Properties

Label 8024.2.a.y.1.1
Level 8024
Weight 2
Character 8024.1
Self dual Yes
Analytic conductor 64.072
Analytic rank 1
Dimension 23
CM No

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Newspace parameters

Level: \( N \) = \( 8024 = 2^{3} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8024.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0719625819\)
Analytic rank: \(1\)
Dimension: \(23\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-3.24951 q^{3}\) \(-3.27317 q^{5}\) \(+3.90567 q^{7}\) \(+7.55931 q^{9}\) \(+O(q^{10})\) \(q\)\(-3.24951 q^{3}\) \(-3.27317 q^{5}\) \(+3.90567 q^{7}\) \(+7.55931 q^{9}\) \(+3.39948 q^{11}\) \(+0.485234 q^{13}\) \(+10.6362 q^{15}\) \(-1.00000 q^{17}\) \(-3.70343 q^{19}\) \(-12.6915 q^{21}\) \(+6.21767 q^{23}\) \(+5.71363 q^{25}\) \(-14.8155 q^{27}\) \(+3.88250 q^{29}\) \(-4.41681 q^{31}\) \(-11.0466 q^{33}\) \(-12.7839 q^{35}\) \(-10.0631 q^{37}\) \(-1.57677 q^{39}\) \(-1.01838 q^{41}\) \(+10.8066 q^{43}\) \(-24.7429 q^{45}\) \(-11.2963 q^{47}\) \(+8.25428 q^{49}\) \(+3.24951 q^{51}\) \(-9.21459 q^{53}\) \(-11.1271 q^{55}\) \(+12.0343 q^{57}\) \(-1.00000 q^{59}\) \(-10.4523 q^{61}\) \(+29.5242 q^{63}\) \(-1.58825 q^{65}\) \(+0.0650174 q^{67}\) \(-20.2044 q^{69}\) \(+6.83545 q^{71}\) \(+12.0474 q^{73}\) \(-18.5665 q^{75}\) \(+13.2772 q^{77}\) \(-12.5012 q^{79}\) \(+25.4652 q^{81}\) \(-0.493623 q^{83}\) \(+3.27317 q^{85}\) \(-12.6162 q^{87}\) \(+4.81090 q^{89}\) \(+1.89516 q^{91}\) \(+14.3525 q^{93}\) \(+12.1219 q^{95}\) \(+4.67707 q^{97}\) \(+25.6977 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.24951 −1.87610 −0.938052 0.346494i \(-0.887372\pi\)
−0.938052 + 0.346494i \(0.887372\pi\)
\(4\) 0 0
\(5\) −3.27317 −1.46381 −0.731903 0.681409i \(-0.761367\pi\)
−0.731903 + 0.681409i \(0.761367\pi\)
\(6\) 0 0
\(7\) 3.90567 1.47621 0.738103 0.674688i \(-0.235722\pi\)
0.738103 + 0.674688i \(0.235722\pi\)
\(8\) 0 0
\(9\) 7.55931 2.51977
\(10\) 0 0
\(11\) 3.39948 1.02498 0.512491 0.858693i \(-0.328723\pi\)
0.512491 + 0.858693i \(0.328723\pi\)
\(12\) 0 0
\(13\) 0.485234 0.134580 0.0672898 0.997733i \(-0.478565\pi\)
0.0672898 + 0.997733i \(0.478565\pi\)
\(14\) 0 0
\(15\) 10.6362 2.74625
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) −3.70343 −0.849625 −0.424813 0.905281i \(-0.639660\pi\)
−0.424813 + 0.905281i \(0.639660\pi\)
\(20\) 0 0
\(21\) −12.6915 −2.76952
\(22\) 0 0
\(23\) 6.21767 1.29647 0.648237 0.761439i \(-0.275507\pi\)
0.648237 + 0.761439i \(0.275507\pi\)
\(24\) 0 0
\(25\) 5.71363 1.14273
\(26\) 0 0
\(27\) −14.8155 −2.85125
\(28\) 0 0
\(29\) 3.88250 0.720963 0.360482 0.932766i \(-0.382612\pi\)
0.360482 + 0.932766i \(0.382612\pi\)
\(30\) 0 0
\(31\) −4.41681 −0.793283 −0.396642 0.917974i \(-0.629824\pi\)
−0.396642 + 0.917974i \(0.629824\pi\)
\(32\) 0 0
\(33\) −11.0466 −1.92297
\(34\) 0 0
\(35\) −12.7839 −2.16088
\(36\) 0 0
\(37\) −10.0631 −1.65437 −0.827186 0.561929i \(-0.810059\pi\)
−0.827186 + 0.561929i \(0.810059\pi\)
\(38\) 0 0
\(39\) −1.57677 −0.252486
\(40\) 0 0
\(41\) −1.01838 −0.159044 −0.0795220 0.996833i \(-0.525339\pi\)
−0.0795220 + 0.996833i \(0.525339\pi\)
\(42\) 0 0
\(43\) 10.8066 1.64799 0.823996 0.566595i \(-0.191740\pi\)
0.823996 + 0.566595i \(0.191740\pi\)
\(44\) 0 0
\(45\) −24.7429 −3.68845
\(46\) 0 0
\(47\) −11.2963 −1.64774 −0.823869 0.566781i \(-0.808189\pi\)
−0.823869 + 0.566781i \(0.808189\pi\)
\(48\) 0 0
\(49\) 8.25428 1.17918
\(50\) 0 0
\(51\) 3.24951 0.455022
\(52\) 0 0
\(53\) −9.21459 −1.26572 −0.632861 0.774266i \(-0.718119\pi\)
−0.632861 + 0.774266i \(0.718119\pi\)
\(54\) 0 0
\(55\) −11.1271 −1.50037
\(56\) 0 0
\(57\) 12.0343 1.59399
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −10.4523 −1.33828 −0.669139 0.743138i \(-0.733337\pi\)
−0.669139 + 0.743138i \(0.733337\pi\)
\(62\) 0 0
\(63\) 29.5242 3.71970
\(64\) 0 0
\(65\) −1.58825 −0.196998
\(66\) 0 0
\(67\) 0.0650174 0.00794314 0.00397157 0.999992i \(-0.498736\pi\)
0.00397157 + 0.999992i \(0.498736\pi\)
\(68\) 0 0
\(69\) −20.2044 −2.43232
\(70\) 0 0
\(71\) 6.83545 0.811219 0.405610 0.914046i \(-0.367059\pi\)
0.405610 + 0.914046i \(0.367059\pi\)
