Properties

Label 8035.2.a.e.1.2
Level 8035
Weight 2
Character 8035.1
Self dual Yes
Analytic conductor 64.160
Analytic rank 0
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8035.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(153\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 8035.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} +O(q^{10})\) \(q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} -2.71462 q^{10} -1.85768 q^{11} +11.6136 q^{12} -0.473422 q^{13} +12.4637 q^{14} +2.16303 q^{15} +14.0894 q^{16} +5.22842 q^{17} -4.55702 q^{18} +6.43407 q^{19} +5.36914 q^{20} -9.93122 q^{21} +5.04289 q^{22} -6.10480 q^{23} -19.7829 q^{24} +1.00000 q^{25} +1.28516 q^{26} -2.85802 q^{27} -24.6516 q^{28} +10.6754 q^{29} -5.87179 q^{30} -3.89035 q^{31} -19.9554 q^{32} -4.01822 q^{33} -14.1932 q^{34} -4.59135 q^{35} +9.01316 q^{36} -0.772275 q^{37} -17.4660 q^{38} -1.02403 q^{39} -9.14592 q^{40} -10.3158 q^{41} +26.9595 q^{42} -4.44984 q^{43} -9.97416 q^{44} +1.67870 q^{45} +16.5722 q^{46} -3.40537 q^{47} +30.4758 q^{48} +14.0805 q^{49} -2.71462 q^{50} +11.3092 q^{51} -2.54187 q^{52} +11.2491 q^{53} +7.75842 q^{54} -1.85768 q^{55} +41.9921 q^{56} +13.9171 q^{57} -28.9797 q^{58} +11.4392 q^{59} +11.6136 q^{60} +11.4994 q^{61} +10.5608 q^{62} -7.70748 q^{63} +25.9925 q^{64} -0.473422 q^{65} +10.9079 q^{66} -1.03348 q^{67} +28.0721 q^{68} -13.2049 q^{69} +12.4637 q^{70} -13.1791 q^{71} -15.3532 q^{72} -13.9911 q^{73} +2.09643 q^{74} +2.16303 q^{75} +34.5454 q^{76} +8.52927 q^{77} +2.77984 q^{78} -0.947999 q^{79} +14.0894 q^{80} -11.2181 q^{81} +28.0035 q^{82} +5.84937 q^{83} -53.3221 q^{84} +5.22842 q^{85} +12.0796 q^{86} +23.0913 q^{87} +16.9902 q^{88} -14.0004 q^{89} -4.55702 q^{90} +2.17365 q^{91} -32.7775 q^{92} -8.41493 q^{93} +9.24428 q^{94} +6.43407 q^{95} -43.1642 q^{96} -4.41652 q^{97} -38.2231 q^{98} -3.11849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + O(q^{10}) \) \( 153q + 18q^{2} + 7q^{3} + 176q^{4} + 153q^{5} + 19q^{6} + 5q^{7} + 57q^{8} + 206q^{9} + 18q^{10} + 38q^{11} + 14q^{12} + 28q^{13} + 53q^{14} + 7q^{15} + 214q^{16} + 50q^{17} + 47q^{18} + 65q^{19} + 176q^{20} + 109q^{21} + 13q^{22} + 52q^{23} + 66q^{24} + 153q^{25} + 36q^{26} + 19q^{27} + 26q^{28} + 172q^{29} + 19q^{30} + 60q^{31} + 107q^{32} + 4q^{33} + 40q^{34} + 5q^{35} + 241q^{36} + 65q^{37} + 29q^{38} + 56q^{39} + 57q^{40} + 152q^{41} - 19q^{42} + 22q^{43} + 97q^{44} + 206q^{45} + 86q^{46} + 37q^{47} - 4q^{48} + 260q^{49} + 18q^{50} + 102q^{51} - 6q^{52} + 169q^{53} + 64q^{54} + 38q^{55} + 146q^{56} + 40q^{57} - 9q^{58} + 64q^{59} + 14q^{60} + 164q^{61} + 12q^{62} + 19q^{63} + 259q^{64} + 28q^{65} + 6q^{66} + 5q^{67} + 112q^{68} + 119q^{69} + 53q^{70} + 100q^{71} + 77q^{72} + 10q^{73} + 98q^{74} + 7q^{75} + 126q^{76} + 80q^{77} - 4q^{78} + 110q^{79} + 214q^{80} + 305q^{81} - 27q^{82} + 36q^{83} + 172q^{84} + 50q^{85} + 44q^{86} + 23q^{87} + 47q^{88} + 143q^{89} + 47q^{90} + 82q^{91} + 130q^{92} + 31q^{93} + 77q^{94} + 65q^{95} + 57q^{96} + 11q^{97} + 29q^{98} + 99q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71462 −1.91952 −0.959762 0.280816i \(-0.909395\pi\)
−0.959762 + 0.280816i \(0.909395\pi\)
\(3\) 2.16303 1.24883 0.624413 0.781094i \(-0.285338\pi\)
0.624413 + 0.781094i \(0.285338\pi\)
\(4\) 5.36914 2.68457
\(5\) 1.00000 0.447214
\(6\) −5.87179 −2.39715
\(7\) −4.59135 −1.73537 −0.867683 0.497117i \(-0.834392\pi\)
−0.867683 + 0.497117i \(0.834392\pi\)
\(8\) −9.14592 −3.23357
\(9\) 1.67870 0.559566
\(10\) −2.71462 −0.858437
\(11\) −1.85768 −0.560112 −0.280056 0.959984i \(-0.590353\pi\)
−0.280056 + 0.959984i \(0.590353\pi\)
\(12\) 11.6136 3.35256
\(13\) −0.473422 −0.131304 −0.0656519 0.997843i \(-0.520913\pi\)
−0.0656519 + 0.997843i \(0.520913\pi\)
\(14\) 12.4637 3.33108
\(15\) 2.16303 0.558492
\(16\) 14.0894 3.52235
\(17\) 5.22842 1.26808 0.634039 0.773301i \(-0.281396\pi\)
0.634039 + 0.773301i \(0.281396\pi\)
\(18\) −4.55702 −1.07410
\(19\) 6.43407 1.47608 0.738038 0.674759i \(-0.235753\pi\)
0.738038 + 0.674759i \(0.235753\pi\)
\(20\) 5.36914 1.20058
\(21\) −9.93122 −2.16717
\(22\) 5.04289 1.07515
\(23\) −6.10480 −1.27294 −0.636469 0.771302i \(-0.719606\pi\)
−0.636469 + 0.771302i \(0.719606\pi\)
\(24\) −19.7829 −4.03817
\(25\) 1.00000 0.200000
\(26\) 1.28516 0.252041
\(27\) −2.85802 −0.550026
\(28\) −24.6516 −4.65871
\(29\) 10.6754 1.98238 0.991188 0.132461i \(-0.0422878\pi\)
0.991188 + 0.132461i \(0.0422878\pi\)
\(30\) −5.87179 −1.07204
\(31\) −3.89035 −0.698727 −0.349363 0.936987i \(-0.613602\pi\)
−0.349363 + 0.936987i \(0.613602\pi\)
\(32\) −19.9554 −3.52765
\(33\) −4.01822 −0.699483
\(34\) −14.1932 −2.43411
\(35\) −4.59135 −0.776080
\(36\) 9.01316 1.50219
\(37\) −0.772275 −0.126961 −0.0634806 0.997983i \(-0.520220\pi\)
−0.0634806 + 0.997983i \(0.520220\pi\)
\(38\) −17.4660 −2.83336
\(39\) −1.02403 −0.163976
\(40\) −9.14592 −1.44610
\(41\) −10.3158 −1.61106 −0.805532 0.592553i \(-0.798120\pi\)
−0.805532 + 0.592553i \(0.798120\pi\)
\(42\) 26.9595 4.15993
\(43\) −4.44984 −0.678594 −0.339297 0.940679i \(-0.610189\pi\)
−0.339297 + 0.940679i \(0.610189\pi\)
\(44\) −9.97416 −1.50366
\(45\) 1.67870 0.250245
