Properties

Label 4017.2.a.j.1.21
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.21
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.28515 q^{2} -1.00000 q^{3} +3.22190 q^{4} -1.71471 q^{5} -2.28515 q^{6} -3.41344 q^{7} +2.79222 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.28515 q^{2} -1.00000 q^{3} +3.22190 q^{4} -1.71471 q^{5} -2.28515 q^{6} -3.41344 q^{7} +2.79222 q^{8} +1.00000 q^{9} -3.91835 q^{10} -2.39155 q^{11} -3.22190 q^{12} +1.00000 q^{13} -7.80020 q^{14} +1.71471 q^{15} -0.0631677 q^{16} +0.255103 q^{17} +2.28515 q^{18} +5.27925 q^{19} -5.52461 q^{20} +3.41344 q^{21} -5.46505 q^{22} +8.19358 q^{23} -2.79222 q^{24} -2.05979 q^{25} +2.28515 q^{26} -1.00000 q^{27} -10.9977 q^{28} +4.00188 q^{29} +3.91835 q^{30} -1.24439 q^{31} -5.72878 q^{32} +2.39155 q^{33} +0.582947 q^{34} +5.85304 q^{35} +3.22190 q^{36} +7.34531 q^{37} +12.0639 q^{38} -1.00000 q^{39} -4.78783 q^{40} +2.94604 q^{41} +7.80020 q^{42} +3.05454 q^{43} -7.70534 q^{44} -1.71471 q^{45} +18.7235 q^{46} -11.6137 q^{47} +0.0631677 q^{48} +4.65154 q^{49} -4.70691 q^{50} -0.255103 q^{51} +3.22190 q^{52} +0.884763 q^{53} -2.28515 q^{54} +4.10081 q^{55} -9.53106 q^{56} -5.27925 q^{57} +9.14489 q^{58} +11.4507 q^{59} +5.52461 q^{60} +7.88600 q^{61} -2.84360 q^{62} -3.41344 q^{63} -12.9648 q^{64} -1.71471 q^{65} +5.46505 q^{66} +7.71850 q^{67} +0.821915 q^{68} -8.19358 q^{69} +13.3750 q^{70} +10.9975 q^{71} +2.79222 q^{72} -8.26216 q^{73} +16.7851 q^{74} +2.05979 q^{75} +17.0092 q^{76} +8.16341 q^{77} -2.28515 q^{78} +5.00055 q^{79} +0.108314 q^{80} +1.00000 q^{81} +6.73214 q^{82} +16.0795 q^{83} +10.9977 q^{84} -0.437426 q^{85} +6.98007 q^{86} -4.00188 q^{87} -6.67773 q^{88} -11.1784 q^{89} -3.91835 q^{90} -3.41344 q^{91} +26.3989 q^{92} +1.24439 q^{93} -26.5390 q^{94} -9.05236 q^{95} +5.72878 q^{96} +16.1374 q^{97} +10.6295 q^{98} -2.39155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.28515 1.61584 0.807922 0.589290i \(-0.200592\pi\)
0.807922 + 0.589290i \(0.200592\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.22190 1.61095
\(5\) −1.71471 −0.766839 −0.383420 0.923574i \(-0.625254\pi\)
−0.383420 + 0.923574i \(0.625254\pi\)
\(6\) −2.28515 −0.932907
\(7\) −3.41344 −1.29016 −0.645079 0.764116i \(-0.723175\pi\)
−0.645079 + 0.764116i \(0.723175\pi\)
\(8\) 2.79222 0.987198
\(9\) 1.00000 0.333333
\(10\) −3.91835 −1.23909
\(11\) −2.39155 −0.721080 −0.360540 0.932744i \(-0.617408\pi\)
−0.360540 + 0.932744i \(0.617408\pi\)
\(12\) −3.22190 −0.930082
\(13\) 1.00000 0.277350
\(14\) −7.80020 −2.08469
\(15\) 1.71471 0.442735
\(16\) −0.0631677 −0.0157919
\(17\) 0.255103 0.0618715 0.0309358 0.999521i \(-0.490151\pi\)
0.0309358 + 0.999521i \(0.490151\pi\)
\(18\) 2.28515 0.538614
\(19\) 5.27925 1.21114 0.605572 0.795791i \(-0.292945\pi\)
0.605572 + 0.795791i \(0.292945\pi\)
\(20\) −5.52461 −1.23534
\(21\) 3.41344 0.744873
\(22\) −5.46505 −1.16515
\(23\) 8.19358 1.70848 0.854239 0.519880i \(-0.174023\pi\)
0.854239 + 0.519880i \(0.174023\pi\)
\(24\) −2.79222 −0.569959
\(25\) −2.05979 −0.411957
\(26\) 2.28515 0.448154
\(27\) −1.00000 −0.192450
\(28\) −10.9977 −2.07838
\(29\) 4.00188 0.743131 0.371565 0.928407i \(-0.378821\pi\)
0.371565 + 0.928407i \(0.378821\pi\)
\(30\) 3.91835 0.715390
\(31\) −1.24439 −0.223498 −0.111749 0.993736i \(-0.535645\pi\)
−0.111749 + 0.993736i \(0.535645\pi\)
\(32\) −5.72878 −1.01272
\(33\) 2.39155 0.416316
\(34\) 0.582947 0.0999746
\(35\) 5.85304 0.989344
\(36\) 3.22190 0.536983
\(37\) 7.34531 1.20756 0.603781 0.797150i \(-0.293660\pi\)
0.603781 + 0.797150i \(0.293660\pi\)
\(38\) 12.0639 1.95702
\(39\) −1.00000 −0.160128
\(40\) −4.78783 −0.757022
\(41\) 2.94604 0.460095 0.230047 0.973179i \(-0.426112\pi\)
0.230047 + 0.973179i \(0.426112\pi\)
\(42\) 7.80020 1.20360
\(43\) 3.05454 0.465813 0.232906 0.972499i \(-0.425176\pi\)
0.232906 + 0.972499i \(0.425176\pi\)
\(44\) −7.70534 −1.16162
\(45\) −1.71471 −0.255613
\(46\) 18.7235 2.76063
\(47\) −11.6137 −1.69403 −0.847016 0.531567i \(-0.821603\pi\)
−0.847016 + 0.531567i \(0.821603\pi\)
\(48\) 0.0631677 0.00911748
\(49\) 4.65154 0.664506
\(50\) −4.70691 −0.665658
\(51\) −0.255103 −0.0357215
\(52\) 3.22190 0.446797
\(53\) 0.884763 0.121532 0.0607658 0.998152i \(-0.480646\pi\)
0.0607658 + 0.998152i \(0.480646\pi\)
\(54\) −2.28515 −0.310969
\(55\) 4.10081 0.552953
\(56\) −9.53106 −1.27364
\(57\) −5.27925 −0.699254
\(58\) 9.14489 1.20078
\(59\) 11.4507 1.49075 0.745376 0.666644i \(-0.232270\pi\)
0.745376 + 0.666644i \(0.232270\pi\)
\(60\) 5.52461 0.713224
\(61\) 7.88600 1.00970 0.504850 0.863207i \(-0.331548\pi\)
0.504850 + 0.863207i \(0.331548\pi\)
\(62\) −2.84360 −0.361138
\(63\) −3.41344 −0.430052
\(64\) −12.9648 −1.62060
\(65\) −1.71471 −0.212683
\(66\) 5.46505 0.672701
\(67\) 7.71850 0.942965 0.471482 0.881875i \(-0.343719\pi\)
0.471482 + 0.881875i \(0.343719\pi\)
\(68\) 0.821915 0.0996718
\(69\) −8.19358 −0.986391
\(70\) 13.3750 1.59862
\(71\) 10.9975 1.30517 0.652584 0.757717i \(-0.273685\pi\)
0.652584 + 0.757717i \(0.273685\pi\)
\(72\) 2.79222 0.329066
