Properties

Label 1.36.a.a.1.3
Level $1$
Weight $36$
Character 1.1
Self dual yes
Analytic conductor $7.760$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 36 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.75951306336\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Defining polynomial: \(x^{3} - 12422194 x - 2645665785\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{12}\cdot 3^{3}\cdot 5\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(3626.53\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +O(q^{10})\) \(q+331573. q^{2} -1.54691e8 q^{3} +7.55810e10 q^{4} +2.12139e12 q^{5} -5.12913e13 q^{6} +3.96640e14 q^{7} +1.36679e16 q^{8} -2.61023e16 q^{9} +7.03395e17 q^{10} -6.82681e17 q^{11} -1.16917e19 q^{12} -1.17949e19 q^{13} +1.31515e20 q^{14} -3.28159e20 q^{15} +1.93496e21 q^{16} -1.33083e21 q^{17} -8.65483e21 q^{18} -3.58945e22 q^{19} +1.60337e23 q^{20} -6.13565e22 q^{21} -2.26359e23 q^{22} +6.92195e23 q^{23} -2.11429e24 q^{24} +1.58990e24 q^{25} -3.91088e24 q^{26} +1.17772e25 q^{27} +2.99785e25 q^{28} -5.67568e25 q^{29} -1.08809e26 q^{30} +1.02960e26 q^{31} +1.71955e26 q^{32} +1.05604e26 q^{33} -4.41267e26 q^{34} +8.41427e26 q^{35} -1.97284e27 q^{36} +4.50412e27 q^{37} -1.19017e28 q^{38} +1.82456e27 q^{39} +2.89948e28 q^{40} -6.23104e27 q^{41} -2.03442e28 q^{42} -2.75822e27 q^{43} -5.15977e28 q^{44} -5.53731e28 q^{45} +2.29513e29 q^{46} +1.41103e29 q^{47} -2.99320e29 q^{48} -2.21495e29 q^{49} +5.27167e29 q^{50} +2.05867e29 q^{51} -8.91472e29 q^{52} -2.48503e30 q^{53} +3.90500e30 q^{54} -1.44823e30 q^{55} +5.42123e30 q^{56} +5.55255e30 q^{57} -1.88190e31 q^{58} +5.47495e30 q^{59} -2.48026e31 q^{60} +2.30979e31 q^{61} +3.41386e31 q^{62} -1.03532e31 q^{63} -9.46893e30 q^{64} -2.50216e31 q^{65} +3.50156e31 q^{66} +1.55814e31 q^{67} -1.00585e32 q^{68} -1.07076e32 q^{69} +2.78995e32 q^{70} -1.13262e32 q^{71} -3.56763e32 q^{72} +3.23524e32 q^{73} +1.49345e33 q^{74} -2.45942e32 q^{75} -2.71294e33 q^{76} -2.70778e32 q^{77} +6.04976e32 q^{78} -1.44166e32 q^{79} +4.10479e33 q^{80} -5.15885e32 q^{81} -2.06605e33 q^{82} +3.50421e33 q^{83} -4.63739e33 q^{84} -2.82320e33 q^{85} -9.14551e32 q^{86} +8.77975e33 q^{87} -9.33079e33 q^{88} +9.37543e33 q^{89} -1.83602e34 q^{90} -4.67833e33 q^{91} +5.23168e34 q^{92} -1.59269e34 q^{93} +4.67858e34 q^{94} -7.61461e34 q^{95} -2.65998e34 q^{96} +3.59603e33 q^{97} -7.34419e34 q^{98} +1.78195e34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + O(q^{10}) \) \( 3q + 139656q^{2} - 104875308q^{3} + 34841262144q^{4} + 892652054010q^{5} - 4786530564384q^{6} + 878422149346056q^{7} + 22336009925337600q^{8} + 150091978876243551q^{9} + 1019870812729298160q^{10} - 1157945428549987044q^{11} - 22548891526776486144q^{12} - 62139610550998650558q^{13} + \)\(13\!\cdots\!28\)\(q^{14} + \)\(70\!\cdots\!20\)\(q^{15} + \)\(21\!\cdots\!48\)\(q^{16} - \)\(39\!\cdots\!94\)\(q^{17} - \)\(23\!\cdots\!08\)\(q^{18} - \)\(32\!\cdots\!40\)\(q^{19} + \)\(14\!\cdots\!80\)\(q^{20} + \)\(22\!\cdots\!76\)\(q^{21} + \)\(22\!\cdots\!12\)\(q^{22} - \)\(51\!\cdots\!08\)\(q^{23} - \)\(37\!\cdots\!20\)\(q^{24} + \)\(64\!\cdots\!25\)\(q^{25} + \)\(42\!\cdots\!36\)\(q^{26} + \)\(27\!\cdots\!00\)\(q^{27} + \)\(10\!\cdots\!08\)\(q^{28} - \)\(38\!\cdots\!10\)\(q^{29} - \)\(23\!\cdots\!80\)\(q^{30} + \)\(10\!\cdots\!56\)\(q^{31} - \)\(92\!\cdots\!44\)\(q^{32} + \)\(11\!\cdots\!84\)\(q^{33} - \)\(55\!\cdots\!12\)\(q^{34} + \)\(15\!\cdots\!60\)\(q^{35} - \)\(60\!\cdots\!52\)\(q^{36} + \)\(24\!\cdots\!06\)\(q^{37} - \)\(12\!\cdots\!00\)\(q^{38} + \)\(18\!\cdots\!12\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} + \)\(23\!\cdots\!06\)\(q^{41} - \)\(33\!\cdots\!88\)\(q^{42} - \)\(47\!\cdots\!08\)\(q^{43} - \)\(80\!\cdots\!12\)\(q^{44} - \)\(11\!\cdots\!30\)\(q^{45} + \)\(31\!\cdots\!56\)\(q^{46} + \)\(16\!\cdots\!56\)\(q^{47} + \)\(44\!\cdots\!92\)\(q^{48} - \)\(59\!\cdots\!21\)\(q^{49} + \)\(37\!\cdots\!00\)\(q^{50} - \)\(18\!\cdots\!04\)\(q^{51} - \)\(51\!\cdots\!44\)\(q^{52} - \)\(16\!\cdots\!58\)\(q^{53} + \)\(44\!\cdots\!60\)\(q^{54} + \)\(30\!\cdots\!20\)\(q^{55} + \)\(56\!\cdots\!40\)\(q^{56} + \)\(40\!\cdots\!00\)\(q^{57} - \)\(23\!\cdots\!00\)\(q^{58} + \)\(43\!\cdots\!80\)\(q^{59} - \)\(40\!\cdots\!40\)\(q^{60} + \)\(23\!\cdots\!06\)\(q^{61} + \)\(29\!\cdots\!12\)\(q^{62} + \)\(45\!\cdots\!92\)\(q^{63} + \)\(93\!\cdots\!84\)\(q^{64} + \)\(75\!\cdots\!20\)\(q^{65} - \)\(75\!\cdots\!68\)\(q^{66} - \)\(18\!\cdots\!44\)\(q^{67} + \)\(21\!\cdots\!08\)\(q^{68} - \)\(32\!\cdots\!48\)\(q^{69} + \)\(22\!\cdots\!60\)\(q^{70} + \)\(34\!\cdots\!56\)\(q^{71} + \)\(31\!\cdots\!00\)\(q^{72} - \)\(28\!\cdots\!58\)\(q^{73} + \)\(21\!\cdots\!08\)\(q^{74} - \)\(15\!\cdots\!00\)\(q^{75} - \)\(27\!\cdots\!20\)\(q^{76} + \)\(69\!\cdots\!12\)\(q^{77} - \)\(22\!\cdots\!16\)\(q^{78} - \)\(42\!\cdots\!60\)\(q^{79} + \)\(68\!\cdots\!60\)\(q^{80} + \)\(18\!\cdots\!63\)\(q^{81} - \)\(40\!\cdots\!88\)\(q^{82} + \)\(14\!\cdots\!92\)\(q^{83} - \)\(13\!\cdots\!52\)\(q^{84} - \)\(87\!\cdots\!40\)\(q^{85} + \)\(14\!\cdots\!96\)\(q^{86} - \)\(78\!\cdots\!00\)\(q^{87} - \)\(18\!\cdots\!00\)\(q^{88} + \)\(30\!\cdots\!70\)\(q^{89} + \)\(28\!\cdots\!20\)\(q^{90} + \)\(10\!\cdots\!96\)\(q^{91} + \)\(83\!\cdots\!56\)\(q^{92} - \)\(40\!\cdots\!16\)\(q^{93} + \)\(19\!\cdots\!68\)\(q^{94} - \)\(84\!\cdots\!00\)\(q^{95} - \)\(32\!\cdots\!84\)\(q^{96} - \)\(10\!\cdots\!94\)\(q^{97} - \)\(13\!\cdots\!92\)\(q^{98} + \)\(30\!\cdots\!52\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 331573. 1.78877 0.894385 0.447298i \(-0.147614\pi\)
0.894385 + 0.447298i \(0.147614\pi\)
\(3\) −1.54691e8 −0.691580 −0.345790 0.938312i \(-0.612389\pi\)
−0.345790 + 0.938312i \(0.612389\pi\)
\(4\) 7.55810e10 2.19970
\(5\) 2.12139e12 1.24350 0.621748 0.783217i \(-0.286423\pi\)
0.621748 + 0.783217i \(0.286423\pi\)
\(6\) −5.12913e13 −1.23708
\(7\) 3.96640e14 0.644438 0.322219 0.946665i \(-0.395571\pi\)
