Properties

Label 4032.2.c.k.2017.1
Level 4032
Weight 2
Character 4032.2017
Analytic conductor 32.196
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.195682095\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2017.1
Root \(-0.866025 - 0.500000i\)
Character \(\chi\) = 4032.2017
Dual form 4032.2.c.k.2017.4

$q$-expansion

\(f(q)\) \(=\) \(q-2.73205i q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-2.73205i q^{5} -1.00000 q^{7} -5.46410i q^{11} -6.73205i q^{13} -2.00000 q^{17} -1.26795i q^{19} -3.46410 q^{23} -2.46410 q^{25} -1.46410i q^{29} -4.00000 q^{31} +2.73205i q^{35} -1.46410i q^{37} +2.00000 q^{41} +5.46410i q^{43} +2.92820 q^{47} +1.00000 q^{49} -12.0000i q^{53} -14.9282 q^{55} +9.66025i q^{59} +11.1244i q^{61} -18.3923 q^{65} +8.00000i q^{67} +2.92820 q^{71} +12.9282 q^{73} +5.46410i q^{77} +10.9282 q^{79} +5.66025i q^{83} +5.46410i q^{85} -11.8564 q^{89} +6.73205i q^{91} -3.46410 q^{95} +8.92820 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{7} + O(q^{10}) \) \( 4q - 4q^{7} - 8q^{17} + 4q^{25} - 16q^{31} + 8q^{41} - 16q^{47} + 4q^{49} - 32q^{55} - 32q^{65} - 16q^{71} + 24q^{73} + 16q^{79} + 8q^{89} + 8q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) − 2.73205i − 1.22181i −0.791704 0.610905i \(-0.790806\pi\)
0.791704 0.610905i \(-0.209194\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 5.46410i − 1.64749i −0.566961 0.823744i \(-0.691881\pi\)
0.566961 0.823744i \(-0.308119\pi\)
\(12\) 0 0
\(13\) − 6.73205i − 1.86713i −0.358402 0.933567i \(-0.616678\pi\)
0.358402 0.933567i \(-0.383322\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) − 1.26795i − 0.290887i −0.989367 0.145444i \(-0.953539\pi\)
0.989367 0.145444i \(-0.0464610\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.46410 −0.722315 −0.361158 0.932505i \(-0.617618\pi\)
−0.361158 + 0.932505i \(0.617618\pi\)
\(24\) 0 0
\(25\) −2.46410 −0.492820
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 1.46410i − 0.271877i −0.990717 0.135938i \(-0.956595\pi\)
0.990717 0.135938i \(-0.0434049\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.73205i 0.461801i
\(36\) 0 0
\(37\) − 1.46410i − 0.240697i −0.992732 0.120348i \(-0.961599\pi\)
0.992732 0.120348i \(-0.0384012\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 5.46410i 0.833268i 0.909074 + 0.416634i \(0.136790\pi\)
−0.909074 + 0.416634i \(0.863210\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 2.92820 0.427122 0.213561 0.976930i \(-0.431494\pi\)
0.213561 + 0.976930i \(0.431494\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 12.0000i − 1.64833i −0.566352 0.824163i \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 0 0
\(55\) −14.9282 −2.01292
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 9.66025i 1.25766i 0.777544 + 0.628829i \(0.216465\pi\)
−0.777544 + 0.628829i \(0.783535\pi\)
\(60\) 0 0
\(61\) 11.1244i 1.42433i 0.702013 + 0.712164i \(0.252285\pi\)
−0.702013 + 0.712164i \(0.747715\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −18.3923 −2.28128
\(66\) 0 0
\(67\) 8.00000i 0.977356i 0.872464 + 0.488678i \(0.162521\pi\)
−0.872464 + 0.488678i \(0.837479\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.92820 0.347514 0.173757 0.984789i \(-0.444409\pi\)
0.173757 + 0.984789i \(0.444409\pi\)
\(72\) 0 0
\(73\) 12.9282 1.51313 0.756566 0.653917i \(-0.226876\pi\)
0.756566 + 0.653917i \(0.226876\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.46410i 0.622692i
\(78\) 0 0
\(79\) 10.9282 1.22952 0.614759 0.788715i \(-0.289253\pi\)
0.614759 + 0.788715i \(0.289253\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.66025i 0.621294i 0.950525 + 0.310647i \(0.100546\pi\)
−0.950525 + 0.310647i \(0.899454\pi\)
\(84\) 0 0
