Properties

Label 1.106.a.a.1.5
Level 1
Weight 106
Character 1.1
Self dual yes
Analytic conductor 69.819
Analytic rank 1
Dimension 8
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 106 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(69.8187388595\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} - \)\(10\!\cdots\!04\)\( x^{6} - \)\(62\!\cdots\!96\)\( x^{5} + \)\(32\!\cdots\!36\)\( x^{4} - \)\(88\!\cdots\!20\)\( x^{3} - \)\(32\!\cdots\!00\)\( x^{2} + \)\(21\!\cdots\!00\)\( x + \)\(48\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(1.99379e13\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} +O(q^{10})\) \(q+1.72418e15 q^{2} -1.28608e25 q^{3} -3.75920e31 q^{4} -7.91382e36 q^{5} -2.21743e40 q^{6} +2.76433e44 q^{7} -1.34757e47 q^{8} +4.01631e49 q^{9} -1.36449e52 q^{10} -6.07175e54 q^{11} +4.83463e56 q^{12} +2.29543e58 q^{13} +4.76621e59 q^{14} +1.01778e62 q^{15} +1.29257e63 q^{16} -1.76894e64 q^{17} +6.92484e64 q^{18} +1.67507e67 q^{19} +2.97496e68 q^{20} -3.55515e69 q^{21} -1.04688e70 q^{22} +4.70564e71 q^{23} +1.73308e72 q^{24} +3.79766e73 q^{25} +3.95773e73 q^{26} +1.09411e75 q^{27} -1.03917e76 q^{28} -2.66735e76 q^{29} +1.75484e77 q^{30} -3.05391e78 q^{31} +7.69500e78 q^{32} +7.80875e79 q^{33} -3.04998e79 q^{34} -2.18764e81 q^{35} -1.50981e81 q^{36} +8.35117e81 q^{37} +2.88812e82 q^{38} -2.95210e83 q^{39} +1.06644e84 q^{40} -4.13967e84 q^{41} -6.12972e84 q^{42} +2.16424e85 q^{43} +2.28250e86 q^{44} -3.17843e86 q^{45} +8.11337e86 q^{46} -2.62376e87 q^{47} -1.66234e88 q^{48} +2.20535e88 q^{49} +6.54785e88 q^{50} +2.27500e89 q^{51} -8.62898e89 q^{52} -2.71935e90 q^{53} +1.88645e90 q^{54} +4.80507e91 q^{55} -3.72512e91 q^{56} -2.15427e92 q^{57} -4.59900e91 q^{58} +1.20365e93 q^{59} -3.82604e93 q^{60} +7.31250e93 q^{61} -5.26549e93 q^{62} +1.11024e94 q^{63} -3.91652e94 q^{64} -1.81656e95 q^{65} +1.34637e95 q^{66} -2.41093e95 q^{67} +6.64982e95 q^{68} -6.05182e96 q^{69} -3.77189e96 q^{70} -9.07767e96 q^{71} -5.41224e96 q^{72} -9.30512e97 q^{73} +1.43989e97 q^{74} -4.88409e98 q^{75} -6.29692e98 q^{76} -1.67843e99 q^{77} -5.08996e98 q^{78} +5.92503e99 q^{79} -1.02292e100 q^{80} -1.91011e100 q^{81} -7.13754e99 q^{82} -1.53405e99 q^{83} +1.33645e101 q^{84} +1.39991e101 q^{85} +3.73155e100 q^{86} +3.43042e101 q^{87} +8.18209e101 q^{88} +2.87836e102 q^{89} -5.48019e101 q^{90} +6.34533e102 q^{91} -1.76894e103 q^{92} +3.92757e103 q^{93} -4.52384e102 q^{94} -1.32562e104 q^{95} -9.89637e103 q^{96} +8.84441e103 q^{97} +3.80242e103 q^{98} -2.43860e104 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + O(q^{10}) \) \( 8q - 9175032489175920q^{2} - \)\(35\!\cdots\!80\)\(q^{3} + \)\(12\!\cdots\!76\)\(q^{4} + \)\(74\!\cdots\!00\)\(q^{5} - \)\(13\!\cdots\!64\)\(q^{6} + \)\(70\!\cdots\!00\)\(q^{7} - \)\(70\!\cdots\!60\)\(q^{8} + \)\(31\!\cdots\!84\)\(q^{9} + \)\(44\!\cdots\!00\)\(q^{10} - \)\(91\!\cdots\!84\)\(q^{11} + \)\(15\!\cdots\!60\)\(q^{12} + \)\(40\!\cdots\!40\)\(q^{13} - \)\(16\!\cdots\!28\)\(q^{14} - \)\(85\!\cdots\!00\)\(q^{15} + \)\(88\!\cdots\!48\)\(q^{16} - \)\(47\!\cdots\!60\)\(q^{17} - \)\(26\!\cdots\!80\)\(q^{18} - \)\(18\!\cdots\!20\)\(q^{19} - \)\(43\!\cdots\!00\)\(q^{20} + \)\(34\!\cdots\!56\)\(q^{21} + \)\(61\!\cdots\!60\)\(q^{22} + \)\(35\!\cdots\!60\)\(q^{23} - \)\(85\!\cdots\!60\)\(q^{24} + \)\(36\!\cdots\!00\)\(q^{25} - \)\(17\!\cdots\!24\)\(q^{26} + \)\(41\!\cdots\!40\)\(q^{27} - \)\(10\!\cdots\!60\)\(q^{28} - \)\(13\!\cdots\!80\)\(q^{29} + \)\(36\!\cdots\!00\)\(q^{30} + \)\(21\!\cdots\!16\)\(q^{31} + \)\(10\!\cdots\!80\)\(q^{32} - \)\(11\!\cdots\!60\)\(q^{33} + \)\(62\!\cdots\!52\)\(q^{34} - \)\(18\!\cdots\!00\)\(q^{35} + \)\(16\!\cdots\!48\)\(q^{36} - \)\(23\!\cdots\!80\)\(q^{37} + \)\(81\!\cdots\!60\)\(q^{38} + \)\(97\!\cdots\!48\)\(q^{39} + \)\(16\!\cdots\!00\)\(q^{40} - \)\(91\!\cdots\!84\)\(q^{41} - \)\(99\!\cdots\!60\)\(q^{42} + \)\(30\!\cdots\!00\)\(q^{43} - \)\(61\!\cdots\!48\)\(q^{44} - \)\(72\!\cdots\!00\)\(q^{45} - \)\(19\!\cdots\!84\)\(q^{46} - \)\(19\!\cdots\!40\)\(q^{47} + \)\(47\!\cdots\!60\)\(q^{48} + \)\(90\!\cdots\!56\)\(q^{49} + \)\(12\!\cdots\!00\)\(q^{50} - \)\(10\!\cdots\!04\)\(q^{51} + \)\(26\!\cdots\!00\)\(q^{52} - \)\(50\!\cdots\!80\)\(q^{53} - \)\(33\!\cdots\!20\)\(q^{54} + \)\(18\!\cdots\!00\)\(q^{55} + \)\(77\!\cdots\!80\)\(q^{56} - \)\(17\!\cdots\!20\)\(q^{57} + \)\(52\!\cdots\!40\)\(q^{58} - \)\(80\!\cdots\!60\)\(q^{59} - \)\(49\!\cdots\!00\)\(q^{60} + \)\(93\!\cdots\!16\)\(q^{61} - \)\(24\!\cdots\!40\)\(q^{62} - \)\(69\!\cdots\!20\)\(q^{63} - \)\(97\!\cdots\!04\)\(q^{64} - \)\(36\!\cdots\!00\)\(q^{65} + \)\(15\!\cdots\!72\)\(q^{66} - \)\(11\!\cdots\!60\)\(q^{67} - \)\(97\!\cdots\!80\)\(q^{68} - \)\(15\!\cdots\!32\)\(q^{69} - \)\(42\!\cdots\!00\)\(q^{70} - \)\(50\!\cdots\!84\)\(q^{71} - \)\(31\!\cdots\!80\)\(q^{72} - \)\(30\!\cdots\!40\)\(q^{73} - \)\(92\!\cdots\!88\)\(q^{74} - \)\(20\!\cdots\!00\)\(q^{75} - \)\(31\!\cdots\!40\)\(q^{76} - \)\(59\!\cdots\!00\)\(q^{77} - \)\(21\!\cdots\!00\)\(q^{78} - \)\(15\!\cdots\!80\)\(q^{79} - \)\(36\!\cdots\!00\)\(q^{80} - \)\(16\!\cdots\!72\)\(q^{81} + \)\(40\!\cdots\!60\)\(q^{82} - \)\(27\!\cdots\!20\)\(q^{83} + \)\(24\!\cdots\!32\)\(q^{84} + \)\(11\!\cdots\!00\)\(q^{85} + \)\(20\!\cdots\!96\)\(q^{86} + \)\(24\!\cdots\!20\)\(q^{87} + \)\(65\!\cdots\!80\)\(q^{88} + \)\(45\!\cdots\!60\)\(q^{89} + \)\(27\!\cdots\!00\)\(q^{90} + \)\(27\!\cdots\!96\)\(q^{91} + \)\(11\!\cdots\!40\)\(q^{92} - \)\(18\!\cdots\!60\)\(q^{93} - \)\(14\!\cdots\!08\)\(q^{94} - \)\(19\!\cdots\!00\)\(q^{95} - \)\(72\!\cdots\!64\)\(q^{96} - \)\(76\!\cdots\!40\)\(q^{97} - \)\(13\!\cdots\!40\)\(q^{98} - \)\(25\!\cdots\!32\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.72418e15 0.270712 0.135356 0.990797i \(-0.456782\pi\)
0.135356 + 0.990797i \(0.456782\pi\)
\(3\) −1.28608e25 −1.14922 −0.574608 0.818429i \(-0.694845\pi\)
−0.574608 + 0.818429i \(0.694845\pi\)
\(4\) −3.75920e31 −0.926715
\(5\) −7.91382e36 −1.59390 −0.796949 0.604046i \(-0.793554\pi\)
−0.796949 + 0.604046i \(0.793554\pi\)