\(72\) 0 0
\(73\) 12.0474 1.41004 0.705022 0.709185i \(-0.250937\pi\)
0.705022 + 0.709185i \(0.250937\pi\)
\(74\) 0 0
\(75\) −18.5665 −2.14387
\(76\) 0 0
\(77\) 13.2772 1.51308
\(78\) 0 0
\(79\) −12.5012 −1.40649 −0.703245 0.710947i \(-0.748266\pi\)
−0.703245 + 0.710947i \(0.748266\pi\)
\(80\) 0 0
\(81\) 25.4652 2.82947
\(82\) 0 0
\(83\) −0.493623 −0.0541822 −0.0270911 0.999633i \(-0.508624\pi\)
−0.0270911 + 0.999633i \(0.508624\pi\)
\(84\) 0 0
\(85\) 3.27317 0.355025
\(86\) 0 0
\(87\) −12.6162 −1.35260
\(88\) 0 0
\(89\) 4.81090 0.509954 0.254977 0.966947i \(-0.417932\pi\)
0.254977 + 0.966947i \(0.417932\pi\)
\(90\) 0 0
\(91\) 1.89516 0.198667
\(92\) 0 0
\(93\) 14.3525 1.48828
\(94\) 0 0
\(95\) 12.1219 1.24369
\(96\) 0 0
\(97\) 4.67707 0.474884 0.237442 0.971402i \(-0.423691\pi\)
0.237442 + 0.971402i \(0.423691\pi\)
\(98\) 0 0
\(99\) 25.6977 2.58272
\(100\) 0 0
\(101\) −0.466630 −0.0464314 −0.0232157 0.999730i \(-0.507390\pi\)
−0.0232157 + 0.999730i \(0.507390\pi\)
\(102\) 0 0
\(103\) −11.0563 −1.08941 −0.544703 0.838629i \(-0.683358\pi\)
−0.544703 + 0.838629i \(0.683358\pi\)
\(104\) 0 0
\(105\) 41.5415 4.05403
\(106\) 0 0
\(107\) −9.42189 −0.910848 −0.455424 0.890275i \(-0.650512\pi\)
−0.455424 + 0.890275i \(0.650512\pi\)
\(108\) 0 0
\(109\) −2.12000 −0.203059 −0.101529 0.994833i \(-0.532374\pi\)
−0.101529 + 0.994833i \(0.532374\pi\)
\(110\) 0 0
\(111\) 32.7003 3.10377
\(112\) 0 0
\(113\) 6.33823 0.596250 0.298125 0.954527i \(-0.403639\pi\)
0.298125 + 0.954527i \(0.403639\pi\)
\(114\) 0 0
\(115\) −20.3515 −1.89778
\(116\) 0 0
\(117\) 3.66803 0.339110
\(118\) 0 0
\(119\) −3.90567 −0.358032
\(120\) 0 0
\(121\) 0.556448 0.0505862
\(122\) 0 0
\(123\) 3.30923 0.298383
\(124\) 0 0
\(125\) −2.33582 −0.208922
\(126\) 0 0
\(127\) 9.95463 0.883330 0.441665 0.897180i \(-0.354388\pi\)
0.441665 + 0.897180i \(0.354388\pi\)
\(128\) 0 0
\(129\) −35.1162 −3.09181
\(130\) 0 0
\(131\) 12.8434 1.12214 0.561068 0.827769i \(-0.310390\pi\)
0.561068 + 0.827769i \(0.310390\pi\)
\(132\) 0 0
\(133\) −14.4644 −1.25422
\(134\) 0 0
\(135\) 48.4936 4.17367
\(136\) 0 0
\(137\) 16.5641 1.41517 0.707585 0.706628i \(-0.249785\pi\)
0.707585 + 0.706628i \(0.249785\pi\)
\(138\) 0 0
\(139\) 11.6558 0.988632 0.494316 0.869282i \(-0.335419\pi\)
0.494316 + 0.869282i \(0.335419\pi\)
\(140\) 0 0
\(141\) 36.7075 3.09133
\(142\) 0 0
\(143\) 1.64954 0.137942
\(144\) 0 0
\(145\) −12.7081 −1.05535
\(146\) 0 0
\(147\) −26.8224 −2.21227
\(148\) 0 0
\(149\) 11.6689 0.955956 0.477978 0.878372i \(-0.341370\pi\)
0.477978 + 0.878372i \(0.341370\pi\)
\(150\) 0 0
\(151\) −19.5354 −1.58977 −0.794886 0.606759i \(-0.792469\pi\)
−0.794886 + 0.606759i \(0.792469\pi\)
\(152\) 0 0
\(153\) −7.55931 −0.611134
\(154\) 0 0
\(155\) 14.4570 1.16121
\(156\) 0 0
\(157\) −6.19012 −0.494025 −0.247013 0.969012i \(-0.579449\pi\)
−0.247013 + 0.969012i \(0.579449\pi\)
\(158\) 0 0
\(159\) 29.9429 2.37463
\(160\) 0 0
\(161\) 24.2842 1.91386
\(162\) 0 0
\(163\) −2.24487 −0.175832 −0.0879159 0.996128i \(-0.528021\pi\)
−0.0879159 + 0.996128i \(0.528021\pi\)
\(164\) 0 0
\(165\) 36.1575 2.81486
\(166\) 0 0
\(167\) −12.0477 −0.932282 −0.466141 0.884710i \(-0.654356\pi\)
−0.466141 + 0.884710i \(0.654356\pi\)
\(168\) 0 0
\(169\) −12.7645 −0.981888
\(170\) 0 0
\(171\) −27.9954 −2.14086
\(172\) 0 0
\(173\) −2.66403 −0.202543 −0.101271 0.994859i \(-0.532291\pi\)
−0.101271 + 0.994859i \(0.532291\pi\)
\(174\) 0 0
\(175\) 22.3156 1.68690
\(176\) 0 0
\(177\) 3.24951 0.244248
\(178\) 0 0
\(179\) −19.9484 −1.49101 −0.745507 0.666497i \(-0.767793\pi\)
−0.745507 + 0.666497i \(0.767793\pi\)
\(180\) 0 0
\(181\) −0.601740 −0.0447270 −0.0223635 0.999750i \(-0.507119\pi\)
−0.0223635 + 0.999750i \(0.507119\pi\)
\(182\) 0 0
\(183\) 33.9648 2.51075
\(184\) 0 0
\(185\) 32.9384 2.42168
\(186\) 0 0
\(187\) −3.39948 −0.248594
\(188\) 0 0
\(189\) −57.8645 −4.20902
\(190\) 0 0
\(191\) −7.21241 −0.521872 −0.260936 0.965356i \(-0.584031\pi\)
−0.260936 + 0.965356i \(0.584031\pi\)
\(192\) 0 0
\(193\) 9.44119 0.679592 0.339796 0.940499i \(-0.389642\pi\)
0.339796 + 0.940499i \(0.389642\pi\)
\(194\) 0 0