\(85\) 5.46410i 0.592665i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −11.8564 −1.25678 −0.628388 0.777900i \(-0.716285\pi\)
−0.628388 + 0.777900i \(0.716285\pi\)
\(90\) 0 0
\(91\) 6.73205i 0.705711i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.46410 −0.355409
\(96\) 0 0
\(97\) 8.92820 0.906522 0.453261 0.891378i \(-0.350261\pi\)
0.453261 + 0.891378i \(0.350261\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.66025i 0.165201i 0.996583 + 0.0826007i \(0.0263226\pi\)
−0.996583 + 0.0826007i \(0.973677\pi\)
\(102\) 0 0
\(103\) −9.85641 −0.971181 −0.485590 0.874187i \(-0.661395\pi\)
−0.485590 + 0.874187i \(0.661395\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 5.07180i − 0.490309i −0.969484 0.245155i \(-0.921161\pi\)
0.969484 0.245155i \(-0.0788387\pi\)
\(108\) 0 0
\(109\) − 12.3923i − 1.18697i −0.804846 0.593484i \(-0.797752\pi\)
0.804846 0.593484i \(-0.202248\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.53590 0.614846 0.307423 0.951573i \(-0.400533\pi\)
0.307423 + 0.951573i \(0.400533\pi\)
\(114\) 0 0
\(115\) 9.46410i 0.882532i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) −18.8564 −1.71422
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 6.92820i − 0.619677i
\(126\) 0 0
\(127\) 11.4641 1.01727 0.508637 0.860981i \(-0.330149\pi\)
0.508637 + 0.860981i \(0.330149\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.7321i 0.937664i 0.883287 + 0.468832i \(0.155325\pi\)
−0.883287 + 0.468832i \(0.844675\pi\)
\(132\) 0 0
\(133\) 1.26795i 0.109945i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −19.8564 −1.69645 −0.848224 0.529638i \(-0.822328\pi\)
−0.848224 + 0.529638i \(0.822328\pi\)
\(138\) 0 0
\(139\) − 9.26795i − 0.786097i −0.919518 0.393049i \(-0.871420\pi\)
0.919518 0.393049i \(-0.128580\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −36.7846 −3.07608
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 1.07180i − 0.0878050i −0.999036 0.0439025i \(-0.986021\pi\)
0.999036 0.0439025i \(-0.0139791\pi\)
\(150\) 0 0
\(151\) 2.39230 0.194683 0.0973415 0.995251i \(-0.468966\pi\)
0.0973415 + 0.995251i \(0.468966\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 10.9282i 0.877774i
\(156\) 0 0
\(157\) 12.1962i 0.973359i 0.873581 + 0.486679i \(0.161792\pi\)
−0.873581 + 0.486679i \(0.838208\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.46410 0.273009
\(162\) 0 0
\(163\) − 13.4641i − 1.05459i −0.849682 0.527295i \(-0.823206\pi\)
0.849682 0.527295i \(-0.176794\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.07180 −0.392467 −0.196234 0.980557i \(-0.562871\pi\)
−0.196234 + 0.980557i \(0.562871\pi\)
\(168\) 0 0
\(169\) −32.3205 −2.48619
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.80385i 0.289201i 0.989490 + 0.144601i \(0.0461897\pi\)
−0.989490 + 0.144601i \(0.953810\pi\)
\(174\) 0 0
\(175\) 2.46410 0.186269
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.92820i 0.218864i 0.993994 + 0.109432i \(0.0349032\pi\)
−0.993994 + 0.109432i \(0.965097\pi\)
\(180\) 0 0
\(181\) − 10.7321i − 0.797707i −0.917015 0.398854i \(-0.869408\pi\)
0.917015 0.398854i \(-0.130592\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.00000 −0.294086
\(186\) 0 0
\(187\) 10.9282i 0.799149i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 16.0000 1.15772 0.578860 0.815427i \(-0.303498\pi\)
0.578860 + 0.815427i \(0.303498\pi\)
\(192\) 0 0
\(193\) 6.53590 0.470464 0.235232 0.971939i \(-0.424415\pi\)
0.235232 + 0.971939i \(0.424415\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 25.8564i − 1.84219i −0.389335 0.921096i \(-0.627295\pi\)
0.389335 0.921096i \(-0.372705\pi\)
\(198\) 0 0
\(199\) 4.00000 0.283552 0.141776 0.989899i \(-0.454719\pi\)
0.141776 + 0.989899i \(0.454719\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.46410i 0.102760i
\(204\) 0 0
