Properties

Label 1.102.a.a.1.5
Level $1$
Weight $102$
Character 1.1
Self dual yes
Analytic conductor $64.601$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 102 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.6006978936\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(15\!\cdots\!64\)\( x^{6} - \)\(13\!\cdots\!76\)\( x^{5} + \)\(79\!\cdots\!56\)\( x^{4} + \)\(16\!\cdots\!20\)\( x^{3} - \)\(12\!\cdots\!00\)\( x^{2} - \)\(46\!\cdots\!00\)\( x + \)\(14\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{119}\cdot 3^{37}\cdot 5^{14}\cdot 7^{7}\cdot 11^{2}\cdot 13^{2}\cdot 17^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-6.74954e12\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +O(q^{10})\) \(q+5.93582e14 q^{2} +2.15060e24 q^{3} -2.18296e30 q^{4} +2.07725e34 q^{5} +1.27656e39 q^{6} -6.15512e42 q^{7} -2.80068e45 q^{8} +3.07894e48 q^{9} +1.23302e49 q^{10} -1.93541e51 q^{11} -4.69467e54 q^{12} +2.07990e56 q^{13} -3.65357e57 q^{14} +4.46732e58 q^{15} +3.87203e60 q^{16} +9.51139e61 q^{17} +1.82761e63 q^{18} -2.07479e64 q^{19} -4.53455e64 q^{20} -1.32372e67 q^{21} -1.14883e66 q^{22} -1.01002e69 q^{23} -6.02314e69 q^{24} -3.90116e70 q^{25} +1.23459e71 q^{26} +3.29646e72 q^{27} +1.34364e73 q^{28} -1.12007e74 q^{29} +2.65172e73 q^{30} -3.39166e75 q^{31} +9.39893e75 q^{32} -4.16230e75 q^{33} +5.64580e76 q^{34} -1.27857e77 q^{35} -6.72122e78 q^{36} -2.80250e78 q^{37} -1.23156e79 q^{38} +4.47304e80 q^{39} -5.81770e79 q^{40} -2.18595e81 q^{41} -7.85736e81 q^{42} +4.27840e82 q^{43} +4.22493e81 q^{44} +6.39572e82 q^{45} -5.99533e83 q^{46} -4.06463e84 q^{47} +8.32719e84 q^{48} +1.52441e85 q^{49} -2.31566e85 q^{50} +2.04552e86 q^{51} -4.54035e86 q^{52} -1.28592e87 q^{53} +1.95672e87 q^{54} -4.02033e85 q^{55} +1.72385e88 q^{56} -4.46205e88 q^{57} -6.64855e88 q^{58} +2.29239e88 q^{59} -9.75199e88 q^{60} +1.48144e90 q^{61} -2.01323e90 q^{62} -1.89513e91 q^{63} -4.23772e90 q^{64} +4.32047e90 q^{65} -2.47067e90 q^{66} -1.12651e92 q^{67} -2.07630e92 q^{68} -2.17216e93 q^{69} -7.58936e91 q^{70} -1.07138e93 q^{71} -8.62313e93 q^{72} +8.88946e92 q^{73} -1.66351e93 q^{74} -8.38982e94 q^{75} +4.52919e94 q^{76} +1.19127e94 q^{77} +2.65512e95 q^{78} +3.94018e95 q^{79} +8.04316e94 q^{80} +2.32892e96 q^{81} -1.29754e96 q^{82} +7.91760e96 q^{83} +2.88963e97 q^{84} +1.97575e96 q^{85} +2.53958e97 q^{86} -2.40883e98 q^{87} +5.42047e96 q^{88} +1.56456e98 q^{89} +3.79639e97 q^{90} -1.28020e99 q^{91} +2.20484e99 q^{92} -7.29409e99 q^{93} -2.41269e99 q^{94} -4.30986e98 q^{95} +2.02133e100 q^{96} +6.75748e99 q^{97} +9.04864e99 q^{98} -5.95903e99 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.93582e14 0.372792 0.186396 0.982475i \(-0.440319\pi\)
0.186396 + 0.982475i \(0.440319\pi\)
\(3\) 2.15060e24 1.72956 0.864781 0.502149i \(-0.167457\pi\)
0.864781 + 0.502149i \(0.167457\pi\)
\(4\) −2.18296e30 −0.861026
\(5\) 2.07725e34 0.104593 0.0522965 0.998632i \(-0.483346\pi\)
0.0522965 + 0.998632i \(0.483346\pi\)
\(6\) 1.27656e39 0.644766
\(7\) −6.15512e42 −1.29356 −0.646778 0.762678i \(-0.723884\pi\)
−0.646778 + 0.762678i \(0.723884\pi\)
\(8\) −2.80068e45 −0.693775
\(9\) 3.07894e48 1.99138
\(10\) 1.23302e49 0.0389914
\(11\) −1.93541e51 −0.0497099 −0.0248550 0.999691i \(-0.507912\pi\)
−0.0248550 + 0.999691i \(0.507912\pi\)
\(12\) −4.69467e54 −1.48920
\(13\) 2.07990e56 1.15852 0.579260 0.815143i \(-0.303341\pi\)
0.579260 + 0.815143i \(0.303341\pi\)
\(14\) −3.65357e57 −0.482227
\(15\) 4.46732e58 0.180900
\(16\) 3.87203e60 0.602393
\(17\) 9.51139e61 0.692745 0.346373 0.938097i \(-0.387413\pi\)
0.346373 + 0.938097i \(0.387413\pi\)
\(18\) 1.82761e63 0.742372
\(19\) −2.07479e64 −0.549437 −0.274719 0.961525i \(-0.588585\pi\)
−0.274719 + 0.961525i \(0.588585\pi\)
\(20\) −4.53455e64 −0.0900573
\(21\) −1.32372e67 −2.23729
\(22\) −1.14883e66 −0.0185314
\(23\) −1.01002e69 −1.72614 −0.863070 0.505084i \(-0.831461\pi\)
−0.863070 + 0.505084i \(0.831461\pi\)
\(24\) −6.02314e69 −1.19993
\(25\) −3.90116e70 −0.989060
\(26\) 1.23459e71 0.431887
\(27\) 3.29646e72 1.71466
\(28\) 1.34364e73 1.11379
\(29\) −1.12007e74 −1.57815 −0.789073 0.614299i \(-0.789439\pi\)
−0.789073 + 0.614299i \(0.789439\pi\)
\(30\) 2.65172e73 0.0674381
\(31\) −3.39166e75 −1.64682 −0.823410 0.567447i \(-0.807931\pi\)
−0.823410 + 0.567447i \(0.807931\pi\)
\(32\) 9.39893e75 0.918342
\(33\) −4.16230e75 −0.0859764
\(34\) 5.64580e76 0.258250
\(35\) −1.27857e77 −0.135297
\(36\) −6.72122e78 −1.71463
\(37\) −2.80250e78 −0.179208 −0.0896041 0.995977i \(-0.528560\pi\)
−0.0896041 + 0.995977i \(0.528560\pi\)
\(38\) −1.23156e79 −0.204826
\(39\) 4.47304e80 2.00373
\(40\) −5.81770e79 −0.0725640
\(41\) −2.18595e81 −0.783531 −0.391765 0.920065i \(-0.628136\pi\)
−0.391765 + 0.920065i \(0.628136\pi\)
\(42\) −7.85736e81 −0.834042
\(43\) 4.27840e82 1.38396 0.691981 0.721916i \(-0.256738\pi\)
0.691981 + 0.721916i \(0.256738\pi\)
\(44\) 4.22493e81 0.0428015
\(45\) 6.39572e82 0.208285
\(46\) −5.99533e83 −0.643491
\(47\) −4.06463e84 −1.47258 −0.736291 0.676665i \(-0.763424\pi\)
−0.736291 + 0.676665i \(0.763424\pi\)
\(48\) 8.32719e84 1.04188
\(49\) 1.52441e85 0.673287
\(50\) −2.31566e85 −0.368714
\(51\) 2.04552e86 1.19815
\(52\) −4.54035e86 −0.997517
\(53\) −1.28592e87 −1.07965 −0.539824 0.841778i \(-0.681509\pi\)
−0.539824 + 0.841778i \(0.681509\pi\)
\(54\) 1.95672e87 0.639212
\(55\) −4.02033e85 −0.00519931
\(56\) 1.72385e88 0.897437
\(57\) −4.46205e88 −0.950286
\(58\) −6.64855e88 −0.588320
\(59\) 2.29239e88 0.0855583 0.0427792 0.999085i \(-0.486379\pi\)
0.0427792 + 0.999085i \(0.486379\pi\)
\(60\) −9.75199e88 −0.155760
\(61\) 1.48144e90 1.02690 0.513451 0.858119i \(-0.328367\pi\)
0.513451 + 0.858119i \(0.328367\pi\)