\(195\) 5.16104 0.369590
\(196\) 0 0
\(197\) 20.7921 1.48138 0.740689 0.671848i \(-0.234499\pi\)
0.740689 + 0.671848i \(0.234499\pi\)
\(198\) 0 0
\(199\) −3.31070 −0.234690 −0.117345 0.993091i \(-0.537438\pi\)
−0.117345 + 0.993091i \(0.537438\pi\)
\(200\) 0 0
\(201\) −0.211275 −0.0149022
\(202\) 0 0
\(203\) 15.1638 1.06429
\(204\) 0 0
\(205\) 3.33332 0.232809
\(206\) 0 0
\(207\) 47.0013 3.26681
\(208\) 0 0
\(209\) −12.5897 −0.870850
\(210\) 0 0
\(211\) −6.41954 −0.441939 −0.220970 0.975281i \(-0.570922\pi\)
−0.220970 + 0.975281i \(0.570922\pi\)
\(212\) 0 0
\(213\) −22.2119 −1.52193
\(214\) 0 0
\(215\) −35.3719 −2.41234
\(216\) 0 0
\(217\) −17.2506 −1.17105
\(218\) 0 0
\(219\) −39.1482 −2.64539
\(220\) 0 0
\(221\) −0.485234 −0.0326404
\(222\) 0 0
\(223\) 16.8176 1.12619 0.563093 0.826393i \(-0.309611\pi\)
0.563093 + 0.826393i \(0.309611\pi\)
\(224\) 0 0
\(225\) 43.1911 2.87940
\(226\) 0 0
\(227\) −11.9033 −0.790047 −0.395023 0.918671i \(-0.629263\pi\)
−0.395023 + 0.918671i \(0.629263\pi\)
\(228\) 0 0
\(229\) 14.4389 0.954149 0.477074 0.878863i \(-0.341697\pi\)
0.477074 + 0.878863i \(0.341697\pi\)
\(230\) 0 0
\(231\) −43.1445 −2.83870
\(232\) 0 0
\(233\) −27.4209 −1.79640 −0.898202 0.439584i \(-0.855126\pi\)
−0.898202 + 0.439584i \(0.855126\pi\)
\(234\) 0 0
\(235\) 36.9747 2.41197
\(236\) 0 0
\(237\) 40.6226 2.63872
\(238\) 0 0
\(239\) −12.1198 −0.783965 −0.391982 0.919973i \(-0.628211\pi\)
−0.391982 + 0.919973i \(0.628211\pi\)
\(240\) 0 0
\(241\) −23.4014 −1.50741 −0.753707 0.657211i \(-0.771736\pi\)
−0.753707 + 0.657211i \(0.771736\pi\)
\(242\) 0 0
\(243\) −38.3029 −2.45713
\(244\) 0 0
\(245\) −27.0177 −1.72609
\(246\) 0 0
\(247\) −1.79703 −0.114342
\(248\) 0 0
\(249\) 1.60403 0.101651
\(250\) 0 0
\(251\) −21.3389 −1.34690 −0.673449 0.739234i \(-0.735188\pi\)
−0.673449 + 0.739234i \(0.735188\pi\)
\(252\) 0 0
\(253\) 21.1368 1.32886
\(254\) 0 0
\(255\) −10.6362 −0.666064
\(256\) 0 0
\(257\) 22.6204 1.41102 0.705510 0.708700i \(-0.250718\pi\)
0.705510 + 0.708700i \(0.250718\pi\)
\(258\) 0 0
\(259\) −39.3034 −2.44219
\(260\) 0 0
\(261\) 29.3490 1.81666
\(262\) 0 0
\(263\) −8.05937 −0.496962 −0.248481 0.968637i \(-0.579931\pi\)
−0.248481 + 0.968637i \(0.579931\pi\)
\(264\) 0 0
\(265\) 30.1609 1.85277
\(266\) 0 0
\(267\) −15.6331 −0.956728
\(268\) 0 0
\(269\) 25.9244 1.58064 0.790318 0.612697i \(-0.209915\pi\)
0.790318 + 0.612697i \(0.209915\pi\)
\(270\) 0 0
\(271\) 6.69681 0.406802 0.203401 0.979095i \(-0.434800\pi\)
0.203401 + 0.979095i \(0.434800\pi\)
\(272\) 0 0
\(273\) −6.15835 −0.372721
\(274\) 0 0
\(275\) 19.4233 1.17127
\(276\) 0 0
\(277\) 4.39800 0.264250 0.132125 0.991233i \(-0.457820\pi\)
0.132125 + 0.991233i \(0.457820\pi\)
\(278\) 0 0
\(279\) −33.3881 −1.99889
\(280\) 0 0
\(281\) 12.1510 0.724869 0.362435 0.932009i \(-0.381946\pi\)
0.362435 + 0.932009i \(0.381946\pi\)
\(282\) 0 0
\(283\) −5.19026 −0.308529 −0.154264 0.988030i \(-0.549301\pi\)
−0.154264 + 0.988030i \(0.549301\pi\)
\(284\) 0 0
\(285\) −39.3904 −2.33328
\(286\) 0 0
\(287\) −3.97745 −0.234782
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) −15.1982 −0.890932
\(292\) 0 0
\(293\) −20.9446 −1.22360 −0.611799 0.791013i \(-0.709554\pi\)
−0.611799 + 0.791013i \(0.709554\pi\)
\(294\) 0 0
\(295\) 3.27317 0.190571
\(296\) 0 0
\(297\) −50.3650 −2.92247
\(298\) 0 0
\(299\) 3.01702 0.174479
\(300\) 0 0
\(301\) 42.2071 2.43278
\(302\) 0 0
\(303\) 1.51632 0.0871103
\(304\) 0 0
\(305\) 34.2121 1.95898
\(306\) 0 0
\(307\) −11.9091 −0.679689 −0.339844 0.940482i \(-0.610374\pi\)
−0.339844 + 0.940482i \(0.610374\pi\)
\(308\) 0 0
\(309\) 35.9274 2.04384
\(310\) 0 0
\(311\) 20.5688 1.16635 0.583174 0.812348i \(-0.301811\pi\)
0.583174 + 0.812348i \(0.301811\pi\)
\(312\) 0 0
\(313\) −12.0134 −0.679039 −0.339519 0.940599i \(-0.610264\pi\)
−0.339519 + 0.940599i \(0.610264\pi\)
\(314\) 0 0
\(315\) −96.6376 −5.44491
\(316\) 0 0
\(317\) 3.01385 0.169274 0.0846372 0.996412i \(-0.473027\pi\)
0.0846372 + 0.996412i \(0.473027\pi\)
\(318\) 0 0
\(319\) 13.1985 0.738973
\(320\) 0 0
\(321\) 30.6165 1.70885
\(322\) 0 0
\(323\) 3.70343 0.206064
\(324\) 0 0
