Properties

Label 6004.2.a.g.1.26
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.26
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.71988 q^{3} -0.592160 q^{5} -2.94575 q^{7} +4.39773 q^{9} +O(q^{10})\) \(q+2.71988 q^{3} -0.592160 q^{5} -2.94575 q^{7} +4.39773 q^{9} +2.40684 q^{11} +3.66568 q^{13} -1.61060 q^{15} -7.66581 q^{17} +1.00000 q^{19} -8.01207 q^{21} -7.91853 q^{23} -4.64935 q^{25} +3.80164 q^{27} -8.53016 q^{29} -0.177489 q^{31} +6.54631 q^{33} +1.74435 q^{35} +4.75848 q^{37} +9.97019 q^{39} +4.20422 q^{41} -5.39793 q^{43} -2.60416 q^{45} +0.161608 q^{47} +1.67743 q^{49} -20.8501 q^{51} -11.3149 q^{53} -1.42523 q^{55} +2.71988 q^{57} -3.61194 q^{59} +10.3097 q^{61} -12.9546 q^{63} -2.17067 q^{65} +10.7657 q^{67} -21.5374 q^{69} -9.67502 q^{71} +6.62788 q^{73} -12.6456 q^{75} -7.08994 q^{77} -1.00000 q^{79} -2.85318 q^{81} -4.26142 q^{83} +4.53939 q^{85} -23.2010 q^{87} -17.0062 q^{89} -10.7982 q^{91} -0.482747 q^{93} -0.592160 q^{95} +14.0216 q^{97} +10.5846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + O(q^{10}) \) \( 27q - 4q^{3} - 10q^{5} - 8q^{7} + 19q^{9} + 3q^{11} - 5q^{13} - 11q^{15} - 17q^{17} + 27q^{19} - 28q^{21} - 11q^{23} + 13q^{25} - 7q^{27} - 39q^{29} - 27q^{31} - 18q^{33} - 5q^{35} - q^{37} - 22q^{39} - 36q^{41} - 2q^{43} - 18q^{45} - 12q^{47} + 15q^{49} + 4q^{51} - 28q^{53} + 5q^{55} - 4q^{57} - 30q^{59} - 6q^{61} - 4q^{63} - 32q^{65} + 13q^{67} - 27q^{69} - 59q^{71} - 30q^{73} - 21q^{75} - 39q^{77} - 27q^{79} - 5q^{81} + 4q^{83} - 3q^{85} + 22q^{87} - 56q^{89} - 8q^{91} - 38q^{93} - 10q^{95} - 30q^{97} + 31q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.71988 1.57032 0.785161 0.619292i \(-0.212580\pi\)
0.785161 + 0.619292i \(0.212580\pi\)
\(4\) 0 0
\(5\) −0.592160 −0.264822 −0.132411 0.991195i \(-0.542272\pi\)
−0.132411 + 0.991195i \(0.542272\pi\)
\(6\) 0 0
\(7\) −2.94575 −1.11339 −0.556694 0.830718i \(-0.687930\pi\)
−0.556694 + 0.830718i \(0.687930\pi\)
\(8\) 0 0
\(9\) 4.39773 1.46591
\(10\) 0 0
\(11\) 2.40684 0.725690 0.362845 0.931850i \(-0.381806\pi\)
0.362845 + 0.931850i \(0.381806\pi\)
\(12\) 0 0
\(13\) 3.66568 1.01668 0.508338 0.861158i \(-0.330260\pi\)
0.508338 + 0.861158i \(0.330260\pi\)
\(14\) 0 0
\(15\) −1.61060 −0.415855
\(16\) 0 0
\(17\) −7.66581 −1.85923 −0.929616 0.368529i \(-0.879862\pi\)
−0.929616 + 0.368529i \(0.879862\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −8.01207 −1.74838
\(22\) 0 0
\(23\) −7.91853 −1.65113 −0.825564 0.564309i \(-0.809143\pi\)
−0.825564 + 0.564309i \(0.809143\pi\)
\(24\) 0 0
\(25\) −4.64935 −0.929869
\(26\) 0 0
\(27\) 3.80164 0.731627
\(28\) 0 0
\(29\) −8.53016 −1.58401 −0.792006 0.610514i \(-0.790963\pi\)
−0.792006 + 0.610514i \(0.790963\pi\)
\(30\) 0 0
\(31\) −0.177489 −0.0318779 −0.0159390 0.999873i \(-0.505074\pi\)
−0.0159390 + 0.999873i \(0.505074\pi\)
\(32\) 0 0
\(33\) 6.54631 1.13957
\(34\) 0 0
\(35\) 1.74435 0.294849
\(36\) 0 0
\(37\) 4.75848 0.782289 0.391145 0.920329i \(-0.372079\pi\)
0.391145 + 0.920329i \(0.372079\pi\)
\(38\) 0 0
\(39\) 9.97019 1.59651
\(40\) 0 0
\(41\) 4.20422 0.656589 0.328294 0.944575i \(-0.393526\pi\)
0.328294 + 0.944575i \(0.393526\pi\)
\(42\) 0 0
\(43\) −5.39793 −0.823177 −0.411588 0.911370i \(-0.635026\pi\)
−0.411588 + 0.911370i \(0.635026\pi\)
\(44\) 0 0
\(45\) −2.60416 −0.388205
\(46\) 0 0
\(47\) 0.161608 0.0235730 0.0117865 0.999931i \(-0.496248\pi\)
0.0117865 + 0.999931i \(0.496248\pi\)
\(48\) 0 0
\(49\) 1.67743 0.239632
\(50\) 0 0
\(51\) −20.8501 −2.91959
\(52\) 0 0
\(53\) −11.3149 −1.55422 −0.777109 0.629366i \(-0.783315\pi\)
−0.777109 + 0.629366i \(0.783315\pi\)
\(54\) 0 0
\(55\) −1.42523 −0.192178
\(56\) 0 0
\(57\) 2.71988 0.360256
\(58\) 0 0
\(59\) −3.61194 −0.470235 −0.235117 0.971967i \(-0.575547\pi\)
−0.235117 + 0.971967i \(0.575547\pi\)
\(60\) 0 0
\(61\) 10.3097 1.32002 0.660010 0.751257i \(-0.270552\pi\)
0.660010 + 0.751257i \(0.270552\pi\)
\(62\) 0 0
\(63\) −12.9546 −1.63213
\(64\) 0 0
\(65\) −2.17067 −0.269238
\(66\) 0 0
\(67\) 10.7657 1.31525 0.657623 0.753347i \(-0.271562\pi\)
0.657623 + 0.753347i \(0.271562\pi\)
\(68\) 0 0
\(69\) −21.5374 −2.59280
\(70\) 0 0
