Properties

Label 6040.2.a.p.1.3
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.89238\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.89238 q^{3}\) \(+1.00000 q^{5}\) \(+0.451178 q^{7}\) \(+5.36583 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.89238 q^{3}\) \(+1.00000 q^{5}\) \(+0.451178 q^{7}\) \(+5.36583 q^{9}\) \(-4.25329 q^{11}\) \(-4.52874 q^{13}\) \(-2.89238 q^{15}\) \(+2.97411 q^{17}\) \(-0.416600 q^{19}\) \(-1.30498 q^{21}\) \(+4.36636 q^{23}\) \(+1.00000 q^{25}\) \(-6.84288 q^{27}\) \(-1.71423 q^{29}\) \(+0.519238 q^{31}\) \(+12.3021 q^{33}\) \(+0.451178 q^{35}\) \(+5.90793 q^{37}\) \(+13.0988 q^{39}\) \(+7.30082 q^{41}\) \(+6.72872 q^{43}\) \(+5.36583 q^{45}\) \(-7.34363 q^{47}\) \(-6.79644 q^{49}\) \(-8.60224 q^{51}\) \(-8.53509 q^{53}\) \(-4.25329 q^{55}\) \(+1.20496 q^{57}\) \(-13.9094 q^{59}\) \(+12.3159 q^{61}\) \(+2.42095 q^{63}\) \(-4.52874 q^{65}\) \(-3.77950 q^{67}\) \(-12.6292 q^{69}\) \(+9.96010 q^{71}\) \(+13.1976 q^{73}\) \(-2.89238 q^{75}\) \(-1.91899 q^{77}\) \(-17.1764 q^{79}\) \(+3.69468 q^{81}\) \(-12.9481 q^{83}\) \(+2.97411 q^{85}\) \(+4.95821 q^{87}\) \(-2.27054 q^{89}\) \(-2.04327 q^{91}\) \(-1.50183 q^{93}\) \(-0.416600 q^{95}\) \(+14.6215 q^{97}\) \(-22.8225 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.89238 −1.66991 −0.834957 0.550315i \(-0.814507\pi\)
−0.834957 + 0.550315i \(0.814507\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 0.451178 0.170529 0.0852646 0.996358i \(-0.472826\pi\)
0.0852646 + 0.996358i \(0.472826\pi\)
\(8\) 0 0
\(9\) 5.36583 1.78861
\(10\) 0 0
\(11\) −4.25329 −1.28242 −0.641208 0.767367i \(-0.721566\pi\)
−0.641208 + 0.767367i \(0.721566\pi\)
\(12\) 0 0
\(13\) −4.52874 −1.25605 −0.628023 0.778195i \(-0.716136\pi\)
−0.628023 + 0.778195i \(0.716136\pi\)
\(14\) 0 0
\(15\) −2.89238 −0.746808
\(16\) 0 0
\(17\) 2.97411 0.721328 0.360664 0.932696i \(-0.382550\pi\)
0.360664 + 0.932696i \(0.382550\pi\)
\(18\) 0 0
\(19\) −0.416600 −0.0955747 −0.0477873 0.998858i \(-0.515217\pi\)
−0.0477873 + 0.998858i \(0.515217\pi\)
\(20\) 0 0
\(21\) −1.30498 −0.284769
\(22\) 0 0
\(23\) 4.36636 0.910449 0.455225 0.890377i \(-0.349559\pi\)
0.455225 + 0.890377i \(0.349559\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −6.84288 −1.31691
\(28\) 0 0
\(29\) −1.71423 −0.318325 −0.159163 0.987252i \(-0.550879\pi\)
−0.159163 + 0.987252i \(0.550879\pi\)
\(30\) 0 0
\(31\) 0.519238 0.0932580 0.0466290 0.998912i \(-0.485152\pi\)
0.0466290 + 0.998912i \(0.485152\pi\)
\(32\) 0 0
\(33\) 12.3021 2.14152
\(34\) 0 0
\(35\) 0.451178 0.0762630
\(36\) 0 0
\(37\) 5.90793 0.971257 0.485629 0.874165i \(-0.338591\pi\)
