Properties

Label 1.102.a.a.1.7
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 1.7
Root \(-2.32579e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.17839e15 q^{2} +6.93716e23 q^{3} +2.21006e30 q^{4} -2.56275e35 q^{5} +1.51118e39 q^{6} +8.01618e42 q^{7} -7.08493e44 q^{8} -1.06489e48 q^{9} +O(q^{10})\) \(q+2.17839e15 q^{2} +6.93716e23 q^{3} +2.21006e30 q^{4} -2.56275e35 q^{5} +1.51118e39 q^{6} +8.01618e42 q^{7} -7.08493e44 q^{8} -1.06489e48 q^{9} -5.58265e50 q^{10} -9.55916e51 q^{11} +1.53316e54 q^{12} +4.33831e54 q^{13} +1.74623e58 q^{14} -1.77782e59 q^{15} -7.14655e60 q^{16} -7.76807e61 q^{17} -2.31974e63 q^{18} +3.75637e64 q^{19} -5.66383e65 q^{20} +5.56095e66 q^{21} -2.08235e67 q^{22} -1.01843e69 q^{23} -4.91493e68 q^{24} +2.62336e70 q^{25} +9.45051e69 q^{26} -1.81131e72 q^{27} +1.77163e73 q^{28} -3.74489e73 q^{29} -3.87277e74 q^{30} -5.68206e74 q^{31} -1.37717e76 q^{32} -6.63134e75 q^{33} -1.69219e77 q^{34} -2.05434e78 q^{35} -2.35348e78 q^{36} -2.65734e79 q^{37} +8.18283e79 q^{38} +3.00955e78 q^{39} +1.81569e80 q^{40} +3.81887e81 q^{41} +1.21139e82 q^{42} -3.91159e82 q^{43} -2.11263e82 q^{44} +2.72905e83 q^{45} -2.21854e84 q^{46} +2.04333e83 q^{47} -4.95767e84 q^{48} +4.16178e85 q^{49} +5.71470e85 q^{50} -5.38883e85 q^{51} +9.58794e84 q^{52} -5.06337e86 q^{53} -3.94573e87 q^{54} +2.44977e87 q^{55} -5.67941e87 q^{56} +2.60585e88 q^{57} -8.15782e88 q^{58} +5.27773e89 q^{59} -3.92909e89 q^{60} -2.08484e90 q^{61} -1.23777e90 q^{62} -8.53636e90 q^{63} -1.18814e91 q^{64} -1.11180e90 q^{65} -1.44456e91 q^{66} -4.63082e91 q^{67} -1.71679e92 q^{68} -7.06501e92 q^{69} -4.47515e93 q^{70} -3.91885e93 q^{71} +7.54468e92 q^{72} +1.42179e94 q^{73} -5.78872e94 q^{74} +1.81987e94 q^{75} +8.30182e94 q^{76} -7.66279e94 q^{77} +6.55597e93 q^{78} -5.87787e95 q^{79} +1.83148e96 q^{80} +3.89931e95 q^{81} +8.31898e96 q^{82} +6.23585e96 q^{83} +1.22901e97 q^{84} +1.99076e97 q^{85} -8.52096e97 q^{86} -2.59789e97 q^{87} +6.77260e96 q^{88} -4.22602e98 q^{89} +5.94492e98 q^{90} +3.47767e97 q^{91} -2.25080e99 q^{92} -3.94174e98 q^{93} +4.45116e98 q^{94} -9.62663e99 q^{95} -9.55364e99 q^{96} +1.04471e100 q^{97} +9.06597e100 q^{98} +1.01795e100 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 434989091795040q^{2} - \)\(12\!\cdots\!60\)\(q^{3} + \)\(90\!\cdots\!96\)\(q^{4} + \)\(38\!\cdots\!00\)\(q^{5} + \)\(24\!\cdots\!36\)\(q^{6} - \)\(57\!\cdots\!00\)\(q^{7} - \)\(61\!\cdots\!20\)\(q^{8} + \)\(52\!\cdots\!84\)\(q^{9} - \)\(37\!\cdots\!00\)\(q^{10} + \)\(46\!\cdots\!96\)\(q^{11} - \)\(72\!\cdots\!80\)\(q^{12} + \)\(25\!\cdots\!80\)\(q^{13} - \)\(48\!\cdots\!88\)\(q^{14} - \)\(29\!\cdots\!00\)\(q^{15} - \)\(10\!\cdots\!72\)\(q^{16} - \)\(39\!\cdots\!20\)\(q^{17} - \)\(72\!\cdots\!60\)\(q^{18} - \)\(21\!\cdots\!80\)\(q^{19} + \)\(17\!\cdots\!00\)\(q^{20} + \)\(40\!\cdots\!36\)\(q^{21} + \)\(61\!\cdots\!20\)\(q^{22} - \)\(13\!\cdots\!80\)\(q^{23} + \)\(10\!\cdots\!60\)\(q^{24} + \)\(77\!\cdots\!00\)\(q^{25} - \)\(97\!\cdots\!44\)\(q^{26} - \)\(59\!\cdots\!20\)\(q^{27} + \)\(92\!\cdots\!80\)\(q^{28} + \)\(15\!\cdots\!80\)\(q^{29} + \)\(11\!\cdots\!00\)\(q^{30} - \)\(65\!\cdots\!44\)\(q^{31} + \)\(12\!\cdots\!60\)\(q^{32} + \)\(43\!\cdots\!80\)\(q^{33} + \)\(95\!\cdots\!12\)\(q^{34} - \)\(11\!\cdots\!00\)\(q^{35} + \)\(19\!\cdots\!08\)\(q^{36} + \)\(39\!\cdots\!40\)\(q^{37} - \)\(70\!\cdots\!80\)\(q^{38} - \)\(26\!\cdots\!32\)\(q^{39} - \)\(76\!\cdots\!00\)\(q^{40} + \)\(56\!\cdots\!36\)\(q^{41} + \)\(30\!\cdots\!80\)\(q^{42} - \)\(28\!\cdots\!00\)\(q^{43} - \)\(20\!\cdots\!48\)\(q^{44} + \)\(71\!\cdots\!00\)\(q^{45} + \)\(10\!\cdots\!76\)\(q^{46} - \)\(45\!\cdots\!80\)\(q^{47} - \)\(58\!\cdots\!80\)\(q^{48} + \)\(12\!\cdots\!56\)\(q^{49} - \)\(40\!\cdots\!00\)\(q^{50} + \)\(11\!\cdots\!36\)\(q^{51} - \)\(73\!\cdots\!00\)\(q^{52} + \)\(13\!\cdots\!40\)\(q^{53} + \)\(68\!\cdots\!20\)\(q^{54} - \)\(14\!\cdots\!00\)\(q^{55} - \)\(23\!\cdots\!80\)\(q^{56} - \)\(66\!\cdots\!40\)\(q^{57} + \)\(29\!\cdots\!80\)\(q^{58} + \)\(21\!\cdots\!60\)\(q^{59} - \)\(34\!\cdots\!00\)\(q^{60} - \)\(33\!\cdots\!04\)\(q^{61} - \)\(58\!\cdots\!80\)\(q^{62} - \)\(20\!\cdots\!40\)\(q^{63} - \)\(74\!\cdots\!04\)\(q^{64} - \)\(16\!\cdots\!00\)\(q^{65} - \)\(74\!\cdots\!68\)\(q^{66} - \)\(61\!\cdots\!20\)\(q^{67} - \)\(21\!\cdots\!60\)\(q^{68} - \)\(53\!\cdots\!72\)\(q^{69} - \)\(12\!\cdots\!00\)\(q^{70} - \)\(15\!\cdots\!24\)\(q^{71} - \)\(55\!\cdots\!60\)\(q^{72} - \)\(20\!\cdots\!80\)\(q^{73} - \)\(14\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} + \)\(64\!\cdots\!40\)\(q^{76} + \)\(25\!\cdots\!00\)\(q^{77} + \)\(12\!\cdots\!00\)\(q^{78} + \)\(14\!\cdots\!80\)\(q^{79} + \)\(60\!\cdots\!00\)\(q^{80} + \)\(14\!\cdots\!08\)\(q^{81} + \)\(30\!\cdots\!20\)\(q^{82} + \)\(33\!\cdots\!60\)\(q^{83} + \)\(57\!\cdots\!32\)\(q^{84} + \)\(17\!\cdots\!00\)\(q^{85} + \)\(67\!\cdots\!16\)\(q^{86} + \)\(25\!\cdots\!40\)\(q^{87} - \)\(36\!\cdots\!40\)\(q^{88} - \)\(62\!\cdots\!60\)\(q^{89} - \)\(47\!\cdots\!00\)\(q^{90} - \)\(36\!\cdots\!44\)\(q^{91} - \)\(46\!\cdots\!20\)\(q^{92} - \)\(39\!\cdots\!20\)\(q^{93} - \)\(17\!\cdots\!88\)\(q^{94} - \)\(26\!\cdots\!00\)\(q^{95} + \)\(46\!\cdots\!56\)\(q^{96} + \)\(64\!\cdots\!20\)\(q^{97} + \)\(20\!\cdots\!20\)\(q^{98} + \)\(22\!\cdots\!08\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17839e15 1.36811 0.684053 0.729432i \(-0.260215\pi\)
0.684053 + 0.729432i \(0.260215\pi\)
\(3\) 6.93716e23 0.557902 0.278951 0.960305i \(-0.410013\pi\)
0.278951 + 0.960305i \(0.410013\pi\)
\(4\) 2.21006e30 0.871716
\(5\) −2.56275e35 −1.29039 −0.645194 0.764019i \(-0.723224\pi\)
−0.645194 + 0.764019i \(0.723224\pi\)
\(6\) 1.51118e39 0.763270
\(7\) 8.01618e42 1.68468 0.842338 0.538949i \(-0.181179\pi\)
0.842338 + 0.538949i \(0.181179\pi\)
\(8\) −7.08493e44 −0.175506
\(9\) −1.06489e48 −0.688745
\(10\) −5.58265e50 −1.76539
\(11\) −9.55916e51 −0.245521 −0.122761 0.992436i \(-0.539175\pi\)
−0.122761 + 0.992436i \(0.539175\pi\)
\(12\) 1.53316e54 0.486332
