(203\) 4.44724e63 1.55579
\(204\) −3.80890e62 −0.116405
\(205\) −3.15084e63 −0.841774
\(206\) −4.90335e62 −0.114589
\(207\) −1.07922e63 −0.220763
\(208\) 1.87485e63 0.335911
\(209\) 7.30515e63 1.14711
\(210\) −1.26430e63 −0.174108
\(211\) −1.25121e64 −1.51204 −0.756019 0.654550i \(-0.772858\pi\)
−0.756019 + 0.654550i \(0.772858\pi\)
\(212\) 2.59749e63 0.275624
\(213\) −1.46096e64 −1.36207
\(214\) −8.37436e62 −0.0686393
\(215\) 3.34267e63 0.241011
\(216\) 4.96606e63 0.315162
\(217\) 1.64985e64 0.922148
\(218\) 1.54766e63 0.0762293
\(219\) 3.62344e63 0.157365
\(220\) 1.97297e64 0.755958
\(221\) 1.35387e63 0.0457921
\(222\) −5.36158e63 −0.160172
\(223\) −3.80868e64 −1.00552 −0.502760 0.864426i \(-0.667682\pi\)
−0.502760 + 0.864426i \(0.667682\pi\)
\(224\) 3.04399e64 0.710595
\(225\) 2.44890e63 0.0505769
\(226\) 7.05786e63 0.129030
\(227\) −8.04148e64 −1.30204 −0.651021 0.759060i \(-0.725659\pi\)
−0.651021 + 0.759060i \(0.725659\pi\)
\(228\) −7.19336e64 −1.03210
\(229\) 3.89160e64 0.495054 0.247527 0.968881i \(-0.420382\pi\)
0.247527 + 0.968881i \(0.420382\pi\)
\(230\) −1.88686e64 −0.212924
\(231\) 1.53691e65 1.53928
\(232\) −3.25983e64 −0.289918
\(233\) −9.97362e64 −0.788070 −0.394035 0.919095i \(-0.628921\pi\)
−0.394035 + 0.919095i \(0.628921\pi\)
\(234\) −9.31072e62 −0.00653954
\(235\) 2.22405e65 1.38925
\(236\) −8.96589e64 −0.498326
\(237\) 2.81081e65 1.39076
\(238\) 7.03972e63 0.0310234
\(239\) −4.18204e62 −0.00164227 −0.000821137 1.00000i \(-0.500261\pi\)
−0.000821137 1.00000i \(0.500261\pi\)
\(240\) −1.89591e65 −0.663755
\(241\) −5.42301e65 −1.69345 −0.846724 0.532033i \(-0.821428\pi\)
−0.846724 + 0.532033i \(0.821428\pi\)
\(242\) 2.07788e63 0.00579026
\(243\) 9.55220e64 0.237646
\(244\) 3.77358e65 0.838558
\(245\) −6.08844e65 −1.20903
\(246\) 8.89076e64 0.157842
\(247\) 2.55688e65 0.406017
\(248\) −1.20934e65 −0.171841
\(249\) 3.85202e65 0.490011
\(250\) 1.43969e65 0.164029
\(251\) −7.66365e65 −0.782363 −0.391181 0.920314i \(-0.627933\pi\)
−0.391181 + 0.920314i \(0.627933\pi\)
\(252\) 2.05376e65 0.187947
\(253\) 2.29371e66 1.88246
\(254\) −1.54374e65 −0.113671
\(255\) −1.36908e65 −0.0904846
\(256\) 1.31021e66 0.777571
\(257\) −2.62578e66 −1.39990 −0.699952 0.714190i \(-0.746795\pi\)
−0.699952 + 0.714190i \(0.746795\pi\)
\(258\) −9.43205e64 −0.0451923
\(259\) −4.20375e66 −1.81089
\(260\) 6.90562e65 0.267569
\(261\) −3.31189e65 −0.115468
\(262\) −1.64883e65 −0.0517477
\(263\) 3.10641e66 0.877962 0.438981 0.898496i \(-0.355339\pi\)
0.438981 + 0.898496i \(0.355339\pi\)
\(264\) −1.12655e66 −0.286843
\(265\) 9.33647e65 0.214250
\(266\) 1.32950e66 0.275069
\(267\) 6.07170e66 1.13305
\(268\) −3.73441e66 −0.628805
\(269\) −2.44880e66 −0.372192 −0.186096 0.982532i \(-0.559583\pi\)
−0.186096 + 0.982532i \(0.559583\pi\)
\(270\) 8.82109e65 0.121065
\(271\) 4.59005e66 0.569065 0.284533 0.958666i \(-0.408162\pi\)
0.284533 + 0.958666i \(0.408162\pi\)
\(272\) 1.05566e66 0.118271
\(273\) 5.37934e66 0.544824
\(274\) −8.78248e65 −0.0804408
\(275\) −5.20475e66 −0.431272
\(276\) −2.25861e67 −1.69372
\(277\) −3.77433e66 −0.256240 −0.128120 0.991759i \(-0.540894\pi\)
−0.128120 + 0.991759i \(0.540894\pi\)
\(278\) −1.55202e66 −0.0954255
\(279\) −1.22865e66 −0.0684404
\(280\) 7.26604e66 0.366819
\(281\) 2.01573e67 0.922591 0.461295 0.887247i \(-0.347385\pi\)
0.461295 + 0.887247i \(0.347385\pi\)
\(282\) −6.27563e66 −0.260500
\(283\) −1.57152e67 −0.591824 −0.295912 0.955215i \(-0.595624\pi\)
−0.295912 + 0.955215i \(0.595624\pi\)
\(284\) 4.14925e67 1.41813
\(285\) −2.58560e67 −0.802283
\(286\) 1.97885e66 0.0557630
\(287\) 6.97080e67 1.78456
\(288\) −2.26688e66 −0.0527393
\(289\) −4.65191e67 −0.983877
\(290\) −5.79036e66 −0.111368
\(291\) 5.67590e66 0.0993064
\(292\) −1.02908e67 −0.163841
\(293\) −5.33382e67 −0.772999 −0.386500 0.922290i \(-0.626316\pi\)
−0.386500 + 0.922290i \(0.626316\pi\)
\(294\) 1.71798e67 0.226708
\(295\) −3.22272e67 −0.387363
\(296\) 3.08135e67 0.337457
\(297\) −1.07231e68 −1.07033
\(298\) −7.93625e66 −0.0722218
\(299\) 8.02824e67 0.666289
\(300\) 5.12510e67 0.388033
