Properties

Label 8036.2.a.t.1.14
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(1.15563\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.15563 q^{3}\) \(+3.94572 q^{5}\) \(-1.66452 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.15563 q^{3}\) \(+3.94572 q^{5}\) \(-1.66452 q^{9}\) \(+1.12534 q^{11}\) \(+3.54416 q^{13}\) \(+4.55979 q^{15}\) \(+3.41735 q^{17}\) \(-1.28335 q^{19}\) \(-3.01618 q^{23}\) \(+10.5687 q^{25}\) \(-5.39046 q^{27}\) \(+7.53562 q^{29}\) \(-0.123190 q^{31}\) \(+1.30048 q^{33}\) \(+0.924137 q^{37}\) \(+4.09574 q^{39}\) \(-1.00000 q^{41}\) \(-3.99122 q^{43}\) \(-6.56772 q^{45}\) \(+1.47225 q^{47}\) \(+3.94919 q^{51}\) \(+8.78256 q^{53}\) \(+4.44029 q^{55}\) \(-1.48308 q^{57}\) \(-3.03142 q^{59}\) \(+12.2049 q^{61}\) \(+13.9842 q^{65}\) \(-2.72904 q^{67}\) \(-3.48559 q^{69}\) \(+5.72921 q^{71}\) \(-7.47002 q^{73}\) \(+12.2135 q^{75}\) \(+10.0679 q^{79}\) \(-1.23581 q^{81}\) \(-13.5564 q^{83}\) \(+13.4839 q^{85}\) \(+8.70838 q^{87}\) \(-0.778550 q^{89}\) \(-0.142362 q^{93}\) \(-5.06375 q^{95}\) \(-5.90424 q^{97}\) \(-1.87316 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.15563 0.667203 0.333602 0.942714i \(-0.391736\pi\)
0.333602 + 0.942714i \(0.391736\pi\)
\(4\) 0 0
\(5\) 3.94572 1.76458 0.882289 0.470708i \(-0.156001\pi\)
0.882289 + 0.470708i \(0.156001\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) −1.66452 −0.554840
\(10\) 0 0
\(11\) 1.12534 0.339304 0.169652 0.985504i \(-0.445736\pi\)
0.169652 + 0.985504i \(0.445736\pi\)
\(12\) 0 0
\(13\) 3.54416 0.982973 0.491486 0.870885i \(-0.336454\pi\)
0.491486 + 0.870885i \(0.336454\pi\)
\(14\) 0 0
\(15\) 4.55979 1.17733
\(16\) 0 0
\(17\) 3.41735 0.828830 0.414415 0.910088i \(-0.363986\pi\)
0.414415 + 0.910088i \(0.363986\pi\)
\(18\) 0 0
\(19\) −1.28335 −0.294421 −0.147211 0.989105i \(-0.547030\pi\)
−0.147211 + 0.989105i \(0.547030\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.01618 −0.628917 −0.314459 0.949271i \(-0.601823\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(24\) 0 0
\(25\) 10.5687 2.11374
\(26\) 0 0
\(27\) −5.39046 −1.03739
\(28\) 0 0
\(29\) 7.53562 1.39933 0.699664 0.714472i \(-0.253333\pi\)
0.699664 + 0.714472i \(0.253333\pi\)
\(30\) 0 0
\(31\) −0.123190 −0.0221256 −0.0110628 0.999939i \(-0.503521\pi\)
−0.0110628 + 0.999939i \(0.503521\pi\)
\(32\) 0 0
\(33\) 1.30048 0.226385
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0.924137 0.151927 0.0759636 0.997111i \(-0.475797\pi\)
0.0759636 + 0.997111i \(0.475797\pi\)
\(38\) 0 0
\(39\) 4.09574 0.655843
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.99122 −0.608655 −0.304327 0.952567i \(-0.598432\pi\)
−0.304327 + 0.952567i \(0.598432\pi\)
\(44\) 0 0
\(45\) −6.56772 −0.979059
\(46\) 0 0
\(47\) 1.47225 0.214749 0.107375 0.994219i \(-0.465756\pi\)
0.107375 + 0.994219i \(0.465756\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 3.94919 0.552998
\(52\) 0 0
\(53\) 8.78256 1.20638 0.603188 0.797599i \(-0.293897\pi\)
0.603188 + 0.797599i \(0.293897\pi\)
\(54\) 0 0
\(55\) 4.44029 0.598729
\(56\) 0 0
\(57\) −1.48308 −0.196439
\(58\) 0 0
\(59\) −3.03142 −0.394658 −0.197329 0.980337i \(-0.563227\pi\)
−0.197329 + 0.980337i \(0.563227\pi\)
\(60\) 0 0
\(61\) 12.2049 1.56267 0.781337 0.624110i \(-0.214538\pi\)
0.781337 + 0.624110i \(0.214538\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.9842 1.73453
\(66\) 0 0
\(67\) −2.72904 −0.333405 −0.166702 0.986007i \(-0.553312\pi\)
−0.166702 + 0.986007i \(0.553312\pi\)
\(68\) 0 0
\(69\) −3.48559 −0.419616
\(70\) 0 0
\(71\) 5.72921 0.679932 0.339966 0.940438i \(-0.389584\pi\)
0.339966 + 0.940438i \(0.389584\pi\)
\(72\) 0 0
\(73\) −7.47002 −0.874300 −0.437150 0.899389i \(-0.644012\pi\)
−0.437150 + 0.899389i \(0.644012\pi\)
\(74\) 0 0
\(75\) 12.2135 1.41029
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0679 1.13273 0.566365 0.824154i \(-0.308349\pi\)
0.566365 + 0.824154i \(0.308349\pi\)
\(80\) 0 0
\(81\) −1.23581 −0.137313
\(82\) 0 0
\(83\) −13.5564 −1.48801 −0.744004 0.668175i \(-0.767076\pi\)
