Properties

Label 2.82.a.a.1.3
Level 2
Weight 82
Character 2.1
Self dual yes
Analytic conductor 83.100
Analytic rank 1
Dimension 3
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 82 \)
Character orbit: \([\chi]\) = 2.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(83.1002571076\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(4.38588e14\)
Character \(\chi\) = 2.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} +O(q^{10})\) \(q-1.09951e12 q^{2} +2.69378e19 q^{3} +1.20893e24 q^{4} +1.65593e28 q^{5} -2.96185e31 q^{6} +2.15367e33 q^{7} -1.32923e36 q^{8} +2.82220e38 q^{9} -1.82071e40 q^{10} -3.85124e40 q^{11} +3.25658e43 q^{12} -8.46841e43 q^{13} -2.36798e45 q^{14} +4.46071e47 q^{15} +1.46150e48 q^{16} -7.68035e49 q^{17} -3.10304e50 q^{18} -7.37973e51 q^{19} +2.00189e52 q^{20} +5.80152e52 q^{21} +4.23448e52 q^{22} -1.05342e55 q^{23} -3.58065e55 q^{24} -1.39380e56 q^{25} +9.31111e55 q^{26} -4.34255e57 q^{27} +2.60363e57 q^{28} -1.79362e59 q^{29} -4.90461e59 q^{30} -4.86617e60 q^{31} -1.60694e60 q^{32} -1.03744e60 q^{33} +8.44463e61 q^{34} +3.56632e61 q^{35} +3.41183e62 q^{36} +2.30511e63 q^{37} +8.11410e63 q^{38} -2.28121e63 q^{39} -2.20111e64 q^{40} -1.35802e65 q^{41} -6.37884e64 q^{42} +2.10516e66 q^{43} -4.65586e64 q^{44} +4.67337e66 q^{45} +1.15824e67 q^{46} +1.03746e68 q^{47} +3.93697e67 q^{48} -2.79115e68 q^{49} +1.53250e68 q^{50} -2.06892e69 q^{51} -1.02377e68 q^{52} +2.99301e69 q^{53} +4.77468e69 q^{54} -6.37737e68 q^{55} -2.86272e69 q^{56} -1.98794e71 q^{57} +1.97211e71 q^{58} -5.68737e71 q^{59} +5.39267e71 q^{60} +5.44662e71 q^{61} +5.35041e72 q^{62} +6.07809e71 q^{63} +1.76685e72 q^{64} -1.40231e72 q^{65} +1.14068e72 q^{66} -5.75193e73 q^{67} -9.28497e73 q^{68} -2.83767e74 q^{69} -3.92121e73 q^{70} +4.64836e74 q^{71} -3.75135e74 q^{72} +4.70398e75 q^{73} -2.53449e75 q^{74} -3.75460e75 q^{75} -8.92155e75 q^{76} -8.29429e73 q^{77} +2.50821e75 q^{78} -4.20695e76 q^{79} +2.42014e76 q^{80} -2.42123e77 q^{81} +1.49315e77 q^{82} -7.46283e77 q^{83} +7.01361e76 q^{84} -1.27181e78 q^{85} -2.31465e78 q^{86} -4.83163e78 q^{87} +5.11917e76 q^{88} +5.59868e78 q^{89} -5.13842e78 q^{90} -1.82382e77 q^{91} -1.27350e79 q^{92} -1.31084e80 q^{93} -1.14070e80 q^{94} -1.22203e80 q^{95} -4.32874e79 q^{96} -1.28380e80 q^{97} +3.06890e80 q^{98} -1.08690e79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3298534883328q^{2} + 12604360672390214988q^{3} + \)\(36\!\cdots\!28\)\(q^{4} - \)\(20\!\cdots\!50\)\(q^{5} - \)\(13\!\cdots\!88\)\(q^{6} - \)\(55\!\cdots\!24\)\(q^{7} - \)\(39\!\cdots\!28\)\(q^{8} - \)\(11\!\cdots\!61\)\(q^{9} + O(q^{10}) \) \( 3q - 3298534883328q^{2} + 12604360672390214988q^{3} + \)\(36\!\cdots\!28\)\(q^{4} - \)\(20\!\cdots\!50\)\(q^{5} - \)\(13\!\cdots\!88\)\(q^{6} - \)\(55\!\cdots\!24\)\(q^{7} - \)\(39\!\cdots\!28\)\(q^{8} - \)\(11\!\cdots\!61\)\(q^{9} + \)\(23\!\cdots\!00\)\(q^{10} + \)\(12\!\cdots\!36\)\(q^{11} + \)\(15\!\cdots\!88\)\(q^{12} - \)\(20\!\cdots\!42\)\(q^{13} + \)\(60\!\cdots\!24\)\(q^{14} + \)\(25\!\cdots\!00\)\(q^{15} + \)\(43\!\cdots\!28\)\(q^{16} + \)\(13\!\cdots\!46\)\(q^{17} + \)\(12\!\cdots\!36\)\(q^{18} + \)\(47\!\cdots\!60\)\(q^{19} - \)\(25\!\cdots\!00\)\(q^{20} - \)\(51\!\cdots\!04\)\(q^{21} - \)\(14\!\cdots\!36\)\(q^{22} - \)\(30\!\cdots\!72\)\(q^{23} - \)\(16\!\cdots\!88\)\(q^{24} + \)\(28\!\cdots\!25\)\(q^{25} + \)\(22\!\cdots\!92\)\(q^{26} - \)\(62\!\cdots\!20\)\(q^{27} - \)\(66\!\cdots\!24\)\(q^{28} + \)\(21\!\cdots\!90\)\(q^{29} - \)\(28\!\cdots\!00\)\(q^{30} - \)\(38\!\cdots\!04\)\(q^{31} - \)\(48\!\cdots\!28\)\(q^{32} + \)\(81\!\cdots\!56\)\(q^{33} - \)\(15\!\cdots\!96\)\(q^{34} + \)\(79\!\cdots\!00\)\(q^{35} - \)\(14\!\cdots\!36\)\(q^{36} - \)\(96\!\cdots\!14\)\(q^{37} - \)\(52\!\cdots\!60\)\(q^{38} + \)\(36\!\cdots\!68\)\(q^{39} + \)\(27\!\cdots\!00\)\(q^{40} + \)\(31\!\cdots\!26\)\(q^{41} + \)\(57\!\cdots\!04\)\(q^{42} + \)\(90\!\cdots\!68\)\(q^{43} + \)\(15\!\cdots\!36\)\(q^{44} + \)\(18\!\cdots\!50\)\(q^{45} + \)\(33\!\cdots\!72\)\(q^{46} + \)\(16\!\cdots\!56\)\(q^{47} + \)\(18\!\cdots\!88\)\(q^{48} + \)\(84\!\cdots\!71\)\(q^{49} - \)\(30\!\cdots\!00\)\(q^{50} - \)\(77\!\cdots\!84\)\(q^{51} - \)\(24\!\cdots\!92\)\(q^{52} - \)\(90\!\cdots\!62\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(47\!\cdots\!00\)\(q^{55} + \)\(73\!\cdots\!24\)\(q^{56} - \)\(21\!\cdots\!40\)\(q^{57} - \)\(23\!\cdots\!40\)\(q^{58} + \)\(17\!\cdots\!80\)\(q^{59} + \)\(31\!\cdots\!00\)\(q^{60} + \)\(36\!\cdots\!86\)\(q^{61} + \)\(42\!\cdots\!04\)\(q^{62} + \)\(97\!\cdots\!88\)\(q^{63} + \)\(53\!\cdots\!28\)\(q^{64} - \)\(44\!\cdots\!00\)\(q^{65} - \)\(89\!\cdots\!56\)\(q^{66} - \)\(45\!\cdots\!04\)\(q^{67} + \)\(16\!\cdots\!96\)\(q^{68} - \)\(38\!\cdots\!12\)\(q^{69} - \)\(87\!\cdots\!00\)\(q^{70} - \)\(66\!\cdots\!84\)\(q^{71} + \)\(15\!\cdots\!36\)\(q^{72} + \)\(28\!\cdots\!78\)\(q^{73} + \)\(10\!\cdots\!64\)\(q^{74} + \)\(10\!\cdots\!00\)\(q^{75} + \)\(57\!\cdots\!60\)\(q^{76} - \)\(30\!\cdots\!88\)\(q^{77} - \)\(40\!\cdots\!68\)\(q^{78} - \)\(16\!\cdots\!60\)\(q^{79} - \)\(30\!\cdots\!00\)\(q^{80} - \)\(29\!\cdots\!37\)\(q^{81} - \)\(34\!\cdots\!76\)\(q^{82} - \)\(15\!\cdots\!52\)\(q^{83} - \)\(62\!\cdots\!04\)\(q^{84} - \)\(52\!\cdots\!00\)\(q^{85} - \)\(10\!\cdots\!68\)\(q^{86} - \)\(55\!\cdots\!60\)\(q^{87} - \)\(17\!\cdots\!36\)\(q^{88} - \)\(86\!\cdots\!30\)\(q^{89} - \)\(20\!\cdots\!00\)\(q^{90} - \)\(58\!\cdots\!64\)\(q^{91} - \)\(36\!\cdots\!72\)\(q^{92} - \)\(24\!\cdots\!84\)\(q^{93} - \)\(17\!\cdots\!56\)\(q^{94} - \)\(43\!\cdots\!00\)\(q^{95} - \)\(20\!\cdots\!88\)\(q^{96} - \)\(53\!\cdots\!94\)\(q^{97} - \)\(93\!\cdots\!96\)\(q^{98} - \)\(54\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09951e12 −0.707107
\(3\) 2.69378e19 1.27924 0.639620 0.768692i \(-0.279092\pi\)
0.639620 + 0.768692i \(0.279092\pi\)
\(4\) 1.20893e24 0.500000
\(5\) 1.65593e28 0.814247 0.407124 0.913373i \(-0.366532\pi\)
0.407124 + 0.913373i \(0.366532\pi\)
\(6\) −2.96185e31 −0.904559
\(7\) 2.15367e33 0.127852 0.0639261 0.997955i \(-0.479638\pi\)