\(6\) −2.21743e40 −0.311107
\(7\) 2.76433e44 1.18561 0.592807 0.805345i \(-0.298020\pi\)
0.592807 + 0.805345i \(0.298020\pi\)
\(8\) −1.34757e47 −0.521586
\(9\) 4.01631e49 0.320697
\(10\) −1.36449e52 −0.431488
\(11\) −6.07175e54 −1.28884 −0.644419 0.764673i \(-0.722901\pi\)
−0.644419 + 0.764673i \(0.722901\pi\)
\(12\) 4.83463e56 1.06500
\(13\) 2.29543e58 0.756550 0.378275 0.925693i \(-0.376517\pi\)
0.378275 + 0.925693i \(0.376517\pi\)
\(14\) 4.76621e59 0.320960
\(15\) 1.01778e62 1.83173
\(16\) 1.29257e63 0.785515
\(17\) −1.76894e64 −0.445806 −0.222903 0.974841i \(-0.571553\pi\)
−0.222903 + 0.974841i \(0.571553\pi\)
\(18\) 6.92484e64 0.0868167
\(19\) 1.67507e67 1.22876 0.614382 0.789008i \(-0.289405\pi\)
0.614382 + 0.789008i \(0.289405\pi\)
\(20\) 2.97496e68 1.47709
\(21\) −3.55515e69 −1.36253
\(22\) −1.04688e70 −0.348904
\(23\) 4.70564e71 1.52022 0.760111 0.649793i \(-0.225144\pi\)
0.760111 + 0.649793i \(0.225144\pi\)
\(24\) 1.73308e72 0.599414
\(25\) 3.79766e73 1.54051
\(26\) 3.95773e73 0.204807
\(27\) 1.09411e75 0.780666
\(28\) −1.03917e76 −1.09873
\(29\) −2.66735e76 −0.446874 −0.223437 0.974718i \(-0.571728\pi\)
−0.223437 + 0.974718i \(0.571728\pi\)
\(30\) 1.75484e77 0.495873
\(31\) −3.05391e78 −1.54300 −0.771502 0.636227i \(-0.780494\pi\)
−0.771502 + 0.636227i \(0.780494\pi\)
\(32\) 7.69500e78 0.734234
\(33\) 7.80875e79 1.48115
\(34\) −3.04998e79 −0.120685
\(35\) −2.18764e81 −1.88975
\(36\) −1.50981e81 −0.297195
\(37\) 8.35117e81 0.390083 0.195041 0.980795i \(-0.437516\pi\)
0.195041 + 0.980795i \(0.437516\pi\)
\(38\) 2.88812e82 0.332642
\(39\) −2.95210e83 −0.869439
\(40\) 1.06644e84 0.831354
\(41\) −4.13967e84 −0.882700 −0.441350 0.897335i \(-0.645500\pi\)
−0.441350 + 0.897335i \(0.645500\pi\)
\(42\) −6.12972e84 −0.368853
\(43\) 2.16424e85 0.378628 0.189314 0.981917i \(-0.439374\pi\)
0.189314 + 0.981917i \(0.439374\pi\)
\(44\) 2.28250e86 1.19438
\(45\) −3.17843e86 −0.511159
\(46\) 8.11337e86 0.411543
\(47\) −2.62376e87 −0.430316 −0.215158 0.976579i \(-0.569027\pi\)
−0.215158 + 0.976579i \(0.569027\pi\)
\(48\) −1.66234e88 −0.902727
\(49\) 2.20535e88 0.405680
\(50\) 6.54785e88 0.417036
\(51\) 2.27500e89 0.512327
\(52\) −8.62898e89 −0.701106
\(53\) −2.71935e90 −0.812796 −0.406398 0.913696i \(-0.633215\pi\)
−0.406398 + 0.913696i \(0.633215\pi\)
\(54\) 1.88645e90 0.211336
\(55\) 4.80507e91 2.05428
\(56\) −3.72512e91 −0.618399
\(57\) −2.15427e92 −1.41212
\(58\) −4.59900e91 −0.120974
\(59\) 1.20365e93 1.29053 0.645266 0.763958i \(-0.276746\pi\)
0.645266 + 0.763958i \(0.276746\pi\)
\(60\) −3.82604e93 −1.69749
\(61\) 7.31250e93 1.36223 0.681114 0.732178i \(-0.261496\pi\)
0.681114 + 0.732178i \(0.261496\pi\)
\(62\) −5.26549e93 −0.417710
\(63\) 1.11024e94 0.380223
\(64\) −3.91652e94 −0.586749
\(65\) −1.81656e95 −1.20586
\(66\) 1.34637e95 0.400966
\(67\) −2.41093e95 −0.326030 −0.163015 0.986624i \(-0.552122\pi\)
−0.163015 + 0.986624i \(0.552122\pi\)
\(68\) 6.64982e95 0.413135
\(69\) −6.05182e96 −1.74706
\(70\) −3.77189e96 −0.511578
\(71\) −9.07767e96 −0.584671 −0.292335 0.956316i \(-0.594432\pi\)
−0.292335 + 0.956316i \(0.594432\pi\)
\(72\) −5.41224e96 −0.167271
\(73\) −9.30512e97 −1.39403 −0.697014 0.717057i \(-0.745489\pi\)
−0.697014 + 0.717057i \(0.745489\pi\)
\(74\) 1.43989e97 0.105600
\(75\) −4.88409e98 −1.77038
\(76\) −6.29692e98 −1.13871
\(77\) −1.67843e99 −1.52806
\(78\) −5.08996e98 −0.235368
\(79\) 5.92503e99 1.40368 0.701840 0.712335i \(-0.252362\pi\)
0.701840 + 0.712335i \(0.252362\pi\)
\(80\) −1.02292e100 −1.25203
\(81\) −1.91011e100 −1.21785
\(82\) −7.13754e99 −0.238958
\(83\) −1.53405e99 −0.0271793 −0.0135897 0.999908i \(-0.504326\pi\)
−0.0135897 + 0.999908i \(0.504326\pi\)
\(84\) 1.33645e101 1.26267
\(85\) 1.39991e101 0.710569
\(86\) 3.73155e100 0.102499
\(87\) 3.43042e101 0.513555
\(88\) 8.18209e101 0.672239
\(89\) 2.87836e102 1.30668 0.653342 0.757063i \(-0.273366\pi\)
0.653342 + 0.757063i \(0.273366\pi\)
\(90\) −5.48019e101 −0.138377
\(91\) 6.34533e102 0.896976
\(92\) −1.76894e103 −1.40881
\(93\) 3.92757e103 1.77324
\(94\) −4.52384e102 −0.116492
\(95\) −1.32562e104 −1.95853
\(96\) −9.89637e103 −0.843794
\(97\) 8.84441e103 0.437676 0.218838 0.975761i \(-0.429773\pi\)
0.218838 + 0.975761i \(0.429773\pi\)
\(98\) 3.80242e103 0.109822
\(99\) −2.43860e104 −0.413327
\(100\) −1.42762e105 −1.42762
\(101\) −1.30055e105 −0.771357 −0.385679 0.922633i \(-0.626033\pi\)
−0.385679 + 0.922633i \(0.626033\pi\)
\(102\) 3.92251e104 0.138693
\(103\) 4.74349e105 1.00495 0.502475 0.864592i \(-0.332423\pi\)
0.502475 + 0.864592i \(0.332423\pi\)
\(104\) −3.09324e105 −0.394606
\(105\) 2.81348e106 2.17173
\(106\) −4.68865e105 −0.220034
\(107\) 2.56647e106 0.735679 0.367839 0.929889i \(-0.380098\pi\)
0.367839 + 0.929889i \(0.380098\pi\)
\(108\) −4.11300e106 −0.723454
\(109\) 5.73392e106 0.621671 0.310836 0.950464i \(-0.399391\pi\)
0.310836 + 0.950464i \(0.399391\pi\)
\(110\) 8.28482e106 0.556118
\(111\) −1.07403e107 −0.448289
\(112\) 3.57309e107 0.931317
\(113\) −4.20335e107 −0.687032 −0.343516 0.939147i \(-0.611618\pi\)
−0.343516 + 0.939147i \(0.611618\pi\)
\(114\) −3.71435e107 −0.382277
\(115\) −3.72396e108 −2.42308
\(116\) 1.00271e108 0.414125
\(117\) 9.21915e107 0.242624
\(118\) 2.07531e108 0.349363
\(119\) −4.88995e108 −0.528553
\(120\) −1.37152e109 −0.955406
\(121\) 1.46724e109 0.661103
\(122\) 1.26081e109 0.368772
\(123\) 5.32394e109 1.01441
\(124\) 1.14803e110 1.42992
\(125\) −1.05449e110 −0.861522
\(126\) 1.91426e109 0.102931
\(127\) 4.07032e110 1.44522 0.722610 0.691256i \(-0.242942\pi\)
0.722610 + 0.691256i \(0.242942\pi\)
\(128\) −3.79674e110 −0.893074
\(129\) −2.78339e110 −0.435125
\(130\) −3.13208e110 −0.326442
\(131\) −6.75209e110 −0.470647 −0.235323 0.971917i \(-0.575615\pi\)
−0.235323 + 0.971917i \(0.575615\pi\)
\(132\) −2.93547e111 −1.37261
\(133\) 4.63045e111 1.45684
\(134\) −4.15689e110 −0.0882604
\(135\) −8.65862e111 −1.24430
\(136\) 2.38377e111 0.232526
\(137\) −1.29262e112 −0.858303 −0.429152 0.903232i \(-0.641187\pi\)
−0.429152 + 0.903232i \(0.641187\pi\)
