Properties

Label 4005.2.a.p.1.5
Level 4005
Weight 2
Character 4005.1
Self dual Yes
Analytic conductor 31.980
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4005 = 3^{2} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4005.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9800860095\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.151894\)
Character \(\chi\) = 4005.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.151894 q^{2} -1.97693 q^{4} +1.00000 q^{5} +2.88745 q^{7} +0.604071 q^{8} +O(q^{10})\) \(q-0.151894 q^{2} -1.97693 q^{4} +1.00000 q^{5} +2.88745 q^{7} +0.604071 q^{8} -0.151894 q^{10} -2.75596 q^{11} +2.78878 q^{13} -0.438585 q^{14} +3.86210 q^{16} -6.24918 q^{17} -0.721848 q^{19} -1.97693 q^{20} +0.418614 q^{22} +0.0986719 q^{23} +1.00000 q^{25} -0.423598 q^{26} -5.70828 q^{28} -6.61485 q^{29} -0.885417 q^{31} -1.79477 q^{32} +0.949212 q^{34} +2.88745 q^{35} -4.03281 q^{37} +0.109644 q^{38} +0.604071 q^{40} -9.13960 q^{41} +4.57497 q^{43} +5.44834 q^{44} -0.0149877 q^{46} +6.64268 q^{47} +1.33735 q^{49} -0.151894 q^{50} -5.51321 q^{52} -0.765878 q^{53} -2.75596 q^{55} +1.74422 q^{56} +1.00476 q^{58} -2.79467 q^{59} -8.50106 q^{61} +0.134489 q^{62} -7.45159 q^{64} +2.78878 q^{65} +4.23461 q^{67} +12.3542 q^{68} -0.438585 q^{70} +2.60032 q^{71} -9.47269 q^{73} +0.612559 q^{74} +1.42704 q^{76} -7.95770 q^{77} +13.2707 q^{79} +3.86210 q^{80} +1.38825 q^{82} +11.3012 q^{83} -6.24918 q^{85} -0.694910 q^{86} -1.66480 q^{88} -1.00000 q^{89} +8.05244 q^{91} -0.195067 q^{92} -1.00898 q^{94} -0.721848 q^{95} -11.6151 q^{97} -0.203135 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} + O(q^{10}) \) \( 8q - q^{2} + 7q^{4} + 8q^{5} - 6q^{7} - 3q^{8} - q^{10} - 14q^{11} - 7q^{13} - 15q^{14} + 9q^{16} - 17q^{17} + 17q^{19} + 7q^{20} + 2q^{22} + q^{23} + 8q^{25} - 3q^{26} - 29q^{28} - 10q^{29} + q^{31} - 2q^{32} - 16q^{34} - 6q^{35} - 11q^{37} + 30q^{38} - 3q^{40} - 15q^{41} - 5q^{43} - 7q^{44} - 12q^{46} - 12q^{47} + 4q^{49} - q^{50} - 14q^{52} + q^{53} - 14q^{55} - 3q^{56} - 37q^{58} - 26q^{59} + 13q^{61} - 22q^{62} - 15q^{64} - 7q^{65} - 25q^{67} - 23q^{68} - 15q^{70} - 28q^{71} - 17q^{73} + 5q^{74} + 8q^{76} - 7q^{79} + 9q^{80} + 5q^{82} - 44q^{83} - 17q^{85} + 13q^{86} - 66q^{88} - 8q^{89} + 27q^{91} - 15q^{92} - 27q^{94} + 17q^{95} + q^{97} + 34q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.151894 −0.107405 −0.0537026 0.998557i \(-0.517102\pi\)
−0.0537026 + 0.998557i \(0.517102\pi\)
\(3\) 0 0
\(4\) −1.97693 −0.988464
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.88745 1.09135 0.545676 0.837996i \(-0.316273\pi\)
0.545676 + 0.837996i \(0.316273\pi\)
\(8\) 0.604071 0.213571
\(9\) 0 0
\(10\) −0.151894 −0.0480330
\(11\) −2.75596 −0.830955 −0.415477 0.909604i \(-0.636385\pi\)
−0.415477 + 0.909604i \(0.636385\pi\)
\(12\) 0 0
\(13\) 2.78878 0.773467 0.386734 0.922192i \(-0.373603\pi\)
0.386734 + 0.922192i \(0.373603\pi\)
\(14\) −0.438585 −0.117217
\(15\) 0 0
\(16\) 3.86210 0.965525
\(17\) −6.24918 −1.51565 −0.757825 0.652458i \(-0.773738\pi\)
−0.757825 + 0.652458i \(0.773738\pi\)
\(18\) 0 0
\(19\) −0.721848 −0.165603 −0.0828017 0.996566i \(-0.526387\pi\)
−0.0828017 + 0.996566i \(0.526387\pi\)
\(20\) −1.97693 −0.442055
\(21\) 0 0
\(22\) 0.418614 0.0892488
\(23\) 0.0986719 0.0205745 0.0102873 0.999947i \(-0.496725\pi\)
0.0102873 + 0.999947i \(0.496725\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −0.423598 −0.0830743
\(27\) 0 0
\(28\) −5.70828 −1.07876
\(29\) −6.61485 −1.22835 −0.614174 0.789171i \(-0.710511\pi\)
−0.614174 + 0.789171i \(0.710511\pi\)
\(30\) 0 0
\(31\) −0.885417 −0.159026 −0.0795128 0.996834i \(-0.525336\pi\)
−0.0795128 + 0.996834i \(0.525336\pi\)
\(32\) −1.79477 −0.317274
\(33\) 0 0
\(34\) 0.949212 0.162789
\(35\) 2.88745 0.488068
\(36\) 0 0
\(37\) −4.03281 −0.662990 −0.331495 0.943457i \(-0.607553\pi\)
−0.331495 + 0.943457i \(0.607553\pi\)
\(38\) 0.109644 0.0177867
\(39\) 0 0
\(40\) 0.604071 0.0955120
\(41\) −9.13960 −1.42737 −0.713683 0.700469i \(-0.752974\pi\)
−0.713683 + 0.700469i \(0.752974\pi\)
\(42\) 0 0
\(43\) 4.57497 0.697676 0.348838 0.937183i \(-0.386576\pi\)
0.348838 + 0.937183i \(0.386576\pi\)
\(44\) 5.44834 0.821369
\(45\) 0 0
\(46\) −0.0149877 −0.00220981
\(47\) 6.64268 0.968934 0.484467 0.874809i \(-0.339014\pi\)
0.484467 + 0.874809i \(0.339014\pi\)
\(48\) 0 0
\(49\) 1.33735 0.191050
\(50\) −0.151894 −0.0214810
\(51\) 0 0
\(52\) −5.51321 −0.764544
\(53\) −0.765878 −0.105201 −0.0526007 0.998616i \(-0.516751\pi\)
−0.0526007 + 0.998616i \(0.516751\pi\)