0.0639261 + 0.997955i \(0.479638\pi\)
\(8\) −1.32923e36 −0.353553
\(9\) 2.82220e38 0.636453
\(10\) −1.82071e40 −0.575760
\(11\) −3.85124e40 −0.0256564 −0.0128282 0.999918i \(-0.504083\pi\)
−0.0128282 + 0.999918i \(0.504083\pi\)
\(12\) 3.25658e43 0.639620
\(13\) −8.46841e43 −0.0650273 −0.0325137 0.999471i \(-0.510351\pi\)
−0.0325137 + 0.999471i \(0.510351\pi\)
\(14\) −2.36798e45 −0.0904052
\(15\) 4.46071e47 1.04162
\(16\) 1.46150e48 0.250000
\(17\) −7.68035e49 −1.12772 −0.563858 0.825872i \(-0.690683\pi\)
−0.563858 + 0.825872i \(0.690683\pi\)
\(18\) −3.10304e50 −0.450041
\(19\) −7.37973e51 −1.19817 −0.599087 0.800684i \(-0.704469\pi\)
−0.599087 + 0.800684i \(0.704469\pi\)
\(20\) 2.00189e52 0.407124
\(21\) 5.80152e52 0.163554
\(22\) 4.23448e52 0.0181418
\(23\) −1.05342e55 −0.745800 −0.372900 0.927872i \(-0.621637\pi\)
−0.372900 + 0.927872i \(0.621637\pi\)
\(24\) −3.58065e55 −0.452279
\(25\) −1.39380e56 −0.337001
\(26\) 9.31111e55 0.0459813
\(27\) −4.34255e57 −0.465063
\(28\) 2.60363e57 0.0639261
\(29\) −1.79362e59 −1.06319 −0.531597 0.846998i \(-0.678408\pi\)
−0.531597 + 0.846998i \(0.678408\pi\)
\(30\) −4.90461e59 −0.736535
\(31\) −4.86617e60 −1.93659 −0.968297 0.249800i \(-0.919635\pi\)
−0.968297 + 0.249800i \(0.919635\pi\)
\(32\) −1.60694e60 −0.176777
\(33\) −1.03744e60 −0.0328207
\(34\) 8.44463e61 0.797416
\(35\) 3.56632e61 0.104103
\(36\) 3.41183e62 0.318227
\(37\) 2.30511e63 0.708796 0.354398 0.935095i \(-0.384686\pi\)
0.354398 + 0.935095i \(0.384686\pi\)
\(38\) 8.11410e63 0.847236
\(39\) −2.28121e63 −0.0831855
\(40\) −2.20111e64 −0.287880
\(41\) −1.35802e65 −0.653369 −0.326684 0.945133i \(-0.605931\pi\)
−0.326684 + 0.945133i \(0.605931\pi\)
\(42\) −6.37884e64 −0.115650
\(43\) 2.10516e66 1.47168 0.735838 0.677158i \(-0.236788\pi\)
0.735838 + 0.677158i \(0.236788\pi\)
\(44\) −4.65586e64 −0.0128282
\(45\) 4.67337e66 0.518231
\(46\) 1.15824e67 0.527360
\(47\) 1.03746e68 1.97700 0.988501 0.151212i \(-0.0483177\pi\)
0.988501 + 0.151212i \(0.0483177\pi\)
\(48\) 3.93697e67 0.319810
\(49\) −2.79115e68 −0.983654
\(50\) 1.53250e68 0.238296
\(51\) −2.06892e69 −1.44262
\(52\) −1.02377e68 −0.0325137
\(53\) 2.99301e69 0.439476 0.219738 0.975559i \(-0.429480\pi\)
0.219738 + 0.975559i \(0.429480\pi\)
\(54\) 4.77468e69 0.328849
\(55\) −6.37737e68 −0.0208907
\(56\) −2.86272e69 −0.0452026
\(57\) −1.98794e71 −1.53275
\(58\) 1.97211e71 0.751791
\(59\) −5.68737e71 −1.08494 −0.542469 0.840076i \(-0.682510\pi\)
−0.542469 + 0.840076i \(0.682510\pi\)
\(60\) 5.39267e71 0.520809
\(61\) 5.44662e71 0.269320 0.134660 0.990892i \(-0.457006\pi\)
0.134660 + 0.990892i \(0.457006\pi\)
\(62\) 5.35041e72 1.36938
\(63\) 6.07809e71 0.0813720
\(64\) 1.76685e72 0.125000
\(65\) −1.40231e72 −0.0529484
\(66\) 1.14068e72 0.0232078
\(67\) −5.75193e73 −0.636479 −0.318240 0.948010i \(-0.603092\pi\)
−0.318240 + 0.948010i \(0.603092\pi\)
\(68\) −9.28497e73 −0.563858
\(69\) −2.83767e74 −0.954057
\(70\) −3.92121e73 −0.0736122
\(71\) 4.64836e74 0.491289 0.245644 0.969360i \(-0.421000\pi\)
0.245644 + 0.969360i \(0.421000\pi\)
\(72\) −3.75135e74 −0.225020
\(73\) 4.70398e75 1.61395 0.806974 0.590587i \(-0.201104\pi\)
0.806974 + 0.590587i \(0.201104\pi\)
\(74\) −2.53449e75 −0.501195
\(75\) −3.75460e75 −0.431105
\(76\) −8.92155e75 −0.599087
\(77\) −8.29429e73 −0.00328023
\(78\) 2.50821e75 0.0588211
\(79\) −4.20695e76 −0.588939 −0.294469 0.955661i \(-0.595143\pi\)
−0.294469 + 0.955661i \(0.595143\pi\)
\(80\) 2.42014e76 0.203562
\(81\) −2.42123e77 −1.23138
\(82\) 1.49315e77 0.462002
\(83\) −7.46283e77 −1.41332 −0.706661 0.707552i \(-0.749799\pi\)
−0.706661 + 0.707552i \(0.749799\pi\)
\(84\) 7.01361e76 0.0817768
\(85\) −1.27181e78 −0.918240
\(86\) −2.31465e78 −1.04063
\(87\) −4.83163e78 −1.36008
\(88\) 5.11917e76 0.00907092
\(89\) 5.59868e78 0.627755 0.313878 0.949463i \(-0.398372\pi\)
0.313878 + 0.949463i \(0.398372\pi\)
\(90\) −5.13842e78 −0.366444
\(91\) −1.82382e77 −0.00831389
\(92\) −1.27350e79 −0.372900
\(93\) −1.31084e80 −2.47737
\(94\) −1.14070e80 −1.39795
\(95\) −1.22203e80 −0.975610
\(96\) −4.32874e79 −0.226140
\(97\) −1.28380e80 −0.440800 −0.220400 0.975410i \(-0.570736\pi\)
−0.220400 + 0.975410i \(0.570736\pi\)
\(98\) 3.06890e80 0.695548
\(99\) −1.08690e79 −0.0163291
\(100\) −1.68501e80 −0.168501
\(101\) −7.72319e79 −0.0516156 −0.0258078 0.999667i \(-0.508216\pi\)
−0.0258078 + 0.999667i \(0.508216\pi\)
\(102\) 2.27480e81 1.02009
\(103\) −3.15136e80 −0.0951897 −0.0475948 0.998867i \(-0.515156\pi\)
−0.0475948 + 0.998867i \(0.515156\pi\)
\(104\) 1.12564e80 0.0229906
\(105\) 9.60690e80 0.133173
\(106\) −3.29085e81 −0.310757
\(107\) 1.69471e82 1.09409 0.547045 0.837103i \(-0.315753\pi\)
0.547045 + 0.837103i \(0.315753\pi\)
\(108\) −5.24982e81 −0.232532
\(109\) 4.82859e82 1.47247 0.736236 0.676725i \(-0.236601\pi\)
0.736236 + 0.676725i \(0.236601\pi\)
\(110\) 7.01199e80 0.0147719
\(111\) 6.20946e82 0.906720
\(112\) 3.14759e81 0.0319631
\(113\) 7.06228e82 0.500343 0.250172 0.968202i \(-0.419513\pi\)
0.250172 + 0.968202i \(0.419513\pi\)
\(114\) 2.18576e83 1.08382
\(115\) −1.74438e83 −0.607266
\(116\) −2.16836e83 −0.531597
\(117\) −2.38996e82 −0.0413869
\(118\) 6.25333e83 0.767167
\(119\) −1.65409e83 −0.144181
\(120\) −5.92930e83 −0.368267
\(121\) −2.25176e84 −0.999342
\(122\) −5.98862e83 −0.190438
\(123\) −3.65820e84 −0.835815
\(124\) −5.88284e84 −0.968297
\(125\) −9.15680e84 −1.08865
\(126\) −6.68293e83 −0.0575387
\(127\) −1.77729e84 −0.111098 −0.0555491 0.998456i \(-0.517691\pi\)
−0.0555491 + 0.998456i \(0.517691\pi\)
\(128\) −1.94267e84 −0.0883883
\(129\) 5.67084e85 1.88263
\(130\) 1.54185e84 0.0374401
\(131\) −2.55142e85 −0.454250 −0.227125 0.973866i \(-0.572933\pi\)
−0.227125 + 0.973866i \(0.572933\pi\)
\(132\) −1.25419e84 −0.0164104
\(133\) −1.58935e85 −0.153189
\(134\) 6.32432e85 0.450059
\(135\) −7.19095e85 −0.378676
\(136\) 1.02089e86 0.398708
\(137\) −6.97596e85 −0.202498 −0.101249 0.994861i \(-0.532284\pi\)
−0.101249 + 0.994861i \(0.532284\pi\)
\(138\) 3.12005e86 0.674620
\(139\) 4.07982e86 0.658478 0.329239 0.944247i \(-0.393208\pi\)