\(325\) 2.77244 0.153788
\(326\) 0 0
\(327\) 6.88894 0.380959
\(328\) 0 0
\(329\) −44.1197 −2.43240
\(330\) 0 0
\(331\) −25.0259 −1.37555 −0.687774 0.725925i \(-0.741412\pi\)
−0.687774 + 0.725925i \(0.741412\pi\)
\(332\) 0 0
\(333\) −76.0704 −4.16863
\(334\) 0 0
\(335\) −0.212813 −0.0116272
\(336\) 0 0
\(337\) 22.9880 1.25224 0.626118 0.779728i \(-0.284643\pi\)
0.626118 + 0.779728i \(0.284643\pi\)
\(338\) 0 0
\(339\) −20.5961 −1.11863
\(340\) 0 0
\(341\) −15.0149 −0.813100
\(342\) 0 0
\(343\) 4.89882 0.264512
\(344\) 0 0
\(345\) 66.1323 3.56044
\(346\) 0 0
\(347\) 30.6131 1.64340 0.821699 0.569922i \(-0.193026\pi\)
0.821699 + 0.569922i \(0.193026\pi\)
\(348\) 0 0
\(349\) −10.4253 −0.558052 −0.279026 0.960284i \(-0.590012\pi\)
−0.279026 + 0.960284i \(0.590012\pi\)
\(350\) 0 0
\(351\) −7.18898 −0.383720
\(352\) 0 0
\(353\) 34.3238 1.82687 0.913435 0.406984i \(-0.133420\pi\)
0.913435 + 0.406984i \(0.133420\pi\)
\(354\) 0 0
\(355\) −22.3736 −1.18747
\(356\) 0 0
\(357\) 12.6915 0.671706
\(358\) 0 0
\(359\) −22.7419 −1.20027 −0.600135 0.799899i \(-0.704886\pi\)
−0.600135 + 0.799899i \(0.704886\pi\)
\(360\) 0 0
\(361\) −5.28461 −0.278137
\(362\) 0 0
\(363\) −1.80818 −0.0949050
\(364\) 0 0
\(365\) −39.4332 −2.06403
\(366\) 0 0
\(367\) −9.85462 −0.514407 −0.257203 0.966357i \(-0.582801\pi\)
−0.257203 + 0.966357i \(0.582801\pi\)
\(368\) 0 0
\(369\) −7.69823 −0.400754
\(370\) 0 0
\(371\) −35.9892 −1.86847
\(372\) 0 0
\(373\) −9.13888 −0.473193 −0.236597 0.971608i \(-0.576032\pi\)
−0.236597 + 0.971608i \(0.576032\pi\)
\(374\) 0 0
\(375\) 7.59027 0.391960
\(376\) 0 0
\(377\) 1.88392 0.0970270
\(378\) 0 0
\(379\) −2.44145 −0.125409 −0.0627044 0.998032i \(-0.519973\pi\)
−0.0627044 + 0.998032i \(0.519973\pi\)
\(380\) 0 0
\(381\) −32.3476 −1.65722
\(382\) 0 0
\(383\) −34.9624 −1.78650 −0.893248 0.449563i \(-0.851580\pi\)
−0.893248 + 0.449563i \(0.851580\pi\)
\(384\) 0 0
\(385\) −43.4587 −2.21486
\(386\) 0 0
\(387\) 81.6905 4.15256
\(388\) 0 0
\(389\) −14.4956 −0.734957 −0.367479 0.930032i \(-0.619779\pi\)
−0.367479 + 0.930032i \(0.619779\pi\)
\(390\) 0 0
\(391\) −6.21767 −0.314441
\(392\) 0 0
\(393\) −41.7349 −2.10525
\(394\) 0 0
\(395\) 40.9184 2.05883
\(396\) 0 0
\(397\) 5.90766 0.296497 0.148249 0.988950i \(-0.452636\pi\)
0.148249 + 0.988950i \(0.452636\pi\)
\(398\) 0 0
\(399\) 47.0022 2.35305
\(400\) 0 0
\(401\) −35.3278 −1.76419 −0.882094 0.471074i \(-0.843866\pi\)
−0.882094 + 0.471074i \(0.843866\pi\)
\(402\) 0 0
\(403\) −2.14319 −0.106760
\(404\) 0 0
\(405\) −83.3519 −4.14179
\(406\) 0 0
\(407\) −34.2094 −1.69570
\(408\) 0 0
\(409\) −23.1393 −1.14416 −0.572082 0.820197i \(-0.693864\pi\)
−0.572082 + 0.820197i \(0.693864\pi\)
\(410\) 0 0
\(411\) −53.8253 −2.65501
\(412\) 0 0
\(413\) −3.90567 −0.192186
\(414\) 0 0
\(415\) 1.61571 0.0793121
\(416\) 0 0
\(417\) −37.8756 −1.85478
\(418\) 0 0
\(419\) 7.38925 0.360988 0.180494 0.983576i \(-0.442230\pi\)
0.180494 + 0.983576i \(0.442230\pi\)
\(420\) 0 0
\(421\) −14.8612 −0.724289 −0.362145 0.932122i \(-0.617955\pi\)
−0.362145 + 0.932122i \(0.617955\pi\)
\(422\) 0 0
\(423\) −85.3923 −4.15192
\(424\) 0 0
\(425\) −5.71363 −0.277152
\(426\) 0 0
\(427\) −40.8232 −1.97557
\(428\) 0 0
\(429\) −5.36020 −0.258793
\(430\) 0 0
\(431\) 32.6450 1.57245 0.786227 0.617938i \(-0.212032\pi\)
0.786227 + 0.617938i \(0.212032\pi\)
\(432\) 0 0
\(433\) −28.4878 −1.36903 −0.684517 0.728997i \(-0.739987\pi\)
−0.684517 + 0.728997i \(0.739987\pi\)
\(434\) 0 0
\(435\) 41.2950 1.97995
\(436\) 0 0
\(437\) −23.0267 −1.10152
\(438\) 0 0
\(439\) 8.24123 0.393332 0.196666 0.980471i \(-0.436988\pi\)
0.196666 + 0.980471i \(0.436988\pi\)
\(440\) 0 0
\(441\) 62.3967 2.97127
\(442\) 0 0
\(443\) 7.15433 0.339912 0.169956 0.985452i \(-0.445637\pi\)
0.169956 + 0.985452i \(0.445637\pi\)
\(444\) 0 0
\(445\) −15.7469 −0.746474
\(446\) 0 0
\(447\) −37.9183 −1.79347
\(448\) 0 0
\(449\) 17.6625 0.833546 0.416773 0.909011i \(-0.363161\pi\)
0.416773 + 0.909011i \(0.363161\pi\)
\(450\) 0 0
\(451\) −3.46195 −0.163017
\(452\) 0 0
\(453\) 63.4806 2.98258
\(454\) 0 0
\(455\) −6.20319 −0.290810
\(456\) 0 0
