Properties

Label 6027.2.a.y.1.6
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-1.32604\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.32604 q^{2} -1.00000 q^{3} +3.41045 q^{4} -0.0978008 q^{5} -2.32604 q^{6} +3.28076 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.32604 q^{2} -1.00000 q^{3} +3.41045 q^{4} -0.0978008 q^{5} -2.32604 q^{6} +3.28076 q^{8} +1.00000 q^{9} -0.227488 q^{10} -0.582422 q^{11} -3.41045 q^{12} -3.95129 q^{13} +0.0978008 q^{15} +0.810278 q^{16} +3.98906 q^{17} +2.32604 q^{18} +4.96154 q^{19} -0.333545 q^{20} -1.35474 q^{22} +7.14176 q^{23} -3.28076 q^{24} -4.99044 q^{25} -9.19086 q^{26} -1.00000 q^{27} +2.15477 q^{29} +0.227488 q^{30} +3.43209 q^{31} -4.67679 q^{32} +0.582422 q^{33} +9.27871 q^{34} +3.41045 q^{36} -2.57517 q^{37} +11.5407 q^{38} +3.95129 q^{39} -0.320861 q^{40} -1.00000 q^{41} +3.59636 q^{43} -1.98632 q^{44} -0.0978008 q^{45} +16.6120 q^{46} +2.71266 q^{47} -0.810278 q^{48} -11.6079 q^{50} -3.98906 q^{51} -13.4757 q^{52} +12.7249 q^{53} -2.32604 q^{54} +0.0569614 q^{55} -4.96154 q^{57} +5.01208 q^{58} +2.48011 q^{59} +0.333545 q^{60} +12.5132 q^{61} +7.98318 q^{62} -12.4989 q^{64} +0.386440 q^{65} +1.35474 q^{66} -5.99051 q^{67} +13.6045 q^{68} -7.14176 q^{69} -0.246186 q^{71} +3.28076 q^{72} +3.11493 q^{73} -5.98994 q^{74} +4.99044 q^{75} +16.9211 q^{76} +9.19086 q^{78} +2.27858 q^{79} -0.0792458 q^{80} +1.00000 q^{81} -2.32604 q^{82} +6.99712 q^{83} -0.390133 q^{85} +8.36527 q^{86} -2.15477 q^{87} -1.91079 q^{88} -4.58259 q^{89} -0.227488 q^{90} +24.3566 q^{92} -3.43209 q^{93} +6.30975 q^{94} -0.485242 q^{95} +4.67679 q^{96} +10.2253 q^{97} -0.582422 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.32604 1.64476 0.822379 0.568941i \(-0.192647\pi\)
0.822379 + 0.568941i \(0.192647\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.41045 1.70523
\(5\) −0.0978008 −0.0437378 −0.0218689 0.999761i \(-0.506962\pi\)
−0.0218689 + 0.999761i \(0.506962\pi\)
\(6\) −2.32604 −0.949601
\(7\) 0 0
\(8\) 3.28076 1.15993
\(9\) 1.00000 0.333333
\(10\) −0.227488 −0.0719381
\(11\) −0.582422 −0.175607 −0.0878035 0.996138i \(-0.527985\pi\)
−0.0878035 + 0.996138i \(0.527985\pi\)
\(12\) −3.41045 −0.984513
\(13\) −3.95129 −1.09589 −0.547946 0.836514i \(-0.684590\pi\)
−0.547946 + 0.836514i \(0.684590\pi\)
\(14\) 0 0
\(15\) 0.0978008 0.0252520
\(16\) 0.810278 0.202570
\(17\) 3.98906 0.967489 0.483745 0.875209i \(-0.339276\pi\)
0.483745 + 0.875209i \(0.339276\pi\)
\(18\) 2.32604 0.548252
\(19\) 4.96154 1.13826 0.569128 0.822249i \(-0.307281\pi\)
0.569128 + 0.822249i \(0.307281\pi\)
\(20\) −0.333545 −0.0745829
\(21\) 0 0
\(22\) −1.35474 −0.288831
\(23\) 7.14176 1.48916 0.744580 0.667533i \(-0.232650\pi\)
0.744580 + 0.667533i \(0.232650\pi\)
\(24\) −3.28076 −0.669683
\(25\) −4.99044 −0.998087
\(26\) −9.19086 −1.80248
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.15477 0.400131 0.200065 0.979783i \(-0.435885\pi\)
0.200065 + 0.979783i \(0.435885\pi\)
\(30\) 0.227488 0.0415335
\(31\) 3.43209 0.616422 0.308211 0.951318i \(-0.400270\pi\)
0.308211 + 0.951318i \(0.400270\pi\)
\(32\) −4.67679 −0.826748
\(33\) 0.582422 0.101387
\(34\) 9.27871 1.59129
\(35\) 0 0
\(36\) 3.41045 0.568409
\(37\) −2.57517 −0.423355 −0.211678 0.977340i \(-0.567893\pi\)
−0.211678 + 0.977340i \(0.567893\pi\)
\(38\) 11.5407 1.87215
\(39\) 3.95129 0.632713
\(40\) −0.320861 −0.0507326
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 3.59636 0.548440 0.274220 0.961667i \(-0.411580\pi\)
0.274220 + 0.961667i \(0.411580\pi\)
\(44\) −1.98632 −0.299450
\(45\) −0.0978008 −0.0145793
\(46\) 16.6120 2.44931
\(47\) 2.71266 0.395682 0.197841 0.980234i \(-0.436607\pi\)
0.197841 + 0.980234i \(0.436607\pi\)
\(48\) −0.810278 −0.116954
\(49\) 0 0
\(50\) −11.6079 −1.64161
\(51\) −3.98906 −0.558580
\(52\) −13.4757 −1.86874
\(53\) 12.7249 1.74790 0.873952 0.486012i \(-0.161549\pi\)
0.873952 + 0.486012i \(0.161549\pi\)
\(54\) −2.32604 −0.316534
\(55\) 0.0569614 0.00768067
\(56\) 0 0
\(57\) −4.96154 −0.657172
\(58\) 5.01208 0.658118
\(59\) 2.48011 0.322882 0.161441 0.986882i \(-0.448386\pi\)
0.161441 + 0.986882i \(0.448386\pi\)
\(60\) 0.333545 0.0430604
\(61\) 12.5132 1.60215 0.801076 0.598563i \(-0.204261\pi\)
0.801076 + 0.598563i \(0.204261\pi\)
\(62\) 7.98318 1.01387
\(63\) 0 0
\(64\) −12.4989 −1.56237
\(65\) 0.386440 0.0479319
\(66\) 1.35474 0.166757
\(67\) −5.99051 −0.731858 −0.365929 0.930643i \(-0.619249\pi\)
−0.365929 + 0.930643i \(0.619249\pi\)
\(68\) 13.6045 1.64979
\(69\) −7.14176 −0.859767
\(70\) 0 0
\(71\) −0.246186 −0.0292169 −0.0146084 0.999893i \(-0.504650\pi\)
−0.0146084 + 0.999893i \(0.504650\pi\)
\(72\) 3.28076 0.386642
\(73\) 3.11493 0.364575 0.182287 0.983245i \(-0.441650\pi\)
0.182287 + 0.983245i \(0.441650\pi\)
\(74\) −5.98994 −0.696316
\(75\) 4.99044 0.576246