\(301\) −7.39521e67 −0.510942
\(302\) −1.13745e67 −0.0717365
\(303\) 1.86067e68 1.07151
\(304\) 1.99367e68 1.04865
\(305\) 1.35638e68 0.651834
\(306\) −5.24252e65 −0.00230251
\(307\) −2.80514e67 −0.112629 −0.0563144 0.998413i \(-0.517935\pi\)
−0.0563144 + 0.998413i \(0.517935\pi\)
\(308\) −4.36493e68 −1.60263
\(309\) −2.10971e68 −0.708542
\(310\) −2.14812e67 −0.0660103
\(311\) −7.41937e67 −0.208668 −0.104334 0.994542i \(-0.533271\pi\)
−0.104334 + 0.994542i \(0.533271\pi\)
\(312\) −3.94306e67 −0.101527
\(313\) 4.59840e68 1.08427 0.542135 0.840291i \(-0.317616\pi\)
0.542135 + 0.840291i \(0.317616\pi\)
\(314\) −3.70279e67 −0.0799768
\(315\) 7.38208e67 0.146096
\(316\) −7.98290e68 −1.44799
\(317\) −3.97467e67 −0.0660955 −0.0330477 0.999454i \(-0.510521\pi\)
−0.0330477 + 0.999454i \(0.510521\pi\)
\(318\) −2.63448e67 −0.0401744
\(319\) 7.03889e68 0.984601
\(320\) 5.11511e68 0.656494
\(321\) −3.60315e68 −0.424418
\(322\) 4.17443e68 0.451399
\(323\) 1.43968e68 0.142954
\(324\) 9.27904e68 0.846283
\(325\) −1.82172e68 −0.152647
\(326\) 2.33425e67 0.0179748
\(327\) 6.65895e68 0.471349
\(328\) −5.10960e68 −0.332549
\(329\) −4.92041e69 −2.94520
\(330\) −2.00107e68 −0.110187
\(331\) 2.81395e69 1.42576 0.712879 0.701287i \(-0.247391\pi\)
0.712879 + 0.701287i \(0.247391\pi\)
\(332\) −1.09400e69 −0.510176
\(333\) 3.13056e68 0.134402
\(334\) 2.48631e68 0.0982939
\(335\) −1.34231e69 −0.488787
\(336\) 4.19443e69 1.40716
\(337\) −3.53381e69 −1.09250 −0.546249 0.837623i \(-0.683945\pi\)
−0.546249 + 0.837623i \(0.683945\pi\)
\(338\) −4.63282e68 −0.132019
\(339\) 3.03671e69 0.797833
\(340\) 3.88829e68 0.0942082
\(341\) 2.61130e69 0.583594
\(342\) −9.90083e67 −0.0204152
\(343\) 5.00907e69 0.953167
\(344\) 5.42069e68 0.0952132
\(345\) −8.11842e69 −1.31658
\(346\) 8.22099e68 0.123121
\(347\) 7.81225e69 1.08073 0.540363 0.841432i \(-0.318287\pi\)
0.540363 + 0.841432i \(0.318287\pi\)
\(348\) −6.93117e69 −0.885885
\(349\) −1.46742e70 −1.73323 −0.866614 0.498978i \(-0.833709\pi\)
−0.866614 + 0.498978i \(0.833709\pi\)
\(350\) −9.47235e68 −0.103416
\(351\) −3.75320e69 −0.378840
\(352\) 4.81788e69 0.449710
\(353\) 3.73450e69 0.322425 0.161212 0.986920i \(-0.448460\pi\)
0.161212 + 0.986920i \(0.448460\pi\)
\(354\) 9.09358e68 0.0726349
\(355\) 1.49142e70 1.10235
\(356\) −1.72441e70 −1.17968
\(357\) 3.02891e69 0.191827
\(358\) −1.17853e69 −0.0691129
\(359\) 2.97159e70 1.61396 0.806979 0.590580i \(-0.201101\pi\)
0.806979 + 0.590580i \(0.201101\pi\)
\(360\) −5.41107e68 −0.0272248
\(361\) 5.73832e69 0.267508
\(362\) −3.15415e69 −0.136269
\(363\) 8.94029e68 0.0358030
\(364\) −1.52777e70 −0.567245
\(365\) −3.69897e69 −0.127358
\(366\) −3.82732e69 −0.122226
\(367\) −5.08197e70 −1.50562 −0.752811 0.658237i \(-0.771302\pi\)
−0.752811 + 0.658237i \(0.771302\pi\)
\(368\) 6.25985e70 1.72087
\(369\) −5.19120e69 −0.132447
\(370\) 5.47333e69 0.129630
\(371\) −2.06556e70 −0.454210
\(372\) −2.57134e70 −0.525083
\(373\) −8.75772e70 −1.66111 −0.830554 0.556938i \(-0.811976\pi\)
−0.830554 + 0.556938i \(0.811976\pi\)
\(374\) 1.11421e69 0.0196336
\(375\) 6.19442e70 1.01424
\(376\) 3.60666e70 0.548833
\(377\) 2.46368e70 0.348496
\(378\) −1.95154e70 −0.256658
\(379\) 1.26223e71 1.54369 0.771847 0.635808i \(-0.219333\pi\)
0.771847 + 0.635808i \(0.219333\pi\)
\(380\) 7.34329e70 0.835299
\(381\) −6.64211e70 −0.702860
\(382\) 2.83044e70 0.278684
\(383\) −5.28430e69 −0.0484196 −0.0242098 0.999707i \(-0.507707\pi\)
−0.0242098 + 0.999707i \(0.507707\pi\)
\(384\) −6.29932e70 −0.537261
\(385\) −1.56894e71 −1.24577
\(386\) 1.03379e70 0.0764334
\(387\) 5.50725e69 0.0379213
\(388\) −1.61200e70 −0.103393
\(389\) 2.99174e70 0.178776 0.0893882 0.995997i \(-0.471509\pi\)
0.0893882 + 0.995997i \(0.471509\pi\)
\(390\) −7.00397e69 −0.0390002
\(391\) 4.52040e70 0.234594
\(392\) −9.87338e70 −0.477638
\(393\) −7.09426e70 −0.319972
\(394\) −3.25438e69 −0.0136874
\(395\) −2.86939e71 −1.12556
\(396\) 3.25059e70 0.118945
\(397\) 4.68857e71 1.60067 0.800335 0.599553i \(-0.204655\pi\)
0.800335 + 0.599553i \(0.204655\pi\)
\(398\) −1.84719e70 −0.0588474