\(54\) 0 0
\(55\) −2.75596 −0.371614
\(56\) 1.74422 0.233082
\(57\) 0 0
\(58\) 1.00476 0.131931
\(59\) −2.79467 −0.363836 −0.181918 0.983314i \(-0.558230\pi\)
−0.181918 + 0.983314i \(0.558230\pi\)
\(60\) 0 0
\(61\) −8.50106 −1.08845 −0.544225 0.838939i \(-0.683176\pi\)
−0.544225 + 0.838939i \(0.683176\pi\)
\(62\) 0.134489 0.0170802
\(63\) 0 0
\(64\) −7.45159 −0.931449
\(65\) 2.78878 0.345905
\(66\) 0 0
\(67\) 4.23461 0.517339 0.258670 0.965966i \(-0.416716\pi\)
0.258670 + 0.965966i \(0.416716\pi\)
\(68\) 12.3542 1.49816
\(69\) 0 0
\(70\) −0.438585 −0.0524210
\(71\) 2.60032 0.308601 0.154300 0.988024i \(-0.450688\pi\)
0.154300 + 0.988024i \(0.450688\pi\)
\(72\) 0 0
\(73\) −9.47269 −1.10869 −0.554347 0.832285i \(-0.687032\pi\)
−0.554347 + 0.832285i \(0.687032\pi\)
\(74\) 0.612559 0.0712085
\(75\) 0 0
\(76\) 1.42704 0.163693
\(77\) −7.95770 −0.906864
\(78\) 0 0
\(79\) 13.2707 1.49307 0.746536 0.665345i \(-0.231716\pi\)
0.746536 + 0.665345i \(0.231716\pi\)
\(80\) 3.86210 0.431796
\(81\) 0 0
\(82\) 1.38825 0.153306
\(83\) 11.3012 1.24046 0.620232 0.784418i \(-0.287038\pi\)
0.620232 + 0.784418i \(0.287038\pi\)
\(84\) 0 0
\(85\) −6.24918 −0.677819
\(86\) −0.694910 −0.0749340
\(87\) 0 0
\(88\) −1.66480 −0.177468
\(89\) −1.00000 −0.106000
\(90\) 0 0
\(91\) 8.05244 0.844125
\(92\) −0.195067 −0.0203372
\(93\) 0 0
\(94\) −1.00898 −0.104069
\(95\) −0.721848 −0.0740601
\(96\) 0 0
\(97\) −11.6151 −1.17933 −0.589667 0.807646i \(-0.700741\pi\)
−0.589667 + 0.807646i \(0.700741\pi\)
\(98\) −0.203135 −0.0205198
\(99\) 0 0
\(100\) −1.97693 −0.197693
\(101\) −12.1795 −1.21191 −0.605953 0.795501i \(-0.707208\pi\)
−0.605953 + 0.795501i \(0.707208\pi\)
\(102\) 0 0
\(103\) 9.71335 0.957085 0.478542 0.878064i \(-0.341165\pi\)
0.478542 + 0.878064i \(0.341165\pi\)
\(104\) 1.68462 0.165190
\(105\) 0 0
\(106\) 0.116332 0.0112992
\(107\) −8.02137 −0.775455 −0.387727 0.921774i \(-0.626740\pi\)
−0.387727 + 0.921774i \(0.626740\pi\)
\(108\) 0 0
\(109\) 4.86470 0.465953 0.232977 0.972482i \(-0.425153\pi\)
0.232977 + 0.972482i \(0.425153\pi\)
\(110\) 0.418614 0.0399133
\(111\) 0 0
\(112\) 11.1516 1.05373
\(113\) 3.12496 0.293971 0.146986 0.989139i \(-0.453043\pi\)
0.146986 + 0.989139i \(0.453043\pi\)
\(114\) 0 0
\(115\) 0.0986719 0.00920120
\(116\) 13.0771 1.21418
\(117\) 0 0
\(118\) 0.424494 0.0390778
\(119\) −18.0442 −1.65411
\(120\) 0 0
\(121\) −3.40466 −0.309514
\(122\) 1.29126 0.116905
\(123\) 0 0
\(124\) 1.75041 0.157191
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −12.6401 −1.12162 −0.560812 0.827943i \(-0.689511\pi\)
−0.560812 + 0.827943i \(0.689511\pi\)
\(128\) 4.72139 0.417316
\(129\) 0 0
\(130\) −0.423598 −0.0371520
\(131\) −16.2432 −1.41917 −0.709587 0.704618i \(-0.751119\pi\)
−0.709587 + 0.704618i \(0.751119\pi\)
\(132\) 0 0
\(133\) −2.08430 −0.180732
\(134\) −0.643210 −0.0555649
\(135\) 0 0
\(136\) −3.77495 −0.323699
\(137\) 11.5123 0.983563 0.491781 0.870719i \(-0.336346\pi\)
0.491781 + 0.870719i \(0.336346\pi\)
\(138\) 0 0
\(139\) −9.18537 −0.779093 −0.389547 0.921007i \(-0.627368\pi\)
−0.389547 + 0.921007i \(0.627368\pi\)
\(140\) −5.70828 −0.482437
\(141\) 0 0
\(142\) −0.394972 −0.0331453
\(143\) −7.68577 −0.642716
\(144\) 0 0
\(145\) −6.61485 −0.549334
\(146\) 1.43884 0.119080
\(147\) 0 0
\(148\) 7.97258 0.655342
\(149\) 3.25326 0.266517 0.133259 0.991081i \(-0.457456\pi\)
0.133259 + 0.991081i \(0.457456\pi\)
\(150\) 0 0
\(151\) −11.3089 −0.920308 −0.460154 0.887839i \(-0.652206\pi\)
−0.460154 + 0.887839i \(0.652206\pi\)
\(152\) −0.436048 −0.0353681
\(153\) 0 0
\(154\) 1.20873 0.0974019
\(155\) −0.885417 −0.0711184
\(156\) 0 0
\(157\) 10.3585 0.826700 0.413350 0.910572i \(-0.364359\pi\)
0.413350 + 0.910572i \(0.364359\pi\)
\(158\) −2.01574 −0.160364
\(159\) 0 0
\(160\) −1.79477 −0.141889
\(161\) 0.284910 0.0224540
\(162\) 0 0
\(163\) −8.75633 −0.685849 −0.342924 0.939363i \(-0.611417\pi\)
−0.342924 + 0.939363i \(0.611417\pi\)
\(164\) 18.0683 1.41090
\(165\) 0 0
\(166\) −1.71658 −0.133232
\(167\) −21.8241 −1.68880 −0.844399 0.535715i \(-0.820042\pi\)
−0.844399 + 0.535715i \(0.820042\pi\)
\(168\) 0 0
\(169\) −5.22273 −0.401749
\(170\) 0.949212 0.0728012
\(171\) 0 0
\(172\) −9.04439 −0.689628
\(173\) 8.11969 0.617329 0.308664 0.951171i \(-0.400118\pi\)
0.308664 + 0.951171i \(0.400118\pi\)
\(174\) 0 0
\(175\) 2.88745 0.218270
\(176\) −10.6438 −0.802308
\(177\) 0 0
\(178\) 0.151894 0.0113849
\(179\) −14.6946 −1.09832 −0.549161 0.835716i \(-0.685053\pi\)
−0.549161 + 0.835716i \(0.685053\pi\)
\(180\) 0 0
\(181\) 9.35948 0.695685 0.347842 0.937553i \(-0.386914\pi\)