\(62\) −2.01323e90 −0.613921
\(63\) −1.89513e91 −2.57597
\(64\) −4.23772e90 −0.260042
\(65\) 4.32047e90 0.121173
\(66\) −2.47067e90 −0.0320513
\(67\) −1.12651e92 −0.683844 −0.341922 0.939728i \(-0.611078\pi\)
−0.341922 + 0.939728i \(0.611078\pi\)
\(68\) −2.07630e92 −0.596472
\(69\) −2.17216e93 −2.98547
\(70\) −7.58936e91 −0.0504376
\(71\) −1.07138e93 −0.347852 −0.173926 0.984759i \(-0.555645\pi\)
−0.173926 + 0.984759i \(0.555645\pi\)
\(72\) −8.62313e93 −1.38157
\(73\) 8.88946e92 0.0709694 0.0354847 0.999370i \(-0.488703\pi\)
0.0354847 + 0.999370i \(0.488703\pi\)
\(74\) −1.66351e93 −0.0668074
\(75\) −8.38982e94 −1.71064
\(76\) 4.52919e94 0.473080
\(77\) 1.19127e94 0.0643026
\(78\) 2.65512e95 0.746975
\(79\) 3.94018e95 0.582570 0.291285 0.956636i \(-0.405917\pi\)
0.291285 + 0.956636i \(0.405917\pi\)
\(80\) 8.04316e94 0.0630060
\(81\) 2.32892e96 0.974228
\(82\) −1.29754e96 −0.292094
\(83\) 7.91760e96 0.966385 0.483192 0.875514i \(-0.339477\pi\)
0.483192 + 0.875514i \(0.339477\pi\)
\(84\) 2.88963e97 1.92636
\(85\) 1.97575e96 0.0724563
\(86\) 2.53958e97 0.515930
\(87\) −2.40883e98 −2.72950
\(88\) 5.42047e96 0.0344875
\(89\) 1.56456e98 0.562596 0.281298 0.959620i \(-0.409235\pi\)
0.281298 + 0.959620i \(0.409235\pi\)
\(90\) 3.79639e97 0.0776469
\(91\) −1.28020e99 −1.49861
\(92\) 2.20484e99 1.48625
\(93\) −7.29409e99 −2.84828
\(94\) −2.41269e99 −0.548966
\(95\) −4.30986e98 −0.0574673
\(96\) 2.02133e100 1.58833
\(97\) 6.75748e99 0.314639 0.157319 0.987548i \(-0.449715\pi\)
0.157319 + 0.987548i \(0.449715\pi\)
\(98\) 9.04864e99 0.250996
\(99\) −5.95903e99 −0.0989916
\(100\) 8.51607e100 0.851607
\(101\) 6.91980e100 0.418663 0.209331 0.977845i \(-0.432871\pi\)
0.209331 + 0.977845i \(0.432871\pi\)
\(102\) 1.21418e101 0.446659
\(103\) 3.86032e101 0.867647 0.433823 0.900998i \(-0.357164\pi\)
0.433823 + 0.900998i \(0.357164\pi\)
\(104\) −5.82514e101 −0.803753
\(105\) −2.74969e101 −0.234004
\(106\) −7.63299e101 −0.402484
\(107\) −2.00326e102 −0.657441 −0.328720 0.944427i \(-0.606617\pi\)
−0.328720 + 0.944427i \(0.606617\pi\)
\(108\) −7.19605e102 −1.47637
\(109\) 7.50780e102 0.967107 0.483553 0.875315i \(-0.339346\pi\)
0.483553 + 0.875315i \(0.339346\pi\)
\(110\) −2.38640e100 −0.00193826
\(111\) −6.02705e102 −0.309952
\(112\) −2.38328e103 −0.779229
\(113\) 2.79242e103 0.582800 0.291400 0.956601i \(-0.405879\pi\)
0.291400 + 0.956601i \(0.405879\pi\)
\(114\) −2.64860e103 −0.354259
\(115\) −2.09807e103 −0.180542
\(116\) 2.44507e104 1.35883
\(117\) 6.40391e104 2.30706
\(118\) 1.36072e103 0.0318954
\(119\) −5.85437e104 −0.896105
\(120\) −1.25115e104 −0.125504
\(121\) −1.51212e105 −0.997529
\(122\) 8.79360e104 0.382820
\(123\) −4.70111e105 −1.35517
\(124\) 7.40385e105 1.41796
\(125\) −1.62969e105 −0.208042
\(126\) −1.12491e106 −0.960299
\(127\) −2.25447e106 −1.29109 −0.645544 0.763723i \(-0.723369\pi\)
−0.645544 + 0.763723i \(0.723369\pi\)
\(128\) −2.63446e106 −1.01528
\(129\) 9.20112e106 2.39365
\(130\) 2.56456e105 0.0451724
\(131\) 4.52448e106 0.541213 0.270606 0.962690i \(-0.412776\pi\)
0.270606 + 0.962690i \(0.412776\pi\)
\(132\) 9.08613e105 0.0740279
\(133\) 1.27706e107 0.710728
\(134\) −6.68676e106 −0.254931
\(135\) 6.84757e106 0.179342
\(136\) −2.66383e107 −0.480610
\(137\) 1.30756e108 1.62957 0.814787 0.579761i \(-0.196854\pi\)
0.814787 + 0.579761i \(0.196854\pi\)
\(138\) −1.28935e108 −1.11296
\(139\) −1.97428e107 −0.118348 −0.0591742 0.998248i \(-0.518847\pi\)
−0.0591742 + 0.998248i \(0.518847\pi\)
\(140\) 2.79107e107 0.116494
\(141\) −8.74139e108 −2.54692
\(142\) −6.35950e107 −0.129677
\(143\) −4.02547e107 −0.0575900
\(144\) 1.19218e109 1.19960
\(145\) −2.32667e108 −0.165063
\(146\) 5.27663e107 0.0264568
\(147\) 3.27840e109 1.16449
\(148\) 6.11774e108 0.154303
\(149\) 3.36638e109 0.604305 0.302153 0.953260i \(-0.402295\pi\)
0.302153 + 0.953260i \(0.402295\pi\)
\(150\) −4.98005e109 −0.637713
\(151\) −7.09829e109 −0.649857 −0.324929 0.945739i \(-0.605340\pi\)
−0.324929 + 0.945739i \(0.605340\pi\)
\(152\) 5.81083e109 0.381186
\(153\) 2.92851e110 1.37952
\(154\) 7.07116e108 0.0239715
\(155\) −7.04530e109 −0.172246
\(156\) −9.76447e110 −1.72527
\(157\) −3.72274e110 −0.476354 −0.238177 0.971222i \(-0.576550\pi\)
−0.238177 + 0.971222i \(0.576550\pi\)
\(158\) 2.33882e110 0.217177
\(159\) −2.76550e111 −1.86732
\(160\) 1.95239e110 0.0960522
\(161\) 6.21682e111 2.23286
\(162\) 1.38240e111 0.363184
\(163\) −4.16933e111 −0.802771 −0.401386 0.915909i \(-0.631471\pi\)
−0.401386 + 0.915909i \(0.631471\pi\)
\(164\) 4.77185e111 0.674641
\(165\) −8.64611e109 −0.00899253
\(166\) 4.69975e111 0.360260
\(167\) −9.93308e111 −0.562215 −0.281107 0.959676i \(-0.590702\pi\)
−0.281107 + 0.959676i \(0.590702\pi\)
\(168\) 3.70731e112 1.55217
\(169\) 1.10286e112 0.342171
\(170\) 1.17277e111 0.0270111
\(171\) −6.38818e112 −1.09414
\(172\) −9.33958e112 −1.19163
\(173\) −5.87533e112 −0.559377 −0.279688 0.960091i \(-0.590231\pi\)
−0.279688 + 0.960091i \(0.590231\pi\)
\(174\) −1.42984e113 −1.01754
\(175\) 2.40121e113 1.27940
\(176\) −7.49398e111 −0.0299449
\(177\) 4.93002e112 0.147978
\(178\) 9.28695e112 0.209731
\(179\) 2.72675e113 0.464053 0.232027 0.972709i \(-0.425464\pi\)
0.232027 + 0.972709i \(0.425464\pi\)
\(180\) −1.39616e113 −0.179339
\(181\) −4.92080e113 −0.477823 −0.238912 0.971041i \(-0.576791\pi\)
−0.238912 + 0.971041i \(0.576791\pi\)
\(182\) −7.59907e113 −0.558670
\(183\) 3.18599e114 1.77609
\(184\) 2.82875e114 1.19755
\(185\) −5.82147e112 −0.0187439
\(186\) −4.32964e114 −1.06181
\(187\) −1.84085e113 −0.0344363
\(188\) 8.87293e114 1.26793
\(189\) −2.02901e115 −2.21801
\(190\) −2.55826e113 −0.0214233
\(191\) −2.75631e115 −1.77069 −0.885346 0.464933i \(-0.846079\pi\)