0.322219 + 0.946665i \(0.395571\pi\)
\(8\) 1.36679e16 2.14598
\(9\) −2.61023e16 −0.521717
\(10\) 7.03395e17 2.22433
\(11\) −6.82681e17 −0.407236 −0.203618 0.979050i \(-0.565270\pi\)
−0.203618 + 0.979050i \(0.565270\pi\)
\(12\) −1.16917e19 −1.52127
\(13\) −1.17949e19 −0.378169 −0.189085 0.981961i \(-0.560552\pi\)
−0.189085 + 0.981961i \(0.560552\pi\)
\(14\) 1.31515e20 1.15275
\(15\) −3.28159e20 −0.859977
\(16\) 1.93496e21 1.63897
\(17\) −1.33083e21 −0.390181 −0.195090 0.980785i \(-0.562500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(18\) −8.65483e21 −0.933232
\(19\) −3.58945e22 −1.50259 −0.751294 0.659967i \(-0.770570\pi\)
−0.751294 + 0.659967i \(0.770570\pi\)
\(20\) 1.60337e23 2.73532
\(21\) −6.13565e22 −0.445680
\(22\) −2.26359e23 −0.728451
\(23\) 6.92195e23 1.02327 0.511636 0.859202i \(-0.329039\pi\)
0.511636 + 0.859202i \(0.329039\pi\)
\(24\) −2.11429e24 −1.48412
\(25\) 1.58990e24 0.546284
\(26\) −3.91088e24 −0.676457
\(27\) 1.17772e25 1.05239
\(28\) 2.99785e25 1.41757
\(29\) −5.67568e25 −1.45229 −0.726144 0.687542i \(-0.758690\pi\)
−0.726144 + 0.687542i \(0.758690\pi\)
\(30\) −1.08809e26 −1.53830
\(31\) 1.02960e26 0.820043 0.410022 0.912076i \(-0.365521\pi\)
0.410022 + 0.912076i \(0.365521\pi\)
\(32\) 1.71955e26 0.785760
\(33\) 1.05604e26 0.281636
\(34\) −4.41267e26 −0.697943
\(35\) 8.41427e26 0.801356
\(36\) −1.97284e27 −1.14762
\(37\) 4.50412e27 1.62211 0.811054 0.584971i \(-0.198894\pi\)
0.811054 + 0.584971i \(0.198894\pi\)
\(38\) −1.19017e28 −2.68779
\(39\) 1.82456e27 0.261534
\(40\) 2.89948e28 2.66852
\(41\) −6.23104e27 −0.372257 −0.186129 0.982525i \(-0.559594\pi\)
−0.186129 + 0.982525i \(0.559594\pi\)
\(42\) −2.03442e28 −0.797219
\(43\) −2.75822e27 −0.0716029 −0.0358014 0.999359i \(-0.511398\pi\)
−0.0358014 + 0.999359i \(0.511398\pi\)
\(44\) −5.15977e28 −0.895795
\(45\) −5.53731e28 −0.648754
\(46\) 2.29513e29 1.83040
\(47\) 1.41103e29 0.772365 0.386182 0.922422i \(-0.373793\pi\)
0.386182 + 0.922422i \(0.373793\pi\)
\(48\) −2.99320e29 −1.13348
\(49\) −2.21495e29 −0.584700
\(50\) 5.27167e29 0.977177
\(51\) 2.05867e29 0.269841
\(52\) −8.91472e29 −0.831858
\(53\) −2.48503e30 −1.66151 −0.830755 0.556638i \(-0.812091\pi\)
−0.830755 + 0.556638i \(0.812091\pi\)
\(54\) 3.90500e30 1.88248
\(55\) −1.44823e30 −0.506396
\(56\) 5.42123e30 1.38295
\(57\) 5.55255e30 1.03916
\(58\) −1.88190e31 −2.59781
\(59\) 5.47495e30 0.560364 0.280182 0.959947i \(-0.409605\pi\)
0.280182 + 0.959947i \(0.409605\pi\)
\(60\) −2.48026e31 −1.89169
\(61\) 2.30979e31 1.31917 0.659585 0.751630i \(-0.270732\pi\)
0.659585 + 0.751630i \(0.270732\pi\)
\(62\) 3.41386e31 1.46687
\(63\) −1.03532e31 −0.336214
\(64\) −9.46893e30 −0.233427
\(65\) −2.50216e31 −0.470252
\(66\) 3.50156e31 0.503782
\(67\) 1.55814e31 0.172304 0.0861522 0.996282i \(-0.472543\pi\)
0.0861522 + 0.996282i \(0.472543\pi\)
\(68\) −1.00585e32 −0.858279
\(69\) −1.07076e32 −0.707675
\(70\) 2.78995e32 1.43344
\(71\) −1.13262e32 −0.454008 −0.227004 0.973894i \(-0.572893\pi\)
−0.227004 + 0.973894i \(0.572893\pi\)
\(72\) −3.56763e32 −1.11960
\(73\) 3.23524e32 0.797548 0.398774 0.917049i \(-0.369436\pi\)
0.398774 + 0.917049i \(0.369436\pi\)
\(74\) 1.49345e33 2.90158
\(75\) −2.45942e32 −0.377799
\(76\) −2.71294e33 −3.30524
\(77\) −2.70778e32 −0.262438
\(78\) 6.04976e32 0.467824
\(79\) −1.44166e32 −0.0892050 −0.0446025 0.999005i \(-0.514202\pi\)
−0.0446025 + 0.999005i \(0.514202\pi\)
\(80\) 4.10479e33 2.03806
\(81\) −5.15885e32 −0.206094
\(82\) −2.06605e33 −0.665882
\(83\) 3.50421e33 0.913532 0.456766 0.889587i \(-0.349008\pi\)
0.456766 + 0.889587i \(0.349008\pi\)
\(84\) −4.63739e33 −0.980361
\(85\) −2.82320e33 −0.485188
\(86\) −9.14551e32 −0.128081
\(87\) 8.77975e33 1.00437
\(88\) −9.33079e33 −0.873920
\(89\) 9.37543e33 0.720553 0.360277 0.932846i \(-0.382682\pi\)
0.360277 + 0.932846i \(0.382682\pi\)
\(90\) −1.83602e34 −1.16047
\(91\) −4.67833e33 −0.243706
\(92\) 5.23168e34 2.25089
\(93\) −1.59269e34 −0.567126
\(94\) 4.67858e34 1.38158
\(95\) −7.61461e34 −1.86846
\(96\) −2.65998e34 −0.543416
\(97\) 3.59603e33 0.0612799 0.0306399 0.999530i \(-0.490245\pi\)
0.0306399 + 0.999530i \(0.490245\pi\)
\(98\) −7.34419e34 −1.04589
\(99\) 1.78195e34 0.212462
\(100\) 1.20166e35 1.20166
\(101\) 7.27571e34 0.611296 0.305648 0.952145i \(-0.401127\pi\)
0.305648 + 0.952145i \(0.401127\pi\)
\(102\) 6.82599e34 0.482683
\(103\) 9.48038e34 0.565164 0.282582 0.959243i \(-0.408809\pi\)
0.282582 + 0.959243i \(0.408809\pi\)
\(104\) −1.61211e35 −0.811544
\(105\) −1.30161e35 −0.554202
\(106\) −8.23968e35 −2.97206
\(107\) 5.43957e35 1.66475 0.832374 0.554214i \(-0.186981\pi\)
0.832374 + 0.554214i \(0.186981\pi\)
\(108\) 8.90133e35 2.31494
\(109\) −2.19201e35 −0.485153 −0.242577 0.970132i \(-0.577993\pi\)
−0.242577 + 0.970132i \(0.577993\pi\)
\(110\) −4.80194e35 −0.905826
\(111\) −6.96746e35 −1.12182
\(112\) 7.67481e35 1.05621
\(113\) −3.57083e35 −0.420627 −0.210313 0.977634i \(-0.567448\pi\)
−0.210313 + 0.977634i \(0.567448\pi\)
\(114\) 1.84108e36 1.85882
\(115\) 1.46841e36 1.27244
\(116\) −4.28974e36 −3.19460
\(117\) 3.07875e35 0.197297
\(118\) 1.81535e36 1.00236
\(119\) −5.27859e35 −0.251447
\(120\) −4.48523e36 −1.84550
\(121\) −2.34419e36 −0.834159
\(122\) 7.65865e36 2.35969
\(123\) 9.63884e35 0.257446
\(124\) 7.78179e36 1.80385
\(125\) −2.80126e36 −0.564194
\(126\) −3.43285e36 −0.601410
\(127\) −2.98205e36 −0.454935 −0.227467 0.973786i \(-0.573045\pi\)
−0.227467 + 0.973786i \(0.573045\pi\)
\(128\) −9.04797e36 −1.20331
\(129\) 4.26671e35 0.0495191
\(130\) −8.29648e36 −0.841173
\(131\) 1.67513e37 1.48525 0.742627 0.669705i \(-0.233579\pi\)
0.742627 + 0.669705i \(0.233579\pi\)
\(132\) 7.98169e36 0.619514
\(133\) −1.42372e37 −0.968325
\(134\) 5.16636e36 0.308213
\(135\) 2.49840e37 1.30864
\(136\) −1.81896e37 −0.837321
\(137\) 7.05739e36 0.285782 0.142891 0.989738i \(-0.454360\pi\)
0.142891 + 0.989738i \(0.454360\pi\)