\(205\) − 5.46410i − 0.381629i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −6.92820 −0.479234
\(210\) 0 0
\(211\) 16.7846i 1.15550i 0.816214 + 0.577750i \(0.196069\pi\)
−0.816214 + 0.577750i \(0.803931\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 14.9282 1.01810
\(216\) 0 0
\(217\) 4.00000 0.271538
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13.4641i 0.905693i
\(222\) 0 0
\(223\) 6.92820 0.463947 0.231973 0.972722i \(-0.425482\pi\)
0.231973 + 0.972722i \(0.425482\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 3.80385i − 0.252470i −0.992000 0.126235i \(-0.959711\pi\)
0.992000 0.126235i \(-0.0402894\pi\)
\(228\) 0 0
\(229\) − 17.2679i − 1.14110i −0.821263 0.570549i \(-0.806730\pi\)
0.821263 0.570549i \(-0.193270\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) − 8.00000i − 0.521862i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −12.5359 −0.810880 −0.405440 0.914122i \(-0.632882\pi\)
−0.405440 + 0.914122i \(0.632882\pi\)
\(240\) 0 0
\(241\) −18.7846 −1.21002 −0.605012 0.796217i \(-0.706832\pi\)
−0.605012 + 0.796217i \(0.706832\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 2.73205i − 0.174544i
\(246\) 0 0
\(247\) −8.53590 −0.543126
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.8038i 0.997530i 0.866737 + 0.498765i \(0.166213\pi\)
−0.866737 + 0.498765i \(0.833787\pi\)
\(252\) 0 0
\(253\) 18.9282i 1.19001i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 1.46410i 0.0909748i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 10.9282 0.673862 0.336931 0.941529i \(-0.390611\pi\)
0.336931 + 0.941529i \(0.390611\pi\)
\(264\) 0 0
\(265\) −32.7846 −2.01394
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.5885i 0.767532i 0.923430 + 0.383766i \(0.125373\pi\)
−0.923430 + 0.383766i \(0.874627\pi\)
\(270\) 0 0
\(271\) −14.9282 −0.906824 −0.453412 0.891301i \(-0.649793\pi\)
−0.453412 + 0.891301i \(0.649793\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 13.4641i 0.811916i
\(276\) 0 0
\(277\) − 4.00000i − 0.240337i −0.992754 0.120168i \(-0.961657\pi\)
0.992754 0.120168i \(-0.0383434\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 16.5885i 0.986081i 0.870006 + 0.493041i \(0.164115\pi\)
−0.870006 + 0.493041i \(0.835885\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 12.1962i − 0.712507i −0.934389 0.356253i \(-0.884054\pi\)
0.934389 0.356253i \(-0.115946\pi\)
\(294\) 0 0
\(295\) 26.3923 1.53662
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 23.3205i 1.34866i
\(300\) 0 0
\(301\) − 5.46410i − 0.314946i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 30.3923 1.74026
\(306\) 0 0
\(307\) − 8.58846i − 0.490169i −0.969502 0.245085i \(-0.921184\pi\)
0.969502 0.245085i \(-0.0788157\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −5.85641 −0.332086 −0.166043 0.986118i \(-0.553099\pi\)
−0.166043 + 0.986118i \(0.553099\pi\)
\(312\) 0 0
\(313\) 19.8564 1.12235 0.561175 0.827697i \(-0.310349\pi\)
0.561175 + 0.827697i \(0.310349\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 28.7846i 1.61670i 0.588699 + 0.808352i \(0.299640\pi\)
−0.588699 + 0.808352i \(0.700360\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.53590i 0.141101i
\(324\) 0 0
\(325\) 16.5885i 0.920162i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.92820 −0.161437
\(330\) 0 0
\(331\) − 16.3923i − 0.901003i −0.892776 0.450501i \(-0.851245\pi\)
0.892776 0.450501i \(-0.148755\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 21.8564 1.19414
\(336\) 0 0
\(337\) 16.3923 0.892946 0.446473 0.894797i \(-0.352680\pi\)
0.446473 + 0.894797i \(0.352680\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 21.8564i 1.18359i
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 35.3205i 1.89610i 0.318115 + 0.948052i \(0.396950\pi\)
−0.318115 + 0.948052i \(0.603050\pi\)
