Properties

Label 8008.2.a.u.1.10
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 1
Dimension 10
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: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(2.97233\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.97233 q^{3} -3.07774 q^{5} -1.00000 q^{7} +5.83476 q^{9} +O(q^{10})\) \(q+2.97233 q^{3} -3.07774 q^{5} -1.00000 q^{7} +5.83476 q^{9} -1.00000 q^{11} -1.00000 q^{13} -9.14806 q^{15} +2.23499 q^{17} +0.103324 q^{19} -2.97233 q^{21} -2.91620 q^{23} +4.47248 q^{25} +8.42585 q^{27} +5.61031 q^{29} -0.191615 q^{31} -2.97233 q^{33} +3.07774 q^{35} -6.04946 q^{37} -2.97233 q^{39} -10.4530 q^{41} +4.42785 q^{43} -17.9579 q^{45} -4.29716 q^{47} +1.00000 q^{49} +6.64315 q^{51} -0.962428 q^{53} +3.07774 q^{55} +0.307112 q^{57} +7.41338 q^{59} -6.36668 q^{61} -5.83476 q^{63} +3.07774 q^{65} -10.9683 q^{67} -8.66791 q^{69} +0.646837 q^{71} +2.81140 q^{73} +13.2937 q^{75} +1.00000 q^{77} -13.8459 q^{79} +7.54015 q^{81} +1.79514 q^{83} -6.87873 q^{85} +16.6757 q^{87} +2.92179 q^{89} +1.00000 q^{91} -0.569544 q^{93} -0.318003 q^{95} -1.39715 q^{97} -5.83476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} + O(q^{10}) \) \( 10q + 2q^{3} - 4q^{5} - 10q^{7} + 6q^{9} - 10q^{11} - 10q^{13} - 4q^{15} - 3q^{17} + 13q^{19} - 2q^{21} + 6q^{25} + 14q^{27} - 3q^{29} - q^{31} - 2q^{33} + 4q^{35} - 5q^{37} - 2q^{39} + 4q^{41} + 19q^{43} - 11q^{45} + q^{47} + 10q^{49} + 15q^{51} - 6q^{53} + 4q^{55} - 6q^{57} + 4q^{59} - 18q^{61} - 6q^{63} + 4q^{65} + q^{67} - 11q^{69} - 21q^{71} - 10q^{73} + 10q^{77} + 3q^{79} - 30q^{81} + 6q^{83} - 33q^{85} - 9q^{87} - 22q^{89} + 10q^{91} - 34q^{93} - 3q^{95} - 9q^{97} - 6q^{99} + O(q^{100}) \)

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
\(3\) 2.97233 1.71608 0.858038 0.513585i \(-0.171683\pi\)
0.858038 + 0.513585i \(0.171683\pi\)
\(4\) 0 0
\(5\) −3.07774 −1.37641 −0.688203 0.725518i \(-0.741600\pi\)
−0.688203 + 0.725518i \(0.741600\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 5.83476 1.94492
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −9.14806 −2.36202
\(16\) 0 0
\(17\) 2.23499 0.542066 0.271033 0.962570i \(-0.412635\pi\)
0.271033 + 0.962570i \(0.412635\pi\)
\(18\) 0 0
\(19\) 0.103324 0.0237041 0.0118520 0.999930i \(-0.496227\pi\)
0.0118520 + 0.999930i \(0.496227\pi\)
\(20\) 0 0
\(21\) −2.97233 −0.648616
\(22\) 0 0
\(23\) −2.91620 −0.608069 −0.304035 0.952661i \(-0.598334\pi\)
−0.304035 + 0.952661i \(0.598334\pi\)
\(24\) 0 0
\(25\) 4.47248 0.894496
\(26\) 0 0
\(27\) 8.42585 1.62156
\(28\) 0 0
\(29\) 5.61031 1.04181 0.520904 0.853615i \(-0.325595\pi\)
0.520904 + 0.853615i \(0.325595\pi\)
\(30\) 0 0
\(31\) −0.191615 −0.0344151 −0.0172075 0.999852i \(-0.505478\pi\)
−0.0172075 + 0.999852i \(0.505478\pi\)
\(32\) 0 0
\(33\) −2.97233 −0.517417
\(34\) 0 0
\(35\) 3.07774 0.520233
\(36\) 0 0
\(37\) −6.04946 −0.994525 −0.497262 0.867600i \(-0.665661\pi\)
−0.497262 + 0.867600i \(0.665661\pi\)
\(38\) 0 0
\(39\) −2.97233 −0.475954
\(40\) 0 0
\(41\) −10.4530 −1.63248 −0.816240 0.577713i \(-0.803945\pi\)
−0.816240 + 0.577713i \(0.803945\pi\)
\(42\) 0 0
\(43\) 4.42785 0.675241 0.337621 0.941282i \(-0.390378\pi\)
0.337621 + 0.941282i \(0.390378\pi\)
\(44\) 0 0
\(45\) −17.9579 −2.67700
\(46\) 0 0
\(47\) −4.29716 −0.626805 −0.313402 0.949620i \(-0.601469\pi\)
−0.313402 + 0.949620i \(0.601469\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 6.64315 0.930226
\(52\) 0 0
\(53\) −0.962428 −0.132200 −0.0660998 0.997813i \(-0.521056\pi\)
−0.0660998 + 0.997813i \(0.521056\pi\)
\(54\) 0 0
\(55\) 3.07774 0.415002
\(56\) 0 0
\(57\) 0.307112 0.0406780
\(58\) 0 0
\(59\) 7.41338 0.965141 0.482570 0.875857i \(-0.339703\pi\)
0.482570 + 0.875857i \(0.339703\pi\)
\(60\) 0 0
\(61\) −6.36668 −0.815169 −0.407585 0.913167i \(-0.633629\pi\)
−0.407585 + 0.913167i \(0.633629\pi\)
\(62\) 0 0
\(63\) −5.83476 −0.735111
\(64\) 0 0
\(65\) 3.07774 0.381747
\(66\) 0 0
\(67\) −10.9683 −1.33999 −0.669994 0.742367i \(-0.733703\pi\)
−0.669994 + 0.742367i \(0.733703\pi\)
\(68\) 0 0
\(69\) −8.66791 −1.04349
\(70\) 0 0
\(71\) 0.646837 0.0767655 0.0383827 0.999263i \(-0.487779\pi\)