\(457\) 33.3504 1.56006 0.780032 0.625740i \(-0.215203\pi\)
0.780032 + 0.625740i \(0.215203\pi\)
\(458\) 0 0
\(459\) 14.8155 0.691529
\(460\) 0 0
\(461\) 29.7900 1.38746 0.693730 0.720236i \(-0.255966\pi\)
0.693730 + 0.720236i \(0.255966\pi\)
\(462\) 0 0
\(463\) −34.1663 −1.58784 −0.793922 0.608020i \(-0.791964\pi\)
−0.793922 + 0.608020i \(0.791964\pi\)
\(464\) 0 0
\(465\) −46.9781 −2.17856
\(466\) 0 0
\(467\) 34.1411 1.57986 0.789931 0.613196i \(-0.210116\pi\)
0.789931 + 0.613196i \(0.210116\pi\)
\(468\) 0 0
\(469\) 0.253937 0.0117257
\(470\) 0 0
\(471\) 20.1148 0.926843
\(472\) 0 0
\(473\) 36.7368 1.68916
\(474\) 0 0
\(475\) −21.1600 −0.970888
\(476\) 0 0
\(477\) −69.6559 −3.18933
\(478\) 0 0
\(479\) −6.59355 −0.301267 −0.150633 0.988590i \(-0.548131\pi\)
−0.150633 + 0.988590i \(0.548131\pi\)
\(480\) 0 0
\(481\) −4.88298 −0.222645
\(482\) 0 0
\(483\) −78.9116 −3.59060
\(484\) 0 0
\(485\) −15.3088 −0.695138
\(486\) 0 0
\(487\) −28.4263 −1.28812 −0.644059 0.764976i \(-0.722751\pi\)
−0.644059 + 0.764976i \(0.722751\pi\)
\(488\) 0 0
\(489\) 7.29473 0.329879
\(490\) 0 0
\(491\) −38.6046 −1.74220 −0.871100 0.491106i \(-0.836593\pi\)
−0.871100 + 0.491106i \(0.836593\pi\)
\(492\) 0 0
\(493\) −3.88250 −0.174859
\(494\) 0 0
\(495\) −84.1129 −3.78059
\(496\) 0 0
\(497\) 26.6971 1.19753
\(498\) 0 0
\(499\) 11.5655 0.517741 0.258870 0.965912i \(-0.416650\pi\)
0.258870 + 0.965912i \(0.416650\pi\)
\(500\) 0 0
\(501\) 39.1492 1.74906
\(502\) 0 0
\(503\) −5.10352 −0.227555 −0.113777 0.993506i \(-0.536295\pi\)
−0.113777 + 0.993506i \(0.536295\pi\)
\(504\) 0 0
\(505\) 1.52736 0.0679666
\(506\) 0 0
\(507\) 41.4785 1.84213
\(508\) 0 0
\(509\) −15.0021 −0.664957 −0.332478 0.943111i \(-0.607885\pi\)
−0.332478 + 0.943111i \(0.607885\pi\)
\(510\) 0 0
\(511\) 47.0533 2.08152
\(512\) 0 0
\(513\) 54.8682 2.42249
\(514\) 0 0
\(515\) 36.1890 1.59468
\(516\) 0 0
\(517\) −38.4016 −1.68890
\(518\) 0 0
\(519\) 8.65679 0.379991
\(520\) 0 0
\(521\) 27.3367 1.19764 0.598820 0.800883i \(-0.295636\pi\)
0.598820 + 0.800883i \(0.295636\pi\)
\(522\) 0 0
\(523\) −11.1570 −0.487863 −0.243932 0.969792i \(-0.578437\pi\)
−0.243932 + 0.969792i \(0.578437\pi\)
\(524\) 0 0
\(525\) −72.5146 −3.16480
\(526\) 0 0
\(527\) 4.41681 0.192399
\(528\) 0 0
\(529\) 15.6594 0.680843
\(530\) 0 0
\(531\) −7.55931 −0.328046
\(532\) 0 0
\(533\) −0.494152 −0.0214041
\(534\) 0 0
\(535\) 30.8394 1.33330
\(536\) 0 0
\(537\) 64.8226 2.79730
\(538\) 0 0
\(539\) 28.0603 1.20864
\(540\) 0 0
\(541\) 17.1623 0.737863 0.368932 0.929457i \(-0.379724\pi\)
0.368932 + 0.929457i \(0.379724\pi\)
\(542\) 0 0
\(543\) 1.95536 0.0839125
\(544\) 0 0
\(545\) 6.93910 0.297238
\(546\) 0 0
\(547\) −41.1503 −1.75946 −0.879730 0.475474i \(-0.842277\pi\)
−0.879730 + 0.475474i \(0.842277\pi\)
\(548\) 0 0
\(549\) −79.0120 −3.37215
\(550\) 0 0
\(551\) −14.3786 −0.612548
\(552\) 0 0
\(553\) −48.8254 −2.07627
\(554\) 0 0
\(555\) −107.034 −4.54332
\(556\) 0 0
\(557\) −15.4273 −0.653674 −0.326837 0.945081i \(-0.605983\pi\)
−0.326837 + 0.945081i \(0.605983\pi\)
\(558\) 0 0
\(559\) 5.24373 0.221786
\(560\) 0 0
\(561\) 11.0466 0.466389
\(562\) 0 0
\(563\) −0.443135 −0.0186759 −0.00933795 0.999956i \(-0.502972\pi\)
−0.00933795 + 0.999956i \(0.502972\pi\)
\(564\) 0 0
\(565\) −20.7461 −0.872794
\(566\) 0 0
\(567\) 99.4587 4.17687
\(568\) 0 0
\(569\) −42.7667 −1.79287 −0.896436 0.443173i \(-0.853853\pi\)
−0.896436 + 0.443173i \(0.853853\pi\)
\(570\) 0 0
\(571\) 18.3309 0.767124 0.383562 0.923515i \(-0.374697\pi\)
0.383562 + 0.923515i \(0.374697\pi\)
\(572\) 0 0
\(573\) 23.4368 0.979086
\(574\) 0 0
\(575\) 35.5254 1.48151
\(576\) 0 0
\(577\) −24.7504 −1.03037 −0.515186 0.857078i \(-0.672277\pi\)
−0.515186 + 0.857078i \(0.672277\pi\)
\(578\) 0 0
\(579\) −30.6792 −1.27499
\(580\) 0 0
\(581\) −1.92793 −0.0799840
\(582\) 0 0
\(583\) −31.3248 −1.29734
\(584\) 0 0
\(585\) −12.0061 −0.496390
\(586\) 0 0
\(587\) −25.2350 −1.04156 −0.520781 0.853691i \(-0.674359\pi\)
−0.520781 + 0.853691i \(0.674359\pi\)
\(588\) 0 0
\(589\) 16.3574 0.673993
\(590\) 0 0
\(591\) −67.5642 −2.77922
\(592\) 0 0
\(593\) 19.9986 0.821245 0.410622 0.911806i \(-0.365311\pi\)
