Properties

Label 4012.2.a.g.1.2
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.43162\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.43162 q^{3}\) \(-0.659543 q^{5}\) \(+4.52406 q^{7}\) \(+2.91279 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.43162 q^{3}\) \(-0.659543 q^{5}\) \(+4.52406 q^{7}\) \(+2.91279 q^{9}\) \(+0.926475 q^{11}\) \(+3.23177 q^{13}\) \(+1.60376 q^{15}\) \(-1.00000 q^{17}\) \(-5.97818 q^{19}\) \(-11.0008 q^{21}\) \(+1.60970 q^{23}\) \(-4.56500 q^{25}\) \(+0.212065 q^{27}\) \(-9.97474 q^{29}\) \(-9.56778 q^{31}\) \(-2.25284 q^{33}\) \(-2.98381 q^{35}\) \(+7.27511 q^{37}\) \(-7.85845 q^{39}\) \(-5.10111 q^{41}\) \(+3.90210 q^{43}\) \(-1.92111 q^{45}\) \(-10.6913 q^{47}\) \(+13.4671 q^{49}\) \(+2.43162 q^{51}\) \(+6.72672 q^{53}\) \(-0.611049 q^{55}\) \(+14.5367 q^{57}\) \(+1.00000 q^{59}\) \(+11.7849 q^{61}\) \(+13.1776 q^{63}\) \(-2.13149 q^{65}\) \(+8.56754 q^{67}\) \(-3.91418 q^{69}\) \(+3.27076 q^{71}\) \(-10.1628 q^{73}\) \(+11.1004 q^{75}\) \(+4.19143 q^{77}\) \(+1.91728 q^{79}\) \(-9.25403 q^{81}\) \(-7.51691 q^{83}\) \(+0.659543 q^{85}\) \(+24.2548 q^{87}\) \(-10.3308 q^{89}\) \(+14.6207 q^{91}\) \(+23.2652 q^{93}\) \(+3.94287 q^{95}\) \(-8.67239 q^{97}\) \(+2.69862 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.43162 −1.40390 −0.701949 0.712227i \(-0.747687\pi\)
−0.701949 + 0.712227i \(0.747687\pi\)
\(4\) 0 0
\(5\) −0.659543 −0.294956 −0.147478 0.989065i \(-0.547116\pi\)
−0.147478 + 0.989065i \(0.547116\pi\)
\(6\) 0 0
\(7\) 4.52406 1.70993 0.854967 0.518682i \(-0.173577\pi\)
0.854967 + 0.518682i \(0.173577\pi\)
\(8\) 0 0
\(9\) 2.91279 0.970930
\(10\) 0 0
\(11\) 0.926475 0.279343 0.139671 0.990198i \(-0.455395\pi\)
0.139671 + 0.990198i \(0.455395\pi\)
\(12\) 0 0
\(13\) 3.23177 0.896333 0.448166 0.893950i \(-0.352077\pi\)
0.448166 + 0.893950i \(0.352077\pi\)
\(14\) 0 0
\(15\) 1.60376 0.414089
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −5.97818 −1.37149 −0.685745 0.727842i \(-0.740523\pi\)
−0.685745 + 0.727842i \(0.740523\pi\)
\(20\) 0 0
\(21\) −11.0008 −2.40057
\(22\) 0 0
\(23\) 1.60970 0.335646 0.167823 0.985817i \(-0.446326\pi\)
0.167823 + 0.985817i \(0.446326\pi\)
\(24\) 0 0
\(25\) −4.56500 −0.913001
\(26\) 0 0
\(27\) 0.212065 0.0408120
\(28\) 0 0
\(29\) −9.97474 −1.85226 −0.926131 0.377202i \(-0.876886\pi\)
−0.926131 + 0.377202i \(0.876886\pi\)
\(30\) 0 0
\(31\) −9.56778 −1.71842 −0.859212 0.511620i \(-0.829046\pi\)
−0.859212 + 0.511620i \(0.829046\pi\)
\(32\) 0 0
\(33\) −2.25284 −0.392169
\(34\) 0 0
\(35\) −2.98381 −0.504356
\(36\) 0 0
\(37\) 7.27511 1.19602 0.598010 0.801488i \(-0.295958\pi\)
0.598010 + 0.801488i \(0.295958\pi\)
\(38\) 0 0
\(39\) −7.85845 −1.25836
\(40\) 0 0
\(41\) −5.10111 −0.796660 −0.398330 0.917242i \(-0.630410\pi\)
−0.398330 + 0.917242i \(0.630410\pi\)
\(42\) 0 0
\(43\) 3.90210 0.595065 0.297533 0.954712i \(-0.403836\pi\)
0.297533 + 0.954712i \(0.403836\pi\)
\(44\) 0 0
\(45\) −1.92111 −0.286382
\(46\) 0 0
\(47\) −10.6913 −1.55948 −0.779742 0.626101i \(-0.784650\pi\)
−0.779742 + 0.626101i \(0.784650\pi\)
\(48\) 0 0
\(49\) 13.4671 1.92388
\(50\) 0 0
\(51\) 2.43162 0.340495
\(52\) 0 0
\(53\) 6.72672 0.923987 0.461993 0.886883i \(-0.347134\pi\)
0.461993 + 0.886883i \(0.347134\pi\)
\(54\) 0 0
\(55\) −0.611049 −0.0823939
\(56\) 0 0
\(57\) 14.5367 1.92543
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 11.7849 1.50890 0.754451 0.656357i \(-0.227903\pi\)
0.754451 + 0.656357i \(0.227903\pi\)
\(62\) 0 0
\(63\) 13.1776 1.66023
\(64\) 0 0
\(65\) −2.13149 −0.264379
\(66\) 0 0
\(67\) 8.56754 1.04669 0.523346 0.852121i \(-0.324684\pi\)
0.523346 + 0.852121i \(0.324684\pi\)
\(68\) 0 0
\(69\) −3.91418 −0.471212
\(70\) 0 0
\(71\) 3.27076 0.388168 0.194084 0.980985i \(-0.437827\pi\)
0.194084 + 0.980985i \(0.437827\pi\)
\(72\) 0 0
\(73\) −10.1628 −1.18946 −0.594731 0.803925i \(-0.702741\pi\)
−0.594731 + 0.803925i \(0.702741\pi\)
\(74\) 0 0
\(75\) 11.1004 1.28176
\(76\) 0 0
\(77\) 4.19143 0.477658
\(78\) 0 0
\(79\) 1.91728 0.215711 0.107855 0.994167i \(-0.465602\pi\)
0.107855 + 0.994167i \(0.465602\pi\)