\(76\) 16.9211 1.94098
\(77\) 0 0
\(78\) 9.19086 1.04066
\(79\) 2.27858 0.256360 0.128180 0.991751i \(-0.459086\pi\)
0.128180 + 0.991751i \(0.459086\pi\)
\(80\) −0.0792458 −0.00885995
\(81\) 1.00000 0.111111
\(82\) −2.32604 −0.256868
\(83\) 6.99712 0.768034 0.384017 0.923326i \(-0.374540\pi\)
0.384017 + 0.923326i \(0.374540\pi\)
\(84\) 0 0
\(85\) −0.390133 −0.0423159
\(86\) 8.36527 0.902050
\(87\) −2.15477 −0.231016
\(88\) −1.91079 −0.203691
\(89\) −4.58259 −0.485754 −0.242877 0.970057i \(-0.578091\pi\)
−0.242877 + 0.970057i \(0.578091\pi\)
\(90\) −0.227488 −0.0239794
\(91\) 0 0
\(92\) 24.3566 2.53936
\(93\) −3.43209 −0.355892
\(94\) 6.30975 0.650801
\(95\) −0.485242 −0.0497848
\(96\) 4.67679 0.477323
\(97\) 10.2253 1.03822 0.519109 0.854708i \(-0.326264\pi\)
0.519109 + 0.854708i \(0.326264\pi\)
\(98\) 0 0
\(99\) −0.582422 −0.0585357
\(100\) −17.0196 −1.70196
\(101\) 9.97712 0.992761 0.496380 0.868105i \(-0.334662\pi\)
0.496380 + 0.868105i \(0.334662\pi\)
\(102\) −9.27871 −0.918729
\(103\) −10.2103 −1.00605 −0.503023 0.864273i \(-0.667779\pi\)
−0.503023 + 0.864273i \(0.667779\pi\)
\(104\) −12.9633 −1.27115
\(105\) 0 0
\(106\) 29.5987 2.87488
\(107\) 14.5942 1.41087 0.705436 0.708773i \(-0.250751\pi\)
0.705436 + 0.708773i \(0.250751\pi\)
\(108\) −3.41045 −0.328171
\(109\) 1.33598 0.127964 0.0639820 0.997951i \(-0.479620\pi\)
0.0639820 + 0.997951i \(0.479620\pi\)
\(110\) 0.132494 0.0126328
\(111\) 2.57517 0.244424
\(112\) 0 0
\(113\) −11.0543 −1.03990 −0.519952 0.854195i \(-0.674050\pi\)
−0.519952 + 0.854195i \(0.674050\pi\)
\(114\) −11.5407 −1.08089
\(115\) −0.698470 −0.0651327
\(116\) 7.34874 0.682313
\(117\) −3.95129 −0.365297
\(118\) 5.76882 0.531063
\(119\) 0 0
\(120\) 0.320861 0.0292905
\(121\) −10.6608 −0.969162
\(122\) 29.1062 2.63515
\(123\) 1.00000 0.0901670
\(124\) 11.7050 1.05114
\(125\) 0.977072 0.0873920
\(126\) 0 0
\(127\) 16.7303 1.48457 0.742287 0.670082i \(-0.233741\pi\)
0.742287 + 0.670082i \(0.233741\pi\)
\(128\) −19.7194 −1.74297
\(129\) −3.59636 −0.316642
\(130\) 0.898873 0.0788364
\(131\) 12.9305 1.12975 0.564874 0.825177i \(-0.308925\pi\)
0.564874 + 0.825177i \(0.308925\pi\)
\(132\) 1.98632 0.172887
\(133\) 0 0
\(134\) −13.9342 −1.20373
\(135\) 0.0978008 0.00841735
\(136\) 13.0872 1.12222
\(137\) 21.9250 1.87318 0.936588 0.350433i \(-0.113966\pi\)
0.936588 + 0.350433i \(0.113966\pi\)
\(138\) −16.6120 −1.41411
\(139\) −10.9812 −0.931417 −0.465709 0.884938i \(-0.654201\pi\)
−0.465709 + 0.884938i \(0.654201\pi\)
\(140\) 0 0
\(141\) −2.71266 −0.228447
\(142\) −0.572638 −0.0480547
\(143\) 2.30132 0.192446
\(144\) 0.810278 0.0675232
\(145\) −0.210738 −0.0175009
\(146\) 7.24544 0.599637
\(147\) 0 0
\(148\) −8.78249 −0.721916
\(149\) −8.01535 −0.656643 −0.328321 0.944566i \(-0.606483\pi\)
−0.328321 + 0.944566i \(0.606483\pi\)
\(150\) 11.6079 0.947784
\(151\) 8.48267 0.690310 0.345155 0.938546i \(-0.387826\pi\)
0.345155 + 0.938546i \(0.387826\pi\)
\(152\) 16.2776 1.32029
\(153\) 3.98906 0.322496
\(154\) 0 0
\(155\) −0.335661 −0.0269610
\(156\) 13.4757 1.07892
\(157\) −11.6378 −0.928795 −0.464398 0.885627i \(-0.653729\pi\)
−0.464398 + 0.885627i \(0.653729\pi\)
\(158\) 5.30006 0.421650
\(159\) −12.7249 −1.00915
\(160\) 0.457394 0.0361601
\(161\) 0 0
\(162\) 2.32604 0.182751
\(163\) −17.5198 −1.37225 −0.686127 0.727482i \(-0.740691\pi\)
−0.686127 + 0.727482i \(0.740691\pi\)
\(164\) −3.41045 −0.266312
\(165\) −0.0569614 −0.00443444
\(166\) 16.2756 1.26323
\(167\) −13.2750 −1.02725 −0.513626 0.858014i \(-0.671698\pi\)
−0.513626 + 0.858014i \(0.671698\pi\)
\(168\) 0 0
\(169\) 2.61273 0.200979
\(170\) −0.907465 −0.0695994
\(171\) 4.96154 0.379418
\(172\) 12.2652 0.935214
\(173\) −20.1883 −1.53489 −0.767444 0.641116i \(-0.778472\pi\)
−0.767444 + 0.641116i \(0.778472\pi\)
\(174\) −5.01208 −0.379965
\(175\) 0 0
\(176\) −0.471924 −0.0355726
\(177\) −2.48011 −0.186416
\(178\) −10.6593 −0.798947
\(179\) 0.347661 0.0259854 0.0129927 0.999916i \(-0.495864\pi\)
0.0129927 + 0.999916i \(0.495864\pi\)
\(180\) −0.333545 −0.0248610
\(181\) 1.09311 0.0812503 0.0406251 0.999174i \(-0.487065\pi\)
0.0406251 + 0.999174i \(0.487065\pi\)
\(182\) 0 0
\(183\) −12.5132 −0.925003
\(184\) 23.4304 1.72732
\(185\) 0.251853 0.0185166
\(186\) −7.98318 −0.585355
\(187\) −2.32332 −0.169898
\(188\) 9.25140 0.674728
\(189\) 0 0
\(190\) −1.12869 −0.0818839
\(191\) −7.50981 −0.543391 −0.271695 0.962383i \(-0.587584\pi\)
−0.271695 + 0.962383i \(0.587584\pi\)
\(192\) 12.4989 0.902034
\(193\) −1.85067 −0.133214 −0.0666071 0.997779i \(-0.521217\pi\)
−0.0666071 + 0.997779i \(0.521217\pi\)
\(194\) 23.7843 1.70762
\(195\) −0.386440 −0.0276735
\(196\) 0 0
\(197\) 18.9892 1.35293 0.676464 0.736476i \(-0.263512\pi\)
0.676464 + 0.736476i \(0.263512\pi\)
\(198\) −1.35474 −0.0962769
\(199\) 19.0072 1.34738 0.673691 0.739013i \(-0.264708\pi\)
