Properties

Label 6026.2.a.h.1.5
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.26660 q^{3} +1.00000 q^{4} +3.87731 q^{5} +2.26660 q^{6} +1.72764 q^{7} -1.00000 q^{8} +2.13746 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.26660 q^{3} +1.00000 q^{4} +3.87731 q^{5} +2.26660 q^{6} +1.72764 q^{7} -1.00000 q^{8} +2.13746 q^{9} -3.87731 q^{10} -0.520561 q^{11} -2.26660 q^{12} -3.00911 q^{13} -1.72764 q^{14} -8.78830 q^{15} +1.00000 q^{16} -2.56209 q^{17} -2.13746 q^{18} -2.36780 q^{19} +3.87731 q^{20} -3.91587 q^{21} +0.520561 q^{22} -1.00000 q^{23} +2.26660 q^{24} +10.0335 q^{25} +3.00911 q^{26} +1.95503 q^{27} +1.72764 q^{28} -4.33964 q^{29} +8.78830 q^{30} +4.96174 q^{31} -1.00000 q^{32} +1.17990 q^{33} +2.56209 q^{34} +6.69861 q^{35} +2.13746 q^{36} -3.95452 q^{37} +2.36780 q^{38} +6.82043 q^{39} -3.87731 q^{40} +6.89824 q^{41} +3.91587 q^{42} +0.963705 q^{43} -0.520561 q^{44} +8.28759 q^{45} +1.00000 q^{46} -5.02747 q^{47} -2.26660 q^{48} -4.01525 q^{49} -10.0335 q^{50} +5.80723 q^{51} -3.00911 q^{52} +11.3159 q^{53} -1.95503 q^{54} -2.01837 q^{55} -1.72764 q^{56} +5.36684 q^{57} +4.33964 q^{58} -7.77077 q^{59} -8.78830 q^{60} -3.89047 q^{61} -4.96174 q^{62} +3.69277 q^{63} +1.00000 q^{64} -11.6672 q^{65} -1.17990 q^{66} -1.15425 q^{67} -2.56209 q^{68} +2.26660 q^{69} -6.69861 q^{70} -10.7198 q^{71} -2.13746 q^{72} -11.5928 q^{73} +3.95452 q^{74} -22.7420 q^{75} -2.36780 q^{76} -0.899343 q^{77} -6.82043 q^{78} -6.96733 q^{79} +3.87731 q^{80} -10.8436 q^{81} -6.89824 q^{82} +0.507436 q^{83} -3.91587 q^{84} -9.93403 q^{85} -0.963705 q^{86} +9.83621 q^{87} +0.520561 q^{88} +0.862086 q^{89} -8.28759 q^{90} -5.19866 q^{91} -1.00000 q^{92} -11.2463 q^{93} +5.02747 q^{94} -9.18069 q^{95} +2.26660 q^{96} +17.8161 q^{97} +4.01525 q^{98} -1.11268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + O(q^{10}) \) \( 24q - 24q^{2} - q^{3} + 24q^{4} - q^{5} + q^{6} - 7q^{7} - 24q^{8} + 27q^{9} + q^{10} - 4q^{11} - q^{12} - 5q^{13} + 7q^{14} - 6q^{15} + 24q^{16} + 5q^{17} - 27q^{18} - 20q^{19} - q^{20} + 4q^{22} - 24q^{23} + q^{24} + q^{25} + 5q^{26} - q^{27} - 7q^{28} - 6q^{29} + 6q^{30} - 23q^{31} - 24q^{32} - 6q^{33} - 5q^{34} + 5q^{35} + 27q^{36} - 6q^{37} + 20q^{38} - 39q^{39} + q^{40} - q^{41} - 44q^{43} - 4q^{44} - 13q^{45} + 24q^{46} + 32q^{47} - q^{48} - 13q^{49} - q^{50} - 44q^{51} - 5q^{52} + 21q^{53} + q^{54} - 13q^{55} + 7q^{56} + 10q^{57} + 6q^{58} - 24q^{59} - 6q^{60} - 40q^{61} + 23q^{62} - 54q^{63} + 24q^{64} - 29q^{65} + 6q^{66} - 17q^{67} + 5q^{68} + q^{69} - 5q^{70} + 4q^{71} - 27q^{72} - 16q^{73} + 6q^{74} - 36q^{75} - 20q^{76} + 24q^{77} + 39q^{78} - 53q^{79} - q^{80} + 24q^{81} + q^{82} - 9q^{83} - 37q^{85} + 44q^{86} + 7q^{87} + 4q^{88} - 46q^{89} + 13q^{90} - 44q^{91} - 24q^{92} + 23q^{93} - 32q^{94} + 28q^{95} + q^{96} - 20q^{97} + 13q^{98} - 78q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.26660 −1.30862 −0.654310 0.756226i \(-0.727041\pi\)
−0.654310 + 0.756226i \(0.727041\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.87731 1.73399 0.866993 0.498320i \(-0.166050\pi\)
0.866993 + 0.498320i \(0.166050\pi\)
\(6\) 2.26660 0.925334
\(7\) 1.72764 0.652988 0.326494 0.945199i \(-0.394133\pi\)
0.326494 + 0.945199i \(0.394133\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.13746 0.712487
\(10\) −3.87731 −1.22611
\(11\) −0.520561 −0.156955 −0.0784774 0.996916i \(-0.525006\pi\)
−0.0784774 + 0.996916i \(0.525006\pi\)
\(12\) −2.26660 −0.654310
\(13\) −3.00911 −0.834576 −0.417288 0.908774i \(-0.637019\pi\)
−0.417288 + 0.908774i \(0.637019\pi\)
\(14\) −1.72764 −0.461732
\(15\) −8.78830 −2.26913
\(16\) 1.00000 0.250000
\(17\) −2.56209 −0.621399 −0.310700 0.950508i \(-0.600563\pi\)
−0.310700 + 0.950508i \(0.600563\pi\)
\(18\) −2.13746 −0.503804
\(19\) −2.36780 −0.543210 −0.271605 0.962409i \(-0.587554\pi\)
−0.271605 + 0.962409i \(0.587554\pi\)
\(20\) 3.87731 0.866993
\(21\) −3.91587 −0.854513
\(22\) 0.520561 0.110984
\(23\) −1.00000 −0.208514
\(24\) 2.26660 0.462667
\(25\) 10.0335 2.00671
\(26\) 3.00911 0.590135
\(27\) 1.95503 0.376246
\(28\) 1.72764 0.326494
\(29\) −4.33964 −0.805851 −0.402925 0.915233i \(-0.632007\pi\)
−0.402925 + 0.915233i \(0.632007\pi\)
\(30\) 8.78830 1.60452
\(31\) 4.96174 0.891155 0.445578 0.895243i \(-0.352998\pi\)
0.445578 + 0.895243i \(0.352998\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.17990 0.205394
\(34\) 2.56209 0.439396
\(35\) 6.69861 1.13227
\(36\) 2.13746 0.356243
\(37\) −3.95452 −0.650119 −0.325060 0.945694i \(-0.605384\pi\)
−0.325060 + 0.945694i \(0.605384\pi\)
\(38\) 2.36780 0.384108
\(39\) 6.82043 1.09214
\(40\) −3.87731 −0.613057
\(41\) 6.89824 1.07732 0.538662 0.842522i \(-0.318930\pi\)
0.538662 + 0.842522i \(0.318930\pi\)
\(42\) 3.91587 0.604232
\(43\) 0.963705 0.146964 0.0734818 0.997297i \(-0.476589\pi\)
0.0734818 + 0.997297i \(0.476589\pi\)
\(44\) −0.520561 −0.0784774
\(45\) 8.28759 1.23544
\(46\) 1.00000 0.147442
\(47\) −5.02747 −0.733332 −0.366666 0.930353i \(-0.619501\pi\)
−0.366666 + 0.930353i \(0.619501\pi\)
\(48\) −2.26660 −0.327155
\(49\) −4.01525 −0.573607
\(50\) −10.0335 −1.41896
\(51\) 5.80723 0.813175
\(52\) −3.00911 −0.417288