\(80\) 0 0
\(81\) −9.25403 −1.02823
\(82\) 0 0
\(83\) −7.51691 −0.825089 −0.412544 0.910938i \(-0.635360\pi\)
−0.412544 + 0.910938i \(0.635360\pi\)
\(84\) 0 0
\(85\) 0.659543 0.0715374
\(86\) 0 0
\(87\) 24.2548 2.60039
\(88\) 0 0
\(89\) −10.3308 −1.09507 −0.547534 0.836784i \(-0.684433\pi\)
−0.547534 + 0.836784i \(0.684433\pi\)
\(90\) 0 0
\(91\) 14.6207 1.53267
\(92\) 0 0
\(93\) 23.2652 2.41249
\(94\) 0 0
\(95\) 3.94287 0.404530
\(96\) 0 0
\(97\) −8.67239 −0.880548 −0.440274 0.897864i \(-0.645119\pi\)
−0.440274 + 0.897864i \(0.645119\pi\)
\(98\) 0 0
\(99\) 2.69862 0.271222
\(100\) 0 0
\(101\) −0.575188 −0.0572333 −0.0286167 0.999590i \(-0.509110\pi\)
−0.0286167 + 0.999590i \(0.509110\pi\)
\(102\) 0 0
\(103\) 0.613304 0.0604307 0.0302153 0.999543i \(-0.490381\pi\)
0.0302153 + 0.999543i \(0.490381\pi\)
\(104\) 0 0
\(105\) 7.25550 0.708065
\(106\) 0 0
\(107\) −1.21744 −0.117694 −0.0588471 0.998267i \(-0.518742\pi\)
−0.0588471 + 0.998267i \(0.518742\pi\)
\(108\) 0 0
\(109\) −16.7472 −1.60409 −0.802044 0.597265i \(-0.796254\pi\)
−0.802044 + 0.597265i \(0.796254\pi\)
\(110\) 0 0
\(111\) −17.6903 −1.67909
\(112\) 0 0
\(113\) −1.50728 −0.141793 −0.0708964 0.997484i \(-0.522586\pi\)
−0.0708964 + 0.997484i \(0.522586\pi\)
\(114\) 0 0
\(115\) −1.06167 −0.0990008
\(116\) 0 0
\(117\) 9.41347 0.870276
\(118\) 0 0
\(119\) −4.52406 −0.414720
\(120\) 0 0
\(121\) −10.1416 −0.921968
\(122\) 0 0
\(123\) 12.4040 1.11843
\(124\) 0 0
\(125\) 6.30853 0.564252
\(126\) 0 0
\(127\) −6.53260 −0.579674 −0.289837 0.957076i \(-0.593601\pi\)
−0.289837 + 0.957076i \(0.593601\pi\)
\(128\) 0 0
\(129\) −9.48844 −0.835411
\(130\) 0 0
\(131\) −15.7524 −1.37629 −0.688145 0.725573i \(-0.741575\pi\)
−0.688145 + 0.725573i \(0.741575\pi\)
\(132\) 0 0
\(133\) −27.0457 −2.34516
\(134\) 0 0
\(135\) −0.139866 −0.0120378
\(136\) 0 0
\(137\) 16.4626 1.40650 0.703249 0.710943i \(-0.251732\pi\)
0.703249 + 0.710943i \(0.251732\pi\)
\(138\) 0 0
\(139\) −12.9745 −1.10048 −0.550241 0.835006i \(-0.685464\pi\)
−0.550241 + 0.835006i \(0.685464\pi\)
\(140\) 0 0
\(141\) 25.9972 2.18936
\(142\) 0 0
\(143\) 2.99416 0.250384
\(144\) 0 0
\(145\) 6.57876 0.546337
\(146\) 0 0
\(147\) −32.7470 −2.70093
\(148\) 0 0
\(149\) 12.1896 0.998613 0.499307 0.866425i \(-0.333588\pi\)
0.499307 + 0.866425i \(0.333588\pi\)
\(150\) 0 0
\(151\) −10.1800 −0.828440 −0.414220 0.910177i \(-0.635946\pi\)
−0.414220 + 0.910177i \(0.635946\pi\)
\(152\) 0 0
\(153\) −2.91279 −0.235485
\(154\) 0 0
\(155\) 6.31036 0.506860
\(156\) 0 0
\(157\) 24.4088 1.94803 0.974017 0.226475i \(-0.0727202\pi\)
0.974017 + 0.226475i \(0.0727202\pi\)
\(158\) 0 0
\(159\) −16.3569 −1.29718
\(160\) 0 0
\(161\) 7.28238 0.573932
\(162\) 0 0
\(163\) 12.7751 1.00062 0.500310 0.865846i \(-0.333219\pi\)
0.500310 + 0.865846i \(0.333219\pi\)
\(164\) 0 0
\(165\) 1.48584 0.115673
\(166\) 0 0
\(167\) −13.8864 −1.07456 −0.537282 0.843403i \(-0.680549\pi\)
−0.537282 + 0.843403i \(0.680549\pi\)
\(168\) 0 0
\(169\) −2.55564 −0.196588
\(170\) 0 0
\(171\) −17.4132 −1.33162
\(172\) 0 0
\(173\) 21.9279 1.66714 0.833572 0.552410i \(-0.186292\pi\)
0.833572 + 0.552410i \(0.186292\pi\)
\(174\) 0 0
\(175\) −20.6524 −1.56117
\(176\) 0 0
\(177\) −2.43162 −0.182772
\(178\) 0 0
\(179\) −18.0677 −1.35044 −0.675220 0.737616i \(-0.735951\pi\)
−0.675220 + 0.737616i \(0.735951\pi\)
\(180\) 0 0
\(181\) 1.16416 0.0865311 0.0432656 0.999064i \(-0.486224\pi\)
0.0432656 + 0.999064i \(0.486224\pi\)
\(182\) 0 0
\(183\) −28.6564 −2.11834
\(184\) 0 0
\(185\) −4.79824 −0.352774
\(186\) 0 0
\(187\) −0.926475 −0.0677505
\(188\) 0 0
\(189\) 0.959397 0.0697858
\(190\) 0 0
\(191\) −3.22483 −0.233340 −0.116670 0.993171i \(-0.537222\pi\)
−0.116670 + 0.993171i \(0.537222\pi\)
\(192\) 0 0
\(193\) 8.61564 0.620167 0.310084 0.950709i \(-0.399643\pi\)
0.310084 + 0.950709i \(0.399643\pi\)
\(194\) 0 0
\(195\) 5.18298 0.371161
\(196\) 0 0
\(197\) −20.4722 −1.45859 −0.729294 0.684201i \(-0.760151\pi\)
−0.729294 + 0.684201i \(0.760151\pi\)
\(198\) 0 0
\(199\) −8.87410 −0.629068 −0.314534 0.949246i \(-0.601848\pi\)