\(138\) −1.04344e112 −0.472952
\(139\) 5.20344e112 1.61441 0.807204 0.590273i \(-0.200980\pi\)
0.807204 + 0.590273i \(0.200980\pi\)
\(140\) 8.22379e112 1.75126
\(141\) 3.37437e112 0.494526
\(142\) −1.56516e112 −0.158278
\(143\) −1.39373e113 −0.975070
\(144\) 5.19135e112 0.251913
\(145\) 2.11089e113 0.712272
\(146\) −1.60437e113 −0.377381
\(147\) −2.83625e113 −0.466213
\(148\) −3.13937e113 −0.361495
\(149\) −5.94493e113 −0.480693 −0.240347 0.970687i \(-0.577261\pi\)
−0.240347 + 0.970687i \(0.577261\pi\)
\(150\) −8.42105e113 −0.479264
\(151\) −1.55664e113 −0.0625026 −0.0312513 0.999512i \(-0.509949\pi\)
−0.0312513 + 0.999512i \(0.509949\pi\)
\(152\) −2.25727e114 −0.640906
\(153\) −7.10462e113 −0.142969
\(154\) −2.89393e114 −0.413666
\(155\) 2.41681e115 2.45939
\(156\) 1.10975e115 0.805722
\(157\) −2.92893e115 −1.52047 −0.760233 0.649651i \(-0.774915\pi\)
−0.760233 + 0.649651i \(0.774915\pi\)
\(158\) 1.02158e115 0.379993
\(159\) 3.49729e115 0.934078
\(160\) −6.08968e115 −1.17029
\(161\) 1.30080e116 1.80240
\(162\) −3.29337e115 −0.329687
\(163\) −4.30034e115 −0.311640 −0.155820 0.987785i \(-0.549802\pi\)
−0.155820 + 0.987785i \(0.549802\pi\)
\(164\) 1.55619e116 0.818011
\(165\) −6.17970e116 −2.36081
\(166\) −2.64497e114 −0.00735778
\(167\) −5.37632e116 −1.09111 −0.545557 0.838074i \(-0.683682\pi\)
−0.545557 + 0.838074i \(0.683682\pi\)
\(168\) 4.79080e116 0.710674
\(169\) −3.93661e116 −0.427632
\(170\) 2.41370e116 0.192360
\(171\) 6.72759e116 0.394062
\(172\) −8.13583e116 −0.350880
\(173\) 3.98690e117 1.26828 0.634139 0.773219i \(-0.281355\pi\)
0.634139 + 0.773219i \(0.281355\pi\)
\(174\) 5.91467e116 0.139026
\(175\) 1.04980e118 1.82645
\(176\) −7.84816e117 −1.01240
\(177\) −1.54799e118 −1.48310
\(178\) 4.96282e117 0.353735
\(179\) 2.27492e118 1.20832 0.604160 0.796863i \(-0.293509\pi\)
0.604160 + 0.796863i \(0.293509\pi\)
\(180\) 1.19484e118 0.473699
\(181\) −2.97655e118 −0.882242 −0.441121 0.897448i \(-0.645419\pi\)
−0.441121 + 0.897448i \(0.645419\pi\)
\(182\) 1.09405e118 0.242823
\(183\) −9.40445e118 −1.56549
\(184\) −6.34116e118 −0.792926
\(185\) −6.60896e118 −0.621752
\(186\) 6.77184e118 0.480039
\(187\) 1.07406e119 0.574571
\(188\) 9.86326e118 0.398780
\(189\) 3.02449e119 0.925568
\(190\) −2.28561e119 −0.530197
\(191\) −3.30349e119 −0.581730 −0.290865 0.956764i \(-0.593943\pi\)
−0.290865 + 0.956764i \(0.593943\pi\)
\(192\) 5.03696e119 0.674301
\(193\) 5.23171e119 0.533194 0.266597 0.963808i \(-0.414101\pi\)
0.266597 + 0.963808i \(0.414101\pi\)
\(194\) 1.52494e119 0.118484
\(195\) 2.33624e120 1.38580
\(196\) −8.29035e119 −0.375949
\(197\) −1.35909e120 −0.471814 −0.235907 0.971776i \(-0.575806\pi\)
−0.235907 + 0.971776i \(0.575806\pi\)
\(198\) −4.20459e119 −0.111893
\(199\) −6.37670e120 −1.30259 −0.651297 0.758823i \(-0.725775\pi\)
−0.651297 + 0.758823i \(0.725775\pi\)
\(200\) −5.11759e120 −0.803509
\(201\) 3.10065e120 0.374679
\(202\) −2.24239e120 −0.208816
\(203\) −7.37345e120 −0.529820
\(204\) −8.55219e120 −0.474781
\(205\) 3.27606e121 1.40693
\(206\) 8.17864e120 0.272052
\(207\) 1.88993e121 0.487531
\(208\) 2.96700e121 0.594282
\(209\) −1.01706e122 −1.58368
\(210\) 4.85095e121 0.587914
\(211\) 3.13721e121 0.296288 0.148144 0.988966i \(-0.452670\pi\)
0.148144 + 0.988966i \(0.452670\pi\)
\(212\) 1.02226e122 0.753230
\(213\) 1.16746e122 0.671913
\(214\) 4.42506e121 0.199157
\(215\) −1.71274e122 −0.603494
\(216\) −1.47439e122 −0.407184
\(217\) −8.44202e122 −1.82941
\(218\) 9.88632e121 0.168294
\(219\) 1.19671e123 1.60204
\(220\) −1.80632e123 −1.90373
\(221\) −4.06048e122 −0.337274
\(222\) −1.85181e122 −0.121357
\(223\) 4.92657e122 0.255000 0.127500 0.991839i \(-0.459305\pi\)
0.127500 + 0.991839i \(0.459305\pi\)
\(224\) 2.12715e123 0.870518
\(225\) 1.52526e123 0.494038
\(226\) −7.24733e122 −0.185988
\(227\) 4.08331e123 0.831104 0.415552 0.909569i \(-0.363588\pi\)
0.415552 + 0.909569i \(0.363588\pi\)
\(228\) 8.09834e123 1.30863
\(229\) −1.31242e124 −1.68543 −0.842716 0.538359i \(-0.819045\pi\)
−0.842716 + 0.538359i \(0.819045\pi\)
\(230\) −6.42078e123 −0.655958
\(231\) 2.15860e124 1.75607
\(232\) 3.59443e123 0.233083
\(233\) −1.99296e124 −1.03113 −0.515565 0.856850i \(-0.672418\pi\)
−0.515565 + 0.856850i \(0.672418\pi\)
\(234\) 1.58955e123 0.0656812
\(235\) 2.07640e124 0.685879
\(236\) −4.52476e124 −1.19596
\(237\) −7.62005e124 −1.61313
\(238\) −8.43116e123 −0.143086
\(239\) −8.89501e124 −1.21131 −0.605657 0.795726i \(-0.707090\pi\)
−0.605657 + 0.795726i \(0.707090\pi\)
\(240\) 1.31555e125 1.43885
\(241\) 1.87728e125 1.65057 0.825284 0.564718i \(-0.191015\pi\)
0.825284 + 0.564718i \(0.191015\pi\)
\(242\) 2.52979e124 0.178969
\(243\) 1.08631e125 0.618908
\(244\) −2.74892e125 −1.26240
\(245\) −1.74527e125 −0.646612
\(246\) 9.17944e124 0.274614
\(247\) 3.84500e125 0.929622
\(248\) 4.11534e125 0.804809
\(249\) 1.97290e124 0.0312349
\(250\) −1.81813e125 −0.233225
\(251\) 1.01406e126 1.05485 0.527426 0.849601i \(-0.323157\pi\)
0.527426 + 0.849601i \(0.323157\pi\)
\(252\) −4.17362e125 −0.352358
\(253\) −2.85715e126 −1.95932
\(254\) 7.01798e125 0.391239
\(255\) −1.80039e126 −0.816597
\(256\) 9.34104e125 0.344983
\(257\) −4.56506e126 −1.37391 −0.686954 0.726701i \(-0.741053\pi\)
−0.686954 + 0.726701i \(0.741053\pi\)
\(258\) −4.79906e125 −0.117794
\(259\) 2.30854e126 0.462487
\(260\) 6.82881e126 1.11749
\(261\) −1.07129e126 −0.143311
\(262\) −1.16418e126 −0.127410
\(263\) 1.42574e127 1.27751 0.638756 0.769410i \(-0.279449\pi\)
0.638756 + 0.769410i \(0.279449\pi\)
\(264\) −1.05228e127 −0.772548
\(265\) 2.15204e127 1.29551
\(266\) 7.98373e126 0.394385
\(267\) −3.70180e127 −1.50166
\(268\) 9.06318e126 0.302137
\(269\) 1.86088e127 0.510179 0.255089 0.966917i \(-0.417895\pi\)
0.255089 + 0.966917i \(0.417895\pi\)
\(270\) −1.49290e127 −0.336848
\(271\) 4.04456e127 0.751595 0.375797 0.926702i \(-0.377369\pi\)
0.375797 + 0.926702i \(0.377369\pi\)
\(272\) −2.28648e127 −0.350187
\(273\) −8.16059e127 −1.03082
\(274\) −2.22871e127 −0.232353
\(275\) −2.30584e128 −1.98547
