Properties

Label 1.76.a.a.1.2
Level $1$
Weight $76$
Character 1.1
Self dual yes
Analytic conductor $35.623$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1 \)
Weight: \( k \) \(=\) \( 76 \)
Character orbit: \([\chi]\) \(=\) 1.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(35.6228392822\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
Defining polynomial: \(x^{6} - 3 x^{5} - 38457853073924058692 x^{4} - 10276556354621685339901678086 x^{3} + 371187556674475060057870954681799784505 x^{2} + 52686123927652036687598761277591247931691204025 x - 675344021115865838575279495800656435684060652010336995750\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.89081e9\) of defining polynomial
Character \(\chi\) \(=\) 1.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.89652e11 q^{2} +1.03577e18 q^{3} +4.61192e22 q^{4} -2.47463e26 q^{5} -3.00013e29 q^{6} -6.83079e31 q^{7} -2.41577e33 q^{8} +4.64556e35 q^{9} +O(q^{10})\) \(q-2.89652e11 q^{2} +1.03577e18 q^{3} +4.61192e22 q^{4} -2.47463e26 q^{5} -3.00013e29 q^{6} -6.83079e31 q^{7} -2.41577e33 q^{8} +4.64556e35 q^{9} +7.16781e37 q^{10} -1.33402e39 q^{11} +4.77689e40 q^{12} +2.92609e41 q^{13} +1.97855e43 q^{14} -2.56315e44 q^{15} -1.04260e45 q^{16} +4.46232e44 q^{17} -1.34559e47 q^{18} -8.32041e47 q^{19} -1.14128e49 q^{20} -7.07514e49 q^{21} +3.86400e50 q^{22} +1.13411e51 q^{23} -2.50218e51 q^{24} +3.47681e52 q^{25} -8.47548e52 q^{26} -1.48852e53 q^{27} -3.15030e54 q^{28} +3.24261e54 q^{29} +7.42421e55 q^{30} -1.48783e56 q^{31} +3.93257e56 q^{32} -1.38174e57 q^{33} -1.29252e56 q^{34} +1.69037e58 q^{35} +2.14249e58 q^{36} +2.52569e58 q^{37} +2.41002e59 q^{38} +3.03076e59 q^{39} +5.97813e59 q^{40} -1.57021e60 q^{41} +2.04933e61 q^{42} +2.24744e61 q^{43} -6.15237e61 q^{44} -1.14960e62 q^{45} -3.28497e62 q^{46} +3.99901e62 q^{47} -1.07990e63 q^{48} +2.25410e63 q^{49} -1.00706e64 q^{50} +4.62195e62 q^{51} +1.34949e64 q^{52} +2.56197e64 q^{53} +4.31152e64 q^{54} +3.30120e65 q^{55} +1.65016e65 q^{56} -8.61804e65 q^{57} -9.39227e65 q^{58} +1.98202e66 q^{59} -1.18210e67 q^{60} -1.77334e66 q^{61} +4.30953e67 q^{62} -3.17328e67 q^{63} -7.45191e67 q^{64} -7.24099e67 q^{65} +4.00222e68 q^{66} +3.79112e68 q^{67} +2.05799e67 q^{68} +1.17468e69 q^{69} -4.89618e69 q^{70} +1.15990e69 q^{71} -1.12226e69 q^{72} -5.75070e69 q^{73} -7.31570e69 q^{74} +3.60118e70 q^{75} -3.83730e70 q^{76} +9.11239e70 q^{77} -8.77866e70 q^{78} +6.59713e70 q^{79} +2.58005e71 q^{80} -4.36750e71 q^{81} +4.54813e71 q^{82} +1.04387e72 q^{83} -3.26300e72 q^{84} -1.10426e71 q^{85} -6.50974e72 q^{86} +3.35860e72 q^{87} +3.22267e72 q^{88} +1.34676e73 q^{89} +3.32984e73 q^{90} -1.99875e73 q^{91} +5.23043e73 q^{92} -1.54105e74 q^{93} -1.15832e74 q^{94} +2.05899e74 q^{95} +4.07324e74 q^{96} -5.17927e74 q^{97} -6.52905e74 q^{98} -6.19725e74 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + O(q^{10}) \) \( 6q - 57080822040q^{2} - 785092363818710040q^{3} + \)\(17\!\cdots\!28\)\(q^{4} - \)\(38\!\cdots\!40\)\(q^{5} + \)\(31\!\cdots\!92\)\(q^{6} + \)\(19\!\cdots\!00\)\(q^{7} + \)\(44\!\cdots\!20\)\(q^{8} + \)\(21\!\cdots\!82\)\(q^{9} + \)\(13\!\cdots\!60\)\(q^{10} - \)\(94\!\cdots\!88\)\(q^{11} - \)\(11\!\cdots\!80\)\(q^{12} + \)\(53\!\cdots\!20\)\(q^{13} + \)\(82\!\cdots\!76\)\(q^{14} - \)\(30\!\cdots\!80\)\(q^{15} + \)\(26\!\cdots\!16\)\(q^{16} + \)\(18\!\cdots\!80\)\(q^{17} - \)\(43\!\cdots\!40\)\(q^{18} + \)\(10\!\cdots\!80\)\(q^{19} + \)\(92\!\cdots\!80\)\(q^{20} - \)\(10\!\cdots\!28\)\(q^{21} + \)\(15\!\cdots\!20\)\(q^{22} + \)\(15\!\cdots\!80\)\(q^{23} - \)\(76\!\cdots\!60\)\(q^{24} + \)\(19\!\cdots\!50\)\(q^{25} + \)\(11\!\cdots\!52\)\(q^{26} - \)\(10\!\cdots\!20\)\(q^{27} + \)\(14\!\cdots\!20\)\(q^{28} + \)\(14\!\cdots\!20\)\(q^{29} - \)\(25\!\cdots\!80\)\(q^{30} - \)\(41\!\cdots\!88\)\(q^{31} + \)\(11\!\cdots\!60\)\(q^{32} + \)\(59\!\cdots\!20\)\(q^{33} + \)\(30\!\cdots\!56\)\(q^{34} + \)\(27\!\cdots\!60\)\(q^{35} + \)\(17\!\cdots\!16\)\(q^{36} + \)\(98\!\cdots\!40\)\(q^{37} + \)\(12\!\cdots\!80\)\(q^{38} + \)\(24\!\cdots\!44\)\(q^{39} + \)\(88\!\cdots\!00\)\(q^{40} + \)\(50\!\cdots\!12\)\(q^{41} + \)\(43\!\cdots\!80\)\(q^{42} + \)\(27\!\cdots\!00\)\(q^{43} - \)\(86\!\cdots\!44\)\(q^{44} - \)\(23\!\cdots\!80\)\(q^{45} - \)\(82\!\cdots\!88\)\(q^{46} - \)\(13\!\cdots\!80\)\(q^{47} - \)\(82\!\cdots\!20\)\(q^{48} - \)\(57\!\cdots\!42\)\(q^{49} + \)\(31\!\cdots\!00\)\(q^{50} + \)\(28\!\cdots\!32\)\(q^{51} + \)\(41\!\cdots\!00\)\(q^{52} + \)\(64\!\cdots\!60\)\(q^{53} + \)\(78\!\cdots\!80\)\(q^{54} + \)\(43\!\cdots\!20\)\(q^{55} + \)\(28\!\cdots\!20\)\(q^{56} - \)\(67\!\cdots\!40\)\(q^{57} - \)\(17\!\cdots\!80\)\(q^{58} - \)\(24\!\cdots\!60\)\(q^{59} - \)\(31\!\cdots\!40\)\(q^{60} - \)\(25\!\cdots\!88\)\(q^{61} - \)\(29\!\cdots\!80\)\(q^{62} + \)\(42\!\cdots\!40\)\(q^{63} + \)\(47\!\cdots\!48\)\(q^{64} + \)\(12\!\cdots\!20\)\(q^{65} + \)\(93\!\cdots\!84\)\(q^{66} + \)\(95\!\cdots\!80\)\(q^{67} + \)\(12\!\cdots\!60\)\(q^{68} - \)\(14\!\cdots\!36\)\(q^{69} - \)\(34\!\cdots\!40\)\(q^{70} - \)\(25\!\cdots\!88\)\(q^{71} - \)\(21\!\cdots\!60\)\(q^{72} - \)\(30\!\cdots\!20\)\(q^{73} - \)\(24\!\cdots\!84\)\(q^{74} + \)\(19\!\cdots\!00\)\(q^{75} + \)\(10\!\cdots\!40\)\(q^{76} + \)\(15\!\cdots\!00\)\(q^{77} + \)\(13\!\cdots\!00\)\(q^{78} + \)\(11\!\cdots\!20\)\(q^{79} + \)\(12\!\cdots\!60\)\(q^{80} + \)\(29\!\cdots\!86\)\(q^{81} - \)\(25\!\cdots\!80\)\(q^{82} - \)\(79\!\cdots\!60\)\(q^{83} - \)\(91\!\cdots\!64\)\(q^{84} - \)\(36\!\cdots\!40\)\(q^{85} + \)\(72\!\cdots\!32\)\(q^{86} - \)\(14\!\cdots\!60\)\(q^{87} - \)\(48\!\cdots\!60\)\(q^{88} + \)\(53\!\cdots\!60\)\(q^{89} + \)\(85\!\cdots\!20\)\(q^{90} + \)\(34\!\cdots\!32\)\(q^{91} + \)\(18\!\cdots\!80\)\(q^{92} - \)\(16\!\cdots\!80\)\(q^{93} - \)\(29\!\cdots\!04\)\(q^{94} + \)\(19\!\cdots\!00\)\(q^{95} - \)\(89\!\cdots\!08\)\(q^{96} - \)\(74\!\cdots\!80\)\(q^{97} - \)\(16\!\cdots\!20\)\(q^{98} - \)\(18\!\cdots\!36\)\(q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.89652e11 −1.49022 −0.745112 0.666940i \(-0.767604\pi\)