−0.314534 + 0.949246i \(0.601848\pi\)
\(200\) 0 0
\(201\) −20.8330 −1.46945
\(202\) 0 0
\(203\) −45.1263 −3.16725
\(204\) 0 0
\(205\) 3.36440 0.234980
\(206\) 0 0
\(207\) 4.68871 0.325888
\(208\) 0 0
\(209\) −5.53864 −0.383115
\(210\) 0 0
\(211\) 13.3596 0.919714 0.459857 0.887993i \(-0.347901\pi\)
0.459857 + 0.887993i \(0.347901\pi\)
\(212\) 0 0
\(213\) −7.95326 −0.544948
\(214\) 0 0
\(215\) −2.57360 −0.175518
\(216\) 0 0
\(217\) −43.2852 −2.93839
\(218\) 0 0
\(219\) 24.7120 1.66988
\(220\) 0 0
\(221\) −3.23177 −0.217393
\(222\) 0 0
\(223\) 3.53538 0.236747 0.118373 0.992969i \(-0.462232\pi\)
0.118373 + 0.992969i \(0.462232\pi\)
\(224\) 0 0
\(225\) −13.2969 −0.886459
\(226\) 0 0
\(227\) −1.71094 −0.113559 −0.0567795 0.998387i \(-0.518083\pi\)
−0.0567795 + 0.998387i \(0.518083\pi\)
\(228\) 0 0
\(229\) −17.1742 −1.13491 −0.567453 0.823406i \(-0.692071\pi\)
−0.567453 + 0.823406i \(0.692071\pi\)
\(230\) 0 0
\(231\) −10.1920 −0.670583
\(232\) 0 0
\(233\) 2.81952 0.184713 0.0923563 0.995726i \(-0.470560\pi\)
0.0923563 + 0.995726i \(0.470560\pi\)
\(234\) 0 0
\(235\) 7.05136 0.459980
\(236\) 0 0
\(237\) −4.66209 −0.302836
\(238\) 0 0
\(239\) −30.2810 −1.95872 −0.979359 0.202128i \(-0.935214\pi\)
−0.979359 + 0.202128i \(0.935214\pi\)
\(240\) 0 0
\(241\) 28.8307 1.85715 0.928573 0.371150i \(-0.121037\pi\)
0.928573 + 0.371150i \(0.121037\pi\)
\(242\) 0 0
\(243\) 21.8661 1.40271
\(244\) 0 0
\(245\) −8.88215 −0.567460
\(246\) 0 0
\(247\) −19.3201 −1.22931
\(248\) 0 0
\(249\) 18.2783 1.15834
\(250\) 0 0
\(251\) −10.4833 −0.661703 −0.330851 0.943683i \(-0.607336\pi\)
−0.330851 + 0.943683i \(0.607336\pi\)
\(252\) 0 0
\(253\) 1.49135 0.0937601
\(254\) 0 0
\(255\) −1.60376 −0.100431
\(256\) 0 0
\(257\) 17.3095 1.07974 0.539868 0.841750i \(-0.318474\pi\)
0.539868 + 0.841750i \(0.318474\pi\)
\(258\) 0 0
\(259\) 32.9130 2.04512
\(260\) 0 0
\(261\) −29.0543 −1.79842
\(262\) 0 0
\(263\) −17.9275 −1.10546 −0.552729 0.833361i \(-0.686413\pi\)
−0.552729 + 0.833361i \(0.686413\pi\)
\(264\) 0 0
\(265\) −4.43656 −0.272536
\(266\) 0 0
\(267\) 25.1207 1.53736
\(268\) 0 0
\(269\) 7.25146 0.442129 0.221065 0.975259i \(-0.429047\pi\)
0.221065 + 0.975259i \(0.429047\pi\)
\(270\) 0 0
\(271\) −3.27173 −0.198743 −0.0993716 0.995050i \(-0.531683\pi\)
−0.0993716 + 0.995050i \(0.531683\pi\)
\(272\) 0 0
\(273\) −35.5521 −2.15171
\(274\) 0 0
\(275\) −4.22936 −0.255040
\(276\) 0 0
\(277\) 32.3349 1.94282 0.971408 0.237415i \(-0.0763000\pi\)
0.971408 + 0.237415i \(0.0763000\pi\)
\(278\) 0 0
\(279\) −27.8689 −1.66847
\(280\) 0 0
\(281\) 21.3290 1.27238 0.636190 0.771533i \(-0.280510\pi\)
0.636190 + 0.771533i \(0.280510\pi\)
\(282\) 0 0
\(283\) 4.94883 0.294177 0.147089 0.989123i \(-0.453010\pi\)
0.147089 + 0.989123i \(0.453010\pi\)
\(284\) 0 0
\(285\) −9.58756 −0.567918
\(286\) 0 0
\(287\) −23.0777 −1.36224
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 21.0880 1.23620
\(292\) 0 0
\(293\) −14.0323 −0.819774 −0.409887 0.912136i \(-0.634432\pi\)
−0.409887 + 0.912136i \(0.634432\pi\)
\(294\) 0 0
\(295\) −0.659543 −0.0384001
\(296\) 0 0
\(297\) 0.196473 0.0114005
\(298\) 0 0
\(299\) 5.20218 0.300850
\(300\) 0 0
\(301\) 17.6534 1.01752
\(302\) 0 0
\(303\) 1.39864 0.0803497
\(304\) 0 0
\(305\) −7.77264 −0.445060
\(306\) 0 0
\(307\) −8.50528 −0.485422 −0.242711 0.970099i \(-0.578037\pi\)
−0.242711 + 0.970099i \(0.578037\pi\)
\(308\) 0 0
\(309\) −1.49132 −0.0848385
\(310\) 0 0
\(311\) −30.3572 −1.72140 −0.860699 0.509115i \(-0.829973\pi\)
−0.860699 + 0.509115i \(0.829973\pi\)
\(312\) 0 0
\(313\) 1.10775 0.0626137 0.0313068 0.999510i \(-0.490033\pi\)
0.0313068 + 0.999510i \(0.490033\pi\)
\(314\) 0 0
\(315\) −8.69121 −0.489694
\(316\) 0 0
\(317\) −15.8068 −0.887798 −0.443899 0.896077i \(-0.646405\pi\)
−0.443899 + 0.896077i \(0.646405\pi\)
\(318\) 0 0
\(319\) −9.24134 −0.517416
\(320\) 0 0
\(321\) 2.96035 0.165231
\(322\) 0 0
\(323\) 5.97818 0.332635
\(324\) 0 0
\(325\) −14.7531 −0.818352
\(326\) 0 0
\(327\) 40.7228 2.25198
\(328\) 0 0
\(329\) −48.3680 −2.66662
\(330\) 0 0
\(331\) −13.8429 −0.760875 −0.380437 0.924807i \(-0.624227\pi\)
