Properties

Label 8008.2.a.i.1.1
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.254102\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.93543 q^{3} +2.25410 q^{5} -1.00000 q^{7} +0.745898 q^{9} +O(q^{10})\) \(q-1.93543 q^{3} +2.25410 q^{5} -1.00000 q^{7} +0.745898 q^{9} -1.00000 q^{11} +1.00000 q^{13} -4.36266 q^{15} +0.616763 q^{17} +2.42723 q^{19} +1.93543 q^{21} -7.69774 q^{23} +0.0809744 q^{25} +4.36266 q^{27} +8.37907 q^{29} -3.31867 q^{31} +1.93543 q^{33} -2.25410 q^{35} +4.68133 q^{37} -1.93543 q^{39} -12.2171 q^{41} +2.23769 q^{43} +1.68133 q^{45} -4.85446 q^{47} +1.00000 q^{49} -1.19370 q^{51} +6.99583 q^{53} -2.25410 q^{55} -4.69774 q^{57} +10.0440 q^{59} +2.74590 q^{61} -0.745898 q^{63} +2.25410 q^{65} -5.42723 q^{67} +14.8984 q^{69} -2.38324 q^{71} -4.98359 q^{73} -0.156721 q^{75} +1.00000 q^{77} -9.31450 q^{79} -10.6813 q^{81} -3.95184 q^{83} +1.39025 q^{85} -16.2171 q^{87} +6.91903 q^{89} -1.00000 q^{91} +6.42306 q^{93} +5.47122 q^{95} +17.2775 q^{97} -0.745898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} + O(q^{10}) \) \( 3q + 2q^{3} + 6q^{5} - 3q^{7} + 3q^{9} - 3q^{11} + 3q^{13} + q^{15} - 13q^{17} + q^{19} - 2q^{21} - 13q^{23} + 5q^{25} - q^{27} + 8q^{29} - 17q^{31} - 2q^{33} - 6q^{35} + 7q^{37} + 2q^{39} - 10q^{41} + 9q^{43} - 2q^{45} - 2q^{47} + 3q^{49} - 27q^{51} - 11q^{53} - 6q^{55} - 4q^{57} + 9q^{59} + 9q^{61} - 3q^{63} + 6q^{65} - 10q^{67} + 11q^{69} - 22q^{71} - 18q^{73} + 2q^{75} + 3q^{77} - 3q^{79} - 25q^{81} - q^{83} - 28q^{85} - 22q^{87} + 16q^{89} - 3q^{91} - 19q^{93} - 11q^{95} + q^{97} - 3q^{99} + O(q^{100}) \)

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
\(3\) −1.93543 −1.11742 −0.558711 0.829362i \(-0.688704\pi\)
−0.558711 + 0.829362i \(0.688704\pi\)
\(4\) 0 0
\(5\) 2.25410 1.00806 0.504032 0.863685i \(-0.331849\pi\)
0.504032 + 0.863685i \(0.331849\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0.745898 0.248633
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −4.36266 −1.12643
\(16\) 0 0
\(17\) 0.616763 0.149587 0.0747935 0.997199i \(-0.476170\pi\)
0.0747935 + 0.997199i \(0.476170\pi\)
\(18\) 0 0
\(19\) 2.42723 0.556845 0.278422 0.960459i \(-0.410189\pi\)
0.278422 + 0.960459i \(0.410189\pi\)
\(20\) 0 0
\(21\) 1.93543 0.422346
\(22\) 0 0
\(23\) −7.69774 −1.60509 −0.802545 0.596592i \(-0.796521\pi\)
−0.802545 + 0.596592i \(0.796521\pi\)
\(24\) 0 0
\(25\) 0.0809744 0.0161949
\(26\) 0 0
\(27\) 4.36266 0.839595
\(28\) 0 0
\(29\) 8.37907 1.55595 0.777977 0.628293i \(-0.216246\pi\)
0.777977 + 0.628293i \(0.216246\pi\)
\(30\) 0 0
\(31\) −3.31867 −0.596051 −0.298025 0.954558i \(-0.596328\pi\)
−0.298025 + 0.954558i \(0.596328\pi\)
\(32\) 0 0
\(33\) 1.93543 0.336916
\(34\) 0 0
\(35\) −2.25410 −0.381013
\(36\) 0 0
\(37\) 4.68133 0.769606 0.384803 0.922999i \(-0.374269\pi\)
0.384803 + 0.922999i \(0.374269\pi\)
\(38\) 0 0
\(39\) −1.93543 −0.309917
\(40\) 0 0
\(41\) −12.2171 −1.90799 −0.953997 0.299817i \(-0.903074\pi\)
−0.953997 + 0.299817i \(0.903074\pi\)
\(42\) 0 0
\(43\) 2.23769 0.341245 0.170623 0.985336i \(-0.445422\pi\)
0.170623 + 0.985336i \(0.445422\pi\)
\(44\) 0 0
\(45\) 1.68133 0.250638
\(46\) 0 0
\(47\) −4.85446 −0.708095 −0.354048 0.935227i \(-0.615195\pi\)
−0.354048 + 0.935227i \(0.615195\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −1.19370 −0.167152
\(52\) 0 0
\(53\) 6.99583 0.960951 0.480476 0.877008i \(-0.340464\pi\)
0.480476 + 0.877008i \(0.340464\pi\)
\(54\) 0 0
\(55\) −2.25410 −0.303943
\(56\) 0 0
\(57\) −4.69774 −0.622231
\(58\) 0 0
\(59\) 10.0440 1.30762 0.653808 0.756660i \(-0.273170\pi\)
0.653808 + 0.756660i \(0.273170\pi\)
\(60\) 0 0
\(61\) 2.74590 0.351576 0.175788 0.984428i \(-0.443753\pi\)
0.175788 + 0.984428i \(0.443753\pi\)
\(62\) 0 0
\(63\) −0.745898 −0.0939744
\(64\) 0 0
\(65\) 2.25410 0.279587
\(66\) 0 0
\(67\) −5.42723 −0.663042 −0.331521 0.943448i \(-0.607562\pi\)
−0.331521 + 0.943448i \(0.607562\pi\)
\(68\) 0 0
\(69\) 14.8984 1.79356
\(70\) 0 0
\(71\) −2.38324 −0.282838 −0.141419 0.989950i \(-0.545167\pi\)
−0.141419 + 0.989950i \(0.545167\pi\)
\(72\) 0 0
\(73\) −4.98359 −0.583285 −0.291643 0.956527i \(-0.594202\pi\)