\(71\) −9.67502 −1.14821 −0.574107 0.818780i \(-0.694651\pi\)
−0.574107 + 0.818780i \(0.694651\pi\)
\(72\) 0 0
\(73\) 6.62788 0.775735 0.387868 0.921715i \(-0.373212\pi\)
0.387868 + 0.921715i \(0.373212\pi\)
\(74\) 0 0
\(75\) −12.6456 −1.46019
\(76\) 0 0
\(77\) −7.08994 −0.807974
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −2.85318 −0.317020
\(82\) 0 0
\(83\) −4.26142 −0.467752 −0.233876 0.972266i \(-0.575141\pi\)
−0.233876 + 0.972266i \(0.575141\pi\)
\(84\) 0 0
\(85\) 4.53939 0.492365
\(86\) 0 0
\(87\) −23.2010 −2.48741
\(88\) 0 0
\(89\) −17.0062 −1.80266 −0.901329 0.433136i \(-0.857407\pi\)
−0.901329 + 0.433136i \(0.857407\pi\)
\(90\) 0 0
\(91\) −10.7982 −1.13195
\(92\) 0 0
\(93\) −0.482747 −0.0500586
\(94\) 0 0
\(95\) −0.592160 −0.0607543
\(96\) 0 0
\(97\) 14.0216 1.42368 0.711838 0.702344i \(-0.247863\pi\)
0.711838 + 0.702344i \(0.247863\pi\)
\(98\) 0 0
\(99\) 10.5846 1.06379
\(100\) 0 0
\(101\) −0.260123 −0.0258832 −0.0129416 0.999916i \(-0.504120\pi\)
−0.0129416 + 0.999916i \(0.504120\pi\)
\(102\) 0 0
\(103\) −14.3067 −1.40968 −0.704842 0.709365i \(-0.748982\pi\)
−0.704842 + 0.709365i \(0.748982\pi\)
\(104\) 0 0
\(105\) 4.74442 0.463008
\(106\) 0 0
\(107\) 3.17406 0.306848 0.153424 0.988160i \(-0.450970\pi\)
0.153424 + 0.988160i \(0.450970\pi\)
\(108\) 0 0
\(109\) 8.92663 0.855017 0.427508 0.904011i \(-0.359391\pi\)
0.427508 + 0.904011i \(0.359391\pi\)
\(110\) 0 0
\(111\) 12.9425 1.22845
\(112\) 0 0
\(113\) −3.65897 −0.344207 −0.172103 0.985079i \(-0.555056\pi\)
−0.172103 + 0.985079i \(0.555056\pi\)
\(114\) 0 0
\(115\) 4.68903 0.437255
\(116\) 0 0
\(117\) 16.1206 1.49035
\(118\) 0 0
\(119\) 22.5815 2.07005
\(120\) 0 0
\(121\) −5.20712 −0.473375
\(122\) 0 0
\(123\) 11.4350 1.03106
\(124\) 0 0
\(125\) 5.71395 0.511072
\(126\) 0 0
\(127\) −0.414767 −0.0368047 −0.0184023 0.999831i \(-0.505858\pi\)
−0.0184023 + 0.999831i \(0.505858\pi\)
\(128\) 0 0
\(129\) −14.6817 −1.29265
\(130\) 0 0
\(131\) 9.27389 0.810264 0.405132 0.914258i \(-0.367226\pi\)
0.405132 + 0.914258i \(0.367226\pi\)
\(132\) 0 0
\(133\) −2.94575 −0.255429
\(134\) 0 0
\(135\) −2.25118 −0.193751
\(136\) 0 0
\(137\) 2.07279 0.177090 0.0885451 0.996072i \(-0.471778\pi\)
0.0885451 + 0.996072i \(0.471778\pi\)
\(138\) 0 0
\(139\) 16.2159 1.37541 0.687707 0.725988i \(-0.258617\pi\)
0.687707 + 0.725988i \(0.258617\pi\)
\(140\) 0 0
\(141\) 0.439554 0.0370172
\(142\) 0 0
\(143\) 8.82270 0.737791
\(144\) 0 0
\(145\) 5.05122 0.419481
\(146\) 0 0
\(147\) 4.56239 0.376300
\(148\) 0 0
\(149\) −3.12243 −0.255800 −0.127900 0.991787i \(-0.540824\pi\)
−0.127900 + 0.991787i \(0.540824\pi\)
\(150\) 0 0
\(151\) −19.9817 −1.62608 −0.813042 0.582205i \(-0.802190\pi\)
−0.813042 + 0.582205i \(0.802190\pi\)
\(152\) 0 0
\(153\) −33.7122 −2.72547
\(154\) 0 0
\(155\) 0.105102 0.00844197
\(156\) 0 0
\(157\) −21.6630 −1.72890 −0.864448 0.502721i \(-0.832332\pi\)
−0.864448 + 0.502721i \(0.832332\pi\)
\(158\) 0 0
\(159\) −30.7751 −2.44062
\(160\) 0 0
\(161\) 23.3260 1.83835
\(162\) 0 0
\(163\) 6.13425 0.480471 0.240236 0.970715i \(-0.422775\pi\)
0.240236 + 0.970715i \(0.422775\pi\)
\(164\) 0 0
\(165\) −3.87646 −0.301782
\(166\) 0 0
\(167\) 22.8505 1.76823 0.884113 0.467273i \(-0.154764\pi\)
0.884113 + 0.467273i \(0.154764\pi\)
\(168\) 0 0
\(169\) 0.437185 0.0336296
\(170\) 0 0
\(171\) 4.39773 0.336303
\(172\) 0 0
\(173\) −22.3280 −1.69756 −0.848782 0.528743i \(-0.822663\pi\)
−0.848782 + 0.528743i \(0.822663\pi\)
\(174\) 0 0
\(175\) 13.6958 1.03531
\(176\) 0 0
\(177\) −9.82403 −0.738419
\(178\) 0 0
\(179\) 20.4749 1.53037 0.765183 0.643812i \(-0.222648\pi\)
0.765183 + 0.643812i \(0.222648\pi\)
\(180\) 0 0
\(181\) 25.3923 1.88740 0.943699 0.330805i \(-0.107320\pi\)
0.943699 + 0.330805i \(0.107320\pi\)
\(182\) 0 0
\(183\) 28.0411 2.07285
\(184\) 0 0
\(185\) −2.81778 −0.207167
\(186\) 0 0
\(187\) −18.4504 −1.34923
\(188\) 0 0
\(189\) −11.1987 −0.814584
\(190\) 0 0
\(191\) 3.56106 0.257670 0.128835 0.991666i \(-0.458876\pi\)
0.128835 + 0.991666i \(0.458876\pi\)
\(192\) 0 0
\(193\) 10.2826 0.740158 0.370079 0.929000i \(-0.379331\pi\)
0.370079 + 0.929000i \(0.379331\pi\)