−0.380437 + 0.924807i \(0.624227\pi\)
\(332\) 0 0
\(333\) 21.1909 1.16125
\(334\) 0 0
\(335\) −5.65065 −0.308728
\(336\) 0 0
\(337\) −14.7012 −0.800826 −0.400413 0.916335i \(-0.631133\pi\)
−0.400413 + 0.916335i \(0.631133\pi\)
\(338\) 0 0
\(339\) 3.66513 0.199063
\(340\) 0 0
\(341\) −8.86430 −0.480029
\(342\) 0 0
\(343\) 29.2577 1.57977
\(344\) 0 0
\(345\) 2.58157 0.138987
\(346\) 0 0
\(347\) −24.7768 −1.33009 −0.665044 0.746804i \(-0.731587\pi\)
−0.665044 + 0.746804i \(0.731587\pi\)
\(348\) 0 0
\(349\) −33.3293 −1.78408 −0.892038 0.451960i \(-0.850725\pi\)
−0.892038 + 0.451960i \(0.850725\pi\)
\(350\) 0 0
\(351\) 0.685347 0.0365811
\(352\) 0 0
\(353\) −2.86087 −0.152269 −0.0761343 0.997098i \(-0.524258\pi\)
−0.0761343 + 0.997098i \(0.524258\pi\)
\(354\) 0 0
\(355\) −2.15721 −0.114493
\(356\) 0 0
\(357\) 11.0008 0.582225
\(358\) 0 0
\(359\) −16.4655 −0.869014 −0.434507 0.900668i \(-0.643077\pi\)
−0.434507 + 0.900668i \(0.643077\pi\)
\(360\) 0 0
\(361\) 16.7387 0.880983
\(362\) 0 0
\(363\) 24.6607 1.29435
\(364\) 0 0
\(365\) 6.70277 0.350839
\(366\) 0 0
\(367\) 4.06526 0.212205 0.106102 0.994355i \(-0.466163\pi\)
0.106102 + 0.994355i \(0.466163\pi\)
\(368\) 0 0
\(369\) −14.8585 −0.773500
\(370\) 0 0
\(371\) 30.4321 1.57996
\(372\) 0 0
\(373\) −1.59492 −0.0825818 −0.0412909 0.999147i \(-0.513147\pi\)
−0.0412909 + 0.999147i \(0.513147\pi\)
\(374\) 0 0
\(375\) −15.3400 −0.792152
\(376\) 0 0
\(377\) −32.2361 −1.66024
\(378\) 0 0
\(379\) −6.89588 −0.354218 −0.177109 0.984191i \(-0.556674\pi\)
−0.177109 + 0.984191i \(0.556674\pi\)
\(380\) 0 0
\(381\) 15.8848 0.813804
\(382\) 0 0
\(383\) −25.7469 −1.31560 −0.657802 0.753191i \(-0.728514\pi\)
−0.657802 + 0.753191i \(0.728514\pi\)
\(384\) 0 0
\(385\) −2.76443 −0.140888
\(386\) 0 0
\(387\) 11.3660 0.577766
\(388\) 0 0
\(389\) 20.2675 1.02760 0.513801 0.857910i \(-0.328237\pi\)
0.513801 + 0.857910i \(0.328237\pi\)
\(390\) 0 0
\(391\) −1.60970 −0.0814060
\(392\) 0 0
\(393\) 38.3038 1.93217
\(394\) 0 0
\(395\) −1.26453 −0.0636252
\(396\) 0 0
\(397\) −1.26935 −0.0637069 −0.0318534 0.999493i \(-0.510141\pi\)
−0.0318534 + 0.999493i \(0.510141\pi\)
\(398\) 0 0
\(399\) 65.7649 3.29236
\(400\) 0 0
\(401\) 4.91694 0.245540 0.122770 0.992435i \(-0.460822\pi\)
0.122770 + 0.992435i \(0.460822\pi\)
\(402\) 0 0
\(403\) −30.9209 −1.54028
\(404\) 0 0
\(405\) 6.10343 0.303282
\(406\) 0 0
\(407\) 6.74020 0.334099
\(408\) 0 0
\(409\) 12.0913 0.597877 0.298939 0.954272i \(-0.403367\pi\)
0.298939 + 0.954272i \(0.403367\pi\)
\(410\) 0 0
\(411\) −40.0309 −1.97458
\(412\) 0 0
\(413\) 4.52406 0.222615
\(414\) 0 0
\(415\) 4.95772 0.243365
\(416\) 0 0
\(417\) 31.5491 1.54497
\(418\) 0 0
\(419\) 19.4653 0.950944 0.475472 0.879731i \(-0.342277\pi\)
0.475472 + 0.879731i \(0.342277\pi\)
\(420\) 0 0
\(421\) −14.5271 −0.708007 −0.354003 0.935244i \(-0.615180\pi\)
−0.354003 + 0.935244i \(0.615180\pi\)
\(422\) 0 0
\(423\) −31.1415 −1.51415
\(424\) 0 0
\(425\) 4.56500 0.221435
\(426\) 0 0
\(427\) 53.3156 2.58012
\(428\) 0 0
\(429\) −7.28066 −0.351513
\(430\) 0 0
\(431\) −18.3916 −0.885894 −0.442947 0.896548i \(-0.646067\pi\)
−0.442947 + 0.896548i \(0.646067\pi\)
\(432\) 0 0
\(433\) −22.5998 −1.08608 −0.543038 0.839708i \(-0.682726\pi\)
−0.543038 + 0.839708i \(0.682726\pi\)
\(434\) 0 0
\(435\) −15.9971 −0.767001
\(436\) 0 0
\(437\) −9.62308 −0.460334
\(438\) 0 0
\(439\) −1.53199 −0.0731179 −0.0365590 0.999331i \(-0.511640\pi\)
−0.0365590 + 0.999331i \(0.511640\pi\)
\(440\) 0 0
\(441\) 39.2269 1.86795
\(442\) 0 0
\(443\) −38.5765 −1.83282 −0.916412 0.400236i \(-0.868928\pi\)
−0.916412 + 0.400236i \(0.868928\pi\)
\(444\) 0 0
\(445\) 6.81363 0.322997
\(446\) 0 0
\(447\) −29.6406 −1.40195
\(448\) 0 0
\(449\) 2.33464 0.110178 0.0550892 0.998481i \(-0.482456\pi\)
0.0550892 + 0.998481i \(0.482456\pi\)
\(450\) 0 0
\(451\) −4.72605 −0.222541
\(452\) 0 0
\(453\) 24.7540 1.16305
\(454\) 0 0
\(455\) −9.64300 −0.452071
\(456\) 0 0
\(457\) 31.7737 1.48631 0.743155 0.669119i \(-0.233329\pi\)
0.743155 + 0.669119i \(0.233329\pi\)
\(458\) 0 0
\(459\) −0.212065 −0.00989836
\(460\) 0 0