−0.291643 + 0.956527i \(0.594202\pi\)
\(74\) 0 0
\(75\) −0.156721 −0.0180965
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −9.31450 −1.04796 −0.523982 0.851730i \(-0.675554\pi\)
−0.523982 + 0.851730i \(0.675554\pi\)
\(80\) 0 0
\(81\) −10.6813 −1.18681
\(82\) 0 0
\(83\) −3.95184 −0.433771 −0.216885 0.976197i \(-0.569590\pi\)
−0.216885 + 0.976197i \(0.569590\pi\)
\(84\) 0 0
\(85\) 1.39025 0.150793
\(86\) 0 0
\(87\) −16.2171 −1.73866
\(88\) 0 0
\(89\) 6.91903 0.733415 0.366708 0.930336i \(-0.380485\pi\)
0.366708 + 0.930336i \(0.380485\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 6.42306 0.666040
\(94\) 0 0
\(95\) 5.47122 0.561335
\(96\) 0 0
\(97\) 17.2775 1.75427 0.877133 0.480247i \(-0.159453\pi\)
0.877133 + 0.480247i \(0.159453\pi\)
\(98\) 0 0
\(99\) −0.745898 −0.0749656
\(100\) 0 0
\(101\) −8.93543 −0.889109 −0.444554 0.895752i \(-0.646638\pi\)
−0.444554 + 0.895752i \(0.646638\pi\)
\(102\) 0 0
\(103\) −14.7253 −1.45093 −0.725465 0.688260i \(-0.758375\pi\)
−0.725465 + 0.688260i \(0.758375\pi\)
\(104\) 0 0
\(105\) 4.36266 0.425752
\(106\) 0 0
\(107\) 10.6496 1.02953 0.514767 0.857330i \(-0.327879\pi\)
0.514767 + 0.857330i \(0.327879\pi\)
\(108\) 0 0
\(109\) 9.91903 0.950070 0.475035 0.879967i \(-0.342435\pi\)
0.475035 + 0.879967i \(0.342435\pi\)
\(110\) 0 0
\(111\) −9.06040 −0.859975
\(112\) 0 0
\(113\) −19.6168 −1.84539 −0.922695 0.385531i \(-0.874018\pi\)
−0.922695 + 0.385531i \(0.874018\pi\)
\(114\) 0 0
\(115\) −17.3515 −1.61803
\(116\) 0 0
\(117\) 0.745898 0.0689583
\(118\) 0 0
\(119\) −0.616763 −0.0565386
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 23.6454 2.13203
\(124\) 0 0
\(125\) −11.0880 −0.991739
\(126\) 0 0
\(127\) 19.6936 1.74752 0.873761 0.486356i \(-0.161674\pi\)
0.873761 + 0.486356i \(0.161674\pi\)
\(128\) 0 0
\(129\) −4.33091 −0.381315
\(130\) 0 0
\(131\) −13.1044 −1.14494 −0.572468 0.819927i \(-0.694014\pi\)
−0.572468 + 0.819927i \(0.694014\pi\)
\(132\) 0 0
\(133\) −2.42723 −0.210467
\(134\) 0 0
\(135\) 9.83388 0.846366
\(136\) 0 0
\(137\) 5.40665 0.461922 0.230961 0.972963i \(-0.425813\pi\)
0.230961 + 0.972963i \(0.425813\pi\)
\(138\) 0 0
\(139\) −1.36266 −0.115579 −0.0577897 0.998329i \(-0.518405\pi\)
−0.0577897 + 0.998329i \(0.518405\pi\)
\(140\) 0 0
\(141\) 9.39547 0.791242
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) 18.8873 1.56850
\(146\) 0 0
\(147\) −1.93543 −0.159632
\(148\) 0 0
\(149\) 0.0481609 0.00394550 0.00197275 0.999998i \(-0.499372\pi\)
0.00197275 + 0.999998i \(0.499372\pi\)
\(150\) 0 0
\(151\) −13.2335 −1.07693 −0.538465 0.842648i \(-0.680995\pi\)
−0.538465 + 0.842648i \(0.680995\pi\)
\(152\) 0 0
\(153\) 0.460042 0.0371922
\(154\) 0 0
\(155\) −7.48062 −0.600858
\(156\) 0 0
\(157\) −16.8021 −1.34096 −0.670478 0.741930i \(-0.733911\pi\)
−0.670478 + 0.741930i \(0.733911\pi\)
\(158\) 0 0
\(159\) −13.5400 −1.07379
\(160\) 0 0
\(161\) 7.69774 0.606667
\(162\) 0 0
\(163\) −4.93543 −0.386573 −0.193286 0.981142i \(-0.561915\pi\)
−0.193286 + 0.981142i \(0.561915\pi\)
\(164\) 0 0
\(165\) 4.36266 0.339633
\(166\) 0 0
\(167\) −13.7623 −1.06496 −0.532480 0.846443i \(-0.678740\pi\)
−0.532480 + 0.846443i \(0.678740\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.81047 0.138450
\(172\) 0 0
\(173\) −1.53996 −0.117081 −0.0585404 0.998285i \(-0.518645\pi\)
−0.0585404 + 0.998285i \(0.518645\pi\)
\(174\) 0 0
\(175\) −0.0809744 −0.00612109
\(176\) 0 0
\(177\) −19.4395 −1.46116
\(178\) 0 0
\(179\) 3.43947 0.257078 0.128539 0.991704i \(-0.458971\pi\)
0.128539 + 0.991704i \(0.458971\pi\)
\(180\) 0 0
\(181\) 5.15672 0.383296 0.191648 0.981464i \(-0.438617\pi\)
0.191648 + 0.981464i \(0.438617\pi\)
\(182\) 0 0
\(183\) −5.31450 −0.392859
\(184\) 0 0
\(185\) 10.5522 0.775813
\(186\) 0 0
\(187\) −0.616763 −0.0451022
\(188\) 0 0
\(189\) −4.36266 −0.317337
\(190\) 0 0
\(191\) −2.33508 −0.168960 −0.0844801 0.996425i \(-0.526923\pi\)
−0.0844801 + 0.996425i \(0.526923\pi\)
\(192\) 0 0
\(193\) −18.8339 −1.35569 −0.677846 0.735204i \(-0.737086\pi\)
−0.677846 + 0.735204i \(0.737086\pi\)
\(194\) 0 0
\(195\) −4.36266 −0.312417
\(196\) 0 0