\(13\) 4.33831e54 0.0241647 0.0120823 0.999927i \(-0.496154\pi\)
0.0120823 + 0.999927i \(0.496154\pi\)
\(14\) 1.74623e58 2.30482
\(15\) −1.77782e59 −0.719911
\(16\) −7.14655e60 −1.11183
\(17\) −7.76807e61 −0.565773 −0.282887 0.959153i \(-0.591292\pi\)
−0.282887 + 0.959153i \(0.591292\pi\)
\(18\) −2.31974e63 −0.942277
\(19\) 3.75637e64 0.994745 0.497372 0.867537i \(-0.334298\pi\)
0.497372 + 0.867537i \(0.334298\pi\)
\(20\) −5.66383e65 −1.12485
\(21\) 5.56095e66 0.939885
\(22\) −2.08235e67 −0.335899
\(23\) −1.01843e69 −1.74051 −0.870254 0.492604i \(-0.836045\pi\)
−0.870254 + 0.492604i \(0.836045\pi\)
\(24\) −4.91493e68 −0.0979150
\(25\) 2.62336e70 0.665102
\(26\) 9.45051e69 0.0330599
\(27\) −1.81131e72 −0.942155
\(28\) 1.77163e73 1.46856
\(29\) −3.74489e73 −0.527643 −0.263822 0.964571i \(-0.584983\pi\)
−0.263822 + 0.964571i \(0.584983\pi\)
\(30\) −3.87277e74 −0.984914
\(31\) −5.68206e74 −0.275893 −0.137946 0.990440i \(-0.544050\pi\)
−0.137946 + 0.990440i \(0.544050\pi\)
\(32\) −1.37717e76 −1.34559
\(33\) −6.63134e75 −0.136977
\(34\) −1.69219e77 −0.774038
\(35\) −2.05434e78 −2.17389
\(36\) −2.35348e78 −0.600390
\(37\) −2.65734e79 −1.69926 −0.849632 0.527377i \(-0.823176\pi\)
−0.849632 + 0.527377i \(0.823176\pi\)
\(38\) 8.18283e79 1.36092
\(39\) 3.00955e78 0.0134815
\(40\) 1.81569e80 0.226471
\(41\) 3.81887e81 1.36883 0.684417 0.729091i \(-0.260057\pi\)
0.684417 + 0.729091i \(0.260057\pi\)
\(42\) 1.21139e82 1.28586
\(43\) −3.91159e82 −1.26531 −0.632654 0.774434i \(-0.718035\pi\)
−0.632654 + 0.774434i \(0.718035\pi\)
\(44\) −2.11263e82 −0.214025
\(45\) 2.72905e83 0.888749
\(46\) −2.21854e84 −2.38120
\(47\) 2.04333e83 0.0740281 0.0370140 0.999315i \(-0.488215\pi\)
0.0370140 + 0.999315i \(0.488215\pi\)
\(48\) −4.95767e84 −0.620291
\(49\) 4.16178e85 1.83814
\(50\) 5.71470e85 0.909931
\(51\) −5.38883e85 −0.315646
\(52\) 9.58794e84 0.0210648
\(53\) −5.06337e86 −0.425116 −0.212558 0.977148i \(-0.568180\pi\)
−0.212558 + 0.977148i \(0.568180\pi\)
\(54\) −3.94573e87 −1.28897
\(55\) 2.44977e87 0.316818
\(56\) −5.67941e87 −0.295670
\(57\) 2.60585e88 0.554970
\(58\) −8.15782e88 −0.721873
\(59\) 5.27773e89 1.96979 0.984897 0.173141i \(-0.0553918\pi\)
0.984897 + 0.173141i \(0.0553918\pi\)
\(60\) −3.92909e89 −0.627558
\(61\) −2.08484e90 −1.44516 −0.722581 0.691286i \(-0.757045\pi\)
−0.722581 + 0.691286i \(0.757045\pi\)
\(62\) −1.23777e90 −0.377451
\(63\) −8.53636e90 −1.16031
\(64\) −1.18814e91 −0.729087
\(65\) −1.11180e90 −0.0311818
\(66\) −1.44456e91 −0.187399
\(67\) −4.63082e91 −0.281113 −0.140556 0.990073i \(-0.544889\pi\)
−0.140556 + 0.990073i \(0.544889\pi\)
\(68\) −1.71679e92 −0.493194
\(69\) −7.06501e92 −0.971033
\(70\) −4.47515e93 −2.97411
\(71\) −3.91885e93 −1.27237 −0.636183 0.771538i \(-0.719488\pi\)
−0.636183 + 0.771538i \(0.719488\pi\)
\(72\) 7.54468e92 0.120879
\(73\) 1.42179e94 1.13509 0.567546 0.823341i \(-0.307893\pi\)
0.567546 + 0.823341i \(0.307893\pi\)
\(74\) −5.78872e94 −2.32477
\(75\) 1.81987e94 0.371062
\(76\) 8.30182e94 0.867135
\(77\) −7.66279e94 −0.413624
\(78\) 6.55597e93 0.0184442
\(79\) −5.87787e95 −0.869064 −0.434532 0.900656i \(-0.643086\pi\)
−0.434532 + 0.900656i \(0.643086\pi\)
\(80\) 1.83148e96 1.43469
\(81\) 3.89931e95 0.163115
\(82\) 8.31898e96 1.87271
\(83\) 6.23585e96 0.761118 0.380559 0.924757i \(-0.375732\pi\)
0.380559 + 0.924757i \(0.375732\pi\)
\(84\) 1.22901e97 0.819313
\(85\) 1.99076e97 0.730067
\(86\) −8.52096e97 −1.73108
\(87\) −2.59789e97 −0.294373
\(88\) 6.77260e96 0.0430904
\(89\) −4.22602e98 −1.51963 −0.759813 0.650142i \(-0.774709\pi\)
−0.759813 + 0.650142i \(0.774709\pi\)
\(90\) 5.94492e98 1.21590
\(91\) 3.47767e97 0.0407097
\(92\) −2.25080e99 −1.51723
\(93\) −3.94174e98 −0.153921
\(94\) 4.45116e98 0.101278
\(95\) −9.62663e99 −1.28361
\(96\) −9.55364e99 −0.750709
\(97\) 1.04471e100 0.486432 0.243216 0.969972i \(-0.421798\pi\)
0.243216 + 0.969972i \(0.421798\pi\)
\(98\) 9.06597e100 2.51477
\(99\) 1.01795e100 0.169102
\(100\) 5.79780e100 0.579780
\(101\) 1.04695e101 0.633425 0.316713 0.948522i \(-0.397421\pi\)
0.316713 + 0.948522i \(0.397421\pi\)
\(102\) −1.17390e101 −0.431838
\(103\) 2.23897e101 0.503232 0.251616 0.967827i \(-0.419038\pi\)
0.251616 + 0.967827i \(0.419038\pi\)
\(104\) −3.07366e99 −0.00424104
\(105\) −1.42513e102 −1.21282
\(106\) −1.10300e102 −0.581605
\(107\) 5.38178e101 0.176622 0.0883111 0.996093i \(-0.471853\pi\)
0.0883111 + 0.996093i \(0.471853\pi\)
\(108\) −4.00311e102 −0.821292
\(109\) 6.37162e102 0.820752 0.410376 0.911916i \(-0.365397\pi\)
0.410376 + 0.911916i \(0.365397\pi\)
\(110\) 5.33654e102 0.433440
\(111\) −1.84344e103 −0.948023
\(112\) −5.72880e103 −1.87307
\(113\) −4.48141e102 −0.0935305 −0.0467653 0.998906i \(-0.514891\pi\)
−0.0467653 + 0.998906i \(0.514891\pi\)
\(114\) 5.67655e103 0.759259
\(115\) 2.60998e104 2.24593
\(116\) −8.27645e103 −0.459955
\(117\) −4.61983e102 −0.0166433
\(118\) 1.14969e105 2.69489
\(119\) −6.22703e104 −0.953145
\(120\) 1.25957e104 0.126348
\(121\) −1.42449e105 −0.939719
\(122\) −4.54159e105 −1.97714
\(123\) 2.64921e105 0.763675
\(124\) −1.25577e105 −0.240500
\(125\) 3.38523e105 0.432148
\(126\) −1.85955e106 −1.58743
\(127\) 1.89098e106 1.08293 0.541463 0.840725i \(-0.317871\pi\)
0.541463 + 0.840725i \(0.317871\pi\)
\(128\) 9.03309e105 0.348123
\(129\) −2.71353e106 −0.705919
\(130\) −2.42193e105 −0.0426601
\(131\) 1.48779e106 0.177967 0.0889836 0.996033i \(-0.471638\pi\)
0.0889836 + 0.996033i \(0.471638\pi\)
\(132\) −1.46557e106 −0.119405
\(133\) 3.01118e107 1.67582
\(134\) −1.00877e107 −0.384592
\(135\) 4.64192e107 1.21575
\(136\) 5.50362e106 0.0992965
\(137\) 2.05438e106 0.0256031 0.0128016 0.999918i \(-0.495925\pi\)
0.0128016 + 0.999918i \(0.495925\pi\)
\(138\) −1.53903e108 −1.32848
\(139\) 1.46512e108 0.878265 0.439133 0.898422i \(-0.355286\pi\)
0.439133 + 0.898422i \(0.355286\pi\)
\(140\) −4.54023e108 −1.89501
\(141\) 1.41749e107 0.0413004
\(142\) −8.53677e108 −1.74073
\(143\) −4.14706e106 −0.00593294
\(144\) 7.61030e108 0.765765
\(145\) 9.59721e108 0.680865