−0.885346 + 0.464933i \(0.846079\pi\)
\(192\) −9.11364e114 −0.449759
\(193\) 4.98329e115 1.89179 0.945893 0.324479i \(-0.105189\pi\)
0.945893 + 0.324479i \(0.105189\pi\)
\(194\) 4.01112e114 0.117295
\(195\) 9.29160e114 0.209577
\(196\) −3.32773e115 −0.579718
\(197\) 7.76102e115 1.04562 0.522810 0.852449i \(-0.324884\pi\)
0.522810 + 0.852449i \(0.324884\pi\)
\(198\) −3.53718e114 −0.0369032
\(199\) 3.53197e115 0.285717 0.142859 0.989743i \(-0.454371\pi\)
0.142859 + 0.989743i \(0.454371\pi\)
\(200\) 1.09259e116 0.686186
\(201\) −2.42267e116 −1.18275
\(202\) 4.10747e115 0.156074
\(203\) 6.89418e116 2.04142
\(204\) −4.46529e116 −1.03164
\(205\) −4.54076e115 −0.0819518
\(206\) 2.29142e116 0.323452
\(207\) −3.10981e117 −3.43741
\(208\) 8.05345e116 0.697884
\(209\) 4.01558e115 0.0273125
\(210\) −1.63217e116 −0.0872349
\(211\) 2.23121e117 0.938158 0.469079 0.883156i \(-0.344586\pi\)
0.469079 + 0.883156i \(0.344586\pi\)
\(212\) 2.80711e117 0.929606
\(213\) −2.30410e117 −0.601632
\(214\) −1.18910e117 −0.245088
\(215\) 8.88728e116 0.144753
\(216\) −9.23233e117 −1.18959
\(217\) 2.08760e118 2.13025
\(218\) 4.45650e117 0.360529
\(219\) 1.91177e117 0.122746
\(220\) 8.77622e115 0.00447674
\(221\) 1.97828e118 0.802560
\(222\) −3.57755e117 −0.115547
\(223\) −3.91127e118 −1.00675 −0.503376 0.864068i \(-0.667909\pi\)
−0.503376 + 0.864068i \(0.667909\pi\)
\(224\) −5.78515e118 −1.18793
\(225\) −1.20114e119 −1.96960
\(226\) 1.65753e118 0.217263
\(227\) 7.18962e118 0.754050 0.377025 0.926203i \(-0.376947\pi\)
0.377025 + 0.926203i \(0.376947\pi\)
\(228\) 9.74048e118 0.818221
\(229\) 2.25539e118 0.151890 0.0759452 0.997112i \(-0.475803\pi\)
0.0759452 + 0.997112i \(0.475803\pi\)
\(230\) −1.24538e118 −0.0673046
\(231\) 2.56194e118 0.111215
\(232\) 3.13696e119 1.09488
\(233\) −4.34636e119 −1.22082 −0.610410 0.792085i \(-0.708995\pi\)
−0.610410 + 0.792085i \(0.708995\pi\)
\(234\) 3.80125e119 0.860053
\(235\) −8.44324e118 −0.154022
\(236\) −5.00420e118 −0.0736680
\(237\) 8.47375e119 1.00759
\(238\) −3.47505e119 −0.334061
\(239\) 5.86452e119 0.456183 0.228091 0.973640i \(-0.426752\pi\)
0.228091 + 0.973640i \(0.426752\pi\)
\(240\) 1.72976e119 0.108973
\(241\) −2.33319e120 −1.19149 −0.595743 0.803175i \(-0.703142\pi\)
−0.595743 + 0.803175i \(0.703142\pi\)
\(242\) −8.97569e119 −0.371871
\(243\) −8.82029e118 −0.0296733
\(244\) −3.23394e120 −0.884189
\(245\) 3.16658e119 0.0704211
\(246\) −2.79050e120 −0.505194
\(247\) −4.31537e120 −0.636535
\(248\) 9.49893e120 1.14252
\(249\) 1.70276e121 1.67142
\(250\) −9.67358e119 −0.0775563
\(251\) −2.88476e121 −1.89055 −0.945273 0.326280i \(-0.894205\pi\)
−0.945273 + 0.326280i \(0.894205\pi\)
\(252\) 4.13699e121 2.21798
\(253\) 1.95481e120 0.0858063
\(254\) −1.33821e121 −0.481307
\(255\) 4.24905e120 0.125318
\(256\) −4.89376e120 −0.118447
\(257\) 1.22979e120 0.0244461 0.0122230 0.999925i \(-0.496109\pi\)
0.0122230 + 0.999925i \(0.496109\pi\)
\(258\) 5.46162e121 0.892332
\(259\) 1.72497e121 0.231816
\(260\) −9.43142e120 −0.104333
\(261\) −3.44864e122 −3.14270
\(262\) 2.68565e121 0.201760
\(263\) −3.92088e121 −0.243006 −0.121503 0.992591i \(-0.538771\pi\)
−0.121503 + 0.992591i \(0.538771\pi\)
\(264\) 1.16573e121 0.0596483
\(265\) −2.67117e121 −0.112924
\(266\) 7.58040e121 0.264954
\(267\) 3.36474e122 0.973045
\(268\) 2.45912e122 0.588808
\(269\) 4.57510e122 0.907634 0.453817 0.891095i \(-0.350062\pi\)
0.453817 + 0.891095i \(0.350062\pi\)
\(270\) 4.06459e121 0.0668570
\(271\) −1.82542e122 −0.249123 −0.124562 0.992212i \(-0.539752\pi\)
−0.124562 + 0.992212i \(0.539752\pi\)
\(272\) 3.68284e122 0.417305
\(273\) −2.75321e123 −2.59194
\(274\) 7.76146e122 0.607492
\(275\) 7.55035e121 0.0491661
\(276\) 4.74173e123 2.57056
\(277\) 1.06562e123 0.481256 0.240628 0.970617i \(-0.422647\pi\)
0.240628 + 0.970617i \(0.422647\pi\)
\(278\) −1.17190e122 −0.0441193
\(279\) −1.04427e124 −3.27945
\(280\) 3.58086e122 0.0938656
\(281\) 3.52617e123 0.772029 0.386015 0.922493i \(-0.373851\pi\)
0.386015 + 0.922493i \(0.373851\pi\)
\(282\) −5.18874e123 −0.949471
\(283\) −5.45476e123 −0.834758 −0.417379 0.908732i \(-0.637051\pi\)
−0.417379 + 0.908732i \(0.637051\pi\)
\(284\) 2.33877e123 0.299510
\(285\) −9.26877e122 −0.0993933
\(286\) −2.38945e122 −0.0214691
\(287\) 1.34548e124 1.01354
\(288\) 2.89388e124 1.82877
\(289\) −9.80463e123 −0.520104
\(290\) −1.38107e123 −0.0615341
\(291\) 1.45326e124 0.544187
\(292\) −1.94053e123 −0.0611065
\(293\) −3.35595e124 −0.889203 −0.444601 0.895729i \(-0.646655\pi\)
−0.444601 + 0.895729i \(0.646655\pi\)
\(294\) 1.94600e124 0.434113
\(295\) 4.76186e122 0.00894880
\(296\) 7.84889e123 0.124330
\(297\) −6.38002e123 −0.0852357
\(298\) 1.99822e124 0.225280
\(299\) −2.10075e125 −1.99977
\(300\) 1.83147e125 1.47291
\(301\) −2.63340e125 −1.79023
\(302\) −4.21342e124 −0.242261
\(303\) 1.48817e125 0.724103
\(304\) −8.03367e124 −0.330977
\(305\) 3.07732e124 0.107407
\(306\) 1.73831e125 0.514275
\(307\) 7.02970e124 0.176380 0.0881900 0.996104i \(-0.471892\pi\)
0.0881900 + 0.996104i \(0.471892\pi\)
\(308\) −2.60049e124 −0.0553662
\(309\) 8.30199e125 1.50065
\(310\) −4.18197e124 −0.0642118
\(311\) 1.14224e126 1.49058 0.745291 0.666739i \(-0.232310\pi\)
0.745291 + 0.666739i \(0.232310\pi\)
\(312\) −1.25275e126 −1.39014
\(313\) −6.45867e125 −0.609753 −0.304876 0.952392i \(-0.598615\pi\)
−0.304876 + 0.952392i \(0.598615\pi\)
\(314\) −2.20975e125 −0.177581
\(315\) −3.93664e125 −0.269428
\(316\) −8.60126e125 −0.501608
\(317\) 2.85359e126 1.41873 0.709364 0.704843i \(-0.248982\pi\)
0.709364 + 0.704843i \(0.248982\pi\)
\(318\) −1.64155e126 −0.696121
\(319\) 2.16780e125 0.0784495
\(320\) −8.80279e124 −0.0271986