\(197\) 3.94661 0.281184 0.140592 0.990068i \(-0.455099\pi\)
0.140592 + 0.990068i \(0.455099\pi\)
\(198\) 0 0
\(199\) 20.4189 1.44746 0.723728 0.690085i \(-0.242427\pi\)
0.723728 + 0.690085i \(0.242427\pi\)
\(200\) 0 0
\(201\) 10.5040 0.740897
\(202\) 0 0
\(203\) −8.37907 −0.588095
\(204\) 0 0
\(205\) −27.5386 −1.92338
\(206\) 0 0
\(207\) −5.74173 −0.399078
\(208\) 0 0
\(209\) −2.42723 −0.167895
\(210\) 0 0
\(211\) 3.72949 0.256749 0.128374 0.991726i \(-0.459024\pi\)
0.128374 + 0.991726i \(0.459024\pi\)
\(212\) 0 0
\(213\) 4.61259 0.316050
\(214\) 0 0
\(215\) 5.04399 0.343997
\(216\) 0 0
\(217\) 3.31867 0.225286
\(218\) 0 0
\(219\) 9.64541 0.651776
\(220\) 0 0
\(221\) 0.616763 0.0414880
\(222\) 0 0
\(223\) 27.1484 1.81799 0.908995 0.416807i \(-0.136851\pi\)
0.908995 + 0.416807i \(0.136851\pi\)
\(224\) 0 0
\(225\) 0.0603987 0.00402658
\(226\) 0 0
\(227\) −22.1002 −1.46684 −0.733422 0.679774i \(-0.762078\pi\)
−0.733422 + 0.679774i \(0.762078\pi\)
\(228\) 0 0
\(229\) 11.7787 0.778359 0.389180 0.921162i \(-0.372759\pi\)
0.389180 + 0.921162i \(0.372759\pi\)
\(230\) 0 0
\(231\) −1.93543 −0.127342
\(232\) 0 0
\(233\) −21.5798 −1.41374 −0.706869 0.707344i \(-0.749893\pi\)
−0.706869 + 0.707344i \(0.749893\pi\)
\(234\) 0 0
\(235\) −10.9424 −0.713806
\(236\) 0 0
\(237\) 18.0276 1.17102
\(238\) 0 0
\(239\) −5.61259 −0.363049 −0.181524 0.983386i \(-0.558103\pi\)
−0.181524 + 0.983386i \(0.558103\pi\)
\(240\) 0 0
\(241\) −10.8545 −0.699197 −0.349599 0.936900i \(-0.613682\pi\)
−0.349599 + 0.936900i \(0.613682\pi\)
\(242\) 0 0
\(243\) 7.58501 0.486579
\(244\) 0 0
\(245\) 2.25410 0.144009
\(246\) 0 0
\(247\) 2.42723 0.154441
\(248\) 0 0
\(249\) 7.64852 0.484705
\(250\) 0 0
\(251\) −18.8175 −1.18775 −0.593874 0.804558i \(-0.702402\pi\)
−0.593874 + 0.804558i \(0.702402\pi\)
\(252\) 0 0
\(253\) 7.69774 0.483953
\(254\) 0 0
\(255\) −2.69073 −0.168500
\(256\) 0 0
\(257\) 24.6290 1.53631 0.768157 0.640261i \(-0.221174\pi\)
0.768157 + 0.640261i \(0.221174\pi\)
\(258\) 0 0
\(259\) −4.68133 −0.290884
\(260\) 0 0
\(261\) 6.24993 0.386861
\(262\) 0 0
\(263\) −8.96825 −0.553006 −0.276503 0.961013i \(-0.589176\pi\)
−0.276503 + 0.961013i \(0.589176\pi\)
\(264\) 0 0
\(265\) 15.7693 0.968701
\(266\) 0 0
\(267\) −13.3913 −0.819535
\(268\) 0 0
\(269\) 28.7253 1.75141 0.875707 0.482843i \(-0.160396\pi\)
0.875707 + 0.482843i \(0.160396\pi\)
\(270\) 0 0
\(271\) 22.0674 1.34050 0.670250 0.742136i \(-0.266187\pi\)
0.670250 + 0.742136i \(0.266187\pi\)
\(272\) 0 0
\(273\) 1.93543 0.117138
\(274\) 0 0
\(275\) −0.0809744 −0.00488294
\(276\) 0 0
\(277\) −5.11273 −0.307194 −0.153597 0.988134i \(-0.549086\pi\)
−0.153597 + 0.988134i \(0.549086\pi\)
\(278\) 0 0
\(279\) −2.47539 −0.148198
\(280\) 0 0
\(281\) 15.0286 0.896534 0.448267 0.893900i \(-0.352041\pi\)
0.448267 + 0.893900i \(0.352041\pi\)
\(282\) 0 0
\(283\) −27.1372 −1.61314 −0.806570 0.591139i \(-0.798678\pi\)
−0.806570 + 0.591139i \(0.798678\pi\)
\(284\) 0 0
\(285\) −10.5892 −0.627249
\(286\) 0 0
\(287\) 12.2171 0.721154
\(288\) 0 0
\(289\) −16.6196 −0.977624
\(290\) 0 0
\(291\) −33.4395 −1.96026
\(292\) 0 0
\(293\) 14.8873 0.869724 0.434862 0.900497i \(-0.356797\pi\)
0.434862 + 0.900497i \(0.356797\pi\)
\(294\) 0 0
\(295\) 22.6402 1.31816
\(296\) 0 0
\(297\) −4.36266 −0.253147
\(298\) 0 0
\(299\) −7.69774 −0.445172
\(300\) 0 0
\(301\) −2.23769 −0.128979
\(302\) 0 0
\(303\) 17.2939 0.993510
\(304\) 0 0
\(305\) 6.18953 0.354412
\(306\) 0 0
\(307\) −6.96302 −0.397400 −0.198700 0.980060i \(-0.563672\pi\)
−0.198700 + 0.980060i \(0.563672\pi\)
\(308\) 0 0
\(309\) 28.4999 1.62130
\(310\) 0 0
\(311\) −29.7899 −1.68923 −0.844615 0.535374i \(-0.820171\pi\)
−0.844615 + 0.535374i \(0.820171\pi\)
\(312\) 0 0
\(313\) 15.1484 0.856237 0.428119 0.903723i \(-0.359177\pi\)
0.428119 + 0.903723i \(0.359177\pi\)
\(314\) 0 0
\(315\) −1.68133 −0.0947322
\(316\) 0 0
\(317\) −8.68133 −0.487592 −0.243796 0.969827i \(-0.578393\pi\)
−0.243796 + 0.969827i \(0.578393\pi\)
\(318\) 0 0
\(319\) −8.37907 −0.469138
\(320\) 0 0
\(321\) −20.6115 −1.15042
\(322\) 0 0
\(323\) 1.49702 0.0832967
\(324\) 0 0
\(325\) 0.0809744 0.00449165
\(326\) 0 0