\(348\) 0 0
\(349\) − 14.0526i − 0.752216i −0.926576 0.376108i \(-0.877262\pi\)
0.926576 0.376108i \(-0.122738\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −0.928203 −0.0494033 −0.0247016 0.999695i \(-0.507864\pi\)
−0.0247016 + 0.999695i \(0.507864\pi\)
\(354\) 0 0
\(355\) − 8.00000i − 0.424596i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −27.4641 −1.44950 −0.724750 0.689012i \(-0.758045\pi\)
−0.724750 + 0.689012i \(0.758045\pi\)
\(360\) 0 0
\(361\) 17.3923 0.915384
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 35.3205i − 1.84876i
\(366\) 0 0
\(367\) −20.7846 −1.08495 −0.542474 0.840073i \(-0.682512\pi\)
−0.542474 + 0.840073i \(0.682512\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.0000i 0.623009i
\(372\) 0 0
\(373\) − 30.9282i − 1.60140i −0.599064 0.800701i \(-0.704461\pi\)
0.599064 0.800701i \(-0.295539\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −9.85641 −0.507631
\(378\) 0 0
\(379\) − 14.2487i − 0.731907i −0.930633 0.365954i \(-0.880743\pi\)
0.930633 0.365954i \(-0.119257\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −32.7846 −1.67522 −0.837608 0.546272i \(-0.816046\pi\)
−0.837608 + 0.546272i \(0.816046\pi\)
\(384\) 0 0
\(385\) 14.9282 0.760812
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 23.3205i − 1.18240i −0.806526 0.591198i \(-0.798655\pi\)
0.806526 0.591198i \(-0.201345\pi\)
\(390\) 0 0
\(391\) 6.92820 0.350374
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) − 29.8564i − 1.50224i
\(396\) 0 0
\(397\) 4.87564i 0.244702i 0.992487 + 0.122351i \(0.0390433\pi\)
−0.992487 + 0.122351i \(0.960957\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.4641 −0.672365 −0.336183 0.941797i \(-0.609136\pi\)
−0.336183 + 0.941797i \(0.609136\pi\)
\(402\) 0 0
\(403\) 26.9282i 1.34139i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) 0 0
\(409\) −3.07180 −0.151891 −0.0759453 0.997112i \(-0.524197\pi\)
−0.0759453 + 0.997112i \(0.524197\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 9.66025i − 0.475350i
\(414\) 0 0
\(415\) 15.4641 0.759103
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 23.8038i − 1.16289i −0.813584 0.581447i \(-0.802487\pi\)
0.813584 0.581447i \(-0.197513\pi\)
\(420\) 0 0
\(421\) − 25.8564i − 1.26016i −0.776529 0.630082i \(-0.783021\pi\)
0.776529 0.630082i \(-0.216979\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.92820 0.239053
\(426\) 0 0
\(427\) − 11.1244i − 0.538345i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −35.4641 −1.70825 −0.854123 0.520071i \(-0.825905\pi\)
−0.854123 + 0.520071i \(0.825905\pi\)
\(432\) 0 0
\(433\) 15.8564 0.762010 0.381005 0.924573i \(-0.375578\pi\)
0.381005 + 0.924573i \(0.375578\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.39230i 0.210112i
\(438\) 0 0
\(439\) −30.9282 −1.47612 −0.738061 0.674734i \(-0.764258\pi\)
−0.738061 + 0.674734i \(0.764258\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 24.0000i − 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) 0 0
\(445\) 32.3923i 1.53554i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) 0 0
\(451\) − 10.9282i − 0.514589i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 18.3923 0.862245
\(456\) 0 0
\(457\) 15.3205 0.716663 0.358332 0.933594i \(-0.383346\pi\)
0.358332 + 0.933594i \(0.383346\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 24.1962i 1.12693i 0.826141 + 0.563464i \(0.190531\pi\)
−0.826141 + 0.563464i \(0.809469\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 0.875644i − 0.0405200i −0.999795 0.0202600i \(-0.993551\pi\)
0.999795 0.0202600i \(-0.00644940\pi\)
\(468\) 0 0
\(469\) − 8.00000i − 0.369406i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 29.8564 1.37280
\(474\) 0 0
