Properties

Label 1.30.a.a.1.1
Level $1$
Weight $30$
Character 1.1
Self dual yes
Analytic conductor $5.328$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(5.32780423830\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{51349}) \)
Defining polynomial: \(x^{2} - x - 12837\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2^{6}\cdot 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(113.802\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-17433.9 q^{2} +9.52434e6 q^{3} -2.32930e8 q^{4} -1.12623e10 q^{5} -1.66046e11 q^{6} -2.98628e12 q^{7} +1.34206e13 q^{8} +2.20826e13 q^{9} +O(q^{10})\) \(q-17433.9 q^{2} +9.52434e6 q^{3} -2.32930e8 q^{4} -1.12623e10 q^{5} -1.66046e11 q^{6} -2.98628e12 q^{7} +1.34206e13 q^{8} +2.20826e13 q^{9} +1.96347e14 q^{10} -1.25811e15 q^{11} -2.21850e15 q^{12} +6.09036e15 q^{13} +5.20625e16 q^{14} -1.07266e17 q^{15} -1.08921e17 q^{16} +8.28952e16 q^{17} -3.84986e17 q^{18} +3.72257e18 q^{19} +2.62334e18 q^{20} -2.84423e19 q^{21} +2.19338e19 q^{22} -1.69513e19 q^{23} +1.27823e20 q^{24} -5.94240e19 q^{25} -1.06179e20 q^{26} -4.43337e20 q^{27} +6.95594e20 q^{28} -8.81402e20 q^{29} +1.87007e21 q^{30} +3.71093e21 q^{31} -5.30623e21 q^{32} -1.19827e22 q^{33} -1.44519e21 q^{34} +3.36325e22 q^{35} -5.14369e21 q^{36} +1.97746e22 q^{37} -6.48990e22 q^{38} +5.80066e22 q^{39} -1.51148e23 q^{40} -1.00635e23 q^{41} +4.95861e23 q^{42} -1.61886e23 q^{43} +2.93051e23 q^{44} -2.48702e23 q^{45} +2.95527e23 q^{46} -2.61745e24 q^{47} -1.03740e24 q^{48} +5.69796e24 q^{49} +1.03599e24 q^{50} +7.89521e23 q^{51} -1.41863e24 q^{52} -1.44856e25 q^{53} +7.72909e24 q^{54} +1.41693e25 q^{55} -4.00778e25 q^{56} +3.54550e25 q^{57} +1.53663e25 q^{58} +5.87125e24 q^{59} +2.49855e25 q^{60} -6.18692e25 q^{61} -6.46960e25 q^{62} -6.59448e25 q^{63} +1.50985e26 q^{64} -6.85917e25 q^{65} +2.08905e26 q^{66} +1.29243e26 q^{67} -1.93088e25 q^{68} -1.61450e26 q^{69} -5.86346e26 q^{70} -3.63672e26 q^{71} +2.96362e26 q^{72} +1.45255e27 q^{73} -3.44748e26 q^{74} -5.65975e26 q^{75} -8.67098e26 q^{76} +3.75707e27 q^{77} -1.01128e27 q^{78} -3.93709e27 q^{79} +1.22670e27 q^{80} -5.73802e27 q^{81} +1.75447e27 q^{82} +6.61171e27 q^{83} +6.62507e27 q^{84} -9.33594e26 q^{85} +2.82231e27 q^{86} -8.39477e27 q^{87} -1.68846e28 q^{88} +6.47986e27 q^{89} +4.33584e27 q^{90} -1.81875e28 q^{91} +3.94847e27 q^{92} +3.53442e28 q^{93} +4.56324e28 q^{94} -4.19249e28 q^{95} -5.05383e28 q^{96} +9.52029e28 q^{97} -9.93377e28 q^{98} -2.77823e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 8640q^{2} - 4967640q^{3} - 89952256q^{4} - 17477788500q^{5} - 543908756736q^{6} - 3020312682800q^{7} + 3150297169920q^{8} + 163469569523706q^{9} + O(q^{10}) \) \( 2q + 8640q^{2} - 4967640q^{3} - 89952256q^{4} - 17477788500q^{5} - 543908756736q^{6} - 3020312682800q^{7} + 3150297169920q^{8} + 163469569523706q^{9} + 34285866768000q^{10} - 2055380519588616q^{11} - 4290530276229120q^{12} + 17139371179332220q^{13} + 51175123348059648q^{14} - 17192351392506000q^{15} - 453469082063208448q^{16} - 664795927907749980q^{17} + 3301524864881760960q^{18} + 1232169445452155080q^{19} + 1734668101813248000q^{20} - 27949113476248821696q^{21} + 1145797484912974080q^{22} - 18588430504374379920q^{23} + \)\(27\!\cdots\!40\)\(q^{24} - \)\(20\!\cdots\!50\)\(q^{25} + \)\(18\!\cdots\!64\)\(q^{26} - \)\(14\!\cdots\!80\)\(q^{27} + \)\(69\!\cdots\!20\)\(q^{28} + \)\(99\!\cdots\!20\)\(q^{29} + \)\(42\!\cdots\!00\)\(q^{30} - \)\(10\!\cdots\!56\)\(q^{31} - \)\(87\!\cdots\!60\)\(q^{32} - \)\(42\!\cdots\!80\)\(q^{33} - \)\(20\!\cdots\!92\)\(q^{34} + \)\(33\!\cdots\!00\)\(q^{35} + \)\(15\!\cdots\!32\)\(q^{36} + \)\(98\!\cdots\!60\)\(q^{37} - \)\(12\!\cdots\!20\)\(q^{38} - \)\(10\!\cdots\!28\)\(q^{39} - \)\(87\!\cdots\!00\)\(q^{40} - \)\(10\!\cdots\!76\)\(q^{41} + \)\(50\!\cdots\!20\)\(q^{42} + \)\(51\!\cdots\!00\)\(q^{43} + \)\(17\!\cdots\!48\)\(q^{44} - \)\(11\!\cdots\!00\)\(q^{45} + \)\(25\!\cdots\!64\)\(q^{46} - \)\(45\!\cdots\!20\)\(q^{47} + \)\(39\!\cdots\!80\)\(q^{48} + \)\(24\!\cdots\!14\)\(q^{49} - \)\(28\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!84\)\(q^{51} + \)\(16\!\cdots\!00\)\(q^{52} - \)\(16\!\cdots\!40\)\(q^{53} - \)\(19\!\cdots\!20\)\(q^{54} + \)\(19\!\cdots\!00\)\(q^{55} - \)\(39\!\cdots\!20\)\(q^{56} + \)\(71\!\cdots\!40\)\(q^{57} + \)\(64\!\cdots\!20\)\(q^{58} - \)\(83\!\cdots\!60\)\(q^{59} + \)\(37\!\cdots\!00\)\(q^{60} - \)\(15\!\cdots\!16\)\(q^{61} - \)\(18\!\cdots\!20\)\(q^{62} - \)\(70\!\cdots\!60\)\(q^{63} + \)\(24\!\cdots\!84\)\(q^{64} - \)\(13\!\cdots\!00\)\(q^{65} + \)\(51\!\cdots\!88\)\(q^{66} + \)\(24\!\cdots\!20\)\(q^{67} - \)\(12\!\cdots\!40\)\(q^{68} - \)\(13\!\cdots\!28\)\(q^{69} - \)\(58\!\cdots\!00\)\(q^{70} - \)\(18\!\cdots\!36\)\(q^{71} - \)\(11\!\cdots\!40\)\(q^{72} + \)\(99\!\cdots\!80\)\(q^{73} + \)\(17\!\cdots\!28\)\(q^{74} + \)\(15\!\cdots\!00\)\(q^{75} - \)\(12\!\cdots\!40\)\(q^{76} + \)\(37\!\cdots\!00\)\(q^{77} - \)\(51\!\cdots\!00\)\(q^{78} - \)\(72\!\cdots\!80\)\(q^{79} + \)\(33\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!58\)\(q^{81} + \)\(15\!\cdots\!80\)\(q^{82} + \)\(22\!\cdots\!40\)\(q^{83} + \)\(66\!\cdots\!88\)\(q^{84} + \)\(37\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!64\)\(q^{86} - \)\(35\!\cdots\!40\)\(q^{87} - \)\(86\!\cdots\!60\)\(q^{88} + \)\(58\!\cdots\!60\)\(q^{89} - \)\(18\!\cdots\!00\)\(q^{90} - \)\(18\!\cdots\!96\)\(q^{91} + \)\(37\!\cdots\!20\)\(q^{92} + \)\(10\!\cdots\!20\)\(q^{93} - \)\(40\!\cdots\!12\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} - \)\(25\!\cdots\!16\)\(q^{96} + \)\(10\!\cdots\!80\)\(q^{97} - \)\(18\!\cdots\!20\)\(q^{98} - \)\(14\!\cdots\!48\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −17433.9 −0.752419 −0.376209 0.926535i \(-0.622773\pi\)
−0.376209 + 0.926535i \(0.622773\pi\)
\(3\) 9.52434e6 1.14968 0.574839 0.818266i \(-0.305065\pi\)
0.574839 + 0.818266i \(0.305065\pi\)
\(4\) −2.32930e8 −0.433866
\(5\) −1.12623e10 −0.825209 −0.412604 0.910910i \(-0.635381\pi\)