\(194\) 0 0
\(195\) −5.90394 −0.422790
\(196\) 0 0
\(197\) 1.29975 0.0926034 0.0463017 0.998928i \(-0.485256\pi\)
0.0463017 + 0.998928i \(0.485256\pi\)
\(198\) 0 0
\(199\) −22.1902 −1.57302 −0.786511 0.617577i \(-0.788114\pi\)
−0.786511 + 0.617577i \(0.788114\pi\)
\(200\) 0 0
\(201\) 29.2815 2.06536
\(202\) 0 0
\(203\) 25.1277 1.76362
\(204\) 0 0
\(205\) −2.48957 −0.173879
\(206\) 0 0
\(207\) −34.8235 −2.42040
\(208\) 0 0
\(209\) 2.40684 0.166485
\(210\) 0 0
\(211\) −21.3451 −1.46946 −0.734728 0.678362i \(-0.762690\pi\)
−0.734728 + 0.678362i \(0.762690\pi\)
\(212\) 0 0
\(213\) −26.3149 −1.80306
\(214\) 0 0
\(215\) 3.19644 0.217995
\(216\) 0 0
\(217\) 0.522837 0.0354925
\(218\) 0 0
\(219\) 18.0270 1.21815
\(220\) 0 0
\(221\) −28.1004 −1.89024
\(222\) 0 0
\(223\) 9.26500 0.620430 0.310215 0.950666i \(-0.399599\pi\)
0.310215 + 0.950666i \(0.399599\pi\)
\(224\) 0 0
\(225\) −20.4466 −1.36310
\(226\) 0 0
\(227\) −0.840113 −0.0557602 −0.0278801 0.999611i \(-0.508876\pi\)
−0.0278801 + 0.999611i \(0.508876\pi\)
\(228\) 0 0
\(229\) −14.6086 −0.965361 −0.482680 0.875797i \(-0.660337\pi\)
−0.482680 + 0.875797i \(0.660337\pi\)
\(230\) 0 0
\(231\) −19.2838 −1.26878
\(232\) 0 0
\(233\) −0.183054 −0.0119923 −0.00599614 0.999982i \(-0.501909\pi\)
−0.00599614 + 0.999982i \(0.501909\pi\)
\(234\) 0 0
\(235\) −0.0956979 −0.00624264
\(236\) 0 0
\(237\) −2.71988 −0.176675
\(238\) 0 0
\(239\) −14.2417 −0.921217 −0.460608 0.887604i \(-0.652369\pi\)
−0.460608 + 0.887604i \(0.652369\pi\)
\(240\) 0 0
\(241\) −22.3242 −1.43803 −0.719014 0.694995i \(-0.755406\pi\)
−0.719014 + 0.694995i \(0.755406\pi\)
\(242\) 0 0
\(243\) −19.1652 −1.22945
\(244\) 0 0
\(245\) −0.993305 −0.0634599
\(246\) 0 0
\(247\) 3.66568 0.233241
\(248\) 0 0
\(249\) −11.5905 −0.734521
\(250\) 0 0
\(251\) −24.3574 −1.53743 −0.768713 0.639594i \(-0.779102\pi\)
−0.768713 + 0.639594i \(0.779102\pi\)
\(252\) 0 0
\(253\) −19.0586 −1.19821
\(254\) 0 0
\(255\) 12.3466 0.773172
\(256\) 0 0
\(257\) 3.09664 0.193163 0.0965817 0.995325i \(-0.469209\pi\)
0.0965817 + 0.995325i \(0.469209\pi\)
\(258\) 0 0
\(259\) −14.0173 −0.870991
\(260\) 0 0
\(261\) −37.5133 −2.32202
\(262\) 0 0
\(263\) −11.3064 −0.697181 −0.348590 0.937275i \(-0.613340\pi\)
−0.348590 + 0.937275i \(0.613340\pi\)
\(264\) 0 0
\(265\) 6.70022 0.411591
\(266\) 0 0
\(267\) −46.2549 −2.83075
\(268\) 0 0
\(269\) 13.0366 0.794855 0.397428 0.917634i \(-0.369903\pi\)
0.397428 + 0.917634i \(0.369903\pi\)
\(270\) 0 0
\(271\) −9.63428 −0.585241 −0.292620 0.956229i \(-0.594527\pi\)
−0.292620 + 0.956229i \(0.594527\pi\)
\(272\) 0 0
\(273\) −29.3697 −1.77753
\(274\) 0 0
\(275\) −11.1902 −0.674797
\(276\) 0 0
\(277\) −0.298797 −0.0179530 −0.00897648 0.999960i \(-0.502857\pi\)
−0.00897648 + 0.999960i \(0.502857\pi\)
\(278\) 0 0
\(279\) −0.780547 −0.0467301
\(280\) 0 0
\(281\) 5.74039 0.342443 0.171221 0.985233i \(-0.445229\pi\)
0.171221 + 0.985233i \(0.445229\pi\)
\(282\) 0 0
\(283\) 25.1521 1.49514 0.747570 0.664183i \(-0.231221\pi\)
0.747570 + 0.664183i \(0.231221\pi\)
\(284\) 0 0
\(285\) −1.61060 −0.0954038
\(286\) 0 0
\(287\) −12.3846 −0.731038
\(288\) 0 0
\(289\) 41.7647 2.45675
\(290\) 0 0
\(291\) 38.1369 2.23563
\(292\) 0 0
\(293\) −22.6981 −1.32604 −0.663020 0.748602i \(-0.730725\pi\)
−0.663020 + 0.748602i \(0.730725\pi\)
\(294\) 0 0
\(295\) 2.13885 0.124528
\(296\) 0 0
\(297\) 9.14995 0.530934
\(298\) 0 0
\(299\) −29.0268 −1.67866
\(300\) 0 0
\(301\) 15.9009 0.916515
\(302\) 0 0
\(303\) −0.707502 −0.0406449
\(304\) 0 0
\(305\) −6.10498 −0.349570
\(306\) 0 0
\(307\) 25.1284 1.43415 0.717077 0.696994i \(-0.245480\pi\)
0.717077 + 0.696994i \(0.245480\pi\)
\(308\) 0 0
\(309\) −38.9125 −2.21366
\(310\) 0 0
\(311\) −26.1490 −1.48277 −0.741387 0.671078i \(-0.765832\pi\)
−0.741387 + 0.671078i \(0.765832\pi\)
\(312\) 0 0
\(313\) 0.369964 0.0209116 0.0104558 0.999945i \(-0.496672\pi\)
0.0104558 + 0.999945i \(0.496672\pi\)
\(314\) 0 0
\(315\) 7.67119 0.432222
\(316\) 0 0
\(317\) 29.1437 1.63687 0.818437 0.574596i \(-0.194841\pi\)
0.818437 + 0.574596i \(0.194841\pi\)
\(318\) 0 0
\(319\) −20.5307 −1.14950
\(320\) 0 0
\(321\) 8.63304 0.481850