\(475\) 3.12436i 0.143355i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.85641 −0.450351 −0.225175 0.974318i \(-0.572295\pi\)
−0.225175 + 0.974318i \(0.572295\pi\)
\(480\) 0 0
\(481\) −9.85641 −0.449413
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 24.3923i − 1.10760i
\(486\) 0 0
\(487\) 21.6077 0.979138 0.489569 0.871965i \(-0.337154\pi\)
0.489569 + 0.871965i \(0.337154\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 32.7846i − 1.47955i −0.672855 0.739774i \(-0.734932\pi\)
0.672855 0.739774i \(-0.265068\pi\)
\(492\) 0 0
\(493\) 2.92820i 0.131880i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.92820 −0.131348
\(498\) 0 0
\(499\) − 13.0718i − 0.585174i −0.956239 0.292587i \(-0.905484\pi\)
0.956239 0.292587i \(-0.0945161\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 30.9282 1.37902 0.689510 0.724276i \(-0.257826\pi\)
0.689510 + 0.724276i \(0.257826\pi\)
\(504\) 0 0
\(505\) 4.53590 0.201845
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.12436i 0.138485i 0.997600 + 0.0692423i \(0.0220582\pi\)
−0.997600 + 0.0692423i \(0.977942\pi\)
\(510\) 0 0
\(511\) −12.9282 −0.571910
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 26.9282i 1.18660i
\(516\) 0 0
\(517\) − 16.0000i − 0.703679i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.7846 0.647726 0.323863 0.946104i \(-0.395018\pi\)
0.323863 + 0.946104i \(0.395018\pi\)
\(522\) 0 0
\(523\) 3.41154i 0.149176i 0.997214 + 0.0745882i \(0.0237642\pi\)
−0.997214 + 0.0745882i \(0.976236\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −11.0000 −0.478261
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 13.4641i − 0.583195i
\(534\) 0 0
\(535\) −13.8564 −0.599065
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 5.46410i − 0.235356i
\(540\) 0 0
\(541\) − 4.00000i − 0.171973i −0.996296 0.0859867i \(-0.972596\pi\)
0.996296 0.0859867i \(-0.0274043\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −33.8564 −1.45025
\(546\) 0 0
\(547\) − 46.2487i − 1.97745i −0.149736 0.988726i \(-0.547842\pi\)
0.149736 0.988726i \(-0.452158\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.85641 −0.0790856
\(552\) 0 0
\(553\) −10.9282 −0.464714
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 23.7128i − 1.00474i −0.864652 0.502372i \(-0.832461\pi\)
0.864652 0.502372i \(-0.167539\pi\)
\(558\) 0 0
\(559\) 36.7846 1.55582
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 34.0526i − 1.43514i −0.696484 0.717572i \(-0.745253\pi\)
0.696484 0.717572i \(-0.254747\pi\)
\(564\) 0 0
\(565\) − 17.8564i − 0.751225i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 5.46410 0.229067 0.114534 0.993419i \(-0.463463\pi\)
0.114534 + 0.993419i \(0.463463\pi\)
\(570\) 0 0
\(571\) 25.1769i 1.05362i 0.849983 + 0.526811i \(0.176612\pi\)
−0.849983 + 0.526811i \(0.823388\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 8.53590 0.355972
\(576\) 0 0
\(577\) −31.0718 −1.29354 −0.646768 0.762687i \(-0.723880\pi\)
−0.646768 + 0.762687i \(0.723880\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) − 5.66025i − 0.234827i
\(582\) 0 0
\(583\) −65.5692 −2.71560
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 33.2679i 1.37312i 0.727075 + 0.686558i \(0.240879\pi\)
−0.727075 + 0.686558i \(0.759121\pi\)
\(588\) 0 0
\(589\) 5.07180i 0.208980i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −12.1436 −0.498678 −0.249339 0.968416i \(-0.580213\pi\)
−0.249339 + 0.968416i \(0.580213\pi\)
\(594\) 0 0
\(595\) − 5.46410i − 0.224006i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.7128 1.13231 0.566157 0.824297i \(-0.308429\pi\)
0.566157 + 0.824297i \(0.308429\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 51.5167i 2.09445i
\(606\) 0 0
\(607\) 27.7128 1.12483 0.562414 0.826856i \(-0.309873\pi\)
0.562414 + 0.826856i \(0.309873\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 19.7128i − 0.797495i