0.329239 + 0.944247i \(0.393208\pi\)
\(140\) 4.31142e85 0.0520517
\(141\) 2.79469e87 2.52906
\(142\) −5.11093e86 −0.347394
\(143\) 3.26138e84 0.00166837
\(144\) 4.12465e86 0.159113
\(145\) −2.97011e87 −0.865703
\(146\) −5.17208e87 −1.14123
\(147\) −7.51876e87 −1.25833
\(148\) 2.78670e87 0.354398
\(149\) −4.93272e87 −0.477576 −0.238788 0.971072i \(-0.576750\pi\)
−0.238788 + 0.971072i \(0.576750\pi\)
\(150\) 4.12823e87 0.304837
\(151\) −1.01232e88 −0.571152 −0.285576 0.958356i \(-0.592185\pi\)
−0.285576 + 0.958356i \(0.592185\pi\)
\(152\) 9.80934e87 0.423618
\(153\) −2.16755e88 −0.717739
\(154\) 9.11967e85 0.00231948
\(155\) −8.05803e88 −1.57687
\(156\) −2.75781e87 −0.0415928
\(157\) 1.17061e89 1.36294 0.681471 0.731845i \(-0.261340\pi\)
0.681471 + 0.731845i \(0.261340\pi\)
\(158\) 4.62559e88 0.416442
\(159\) 8.06252e88 0.562195
\(160\) −2.66097e88 −0.143940
\(161\) −2.26871e88 −0.0953522
\(162\) 2.66217e89 0.870717
\(163\) 1.93542e89 0.493375 0.246687 0.969095i \(-0.420658\pi\)
0.246687 + 0.969095i \(0.420658\pi\)
\(164\) −1.64174e89 −0.326684
\(165\) −1.71793e88 −0.0267242
\(166\) 8.20547e89 0.999369
\(167\) 2.65462e89 0.253505 0.126752 0.991934i \(-0.459545\pi\)
0.126752 + 0.991934i \(0.459545\pi\)
\(168\) −7.71154e88 −0.0578250
\(169\) −1.68877e90 −0.995771
\(170\) 1.39837e90 0.649294
\(171\) −2.08271e90 −0.762581
\(172\) 2.54498e90 0.735838
\(173\) −4.22319e90 −0.965547 −0.482773 0.875745i \(-0.660371\pi\)
−0.482773 + 0.875745i \(0.660371\pi\)
\(174\) 5.31244e90 0.961721
\(175\) −3.00179e89 −0.0430863
\(176\) −5.62859e88 −0.00641411
\(177\) −1.53205e91 −1.38790
\(178\) −6.15581e90 −0.443890
\(179\) −2.47654e91 −1.42330 −0.711652 0.702532i \(-0.752053\pi\)
−0.711652 + 0.702532i \(0.752053\pi\)
\(180\) 5.64975e90 0.259115
\(181\) −2.31583e91 −0.848643 −0.424321 0.905512i \(-0.639487\pi\)
−0.424321 + 0.905512i \(0.639487\pi\)
\(182\) 2.00531e89 0.00587881
\(183\) 1.46720e91 0.344525
\(184\) 1.40023e91 0.263680
\(185\) 3.81709e91 0.577135
\(186\) 1.44128e92 1.75176
\(187\) 2.95788e90 0.0289332
\(188\) 1.25421e92 0.988501
\(189\) −9.35241e90 −0.0594594
\(190\) 1.34364e92 0.689860
\(191\) −1.10964e92 −0.460607 −0.230304 0.973119i \(-0.573972\pi\)
−0.230304 + 0.973119i \(0.573972\pi\)
\(192\) 4.75950e91 0.159905
\(193\) −5.11836e92 −1.39335 −0.696675 0.717387i \(-0.745338\pi\)
−0.696675 + 0.717387i \(0.745338\pi\)
\(194\) 1.41155e92 0.311692
\(195\) −3.77751e91 −0.0677336
\(196\) −3.37430e92 −0.491827
\(197\) 1.19905e93 1.42218 0.711092 0.703099i \(-0.248201\pi\)
0.711092 + 0.703099i \(0.248201\pi\)
\(198\) 1.19506e91 0.0115464
\(199\) −8.67630e92 −0.683573 −0.341786 0.939778i \(-0.611032\pi\)
−0.341786 + 0.939778i \(0.611032\pi\)
\(200\) 1.85268e92 0.119148
\(201\) −1.54945e93 −0.814209
\(202\) 8.49173e91 0.0364977
\(203\) −3.86287e92 −0.135932
\(204\) −2.50117e93 −0.721309
\(205\) −2.24878e93 −0.532004
\(206\) 3.46495e92 0.0673093
\(207\) −2.97295e93 −0.474667
\(208\) −1.23766e92 −0.0162568
\(209\) 2.84211e92 0.0307409
\(210\) −1.05629e93 −0.0941676
\(211\) 1.56322e94 1.14969 0.574845 0.818262i \(-0.305062\pi\)
0.574845 + 0.818262i \(0.305062\pi\)
\(212\) 3.61833e93 0.219738
\(213\) 1.25217e94 0.628476
\(214\) −1.86336e94 −0.773639
\(215\) 3.48599e94 1.19831
\(216\) 5.77223e93 0.164425
\(217\) −1.04801e94 −0.247598
\(218\) −5.30909e94 −1.04119
\(219\) 1.26715e95 2.06463
\(220\) −7.70977e92 −0.0104453
\(221\) 6.50403e93 0.0733324
\(222\) −6.82737e94 −0.641148
\(223\) 1.51413e95 1.18527 0.592633 0.805472i \(-0.298088\pi\)
0.592633 + 0.805472i \(0.298088\pi\)
\(224\) −3.46081e93 −0.0226013
\(225\) −3.93360e94 −0.214485
\(226\) −7.76506e94 −0.353796
\(227\) −3.54890e95 −1.35222 −0.676109 0.736801i \(-0.736335\pi\)
−0.676109 + 0.736801i \(0.736335\pi\)
\(228\) −2.40327e95 −0.766375
\(229\) −7.16704e95 −1.91427 −0.957133 0.289647i \(-0.906462\pi\)
−0.957133 + 0.289647i \(0.906462\pi\)
\(230\) 1.91797e95 0.429402
\(231\) −2.23430e93 −0.00419620
\(232\) 2.38413e95 0.375896
\(233\) −1.74206e94 −0.0230754 −0.0115377 0.999933i \(-0.503673\pi\)
−0.0115377 + 0.999933i \(0.503673\pi\)
\(234\) 2.62779e94 0.0292649
\(235\) 1.71796e96 1.60977
\(236\) −6.87561e95 −0.542469
\(237\) −1.13326e96 −0.753393
\(238\) 1.81870e95 0.101951
\(239\) 2.85641e96 1.35116 0.675579 0.737288i \(-0.263894\pi\)
0.675579 + 0.737288i \(0.263894\pi\)
\(240\) 6.51934e95 0.260404
\(241\) 1.64482e96 0.555174 0.277587 0.960700i \(-0.410465\pi\)
0.277587 + 0.960700i \(0.410465\pi\)
\(242\) 2.47583e96 0.706641
\(243\) −4.59666e96 −1.11017
\(244\) 6.58456e95 0.134660
\(245\) −4.62195e96 −0.800938
\(246\) 4.02223e96 0.591011
\(247\) 6.24946e95 0.0779140
\(248\) 6.46825e96 0.684690
\(249\) −2.01033e97 −1.80798
\(250\) 1.00680e97 0.769792
\(251\) 2.49036e97 1.61986 0.809928 0.586530i \(-0.199506\pi\)
0.809928 + 0.586530i \(0.199506\pi\)
\(252\) 7.34796e95 0.0406860
\(253\) 4.05695e95 0.0191346
\(254\) 1.95415e96 0.0785583
\(255\) −3.42598e97 −1.17465
\(256\) 2.13599e96 0.0625000
\(257\) −6.39309e97 −1.59742 −0.798710 0.601716i \(-0.794484\pi\)
−0.798710 + 0.601716i \(0.794484\pi\)
\(258\) −6.23515e97 −1.33122
\(259\) 4.96444e96 0.0906212
\(260\) −1.69529e96 −0.0264742
\(261\) −5.06197e97 −0.676673
\(262\) 2.80532e97 0.321203
\(263\) 1.31373e98 1.28914 0.644569 0.764546i \(-0.277037\pi\)
0.644569 + 0.764546i \(0.277037\pi\)
\(264\) 1.37899e96 0.0116039
\(265\) 4.95621e97 0.357842
\(266\) 1.74751e97 0.108321
\(267\) 1.50816e98 0.803049
\(268\) −6.95366e97 −0.318240
\(269\) 1.34185e98 0.528126 0.264063 0.964505i \(-0.414937\pi\)
0.264063 + 0.964505i \(0.414937\pi\)
\(270\) 7.90653e97 0.267765
\(271\) 2.31481e98 0.674930 0.337465 0.941338i \(-0.390431\pi\)
0.337465 + 0.941338i \(0.390431\pi\)
\(272\) −1.12248e98 −0.281929
\(273\) −4.91296e96 −0.0106355
\(274\) 7.67015e97 0.143188
\(275\) 5.36787e96 0.00864624
\(276\) −3.43054e98 −0.477028
\(277\) 1.19697e99 1.43765 0.718827 0.695189i \(-0.244680\pi\)
0.718827 + 0.695189i \(0.244680\pi\)
\(278\) −4.48581e98 −0.465615
\(279\) −1.37333e99 −1.23255