\(399\) 5.72028e71 1.70084
\(400\) −1.42045e71 −0.394253
\(401\) 1.15088e70 0.0298236 0.0149118 0.999889i \(-0.495253\pi\)
0.0149118 + 0.999889i \(0.495253\pi\)
\(402\) 3.78760e70 0.0916532
\(403\) 9.13981e70 0.206561
\(404\) −5.28445e71 −1.11561
\(405\) 3.33528e71 0.657839
\(406\) 1.28104e71 0.236100
\(407\) −6.65350e71 −1.14605
\(408\) −2.22019e70 −0.0357467
\(409\) −5.99712e71 −0.902717 −0.451358 0.892343i \(-0.649060\pi\)
−0.451358 + 0.892343i \(0.649060\pi\)
\(410\) −9.07607e70 −0.127744
\(411\) −3.77875e71 −0.497391
\(412\) 5.99174e71 0.737700
\(413\) 7.12983e71 0.821207
\(414\) −3.10872e70 −0.0335021
\(415\) −3.93230e71 −0.396574
\(416\) 1.68631e71 0.159173
\(417\) −6.67770e71 −0.590046
\(418\) 2.10426e71 0.174081
\(419\) −6.48026e71 −0.502004 −0.251002 0.967987i \(-0.580760\pi\)
−0.251002 + 0.967987i \(0.580760\pi\)
\(420\) 1.54493e72 1.12087
\(421\) 1.99937e72 1.35874 0.679369 0.733797i \(-0.262254\pi\)
0.679369 + 0.733797i \(0.262254\pi\)
\(422\) −3.60413e71 −0.229461
\(423\) 3.66426e71 0.218588
\(424\) 1.51406e71 0.0846412
\(425\) −1.02574e71 −0.0537455
\(426\) −4.20834e71 −0.206703
\(427\) −3.00081e72 −1.38189
\(428\) 1.02332e72 0.441884
\(429\) 8.51417e71 0.344800
\(430\) 9.62864e70 0.0365749
\(431\) −3.24265e72 −1.15551 −0.577756 0.816209i \(-0.696072\pi\)
−0.577756 + 0.816209i \(0.696072\pi\)
\(432\) −2.92648e72 −0.978459
\(433\) 1.58622e72 0.497675 0.248838 0.968545i \(-0.419951\pi\)
0.248838 + 0.968545i \(0.419951\pi\)
\(434\) 4.75241e71 0.139942
\(435\) −2.49136e72 −0.688623
\(436\) −1.89119e72 −0.490746
\(437\) 8.53707e72 2.08003
\(438\) 1.04374e71 0.0238811
\(439\) 1.49705e72 0.321708 0.160854 0.986978i \(-0.448575\pi\)
0.160854 + 0.986978i \(0.448575\pi\)
\(440\) 1.15004e72 0.232147
\(441\) −1.00311e72 −0.190233
\(442\) 3.89986e70 0.00694923
\(443\) 3.40583e72 0.570322 0.285161 0.958480i \(-0.407953\pi\)
0.285161 + 0.958480i \(0.407953\pi\)
\(444\) 6.55168e72 1.03115
\(445\) −6.19825e72 −0.917000
\(446\) −1.09710e72 −0.152594
\(447\) −3.41465e72 −0.446570
\(448\) −1.13165e73 −1.39176
\(449\) 8.20452e72 0.949027 0.474514 0.880248i \(-0.342624\pi\)
0.474514 + 0.880248i \(0.342624\pi\)
\(450\) 7.05411e70 0.00767535
\(451\) 1.10331e73 1.12938
\(452\) −8.62449e72 −0.830666
\(453\) −4.89398e72 −0.443569
\(454\) −2.31636e72 −0.197593
\(455\) −5.49146e72 −0.440935
\(456\) −4.19297e72 −0.316948
\(457\) −1.34921e73 −0.960247 −0.480124 0.877201i \(-0.659408\pi\)
−0.480124 + 0.877201i \(0.659408\pi\)
\(458\) 1.12098e72 0.0751275
\(459\) −2.11329e72 −0.133386
\(460\) 2.30569e73 1.37076
\(461\) 3.22702e73 1.80728 0.903641 0.428290i \(-0.140884\pi\)
0.903641 + 0.428290i \(0.140884\pi\)
\(462\) 4.42710e72 0.233596
\(463\) −7.30279e72 −0.363088 −0.181544 0.983383i \(-0.558109\pi\)
−0.181544 + 0.983383i \(0.558109\pi\)
\(464\) 1.92101e73 0.900087
\(465\) −9.24248e72 −0.408162
\(466\) −2.87292e72 −0.119594
\(467\) −4.40634e73 −1.72927 −0.864636 0.502398i \(-0.832451\pi\)
−0.864636 + 0.502398i \(0.832451\pi\)
\(468\) 1.13774e72 0.0421000
\(469\) 2.96967e73 1.03623
\(470\) 6.40644e72 0.210827
\(471\) −1.59316e73 −0.494522
\(472\) −5.22617e72 −0.153031
\(473\) −1.17048e73 −0.323357
\(474\) 8.09659e72 0.211056
\(475\) −1.93718e73 −0.476535
\(476\) −8.60231e72 −0.199721
\(477\) 1.53824e72 0.0337107
\(478\) −1.20464e70 −0.000249225 0
\(479\) −3.18111e73 −0.621373 −0.310687 0.950512i \(-0.600559\pi\)
−0.310687 + 0.950512i \(0.600559\pi\)
\(480\) −1.70525e73 −0.314524
\(481\) −2.32879e73 −0.405640
\(482\) −1.56211e73 −0.256991
\(483\) 1.79609e74 2.79114
\(484\) −2.53911e72 −0.0372764
\(485\) −5.79420e72 −0.0803703
\(486\) 2.75153e72 0.0360643
\(487\) 6.34796e73 0.786299 0.393149 0.919475i \(-0.371386\pi\)
0.393149 + 0.919475i \(0.371386\pi\)
\(488\) 2.19960e73 0.257512
\(489\) 1.00433e73 0.111144
\(490\) −1.75379e73 −0.183478
\(491\) −6.91619e73 −0.684110 −0.342055 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(492\) −1.08642e74 −1.01615
\(493\) 1.38721e73 0.122702
\(494\) 7.36514e72 0.0616155
\(495\) 1.16840e73 0.0924590
\(496\) 7.12658e73 0.533501