0.0383827 + 0.999263i \(0.487779\pi\)
\(72\) 0 0
\(73\) 2.81140 0.329049 0.164525 0.986373i \(-0.447391\pi\)
0.164525 + 0.986373i \(0.447391\pi\)
\(74\) 0 0
\(75\) 13.2937 1.53502
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) −13.8459 −1.55779 −0.778895 0.627155i \(-0.784219\pi\)
−0.778895 + 0.627155i \(0.784219\pi\)
\(80\) 0 0
\(81\) 7.54015 0.837795
\(82\) 0 0
\(83\) 1.79514 0.197042 0.0985210 0.995135i \(-0.468589\pi\)
0.0985210 + 0.995135i \(0.468589\pi\)
\(84\) 0 0
\(85\) −6.87873 −0.746103
\(86\) 0 0
\(87\) 16.6757 1.78782
\(88\) 0 0
\(89\) 2.92179 0.309709 0.154855 0.987937i \(-0.450509\pi\)
0.154855 + 0.987937i \(0.450509\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) −0.569544 −0.0590589
\(94\) 0 0
\(95\) −0.318003 −0.0326265
\(96\) 0 0
\(97\) −1.39715 −0.141859 −0.0709296 0.997481i \(-0.522597\pi\)
−0.0709296 + 0.997481i \(0.522597\pi\)
\(98\) 0 0
\(99\) −5.83476 −0.586416
\(100\) 0 0
\(101\) −13.2388 −1.31731 −0.658656 0.752444i \(-0.728875\pi\)
−0.658656 + 0.752444i \(0.728875\pi\)
\(102\) 0 0
\(103\) 9.76380 0.962056 0.481028 0.876705i \(-0.340264\pi\)
0.481028 + 0.876705i \(0.340264\pi\)
\(104\) 0 0
\(105\) 9.14806 0.892760
\(106\) 0 0
\(107\) 5.03968 0.487204 0.243602 0.969875i \(-0.421671\pi\)
0.243602 + 0.969875i \(0.421671\pi\)
\(108\) 0 0
\(109\) −10.5141 −1.00706 −0.503532 0.863977i \(-0.667966\pi\)
−0.503532 + 0.863977i \(0.667966\pi\)
\(110\) 0 0
\(111\) −17.9810 −1.70668
\(112\) 0 0
\(113\) −0.483443 −0.0454785 −0.0227393 0.999741i \(-0.507239\pi\)
−0.0227393 + 0.999741i \(0.507239\pi\)
\(114\) 0 0
\(115\) 8.97529 0.836950
\(116\) 0 0
\(117\) −5.83476 −0.539424
\(118\) 0 0
\(119\) −2.23499 −0.204882
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −31.0697 −2.80146
\(124\) 0 0
\(125\) 1.62357 0.145217
\(126\) 0 0
\(127\) −4.50838 −0.400054 −0.200027 0.979790i \(-0.564103\pi\)
−0.200027 + 0.979790i \(0.564103\pi\)
\(128\) 0 0
\(129\) 13.1611 1.15877
\(130\) 0 0
\(131\) −10.8575 −0.948627 −0.474314 0.880356i \(-0.657304\pi\)
−0.474314 + 0.880356i \(0.657304\pi\)
\(132\) 0 0
\(133\) −0.103324 −0.00895930
\(134\) 0 0
\(135\) −25.9326 −2.23192
\(136\) 0 0
\(137\) −11.5054 −0.982971 −0.491486 0.870886i \(-0.663546\pi\)
−0.491486 + 0.870886i \(0.663546\pi\)
\(138\) 0 0
\(139\) −3.51308 −0.297976 −0.148988 0.988839i \(-0.547602\pi\)
−0.148988 + 0.988839i \(0.547602\pi\)
\(140\) 0 0
\(141\) −12.7726 −1.07565
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −17.2671 −1.43395
\(146\) 0 0
\(147\) 2.97233 0.245154
\(148\) 0 0
\(149\) −8.93487 −0.731973 −0.365986 0.930620i \(-0.619268\pi\)
−0.365986 + 0.930620i \(0.619268\pi\)
\(150\) 0 0
\(151\) 2.73619 0.222668 0.111334 0.993783i \(-0.464488\pi\)
0.111334 + 0.993783i \(0.464488\pi\)
\(152\) 0 0
\(153\) 13.0407 1.05427
\(154\) 0 0
\(155\) 0.589741 0.0473691
\(156\) 0 0
\(157\) 6.99619 0.558357 0.279178 0.960239i \(-0.409938\pi\)
0.279178 + 0.960239i \(0.409938\pi\)
\(158\) 0 0
\(159\) −2.86066 −0.226865
\(160\) 0 0
\(161\) 2.91620 0.229828
\(162\) 0 0
\(163\) −5.19927 −0.407238 −0.203619 0.979050i \(-0.565270\pi\)
−0.203619 + 0.979050i \(0.565270\pi\)
\(164\) 0 0
\(165\) 9.14806 0.712176
\(166\) 0 0
\(167\) −22.5642 −1.74607 −0.873036 0.487656i \(-0.837852\pi\)
−0.873036 + 0.487656i \(0.837852\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0.602869 0.0461026
\(172\) 0 0
\(173\) −23.1188 −1.75769 −0.878844 0.477109i \(-0.841685\pi\)
−0.878844 + 0.477109i \(0.841685\pi\)
\(174\) 0 0
\(175\) −4.47248 −0.338088
\(176\) 0 0
\(177\) 22.0350 1.65626
\(178\) 0 0
\(179\) −17.0313 −1.27298 −0.636488 0.771286i \(-0.719614\pi\)
−0.636488 + 0.771286i \(0.719614\pi\)
\(180\) 0 0
\(181\) −2.10710 −0.156619 −0.0783097 0.996929i \(-0.524952\pi\)
−0.0783097 + 0.996929i \(0.524952\pi\)
\(182\) 0 0
\(183\) −18.9239 −1.39889
\(184\) 0 0
\(185\) 18.6187 1.36887
\(186\) 0 0
\(187\) −2.23499 −0.163439
\(188\) 0 0
\(189\) −8.42585 −0.612891
\(190\) 0 0
\(191\) −11.2206 −0.811893 −0.405947 0.913897i \(-0.633058\pi\)
−0.405947 + 0.913897i \(0.633058\pi\)
\(192\) 0 0
\(193\) 14.5364 1.04635 0.523177 0.852224i \(-0.324747\pi\)
