Properties

Label 1.106.a.a.1.7
Level 1
Weight 106
Character 1.1
Self dual yes
Analytic conductor 69.819
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 106 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(69.8187388595\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(10\!\cdots\!04\)\( x^{6} - \)\(62\!\cdots\!96\)\( x^{5} + \)\(32\!\cdots\!36\)\( x^{4} - \)\(88\!\cdots\!20\)\( x^{3} - \)\(32\!\cdots\!00\)\( x^{2} + \)\(21\!\cdots\!00\)\( x + \)\(48\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(4.91848e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +O(q^{10})\) \(q+5.93573e15 q^{2} +1.55541e25 q^{3} -5.33194e30 q^{4} +1.46253e36 q^{5} +9.23248e40 q^{6} +8.76445e43 q^{7} -2.72431e47 q^{8} +1.16692e50 q^{9} +8.68120e51 q^{10} -7.28669e54 q^{11} -8.29334e55 q^{12} -4.19396e58 q^{13} +5.20234e59 q^{14} +2.27483e61 q^{15} -1.40079e63 q^{16} +8.65740e63 q^{17} +6.92655e65 q^{18} -9.21112e66 q^{19} -7.79814e66 q^{20} +1.36323e69 q^{21} -4.32518e70 q^{22} -1.62076e69 q^{23} -4.23741e72 q^{24} -2.25129e73 q^{25} -2.48942e74 q^{26} -1.32898e74 q^{27} -4.67316e74 q^{28} +9.56136e76 q^{29} +1.35028e77 q^{30} -1.52589e78 q^{31} +2.73642e78 q^{32} -1.13338e80 q^{33} +5.13880e79 q^{34} +1.28183e80 q^{35} -6.22198e80 q^{36} -2.78360e82 q^{37} -5.46747e82 q^{38} -6.52332e83 q^{39} -3.98439e83 q^{40} +5.59619e84 q^{41} +8.09176e84 q^{42} +2.87167e84 q^{43} +3.88522e85 q^{44} +1.70667e86 q^{45} -9.62038e84 q^{46} +8.04149e87 q^{47} -2.17879e88 q^{48} -4.66803e88 q^{49} -1.33630e89 q^{50} +1.34658e89 q^{51} +2.23620e89 q^{52} +5.94866e90 q^{53} -7.88847e89 q^{54} -1.06570e91 q^{55} -2.38771e91 q^{56} -1.43271e92 q^{57} +5.67537e92 q^{58} -1.24710e93 q^{59} -1.21293e92 q^{60} +3.83239e93 q^{61} -9.05730e93 q^{62} +1.02275e94 q^{63} +7.30653e94 q^{64} -6.13380e94 q^{65} -6.72742e95 q^{66} -7.25169e95 q^{67} -4.61608e94 q^{68} -2.52094e94 q^{69} +7.60859e95 q^{70} -3.02377e96 q^{71} -3.17906e97 q^{72} -1.13078e98 q^{73} -1.65227e98 q^{74} -3.50167e98 q^{75} +4.91132e97 q^{76} -6.38639e98 q^{77} -3.87206e99 q^{78} +1.66730e99 q^{79} -2.04869e99 q^{80} -1.66813e100 q^{81} +3.32175e100 q^{82} -3.34613e100 q^{83} -7.26866e99 q^{84} +1.26617e100 q^{85} +1.70454e100 q^{86} +1.48718e102 q^{87} +1.98512e102 q^{88} +3.73253e101 q^{89} +1.01303e102 q^{90} -3.67578e102 q^{91} +8.64179e99 q^{92} -2.37339e103 q^{93} +4.77321e103 q^{94} -1.34716e103 q^{95} +4.25625e103 q^{96} -2.81285e104 q^{97} -2.77082e104 q^{98} -8.50302e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.93573e15 0.931964 0.465982 0.884794i \(-0.345701\pi\)
0.465982 + 0.884794i \(0.345701\pi\)
\(3\) 1.55541e25 1.38988 0.694942 0.719066i \(-0.255430\pi\)
0.694942 + 0.719066i \(0.255430\pi\)
\(4\) −5.33194e30 −0.131443
\(5\) 1.46253e36 0.294564 0.147282 0.989095i \(-0.452947\pi\)
0.147282 + 0.989095i \(0.452947\pi\)
\(6\) 9.23248e40 1.29532
\(7\) 8.76445e43 0.375905 0.187952 0.982178i \(-0.439815\pi\)
0.187952 + 0.982178i \(0.439815\pi\)
\(8\) −2.72431e47 −1.05446
\(9\) 1.16692e50 0.931775
\(10\) 8.68120e51 0.274524
\(11\) −7.28669e54 −1.54673 −0.773365 0.633961i \(-0.781428\pi\)
−0.773365 + 0.633961i \(0.781428\pi\)
\(12\) −8.29334e55 −0.182690
\(13\) −4.19396e58 −1.38229 −0.691144 0.722717i \(-0.742893\pi\)
−0.691144 + 0.722717i \(0.742893\pi\)
\(14\) 5.20234e59 0.350330
\(15\) 2.27483e61 0.409410
\(16\) −1.40079e63 −0.851280
\(17\) 8.65740e63 0.218182 0.109091 0.994032i \(-0.465206\pi\)
0.109091 + 0.994032i \(0.465206\pi\)
\(18\) 6.92655e65 0.868381
\(19\) −9.21112e66 −0.675692 −0.337846 0.941201i \(-0.609698\pi\)
−0.337846 + 0.941201i \(0.609698\pi\)
\(20\) −7.79814e66 −0.0387183
\(21\) 1.36323e69 0.522463
\(22\) −4.32518e70 −1.44150
\(23\) −1.62076e69 −0.00523609 −0.00261804 0.999997i \(-0.500833\pi\)
−0.00261804 + 0.999997i \(0.500833\pi\)
\(24\) −4.23741e72 −1.46558
\(25\) −2.25129e73 −0.913232
\(26\) −2.48942e74 −1.28824
\(27\) −1.32898e74 −0.0948246
\(28\) −4.67316e74 −0.0494099
\(29\) 9.56136e76 1.60186 0.800931 0.598757i \(-0.204338\pi\)
0.800931 + 0.598757i \(0.204338\pi\)
\(30\) 1.35028e77 0.381556
\(31\) −1.52589e78 −0.770967 −0.385483 0.922715i \(-0.625965\pi\)
−0.385483 + 0.922715i \(0.625965\pi\)
\(32\) 2.73642e78 0.261101
\(33\) −1.13338e80 −2.14977
\(34\) 5.13880e79 0.203338
\(35\) 1.28183e80 0.110728
\(36\) −6.22198e80 −0.122475
\(37\) −2.78360e82 −1.30022 −0.650109 0.759841i \(-0.725277\pi\)
−0.650109 + 0.759841i \(0.725277\pi\)
\(38\) −5.46747e82 −0.629721
\(39\) −6.52332e83 −1.92122
\(40\) −3.98439e83 −0.310608
\(41\) 5.59619e84 1.19327 0.596636 0.802512i \(-0.296503\pi\)
0.596636 + 0.802512i \(0.296503\pi\)
\(42\) 8.09176e84 0.486917
\(43\) 2.87167e84 0.0502389 0.0251195 0.999684i \(-0.492003\pi\)
0.0251195 + 0.999684i \(0.492003\pi\)
\(44\) 3.88522e85 0.203306
\(45\) 1.70667e86 0.274468
\(46\) −9.62038e84 −0.00487985
\(47\) 8.04149e87 1.31886 0.659431 0.751765i \(-0.270797\pi\)
0.659431 + 0.751765i \(0.270797\pi\)
\(48\) −2.17879e88 −1.18318
\(49\) −4.66803e88 −0.858696
\(50\) −1.33630e89 −0.851099
\(51\) 1.34658e89 0.303248
\(52\) 2.23620e89 0.181691
\(53\) 5.94866e90 1.77802 0.889008 0.457892i \(-0.151395\pi\)
0.889008 + 0.457892i \(0.151395\pi\)
\(54\) −7.88847e89 −0.0883732
\(55\) −1.06570e91 −0.455612
\(56\) −2.38771e91 −0.396378
\(57\) −1.43271e92 −0.939133
\(58\) 5.67537e92 1.49288
\(59\) −1.24710e93 −1.33712 −0.668559 0.743659i \(-0.733089\pi\)
−0.668559 + 0.743659i \(0.733089\pi\)
\(60\) −1.21293e92 −0.0538139
\(61\) 3.83239e93 0.713927 0.356963 0.934118i \(-0.383812\pi\)
0.356963 + 0.934118i \(0.383812\pi\)
\(62\) −9.05730e93 −0.718513
\(63\) 1.02275e94 0.350259
\(64\) 7.30653e94 1.09462
\(65\) −6.13380e94 −0.407173