\(280\) −4.74046e97 −0.0368061
\(281\) 2.35229e99 1.58083 0.790415 0.612571i \(-0.209865\pi\)
0.790415 + 0.612571i \(0.209865\pi\)
\(282\) −3.07279e99 −1.78832
\(283\) −1.76801e99 −0.891524 −0.445762 0.895152i \(-0.647067\pi\)
−0.445762 + 0.895152i \(0.647067\pi\)
\(284\) 5.61952e98 0.245644
\(285\) −3.29189e99 −1.24804
\(286\) −3.58593e96 −0.00117972
\(287\) −2.92472e98 −0.0835347
\(288\) −4.53511e98 −0.112510
\(289\) 1.26044e99 0.271743
\(290\) 3.26567e99 0.612144
\(291\) −3.45827e99 −0.563888
\(292\) 5.68676e99 0.806974
\(293\) 7.41514e99 0.916180 0.458090 0.888906i \(-0.348534\pi\)
0.458090 + 0.888906i \(0.348534\pi\)
\(294\) 8.26696e99 0.889773
\(295\) −9.41788e99 −0.883408
\(296\) −3.06401e99 −0.250597
\(297\) 1.67242e98 0.0119319
\(298\) 5.42358e99 0.337697
\(299\) 8.92075e98 0.0484974
\(300\) −4.53904e99 −0.215552
\(301\) 4.53381e99 0.188157
\(302\) 1.11306e100 0.403866
\(303\) −2.08046e99 −0.0660287
\(304\) −1.07855e100 −0.299543
\(305\) 9.01921e99 0.219293
\(306\) 2.38325e100 0.507518
\(307\) 3.35912e100 0.626789 0.313395 0.949623i \(-0.398534\pi\)
0.313395 + 0.949623i \(0.398534\pi\)
\(308\) −1.00272e98 −0.00164012
\(309\) −8.48907e99 −0.121770
\(310\) 8.85990e100 1.11501
\(311\) −1.52457e101 −1.68404 −0.842019 0.539448i \(-0.818633\pi\)
−0.842019 + 0.539448i \(0.818633\pi\)
\(312\) 3.03224e99 0.0294105
\(313\) −1.80423e101 −1.53726 −0.768628 0.639696i \(-0.779060\pi\)
−0.768628 + 0.639696i \(0.779060\pi\)
\(314\) −1.28710e101 −0.963746
\(315\) 1.00649e100 0.0662570
\(316\) −5.08589e100 −0.294469
\(317\) −9.83506e100 −0.501045 −0.250523 0.968111i \(-0.580602\pi\)
−0.250523 + 0.968111i \(0.580602\pi\)
\(318\) −8.86483e100 −0.397532
\(319\) 6.90767e99 0.0272778
\(320\) 2.92577e100 0.101781
\(321\) 4.56519e101 1.39960
\(322\) 2.49447e100 0.0674242
\(323\) 5.66789e101 1.35120
\(324\) −2.92708e101 −0.615690
\(325\) 1.18033e100 0.0219143
\(326\) −2.12802e101 −0.348869
\(327\) 1.30072e102 1.88364
\(328\) 1.80511e101 0.231001
\(329\) 2.23434e101 0.252764
\(330\) 1.88888e100 0.0188969
\(331\) −7.65599e99 −0.00677591 −0.00338795 0.999994i \(-0.501078\pi\)
−0.00338795 + 0.999994i \(0.501078\pi\)
\(332\) −9.02201e101 −0.706661
\(333\) 6.50548e101 0.451116
\(334\) −2.91879e101 −0.179255
\(335\) −9.52479e101 −0.518252
\(336\) 8.47893e100 0.0408884
\(337\) −4.29366e102 −1.83576 −0.917881 0.396856i \(-0.870101\pi\)
−0.917881 + 0.396856i \(0.870101\pi\)
\(338\) 1.85683e102 0.704117
\(339\) 1.90242e102 0.640059
\(340\) −1.53753e102 −0.459120
\(341\) 1.87408e101 0.0496861
\(342\) 2.28996e102 0.539226
\(343\) −1.21223e102 −0.253615
\(344\) −2.79823e102 −0.520316
\(345\) −4.69898e102 −0.776838
\(346\) 4.64344e102 0.682745
\(347\) 1.89134e101 0.0247415 0.0123708 0.999923i \(-0.496062\pi\)
0.0123708 + 0.999923i \(0.496062\pi\)
\(348\) −5.84109e102 −0.680040
\(349\) −1.37592e103 −1.42614 −0.713070 0.701093i \(-0.752696\pi\)
−0.713070 + 0.701093i \(0.752696\pi\)
\(350\) 3.30051e101 0.0304666
\(351\) 3.67745e101 0.0302418
\(352\) 6.18870e100 0.00453546
\(353\) 2.78332e103 1.81839 0.909195 0.416371i \(-0.136698\pi\)
0.909195 + 0.416371i \(0.136698\pi\)
\(354\) 1.68451e103 0.981390
\(355\) 7.69735e102 0.400031
\(356\) 6.76839e102 0.313878
\(357\) −4.45577e102 −0.184442
\(358\) 2.72298e103 1.00643
\(359\) −5.09879e103 −1.68322 −0.841612 0.540082i \(-0.818393\pi\)
−0.841612 + 0.540082i \(0.818393\pi\)
\(360\) −6.21197e102 −0.183222
\(361\) 1.65253e103 0.435619
\(362\) 2.54629e103 0.600081
\(363\) −6.06575e103 −1.27840
\(364\) −2.20486e101 −0.00415695
\(365\) 7.78946e103 1.31415
\(366\) −1.61320e103 −0.243616
\(367\) 7.65169e103 1.03462 0.517311 0.855798i \(-0.326933\pi\)
0.517311 + 0.855798i \(0.326933\pi\)
\(368\) −1.53957e103 −0.186450
\(369\) −3.83260e103 −0.415839
\(370\) −4.19694e103 −0.408096
\(371\) 6.44595e102 0.0561880
\(372\) −1.58471e104 −1.23868
\(373\) 1.10313e104 0.773430 0.386715 0.922199i \(-0.373610\pi\)
0.386715 + 0.922199i \(0.373610\pi\)
\(374\) −3.25223e102 −0.0204588
\(375\) −2.46664e104 −1.39264
\(376\) −1.37902e104 −0.698976
\(377\) 1.51891e103 0.0691367
\(378\) 1.02831e103 0.0420441
\(379\) −2.28475e104 −0.839365 −0.419682 0.907671i \(-0.637859\pi\)
−0.419682 + 0.907671i \(0.637859\pi\)
\(380\) −1.47734e104 −0.487805
\(381\) −4.78763e103 −0.142121
\(382\) 1.22006e104 0.325699
\(383\) 7.62871e104 1.83189 0.915947 0.401298i \(-0.131441\pi\)
0.915947 + 0.401298i \(0.131441\pi\)
\(384\) −5.23313e103 −0.113070
\(385\) −1.37347e102 −0.00267092
\(386\) 5.62770e104 0.985247
\(387\) 5.94118e104 0.936653
\(388\) −1.55202e104 −0.220400
\(389\) 6.74768e104 0.863368 0.431684 0.902025i \(-0.357920\pi\)
0.431684 + 0.902025i \(0.357920\pi\)
\(390\) 4.15342e103 0.0478949
\(391\) 8.09060e104 0.841051
\(392\) 3.71008e104 0.347774
\(393\) −6.87298e104 −0.581094
\(394\) −1.31837e105 −1.00564
\(395\) −6.96641e104 −0.479542
\(396\) −1.31398e103 −0.00816456
\(397\) −2.50030e105 −1.40274 −0.701368 0.712799i \(-0.747427\pi\)
−0.701368 + 0.712799i \(0.747427\pi\)
\(398\) 9.53969e104 0.483359
\(399\) −4.28136e104 −0.195966
\(400\) −2.03705e104 −0.0842503
\(401\) 7.15970e103 0.0267638 0.0133819 0.999910i \(-0.495740\pi\)
0.0133819 + 0.999910i \(0.495740\pi\)
\(402\) 1.70363e105 0.575733
\(403\) 4.12087e104 0.125932
\(404\) −9.33676e103 −0.0258078
\(405\) −4.00938e105 −1.00265
\(406\) 4.24727e104 0.0961182
\(407\) −8.87751e103 −0.0181852
\(408\) 2.75007e105 0.510043
\(409\) −5.18525e105 −0.870914 −0.435457 0.900209i \(-0.643413\pi\)
−0.435457 + 0.900209i \(0.643413\pi\)
\(410\) 2.47256e105 0.376184
\(411\) −1.87917e105 −0.259044
\(412\) −3.80976e104 −0.0475948
\(413\) −1.22487e105 −0.138712
\(414\) 3.26880e105 0.335640
\(415\) −1.23579e106 −1.15079
\(416\) 1.36082e104 0.0114953
\(417\) 1.09901e106 0.842351
\(418\) −3.12493e104 −0.0217371
\(419\) 1.13062e106 0.713919 0.356960 0.934120i \(-0.383813\pi\)
0.356960 + 0.934120i \(0.383813\pi\)
\(420\) 1.16140e105 0.0665866
\(421\) 2.52430e106 1.31437 0.657183 0.753731i \(-0.271748\pi\)
0.657183 + 0.753731i \(0.271748\pi\)
\(422\) −1.71878e106 −0.812953