0.673691 + 0.739013i \(0.264708\pi\)
\(200\) −16.3724 −1.15771
\(201\) 5.99051 0.422538
\(202\) 23.2072 1.63285
\(203\) 0 0
\(204\) −13.6045 −0.952506
\(205\) 0.0978008 0.00683070
\(206\) −23.7495 −1.65470
\(207\) 7.14176 0.496387
\(208\) −3.20165 −0.221994
\(209\) −2.88971 −0.199886
\(210\) 0 0
\(211\) 23.1684 1.59498 0.797489 0.603334i \(-0.206161\pi\)
0.797489 + 0.603334i \(0.206161\pi\)
\(212\) 43.3978 2.98057
\(213\) 0.246186 0.0168684
\(214\) 33.9466 2.32054
\(215\) −0.351727 −0.0239876
\(216\) −3.28076 −0.223228
\(217\) 0 0
\(218\) 3.10755 0.210470
\(219\) −3.11493 −0.210487
\(220\) 0.194264 0.0130973
\(221\) −15.7620 −1.06026
\(222\) 5.98994 0.402018
\(223\) 7.61730 0.510092 0.255046 0.966929i \(-0.417909\pi\)
0.255046 + 0.966929i \(0.417909\pi\)
\(224\) 0 0
\(225\) −4.99044 −0.332696
\(226\) −25.7128 −1.71039
\(227\) 20.5812 1.36603 0.683013 0.730407i \(-0.260669\pi\)
0.683013 + 0.730407i \(0.260669\pi\)
\(228\) −16.9211 −1.12063
\(229\) −10.9117 −0.721063 −0.360531 0.932747i \(-0.617405\pi\)
−0.360531 + 0.932747i \(0.617405\pi\)
\(230\) −1.62467 −0.107127
\(231\) 0 0
\(232\) 7.06929 0.464122
\(233\) 19.1646 1.25552 0.627758 0.778409i \(-0.283973\pi\)
0.627758 + 0.778409i \(0.283973\pi\)
\(234\) −9.19086 −0.600825
\(235\) −0.265300 −0.0173063
\(236\) 8.45828 0.550587
\(237\) −2.27858 −0.148010
\(238\) 0 0
\(239\) 23.8019 1.53961 0.769807 0.638277i \(-0.220352\pi\)
0.769807 + 0.638277i \(0.220352\pi\)
\(240\) 0.0792458 0.00511530
\(241\) 20.7925 1.33936 0.669681 0.742649i \(-0.266431\pi\)
0.669681 + 0.742649i \(0.266431\pi\)
\(242\) −24.7974 −1.59404
\(243\) −1.00000 −0.0641500
\(244\) 42.6757 2.73203
\(245\) 0 0
\(246\) 2.32604 0.148303
\(247\) −19.6045 −1.24740
\(248\) 11.2599 0.715004
\(249\) −6.99712 −0.443424
\(250\) 2.27271 0.143739
\(251\) −26.1674 −1.65167 −0.825835 0.563912i \(-0.809296\pi\)
−0.825835 + 0.563912i \(0.809296\pi\)
\(252\) 0 0
\(253\) −4.15952 −0.261507
\(254\) 38.9153 2.44176
\(255\) 0.390133 0.0244311
\(256\) −20.8703 −1.30439
\(257\) −26.6554 −1.66272 −0.831359 0.555735i \(-0.812437\pi\)
−0.831359 + 0.555735i \(0.812437\pi\)
\(258\) −8.36527 −0.520799
\(259\) 0 0
\(260\) 1.31793 0.0817348
\(261\) 2.15477 0.133377
\(262\) 30.0769 1.85816
\(263\) −14.4582 −0.891533 −0.445767 0.895149i \(-0.647069\pi\)
−0.445767 + 0.895149i \(0.647069\pi\)
\(264\) 1.91079 0.117601
\(265\) −1.24451 −0.0764495
\(266\) 0 0
\(267\) 4.58259 0.280450
\(268\) −20.4304 −1.24798
\(269\) 0.964369 0.0587986 0.0293993 0.999568i \(-0.490641\pi\)
0.0293993 + 0.999568i \(0.490641\pi\)
\(270\) 0.227488 0.0138445
\(271\) −23.3860 −1.42060 −0.710298 0.703901i \(-0.751440\pi\)
−0.710298 + 0.703901i \(0.751440\pi\)
\(272\) 3.23225 0.195984
\(273\) 0 0
\(274\) 50.9983 3.08092
\(275\) 2.90654 0.175271
\(276\) −24.3566 −1.46610
\(277\) 1.72664 0.103744 0.0518720 0.998654i \(-0.483481\pi\)
0.0518720 + 0.998654i \(0.483481\pi\)
\(278\) −25.5428 −1.53196
\(279\) 3.43209 0.205474
\(280\) 0 0
\(281\) −15.4609 −0.922322 −0.461161 0.887316i \(-0.652567\pi\)
−0.461161 + 0.887316i \(0.652567\pi\)
\(282\) −6.30975 −0.375740
\(283\) 1.79710 0.106826 0.0534132 0.998572i \(-0.482990\pi\)
0.0534132 + 0.998572i \(0.482990\pi\)
\(284\) −0.839605 −0.0498214
\(285\) 0.485242 0.0287433
\(286\) 5.35296 0.316527
\(287\) 0 0
\(288\) −4.67679 −0.275583
\(289\) −1.08739 −0.0639643
\(290\) −0.490185 −0.0287847
\(291\) −10.2253 −0.599415
\(292\) 10.6233 0.621682
\(293\) −12.3247 −0.720018 −0.360009 0.932949i \(-0.617226\pi\)
−0.360009 + 0.932949i \(0.617226\pi\)
\(294\) 0 0
\(295\) −0.242556 −0.0141222
\(296\) −8.44852 −0.491060
\(297\) 0.582422 0.0337956
\(298\) −18.6440 −1.08002
\(299\) −28.2192 −1.63196
\(300\) 17.0196 0.982629
\(301\) 0 0
\(302\) 19.7310 1.13539
\(303\) −9.97712 −0.573171
\(304\) 4.02023 0.230576
\(305\) −1.22380 −0.0700746
\(306\) 9.27871 0.530428
\(307\) 8.89441 0.507631 0.253815 0.967253i \(-0.418314\pi\)
0.253815 + 0.967253i \(0.418314\pi\)
\(308\) 0 0
\(309\) 10.2103 0.580841
\(310\) −0.780761 −0.0443443
\(311\) −7.36424 −0.417588 −0.208794 0.977960i \(-0.566954\pi\)
−0.208794 + 0.977960i \(0.566954\pi\)
\(312\) 12.9633 0.733900
\(313\) −9.03728 −0.510817 −0.255409 0.966833i \(-0.582210\pi\)
−0.255409 + 0.966833i \(0.582210\pi\)
\(314\) −27.0699 −1.52764
\(315\) 0 0
\(316\) 7.77098 0.437152
\(317\) −0.357106 −0.0200571 −0.0100285 0.999950i \(-0.503192\pi\)
−0.0100285 + 0.999950i \(0.503192\pi\)
\(318\) −29.5987 −1.65981
\(319\) −1.25499 −0.0702658
\(320\) 1.22241 0.0683346
\(321\) −14.5942 −0.814568
\(322\) 0 0
\(323\) 19.7919 1.10125
\(324\) 3.41045 0.189470
\(325\) 19.7187 1.09380
\(326\) −40.7516 −2.25702
\(327\) −1.33598 −0.0738801
\(328\) −3.28076 −0.181150
\(329\) 0 0
\(330\) −0.132494 −0.00729357
\(331\) −11.3319 −0.622858 −0.311429 0.950269i \(-0.600808\pi\)