\(322\) 0 0
\(323\) −7.66581 −0.426537
\(324\) 0 0
\(325\) −17.0430 −0.945376
\(326\) 0 0
\(327\) 24.2793 1.34265
\(328\) 0 0
\(329\) −0.476057 −0.0262459
\(330\) 0 0
\(331\) 31.7588 1.74562 0.872811 0.488058i \(-0.162295\pi\)
0.872811 + 0.488058i \(0.162295\pi\)
\(332\) 0 0
\(333\) 20.9265 1.14676
\(334\) 0 0
\(335\) −6.37504 −0.348306
\(336\) 0 0
\(337\) 14.7789 0.805058 0.402529 0.915407i \(-0.368131\pi\)
0.402529 + 0.915407i \(0.368131\pi\)
\(338\) 0 0
\(339\) −9.95194 −0.540515
\(340\) 0 0
\(341\) −0.427187 −0.0231335
\(342\) 0 0
\(343\) 15.6790 0.846584
\(344\) 0 0
\(345\) 12.7536 0.686630
\(346\) 0 0
\(347\) −20.6479 −1.10844 −0.554220 0.832370i \(-0.686983\pi\)
−0.554220 + 0.832370i \(0.686983\pi\)
\(348\) 0 0
\(349\) −34.8066 −1.86315 −0.931576 0.363546i \(-0.881566\pi\)
−0.931576 + 0.363546i \(0.881566\pi\)
\(350\) 0 0
\(351\) 13.9356 0.743827
\(352\) 0 0
\(353\) 11.3935 0.606415 0.303207 0.952925i \(-0.401942\pi\)
0.303207 + 0.952925i \(0.401942\pi\)
\(354\) 0 0
\(355\) 5.72916 0.304072
\(356\) 0 0
\(357\) 61.4190 3.25064
\(358\) 0 0
\(359\) 22.8684 1.20695 0.603474 0.797383i \(-0.293783\pi\)
0.603474 + 0.797383i \(0.293783\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −14.1627 −0.743350
\(364\) 0 0
\(365\) −3.92477 −0.205432
\(366\) 0 0
\(367\) −6.76747 −0.353259 −0.176629 0.984277i \(-0.556519\pi\)
−0.176629 + 0.984277i \(0.556519\pi\)
\(368\) 0 0
\(369\) 18.4890 0.962500
\(370\) 0 0
\(371\) 33.3308 1.73045
\(372\) 0 0
\(373\) −26.8854 −1.39207 −0.696036 0.718007i \(-0.745055\pi\)
−0.696036 + 0.718007i \(0.745055\pi\)
\(374\) 0 0
\(375\) 15.5412 0.802547
\(376\) 0 0
\(377\) −31.2688 −1.61043
\(378\) 0 0
\(379\) −31.9811 −1.64276 −0.821379 0.570383i \(-0.806795\pi\)
−0.821379 + 0.570383i \(0.806795\pi\)
\(380\) 0 0
\(381\) −1.12812 −0.0577951
\(382\) 0 0
\(383\) 31.4537 1.60721 0.803604 0.595165i \(-0.202913\pi\)
0.803604 + 0.595165i \(0.202913\pi\)
\(384\) 0 0
\(385\) 4.19838 0.213969
\(386\) 0 0
\(387\) −23.7386 −1.20670
\(388\) 0 0
\(389\) −15.9989 −0.811175 −0.405588 0.914056i \(-0.632933\pi\)
−0.405588 + 0.914056i \(0.632933\pi\)
\(390\) 0 0
\(391\) 60.7020 3.06983
\(392\) 0 0
\(393\) 25.2238 1.27237
\(394\) 0 0
\(395\) 0.592160 0.0297948
\(396\) 0 0
\(397\) −10.3054 −0.517214 −0.258607 0.965983i \(-0.583263\pi\)
−0.258607 + 0.965983i \(0.583263\pi\)
\(398\) 0 0
\(399\) −8.01207 −0.401105
\(400\) 0 0
\(401\) 33.0946 1.65266 0.826332 0.563183i \(-0.190424\pi\)
0.826332 + 0.563183i \(0.190424\pi\)
\(402\) 0 0
\(403\) −0.650616 −0.0324095
\(404\) 0 0
\(405\) 1.68954 0.0839538
\(406\) 0 0
\(407\) 11.4529 0.567699
\(408\) 0 0
\(409\) −19.7646 −0.977295 −0.488647 0.872481i \(-0.662510\pi\)
−0.488647 + 0.872481i \(0.662510\pi\)
\(410\) 0 0
\(411\) 5.63772 0.278088
\(412\) 0 0
\(413\) 10.6399 0.523554
\(414\) 0 0
\(415\) 2.52344 0.123871
\(416\) 0 0
\(417\) 44.1052 2.15984
\(418\) 0 0
\(419\) −31.1608 −1.52231 −0.761153 0.648573i \(-0.775366\pi\)
−0.761153 + 0.648573i \(0.775366\pi\)
\(420\) 0 0
\(421\) 30.0185 1.46301 0.731506 0.681835i \(-0.238818\pi\)
0.731506 + 0.681835i \(0.238818\pi\)
\(422\) 0 0
\(423\) 0.710709 0.0345559
\(424\) 0 0
\(425\) 35.6410 1.72884
\(426\) 0 0
\(427\) −30.3697 −1.46969
\(428\) 0 0
\(429\) 23.9966 1.15857
\(430\) 0 0
\(431\) 2.56995 0.123790 0.0618952 0.998083i \(-0.480286\pi\)
0.0618952 + 0.998083i \(0.480286\pi\)
\(432\) 0 0
\(433\) −11.3974 −0.547723 −0.273861 0.961769i \(-0.588301\pi\)
−0.273861 + 0.961769i \(0.588301\pi\)
\(434\) 0 0
\(435\) 13.7387 0.658720
\(436\) 0 0
\(437\) −7.91853 −0.378795
\(438\) 0 0
\(439\) −28.6807 −1.36886 −0.684428 0.729080i \(-0.739948\pi\)
−0.684428 + 0.729080i \(0.739948\pi\)
\(440\) 0 0
\(441\) 7.37687 0.351279
\(442\) 0 0
\(443\) 19.3206 0.917950 0.458975 0.888449i \(-0.348217\pi\)
0.458975 + 0.888449i \(0.348217\pi\)
\(444\) 0 0
\(445\) 10.0704 0.477383
\(446\) 0 0
\(447\) −8.49263 −0.401688
\(448\) 0 0
\(449\) 22.0959 1.04277 0.521386 0.853321i \(-0.325415\pi\)
0.521386 + 0.853321i \(0.325415\pi\)
\(450\) 0 0
\(451\) 10.1189 0.476480
\(452\) 0 0
\(453\) −54.3476 −2.55347
\(454\) 0 0
\(455\) 6.39423 0.299766
\(456\) 0 0