−0.745112 + 0.666940i \(0.767604\pi\)
\(3\) 1.03577e18 1.32806 0.664029 0.747707i \(-0.268845\pi\)
0.664029 + 0.747707i \(0.268845\pi\)
\(4\) 4.61192e22 1.22076
\(5\) −2.47463e26 −1.52102 −0.760510 0.649326i \(-0.775051\pi\)
−0.760510 + 0.649326i \(0.775051\pi\)
\(6\) −3.00013e29 −1.97910
\(7\) −6.83079e31 −1.39090 −0.695448 0.718577i \(-0.744794\pi\)
−0.695448 + 0.718577i \(0.744794\pi\)
\(8\) −2.41577e33 −0.328989
\(9\) 4.64556e35 0.763737
\(10\) 7.16781e37 2.26666
\(11\) −1.33402e39 −1.18287 −0.591433 0.806354i \(-0.701438\pi\)
−0.591433 + 0.806354i \(0.701438\pi\)
\(12\) 4.77689e40 1.62125
\(13\) 2.92609e41 0.493642 0.246821 0.969061i \(-0.420614\pi\)
0.246821 + 0.969061i \(0.420614\pi\)
\(14\) 1.97855e43 2.07274
\(15\) −2.56315e44 −2.02000
\(16\) −1.04260e45 −0.730498
\(17\) 4.46232e44 0.0321904 0.0160952 0.999870i \(-0.494877\pi\)
0.0160952 + 0.999870i \(0.494877\pi\)
\(18\) −1.34559e47 −1.13814
\(19\) −8.32041e47 −0.926583 −0.463292 0.886206i \(-0.653332\pi\)
−0.463292 + 0.886206i \(0.653332\pi\)
\(20\) −1.14128e49 −1.85681
\(21\) −7.07514e49 −1.84719
\(22\) 3.86400e50 1.76273
\(23\) 1.13411e51 0.976927 0.488463 0.872584i \(-0.337558\pi\)
0.488463 + 0.872584i \(0.337558\pi\)
\(24\) −2.50218e51 −0.436916
\(25\) 3.47681e52 1.31350
\(26\) −8.47548e52 −0.735637
\(27\) −1.48852e53 −0.313771
\(28\) −3.15030e54 −1.69796
\(29\) 3.24261e54 0.468781 0.234390 0.972143i \(-0.424691\pi\)
0.234390 + 0.972143i \(0.424691\pi\)
\(30\) 7.42421e55 3.01025
\(31\) −1.48783e56 −1.76397 −0.881983 0.471282i \(-0.843792\pi\)
−0.881983 + 0.471282i \(0.843792\pi\)
\(32\) 3.93257e56 1.41759
\(33\) −1.38174e57 −1.57091
\(34\) −1.29252e56 −0.0479709
\(35\) 1.69037e58 2.11558
\(36\) 2.14249e58 0.932343
\(37\) 2.52569e58 0.393383 0.196691 0.980465i \(-0.436980\pi\)
0.196691 + 0.980465i \(0.436980\pi\)
\(38\) 2.41002e59 1.38082
\(39\) 3.03076e59 0.655585
\(40\) 5.97813e59 0.500398
\(41\) −1.57021e60 −0.520669 −0.260335 0.965518i \(-0.583833\pi\)
−0.260335 + 0.965518i \(0.583833\pi\)
\(42\) 2.04933e61 2.75272
\(43\) 2.24744e61 1.24917 0.624584 0.780958i \(-0.285269\pi\)
0.624584 + 0.780958i \(0.285269\pi\)
\(44\) −6.15237e61 −1.44400
\(45\) −1.14960e62 −1.16166
\(46\) −3.28497e62 −1.45584
\(47\) 3.99901e62 0.791194 0.395597 0.918424i \(-0.370538\pi\)
0.395597 + 0.918424i \(0.370538\pi\)
\(48\) −1.07990e63 −0.970144
\(49\) 2.25410e63 0.934590
\(50\) −1.00706e64 −1.95741
\(51\) 4.62195e62 0.0427507
\(52\) 1.34949e64 0.602621
\(53\) 2.56197e64 0.560053 0.280027 0.959992i \(-0.409657\pi\)
0.280027 + 0.959992i \(0.409657\pi\)
\(54\) 4.31152e64 0.467589
\(55\) 3.30120e65 1.79916
\(56\) 1.65016e65 0.457589
\(57\) −8.61804e65 −1.23056
\(58\) −9.39227e65 −0.698588
\(59\) 1.98202e66 0.776528 0.388264 0.921548i \(-0.373075\pi\)
0.388264 + 0.921548i \(0.373075\pi\)
\(60\) −1.18210e67 −2.46595
\(61\) −1.77334e66 −0.199032 −0.0995159 0.995036i \(-0.531729\pi\)
−0.0995159 + 0.995036i \(0.531729\pi\)
\(62\) 4.30953e67 2.62870
\(63\) −3.17328e67 −1.06228
\(64\) −7.45191e67 −1.38203
\(65\) −7.24099e67 −0.750840
\(66\) 4.00222e68 2.34101
\(67\) 3.79112e68 1.26172 0.630860 0.775897i \(-0.282702\pi\)
0.630860 + 0.775897i \(0.282702\pi\)
\(68\) 2.05799e67 0.0392969
\(69\) 1.17468e69 1.29741
\(70\) −4.89618e69 −3.15269
\(71\) 1.15990e69 0.438765 0.219383 0.975639i \(-0.429596\pi\)
0.219383 + 0.975639i \(0.429596\pi\)
\(72\) −1.12226e69 −0.251261
\(73\) −5.75070e69 −0.767562 −0.383781 0.923424i \(-0.625378\pi\)
−0.383781 + 0.923424i \(0.625378\pi\)
\(74\) −7.31570e69 −0.586228
\(75\) 3.60118e70 1.74441
\(76\) −3.83730e70 −1.13114
\(77\) 9.11239e70 1.64524
\(78\) −8.77866e70 −0.976968
\(79\) 6.59713e70 0.455344 0.227672 0.973738i \(-0.426889\pi\)
0.227672 + 0.973738i \(0.426889\pi\)
\(80\) 2.58005e71 1.11110
\(81\) −4.36750e71 −1.18044
\(82\) 4.54813e71 0.775913
\(83\) 1.04387e72 1.13036 0.565182 0.824966i \(-0.308806\pi\)
0.565182 + 0.824966i \(0.308806\pi\)
\(84\) −3.26300e72 −2.25498
\(85\) −1.10426e71 −0.0489622
\(86\) −6.50974e72 −1.86154
\(87\) 3.35860e72 0.622567
\(88\) 3.22267e72 0.389149
\(89\) 1.34676e73 1.06455 0.532274 0.846572i \(-0.321338\pi\)
0.532274 + 0.846572i \(0.321338\pi\)
\(90\) 3.32984e73 1.73113
\(91\) −1.99875e73 −0.686605
\(92\) 5.23043e73 1.19260
\(93\) −1.54105e74 −2.34265
\(94\) −1.15832e74 −1.17906
\(95\) 2.05899e74 1.40935
\(96\) 4.07324e74 1.88265
\(97\) −5.17927e74 −1.62304 −0.811519 0.584326i \(-0.801359\pi\)
−0.811519 + 0.584326i \(0.801359\pi\)
\(98\) −6.52905e74 −1.39275
\(99\) −6.19725e74 −0.903398
\(100\) 1.60348e75 1.60348
\(101\) 4.46775e74 0.307636 0.153818 0.988099i \(-0.450843\pi\)
0.153818 + 0.988099i \(0.450843\pi\)
\(102\) −1.33875e74 −0.0637081
\(103\) 1.77263e74 0.0585089 0.0292544 0.999572i \(-0.490687\pi\)
0.0292544 + 0.999572i \(0.490687\pi\)
\(104\) −7.06876e74 −0.162403
\(105\) 1.75083e76 2.80961
\(106\) −7.42080e75 −0.834604
\(107\) −1.64232e76 −1.29887 −0.649434 0.760418i \(-0.724994\pi\)
−0.649434 + 0.760418i \(0.724994\pi\)
\(108\) −6.86493e75 −0.383041
\(109\) 9.19334e75 0.363061 0.181531 0.983385i \(-0.441895\pi\)
0.181531 + 0.983385i \(0.441895\pi\)
\(110\) −9.56197e76 −2.68115
\(111\) 2.61604e76 0.522435
\(112\) 7.12180e76 1.01605
\(113\) 4.17267e76 0.426553 0.213276 0.976992i \(-0.431587\pi\)
0.213276 + 0.976992i \(0.431587\pi\)
\(114\) 2.49623e77 1.83380
\(115\) −2.80651e77 −1.48592
\(116\) 1.49546e77 0.572271
\(117\) 1.35933e77 0.377013
\(118\) −5.74095e77 −1.15720
\(119\) −3.04812e76 −0.0447735
\(120\) 6.19198e77 0.664557
\(121\) 5.07704e77 0.399171
\(122\) 5.13650e77 0.296602
\(123\) −1.62637e78 −0.691479
\(124\) −6.86176e78 −2.15339
\(125\) −2.05353e78 −0.476843
\(126\) 9.19146e78 1.58303
\(127\) −3.66800e78 −0.469667 −0.234834 0.972036i \(-0.575455\pi\)
−0.234834 + 0.972036i \(0.575455\pi\)
\(128\) 6.72776e78 0.641943
\(129\) 2.32783e79 1.65897
\(130\) 2.09737e79 1.11892
\(131\) −1.61112e79 −0.644843 −0.322422 0.946596i \(-0.604497\pi\)
−0.322422 + 0.946596i \(0.604497\pi\)