\(46\) 16.5722 2.44343
\(47\) −3.40537 −0.496725 −0.248362 0.968667i \(-0.579892\pi\)
−0.248362 + 0.968667i \(0.579892\pi\)
\(48\) 30.4758 4.39880
\(49\) 14.0805 2.01150
\(50\) −2.71462 −0.383905
\(51\) 11.3092 1.58361
\(52\) −2.54187 −0.352494
\(53\) 11.2491 1.54518 0.772592 0.634903i \(-0.218960\pi\)
0.772592 + 0.634903i \(0.218960\pi\)
\(54\) 7.75842 1.05579
\(55\) −1.85768 −0.250490
\(56\) 41.9921 5.61143
\(57\) 13.9171 1.84336
\(58\) −28.9797 −3.80522
\(59\) 11.4392 1.48926 0.744630 0.667478i \(-0.232626\pi\)
0.744630 + 0.667478i \(0.232626\pi\)
\(60\) 11.6136 1.49931
\(61\) 11.4994 1.47235 0.736175 0.676792i \(-0.236630\pi\)
0.736175 + 0.676792i \(0.236630\pi\)
\(62\) 10.5608 1.34122
\(63\) −7.70748 −0.971052
\(64\) 25.9925 3.24907
\(65\) −0.473422 −0.0587208
\(66\) 10.9079 1.34267
\(67\) −1.03348 −0.126260 −0.0631298 0.998005i \(-0.520108\pi\)
−0.0631298 + 0.998005i \(0.520108\pi\)
\(68\) 28.0721 3.40425
\(69\) −13.2049 −1.58968
\(70\) 12.4637 1.48970
\(71\) −13.1791 −1.56407 −0.782036 0.623234i \(-0.785819\pi\)
−0.782036 + 0.623234i \(0.785819\pi\)
\(72\) −15.3532 −1.80940
\(73\) −13.9911 −1.63754 −0.818769 0.574123i \(-0.805343\pi\)
−0.818769 + 0.574123i \(0.805343\pi\)
\(74\) 2.09643 0.243705
\(75\) 2.16303 0.249765
\(76\) 34.5454 3.96263
\(77\) 8.52927 0.972000
\(78\) 2.77984 0.314755
\(79\) −0.947999 −0.106658 −0.0533291 0.998577i \(-0.516983\pi\)
−0.0533291 + 0.998577i \(0.516983\pi\)
\(80\) 14.0894 1.57524
\(81\) −11.2181 −1.24645
\(82\) 28.0035 3.09247
\(83\) 5.84937 0.642052 0.321026 0.947070i \(-0.395972\pi\)
0.321026 + 0.947070i \(0.395972\pi\)
\(84\) −53.3221 −5.81792
\(85\) 5.22842 0.567102
\(86\) 12.0796 1.30258
\(87\) 23.0913 2.47564
\(88\) 16.9902 1.81116
\(89\) −14.0004 −1.48404 −0.742021 0.670377i \(-0.766133\pi\)
−0.742021 + 0.670377i \(0.766133\pi\)
\(90\) −4.55702 −0.480352
\(91\) 2.17365 0.227860
\(92\) −32.7775 −3.41729
\(93\) −8.41493 −0.872588
\(94\) 9.24428 0.953475
\(95\) 6.43407 0.660121
\(96\) −43.1642 −4.40542
\(97\) −4.41652 −0.448430 −0.224215 0.974540i \(-0.571982\pi\)
−0.224215 + 0.974540i \(0.571982\pi\)
\(98\) −38.2231 −3.86112
\(99\) −3.11849 −0.313420
\(100\) 5.36914 0.536914
\(101\) 10.8134 1.07597 0.537986 0.842954i \(-0.319185\pi\)
0.537986 + 0.842954i \(0.319185\pi\)
\(102\) −30.7002 −3.03977
\(103\) −3.23224 −0.318482 −0.159241 0.987240i \(-0.550905\pi\)
−0.159241 + 0.987240i \(0.550905\pi\)
\(104\) 4.32988 0.424580
\(105\) −9.93122 −0.969188
\(106\) −30.5370 −2.96602
\(107\) 6.02632 0.582586 0.291293 0.956634i \(-0.405915\pi\)
0.291293 + 0.956634i \(0.405915\pi\)
\(108\) −15.3451 −1.47658
\(109\) 10.0825 0.965729 0.482865 0.875695i \(-0.339596\pi\)
0.482865 + 0.875695i \(0.339596\pi\)
\(110\) 5.04289 0.480821
\(111\) −1.67045 −0.158552
\(112\) −64.6893 −6.11256
\(113\) 10.6378 1.00072 0.500359 0.865818i \(-0.333201\pi\)
0.500359 + 0.865818i \(0.333201\pi\)
\(114\) −37.7795 −3.53838
\(115\) −6.10480 −0.569275
\(116\) 57.3178 5.32183
\(117\) −0.794733 −0.0734731
\(118\) −31.0531 −2.85867
\(119\) −24.0055 −2.20058
\(120\) −19.7829 −1.80592
\(121\) −7.54902 −0.686274
\(122\) −31.2165 −2.82621
\(123\) −22.3135 −2.01194
\(124\) −20.8878 −1.87578
\(125\) 1.00000 0.0894427
\(126\) 20.9229 1.86396
\(127\) −7.34283 −0.651571 −0.325786 0.945444i \(-0.605629\pi\)
−0.325786 + 0.945444i \(0.605629\pi\)
\(128\) −30.6489 −2.70901
\(129\) −9.62513 −0.847445
\(130\) 1.28516 0.112716
\(131\) 1.66472 0.145448 0.0727238 0.997352i \(-0.476831\pi\)
0.0727238 + 0.997352i \(0.476831\pi\)
\(132\) −21.5744 −1.87781
\(133\) −29.5410 −2.56153
\(134\) 2.80550 0.242358
\(135\) −2.85802 −0.245979
\(136\) −47.8187 −4.10042
\(137\) 12.9232 1.10410 0.552052 0.833810i \(-0.313845\pi\)
0.552052 + 0.833810i \(0.313845\pi\)
\(138\) 35.8461 3.05142
\(139\) 13.2138 1.12078 0.560391 0.828228i \(-0.310651\pi\)
0.560391 + 0.828228i \(0.310651\pi\)
\(140\) −24.6516 −2.08344
\(141\) −7.36592 −0.620323
\(142\) 35.7762 3.00227
\(143\) 0.879469 0.0735449
\(144\) 23.6518 1.97098
\(145\) 10.6754 0.886546
\(146\) 37.9805 3.14329
\(147\) 30.4565 2.51201
\(148\) −4.14645 −0.340836
\(149\) −2.56859 −0.210427 −0.105214 0.994450i \(-0.533553\pi\)
−0.105214 + 0.994450i \(0.533553\pi\)
\(150\) −5.87179 −0.479430
\(151\) 11.4536 0.932085 0.466042 0.884762i \(-0.345679\pi\)
0.466042 + 0.884762i \(0.345679\pi\)
\(152\) −58.8455 −4.77300
\(153\) 8.77694 0.709573
\(154\) −23.1537 −1.86578
\(155\) −3.89035 −0.312480
\(156\) −5.49814 −0.440204
\(157\) 5.26533 0.420219 0.210110 0.977678i \(-0.432618\pi\)
0.210110 + 0.977678i \(0.432618\pi\)
\(158\) 2.57345 0.204733
\(159\) 24.3322 1.92967
\(160\) −19.9554 −1.57761
\(161\) 28.0292 2.20901
\(162\) 30.4527 2.39259
\(163\) 1.84492 0.144505 0.0722527 0.997386i \(-0.476981\pi\)
0.0722527 + 0.997386i \(0.476981\pi\)
\(164\) −55.3872 −4.32501
\(165\) −4.01822 −0.312818
\(166\) −15.8788 −1.23243
\(167\) 13.3144 1.03030 0.515150 0.857100i \(-0.327736\pi\)
0.515150 + 0.857100i \(0.327736\pi\)
\(168\) 90.8302 7.00770
\(169\) −12.7759 −0.982759
\(170\) −14.1932 −1.08857
\(171\) 10.8008 0.825961
\(172\) −23.8918 −1.82173
\(173\) 7.40702 0.563146 0.281573 0.959540i \(-0.409144\pi\)