\(457\) 17.4439 0.815991 0.407996 0.912984i \(-0.366228\pi\)
0.407996 + 0.912984i \(0.366228\pi\)
\(458\) 0 0
\(459\) −29.1427 −1.36026
\(460\) 0 0
\(461\) −28.5439 −1.32942 −0.664712 0.747100i \(-0.731446\pi\)
−0.664712 + 0.747100i \(0.731446\pi\)
\(462\) 0 0
\(463\) 12.3512 0.574011 0.287005 0.957929i \(-0.407340\pi\)
0.287005 + 0.957929i \(0.407340\pi\)
\(464\) 0 0
\(465\) 0.285864 0.0132566
\(466\) 0 0
\(467\) −29.7802 −1.37807 −0.689033 0.724730i \(-0.741964\pi\)
−0.689033 + 0.724730i \(0.741964\pi\)
\(468\) 0 0
\(469\) −31.7132 −1.46438
\(470\) 0 0
\(471\) −58.9207 −2.71492
\(472\) 0 0
\(473\) −12.9920 −0.597371
\(474\) 0 0
\(475\) −4.64935 −0.213327
\(476\) 0 0
\(477\) −49.7597 −2.27834
\(478\) 0 0
\(479\) −2.69120 −0.122964 −0.0614821 0.998108i \(-0.519583\pi\)
−0.0614821 + 0.998108i \(0.519583\pi\)
\(480\) 0 0
\(481\) 17.4430 0.795334
\(482\) 0 0
\(483\) 63.4438 2.88679
\(484\) 0 0
\(485\) −8.30301 −0.377020
\(486\) 0 0
\(487\) 40.6509 1.84207 0.921034 0.389482i \(-0.127346\pi\)
0.921034 + 0.389482i \(0.127346\pi\)
\(488\) 0 0
\(489\) 16.6844 0.754494
\(490\) 0 0
\(491\) 7.70487 0.347716 0.173858 0.984771i \(-0.444377\pi\)
0.173858 + 0.984771i \(0.444377\pi\)
\(492\) 0 0
\(493\) 65.3906 2.94505
\(494\) 0 0
\(495\) −6.26779 −0.281716
\(496\) 0 0
\(497\) 28.5002 1.27841
\(498\) 0 0
\(499\) −18.8438 −0.843566 −0.421783 0.906697i \(-0.638596\pi\)
−0.421783 + 0.906697i \(0.638596\pi\)
\(500\) 0 0
\(501\) 62.1506 2.77668
\(502\) 0 0
\(503\) 12.2068 0.544273 0.272136 0.962259i \(-0.412270\pi\)
0.272136 + 0.962259i \(0.412270\pi\)
\(504\) 0 0
\(505\) 0.154034 0.00685444
\(506\) 0 0
\(507\) 1.18909 0.0528093
\(508\) 0 0
\(509\) −18.5816 −0.823613 −0.411807 0.911271i \(-0.635102\pi\)
−0.411807 + 0.911271i \(0.635102\pi\)
\(510\) 0 0
\(511\) −19.5241 −0.863694
\(512\) 0 0
\(513\) 3.80164 0.167847
\(514\) 0 0
\(515\) 8.47186 0.373315
\(516\) 0 0
\(517\) 0.388965 0.0171067
\(518\) 0 0
\(519\) −60.7293 −2.66572
\(520\) 0 0
\(521\) 16.0856 0.704725 0.352362 0.935864i \(-0.385378\pi\)
0.352362 + 0.935864i \(0.385378\pi\)
\(522\) 0 0
\(523\) −5.11684 −0.223744 −0.111872 0.993723i \(-0.535685\pi\)
−0.111872 + 0.993723i \(0.535685\pi\)
\(524\) 0 0
\(525\) 37.2509 1.62576
\(526\) 0 0
\(527\) 1.36060 0.0592684
\(528\) 0 0
\(529\) 39.7031 1.72622
\(530\) 0 0
\(531\) −15.8843 −0.689321
\(532\) 0 0
\(533\) 15.4113 0.667538
\(534\) 0 0
\(535\) −1.87955 −0.0812600
\(536\) 0 0
\(537\) 55.6892 2.40317
\(538\) 0 0
\(539\) 4.03730 0.173899
\(540\) 0 0
\(541\) −17.3642 −0.746547 −0.373274 0.927721i \(-0.621765\pi\)
−0.373274 + 0.927721i \(0.621765\pi\)
\(542\) 0 0
\(543\) 69.0640 2.96382
\(544\) 0 0
\(545\) −5.28599 −0.226427
\(546\) 0 0
\(547\) −19.6927 −0.841998 −0.420999 0.907061i \(-0.638320\pi\)
−0.420999 + 0.907061i \(0.638320\pi\)
\(548\) 0 0
\(549\) 45.3392 1.93503
\(550\) 0 0
\(551\) −8.53016 −0.363397
\(552\) 0 0
\(553\) 2.94575 0.125266
\(554\) 0 0
\(555\) −7.66401 −0.325319
\(556\) 0 0
\(557\) −41.4631 −1.75685 −0.878423 0.477883i \(-0.841404\pi\)
−0.878423 + 0.477883i \(0.841404\pi\)
\(558\) 0 0
\(559\) −19.7871 −0.836904
\(560\) 0 0
\(561\) −50.1828 −2.11872
\(562\) 0 0
\(563\) −17.7121 −0.746477 −0.373238 0.927735i \(-0.621753\pi\)
−0.373238 + 0.927735i \(0.621753\pi\)
\(564\) 0 0
\(565\) 2.16669 0.0911535
\(566\) 0 0
\(567\) 8.40474 0.352966
\(568\) 0 0
\(569\) −5.44969 −0.228463 −0.114232 0.993454i \(-0.536441\pi\)
−0.114232 + 0.993454i \(0.536441\pi\)
\(570\) 0 0
\(571\) −8.56064 −0.358252 −0.179126 0.983826i \(-0.557327\pi\)
−0.179126 + 0.983826i \(0.557327\pi\)
\(572\) 0 0
\(573\) 9.68566 0.404624
\(574\) 0 0
\(575\) 36.8160 1.53533
\(576\) 0 0
\(577\) 19.4759 0.810794 0.405397 0.914141i \(-0.367133\pi\)
0.405397 + 0.914141i \(0.367133\pi\)
\(578\) 0 0
\(579\) 27.9674 1.16229
\(580\) 0 0
\(581\) 12.5531 0.520789
\(582\) 0 0
\(583\) −27.2331 −1.12788
\(584\) 0 0
\(585\) −9.54600 −0.394678
\(586\) 0 0
\(587\) −2.10064 −0.0867027 −0.0433513 0.999060i \(-0.513803\pi\)
−0.0433513 + 0.999060i \(0.513803\pi\)
\(588\) 0 0
\(589\) −0.177489 −0.00731329
\(590\) 0 0
\(591\) 3.53516 0.145417
\(592\) 0 0
\(593\) 38.5015 1.58107 0.790534 0.612418i \(-0.209803\pi\)