\(423\) 2.92792e106 1.25827
\(424\) −3.97839e105 −0.155378
\(425\) 1.07049e106 0.380041
\(426\) −1.37677e106 −0.444400
\(427\) 1.17302e105 0.0344332
\(428\) 2.04878e106 0.547045
\(429\) 8.78546e103 0.00213424
\(430\) −3.83289e106 −0.847332
\(431\) 2.23744e105 0.0450217 0.0225108 0.999747i \(-0.492834\pi\)
0.0225108 + 0.999747i \(0.492834\pi\)
\(432\) −6.34664e105 −0.116266
\(433\) −4.63717e106 −0.773559 −0.386780 0.922172i \(-0.626413\pi\)
−0.386780 + 0.922172i \(0.626413\pi\)
\(434\) 1.15230e106 0.175078
\(435\) −8.00084e106 −1.10744
\(436\) 5.83740e106 0.736236
\(437\) 7.77392e106 0.893598
\(438\) −1.39325e107 −1.45991
\(439\) −8.66735e106 −0.828082 −0.414041 0.910258i \(-0.635883\pi\)
−0.414041 + 0.910258i \(0.635883\pi\)
\(440\) 8.47698e104 0.00738597
\(441\) −7.87720e106 −0.626050
\(442\) −7.15126e105 −0.0518538
\(443\) 9.95720e106 0.658850 0.329425 0.944182i \(-0.393145\pi\)
0.329425 + 0.944182i \(0.393145\pi\)
\(444\) 7.50678e106 0.453360
\(445\) 9.27101e106 0.511148
\(446\) −1.66480e107 −0.838110
\(447\) −1.32877e107 −0.610934
\(448\) 3.80520e105 0.0159815
\(449\) 3.96267e107 1.52059 0.760294 0.649579i \(-0.225055\pi\)
0.760294 + 0.649579i \(0.225055\pi\)
\(450\) 4.32504e106 0.151664
\(451\) 5.23004e105 0.0167631
\(452\) 8.53777e106 0.250172
\(453\) −2.72697e107 −0.730641
\(454\) 3.90206e107 0.956163
\(455\) −3.02011e105 −0.00676957
\(456\) 2.64242e107 0.541909
\(457\) 4.31708e107 0.810184 0.405092 0.914276i \(-0.367240\pi\)
0.405092 + 0.914276i \(0.367240\pi\)
\(458\) 7.88024e107 1.35359
\(459\) 3.33523e107 0.524459
\(460\) −2.10883e107 −0.303633
\(461\) −8.16084e107 −1.07609 −0.538043 0.842917i \(-0.680836\pi\)
−0.538043 + 0.842917i \(0.680836\pi\)
\(462\) 2.45664e105 0.00296716
\(463\) −6.62658e107 −0.733262 −0.366631 0.930366i \(-0.619489\pi\)
−0.366631 + 0.930366i \(0.619489\pi\)
\(464\) −2.62138e107 −0.265798
\(465\) −2.17066e108 −2.01719
\(466\) 1.91542e106 0.0163167
\(467\) −8.07914e107 −0.631003 −0.315502 0.948925i \(-0.602173\pi\)
−0.315502 + 0.948925i \(0.602173\pi\)
\(468\) −2.88928e106 −0.0206934
\(469\) −1.23878e107 −0.0813753
\(470\) −1.88891e108 −1.13828
\(471\) 3.15338e108 1.74353
\(472\) 7.55981e107 0.383584
\(473\) −8.10746e106 −0.0377580
\(474\) 1.24603e108 0.532730
\(475\) 1.02859e108 0.403786
\(476\) −1.99968e107 −0.0720905
\(477\) 8.44688e107 0.279706
\(478\) −3.14066e108 −0.955413
\(479\) 4.07310e107 0.113851 0.0569254 0.998378i \(-0.481870\pi\)
0.0569254 + 0.998378i \(0.481870\pi\)
\(480\) −7.16809e107 −0.184134
\(481\) −1.95206e107 −0.0460911
\(482\) −1.80850e108 −0.392568
\(483\) −6.11141e107 −0.121978
\(484\) −2.72221e108 −0.499671
\(485\) −2.12588e108 −0.358920
\(486\) 5.05408e108 0.785007
\(487\) 8.18293e108 1.16946 0.584731 0.811227i \(-0.301200\pi\)
0.584731 + 0.811227i \(0.301200\pi\)
\(488\) −7.23980e107 −0.0952190
\(489\) 5.21360e108 0.631145
\(490\) 5.08189e108 0.566348
\(491\) −4.58698e107 −0.0470681 −0.0235341 0.999723i \(-0.507492\pi\)
−0.0235341 + 0.999723i \(0.507492\pi\)
\(492\) −4.42249e108 −0.417908
\(493\) 1.37757e109 1.19898
\(494\) −6.87135e107 −0.0550935
\(495\) −1.79982e107 −0.0132959
\(496\) −7.11192e108 −0.484149
\(497\) 1.00110e108 0.0628124
\(498\) 2.21038e109 1.27843
\(499\) −1.29605e109 −0.691116 −0.345558 0.938397i \(-0.612310\pi\)
−0.345558 + 0.938397i \(0.612310\pi\)
\(500\) −1.10699e109 −0.544325
\(501\) 7.15098e108 0.324293
\(502\) −2.73818e109 −1.14541
\(503\) −3.21057e109 −1.23902 −0.619511 0.784988i \(-0.712669\pi\)
−0.619511 + 0.784988i \(0.712669\pi\)
\(504\) −8.07917e107 −0.0287694
\(505\) −1.27890e108 −0.0420279
\(506\) −4.46067e107 −0.0135302
\(507\) −4.54919e109 −1.27383
\(508\) −2.14861e108 −0.0555491
\(509\) −4.21642e109 −1.00664 −0.503319 0.864100i \(-0.667888\pi\)
−0.503319 + 0.864100i \(0.667888\pi\)
\(510\) 3.76691e109 0.830602
\(511\) 1.01308e109 0.206347
\(512\) −2.34854e108 −0.0441942
\(513\) 3.20468e109 0.557226
\(514\) 7.02927e109 1.12955
\(515\) −5.21842e108 −0.0775079
\(516\) 6.85562e109 0.941313
\(517\) −3.99549e108 −0.0507228
\(518\) −5.45846e108 −0.0640789
\(519\) −1.13764e110 −1.23517
\(520\) 1.86399e108 0.0187201
\(521\) 6.70105e109 0.622609 0.311304 0.950310i \(-0.399234\pi\)
0.311304 + 0.950310i \(0.399234\pi\)
\(522\) 5.56569e109 0.478480
\(523\) 1.39503e110 1.10986 0.554928 0.831898i \(-0.312746\pi\)
0.554928 + 0.831898i \(0.312746\pi\)
\(524\) −3.08448e109 −0.227125
\(525\) −8.08618e108 −0.0551178
\(526\) −1.44447e110 −0.911559
\(527\) 3.73739e110 2.18393
\(528\) −1.51622e108 −0.00820518
\(529\) −8.85370e109 −0.443782
\(530\) −5.44941e109 −0.253033
\(531\) −1.60509e110 −0.690513
\(532\) −1.92141e109 −0.0765946
\(533\) 1.15002e109 0.0424869
\(534\) −1.65824e110 −0.567842
\(535\) 2.80632e110 0.890860
\(536\) 7.64563e109 0.225029
\(537\) −6.67126e110 −1.82075
\(538\) −1.47538e110 −0.373441
\(539\) 1.07494e109 0.0252370
\(540\) −8.69332e109 −0.189338
\(541\) 7.78185e109 0.157251 0.0786256 0.996904i \(-0.474947\pi\)
0.0786256 + 0.996904i \(0.474947\pi\)
\(542\) −2.54516e110 −0.477247
\(543\) −6.23835e110 −1.08562
\(544\) 1.23418e110 0.199354
\(545\) 7.99580e110 1.19896
\(546\) 5.40186e108 0.00752041
\(547\) −2.81651e110 −0.364103 −0.182051 0.983289i \(-0.558274\pi\)
−0.182051 + 0.983289i \(0.558274\pi\)
\(548\) −8.43342e109 −0.101249
\(549\) 1.53715e110 0.171410
\(550\) −5.90203e108 −0.00611382
\(551\) 1.32365e111 1.27389
\(552\) 3.77191e110 0.337310
\(553\) −9.06038e109 −0.0752971
\(554\) −1.31609e111 −1.01657
\(555\) 1.02824e111 0.738294
\(556\) 4.93220e110 0.329239
\(557\) −3.50511e110 −0.217554 −0.108777 0.994066i \(-0.534693\pi\)
−0.108777 + 0.994066i \(0.534693\pi\)
\(558\) 1.50999e111 0.871546
\(559\) −1.78273e110 −0.0956992
\(560\) 5.21219e109 0.0260258
\(561\) 7.96790e109 0.0370124
\(562\) −2.58637e111 −1.11782
\(563\) −2.55312e111 −1.02679 −0.513395 0.858152i \(-0.671612\pi\)
−0.513395 + 0.858152i \(0.671612\pi\)
\(564\) 3.37857e111 1.26453
\(565\) 1.16946e111 0.407403
\(566\) 1.94394e111 0.630403
\(567\) −5.21452e110 −0.157435
\(568\) −6.17873e110 −0.173697