−0.311429 + 0.950269i \(0.600808\pi\)
\(332\) 23.8633 1.30967
\(333\) −2.57517 −0.141118
\(334\) −30.8782 −1.68958
\(335\) 0.585877 0.0320099
\(336\) 0 0
\(337\) −5.50898 −0.300093 −0.150047 0.988679i \(-0.547942\pi\)
−0.150047 + 0.988679i \(0.547942\pi\)
\(338\) 6.07730 0.330562
\(339\) 11.0543 0.600389
\(340\) −1.33053 −0.0721581
\(341\) −1.99893 −0.108248
\(342\) 11.5407 0.624051
\(343\) 0 0
\(344\) 11.7988 0.636149
\(345\) 0.698470 0.0376044
\(346\) −46.9587 −2.52452
\(347\) 8.24953 0.442858 0.221429 0.975177i \(-0.428928\pi\)
0.221429 + 0.975177i \(0.428928\pi\)
\(348\) −7.34874 −0.393934
\(349\) 16.3307 0.874162 0.437081 0.899422i \(-0.356012\pi\)
0.437081 + 0.899422i \(0.356012\pi\)
\(350\) 0 0
\(351\) 3.95129 0.210904
\(352\) 2.72387 0.145183
\(353\) −9.97755 −0.531051 −0.265526 0.964104i \(-0.585545\pi\)
−0.265526 + 0.964104i \(0.585545\pi\)
\(354\) −5.76882 −0.306609
\(355\) 0.0240772 0.00127788
\(356\) −15.6287 −0.828320
\(357\) 0 0
\(358\) 0.808672 0.0427397
\(359\) 12.3374 0.651141 0.325571 0.945518i \(-0.394444\pi\)
0.325571 + 0.945518i \(0.394444\pi\)
\(360\) −0.320861 −0.0169109
\(361\) 5.61687 0.295625
\(362\) 2.54262 0.133637
\(363\) 10.6608 0.559546
\(364\) 0 0
\(365\) −0.304642 −0.0159457
\(366\) −29.1062 −1.52140
\(367\) −10.5212 −0.549204 −0.274602 0.961558i \(-0.588546\pi\)
−0.274602 + 0.961558i \(0.588546\pi\)
\(368\) 5.78682 0.301659
\(369\) −1.00000 −0.0520579
\(370\) 0.585821 0.0304554
\(371\) 0 0
\(372\) −11.7050 −0.606876
\(373\) −23.2163 −1.20209 −0.601046 0.799214i \(-0.705249\pi\)
−0.601046 + 0.799214i \(0.705249\pi\)
\(374\) −5.40413 −0.279441
\(375\) −0.977072 −0.0504558
\(376\) 8.89960 0.458962
\(377\) −8.51413 −0.438500
\(378\) 0 0
\(379\) −8.66512 −0.445097 −0.222549 0.974922i \(-0.571438\pi\)
−0.222549 + 0.974922i \(0.571438\pi\)
\(380\) −1.65490 −0.0848943
\(381\) −16.7303 −0.857119
\(382\) −17.4681 −0.893746
\(383\) −7.45570 −0.380969 −0.190484 0.981690i \(-0.561006\pi\)
−0.190484 + 0.981690i \(0.561006\pi\)
\(384\) 19.7194 1.00630
\(385\) 0 0
\(386\) −4.30473 −0.219105
\(387\) 3.59636 0.182813
\(388\) 34.8727 1.77040
\(389\) −8.66253 −0.439208 −0.219604 0.975589i \(-0.570476\pi\)
−0.219604 + 0.975589i \(0.570476\pi\)
\(390\) −0.898873 −0.0455162
\(391\) 28.4889 1.44075
\(392\) 0 0
\(393\) −12.9305 −0.652260
\(394\) 44.1697 2.22524
\(395\) −0.222847 −0.0112126
\(396\) −1.98632 −0.0998165
\(397\) −14.6556 −0.735546 −0.367773 0.929916i \(-0.619880\pi\)
−0.367773 + 0.929916i \(0.619880\pi\)
\(398\) 44.2114 2.21611
\(399\) 0 0
\(400\) −4.04364 −0.202182
\(401\) −14.6728 −0.732722 −0.366361 0.930473i \(-0.619397\pi\)
−0.366361 + 0.930473i \(0.619397\pi\)
\(402\) 13.9342 0.694973
\(403\) −13.5612 −0.675532
\(404\) 34.0265 1.69288
\(405\) −0.0978008 −0.00485976
\(406\) 0 0
\(407\) 1.49984 0.0743441
\(408\) −13.0872 −0.647911
\(409\) 2.76287 0.136615 0.0683075 0.997664i \(-0.478240\pi\)
0.0683075 + 0.997664i \(0.478240\pi\)
\(410\) 0.227488 0.0112348
\(411\) −21.9250 −1.08148
\(412\) −34.8216 −1.71554
\(413\) 0 0
\(414\) 16.6120 0.816436
\(415\) −0.684324 −0.0335921
\(416\) 18.4794 0.906026
\(417\) 10.9812 0.537754
\(418\) −6.72158 −0.328763
\(419\) −30.1742 −1.47411 −0.737054 0.675834i \(-0.763784\pi\)
−0.737054 + 0.675834i \(0.763784\pi\)
\(420\) 0 0
\(421\) −6.93295 −0.337891 −0.168946 0.985625i \(-0.554036\pi\)
−0.168946 + 0.985625i \(0.554036\pi\)
\(422\) 53.8906 2.62335
\(423\) 2.71266 0.131894
\(424\) 41.7475 2.02744
\(425\) −19.9071 −0.965639
\(426\) 0.572638 0.0277444
\(427\) 0 0
\(428\) 49.7727 2.40586
\(429\) −2.30132 −0.111109
\(430\) −0.818130 −0.0394537
\(431\) −18.9984 −0.915119 −0.457559 0.889179i \(-0.651276\pi\)
−0.457559 + 0.889179i \(0.651276\pi\)
\(432\) −0.810278 −0.0389845
\(433\) 28.4832 1.36881 0.684407 0.729100i \(-0.260061\pi\)
0.684407 + 0.729100i \(0.260061\pi\)
\(434\) 0 0
\(435\) 0.210738 0.0101041
\(436\) 4.55631 0.218208
\(437\) 35.4341 1.69504
\(438\) −7.24544 −0.346200
\(439\) −18.3921 −0.877809 −0.438904 0.898534i \(-0.644633\pi\)
−0.438904 + 0.898534i \(0.644633\pi\)
\(440\) 0.186877 0.00890900
\(441\) 0 0
\(442\) −36.6629 −1.74388
\(443\) 5.49006 0.260841 0.130420 0.991459i \(-0.458367\pi\)
0.130420 + 0.991459i \(0.458367\pi\)
\(444\) 8.78249 0.416798
\(445\) 0.448181 0.0212458
\(446\) 17.7181 0.838978
\(447\) 8.01535 0.379113
\(448\) 0 0
\(449\) −25.1872 −1.18866 −0.594329 0.804222i \(-0.702582\pi\)
−0.594329 + 0.804222i \(0.702582\pi\)
\(450\) −11.6079 −0.547204
\(451\) 0.582422 0.0274252
\(452\) −37.7003 −1.77327
\(453\) −8.48267 −0.398551
\(454\) 47.8728 2.24678
\(455\) 0 0
\(456\) −16.2776 −0.762270
\(457\) 37.8522 1.77065 0.885326 0.464971i \(-0.153935\pi\)
0.885326 + 0.464971i \(0.153935\pi\)
\(458\) −25.3809 −1.18597
\(459\) −3.98906 −0.186193
\(460\) −2.38210 −0.111066