\(53\) 11.3159 1.55436 0.777180 0.629279i \(-0.216650\pi\)
0.777180 + 0.629279i \(0.216650\pi\)
\(54\) −1.95503 −0.266046
\(55\) −2.01837 −0.272158
\(56\) −1.72764 −0.230866
\(57\) 5.36684 0.710856
\(58\) 4.33964 0.569822
\(59\) −7.77077 −1.01167 −0.505834 0.862631i \(-0.668815\pi\)
−0.505834 + 0.862631i \(0.668815\pi\)
\(60\) −8.78830 −1.13456
\(61\) −3.89047 −0.498124 −0.249062 0.968488i \(-0.580122\pi\)
−0.249062 + 0.968488i \(0.580122\pi\)
\(62\) −4.96174 −0.630142
\(63\) 3.69277 0.465245
\(64\) 1.00000 0.125000
\(65\) −11.6672 −1.44714
\(66\) −1.17990 −0.145236
\(67\) −1.15425 −0.141014 −0.0705071 0.997511i \(-0.522462\pi\)
−0.0705071 + 0.997511i \(0.522462\pi\)
\(68\) −2.56209 −0.310700
\(69\) 2.26660 0.272866
\(70\) −6.69861 −0.800637
\(71\) −10.7198 −1.27221 −0.636106 0.771602i \(-0.719456\pi\)
−0.636106 + 0.771602i \(0.719456\pi\)
\(72\) −2.13746 −0.251902
\(73\) −11.5928 −1.35684 −0.678419 0.734675i \(-0.737334\pi\)
−0.678419 + 0.734675i \(0.737334\pi\)
\(74\) 3.95452 0.459704
\(75\) −22.7420 −2.62602
\(76\) −2.36780 −0.271605
\(77\) −0.899343 −0.102490
\(78\) −6.82043 −0.772262
\(79\) −6.96733 −0.783886 −0.391943 0.919990i \(-0.628197\pi\)
−0.391943 + 0.919990i \(0.628197\pi\)
\(80\) 3.87731 0.433496
\(81\) −10.8436 −1.20485
\(82\) −6.89824 −0.761784
\(83\) 0.507436 0.0556983 0.0278492 0.999612i \(-0.491134\pi\)
0.0278492 + 0.999612i \(0.491134\pi\)
\(84\) −3.91587 −0.427256
\(85\) −9.93403 −1.07750
\(86\) −0.963705 −0.103919
\(87\) 9.83621 1.05455
\(88\) 0.520561 0.0554919
\(89\) 0.862086 0.0913809 0.0456904 0.998956i \(-0.485451\pi\)
0.0456904 + 0.998956i \(0.485451\pi\)
\(90\) −8.28759 −0.873589
\(91\) −5.19866 −0.544968
\(92\) −1.00000 −0.104257
\(93\) −11.2463 −1.16618
\(94\) 5.02747 0.518544
\(95\) −9.18069 −0.941919
\(96\) 2.26660 0.231334
\(97\) 17.8161 1.80895 0.904477 0.426522i \(-0.140261\pi\)
0.904477 + 0.426522i \(0.140261\pi\)
\(98\) 4.01525 0.405601
\(99\) −1.11268 −0.111828
\(100\) 10.0335 1.00335
\(101\) −7.99939 −0.795969 −0.397984 0.917392i \(-0.630290\pi\)
−0.397984 + 0.917392i \(0.630290\pi\)
\(102\) −5.80723 −0.575002
\(103\) −9.62187 −0.948071 −0.474036 0.880506i \(-0.657203\pi\)
−0.474036 + 0.880506i \(0.657203\pi\)
\(104\) 3.00911 0.295067
\(105\) −15.1830 −1.48171
\(106\) −11.3159 −1.09910
\(107\) −10.5980 −1.02455 −0.512273 0.858823i \(-0.671196\pi\)
−0.512273 + 0.858823i \(0.671196\pi\)
\(108\) 1.95503 0.188123
\(109\) 10.0733 0.964848 0.482424 0.875938i \(-0.339756\pi\)
0.482424 + 0.875938i \(0.339756\pi\)
\(110\) 2.01837 0.192444
\(111\) 8.96330 0.850759
\(112\) 1.72764 0.163247
\(113\) 20.6962 1.94693 0.973466 0.228830i \(-0.0734899\pi\)
0.973466 + 0.228830i \(0.0734899\pi\)
\(114\) −5.36684 −0.502651
\(115\) −3.87731 −0.361561
\(116\) −4.33964 −0.402925
\(117\) −6.43185 −0.594625
\(118\) 7.77077 0.715358
\(119\) −4.42638 −0.405766
\(120\) 8.78830 0.802258
\(121\) −10.7290 −0.975365
\(122\) 3.89047 0.352227
\(123\) −15.6355 −1.40981
\(124\) 4.96174 0.445578
\(125\) 19.5166 1.74562
\(126\) −3.69277 −0.328978
\(127\) −10.3445 −0.917926 −0.458963 0.888455i \(-0.651779\pi\)
−0.458963 + 0.888455i \(0.651779\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.18433 −0.192320
\(130\) 11.6672 1.02329
\(131\) −1.00000 −0.0873704
\(132\) 1.17990 0.102697
\(133\) −4.09071 −0.354710
\(134\) 1.15425 0.0997120
\(135\) 7.58026 0.652405
\(136\) 2.56209 0.219698
\(137\) 11.9437 1.02042 0.510211 0.860050i \(-0.329567\pi\)
0.510211 + 0.860050i \(0.329567\pi\)
\(138\) −2.26660 −0.192946
\(139\) −11.8835 −1.00794 −0.503971 0.863721i \(-0.668128\pi\)
−0.503971 + 0.863721i \(0.668128\pi\)
\(140\) 6.69861 0.566136
\(141\) 11.3952 0.959653
\(142\) 10.7198 0.899589
\(143\) 1.56642 0.130991
\(144\) 2.13746 0.178122
\(145\) −16.8261 −1.39733
\(146\) 11.5928 0.959429
\(147\) 9.10095 0.750634
\(148\) −3.95452 −0.325060
\(149\) −18.0698 −1.48033 −0.740166 0.672424i \(-0.765253\pi\)
−0.740166 + 0.672424i \(0.765253\pi\)
\(150\) 22.7420 1.85687
\(151\) −2.28863 −0.186246 −0.0931232 0.995655i \(-0.529685\pi\)
−0.0931232 + 0.995655i \(0.529685\pi\)
\(152\) 2.36780 0.192054
\(153\) −5.47637 −0.442739
\(154\) 0.899343 0.0724711
\(155\) 19.2382 1.54525
\(156\) 6.82043 0.546072
\(157\) 2.34717 0.187324 0.0936621 0.995604i \(-0.470143\pi\)
0.0936621 + 0.995604i \(0.470143\pi\)
\(158\) 6.96733 0.554291
\(159\) −25.6486 −2.03407
\(160\) −3.87731 −0.306528
\(161\) −1.72764 −0.136157
\(162\) 10.8436 0.851957
\(163\) 9.12204 0.714493 0.357246 0.934010i \(-0.383716\pi\)
0.357246 + 0.934010i \(0.383716\pi\)
\(164\) 6.89824 0.538662
\(165\) 4.57484 0.356151
\(166\) −0.507436 −0.0393847
\(167\) −1.50626 −0.116558 −0.0582790 0.998300i \(-0.518561\pi\)
−0.0582790 + 0.998300i \(0.518561\pi\)
\(168\) 3.91587 0.302116
\(169\) −3.94527 −0.303482
\(170\) 9.93403 0.761906
\(171\) −5.06107 −0.387030
\(172\) 0.963705 0.0734818
\(173\) −7.42542 −0.564544 −0.282272 0.959334i \(-0.591088\pi\)
−0.282272 + 0.959334i \(0.591088\pi\)
\(174\) −9.83621 −0.745681
\(175\) 17.3344 1.31035
\(176\) −0.520561 −0.0392387
\(177\) 17.6132 1.32389
\(178\) −0.862086 −0.0646161
\(179\) 2.57918 0.192777 0.0963885 0.995344i \(-0.469271\pi\)
0.0963885 + 0.995344i \(0.469271\pi\)