\(132\) −6.37245e79 −1.91772
\(133\) 5.68349e79 1.28878
\(134\) −1.09810e80 −1.88024
\(135\) 3.68353e79 0.477253
\(136\) −1.07799e78 −0.0105903
\(137\) 4.52829e79 0.337997 0.168998 0.985616i \(-0.445947\pi\)
0.168998 + 0.985616i \(0.445947\pi\)
\(138\) −3.40248e80 −1.93344
\(139\) −2.07054e79 −0.0897490 −0.0448745 0.998993i \(-0.514289\pi\)
−0.0448745 + 0.998993i \(0.514289\pi\)
\(140\) 7.79584e80 2.58262
\(141\) 4.14206e80 1.05075
\(142\) −3.35967e80 −0.653858
\(143\) −3.90346e80 −0.583913
\(144\) −4.84347e80 −0.557908
\(145\) −8.02425e80 −0.713025
\(146\) 1.66570e81 1.14384
\(147\) 2.33474e81 1.24119
\(148\) 1.16483e81 0.480228
\(149\) −3.52371e81 −1.12854 −0.564268 0.825591i \(-0.690842\pi\)
−0.564268 + 0.825591i \(0.690842\pi\)
\(150\) −1.04309e82 −2.59955
\(151\) 4.34097e81 0.843239 0.421620 0.906773i \(-0.361462\pi\)
0.421620 + 0.906773i \(0.361462\pi\)
\(152\) 2.01002e81 0.304835
\(153\) 2.07300e80 0.0245850
\(154\) −2.63942e82 −2.45178
\(155\) 3.68183e82 2.68303
\(156\) 1.39776e82 0.800315
\(157\) 4.23236e82 1.90698 0.953490 0.301425i \(-0.0974622\pi\)
0.953490 + 0.301425i \(0.0974622\pi\)
\(158\) −1.91087e82 −0.678564
\(159\) 2.65362e82 0.743783
\(160\) −9.73164e82 −2.15619
\(161\) −7.74688e82 −1.35880
\(162\) 1.26505e83 1.75912
\(163\) −1.60838e83 −1.77564 −0.887818 0.460194i \(-0.847780\pi\)
−0.887818 + 0.460194i \(0.847780\pi\)
\(164\) −7.24166e82 −0.635615
\(165\) 3.41928e83 2.38939
\(166\) −3.02359e83 −1.68449
\(167\) 2.02081e83 0.898787 0.449394 0.893334i \(-0.351640\pi\)
0.449394 + 0.893334i \(0.351640\pi\)
\(168\) 1.70919e83 0.607704
\(169\) −2.65739e83 −0.756317
\(170\) 3.19851e82 0.0729647
\(171\) −3.86529e83 −0.707665
\(172\) 1.03650e84 1.52494
\(173\) 1.28506e84 1.52123 0.760615 0.649203i \(-0.224898\pi\)
0.760615 + 0.649203i \(0.224898\pi\)
\(174\) −9.72824e83 −0.927764
\(175\) −2.37494e84 −1.82694
\(176\) 1.39085e84 0.864081
\(177\) 2.05292e84 1.03127
\(178\) −3.90091e84 −1.58641
\(179\) 2.87264e84 0.946873 0.473437 0.880828i \(-0.343013\pi\)
0.473437 + 0.880828i \(0.343013\pi\)
\(180\) −5.30187e84 −1.41811
\(181\) −4.04728e84 −0.879462 −0.439731 0.898130i \(-0.644926\pi\)
−0.439731 + 0.898130i \(0.644926\pi\)
\(182\) 5.78942e84 1.02319
\(183\) −1.83677e84 −0.264326
\(184\) −2.73975e84 −0.321398
\(185\) −6.25014e84 −0.598343
\(186\) 4.46369e85 3.49107
\(187\) −5.95281e83 −0.0380769
\(188\) 1.84431e85 0.965862
\(189\) 1.01678e85 0.436423
\(190\) −5.96390e85 −2.10025
\(191\) −5.46188e85 −1.57976 −0.789880 0.613262i \(-0.789857\pi\)
−0.789880 + 0.613262i \(0.789857\pi\)
\(192\) −7.71847e85 −1.83542
\(193\) 2.91758e85 0.570983 0.285491 0.958381i \(-0.407843\pi\)
0.285491 + 0.958381i \(0.407843\pi\)
\(194\) 1.50018e86 2.41869
\(195\) −7.50001e85 −0.997158
\(196\) 1.03957e86 1.14091
\(197\) −1.89682e86 −1.72006 −0.860030 0.510244i \(-0.829555\pi\)
−0.860030 + 0.510244i \(0.829555\pi\)
\(198\) 1.79504e86 1.34626
\(199\) −8.15036e85 −0.506042 −0.253021 0.967461i \(-0.581424\pi\)
−0.253021 + 0.967461i \(0.581424\pi\)
\(200\) −8.39917e85 −0.432127
\(201\) 3.92674e86 1.67564
\(202\) −1.29409e86 −0.458446
\(203\) −2.21496e86 −0.652025
\(204\) 2.13160e85 0.0521885
\(205\) 3.88568e86 0.791948
\(206\) −5.13445e85 −0.0871913
\(207\) 5.26858e86 0.746115
\(208\) −3.05075e86 −0.360605
\(209\) 1.10996e87 1.09602
\(210\) −5.07132e87 −4.18695
\(211\) −4.45152e86 −0.307550 −0.153775 0.988106i \(-0.549143\pi\)
−0.153775 + 0.988106i \(0.549143\pi\)
\(212\) 1.18156e87 0.683693
\(213\) 1.20139e87 0.582705
\(214\) 4.75700e87 1.93560
\(215\) −5.56157e87 −1.90001
\(216\) 3.59592e86 0.103227
\(217\) 1.01631e88 2.45349
\(218\) −2.66287e87 −0.541042
\(219\) −5.95641e87 −1.01937
\(220\) 1.52248e88 2.19635
\(221\) 1.30572e86 0.0158905
\(222\) −7.57740e87 −0.778545
\(223\) −1.26594e88 −1.09896 −0.549480 0.835507i \(-0.685174\pi\)
−0.549480 + 0.835507i \(0.685174\pi\)
\(224\) −2.68625e88 −1.97172
\(225\) 1.61517e88 1.00317
\(226\) −1.20862e88 −0.635659
\(227\) 2.80119e88 1.24845 0.624227 0.781243i \(-0.285414\pi\)
0.624227 + 0.781243i \(0.285414\pi\)
\(228\) −3.97457e88 −1.50222
\(229\) −2.13293e88 −0.684142 −0.342071 0.939674i \(-0.611128\pi\)
−0.342071 + 0.939674i \(0.611128\pi\)
\(230\) 8.12909e88 2.21436
\(231\) 9.43835e88 2.18498
\(232\) −7.83339e87 −0.154223
\(233\) −8.75869e88 −1.46755 −0.733774 0.679394i \(-0.762243\pi\)
−0.733774 + 0.679394i \(0.762243\pi\)
\(234\) −3.93733e88 −0.561833
\(235\) −9.89607e88 −1.20342
\(236\) 9.14090e88 0.947958
\(237\) 6.83312e88 0.604723
\(238\) 8.82893e87 0.0667225
\(239\) 6.42047e88 0.414615 0.207308 0.978276i \(-0.433530\pi\)
0.207308 + 0.978276i \(0.433530\pi\)
\(240\) 2.67235e89 1.47561
\(241\) −2.34435e89 −1.10760 −0.553800 0.832650i \(-0.686823\pi\)
−0.553800 + 0.832650i \(0.686823\pi\)
\(242\) −1.47057e89 −0.594854
\(243\) −3.61832e89 −1.25392
\(244\) −8.17848e88 −0.242971
\(245\) −5.57807e89 −1.42153
\(246\) 4.71082e89 1.03046
\(247\) −2.43463e89 −0.457401
\(248\) 3.59426e89 0.580324
\(249\) 1.08121e90 1.50119
\(250\) 5.94808e89 0.710602
\(251\) 1.57600e90 1.62103 0.810517 0.585715i \(-0.199186\pi\)
0.810517 + 0.585715i \(0.199186\pi\)
\(252\) −1.46349e90 −1.29679
\(253\) −1.51292e90 −1.15557
\(254\) 1.06244e90 0.699909
\(255\) −1.14376e89 −0.0650247
\(256\) 8.66544e89 0.425394
\(257\) 9.26893e89 0.393131 0.196566 0.980491i \(-0.437021\pi\)
0.196566 + 0.980491i \(0.437021\pi\)
\(258\) −6.74260e90 −2.47223
\(259\) −1.72525e90 −0.547154
\(260\) −3.33949e90 −0.916599
\(261\) 1.50637e90 0.358025
\(262\) 4.66663e90 0.960960
\(263\) 9.67293e90 1.72670 0.863351 0.504603i \(-0.168361\pi\)
0.863351 + 0.504603i \(0.168361\pi\)
\(264\) 3.33795e90 0.516813
\(265\) −6.33993e90 −0.851852
\(266\) −1.64623e91 −1.92057
\(267\) 1.39494e91 1.41378
\(268\) 1.74843e91 1.54026
\(269\) −8.00260e90 −0.613085 −0.306542 0.951857i \(-0.599172\pi\)
−0.306542 + 0.951857i \(0.599172\pi\)
\(270\) −1.06694e91 −0.711213
\(271\) 1.96164e91 1.13834 0.569168 0.822222i \(-0.307266\pi\)
0.569168 + 0.822222i \(0.307266\pi\)
\(272\) −4.65243e89 −0.0235150