\(461\) −9.06531 −0.422213 −0.211107 0.977463i \(-0.567707\pi\)
−0.211107 + 0.977463i \(0.567707\pi\)
\(462\) 0 0
\(463\) 6.59721 0.306598 0.153299 0.988180i \(-0.451010\pi\)
0.153299 + 0.988180i \(0.451010\pi\)
\(464\) 1.74596 0.0810543
\(465\) 0.335661 0.0155659
\(466\) 44.5776 2.06502
\(467\) −4.20780 −0.194714 −0.0973569 0.995250i \(-0.531039\pi\)
−0.0973569 + 0.995250i \(0.531039\pi\)
\(468\) −13.4757 −0.622914
\(469\) 0 0
\(470\) −0.617099 −0.0284646
\(471\) 11.6378 0.536240
\(472\) 8.13664 0.374519
\(473\) −2.09460 −0.0963098
\(474\) −5.30006 −0.243440
\(475\) −24.7602 −1.13608
\(476\) 0 0
\(477\) 12.7249 0.582635
\(478\) 55.3640 2.53229
\(479\) 8.07101 0.368774 0.184387 0.982854i \(-0.440970\pi\)
0.184387 + 0.982854i \(0.440970\pi\)
\(480\) −0.457394 −0.0208771
\(481\) 10.1752 0.463951
\(482\) 48.3641 2.20292
\(483\) 0 0
\(484\) −36.3581 −1.65264
\(485\) −1.00004 −0.0454094
\(486\) −2.32604 −0.105511
\(487\) −24.1297 −1.09342 −0.546711 0.837322i \(-0.684120\pi\)
−0.546711 + 0.837322i \(0.684120\pi\)
\(488\) 41.0529 1.85838
\(489\) 17.5198 0.792271
\(490\) 0 0
\(491\) 37.6556 1.69937 0.849687 0.527287i \(-0.176791\pi\)
0.849687 + 0.527287i \(0.176791\pi\)
\(492\) 3.41045 0.153755
\(493\) 8.59551 0.387122
\(494\) −45.6008 −2.05168
\(495\) 0.0569614 0.00256022
\(496\) 2.78095 0.124868
\(497\) 0 0
\(498\) −16.2756 −0.729325
\(499\) 34.3383 1.53719 0.768596 0.639735i \(-0.220956\pi\)
0.768596 + 0.639735i \(0.220956\pi\)
\(500\) 3.33226 0.149023
\(501\) 13.2750 0.593084
\(502\) −60.8663 −2.71660
\(503\) −33.8797 −1.51062 −0.755310 0.655368i \(-0.772514\pi\)
−0.755310 + 0.655368i \(0.772514\pi\)
\(504\) 0 0
\(505\) −0.975770 −0.0434212
\(506\) −9.67521 −0.430116
\(507\) −2.61273 −0.116035
\(508\) 57.0579 2.53153
\(509\) 12.2614 0.543476 0.271738 0.962371i \(-0.412402\pi\)
0.271738 + 0.962371i \(0.412402\pi\)
\(510\) 0.907465 0.0401832
\(511\) 0 0
\(512\) −9.10617 −0.402439
\(513\) −4.96154 −0.219057
\(514\) −62.0015 −2.73477
\(515\) 0.998571 0.0440023
\(516\) −12.2652 −0.539946
\(517\) −1.57991 −0.0694846
\(518\) 0 0
\(519\) 20.1883 0.886168
\(520\) 1.26782 0.0555975
\(521\) 29.4757 1.29135 0.645676 0.763611i \(-0.276576\pi\)
0.645676 + 0.763611i \(0.276576\pi\)
\(522\) 5.01208 0.219373
\(523\) 41.1371 1.79880 0.899399 0.437129i \(-0.144005\pi\)
0.899399 + 0.437129i \(0.144005\pi\)
\(524\) 44.0990 1.92647
\(525\) 0 0
\(526\) −33.6304 −1.46636
\(527\) 13.6908 0.596382
\(528\) 0.471924 0.0205379
\(529\) 28.0048 1.21760
\(530\) −2.89477 −0.125741
\(531\) 2.48011 0.107627
\(532\) 0 0
\(533\) 3.95129 0.171150
\(534\) 10.6593 0.461272
\(535\) −1.42732 −0.0617085
\(536\) −19.6535 −0.848900
\(537\) −0.347661 −0.0150027
\(538\) 2.24316 0.0967095
\(539\) 0 0
\(540\) 0.333545 0.0143535
\(541\) −15.5031 −0.666529 −0.333264 0.942833i \(-0.608150\pi\)
−0.333264 + 0.942833i \(0.608150\pi\)
\(542\) −54.3967 −2.33654
\(543\) −1.09311 −0.0469099
\(544\) −18.6560 −0.799870
\(545\) −0.130660 −0.00559687
\(546\) 0 0
\(547\) 25.8851 1.10677 0.553384 0.832926i \(-0.313336\pi\)
0.553384 + 0.832926i \(0.313336\pi\)
\(548\) 74.7740 3.19419
\(549\) 12.5132 0.534051
\(550\) 6.76072 0.288278
\(551\) 10.6910 0.455451
\(552\) −23.4304 −0.997266
\(553\) 0 0
\(554\) 4.01624 0.170634
\(555\) −0.251853 −0.0106906
\(556\) −37.4510 −1.58828
\(557\) −19.3798 −0.821148 −0.410574 0.911827i \(-0.634672\pi\)
−0.410574 + 0.911827i \(0.634672\pi\)
\(558\) 7.98318 0.337955
\(559\) −14.2103 −0.601031
\(560\) 0 0
\(561\) 2.32332 0.0980906
\(562\) −35.9627 −1.51700
\(563\) 2.07786 0.0875715 0.0437857 0.999041i \(-0.486058\pi\)
0.0437857 + 0.999041i \(0.486058\pi\)
\(564\) −9.25140 −0.389554
\(565\) 1.08112 0.0454832
\(566\) 4.18012 0.175704
\(567\) 0 0
\(568\) −0.807678 −0.0338894
\(569\) −3.58169 −0.150152 −0.0750762 0.997178i \(-0.523920\pi\)
−0.0750762 + 0.997178i \(0.523920\pi\)
\(570\) 1.12869 0.0472757
\(571\) 34.8356 1.45783 0.728913 0.684607i \(-0.240026\pi\)
0.728913 + 0.684607i \(0.240026\pi\)
\(572\) 7.84855 0.328164
\(573\) 7.50981 0.313727
\(574\) 0 0
\(575\) −35.6405 −1.48631
\(576\) −12.4989 −0.520790
\(577\) 10.9314 0.455080 0.227540 0.973769i \(-0.426932\pi\)
0.227540 + 0.973769i \(0.426932\pi\)
\(578\) −2.52932 −0.105206
\(579\) 1.85067 0.0769112
\(580\) −0.718712 −0.0298429
\(581\) 0 0
\(582\) −23.7843 −0.985892
\(583\) −7.41129 −0.306944
\(584\) 10.2193 0.422879
\(585\) 0.386440 0.0159773
\(586\) −28.6678 −1.18426
\(587\) −12.0086 −0.495647 −0.247823 0.968805i \(-0.579715\pi\)
−0.247823 + 0.968805i \(0.579715\pi\)
\(588\) 0 0
\(589\) 17.0285 0.701646
\(590\) −0.564195 −0.0232275
\(591\) −18.9892 −0.781113
\(592\) −2.08660 −0.0857589
\(593\) 28.7042 1.17874 0.589370 0.807863i \(-0.299376\pi\)
0.589370 + 0.807863i \(0.299376\pi\)
\(594\) 1.35474 0.0555855
\(595\) 0 0
\(596\) −27.3360 −1.11972
\(597\) −19.0072 −0.777911