0.281573 + 0.959540i \(0.409144\pi\)
\(174\) −62.6839 −4.75205
\(175\) −4.59135 −0.347073
\(176\) −26.1736 −1.97291
\(177\) 24.7434 1.85983
\(178\) 38.0058 2.84865
\(179\) −6.72200 −0.502426 −0.251213 0.967932i \(-0.580829\pi\)
−0.251213 + 0.967932i \(0.580829\pi\)
\(180\) 9.01316 0.671801
\(181\) 15.6894 1.16618 0.583090 0.812407i \(-0.301843\pi\)
0.583090 + 0.812407i \(0.301843\pi\)
\(182\) −5.90062 −0.437383
\(183\) 24.8736 1.83871
\(184\) 55.8340 4.11614
\(185\) −0.772275 −0.0567788
\(186\) 22.8433 1.67495
\(187\) −9.71275 −0.710266
\(188\) −18.2839 −1.33349
\(189\) 13.1222 0.954496
\(190\) −17.4660 −1.26712
\(191\) −14.8665 −1.07570 −0.537852 0.843039i \(-0.680764\pi\)
−0.537852 + 0.843039i \(0.680764\pi\)
\(192\) 56.2226 4.05752
\(193\) 13.6442 0.982128 0.491064 0.871123i \(-0.336608\pi\)
0.491064 + 0.871123i \(0.336608\pi\)
\(194\) 11.9892 0.860771
\(195\) −1.02403 −0.0733321
\(196\) 75.6001 5.40000
\(197\) 7.06266 0.503194 0.251597 0.967832i \(-0.419044\pi\)
0.251597 + 0.967832i \(0.419044\pi\)
\(198\) 8.46549 0.601616
\(199\) −5.74325 −0.407128 −0.203564 0.979062i \(-0.565252\pi\)
−0.203564 + 0.979062i \(0.565252\pi\)
\(200\) −9.14592 −0.646714
\(201\) −2.23545 −0.157676
\(202\) −29.3542 −2.06535
\(203\) −49.0146 −3.44015
\(204\) 60.7208 4.25131
\(205\) −10.3158 −0.720489
\(206\) 8.77430 0.611334
\(207\) −10.2481 −0.712292
\(208\) −6.67023 −0.462497
\(209\) −11.9525 −0.826768
\(210\) 26.9595 1.86038
\(211\) −17.2763 −1.18935 −0.594675 0.803966i \(-0.702719\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(212\) 60.3981 4.14816
\(213\) −28.5068 −1.95325
\(214\) −16.3591 −1.11829
\(215\) −4.44984 −0.303476
\(216\) 26.1392 1.77855
\(217\) 17.8619 1.21255
\(218\) −27.3701 −1.85374
\(219\) −30.2632 −2.04500
\(220\) −9.97416 −0.672458
\(221\) −2.47525 −0.166504
\(222\) 4.53464 0.304345
\(223\) 8.27151 0.553901 0.276951 0.960884i \(-0.410676\pi\)
0.276951 + 0.960884i \(0.410676\pi\)
\(224\) 91.6223 6.12177
\(225\) 1.67870 0.111913
\(226\) −28.8775 −1.92090
\(227\) −28.3564 −1.88208 −0.941039 0.338298i \(-0.890149\pi\)
−0.941039 + 0.338298i \(0.890149\pi\)
\(228\) 74.7227 4.94863
\(229\) 1.40391 0.0927727 0.0463864 0.998924i \(-0.485229\pi\)
0.0463864 + 0.998924i \(0.485229\pi\)
\(230\) 16.5722 1.09274
\(231\) 18.4491 1.21386
\(232\) −97.6366 −6.41016
\(233\) 8.57750 0.561930 0.280965 0.959718i \(-0.409345\pi\)
0.280965 + 0.959718i \(0.409345\pi\)
\(234\) 2.15739 0.141033
\(235\) −3.40537 −0.222142
\(236\) 61.4188 3.99802
\(237\) −2.05055 −0.133198
\(238\) 65.1657 4.22407
\(239\) 22.9997 1.48773 0.743863 0.668332i \(-0.232991\pi\)
0.743863 + 0.668332i \(0.232991\pi\)
\(240\) 30.4758 1.96720
\(241\) −1.99067 −0.128230 −0.0641150 0.997943i \(-0.520422\pi\)
−0.0641150 + 0.997943i \(0.520422\pi\)
\(242\) 20.4927 1.31732
\(243\) −15.6910 −1.00658
\(244\) 61.7420 3.95262
\(245\) 14.0805 0.899569
\(246\) 60.5725 3.86196
\(247\) −3.04603 −0.193814
\(248\) 35.5808 2.25938
\(249\) 12.6524 0.801811
\(250\) −2.71462 −0.171687
\(251\) 26.6081 1.67949 0.839745 0.542981i \(-0.182704\pi\)
0.839745 + 0.542981i \(0.182704\pi\)
\(252\) −41.3826 −2.60686
\(253\) 11.3408 0.712988
\(254\) 19.9330 1.25071
\(255\) 11.3092 0.708212
\(256\) 31.2150 1.95094
\(257\) −12.8591 −0.802128 −0.401064 0.916050i \(-0.631360\pi\)
−0.401064 + 0.916050i \(0.631360\pi\)
\(258\) 26.1285 1.62669
\(259\) 3.54578 0.220324
\(260\) −2.54187 −0.157640
\(261\) 17.9208 1.10927
\(262\) −4.51908 −0.279190
\(263\) −5.06534 −0.312342 −0.156171 0.987730i \(-0.549915\pi\)
−0.156171 + 0.987730i \(0.549915\pi\)
\(264\) 36.7503 2.26183
\(265\) 11.2491 0.691027
\(266\) 80.1926 4.91692
\(267\) −30.2833 −1.85331
\(268\) −5.54889 −0.338953
\(269\) 13.4607 0.820715 0.410358 0.911925i \(-0.365404\pi\)
0.410358 + 0.911925i \(0.365404\pi\)
\(270\) 7.75842 0.472162
\(271\) 1.68890 0.102593 0.0512967 0.998683i \(-0.483665\pi\)
0.0512967 + 0.998683i \(0.483665\pi\)
\(272\) 73.6652 4.46661
\(273\) 4.70166 0.284558
\(274\) −35.0815 −2.11935
\(275\) −1.85768 −0.112022
\(276\) −70.8987 −4.26760
\(277\) 20.8013 1.24983 0.624914 0.780694i \(-0.285134\pi\)
0.624914 + 0.780694i \(0.285134\pi\)
\(278\) −35.8704 −2.15137
\(279\) −6.53071 −0.390984
\(280\) 41.9921 2.50951
\(281\) 20.4815 1.22183 0.610913 0.791697i \(-0.290802\pi\)
0.610913 + 0.791697i \(0.290802\pi\)
\(282\) 19.9957 1.19072
\(283\) −28.8233 −1.71336 −0.856682 0.515845i \(-0.827478\pi\)
−0.856682 + 0.515845i \(0.827478\pi\)
\(284\) −70.7604 −4.19886
\(285\) 13.9171 0.824376
\(286\) −2.38742 −0.141171
\(287\) 47.3636 2.79579
\(288\) −33.4991 −1.97395
\(289\) 10.3364 0.608023
\(290\) −28.9797 −1.70175
\(291\) −9.55306 −0.560010
\(292\) −75.1203 −4.39608
\(293\) 18.0456 1.05423 0.527116 0.849793i \(-0.323273\pi\)
0.527116 + 0.849793i \(0.323273\pi\)
\(294\) −82.6777 −4.82186
\(295\) 11.4392 0.666017
\(296\) 7.06317 0.410538
\(297\) 5.30929 0.308076
\(298\) 6.97275 0.403920
\(299\) 2.89015 0.167142
\(300\) 11.6136 0.670512
\(301\) 20.4307 1.17761
\(302\) −31.0923 −1.78916
\(303\) 23.3897 1.34370
\(304\) 90.6520 5.19925
\(305\) 11.4994 0.658455
\(306\) −23.8260 −1.36204
\(307\) 24.7404 1.41201 0.706004 0.708208i \(-0.250496\pi\)
0.706004 + 0.708208i \(0.250496\pi\)