\(461\) −29.1108 −1.35582 −0.677912 0.735143i \(-0.737115\pi\)
−0.677912 + 0.735143i \(0.737115\pi\)
\(462\) 0 0
\(463\) −26.7217 −1.24186 −0.620932 0.783865i \(-0.713246\pi\)
−0.620932 + 0.783865i \(0.713246\pi\)
\(464\) 0 0
\(465\) −15.3444 −0.711580
\(466\) 0 0
\(467\) 6.05007 0.279964 0.139982 0.990154i \(-0.455296\pi\)
0.139982 + 0.990154i \(0.455296\pi\)
\(468\) 0 0
\(469\) 38.7601 1.78977
\(470\) 0 0
\(471\) −59.3530 −2.73484
\(472\) 0 0
\(473\) 3.61520 0.166227
\(474\) 0 0
\(475\) 27.2904 1.25217
\(476\) 0 0
\(477\) 19.5935 0.897126
\(478\) 0 0
\(479\) −10.7376 −0.490611 −0.245306 0.969446i \(-0.578888\pi\)
−0.245306 + 0.969446i \(0.578888\pi\)
\(480\) 0 0
\(481\) 23.5115 1.07203
\(482\) 0 0
\(483\) −17.7080 −0.805742
\(484\) 0 0
\(485\) 5.71981 0.259723
\(486\) 0 0
\(487\) 8.22178 0.372564 0.186282 0.982496i \(-0.440356\pi\)
0.186282 + 0.982496i \(0.440356\pi\)
\(488\) 0 0
\(489\) −31.0641 −1.40477
\(490\) 0 0
\(491\) 19.3071 0.871318 0.435659 0.900112i \(-0.356515\pi\)
0.435659 + 0.900112i \(0.356515\pi\)
\(492\) 0 0
\(493\) 9.97474 0.449240
\(494\) 0 0
\(495\) −1.77986 −0.0799987
\(496\) 0 0
\(497\) 14.7971 0.663742
\(498\) 0 0
\(499\) 13.5287 0.605626 0.302813 0.953050i \(-0.402074\pi\)
0.302813 + 0.953050i \(0.402074\pi\)
\(500\) 0 0
\(501\) 33.7665 1.50858
\(502\) 0 0
\(503\) 19.0595 0.849823 0.424912 0.905235i \(-0.360305\pi\)
0.424912 + 0.905235i \(0.360305\pi\)
\(504\) 0 0
\(505\) 0.379361 0.0168813
\(506\) 0 0
\(507\) 6.21435 0.275989
\(508\) 0 0
\(509\) 4.86980 0.215850 0.107925 0.994159i \(-0.465579\pi\)
0.107925 + 0.994159i \(0.465579\pi\)
\(510\) 0 0
\(511\) −45.9770 −2.03390
\(512\) 0 0
\(513\) −1.26777 −0.0559732
\(514\) 0 0
\(515\) −0.404500 −0.0178244
\(516\) 0 0
\(517\) −9.90520 −0.435630
\(518\) 0 0
\(519\) −53.3203 −2.34050
\(520\) 0 0
\(521\) 31.7482 1.39091 0.695457 0.718568i \(-0.255202\pi\)
0.695457 + 0.718568i \(0.255202\pi\)
\(522\) 0 0
\(523\) 28.4375 1.24348 0.621742 0.783222i \(-0.286425\pi\)
0.621742 + 0.783222i \(0.286425\pi\)
\(524\) 0 0
\(525\) 50.2187 2.19173
\(526\) 0 0
\(527\) 9.56778 0.416779
\(528\) 0 0
\(529\) −20.4089 −0.887342
\(530\) 0 0
\(531\) 2.91279 0.126404
\(532\) 0 0
\(533\) −16.4856 −0.714072
\(534\) 0 0
\(535\) 0.802952 0.0347146
\(536\) 0 0
\(537\) 43.9337 1.89588
\(538\) 0 0
\(539\) 12.4770 0.537421
\(540\) 0 0
\(541\) −28.9579 −1.24500 −0.622498 0.782621i \(-0.713882\pi\)
−0.622498 + 0.782621i \(0.713882\pi\)
\(542\) 0 0
\(543\) −2.83079 −0.121481
\(544\) 0 0
\(545\) 11.0455 0.473136
\(546\) 0 0
\(547\) 18.8154 0.804489 0.402245 0.915532i \(-0.368230\pi\)
0.402245 + 0.915532i \(0.368230\pi\)
\(548\) 0 0
\(549\) 34.3269 1.46504
\(550\) 0 0
\(551\) 59.6308 2.54036
\(552\) 0 0
\(553\) 8.67388 0.368851
\(554\) 0 0
\(555\) 11.6675 0.495259
\(556\) 0 0
\(557\) −21.6557 −0.917580 −0.458790 0.888545i \(-0.651717\pi\)
−0.458790 + 0.888545i \(0.651717\pi\)
\(558\) 0 0
\(559\) 12.6107 0.533376
\(560\) 0 0
\(561\) 2.25284 0.0951148
\(562\) 0 0
\(563\) −9.14610 −0.385462 −0.192731 0.981252i \(-0.561734\pi\)
−0.192731 + 0.981252i \(0.561734\pi\)
\(564\) 0 0
\(565\) 0.994114 0.0418227
\(566\) 0 0
\(567\) −41.8658 −1.75820
\(568\) 0 0
\(569\) −9.79514 −0.410634 −0.205317 0.978696i \(-0.565823\pi\)
−0.205317 + 0.978696i \(0.565823\pi\)
\(570\) 0 0
\(571\) 41.9362 1.75497 0.877487 0.479600i \(-0.159218\pi\)
0.877487 + 0.479600i \(0.159218\pi\)
\(572\) 0 0
\(573\) 7.84156 0.327586
\(574\) 0 0
\(575\) −7.34828 −0.306445
\(576\) 0 0
\(577\) −4.46746 −0.185983 −0.0929913 0.995667i \(-0.529643\pi\)
−0.0929913 + 0.995667i \(0.529643\pi\)
\(578\) 0 0
\(579\) −20.9500 −0.870651
\(580\) 0 0
\(581\) −34.0070 −1.41085
\(582\) 0 0
\(583\) 6.23214 0.258109
\(584\) 0 0
\(585\) −6.20859 −0.256693
\(586\) 0 0
\(587\) −36.6889 −1.51431 −0.757157 0.653233i \(-0.773412\pi\)
−0.757157 + 0.653233i \(0.773412\pi\)
\(588\) 0 0
\(589\) 57.1979 2.35680
\(590\) 0 0
\(591\) 49.7808 2.04771
\(592\) 0 0
\(593\) 10.9356 0.449070 0.224535 0.974466i \(-0.427914\pi\)
0.224535 + 0.974466i \(0.427914\pi\)
\(594\) 0 0
\(595\) 2.98381 0.122324
\(596\) 0 0
