Properties

Label 8046.2.a.h.1.9
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 1
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-1.55687\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.71034 q^{5} +1.67819 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +2.71034 q^{5} +1.67819 q^{7} +1.00000 q^{8} +2.71034 q^{10} -4.37358 q^{11} -2.34775 q^{13} +1.67819 q^{14} +1.00000 q^{16} -4.09598 q^{17} -7.26207 q^{19} +2.71034 q^{20} -4.37358 q^{22} +0.0981648 q^{23} +2.34593 q^{25} -2.34775 q^{26} +1.67819 q^{28} -5.89425 q^{29} -1.88042 q^{31} +1.00000 q^{32} -4.09598 q^{34} +4.54847 q^{35} -3.13510 q^{37} -7.26207 q^{38} +2.71034 q^{40} -0.419725 q^{41} -0.0900380 q^{43} -4.37358 q^{44} +0.0981648 q^{46} -1.12980 q^{47} -4.18367 q^{49} +2.34593 q^{50} -2.34775 q^{52} +12.5105 q^{53} -11.8539 q^{55} +1.67819 q^{56} -5.89425 q^{58} -7.63266 q^{59} +3.77438 q^{61} -1.88042 q^{62} +1.00000 q^{64} -6.36319 q^{65} +3.12705 q^{67} -4.09598 q^{68} +4.54847 q^{70} -3.20185 q^{71} +1.15506 q^{73} -3.13510 q^{74} -7.26207 q^{76} -7.33971 q^{77} -15.5113 q^{79} +2.71034 q^{80} -0.419725 q^{82} -14.9118 q^{83} -11.1015 q^{85} -0.0900380 q^{86} -4.37358 q^{88} +7.11363 q^{89} -3.93997 q^{91} +0.0981648 q^{92} -1.12980 q^{94} -19.6827 q^{95} -4.78642 q^{97} -4.18367 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} + O(q^{10}) \) \( 9q + 9q^{2} + 9q^{4} - 4q^{5} - 4q^{7} + 9q^{8} - 4q^{10} - 4q^{11} - 8q^{13} - 4q^{14} + 9q^{16} - q^{17} - 10q^{19} - 4q^{20} - 4q^{22} - 8q^{23} - 3q^{25} - 8q^{26} - 4q^{28} - 4q^{29} - 17q^{31} + 9q^{32} - q^{34} - 10q^{35} - 11q^{37} - 10q^{38} - 4q^{40} - 16q^{43} - 4q^{44} - 8q^{46} - 7q^{47} - 5q^{49} - 3q^{50} - 8q^{52} - 12q^{53} - 23q^{55} - 4q^{56} - 4q^{58} - 6q^{59} - 13q^{61} - 17q^{62} + 9q^{64} + 24q^{65} - 14q^{67} - q^{68} - 10q^{70} - 30q^{71} - 12q^{73} - 11q^{74} - 10q^{76} - 12q^{77} - 35q^{79} - 4q^{80} - 5q^{83} - 27q^{85} - 16q^{86} - 4q^{88} - 23q^{89} - 28q^{91} - 8q^{92} - 7q^{94} - 32q^{95} - 21q^{97} - 5q^{98} + O(q^{100}) \)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 2.71034 1.21210 0.606050 0.795426i \(-0.292753\pi\)
0.606050 + 0.795426i \(0.292753\pi\)
\(6\) 0 0
\(7\) 1.67819 0.634297 0.317148 0.948376i \(-0.397275\pi\)
0.317148 + 0.948376i \(0.397275\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 2.71034 0.857084
\(11\) −4.37358 −1.31869 −0.659343 0.751843i \(-0.729165\pi\)
−0.659343 + 0.751843i \(0.729165\pi\)
\(12\) 0 0
\(13\) −2.34775 −0.651148 −0.325574 0.945517i \(-0.605557\pi\)
−0.325574 + 0.945517i \(0.605557\pi\)
\(14\) 1.67819 0.448515
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −4.09598 −0.993420 −0.496710 0.867916i \(-0.665459\pi\)
−0.496710 + 0.867916i \(0.665459\pi\)
\(18\) 0 0
\(19\) −7.26207 −1.66603 −0.833016 0.553249i \(-0.813388\pi\)
−0.833016 + 0.553249i \(0.813388\pi\)
\(20\) 2.71034 0.606050
\(21\) 0 0
\(22\) −4.37358 −0.932451
\(23\) 0.0981648 0.0204688 0.0102344 0.999948i \(-0.496742\pi\)
0.0102344 + 0.999948i \(0.496742\pi\)
\(24\) 0 0
\(25\) 2.34593 0.469187
\(26\) −2.34775 −0.460431
\(27\) 0 0
\(28\) 1.67819 0.317148
\(29\) −5.89425 −1.09454 −0.547268 0.836958i \(-0.684332\pi\)
−0.547268 + 0.836958i \(0.684332\pi\)
\(30\) 0 0
\(31\) −1.88042 −0.337734 −0.168867 0.985639i \(-0.554011\pi\)
−0.168867 + 0.985639i \(0.554011\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −4.09598 −0.702454
\(35\) 4.54847 0.768831
\(36\) 0 0
\(37\) −3.13510 −0.515407 −0.257704 0.966224i \(-0.582966\pi\)
−0.257704 + 0.966224i \(0.582966\pi\)
\(38\) −7.26207 −1.17806
\(39\) 0 0
\(40\) 2.71034 0.428542
\(41\) −0.419725 −0.0655501 −0.0327750 0.999463i \(-0.510434\pi\)
−0.0327750 + 0.999463i \(0.510434\pi\)
\(42\) 0 0
\(43\) −0.0900380 −0.0137307 −0.00686534 0.999976i \(-0.502185\pi\)
−0.00686534 + 0.999976i \(0.502185\pi\)
\(44\) −4.37358 −0.659343
\(45\) 0 0
\(46\) 0.0981648 0.0144736
\(47\) −1.12980 −0.164799 −0.0823993 0.996599i \(-0.526258\pi\)
−0.0823993 + 0.996599i \(0.526258\pi\)
\(48\) 0 0
\(49\) −4.18367 −0.597668
\(50\) 2.34593 0.331765
\(51\) 0 0
\(52\) −2.34775 −0.325574
\(53\) 12.5105 1.71845 0.859227 0.511595i \(-0.170945\pi\)
0.859227 + 0.511595i \(0.170945\pi\)
\(54\) 0 0
\(55\) −11.8539 −1.59838
\(56\) 1.67819 0.224258
\(57\) 0 0
\(58\) −5.89425 −0.773953
\(59\) −7.63266 −0.993687 −0.496844 0.867840i \(-0.665508\pi\)
−0.496844 + 0.867840i \(0.665508\pi\)
\(60\) 0 0
\(61\) 3.77438 0.483260 0.241630 0.970368i \(-0.422318\pi\)
0.241630 + 0.970368i \(0.422318\pi\)