−0.412604 + 0.910910i \(0.635381\pi\)
\(6\) −1.66046e11 −0.865040
\(7\) −2.98628e12 −1.66421 −0.832106 0.554616i \(-0.812865\pi\)
−0.832106 + 0.554616i \(0.812865\pi\)
\(8\) 1.34206e13 1.07887
\(9\) 2.20826e13 0.321761
\(10\) 1.96347e14 0.620903
\(11\) −1.25811e15 −0.998906 −0.499453 0.866341i \(-0.666466\pi\)
−0.499453 + 0.866341i \(0.666466\pi\)
\(12\) −2.21850e15 −0.498806
\(13\) 6.09036e15 0.429007 0.214503 0.976723i \(-0.431187\pi\)
0.214503 + 0.976723i \(0.431187\pi\)
\(14\) 5.20625e16 1.25219
\(15\) −1.07266e17 −0.948725
\(16\) −1.08921e17 −0.377895
\(17\) 8.28952e16 0.119404 0.0597021 0.998216i \(-0.480985\pi\)
0.0597021 + 0.998216i \(0.480985\pi\)
\(18\) −3.84986e17 −0.242099
\(19\) 3.72257e18 1.06885 0.534424 0.845217i \(-0.320529\pi\)
0.534424 + 0.845217i \(0.320529\pi\)
\(20\) 2.62334e18 0.358030
\(21\) −2.84423e19 −1.91331
\(22\) 2.19338e19 0.751596
\(23\) −1.69513e19 −0.304894 −0.152447 0.988312i \(-0.548715\pi\)
−0.152447 + 0.988312i \(0.548715\pi\)
\(24\) 1.27823e20 1.24035
\(25\) −5.94240e19 −0.319030
\(26\) −1.06179e20 −0.322793
\(27\) −4.43337e20 −0.779757
\(28\) 6.95594e20 0.722045
\(29\) −8.81402e20 −0.550051 −0.275026 0.961437i \(-0.588686\pi\)
−0.275026 + 0.961437i \(0.588686\pi\)
\(30\) 1.87007e21 0.713839
\(31\) 3.71093e21 0.880518 0.440259 0.897871i \(-0.354887\pi\)
0.440259 + 0.897871i \(0.354887\pi\)
\(32\) −5.30623e21 −0.794532
\(33\) −1.19827e22 −1.14842
\(34\) −1.44519e21 −0.0898420
\(35\) 3.36325e22 1.37332
\(36\) −5.14369e21 −0.139601
\(37\) 1.97746e22 0.360730 0.180365 0.983600i \(-0.442272\pi\)
0.180365 + 0.983600i \(0.442272\pi\)
\(38\) −6.48990e22 −0.804221
\(39\) 5.80066e22 0.493220
\(40\) −1.51148e23 −0.890291
\(41\) −1.00635e23 −0.414367 −0.207183 0.978302i \(-0.566430\pi\)
−0.207183 + 0.978302i \(0.566430\pi\)
\(42\) 4.95861e23 1.43961
\(43\) −1.61886e23 −0.334131 −0.167066 0.985946i \(-0.553429\pi\)
−0.167066 + 0.985946i \(0.553429\pi\)
\(44\) 2.93051e23 0.433391
\(45\) −2.48702e23 −0.265520
\(46\) 2.95527e23 0.229408
\(47\) −2.61745e24 −1.48751 −0.743755 0.668453i \(-0.766957\pi\)
−0.743755 + 0.668453i \(0.766957\pi\)
\(48\) −1.03740e24 −0.434458
\(49\) 5.69796e24 1.76960
\(50\) 1.03599e24 0.240045
\(51\) 7.89521e23 0.137277
\(52\) −1.41863e24 −0.186131
\(53\) −1.44856e25 −1.44190 −0.720951 0.692986i \(-0.756295\pi\)
−0.720951 + 0.692986i \(0.756295\pi\)
\(54\) 7.72909e24 0.586704
\(55\) 1.41693e25 0.824306
\(56\) −4.00778e25 −1.79547
\(57\) 3.54550e25 1.22883
\(58\) 1.53663e25 0.413869
\(59\) 5.87125e24 0.123417 0.0617087 0.998094i \(-0.480345\pi\)
0.0617087 + 0.998094i \(0.480345\pi\)
\(60\) 2.49855e25 0.411619
\(61\) −6.18692e25 −0.802032 −0.401016 0.916071i \(-0.631343\pi\)
−0.401016 + 0.916071i \(0.631343\pi\)
\(62\) −6.46960e25 −0.662519
\(63\) −6.59448e25 −0.535479
\(64\) 1.50985e26 0.975716
\(65\) −6.85917e25 −0.354020
\(66\) 2.08905e26 0.864094
\(67\) 1.29243e26 0.429854 0.214927 0.976630i \(-0.431049\pi\)
0.214927 + 0.976630i \(0.431049\pi\)
\(68\) −1.93088e25 −0.0518054
\(69\) −1.61450e26 −0.350531
\(70\) −5.86346e26 −1.03331
\(71\) −3.63672e26 −0.521751 −0.260876 0.965372i \(-0.584011\pi\)
−0.260876 + 0.965372i \(0.584011\pi\)
\(72\) 2.96362e26 0.347138
\(73\) 1.45255e27 1.39299 0.696496 0.717561i \(-0.254741\pi\)
0.696496 + 0.717561i \(0.254741\pi\)
\(74\) −3.44748e26 −0.271420
\(75\) −5.65975e26 −0.366783
\(76\) −8.67098e26 −0.463736
\(77\) 3.75707e27 1.66239
\(78\) −1.01128e27 −0.371108
\(79\) −3.93709e27 −1.20111 −0.600554 0.799584i \(-0.705053\pi\)
−0.600554 + 0.799584i \(0.705053\pi\)
\(80\) 1.22670e27 0.311842
\(81\) −5.73802e27 −1.21823
\(82\) 1.75447e27 0.311778
\(83\) 6.61171e27 0.985556 0.492778 0.870155i \(-0.335982\pi\)
0.492778 + 0.870155i \(0.335982\pi\)
\(84\) 6.62507e27 0.830120
\(85\) −9.33594e26 −0.0985335
\(86\) 2.82231e27 0.251407
\(87\) −8.39477e27 −0.632382
\(88\) −1.68846e28 −1.07769
\(89\) 6.47986e27 0.351084 0.175542 0.984472i \(-0.443832\pi\)
0.175542 + 0.984472i \(0.443832\pi\)
\(90\) 4.33584e27 0.199782
\(91\) −1.81875e28 −0.713959
\(92\) 3.94847e27 0.132283
\(93\) 3.53442e28 1.01231
\(94\) 4.56324e28 1.11923
\(95\) −4.19249e28 −0.882023
\(96\) −5.05383e28 −0.913457
\(97\) 9.52029e28 1.48068 0.740338 0.672235i \(-0.234666\pi\)
0.740338 + 0.672235i \(0.234666\pi\)
\(98\) −9.93377e28 −1.33148
\(99\) −2.77823e28 −0.321409
\(100\) 1.38416e28 0.138416
\(101\) 4.65862e28 0.403271 0.201635 0.979461i \(-0.435374\pi\)
0.201635 + 0.979461i \(0.435374\pi\)
\(102\) −1.37644e28 −0.103289
\(103\) −1.34288e29 −0.874775 −0.437388 0.899273i \(-0.644096\pi\)
−0.437388 + 0.899273i \(0.644096\pi\)
\(104\) 8.17365e28 0.462842
\(105\) 3.20327e29 1.57888
\(106\) 2.52540e29 1.08491
\(107\) −4.69036e29 −1.75850 −0.879248 0.476364i \(-0.841955\pi\)
−0.879248 + 0.476364i \(0.841955\pi\)
\(108\) 1.03266e29 0.338310
\(109\) −5.33865e29 −1.53020 −0.765098 0.643913i \(-0.777310\pi\)
−0.765098 + 0.643913i \(0.777310\pi\)
\(110\) −2.47026e29 −0.620223
\(111\) 1.88340e29 0.414723
\(112\) 3.25268e29 0.628897
\(113\) 7.95436e29 1.35197 0.675987 0.736914i \(-0.263718\pi\)
0.675987 + 0.736914i \(0.263718\pi\)
\(114\) −6.18120e29 −0.924596
\(115\) 1.90911e29 0.251602
\(116\) 2.05305e29 0.238648
\(117\) 1.34491e29 0.138038
\(118\) −1.02359e29 −0.0928615
\(119\) −2.47548e29 −0.198714
\(120\) −1.43958e30 −1.02355
\(121\) −3.46951e27 −0.00218716
\(122\) 1.07862e30 0.603464
\(123\) −9.58486e29 −0.476389
\(124\) −8.64387e29 −0.382027
\(125\) 2.76703e30 1.08848
\(126\) 1.14968e30 0.402905
\(127\) 1.93923e29 0.0606003 0.0303002 0.999541i \(-0.490354\pi\)
0.0303002 + 0.999541i \(0.490354\pi\)
\(128\) 2.16508e29 0.0603851
\(129\) −1.54186e30 −0.384143
\(130\) 1.19582e30 0.266372
\(131\) −2.32229e30 −0.462894 −0.231447 0.972847i \(-0.574346\pi\)
−0.231447 + 0.972847i \(0.574346\pi\)
\(132\) 2.79112e30 0.498260
\(133\) −1.11166e31 −1.77879
\(134\) −2.25320e30 −0.323430
\(135\) 4.99301e30 0.643462
\(136\) 1.11251e30 0.128821