0.790534 + 0.612418i \(0.209803\pi\)
\(594\) 0 0
\(595\) −13.3719 −0.548194
\(596\) 0 0
\(597\) −60.3546 −2.47015
\(598\) 0 0
\(599\) 25.3020 1.03381 0.516905 0.856043i \(-0.327084\pi\)
0.516905 + 0.856043i \(0.327084\pi\)
\(600\) 0 0
\(601\) −13.8150 −0.563527 −0.281763 0.959484i \(-0.590919\pi\)
−0.281763 + 0.959484i \(0.590919\pi\)
\(602\) 0 0
\(603\) 47.3448 1.92803
\(604\) 0 0
\(605\) 3.08345 0.125360
\(606\) 0 0
\(607\) −25.6662 −1.04176 −0.520879 0.853631i \(-0.674396\pi\)
−0.520879 + 0.853631i \(0.674396\pi\)
\(608\) 0 0
\(609\) 68.3442 2.76945
\(610\) 0 0
\(611\) 0.592404 0.0239661
\(612\) 0 0
\(613\) 30.6385 1.23748 0.618738 0.785597i \(-0.287644\pi\)
0.618738 + 0.785597i \(0.287644\pi\)
\(614\) 0 0
\(615\) −6.77132 −0.273046
\(616\) 0 0
\(617\) −6.40157 −0.257718 −0.128859 0.991663i \(-0.541131\pi\)
−0.128859 + 0.991663i \(0.541131\pi\)
\(618\) 0 0
\(619\) −11.3704 −0.457014 −0.228507 0.973542i \(-0.573384\pi\)
−0.228507 + 0.973542i \(0.573384\pi\)
\(620\) 0 0
\(621\) −30.1034 −1.20801
\(622\) 0 0
\(623\) 50.0961 2.00706
\(624\) 0 0
\(625\) 19.8632 0.794526
\(626\) 0 0
\(627\) 6.54631 0.261434
\(628\) 0 0
\(629\) −36.4776 −1.45446
\(630\) 0 0
\(631\) 31.5680 1.25670 0.628352 0.777929i \(-0.283730\pi\)
0.628352 + 0.777929i \(0.283730\pi\)
\(632\) 0 0
\(633\) −58.0560 −2.30752
\(634\) 0 0
\(635\) 0.245609 0.00974668
\(636\) 0 0
\(637\) 6.14890 0.243628
\(638\) 0 0
\(639\) −42.5481 −1.68318
\(640\) 0 0
\(641\) 30.0046 1.18511 0.592556 0.805529i \(-0.298119\pi\)
0.592556 + 0.805529i \(0.298119\pi\)
\(642\) 0 0
\(643\) 7.71725 0.304339 0.152169 0.988354i \(-0.451374\pi\)
0.152169 + 0.988354i \(0.451374\pi\)
\(644\) 0 0
\(645\) 8.69391 0.342322
\(646\) 0 0
\(647\) −9.12449 −0.358721 −0.179360 0.983783i \(-0.557403\pi\)
−0.179360 + 0.983783i \(0.557403\pi\)
\(648\) 0 0
\(649\) −8.69336 −0.341244
\(650\) 0 0
\(651\) 1.42205 0.0557346
\(652\) 0 0
\(653\) 26.6714 1.04373 0.521866 0.853028i \(-0.325236\pi\)
0.521866 + 0.853028i \(0.325236\pi\)
\(654\) 0 0
\(655\) −5.49162 −0.214576
\(656\) 0 0
\(657\) 29.1476 1.13716
\(658\) 0 0
\(659\) 30.8681 1.20245 0.601225 0.799080i \(-0.294680\pi\)
0.601225 + 0.799080i \(0.294680\pi\)
\(660\) 0 0
\(661\) −35.0682 −1.36399 −0.681997 0.731355i \(-0.738888\pi\)
−0.681997 + 0.731355i \(0.738888\pi\)
\(662\) 0 0
\(663\) −76.4296 −2.96828
\(664\) 0 0
\(665\) 1.74435 0.0676431
\(666\) 0 0
\(667\) 67.5463 2.61540
\(668\) 0 0
\(669\) 25.1997 0.974275
\(670\) 0 0
\(671\) 24.8138 0.957925
\(672\) 0 0
\(673\) 27.1644 1.04711 0.523556 0.851991i \(-0.324605\pi\)
0.523556 + 0.851991i \(0.324605\pi\)
\(674\) 0 0
\(675\) −17.6752 −0.680317
\(676\) 0 0
\(677\) 36.2990 1.39508 0.697541 0.716544i \(-0.254277\pi\)
0.697541 + 0.716544i \(0.254277\pi\)
\(678\) 0 0
\(679\) −41.3040 −1.58510
\(680\) 0 0
\(681\) −2.28500 −0.0875615
\(682\) 0 0
\(683\) 37.9871 1.45354 0.726768 0.686883i \(-0.241022\pi\)
0.726768 + 0.686883i \(0.241022\pi\)
\(684\) 0 0
\(685\) −1.22742 −0.0468973
\(686\) 0 0
\(687\) −39.7335 −1.51593
\(688\) 0 0
\(689\) −41.4767 −1.58014
\(690\) 0 0
\(691\) 6.16824 0.234651 0.117325 0.993094i \(-0.462568\pi\)
0.117325 + 0.993094i \(0.462568\pi\)
\(692\) 0 0
\(693\) −31.1796 −1.18442
\(694\) 0 0
\(695\) −9.60240 −0.364240
\(696\) 0 0
\(697\) −32.2288 −1.22075
\(698\) 0 0
\(699\) −0.497885 −0.0188317
\(700\) 0 0
\(701\) −4.13482 −0.156170 −0.0780851 0.996947i \(-0.524881\pi\)
−0.0780851 + 0.996947i \(0.524881\pi\)
\(702\) 0 0
\(703\) 4.75848 0.179469
\(704\) 0 0
\(705\) −0.260286 −0.00980295
\(706\) 0 0
\(707\) 0.766256 0.0288180
\(708\) 0 0
\(709\) −2.21199 −0.0830730 −0.0415365 0.999137i \(-0.513225\pi\)
−0.0415365 + 0.999137i \(0.513225\pi\)
\(710\) 0 0
\(711\) −4.39773 −0.164928
\(712\) 0 0
\(713\) 1.40545 0.0526345
\(714\) 0 0
\(715\) −5.22445 −0.195383
\(716\) 0 0
\(717\) −38.7356 −1.44661
\(718\) 0 0
\(719\) 18.4892 0.689532 0.344766 0.938689i \(-0.387958\pi\)
0.344766 + 0.938689i \(0.387958\pi\)
\(720\) 0 0
\(721\) 42.1440 1.56952
\(722\) 0 0
\(723\) −60.7191 −2.25817
\(724\) 0 0
\(725\) 39.6597 1.47292
\(726\) 0 0
\(727\) −18.0772 −0.670447 −0.335224 0.942139i \(-0.608812\pi\)