\(62\) −1.88042 −0.238814
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.36319 −0.789256
\(66\) 0 0
\(67\) 3.12705 0.382030 0.191015 0.981587i \(-0.438822\pi\)
0.191015 + 0.981587i \(0.438822\pi\)
\(68\) −4.09598 −0.496710
\(69\) 0 0
\(70\) 4.54847 0.543646
\(71\) −3.20185 −0.379990 −0.189995 0.981785i \(-0.560847\pi\)
−0.189995 + 0.981785i \(0.560847\pi\)
\(72\) 0 0
\(73\) 1.15506 0.135190 0.0675951 0.997713i \(-0.478467\pi\)
0.0675951 + 0.997713i \(0.478467\pi\)
\(74\) −3.13510 −0.364448
\(75\) 0 0
\(76\) −7.26207 −0.833016
\(77\) −7.33971 −0.836437
\(78\) 0 0
\(79\) −15.5113 −1.74516 −0.872578 0.488475i \(-0.837553\pi\)
−0.872578 + 0.488475i \(0.837553\pi\)
\(80\) 2.71034 0.303025
\(81\) 0 0
\(82\) −0.419725 −0.0463509
\(83\) −14.9118 −1.63678 −0.818389 0.574665i \(-0.805132\pi\)
−0.818389 + 0.574665i \(0.805132\pi\)
\(84\) 0 0
\(85\) −11.1015 −1.20412
\(86\) −0.0900380 −0.00970905
\(87\) 0 0
\(88\) −4.37358 −0.466226
\(89\) 7.11363 0.754043 0.377022 0.926204i \(-0.376948\pi\)
0.377022 + 0.926204i \(0.376948\pi\)
\(90\) 0 0
\(91\) −3.93997 −0.413021
\(92\) 0.0981648 0.0102344
\(93\) 0 0
\(94\) −1.12980 −0.116530
\(95\) −19.6827 −2.01940
\(96\) 0 0
\(97\) −4.78642 −0.485987 −0.242994 0.970028i \(-0.578129\pi\)
−0.242994 + 0.970028i \(0.578129\pi\)
\(98\) −4.18367 −0.422615
\(99\) 0 0
\(100\) 2.34593 0.234593
\(101\) −3.25163 −0.323550 −0.161775 0.986828i \(-0.551722\pi\)
−0.161775 + 0.986828i \(0.551722\pi\)
\(102\) 0 0
\(103\) −6.91855 −0.681705 −0.340852 0.940117i \(-0.610716\pi\)
−0.340852 + 0.940117i \(0.610716\pi\)
\(104\) −2.34775 −0.230216
\(105\) 0 0
\(106\) 12.5105 1.21513
\(107\) 2.61340 0.252647 0.126323 0.991989i \(-0.459682\pi\)
0.126323 + 0.991989i \(0.459682\pi\)
\(108\) 0 0
\(109\) −8.13251 −0.778953 −0.389477 0.921036i \(-0.627344\pi\)
−0.389477 + 0.921036i \(0.627344\pi\)
\(110\) −11.8539 −1.13022
\(111\) 0 0
\(112\) 1.67819 0.158574
\(113\) 6.09305 0.573186 0.286593 0.958052i \(-0.407477\pi\)
0.286593 + 0.958052i \(0.407477\pi\)
\(114\) 0 0
\(115\) 0.266060 0.0248102
\(116\) −5.89425 −0.547268
\(117\) 0 0
\(118\) −7.63266 −0.702643
\(119\) −6.87383 −0.630123
\(120\) 0 0
\(121\) 8.12823 0.738930
\(122\) 3.77438 0.341717
\(123\) 0 0
\(124\) −1.88042 −0.168867
\(125\) −7.19342 −0.643399
\(126\) 0 0
\(127\) 3.03062 0.268924 0.134462 0.990919i \(-0.457069\pi\)
0.134462 + 0.990919i \(0.457069\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) −6.36319 −0.558089
\(131\) 22.8099 1.99291 0.996454 0.0841386i \(-0.0268138\pi\)
0.996454 + 0.0841386i \(0.0268138\pi\)
\(132\) 0 0
\(133\) −12.1871 −1.05676
\(134\) 3.12705 0.270136
\(135\) 0 0
\(136\) −4.09598 −0.351227
\(137\) 12.4026 1.05962 0.529812 0.848115i \(-0.322262\pi\)
0.529812 + 0.848115i \(0.322262\pi\)
\(138\) 0 0
\(139\) 16.1737 1.37184 0.685918 0.727679i \(-0.259401\pi\)
0.685918 + 0.727679i \(0.259401\pi\)
\(140\) 4.54847 0.384415
\(141\) 0 0
\(142\) −3.20185 −0.268693
\(143\) 10.2681 0.858659
\(144\) 0 0
\(145\) −15.9754 −1.32669
\(146\) 1.15506 0.0955938
\(147\) 0 0
\(148\) −3.13510 −0.257704
\(149\) −1.00000 −0.0819232
\(150\) 0 0
\(151\) 10.5180 0.855946 0.427973 0.903791i \(-0.359228\pi\)
0.427973 + 0.903791i \(0.359228\pi\)
\(152\) −7.26207 −0.589031
\(153\) 0 0
\(154\) −7.33971 −0.591451
\(155\) −5.09658 −0.409367
\(156\) 0 0
\(157\) 19.1463 1.52804 0.764020 0.645193i \(-0.223223\pi\)
0.764020 + 0.645193i \(0.223223\pi\)
\(158\) −15.5113 −1.23401
\(159\) 0 0
\(160\) 2.71034 0.214271
\(161\) 0.164739 0.0129833
\(162\) 0 0
\(163\) −6.53078 −0.511530 −0.255765 0.966739i \(-0.582327\pi\)
−0.255765 + 0.966739i \(0.582327\pi\)
\(164\) −0.419725 −0.0327750
\(165\) 0 0
\(166\) −14.9118 −1.15738
\(167\) −11.7228 −0.907134 −0.453567 0.891222i \(-0.649849\pi\)
−0.453567 + 0.891222i \(0.649849\pi\)
\(168\) 0 0
\(169\) −7.48808 −0.576006
\(170\) −11.1015 −0.851445
\(171\) 0 0
\(172\) −0.0900380 −0.00686534
\(173\) −1.93624 −0.147210 −0.0736049 0.997287i \(-0.523450\pi\)
−0.0736049 + 0.997287i \(0.523450\pi\)
\(174\) 0 0
\(175\) 3.93692 0.297604
\(176\) −4.37358 −0.329671
\(177\) 0 0
\(178\) 7.11363 0.533189
\(179\) 13.5559 1.01321 0.506606 0.862178i \(-0.330900\pi\)
0.506606 + 0.862178i \(0.330900\pi\)
\(180\) 0 0
\(181\) 14.9431 1.11071 0.555354 0.831614i \(-0.312583\pi\)
0.555354 + 0.831614i \(0.312583\pi\)
\(182\) −3.93997 −0.292050
\(183\) 0 0
\(184\) 0.0981648 0.00723681
\(185\) −8.49718 −0.624725
\(186\) 0 0
\(187\) 17.9141 1.31001
\(188\) −1.12980 −0.0823993
\(189\) 0 0
\(190\) −19.6827 −1.42793