−0.744004 + 0.668175i \(0.767076\pi\)
\(84\) 0 0
\(85\) 13.4839 1.46253
\(86\) 0 0
\(87\) 8.70838 0.933636
\(88\) 0 0
\(89\) −0.778550 −0.0825262 −0.0412631 0.999148i \(-0.513138\pi\)
−0.0412631 + 0.999148i \(0.513138\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −0.142362 −0.0147622
\(94\) 0 0
\(95\) −5.06375 −0.519530
\(96\) 0 0
\(97\) −5.90424 −0.599484 −0.299742 0.954020i \(-0.596901\pi\)
−0.299742 + 0.954020i \(0.596901\pi\)
\(98\) 0 0
\(99\) −1.87316 −0.188260
\(100\) 0 0
\(101\) 0.701602 0.0698120 0.0349060 0.999391i \(-0.488887\pi\)
0.0349060 + 0.999391i \(0.488887\pi\)
\(102\) 0 0
\(103\) −10.1863 −1.00369 −0.501844 0.864958i \(-0.667345\pi\)
−0.501844 + 0.864958i \(0.667345\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.70206 −0.937934 −0.468967 0.883216i \(-0.655374\pi\)
−0.468967 + 0.883216i \(0.655374\pi\)
\(108\) 0 0
\(109\) 8.43965 0.808371 0.404186 0.914677i \(-0.367555\pi\)
0.404186 + 0.914677i \(0.367555\pi\)
\(110\) 0 0
\(111\) 1.06796 0.101366
\(112\) 0 0
\(113\) 1.43990 0.135455 0.0677274 0.997704i \(-0.478425\pi\)
0.0677274 + 0.997704i \(0.478425\pi\)
\(114\) 0 0
\(115\) −11.9010 −1.10977
\(116\) 0 0
\(117\) −5.89932 −0.545393
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −9.73360 −0.884873
\(122\) 0 0
\(123\) −1.15563 −0.104200
\(124\) 0 0
\(125\) 21.9724 1.96528
\(126\) 0 0
\(127\) −12.4802 −1.10744 −0.553718 0.832704i \(-0.686791\pi\)
−0.553718 + 0.832704i \(0.686791\pi\)
\(128\) 0 0
\(129\) −4.61237 −0.406097
\(130\) 0 0
\(131\) 20.1838 1.76346 0.881732 0.471751i \(-0.156378\pi\)
0.881732 + 0.471751i \(0.156378\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −21.2692 −1.83056
\(136\) 0 0
\(137\) 9.14237 0.781085 0.390542 0.920585i \(-0.372287\pi\)
0.390542 + 0.920585i \(0.372287\pi\)
\(138\) 0 0
\(139\) 21.1559 1.79442 0.897210 0.441604i \(-0.145590\pi\)
0.897210 + 0.441604i \(0.145590\pi\)
\(140\) 0 0
\(141\) 1.70137 0.143281
\(142\) 0 0
\(143\) 3.98840 0.333527
\(144\) 0 0
\(145\) 29.7334 2.46922
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.12932 0.502134 0.251067 0.967970i \(-0.419219\pi\)
0.251067 + 0.967970i \(0.419219\pi\)
\(150\) 0 0
\(151\) 7.97172 0.648730 0.324365 0.945932i \(-0.394849\pi\)
0.324365 + 0.945932i \(0.394849\pi\)
\(152\) 0 0
\(153\) −5.68825 −0.459868
\(154\) 0 0
\(155\) −0.486073 −0.0390423
\(156\) 0 0
\(157\) −11.2658 −0.899109 −0.449555 0.893253i \(-0.648417\pi\)
−0.449555 + 0.893253i \(0.648417\pi\)
\(158\) 0 0
\(159\) 10.1494 0.804898
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.74597 0.136755 0.0683775 0.997660i \(-0.478218\pi\)
0.0683775 + 0.997660i \(0.478218\pi\)
\(164\) 0 0
\(165\) 5.13133 0.399474
\(166\) 0 0
\(167\) −14.2797 −1.10499 −0.552497 0.833515i \(-0.686325\pi\)
−0.552497 + 0.833515i \(0.686325\pi\)
\(168\) 0 0
\(169\) −0.438935 −0.0337642
\(170\) 0 0
\(171\) 2.13617 0.163357
\(172\) 0 0
\(173\) −4.43511 −0.337195 −0.168597 0.985685i \(-0.553924\pi\)
−0.168597 + 0.985685i \(0.553924\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −3.50320 −0.263317
\(178\) 0 0
\(179\) 1.00948 0.0754519 0.0377260 0.999288i \(-0.487989\pi\)
0.0377260 + 0.999288i \(0.487989\pi\)
\(180\) 0 0
\(181\) 14.8421 1.10320 0.551602 0.834107i \(-0.314017\pi\)
0.551602 + 0.834107i \(0.314017\pi\)
\(182\) 0 0
\(183\) 14.1043 1.04262
\(184\) 0 0
\(185\) 3.64638 0.268087
\(186\) 0 0
\(187\) 3.84570 0.281225
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.13720 0.299358 0.149679 0.988735i \(-0.452176\pi\)
0.149679 + 0.988735i \(0.452176\pi\)
\(192\) 0 0
\(193\) 9.94820 0.716087 0.358044 0.933705i \(-0.383444\pi\)
0.358044 + 0.933705i \(0.383444\pi\)
\(194\) 0 0
\(195\) 16.1606 1.15729
\(196\) 0 0
\(197\) 4.84994 0.345544 0.172772 0.984962i \(-0.444728\pi\)
0.172772 + 0.984962i \(0.444728\pi\)
\(198\) 0 0
\(199\) 27.3865 1.94137 0.970687 0.240345i \(-0.0772607\pi\)
0.970687 + 0.240345i \(0.0772607\pi\)
\(200\) 0 0
\(201\) −3.15375 −0.222449
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.94572 −0.275581