\(66\) −6.72742e95 −2.00351
\(67\) −7.25169e95 −0.980646 −0.490323 0.871541i \(-0.663121\pi\)
−0.490323 + 0.871541i \(0.663121\pi\)
\(68\) −4.61608e94 −0.0286784
\(69\) −2.52094e94 −0.00727755
\(70\) 7.60859e95 0.103195
\(71\) −3.02377e96 −0.194754 −0.0973768 0.995248i \(-0.531045\pi\)
−0.0973768 + 0.995248i \(0.531045\pi\)
\(72\) −3.17906e97 −0.982523
\(73\) −1.13078e98 −1.69405 −0.847026 0.531551i \(-0.821609\pi\)
−0.847026 + 0.531551i \(0.821609\pi\)
\(74\) −1.65227e98 −1.21176
\(75\) −3.50167e98 −1.26929
\(76\) 4.91132e97 0.0888146
\(77\) −6.38639e98 −0.581423
\(78\) −3.87206e99 −1.79051
\(79\) 1.66730e99 0.394994 0.197497 0.980303i \(-0.436719\pi\)
0.197497 + 0.980303i \(0.436719\pi\)
\(80\) −2.04869e99 −0.250757
\(81\) −1.66813e100 −1.06357
\(82\) 3.32175e100 1.11209
\(83\) −3.34613e100 −0.592847 −0.296423 0.955057i \(-0.595794\pi\)
−0.296423 + 0.955057i \(0.595794\pi\)
\(84\) −7.26866e99 −0.0686739
\(85\) 1.26617e100 0.0642687
\(86\) 1.70454e100 0.0468209
\(87\) 1.48718e102 2.22640
\(88\) 1.98512e102 1.63097
\(89\) 3.73253e101 0.169445 0.0847224 0.996405i \(-0.473000\pi\)
0.0847224 + 0.996405i \(0.473000\pi\)
\(90\) 1.01303e102 0.255794
\(91\) −3.67578e102 −0.519608
\(92\) 8.64179e99 0.000688245 0
\(93\) −2.37339e103 −1.07155
\(94\) 4.77321e103 1.22913
\(95\) −1.34716e103 −0.199035
\(96\) 4.25625e103 0.362900
\(97\) −2.81285e104 −1.39197 −0.695986 0.718055i \(-0.745033\pi\)
−0.695986 + 0.718055i \(0.745033\pi\)
\(98\) −2.77082e104 −0.800274
\(99\) −8.50302e104 −1.44120
\(100\) 1.20038e104 0.120038
\(101\) 2.44200e104 0.144835 0.0724175 0.997374i \(-0.476929\pi\)
0.0724175 + 0.997374i \(0.476929\pi\)
\(102\) 7.99293e104 0.282616
\(103\) −5.07710e105 −1.07563 −0.537814 0.843064i \(-0.680750\pi\)
−0.537814 + 0.843064i \(0.680750\pi\)
\(104\) 1.14256e106 1.45757
\(105\) 1.99377e105 0.153899
\(106\) 3.53096e106 1.65705
\(107\) −8.73746e105 −0.250459 −0.125230 0.992128i \(-0.539967\pi\)
−0.125230 + 0.992128i \(0.539967\pi\)
\(108\) 7.08605e104 0.0124640
\(109\) 1.52768e107 1.65631 0.828156 0.560497i \(-0.189390\pi\)
0.828156 + 0.560497i \(0.189390\pi\)
\(110\) −6.32572e106 −0.424614
\(111\) −4.32963e107 −1.80715
\(112\) −1.22771e107 −0.320000
\(113\) 1.04871e108 1.71411 0.857054 0.515227i \(-0.172292\pi\)
0.857054 + 0.515227i \(0.172292\pi\)
\(114\) −8.50415e107 −0.875238
\(115\) −2.37041e105 −0.00154237
\(116\) −5.09806e107 −0.210553
\(117\) −4.89404e108 −1.28798
\(118\) −7.40243e108 −1.24615
\(119\) 7.58774e107 0.0820157
\(120\) −6.19735e108 −0.431708
\(121\) 3.09021e109 1.39237
\(122\) 2.27481e109 0.665354
\(123\) 8.70435e109 1.65851
\(124\) 8.13598e108 0.101338
\(125\) −6.89801e109 −0.563570
\(126\) 6.07074e109 0.326428
\(127\) −1.89039e110 −0.671208 −0.335604 0.942003i \(-0.608940\pi\)
−0.335604 + 0.942003i \(0.608940\pi\)
\(128\) 3.22693e110 0.759043
\(129\) 4.46661e109 0.0698262
\(130\) −3.64086e110 −0.379470
\(131\) −1.66200e111 −1.15848 −0.579240 0.815157i \(-0.696650\pi\)
−0.579240 + 0.815157i \(0.696650\pi\)
\(132\) 6.04310e110 0.282572
\(133\) −8.07305e110 −0.253996
\(134\) −4.30441e111 −0.913927
\(135\) −1.94368e110 −0.0279320
\(136\) −2.35854e111 −0.230065
\(137\) 1.41306e112 0.938276 0.469138 0.883125i \(-0.344565\pi\)
0.469138 + 0.883125i \(0.344565\pi\)
\(138\) −1.49636e110 −0.00678242
\(139\) −2.16214e112 −0.670821 −0.335410 0.942072i \(-0.608875\pi\)
−0.335410 + 0.942072i \(0.608875\pi\)
\(140\) −6.83464e110 −0.0145544
\(141\) 1.25078e113 1.83306
\(142\) −1.79483e112 −0.181503
\(143\) 3.05601e113 2.13803
\(144\) −1.63461e113 −0.793202
\(145\) 1.39838e113 0.471851
\(146\) −6.71199e113 −1.57880
\(147\) −7.26069e113 −1.19349
\(148\) 1.48420e113 0.170904
\(149\) −5.65399e113 −0.457169 −0.228584 0.973524i \(-0.573410\pi\)
−0.228584 + 0.973524i \(0.573410\pi\)
\(150\) −2.07850e114 −1.18293
\(151\) 2.64543e114 1.06220 0.531100 0.847309i \(-0.321779\pi\)
0.531100 + 0.847309i \(0.321779\pi\)
\(152\) 2.50939e114 0.712493
\(153\) 1.01025e114 0.203297
\(154\) −3.79079e114 −0.541865
\(155\) −2.23167e114 −0.227099
\(156\) 3.47820e114 0.252530
\(157\) −1.17083e115 −0.607801 −0.303901 0.952704i \(-0.598289\pi\)
−0.303901 + 0.952704i \(0.598289\pi\)
\(158\) 9.89662e114 0.368120
\(159\) 9.25258e115 2.47123
\(160\) 4.00210e114 0.0769111
\(161\) −1.42051e113 −0.00196827
\(162\) −9.90156e115 −0.991210
\(163\) 1.03779e115 0.0752071 0.0376035 0.999293i \(-0.488028\pi\)
0.0376035 + 0.999293i \(0.488028\pi\)
\(164\) −2.98386e115 −0.156847
\(165\) −1.65760e116 −0.633247
\(166\) −1.98617e116 −0.552512
\(167\) −3.53472e116 −0.717364 −0.358682 0.933460i \(-0.616774\pi\)
−0.358682 + 0.933460i \(0.616774\pi\)
\(168\) −3.71386e116 −0.550919
\(169\) 8.38371e116 0.910719
\(170\) 7.51566e115 0.0598961
\(171\) −1.07487e117 −0.629593
\(172\) −1.53116e115 −0.00660353
\(173\) 2.29574e117 0.730302 0.365151 0.930948i \(-0.381017\pi\)
0.365151 + 0.930948i \(0.381017\pi\)
\(174\) 8.82751e117 2.07493
\(175\) −1.97313e117 −0.343288
\(176\) 1.02071e118 1.31670
\(177\) −1.93975e118 −1.85844
\(178\) 2.21553e117 0.157916
\(179\) −6.76216e117 −0.359171 −0.179586 0.983742i \(-0.557476\pi\)
−0.179586 + 0.983742i \(0.557476\pi\)
\(180\) −9.09984e116 −0.0360767
\(181\) −1.36028e118 −0.403184 −0.201592 0.979470i \(-0.564612\pi\)
−0.201592 + 0.979470i \(0.564612\pi\)
\(182\) −2.18184e118 −0.484256
\(183\) 5.96093e118 0.992275
\(184\) 4.41545e116 0.00552127
\(185\) −4.07111e118 −0.382998
\(186\) −1.40878e119 −0.998650
\(187\) −6.30838e118 −0.337469
\(188\) −4.28768e118 −0.173355
\(189\) −1.16478e118 −0.0356450
\(190\) −7.99636e118 −0.185493
\(191\) 6.87230e119 1.21018 0.605091 0.796157i \(-0.293137\pi\)
0.605091 + 0.796157i \(0.293137\pi\)