\(276\) 2.27500e128 1.61903
\(277\) −1.03896e128 −0.611519 −0.305760 0.952109i \(-0.598910\pi\)
−0.305760 + 0.952109i \(0.598910\pi\)
\(278\) 8.97167e127 0.437040
\(279\) −1.22654e128 −0.494837
\(280\) 2.94799e128 0.985665
\(281\) 1.51367e128 0.419710 0.209855 0.977732i \(-0.432701\pi\)
0.209855 + 0.977732i \(0.432701\pi\)
\(282\) 5.81802e127 0.133874
\(283\) −5.26985e128 −1.00696 −0.503478 0.864008i \(-0.667947\pi\)
−0.503478 + 0.864008i \(0.667947\pi\)
\(284\) 3.41248e128 0.541823
\(285\) 1.70485e129 2.25077
\(286\) −2.40304e128 −0.263964
\(287\) −1.14434e129 −1.04654
\(288\) 3.09055e128 0.235467
\(289\) −1.26156e129 −0.801257
\(290\) 3.63956e128 0.192821
\(291\) −1.13746e129 −0.502985
\(292\) 3.49798e129 1.29187
\(293\) −8.63812e128 −0.266606 −0.133303 0.991075i \(-0.542558\pi\)
−0.133303 + 0.991075i \(0.542558\pi\)
\(294\) −4.89021e128 −0.126210
\(295\) −9.52545e129 −2.05698
\(296\) −1.12537e129 −0.203461
\(297\) −6.64319e129 −1.00615
\(298\) −1.02501e129 −0.130130
\(299\) 1.08015e130 1.15012
\(300\) 1.83603e130 1.64064
\(301\) 5.98269e129 0.448906
\(302\) −2.68393e128 −0.0169202
\(303\) 1.67261e130 0.886456
\(304\) 2.16514e130 0.965213
\(305\) −5.78698e130 −2.17125
\(306\) −1.22497e129 −0.0387034
\(307\) −1.83896e130 −0.489562 −0.244781 0.969578i \(-0.578716\pi\)
−0.244781 + 0.969578i \(0.578716\pi\)
\(308\) 6.30957e130 1.41608
\(309\) −6.10051e130 −1.15490
\(310\) 4.16701e130 0.665788
\(311\) 1.34727e130 0.181776 0.0908878 0.995861i \(-0.471030\pi\)
0.0908878 + 0.995861i \(0.471030\pi\)
\(312\) 3.97815e130 0.453487
\(313\) −1.30348e131 −1.25611 −0.628056 0.778168i \(-0.716149\pi\)
−0.628056 + 0.778168i \(0.716149\pi\)
\(314\) −5.05000e130 −0.411609
\(315\) −8.78624e130 −0.606037
\(316\) −2.22734e131 −1.30081
\(317\) 1.73457e131 0.858183 0.429091 0.903261i \(-0.358834\pi\)
0.429091 + 0.903261i \(0.358834\pi\)
\(318\) 6.02997e130 0.252866
\(319\) 1.61955e131 0.575948
\(320\) 3.09947e131 0.935218
\(321\) −3.30069e131 −0.845454
\(322\) 2.24281e131 0.487931
\(323\) −2.96310e131 −0.547790
\(324\) 7.18047e131 1.12860
\(325\) 8.71725e131 1.16547
\(326\) −7.41456e130 −0.0843648
\(327\) −7.37428e131 −0.714434
\(328\) 5.57848e131 0.460404
\(329\) −7.25295e131 −0.510188
\(330\) −1.06549e132 −0.639100
\(331\) −6.66098e131 −0.340854 −0.170427 0.985370i \(-0.554515\pi\)
−0.170427 + 0.985370i \(0.554515\pi\)
\(332\) 5.76679e130 0.0251875
\(333\) 3.35409e131 0.125098
\(334\) −9.26975e131 −0.295378
\(335\) 1.90797e132 0.519659
\(336\) −4.59527e132 −1.07028
\(337\) −4.68436e132 −0.933427 −0.466713 0.884409i \(-0.654562\pi\)
−0.466713 + 0.884409i \(0.654562\pi\)
\(338\) −6.78743e131 −0.115765
\(339\) 5.40584e132 0.789548
\(340\) −5.26254e132 −0.658495
\(341\) 1.85426e133 1.98868
\(342\) 1.15996e132 0.106677
\(343\) −8.93110e132 −0.704634
\(344\) −2.91646e132 −0.197487
\(345\) 4.78930e133 2.78464
\(346\) 6.87413e132 0.343339
\(347\) −2.93933e133 −1.26169 −0.630843 0.775911i \(-0.717291\pi\)
−0.630843 + 0.775911i \(0.717291\pi\)
\(348\) −1.28957e133 −0.475919
\(349\) −2.97134e133 −0.943230 −0.471615 0.881804i \(-0.656329\pi\)
−0.471615 + 0.881804i \(0.656329\pi\)
\(350\) 1.81004e133 0.494443
\(351\) 2.51146e133 0.590613
\(352\) −4.67221e133 −0.946309
\(353\) −3.13067e133 −0.546343 −0.273171 0.961965i \(-0.588073\pi\)
−0.273171 + 0.961965i \(0.588073\pi\)
\(354\) −2.66901e133 −0.401494
\(355\) 7.18390e133 0.931906
\(356\) −1.08204e134 −1.21092
\(357\) 6.28886e133 0.607422
\(358\) 3.92237e133 0.327107
\(359\) −9.32496e133 −0.671721 −0.335860 0.941912i \(-0.609027\pi\)
−0.335860 + 0.941912i \(0.609027\pi\)
\(360\) 4.28315e133 0.266613
\(361\) 9.47505e133 0.509863
\(362\) −5.13211e133 −0.238834
\(363\) −1.88698e134 −0.759750
\(364\) −2.38534e134 −0.831241
\(365\) 7.36390e134 2.22194
\(366\) −1.62150e134 −0.423799
\(367\) 7.95942e134 1.80266 0.901329 0.433136i \(-0.142593\pi\)
0.901329 + 0.433136i \(0.142593\pi\)
\(368\) 6.08236e134 1.19416
\(369\) −1.66262e134 −0.283080
\(370\) −1.13950e134 −0.168316
\(371\) −7.51718e134 −0.963661
\(372\) −1.47645e135 −1.64329
\(373\) −1.34599e135 −1.30115 −0.650574 0.759443i \(-0.725472\pi\)
−0.650574 + 0.759443i \(0.725472\pi\)
\(374\) 1.85187e134 0.155544
\(375\) 1.35616e135 0.990075
\(376\) 3.53569e134 0.224446
\(377\) −6.12271e134 −0.338083
\(378\) 5.21478e134 0.250563
\(379\) −2.25026e135 −0.941182 −0.470591 0.882351i \(-0.655959\pi\)
−0.470591 + 0.882351i \(0.655959\pi\)
\(380\) 4.98327e135 1.81500
\(381\) −5.23476e135 −1.66087
\(382\) −5.69582e134 −0.157481
\(383\) −5.53878e135 −1.33499 −0.667495 0.744614i \(-0.732634\pi\)
−0.667495 + 0.744614i \(0.732634\pi\)
\(384\) 4.88291e135 1.02634
\(385\) 1.32828e136 2.43558
\(386\) 9.02041e134 0.144342
\(387\) 8.69227e134 0.121425
\(388\) −3.32479e135 −0.405601
\(389\) 4.13994e135 0.441204 0.220602 0.975364i \(-0.429198\pi\)
0.220602 + 0.975364i \(0.429198\pi\)
\(390\) 4.02810e135 0.375153
\(391\) −8.32401e135 −0.677724
\(392\) −2.97185e135 −0.211597
\(393\) 8.68371e135 0.540875
\(394\) −2.34332e135 −0.127726
\(395\) −4.68896e136 −2.23732
\(396\) 9.16720e135 0.383036
\(397\) 2.52452e136 0.924012 0.462006 0.886877i \(-0.347130\pi\)
0.462006 + 0.886877i \(0.347130\pi\)
\(398\) −1.09946e136 −0.352628
\(399\) −5.95512e136 −1.67422
\(400\) 4.90873e136 1.21010
\(401\) −8.02537e135 −0.173534 −0.0867672 0.996229i \(-0.527654\pi\)
−0.0867672 + 0.996229i \(0.527654\pi\)
\(402\) 5.34608e135 0.101430
\(403\) −7.01003e136 −1.16736
\(404\) 4.88904e136 0.714828
\(405\) 1.51162e137 1.94113
\(406\) −1.27132e136 −0.143429
\(407\) −5.07062e136 −0.502753
\(408\) −3.06571e136 −0.267222
\(409\) −3.44614e136 −0.264155 −0.132077 0.991239i \(-0.542165\pi\)
−0.132077 + 0.991239i \(0.542165\pi\)
\(410\) 5.64852e136 0.380875
\(411\) 1.66241e137 0.986376
\(412\) −1.78318e137 −0.931301
\(413\) 3.32728e137 1.53007
\(414\) 3.25858e136 0.131981
\(415\) 1.21402e136 0.0433211
\(416\) 1.76633e137 0.555485
\(417\) −6.69203e137 −1.85530
\(418\) −1.75360e137 −0.428721
\(419\) −1.84518e137 −0.397926 −0.198963 0.980007i \(-0.563757\pi\)