\(191\) −3.69535 −0.267386 −0.133693 0.991023i \(-0.542684\pi\)
−0.133693 + 0.991023i \(0.542684\pi\)
\(192\) 0 0
\(193\) 7.65239 0.550831 0.275416 0.961325i \(-0.411185\pi\)
0.275416 + 0.961325i \(0.411185\pi\)
\(194\) −4.78642 −0.343645
\(195\) 0 0
\(196\) −4.18367 −0.298834
\(197\) −18.2992 −1.30376 −0.651882 0.758321i \(-0.726020\pi\)
−0.651882 + 0.758321i \(0.726020\pi\)
\(198\) 0 0
\(199\) 12.9256 0.916269 0.458134 0.888883i \(-0.348518\pi\)
0.458134 + 0.888883i \(0.348518\pi\)
\(200\) 2.34593 0.165883
\(201\) 0 0
\(202\) −3.25163 −0.228784
\(203\) −9.89168 −0.694260
\(204\) 0 0
\(205\) −1.13760 −0.0794532
\(206\) −6.91855 −0.482038
\(207\) 0 0
\(208\) −2.34775 −0.162787
\(209\) 31.7613 2.19697
\(210\) 0 0
\(211\) −12.7410 −0.877126 −0.438563 0.898700i \(-0.644512\pi\)
−0.438563 + 0.898700i \(0.644512\pi\)
\(212\) 12.5105 0.859227
\(213\) 0 0
\(214\) 2.61340 0.178648
\(215\) −0.244034 −0.0166429
\(216\) 0 0
\(217\) −3.15571 −0.214223
\(218\) −8.13251 −0.550803
\(219\) 0 0
\(220\) −11.8539 −0.799189
\(221\) 9.61632 0.646864
\(222\) 0 0
\(223\) −10.0497 −0.672980 −0.336490 0.941687i \(-0.609240\pi\)
−0.336490 + 0.941687i \(0.609240\pi\)
\(224\) 1.67819 0.112129
\(225\) 0 0
\(226\) 6.09305 0.405303
\(227\) 9.51471 0.631514 0.315757 0.948840i \(-0.397742\pi\)
0.315757 + 0.948840i \(0.397742\pi\)
\(228\) 0 0
\(229\) 17.3081 1.14375 0.571875 0.820341i \(-0.306216\pi\)
0.571875 + 0.820341i \(0.306216\pi\)
\(230\) 0.266060 0.0175435
\(231\) 0 0
\(232\) −5.89425 −0.386977
\(233\) −21.8741 −1.43302 −0.716511 0.697576i \(-0.754262\pi\)
−0.716511 + 0.697576i \(0.754262\pi\)
\(234\) 0 0
\(235\) −3.06215 −0.199752
\(236\) −7.63266 −0.496844
\(237\) 0 0
\(238\) −6.87383 −0.445564
\(239\) 25.8220 1.67029 0.835143 0.550032i \(-0.185385\pi\)
0.835143 + 0.550032i \(0.185385\pi\)
\(240\) 0 0
\(241\) −12.3157 −0.793327 −0.396663 0.917964i \(-0.629832\pi\)
−0.396663 + 0.917964i \(0.629832\pi\)
\(242\) 8.12823 0.522503
\(243\) 0 0
\(244\) 3.77438 0.241630
\(245\) −11.3392 −0.724433
\(246\) 0 0
\(247\) 17.0495 1.08483
\(248\) −1.88042 −0.119407
\(249\) 0 0
\(250\) −7.19342 −0.454952
\(251\) 24.1336 1.52330 0.761649 0.647990i \(-0.224390\pi\)
0.761649 + 0.647990i \(0.224390\pi\)
\(252\) 0 0
\(253\) −0.429332 −0.0269919
\(254\) 3.03062 0.190158
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −1.94139 −0.121101 −0.0605504 0.998165i \(-0.519286\pi\)
−0.0605504 + 0.998165i \(0.519286\pi\)
\(258\) 0 0
\(259\) −5.26129 −0.326921
\(260\) −6.36319 −0.394628
\(261\) 0 0
\(262\) 22.8099 1.40920
\(263\) −12.2957 −0.758187 −0.379093 0.925358i \(-0.623764\pi\)
−0.379093 + 0.925358i \(0.623764\pi\)
\(264\) 0 0
\(265\) 33.9078 2.08294
\(266\) −12.1871 −0.747241
\(267\) 0 0
\(268\) 3.12705 0.191015
\(269\) −5.20845 −0.317565 −0.158782 0.987314i \(-0.550757\pi\)
−0.158782 + 0.987314i \(0.550757\pi\)
\(270\) 0 0
\(271\) 9.53266 0.579068 0.289534 0.957168i \(-0.406500\pi\)
0.289534 + 0.957168i \(0.406500\pi\)
\(272\) −4.09598 −0.248355
\(273\) 0 0
\(274\) 12.4026 0.749268
\(275\) −10.2601 −0.618710
\(276\) 0 0
\(277\) 12.2562 0.736404 0.368202 0.929746i \(-0.379973\pi\)
0.368202 + 0.929746i \(0.379973\pi\)
\(278\) 16.1737 0.970034
\(279\) 0 0
\(280\) 4.54847 0.271823
\(281\) 1.20525 0.0718992 0.0359496 0.999354i \(-0.488554\pi\)
0.0359496 + 0.999354i \(0.488554\pi\)
\(282\) 0 0
\(283\) −24.3087 −1.44500 −0.722500 0.691371i \(-0.757007\pi\)
−0.722500 + 0.691371i \(0.757007\pi\)
\(284\) −3.20185 −0.189995
\(285\) 0 0
\(286\) 10.2681 0.607164
\(287\) −0.704379 −0.0415782
\(288\) 0 0
\(289\) −0.222971 −0.0131159
\(290\) −15.9754 −0.938109
\(291\) 0 0
\(292\) 1.15506 0.0675951
\(293\) 9.58867 0.560176 0.280088 0.959974i \(-0.409636\pi\)
0.280088 + 0.959974i \(0.409636\pi\)
\(294\) 0 0
\(295\) −20.6871 −1.20445
\(296\) −3.13510 −0.182224
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −0.230466 −0.0133282
\(300\) 0 0
\(301\) −0.151101 −0.00870932
\(302\) 10.5180 0.605246
\(303\) 0 0
\(304\) −7.26207 −0.416508
\(305\) 10.2299 0.585760
\(306\) 0 0
\(307\) −20.9118 −1.19350 −0.596750 0.802427i \(-0.703542\pi\)
−0.596750 + 0.802427i \(0.703542\pi\)
\(308\) −7.33971 −0.418219
\(309\) 0 0
\(310\) −5.09658 −0.289466
\(311\) 13.7307 0.778598 0.389299 0.921111i \(-0.372717\pi\)
0.389299 + 0.921111i \(0.372717\pi\)
\(312\) 0 0
\(313\) −27.3384 −1.54526 −0.772628 0.634859i \(-0.781058\pi\)
−0.772628 + 0.634859i \(0.781058\pi\)
\(314\) 19.1463 1.08049
\(315\) 0 0
\(316\) −15.5113 −0.872578
\(317\) 19.0031 1.06732 0.533659 0.845700i \(-0.320817\pi\)