\(180\) 8.28759 0.617721
\(181\) 10.8090 0.803425 0.401712 0.915766i \(-0.368415\pi\)
0.401712 + 0.915766i \(0.368415\pi\)
\(182\) 5.19866 0.385351
\(183\) 8.81813 0.651855
\(184\) 1.00000 0.0737210
\(185\) −15.3329 −1.12730
\(186\) 11.2463 0.824616
\(187\) 1.33373 0.0975316
\(188\) −5.02747 −0.366666
\(189\) 3.37759 0.245684
\(190\) 9.18069 0.666037
\(191\) −6.53654 −0.472967 −0.236484 0.971635i \(-0.575995\pi\)
−0.236484 + 0.971635i \(0.575995\pi\)
\(192\) −2.26660 −0.163578
\(193\) 5.20786 0.374870 0.187435 0.982277i \(-0.439983\pi\)
0.187435 + 0.982277i \(0.439983\pi\)
\(194\) −17.8161 −1.27912
\(195\) 26.4449 1.89376
\(196\) −4.01525 −0.286804
\(197\) −5.47004 −0.389724 −0.194862 0.980831i \(-0.562426\pi\)
−0.194862 + 0.980831i \(0.562426\pi\)
\(198\) 1.11268 0.0790745
\(199\) −10.1452 −0.719175 −0.359588 0.933111i \(-0.617083\pi\)
−0.359588 + 0.933111i \(0.617083\pi\)
\(200\) −10.0335 −0.709478
\(201\) 2.61622 0.184534
\(202\) 7.99939 0.562835
\(203\) −7.49735 −0.526210
\(204\) 5.80723 0.406588
\(205\) 26.7466 1.86807
\(206\) 9.62187 0.670388
\(207\) −2.13746 −0.148564
\(208\) −3.00911 −0.208644
\(209\) 1.23258 0.0852595
\(210\) 15.1830 1.04773
\(211\) −22.5482 −1.55228 −0.776140 0.630560i \(-0.782825\pi\)
−0.776140 + 0.630560i \(0.782825\pi\)
\(212\) 11.3159 0.777180
\(213\) 24.2976 1.66484
\(214\) 10.5980 0.724463
\(215\) 3.73658 0.254833
\(216\) −1.95503 −0.133023
\(217\) 8.57212 0.581913
\(218\) −10.0733 −0.682251
\(219\) 26.2763 1.77558
\(220\) −2.01837 −0.136079
\(221\) 7.70962 0.518605
\(222\) −8.96330 −0.601577
\(223\) 4.64685 0.311176 0.155588 0.987822i \(-0.450273\pi\)
0.155588 + 0.987822i \(0.450273\pi\)
\(224\) −1.72764 −0.115433
\(225\) 21.4463 1.42975
\(226\) −20.6962 −1.37669
\(227\) −21.1266 −1.40222 −0.701110 0.713053i \(-0.747312\pi\)
−0.701110 + 0.713053i \(0.747312\pi\)
\(228\) 5.36684 0.355428
\(229\) 21.6357 1.42973 0.714864 0.699263i \(-0.246488\pi\)
0.714864 + 0.699263i \(0.246488\pi\)
\(230\) 3.87731 0.255662
\(231\) 2.03845 0.134120
\(232\) 4.33964 0.284911
\(233\) 2.02031 0.132355 0.0661776 0.997808i \(-0.478920\pi\)
0.0661776 + 0.997808i \(0.478920\pi\)
\(234\) 6.43185 0.420463
\(235\) −19.4931 −1.27159
\(236\) −7.77077 −0.505834
\(237\) 15.7921 1.02581
\(238\) 4.42638 0.286920
\(239\) 15.6203 1.01039 0.505196 0.863004i \(-0.331420\pi\)
0.505196 + 0.863004i \(0.331420\pi\)
\(240\) −8.78830 −0.567282
\(241\) 18.0541 1.16296 0.581482 0.813559i \(-0.302473\pi\)
0.581482 + 0.813559i \(0.302473\pi\)
\(242\) 10.7290 0.689687
\(243\) 18.7131 1.20044
\(244\) −3.89047 −0.249062
\(245\) −15.5684 −0.994627
\(246\) 15.6355 0.996885
\(247\) 7.12496 0.453351
\(248\) −4.96174 −0.315071
\(249\) −1.15015 −0.0728880
\(250\) −19.5166 −1.23434
\(251\) −17.2048 −1.08596 −0.542978 0.839747i \(-0.682703\pi\)
−0.542978 + 0.839747i \(0.682703\pi\)
\(252\) 3.69277 0.232623
\(253\) 0.520561 0.0327274
\(254\) 10.3445 0.649072
\(255\) 22.5164 1.41003
\(256\) 1.00000 0.0625000
\(257\) 12.5621 0.783601 0.391800 0.920050i \(-0.371852\pi\)
0.391800 + 0.920050i \(0.371852\pi\)
\(258\) 2.18433 0.135990
\(259\) −6.83200 −0.424520
\(260\) −11.6672 −0.723572
\(261\) −9.27580 −0.574158
\(262\) 1.00000 0.0617802
\(263\) −25.2644 −1.55787 −0.778935 0.627105i \(-0.784240\pi\)
−0.778935 + 0.627105i \(0.784240\pi\)
\(264\) −1.17990 −0.0726179
\(265\) 43.8753 2.69524
\(266\) 4.09071 0.250818
\(267\) −1.95400 −0.119583
\(268\) −1.15425 −0.0705071
\(269\) 2.59240 0.158061 0.0790306 0.996872i \(-0.474818\pi\)
0.0790306 + 0.996872i \(0.474818\pi\)
\(270\) −7.58026 −0.461320
\(271\) 13.5472 0.822933 0.411466 0.911425i \(-0.365017\pi\)
0.411466 + 0.911425i \(0.365017\pi\)
\(272\) −2.56209 −0.155350
\(273\) 11.7833 0.713156
\(274\) −11.9437 −0.721547
\(275\) −5.22306 −0.314962
\(276\) 2.26660 0.136433
\(277\) 6.77010 0.406776 0.203388 0.979098i \(-0.434805\pi\)
0.203388 + 0.979098i \(0.434805\pi\)
\(278\) 11.8835 0.712723
\(279\) 10.6055 0.634936
\(280\) −6.69861 −0.400318
\(281\) −19.7839 −1.18021 −0.590104 0.807327i \(-0.700913\pi\)
−0.590104 + 0.807327i \(0.700913\pi\)
\(282\) −11.3952 −0.678577
\(283\) −22.0120 −1.30848 −0.654239 0.756288i \(-0.727011\pi\)
−0.654239 + 0.756288i \(0.727011\pi\)
\(284\) −10.7198 −0.636106
\(285\) 20.8089 1.23261
\(286\) −1.56642 −0.0926245
\(287\) 11.9177 0.703480
\(288\) −2.13746 −0.125951
\(289\) −10.4357 −0.613863
\(290\) 16.8261 0.988064
\(291\) −40.3820 −2.36723
\(292\) −11.5928 −0.678419
\(293\) −32.6010 −1.90457 −0.952286 0.305206i \(-0.901275\pi\)
−0.952286 + 0.305206i \(0.901275\pi\)
\(294\) −9.10095 −0.530778
\(295\) −30.1297 −1.75422
\(296\) 3.95452 0.229852
\(297\) −1.01771 −0.0590536
\(298\) 18.0698 1.04675
\(299\) 3.00911 0.174021
\(300\) −22.7420 −1.31301
\(301\) 1.66494 0.0959655
\(302\) 2.28863 0.131696
\(303\) 18.1314 1.04162
\(304\) −2.36780 −0.135803
\(305\) −15.0846 −0.863740
\(306\) 5.47637 0.313063
\(307\) 12.8481 0.733277 0.366639 0.930363i \(-0.380509\pi\)
0.366639 + 0.930363i \(0.380509\pi\)
\(308\) −0.899343 −0.0512448
\(309\) 21.8089 1.24067
\(310\) −19.2382 −1.09266
\(311\) −5.61834 −0.318587 −0.159294 0.987231i \(-0.550922\pi\)
−0.159294 + 0.987231i \(0.550922\pi\)
\(312\) −6.82043 −0.386131