0.523177 + 0.852224i \(0.324747\pi\)
\(194\) 0 0
\(195\) 9.14806 0.655107
\(196\) 0 0
\(197\) 10.4063 0.741417 0.370708 0.928749i \(-0.379115\pi\)
0.370708 + 0.928749i \(0.379115\pi\)
\(198\) 0 0
\(199\) 12.4838 0.884954 0.442477 0.896780i \(-0.354100\pi\)
0.442477 + 0.896780i \(0.354100\pi\)
\(200\) 0 0
\(201\) −32.6013 −2.29952
\(202\) 0 0
\(203\) −5.61031 −0.393766
\(204\) 0 0
\(205\) 32.1715 2.24696
\(206\) 0 0
\(207\) −17.0153 −1.18265
\(208\) 0 0
\(209\) −0.103324 −0.00714705
\(210\) 0 0
\(211\) 0.779158 0.0536394 0.0268197 0.999640i \(-0.491462\pi\)
0.0268197 + 0.999640i \(0.491462\pi\)
\(212\) 0 0
\(213\) 1.92262 0.131735
\(214\) 0 0
\(215\) −13.6278 −0.929407
\(216\) 0 0
\(217\) 0.191615 0.0130077
\(218\) 0 0
\(219\) 8.35641 0.564674
\(220\) 0 0
\(221\) −2.23499 −0.150342
\(222\) 0 0
\(223\) −16.3416 −1.09432 −0.547158 0.837030i \(-0.684290\pi\)
−0.547158 + 0.837030i \(0.684290\pi\)
\(224\) 0 0
\(225\) 26.0958 1.73972
\(226\) 0 0
\(227\) −11.7555 −0.780238 −0.390119 0.920764i \(-0.627566\pi\)
−0.390119 + 0.920764i \(0.627566\pi\)
\(228\) 0 0
\(229\) 10.0978 0.667283 0.333641 0.942700i \(-0.391723\pi\)
0.333641 + 0.942700i \(0.391723\pi\)
\(230\) 0 0
\(231\) 2.97233 0.195565
\(232\) 0 0
\(233\) 20.7608 1.36009 0.680043 0.733172i \(-0.261961\pi\)
0.680043 + 0.733172i \(0.261961\pi\)
\(234\) 0 0
\(235\) 13.2255 0.862739
\(236\) 0 0
\(237\) −41.1547 −2.67329
\(238\) 0 0
\(239\) −13.1024 −0.847521 −0.423761 0.905774i \(-0.639290\pi\)
−0.423761 + 0.905774i \(0.639290\pi\)
\(240\) 0 0
\(241\) 5.60987 0.361363 0.180682 0.983542i \(-0.442170\pi\)
0.180682 + 0.983542i \(0.442170\pi\)
\(242\) 0 0
\(243\) −2.86572 −0.183836
\(244\) 0 0
\(245\) −3.07774 −0.196630
\(246\) 0 0
\(247\) −0.103324 −0.00657433
\(248\) 0 0
\(249\) 5.33575 0.338139
\(250\) 0 0
\(251\) −17.8824 −1.12872 −0.564362 0.825527i \(-0.690878\pi\)
−0.564362 + 0.825527i \(0.690878\pi\)
\(252\) 0 0
\(253\) 2.91620 0.183340
\(254\) 0 0
\(255\) −20.4459 −1.28037
\(256\) 0 0
\(257\) −18.0040 −1.12306 −0.561529 0.827457i \(-0.689787\pi\)
−0.561529 + 0.827457i \(0.689787\pi\)
\(258\) 0 0
\(259\) 6.04946 0.375895
\(260\) 0 0
\(261\) 32.7348 2.02623
\(262\) 0 0
\(263\) 21.0315 1.29686 0.648429 0.761275i \(-0.275427\pi\)
0.648429 + 0.761275i \(0.275427\pi\)
\(264\) 0 0
\(265\) 2.96210 0.181961
\(266\) 0 0
\(267\) 8.68453 0.531485
\(268\) 0 0
\(269\) 21.5117 1.31159 0.655795 0.754939i \(-0.272333\pi\)
0.655795 + 0.754939i \(0.272333\pi\)
\(270\) 0 0
\(271\) 2.67313 0.162381 0.0811907 0.996699i \(-0.474128\pi\)
0.0811907 + 0.996699i \(0.474128\pi\)
\(272\) 0 0
\(273\) 2.97233 0.179894
\(274\) 0 0
\(275\) −4.47248 −0.269701
\(276\) 0 0
\(277\) 7.37325 0.443016 0.221508 0.975159i \(-0.428902\pi\)
0.221508 + 0.975159i \(0.428902\pi\)
\(278\) 0 0
\(279\) −1.11803 −0.0669346
\(280\) 0 0
\(281\) −5.42569 −0.323669 −0.161835 0.986818i \(-0.551741\pi\)
−0.161835 + 0.986818i \(0.551741\pi\)
\(282\) 0 0
\(283\) 13.7443 0.817016 0.408508 0.912755i \(-0.366049\pi\)
0.408508 + 0.912755i \(0.366049\pi\)
\(284\) 0 0
\(285\) −0.945212 −0.0559895
\(286\) 0 0
\(287\) 10.4530 0.617019
\(288\) 0 0
\(289\) −12.0048 −0.706165
\(290\) 0 0
\(291\) −4.15280 −0.243441
\(292\) 0 0
\(293\) 5.02676 0.293667 0.146833 0.989161i \(-0.453092\pi\)
0.146833 + 0.989161i \(0.453092\pi\)
\(294\) 0 0
\(295\) −22.8165 −1.32843
\(296\) 0 0
\(297\) −8.42585 −0.488917
\(298\) 0 0
\(299\) 2.91620 0.168648
\(300\) 0 0
\(301\) −4.42785 −0.255217
\(302\) 0 0
\(303\) −39.3502 −2.26061
\(304\) 0 0
\(305\) 19.5950 1.12200
\(306\) 0 0
\(307\) 34.6980 1.98032 0.990161 0.139935i \(-0.0446893\pi\)
0.990161 + 0.139935i \(0.0446893\pi\)
\(308\) 0 0
\(309\) 29.0213 1.65096
\(310\) 0 0
\(311\) 15.7071 0.890670 0.445335 0.895364i \(-0.353085\pi\)
0.445335 + 0.895364i \(0.353085\pi\)
\(312\) 0 0
\(313\) −12.3047 −0.695503 −0.347752 0.937587i \(-0.613055\pi\)
−0.347752 + 0.937587i \(0.613055\pi\)
\(314\) 0 0
\(315\) 17.9579 1.01181
\(316\) 0 0
\(317\) −18.4765 −1.03774 −0.518872 0.854852i \(-0.673648\pi\)
−0.518872 + 0.854852i \(0.673648\pi\)
\(318\) 0 0
\(319\) −5.61031 −0.314117
\(320\) 0 0
\(321\) 14.9796 0.836080
\(322\) 0 0