\(146\) 3.09721e109 1.55293
\(147\) 2.88709e109 1.02550
\(148\) −5.87290e109 −1.48128
\(149\) −4.96513e109 −0.891300 −0.445650 0.895207i \(-0.647027\pi\)
−0.445650 + 0.895207i \(0.647027\pi\)
\(150\) 3.96438e109 0.507652
\(151\) 1.14116e110 1.04474 0.522372 0.852717i \(-0.325047\pi\)
0.522372 + 0.852717i \(0.325047\pi\)
\(152\) −2.66136e109 −0.174583
\(153\) 8.27215e109 0.389674
\(154\) −1.66925e110 −0.565882
\(155\) 1.45617e110 0.356009
\(156\) 6.65130e108 0.0117521
\(157\) −7.80595e110 −0.998834 −0.499417 0.866362i \(-0.666452\pi\)
−0.499417 + 0.866362i \(0.666452\pi\)
\(158\) −1.28043e111 −1.18897
\(159\) −3.51254e110 −0.237173
\(160\) 3.52934e111 1.73634
\(161\) −8.16393e111 −2.93219
\(162\) 8.49419e110 0.223159
\(163\) 1.02381e112 1.97127 0.985636 0.168885i \(-0.0540167\pi\)
0.985636 + 0.168885i \(0.0540167\pi\)
\(164\) 8.43995e111 1.19323
\(165\) 1.69944e111 0.176753
\(166\) 1.35841e112 1.04129
\(167\) −9.04519e111 −0.511960 −0.255980 0.966682i \(-0.582398\pi\)
−0.255980 + 0.966682i \(0.582398\pi\)
\(168\) −3.93989e111 −0.164955
\(169\) −3.22125e112 −0.999416
\(170\) 4.33664e112 0.998810
\(171\) −4.00013e112 −0.685126
\(172\) −8.64487e112 −1.10299
\(173\) −6.97539e112 −0.664110 −0.332055 0.943260i \(-0.607742\pi\)
−0.332055 + 0.943260i \(0.607742\pi\)
\(174\) −5.65921e112 −0.402734
\(175\) 2.10294e113 1.12048
\(176\) 6.83150e112 0.272977
\(177\) 3.66125e113 1.09895
\(178\) −9.20591e113 −2.07901
\(179\) −4.15404e111 −0.00706956 −0.00353478 0.999994i \(-0.501125\pi\)
−0.00353478 + 0.999994i \(0.501125\pi\)
\(180\) 6.03137e113 0.774737
\(181\) 6.83567e113 0.663763 0.331882 0.943321i \(-0.392317\pi\)
0.331882 + 0.943321i \(0.392317\pi\)
\(182\) 7.57570e112 0.0556952
\(183\) −1.44629e114 −0.806260
\(184\) 7.21551e113 0.305469
\(185\) 6.81010e114 2.19271
\(186\) −8.58662e113 −0.210581
\(187\) 7.42562e113 0.138909
\(188\) 4.51589e113 0.0645315
\(189\) −1.45198e115 −1.58723
\(190\) −2.09705e115 −1.75611
\(191\) −6.49031e114 −0.416946 −0.208473 0.978028i \(-0.566849\pi\)
−0.208473 + 0.978028i \(0.566849\pi\)
\(192\) −8.24232e114 −0.406759
\(193\) 1.58395e115 0.601307 0.300654 0.953733i \(-0.402795\pi\)
0.300654 + 0.953733i \(0.402795\pi\)
\(194\) 2.27578e115 0.665491
\(195\) −7.71272e113 −0.0173964
\(196\) 9.19781e115 1.60233
\(197\) −4.98876e115 −0.672122 −0.336061 0.941840i \(-0.609095\pi\)
−0.336061 + 0.941840i \(0.609095\pi\)
\(198\) 2.21748e115 0.231349
\(199\) 9.90704e115 0.801426 0.400713 0.916204i \(-0.368762\pi\)
0.400713 + 0.916204i \(0.368762\pi\)
\(200\) −1.85864e115 −0.116729
\(201\) −3.21247e115 −0.156833
\(202\) 2.28065e116 0.866593
\(203\) −3.00197e116 −0.888909
\(204\) −1.19097e116 −0.275154
\(205\) −9.78681e116 −1.76633
\(206\) 4.87734e116 0.688475
\(207\) 1.08452e117 1.19877
\(208\) −3.10039e115 −0.0268670
\(209\) −3.59077e116 −0.244231
\(210\) −3.10448e117 −1.65926
\(211\) 1.83494e117 0.771541 0.385770 0.922595i \(-0.373936\pi\)
0.385770 + 0.922595i \(0.373936\pi\)
\(212\) −1.11904e117 −0.370581
\(213\) −2.71857e117 −0.709856
\(214\) 1.17236e117 0.241638
\(215\) 1.00244e118 1.63274
\(216\) 1.28330e117 0.165354
\(217\) −4.55485e117 −0.464790
\(218\) 1.38799e118 1.12288
\(219\) 9.86319e117 0.633271
\(220\) 5.41415e117 0.276175
\(221\) −3.37003e116 −0.0136717
\(222\) −4.01573e118 −1.29700
\(223\) 2.97933e118 0.766871 0.383436 0.923568i \(-0.374741\pi\)
0.383436 + 0.923568i \(0.374741\pi\)
\(224\) −1.10396e119 −2.26689
\(225\) −2.79360e118 −0.458086
\(226\) −9.76224e117 −0.127960
\(227\) −7.51975e118 −0.788674 −0.394337 0.918966i \(-0.629026\pi\)
−0.394337 + 0.918966i \(0.629026\pi\)
\(228\) 5.75910e118 0.483777
\(229\) −2.60468e118 −0.175413 −0.0877067 0.996146i \(-0.527954\pi\)
−0.0877067 + 0.996146i \(0.527954\pi\)
\(230\) 5.68554e119 3.07267
\(231\) −5.31580e118 −0.230762
\(232\) 2.65323e118 0.0926044
\(233\) −3.69783e119 −1.03866 −0.519330 0.854574i \(-0.673818\pi\)
−0.519330 + 0.854574i \(0.673818\pi\)
\(234\) −1.00638e118 −0.0227698
\(235\) −5.23653e118 −0.0955250
\(236\) 1.16641e120 1.71710
\(237\) −4.07757e119 −0.484853
\(238\) −1.35649e120 −1.30400
\(239\) −2.15076e119 −0.167301 −0.0836504 0.996495i \(-0.526658\pi\)
−0.0836504 + 0.996495i \(0.526658\pi\)
\(240\) 1.27053e120 0.800416
\(241\) 2.22189e120 1.13465 0.567324 0.823495i \(-0.307979\pi\)
0.567324 + 0.823495i \(0.307979\pi\)
\(242\) −3.10309e120 −1.28564
\(243\) 3.07102e120 1.03316
\(244\) −4.60764e120 −1.25977
\(245\) −1.06656e121 −2.37191
\(246\) 5.77101e120 1.04479
\(247\) 1.62963e119 0.0240377
\(248\) 4.02570e119 0.0484208
\(249\) 4.32591e120 0.424630
\(250\) 7.37434e120 0.591225
\(251\) 8.35823e120 0.547761 0.273881 0.961764i \(-0.411693\pi\)
0.273881 + 0.961764i \(0.411693\pi\)
\(252\) −1.88659e121 −1.01146
\(253\) 9.73534e120 0.427331
\(254\) 4.11928e121 1.48156
\(255\) 1.38102e121 0.407306
\(256\) 4.98005e121 1.20536
\(257\) −1.29393e121 −0.257210 −0.128605 0.991696i \(-0.541050\pi\)
−0.128605 + 0.991696i \(0.541050\pi\)
\(258\) −5.91112e121 −0.965772
\(259\) −2.13018e122 −2.86271
\(260\) −2.45715e120 −0.0271817
\(261\) 3.98790e121 0.363412
\(262\) 3.24097e121 0.243478
\(263\) −1.95610e122 −1.21235 −0.606173 0.795333i \(-0.707296\pi\)
−0.606173 + 0.795333i \(0.707296\pi\)
\(264\) 4.69826e120 0.0240402
\(265\) 1.29761e122 0.548565
\(266\) 6.55950e122 2.29271
\(267\) −2.93166e122 −0.847802
\(268\) −1.02344e122 −0.245050
\(269\) −2.01646e122 −0.400037 −0.200018 0.979792i \(-0.564100\pi\)
−0.200018 + 0.979792i \(0.564100\pi\)
\(270\) 1.01119e123 1.66327
\(271\) −8.55915e122 −1.16810 −0.584052 0.811716i \(-0.698534\pi\)
−0.584052 + 0.811716i \(0.698534\pi\)
\(272\) 5.55149e122 0.629042
\(273\) 2.41251e121 0.0227120
\(274\) 4.47524e121 0.0350278
\(275\) −2.50772e122 −0.163297
\(276\) −1.56141e123 −0.846465
\(277\) 2.86983e122 0.129607 0.0648035 0.997898i \(-0.479358\pi\)
0.0648035 + 0.997898i \(0.479358\pi\)
\(278\) 3.19160e123 1.20156
\(279\) 6.05078e122 0.190020
\(280\) 1.45549e123 0.381530
\(281\) −8.77608e123 −1.92146 −0.960730 0.277484i \(-0.910500\pi\)