0.533659 + 0.845700i \(0.320817\pi\)
\(318\) 0 0
\(319\) 25.7790 1.44335
\(320\) 2.71034 0.151513
\(321\) 0 0
\(322\) 0.164739 0.00918056
\(323\) 29.7453 1.65507
\(324\) 0 0
\(325\) −5.50766 −0.305510
\(326\) −6.53078 −0.361707
\(327\) 0 0
\(328\) −0.419725 −0.0231754
\(329\) −1.89602 −0.104531
\(330\) 0 0
\(331\) −24.2079 −1.33059 −0.665294 0.746581i \(-0.731694\pi\)
−0.665294 + 0.746581i \(0.731694\pi\)
\(332\) −14.9118 −0.818389
\(333\) 0 0
\(334\) −11.7228 −0.641440
\(335\) 8.47536 0.463059
\(336\) 0 0
\(337\) −21.7597 −1.18533 −0.592663 0.805450i \(-0.701924\pi\)
−0.592663 + 0.805450i \(0.701924\pi\)
\(338\) −7.48808 −0.407298
\(339\) 0 0
\(340\) −11.1015 −0.602062
\(341\) 8.22418 0.445364
\(342\) 0 0
\(343\) −18.7683 −1.01340
\(344\) −0.0900380 −0.00485453
\(345\) 0 0
\(346\) −1.93624 −0.104093
\(347\) −11.4110 −0.612574 −0.306287 0.951939i \(-0.599087\pi\)
−0.306287 + 0.951939i \(0.599087\pi\)
\(348\) 0 0
\(349\) 29.2720 1.56689 0.783446 0.621460i \(-0.213460\pi\)
0.783446 + 0.621460i \(0.213460\pi\)
\(350\) 3.93692 0.210437
\(351\) 0 0
\(352\) −4.37358 −0.233113
\(353\) 25.2789 1.34546 0.672730 0.739888i \(-0.265121\pi\)
0.672730 + 0.739888i \(0.265121\pi\)
\(354\) 0 0
\(355\) −8.67810 −0.460586
\(356\) 7.11363 0.377022
\(357\) 0 0
\(358\) 13.5559 0.716449
\(359\) 3.38548 0.178679 0.0893393 0.996001i \(-0.471524\pi\)
0.0893393 + 0.996001i \(0.471524\pi\)
\(360\) 0 0
\(361\) 33.7376 1.77566
\(362\) 14.9431 0.785389
\(363\) 0 0
\(364\) −3.93997 −0.206510
\(365\) 3.13062 0.163864
\(366\) 0 0
\(367\) 7.07969 0.369557 0.184778 0.982780i \(-0.440843\pi\)
0.184778 + 0.982780i \(0.440843\pi\)
\(368\) 0.0981648 0.00511719
\(369\) 0 0
\(370\) −8.49718 −0.441747
\(371\) 20.9951 1.09001
\(372\) 0 0
\(373\) 7.58277 0.392621 0.196311 0.980542i \(-0.437104\pi\)
0.196311 + 0.980542i \(0.437104\pi\)
\(374\) 17.9141 0.926316
\(375\) 0 0
\(376\) −1.12980 −0.0582651
\(377\) 13.8382 0.712704
\(378\) 0 0
\(379\) −37.0298 −1.90210 −0.951048 0.309044i \(-0.899991\pi\)
−0.951048 + 0.309044i \(0.899991\pi\)
\(380\) −19.6827 −1.00970
\(381\) 0 0
\(382\) −3.69535 −0.189071
\(383\) 9.47515 0.484158 0.242079 0.970257i \(-0.422171\pi\)
0.242079 + 0.970257i \(0.422171\pi\)
\(384\) 0 0
\(385\) −19.8931 −1.01385
\(386\) 7.65239 0.389496
\(387\) 0 0
\(388\) −4.78642 −0.242994
\(389\) 8.01018 0.406132 0.203066 0.979165i \(-0.434909\pi\)
0.203066 + 0.979165i \(0.434909\pi\)
\(390\) 0 0
\(391\) −0.402081 −0.0203341
\(392\) −4.18367 −0.211307
\(393\) 0 0
\(394\) −18.2992 −0.921900
\(395\) −42.0408 −2.11530
\(396\) 0 0
\(397\) −16.4377 −0.824984 −0.412492 0.910961i \(-0.635342\pi\)
−0.412492 + 0.910961i \(0.635342\pi\)
\(398\) 12.9256 0.647900
\(399\) 0 0
\(400\) 2.34593 0.117297
\(401\) 17.7661 0.887199 0.443599 0.896225i \(-0.353701\pi\)
0.443599 + 0.896225i \(0.353701\pi\)
\(402\) 0 0
\(403\) 4.41475 0.219914
\(404\) −3.25163 −0.161775
\(405\) 0 0
\(406\) −9.89168 −0.490916
\(407\) 13.7116 0.679660
\(408\) 0 0
\(409\) −24.3199 −1.20254 −0.601270 0.799046i \(-0.705338\pi\)
−0.601270 + 0.799046i \(0.705338\pi\)
\(410\) −1.13760 −0.0561819
\(411\) 0 0
\(412\) −6.91855 −0.340852
\(413\) −12.8091 −0.630293
\(414\) 0 0
\(415\) −40.4159 −1.98394
\(416\) −2.34775 −0.115108
\(417\) 0 0
\(418\) 31.7613 1.55349
\(419\) −23.5738 −1.15166 −0.575829 0.817570i \(-0.695321\pi\)
−0.575829 + 0.817570i \(0.695321\pi\)
\(420\) 0 0
\(421\) −0.218135 −0.0106312 −0.00531562 0.999986i \(-0.501692\pi\)
−0.00531562 + 0.999986i \(0.501692\pi\)
\(422\) −12.7410 −0.620222
\(423\) 0 0
\(424\) 12.5105 0.607565
\(425\) −9.60889 −0.466100
\(426\) 0 0
\(427\) 6.33414 0.306530
\(428\) 2.61340 0.126323
\(429\) 0 0
\(430\) −0.244034 −0.0117683
\(431\) 16.3041 0.785339 0.392670 0.919680i \(-0.371552\pi\)
0.392670 + 0.919680i \(0.371552\pi\)
\(432\) 0 0
\(433\) 16.4350 0.789815 0.394908 0.918721i \(-0.370777\pi\)
0.394908 + 0.918721i \(0.370777\pi\)
\(434\) −3.15571 −0.151479
\(435\) 0 0
\(436\) −8.13251 −0.389477
\(437\) −0.712879 −0.0341016
\(438\) 0 0
\(439\) −25.1285 −1.19932 −0.599660 0.800255i \(-0.704697\pi\)
−0.599660 + 0.800255i \(0.704697\pi\)
\(440\) −11.8539 −0.565112
\(441\) 0 0
\(442\) 9.61632 0.457402
\(443\) 26.4593 1.25712 0.628560 0.777761i \(-0.283645\pi\)
0.628560 + 0.777761i \(0.283645\pi\)
\(444\) 0 0
\(445\) 19.2803 0.913976
\(446\) −10.0497 −0.475869
\(447\) 0 0
\(448\) 1.67819 0.0792871
\(449\) 11.6779 0.551112 0.275556 0.961285i \(-0.411138\pi\)
0.275556 + 0.961285i \(0.411138\pi\)
\(450\) 0 0