\(308\) 45.7948 2.60940
\(309\) −6.99144 −0.397729
\(310\) 10.5608 0.599813
\(311\) 20.4487 1.15954 0.579770 0.814780i \(-0.303143\pi\)
0.579770 + 0.814780i \(0.303143\pi\)
\(312\) 9.36567 0.530227
\(313\) −7.29020 −0.412067 −0.206033 0.978545i \(-0.566056\pi\)
−0.206033 + 0.978545i \(0.566056\pi\)
\(314\) −14.2934 −0.806621
\(315\) −7.70748 −0.434267
\(316\) −5.08994 −0.286332
\(317\) 18.2687 1.02607 0.513036 0.858367i \(-0.328521\pi\)
0.513036 + 0.858367i \(0.328521\pi\)
\(318\) −66.0525 −3.70404
\(319\) −19.8315 −1.11035
\(320\) 25.9925 1.45303
\(321\) 13.0351 0.727548
\(322\) −76.0886 −4.24025
\(323\) 33.6400 1.87178
\(324\) −60.2314 −3.34619
\(325\) −0.473422 −0.0262608
\(326\) −5.00825 −0.277381
\(327\) 21.8088 1.20603
\(328\) 94.3478 5.20949
\(329\) 15.6353 0.862000
\(330\) 10.9079 0.600462
\(331\) 16.0487 0.882114 0.441057 0.897479i \(-0.354604\pi\)
0.441057 + 0.897479i \(0.354604\pi\)
\(332\) 31.4061 1.72363
\(333\) −1.29642 −0.0710431
\(334\) −36.1435 −1.97768
\(335\) −1.03348 −0.0564650
\(336\) −139.925 −7.63352
\(337\) 0.487635 0.0265631 0.0132816 0.999912i \(-0.495772\pi\)
0.0132816 + 0.999912i \(0.495772\pi\)
\(338\) 34.6816 1.88643
\(339\) 23.0099 1.24972
\(340\) 28.0721 1.52243
\(341\) 7.22703 0.391366
\(342\) −29.3202 −1.58545
\(343\) −32.5090 −1.75532
\(344\) 40.6978 2.19428
\(345\) −13.2049 −0.710925
\(346\) −20.1072 −1.08097
\(347\) 21.5002 1.15419 0.577096 0.816676i \(-0.304186\pi\)
0.577096 + 0.816676i \(0.304186\pi\)
\(348\) 123.980 6.64604
\(349\) 32.5827 1.74411 0.872055 0.489408i \(-0.162787\pi\)
0.872055 + 0.489408i \(0.162787\pi\)
\(350\) 12.4637 0.666215
\(351\) 1.35305 0.0722204
\(352\) 37.0708 1.97588
\(353\) 10.2565 0.545900 0.272950 0.962028i \(-0.412001\pi\)
0.272950 + 0.962028i \(0.412001\pi\)
\(354\) −67.1687 −3.56998
\(355\) −13.1791 −0.699474
\(356\) −75.1702 −3.98401
\(357\) −51.9246 −2.74814
\(358\) 18.2477 0.964419
\(359\) −1.38544 −0.0731206 −0.0365603 0.999331i \(-0.511640\pi\)
−0.0365603 + 0.999331i \(0.511640\pi\)
\(360\) −15.3532 −0.809186
\(361\) 22.3972 1.17880
\(362\) −42.5906 −2.23851
\(363\) −16.3287 −0.857037
\(364\) 11.6706 0.611707
\(365\) −13.9911 −0.732329
\(366\) −67.5222 −3.52944
\(367\) −18.0906 −0.944323 −0.472162 0.881512i \(-0.656526\pi\)
−0.472162 + 0.881512i \(0.656526\pi\)
\(368\) −86.0128 −4.48373
\(369\) −17.3172 −0.901496
\(370\) 2.09643 0.108988
\(371\) −51.6486 −2.68146
\(372\) −45.1810 −2.34252
\(373\) −10.8785 −0.563265 −0.281633 0.959522i \(-0.590876\pi\)
−0.281633 + 0.959522i \(0.590876\pi\)
\(374\) 26.3664 1.36337
\(375\) 2.16303 0.111698
\(376\) 31.1453 1.60619
\(377\) −5.05399 −0.260294
\(378\) −35.6216 −1.83218
\(379\) 28.8532 1.48209 0.741044 0.671457i \(-0.234331\pi\)
0.741044 + 0.671457i \(0.234331\pi\)
\(380\) 34.5454 1.77214
\(381\) −15.8828 −0.813699
\(382\) 40.3569 2.06484
\(383\) 22.4715 1.14824 0.574120 0.818771i \(-0.305344\pi\)
0.574120 + 0.818771i \(0.305344\pi\)
\(384\) −66.2945 −3.38308
\(385\) 8.52927 0.434692
\(386\) −37.0387 −1.88522
\(387\) −7.46993 −0.379718
\(388\) −23.7129 −1.20384
\(389\) −3.04352 −0.154313 −0.0771564 0.997019i \(-0.524584\pi\)
−0.0771564 + 0.997019i \(0.524584\pi\)
\(390\) 2.77984 0.140763
\(391\) −31.9185 −1.61419
\(392\) −128.779 −6.50432
\(393\) 3.60085 0.181639
\(394\) −19.1724 −0.965892
\(395\) −0.947999 −0.0476990
\(396\) −16.7436 −0.841397
\(397\) −3.22830 −0.162024 −0.0810119 0.996713i \(-0.525815\pi\)
−0.0810119 + 0.996713i \(0.525815\pi\)
\(398\) 15.5907 0.781492
\(399\) −63.8981 −3.19891
\(400\) 14.0894 0.704469
\(401\) −6.54361 −0.326772 −0.163386 0.986562i \(-0.552242\pi\)
−0.163386 + 0.986562i \(0.552242\pi\)
\(402\) 6.06838 0.302663
\(403\) 1.84178 0.0917455
\(404\) 58.0586 2.88852
\(405\) −11.2181 −0.557430
\(406\) 133.056 6.60345
\(407\) 1.43464 0.0711125
\(408\) −103.433 −5.12071
\(409\) −14.5883 −0.721347 −0.360674 0.932692i \(-0.617453\pi\)
−0.360674 + 0.932692i \(0.617453\pi\)
\(410\) 28.0035 1.38300
\(411\) 27.9533 1.37883
\(412\) −17.3544 −0.854988
\(413\) −52.5214 −2.58441
\(414\) 27.8197 1.36726
\(415\) 5.84937 0.287134
\(416\) 9.44735 0.463194
\(417\) 28.5819 1.39966
\(418\) 32.4463 1.58700
\(419\) 14.1897 0.693210 0.346605 0.938011i \(-0.387334\pi\)
0.346605 + 0.938011i \(0.387334\pi\)
\(420\) −53.3221 −2.60185
\(421\) −9.79635 −0.477445 −0.238722 0.971088i \(-0.576729\pi\)
−0.238722 + 0.971088i \(0.576729\pi\)
\(422\) 46.8985 2.28299
\(423\) −5.71659 −0.277950
\(424\) −102.883 −4.99646
\(425\) 5.22842 0.253616
\(426\) 77.3850 3.74931
\(427\) −52.7978 −2.55507
\(428\) 32.3561 1.56399
\(429\) 1.90232 0.0918447
\(430\) 12.0796 0.582530
\(431\) 17.1929 0.828151 0.414076 0.910242i \(-0.364105\pi\)
0.414076 + 0.910242i \(0.364105\pi\)
\(432\) −40.2677 −1.93738
\(433\) 31.4216 1.51002 0.755012 0.655711i \(-0.227631\pi\)
0.755012 + 0.655711i \(0.227631\pi\)
\(434\) −48.4883 −2.32751
\(435\) 23.0913 1.10714
\(436\) 54.1344 2.59257
\(437\) −39.2787 −1.87895
\(438\) 82.1530 3.92542
\(439\) 20.0153 0.955279 0.477640 0.878556i \(-0.341493\pi\)
0.477640 + 0.878556i \(0.341493\pi\)
\(440\) 16.9902 0.809977
\(441\) 23.6369 1.12556
\(442\) 6.71936 0.319607