\(73\) −8.26216 −0.967012 −0.483506 0.875341i \(-0.660637\pi\)
−0.483506 + 0.875341i \(0.660637\pi\)
\(74\) 16.7851 1.95123
\(75\) 2.05979 0.237844
\(76\) 17.0092 1.95109
\(77\) 8.16341 0.930307
\(78\) −2.28515 −0.258742
\(79\) 5.00055 0.562606 0.281303 0.959619i \(-0.409233\pi\)
0.281303 + 0.959619i \(0.409233\pi\)
\(80\) 0.108314 0.0121099
\(81\) 1.00000 0.111111
\(82\) 6.73214 0.743441
\(83\) 16.0795 1.76496 0.882479 0.470351i \(-0.155873\pi\)
0.882479 + 0.470351i \(0.155873\pi\)
\(84\) 10.9977 1.19995
\(85\) −0.437426 −0.0474455
\(86\) 6.98007 0.752680
\(87\) −4.00188 −0.429047
\(88\) −6.67773 −0.711849
\(89\) −11.1784 −1.18490 −0.592452 0.805606i \(-0.701840\pi\)
−0.592452 + 0.805606i \(0.701840\pi\)
\(90\) −3.91835 −0.413031
\(91\) −3.41344 −0.357825
\(92\) 26.3989 2.75227
\(93\) 1.24439 0.129037
\(94\) −26.5390 −2.73729
\(95\) −9.05236 −0.928753
\(96\) 5.72878 0.584691
\(97\) 16.1374 1.63851 0.819254 0.573431i \(-0.194388\pi\)
0.819254 + 0.573431i \(0.194388\pi\)
\(98\) 10.6295 1.07374
\(99\) −2.39155 −0.240360
\(100\) −6.63642 −0.663642
\(101\) 7.78769 0.774904 0.387452 0.921890i \(-0.373355\pi\)
0.387452 + 0.921890i \(0.373355\pi\)
\(102\) −0.582947 −0.0577204
\(103\) −1.00000 −0.0985329
\(104\) 2.79222 0.273799
\(105\) −5.85304 −0.571198
\(106\) 2.02181 0.196376
\(107\) −12.7489 −1.23248 −0.616241 0.787558i \(-0.711345\pi\)
−0.616241 + 0.787558i \(0.711345\pi\)
\(108\) −3.22190 −0.310027
\(109\) −4.89646 −0.468996 −0.234498 0.972117i \(-0.575345\pi\)
−0.234498 + 0.972117i \(0.575345\pi\)
\(110\) 9.37095 0.893485
\(111\) −7.34531 −0.697186
\(112\) 0.215619 0.0203741
\(113\) −6.75655 −0.635603 −0.317802 0.948157i \(-0.602945\pi\)
−0.317802 + 0.948157i \(0.602945\pi\)
\(114\) −12.0639 −1.12988
\(115\) −14.0496 −1.31013
\(116\) 12.8937 1.19715
\(117\) 1.00000 0.0924500
\(118\) 26.1665 2.40882
\(119\) −0.870777 −0.0798240
\(120\) 4.78783 0.437067
\(121\) −5.28048 −0.480044
\(122\) 18.0207 1.63152
\(123\) −2.94604 −0.265636
\(124\) −4.00928 −0.360044
\(125\) 12.1055 1.08274
\(126\) −7.80020 −0.694897
\(127\) 11.3175 1.00427 0.502133 0.864790i \(-0.332549\pi\)
0.502133 + 0.864790i \(0.332549\pi\)
\(128\) −18.1689 −1.60592
\(129\) −3.05454 −0.268937
\(130\) −3.91835 −0.343662
\(131\) 19.1731 1.67516 0.837580 0.546314i \(-0.183969\pi\)
0.837580 + 0.546314i \(0.183969\pi\)
\(132\) 7.70534 0.670663
\(133\) −18.0204 −1.56257
\(134\) 17.6379 1.52368
\(135\) 1.71471 0.147578
\(136\) 0.712302 0.0610794
\(137\) 17.2171 1.47095 0.735476 0.677550i \(-0.236958\pi\)
0.735476 + 0.677550i \(0.236958\pi\)
\(138\) −18.7235 −1.59385
\(139\) −11.2343 −0.952880 −0.476440 0.879207i \(-0.658073\pi\)
−0.476440 + 0.879207i \(0.658073\pi\)
\(140\) 18.8579 1.59378
\(141\) 11.6137 0.978050
\(142\) 25.1310 2.10895
\(143\) −2.39155 −0.199992
\(144\) −0.0631677 −0.00526398
\(145\) −6.86205 −0.569862
\(146\) −18.8802 −1.56254
\(147\) −4.65154 −0.383653
\(148\) 23.6658 1.94532
\(149\) 1.54149 0.126284 0.0631420 0.998005i \(-0.479888\pi\)
0.0631420 + 0.998005i \(0.479888\pi\)
\(150\) 4.70691 0.384318
\(151\) 9.37962 0.763303 0.381651 0.924306i \(-0.375356\pi\)
0.381651 + 0.924306i \(0.375356\pi\)
\(152\) 14.7408 1.19564
\(153\) 0.255103 0.0206238
\(154\) 18.6546 1.50323
\(155\) 2.13375 0.171387
\(156\) −3.22190 −0.257958
\(157\) −20.7437 −1.65553 −0.827764 0.561077i \(-0.810387\pi\)
−0.827764 + 0.561077i \(0.810387\pi\)
\(158\) 11.4270 0.909083
\(159\) −0.884763 −0.0701663
\(160\) 9.82317 0.776590
\(161\) −27.9682 −2.20421
\(162\) 2.28515 0.179538
\(163\) 12.2878 0.962453 0.481226 0.876596i \(-0.340192\pi\)
0.481226 + 0.876596i \(0.340192\pi\)
\(164\) 9.49185 0.741189
\(165\) −4.10081 −0.319247
\(166\) 36.7441 2.85190
\(167\) −25.1607 −1.94699 −0.973495 0.228708i \(-0.926550\pi\)
−0.973495 + 0.228708i \(0.926550\pi\)
\(168\) 9.53106 0.735337
\(169\) 1.00000 0.0769231
\(170\) −0.999583 −0.0766645
\(171\) 5.27925 0.403714
\(172\) 9.84141 0.750401
\(173\) 2.99711 0.227866 0.113933 0.993488i \(-0.463655\pi\)
0.113933 + 0.993488i \(0.463655\pi\)
\(174\) −9.14489 −0.693272
\(175\) 7.03095 0.531490
\(176\) 0.151069 0.0113872
\(177\) −11.4507 −0.860686
\(178\) −25.5442 −1.91462
\(179\) −19.1346 −1.43018 −0.715092 0.699030i \(-0.753615\pi\)
−0.715092 + 0.699030i \(0.753615\pi\)
\(180\) −5.52461 −0.411780
\(181\) −11.5217 −0.856405 −0.428202 0.903683i \(-0.640853\pi\)
−0.428202 + 0.903683i \(0.640853\pi\)
\(182\) −7.80020 −0.578190
\(183\) −7.88600 −0.582950
\(184\) 22.8782 1.68661
\(185\) −12.5950 −0.926006
\(186\) 2.84360 0.208503
\(187\) −0.610091 −0.0446143
\(188\) −37.4182 −2.72900
\(189\) 3.41344 0.248291
\(190\) −20.6860 −1.50072
\(191\) −16.4594 −1.19096 −0.595480 0.803370i \(-0.703038\pi\)
−0.595480 + 0.803370i \(0.703038\pi\)
\(192\) 12.9648 0.935652
\(193\) 19.1523 1.37861 0.689306 0.724470i \(-0.257915\pi\)
0.689306 + 0.724470i \(0.257915\pi\)
\(194\) 36.8764 2.64757
\(195\) 1.71471 0.122793
\(196\) 14.9868 1.07049
\(197\) 23.2375 1.65560 0.827802 0.561020i \(-0.189591\pi\)
0.827802 + 0.561020i \(0.189591\pi\)
\(198\) −5.46505 −0.388384
