Properties

Label 6036.2.a.i.1.16
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+1.62125 q^{5}\) \(+5.08723 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+1.62125 q^{5}\) \(+5.08723 q^{7}\) \(+1.00000 q^{9}\) \(-4.78702 q^{11}\) \(+3.75038 q^{13}\) \(-1.62125 q^{15}\) \(+8.05516 q^{17}\) \(+2.54548 q^{19}\) \(-5.08723 q^{21}\) \(-6.47688 q^{23}\) \(-2.37155 q^{25}\) \(-1.00000 q^{27}\) \(+1.84482 q^{29}\) \(+11.0732 q^{31}\) \(+4.78702 q^{33}\) \(+8.24767 q^{35}\) \(-2.26721 q^{37}\) \(-3.75038 q^{39}\) \(+3.95793 q^{41}\) \(-9.87920 q^{43}\) \(+1.62125 q^{45}\) \(-1.11380 q^{47}\) \(+18.8800 q^{49}\) \(-8.05516 q^{51}\) \(+5.65830 q^{53}\) \(-7.76096 q^{55}\) \(-2.54548 q^{57}\) \(-9.39418 q^{59}\) \(+4.19568 q^{61}\) \(+5.08723 q^{63}\) \(+6.08030 q^{65}\) \(+0.706924 q^{67}\) \(+6.47688 q^{69}\) \(+14.2100 q^{71}\) \(+16.1734 q^{73}\) \(+2.37155 q^{75}\) \(-24.3527 q^{77}\) \(+2.99763 q^{79}\) \(+1.00000 q^{81}\) \(-11.2872 q^{83}\) \(+13.0594 q^{85}\) \(-1.84482 q^{87}\) \(-5.82489 q^{89}\) \(+19.0790 q^{91}\) \(-11.0732 q^{93}\) \(+4.12685 q^{95}\) \(-8.69438 q^{97}\) \(-4.78702 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 1.62125 0.725045 0.362522 0.931975i \(-0.381916\pi\)
0.362522 + 0.931975i \(0.381916\pi\)
\(6\) 0 0
\(7\) 5.08723 1.92279 0.961397 0.275165i \(-0.0887326\pi\)
0.961397 + 0.275165i \(0.0887326\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.78702 −1.44334 −0.721671 0.692236i \(-0.756626\pi\)
−0.721671 + 0.692236i \(0.756626\pi\)
\(12\) 0 0
\(13\) 3.75038 1.04017 0.520084 0.854115i \(-0.325901\pi\)
0.520084 + 0.854115i \(0.325901\pi\)
\(14\) 0 0
\(15\) −1.62125 −0.418605
\(16\) 0 0
\(17\) 8.05516 1.95366 0.976832 0.214009i \(-0.0686520\pi\)
0.976832 + 0.214009i \(0.0686520\pi\)
\(18\) 0 0
\(19\) 2.54548 0.583972 0.291986 0.956423i \(-0.405684\pi\)
0.291986 + 0.956423i \(0.405684\pi\)
\(20\) 0 0
\(21\) −5.08723 −1.11013
\(22\) 0 0
\(23\) −6.47688 −1.35052 −0.675261 0.737579i \(-0.735969\pi\)
−0.675261 + 0.737579i \(0.735969\pi\)
\(24\) 0 0
\(25\) −2.37155 −0.474310
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.84482 0.342574 0.171287 0.985221i \(-0.445207\pi\)
0.171287 + 0.985221i \(0.445207\pi\)
\(30\) 0 0
\(31\) 11.0732 1.98881 0.994403 0.105657i \(-0.0336945\pi\)
0.994403 + 0.105657i \(0.0336945\pi\)
\(32\) 0 0
\(33\) 4.78702 0.833314
\(34\) 0 0
\(35\) 8.24767 1.39411
\(36\) 0 0
\(37\) −2.26721 −0.372727 −0.186364 0.982481i \(-0.559670\pi\)
−0.186364 + 0.982481i \(0.559670\pi\)
\(38\) 0 0
\(39\) −3.75038 −0.600541
\(40\) 0 0
\(41\) 3.95793 0.618126 0.309063 0.951042i \(-0.399985\pi\)
0.309063 + 0.951042i \(0.399985\pi\)
\(42\) 0 0
\(43\) −9.87920 −1.50656 −0.753282 0.657698i \(-0.771530\pi\)
−0.753282 + 0.657698i \(0.771530\pi\)
\(44\) 0 0
\(45\) 1.62125 0.241682
\(46\) 0 0
\(47\) −1.11380 −0.162464 −0.0812320 0.996695i \(-0.525885\pi\)
−0.0812320 + 0.996695i \(0.525885\pi\)
\(48\) 0 0
\(49\) 18.8800 2.69714
\(50\) 0 0
\(51\) −8.05516 −1.12795
\(52\) 0 0
\(53\) 5.65830 0.777228 0.388614 0.921401i \(-0.372954\pi\)
0.388614 + 0.921401i \(0.372954\pi\)
\(54\) 0 0
\(55\) −7.76096 −1.04649
\(56\) 0 0
\(57\) −2.54548 −0.337156
\(58\) 0 0
\(59\) −9.39418 −1.22302 −0.611509 0.791237i \(-0.709437\pi\)
−0.611509 + 0.791237i \(0.709437\pi\)
\(60\) 0 0
\(61\) 4.19568 0.537201 0.268601 0.963252i \(-0.413439\pi\)
0.268601 + 0.963252i \(0.413439\pi\)
\(62\) 0 0
\(63\) 5.08723 0.640931
\(64\) 0 0
\(65\) 6.08030 0.754168
\(66\) 0 0
\(67\) 0.706924 0.0863645 0.0431822 0.999067i \(-0.486250\pi\)
0.0431822 + 0.999067i \(0.486250\pi\)
\(68\) 0 0
\(69\) 6.47688 0.779724
\(70\) 0 0
\(71\) 14.2100 1.68642 0.843210 0.537585i \(-0.180663\pi\)
0.843210 + 0.537585i \(0.180663\pi\)
\(72\) 0 0
\(73\) 16.1734 1.89295 0.946476 0.322775i \(-0.104616\pi\)
0.946476 + 0.322775i \(0.104616\pi\)
\(74\) 0 0
\(75\) 2.37155 0.273843
\(76\) 0 0
\(77\) −24.3527 −2.77525
\(78\) 0 0
\(79\) 2.99763 0.337260 0.168630 0.985679i \(-0.446066\pi\)
0.168630 + 0.985679i \(0.446066\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −11.2872 −1.23893 −0.619465 0.785024i \(-0.712650\pi\)
