Properties

Label 6008.2.a.e.1.9
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.41806 q^{3} +0.877422 q^{5} +2.89114 q^{7} +2.84699 q^{9} +O(q^{10})\) \(q-2.41806 q^{3} +0.877422 q^{5} +2.89114 q^{7} +2.84699 q^{9} +1.81257 q^{11} -3.69719 q^{13} -2.12166 q^{15} -5.52490 q^{17} -3.24113 q^{19} -6.99093 q^{21} -2.45930 q^{23} -4.23013 q^{25} +0.369983 q^{27} +2.86650 q^{29} -7.81129 q^{31} -4.38289 q^{33} +2.53675 q^{35} +4.93159 q^{37} +8.94002 q^{39} +12.1443 q^{41} +6.06072 q^{43} +2.49801 q^{45} +4.72506 q^{47} +1.35868 q^{49} +13.3595 q^{51} -1.39504 q^{53} +1.59039 q^{55} +7.83723 q^{57} -8.45080 q^{59} +13.2787 q^{61} +8.23105 q^{63} -3.24400 q^{65} -8.83863 q^{67} +5.94672 q^{69} -3.13219 q^{71} +9.61295 q^{73} +10.2287 q^{75} +5.24039 q^{77} +0.251676 q^{79} -9.43561 q^{81} +1.82717 q^{83} -4.84767 q^{85} -6.93136 q^{87} +3.65191 q^{89} -10.6891 q^{91} +18.8881 q^{93} -2.84384 q^{95} +11.3340 q^{97} +5.16037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

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
\(3\) −2.41806 −1.39606 −0.698032 0.716066i \(-0.745941\pi\)
−0.698032 + 0.716066i \(0.745941\pi\)
\(4\) 0 0
\(5\) 0.877422 0.392395 0.196198 0.980564i \(-0.437141\pi\)
0.196198 + 0.980564i \(0.437141\pi\)
\(6\) 0 0
\(7\) 2.89114 1.09275 0.546374 0.837541i \(-0.316008\pi\)
0.546374 + 0.837541i \(0.316008\pi\)
\(8\) 0 0
\(9\) 2.84699 0.948997
\(10\) 0 0
\(11\) 1.81257 0.546510 0.273255 0.961942i \(-0.411900\pi\)
0.273255 + 0.961942i \(0.411900\pi\)
\(12\) 0 0
\(13\) −3.69719 −1.02542 −0.512709 0.858563i \(-0.671358\pi\)
−0.512709 + 0.858563i \(0.671358\pi\)
\(14\) 0 0
\(15\) −2.12166 −0.547809
\(16\) 0 0
\(17\) −5.52490 −1.33998 −0.669992 0.742368i \(-0.733703\pi\)
−0.669992 + 0.742368i \(0.733703\pi\)
\(18\) 0 0
\(19\) −3.24113 −0.743566 −0.371783 0.928320i \(-0.621253\pi\)
−0.371783 + 0.928320i \(0.621253\pi\)
\(20\) 0 0
\(21\) −6.99093 −1.52555
\(22\) 0 0
\(23\) −2.45930 −0.512799 −0.256400 0.966571i \(-0.582536\pi\)
−0.256400 + 0.966571i \(0.582536\pi\)
\(24\) 0 0
\(25\) −4.23013 −0.846026
\(26\) 0 0
\(27\) 0.369983 0.0712033
\(28\) 0 0
\(29\) 2.86650 0.532296 0.266148 0.963932i \(-0.414249\pi\)
0.266148 + 0.963932i \(0.414249\pi\)
\(30\) 0 0
\(31\) −7.81129 −1.40295 −0.701474 0.712695i \(-0.747474\pi\)
−0.701474 + 0.712695i \(0.747474\pi\)
\(32\) 0 0
\(33\) −4.38289 −0.762963
\(34\) 0 0
\(35\) 2.53675 0.428789
\(36\) 0 0
\(37\) 4.93159 0.810749 0.405374 0.914151i \(-0.367141\pi\)
0.405374 + 0.914151i \(0.367141\pi\)
\(38\) 0 0
\(39\) 8.94002 1.43155
\(40\) 0 0
\(41\) 12.1443 1.89663 0.948314 0.317333i \(-0.102787\pi\)
0.948314 + 0.317333i \(0.102787\pi\)
\(42\) 0 0
\(43\) 6.06072 0.924251 0.462126 0.886814i \(-0.347087\pi\)
0.462126 + 0.886814i \(0.347087\pi\)
\(44\) 0 0
\(45\) 2.49801 0.372382
\(46\) 0 0
\(47\) 4.72506 0.689221 0.344610 0.938746i \(-0.388011\pi\)
0.344610 + 0.938746i \(0.388011\pi\)
\(48\) 0 0
\(49\) 1.35868 0.194097
\(50\) 0 0
\(51\) 13.3595 1.87071
\(52\) 0 0
\(53\) −1.39504 −0.191623 −0.0958115 0.995399i \(-0.530545\pi\)
−0.0958115 + 0.995399i \(0.530545\pi\)
\(54\) 0 0
\(55\) 1.59039 0.214448
\(56\) 0 0
\(57\) 7.83723 1.03807
\(58\) 0 0
\(59\) −8.45080 −1.10020 −0.550100 0.835098i \(-0.685411\pi\)
−0.550100 + 0.835098i \(0.685411\pi\)
\(60\) 0 0
\(61\) 13.2787 1.70017 0.850084 0.526648i \(-0.176551\pi\)
0.850084 + 0.526648i \(0.176551\pi\)
\(62\) 0 0
\(63\) 8.23105 1.03701
\(64\) 0 0
\(65\) −3.24400 −0.402369
\(66\) 0 0
\(67\) −8.83863 −1.07981 −0.539906 0.841726i \(-0.681540\pi\)
−0.539906 + 0.841726i \(0.681540\pi\)
\(68\) 0 0
\(69\) 5.94672 0.715901
\(70\) 0 0
\(71\) −3.13219 −0.371723 −0.185861 0.982576i \(-0.559508\pi\)
−0.185861 + 0.982576i \(0.559508\pi\)
\(72\) 0 0
\(73\) 9.61295 1.12511 0.562556 0.826759i \(-0.309818\pi\)
0.562556 + 0.826759i \(0.309818\pi\)
\(74\) 0 0
\(75\) 10.2287 1.18111
\(76\) 0 0
\(77\) 5.24039 0.597197
\(78\) 0 0
\(79\) 0.251676 0.0283157 0.0141579 0.999900i \(-0.495493\pi\)
0.0141579 + 0.999900i \(0.495493\pi\)
\(80\) 0 0
\(81\) −9.43561 −1.04840
\(82\) 0 0