\(323\) 0.230928 0.0128492
\(324\) 0 0
\(325\) −4.47248 −0.248088
\(326\) 0 0
\(327\) −31.2513 −1.72820
\(328\) 0 0
\(329\) 4.29716 0.236910
\(330\) 0 0
\(331\) −17.5194 −0.962952 −0.481476 0.876459i \(-0.659899\pi\)
−0.481476 + 0.876459i \(0.659899\pi\)
\(332\) 0 0
\(333\) −35.2971 −1.93427
\(334\) 0 0
\(335\) 33.7575 1.84437
\(336\) 0 0
\(337\) 15.4363 0.840870 0.420435 0.907323i \(-0.361877\pi\)
0.420435 + 0.907323i \(0.361877\pi\)
\(338\) 0 0
\(339\) −1.43695 −0.0780446
\(340\) 0 0
\(341\) 0.191615 0.0103765
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 26.6776 1.43627
\(346\) 0 0
\(347\) 12.6121 0.677055 0.338527 0.940956i \(-0.390071\pi\)
0.338527 + 0.940956i \(0.390071\pi\)
\(348\) 0 0
\(349\) 21.0583 1.12722 0.563612 0.826040i \(-0.309411\pi\)
0.563612 + 0.826040i \(0.309411\pi\)
\(350\) 0 0
\(351\) −8.42585 −0.449739
\(352\) 0 0
\(353\) −3.45477 −0.183879 −0.0919394 0.995765i \(-0.529307\pi\)
−0.0919394 + 0.995765i \(0.529307\pi\)
\(354\) 0 0
\(355\) −1.99080 −0.105661
\(356\) 0 0
\(357\) −6.64315 −0.351593
\(358\) 0 0
\(359\) −1.30709 −0.0689855 −0.0344927 0.999405i \(-0.510982\pi\)
−0.0344927 + 0.999405i \(0.510982\pi\)
\(360\) 0 0
\(361\) −18.9893 −0.999438
\(362\) 0 0
\(363\) 2.97233 0.156007
\(364\) 0 0
\(365\) −8.65275 −0.452906
\(366\) 0 0
\(367\) 2.43609 0.127163 0.0635813 0.997977i \(-0.479748\pi\)
0.0635813 + 0.997977i \(0.479748\pi\)
\(368\) 0 0
\(369\) −60.9906 −3.17504
\(370\) 0 0
\(371\) 0.962428 0.0499668
\(372\) 0 0
\(373\) −13.6475 −0.706640 −0.353320 0.935502i \(-0.614947\pi\)
−0.353320 + 0.935502i \(0.614947\pi\)
\(374\) 0 0
\(375\) 4.82580 0.249203
\(376\) 0 0
\(377\) −5.61031 −0.288945
\(378\) 0 0
\(379\) −16.0155 −0.822662 −0.411331 0.911486i \(-0.634936\pi\)
−0.411331 + 0.911486i \(0.634936\pi\)
\(380\) 0 0
\(381\) −13.4004 −0.686524
\(382\) 0 0
\(383\) −36.6095 −1.87066 −0.935330 0.353777i \(-0.884897\pi\)
−0.935330 + 0.353777i \(0.884897\pi\)
\(384\) 0 0
\(385\) −3.07774 −0.156856
\(386\) 0 0
\(387\) 25.8355 1.31329
\(388\) 0 0
\(389\) −16.3212 −0.827517 −0.413758 0.910387i \(-0.635784\pi\)
−0.413758 + 0.910387i \(0.635784\pi\)
\(390\) 0 0
\(391\) −6.51768 −0.329613
\(392\) 0 0
\(393\) −32.2722 −1.62792
\(394\) 0 0
\(395\) 42.6142 2.14415
\(396\) 0 0
\(397\) −10.2818 −0.516031 −0.258016 0.966141i \(-0.583069\pi\)
−0.258016 + 0.966141i \(0.583069\pi\)
\(398\) 0 0
\(399\) −0.307112 −0.0153749
\(400\) 0 0
\(401\) −18.5310 −0.925393 −0.462697 0.886517i \(-0.653118\pi\)
−0.462697 + 0.886517i \(0.653118\pi\)
\(402\) 0 0
\(403\) 0.191615 0.00954502
\(404\) 0 0
\(405\) −23.2066 −1.15315
\(406\) 0 0
\(407\) 6.04946 0.299860
\(408\) 0 0
\(409\) 30.9073 1.52827 0.764135 0.645057i \(-0.223166\pi\)
0.764135 + 0.645057i \(0.223166\pi\)
\(410\) 0 0
\(411\) −34.1978 −1.68685
\(412\) 0 0
\(413\) −7.41338 −0.364789
\(414\) 0 0
\(415\) −5.52497 −0.271210
\(416\) 0 0
\(417\) −10.4421 −0.511349
\(418\) 0 0
\(419\) 2.04604 0.0999554 0.0499777 0.998750i \(-0.484085\pi\)
0.0499777 + 0.998750i \(0.484085\pi\)
\(420\) 0 0
\(421\) −17.9547 −0.875056 −0.437528 0.899205i \(-0.644146\pi\)
−0.437528 + 0.899205i \(0.644146\pi\)
\(422\) 0 0
\(423\) −25.0729 −1.21909
\(424\) 0 0
\(425\) 9.99596 0.484875
\(426\) 0 0
\(427\) 6.36668 0.308105
\(428\) 0 0
\(429\) 2.97233 0.143506
\(430\) 0 0
\(431\) −31.2834 −1.50687 −0.753434 0.657523i \(-0.771604\pi\)
−0.753434 + 0.657523i \(0.771604\pi\)
\(432\) 0 0
\(433\) 2.28678 0.109896 0.0549478 0.998489i \(-0.482501\pi\)
0.0549478 + 0.998489i \(0.482501\pi\)
\(434\) 0 0
\(435\) −51.3234 −2.46077
\(436\) 0 0
\(437\) −0.301312 −0.0144137
\(438\) 0 0
\(439\) 4.92870 0.235234 0.117617 0.993059i \(-0.462474\pi\)
0.117617 + 0.993059i \(0.462474\pi\)
\(440\) 0 0
\(441\) 5.83476 0.277846
\(442\) 0 0
\(443\) −10.1997 −0.484602 −0.242301 0.970201i \(-0.577902\pi\)
−0.242301 + 0.970201i \(0.577902\pi\)
\(444\) 0 0
\(445\) −8.99251 −0.426286
\(446\) 0 0
\(447\) −26.5574 −1.25612
\(448\) 0 0
\(449\) −12.7827 −0.603254 −0.301627 0.953426i \(-0.597530\pi\)
−0.301627 + 0.953426i \(0.597530\pi\)
\(450\) 0 0
\(451\) 10.4530 0.492211
\(452\) 0 0
\(453\) 8.13287 0.382116
\(454\) 0 0