−0.619465 + 0.785024i \(0.712650\pi\)
\(84\) 0 0
\(85\) 13.0594 1.41649
\(86\) 0 0
\(87\) −1.84482 −0.197785
\(88\) 0 0
\(89\) −5.82489 −0.617437 −0.308719 0.951153i \(-0.599900\pi\)
−0.308719 + 0.951153i \(0.599900\pi\)
\(90\) 0 0
\(91\) 19.0790 2.00003
\(92\) 0 0
\(93\) −11.0732 −1.14824
\(94\) 0 0
\(95\) 4.12685 0.423406
\(96\) 0 0
\(97\) −8.69438 −0.882781 −0.441391 0.897315i \(-0.645515\pi\)
−0.441391 + 0.897315i \(0.645515\pi\)
\(98\) 0 0
\(99\) −4.78702 −0.481114
\(100\) 0 0
\(101\) −7.46387 −0.742683 −0.371342 0.928496i \(-0.621102\pi\)
−0.371342 + 0.928496i \(0.621102\pi\)
\(102\) 0 0
\(103\) −4.05463 −0.399515 −0.199757 0.979845i \(-0.564015\pi\)
−0.199757 + 0.979845i \(0.564015\pi\)
\(104\) 0 0
\(105\) −8.24767 −0.804891
\(106\) 0 0
\(107\) 8.22324 0.794971 0.397485 0.917608i \(-0.369883\pi\)
0.397485 + 0.917608i \(0.369883\pi\)
\(108\) 0 0
\(109\) −4.91908 −0.471162 −0.235581 0.971855i \(-0.575699\pi\)
−0.235581 + 0.971855i \(0.575699\pi\)
\(110\) 0 0
\(111\) 2.26721 0.215194
\(112\) 0 0
\(113\) −10.3271 −0.971495 −0.485747 0.874099i \(-0.661453\pi\)
−0.485747 + 0.874099i \(0.661453\pi\)
\(114\) 0 0
\(115\) −10.5006 −0.979189
\(116\) 0 0
\(117\) 3.75038 0.346723
\(118\) 0 0
\(119\) 40.9785 3.75649
\(120\) 0 0
\(121\) 11.9156 1.08324
\(122\) 0 0
\(123\) −3.95793 −0.356875
\(124\) 0 0
\(125\) −11.9511 −1.06894
\(126\) 0 0
\(127\) 12.1345 1.07676 0.538379 0.842703i \(-0.319037\pi\)
0.538379 + 0.842703i \(0.319037\pi\)
\(128\) 0 0
\(129\) 9.87920 0.869815
\(130\) 0 0
\(131\) −8.79470 −0.768396 −0.384198 0.923251i \(-0.625522\pi\)
−0.384198 + 0.923251i \(0.625522\pi\)
\(132\) 0 0
\(133\) 12.9494 1.12286
\(134\) 0 0
\(135\) −1.62125 −0.139535
\(136\) 0 0
\(137\) 3.83330 0.327501 0.163750 0.986502i \(-0.447641\pi\)
0.163750 + 0.986502i \(0.447641\pi\)
\(138\) 0 0
\(139\) 1.81069 0.153580 0.0767902 0.997047i \(-0.475533\pi\)
0.0767902 + 0.997047i \(0.475533\pi\)
\(140\) 0 0
\(141\) 1.11380 0.0937986
\(142\) 0 0
\(143\) −17.9531 −1.50132
\(144\) 0 0
\(145\) 2.99091 0.248382
\(146\) 0 0
\(147\) −18.8800 −1.55719
\(148\) 0 0
\(149\) −19.9656 −1.63564 −0.817822 0.575472i \(-0.804819\pi\)
−0.817822 + 0.575472i \(0.804819\pi\)
\(150\) 0 0
\(151\) −12.5577 −1.02193 −0.510966 0.859601i \(-0.670712\pi\)
−0.510966 + 0.859601i \(0.670712\pi\)
\(152\) 0 0
\(153\) 8.05516 0.651221
\(154\) 0 0
\(155\) 17.9524 1.44197
\(156\) 0 0
\(157\) 24.4197 1.94890 0.974452 0.224597i \(-0.0721066\pi\)
0.974452 + 0.224597i \(0.0721066\pi\)
\(158\) 0 0
\(159\) −5.65830 −0.448733
\(160\) 0 0
\(161\) −32.9494 −2.59678
\(162\) 0 0
\(163\) 1.07379 0.0841057 0.0420528 0.999115i \(-0.486610\pi\)
0.0420528 + 0.999115i \(0.486610\pi\)
\(164\) 0 0
\(165\) 7.76096 0.604190
\(166\) 0 0
\(167\) −7.25268 −0.561230 −0.280615 0.959820i \(-0.590538\pi\)
−0.280615 + 0.959820i \(0.590538\pi\)
\(168\) 0 0
\(169\) 1.06533 0.0819485
\(170\) 0 0
\(171\) 2.54548 0.194657
\(172\) 0 0
\(173\) 10.7486 0.817197 0.408599 0.912714i \(-0.366018\pi\)
0.408599 + 0.912714i \(0.366018\pi\)
\(174\) 0 0
\(175\) −12.0646 −0.912001
\(176\) 0 0
\(177\) 9.39418 0.706110
\(178\) 0 0
\(179\) −5.28959 −0.395363 −0.197681 0.980266i \(-0.563341\pi\)
−0.197681 + 0.980266i \(0.563341\pi\)
\(180\) 0 0
\(181\) −7.10431 −0.528059 −0.264030 0.964515i \(-0.585052\pi\)
−0.264030 + 0.964515i \(0.585052\pi\)
\(182\) 0 0
\(183\) −4.19568 −0.310153
\(184\) 0 0
\(185\) −3.67571 −0.270244
\(186\) 0 0
\(187\) −38.5603 −2.81981
\(188\) 0 0
\(189\) −5.08723 −0.370042
\(190\) 0 0
\(191\) 16.2208 1.17369 0.586846 0.809698i \(-0.300369\pi\)
0.586846 + 0.809698i \(0.300369\pi\)
\(192\) 0 0
\(193\) −15.9161 −1.14567 −0.572834 0.819671i \(-0.694156\pi\)
−0.572834 + 0.819671i \(0.694156\pi\)
\(194\) 0 0
\(195\) −6.08030 −0.435419
\(196\) 0 0
\(197\) 6.48555 0.462077 0.231038 0.972945i \(-0.425788\pi\)
0.231038 + 0.972945i \(0.425788\pi\)
\(198\) 0 0
\(199\) 14.1090 1.00016 0.500081 0.865979i \(-0.333304\pi\)
0.500081 + 0.865979i \(0.333304\pi\)
\(200\) 0 0
\(201\) −0.706924 −0.0498625