\(137\) 1.26990e31 1.32228 0.661139 0.750263i \(-0.270073\pi\)
0.661139 + 0.750263i \(0.270073\pi\)
\(138\) 2.81470e30 0.263746
\(139\) 1.14547e31 0.966648 0.483324 0.875442i \(-0.339429\pi\)
0.483324 + 0.875442i \(0.339429\pi\)
\(140\) −7.83402e30 −0.595838
\(141\) −2.49295e31 −1.71016
\(142\) 6.34022e30 0.392575
\(143\) −7.66234e30 −0.428538
\(144\) −2.40525e30 −0.121592
\(145\) 9.92666e30 0.453907
\(146\) −2.53236e31 −1.04811
\(147\) 5.42693e31 2.03448
\(148\) −4.60609e30 −0.156508
\(149\) −5.74280e31 −1.76979 −0.884897 0.465787i \(-0.845771\pi\)
−0.884897 + 0.465787i \(0.845771\pi\)
\(150\) 9.86715e30 0.275974
\(151\) 5.07974e31 1.29026 0.645128 0.764075i \(-0.276804\pi\)
0.645128 + 0.764075i \(0.276804\pi\)
\(152\) 4.99593e31 1.15315
\(153\) 1.83054e30 0.0384197
\(154\) −6.55003e31 −1.25082
\(155\) −4.17938e31 −0.726611
\(156\) −1.35115e31 −0.213991
\(157\) −9.31373e30 −0.134455 −0.0672277 0.997738i \(-0.521415\pi\)
−0.0672277 + 0.997738i \(0.521415\pi\)
\(158\) 6.86388e31 0.903736
\(159\) −1.37965e32 −1.65772
\(160\) 5.97606e31 0.655655
\(161\) 5.06213e31 0.507409
\(162\) 1.00036e32 0.916620
\(163\) −4.45351e31 −0.373235 −0.186617 0.982433i \(-0.559752\pi\)
−0.186617 + 0.982433i \(0.559752\pi\)
\(164\) 2.34410e31 0.179780
\(165\) 1.34953e32 0.947687
\(166\) −1.15268e32 −0.741551
\(167\) 1.74608e32 1.02962 0.514808 0.857305i \(-0.327863\pi\)
0.514808 + 0.857305i \(0.327863\pi\)
\(168\) −3.81714e32 −2.06421
\(169\) −1.64446e32 −0.815953
\(170\) 1.62762e31 0.0741384
\(171\) 8.22040e31 0.343914
\(172\) 3.77081e31 0.144968
\(173\) 4.75360e31 0.168017 0.0840086 0.996465i \(-0.473228\pi\)
0.0840086 + 0.996465i \(0.473228\pi\)
\(174\) 1.46354e32 0.475816
\(175\) 1.77457e32 0.530935
\(176\) 1.37034e32 0.377481
\(177\) 5.59197e31 0.141890
\(178\) −1.12969e32 −0.264162
\(179\) −6.60198e32 −1.42333 −0.711664 0.702520i \(-0.752058\pi\)
−0.711664 + 0.702520i \(0.752058\pi\)
\(180\) 5.79301e31 0.115200
\(181\) 5.34310e32 0.980515 0.490257 0.871578i \(-0.336903\pi\)
0.490257 + 0.871578i \(0.336903\pi\)
\(182\) 3.17079e32 0.537196
\(183\) −5.89263e32 −0.922079
\(184\) −2.27497e32 −0.328941
\(185\) −2.22708e32 −0.297677
\(186\) −6.16187e32 −0.761683
\(187\) −1.04291e32 −0.119274
\(188\) 6.09683e32 0.645379
\(189\) 1.32393e33 1.29768
\(190\) 7.30915e32 0.663651
\(191\) −9.58754e32 −0.806721 −0.403360 0.915041i \(-0.632158\pi\)
−0.403360 + 0.915041i \(0.632158\pi\)
\(192\) 1.43803e33 1.12176
\(193\) 7.81683e31 0.0565522 0.0282761 0.999600i \(-0.490998\pi\)
0.0282761 + 0.999600i \(0.490998\pi\)
\(194\) −1.65976e33 −1.11409
\(195\) −6.53291e32 −0.407010
\(196\) −1.32722e33 −0.767770
\(197\) −5.60393e32 −0.301115 −0.150557 0.988601i \(-0.548107\pi\)
−0.150557 + 0.988601i \(0.548107\pi\)
\(198\) 4.84354e32 0.241834
\(199\) 8.91542e32 0.413783 0.206891 0.978364i \(-0.433665\pi\)
0.206891 + 0.978364i \(0.433665\pi\)
\(200\) −7.97508e32 −0.344192
\(201\) 1.23095e33 0.494194
\(202\) −8.12179e32 −0.303429
\(203\) 2.63211e33 0.915402
\(204\) −1.83903e32 −0.0595596
\(205\) 1.13339e33 0.341939
\(206\) 2.34116e33 0.658198
\(207\) −3.74329e32 −0.0981032
\(208\) −6.63367e32 −0.162120
\(209\) −4.68340e33 −1.06768
\(210\) −5.58456e33 −1.18798
\(211\) 1.07645e33 0.213746 0.106873 0.994273i \(-0.465916\pi\)
0.106873 + 0.994273i \(0.465916\pi\)
\(212\) 3.37412e33 0.625592
\(213\) −3.46373e33 −0.599846
\(214\) 8.17713e33 1.32313
\(215\) 1.82322e33 0.275728
\(216\) −5.94986e33 −0.841254
\(217\) −1.10819e34 −1.46537
\(218\) 9.30735e33 1.15135
\(219\) 1.38345e34 1.60149
\(220\) −3.30045e33 −0.357638
\(221\) 5.04861e32 0.0512253
\(222\) −3.28350e33 −0.312046
\(223\) −3.94073e33 −0.350878 −0.175439 0.984490i \(-0.556134\pi\)
−0.175439 + 0.984490i \(0.556134\pi\)
\(224\) 1.58459e34 1.32227
\(225\) −1.31224e33 −0.102652
\(226\) −1.38676e34 −1.01725
\(227\) −2.60531e34 −1.79260 −0.896302 0.443445i \(-0.853756\pi\)
−0.896302 + 0.443445i \(0.853756\pi\)
\(228\) −8.25853e33 −0.533148
\(229\) 1.02479e34 0.620898 0.310449 0.950590i \(-0.399521\pi\)
0.310449 + 0.950590i \(0.399521\pi\)
\(230\) −3.32833e33 −0.189310
\(231\) 3.57836e34 1.91122
\(232\) −1.18290e34 −0.593432
\(233\) 1.94574e34 0.917113 0.458557 0.888665i \(-0.348367\pi\)
0.458557 + 0.888665i \(0.348367\pi\)
\(234\) −2.34470e33 −0.103862
\(235\) 2.94786e34 1.22751
\(236\) −1.36759e33 −0.0535465
\(237\) −3.74981e34 −1.38089
\(238\) 4.31573e33 0.149516
\(239\) −4.56285e34 −1.48753 −0.743766 0.668440i \(-0.766963\pi\)
−0.743766 + 0.668440i \(0.766963\pi\)
\(240\) 1.16835e34 0.358518
\(241\) 2.90791e34 0.840107 0.420053 0.907499i \(-0.362011\pi\)
0.420053 + 0.907499i \(0.362011\pi\)
\(242\) 6.04870e31 0.00164566
\(243\) −2.42245e34 −0.620817
\(244\) 1.44112e34 0.347974
\(245\) −6.41724e34 −1.46029
\(246\) 1.67101e34 0.358444
\(247\) 2.26718e34 0.458543
\(248\) 4.98030e34 0.949963
\(249\) 6.29721e34 1.13307
\(250\) −4.82401e34 −0.818990
\(251\) −1.72418e34 −0.276256 −0.138128 0.990414i \(-0.544109\pi\)
−0.138128 + 0.990414i \(0.544109\pi\)
\(252\) 1.53605e34 0.232326
\(253\) 2.13266e34 0.304561
\(254\) −3.38083e33 −0.0455968
\(255\) −8.89186e33 −0.113282
\(256\) −8.48339e34 −1.02115
\(257\) 4.22826e33 0.0480985 0.0240493 0.999711i \(-0.492344\pi\)
0.0240493 + 0.999711i \(0.492344\pi\)
\(258\) 2.68806e34 0.289037
\(259\) −5.90524e34 −0.600331
\(260\) 1.59771e34 0.153597
\(261\) −1.94636e34 −0.176985
\(262\) 4.04865e34 0.348290
\(263\) −3.28330e34 −0.267271 −0.133635 0.991031i \(-0.542665\pi\)
−0.133635 + 0.991031i \(0.542665\pi\)
\(264\) −1.60815e35 −1.23899
\(265\) 1.63142e35 1.18987
\(266\) 1.93806e35 1.33840
\(267\) 6.17164e34 0.403633
\(268\) −3.01045e34 −0.186499
\(269\) 2.79966e35 1.64322 0.821612 0.570048i \(-0.193075\pi\)
0.821612 + 0.570048i \(0.193075\pi\)
\(270\) −8.70477e34 −0.484153
\(271\) −3.70768e35 −1.95455 −0.977277 0.211965i \(-0.932014\pi\)
−0.977277 + 0.211965i \(0.932014\pi\)
\(272\) −9.02901e33 −0.0451223
\(273\) −1.73224e35 −0.820823
\(274\) −2.21394e35 −0.994907