\(206\) 0 0
\(207\) 5.02049 0.348948
\(208\) 0 0
\(209\) −1.44421 −0.0998984
\(210\) 0 0
\(211\) −20.1342 −1.38610 −0.693048 0.720891i \(-0.743733\pi\)
−0.693048 + 0.720891i \(0.743733\pi\)
\(212\) 0 0
\(213\) 6.62084 0.453653
\(214\) 0 0
\(215\) −15.7482 −1.07402
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −8.63258 −0.583336
\(220\) 0 0
\(221\) 12.1116 0.814717
\(222\) 0 0
\(223\) −1.11801 −0.0748676 −0.0374338 0.999299i \(-0.511918\pi\)
−0.0374338 + 0.999299i \(0.511918\pi\)
\(224\) 0 0
\(225\) −17.5918 −1.17279
\(226\) 0 0
\(227\) 17.8238 1.18301 0.591503 0.806303i \(-0.298535\pi\)
0.591503 + 0.806303i \(0.298535\pi\)
\(228\) 0 0
\(229\) −18.6566 −1.23287 −0.616433 0.787408i \(-0.711423\pi\)
−0.616433 + 0.787408i \(0.711423\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5.63485 −0.369151 −0.184575 0.982818i \(-0.559091\pi\)
−0.184575 + 0.982818i \(0.559091\pi\)
\(234\) 0 0
\(235\) 5.80907 0.378942
\(236\) 0 0
\(237\) 11.6348 0.755761
\(238\) 0 0
\(239\) −9.13621 −0.590972 −0.295486 0.955347i \(-0.595482\pi\)
−0.295486 + 0.955347i \(0.595482\pi\)
\(240\) 0 0
\(241\) −23.6516 −1.52353 −0.761766 0.647852i \(-0.775668\pi\)
−0.761766 + 0.647852i \(0.775668\pi\)
\(242\) 0 0
\(243\) 14.7432 0.945779
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.54841 −0.289408
\(248\) 0 0
\(249\) −15.6662 −0.992804
\(250\) 0 0
\(251\) −8.96988 −0.566174 −0.283087 0.959094i \(-0.591359\pi\)
−0.283087 + 0.959094i \(0.591359\pi\)
\(252\) 0 0
\(253\) −3.39424 −0.213394
\(254\) 0 0
\(255\) 15.5824 0.975808
\(256\) 0 0
\(257\) −9.23528 −0.576081 −0.288040 0.957618i \(-0.593004\pi\)
−0.288040 + 0.957618i \(0.593004\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −12.5432 −0.776403
\(262\) 0 0
\(263\) 28.0521 1.72976 0.864882 0.501975i \(-0.167393\pi\)
0.864882 + 0.501975i \(0.167393\pi\)
\(264\) 0 0
\(265\) 34.6535 2.12875
\(266\) 0 0
\(267\) −0.899716 −0.0550617
\(268\) 0 0
\(269\) 7.96236 0.485474 0.242737 0.970092i \(-0.421955\pi\)
0.242737 + 0.970092i \(0.421955\pi\)
\(270\) 0 0
\(271\) 4.72220 0.286853 0.143426 0.989661i \(-0.454188\pi\)
0.143426 + 0.989661i \(0.454188\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 11.8934 0.717200
\(276\) 0 0
\(277\) 5.92448 0.355968 0.177984 0.984033i \(-0.443043\pi\)
0.177984 + 0.984033i \(0.443043\pi\)
\(278\) 0 0
\(279\) 0.205052 0.0122761
\(280\) 0 0
\(281\) −15.3710 −0.916956 −0.458478 0.888706i \(-0.651605\pi\)
−0.458478 + 0.888706i \(0.651605\pi\)
\(282\) 0 0
\(283\) −0.0322261 −0.00191564 −0.000957822 1.00000i \(-0.500305\pi\)
−0.000957822 1.00000i \(0.500305\pi\)
\(284\) 0 0
\(285\) −5.85182 −0.346632
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −5.32170 −0.313041
\(290\) 0 0
\(291\) −6.82311 −0.399978
\(292\) 0 0
\(293\) −3.21017 −0.187540 −0.0937700 0.995594i \(-0.529892\pi\)
−0.0937700 + 0.995594i \(0.529892\pi\)
\(294\) 0 0
\(295\) −11.9611 −0.696404
\(296\) 0 0
\(297\) −6.06612 −0.351992
\(298\) 0 0
\(299\) −10.6898 −0.618209
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0.810792 0.0465788
\(304\) 0 0
\(305\) 48.1569 2.75746
\(306\) 0 0
\(307\) −17.0753 −0.974540 −0.487270 0.873251i \(-0.662007\pi\)
−0.487270 + 0.873251i \(0.662007\pi\)
\(308\) 0 0
\(309\) −11.7716 −0.669663
\(310\) 0 0
\(311\) 20.9903 1.19025 0.595126 0.803632i \(-0.297102\pi\)
0.595126 + 0.803632i \(0.297102\pi\)
\(312\) 0 0
\(313\) 2.67884 0.151417 0.0757085 0.997130i \(-0.475878\pi\)
0.0757085 + 0.997130i \(0.475878\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 21.2252 1.19212 0.596062 0.802939i \(-0.296731\pi\)
0.596062 + 0.802939i \(0.296731\pi\)
\(318\) 0 0
\(319\) 8.48017 0.474798
\(320\) 0 0
\(321\) −11.2120 −0.625793
\(322\) 0 0
\(323\) −4.38567 −0.244025
\(324\) 0 0
\(325\) 37.4571 2.07775
\(326\) 0 0
\(327\) 9.75311 0.539348
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −7.04279 −0.387107 −0.193553 0.981090i \(-0.562001\pi\)
−0.193553 + 0.981090i \(0.562001\pi\)
\(332\) 0 0
\(333\) −1.53824 −0.0842952
\(334\) 0 0