\(192\) 1.13646e120 1.52139
\(193\) 1.79504e120 1.82943 0.914714 0.404103i \(-0.132416\pi\)
0.914714 + 0.404103i \(0.132416\pi\)
\(194\) −1.66963e120 −1.29727
\(195\) −9.54056e119 −0.565922
\(196\) 2.48897e119 0.112869
\(197\) 7.42365e119 0.257715 0.128858 0.991663i \(-0.458869\pi\)
0.128858 + 0.991663i \(0.458869\pi\)
\(198\) −5.04716e120 −1.34315
\(199\) −4.51807e120 −0.922926 −0.461463 0.887160i \(-0.652675\pi\)
−0.461463 + 0.887160i \(0.652675\pi\)
\(200\) 6.13321e120 0.962970
\(201\) −1.12793e121 −1.36298
\(202\) 1.44950e120 0.134981
\(203\) 8.38001e120 0.602147
\(204\) −7.17988e119 −0.0398596
\(205\) 8.18461e120 0.351496
\(206\) −3.01363e121 −1.00245
\(207\) −1.89130e119 −0.00487886
\(208\) 5.87484e121 1.17671
\(209\) 6.71186e121 1.04511
\(210\) 1.18345e121 0.143429
\(211\) −3.56693e120 −0.0336872 −0.0168436 0.999858i \(-0.505362\pi\)
−0.0168436 + 0.999858i \(0.505362\pi\)
\(212\) −3.17179e121 −0.233707
\(213\) −4.70320e121 −0.270685
\(214\) −5.18632e121 −0.233419
\(215\) 4.19991e120 0.0147986
\(216\) 3.62055e121 0.0999892
\(217\) −1.33736e122 −0.289810
\(218\) 9.06792e122 1.54362
\(219\) −1.75882e123 −2.35454
\(220\) 5.68226e121 0.0598867
\(221\) −3.63088e122 −0.301590
\(222\) −2.56995e123 −1.68420
\(223\) 2.69470e123 1.39478 0.697388 0.716694i \(-0.254345\pi\)
0.697388 + 0.716694i \(0.254345\pi\)
\(224\) 2.39832e122 0.0981491
\(225\) −2.62709e123 −0.850927
\(226\) 6.22487e123 1.59749
\(227\) 7.89252e123 1.60642 0.803208 0.595698i \(-0.203125\pi\)
0.803208 + 0.595698i \(0.203125\pi\)
\(228\) 7.63910e122 0.123442
\(229\) 7.09479e123 0.911123 0.455561 0.890204i \(-0.349439\pi\)
0.455561 + 0.890204i \(0.349439\pi\)
\(230\) −1.40701e121 −0.00143743
\(231\) −9.93343e123 −0.808110
\(232\) −2.60481e124 −1.68911
\(233\) 7.64294e123 0.395434 0.197717 0.980259i \(-0.436647\pi\)
0.197717 + 0.980259i \(0.436647\pi\)
\(234\) −2.90497e124 −1.20035
\(235\) 1.17609e124 0.388490
\(236\) 6.64945e123 0.175754
\(237\) 2.59333e124 0.548996
\(238\) 4.50388e123 0.0764357
\(239\) −8.75129e124 −1.19174 −0.595871 0.803080i \(-0.703193\pi\)
−0.595871 + 0.803080i \(0.703193\pi\)
\(240\) −3.18655e124 −0.348523
\(241\) 6.50591e124 0.572023 0.286011 0.958226i \(-0.407671\pi\)
0.286011 + 0.958226i \(0.407671\pi\)
\(242\) 1.83426e125 1.29764
\(243\) −2.42818e125 −1.38341
\(244\) −2.04341e124 −0.0938404
\(245\) −6.82714e124 −0.252941
\(246\) 5.16667e125 1.54567
\(247\) 3.86311e125 0.934000
\(248\) 4.15701e125 0.812957
\(249\) −5.20459e125 −0.823988
\(250\) −4.09447e125 −0.525227
\(251\) −1.04222e125 −0.108415 −0.0542077 0.998530i \(-0.517263\pi\)
−0.0542077 + 0.998530i \(0.517263\pi\)
\(252\) −5.45322e124 −0.0460389
\(253\) 1.18100e124 0.00809882
\(254\) −1.12209e126 −0.625542
\(255\) 1.96942e125 0.0893260
\(256\) −1.04846e126 −0.387216
\(257\) −3.16211e126 −0.951675 −0.475838 0.879533i \(-0.657855\pi\)
−0.475838 + 0.879533i \(0.657855\pi\)
\(258\) 2.65126e125 0.0650756
\(259\) −2.43967e126 −0.488758
\(260\) 3.27051e125 0.0535198
\(261\) 1.11574e127 1.49257
\(262\) −9.86519e126 −1.07966
\(263\) 2.05656e126 0.184274 0.0921371 0.995746i \(-0.470630\pi\)
0.0921371 + 0.995746i \(0.470630\pi\)
\(264\) 3.08767e127 2.26686
\(265\) 8.70010e126 0.523740
\(266\) −4.79194e126 −0.236715
\(267\) 5.80561e126 0.235508
\(268\) 3.86656e126 0.128899
\(269\) −3.70566e127 −1.01595 −0.507974 0.861373i \(-0.669605\pi\)
−0.507974 + 0.861373i \(0.669605\pi\)
\(270\) −1.15371e126 −0.0260316
\(271\) −8.71045e127 −1.61865 −0.809324 0.587362i \(-0.800167\pi\)
−0.809324 + 0.587362i \(0.800167\pi\)
\(272\) −1.21272e127 −0.185734
\(273\) −5.71733e127 −0.722195
\(274\) 8.38754e127 0.874440
\(275\) 1.64045e128 1.41252
\(276\) 1.34415e125 0.000956580 0
\(277\) −6.76019e127 −0.397897 −0.198949 0.980010i \(-0.563753\pi\)
−0.198949 + 0.980010i \(0.563753\pi\)
\(278\) −1.28339e128 −0.625181
\(279\) −1.78060e128 −0.718368
\(280\) −3.49210e127 −0.116759
\(281\) −1.03457e128 −0.286866 −0.143433 0.989660i \(-0.545814\pi\)
−0.143433 + 0.989660i \(0.545814\pi\)
\(282\) 7.42429e128 1.70835
\(283\) −1.78925e128 −0.341887 −0.170943 0.985281i \(-0.554682\pi\)
−0.170943 + 0.985281i \(0.554682\pi\)
\(284\) 1.61226e127 0.0255989
\(285\) −2.09538e128 −0.276635
\(286\) 1.81396e129 1.99256
\(287\) 4.90475e128 0.448557
\(288\) 3.19320e128 0.243288
\(289\) −1.49953e129 −0.952397
\(290\) 8.30041e128 0.439749
\(291\) −4.37513e129 −1.93468
\(292\) 6.02924e128 0.222671
\(293\) −1.69501e129 −0.523145 −0.261572 0.965184i \(-0.584241\pi\)
−0.261572 + 0.965184i \(0.584241\pi\)
\(294\) −4.30975e129 −1.11229
\(295\) −1.82392e129 −0.393868
\(296\) 7.58339e129 1.37103
\(297\) 9.68388e128 0.146668
\(298\) −3.35606e129 −0.426065
\(299\) 6.79740e127 0.00723778
\(300\) 1.86707e129 0.166838
\(301\) 2.51686e128 0.0188850
\(302\) 1.57025e130 0.989932
\(303\) 3.79830e129 0.201304
\(304\) 1.29028e130 0.575203
\(305\) 5.60500e129 0.210297
\(306\) 5.99659e129 0.189465
\(307\) 4.16550e129 0.110893 0.0554463 0.998462i \(-0.482342\pi\)
0.0554463 + 0.998462i \(0.482342\pi\)
\(308\) 3.40518e129 0.0764237
\(309\) −7.89696e130 −1.49500
\(310\) −1.32466e130 −0.211648
\(311\) −7.28115e130 −0.982381 −0.491190 0.871052i \(-0.663438\pi\)
−0.491190 + 0.871052i \(0.663438\pi\)
\(312\) 1.77715e131 2.02586
\(313\) −1.68114e131 −1.62004 −0.810019 0.586403i \(-0.800543\pi\)
−0.810019 + 0.586403i \(0.800543\pi\)
\(314\) −6.94972e130 −0.566449
\(315\) 1.49580e130 0.103174
\(316\) −8.88993e129 −0.0519190
\(317\) 1.20789e131 0.597609 0.298804 0.954314i \(-0.403412\pi\)
0.298804 + 0.954314i \(0.403412\pi\)
\(318\) 5.49208e131 2.30310
\(319\) −6.96707e131 −2.47765
\(320\) 1.06860e131 0.322435
\(321\) −1.35903e131 −0.348109