\(83\) 1.82717 0.200558 0.100279 0.994959i \(-0.468026\pi\)
0.100279 + 0.994959i \(0.468026\pi\)
\(84\) 0 0
\(85\) −4.84767 −0.525804
\(86\) 0 0
\(87\) −6.93136 −0.743120
\(88\) 0 0
\(89\) 3.65191 0.387102 0.193551 0.981090i \(-0.437999\pi\)
0.193551 + 0.981090i \(0.437999\pi\)
\(90\) 0 0
\(91\) −10.6891 −1.12052
\(92\) 0 0
\(93\) 18.8881 1.95861
\(94\) 0 0
\(95\) −2.84384 −0.291772
\(96\) 0 0
\(97\) 11.3340 1.15080 0.575399 0.817873i \(-0.304847\pi\)
0.575399 + 0.817873i \(0.304847\pi\)
\(98\) 0 0
\(99\) 5.16037 0.518636
\(100\) 0 0
\(101\) 8.02240 0.798259 0.399129 0.916895i \(-0.369312\pi\)
0.399129 + 0.916895i \(0.369312\pi\)
\(102\) 0 0
\(103\) −0.398605 −0.0392757 −0.0196379 0.999807i \(-0.506251\pi\)
−0.0196379 + 0.999807i \(0.506251\pi\)
\(104\) 0 0
\(105\) −6.13400 −0.598617
\(106\) 0 0
\(107\) −4.81810 −0.465783 −0.232891 0.972503i \(-0.574819\pi\)
−0.232891 + 0.972503i \(0.574819\pi\)
\(108\) 0 0
\(109\) −12.3186 −1.17990 −0.589952 0.807439i \(-0.700853\pi\)
−0.589952 + 0.807439i \(0.700853\pi\)
\(110\) 0 0
\(111\) −11.9249 −1.13186
\(112\) 0 0
\(113\) 14.5143 1.36539 0.682694 0.730705i \(-0.260808\pi\)
0.682694 + 0.730705i \(0.260808\pi\)
\(114\) 0 0
\(115\) −2.15784 −0.201220
\(116\) 0 0
\(117\) −10.5259 −0.973118
\(118\) 0 0
\(119\) −15.9732 −1.46427
\(120\) 0 0
\(121\) −7.71460 −0.701327
\(122\) 0 0
\(123\) −29.3657 −2.64782
\(124\) 0 0
\(125\) −8.09872 −0.724372
\(126\) 0 0
\(127\) 12.5119 1.11025 0.555124 0.831767i \(-0.312671\pi\)
0.555124 + 0.831767i \(0.312671\pi\)
\(128\) 0 0
\(129\) −14.6552 −1.29031
\(130\) 0 0
\(131\) 10.9192 0.954016 0.477008 0.878899i \(-0.341721\pi\)
0.477008 + 0.878899i \(0.341721\pi\)
\(132\) 0 0
\(133\) −9.37055 −0.812530
\(134\) 0 0
\(135\) 0.324632 0.0279398
\(136\) 0 0
\(137\) −10.2321 −0.874189 −0.437095 0.899416i \(-0.643993\pi\)
−0.437095 + 0.899416i \(0.643993\pi\)
\(138\) 0 0
\(139\) −14.0747 −1.19380 −0.596901 0.802315i \(-0.703601\pi\)
−0.596901 + 0.802315i \(0.703601\pi\)
\(140\) 0 0
\(141\) −11.4255 −0.962197
\(142\) 0 0
\(143\) −6.70142 −0.560401
\(144\) 0 0
\(145\) 2.51513 0.208870
\(146\) 0 0
\(147\) −3.28537 −0.270972
\(148\) 0 0
\(149\) 16.6740 1.36599 0.682995 0.730423i \(-0.260677\pi\)
0.682995 + 0.730423i \(0.260677\pi\)
\(150\) 0 0
\(151\) −1.91103 −0.155517 −0.0777586 0.996972i \(-0.524776\pi\)
−0.0777586 + 0.996972i \(0.524776\pi\)
\(152\) 0 0
\(153\) −15.7293 −1.27164
\(154\) 0 0
\(155\) −6.85380 −0.550510
\(156\) 0 0
\(157\) 12.2750 0.979654 0.489827 0.871820i \(-0.337060\pi\)
0.489827 + 0.871820i \(0.337060\pi\)
\(158\) 0 0
\(159\) 3.37327 0.267518
\(160\) 0 0
\(161\) −7.11018 −0.560360
\(162\) 0 0
\(163\) 1.44567 0.113234 0.0566170 0.998396i \(-0.481969\pi\)
0.0566170 + 0.998396i \(0.481969\pi\)
\(164\) 0 0
\(165\) −3.84565 −0.299383
\(166\) 0 0
\(167\) −16.0957 −1.24552 −0.622762 0.782411i \(-0.713990\pi\)
−0.622762 + 0.782411i \(0.713990\pi\)
\(168\) 0 0
\(169\) 0.669243 0.0514803
\(170\) 0 0
\(171\) −9.22747 −0.705642
\(172\) 0 0
\(173\) 11.5761 0.880113 0.440057 0.897970i \(-0.354958\pi\)
0.440057 + 0.897970i \(0.354958\pi\)
\(174\) 0 0
\(175\) −12.2299 −0.924493
\(176\) 0 0
\(177\) 20.4345 1.53595
\(178\) 0 0
\(179\) 18.4469 1.37879 0.689395 0.724386i \(-0.257877\pi\)
0.689395 + 0.724386i \(0.257877\pi\)
\(180\) 0 0
\(181\) 5.30694 0.394462 0.197231 0.980357i \(-0.436805\pi\)
0.197231 + 0.980357i \(0.436805\pi\)
\(182\) 0 0
\(183\) −32.1087 −2.37354
\(184\) 0 0
\(185\) 4.32709 0.318134
\(186\) 0 0
\(187\) −10.0143 −0.732315
\(188\) 0 0
\(189\) 1.06967 0.0778072
\(190\) 0 0
\(191\) 1.03520 0.0749044 0.0374522 0.999298i \(-0.488076\pi\)
0.0374522 + 0.999298i \(0.488076\pi\)
\(192\) 0 0
\(193\) 16.1227 1.16054 0.580268 0.814425i \(-0.302948\pi\)
0.580268 + 0.814425i \(0.302948\pi\)
\(194\) 0 0
\(195\) 7.84417 0.561733
\(196\) 0 0
\(197\) 16.7147 1.19088 0.595438 0.803401i \(-0.296978\pi\)
0.595438 + 0.803401i \(0.296978\pi\)
\(198\) 0 0
\(199\) 0.914111 0.0647996 0.0323998 0.999475i \(-0.489685\pi\)
0.0323998 + 0.999475i \(0.489685\pi\)
\(200\) 0 0
\(201\) 21.3723 1.50749