\(138\) −3.55036e37 −1.26587
\(139\) 5.54070e36 0.174103 0.0870514 0.996204i \(-0.472256\pi\)
0.0870514 + 0.996204i \(0.472256\pi\)
\(140\) 6.35959e37 1.76274
\(141\) −2.18273e37 −0.534152
\(142\) −3.75546e37 −0.812115
\(143\) 8.05216e36 0.154004
\(144\) −5.05068e37 −0.855080
\(145\) −1.20403e38 −1.80592
\(146\) 1.07272e38 1.42663
\(147\) 3.42633e37 0.404367
\(148\) 3.40426e38 3.56815
\(149\) −1.26594e38 −1.17938 −0.589689 0.807631i \(-0.700750\pi\)
−0.589689 + 0.807631i \(0.700750\pi\)
\(150\) −8.15479e37 −0.675796
\(151\) 1.46030e38 1.07732 0.538661 0.842523i \(-0.318930\pi\)
0.538661 + 0.842523i \(0.318930\pi\)
\(152\) −4.90602e38 −3.22453
\(153\) 3.47377e37 0.203564
\(154\) −8.97829e37 −0.469441
\(155\) 2.18417e38 1.01972
\(156\) 1.37902e38 0.575296
\(157\) −2.57702e38 −0.961332 −0.480666 0.876904i \(-0.659605\pi\)
−0.480666 + 0.876904i \(0.659605\pi\)
\(158\) −4.78016e37 −0.159567
\(159\) 3.84410e38 1.14907
\(160\) 3.64783e38 0.977091
\(161\) 2.74552e38 0.659436
\(162\) −1.71054e38 −0.368655
\(163\) −1.00523e39 −1.94529 −0.972643 0.232306i \(-0.925373\pi\)
−0.972643 + 0.232306i \(0.925373\pi\)
\(164\) −4.70948e38 −0.818853
\(165\) 2.24028e38 0.350213
\(166\) 1.16190e39 1.63410
\(167\) 4.87583e38 0.617320 0.308660 0.951172i \(-0.400119\pi\)
0.308660 + 0.951172i \(0.400119\pi\)
\(168\) −8.38614e38 −0.956422
\(169\) −8.33666e38 −0.856988
\(170\) −9.36097e38 −0.867890
\(171\) 9.36930e38 0.783926
\(172\) −2.08469e38 −0.157505
\(173\) −3.15688e37 −0.0215502 −0.0107751 0.999942i \(-0.503430\pi\)
−0.0107751 + 0.999942i \(0.503430\pi\)
\(174\) 2.91113e39 1.79659
\(175\) 6.30617e38 0.352046
\(176\) −1.32096e39 −0.667447
\(177\) −8.46924e38 −0.387536
\(178\) 3.10864e39 1.28890
\(179\) −4.86041e38 −0.182702 −0.0913512 0.995819i \(-0.529119\pi\)
−0.0913512 + 0.995819i \(0.529119\pi\)
\(180\) −4.18516e39 −1.42706
\(181\) −4.89892e39 −1.51609 −0.758045 0.652202i \(-0.773845\pi\)
−0.758045 + 0.652202i \(0.773845\pi\)
\(182\) −1.55121e39 −0.435935
\(183\) −3.57303e39 −0.912311
\(184\) 9.46084e39 2.19593
\(185\) 9.55498e39 2.01709
\(186\) −5.28093e39 −1.01446
\(187\) 9.08530e38 0.158895
\(188\) 1.06647e40 1.69897
\(189\) 4.67131e39 0.678199
\(190\) −2.52480e40 −3.34225
\(191\) −8.79853e39 −1.06249 −0.531246 0.847217i \(-0.678276\pi\)
−0.531246 + 0.847217i \(0.678276\pi\)
\(192\) 1.46476e39 0.161434
\(193\) 1.65403e40 1.66452 0.832262 0.554383i \(-0.187046\pi\)
0.832262 + 0.554383i \(0.187046\pi\)
\(194\) 1.19235e39 0.109616
\(195\) 3.87060e39 0.325217
\(196\) −1.67408e40 −1.28616
\(197\) 3.96581e36 0.000278723 0 0.000139362 1.00000i \(-0.499956\pi\)
0.000139362 1.00000i \(0.499956\pi\)
\(198\) 5.90848e39 0.380045
\(199\) −1.61546e40 −0.951409 −0.475705 0.879605i \(-0.657807\pi\)
−0.475705 + 0.879605i \(0.657807\pi\)
\(200\) 2.17305e40 1.17232
\(201\) −2.41029e39 −0.119162
\(202\) 2.41243e40 1.09347
\(203\) −2.25120e40 −0.935909
\(204\) 1.55596e40 0.593569
\(205\) −1.32184e40 −0.462901
\(206\) 3.14344e40 1.01095
\(207\) −1.80679e40 −0.533859
\(208\) −2.28226e40 −0.619808
\(209\) 2.45045e40 0.611908
\(210\) −4.31579e40 −0.991339
\(211\) 2.70344e40 0.571444 0.285722 0.958313i \(-0.407767\pi\)
0.285722 + 0.958313i \(0.407767\pi\)
\(212\) −1.87821e41 −3.65482
\(213\) 1.75206e40 0.313983
\(214\) 1.80362e41 2.97785
\(215\) −5.85124e39 −0.0890379
\(216\) 1.60969e41 2.25841
\(217\) 4.08379e40 0.528467
\(218\) −7.26812e40 −0.867827
\(219\) −5.00462e40 −0.551569
\(220\) −1.09459e41 −1.11392
\(221\) 1.56970e40 0.147554
\(222\) −2.31022e41 −2.00667
\(223\) 1.60448e41 1.28825 0.644124 0.764921i \(-0.277222\pi\)
0.644124 + 0.764921i \(0.277222\pi\)
\(224\) 6.82042e40 0.506374
\(225\) −4.15000e40 −0.285006
\(226\) −1.18399e41 −0.752405
\(227\) −1.32023e41 −0.776597 −0.388299 0.921534i \(-0.626937\pi\)
−0.388299 + 0.921534i \(0.626937\pi\)
\(228\) 4.19667e41 2.28584
\(229\) −1.27675e41 −0.644147 −0.322073 0.946715i \(-0.604380\pi\)
−0.322073 + 0.946715i \(0.604380\pi\)
\(230\) 4.86887e41 2.27610
\(231\) 4.18869e40 0.181497
\(232\) −7.75745e41 −3.11659
\(233\) −1.15249e41 −0.429445 −0.214722 0.976675i \(-0.568885\pi\)
−0.214722 + 0.976675i \(0.568885\pi\)
\(234\) 1.02083e41 0.352919
\(235\) 2.99333e41 0.960433
\(236\) 4.13802e41 1.23263
\(237\) 2.23012e40 0.0616924
\(238\) −1.75024e41 −0.449781
\(239\) 1.42881e41 0.341201 0.170601 0.985340i \(-0.445429\pi\)
0.170601 + 0.985340i \(0.445429\pi\)
\(240\) −6.34973e41 −1.40948
\(241\) −1.47367e41 −0.304160 −0.152080 0.988368i \(-0.548597\pi\)
−0.152080 + 0.988368i \(0.548597\pi\)
\(242\) −7.77271e41 −1.49212
\(243\) −5.09429e41 −0.909859
\(244\) 1.74576e42 2.90177
\(245\) −4.69877e41 −0.727073
\(246\) 3.19598e41 0.460511
\(247\) 4.23373e41 0.568233
\(248\) 1.40724e42 1.75980
\(249\) −5.42069e41 −0.631781
\(250\) −9.28823e41 −1.00921
\(251\) 1.16925e42 1.18473 0.592363 0.805671i \(-0.298195\pi\)
0.592363 + 0.805671i \(0.298195\pi\)
\(252\) −7.82507e41 −0.739569
\(253\) −4.72548e41 −0.416713
\(254\) −9.88766e41 −0.813773
\(255\) 4.36723e41 0.335546
\(256\) −2.67471e42 −1.91901
\(257\) 6.14627e41 0.411890 0.205945 0.978564i \(-0.433973\pi\)
0.205945 + 0.978564i \(0.433973\pi\)
\(258\) 1.41473e41 0.0885783
\(259\) 1.78651e42 1.04535
\(260\) −1.89116e42 −1.03441
\(261\) 1.48148e42 0.757684
\(262\) 5.55428e42 2.65678
\(263\) 5.29428e41 0.236909 0.118454 0.992959i \(-0.462206\pi\)
0.118454 + 0.992959i \(0.462206\pi\)
\(264\) 1.44339e42 0.604386
\(265\) −5.27170e42 −2.06608
\(266\) −4.72067e42 −1.73211
\(267\) −1.45029e42 −0.498320
\(268\) 1.17766e42 0.379018
\(269\) 2.61222e42 0.787670 0.393835 0.919181i \(-0.371148\pi\)
0.393835 + 0.919181i \(0.371148\pi\)
\(270\) 8.28402e42 2.34086
\(271\) −6.35646e42 −1.68365 −0.841827 0.539748i \(-0.818520\pi\)
−0.841827 + 0.539748i \(0.818520\pi\)
\(272\) −2.57509e42 −0.639495
\(273\) 7.23695e41 0.168542
\(274\) 2.34004e42 0.511197
\(275\) −1.08539e42 −0.222466
\(276\) −8.09293e42 −1.55667