\(612\) 0 0
\(613\) 39.3205i 1.58814i 0.607826 + 0.794070i \(0.292042\pi\)
−0.607826 + 0.794070i \(0.707958\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.3923 0.981997 0.490999 0.871160i \(-0.336632\pi\)
0.490999 + 0.871160i \(0.336632\pi\)
\(618\) 0 0
\(619\) − 24.1962i − 0.972525i −0.873813 0.486263i \(-0.838360\pi\)
0.873813 0.486263i \(-0.161640\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 11.8564 0.475017
\(624\) 0 0
\(625\) −31.2487 −1.24995
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.92820i 0.116755i
\(630\) 0 0
\(631\) 49.5692 1.97332 0.986660 0.162796i \(-0.0520513\pi\)
0.986660 + 0.162796i \(0.0520513\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 31.3205i − 1.24292i
\(636\) 0 0
\(637\) − 6.73205i − 0.266734i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22.2487 0.878771 0.439386 0.898299i \(-0.355196\pi\)
0.439386 + 0.898299i \(0.355196\pi\)
\(642\) 0 0
\(643\) 14.3397i 0.565504i 0.959193 + 0.282752i \(0.0912474\pi\)
−0.959193 + 0.282752i \(0.908753\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.85641 −0.0729829 −0.0364914 0.999334i \(-0.511618\pi\)
−0.0364914 + 0.999334i \(0.511618\pi\)
\(648\) 0 0
\(649\) 52.7846 2.07198
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.5359i 1.50803i 0.656859 + 0.754013i \(0.271885\pi\)
−0.656859 + 0.754013i \(0.728115\pi\)
\(654\) 0 0
\(655\) 29.3205 1.14565
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) − 3.32051i − 0.129349i −0.997906 0.0646743i \(-0.979399\pi\)
0.997906 0.0646743i \(-0.0206009\pi\)
\(660\) 0 0
\(661\) 28.9808i 1.12722i 0.826041 + 0.563611i \(0.190588\pi\)
−0.826041 + 0.563611i \(0.809412\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 3.46410 0.134332
\(666\) 0 0
\(667\) 5.07180i 0.196381i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 60.7846 2.34656
\(672\) 0 0
\(673\) 4.14359 0.159724 0.0798619 0.996806i \(-0.474552\pi\)
0.0798619 + 0.996806i \(0.474552\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 14.4449i 0.555161i 0.960702 + 0.277581i \(0.0895326\pi\)
−0.960702 + 0.277581i \(0.910467\pi\)
\(678\) 0 0
\(679\) −8.92820 −0.342633
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 30.6410i − 1.17245i −0.810150 0.586223i \(-0.800614\pi\)
0.810150 0.586223i \(-0.199386\pi\)
\(684\) 0 0
\(685\) 54.2487i 2.07274i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −80.7846 −3.07765
\(690\) 0 0
\(691\) 11.1244i 0.423190i 0.977357 + 0.211595i \(0.0678658\pi\)
−0.977357 + 0.211595i \(0.932134\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −25.3205 −0.960462
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19.6077i 0.740572i 0.928918 + 0.370286i \(0.120740\pi\)
−0.928918 + 0.370286i \(0.879260\pi\)
\(702\) 0 0
\(703\) −1.85641 −0.0700157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 1.66025i − 0.0624403i
\(708\) 0 0
\(709\) 48.1051i 1.80663i 0.428982 + 0.903313i \(0.358872\pi\)
−0.428982 + 0.903313i \(0.641128\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 13.8564 0.518927
\(714\) 0 0
\(715\) 100.497i 3.75839i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 21.0718 0.785845 0.392923 0.919572i \(-0.371464\pi\)
0.392923 + 0.919572i \(0.371464\pi\)
\(720\) 0 0
\(721\) 9.85641 0.367072
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.60770i 0.133986i
\(726\) 0 0
\(727\) −10.9282 −0.405305 −0.202652 0.979251i \(-0.564956\pi\)
−0.202652 + 0.979251i \(0.564956\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 10.9282i − 0.404194i
\(732\) 0 0
\(733\) − 13.6603i − 0.504553i −0.967655 0.252276i \(-0.918821\pi\)
0.967655 0.252276i \(-0.0811792\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 43.7128 1.61018
\(738\) 0 0