\(443\) −13.3353 −0.633578 −0.316789 0.948496i \(-0.602605\pi\)
−0.316789 + 0.948496i \(0.602605\pi\)
\(444\) −8.96890 −0.425645
\(445\) −14.0004 −0.663684
\(446\) −22.4540 −1.06323
\(447\) −5.55594 −0.262787
\(448\) −119.341 −5.63832
\(449\) −4.24194 −0.200189 −0.100095 0.994978i \(-0.531915\pi\)
−0.100095 + 0.994978i \(0.531915\pi\)
\(450\) −4.55702 −0.214820
\(451\) 19.1635 0.902376
\(452\) 57.1158 2.68650
\(453\) 24.7746 1.16401
\(454\) 76.9766 3.61269
\(455\) 2.17365 0.101902
\(456\) −127.284 −5.96064
\(457\) 5.40125 0.252660 0.126330 0.991988i \(-0.459680\pi\)
0.126330 + 0.991988i \(0.459680\pi\)
\(458\) −3.81107 −0.178079
\(459\) −14.9429 −0.697476
\(460\) −32.7775 −1.52826
\(461\) −11.3261 −0.527510 −0.263755 0.964590i \(-0.584961\pi\)
−0.263755 + 0.964590i \(0.584961\pi\)
\(462\) −50.0821 −2.33003
\(463\) −1.91560 −0.0890255 −0.0445128 0.999009i \(-0.514174\pi\)
−0.0445128 + 0.999009i \(0.514174\pi\)
\(464\) 150.410 6.98262
\(465\) −8.41493 −0.390233
\(466\) −23.2846 −1.07864
\(467\) 2.00150 0.0926183 0.0463091 0.998927i \(-0.485254\pi\)
0.0463091 + 0.998927i \(0.485254\pi\)
\(468\) −4.26703 −0.197244
\(469\) 4.74506 0.219107
\(470\) 9.24428 0.426407
\(471\) 11.3891 0.524781
\(472\) −104.622 −4.81563
\(473\) 8.26638 0.380089
\(474\) 5.56646 0.255676
\(475\) 6.43407 0.295215
\(476\) −128.889 −5.90761
\(477\) 18.8839 0.864632
\(478\) −62.4353 −2.85573
\(479\) 43.6414 1.99402 0.997012 0.0772433i \(-0.0246118\pi\)
0.997012 + 0.0772433i \(0.0246118\pi\)
\(480\) −43.1642 −1.97017
\(481\) 0.365612 0.0166705
\(482\) 5.40389 0.246141
\(483\) 60.6281 2.75867
\(484\) −40.5317 −1.84235
\(485\) −4.41652 −0.200544
\(486\) 42.5949 1.93215
\(487\) −18.1831 −0.823954 −0.411977 0.911194i \(-0.635162\pi\)
−0.411977 + 0.911194i \(0.635162\pi\)
\(488\) −105.173 −4.76095
\(489\) 3.99062 0.180462
\(490\) −38.2231 −1.72674
\(491\) −10.6416 −0.480248 −0.240124 0.970742i \(-0.577188\pi\)
−0.240124 + 0.970742i \(0.577188\pi\)
\(492\) −119.804 −5.40119
\(493\) 55.8156 2.51381
\(494\) 8.26881 0.372031
\(495\) −3.11849 −0.140166
\(496\) −54.8126 −2.46116
\(497\) 60.5098 2.71424
\(498\) −34.3463 −1.53909
\(499\) 12.2641 0.549014 0.274507 0.961585i \(-0.411485\pi\)
0.274507 + 0.961585i \(0.411485\pi\)
\(500\) 5.36914 0.240115
\(501\) 28.7995 1.28666
\(502\) −72.2309 −3.22382
\(503\) 35.5286 1.58414 0.792070 0.610430i \(-0.209003\pi\)
0.792070 + 0.610430i \(0.209003\pi\)
\(504\) 70.4920 3.13996
\(505\) 10.8134 0.481189
\(506\) −30.7858 −1.36860
\(507\) −27.6346 −1.22730
\(508\) −39.4247 −1.74919
\(509\) −15.3898 −0.682143 −0.341072 0.940037i \(-0.610790\pi\)
−0.341072 + 0.940037i \(0.610790\pi\)
\(510\) −30.7002 −1.35943
\(511\) 64.2381 2.84173
\(512\) −23.4388 −1.03586
\(513\) −18.3887 −0.811880
\(514\) 34.9075 1.53970
\(515\) −3.23224 −0.142430
\(516\) −51.6786 −2.27503
\(517\) 6.32610 0.278222
\(518\) −9.62544 −0.422918
\(519\) 16.0216 0.703271
\(520\) 4.32988 0.189878
\(521\) −3.45053 −0.151171 −0.0755853 0.997139i \(-0.524083\pi\)
−0.0755853 + 0.997139i \(0.524083\pi\)
\(522\) −48.6481 −2.12927
\(523\) −33.8358 −1.47954 −0.739768 0.672862i \(-0.765065\pi\)
−0.739768 + 0.672862i \(0.765065\pi\)
\(524\) 8.93813 0.390464
\(525\) −9.93122 −0.433434
\(526\) 13.7504 0.599548
\(527\) −20.3404 −0.886041
\(528\) −56.6143 −2.46382
\(529\) 14.2685 0.620371
\(530\) −30.5370 −1.32644
\(531\) 19.2030 0.833338
\(532\) −158.610 −6.87661
\(533\) 4.88375 0.211539
\(534\) 82.2076 3.55747
\(535\) 6.02632 0.260540
\(536\) 9.45212 0.408269
\(537\) −14.5399 −0.627443
\(538\) −36.5407 −1.57538
\(539\) −26.1571 −1.12666
\(540\) −15.3451 −0.660348
\(541\) −0.0378167 −0.00162587 −0.000812934 1.00000i \(-0.500259\pi\)
−0.000812934 1.00000i \(0.500259\pi\)
\(542\) −4.58471 −0.196930
\(543\) 33.9365 1.45636
\(544\) −104.335 −4.47334
\(545\) 10.0825 0.431887
\(546\) −12.7632 −0.546215
\(547\) −34.8702 −1.49094 −0.745470 0.666539i \(-0.767775\pi\)
−0.745470 + 0.666539i \(0.767775\pi\)
\(548\) 69.3865 2.96404
\(549\) 19.3040 0.823876
\(550\) 5.04289 0.215030
\(551\) 68.6864 2.92614
\(552\) 120.771 5.14034
\(553\) 4.35260 0.185091
\(554\) −56.4675 −2.39907
\(555\) −1.67045 −0.0709068
\(556\) 70.9468 3.00882
\(557\) 22.5273 0.954513 0.477257 0.878764i \(-0.341631\pi\)
0.477257 + 0.878764i \(0.341631\pi\)
\(558\) 17.7284 0.750502
\(559\) 2.10665 0.0891019
\(560\) −64.6893 −2.73362
\(561\) −21.0090 −0.886999
\(562\) −55.5995 −2.34533
\(563\) −30.8732 −1.30115 −0.650576 0.759441i \(-0.725472\pi\)
−0.650576 + 0.759441i \(0.725472\pi\)
\(564\) −39.5487 −1.66530
\(565\) 10.6378 0.447535
\(566\) 78.2441 3.28884
\(567\) 51.5061 2.16305
\(568\) 120.535 5.05754
\(569\) −33.0178 −1.38418 −0.692088 0.721813i \(-0.743309\pi\)
−0.692088 + 0.721813i \(0.743309\pi\)
\(570\) −37.7795 −1.58241
\(571\) −24.9929 −1.04592 −0.522961 0.852357i \(-0.675173\pi\)
−0.522961 + 0.852357i \(0.675173\pi\)
\(572\) 4.72199 0.197436
\(573\) −32.1567 −1.34337
\(574\) −128.574 −5.36657
\(575\) −6.10480 −0.254588
\(576\) 43.6336 1.81807
\(577\) −39.1167 −1.62845 −0.814225 0.580550i \(-0.802838\pi\)
−0.814225 + 0.580550i \(0.802838\pi\)
\(578\) −28.0594 −1.16712
\(579\) 29.5127 1.22651
\(580\) 57.3178 2.37999
\(581\) −26.8565 −1.11420