\(497\) −3.29955e74 −2.33698
\(498\) 1.10958e73 0.0743622
\(499\) 1.91941e74 1.21732 0.608659 0.793432i \(-0.291708\pi\)
0.608659 + 0.793432i \(0.291708\pi\)
\(500\) −1.75926e74 −1.05598
\(501\) 1.06976e74 0.607782
\(502\) −2.20753e73 −0.118728
\(503\) 2.48789e74 1.26681 0.633406 0.773820i \(-0.281656\pi\)
0.633406 + 0.773820i \(0.281656\pi\)
\(504\) 1.19712e73 0.0577164
\(505\) −1.89945e74 −0.867194
\(506\) 6.60709e73 0.285674
\(507\) −1.99332e74 −0.816314
\(508\) 1.88641e74 0.731785
\(509\) 3.43699e74 1.26311 0.631553 0.775333i \(-0.282418\pi\)
0.631553 + 0.775333i \(0.282418\pi\)
\(510\) −3.94367e72 −0.0137316
\(511\) 8.18345e73 0.269999
\(512\) 2.20863e74 0.690557
\(513\) −3.99108e74 −1.18267
\(514\) −7.56362e73 −0.212444
\(515\) 2.15369e74 0.573435
\(516\) 1.15257e74 0.290937
\(517\) −7.78780e74 −1.86391
\(518\) −1.21090e74 −0.274814
\(519\) 3.53716e74 0.761294
\(520\) 4.02524e73 0.0821675
\(521\) −3.30970e74 −0.640842 −0.320421 0.947275i \(-0.603824\pi\)
−0.320421 + 0.947275i \(0.603824\pi\)
\(522\) −9.53996e72 −0.0175230
\(523\) −5.36017e74 −0.934076 −0.467038 0.884237i \(-0.654679\pi\)
−0.467038 + 0.884237i \(0.654679\pi\)
\(524\) 2.01482e74 0.333140
\(525\) −4.07557e74 −0.639451
\(526\) 8.94808e73 0.133236
\(527\) 5.14629e73 0.0727281
\(528\) 6.63875e74 0.890540
\(529\) 1.89523e75 2.41340
\(530\) 2.68939e73 0.0325138
\(531\) −5.30963e73 −0.0609487
\(532\) −1.62460e75 −1.77083
\(533\) 3.86169e74 0.399741
\(534\) 1.74897e74 0.171948
\(535\) 3.67825e74 0.343489
\(536\) −2.17677e74 −0.193099
\(537\) −5.07076e74 −0.427346
\(538\) −7.05383e73 −0.0564823
\(539\) 2.13194e75 1.62212
\(540\) −1.07791e75 −0.779389
\(541\) −9.01034e74 −0.619179 −0.309590 0.950870i \(-0.600192\pi\)
−0.309590 + 0.950870i \(0.600192\pi\)
\(542\) 1.32217e74 0.0863591
\(543\) −1.35710e75 −0.842592
\(544\) 9.49497e73 0.0560433
\(545\) −6.79775e74 −0.381471
\(546\) 1.54953e74 0.0826804
\(547\) −3.28535e75 −1.66698 −0.833491 0.552534i \(-0.813661\pi\)
−0.833491 + 0.552534i \(0.813661\pi\)
\(548\) 1.07319e75 0.517859
\(549\) 2.23472e74 0.102561
\(550\) −1.49924e74 −0.0654481
\(551\) 2.61983e75 1.08794
\(552\) −1.31653e75 −0.520124
\(553\) 6.34814e75 2.38619
\(554\) −1.08720e74 −0.0388859
\(555\) 2.35495e75 0.801540
\(556\) 1.89652e75 0.614327
\(557\) −5.67764e75 −1.75045 −0.875226 0.483715i \(-0.839287\pi\)
−0.875226 + 0.483715i \(0.839287\pi\)
\(558\) −3.53915e73 −0.0103862
\(559\) −4.09680e74 −0.114451
\(560\) −4.28185e75 −1.13884
\(561\) 4.79401e74 0.121400
\(562\) 5.80636e74 0.140009
\(563\) 1.20573e74 0.0276866 0.0138433 0.999904i \(-0.495593\pi\)
0.0138433 + 0.999904i \(0.495593\pi\)
\(564\) 7.66863e75 1.67704
\(565\) −3.10001e75 −0.645700
\(566\) −4.52679e74 −0.0898129
\(567\) −7.37885e75 −1.39462
\(568\) 2.41857e75 0.435492
\(569\) −3.59495e75 −0.616745 −0.308372 0.951266i \(-0.599784\pi\)
−0.308372 + 0.951266i \(0.599784\pi\)
\(570\) −7.44788e74 −0.121751
\(571\) −5.41913e75 −0.844183 −0.422092 0.906553i \(-0.638704\pi\)
−0.422092 + 0.906553i \(0.638704\pi\)
\(572\) −2.41809e75 −0.358989
\(573\) 1.21782e76 1.72319
\(574\) 2.00795e75 0.270817
\(575\) −6.08246e75 −0.782012
\(576\) 8.42744e74 0.103295
\(577\) 4.19846e75 0.490631 0.245316 0.969443i \(-0.421108\pi\)
0.245316 + 0.969443i \(0.421108\pi\)
\(578\) −1.33999e75 −0.149309
\(579\) 4.44800e75 0.472611
\(580\) 7.07564e75 0.716961
\(581\) 8.69968e75 0.840736
\(582\) 1.63495e74 0.0150704
\(583\) −3.26928e75 −0.287453
\(584\) −5.99847e74 −0.0503138
\(585\) 4.08953e74 0.0327255
\(586\) −1.53642e75 −0.117307
\(587\) −4.18417e75 −0.304833 −0.152417 0.988316i \(-0.548706\pi\)
−0.152417 + 0.988316i \(0.548706\pi\)
\(588\) −2.09932e76 −1.45949
\(589\) 9.71910e75 0.644845
\(590\) −9.28312e74 −0.0587846
\(591\) −1.40023e75 −0.0846337
\(592\) −1.81583e76 −1.04768
\(593\) 4.80739e75 0.264792 0.132396 0.991197i \(-0.457733\pi\)
0.132396 + 0.991197i \(0.457733\pi\)
\(594\) −3.08881e75 −0.162429
\(595\) −3.09204e75 −0.155249
\(596\) 9.69785e75 0.464947
\(597\) −7.94772e75 −0.363872
\(598\) 2.31255e75 0.101113
\(599\) 3.85877e75 0.161143 0.0805714 0.996749i \(-0.474325\pi\)