0.485629 + 0.874165i \(0.338591\pi\)
\(38\) 0 0
\(39\) 13.0988 2.09749
\(40\) 0 0
\(41\) 7.30082 1.14020 0.570098 0.821577i \(-0.306905\pi\)
0.570098 + 0.821577i \(0.306905\pi\)
\(42\) 0 0
\(43\) 6.72872 1.02612 0.513060 0.858353i \(-0.328512\pi\)
0.513060 + 0.858353i \(0.328512\pi\)
\(44\) 0 0
\(45\) 5.36583 0.799891
\(46\) 0 0
\(47\) −7.34363 −1.07118 −0.535589 0.844479i \(-0.679910\pi\)
−0.535589 + 0.844479i \(0.679910\pi\)
\(48\) 0 0
\(49\) −6.79644 −0.970920
\(50\) 0 0
\(51\) −8.60224 −1.20455
\(52\) 0 0
\(53\) −8.53509 −1.17238 −0.586192 0.810172i \(-0.699374\pi\)
−0.586192 + 0.810172i \(0.699374\pi\)
\(54\) 0 0
\(55\) −4.25329 −0.573513
\(56\) 0 0
\(57\) 1.20496 0.159601
\(58\) 0 0
\(59\) −13.9094 −1.81085 −0.905427 0.424503i \(-0.860449\pi\)
−0.905427 + 0.424503i \(0.860449\pi\)
\(60\) 0 0
\(61\) 12.3159 1.57688 0.788442 0.615109i \(-0.210888\pi\)
0.788442 + 0.615109i \(0.210888\pi\)
\(62\) 0 0
\(63\) 2.42095 0.305011
\(64\) 0 0
\(65\) −4.52874 −0.561721
\(66\) 0 0
\(67\) −3.77950 −0.461739 −0.230869 0.972985i \(-0.574157\pi\)
−0.230869 + 0.972985i \(0.574157\pi\)
\(68\) 0 0
\(69\) −12.6292 −1.52037
\(70\) 0 0
\(71\) 9.96010 1.18205 0.591023 0.806654i \(-0.298724\pi\)
0.591023 + 0.806654i \(0.298724\pi\)
\(72\) 0 0
\(73\) 13.1976 1.54467 0.772333 0.635218i \(-0.219090\pi\)
0.772333 + 0.635218i \(0.219090\pi\)
\(74\) 0 0
\(75\) −2.89238 −0.333983
\(76\) 0 0
\(77\) −1.91899 −0.218689
\(78\) 0 0
\(79\) −17.1764 −1.93250 −0.966248 0.257612i \(-0.917064\pi\)
−0.966248 + 0.257612i \(0.917064\pi\)
\(80\) 0 0
\(81\) 3.69468 0.410520
\(82\) 0 0
\(83\) −12.9481 −1.42123 −0.710617 0.703579i \(-0.751584\pi\)
−0.710617 + 0.703579i \(0.751584\pi\)
\(84\) 0 0
\(85\) 2.97411 0.322588
\(86\) 0 0
\(87\) 4.95821 0.531575
\(88\) 0 0
\(89\) −2.27054 −0.240676 −0.120338 0.992733i \(-0.538398\pi\)
−0.120338 + 0.992733i \(0.538398\pi\)
\(90\) 0 0
\(91\) −2.04327 −0.214193
\(92\) 0 0
\(93\) −1.50183 −0.155733
\(94\) 0 0
\(95\) −0.416600 −0.0427423
\(96\) 0 0
\(97\) 14.6215 1.48459 0.742295 0.670073i \(-0.233737\pi\)
0.742295 + 0.670073i \(0.233737\pi\)
\(98\) 0 0
\(99\) −22.8225 −2.29374
\(100\) 0 0
\(101\) 8.49145 0.844931 0.422465 0.906379i \(-0.361165\pi\)
0.422465 + 0.906379i \(0.361165\pi\)
\(102\) 0 0
\(103\) −1.32253 −0.130313 −0.0651565 0.997875i \(-0.520755\pi\)
−0.0651565 + 0.997875i \(0.520755\pi\)
\(104\) 0 0
\(105\) −1.30498 −0.127353
\(106\) 0 0
\(107\) 8.30393 0.802771 0.401386 0.915909i \(-0.368529\pi\)
0.401386 + 0.915909i \(0.368529\pi\)
\(108\) 0 0
\(109\) −8.11894 −0.777654 −0.388827 0.921311i \(-0.627120\pi\)