\(451\) 1.83570 0.0864399
\(452\) 6.09305 0.286593
\(453\) 0 0
\(454\) 9.51471 0.446548
\(455\) −10.6786 −0.500623
\(456\) 0 0
\(457\) 11.2598 0.526709 0.263355 0.964699i \(-0.415171\pi\)
0.263355 + 0.964699i \(0.415171\pi\)
\(458\) 17.3081 0.808753
\(459\) 0 0
\(460\) 0.266060 0.0124051
\(461\) −14.7144 −0.685318 −0.342659 0.939460i \(-0.611328\pi\)
−0.342659 + 0.939460i \(0.611328\pi\)
\(462\) 0 0
\(463\) 15.2474 0.708607 0.354303 0.935131i \(-0.384718\pi\)
0.354303 + 0.935131i \(0.384718\pi\)
\(464\) −5.89425 −0.273634
\(465\) 0 0
\(466\) −21.8741 −1.01330
\(467\) −31.9586 −1.47887 −0.739433 0.673230i \(-0.764906\pi\)
−0.739433 + 0.673230i \(0.764906\pi\)
\(468\) 0 0
\(469\) 5.24779 0.242320
\(470\) −3.06215 −0.141246
\(471\) 0 0
\(472\) −7.63266 −0.351322
\(473\) 0.393789 0.0181064
\(474\) 0 0
\(475\) −17.0363 −0.781680
\(476\) −6.87383 −0.315062
\(477\) 0 0
\(478\) 25.8220 1.18107
\(479\) 10.9302 0.499413 0.249706 0.968322i \(-0.419666\pi\)
0.249706 + 0.968322i \(0.419666\pi\)
\(480\) 0 0
\(481\) 7.36042 0.335606
\(482\) −12.3157 −0.560967
\(483\) 0 0
\(484\) 8.12823 0.369465
\(485\) −12.9728 −0.589065
\(486\) 0 0
\(487\) −34.7186 −1.57325 −0.786626 0.617430i \(-0.788174\pi\)
−0.786626 + 0.617430i \(0.788174\pi\)
\(488\) 3.77438 0.170858
\(489\) 0 0
\(490\) −11.3392 −0.512252
\(491\) −33.3466 −1.50491 −0.752456 0.658642i \(-0.771131\pi\)
−0.752456 + 0.658642i \(0.771131\pi\)
\(492\) 0 0
\(493\) 24.1427 1.08733
\(494\) 17.0495 0.767093
\(495\) 0 0
\(496\) −1.88042 −0.0844334
\(497\) −5.37332 −0.241026
\(498\) 0 0
\(499\) −23.1107 −1.03458 −0.517289 0.855811i \(-0.673059\pi\)
−0.517289 + 0.855811i \(0.673059\pi\)
\(500\) −7.19342 −0.321699
\(501\) 0 0
\(502\) 24.1336 1.07713
\(503\) 31.7411 1.41527 0.707633 0.706580i \(-0.249763\pi\)
0.707633 + 0.706580i \(0.249763\pi\)
\(504\) 0 0
\(505\) −8.81303 −0.392175
\(506\) −0.429332 −0.0190861
\(507\) 0 0
\(508\) 3.03062 0.134462
\(509\) 15.5438 0.688965 0.344483 0.938793i \(-0.388054\pi\)
0.344483 + 0.938793i \(0.388054\pi\)
\(510\) 0 0
\(511\) 1.93842 0.0857506
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −1.94139 −0.0856311
\(515\) −18.7516 −0.826294
\(516\) 0 0
\(517\) 4.94129 0.217318
\(518\) −5.26129 −0.231168
\(519\) 0 0
\(520\) −6.36319 −0.279044
\(521\) 18.6011 0.814929 0.407465 0.913221i \(-0.366413\pi\)
0.407465 + 0.913221i \(0.366413\pi\)
\(522\) 0 0
\(523\) −16.4760 −0.720444 −0.360222 0.932867i \(-0.617299\pi\)
−0.360222 + 0.932867i \(0.617299\pi\)
\(524\) 22.8099 0.996454
\(525\) 0 0
\(526\) −12.2957 −0.536119
\(527\) 7.70216 0.335511
\(528\) 0 0
\(529\) −22.9904 −0.999581
\(530\) 33.9078 1.47286
\(531\) 0 0
\(532\) −12.1871 −0.528379
\(533\) 0.985408 0.0426828
\(534\) 0 0
\(535\) 7.08319 0.306233
\(536\) 3.12705 0.135068
\(537\) 0 0
\(538\) −5.20845 −0.224552
\(539\) 18.2977 0.788136
\(540\) 0 0
\(541\) 17.8765 0.768573 0.384286 0.923214i \(-0.374448\pi\)
0.384286 + 0.923214i \(0.374448\pi\)
\(542\) 9.53266 0.409463
\(543\) 0 0
\(544\) −4.09598 −0.175614
\(545\) −22.0419 −0.944169
\(546\) 0 0
\(547\) −27.9324 −1.19430 −0.597152 0.802128i \(-0.703701\pi\)
−0.597152 + 0.802128i \(0.703701\pi\)
\(548\) 12.4026 0.529812
\(549\) 0 0
\(550\) −10.2601 −0.437494
\(551\) 42.8044 1.82353
\(552\) 0 0
\(553\) −26.0309 −1.10695
\(554\) 12.2562 0.520716
\(555\) 0 0
\(556\) 16.1737 0.685918
\(557\) −17.0091 −0.720700 −0.360350 0.932817i \(-0.617343\pi\)
−0.360350 + 0.932817i \(0.617343\pi\)
\(558\) 0 0
\(559\) 0.211387 0.00894070
\(560\) 4.54847 0.192208
\(561\) 0 0
\(562\) 1.20525 0.0508404
\(563\) −36.1048 −1.52164 −0.760818 0.648965i \(-0.775202\pi\)
−0.760818 + 0.648965i \(0.775202\pi\)
\(564\) 0 0
\(565\) 16.5142 0.694758
\(566\) −24.3087 −1.02177
\(567\) 0 0
\(568\) −3.20185 −0.134347
\(569\) −6.41843 −0.269074 −0.134537 0.990909i \(-0.542955\pi\)
−0.134537 + 0.990909i \(0.542955\pi\)
\(570\) 0 0
\(571\) 16.2900 0.681716 0.340858 0.940115i \(-0.389282\pi\)
0.340858 + 0.940115i \(0.389282\pi\)
\(572\) 10.2681 0.429329
\(573\) 0 0
\(574\) −0.704379 −0.0294002
\(575\) 0.230288 0.00960368
\(576\) 0 0
\(577\) 14.1764 0.590170 0.295085 0.955471i \(-0.404652\pi\)
0.295085 + 0.955471i \(0.404652\pi\)
\(578\) −0.222971 −0.00927438
\(579\) 0 0
\(580\) −15.9754 −0.663343
\(581\) −25.0248 −1.03820
\(582\) 0 0
\(583\) −54.7159 −2.26610
\(584\) 1.15506 0.0477969
\(585\) 0 0
\(586\) 9.58867 0.396104
\(587\) −16.5294 −0.682242 −0.341121 0.940019i \(-0.610807\pi\)
−0.341121 + 0.940019i \(0.610807\pi\)
\(588\) 0 0
\(589\) 13.6557 0.562675