0.410622 + 0.911806i \(0.365311\pi\)
\(594\) 0 0
\(595\) 12.7839 0.524090
\(596\) 0 0
\(597\) 10.7582 0.440302
\(598\) 0 0
\(599\) 34.3922 1.40523 0.702615 0.711571i \(-0.252016\pi\)
0.702615 + 0.711571i \(0.252016\pi\)
\(600\) 0 0
\(601\) −9.24784 −0.377227 −0.188614 0.982051i \(-0.560399\pi\)
−0.188614 + 0.982051i \(0.560399\pi\)
\(602\) 0 0
\(603\) 0.491486 0.0200149
\(604\) 0 0
\(605\) −1.82135 −0.0740483
\(606\) 0 0
\(607\) 17.4645 0.708861 0.354430 0.935082i \(-0.384675\pi\)
0.354430 + 0.935082i \(0.384675\pi\)
\(608\) 0 0
\(609\) −49.2749 −1.99672
\(610\) 0 0
\(611\) −5.48136 −0.221752
\(612\) 0 0
\(613\) −14.0627 −0.567986 −0.283993 0.958826i \(-0.591659\pi\)
−0.283993 + 0.958826i \(0.591659\pi\)
\(614\) 0 0
\(615\) −10.8317 −0.436775
\(616\) 0 0
\(617\) 13.9872 0.563103 0.281551 0.959546i \(-0.409151\pi\)
0.281551 + 0.959546i \(0.409151\pi\)
\(618\) 0 0
\(619\) 31.2197 1.25483 0.627413 0.778686i \(-0.284114\pi\)
0.627413 + 0.778686i \(0.284114\pi\)
\(620\) 0 0
\(621\) −92.1179 −3.69656
\(622\) 0 0
\(623\) 18.7898 0.752798
\(624\) 0 0
\(625\) −20.9226 −0.836904
\(626\) 0 0
\(627\) 40.9104 1.63381
\(628\) 0 0
\(629\) 10.0631 0.401244
\(630\) 0 0
\(631\) −21.7763 −0.866899 −0.433450 0.901178i \(-0.642704\pi\)
−0.433450 + 0.901178i \(0.642704\pi\)
\(632\) 0 0
\(633\) 20.8603 0.829124
\(634\) 0 0
\(635\) −32.5832 −1.29302
\(636\) 0 0
\(637\) 4.00526 0.158694
\(638\) 0 0
\(639\) 51.6713 2.04408
\(640\) 0 0
\(641\) 27.9602 1.10436 0.552181 0.833725i \(-0.313796\pi\)
0.552181 + 0.833725i \(0.313796\pi\)
\(642\) 0 0
\(643\) −24.2376 −0.955838 −0.477919 0.878404i \(-0.658609\pi\)
−0.477919 + 0.878404i \(0.658609\pi\)
\(644\) 0 0
\(645\) 114.941 4.52580
\(646\) 0 0
\(647\) −20.8486 −0.819643 −0.409822 0.912166i \(-0.634409\pi\)
−0.409822 + 0.912166i \(0.634409\pi\)
\(648\) 0 0
\(649\) −3.39948 −0.133441
\(650\) 0 0
\(651\) 56.0561 2.19701
\(652\) 0 0
\(653\) 10.0708 0.394101 0.197050 0.980393i \(-0.436864\pi\)
0.197050 + 0.980393i \(0.436864\pi\)
\(654\) 0 0
\(655\) −42.0387 −1.64259
\(656\) 0 0
\(657\) 91.0702 3.55299
\(658\) 0 0
\(659\) −40.3746 −1.57277 −0.786386 0.617735i \(-0.788050\pi\)
−0.786386 + 0.617735i \(0.788050\pi\)
\(660\) 0 0
\(661\) −16.2897 −0.633594 −0.316797 0.948493i \(-0.602607\pi\)
−0.316797 + 0.948493i \(0.602607\pi\)
\(662\) 0 0
\(663\) 1.57677 0.0612367
\(664\) 0 0
\(665\) 47.3444 1.83594
\(666\) 0 0
\(667\) 24.1401 0.934709
\(668\) 0 0
\(669\) −54.6488 −2.11284
\(670\) 0 0
\(671\) −35.5323 −1.37171
\(672\) 0 0
\(673\) −16.4101 −0.632564 −0.316282 0.948665i \(-0.602435\pi\)
−0.316282 + 0.948665i \(0.602435\pi\)
\(674\) 0 0
\(675\) −84.6503 −3.25819
\(676\) 0 0
\(677\) 34.1140 1.31111 0.655554 0.755148i \(-0.272435\pi\)
0.655554 + 0.755148i \(0.272435\pi\)
\(678\) 0 0
\(679\) 18.2671 0.701027
\(680\) 0 0
\(681\) 38.6797 1.48221
\(682\) 0 0
\(683\) 20.3349 0.778095 0.389048 0.921218i \(-0.372804\pi\)
0.389048 + 0.921218i \(0.372804\pi\)
\(684\) 0 0
\(685\) −54.2172 −2.07153
\(686\) 0 0
\(687\) −46.9193 −1.79008
\(688\) 0 0
\(689\) −4.47123 −0.170340
\(690\) 0 0
\(691\) −6.31432 −0.240208 −0.120104 0.992761i \(-0.538323\pi\)
−0.120104 + 0.992761i \(0.538323\pi\)
\(692\) 0 0
\(693\) 100.367 3.81262
\(694\) 0 0
\(695\) −38.1514 −1.44716
\(696\) 0 0
\(697\) 1.01838 0.0385738
\(698\) 0 0
\(699\) 89.1045 3.37024
\(700\) 0 0
\(701\) −5.90253 −0.222936 −0.111468 0.993768i \(-0.535555\pi\)
−0.111468 + 0.993768i \(0.535555\pi\)
\(702\) 0 0
\(703\) 37.2682 1.40560
\(704\) 0 0
\(705\) −120.150 −4.52510
\(706\) 0 0
\(707\) −1.82251 −0.0685424
\(708\) 0 0
\(709\) 7.40979 0.278281 0.139140 0.990273i \(-0.455566\pi\)
0.139140 + 0.990273i \(0.455566\pi\)
\(710\) 0 0
\(711\) −94.5001 −3.54403
\(712\) 0 0
\(713\) −27.4623 −1.02847
\(714\) 0 0
\(715\) −5.39923 −0.201920
\(716\) 0 0
\(717\) 39.3834 1.47080
\(718\) 0 0
\(719\) −6.39091 −0.238341 −0.119170 0.992874i \(-0.538023\pi\)
−0.119170 + 0.992874i \(0.538023\pi\)
\(720\) 0 0
\(721\) −43.1821 −1.60819
\(722\) 0 0
\(723\) 76.0429 2.82807
\(724\) 0 0
\(725\) 22.1832 0.823863
\(726\) 0 0