\(199\) −16.9857 −1.20408 −0.602041 0.798465i \(-0.705646\pi\)
−0.602041 + 0.798465i \(0.705646\pi\)
\(200\) −5.75137 −0.406683
\(201\) −7.71850 −0.544421
\(202\) 17.7960 1.25212
\(203\) −13.6602 −0.958756
\(204\) −0.821915 −0.0575456
\(205\) −5.05160 −0.352819
\(206\) −2.28515 −0.159214
\(207\) 8.19358 0.569493
\(208\) −0.0631677 −0.00437989
\(209\) −12.6256 −0.873331
\(210\) −13.3750 −0.922966
\(211\) −7.92265 −0.545418 −0.272709 0.962097i \(-0.587920\pi\)
−0.272709 + 0.962097i \(0.587920\pi\)
\(212\) 2.85062 0.195781
\(213\) −10.9975 −0.753539
\(214\) −29.1331 −1.99150
\(215\) −5.23763 −0.357204
\(216\) −2.79222 −0.189986
\(217\) 4.24763 0.288348
\(218\) −11.1891 −0.757824
\(219\) 8.26216 0.558305
\(220\) 13.2124 0.890779
\(221\) 0.255103 0.0171601
\(222\) −16.7851 −1.12654
\(223\) 7.13905 0.478066 0.239033 0.971011i \(-0.423170\pi\)
0.239033 + 0.971011i \(0.423170\pi\)
\(224\) 19.5548 1.30656
\(225\) −2.05979 −0.137319
\(226\) −15.4397 −1.02703
\(227\) 22.8763 1.51836 0.759178 0.650883i \(-0.225601\pi\)
0.759178 + 0.650883i \(0.225601\pi\)
\(228\) −17.0092 −1.12646
\(229\) −23.8110 −1.57347 −0.786736 0.617289i \(-0.788231\pi\)
−0.786736 + 0.617289i \(0.788231\pi\)
\(230\) −32.1053 −2.11696
\(231\) −8.16341 −0.537113
\(232\) 11.1741 0.733617
\(233\) −12.3701 −0.810395 −0.405198 0.914229i \(-0.632797\pi\)
−0.405198 + 0.914229i \(0.632797\pi\)
\(234\) 2.28515 0.149385
\(235\) 19.9141 1.29905
\(236\) 36.8929 2.40153
\(237\) −5.00055 −0.324821
\(238\) −1.98985 −0.128983
\(239\) 7.04450 0.455671 0.227835 0.973700i \(-0.426835\pi\)
0.227835 + 0.973700i \(0.426835\pi\)
\(240\) −0.108314 −0.00699164
\(241\) 1.57911 0.101719 0.0508597 0.998706i \(-0.483804\pi\)
0.0508597 + 0.998706i \(0.483804\pi\)
\(242\) −12.0667 −0.775675
\(243\) −1.00000 −0.0641500
\(244\) 25.4079 1.62657
\(245\) −7.97602 −0.509569
\(246\) −6.73214 −0.429226
\(247\) 5.27925 0.335911
\(248\) −3.47460 −0.220637
\(249\) −16.0795 −1.01900
\(250\) 27.6627 1.74955
\(251\) −9.65990 −0.609727 −0.304864 0.952396i \(-0.598611\pi\)
−0.304864 + 0.952396i \(0.598611\pi\)
\(252\) −10.9977 −0.692793
\(253\) −19.5954 −1.23195
\(254\) 25.8622 1.62274
\(255\) 0.437426 0.0273927
\(256\) −15.5890 −0.974311
\(257\) −17.5266 −1.09328 −0.546639 0.837369i \(-0.684093\pi\)
−0.546639 + 0.837369i \(0.684093\pi\)
\(258\) −6.98007 −0.434560
\(259\) −25.0727 −1.55794
\(260\) −5.52461 −0.342622
\(261\) 4.00188 0.247710
\(262\) 43.8133 2.70680
\(263\) 24.8504 1.53234 0.766170 0.642638i \(-0.222160\pi\)
0.766170 + 0.642638i \(0.222160\pi\)
\(264\) 6.67773 0.410986
\(265\) −1.51711 −0.0931952
\(266\) −41.1792 −2.52486
\(267\) 11.1784 0.684104
\(268\) 24.8682 1.51907
\(269\) 9.71874 0.592562 0.296281 0.955101i \(-0.404253\pi\)
0.296281 + 0.955101i \(0.404253\pi\)
\(270\) 3.91835 0.238463
\(271\) −1.14079 −0.0692982 −0.0346491 0.999400i \(-0.511031\pi\)
−0.0346491 + 0.999400i \(0.511031\pi\)
\(272\) −0.0161143 −0.000977071 0
\(273\) 3.41344 0.206591
\(274\) 39.3435 2.37683
\(275\) 4.92608 0.297054
\(276\) −26.3989 −1.58903
\(277\) 10.0010 0.600900 0.300450 0.953798i \(-0.402863\pi\)
0.300450 + 0.953798i \(0.402863\pi\)
\(278\) −25.6720 −1.53970
\(279\) −1.24439 −0.0744994
\(280\) 16.3429 0.976678
\(281\) −1.05334 −0.0628371 −0.0314185 0.999506i \(-0.510002\pi\)
−0.0314185 + 0.999506i \(0.510002\pi\)
\(282\) 26.5390 1.58038
\(283\) 33.1797 1.97233 0.986163 0.165778i \(-0.0530135\pi\)
0.986163 + 0.165778i \(0.0530135\pi\)
\(284\) 35.4329 2.10256
\(285\) 9.05236 0.536216
\(286\) −5.46505 −0.323155
\(287\) −10.0561 −0.593594
\(288\) −5.72878 −0.337572
\(289\) −16.9349 −0.996172
\(290\) −15.6808 −0.920808
\(291\) −16.1374 −0.945993
\(292\) −26.6198 −1.55781
\(293\) 3.76067 0.219701 0.109850 0.993948i \(-0.464963\pi\)
0.109850 + 0.993948i \(0.464963\pi\)
\(294\) −10.6295 −0.619923
\(295\) −19.6345 −1.14317
\(296\) 20.5097 1.19210
\(297\) 2.39155 0.138772
\(298\) 3.52254 0.204055
\(299\) 8.19358 0.473847
\(300\) 6.63642 0.383154
\(301\) −10.4265 −0.600972
\(302\) 21.4338 1.23338
\(303\) −7.78769 −0.447391
\(304\) −0.333478 −0.0191263
\(305\) −13.5222 −0.774277
\(306\) 0.582947 0.0333249
\(307\) −10.5794 −0.603796 −0.301898 0.953340i \(-0.597620\pi\)
−0.301898 + 0.953340i \(0.597620\pi\)
\(308\) 26.3017 1.49868
\(309\) 1.00000 0.0568880
\(310\) 4.87594 0.276935
\(311\) 26.1467 1.48265 0.741323 0.671149i \(-0.234199\pi\)
0.741323 + 0.671149i \(0.234199\pi\)
\(312\) −2.79222 −0.158078
\(313\) −23.8126 −1.34597 −0.672985 0.739656i \(-0.734988\pi\)
−0.672985 + 0.739656i \(0.734988\pi\)
\(314\) −47.4024 −2.67507
\(315\) 5.85304 0.329781
\(316\) 16.1113 0.906330
\(317\) −20.7133 −1.16337 −0.581686 0.813413i \(-0.697607\pi\)
−0.581686 + 0.813413i \(0.697607\pi\)
\(318\) −2.02181 −0.113378
\(319\) −9.57071 −0.535857
\(320\) 22.2308 1.24274
\(321\) 12.7489 0.711573
\(322\) −63.9116 −3.56165
\(323\) 1.34675 0.0749353
\(324\) 3.22190 0.178994
\(325\) −2.05979 −0.114256
\(326\) 28.0794 1.55517
\(327\) 4.89646 0.270775
\(328\) 8.22599 0.454205
\(329\) 39.6426 2.18557
\(330\) −9.37095 −0.515854