0.347842 + 0.937553i \(0.386914\pi\)
\(182\) −1.22312 −0.0906634
\(183\) 0 0
\(184\) 0.0596048 0.00439413
\(185\) −4.03281 −0.296498
\(186\) 0 0
\(187\) 17.2225 1.25944
\(188\) −13.1321 −0.957757
\(189\) 0 0
\(190\) 0.109644 0.00795443
\(191\) −10.6961 −0.773943 −0.386971 0.922092i \(-0.626479\pi\)
−0.386971 + 0.922092i \(0.626479\pi\)
\(192\) 0 0
\(193\) 19.0333 1.37005 0.685024 0.728521i \(-0.259792\pi\)
0.685024 + 0.728521i \(0.259792\pi\)
\(194\) 1.76426 0.126667
\(195\) 0 0
\(196\) −2.64385 −0.188846
\(197\) 21.9152 1.56139 0.780695 0.624912i \(-0.214865\pi\)
0.780695 + 0.624912i \(0.214865\pi\)
\(198\) 0 0
\(199\) 13.0013 0.921639 0.460819 0.887494i \(-0.347556\pi\)
0.460819 + 0.887494i \(0.347556\pi\)
\(200\) 0.604071 0.0427143
\(201\) 0 0
\(202\) 1.84999 0.130165
\(203\) −19.1000 −1.34056
\(204\) 0 0
\(205\) −9.13960 −0.638338
\(206\) −1.47540 −0.102796
\(207\) 0 0
\(208\) 10.7705 0.746802
\(209\) 1.98939 0.137609
\(210\) 0 0
\(211\) 0.914119 0.0629306 0.0314653 0.999505i \(-0.489983\pi\)
0.0314653 + 0.999505i \(0.489983\pi\)
\(212\) 1.51409 0.103988
\(213\) 0 0
\(214\) 1.21840 0.0832878
\(215\) 4.57497 0.312010
\(216\) 0 0
\(217\) −2.55660 −0.173553
\(218\) −0.738917 −0.0500458
\(219\) 0 0
\(220\) 5.44834 0.367327
\(221\) −17.4276 −1.17230
\(222\) 0 0
\(223\) −8.67837 −0.581147 −0.290573 0.956853i \(-0.593846\pi\)
−0.290573 + 0.956853i \(0.593846\pi\)
\(224\) −5.18231 −0.346257
\(225\) 0 0
\(226\) −0.474662 −0.0315740
\(227\) −18.0379 −1.19722 −0.598608 0.801042i \(-0.704279\pi\)
−0.598608 + 0.801042i \(0.704279\pi\)
\(228\) 0 0
\(229\) −24.4494 −1.61566 −0.807831 0.589414i \(-0.799359\pi\)
−0.807831 + 0.589414i \(0.799359\pi\)
\(230\) −0.0149877 −0.000988257 0
\(231\) 0 0
\(232\) −3.99584 −0.262340
\(233\) 17.4971 1.14627 0.573136 0.819460i \(-0.305727\pi\)
0.573136 + 0.819460i \(0.305727\pi\)
\(234\) 0 0
\(235\) 6.64268 0.433321
\(236\) 5.52487 0.359638
\(237\) 0 0
\(238\) 2.74080 0.177660
\(239\) −7.31086 −0.472900 −0.236450 0.971644i \(-0.575984\pi\)
−0.236450 + 0.971644i \(0.575984\pi\)
\(240\) 0 0
\(241\) −26.6186 −1.71466 −0.857328 0.514771i \(-0.827877\pi\)
−0.857328 + 0.514771i \(0.827877\pi\)
\(242\) 0.517147 0.0332434
\(243\) 0 0
\(244\) 16.8060 1.07589
\(245\) 1.33735 0.0854402
\(246\) 0 0
\(247\) −2.01307 −0.128089
\(248\) −0.534855 −0.0339633
\(249\) 0 0
\(250\) −0.151894 −0.00960661
\(251\) −21.3903 −1.35015 −0.675073 0.737751i \(-0.735888\pi\)
−0.675073 + 0.737751i \(0.735888\pi\)
\(252\) 0 0
\(253\) −0.271936 −0.0170965
\(254\) 1.91995 0.120468
\(255\) 0 0
\(256\) 14.1860 0.886627
\(257\) 13.8639 0.864809 0.432404 0.901680i \(-0.357665\pi\)
0.432404 + 0.901680i \(0.357665\pi\)
\(258\) 0 0
\(259\) −11.6445 −0.723556
\(260\) −5.51321 −0.341915
\(261\) 0 0
\(262\) 2.46724 0.152427
\(263\) −20.0797 −1.23817 −0.619085 0.785324i \(-0.712496\pi\)
−0.619085 + 0.785324i \(0.712496\pi\)
\(264\) 0 0
\(265\) −0.765878 −0.0470475
\(266\) 0.316592 0.0194115
\(267\) 0 0
\(268\) −8.37151 −0.511371
\(269\) −10.7150 −0.653303 −0.326652 0.945145i \(-0.605920\pi\)
−0.326652 + 0.945145i \(0.605920\pi\)
\(270\) 0 0
\(271\) −27.3435 −1.66100 −0.830500 0.557019i \(-0.811945\pi\)
−0.830500 + 0.557019i \(0.811945\pi\)
\(272\) −24.1350 −1.46340
\(273\) 0 0
\(274\) −1.74865 −0.105640
\(275\) −2.75596 −0.166191
\(276\) 0 0
\(277\) −16.5306 −0.993229 −0.496614 0.867971i \(-0.665424\pi\)
−0.496614 + 0.867971i \(0.665424\pi\)
\(278\) 1.39520 0.0836786
\(279\) 0 0
\(280\) 1.74422 0.104237
\(281\) −6.73948 −0.402044 −0.201022 0.979587i \(-0.564426\pi\)
−0.201022 + 0.979587i \(0.564426\pi\)
\(282\) 0 0
\(283\) −5.58139 −0.331779 −0.165890 0.986144i \(-0.553050\pi\)
−0.165890 + 0.986144i \(0.553050\pi\)
\(284\) −5.14064 −0.305041
\(285\) 0 0
\(286\) 1.16742 0.0690310
\(287\) −26.3901 −1.55776
\(288\) 0 0
\(289\) 22.0523 1.29719
\(290\) 1.00476 0.0590012
\(291\) 0 0
\(292\) 18.7268 1.09591
\(293\) −7.53464 −0.440178 −0.220089 0.975480i \(-0.570635\pi\)
−0.220089 + 0.975480i \(0.570635\pi\)
\(294\) 0 0
\(295\) −2.79467 −0.162712
\(296\) −2.43610 −0.141596
\(297\) 0 0
\(298\) −0.494149 −0.0286253
\(299\) 0.275174 0.0159137
\(300\) 0 0
\(301\) 13.2100 0.761411
\(302\) 1.71776 0.0988458
\(303\) 0 0
\(304\) −2.78785 −0.159894
\(305\) −8.50106 −0.486769
\(306\) 0 0
\(307\) −10.4478 −0.596289 −0.298144 0.954521i \(-0.596368\pi\)
−0.298144 + 0.954521i \(0.596368\pi\)
\(308\) 15.7318 0.896403
\(309\) 0 0
\(310\) 0.134489 0.00763848
\(311\) 26.2433 1.48812 0.744061 0.668111i \(-0.232897\pi\)
0.744061 + 0.668111i \(0.232897\pi\)