\(455\) −3.07774 −0.144287
\(456\) 0 0
\(457\) −24.0107 −1.12317 −0.561587 0.827418i \(-0.689809\pi\)
−0.561587 + 0.827418i \(0.689809\pi\)
\(458\) 0 0
\(459\) 18.8317 0.878990
\(460\) 0 0
\(461\) −5.33623 −0.248533 −0.124267 0.992249i \(-0.539658\pi\)
−0.124267 + 0.992249i \(0.539658\pi\)
\(462\) 0 0
\(463\) −20.3381 −0.945192 −0.472596 0.881279i \(-0.656683\pi\)
−0.472596 + 0.881279i \(0.656683\pi\)
\(464\) 0 0
\(465\) 1.75291 0.0812891
\(466\) 0 0
\(467\) −11.5450 −0.534240 −0.267120 0.963663i \(-0.586072\pi\)
−0.267120 + 0.963663i \(0.586072\pi\)
\(468\) 0 0
\(469\) 10.9683 0.506468
\(470\) 0 0
\(471\) 20.7950 0.958183
\(472\) 0 0
\(473\) −4.42785 −0.203593
\(474\) 0 0
\(475\) 0.462113 0.0212032
\(476\) 0 0
\(477\) −5.61554 −0.257118
\(478\) 0 0
\(479\) 29.8689 1.36475 0.682373 0.731004i \(-0.260948\pi\)
0.682373 + 0.731004i \(0.260948\pi\)
\(480\) 0 0
\(481\) 6.04946 0.275831
\(482\) 0 0
\(483\) 8.66791 0.394403
\(484\) 0 0
\(485\) 4.30007 0.195256
\(486\) 0 0
\(487\) −17.4372 −0.790155 −0.395077 0.918648i \(-0.629282\pi\)
−0.395077 + 0.918648i \(0.629282\pi\)
\(488\) 0 0
\(489\) −15.4540 −0.698852
\(490\) 0 0
\(491\) 8.31828 0.375399 0.187699 0.982227i \(-0.439897\pi\)
0.187699 + 0.982227i \(0.439897\pi\)
\(492\) 0 0
\(493\) 12.5390 0.564728
\(494\) 0 0
\(495\) 17.9579 0.807146
\(496\) 0 0
\(497\) −0.646837 −0.0290146
\(498\) 0 0
\(499\) 25.9215 1.16041 0.580204 0.814471i \(-0.302973\pi\)
0.580204 + 0.814471i \(0.302973\pi\)
\(500\) 0 0
\(501\) −67.0684 −2.99639
\(502\) 0 0
\(503\) −25.0915 −1.11878 −0.559388 0.828906i \(-0.688964\pi\)
−0.559388 + 0.828906i \(0.688964\pi\)
\(504\) 0 0
\(505\) 40.7457 1.81316
\(506\) 0 0
\(507\) 2.97233 0.132006
\(508\) 0 0
\(509\) 15.7067 0.696189 0.348094 0.937460i \(-0.386829\pi\)
0.348094 + 0.937460i \(0.386829\pi\)
\(510\) 0 0
\(511\) −2.81140 −0.124369
\(512\) 0 0
\(513\) 0.870590 0.0384375
\(514\) 0 0
\(515\) −30.0504 −1.32418
\(516\) 0 0
\(517\) 4.29716 0.188989
\(518\) 0 0
\(519\) −68.7167 −3.01633
\(520\) 0 0
\(521\) −5.67235 −0.248510 −0.124255 0.992250i \(-0.539654\pi\)
−0.124255 + 0.992250i \(0.539654\pi\)
\(522\) 0 0
\(523\) 17.4581 0.763388 0.381694 0.924289i \(-0.375341\pi\)
0.381694 + 0.924289i \(0.375341\pi\)
\(524\) 0 0
\(525\) −13.2937 −0.580184
\(526\) 0 0
\(527\) −0.428258 −0.0186552
\(528\) 0 0
\(529\) −14.4958 −0.630252
\(530\) 0 0
\(531\) 43.2553 1.87712
\(532\) 0 0
\(533\) 10.4530 0.452768
\(534\) 0 0
\(535\) −15.5108 −0.670592
\(536\) 0 0
\(537\) −50.6226 −2.18453
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 34.7310 1.49320 0.746602 0.665271i \(-0.231684\pi\)
0.746602 + 0.665271i \(0.231684\pi\)
\(542\) 0 0
\(543\) −6.26299 −0.268771
\(544\) 0 0
\(545\) 32.3595 1.38613
\(546\) 0 0
\(547\) 4.87867 0.208597 0.104298 0.994546i \(-0.466740\pi\)
0.104298 + 0.994546i \(0.466740\pi\)
\(548\) 0 0
\(549\) −37.1480 −1.58544
\(550\) 0 0
\(551\) 0.579678 0.0246951
\(552\) 0 0
\(553\) 13.8459 0.588789
\(554\) 0 0
\(555\) 55.3408 2.34909
\(556\) 0 0
\(557\) 42.6830 1.80854 0.904269 0.426962i \(-0.140416\pi\)
0.904269 + 0.426962i \(0.140416\pi\)
\(558\) 0 0
\(559\) −4.42785 −0.187278
\(560\) 0 0
\(561\) −6.64315 −0.280474
\(562\) 0 0
\(563\) −9.22792 −0.388911 −0.194455 0.980911i \(-0.562294\pi\)
−0.194455 + 0.980911i \(0.562294\pi\)
\(564\) 0 0
\(565\) 1.48791 0.0625969
\(566\) 0 0
\(567\) −7.54015 −0.316657
\(568\) 0 0
\(569\) 39.3733 1.65061 0.825307 0.564684i \(-0.191002\pi\)
0.825307 + 0.564684i \(0.191002\pi\)
\(570\) 0 0
\(571\) 36.5144 1.52808 0.764039 0.645170i \(-0.223213\pi\)
0.764039 + 0.645170i \(0.223213\pi\)
\(572\) 0 0
\(573\) −33.3513 −1.39327
\(574\) 0 0
\(575\) −13.0426 −0.543915
\(576\) 0 0
\(577\) 7.24618 0.301663 0.150831 0.988560i \(-0.451805\pi\)
0.150831 + 0.988560i \(0.451805\pi\)
\(578\) 0 0
\(579\) 43.2070 1.79562
\(580\) 0 0
\(581\) −1.79514 −0.0744749
\(582\) 0 0
\(583\) 0.962428 0.0398597
\(584\) 0 0
\(585\) 17.9579 0.742467
\(586\) 0 0
\(587\) −11.6928 −0.482612 −0.241306 0.970449i \(-0.577576\pi\)
−0.241306 + 0.970449i \(0.577576\pi\)
\(588\) 0 0
\(589\) −0.0197984 −0.000815778 0
\(590\) 0 0
\(591\) 30.9309 1.27233
\(592\) 0 0