−0.388827 + 0.921311i \(0.627120\pi\)
\(110\) 0 0
\(111\) −17.0879 −1.62192
\(112\) 0 0
\(113\) 5.99555 0.564014 0.282007 0.959412i \(-0.409000\pi\)
0.282007 + 0.959412i \(0.409000\pi\)
\(114\) 0 0
\(115\) 4.36636 0.407165
\(116\) 0 0
\(117\) −24.3005 −2.24658
\(118\) 0 0
\(119\) 1.34185 0.123007
\(120\) 0 0
\(121\) 7.09047 0.644588
\(122\) 0 0
\(123\) −21.1167 −1.90403
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 3.64749 0.323662 0.161831 0.986818i \(-0.448260\pi\)
0.161831 + 0.986818i \(0.448260\pi\)
\(128\) 0 0
\(129\) −19.4620 −1.71353
\(130\) 0 0
\(131\) 7.37463 0.644324 0.322162 0.946684i \(-0.395590\pi\)
0.322162 + 0.946684i \(0.395590\pi\)
\(132\) 0 0
\(133\) −0.187961 −0.0162983
\(134\) 0 0
\(135\) −6.84288 −0.588942
\(136\) 0 0
\(137\) 22.7441 1.94316 0.971579 0.236714i \(-0.0760706\pi\)
0.971579 + 0.236714i \(0.0760706\pi\)
\(138\) 0 0
\(139\) 14.9027 1.26403 0.632014 0.774957i \(-0.282229\pi\)
0.632014 + 0.774957i \(0.282229\pi\)
\(140\) 0 0
\(141\) 21.2405 1.78878
\(142\) 0 0
\(143\) 19.2620 1.61077
\(144\) 0 0
\(145\) −1.71423 −0.142359
\(146\) 0 0
\(147\) 19.6579 1.62135
\(148\) 0 0
\(149\) 1.10295 0.0903569 0.0451785 0.998979i \(-0.485614\pi\)
0.0451785 + 0.998979i \(0.485614\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) 15.9586 1.29018
\(154\) 0 0
\(155\) 0.519238 0.0417062
\(156\) 0 0
\(157\) −9.71155 −0.775066 −0.387533 0.921856i \(-0.626673\pi\)
−0.387533 + 0.921856i \(0.626673\pi\)
\(158\) 0 0
\(159\) 24.6867 1.95778
\(160\) 0 0
\(161\) 1.97001 0.155258
\(162\) 0 0
\(163\) −9.78801 −0.766656 −0.383328 0.923612i \(-0.625222\pi\)
−0.383328 + 0.923612i \(0.625222\pi\)
\(164\) 0 0
\(165\) 12.3021 0.957718
\(166\) 0 0
\(167\) 4.81946 0.372941 0.186471 0.982461i \(-0.440295\pi\)
0.186471 + 0.982461i \(0.440295\pi\)
\(168\) 0 0
\(169\) 7.50945 0.577650
\(170\) 0 0
\(171\) −2.23541 −0.170946
\(172\) 0 0
\(173\) 19.0278 1.44666 0.723329 0.690503i \(-0.242611\pi\)
0.723329 + 0.690503i \(0.242611\pi\)
\(174\) 0 0
\(175\) 0.451178 0.0341059
\(176\) 0 0
\(177\) 40.2313 3.02397
\(178\) 0 0
\(179\) −13.0012 −0.971756 −0.485878 0.874027i \(-0.661500\pi\)
−0.485878 + 0.874027i \(0.661500\pi\)
\(180\) 0 0
\(181\) −20.5584 −1.52809 −0.764045 0.645163i \(-0.776790\pi\)
−0.764045 + 0.645163i \(0.776790\pi\)
\(182\) 0 0
\(183\) −35.6221 −2.63326
\(184\) 0 0
\(185\) 5.90793 0.434359
\(186\) 0 0
\(187\) −12.6498 −0.925041
\(188\) 0 0
\(189\) −3.08736 −0.224572
\(190\) 0 0
\(191\) −18.9544 −1.37149 −0.685747 0.727840i \(-0.740524\pi\)
−0.685747 + 0.727840i \(0.740524\pi\)
\(192\) 0 0
\(193\) −27.7140 −1.99490 −0.997449 0.0713838i \(-0.977258\pi\)