\(727\) 51.9050 1.92505 0.962524 0.271196i \(-0.0874190\pi\)
0.962524 + 0.271196i \(0.0874190\pi\)
\(728\) 0 0
\(729\) 48.0699 1.78037
\(730\) 0 0
\(731\) −10.8066 −0.399697
\(732\) 0 0
\(733\) 42.8155 1.58143 0.790713 0.612187i \(-0.209710\pi\)
0.790713 + 0.612187i \(0.209710\pi\)
\(734\) 0 0
\(735\) 87.7941 3.23833
\(736\) 0 0
\(737\) 0.221025 0.00814156
\(738\) 0 0
\(739\) 30.8483 1.13477 0.567387 0.823451i \(-0.307954\pi\)
0.567387 + 0.823451i \(0.307954\pi\)
\(740\) 0 0
\(741\) 5.83946 0.214518
\(742\) 0 0
\(743\) −12.9551 −0.475277 −0.237638 0.971354i \(-0.576373\pi\)
−0.237638 + 0.971354i \(0.576373\pi\)
\(744\) 0 0
\(745\) −38.1944 −1.39933
\(746\) 0 0
\(747\) −3.73145 −0.136527
\(748\) 0 0
\(749\) −36.7988 −1.34460
\(750\) 0 0
\(751\) −0.866086 −0.0316039 −0.0158020 0.999875i \(-0.505030\pi\)
−0.0158020 + 0.999875i \(0.505030\pi\)
\(752\) 0 0
\(753\) 69.3408 2.52692
\(754\) 0 0
\(755\) 63.9428 2.32712
\(756\) 0 0
\(757\) 27.0762 0.984103 0.492051 0.870566i \(-0.336247\pi\)
0.492051 + 0.870566i \(0.336247\pi\)
\(758\) 0 0
\(759\) −68.6843 −2.49308
\(760\) 0 0
\(761\) −9.88322 −0.358266 −0.179133 0.983825i \(-0.557329\pi\)
−0.179133 + 0.983825i \(0.557329\pi\)
\(762\) 0 0
\(763\) −8.28001 −0.299756
\(764\) 0 0
\(765\) 24.7429 0.894581
\(766\) 0 0
\(767\) −0.485234 −0.0175208
\(768\) 0 0
\(769\) −40.2120 −1.45008 −0.725040 0.688706i \(-0.758179\pi\)
−0.725040 + 0.688706i \(0.758179\pi\)
\(770\) 0 0
\(771\) −73.5051 −2.64722
\(772\) 0 0
\(773\) 20.2285 0.727568 0.363784 0.931483i \(-0.381485\pi\)
0.363784 + 0.931483i \(0.381485\pi\)
\(774\) 0 0
\(775\) −25.2360 −0.906505
\(776\) 0 0
\(777\) 127.717 4.58181
\(778\) 0 0
\(779\) 3.77149 0.135128
\(780\) 0 0
\(781\) 23.2370 0.831484
\(782\) 0 0
\(783\) −57.5213 −2.05564
\(784\) 0 0
\(785\) 20.2613 0.723156
\(786\) 0 0
\(787\) 10.1726 0.362615 0.181307 0.983426i \(-0.441967\pi\)
0.181307 + 0.983426i \(0.441967\pi\)
\(788\) 0 0
\(789\) 26.1890 0.932353
\(790\) 0 0
\(791\) 24.7550 0.880188
\(792\) 0 0
\(793\) −5.07180 −0.180105
\(794\) 0 0
\(795\) −98.0081 −3.47599
\(796\) 0 0
\(797\) 36.5236 1.29373 0.646866 0.762603i \(-0.276079\pi\)
0.646866 + 0.762603i \(0.276079\pi\)
\(798\) 0 0
\(799\) 11.2963 0.399635
\(800\) 0 0
\(801\) 36.3671 1.28497
\(802\) 0 0
\(803\) 40.9549 1.44527
\(804\) 0 0
\(805\) −79.4862 −2.80152
\(806\) 0 0
\(807\) −84.2414 −2.96544
\(808\) 0 0
\(809\) −20.0498 −0.704912 −0.352456 0.935828i \(-0.614653\pi\)
−0.352456 + 0.935828i \(0.614653\pi\)
\(810\) 0 0
\(811\) −8.67887 −0.304756 −0.152378 0.988322i \(-0.548693\pi\)
−0.152378 + 0.988322i \(0.548693\pi\)
\(812\) 0 0
\(813\) −21.7613 −0.763204
\(814\) 0 0
\(815\) 7.34784 0.257384
\(816\) 0 0
\(817\) −40.0215 −1.40018
\(818\) 0 0
\(819\) 14.3261 0.500596
\(820\) 0 0
\(821\) 11.5975 0.404755 0.202378 0.979308i \(-0.435133\pi\)
0.202378 + 0.979308i \(0.435133\pi\)
\(822\) 0 0
\(823\) −41.3897 −1.44275 −0.721377 0.692543i \(-0.756490\pi\)
−0.721377 + 0.692543i \(0.756490\pi\)
\(824\) 0 0
\(825\) −63.1163 −2.19743
\(826\) 0 0
\(827\) 19.1665 0.666484 0.333242 0.942841i \(-0.391857\pi\)
0.333242 + 0.942841i \(0.391857\pi\)
\(828\) 0 0
\(829\) −14.0287 −0.487238 −0.243619 0.969871i \(-0.578335\pi\)
−0.243619 + 0.969871i \(0.578335\pi\)
\(830\) 0 0
\(831\) −14.2913 −0.495761
\(832\) 0 0
\(833\) −8.25428 −0.285994
\(834\) 0 0
\(835\) 39.4343 1.36468
\(836\) 0 0
\(837\) 65.4373 2.26185
\(838\) 0 0
\(839\) 12.1966 0.421072 0.210536 0.977586i \(-0.432479\pi\)
0.210536 + 0.977586i \(0.432479\pi\)
\(840\) 0 0
\(841\) −13.9262 −0.480212
\(842\) 0 0
\(843\) −39.4849 −1.35993
\(844\) 0 0
\(845\) 41.7805 1.43729
\(846\) 0 0
\(847\) 2.17330 0.0746756
\(848\) 0 0
\(849\) 16.8658 0.578833
\(850\) 0 0
\(851\) −62.5693 −2.14485
\(852\) 0 0
\(853\) −34.2167 −1.17156 −0.585779 0.810471i \(-0.699211\pi\)
−0.585779 + 0.810471i \(0.699211\pi\)
\(854\) 0 0
\(855\) 91.6335 3.13380
\(856\) 0 0
\(857\) 32.4959 1.11004 0.555019 0.831838i \(-0.312711\pi\)
0.555019 + 0.831838i \(0.312711\pi\)
\(858\) 0 0
\(859\) −12.1451 −0.414387 −0.207194 0.978300i \(-0.566433\pi\)
−0.207194 + 0.978300i \(0.566433\pi\)
\(860\) 0 0
\(861\) 12.9248 0.440475