\(593\) 36.5638 1.50150 0.750748 0.660588i \(-0.229693\pi\)
0.750748 + 0.660588i \(0.229693\pi\)
\(594\) 0 0
\(595\) 6.87873 0.282000
\(596\) 0 0
\(597\) 37.1061 1.51865
\(598\) 0 0
\(599\) 36.3081 1.48351 0.741754 0.670672i \(-0.233994\pi\)
0.741754 + 0.670672i \(0.233994\pi\)
\(600\) 0 0
\(601\) −0.848823 −0.0346242 −0.0173121 0.999850i \(-0.505511\pi\)
−0.0173121 + 0.999850i \(0.505511\pi\)
\(602\) 0 0
\(603\) −63.9972 −2.60617
\(604\) 0 0
\(605\) −3.07774 −0.125128
\(606\) 0 0
\(607\) 33.9714 1.37886 0.689429 0.724353i \(-0.257862\pi\)
0.689429 + 0.724353i \(0.257862\pi\)
\(608\) 0 0
\(609\) −16.6757 −0.675733
\(610\) 0 0
\(611\) 4.29716 0.173844
\(612\) 0 0
\(613\) 24.9217 1.00658 0.503288 0.864119i \(-0.332123\pi\)
0.503288 + 0.864119i \(0.332123\pi\)
\(614\) 0 0
\(615\) 95.6245 3.85595
\(616\) 0 0
\(617\) 35.9790 1.44846 0.724229 0.689559i \(-0.242196\pi\)
0.724229 + 0.689559i \(0.242196\pi\)
\(618\) 0 0
\(619\) 31.4024 1.26217 0.631085 0.775714i \(-0.282610\pi\)
0.631085 + 0.775714i \(0.282610\pi\)
\(620\) 0 0
\(621\) −24.5714 −0.986018
\(622\) 0 0
\(623\) −2.92179 −0.117059
\(624\) 0 0
\(625\) −27.3593 −1.09437
\(626\) 0 0
\(627\) −0.307112 −0.0122649
\(628\) 0 0
\(629\) −13.5205 −0.539098
\(630\) 0 0
\(631\) 11.1345 0.443256 0.221628 0.975131i \(-0.428863\pi\)
0.221628 + 0.975131i \(0.428863\pi\)
\(632\) 0 0
\(633\) 2.31592 0.0920494
\(634\) 0 0
\(635\) 13.8756 0.550637
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 3.77414 0.149303
\(640\) 0 0
\(641\) −9.52274 −0.376126 −0.188063 0.982157i \(-0.560221\pi\)
−0.188063 + 0.982157i \(0.560221\pi\)
\(642\) 0 0
\(643\) 24.4989 0.966142 0.483071 0.875581i \(-0.339521\pi\)
0.483071 + 0.875581i \(0.339521\pi\)
\(644\) 0 0
\(645\) −40.5063 −1.59493
\(646\) 0 0
\(647\) 27.8307 1.09414 0.547069 0.837087i \(-0.315743\pi\)
0.547069 + 0.837087i \(0.315743\pi\)
\(648\) 0 0
\(649\) −7.41338 −0.291001
\(650\) 0 0
\(651\) 0.569544 0.0223222
\(652\) 0 0
\(653\) −7.00807 −0.274247 −0.137123 0.990554i \(-0.543786\pi\)
−0.137123 + 0.990554i \(0.543786\pi\)
\(654\) 0 0
\(655\) 33.4167 1.30570
\(656\) 0 0
\(657\) 16.4038 0.639975
\(658\) 0 0
\(659\) −21.7284 −0.846419 −0.423209 0.906032i \(-0.639097\pi\)
−0.423209 + 0.906032i \(0.639097\pi\)
\(660\) 0 0
\(661\) −23.5817 −0.917223 −0.458612 0.888637i \(-0.651653\pi\)
−0.458612 + 0.888637i \(0.651653\pi\)
\(662\) 0 0
\(663\) −6.64315 −0.257998
\(664\) 0 0
\(665\) 0.318003 0.0123316
\(666\) 0 0
\(667\) −16.3608 −0.633491
\(668\) 0 0
\(669\) −48.5727 −1.87793
\(670\) 0 0
\(671\) 6.36668 0.245783
\(672\) 0 0
\(673\) −6.49704 −0.250443 −0.125221 0.992129i \(-0.539964\pi\)
−0.125221 + 0.992129i \(0.539964\pi\)
\(674\) 0 0
\(675\) 37.6844 1.45047
\(676\) 0 0
\(677\) −21.8837 −0.841061 −0.420530 0.907279i \(-0.638156\pi\)
−0.420530 + 0.907279i \(0.638156\pi\)
\(678\) 0 0
\(679\) 1.39715 0.0536177
\(680\) 0 0
\(681\) −34.9412 −1.33895
\(682\) 0 0
\(683\) 14.9527 0.572148 0.286074 0.958207i \(-0.407650\pi\)
0.286074 + 0.958207i \(0.407650\pi\)
\(684\) 0 0
\(685\) 35.4106 1.35297
\(686\) 0 0
\(687\) 30.0141 1.14511
\(688\) 0 0
\(689\) 0.962428 0.0366656
\(690\) 0 0
\(691\) 17.8548 0.679229 0.339615 0.940565i \(-0.389703\pi\)
0.339615 + 0.940565i \(0.389703\pi\)
\(692\) 0 0
\(693\) 5.83476 0.221644
\(694\) 0 0
\(695\) 10.8124 0.410136
\(696\) 0 0
\(697\) −23.3623 −0.884911
\(698\) 0 0
\(699\) 61.7080 2.33401
\(700\) 0 0
\(701\) −26.1625 −0.988143 −0.494071 0.869421i \(-0.664492\pi\)
−0.494071 + 0.869421i \(0.664492\pi\)
\(702\) 0 0
\(703\) −0.625052 −0.0235743
\(704\) 0 0
\(705\) 39.3107 1.48053
\(706\) 0 0
\(707\) 13.2388 0.497897
\(708\) 0 0
\(709\) 38.3064 1.43863 0.719314 0.694685i \(-0.244456\pi\)
0.719314 + 0.694685i \(0.244456\pi\)
\(710\) 0 0
\(711\) −80.7877 −3.02978
\(712\) 0 0
\(713\) 0.558787 0.0209267
\(714\) 0 0
\(715\) −3.07774 −0.115101
\(716\) 0 0
\(717\) −38.9446 −1.45441
\(718\) 0 0
\(719\) 23.2718 0.867893 0.433946 0.900939i \(-0.357121\pi\)
0.433946 + 0.900939i \(0.357121\pi\)
\(720\) 0 0
\(721\) −9.76380 −0.363623
\(722\) 0 0
\(723\) 16.6744 0.620127
\(724\) 0 0
\(725\) 25.0920 0.931893
\(726\) 0 0