\(313\) 11.6656 0.659381 0.329690 0.944089i \(-0.393056\pi\)
0.329690 + 0.944089i \(0.393056\pi\)
\(314\) −2.34717 −0.132458
\(315\) 14.3180 0.806728
\(316\) −6.96733 −0.391943
\(317\) 22.9683 1.29003 0.645015 0.764170i \(-0.276851\pi\)
0.645015 + 0.764170i \(0.276851\pi\)
\(318\) 25.6486 1.43830
\(319\) 2.25904 0.126482
\(320\) 3.87731 0.216748
\(321\) 24.0213 1.34074
\(322\) 1.72764 0.0962778
\(323\) 6.06652 0.337550
\(324\) −10.8436 −0.602425
\(325\) −30.1920 −1.67475
\(326\) −9.12204 −0.505223
\(327\) −22.8321 −1.26262
\(328\) −6.89824 −0.380892
\(329\) −8.68568 −0.478857
\(330\) −4.57484 −0.251837
\(331\) −20.2179 −1.11127 −0.555637 0.831425i \(-0.687526\pi\)
−0.555637 + 0.831425i \(0.687526\pi\)
\(332\) 0.507436 0.0278492
\(333\) −8.45263 −0.463201
\(334\) 1.50626 0.0824189
\(335\) −4.47539 −0.244516
\(336\) −3.91587 −0.213628
\(337\) −16.3376 −0.889964 −0.444982 0.895540i \(-0.646790\pi\)
−0.444982 + 0.895540i \(0.646790\pi\)
\(338\) 3.94527 0.214594
\(339\) −46.9099 −2.54780
\(340\) −9.93403 −0.538749
\(341\) −2.58289 −0.139871
\(342\) 5.06107 0.273672
\(343\) −19.0304 −1.02755
\(344\) −0.963705 −0.0519595
\(345\) 8.78830 0.473146
\(346\) 7.42542 0.399193
\(347\) 0.738035 0.0396198 0.0198099 0.999804i \(-0.493694\pi\)
0.0198099 + 0.999804i \(0.493694\pi\)
\(348\) 9.83621 0.527276
\(349\) −12.9354 −0.692415 −0.346207 0.938158i \(-0.612531\pi\)
−0.346207 + 0.938158i \(0.612531\pi\)
\(350\) −17.3344 −0.926561
\(351\) −5.88290 −0.314006
\(352\) 0.520561 0.0277460
\(353\) 21.5573 1.14738 0.573690 0.819073i \(-0.305511\pi\)
0.573690 + 0.819073i \(0.305511\pi\)
\(354\) −17.6132 −0.936132
\(355\) −41.5642 −2.20600
\(356\) 0.862086 0.0456904
\(357\) 10.0328 0.530994
\(358\) −2.57918 −0.136314
\(359\) 11.8701 0.626481 0.313241 0.949674i \(-0.398585\pi\)
0.313241 + 0.949674i \(0.398585\pi\)
\(360\) −8.28759 −0.436795
\(361\) −13.3935 −0.704923
\(362\) −10.8090 −0.568107
\(363\) 24.3184 1.27638
\(364\) −5.19866 −0.272484
\(365\) −44.9490 −2.35274
\(366\) −8.81813 −0.460931
\(367\) 18.9022 0.986684 0.493342 0.869835i \(-0.335775\pi\)
0.493342 + 0.869835i \(0.335775\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 14.7447 0.767579
\(370\) 15.3329 0.797120
\(371\) 19.5498 1.01498
\(372\) −11.2463 −0.583092
\(373\) 4.12490 0.213579 0.106790 0.994282i \(-0.465943\pi\)
0.106790 + 0.994282i \(0.465943\pi\)
\(374\) −1.33373 −0.0689653
\(375\) −44.2362 −2.28435
\(376\) 5.02747 0.259272
\(377\) 13.0584 0.672544
\(378\) −3.37759 −0.173725
\(379\) −2.12205 −0.109002 −0.0545011 0.998514i \(-0.517357\pi\)
−0.0545011 + 0.998514i \(0.517357\pi\)
\(380\) −9.18069 −0.470959
\(381\) 23.4468 1.20122
\(382\) 6.53654 0.334439
\(383\) 27.2960 1.39476 0.697380 0.716701i \(-0.254349\pi\)
0.697380 + 0.716701i \(0.254349\pi\)
\(384\) 2.26660 0.115667
\(385\) −3.48703 −0.177716
\(386\) −5.20786 −0.265073
\(387\) 2.05988 0.104710
\(388\) 17.8161 0.904477
\(389\) 25.3143 1.28349 0.641743 0.766920i \(-0.278212\pi\)
0.641743 + 0.766920i \(0.278212\pi\)
\(390\) −26.4449 −1.33909
\(391\) 2.56209 0.129571
\(392\) 4.01525 0.202801
\(393\) 2.26660 0.114335
\(394\) 5.47004 0.275577
\(395\) −27.0145 −1.35925
\(396\) −1.11268 −0.0559141
\(397\) −29.4192 −1.47651 −0.738253 0.674524i \(-0.764349\pi\)
−0.738253 + 0.674524i \(0.764349\pi\)
\(398\) 10.1452 0.508534
\(399\) 9.27199 0.464180
\(400\) 10.0335 0.501677
\(401\) 15.9525 0.796631 0.398315 0.917249i \(-0.369595\pi\)
0.398315 + 0.917249i \(0.369595\pi\)
\(402\) −2.61622 −0.130485
\(403\) −14.9304 −0.743737
\(404\) −7.99939 −0.397984
\(405\) −42.0442 −2.08919
\(406\) 7.49735 0.372087
\(407\) 2.05857 0.102039
\(408\) −5.80723 −0.287501
\(409\) −18.0172 −0.890894 −0.445447 0.895308i \(-0.646955\pi\)
−0.445447 + 0.895308i \(0.646955\pi\)
\(410\) −26.7466 −1.32092
\(411\) −27.0716 −1.33534
\(412\) −9.62187 −0.474036
\(413\) −13.4251 −0.660607
\(414\) 2.13746 0.105050
\(415\) 1.96749 0.0965801
\(416\) 3.00911 0.147534
\(417\) 26.9350 1.31901
\(418\) −1.23258 −0.0602876
\(419\) −16.9697 −0.829023 −0.414512 0.910044i \(-0.636048\pi\)
−0.414512 + 0.910044i \(0.636048\pi\)
\(420\) −15.1830 −0.740857
\(421\) 26.8188 1.30707 0.653534 0.756897i \(-0.273286\pi\)
0.653534 + 0.756897i \(0.273286\pi\)
\(422\) 22.5482 1.09763
\(423\) −10.7460 −0.522489
\(424\) −11.3159 −0.549549
\(425\) −25.7069 −1.24697
\(426\) −24.2976 −1.17722
\(427\) −6.72135 −0.325269
\(428\) −10.5980 −0.512273
\(429\) −3.55045 −0.171417
\(430\) −3.73658 −0.180194
\(431\) 40.0814 1.93065 0.965326 0.261047i \(-0.0840676\pi\)
0.965326 + 0.261047i \(0.0840676\pi\)
\(432\) 1.95503 0.0940614
\(433\) −21.4108 −1.02894 −0.514469 0.857509i \(-0.672011\pi\)
−0.514469 + 0.857509i \(0.672011\pi\)
\(434\) −8.57212 −0.411475
\(435\) 38.1380 1.82858
\(436\) 10.0733 0.482424
\(437\) 2.36780 0.113267
\(438\) −26.2763 −1.25553
\(439\) −32.0137 −1.52793 −0.763966 0.645256i \(-0.776751\pi\)
−0.763966 + 0.645256i \(0.776751\pi\)
\(440\) 2.01837 0.0962222
\(441\) −8.58243 −0.408687
\(442\) −7.70962 −0.366709
\(443\) −13.0783 −0.621367 −0.310683 0.950513i \(-0.600558\pi\)
−0.310683 + 0.950513i \(0.600558\pi\)
\(444\) 8.96330 0.425379
\(445\) 3.34257 0.158453
\(446\) −4.64685 −0.220035
\(447\) 40.9568 1.93719