\(582\) 25.9329 1.07495
\(583\) −20.8973 −0.865477
\(584\) 127.962 5.29510
\(585\) −0.794733 −0.0328582
\(586\) −48.9867 −2.02362
\(587\) 11.0489 0.456037 0.228019 0.973657i \(-0.426775\pi\)
0.228019 + 0.973657i \(0.426775\pi\)
\(588\) 163.525 6.74367
\(589\) −25.0307 −1.03137
\(590\) −31.0531 −1.27844
\(591\) 15.2767 0.628401
\(592\) −10.8809 −0.447201
\(593\) 19.0114 0.780704 0.390352 0.920666i \(-0.372353\pi\)
0.390352 + 0.920666i \(0.372353\pi\)
\(594\) −14.4127 −0.591359
\(595\) −24.0055 −0.984130
\(596\) −13.7911 −0.564907
\(597\) −12.4228 −0.508432
\(598\) −7.84564 −0.320832
\(599\) 16.1809 0.661133 0.330566 0.943783i \(-0.392760\pi\)
0.330566 + 0.943783i \(0.392760\pi\)
\(600\) −19.7829 −0.807633
\(601\) 25.5018 1.04024 0.520120 0.854093i \(-0.325887\pi\)
0.520120 + 0.854093i \(0.325887\pi\)
\(602\) −55.4616 −2.26045
\(603\) −1.73490 −0.0706505
\(604\) 61.4962 2.50225
\(605\) −7.54902 −0.306911
\(606\) −63.4940 −2.57927
\(607\) 5.88688 0.238941 0.119470 0.992838i \(-0.461880\pi\)
0.119470 + 0.992838i \(0.461880\pi\)
\(608\) −128.395 −5.20708
\(609\) −106.020 −4.29615
\(610\) −31.2165 −1.26392
\(611\) 1.61218 0.0652218
\(612\) 47.1246 1.90490
\(613\) −17.0543 −0.688817 −0.344408 0.938820i \(-0.611920\pi\)
−0.344408 + 0.938820i \(0.611920\pi\)
\(614\) −67.1606 −2.71038
\(615\) −22.3135 −0.899766
\(616\) −78.0080 −3.14303
\(617\) 48.9846 1.97205 0.986023 0.166608i \(-0.0532815\pi\)
0.986023 + 0.166608i \(0.0532815\pi\)
\(618\) 18.9791 0.763450
\(619\) −3.64627 −0.146556 −0.0732780 0.997312i \(-0.523346\pi\)
−0.0732780 + 0.997312i \(0.523346\pi\)
\(620\) −20.8878 −0.838875
\(621\) 17.4476 0.700149
\(622\) −55.5104 −2.22576
\(623\) 64.2808 2.57536
\(624\) −14.4279 −0.577579
\(625\) 1.00000 0.0400000
\(626\) 19.7901 0.790972
\(627\) −25.8535 −1.03249
\(628\) 28.2703 1.12811
\(629\) −4.03778 −0.160997
\(630\) 20.9229 0.833587
\(631\) −18.8477 −0.750316 −0.375158 0.926961i \(-0.622412\pi\)
−0.375158 + 0.926961i \(0.622412\pi\)
\(632\) 8.67033 0.344887
\(633\) −37.3692 −1.48529
\(634\) −49.5925 −1.96957
\(635\) −7.34283 −0.291392
\(636\) 130.643 5.18032
\(637\) −6.66602 −0.264117
\(638\) 53.8350 2.13135
\(639\) −22.1237 −0.875201
\(640\) −30.6489 −1.21151
\(641\) 9.33283 0.368624 0.184312 0.982868i \(-0.440994\pi\)
0.184312 + 0.982868i \(0.440994\pi\)
\(642\) −35.3853 −1.39655
\(643\) 13.2374 0.522030 0.261015 0.965335i \(-0.415943\pi\)
0.261015 + 0.965335i \(0.415943\pi\)
\(644\) 150.493 5.93025
\(645\) −9.62513 −0.378989
\(646\) −91.3197 −3.59293
\(647\) 5.29686 0.208241 0.104121 0.994565i \(-0.466797\pi\)
0.104121 + 0.994565i \(0.466797\pi\)
\(648\) 102.600 4.03049
\(649\) −21.2504 −0.834152
\(650\) 1.28516 0.0504081
\(651\) 38.6359 1.51426
\(652\) 9.90564 0.387935
\(653\) 12.8603 0.503262 0.251631 0.967823i \(-0.419033\pi\)
0.251631 + 0.967823i \(0.419033\pi\)
\(654\) −59.2024 −2.31500
\(655\) 1.66472 0.0650461
\(656\) −145.344 −5.67472
\(657\) −23.4869 −0.916310
\(658\) −42.4437 −1.65463
\(659\) 39.0287 1.52034 0.760172 0.649722i \(-0.225115\pi\)
0.760172 + 0.649722i \(0.225115\pi\)
\(660\) −21.5744 −0.839782
\(661\) −14.7477 −0.573620 −0.286810 0.957987i \(-0.592595\pi\)
−0.286810 + 0.957987i \(0.592595\pi\)
\(662\) −43.5660 −1.69324
\(663\) −5.35404 −0.207934
\(664\) −53.4979 −2.07612
\(665\) −29.5410 −1.14555
\(666\) 3.51927 0.136369
\(667\) −65.1713 −2.52344
\(668\) 71.4869 2.76591
\(669\) 17.8915 0.691726
\(670\) 2.80550 0.108386
\(671\) −21.3623 −0.824681
\(672\) 198.182 7.64503
\(673\) 49.3395 1.90190 0.950950 0.309346i \(-0.100110\pi\)
0.950950 + 0.309346i \(0.100110\pi\)
\(674\) −1.32374 −0.0509886
\(675\) −2.85802 −0.110005
\(676\) −68.5954 −2.63829
\(677\) 47.2300 1.81520 0.907599 0.419838i \(-0.137913\pi\)
0.907599 + 0.419838i \(0.137913\pi\)
\(678\) −62.4629 −2.39887
\(679\) 20.2778 0.778190
\(680\) −47.8187 −1.83376
\(681\) −61.3357 −2.35039
\(682\) −19.6186 −0.751235
\(683\) 23.4646 0.897847 0.448923 0.893570i \(-0.351808\pi\)
0.448923 + 0.893570i \(0.351808\pi\)
\(684\) 57.9913 2.21735
\(685\) 12.9232 0.493770
\(686\) 88.2493 3.36937
\(687\) 3.03669 0.115857
\(688\) −62.6954 −2.39024
\(689\) −5.32558 −0.202889
\(690\) 35.8461 1.36464
\(691\) −51.4409 −1.95690 −0.978452 0.206475i \(-0.933801\pi\)
−0.978452 + 0.206475i \(0.933801\pi\)
\(692\) 39.7694 1.51180
\(693\) 14.3181 0.543898
\(694\) −58.3648 −2.21550
\(695\) 13.2138 0.501229
\(696\) −211.191 −8.00517
\(697\) −53.9356 −2.04295
\(698\) −88.4494 −3.34786
\(699\) 18.5534 0.701753
\(700\) −24.6516 −0.931743
\(701\) 46.4415 1.75407 0.877036 0.480425i \(-0.159518\pi\)
0.877036 + 0.480425i \(0.159518\pi\)
\(702\) −3.67301 −0.138629
\(703\) −4.96887 −0.187404
\(704\) −48.2859 −1.81984
\(705\) −7.36592 −0.277417
\(706\) −27.8426 −1.04787
\(707\) −49.6480 −1.86721
\(708\) 132.851 4.99283
\(709\) −17.2120 −0.646409 −0.323205 0.946329i \(-0.604760\pi\)
−0.323205 + 0.946329i \(0.604760\pi\)
\(710\) 35.7762 1.34266
\(711\) −1.59140 −0.0596823
\(712\) 128.047 4.79876
\(713\) 23.7498 0.889436
\(714\) 140.955 5.27512
\(715\) 0.879469 0.0328903
\(716\) −36.0914 −1.34880
\(717\) 49.7490 1.85791
\(718\) 3.76093 0.140357
\(719\) 30.6922 1.14463 0.572313 0.820035i \(-0.306046\pi\)