\(322\) −8.43174e128 −0.00183436
\(323\) −7.97444e130 −0.147424
\(324\) 8.89437e130 0.139798
\(325\) 9.44182e131 1.26235
\(326\) 6.16002e130 0.0700903
\(327\) 2.37617e132 2.30208
\(328\) −1.52457e132 −1.25826
\(329\) 7.04793e131 0.495766
\(330\) −9.83907e131 −0.590164
\(331\) −1.75907e132 −0.900146 −0.450073 0.892992i \(-0.648602\pi\)
−0.450073 + 0.892992i \(0.648602\pi\)
\(332\) 1.78414e131 0.0779253
\(333\) −3.24825e132 −1.21151
\(334\) −2.09811e132 −0.668558
\(335\) −1.06058e132 −0.288863
\(336\) −1.90959e132 −0.444763
\(337\) −5.46915e132 −1.08981 −0.544904 0.838498i \(-0.683434\pi\)
−0.544904 + 0.838498i \(0.683434\pi\)
\(338\) 4.97634e132 0.848757
\(339\) 1.63117e133 2.38241
\(340\) −6.75116e130 −0.00844764
\(341\) 1.11187e133 1.19248
\(342\) −6.38013e132 −0.586758
\(343\) −8.85579e132 −0.698692
\(344\) −7.82331e131 −0.0529751
\(345\) −3.68696e130 −0.00214371
\(346\) 1.36269e133 0.680615
\(347\) 1.69890e133 0.729238 0.364619 0.931157i \(-0.381199\pi\)
0.364619 + 0.931157i \(0.381199\pi\)
\(348\) −7.92957e132 −0.292644
\(349\) −1.33296e133 −0.423137 −0.211568 0.977363i \(-0.567857\pi\)
−0.211568 + 0.977363i \(0.567857\pi\)
\(350\) −1.17120e133 −0.319932
\(351\) 5.57369e132 0.131075
\(352\) −1.99394e133 −0.403853
\(353\) 4.25860e133 0.743181 0.371591 0.928397i \(-0.378812\pi\)
0.371591 + 0.928397i \(0.378812\pi\)
\(354\) −1.15138e134 −1.73200
\(355\) −4.42236e132 −0.0573675
\(356\) −1.99016e132 −0.0222722
\(357\) 1.18020e133 0.113992
\(358\) −4.01383e133 −0.334735
\(359\) 1.29130e134 0.930187 0.465093 0.885262i \(-0.346021\pi\)
0.465093 + 0.885262i \(0.346021\pi\)
\(360\) −4.64948e133 −0.289416
\(361\) −1.00990e134 −0.543441
\(362\) −8.07426e133 −0.375753
\(363\) 4.80653e134 1.93524
\(364\) 1.95990e133 0.0682986
\(365\) −1.65380e134 −0.499008
\(366\) 3.53825e134 0.924765
\(367\) −4.52119e134 −1.02396 −0.511982 0.858996i \(-0.671088\pi\)
−0.511982 + 0.858996i \(0.671088\pi\)
\(368\) 2.27034e132 0.00445738
\(369\) 6.53033e134 1.11186
\(370\) −2.41650e134 −0.356941
\(371\) 5.21367e134 0.668364
\(372\) 1.26548e134 0.140848
\(373\) 2.53939e134 0.245480 0.122740 0.992439i \(-0.460832\pi\)
0.122740 + 0.992439i \(0.460832\pi\)
\(374\) −3.74448e134 −0.314509
\(375\) −1.07292e135 −0.783297
\(376\) −2.19075e135 −1.39069
\(377\) −4.01000e135 −2.21423
\(378\) −6.91381e133 −0.0332199
\(379\) 4.23774e135 1.77246 0.886228 0.463250i \(-0.153317\pi\)
0.886228 + 0.463250i \(0.153317\pi\)
\(380\) 7.18296e133 0.0261616
\(381\) −2.94033e135 −0.932901
\(382\) 4.07921e135 1.12785
\(383\) 1.40505e135 0.338653 0.169327 0.985560i \(-0.445841\pi\)
0.169327 + 0.985560i \(0.445841\pi\)
\(384\) 5.01919e135 1.05498
\(385\) −9.34030e134 −0.171266
\(386\) 1.06549e136 1.70496
\(387\) 3.35102e134 0.0468114
\(388\) 1.49980e135 0.182964
\(389\) −1.50971e136 −1.60894 −0.804468 0.593996i \(-0.797549\pi\)
−0.804468 + 0.593996i \(0.797549\pi\)
\(390\) −5.66302e135 −0.527420
\(391\) −1.40316e133 −0.00114242
\(392\) 1.27171e136 0.905464
\(393\) −2.58509e136 −1.61015
\(394\) 4.40648e135 0.240182
\(395\) 2.43848e135 0.116351
\(396\) 4.53376e135 0.189436
\(397\) 3.01792e136 1.10460 0.552301 0.833645i \(-0.313750\pi\)
0.552301 + 0.833645i \(0.313750\pi\)
\(398\) −2.68181e136 −0.860134
\(399\) −1.25569e136 −0.353024
\(400\) 3.15357e136 0.777416
\(401\) −7.19899e136 −1.55665 −0.778326 0.627860i \(-0.783931\pi\)
−0.778326 + 0.627860i \(0.783931\pi\)
\(402\) −6.69511e136 −1.27025
\(403\) 6.39954e136 1.06570
\(404\) −1.30206e135 −0.0190375
\(405\) −2.43969e136 −0.313290
\(406\) 4.97415e136 0.561180
\(407\) 2.02832e137 2.01109
\(408\) −3.66849e136 −0.319764
\(409\) −1.05041e137 −0.805163 −0.402581 0.915384i \(-0.631887\pi\)
−0.402581 + 0.915384i \(0.631887\pi\)
\(410\) 4.85816e136 0.327581
\(411\) 2.19788e137 1.30409
\(412\) 2.70708e136 0.141383
\(413\) −1.09301e137 −0.502629
\(414\) −1.12263e135 −0.00454692
\(415\) −4.89382e136 −0.174632
\(416\) −1.14764e137 −0.360917
\(417\) −3.36301e137 −0.932363
\(418\) 3.98398e137 0.974008
\(419\) −5.13603e137 −1.10762 −0.553811 0.832643i \(-0.686827\pi\)
−0.553811 + 0.832643i \(0.686827\pi\)
\(420\) −1.06307e136 −0.0202289
\(421\) −3.41684e137 −0.573871 −0.286935 0.957950i \(-0.592636\pi\)
−0.286935 + 0.957950i \(0.592636\pi\)
\(422\) −2.11723e136 −0.0313953
\(423\) 9.38382e137 1.22888
\(424\) −1.62060e138 −1.87485
\(425\) −1.94903e137 −0.199251
\(426\) −2.79169e137 −0.252269
\(427\) 3.35888e137 0.268368
\(428\) 4.65877e136 0.0329210
\(429\) 4.75334e138 2.97161
\(430\) 2.49295e136 0.0137918
\(431\) 2.04799e138 1.00293 0.501466 0.865177i \(-0.332794\pi\)
0.501466 + 0.865177i \(0.332794\pi\)
\(432\) 1.86162e137 0.0807223
\(433\) −3.08552e138 −1.18499 −0.592494 0.805575i \(-0.701857\pi\)
−0.592494 + 0.805575i \(0.701857\pi\)
\(434\) −7.93822e137 −0.270092
\(435\) 2.17505e138 0.655818
\(436\) −8.14552e137 −0.217710
\(437\) 1.49290e136 0.00353798
\(438\) −1.04399e139 −2.19434
\(439\) 2.64684e138 0.493561 0.246780 0.969071i \(-0.420627\pi\)
0.246780 + 0.969071i \(0.420627\pi\)
\(440\) 2.90330e138 0.480426
\(441\) −5.44724e138 −0.800111
\(442\) −2.15519e138 −0.281072
\(443\) 1.00847e138 0.116806 0.0584032 0.998293i \(-0.481399\pi\)
0.0584032 + 0.998293i \(0.481399\pi\)
\(444\) 2.30854e138 0.237537
\(445\) 5.45895e137 0.0499124
\(446\) 1.59950e139 1.29988
\(447\) −8.79426e138 −0.635411
\(448\) 6.40377e138 0.411472
\(449\) −4.95920e137 −0.0283452 −0.0141726 0.999900i \(-0.504511\pi\)
−0.0141726 + 0.999900i \(0.504511\pi\)
\(450\) −1.55937e139 −0.793033
\(451\) −4.07777e139 −1.84567
\(452\) −5.59167e138 −0.225307
\(453\) 4.11472e139 1.47633
\(454\) 4.68479e139 1.49712
\(455\) −5.37594e138 −0.153058
\(456\) 3.90313e139 0.990282