−0.335224 + 0.942139i \(0.608812\pi\)
\(728\) 0 0
\(729\) −43.5675 −1.61361
\(730\) 0 0
\(731\) 41.3795 1.53048
\(732\) 0 0
\(733\) −10.5169 −0.388452 −0.194226 0.980957i \(-0.562220\pi\)
−0.194226 + 0.980957i \(0.562220\pi\)
\(734\) 0 0
\(735\) −2.70167 −0.0996524
\(736\) 0 0
\(737\) 25.9114 0.954460
\(738\) 0 0
\(739\) −21.8505 −0.803784 −0.401892 0.915687i \(-0.631647\pi\)
−0.401892 + 0.915687i \(0.631647\pi\)
\(740\) 0 0
\(741\) 9.97019 0.366264
\(742\) 0 0
\(743\) 44.1742 1.62059 0.810297 0.586019i \(-0.199306\pi\)
0.810297 + 0.586019i \(0.199306\pi\)
\(744\) 0 0
\(745\) 1.84898 0.0677414
\(746\) 0 0
\(747\) −18.7406 −0.685682
\(748\) 0 0
\(749\) −9.34997 −0.341641
\(750\) 0 0
\(751\) −22.2521 −0.811991 −0.405995 0.913875i \(-0.633075\pi\)
−0.405995 + 0.913875i \(0.633075\pi\)
\(752\) 0 0
\(753\) −66.2491 −2.41425
\(754\) 0 0
\(755\) 11.8323 0.430623
\(756\) 0 0
\(757\) −15.9029 −0.578002 −0.289001 0.957329i \(-0.593323\pi\)
−0.289001 + 0.957329i \(0.593323\pi\)
\(758\) 0 0
\(759\) −51.8371 −1.88157
\(760\) 0 0
\(761\) −6.41785 −0.232647 −0.116323 0.993211i \(-0.537111\pi\)
−0.116323 + 0.993211i \(0.537111\pi\)
\(762\) 0 0
\(763\) −26.2956 −0.951965
\(764\) 0 0
\(765\) 19.9630 0.721763
\(766\) 0 0
\(767\) −13.2402 −0.478076
\(768\) 0 0
\(769\) −21.1031 −0.760999 −0.380499 0.924781i \(-0.624248\pi\)
−0.380499 + 0.924781i \(0.624248\pi\)
\(770\) 0 0
\(771\) 8.42249 0.303329
\(772\) 0 0
\(773\) −18.1093 −0.651348 −0.325674 0.945482i \(-0.605591\pi\)
−0.325674 + 0.945482i \(0.605591\pi\)
\(774\) 0 0
\(775\) 0.825206 0.0296423
\(776\) 0 0
\(777\) −38.1253 −1.36774
\(778\) 0 0
\(779\) 4.20422 0.150632
\(780\) 0 0
\(781\) −23.2862 −0.833247
\(782\) 0 0
\(783\) −32.4286 −1.15891
\(784\) 0 0
\(785\) 12.8280 0.457850
\(786\) 0 0
\(787\) 41.2633 1.47088 0.735440 0.677590i \(-0.236976\pi\)
0.735440 + 0.677590i \(0.236976\pi\)
\(788\) 0 0
\(789\) −30.7519 −1.09480
\(790\) 0 0
\(791\) 10.7784 0.383236
\(792\) 0 0
\(793\) 37.7920 1.34203
\(794\) 0 0
\(795\) 18.2238 0.646330
\(796\) 0 0
\(797\) 37.4139 1.32527 0.662635 0.748943i \(-0.269438\pi\)
0.662635 + 0.748943i \(0.269438\pi\)
\(798\) 0 0
\(799\) −1.23886 −0.0438277
\(800\) 0 0
\(801\) −74.7888 −2.64253
\(802\) 0 0
\(803\) 15.9523 0.562943
\(804\) 0 0
\(805\) −13.8127 −0.486834
\(806\) 0 0
\(807\) 35.4579 1.24818
\(808\) 0 0
\(809\) −56.7517 −1.99528 −0.997642 0.0686296i \(-0.978137\pi\)
−0.997642 + 0.0686296i \(0.978137\pi\)
\(810\) 0 0
\(811\) 11.8384 0.415702 0.207851 0.978161i \(-0.433353\pi\)
0.207851 + 0.978161i \(0.433353\pi\)
\(812\) 0 0
\(813\) −26.2040 −0.919016
\(814\) 0 0
\(815\) −3.63245 −0.127239
\(816\) 0 0
\(817\) −5.39793 −0.188850
\(818\) 0 0
\(819\) −47.4873 −1.65934
\(820\) 0 0
\(821\) −21.1755 −0.739031 −0.369515 0.929225i \(-0.620476\pi\)
−0.369515 + 0.929225i \(0.620476\pi\)
\(822\) 0 0
\(823\) 9.02961 0.314752 0.157376 0.987539i \(-0.449696\pi\)
0.157376 + 0.987539i \(0.449696\pi\)
\(824\) 0 0
\(825\) −30.4361 −1.05965
\(826\) 0 0
\(827\) 8.40374 0.292227 0.146113 0.989268i \(-0.453324\pi\)
0.146113 + 0.989268i \(0.453324\pi\)
\(828\) 0 0
\(829\) 37.3540 1.29736 0.648679 0.761062i \(-0.275322\pi\)
0.648679 + 0.761062i \(0.275322\pi\)
\(830\) 0 0
\(831\) −0.812691 −0.0281919
\(832\) 0 0
\(833\) −12.8588 −0.445532
\(834\) 0 0
\(835\) −13.5312 −0.468265
\(836\) 0 0
\(837\) −0.674749 −0.0233227
\(838\) 0 0
\(839\) −9.96301 −0.343961 −0.171981 0.985100i \(-0.555017\pi\)
−0.171981 + 0.985100i \(0.555017\pi\)
\(840\) 0 0
\(841\) 43.7637 1.50909
\(842\) 0 0
\(843\) 15.6131 0.537745
\(844\) 0 0
\(845\) −0.258883 −0.00890586
\(846\) 0 0
\(847\) 15.3389 0.527050
\(848\) 0 0
\(849\) 68.4107 2.34785
\(850\) 0 0
\(851\) −37.6802 −1.29166
\(852\) 0 0
\(853\) −45.2551 −1.54951 −0.774753 0.632264i \(-0.782126\pi\)
−0.774753 + 0.632264i \(0.782126\pi\)
\(854\) 0 0
\(855\) −2.60416 −0.0890603
\(856\) 0 0
\(857\) −31.0656 −1.06118 −0.530590 0.847629i \(-0.678030\pi\)
−0.530590 + 0.847629i \(0.678030\pi\)
\(858\) 0 0
\(859\) 35.6714 1.21709 0.608546 0.793519i \(-0.291753\pi\)
0.608546 + 0.793519i \(0.291753\pi\)
\(860\) 0 0
\(861\) −33.6845 −1.14796