\(331\) −7.55226 −0.415110 −0.207555 0.978223i \(-0.566551\pi\)
−0.207555 + 0.978223i \(0.566551\pi\)
\(332\) 51.8066 2.84326
\(333\) 7.34531 0.402521
\(334\) −57.4958 −3.14603
\(335\) −13.2350 −0.723103
\(336\) −0.215619 −0.0117630
\(337\) 18.4564 1.00538 0.502692 0.864466i \(-0.332343\pi\)
0.502692 + 0.864466i \(0.332343\pi\)
\(338\) 2.28515 0.124296
\(339\) 6.75655 0.366966
\(340\) −1.40934 −0.0764323
\(341\) 2.97601 0.161160
\(342\) 12.0639 0.652339
\(343\) 8.01631 0.432840
\(344\) 8.52894 0.459849
\(345\) 14.0496 0.756403
\(346\) 6.84883 0.368196
\(347\) 34.9200 1.87460 0.937302 0.348519i \(-0.113315\pi\)
0.937302 + 0.348519i \(0.113315\pi\)
\(348\) −12.8937 −0.691173
\(349\) −18.2434 −0.976546 −0.488273 0.872691i \(-0.662373\pi\)
−0.488273 + 0.872691i \(0.662373\pi\)
\(350\) 16.0667 0.858804
\(351\) −1.00000 −0.0533761
\(352\) 13.7007 0.730249
\(353\) 36.3598 1.93524 0.967619 0.252416i \(-0.0812251\pi\)
0.967619 + 0.252416i \(0.0812251\pi\)
\(354\) −26.1665 −1.39073
\(355\) −18.8575 −1.00085
\(356\) −36.0155 −1.90882
\(357\) 0.870777 0.0460864
\(358\) −43.7253 −2.31095
\(359\) 2.67100 0.140970 0.0704850 0.997513i \(-0.477545\pi\)
0.0704850 + 0.997513i \(0.477545\pi\)
\(360\) −4.78783 −0.252341
\(361\) 8.87049 0.466868
\(362\) −26.3289 −1.38382
\(363\) 5.28048 0.277153
\(364\) −10.9977 −0.576438
\(365\) 14.1672 0.741543
\(366\) −18.0207 −0.941956
\(367\) 15.2213 0.794547 0.397274 0.917700i \(-0.369956\pi\)
0.397274 + 0.917700i \(0.369956\pi\)
\(368\) −0.517570 −0.0269802
\(369\) 2.94604 0.153365
\(370\) −28.7815 −1.49628
\(371\) −3.02008 −0.156795
\(372\) 4.00928 0.207872
\(373\) −0.625827 −0.0324041 −0.0162021 0.999869i \(-0.505157\pi\)
−0.0162021 + 0.999869i \(0.505157\pi\)
\(374\) −1.39415 −0.0720897
\(375\) −12.1055 −0.625123
\(376\) −32.4280 −1.67235
\(377\) 4.00188 0.206107
\(378\) 7.80020 0.401199
\(379\) 26.0071 1.33589 0.667946 0.744209i \(-0.267174\pi\)
0.667946 + 0.744209i \(0.267174\pi\)
\(380\) −29.1658 −1.49617
\(381\) −11.3175 −0.579813
\(382\) −37.6121 −1.92440
\(383\) −9.03498 −0.461666 −0.230833 0.972993i \(-0.574145\pi\)
−0.230833 + 0.972993i \(0.574145\pi\)
\(384\) 18.1689 0.927176
\(385\) −13.9978 −0.713396
\(386\) 43.7658 2.22762
\(387\) 3.05454 0.155271
\(388\) 51.9931 2.63955
\(389\) 16.7774 0.850646 0.425323 0.905042i \(-0.360160\pi\)
0.425323 + 0.905042i \(0.360160\pi\)
\(390\) 3.91835 0.198414
\(391\) 2.09020 0.105706
\(392\) 12.9881 0.655999
\(393\) −19.1731 −0.967155
\(394\) 53.1011 2.67520
\(395\) −8.57447 −0.431429
\(396\) −7.70534 −0.387208
\(397\) −2.34156 −0.117519 −0.0587597 0.998272i \(-0.518715\pi\)
−0.0587597 + 0.998272i \(0.518715\pi\)
\(398\) −38.8148 −1.94561
\(399\) 18.0204 0.902148
\(400\) 0.130112 0.00650560
\(401\) 22.7341 1.13529 0.567644 0.823274i \(-0.307855\pi\)
0.567644 + 0.823274i \(0.307855\pi\)
\(402\) −17.6379 −0.879699
\(403\) −1.24439 −0.0619873
\(404\) 25.0912 1.24833
\(405\) −1.71471 −0.0852044
\(406\) −31.2155 −1.54920
\(407\) −17.5667 −0.870748
\(408\) −0.712302 −0.0352642
\(409\) −28.2430 −1.39653 −0.698264 0.715841i \(-0.746044\pi\)
−0.698264 + 0.715841i \(0.746044\pi\)
\(410\) −11.5436 −0.570100
\(411\) −17.2171 −0.849255
\(412\) −3.22190 −0.158732
\(413\) −39.0862 −1.92330
\(414\) 18.7235 0.920211
\(415\) −27.5717 −1.35344
\(416\) −5.72878 −0.280877
\(417\) 11.2343 0.550145
\(418\) −28.8514 −1.41117
\(419\) −31.9451 −1.56062 −0.780310 0.625392i \(-0.784939\pi\)
−0.780310 + 0.625392i \(0.784939\pi\)
\(420\) −18.8579 −0.920171
\(421\) 12.3594 0.602358 0.301179 0.953568i \(-0.402620\pi\)
0.301179 + 0.953568i \(0.402620\pi\)
\(422\) −18.1044 −0.881309
\(423\) −11.6137 −0.564677
\(424\) 2.47045 0.119976
\(425\) −0.525457 −0.0254884
\(426\) −25.1310 −1.21760
\(427\) −26.9184 −1.30267
\(428\) −41.0756 −1.98546
\(429\) 2.39155 0.115465
\(430\) −11.9688 −0.577185
\(431\) 16.7482 0.806734 0.403367 0.915038i \(-0.367840\pi\)
0.403367 + 0.915038i \(0.367840\pi\)
\(432\) 0.0631677 0.00303916
\(433\) −28.9389 −1.39072 −0.695359 0.718663i \(-0.744754\pi\)
−0.695359 + 0.718663i \(0.744754\pi\)
\(434\) 9.70646 0.465925
\(435\) 6.86205 0.329010
\(436\) −15.7759 −0.755529
\(437\) 43.2559 2.06921
\(438\) 18.8802 0.902133
\(439\) 7.25628 0.346323 0.173162 0.984893i \(-0.444602\pi\)
0.173162 + 0.984893i \(0.444602\pi\)
\(440\) 11.4503 0.545874
\(441\) 4.65154 0.221502
\(442\) 0.582947 0.0277280
\(443\) 14.8478 0.705441 0.352721 0.935729i \(-0.385257\pi\)
0.352721 + 0.935729i \(0.385257\pi\)
\(444\) −23.6658 −1.12313
\(445\) 19.1676 0.908631
\(446\) 16.3138 0.772480
\(447\) −1.54149 −0.0729102
\(448\) 44.2544 2.09083
\(449\) −20.2016 −0.953375 −0.476687 0.879073i \(-0.658163\pi\)
−0.476687 + 0.879073i \(0.658163\pi\)
\(450\) −4.70691 −0.221886
\(451\) −7.04561 −0.331765
\(452\) −21.7689 −1.02392
\(453\) −9.37962 −0.440693
\(454\) 52.2758 2.45343
\(455\) 5.85304 0.274395
\(456\) −14.7408 −0.690302
\(457\) −18.7638 −0.877733 −0.438867 0.898552i \(-0.644620\pi\)
−0.438867 + 0.898552i \(0.644620\pi\)
\(458\) −54.4116 −2.54248
\(459\) −0.255103 −0.0119072