\(739\) − 3.32051i − 0.122147i −0.998133 0.0610734i \(-0.980548\pi\)
0.998133 0.0610734i \(-0.0194524\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32.2487 1.18309 0.591545 0.806272i \(-0.298518\pi\)
0.591545 + 0.806272i \(0.298518\pi\)
\(744\) 0 0
\(745\) −2.92820 −0.107281
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.07180i 0.185319i
\(750\) 0 0
\(751\) −24.2487 −0.884848 −0.442424 0.896806i \(-0.645881\pi\)
−0.442424 + 0.896806i \(0.645881\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 6.53590i − 0.237866i
\(756\) 0 0
\(757\) − 10.2487i − 0.372496i −0.982503 0.186248i \(-0.940367\pi\)
0.982503 0.186248i \(-0.0596327\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21.7128 0.787089 0.393544 0.919306i \(-0.371249\pi\)
0.393544 + 0.919306i \(0.371249\pi\)
\(762\) 0 0
\(763\) 12.3923i 0.448632i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 65.0333 2.34822
\(768\) 0 0
\(769\) −10.7846 −0.388903 −0.194451 0.980912i \(-0.562293\pi\)
−0.194451 + 0.980912i \(0.562293\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 20.8756i − 0.750845i −0.926854 0.375422i \(-0.877498\pi\)
0.926854 0.375422i \(-0.122502\pi\)
\(774\) 0 0
\(775\) 9.85641 0.354053
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) − 2.53590i − 0.0908580i
\(780\) 0 0
\(781\) − 16.0000i − 0.572525i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 33.3205 1.18926
\(786\) 0 0
\(787\) 20.5885i 0.733899i 0.930241 + 0.366950i \(0.119598\pi\)
−0.930241 + 0.366950i \(0.880402\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.53590 −0.232390
\(792\) 0 0
\(793\) 74.8897 2.65941
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 12.9808i − 0.459802i −0.973214 0.229901i \(-0.926160\pi\)
0.973214 0.229901i \(-0.0738403\pi\)
\(798\) 0 0
\(799\) −5.85641 −0.207185
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 70.6410i − 2.49287i
\(804\) 0 0
\(805\) − 9.46410i − 0.333566i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −23.3205 −0.819905 −0.409953 0.912107i \(-0.634455\pi\)
−0.409953 + 0.912107i \(0.634455\pi\)
\(810\) 0 0
\(811\) − 27.1244i − 0.952465i −0.879319 0.476232i \(-0.842002\pi\)
0.879319 0.476232i \(-0.157998\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −36.7846 −1.28851
\(816\) 0 0
\(817\) 6.92820 0.242387
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 6.92820i 0.241796i 0.992665 + 0.120898i \(0.0385774\pi\)
−0.992665 + 0.120898i \(0.961423\pi\)
\(822\) 0 0
\(823\) 2.92820 0.102071 0.0510354 0.998697i \(-0.483748\pi\)
0.0510354 + 0.998697i \(0.483748\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 13.8564i 0.481834i 0.970546 + 0.240917i \(0.0774482\pi\)
−0.970546 + 0.240917i \(0.922552\pi\)
\(828\) 0 0
\(829\) 40.9808i 1.42332i 0.702524 + 0.711660i \(0.252056\pi\)
−0.702524 + 0.711660i \(0.747944\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.00000 −0.0692959
\(834\) 0 0
\(835\) 13.8564i 0.479521i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −39.7128 −1.37104 −0.685519 0.728054i \(-0.740425\pi\)
−0.685519 + 0.728054i \(0.740425\pi\)
\(840\) 0 0
\(841\) 26.8564 0.926083
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 88.3013i 3.03766i
\(846\) 0 0
\(847\) 18.8564 0.647914
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 5.07180i 0.173859i
\(852\) 0 0
\(853\) − 4.98076i − 0.170538i −0.996358 0.0852690i \(-0.972825\pi\)
0.996358 0.0852690i \(-0.0271750\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 30.7846 1.05158 0.525791 0.850614i \(-0.323769\pi\)
0.525791 + 0.850614i \(0.323769\pi\)
\(858\) 0 0
\(859\) − 30.4449i − 1.03877i −0.854542 0.519383i \(-0.826162\pi\)
0.854542 0.519383i \(-0.173838\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 10.3923 0.353349
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) − 59.7128i − 2.02562i