\(312\) 0 0
\(313\) 12.4586 0.704203 0.352101 0.935962i \(-0.385467\pi\)
0.352101 + 0.935962i \(0.385467\pi\)
\(314\) −1.57340 −0.0887918
\(315\) 0 0
\(316\) −26.2352 −1.47585
\(317\) 13.7370 0.771548 0.385774 0.922593i \(-0.373934\pi\)
0.385774 + 0.922593i \(0.373934\pi\)
\(318\) 0 0
\(319\) 18.2303 1.02070
\(320\) −7.45159 −0.416556
\(321\) 0 0
\(322\) −0.0432761 −0.00241168
\(323\) 4.51096 0.250997
\(324\) 0 0
\(325\) 2.78878 0.154693
\(326\) 1.33003 0.0736637
\(327\) 0 0
\(328\) −5.52097 −0.304844
\(329\) 19.1804 1.05745
\(330\) 0 0
\(331\) 19.4675 1.07003 0.535016 0.844842i \(-0.320306\pi\)
0.535016 + 0.844842i \(0.320306\pi\)
\(332\) −22.3416 −1.22616
\(333\) 0 0
\(334\) 3.31494 0.181386
\(335\) 4.23461 0.231361
\(336\) 0 0
\(337\) −29.0718 −1.58364 −0.791821 0.610753i \(-0.790867\pi\)
−0.791821 + 0.610753i \(0.790867\pi\)
\(338\) 0.793301 0.0431499
\(339\) 0 0
\(340\) 12.3542 0.670000
\(341\) 2.44018 0.132143
\(342\) 0 0
\(343\) −16.3506 −0.882849
\(344\) 2.76361 0.149004
\(345\) 0 0
\(346\) −1.23333 −0.0663043
\(347\) 5.62285 0.301850 0.150925 0.988545i \(-0.451775\pi\)
0.150925 + 0.988545i \(0.451775\pi\)
\(348\) 0 0
\(349\) −2.35987 −0.126321 −0.0631605 0.998003i \(-0.520118\pi\)
−0.0631605 + 0.998003i \(0.520118\pi\)
\(350\) −0.438585 −0.0234434
\(351\) 0 0
\(352\) 4.94633 0.263640
\(353\) −25.8602 −1.37640 −0.688201 0.725520i \(-0.741599\pi\)
−0.688201 + 0.725520i \(0.741599\pi\)
\(354\) 0 0
\(355\) 2.60032 0.138010
\(356\) 1.97693 0.104777
\(357\) 0 0
\(358\) 2.23201 0.117966
\(359\) 22.6920 1.19764 0.598819 0.800884i \(-0.295637\pi\)
0.598819 + 0.800884i \(0.295637\pi\)
\(360\) 0 0
\(361\) −18.4789 −0.972576
\(362\) −1.42165 −0.0747201
\(363\) 0 0
\(364\) −15.9191 −0.834387
\(365\) −9.47269 −0.495823
\(366\) 0 0
\(367\) −27.4660 −1.43372 −0.716858 0.697219i \(-0.754420\pi\)
−0.716858 + 0.697219i \(0.754420\pi\)
\(368\) 0.381081 0.0198652
\(369\) 0 0
\(370\) 0.612559 0.0318454
\(371\) −2.21143 −0.114812
\(372\) 0 0
\(373\) −3.63459 −0.188192 −0.0940958 0.995563i \(-0.529996\pi\)
−0.0940958 + 0.995563i \(0.529996\pi\)
\(374\) −2.61599 −0.135270
\(375\) 0 0
\(376\) 4.01265 0.206937
\(377\) −18.4473 −0.950086
\(378\) 0 0
\(379\) −9.48226 −0.487071 −0.243536 0.969892i \(-0.578307\pi\)
−0.243536 + 0.969892i \(0.578307\pi\)
\(380\) 1.42704 0.0732057
\(381\) 0 0
\(382\) 1.62467 0.0831255
\(383\) 10.9355 0.558776 0.279388 0.960178i \(-0.409868\pi\)
0.279388 + 0.960178i \(0.409868\pi\)
\(384\) 0 0
\(385\) −7.95770 −0.405562
\(386\) −2.89104 −0.147150
\(387\) 0 0
\(388\) 22.9622 1.16573
\(389\) 11.3628 0.576117 0.288059 0.957613i \(-0.406990\pi\)
0.288059 + 0.957613i \(0.406990\pi\)
\(390\) 0 0
\(391\) −0.616619 −0.0311837
\(392\) 0.807855 0.0408028
\(393\) 0 0
\(394\) −3.32878 −0.167701
\(395\) 13.2707 0.667722
\(396\) 0 0
\(397\) 0.601588 0.0301929 0.0150964 0.999886i \(-0.495194\pi\)
0.0150964 + 0.999886i \(0.495194\pi\)
\(398\) −1.97482 −0.0989888
\(399\) 0 0
\(400\) 3.86210 0.193105
\(401\) 20.5405 1.02574 0.512872 0.858465i \(-0.328582\pi\)
0.512872 + 0.858465i \(0.328582\pi\)
\(402\) 0 0
\(403\) −2.46923 −0.123001
\(404\) 24.0780 1.19793
\(405\) 0 0
\(406\) 2.90118 0.143983
\(407\) 11.1143 0.550915
\(408\) 0 0
\(409\) 29.6541 1.46630 0.733150 0.680067i \(-0.238049\pi\)
0.733150 + 0.680067i \(0.238049\pi\)
\(410\) 1.38825 0.0685607
\(411\) 0 0
\(412\) −19.2026 −0.946044
\(413\) −8.06947 −0.397073
\(414\) 0 0
\(415\) 11.3012 0.554753
\(416\) −5.00521 −0.245401
\(417\) 0 0
\(418\) −0.302176 −0.0147799
\(419\) −6.46993 −0.316077 −0.158038 0.987433i \(-0.550517\pi\)
−0.158038 + 0.987433i \(0.550517\pi\)
\(420\) 0 0
\(421\) −30.5926 −1.49099 −0.745496 0.666511i \(-0.767787\pi\)
−0.745496 + 0.666511i \(0.767787\pi\)
\(422\) −0.138849 −0.00675907
\(423\) 0 0
\(424\) −0.462645 −0.0224680
\(425\) −6.24918 −0.303130
\(426\) 0 0
\(427\) −24.5464 −1.18788
\(428\) 15.8577 0.766509
\(429\) 0 0
\(430\) −0.694910 −0.0335115
\(431\) 15.6618 0.754402 0.377201 0.926131i \(-0.376887\pi\)
0.377201 + 0.926131i \(0.376887\pi\)
\(432\) 0 0
\(433\) 31.2050 1.49962 0.749809 0.661655i \(-0.230146\pi\)
0.749809 + 0.661655i \(0.230146\pi\)
\(434\) 0.388331 0.0186405
\(435\) 0 0
\(436\) −9.61715 −0.460578
\(437\) −0.0712262 −0.00340721
\(438\) 0 0
\(439\) −17.2377 −0.822711 −0.411355 0.911475i \(-0.634944\pi\)
−0.411355 + 0.911475i \(0.634944\pi\)
\(440\) −1.66480 −0.0793661
\(441\) 0 0
\(442\) 2.64714 0.125912
\(443\) −1.62298 −0.0771101 −0.0385551 0.999256i \(-0.512275\pi\)
−0.0385551 + 0.999256i \(0.512275\pi\)
\(444\) 0 0
\(445\) −1.00000 −0.0474045