\(597\) 21.5785 0.883148
\(598\) 0 0
\(599\) −11.4308 −0.467051 −0.233526 0.972351i \(-0.575026\pi\)
−0.233526 + 0.972351i \(0.575026\pi\)
\(600\) 0 0
\(601\) 9.92517 0.404856 0.202428 0.979297i \(-0.435117\pi\)
0.202428 + 0.979297i \(0.435117\pi\)
\(602\) 0 0
\(603\) 24.9554 1.01626
\(604\) 0 0
\(605\) 6.68885 0.271940
\(606\) 0 0
\(607\) 31.4164 1.27515 0.637575 0.770388i \(-0.279938\pi\)
0.637575 + 0.770388i \(0.279938\pi\)
\(608\) 0 0
\(609\) 109.730 4.44649
\(610\) 0 0
\(611\) −34.5518 −1.39782
\(612\) 0 0
\(613\) −31.5185 −1.27302 −0.636509 0.771269i \(-0.719622\pi\)
−0.636509 + 0.771269i \(0.719622\pi\)
\(614\) 0 0
\(615\) −8.18095 −0.329888
\(616\) 0 0
\(617\) −16.5466 −0.666139 −0.333070 0.942902i \(-0.608084\pi\)
−0.333070 + 0.942902i \(0.608084\pi\)
\(618\) 0 0
\(619\) −44.9036 −1.80483 −0.902414 0.430870i \(-0.858207\pi\)
−0.902414 + 0.430870i \(0.858207\pi\)
\(620\) 0 0
\(621\) 0.341361 0.0136984
\(622\) 0 0
\(623\) −46.7374 −1.87249
\(624\) 0 0
\(625\) 18.6643 0.746571
\(626\) 0 0
\(627\) 13.4679 0.537855
\(628\) 0 0
\(629\) −7.27511 −0.290078
\(630\) 0 0
\(631\) 42.7887 1.70339 0.851696 0.524036i \(-0.175574\pi\)
0.851696 + 0.524036i \(0.175574\pi\)
\(632\) 0 0
\(633\) −32.4855 −1.29118
\(634\) 0 0
\(635\) 4.30853 0.170979
\(636\) 0 0
\(637\) 43.5227 1.72443
\(638\) 0 0
\(639\) 9.52704 0.376884
\(640\) 0 0
\(641\) 21.2110 0.837785 0.418893 0.908036i \(-0.362418\pi\)
0.418893 + 0.908036i \(0.362418\pi\)
\(642\) 0 0
\(643\) −34.5875 −1.36400 −0.682000 0.731353i \(-0.738889\pi\)
−0.682000 + 0.731353i \(0.738889\pi\)
\(644\) 0 0
\(645\) 6.25803 0.246410
\(646\) 0 0
\(647\) 31.0218 1.21959 0.609797 0.792558i \(-0.291251\pi\)
0.609797 + 0.792558i \(0.291251\pi\)
\(648\) 0 0
\(649\) 0.926475 0.0363673
\(650\) 0 0
\(651\) 105.253 4.12520
\(652\) 0 0
\(653\) 18.2139 0.712766 0.356383 0.934340i \(-0.384010\pi\)
0.356383 + 0.934340i \(0.384010\pi\)
\(654\) 0 0
\(655\) 10.3894 0.405946
\(656\) 0 0
\(657\) −29.6020 −1.15488
\(658\) 0 0
\(659\) 49.8036 1.94007 0.970036 0.242963i \(-0.0781194\pi\)
0.970036 + 0.242963i \(0.0781194\pi\)
\(660\) 0 0
\(661\) 29.2053 1.13596 0.567978 0.823044i \(-0.307726\pi\)
0.567978 + 0.823044i \(0.307726\pi\)
\(662\) 0 0
\(663\) 7.85845 0.305197
\(664\) 0 0
\(665\) 17.8378 0.691719
\(666\) 0 0
\(667\) −16.0563 −0.621704
\(668\) 0 0
\(669\) −8.59672 −0.332368
\(670\) 0 0
\(671\) 10.9184 0.421501
\(672\) 0 0
\(673\) −23.2178 −0.894980 −0.447490 0.894289i \(-0.647682\pi\)
−0.447490 + 0.894289i \(0.647682\pi\)
\(674\) 0 0
\(675\) −0.968079 −0.0372614
\(676\) 0 0
\(677\) 19.0796 0.733289 0.366644 0.930361i \(-0.380507\pi\)
0.366644 + 0.930361i \(0.380507\pi\)
\(678\) 0 0
\(679\) −39.2344 −1.50568
\(680\) 0 0
\(681\) 4.16036 0.159425
\(682\) 0 0
\(683\) 18.2093 0.696758 0.348379 0.937354i \(-0.386732\pi\)
0.348379 + 0.937354i \(0.386732\pi\)
\(684\) 0 0
\(685\) −10.8578 −0.414856
\(686\) 0 0
\(687\) 41.7613 1.59329
\(688\) 0 0
\(689\) 21.7392 0.828199
\(690\) 0 0
\(691\) −27.4291 −1.04345 −0.521727 0.853113i \(-0.674712\pi\)
−0.521727 + 0.853113i \(0.674712\pi\)
\(692\) 0 0
\(693\) 12.2087 0.463772
\(694\) 0 0
\(695\) 8.55723 0.324594
\(696\) 0 0
\(697\) 5.10111 0.193218
\(698\) 0 0
\(699\) −6.85600 −0.259318
\(700\) 0 0
\(701\) 2.48782 0.0939635 0.0469818 0.998896i \(-0.485040\pi\)
0.0469818 + 0.998896i \(0.485040\pi\)
\(702\) 0 0
\(703\) −43.4919 −1.64033
\(704\) 0 0
\(705\) −17.1462 −0.645765
\(706\) 0 0
\(707\) −2.60219 −0.0978652
\(708\) 0 0
\(709\) 15.3157 0.575195 0.287597 0.957751i \(-0.407144\pi\)
0.287597 + 0.957751i \(0.407144\pi\)
\(710\) 0 0
\(711\) 5.58462 0.209440
\(712\) 0 0
\(713\) −15.4012 −0.576781
\(714\) 0 0
\(715\) −1.97477 −0.0738523
\(716\) 0 0
\(717\) 73.6321 2.74984
\(718\) 0 0
\(719\) −8.68177 −0.323775 −0.161888 0.986809i \(-0.551758\pi\)
−0.161888 + 0.986809i \(0.551758\pi\)
\(720\) 0 0
\(721\) 2.77463 0.103332
\(722\) 0 0
\(723\) −70.1053 −2.60724
\(724\) 0 0
\(725\) 45.5347 1.69112
\(726\) 0 0
\(727\) −16.6679 −0.618177 −0.309089 0.951033i \(-0.600024\pi\)
−0.309089 + 0.951033i \(0.600024\pi\)
\(728\) 0 0