\(275\) 7.47620e34 0.318681
\(276\) 3.76065e34 0.152083
\(277\) 3.33125e35 1.27835 0.639176 0.769060i \(-0.279275\pi\)
0.639176 + 0.769060i \(0.279275\pi\)
\(278\) −1.99700e35 −0.727324
\(279\) 8.19470e34 0.283317
\(280\) 4.51370e35 1.48163
\(281\) −5.19345e35 −1.61888 −0.809440 0.587203i \(-0.800229\pi\)
−0.809440 + 0.587203i \(0.800229\pi\)
\(282\) 4.34618e35 1.28676
\(283\) −1.04587e34 −0.0294154 −0.0147077 0.999892i \(-0.504682\pi\)
−0.0147077 + 0.999892i \(0.504682\pi\)
\(284\) 8.47100e34 0.226370
\(285\) −3.99307e35 −1.01404
\(286\) 1.33585e35 0.322440
\(287\) 3.00526e35 0.689595
\(288\) −1.17175e35 −0.255650
\(289\) −4.75097e35 −0.985743
\(290\) −1.73060e35 −0.341528
\(291\) 9.06744e35 1.70230
\(292\) −3.38341e35 −0.604371
\(293\) −3.74269e35 −0.636214 −0.318107 0.948055i \(-0.603047\pi\)
−0.318107 + 0.948055i \(0.603047\pi\)
\(294\) −9.46125e35 −1.53078
\(295\) −6.61240e34 −0.101845
\(296\) 2.65387e35 0.389180
\(297\) 5.57766e35 0.778904
\(298\) 1.00119e36 1.33163
\(299\) −1.03240e35 −0.130802
\(300\) 1.31832e35 0.159134
\(301\) 4.83437e35 0.556065
\(302\) −8.85597e35 −0.970813
\(303\) 4.43702e35 0.463632
\(304\) −4.05465e35 −0.403912
\(305\) 6.96792e35 0.661844
\(306\) −3.19135e34 −0.0289077
\(307\) −5.37563e35 −0.464433 −0.232217 0.972664i \(-0.574598\pi\)
−0.232217 + 0.972664i \(0.574598\pi\)
\(308\) −8.75133e35 −0.721255
\(309\) −1.27900e36 −1.00571
\(310\) 7.28629e35 0.546716
\(311\) −4.11459e35 −0.294646 −0.147323 0.989088i \(-0.547066\pi\)
−0.147323 + 0.989088i \(0.547066\pi\)
\(312\) 7.78486e35 0.532119
\(313\) −1.66582e36 −1.08702 −0.543508 0.839404i \(-0.682904\pi\)
−0.543508 + 0.839404i \(0.682904\pi\)
\(314\) 1.62375e35 0.101167
\(315\) 7.42693e35 0.441882
\(316\) 9.17065e35 0.521120
\(317\) 2.49069e36 1.35195 0.675975 0.736925i \(-0.263723\pi\)
0.675975 + 0.736925i \(0.263723\pi\)
\(318\) 2.40528e36 1.24730
\(319\) 1.10890e36 0.549449
\(320\) −1.70044e36 −0.805170
\(321\) −4.46726e36 −2.02171
\(322\) −8.82527e35 −0.381784
\(323\) 3.08583e35 0.127625
\(324\) 1.33656e36 0.528549
\(325\) −3.61914e35 −0.136866
\(326\) 7.76421e35 0.280829
\(327\) −5.08471e36 −1.75923
\(328\) −1.35059e36 −0.447047
\(329\) 7.81644e36 2.47553
\(330\) −2.35276e36 −0.713058
\(331\) 1.70323e36 0.494046 0.247023 0.969010i \(-0.420548\pi\)
0.247023 + 0.969010i \(0.420548\pi\)
\(332\) −1.54006e36 −0.427599
\(333\) 4.36674e35 0.116069
\(334\) −3.04410e36 −0.774703
\(335\) −1.45557e36 −0.354719
\(336\) 3.09796e36 0.723030
\(337\) 1.36026e36 0.304080 0.152040 0.988374i \(-0.451416\pi\)
0.152040 + 0.988374i \(0.451416\pi\)
\(338\) 2.86693e36 0.613939
\(339\) 7.57600e36 1.55433
\(340\) 2.17462e35 0.0427503
\(341\) −4.66876e36 −0.879555
\(342\) −1.43314e36 −0.258767
\(343\) −7.40016e36 −1.28078
\(344\) −2.17261e36 −0.360483
\(345\) 1.81831e36 0.289261
\(346\) −8.28738e35 −0.126419
\(347\) −6.83587e36 −1.00004 −0.500019 0.866015i \(-0.666674\pi\)
−0.500019 + 0.866015i \(0.666674\pi\)
\(348\) 1.95539e36 0.274369
\(349\) 4.60521e36 0.619842 0.309921 0.950762i \(-0.399697\pi\)
0.309921 + 0.950762i \(0.399697\pi\)
\(350\) −3.09377e36 −0.399485
\(351\) −2.70008e36 −0.334521
\(352\) 6.67582e36 0.793663
\(353\) 1.14489e37 1.30627 0.653134 0.757243i \(-0.273454\pi\)
0.653134 + 0.757243i \(0.273454\pi\)
\(354\) −9.74899e35 −0.106761
\(355\) 4.09580e36 0.430554
\(356\) −1.50935e36 −0.152323
\(357\) −2.35773e36 −0.228457
\(358\) 1.15098e37 1.07094
\(359\) −1.33540e37 −1.19328 −0.596638 0.802510i \(-0.703497\pi\)
−0.596638 + 0.802510i \(0.703497\pi\)
\(360\) −3.33774e36 −0.286461
\(361\) 1.72772e36 0.142436
\(362\) −9.31511e36 −0.737758
\(363\) −3.30447e34 −0.00251453
\(364\) 4.23642e36 0.309762
\(365\) −1.63591e37 −1.14951
\(366\) 1.02732e37 0.693790
\(367\) −1.51022e37 −0.980353 −0.490177 0.871623i \(-0.663068\pi\)
−0.490177 + 0.871623i \(0.663068\pi\)
\(368\) 1.84635e36 0.115218
\(369\) −2.22229e36 −0.133327
\(370\) 3.88267e36 0.223978
\(371\) 4.32580e37 2.39963
\(372\) −8.23271e36 −0.439208
\(373\) −1.09297e36 −0.0560828 −0.0280414 0.999607i \(-0.508927\pi\)
−0.0280414 + 0.999607i \(0.508927\pi\)
\(374\) 1.81820e36 0.0897437
\(375\) 2.63541e37 1.25140
\(376\) −3.51279e37 −1.60483
\(377\) −5.36806e36 −0.235976
\(378\) −2.30812e37 −0.976400
\(379\) 1.45750e37 0.593392 0.296696 0.954972i \(-0.404115\pi\)
0.296696 + 0.954972i \(0.404115\pi\)
\(380\) 9.76556e36 0.382679
\(381\) 1.84699e36 0.0696709
\(382\) 1.67148e37 0.606992
\(383\) −5.82118e36 −0.203530 −0.101765 0.994808i \(-0.532449\pi\)
−0.101765 + 0.994808i \(0.532449\pi\)
\(384\) 2.06210e36 0.0694235
\(385\) −4.23134e37 −1.37182
\(386\) −1.36278e36 −0.0425510
\(387\) −3.57486e36 −0.107510
\(388\) −2.21756e37 −0.642414
\(389\) −6.42121e36 −0.179204 −0.0896020 0.995978i \(-0.528560\pi\)
−0.0896020 + 0.995978i \(0.528560\pi\)
\(390\) 1.13894e37 0.306242
\(391\) −1.40518e36 −0.0364057
\(392\) 7.64702e37 1.90917
\(393\) −2.21182e37 −0.532180
\(394\) 9.76983e36 0.226564
\(395\) 4.43408e37 0.991165
\(396\) 6.47133e36 0.139448
\(397\) 6.76912e37 1.40627 0.703137 0.711054i \(-0.251782\pi\)
0.703137 + 0.711054i \(0.251782\pi\)
\(398\) −1.55431e37 −0.311338
\(399\) −1.05879e38 −2.04504
\(400\) 6.47251e36 0.120560
\(401\) −8.28993e37 −1.48922 −0.744608 0.667502i \(-0.767364\pi\)
−0.744608 + 0.667502i \(0.767364\pi\)
\(402\) −2.14603e37 −0.371841
\(403\) 2.26009e37 0.377748
\(404\) −1.08513e37 −0.174965
\(405\) 6.46236e37 1.00529
\(406\) −4.58880e37 −0.688766
\(407\) −2.48786e37 −0.360335
\(408\) 1.05959e37 0.148103
\(409\) 2.19435e37 0.296018 0.148009 0.988986i \(-0.452714\pi\)
0.148009 + 0.988986i \(0.452714\pi\)
\(410\) −1.97594e37 −0.257282
\(411\) 1.20950e38 1.52019
\(412\) 3.12796e37 0.379535
\(413\) −1.75332e37 −0.205393
\(414\) 6.52601e36 0.0738147
\(415\) −7.44633e37 −0.813289
\(416\) −3.23169e37 −0.340860
\(417\) 1.09098e38 1.11133
\(418\) 8.16500e37 0.803341
\(419\) −1.94941e37 −0.185268 −0.0926338 0.995700i \(-0.529529\pi\)
−0.0926338 + 0.995700i \(0.529529\pi\)
\(420\) −7.46138e37 −0.685022