\(277\) 1.32088e41 0.0238488 0.0119244 0.999929i \(-0.496204\pi\)
0.0119244 + 0.999929i \(0.496204\pi\)
\(278\) 1.83715e42 0.311430
\(279\) −2.68748e42 −0.427831
\(280\) 1.15005e43 1.71970
\(281\) 1.21053e43 1.70065 0.850324 0.526260i \(-0.176406\pi\)
0.850324 + 0.526260i \(0.176406\pi\)
\(282\) −7.23734e42 −0.955475
\(283\) 1.08291e41 0.0134378 0.00671891 0.999977i \(-0.497861\pi\)
0.00671891 + 0.999977i \(0.497861\pi\)
\(284\) −8.56046e42 −0.998680
\(285\) 1.17791e43 1.29219
\(286\) 2.66988e42 0.275477
\(287\) −2.47148e42 −0.239896
\(288\) −4.48842e42 −0.409945
\(289\) −9.86245e42 −0.847759
\(290\) −3.99224e43 −3.23037
\(291\) −5.56273e41 −0.0423799
\(292\) 2.44523e43 1.75437
\(293\) −2.38381e42 −0.161097 −0.0805486 0.996751i \(-0.525667\pi\)
−0.0805486 + 0.996751i \(0.525667\pi\)
\(294\) 1.13608e43 0.723319
\(295\) 1.16145e43 0.696811
\(296\) 6.15617e43 3.48102
\(297\) −8.04007e42 −0.428570
\(298\) −4.19751e43 −2.10963
\(299\) −8.16438e42 −0.386970
\(300\) −1.85886e43 −0.831044
\(301\) −1.09402e42 −0.0461436
\(302\) 4.84196e43 1.92708
\(303\) −1.12548e43 −0.422760
\(304\) −6.94543e43 −2.46270
\(305\) 4.89996e43 1.64038
\(306\) 1.15181e43 0.364129
\(307\) −4.84424e43 −1.44645 −0.723226 0.690611i \(-0.757342\pi\)
−0.723226 + 0.690611i \(0.757342\pi\)
\(308\) −2.04657e43 −0.577284
\(309\) −1.46653e43 −0.390856
\(310\) 7.24212e43 1.82405
\(311\) 1.85715e43 0.442119 0.221060 0.975260i \(-0.429048\pi\)
0.221060 + 0.975260i \(0.429048\pi\)
\(312\) 2.49379e43 0.561248
\(313\) 2.67734e43 0.569740 0.284870 0.958566i \(-0.408049\pi\)
0.284870 + 0.958566i \(0.408049\pi\)
\(314\) −8.54470e43 −1.71960
\(315\) −2.19632e43 −0.418081
\(316\) −1.08962e43 −0.196224
\(317\) −2.42612e43 −0.413405 −0.206703 0.978404i \(-0.566273\pi\)
−0.206703 + 0.978404i \(0.566273\pi\)
\(318\) 1.27460e44 2.05542
\(319\) 3.87468e43 0.591423
\(320\) −2.00873e43 −0.290266
\(321\) −8.41452e43 −1.15131
\(322\) 9.10342e43 1.17958
\(323\) 4.77694e43 0.586281
\(324\) −3.89911e43 −0.453344
\(325\) −1.87527e43 −0.206588
\(326\) −3.33308e44 −3.47967
\(327\) 3.39084e43 0.335522
\(328\) −8.51651e43 −0.798857
\(329\) 5.59669e43 0.497741
\(330\) 7.42816e43 0.626451
\(331\) 1.83689e44 1.46924 0.734620 0.678479i \(-0.237361\pi\)
0.734620 + 0.678479i \(0.237361\pi\)
\(332\) 2.64852e44 2.00950
\(333\) −1.17568e44 −0.846282
\(334\) 1.61669e44 1.10424
\(335\) 3.30541e43 0.214260
\(336\) −1.18722e44 −0.730457
\(337\) 9.63203e42 0.0562593 0.0281297 0.999604i \(-0.491045\pi\)
0.0281297 + 0.999604i \(0.491045\pi\)
\(338\) −2.76421e44 −1.53295
\(339\) 5.52375e43 0.290897
\(340\) −2.13380e44 −1.06727
\(341\) −7.02885e43 −0.333951
\(342\) 3.10661e44 1.40226
\(343\) −2.38109e44 −1.02124
\(344\) −3.76990e43 −0.153659
\(345\) −2.27150e44 −0.879992
\(346\) −1.04674e43 −0.0385483
\(347\) 2.05198e44 0.718468 0.359234 0.933247i \(-0.383038\pi\)
0.359234 + 0.933247i \(0.383038\pi\)
\(348\) 6.63583e44 2.20932
\(349\) −1.00117e44 −0.317003 −0.158501 0.987359i \(-0.550666\pi\)
−0.158501 + 0.987359i \(0.550666\pi\)
\(350\) 2.09096e44 0.629730
\(351\) −1.38911e44 −0.397981
\(352\) −1.17390e44 −0.319990
\(353\) −2.71539e44 −0.704328 −0.352164 0.935938i \(-0.614554\pi\)
−0.352164 + 0.935938i \(0.614554\pi\)
\(354\) −2.80817e44 −0.693213
\(355\) −2.40272e44 −0.564557
\(356\) 7.08605e44 1.58500
\(357\) 8.16550e43 0.173896
\(358\) −1.61158e44 −0.326813
\(359\) 8.81356e44 1.70215 0.851076 0.525043i \(-0.175951\pi\)
0.851076 + 0.525043i \(0.175951\pi\)
\(360\) −7.56833e44 −1.39221
\(361\) 7.17758e44 1.25777
\(362\) −1.62435e45 −2.71194
\(363\) 3.62625e44 0.576888
\(364\) −3.53593e44 −0.536080
\(365\) 6.86320e44 0.991749
\(366\) −1.18472e45 −1.63191
\(367\) −1.11298e45 −1.46161 −0.730806 0.682585i \(-0.760856\pi\)
−0.730806 + 0.682585i \(0.760856\pi\)
\(368\) 1.33937e45 1.67712
\(369\) 1.62645e44 0.194213
\(370\) 3.16817e45 3.60810
\(371\) −9.85661e44 −1.07074
\(372\) −1.20377e45 −1.24750
\(373\) −5.50495e44 −0.544313 −0.272157 0.962253i \(-0.587737\pi\)
−0.272157 + 0.962253i \(0.587737\pi\)
\(374\) 3.01244e44 0.284227
\(375\) 4.33329e44 0.390185
\(376\) 1.92857e45 1.65748
\(377\) 6.69441e44 0.549211
\(378\) 1.54888e45 1.21314
\(379\) −1.81534e45 −1.35760 −0.678799 0.734325i \(-0.737499\pi\)
−0.678799 + 0.734325i \(0.737499\pi\)
\(380\) −5.75520e45 −4.11006
\(381\) 4.61295e44 0.314624
\(382\) −2.91736e45 −1.90056
\(383\) 5.42819e44 0.337813 0.168907 0.985632i \(-0.445976\pi\)
0.168907 + 0.985632i \(0.445976\pi\)
\(384\) 1.39964e45 0.832184
\(385\) −5.74426e44 −0.326341
\(386\) 5.48431e45 2.97745
\(387\) 7.19958e43 0.0373564
\(388\) 2.71792e44 0.134797
\(389\) 2.27596e45 1.07906 0.539532 0.841965i \(-0.318601\pi\)
0.539532 + 0.841965i \(0.318601\pi\)
\(390\) 1.28339e45 0.581738
\(391\) −9.21192e44 −0.399261
\(392\) −3.02737e45 −1.25476
\(393\) −2.59127e45 −1.02717
\(394\) 1.31496e42 0.000498572 0
\(395\) −3.05832e44 −0.110926
\(396\) 1.34682e45 0.467352
\(397\) 2.97575e45 0.988013 0.494006 0.869458i \(-0.335532\pi\)
0.494006 + 0.869458i \(0.335532\pi\)
\(398\) −5.35643e45 −1.70185
\(399\) 2.20236e45 0.669674
\(400\) 3.07638e45 0.895345
\(401\) −3.35408e45 −0.934429 −0.467215 0.884144i \(-0.654742\pi\)
−0.467215 + 0.884144i \(0.654742\pi\)
\(402\) −7.99189e44 −0.213154
\(403\) −1.21440e45 −0.310115
\(404\) 5.49906e45 1.34467
\(405\) −1.09439e45 −0.256277
\(406\) −7.46438e45 −1.67413
\(407\) −3.07488e45 −0.660580
\(408\) 2.81376e45 0.579074
\(409\) 8.75180e45 1.72560 0.862799 0.505547i \(-0.168709\pi\)
0.862799 + 0.505547i \(0.168709\pi\)
\(410\) −4.38288e45 −0.828022
\(411\) −1.09171e45 −0.197641
\(412\) 7.16537e45 1.24319
\(413\) 2.17158e45 0.361119
\(414\) −5.99083e45 −0.954951
\(415\) 7.43379e45 1.13597
\(416\) −2.02819e45 −0.297150
\(417\) −8.57095e44 −0.120406
\(418\) 8.12503e45 1.09456
\(419\) 1.99625e45 0.257911 0.128955 0.991650i \(-0.458838\pi\)
0.128955 + 0.991650i \(0.458838\pi\)
\(420\) −9.83770e45 −1.21908
\(421\) −1.23389e46 −1.46670 −0.733348 0.679854i \(-0.762043\pi\)