\(202\) 0 0
\(203\) 9.38503 0.658700
\(204\) 0 0
\(205\) 6.41680 0.448169
\(206\) 0 0
\(207\) −6.47688 −0.450174
\(208\) 0 0
\(209\) −12.1853 −0.842872
\(210\) 0 0
\(211\) 3.02938 0.208551 0.104276 0.994548i \(-0.466748\pi\)
0.104276 + 0.994548i \(0.466748\pi\)
\(212\) 0 0
\(213\) −14.2100 −0.973655
\(214\) 0 0
\(215\) −16.0166 −1.09233
\(216\) 0 0
\(217\) 56.3320 3.82406
\(218\) 0 0
\(219\) −16.1734 −1.09290
\(220\) 0 0
\(221\) 30.2099 2.03214
\(222\) 0 0
\(223\) −18.1230 −1.21360 −0.606801 0.794853i \(-0.707548\pi\)
−0.606801 + 0.794853i \(0.707548\pi\)
\(224\) 0 0
\(225\) −2.37155 −0.158103
\(226\) 0 0
\(227\) 7.36207 0.488638 0.244319 0.969695i \(-0.421436\pi\)
0.244319 + 0.969695i \(0.421436\pi\)
\(228\) 0 0
\(229\) −28.8730 −1.90798 −0.953990 0.299839i \(-0.903067\pi\)
−0.953990 + 0.299839i \(0.903067\pi\)
\(230\) 0 0
\(231\) 24.3527 1.60229
\(232\) 0 0
\(233\) 22.1642 1.45202 0.726011 0.687683i \(-0.241372\pi\)
0.726011 + 0.687683i \(0.241372\pi\)
\(234\) 0 0
\(235\) −1.80574 −0.117794
\(236\) 0 0
\(237\) −2.99763 −0.194717
\(238\) 0 0
\(239\) −8.28176 −0.535702 −0.267851 0.963460i \(-0.586314\pi\)
−0.267851 + 0.963460i \(0.586314\pi\)
\(240\) 0 0
\(241\) 1.60328 0.103277 0.0516383 0.998666i \(-0.483556\pi\)
0.0516383 + 0.998666i \(0.483556\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 30.6091 1.95554
\(246\) 0 0
\(247\) 9.54649 0.607429
\(248\) 0 0
\(249\) 11.2872 0.715296
\(250\) 0 0
\(251\) 28.7613 1.81540 0.907698 0.419623i \(-0.137838\pi\)
0.907698 + 0.419623i \(0.137838\pi\)
\(252\) 0 0
\(253\) 31.0050 1.94927
\(254\) 0 0
\(255\) −13.0594 −0.817813
\(256\) 0 0
\(257\) 14.8466 0.926104 0.463052 0.886331i \(-0.346754\pi\)
0.463052 + 0.886331i \(0.346754\pi\)
\(258\) 0 0
\(259\) −11.5338 −0.716677
\(260\) 0 0
\(261\) 1.84482 0.114191
\(262\) 0 0
\(263\) −12.6492 −0.779982 −0.389991 0.920819i \(-0.627522\pi\)
−0.389991 + 0.920819i \(0.627522\pi\)
\(264\) 0 0
\(265\) 9.17352 0.563525
\(266\) 0 0
\(267\) 5.82489 0.356478
\(268\) 0 0
\(269\) 12.5501 0.765194 0.382597 0.923915i \(-0.375030\pi\)
0.382597 + 0.923915i \(0.375030\pi\)
\(270\) 0 0
\(271\) −23.0080 −1.39764 −0.698818 0.715299i \(-0.746290\pi\)
−0.698818 + 0.715299i \(0.746290\pi\)
\(272\) 0 0
\(273\) −19.0790 −1.15472
\(274\) 0 0
\(275\) 11.3527 0.684592
\(276\) 0 0
\(277\) 20.6993 1.24370 0.621849 0.783137i \(-0.286382\pi\)
0.621849 + 0.783137i \(0.286382\pi\)
\(278\) 0 0
\(279\) 11.0732 0.662935
\(280\) 0 0
\(281\) −30.9147 −1.84422 −0.922110 0.386929i \(-0.873536\pi\)
−0.922110 + 0.386929i \(0.873536\pi\)
\(282\) 0 0
\(283\) −15.7644 −0.937097 −0.468548 0.883438i \(-0.655223\pi\)
−0.468548 + 0.883438i \(0.655223\pi\)
\(284\) 0 0
\(285\) −4.12685 −0.244453
\(286\) 0 0
\(287\) 20.1349 1.18853
\(288\) 0 0
\(289\) 47.8856 2.81680
\(290\) 0 0
\(291\) 8.69438 0.509674
\(292\) 0 0
\(293\) −9.59637 −0.560626 −0.280313 0.959909i \(-0.590438\pi\)
−0.280313 + 0.959909i \(0.590438\pi\)
\(294\) 0 0
\(295\) −15.2303 −0.886743
\(296\) 0 0
\(297\) 4.78702 0.277771
\(298\) 0 0
\(299\) −24.2907 −1.40477
\(300\) 0 0
\(301\) −50.2578 −2.89681
\(302\) 0 0
\(303\) 7.46387 0.428788
\(304\) 0 0
\(305\) 6.80224 0.389495
\(306\) 0 0
\(307\) 20.3194 1.15969 0.579844 0.814727i \(-0.303113\pi\)
0.579844 + 0.814727i \(0.303113\pi\)
\(308\) 0 0
\(309\) 4.05463 0.230660
\(310\) 0 0
\(311\) −21.7343 −1.23244 −0.616218 0.787575i \(-0.711336\pi\)
−0.616218 + 0.787575i \(0.711336\pi\)
\(312\) 0 0
\(313\) −10.0035 −0.565432 −0.282716 0.959204i \(-0.591235\pi\)
−0.282716 + 0.959204i \(0.591235\pi\)
\(314\) 0 0
\(315\) 8.24767 0.464704
\(316\) 0 0
\(317\) 4.74953 0.266760 0.133380 0.991065i \(-0.457417\pi\)
0.133380 + 0.991065i \(0.457417\pi\)
\(318\) 0 0
\(319\) −8.83120 −0.494452
\(320\) 0 0
\(321\) −8.22324 −0.458977
\(322\) 0 0
\(323\) 20.5042 1.14088
\(324\) 0 0
\(325\) −8.89421 −0.493362
\(326\) 0 0
\(327\) 4.91908 0.272026
\(328\) 0 0
\(329\) −5.66614 −0.312385
\(330\) 0 0
\(331\) −5.77266 −0.317294 −0.158647 0.987335i \(-0.550713\pi\)
−0.158647 + 0.987335i \(0.550713\pi\)
\(332\) 0 0