\(590\) −20.6871 −0.851674
\(591\) 0 0
\(592\) −3.13510 −0.128852
\(593\) 32.0924 1.31788 0.658939 0.752196i \(-0.271005\pi\)
0.658939 + 0.752196i \(0.271005\pi\)
\(594\) 0 0
\(595\) −18.6304 −0.763772
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) −0.230466 −0.00942446
\(599\) −22.1189 −0.903754 −0.451877 0.892080i \(-0.649245\pi\)
−0.451877 + 0.892080i \(0.649245\pi\)
\(600\) 0 0
\(601\) −22.2111 −0.906009 −0.453004 0.891508i \(-0.649648\pi\)
−0.453004 + 0.891508i \(0.649648\pi\)
\(602\) −0.151101 −0.00615842
\(603\) 0 0
\(604\) 10.5180 0.427973
\(605\) 22.0303 0.895658
\(606\) 0 0
\(607\) −5.78678 −0.234878 −0.117439 0.993080i \(-0.537468\pi\)
−0.117439 + 0.993080i \(0.537468\pi\)
\(608\) −7.26207 −0.294516
\(609\) 0 0
\(610\) 10.2299 0.414195
\(611\) 2.65249 0.107308
\(612\) 0 0
\(613\) −28.4581 −1.14941 −0.574706 0.818360i \(-0.694884\pi\)
−0.574706 + 0.818360i \(0.694884\pi\)
\(614\) −20.9118 −0.843932
\(615\) 0 0
\(616\) −7.33971 −0.295725
\(617\) −13.5829 −0.546826 −0.273413 0.961897i \(-0.588153\pi\)
−0.273413 + 0.961897i \(0.588153\pi\)
\(618\) 0 0
\(619\) 23.0851 0.927870 0.463935 0.885869i \(-0.346437\pi\)
0.463935 + 0.885869i \(0.346437\pi\)
\(620\) −5.09658 −0.204683
\(621\) 0 0
\(622\) 13.7307 0.550552
\(623\) 11.9380 0.478287
\(624\) 0 0
\(625\) −31.2263 −1.24905
\(626\) −27.3384 −1.09266
\(627\) 0 0
\(628\) 19.1463 0.764020
\(629\) 12.8413 0.512016
\(630\) 0 0
\(631\) −29.5613 −1.17682 −0.588409 0.808563i \(-0.700246\pi\)
−0.588409 + 0.808563i \(0.700246\pi\)
\(632\) −15.5113 −0.617006
\(633\) 0 0
\(634\) 19.0031 0.754708
\(635\) 8.21400 0.325963
\(636\) 0 0
\(637\) 9.82221 0.389170
\(638\) 25.7790 1.02060
\(639\) 0 0
\(640\) 2.71034 0.107136
\(641\) 3.36162 0.132776 0.0663881 0.997794i \(-0.478852\pi\)
0.0663881 + 0.997794i \(0.478852\pi\)
\(642\) 0 0
\(643\) −37.2776 −1.47009 −0.735043 0.678020i \(-0.762838\pi\)
−0.735043 + 0.678020i \(0.762838\pi\)
\(644\) 0.164739 0.00649164
\(645\) 0 0
\(646\) 29.7453 1.17031
\(647\) 17.7157 0.696478 0.348239 0.937406i \(-0.386780\pi\)
0.348239 + 0.937406i \(0.386780\pi\)
\(648\) 0 0
\(649\) 33.3821 1.31036
\(650\) −5.50766 −0.216028
\(651\) 0 0
\(652\) −6.53078 −0.255765
\(653\) 31.2042 1.22111 0.610557 0.791972i \(-0.290946\pi\)
0.610557 + 0.791972i \(0.290946\pi\)
\(654\) 0 0
\(655\) 61.8225 2.41560
\(656\) −0.419725 −0.0163875
\(657\) 0 0
\(658\) −1.89602 −0.0739147
\(659\) 42.2097 1.64426 0.822128 0.569303i \(-0.192787\pi\)
0.822128 + 0.569303i \(0.192787\pi\)
\(660\) 0 0
\(661\) −11.0759 −0.430801 −0.215401 0.976526i \(-0.569106\pi\)
−0.215401 + 0.976526i \(0.569106\pi\)
\(662\) −24.2079 −0.940868
\(663\) 0 0
\(664\) −14.9118 −0.578688
\(665\) −33.0313 −1.28090
\(666\) 0 0
\(667\) −0.578608 −0.0224038
\(668\) −11.7228 −0.453567
\(669\) 0 0
\(670\) 8.47536 0.327432
\(671\) −16.5076 −0.637268
\(672\) 0 0
\(673\) 17.6065 0.678680 0.339340 0.940664i \(-0.389796\pi\)
0.339340 + 0.940664i \(0.389796\pi\)
\(674\) −21.7597 −0.838152
\(675\) 0 0
\(676\) −7.48808 −0.288003
\(677\) 21.4160 0.823083 0.411542 0.911391i \(-0.364990\pi\)
0.411542 + 0.911391i \(0.364990\pi\)
\(678\) 0 0
\(679\) −8.03253 −0.308260
\(680\) −11.1015 −0.425722
\(681\) 0 0
\(682\) 8.22418 0.314920
\(683\) −41.4123 −1.58460 −0.792298 0.610134i \(-0.791116\pi\)
−0.792298 + 0.610134i \(0.791116\pi\)
\(684\) 0 0
\(685\) 33.6152 1.28437
\(686\) −18.7683 −0.716579
\(687\) 0 0
\(688\) −0.0900380 −0.00343267
\(689\) −29.3716 −1.11897
\(690\) 0 0
\(691\) 15.2709 0.580932 0.290466 0.956885i \(-0.406190\pi\)
0.290466 + 0.956885i \(0.406190\pi\)
\(692\) −1.93624 −0.0736049
\(693\) 0 0
\(694\) −11.4110 −0.433155
\(695\) 43.8362 1.66280
\(696\) 0 0
\(697\) 1.71918 0.0651188
\(698\) 29.2720 1.10796
\(699\) 0 0
\(700\) 3.93692 0.148802
\(701\) −37.9423 −1.43306 −0.716531 0.697555i \(-0.754271\pi\)
−0.716531 + 0.697555i \(0.754271\pi\)
\(702\) 0 0
\(703\) 22.7673 0.858685
\(704\) −4.37358 −0.164836
\(705\) 0 0
\(706\) 25.2789 0.951384
\(707\) −5.45686 −0.205226
\(708\) 0 0
\(709\) −26.1329 −0.981441 −0.490721 0.871317i \(-0.663266\pi\)
−0.490721 + 0.871317i \(0.663266\pi\)
\(710\) −8.67810 −0.325683
\(711\) 0 0
\(712\) 7.11363 0.266595
\(713\) −0.184591 −0.00691299
\(714\) 0 0
\(715\) 27.8299 1.04078
\(716\) 13.5559 0.506606
\(717\) 0 0
\(718\) 3.38548 0.126345
\(719\) −2.05961 −0.0768107 −0.0384053 0.999262i \(-0.512228\pi\)
−0.0384053 + 0.999262i \(0.512228\pi\)
\(720\) 0 0
\(721\) −11.6106 −0.432403
\(722\) 33.7376 1.25558
\(723\) 0 0
\(724\) 14.9431 0.555354
\(725\) −13.8275 −0.513541