\(569\) 2.41238e111 0.631538 0.315769 0.948836i \(-0.397738\pi\)
0.315769 + 0.948836i \(0.397738\pi\)
\(570\) 3.61947e111 0.882496
\(571\) −4.06873e111 −0.924052 −0.462026 0.886866i \(-0.652877\pi\)
−0.462026 + 0.886866i \(0.652877\pi\)
\(572\) 3.94277e108 0.000834185 0
\(573\) −2.98913e111 −0.589227
\(574\) 3.21576e110 0.0590680
\(575\) 1.46825e111 0.251335
\(576\) 4.98640e110 0.0795567
\(577\) −6.19248e111 −0.920967 −0.460484 0.887668i \(-0.652324\pi\)
−0.460484 + 0.887668i \(0.652324\pi\)
\(578\) −1.38586e111 −0.192151
\(579\) −1.37878e112 −1.78243
\(580\) −3.59065e111 −0.432851
\(581\) −1.60725e111 −0.180696
\(582\) 3.80241e111 0.398729
\(583\) −1.15268e110 −0.0112754
\(584\) −6.25266e111 −0.570617
\(585\) −3.95760e110 −0.0336992
\(586\) −8.15303e111 −0.647837
\(587\) −9.44491e110 −0.0700414 −0.0350207 0.999387i \(-0.511150\pi\)
−0.0350207 + 0.999387i \(0.511150\pi\)
\(588\) −9.08962e111 −0.629164
\(589\) 3.59110e112 2.32038
\(590\) 1.03551e112 0.624664
\(591\) 3.22999e112 1.81931
\(592\) 3.36892e111 0.177199
\(593\) 3.51703e112 1.72767 0.863836 0.503773i \(-0.168055\pi\)
0.863836 + 0.503773i \(0.168055\pi\)
\(594\) −1.83884e110 −0.00843710
\(595\) −2.73906e111 −0.117399
\(596\) −5.96329e111 −0.238788
\(597\) −2.33721e112 −0.874453
\(598\) −9.80847e110 −0.0342928
\(599\) −8.52279e111 −0.278481 −0.139240 0.990259i \(-0.544466\pi\)
−0.139240 + 0.990259i \(0.544466\pi\)
\(600\) 4.99073e111 0.152419
\(601\) −1.13950e112 −0.325312 −0.162656 0.986683i \(-0.552006\pi\)
−0.162656 + 0.986683i \(0.552006\pi\)
\(602\) −4.98498e111 −0.133047
\(603\) −1.62331e112 −0.405089
\(604\) −1.22382e112 −0.285576
\(605\) −3.72875e112 −0.813712
\(606\) 2.28749e111 0.0466893
\(607\) 5.48765e112 1.04772 0.523859 0.851805i \(-0.324492\pi\)
0.523859 + 0.851805i \(0.324492\pi\)
\(608\) 1.18588e112 0.211809
\(609\) −1.04057e112 −0.173889
\(610\) −9.91673e111 −0.155064
\(611\) −8.78562e111 −0.128559
\(612\) −2.62041e112 −0.358869
\(613\) 3.54802e112 0.454817 0.227408 0.973799i \(-0.426975\pi\)
0.227408 + 0.973799i \(0.426975\pi\)
\(614\) −3.69339e112 −0.443207
\(615\) −6.05772e112 −0.680561
\(616\) 1.10250e110 0.00115974
\(617\) −9.42261e112 −0.928159 −0.464079 0.885794i \(-0.653615\pi\)
−0.464079 + 0.885794i \(0.653615\pi\)
\(618\) 9.33383e111 0.0861047
\(619\) 3.52629e111 0.0304682 0.0152341 0.999884i \(-0.495151\pi\)
0.0152341 + 0.999884i \(0.495151\pi\)
\(620\) −9.74156e112 −0.788434
\(621\) 4.57451e112 0.346844
\(622\) 1.67628e113 1.19079
\(623\) 1.20577e112 0.0802599
\(624\) −3.33399e111 −0.0207964
\(625\) −9.39837e112 −0.549429
\(626\) 1.98377e113 1.08700
\(627\) 7.65602e111 0.0393249
\(628\) 1.41519e113 0.681471
\(629\) −1.77040e113 −0.799321
\(630\) −1.10665e112 −0.0468507
\(631\) −1.55289e113 −0.616527 −0.308263 0.951301i \(-0.599748\pi\)
−0.308263 + 0.951301i \(0.599748\pi\)
\(632\) 5.59199e112 0.208221
\(633\) 4.21098e113 1.47073
\(634\) 1.08138e113 0.354293
\(635\) −2.94306e112 −0.0904615
\(636\) 9.74699e112 0.281098
\(637\) 2.36366e112 0.0639644
\(638\) −7.59506e111 −0.0192883
\(639\) 1.31186e113 0.312682
\(640\) −3.21692e112 −0.0719700
\(641\) 4.55438e113 0.956487 0.478244 0.878227i \(-0.341274\pi\)
0.478244 + 0.878227i \(0.341274\pi\)
\(642\) −5.01948e113 −0.989669
\(643\) −8.10226e113 −1.49990 −0.749949 0.661496i \(-0.769922\pi\)
−0.749949 + 0.661496i \(0.769922\pi\)
\(644\) −2.74270e112 −0.0476761
\(645\) 9.39050e113 1.53292
\(646\) −6.23191e113 −0.955442
\(647\) −7.61202e113 −1.09617 −0.548083 0.836424i \(-0.684642\pi\)
−0.548083 + 0.836424i \(0.684642\pi\)
\(648\) 3.21836e113 0.435359
\(649\) 2.19034e112 0.0278356
\(650\) −1.29779e112 −0.0154957
\(651\) −2.82312e113 −0.316737
\(652\) 2.33978e113 0.246687
\(653\) 9.46822e113 0.938176 0.469088 0.883151i \(-0.344583\pi\)
0.469088 + 0.883151i \(0.344583\pi\)
\(654\) −1.43015e114 −1.33194
\(655\) −4.22497e113 −0.369872
\(656\) −1.98474e113 −0.163342
\(657\) 1.32756e114 1.02720
\(658\) −2.45668e113 −0.178731
\(659\) −1.13280e114 −0.774986 −0.387493 0.921873i \(-0.626659\pi\)
−0.387493 + 0.921873i \(0.626659\pi\)
\(660\) −2.07684e112 −0.0133621
\(661\) −2.33352e114 −1.41206 −0.706029 0.708183i \(-0.749515\pi\)
−0.706029 + 0.708183i \(0.749515\pi\)
\(662\) 8.41785e111 0.00479129
\(663\) 1.75205e113 0.0938097
\(664\) 9.91981e113 0.499685
\(665\) −2.63185e113 −0.124734
\(666\) −7.15285e113 −0.318987
\(667\) 1.88943e114 0.792930
\(668\) 3.20924e113 0.126752
\(669\) 4.07874e114 1.51624
\(670\) 1.04726e114 0.366459
\(671\) −2.09762e112 −0.00690979
\(672\) −9.32268e112 −0.0289125
\(673\) 3.04730e114 0.889827 0.444914 0.895573i \(-0.353234\pi\)
0.444914 + 0.895573i \(0.353234\pi\)
\(674\) 4.72092e114 1.29808
\(675\) 6.05266e113 0.156727
\(676\) −2.04160e114 −0.497886
\(677\) 1.93415e114 0.444272 0.222136 0.975016i \(-0.428697\pi\)
0.222136 + 0.975016i \(0.428697\pi\)
\(678\) −2.09174e114 −0.452590
\(679\) −2.76488e113 −0.0563572
\(680\) 1.69053e114 0.324647
\(681\) −9.55998e114 −1.72981
\(682\) −2.06057e113 −0.0351334
\(683\) 3.94780e114 0.634331 0.317166 0.948370i \(-0.397269\pi\)
0.317166 + 0.948370i \(0.397269\pi\)
\(684\) −2.51784e114 −0.381291
\(685\) −1.15517e114 −0.164884
\(686\) 1.33286e114 0.179333
\(687\) −1.93064e115 −2.44881
\(688\) 3.07669e114 0.367919
\(689\) −2.53460e113 −0.0285780
\(690\) 5.16659e114 0.549308
\(691\) −1.75270e115 −1.75730 −0.878649 0.477468i \(-0.841555\pi\)
−0.878649 + 0.477468i \(0.841555\pi\)
\(692\) −5.10552e114 −0.482773
\(693\) −2.34082e112 −0.00208772
\(694\) −2.07955e113 −0.0174949
\(695\) 6.75589e114 0.536164
\(696\) 6.42234e114 0.480861
\(697\) 1.04300e115 0.736815
\(698\) 1.51284e115 1.00843
\(699\) −4.69273e113 −0.0295189
\(700\) −3.62894e113 −0.0215432
\(701\) 6.82707e114 0.382521 0.191260 0.981539i \(-0.438743\pi\)
0.191260 + 0.981539i \(0.438743\pi\)
\(702\) −4.04339e113 −0.0213842
\(703\) −1.70111e115 −0.849261
\(704\) −6.80454e112 −0.00320705
\(705\) 4.62780e115 2.05928
\(706\) −3.06029e115 −1.28580
\(707\) −1.66332e113 −0.00659917
\(708\) −1.85214e115 −0.693948
\(709\) 2.03694e114 0.0720783 0.0360392 0.999350i \(-0.488526\pi\)