\(202\) 0 0
\(203\) 8.28746 0.581665
\(204\) 0 0
\(205\) 10.6557 0.744228
\(206\) 0 0
\(207\) −7.00160 −0.486645
\(208\) 0 0
\(209\) −5.87477 −0.406366
\(210\) 0 0
\(211\) −0.300114 −0.0206607 −0.0103303 0.999947i \(-0.503288\pi\)
−0.0103303 + 0.999947i \(0.503288\pi\)
\(212\) 0 0
\(213\) 7.57381 0.518949
\(214\) 0 0
\(215\) 5.31781 0.362672
\(216\) 0 0
\(217\) −22.5835 −1.53307
\(218\) 0 0
\(219\) −23.2447 −1.57073
\(220\) 0 0
\(221\) 20.4266 1.37404
\(222\) 0 0
\(223\) 8.48842 0.568426 0.284213 0.958761i \(-0.408268\pi\)
0.284213 + 0.958761i \(0.408268\pi\)
\(224\) 0 0
\(225\) −12.0431 −0.802876
\(226\) 0 0
\(227\) 11.1657 0.741095 0.370548 0.928814i \(-0.379170\pi\)
0.370548 + 0.928814i \(0.379170\pi\)
\(228\) 0 0
\(229\) 6.26396 0.413934 0.206967 0.978348i \(-0.433641\pi\)
0.206967 + 0.978348i \(0.433641\pi\)
\(230\) 0 0
\(231\) −12.6715 −0.833726
\(232\) 0 0
\(233\) −13.1058 −0.858586 −0.429293 0.903165i \(-0.641237\pi\)
−0.429293 + 0.903165i \(0.641237\pi\)
\(234\) 0 0
\(235\) 4.14587 0.270447
\(236\) 0 0
\(237\) −0.608566 −0.0395306
\(238\) 0 0
\(239\) −19.4793 −1.26001 −0.630006 0.776590i \(-0.716948\pi\)
−0.630006 + 0.776590i \(0.716948\pi\)
\(240\) 0 0
\(241\) 21.3358 1.37436 0.687180 0.726487i \(-0.258848\pi\)
0.687180 + 0.726487i \(0.258848\pi\)
\(242\) 0 0
\(243\) 21.7059 1.39243
\(244\) 0 0
\(245\) 1.19214 0.0761629
\(246\) 0 0
\(247\) 11.9831 0.762465
\(248\) 0 0
\(249\) −4.41820 −0.279992
\(250\) 0 0
\(251\) 11.0562 0.697859 0.348929 0.937149i \(-0.386545\pi\)
0.348929 + 0.937149i \(0.386545\pi\)
\(252\) 0 0
\(253\) −4.45765 −0.280250
\(254\) 0 0
\(255\) 11.7219 0.734056
\(256\) 0 0
\(257\) 24.9376 1.55556 0.777781 0.628535i \(-0.216345\pi\)
0.777781 + 0.628535i \(0.216345\pi\)
\(258\) 0 0
\(259\) 14.2579 0.885944
\(260\) 0 0
\(261\) 8.16091 0.505148
\(262\) 0 0
\(263\) −20.4803 −1.26287 −0.631436 0.775428i \(-0.717534\pi\)
−0.631436 + 0.775428i \(0.717534\pi\)
\(264\) 0 0
\(265\) −1.22404 −0.0751919
\(266\) 0 0
\(267\) −8.83053 −0.540420
\(268\) 0 0
\(269\) −19.3651 −1.18071 −0.590356 0.807143i \(-0.701013\pi\)
−0.590356 + 0.807143i \(0.701013\pi\)
\(270\) 0 0
\(271\) 5.00825 0.304230 0.152115 0.988363i \(-0.451392\pi\)
0.152115 + 0.988363i \(0.451392\pi\)
\(272\) 0 0
\(273\) 25.8468 1.56432
\(274\) 0 0
\(275\) −7.66740 −0.462362
\(276\) 0 0
\(277\) 3.09507 0.185965 0.0929825 0.995668i \(-0.470360\pi\)
0.0929825 + 0.995668i \(0.470360\pi\)
\(278\) 0 0
\(279\) −22.2387 −1.33139
\(280\) 0 0
\(281\) −20.0408 −1.19553 −0.597767 0.801670i \(-0.703945\pi\)
−0.597767 + 0.801670i \(0.703945\pi\)
\(282\) 0 0
\(283\) 20.1114 1.19550 0.597749 0.801683i \(-0.296062\pi\)
0.597749 + 0.801683i \(0.296062\pi\)
\(284\) 0 0
\(285\) 6.87656 0.407332
\(286\) 0 0
\(287\) 35.1110 2.07254
\(288\) 0 0
\(289\) 13.5245 0.795559
\(290\) 0 0
\(291\) −27.4063 −1.60659
\(292\) 0 0
\(293\) 17.8533 1.04300 0.521500 0.853252i \(-0.325373\pi\)
0.521500 + 0.853252i \(0.325373\pi\)
\(294\) 0 0
\(295\) −7.41492 −0.431714
\(296\) 0 0
\(297\) 0.670620 0.0389133
\(298\) 0 0
\(299\) 9.09251 0.525833
\(300\) 0 0
\(301\) 17.5224 1.00997
\(302\) 0 0
\(303\) −19.3986 −1.11442
\(304\) 0 0
\(305\) 11.6511 0.667137
\(306\) 0 0
\(307\) 29.7019 1.69517 0.847587 0.530656i \(-0.178054\pi\)
0.847587 + 0.530656i \(0.178054\pi\)
\(308\) 0 0
\(309\) 0.963849 0.0548315
\(310\) 0 0
\(311\) 15.7601 0.893671 0.446836 0.894616i \(-0.352551\pi\)
0.446836 + 0.894616i \(0.352551\pi\)
\(312\) 0 0
\(313\) −30.0224 −1.69697 −0.848484 0.529221i \(-0.822484\pi\)
−0.848484 + 0.529221i \(0.822484\pi\)
\(314\) 0 0
\(315\) 7.22210 0.406919
\(316\) 0 0
\(317\) 1.05026 0.0589884 0.0294942 0.999565i \(-0.490610\pi\)
0.0294942 + 0.999565i \(0.490610\pi\)
\(318\) 0 0
\(319\) 5.19573 0.290905
\(320\) 0 0
\(321\) 11.6504 0.650263
\(322\) 0 0
\(323\) 17.9069 0.996367
\(324\) 0 0
\(325\) 15.6396 0.867530
\(326\) 0 0
\(327\) 29.7869 1.64722
\(328\) 0 0
\(329\) 13.6608 0.753145
\(330\) 0 0
\(331\) 11.9827 0.658630 0.329315 0.944220i \(-0.393182\pi\)
0.329315 + 0.944220i \(0.393182\pi\)
\(332\) 0 0
\(333\) 14.0402 0.769398