−0.960730 + 0.277484i \(0.910500\pi\)
\(282\) 3.08784e122 0.0565034
\(283\) −3.53849e123 −0.541506 −0.270753 0.962649i \(-0.587273\pi\)
−0.270753 + 0.962649i \(0.587273\pi\)
\(284\) −8.66091e123 −1.10914
\(285\) −6.67814e123 −0.716127
\(286\) −9.03389e121 −0.00811690
\(287\) 3.06128e124 2.30604
\(288\) 1.46654e124 0.926770
\(289\) −1.28170e124 −0.679900
\(290\) 2.09064e124 0.931496
\(291\) 7.24730e123 0.271382
\(292\) 3.14225e124 0.989479
\(293\) −3.24042e124 −0.858592 −0.429296 0.903164i \(-0.641238\pi\)
−0.429296 + 0.903164i \(0.641238\pi\)
\(294\) 6.28921e124 1.40299
\(295\) −1.35255e125 −2.54180
\(296\) 1.88271e124 0.298230
\(297\) 1.73146e124 0.231319
\(298\) −1.08160e125 −1.21939
\(299\) −4.41827e123 −0.0420588
\(300\) 4.02203e124 0.323461
\(301\) −3.13560e125 −2.13164
\(302\) 2.48588e125 1.42932
\(303\) 7.26284e124 0.353389
\(304\) −2.68451e125 −1.10598
\(305\) 5.34293e125 1.86482
\(306\) 1.80199e125 0.533115
\(307\) −8.81457e124 −0.221163 −0.110582 0.993867i \(-0.535271\pi\)
−0.110582 + 0.993867i \(0.535271\pi\)
\(308\) −1.69353e125 −0.360563
\(309\) 1.55321e125 0.280754
\(310\) 3.17210e125 0.487058
\(311\) −2.64772e125 −0.345519 −0.172760 0.984964i \(-0.555268\pi\)
−0.172760 + 0.984964i \(0.555268\pi\)
\(312\) −2.13225e123 −0.00236609
\(313\) 2.92546e125 0.276189 0.138094 0.990419i \(-0.455902\pi\)
0.138094 + 0.990419i \(0.455902\pi\)
\(314\) −1.70044e126 −1.36651
\(315\) 2.18765e126 1.49725
\(316\) −1.29905e126 −0.757577
\(317\) 1.43032e126 0.711116 0.355558 0.934654i \(-0.384291\pi\)
0.355558 + 0.934654i \(0.384291\pi\)
\(318\) −7.65166e125 −0.324479
\(319\) 3.57980e125 0.129548
\(320\) 3.04491e126 0.940806
\(321\) 3.73342e125 0.0985379
\(322\) −1.77842e127 −4.01155
\(323\) −2.91798e126 −0.562800
\(324\) 8.61771e125 0.142190
\(325\) 1.13810e125 0.0160720
\(326\) 2.23026e127 2.69691
\(327\) 4.42009e126 0.457899
\(328\) −2.70565e126 −0.240238
\(329\) 1.63797e126 0.124713
\(330\) 3.70204e126 0.241817
\(331\) 2.56318e126 0.143703 0.0718514 0.997415i \(-0.477109\pi\)
0.0718514 + 0.997415i \(0.477109\pi\)
\(332\) 1.37816e127 0.663479
\(333\) 2.82978e127 1.17036
\(334\) −1.97039e127 −0.700415
\(335\) 1.18676e127 0.362744
\(336\) −3.97416e127 −1.04499
\(337\) −6.28379e127 −1.42204 −0.711020 0.703172i \(-0.751767\pi\)
−0.711020 + 0.703172i \(0.751767\pi\)
\(338\) −7.01713e127 −1.36731
\(339\) −3.10883e126 −0.0521809
\(340\) 4.39970e127 0.636412
\(341\) 5.43157e126 0.0677376
\(342\) −8.71382e127 −0.937325
\(343\) 1.52119e128 1.41199
\(344\) 2.77134e127 0.222069
\(345\) 1.81058e128 1.25301
\(346\) −1.51951e128 −0.908573
\(347\) −7.50746e126 −0.0388021 −0.0194010 0.999812i \(-0.506176\pi\)
−0.0194010 + 0.999812i \(0.506176\pi\)
\(348\) −5.74150e127 −0.256610
\(349\) −1.53174e128 −0.592243 −0.296121 0.955150i \(-0.595693\pi\)
−0.296121 + 0.955150i \(0.595693\pi\)
\(350\) 4.58101e128 1.53294
\(351\) −7.85801e126 −0.0227669
\(352\) 1.31646e128 0.330371
\(353\) −8.51845e128 −1.85241 −0.926206 0.377017i \(-0.876950\pi\)
−0.926206 + 0.377017i \(0.876950\pi\)
\(354\) 7.97561e128 1.50348
\(355\) 1.00430e129 1.64185
\(356\) −9.33978e128 −1.32468
\(357\) −4.31978e128 −0.531762
\(358\) −9.04909e126 −0.00967191
\(359\) −6.93817e128 −0.644133 −0.322066 0.946717i \(-0.604377\pi\)
−0.322066 + 0.946717i \(0.604377\pi\)
\(360\) −1.93351e128 −0.155980
\(361\) −1.49481e127 −0.0104827
\(362\) 1.48907e129 0.908099
\(363\) −9.88191e128 −0.524271
\(364\) 7.68587e127 0.0354873
\(365\) −3.64369e129 −1.46471
\(366\) −3.15057e129 −1.10305
\(367\) −3.99074e128 −0.121735 −0.0608677 0.998146i \(-0.519387\pi\)
−0.0608677 + 0.998146i \(0.519387\pi\)
\(368\) 7.27827e129 1.93514
\(369\) −4.06669e129 −0.942777
\(370\) 1.48350e130 2.99986
\(371\) −4.05889e129 −0.716184
\(372\) −8.71149e128 −0.134176
\(373\) 9.72150e129 1.30749 0.653743 0.756716i \(-0.273198\pi\)
0.653743 + 0.756716i \(0.273198\pi\)
\(374\) 1.61759e129 0.190043
\(375\) 2.34839e129 0.241097
\(376\) −1.44768e128 −0.0129923
\(377\) −1.62465e128 −0.0127503
\(378\) −3.16297e130 −2.17149
\(379\) −5.91099e129 −0.355124 −0.177562 0.984110i \(-0.556821\pi\)
−0.177562 + 0.984110i \(0.556821\pi\)
\(380\) −2.12755e130 −1.11894
\(381\) 1.31180e130 0.604167
\(382\) −1.41384e130 −0.570427
\(383\) −1.38327e130 −0.489066 −0.244533 0.969641i \(-0.578635\pi\)
−0.244533 + 0.969641i \(0.578635\pi\)
\(384\) 6.26640e129 0.194219
\(385\) 1.96378e130 0.533735
\(386\) 3.45045e130 0.822652
\(387\) 4.16542e130 0.871475
\(388\) 2.30887e130 0.424031
\(389\) −7.55228e130 −1.21793 −0.608966 0.793196i \(-0.708416\pi\)
−0.608966 + 0.793196i \(0.708416\pi\)
\(390\) −1.68013e129 −0.0238002
\(391\) 7.91124e130 0.984733
\(392\) −2.94859e130 −0.322603
\(393\) 1.03210e130 0.0992883
\(394\) −1.08674e131 −0.919535
\(395\) 1.50635e131 1.12143
\(396\) 2.24973e130 0.147409
\(397\) −1.85454e131 −1.06983 −0.534917 0.844905i \(-0.679657\pi\)
−0.534917 + 0.844905i \(0.679657\pi\)
\(398\) 2.15813e131 1.09644
\(399\) 2.08890e131 0.934946
\(400\) −1.87480e131 −0.739478
\(401\) −2.80194e131 −0.974245 −0.487123 0.873334i \(-0.661954\pi\)
−0.487123 + 0.873334i \(0.661954\pi\)
\(402\) −6.99800e130 −0.214565
\(403\) −2.46506e129 −0.00666687
\(404\) 2.31382e131 0.552167
\(405\) −9.99293e130 −0.210482
\(406\) −6.53946e131 −1.21612
\(407\) 2.54020e131 0.417205
\(408\) 3.81795e130 0.0553977
\(409\) −1.45497e129 −0.00186564 −0.000932820 1.00000i \(-0.500297\pi\)
−0.000932820 1.00000i \(0.500297\pi\)
\(410\) −2.13194e132 −2.41652
\(411\) 1.42516e130 0.0142840
\(412\) 4.94826e131 0.438675
\(413\) 4.23073e132 3.31847
\(414\) 2.36250e132 1.64004
\(415\) −1.59809e132 −0.982138
\(416\) −5.97459e130 −0.0325158
\(417\) 1.01638e132 0.489986
\(418\) −7.82209e131 −0.334134
\(419\) 2.79270e131 0.105734 0.0528671 0.998602i \(-0.483164\pi\)
0.0528671 + 0.998602i \(0.483164\pi\)
\(420\) −3.14963e132 −1.05723
\(421\) −3.06040e132 −0.911029 −0.455514 0.890228i \(-0.650545\pi\)
−0.455514 + 0.890228i \(0.650545\pi\)
\(422\) 3.99722e132 1.05555
\(423\) −2.17592e131 −0.0509865