\(862\) 0 0
\(863\) −0.775147 −0.0263863 −0.0131931 0.999913i \(-0.504200\pi\)
−0.0131931 + 0.999913i \(0.504200\pi\)
\(864\) 0 0
\(865\) 8.71982 0.296483
\(866\) 0 0
\(867\) −3.24951 −0.110359
\(868\) 0 0
\(869\) −42.4974 −1.44163
\(870\) 0 0
\(871\) 0.0315486 0.00106898
\(872\) 0 0
\(873\) 35.3554 1.19660
\(874\) 0 0
\(875\) −9.12295 −0.308412
\(876\) 0 0
\(877\) −32.2510 −1.08904 −0.544520 0.838748i \(-0.683288\pi\)
−0.544520 + 0.838748i \(0.683288\pi\)
\(878\) 0 0
\(879\) 68.0598 2.29560
\(880\) 0 0
\(881\) 13.4840 0.454287 0.227143 0.973861i \(-0.427061\pi\)
0.227143 + 0.973861i \(0.427061\pi\)
\(882\) 0 0
\(883\) 31.3597 1.05534 0.527669 0.849450i \(-0.323066\pi\)
0.527669 + 0.849450i \(0.323066\pi\)
\(884\) 0 0
\(885\) −10.6362 −0.357532
\(886\) 0 0
\(887\) −19.4434 −0.652846 −0.326423 0.945224i \(-0.605843\pi\)
−0.326423 + 0.945224i \(0.605843\pi\)
\(888\) 0 0
\(889\) 38.8795 1.30398
\(890\) 0 0
\(891\) 86.5684 2.90015
\(892\) 0 0
\(893\) 41.8351 1.39996
\(894\) 0 0
\(895\) 65.2945 2.18256
\(896\) 0 0
\(897\) −9.80384 −0.327341
\(898\) 0 0
\(899\) −17.1483 −0.571928
\(900\) 0 0
\(901\) 9.21459 0.306983
\(902\) 0 0
\(903\) −137.152 −4.56414
\(904\) 0 0
\(905\) 1.96960 0.0654716
\(906\) 0 0
\(907\) −32.8247 −1.08993 −0.544963 0.838460i \(-0.683456\pi\)
−0.544963 + 0.838460i \(0.683456\pi\)
\(908\) 0 0
\(909\) −3.52740 −0.116997
\(910\) 0 0
\(911\) 50.5267 1.67402 0.837012 0.547184i \(-0.184300\pi\)
0.837012 + 0.547184i \(0.184300\pi\)
\(912\) 0 0
\(913\) −1.67806 −0.0555357
\(914\) 0 0
\(915\) −111.172 −3.67525
\(916\) 0 0
\(917\) 50.1623 1.65651
\(918\) 0 0
\(919\) −25.2507 −0.832944 −0.416472 0.909148i \(-0.636734\pi\)
−0.416472 + 0.909148i \(0.636734\pi\)
\(920\) 0 0
\(921\) 38.6987 1.27517
\(922\) 0 0
\(923\) 3.31679 0.109174
\(924\) 0 0
\(925\) −57.4971 −1.89049
\(926\) 0 0
\(927\) −83.5777 −2.74505
\(928\) 0 0
\(929\) 17.0317 0.558793 0.279396 0.960176i \(-0.409866\pi\)
0.279396 + 0.960176i \(0.409866\pi\)
\(930\) 0 0
\(931\) −30.5692 −1.00186
\(932\) 0 0
\(933\) −66.8384 −2.18819
\(934\) 0 0
\(935\) 11.1271 0.363894
\(936\) 0 0
\(937\) −22.4932 −0.734822 −0.367411 0.930059i \(-0.619756\pi\)
−0.367411 + 0.930059i \(0.619756\pi\)
\(938\) 0 0
\(939\) 39.0377 1.27395
\(940\) 0 0
\(941\) 2.17649 0.0709516 0.0354758 0.999371i \(-0.488705\pi\)
0.0354758 + 0.999371i \(0.488705\pi\)
\(942\) 0 0
\(943\) −6.33194 −0.206196
\(944\) 0 0
\(945\) 189.400 6.16119
\(946\) 0 0
\(947\) 8.36870 0.271946 0.135973 0.990713i \(-0.456584\pi\)
0.135973 + 0.990713i \(0.456584\pi\)
\(948\) 0 0
\(949\) 5.84582 0.189763
\(950\) 0 0
\(951\) −9.79352 −0.317577
\(952\) 0 0
\(953\) 33.0999 1.07221 0.536105 0.844151i \(-0.319895\pi\)
0.536105 + 0.844151i \(0.319895\pi\)
\(954\) 0 0
\(955\) 23.6074 0.763918
\(956\) 0 0
\(957\) −42.8886 −1.38639
\(958\) 0 0
\(959\) 64.6941 2.08908
\(960\) 0 0
\(961\) −11.4917 −0.370702
\(962\) 0 0
\(963\) −71.2229 −2.29513
\(964\) 0 0
\(965\) −30.9026 −0.994790
\(966\) 0 0
\(967\) −60.9480 −1.95996 −0.979979 0.199103i \(-0.936197\pi\)
−0.979979 + 0.199103i \(0.936197\pi\)
\(968\) 0 0
\(969\) −12.0343 −0.386598
\(970\) 0 0
\(971\) 18.2388 0.585311 0.292656 0.956218i \(-0.405461\pi\)
0.292656 + 0.956218i \(0.405461\pi\)
\(972\) 0 0
\(973\) 45.5238 1.45942
\(974\) 0 0
\(975\) −9.00908 −0.288522
\(976\) 0 0
\(977\) 19.5927 0.626828 0.313414 0.949617i \(-0.398527\pi\)
0.313414 + 0.949617i \(0.398527\pi\)
\(978\) 0 0
\(979\) 16.3545 0.522694
\(980\) 0 0
\(981\) −16.0257 −0.511661
\(982\) 0 0
\(983\) −44.1384 −1.40780 −0.703898 0.710301i \(-0.748559\pi\)
−0.703898 + 0.710301i \(0.748559\pi\)
\(984\) 0 0
\(985\) −68.0561 −2.16845
\(986\) 0 0
\(987\) 143.367 4.56344
\(988\) 0 0
\(989\) 67.1919 2.13658
\(990\) 0 0
\(991\) −34.0662 −1.08215 −0.541074 0.840975i \(-0.681982\pi\)
−0.541074 + 0.840975i \(0.681982\pi\)
\(992\) 0 0
\(993\) 81.3219 2.58067
\(994\) 0 0
\(995\) 10.8365 0.343540
\(996\) 0 0
\(997\) 28.3098 0.896579 0.448289 0.893888i \(-0.352033\pi\)
0.448289 + 0.893888i \(0.352033\pi\)
\(998\) 0 0
\(999\) 149.091 4.71702
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 \(a_p\))