\(448\) 1.72764 0.0816235
\(449\) −32.5448 −1.53588 −0.767942 0.640519i \(-0.778719\pi\)
−0.767942 + 0.640519i \(0.778719\pi\)
\(450\) −21.4463 −1.01099
\(451\) −3.59095 −0.169091
\(452\) 20.6962 0.973466
\(453\) 5.18741 0.243726
\(454\) 21.1266 0.991520
\(455\) −20.1568 −0.944967
\(456\) −5.36684 −0.251326
\(457\) 25.8113 1.20740 0.603701 0.797211i \(-0.293692\pi\)
0.603701 + 0.797211i \(0.293692\pi\)
\(458\) −21.6357 −1.01097
\(459\) −5.00897 −0.233799
\(460\) −3.87731 −0.180781
\(461\) 10.2354 0.476710 0.238355 0.971178i \(-0.423392\pi\)
0.238355 + 0.971178i \(0.423392\pi\)
\(462\) −2.03845 −0.0948371
\(463\) −5.29908 −0.246269 −0.123134 0.992390i \(-0.539295\pi\)
−0.123134 + 0.992390i \(0.539295\pi\)
\(464\) −4.33964 −0.201463
\(465\) −43.6053 −2.02215
\(466\) −2.02031 −0.0935893
\(467\) −32.4550 −1.50184 −0.750919 0.660394i \(-0.770389\pi\)
−0.750919 + 0.660394i \(0.770389\pi\)
\(468\) −6.43185 −0.297312
\(469\) −1.99413 −0.0920805
\(470\) 19.4931 0.899148
\(471\) −5.32008 −0.245136
\(472\) 7.77077 0.357679
\(473\) −0.501667 −0.0230667
\(474\) −15.7921 −0.725356
\(475\) −23.7574 −1.09006
\(476\) −4.42638 −0.202883
\(477\) 24.1873 1.10746
\(478\) −15.6203 −0.714456
\(479\) −28.5289 −1.30352 −0.651759 0.758426i \(-0.725969\pi\)
−0.651759 + 0.758426i \(0.725969\pi\)
\(480\) 8.78830 0.401129
\(481\) 11.8996 0.542574
\(482\) −18.0541 −0.822340
\(483\) 3.91587 0.178178
\(484\) −10.7290 −0.487683
\(485\) 69.0787 3.13670
\(486\) −18.7131 −0.848842
\(487\) −0.448101 −0.0203054 −0.0101527 0.999948i \(-0.503232\pi\)
−0.0101527 + 0.999948i \(0.503232\pi\)
\(488\) 3.89047 0.176113
\(489\) −20.6760 −0.935000
\(490\) 15.5684 0.703307
\(491\) 12.2653 0.553527 0.276763 0.960938i \(-0.410738\pi\)
0.276763 + 0.960938i \(0.410738\pi\)
\(492\) −15.6355 −0.704904
\(493\) 11.1186 0.500755
\(494\) −7.12496 −0.320567
\(495\) −4.31419 −0.193909
\(496\) 4.96174 0.222789
\(497\) −18.5201 −0.830739
\(498\) 1.15015 0.0515396
\(499\) −7.59920 −0.340187 −0.170094 0.985428i \(-0.554407\pi\)
−0.170094 + 0.985428i \(0.554407\pi\)
\(500\) 19.5166 0.872808
\(501\) 3.41409 0.152530
\(502\) 17.2048 0.767887
\(503\) −6.07364 −0.270810 −0.135405 0.990790i \(-0.543234\pi\)
−0.135405 + 0.990790i \(0.543234\pi\)
\(504\) −3.69277 −0.164489
\(505\) −31.0161 −1.38020
\(506\) −0.520561 −0.0231417
\(507\) 8.94233 0.397143
\(508\) −10.3445 −0.458963
\(509\) −38.2864 −1.69702 −0.848508 0.529182i \(-0.822499\pi\)
−0.848508 + 0.529182i \(0.822499\pi\)
\(510\) −22.5164 −0.997045
\(511\) −20.0283 −0.885998
\(512\) −1.00000 −0.0441942
\(513\) −4.62912 −0.204381
\(514\) −12.5621 −0.554089
\(515\) −37.3070 −1.64394
\(516\) −2.18433 −0.0961598
\(517\) 2.61710 0.115100
\(518\) 6.83200 0.300181
\(519\) 16.8304 0.738774
\(520\) 11.6672 0.511643
\(521\) 19.2057 0.841416 0.420708 0.907196i \(-0.361782\pi\)
0.420708 + 0.907196i \(0.361782\pi\)
\(522\) 9.27580 0.405991
\(523\) 33.5569 1.46734 0.733671 0.679505i \(-0.237805\pi\)
0.733671 + 0.679505i \(0.237805\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −39.2900 −1.71476
\(526\) 25.2644 1.10158
\(527\) −12.7125 −0.553763
\(528\) 1.17990 0.0513486
\(529\) 1.00000 0.0434783
\(530\) −43.8753 −1.90582
\(531\) −16.6097 −0.720800
\(532\) −4.09071 −0.177355
\(533\) −20.7576 −0.899110
\(534\) 1.95400 0.0845579
\(535\) −41.0916 −1.77655
\(536\) 1.15425 0.0498560
\(537\) −5.84596 −0.252272
\(538\) −2.59240 −0.111766
\(539\) 2.09018 0.0900304
\(540\) 7.58026 0.326202
\(541\) 11.8029 0.507446 0.253723 0.967277i \(-0.418345\pi\)
0.253723 + 0.967277i \(0.418345\pi\)
\(542\) −13.5472 −0.581901
\(543\) −24.4996 −1.05138
\(544\) 2.56209 0.109849
\(545\) 39.0574 1.67303
\(546\) −11.7833 −0.504278
\(547\) 10.5561 0.451347 0.225673 0.974203i \(-0.427542\pi\)
0.225673 + 0.974203i \(0.427542\pi\)
\(548\) 11.9437 0.510211
\(549\) −8.31573 −0.354907
\(550\) 5.22306 0.222712
\(551\) 10.2754 0.437746
\(552\) −2.26660 −0.0964728
\(553\) −12.0371 −0.511868
\(554\) −6.77010 −0.287634
\(555\) 34.7535 1.47520
\(556\) −11.8835 −0.503971
\(557\) −9.14370 −0.387431 −0.193716 0.981058i \(-0.562054\pi\)
−0.193716 + 0.981058i \(0.562054\pi\)
\(558\) −10.6055 −0.448968
\(559\) −2.89989 −0.122652
\(560\) 6.69861 0.283068
\(561\) −3.02302 −0.127632
\(562\) 19.7839 0.834533
\(563\) 20.8557 0.878961 0.439481 0.898252i \(-0.355163\pi\)
0.439481 + 0.898252i \(0.355163\pi\)
\(564\) 11.3952 0.479827
\(565\) 80.2455 3.37595
\(566\) 22.0120 0.925233
\(567\) −18.7339 −0.786752
\(568\) 10.7198 0.449795
\(569\) 2.43181 0.101947 0.0509734 0.998700i \(-0.483768\pi\)
0.0509734 + 0.998700i \(0.483768\pi\)
\(570\) −20.8089 −0.871590
\(571\) −5.94569 −0.248819 −0.124410 0.992231i \(-0.539704\pi\)
−0.124410 + 0.992231i \(0.539704\pi\)
\(572\) 1.56642 0.0654954
\(573\) 14.8157 0.618935
\(574\) −11.9177 −0.497435
\(575\) −10.0335 −0.418427
\(576\) 2.13746 0.0890608
\(577\) −37.9620 −1.58038 −0.790190 0.612862i \(-0.790018\pi\)
−0.790190 + 0.612862i \(0.790018\pi\)
\(578\) 10.4357 0.434067
\(579\) −11.8041 −0.490563
\(580\) −16.8261 −0.698667
\(581\) 0.876668 0.0363703
\(582\) 40.3820 1.67389
\(583\) −5.89061 −0.243964
\(584\) 11.5928 0.479715
\(585\) −24.9383 −1.03107
\(586\) 32.6010 1.34674