\(333\) −2.26721 −0.124242
\(334\) 0 0
\(335\) 1.14610 0.0626181
\(336\) 0 0
\(337\) 18.3300 0.998496 0.499248 0.866459i \(-0.333610\pi\)
0.499248 + 0.866459i \(0.333610\pi\)
\(338\) 0 0
\(339\) 10.3271 0.560893
\(340\) 0 0
\(341\) −53.0077 −2.87053
\(342\) 0 0
\(343\) 60.4361 3.26324
\(344\) 0 0
\(345\) 10.5006 0.565335
\(346\) 0 0
\(347\) −25.3602 −1.36140 −0.680702 0.732560i \(-0.738325\pi\)
−0.680702 + 0.732560i \(0.738325\pi\)
\(348\) 0 0
\(349\) −7.44859 −0.398714 −0.199357 0.979927i \(-0.563885\pi\)
−0.199357 + 0.979927i \(0.563885\pi\)
\(350\) 0 0
\(351\) −3.75038 −0.200180
\(352\) 0 0
\(353\) −20.2269 −1.07657 −0.538284 0.842764i \(-0.680927\pi\)
−0.538284 + 0.842764i \(0.680927\pi\)
\(354\) 0 0
\(355\) 23.0380 1.22273
\(356\) 0 0
\(357\) −40.9785 −2.16881
\(358\) 0 0
\(359\) 4.20284 0.221818 0.110909 0.993831i \(-0.464624\pi\)
0.110909 + 0.993831i \(0.464624\pi\)
\(360\) 0 0
\(361\) −12.5206 −0.658977
\(362\) 0 0
\(363\) −11.9156 −0.625407
\(364\) 0 0
\(365\) 26.2211 1.37247
\(366\) 0 0
\(367\) 13.7248 0.716430 0.358215 0.933639i \(-0.383386\pi\)
0.358215 + 0.933639i \(0.383386\pi\)
\(368\) 0 0
\(369\) 3.95793 0.206042
\(370\) 0 0
\(371\) 28.7851 1.49445
\(372\) 0 0
\(373\) 36.3665 1.88299 0.941493 0.337032i \(-0.109423\pi\)
0.941493 + 0.337032i \(0.109423\pi\)
\(374\) 0 0
\(375\) 11.9511 0.617153
\(376\) 0 0
\(377\) 6.91877 0.356335
\(378\) 0 0
\(379\) 16.9142 0.868822 0.434411 0.900715i \(-0.356957\pi\)
0.434411 + 0.900715i \(0.356957\pi\)
\(380\) 0 0
\(381\) −12.1345 −0.621667
\(382\) 0 0
\(383\) 9.23564 0.471919 0.235960 0.971763i \(-0.424177\pi\)
0.235960 + 0.971763i \(0.424177\pi\)
\(384\) 0 0
\(385\) −39.4818 −2.01218
\(386\) 0 0
\(387\) −9.87920 −0.502188
\(388\) 0 0
\(389\) 20.0808 1.01814 0.509069 0.860726i \(-0.329990\pi\)
0.509069 + 0.860726i \(0.329990\pi\)
\(390\) 0 0
\(391\) −52.1723 −2.63847
\(392\) 0 0
\(393\) 8.79470 0.443634
\(394\) 0 0
\(395\) 4.85991 0.244529
\(396\) 0 0
\(397\) 8.03548 0.403289 0.201645 0.979459i \(-0.435371\pi\)
0.201645 + 0.979459i \(0.435371\pi\)
\(398\) 0 0
\(399\) −12.9494 −0.648282
\(400\) 0 0
\(401\) −20.6983 −1.03362 −0.516812 0.856099i \(-0.672881\pi\)
−0.516812 + 0.856099i \(0.672881\pi\)
\(402\) 0 0
\(403\) 41.5287 2.06869
\(404\) 0 0
\(405\) 1.62125 0.0805605
\(406\) 0 0
\(407\) 10.8532 0.537973
\(408\) 0 0
\(409\) 24.7004 1.22136 0.610679 0.791878i \(-0.290897\pi\)
0.610679 + 0.791878i \(0.290897\pi\)
\(410\) 0 0
\(411\) −3.83330 −0.189083
\(412\) 0 0
\(413\) −47.7904 −2.35161
\(414\) 0 0
\(415\) −18.2993 −0.898279
\(416\) 0 0
\(417\) −1.81069 −0.0886697
\(418\) 0 0
\(419\) 25.5548 1.24843 0.624217 0.781251i \(-0.285418\pi\)
0.624217 + 0.781251i \(0.285418\pi\)
\(420\) 0 0
\(421\) −12.2638 −0.597701 −0.298850 0.954300i \(-0.596603\pi\)
−0.298850 + 0.954300i \(0.596603\pi\)
\(422\) 0 0
\(423\) −1.11380 −0.0541546
\(424\) 0 0
\(425\) −19.1032 −0.926643
\(426\) 0 0
\(427\) 21.3444 1.03293
\(428\) 0 0
\(429\) 17.9531 0.866786
\(430\) 0 0
\(431\) 16.4921 0.794398 0.397199 0.917733i \(-0.369982\pi\)
0.397199 + 0.917733i \(0.369982\pi\)
\(432\) 0 0
\(433\) −20.3288 −0.976939 −0.488469 0.872581i \(-0.662445\pi\)
−0.488469 + 0.872581i \(0.662445\pi\)
\(434\) 0 0
\(435\) −2.99091 −0.143403
\(436\) 0 0
\(437\) −16.4867 −0.788667
\(438\) 0 0
\(439\) 23.8416 1.13790 0.568949 0.822373i \(-0.307350\pi\)
0.568949 + 0.822373i \(0.307350\pi\)
\(440\) 0 0
\(441\) 18.8800 0.899045
\(442\) 0 0
\(443\) −17.8300 −0.847131 −0.423565 0.905865i \(-0.639222\pi\)
−0.423565 + 0.905865i \(0.639222\pi\)
\(444\) 0 0
\(445\) −9.44360 −0.447670
\(446\) 0 0
\(447\) 19.9656 0.944339
\(448\) 0 0
\(449\) 19.1086 0.901788 0.450894 0.892577i \(-0.351105\pi\)
0.450894 + 0.892577i \(0.351105\pi\)
\(450\) 0 0
\(451\) −18.9467 −0.892167
\(452\) 0 0
\(453\) 12.5577 0.590012
\(454\) 0 0
\(455\) 30.9319 1.45011
\(456\) 0 0
\(457\) 27.9632 1.30806 0.654031 0.756467i \(-0.273076\pi\)
0.654031 + 0.756467i \(0.273076\pi\)
\(458\) 0 0
\(459\) −8.05516 −0.375983
\(460\) 0 0
\(461\) 6.83764 0.318461 0.159230 0.987241i \(-0.449099\pi\)