−0.997449 + 0.0713838i \(0.977258\pi\)
\(194\) 0 0
\(195\) 13.0988 0.938025
\(196\) 0 0
\(197\) 7.09673 0.505621 0.252810 0.967516i \(-0.418645\pi\)
0.252810 + 0.967516i \(0.418645\pi\)
\(198\) 0 0
\(199\) −22.7907 −1.61559 −0.807794 0.589465i \(-0.799338\pi\)
−0.807794 + 0.589465i \(0.799338\pi\)
\(200\) 0 0
\(201\) 10.9317 0.771064
\(202\) 0 0
\(203\) −0.773424 −0.0542838
\(204\) 0 0
\(205\) 7.30082 0.509911
\(206\) 0 0
\(207\) 23.4292 1.62844
\(208\) 0 0
\(209\) 1.77192 0.122566
\(210\) 0 0
\(211\) 17.0733 1.17537 0.587687 0.809089i \(-0.300039\pi\)
0.587687 + 0.809089i \(0.300039\pi\)
\(212\) 0 0
\(213\) −28.8084 −1.97392
\(214\) 0 0
\(215\) 6.72872 0.458895
\(216\) 0 0
\(217\) 0.234269 0.0159032
\(218\) 0 0
\(219\) −38.1725 −2.57946
\(220\) 0 0
\(221\) −13.4690 −0.906020
\(222\) 0 0
\(223\) −1.97058 −0.131960 −0.0659800 0.997821i \(-0.521017\pi\)
−0.0659800 + 0.997821i \(0.521017\pi\)
\(224\) 0 0
\(225\) 5.36583 0.357722
\(226\) 0 0
\(227\) −20.8242 −1.38215 −0.691074 0.722784i \(-0.742862\pi\)
−0.691074 + 0.722784i \(0.742862\pi\)
\(228\) 0 0
\(229\) −11.3583 −0.750580 −0.375290 0.926908i \(-0.622457\pi\)
−0.375290 + 0.926908i \(0.622457\pi\)
\(230\) 0 0
\(231\) 5.55044 0.365192
\(232\) 0 0
\(233\) −5.39183 −0.353231 −0.176615 0.984280i \(-0.556515\pi\)
−0.176615 + 0.984280i \(0.556515\pi\)
\(234\) 0 0
\(235\) −7.34363 −0.479046
\(236\) 0 0
\(237\) 49.6806 3.22710
\(238\) 0 0
\(239\) −2.49168 −0.161173 −0.0805865 0.996748i \(-0.525679\pi\)
−0.0805865 + 0.996748i \(0.525679\pi\)
\(240\) 0 0
\(241\) −26.3996 −1.70055 −0.850275 0.526339i \(-0.823564\pi\)
−0.850275 + 0.526339i \(0.823564\pi\)
\(242\) 0 0
\(243\) 9.84225 0.631380
\(244\) 0 0
\(245\) −6.79644 −0.434209
\(246\) 0 0
\(247\) 1.88667 0.120046
\(248\) 0 0
\(249\) 37.4506 2.37334
\(250\) 0 0
\(251\) −4.13027 −0.260700 −0.130350 0.991468i \(-0.541610\pi\)
−0.130350 + 0.991468i \(0.541610\pi\)
\(252\) 0 0
\(253\) −18.5714 −1.16757
\(254\) 0 0
\(255\) −8.60224 −0.538693
\(256\) 0 0
\(257\) −9.57443 −0.597237 −0.298618 0.954373i \(-0.596526\pi\)
−0.298618 + 0.954373i \(0.596526\pi\)
\(258\) 0 0
\(259\) 2.66553 0.165628
\(260\) 0 0
\(261\) −9.19829 −0.569360
\(262\) 0 0
\(263\) 1.21730 0.0750620 0.0375310 0.999295i \(-0.488051\pi\)
0.0375310 + 0.999295i \(0.488051\pi\)
\(264\) 0 0
\(265\) −8.53509 −0.524307
\(266\) 0 0
\(267\) 6.56724 0.401909
\(268\) 0 0
\(269\) −29.3682 −1.79061 −0.895304 0.445456i \(-0.853042\pi\)
−0.895304 + 0.445456i \(0.853042\pi\)
\(270\) 0 0
\(271\) 20.6624 1.25515 0.627577 0.778554i \(-0.284047\pi\)
0.627577 + 0.778554i \(0.284047\pi\)
\(272\) 0 0
\(273\) 5.90989 0.357683