\(421\) −3.14435e37 −0.278895 −0.139447 0.990229i \(-0.544533\pi\)
−0.139447 + 0.990229i \(0.544533\pi\)
\(422\) −1.87667e37 −0.160827
\(423\) −5.78001e37 −0.478623
\(424\) −1.94406e38 −1.55562
\(425\) −4.92597e36 −0.0380936
\(426\) 6.03863e37 0.451336
\(427\) 1.84759e38 1.33475
\(428\) 1.09253e38 0.762951
\(429\) −7.29787e37 −0.492680
\(430\) −3.17858e37 −0.207463
\(431\) −2.71956e38 −1.71624 −0.858120 0.513449i \(-0.828367\pi\)
−0.858120 + 0.513449i \(0.828367\pi\)
\(432\) 4.82886e37 0.294666
\(433\) 1.20292e38 0.709842 0.354921 0.934896i \(-0.384508\pi\)
0.354921 + 0.934896i \(0.384508\pi\)
\(434\) 1.93200e38 1.10257
\(435\) 9.45448e37 0.521847
\(436\) 1.24353e38 0.663900
\(437\) −6.31025e37 −0.325886
\(438\) −2.41190e38 −1.20499
\(439\) −6.48441e37 −0.313426 −0.156713 0.987644i \(-0.550090\pi\)
−0.156713 + 0.987644i \(0.550090\pi\)
\(440\) 1.90161e38 0.889317
\(441\) 1.25826e38 0.569390
\(442\) −8.80171e36 −0.0385429
\(443\) −1.25901e38 −0.533550 −0.266775 0.963759i \(-0.585958\pi\)
−0.266775 + 0.963759i \(0.585958\pi\)
\(444\) −4.38699e37 −0.179934
\(445\) −7.29785e37 −0.289717
\(446\) 6.87022e37 0.264007
\(447\) −5.46963e38 −2.03469
\(448\) −4.50883e38 −1.62380
\(449\) 4.32701e38 1.50874 0.754372 0.656447i \(-0.227941\pi\)
0.754372 + 0.656447i \(0.227941\pi\)
\(450\) 2.28774e37 0.0772370
\(451\) 1.26610e38 0.413914
\(452\) −1.85281e38 −0.586575
\(453\) 4.83812e38 1.48338
\(454\) 4.54207e38 1.34879
\(455\) 2.04834e38 0.589165
\(456\) 4.75829e38 1.32575
\(457\) −5.34446e38 −1.44251 −0.721255 0.692670i \(-0.756434\pi\)
−0.721255 + 0.692670i \(0.756434\pi\)
\(458\) −1.78661e38 −0.467176
\(459\) −3.67505e37 −0.0931063
\(460\) −4.44690e37 −0.109161
\(461\) −2.70831e38 −0.644220 −0.322110 0.946702i \(-0.604392\pi\)
−0.322110 + 0.946702i \(0.604392\pi\)
\(462\) −6.23847e38 −1.43804
\(463\) 5.36275e38 1.19802 0.599009 0.800742i \(-0.295561\pi\)
0.599009 + 0.800742i \(0.295561\pi\)
\(464\) 9.60030e37 0.207862
\(465\) −3.98058e38 −0.835370
\(466\) −3.39218e38 −0.690054
\(467\) 9.88390e38 1.94910 0.974549 0.224177i \(-0.0719693\pi\)
0.974549 + 0.224177i \(0.0719693\pi\)
\(468\) −3.13270e37 −0.0598899
\(469\) −3.85954e38 −0.715368
\(470\) −5.13928e38 −0.923599
\(471\) −8.87071e37 −0.154581
\(472\) 7.87958e37 0.133151
\(473\) 2.03670e38 0.333765
\(474\) 6.53739e38 1.03901
\(475\) −2.21210e38 −0.340995
\(476\) 5.76614e37 0.0862152
\(477\) −3.19879e38 −0.463948
\(478\) 7.95483e38 1.11925
\(479\) −1.66145e38 −0.226789 −0.113395 0.993550i \(-0.536172\pi\)
−0.113395 + 0.993550i \(0.536172\pi\)
\(480\) 5.69180e38 0.753793
\(481\) 1.20434e38 0.154756
\(482\) −5.06963e38 −0.632112
\(483\) 4.82135e38 0.583358
\(484\) 8.08152e35 0.000948932 0
\(485\) −1.07221e39 −1.22187
\(486\) 4.22328e38 0.467115
\(487\) −5.21209e38 −0.559554 −0.279777 0.960065i \(-0.590260\pi\)
−0.279777 + 0.960065i \(0.590260\pi\)
\(488\) −8.30323e38 −0.865286
\(489\) −4.24167e38 −0.429100
\(490\) 1.11878e39 1.09875
\(491\) −6.08070e38 −0.579791 −0.289896 0.957058i \(-0.593621\pi\)
−0.289896 + 0.957058i \(0.593621\pi\)
\(492\) 2.23260e38 0.206689
\(493\) −7.30640e37 −0.0656785
\(494\) −3.95258e38 −0.345017
\(495\) 3.12894e38 0.265230
\(496\) −4.04197e38 −0.332743
\(497\) 1.08602e39 0.868305
\(498\) −1.09785e39 −0.852545
\(499\) 1.92541e39 1.45233 0.726165 0.687521i \(-0.241301\pi\)
0.726165 + 0.687521i \(0.241301\pi\)
\(500\) −6.44524e38 −0.472252
\(501\) 1.66303e39 1.18373
\(502\) 3.00591e38 0.207861
\(503\) 1.47205e39 0.988981 0.494490 0.869183i \(-0.335355\pi\)
0.494490 + 0.869183i \(0.335355\pi\)
\(504\) −8.85021e38 −0.577711
\(505\) −5.24669e38 −0.332783
\(506\) −3.71806e38 −0.229157
\(507\) −1.56624e39 −0.938084
\(508\) −4.51704e37 −0.0262924
\(509\) 9.86933e37 0.0558316 0.0279158 0.999610i \(-0.491113\pi\)
0.0279158 + 0.999610i \(0.491113\pi\)
\(510\) 1.55020e38 0.0852354
\(511\) −4.33771e39 −2.31823
\(512\) 1.36275e39 0.707948
\(513\) −1.65035e39 −0.833441
\(514\) −7.37152e37 −0.0361903
\(515\) 1.51239e39 0.721872
\(516\) 3.59145e38 0.166667
\(517\) 3.29304e39 1.48588
\(518\) 1.02951e39 0.451701
\(519\) 4.52749e38 0.193166
\(520\) −9.20545e38 −0.381941
\(521\) 1.36208e39 0.549613 0.274806 0.961500i \(-0.411386\pi\)
0.274806 + 0.961500i \(0.411386\pi\)
\(522\) 3.39327e38 0.133167
\(523\) −3.92619e39 −1.49864 −0.749320 0.662208i \(-0.769619\pi\)
−0.749320 + 0.662208i \(0.769619\pi\)
\(524\) 5.40930e38 0.200834
\(525\) 1.69016e39 0.610404
\(526\) 5.72407e38 0.201100
\(527\) 3.07618e38 0.105138
\(528\) 1.30516e39 0.433982
\(529\) −2.80371e39 −0.907039
\(530\) −2.84419e39 −0.895281
\(531\) 1.29652e38 0.0397109
\(532\) 2.58940e39 0.771756
\(533\) −6.12906e38 −0.177766
\(534\) −1.07596e39 −0.303701
\(535\) 5.28245e39 1.45113
\(536\) 1.73452e39 0.463756
\(537\) −6.28794e39 −1.63637
\(538\) −4.88089e39 −1.23639
\(539\) −7.16866e39 −1.76767
\(540\) −1.16302e39 −0.279176
\(541\) 3.64331e39 0.851405 0.425702 0.904863i \(-0.360027\pi\)
0.425702 + 0.904863i \(0.360027\pi\)
\(542\) 6.46394e39 1.47064
\(543\) 5.08895e39 1.12728
\(544\) −4.39861e38 −0.0948706
\(545\) 6.01257e39 1.26273
\(546\) 3.01997e39 0.617603
\(547\) −9.64716e38 −0.192125 −0.0960624 0.995375i \(-0.530625\pi\)
−0.0960624 + 0.995375i \(0.530625\pi\)
\(548\) −2.95799e39 −0.573691
\(549\) −1.36623e39 −0.258063
\(550\) −1.30339e39 −0.239782
\(551\) −3.28108e39 −0.587921
\(552\) −2.16676e39 −0.378176
\(553\) 1.17572e40 1.99890
\(554\) −5.80767e39 −0.961857
\(555\) −2.12115e39 −0.342233
\(556\) −2.66814e39 −0.419395
\(557\) −4.34857e39 −0.665956 −0.332978 0.942935i \(-0.608054\pi\)
−0.332978 + 0.942935i \(0.608054\pi\)
\(558\) −1.42866e39 −0.213173
\(559\) −9.85944e38 −0.143345
\(560\) −3.66328e39 −0.518972
\(561\) −9.93305e38 −0.137126
\(562\) 9.05422e39 1.21808
\(563\) −5.22292e39 −0.684765 −0.342382 0.939561i \(-0.611234\pi\)
−0.342382 + 0.939561i \(0.611234\pi\)
\(564\) 5.80682e39 0.741979
\(565\) −8.95848e39 −1.11566
\(566\) 1.82336e38 0.0221327
\(567\) 1.71353e40 2.02740