0.159230 + 0.987241i \(0.449099\pi\)
\(462\) 0 0
\(463\) −29.5091 −1.37140 −0.685702 0.727882i \(-0.740505\pi\)
−0.685702 + 0.727882i \(0.740505\pi\)
\(464\) 0 0
\(465\) −17.9524 −0.832523
\(466\) 0 0
\(467\) 24.3776 1.12806 0.564030 0.825754i \(-0.309250\pi\)
0.564030 + 0.825754i \(0.309250\pi\)
\(468\) 0 0
\(469\) 3.59629 0.166061
\(470\) 0 0
\(471\) −24.4197 −1.12520
\(472\) 0 0
\(473\) 47.2920 2.17449
\(474\) 0 0
\(475\) −6.03673 −0.276984
\(476\) 0 0
\(477\) 5.65830 0.259076
\(478\) 0 0
\(479\) 15.5820 0.711960 0.355980 0.934494i \(-0.384147\pi\)
0.355980 + 0.934494i \(0.384147\pi\)
\(480\) 0 0
\(481\) −8.50289 −0.387699
\(482\) 0 0
\(483\) 32.9494 1.49925
\(484\) 0 0
\(485\) −14.0958 −0.640056
\(486\) 0 0
\(487\) −29.1356 −1.32026 −0.660131 0.751151i \(-0.729499\pi\)
−0.660131 + 0.751151i \(0.729499\pi\)
\(488\) 0 0
\(489\) −1.07379 −0.0485584
\(490\) 0 0
\(491\) 15.3303 0.691849 0.345924 0.938262i \(-0.387565\pi\)
0.345924 + 0.938262i \(0.387565\pi\)
\(492\) 0 0
\(493\) 14.8603 0.669275
\(494\) 0 0
\(495\) −7.76096 −0.348829
\(496\) 0 0
\(497\) 72.2897 3.24264
\(498\) 0 0
\(499\) −20.9521 −0.937947 −0.468974 0.883212i \(-0.655376\pi\)
−0.468974 + 0.883212i \(0.655376\pi\)
\(500\) 0 0
\(501\) 7.25268 0.324026
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −12.1008 −0.538478
\(506\) 0 0
\(507\) −1.06533 −0.0473130
\(508\) 0 0
\(509\) 21.6036 0.957564 0.478782 0.877934i \(-0.341078\pi\)
0.478782 + 0.877934i \(0.341078\pi\)
\(510\) 0 0
\(511\) 82.2778 3.63975
\(512\) 0 0
\(513\) −2.54548 −0.112385
\(514\) 0 0
\(515\) −6.57357 −0.289666
\(516\) 0 0
\(517\) 5.33177 0.234491
\(518\) 0 0
\(519\) −10.7486 −0.471809
\(520\) 0 0
\(521\) 34.5773 1.51486 0.757430 0.652916i \(-0.226455\pi\)
0.757430 + 0.652916i \(0.226455\pi\)
\(522\) 0 0
\(523\) 16.6517 0.728130 0.364065 0.931374i \(-0.381389\pi\)
0.364065 + 0.931374i \(0.381389\pi\)
\(524\) 0 0
\(525\) 12.0646 0.526544
\(526\) 0 0
\(527\) 89.1964 3.88546
\(528\) 0 0
\(529\) 18.9499 0.823910
\(530\) 0 0
\(531\) −9.39418 −0.407673
\(532\) 0 0
\(533\) 14.8437 0.642954
\(534\) 0 0
\(535\) 13.3319 0.576389
\(536\) 0 0
\(537\) 5.28959 0.228263
\(538\) 0 0
\(539\) −90.3788 −3.89289
\(540\) 0 0
\(541\) −12.2237 −0.525536 −0.262768 0.964859i \(-0.584635\pi\)
−0.262768 + 0.964859i \(0.584635\pi\)
\(542\) 0 0
\(543\) 7.10431 0.304875
\(544\) 0 0
\(545\) −7.97505 −0.341614
\(546\) 0 0
\(547\) 42.3294 1.80988 0.904938 0.425544i \(-0.139917\pi\)
0.904938 + 0.425544i \(0.139917\pi\)
\(548\) 0 0
\(549\) 4.19568 0.179067
\(550\) 0 0
\(551\) 4.69594 0.200054
\(552\) 0 0
\(553\) 15.2497 0.648482
\(554\) 0 0
\(555\) 3.67571 0.156025
\(556\) 0 0
\(557\) 17.4486 0.739321 0.369661 0.929167i \(-0.379474\pi\)
0.369661 + 0.929167i \(0.379474\pi\)
\(558\) 0 0
\(559\) −37.0507 −1.56708
\(560\) 0 0
\(561\) 38.5603 1.62802
\(562\) 0 0
\(563\) −36.4161 −1.53475 −0.767377 0.641196i \(-0.778438\pi\)
−0.767377 + 0.641196i \(0.778438\pi\)
\(564\) 0 0
\(565\) −16.7429 −0.704377
\(566\) 0 0
\(567\) 5.08723 0.213644
\(568\) 0 0
\(569\) 30.2694 1.26896 0.634481 0.772939i \(-0.281214\pi\)
0.634481 + 0.772939i \(0.281214\pi\)
\(570\) 0 0
\(571\) 18.3774 0.769068 0.384534 0.923111i \(-0.374362\pi\)
0.384534 + 0.923111i \(0.374362\pi\)
\(572\) 0 0
\(573\) −16.2208 −0.677632
\(574\) 0 0
\(575\) 15.3602 0.640567
\(576\) 0 0
\(577\) −11.9921 −0.499236 −0.249618 0.968344i \(-0.580305\pi\)
−0.249618 + 0.968344i \(0.580305\pi\)
\(578\) 0 0
\(579\) 15.9161 0.661452
\(580\) 0 0
\(581\) −57.4206 −2.38221
\(582\) 0 0
\(583\) −27.0864 −1.12181
\(584\) 0 0
\(585\) 6.08030 0.251389
\(586\) 0 0
\(587\) −0.765014 −0.0315755 −0.0157877 0.999875i \(-0.505026\pi\)
−0.0157877 + 0.999875i \(0.505026\pi\)
\(588\) 0 0
\(589\) 28.1866 1.16141
\(590\) 0 0
\(591\) −6.48555 −0.266780
\(592\) 0 0
\(593\) −19.5386 −0.802353 −0.401176 0.916001i \(-0.631399\pi\)
−0.401176 + 0.916001i \(0.631399\pi\)
\(594\) 0 0
\(595\) 66.4363 2.72362
\(596\) 0 0
\(597\) −14.1090 −0.577443
\(598\) 0 0
\(599\) −12.3808 −0.505864 −0.252932 0.967484i \(-0.581395\pi\)