−0.733348 + 0.679854i \(0.762043\pi\)
\(422\) 8.96388e45 1.02218
\(423\) −3.68311e45 −0.402956
\(424\) −3.39650e46 −3.56557
\(425\) −2.11588e45 −0.213150
\(426\) 5.80936e45 0.561643
\(427\) 9.16156e45 0.850122
\(428\) 4.11129e46 3.66194
\(429\) −1.24559e45 −0.106506
\(430\) −1.94012e45 −0.159268
\(431\) −1.20357e46 −0.948677 −0.474339 0.880343i \(-0.657313\pi\)
−0.474339 + 0.880343i \(0.657313\pi\)
\(432\) 2.27884e46 1.72484
\(433\) −2.06332e46 −1.49979 −0.749893 0.661559i \(-0.769895\pi\)
−0.749893 + 0.661559i \(0.769895\pi\)
\(434\) 1.35407e46 0.945305
\(435\) 1.86252e46 1.24894
\(436\) −1.65674e46 −1.06719
\(437\) −2.48460e46 −1.53756
\(438\) −1.65940e46 −0.986629
\(439\) 3.14998e46 1.79961 0.899805 0.436293i \(-0.143709\pi\)
0.899805 + 0.436293i \(0.143709\pi\)
\(440\) −1.97942e46 −1.08672
\(441\) 5.78154e45 0.305048
\(442\) 5.20470e45 0.263941
\(443\) −2.49595e46 −1.21667 −0.608333 0.793682i \(-0.708161\pi\)
−0.608333 + 0.793682i \(0.708161\pi\)
\(444\) −5.26608e46 −2.46766
\(445\) 1.98889e46 0.896006
\(446\) 5.32003e46 2.30438
\(447\) 1.95829e46 0.815634
\(448\) −3.75576e45 −0.150429
\(449\) 3.14792e46 1.21259 0.606294 0.795241i \(-0.292656\pi\)
0.606294 + 0.795241i \(0.292656\pi\)
\(450\) −1.37603e46 −0.509810
\(451\) 4.25381e45 0.151596
\(452\) −2.69887e46 −0.925252
\(453\) −2.25895e46 −0.745054
\(454\) −4.37752e46 −1.38915
\(455\) −9.92455e45 −0.303048
\(456\) 7.58916e46 2.23002
\(457\) 3.21994e46 0.910572 0.455286 0.890345i \(-0.349537\pi\)
0.455286 + 0.890345i \(0.349537\pi\)
\(458\) −4.23336e46 −1.15223
\(459\) −1.56734e46 −0.410622
\(460\) 1.10984e47 2.79898
\(461\) 8.96567e45 0.217679 0.108840 0.994059i \(-0.465287\pi\)
0.108840 + 0.994059i \(0.465287\pi\)
\(462\) 1.38886e46 0.324656
\(463\) −2.74379e46 −0.617566 −0.308783 0.951133i \(-0.599922\pi\)
−0.308783 + 0.951133i \(0.599922\pi\)
\(464\) −1.09822e47 −2.38026
\(465\) −3.37871e46 −0.705219
\(466\) −3.82134e46 −0.768178
\(467\) −8.40024e46 −1.62647 −0.813235 0.581935i \(-0.802296\pi\)
−0.813235 + 0.581935i \(0.802296\pi\)
\(468\) 2.32695e46 0.433994
\(469\) 6.18019e45 0.111039
\(470\) 9.92509e46 1.71799
\(471\) 3.98641e46 0.664838
\(472\) 7.48309e46 1.20253
\(473\) 1.88298e45 0.0291592
\(474\) 7.39447e45 0.110353
\(475\) −5.70686e46 −0.820841
\(476\) −3.98962e46 −0.553107
\(477\) 6.48649e46 0.866839
\(478\) 4.73755e46 0.610331
\(479\) 1.51913e47 1.88679 0.943395 0.331671i \(-0.107612\pi\)
0.943395 + 0.331671i \(0.107612\pi\)
\(480\) −5.64286e46 −0.675736
\(481\) −5.31257e46 −0.613431
\(482\) −4.88629e46 −0.544072
\(483\) −4.24707e46 −0.456052
\(484\) −1.77176e47 −1.83490
\(485\) 7.62857e45 0.0762014
\(486\) −1.68913e47 −1.62753
\(487\) −9.57009e46 −0.889527 −0.444764 0.895648i \(-0.646712\pi\)
−0.444764 + 0.895648i \(0.646712\pi\)
\(488\) 3.15699e47 2.83091
\(489\) 1.55500e47 1.34532
\(490\) −1.55799e47 −1.30057
\(491\) −9.00218e46 −0.725139 −0.362570 0.931957i \(-0.618100\pi\)
−0.362570 + 0.931957i \(0.618100\pi\)
\(492\) 7.28514e46 0.566302
\(493\) 7.55335e46 0.566655
\(494\) 1.40379e47 1.01644
\(495\) 3.78021e46 0.264196
\(496\) 1.99222e47 1.34403
\(497\) −4.49242e46 −0.292580
\(498\) −1.79736e47 −1.13011
\(499\) −1.31845e47 −0.800394 −0.400197 0.916429i \(-0.631058\pi\)
−0.400197 + 0.916429i \(0.631058\pi\)
\(500\) −2.11722e47 −1.24106
\(501\) −7.54246e46 −0.426926
\(502\) 3.87693e47 2.11920
\(503\) 3.29261e46 0.173820 0.0869101 0.996216i \(-0.472301\pi\)
0.0869101 + 0.996216i \(0.472301\pi\)
\(504\) −1.41507e47 −0.721510
\(505\) 1.54346e47 0.760144
\(506\) −1.56684e47 −0.745404
\(507\) 1.28960e47 0.592676
\(508\) −2.25386e47 −1.00072
\(509\) 1.43449e47 0.615370 0.307685 0.951488i \(-0.400446\pi\)
0.307685 + 0.951488i \(0.400446\pi\)
\(510\) 1.44806e47 0.600215
\(511\) 1.28323e47 0.513970
\(512\) −5.75978e47 −2.22937
\(513\) −4.22737e47 −1.58131
\(514\) 2.03794e47 0.736777
\(515\) 2.01115e47 0.702779
\(516\) 3.22482e46 0.108927
\(517\) −9.63280e46 −0.314534
\(518\) 5.92360e47 1.86989
\(519\) 4.88340e45 0.0149037
\(520\) −3.41992e47 −1.00915
\(521\) −2.33055e47 −0.664966 −0.332483 0.943109i \(-0.607886\pi\)
−0.332483 + 0.943109i \(0.607886\pi\)
\(522\) 4.91220e47 1.35532
\(523\) −4.26380e47 −1.13767 −0.568836 0.822451i \(-0.692606\pi\)
−0.568836 + 0.822451i \(0.692606\pi\)
\(524\) 1.26608e48 3.26711
\(525\) −9.75506e46 −0.243468
\(526\) 1.75544e47 0.423776
\(527\) −1.37021e47 −0.319965
\(528\) 2.04340e47 0.461593
\(529\) 2.15467e46 0.0470875
\(530\) −1.74795e48 −3.69575
\(531\) −1.42909e47 −0.292351
\(532\) −1.07606e48 −2.13002
\(533\) 7.34945e46 0.140776
\(534\) −4.80878e47 −0.891380
\(535\) 1.15394e48 2.07011
\(536\) 2.12964e47 0.369762
\(537\) 7.51860e46 0.126353
\(538\) 8.66140e47 1.40896
\(539\) 1.51211e47 0.238111
\(540\) 1.88832e48 2.87862
\(541\) −5.43835e45 −0.00802629 −0.00401314 0.999992i \(-0.501277\pi\)
−0.00401314 + 0.999992i \(0.501277\pi\)
\(542\) −2.10763e48 −3.01167
\(543\) 7.57817e47 1.04850
\(544\) −2.28842e47 −0.306588
\(545\) −4.65010e47 −0.603286
\(546\) 2.39958e47 0.301484
\(547\) −4.15694e47 −0.505820 −0.252910 0.967490i \(-0.581388\pi\)
−0.252910 + 0.967490i \(0.581388\pi\)
\(548\) 5.33405e47 0.628633
\(549\) −6.02909e47 −0.688233
\(550\) −3.59887e47 −0.397941
\(551\) 2.03726e48 2.18219
\(552\) −1.46350e48 −1.51866
\(553\) −5.71821e46 −0.0574871
\(554\) 4.37967e46 0.0426600
\(555\) −1.47807e48 −1.39498
\(556\) 4.18772e47 0.382973
\(557\) 1.81613e45 0.00160947 0.000804733 1.00000i \(-0.499744\pi\)
0.000804733 1.00000i \(0.499744\pi\)
\(558\) −8.91097e47 −0.765291
\(559\) 3.25329e46 0.0270780
\(560\) 1.62812e48 1.31340
\(561\) −1.40541e47 −0.109889
\(562\) 4.01379e48 3.04207
\(563\) −2.19502e48 −1.61266 −0.806329 0.591468i \(-0.798549\pi\)
−0.806329 + 0.591468i \(0.798549\pi\)
\(564\) −1.64973e48 −1.17497
\(565\) −7.57512e47 −0.523048
\(566\) 3.59063e46 0.0240372
\(567\) −2.04621e47 −0.132815
\(568\) −1.54805e48 −0.974293