\(273\) −2.07025e91 −0.911851
\(274\) −1.31163e91 −0.503691
\(275\) −4.63812e91 −1.55370
\(276\) 5.41753e91 1.58384
\(277\) 5.38580e91 1.37486 0.687431 0.726249i \(-0.258738\pi\)
0.687431 + 0.726249i \(0.258738\pi\)
\(278\) 5.99737e90 0.133746
\(279\) −6.91180e91 −1.34720
\(280\) −4.08354e91 −0.696001
\(281\) 9.87766e90 0.147288 0.0736440 0.997285i \(-0.476537\pi\)
0.0736440 + 0.997285i \(0.476537\pi\)
\(282\) −1.19976e92 −1.56585
\(283\) −2.10001e91 −0.240010 −0.120005 0.992773i \(-0.538291\pi\)
−0.120005 + 0.992773i \(0.538291\pi\)
\(284\) 5.34936e91 0.535629
\(285\) 2.13264e92 1.87170
\(286\) 1.13064e92 0.870160
\(287\) 1.07257e92 0.724197
\(288\) 1.82690e92 1.08267
\(289\) −1.91964e92 −0.998964
\(290\) 2.32424e92 1.06257
\(291\) −5.36454e92 −2.15549
\(292\) −2.65218e92 −0.937013
\(293\) 3.34446e92 1.03942 0.519710 0.854343i \(-0.326040\pi\)
0.519710 + 0.854343i \(0.326040\pi\)
\(294\) −6.76261e92 −1.84965
\(295\) −4.90476e92 −1.18111
\(296\) −6.10148e91 −0.129418
\(297\) 1.98571e92 0.371149
\(298\) 1.02065e93 1.68177
\(299\) 3.31852e92 0.482252
\(300\) 1.66084e93 2.12951
\(301\) −1.53518e93 −1.73746
\(302\) −1.25737e93 −1.25661
\(303\) 4.62756e92 0.408558
\(304\) 8.67487e92 0.676868
\(305\) 4.38835e92 0.302731
\(306\) −6.00447e91 −0.0366371
\(307\) −9.57957e92 −0.517198 −0.258599 0.965985i \(-0.583261\pi\)
−0.258599 + 0.965985i \(0.583261\pi\)
\(308\) 4.20256e93 2.00845
\(309\) 1.83604e92 0.0777032
\(310\) −1.06645e94 −3.99831
\(311\) 5.25070e93 1.74463 0.872313 0.488948i \(-0.162619\pi\)
0.872313 + 0.488948i \(0.162619\pi\)
\(312\) −7.32162e92 −0.215680
\(313\) 5.81690e93 1.51977 0.759887 0.650055i \(-0.225254\pi\)
0.759887 + 0.650055i \(0.225254\pi\)
\(314\) −1.22591e94 −2.84183
\(315\) 7.85269e93 1.61575
\(316\) 3.04254e93 0.555868
\(317\) −4.47378e93 −0.726026 −0.363013 0.931784i \(-0.618252\pi\)
−0.363013 + 0.931784i \(0.618252\pi\)
\(318\) −7.68625e93 −1.10840
\(319\) −4.32569e93 −0.554504
\(320\) 1.84407e94 2.10210
\(321\) −1.70106e94 −1.72497
\(322\) 2.24390e94 2.02492
\(323\) −3.71283e92 −0.0298271
\(324\) −2.01426e94 −1.44104
\(325\) 1.01735e94 0.648400
\(326\) 4.65871e94 2.64609
\(327\) 9.52220e93 0.482166
\(328\) 3.79325e93 0.171294
\(329\) −2.73164e94 −1.10047
\(330\) −9.90401e94 −3.56073
\(331\) 9.70530e93 0.311501 0.155750 0.987796i \(-0.450220\pi\)
0.155750 + 0.987796i \(0.450220\pi\)
\(332\) 4.81424e94 1.37991
\(333\) 1.17332e94 0.300441
\(334\) −5.85330e94 −1.33939
\(335\) −9.38162e94 −1.91910
\(336\) 7.37655e94 1.34937
\(337\) −2.56870e94 −0.420332 −0.210166 0.977666i \(-0.567400\pi\)
−0.210166 + 0.977666i \(0.567400\pi\)
\(338\) 7.69718e94 1.12708
\(339\) 4.32194e94 0.566487
\(340\) −5.09275e93 −0.0597714
\(341\) 1.98479e95 2.08653
\(342\) 1.11959e95 1.05458
\(343\) 1.07763e94 0.0909786
\(344\) −5.42929e94 −0.410962
\(345\) −2.90690e95 −1.97339
\(346\) −3.72220e95 −2.26697
\(347\) −7.33722e94 −0.401030 −0.200515 0.979691i \(-0.564261\pi\)
−0.200515 + 0.979691i \(0.564261\pi\)
\(348\) 1.54896e95 0.760008
\(349\) 1.66138e95 0.732008 0.366004 0.930613i \(-0.380726\pi\)
0.366004 + 0.930613i \(0.380726\pi\)
\(350\) 6.87904e95 2.72255
\(351\) −4.35555e94 −0.154891
\(352\) −5.24611e95 −1.67682
\(353\) 1.37439e95 0.394965 0.197482 0.980306i \(-0.436723\pi\)
0.197482 + 0.980306i \(0.436723\pi\)
\(354\) −5.94631e95 −1.53683
\(355\) −2.87032e95 −0.667370
\(356\) 6.21115e95 1.29956
\(357\) −3.15715e94 −0.0594617
\(358\) −8.32064e95 −1.41105
\(359\) 5.50724e95 0.841187 0.420593 0.907249i \(-0.361822\pi\)
0.420593 + 0.907249i \(0.361822\pi\)
\(360\) 2.77717e95 0.382172
\(361\) −1.14052e95 −0.141443
\(362\) 1.17230e96 1.31059
\(363\) 5.25865e95 0.530122
\(364\) −9.21808e95 −0.838183
\(365\) 1.42309e96 1.16748
\(366\) 5.32024e95 0.393904
\(367\) −6.49521e95 −0.434126 −0.217063 0.976158i \(-0.569648\pi\)
−0.217063 + 0.976158i \(0.569648\pi\)
\(368\) −1.18243e96 −0.713643
\(369\) −7.29448e95 −0.397654
\(370\) 1.81037e96 0.891665
\(371\) −1.75003e96 −0.778975
\(372\) −7.10721e96 −2.85982
\(373\) 5.22192e96 1.89998 0.949991 0.312279i \(-0.101092\pi\)
0.949991 + 0.312279i \(0.101092\pi\)
\(374\) 1.72424e95 0.0567431
\(375\) −2.12699e96 −0.633274
\(376\) −9.66069e95 −0.260294
\(377\) 9.48817e95 0.231410
\(378\) −2.94511e96 −0.650368
\(379\) 6.94041e94 0.0138808 0.00694041 0.999976i \(-0.497791\pi\)
0.00694041 + 0.999976i \(0.497791\pi\)
\(380\) 9.49590e96 1.72049
\(381\) −3.79921e96 −0.623745
\(382\) 1.58204e97 2.35419
\(383\) 9.05321e96 1.22137 0.610687 0.791872i \(-0.290894\pi\)
0.610687 + 0.791872i \(0.290894\pi\)
\(384\) 6.96842e96 0.852537
\(385\) −2.25498e97 −2.50245
\(386\) −8.45081e96 −0.850892
\(387\) 1.04406e97 0.954035
\(388\) −2.38864e97 −1.98135
\(389\) −1.69852e97 −1.27927 −0.639634 0.768679i \(-0.720914\pi\)
−0.639634 + 0.768679i \(0.720914\pi\)
\(390\) 2.17239e97 1.48599
\(391\) 5.06077e95 0.0314477
\(392\) −5.44540e96 −0.307469
\(393\) −1.66875e97 −0.856389
\(394\) 5.49418e97 2.56327
\(395\) −1.63255e97 −0.692587
\(396\) −2.85812e97 −1.10284
\(397\) −1.70232e97 −0.597582 −0.298791 0.954319i \(-0.596583\pi\)
−0.298791 + 0.954319i \(0.596583\pi\)
\(398\) 2.36077e97 0.754115
\(399\) 5.88680e97 1.71157
\(400\) −3.62493e97 −0.959511
\(401\) 5.80652e97 1.39959 0.699797 0.714342i \(-0.253274\pi\)
0.699797 + 0.714342i \(0.253274\pi\)
\(402\) −1.13739e98 −2.49707
\(403\) −4.35353e97 −0.870768
\(404\) 2.06049e97 0.375551
\(405\) 1.08080e98 1.79548
\(406\) 6.41566e97 0.971662
\(407\) −3.36931e97 −0.465319
\(408\) −1.11655e96 −0.0140645
\(409\) 1.31385e98 1.50981 0.754903 0.655837i \(-0.227684\pi\)
0.754903 + 0.655837i \(0.227684\pi\)
\(410\) −1.12549e98 −1.18018
\(411\) 4.69027e97 0.448879
\(412\) 8.17522e96 0.0714256
\(413\) −1.35387e98 −1.08007
\(414\) −1.52605e98 −1.11188
\(415\) −2.58319e98 −1.71931
\(416\) 1.15071e98 0.699784
\(417\) −2.14461e97 −0.119192
\(418\) −3.21501e98 −1.63332
\(419\) −1.12448e98 −0.522306 −0.261153 0.965297i \(-0.584103\pi\)
−0.261153 + 0.965297i \(0.584103\pi\)
\(420\) 8.07470e98 3.42987
