Properties

Label 1.102.a.a.1.4
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 1.4
Root \(2.10926e12\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} +O(q^{10})\) \(q-2.56863e14 q^{2} -3.45553e23 q^{3} -2.46932e30 q^{4} +1.16158e35 q^{5} +8.87596e37 q^{6} +2.79663e42 q^{7} +1.28550e45 q^{8} -1.42673e48 q^{9} -2.98366e49 q^{10} -9.95717e51 q^{11} +8.53281e53 q^{12} -1.44350e56 q^{13} -7.18350e56 q^{14} -4.01386e58 q^{15} +5.93028e60 q^{16} +1.59801e62 q^{17} +3.66473e62 q^{18} +1.62028e64 q^{19} -2.86831e65 q^{20} -9.66383e65 q^{21} +2.55763e66 q^{22} +7.65727e68 q^{23} -4.44208e68 q^{24} -2.59504e70 q^{25} +3.70781e70 q^{26} +1.02728e72 q^{27} -6.90578e72 q^{28} -7.16454e72 q^{29} +1.03101e73 q^{30} +1.90510e75 q^{31} -4.78240e75 q^{32} +3.44073e75 q^{33} -4.10469e76 q^{34} +3.24850e77 q^{35} +3.52305e78 q^{36} -1.10721e79 q^{37} -4.16190e78 q^{38} +4.98805e79 q^{39} +1.49321e80 q^{40} -1.87777e81 q^{41} +2.48228e80 q^{42} +9.41841e81 q^{43} +2.45875e82 q^{44} -1.65725e83 q^{45} -1.96687e83 q^{46} +3.14875e84 q^{47} -2.04922e84 q^{48} -1.48202e85 q^{49} +6.66570e84 q^{50} -5.52197e85 q^{51} +3.56447e86 q^{52} -4.00521e86 q^{53} -2.63870e86 q^{54} -1.15660e87 q^{55} +3.59507e87 q^{56} -5.59893e87 q^{57} +1.84030e87 q^{58} -2.34450e89 q^{59} +9.91152e88 q^{60} -4.02186e89 q^{61} -4.89350e89 q^{62} -3.99002e90 q^{63} -1.38066e91 q^{64} -1.67674e91 q^{65} -8.83794e89 q^{66} -3.05726e92 q^{67} -3.94600e92 q^{68} -2.64599e92 q^{69} -8.34418e91 q^{70} -5.37677e93 q^{71} -1.83406e93 q^{72} -2.11035e94 q^{73} +2.84401e93 q^{74} +8.96724e93 q^{75} -4.00100e94 q^{76} -2.78465e94 q^{77} -1.28124e94 q^{78} +8.91772e95 q^{79} +6.88848e95 q^{80} +1.85093e96 q^{81} +4.82328e95 q^{82} +7.50442e96 q^{83} +2.38631e96 q^{84} +1.85621e97 q^{85} -2.41924e96 q^{86} +2.47573e96 q^{87} -1.28000e97 q^{88} -3.83813e98 q^{89} +4.25686e97 q^{90} -4.03693e98 q^{91} -1.89083e99 q^{92} -6.58314e98 q^{93} -8.08797e98 q^{94} +1.88208e99 q^{95} +1.65257e99 q^{96} +1.03291e100 q^{97} +3.80676e99 q^{98} +1.42062e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.56863e14 −0.161319 −0.0806596 0.996742i \(-0.525703\pi\)
−0.0806596 + 0.996742i \(0.525703\pi\)
\(3\) −3.45553e23 −0.277902 −0.138951 0.990299i \(-0.544373\pi\)
−0.138951 + 0.990299i \(0.544373\pi\)
\(4\) −2.46932e30 −0.973976
\(5\) 1.16158e35 0.584875 0.292437 0.956285i \(-0.405534\pi\)
0.292437 + 0.956285i \(0.405534\pi\)
\(6\) 8.87596e37 0.0448309
\(7\) 2.79663e42 0.587738 0.293869 0.955846i \(-0.405057\pi\)
0.293869 + 0.955846i \(0.405057\pi\)
\(8\) 1.28550e45 0.318440
\(9\) −1.42673e48 −0.922771
\(10\) −2.98366e49 −0.0943515
\(11\) −9.95717e51 −0.255744 −0.127872 0.991791i \(-0.540815\pi\)
−0.127872 + 0.991791i \(0.540815\pi\)
\(12\) 8.53281e53 0.270669
\(13\) −1.44350e56 −0.804039 −0.402020 0.915631i \(-0.631692\pi\)
−0.402020 + 0.915631i \(0.631692\pi\)
\(14\) −7.18350e56 −0.0948135
\(15\) −4.01386e58 −0.162538
\(16\) 5.93028e60 0.922606
\(17\) 1.59801e62 1.16388 0.581941 0.813231i \(-0.302293\pi\)
0.581941 + 0.813231i \(0.302293\pi\)
\(18\) 3.66473e62 0.148861
\(19\) 1.62028e64 0.429076 0.214538 0.976716i \(-0.431175\pi\)
0.214538 + 0.976716i \(0.431175\pi\)
\(20\) −2.86831e65 −0.569654
\(21\) −9.66383e65 −0.163333
\(22\) 2.55763e66 0.0412564
\(23\) 7.65727e68 1.30863 0.654317 0.756220i \(-0.272956\pi\)
0.654317 + 0.756220i \(0.272956\pi\)
\(24\) −4.44208e68 −0.0884951
\(25\) −2.59504e70 −0.657922
\(26\) 3.70781e70 0.129707
\(27\) 1.02728e72 0.534341
\(28\) −6.90578e72 −0.572443
\(29\) −7.16454e72 −0.100946 −0.0504730 0.998725i \(-0.516073\pi\)
−0.0504730 + 0.998725i \(0.516073\pi\)
\(30\) 1.03101e73 0.0262204
\(31\) 1.90510e75 0.925024 0.462512 0.886613i \(-0.346948\pi\)
0.462512 + 0.886613i \(0.346948\pi\)
\(32\) −4.78240e75 −0.467274
\(33\) 3.44073e75 0.0710716
\(34\) −4.10469e76 −0.187757
\(35\) 3.24850e77 0.343753
\(36\) 3.52305e78 0.898757
\(37\) −1.10721e79 −0.708017 −0.354009 0.935242i \(-0.615182\pi\)
−0.354009 + 0.935242i \(0.615182\pi\)
\(38\) −4.16190e78 −0.0692182
\(39\) 4.98805e79 0.223444
\(40\) 1.49321e80 0.186248
\(41\) −1.87777e81 −0.673064 −0.336532 0.941672i \(-0.609254\pi\)
−0.336532 + 0.941672i \(0.609254\pi\)
\(42\) 2.48228e80 0.0263488
\(43\) 9.41841e81 0.304664 0.152332 0.988329i \(-0.451322\pi\)
0.152332 + 0.988329i \(0.451322\pi\)
\(44\) 2.45875e82 0.249088
\(45\) −1.65725e83 −0.539705
\(46\) −1.96687e83 −0.211108
\(47\) 3.14875e84 1.14077 0.570383 0.821379i \(-0.306795\pi\)
0.570383 + 0.821379i \(0.306795\pi\)
\(48\) −2.04922e84 −0.256393
\(49\) −1.48202e85 −0.654564
\(50\) 6.66570e84 0.106135
\(51\) −5.52197e85 −0.323445
\(52\) 3.56447e86 0.783115
\(53\) −4.00521e86 −0.336275 −0.168137 0.985764i \(-0.553775\pi\)
−0.168137 + 0.985764i \(0.553775\pi\)
\(54\) −2.63870e86 −0.0861995
\(55\) −1.15660e87 −0.149578
\(56\) 3.59507e87 0.187160
\(57\) −5.59893e87 −0.119241
\(58\) 1.84030e87 0.0162846
\(59\) −2.34450e89 −0.875031 −0.437516 0.899211i \(-0.644142\pi\)
−0.437516 + 0.899211i \(0.644142\pi\)
\(60\) 9.91152e88 0.158308
\(61\) −4.02186e89 −0.278785 −0.139393 0.990237i \(-0.544515\pi\)
−0.139393 + 0.990237i \(0.544515\pi\)
\(62\) −4.89350e89 −0.149224
\(63\) −3.99002e90 −0.542348
\(64\) −1.38066e91 −0.847225
\(65\) −1.67674e91 −0.470262
\(66\) −8.83794e89 −0.0114652
\(67\) −3.05726e92 −1.85590 −0.927951 0.372702i \(-0.878432\pi\)
−0.927951 + 0.372702i \(0.878432\pi\)
\(68\) −3.94600e92 −1.13359
\(69\) −2.64599e92 −0.363672
\(70\) −8.34418e91 −0.0554540
\(71\) −5.37677e93 −1.74572 −0.872861 0.487968i \(-0.837738\pi\)
−0.872861 + 0.487968i \(0.837738\pi\)
\(72\) −1.83406e93 −0.293847