−0.252932 + 0.967484i \(0.581395\pi\)
\(600\) 0 0
\(601\) 39.1993 1.59897 0.799487 0.600683i \(-0.205105\pi\)
0.799487 + 0.600683i \(0.205105\pi\)
\(602\) 0 0
\(603\) 0.706924 0.0287882
\(604\) 0 0
\(605\) 19.3182 0.785395
\(606\) 0 0
\(607\) 4.83993 0.196447 0.0982234 0.995164i \(-0.468684\pi\)
0.0982234 + 0.995164i \(0.468684\pi\)
\(608\) 0 0
\(609\) −9.38503 −0.380301
\(610\) 0 0
\(611\) −4.17716 −0.168990
\(612\) 0 0
\(613\) −6.04924 −0.244327 −0.122163 0.992510i \(-0.538983\pi\)
−0.122163 + 0.992510i \(0.538983\pi\)
\(614\) 0 0
\(615\) −6.41680 −0.258750
\(616\) 0 0
\(617\) 32.0507 1.29031 0.645156 0.764051i \(-0.276792\pi\)
0.645156 + 0.764051i \(0.276792\pi\)
\(618\) 0 0
\(619\) −10.8170 −0.434772 −0.217386 0.976086i \(-0.569753\pi\)
−0.217386 + 0.976086i \(0.569753\pi\)
\(620\) 0 0
\(621\) 6.47688 0.259908
\(622\) 0 0
\(623\) −29.6326 −1.18720
\(624\) 0 0
\(625\) −7.51799 −0.300720
\(626\) 0 0
\(627\) 12.1853 0.486632
\(628\) 0 0
\(629\) −18.2627 −0.728183
\(630\) 0 0
\(631\) −5.54692 −0.220819 −0.110410 0.993886i \(-0.535216\pi\)
−0.110410 + 0.993886i \(0.535216\pi\)
\(632\) 0 0
\(633\) −3.02938 −0.120407
\(634\) 0 0
\(635\) 19.6730 0.780698
\(636\) 0 0
\(637\) 70.8069 2.80547
\(638\) 0 0
\(639\) 14.2100 0.562140
\(640\) 0 0
\(641\) 14.4980 0.572635 0.286318 0.958135i \(-0.407569\pi\)
0.286318 + 0.958135i \(0.407569\pi\)
\(642\) 0 0
\(643\) 34.5051 1.36075 0.680373 0.732866i \(-0.261818\pi\)
0.680373 + 0.732866i \(0.261818\pi\)
\(644\) 0 0
\(645\) 16.0166 0.630655
\(646\) 0 0
\(647\) 0.260969 0.0102597 0.00512987 0.999987i \(-0.498367\pi\)
0.00512987 + 0.999987i \(0.498367\pi\)
\(648\) 0 0
\(649\) 44.9702 1.76523
\(650\) 0 0
\(651\) −56.3320 −2.20782
\(652\) 0 0
\(653\) −6.80054 −0.266126 −0.133063 0.991108i \(-0.542481\pi\)
−0.133063 + 0.991108i \(0.542481\pi\)
\(654\) 0 0
\(655\) −14.2584 −0.557121
\(656\) 0 0
\(657\) 16.1734 0.630984
\(658\) 0 0
\(659\) −32.0742 −1.24943 −0.624717 0.780852i \(-0.714786\pi\)
−0.624717 + 0.780852i \(0.714786\pi\)
\(660\) 0 0
\(661\) −2.65863 −0.103409 −0.0517043 0.998662i \(-0.516465\pi\)
−0.0517043 + 0.998662i \(0.516465\pi\)
\(662\) 0 0
\(663\) −30.2099 −1.17326
\(664\) 0 0
\(665\) 20.9943 0.814122
\(666\) 0 0
\(667\) −11.9487 −0.462654
\(668\) 0 0
\(669\) 18.1230 0.700674
\(670\) 0 0
\(671\) −20.0848 −0.775365
\(672\) 0 0
\(673\) −12.8856 −0.496704 −0.248352 0.968670i \(-0.579889\pi\)
−0.248352 + 0.968670i \(0.579889\pi\)
\(674\) 0 0
\(675\) 2.37155 0.0912811
\(676\) 0 0
\(677\) −8.88973 −0.341660 −0.170830 0.985301i \(-0.554645\pi\)
−0.170830 + 0.985301i \(0.554645\pi\)
\(678\) 0 0
\(679\) −44.2304 −1.69741
\(680\) 0 0
\(681\) −7.36207 −0.282115
\(682\) 0 0
\(683\) 34.8155 1.33218 0.666089 0.745872i \(-0.267967\pi\)
0.666089 + 0.745872i \(0.267967\pi\)
\(684\) 0 0
\(685\) 6.21473 0.237453
\(686\) 0 0
\(687\) 28.8730 1.10157
\(688\) 0 0
\(689\) 21.2208 0.808447
\(690\) 0 0
\(691\) 1.97469 0.0751209 0.0375605 0.999294i \(-0.488041\pi\)
0.0375605 + 0.999294i \(0.488041\pi\)
\(692\) 0 0
\(693\) −24.3527 −0.925083
\(694\) 0 0
\(695\) 2.93557 0.111353
\(696\) 0 0
\(697\) 31.8818 1.20761
\(698\) 0 0
\(699\) −22.1642 −0.838326
\(700\) 0 0
\(701\) 13.5969 0.513549 0.256774 0.966471i \(-0.417340\pi\)
0.256774 + 0.966471i \(0.417340\pi\)
\(702\) 0 0
\(703\) −5.77113 −0.217662
\(704\) 0 0
\(705\) 1.80574 0.0680082
\(706\) 0 0
\(707\) −37.9705 −1.42803
\(708\) 0 0
\(709\) −36.6935 −1.37805 −0.689027 0.724735i \(-0.741962\pi\)
−0.689027 + 0.724735i \(0.741962\pi\)
\(710\) 0 0
\(711\) 2.99763 0.112420
\(712\) 0 0
\(713\) −71.7198 −2.68593
\(714\) 0 0
\(715\) −29.1065 −1.08852
\(716\) 0 0
\(717\) 8.28176 0.309288
\(718\) 0 0
\(719\) −12.7127 −0.474104 −0.237052 0.971497i \(-0.576181\pi\)
−0.237052 + 0.971497i \(0.576181\pi\)
\(720\) 0 0
\(721\) −20.6269 −0.768184
\(722\) 0 0
\(723\) −1.60328 −0.0596267
\(724\) 0 0
\(725\) −4.37508 −0.162487
\(726\) 0 0
\(727\) −21.6489 −0.802914 −0.401457 0.915878i \(-0.631496\pi\)
−0.401457 + 0.915878i \(0.631496\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −79.5785 −2.94332
\(732\) 0 0