\(457\) −1.67962e139 −0.379848 −0.189924 0.981799i \(-0.560824\pi\)
−0.189924 + 0.981799i \(0.560824\pi\)
\(458\) 4.21128e139 0.849134
\(459\) −1.15055e138 −0.0206890
\(460\) 1.26389e136 0.000202732 0
\(461\) 2.43974e139 0.349176 0.174588 0.984642i \(-0.444141\pi\)
0.174588 + 0.984642i \(0.444141\pi\)
\(462\) −5.89622e139 −0.753130
\(463\) −8.04930e139 −0.917817 −0.458909 0.888484i \(-0.651759\pi\)
−0.458909 + 0.888484i \(0.651759\pi\)
\(464\) −1.33934e140 −1.36363
\(465\) −3.47116e139 −0.315642
\(466\) 4.53664e139 0.368531
\(467\) −6.71585e139 −0.487489 −0.243744 0.969840i \(-0.578376\pi\)
−0.243744 + 0.969840i \(0.578376\pi\)
\(468\) 2.60947e139 0.169295
\(469\) −6.35571e139 −0.368629
\(470\) 6.98098e139 0.362059
\(471\) −1.82112e140 −0.844773
\(472\) 3.39748e140 1.40994
\(473\) −2.09250e139 −0.0777060
\(474\) 1.53933e140 0.511644
\(475\) 2.07369e140 0.617063
\(476\) −4.04574e138 −0.0107803
\(477\) 6.94163e140 1.65671
\(478\) −5.19453e140 −1.11066
\(479\) −7.93981e140 −1.52123 −0.760616 0.649202i \(-0.775103\pi\)
−0.760616 + 0.649202i \(0.775103\pi\)
\(480\) 6.22490e139 0.106897
\(481\) 1.16743e141 1.79728
\(482\) 3.86173e140 0.533105
\(483\) −2.20947e138 −0.00273566
\(484\) −1.64768e140 −0.183017
\(485\) −4.11389e140 −0.410026
\(486\) −1.44130e141 −1.28929
\(487\) −6.81986e140 −0.547652 −0.273826 0.961779i \(-0.588289\pi\)
−0.273826 + 0.961779i \(0.588289\pi\)
\(488\) −1.04406e141 −0.752810
\(489\) 1.61418e140 0.104529
\(490\) −4.05241e140 −0.235732
\(491\) 7.17413e140 0.374965 0.187483 0.982268i \(-0.439967\pi\)
0.187483 + 0.982268i \(0.439967\pi\)
\(492\) −4.64111e140 −0.217999
\(493\) 8.27766e140 0.349498
\(494\) 2.29304e141 0.870455
\(495\) −1.24359e141 −0.424528
\(496\) 2.13745e141 0.656309
\(497\) −2.65017e140 −0.0732088
\(498\) −3.08930e141 −0.767927
\(499\) 5.28030e141 1.18135 0.590677 0.806908i \(-0.298861\pi\)
0.590677 + 0.806908i \(0.298861\pi\)
\(500\) 3.67798e140 0.0740771
\(501\) −5.49792e141 −0.997052
\(502\) −6.18636e140 −0.101039
\(503\) 6.45019e141 0.948971 0.474486 0.880263i \(-0.342634\pi\)
0.474486 + 0.880263i \(0.342634\pi\)
\(504\) −2.78627e141 −0.369335
\(505\) 3.57150e140 0.0426632
\(506\) 7.01008e139 0.00754781
\(507\) 1.30401e142 1.26579
\(508\) 1.00795e141 0.0882253
\(509\) 5.45984e141 0.431019 0.215509 0.976502i \(-0.430859\pi\)
0.215509 + 0.976502i \(0.430859\pi\)
\(510\) 1.16899e141 0.0832486
\(511\) −9.91064e141 −0.636802
\(512\) −1.93134e142 −1.11991
\(513\) 1.22414e141 0.0640722
\(514\) −1.87695e142 −0.886927
\(515\) −7.42543e141 −0.316841
\(516\) −2.38157e140 −0.00917814
\(517\) −5.85959e142 −2.03992
\(518\) −1.44812e142 −0.455505
\(519\) 3.57081e142 1.01503
\(520\) 1.67104e142 0.429349
\(521\) 4.91559e142 1.14181 0.570906 0.821015i \(-0.306592\pi\)
0.570906 + 0.821015i \(0.306592\pi\)
\(522\) 6.62273e142 1.39103
\(523\) 2.21300e142 0.420381 0.210190 0.977660i \(-0.432592\pi\)
0.210190 + 0.977660i \(0.432592\pi\)
\(524\) 8.86169e141 0.152273
\(525\) −3.06902e142 −0.477130
\(526\) 1.22072e142 0.171737
\(527\) −1.32103e142 −0.168211
\(528\) 1.58762e143 1.83006
\(529\) −9.58100e142 −0.999973
\(530\) 5.16414e142 0.488107
\(531\) −1.45527e143 −1.24589
\(532\) 4.30450e141 0.0333858
\(533\) −2.34702e143 −1.64945
\(534\) 3.44605e142 0.219485
\(535\) −1.27788e142 −0.0737764
\(536\) 1.97558e143 1.03406
\(537\) −1.05179e143 −0.499206
\(538\) −2.19958e143 −0.946827
\(539\) 3.40145e143 1.32817
\(540\) 1.03636e141 0.00367145
\(541\) 6.21110e142 0.199670 0.0998348 0.995004i \(-0.468169\pi\)
0.0998348 + 0.995004i \(0.468169\pi\)
\(542\) −5.17028e143 −1.50852
\(543\) −2.11579e143 −0.560379
\(544\) 2.36903e142 0.0569676
\(545\) 2.23429e143 0.487891
\(546\) −3.39365e143 −0.673060
\(547\) 9.88009e143 1.78003 0.890013 0.455936i \(-0.150695\pi\)
0.890013 + 0.455936i \(0.150695\pi\)
\(548\) −7.53435e142 −0.123329
\(549\) 4.47212e143 0.665219
\(550\) 9.73724e143 1.31642
\(551\) −8.80709e143 −1.08236
\(552\) 6.86782e141 0.00767392
\(553\) 1.46129e143 0.148480
\(554\) −4.01267e143 −0.370826
\(555\) −6.33223e143 −0.532323
\(556\) 1.15284e143 0.0881744
\(557\) 2.14551e144 1.49325 0.746626 0.665244i \(-0.231672\pi\)
0.746626 + 0.665244i \(0.231672\pi\)
\(558\) −1.05692e144 −0.669493
\(559\) −1.20437e143 −0.0694446
\(560\) −1.79557e143 −0.0942607
\(561\) −9.81210e143 −0.469042
\(562\) −6.14094e143 −0.267349
\(563\) −9.74563e143 −0.386473 −0.193237 0.981152i \(-0.561898\pi\)
−0.193237 + 0.981152i \(0.561898\pi\)
\(564\) −6.66909e143 −0.240943
\(565\) 1.53378e144 0.504915
\(566\) −1.06205e144 −0.318626
\(567\) −1.46202e144 −0.399801
\(568\) 8.23768e143 0.205361
\(569\) −3.93707e144 −0.894909 −0.447454 0.894307i \(-0.647669\pi\)
−0.447454 + 0.894307i \(0.647669\pi\)
\(570\) −1.24376e144 −0.257814
\(571\) −1.88688e144 −0.356738 −0.178369 0.983964i \(-0.557082\pi\)
−0.178369 + 0.983964i \(0.557082\pi\)
\(572\) −1.62945e144 −0.281027
\(573\) 1.06892e145 1.68201
\(574\) 2.91133e144 0.418039
\(575\) 3.64880e142 0.00478176
\(576\) 8.52617e144 1.01994
\(577\) 1.05199e145 1.14889 0.574446 0.818542i \(-0.305217\pi\)
0.574446 + 0.818542i \(0.305217\pi\)
\(578\) −8.90079e144 −0.887600
\(579\) 2.79202e145 2.54269
\(580\) −7.45609e143 −0.0620213
\(581\) −2.93270e144 −0.222854
\(582\) −2.59696e145 −1.80305
\(583\) −4.33460e145 −2.75011
\(584\) 3.08058e145 1.78632
\(585\) −7.15769e144 −0.379393
\(586\) −1.00611e145 −0.487552
\(587\) −3.35704e145 −1.48750 −0.743748 0.668460i \(-0.766954\pi\)
−0.743748 + 0.668460i \(0.766954\pi\)
\(588\) 3.87136e144 0.156875
\(589\) 1.40552e145 0.520936
\(590\) −1.08263e145 −0.367071
\(591\) 1.15468e145 0.358194
\(592\) 3.89923e145 1.10685
\(593\) 9.74195e143 0.0253090 0.0126545 0.999920i \(-0.495972\pi\)