\(726\) 0 0
\(727\) −10.4096 −0.386073 −0.193036 0.981192i \(-0.561833\pi\)
−0.193036 + 0.981192i \(0.561833\pi\)
\(728\) −3.93997 −0.146025
\(729\) 0 0
\(730\) 3.13062 0.115869
\(731\) 0.368794 0.0136403
\(732\) 0 0
\(733\) −18.8723 −0.697065 −0.348533 0.937297i \(-0.613320\pi\)
−0.348533 + 0.937297i \(0.613320\pi\)
\(734\) 7.07969 0.261316
\(735\) 0 0
\(736\) 0.0981648 0.00361840
\(737\) −13.6764 −0.503777
\(738\) 0 0
\(739\) −22.8498 −0.840544 −0.420272 0.907398i \(-0.638065\pi\)
−0.420272 + 0.907398i \(0.638065\pi\)
\(740\) −8.49718 −0.312362
\(741\) 0 0
\(742\) 20.9951 0.770753
\(743\) −40.5510 −1.48767 −0.743837 0.668362i \(-0.766996\pi\)
−0.743837 + 0.668362i \(0.766996\pi\)
\(744\) 0 0
\(745\) −2.71034 −0.0992991
\(746\) 7.58277 0.277625
\(747\) 0 0
\(748\) 17.9141 0.655004
\(749\) 4.38578 0.160253
\(750\) 0 0
\(751\) 18.7741 0.685078 0.342539 0.939504i \(-0.388713\pi\)
0.342539 + 0.939504i \(0.388713\pi\)
\(752\) −1.12980 −0.0411997
\(753\) 0 0
\(754\) 13.8382 0.503958
\(755\) 28.5075 1.03749
\(756\) 0 0
\(757\) −10.1211 −0.367857 −0.183928 0.982940i \(-0.558881\pi\)
−0.183928 + 0.982940i \(0.558881\pi\)
\(758\) −37.0298 −1.34498
\(759\) 0 0
\(760\) −19.6827 −0.713965
\(761\) 20.0772 0.727799 0.363899 0.931438i \(-0.381445\pi\)
0.363899 + 0.931438i \(0.381445\pi\)
\(762\) 0 0
\(763\) −13.6479 −0.494087
\(764\) −3.69535 −0.133693
\(765\) 0 0
\(766\) 9.47515 0.342351
\(767\) 17.9195 0.647037
\(768\) 0 0
\(769\) 6.24889 0.225341 0.112670 0.993632i \(-0.464060\pi\)
0.112670 + 0.993632i \(0.464060\pi\)
\(770\) −19.8931 −0.716897
\(771\) 0 0
\(772\) 7.65239 0.275416
\(773\) −1.11866 −0.0402353 −0.0201176 0.999798i \(-0.506404\pi\)
−0.0201176 + 0.999798i \(0.506404\pi\)
\(774\) 0 0
\(775\) −4.41134 −0.158460
\(776\) −4.78642 −0.171822
\(777\) 0 0
\(778\) 8.01018 0.287179
\(779\) 3.04807 0.109209
\(780\) 0 0
\(781\) 14.0036 0.501087
\(782\) −0.402081 −0.0143784
\(783\) 0 0
\(784\) −4.18367 −0.149417
\(785\) 51.8929 1.85214
\(786\) 0 0
\(787\) 37.0689 1.32136 0.660682 0.750666i \(-0.270267\pi\)
0.660682 + 0.750666i \(0.270267\pi\)
\(788\) −18.2992 −0.651882
\(789\) 0 0
\(790\) −42.0408 −1.49575
\(791\) 10.2253 0.363570
\(792\) 0 0
\(793\) −8.86130 −0.314674
\(794\) −16.4377 −0.583352
\(795\) 0 0
\(796\) 12.9256 0.458134
\(797\) −32.5071 −1.15146 −0.575730 0.817640i \(-0.695282\pi\)
−0.575730 + 0.817640i \(0.695282\pi\)
\(798\) 0 0
\(799\) 4.62765 0.163714
\(800\) 2.34593 0.0829413
\(801\) 0 0
\(802\) 17.7661 0.627344
\(803\) −5.05177 −0.178273
\(804\) 0 0
\(805\) 0.446499 0.0157370
\(806\) 4.41475 0.155503
\(807\) 0 0
\(808\) −3.25163 −0.114392
\(809\) 2.43628 0.0856552 0.0428276 0.999082i \(-0.486363\pi\)
0.0428276 + 0.999082i \(0.486363\pi\)
\(810\) 0 0
\(811\) −38.2685 −1.34379 −0.671894 0.740647i \(-0.734519\pi\)
−0.671894 + 0.740647i \(0.734519\pi\)
\(812\) −9.89168 −0.347130
\(813\) 0 0
\(814\) 13.7116 0.480592
\(815\) −17.7006 −0.620026
\(816\) 0 0
\(817\) 0.653862 0.0228757
\(818\) −24.3199 −0.850325
\(819\) 0 0
\(820\) −1.13760 −0.0397266
\(821\) 0.603988 0.0210793 0.0105397 0.999944i \(-0.496645\pi\)
0.0105397 + 0.999944i \(0.496645\pi\)
\(822\) 0 0
\(823\) −9.46449 −0.329911 −0.164956 0.986301i \(-0.552748\pi\)
−0.164956 + 0.986301i \(0.552748\pi\)
\(824\) −6.91855 −0.241019
\(825\) 0 0
\(826\) −12.8091 −0.445684
\(827\) −9.04512 −0.314530 −0.157265 0.987556i \(-0.550268\pi\)
−0.157265 + 0.987556i \(0.550268\pi\)
\(828\) 0 0
\(829\) −22.2814 −0.773864 −0.386932 0.922108i \(-0.626465\pi\)
−0.386932 + 0.922108i \(0.626465\pi\)
\(830\) −40.4159 −1.40286
\(831\) 0 0
\(832\) −2.34775 −0.0813935
\(833\) 17.1362 0.593735
\(834\) 0 0
\(835\) −31.7726 −1.09954
\(836\) 31.7613 1.09849
\(837\) 0 0
\(838\) −23.5738 −0.814345
\(839\) 3.95317 0.136479 0.0682393 0.997669i \(-0.478262\pi\)
0.0682393 + 0.997669i \(0.478262\pi\)
\(840\) 0 0
\(841\) 5.74221 0.198007
\(842\) −0.218135 −0.00751742
\(843\) 0 0
\(844\) −12.7410 −0.438563
\(845\) −20.2952 −0.698178
\(846\) 0 0
\(847\) 13.6407 0.468701
\(848\) 12.5105 0.429613
\(849\) 0 0
\(850\) −9.60889 −0.329582
\(851\) −0.307756 −0.0105498
\(852\) 0 0
\(853\) 6.31219 0.216125 0.108063 0.994144i \(-0.465535\pi\)
0.108063 + 0.994144i \(0.465535\pi\)
\(854\) 6.33414 0.216750
\(855\) 0 0
\(856\) 2.61340 0.0893241
\(857\) −22.0163 −0.752064 −0.376032 0.926607i \(-0.622712\pi\)
−0.376032 + 0.926607i \(0.622712\pi\)
\(858\) 0 0
\(859\) −48.1678 −1.64346 −0.821732 0.569875i \(-0.806992\pi\)
−0.821732 + 0.569875i \(0.806992\pi\)