\(327\) −19.1976 −1.06163
\(328\) 0 0
\(329\) 4.85446 0.267635
\(330\) 0 0
\(331\) −6.25410 −0.343757 −0.171878 0.985118i \(-0.554984\pi\)
−0.171878 + 0.985118i \(0.554984\pi\)
\(332\) 0 0
\(333\) 3.49180 0.191349
\(334\) 0 0
\(335\) −12.2335 −0.668389
\(336\) 0 0
\(337\) 26.3051 1.43293 0.716465 0.697623i \(-0.245759\pi\)
0.716465 + 0.697623i \(0.245759\pi\)
\(338\) 0 0
\(339\) 37.9669 2.06208
\(340\) 0 0
\(341\) 3.31867 0.179716
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 33.5826 1.80803
\(346\) 0 0
\(347\) 8.08097 0.433809 0.216905 0.976193i \(-0.430404\pi\)
0.216905 + 0.976193i \(0.430404\pi\)
\(348\) 0 0
\(349\) −33.6126 −1.79924 −0.899620 0.436673i \(-0.856157\pi\)
−0.899620 + 0.436673i \(0.856157\pi\)
\(350\) 0 0
\(351\) 4.36266 0.232862
\(352\) 0 0
\(353\) −0.585009 −0.0311369 −0.0155684 0.999879i \(-0.504956\pi\)
−0.0155684 + 0.999879i \(0.504956\pi\)
\(354\) 0 0
\(355\) −5.37206 −0.285119
\(356\) 0 0
\(357\) 1.19370 0.0631775
\(358\) 0 0
\(359\) −10.9201 −0.576340 −0.288170 0.957579i \(-0.593047\pi\)
−0.288170 + 0.957579i \(0.593047\pi\)
\(360\) 0 0
\(361\) −13.1086 −0.689924
\(362\) 0 0
\(363\) −1.93543 −0.101584
\(364\) 0 0
\(365\) −11.2335 −0.587990
\(366\) 0 0
\(367\) −18.5316 −0.967343 −0.483671 0.875250i \(-0.660697\pi\)
−0.483671 + 0.875250i \(0.660697\pi\)
\(368\) 0 0
\(369\) −9.11273 −0.474390
\(370\) 0 0
\(371\) −6.99583 −0.363205
\(372\) 0 0
\(373\) −29.9505 −1.55078 −0.775389 0.631483i \(-0.782446\pi\)
−0.775389 + 0.631483i \(0.782446\pi\)
\(374\) 0 0
\(375\) 21.4600 1.10819
\(376\) 0 0
\(377\) 8.37907 0.431544
\(378\) 0 0
\(379\) 36.6524 1.88271 0.941354 0.337420i \(-0.109554\pi\)
0.941354 + 0.337420i \(0.109554\pi\)
\(380\) 0 0
\(381\) −38.1156 −1.95272
\(382\) 0 0
\(383\) −26.9641 −1.37780 −0.688900 0.724856i \(-0.741906\pi\)
−0.688900 + 0.724856i \(0.741906\pi\)
\(384\) 0 0
\(385\) 2.25410 0.114880
\(386\) 0 0
\(387\) 1.66909 0.0848448
\(388\) 0 0
\(389\) −26.8175 −1.35970 −0.679850 0.733351i \(-0.737955\pi\)
−0.679850 + 0.733351i \(0.737955\pi\)
\(390\) 0 0
\(391\) −4.74768 −0.240100
\(392\) 0 0
\(393\) 25.3627 1.27938
\(394\) 0 0
\(395\) −20.9958 −1.05641
\(396\) 0 0
\(397\) 1.85863 0.0932818 0.0466409 0.998912i \(-0.485148\pi\)
0.0466409 + 0.998912i \(0.485148\pi\)
\(398\) 0 0
\(399\) 4.69774 0.235181
\(400\) 0 0
\(401\) 26.2827 1.31250 0.656249 0.754545i \(-0.272142\pi\)
0.656249 + 0.754545i \(0.272142\pi\)
\(402\) 0 0
\(403\) −3.31867 −0.165315
\(404\) 0 0
\(405\) −24.0768 −1.19639
\(406\) 0 0
\(407\) −4.68133 −0.232045
\(408\) 0 0
\(409\) −32.9424 −1.62890 −0.814449 0.580235i \(-0.802961\pi\)
−0.814449 + 0.580235i \(0.802961\pi\)
\(410\) 0 0
\(411\) −10.4642 −0.516161
\(412\) 0 0
\(413\) −10.0440 −0.494233
\(414\) 0 0
\(415\) −8.90785 −0.437269
\(416\) 0 0
\(417\) 2.63734 0.129151
\(418\) 0 0
\(419\) 28.5204 1.39331 0.696657 0.717404i \(-0.254670\pi\)
0.696657 + 0.717404i \(0.254670\pi\)
\(420\) 0 0
\(421\) −17.4178 −0.848893 −0.424447 0.905453i \(-0.639531\pi\)
−0.424447 + 0.905453i \(0.639531\pi\)
\(422\) 0 0
\(423\) −3.62093 −0.176056
\(424\) 0 0
\(425\) 0.0499420 0.00242254
\(426\) 0 0
\(427\) −2.74590 −0.132883
\(428\) 0 0
\(429\) 1.93543 0.0934436
\(430\) 0 0
\(431\) −7.45065 −0.358885 −0.179442 0.983768i \(-0.557429\pi\)
−0.179442 + 0.983768i \(0.557429\pi\)
\(432\) 0 0
\(433\) −32.7058 −1.57174 −0.785870 0.618391i \(-0.787785\pi\)
−0.785870 + 0.618391i \(0.787785\pi\)
\(434\) 0 0
\(435\) −36.5550 −1.75268
\(436\) 0 0
\(437\) −18.6842 −0.893785
\(438\) 0 0
\(439\) −17.2335 −0.822511 −0.411256 0.911520i \(-0.634910\pi\)
−0.411256 + 0.911520i \(0.634910\pi\)
\(440\) 0 0
\(441\) 0.745898 0.0355190
\(442\) 0 0
\(443\) −30.3491 −1.44193 −0.720965 0.692972i \(-0.756301\pi\)
−0.720965 + 0.692972i \(0.756301\pi\)
\(444\) 0 0
\(445\) 15.5962 0.739330
\(446\) 0 0
\(447\) −0.0932122 −0.00440879
\(448\) 0 0
\(449\) −20.8656 −0.984710 −0.492355 0.870394i \(-0.663864\pi\)
−0.492355 + 0.870394i \(0.663864\pi\)
\(450\) 0 0
\(451\) 12.2171 0.575282
\(452\) 0 0
\(453\) 25.6126 1.20338
\(454\) 0 0
\(455\) −2.25410 −0.105674
\(456\) 0 0
\(457\) −21.3697 −0.999631 −0.499816 0.866132i \(-0.666599\pi\)