\(727\) −39.2543 −1.45586 −0.727931 0.685650i \(-0.759518\pi\)
−0.727931 + 0.685650i \(0.759518\pi\)
\(728\) 0 0
\(729\) −31.1383 −1.15327
\(730\) 0 0
\(731\) 9.89623 0.366025
\(732\) 0 0
\(733\) 14.0120 0.517544 0.258772 0.965938i \(-0.416682\pi\)
0.258772 + 0.965938i \(0.416682\pi\)
\(734\) 0 0
\(735\) −9.14806 −0.337431
\(736\) 0 0
\(737\) 10.9683 0.404021
\(738\) 0 0
\(739\) 26.3673 0.969935 0.484968 0.874532i \(-0.338831\pi\)
0.484968 + 0.874532i \(0.338831\pi\)
\(740\) 0 0
\(741\) −0.307112 −0.0112821
\(742\) 0 0
\(743\) −7.72910 −0.283553 −0.141777 0.989899i \(-0.545281\pi\)
−0.141777 + 0.989899i \(0.545281\pi\)
\(744\) 0 0
\(745\) 27.4992 1.00749
\(746\) 0 0
\(747\) 10.4742 0.383231
\(748\) 0 0
\(749\) −5.03968 −0.184146
\(750\) 0 0
\(751\) 28.5477 1.04172 0.520860 0.853642i \(-0.325611\pi\)
0.520860 + 0.853642i \(0.325611\pi\)
\(752\) 0 0
\(753\) −53.1523 −1.93698
\(754\) 0 0
\(755\) −8.42129 −0.306482
\(756\) 0 0
\(757\) 12.4235 0.451541 0.225770 0.974181i \(-0.427510\pi\)
0.225770 + 0.974181i \(0.427510\pi\)
\(758\) 0 0
\(759\) 8.66791 0.314625
\(760\) 0 0
\(761\) −40.9895 −1.48587 −0.742934 0.669365i \(-0.766566\pi\)
−0.742934 + 0.669365i \(0.766566\pi\)
\(762\) 0 0
\(763\) 10.5141 0.380635
\(764\) 0 0
\(765\) −40.1357 −1.45111
\(766\) 0 0
\(767\) −7.41338 −0.267682
\(768\) 0 0
\(769\) 11.9596 0.431276 0.215638 0.976473i \(-0.430817\pi\)
0.215638 + 0.976473i \(0.430817\pi\)
\(770\) 0 0
\(771\) −53.5139 −1.92726
\(772\) 0 0
\(773\) 30.1629 1.08488 0.542442 0.840093i \(-0.317500\pi\)
0.542442 + 0.840093i \(0.317500\pi\)
\(774\) 0 0
\(775\) −0.856994 −0.0307841
\(776\) 0 0
\(777\) 17.9810 0.645065
\(778\) 0 0
\(779\) −1.08004 −0.0386964
\(780\) 0 0
\(781\) −0.646837 −0.0231457
\(782\) 0 0
\(783\) 47.2716 1.68935
\(784\) 0 0
\(785\) −21.5325 −0.768526
\(786\) 0 0
\(787\) −25.0804 −0.894018 −0.447009 0.894529i \(-0.647511\pi\)
−0.447009 + 0.894529i \(0.647511\pi\)
\(788\) 0 0
\(789\) 62.5126 2.22551
\(790\) 0 0
\(791\) 0.483443 0.0171893
\(792\) 0 0
\(793\) 6.36668 0.226087
\(794\) 0 0
\(795\) 8.80436 0.312258
\(796\) 0 0
\(797\) 8.08469 0.286374 0.143187 0.989696i \(-0.454265\pi\)
0.143187 + 0.989696i \(0.454265\pi\)
\(798\) 0 0
\(799\) −9.60412 −0.339769
\(800\) 0 0
\(801\) 17.0479 0.602360
\(802\) 0 0
\(803\) −2.81140 −0.0992121
\(804\) 0 0
\(805\) −8.97529 −0.316337
\(806\) 0 0
\(807\) 63.9399 2.25079
\(808\) 0 0
\(809\) −21.0463 −0.739948 −0.369974 0.929042i \(-0.620633\pi\)
−0.369974 + 0.929042i \(0.620633\pi\)
\(810\) 0 0
\(811\) 44.2012 1.55211 0.776057 0.630663i \(-0.217217\pi\)
0.776057 + 0.630663i \(0.217217\pi\)
\(812\) 0 0
\(813\) 7.94545 0.278659
\(814\) 0 0
\(815\) 16.0020 0.560525
\(816\) 0 0
\(817\) 0.457502 0.0160060
\(818\) 0 0
\(819\) 5.83476 0.203883
\(820\) 0 0
\(821\) 19.4852 0.680039 0.340020 0.940418i \(-0.389566\pi\)
0.340020 + 0.940418i \(0.389566\pi\)
\(822\) 0 0
\(823\) −8.93217 −0.311356 −0.155678 0.987808i \(-0.549756\pi\)
−0.155678 + 0.987808i \(0.549756\pi\)
\(824\) 0 0
\(825\) −13.2937 −0.462827
\(826\) 0 0
\(827\) −13.5672 −0.471779 −0.235890 0.971780i \(-0.575800\pi\)
−0.235890 + 0.971780i \(0.575800\pi\)
\(828\) 0 0
\(829\) −44.8746 −1.55856 −0.779279 0.626677i \(-0.784415\pi\)
−0.779279 + 0.626677i \(0.784415\pi\)
\(830\) 0 0
\(831\) 21.9158 0.760249
\(832\) 0 0
\(833\) 2.23499 0.0774380
\(834\) 0 0
\(835\) 69.4468 2.40331
\(836\) 0 0
\(837\) −1.61452 −0.0558060
\(838\) 0 0
\(839\) 11.8501 0.409111 0.204556 0.978855i \(-0.434425\pi\)
0.204556 + 0.978855i \(0.434425\pi\)
\(840\) 0 0
\(841\) 2.47554 0.0853635
\(842\) 0 0
\(843\) −16.1270 −0.555442
\(844\) 0 0
\(845\) −3.07774 −0.105877
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) 0 0
\(849\) 40.8527 1.40206
\(850\) 0 0
\(851\) 17.6414 0.604740
\(852\) 0 0
\(853\) 14.0146 0.479850 0.239925 0.970791i \(-0.422877\pi\)
0.239925 + 0.970791i \(0.422877\pi\)
\(854\) 0 0
\(855\) −1.85547 −0.0634559
\(856\) 0 0
\(857\) −44.1020 −1.50650 −0.753248 0.657737i \(-0.771514\pi\)
−0.753248 + 0.657737i \(0.771514\pi\)
\(858\) 0 0
\(859\) 46.0462 1.57108 0.785539 0.618812i \(-0.212386\pi\)
0.785539 + 0.618812i \(0.212386\pi\)
\(860\) 0 0
\(861\) 31.0697 1.05885