\(460\) −45.2663 −2.11055
\(461\) 33.5705 1.56353 0.781767 0.623571i \(-0.214319\pi\)
0.781767 + 0.623571i \(0.214319\pi\)
\(462\) −18.6546 −0.867890
\(463\) 33.6119 1.56208 0.781038 0.624483i \(-0.214690\pi\)
0.781038 + 0.624483i \(0.214690\pi\)
\(464\) −0.252790 −0.0117355
\(465\) −2.13375 −0.0989505
\(466\) −28.2676 −1.30947
\(467\) −28.2426 −1.30691 −0.653455 0.756965i \(-0.726681\pi\)
−0.653455 + 0.756965i \(0.726681\pi\)
\(468\) 3.22190 0.148932
\(469\) −26.3466 −1.21657
\(470\) 45.5066 2.09906
\(471\) 20.7437 0.955819
\(472\) 31.9728 1.47167
\(473\) −7.30509 −0.335888
\(474\) −11.4270 −0.524860
\(475\) −10.8741 −0.498939
\(476\) −2.80555 −0.128592
\(477\) 0.884763 0.0405105
\(478\) 16.0977 0.736293
\(479\) 18.0801 0.826101 0.413051 0.910708i \(-0.364463\pi\)
0.413051 + 0.910708i \(0.364463\pi\)
\(480\) −9.82317 −0.448365
\(481\) 7.34531 0.334917
\(482\) 3.60850 0.164363
\(483\) 27.9682 1.27260
\(484\) −17.0132 −0.773326
\(485\) −27.6709 −1.25647
\(486\) −2.28515 −0.103656
\(487\) 11.3088 0.512449 0.256225 0.966617i \(-0.417521\pi\)
0.256225 + 0.966617i \(0.417521\pi\)
\(488\) 22.0194 0.996773
\(489\) −12.2878 −0.555672
\(490\) −18.2264 −0.823384
\(491\) −11.1297 −0.502278 −0.251139 0.967951i \(-0.580805\pi\)
−0.251139 + 0.967951i \(0.580805\pi\)
\(492\) −9.49185 −0.427926
\(493\) 1.02089 0.0459786
\(494\) 12.0639 0.542779
\(495\) 4.10081 0.184318
\(496\) 0.0786050 0.00352947
\(497\) −37.5394 −1.68387
\(498\) −36.7441 −1.64654
\(499\) −33.5896 −1.50368 −0.751838 0.659348i \(-0.770833\pi\)
−0.751838 + 0.659348i \(0.770833\pi\)
\(500\) 39.0025 1.74425
\(501\) 25.1607 1.12410
\(502\) −22.0743 −0.985224
\(503\) −29.6226 −1.32080 −0.660402 0.750912i \(-0.729614\pi\)
−0.660402 + 0.750912i \(0.729614\pi\)
\(504\) −9.53106 −0.424547
\(505\) −13.3536 −0.594227
\(506\) −44.7783 −1.99064
\(507\) −1.00000 −0.0444116
\(508\) 36.4638 1.61782
\(509\) −6.23103 −0.276185 −0.138093 0.990419i \(-0.544097\pi\)
−0.138093 + 0.990419i \(0.544097\pi\)
\(510\) 0.999583 0.0442623
\(511\) 28.2023 1.24760
\(512\) 0.714630 0.0315825
\(513\) −5.27925 −0.233085
\(514\) −40.0508 −1.76657
\(515\) 1.71471 0.0755589
\(516\) −9.84141 −0.433244
\(517\) 27.7748 1.22153
\(518\) −57.2949 −2.51739
\(519\) −2.99711 −0.131558
\(520\) −4.78783 −0.209960
\(521\) −36.8476 −1.61432 −0.807161 0.590332i \(-0.798997\pi\)
−0.807161 + 0.590332i \(0.798997\pi\)
\(522\) 9.14489 0.400261
\(523\) −4.70510 −0.205740 −0.102870 0.994695i \(-0.532802\pi\)
−0.102870 + 0.994695i \(0.532802\pi\)
\(524\) 61.7738 2.69860
\(525\) −7.03095 −0.306856
\(526\) 56.7868 2.47602
\(527\) −0.317446 −0.0138282
\(528\) −0.151069 −0.00657443
\(529\) 44.1347 1.91890
\(530\) −3.46682 −0.150589
\(531\) 11.4507 0.496917
\(532\) −58.0598 −2.51721
\(533\) 2.94604 0.127607
\(534\) 25.5442 1.10541
\(535\) 21.8606 0.945115
\(536\) 21.5517 0.930893
\(537\) 19.1346 0.825718
\(538\) 22.2088 0.957488
\(539\) −11.1244 −0.479162
\(540\) 5.52461 0.237741
\(541\) 18.2189 0.783294 0.391647 0.920116i \(-0.371906\pi\)
0.391647 + 0.920116i \(0.371906\pi\)
\(542\) −2.60688 −0.111975
\(543\) 11.5217 0.494446
\(544\) −1.46143 −0.0626582
\(545\) 8.39599 0.359645
\(546\) 7.80020 0.333818
\(547\) −4.53208 −0.193778 −0.0968889 0.995295i \(-0.530889\pi\)
−0.0968889 + 0.995295i \(0.530889\pi\)
\(548\) 55.4716 2.36963
\(549\) 7.88600 0.336566
\(550\) 11.2568 0.479993
\(551\) 21.1269 0.900038
\(552\) −22.8782 −0.973763
\(553\) −17.0691 −0.725850
\(554\) 22.8537 0.970959
\(555\) 12.5950 0.534630
\(556\) −36.1957 −1.53504
\(557\) −42.3256 −1.79339 −0.896697 0.442645i \(-0.854040\pi\)
−0.896697 + 0.442645i \(0.854040\pi\)
\(558\) −2.84360 −0.120379
\(559\) 3.05454 0.129193
\(560\) −0.369723 −0.0156236
\(561\) 0.610091 0.0257581
\(562\) −2.40704 −0.101535
\(563\) 0.157148 0.00662302 0.00331151 0.999995i \(-0.498946\pi\)
0.00331151 + 0.999995i \(0.498946\pi\)
\(564\) 37.4182 1.57559
\(565\) 11.5855 0.487405
\(566\) 75.8204 3.18697
\(567\) −3.41344 −0.143351
\(568\) 30.7075 1.28846
\(569\) −4.28598 −0.179677 −0.0898387 0.995956i \(-0.528635\pi\)
−0.0898387 + 0.995956i \(0.528635\pi\)
\(570\) 20.6860 0.866440
\(571\) 38.8367 1.62527 0.812633 0.582776i \(-0.198033\pi\)
0.812633 + 0.582776i \(0.198033\pi\)
\(572\) −7.70534 −0.322176
\(573\) 16.4594 0.687601
\(574\) −22.9797 −0.959156
\(575\) −16.8770 −0.703820
\(576\) −12.9648 −0.540199
\(577\) 37.4133 1.55754 0.778769 0.627311i \(-0.215844\pi\)
0.778769 + 0.627311i \(0.215844\pi\)
\(578\) −38.6988 −1.60966
\(579\) −19.1523 −0.795943
\(580\) −22.1088 −0.918019
\(581\) −54.8865 −2.27707
\(582\) −36.8764 −1.52858
\(583\) −2.11596 −0.0876340
\(584\) −23.0697 −0.954633
\(585\) −1.71471 −0.0708943
\(586\) 8.59368 0.355002
\(587\) 40.4137 1.66805 0.834026 0.551724i \(-0.186030\pi\)
0.834026 + 0.551724i \(0.186030\pi\)
\(588\) −14.9868 −0.618045
\(589\) −6.56942 −0.270688
\(590\) −44.8678 −1.84718
\(591\) −23.2375 −0.955864
\(592\) −0.463987 −0.0190697
\(593\) 0.923076 0.0379062 0.0189531 0.999820i \(-0.493967\pi\)
0.0189531 + 0.999820i \(0.493967\pi\)
\(594\) 5.46505 0.224234