−0.499816 + 0.866132i \(0.666599\pi\)
\(458\) 0 0
\(459\) 2.69073 0.125592
\(460\) 0 0
\(461\) 27.2007 1.26686 0.633432 0.773799i \(-0.281646\pi\)
0.633432 + 0.773799i \(0.281646\pi\)
\(462\) 0 0
\(463\) −33.8269 −1.57207 −0.786034 0.618183i \(-0.787869\pi\)
−0.786034 + 0.618183i \(0.787869\pi\)
\(464\) 0 0
\(465\) 14.4782 0.671412
\(466\) 0 0
\(467\) 13.6772 0.632904 0.316452 0.948609i \(-0.397508\pi\)
0.316452 + 0.948609i \(0.397508\pi\)
\(468\) 0 0
\(469\) 5.42723 0.250606
\(470\) 0 0
\(471\) 32.5194 1.49841
\(472\) 0 0
\(473\) −2.23769 −0.102889
\(474\) 0 0
\(475\) 0.196543 0.00901803
\(476\) 0 0
\(477\) 5.21818 0.238924
\(478\) 0 0
\(479\) 0.339245 0.0155005 0.00775025 0.999970i \(-0.497533\pi\)
0.00775025 + 0.999970i \(0.497533\pi\)
\(480\) 0 0
\(481\) 4.68133 0.213450
\(482\) 0 0
\(483\) −14.8984 −0.677903
\(484\) 0 0
\(485\) 38.9453 1.76841
\(486\) 0 0
\(487\) −20.8984 −0.946999 −0.473500 0.880794i \(-0.657009\pi\)
−0.473500 + 0.880794i \(0.657009\pi\)
\(488\) 0 0
\(489\) 9.55220 0.431965
\(490\) 0 0
\(491\) 18.6373 0.841091 0.420546 0.907271i \(-0.361839\pi\)
0.420546 + 0.907271i \(0.361839\pi\)
\(492\) 0 0
\(493\) 5.16790 0.232750
\(494\) 0 0
\(495\) −1.68133 −0.0755702
\(496\) 0 0
\(497\) 2.38324 0.106903
\(498\) 0 0
\(499\) −5.85552 −0.262129 −0.131064 0.991374i \(-0.541839\pi\)
−0.131064 + 0.991374i \(0.541839\pi\)
\(500\) 0 0
\(501\) 26.6360 1.19001
\(502\) 0 0
\(503\) 29.1372 1.29916 0.649582 0.760292i \(-0.274944\pi\)
0.649582 + 0.760292i \(0.274944\pi\)
\(504\) 0 0
\(505\) −20.1414 −0.896279
\(506\) 0 0
\(507\) −1.93543 −0.0859556
\(508\) 0 0
\(509\) −37.0192 −1.64085 −0.820425 0.571755i \(-0.806263\pi\)
−0.820425 + 0.571755i \(0.806263\pi\)
\(510\) 0 0
\(511\) 4.98359 0.220461
\(512\) 0 0
\(513\) 10.5892 0.467524
\(514\) 0 0
\(515\) −33.1924 −1.46263
\(516\) 0 0
\(517\) 4.85446 0.213499
\(518\) 0 0
\(519\) 2.98048 0.130829
\(520\) 0 0
\(521\) 13.7201 0.601088 0.300544 0.953768i \(-0.402832\pi\)
0.300544 + 0.953768i \(0.402832\pi\)
\(522\) 0 0
\(523\) −22.4754 −0.982780 −0.491390 0.870940i \(-0.663511\pi\)
−0.491390 + 0.870940i \(0.663511\pi\)
\(524\) 0 0
\(525\) 0.156721 0.00683984
\(526\) 0 0
\(527\) −2.04683 −0.0891614
\(528\) 0 0
\(529\) 36.2552 1.57631
\(530\) 0 0
\(531\) 7.49180 0.325116
\(532\) 0 0
\(533\) −12.2171 −0.529182
\(534\) 0 0
\(535\) 24.0052 1.03784
\(536\) 0 0
\(537\) −6.65686 −0.287265
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 2.51654 0.108195 0.0540973 0.998536i \(-0.482772\pi\)
0.0540973 + 0.998536i \(0.482772\pi\)
\(542\) 0 0
\(543\) −9.98048 −0.428304
\(544\) 0 0
\(545\) 22.3585 0.957733
\(546\) 0 0
\(547\) −33.1924 −1.41920 −0.709602 0.704603i \(-0.751125\pi\)
−0.709602 + 0.704603i \(0.751125\pi\)
\(548\) 0 0
\(549\) 2.04816 0.0874134
\(550\) 0 0
\(551\) 20.3379 0.866424
\(552\) 0 0
\(553\) 9.31450 0.396093
\(554\) 0 0
\(555\) −20.4231 −0.866911
\(556\) 0 0
\(557\) −14.3309 −0.607220 −0.303610 0.952796i \(-0.598192\pi\)
−0.303610 + 0.952796i \(0.598192\pi\)
\(558\) 0 0
\(559\) 2.23769 0.0946444
\(560\) 0 0
\(561\) 1.19370 0.0503982
\(562\) 0 0
\(563\) 28.8050 1.21398 0.606992 0.794708i \(-0.292376\pi\)
0.606992 + 0.794708i \(0.292376\pi\)
\(564\) 0 0
\(565\) −44.2182 −1.86027
\(566\) 0 0
\(567\) 10.6813 0.448574
\(568\) 0 0
\(569\) −24.8873 −1.04333 −0.521664 0.853151i \(-0.674689\pi\)
−0.521664 + 0.853151i \(0.674689\pi\)
\(570\) 0 0
\(571\) 8.17730 0.342209 0.171105 0.985253i \(-0.445266\pi\)
0.171105 + 0.985253i \(0.445266\pi\)
\(572\) 0 0
\(573\) 4.51938 0.188800
\(574\) 0 0
\(575\) −0.623320 −0.0259942
\(576\) 0 0
\(577\) −37.7100 −1.56989 −0.784943 0.619567i \(-0.787308\pi\)
−0.784943 + 0.619567i \(0.787308\pi\)
\(578\) 0 0
\(579\) 36.4517 1.51488
\(580\) 0 0
\(581\) 3.95184 0.163950
\(582\) 0 0
\(583\) −6.99583 −0.289738
\(584\) 0 0
\(585\) 1.68133 0.0695145
\(586\) 0 0
\(587\) −18.2499 −0.753255 −0.376628 0.926365i \(-0.622916\pi\)
−0.376628 + 0.926365i \(0.622916\pi\)
\(588\) 0 0
\(589\) −8.05517 −0.331908
\(590\) 0 0
\(591\) −7.63840 −0.314202
\(592\) 0 0
\(593\) 6.07965 0.249661 0.124831 0.992178i \(-0.460161\pi\)