0.0126545 + 0.999920i \(0.495972\pi\)
\(594\) 5.74809e144 0.136689
\(595\) 1.10973e144 0.0241589
\(596\) 3.01468e144 0.0600914
\(597\) −7.02744e145 −1.28276
\(598\) 4.03475e143 0.00674535
\(599\) 7.73768e145 1.18496 0.592478 0.805586i \(-0.298150\pi\)
0.592478 + 0.805586i \(0.298150\pi\)
\(600\) 9.53963e145 1.33842
\(601\) −7.70795e145 −0.990899 −0.495449 0.868637i \(-0.664997\pi\)
−0.495449 + 0.868637i \(0.664997\pi\)
\(602\) 1.49394e144 0.0176002
\(603\) −8.46218e145 −0.913741
\(604\) −1.41053e145 −0.139618
\(605\) 4.51953e145 0.410144
\(606\) 2.25457e145 0.187608
\(607\) 2.37938e146 1.81576 0.907880 0.419231i \(-0.137700\pi\)
0.907880 + 0.419231i \(0.137700\pi\)
\(608\) −2.52055e145 −0.176424
\(609\) 1.30343e146 0.836914
\(610\) 3.32698e145 0.195990
\(611\) −3.37257e146 −1.82305
\(612\) −5.38661e144 −0.0267218
\(613\) −4.21329e146 −1.91843 −0.959217 0.282672i \(-0.908779\pi\)
−0.959217 + 0.282672i \(0.908779\pi\)
\(614\) 2.47253e145 0.103348
\(615\) 1.27304e146 0.488538
\(616\) 1.73985e146 0.613090
\(617\) −2.51057e146 −0.812457 −0.406228 0.913772i \(-0.633156\pi\)
−0.406228 + 0.913772i \(0.633156\pi\)
\(618\) −4.68742e146 −1.39328
\(619\) 4.37224e146 1.19384 0.596919 0.802302i \(-0.296392\pi\)
0.596919 + 0.802302i \(0.296392\pi\)
\(620\) 1.18991e145 0.0298505
\(621\) 2.15396e143 0.000496510 0
\(622\) −4.32190e146 −0.915544
\(623\) 3.27136e145 0.0636950
\(624\) 9.13777e146 1.63550
\(625\) 4.54100e146 0.747224
\(626\) −9.97877e146 −1.50982
\(627\) 1.04397e147 1.45258
\(628\) 6.24279e145 0.0798909
\(629\) −2.40988e146 −0.283685
\(630\) 8.87865e145 0.0961542
\(631\) 1.17893e147 1.17475 0.587375 0.809315i \(-0.300161\pi\)
0.587375 + 0.809315i \(0.300161\pi\)
\(632\) −4.54223e146 −0.416507
\(633\) −5.54803e145 −0.0468213
\(634\) 7.16972e146 0.556950
\(635\) −2.76476e146 −0.197714
\(636\) −4.93342e146 −0.324825
\(637\) 1.95775e147 1.18696
\(638\) −4.13547e147 −2.30908
\(639\) −3.52851e146 −0.181467
\(640\) 4.71949e146 0.223587
\(641\) −1.42300e147 −0.621096 −0.310548 0.950558i \(-0.600513\pi\)
−0.310548 + 0.950558i \(0.600513\pi\)
\(642\) −8.06684e146 −0.324425
\(643\) −3.56269e147 −1.32039 −0.660195 0.751095i \(-0.729526\pi\)
−0.660195 + 0.751095i \(0.729526\pi\)
\(644\) 7.57406e143 0.000258714 0
\(645\) 6.53257e145 0.0205683
\(646\) −4.73341e146 −0.137394
\(647\) −2.08851e147 −0.558934 −0.279467 0.960155i \(-0.590158\pi\)
−0.279467 + 0.960155i \(0.590158\pi\)
\(648\) 4.54450e147 1.12150
\(649\) 9.08722e147 2.06816
\(650\) 5.60441e147 1.17646
\(651\) −2.08014e147 −0.402802
\(652\) −5.53342e145 −0.00988541
\(653\) −7.12364e147 −1.17425 −0.587124 0.809497i \(-0.699740\pi\)
−0.587124 + 0.809497i \(0.699740\pi\)
\(654\) 1.41043e148 2.14546
\(655\) −2.43073e147 −0.341247
\(656\) −7.83906e147 −1.01581
\(657\) −1.31953e148 −1.57848
\(658\) 4.18346e147 0.462036
\(659\) 2.60531e147 0.265690 0.132845 0.991137i \(-0.457589\pi\)
0.132845 + 0.991137i \(0.457589\pi\)
\(660\) 8.83824e146 0.0832356
\(661\) 1.69983e148 1.47852 0.739262 0.673418i \(-0.235175\pi\)
0.739262 + 0.673418i \(0.235175\pi\)
\(662\) −1.04413e148 −0.838903
\(663\) −5.64750e147 −0.419175
\(664\) 9.11587e147 0.625136
\(665\) −1.18071e147 −0.0748181
\(666\) −1.92807e148 −1.12909
\(667\) −1.54967e146 −0.00838749
\(668\) 1.88469e147 0.0942922
\(669\) 4.19135e148 1.93858
\(670\) −6.29533e147 −0.269210
\(671\) −2.79255e148 −1.10425
\(672\) 3.73037e147 0.136416
\(673\) −5.70050e148 −1.92807 −0.964033 0.265783i \(-0.914369\pi\)
−0.964033 + 0.265783i \(0.914369\pi\)
\(674\) −3.24634e148 −1.01566
\(675\) 2.99192e147 0.0865969
\(676\) −4.47015e147 −0.119707
\(677\) −1.15809e148 −0.286971 −0.143486 0.989652i \(-0.545831\pi\)
−0.143486 + 0.989652i \(0.545831\pi\)
\(678\) 9.68221e148 2.22032
\(679\) −2.46531e148 −0.523249
\(680\) −3.44944e147 −0.0677690
\(681\) 1.22761e149 2.23273
\(682\) 6.59977e148 1.11135
\(683\) −4.36434e148 −0.680506 −0.340253 0.940334i \(-0.610513\pi\)
−0.340253 + 0.940334i \(0.610513\pi\)
\(684\) 5.73114e147 0.0827553
\(685\) 2.06665e148 0.276383
\(686\) −5.25656e148 −0.651156
\(687\) 1.10353e149 1.26635
\(688\) −4.02259e147 −0.0427674
\(689\) −2.49484e149 −2.45773
\(690\) −2.18848e146 −0.00199786
\(691\) 9.93176e148 0.840289 0.420144 0.907457i \(-0.361979\pi\)
0.420144 + 0.907457i \(0.361979\pi\)
\(692\) −1.22408e148 −0.0959927
\(693\) −7.45243e148 −0.541755
\(694\) 1.00842e149 0.679624
\(695\) −3.16220e148 −0.197600
\(696\) −4.05154e149 −2.34766
\(697\) 4.84484e148 0.260351
\(698\) −7.91206e148 −0.394348
\(699\) 1.18879e149 0.549608
\(700\) 1.05206e148 0.0451226
\(701\) 8.46981e148 0.337037 0.168519 0.985698i \(-0.446102\pi\)
0.168519 + 0.985698i \(0.446102\pi\)
\(702\) 3.30839e148 0.122157
\(703\) 2.56401e149 0.878547
\(704\) −5.32404e149 −1.69308
\(705\) 1.82931e149 0.539955
\(706\) 2.52779e149 0.692619
\(707\) 2.14028e148 0.0544441
\(708\) 1.03426e149 0.244278
\(709\) 5.21147e149 1.14296 0.571482 0.820615i \(-0.306369\pi\)
0.571482 + 0.820615i \(0.306369\pi\)
\(710\) −2.62500e148 −0.0534645
\(711\) 1.94561e149 0.368046
\(712\) −1.01686e149 −0.178673
\(713\) 2.47311e147 0.00403685
\(714\) 7.00536e148 0.106237
\(715\) 4.46951e149 0.629786
\(716\) 3.60554e148 0.0472104
\(717\) −1.36118e150 −1.65638
\(718\) 7.66483e149 0.866901
\(719\) −1.22999e150 −1.29311 −0.646553 0.762869i \(-0.723790\pi\)
−0.646553 + 0.762869i \(0.723790\pi\)
\(720\) −2.39067e149 −0.233649
\(721\) −4.44980e149 −0.404333
\(722\) −5.99452e149 −0.506467
\(723\) 1.01193e150 0.795045
\(724\) 7.25294e148 0.0529955
\(725\) −2.15254e150 −1.46287
\(726\) 2.85303e150 1.80357
\(727\) 6.70077e149 0.394065 0.197033 0.980397i \(-0.436870\pi\)
0.197033 + 0.980397i \(0.436870\pi\)