\(587\) −20.5285 −0.847300 −0.423650 0.905826i \(-0.639251\pi\)
−0.423650 + 0.905826i \(0.639251\pi\)
\(588\) 9.10095 0.375317
\(589\) −11.7484 −0.484085
\(590\) 30.1297 1.24042
\(591\) 12.3984 0.510001
\(592\) −3.95452 −0.162530
\(593\) 24.2992 0.997847 0.498923 0.866646i \(-0.333729\pi\)
0.498923 + 0.866646i \(0.333729\pi\)
\(594\) 1.01771 0.0417572
\(595\) −17.1625 −0.703592
\(596\) −18.0698 −0.740166
\(597\) 22.9951 0.941127
\(598\) −3.00911 −0.123052
\(599\) −28.2594 −1.15465 −0.577323 0.816516i \(-0.695903\pi\)
−0.577323 + 0.816516i \(0.695903\pi\)
\(600\) 22.7420 0.928437
\(601\) −7.18116 −0.292926 −0.146463 0.989216i \(-0.546789\pi\)
−0.146463 + 0.989216i \(0.546789\pi\)
\(602\) −1.66494 −0.0678578
\(603\) −2.46716 −0.100471
\(604\) −2.28863 −0.0931232
\(605\) −41.5997 −1.69127
\(606\) −18.1314 −0.736537
\(607\) 6.15770 0.249933 0.124967 0.992161i \(-0.460118\pi\)
0.124967 + 0.992161i \(0.460118\pi\)
\(608\) 2.36780 0.0960269
\(609\) 16.9935 0.688610
\(610\) 15.0846 0.610756
\(611\) 15.1282 0.612022
\(612\) −5.47637 −0.221369
\(613\) −5.11650 −0.206654 −0.103327 0.994647i \(-0.532949\pi\)
−0.103327 + 0.994647i \(0.532949\pi\)
\(614\) −12.8481 −0.518505
\(615\) −60.6238 −2.44459
\(616\) 0.899343 0.0362356
\(617\) −37.9377 −1.52732 −0.763658 0.645621i \(-0.776599\pi\)
−0.763658 + 0.645621i \(0.776599\pi\)
\(618\) −21.8089 −0.877283
\(619\) −11.4521 −0.460297 −0.230149 0.973155i \(-0.573921\pi\)
−0.230149 + 0.973155i \(0.573921\pi\)
\(620\) 19.2382 0.772625
\(621\) −1.95503 −0.0784527
\(622\) 5.61834 0.225275
\(623\) 1.48938 0.0596706
\(624\) 6.82043 0.273036
\(625\) 25.5041 1.02017
\(626\) −11.6656 −0.466253
\(627\) −2.79377 −0.111572
\(628\) 2.34717 0.0936621
\(629\) 10.1319 0.403983
\(630\) −14.3180 −0.570443
\(631\) −3.76754 −0.149983 −0.0749917 0.997184i \(-0.523893\pi\)
−0.0749917 + 0.997184i \(0.523893\pi\)
\(632\) 6.96733 0.277145
\(633\) 51.1076 2.03135
\(634\) −22.9683 −0.912189
\(635\) −40.1088 −1.59167
\(636\) −25.6486 −1.01703
\(637\) 12.0823 0.478719
\(638\) −2.25904 −0.0894364
\(639\) −22.9132 −0.906434
\(640\) −3.87731 −0.153264
\(641\) −24.1133 −0.952417 −0.476209 0.879332i \(-0.657989\pi\)
−0.476209 + 0.879332i \(0.657989\pi\)
\(642\) −24.0213 −0.948047
\(643\) −43.8511 −1.72932 −0.864659 0.502359i \(-0.832465\pi\)
−0.864659 + 0.502359i \(0.832465\pi\)
\(644\) −1.72764 −0.0680787
\(645\) −8.46933 −0.333479
\(646\) −6.06652 −0.238684
\(647\) 41.5450 1.63330 0.816652 0.577131i \(-0.195828\pi\)
0.816652 + 0.577131i \(0.195828\pi\)
\(648\) 10.8436 0.425979
\(649\) 4.04516 0.158786
\(650\) 30.1920 1.18423
\(651\) −19.4295 −0.761504
\(652\) 9.12204 0.357246
\(653\) 40.4930 1.58461 0.792307 0.610122i \(-0.208880\pi\)
0.792307 + 0.610122i \(0.208880\pi\)
\(654\) 22.8321 0.892807
\(655\) −3.87731 −0.151499
\(656\) 6.89824 0.269331
\(657\) −24.7792 −0.966729
\(658\) 8.68568 0.338603
\(659\) 13.0424 0.508061 0.254031 0.967196i \(-0.418244\pi\)
0.254031 + 0.967196i \(0.418244\pi\)
\(660\) 4.57484 0.178075
\(661\) 0.915376 0.0356040 0.0178020 0.999842i \(-0.494333\pi\)
0.0178020 + 0.999842i \(0.494333\pi\)
\(662\) 20.2179 0.785789
\(663\) −17.4746 −0.678657
\(664\) −0.507436 −0.0196923
\(665\) −15.8610 −0.615061
\(666\) 8.45263 0.327533
\(667\) 4.33964 0.168031
\(668\) −1.50626 −0.0582790
\(669\) −10.5325 −0.407211
\(670\) 4.47539 0.172899
\(671\) 2.02523 0.0781830
\(672\) 3.91587 0.151058
\(673\) −48.0329 −1.85153 −0.925766 0.378098i \(-0.876578\pi\)
−0.925766 + 0.378098i \(0.876578\pi\)
\(674\) 16.3376 0.629299
\(675\) 19.6159 0.755015
\(676\) −3.94527 −0.151741
\(677\) 4.90521 0.188522 0.0942612 0.995547i \(-0.469951\pi\)
0.0942612 + 0.995547i \(0.469951\pi\)
\(678\) 46.9099 1.80156
\(679\) 30.7799 1.18123
\(680\) 9.93403 0.380953
\(681\) 47.8855 1.83497
\(682\) 2.58289 0.0989039
\(683\) −16.0178 −0.612905 −0.306453 0.951886i \(-0.599142\pi\)
−0.306453 + 0.951886i \(0.599142\pi\)
\(684\) −5.06107 −0.193515
\(685\) 46.3095 1.76940
\(686\) 19.0304 0.726585
\(687\) −49.0394 −1.87097
\(688\) 0.963705 0.0367409
\(689\) −34.0508 −1.29723
\(690\) −8.78830 −0.334565
\(691\) 10.2099 0.388405 0.194202 0.980961i \(-0.437788\pi\)
0.194202 + 0.980961i \(0.437788\pi\)
\(692\) −7.42542 −0.282272
\(693\) −1.92231 −0.0730225
\(694\) −0.738035 −0.0280154
\(695\) −46.0759 −1.74776
\(696\) −9.83621 −0.372841
\(697\) −17.6739 −0.669449
\(698\) 12.9354 0.489611
\(699\) −4.57924 −0.173203
\(700\) 17.3344 0.655177
\(701\) −26.4719 −0.999830 −0.499915 0.866074i \(-0.666635\pi\)
−0.499915 + 0.866074i \(0.666635\pi\)
\(702\) 5.88290 0.222036
\(703\) 9.36351 0.353151
\(704\) −0.520561 −0.0196194
\(705\) 44.1829 1.66402
\(706\) −21.5573 −0.811320
\(707\) −13.8201 −0.519758
\(708\) 17.6132 0.661945
\(709\) −29.7925 −1.11888 −0.559441 0.828870i \(-0.688984\pi\)
−0.559441 + 0.828870i \(0.688984\pi\)
\(710\) 41.5642 1.55988
\(711\) −14.8924 −0.558508
\(712\) −0.862086 −0.0323080
\(713\) −4.96174 −0.185819
\(714\) −10.0328 −0.375469
\(715\) 6.07351 0.227136
\(716\) 2.57918 0.0963885
\(717\) −35.4049 −1.32222
\(718\) −11.8701 −0.442989
\(719\) 17.7465 0.661835 0.330917 0.943660i \(-0.392642\pi\)
0.330917 + 0.943660i \(0.392642\pi\)
\(720\) 8.28759 0.308860