0.124831 + 0.992178i \(0.460161\pi\)
\(594\) 0 0
\(595\) −1.39025 −0.0569945
\(596\) 0 0
\(597\) −39.5194 −1.61742
\(598\) 0 0
\(599\) −42.7498 −1.74671 −0.873355 0.487085i \(-0.838060\pi\)
−0.873355 + 0.487085i \(0.838060\pi\)
\(600\) 0 0
\(601\) 19.8831 0.811049 0.405524 0.914084i \(-0.367089\pi\)
0.405524 + 0.914084i \(0.367089\pi\)
\(602\) 0 0
\(603\) −4.04816 −0.164854
\(604\) 0 0
\(605\) 2.25410 0.0916423
\(606\) 0 0
\(607\) 1.68656 0.0684553 0.0342277 0.999414i \(-0.489103\pi\)
0.0342277 + 0.999414i \(0.489103\pi\)
\(608\) 0 0
\(609\) 16.2171 0.657151
\(610\) 0 0
\(611\) −4.85446 −0.196390
\(612\) 0 0
\(613\) 4.65970 0.188203 0.0941017 0.995563i \(-0.470002\pi\)
0.0941017 + 0.995563i \(0.470002\pi\)
\(614\) 0 0
\(615\) 53.2992 2.14923
\(616\) 0 0
\(617\) −2.31344 −0.0931356 −0.0465678 0.998915i \(-0.514828\pi\)
−0.0465678 + 0.998915i \(0.514828\pi\)
\(618\) 0 0
\(619\) −13.2859 −0.534004 −0.267002 0.963696i \(-0.586033\pi\)
−0.267002 + 0.963696i \(0.586033\pi\)
\(620\) 0 0
\(621\) −33.5826 −1.34762
\(622\) 0 0
\(623\) −6.91903 −0.277205
\(624\) 0 0
\(625\) −25.3983 −1.01593
\(626\) 0 0
\(627\) 4.69774 0.187610
\(628\) 0 0
\(629\) 2.88727 0.115123
\(630\) 0 0
\(631\) −26.5868 −1.05840 −0.529202 0.848496i \(-0.677509\pi\)
−0.529202 + 0.848496i \(0.677509\pi\)
\(632\) 0 0
\(633\) −7.21818 −0.286897
\(634\) 0 0
\(635\) 44.3913 1.76162
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −1.77765 −0.0703228
\(640\) 0 0
\(641\) −11.2346 −0.443739 −0.221870 0.975076i \(-0.571216\pi\)
−0.221870 + 0.975076i \(0.571216\pi\)
\(642\) 0 0
\(643\) −8.96408 −0.353509 −0.176754 0.984255i \(-0.556560\pi\)
−0.176754 + 0.984255i \(0.556560\pi\)
\(644\) 0 0
\(645\) −9.76231 −0.384390
\(646\) 0 0
\(647\) −36.5522 −1.43702 −0.718508 0.695519i \(-0.755174\pi\)
−0.718508 + 0.695519i \(0.755174\pi\)
\(648\) 0 0
\(649\) −10.0440 −0.394261
\(650\) 0 0
\(651\) −6.42306 −0.251740
\(652\) 0 0
\(653\) −42.9903 −1.68234 −0.841171 0.540769i \(-0.818133\pi\)
−0.841171 + 0.540769i \(0.818133\pi\)
\(654\) 0 0
\(655\) −29.5386 −1.15417
\(656\) 0 0
\(657\) −3.71725 −0.145024
\(658\) 0 0
\(659\) 22.3502 0.870638 0.435319 0.900276i \(-0.356636\pi\)
0.435319 + 0.900276i \(0.356636\pi\)
\(660\) 0 0
\(661\) 1.91619 0.0745310 0.0372655 0.999305i \(-0.488135\pi\)
0.0372655 + 0.999305i \(0.488135\pi\)
\(662\) 0 0
\(663\) −1.19370 −0.0463596
\(664\) 0 0
\(665\) −5.47122 −0.212165
\(666\) 0 0
\(667\) −64.4999 −2.49744
\(668\) 0 0
\(669\) −52.5439 −2.03146
\(670\) 0 0
\(671\) −2.74590 −0.106004
\(672\) 0 0
\(673\) 40.4259 1.55830 0.779152 0.626835i \(-0.215650\pi\)
0.779152 + 0.626835i \(0.215650\pi\)
\(674\) 0 0
\(675\) 0.353264 0.0135971
\(676\) 0 0
\(677\) 16.8422 0.647299 0.323650 0.946177i \(-0.395090\pi\)
0.323650 + 0.946177i \(0.395090\pi\)
\(678\) 0 0
\(679\) −17.2775 −0.663050
\(680\) 0 0
\(681\) 42.7735 1.63908
\(682\) 0 0
\(683\) 7.92425 0.303213 0.151607 0.988441i \(-0.451555\pi\)
0.151607 + 0.988441i \(0.451555\pi\)
\(684\) 0 0
\(685\) 12.1871 0.465647
\(686\) 0 0
\(687\) −22.7969 −0.869756
\(688\) 0 0
\(689\) 6.99583 0.266520
\(690\) 0 0
\(691\) 29.9477 1.13926 0.569632 0.821900i \(-0.307086\pi\)
0.569632 + 0.821900i \(0.307086\pi\)
\(692\) 0 0
\(693\) 0.745898 0.0283343
\(694\) 0 0
\(695\) −3.07158 −0.116512
\(696\) 0 0
\(697\) −7.53507 −0.285411
\(698\) 0 0
\(699\) 41.7662 1.57974
\(700\) 0 0
\(701\) −35.1044 −1.32587 −0.662937 0.748675i \(-0.730690\pi\)
−0.662937 + 0.748675i \(0.730690\pi\)
\(702\) 0 0
\(703\) 11.3627 0.428551
\(704\) 0 0
\(705\) 21.1784 0.797623
\(706\) 0 0
\(707\) 8.93543 0.336052
\(708\) 0 0
\(709\) −24.9969 −0.938778 −0.469389 0.882992i \(-0.655526\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(710\) 0 0
\(711\) −6.94767 −0.260558
\(712\) 0 0
\(713\) 25.5462 0.956714
\(714\) 0 0
\(715\) −2.25410 −0.0842986
\(716\) 0 0
\(717\) 10.8628 0.405679
\(718\) 0 0
\(719\) 27.0950 1.01047 0.505236 0.862981i \(-0.331405\pi\)
0.505236 + 0.862981i \(0.331405\pi\)
\(720\) 0 0
\(721\) 14.7253 0.548400
\(722\) 0 0
\(723\) 21.0081 0.781298
\(724\) 0 0
\(725\) 0.678490 0.0251985
\(726\) 0 0
\(727\) −13.2070 −0.489821 −0.244910 0.969546i \(-0.578759\pi\)