\(446\) 1.31819 0.0624181
\(447\) 0 0
\(448\) −21.5161 −1.01654
\(449\) 37.6589 1.77723 0.888617 0.458650i \(-0.151667\pi\)
0.888617 + 0.458650i \(0.151667\pi\)
\(450\) 0 0
\(451\) 25.1884 1.18608
\(452\) −6.17781 −0.290580
\(453\) 0 0
\(454\) 2.73984 0.128587
\(455\) 8.05244 0.377504
\(456\) 0 0
\(457\) −20.4355 −0.955933 −0.477966 0.878378i \(-0.658626\pi\)
−0.477966 + 0.878378i \(0.658626\pi\)
\(458\) 3.71371 0.173530
\(459\) 0 0
\(460\) −0.195067 −0.00909506
\(461\) −39.5268 −1.84095 −0.920474 0.390803i \(-0.872197\pi\)
−0.920474 + 0.390803i \(0.872197\pi\)
\(462\) 0 0
\(463\) 16.4046 0.762387 0.381194 0.924495i \(-0.375513\pi\)
0.381194 + 0.924495i \(0.375513\pi\)
\(464\) −25.5472 −1.18600
\(465\) 0 0
\(466\) −2.65770 −0.123115
\(467\) 1.41022 0.0652573 0.0326286 0.999468i \(-0.489612\pi\)
0.0326286 + 0.999468i \(0.489612\pi\)
\(468\) 0 0
\(469\) 12.2272 0.564600
\(470\) −1.00898 −0.0465409
\(471\) 0 0
\(472\) −1.68818 −0.0777048
\(473\) −12.6085 −0.579737
\(474\) 0 0
\(475\) −0.721848 −0.0331207
\(476\) 35.6721 1.63503
\(477\) 0 0
\(478\) 1.11047 0.0507919
\(479\) 5.09893 0.232976 0.116488 0.993192i \(-0.462836\pi\)
0.116488 + 0.993192i \(0.462836\pi\)
\(480\) 0 0
\(481\) −11.2466 −0.512801
\(482\) 4.04320 0.184163
\(483\) 0 0
\(484\) 6.73077 0.305944
\(485\) −11.6151 −0.527414
\(486\) 0 0
\(487\) −30.3129 −1.37361 −0.686803 0.726843i \(-0.740987\pi\)
−0.686803 + 0.726843i \(0.740987\pi\)
\(488\) −5.13524 −0.232462
\(489\) 0 0
\(490\) −0.203135 −0.00917672
\(491\) 16.6019 0.749234 0.374617 0.927180i \(-0.377774\pi\)
0.374617 + 0.927180i \(0.377774\pi\)
\(492\) 0 0
\(493\) 41.3374 1.86174
\(494\) 0.305773 0.0137574
\(495\) 0 0
\(496\) −3.41957 −0.153543
\(497\) 7.50827 0.336792
\(498\) 0 0
\(499\) 37.3084 1.67015 0.835077 0.550133i \(-0.185423\pi\)
0.835077 + 0.550133i \(0.185423\pi\)
\(500\) −1.97693 −0.0884109
\(501\) 0 0
\(502\) 3.24906 0.145013
\(503\) 25.3041 1.12825 0.564127 0.825688i \(-0.309213\pi\)
0.564127 + 0.825688i \(0.309213\pi\)
\(504\) 0 0
\(505\) −12.1795 −0.541981
\(506\) 0.0413054 0.00183625
\(507\) 0 0
\(508\) 24.9885 1.10869
\(509\) 2.56999 0.113913 0.0569563 0.998377i \(-0.481860\pi\)
0.0569563 + 0.998377i \(0.481860\pi\)
\(510\) 0 0
\(511\) −27.3519 −1.20998
\(512\) −11.5976 −0.512544
\(513\) 0 0
\(514\) −2.10585 −0.0928849
\(515\) 9.71335 0.428021
\(516\) 0 0
\(517\) −18.3070 −0.805140
\(518\) 1.76873 0.0777136
\(519\) 0 0
\(520\) 1.68462 0.0738754
\(521\) 40.9730 1.79506 0.897530 0.440954i \(-0.145360\pi\)
0.897530 + 0.440954i \(0.145360\pi\)
\(522\) 0 0
\(523\) −2.35708 −0.103068 −0.0515340 0.998671i \(-0.516411\pi\)
−0.0515340 + 0.998671i \(0.516411\pi\)
\(524\) 32.1116 1.40280
\(525\) 0 0
\(526\) 3.04999 0.132986
\(527\) 5.53313 0.241027
\(528\) 0 0
\(529\) −22.9903 −0.999577
\(530\) 0.116332 0.00505315
\(531\) 0 0
\(532\) 4.12051 0.178647
\(533\) −25.4883 −1.10402
\(534\) 0 0
\(535\) −8.02137 −0.346794
\(536\) 2.55800 0.110489
\(537\) 0 0
\(538\) 1.62754 0.0701681
\(539\) −3.68569 −0.158754
\(540\) 0 0
\(541\) −6.28140 −0.270058 −0.135029 0.990842i \(-0.543113\pi\)
−0.135029 + 0.990842i \(0.543113\pi\)
\(542\) 4.15331 0.178400
\(543\) 0 0
\(544\) 11.2159 0.480876
\(545\) 4.86470 0.208381
\(546\) 0 0
\(547\) −37.6741 −1.61083 −0.805414 0.592712i \(-0.798057\pi\)
−0.805414 + 0.592712i \(0.798057\pi\)
\(548\) −22.7590 −0.972217
\(549\) 0 0
\(550\) 0.418614 0.0178498
\(551\) 4.77492 0.203418
\(552\) 0 0
\(553\) 38.3185 1.62947
\(554\) 2.51090 0.106678
\(555\) 0 0
\(556\) 18.1588 0.770106
\(557\) 27.6895 1.17324 0.586622 0.809861i \(-0.300458\pi\)
0.586622 + 0.809861i \(0.300458\pi\)
\(558\) 0 0
\(559\) 12.7586 0.539630
\(560\) 11.1516 0.471242
\(561\) 0 0
\(562\) 1.02369 0.0431816
\(563\) 31.6924 1.33567 0.667837 0.744308i \(-0.267220\pi\)
0.667837 + 0.744308i \(0.267220\pi\)
\(564\) 0 0
\(565\) 3.12496 0.131468
\(566\) 0.847778 0.0356348
\(567\) 0 0
\(568\) 1.57077 0.0659082
\(569\) 9.29551 0.389688 0.194844 0.980834i \(-0.437580\pi\)
0.194844 + 0.980834i \(0.437580\pi\)
\(570\) 0 0
\(571\) 43.4044 1.81642 0.908208 0.418519i \(-0.137451\pi\)
0.908208 + 0.418519i \(0.137451\pi\)
\(572\) 15.1942 0.635302
\(573\) 0 0
\(574\) 4.00850 0.167311
\(575\) 0.0986719 0.00411490
\(576\) 0 0
\(577\) 25.8713 1.07704 0.538519 0.842613i \(-0.318984\pi\)
0.538519 + 0.842613i \(0.318984\pi\)
\(578\) −3.34960 −0.139325
\(579\) 0 0
\(580\) 13.0771 0.542996
\(581\) 32.6315 1.35378
\(582\) 0 0
\(583\) 2.11073 0.0874176
\(584\) −5.72218 −0.236785
\(585\) 0 0
\(586\) 1.14446 0.0472774