\(321\) −4.30821e126 −1.13708
\(322\) 3.69019e126 0.832391
\(323\) −1.97342e126 −0.380620
\(324\) −5.08394e126 −0.838836
\(325\) −8.11403e126 −1.14585
\(326\) −2.47484e126 −0.299266
\(327\) 1.61463e127 1.67267
\(328\) 6.12215e126 0.543594
\(329\) 2.50183e127 1.90487
\(330\) −5.13218e124 −0.00335234
\(331\) 1.94587e127 1.09094 0.545469 0.838131i \(-0.316351\pi\)
0.545469 + 0.838131i \(0.316351\pi\)
\(332\) −1.72838e127 −0.832083
\(333\) −8.62873e126 −0.356873
\(334\) −5.89610e126 −0.209589
\(335\) −2.34004e126 −0.0715253
\(336\) −5.12548e127 −1.34772
\(337\) −3.84815e127 −0.870848 −0.435424 0.900225i \(-0.643402\pi\)
−0.435424 + 0.900225i \(0.643402\pi\)
\(338\) 6.54640e126 0.127558
\(339\) 6.00537e127 1.00799
\(340\) −4.31298e126 −0.0623868
\(341\) 6.56425e126 0.0818633
\(342\) −3.79191e127 −0.407887
\(343\) 4.55307e127 0.422621
\(344\) −1.19824e128 −0.960159
\(345\) −4.51210e127 −0.312259
\(346\) −3.48749e127 −0.208531
\(347\) −5.10458e127 −0.263828 −0.131914 0.991261i \(-0.542112\pi\)
−0.131914 + 0.991261i \(0.542112\pi\)
\(348\) 5.25838e128 2.35017
\(349\) −2.94005e128 −1.13677 −0.568383 0.822764i \(-0.692431\pi\)
−0.568383 + 0.822764i \(0.692431\pi\)
\(350\) 1.42531e128 0.476952
\(351\) 6.85633e128 1.98647
\(352\) −1.81908e127 −0.0456507
\(353\) −3.11192e128 −0.676714 −0.338357 0.941018i \(-0.609871\pi\)
−0.338357 + 0.941018i \(0.609871\pi\)
\(354\) 2.92637e127 0.0551651
\(355\) −2.22551e127 −0.0363829
\(356\) −3.41537e128 −0.484410
\(357\) −1.25904e129 −1.54987
\(358\) 1.61855e128 0.172995
\(359\) 1.27605e129 1.18467 0.592336 0.805691i \(-0.298206\pi\)
0.592336 + 0.805691i \(0.298206\pi\)
\(360\) −1.79124e128 −0.144503
\(361\) −9.95504e128 −0.698119
\(362\) −2.92090e128 −0.178129
\(363\) −3.25197e129 −1.72529
\(364\) 2.79464e129 1.29034
\(365\) 1.84656e127 0.00742290
\(366\) 1.89115e129 0.662112
\(367\) 3.07513e129 0.938052 0.469026 0.883184i \(-0.344605\pi\)
0.469026 + 0.883184i \(0.344605\pi\)
\(368\) −3.91084e129 −1.03981
\(369\) −6.73043e129 −1.56031
\(370\) −3.45552e127 −0.00698758
\(371\) 7.91499e129 1.39659
\(372\) 1.59227e130 2.45244
\(373\) −9.10110e128 −0.122405 −0.0612023 0.998125i \(-0.519493\pi\)
−0.0612023 + 0.998125i \(0.519493\pi\)
\(374\) −1.09269e128 −0.0128376
\(375\) −3.50482e129 −0.359821
\(376\) 1.13837e130 1.02164
\(377\) −2.32964e130 −1.82832
\(378\) −1.20439e130 −0.826856
\(379\) 1.67118e130 1.00402 0.502011 0.864861i \(-0.332594\pi\)
0.502011 + 0.864861i \(0.332594\pi\)
\(380\) 9.40825e128 0.0494809
\(381\) −4.84845e130 −2.23302
\(382\) −1.63610e130 −0.660099
\(383\) 4.34816e130 1.53733 0.768666 0.639650i \(-0.220921\pi\)
0.768666 + 0.639650i \(0.220921\pi\)
\(384\) −5.66566e130 −1.75600
\(385\) 2.47456e128 0.00672560
\(386\) 2.95799e130 0.705242
\(387\) 1.31730e131 2.75600
\(388\) −1.47513e130 −0.270912
\(389\) −2.46326e130 −0.397242 −0.198621 0.980076i \(-0.563646\pi\)
−0.198621 + 0.980076i \(0.563646\pi\)
\(390\) 5.51533e129 0.0781284
\(391\) −9.60674e130 −1.19578
\(392\) −4.26939e130 −0.467110
\(393\) 9.73034e130 0.936061
\(394\) 4.60680e130 0.389799
\(395\) 8.18472e129 0.0609327
\(396\) 1.30083e130 0.0852343
\(397\) 1.12850e131 0.651001 0.325500 0.945542i \(-0.394467\pi\)
0.325500 + 0.945542i \(0.394467\pi\)
\(398\) 2.09651e130 0.106513
\(399\) 2.74644e131 1.22925
\(400\) −1.51054e131 −0.595803
\(401\) −2.71882e131 −0.945343 −0.472672 0.881239i \(-0.656710\pi\)
−0.472672 + 0.881239i \(0.656710\pi\)
\(402\) −1.43805e131 −0.440920
\(403\) −7.05431e131 −1.90788
\(404\) −1.51057e131 −0.360480
\(405\) 4.83773e130 0.101897
\(406\) 4.09226e131 0.761025
\(407\) 5.42399e129 0.00890843
\(408\) −5.72884e131 −0.831244
\(409\) 4.67974e131 0.600059 0.300030 0.953930i \(-0.403003\pi\)
0.300030 + 0.953930i \(0.403003\pi\)
\(410\) −2.69532e130 −0.0305510
\(411\) 2.81204e132 2.81845
\(412\) −8.42692e131 −0.747067
\(413\) −1.41099e131 −0.110674
\(414\) −1.84593e132 −1.28144
\(415\) 1.64468e131 0.101077
\(416\) 1.95489e132 1.06392
\(417\) −4.24589e131 −0.204691
\(418\) 2.38358e130 0.0101819
\(419\) 1.77543e132 0.672194 0.336097 0.941827i \(-0.390893\pi\)
0.336097 + 0.941827i \(0.390893\pi\)
\(420\) 6.00246e131 0.201484
\(421\) 2.58058e132 0.768194 0.384097 0.923293i \(-0.374513\pi\)
0.384097 + 0.923293i \(0.374513\pi\)
\(422\) 1.32441e132 0.349738
\(423\) −1.25148e133 −2.93248
\(424\) 3.60145e132 0.749034
\(425\) −3.71054e132 −0.685167
\(426\) −1.36767e132 −0.224284
\(427\) −9.11847e132 −1.32835
\(428\) 4.37304e132 0.566074
\(429\) −8.65718e131 −0.0996054
\(430\) 5.27534e131 0.0539626
\(431\) −6.70076e132 −0.609568 −0.304784 0.952422i \(-0.598584\pi\)
−0.304784 + 0.952422i \(0.598584\pi\)
\(432\) 1.27640e133 1.03290
\(433\) 2.06034e133 1.48354 0.741771 0.670653i \(-0.233986\pi\)
0.741771 + 0.670653i \(0.233986\pi\)
\(434\) 1.23916e133 0.794141
\(435\) −5.00373e132 −0.285487
\(436\) −1.63892e133 −0.832704
\(437\) 2.09559e133 0.948406
\(438\) 1.13479e132 0.0457587
\(439\) −2.98273e133 −1.07190 −0.535952 0.844249i \(-0.680047\pi\)
−0.535952 + 0.844249i \(0.680047\pi\)
\(440\) 1.12596e131 0.00360715
\(441\) 4.69358e133 1.34077
\(442\) 1.17427e133 0.299188
\(443\) −8.60604e133 −1.95621 −0.978105 0.208113i \(-0.933268\pi\)
−0.978105 + 0.208113i \(0.933268\pi\)
\(444\) 1.31568e133 0.266877
\(445\) 3.24997e132 0.0588436
\(446\) −2.32166e133 −0.375308
\(447\) 7.23973e133 1.04518
\(448\) 2.60837e133 0.336379
\(449\) −7.10386e133 −0.818567 −0.409283 0.912407i \(-0.634221\pi\)
−0.409283 + 0.912407i \(0.634221\pi\)
\(450\) −7.12978e133 −0.734250
\(451\) 4.23072e132 0.0389493
\(452\) −6.09574e133 −0.501806
\(453\) −1.52656e134 −1.12397
\(454\) 4.26763e133 0.281104
\(455\) −2.65930e133 −0.156744
\(456\) 1.24968e134 0.659285