−0.198963 + 0.980007i \(0.563757\pi\)
\(420\) −1.05764e138 −2.01257
\(421\) 6.84171e137 1.14909 0.574546 0.818473i \(-0.305179\pi\)
0.574546 + 0.818473i \(0.305179\pi\)
\(422\) 5.40911e136 0.0802088
\(423\) −1.05378e137 −0.138001
\(424\) 3.66450e137 0.423942
\(425\) −6.71784e137 −0.686769
\(426\) 2.01291e137 0.181895
\(427\) 2.02142e138 1.61508
\(428\) −9.64789e137 −0.681765
\(429\) 1.79244e138 1.12057
\(430\) −2.95308e137 −0.163373
\(431\) 7.02164e137 0.343860 0.171930 0.985109i \(-0.445000\pi\)
0.171930 + 0.985109i \(0.445000\pi\)
\(432\) 1.41422e138 0.613225
\(433\) −7.67228e137 −0.294652 −0.147326 0.989088i \(-0.547067\pi\)
−0.147326 + 0.989088i \(0.547067\pi\)
\(434\) −1.45556e138 −0.495243
\(435\) −2.71477e138 −0.818555
\(436\) −2.15550e138 −0.576112
\(437\) 7.88227e138 1.86800
\(438\) 2.06335e138 0.433692
\(439\) −1.85235e138 −0.345411 −0.172705 0.984974i \(-0.555251\pi\)
−0.172705 + 0.984974i \(0.555251\pi\)
\(440\) −6.47515e138 −1.07148
\(441\) 8.85736e137 0.130100
\(442\) −7.00101e137 −0.0913043
\(443\) −6.11745e138 −0.708557 −0.354278 0.935140i \(-0.615273\pi\)
−0.354278 + 0.935140i \(0.615273\pi\)
\(444\) 4.03748e138 0.415436
\(445\) −2.27788e139 −2.08272
\(446\) 8.49431e137 0.0690316
\(447\) 7.64565e138 0.552420
\(448\) −1.08266e139 −0.695657
\(449\) 2.64878e139 1.51396 0.756979 0.653440i \(-0.226675\pi\)
0.756979 + 0.653440i \(0.226675\pi\)
\(450\) 2.62982e138 0.133742
\(451\) 2.51351e139 1.13766
\(452\) 1.58012e139 0.636683
\(453\) 2.00196e138 0.0718290
\(454\) 7.04037e138 0.224990
\(455\) −5.02157e139 −1.42969
\(456\) 2.90302e139 0.736539
\(457\) −3.40764e139 −0.770642 −0.385321 0.922783i \(-0.625909\pi\)
−0.385321 + 0.922783i \(0.625909\pi\)
\(458\) −2.26286e139 −0.456267
\(459\) −1.93543e139 −0.348025
\(460\) 1.39991e140 2.24551
\(461\) 1.76000e139 0.251891 0.125946 0.992037i \(-0.459804\pi\)
0.125946 + 0.992037i \(0.459804\pi\)
\(462\) 3.72182e139 0.475391
\(463\) −3.51403e139 −0.400685 −0.200342 0.979726i \(-0.564205\pi\)
−0.200342 + 0.979726i \(0.564205\pi\)
\(464\) −3.44773e139 −0.351026
\(465\) −3.10820e140 −2.82637
\(466\) −3.43623e139 −0.279140
\(467\) 5.51524e139 0.400339 0.200170 0.979761i \(-0.435851\pi\)
0.200170 + 0.979761i \(0.435851\pi\)
\(468\) −3.46566e139 −0.224843
\(469\) −6.66462e139 −0.386546
\(470\) 3.58009e139 0.185676
\(471\) 3.76683e140 1.74734
\(472\) −1.62200e140 −0.673123
\(473\) −1.31408e140 −0.487989
\(474\) −1.31383e140 −0.436695
\(475\) 6.36134e140 1.89293
\(476\) 1.83823e140 0.489818
\(477\) −1.09217e140 −0.260661
\(478\) −1.53366e140 −0.327918
\(479\) 1.76670e140 0.338493 0.169246 0.985574i \(-0.445867\pi\)
0.169246 + 0.985574i \(0.445867\pi\)
\(480\) 7.83181e140 1.34492
\(481\) 1.91695e140 0.295117
\(482\) 3.23676e140 0.446829
\(483\) −1.67292e141 −2.07134
\(484\) −5.51565e140 −0.612654
\(485\) −6.99931e140 −0.697612
\(486\) 1.87300e140 0.167546
\(487\) 7.86002e140 0.631180 0.315590 0.948896i \(-0.397798\pi\)
0.315590 + 0.948896i \(0.397798\pi\)
\(488\) −9.85408e140 −0.710518
\(489\) 5.53057e140 0.358142
\(490\) −3.00917e140 −0.175046
\(491\) 8.16969e140 0.426999 0.213500 0.976943i \(-0.431514\pi\)
0.213500 + 0.976943i \(0.431514\pi\)
\(492\) −2.00138e141 −0.940072
\(493\) 4.71839e140 0.199219
\(494\) 6.62948e140 0.251660
\(495\) 1.92987e141 0.658801
\(496\) −3.94739e141 −1.21205
\(497\) −2.50937e141 −0.693193
\(498\) 3.40164e139 0.00845567
\(499\) 3.10828e141 0.695411 0.347706 0.937604i \(-0.386961\pi\)
0.347706 + 0.937604i \(0.386961\pi\)
\(500\) 3.96404e141 0.798386
\(501\) 6.91437e141 1.25393
\(502\) 1.74842e141 0.285562
\(503\) −1.58808e141 −0.233643 −0.116821 0.993153i \(-0.537271\pi\)
−0.116821 + 0.993153i \(0.537271\pi\)
\(504\) −1.49612e141 −0.198319
\(505\) 1.02923e142 1.22946
\(506\) −4.92624e141 −0.530412
\(507\) 5.06279e141 0.491442
\(508\) −1.53012e142 −1.33931
\(509\) −4.45459e141 −0.351661 −0.175831 0.984420i \(-0.556261\pi\)
−0.175831 + 0.984420i \(0.556261\pi\)
\(510\) −3.10420e141 −0.221063
\(511\) −2.57224e142 −1.65278
\(512\) 1.70120e142 0.986465
\(513\) 1.83272e142 0.959254
\(514\) −7.87099e141 −0.371934
\(515\) −3.75391e142 −1.60179
\(516\) 1.04633e142 0.403237
\(517\) 1.59308e142 0.554607
\(518\) 3.98034e141 0.125201
\(519\) −5.12746e142 −1.45753
\(520\) 2.44793e142 0.628961
\(521\) 4.14489e142 0.962792 0.481396 0.876503i \(-0.340130\pi\)
0.481396 + 0.876503i \(0.340130\pi\)
\(522\) −1.84710e141 −0.0387962
\(523\) 4.05731e142 0.770725 0.385362 0.922765i \(-0.374076\pi\)
0.385362 + 0.922765i \(0.374076\pi\)
\(524\) 2.53825e142 0.436155
\(525\) −1.35012e143 −2.09899
\(526\) 2.45824e142 0.345838
\(527\) 5.40219e142 0.687880
\(528\) 1.00934e143 1.16347
\(529\) 1.25618e143 1.31108
\(530\) 3.71051e142 0.350712
\(531\) 4.83422e142 0.413870
\(532\) −1.74068e143 −1.35008
\(533\) −9.50231e142 −0.667807
\(534\) −6.38258e142 −0.406518
\(535\) −2.03106e143 −1.17260
\(536\) 3.24889e142 0.170053
\(537\) −2.92572e143 −1.38862
\(538\) 3.20849e142 0.138112
\(539\) −1.33903e143 −0.522855
\(540\) 3.25495e143 1.15311
\(541\) 1.47517e143 0.474225 0.237112 0.971482i \(-0.423799\pi\)
0.237112 + 0.971482i \(0.423799\pi\)
\(542\) 6.97356e142 0.203466
\(543\) 3.82808e143 1.01389
\(544\) −1.36120e143 −0.327326
\(545\) −4.53772e143 −0.990881
\(546\) −1.40703e143 −0.279056
\(547\) −5.05802e142 −0.0911268 −0.0455634 0.998961i \(-0.514508\pi\)
−0.0455634 + 0.998961i \(0.514508\pi\)
\(548\) 4.85922e143 0.795402
\(549\) 2.93693e143 0.436863
\(550\) −3.97569e143 −0.537492
\(551\) −4.46800e143 −0.549103
\(552\) 8.15523e143 0.911244
\(553\) 1.63787e144 1.66422
\(554\) −1.79135e143 −0.165546
\(555\) 8.49964e143 0.714528
\(556\) −1.95608e144 −1.49610
\(557\) 7.98264e143 0.555583 0.277792 0.960641i \(-0.410398\pi\)
0.277792 + 0.960641i \(0.410398\pi\)
\(558\) −2.11478e143 −0.133959
\(559\) 4.96786e143 0.286451
\(560\) −2.82768e144 −1.48443
\(561\) −1.38132e144 −0.660306
\(562\) 2.60984e143 0.113621
\(563\) 3.83728e143 0.152171 0.0760856 0.997101i \(-0.475758\pi\)
0.0760856 + 0.997101i \(0.475758\pi\)
\(564\) −1.26849e144 −0.458284