0.0805714 + 0.996749i \(0.474325\pi\)
\(600\) 2.98739e75 0.119161
\(601\) 2.69061e76 1.02519 0.512593 0.858632i \(-0.328685\pi\)
0.512593 + 0.858632i \(0.328685\pi\)
\(602\) −2.13020e75 −0.0775386
\(603\) −2.21153e75 −0.0769072
\(604\) 1.38992e76 0.461823
\(605\) −9.12663e74 −0.0289760
\(606\) 5.35971e75 0.162609
\(607\) −2.83247e76 −0.821252 −0.410626 0.911804i \(-0.634690\pi\)
−0.410626 + 0.911804i \(0.634690\pi\)
\(608\) 1.79319e76 0.496909
\(609\) 5.51179e76 1.45988
\(610\) 3.90709e75 0.0989198
\(611\) −2.72581e76 −0.659724
\(612\) 6.40619e74 0.0148230
\(613\) −5.22770e76 −1.15651 −0.578253 0.815858i \(-0.696265\pi\)
−0.578253 + 0.815858i \(0.696265\pi\)
\(614\) −8.08026e74 −0.0170921
\(615\) −3.90507e76 −0.789883
\(616\) −2.54429e76 −0.492150
\(617\) 3.43035e76 0.634595 0.317297 0.948326i \(-0.397225\pi\)
0.317297 + 0.948326i \(0.397225\pi\)
\(618\) −6.07708e75 −0.107526
\(619\) −1.83217e76 −0.310080 −0.155040 0.987908i \(-0.549551\pi\)
−0.155040 + 0.987908i \(0.549551\pi\)
\(620\) 2.62493e76 0.424959
\(621\) −1.25314e77 −1.94080
\(622\) −2.13716e75 −0.0316667
\(623\) 1.37128e77 1.94404
\(624\) 2.32363e76 0.315203
\(625\) −3.06276e76 −0.397568
\(626\) 1.32458e76 0.164545
\(627\) 9.05380e76 1.07640
\(628\) 4.52470e76 0.514872
\(629\) −1.31126e76 −0.142822
\(630\) 2.12642e75 0.0221710
\(631\) 3.00198e76 0.299640 0.149820 0.988713i \(-0.452131\pi\)
0.149820 + 0.988713i \(0.452131\pi\)
\(632\) −4.65319e76 −0.444663
\(633\) −1.55071e77 −1.41883
\(634\) −1.14491e75 −0.0100304
\(635\) 6.78055e76 0.568836
\(636\) 3.21925e76 0.258633
\(637\) 7.46201e76 0.574145
\(638\) 2.02757e76 0.149419
\(639\) 2.45720e76 0.173447
\(640\) 6.43062e76 0.434814
\(641\) −7.84590e76 −0.508214 −0.254107 0.967176i \(-0.581782\pi\)
−0.254107 + 0.967176i \(0.581782\pi\)
\(642\) −1.03789e76 −0.0644080
\(643\) −1.61526e77 −0.960374 −0.480187 0.877166i \(-0.659431\pi\)
−0.480187 + 0.877166i \(0.659431\pi\)
\(644\) −5.10102e77 −2.90600
\(645\) 4.14282e76 0.226154
\(646\) 4.14704e75 0.0216942
\(647\) 1.73743e77 0.871044 0.435522 0.900178i \(-0.356564\pi\)
0.435522 + 0.900178i \(0.356564\pi\)
\(648\) 5.40870e76 0.259884
\(649\) 1.12848e77 0.519713
\(650\) −5.24749e75 −0.0231651
\(651\) 2.04477e77 0.865302
\(652\) −2.85238e76 −0.115717
\(653\) 1.79111e77 0.696641 0.348320 0.937376i \(-0.386752\pi\)
0.348320 + 0.937376i \(0.386752\pi\)
\(654\) 1.91813e76 0.0715301
\(655\) 7.24213e76 0.258959
\(656\) 3.01107e77 1.03244
\(657\) −6.09427e75 −0.0200389
\(658\) −1.41734e77 −0.446952
\(659\) −5.64076e77 −1.70604 −0.853018 0.521881i \(-0.825231\pi\)
−0.853018 + 0.521881i \(0.825231\pi\)
\(660\) 2.44525e77 0.709357
\(661\) 5.54552e76 0.154313 0.0771565 0.997019i \(-0.475416\pi\)
0.0771565 + 0.997019i \(0.475416\pi\)
\(662\) 8.10563e76 0.216368
\(663\) 1.67795e76 0.0429693
\(664\) −6.37687e76 −0.156670
\(665\) −5.83951e77 −1.37652
\(666\) 9.01763e75 0.0203963
\(667\) 8.22590e77 1.78535
\(668\) −3.03819e77 −0.632793
\(669\) −4.72037e77 −0.943535
\(670\) −3.86654e76 −0.0741764
\(671\) −4.74955e77 −0.874546
\(672\) 3.77263e77 0.666791
\(673\) −7.57599e77 −1.28536 −0.642680 0.766135i \(-0.722178\pi\)
−0.642680 + 0.766135i \(0.722178\pi\)
\(674\) −1.01792e77 −0.165793
\(675\) 2.84355e77 0.444639
\(676\) 5.66116e77 0.849907
\(677\) 9.51246e77 1.37121 0.685606 0.727973i \(-0.259537\pi\)
0.685606 + 0.727973i \(0.259537\pi\)
\(678\) 8.74732e76 0.121076
\(679\) 1.28189e77 0.170385
\(680\) 2.26646e76 0.0289304
\(681\) −9.96638e77 −1.22178
\(682\) 7.52190e76 0.0885640
\(683\) 9.13435e77 1.03302 0.516510 0.856281i \(-0.327231\pi\)
0.516510 + 0.856281i \(0.327231\pi\)
\(684\) 1.20985e77 0.131428
\(685\) 3.85751e77 0.402546
\(686\) 1.44287e77 0.144649
\(687\) 4.82314e77 0.464537
\(688\) −3.19439e77 −0.295601
\(689\) −1.14428e77 −0.101743
\(690\) −2.33853e77 −0.199799
\(691\) −1.64704e78 −1.35225 −0.676127 0.736785i \(-0.736343\pi\)
−0.676127 + 0.736785i \(0.736343\pi\)
\(692\) −1.00458e78 −0.792623
\(693\) −2.58493e77 −0.196013
\(694\) 2.25034e77 0.164007
\(695\) 6.81689e77 0.477534