\(729\) −25.4080 −0.941039
\(730\) 0 0
\(731\) −3.90210 −0.144325
\(732\) 0 0
\(733\) −21.7078 −0.801795 −0.400898 0.916123i \(-0.631302\pi\)
−0.400898 + 0.916123i \(0.631302\pi\)
\(734\) 0 0
\(735\) 21.5980 0.796656
\(736\) 0 0
\(737\) 7.93760 0.292385
\(738\) 0 0
\(739\) −28.9300 −1.06421 −0.532104 0.846679i \(-0.678599\pi\)
−0.532104 + 0.846679i \(0.678599\pi\)
\(740\) 0 0
\(741\) 46.9793 1.72583
\(742\) 0 0
\(743\) 37.1684 1.36358 0.681789 0.731549i \(-0.261202\pi\)
0.681789 + 0.731549i \(0.261202\pi\)
\(744\) 0 0
\(745\) −8.03958 −0.294547
\(746\) 0 0
\(747\) −21.8952 −0.801103
\(748\) 0 0
\(749\) −5.50776 −0.201249
\(750\) 0 0
\(751\) 18.3083 0.668081 0.334040 0.942559i \(-0.391588\pi\)
0.334040 + 0.942559i \(0.391588\pi\)
\(752\) 0 0
\(753\) 25.4915 0.928963
\(754\) 0 0
\(755\) 6.71417 0.244354
\(756\) 0 0
\(757\) −43.3774 −1.57658 −0.788289 0.615305i \(-0.789033\pi\)
−0.788289 + 0.615305i \(0.789033\pi\)
\(758\) 0 0
\(759\) −3.62639 −0.131630
\(760\) 0 0
\(761\) −17.9239 −0.649739 −0.324870 0.945759i \(-0.605320\pi\)
−0.324870 + 0.945759i \(0.605320\pi\)
\(762\) 0 0
\(763\) −75.7652 −2.74289
\(764\) 0 0
\(765\) 1.92111 0.0694578
\(766\) 0 0
\(767\) 3.23177 0.116693
\(768\) 0 0
\(769\) −31.3505 −1.13053 −0.565264 0.824910i \(-0.691226\pi\)
−0.565264 + 0.824910i \(0.691226\pi\)
\(770\) 0 0
\(771\) −42.0901 −1.51584
\(772\) 0 0
\(773\) −9.21456 −0.331425 −0.165712 0.986174i \(-0.552992\pi\)
−0.165712 + 0.986174i \(0.552992\pi\)
\(774\) 0 0
\(775\) 43.6769 1.56892
\(776\) 0 0
\(777\) −80.0321 −2.87114
\(778\) 0 0
\(779\) 30.4954 1.09261
\(780\) 0 0
\(781\) 3.03028 0.108432
\(782\) 0 0
\(783\) −2.11530 −0.0755945
\(784\) 0 0
\(785\) −16.0986 −0.574585
\(786\) 0 0
\(787\) 1.87853 0.0669625 0.0334813 0.999439i \(-0.489341\pi\)
0.0334813 + 0.999439i \(0.489341\pi\)
\(788\) 0 0
\(789\) 43.5929 1.55195
\(790\) 0 0
\(791\) −6.81902 −0.242456
\(792\) 0 0
\(793\) 38.0861 1.35248
\(794\) 0 0
\(795\) 10.7880 0.382612
\(796\) 0 0
\(797\) −22.3282 −0.790905 −0.395452 0.918486i \(-0.629412\pi\)
−0.395452 + 0.918486i \(0.629412\pi\)
\(798\) 0 0
\(799\) 10.6913 0.378230
\(800\) 0 0
\(801\) −30.0916 −1.06323
\(802\) 0 0
\(803\) −9.41554 −0.332267
\(804\) 0 0
\(805\) −4.80304 −0.169285
\(806\) 0 0
\(807\) −17.6328 −0.620704
\(808\) 0 0
\(809\) 4.11252 0.144588 0.0722942 0.997383i \(-0.476968\pi\)
0.0722942 + 0.997383i \(0.476968\pi\)
\(810\) 0 0
\(811\) 4.98960 0.175208 0.0876042 0.996155i \(-0.472079\pi\)
0.0876042 + 0.996155i \(0.472079\pi\)
\(812\) 0 0
\(813\) 7.95560 0.279015
\(814\) 0 0
\(815\) −8.42570 −0.295139
\(816\) 0 0
\(817\) −23.3275 −0.816126
\(818\) 0 0
\(819\) 42.5871 1.48811
\(820\) 0 0
\(821\) −39.4527 −1.37691 −0.688455 0.725279i \(-0.741711\pi\)
−0.688455 + 0.725279i \(0.741711\pi\)
\(822\) 0 0
\(823\) 2.61869 0.0912819 0.0456410 0.998958i \(-0.485467\pi\)
0.0456410 + 0.998958i \(0.485467\pi\)
\(824\) 0 0
\(825\) 10.2842 0.358050
\(826\) 0 0
\(827\) 16.7544 0.582608 0.291304 0.956630i \(-0.405911\pi\)
0.291304 + 0.956630i \(0.405911\pi\)
\(828\) 0 0
\(829\) 25.0348 0.869495 0.434748 0.900552i \(-0.356838\pi\)
0.434748 + 0.900552i \(0.356838\pi\)
\(830\) 0 0
\(831\) −78.6263 −2.72752
\(832\) 0 0
\(833\) −13.4671 −0.466609
\(834\) 0 0
\(835\) 9.15869 0.316949
\(836\) 0 0
\(837\) −2.02899 −0.0701323
\(838\) 0 0
\(839\) 17.3197 0.597941 0.298971 0.954262i \(-0.403357\pi\)
0.298971 + 0.954262i \(0.403357\pi\)
\(840\) 0 0
\(841\) 70.4954 2.43088
\(842\) 0 0
\(843\) −51.8640 −1.78629
\(844\) 0 0
\(845\) 1.68555 0.0579848
\(846\) 0 0
\(847\) −45.8814 −1.57650
\(848\) 0 0
\(849\) −12.0337 −0.412995
\(850\) 0 0
\(851\) 11.7107 0.401439
\(852\) 0 0
\(853\) −51.3757 −1.75907 −0.879535 0.475833i \(-0.842147\pi\)
−0.879535 + 0.475833i \(0.842147\pi\)
\(854\) 0 0
\(855\) 11.4847 0.392770
\(856\) 0 0
\(857\) −6.72178 −0.229612 −0.114806 0.993388i \(-0.536625\pi\)
−0.114806 + 0.993388i \(0.536625\pi\)
\(858\) 0 0
\(859\) 14.2503 0.486212 0.243106 0.970000i \(-0.421834\pi\)
0.243106 + 0.970000i \(0.421834\pi\)
\(860\) 0 0
\(861\) 56.1164 1.91244
\(862\) 0 0