\(274\) 0 0
\(275\) −4.25329 −0.256483
\(276\) 0 0
\(277\) −23.5077 −1.41244 −0.706221 0.707992i \(-0.749601\pi\)
−0.706221 + 0.707992i \(0.749601\pi\)
\(278\) 0 0
\(279\) 2.78615 0.166802
\(280\) 0 0
\(281\) −26.8257 −1.60028 −0.800142 0.599810i \(-0.795243\pi\)
−0.800142 + 0.599810i \(0.795243\pi\)
\(282\) 0 0
\(283\) 25.2537 1.50118 0.750589 0.660769i \(-0.229770\pi\)
0.750589 + 0.660769i \(0.229770\pi\)
\(284\) 0 0
\(285\) 1.20496 0.0713759
\(286\) 0 0
\(287\) 3.29397 0.194437
\(288\) 0 0
\(289\) −8.15467 −0.479686
\(290\) 0 0
\(291\) −42.2909 −2.47914
\(292\) 0 0
\(293\) 3.08761 0.180380 0.0901900 0.995925i \(-0.471253\pi\)
0.0901900 + 0.995925i \(0.471253\pi\)
\(294\) 0 0
\(295\) −13.9094 −0.809838
\(296\) 0 0
\(297\) 29.1048 1.68883
\(298\) 0 0
\(299\) −19.7741 −1.14357
\(300\) 0 0
\(301\) 3.03585 0.174984
\(302\) 0 0
\(303\) −24.5605 −1.41096
\(304\) 0 0
\(305\) 12.3159 0.705204
\(306\) 0 0
\(307\) −20.5478 −1.17273 −0.586363 0.810048i \(-0.699441\pi\)
−0.586363 + 0.810048i \(0.699441\pi\)
\(308\) 0 0
\(309\) 3.82526 0.217611
\(310\) 0 0
\(311\) 15.8529 0.898933 0.449467 0.893297i \(-0.351614\pi\)
0.449467 + 0.893297i \(0.351614\pi\)
\(312\) 0 0
\(313\) 27.8519 1.57428 0.787140 0.616775i \(-0.211561\pi\)
0.787140 + 0.616775i \(0.211561\pi\)
\(314\) 0 0
\(315\) 2.42095 0.136405
\(316\) 0 0
\(317\) 3.01896 0.169562 0.0847808 0.996400i \(-0.472981\pi\)
0.0847808 + 0.996400i \(0.472981\pi\)
\(318\) 0 0
\(319\) 7.29113 0.408225
\(320\) 0 0
\(321\) −24.0181 −1.34056
\(322\) 0 0
\(323\) −1.23902 −0.0689406
\(324\) 0 0
\(325\) −4.52874 −0.251209
\(326\) 0 0
\(327\) 23.4830 1.29861
\(328\) 0 0
\(329\) −3.31329 −0.182667
\(330\) 0 0
\(331\) 25.2754 1.38926 0.694631 0.719366i \(-0.255568\pi\)
0.694631 + 0.719366i \(0.255568\pi\)
\(332\) 0 0
\(333\) 31.7010 1.73720
\(334\) 0 0
\(335\) −3.77950 −0.206496
\(336\) 0 0
\(337\) −11.0237 −0.600499 −0.300249 0.953861i \(-0.597070\pi\)
−0.300249 + 0.953861i \(0.597070\pi\)
\(338\) 0 0
\(339\) −17.3414 −0.941855
\(340\) 0 0
\(341\) −2.20847 −0.119595
\(342\) 0 0
\(343\) −6.22465 −0.336100
\(344\) 0 0
\(345\) −12.6292 −0.679931
\(346\) 0 0
\(347\) −9.11433 −0.489283 −0.244641 0.969614i \(-0.578670\pi\)
−0.244641 + 0.969614i \(0.578670\pi\)
\(348\) 0 0
\(349\) −30.4330 −1.62904 −0.814522 0.580133i \(-0.803001\pi\)
−0.814522 + 0.580133i \(0.803001\pi\)
\(350\) 0 0
\(351\) 30.9896 1.65410
\(352\) 0 0
\(353\) 20.9558 1.11536 0.557682 0.830054i \(-0.311691\pi\)
0.557682 + 0.830054i \(0.311691\pi\)
\(354\) 0 0
\(355\) 9.96010 0.528627
\(356\) 0 0
\(357\) −3.88114 −0.205412
\(358\) 0 0