\(335\) −10.7680 −0.588319
\(336\) 0 0
\(337\) −18.8099 −1.02464 −0.512322 0.858794i \(-0.671214\pi\)
−0.512322 + 0.858794i \(0.671214\pi\)
\(338\) 0 0
\(339\) 1.66400 0.0903759
\(340\) 0 0
\(341\) −0.138631 −0.00750730
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −13.7531 −0.740445
\(346\) 0 0
\(347\) −4.68569 −0.251541 −0.125771 0.992059i \(-0.540140\pi\)
−0.125771 + 0.992059i \(0.540140\pi\)
\(348\) 0 0
\(349\) 30.1321 1.61294 0.806468 0.591277i \(-0.201376\pi\)
0.806468 + 0.591277i \(0.201376\pi\)
\(350\) 0 0
\(351\) −19.1046 −1.01973
\(352\) 0 0
\(353\) −10.3867 −0.552829 −0.276414 0.961039i \(-0.589146\pi\)
−0.276414 + 0.961039i \(0.589146\pi\)
\(354\) 0 0
\(355\) 22.6058 1.19979
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −17.5176 −0.924542 −0.462271 0.886739i \(-0.652965\pi\)
−0.462271 + 0.886739i \(0.652965\pi\)
\(360\) 0 0
\(361\) −17.3530 −0.913316
\(362\) 0 0
\(363\) −11.2484 −0.590390
\(364\) 0 0
\(365\) −29.4746 −1.54277
\(366\) 0 0
\(367\) 7.27107 0.379547 0.189773 0.981828i \(-0.439225\pi\)
0.189773 + 0.981828i \(0.439225\pi\)
\(368\) 0 0
\(369\) 1.66452 0.0866514
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −33.3781 −1.72825 −0.864126 0.503275i \(-0.832128\pi\)
−0.864126 + 0.503275i \(0.832128\pi\)
\(374\) 0 0
\(375\) 25.3920 1.31124
\(376\) 0 0
\(377\) 26.7074 1.37550
\(378\) 0 0
\(379\) −8.88493 −0.456388 −0.228194 0.973616i \(-0.573282\pi\)
−0.228194 + 0.973616i \(0.573282\pi\)
\(380\) 0 0
\(381\) −14.4225 −0.738885
\(382\) 0 0
\(383\) −18.8596 −0.963679 −0.481840 0.876259i \(-0.660031\pi\)
−0.481840 + 0.876259i \(0.660031\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6.64346 0.337706
\(388\) 0 0
\(389\) −34.3262 −1.74041 −0.870203 0.492693i \(-0.836013\pi\)
−0.870203 + 0.492693i \(0.836013\pi\)
\(390\) 0 0
\(391\) −10.3074 −0.521265
\(392\) 0 0
\(393\) 23.3250 1.17659
\(394\) 0 0
\(395\) 39.7252 1.99879
\(396\) 0 0
\(397\) −10.5501 −0.529495 −0.264747 0.964318i \(-0.585289\pi\)
−0.264747 + 0.964318i \(0.585289\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 31.5621 1.57614 0.788068 0.615589i \(-0.211082\pi\)
0.788068 + 0.615589i \(0.211082\pi\)
\(402\) 0 0
\(403\) −0.436605 −0.0217488
\(404\) 0 0
\(405\) −4.87617 −0.242299
\(406\) 0 0
\(407\) 1.03997 0.0515495
\(408\) 0 0
\(409\) 20.1166 0.994703 0.497351 0.867549i \(-0.334306\pi\)
0.497351 + 0.867549i \(0.334306\pi\)
\(410\) 0 0
\(411\) 10.5652 0.521142
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −53.4897 −2.62571
\(416\) 0 0
\(417\) 24.4484 1.19724
\(418\) 0 0
\(419\) −22.6059 −1.10437 −0.552186 0.833721i \(-0.686206\pi\)
−0.552186 + 0.833721i \(0.686206\pi\)
\(420\) 0 0
\(421\) 3.68375 0.179535 0.0897674 0.995963i \(-0.471388\pi\)
0.0897674 + 0.995963i \(0.471388\pi\)
\(422\) 0 0
\(423\) −2.45058 −0.119151
\(424\) 0 0
\(425\) 36.1169 1.75193
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 4.60912 0.222530
\(430\) 0 0
\(431\) 40.2662 1.93956 0.969778 0.243988i \(-0.0784559\pi\)
0.969778 + 0.243988i \(0.0784559\pi\)
\(432\) 0 0
\(433\) 33.0742 1.58945 0.794723 0.606972i \(-0.207616\pi\)
0.794723 + 0.606972i \(0.207616\pi\)
\(434\) 0 0
\(435\) 34.3608 1.64747
\(436\) 0 0
\(437\) 3.87083 0.185167
\(438\) 0 0
\(439\) −10.1150 −0.482761 −0.241381 0.970431i \(-0.577600\pi\)
−0.241381 + 0.970431i \(0.577600\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.16423 −0.102826 −0.0514128 0.998677i \(-0.516372\pi\)
−0.0514128 + 0.998677i \(0.516372\pi\)
\(444\) 0 0
\(445\) −3.07194 −0.145624
\(446\) 0 0
\(447\) 7.08323 0.335025
\(448\) 0 0
\(449\) −34.2656 −1.61709 −0.808547 0.588431i \(-0.799746\pi\)
−0.808547 + 0.588431i \(0.799746\pi\)
\(450\) 0 0
\(451\) −1.12534 −0.0529904
\(452\) 0 0
\(453\) 9.21236 0.432835
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.3160 −0.763230 −0.381615 0.924321i \(-0.624632\pi\)
−0.381615 + 0.924321i \(0.624632\pi\)
\(458\) 0 0
\(459\) −18.4211 −0.859823
\(460\) 0 0
\(461\) −9.68932 −0.451277 −0.225638 0.974211i \(-0.572447\pi\)
−0.225638 + 0.974211i \(0.572447\pi\)