\(421\) 2.85953e98 1.11100 0.555502 0.831515i \(-0.312526\pi\)
0.555502 + 0.831515i \(0.312526\pi\)
\(422\) 1.28939e98 0.458318
\(423\) 1.85776e98 0.604264
\(424\) −6.18913e97 −0.184251
\(425\) 1.55146e97 0.0422821
\(426\) −3.47985e98 −0.868361
\(427\) 1.21133e98 0.276832
\(428\) −7.57423e98 −1.58561
\(429\) −4.04309e98 −0.775469
\(430\) 1.61092e99 2.83144
\(431\) 1.27153e98 0.204847 0.102424 0.994741i \(-0.467340\pi\)
0.102424 + 0.994741i \(0.467340\pi\)
\(432\) 1.55193e98 0.229210
\(433\) 1.29434e98 0.175287 0.0876437 0.996152i \(-0.472066\pi\)
0.0876437 + 0.996152i \(0.472066\pi\)
\(434\) −2.94375e99 −3.65625
\(435\) −8.31129e98 −0.946938
\(436\) 4.23989e98 0.443212
\(437\) −9.43627e98 −0.905204
\(438\) 1.72528e99 1.51908
\(439\) 2.23963e99 1.81033 0.905165 0.425060i \(-0.139747\pi\)
0.905165 + 0.425060i \(0.139747\pi\)
\(440\) −7.97492e98 −0.591904
\(441\) 1.04716e99 0.713780
\(442\) −3.78203e97 −0.0236805
\(443\) −4.21179e98 −0.242285 −0.121143 0.992635i \(-0.538656\pi\)
−0.121143 + 0.992635i \(0.538656\pi\)
\(444\) 1.20649e99 0.637770
\(445\) −3.33273e99 −1.61920
\(446\) 3.66683e99 1.63770
\(447\) −3.64976e99 −1.49876
\(448\) 5.09024e99 1.92226
\(449\) −1.69484e99 −0.588696 −0.294348 0.955698i \(-0.595103\pi\)
−0.294348 + 0.955698i \(0.595103\pi\)
\(450\) −4.67837e99 −1.49495
\(451\) 2.09468e99 0.615882
\(452\) 1.92440e99 0.520721
\(453\) 4.49625e99 1.11987
\(454\) −8.11368e99 −1.86047
\(455\) 4.94617e99 1.04434
\(456\) 2.08192e99 0.404839
\(457\) −4.57890e99 −0.820169 −0.410085 0.912047i \(-0.634501\pi\)
−0.410085 + 0.912047i \(0.634501\pi\)
\(458\) 6.17807e99 1.01952
\(459\) −6.64225e97 −0.0101004
\(460\) −1.29434e100 −1.81396
\(461\) −2.39771e99 −0.309750 −0.154875 0.987934i \(-0.549497\pi\)
−0.154875 + 0.987934i \(0.549497\pi\)
\(462\) −2.73383e100 −3.25610
\(463\) 4.76071e99 0.522859 0.261430 0.965223i \(-0.415806\pi\)
0.261430 + 0.965223i \(0.415806\pi\)
\(464\) −3.38075e99 −0.342443
\(465\) 3.81353e100 3.56321
\(466\) 2.53697e100 2.18697
\(467\) −1.60644e100 −1.27786 −0.638928 0.769266i \(-0.720622\pi\)
−0.638928 + 0.769266i \(0.720622\pi\)
\(468\) 6.26913e99 0.460244
\(469\) −2.58964e100 −1.75492
\(470\) 2.86641e100 1.79337
\(471\) 4.38376e100 2.53258
\(472\) −4.78809e99 −0.255469
\(473\) −2.99812e100 −1.47760
\(474\) −1.97923e100 −0.901172
\(475\) −2.89285e100 −1.21707
\(476\) −1.40577e99 −0.0546579
\(477\) 1.19018e100 0.427733
\(478\) −1.85970e100 −0.617869
\(479\) 2.55062e100 0.783546 0.391773 0.920062i \(-0.371862\pi\)
0.391773 + 0.920062i \(0.371862\pi\)
\(480\) −1.00798e101 −2.86354
\(481\) 7.39040e99 0.194190
\(482\) 6.79044e100 1.65057
\(483\) −8.02400e100 −1.80457
\(484\) 2.34149e100 0.487294
\(485\) 1.28168e101 2.46867
\(486\) 1.04805e101 1.86863
\(487\) −6.41200e100 −1.05842 −0.529210 0.848491i \(-0.677512\pi\)
−0.529210 + 0.848491i \(0.677512\pi\)
\(488\) 4.28397e99 0.0654792
\(489\) −1.66592e101 −2.35815
\(490\) 1.61570e101 2.11840
\(491\) −8.97077e100 −1.08962 −0.544808 0.838561i \(-0.683398\pi\)
−0.544808 + 0.838561i \(0.683398\pi\)
\(492\) −7.50071e100 −0.844133
\(493\) 1.44696e99 0.0150902
\(494\) 7.05194e100 0.681629
\(495\) 1.53359e101 1.37409
\(496\) 1.55122e101 1.28857
\(497\) −7.92303e100 −0.610276
\(498\) −3.13175e101 −2.23710
\(499\) 1.62083e101 1.07391 0.536955 0.843611i \(-0.319574\pi\)
0.536955 + 0.843611i \(0.319574\pi\)
\(500\) −9.47070e100 −0.582113
\(501\) 2.09309e101 1.19364
\(502\) −4.56492e101 −2.41570
\(503\) −1.09505e99 −0.00537818 −0.00268909 0.999996i \(-0.500856\pi\)
−0.00268909 + 0.999996i \(0.500856\pi\)
\(504\) 7.66591e100 0.349477
\(505\) −1.10560e101 −0.467920
\(506\) 4.38221e101 1.72206
\(507\) −2.75245e101 −1.00443
\(508\) −1.69165e101 −0.573353
\(509\) 1.18985e101 0.374608 0.187304 0.982302i \(-0.440025\pi\)
0.187304 + 0.982302i \(0.440025\pi\)
\(510\) 3.31292e100 0.0969013
\(511\) 3.92818e101 1.06760
\(512\) −5.05163e101 −1.27588
\(513\) 1.23851e101 0.290735
\(514\) −2.68476e101 −0.585853
\(515\) −4.38660e100 −0.0889932
\(516\) 1.07358e102 2.02521
\(517\) −5.33475e101 −0.935876
\(518\) 4.99720e101 0.815382
\(519\) 1.33103e102 2.02028
\(520\) 1.74926e101 0.247018
\(521\) 5.83254e100 0.0766378 0.0383189 0.999266i \(-0.487800\pi\)
0.0383189 + 0.999266i \(0.487800\pi\)
\(522\) −4.36323e101 −0.533537
\(523\) −3.14042e101 −0.357416 −0.178708 0.983902i \(-0.557192\pi\)
−0.178708 + 0.983902i \(0.557192\pi\)
\(524\) −7.43035e101 −0.787202
\(525\) −2.45989e102 −2.42629
\(526\) −2.80178e102 −2.57317
\(527\) −6.63918e100 −0.0567828
\(528\) 1.44060e102 1.14755
\(529\) −6.14737e100 −0.0456144
\(530\) 1.83637e102 1.26945
\(531\) 9.20757e101 0.593063
\(532\) 2.62118e102 1.57330
\(533\) −4.59457e101 −0.257024
\(534\) −4.04045e102 −2.10685
\(535\) 4.06412e102 1.97560
\(536\) −9.15847e101 −0.415091
\(537\) 2.97539e102 1.25750
\(538\) 2.31797e102 0.913633
\(539\) −3.00701e102 −1.10549
\(540\) 1.69882e102 0.582613
\(541\) 1.36286e102 0.436069 0.218034 0.975941i \(-0.430036\pi\)
0.218034 + 0.975941i \(0.430036\pi\)
\(542\) −5.68191e102 −1.69637
\(543\) −4.19206e102 −1.16798
\(544\) 1.75484e101 0.0456329
\(545\) −2.27501e102 −0.552223
\(546\) 5.99652e102 1.35886
\(547\) −3.83088e102 −0.810539 −0.405269 0.914197i \(-0.632822\pi\)
−0.405269 + 0.914197i \(0.632822\pi\)
\(548\) 2.08841e102 0.412614
\(549\) −8.23813e101 −0.152008
\(550\) 1.34344e103 2.31535
\(551\) −2.69798e102 −0.434364
\(552\) −2.83776e102 −0.426835
\(553\) −4.50636e102 −0.633336
\(554\) −1.56001e103 −2.04885
\(555\) −6.47372e102 −0.794634
\(556\) −9.54918e101 −0.109562
\(557\) 9.23735e102 0.990781 0.495390 0.868670i \(-0.335025\pi\)
0.495390 + 0.868670i \(0.335025\pi\)
\(558\) 2.00202e103 2.00764
\(559\) 6.57621e102 0.616642
\(560\) −1.76238e103 −1.54543
\(561\) −6.16575e101 −0.0505683
\(562\) −2.86108e102 −0.219492
\(563\) 4.61463e102 0.331186 0.165593 0.986194i \(-0.447046\pi\)
0.165593 + 0.986194i \(0.447046\pi\)
\(564\) 1.91029e103 1.28272
\(565\) −1.03258e103 −0.648795
\(566\) 6.08271e102 0.357669
\(567\) 2.98335e103 1.64187