\(73\) −2.11035e94 −1.68480 −0.842402 0.538850i \(-0.818859\pi\)
−0.842402 + 0.538850i \(0.818859\pi\)
\(74\) 2.84401e93 0.114217
\(75\) 8.96724e93 0.182837
\(76\) −4.00100e94 −0.417910
\(77\) −2.78465e94 −0.150310
\(78\) −1.28124e94 −0.0360458
\(79\) 8.91772e95 1.31852 0.659259 0.751916i \(-0.270870\pi\)
0.659259 + 0.751916i \(0.270870\pi\)
\(80\) 6.88848e95 0.539608
\(81\) 1.85093e96 0.774277
\(82\) 4.82328e95 0.108578
\(83\) 7.50442e96 0.915954 0.457977 0.888964i \(-0.348574\pi\)
0.457977 + 0.888964i \(0.348574\pi\)
\(84\) 2.38631e96 0.159083
\(85\) 1.85621e97 0.680725
\(86\) −2.41924e96 −0.0491481
\(87\) 2.47573e96 0.0280531
\(88\) −1.28000e97 −0.0814392
\(89\) −3.83813e98 −1.38014 −0.690072 0.723741i \(-0.742421\pi\)
−0.690072 + 0.723741i \(0.742421\pi\)
\(90\) 4.25686e97 0.0870648
\(91\) −4.03693e98 −0.472565
\(92\) −1.89083e99 −1.27458
\(93\) −6.58314e98 −0.257066
\(94\) −8.08797e98 −0.184028
\(95\) 1.88208e99 0.250956
\(96\) 1.65257e99 0.129856
\(97\) 1.03291e100 0.480937 0.240469 0.970657i \(-0.422699\pi\)
0.240469 + 0.970657i \(0.422699\pi\)
\(98\) 3.80676e99 0.105594
\(99\) 1.42062e100 0.235993
\(100\) 6.40800e100 0.640800
\(101\) 2.39177e101 1.44707 0.723535 0.690288i \(-0.242516\pi\)
0.723535 + 0.690288i \(0.242516\pi\)
\(102\) 1.41839e100 0.0521778
\(103\) −1.67545e101 −0.376575 −0.188288 0.982114i \(-0.560294\pi\)
−0.188288 + 0.982114i \(0.560294\pi\)
\(104\) −1.85562e101 −0.256039
\(105\) −1.12253e101 −0.0955295
\(106\) 1.02879e101 0.0542476
\(107\) −9.91379e101 −0.325356 −0.162678 0.986679i \(-0.552013\pi\)
−0.162678 + 0.986679i \(0.552013\pi\)
\(108\) −2.53668e102 −0.520435
\(109\) −1.40368e103 −1.80814 −0.904068 0.427390i \(-0.859433\pi\)
−0.904068 + 0.427390i \(0.859433\pi\)
\(110\) 2.97088e101 0.0241298
\(111\) 3.82600e102 0.196759
\(112\) 1.65848e103 0.542251
\(113\) 1.51940e102 0.0317110 0.0158555 0.999874i \(-0.494953\pi\)
0.0158555 + 0.999874i \(0.494953\pi\)
\(114\) 1.43816e102 0.0192358
\(115\) 8.89451e103 0.765387
\(116\) 1.76916e103 0.0983191
\(117\) 2.05948e104 0.741944
\(118\) 6.02215e103 0.141159
\(119\) 4.46904e104 0.684058
\(120\) −5.15982e103 −0.0517585
\(121\) −1.41672e105 −0.934595
\(122\) 1.03306e104 0.0449734
\(123\) 6.48867e104 0.187046
\(124\) −4.70432e105 −0.900952
\(125\) −7.59596e105 −0.969676
\(126\) 1.02489e105 0.0874911
\(127\) −1.19794e106 −0.686034 −0.343017 0.939329i \(-0.611449\pi\)
−0.343017 + 0.939329i \(0.611449\pi\)
\(128\) 1.56712e106 0.603948
\(129\) −3.25456e105 −0.0846665
\(130\) 4.30691e105 0.0758623
\(131\) 1.15584e107 1.38261 0.691304 0.722564i \(-0.257037\pi\)
0.691304 + 0.722564i \(0.257037\pi\)
\(132\) −8.49627e105 −0.0692221
\(133\) 4.53133e106 0.252184
\(134\) 7.85297e106 0.299393
\(135\) 1.19326e107 0.312522
\(136\) 2.05424e107 0.370627
\(137\) −3.40012e107 −0.423746 −0.211873 0.977297i \(-0.567956\pi\)
−0.211873 + 0.977297i \(0.567956\pi\)
\(138\) 6.79657e106 0.0586672
\(139\) −2.26071e108 −1.35518 −0.677592 0.735438i \(-0.736976\pi\)
−0.677592 + 0.735438i \(0.736976\pi\)
\(140\) −8.02159e107 −0.334807
\(141\) −1.08806e108 −0.317021
\(142\) 1.38109e108 0.281619
\(143\) 1.43732e108 0.205628
\(144\) −8.46088e108 −0.851353
\(145\) −8.32217e107 −0.0590408
\(146\) 5.42069e108 0.271791
\(147\) 5.12116e108 0.181904
\(148\) 2.73406e109 0.689592
\(149\) 8.38640e109 1.50546 0.752730 0.658330i \(-0.228737\pi\)
0.752730 + 0.658330i \(0.228737\pi\)
\(150\) −2.30335e108 −0.0294952
\(151\) −9.80255e108 −0.0897436 −0.0448718 0.998993i \(-0.514288\pi\)
−0.0448718 + 0.998993i \(0.514288\pi\)
\(152\) 2.08288e109 0.136635
\(153\) −2.27992e110 −1.07400
\(154\) 7.15273e108 0.0242480
\(155\) 2.21292e110 0.541023
\(156\) −1.23171e110 −0.217629
\(157\) −1.27999e111 −1.63785 −0.818923 0.573903i \(-0.805429\pi\)
−0.818923 + 0.573903i \(0.805429\pi\)
\(158\) −2.29063e110 −0.212702
\(159\) 1.38401e110 0.0934512
\(160\) −5.55513e110 −0.273297
\(161\) 2.14146e111 0.769135
\(162\) −4.75434e110 −0.124906
\(163\) 1.59995e111 0.308058 0.154029 0.988066i \(-0.450775\pi\)
0.154029 + 0.988066i \(0.450775\pi\)
\(164\) 4.63681e111 0.655548
\(165\) 3.99667e110 0.0415680
\(166\) −1.92761e111 −0.147761
\(167\) 2.33044e112 1.31904 0.659518 0.751689i \(-0.270761\pi\)
0.659518 + 0.751689i \(0.270761\pi\)
\(168\) −1.24229e111 −0.0520119
\(169\) −1.13945e112 −0.353521
\(170\) −4.76791e111 −0.109814
\(171\) −2.31170e112 −0.395939
\(172\) −2.32571e112 −0.296735
\(173\) −8.33103e112 −0.793178 −0.396589 0.917996i \(-0.629806\pi\)
−0.396589 + 0.917996i \(0.629806\pi\)
\(174\) −6.35922e110 −0.00452550
\(175\) −7.25738e112 −0.386686
\(176\) −5.90488e112 −0.235951
\(177\) 8.10148e112 0.243173
\(178\) 9.85873e112 0.222644
\(179\) −3.61084e113 −0.614512 −0.307256 0.951627i \(-0.599411\pi\)
−0.307256 + 0.951627i \(0.599411\pi\)
\(180\) 4.09229e113 0.525660
\(181\) 1.67890e114 1.63026 0.815132 0.579275i \(-0.196664\pi\)
0.815132 + 0.579275i \(0.196664\pi\)
\(182\) 1.03694e113 0.0762338
\(183\) 1.38976e113 0.0774748
\(184\) 9.84344e113 0.416722
\(185\) −1.28611e114 −0.414101
\(186\) 1.69096e113 0.0414697
\(187\) −1.59117e114 −0.297656
\(188\) −7.77529e114 −1.11108
\(189\) 2.87292e114 0.314053
\(190\) −4.83437e113 −0.0404840
\(191\) −2.24809e114 −0.144421 −0.0722103 0.997389i \(-0.523005\pi\)
−0.0722103 + 0.997389i \(0.523005\pi\)
\(192\) 4.77092e114 0.235445
\(193\) −3.98577e115 −1.51310 −0.756551 0.653934i \(-0.773117\pi\)
−0.756551 + 0.653934i \(0.773117\pi\)
\(194\) −2.65315e114 −0.0775844
\(195\) 5.79400e114 0.130687
\(196\) 3.65959e115 0.637529
\(197\) 9.87434e115 1.33034 0.665171 0.746691i \(-0.268358\pi\)
0.665171 + 0.746691i \(0.268358\pi\)
\(198\) −3.64903e114 −0.0380702