\(424\) 3.58736e131 0.0746104
\(425\) −2.03785e132 −0.376297
\(426\) −5.92209e132 −0.971158
\(427\) −1.67125e133 −2.43463
\(428\) 1.18941e132 0.153964
\(429\) −2.87688e130 −0.00331000
\(430\) 2.18370e133 2.23376
\(431\) −2.83557e132 −0.257951 −0.128976 0.991648i \(-0.541169\pi\)
−0.128976 + 0.991648i \(0.541169\pi\)
\(432\) 1.29446e133 1.04751
\(433\) 1.37181e133 0.987767 0.493883 0.869528i \(-0.335577\pi\)
0.493883 + 0.869528i \(0.335577\pi\)
\(434\) −9.92221e132 −0.635883
\(435\) 6.65773e132 0.379856
\(436\) 1.40817e133 0.715463
\(437\) −3.82561e133 −1.73136
\(438\) 2.14858e133 0.866382
\(439\) 2.79760e132 0.100537 0.0502686 0.998736i \(-0.483992\pi\)
0.0502686 + 0.998736i \(0.483992\pi\)
\(440\) −1.73564e132 −0.0556033
\(441\) −4.43185e133 −1.26601
\(442\) −7.34122e131 −0.0187044
\(443\) 1.81372e133 0.412270 0.206135 0.978524i \(-0.433911\pi\)
0.206135 + 0.978524i \(0.433911\pi\)
\(444\) −4.07412e133 −0.826407
\(445\) 1.08302e134 1.96091
\(446\) 6.49012e133 1.04916
\(447\) −3.44439e133 −0.497258
\(448\) −9.52436e133 −1.22828
\(449\) −4.40637e133 −0.507740 −0.253870 0.967238i \(-0.581703\pi\)
−0.253870 + 0.967238i \(0.581703\pi\)
\(450\) −6.08553e133 −0.626710
\(451\) −3.65052e133 −0.336078
\(452\) −9.90421e132 −0.0815321
\(453\) 7.91640e133 0.582866
\(454\) −1.63809e134 −1.07899
\(455\) −8.91238e132 −0.0525313
\(456\) −1.84623e133 −0.0974005
\(457\) 2.56573e134 1.21183 0.605916 0.795529i \(-0.292807\pi\)
0.605916 + 0.795529i \(0.292807\pi\)
\(458\) −5.67400e133 −0.239984
\(459\) 1.40704e134 0.533046
\(460\) 5.76822e134 1.95781
\(461\) −2.76855e134 −0.842084 −0.421042 0.907041i \(-0.638336\pi\)
−0.421042 + 0.907041i \(0.638336\pi\)
\(462\) −1.15799e134 −0.315707
\(463\) 6.40865e134 1.56649 0.783243 0.621715i \(-0.213564\pi\)
0.783243 + 0.621715i \(0.213564\pi\)
\(464\) 2.67631e134 0.586648
\(465\) 1.01017e134 0.198618
\(466\) −8.05530e134 −1.42100
\(467\) −7.65000e134 −1.21104 −0.605521 0.795829i \(-0.707035\pi\)
−0.605521 + 0.795829i \(0.707035\pi\)
\(468\) −1.02101e133 −0.0145082
\(469\) −3.71215e134 −0.473584
\(470\) −1.14072e134 −0.130688
\(471\) −5.41511e134 −0.557251
\(472\) −3.73924e134 −0.345710
\(473\) 3.73915e134 0.310660
\(474\) −8.88251e134 −0.663330
\(475\) 9.85433e134 0.661607
\(476\) −1.37621e135 −0.830872
\(477\) 5.39193e134 0.292797
\(478\) −4.68518e134 −0.228885
\(479\) 4.32936e135 1.90318 0.951592 0.307364i \(-0.0994470\pi\)
0.951592 + 0.307364i \(0.0994470\pi\)
\(480\) 2.44836e135 0.968706
\(481\) −1.15284e134 −0.0410622
\(482\) 4.84013e135 1.55232
\(483\) −5.66344e135 −1.63588
\(484\) −3.14821e135 −0.819169
\(485\) −2.67732e135 −0.627687
\(486\) 6.68987e135 1.41347
\(487\) −2.22301e135 −0.423379 −0.211689 0.977337i \(-0.567896\pi\)
−0.211689 + 0.977337i \(0.567896\pi\)
\(488\) 1.47710e135 0.253634
\(489\) 7.10235e135 1.09978
\(490\) −2.32338e136 −3.24502
\(491\) 7.43679e135 0.937066 0.468533 0.883446i \(-0.344783\pi\)
0.468533 + 0.883446i \(0.344783\pi\)
\(492\) 5.85493e135 0.665708
\(493\) 2.90906e135 0.298527
\(494\) 3.54996e134 0.0328861
\(495\) −2.60874e135 −0.218207
\(496\) 4.06071e135 0.306745
\(497\) −3.14142e136 −2.14352
\(498\) 9.42350e135 0.580939
\(499\) −1.25878e135 −0.0701248 −0.0350624 0.999385i \(-0.511163\pi\)
−0.0350624 + 0.999385i \(0.511163\pi\)
\(500\) 7.48158e135 0.376711
\(501\) −6.27479e135 −0.285623
\(502\) 1.82075e136 0.749396
\(503\) −1.27338e136 −0.473995 −0.236997 0.971510i \(-0.576163\pi\)
−0.236997 + 0.971510i \(0.576163\pi\)
\(504\) 6.04795e135 0.203642
\(505\) −2.68306e136 −0.817365
\(506\) 2.12073e136 0.584635
\(507\) −2.23463e136 −0.557576
\(508\) 4.17918e136 0.944004
\(509\) 1.09464e136 0.223885 0.111943 0.993715i \(-0.464293\pi\)
0.111943 + 0.993715i \(0.464293\pi\)
\(510\) 3.00840e136 0.557238
\(511\) 1.13973e137 1.91226
\(512\) 8.55831e136 1.30093
\(513\) −6.80395e136 −0.937203
\(514\) −2.81868e136 −0.351891
\(515\) −5.73791e136 −0.649364
\(516\) −5.99708e136 −0.615361
\(517\) −1.95325e135 −0.0181755
\(518\) −4.64034e137 −3.91649
\(519\) −4.83893e136 −0.370508
\(520\) 7.87702e134 0.00547259
\(521\) 2.10093e137 1.32467 0.662335 0.749208i \(-0.269566\pi\)
0.662335 + 0.749208i \(0.269566\pi\)
\(522\) 8.68719e136 0.497186
\(523\) 1.58385e137 0.822958 0.411479 0.911419i \(-0.365012\pi\)
0.411479 + 0.911419i \(0.365012\pi\)
\(524\) 3.28810e136 0.155137
\(525\) 1.45884e137 0.625119
\(526\) −4.26115e137 −1.65862
\(527\) 4.41387e136 0.156093
\(528\) 4.73912e136 0.152295
\(529\) 6.94819e137 2.02937
\(530\) 2.82670e137 0.750496
\(531\) −5.62021e137 −1.35669
\(532\) 6.65489e137 1.46084
\(533\) 1.65675e136 0.0330774
\(534\) −6.38628e137 −1.15988
\(535\) −1.37921e137 −0.227911
\(536\) 3.28090e136 0.0493369
\(537\) −2.88172e135 −0.00394412
\(538\) −4.39263e137 −0.547293
\(539\) −3.97831e137 −0.451301
\(540\) 1.02589e138 1.05979
\(541\) 2.27932e137 0.214458 0.107229 0.994234i \(-0.465802\pi\)
0.107229 + 0.994234i \(0.465802\pi\)
\(542\) −1.86451e138 −1.59809
\(543\) 4.74201e137 0.370315
\(544\) 1.06979e138 0.761300
\(545\) −1.63289e138 −1.05909
\(546\) 5.25538e136 0.0310725
\(547\) −2.09237e137 −0.112792 −0.0563959 0.998408i \(-0.517961\pi\)
−0.0563959 + 0.998408i \(0.517961\pi\)
\(548\) 4.54032e136 0.0223187
\(549\) 2.22013e138 0.995349
\(550\) −5.46277e137 −0.223407
\(551\) −1.40672e138 −0.524871
\(552\) 5.00551e137 0.170422
\(553\) −4.71180e138 −1.46409
\(554\) 6.25160e137 0.177316
\(555\) 4.72427e138 1.22332
\(556\) 3.23801e138 0.765598
\(557\) −1.72569e138 −0.372629 −0.186314 0.982490i \(-0.559654\pi\)
−0.186314 + 0.982490i \(0.559654\pi\)
\(558\) 1.31809e138 0.259968
\(559\) −1.69697e137 −0.0305758
\(560\) 1.46815e139 2.41699
\(561\) 5.15127e137 0.0774978
\(562\) −1.91177e139 −2.62876
\(563\) 1.04160e139 1.30927 0.654633 0.755946i \(-0.272823\pi\)
0.654633 + 0.755946i \(0.272823\pi\)
\(564\) 3.13274e137 0.0360023
\(565\) 1.14847e138 0.120691
\(566\) −7.70820e138 −0.740838
\(567\) 3.12575e138 0.274796
\(568\) 2.77648e138 0.223307
\(569\) −2.38659e139 −1.75634 −0.878170 0.478348i \(-0.841236\pi\)