\(462\) 0 0
\(463\) 23.0970 1.07341 0.536705 0.843770i \(-0.319669\pi\)
0.536705 + 0.843770i \(0.319669\pi\)
\(464\) 0 0
\(465\) −0.561720 −0.0260491
\(466\) 0 0
\(467\) −22.0946 −1.02242 −0.511208 0.859457i \(-0.670802\pi\)
−0.511208 + 0.859457i \(0.670802\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −13.0191 −0.599889
\(472\) 0 0
\(473\) −4.49150 −0.206519
\(474\) 0 0
\(475\) −13.5634 −0.622329
\(476\) 0 0
\(477\) −14.6187 −0.669346
\(478\) 0 0
\(479\) 20.8078 0.950732 0.475366 0.879788i \(-0.342316\pi\)
0.475366 + 0.879788i \(0.342316\pi\)
\(480\) 0 0
\(481\) 3.27529 0.149340
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −23.2964 −1.05784
\(486\) 0 0
\(487\) −29.1355 −1.32025 −0.660127 0.751154i \(-0.729497\pi\)
−0.660127 + 0.751154i \(0.729497\pi\)
\(488\) 0 0
\(489\) 2.01770 0.0912434
\(490\) 0 0
\(491\) −15.8054 −0.713287 −0.356644 0.934240i \(-0.616079\pi\)
−0.356644 + 0.934240i \(0.616079\pi\)
\(492\) 0 0
\(493\) 25.7519 1.15981
\(494\) 0 0
\(495\) −7.39095 −0.332199
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −39.5339 −1.76978 −0.884890 0.465800i \(-0.845767\pi\)
−0.884890 + 0.465800i \(0.845767\pi\)
\(500\) 0 0
\(501\) −16.5020 −0.737255
\(502\) 0 0
\(503\) −38.5115 −1.71715 −0.858573 0.512692i \(-0.828648\pi\)
−0.858573 + 0.512692i \(0.828648\pi\)
\(504\) 0 0
\(505\) 2.76832 0.123189
\(506\) 0 0
\(507\) −0.507246 −0.0225276
\(508\) 0 0
\(509\) 17.2109 0.762858 0.381429 0.924398i \(-0.375432\pi\)
0.381429 + 0.924398i \(0.375432\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 6.91786 0.305431
\(514\) 0 0
\(515\) −40.1923 −1.77108
\(516\) 0 0
\(517\) 1.65678 0.0728653
\(518\) 0 0
\(519\) −5.12534 −0.224977
\(520\) 0 0
\(521\) −7.94448 −0.348054 −0.174027 0.984741i \(-0.555678\pi\)
−0.174027 + 0.984741i \(0.555678\pi\)
\(522\) 0 0
\(523\) 7.98595 0.349201 0.174601 0.984639i \(-0.444137\pi\)
0.174601 + 0.984639i \(0.444137\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.420983 −0.0183383
\(528\) 0 0
\(529\) −13.9027 −0.604463
\(530\) 0 0
\(531\) 5.04586 0.218972
\(532\) 0 0
\(533\) −3.54416 −0.153515
\(534\) 0 0
\(535\) −38.2816 −1.65506
\(536\) 0 0
\(537\) 1.16658 0.0503418
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.815853 −0.0350763 −0.0175381 0.999846i \(-0.505583\pi\)
−0.0175381 + 0.999846i \(0.505583\pi\)
\(542\) 0 0
\(543\) 17.1520 0.736061
\(544\) 0 0
\(545\) 33.3005 1.42643
\(546\) 0 0
\(547\) 24.0249 1.02723 0.513616 0.858020i \(-0.328306\pi\)
0.513616 + 0.858020i \(0.328306\pi\)
\(548\) 0 0
\(549\) −20.3152 −0.867033
\(550\) 0 0
\(551\) −9.67086 −0.411992
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 4.21387 0.178869
\(556\) 0 0
\(557\) 8.69660 0.368487 0.184243 0.982881i \(-0.441017\pi\)
0.184243 + 0.982881i \(0.441017\pi\)
\(558\) 0 0
\(559\) −14.1455 −0.598291
\(560\) 0 0
\(561\) 4.44421 0.187634
\(562\) 0 0
\(563\) 32.9095 1.38697 0.693486 0.720470i \(-0.256074\pi\)
0.693486 + 0.720470i \(0.256074\pi\)
\(564\) 0 0
\(565\) 5.68146 0.239021
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −19.8229 −0.831020 −0.415510 0.909589i \(-0.636397\pi\)
−0.415510 + 0.909589i \(0.636397\pi\)
\(570\) 0 0
\(571\) −5.62422 −0.235366 −0.117683 0.993051i \(-0.537547\pi\)
−0.117683 + 0.993051i \(0.537547\pi\)
\(572\) 0 0
\(573\) 4.78108 0.199732
\(574\) 0 0
\(575\) −31.8771 −1.32937
\(576\) 0 0
\(577\) 17.7611 0.739404 0.369702 0.929150i \(-0.379460\pi\)
0.369702 + 0.929150i \(0.379460\pi\)
\(578\) 0 0
\(579\) 11.4964 0.477776
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 9.88340 0.409329
\(584\) 0 0
\(585\) −23.2771 −0.962388
\(586\) 0 0
\(587\) −24.6592 −1.01779 −0.508897 0.860827i \(-0.669947\pi\)
−0.508897 + 0.860827i \(0.669947\pi\)
\(588\) 0 0
\(589\) 0.158096 0.00651424
\(590\) 0 0
\(591\) 5.60474 0.230548
\(592\) 0 0
\(593\) 33.2007 1.36339 0.681695 0.731637i \(-0.261243\pi\)
0.681695 + 0.731637i \(0.261243\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 31.6486 1.29529
\(598\) 0 0