−0.244910 + 0.969546i \(0.578759\pi\)
\(728\) 0 0
\(729\) 17.3637 0.643101
\(730\) 0 0
\(731\) 1.38013 0.0510459
\(732\) 0 0
\(733\) 41.6454 1.53821 0.769104 0.639124i \(-0.220703\pi\)
0.769104 + 0.639124i \(0.220703\pi\)
\(734\) 0 0
\(735\) −4.36266 −0.160919
\(736\) 0 0
\(737\) 5.42723 0.199915
\(738\) 0 0
\(739\) −10.9201 −0.401702 −0.200851 0.979622i \(-0.564371\pi\)
−0.200851 + 0.979622i \(0.564371\pi\)
\(740\) 0 0
\(741\) −4.69774 −0.172576
\(742\) 0 0
\(743\) −4.03281 −0.147950 −0.0739748 0.997260i \(-0.523568\pi\)
−0.0739748 + 0.997260i \(0.523568\pi\)
\(744\) 0 0
\(745\) 0.108560 0.00397732
\(746\) 0 0
\(747\) −2.94767 −0.107850
\(748\) 0 0
\(749\) −10.6496 −0.389127
\(750\) 0 0
\(751\) 6.38191 0.232879 0.116440 0.993198i \(-0.462852\pi\)
0.116440 + 0.993198i \(0.462852\pi\)
\(752\) 0 0
\(753\) 36.4200 1.32722
\(754\) 0 0
\(755\) −29.8297 −1.08561
\(756\) 0 0
\(757\) −39.1114 −1.42153 −0.710764 0.703431i \(-0.751651\pi\)
−0.710764 + 0.703431i \(0.751651\pi\)
\(758\) 0 0
\(759\) −14.8984 −0.540779
\(760\) 0 0
\(761\) −21.8625 −0.792516 −0.396258 0.918139i \(-0.629691\pi\)
−0.396258 + 0.918139i \(0.629691\pi\)
\(762\) 0 0
\(763\) −9.91903 −0.359093
\(764\) 0 0
\(765\) 1.03698 0.0374922
\(766\) 0 0
\(767\) 10.0440 0.362668
\(768\) 0 0
\(769\) −42.4364 −1.53029 −0.765147 0.643856i \(-0.777334\pi\)
−0.765147 + 0.643856i \(0.777334\pi\)
\(770\) 0 0
\(771\) −47.6678 −1.71671
\(772\) 0 0
\(773\) −6.20700 −0.223250 −0.111625 0.993750i \(-0.535606\pi\)
−0.111625 + 0.993750i \(0.535606\pi\)
\(774\) 0 0
\(775\) −0.268727 −0.00965297
\(776\) 0 0
\(777\) 9.06040 0.325040
\(778\) 0 0
\(779\) −29.6537 −1.06246
\(780\) 0 0
\(781\) 2.38324 0.0852789
\(782\) 0 0
\(783\) 36.5550 1.30637
\(784\) 0 0
\(785\) −37.8737 −1.35177
\(786\) 0 0
\(787\) 24.3913 0.869456 0.434728 0.900562i \(-0.356844\pi\)
0.434728 + 0.900562i \(0.356844\pi\)
\(788\) 0 0
\(789\) 17.3574 0.617941
\(790\) 0 0
\(791\) 19.6168 0.697492
\(792\) 0 0
\(793\) 2.74590 0.0975097
\(794\) 0 0
\(795\) −30.5204 −1.08245
\(796\) 0 0
\(797\) 32.6178 1.15538 0.577691 0.816255i \(-0.303954\pi\)
0.577691 + 0.816255i \(0.303954\pi\)
\(798\) 0 0
\(799\) −2.99405 −0.105922
\(800\) 0 0
\(801\) 5.16089 0.182351
\(802\) 0 0
\(803\) 4.98359 0.175867
\(804\) 0 0
\(805\) 17.3515 0.611559
\(806\) 0 0
\(807\) −55.5959 −1.95707
\(808\) 0 0
\(809\) 5.77242 0.202948 0.101474 0.994838i \(-0.467644\pi\)
0.101474 + 0.994838i \(0.467644\pi\)
\(810\) 0 0
\(811\) 18.2653 0.641381 0.320690 0.947184i \(-0.396085\pi\)
0.320690 + 0.947184i \(0.396085\pi\)
\(812\) 0 0
\(813\) −42.7100 −1.49790
\(814\) 0 0
\(815\) −11.1250 −0.389691
\(816\) 0 0
\(817\) 5.43140 0.190021
\(818\) 0 0
\(819\) −0.745898 −0.0260638
\(820\) 0 0
\(821\) −40.7927 −1.42368 −0.711838 0.702344i \(-0.752137\pi\)
−0.711838 + 0.702344i \(0.752137\pi\)
\(822\) 0 0
\(823\) −41.0521 −1.43098 −0.715492 0.698620i \(-0.753798\pi\)
−0.715492 + 0.698620i \(0.753798\pi\)
\(824\) 0 0
\(825\) 0.156721 0.00545631
\(826\) 0 0
\(827\) −1.52461 −0.0530159 −0.0265079 0.999649i \(-0.508439\pi\)
−0.0265079 + 0.999649i \(0.508439\pi\)
\(828\) 0 0
\(829\) 25.4067 0.882410 0.441205 0.897406i \(-0.354551\pi\)
0.441205 + 0.897406i \(0.354551\pi\)
\(830\) 0 0
\(831\) 9.89534 0.343266
\(832\) 0 0
\(833\) 0.616763 0.0213696
\(834\) 0 0
\(835\) −31.0216 −1.07355
\(836\) 0 0
\(837\) −14.4782 −0.500441
\(838\) 0 0
\(839\) 28.1648 0.972357 0.486178 0.873860i \(-0.338391\pi\)
0.486178 + 0.873860i \(0.338391\pi\)
\(840\) 0 0
\(841\) 41.2088 1.42099
\(842\) 0 0
\(843\) −29.0869 −1.00181
\(844\) 0 0
\(845\) 2.25410 0.0775435
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 52.5222 1.80256
\(850\) 0 0
\(851\) −36.0357 −1.23529
\(852\) 0 0
\(853\) 8.78049 0.300638 0.150319 0.988638i \(-0.451970\pi\)
0.150319 + 0.988638i \(0.451970\pi\)
\(854\) 0 0
\(855\) 4.08097 0.139566
\(856\) 0 0
\(857\) −41.5561 −1.41953 −0.709765 0.704439i \(-0.751199\pi\)
−0.709765 + 0.704439i \(0.751199\pi\)
\(858\) 0 0
\(859\) −23.7941 −0.811843 −0.405921 0.913908i \(-0.633049\pi\)
−0.405921 + 0.913908i \(0.633049\pi\)
\(860\) 0 0
\(861\) −23.6454 −0.805833