\(359\) −20.8189 −1.09878 −0.549390 0.835566i \(-0.685140\pi\)
−0.549390 + 0.835566i \(0.685140\pi\)
\(360\) 0 0
\(361\) −18.8264 −0.990865
\(362\) 0 0
\(363\) −20.5083 −1.07641
\(364\) 0 0
\(365\) 13.1976 0.690796
\(366\) 0 0
\(367\) −10.6761 −0.557289 −0.278645 0.960394i \(-0.589885\pi\)
−0.278645 + 0.960394i \(0.589885\pi\)
\(368\) 0 0
\(369\) 39.1750 2.03937
\(370\) 0 0
\(371\) −3.85085 −0.199926
\(372\) 0 0
\(373\) 23.0816 1.19512 0.597559 0.801825i \(-0.296137\pi\)
0.597559 + 0.801825i \(0.296137\pi\)
\(374\) 0 0
\(375\) −2.89238 −0.149362
\(376\) 0 0
\(377\) 7.76331 0.399831
\(378\) 0 0
\(379\) 10.8675 0.558224 0.279112 0.960259i \(-0.409960\pi\)
0.279112 + 0.960259i \(0.409960\pi\)
\(380\) 0 0
\(381\) −10.5499 −0.540488
\(382\) 0 0
\(383\) −17.6815 −0.903482 −0.451741 0.892149i \(-0.649197\pi\)
−0.451741 + 0.892149i \(0.649197\pi\)
\(384\) 0 0
\(385\) −1.91899 −0.0978008
\(386\) 0 0
\(387\) 36.1052 1.83533
\(388\) 0 0
\(389\) −19.8691 −1.00740 −0.503701 0.863878i \(-0.668029\pi\)
−0.503701 + 0.863878i \(0.668029\pi\)
\(390\) 0 0
\(391\) 12.9860 0.656732
\(392\) 0 0
\(393\) −21.3302 −1.07597
\(394\) 0 0
\(395\) −17.1764 −0.864239
\(396\) 0 0
\(397\) 31.7296 1.59246 0.796231 0.604993i \(-0.206824\pi\)
0.796231 + 0.604993i \(0.206824\pi\)
\(398\) 0 0
\(399\) 0.543653 0.0272167
\(400\) 0 0
\(401\) −35.3388 −1.76474 −0.882368 0.470560i \(-0.844052\pi\)
−0.882368 + 0.470560i \(0.844052\pi\)
\(402\) 0 0
\(403\) −2.35149 −0.117136
\(404\) 0 0
\(405\) 3.69468 0.183590
\(406\) 0 0
\(407\) −25.1281 −1.24555
\(408\) 0 0
\(409\) −19.4214 −0.960326 −0.480163 0.877179i \(-0.659422\pi\)
−0.480163 + 0.877179i \(0.659422\pi\)
\(410\) 0 0
\(411\) −65.7844 −3.24491
\(412\) 0 0
\(413\) −6.27563 −0.308803
\(414\) 0 0
\(415\) −12.9481 −0.635595
\(416\) 0 0
\(417\) −43.1041 −2.11082
\(418\) 0 0
\(419\) −4.14059 −0.202281 −0.101141 0.994872i \(-0.532249\pi\)
−0.101141 + 0.994872i \(0.532249\pi\)
\(420\) 0 0
\(421\) 3.31113 0.161374 0.0806872 0.996739i \(-0.474289\pi\)
0.0806872 + 0.996739i \(0.474289\pi\)
\(422\) 0 0
\(423\) −39.4047 −1.91592
\(424\) 0 0
\(425\) 2.97411 0.144266
\(426\) 0 0
\(427\) 5.55664 0.268905
\(428\) 0 0
\(429\) −55.7130 −2.68985
\(430\) 0 0
\(431\) −18.9816 −0.914312 −0.457156 0.889387i \(-0.651132\pi\)
−0.457156 + 0.889387i \(0.651132\pi\)
\(432\) 0 0
\(433\) −18.9959 −0.912884 −0.456442 0.889753i \(-0.650876\pi\)
−0.456442 + 0.889753i \(0.650876\pi\)
\(434\) 0 0
\(435\) 4.95821 0.237728
\(436\) 0 0
\(437\) −1.81903 −0.0870159
\(438\) 0 0
\(439\) 11.5187 0.549759 0.274879 0.961479i \(-0.411362\pi\)
0.274879 + 0.961479i \(0.411362\pi\)
\(440\) 0 0