−0.878170 + 0.478348i \(0.841236\pi\)
\(570\) −1.45476e139 −0.979739
\(571\) −2.74087e139 −1.68953 −0.844764 0.535139i \(-0.820259\pi\)
−0.844764 + 0.535139i \(0.820259\pi\)
\(572\) −9.16526e136 −0.00517184
\(573\) −4.50243e138 −0.232615
\(574\) 6.66865e139 3.15491
\(575\) −2.67172e139 −1.15761
\(576\) 1.26524e139 0.502155
\(577\) 3.12739e139 1.13711 0.568557 0.822644i \(-0.307502\pi\)
0.568557 + 0.822644i \(0.307502\pi\)
\(578\) −2.79204e139 −0.930176
\(579\) 1.09881e139 0.335471
\(580\) 2.12104e139 0.593521
\(581\) 4.99877e139 1.28224
\(582\) 1.57874e139 0.371279
\(583\) 4.84015e138 0.104375
\(584\) −1.00733e139 −0.199215
\(585\) 1.18394e138 0.0214763
\(586\) −7.05889e139 −1.17465
\(587\) 6.93226e138 0.105840 0.0529201 0.998599i \(-0.483147\pi\)
0.0529201 + 0.998599i \(0.483147\pi\)
\(588\) 6.38066e139 0.893945
\(589\) −2.13439e139 −0.274443
\(590\) −2.94637e140 −3.47745
\(591\) −3.46078e139 −0.374979
\(592\) 1.89908e140 1.88929
\(593\) −5.93058e139 −0.541795 −0.270898 0.962608i \(-0.587320\pi\)
−0.270898 + 0.962608i \(0.587320\pi\)
\(594\) 3.77178e139 0.316469
\(595\) 1.59583e140 1.22993
\(596\) −1.09733e140 −0.776961
\(597\) 6.87266e139 0.447117
\(598\) −9.62469e138 −0.0575410
\(599\) 1.91583e140 1.05269 0.526346 0.850270i \(-0.323562\pi\)
0.526346 + 0.850270i \(0.323562\pi\)
\(600\) −1.28936e139 −0.0651235
\(601\) −1.85009e140 −0.859078 −0.429539 0.903048i \(-0.641324\pi\)
−0.429539 + 0.903048i \(0.641324\pi\)
\(602\) −6.83055e140 −2.91631
\(603\) 4.93132e139 0.193615
\(604\) 2.52203e140 0.910721
\(605\) 3.65061e140 1.21260
\(606\) 1.58213e140 0.483474
\(607\) 3.03046e140 0.852077 0.426039 0.904705i \(-0.359909\pi\)
0.426039 + 0.904705i \(0.359909\pi\)
\(608\) −5.17316e140 −1.33852
\(609\) −2.08252e140 −0.495924
\(610\) 1.16390e141 2.55127
\(611\) 8.86459e137 0.00178887
\(612\) 1.82820e140 0.339685
\(613\) 2.63225e139 0.0450375 0.0225187 0.999746i \(-0.492831\pi\)
0.0225187 + 0.999746i \(0.492831\pi\)
\(614\) −1.92015e140 −0.302575
\(615\) −6.78926e140 −0.985438
\(616\) 5.42904e139 0.0725933
\(617\) −9.13650e140 −1.12559 −0.562794 0.826597i \(-0.690273\pi\)
−0.562794 + 0.826597i \(0.690273\pi\)
\(618\) 3.38348e140 0.384102
\(619\) −3.85006e140 −0.402800 −0.201400 0.979509i \(-0.564549\pi\)
−0.201400 + 0.979509i \(0.564549\pi\)
\(620\) 3.21823e140 0.310339
\(621\) 1.84469e141 1.63983
\(622\) −5.76775e140 −0.472707
\(623\) −3.38766e141 −2.56008
\(624\) −2.15079e139 −0.0149891
\(625\) −1.90228e141 −1.22274
\(626\) 6.37279e140 0.377856
\(627\) −2.49098e140 −0.136257
\(628\) −1.72516e141 −0.870700
\(629\) 2.06424e141 0.961398
\(630\) 4.76555e141 2.04840
\(631\) 3.45766e141 1.37183 0.685914 0.727683i \(-0.259403\pi\)
0.685914 + 0.727683i \(0.259403\pi\)
\(632\) 4.16443e140 0.152526
\(633\) 1.27293e141 0.430444
\(634\) 3.11579e141 0.972882
\(635\) −4.84610e141 −1.39739
\(636\) −7.76293e140 −0.206748
\(637\) 1.80551e140 0.0444180
\(638\) 7.79819e140 0.177235
\(639\) 4.17315e141 0.876336
\(640\) −2.31495e141 −0.449214
\(641\) −7.54846e141 −1.35372 −0.676858 0.736113i \(-0.736659\pi\)
−0.676858 + 0.736113i \(0.736659\pi\)
\(642\) 8.13284e140 0.134810
\(643\) 2.67416e141 0.409764 0.204882 0.978787i \(-0.434319\pi\)
0.204882 + 0.978787i \(0.434319\pi\)
\(644\) −1.80428e142 −2.55604
\(645\) 6.95409e141 0.910909
\(646\) −6.35648e141 −0.769971
\(647\) 5.28331e141 0.591888 0.295944 0.955205i \(-0.404366\pi\)
0.295944 + 0.955205i \(0.404366\pi\)
\(648\) −2.76263e140 −0.0286276
\(649\) −5.04507e141 −0.483626
\(650\) 2.47921e140 0.0219882
\(651\) −3.15977e141 −0.259308
\(652\) 2.26269e142 1.71839
\(653\) 1.07024e142 0.752255 0.376127 0.926568i \(-0.377256\pi\)
0.376127 + 0.926568i \(0.377256\pi\)
\(654\) 9.62867e141 0.626455
\(655\) −3.81282e141 −0.229647
\(656\) −2.72918e142 −1.52191
\(657\) −1.51405e142 −0.781790
\(658\) 3.56813e141 0.170621
\(659\) 5.07673e141 0.224838 0.112419 0.993661i \(-0.464140\pi\)
0.112419 + 0.993661i \(0.464140\pi\)
\(660\) 3.75588e141 0.154079
\(661\) 3.54834e142 1.34850 0.674251 0.738503i \(-0.264467\pi\)
0.674251 + 0.738503i \(0.264467\pi\)
\(662\) 5.58360e141 0.196601
\(663\) −2.33784e140 −0.00762749
\(664\) −4.41806e141 −0.133581
\(665\) −7.71688e142 −2.16246
\(666\) 6.16436e142 1.60118
\(667\) 3.81391e142 0.918367
\(668\) −1.99904e142 −0.446284
\(669\) 2.06681e142 0.427839
\(670\) 2.58523e142 0.496273
\(671\) 1.99293e142 0.354818
\(672\) −7.65837e142 −1.26470
\(673\) 9.39782e142 1.43968 0.719841 0.694139i \(-0.244215\pi\)
0.719841 + 0.694139i \(0.244215\pi\)
\(674\) −1.36885e143 −1.94550
\(675\) −4.75172e142 −0.626629
\(676\) −7.11918e142 −0.871207
\(677\) −8.56774e142 −0.973058 −0.486529 0.873664i \(-0.661737\pi\)
−0.486529 + 0.873664i \(0.661737\pi\)
\(678\) −6.77222e141 −0.0713890
\(679\) 8.37457e142 0.819481
\(680\) −1.41044e142 −0.128131
\(681\) −5.21657e142 −0.440003
\(682\) 1.18321e142 0.0926722
\(683\) 1.57442e143 1.14518 0.572592 0.819841i \(-0.305938\pi\)
0.572592 + 0.819841i \(0.305938\pi\)
\(684\) −8.84054e142 −0.597235
\(685\) −5.26487e141 −0.0330380
\(686\) 3.31374e143 1.93175
\(687\) −1.80691e142 −0.0978635
\(688\) 2.79544e143 1.40680
\(689\) −2.19665e141 −0.0102728
\(690\) 3.94415e143 1.71425
\(691\) −3.69642e143 −1.49327 −0.746637 0.665232i \(-0.768333\pi\)
−0.746637 + 0.665232i \(0.768333\pi\)
\(692\) −1.54160e143 −0.578916
\(693\) 8.16004e142 0.284881
\(694\) −1.63542e142 −0.0530854
\(695\) −3.75473e143 −1.13330
\(696\) 1.84059e142 0.0516642
\(697\) −2.96653e143 −0.774450
\(698\) −3.33671e143 −0.810251
\(699\) −2.56524e143 −0.579470
\(700\) 4.64762e143 0.976742
\(701\) 6.83715e143 1.33695 0.668475 0.743735i \(-0.266948\pi\)
0.668475 + 0.743735i \(0.266948\pi\)
\(702\) −1.71178e142 −0.0311475
\(703\) −9.98197e143 −1.69033
\(704\) 1.13576e143 0.179006
\(705\) −3.63267e142 −0.0532936
\(706\) −1.85565e144 −2.53430
\(707\) 8.39252e143 1.06712
\(708\) 8.09159e143 0.957975
\(709\) −4.57737e143 −0.504640 −0.252320 0.967644i \(-0.581194\pi\)
−0.252320 + 0.967644i \(0.581194\pi\)
\(710\) 2.18776e144 2.24622