\(696\) −4.04014e77 −0.272046
\(697\) 2.17437e77 0.140745
\(698\) −4.22694e77 −0.263028
\(699\) −1.23610e78 −0.739489
\(700\) 1.15749e78 0.665766
\(701\) 2.19900e78 1.21613 0.608066 0.793886i \(-0.291946\pi\)
0.608066 + 0.793886i \(0.291946\pi\)
\(702\) −1.08112e77 −0.0574913
\(703\) −2.47639e78 −1.26633
\(704\) −1.79112e78 −0.880798
\(705\) 2.75643e78 1.30361
\(706\) 1.07573e77 0.0489299
\(707\) 4.20228e78 1.83845
\(708\) −1.11121e78 −0.467607
\(709\) −5.02468e77 −0.203393 −0.101697 0.994815i \(-0.532427\pi\)
−0.101697 + 0.994815i \(0.532427\pi\)
\(710\) 4.29605e77 0.167288
\(711\) −4.72750e77 −0.177099
\(712\) −1.00515e78 −0.362268
\(713\) 3.05166e78 1.05821
\(714\) 8.72482e76 0.0291109
\(715\) −8.69163e77 −0.279052
\(716\) 1.44013e78 0.444933
\(717\) −5.18310e75 −0.00154104
\(718\) 8.55974e77 0.244928
\(719\) −5.31416e78 −1.46349 −0.731745 0.681578i \(-0.761294\pi\)
−0.731745 + 0.681578i \(0.761294\pi\)
\(720\) 3.18872e77 0.0845227
\(721\) −4.76474e78 −1.21568
\(722\) 1.65293e77 0.0405959
\(723\) −6.72113e78 −1.58905
\(724\) 3.85427e78 0.877267
\(725\) −1.86657e78 −0.409024
\(726\) 2.57527e76 0.00543332
\(727\) 3.83847e78 0.779761 0.389880 0.920865i \(-0.372516\pi\)
0.389880 + 0.920865i \(0.372516\pi\)
\(728\) −8.90530e77 −0.174195
\(729\) 5.78264e78 1.08923
\(730\) −1.06550e77 −0.0193274
\(731\) −2.30675e77 −0.0402970
\(732\) 4.67686e78 0.786865
\(733\) 4.93828e78 0.800233 0.400116 0.916464i \(-0.368970\pi\)
0.400116 + 0.916464i \(0.368970\pi\)
\(734\) −1.46387e78 −0.228487
\(735\) −7.54584e78 −1.13450
\(736\) 5.63035e78 0.815447
\(737\) 4.70026e78 0.655791
\(738\) −1.49534e77 −0.0200997
\(739\) −7.07383e78 −0.916078 −0.458039 0.888932i \(-0.651448\pi\)
−0.458039 + 0.888932i \(0.651448\pi\)
\(740\) −6.68824e78 −0.834525
\(741\) 3.16892e78 0.380988
\(742\) −5.94990e77 −0.0689291
\(743\) 9.59859e78 1.07156 0.535778 0.844359i \(-0.320018\pi\)
0.535778 + 0.844359i \(0.320018\pi\)
\(744\) −1.49882e78 −0.161248
\(745\) 3.48582e78 0.361416
\(746\) −2.52268e78 −0.252083
\(747\) −6.47870e77 −0.0623981
\(748\) −1.36153e78 −0.126396
\(749\) −8.13762e78 −0.728195
\(750\) 1.78431e78 0.153917
\(751\) −6.76425e78 −0.562499 −0.281249 0.959635i \(-0.590749\pi\)
−0.281249 + 0.959635i \(0.590749\pi\)
\(752\) −2.12540e79 −1.70392
\(753\) −9.49811e78 −0.734134
\(754\) 7.09669e77 0.0528864
\(755\) 4.99598e78 0.358988
\(756\) 2.38473e79 1.65230
\(757\) −6.22716e78 −0.416057 −0.208029 0.978123i \(-0.566705\pi\)
−0.208029 + 0.978123i \(0.566705\pi\)
\(758\) 3.63589e78 0.234265
\(759\) 2.84276e79 1.76641
\(760\) 4.28036e78 0.256512
\(761\) −6.20793e77 −0.0358814 −0.0179407 0.999839i \(-0.505711\pi\)
−0.0179407 + 0.999839i \(0.505711\pi\)
\(762\) −1.91327e78 −0.106663
\(763\) 1.50391e79 0.808717
\(764\) −3.45871e79 −1.79410
\(765\) 2.30266e77 0.0115223
\(766\) −1.52215e77 −0.00734797
\(767\) 3.94978e78 0.183950
\(768\) 1.62383e79 0.729638
\(769\) 2.93043e79 1.27045 0.635224 0.772328i \(-0.280908\pi\)
0.635224 + 0.772328i \(0.280908\pi\)
\(770\) −4.51937e78 −0.189053
\(771\) −3.25432e79 −1.31361
\(772\) −1.26326e79 −0.492060
\(773\) 9.72409e78 0.365521 0.182761 0.983157i \(-0.441497\pi\)
0.182761 + 0.983157i \(0.441497\pi\)
\(774\) 1.58638e77 0.00575479
\(775\) −6.92463e78 −0.242437
\(776\) −9.39623e77 −0.0317509
\(777\) −5.21001e79 −1.69926
\(778\) 8.61777e77 0.0271304
\(779\) 4.10644e79 1.24792
\(780\) 8.55863e78 0.251074
\(781\) −5.22238e79 −1.47899
\(782\) 1.30211e78 0.0356010
\(783\) −3.84561e79 −1.01512
\(784\) 5.81835e79 1.48289
\(785\) 1.62637e79 0.400224
\(786\) −2.04352e78 −0.0485577
\(787\) −1.67187e79 −0.383617 −0.191808 0.981432i \(-0.561435\pi\)
−0.191808 + 0.981432i \(0.561435\pi\)
\(788\) 3.97675e78 0.0881165
\(789\) 3.85000e79 0.823840
\(790\) −8.26535e78 −0.170811
\(791\) 6.85834e79 1.36888
\(792\) 1.89475e78 0.0365266
\(793\) −1.66239e79 −0.309543
\(794\) 1.35055e79 0.242911
\(795\) 1.15714e79 0.201043
\(796\) 2.25721e79 0.378846
\(797\) −4.63054e79 −0.750806 −0.375403 0.926862i \(-0.622496\pi\)
−0.375403 + 0.926862i \(0.622496\pi\)
\(798\) 1.64774e79 0.258112