\(457\) 1.42058e134 0.670962 0.335481 0.942047i \(-0.391101\pi\)
0.335481 + 0.942047i \(0.391101\pi\)
\(458\) 1.33876e133 0.0566235
\(459\) 3.13540e134 1.18782
\(460\) 4.58000e133 0.155452
\(461\) 6.35945e134 1.93430 0.967148 0.254214i \(-0.0818168\pi\)
0.967148 + 0.254214i \(0.0818168\pi\)
\(462\) 1.52072e133 0.0414601
\(463\) −4.26577e134 −1.04270 −0.521348 0.853344i \(-0.674571\pi\)
−0.521348 + 0.853344i \(0.674571\pi\)
\(464\) −4.33696e134 −0.950664
\(465\) −1.51516e134 −0.297910
\(466\) −2.57992e134 −0.455112
\(467\) 7.39973e134 1.17142 0.585711 0.810520i \(-0.300815\pi\)
0.585711 + 0.810520i \(0.300815\pi\)
\(468\) −1.39795e135 −1.98644
\(469\) 6.93379e134 0.884591
\(470\) −5.01176e133 −0.0574180
\(471\) −8.00612e134 −0.823885
\(472\) −6.42025e133 −0.0593582
\(473\) −8.28047e133 −0.0687966
\(474\) 5.02987e134 0.375621
\(475\) 8.09409e134 0.543427
\(476\) 1.27799e135 0.771570
\(477\) −3.95928e135 −2.15000
\(478\) 3.48108e134 0.170061
\(479\) −7.32367e134 −0.321948 −0.160974 0.986959i \(-0.551464\pi\)
−0.160974 + 0.986959i \(0.551464\pi\)
\(480\) 4.19881e134 0.166128
\(481\) −5.82892e134 −0.207617
\(482\) −1.38494e135 −0.444176
\(483\) 1.33699e136 3.86187
\(484\) 3.30090e135 0.858899
\(485\) 1.40369e134 0.0329090
\(486\) −5.23557e133 −0.0110620
\(487\) −5.67086e135 −1.08003 −0.540016 0.841655i \(-0.681582\pi\)
−0.540016 + 0.841655i \(0.681582\pi\)
\(488\) −4.14905e135 −0.712439
\(489\) −8.96655e135 −1.38844
\(490\) 1.87963e134 0.0262524
\(491\) 1.09683e135 0.138205 0.0691027 0.997610i \(-0.477986\pi\)
0.0691027 + 0.997610i \(0.477986\pi\)
\(492\) 1.02623e136 1.16683
\(493\) −1.06535e136 −1.09325
\(494\) −2.56153e135 −0.237295
\(495\) −1.23784e134 −0.0103538
\(496\) −1.31326e136 −0.992032
\(497\) 6.59444e135 0.449967
\(498\) 1.01073e136 0.623093
\(499\) 1.68834e136 0.940550 0.470275 0.882520i \(-0.344155\pi\)
0.470275 + 0.882520i \(0.344155\pi\)
\(500\) 3.55756e135 0.179129
\(501\) −2.13621e136 −0.972385
\(502\) −1.71235e136 −0.704780
\(503\) −4.59541e136 −1.71057 −0.855285 0.518158i \(-0.826618\pi\)
−0.855285 + 0.518158i \(0.826618\pi\)
\(504\) 5.30764e136 1.78714
\(505\) 1.43741e135 0.0437892
\(506\) 1.16034e135 0.0319879
\(507\) 2.37181e136 0.591805
\(508\) 4.92141e136 1.11166
\(509\) 3.06425e136 0.626724 0.313362 0.949634i \(-0.398545\pi\)
0.313362 + 0.949634i \(0.398545\pi\)
\(510\) 2.52216e135 0.0467174
\(511\) −5.47157e135 −0.0918029
\(512\) 6.38865e136 0.971128
\(513\) −6.83949e136 −0.942099
\(514\) 7.29983e134 0.00911329
\(515\) 8.01882e135 0.0907498
\(516\) −2.00857e137 −2.06099
\(517\) 7.86674e135 0.0732019
\(518\) 1.02391e136 0.0864191
\(519\) −1.26355e137 −0.967476
\(520\) −1.21002e136 −0.0840669
\(521\) 4.01949e136 0.253435 0.126717 0.991939i \(-0.459556\pi\)
0.126717 + 0.991939i \(0.459556\pi\)
\(522\) −2.04705e137 −1.17157
\(523\) 1.74801e137 0.908256 0.454128 0.890937i \(-0.349951\pi\)
0.454128 + 0.890937i \(0.349951\pi\)
\(524\) −9.87676e136 −0.465999
\(525\) 5.16403e137 2.21281
\(526\) −2.32736e136 −0.0905908
\(527\) −3.22594e137 −1.14083
\(528\) −1.61165e136 −0.0517915
\(529\) 6.77766e137 1.97956
\(530\) −1.58556e136 −0.0420970
\(531\) 7.05815e136 0.170379
\(532\) −2.78777e137 −0.611956
\(533\) −4.54657e137 −0.907737
\(534\) 1.99725e137 0.362743
\(535\) −4.16126e136 −0.0687637
\(536\) 3.15499e137 0.474434
\(537\) 5.86415e137 0.802609
\(538\) 2.71570e137 0.338359
\(539\) −2.95037e136 −0.0334691
\(540\) −1.49480e137 −0.154418
\(541\) −1.25633e138 −1.18207 −0.591034 0.806647i \(-0.701280\pi\)
−0.591034 + 0.806647i \(0.701280\pi\)
\(542\) −1.08354e137 −0.0928711
\(543\) −1.05827e138 −0.826425
\(544\) 8.93969e137 0.636177
\(545\) 1.55955e137 0.101153
\(546\) −1.63426e138 −0.966254
\(547\) −2.40142e138 −1.29452 −0.647259 0.762270i \(-0.724085\pi\)
−0.647259 + 0.762270i \(0.724085\pi\)
\(548\) −2.85436e138 −1.40311
\(549\) 4.56129e138 2.04496
\(550\) 4.48175e136 0.0183287
\(551\) 2.32392e138 0.867093
\(552\) 6.08351e138 2.07124
\(553\) −2.42523e138 −0.753587
\(554\) 6.32536e137 0.179408
\(555\) −1.25197e137 −0.0324188
\(556\) 4.30979e137 0.101901
\(557\) −2.32646e138 −0.502353 −0.251176 0.967941i \(-0.580817\pi\)
−0.251176 + 0.967941i \(0.580817\pi\)
\(558\) −6.19861e138 −1.22255
\(559\) 8.89866e138 1.60335
\(560\) −4.95066e137 −0.0815019
\(561\) −3.95892e137 −0.0595597
\(562\) 2.09307e138 0.287806
\(563\) −1.12700e139 −1.41661 −0.708306 0.705906i \(-0.750540\pi\)
−0.708306 + 0.705906i \(0.750540\pi\)
\(564\) 1.90821e139 2.19297
\(565\) 5.80054e137 0.0609568
\(566\) −3.23785e138 −0.311191
\(567\) −1.43348e139 −1.26022
\(568\) 3.00058e138 0.241331
\(569\) −6.22965e138 −0.458452 −0.229226 0.973373i \(-0.573620\pi\)
−0.229226 + 0.973373i \(0.573620\pi\)
\(570\) −5.50178e137 −0.0370530
\(571\) −1.06373e139 −0.655704 −0.327852 0.944729i \(-0.606325\pi\)
−0.327852 + 0.944729i \(0.606325\pi\)
\(572\) 8.78745e137 0.0495865
\(573\) −5.92772e139 −3.06252
\(574\) 7.98653e138 0.377840
\(575\) 3.94026e139 1.70726
\(576\) −1.30477e139 −0.517844
\(577\) 3.61142e139 1.31310 0.656552 0.754281i \(-0.272014\pi\)
0.656552 + 0.754281i \(0.272014\pi\)
\(578\) −5.81986e138 −0.193890
\(579\) 1.07171e140 3.27196
\(580\) 5.07902e138 0.142124
\(581\) −4.87338e139 −1.25007
\(582\) 8.62632e138 0.202869
\(583\) 2.48879e138 0.0536692
\(584\) −2.48965e138 −0.0492368
\(585\) 1.33025e139 0.241302
\(586\) −1.99203e139 −0.331487
\(587\) −9.37398e139 −1.43120 −0.715599 0.698511i \(-0.753846\pi\)
−0.715599 + 0.698511i \(0.753846\pi\)
\(588\) −7.15662e139 −1.00266
\(589\) 7.03699e139 0.904824
\(590\) 2.82656e137 0.00333604
\(591\) 1.66908e140 1.80847
\(592\) −1.08514e139 −0.107954
\(593\) −1.79083e140 −1.63603 −0.818015 0.575197i \(-0.804926\pi\)