\(199\) 4.01699e115 0.324953 0.162476 0.986712i \(-0.448052\pi\)
0.162476 + 0.986712i \(0.448052\pi\)
\(200\) −3.33593e115 −0.209509
\(201\) 1.05645e116 0.515758
\(202\) −6.14356e115 −0.233440
\(203\) −2.00366e115 −0.0593299
\(204\) 1.36355e116 0.315027
\(205\) −2.18117e116 −0.393658
\(206\) 4.30361e115 0.0607489
\(207\) −1.09248e117 −1.20757
\(208\) −8.56035e116 −0.741811
\(209\) −1.61334e116 −0.109734
\(210\) 2.88336e115 0.0154108
\(211\) 4.53257e116 0.190581 0.0952907 0.995449i \(-0.469622\pi\)
0.0952907 + 0.995449i \(0.469622\pi\)
\(212\) 9.89016e116 0.327523
\(213\) 1.85796e117 0.485139
\(214\) 2.54648e116 0.0524862
\(215\) 1.09402e117 0.178190
\(216\) 1.32057e117 0.170156
\(217\) 5.32787e117 0.543672
\(218\) 3.60554e117 0.291687
\(219\) 7.29236e117 0.468209
\(220\) 2.85602e117 0.145685
\(221\) −2.30673e118 −0.935807
\(222\) −9.82757e116 −0.0317410
\(223\) −3.52241e118 −0.906660 −0.453330 0.891343i \(-0.649764\pi\)
−0.453330 + 0.891343i \(0.649764\pi\)
\(224\) −1.33746e118 −0.274635
\(225\) 3.70242e118 0.607111
\(226\) −3.90276e116 −0.00511559
\(227\) −1.25414e119 −1.31535 −0.657674 0.753302i \(-0.728460\pi\)
−0.657674 + 0.753302i \(0.728460\pi\)
\(228\) 1.38256e118 0.116138
\(229\) 5.60999e118 0.377807 0.188904 0.981996i \(-0.439507\pi\)
0.188904 + 0.981996i \(0.439507\pi\)
\(230\) −2.28467e118 −0.123472
\(231\) 9.62244e117 0.0417715
\(232\) −9.21003e117 −0.0321453
\(233\) 4.54576e119 1.27683 0.638415 0.769693i \(-0.279591\pi\)
0.638415 + 0.769693i \(0.279591\pi\)
\(234\) −5.29003e118 −0.119690
\(235\) 3.65752e119 0.667205
\(236\) 5.78933e119 0.852260
\(237\) −3.08154e119 −0.366418
\(238\) −1.14793e119 −0.110352
\(239\) −1.02709e120 −0.798939 −0.399469 0.916747i \(-0.630806\pi\)
−0.399469 + 0.916747i \(0.630806\pi\)
\(240\) −2.38033e119 −0.149958
\(241\) −8.90997e119 −0.455005 −0.227502 0.973778i \(-0.573056\pi\)
−0.227502 + 0.973778i \(0.573056\pi\)
\(242\) 3.63903e119 0.150768
\(243\) −2.22790e120 −0.749514
\(244\) 9.93126e119 0.271530
\(245\) −1.72148e120 −0.382838
\(246\) −1.66670e119 −0.0301741
\(247\) −2.33888e120 −0.344994
\(248\) 2.44901e120 0.294565
\(249\) −2.59317e120 −0.254545
\(250\) 1.95112e120 0.156427
\(251\) 2.54170e121 1.66572 0.832860 0.553484i \(-0.186702\pi\)
0.832860 + 0.553484i \(0.186702\pi\)
\(252\) 9.85266e120 0.528234
\(253\) −7.62448e120 −0.334675
\(254\) 3.07705e120 0.110671
\(255\) −6.41419e120 −0.189174
\(256\) 3.09786e121 0.749797
\(257\) −6.07536e121 −1.20767 −0.603836 0.797108i \(-0.706362\pi\)
−0.603836 + 0.797108i \(0.706362\pi\)
\(258\) 8.35974e119 0.0136583
\(259\) −3.09646e121 −0.416129
\(260\) 4.14040e121 0.458024
\(261\) 1.02218e121 0.0931501
\(262\) −2.96893e121 −0.223041
\(263\) −2.58199e122 −1.60026 −0.800128 0.599829i \(-0.795235\pi\)
−0.800128 + 0.599829i \(0.795235\pi\)
\(264\) 4.42306e120 0.0226321
\(265\) −4.65236e121 −0.196678
\(266\) −1.16393e121 −0.0406822
\(267\) 1.32628e122 0.383544
\(268\) 7.54937e122 1.80760
\(269\) −2.19706e122 −0.435865 −0.217932 0.975964i \(-0.569931\pi\)
−0.217932 + 0.975964i \(0.569931\pi\)
\(270\) −3.06505e121 −0.0504159
\(271\) −2.27556e122 −0.310555 −0.155278 0.987871i \(-0.549627\pi\)
−0.155278 + 0.987871i \(0.549627\pi\)
\(272\) 9.47664e122 1.07380
\(273\) 1.39497e122 0.131326
\(274\) 8.73363e121 0.0683583
\(275\) 2.58393e122 0.168259
\(276\) 6.53381e122 0.354207
\(277\) −2.83013e123 −1.27814 −0.639070 0.769148i \(-0.720681\pi\)
−0.639070 + 0.769148i \(0.720681\pi\)
\(278\) 5.80693e122 0.218617
\(279\) −2.71806e123 −0.853586
\(280\) 4.17595e122 0.109465
\(281\) −5.27048e123 −1.15393 −0.576967 0.816768i \(-0.695764\pi\)
−0.576967 + 0.816768i \(0.695764\pi\)
\(282\) 2.79482e122 0.0511416
\(283\) −4.08346e123 −0.624904 −0.312452 0.949934i \(-0.601150\pi\)
−0.312452 + 0.949934i \(0.601150\pi\)
\(284\) 1.32770e124 1.70029
\(285\) −6.50359e122 −0.0697409
\(286\) −3.69193e122 −0.0331718
\(287\) −5.25141e123 −0.395586
\(288\) 6.82317e123 0.431187
\(289\) 6.68506e123 0.354621
\(290\) 2.13765e122 0.00952442
\(291\) −3.56924e123 −0.133653
\(292\) 5.21112e124 1.64096
\(293\) −6.02275e123 −0.159580 −0.0797902 0.996812i \(-0.525425\pi\)
−0.0797902 + 0.996812i \(0.525425\pi\)
\(294\) −1.31543e123 −0.0293447
\(295\) −2.72332e124 −0.511784
\(296\) −1.42332e124 −0.225461
\(297\) −1.02288e124 −0.136654
\(298\) −2.15415e124 −0.242860
\(299\) −1.10533e125 −1.05219
\(300\) −2.21430e124 −0.178079
\(301\) 2.63398e124 0.179062
\(302\) 2.51791e123 0.0144774
\(303\) −8.26481e124 −0.402143
\(304\) 9.60873e124 0.395868
\(305\) −4.67169e124 −0.163054
\(306\) 5.85627e124 0.173256
\(307\) 2.01247e125 0.504943 0.252471 0.967604i \(-0.418757\pi\)
0.252471 + 0.967604i \(0.418757\pi\)
\(308\) 6.87620e124 0.146399
\(309\) 5.78957e124 0.104651
\(310\) −5.68418e124 −0.0872775
\(311\) 9.00803e125 1.17552 0.587760 0.809035i \(-0.300010\pi\)
0.587760 + 0.809035i \(0.300010\pi\)
\(312\) 6.41214e124 0.0711535
\(313\) 4.50650e125 0.425452 0.212726 0.977112i \(-0.431766\pi\)
0.212726 + 0.977112i \(0.431766\pi\)
\(314\) 3.28781e125 0.264216
\(315\) −4.63472e125 −0.317205
\(316\) −2.20207e126 −1.28420
\(317\) −1.39121e126 −0.691671 −0.345835 0.938295i \(-0.612404\pi\)
−0.345835 + 0.938295i \(0.612404\pi\)
\(318\) −3.55501e124 −0.0150755
\(319\) 7.13386e124 0.0258163
\(320\) −1.60375e126 −0.495520
\(321\) 3.42574e125 0.0904170
\(322\) −5.50060e125 −0.124076
\(323\) 2.58923e126 0.499394
\(324\) −4.57054e126 −0.754127
\(325\) 3.74594e126 0.528995
\(326\) −4.10968e125 −0.0496957
\(327\) 4.85046e126 0.502484
\(328\) −2.41387e126 −0.214331
\(329\) 8.80590e126 0.670472
\(330\) −1.02660e125 −0.00670572
\(331\) 2.75350e127 1.54373 0.771864 0.635788i \(-0.219325\pi\)