\(568\) −4.88070e39 −0.562900
\(569\) 8.52031e39 0.957916 0.478958 0.877838i \(-0.341015\pi\)
0.478958 + 0.877838i \(0.341015\pi\)
\(570\) 6.96148e39 0.762985
\(571\) 8.06636e38 0.0861894 0.0430947 0.999071i \(-0.486278\pi\)
0.0430947 + 0.999071i \(0.486278\pi\)
\(572\) 1.78479e39 0.185928
\(573\) −9.13149e39 −0.927470
\(574\) −5.23933e39 −0.518864
\(575\) 1.00732e39 0.0972706
\(576\) 3.33413e39 0.313948
\(577\) −1.60079e40 −1.46989 −0.734947 0.678125i \(-0.762793\pi\)
−0.734947 + 0.678125i \(0.762793\pi\)
\(578\) 8.28280e39 0.741691
\(579\) 7.44501e38 0.0650169
\(580\) −2.31221e39 −0.196935
\(581\) −1.97444e40 −1.64017
\(582\) −1.58081e40 −1.28084
\(583\) 1.82244e40 1.44032
\(584\) 1.94941e40 1.50285
\(585\) −1.51468e39 −0.113910
\(586\) 6.52496e39 0.478699
\(587\) −7.25470e39 −0.519239 −0.259619 0.965711i \(-0.583597\pi\)
−0.259619 + 0.965711i \(0.583597\pi\)
\(588\) −1.26409e40 −0.882689
\(589\) 1.38142e40 0.941140
\(590\) 1.15280e39 0.0766302
\(591\) −5.33737e39 −0.346185
\(592\) −2.15386e39 −0.136318
\(593\) 4.67095e39 0.288478 0.144239 0.989543i \(-0.453927\pi\)
0.144239 + 0.989543i \(0.453927\pi\)
\(594\) −9.72404e39 −0.586062
\(595\) 2.78797e39 0.163981
\(596\) 1.33767e40 0.767853
\(597\) 8.49135e39 0.475717
\(598\) 1.79987e39 0.0984178
\(599\) 3.02320e40 1.61353 0.806766 0.590871i \(-0.201216\pi\)
0.806766 + 0.590871i \(0.201216\pi\)
\(600\) −7.59574e39 −0.395710
\(601\) −1.75696e40 −0.893476 −0.446738 0.894665i \(-0.647414\pi\)
−0.446738 + 0.894665i \(0.647414\pi\)
\(602\) −8.42819e39 −0.418394
\(603\) 2.85401e39 0.138310
\(604\) −1.18322e40 −0.559798
\(605\) 3.90748e37 0.00180486
\(606\) −7.73546e39 −0.348846
\(607\) −2.78325e40 −1.22551 −0.612755 0.790273i \(-0.709939\pi\)
−0.612755 + 0.790273i \(0.709939\pi\)
\(608\) −1.97528e40 −0.849234
\(609\) 2.50691e40 1.05242
\(610\) −1.21478e40 −0.497984
\(611\) −1.59412e40 −0.638152
\(612\) −4.26387e38 −0.0166690
\(613\) 2.63728e40 1.00688 0.503441 0.864030i \(-0.332067\pi\)
0.503441 + 0.864030i \(0.332067\pi\)
\(614\) 9.37183e39 0.349448
\(615\) 1.07948e40 0.393120
\(616\) 5.04222e40 1.79350
\(617\) 9.21532e38 0.0320166 0.0160083 0.999872i \(-0.494904\pi\)
0.0160083 + 0.999872i \(0.494904\pi\)
\(618\) 2.22980e40 0.756716
\(619\) −4.42763e40 −1.46777 −0.733883 0.679276i \(-0.762294\pi\)
−0.733883 + 0.679276i \(0.762294\pi\)
\(620\) 9.73502e39 0.315252
\(621\) 7.51514e39 0.237744
\(622\) 7.17333e39 0.221697
\(623\) −1.93507e40 −0.584278
\(624\) −6.31813e39 −0.186385
\(625\) −2.00947e40 −0.579189
\(626\) 2.90418e40 0.817891
\(627\) −4.46063e40 −1.22749
\(628\) 2.16945e39 0.0583356
\(629\) 1.63922e39 0.0430727
\(630\) −1.29480e40 −0.332480
\(631\) 4.23643e40 1.06310 0.531551 0.847026i \(-0.321609\pi\)
0.531551 + 0.847026i \(0.321609\pi\)
\(632\) −5.28382e40 −1.29584
\(633\) 1.02525e40 0.245739
\(634\) −4.34225e40 −1.01723
\(635\) −2.18403e39 −0.0500079
\(636\) 3.21363e40 0.719229
\(637\) 3.47026e40 0.759172
\(638\) −1.93325e40 −0.413416
\(639\) −8.03081e39 −0.167879
\(640\) −2.43839e39 −0.0498303
\(641\) −4.13775e40 −0.826652 −0.413326 0.910583i \(-0.635633\pi\)
−0.413326 + 0.910583i \(0.635633\pi\)
\(642\) 7.78818e40 1.52117
\(643\) 9.84722e40 1.88042 0.940209 0.340598i \(-0.110630\pi\)
0.940209 + 0.340598i \(0.110630\pi\)
\(644\) −1.17912e40 −0.220147
\(645\) 1.73649e40 0.316998
\(646\) −5.37981e39 −0.0960275
\(647\) −6.78001e39 −0.118336 −0.0591682 0.998248i \(-0.518845\pi\)
−0.0591682 + 0.998248i \(0.518845\pi\)
\(648\) −7.70079e40 −1.31431
\(649\) −7.38667e39 −0.123282
\(650\) 6.30957e39 0.102981
\(651\) −1.05548e41 −1.68470
\(652\) 1.03736e40 0.161934
\(653\) 3.23913e40 0.494524 0.247262 0.968949i \(-0.420469\pi\)
0.247262 + 0.968949i \(0.420469\pi\)
\(654\) 8.86464e40 1.32368
\(655\) 2.61544e40 0.381984
\(656\) 1.09613e40 0.156587
\(657\) 3.20760e40 0.448211
\(658\) −1.36271e41 −1.86264
\(659\) −1.40926e40 −0.188431 −0.0942156 0.995552i \(-0.530034\pi\)
−0.0942156 + 0.995552i \(0.530034\pi\)
\(660\) −3.14346e40 −0.411169
\(661\) −9.56737e40 −1.22425 −0.612127 0.790759i \(-0.709686\pi\)
−0.612127 + 0.790759i \(0.709686\pi\)
\(662\) −2.96940e40 −0.371730
\(663\) 4.80847e39 0.0588926
\(664\) 8.87333e40 1.06328
\(665\) 1.25199e41 1.46787
\(666\) −7.61293e39 −0.0873324
\(667\) 1.49409e40 0.167708
\(668\) −4.06714e40 −0.446715
\(669\) −3.75328e40 −0.403397
\(670\) 2.53764e40 0.266898
\(671\) 7.78382e40 0.801154
\(672\) 1.50922e41 1.52019
\(673\) −1.43434e40 −0.141394 −0.0706972 0.997498i \(-0.522522\pi\)
−0.0706972 + 0.997498i \(0.522522\pi\)
\(674\) −2.37146e40 −0.228796
\(675\) 2.63449e40 0.248766
\(676\) 3.83043e40 0.354014
\(677\) 8.89678e40 0.804817 0.402408 0.915460i \(-0.368173\pi\)
0.402408 + 0.915460i \(0.368173\pi\)
\(678\) −1.32079e41 −1.16951
\(679\) −2.84302e41 −2.46416
\(680\) −1.25294e40 −0.106305
\(681\) −2.48138e41 −2.06092
\(682\) 8.13947e40 0.661794
\(683\) 1.49228e41 1.18782 0.593910 0.804531i \(-0.297583\pi\)
0.593910 + 0.804531i \(0.297583\pi\)
\(684\) −1.91478e40 −0.149212
\(685\) −1.43021e41 −1.09116
\(686\) 1.29014e41 0.963687
\(687\) 9.76045e40 0.713834
\(688\) 1.76328e40 0.126266
\(689\) −8.82224e40 −0.618586
\(690\) −3.17002e40 −0.217645
\(691\) 2.54015e41 1.70776 0.853880 0.520469i \(-0.174243\pi\)
0.853880 + 0.520469i \(0.174243\pi\)
\(692\) −1.10725e40 −0.0728969
\(693\) 8.29658e40 0.534893
\(694\) 1.19176e41 0.752447
\(695\) −1.29007e41 −0.797686
\(696\) −1.12663e41 −0.682257
\(697\) −8.34219e39 −0.0494772
\(698\) −8.02868e40 −0.466381
\(699\) 1.85318e41 1.05439
\(700\) −4.13350e40 −0.230354
\(701\) −1.56415e40 −0.0853824 −0.0426912 0.999088i \(-0.513593\pi\)
−0.0426912 + 0.999088i \(0.513593\pi\)
\(702\) 4.70729e40 0.251700
\(703\) 7.36123e40 0.385565
\(704\) −1.89955e41 −0.974649
\(705\) 2.80765e41 1.41124
\(706\) −1.99600e41 −0.982860
\(707\) −1.39119e41 −0.671129
\(708\) −1.30254e40 −0.0615613
\(709\) −7.96882e40 −0.368998 −0.184499 0.982833i \(-0.559066\pi\)
−0.184499 + 0.982833i \(0.559066\pi\)