\(595\) 1.49313 0.0612122
\(596\) 4.96654 0.203437
\(597\) 16.9857 0.695177
\(598\) 18.7235 0.765662
\(599\) 8.63432 0.352789 0.176394 0.984320i \(-0.443557\pi\)
0.176394 + 0.984320i \(0.443557\pi\)
\(600\) 5.75137 0.234799
\(601\) −30.3188 −1.23673 −0.618364 0.785892i \(-0.712204\pi\)
−0.618364 + 0.785892i \(0.712204\pi\)
\(602\) −23.8260 −0.971076
\(603\) 7.71850 0.314322
\(604\) 30.2202 1.22964
\(605\) 9.05447 0.368116
\(606\) −17.7960 −0.722914
\(607\) −2.17453 −0.0882613 −0.0441307 0.999026i \(-0.514052\pi\)
−0.0441307 + 0.999026i \(0.514052\pi\)
\(608\) −30.2437 −1.22654
\(609\) 13.6602 0.553538
\(610\) −30.9001 −1.25111
\(611\) −11.6137 −0.469840
\(612\) 0.821915 0.0332239
\(613\) 29.7489 1.20155 0.600774 0.799419i \(-0.294859\pi\)
0.600774 + 0.799419i \(0.294859\pi\)
\(614\) −24.1754 −0.975640
\(615\) 5.05160 0.203700
\(616\) 22.7940 0.918397
\(617\) 11.2602 0.453319 0.226659 0.973974i \(-0.427220\pi\)
0.226659 + 0.973974i \(0.427220\pi\)
\(618\) 2.28515 0.0919221
\(619\) 44.5760 1.79166 0.895829 0.444398i \(-0.146582\pi\)
0.895829 + 0.444398i \(0.146582\pi\)
\(620\) 6.87474 0.276096
\(621\) −8.19358 −0.328797
\(622\) 59.7491 2.39572
\(623\) 38.1566 1.52871
\(624\) 0.0631677 0.00252873
\(625\) −10.4584 −0.418334
\(626\) −54.4154 −2.17488
\(627\) 12.6256 0.504218
\(628\) −66.8341 −2.66697
\(629\) 1.87381 0.0747136
\(630\) 13.3750 0.532875
\(631\) −17.9206 −0.713408 −0.356704 0.934217i \(-0.616100\pi\)
−0.356704 + 0.934217i \(0.616100\pi\)
\(632\) 13.9626 0.555404
\(633\) 7.92265 0.314897
\(634\) −47.3328 −1.87983
\(635\) −19.4062 −0.770111
\(636\) −2.85062 −0.113034
\(637\) 4.65154 0.184301
\(638\) −21.8705 −0.865860
\(639\) 10.9975 0.435056
\(640\) 31.1542 1.23148
\(641\) 16.8217 0.664417 0.332209 0.943206i \(-0.392206\pi\)
0.332209 + 0.943206i \(0.392206\pi\)
\(642\) 29.1331 1.14979
\(643\) −38.0452 −1.50036 −0.750178 0.661236i \(-0.770032\pi\)
−0.750178 + 0.661236i \(0.770032\pi\)
\(644\) −90.1108 −3.55086
\(645\) 5.23763 0.206232
\(646\) 3.07753 0.121084
\(647\) −16.3953 −0.644567 −0.322283 0.946643i \(-0.604450\pi\)
−0.322283 + 0.946643i \(0.604450\pi\)
\(648\) 2.79222 0.109689
\(649\) −27.3849 −1.07495
\(650\) −4.70691 −0.184620
\(651\) −4.24763 −0.166478
\(652\) 39.5900 1.55046
\(653\) 14.4785 0.566588 0.283294 0.959033i \(-0.408573\pi\)
0.283294 + 0.959033i \(0.408573\pi\)
\(654\) 11.1891 0.437530
\(655\) −32.8762 −1.28458
\(656\) −0.186095 −0.00726578
\(657\) −8.26216 −0.322337
\(658\) 90.5892 3.53154
\(659\) 12.9251 0.503489 0.251745 0.967794i \(-0.418996\pi\)
0.251745 + 0.967794i \(0.418996\pi\)
\(660\) −13.2124 −0.514291
\(661\) −43.1292 −1.67753 −0.838766 0.544491i \(-0.816723\pi\)
−0.838766 + 0.544491i \(0.816723\pi\)
\(662\) −17.2580 −0.670753
\(663\) −0.255103 −0.00990737
\(664\) 44.8976 1.74236
\(665\) 30.8996 1.19824
\(666\) 16.7851 0.650410
\(667\) 32.7897 1.26962
\(668\) −81.0651 −3.13650
\(669\) −7.13905 −0.276012
\(670\) −30.2438 −1.16842
\(671\) −18.8598 −0.728074
\(672\) −19.5548 −0.754344
\(673\) 41.2697 1.59083 0.795414 0.606066i \(-0.207253\pi\)
0.795414 + 0.606066i \(0.207253\pi\)
\(674\) 42.1756 1.62454
\(675\) 2.05979 0.0792812
\(676\) 3.22190 0.123919
\(677\) 12.2927 0.472445 0.236223 0.971699i \(-0.424091\pi\)
0.236223 + 0.971699i \(0.424091\pi\)
\(678\) 15.4397 0.592959
\(679\) −55.0841 −2.11393
\(680\) −1.22139 −0.0468381
\(681\) −22.8763 −0.876623
\(682\) 6.80063 0.260409
\(683\) 26.7405 1.02320 0.511599 0.859224i \(-0.329053\pi\)
0.511599 + 0.859224i \(0.329053\pi\)
\(684\) 17.0092 0.650363
\(685\) −29.5222 −1.12798
\(686\) 18.3185 0.699402
\(687\) 23.8110 0.908445
\(688\) −0.192948 −0.00735609
\(689\) 0.884763 0.0337068
\(690\) 32.1053 1.22223
\(691\) −10.3840 −0.395027 −0.197514 0.980300i \(-0.563287\pi\)
−0.197514 + 0.980300i \(0.563287\pi\)
\(692\) 9.65638 0.367080
\(693\) 8.16341 0.310102
\(694\) 79.7973 3.02907
\(695\) 19.2635 0.730706
\(696\) −11.1741 −0.423554
\(697\) 0.751544 0.0284667
\(698\) −41.6888 −1.57795
\(699\) 12.3701 0.467882
\(700\) 22.6530 0.856203
\(701\) −1.89474 −0.0715634 −0.0357817 0.999360i \(-0.511392\pi\)
−0.0357817 + 0.999360i \(0.511392\pi\)
\(702\) −2.28515 −0.0862473
\(703\) 38.7777 1.46253
\(704\) 31.0059 1.16858
\(705\) −19.9141 −0.750007
\(706\) 83.0875 3.12704
\(707\) −26.5828 −0.999749
\(708\) −36.8929 −1.38652
\(709\) 1.58262 0.0594365 0.0297182 0.999558i \(-0.490539\pi\)
0.0297182 + 0.999558i \(0.490539\pi\)
\(710\) −43.0922 −1.61722
\(711\) 5.00055 0.187535
\(712\) −31.2124 −1.16973
\(713\) −10.1960 −0.381842
\(714\) 1.98985 0.0744684
\(715\) 4.10081 0.153361
\(716\) −61.6496 −2.30395
\(717\) −7.04450 −0.263082
\(718\) 6.10362 0.227785
\(719\) 37.4439 1.39642 0.698211 0.715892i \(-0.253980\pi\)
0.698211 + 0.715892i \(0.253980\pi\)
\(720\) 0.108314 0.00403663
\(721\) 3.41344 0.127123
\(722\) 20.2704 0.754386
\(723\) −1.57911 −0.0587277
\(724\) −37.1219 −1.37962
\(725\) −8.24302 −0.306138
\(726\) 12.0667 0.447836
\(727\) −37.5084 −1.39111 −0.695555 0.718473i \(-0.744842\pi\)
−0.695555 + 0.718473i \(0.744842\pi\)
\(728\) −9.53106 −0.353244