\(587\) −35.2942 −1.45675 −0.728373 0.685180i \(-0.759723\pi\)
−0.728373 + 0.685180i \(0.759723\pi\)
\(588\) 0 0
\(589\) 0.639137 0.0263352
\(590\) 0.424494 0.0174761
\(591\) 0 0
\(592\) −15.5751 −0.640134
\(593\) −22.4865 −0.923411 −0.461706 0.887033i \(-0.652762\pi\)
−0.461706 + 0.887033i \(0.652762\pi\)
\(594\) 0 0
\(595\) −18.0442 −0.739739
\(596\) −6.43145 −0.263443
\(597\) 0 0
\(598\) −0.0417972 −0.00170921
\(599\) −37.4414 −1.52982 −0.764908 0.644140i \(-0.777215\pi\)
−0.764908 + 0.644140i \(0.777215\pi\)
\(600\) 0 0
\(601\) 35.1825 1.43513 0.717563 0.696494i \(-0.245258\pi\)
0.717563 + 0.696494i \(0.245258\pi\)
\(602\) −2.00652 −0.0817794
\(603\) 0 0
\(604\) 22.3569 0.909691
\(605\) −3.40466 −0.138419
\(606\) 0 0
\(607\) −44.2600 −1.79646 −0.898230 0.439526i \(-0.855146\pi\)
−0.898230 + 0.439526i \(0.855146\pi\)
\(608\) 1.29555 0.0525416
\(609\) 0 0
\(610\) 1.29126 0.0522815
\(611\) 18.5249 0.749439
\(612\) 0 0
\(613\) 11.3225 0.457313 0.228657 0.973507i \(-0.426567\pi\)
0.228657 + 0.973507i \(0.426567\pi\)
\(614\) 1.58696 0.0640445
\(615\) 0 0
\(616\) −4.80702 −0.193680
\(617\) −13.3243 −0.536415 −0.268208 0.963361i \(-0.586431\pi\)
−0.268208 + 0.963361i \(0.586431\pi\)
\(618\) 0 0
\(619\) 13.8176 0.555378 0.277689 0.960671i \(-0.410432\pi\)
0.277689 + 0.960671i \(0.410432\pi\)
\(620\) 1.75041 0.0702980
\(621\) 0 0
\(622\) −3.98620 −0.159832
\(623\) −2.88745 −0.115683
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −1.89239 −0.0756350
\(627\) 0 0
\(628\) −20.4781 −0.817163
\(629\) 25.2018 1.00486
\(630\) 0 0
\(631\) 45.8580 1.82558 0.912789 0.408431i \(-0.133924\pi\)
0.912789 + 0.408431i \(0.133924\pi\)
\(632\) 8.01645 0.318877
\(633\) 0 0
\(634\) −2.08657 −0.0828682
\(635\) −12.6401 −0.501606
\(636\) 0 0
\(637\) 3.72957 0.147771
\(638\) −2.76907 −0.109629
\(639\) 0 0
\(640\) 4.72139 0.186629
\(641\) 33.8076 1.33532 0.667661 0.744466i \(-0.267296\pi\)
0.667661 + 0.744466i \(0.267296\pi\)
\(642\) 0 0
\(643\) 43.4445 1.71328 0.856642 0.515912i \(-0.172547\pi\)
0.856642 + 0.515912i \(0.172547\pi\)
\(644\) −0.563247 −0.0221950
\(645\) 0 0
\(646\) −0.685187 −0.0269583
\(647\) −3.44794 −0.135553 −0.0677763 0.997701i \(-0.521590\pi\)
−0.0677763 + 0.997701i \(0.521590\pi\)
\(648\) 0 0
\(649\) 7.70202 0.302331
\(650\) −0.423598 −0.0166149
\(651\) 0 0
\(652\) 17.3106 0.677937
\(653\) −17.8067 −0.696831 −0.348415 0.937340i \(-0.613280\pi\)
−0.348415 + 0.937340i \(0.613280\pi\)
\(654\) 0 0
\(655\) −16.2432 −0.634674
\(656\) −35.2981 −1.37816
\(657\) 0 0
\(658\) −2.91338 −0.113575
\(659\) −16.5625 −0.645185 −0.322593 0.946538i \(-0.604554\pi\)
−0.322593 + 0.946538i \(0.604554\pi\)
\(660\) 0 0
\(661\) 2.05302 0.0798534 0.0399267 0.999203i \(-0.487288\pi\)
0.0399267 + 0.999203i \(0.487288\pi\)
\(662\) −2.95700 −0.114927
\(663\) 0 0
\(664\) 6.82671 0.264928
\(665\) −2.08430 −0.0808257
\(666\) 0 0
\(667\) −0.652700 −0.0252726
\(668\) 43.1446 1.66932
\(669\) 0 0
\(670\) −0.643210 −0.0248494
\(671\) 23.4286 0.904452
\(672\) 0 0
\(673\) −30.6267 −1.18057 −0.590286 0.807194i \(-0.700985\pi\)
−0.590286 + 0.807194i \(0.700985\pi\)
\(674\) 4.41583 0.170091
\(675\) 0 0
\(676\) 10.3250 0.397114
\(677\) 25.7858 0.991029 0.495515 0.868600i \(-0.334979\pi\)
0.495515 + 0.868600i \(0.334979\pi\)
\(678\) 0 0
\(679\) −33.5380 −1.28707
\(680\) −3.77495 −0.144763
\(681\) 0 0
\(682\) −0.370648 −0.0141928
\(683\) −38.0328 −1.45528 −0.727642 0.685957i \(-0.759384\pi\)
−0.727642 + 0.685957i \(0.759384\pi\)
\(684\) 0 0
\(685\) 11.5123 0.439863
\(686\) 2.48356 0.0948226
\(687\) 0 0
\(688\) 17.6690 0.673624
\(689\) −2.13586 −0.0813698
\(690\) 0 0
\(691\) 40.2662 1.53180 0.765899 0.642961i \(-0.222294\pi\)
0.765899 + 0.642961i \(0.222294\pi\)
\(692\) −16.0521 −0.610207
\(693\) 0 0
\(694\) −0.854076 −0.0324203
\(695\) −9.18537 −0.348421
\(696\) 0 0
\(697\) 57.1150 2.16339
\(698\) 0.358450 0.0135675
\(699\) 0 0
\(700\) −5.70828 −0.215753
\(701\) 37.7180 1.42459 0.712295 0.701880i \(-0.247656\pi\)
0.712295 + 0.701880i \(0.247656\pi\)
\(702\) 0 0
\(703\) 2.91108 0.109793
\(704\) 20.5363 0.773992
\(705\) 0 0
\(706\) 3.92801 0.147833
\(707\) −35.1677 −1.32262
\(708\) 0 0
\(709\) 38.5655 1.44836 0.724178 0.689613i \(-0.242219\pi\)
0.724178 + 0.689613i \(0.242219\pi\)
\(710\) −0.394972 −0.0148230
\(711\) 0 0
\(712\) −0.604071 −0.0226385
\(713\) −0.0873658 −0.00327188
\(714\) 0 0
\(715\) −7.68577 −0.287431
\(716\) 29.0501 1.08565
\(717\) 0 0
\(718\) −3.44677 −0.128632
\(719\) −10.0993 −0.376641 −0.188321 0.982108i \(-0.560304\pi\)
−0.188321 + 0.982108i \(0.560304\pi\)
\(720\) 0 0
\(721\) 28.0468 1.04452