\(568\) −2.80205e102 −0.144349
\(569\) 1.88669e103 0.909893 0.454947 0.890519i \(-0.349658\pi\)
0.454947 + 0.890519i \(0.349658\pi\)
\(570\) −6.17724e103 −2.78925
\(571\) 4.67402e103 1.97623 0.988113 0.153727i \(-0.0491277\pi\)
0.988113 + 0.153727i \(0.0491277\pi\)
\(572\) −1.80024e103 −0.712820
\(573\) −5.65726e103 −2.09801
\(574\) −3.10673e103 −1.07921
\(575\) 3.94309e103 1.28319
\(576\) −3.46182e103 −1.05551
\(577\) −3.64917e103 −1.04256 −0.521280 0.853386i \(-0.674545\pi\)
−0.521280 + 0.853386i \(0.674545\pi\)
\(578\) 5.56026e103 1.48868
\(579\) 3.02194e103 0.758298
\(580\) −3.70072e103 −0.870435
\(581\) −7.13046e103 −1.57222
\(582\) 1.55385e104 3.21216
\(583\) −3.41771e103 −0.662468
\(584\) 1.38924e103 0.252519
\(585\) −3.36384e103 −0.573444
\(586\) −9.68730e103 −1.54897
\(587\) 1.17897e104 1.76838 0.884190 0.467128i \(-0.154711\pi\)
0.884190 + 0.467128i \(0.154711\pi\)
\(588\) 1.07676e104 1.51520
\(589\) 1.23794e104 1.63446
\(590\) 1.42067e104 1.76012
\(591\) −1.96468e104 −2.28434
\(592\) −2.63329e103 −0.287365
\(593\) −1.02656e104 −1.05156 −0.525779 0.850621i \(-0.676226\pi\)
−0.525779 + 0.850621i \(0.676226\pi\)
\(594\) −5.75164e103 −0.553096
\(595\) 7.54296e102 0.0681014
\(596\) −1.62511e104 −1.37768
\(597\) −8.44191e103 −0.672053
\(598\) −9.61214e103 −0.718663
\(599\) 7.18476e103 0.504553 0.252276 0.967655i \(-0.418821\pi\)
0.252276 + 0.967655i \(0.418821\pi\)
\(600\) −8.69962e103 −0.573890
\(601\) −4.70305e103 −0.291465 −0.145733 0.989324i \(-0.546554\pi\)
−0.145733 + 0.989324i \(0.546554\pi\)
\(602\) 4.44667e104 2.58920
\(603\) 1.76119e104 0.963621
\(604\) 2.00202e104 1.02940
\(605\) −1.25638e104 −0.607147
\(606\) −1.34038e104 −0.608843
\(607\) 4.85988e103 0.207515 0.103757 0.994603i \(-0.466913\pi\)
0.103757 + 0.994603i \(0.466913\pi\)
\(608\) −3.27205e104 −1.31352
\(609\) −2.29419e104 −0.865926
\(610\) −1.27109e104 −0.451137
\(611\) 1.17015e104 0.390567
\(612\) 9.56049e102 0.0300125
\(613\) 2.87536e104 0.849033 0.424517 0.905420i \(-0.360444\pi\)
0.424517 + 0.905420i \(0.360444\pi\)
\(614\) 2.77474e104 0.770741
\(615\) 4.02467e104 1.05175
\(616\) −2.20134e104 −0.541266
\(617\) −5.46413e104 −1.26423 −0.632117 0.774873i \(-0.717814\pi\)
−0.632117 + 0.774873i \(0.717814\pi\)
\(618\) −5.31812e103 −0.115795
\(619\) 8.19299e104 1.67897 0.839486 0.543382i \(-0.182856\pi\)
0.839486 + 0.543382i \(0.182856\pi\)
\(620\) 1.69803e105 3.27534
\(621\) −1.68815e104 −0.306532
\(622\) −1.52087e105 −2.59988
\(623\) −9.19943e104 −1.48067
\(624\) −3.15988e104 −0.478904
\(625\) −4.12132e104 −0.588215
\(626\) −1.68488e105 −2.26480
\(627\) 1.14966e105 1.45558
\(628\) 1.95193e105 2.32797
\(629\) 1.12704e103 0.0126631
\(630\) −2.27455e105 −2.40782
\(631\) −1.20642e103 −0.0120336 −0.00601682 0.999982i \(-0.501915\pi\)
−0.00601682 + 0.999982i \(0.501915\pi\)
\(632\) −1.59371e104 −0.149803
\(633\) −4.61075e104 −0.408444
\(634\) 1.29584e105 1.08194
\(635\) 9.07695e104 0.714373
\(636\) 1.22383e105 0.907984
\(637\) 6.59572e104 0.461353
\(638\) 1.25294e105 0.826335
\(639\) 5.38837e104 0.335101
\(640\) −1.66487e105 −0.976408
\(641\) 1.53129e105 0.846994 0.423497 0.905898i \(-0.360802\pi\)
0.423497 + 0.905898i \(0.360802\pi\)
\(642\) 4.92716e105 2.57059
\(643\) −3.28939e105 −1.61884 −0.809420 0.587231i \(-0.800218\pi\)
−0.809420 + 0.587231i \(0.800218\pi\)
\(644\) −3.57280e105 −1.65878
\(645\) −5.76052e105 −2.52332
\(646\) 1.07543e104 0.0444490
\(647\) 4.12602e105 1.60924 0.804621 0.593789i \(-0.202369\pi\)
0.804621 + 0.593789i \(0.202369\pi\)
\(648\) 1.05509e105 0.388352
\(649\) −2.64404e105 −0.918528
\(650\) −2.94676e105 −0.966261
\(651\) 1.05266e106 3.25838
\(652\) −7.41773e105 −2.16763
\(653\) −5.94027e105 −1.63894 −0.819468 0.573125i \(-0.805731\pi\)
−0.819468 + 0.573125i \(0.805731\pi\)
\(654\) −2.75812e105 −0.718535
\(655\) 3.98692e105 0.980819
\(656\) 1.63710e105 0.380348
\(657\) −2.67152e105 −0.586215
\(658\) 7.91225e105 1.63994
\(659\) −8.96994e105 −1.75625 −0.878126 0.478430i \(-0.841206\pi\)
−0.878126 + 0.478430i \(0.841206\pi\)
\(660\) 1.57695e106 2.91688
\(661\) 7.06992e105 1.23555 0.617774 0.786355i \(-0.288034\pi\)
0.617774 + 0.786355i \(0.288034\pi\)
\(662\) −2.81116e105 −0.464206
\(663\) 1.35242e104 0.0211036
\(664\) −2.52175e105 −0.371877
\(665\) −1.40645e106 −1.96026
\(666\) −3.39855e105 −0.447724
\(667\) 3.67748e105 0.457964
\(668\) 9.31979e105 1.09721
\(669\) −1.31123e106 −1.45948
\(670\) 2.71740e106 2.85989
\(671\) 2.36566e105 0.235428
\(672\) −2.78234e106 −2.61856
\(673\) 7.44927e105 0.663054 0.331527 0.943446i \(-0.392436\pi\)
0.331527 + 0.943446i \(0.392436\pi\)
\(674\) 7.44029e105 0.626389
\(675\) −5.17530e105 −0.412139
\(676\) −1.22557e106 −0.923285
\(677\) −9.15284e104 −0.0652350 −0.0326175 0.999468i \(-0.510384\pi\)
−0.0326175 + 0.999468i \(0.510384\pi\)
\(678\) −1.25186e106 −0.844192
\(679\) 3.53785e106 2.25748
\(680\) 2.66763e104 0.0161080
\(681\) 2.90139e106 1.65802
\(682\) −5.74898e106 −3.10940
\(683\) 3.43532e105 0.175870 0.0879348 0.996126i \(-0.471973\pi\)
0.0879348 + 0.996126i \(0.471973\pi\)
\(684\) −1.78264e106 −0.863893
\(685\) −1.12058e106 −0.514100
\(686\) −3.12137e105 −0.135578
\(687\) −2.20923e106 −0.908579
\(688\) −2.34318e106 −0.912515
\(689\) 7.49657e105 0.276466
\(690\) 8.41988e106 2.94080
\(691\) 1.22859e106 0.406424 0.203212 0.979135i \(-0.434862\pi\)
0.203212 + 0.979135i \(0.434862\pi\)
\(692\) 5.92659e106 1.85706
\(693\) 4.23321e106 1.25653
\(694\) 2.12524e106 0.597623
\(695\) 5.12383e105 0.136510
\(696\) −8.11360e105 −0.204818
\(697\) −7.00677e104 −0.0167606
\(698\) −4.81222e106 −1.09086
\(699\) −9.07200e106 −1.94899
\(700\) −1.09530e107 −2.23027
\(701\) 1.96377e106 0.379022 0.189511 0.981879i \(-0.439310\pi\)
0.189511 + 0.981879i \(0.439310\pi\)
\(702\) 1.26159e106 0.230822
\(703\) −2.10148e106 −0.364502
\(704\) 9.94096e106 1.63476
\(705\) −1.02501e107 −1.59821
\(706\) −3.98094e106 −0.588586
\(707\) −3.05182e106 −0.427889
\(708\) 9.46789e106 1.25894
\(709\) 4.23404e106 0.533976 0.266988 0.963700i \(-0.413972\pi\)