\(565\) 3.32645e144 1.09506
\(566\) −9.08618e143 −0.272596
\(567\) −5.28017e144 −1.44390
\(568\) 1.22328e144 0.304956
\(569\) −7.81233e144 −1.77577 −0.887884 0.460067i \(-0.847825\pi\)
−0.887884 + 0.460067i \(0.847825\pi\)
\(570\) 2.93947e144 0.609311
\(571\) 5.50316e144 1.04044 0.520220 0.854033i \(-0.325850\pi\)
0.520220 + 0.854033i \(0.325850\pi\)
\(572\) 5.23930e144 0.903612
\(573\) 4.24855e144 0.668533
\(574\) −1.97305e144 −0.283312
\(575\) 1.78704e145 2.34192
\(576\) −1.57300e144 −0.188169
\(577\) −6.56179e144 −0.716625 −0.358312 0.933602i \(-0.616648\pi\)
−0.358312 + 0.933602i \(0.616648\pi\)
\(578\) −2.17516e144 −0.216910
\(579\) −6.72839e144 −0.612755
\(580\) −7.93527e144 −0.660073
\(581\) −4.24061e143 −0.0322242
\(582\) −1.96119e144 −0.136164
\(583\) 1.65112e145 1.04756
\(584\) 1.25393e145 0.727105
\(585\) −7.29586e144 −0.386717
\(586\) −1.48937e144 −0.0721734
\(587\) −1.42844e145 −0.632939 −0.316469 0.948603i \(-0.602497\pi\)
−0.316469 + 0.948603i \(0.602497\pi\)
\(588\) 1.06620e145 0.432047
\(589\) −5.11551e145 −1.89599
\(590\) −1.64236e145 −0.556850
\(591\) 1.74790e145 0.542216
\(592\) 1.07945e145 0.306416
\(593\) −5.51029e145 −1.43154 −0.715769 0.698337i \(-0.753924\pi\)
−0.715769 + 0.698337i \(0.753924\pi\)
\(594\) −1.14541e145 −0.272378
\(595\) 3.86981e145 0.842460
\(596\) 2.23482e145 0.445465
\(597\) 8.20093e145 1.49696
\(598\) 1.86237e145 0.311353
\(599\) −1.15611e146 −1.77048 −0.885238 0.465138i \(-0.846005\pi\)
−0.885238 + 0.465138i \(0.846005\pi\)
\(600\) 6.58162e145 0.923406
\(601\) 1.32026e146 1.69727 0.848633 0.528982i \(-0.177426\pi\)
0.848633 + 0.528982i \(0.177426\pi\)
\(602\) 1.03152e145 0.121524
\(603\) −9.68305e144 −0.104557
\(604\) 5.85172e144 0.0579221
\(605\) −1.16115e146 −1.05373
\(606\) 2.88389e145 0.239975
\(607\) −1.59602e146 −1.21796 −0.608980 0.793185i \(-0.708421\pi\)
−0.608980 + 0.793185i \(0.708421\pi\)
\(608\) 1.28897e146 0.902201
\(609\) 9.48283e145 0.608878
\(610\) −9.97780e145 −0.587785
\(611\) −6.02266e145 −0.325555
\(612\) 2.67077e145 0.132491
\(613\) 6.35553e145 0.289386 0.144693 0.989477i \(-0.453781\pi\)
0.144693 + 0.989477i \(0.453781\pi\)
\(614\) −3.17070e145 −0.132530
\(615\) −4.21327e146 −1.61687
\(616\) 2.26180e146 0.797016
\(617\) 3.62889e146 1.17436 0.587182 0.809455i \(-0.300237\pi\)
0.587182 + 0.809455i \(0.300237\pi\)
\(618\) −1.05184e146 −0.312647
\(619\) −4.93925e146 −1.34866 −0.674329 0.738431i \(-0.735567\pi\)
−0.674329 + 0.738431i \(0.735567\pi\)
\(620\) −9.08526e146 −2.27915
\(621\) 5.14851e146 1.18679
\(622\) 2.32295e145 0.0492089
\(623\) 7.95676e146 1.54922
\(624\) −3.81579e146 −0.682958
\(625\) −1.01691e146 −0.167333
\(626\) −2.24744e146 −0.340045
\(627\) 1.30802e147 1.81999
\(628\) 1.10104e147 1.40904
\(629\) −1.47727e146 −0.173901
\(630\) −1.51491e146 −0.164062
\(631\) 1.66165e147 1.65576 0.827882 0.560903i \(-0.189546\pi\)
0.827882 + 0.560903i \(0.189546\pi\)
\(632\) −7.98436e146 −0.732139
\(633\) −4.03469e146 −0.340499
\(634\) 2.99071e146 0.232321
\(635\) −3.22118e147 −2.30353
\(636\) −1.31470e147 −0.865624
\(637\) 5.06222e146 0.306917
\(638\) 2.79240e146 0.155916
\(639\) −3.64587e146 −0.187502
\(640\) 3.00467e147 1.42347
\(641\) −1.30831e147 −0.571037 −0.285519 0.958373i \(-0.592166\pi\)
−0.285519 + 0.958373i \(0.592166\pi\)
\(642\) −5.69098e146 −0.228875
\(643\) 8.82411e146 0.327035 0.163518 0.986540i \(-0.447716\pi\)
0.163518 + 0.986540i \(0.447716\pi\)
\(644\) −4.88995e147 −1.67031
\(645\) 2.20272e147 0.693545
\(646\) −5.10893e146 −0.148294
\(647\) −1.73337e147 −0.463893 −0.231946 0.972729i \(-0.574509\pi\)
−0.231946 + 0.972729i \(0.574509\pi\)
\(648\) 2.57399e147 0.635213
\(649\) −7.30826e147 −1.66329
\(650\) 1.50301e147 0.315509
\(651\) 1.08571e148 2.10238
\(652\) 1.61658e147 0.288801
\(653\) 4.30837e147 0.710184 0.355092 0.934831i \(-0.384450\pi\)
0.355092 + 0.934831i \(0.384450\pi\)
\(654\) −1.27146e147 −0.193406
\(655\) 5.34348e147 0.750163
\(656\) −5.35081e147 −0.693374
\(657\) −3.73722e147 −0.447061
\(658\) −1.25054e147 −0.138114
\(659\) −1.06978e148 −1.09096 −0.545482 0.838123i \(-0.683653\pi\)
−0.545482 + 0.838123i \(0.683653\pi\)
\(660\) 2.32308e148 2.18780
\(661\) 3.16357e147 0.275170 0.137585 0.990490i \(-0.456066\pi\)
0.137585 + 0.990490i \(0.456066\pi\)
\(662\) −1.14847e147 −0.0922734
\(663\) 5.22210e147 0.387601
\(664\) 2.06723e146 0.0141763
\(665\) −3.66445e148 −2.32206
\(666\) 5.78305e146 0.0338657
\(667\) −1.25516e148 −0.679348
\(668\) 2.02107e148 1.01115
\(669\) −6.33596e147 −0.293050
\(670\) 3.28968e147 0.140678
\(671\) −4.43997e148 −1.75569
\(672\) −2.73569e148 −1.00041
\(673\) 4.25179e148 1.43807 0.719037 0.694972i \(-0.244583\pi\)
0.719037 + 0.694972i \(0.244583\pi\)
\(674\) −8.07668e147 −0.252690
\(675\) 4.15507e148 1.20263
\(676\) 1.47985e148 0.396293
\(677\) 9.84342e147 0.243916 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(678\) 9.32064e147 0.213740
\(679\) 2.44489e148 0.518915
\(680\) −1.88647e148 −0.370623
\(681\) −5.25146e148 −0.955118
\(682\) 3.19708e148 0.538361
\(683\) −5.19588e148 −0.810163 −0.405082 0.914281i \(-0.632757\pi\)
−0.405082 + 0.914281i \(0.632757\pi\)
\(684\) −2.52904e148 −0.365183
\(685\) 1.02295e149 1.36805
\(686\) −1.53988e148 −0.190753
\(687\) 1.68788e149 1.93693
\(688\) 2.79743e148 0.297418
\(689\) −6.24206e148 −0.614920
\(690\) 8.25762e148 0.753837
\(691\) 1.83656e148 0.155385 0.0776924 0.996977i \(-0.475245\pi\)
0.0776924 + 0.996977i \(0.475245\pi\)
\(692\) −1.49875e149 −1.17533
\(693\) −6.74111e148 −0.490046
\(694\) −5.06794e148 −0.341554
\(695\) −4.11790e149 −2.57320
\(696\) −4.62272e148 −0.267863
\(697\) 7.32284e148 0.393513
\(698\) −5.12313e148 −0.255344
\(699\) 2.56311e149 1.18499
\(700\) −3.94640e149 −1.69260
\(701\) 4.14109e149 1.64785 0.823927 0.566696i \(-0.191779\pi\)
0.823927 + 0.566696i \(0.191779\pi\)
\(702\) 4.33021e148 0.159886
\(703\) 1.39888e149 0.479320
\(704\) 2.37802e149 0.756224
\(705\) −2.67041e149 −0.788224
\(706\) −5.39784e148 −0.147902
\(707\) −3.59516e149 −0.914531
\(708\) 5.81919e149 1.37441