\(441\) −36.4686 −1.73660
\(442\) 0 0
\(443\) −36.6022 −1.73902 −0.869512 0.493911i \(-0.835567\pi\)
−0.869512 + 0.493911i \(0.835567\pi\)
\(444\) 0 0
\(445\) −2.27054 −0.107634
\(446\) 0 0
\(447\) −3.19014 −0.150888
\(448\) 0 0
\(449\) 20.0117 0.944412 0.472206 0.881488i \(-0.343458\pi\)
0.472206 + 0.881488i \(0.343458\pi\)
\(450\) 0 0
\(451\) −31.0525 −1.46220
\(452\) 0 0
\(453\) −2.89238 −0.135896
\(454\) 0 0
\(455\) −2.04327 −0.0957898
\(456\) 0 0
\(457\) 1.42946 0.0668672 0.0334336 0.999441i \(-0.489356\pi\)
0.0334336 + 0.999441i \(0.489356\pi\)
\(458\) 0 0
\(459\) −20.3515 −0.949926
\(460\) 0 0
\(461\) −22.2114 −1.03449 −0.517244 0.855838i \(-0.673042\pi\)
−0.517244 + 0.855838i \(0.673042\pi\)
\(462\) 0 0
\(463\) 15.8050 0.734522 0.367261 0.930118i \(-0.380296\pi\)
0.367261 + 0.930118i \(0.380296\pi\)
\(464\) 0 0
\(465\) −1.50183 −0.0696458
\(466\) 0 0
\(467\) −10.1175 −0.468182 −0.234091 0.972215i \(-0.575211\pi\)
−0.234091 + 0.972215i \(0.575211\pi\)
\(468\) 0 0
\(469\) −1.70523 −0.0787400
\(470\) 0 0
\(471\) 28.0895 1.29429
\(472\) 0 0
\(473\) −28.6192 −1.31591
\(474\) 0 0
\(475\) −0.416600 −0.0191149
\(476\) 0 0
\(477\) −45.7979 −2.09694
\(478\) 0 0
\(479\) −4.25747 −0.194529 −0.0972644 0.995259i \(-0.531009\pi\)
−0.0972644 + 0.995259i \(0.531009\pi\)
\(480\) 0 0
\(481\) −26.7554 −1.21994
\(482\) 0 0
\(483\) −5.69800 −0.259268
\(484\) 0 0
\(485\) 14.6215 0.663929
\(486\) 0 0
\(487\) −22.5398 −1.02138 −0.510689 0.859766i \(-0.670610\pi\)
−0.510689 + 0.859766i \(0.670610\pi\)
\(488\) 0 0
\(489\) 28.3106 1.28025
\(490\) 0 0
\(491\) 34.1919 1.54306 0.771529 0.636194i \(-0.219492\pi\)
0.771529 + 0.636194i \(0.219492\pi\)
\(492\) 0 0
\(493\) −5.09832 −0.229617
\(494\) 0 0
\(495\) −22.8225 −1.02579
\(496\) 0 0
\(497\) 4.49378 0.201574
\(498\) 0 0
\(499\) −20.9147 −0.936273 −0.468136 0.883656i \(-0.655074\pi\)
−0.468136 + 0.883656i \(0.655074\pi\)
\(500\) 0 0
\(501\) −13.9397 −0.622780
\(502\) 0 0
\(503\) 8.21327 0.366212 0.183106 0.983093i \(-0.441385\pi\)
0.183106 + 0.983093i \(0.441385\pi\)
\(504\) 0 0
\(505\) 8.49145 0.377865
\(506\) 0 0
\(507\) −21.7201 −0.964626
\(508\) 0 0
\(509\) 6.57506 0.291434 0.145717 0.989326i \(-0.453451\pi\)
0.145717 + 0.989326i \(0.453451\pi\)
\(510\) 0 0
\(511\) 5.95448 0.263411
\(512\) 0 0
\(513\) 2.85075 0.125864
\(514\) 0 0
\(515\) −1.32253 −0.0582777
\(516\) 0 0
\(517\) 31.2346 1.37370
\(518\) 0 0
\(519\) −55.0356 −2.41580
\(520\) 0 0
\(521\) 22.9988 1.00760 0.503798 0.863822i \(-0.331936\pi\)
0.503798 + 0.863822i \(0.331936\pi\)
\(522\) 0 0
\(523\) −18.6672 −0.816260 −0.408130 0.912924i \(-0.633819\pi\)