\(862\) 0 0
\(863\) −48.4201 −1.64824 −0.824120 0.566415i \(-0.808330\pi\)
−0.824120 + 0.566415i \(0.808330\pi\)
\(864\) 0 0
\(865\) 13.2217 0.449552
\(866\) 0 0
\(867\) 113.595 3.85788
\(868\) 0 0
\(869\) −2.40684 −0.0816465
\(870\) 0 0
\(871\) 39.4637 1.33718
\(872\) 0 0
\(873\) 61.6631 2.08698
\(874\) 0 0
\(875\) −16.8319 −0.569021
\(876\) 0 0
\(877\) 36.4341 1.23029 0.615146 0.788413i \(-0.289097\pi\)
0.615146 + 0.788413i \(0.289097\pi\)
\(878\) 0 0
\(879\) −61.7361 −2.08231
\(880\) 0 0
\(881\) 31.9437 1.07621 0.538106 0.842877i \(-0.319140\pi\)
0.538106 + 0.842877i \(0.319140\pi\)
\(882\) 0 0
\(883\) 36.3025 1.22168 0.610838 0.791756i \(-0.290833\pi\)
0.610838 + 0.791756i \(0.290833\pi\)
\(884\) 0 0
\(885\) 5.81740 0.195550
\(886\) 0 0
\(887\) −19.6571 −0.660022 −0.330011 0.943977i \(-0.607052\pi\)
−0.330011 + 0.943977i \(0.607052\pi\)
\(888\) 0 0
\(889\) 1.22180 0.0409779
\(890\) 0 0
\(891\) −6.86714 −0.230058
\(892\) 0 0
\(893\) 0.161608 0.00540801
\(894\) 0 0
\(895\) −12.1244 −0.405275
\(896\) 0 0
\(897\) −78.9492 −2.63604
\(898\) 0 0
\(899\) 1.51401 0.0504950
\(900\) 0 0
\(901\) 86.7377 2.88965
\(902\) 0 0
\(903\) 43.2486 1.43922
\(904\) 0 0
\(905\) −15.0363 −0.499824
\(906\) 0 0
\(907\) 12.0743 0.400921 0.200461 0.979702i \(-0.435756\pi\)
0.200461 + 0.979702i \(0.435756\pi\)
\(908\) 0 0
\(909\) −1.14395 −0.0379424
\(910\) 0 0
\(911\) 42.3744 1.40393 0.701963 0.712213i \(-0.252307\pi\)
0.701963 + 0.712213i \(0.252307\pi\)
\(912\) 0 0
\(913\) −10.2566 −0.339443
\(914\) 0 0
\(915\) −16.6048 −0.548937
\(916\) 0 0
\(917\) −27.3185 −0.902138
\(918\) 0 0
\(919\) −38.5524 −1.27172 −0.635862 0.771802i \(-0.719355\pi\)
−0.635862 + 0.771802i \(0.719355\pi\)
\(920\) 0 0
\(921\) 68.3462 2.25208
\(922\) 0 0
\(923\) −35.4655 −1.16736
\(924\) 0 0
\(925\) −22.1238 −0.727427
\(926\) 0 0
\(927\) −62.9171 −2.06647
\(928\) 0 0
\(929\) −0.245863 −0.00806651 −0.00403326 0.999992i \(-0.501284\pi\)
−0.00403326 + 0.999992i \(0.501284\pi\)
\(930\) 0 0
\(931\) 1.67743 0.0549754
\(932\) 0 0
\(933\) −71.1220 −2.32843
\(934\) 0 0
\(935\) 10.9256 0.357305
\(936\) 0 0
\(937\) −29.6860 −0.969798 −0.484899 0.874570i \(-0.661144\pi\)
−0.484899 + 0.874570i \(0.661144\pi\)
\(938\) 0 0
\(939\) 1.00626 0.0328380
\(940\) 0 0
\(941\) −22.7390 −0.741270 −0.370635 0.928779i \(-0.620860\pi\)
−0.370635 + 0.928779i \(0.620860\pi\)
\(942\) 0 0
\(943\) −33.2912 −1.08411
\(944\) 0 0
\(945\) 6.63141 0.215720
\(946\) 0 0
\(947\) −31.4595 −1.02230 −0.511149 0.859492i \(-0.670780\pi\)
−0.511149 + 0.859492i \(0.670780\pi\)
\(948\) 0 0
\(949\) 24.2957 0.788671
\(950\) 0 0
\(951\) 79.2673 2.57042
\(952\) 0 0
\(953\) −11.8602 −0.384191 −0.192095 0.981376i \(-0.561528\pi\)
−0.192095 + 0.981376i \(0.561528\pi\)
\(954\) 0 0
\(955\) −2.10872 −0.0682365
\(956\) 0 0
\(957\) −55.8411 −1.80509
\(958\) 0 0
\(959\) −6.10591 −0.197170
\(960\) 0 0
\(961\) −30.9685 −0.998984
\(962\) 0 0
\(963\) 13.9586 0.449811
\(964\) 0 0
\(965\) −6.08894 −0.196010
\(966\) 0 0
\(967\) 55.9859 1.80038 0.900192 0.435494i \(-0.143426\pi\)
0.900192 + 0.435494i \(0.143426\pi\)
\(968\) 0 0
\(969\) −20.8501 −0.669800
\(970\) 0 0
\(971\) −22.5950 −0.725108 −0.362554 0.931963i \(-0.618095\pi\)
−0.362554 + 0.931963i \(0.618095\pi\)
\(972\) 0 0
\(973\) −47.7679 −1.53137
\(974\) 0 0
\(975\) −46.3549 −1.48454
\(976\) 0 0
\(977\) 20.4344 0.653753 0.326876 0.945067i \(-0.394004\pi\)
0.326876 + 0.945067i \(0.394004\pi\)
\(978\) 0 0
\(979\) −40.9313 −1.30817
\(980\) 0 0
\(981\) 39.2569 1.25338
\(982\) 0 0
\(983\) 45.8372 1.46198 0.730990 0.682388i \(-0.239058\pi\)
0.730990 + 0.682388i \(0.239058\pi\)
\(984\) 0 0
\(985\) −0.769660 −0.0245234
\(986\) 0 0
\(987\) −1.29482 −0.0412145
\(988\) 0 0
\(989\) 42.7437 1.35917
\(990\) 0 0
\(991\) 16.4265 0.521804 0.260902 0.965365i \(-0.415980\pi\)
0.260902 + 0.965365i \(0.415980\pi\)
\(992\) 0 0
\(993\) 86.3800 2.74119
\(994\) 0 0
\(995\) 13.1401 0.416570
\(996\) 0 0
\(997\) 23.1395 0.732836 0.366418 0.930450i \(-0.380584\pi\)
0.366418 + 0.930450i \(0.380584\pi\)
\(998\) 0 0
\(999\) 18.0900 0.572344
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 \(a_p\))