0.266988 + 0.963700i \(0.413972\pi\)
\(710\) 8.31393e106 0.994531
\(711\) 3.06474e106 0.347763
\(712\) −3.25346e106 −0.350224
\(713\) −1.68737e107 −1.72326
\(714\) 9.14475e105 0.0886113
\(715\) 9.65960e106 0.888143
\(716\) 1.32484e107 1.15591
\(717\) 6.65014e106 0.550633
\(718\) −1.59518e107 −1.25356
\(719\) 1.27678e107 0.952316 0.476158 0.879360i \(-0.342029\pi\)
0.476158 + 0.879360i \(0.342029\pi\)
\(720\) 1.19858e107 0.848590
\(721\) −1.21085e106 −0.0813797
\(722\) 3.30354e106 0.210782
\(723\) −2.42821e107 −1.47096
\(724\) −1.86657e107 −1.07362
\(725\) 1.12739e107 0.615744
\(726\) −1.52318e107 −0.790000
\(727\) 3.59224e107 1.76939 0.884697 0.466166i \(-0.154365\pi\)
0.884697 + 0.466166i \(0.154365\pi\)
\(728\) 4.82852e106 0.225885
\(729\) −1.09114e107 −0.484841
\(730\) −4.12199e107 −1.73980
\(731\) 1.00288e106 0.0402112
\(732\) −8.47104e106 −0.322679
\(733\) 4.68165e107 1.69434 0.847168 0.531325i \(-0.178306\pi\)
0.847168 + 0.531325i \(0.178306\pi\)
\(734\) 1.88135e107 0.646945
\(735\) −5.77761e107 −1.88787
\(736\) 4.45997e107 1.38489
\(737\) −5.05742e107 −1.49244
\(738\) 2.11286e107 0.592593
\(739\) −9.15146e106 −0.243963 −0.121982 0.992532i \(-0.538925\pi\)
−0.121982 + 0.992532i \(0.538925\pi\)
\(740\) −2.88252e107 −0.730436
\(741\) −2.52172e107 −0.607454
\(742\) 5.06899e107 1.16085
\(743\) −8.16406e106 −0.177757 −0.0888783 0.996042i \(-0.528328\pi\)
−0.0888783 + 0.996042i \(0.528328\pi\)
\(744\) 3.72283e107 0.770704
\(745\) 8.71989e107 1.71653
\(746\) −1.51254e108 −2.83140
\(747\) 4.84936e107 0.863300
\(748\) −2.74539e106 −0.0464830
\(749\) 1.12183e108 1.80659
\(750\) 6.16085e107 0.943720
\(751\) −9.35487e107 −1.36314 −0.681570 0.731753i \(-0.738702\pi\)
−0.681570 + 0.731753i \(0.738702\pi\)
\(752\) −4.16938e107 −0.577966
\(753\) 1.63238e108 2.15283
\(754\) −2.74827e107 −0.344852
\(755\) −1.07423e108 −1.28258
\(756\) 4.68929e107 0.532770
\(757\) 1.82140e107 0.196929 0.0984645 0.995141i \(-0.468607\pi\)
0.0984645 + 0.995141i \(0.468607\pi\)
\(758\) −2.01030e106 −0.0206855
\(759\) −1.56704e108 −1.53467
\(760\) −4.97405e107 −0.463661
\(761\) −8.22984e107 −0.730242 −0.365121 0.930960i \(-0.618972\pi\)
−0.365121 + 0.930960i \(0.618972\pi\)
\(762\) 1.10045e108 0.929519
\(763\) −6.27978e107 −0.504980
\(764\) −2.51897e108 −1.92851
\(765\) −5.12990e106 −0.0373943
\(766\) −2.62228e108 −1.82012
\(767\) 5.79957e107 0.383327
\(768\) 8.97541e107 0.564948
\(769\) 2.74612e108 1.64620 0.823098 0.567900i \(-0.192244\pi\)
0.823098 + 0.567900i \(0.192244\pi\)
\(770\) 6.53158e108 3.72920
\(771\) 9.60049e107 0.522101
\(772\) 1.34556e108 0.697036
\(773\) 1.64531e108 0.811924 0.405962 0.913890i \(-0.366937\pi\)
0.405962 + 0.913890i \(0.366937\pi\)
\(774\) −3.02414e108 −1.42172
\(775\) −5.17291e108 −2.31697
\(776\) 1.25119e108 0.533961
\(777\) −1.78696e108 −0.726652
\(778\) 4.91981e108 1.90640
\(779\) 1.30648e108 0.482443
\(780\) −3.45895e108 −1.21730
\(781\) −1.54732e108 −0.519000
\(782\) −1.46586e107 −0.0468640
\(783\) −4.82669e107 −0.147090
\(784\) −2.35013e108 −0.682716
\(785\) −1.04735e109 −2.90055
\(786\) 4.83357e108 1.27621
\(787\) 6.95067e108 1.74974 0.874872 0.484354i \(-0.160945\pi\)
0.874872 + 0.484354i \(0.160945\pi\)
\(788\) −8.74800e108 −2.09979
\(789\) 1.00189e109 2.29316
\(790\) 4.72870e108 1.03211
\(791\) −2.85027e108 −0.593290
\(792\) 1.49711e108 0.297208
\(793\) −5.18895e107 −0.0982505
\(794\) 4.93080e108 0.890531
\(795\) −6.56672e108 −1.13131
\(796\) −3.75888e108 −0.617758
\(797\) −1.73186e108 −0.271534 −0.135767 0.990741i \(-0.543350\pi\)
−0.135767 + 0.990741i \(0.543350\pi\)
\(798\) −1.70512e109 −2.55063
\(799\) 1.78449e107 0.0254689
\(800\) 1.36728e109 1.86201
\(801\) 6.25645e108 0.813033
\(802\) −1.68187e109 −2.08571
\(803\) 7.67153e108 0.907923
\(804\) 1.81098e109 2.04556
\(805\) 1.91707e109 2.06677
\(806\) 1.26101e109 1.29764
\(807\) −8.28886e108 −0.814212
\(808\) −1.07930e108 −0.101209
\(809\) −7.97983e108 −0.714371 −0.357186 0.934033i \(-0.616264\pi\)
−0.357186 + 0.934033i \(0.616264\pi\)
\(810\) −3.13054e109 −2.67566
\(811\) −1.17079e109 −0.955426 −0.477713 0.878516i \(-0.658534\pi\)
−0.477713 + 0.878516i \(0.658534\pi\)
\(812\) −1.02152e109 −0.795969
\(813\) 2.03181e109 1.51177
\(814\) 9.75927e108 0.693429
\(815\) 3.98015e109 2.70078
\(816\) −4.81885e107 −0.0312293
\(817\) −1.86996e109 −1.15746
\(818\) −3.80558e109 −2.24995
\(819\) −9.28532e108 −0.524385
\(820\) 1.79204e109 0.966783
\(821\) 2.89556e107 0.0149233 0.00746163 0.999972i \(-0.497625\pi\)
0.00746163 + 0.999972i \(0.497625\pi\)
\(822\) −1.35854e109 −0.668930
\(823\) −1.93713e109 −0.911307 −0.455654 0.890157i \(-0.650594\pi\)
−0.455654 + 0.890157i \(0.650594\pi\)
\(824\) −4.28226e107 −0.0192488
\(825\) −4.80403e109 −2.06340
\(826\) 3.92152e109 1.60954
\(827\) 5.09906e108 0.200002 0.100001 0.994987i \(-0.468115\pi\)
0.100001 + 0.994987i \(0.468115\pi\)
\(828\) 2.42983e109 0.910830
\(829\) −2.40363e109 −0.861139 −0.430570 0.902557i \(-0.641687\pi\)
−0.430570 + 0.902557i \(0.641687\pi\)
\(830\) 7.48226e109 2.56215
\(831\) 5.57846e109 1.82590
\(832\) −2.18050e109 −0.682230
\(833\) 1.00585e108 0.0300848
\(834\) 6.21190e108 0.177622
\(835\) −5.00075e109 −1.36707
\(836\) 5.11902e109 1.33799
\(837\) 2.21467e109 0.553482
\(838\) 3.25707e109 0.778353
\(839\) −3.09581e109 −0.707457 −0.353729 0.935348i \(-0.615086\pi\)
−0.353729 + 0.935348i \(0.615086\pi\)
\(840\) −4.22961e109 −0.924330
\(841\) −3.73320e109 −0.780245
\(842\) −8.28267e109 −1.65564
\(843\) 1.02310e109 0.195607
\(844\) −2.05300e109 −0.375446
\(845\) 6.57606e109 1.15037
\(846\) −5.38104e109 −0.900488
\(847\) −3.46802e109 −0.555205
\(848\) −2.67112e109 −0.409118
\(849\) −2.17513e109 −0.318747
\(850\) −4.49384e108 −0.0630098
\(851\) 2.86441e109 0.384306
\(852\) 5.54071e109 0.711346
\(853\) 7.93997e109 0.975506 0.487753 0.872982i \(-0.337817\pi\)
0.487753 + 0.872982i \(0.337817\pi\)
\(854\) −3.50864e109 −0.412542
\(855\) 9.56516e109 1.07637
\(856\) 3.96745e109 0.427313
\(857\) −1.00473e110 −1.03579 −0.517893 0.855445i \(-0.673284\pi\)