\(862\) 0 0
\(863\) 19.6060 0.667396 0.333698 0.942680i \(-0.391703\pi\)
0.333698 + 0.942680i \(0.391703\pi\)
\(864\) 0 0
\(865\) 71.1536 2.41929
\(866\) 0 0
\(867\) −35.6823 −1.21183
\(868\) 0 0
\(869\) 13.8459 0.469691
\(870\) 0 0
\(871\) 10.9683 0.371646
\(872\) 0 0
\(873\) −8.15204 −0.275905
\(874\) 0 0
\(875\) −1.62357 −0.0548868
\(876\) 0 0
\(877\) −31.2707 −1.05594 −0.527968 0.849264i \(-0.677046\pi\)
−0.527968 + 0.849264i \(0.677046\pi\)
\(878\) 0 0
\(879\) 14.9412 0.503954
\(880\) 0 0
\(881\) −44.1429 −1.48721 −0.743606 0.668618i \(-0.766886\pi\)
−0.743606 + 0.668618i \(0.766886\pi\)
\(882\) 0 0
\(883\) 5.06210 0.170353 0.0851767 0.996366i \(-0.472855\pi\)
0.0851767 + 0.996366i \(0.472855\pi\)
\(884\) 0 0
\(885\) −67.8181 −2.27968
\(886\) 0 0
\(887\) 8.15920 0.273959 0.136980 0.990574i \(-0.456261\pi\)
0.136980 + 0.990574i \(0.456261\pi\)
\(888\) 0 0
\(889\) 4.50838 0.151206
\(890\) 0 0
\(891\) −7.54015 −0.252605
\(892\) 0 0
\(893\) −0.443998 −0.0148578
\(894\) 0 0
\(895\) 52.4178 1.75213
\(896\) 0 0
\(897\) 8.66791 0.289413
\(898\) 0 0
\(899\) −1.07502 −0.0358539
\(900\) 0 0
\(901\) −2.15102 −0.0716609
\(902\) 0 0
\(903\) −13.1611 −0.437972
\(904\) 0 0
\(905\) 6.48510 0.215572
\(906\) 0 0
\(907\) 33.9941 1.12876 0.564378 0.825517i \(-0.309116\pi\)
0.564378 + 0.825517i \(0.309116\pi\)
\(908\) 0 0
\(909\) −77.2454 −2.56207
\(910\) 0 0
\(911\) −55.5974 −1.84202 −0.921012 0.389534i \(-0.872636\pi\)
−0.921012 + 0.389534i \(0.872636\pi\)
\(912\) 0 0
\(913\) −1.79514 −0.0594104
\(914\) 0 0
\(915\) 58.2428 1.92545
\(916\) 0 0
\(917\) 10.8575 0.358547
\(918\) 0 0
\(919\) −11.5725 −0.381741 −0.190870 0.981615i \(-0.561131\pi\)
−0.190870 + 0.981615i \(0.561131\pi\)
\(920\) 0 0
\(921\) 103.134 3.39838
\(922\) 0 0
\(923\) −0.646837 −0.0212909
\(924\) 0 0
\(925\) −27.0561 −0.889598
\(926\) 0 0
\(927\) 56.9694 1.87112
\(928\) 0 0
\(929\) 21.2354 0.696712 0.348356 0.937362i \(-0.386740\pi\)
0.348356 + 0.937362i \(0.386740\pi\)
\(930\) 0 0
\(931\) 0.103324 0.00338630
\(932\) 0 0
\(933\) 46.6868 1.52846
\(934\) 0 0
\(935\) 6.87873 0.224958
\(936\) 0 0
\(937\) −17.8920 −0.584505 −0.292253 0.956341i \(-0.594405\pi\)
−0.292253 + 0.956341i \(0.594405\pi\)
\(938\) 0 0
\(939\) −36.5737 −1.19354
\(940\) 0 0
\(941\) −16.7344 −0.545526 −0.272763 0.962081i \(-0.587937\pi\)
−0.272763 + 0.962081i \(0.587937\pi\)
\(942\) 0 0
\(943\) 30.4829 0.992660
\(944\) 0 0
\(945\) 25.9326 0.843587
\(946\) 0 0
\(947\) −6.43614 −0.209147 −0.104573 0.994517i \(-0.533348\pi\)
−0.104573 + 0.994517i \(0.533348\pi\)
\(948\) 0 0
\(949\) −2.81140 −0.0912619
\(950\) 0 0
\(951\) −54.9183 −1.78085
\(952\) 0 0
\(953\) 47.0679 1.52468 0.762339 0.647177i \(-0.224051\pi\)
0.762339 + 0.647177i \(0.224051\pi\)
\(954\) 0 0
\(955\) 34.5340 1.11750
\(956\) 0 0
\(957\) −16.6757 −0.539049
\(958\) 0 0
\(959\) 11.5054 0.371528
\(960\) 0 0
\(961\) −30.9633 −0.998816
\(962\) 0 0
\(963\) 29.4053 0.947574
\(964\) 0 0
\(965\) −44.7393 −1.44021
\(966\) 0 0
\(967\) 34.9496 1.12390 0.561952 0.827170i \(-0.310051\pi\)
0.561952 + 0.827170i \(0.310051\pi\)
\(968\) 0 0
\(969\) 0.686395 0.0220502
\(970\) 0 0
\(971\) 22.8109 0.732037 0.366018 0.930608i \(-0.380721\pi\)
0.366018 + 0.930608i \(0.380721\pi\)
\(972\) 0 0
\(973\) 3.51308 0.112624
\(974\) 0 0
\(975\) −13.2937 −0.425739
\(976\) 0 0
\(977\) −34.7413 −1.11147 −0.555736 0.831359i \(-0.687564\pi\)
−0.555736 + 0.831359i \(0.687564\pi\)
\(978\) 0 0
\(979\) −2.92179 −0.0933808
\(980\) 0 0
\(981\) −61.3470 −1.95866
\(982\) 0 0
\(983\) −3.76311 −0.120025 −0.0600123 0.998198i \(-0.519114\pi\)
−0.0600123 + 0.998198i \(0.519114\pi\)
\(984\) 0 0
\(985\) −32.0278 −1.02049
\(986\) 0 0
\(987\) 12.7726 0.406556
\(988\) 0 0
\(989\) −12.9125 −0.410593
\(990\) 0 0
\(991\) 36.6661 1.16474 0.582368 0.812925i \(-0.302126\pi\)
0.582368 + 0.812925i \(0.302126\pi\)
\(992\) 0 0
\(993\) −52.0734 −1.65250
\(994\) 0 0
\(995\) −38.4219 −1.21806
\(996\) 0 0
\(997\) 12.3542 0.391261 0.195631 0.980678i \(-0.437325\pi\)
0.195631 + 0.980678i \(0.437325\pi\)
\(998\) 0 0
\(999\) −50.9718 −1.61268
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 \(a_p\))