\(733\) 3.39863 0.125531 0.0627657 0.998028i \(-0.480008\pi\)
0.0627657 + 0.998028i \(0.480008\pi\)
\(734\) 0 0
\(735\) −30.6091 −1.12903
\(736\) 0 0
\(737\) −3.38406 −0.124653
\(738\) 0 0
\(739\) −18.8891 −0.694848 −0.347424 0.937708i \(-0.612944\pi\)
−0.347424 + 0.937708i \(0.612944\pi\)
\(740\) 0 0
\(741\) −9.54649 −0.350699
\(742\) 0 0
\(743\) −31.3785 −1.15116 −0.575582 0.817744i \(-0.695224\pi\)
−0.575582 + 0.817744i \(0.695224\pi\)
\(744\) 0 0
\(745\) −32.3692 −1.18591
\(746\) 0 0
\(747\) −11.2872 −0.412977
\(748\) 0 0
\(749\) 41.8336 1.52857
\(750\) 0 0
\(751\) −12.2331 −0.446393 −0.223197 0.974773i \(-0.571649\pi\)
−0.223197 + 0.974773i \(0.571649\pi\)
\(752\) 0 0
\(753\) −28.7613 −1.04812
\(754\) 0 0
\(755\) −20.3592 −0.740946
\(756\) 0 0
\(757\) −43.3208 −1.57452 −0.787261 0.616620i \(-0.788502\pi\)
−0.787261 + 0.616620i \(0.788502\pi\)
\(758\) 0 0
\(759\) −31.0050 −1.12541
\(760\) 0 0
\(761\) −12.9918 −0.470951 −0.235475 0.971880i \(-0.575665\pi\)
−0.235475 + 0.971880i \(0.575665\pi\)
\(762\) 0 0
\(763\) −25.0245 −0.905948
\(764\) 0 0
\(765\) 13.0594 0.472164
\(766\) 0 0
\(767\) −35.2317 −1.27214
\(768\) 0 0
\(769\) −10.8066 −0.389697 −0.194848 0.980833i \(-0.562421\pi\)
−0.194848 + 0.980833i \(0.562421\pi\)
\(770\) 0 0
\(771\) −14.8466 −0.534687
\(772\) 0 0
\(773\) −42.1613 −1.51643 −0.758217 0.652002i \(-0.773929\pi\)
−0.758217 + 0.652002i \(0.773929\pi\)
\(774\) 0 0
\(775\) −26.2607 −0.943311
\(776\) 0 0
\(777\) 11.5338 0.413774
\(778\) 0 0
\(779\) 10.0748 0.360968
\(780\) 0 0
\(781\) −68.0237 −2.43408
\(782\) 0 0
\(783\) −1.84482 −0.0659285
\(784\) 0 0
\(785\) 39.5904 1.41304
\(786\) 0 0
\(787\) 42.5411 1.51643 0.758214 0.652006i \(-0.226072\pi\)
0.758214 + 0.652006i \(0.226072\pi\)
\(788\) 0 0
\(789\) 12.6492 0.450323
\(790\) 0 0
\(791\) −52.5365 −1.86798
\(792\) 0 0
\(793\) 15.7354 0.558779
\(794\) 0 0
\(795\) −9.17352 −0.325351
\(796\) 0 0
\(797\) −19.3105 −0.684011 −0.342006 0.939698i \(-0.611106\pi\)
−0.342006 + 0.939698i \(0.611106\pi\)
\(798\) 0 0
\(799\) −8.97181 −0.317400
\(800\) 0 0
\(801\) −5.82489 −0.205812
\(802\) 0 0
\(803\) −77.4224 −2.73218
\(804\) 0 0
\(805\) −53.4192 −1.88278
\(806\) 0 0
\(807\) −12.5501 −0.441785
\(808\) 0 0
\(809\) 10.3817 0.365003 0.182501 0.983206i \(-0.441581\pi\)
0.182501 + 0.983206i \(0.441581\pi\)
\(810\) 0 0
\(811\) −3.30087 −0.115909 −0.0579546 0.998319i \(-0.518458\pi\)
−0.0579546 + 0.998319i \(0.518458\pi\)
\(812\) 0 0
\(813\) 23.0080 0.806926
\(814\) 0 0
\(815\) 1.74088 0.0609804
\(816\) 0 0
\(817\) −25.1473 −0.879791
\(818\) 0 0
\(819\) 19.0790 0.666676
\(820\) 0 0
\(821\) 23.1377 0.807511 0.403755 0.914867i \(-0.367705\pi\)
0.403755 + 0.914867i \(0.367705\pi\)
\(822\) 0 0
\(823\) −30.8167 −1.07420 −0.537102 0.843517i \(-0.680481\pi\)
−0.537102 + 0.843517i \(0.680481\pi\)
\(824\) 0 0
\(825\) −11.3527 −0.395249
\(826\) 0 0
\(827\) −42.7231 −1.48563 −0.742815 0.669497i \(-0.766510\pi\)
−0.742815 + 0.669497i \(0.766510\pi\)
\(828\) 0 0
\(829\) 11.6954 0.406198 0.203099 0.979158i \(-0.434899\pi\)
0.203099 + 0.979158i \(0.434899\pi\)
\(830\) 0 0
\(831\) −20.6993 −0.718050
\(832\) 0 0
\(833\) 152.081 5.26930
\(834\) 0 0
\(835\) −11.7584 −0.406916
\(836\) 0 0
\(837\) −11.0732 −0.382746
\(838\) 0 0
\(839\) −31.7883 −1.09745 −0.548727 0.836002i \(-0.684887\pi\)
−0.548727 + 0.836002i \(0.684887\pi\)
\(840\) 0 0
\(841\) −25.5966 −0.882643
\(842\) 0 0
\(843\) 30.9147 1.06476
\(844\) 0 0
\(845\) 1.72717 0.0594163
\(846\) 0 0
\(847\) 60.6175 2.08284
\(848\) 0 0
\(849\) 15.7644 0.541033
\(850\) 0 0
\(851\) 14.6844 0.503376
\(852\) 0 0
\(853\) 1.86112 0.0637234 0.0318617 0.999492i \(-0.489856\pi\)
0.0318617 + 0.999492i \(0.489856\pi\)
\(854\) 0 0
\(855\) 4.12685 0.141135
\(856\) 0 0
\(857\) −35.0269 −1.19650 −0.598249 0.801311i \(-0.704136\pi\)
−0.598249 + 0.801311i \(0.704136\pi\)
\(858\) 0 0
\(859\) −47.9439 −1.63582 −0.817912 0.575344i \(-0.804868\pi\)
−0.817912 + 0.575344i \(0.804868\pi\)
\(860\) 0 0
\(861\) −20.1349 −0.686197
\(862\) 0 0
\(863\) −22.5634 −0.768068 −0.384034 0.923319i \(-0.625466\pi\)