0.0360392 + 0.999350i \(0.488526\pi\)
\(710\) −8.46333e114 −0.282864
\(711\) −1.18729e115 −0.374832
\(712\) −7.44192e114 −0.221945
\(713\) 5.12610e115 1.44431
\(714\) 4.89917e114 0.130420
\(715\) 5.40062e112 0.00135847
\(716\) −2.99395e115 −0.711652
\(717\) 7.69456e115 1.72845
\(718\) 5.60618e115 1.19022
\(719\) −5.76168e115 −1.15619 −0.578095 0.815969i \(-0.696204\pi\)
−0.578095 + 0.815969i \(0.696204\pi\)
\(720\) 6.83013e114 0.129558
\(721\) −6.78698e113 −0.0121702
\(722\) −1.81697e115 −0.308029
\(723\) 4.43080e115 0.710201
\(724\) −2.79967e115 −0.424321
\(725\) 2.49996e115 0.358297
\(726\) 6.66936e115 0.903963
\(727\) −1.53192e116 −1.96378 −0.981889 0.189456i \(-0.939328\pi\)
−0.981889 + 0.189456i \(0.939328\pi\)
\(728\) 2.42427e113 0.00293941
\(729\) −1.64605e115 −0.188789
\(730\) −8.56460e115 −0.929247
\(731\) −1.61683e116 −1.65963
\(732\) 1.77374e115 0.172262
\(733\) 1.27965e116 1.17592 0.587961 0.808889i \(-0.299931\pi\)
0.587961 + 0.808889i \(0.299931\pi\)
\(734\) −8.41312e115 −0.731588
\(735\) −1.24505e116 −1.02459
\(736\) 1.69277e115 0.131840
\(737\) 2.21520e114 0.0163298
\(738\) 4.21398e115 0.294042
\(739\) 3.22829e115 0.213242 0.106621 0.994300i \(-0.465997\pi\)
0.106621 + 0.994300i \(0.465997\pi\)
\(740\) 4.61458e115 0.288568
\(741\) 1.68347e115 0.0996707
\(742\) −7.08740e114 −0.0397309
\(743\) 2.55795e116 1.35783 0.678913 0.734219i \(-0.262451\pi\)
0.678913 + 0.734219i \(0.262451\pi\)
\(744\) 1.74241e116 0.875882
\(745\) −8.16823e115 −0.388865
\(746\) −1.21291e116 −0.546897
\(747\) −2.10616e116 −0.899513
\(748\) 3.57586e114 0.0144666
\(749\) 3.64985e115 0.139882
\(750\) 2.71210e116 0.984748
\(751\) −3.19459e116 −1.09900 −0.549499 0.835494i \(-0.685182\pi\)
−0.549499 + 0.835494i \(0.685182\pi\)
\(752\) 1.51625e116 0.494251
\(753\) 6.70849e116 2.07218
\(754\) −1.67006e115 −0.0488870
\(755\) −1.67633e116 −0.465059
\(756\) −1.13064e115 −0.0297297
\(757\) −2.48299e116 −0.618860 −0.309430 0.950922i \(-0.600138\pi\)
−0.309430 + 0.950922i \(0.600138\pi\)
\(758\) 2.51211e116 0.593520
\(759\) 1.09285e115 0.0244777
\(760\) 1.62436e116 0.344930
\(761\) 6.23857e116 1.25605 0.628025 0.778194i \(-0.283864\pi\)
0.628025 + 0.778194i \(0.283864\pi\)
\(762\) 5.26405e115 0.100495
\(763\) 1.03992e116 0.188259
\(764\) −1.34147e116 −0.230304
\(765\) −3.58931e116 −0.584417
\(766\) −8.38785e116 −1.29535
\(767\) 4.81630e115 0.0705507
\(768\) 5.75389e115 0.0799525
\(769\) −8.17099e116 −1.07710 −0.538552 0.842592i \(-0.681029\pi\)
−0.538552 + 0.842592i \(0.681029\pi\)
\(770\) 1.51015e114 0.00188863
\(771\) −1.72216e117 −2.04348
\(772\) −6.18772e116 −0.696675
\(773\) 1.05233e117 1.12431 0.562153 0.827033i \(-0.309973\pi\)
0.562153 + 0.827033i \(0.309973\pi\)
\(774\) −6.53240e116 −0.662314
\(775\) 6.78249e116 0.652634
\(776\) 1.70646e116 0.155846
\(777\) 1.33731e116 0.115926
\(778\) −7.41915e116 −0.610493
\(779\) 1.00218e117 0.782849
\(780\) −4.56673e115 −0.0338668
\(781\) −1.79019e115 −0.0126047
\(782\) −8.89571e116 −0.594713
\(783\) 7.78889e116 0.494452
\(784\) −4.07927e116 −0.245913
\(785\) 1.93845e117 1.10977
\(786\) 7.55692e116 0.410896
\(787\) −2.70781e117 −1.39843 −0.699216 0.714910i \(-0.746468\pi\)
−0.699216 + 0.714910i \(0.746468\pi\)
\(788\) 1.44957e117 0.711092
\(789\) 3.53892e117 1.64912
\(790\) 7.65964e116 0.339087
\(791\) 1.52098e116 0.0639700
\(792\) 1.44473e115 0.00577322
\(793\) −4.61242e115 −0.0175132
\(794\) 2.74911e117 0.991885
\(795\) 1.33510e117 0.457766
\(796\) −1.04890e117 −0.341786
\(797\) −2.00940e117 −0.622306 −0.311153 0.950360i \(-0.600715\pi\)
−0.311153 + 0.950360i \(0.600715\pi\)
\(798\) 4.70741e116 0.138569
\(799\) −7.96804e117 −2.22950
\(800\) 2.23976e116 0.0595739
\(801\) 1.58006e117 0.399537
\(802\) −7.87217e115 −0.0189249
\(803\) −1.81161e116 −0.0414082
\(804\) −1.87317e117 −0.407105
\(805\) −3.75682e116 −0.0776403
\(806\) −4.53095e116 −0.0890471
\(807\) 3.61466e117 0.675599
\(808\) 1.02659e116 0.0182489
\(809\) 6.39070e117 1.08052 0.540261 0.841498i \(-0.318326\pi\)
0.540261 + 0.841498i \(0.318326\pi\)
\(810\) 4.40836e117 0.708980
\(811\) −1.12578e118 −1.72230 −0.861151 0.508350i \(-0.830256\pi\)
−0.861151 + 0.508350i \(0.830256\pi\)
\(812\) −4.66993e116 −0.0679659
\(813\) 6.23559e117 0.863397
\(814\) 9.76093e115 0.0128589
\(815\) 3.20492e117 0.401729
\(816\) −3.02373e117 −0.360655
\(817\) −1.55355e118 −1.76332
\(818\) 5.70124e117 0.615829
\(819\) −5.14718e115 −0.00529141
\(820\) −2.71860e117 −0.266002
\(821\) −1.95190e118 −1.81785 −0.908927 0.416955i \(-0.863097\pi\)
−0.908927 + 0.416955i \(0.863097\pi\)
\(822\) 2.06617e117 0.183171
\(823\) −7.18378e117 −0.606261 −0.303131 0.952949i \(-0.598032\pi\)
−0.303131 + 0.952949i \(0.598032\pi\)
\(824\) 4.18887e116 0.0336546
\(825\) 1.44599e116 0.0110606
\(826\) 1.34676e117 0.0980841
\(827\) 1.72528e118 1.19643 0.598214 0.801336i \(-0.295877\pi\)
0.598214 + 0.801336i \(0.295877\pi\)
\(828\) −3.59408e117 −0.237333
\(829\) −2.41901e118 −1.52118 −0.760589 0.649234i \(-0.775090\pi\)
−0.760589 + 0.649234i \(0.775090\pi\)
\(830\) 1.35877e118 0.813734
\(831\) 3.22439e118 1.83910
\(832\) −1.49624e116 −0.00812842
\(833\) 2.14370e118 1.10928
\(834\) −1.20838e118 −0.595632
\(835\) 4.39587e117 0.206416
\(836\) 3.43590e116 0.0153704
\(837\) 2.11316e118 0.900639
\(838\) −1.24313e118 −0.504817
\(839\) 3.03813e118 1.17556 0.587782 0.809019i \(-0.300001\pi\)
0.587782 + 0.809019i \(0.300001\pi\)
\(840\) −1.27698e117 −0.0470838
\(841\) 3.71065e117 0.130380
\(842\) −2.77550e118 −0.929397
\(843\) 6.33657e118 2.02226
\(844\) 1.88982e118 0.574845
\(845\) −2.79649e118 −0.810804
\(846\) −3.21928e118 −0.889731
\(847\) −4.84954e117 −0.127768
\(848\) 4.37429e117 0.109869
\(849\) −4.76262e118 −1.14047
\(850\) −1.17702e118 −0.268730
\(851\) −2.42824e118 −0.528620
\(852\) 1.51378e118 0.314238
\(853\) −6.30022e118 −1.24715 −0.623577 0.781762i \(-0.714321\pi\)
−0.623577 + 0.781762i \(0.714321\pi\)
\(854\) −1.28975e117 −0.0243479
\(855\) −3.44882e118 −0.620930
\(856\) −2.25266e118 −0.386819