\(334\) 0 0
\(335\) −7.75521 −0.423713
\(336\) 0 0
\(337\) 13.8991 0.757130 0.378565 0.925575i \(-0.376418\pi\)
0.378565 + 0.925575i \(0.376418\pi\)
\(338\) 0 0
\(339\) −35.0963 −1.90617
\(340\) 0 0
\(341\) −14.1585 −0.766725
\(342\) 0 0
\(343\) −16.3098 −0.880648
\(344\) 0 0
\(345\) 5.21779 0.280916
\(346\) 0 0
\(347\) −3.07712 −0.165189 −0.0825943 0.996583i \(-0.526321\pi\)
−0.0825943 + 0.996583i \(0.526321\pi\)
\(348\) 0 0
\(349\) 33.6214 1.79971 0.899857 0.436185i \(-0.143671\pi\)
0.899857 + 0.436185i \(0.143671\pi\)
\(350\) 0 0
\(351\) −1.36790 −0.0730131
\(352\) 0 0
\(353\) −21.8629 −1.16365 −0.581823 0.813315i \(-0.697660\pi\)
−0.581823 + 0.813315i \(0.697660\pi\)
\(354\) 0 0
\(355\) −2.74825 −0.145862
\(356\) 0 0
\(357\) 38.6242 2.04421
\(358\) 0 0
\(359\) −34.0907 −1.79924 −0.899619 0.436675i \(-0.856156\pi\)
−0.899619 + 0.436675i \(0.856156\pi\)
\(360\) 0 0
\(361\) −8.49508 −0.447110
\(362\) 0 0
\(363\) 18.6543 0.979098
\(364\) 0 0
\(365\) 8.43462 0.441488
\(366\) 0 0
\(367\) −25.2588 −1.31850 −0.659248 0.751926i \(-0.729125\pi\)
−0.659248 + 0.751926i \(0.729125\pi\)
\(368\) 0 0
\(369\) 34.5748 1.79989
\(370\) 0 0
\(371\) −4.03324 −0.209396
\(372\) 0 0
\(373\) 6.58372 0.340892 0.170446 0.985367i \(-0.445479\pi\)
0.170446 + 0.985367i \(0.445479\pi\)
\(374\) 0 0
\(375\) 19.5832 1.01127
\(376\) 0 0
\(377\) −10.5980 −0.545826
\(378\) 0 0
\(379\) −9.88202 −0.507605 −0.253803 0.967256i \(-0.581681\pi\)
−0.253803 + 0.967256i \(0.581681\pi\)
\(380\) 0 0
\(381\) −30.2544 −1.54998
\(382\) 0 0
\(383\) 36.7773 1.87923 0.939615 0.342233i \(-0.111183\pi\)
0.939615 + 0.342233i \(0.111183\pi\)
\(384\) 0 0
\(385\) 4.59803 0.234337
\(386\) 0 0
\(387\) 17.2548 0.877112
\(388\) 0 0
\(389\) −12.8853 −0.653308 −0.326654 0.945144i \(-0.605921\pi\)
−0.326654 + 0.945144i \(0.605921\pi\)
\(390\) 0 0
\(391\) 13.5874 0.687143
\(392\) 0 0
\(393\) −26.4033 −1.33187
\(394\) 0 0
\(395\) 0.220826 0.0111110
\(396\) 0 0
\(397\) −4.80575 −0.241194 −0.120597 0.992702i \(-0.538481\pi\)
−0.120597 + 0.992702i \(0.538481\pi\)
\(398\) 0 0
\(399\) 22.6585 1.13434
\(400\) 0 0
\(401\) 7.39828 0.369452 0.184726 0.982790i \(-0.440860\pi\)
0.184726 + 0.982790i \(0.440860\pi\)
\(402\) 0 0
\(403\) 28.8798 1.43861
\(404\) 0 0
\(405\) −8.27902 −0.411388
\(406\) 0 0
\(407\) 8.93885 0.443082
\(408\) 0 0
\(409\) 11.7161 0.579323 0.289662 0.957129i \(-0.406457\pi\)
0.289662 + 0.957129i \(0.406457\pi\)
\(410\) 0 0
\(411\) 24.7418 1.22042
\(412\) 0 0
\(413\) −24.4324 −1.20224
\(414\) 0 0
\(415\) 1.60320 0.0786980
\(416\) 0 0
\(417\) 34.0334 1.66662
\(418\) 0 0
\(419\) 16.9433 0.827734 0.413867 0.910337i \(-0.364178\pi\)
0.413867 + 0.910337i \(0.364178\pi\)
\(420\) 0 0
\(421\) 15.2552 0.743493 0.371747 0.928334i \(-0.378759\pi\)
0.371747 + 0.928334i \(0.378759\pi\)
\(422\) 0 0
\(423\) 13.4522 0.654069
\(424\) 0 0
\(425\) 23.3710 1.13366
\(426\) 0 0
\(427\) 38.3906 1.85785
\(428\) 0 0
\(429\) 16.2044 0.782356
\(430\) 0 0
\(431\) −18.2726 −0.880158 −0.440079 0.897959i \(-0.645050\pi\)
−0.440079 + 0.897959i \(0.645050\pi\)
\(432\) 0 0
\(433\) 9.76978 0.469506 0.234753 0.972055i \(-0.424572\pi\)
0.234753 + 0.972055i \(0.424572\pi\)
\(434\) 0 0
\(435\) −6.08173 −0.291597
\(436\) 0 0
\(437\) 7.97091 0.381300
\(438\) 0 0
\(439\) 24.4162 1.16532 0.582660 0.812716i \(-0.302012\pi\)
0.582660 + 0.812716i \(0.302012\pi\)
\(440\) 0 0
\(441\) 3.86815 0.184198
\(442\) 0 0
\(443\) 25.3693 1.20533 0.602667 0.797993i \(-0.294105\pi\)
0.602667 + 0.797993i \(0.294105\pi\)
\(444\) 0 0
\(445\) 3.20427 0.151897
\(446\) 0 0
\(447\) −40.3187 −1.90701
\(448\) 0 0
\(449\) −36.5235 −1.72365 −0.861825 0.507207i \(-0.830678\pi\)
−0.861825 + 0.507207i \(0.830678\pi\)
\(450\) 0 0
\(451\) 22.0125 1.03653
\(452\) 0 0
\(453\) 4.62097 0.217112
\(454\) 0 0
\(455\) −9.37885 −0.439687
\(456\) 0 0
\(457\) 35.5234 1.66171 0.830857 0.556485i \(-0.187850\pi\)
0.830857 + 0.556485i \(0.187850\pi\)
\(458\) 0 0
\(459\) −2.04412 −0.0954114
\(460\) 0 0
\(461\) 36.3542 1.69318 0.846591 0.532244i \(-0.178651\pi\)
0.846591 + 0.532244i \(0.178651\pi\)