\(722\) 2.80684 0.104460
\(723\) 0 0
\(724\) −18.5030 −0.687660
\(725\) −6.61485 −0.245669
\(726\) 0 0
\(727\) 10.8207 0.401319 0.200659 0.979661i \(-0.435692\pi\)
0.200659 + 0.979661i \(0.435692\pi\)
\(728\) 4.86424 0.180281
\(729\) 0 0
\(730\) 1.43884 0.0532540
\(731\) −28.5898 −1.05743
\(732\) 0 0
\(733\) 18.8978 0.698005 0.349002 0.937122i \(-0.386521\pi\)
0.349002 + 0.937122i \(0.386521\pi\)
\(734\) 4.17192 0.153988
\(735\) 0 0
\(736\) −0.177094 −0.00652775
\(737\) −11.6704 −0.429886
\(738\) 0 0
\(739\) 32.8181 1.20723 0.603617 0.797275i \(-0.293726\pi\)
0.603617 + 0.797275i \(0.293726\pi\)
\(740\) 7.97258 0.293078
\(741\) 0 0
\(742\) 0.335903 0.0123314
\(743\) 22.4436 0.823374 0.411687 0.911325i \(-0.364940\pi\)
0.411687 + 0.911325i \(0.364940\pi\)
\(744\) 0 0
\(745\) 3.25326 0.119190
\(746\) 0.552071 0.0202128
\(747\) 0 0
\(748\) −34.0477 −1.24491
\(749\) −23.1613 −0.846294
\(750\) 0 0
\(751\) 11.1004 0.405058 0.202529 0.979276i \(-0.435084\pi\)
0.202529 + 0.979276i \(0.435084\pi\)
\(752\) 25.6547 0.935531
\(753\) 0 0
\(754\) 2.80204 0.102044
\(755\) −11.3089 −0.411574
\(756\) 0 0
\(757\) −17.6253 −0.640601 −0.320300 0.947316i \(-0.603784\pi\)
−0.320300 + 0.947316i \(0.603784\pi\)
\(758\) 1.44030 0.0523140
\(759\) 0 0
\(760\) −0.436048 −0.0158171
\(761\) 8.04139 0.291500 0.145750 0.989321i \(-0.453440\pi\)
0.145750 + 0.989321i \(0.453440\pi\)
\(762\) 0 0
\(763\) 14.0466 0.508519
\(764\) 21.1454 0.765015
\(765\) 0 0
\(766\) −1.66103 −0.0600155
\(767\) −7.79372 −0.281415
\(768\) 0 0
\(769\) 13.1830 0.475392 0.237696 0.971340i \(-0.423608\pi\)
0.237696 + 0.971340i \(0.423608\pi\)
\(770\) 1.20873 0.0435595
\(771\) 0 0
\(772\) −37.6275 −1.35424
\(773\) 21.9320 0.788840 0.394420 0.918930i \(-0.370946\pi\)
0.394420 + 0.918930i \(0.370946\pi\)
\(774\) 0 0
\(775\) −0.885417 −0.0318051
\(776\) −7.01634 −0.251872
\(777\) 0 0
\(778\) −1.72594 −0.0618780
\(779\) 6.59741 0.236377
\(780\) 0 0
\(781\) −7.16638 −0.256433
\(782\) 0.0936606 0.00334930
\(783\) 0 0
\(784\) 5.16498 0.184464
\(785\) 10.3585 0.369711
\(786\) 0 0
\(787\) 17.3072 0.616937 0.308468 0.951235i \(-0.400184\pi\)
0.308468 + 0.951235i \(0.400184\pi\)
\(788\) −43.3247 −1.54338
\(789\) 0 0
\(790\) −2.01574 −0.0717168
\(791\) 9.02315 0.320826
\(792\) 0 0
\(793\) −23.7076 −0.841880
\(794\) −0.0913776 −0.00324287
\(795\) 0 0
\(796\) −25.7027 −0.911007
\(797\) −18.0296 −0.638642 −0.319321 0.947647i \(-0.603455\pi\)
−0.319321 + 0.947647i \(0.603455\pi\)
\(798\) 0 0
\(799\) −41.5113 −1.46856
\(800\) −1.79477 −0.0634547
\(801\) 0 0
\(802\) −3.11997 −0.110170
\(803\) 26.1064 0.921275
\(804\) 0 0
\(805\) 0.284910 0.0100418
\(806\) 0.375061 0.0132110
\(807\) 0 0
\(808\) −7.35728 −0.258828
\(809\) −10.9470 −0.384875 −0.192438 0.981309i \(-0.561639\pi\)
−0.192438 + 0.981309i \(0.561639\pi\)
\(810\) 0 0
\(811\) −45.8898 −1.61141 −0.805705 0.592318i \(-0.798213\pi\)
−0.805705 + 0.592318i \(0.798213\pi\)
\(812\) 37.7594 1.32510
\(813\) 0 0
\(814\) −1.68819 −0.0591711
\(815\) −8.75633 −0.306721
\(816\) 0 0
\(817\) −3.30244 −0.115538
\(818\) −4.50427 −0.157488
\(819\) 0 0
\(820\) 18.0683 0.630974
\(821\) −2.44052 −0.0851747 −0.0425874 0.999093i \(-0.513560\pi\)
−0.0425874 + 0.999093i \(0.513560\pi\)
\(822\) 0 0
\(823\) −24.4911 −0.853708 −0.426854 0.904321i \(-0.640378\pi\)
−0.426854 + 0.904321i \(0.640378\pi\)
\(824\) 5.86755 0.204406
\(825\) 0 0
\(826\) 1.22570 0.0426477
\(827\) −32.8082 −1.14085 −0.570426 0.821349i \(-0.693222\pi\)
−0.570426 + 0.821349i \(0.693222\pi\)
\(828\) 0 0
\(829\) −1.25808 −0.0436948 −0.0218474 0.999761i \(-0.506955\pi\)
−0.0218474 + 0.999761i \(0.506955\pi\)
\(830\) −1.71658 −0.0595833
\(831\) 0 0
\(832\) −20.7808 −0.720445
\(833\) −8.35735 −0.289565
\(834\) 0 0
\(835\) −21.8241 −0.755253
\(836\) −3.93288 −0.136021
\(837\) 0 0
\(838\) 0.982742 0.0339483
\(839\) −31.3237 −1.08142 −0.540708 0.841211i \(-0.681843\pi\)
−0.540708 + 0.841211i \(0.681843\pi\)
\(840\) 0 0
\(841\) 14.7563 0.508837
\(842\) 4.64682 0.160140
\(843\) 0 0
\(844\) −1.80715 −0.0622046
\(845\) −5.22273 −0.179667
\(846\) 0 0
\(847\) −9.83077 −0.337789
\(848\) −2.95790 −0.101575
\(849\) 0 0
\(850\) 0.949212 0.0325577
\(851\) −0.397925 −0.0136407
\(852\) 0 0
\(853\) −45.1227 −1.54497 −0.772486 0.635032i \(-0.780987\pi\)
−0.772486 + 0.635032i \(0.780987\pi\)
\(854\) 3.72844 0.127585
\(855\) 0 0
\(856\) −4.84547 −0.165615
\(857\) −18.5362 −0.633186 −0.316593 0.948562i \(-0.602539\pi\)
−0.316593 + 0.948562i \(0.602539\pi\)
\(858\) 0 0
\(859\) −15.7802 −0.538415 −0.269207 0.963082i \(-0.586762\pi\)