\(569\) 1.19614e48 0.729993 0.364996 0.931009i \(-0.381070\pi\)
0.364996 + 0.931009i \(0.381070\pi\)
\(570\) 3.90564e48 2.31143
\(571\) −1.26426e48 −0.725610 −0.362805 0.931865i \(-0.618181\pi\)
−0.362805 + 0.931865i \(0.618181\pi\)
\(572\) 6.08590e47 0.338762
\(573\) 1.36105e48 0.734799
\(574\) −8.19476e47 −0.429120
\(575\) 1.10052e48 0.558998
\(576\) 2.47161e47 0.121783
\(577\) 2.42022e48 1.15686 0.578428 0.815734i \(-0.303667\pi\)
0.578428 + 0.815734i \(0.303667\pi\)
\(578\) −3.27012e48 −1.51645
\(579\) −2.55863e48 −1.15115
\(580\) −9.10019e48 −3.97247
\(581\) 1.38991e48 0.588715
\(582\) −1.84445e47 −0.0758080
\(583\) 1.69648e48 0.676626
\(584\) 4.42189e48 1.71153
\(585\) 6.53121e47 0.245339
\(586\) −7.90407e47 −0.288166
\(587\) −1.04500e48 −0.369787 −0.184893 0.982759i \(-0.559194\pi\)
−0.184893 + 0.982759i \(0.559194\pi\)
\(588\) 2.58965e48 0.889485
\(589\) −3.69568e48 −1.23219
\(590\) 3.85105e48 1.24643
\(591\) −6.13475e44 −0.000192760 0
\(592\) 8.71527e48 2.65859
\(593\) 4.87793e48 1.44470 0.722351 0.691526i \(-0.243061\pi\)
0.722351 + 0.691526i \(0.243061\pi\)
\(594\) −2.66587e48 −0.766613
\(595\) −1.11979e48 −0.312674
\(596\) −9.56809e48 −2.59427
\(597\) 2.49897e48 0.657976
\(598\) −2.70709e48 −0.692201
\(599\) 8.48111e47 0.210612 0.105306 0.994440i \(-0.466418\pi\)
0.105306 + 0.994440i \(0.466418\pi\)
\(600\) −3.36151e48 −0.810751
\(601\) −6.23099e48 −1.45967 −0.729834 0.683624i \(-0.760403\pi\)
−0.729834 + 0.683624i \(0.760403\pi\)
\(602\) −3.62747e47 −0.0825402
\(603\) −4.06710e47 −0.0898942
\(604\) 1.10371e49 2.36978
\(605\) −4.97293e48 −1.03727
\(606\) −3.73181e48 −0.756220
\(607\) 2.65746e48 0.523197 0.261598 0.965177i \(-0.415750\pi\)
0.261598 + 0.965177i \(0.415750\pi\)
\(608\) −6.17224e48 −1.18067
\(609\) 3.48240e48 0.647256
\(610\) 1.62470e49 2.93427
\(611\) −1.66429e48 −0.292085
\(612\) 2.62551e48 0.447779
\(613\) 5.89105e48 0.976415 0.488208 0.872727i \(-0.337651\pi\)
0.488208 + 0.872727i \(0.337651\pi\)
\(614\) −1.60622e49 −2.58737
\(615\) 2.04477e48 0.320133
\(616\) −3.70097e48 −0.563187
\(617\) −2.86204e48 −0.423337 −0.211668 0.977342i \(-0.567890\pi\)
−0.211668 + 0.977342i \(0.567890\pi\)
\(618\) −4.86261e48 −0.699151
\(619\) −9.42149e48 −1.31684 −0.658420 0.752651i \(-0.728775\pi\)
−0.658420 + 0.752651i \(0.728775\pi\)
\(620\) 1.65082e49 2.24308
\(621\) 8.15212e48 1.07688
\(622\) 6.15780e48 0.790850
\(623\) 3.71867e48 0.464352
\(624\) 3.53045e48 0.428647
\(625\) −1.05698e49 −1.24786
\(626\) 8.87733e48 1.01913
\(627\) −3.79062e48 −0.423183
\(628\) −1.94774e49 −2.11464
\(629\) −5.99421e48 −0.632915
\(630\) −7.28240e48 −0.747851
\(631\) 8.74950e48 0.873915 0.436958 0.899482i \(-0.356056\pi\)
0.436958 + 0.899482i \(0.356056\pi\)
\(632\) −1.97045e48 −0.191432
\(633\) −4.18197e48 −0.395199
\(634\) −8.04438e48 −0.739487
\(635\) −6.32607e48 −0.565710
\(636\) 2.90541e49 2.52760
\(637\) 2.61252e48 0.221116
\(638\) 1.28474e49 1.05792
\(639\) 2.95640e48 0.236864
\(640\) −1.91942e49 −1.49631
\(641\) 5.35983e48 0.406571 0.203285 0.979120i \(-0.434838\pi\)
0.203285 + 0.979120i \(0.434838\pi\)
\(642\) −2.79003e49 −2.05942
\(643\) 2.04799e49 1.47108 0.735538 0.677483i \(-0.236929\pi\)
0.735538 + 0.677483i \(0.236929\pi\)
\(644\) 2.07509e49 1.45056
\(645\) 9.05133e47 0.0615768
\(646\) 1.58391e49 1.04872
\(647\) 2.13324e49 1.37472 0.687360 0.726317i \(-0.258769\pi\)
0.687360 + 0.726317i \(0.258769\pi\)
\(648\) −7.05105e48 −0.442274
\(649\) −3.73764e48 −0.228200
\(650\) −6.21789e48 −0.369538
\(651\) −6.31724e48 −0.365477
\(652\) −7.59765e49 −4.27904
\(653\) −2.78018e49 −1.52438 −0.762189 0.647354i \(-0.775876\pi\)
−0.762189 + 0.647354i \(0.775876\pi\)
\(654\) 1.12431e49 0.600172
\(655\) 3.55360e49 1.84691
\(656\) −1.20568e49 −0.610119
\(657\) −8.44474e48 −0.416095
\(658\) 1.85571e49 0.890344
\(659\) −2.64746e49 −1.23690 −0.618450 0.785824i \(-0.712239\pi\)
−0.618450 + 0.785824i \(0.712239\pi\)
\(660\) 1.69322e49 0.770363
\(661\) 2.31405e49 1.02529 0.512646 0.858600i \(-0.328665\pi\)
0.512646 + 0.858600i \(0.328665\pi\)
\(662\) 6.09062e49 2.62813
\(663\) −2.42818e48 −0.102046
\(664\) 4.78952e49 1.96042
\(665\) −3.02026e49 −1.20411
\(666\) −3.89824e49 −1.51380
\(667\) −3.92868e49 −1.48609
\(668\) 3.68520e49 1.35792
\(669\) −2.48198e49 −0.890927
\(670\) 1.09599e49 0.383262
\(671\) −1.57685e49 −0.537213
\(672\) −1.05506e49 −0.350198
\(673\) 3.41502e49 1.10441 0.552204 0.833709i \(-0.313787\pi\)
0.552204 + 0.833709i \(0.313787\pi\)
\(674\) 3.19372e48 0.100635
\(675\) 1.87245e49 0.574904
\(676\) −6.30093e49 −1.88511
\(677\) 1.81760e49 0.529903 0.264951 0.964262i \(-0.414644\pi\)
0.264951 + 0.964262i \(0.414644\pi\)
\(678\) 1.83153e49 0.520348
\(679\) 1.42633e48 0.0394911
\(680\) −3.85871e49 −1.04121
\(681\) 2.04227e49 0.537079
\(682\) −2.33058e49 −0.597361
\(683\) −1.52341e49 −0.380587 −0.190294 0.981727i \(-0.560944\pi\)
−0.190294 + 0.981727i \(0.560944\pi\)
\(684\) 7.08142e49 1.72440
\(685\) 1.49715e49 0.355368
\(686\) −7.89504e49 −1.82676
\(687\) 1.97501e49 0.445479
\(688\) −5.33703e48 −0.117355
\(689\) 2.93107e49 0.628332
\(690\) −7.53168e49 −1.57410
\(691\) −1.25243e49 −0.255203 −0.127602 0.991825i \(-0.540728\pi\)
−0.127602 + 0.991825i \(0.540728\pi\)
\(692\) −2.38600e48 −0.0474039
\(693\) 7.06795e48 0.136918
\(694\) 6.80382e49 1.28517
\(695\) 1.17540e49 0.216496
\(696\) 1.20001e50 2.15537
\(697\) 8.29244e48 0.145247
\(698\) −3.31961e49 −0.567045
\(699\) 1.78279e49 0.296995
\(700\) 4.76627e49 0.774395
\(701\) 4.20207e49 0.665883 0.332942 0.942947i \(-0.391959\pi\)
0.332942 + 0.942947i \(0.391959\pi\)
\(702\) −4.60592e49 −0.711896
\(703\) −1.61673e50 −2.43736
\(704\) 6.46426e48 0.0950598
\(705\) −4.63041e49 −0.664216
\(706\) −9.00351e49 −1.25988
\(707\) 2.88584e49 0.393942
\(708\) −6.40114e49 −0.852463
\(709\) 9.39998e48 0.122129 0.0610644 0.998134i \(-0.480551\pi\)
0.0610644 + 0.998134i \(0.480551\pi\)
\(710\) −7.96679e49 −1.00986