\(462\) 0 0
\(463\) −18.9330 −0.879892 −0.439946 0.898024i \(-0.645002\pi\)
−0.439946 + 0.898024i \(0.645002\pi\)
\(464\) 0 0
\(465\) 16.5729 0.768548
\(466\) 0 0
\(467\) 8.70155 0.402660 0.201330 0.979523i \(-0.435474\pi\)
0.201330 + 0.979523i \(0.435474\pi\)
\(468\) 0 0
\(469\) −25.5537 −1.17996
\(470\) 0 0
\(471\) −29.6817 −1.36766
\(472\) 0 0
\(473\) 10.9855 0.505113
\(474\) 0 0
\(475\) 13.7104 0.629076
\(476\) 0 0
\(477\) −3.97166 −0.181850
\(478\) 0 0
\(479\) −23.9779 −1.09558 −0.547790 0.836616i \(-0.684531\pi\)
−0.547790 + 0.836616i \(0.684531\pi\)
\(480\) 0 0
\(481\) −18.2331 −0.831356
\(482\) 0 0
\(483\) 17.1928 0.782299
\(484\) 0 0
\(485\) 9.94474 0.451567
\(486\) 0 0
\(487\) −7.37041 −0.333985 −0.166993 0.985958i \(-0.553406\pi\)
−0.166993 + 0.985958i \(0.553406\pi\)
\(488\) 0 0
\(489\) −3.49572 −0.158082
\(490\) 0 0
\(491\) −27.4776 −1.24005 −0.620023 0.784584i \(-0.712877\pi\)
−0.620023 + 0.784584i \(0.712877\pi\)
\(492\) 0 0
\(493\) −15.8371 −0.713269
\(494\) 0 0
\(495\) 4.52782 0.203510
\(496\) 0 0
\(497\) −9.05560 −0.406199
\(498\) 0 0
\(499\) −26.7649 −1.19816 −0.599082 0.800688i \(-0.704468\pi\)
−0.599082 + 0.800688i \(0.704468\pi\)
\(500\) 0 0
\(501\) 38.9204 1.73883
\(502\) 0 0
\(503\) 0.279986 0.0124840 0.00624199 0.999981i \(-0.498013\pi\)
0.00624199 + 0.999981i \(0.498013\pi\)
\(504\) 0 0
\(505\) 7.03903 0.313233
\(506\) 0 0
\(507\) −1.61827 −0.0718698
\(508\) 0 0
\(509\) −23.4582 −1.03977 −0.519883 0.854237i \(-0.674025\pi\)
−0.519883 + 0.854237i \(0.674025\pi\)
\(510\) 0 0
\(511\) 27.7924 1.22946
\(512\) 0 0
\(513\) −1.19916 −0.0529444
\(514\) 0 0
\(515\) −0.349745 −0.0154116
\(516\) 0 0
\(517\) 8.56450 0.376666
\(518\) 0 0
\(519\) −27.9916 −1.22870
\(520\) 0 0
\(521\) −11.4150 −0.500102 −0.250051 0.968233i \(-0.580447\pi\)
−0.250051 + 0.968233i \(0.580447\pi\)
\(522\) 0 0
\(523\) −1.93823 −0.0847530 −0.0423765 0.999102i \(-0.513493\pi\)
−0.0423765 + 0.999102i \(0.513493\pi\)
\(524\) 0 0
\(525\) 29.5726 1.29065
\(526\) 0 0
\(527\) 43.1566 1.87993
\(528\) 0 0
\(529\) −16.9518 −0.737037
\(530\) 0 0
\(531\) −24.0594 −1.04409
\(532\) 0 0
\(533\) −44.9000 −1.94483
\(534\) 0 0
\(535\) −4.22750 −0.182771
\(536\) 0 0
\(537\) −44.6057 −1.92488
\(538\) 0 0
\(539\) 2.46270 0.106076
\(540\) 0 0
\(541\) 23.1820 0.996671 0.498335 0.866984i \(-0.333945\pi\)
0.498335 + 0.866984i \(0.333945\pi\)
\(542\) 0 0
\(543\) −12.8325 −0.550694
\(544\) 0 0
\(545\) −10.8086 −0.462988
\(546\) 0 0
\(547\) 22.0059 0.940903 0.470451 0.882426i \(-0.344091\pi\)
0.470451 + 0.882426i \(0.344091\pi\)
\(548\) 0 0
\(549\) 37.8044 1.61345
\(550\) 0 0
\(551\) −9.29071 −0.395797
\(552\) 0 0
\(553\) 0.727630 0.0309420
\(554\) 0 0
\(555\) −10.4631 −0.444135
\(556\) 0 0
\(557\) 31.8515 1.34959 0.674795 0.738005i \(-0.264232\pi\)
0.674795 + 0.738005i \(0.264232\pi\)
\(558\) 0 0
\(559\) −22.4077 −0.947743
\(560\) 0 0
\(561\) 24.2150 1.02236
\(562\) 0 0
\(563\) 20.0243 0.843925 0.421963 0.906613i \(-0.361341\pi\)
0.421963 + 0.906613i \(0.361341\pi\)
\(564\) 0 0
\(565\) 12.7351 0.535772
\(566\) 0 0
\(567\) −27.2797 −1.14564
\(568\) 0 0
\(569\) −27.1337 −1.13750 −0.568752 0.822509i \(-0.692574\pi\)
−0.568752 + 0.822509i \(0.692574\pi\)
\(570\) 0 0
\(571\) 6.72437 0.281406 0.140703 0.990052i \(-0.455064\pi\)
0.140703 + 0.990052i \(0.455064\pi\)
\(572\) 0 0
\(573\) −2.50317 −0.104571
\(574\) 0 0
\(575\) 10.4032 0.433842
\(576\) 0 0
\(577\) −15.3510 −0.639069 −0.319535 0.947575i \(-0.603527\pi\)
−0.319535 + 0.947575i \(0.603527\pi\)
\(578\) 0 0
\(579\) −38.9856 −1.62018
\(580\) 0 0
\(581\) 5.28260 0.219159
\(582\) 0 0
\(583\) −2.52860 −0.104724
\(584\) 0 0
\(585\) −9.23564 −0.381847
\(586\) 0 0
\(587\) −4.56946 −0.188602 −0.0943008 0.995544i \(-0.530062\pi\)
−0.0943008 + 0.995544i \(0.530062\pi\)
\(588\) 0 0
\(589\) 25.3174 1.04318
\(590\) 0 0
\(591\) −40.4172 −1.66254
\(592\) 0 0
\(593\) −13.9698 −0.573672 −0.286836 0.957980i \(-0.592603\pi\)
−0.286836 + 0.957980i \(0.592603\pi\)
\(594\) 0 0
\(595\) −14.0153 −0.574571
\(596\) 0 0
\(597\) −2.21037 −0.0904644