0.771864 + 0.635788i \(0.219325\pi\)
\(332\) −1.85308e127 −0.892117
\(333\) 1.57969e127 0.653337
\(334\) −5.98604e126 −0.212786
\(335\) −3.55124e127 −1.08547
\(336\) −5.73092e126 −0.150692
\(337\) 7.77367e126 0.175920 0.0879602 0.996124i \(-0.471965\pi\)
0.0879602 + 0.996124i \(0.471965\pi\)
\(338\) 2.92681e126 0.0570297
\(339\) −5.25031e125 −0.00881252
\(340\) −4.58358e127 −0.663010
\(341\) −1.89694e127 −0.236569
\(342\) 5.93789e126 0.0638725
\(343\) −1.04766e128 −0.972450
\(344\) 1.21074e127 0.0970172
\(345\) −3.07352e127 −0.212702
\(346\) 2.13993e127 0.127955
\(347\) 2.37286e128 1.22640 0.613202 0.789926i \(-0.289881\pi\)
0.613202 + 0.789926i \(0.289881\pi\)
\(348\) −6.11337e126 −0.0273230
\(349\) 3.72904e128 1.44183 0.720913 0.693026i \(-0.243723\pi\)
0.720913 + 0.693026i \(0.243723\pi\)
\(350\) 1.86415e127 0.0623799
\(351\) −1.48288e128 −0.429631
\(352\) 4.76192e127 0.119503
\(353\) 7.61652e126 0.0165628 0.00828140 0.999966i \(-0.497364\pi\)
0.00828140 + 0.999966i \(0.497364\pi\)
\(354\) −2.08097e127 −0.0392284
\(355\) −6.24554e128 −1.02103
\(356\) 9.47758e128 1.34423
\(357\) −1.54429e128 −0.190101
\(358\) 9.27491e127 0.0991327
\(359\) −1.27355e129 −1.18235 −0.591175 0.806543i \(-0.701336\pi\)
−0.591175 + 0.806543i \(0.701336\pi\)
\(360\) −2.13040e128 −0.171864
\(361\) −1.16345e129 −0.815894
\(362\) −4.31248e128 −0.262993
\(363\) 4.89552e128 0.259725
\(364\) 9.96849e128 0.460267
\(365\) −2.45133e129 −0.985398
\(366\) −3.56978e127 −0.0124982
\(367\) 1.66816e129 0.508863 0.254431 0.967091i \(-0.418112\pi\)
0.254431 + 0.967091i \(0.418112\pi\)
\(368\) 4.54098e129 1.20735
\(369\) 2.67906e129 0.621084
\(370\) 3.30354e128 0.0668025
\(371\) −1.12011e129 −0.197641
\(372\) 1.62559e129 0.250376
\(373\) −3.54244e129 −0.476438 −0.238219 0.971211i \(-0.576564\pi\)
−0.238219 + 0.971211i \(0.576564\pi\)
\(374\) 4.08711e128 0.0480176
\(375\) 2.62480e129 0.269475
\(376\) 4.04773e129 0.363266
\(377\) 1.03420e129 0.0811646
\(378\) −7.37946e128 −0.0506627
\(379\) −1.58386e130 −0.951561 −0.475781 0.879564i \(-0.657834\pi\)
−0.475781 + 0.879564i \(0.657834\pi\)
\(380\) −4.64747e129 −0.244425
\(381\) 4.13950e129 0.190650
\(382\) 5.77451e128 0.0232978
\(383\) −3.23739e130 −1.14461 −0.572305 0.820041i \(-0.693951\pi\)
−0.572305 + 0.820041i \(0.693951\pi\)
\(384\) −5.41524e129 −0.167838
\(385\) −3.23459e129 −0.0879128
\(386\) 1.02380e130 0.244093
\(387\) −1.34375e130 −0.281135
\(388\) −2.55058e130 −0.468421
\(389\) 8.82272e130 1.42281 0.711406 0.702781i \(-0.248059\pi\)
0.711406 + 0.702781i \(0.248059\pi\)
\(390\) −1.48826e129 −0.0210823
\(391\) 1.22364e131 1.52310
\(392\) −1.90514e130 −0.208440
\(393\) −3.99405e130 −0.384229
\(394\) −2.53635e130 −0.214610
\(395\) 1.03586e131 0.771167
\(396\) −3.50796e130 −0.229852
\(397\) 5.46354e130 0.315176 0.157588 0.987505i \(-0.449628\pi\)
0.157588 + 0.987505i \(0.449628\pi\)
\(398\) −1.03181e130 −0.0524211
\(399\) −1.56581e130 −0.0700824
\(400\) −1.53893e131 −0.607002
\(401\) 1.18778e130 0.0412996 0.0206498 0.999787i \(-0.493426\pi\)
0.0206498 + 0.999787i \(0.493426\pi\)
\(402\) −2.71361e130 −0.0832017
\(403\) −2.75002e131 −0.743756
\(404\) −5.90604e131 −1.40941
\(405\) 2.15000e131 0.452855
\(406\) 5.14665e129 0.00957105
\(407\) 1.10247e131 0.181071
\(408\) −7.09849e130 −0.102998
\(409\) 6.47684e131 0.830493 0.415247 0.909709i \(-0.363695\pi\)
0.415247 + 0.909709i \(0.363695\pi\)
\(410\) 5.60261e130 0.0635046
\(411\) 1.17492e131 0.117760
\(412\) 4.13723e131 0.366775
\(413\) −6.55670e131 −0.514289
\(414\) 2.80618e131 0.194804
\(415\) 8.71696e131 0.535718
\(416\) 6.90339e131 0.375707
\(417\) 7.81196e131 0.376608
\(418\) 4.14408e130 0.0177021
\(419\) 3.66872e131 0.138901 0.0694507 0.997585i \(-0.477875\pi\)
0.0694507 + 0.997585i \(0.477875\pi\)
\(420\) 2.77188e131 0.0930435
\(421\) −1.22752e132 −0.365412 −0.182706 0.983168i \(-0.558486\pi\)
−0.182706 + 0.983168i \(0.558486\pi\)
\(422\) −1.16425e131 −0.0307445
\(423\) −4.49241e132 −1.05267
\(424\) −5.14871e131 −0.107083
\(425\) −4.14691e132 −0.765743
\(426\) −4.77240e131 −0.0782623
\(427\) −1.12476e132 −0.163853
\(428\) 2.44803e132 0.316889
\(429\) −4.96669e131 −0.0571444
\(430\) −2.81013e131 −0.0287455
\(431\) 1.06447e133 0.968344 0.484172 0.874973i \(-0.339121\pi\)
0.484172 + 0.874973i \(0.339121\pi\)
\(432\) 6.09205e132 0.492986
\(433\) −2.64916e133 −1.90752 −0.953762 0.300564i \(-0.902825\pi\)
−0.953762 + 0.300564i \(0.902825\pi\)
\(434\) −1.36853e132 −0.0877048
\(435\) 2.87575e131 0.0164075
\(436\) 3.46615e133 1.76108
\(437\) 1.24070e133 0.561504
\(438\) −1.87313e132 −0.0755312
\(439\) 1.51769e133 0.545411 0.272706 0.962098i \(-0.412081\pi\)
0.272706 + 0.962098i \(0.412081\pi\)
\(440\) −1.48681e132 −0.0476317
\(441\) 2.11444e133 0.604012
\(442\) 5.92512e132 0.150964
\(443\) −5.30570e133 −1.20602 −0.603010 0.797733i \(-0.706032\pi\)
−0.603010 + 0.797733i \(0.706032\pi\)
\(444\) −9.44763e132 −0.191639
\(445\) −4.45828e133 −0.807211
\(446\) 9.04776e132 0.146262
\(447\) −2.89794e133 −0.418369
\(448\) −3.86120e133 −0.497947
\(449\) 5.37070e131 0.00618857 0.00309429 0.999995i \(-0.499015\pi\)
0.00309429 + 0.999995i \(0.499015\pi\)
\(450\) −9.51013e132 −0.0979387
\(451\) 1.86972e133 0.172132
\(452\) −3.75188e132 −0.0308857
\(453\) 3.38730e132 0.0249399
\(454\) 3.22142e133 0.212191
\(455\) −4.68921e133 −0.276391
\(456\) −7.19743e132 −0.0379711
\(457\) 2.17557e134 1.02755 0.513777 0.857924i \(-0.328246\pi\)
0.513777 + 0.857924i \(0.328246\pi\)
\(458\) −1.44100e133 −0.0609476
\(459\) 1.64160e134 0.621910
\(460\) −2.19634e134 −0.745469
\(461\) 3.26419e134 0.992838 0.496419 0.868083i \(-0.334648\pi\)