\(598\) −65.6390 −2.68418
\(599\) −31.7023 −1.29532 −0.647661 0.761929i \(-0.724253\pi\)
−0.647661 + 0.761929i \(0.724253\pi\)
\(600\) 16.3724 0.668402
\(601\) 11.5206 0.469933 0.234967 0.972003i \(-0.424502\pi\)
0.234967 + 0.972003i \(0.424502\pi\)
\(602\) 0 0
\(603\) −5.99051 −0.243953
\(604\) 28.9297 1.17713
\(605\) 1.04263 0.0423891
\(606\) −23.2072 −0.942726
\(607\) −0.0495832 −0.00201252 −0.00100626 0.999999i \(-0.500320\pi\)
−0.00100626 + 0.999999i \(0.500320\pi\)
\(608\) −23.2041 −0.941050
\(609\) 0 0
\(610\) −2.84661 −0.115256
\(611\) −10.7185 −0.433625
\(612\) 13.6045 0.549929
\(613\) −35.4076 −1.43010 −0.715050 0.699073i \(-0.753596\pi\)
−0.715050 + 0.699073i \(0.753596\pi\)
\(614\) 20.6887 0.834929
\(615\) −0.0978008 −0.00394371
\(616\) 0 0
\(617\) −27.3399 −1.10066 −0.550332 0.834946i \(-0.685499\pi\)
−0.550332 + 0.834946i \(0.685499\pi\)
\(618\) 23.7495 0.955343
\(619\) −40.2579 −1.61810 −0.809051 0.587739i \(-0.800018\pi\)
−0.809051 + 0.587739i \(0.800018\pi\)
\(620\) −1.14476 −0.0459746
\(621\) −7.14176 −0.286589
\(622\) −17.1295 −0.686830
\(623\) 0 0
\(624\) 3.20165 0.128168
\(625\) 24.8566 0.994265
\(626\) −21.0211 −0.840171
\(627\) 2.88971 0.115404
\(628\) −39.6901 −1.58381
\(629\) −10.2725 −0.409592
\(630\) 0 0
\(631\) −42.6224 −1.69677 −0.848385 0.529380i \(-0.822425\pi\)
−0.848385 + 0.529380i \(0.822425\pi\)
\(632\) 7.47548 0.297359
\(633\) −23.1684 −0.920861
\(634\) −0.830643 −0.0329890
\(635\) −1.63624 −0.0649321
\(636\) −43.3978 −1.72083
\(637\) 0 0
\(638\) −2.91915 −0.115570
\(639\) −0.246186 −0.00973896
\(640\) 1.92858 0.0762337
\(641\) 35.9301 1.41915 0.709577 0.704628i \(-0.248886\pi\)
0.709577 + 0.704628i \(0.248886\pi\)
\(642\) −33.9466 −1.33977
\(643\) −18.9359 −0.746760 −0.373380 0.927678i \(-0.621801\pi\)
−0.373380 + 0.927678i \(0.621801\pi\)
\(644\) 0 0
\(645\) 0.351727 0.0138492
\(646\) 46.0367 1.81129
\(647\) 0.964507 0.0379187 0.0189593 0.999820i \(-0.493965\pi\)
0.0189593 + 0.999820i \(0.493965\pi\)
\(648\) 3.28076 0.128881
\(649\) −1.44447 −0.0567004
\(650\) 45.8664 1.79903
\(651\) 0 0
\(652\) −59.7503 −2.34000
\(653\) −4.40352 −0.172323 −0.0861615 0.996281i \(-0.527460\pi\)
−0.0861615 + 0.996281i \(0.527460\pi\)
\(654\) −3.10755 −0.121515
\(655\) −1.26462 −0.0494127
\(656\) −0.810278 −0.0316360
\(657\) 3.11493 0.121525
\(658\) 0 0
\(659\) −11.0759 −0.431455 −0.215728 0.976454i \(-0.569212\pi\)
−0.215728 + 0.976454i \(0.569212\pi\)
\(660\) −0.194264 −0.00756171
\(661\) 45.7318 1.77876 0.889381 0.457167i \(-0.151136\pi\)
0.889381 + 0.457167i \(0.151136\pi\)
\(662\) −26.3584 −1.02445
\(663\) 15.7620 0.612144
\(664\) 22.9559 0.890862
\(665\) 0 0
\(666\) −5.98994 −0.232105
\(667\) 15.3889 0.595859
\(668\) −45.2738 −1.75170
\(669\) −7.61730 −0.294502
\(670\) 1.36277 0.0526485
\(671\) −7.28797 −0.281349
\(672\) 0 0
\(673\) 42.4285 1.63550 0.817750 0.575574i \(-0.195221\pi\)
0.817750 + 0.575574i \(0.195221\pi\)
\(674\) −12.8141 −0.493580
\(675\) 4.99044 0.192082
\(676\) 8.91058 0.342715
\(677\) −12.5797 −0.483478 −0.241739 0.970341i \(-0.577718\pi\)
−0.241739 + 0.970341i \(0.577718\pi\)
\(678\) 25.7128 0.987494
\(679\) 0 0
\(680\) −1.27994 −0.0490833
\(681\) −20.5812 −0.788675
\(682\) −4.64958 −0.178042
\(683\) −0.545437 −0.0208706 −0.0104353 0.999946i \(-0.503322\pi\)
−0.0104353 + 0.999946i \(0.503322\pi\)
\(684\) 16.9211 0.646994
\(685\) −2.14428 −0.0819286
\(686\) 0 0
\(687\) 10.9117 0.416306
\(688\) 2.91405 0.111097
\(689\) −50.2800 −1.91551
\(690\) 1.62467 0.0618500
\(691\) −40.0206 −1.52246 −0.761228 0.648484i \(-0.775403\pi\)
−0.761228 + 0.648484i \(0.775403\pi\)
\(692\) −68.8512 −2.61733
\(693\) 0 0
\(694\) 19.1887 0.728393
\(695\) 1.07397 0.0407382
\(696\) −7.06929 −0.267961
\(697\) −3.98906 −0.151096
\(698\) 37.9858 1.43778
\(699\) −19.1646 −0.724872
\(700\) 0 0
\(701\) −33.0999 −1.25017 −0.625083 0.780558i \(-0.714935\pi\)
−0.625083 + 0.780558i \(0.714935\pi\)
\(702\) 9.19086 0.346887
\(703\) −12.7768 −0.481886
\(704\) 7.27967 0.274363
\(705\) 0.265300 0.00999179
\(706\) −23.2082 −0.873450
\(707\) 0 0
\(708\) −8.45828 −0.317882
\(709\) 18.6301 0.699669 0.349835 0.936811i \(-0.386238\pi\)
0.349835 + 0.936811i \(0.386238\pi\)
\(710\) 0.0560044 0.00210181
\(711\) 2.27858 0.0854534
\(712\) −15.0344 −0.563438
\(713\) 24.5112 0.917952
\(714\) 0 0
\(715\) −0.225071 −0.00841718
\(716\) 1.18568 0.0443110
\(717\) −23.8019 −0.888897
\(718\) 28.6972 1.07097
\(719\) −1.94161 −0.0724099 −0.0362050 0.999344i \(-0.511527\pi\)
−0.0362050 + 0.999344i \(0.511527\pi\)
\(720\) −0.0792458 −0.00295332
\(721\) 0 0
\(722\) 13.0650 0.486231
\(723\) −20.7925 −0.773281
\(724\) 3.72800 0.138550
\(725\) −10.7532 −0.399365
\(726\) 24.7974 0.920317
\(727\) −29.7690 −1.10407 −0.552036 0.833820i \(-0.686149\pi\)