\(711\) 3.76307e48 0.0465398
\(712\) 1.28142e50 1.54629
\(713\) 7.12681e49 0.839128
\(714\) 2.70746e49 0.311059
\(715\) 1.70817e49 0.191503
\(716\) −3.67354e49 −0.401890
\(717\) −2.21023e49 −0.235968
\(718\) 2.92234e50 3.04476
\(719\) −7.29315e49 −0.741583 −0.370792 0.928716i \(-0.620914\pi\)
−0.370792 + 0.928716i \(0.620914\pi\)
\(720\) −1.07145e50 −1.06329
\(721\) 3.76030e49 0.364213
\(722\) 2.37989e50 2.24987
\(723\) 2.27963e49 0.210351
\(724\) −3.70265e50 −3.33494
\(725\) −9.02375e49 −0.793363
\(726\) 1.20237e50 1.03192
\(727\) −4.92620e49 −0.412724 −0.206362 0.978476i \(-0.566162\pi\)
−0.206362 + 0.978476i \(0.566162\pi\)
\(728\) −6.39429e49 −0.522990
\(729\) 1.04614e50 0.835334
\(730\) 2.27565e50 1.77401
\(731\) 3.67071e48 0.0279380
\(732\) −2.70054e50 −2.00681
\(733\) −1.28080e50 −0.929310 −0.464655 0.885492i \(-0.653822\pi\)
−0.464655 + 0.885492i \(0.653822\pi\)
\(734\) −3.69035e50 −2.61449
\(735\) 7.26857e49 0.502829
\(736\) 1.19026e50 0.804047
\(737\) −1.06371e49 −0.0701685
\(738\) 5.39286e49 0.347402
\(739\) 1.99479e50 1.25493 0.627466 0.778644i \(-0.284092\pi\)
0.627466 + 0.778644i \(0.284092\pi\)
\(740\) 7.22175e50 4.43698
\(741\) −6.54918e49 −0.392978
\(742\) −3.26819e50 −1.91531
\(743\) 1.05855e50 0.605907 0.302954 0.953005i \(-0.402027\pi\)
0.302954 + 0.953005i \(0.402027\pi\)
\(744\) −2.17687e50 −1.21704
\(745\) −2.68554e50 −1.46655
\(746\) −1.82529e50 −0.973651
\(747\) −9.14681e49 −0.476606
\(748\) 6.86676e49 0.349522
\(749\) 2.15755e50 1.07283
\(750\) 1.43680e50 0.697951
\(751\) −1.20549e50 −0.572090 −0.286045 0.958216i \(-0.592341\pi\)
−0.286045 + 0.958216i \(0.592341\pi\)
\(752\) 2.73027e50 1.26588
\(753\) −1.80872e50 −0.819333
\(754\) 2.21969e50 0.982411
\(755\) 3.09786e50 1.33965
\(756\) 3.53062e50 1.49183
\(757\) 1.18495e50 0.489240 0.244620 0.969619i \(-0.421337\pi\)
0.244620 + 0.969619i \(0.421337\pi\)
\(758\) −6.01917e50 −2.42843
\(759\) 7.30989e49 0.288190
\(760\) −1.04076e51 −4.00969
\(761\) 2.89900e50 1.09148 0.545741 0.837954i \(-0.316248\pi\)
0.545741 + 0.837954i \(0.316248\pi\)
\(762\) 1.52953e50 0.562789
\(763\) −8.69439e49 −0.312651
\(764\) −6.65002e50 −2.33716
\(765\) 7.36920e49 0.253131
\(766\) 1.79984e50 0.604270
\(767\) −6.45766e49 −0.211912
\(768\) 4.13754e50 1.32715
\(769\) 6.18664e49 0.193974 0.0969870 0.995286i \(-0.469079\pi\)
0.0969870 + 0.995286i \(0.469079\pi\)
\(770\) −1.90464e50 −0.583748
\(771\) −9.50771e49 −0.284855
\(772\) 1.25013e51 3.66145
\(773\) −6.37753e50 −1.82604 −0.913022 0.407911i \(-0.866257\pi\)
−0.913022 + 0.407911i \(0.866257\pi\)
\(774\) 2.38719e49 0.0668221
\(775\) 1.63695e50 0.447977
\(776\) 4.91501e49 0.131506
\(777\) −2.76357e50 −0.722941
\(778\) 7.54649e50 1.93020
\(779\) 2.23660e50 0.559349
\(780\) 2.92544e50 0.715379
\(781\) 7.73218e49 0.184888
\(782\) −3.05443e50 −0.714186
\(783\) −6.68436e50 −1.52837
\(784\) −4.28584e50 −0.958307
\(785\) −5.46685e50 −1.19541
\(786\) −8.59196e50 −1.83737
\(787\) 6.23653e50 1.30432 0.652161 0.758080i \(-0.273862\pi\)
0.652161 + 0.758080i \(0.273862\pi\)
\(788\) 2.99740e47 0.000613107 0
\(789\) −8.18976e49 −0.163841
\(790\) −1.01406e50 −0.198421
\(791\) −1.41634e50 −0.271068
\(792\) 2.43555e50 0.455939
\(793\) −2.72438e50 −0.498869
\(794\) 9.86679e50 1.76733
\(795\) 8.15483e50 1.42886
\(796\) −1.22098e51 −2.09281
\(797\) 9.07097e50 1.52101 0.760507 0.649329i \(-0.224950\pi\)
0.760507 + 0.649329i \(0.224950\pi\)
\(798\) 7.30245e50 1.19789
\(799\) −1.87783e50 −0.301362
\(800\) 2.73391e50 0.429249
\(801\) −2.44720e50 −0.375925
\(802\) −1.11212e51 −1.67148
\(803\) −2.20864e50 −0.324790
\(804\) −1.82172e50 −0.262121
\(805\) 5.82432e50 0.820006
\(806\) −4.02662e50 −0.554724
\(807\) −4.04086e50 −0.544736
\(808\) 9.94435e50 1.31183
\(809\) 1.43609e51 1.85389 0.926943 0.375202i \(-0.122427\pi\)
0.926943 + 0.375202i \(0.122427\pi\)
\(810\) −3.62871e50 −0.458421
\(811\) 6.18627e50 0.764828 0.382414 0.923991i \(-0.375093\pi\)
0.382414 + 0.923991i \(0.375093\pi\)
\(812\) −1.70148e51 −2.05872
\(813\) 9.83286e50 1.16438
\(814\) −1.01955e51 −1.18163
\(815\) −2.13249e51 −2.41896
\(816\) 3.98343e50 0.442262
\(817\) 9.90049e49 0.107590
\(818\) 2.90186e51 3.08670
\(819\) 1.22115e50 0.127146
\(820\) −9.99063e50 −1.01824
\(821\) −9.87204e50 −0.984922 −0.492461 0.870335i \(-0.663903\pi\)
−0.492461 + 0.870335i \(0.663903\pi\)
\(822\) −3.61983e50 −0.353534
\(823\) −1.56871e51 −1.49985 −0.749923 0.661525i \(-0.769909\pi\)
−0.749923 + 0.661525i \(0.769909\pi\)
\(824\) 1.29577e51 1.21283
\(825\) 1.67900e50 0.153853
\(826\) 7.20039e50 0.645960
\(827\) −3.34712e49 −0.0293985 −0.0146992 0.999892i \(-0.504679\pi\)
−0.0146992 + 0.999892i \(0.504679\pi\)
\(828\) −1.36559e51 −1.17433
\(829\) −1.24277e51 −1.04638 −0.523188 0.852217i \(-0.675257\pi\)
−0.523188 + 0.852217i \(0.675257\pi\)
\(830\) 2.46485e51 2.03200
\(831\) −2.04327e49 −0.0164933
\(832\) 1.11685e50 0.0882749
\(833\) 2.94772e50 0.228139
\(834\) −2.84190e50 −0.215379
\(835\) 1.03435e51 0.767635
\(836\) 1.85208e51 1.34601
\(837\) 1.21258e51 0.863005
\(838\) 6.61903e50 0.461343
\(839\) 7.06560e50 0.482297 0.241149 0.970488i \(-0.422476\pi\)
0.241149 + 0.970488i \(0.422476\pi\)
\(840\) −1.77902e51 −1.18931
\(841\) 1.69401e51 1.10914
\(842\) −4.09125e51 −2.62358
\(843\) −1.87258e51 −1.17613
\(844\) 2.04329e51 1.25700
\(845\) −1.76853e51 −1.06566
\(846\) −1.22122e51 −0.720796
\(847\) −9.29800e50 −0.537564
\(848\) −4.80842e51 −2.72317
\(849\) −1.67516e49 −0.00929333
\(850\) −7.01568e50 −0.381275
\(851\) 3.11773e51 1.65986
\(852\) 1.32422e51 0.690667
\(853\) −4.40952e50 −0.225311 −0.112656 0.993634i \(-0.535936\pi\)
−0.112656 + 0.993634i \(0.535936\pi\)
\(854\) 3.03773e51 1.52067
\(855\) 1.98759e51 0.974810
\(856\) 7.43474e51 3.57252
\(857\) −2.01998e51 −0.951004 −0.475502 0.879715i \(-0.657733\pi\)
−0.475502 + 0.879715i \(0.657733\pi\)
\(858\) −4.13006e50 −0.190515
\(859\) −2.47558e51 −1.11891 −0.559456 0.828860i \(-0.688990\pi\)