0.496419 + 0.868083i \(0.334648\pi\)
\(462\) −2.47165e132 −0.00673855
\(463\) 2.23237e134 0.545664 0.272832 0.962062i \(-0.412040\pi\)
0.272832 + 0.962062i \(0.412040\pi\)
\(464\) −4.24877e133 −0.0931334
\(465\) −7.64682e133 −0.150351
\(466\) −1.16764e134 −0.205977
\(467\) 1.51582e134 0.239963 0.119982 0.992776i \(-0.461716\pi\)
0.119982 + 0.992776i \(0.461716\pi\)
\(468\) −5.08551e134 −0.722636
\(469\) −8.55003e134 −1.09078
\(470\) −9.39480e133 −0.107633
\(471\) 4.42303e134 0.455160
\(472\) −3.01386e134 −0.278645
\(473\) −9.37807e133 −0.0779158
\(474\) 7.91533e133 0.0591103
\(475\) −4.20471e134 −0.282298
\(476\) −1.10355e135 −0.666256
\(477\) 5.71434e134 0.310304
\(478\) 2.63820e134 0.128884
\(479\) 1.07969e135 0.474632 0.237316 0.971432i \(-0.423732\pi\)
0.237316 + 0.971432i \(0.423732\pi\)
\(480\) 1.91959e134 0.0759496
\(481\) 1.59826e135 0.569273
\(482\) 2.28864e134 0.0734010
\(483\) −7.39986e134 −0.213744
\(484\) 3.49834e135 0.910273
\(485\) 1.19980e135 0.281288
\(486\) 5.72265e134 0.120911
\(487\) 1.89475e135 0.360861 0.180430 0.983588i \(-0.442251\pi\)
0.180430 + 0.983588i \(0.442251\pi\)
\(488\) −5.17010e134 −0.0887765
\(489\) −5.52867e134 −0.0856098
\(490\) 4.42184e134 0.0617591
\(491\) −1.35592e136 −1.70851 −0.854257 0.519852i \(-0.825987\pi\)
−0.854257 + 0.519852i \(0.825987\pi\)
\(492\) −1.60226e135 −0.182178
\(493\) −1.14490e135 −0.117489
\(494\) 6.00770e134 0.0556541
\(495\) 1.65015e135 0.138026
\(496\) 1.12978e136 0.853433
\(497\) −1.50368e136 −1.02603
\(498\) 6.66089e134 0.0410630
\(499\) −3.19004e136 −1.77713 −0.888563 0.458755i \(-0.848295\pi\)
−0.888563 + 0.458755i \(0.848295\pi\)
\(500\) 1.87569e136 0.944441
\(501\) −8.05290e135 −0.366562
\(502\) −6.52869e135 −0.268713
\(503\) 4.79960e136 1.78658 0.893288 0.449485i \(-0.148392\pi\)
0.893288 + 0.449485i \(0.148392\pi\)
\(504\) −5.12918e135 −0.172705
\(505\) 2.77822e136 0.846354
\(506\) 1.95844e135 0.0539896
\(507\) 3.93739e135 0.0982440
\(508\) 2.95809e136 0.668181
\(509\) 1.97121e136 0.403167 0.201583 0.979471i \(-0.435391\pi\)
0.201583 + 0.979471i \(0.435391\pi\)
\(510\) 1.64757e135 0.0305175
\(511\) −5.90185e136 −0.990223
\(512\) −4.76885e136 −0.724905
\(513\) 1.66448e136 0.229273
\(514\) 1.56053e136 0.194821
\(515\) −1.94616e136 −0.220249
\(516\) 8.03655e135 0.0824631
\(517\) −3.13527e136 −0.291744
\(518\) 7.95366e135 0.0671296
\(519\) 2.87881e136 0.220425
\(520\) −2.15545e136 −0.149750
\(521\) −1.89189e137 −1.19286 −0.596430 0.802665i \(-0.703415\pi\)
−0.596430 + 0.802665i \(0.703415\pi\)
\(522\) −2.62561e135 −0.0150269
\(523\) 6.85650e136 0.356260 0.178130 0.984007i \(-0.442995\pi\)
0.178130 + 0.984007i \(0.442995\pi\)
\(524\) −2.85415e137 −1.34663
\(525\) 2.50781e136 0.107461
\(526\) 6.63217e136 0.258152
\(527\) 3.04438e137 1.07662
\(528\) 2.04045e136 0.0655711
\(529\) 2.43956e137 0.712525
\(530\) 1.19502e136 0.0317280
\(531\) 3.34496e137 0.807453
\(532\) −1.11893e137 −0.245621
\(533\) 2.71055e137 0.541170
\(534\) −3.40671e136 −0.0618731
\(535\) −1.15156e137 −0.190293
\(536\) −3.93011e137 −0.590994
\(537\) 1.24774e137 0.170774
\(538\) 5.64342e136 0.0703134
\(539\) 1.47567e137 0.167401
\(540\) −2.94655e137 −0.304389
\(541\) −1.17231e137 −0.110301 −0.0551506 0.998478i \(-0.517564\pi\)
−0.0551506 + 0.998478i \(0.517564\pi\)
\(542\) 5.84506e136 0.0500986
\(543\) −5.80150e137 −0.453053
\(544\) −7.64232e137 −0.543852
\(545\) −1.63049e138 −1.05753
\(546\) −3.58317e136 −0.0211855
\(547\) −1.71733e136 −0.00925751 −0.00462875 0.999989i \(-0.501473\pi\)
−0.00462875 + 0.999989i \(0.501473\pi\)
\(548\) 8.39599e137 0.412718
\(549\) 5.73808e137 0.257255
\(550\) −6.63715e136 −0.0271435
\(551\) −1.16086e137 −0.0433135
\(552\) −3.40143e137 −0.115808
\(553\) 2.49396e138 0.774943
\(554\) 7.26956e137 0.206189
\(555\) 4.44419e137 0.115079
\(556\) 5.58243e138 1.31992
\(557\) −1.70337e138 −0.367808 −0.183904 0.982944i \(-0.558874\pi\)
−0.183904 + 0.982944i \(0.558874\pi\)
\(558\) 6.98169e137 0.137700
\(559\) −1.35955e138 −0.244961
\(560\) 1.92645e138 0.317149
\(561\) 5.49831e137 0.0827190
\(562\) 1.35379e138 0.186152
\(563\) −1.19099e139 −1.49705 −0.748523 0.663109i \(-0.769237\pi\)
−0.748523 + 0.663109i \(0.769237\pi\)
\(564\) 2.68677e138 0.308771
\(565\) 1.76489e137 0.0185469
\(566\) 1.04889e138 0.100809
\(567\) 5.17636e138 0.455072
\(568\) −6.91185e138 −0.555909
\(569\) −2.22588e139 −1.63807 −0.819034 0.573745i \(-0.805490\pi\)
−0.819034 + 0.573745i \(0.805490\pi\)
\(570\) 1.67053e137 0.0112506
\(571\) 7.96541e138 0.491004 0.245502 0.969396i \(-0.421047\pi\)
0.245502 + 0.969396i \(0.421047\pi\)
\(572\) −3.54920e138 −0.200277
\(573\) 7.76834e137 0.0401347
\(574\) 1.34889e138 0.0638156
\(575\) −1.98710e139 −0.860979
\(576\) 1.96983e139 0.781795
\(577\) 2.07485e139 0.754411 0.377205 0.926130i \(-0.376885\pi\)
0.377205 + 0.926130i \(0.376885\pi\)
\(578\) −1.71714e138 −0.0572072
\(579\) 1.37729e139 0.420494
\(580\) 2.05501e138 0.0575043
\(581\) 2.09871e139 0.538341
\(582\) 9.16804e137 0.0215608
\(583\) 3.98806e138 0.0860002
\(584\) −2.71285e139 −0.536509
\(585\) 2.39224e139 0.433944
\(586\) 1.54702e138 0.0257434
\(587\) 2.85396e139 0.435736 0.217868 0.975978i \(-0.430090\pi\)
0.217868 + 0.975978i \(0.430090\pi\)
\(588\) −1.26458e139 −0.177170
\(589\) 3.08681e139 0.396906
\(590\) 6.99519e138 0.0825606
\(591\) −3.41210e139 −0.369704
\(592\) −6.56608e139 −0.653220
\(593\) −1.04560e140 −0.955220 −0.477610 0.878572i \(-0.658497\pi\)
−0.477610 + 0.878572i \(0.658497\pi\)
\(594\) 2.62740e138 0.0220450
\(595\) 5.19113e139 0.400088
\(596\) −2.07087e140 −1.46628
\(597\) −1.38808e139 −0.0903048
\(598\) 2.83917e139 0.169739