\(799\) −1.53480e79 −0.232282
\(800\) −1.27760e79 −0.186819
\(801\) −1.02120e79 −0.144283
\(802\) 3.31513e77 0.00452591
\(803\) 1.29524e79 0.170873
\(804\) −4.62833e79 −0.590042
\(805\) −1.83352e80 −2.25891
\(806\) 2.63274e78 0.0313469
\(807\) −3.03498e79 −0.349248
\(808\) −3.08027e79 −0.342592
\(809\) 1.81292e80 1.94892 0.974459 0.224565i \(-0.0720962\pi\)
0.974459 + 0.224565i \(0.0720962\pi\)
\(810\) 9.60735e78 0.0998310
\(811\) 1.57811e80 1.58512 0.792562 0.609791i \(-0.208747\pi\)
0.792562 + 0.609791i \(0.208747\pi\)
\(812\) −1.56539e80 −1.51996
\(813\) 5.68878e79 0.533985
\(814\) −1.91655e79 −0.173920
\(815\) −1.02527e79 −0.0899504
\(816\) 1.30835e79 0.110980
\(817\) −4.35645e79 −0.357295
\(818\) −1.72748e79 −0.136993
\(819\) −9.04751e78 −0.0693780
\(820\) 1.10907e80 0.822388
\(821\) 5.17464e79 0.371059 0.185530 0.982639i \(-0.440600\pi\)
0.185530 + 0.982639i \(0.440600\pi\)
\(822\) −1.08848e79 −0.0754820
\(823\) 1.22160e80 0.819279 0.409640 0.912247i \(-0.365654\pi\)
0.409640 + 0.912247i \(0.365654\pi\)
\(824\) 3.49255e79 0.226540
\(825\) −6.45062e79 −0.404686
\(826\) 2.05376e79 0.124623
\(827\) 5.64616e79 0.331400 0.165700 0.986176i \(-0.447012\pi\)
0.165700 + 0.986176i \(0.447012\pi\)
\(828\) 3.79876e79 0.215679
\(829\) −1.62760e80 −0.893921 −0.446961 0.894554i \(-0.647494\pi\)
−0.446961 + 0.894554i \(0.647494\pi\)
\(830\) −1.13271e79 −0.0601826
\(831\) −4.67780e79 −0.240444
\(832\) −6.26910e79 −0.311755
\(833\) 4.20158e79 0.202151
\(834\) −1.92353e79 −0.0895430
\(835\) −1.09205e80 −0.491888
\(836\) −2.57134e80 −1.12070
\(837\) −1.42665e80 −0.601682
\(838\) −1.86665e79 −0.0761821
\(839\) −7.61754e79 −0.300858 −0.150429 0.988621i \(-0.548065\pi\)
−0.150429 + 0.988621i \(0.548065\pi\)
\(840\) 9.00533e79 0.344207
\(841\) −1.78931e79 −0.0661906
\(842\) 5.75923e79 0.206197
\(843\) 2.49824e80 0.865717
\(844\) 4.40414e80 1.47722
\(845\) 2.03486e80 0.660656
\(846\) 1.05550e79 0.0331721
\(847\) 2.01914e79 0.0614289
\(848\) −8.92230e79 −0.262779
\(849\) −1.94770e80 −0.555341
\(850\) −2.95467e78 −0.00815620
\(851\) −7.77552e80 −2.07810
\(852\) 5.14246e80 1.33071
\(853\) 6.55715e80 1.64292 0.821461 0.570265i \(-0.193160\pi\)
0.821461 + 0.570265i \(0.193160\pi\)
\(854\) −8.64390e79 −0.209710
\(855\) 4.34872e79 0.102163
\(856\) 5.96488e79 0.135698
\(857\) −2.43562e80 −0.536584 −0.268292 0.963338i \(-0.586459\pi\)
−0.268292 + 0.963338i \(0.586459\pi\)
\(858\) 2.45252e79 0.0523254
\(859\) −2.70552e80 −0.559035 −0.279517 0.960141i \(-0.590174\pi\)
−0.279517 + 0.960141i \(0.590174\pi\)
\(860\) −1.17659e80 −0.235460
\(861\) 8.63942e80 1.67455
\(862\) −9.34051e79 −0.175356
\(863\) −9.09815e80 −1.65446 −0.827230 0.561863i \(-0.810085\pi\)
−0.827230 + 0.561863i \(0.810085\pi\)
\(864\) −2.63219e80 −0.463649
\(865\) −3.61089e80 −0.616128
\(866\) 4.56914e79 0.0755252
\(867\) −5.76545e80 −0.923226
\(868\) −5.80730e80 −0.900911
\(869\) 1.00475e81 1.51013
\(870\) −7.17641e79 −0.104503
\(871\) 1.64514e80 0.232115
\(872\) −1.10236e80 −0.150703
\(873\) −9.54629e78 −0.0126457
\(874\) 2.45912e80 0.315657
\(875\) 1.39899e81 1.74018
\(876\) −1.27542e80 −0.153741
\(877\) 1.05076e81 1.22749 0.613743 0.789506i \(-0.289663\pi\)
0.613743 + 0.789506i \(0.289663\pi\)
\(878\) 4.31228e79 0.0488211
\(879\) −6.61059e80 −0.725348
\(880\) −6.77712e80 −0.720729
\(881\) 6.98981e80 0.720490 0.360245 0.932858i \(-0.382693\pi\)
0.360245 + 0.932858i \(0.382693\pi\)
\(882\) −2.88947e79 −0.0288690
\(883\) −7.95621e80 −0.770525 −0.385263 0.922807i \(-0.625889\pi\)
−0.385263 + 0.922807i \(0.625889\pi\)
\(884\) −4.76551e79 −0.0447375
\(885\) −3.99415e80 −0.363484
\(886\) 9.81055e79 0.0865498
\(887\) 2.23142e81 1.90846 0.954228 0.299079i \(-0.0966794\pi\)
0.954228 + 0.299079i \(0.0966794\pi\)
\(888\) 3.81894e80 0.316655
\(889\) −1.50010e81 −1.20593
\(890\) −1.78542e80 −0.139160
\(891\) −1.16789e81 −0.882603
\(892\) 1.34062e81 0.982364
\(893\) −2.89857e81 −2.05954
\(894\) −9.83596e79 −0.0677696
\(895\) 5.17645e80 0.345858
\(896\) −1.42269e81 −0.921804
\(897\) 9.94997e80 0.625215
\(898\) 2.36333e80 0.144021
\(899\) 9.36484e80 0.553489