\(598\) 0 0
\(599\) −5.33124 −0.217829 −0.108914 0.994051i \(-0.534737\pi\)
−0.108914 + 0.994051i \(0.534737\pi\)
\(600\) 0 0
\(601\) 39.0067 1.59111 0.795557 0.605878i \(-0.207178\pi\)
0.795557 + 0.605878i \(0.207178\pi\)
\(602\) 0 0
\(603\) −25.1635 −1.02474
\(604\) 0 0
\(605\) −6.76896 −0.275197
\(606\) 0 0
\(607\) 21.2493 0.862481 0.431240 0.902237i \(-0.358076\pi\)
0.431240 + 0.902237i \(0.358076\pi\)
\(608\) 0 0
\(609\) −20.0395 −0.812043
\(610\) 0 0
\(611\) −17.4695 −0.706739
\(612\) 0 0
\(613\) 19.8698 0.802532 0.401266 0.915962i \(-0.368570\pi\)
0.401266 + 0.915962i \(0.368570\pi\)
\(614\) 0 0
\(615\) −25.7661 −1.03899
\(616\) 0 0
\(617\) 20.7854 0.836789 0.418395 0.908265i \(-0.362593\pi\)
0.418395 + 0.908265i \(0.362593\pi\)
\(618\) 0 0
\(619\) 9.46068 0.380257 0.190128 0.981759i \(-0.439110\pi\)
0.190128 + 0.981759i \(0.439110\pi\)
\(620\) 0 0
\(621\) −0.909900 −0.0365130
\(622\) 0 0
\(623\) 10.5582 0.423005
\(624\) 0 0
\(625\) 14.0447 0.561786
\(626\) 0 0
\(627\) 14.2055 0.567314
\(628\) 0 0
\(629\) −27.2465 −1.08639
\(630\) 0 0
\(631\) −2.06357 −0.0821493 −0.0410747 0.999156i \(-0.513078\pi\)
−0.0410747 + 0.999156i \(0.513078\pi\)
\(632\) 0 0
\(633\) 0.725691 0.0288436
\(634\) 0 0
\(635\) 10.9782 0.435656
\(636\) 0 0
\(637\) −5.02331 −0.199031
\(638\) 0 0
\(639\) −8.91732 −0.352764
\(640\) 0 0
\(641\) 46.0857 1.82028 0.910138 0.414306i \(-0.135976\pi\)
0.910138 + 0.414306i \(0.135976\pi\)
\(642\) 0 0
\(643\) 47.7595 1.88345 0.941725 0.336383i \(-0.109204\pi\)
0.941725 + 0.336383i \(0.109204\pi\)
\(644\) 0 0
\(645\) −12.8588 −0.506313
\(646\) 0 0
\(647\) −8.44393 −0.331965 −0.165983 0.986129i \(-0.553080\pi\)
−0.165983 + 0.986129i \(0.553080\pi\)
\(648\) 0 0
\(649\) −15.3177 −0.601271
\(650\) 0 0
\(651\) 54.6082 2.14026
\(652\) 0 0
\(653\) −3.60473 −0.141064 −0.0705320 0.997510i \(-0.522470\pi\)
−0.0705320 + 0.997510i \(0.522470\pi\)
\(654\) 0 0
\(655\) 9.58076 0.374351
\(656\) 0 0
\(657\) 27.3680 1.06773
\(658\) 0 0
\(659\) −5.14378 −0.200373 −0.100187 0.994969i \(-0.531944\pi\)
−0.100187 + 0.994969i \(0.531944\pi\)
\(660\) 0 0
\(661\) −7.81877 −0.304115 −0.152057 0.988372i \(-0.548590\pi\)
−0.152057 + 0.988372i \(0.548590\pi\)
\(662\) 0 0
\(663\) −49.3927 −1.91825
\(664\) 0 0
\(665\) −8.22193 −0.318833
\(666\) 0 0
\(667\) −7.04959 −0.272961
\(668\) 0 0
\(669\) −20.5255 −0.793560
\(670\) 0 0
\(671\) 24.0686 0.929158
\(672\) 0 0
\(673\) 20.5503 0.792157 0.396078 0.918217i \(-0.370371\pi\)
0.396078 + 0.918217i \(0.370371\pi\)
\(674\) 0 0
\(675\) −1.56508 −0.0602399
\(676\) 0 0
\(677\) −38.4948 −1.47948 −0.739738 0.672895i \(-0.765051\pi\)
−0.739738 + 0.672895i \(0.765051\pi\)
\(678\) 0 0
\(679\) 32.7683 1.25753
\(680\) 0 0
\(681\) −26.9993 −1.03462
\(682\) 0 0
\(683\) 17.9996 0.688735 0.344368 0.938835i \(-0.388093\pi\)
0.344368 + 0.938835i \(0.388093\pi\)
\(684\) 0 0
\(685\) −8.97789 −0.343028
\(686\) 0 0
\(687\) −15.1466 −0.577879
\(688\) 0 0
\(689\) 5.15772 0.196493
\(690\) 0 0
\(691\) −8.55829 −0.325573 −0.162786 0.986661i \(-0.552048\pi\)
−0.162786 + 0.986661i \(0.552048\pi\)
\(692\) 0 0
\(693\) 14.9193 0.566739
\(694\) 0 0
\(695\) −12.3495 −0.468442
\(696\) 0 0
\(697\) −67.0963 −2.54145
\(698\) 0 0
\(699\) 31.6904 1.19864
\(700\) 0 0
\(701\) 8.80365 0.332509 0.166255 0.986083i \(-0.446833\pi\)
0.166255 + 0.986083i \(0.446833\pi\)
\(702\) 0 0
\(703\) −15.9839 −0.602845
\(704\) 0 0
\(705\) −10.0250 −0.377562
\(706\) 0 0
\(707\) 23.1939 0.872295
\(708\) 0 0
\(709\) −21.8018 −0.818784 −0.409392 0.912359i \(-0.634259\pi\)
−0.409392 + 0.912359i \(0.634259\pi\)
\(710\) 0 0
\(711\) 0.716519 0.0268716
\(712\) 0 0
\(713\) 19.2103 0.719431
\(714\) 0 0
\(715\) −5.87997 −0.219899
\(716\) 0 0
\(717\) 47.1021 1.75906
\(718\) 0 0
\(719\) 34.8234 1.29869 0.649347 0.760492i \(-0.275042\pi\)
0.649347 + 0.760492i \(0.275042\pi\)
\(720\) 0 0
\(721\) −1.15242 −0.0429185
\(722\) 0 0
\(723\) −51.5912 −1.91870
\(724\) 0 0
\(725\) −12.1257 −0.450337
\(726\) 0 0
\(727\) 10.3070 0.382265 0.191133 0.981564i \(-0.438784\pi\)
0.191133 + 0.981564i \(0.438784\pi\)