\(729\) 1.00000 0.0370370
\(730\) 32.3741 1.19822
\(731\) 0.779221 0.0288205
\(732\) −25.4079 −0.939103
\(733\) −10.9898 −0.405916 −0.202958 0.979187i \(-0.565055\pi\)
−0.202958 + 0.979187i \(0.565055\pi\)
\(734\) 34.7830 1.28386
\(735\) 7.97602 0.294200
\(736\) −46.9392 −1.73020
\(737\) −18.4592 −0.679953
\(738\) 6.73214 0.247814
\(739\) 1.70284 0.0626401 0.0313201 0.999509i \(-0.490029\pi\)
0.0313201 + 0.999509i \(0.490029\pi\)
\(740\) −40.5799 −1.49175
\(741\) −5.27925 −0.193938
\(742\) −6.90133 −0.253356
\(743\) 27.3427 1.00311 0.501554 0.865126i \(-0.332762\pi\)
0.501554 + 0.865126i \(0.332762\pi\)
\(744\) 3.47460 0.127385
\(745\) −2.64321 −0.0968396
\(746\) −1.43011 −0.0523600
\(747\) 16.0795 0.588320
\(748\) −1.96565 −0.0718714
\(749\) 43.5175 1.59009
\(750\) −27.6627 −1.01010
\(751\) 18.7547 0.684368 0.342184 0.939633i \(-0.388833\pi\)
0.342184 + 0.939633i \(0.388833\pi\)
\(752\) 0.733611 0.0267520
\(753\) 9.65990 0.352026
\(754\) 9.14489 0.333037
\(755\) −16.0833 −0.585331
\(756\) 10.9977 0.399984
\(757\) −29.3854 −1.06803 −0.534015 0.845475i \(-0.679318\pi\)
−0.534015 + 0.845475i \(0.679318\pi\)
\(758\) 59.4300 2.15859
\(759\) 19.5954 0.711267
\(760\) −25.2762 −0.916863
\(761\) 35.8984 1.30132 0.650658 0.759371i \(-0.274493\pi\)
0.650658 + 0.759371i \(0.274493\pi\)
\(762\) −25.8622 −0.936887
\(763\) 16.7138 0.605079
\(764\) −53.0305 −1.91857
\(765\) −0.437426 −0.0158152
\(766\) −20.6463 −0.745980
\(767\) 11.4507 0.413460
\(768\) 15.5890 0.562518
\(769\) 31.8777 1.14954 0.574769 0.818316i \(-0.305092\pi\)
0.574769 + 0.818316i \(0.305092\pi\)
\(770\) −31.9871 −1.15274
\(771\) 17.5266 0.631204
\(772\) 61.7068 2.22088
\(773\) −21.5690 −0.775781 −0.387891 0.921705i \(-0.626796\pi\)
−0.387891 + 0.921705i \(0.626796\pi\)
\(774\) 6.98007 0.250893
\(775\) 2.56317 0.0920717
\(776\) 45.0592 1.61753
\(777\) 25.0727 0.899480
\(778\) 38.3387 1.37451
\(779\) 15.5529 0.557241
\(780\) 5.52461 0.197813
\(781\) −26.3012 −0.941130
\(782\) 4.77642 0.170805
\(783\) −4.00188 −0.143016
\(784\) −0.293827 −0.0104938
\(785\) 35.5693 1.26952
\(786\) −43.8133 −1.56277
\(787\) −41.3153 −1.47273 −0.736366 0.676583i \(-0.763460\pi\)
−0.736366 + 0.676583i \(0.763460\pi\)
\(788\) 74.8689 2.66709
\(789\) −24.8504 −0.884697
\(790\) −19.5939 −0.697121
\(791\) 23.0631 0.820028
\(792\) −6.67773 −0.237283
\(793\) 7.88600 0.280040
\(794\) −5.35081 −0.189893
\(795\) 1.51711 0.0538063
\(796\) −54.7261 −1.93972
\(797\) −24.4599 −0.866415 −0.433207 0.901294i \(-0.642618\pi\)
−0.433207 + 0.901294i \(0.642618\pi\)
\(798\) 41.1792 1.45773
\(799\) −2.96269 −0.104812
\(800\) 11.8001 0.417195
\(801\) −11.1784 −0.394968
\(802\) 51.9508 1.83445
\(803\) 19.7594 0.697293
\(804\) −24.8682 −0.877035
\(805\) 47.9573 1.69027
\(806\) −2.84360 −0.100162
\(807\) −9.71874 −0.342116
\(808\) 21.7449 0.764984
\(809\) −40.7164 −1.43151 −0.715755 0.698351i \(-0.753917\pi\)
−0.715755 + 0.698351i \(0.753917\pi\)
\(810\) −3.91835 −0.137677
\(811\) 13.7546 0.482988 0.241494 0.970402i \(-0.422363\pi\)
0.241494 + 0.970402i \(0.422363\pi\)
\(812\) −44.0117 −1.54451
\(813\) 1.14079 0.0400093
\(814\) −40.1425 −1.40699
\(815\) −21.0699 −0.738047
\(816\) 0.0161143 0.000564112 0
\(817\) 16.1257 0.564166
\(818\) −64.5394 −2.25657
\(819\) −3.41344 −0.119275
\(820\) −16.2757 −0.568373
\(821\) −16.5883 −0.578937 −0.289469 0.957188i \(-0.593479\pi\)
−0.289469 + 0.957188i \(0.593479\pi\)
\(822\) −39.3435 −1.37226
\(823\) −4.73370 −0.165007 −0.0825033 0.996591i \(-0.526291\pi\)
−0.0825033 + 0.996591i \(0.526291\pi\)
\(824\) −2.79222 −0.0972715
\(825\) −4.92608 −0.171504
\(826\) −89.3177 −3.10776
\(827\) 26.1246 0.908443 0.454221 0.890889i \(-0.349917\pi\)
0.454221 + 0.890889i \(0.349917\pi\)
\(828\) 26.3989 0.917424
\(829\) −16.7899 −0.583136 −0.291568 0.956550i \(-0.594177\pi\)
−0.291568 + 0.956550i \(0.594177\pi\)
\(830\) −63.0053 −2.18695
\(831\) −10.0010 −0.346930
\(832\) −12.9648 −0.449473
\(833\) 1.18662 0.0411140
\(834\) 25.6720 0.888949
\(835\) 43.1431 1.49303
\(836\) −40.6784 −1.40689
\(837\) 1.24439 0.0430123
\(838\) −72.9993 −2.52172
\(839\) 51.6191 1.78209 0.891044 0.453916i \(-0.149973\pi\)
0.891044 + 0.453916i \(0.149973\pi\)
\(840\) −16.3429 −0.563885
\(841\) −12.9849 −0.447757
\(842\) 28.2430 0.973317
\(843\) 1.05334 0.0362790
\(844\) −25.5260 −0.878640
\(845\) −1.71471 −0.0589877
\(846\) −26.5390 −0.912430
\(847\) 18.0246 0.619332
\(848\) −0.0558885 −0.00191922
\(849\) −33.1797 −1.13872
\(850\) −1.20075 −0.0411853
\(851\) 60.1844 2.06309
\(852\) −35.4329 −1.21391
\(853\) −30.2009 −1.03406 −0.517029 0.855968i \(-0.672962\pi\)
−0.517029 + 0.855968i \(0.672962\pi\)
\(854\) −61.5124 −2.10491
\(855\) −9.05236 −0.309584
\(856\) −35.5977 −1.21670
\(857\) 48.4034 1.65343 0.826715 0.562621i \(-0.190207\pi\)
0.826715 + 0.562621i \(0.190207\pi\)
\(858\) 5.46505 0.186574
\(859\) 19.7181 0.672774 0.336387 0.941724i \(-0.390795\pi\)
0.336387 + 0.941724i \(0.390795\pi\)
\(860\) −16.8751 −0.575437
\(861\) 10.0561 0.342712
\(862\) 38.2722 1.30356