\(721\) −16.6232 −0.619079
\(722\) 13.3935 0.498456
\(723\) −40.9213 −1.52188
\(724\) 10.8090 0.401712
\(725\) −43.5419 −1.61711
\(726\) −24.3184 −0.902539
\(727\) −16.9300 −0.627900 −0.313950 0.949439i \(-0.601652\pi\)
−0.313950 + 0.949439i \(0.601652\pi\)
\(728\) 5.19866 0.192675
\(729\) −9.88406 −0.366076
\(730\) 44.9490 1.66364
\(731\) −2.46910 −0.0913231
\(732\) 8.81813 0.325928
\(733\) −19.4367 −0.717911 −0.358956 0.933355i \(-0.616867\pi\)
−0.358956 + 0.933355i \(0.616867\pi\)
\(734\) −18.9022 −0.697691
\(735\) 35.2872 1.30159
\(736\) 1.00000 0.0368605
\(737\) 0.600857 0.0221329
\(738\) −14.7447 −0.542761
\(739\) −21.5119 −0.791329 −0.395664 0.918395i \(-0.629486\pi\)
−0.395664 + 0.918395i \(0.629486\pi\)
\(740\) −15.3329 −0.563649
\(741\) −16.1494 −0.593264
\(742\) −19.5498 −0.717697
\(743\) 19.5195 0.716101 0.358051 0.933702i \(-0.383442\pi\)
0.358051 + 0.933702i \(0.383442\pi\)
\(744\) 11.2463 0.412308
\(745\) −70.0620 −2.56687
\(746\) −4.12490 −0.151023
\(747\) 1.08462 0.0396843
\(748\) 1.33373 0.0487658
\(749\) −18.3095 −0.669015
\(750\) 44.2362 1.61528
\(751\) −13.8384 −0.504972 −0.252486 0.967601i \(-0.581248\pi\)
−0.252486 + 0.967601i \(0.581248\pi\)
\(752\) −5.02747 −0.183333
\(753\) 38.9963 1.42110
\(754\) −13.0584 −0.475560
\(755\) −8.87374 −0.322949
\(756\) 3.37759 0.122842
\(757\) −25.6057 −0.930655 −0.465327 0.885139i \(-0.654063\pi\)
−0.465327 + 0.885139i \(0.654063\pi\)
\(758\) 2.12205 0.0770762
\(759\) −1.17990 −0.0428277
\(760\) 9.18069 0.333019
\(761\) 42.9990 1.55871 0.779357 0.626580i \(-0.215546\pi\)
0.779357 + 0.626580i \(0.215546\pi\)
\(762\) −23.4468 −0.849388
\(763\) 17.4031 0.630034
\(764\) −6.53654 −0.236484
\(765\) −21.2336 −0.767702
\(766\) −27.2960 −0.986244
\(767\) 23.3831 0.844315
\(768\) −2.26660 −0.0817888
\(769\) 31.6929 1.14287 0.571437 0.820646i \(-0.306386\pi\)
0.571437 + 0.820646i \(0.306386\pi\)
\(770\) 3.48703 0.125664
\(771\) −28.4732 −1.02544
\(772\) 5.20786 0.187435
\(773\) 33.2594 1.19626 0.598129 0.801400i \(-0.295911\pi\)
0.598129 + 0.801400i \(0.295911\pi\)
\(774\) −2.05988 −0.0740409
\(775\) 49.7838 1.78829
\(776\) −17.8161 −0.639562
\(777\) 15.4854 0.555535
\(778\) −25.3143 −0.907561
\(779\) −16.3337 −0.585214
\(780\) 26.4449 0.946881
\(781\) 5.58033 0.199680
\(782\) −2.56209 −0.0916203
\(783\) −8.48412 −0.303198
\(784\) −4.01525 −0.143402
\(785\) 9.10069 0.324818
\(786\) −2.26660 −0.0808468
\(787\) 37.3813 1.33250 0.666249 0.745729i \(-0.267899\pi\)
0.666249 + 0.745729i \(0.267899\pi\)
\(788\) −5.47004 −0.194862
\(789\) 57.2642 2.03866
\(790\) 27.0145 0.961132
\(791\) 35.7556 1.27132
\(792\) 1.11268 0.0395373
\(793\) 11.7069 0.415723
\(794\) 29.4192 1.04405
\(795\) −99.4475 −3.52704
\(796\) −10.1452 −0.359588
\(797\) 1.26842 0.0449297 0.0224648 0.999748i \(-0.492849\pi\)
0.0224648 + 0.999748i \(0.492849\pi\)
\(798\) −9.27199 −0.328225
\(799\) 12.8809 0.455692
\(800\) −10.0335 −0.354739
\(801\) 1.84267 0.0651077
\(802\) −15.9525 −0.563303
\(803\) 6.03477 0.212962
\(804\) 2.61622 0.0922669
\(805\) −6.69861 −0.236095
\(806\) 14.9304 0.525902
\(807\) −5.87592 −0.206842
\(808\) 7.99939 0.281418
\(809\) −3.72033 −0.130800 −0.0653999 0.997859i \(-0.520832\pi\)
−0.0653999 + 0.997859i \(0.520832\pi\)
\(810\) 42.0442 1.47728
\(811\) −24.6799 −0.866629 −0.433315 0.901243i \(-0.642656\pi\)
−0.433315 + 0.901243i \(0.642656\pi\)
\(812\) −7.49735 −0.263105
\(813\) −30.7060 −1.07691
\(814\) −2.05857 −0.0721527
\(815\) 35.3690 1.23892
\(816\) 5.80723 0.203294
\(817\) −2.28186 −0.0798322
\(818\) 18.0172 0.629957
\(819\) −11.1119 −0.388283
\(820\) 26.7466 0.934033
\(821\) 1.22557 0.0427728 0.0213864 0.999771i \(-0.493192\pi\)
0.0213864 + 0.999771i \(0.493192\pi\)
\(822\) 27.0716 0.944231
\(823\) 25.5294 0.889897 0.444949 0.895556i \(-0.353222\pi\)
0.444949 + 0.895556i \(0.353222\pi\)
\(824\) 9.62187 0.335194
\(825\) 11.8386 0.412166
\(826\) 13.4251 0.467120
\(827\) 17.8283 0.619951 0.309976 0.950744i \(-0.399679\pi\)
0.309976 + 0.950744i \(0.399679\pi\)
\(828\) −2.13746 −0.0742819
\(829\) −49.5827 −1.72208 −0.861038 0.508540i \(-0.830185\pi\)
−0.861038 + 0.508540i \(0.830185\pi\)
\(830\) −1.96749 −0.0682925
\(831\) −15.3451 −0.532315
\(832\) −3.00911 −0.104322
\(833\) 10.2874 0.356439
\(834\) −26.9350 −0.932683
\(835\) −5.84024 −0.202110
\(836\) 1.23258 0.0426298
\(837\) 9.70036 0.335293
\(838\) 16.9697 0.586208
\(839\) 35.9953 1.24270 0.621348 0.783534i \(-0.286585\pi\)
0.621348 + 0.783534i \(0.286585\pi\)
\(840\) 15.1830 0.523865
\(841\) −10.1675 −0.350605
\(842\) −26.8188 −0.924237
\(843\) 44.8421 1.54444
\(844\) −22.5482 −0.776140
\(845\) −15.2970 −0.526234
\(846\) 10.7460 0.369456
\(847\) −18.5359 −0.636901
\(848\) 11.3159 0.388590
\(849\) 49.8923 1.71230
\(850\) 25.7069 0.881738
\(851\) 3.95452 0.135559
\(852\) 24.2976 0.832421
\(853\) −0.111598 −0.00382105 −0.00191052 0.999998i \(-0.500608\pi\)
−0.00191052 + 0.999998i \(0.500608\pi\)
\(854\) 6.72135 0.230000
\(855\) −19.6234 −0.671105
\(856\) 10.5980 0.362231
\(857\) −39.8806 −1.36230 −0.681148 0.732145i \(-0.738519\pi\)
−0.681148 + 0.732145i \(0.738519\pi\)
\(858\) 3.55045 0.121210
\(859\) −18.7197 −0.638706 −0.319353 0.947636i \(-0.603466\pi\)