\(728\) 0 0
\(729\) −24.1792 −0.895526
\(730\) 0 0
\(731\) −33.4849 −1.23848
\(732\) 0 0
\(733\) −3.83455 −0.141632 −0.0708162 0.997489i \(-0.522560\pi\)
−0.0708162 + 0.997489i \(0.522560\pi\)
\(734\) 0 0
\(735\) −2.88265 −0.106328
\(736\) 0 0
\(737\) −16.0206 −0.590127
\(738\) 0 0
\(739\) 23.1903 0.853069 0.426535 0.904471i \(-0.359734\pi\)
0.426535 + 0.904471i \(0.359734\pi\)
\(740\) 0 0
\(741\) −28.9758 −1.06445
\(742\) 0 0
\(743\) 2.71053 0.0994396 0.0497198 0.998763i \(-0.484167\pi\)
0.0497198 + 0.998763i \(0.484167\pi\)
\(744\) 0 0
\(745\) 14.6302 0.536008
\(746\) 0 0
\(747\) 5.20194 0.190329
\(748\) 0 0
\(749\) −13.9298 −0.508983
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −26.7344 −0.974256
\(754\) 0 0
\(755\) −1.67678 −0.0610242
\(756\) 0 0
\(757\) −20.6147 −0.749254 −0.374627 0.927176i \(-0.622229\pi\)
−0.374627 + 0.927176i \(0.622229\pi\)
\(758\) 0 0
\(759\) 10.7788 0.391247
\(760\) 0 0
\(761\) 24.5508 0.889968 0.444984 0.895539i \(-0.353209\pi\)
0.444984 + 0.895539i \(0.353209\pi\)
\(762\) 0 0
\(763\) −35.6146 −1.28934
\(764\) 0 0
\(765\) −13.8013 −0.498986
\(766\) 0 0
\(767\) 31.2443 1.12816
\(768\) 0 0
\(769\) 45.6604 1.64655 0.823277 0.567639i \(-0.192143\pi\)
0.823277 + 0.567639i \(0.192143\pi\)
\(770\) 0 0
\(771\) −60.3004 −2.17167
\(772\) 0 0
\(773\) −8.27916 −0.297781 −0.148890 0.988854i \(-0.547570\pi\)
−0.148890 + 0.988854i \(0.547570\pi\)
\(774\) 0 0
\(775\) 33.0428 1.18693
\(776\) 0 0
\(777\) −34.4764 −1.23683
\(778\) 0 0
\(779\) −39.3614 −1.41027
\(780\) 0 0
\(781\) −5.67731 −0.203150
\(782\) 0 0
\(783\) 1.06056 0.0379013
\(784\) 0 0
\(785\) 10.7704 0.384412
\(786\) 0 0
\(787\) −1.10988 −0.0395628 −0.0197814 0.999804i \(-0.506297\pi\)
−0.0197814 + 0.999804i \(0.506297\pi\)
\(788\) 0 0
\(789\) 49.5226 1.76305
\(790\) 0 0
\(791\) 41.9628 1.49202
\(792\) 0 0
\(793\) −49.0940 −1.74338
\(794\) 0 0
\(795\) 2.95979 0.104973
\(796\) 0 0
\(797\) 4.23483 0.150005 0.0750027 0.997183i \(-0.476103\pi\)
0.0750027 + 0.997183i \(0.476103\pi\)
\(798\) 0 0
\(799\) −26.1055 −0.923546
\(800\) 0 0
\(801\) 10.3970 0.367359
\(802\) 0 0
\(803\) 17.4241 0.614884
\(804\) 0 0
\(805\) −6.23863 −0.219883
\(806\) 0 0
\(807\) 46.8259 1.64835
\(808\) 0 0
\(809\) 3.13975 0.110388 0.0551938 0.998476i \(-0.482422\pi\)
0.0551938 + 0.998476i \(0.482422\pi\)
\(810\) 0 0
\(811\) 27.2914 0.958329 0.479165 0.877725i \(-0.340940\pi\)
0.479165 + 0.877725i \(0.340940\pi\)
\(812\) 0 0
\(813\) −12.1102 −0.424724
\(814\) 0 0
\(815\) 1.26847 0.0444325
\(816\) 0 0
\(817\) −19.6436 −0.687242
\(818\) 0 0
\(819\) −30.4318 −1.06337
\(820\) 0 0
\(821\) 33.7072 1.17639 0.588195 0.808719i \(-0.299839\pi\)
0.588195 + 0.808719i \(0.299839\pi\)
\(822\) 0 0
\(823\) −54.9615 −1.91584 −0.957919 0.287040i \(-0.907329\pi\)
−0.957919 + 0.287040i \(0.907329\pi\)
\(824\) 0 0
\(825\) 18.5402 0.645487
\(826\) 0 0
\(827\) 36.5563 1.27119 0.635594 0.772024i \(-0.280755\pi\)
0.635594 + 0.772024i \(0.280755\pi\)
\(828\) 0 0
\(829\) −7.26003 −0.252151 −0.126076 0.992021i \(-0.540238\pi\)
−0.126076 + 0.992021i \(0.540238\pi\)
\(830\) 0 0
\(831\) −7.48406 −0.259619
\(832\) 0 0
\(833\) −7.50658 −0.260087
\(834\) 0 0
\(835\) −14.1227 −0.488738
\(836\) 0 0
\(837\) −2.89004 −0.0998946
\(838\) 0 0
\(839\) 53.5396 1.84839 0.924197 0.381916i \(-0.124736\pi\)
0.924197 + 0.381916i \(0.124736\pi\)
\(840\) 0 0
\(841\) −20.7832 −0.716661
\(842\) 0 0
\(843\) 48.4598 1.66904
\(844\) 0 0
\(845\) 0.587209 0.0202006
\(846\) 0 0
\(847\) −22.3040 −0.766373
\(848\) 0 0
\(849\) −48.6305 −1.66899
\(850\) 0 0
\(851\) −12.1283 −0.415751
\(852\) 0 0
\(853\) −6.02428 −0.206267 −0.103134 0.994667i \(-0.532887\pi\)
−0.103134 + 0.994667i \(0.532887\pi\)
\(854\) 0 0
\(855\) −8.09638 −0.276890
\(856\) 0 0
\(857\) −4.27674 −0.146090 −0.0730452 0.997329i \(-0.523272\pi\)
−0.0730452 + 0.997329i \(0.523272\pi\)
\(858\) 0 0
\(859\) 50.7405 1.73124 0.865622 0.500698i \(-0.166923\pi\)
0.865622 + 0.500698i \(0.166923\pi\)
\(860\) 0 0
\(861\) −84.9003 −2.89339
\(862\) 0 0
\(863\) −17.9238 −0.610133 −0.305066 0.952331i \(-0.598679\pi\)