\(711\) 6.25929e143 0.598563
\(712\) 2.99411e143 0.266703
\(713\) 5.78679e143 0.480194
\(714\) −9.41016e143 −0.727507
\(715\) 1.06279e142 0.00765580
\(716\) −9.18068e141 −0.00616265
\(717\) −1.49202e143 −0.0933375
\(718\) −1.51140e144 −0.881243
\(719\) −8.91079e142 −0.0484292 −0.0242146 0.999707i \(-0.507708\pi\)
−0.0242146 + 0.999707i \(0.507708\pi\)
\(720\) −1.95033e144 −0.988135
\(721\) 1.79480e144 0.847783
\(722\) −3.25628e142 −0.0143414
\(723\) 1.54136e144 0.633023
\(724\) 1.51073e144 0.578613
\(725\) −9.82422e143 −0.350937
\(726\) −2.15266e144 −0.717259
\(727\) 5.09087e144 1.58236 0.791178 0.611585i \(-0.209468\pi\)
0.791178 + 0.611585i \(0.209468\pi\)
\(728\) −2.46390e142 −0.00714478
\(729\) 1.52753e144 0.413286
\(730\) −7.93736e144 −2.00388
\(731\) 3.03855e144 0.715878
\(732\) −3.19639e144 −0.702830
\(733\) −8.05963e144 −1.65411 −0.827055 0.562121i \(-0.809985\pi\)
−0.827055 + 0.562121i \(0.809985\pi\)
\(734\) −8.69337e143 −0.166547
\(735\) −7.39889e144 −1.32329
\(736\) 1.40255e145 2.34201
\(737\) 4.42667e143 0.0690191
\(738\) −8.85881e144 −1.28982
\(739\) 5.87280e143 0.0798547 0.0399274 0.999203i \(-0.487287\pi\)
0.0399274 + 0.999203i \(0.487287\pi\)
\(740\) 1.50508e145 1.91142
\(741\) 1.13050e143 0.0134107
\(742\) −8.84182e144 −0.979816
\(743\) 4.30726e144 0.445929 0.222965 0.974827i \(-0.428427\pi\)
0.222965 + 0.974827i \(0.428427\pi\)
\(744\) 2.79269e143 0.0270141
\(745\) 1.27244e145 1.15012
\(746\) 2.11772e145 1.78878
\(747\) −6.64051e144 −0.524217
\(748\) 1.64111e144 0.121090
\(749\) 4.31413e144 0.297551
\(750\) 5.11570e144 0.329846
\(751\) −1.39247e145 −0.839402 −0.419701 0.907662i \(-0.637865\pi\)
−0.419701 + 0.907662i \(0.637865\pi\)
\(752\) −1.46027e144 −0.0823064
\(753\) 5.79823e144 0.305597
\(754\) −3.53912e143 −0.0174438
\(755\) −2.92450e145 −1.34813
\(756\) −3.20896e145 −1.38361
\(757\) −4.28990e145 −1.73024 −0.865118 0.501568i \(-0.832757\pi\)
−0.865118 + 0.501568i \(0.832757\pi\)
\(758\) −1.28764e145 −0.485848
\(759\) 6.75356e144 0.238409
\(760\) 6.82040e144 0.225280
\(761\) 2.43861e145 0.753732 0.376866 0.926268i \(-0.377002\pi\)
0.376866 + 0.926268i \(0.377002\pi\)
\(762\) 2.85761e145 0.826564
\(763\) 5.10761e145 1.38270
\(764\) −1.43440e145 −0.363459
\(765\) −2.11994e145 −0.502830
\(766\) −3.01329e145 −0.669095
\(767\) 2.28964e144 0.0475995
\(768\) 3.45474e145 0.672471
\(769\) 2.73166e145 0.497905 0.248952 0.968516i \(-0.419914\pi\)
0.248952 + 0.968516i \(0.419914\pi\)
\(770\) 4.27787e145 0.730207
\(771\) −8.97619e144 −0.143498
\(772\) 3.50062e145 0.524169
\(773\) −3.79729e145 −0.532611 −0.266305 0.963889i \(-0.585803\pi\)
−0.266305 + 0.963889i \(0.585803\pi\)
\(774\) 9.07389e145 1.19227
\(775\) −1.49061e145 −0.183497
\(776\) −7.40168e144 −0.0853716
\(777\) −1.47774e146 −1.59711
\(778\) −1.64518e146 −1.66626
\(779\) 1.43451e146 1.36164
\(780\) −1.70456e144 −0.0151647
\(781\) 3.74609e145 0.312393
\(782\) 1.72337e146 1.34722
\(783\) 6.78315e145 0.497122
\(784\) −2.97424e146 −2.04369
\(785\) 2.00047e146 1.28888
\(786\) 2.24831e145 0.135837
\(787\) −2.95088e146 −1.67197 −0.835984 0.548754i \(-0.815103\pi\)
−0.835984 + 0.548754i \(0.815103\pi\)
\(788\) −1.10255e146 −0.585900
\(789\) −1.35698e146 −0.676370
\(790\) 3.28141e146 1.53424
\(791\) −3.59238e145 −0.157569
\(792\) −7.21208e144 −0.0296783
\(793\) −9.04470e144 −0.0349219
\(794\) −4.03991e146 −1.46365
\(795\) 9.00174e145 0.306046
\(796\) 2.18952e146 0.698616
\(797\) −9.14143e145 −0.273759 −0.136880 0.990588i \(-0.543707\pi\)
−0.136880 + 0.990588i \(0.543707\pi\)
\(798\) 4.55043e146 1.27911
\(799\) −1.58727e145 −0.0418831
\(800\) −3.61282e146 −0.894956
\(801\) 4.50026e146 1.04663
\(802\) −6.10371e146 −1.33287
\(803\) −1.35911e146 −0.278689
\(804\) −7.09977e145 −0.136714
\(805\) 2.09221e147 3.78367
\(806\) −5.36984e144 −0.00912099
\(807\) −1.39885e146 −0.223181
\(808\) −7.41755e145 −0.111170
\(809\) −4.26379e146 −0.600337 −0.300168 0.953886i \(-0.597043\pi\)
−0.300168 + 0.953886i \(0.597043\pi\)
\(810\) −2.17685e146 −0.287961
\(811\) 1.42871e147 1.77579 0.887897 0.460043i \(-0.152166\pi\)
0.887897 + 0.460043i \(0.152166\pi\)
\(812\) −6.63455e146 −0.774876
\(813\) −5.93762e146 −0.651688
\(814\) 5.53353e146 0.570781
\(815\) −2.62377e147 −2.54371
\(816\) 3.85115e146 0.350944
\(817\) −1.46934e147 −1.25866
\(818\) −3.16949e144 −0.00255240
\(819\) −3.70334e145 −0.0280386
\(820\) −2.16295e147 −1.53974
\(821\) −5.19552e145 −0.0347776 −0.0173888 0.999849i \(-0.505535\pi\)
−0.0173888 + 0.999849i \(0.505535\pi\)
\(822\) 3.10455e145 0.0195421
\(823\) 1.81447e146 0.107413 0.0537067 0.998557i \(-0.482896\pi\)
0.0537067 + 0.998557i \(0.482896\pi\)
\(824\) −1.58629e146 −0.0883200
\(825\) −1.73964e146 −0.0911036
\(826\) 9.21615e147 4.54002
\(827\) 2.36634e147 1.09660 0.548302 0.836280i \(-0.315274\pi\)
0.548302 + 0.836280i \(0.315274\pi\)
\(828\) 2.39685e147 1.04498
\(829\) −3.79588e147 −1.55707 −0.778536 0.627600i \(-0.784037\pi\)
−0.778536 + 0.627600i \(0.784037\pi\)
\(830\) −3.48126e147 −1.34367
\(831\) 1.99085e146 0.0723080
\(832\) −5.15453e145 −0.0176182
\(833\) −3.23290e147 −1.03997
\(834\) 2.21406e147 0.670354
\(835\) 2.31805e147 0.660627
\(836\) −7.93584e146 −0.212900
\(837\) 1.02920e147 0.259934
\(838\) 6.08357e146 0.144656
\(839\) −2.25603e145 −0.00505087 −0.00252543 0.999997i \(-0.500804\pi\)
−0.00252543 + 0.999997i \(0.500804\pi\)
\(840\) 1.00970e147 0.212856
\(841\) −3.63488e147 −0.721592
\(842\) −6.66673e147 −1.24638
\(843\) −6.08810e147 −1.07199
\(844\) 4.05534e147 0.672565
\(845\) 8.25526e147 1.28963
\(846\) −4.74000e146 −0.0697549
\(847\) −1.14190e148 −1.58312
\(848\) 3.61856e147 0.472656
\(849\) −2.45471e147 −0.302107
\(850\) −4.43922e147 −0.514815
\(851\) 2.70632e148 2.95758
\(852\) −6.00821e147 −0.618793
\(853\) 1.31386e148 1.27533 0.637664 0.770315i \(-0.279901\pi\)
0.637664 + 0.770315i \(0.279901\pi\)
\(854\) −3.64062e148 −3.33084
\(855\) 1.02513e148 0.884078
\(856\) −3.81295e146 −0.0309982
\(857\) −1.22789e148 −0.941081 −0.470541 0.882378i \(-0.655941\pi\)