\(728\) 1.00139e150 0.547908
\(729\) −1.68770e150 −0.859213
\(730\) −9.81650e149 −0.465057
\(731\) 2.48612e148 0.0109612
\(732\) −3.17834e149 −0.130427
\(733\) 3.97348e149 0.151779 0.0758897 0.997116i \(-0.475820\pi\)
0.0758897 + 0.997116i \(0.475820\pi\)
\(734\) −2.68366e150 −0.954297
\(735\) −1.06190e150 −0.351559
\(736\) −4.43508e147 −0.00136715
\(737\) 5.28408e150 1.51679
\(738\) 3.87623e150 1.03622
\(739\) −6.00249e150 −1.49451 −0.747254 0.664538i \(-0.768628\pi\)
−0.747254 + 0.664538i \(0.768628\pi\)
\(740\) 2.17069e149 0.0503423
\(741\) 6.00871e150 1.29815
\(742\) 3.09469e150 0.622892
\(743\) −2.11116e148 −0.00395922 −0.00197961 0.999998i \(-0.500630\pi\)
−0.00197961 + 0.999998i \(0.500630\pi\)
\(744\) 6.46584e150 1.12991
\(745\) −8.26915e149 −0.134666
\(746\) 1.50731e150 0.228779
\(747\) −3.90468e150 −0.552400
\(748\) 3.36359e149 0.0443578
\(749\) −7.65791e149 −0.0941488
\(750\) −6.36857e150 −0.730004
\(751\) −1.19849e151 −1.28097 −0.640483 0.767972i \(-0.721266\pi\)
−0.640483 + 0.767972i \(0.721266\pi\)
\(752\) −1.12644e151 −1.12272
\(753\) −1.62108e150 −0.150685
\(754\) −2.38023e151 −2.06359
\(755\) 3.86902e150 0.312886
\(756\) 6.21053e148 0.00468527
\(757\) 1.35251e151 0.951933 0.475966 0.879464i \(-0.342098\pi\)
0.475966 + 0.879464i \(0.342098\pi\)
\(758\) 2.51540e151 1.65187
\(759\) 1.83693e149 0.0112564
\(760\) 3.67007e150 0.209875
\(761\) 1.16327e151 0.620848 0.310424 0.950598i \(-0.399529\pi\)
0.310424 + 0.950598i \(0.399529\pi\)
\(762\) −1.74530e151 −0.869430
\(763\) 1.33893e151 0.622615
\(764\) −3.66427e150 −0.159069
\(765\) 1.47753e150 0.0598840
\(766\) 8.33997e150 0.315613
\(767\) 5.23028e151 1.84828
\(768\) −1.63078e151 −0.538185
\(769\) 9.66156e149 0.0297793 0.0148896 0.999889i \(-0.495260\pi\)
0.0148896 + 0.999889i \(0.495260\pi\)
\(770\) −5.54415e150 −0.159614
\(771\) −4.91838e151 −1.32272
\(772\) −9.57105e150 −0.240465
\(773\) 4.94920e150 0.116175 0.0580873 0.998312i \(-0.481500\pi\)
0.0580873 + 0.998312i \(0.481500\pi\)
\(774\) 1.98907e150 0.0436265
\(775\) 3.43523e151 0.704071
\(776\) 7.66307e151 1.46779
\(777\) −3.79469e151 −0.679317
\(778\) −8.96121e151 −1.49947
\(779\) −5.15472e151 −0.806285
\(780\) 5.08697e150 0.0743863
\(781\) 2.20333e151 0.301231
\(782\) −8.32875e148 −0.00106470
\(783\) −1.27069e151 −0.151896
\(784\) 6.53891e151 0.730991
\(785\) −1.71237e151 −0.179037
\(786\) −1.53444e152 −1.50060
\(787\) −3.96812e151 −0.363004 −0.181502 0.983391i \(-0.558096\pi\)
−0.181502 + 0.983391i \(0.558096\pi\)
\(788\) −3.95825e150 −0.0338748
\(789\) 3.19879e151 0.256120
\(790\) 1.44741e151 0.108435
\(791\) 9.19139e151 0.644341
\(792\) 2.31648e152 1.51970
\(793\) −1.60729e152 −0.986852
\(794\) 1.79135e152 1.02945
\(795\) 1.35322e152 0.727938
\(796\) 2.40901e151 0.121312
\(797\) −2.62714e152 −1.23857 −0.619287 0.785165i \(-0.712578\pi\)
−0.619287 + 0.785165i \(0.712578\pi\)
\(798\) −7.45342e151 −0.329006
\(799\) 6.96185e151 0.287752
\(800\) −6.16047e151 −0.238446
\(801\) 4.35558e151 0.157884
\(802\) −4.27312e152 −1.45074
\(803\) 8.23963e152 2.62024
\(804\) 6.01407e151 0.179154
\(805\) −2.07754e149 −0.000579782 0
\(806\) 3.79859e152 0.993192
\(807\) −5.76382e152 −1.41205
\(808\) −6.65275e151 −0.152723
\(809\) 1.80159e152 0.387578 0.193789 0.981043i \(-0.437922\pi\)
0.193789 + 0.981043i \(0.437922\pi\)
\(810\) −1.44814e152 −0.291975
\(811\) −7.80264e152 −1.47451 −0.737253 0.675617i \(-0.763877\pi\)
−0.737253 + 0.675617i \(0.763877\pi\)
\(812\) −4.46817e151 −0.0791477
\(813\) −1.35483e153 −2.24973
\(814\) 1.20396e153 1.87426
\(815\) 1.51780e151 0.0221533
\(816\) −1.88627e152 −0.258149
\(817\) −2.64513e151 −0.0339460
\(818\) −6.23493e152 −0.750383
\(819\) −4.28935e152 −0.484158
\(820\) −4.36399e151 −0.0462015
\(821\) 3.35866e152 0.333542 0.166771 0.985996i \(-0.446666\pi\)
0.166771 + 0.985996i \(0.446666\pi\)
\(822\) 1.30460e153 1.21537
\(823\) −8.67106e152 −0.757846 −0.378923 0.925428i \(-0.623705\pi\)
−0.378923 + 0.925428i \(0.623705\pi\)
\(824\) 1.38316e153 1.13421
\(825\) 2.55156e153 1.96324
\(826\) −6.48783e152 −0.468432
\(827\) 2.50977e153 1.70057 0.850284 0.526324i \(-0.176430\pi\)
0.850284 + 0.526324i \(0.176430\pi\)
\(828\) 1.00843e150 0.000641289 0
\(829\) 8.67655e152 0.517886 0.258943 0.965893i \(-0.416626\pi\)
0.258943 + 0.965893i \(0.416626\pi\)
\(830\) −2.90484e152 −0.162750
\(831\) −1.05149e153 −0.553031
\(832\) −3.06433e153 −1.51308
\(833\) −4.04130e152 −0.187352
\(834\) −1.99619e153 −0.868929
\(835\) −5.16964e152 −0.211310
\(836\) −3.57873e152 −0.137372
\(837\) 2.02788e152 0.0731066
\(838\) −3.04861e153 −1.03226
\(839\) 1.69754e152 0.0539904 0.0269952 0.999636i \(-0.491406\pi\)
0.0269952 + 0.999636i \(0.491406\pi\)
\(840\) −5.43163e152 −0.162281
\(841\) 5.57918e153 1.56596
\(842\) −2.02814e153 −0.534827
\(843\) −1.60918e153 −0.398710
\(844\) 1.90187e151 0.00442794
\(845\) 1.22614e153 0.268265
\(846\) 5.56998e153 1.14527
\(847\) 2.70840e153 0.523400
\(848\) −8.33279e153 −1.51359
\(849\) −2.78301e153 −0.475183
\(850\) −1.15689e153 −0.185695
\(851\) 4.51155e151 0.00680806
\(852\) 2.50772e152 0.0355795
\(853\) 5.71396e153 0.762278 0.381139 0.924518i \(-0.375532\pi\)
0.381139 + 0.924518i \(0.375532\pi\)
\(854\) 1.99374e153 0.250110
\(855\) −1.57203e153 −0.185456
\(856\) 2.38035e153 0.264100
\(857\) −1.55632e154 −1.62407 −0.812035 0.583609i \(-0.801640\pi\)
−0.812035 + 0.583609i \(0.801640\pi\)
\(858\) 2.82145e154 2.76943
\(859\) −9.58283e153 −0.884815 −0.442408 0.896814i \(-0.645876\pi\)
−0.442408 + 0.896814i \(0.645876\pi\)
\(860\) −2.23937e151 −0.00194517
\(861\) 7.62889e153 0.623441
\(862\) 1.21563e154 0.934697
\(863\) 5.02429e153 0.363503 0.181751 0.983345i \(-0.441823\pi\)