\(863\) −6.82452 −0.232310 −0.116155 0.993231i \(-0.537057\pi\)
−0.116155 + 0.993231i \(0.537057\pi\)
\(864\) 5.72878 0.194897
\(865\) −5.13916 −0.174737
\(866\) −66.1298 −2.24718
\(867\) 16.9349 0.575140
\(868\) 13.6854 0.464514
\(869\) −11.9591 −0.405684
\(870\) 15.6808 0.531629
\(871\) 7.71850 0.261531
\(872\) −13.6720 −0.462992
\(873\) 16.1374 0.546169
\(874\) 98.8462 3.34352
\(875\) −41.3212 −1.39691
\(876\) 26.6198 0.899401
\(877\) 28.9327 0.976987 0.488494 0.872567i \(-0.337547\pi\)
0.488494 + 0.872567i \(0.337547\pi\)
\(878\) 16.5817 0.559604
\(879\) −3.76067 −0.126844
\(880\) −0.259039 −0.00873219
\(881\) 10.8292 0.364845 0.182422 0.983220i \(-0.441606\pi\)
0.182422 + 0.983220i \(0.441606\pi\)
\(882\) 10.6295 0.357912
\(883\) −5.10725 −0.171873 −0.0859364 0.996301i \(-0.527388\pi\)
−0.0859364 + 0.996301i \(0.527388\pi\)
\(884\) 0.821915 0.0276440
\(885\) 19.6345 0.660008
\(886\) 33.9295 1.13988
\(887\) −18.9905 −0.637637 −0.318818 0.947816i \(-0.603286\pi\)
−0.318818 + 0.947816i \(0.603286\pi\)
\(888\) −20.5097 −0.688261
\(889\) −38.6316 −1.29566
\(890\) 43.8008 1.46820
\(891\) −2.39155 −0.0801200
\(892\) 23.0013 0.770141
\(893\) −61.3116 −2.05172
\(894\) −3.52254 −0.117811
\(895\) 32.8101 1.09672
\(896\) 62.0182 2.07188
\(897\) −8.19358 −0.273576
\(898\) −46.1637 −1.54050
\(899\) −4.97988 −0.166088
\(900\) −6.63642 −0.221214
\(901\) 0.225705 0.00751934
\(902\) −16.1003 −0.536080
\(903\) 10.4265 0.346971
\(904\) −18.8658 −0.627466
\(905\) 19.7564 0.656725
\(906\) −21.4338 −0.712091
\(907\) −51.8495 −1.72163 −0.860817 0.508915i \(-0.830047\pi\)
−0.860817 + 0.508915i \(0.830047\pi\)
\(908\) 73.7052 2.44599
\(909\) 7.78769 0.258301
\(910\) 13.3750 0.443379
\(911\) 40.7226 1.34920 0.674600 0.738184i \(-0.264316\pi\)
0.674600 + 0.738184i \(0.264316\pi\)
\(912\) 0.333478 0.0110426
\(913\) −38.4551 −1.27268
\(914\) −42.8780 −1.41828
\(915\) 13.5222 0.447029
\(916\) −76.7165 −2.53478
\(917\) −65.4461 −2.16122
\(918\) −0.582947 −0.0192401
\(919\) 35.2784 1.16373 0.581863 0.813287i \(-0.302324\pi\)
0.581863 + 0.813287i \(0.302324\pi\)
\(920\) −39.2295 −1.29336
\(921\) 10.5794 0.348602
\(922\) 76.7135 2.52642
\(923\) 10.9975 0.361988
\(924\) −26.3017 −0.865261
\(925\) −15.1298 −0.497464
\(926\) 76.8081 2.52407
\(927\) −1.00000 −0.0328443
\(928\) −22.9259 −0.752580
\(929\) 25.9916 0.852755 0.426378 0.904545i \(-0.359789\pi\)
0.426378 + 0.904545i \(0.359789\pi\)
\(930\) −4.87594 −0.159888
\(931\) 24.5567 0.804812
\(932\) −39.8554 −1.30551
\(933\) −26.1467 −0.856006
\(934\) −64.5384 −2.11176
\(935\) 1.04613 0.0342120
\(936\) 2.79222 0.0912665
\(937\) 10.1078 0.330206 0.165103 0.986276i \(-0.447204\pi\)
0.165103 + 0.986276i \(0.447204\pi\)
\(938\) −60.2059 −1.96579
\(939\) 23.8126 0.777096
\(940\) 64.1611 2.09271
\(941\) −20.7920 −0.677801 −0.338901 0.940822i \(-0.610055\pi\)
−0.338901 + 0.940822i \(0.610055\pi\)
\(942\) 47.4024 1.54445
\(943\) 24.1386 0.786062
\(944\) −0.723314 −0.0235419
\(945\) −5.85304 −0.190399
\(946\) −16.6932 −0.542743
\(947\) −13.6641 −0.444022 −0.222011 0.975044i \(-0.571262\pi\)
−0.222011 + 0.975044i \(0.571262\pi\)
\(948\) −16.1113 −0.523270
\(949\) −8.26216 −0.268201
\(950\) −24.8490 −0.806208
\(951\) 20.7133 0.671673
\(952\) −2.43140 −0.0788021
\(953\) −16.2720 −0.527101 −0.263551 0.964646i \(-0.584894\pi\)
−0.263551 + 0.964646i \(0.584894\pi\)
\(954\) 2.02181 0.0654586
\(955\) 28.2230 0.913274
\(956\) 22.6967 0.734063
\(957\) 9.57071 0.309377
\(958\) 41.3157 1.33485
\(959\) −58.7693 −1.89776
\(960\) −22.2308 −0.717495
\(961\) −29.4515 −0.950049
\(962\) 16.7851 0.541174
\(963\) −12.7489 −0.410827
\(964\) 5.08773 0.163865
\(965\) −32.8406 −1.05717
\(966\) 63.9116 2.05632
\(967\) −25.4364 −0.817980 −0.408990 0.912539i \(-0.634119\pi\)
−0.408990 + 0.912539i \(0.634119\pi\)
\(968\) −14.7443 −0.473898
\(969\) −1.34675 −0.0432639
\(970\) −63.2321 −2.03026
\(971\) −17.3076 −0.555427 −0.277714 0.960664i \(-0.589577\pi\)
−0.277714 + 0.960664i \(0.589577\pi\)
\(972\) −3.22190 −0.103342
\(973\) 38.3475 1.22936
\(974\) 25.8422 0.828038
\(975\) 2.05979 0.0659659
\(976\) −0.498141 −0.0159451
\(977\) 43.1051 1.37906 0.689528 0.724259i \(-0.257818\pi\)
0.689528 + 0.724259i \(0.257818\pi\)
\(978\) −28.0794 −0.897879
\(979\) 26.7336 0.854410
\(980\) −25.6979 −0.820890
\(981\) −4.89646 −0.156332
\(982\) −25.4331 −0.811602
\(983\) 6.61327 0.210931 0.105465 0.994423i \(-0.466367\pi\)
0.105465 + 0.994423i \(0.466367\pi\)
\(984\) −8.22599 −0.262235
\(985\) −39.8455 −1.26958
\(986\) 2.33289 0.0742942
\(987\) −39.6426 −1.26184
\(988\) 17.0092 0.541135
\(989\) 25.0276 0.795831
\(990\) 9.37095 0.297828
\(991\) 19.0075 0.603792 0.301896 0.953341i \(-0.402380\pi\)
0.301896 + 0.953341i \(0.402380\pi\)
\(992\) 7.12881 0.226340
\(993\) 7.55226 0.239664
\(994\) −85.7830 −2.72087
\(995\) 29.1254 0.923338
\(996\) −51.8066 −1.64156
\(997\) −29.3510 −0.929555 −0.464778 0.885427i \(-0.653866\pi\)
−0.464778 + 0.885427i \(0.653866\pi\)
\(998\) −76.7572 −2.42971
\(999\) −7.34531 −0.232395
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 \(a_p\))