−0.818015 + 0.575197i \(0.804926\pi\)
\(594\) −3.78707e138 −0.0317751
\(595\) −1.21610e139 −0.0937263
\(596\) −7.34868e139 −0.520323
\(597\) 7.59584e139 0.494165
\(598\) −1.24697e140 −0.745497
\(599\) −8.24207e139 −0.452879 −0.226439 0.974025i \(-0.572709\pi\)
−0.226439 + 0.974025i \(0.572709\pi\)
\(600\) 2.34972e140 1.18680
\(601\) 1.29641e140 0.601980 0.300990 0.953627i \(-0.402683\pi\)
0.300990 + 0.953627i \(0.402683\pi\)
\(602\) −1.56314e140 −0.667384
\(603\) −3.46846e140 −1.36180
\(604\) 1.54953e140 0.559544
\(605\) −3.14105e139 −0.104335
\(606\) 8.83353e139 0.269940
\(607\) 4.97901e140 1.39996 0.699978 0.714164i \(-0.253193\pi\)
0.699978 + 0.714164i \(0.253193\pi\)
\(608\) −1.95008e140 −0.504572
\(609\) 1.48266e141 3.53076
\(610\) 1.82665e139 0.0400403
\(611\) −8.45404e140 −1.70602
\(612\) −6.39281e140 −1.18781
\(613\) 2.08079e140 0.356019 0.178010 0.984029i \(-0.443034\pi\)
0.178010 + 0.984029i \(0.443034\pi\)
\(614\) 4.17271e139 0.0657530
\(615\) −9.76536e139 −0.141741
\(616\) −3.33636e139 −0.0446115
\(617\) −8.92522e140 −1.09956 −0.549779 0.835310i \(-0.685288\pi\)
−0.549779 + 0.835310i \(0.685288\pi\)
\(618\) 4.92792e140 0.559429
\(619\) 4.62079e140 0.483436 0.241718 0.970347i \(-0.422289\pi\)
0.241718 + 0.970347i \(0.422289\pi\)
\(620\) 1.53796e140 0.148308
\(621\) −3.32951e141 −2.95974
\(622\) 6.78011e140 0.555677
\(623\) −9.63005e140 −0.727750
\(624\) 1.73197e141 1.20703
\(625\) 1.50488e141 0.967301
\(626\) −3.83375e140 −0.227311
\(627\) 8.63591e139 0.0472386
\(628\) 8.12660e140 0.410154
\(629\) −2.66556e140 −0.124146
\(630\) −2.33672e140 −0.100441
\(631\) −3.56470e141 −1.41430 −0.707148 0.707066i \(-0.750018\pi\)
−0.707148 + 0.707066i \(0.750018\pi\)
\(632\) −1.10352e141 −0.404173
\(633\) 4.79844e141 1.62260
\(634\) 1.69384e141 0.528890
\(635\) −4.68308e140 −0.135039
\(636\) 6.03697e141 1.60781
\(637\) 3.17063e141 0.780017
\(638\) 1.28677e140 0.0292453
\(639\) −3.29871e141 −0.692708
\(640\) −5.47241e140 −0.106192
\(641\) −1.80821e140 −0.0324278 −0.0162139 0.999869i \(-0.505161\pi\)
−0.0162139 + 0.999869i \(0.505161\pi\)
\(642\) −2.55728e141 −0.423896
\(643\) 5.93023e140 0.0908693 0.0454347 0.998967i \(-0.485533\pi\)
0.0454347 + 0.998967i \(0.485533\pi\)
\(644\) −1.35711e142 −1.92255
\(645\) 1.91130e141 0.250359
\(646\) −1.17139e141 −0.141892
\(647\) −1.30820e142 −1.46558 −0.732788 0.680457i \(-0.761781\pi\)
−0.732788 + 0.680457i \(0.761781\pi\)
\(648\) −6.52255e141 −0.675895
\(649\) −4.43672e139 −0.00425310
\(650\) −4.81634e141 −0.427162
\(651\) 4.48960e142 3.68441
\(652\) 9.10148e141 0.691207
\(653\) −2.39043e142 −1.68020 −0.840100 0.542431i \(-0.817504\pi\)
−0.840100 + 0.542431i \(0.817504\pi\)
\(654\) 9.58414e141 0.623558
\(655\) 9.39845e140 0.0566071
\(656\) −8.46408e141 −0.471993
\(657\) 2.73702e141 0.141327
\(658\) 1.48504e142 0.710119
\(659\) −2.10277e142 −0.931278 −0.465639 0.884975i \(-0.654175\pi\)
−0.465639 + 0.884975i \(0.654175\pi\)
\(660\) 1.88741e140 0.00774280
\(661\) −1.91977e142 −0.729583 −0.364792 0.931089i \(-0.618860\pi\)
−0.364792 + 0.931089i \(0.618860\pi\)
\(662\) 1.15503e142 0.406693
\(663\) 4.25448e142 1.38808
\(664\) −2.21747e142 −0.670454
\(665\) 2.65277e141 0.0743372
\(666\) −5.12186e141 −0.133039
\(667\) 1.13130e143 2.72410
\(668\) 2.16835e142 0.484082
\(669\) −8.41157e142 −1.74124
\(670\) −1.38900e141 −0.0266640
\(671\) −2.86721e141 −0.0510472
\(672\) −1.24415e143 −2.05459
\(673\) 5.63386e142 0.863069 0.431534 0.902096i \(-0.357972\pi\)
0.431534 + 0.902096i \(0.357972\pi\)
\(674\) −2.28420e142 −0.324645
\(675\) −1.28600e143 −1.69590
\(676\) −2.40751e142 −0.294618
\(677\) 6.51705e141 0.0740157 0.0370078 0.999315i \(-0.488217\pi\)
0.0370078 + 0.999315i \(0.488217\pi\)
\(678\) 3.56469e142 0.375770
\(679\) −4.15931e142 −0.407003
\(680\) −5.53344e141 −0.0502684
\(681\) 1.54620e143 1.30418
\(682\) 3.89643e141 0.0305180
\(683\) 1.77465e142 0.129083 0.0645413 0.997915i \(-0.479442\pi\)
0.0645413 + 0.997915i \(0.479442\pi\)
\(684\) 1.39451e143 0.942084
\(685\) 2.71613e142 0.170442
\(686\) 2.70262e142 0.157550
\(687\) 4.85045e142 0.262704
\(688\) 1.65661e143 0.833689
\(689\) −2.67459e143 −1.25080
\(690\) −2.67831e142 −0.116408
\(691\) −7.60623e142 −0.307275 −0.153638 0.988127i \(-0.549099\pi\)
−0.153638 + 0.988127i \(0.549099\pi\)
\(692\) 1.28256e143 0.481638
\(693\) 3.66785e142 0.128051
\(694\) −3.02999e142 −0.0983530
\(695\) −4.10107e141 −0.0123784
\(696\) 6.74635e143 1.89366
\(697\) −2.07915e143 −0.542787
\(698\) −1.74516e143 −0.423777
\(699\) −9.34728e143 −2.11148
\(700\) −5.24174e143 −1.10160
\(701\) 2.53234e143 0.495179 0.247590 0.968865i \(-0.420362\pi\)
0.247590 + 0.968865i \(0.420362\pi\)
\(702\) 4.06980e143 0.740540
\(703\) 5.81460e142 0.0984637
\(704\) 8.20174e141 0.0129267
\(705\) −1.81580e143 −0.266390
\(706\) −1.84718e143 −0.252274
\(707\) −4.25922e143 −0.541564
\(708\) −1.07620e143 −0.127413
\(709\) −4.79369e143 −0.528488 −0.264244 0.964456i \(-0.585122\pi\)
−0.264244 + 0.964456i \(0.585122\pi\)
\(710\) −1.32102e142 −0.0135633
\(711\) 1.21316e144 1.16012
\(712\) −4.38183e143 −0.390315
\(713\) 3.42565e144 2.84264
\(714\) −7.47345e143 −0.577778
\(715\) −8.36189e141 −0.00602351
\(716\) −5.95240e143 −0.399562
\(717\) 1.26122e144 0.788996
\(718\) 7.57440e143 0.441636
\(719\) 2.96453e143 0.161119 0.0805595 0.996750i \(-0.474329\pi\)
0.0805595 + 0.996750i \(0.474329\pi\)
\(720\) 2.47644e143 0.125469
\(721\) −2.37607e144 −1.12235
\(722\) −5.90914e143 −0.260253
\(723\) −5.01775e144 −2.06075
\(724\) 1.07419e144 0.411418
\(725\) 4.36958e144 1.56088
\(726\) −1.93031e144 −0.643173
\(727\) −5.04268e143 −0.156738 −0.0783689 0.996924i \(-0.524971\pi\)
−0.0783689 + 0.996924i \(0.524971\pi\)