−0.517893 + 0.855445i \(0.673284\pi\)
\(858\) 1.17109e110 1.15562
\(859\) 9.45760e109 0.893383 0.446691 0.894688i \(-0.352602\pi\)
0.446691 + 0.894688i \(0.352602\pi\)
\(860\) −2.56495e110 −2.31946
\(861\) 1.11094e110 0.961775
\(862\) −3.68302e109 −0.305268
\(863\) 1.62638e110 1.29068 0.645339 0.763896i \(-0.276716\pi\)
0.645339 + 0.763896i \(0.276716\pi\)
\(864\) −5.85370e109 −0.444801
\(865\) −3.18005e110 −2.31382
\(866\) −3.74906e109 −0.261217
\(867\) −1.98830e110 −1.32668
\(868\) 4.68712e110 2.99514
\(869\) −8.80068e109 −0.538611
\(870\) 2.40738e110 1.41115
\(871\) 1.10932e110 0.622838
\(872\) −2.22090e109 −0.119443
\(873\) −2.40606e110 −1.23957
\(874\) 2.73323e110 1.34896
\(875\) 1.40272e110 0.663238
\(876\) −2.74705e110 −1.24441
\(877\) 1.83558e110 0.796691 0.398345 0.917236i \(-0.369585\pi\)
0.398345 + 0.917236i \(0.369585\pi\)
\(878\) −6.48714e110 −2.69780
\(879\) 3.46410e110 1.38041
\(880\) −3.44183e110 −1.31429
\(881\) −3.02493e110 −1.10693 −0.553463 0.832874i \(-0.686694\pi\)
−0.553463 + 0.832874i \(0.686694\pi\)
\(882\) −3.03311e110 −1.06369
\(883\) 2.96289e110 0.995838 0.497919 0.867223i \(-0.334098\pi\)
0.497919 + 0.867223i \(0.334098\pi\)
\(884\) 6.02186e108 0.0193986
\(885\) −5.08021e110 −1.56859
\(886\) 1.21995e110 0.361059
\(887\) 4.87676e110 1.38355 0.691776 0.722112i \(-0.256828\pi\)
0.691776 + 0.722112i \(0.256828\pi\)
\(888\) −6.31974e109 −0.171875
\(889\) 2.50554e110 0.653258
\(890\) 9.65331e110 2.41297
\(891\) 5.82632e110 1.39631
\(892\) −5.83843e110 −1.34157
\(893\) −3.32734e110 −0.733107
\(894\) 1.05716e111 2.23349
\(895\) −7.10871e110 −1.44021
\(896\) −4.59559e110 −0.892876
\(897\) 3.43722e110 0.640459
\(898\) 4.90914e110 0.877289
\(899\) −4.82445e110 −0.826913
\(900\) 7.44904e110 1.22463
\(901\) 1.14323e109 0.0180283
\(902\) −6.06728e110 −0.917801
\(903\) −1.59009e111 −2.30745
\(904\) −1.00802e110 −0.140331
\(905\) 1.00155e111 1.33768
\(906\) −1.30235e111 −1.66886
\(907\) −4.17981e110 −0.513906 −0.256953 0.966424i \(-0.582719\pi\)
−0.256953 + 0.966424i \(0.582719\pi\)
\(908\) 1.29188e111 1.52407
\(909\) 2.07552e110 0.234953
\(910\) −1.43267e111 −1.55630
\(911\) −2.43772e110 −0.254123 −0.127062 0.991895i \(-0.540555\pi\)
−0.127062 + 0.991895i \(0.540555\pi\)
\(912\) 8.98518e110 0.898919
\(913\) −1.39254e111 −1.33707
\(914\) 1.32629e111 1.22224
\(915\) 4.54533e110 0.402045
\(916\) −9.83690e110 −0.835176
\(917\) 1.10052e111 0.896909
\(918\) 1.92394e109 0.0150519
\(919\) 5.55089e110 0.416899 0.208449 0.978033i \(-0.433158\pi\)
0.208449 + 0.978033i \(0.433158\pi\)
\(920\) 6.77987e110 0.488852
\(921\) −9.92225e110 −0.686869
\(922\) 6.94500e110 0.461597
\(923\) 3.39397e110 0.216593
\(924\) 4.35289e111 2.66734
\(925\) 8.78134e110 0.516709
\(926\) −1.37895e111 −0.779177
\(927\) 8.23485e109 0.0446854
\(928\) 1.27518e111 0.664540
\(929\) −2.79269e110 −0.139776 −0.0698881 0.997555i \(-0.522264\pi\)
−0.0698881 + 0.997555i \(0.522264\pi\)
\(930\) −1.10460e112 −5.30998
\(931\) −1.87551e111 −0.865975
\(932\) −4.03944e111 −1.79153
\(933\) 5.43852e111 2.31696
\(934\) 4.65309e111 1.90429
\(935\) 1.47310e110 0.0579158
\(936\) −3.28383e110 −0.124033
\(937\) −2.54076e110 −0.0921997 −0.0460998 0.998937i \(-0.514679\pi\)
−0.0460998 + 0.998937i \(0.514679\pi\)
\(938\) 7.50093e111 2.61522
\(939\) 6.02498e111 2.01835
\(940\) −4.56399e111 −1.46910
\(941\) 5.39434e110 0.166850 0.0834252 0.996514i \(-0.473414\pi\)
0.0834252 + 0.996514i \(0.473414\pi\)
\(942\) −1.26976e112 −3.77411
\(943\) −1.78079e111 −0.508656
\(944\) −2.06646e111 −0.567252
\(945\) −2.51614e111 −0.663809
\(946\) 8.68410e111 2.20195
\(947\) −5.12709e111 −1.24953 −0.624765 0.780813i \(-0.714805\pi\)
−0.624765 + 0.780813i \(0.714805\pi\)
\(948\) 3.15138e111 0.738224
\(949\) −1.68271e111 −0.378901
\(950\) 8.37918e111 1.81370
\(951\) −4.63381e111 −0.964205
\(952\) 7.36355e109 0.0147300
\(953\) −1.33636e111 −0.257004 −0.128502 0.991709i \(-0.541017\pi\)
−0.128502 + 0.991709i \(0.541017\pi\)
\(954\) −3.44737e111 −0.637418
\(955\) 1.35161e112 2.40285
\(956\) 2.96107e111 0.506148
\(957\) −4.48043e111 −0.736414
\(958\) −7.38793e111 −1.16766
\(959\) −3.09318e111 −0.470118
\(960\) 1.91004e112 2.79171
\(961\) 1.50222e112 2.11157
\(962\) −2.14064e111 −0.289387
\(963\) −7.62947e111 −0.991993
\(964\) −1.08119e112 −1.35212
\(965\) −7.21992e111 −0.868476
\(966\) 2.32416e112 2.68921
\(967\) −1.07433e112 −1.19577 −0.597883 0.801583i \(-0.703991\pi\)
−0.597883 + 0.801583i \(0.703991\pi\)
\(968\) −1.22650e111 −0.131323
\(969\) −3.84565e110 −0.0396121
\(970\) −3.71240e112 −3.67887
\(971\) −1.38284e112 −1.31841 −0.659206 0.751963i \(-0.729107\pi\)
−0.659206 + 0.751963i \(0.729107\pi\)
\(972\) −1.66874e112 −1.53075
\(973\) 1.41435e111 0.124831
\(974\) 1.85725e112 1.57728
\(975\) 1.05374e112 0.861112
\(976\) 1.84888e111 0.145392
\(977\) 3.40506e111 0.257679 0.128839 0.991665i \(-0.458875\pi\)
0.128839 + 0.991665i \(0.458875\pi\)
\(978\) 4.82535e112 3.51417
\(979\) −1.79660e112 −1.25922
\(980\) −2.57256e112 −1.73535
\(981\) 4.27082e111 0.277283
\(982\) 2.59840e112 1.62377
\(983\) −4.99299e111 −0.300333 −0.150167 0.988661i \(-0.547981\pi\)
−0.150167 + 0.988661i \(0.547981\pi\)
\(984\) 3.92894e111 0.227489
\(985\) 4.69393e112 2.61624
\(986\) −4.19113e110 −0.0224878
\(987\) −2.82936e112 −1.46148
\(988\) −1.12283e112 −0.558379
\(989\) 2.54884e112 1.22034
\(990\) −4.44207e112 −2.04769
\(991\) 1.47616e112 0.655196 0.327598 0.944817i \(-0.393761\pi\)
0.327598 + 0.944817i \(0.393761\pi\)
\(992\) −5.85099e112 −2.50059
\(993\) 1.00525e112 0.413691
\(994\) 2.29492e112 0.909448
\(995\) 2.01691e112 0.769700
\(996\) 4.98646e112 1.83260
\(997\) −2.67429e112 −0.946543 −0.473272 0.880917i \(-0.656927\pi\)
−0.473272 + 0.880917i \(0.656927\pi\)
\(998\) −4.69477e112 −1.60037
\(999\) −3.75954e111 −0.123432
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 1.76.a.a.1.2 6
3.2 odd 2 9.76.a.c.1.5 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1.76.a.a.1.2 6 1.1 even 1 trivial
9.76.a.c.1.5 6 3.2 odd 2