\(599\) 26.3074 1.07489 0.537445 0.843299i \(-0.319389\pi\)
0.537445 + 0.843299i \(0.319389\pi\)
\(600\) 0 0
\(601\) −46.3932 −1.89242 −0.946209 0.323556i \(-0.895122\pi\)
−0.946209 + 0.323556i \(0.895122\pi\)
\(602\) 0 0
\(603\) 4.54253 0.184986
\(604\) 0 0
\(605\) −38.4060 −1.56143
\(606\) 0 0
\(607\) −20.5000 −0.832069 −0.416034 0.909349i \(-0.636580\pi\)
−0.416034 + 0.909349i \(0.636580\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 5.21788 0.211093
\(612\) 0 0
\(613\) −7.94499 −0.320895 −0.160448 0.987044i \(-0.551294\pi\)
−0.160448 + 0.987044i \(0.551294\pi\)
\(614\) 0 0
\(615\) −4.55979 −0.183868
\(616\) 0 0
\(617\) 1.49848 0.0603265 0.0301632 0.999545i \(-0.490397\pi\)
0.0301632 + 0.999545i \(0.490397\pi\)
\(618\) 0 0
\(619\) −18.4540 −0.741731 −0.370865 0.928687i \(-0.620939\pi\)
−0.370865 + 0.928687i \(0.620939\pi\)
\(620\) 0 0
\(621\) 16.2586 0.652435
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 33.8536 1.35415
\(626\) 0 0
\(627\) −1.66898 −0.0666525
\(628\) 0 0
\(629\) 3.15810 0.125922
\(630\) 0 0
\(631\) 46.7823 1.86237 0.931187 0.364543i \(-0.118775\pi\)
0.931187 + 0.364543i \(0.118775\pi\)
\(632\) 0 0
\(633\) −23.2677 −0.924808
\(634\) 0 0
\(635\) −49.2432 −1.95416
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −9.53638 −0.377253
\(640\) 0 0
\(641\) −0.554345 −0.0218953 −0.0109476 0.999940i \(-0.503485\pi\)
−0.0109476 + 0.999940i \(0.503485\pi\)
\(642\) 0 0
\(643\) −16.3700 −0.645572 −0.322786 0.946472i \(-0.604619\pi\)
−0.322786 + 0.946472i \(0.604619\pi\)
\(644\) 0 0
\(645\) −18.1991 −0.716589
\(646\) 0 0
\(647\) 6.20653 0.244004 0.122002 0.992530i \(-0.461069\pi\)
0.122002 + 0.992530i \(0.461069\pi\)
\(648\) 0 0
\(649\) −3.41140 −0.133909
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.86445 0.0729616 0.0364808 0.999334i \(-0.488385\pi\)
0.0364808 + 0.999334i \(0.488385\pi\)
\(654\) 0 0
\(655\) 79.6394 3.11177
\(656\) 0 0
\(657\) 12.4340 0.485097
\(658\) 0 0
\(659\) −35.2076 −1.37149 −0.685747 0.727840i \(-0.740524\pi\)
−0.685747 + 0.727840i \(0.740524\pi\)
\(660\) 0 0
\(661\) 16.1818 0.629397 0.314699 0.949192i \(-0.398097\pi\)
0.314699 + 0.949192i \(0.398097\pi\)
\(662\) 0 0
\(663\) 13.9966 0.543582
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −22.7288 −0.880062
\(668\) 0 0
\(669\) −1.29201 −0.0499519
\(670\) 0 0
\(671\) 13.7347 0.530222
\(672\) 0 0
\(673\) 0.0216325 0.000833870 0 0.000416935 1.00000i \(-0.499867\pi\)
0.000416935 1.00000i \(0.499867\pi\)
\(674\) 0 0
\(675\) −56.9700 −2.19278
\(676\) 0 0
\(677\) 29.8548 1.14741 0.573706 0.819061i \(-0.305505\pi\)
0.573706 + 0.819061i \(0.305505\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 20.5977 0.789305
\(682\) 0 0
\(683\) −23.2050 −0.887913 −0.443956 0.896048i \(-0.646426\pi\)
−0.443956 + 0.896048i \(0.646426\pi\)
\(684\) 0 0
\(685\) 36.0732 1.37829
\(686\) 0 0
\(687\) −21.5602 −0.822572
\(688\) 0 0
\(689\) 31.1268 1.18584
\(690\) 0 0
\(691\) 9.06237 0.344749 0.172374 0.985032i \(-0.444856\pi\)
0.172374 + 0.985032i \(0.444856\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 83.4752 3.16639
\(696\) 0 0
\(697\) −3.41735 −0.129441
\(698\) 0 0
\(699\) −6.51179 −0.246299
\(700\) 0 0
\(701\) 5.46047 0.206239 0.103120 0.994669i \(-0.467118\pi\)
0.103120 + 0.994669i \(0.467118\pi\)
\(702\) 0 0
\(703\) −1.18599 −0.0447306
\(704\) 0 0
\(705\) 6.71313 0.252831
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −36.2012 −1.35956 −0.679782 0.733414i \(-0.737926\pi\)
−0.679782 + 0.733414i \(0.737926\pi\)
\(710\) 0 0
\(711\) −16.7583 −0.628484
\(712\) 0 0
\(713\) 0.371563 0.0139152
\(714\) 0 0
\(715\) 15.7371 0.588534
\(716\) 0 0
\(717\) −10.5581 −0.394299
\(718\) 0 0
\(719\) 42.8296 1.59728 0.798638 0.601812i \(-0.205554\pi\)
0.798638 + 0.601812i \(0.205554\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −27.3325 −1.01651
\(724\) 0 0
\(725\) 79.6415 2.95781
\(726\) 0 0
\(727\) −49.0331 −1.81854 −0.909268 0.416210i \(-0.863358\pi\)
−0.909268 + 0.416210i \(0.863358\pi\)
\(728\) 0 0
\(729\) 20.7452 0.768339