\(709\) 7.22005e149 1.58348 0.791740 0.610858i \(-0.209175\pi\)
0.791740 + 0.610858i \(0.209175\pi\)
\(710\) 1.23864e149 0.252278
\(711\) 2.37967e149 0.450156
\(712\) −3.87878e149 −0.681547
\(713\) −1.43706e150 −2.34571
\(714\) 1.08431e149 0.164437
\(715\) 1.10297e150 1.55416
\(716\) −8.55188e149 −1.11977
\(717\) 1.14397e150 1.39206
\(718\) −1.60779e149 −0.181843
\(719\) −3.81074e149 −0.400629 −0.200314 0.979732i \(-0.564196\pi\)
−0.200314 + 0.979732i \(0.564196\pi\)
\(720\) −4.10834e149 −0.401523
\(721\) 1.31126e150 1.19148
\(722\) 1.63367e149 0.138026
\(723\) −2.41432e150 −1.89686
\(724\) 1.11894e150 0.817587
\(725\) −1.01297e150 −0.688415
\(726\) −3.25350e149 −0.205674
\(727\) −2.71636e150 −1.59746 −0.798731 0.601689i \(-0.794495\pi\)
−0.798731 + 0.601689i \(0.794495\pi\)
\(728\) −8.55074e149 −0.467850
\(729\) 9.95070e149 0.506592
\(730\) 1.26967e150 0.601507
\(731\) −3.82842e149 −0.168794
\(732\) 3.53532e150 1.45077
\(733\) −3.94863e150 −1.50830 −0.754151 0.656701i \(-0.771951\pi\)
−0.754151 + 0.656701i \(0.771951\pi\)
\(734\) 1.37235e150 0.488002
\(735\) 2.24456e150 0.743097
\(736\) 3.62099e150 1.11620
\(737\) 1.46386e150 0.420200
\(738\) −2.86666e149 −0.0766332
\(739\) 1.16910e148 0.00291083 0.00145542 0.999999i \(-0.499537\pi\)
0.00145542 + 0.999999i \(0.499537\pi\)
\(740\) 2.48444e150 0.576187
\(741\) −4.94497e150 −1.06834
\(742\) −1.29610e150 −0.260875
\(743\) 4.78469e150 0.897307 0.448654 0.893706i \(-0.351904\pi\)
0.448654 + 0.893706i \(0.351904\pi\)
\(744\) −5.29265e150 −0.924899
\(745\) 4.70471e150 0.766176
\(746\) −2.32072e150 −0.352237
\(747\) −6.16120e148 −0.00871633
\(748\) −4.03760e150 −0.532464
\(749\) 7.09458e150 0.872231
\(750\) 2.33826e150 0.268026
\(751\) −6.26686e150 −0.669813 −0.334906 0.942251i \(-0.608705\pi\)
−0.334906 + 0.942251i \(0.608705\pi\)
\(752\) −3.39139e150 −0.338019
\(753\) −1.30416e151 −1.21225
\(754\) −1.05567e150 −0.0915232
\(755\) 1.23190e150 0.0996229
\(756\) −1.13697e151 −0.857737
\(757\) −1.16053e151 −0.816815 −0.408408 0.912800i \(-0.633916\pi\)
−0.408408 + 0.912800i \(0.633916\pi\)
\(758\) −3.87985e150 −0.254790
\(759\) 3.67452e151 2.25168
\(760\) 1.78636e151 1.02154
\(761\) −2.34237e151 −1.25015 −0.625074 0.780566i \(-0.714931\pi\)
−0.625074 + 0.780566i \(0.714931\pi\)
\(762\) −9.02567e150 −0.449618
\(763\) 1.58505e151 0.737062
\(764\) 1.24185e151 0.539098
\(765\) 5.62247e150 0.227878
\(766\) −9.54985e150 −0.361399
\(767\) 2.76289e151 0.976353
\(768\) −1.20133e151 −0.396459
\(769\) −2.06829e151 −0.637499 −0.318749 0.947839i \(-0.603263\pi\)
−0.318749 + 0.947839i \(0.603263\pi\)
\(770\) 2.29020e151 0.659341
\(771\) 5.87103e151 1.57892
\(772\) −1.96671e151 −0.494118
\(773\) 6.81430e151 1.59955 0.799775 0.600300i \(-0.204952\pi\)
0.799775 + 0.600300i \(0.204952\pi\)
\(774\) 1.49870e150 0.0328712
\(775\) −1.15977e152 −2.37702
\(776\) −1.19184e151 −0.228286
\(777\) −2.96896e151 −0.531498
\(778\) 7.13800e150 0.119439
\(779\) −6.93423e151 −1.08463
\(780\) −8.78239e151 −1.28424
\(781\) 5.51174e151 0.753546
\(782\) −1.43521e151 −0.183468
\(783\) −2.91839e151 −0.348859
\(784\) 2.85056e151 0.318667
\(785\) 2.31790e152 2.42347
\(786\) 1.49723e151 0.146421
\(787\) −3.75742e151 −0.343729 −0.171865 0.985121i \(-0.554979\pi\)
−0.171865 + 0.985121i \(0.554979\pi\)
\(788\) 5.10909e151 0.437237
\(789\) −1.83362e152 −1.46814
\(790\) −8.08461e151 −0.605671
\(791\) −1.16195e152 −0.814555
\(792\) 3.28618e151 0.215585
\(793\) 1.67853e152 1.03059
\(794\) 4.35274e151 0.250142
\(795\) −2.76769e152 −1.48882
\(796\) 2.39713e152 1.20713
\(797\) 2.91172e152 1.37274 0.686369 0.727253i \(-0.259203\pi\)
0.686369 + 0.727253i \(0.259203\pi\)
\(798\) −1.02677e152 −0.453233
\(799\) 4.64129e151 0.191837
\(800\) 2.92230e152 1.13110
\(801\) 1.15604e152 0.419050
\(802\) −1.38372e151 −0.0469779
\(803\) 5.64984e152 1.79668
\(804\) −1.16560e152 −0.347221
\(805\) −1.02943e153 −2.87284
\(806\) −1.20866e152 −0.316019
\(807\) −2.39323e152 −0.586306
\(808\) 1.75258e152 0.402329
\(809\) −4.11093e152 −0.884387 −0.442194 0.896920i \(-0.645800\pi\)
−0.442194 + 0.896920i \(0.645800\pi\)
\(810\) 2.60631e152 0.525488
\(811\) −4.85458e152 −0.917396 −0.458698 0.888592i \(-0.651684\pi\)
−0.458698 + 0.888592i \(0.651684\pi\)
\(812\) 2.77183e152 0.490992
\(813\) −5.20163e152 −0.863745
\(814\) −8.74267e151 −0.136102
\(815\) 3.40321e152 0.496723
\(816\) 2.94059e152 0.402441
\(817\) 3.62526e152 0.465244
\(818\) −5.94176e151 −0.0715100
\(819\) 2.54848e152 0.287658
\(820\) −1.23154e153 −1.30383
\(821\) 3.03410e152 0.301310 0.150655 0.988586i \(-0.451862\pi\)
0.150655 + 0.988586i \(0.451862\pi\)
\(822\) 2.86630e152 0.267024
\(823\) 4.02257e152 0.351571 0.175785 0.984429i \(-0.443754\pi\)
0.175785 + 0.984429i \(0.443754\pi\)
\(824\) −6.39217e152 −0.524167
\(825\) 2.96550e153 2.28173
\(826\) 5.73684e152 0.414210
\(827\) −8.19205e151 −0.0555077 −0.0277539 0.999615i \(-0.508835\pi\)
−0.0277539 + 0.999615i \(0.508835\pi\)
\(828\) −7.10463e152 −0.451803
\(829\) −1.29914e153 −0.775433 −0.387716 0.921779i \(-0.626736\pi\)
−0.387716 + 0.921779i \(0.626736\pi\)
\(830\) 2.09318e151 0.0117275
\(831\) 1.33618e153 0.702768
\(832\) −8.99010e152 −0.443905
\(833\) −3.90114e152 −0.180854
\(834\) −1.15383e153 −0.502254
\(835\) 4.25472e153 1.73913
\(836\) 3.82334e153 1.46762
\(837\) −3.34132e153 −1.20457
\(838\) −3.18142e152 −0.107724
\(839\) −5.26860e153 −1.67568 −0.837842 0.545913i \(-0.816183\pi\)
−0.837842 + 0.545913i \(0.816183\pi\)
\(840\) −3.79135e153 −1.13274
\(841\) −2.85131e153 −0.800303
\(842\) 1.17963e153 0.311073
\(843\) −1.94670e153 −0.482338
\(844\) −1.17934e153 −0.274574
\(845\) 3.11536e153 0.681602
\(846\) −1.81691e152 −0.0373586
\(847\) 4.05594e153 0.783812
\(848\) −3.51494e153 −0.638463
\(849\) 6.77745e153 1.15721
\(850\) −1.15828e153 −0.185917
\(851\) 3.92976e153 0.593013
\(852\) −4.38872e153 −0.622672
\(853\) 9.25670e153 1.23490 0.617450 0.786610i \(-0.288166\pi\)
0.617450 + 0.786610i \(0.288166\pi\)
\(854\) 3.48529e153 0.437221
\(855\) −5.32409e153 −0.628094
\(856\) −3.45849e153 −0.383720