\(900\) −8.61991e79 −0.0494121
\(901\) −6.44302e79 −0.0358227
\(902\) 3.17810e80 0.171391
\(903\) −9.16541e80 −0.479445
\(904\) −5.02716e80 −0.255089
\(905\) 1.38539e81 0.681924
\(906\) −1.40972e80 −0.0673143
\(907\) −1.64651e81 −0.762716 −0.381358 0.924427i \(-0.624543\pi\)
−0.381358 + 0.924427i \(0.624543\pi\)
\(908\) 2.83053e81 1.27206
\(909\) −3.12946e80 −0.136447
\(910\) −1.58183e80 −0.0669146
\(911\) 1.86319e81 0.764718 0.382359 0.924014i \(-0.375112\pi\)
0.382359 + 0.924014i \(0.375112\pi\)
\(912\) 2.47090e81 0.984006
\(913\) 1.37694e81 0.532072
\(914\) −3.88642e80 −0.145723
\(915\) 1.68106e81 0.611652
\(916\) −1.36981e81 −0.483653
\(917\) −1.60222e81 −0.548992
\(918\) −6.08737e79 −0.0202421
\(919\) −5.59344e81 −1.80510 −0.902552 0.430580i \(-0.858309\pi\)
−0.902552 + 0.430580i \(0.858309\pi\)
\(920\) 1.34397e81 0.420945
\(921\) −3.47661e80 −0.105686
\(922\) 9.29550e80 0.274266
\(923\) −1.82789e81 −0.523483
\(924\) −5.40978e81 −1.50383
\(925\) 1.76437e81 0.476094
\(926\) −2.10358e80 −0.0551008
\(927\) 3.54833e80 0.0902258
\(928\) 1.72783e81 0.426512
\(929\) −5.85958e81 −1.40422 −0.702109 0.712070i \(-0.747758\pi\)
−0.702109 + 0.712070i \(0.747758\pi\)
\(930\) −2.66232e80 −0.0619410
\(931\) 7.93496e81 1.79237
\(932\) 3.51062e81 0.769921
\(933\) −9.19536e80 −0.195805
\(934\) −1.26925e81 −0.262428
\(935\) −4.89393e80 −0.0982514
\(936\) 6.63183e79 0.0129285
\(937\) 2.38829e81 0.452115 0.226057 0.974114i \(-0.427416\pi\)
0.226057 + 0.974114i \(0.427416\pi\)
\(938\) 8.55419e80 0.157254
\(939\) 5.69913e81 1.01743
\(940\) −7.82846e81 −1.35725
\(941\) −8.27740e81 −1.39373 −0.696866 0.717201i \(-0.745423\pi\)
−0.696866 + 0.717201i \(0.745423\pi\)
\(942\) −4.58914e80 −0.0750467
\(943\) 1.28936e82 2.04788
\(944\) 3.07976e81 0.475103
\(945\) 8.57172e81 1.28438
\(946\) −3.37159e80 −0.0490714
\(947\) 6.70100e80 0.0947360 0.0473680 0.998878i \(-0.484917\pi\)
0.0473680 + 0.998878i \(0.484917\pi\)
\(948\) −9.89378e81 −1.35873
\(949\) 4.53347e80 0.0604797
\(950\) −5.58008e80 −0.0723171
\(951\) −4.92610e80 −0.0620210
\(952\) −5.01424e80 −0.0613322
\(953\) −1.01290e82 −1.20368 −0.601839 0.798617i \(-0.705565\pi\)
−0.601839 + 0.798617i \(0.705565\pi\)
\(954\) 4.43093e79 0.00511581
\(955\) −1.24321e82 −1.39460
\(956\) 1.47204e79 0.00160445
\(957\) 8.72380e81 0.923905
\(958\) −9.16326e80 −0.0942972
\(959\) −8.53420e81 −0.853397
\(960\) 6.33952e81 0.616024
\(961\) −7.11575e81 −0.671935
\(962\) −6.70813e80 −0.0615584
\(963\) 6.06014e80 0.0540455
\(964\) 1.90885e82 1.65445
\(965\) −4.54071e81 −0.382492
\(966\) 5.17367e81 0.423572
\(967\) 5.45472e81 0.434055 0.217027 0.976166i \(-0.430364\pi\)
0.217027 + 0.976166i \(0.430364\pi\)
\(968\) −1.48003e80 −0.0114472
\(969\) 1.78430e81 0.134142
\(970\) −1.66903e80 −0.0121967
\(971\) 1.71965e82 1.22155 0.610776 0.791803i \(-0.290858\pi\)
0.610776 + 0.791803i \(0.290858\pi\)
\(972\) −3.36229e81 −0.232173
\(973\) −1.50814e82 −1.01237
\(974\) 1.82854e81 0.119326
\(975\) −2.25778e81 −0.143237
\(976\) −1.29621e82 −0.799479
\(977\) −2.16132e81 −0.129604 −0.0648020 0.997898i \(-0.520642\pi\)
−0.0648020 + 0.997898i \(0.520642\pi\)
\(978\) 2.89300e80 0.0168667
\(979\) 2.17040e82 1.23031
\(980\) 2.14307e82 1.18119
\(981\) −1.11997e81 −0.0600217
\(982\) −1.99222e81 −0.103818
\(983\) −3.94403e81 −0.199856 −0.0999282 0.994995i \(-0.531861\pi\)
−0.0999282 + 0.994995i \(0.531861\pi\)
\(984\) −6.33269e81 −0.312049
\(985\) 1.42941e81 0.0684954
\(986\) 3.99588e80 0.0186208
\(987\) −6.09822e82 −2.76364
\(988\) −8.99997e81 −0.396666
\(989\) −1.36786e82 −0.586334
\(990\) 3.36560e80 0.0140312
\(991\) 4.34814e81 0.176310 0.0881551 0.996107i \(-0.471903\pi\)
0.0881551 + 0.996107i \(0.471903\pi\)
\(992\) 6.40992e81 0.252803
\(993\) 3.48753e82 1.33787
\(994\) −9.50442e81 −0.354650
\(995\) 8.11337e81 0.294487
\(996\) −1.35587e82 −0.478726
\(997\) 3.26514e81 0.112146 0.0560732 0.998427i \(-0.482142\pi\)
0.0560732 + 0.998427i \(0.482142\pi\)
\(998\) 5.52891e81 0.184735
\(999\) 3.63505e82 1.18157
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 \(a_p\))