−0.384034 + 0.923319i \(0.625466\pi\)
\(864\) 0 0
\(865\) 17.4261 0.592505
\(866\) 0 0
\(867\) −47.8856 −1.62628
\(868\) 0 0
\(869\) −14.3498 −0.486782
\(870\) 0 0
\(871\) 2.65123 0.0898335
\(872\) 0 0
\(873\) −8.69438 −0.294260
\(874\) 0 0
\(875\) −60.7982 −2.05535
\(876\) 0 0
\(877\) 2.97906 0.100596 0.0502979 0.998734i \(-0.483983\pi\)
0.0502979 + 0.998734i \(0.483983\pi\)
\(878\) 0 0
\(879\) 9.59637 0.323678
\(880\) 0 0
\(881\) −24.7033 −0.832275 −0.416138 0.909302i \(-0.636617\pi\)
−0.416138 + 0.909302i \(0.636617\pi\)
\(882\) 0 0
\(883\) 22.0936 0.743510 0.371755 0.928331i \(-0.378756\pi\)
0.371755 + 0.928331i \(0.378756\pi\)
\(884\) 0 0
\(885\) 15.2303 0.511961
\(886\) 0 0
\(887\) −7.00169 −0.235094 −0.117547 0.993067i \(-0.537503\pi\)
−0.117547 + 0.993067i \(0.537503\pi\)
\(888\) 0 0
\(889\) 61.7308 2.07038
\(890\) 0 0
\(891\) −4.78702 −0.160371
\(892\) 0 0
\(893\) −2.83514 −0.0948744
\(894\) 0 0
\(895\) −8.57574 −0.286655
\(896\) 0 0
\(897\) 24.2907 0.811044
\(898\) 0 0
\(899\) 20.4281 0.681314
\(900\) 0 0
\(901\) 45.5785 1.51844
\(902\) 0 0
\(903\) 50.2578 1.67247
\(904\) 0 0
\(905\) −11.5179 −0.382867
\(906\) 0 0
\(907\) 16.0503 0.532943 0.266472 0.963843i \(-0.414142\pi\)
0.266472 + 0.963843i \(0.414142\pi\)
\(908\) 0 0
\(909\) −7.46387 −0.247561
\(910\) 0 0
\(911\) 8.69646 0.288127 0.144063 0.989568i \(-0.453983\pi\)
0.144063 + 0.989568i \(0.453983\pi\)
\(912\) 0 0
\(913\) 54.0320 1.78820
\(914\) 0 0
\(915\) −6.80224 −0.224875
\(916\) 0 0
\(917\) −44.7407 −1.47747
\(918\) 0 0
\(919\) 24.0545 0.793484 0.396742 0.917930i \(-0.370141\pi\)
0.396742 + 0.917930i \(0.370141\pi\)
\(920\) 0 0
\(921\) −20.3194 −0.669547
\(922\) 0 0
\(923\) 53.2930 1.75416
\(924\) 0 0
\(925\) 5.37681 0.176788
\(926\) 0 0
\(927\) −4.05463 −0.133172
\(928\) 0 0
\(929\) −2.25584 −0.0740118 −0.0370059 0.999315i \(-0.511782\pi\)
−0.0370059 + 0.999315i \(0.511782\pi\)
\(930\) 0 0
\(931\) 48.0585 1.57505
\(932\) 0 0
\(933\) 21.7343 0.711548
\(934\) 0 0
\(935\) −62.5158 −2.04448
\(936\) 0 0
\(937\) 5.56080 0.181663 0.0908317 0.995866i \(-0.471047\pi\)
0.0908317 + 0.995866i \(0.471047\pi\)
\(938\) 0 0
\(939\) 10.0035 0.326452
\(940\) 0 0
\(941\) −42.0092 −1.36946 −0.684731 0.728796i \(-0.740080\pi\)
−0.684731 + 0.728796i \(0.740080\pi\)
\(942\) 0 0
\(943\) −25.6351 −0.834792
\(944\) 0 0
\(945\) −8.24767 −0.268297
\(946\) 0 0
\(947\) −43.9687 −1.42879 −0.714395 0.699743i \(-0.753298\pi\)
−0.714395 + 0.699743i \(0.753298\pi\)
\(948\) 0 0
\(949\) 60.6563 1.96899
\(950\) 0 0
\(951\) −4.74953 −0.154014
\(952\) 0 0
\(953\) −16.8158 −0.544718 −0.272359 0.962196i \(-0.587804\pi\)
−0.272359 + 0.962196i \(0.587804\pi\)
\(954\) 0 0
\(955\) 26.2979 0.850980
\(956\) 0 0
\(957\) 8.83120 0.285472
\(958\) 0 0
\(959\) 19.5009 0.629717
\(960\) 0 0
\(961\) 91.6157 2.95535
\(962\) 0 0
\(963\) 8.22324 0.264990
\(964\) 0 0
\(965\) −25.8040 −0.830661
\(966\) 0 0
\(967\) −12.9469 −0.416344 −0.208172 0.978092i \(-0.566751\pi\)
−0.208172 + 0.978092i \(0.566751\pi\)
\(968\) 0 0
\(969\) −20.5042 −0.658690
\(970\) 0 0
\(971\) 22.0433 0.707403 0.353702 0.935358i \(-0.384923\pi\)
0.353702 + 0.935358i \(0.384923\pi\)
\(972\) 0 0
\(973\) 9.21139 0.295304
\(974\) 0 0
\(975\) 8.89421 0.284843
\(976\) 0 0
\(977\) −9.91543 −0.317223 −0.158611 0.987341i \(-0.550702\pi\)
−0.158611 + 0.987341i \(0.550702\pi\)
\(978\) 0 0
\(979\) 27.8839 0.891173
\(980\) 0 0
\(981\) −4.91908 −0.157054
\(982\) 0 0
\(983\) 32.2011 1.02705 0.513527 0.858073i \(-0.328338\pi\)
0.513527 + 0.858073i \(0.328338\pi\)
\(984\) 0 0
\(985\) 10.5147 0.335026
\(986\) 0 0
\(987\) 5.66614 0.180355
\(988\) 0 0
\(989\) 63.9863 2.03465
\(990\) 0 0
\(991\) 20.1212 0.639169 0.319585 0.947558i \(-0.396457\pi\)
0.319585 + 0.947558i \(0.396457\pi\)
\(992\) 0 0
\(993\) 5.77266 0.183190
\(994\) 0 0
\(995\) 22.8742 0.725161
\(996\) 0 0
\(997\) −48.8248 −1.54630 −0.773148 0.634226i \(-0.781319\pi\)
−0.773148 + 0.634226i \(0.781319\pi\)
\(998\) 0 0
\(999\) 2.26721 0.0717314
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 \(a_p\))