\(863\) −49.6186 −1.68904 −0.844518 0.535527i \(-0.820113\pi\)
−0.844518 + 0.535527i \(0.820113\pi\)
\(864\) 0 0
\(865\) −14.4624 −0.491735
\(866\) 0 0
\(867\) −2.43162 −0.0825822
\(868\) 0 0
\(869\) 1.77631 0.0602571
\(870\) 0 0
\(871\) 27.6883 0.938183
\(872\) 0 0
\(873\) −25.2608 −0.854950
\(874\) 0 0
\(875\) 28.5402 0.964834
\(876\) 0 0
\(877\) 45.0620 1.52164 0.760818 0.648965i \(-0.224798\pi\)
0.760818 + 0.648965i \(0.224798\pi\)
\(878\) 0 0
\(879\) 34.1212 1.15088
\(880\) 0 0
\(881\) 58.1095 1.95776 0.978879 0.204443i \(-0.0655382\pi\)
0.978879 + 0.204443i \(0.0655382\pi\)
\(882\) 0 0
\(883\) −6.35261 −0.213782 −0.106891 0.994271i \(-0.534090\pi\)
−0.106891 + 0.994271i \(0.534090\pi\)
\(884\) 0 0
\(885\) 1.60376 0.0539098
\(886\) 0 0
\(887\) 19.4738 0.653865 0.326932 0.945048i \(-0.393985\pi\)
0.326932 + 0.945048i \(0.393985\pi\)
\(888\) 0 0
\(889\) −29.5539 −0.991205
\(890\) 0 0
\(891\) −8.57362 −0.287227
\(892\) 0 0
\(893\) 63.9145 2.13882
\(894\) 0 0
\(895\) 11.9164 0.398321
\(896\) 0 0
\(897\) −12.6497 −0.422363
\(898\) 0 0
\(899\) 95.4361 3.18297
\(900\) 0 0
\(901\) −6.72672 −0.224100
\(902\) 0 0
\(903\) −42.9263 −1.42850
\(904\) 0 0
\(905\) −0.767811 −0.0255229
\(906\) 0 0
\(907\) −29.5814 −0.982234 −0.491117 0.871094i \(-0.663411\pi\)
−0.491117 + 0.871094i \(0.663411\pi\)
\(908\) 0 0
\(909\) −1.67540 −0.0555695
\(910\) 0 0
\(911\) −41.5301 −1.37595 −0.687977 0.725732i \(-0.741501\pi\)
−0.687977 + 0.725732i \(0.741501\pi\)
\(912\) 0 0
\(913\) −6.96423 −0.230482
\(914\) 0 0
\(915\) 18.9001 0.624819
\(916\) 0 0
\(917\) −71.2647 −2.35337
\(918\) 0 0
\(919\) 19.7037 0.649965 0.324983 0.945720i \(-0.394642\pi\)
0.324983 + 0.945720i \(0.394642\pi\)
\(920\) 0 0
\(921\) 20.6816 0.681483
\(922\) 0 0
\(923\) 10.5704 0.347928
\(924\) 0 0
\(925\) −33.2109 −1.09197
\(926\) 0 0
\(927\) 1.78643 0.0586739
\(928\) 0 0
\(929\) −28.8855 −0.947701 −0.473851 0.880605i \(-0.657136\pi\)
−0.473851 + 0.880605i \(0.657136\pi\)
\(930\) 0 0
\(931\) −80.5090 −2.63858
\(932\) 0 0
\(933\) 73.8172 2.41667
\(934\) 0 0
\(935\) 0.611049 0.0199835
\(936\) 0 0
\(937\) −6.81226 −0.222547 −0.111273 0.993790i \(-0.535493\pi\)
−0.111273 + 0.993790i \(0.535493\pi\)
\(938\) 0 0
\(939\) −2.69363 −0.0879032
\(940\) 0 0
\(941\) −45.0627 −1.46900 −0.734500 0.678608i \(-0.762583\pi\)
−0.734500 + 0.678608i \(0.762583\pi\)
\(942\) 0 0
\(943\) −8.21125 −0.267395
\(944\) 0 0
\(945\) −0.632763 −0.0205838
\(946\) 0 0
\(947\) 26.6042 0.864519 0.432260 0.901749i \(-0.357716\pi\)
0.432260 + 0.901749i \(0.357716\pi\)
\(948\) 0 0
\(949\) −32.8437 −1.06615
\(950\) 0 0
\(951\) 38.4362 1.24638
\(952\) 0 0
\(953\) 27.0787 0.877164 0.438582 0.898691i \(-0.355481\pi\)
0.438582 + 0.898691i \(0.355481\pi\)
\(954\) 0 0
\(955\) 2.12691 0.0688252
\(956\) 0 0
\(957\) 22.4715 0.726399
\(958\) 0 0
\(959\) 74.4780 2.40502
\(960\) 0 0
\(961\) 60.5424 1.95298
\(962\) 0 0
\(963\) −3.54614 −0.114273
\(964\) 0 0
\(965\) −5.68238 −0.182922
\(966\) 0 0
\(967\) 17.9677 0.577804 0.288902 0.957359i \(-0.406710\pi\)
0.288902 + 0.957359i \(0.406710\pi\)
\(968\) 0 0
\(969\) −14.5367 −0.466986
\(970\) 0 0
\(971\) −41.9029 −1.34473 −0.672364 0.740221i \(-0.734721\pi\)
−0.672364 + 0.740221i \(0.734721\pi\)
\(972\) 0 0
\(973\) −58.6974 −1.88175
\(974\) 0 0
\(975\) 35.8739 1.14888
\(976\) 0 0
\(977\) 2.37095 0.0758535 0.0379267 0.999281i \(-0.487925\pi\)
0.0379267 + 0.999281i \(0.487925\pi\)
\(978\) 0 0
\(979\) −9.57126 −0.305899
\(980\) 0 0
\(981\) −48.7810 −1.55746
\(982\) 0 0
\(983\) 2.01321 0.0642113 0.0321056 0.999484i \(-0.489779\pi\)
0.0321056 + 0.999484i \(0.489779\pi\)
\(984\) 0 0
\(985\) 13.5023 0.430220
\(986\) 0 0
\(987\) 117.613 3.74366
\(988\) 0 0
\(989\) 6.28121 0.199731
\(990\) 0 0
\(991\) −9.09875 −0.289031 −0.144516 0.989503i \(-0.546162\pi\)
−0.144516 + 0.989503i \(0.546162\pi\)
\(992\) 0 0
\(993\) 33.6607 1.06819
\(994\) 0 0
\(995\) 5.85285 0.185548
\(996\) 0 0
\(997\) 58.7618 1.86100 0.930502 0.366286i \(-0.119371\pi\)
0.930502 + 0.366286i \(0.119371\pi\)
\(998\) 0 0
\(999\) 1.54280 0.0488120
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 \(a_p\))