0.572313 + 0.820035i \(0.306046\pi\)
\(720\) 23.6518 0.881451
\(721\) 14.8403 0.552684
\(722\) −60.7998 −2.26273
\(723\) −4.30587 −0.160137
\(724\) 84.2383 3.13069
\(725\) 10.6754 0.396475
\(726\) 44.3263 1.64510
\(727\) 3.97684 0.147493 0.0737465 0.997277i \(-0.476504\pi\)
0.0737465 + 0.997277i \(0.476504\pi\)
\(728\) −19.8800 −0.736802
\(729\) −0.285808 −0.0105855
\(730\) 37.9805 1.40572
\(731\) −23.2656 −0.860510
\(732\) 133.550 4.93614
\(733\) 10.9841 0.405705 0.202853 0.979209i \(-0.434979\pi\)
0.202853 + 0.979209i \(0.434979\pi\)
\(734\) 49.1091 1.81265
\(735\) 30.4565 1.12340
\(736\) 121.824 4.49048
\(737\) 1.91988 0.0707195
\(738\) 47.0095 1.73044
\(739\) 45.6054 1.67762 0.838811 0.544423i \(-0.183251\pi\)
0.838811 + 0.544423i \(0.183251\pi\)
\(740\) −4.14645 −0.152427
\(741\) −6.58866 −0.242040
\(742\) 140.206 5.14713
\(743\) 19.1849 0.703824 0.351912 0.936033i \(-0.385532\pi\)
0.351912 + 0.936033i \(0.385532\pi\)
\(744\) 76.9623 2.82158
\(745\) −2.56859 −0.0941060
\(746\) 29.5308 1.08120
\(747\) 9.81932 0.359270
\(748\) −52.1491 −1.90676
\(749\) −27.6689 −1.01100
\(750\) −5.87179 −0.214408
\(751\) −16.4894 −0.601706 −0.300853 0.953671i \(-0.597271\pi\)
−0.300853 + 0.953671i \(0.597271\pi\)
\(752\) −47.9796 −1.74964
\(753\) 57.5542 2.09739
\(754\) 13.7196 0.499639
\(755\) 11.4536 0.416841
\(756\) 70.4547 2.56241
\(757\) −14.6475 −0.532374 −0.266187 0.963921i \(-0.585764\pi\)
−0.266187 + 0.963921i \(0.585764\pi\)
\(758\) −78.3253 −2.84490
\(759\) 24.5304 0.890398
\(760\) −58.8455 −2.13455
\(761\) −44.8079 −1.62429 −0.812143 0.583458i \(-0.801699\pi\)
−0.812143 + 0.583458i \(0.801699\pi\)
\(762\) 43.1156 1.56191
\(763\) −46.2923 −1.67589
\(764\) −79.8205 −2.88780
\(765\) 8.77694 0.317331
\(766\) −61.0015 −2.20407
\(767\) −5.41558 −0.195545
\(768\) 67.5189 2.43638
\(769\) 34.5856 1.24719 0.623593 0.781749i \(-0.285672\pi\)
0.623593 + 0.781749i \(0.285672\pi\)
\(770\) −23.1537 −0.834401
\(771\) −27.8146 −1.00172
\(772\) 73.2574 2.63659
\(773\) 12.4708 0.448543 0.224271 0.974527i \(-0.428000\pi\)
0.224271 + 0.974527i \(0.428000\pi\)
\(774\) 20.2780 0.728877
\(775\) −3.89035 −0.139745
\(776\) 40.3931 1.45003
\(777\) 7.66963 0.275147
\(778\) 8.26200 0.296207
\(779\) −66.3728 −2.37805
\(780\) −5.49814 −0.196865
\(781\) 24.4826 0.876056
\(782\) 86.6463 3.09847
\(783\) −30.5105 −1.09036
\(784\) 198.385 7.08519
\(785\) 5.26533 0.187928
\(786\) −9.77491 −0.348660
\(787\) −44.7357 −1.59466 −0.797328 0.603547i \(-0.793754\pi\)
−0.797328 + 0.603547i \(0.793754\pi\)
\(788\) 37.9204 1.35086
\(789\) −10.9565 −0.390061
\(790\) 2.57345 0.0915594
\(791\) −48.8418 −1.73661
\(792\) 28.5214 1.01346
\(793\) −5.44408 −0.193325
\(794\) 8.76360 0.311009
\(795\) 24.3322 0.862973
\(796\) −30.8363 −1.09296
\(797\) −45.6179 −1.61587 −0.807935 0.589272i \(-0.799415\pi\)
−0.807935 + 0.589272i \(0.799415\pi\)
\(798\) 173.459 6.14038
\(799\) −17.8047 −0.629886
\(800\) −19.9554 −0.705531
\(801\) −23.5025 −0.830419
\(802\) 17.7634 0.627247
\(803\) 25.9911 0.917205
\(804\) −12.0024 −0.423293
\(805\) 28.0292 0.987901
\(806\) −4.99972 −0.176108
\(807\) 29.1160 1.02493
\(808\) −98.8984 −3.47923
\(809\) −3.88125 −0.136457 −0.0682287 0.997670i \(-0.521735\pi\)
−0.0682287 + 0.997670i \(0.521735\pi\)
\(810\) 30.4527 1.07000
\(811\) 30.9222 1.08582 0.542912 0.839790i \(-0.317322\pi\)
0.542912 + 0.839790i \(0.317322\pi\)
\(812\) −263.166 −9.23532
\(813\) 3.65314 0.128121
\(814\) −3.89450 −0.136502
\(815\) 1.84492 0.0646247
\(816\) 159.340 5.57802
\(817\) −28.6305 −1.00166
\(818\) 39.6017 1.38464
\(819\) 3.64890 0.127503
\(820\) −55.3872 −1.93420
\(821\) 13.3888 0.467273 0.233636 0.972324i \(-0.424937\pi\)
0.233636 + 0.972324i \(0.424937\pi\)
\(822\) −75.8824 −2.64670
\(823\) 13.2266 0.461052 0.230526 0.973066i \(-0.425955\pi\)
0.230526 + 0.973066i \(0.425955\pi\)
\(824\) 29.5618 1.02984
\(825\) −4.01822 −0.139897
\(826\) 142.576 4.96084
\(827\) 25.6976 0.893593 0.446796 0.894636i \(-0.352565\pi\)
0.446796 + 0.894636i \(0.352565\pi\)
\(828\) −55.0235 −1.91220
\(829\) −8.70771 −0.302431 −0.151216 0.988501i \(-0.548319\pi\)
−0.151216 + 0.988501i \(0.548319\pi\)
\(830\) −15.8788 −0.551161
\(831\) 44.9938 1.56082
\(832\) −12.3055 −0.426615
\(833\) 73.6187 2.55074
\(834\) −77.5888 −2.68668
\(835\) 13.3144 0.460764
\(836\) −64.1744 −2.21952
\(837\) 11.1187 0.384318
\(838\) −38.5195 −1.33063
\(839\) 51.3648 1.77331 0.886654 0.462433i \(-0.153023\pi\)
0.886654 + 0.462433i \(0.153023\pi\)
\(840\) 90.8302 3.13394
\(841\) 84.9647 2.92982
\(842\) 26.5933 0.916467
\(843\) 44.3022 1.52585
\(844\) −92.7589 −3.19289
\(845\) −12.7759 −0.439503
\(846\) 15.5183 0.533532
\(847\) 34.6602 1.19094
\(848\) 158.493 5.44267
\(849\) −62.3455 −2.13969
\(850\) −14.1932 −0.486821
\(851\) 4.71458 0.161614
\(852\) −153.057 −5.24364
\(853\) 31.4584 1.07712 0.538558 0.842588i \(-0.318969\pi\)
0.538558 + 0.842588i \(0.318969\pi\)
\(854\) 143.326 4.90451
\(855\) 10.8008 0.369381
\(856\) −55.1162 −1.88383
\(857\) 35.2659 1.20466 0.602329 0.798248i \(-0.294239\pi\)
0.602329 + 0.798248i \(0.294239\pi\)
\(858\) −5.16406 −0.176298
\(859\) −47.8773 −1.63355 −0.816775 0.576956i \(-0.804241\pi\)