−0.552036 + 0.833820i \(0.686149\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.708609 −0.0262268
\(731\) 14.3461 0.530610
\(732\) −42.6757 −1.57734
\(733\) 45.3347 1.67448 0.837238 0.546839i \(-0.184169\pi\)
0.837238 + 0.546839i \(0.184169\pi\)
\(734\) −24.4728 −0.903307
\(735\) 0 0
\(736\) −33.4005 −1.23116
\(737\) 3.48901 0.128519
\(738\) −2.32604 −0.0856226
\(739\) 18.5022 0.680614 0.340307 0.940314i \(-0.389469\pi\)
0.340307 + 0.940314i \(0.389469\pi\)
\(740\) 0.858934 0.0315750
\(741\) 19.6045 0.720189
\(742\) 0 0
\(743\) 3.94213 0.144623 0.0723114 0.997382i \(-0.476962\pi\)
0.0723114 + 0.997382i \(0.476962\pi\)
\(744\) −11.2599 −0.412808
\(745\) 0.783907 0.0287201
\(746\) −54.0019 −1.97715
\(747\) 6.99712 0.256011
\(748\) −7.92357 −0.289714
\(749\) 0 0
\(750\) −2.27271 −0.0829875
\(751\) −41.1338 −1.50099 −0.750496 0.660875i \(-0.770185\pi\)
−0.750496 + 0.660875i \(0.770185\pi\)
\(752\) 2.19801 0.0801532
\(753\) 26.1674 0.953592
\(754\) −19.8042 −0.721226
\(755\) −0.829612 −0.0301927
\(756\) 0 0
\(757\) −16.5287 −0.600747 −0.300373 0.953822i \(-0.597111\pi\)
−0.300373 + 0.953822i \(0.597111\pi\)
\(758\) −20.1554 −0.732077
\(759\) 4.15952 0.150981
\(760\) −1.59197 −0.0577467
\(761\) 5.60469 0.203170 0.101585 0.994827i \(-0.467609\pi\)
0.101585 + 0.994827i \(0.467609\pi\)
\(762\) −38.9153 −1.40975
\(763\) 0 0
\(764\) −25.6118 −0.926604
\(765\) −0.390133 −0.0141053
\(766\) −17.3422 −0.626601
\(767\) −9.79963 −0.353844
\(768\) 20.8703 0.753091
\(769\) −2.94131 −0.106066 −0.0530331 0.998593i \(-0.516889\pi\)
−0.0530331 + 0.998593i \(0.516889\pi\)
\(770\) 0 0
\(771\) 26.6554 0.959971
\(772\) −6.31162 −0.227160
\(773\) 12.8639 0.462683 0.231342 0.972873i \(-0.425688\pi\)
0.231342 + 0.972873i \(0.425688\pi\)
\(774\) 8.36527 0.300683
\(775\) −17.1276 −0.615243
\(776\) 33.5467 1.20425
\(777\) 0 0
\(778\) −20.1494 −0.722390
\(779\) −4.96154 −0.177766
\(780\) −1.31793 −0.0471896
\(781\) 0.143384 0.00513069
\(782\) 66.2663 2.36968
\(783\) −2.15477 −0.0770052
\(784\) 0 0
\(785\) 1.13818 0.0406235
\(786\) −30.0769 −1.07281
\(787\) −10.8028 −0.385078 −0.192539 0.981289i \(-0.561672\pi\)
−0.192539 + 0.981289i \(0.561672\pi\)
\(788\) 64.7619 2.30705
\(789\) 14.4582 0.514727
\(790\) −0.518350 −0.0184421
\(791\) 0 0
\(792\) −1.91079 −0.0678970
\(793\) −49.4434 −1.75578
\(794\) −34.0896 −1.20979
\(795\) 1.24451 0.0441382
\(796\) 64.8230 2.29759
\(797\) 32.2200 1.14129 0.570645 0.821197i \(-0.306693\pi\)
0.570645 + 0.821197i \(0.306693\pi\)
\(798\) 0 0
\(799\) 10.8210 0.382818
\(800\) 23.3392 0.825166
\(801\) −4.58259 −0.161918
\(802\) −34.1294 −1.20515
\(803\) −1.81420 −0.0640218
\(804\) 20.4304 0.720523
\(805\) 0 0
\(806\) −31.5439 −1.11109
\(807\) −0.964369 −0.0339474
\(808\) 32.7326 1.15153
\(809\) −30.0911 −1.05795 −0.528973 0.848639i \(-0.677423\pi\)
−0.528973 + 0.848639i \(0.677423\pi\)
\(810\) −0.227488 −0.00799312
\(811\) −46.8676 −1.64574 −0.822871 0.568228i \(-0.807629\pi\)
−0.822871 + 0.568228i \(0.807629\pi\)
\(812\) 0 0
\(813\) 23.3860 0.820182
\(814\) 3.48867 0.122278
\(815\) 1.71345 0.0600194
\(816\) −3.23225 −0.113151
\(817\) 17.8435 0.624264
\(818\) 6.42653 0.224698
\(819\) 0 0
\(820\) 0.333545 0.0116479
\(821\) −41.4566 −1.44684 −0.723422 0.690406i \(-0.757432\pi\)
−0.723422 + 0.690406i \(0.757432\pi\)
\(822\) −50.9983 −1.77877
\(823\) −36.4738 −1.27140 −0.635699 0.771937i \(-0.719288\pi\)
−0.635699 + 0.771937i \(0.719288\pi\)
\(824\) −33.4975 −1.16694
\(825\) −2.90654 −0.101193
\(826\) 0 0
\(827\) −5.77420 −0.200789 −0.100394 0.994948i \(-0.532010\pi\)
−0.100394 + 0.994948i \(0.532010\pi\)
\(828\) 24.3566 0.846452
\(829\) 19.1399 0.664755 0.332378 0.943146i \(-0.392149\pi\)
0.332378 + 0.943146i \(0.392149\pi\)
\(830\) −1.59176 −0.0552509
\(831\) −1.72664 −0.0598966
\(832\) 49.3870 1.71219
\(833\) 0 0
\(834\) 25.5428 0.884475
\(835\) 1.29831 0.0449297
\(836\) −9.85522 −0.340850
\(837\) −3.43209 −0.118631
\(838\) −70.1864 −2.42455
\(839\) 32.7657 1.13120 0.565599 0.824680i \(-0.308645\pi\)
0.565599 + 0.824680i \(0.308645\pi\)
\(840\) 0 0
\(841\) −24.3570 −0.839895
\(842\) −16.1263 −0.555749
\(843\) 15.4609 0.532503
\(844\) 79.0147 2.71980
\(845\) −0.255527 −0.00879039
\(846\) 6.30975 0.216934
\(847\) 0 0
\(848\) 10.3107 0.354072
\(849\) −1.79710 −0.0616763
\(850\) −46.3048 −1.58824
\(851\) −18.3912 −0.630444
\(852\) 0.839605 0.0287644
\(853\) 42.3085 1.44862 0.724308 0.689477i \(-0.242159\pi\)
0.724308 + 0.689477i \(0.242159\pi\)
\(854\) 0 0
\(855\) −0.485242 −0.0165949
\(856\) 47.8801 1.63651
\(857\) 23.3694 0.798283 0.399141 0.916889i \(-0.369308\pi\)
0.399141 + 0.916889i \(0.369308\pi\)
\(858\) −5.35296 −0.182747
\(859\) −5.02568 −0.171474 −0.0857371 0.996318i \(-0.527324\pi\)
−0.0857371 + 0.996318i \(0.527324\pi\)
\(860\) −1.19955 −0.0409042
\(861\) 0 0
\(862\) −44.1909 −1.50515