\(730\) 0 0
\(731\) −13.6394 −0.504471
\(732\) 0 0
\(733\) 12.6149 0.465942 0.232971 0.972484i \(-0.425155\pi\)
0.232971 + 0.972484i \(0.425155\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.07111 −0.113126
\(738\) 0 0
\(739\) 11.7584 0.432539 0.216270 0.976334i \(-0.430611\pi\)
0.216270 + 0.976334i \(0.430611\pi\)
\(740\) 0 0
\(741\) −5.25628 −0.193094
\(742\) 0 0
\(743\) −0.0548021 −0.00201049 −0.00100525 0.999999i \(-0.500320\pi\)
−0.00100525 + 0.999999i \(0.500320\pi\)
\(744\) 0 0
\(745\) 24.1846 0.886054
\(746\) 0 0
\(747\) 22.5649 0.825606
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 39.3802 1.43700 0.718501 0.695525i \(-0.244828\pi\)
0.718501 + 0.695525i \(0.244828\pi\)
\(752\) 0 0
\(753\) −10.3659 −0.377753
\(754\) 0 0
\(755\) 31.4542 1.14473
\(756\) 0 0
\(757\) 3.34906 0.121724 0.0608618 0.998146i \(-0.480615\pi\)
0.0608618 + 0.998146i \(0.480615\pi\)
\(758\) 0 0
\(759\) −3.92249 −0.142377
\(760\) 0 0
\(761\) 40.4465 1.46618 0.733092 0.680130i \(-0.238077\pi\)
0.733092 + 0.680130i \(0.238077\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −22.4442 −0.811473
\(766\) 0 0
\(767\) −10.7438 −0.387938
\(768\) 0 0
\(769\) 13.4548 0.485194 0.242597 0.970127i \(-0.422001\pi\)
0.242597 + 0.970127i \(0.422001\pi\)
\(770\) 0 0
\(771\) −10.6726 −0.384363
\(772\) 0 0
\(773\) 55.4155 1.99316 0.996579 0.0826452i \(-0.0263368\pi\)
0.996579 + 0.0826452i \(0.0263368\pi\)
\(774\) 0 0
\(775\) −1.30196 −0.0467676
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.28335 0.0459809
\(780\) 0 0
\(781\) 6.44733 0.230704
\(782\) 0 0
\(783\) −40.6204 −1.45166
\(784\) 0 0
\(785\) −44.4517 −1.58655
\(786\) 0 0
\(787\) −34.9091 −1.24438 −0.622188 0.782868i \(-0.713756\pi\)
−0.622188 + 0.782868i \(0.713756\pi\)
\(788\) 0 0
\(789\) 32.4178 1.15410
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 43.2560 1.53607
\(794\) 0 0
\(795\) 40.0466 1.42031
\(796\) 0 0
\(797\) −8.12865 −0.287931 −0.143966 0.989583i \(-0.545986\pi\)
−0.143966 + 0.989583i \(0.545986\pi\)
\(798\) 0 0
\(799\) 5.03118 0.177991
\(800\) 0 0
\(801\) 1.29591 0.0457888
\(802\) 0 0
\(803\) −8.40635 −0.296654
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 9.20154 0.323910
\(808\) 0 0
\(809\) 40.9839 1.44092 0.720458 0.693499i \(-0.243932\pi\)
0.720458 + 0.693499i \(0.243932\pi\)
\(810\) 0 0
\(811\) 5.69788 0.200080 0.100040 0.994983i \(-0.468103\pi\)
0.100040 + 0.994983i \(0.468103\pi\)
\(812\) 0 0
\(813\) 5.45711 0.191389
\(814\) 0 0
\(815\) 6.88911 0.241315
\(816\) 0 0
\(817\) 5.12214 0.179201
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 17.3086 0.604076 0.302038 0.953296i \(-0.402333\pi\)
0.302038 + 0.953296i \(0.402333\pi\)
\(822\) 0 0
\(823\) −47.3436 −1.65030 −0.825148 0.564917i \(-0.808908\pi\)
−0.825148 + 0.564917i \(0.808908\pi\)
\(824\) 0 0
\(825\) 13.7444 0.478518
\(826\) 0 0
\(827\) 50.9924 1.77318 0.886589 0.462558i \(-0.153068\pi\)
0.886589 + 0.462558i \(0.153068\pi\)
\(828\) 0 0
\(829\) 21.9429 0.762110 0.381055 0.924552i \(-0.375561\pi\)
0.381055 + 0.924552i \(0.375561\pi\)
\(830\) 0 0
\(831\) 6.84651 0.237503
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −56.3435 −1.94985
\(836\) 0 0
\(837\) 0.664050 0.0229529
\(838\) 0 0
\(839\) 5.79049 0.199910 0.0999550 0.994992i \(-0.468130\pi\)
0.0999550 + 0.994992i \(0.468130\pi\)
\(840\) 0 0
\(841\) 27.7855 0.958121
\(842\) 0 0
\(843\) −17.7632 −0.611796
\(844\) 0 0
\(845\) −1.73191 −0.0595796
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −0.0372415 −0.00127812
\(850\) 0 0
\(851\) −2.78736 −0.0955496
\(852\) 0 0
\(853\) −6.63091 −0.227038 −0.113519 0.993536i \(-0.536212\pi\)
−0.113519 + 0.993536i \(0.536212\pi\)
\(854\) 0 0
\(855\) 8.42871 0.288256
\(856\) 0 0
\(857\) 3.09276 0.105647 0.0528233 0.998604i \(-0.483178\pi\)
0.0528233 + 0.998604i \(0.483178\pi\)
\(858\) 0 0
\(859\) 11.7716 0.401640 0.200820 0.979628i \(-0.435639\pi\)
0.200820 + 0.979628i \(0.435639\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 32.7828 1.11594 0.557970 0.829861i \(-0.311580\pi\)