\(599\) −1.21440e140 −0.667277 −0.333639 0.942701i \(-0.608277\pi\)
−0.333639 + 0.942701i \(0.608277\pi\)
\(600\) 1.15274e139 0.0582228
\(601\) 2.46874e140 1.14634 0.573171 0.819436i \(-0.305713\pi\)
0.573171 + 0.819436i \(0.305713\pi\)
\(602\) −6.76571e138 −0.0288862
\(603\) 4.36188e140 1.71257
\(604\) 2.42057e139 0.0874081
\(605\) −1.64563e140 −0.546621
\(606\) 2.12292e139 0.0648734
\(607\) 1.09575e140 0.308093 0.154046 0.988064i \(-0.450770\pi\)
0.154046 + 0.988064i \(0.450770\pi\)
\(608\) −7.74884e139 −0.200496
\(609\) 6.92369e138 0.0164879
\(610\) 1.19998e139 0.0263038
\(611\) −4.54522e140 −0.917221
\(612\) 5.62986e140 1.04605
\(613\) 7.23778e140 1.23837 0.619186 0.785244i \(-0.287463\pi\)
0.619186 + 0.785244i \(0.287463\pi\)
\(614\) −5.16929e139 −0.0814570
\(615\) 7.53709e139 0.109398
\(616\) −3.57967e139 −0.0478649
\(617\) −1.53781e141 −1.89453 −0.947265 0.320452i \(-0.896165\pi\)
−0.947265 + 0.320452i \(0.896165\pi\)
\(618\) −1.48712e139 −0.0168822
\(619\) −6.21672e140 −0.650404 −0.325202 0.945644i \(-0.605432\pi\)
−0.325202 + 0.945644i \(0.605432\pi\)
\(620\) −5.46443e140 −0.526944
\(621\) 7.86616e140 0.699257
\(622\) −2.31383e140 −0.189634
\(623\) −1.07338e141 −0.811164
\(624\) 2.95805e140 0.206150
\(625\) 1.41236e140 0.0907829
\(626\) −1.15755e140 −0.0686336
\(627\) 5.57495e139 0.0304951
\(628\) 3.16070e141 1.59522
\(629\) −1.76934e141 −0.824048
\(630\) 1.19049e140 0.0511713
\(631\) 1.33263e141 0.528721 0.264360 0.964424i \(-0.414839\pi\)
0.264360 + 0.964424i \(0.414839\pi\)
\(632\) 1.14637e141 0.419869
\(633\) −1.56624e140 −0.0529629
\(634\) 3.57349e140 0.111580
\(635\) −1.39150e141 −0.401244
\(636\) −3.41757e140 −0.0910193
\(637\) 2.13929e141 0.526295
\(638\) −1.83242e139 −0.00416467
\(639\) 7.67118e141 1.61090
\(640\) 1.82033e141 0.353234
\(641\) −1.00041e142 −1.79410 −0.897049 0.441931i \(-0.854294\pi\)
−0.897049 + 0.441931i \(0.854294\pi\)
\(642\) −8.79944e139 −0.0145860
\(643\) 6.42814e140 0.0984989 0.0492494 0.998787i \(-0.484317\pi\)
0.0492494 + 0.998787i \(0.484317\pi\)
\(644\) −5.28795e141 −0.749119
\(645\) −3.78042e140 −0.0495193
\(646\) −6.65076e140 −0.0805618
\(647\) −1.06846e142 −1.19699 −0.598496 0.801126i \(-0.704235\pi\)
−0.598496 + 0.801126i \(0.704235\pi\)
\(648\) 2.37937e141 0.246561
\(649\) 2.33446e141 0.223784
\(650\) −9.62193e140 −0.0853371
\(651\) −1.84106e141 −0.151087
\(652\) −3.95080e141 −0.300041
\(653\) −8.23618e140 −0.0578909 −0.0289454 0.999581i \(-0.509215\pi\)
−0.0289454 + 0.999581i \(0.509215\pi\)
\(654\) −1.24590e141 −0.0810603
\(655\) 1.34260e142 0.808652
\(656\) −1.11357e142 −0.620973
\(657\) 3.01088e142 1.55469
\(658\) −2.26191e141 −0.108160
\(659\) −1.12345e142 −0.497556 −0.248778 0.968561i \(-0.580029\pi\)
−0.248778 + 0.968561i \(0.580029\pi\)
\(660\) −9.86906e140 −0.0404862
\(661\) 4.11483e142 1.56379 0.781895 0.623410i \(-0.214253\pi\)
0.781895 + 0.623410i \(0.214253\pi\)
\(662\) −7.07271e141 −0.249033
\(663\) 7.97095e141 0.260062
\(664\) 9.64694e141 0.291677
\(665\) 5.26349e141 0.147496
\(666\) −4.05763e141 −0.105396
\(667\) −5.48609e141 −0.132102
\(668\) −5.75461e142 −1.28471
\(669\) 1.21718e142 0.251962
\(670\) 9.12182e141 0.175107
\(671\) 4.00463e141 0.0712976
\(672\) 4.62163e141 0.0763215
\(673\) −1.14033e143 −1.74691 −0.873456 0.486902i \(-0.838127\pi\)
−0.873456 + 0.486902i \(0.838127\pi\)
\(674\) −1.99677e141 −0.0283793
\(675\) −2.66583e142 −0.351555
\(676\) 2.81366e142 0.344321
\(677\) −1.56671e142 −0.177935 −0.0889673 0.996035i \(-0.528357\pi\)
−0.0889673 + 0.996035i \(0.528357\pi\)
\(678\) 1.34861e140 0.00142163
\(679\) 2.88866e142 0.282665
\(680\) 2.38616e142 0.216770
\(681\) 4.33372e142 0.365537
\(682\) 4.87254e141 0.0381632
\(683\) −2.23192e142 −0.162343 −0.0811714 0.996700i \(-0.525866\pi\)
−0.0811714 + 0.996700i \(0.525866\pi\)
\(684\) 5.70833e142 0.385635
\(685\) −3.94950e142 −0.247838
\(686\) 2.69105e142 0.156875
\(687\) −1.93855e142 −0.104993
\(688\) 5.58538e142 0.281084
\(689\) 5.78152e142 0.270378
\(690\) 7.89473e141 0.0343130
\(691\) 2.36035e143 0.953530 0.476765 0.879031i \(-0.341809\pi\)
0.476765 + 0.879031i \(0.341809\pi\)
\(692\) 2.05720e143 0.772537
\(693\) 3.97293e142 0.138702
\(694\) −6.09499e142 −0.197843
\(695\) −2.62599e143 −0.792612
\(696\) 3.18255e141 0.00893323
\(697\) −3.00069e143 −0.783367
\(698\) −9.57851e142 −0.232594
\(699\) −1.57080e143 −0.354833
\(700\) 1.79208e143 0.376623
\(701\) −6.16772e143 −1.20605 −0.603025 0.797723i \(-0.706038\pi\)
−0.603025 + 0.797723i \(0.706038\pi\)
\(702\) 3.80896e142 0.0693078
\(703\) −1.79400e143 −0.303793
\(704\) 1.37475e143 0.216673
\(705\) −1.26387e143 −0.185417
\(706\) −1.95640e141 −0.00267190
\(707\) 6.68888e143 0.850498
\(708\) −2.00052e143 −0.236844
\(709\) 4.62173e143 0.509529 0.254765 0.967003i \(-0.418002\pi\)
0.254765 + 0.967003i \(0.418002\pi\)
\(710\) 1.60425e143 0.164712
\(711\) −1.27231e144 −1.21669
\(712\) −4.93392e143 −0.439494
\(713\) 1.45879e144 1.21052
\(714\) 3.96670e142 0.0306669
\(715\) 1.66955e143 0.120267
\(716\) 8.91634e143 0.598520
\(717\) 3.54913e143 0.222026
\(718\) 3.27127e143 0.190736
\(719\) 3.09556e144 1.68241 0.841203 0.540719i \(-0.181848\pi\)
0.841203 + 0.540719i \(0.181848\pi\)
\(720\) −9.82797e143 −0.497935
\(721\) −4.68562e143 −0.221328
\(722\) 2.98847e143 0.131619
\(723\) 3.07887e143 0.126446
\(724\) −4.14576e144 −1.58784
\(725\) 1.85923e143 0.0664146
\(726\) −1.25748e143 −0.0418987
\(727\) −3.18407e144 −0.989681 −0.494840 0.868984i \(-0.664773\pi\)
−0.494840 + 0.868984i \(0.664773\pi\)
\(728\) −5.18948e143 −0.150484
\(729\) −2.09192e144 −0.565986
\(730\) 6.29655e143 0.158964
\(731\) 1.50507e144 0.354592
\(732\) −3.43177e143 −0.0754586