−0.559456 + 0.828860i \(0.688990\pi\)
\(860\) −4.42243e50 −0.195857
\(861\) 3.82315e50 0.165908
\(862\) −3.99071e51 −1.69696
\(863\) 1.15182e51 0.479948 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(864\) 2.02515e51 0.826926
\(865\) −6.69696e49 −0.0267976
\(866\) −6.84143e51 −2.68277
\(867\) 1.52563e51 0.586293
\(868\) 3.08657e51 1.16247
\(869\) 9.84195e49 0.0363274
\(870\) 6.17563e51 2.23406
\(871\) −1.83781e50 −0.0651602
\(872\) −2.99601e51 −1.04113
\(873\) −9.38647e49 −0.0319708
\(874\) −8.23827e51 −2.75034
\(875\) −1.11109e51 −0.363588
\(876\) −3.78255e51 −1.21328
\(877\) 1.21793e50 0.0382938 0.0191469 0.999817i \(-0.493905\pi\)
0.0191469 + 0.999817i \(0.493905\pi\)
\(878\) 1.04445e52 3.21909
\(879\) 3.68753e50 0.111412
\(880\) −2.80226e51 −0.829969
\(881\) 1.43159e51 0.415663 0.207832 0.978165i \(-0.433359\pi\)
0.207832 + 0.978165i \(0.433359\pi\)
\(882\) 1.91700e51 0.545661
\(883\) 4.21625e51 1.17656 0.588280 0.808658i \(-0.299805\pi\)
0.588280 + 0.808658i \(0.299805\pi\)
\(884\) 1.18639e51 0.324575
\(885\) −1.79665e51 −0.481900
\(886\) −8.27591e51 −2.17634
\(887\) 1.06484e51 0.274549 0.137274 0.990533i \(-0.456166\pi\)
0.137274 + 0.990533i \(0.456166\pi\)
\(888\) −9.52303e51 −2.40740
\(889\) −1.18280e51 −0.293177
\(890\) 6.59463e51 1.60275
\(891\) 3.52185e50 0.0839288
\(892\) 1.21268e52 2.83376
\(893\) −5.06481e51 −1.16055
\(894\) 6.49316e51 1.45898
\(895\) −1.03108e51 −0.227190
\(896\) −3.58879e51 −0.775457
\(897\) 1.26295e51 0.267621
\(898\) 1.04377e52 2.16904
\(899\) −5.84365e51 −1.19094
\(900\) −3.13661e51 −0.626927
\(901\) 3.30714e51 0.648289
\(902\) 1.41045e51 0.271171
\(903\) 1.69235e50 0.0319120
\(904\) −4.88057e51 −0.902658
\(905\) −1.03925e52 −1.88525
\(906\) −7.49007e51 −1.33273
\(907\) 5.18332e51 0.904649 0.452325 0.891853i \(-0.350595\pi\)
0.452325 + 0.891853i \(0.350595\pi\)
\(908\) −9.97841e51 −1.70828
\(909\) −1.89913e51 −0.318923
\(910\) −3.29072e51 −0.542083
\(911\) 9.24676e51 1.49423 0.747116 0.664694i \(-0.231438\pi\)
0.747116 + 0.664694i \(0.231438\pi\)
\(912\) 1.07439e52 1.70315
\(913\) −2.39226e51 −0.372023
\(914\) 1.06765e52 1.62880
\(915\) −7.57978e51 −1.13446
\(916\) −9.64981e51 −1.41693
\(917\) 6.64424e51 0.957154
\(918\) −5.19689e51 −0.734508
\(919\) −4.29279e51 −0.595275 −0.297638 0.954679i \(-0.596199\pi\)
−0.297638 + 0.954679i \(0.596199\pi\)
\(920\) 2.00701e52 2.73063
\(921\) 7.49359e51 1.00034
\(922\) 2.97278e51 0.389378
\(923\) 1.33592e51 0.171692
\(924\) 3.16586e51 0.399238
\(925\) 7.16109e51 0.886132
\(926\) −9.09766e51 −1.10468
\(927\) −2.47460e51 −0.294856
\(928\) −9.75961e51 −1.14115
\(929\) 4.47733e51 0.513740 0.256870 0.966446i \(-0.417309\pi\)
0.256870 + 0.966446i \(0.417309\pi\)
\(930\) −1.12029e52 −1.26147
\(931\) 7.95047e51 0.878564
\(932\) −8.71061e51 −0.944649
\(933\) −2.87284e51 −0.305761
\(934\) −2.78529e52 −2.90938
\(935\) 1.92734e51 0.197586
\(936\) 4.20799e51 0.423397
\(937\) −1.28073e50 −0.0126478 −0.00632388 0.999980i \(-0.502013\pi\)
−0.00632388 + 0.999980i \(0.502013\pi\)
\(938\) 2.04919e51 0.198624
\(939\) −4.14159e51 −0.394021
\(940\) 2.26239e52 2.11266
\(941\) 3.26378e50 0.0299160 0.0149580 0.999888i \(-0.495239\pi\)
0.0149580 + 0.999888i \(0.495239\pi\)
\(942\) 1.32179e52 1.18924
\(943\) −4.31310e51 −0.380921
\(944\) 1.05938e52 0.918420
\(945\) 9.90965e51 0.843338
\(946\) 6.24346e50 0.0521591
\(947\) −1.57573e52 −1.29228 −0.646140 0.763219i \(-0.723618\pi\)
−0.646140 + 0.763219i \(0.723618\pi\)
\(948\) 1.68555e51 0.135705
\(949\) −3.81594e51 −0.301608
\(950\) −1.89224e52 −1.46830
\(951\) 3.75299e51 0.285903
\(952\) −7.21472e51 −0.539601
\(953\) −9.47096e51 −0.695454 −0.347727 0.937596i \(-0.613046\pi\)
−0.347727 + 0.937596i \(0.613046\pi\)
\(954\) 2.15075e52 1.55057
\(955\) −1.86651e52 −1.32121
\(956\) 1.07991e52 0.750540
\(957\) −5.99377e51 −0.409017
\(958\) 5.03703e52 3.37503
\(959\) 2.79924e51 0.184168
\(960\) 3.10731e51 0.200742
\(961\) −5.16308e51 −0.327529
\(962\) −1.76151e52 −1.09729
\(963\) −1.41985e52 −0.868528
\(964\) −1.11381e52 −0.669059
\(965\) 3.50883e52 2.06983
\(966\) −1.40821e52 −0.815773
\(967\) 1.42806e52 0.812424 0.406212 0.913779i \(-0.366849\pi\)
0.406212 + 0.913779i \(0.366849\pi\)
\(968\) −3.20401e52 −1.79009
\(969\) −7.38949e51 −0.405460
\(970\) 2.52943e51 0.136307
\(971\) −4.08920e51 −0.216422 −0.108211 0.994128i \(-0.534512\pi\)
−0.108211 + 0.994128i \(0.534512\pi\)
\(972\) −3.85032e52 −2.00141
\(973\) 2.19766e51 0.112198
\(974\) −3.17319e52 −1.59116
\(975\) 2.90087e51 0.142872
\(976\) 4.46934e52 2.16208
\(977\) 2.55940e52 1.21614 0.608071 0.793883i \(-0.291944\pi\)
0.608071 + 0.793883i \(0.291944\pi\)
\(978\) 5.15597e52 2.40647
\(979\) −6.40042e51 −0.293435
\(980\) −3.55138e52 −1.59934
\(981\) 5.72166e51 0.253113
\(982\) −2.98488e52 −1.29711
\(983\) 1.82270e52 0.778087 0.389044 0.921219i \(-0.372806\pi\)
0.389044 + 0.921219i \(0.372806\pi\)
\(984\) 1.31742e52 0.552474
\(985\) 8.41302e48 0.000346592 0
\(986\) 2.50449e52 1.01361
\(987\) −8.65757e51 −0.344228
\(988\) 3.19989e52 1.24994
\(989\) −1.90922e51 −0.0732693
\(990\) 1.25342e52 0.472585
\(991\) 8.47738e51 0.314031 0.157015 0.987596i \(-0.449813\pi\)
0.157015 + 0.987596i \(0.449813\pi\)
\(992\) 1.77044e52 0.644358
\(993\) −2.84149e52 −1.01610
\(994\) −1.48957e52 −0.523358
\(995\) −3.42702e52 −1.18307
\(996\) −4.09702e52 −1.38973
\(997\) −4.09490e52 −1.36483 −0.682414 0.730966i \(-0.739070\pi\)
−0.682414 + 0.730966i \(0.739070\pi\)
\(998\) −4.37162e52 −1.43172
\(999\) 5.30459e52 1.70709
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 1.36.a.a.1.3 3
3.2 odd 2 9.36.a.b.1.1 3
4.3 odd 2 16.36.a.d.1.2 3
5.2 odd 4 25.36.b.a.24.6 6
5.3 odd 4 25.36.b.a.24.1 6
5.4 even 2 25.36.a.a.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.36.a.a.1.3 3 1.1 even 1 trivial
9.36.a.b.1.1 3 3.2 odd 2
16.36.a.d.1.2 3 4.3 odd 2
25.36.a.a.1.1 3 5.4 even 2
25.36.b.a.24.1 6 5.3 odd 4
25.36.b.a.24.6 6 5.2 odd 4