\(710\) −7.14057e40 −0.323957
\(711\) −8.69411e40 −0.386470
\(712\) 8.69638e40 0.378773
\(713\) −6.29051e40 −0.268465
\(714\) 4.11045e40 0.171896
\(715\) 8.62959e40 0.353633
\(716\) 1.53780e41 0.617533
\(717\) −4.34581e41 −1.71018
\(718\) 2.32812e41 0.897844
\(719\) 6.70217e39 0.0253306 0.0126653 0.999920i \(-0.495968\pi\)
0.0126653 + 0.999920i \(0.495968\pi\)
\(720\) 2.70888e40 0.100339
\(721\) 4.01021e41 1.45581
\(722\) −3.01209e40 −0.107171
\(723\) 2.76960e41 0.965853
\(724\) −1.24457e41 −0.425412
\(725\) 5.23765e40 0.175483
\(726\) 5.76099e38 0.00189198
\(727\) −3.08325e41 −0.992565 −0.496283 0.868161i \(-0.665302\pi\)
−0.496283 + 0.868161i \(0.665302\pi\)
\(728\) −2.44088e41 −0.770267
\(729\) 1.63080e41 0.504490
\(730\) 2.85203e41 0.864912
\(731\) −1.34196e40 −0.0398967
\(732\) 1.37257e41 0.400058
\(733\) −2.79480e41 −0.798626 −0.399313 0.916815i \(-0.630751\pi\)
−0.399313 + 0.916815i \(0.630751\pi\)
\(734\) 2.63290e41 0.737636
\(735\) −6.11199e41 −1.67887
\(736\) 8.99476e40 0.242249
\(737\) −1.62601e41 −0.429384
\(738\) 3.87432e40 0.100318
\(739\) −4.36349e41 −1.10787 −0.553936 0.832560i \(-0.686875\pi\)
−0.553936 + 0.832560i \(0.686875\pi\)
\(740\) 5.18754e40 0.129152
\(741\) 2.15934e41 0.527177
\(742\) −7.54155e41 −1.80553
\(743\) −1.06242e41 −0.249437 −0.124718 0.992192i \(-0.539803\pi\)
−0.124718 + 0.992192i \(0.539803\pi\)
\(744\) 4.74341e41 1.09215
\(745\) 6.46774e41 1.46045
\(746\) 1.90547e40 0.0421977
\(747\) 1.46004e41 0.317114
\(748\) 2.42925e40 0.0517487
\(749\) 1.40067e42 2.92651
\(750\) −4.59455e41 −0.941575
\(751\) −1.53315e41 −0.308181 −0.154091 0.988057i \(-0.549245\pi\)
−0.154091 + 0.988057i \(0.549245\pi\)
\(752\) 2.85095e41 0.562122
\(753\) −1.64216e41 −0.317606
\(754\) 9.35862e40 0.177553
\(755\) −5.72098e41 −1.06473
\(756\) −3.08382e41 −0.563019
\(757\) −1.29063e41 −0.231160 −0.115580 0.993298i \(-0.536873\pi\)
−0.115580 + 0.993298i \(0.536873\pi\)
\(758\) −2.54100e41 −0.446479
\(759\) 2.03122e41 0.350147
\(760\) −5.62659e41 −0.951586
\(761\) −1.01002e42 −1.67592 −0.837962 0.545728i \(-0.816253\pi\)
−0.837962 + 0.545728i \(0.816253\pi\)
\(762\) −3.22002e40 −0.0524217
\(763\) 1.59427e42 2.54657
\(764\) 2.23322e41 0.350008
\(765\) −2.06162e40 −0.0317042
\(766\) 1.01486e41 0.153140
\(767\) 3.57580e40 0.0529469
\(768\) −8.07987e41 −1.17400
\(769\) −8.10252e41 −1.15528 −0.577641 0.816291i \(-0.696027\pi\)
−0.577641 + 0.816291i \(0.696027\pi\)
\(770\) 7.37688e41 1.03218
\(771\) 4.02714e40 0.0552979
\(772\) −1.82077e40 −0.0245361
\(773\) 3.13830e41 0.415042 0.207521 0.978231i \(-0.433461\pi\)
0.207521 + 0.978231i \(0.433461\pi\)
\(774\) 6.23238e40 0.0808929
\(775\) −2.20519e41 −0.280912
\(776\) 1.27768e42 1.59745
\(777\) −5.62435e41 −0.690188
\(778\) 1.11947e41 0.134836
\(779\) −3.74623e41 −0.442895
\(780\) 1.52171e41 0.176588
\(781\) 4.57539e41 0.521180
\(782\) 2.44978e40 0.0273923
\(783\) 3.90758e41 0.428906
\(784\) −6.20626e41 −0.668724
\(785\) 1.04894e41 0.110954
\(786\) 3.85607e41 0.400422
\(787\) 8.07245e41 0.822947 0.411473 0.911422i \(-0.365014\pi\)
0.411473 + 0.911422i \(0.365014\pi\)
\(788\) 1.30532e41 0.130643
\(789\) −3.12712e41 −0.307276
\(790\) −7.73034e41 −0.745771
\(791\) −2.37540e42 −2.24997
\(792\) −3.72856e41 −0.346758
\(793\) −3.76805e41 −0.344077
\(794\) −1.18012e42 −1.05811
\(795\) 1.55382e42 1.36797
\(796\) −2.07667e41 −0.179526
\(797\) 2.35976e41 0.200319 0.100160 0.994971i \(-0.468065\pi\)
0.100160 + 0.994971i \(0.468065\pi\)
\(798\) 1.84588e42 1.53872
\(799\) −2.16974e41 −0.177615
\(800\) 3.15318e41 0.253480
\(801\) 1.43092e41 0.112965
\(802\) 1.44526e42 1.12051
\(803\) −1.82746e42 −1.39147
\(804\) −2.86725e41 −0.214414
\(805\) −5.70115e41 −0.418719
\(806\) −3.94022e41 −0.284225
\(807\) 2.66649e42 1.88918
\(808\) 6.25216e41 0.435076
\(809\) 2.25512e42 1.54140 0.770700 0.637198i \(-0.219907\pi\)
0.770700 + 0.637198i \(0.219907\pi\)
\(810\) −1.12664e42 −0.756403
\(811\) 8.17269e41 0.538967 0.269484 0.963005i \(-0.413147\pi\)
0.269484 + 0.963005i \(0.413147\pi\)
\(812\) −6.13098e41 −0.397162
\(813\) −3.53132e42 −2.24711
\(814\) 4.33731e41 0.271123
\(815\) 5.01570e41 0.307997
\(816\) −8.59953e40 −0.0518761
\(817\) −6.02632e41 −0.357135
\(818\) −3.82560e41 −0.222729
\(819\) −4.01627e41 −0.229724
\(820\) −2.64001e41 −0.148356
\(821\) 8.86919e39 0.00489675 0.00244838 0.999997i \(-0.499221\pi\)
0.00244838 + 0.999997i \(0.499221\pi\)
\(822\) −2.10863e42 −1.14382
\(823\) 4.50695e41 0.240207 0.120103 0.992761i \(-0.461677\pi\)
0.120103 + 0.992761i \(0.461677\pi\)
\(824\) −1.80223e42 −0.943767
\(825\) 7.12058e41 0.366381
\(826\) 3.05672e41 0.154541
\(827\) 1.64298e42 0.816211 0.408106 0.912935i \(-0.366190\pi\)
0.408106 + 0.912935i \(0.366190\pi\)
\(828\) 8.71923e40 0.0425636
\(829\) 9.28693e41 0.445483 0.222742 0.974878i \(-0.428499\pi\)
0.222742 + 0.974878i \(0.428499\pi\)
\(830\) 1.29819e42 0.611934
\(831\) 3.17280e42 1.46970
\(832\) 9.19552e41 0.418589
\(833\) 4.72333e41 0.211298
\(834\) −1.90201e42 −0.836189
\(835\) −1.96650e42 −0.849648
\(836\) 1.09090e42 0.463229
\(837\) −1.64519e42 −0.686590
\(838\) 3.39858e41 0.139399
\(839\) −1.59653e42 −0.643620 −0.321810 0.946804i \(-0.604291\pi\)
−0.321810 + 0.946804i \(0.604291\pi\)
\(840\) 4.29900e42 1.70340
\(841\) −1.79082e42 −0.697444
\(842\) 5.48183e41 0.209846
\(843\) −4.94642e42 −1.86119
\(844\) −2.50737e41 −0.0927371
\(845\) 1.85204e42 0.673332
\(846\) 1.00768e42 0.360125
\(847\) 1.03609e40 0.00363989
\(848\) 1.57778e42 0.544887
\(849\) −9.96121e40 −0.0338182
\(850\) 8.58788e40 0.0286623
\(851\) −3.35205e41 −0.109985
\(852\) 8.06806e41 0.260253
\(853\) −2.50802e42 −0.795373 −0.397686 0.917521i \(-0.630187\pi\)
−0.397686 + 0.917521i \(0.630187\pi\)
\(854\) −3.22106e42 −1.00429
\(855\) −9.25810e41 −0.283801
\(856\) −6.29476e42 −1.89719
\(857\) 4.74569e42 1.40630 0.703149 0.711043i \(-0.251777\pi\)
0.703149 + 0.711043i \(0.251777\pi\)
\(858\) 1.27230e42 0.370702
\(859\) −1.19413e42 −0.342098 −0.171049 0.985263i \(-0.554716\pi\)