0.181751 + 0.983345i \(0.441823\pi\)
\(864\) −3.63665e152 −0.0247588
\(865\) 3.35760e153 0.215121
\(866\) −1.83148e154 −1.10437
\(867\) −2.33238e154 −1.32372
\(868\) 7.13074e152 0.0380933
\(869\) −1.21491e154 −0.610949
\(870\) 1.29105e154 0.611199
\(871\) 3.04133e154 1.35553
\(872\) −4.16188e154 −1.74652
\(873\) −3.28239e154 −1.29701
\(874\) 8.86146e151 0.00329727
\(875\) −6.04572e153 −0.211849
\(876\) 9.37792e153 0.309486
\(877\) 2.68630e154 0.834981 0.417490 0.908681i \(-0.362910\pi\)
0.417490 + 0.908681i \(0.362910\pi\)
\(878\) 1.57109e154 0.459981
\(879\) −2.63643e154 −0.727110
\(880\) 1.49282e154 0.387853
\(881\) −5.37696e151 −0.00131614 −0.000658069 1.00000i \(-0.500209\pi\)
−0.000658069 1.00000i \(0.500209\pi\)
\(882\) −3.23333e154 −0.745675
\(883\) 2.65925e154 0.577861 0.288930 0.957350i \(-0.406700\pi\)
0.288930 + 0.957350i \(0.406700\pi\)
\(884\) 1.93596e153 0.0396418
\(885\) −2.83694e154 −0.547430
\(886\) 5.98600e153 0.108859
\(887\) 4.10224e154 0.703122 0.351561 0.936165i \(-0.385651\pi\)
0.351561 + 0.936165i \(0.385651\pi\)
\(888\) 1.17953e155 1.90558
\(889\) −1.65683e154 −0.252310
\(890\) 3.24028e153 0.0465166
\(891\) 1.21551e155 1.64506
\(892\) −1.43680e154 −0.183333
\(893\) −7.40712e154 −0.891144
\(894\) −5.22004e154 −0.592180
\(895\) −9.88988e153 −0.105799
\(896\) 2.82823e154 0.285328
\(897\) 1.05727e153 0.0100597
\(898\) −2.94365e153 −0.0264167
\(899\) −1.45896e155 −1.23498
\(900\) 1.40075e154 0.111848
\(901\) 5.14999e154 0.387931
\(902\) −2.42045e155 −1.72010
\(903\) 3.91474e153 0.0262480
\(904\) −2.85701e155 −1.80746
\(905\) −1.98946e154 −0.118764
\(906\) 2.44238e155 1.37589
\(907\) −4.27645e154 −0.227353 −0.113677 0.993518i \(-0.536263\pi\)
−0.113677 + 0.993518i \(0.536263\pi\)
\(908\) −4.20825e154 −0.211151
\(909\) 2.84963e154 0.134954
\(910\) −3.19101e154 −0.142645
\(911\) 4.52642e155 1.91003 0.955015 0.296556i \(-0.0958383\pi\)
0.955015 + 0.296556i \(0.0958383\pi\)
\(912\) 2.00691e155 0.799465
\(913\) 2.43822e155 0.916974
\(914\) −9.96974e154 −0.354004
\(915\) 8.71806e154 0.292289
\(916\) −3.78290e154 −0.119760
\(917\) −1.45665e155 −0.435478
\(918\) −6.82937e153 −0.0192814
\(919\) −5.60391e155 −1.49426 −0.747132 0.664676i \(-0.768569\pi\)
−0.747132 + 0.664676i \(0.768569\pi\)
\(920\) 6.45773e152 0.00162637
\(921\) 6.47905e154 0.154128
\(922\) 1.44816e155 0.325419
\(923\) 1.26816e155 0.269206
\(924\) 5.29645e154 0.106220
\(925\) 6.26669e155 1.18740
\(926\) −4.77785e155 −0.855373
\(927\) −5.92460e155 −1.00224
\(928\) 2.61639e155 0.418248
\(929\) 8.70215e155 1.31462 0.657312 0.753619i \(-0.271693\pi\)
0.657312 + 0.753619i \(0.271693\pi\)
\(930\) −2.06038e155 −0.294167
\(931\) 4.29978e155 0.580214
\(932\) −4.07517e154 −0.0519769
\(933\) −1.13252e156 −1.36539
\(934\) −3.98634e155 −0.454322
\(935\) −9.22621e154 −0.0994063
\(936\) 1.33329e156 1.35813
\(937\) −8.48069e155 −0.816775 −0.408388 0.912809i \(-0.633909\pi\)
−0.408388 + 0.912809i \(0.633909\pi\)
\(938\) −3.77258e155 −0.343549
\(939\) −2.61485e156 −2.25166
\(940\) −6.27087e154 −0.0510641
\(941\) 1.20312e156 0.926517 0.463258 0.886223i \(-0.346680\pi\)
0.463258 + 0.886223i \(0.346680\pi\)
\(942\) −1.08096e156 −0.787298
\(943\) −9.07007e153 −0.00624808
\(944\) 1.74692e156 1.13826
\(945\) −1.70353e154 −0.0104998
\(946\) −1.24205e155 −0.0724193
\(947\) −9.05317e155 −0.499375 −0.249687 0.968326i \(-0.580328\pi\)
−0.249687 + 0.968326i \(0.580328\pi\)
\(948\) −1.38275e155 −0.0721614
\(949\) 4.74244e156 2.34167
\(950\) 1.23089e156 0.575081
\(951\) 1.87876e156 0.830606
\(952\) −2.06713e155 −0.0864826
\(953\) −3.42515e155 −0.135613 −0.0678067 0.997698i \(-0.521600\pi\)
−0.0678067 + 0.997698i \(0.521600\pi\)
\(954\) 4.12036e156 1.54400
\(955\) 1.00510e156 0.356476
\(956\) 4.66614e155 0.156646
\(957\) −1.08366e157 −3.44364
\(958\) −4.71285e156 −1.41773
\(959\) 1.23847e156 0.352702
\(960\) 1.66211e156 0.448147
\(961\) −1.58887e156 −0.405610
\(962\) 6.92956e156 1.67500
\(963\) −1.01960e156 −0.233372
\(964\) −3.46891e155 −0.0751881
\(965\) 2.62530e156 0.538884
\(966\) −1.31148e154 −0.00254954
\(967\) −9.59776e156 −1.76718 −0.883588 0.468265i \(-0.844879\pi\)
−0.883588 + 0.468265i \(0.844879\pi\)
\(968\) −8.41868e156 −1.46821
\(969\) −1.24035e156 −0.204902
\(970\) −2.44189e156 −0.382129
\(971\) 8.31538e156 1.23274 0.616372 0.787455i \(-0.288602\pi\)
0.616372 + 0.787455i \(0.288602\pi\)
\(972\) 1.29469e156 0.181839
\(973\) −1.89500e156 −0.252165
\(974\) −4.04808e156 −0.510392
\(975\) 1.46859e157 1.75452
\(976\) −5.36836e156 −0.607752
\(977\) 2.36789e156 0.254037 0.127018 0.991900i \(-0.459459\pi\)
0.127018 + 0.991900i \(0.459459\pi\)
\(978\) 9.58134e155 0.0974174
\(979\) −2.71978e156 −0.262085
\(980\) 3.64019e155 0.0332472
\(981\) 1.78269e157 1.54331
\(982\) 4.25837e156 0.349454
\(983\) 1.74866e157 1.36033 0.680167 0.733057i \(-0.261907\pi\)
0.680167 + 0.733057i \(0.261907\pi\)
\(984\) −2.37133e157 −1.74884
\(985\) 1.08573e156 0.0759138
\(986\) 4.91339e156 0.325719
\(987\) 1.09624e157 0.689057
\(988\) −2.05979e156 −0.122767
\(989\) −4.65428e153 −0.000263055 0
\(990\) −7.38164e156 −0.395645
\(991\) −1.15467e157 −0.586938 −0.293469 0.955969i \(-0.594810\pi\)
−0.293469 + 0.955969i \(0.594810\pi\)
\(992\) −4.17549e156 −0.201300
\(993\) −2.73607e157 −1.25110
\(994\) −1.57307e156 −0.0682280
\(995\) −6.60783e156 −0.271861
\(996\) 2.77506e156 0.108307
\(997\) −2.03200e157 −0.752364 −0.376182 0.926546i \(-0.622763\pi\)
−0.376182 + 0.926546i \(0.622763\pi\)
\(998\) 3.13425e157 1.10098
\(999\) 3.69935e156 0.123293
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1.106.a.a.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.7 8 1.1 even 1 trivial