−0.269207 + 0.963082i \(0.586762\pi\)
\(860\) −9.04439 −0.308411
\(861\) 0 0
\(862\) −2.37893 −0.0810267
\(863\) 29.4551 1.00266 0.501332 0.865255i \(-0.332844\pi\)
0.501332 + 0.865255i \(0.332844\pi\)
\(864\) 0 0
\(865\) 8.11969 0.276078
\(866\) −4.73985 −0.161067
\(867\) 0 0
\(868\) 5.05421 0.171551
\(869\) −36.5736 −1.24067
\(870\) 0 0
\(871\) 11.8094 0.400145
\(872\) 2.93862 0.0995143
\(873\) 0 0
\(874\) 0.0108188 0.000365952 0
\(875\) 2.88745 0.0976135
\(876\) 0 0
\(877\) −36.8048 −1.24281 −0.621405 0.783490i \(-0.713438\pi\)
−0.621405 + 0.783490i \(0.713438\pi\)
\(878\) 2.61830 0.0883634
\(879\) 0 0
\(880\) −10.6438 −0.358803
\(881\) −6.97606 −0.235029 −0.117515 0.993071i \(-0.537493\pi\)
−0.117515 + 0.993071i \(0.537493\pi\)
\(882\) 0 0
\(883\) 42.8921 1.44343 0.721717 0.692188i \(-0.243353\pi\)
0.721717 + 0.692188i \(0.243353\pi\)
\(884\) 34.4530 1.15878
\(885\) 0 0
\(886\) 0.246521 0.00828202
\(887\) −32.4435 −1.08935 −0.544673 0.838649i \(-0.683346\pi\)
−0.544673 + 0.838649i \(0.683346\pi\)
\(888\) 0 0
\(889\) −36.4975 −1.22409
\(890\) 0.151894 0.00509149
\(891\) 0 0
\(892\) 17.1565 0.574443
\(893\) −4.79501 −0.160459
\(894\) 0 0
\(895\) −14.6946 −0.491185
\(896\) 13.6328 0.455439
\(897\) 0 0
\(898\) −5.72015 −0.190884
\(899\) 5.85690 0.195339
\(900\) 0 0
\(901\) 4.78611 0.159448
\(902\) −3.82597 −0.127391
\(903\) 0 0
\(904\) 1.88769 0.0627838
\(905\) 9.35948 0.311120
\(906\) 0 0
\(907\) 31.4521 1.04435 0.522175 0.852838i \(-0.325121\pi\)
0.522175 + 0.852838i \(0.325121\pi\)
\(908\) 35.6596 1.18341
\(909\) 0 0
\(910\) −1.22312 −0.0405459
\(911\) 12.0996 0.400877 0.200438 0.979706i \(-0.435763\pi\)
0.200438 + 0.979706i \(0.435763\pi\)
\(912\) 0 0
\(913\) −31.1456 −1.03077
\(914\) 3.10403 0.102672
\(915\) 0 0
\(916\) 48.3347 1.59702
\(917\) −46.9014 −1.54882
\(918\) 0 0
\(919\) −31.0362 −1.02379 −0.511894 0.859049i \(-0.671056\pi\)
−0.511894 + 0.859049i \(0.671056\pi\)
\(920\) 0.0596048 0.00196511
\(921\) 0 0
\(922\) 6.00388 0.197727
\(923\) 7.25170 0.238692
\(924\) 0 0
\(925\) −4.03281 −0.132598
\(926\) −2.49176 −0.0818843
\(927\) 0 0
\(928\) 11.8721 0.389722
\(929\) 14.0194 0.459963 0.229982 0.973195i \(-0.426133\pi\)
0.229982 + 0.973195i \(0.426133\pi\)
\(930\) 0 0
\(931\) −0.965364 −0.0316385
\(932\) −34.5905 −1.13305
\(933\) 0 0
\(934\) −0.214204 −0.00700897
\(935\) 17.2225 0.563237
\(936\) 0 0
\(937\) 38.5069 1.25797 0.628983 0.777419i \(-0.283471\pi\)
0.628983 + 0.777419i \(0.283471\pi\)
\(938\) −1.85724 −0.0606409
\(939\) 0 0
\(940\) −13.1321 −0.428322
\(941\) −52.9697 −1.72676 −0.863381 0.504552i \(-0.831658\pi\)
−0.863381 + 0.504552i \(0.831658\pi\)
\(942\) 0 0
\(943\) −0.901822 −0.0293674
\(944\) −10.7933 −0.351292
\(945\) 0 0
\(946\) 1.91515 0.0622668
\(947\) 44.2927 1.43932 0.719659 0.694327i \(-0.244298\pi\)
0.719659 + 0.694327i \(0.244298\pi\)
\(948\) 0 0
\(949\) −26.4172 −0.857539
\(950\) 0.109644 0.00355733
\(951\) 0 0
\(952\) −10.9000 −0.353270
\(953\) −11.7349 −0.380130 −0.190065 0.981772i \(-0.560870\pi\)
−0.190065 + 0.981772i \(0.560870\pi\)
\(954\) 0 0
\(955\) −10.6961 −0.346118
\(956\) 14.4530 0.467445
\(957\) 0 0
\(958\) −0.774496 −0.0250228
\(959\) 33.2412 1.07341
\(960\) 0 0
\(961\) −30.2160 −0.974711
\(962\) 1.70829 0.0550775
\(963\) 0 0
\(964\) 52.6231 1.69488
\(965\) 19.0333 0.612704
\(966\) 0 0
\(967\) −50.6434 −1.62858 −0.814291 0.580457i \(-0.802874\pi\)
−0.814291 + 0.580457i \(0.802874\pi\)
\(968\) −2.05666 −0.0661034
\(969\) 0 0
\(970\) 1.76426 0.0566470
\(971\) −14.2579 −0.457556 −0.228778 0.973479i \(-0.573473\pi\)
−0.228778 + 0.973479i \(0.573473\pi\)
\(972\) 0 0
\(973\) −26.5223 −0.850265
\(974\) 4.60433 0.147532
\(975\) 0 0
\(976\) −32.8320 −1.05093
\(977\) 32.2990 1.03334 0.516669 0.856185i \(-0.327172\pi\)
0.516669 + 0.856185i \(0.327172\pi\)
\(978\) 0 0
\(979\) 2.75596 0.0880810
\(980\) −2.64385 −0.0844546
\(981\) 0 0
\(982\) −2.52173 −0.0804716
\(983\) 28.7938 0.918378 0.459189 0.888339i \(-0.348140\pi\)
0.459189 + 0.888339i \(0.348140\pi\)
\(984\) 0 0
\(985\) 21.9152 0.698275
\(986\) −6.27890 −0.199961
\(987\) 0 0
\(988\) 3.97970 0.126611
\(989\) 0.451421 0.0143544
\(990\) 0 0
\(991\) 46.2829 1.47023 0.735113 0.677945i \(-0.237129\pi\)
0.735113 + 0.677945i \(0.237129\pi\)
\(992\) 1.58912 0.0504546
\(993\) 0 0
\(994\) −1.14046 −0.0361732
\(995\) 13.0013 0.412169
\(996\) 0 0
\(997\) 24.8140 0.785866 0.392933 0.919567i \(-0.371460\pi\)
0.392933 + 0.919567i \(0.371460\pi\)
\(998\) −5.66692 −0.179383
\(999\) 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 \(a_p\))