−0.171049 + 0.985263i \(0.554716\pi\)
\(860\) −4.24682e41 −0.119629
\(861\) 2.86231e42 0.792812
\(862\) 4.74125e42 1.29133
\(863\) 5.51388e42 1.47673 0.738364 0.674402i \(-0.235599\pi\)
0.738364 + 0.674402i \(0.235599\pi\)
\(864\) 2.35245e42 0.619542
\(865\) −5.35367e41 −0.138649
\(866\) −2.09716e42 −0.534099
\(867\) −4.52498e42 −1.13329
\(868\) 2.58130e42 0.635774
\(869\) 4.95329e42 1.19979
\(870\) −1.64829e42 −0.392648
\(871\) 7.87134e41 0.184410
\(872\) −7.16481e42 −1.65088
\(873\) 2.10233e42 0.476424
\(874\) 1.10012e42 0.245203
\(875\) −8.26312e42 −1.81145
\(876\) −3.22248e42 −0.694833
\(877\) 3.25016e42 0.689304 0.344652 0.938731i \(-0.387997\pi\)
0.344652 + 0.938731i \(0.387997\pi\)
\(878\) 1.13049e42 0.235828
\(879\) −3.56466e42 −0.731441
\(880\) −1.54333e42 −0.311501
\(881\) 1.07364e42 0.213162 0.106581 0.994304i \(-0.466010\pi\)
0.106581 + 0.994304i \(0.466010\pi\)
\(882\) −2.19363e42 −0.428420
\(883\) 4.03526e42 0.775250 0.387625 0.921817i \(-0.373296\pi\)
0.387625 + 0.921817i \(0.373296\pi\)
\(884\) −1.17597e41 −0.0222249
\(885\) −6.29787e41 −0.117089
\(886\) 2.19495e42 0.401453
\(887\) −1.14783e42 −0.206532 −0.103266 0.994654i \(-0.532929\pi\)
−0.103266 + 0.994654i \(0.532929\pi\)
\(888\) 2.52764e42 0.447432
\(889\) −5.79108e41 −0.100852
\(890\) 1.27230e42 0.217989
\(891\) 7.21906e42 1.21690
\(892\) 9.17913e41 0.152234
\(893\) −9.74365e42 −1.58992
\(894\) 9.53571e42 1.53094
\(895\) 7.43537e42 1.17454
\(896\) −6.46554e41 −0.100494
\(897\) −9.83288e41 −0.150380
\(898\) −7.54366e42 −1.13521
\(899\) −3.27082e42 −0.484330
\(900\) 3.05659e41 0.0445370
\(901\) −1.20078e42 −0.172169
\(902\) −2.20731e42 −0.311436
\(903\) 4.60442e42 0.639296
\(904\) 1.06753e43 1.45860
\(905\) −6.01759e42 −0.809129
\(906\) −8.43472e42 −1.11612
\(907\) −1.34894e43 −1.75666 −0.878328 0.478058i \(-0.841341\pi\)
−0.878328 + 0.478058i \(0.841341\pi\)
\(908\) 6.06854e42 0.777749
\(909\) 1.02874e42 0.129757
\(910\) −3.57106e42 −0.443299
\(911\) 3.01049e42 0.367807 0.183904 0.982944i \(-0.441127\pi\)
0.183904 + 0.982944i \(0.441127\pi\)
\(912\) −3.86179e42 −0.464369
\(913\) −8.31825e42 −0.984477
\(914\) 9.31747e42 1.08537
\(915\) 6.63648e42 0.760908
\(916\) −2.38704e42 −0.269386
\(917\) 6.93499e42 0.770355
\(918\) 6.40704e41 0.0700549
\(919\) 6.28761e42 0.676723 0.338361 0.941016i \(-0.390127\pi\)
0.338361 + 0.941016i \(0.390127\pi\)
\(920\) 2.56215e42 0.271445
\(921\) −5.11993e42 −0.533949
\(922\) 4.72163e42 0.484723
\(923\) −2.21489e42 −0.223835
\(924\) −8.33506e42 −0.829211
\(925\) −1.17509e42 −0.115084
\(926\) −9.34937e42 −0.901412
\(927\) −2.96542e42 −0.281469
\(928\) 4.67692e42 0.437034
\(929\) 1.66684e43 1.53344 0.766720 0.641982i \(-0.221888\pi\)
0.766720 + 0.641982i \(0.221888\pi\)
\(930\) 6.93971e42 0.628548
\(931\) 2.12111e43 1.89144
\(932\) −4.53220e42 −0.397904
\(933\) −3.91887e42 −0.338748
\(934\) −1.72315e43 −1.46654
\(935\) 1.17456e42 0.0984256
\(936\) 1.80495e42 0.148925
\(937\) −1.87621e43 −1.52426 −0.762129 0.647425i \(-0.775846\pi\)
−0.762129 + 0.647425i \(0.775846\pi\)
\(938\) 6.72869e42 0.538257
\(939\) −1.58659e43 −1.24972
\(940\) −6.86646e42 −0.532573
\(941\) 5.14783e42 0.393165 0.196582 0.980487i \(-0.437016\pi\)
0.196582 + 0.980487i \(0.437016\pi\)
\(942\) 1.54651e42 0.116309
\(943\) 1.70590e42 0.126338
\(944\) −6.39501e41 −0.0466388
\(945\) −1.49105e43 −1.07086
\(946\) −3.55077e42 −0.251131
\(947\) −2.96240e42 −0.206333 −0.103167 0.994664i \(-0.532897\pi\)
−0.103167 + 0.994664i \(0.532897\pi\)
\(948\) 8.73443e42 0.599120
\(949\) 8.84653e42 0.597603
\(950\) 3.85656e42 0.256571
\(951\) 2.37222e43 1.55431
\(952\) −3.32225e42 −0.214386
\(953\) 1.30942e43 0.832208 0.416104 0.909317i \(-0.363395\pi\)
0.416104 + 0.909317i \(0.363395\pi\)
\(954\) 5.57674e42 0.349083
\(955\) 1.07978e43 0.665713
\(956\) 1.06282e43 0.645390
\(957\) 1.05615e43 0.631690
\(958\) 2.89656e42 0.170640
\(959\) −3.79229e43 −2.20055
\(960\) −1.61956e43 −0.925686
\(961\) −3.99088e42 −0.224688
\(962\) −2.09964e42 −0.116441
\(963\) −1.03575e43 −0.565816
\(964\) −6.77340e42 −0.364493
\(965\) −8.80359e41 −0.0466674
\(966\) −8.40549e42 −0.438929
\(967\) 2.64169e43 1.35894 0.679468 0.733706i \(-0.262211\pi\)
0.679468 + 0.733706i \(0.262211\pi\)
\(968\) −4.65630e40 −0.00235965
\(969\) 2.93905e42 0.146728
\(970\) 1.86928e43 0.919356
\(971\) −3.41602e43 −1.65517 −0.827583 0.561343i \(-0.810285\pi\)
−0.827583 + 0.561343i \(0.810285\pi\)
\(972\) 5.64261e42 0.269351
\(973\) −3.42069e43 −1.60871
\(974\) 9.08670e42 0.421019
\(975\) −3.44699e42 −0.157352
\(976\) 6.73884e42 0.303084
\(977\) 2.06179e43 0.913636 0.456818 0.889560i \(-0.348989\pi\)
0.456818 + 0.889560i \(0.348989\pi\)
\(978\) 7.39489e42 0.322863
\(979\) −8.15238e42 −0.350700
\(980\) 1.49477e43 0.633571
\(981\) −1.17891e43 −0.492358
\(982\) 1.06010e43 0.436246
\(983\) −1.21841e43 −0.494047 −0.247023 0.969009i \(-0.579452\pi\)
−0.247023 + 0.969009i \(0.579452\pi\)
\(984\) −1.28635e43 −0.513961
\(985\) 6.31134e42 0.248483
\(986\) 1.27379e42 0.0494177
\(987\) 7.44464e43 2.84607
\(988\) −5.28094e42 −0.198946
\(989\) 2.74418e42 0.101875
\(990\) −5.45497e42 −0.199564
\(991\) −1.94686e43 −0.701888 −0.350944 0.936397i \(-0.614139\pi\)
−0.350944 + 0.936397i \(0.614139\pi\)
\(992\) −1.96911e43 −0.699600
\(993\) 1.62221e43 0.567994
\(994\) −1.89337e43 −0.653329
\(995\) −1.00409e43 −0.341457
\(996\) −1.46681e43 −0.491601
\(997\) 2.12798e43 0.702891 0.351446 0.936208i \(-0.385690\pi\)
0.351446 + 0.936208i \(0.385690\pi\)
\(998\) −3.35674e43 −1.09276
\(999\) −8.76679e42 −0.281282
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 1.30.a.a.1.1 2
3.2 odd 2 9.30.a.a.1.2 2
4.3 odd 2 16.30.a.c.1.1 2
5.2 odd 4 25.30.b.a.24.2 4
5.3 odd 4 25.30.b.a.24.3 4
5.4 even 2 25.30.a.a.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.30.a.a.1.1 2 1.1 even 1 trivial
9.30.a.a.1.2 2 3.2 odd 2
16.30.a.c.1.1 2 4.3 odd 2
25.30.a.a.1.2 2 5.4 even 2
25.30.b.a.24.2 4 5.2 odd 4
25.30.b.a.24.3 4 5.3 odd 4