−0.816775 + 0.576956i \(0.804241\pi\)
\(860\) −23.8918 −0.814703
\(861\) 102.449 3.49145
\(862\) −46.6720 −1.58966
\(863\) 10.7149 0.364738 0.182369 0.983230i \(-0.441623\pi\)
0.182369 + 0.983230i \(0.441623\pi\)
\(864\) 57.0329 1.94030
\(865\) 7.40702 0.251846
\(866\) −85.2974 −2.89853
\(867\) 22.3579 0.759315
\(868\) 95.9032 3.25517
\(869\) 1.76108 0.0597406
\(870\) −62.6839 −2.12518
\(871\) 0.489272 0.0165784
\(872\) −92.2138 −3.12275
\(873\) −7.41400 −0.250926
\(874\) 106.626 3.60669
\(875\) −4.59135 −0.155216
\(876\) −162.487 −5.48994
\(877\) 0.488875 0.0165081 0.00825407 0.999966i \(-0.497373\pi\)
0.00825407 + 0.999966i \(0.497373\pi\)
\(878\) −54.3339 −1.83368
\(879\) 39.0331 1.31655
\(880\) −26.1736 −0.882312
\(881\) −45.6713 −1.53870 −0.769352 0.638825i \(-0.779421\pi\)
−0.769352 + 0.638825i \(0.779421\pi\)
\(882\) −64.1650 −2.16055
\(883\) 10.9258 0.367682 0.183841 0.982956i \(-0.441147\pi\)
0.183841 + 0.982956i \(0.441147\pi\)
\(884\) −13.2900 −0.446990
\(885\) 24.7434 0.831739
\(886\) 36.2002 1.21617
\(887\) −52.2265 −1.75359 −0.876797 0.480860i \(-0.840325\pi\)
−0.876797 + 0.480860i \(0.840325\pi\)
\(888\) 15.2778 0.512691
\(889\) 33.7135 1.13071
\(890\) 38.0058 1.27396
\(891\) 20.8396 0.698153
\(892\) 44.4109 1.48699
\(893\) −21.9104 −0.733203
\(894\) 15.0823 0.504426
\(895\) −6.72200 −0.224692
\(896\) 140.720 4.70112
\(897\) 6.25148 0.208731
\(898\) 11.5152 0.384268
\(899\) −41.5311 −1.38514
\(900\) 9.01316 0.300439
\(901\) 58.8151 1.95942
\(902\) −52.0217 −1.73213
\(903\) 44.1923 1.47063
\(904\) −97.2924 −3.23590
\(905\) 15.6894 0.521532
\(906\) −67.2535 −2.23435
\(907\) −47.6697 −1.58285 −0.791423 0.611269i \(-0.790659\pi\)
−0.791423 + 0.611269i \(0.790659\pi\)
\(908\) −152.249 −5.05257
\(909\) 18.1524 0.602077
\(910\) −5.90062 −0.195604
\(911\) 8.80254 0.291641 0.145821 0.989311i \(-0.453418\pi\)
0.145821 + 0.989311i \(0.453418\pi\)
\(912\) 196.083 6.49296
\(913\) −10.8663 −0.359621
\(914\) −14.6623 −0.484986
\(915\) 24.8736 0.822295
\(916\) 7.53777 0.249055
\(917\) −7.64332 −0.252405
\(918\) 40.5643 1.33882
\(919\) −55.7361 −1.83856 −0.919282 0.393600i \(-0.871230\pi\)
−0.919282 + 0.393600i \(0.871230\pi\)
\(920\) 55.8340 1.84079
\(921\) 53.5142 1.76335
\(922\) 30.7461 1.01257
\(923\) 6.23928 0.205368
\(924\) 99.0556 3.25869
\(925\) −0.772275 −0.0253922
\(926\) 5.20012 0.170887
\(927\) −5.42596 −0.178212
\(928\) −213.033 −6.99314
\(929\) 20.6778 0.678417 0.339208 0.940711i \(-0.389841\pi\)
0.339208 + 0.940711i \(0.389841\pi\)
\(930\) 22.8433 0.749062
\(931\) 90.5947 2.96912
\(932\) 46.0538 1.50854
\(933\) 44.2311 1.44806
\(934\) −5.43330 −0.177783
\(935\) −9.71275 −0.317641
\(936\) 7.26856 0.237580
\(937\) −14.6793 −0.479553 −0.239777 0.970828i \(-0.577074\pi\)
−0.239777 + 0.970828i \(0.577074\pi\)
\(938\) −12.8810 −0.420580
\(939\) −15.7689 −0.514600
\(940\) −18.2839 −0.596356
\(941\) −0.641329 −0.0209067 −0.0104534 0.999945i \(-0.503327\pi\)
−0.0104534 + 0.999945i \(0.503327\pi\)
\(942\) −30.9170 −1.00733
\(943\) 62.9761 2.05078
\(944\) 161.172 5.24569
\(945\) 13.1222 0.426864
\(946\) −22.4400 −0.729589
\(947\) 28.8281 0.936788 0.468394 0.883520i \(-0.344833\pi\)
0.468394 + 0.883520i \(0.344833\pi\)
\(948\) −11.0097 −0.357578
\(949\) 6.62371 0.215015
\(950\) −17.4660 −0.566672
\(951\) 39.5157 1.28139
\(952\) 219.552 7.11574
\(953\) 15.9453 0.516520 0.258260 0.966075i \(-0.416851\pi\)
0.258260 + 0.966075i \(0.416851\pi\)
\(954\) −51.2624 −1.65968
\(955\) −14.8665 −0.481070
\(956\) 123.489 3.99391
\(957\) −42.8962 −1.38664
\(958\) −118.470 −3.82758
\(959\) −59.3349 −1.91603
\(960\) 56.2226 1.81458
\(961\) −15.8652 −0.511781
\(962\) −0.992497 −0.0319994
\(963\) 10.1164 0.325995
\(964\) −10.6882 −0.344242
\(965\) 13.6442 0.439221
\(966\) −164.582 −5.29534
\(967\) 44.8189 1.44128 0.720639 0.693311i \(-0.243849\pi\)
0.720639 + 0.693311i \(0.243849\pi\)
\(968\) 69.0427 2.21912
\(969\) 72.7643 2.33753
\(970\) 11.9892 0.384949
\(971\) −46.9691 −1.50731 −0.753656 0.657270i \(-0.771711\pi\)
−0.753656 + 0.657270i \(0.771711\pi\)
\(972\) −84.2470 −2.70222
\(973\) −60.6692 −1.94497
\(974\) 49.3601 1.58160
\(975\) −1.02403 −0.0327951
\(976\) 162.020 5.18612
\(977\) −15.6897 −0.501959 −0.250979 0.967992i \(-0.580753\pi\)
−0.250979 + 0.967992i \(0.580753\pi\)
\(978\) −10.8330 −0.346401
\(979\) 26.0083 0.831230
\(980\) 75.6001 2.41496
\(981\) 16.9255 0.540389
\(982\) 28.8878 0.921846
\(983\) −38.1280 −1.21609 −0.608047 0.793901i \(-0.708047\pi\)
−0.608047 + 0.793901i \(0.708047\pi\)
\(984\) 204.077 6.50574
\(985\) 7.06266 0.225035
\(986\) −151.518 −4.82532
\(987\) 33.8195 1.07649
\(988\) −16.3546 −0.520308
\(989\) 27.1653 0.863807
\(990\) 8.46549 0.269051
\(991\) −36.3979 −1.15622 −0.578108 0.815960i \(-0.696209\pi\)
−0.578108 + 0.815960i \(0.696209\pi\)
\(992\) 77.6335 2.46487
\(993\) 34.7137 1.10161
\(994\) −164.261 −5.21004
\(995\) −5.74325 −0.182073
\(996\) 67.9323 2.15252
\(997\) −9.28675 −0.294114 −0.147057 0.989128i \(-0.546980\pi\)
−0.147057 + 0.989128i \(0.546980\pi\)
\(998\) −33.2922 −1.05385
\(999\) 2.20718 0.0698319
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 \(a_p\))