\(857\) −1.01455e154 −1.05871 −0.529357 0.848399i \(-0.677567\pi\)
−0.529357 + 0.848399i \(0.677567\pi\)
\(858\) 3.09050e153 0.303351
\(859\) 1.04057e154 0.960794 0.480397 0.877051i \(-0.340493\pi\)
0.480397 + 0.877051i \(0.340493\pi\)
\(860\) 6.43854e153 0.559267
\(861\) 1.47171e154 1.20270
\(862\) 1.21066e153 0.0930872
\(863\) −1.59859e154 −1.15656 −0.578282 0.815837i \(-0.696277\pi\)
−0.578282 + 0.815837i \(0.696277\pi\)
\(864\) 8.41921e153 0.573191
\(865\) −3.15516e154 −2.02151
\(866\) −1.32284e153 −0.0797660
\(867\) 1.62247e154 0.920818
\(868\) 3.17352e154 1.69534
\(869\) −3.59753e154 −1.80912
\(870\) −4.68076e153 −0.221593
\(871\) −5.53412e153 −0.246658
\(872\) −7.72684e153 −0.324255
\(873\) 3.55219e153 0.140362
\(874\) 1.35905e154 0.505690
\(875\) −2.91496e154 −1.02143
\(876\) −4.49868e154 −1.48463
\(877\) 1.92505e154 0.598362 0.299181 0.954196i \(-0.403287\pi\)
0.299181 + 0.954196i \(0.403287\pi\)
\(878\) −3.19379e153 −0.0935070
\(879\) 1.11093e154 0.306387
\(880\) 6.21089e154 1.61367
\(881\) −4.86159e154 −1.18999 −0.594995 0.803729i \(-0.702846\pi\)
−0.594995 + 0.803729i \(0.702846\pi\)
\(882\) 1.52717e153 0.0352198
\(883\) −5.99705e154 −1.30317 −0.651584 0.758576i \(-0.725895\pi\)
−0.651584 + 0.758576i \(0.725895\pi\)
\(884\) 1.52642e154 0.312557
\(885\) 1.22505e155 2.36391
\(886\) −1.05476e154 −0.191815
\(887\) 1.04076e154 0.178386 0.0891932 0.996014i \(-0.471571\pi\)
0.0891932 + 0.996014i \(0.471571\pi\)
\(888\) 1.44732e154 0.233821
\(889\) 1.12517e155 1.71347
\(890\) −3.92749e154 −0.563818
\(891\) 1.15977e155 1.56961
\(892\) −1.85200e154 −0.236312
\(893\) −4.39499e154 −0.528757
\(894\) 1.31825e154 0.149547
\(895\) −1.80033e155 −1.92594
\(896\) −1.04955e155 −1.05884
\(897\) −1.38915e155 −1.32174
\(898\) 4.56698e154 0.409847
\(899\) 8.14584e154 0.689529
\(900\) −5.73375e154 −0.457833
\(901\) 4.81037e154 0.362349
\(902\) 4.33374e154 0.307978
\(903\) −7.69421e154 −0.515890
\(904\) 5.66429e154 0.358346
\(905\) 2.35559e155 1.40620
\(906\) 3.45174e153 0.0194450
\(907\) −1.16482e155 −0.619262 −0.309631 0.950857i \(-0.600206\pi\)
−0.309631 + 0.950857i \(0.600206\pi\)
\(908\) −1.53500e155 −0.770196
\(909\) −5.22342e154 −0.247372
\(910\) −8.65810e154 −0.387034
\(911\) −1.37817e155 −0.581551 −0.290776 0.956791i \(-0.593913\pi\)
−0.290776 + 0.956791i \(0.593913\pi\)
\(912\) −2.78454e155 −1.10924
\(913\) 9.31435e153 0.0350297
\(914\) −5.87538e154 −0.208622
\(915\) 7.44251e155 2.49524
\(916\) 4.93366e155 1.56191
\(917\) −1.86650e155 −0.558005
\(918\) −3.33702e154 −0.0942147
\(919\) 4.43843e154 0.118349 0.0591746 0.998248i \(-0.481153\pi\)
0.0591746 + 0.998248i \(0.481153\pi\)
\(920\) 5.01827e155 1.26384
\(921\) 2.36505e155 0.562612
\(922\) 3.03455e154 0.0681901
\(923\) −2.08371e155 −0.442333
\(924\) −8.11461e155 −1.62738
\(925\) 3.17149e155 0.600927
\(926\) −6.05882e154 −0.108470
\(927\) 1.90513e155 0.322284
\(928\) −2.05253e155 −0.328110
\(929\) −7.19518e155 −1.08697 −0.543484 0.839419i \(-0.682895\pi\)
−0.543484 + 0.839419i \(0.682895\pi\)
\(930\) −5.35911e155 −0.765134
\(931\) 3.69411e155 0.498485
\(932\) 7.49196e155 0.955564
\(933\) −1.73270e155 −0.208899
\(934\) 9.50927e154 0.108377
\(935\) −8.49990e155 −0.915808
\(936\) −1.24234e155 −0.126549
\(937\) −1.14815e156 −1.10579 −0.552894 0.833252i \(-0.686476\pi\)
−0.552894 + 0.833252i \(0.686476\pi\)
\(938\) −1.14910e155 −0.104643
\(939\) 1.67638e156 1.44354
\(940\) −7.80560e155 −0.635615
\(941\) 7.99074e155 0.615364 0.307682 0.951489i \(-0.400447\pi\)
0.307682 + 0.951489i \(0.400447\pi\)
\(942\) 6.49469e155 0.473027
\(943\) −1.94798e156 −1.34190
\(944\) 1.55580e156 1.01373
\(945\) −2.39353e156 −1.47526
\(946\) −2.26570e155 −0.132105
\(947\) 2.63160e156 1.45160 0.725798 0.687908i \(-0.241471\pi\)
0.725798 + 0.687908i \(0.241471\pi\)
\(948\) 2.86453e156 1.49491
\(949\) −2.13592e156 −1.05465
\(950\) 1.09681e156 0.512439
\(951\) −2.23079e156 −0.986238
\(952\) 6.58952e155 0.275686
\(953\) 2.53066e156 1.00197 0.500987 0.865455i \(-0.332970\pi\)
0.500987 + 0.865455i \(0.332970\pi\)
\(954\) −1.88310e155 −0.0705642
\(955\) 2.61432e156 0.927218
\(956\) 3.34381e156 1.12254
\(957\) −2.08287e156 −0.661889
\(958\) 3.04612e155 0.0916342
\(959\) −3.57323e156 −1.01762
\(960\) −3.98616e156 −1.07477
\(961\) 5.40913e156 1.38086
\(962\) 3.30517e155 0.0798918
\(963\) 1.03077e156 0.235930
\(964\) −7.05706e156 −1.52961
\(965\) −4.14028e156 −0.849856
\(966\) −2.88443e156 −0.560738
\(967\) −6.77596e156 −1.24762 −0.623808 0.781578i \(-0.714415\pi\)
−0.623808 + 0.781578i \(0.714415\pi\)
\(968\) −1.97720e156 −0.344822
\(969\) 3.81078e156 0.629529
\(970\) −1.20681e156 −0.188852
\(971\) 6.47134e156 0.959366 0.479683 0.877442i \(-0.340752\pi\)
0.479683 + 0.877442i \(0.340752\pi\)
\(972\) −4.08367e156 −0.573551
\(973\) 1.43840e157 1.91406
\(974\) 1.35521e156 0.170868
\(975\) −1.12111e157 −1.33938
\(976\) 9.45191e156 1.07005
\(977\) 5.82573e156 0.625009 0.312504 0.949916i \(-0.398832\pi\)
0.312504 + 0.949916i \(0.398832\pi\)
\(978\) 9.53571e155 0.0969534
\(979\) −1.74767e157 −1.68410
\(980\) 6.56083e156 0.599225
\(981\) 2.30292e156 0.199368
\(982\) 1.40860e156 0.115594
\(983\) 1.53172e157 1.19157 0.595784 0.803144i \(-0.296841\pi\)
0.595784 + 0.803144i \(0.296841\pi\)
\(984\) −7.17436e156 −0.529103
\(985\) 1.07556e157 0.752024
\(986\) 8.13536e155 0.0539311
\(987\) 9.32787e156 0.586316
\(988\) −1.44541e157 −0.861495
\(989\) 1.01841e157 0.575598
\(990\) 3.32744e156 0.178346
\(991\) −3.06213e157 −1.55653 −0.778263 0.627939i \(-0.783899\pi\)
−0.778263 + 0.627939i \(0.783899\pi\)
\(992\) −2.34998e157 −1.13293
\(993\) 8.56654e156 0.391715
\(994\) −4.32661e156 −0.187656
\(995\) 5.04640e157 2.07620
\(996\) −7.41654e155 −0.0289458
\(997\) −4.11854e157 −1.52492 −0.762461 0.647034i \(-0.776009\pi\)
−0.762461 + 0.647034i \(0.776009\pi\)
\(998\) 5.35924e156 0.188256
\(999\) 9.13713e156 0.304524
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 1.106.a.a.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.106.a.a.1.5 8 1.1 even 1 trivial