−0.319353 + 0.947636i \(0.603466\pi\)
\(860\) 3.73658 0.127416
\(861\) −27.0126 −0.920588
\(862\) −40.0814 −1.36518
\(863\) 17.9555 0.611211 0.305606 0.952158i \(-0.401141\pi\)
0.305606 + 0.952158i \(0.401141\pi\)
\(864\) −1.95503 −0.0665115
\(865\) −28.7906 −0.978911
\(866\) 21.4108 0.727568
\(867\) 23.6535 0.803314
\(868\) 8.57212 0.290957
\(869\) 3.62692 0.123035
\(870\) −38.1380 −1.29300
\(871\) 3.47326 0.117687
\(872\) −10.0733 −0.341125
\(873\) 38.0813 1.28886
\(874\) −2.36780 −0.0800920
\(875\) 33.7177 1.13987
\(876\) 26.2763 0.887792
\(877\) −46.0057 −1.55350 −0.776751 0.629808i \(-0.783133\pi\)
−0.776751 + 0.629808i \(0.783133\pi\)
\(878\) 32.0137 1.08041
\(879\) 73.8934 2.49236
\(880\) −2.01837 −0.0680394
\(881\) 5.18136 0.174564 0.0872822 0.996184i \(-0.472182\pi\)
0.0872822 + 0.996184i \(0.472182\pi\)
\(882\) 8.58243 0.288986
\(883\) −1.94149 −0.0653363 −0.0326681 0.999466i \(-0.510400\pi\)
−0.0326681 + 0.999466i \(0.510400\pi\)
\(884\) 7.70962 0.259303
\(885\) 68.2919 2.29561
\(886\) 13.0783 0.439373
\(887\) −37.4192 −1.25641 −0.628207 0.778047i \(-0.716211\pi\)
−0.628207 + 0.778047i \(0.716211\pi\)
\(888\) −8.96330 −0.300789
\(889\) −17.8716 −0.599394
\(890\) −3.34257 −0.112043
\(891\) 5.64477 0.189107
\(892\) 4.64685 0.155588
\(893\) 11.9040 0.398354
\(894\) −40.9568 −1.36980
\(895\) 10.0003 0.334273
\(896\) −1.72764 −0.0577165
\(897\) −6.82043 −0.227728
\(898\) 32.5448 1.08603
\(899\) −21.5322 −0.718138
\(900\) 21.4463 0.714876
\(901\) −28.9924 −0.965877
\(902\) 3.59095 0.119566
\(903\) −3.77374 −0.125582
\(904\) −20.6962 −0.688345
\(905\) 41.9097 1.39313
\(906\) −5.18741 −0.172340
\(907\) 51.9426 1.72473 0.862363 0.506291i \(-0.168984\pi\)
0.862363 + 0.506291i \(0.168984\pi\)
\(908\) −21.1266 −0.701110
\(909\) −17.0984 −0.567117
\(910\) 20.1568 0.668193
\(911\) −19.4383 −0.644019 −0.322009 0.946736i \(-0.604358\pi\)
−0.322009 + 0.946736i \(0.604358\pi\)
\(912\) 5.36684 0.177714
\(913\) −0.264151 −0.00874213
\(914\) −25.8113 −0.853763
\(915\) 34.1906 1.13031
\(916\) 21.6357 0.714864
\(917\) −1.72764 −0.0570518
\(918\) 5.00897 0.165321
\(919\) −6.84642 −0.225842 −0.112921 0.993604i \(-0.536021\pi\)
−0.112921 + 0.993604i \(0.536021\pi\)
\(920\) 3.87731 0.127831
\(921\) −29.1214 −0.959582
\(922\) −10.2354 −0.337085
\(923\) 32.2572 1.06176
\(924\) 2.03845 0.0670600
\(925\) −39.6778 −1.30460
\(926\) 5.29908 0.174138
\(927\) −20.5664 −0.675488
\(928\) 4.33964 0.142456
\(929\) −54.0385 −1.77295 −0.886473 0.462781i \(-0.846852\pi\)
−0.886473 + 0.462781i \(0.846852\pi\)
\(930\) 43.6053 1.42987
\(931\) 9.50730 0.311589
\(932\) 2.02031 0.0661776
\(933\) 12.7345 0.416909
\(934\) 32.4550 1.06196
\(935\) 5.17127 0.169118
\(936\) 6.43185 0.210232
\(937\) 25.6242 0.837105 0.418552 0.908193i \(-0.362538\pi\)
0.418552 + 0.908193i \(0.362538\pi\)
\(938\) 1.99413 0.0651107
\(939\) −26.4413 −0.862879
\(940\) −19.4931 −0.635794
\(941\) 42.4439 1.38363 0.691816 0.722074i \(-0.256811\pi\)
0.691816 + 0.722074i \(0.256811\pi\)
\(942\) 5.32008 0.173338
\(943\) −6.89824 −0.224638
\(944\) −7.77077 −0.252917
\(945\) 13.0960 0.426012
\(946\) 0.501667 0.0163106
\(947\) 6.45606 0.209794 0.104897 0.994483i \(-0.466549\pi\)
0.104897 + 0.994483i \(0.466549\pi\)
\(948\) 15.7921 0.512904
\(949\) 34.8841 1.13238
\(950\) 23.7574 0.770792
\(951\) −52.0599 −1.68816
\(952\) 4.42638 0.143460
\(953\) 23.8899 0.773869 0.386934 0.922107i \(-0.373534\pi\)
0.386934 + 0.922107i \(0.373534\pi\)
\(954\) −24.1873 −0.783093
\(955\) −25.3442 −0.820119
\(956\) 15.6203 0.505196
\(957\) −5.12034 −0.165517
\(958\) 28.5289 0.921727
\(959\) 20.6345 0.666322
\(960\) −8.78830 −0.283641
\(961\) −6.38112 −0.205842
\(962\) −11.8996 −0.383658
\(963\) −22.6527 −0.729975
\(964\) 18.0541 0.581482
\(965\) 20.1925 0.650020
\(966\) −3.91587 −0.125991
\(967\) 32.8246 1.05557 0.527785 0.849378i \(-0.323023\pi\)
0.527785 + 0.849378i \(0.323023\pi\)
\(968\) 10.7290 0.344844
\(969\) −13.7504 −0.441725
\(970\) −69.0787 −2.21798
\(971\) 42.1733 1.35341 0.676703 0.736256i \(-0.263408\pi\)
0.676703 + 0.736256i \(0.263408\pi\)
\(972\) 18.7131 0.600222
\(973\) −20.5304 −0.658174
\(974\) 0.448101 0.0143581
\(975\) 68.4331 2.19161
\(976\) −3.89047 −0.124531
\(977\) −16.8859 −0.540229 −0.270114 0.962828i \(-0.587062\pi\)
−0.270114 + 0.962828i \(0.587062\pi\)
\(978\) 20.6760 0.661145
\(979\) −0.448768 −0.0143427
\(980\) −15.5684 −0.497313
\(981\) 21.5313 0.687442
\(982\) −12.2653 −0.391403
\(983\) 35.3853 1.12862 0.564308 0.825564i \(-0.309143\pi\)
0.564308 + 0.825564i \(0.309143\pi\)
\(984\) 15.6355 0.498443
\(985\) −21.2091 −0.675777
\(986\) −11.1186 −0.354087
\(987\) 19.6869 0.626642
\(988\) 7.12496 0.226675
\(989\) −0.963705 −0.0306440
\(990\) 4.31419 0.137114
\(991\) −29.0792 −0.923731 −0.461865 0.886950i \(-0.652820\pi\)
−0.461865 + 0.886950i \(0.652820\pi\)
\(992\) −4.96174 −0.157535
\(993\) 45.8257 1.45424
\(994\) 18.5201 0.587421
\(995\) −39.3361 −1.24704
\(996\) −1.15015 −0.0364440
\(997\) 15.5376 0.492080 0.246040 0.969260i \(-0.420870\pi\)
0.246040 + 0.969260i \(0.420870\pi\)
\(998\) 7.59920 0.240549
\(999\) −7.73121 −0.244605
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 \(a_p\))