\(862\) 0 0
\(863\) 23.4835 0.799386 0.399693 0.916649i \(-0.369117\pi\)
0.399693 + 0.916649i \(0.369117\pi\)
\(864\) 0 0
\(865\) −3.47122 −0.118025
\(866\) 0 0
\(867\) 32.1661 1.09242
\(868\) 0 0
\(869\) 9.31450 0.315973
\(870\) 0 0
\(871\) −5.42723 −0.183895
\(872\) 0 0
\(873\) 12.8873 0.436168
\(874\) 0 0
\(875\) 11.0880 0.374842
\(876\) 0 0
\(877\) −4.18252 −0.141234 −0.0706169 0.997504i \(-0.522497\pi\)
−0.0706169 + 0.997504i \(0.522497\pi\)
\(878\) 0 0
\(879\) −28.8133 −0.971849
\(880\) 0 0
\(881\) −35.1484 −1.18418 −0.592090 0.805872i \(-0.701697\pi\)
−0.592090 + 0.805872i \(0.701697\pi\)
\(882\) 0 0
\(883\) 5.58812 0.188055 0.0940276 0.995570i \(-0.470026\pi\)
0.0940276 + 0.995570i \(0.470026\pi\)
\(884\) 0 0
\(885\) −43.8185 −1.47294
\(886\) 0 0
\(887\) −14.2911 −0.479848 −0.239924 0.970792i \(-0.577122\pi\)
−0.239924 + 0.970792i \(0.577122\pi\)
\(888\) 0 0
\(889\) −19.6936 −0.660501
\(890\) 0 0
\(891\) 10.6813 0.357838
\(892\) 0 0
\(893\) −11.7829 −0.394299
\(894\) 0 0
\(895\) 7.75291 0.259151
\(896\) 0 0
\(897\) 14.8984 0.497445
\(898\) 0 0
\(899\) −27.8074 −0.927427
\(900\) 0 0
\(901\) 4.31477 0.143746
\(902\) 0 0
\(903\) 4.33091 0.144124
\(904\) 0 0
\(905\) 11.6238 0.386387
\(906\) 0 0
\(907\) 54.2884 1.80262 0.901309 0.433177i \(-0.142608\pi\)
0.901309 + 0.433177i \(0.142608\pi\)
\(908\) 0 0
\(909\) −6.66492 −0.221062
\(910\) 0 0
\(911\) −47.0081 −1.55745 −0.778723 0.627367i \(-0.784132\pi\)
−0.778723 + 0.627367i \(0.784132\pi\)
\(912\) 0 0
\(913\) 3.95184 0.130787
\(914\) 0 0
\(915\) −11.9794 −0.396028
\(916\) 0 0
\(917\) 13.1044 0.432745
\(918\) 0 0
\(919\) 53.8831 1.77744 0.888720 0.458451i \(-0.151595\pi\)
0.888720 + 0.458451i \(0.151595\pi\)
\(920\) 0 0
\(921\) 13.4764 0.444064
\(922\) 0 0
\(923\) −2.38324 −0.0784452
\(924\) 0 0
\(925\) 0.379068 0.0124637
\(926\) 0 0
\(927\) −10.9836 −0.360749
\(928\) 0 0
\(929\) 34.8891 1.14467 0.572336 0.820019i \(-0.306037\pi\)
0.572336 + 0.820019i \(0.306037\pi\)
\(930\) 0 0
\(931\) 2.42723 0.0795492
\(932\) 0 0
\(933\) 57.6563 1.88758
\(934\) 0 0
\(935\) −1.39025 −0.0454659
\(936\) 0 0
\(937\) 18.0726 0.590407 0.295204 0.955434i \(-0.404613\pi\)
0.295204 + 0.955434i \(0.404613\pi\)
\(938\) 0 0
\(939\) −29.3187 −0.956779
\(940\) 0 0
\(941\) 10.8873 0.354915 0.177457 0.984128i \(-0.443213\pi\)
0.177457 + 0.984128i \(0.443213\pi\)
\(942\) 0 0
\(943\) 94.0442 3.06250
\(944\) 0 0
\(945\) −9.83388 −0.319896
\(946\) 0 0
\(947\) 45.2158 1.46932 0.734658 0.678438i \(-0.237343\pi\)
0.734658 + 0.678438i \(0.237343\pi\)
\(948\) 0 0
\(949\) −4.98359 −0.161774
\(950\) 0 0
\(951\) 16.8021 0.544846
\(952\) 0 0
\(953\) −47.2007 −1.52898 −0.764491 0.644635i \(-0.777009\pi\)
−0.764491 + 0.644635i \(0.777009\pi\)
\(954\) 0 0
\(955\) −5.26350 −0.170323
\(956\) 0 0
\(957\) 16.2171 0.524225
\(958\) 0 0
\(959\) −5.40665 −0.174590
\(960\) 0 0
\(961\) −19.9864 −0.644724
\(962\) 0 0
\(963\) 7.94350 0.255976
\(964\) 0 0
\(965\) −42.4535 −1.36663
\(966\) 0 0
\(967\) 43.5163 1.39939 0.699694 0.714442i \(-0.253319\pi\)
0.699694 + 0.714442i \(0.253319\pi\)
\(968\) 0 0
\(969\) −2.89739 −0.0930776
\(970\) 0 0
\(971\) 43.1247 1.38394 0.691969 0.721928i \(-0.256744\pi\)
0.691969 + 0.721928i \(0.256744\pi\)
\(972\) 0 0
\(973\) 1.36266 0.0436849
\(974\) 0 0
\(975\) −0.156721 −0.00501907
\(976\) 0 0
\(977\) −35.4311 −1.13354 −0.566771 0.823875i \(-0.691808\pi\)
−0.566771 + 0.823875i \(0.691808\pi\)
\(978\) 0 0
\(979\) −6.91903 −0.221133
\(980\) 0 0
\(981\) 7.39858 0.236219
\(982\) 0 0
\(983\) −51.0192 −1.62726 −0.813631 0.581382i \(-0.802512\pi\)
−0.813631 + 0.581382i \(0.802512\pi\)
\(984\) 0 0
\(985\) 8.89606 0.283452
\(986\) 0 0
\(987\) −9.39547 −0.299061
\(988\) 0 0
\(989\) −17.2252 −0.547729
\(990\) 0 0
\(991\) 16.0000 0.508257 0.254128 0.967170i \(-0.418211\pi\)
0.254128 + 0.967170i \(0.418211\pi\)
\(992\) 0 0
\(993\) 12.1044 0.384121
\(994\) 0 0
\(995\) 46.0263 1.45913
\(996\) 0 0
\(997\) −26.7240 −0.846357 −0.423179 0.906046i \(-0.639086\pi\)
−0.423179 + 0.906046i \(0.639086\pi\)
\(998\) 0 0
\(999\) 20.4231 0.646157
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 \(a_p\))