\(733\) 8.96985e143 0.184092 0.0920459 0.995755i \(-0.470659\pi\)
0.0920459 + 0.995755i \(0.470659\pi\)
\(734\) −4.28487e143 −0.0820894
\(735\) 5.94862e143 0.106391
\(736\) −3.66202e144 −0.611492
\(737\) 3.04417e144 0.474636
\(738\) −6.88150e143 −0.100193
\(739\) −1.38916e144 −0.188889 −0.0944445 0.995530i \(-0.530107\pi\)
−0.0944445 + 0.995530i \(0.530107\pi\)
\(740\) 3.17582e144 0.403325
\(741\) 8.08205e143 0.0958743
\(742\) 2.87714e143 0.0318834
\(743\) 1.30796e145 1.35413 0.677066 0.735923i \(-0.263251\pi\)
0.677066 + 0.735923i \(0.263251\pi\)
\(744\) −8.46263e143 −0.0818601
\(745\) 9.74145e144 0.880505
\(746\) 9.09921e143 0.0768587
\(747\) −1.07068e145 −0.845215
\(748\) 3.92910e144 0.289910
\(749\) −2.77252e144 −0.191224
\(750\) −6.74214e143 −0.0434714
\(751\) −1.15451e145 −0.695954 −0.347977 0.937503i \(-0.613131\pi\)
−0.347977 + 0.937503i \(0.613131\pi\)
\(752\) 1.86730e145 1.05248
\(753\) −8.78293e144 −0.462906
\(754\) −2.65648e143 −0.0130934
\(755\) −1.13864e144 −0.0524887
\(756\) −7.09417e144 −0.305880
\(757\) −3.83259e145 −1.54579 −0.772896 0.634533i \(-0.781193\pi\)
−0.772896 + 0.634533i \(0.781193\pi\)
\(758\) 4.06835e144 0.153505
\(759\) 2.63466e144 0.0930068
\(760\) 2.41942e144 0.0799144
\(761\) 2.11377e145 0.653329 0.326665 0.945140i \(-0.394075\pi\)
0.326665 + 0.945140i \(0.394075\pi\)
\(762\) −1.06328e144 −0.0307555
\(763\) −3.92558e145 −1.06271
\(764\) 5.55126e144 0.140662
\(765\) −2.64830e145 −0.628153
\(766\) 8.31566e144 0.184648
\(767\) 3.38428e145 0.703560
\(768\) −1.07047e145 −0.208370
\(769\) 9.71643e144 0.177103 0.0885516 0.996072i \(-0.471776\pi\)
0.0885516 + 0.996072i \(0.471776\pi\)
\(770\) 8.30845e143 0.0141820
\(771\) 2.09936e145 0.335614
\(772\) 9.84216e145 1.47373
\(773\) 5.12373e145 0.718657 0.359328 0.933211i \(-0.383006\pi\)
0.359328 + 0.933211i \(0.383006\pi\)
\(774\) 3.45159e144 0.0453524
\(775\) −4.94383e145 −0.608594
\(776\) 1.32780e145 0.153150
\(777\) 1.06999e145 0.115643
\(778\) −2.26623e145 −0.229527
\(779\) −3.04251e145 −0.288796
\(780\) −1.43073e145 −0.127286
\(781\) 5.35375e145 0.446458
\(782\) −3.14307e145 −0.245705
\(783\) −7.35999e144 −0.0539396
\(784\) −8.78879e145 −0.603904
\(785\) −1.48680e146 −0.957935
\(786\) 1.02592e145 0.0619835
\(787\) 1.01267e146 0.573778 0.286889 0.957964i \(-0.407379\pi\)
0.286889 + 0.957964i \(0.407379\pi\)
\(788\) −2.43829e146 −1.29572
\(789\) 8.92214e145 0.444714
\(790\) −2.66074e145 −0.124404
\(791\) 4.24919e144 0.0186377
\(792\) 1.82620e145 0.0751497
\(793\) 5.80554e145 0.224154
\(794\) −1.40338e145 −0.0508440
\(795\) 1.60764e145 0.0546573
\(796\) −9.91924e145 −0.316496
\(797\) −2.74405e146 −0.821764 −0.410882 0.911688i \(-0.634779\pi\)
−0.410882 + 0.911688i \(0.634779\pi\)
\(798\) 4.02199e144 0.0113056
\(799\) 5.03174e146 1.32772
\(800\) 1.24105e146 0.307430
\(801\) 5.47596e146 1.27356
\(802\) −3.05097e144 −0.00666242
\(803\) 2.10131e146 0.430878
\(804\) −2.60870e146 −0.502336
\(805\) 2.48747e146 0.449847
\(806\) 7.06377e145 0.119982
\(807\) 7.59200e145 0.121127
\(808\) 3.07462e146 0.460805
\(809\) −7.66386e146 −1.07906 −0.539532 0.841965i \(-0.681399\pi\)
−0.539532 + 0.841965i \(0.681399\pi\)
\(810\) −5.52254e145 −0.0730542
\(811\) −1.19038e147 −1.47956 −0.739781 0.672848i \(-0.765071\pi\)
−0.739781 + 0.672848i \(0.765071\pi\)
\(812\) 4.94768e145 0.0577859
\(813\) 7.86326e145 0.0863038
\(814\) −2.83183e145 −0.0292103
\(815\) 1.85847e146 0.180175
\(816\) −3.27468e146 −0.298412
\(817\) 1.52605e146 0.130724
\(818\) −1.66366e146 −0.133975
\(819\) 5.75960e146 0.436069
\(820\) 5.38601e146 0.383414
\(821\) −1.88359e147 −1.26083 −0.630414 0.776259i \(-0.717115\pi\)
−0.630414 + 0.776259i \(0.717115\pi\)
\(822\) −3.01793e145 −0.0189969
\(823\) −4.64333e146 −0.274876 −0.137438 0.990510i \(-0.543887\pi\)
−0.137438 + 0.990510i \(0.543887\pi\)
\(824\) −2.15379e146 −0.119917
\(825\) −8.92884e145 −0.0467596
\(826\) 1.68417e146 0.0829648
\(827\) −2.44457e147 −1.13285 −0.566427 0.824112i \(-0.691675\pi\)
−0.566427 + 0.824112i \(0.691675\pi\)
\(828\) 2.69769e147 1.17614
\(829\) 4.20030e147 1.72297 0.861483 0.507786i \(-0.169536\pi\)
0.861483 + 0.507786i \(0.169536\pi\)
\(830\) −2.23906e146 −0.0864216
\(831\) 9.77960e146 0.355197
\(832\) 1.99299e147 0.681202
\(833\) −2.36828e147 −0.761835
\(834\) −2.00660e146 −0.0607541
\(835\) 2.70699e147 0.771470
\(836\) 3.98387e146 0.106878
\(837\) 1.95707e147 0.494278
\(838\) −9.42358e145 −0.0224075
\(839\) −4.27111e147 −0.956228 −0.478114 0.878298i \(-0.658679\pi\)
−0.478114 + 0.878298i \(0.658679\pi\)
\(840\) −1.44301e146 −0.0304205
\(841\) −4.98597e147 −0.989810
\(842\) 3.15304e146 0.0589480
\(843\) 1.82123e147 0.320680
\(844\) −1.11924e147 −0.185622
\(845\) −1.32355e147 −0.206765
\(846\) 1.15393e147 0.169815
\(847\) −3.96205e147 −0.549297
\(848\) −2.37520e147 −0.310249
\(849\) 1.41105e147 0.173662
\(850\) 1.06519e147 0.123529
\(851\) −8.47823e147 −0.926536
\(852\) −4.58790e147 −0.472514
\(853\) 1.65370e147 0.160521 0.0802604 0.996774i \(-0.474425\pi\)
0.0802604 + 0.996774i \(0.474425\pi\)
\(854\) 2.88910e146 0.0264326
\(855\) −2.68522e147 −0.231574
\(856\) −1.27442e147 −0.103607
\(857\) 2.26666e148 1.73722 0.868610 0.495497i \(-0.165014\pi\)
0.868610 + 0.495497i \(0.165014\pi\)
\(858\) 1.27576e146 0.00921849
\(859\) 1.45946e148 0.994344 0.497172 0.867652i \(-0.334372\pi\)
0.497172 + 0.867652i \(0.334372\pi\)
\(860\) −2.70149e147 −0.173553
\(861\) 1.81464e147 0.109934
\(862\) −2.73422e147 −0.156213
\(863\) 1.99479e148 1.07486 0.537430 0.843308i \(-0.319395\pi\)
0.537430 + 0.843308i \(0.319395\pi\)
\(864\) −4.91286e147 −0.249684
\(865\) −9.67714e147 −0.463910