\(863\) 17.7022 0.602591 0.301296 0.953531i \(-0.402581\pi\)
0.301296 + 0.953531i \(0.402581\pi\)
\(864\) 4.67679 0.159108
\(865\) 1.97443 0.0671327
\(866\) 66.2530 2.25137
\(867\) 1.08739 0.0369298
\(868\) 0 0
\(869\) −1.32710 −0.0450186
\(870\) 0.490185 0.0166188
\(871\) 23.6703 0.802037
\(872\) 4.38305 0.148429
\(873\) 10.2253 0.346072
\(874\) 82.4212 2.78794
\(875\) 0 0
\(876\) −10.6233 −0.358928
\(877\) 4.97821 0.168102 0.0840512 0.996461i \(-0.473214\pi\)
0.0840512 + 0.996461i \(0.473214\pi\)
\(878\) −42.7808 −1.44378
\(879\) 12.3247 0.415703
\(880\) 0.0461545 0.00155587
\(881\) −31.4164 −1.05844 −0.529222 0.848483i \(-0.677516\pi\)
−0.529222 + 0.848483i \(0.677516\pi\)
\(882\) 0 0
\(883\) −55.3269 −1.86190 −0.930950 0.365148i \(-0.881019\pi\)
−0.930950 + 0.365148i \(0.881019\pi\)
\(884\) −53.7554 −1.80799
\(885\) 0.242556 0.00815344
\(886\) 12.7701 0.429020
\(887\) 0.897270 0.0301274 0.0150637 0.999887i \(-0.495205\pi\)
0.0150637 + 0.999887i \(0.495205\pi\)
\(888\) 8.44852 0.283514
\(889\) 0 0
\(890\) 1.04249 0.0349442
\(891\) −0.582422 −0.0195119
\(892\) 25.9784 0.869822
\(893\) 13.4590 0.450387
\(894\) 18.6440 0.623549
\(895\) −0.0340015 −0.00113654
\(896\) 0 0
\(897\) 28.2192 0.942212
\(898\) −58.5864 −1.95505
\(899\) 7.39538 0.246650
\(900\) −17.0196 −0.567321
\(901\) 50.7605 1.69108
\(902\) 1.35474 0.0451078
\(903\) 0 0
\(904\) −36.2667 −1.20621
\(905\) −0.106907 −0.00355371
\(906\) −19.7310 −0.655519
\(907\) −16.4250 −0.545383 −0.272691 0.962102i \(-0.587914\pi\)
−0.272691 + 0.962102i \(0.587914\pi\)
\(908\) 70.1913 2.32938
\(909\) 9.97712 0.330920
\(910\) 0 0
\(911\) −54.6545 −1.81078 −0.905391 0.424578i \(-0.860423\pi\)
−0.905391 + 0.424578i \(0.860423\pi\)
\(912\) −4.02023 −0.133123
\(913\) −4.07528 −0.134872
\(914\) 88.0457 2.91229
\(915\) 1.22380 0.0404576
\(916\) −37.2137 −1.22958
\(917\) 0 0
\(918\) −9.27871 −0.306243
\(919\) −38.7201 −1.27726 −0.638629 0.769515i \(-0.720498\pi\)
−0.638629 + 0.769515i \(0.720498\pi\)
\(920\) −2.29152 −0.0755490
\(921\) −8.89441 −0.293081
\(922\) −21.0862 −0.694439
\(923\) 0.972753 0.0320186
\(924\) 0 0
\(925\) 12.8512 0.422545
\(926\) 15.3454 0.504280
\(927\) −10.2103 −0.335349
\(928\) −10.0774 −0.330807
\(929\) 3.66975 0.120400 0.0602002 0.998186i \(-0.480826\pi\)
0.0602002 + 0.998186i \(0.480826\pi\)
\(930\) 0.780761 0.0256022
\(931\) 0 0
\(932\) 65.3600 2.14094
\(933\) 7.36424 0.241094
\(934\) −9.78750 −0.320257
\(935\) 0.227222 0.00743096
\(936\) −12.9633 −0.423718
\(937\) −9.05184 −0.295711 −0.147855 0.989009i \(-0.547237\pi\)
−0.147855 + 0.989009i \(0.547237\pi\)
\(938\) 0 0
\(939\) 9.03728 0.294921
\(940\) −0.904794 −0.0295111
\(941\) 53.8288 1.75477 0.877384 0.479789i \(-0.159287\pi\)
0.877384 + 0.479789i \(0.159287\pi\)
\(942\) 27.0699 0.881985
\(943\) −7.14176 −0.232568
\(944\) 2.00958 0.0654061
\(945\) 0 0
\(946\) −4.87212 −0.158406
\(947\) −24.9164 −0.809674 −0.404837 0.914389i \(-0.632672\pi\)
−0.404837 + 0.914389i \(0.632672\pi\)
\(948\) −7.77098 −0.252390
\(949\) −12.3080 −0.399534
\(950\) −57.5932 −1.86857
\(951\) 0.357106 0.0115800
\(952\) 0 0
\(953\) 14.1959 0.459850 0.229925 0.973208i \(-0.426152\pi\)
0.229925 + 0.973208i \(0.426152\pi\)
\(954\) 29.5987 0.958293
\(955\) 0.734465 0.0237667
\(956\) 81.1751 2.62539
\(957\) 1.25499 0.0405680
\(958\) 18.7735 0.606544
\(959\) 0 0
\(960\) −1.22241 −0.0394530
\(961\) −19.2207 −0.620024
\(962\) 23.6680 0.763087
\(963\) 14.5942 0.470291
\(964\) 70.9118 2.28391
\(965\) 0.180997 0.00582650
\(966\) 0 0
\(967\) −15.5411 −0.499768 −0.249884 0.968276i \(-0.580392\pi\)
−0.249884 + 0.968276i \(0.580392\pi\)
\(968\) −34.9755 −1.12416
\(969\) −19.7919 −0.635807
\(970\) −2.32613 −0.0746874
\(971\) 43.8807 1.40820 0.704100 0.710101i \(-0.251351\pi\)
0.704100 + 0.710101i \(0.251351\pi\)
\(972\) −3.41045 −0.109390
\(973\) 0 0
\(974\) −56.1266 −1.79841
\(975\) −19.7187 −0.631503
\(976\) 10.1392 0.324547
\(977\) −35.5556 −1.13753 −0.568763 0.822501i \(-0.692578\pi\)
−0.568763 + 0.822501i \(0.692578\pi\)
\(978\) 40.7516 1.30309
\(979\) 2.66900 0.0853018
\(980\) 0 0
\(981\) 1.33598 0.0426547
\(982\) 87.5884 2.79506
\(983\) −47.3823 −1.51126 −0.755630 0.654999i \(-0.772669\pi\)
−0.755630 + 0.654999i \(0.772669\pi\)
\(984\) 3.28076 0.104587
\(985\) −1.85716 −0.0591741
\(986\) 19.9935 0.636722
\(987\) 0 0
\(988\) −66.8602 −2.12711
\(989\) 25.6844 0.816715
\(990\) 0.132494 0.00421094
\(991\) −15.5951 −0.495395 −0.247697 0.968837i \(-0.579674\pi\)
−0.247697 + 0.968837i \(0.579674\pi\)
\(992\) −16.0512 −0.509626
\(993\) 11.3319 0.359607
\(994\) 0 0
\(995\) −1.85891 −0.0589315
\(996\) −23.8633 −0.756139
\(997\) 42.2473 1.33799 0.668993 0.743269i \(-0.266726\pi\)
0.668993 + 0.743269i \(0.266726\pi\)
\(998\) 79.8721 2.52831
\(999\) 2.57517 0.0814747
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 \(a_p\))