\(857\) 3.80553e118 0.623292 0.311646 0.950198i \(-0.399120\pi\)
0.311646 + 0.950198i \(0.399120\pi\)
\(858\) −9.65972e115 −0.00150914
\(859\) 2.11862e118 0.315740 0.157870 0.987460i \(-0.449537\pi\)
0.157870 + 0.987460i \(0.449537\pi\)
\(860\) 4.21430e118 0.599154
\(861\) −7.87855e117 −0.106861
\(862\) −2.46009e117 −0.0318351
\(863\) −5.31849e118 −0.656676 −0.328338 0.944560i \(-0.606489\pi\)
−0.328338 + 0.944560i \(0.606489\pi\)
\(864\) 6.97820e117 0.0822123
\(865\) −6.99330e118 −0.786194
\(866\) 5.09863e118 0.546989
\(867\) 3.39534e118 0.347624
\(868\) −1.26697e118 −0.123799
\(869\) 1.62019e117 0.0151101
\(870\) 8.79701e118 0.783079
\(871\) 4.87097e117 0.0413886
\(872\) −6.41829e118 −0.520597
\(873\) −3.62314e118 −0.280548
\(874\) −8.54752e118 −0.631869
\(875\) −1.97207e118 −0.139186
\(876\) 1.53189e119 1.03231
\(877\) −5.34719e118 −0.344066 −0.172033 0.985091i \(-0.555034\pi\)
−0.172033 + 0.985091i \(0.555034\pi\)
\(878\) 9.52985e118 0.585542
\(879\) 1.99748e119 1.17201
\(880\) −9.32054e116 −0.00522267
\(881\) 3.52621e119 1.88705 0.943527 0.331296i \(-0.107486\pi\)
0.943527 + 0.331296i \(0.107486\pi\)
\(882\) 8.66107e118 0.442684
\(883\) 3.55834e118 0.173716 0.0868578 0.996221i \(-0.472317\pi\)
0.0868578 + 0.996221i \(0.472317\pi\)
\(884\) 7.86289e117 0.0366662
\(885\) −2.53697e119 −1.13009
\(886\) −1.09481e119 −0.465877
\(887\) 1.29338e119 0.525801 0.262900 0.964823i \(-0.415321\pi\)
0.262900 + 0.964823i \(0.415321\pi\)
\(888\) −8.25379e118 −0.320574
\(889\) −3.82769e117 −0.0142042
\(890\) −1.01936e119 −0.361436
\(891\) 9.32472e117 0.0315928
\(892\) 1.83047e119 0.592633
\(893\) −7.65616e119 −2.36879
\(894\) 1.46100e119 0.431996
\(895\) −4.10097e119 −1.15892
\(896\) −4.18387e117 −0.0113007
\(897\) 2.40306e118 0.0620398
\(898\) −4.35701e119 −1.07522
\(899\) 8.72808e119 2.05898
\(900\) −4.75543e118 −0.107243
\(901\) −2.29874e119 −0.495604
\(902\) −5.75049e117 −0.0118533
\(903\) 1.22131e119 0.240698
\(904\) −9.38738e118 −0.176898
\(905\) −3.83485e119 −0.691005
\(906\) 2.99834e119 0.516641
\(907\) 4.19243e119 0.690830 0.345415 0.938450i \(-0.387738\pi\)
0.345415 + 0.938450i \(0.387738\pi\)
\(908\) −4.29036e119 −0.676109
\(909\) −2.17964e118 −0.0328509
\(910\) 3.32064e117 0.00478681
\(911\) 9.31240e119 1.28401 0.642003 0.766702i \(-0.278104\pi\)
0.642003 + 0.766702i \(0.278104\pi\)
\(912\) −2.90538e119 −0.383188
\(913\) 2.87411e118 0.0362608
\(914\) −4.74667e119 −0.572886
\(915\) 2.42958e119 0.280528
\(916\) −8.66441e119 −0.957133
\(917\) −5.49492e118 −0.0580769
\(918\) −3.66712e119 −0.370849
\(919\) −6.05994e119 −0.586395 −0.293197 0.956052i \(-0.594719\pi\)
−0.293197 + 0.956052i \(0.594719\pi\)
\(920\) 2.31868e119 0.214701
\(921\) 9.04874e119 0.801813
\(922\) 8.97293e119 0.760908
\(923\) −3.93642e118 −0.0319472
\(924\) −2.70110e117 −0.00209810
\(925\) −3.21287e119 −0.238865
\(926\) 7.28600e119 0.518494
\(927\) −8.89376e118 −0.0605838
\(928\) 2.88224e119 0.187948
\(929\) 1.78670e120 1.11536 0.557681 0.830055i \(-0.311691\pi\)
0.557681 + 0.830055i \(0.311691\pi\)
\(930\) 2.38666e120 1.42637
\(931\) 2.05979e120 1.17859
\(932\) −2.10602e118 −0.0115377
\(933\) −4.10686e120 −2.15429
\(934\) 8.88311e119 0.446187
\(935\) 4.89804e118 0.0235588
\(936\) 3.17680e118 0.0146325
\(937\) 9.18961e119 0.405363 0.202681 0.979245i \(-0.435034\pi\)
0.202681 + 0.979245i \(0.435034\pi\)
\(938\) 1.36205e119 0.0575410
\(939\) −4.86020e120 −1.96652
\(940\) 2.07688e120 0.804885
\(941\) 8.77906e118 0.0325888 0.0162944 0.999867i \(-0.494813\pi\)
0.0162944 + 0.999867i \(0.494813\pi\)
\(942\) −3.46718e120 −1.23286
\(943\) 1.43055e120 0.487283
\(944\) −8.31210e119 −0.271235
\(945\) −1.54869e119 −0.0484147
\(946\) 8.91424e118 0.0266989
\(947\) −5.56825e120 −1.59788 −0.798941 0.601409i \(-0.794606\pi\)
−0.798941 + 0.601409i \(0.794606\pi\)
\(948\) −1.37003e120 −0.376697
\(949\) −3.98352e119 −0.104951
\(950\) −1.13095e120 −0.285520
\(951\) −2.64935e120 −0.640957
\(952\) 2.19867e119 0.0509757
\(953\) 4.55605e119 0.101234 0.0506169 0.998718i \(-0.483881\pi\)
0.0506169 + 0.998718i \(0.483881\pi\)
\(954\) −9.28744e119 −0.197782
\(955\) −1.83749e120 −0.375048
\(956\) 3.45319e120 0.675579
\(957\) 1.86078e119 0.0348948
\(958\) −4.47842e119 −0.0805047
\(959\) −1.50239e119 −0.0258898
\(960\) 7.88140e119 0.130202
\(961\) 1.73657e121 2.75040
\(962\) 2.14631e119 0.0325914
\(963\) 4.78282e120 0.696338
\(964\) 1.98847e120 0.277587
\(965\) −8.47564e120 −1.13453
\(966\) 6.71957e119 0.0862517
\(967\) 5.91369e120 0.727924 0.363962 0.931414i \(-0.381424\pi\)
0.363962 + 0.931414i \(0.381424\pi\)
\(968\) 2.99310e120 0.353321
\(969\) 1.52681e121 1.72851
\(970\) 2.33743e120 0.253795
\(971\) −1.75570e121 −1.82840 −0.914202 0.405258i \(-0.867182\pi\)
−0.914202 + 0.405258i \(0.867182\pi\)
\(972\) −5.55702e120 −0.555084
\(973\) 8.78658e119 0.0841880
\(974\) −8.99723e120 −0.826934
\(975\) 3.17955e119 0.0280336
\(976\) 7.96024e119 0.0673300
\(977\) 3.67319e120 0.298067 0.149034 0.988832i \(-0.452384\pi\)
0.149034 + 0.988832i \(0.452384\pi\)
\(978\) −5.73241e120 −0.446287
\(979\) −2.15618e119 −0.0161060
\(980\) −5.58759e120 −0.400469
\(981\) 1.36273e121 0.937160
\(982\) 5.04344e119 0.0332822
\(983\) −6.03863e120 −0.382403 −0.191201 0.981551i \(-0.561238\pi\)
−0.191201 + 0.981551i \(0.561238\pi\)
\(984\) 4.86258e120 0.295505
\(985\) 1.98554e121 1.15801
\(986\) −1.51465e121 −0.847807
\(987\) 6.01883e120 0.323346
\(988\) 7.55513e119 0.0389570
\(989\) −2.21761e121 −1.09758
\(990\) 1.97893e119 0.00940166
\(991\) −1.08669e121 −0.495591 −0.247796 0.968812i \(-0.579706\pi\)
−0.247796 + 0.968812i \(0.579706\pi\)
\(992\) 7.81964e120 0.342345
\(993\) −2.06236e119 −0.00866801
\(994\) −1.10072e120 −0.0444151
\(995\) −1.43673e121 −0.556597
\(996\) −2.43033e121 −0.903988
\(997\) −3.79923e121 −1.35688 −0.678441 0.734655i \(-0.737344\pi\)
−0.678441 + 0.734655i \(0.737344\pi\)
\(998\) 1.42503e121 0.488693
\(999\) −1.00100e121 −0.329635
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 2.82.a.a.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2.82.a.a.1.3 3 1.1 even 1 trivial