\(870\) 0 0
\(871\) 53.8564 1.82485
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.92820i 0.234216i
\(876\) 0 0
\(877\) 20.3923i 0.688599i 0.938860 + 0.344300i \(0.111884\pi\)
−0.938860 + 0.344300i \(0.888116\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 50.7846 1.71098 0.855488 0.517822i \(-0.173257\pi\)
0.855488 + 0.517822i \(0.173257\pi\)
\(882\) 0 0
\(883\) 5.07180i 0.170680i 0.996352 + 0.0853398i \(0.0271976\pi\)
−0.996352 + 0.0853398i \(0.972802\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −46.6410 −1.56605 −0.783026 0.621989i \(-0.786325\pi\)
−0.783026 + 0.621989i \(0.786325\pi\)
\(888\) 0 0
\(889\) −11.4641 −0.384494
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 3.71281i − 0.124245i
\(894\) 0 0
\(895\) 8.00000 0.267411
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 5.85641i 0.195322i
\(900\) 0 0
\(901\) 24.0000i 0.799556i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −29.3205 −0.974647
\(906\) 0 0
\(907\) − 43.7128i − 1.45146i −0.687980 0.725730i \(-0.741502\pi\)
0.687980 0.725730i \(-0.258498\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −4.53590 −0.150281 −0.0751405 0.997173i \(-0.523941\pi\)
−0.0751405 + 0.997173i \(0.523941\pi\)
\(912\) 0 0
\(913\) 30.9282 1.02357
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 10.7321i − 0.354404i
\(918\) 0 0
\(919\) 7.21539 0.238014 0.119007 0.992893i \(-0.462029\pi\)
0.119007 + 0.992893i \(0.462029\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 19.7128i − 0.648855i
\(924\) 0 0
\(925\) 3.60770i 0.118620i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −37.7128 −1.23732 −0.618659 0.785660i \(-0.712324\pi\)
−0.618659 + 0.785660i \(0.712324\pi\)
\(930\) 0 0
\(931\) − 1.26795i − 0.0415554i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 29.8564 0.976409
\(936\) 0 0
\(937\) 8.64102 0.282290 0.141145 0.989989i \(-0.454922\pi\)
0.141145 + 0.989989i \(0.454922\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 44.9808i 1.46633i 0.680050 + 0.733165i \(0.261958\pi\)
−0.680050 + 0.733165i \(0.738042\pi\)
\(942\) 0 0
\(943\) −6.92820 −0.225613
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 24.3923i 0.792643i 0.918112 + 0.396322i \(0.129714\pi\)
−0.918112 + 0.396322i \(0.870286\pi\)
\(948\) 0 0
\(949\) − 87.0333i − 2.82522i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.8564 0.643212 0.321606 0.946874i \(-0.395777\pi\)
0.321606 + 0.946874i \(0.395777\pi\)
\(954\) 0 0
\(955\) − 43.7128i − 1.41451i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 19.8564 0.641197
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) − 17.8564i − 0.574818i
\(966\) 0 0
\(967\) 15.1769 0.488057 0.244028 0.969768i \(-0.421531\pi\)
0.244028 + 0.969768i \(0.421531\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 55.5167i 1.78161i 0.454381 + 0.890807i \(0.349860\pi\)
−0.454381 + 0.890807i \(0.650140\pi\)
\(972\) 0 0
\(973\) 9.26795i 0.297117i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 28.1436 0.900393 0.450197 0.892929i \(-0.351354\pi\)
0.450197 + 0.892929i \(0.351354\pi\)
\(978\) 0 0
\(979\) 64.7846i 2.07053i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −47.7128 −1.52180 −0.760901 0.648868i \(-0.775243\pi\)
−0.760901 + 0.648868i \(0.775243\pi\)
\(984\) 0 0
\(985\) −70.6410 −2.25081
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 18.9282i − 0.601882i
\(990\) 0 0
\(991\) −24.7846 −0.787309 −0.393655 0.919258i \(-0.628789\pi\)
−0.393655 + 0.919258i \(0.628789\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) − 10.9282i − 0.346447i
\(996\) 0 0
\(997\) − 5.26795i − 0.166838i −0.996515 0.0834188i \(-0.973416\pi\)
0.996515 0.0834188i \(-0.0265839\pi\)
\(998\) 0 0
\(999\) 0 0
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 \(a_p\))