0.557970 + 0.829861i \(0.311580\pi\)
\(864\) 0 0
\(865\) −17.4997 −0.595007
\(866\) 0 0
\(867\) −6.14992 −0.208862
\(868\) 0 0
\(869\) 11.3299 0.384340
\(870\) 0 0
\(871\) −9.67214 −0.327728
\(872\) 0 0
\(873\) 9.82772 0.332618
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.6650 −1.27186 −0.635929 0.771748i \(-0.719383\pi\)
−0.635929 + 0.771748i \(0.719383\pi\)
\(878\) 0 0
\(879\) −3.70976 −0.125127
\(880\) 0 0
\(881\) −57.0582 −1.92234 −0.961170 0.275956i \(-0.911006\pi\)
−0.961170 + 0.275956i \(0.911006\pi\)
\(882\) 0 0
\(883\) −40.5820 −1.36569 −0.682846 0.730562i \(-0.739258\pi\)
−0.682846 + 0.730562i \(0.739258\pi\)
\(884\) 0 0
\(885\) −13.8226 −0.464643
\(886\) 0 0
\(887\) −8.35120 −0.280406 −0.140203 0.990123i \(-0.544775\pi\)
−0.140203 + 0.990123i \(0.544775\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.39072 −0.0465908
\(892\) 0 0
\(893\) −1.88941 −0.0632268
\(894\) 0 0
\(895\) 3.98311 0.133141
\(896\) 0 0
\(897\) −12.3535 −0.412471
\(898\) 0 0
\(899\) −0.928312 −0.0309609
\(900\) 0 0
\(901\) 30.0131 0.999881
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 58.5627 1.94669
\(906\) 0 0
\(907\) −13.9348 −0.462696 −0.231348 0.972871i \(-0.574314\pi\)
−0.231348 + 0.972871i \(0.574314\pi\)
\(908\) 0 0
\(909\) −1.16783 −0.0387345
\(910\) 0 0
\(911\) −9.88485 −0.327500 −0.163750 0.986502i \(-0.552359\pi\)
−0.163750 + 0.986502i \(0.552359\pi\)
\(912\) 0 0
\(913\) −15.2556 −0.504887
\(914\) 0 0
\(915\) 55.6516 1.83979
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 38.6877 1.27619 0.638095 0.769958i \(-0.279723\pi\)
0.638095 + 0.769958i \(0.279723\pi\)
\(920\) 0 0
\(921\) −19.7327 −0.650216
\(922\) 0 0
\(923\) 20.3052 0.668355
\(924\) 0 0
\(925\) 9.76691 0.321134
\(926\) 0 0
\(927\) 16.9553 0.556886
\(928\) 0 0
\(929\) −33.3468 −1.09407 −0.547036 0.837109i \(-0.684244\pi\)
−0.547036 + 0.837109i \(0.684244\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 24.2571 0.794140
\(934\) 0 0
\(935\) 15.1740 0.496244
\(936\) 0 0
\(937\) −25.5278 −0.833957 −0.416979 0.908916i \(-0.636911\pi\)
−0.416979 + 0.908916i \(0.636911\pi\)
\(938\) 0 0
\(939\) 3.09575 0.101026
\(940\) 0 0
\(941\) −16.5550 −0.539679 −0.269839 0.962905i \(-0.586971\pi\)
−0.269839 + 0.962905i \(0.586971\pi\)
\(942\) 0 0
\(943\) 3.01618 0.0982204
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −49.6494 −1.61339 −0.806694 0.590970i \(-0.798745\pi\)
−0.806694 + 0.590970i \(0.798745\pi\)
\(948\) 0 0
\(949\) −26.4750 −0.859413
\(950\) 0 0
\(951\) 24.5284 0.795388
\(952\) 0 0
\(953\) 39.4973 1.27944 0.639721 0.768607i \(-0.279050\pi\)
0.639721 + 0.768607i \(0.279050\pi\)
\(954\) 0 0
\(955\) 16.3242 0.528240
\(956\) 0 0
\(957\) 9.79993 0.316787
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −30.9848 −0.999510
\(962\) 0 0
\(963\) 16.1493 0.520403
\(964\) 0 0
\(965\) 39.2528 1.26359
\(966\) 0 0
\(967\) 27.3053 0.878080 0.439040 0.898468i \(-0.355319\pi\)
0.439040 + 0.898468i \(0.355319\pi\)
\(968\) 0 0
\(969\) −5.06821 −0.162814
\(970\) 0 0
\(971\) −21.9950 −0.705853 −0.352926 0.935651i \(-0.614813\pi\)
−0.352926 + 0.935651i \(0.614813\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 43.2865 1.38628
\(976\) 0 0
\(977\) 8.72454 0.279123 0.139561 0.990213i \(-0.455431\pi\)
0.139561 + 0.990213i \(0.455431\pi\)
\(978\) 0 0
\(979\) −0.876138 −0.0280015
\(980\) 0 0
\(981\) −14.0480 −0.448517
\(982\) 0 0
\(983\) 46.1851 1.47307 0.736537 0.676397i \(-0.236460\pi\)
0.736537 + 0.676397i \(0.236460\pi\)
\(984\) 0 0
\(985\) 19.1365 0.609739
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 12.0382 0.382794
\(990\) 0 0
\(991\) −12.3287 −0.391635 −0.195818 0.980640i \(-0.562736\pi\)
−0.195818 + 0.980640i \(0.562736\pi\)
\(992\) 0 0
\(993\) −8.13886 −0.258279
\(994\) 0 0
\(995\) 108.059 3.42571
\(996\) 0 0
\(997\) 39.9390 1.26488 0.632441 0.774609i \(-0.282053\pi\)
0.632441 + 0.774609i \(0.282053\pi\)
\(998\) 0 0
\(999\) −4.98152 −0.157608
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 \(a_p\))