−0.470541 + 0.882378i \(0.655941\pi\)
\(858\) −6.26695e145 −0.00452844
\(859\) −1.16067e148 −0.790778 −0.395389 0.918514i \(-0.629390\pi\)
−0.395389 + 0.918514i \(0.629390\pi\)
\(860\) 2.21546e148 1.42329
\(861\) 2.12366e148 1.28655
\(862\) −6.17696e147 −0.352905
\(863\) −2.56604e148 −1.38267 −0.691336 0.722534i \(-0.742977\pi\)
−0.691336 + 0.722534i \(0.742977\pi\)
\(864\) 2.49448e148 1.26776
\(865\) 1.78761e148 0.856960
\(866\) 2.98833e148 1.35137
\(867\) −8.89135e147 −0.379318
\(868\) −1.00665e148 −0.405165
\(869\) 5.61874e147 0.213374
\(870\) 1.45031e148 0.519684
\(871\) −2.00899e146 −0.00679300
\(872\) −4.51425e147 −0.144047
\(873\) −1.11250e148 −0.335028
\(874\) −8.33364e148 −2.36869
\(875\) 2.71366e148 0.728030
\(876\) 2.17983e148 0.552032
\(877\) −6.08651e148 −1.45509 −0.727544 0.686061i \(-0.759338\pi\)
−0.727544 + 0.686061i \(0.759338\pi\)
\(878\) 6.09425e147 0.137546
\(879\) −2.24793e148 −0.479010
\(880\) −1.75074e148 −0.352246
\(881\) 4.99456e148 0.948885 0.474443 0.880286i \(-0.342650\pi\)
0.474443 + 0.880286i \(0.342650\pi\)
\(882\) −9.65427e148 −1.73203
\(883\) 9.54085e148 1.61649 0.808243 0.588850i \(-0.200419\pi\)
0.808243 + 0.588850i \(0.200419\pi\)
\(884\) −7.44798e146 −0.0119179
\(885\) −9.38284e148 −1.41808
\(886\) 3.95098e148 0.564030
\(887\) −1.18543e149 −1.59858 −0.799290 0.600946i \(-0.794791\pi\)
−0.799290 + 0.600946i \(0.794791\pi\)
\(888\) 1.30606e148 0.166383
\(889\) 1.51584e149 1.82438
\(890\) 2.35924e149 2.68273
\(891\) −3.72741e147 −0.0400482
\(892\) 6.58450e148 0.668494
\(893\) 7.67550e147 0.0736390
\(894\) −7.50321e148 −0.680303
\(895\) 1.06457e147 0.00912247
\(896\) 7.24109e148 0.586475
\(897\) −3.06502e147 −0.0234647
\(898\) −9.59878e148 −0.694642
\(899\) 2.12787e148 0.145573
\(900\) −6.17403e148 −0.399321
\(901\) 3.93326e148 0.240520
\(902\) −7.95225e148 −0.459790
\(903\) −2.17522e149 −1.18924
\(904\) 3.17505e147 0.0164151
\(905\) −1.75181e149 −0.856512
\(906\) 1.72450e149 0.797422
\(907\) −7.81669e148 −0.341865 −0.170933 0.985283i \(-0.554678\pi\)
−0.170933 + 0.985283i \(0.554678\pi\)
\(908\) −1.66191e149 −0.687500
\(909\) −1.11488e149 −0.436269
\(910\) −1.94146e148 −0.0718684
\(911\) 2.35969e149 0.826373 0.413187 0.910646i \(-0.364416\pi\)
0.413187 + 0.910646i \(0.364416\pi\)
\(912\) −1.86229e149 −0.617031
\(913\) −5.96095e148 −0.186871
\(914\) 5.58914e149 1.65792
\(915\) 3.70647e149 1.04039
\(916\) −5.75651e148 −0.152911
\(917\) 1.19264e149 0.299817
\(918\) 3.06507e149 0.729264
\(919\) −4.79004e149 −1.07871 −0.539356 0.842078i \(-0.681332\pi\)
−0.539356 + 0.842078i \(0.681332\pi\)
\(920\) −1.84915e149 −0.394174
\(921\) −6.11481e148 −0.123388
\(922\) −6.03097e149 −1.15206
\(923\) −1.70012e148 −0.0307463
\(924\) −1.17483e149 −0.201159
\(925\) −6.97118e149 −1.13018
\(926\) 1.39605e150 2.14312
\(927\) −2.38426e149 −0.346598
\(928\) 5.15735e149 0.709993
\(929\) 8.78242e149 1.14504 0.572520 0.819891i \(-0.305966\pi\)
0.572520 + 0.819891i \(0.305966\pi\)
\(930\) 2.20053e149 0.271731
\(931\) 1.56332e150 1.82848
\(932\) −8.17244e149 −0.905416
\(933\) −1.83676e149 −0.192766
\(934\) −1.66647e150 −1.65683
\(935\) −1.90300e149 −0.179247
\(936\) 3.27312e147 0.00292100
\(937\) 7.29911e149 0.617192 0.308596 0.951193i \(-0.400141\pi\)
0.308596 + 0.951193i \(0.400141\pi\)
\(938\) −8.08649e149 −0.647913
\(939\) 2.02944e149 0.154086
\(940\) −1.15731e149 −0.0832707
\(941\) 7.72707e149 0.526913 0.263456 0.964671i \(-0.415138\pi\)
0.263456 + 0.964671i \(0.415138\pi\)
\(942\) −1.17962e150 −0.762380
\(943\) −3.88926e150 −2.38246
\(944\) −3.77176e150 −2.19007
\(945\) 3.72105e150 2.04814
\(946\) 8.14532e149 0.425016
\(947\) 1.31603e150 0.651019 0.325509 0.945539i \(-0.394464\pi\)
0.325509 + 0.945539i \(0.394464\pi\)
\(948\) −9.01168e149 −0.422654
\(949\) 6.16817e148 0.0274292
\(950\) 2.14665e150 0.905149
\(951\) 9.92235e149 0.396733
\(952\) 4.41180e149 0.167282
\(953\) −2.13928e150 −0.769266 −0.384633 0.923070i \(-0.625672\pi\)
−0.384633 + 0.923070i \(0.625672\pi\)
\(954\) 1.17457e150 0.400577
\(955\) 1.66330e150 0.538023
\(956\) −4.75332e149 −0.145839
\(957\) 2.48336e149 0.0722749
\(958\) 9.43103e150 2.60376
\(959\) 1.64683e149 0.0431330
\(960\) 2.11230e150 0.524878
\(961\) −3.91875e150 −0.923883
\(962\) −2.51133e149 −0.0561774
\(963\) −5.73101e149 −0.121648
\(964\) 4.91051e150 0.989092
\(965\) −4.05925e150 −0.775920
\(966\) −1.23372e151 −2.23805
\(967\) −3.54101e150 −0.609664 −0.304832 0.952406i \(-0.598600\pi\)
−0.304832 + 0.952406i \(0.598600\pi\)
\(968\) 1.00924e150 0.164926
\(969\) −2.02424e150 −0.313987
\(970\) −5.83224e150 −0.858742
\(971\) −1.11465e151 −1.55799 −0.778997 0.627028i \(-0.784271\pi\)
−0.778997 + 0.627028i \(0.784271\pi\)
\(972\) 6.78716e150 0.900620
\(973\) 1.17447e151 1.47959
\(974\) −4.84257e150 −0.579227
\(975\) 7.89516e148 0.00896660
\(976\) 1.48994e151 1.60677
\(977\) −1.17628e151 −1.20458 −0.602289 0.798278i \(-0.705744\pi\)
−0.602289 + 0.798278i \(0.705744\pi\)
\(978\) 1.54717e151 1.50461
\(979\) 4.03972e150 0.373100
\(980\) −2.35716e151 −2.06763
\(981\) −6.78509e150 −0.565289
\(982\) 1.62002e151 1.28201
\(983\) −4.21293e150 −0.316688 −0.158344 0.987384i \(-0.550615\pi\)
−0.158344 + 0.987384i \(0.550615\pi\)
\(984\) −1.87695e150 −0.134029
\(985\) 1.27849e151 0.867299
\(986\) 6.33705e150 0.408416
\(987\) 1.13629e150 0.0695779
\(988\) 3.60159e149 0.0209541
\(989\) 3.98369e151 2.20228
\(990\) −5.68284e150 −0.298530
\(991\) −2.05203e151 −1.02439 −0.512193 0.858870i \(-0.671167\pi\)
−0.512193 + 0.858870i \(0.671167\pi\)
\(992\) 7.82517e150 0.371239
\(993\) 1.77812e150 0.0801722
\(994\) −6.84323e151 −2.93257
\(995\) −2.53892e151 −1.03415
\(996\) 9.56053e150 0.370157
\(997\) 4.91493e151 1.80889 0.904444 0.426592i \(-0.140286\pi\)
0.904444 + 0.426592i \(0.140286\pi\)
\(998\) −2.74211e150 −0.0959383
\(999\) 4.81327e151 1.60097
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.1.7 8
3.2 odd 2 9.102.a.b.1.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.102.a.a.1.7 8 1.1 even 1 trivial
9.102.a.b.1.2 8 3.2 odd 2