\(728\) 3.58544e144 1.03970
\(729\) −3.79050e144 −1.02555
\(730\) 1.09609e142 0.00276720
\(731\) 4.06935e144 0.958733
\(732\) −6.95490e144 −1.52926
\(733\) 1.13594e144 0.233134 0.116567 0.993183i \(-0.462811\pi\)
0.116567 + 0.993183i \(0.462811\pi\)
\(734\) 1.82534e144 0.349698
\(735\) 6.81004e143 0.121798
\(736\) −9.49315e144 −1.58519
\(737\) 2.18026e143 0.0339938
\(738\) −3.99507e144 −0.581671
\(739\) 9.39645e144 1.27767 0.638836 0.769343i \(-0.279416\pi\)
0.638836 + 0.769343i \(0.279416\pi\)
\(740\) 1.27080e143 0.0161390
\(741\) −9.28063e144 −1.10093
\(742\) 4.69820e144 0.520636
\(743\) 3.87882e144 0.401574 0.200787 0.979635i \(-0.435650\pi\)
0.200787 + 0.979635i \(0.435650\pi\)
\(744\) 2.04284e145 1.97606
\(745\) 6.99280e143 0.0632061
\(746\) −5.40226e143 −0.0456315
\(747\) 2.43779e145 1.92444
\(748\) 4.01850e143 0.0296506
\(749\) 1.23303e145 0.850436
\(750\) −2.08040e144 −0.134138
\(751\) −1.87721e145 −1.13161 −0.565804 0.824540i \(-0.691434\pi\)
−0.565804 + 0.824540i \(0.691434\pi\)
\(752\) −1.57384e145 −0.887072
\(753\) −6.20397e145 −3.26982
\(754\) −1.38284e145 −0.681581
\(755\) −1.47449e144 −0.0679705
\(756\) 4.42925e145 1.90977
\(757\) −6.72388e144 −0.271193 −0.135596 0.990764i \(-0.543295\pi\)
−0.135596 + 0.990764i \(0.543295\pi\)
\(758\) 9.91984e144 0.374291
\(759\) 4.20402e144 0.148407
\(760\) 1.20705e144 0.0398694
\(761\) 2.75168e144 0.0850496 0.0425248 0.999095i \(-0.486460\pi\)
0.0425248 + 0.999095i \(0.486460\pi\)
\(762\) −2.87796e145 −0.832450
\(763\) −4.62114e145 −1.25101
\(764\) 6.01692e145 1.52461
\(765\) 6.08322e144 0.144288
\(766\) 2.58099e145 0.573105
\(767\) 4.76795e144 0.0991211
\(768\) −1.05245e145 −0.204862
\(769\) −8.90258e144 −0.162269 −0.0811345 0.996703i \(-0.525854\pi\)
−0.0811345 + 0.996703i \(0.525854\pi\)
\(770\) 1.46885e143 0.00250725
\(771\) 2.64479e144 0.0422810
\(772\) −1.08783e146 −1.62888
\(773\) 6.30125e145 0.883816 0.441908 0.897060i \(-0.354302\pi\)
0.441908 + 0.897060i \(0.354302\pi\)
\(774\) 7.81923e145 1.02741
\(775\) 1.32314e146 1.62880
\(776\) −1.89255e145 −0.218289
\(777\) 3.70972e145 0.400940
\(778\) −1.46215e145 −0.148088
\(779\) 4.53540e145 0.430501
\(780\) −2.02832e145 −0.180451
\(781\) 2.07355e144 0.0172917
\(782\) −5.70239e145 −0.445775
\(783\) −3.69228e146 −2.70599
\(784\) 5.90257e145 0.405583
\(785\) −7.73304e144 −0.0498233
\(786\) 5.77576e145 0.348956
\(787\) 1.04521e146 0.592216 0.296108 0.955154i \(-0.404311\pi\)
0.296108 + 0.955154i \(0.404311\pi\)
\(788\) −1.69420e146 −0.900307
\(789\) −8.43223e145 −0.420295
\(790\) 4.85831e144 0.0227152
\(791\) −1.71877e146 −0.753884
\(792\) 1.66893e145 0.0686779
\(793\) 3.08126e146 1.18969
\(794\) 6.69859e145 0.242688
\(795\) −5.74462e145 −0.195309
\(796\) −7.71014e145 −0.246010
\(797\) 4.25964e146 1.27564 0.637820 0.770186i \(-0.279836\pi\)
0.637820 + 0.770186i \(0.279836\pi\)
\(798\) 1.63024e146 0.458254
\(799\) −3.86603e146 −1.02012
\(800\) −3.66667e146 −0.908296
\(801\) 4.81719e146 1.12035
\(802\) −1.61384e146 −0.352416
\(803\) −1.72048e144 −0.00352788
\(804\) 5.28859e146 1.01838
\(805\) 1.29139e146 0.233541
\(806\) −4.18732e146 −0.711240
\(807\) 9.83922e146 1.56981
\(808\) −1.93801e146 −0.290458
\(809\) −3.72784e146 −0.524877 −0.262438 0.964949i \(-0.584527\pi\)
−0.262438 + 0.964949i \(0.584527\pi\)
\(810\) 2.87159e145 0.0379865
\(811\) 1.18387e147 1.47147 0.735735 0.677270i \(-0.236837\pi\)
0.735735 + 0.677270i \(0.236837\pi\)
\(812\) −1.50497e147 −1.75772
\(813\) −3.92575e146 −0.430874
\(814\) 3.21958e144 0.00332099
\(815\) −8.66071e145 −0.0839642
\(816\) 7.92031e146 0.721754
\(817\) −8.87680e146 −0.760401
\(818\) 2.77781e146 0.223697
\(819\) −3.94168e147 −2.98431
\(820\) 9.91231e145 0.0705627
\(821\) −1.48927e147 −0.996885 −0.498442 0.866923i \(-0.666094\pi\)
−0.498442 + 0.866923i \(0.666094\pi\)
\(822\) 1.66918e147 1.05069
\(823\) 2.78199e147 1.64689 0.823443 0.567399i \(-0.192050\pi\)
0.823443 + 0.567399i \(0.192050\pi\)
\(824\) −1.08115e147 −0.601952
\(825\) 1.62378e146 0.0850358
\(826\) −8.37541e145 −0.0412585
\(827\) −2.17061e147 −1.00590 −0.502950 0.864316i \(-0.667752\pi\)
−0.502950 + 0.864316i \(0.667752\pi\)
\(828\) 6.78859e147 2.95970
\(829\) 1.19927e147 0.491941 0.245970 0.969277i \(-0.420893\pi\)
0.245970 + 0.969277i \(0.420893\pi\)
\(830\) 9.76254e145 0.0376807
\(831\) 2.29173e147 0.832361
\(832\) −8.81405e146 −0.301264
\(833\) 1.44993e147 0.466417
\(834\) −2.52029e146 −0.0763071
\(835\) −2.06335e146 −0.0588037
\(836\) −8.76586e145 −0.0235168
\(837\) −1.11805e148 −2.82374
\(838\) 1.05386e147 0.250588
\(839\) −4.40608e147 −0.986445 −0.493223 0.869903i \(-0.664181\pi\)
−0.493223 + 0.869903i \(0.664181\pi\)
\(840\) 7.70099e146 0.162346
\(841\) 7.50833e147 1.49055
\(842\) 1.53179e147 0.286377
\(843\) 7.58338e147 1.33527
\(844\) −4.87064e147 −0.807779
\(845\) 2.29092e146 0.0357886
\(846\) −7.42855e147 −1.09320
\(847\) 9.30728e147 1.29036
\(848\) −4.97912e147 −0.650372
\(849\) −1.17310e148 −1.44377
\(850\) −2.20251e147 −0.255425
\(851\) 2.83059e147 0.309339
\(852\) 5.02976e147 0.518021
\(853\) −1.23230e148 −1.19616 −0.598082 0.801435i \(-0.704070\pi\)
−0.598082 + 0.801435i \(0.704070\pi\)
\(854\) −5.41256e147 −0.495200
\(855\) −1.32698e147 −0.114439
\(856\) 5.61049e147 0.456116
\(857\) 9.78619e147 0.750036 0.375018 0.927018i \(-0.377637\pi\)
0.375018 + 0.927018i \(0.377637\pi\)
\(858\) −5.13875e146 −0.0371321
\(859\) 1.54130e147 0.105010 0.0525052 0.998621i \(-0.483279\pi\)
0.0525052 + 0.998621i \(0.483279\pi\)
\(860\) −1.94006e147 −0.124636
\(861\) 2.89359e148 1.75298
\(862\) −3.97746e147 −0.227242
\(863\) 1.29970e148 0.700321 0.350160 0.936690i \(-0.386127\pi\)
0.350160 + 0.936690i \(0.386127\pi\)