\(866\) 6.80471e147 0.307720
\(867\) −2.31004e147 −0.0985497
\(868\) −1.31562e148 −0.529524
\(869\) −8.87953e147 −0.337203
\(870\) −7.38672e145 −0.00264685
\(871\) 4.41316e148 1.49222
\(872\) −1.80444e148 −0.575783
\(873\) −1.47367e148 −0.443795
\(874\) −3.18688e147 −0.0905813
\(875\) −2.12431e148 −0.569916
\(876\) −1.80072e148 −0.456025
\(877\) −9.73527e147 −0.232739 −0.116369 0.993206i \(-0.537126\pi\)
−0.116369 + 0.993206i \(0.537126\pi\)
\(878\) −3.89837e147 −0.0879854
\(879\) 2.08118e147 0.0443477
\(880\) −6.85897e147 −0.138002
\(881\) 6.24527e147 0.118650 0.0593250 0.998239i \(-0.481105\pi\)
0.0593250 + 0.998239i \(0.481105\pi\)
\(882\) −5.43120e147 −0.0974388
\(883\) −1.09918e149 −1.86232 −0.931159 0.364615i \(-0.881201\pi\)
−0.931159 + 0.364615i \(0.881201\pi\)
\(884\) 5.69605e148 0.911453
\(885\) 9.41050e147 0.142225
\(886\) 1.36284e148 0.194554
\(887\) 1.10849e149 1.49481 0.747407 0.664366i \(-0.231298\pi\)
0.747407 + 0.664366i \(0.231298\pi\)
\(888\) 4.91833e147 0.0626560
\(889\) −3.35018e148 −0.403209
\(890\) 1.14517e148 0.130219
\(891\) −1.84300e148 −0.198017
\(892\) 8.69797e148 0.883065
\(893\) 5.10187e148 0.489475
\(894\) 7.44373e147 0.0674910
\(895\) −4.19427e148 −0.359413
\(896\) 4.38266e148 0.354963
\(897\) 3.81949e148 0.292406
\(898\) −1.37953e146 −0.000998336 0
\(899\) −1.36492e148 −0.0933776
\(900\) −9.14246e148 −0.591312
\(901\) −6.40037e148 −0.391384
\(902\) −4.80262e147 −0.0277682
\(903\) −9.10179e147 −0.0497617
\(904\) 1.95318e147 0.0100981
\(905\) 1.95018e149 0.953500
\(906\) −8.70071e146 −0.00402328
\(907\) −3.76928e149 −1.64851 −0.824253 0.566221i \(-0.808405\pi\)
−0.824253 + 0.566221i \(0.808405\pi\)
\(908\) 3.09688e149 1.28112
\(909\) −3.41239e149 −1.33531
\(910\) 1.20448e148 0.0445872
\(911\) −2.36013e149 −0.826528 −0.413264 0.910611i \(-0.635611\pi\)
−0.413264 + 0.910611i \(0.635611\pi\)
\(912\) −3.32032e148 −0.110012
\(913\) −7.47228e148 −0.234250
\(914\) −5.58822e148 −0.165764
\(915\) 1.61432e148 0.0453131
\(916\) −1.38529e149 −0.367975
\(917\) 3.23247e149 0.812611
\(918\) −4.21666e148 −0.100326
\(919\) 4.61378e149 1.03902 0.519510 0.854464i \(-0.326115\pi\)
0.519510 + 0.854464i \(0.326115\pi\)
\(920\) 1.14339e149 0.243730
\(921\) −6.95416e148 −0.140324
\(922\) −8.38448e148 −0.160164
\(923\) 7.76137e149 1.40363
\(924\) −2.37609e148 −0.0406845
\(925\) 2.87326e149 0.465820
\(926\) −5.73412e148 −0.0880262
\(927\) 2.39041e149 0.347493
\(928\) 3.42637e148 0.0471695
\(929\) −6.15334e148 −0.0802264 −0.0401132 0.999195i \(-0.512772\pi\)
−0.0401132 + 0.999195i \(0.512772\pi\)
\(930\) 1.96418e148 0.0242545
\(931\) −2.40129e149 −0.280857
\(932\) −1.12250e150 −1.24360
\(933\) −3.11275e149 −0.326679
\(934\) −3.89358e148 −0.0387107
\(935\) −1.84826e149 −0.174091
\(936\) 2.64746e149 0.236265
\(937\) 9.87076e149 0.834644 0.417322 0.908759i \(-0.362969\pi\)
0.417322 + 0.908759i \(0.362969\pi\)
\(938\) 2.19618e149 0.175965
\(939\) −1.55723e149 −0.118234
\(940\) −9.03160e149 −0.649842
\(941\) −5.12586e149 −0.349535 −0.174768 0.984610i \(-0.555917\pi\)
−0.174768 + 0.984610i \(0.555917\pi\)
\(942\) −1.13611e149 −0.0734261
\(943\) −1.43786e150 −0.880795
\(944\) −1.39035e150 −0.807309
\(945\) 3.33712e149 0.183681
\(946\) 2.40888e148 0.0125693
\(947\) −7.23652e149 −0.357978 −0.178989 0.983851i \(-0.557283\pi\)
−0.178989 + 0.983851i \(0.557283\pi\)
\(948\) 7.60932e149 0.356882
\(949\) 3.04628e150 1.35465
\(950\) 1.08003e149 0.0455402
\(951\) 4.80736e149 0.192216
\(952\) 5.74496e149 0.217832
\(953\) 1.33924e150 0.481578 0.240789 0.970578i \(-0.422594\pi\)
0.240789 + 0.970578i \(0.422594\pi\)
\(954\) −1.46780e149 −0.0500581
\(955\) −2.61133e149 −0.0844679
\(956\) 2.53621e150 0.778147
\(957\) −2.46512e148 −0.00717440
\(958\) −2.77333e149 −0.0765673
\(959\) −9.50887e149 −0.249052
\(960\) 5.54179e149 0.137706
\(961\) −6.12191e149 −0.144330
\(962\) −4.10533e149 −0.0918348
\(963\) 1.41443e150 0.300229
\(964\) 2.20016e150 0.443164
\(965\) −4.62978e150 −0.884975
\(966\) 1.90075e149 0.0344810
\(967\) 3.91457e150 0.673980 0.336990 0.941508i \(-0.390591\pi\)
0.336990 + 0.941508i \(0.390591\pi\)
\(968\) −1.82120e150 −0.297613
\(969\) −8.94715e149 −0.138782
\(970\) −3.08184e149 −0.0453772
\(971\) −1.14003e151 −1.59348 −0.796740 0.604322i \(-0.793444\pi\)
−0.796740 + 0.604322i \(0.793444\pi\)
\(972\) 5.50141e150 0.730008
\(973\) −6.32238e150 −0.796493
\(974\) −4.86691e149 −0.0582138
\(975\) −1.29442e150 −0.147008
\(976\) −2.38507e150 −0.257209
\(977\) −9.05921e150 −0.927716 −0.463858 0.885910i \(-0.653535\pi\)
−0.463858 + 0.885910i \(0.653535\pi\)
\(978\) 1.42011e149 0.0138105
\(979\) 3.82169e150 0.352964
\(980\) 4.25089e150 0.372875
\(981\) 2.00267e151 1.66849
\(982\) 3.48285e150 0.275616
\(983\) −1.35939e151 −1.02186 −0.510930 0.859623i \(-0.670699\pi\)
−0.510930 + 0.859623i \(0.670699\pi\)
\(984\) 8.34119e149 0.0595629
\(985\) 1.14698e151 0.778084
\(986\) 2.94082e149 0.0189533
\(987\) −3.04290e150 −0.186325
\(988\) 5.77544e150 0.336016
\(989\) 7.21193e150 0.398693
\(990\) −4.23863e149 −0.0222663
\(991\) 1.59255e151 0.795010 0.397505 0.917600i \(-0.369876\pi\)
0.397505 + 0.917600i \(0.369876\pi\)
\(992\) −9.11097e150 −0.432240
\(993\) −9.51478e150 −0.429004
\(994\) 3.86241e150 0.165518
\(995\) 4.66604e150 0.190057
\(996\) 6.40338e150 0.247921
\(997\) −7.11596e148 −0.00261896 −0.00130948 0.999999i \(-0.500417\pi\)
−0.00130948 + 0.999999i \(0.500417\pi\)
\(998\) 8.19401e150 0.286685
\(999\) −1.13742e151 −0.378322
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.1.4 8
3.2 odd 2 9.102.a.b.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.4 8 1.1 even 1 trivial
9.102.a.b.1.5 8 3.2 odd 2