\(860\) −0.244034 −0.00832147
\(861\) 0 0
\(862\) 16.3041 0.555319
\(863\) 23.0500 0.784631 0.392315 0.919831i \(-0.371674\pi\)
0.392315 + 0.919831i \(0.371674\pi\)
\(864\) 0 0
\(865\) −5.24787 −0.178433
\(866\) 16.4350 0.558484
\(867\) 0 0
\(868\) −3.15571 −0.107112
\(869\) 67.8399 2.30131
\(870\) 0 0
\(871\) −7.34152 −0.248758
\(872\) −8.13251 −0.275402
\(873\) 0 0
\(874\) −0.712879 −0.0241135
\(875\) −12.0719 −0.408106
\(876\) 0 0
\(877\) −34.2938 −1.15802 −0.579010 0.815320i \(-0.696561\pi\)
−0.579010 + 0.815320i \(0.696561\pi\)
\(878\) −25.1285 −0.848047
\(879\) 0 0
\(880\) −11.8539 −0.399595
\(881\) −30.3973 −1.02411 −0.512056 0.858952i \(-0.671116\pi\)
−0.512056 + 0.858952i \(0.671116\pi\)
\(882\) 0 0
\(883\) −2.01379 −0.0677695 −0.0338847 0.999426i \(-0.510788\pi\)
−0.0338847 + 0.999426i \(0.510788\pi\)
\(884\) 9.61632 0.323432
\(885\) 0 0
\(886\) 26.4593 0.888919
\(887\) 22.2434 0.746859 0.373429 0.927659i \(-0.378182\pi\)
0.373429 + 0.927659i \(0.378182\pi\)
\(888\) 0 0
\(889\) 5.08595 0.170577
\(890\) 19.2803 0.646279
\(891\) 0 0
\(892\) −10.0497 −0.336490
\(893\) 8.20470 0.274560
\(894\) 0 0
\(895\) 36.7410 1.22811
\(896\) 1.67819 0.0560644
\(897\) 0 0
\(898\) 11.6779 0.389695
\(899\) 11.0837 0.369661
\(900\) 0 0
\(901\) −51.2429 −1.70715
\(902\) 1.83570 0.0611222
\(903\) 0 0
\(904\) 6.09305 0.202652
\(905\) 40.5007 1.34629
\(906\) 0 0
\(907\) −1.68674 −0.0560073 −0.0280036 0.999608i \(-0.508915\pi\)
−0.0280036 + 0.999608i \(0.508915\pi\)
\(908\) 9.51471 0.315757
\(909\) 0 0
\(910\) −10.6786 −0.353994
\(911\) 54.8311 1.81664 0.908318 0.418280i \(-0.137367\pi\)
0.908318 + 0.418280i \(0.137367\pi\)
\(912\) 0 0
\(913\) 65.2178 2.15839
\(914\) 11.2598 0.372440
\(915\) 0 0
\(916\) 17.3081 0.571875
\(917\) 38.2793 1.26409
\(918\) 0 0
\(919\) −52.9869 −1.74788 −0.873939 0.486036i \(-0.838442\pi\)
−0.873939 + 0.486036i \(0.838442\pi\)
\(920\) 0.266060 0.00877173
\(921\) 0 0
\(922\) −14.7144 −0.484593
\(923\) 7.51714 0.247430
\(924\) 0 0
\(925\) −7.35473 −0.241822
\(926\) 15.2474 0.501061
\(927\) 0 0
\(928\) −5.89425 −0.193488
\(929\) 5.24290 0.172014 0.0860069 0.996295i \(-0.472589\pi\)
0.0860069 + 0.996295i \(0.472589\pi\)
\(930\) 0 0
\(931\) 30.3821 0.995734
\(932\) −21.8741 −0.716511
\(933\) 0 0
\(934\) −31.9586 −1.04572
\(935\) 48.5533 1.58786
\(936\) 0 0
\(937\) −36.5730 −1.19479 −0.597393 0.801948i \(-0.703797\pi\)
−0.597393 + 0.801948i \(0.703797\pi\)
\(938\) 5.24779 0.171346
\(939\) 0 0
\(940\) −3.06215 −0.0998762
\(941\) −24.6596 −0.803879 −0.401940 0.915666i \(-0.631664\pi\)
−0.401940 + 0.915666i \(0.631664\pi\)
\(942\) 0 0
\(943\) −0.0412022 −0.00134173
\(944\) −7.63266 −0.248422
\(945\) 0 0
\(946\) 0.393789 0.0128032
\(947\) −34.3077 −1.11485 −0.557425 0.830227i \(-0.688211\pi\)
−0.557425 + 0.830227i \(0.688211\pi\)
\(948\) 0 0
\(949\) −2.71180 −0.0880287
\(950\) −17.0363 −0.552731
\(951\) 0 0
\(952\) −6.87383 −0.222782
\(953\) 31.0422 1.00556 0.502778 0.864415i \(-0.332311\pi\)
0.502778 + 0.864415i \(0.332311\pi\)
\(954\) 0 0
\(955\) −10.0157 −0.324099
\(956\) 25.8220 0.835143
\(957\) 0 0
\(958\) 10.9302 0.353138
\(959\) 20.8139 0.672116
\(960\) 0 0
\(961\) −27.4640 −0.885936
\(962\) 7.36042 0.237309
\(963\) 0 0
\(964\) −12.3157 −0.396663
\(965\) 20.7406 0.667662
\(966\) 0 0
\(967\) 56.2492 1.80885 0.904426 0.426631i \(-0.140300\pi\)
0.904426 + 0.426631i \(0.140300\pi\)
\(968\) 8.12823 0.261251
\(969\) 0 0
\(970\) −12.9728 −0.416532
\(971\) −26.1008 −0.837614 −0.418807 0.908075i \(-0.637552\pi\)
−0.418807 + 0.908075i \(0.637552\pi\)
\(972\) 0 0
\(973\) 27.1426 0.870151
\(974\) −34.7186 −1.11246
\(975\) 0 0
\(976\) 3.77438 0.120815
\(977\) 13.8161 0.442015 0.221008 0.975272i \(-0.429065\pi\)
0.221008 + 0.975272i \(0.429065\pi\)
\(978\) 0 0
\(979\) −31.1121 −0.994346
\(980\) −11.3392 −0.362217
\(981\) 0 0
\(982\) −33.3466 −1.06413
\(983\) −1.02013 −0.0325370 −0.0162685 0.999868i \(-0.505179\pi\)
−0.0162685 + 0.999868i \(0.505179\pi\)
\(984\) 0 0
\(985\) −49.5970 −1.58029
\(986\) 24.1427 0.768861
\(987\) 0 0
\(988\) 17.0495 0.542417
\(989\) −0.00883857 −0.000281050 0
\(990\) 0 0
\(991\) −30.5516 −0.970502 −0.485251 0.874375i \(-0.661272\pi\)
−0.485251 + 0.874375i \(0.661272\pi\)
\(992\) −1.88042 −0.0597034
\(993\) 0 0
\(994\) −5.37332 −0.170431
\(995\) 35.0326 1.11061
\(996\) 0 0
\(997\) 14.1051 0.446714 0.223357 0.974737i \(-0.428298\pi\)
0.223357 + 0.974737i \(0.428298\pi\)
\(998\) −23.1107 −0.731557
\(999\) 0 0
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 \(a_p\))