\(864\) 3.09832e148 1.57465
\(865\) −1.22045e147 −0.0585069
\(866\) 1.22298e148 0.553053
\(867\) −2.10858e148 −0.899552
\(868\) −4.55716e148 −1.83420
\(869\) −7.62588e146 −0.0289595
\(870\) −2.97012e147 −0.106427
\(871\) −2.34303e148 −0.792248
\(872\) −2.10269e148 −0.670955
\(873\) 2.08059e148 0.626567
\(874\) 1.24391e148 0.353558
\(875\) 1.00310e148 0.269114
\(876\) −4.17331e147 −0.105687
\(877\) 3.62999e148 0.867813 0.433906 0.900958i \(-0.357135\pi\)
0.433906 + 0.900958i \(0.357135\pi\)
\(878\) −1.77050e148 −0.399597
\(879\) −7.21731e148 −1.53793
\(880\) −1.55668e146 −0.00313203
\(881\) 3.01535e148 0.572869 0.286434 0.958100i \(-0.407530\pi\)
0.286434 + 0.958100i \(0.407530\pi\)
\(882\) 2.78603e148 0.499829
\(883\) −5.32283e148 −0.901835 −0.450917 0.892566i \(-0.648903\pi\)
−0.450917 + 0.892566i \(0.648903\pi\)
\(884\) −4.31850e148 −0.691025
\(885\) 1.02409e147 0.0154775
\(886\) −5.10840e148 −0.729259
\(887\) 2.38497e147 0.0321618 0.0160809 0.999871i \(-0.494881\pi\)
0.0160809 + 0.999871i \(0.494881\pi\)
\(888\) 1.68798e148 0.215037
\(889\) 1.38765e149 1.67009
\(890\) 1.92913e147 0.0219364
\(891\) −4.50742e147 −0.0484288
\(892\) 8.53815e148 0.866839
\(893\) 8.43327e148 0.809091
\(894\) 4.29738e148 0.389636
\(895\) 5.66414e147 0.0485367
\(896\) 1.62154e149 1.31333
\(897\) −4.51788e149 −3.45872
\(898\) −4.21673e148 −0.305155
\(899\) 3.79890e149 2.59892
\(900\) 2.62205e149 1.69588
\(901\) −1.22309e149 −0.747922
\(902\) 2.51128e147 0.0145200
\(903\) −5.66340e149 −3.09632
\(904\) −7.82067e148 −0.404332
\(905\) −1.02217e148 −0.0499770
\(906\) −9.06138e148 −0.419006
\(907\) −1.47830e149 −0.646541 −0.323270 0.946307i \(-0.604782\pi\)
−0.323270 + 0.946307i \(0.604782\pi\)
\(908\) −1.56947e149 −0.649257
\(909\) 2.13057e149 0.833718
\(910\) −1.57851e148 −0.0584330
\(911\) 4.77532e149 1.67234 0.836170 0.548470i \(-0.184790\pi\)
0.836170 + 0.548470i \(0.184790\pi\)
\(912\) −1.72772e149 −0.572445
\(913\) −1.53238e148 −0.0480389
\(914\) 8.43232e148 0.250129
\(915\) 6.61809e148 0.185767
\(916\) −4.92344e148 −0.130782
\(917\) −2.78487e149 −0.700089
\(918\) 1.86112e149 0.442811
\(919\) −2.19568e148 −0.0494465 −0.0247232 0.999694i \(-0.507870\pi\)
−0.0247232 + 0.999694i \(0.507870\pi\)
\(920\) 5.87601e148 0.125256
\(921\) 1.51181e149 0.305060
\(922\) 3.77486e149 0.721090
\(923\) −2.22836e149 −0.402994
\(924\) −5.59262e148 −0.0957593
\(925\) 1.09330e149 0.177248
\(926\) −2.53209e149 −0.388708
\(927\) 1.18857e150 1.72782
\(928\) −1.05275e150 −1.44928
\(929\) −1.54224e149 −0.201076 −0.100538 0.994933i \(-0.532056\pi\)
−0.100538 + 0.994933i \(0.532056\pi\)
\(930\) −8.99373e148 −0.111058
\(931\) −3.16284e149 −0.369929
\(932\) 9.48794e149 1.05116
\(933\) 2.45649e150 2.57805
\(934\) 4.39235e149 0.436696
\(935\) −3.82389e147 −0.00360180
\(936\) −1.79353e150 −1.60058
\(937\) −2.20649e150 −1.86574 −0.932871 0.360210i \(-0.882705\pi\)
−0.932871 + 0.360210i \(0.882705\pi\)
\(938\) 4.11578e149 0.329768
\(939\) −1.38900e150 −1.05461
\(940\) 1.84313e149 0.132617
\(941\) −2.68784e150 −1.83285 −0.916426 0.400205i \(-0.868939\pi\)
−0.916426 + 0.400205i \(0.868939\pi\)
\(942\) −4.75229e149 −0.307137
\(943\) 2.20787e150 1.35248
\(944\) 8.87621e148 0.0515397
\(945\) −4.21476e149 −0.231988
\(946\) −4.91514e148 −0.0256468
\(947\) −2.21163e149 −0.109406 −0.0547028 0.998503i \(-0.517421\pi\)
−0.0547028 + 0.998503i \(0.517421\pi\)
\(948\) −1.84979e150 −0.867562
\(949\) 1.84892e149 0.0822195
\(950\) 4.80451e149 0.202585
\(951\) 6.13693e150 2.45378
\(952\) 1.63962e150 0.621695
\(953\) 4.98371e150 1.79210 0.896048 0.443957i \(-0.146426\pi\)
0.896048 + 0.443957i \(0.146426\pi\)
\(954\) −2.35016e150 −0.801501
\(955\) −5.72553e149 −0.185202
\(956\) −1.28020e150 −0.392785
\(957\) 4.66208e149 0.135683
\(958\) −4.34720e149 −0.120020
\(959\) −8.04820e150 −2.10794
\(960\) −1.89313e149 −0.0470417
\(961\) 7.26171e150 1.71202
\(962\) −3.45995e149 −0.0773977
\(963\) −6.16793e150 −1.30922
\(964\) 5.09325e150 1.02590
\(965\) 1.03515e150 0.197868
\(966\) 7.93613e150 1.43967
\(967\) −6.03489e150 −1.03904 −0.519520 0.854458i \(-0.673889\pi\)
−0.519520 + 0.854458i \(0.673889\pi\)
\(968\) 4.23497e150 0.692061
\(969\) −4.24403e150 −0.658306
\(970\) 8.33209e148 0.0122682
\(971\) −1.06084e151 −1.48278 −0.741392 0.671072i \(-0.765834\pi\)
−0.741392 + 0.671072i \(0.765834\pi\)
\(972\) 1.92544e149 0.0255495
\(973\) 1.21520e150 0.153090
\(974\) −3.36612e150 −0.402627
\(975\) −1.74500e151 −1.98181
\(976\) 5.73620e150 0.618598
\(977\) 5.88403e149 0.0602559 0.0301279 0.999546i \(-0.490409\pi\)
0.0301279 + 0.999546i \(0.490409\pi\)
\(978\) −5.32239e150 −0.517600
\(979\) −3.02807e149 −0.0279666
\(980\) −6.91252e149 −0.0606344
\(981\) 2.31161e151 1.92588
\(982\) 6.51061e149 0.0515218
\(983\) −5.74386e150 −0.431769 −0.215884 0.976419i \(-0.569263\pi\)
−0.215884 + 0.976419i \(0.569263\pi\)
\(984\) 1.31663e151 0.940180
\(985\) 1.61215e150 0.109365
\(986\) −6.32370e150 −0.407556
\(987\) 5.38043e151 3.29459
\(988\) 9.42029e150 0.548073
\(989\) −4.32129e151 −2.38891
\(990\) −7.34758e148 −0.00385982
\(991\) −6.60511e150 −0.329731 −0.164866 0.986316i \(-0.552719\pi\)
−0.164866 + 0.986316i \(0.552719\pi\)
\(992\) −3.18779e151 −1.51234
\(993\) 4.18479e151 1.88685
\(994\) 3.91434e150 0.167744
\(995\) 7.33676e149 0.0298840
\(996\) −3.71706e151 −1.43914
\(997\) −6.44459e150 −0.237186 −0.118593 0.992943i \(-0.537838\pi\)
−0.118593 + 0.992943i \(0.537838\pi\)
\(998\) 1.00217e151 0.350629
\(999\) −9.23833e150 −0.307281
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 1.102.a.a.1.5 8
3.2 odd 2 9.102.a.b.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.5 8 1.1 even 1 trivial
9.102.a.b.1.4 8 3.2 odd 2