−0.305066 + 0.952331i \(0.598679\pi\)
\(864\) 0 0
\(865\) 10.1571 0.345352
\(866\) 0 0
\(867\) −32.7030 −1.11065
\(868\) 0 0
\(869\) 0.456180 0.0154748
\(870\) 0 0
\(871\) 32.6781 1.10726
\(872\) 0 0
\(873\) 32.2679 1.09210
\(874\) 0 0
\(875\) −23.4145 −0.791555
\(876\) 0 0
\(877\) −30.8516 −1.04179 −0.520893 0.853622i \(-0.674401\pi\)
−0.520893 + 0.853622i \(0.674401\pi\)
\(878\) 0 0
\(879\) −43.1702 −1.45609
\(880\) 0 0
\(881\) 11.5257 0.388310 0.194155 0.980971i \(-0.437804\pi\)
0.194155 + 0.980971i \(0.437804\pi\)
\(882\) 0 0
\(883\) 27.0129 0.909057 0.454529 0.890732i \(-0.349808\pi\)
0.454529 + 0.890732i \(0.349808\pi\)
\(884\) 0 0
\(885\) 17.9297 0.602700
\(886\) 0 0
\(887\) −38.5969 −1.29596 −0.647978 0.761659i \(-0.724385\pi\)
−0.647978 + 0.761659i \(0.724385\pi\)
\(888\) 0 0
\(889\) 36.1735 1.21322
\(890\) 0 0
\(891\) −17.1027 −0.572962
\(892\) 0 0
\(893\) −15.3145 −0.512481
\(894\) 0 0
\(895\) 16.1858 0.541030
\(896\) 0 0
\(897\) −21.9862 −0.734097
\(898\) 0 0
\(899\) −22.3911 −0.746784
\(900\) 0 0
\(901\) 7.70743 0.256772
\(902\) 0 0
\(903\) −42.3701 −1.40999
\(904\) 0 0
\(905\) 4.65643 0.154785
\(906\) 0 0
\(907\) −42.8510 −1.42284 −0.711422 0.702765i \(-0.751948\pi\)
−0.711422 + 0.702765i \(0.751948\pi\)
\(908\) 0 0
\(909\) 22.8397 0.757545
\(910\) 0 0
\(911\) −36.3626 −1.20475 −0.602374 0.798214i \(-0.705778\pi\)
−0.602374 + 0.798214i \(0.705778\pi\)
\(912\) 0 0
\(913\) 3.31187 0.109607
\(914\) 0 0
\(915\) −28.1729 −0.931367
\(916\) 0 0
\(917\) 31.5690 1.04250
\(918\) 0 0
\(919\) −43.3256 −1.42918 −0.714591 0.699543i \(-0.753387\pi\)
−0.714591 + 0.699543i \(0.753387\pi\)
\(920\) 0 0
\(921\) −71.8207 −2.36657
\(922\) 0 0
\(923\) 11.5803 0.381171
\(924\) 0 0
\(925\) −20.8613 −0.685915
\(926\) 0 0
\(927\) −1.13483 −0.0372725
\(928\) 0 0
\(929\) 12.5898 0.413057 0.206529 0.978441i \(-0.433783\pi\)
0.206529 + 0.978441i \(0.433783\pi\)
\(930\) 0 0
\(931\) −4.40366 −0.144324
\(932\) 0 0
\(933\) −38.1087 −1.24762
\(934\) 0 0
\(935\) −8.78673 −0.287357
\(936\) 0 0
\(937\) −12.3585 −0.403734 −0.201867 0.979413i \(-0.564701\pi\)
−0.201867 + 0.979413i \(0.564701\pi\)
\(938\) 0 0
\(939\) 72.5959 2.36908
\(940\) 0 0
\(941\) 15.4472 0.503564 0.251782 0.967784i \(-0.418983\pi\)
0.251782 + 0.967784i \(0.418983\pi\)
\(942\) 0 0
\(943\) −29.8666 −0.972590
\(944\) 0 0
\(945\) 0.938555 0.0305312
\(946\) 0 0
\(947\) −2.98024 −0.0968447 −0.0484223 0.998827i \(-0.515419\pi\)
−0.0484223 + 0.998827i \(0.515419\pi\)
\(948\) 0 0
\(949\) −35.5410 −1.15371
\(950\) 0 0
\(951\) −2.53958 −0.0823516
\(952\) 0 0
\(953\) 45.9731 1.48922 0.744608 0.667502i \(-0.232637\pi\)
0.744608 + 0.667502i \(0.232637\pi\)
\(954\) 0 0
\(955\) 0.908307 0.0293921
\(956\) 0 0
\(957\) −12.5636 −0.406123
\(958\) 0 0
\(959\) −29.5825 −0.955268
\(960\) 0 0
\(961\) 30.0162 0.968264
\(962\) 0 0
\(963\) −13.7171 −0.442027
\(964\) 0 0
\(965\) 14.1464 0.455389
\(966\) 0 0
\(967\) 48.3403 1.55452 0.777260 0.629180i \(-0.216609\pi\)
0.777260 + 0.629180i \(0.216609\pi\)
\(968\) 0 0
\(969\) −43.2999 −1.39099
\(970\) 0 0
\(971\) −57.0021 −1.82928 −0.914642 0.404266i \(-0.867527\pi\)
−0.914642 + 0.404266i \(0.867527\pi\)
\(972\) 0 0
\(973\) −40.6920 −1.30452
\(974\) 0 0
\(975\) −37.8174 −1.21113
\(976\) 0 0
\(977\) 44.6077 1.42713 0.713564 0.700590i \(-0.247080\pi\)
0.713564 + 0.700590i \(0.247080\pi\)
\(978\) 0 0
\(979\) 6.61934 0.211555
\(980\) 0 0
\(981\) −35.0708 −1.11972
\(982\) 0 0
\(983\) 2.95916 0.0943827 0.0471913 0.998886i \(-0.484973\pi\)
0.0471913 + 0.998886i \(0.484973\pi\)
\(984\) 0 0
\(985\) 14.6659 0.467294
\(986\) 0 0
\(987\) −33.0326 −1.05144
\(988\) 0 0
\(989\) −14.9051 −0.473955
\(990\) 0 0
\(991\) 18.8424 0.598548 0.299274 0.954167i \(-0.403256\pi\)
0.299274 + 0.954167i \(0.403256\pi\)
\(992\) 0 0
\(993\) −28.9749 −0.919490
\(994\) 0 0
\(995\) 0.802061 0.0254270
\(996\) 0 0
\(997\) 8.28041 0.262243 0.131122 0.991366i \(-0.458142\pi\)
0.131122 + 0.991366i \(0.458142\pi\)
\(998\) 0 0
\(999\) 1.82461 0.0577280
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 \(a_p\))