−0.408130 + 0.912924i \(0.633819\pi\)
\(524\) 0 0
\(525\) −1.30498 −0.0569538
\(526\) 0 0
\(527\) 1.54427 0.0672696
\(528\) 0 0
\(529\) −3.93490 −0.171082
\(530\) 0 0
\(531\) −74.6357 −3.23891
\(532\) 0 0
\(533\) −33.0635 −1.43214
\(534\) 0 0
\(535\) 8.30393 0.359010
\(536\) 0 0
\(537\) 37.6044 1.62275
\(538\) 0 0
\(539\) 28.9072 1.24512
\(540\) 0 0
\(541\) 0.192302 0.00826770 0.00413385 0.999991i \(-0.498684\pi\)
0.00413385 + 0.999991i \(0.498684\pi\)
\(542\) 0 0
\(543\) 59.4625 2.55178
\(544\) 0 0
\(545\) −8.11894 −0.347777
\(546\) 0 0
\(547\) 34.2014 1.46235 0.731174 0.682191i \(-0.238973\pi\)
0.731174 + 0.682191i \(0.238973\pi\)
\(548\) 0 0
\(549\) 66.0848 2.82043
\(550\) 0 0
\(551\) 0.714150 0.0304238
\(552\) 0 0
\(553\) −7.74962 −0.329547
\(554\) 0 0
\(555\) −17.0879 −0.725343
\(556\) 0 0
\(557\) −23.5418 −0.997497 −0.498749 0.866747i \(-0.666207\pi\)
−0.498749 + 0.866747i \(0.666207\pi\)
\(558\) 0 0
\(559\) −30.4726 −1.28885
\(560\) 0 0
\(561\) 36.5878 1.54474
\(562\) 0 0
\(563\) 1.68157 0.0708695 0.0354348 0.999372i \(-0.488718\pi\)
0.0354348 + 0.999372i \(0.488718\pi\)
\(564\) 0 0
\(565\) 5.99555 0.252235
\(566\) 0 0
\(567\) 1.66696 0.0700057
\(568\) 0 0
\(569\) −5.29042 −0.221786 −0.110893 0.993832i \(-0.535371\pi\)
−0.110893 + 0.993832i \(0.535371\pi\)
\(570\) 0 0
\(571\) 21.0892 0.882556 0.441278 0.897371i \(-0.354525\pi\)
0.441278 + 0.897371i \(0.354525\pi\)
\(572\) 0 0
\(573\) 54.8233 2.29028
\(574\) 0 0
\(575\) 4.36636 0.182090
\(576\) 0 0
\(577\) −10.4200 −0.433791 −0.216895 0.976195i \(-0.569593\pi\)
−0.216895 + 0.976195i \(0.569593\pi\)
\(578\) 0 0
\(579\) 80.1593 3.33131
\(580\) 0 0
\(581\) −5.84188 −0.242362
\(582\) 0 0
\(583\) 36.3022 1.50348
\(584\) 0 0
\(585\) −24.3005 −1.00470
\(586\) 0 0
\(587\) −43.7873 −1.80730 −0.903648 0.428275i \(-0.859121\pi\)
−0.903648 + 0.428275i \(0.859121\pi\)
\(588\) 0 0
\(589\) −0.216315 −0.00891310
\(590\) 0 0
\(591\) −20.5264 −0.844343
\(592\) 0 0
\(593\) −14.2309 −0.584393 −0.292197 0.956358i \(-0.594386\pi\)
−0.292197 + 0.956358i \(0.594386\pi\)
\(594\) 0 0
\(595\) 1.34185 0.0550106
\(596\) 0 0
\(597\) 65.9192 2.69789
\(598\) 0 0
\(599\) 19.0831 0.779716 0.389858 0.920875i \(-0.372524\pi\)
0.389858 + 0.920875i \(0.372524\pi\)
\(600\) 0 0
\(601\) −8.90747 −0.363343 −0.181672 0.983359i \(-0.558151\pi\)
−0.181672 + 0.983359i \(0.558151\pi\)
\(602\) 0 0
\(603\) −20.2801 −0.825871
\(604\) 0 0
\(605\) 7.09047 0.288269
\(606\) 0 0
\(607\) −5.79536 −0.235227 −0.117613 0.993059i \(-0.537524\pi\)
−0.117613 + 0.993059i \(0.537524\pi\)
\(608\) 0 0
\(609\) 2.23703 0.0906492
\(610\) 0 0
\(611\) 33.2574 1.34545
\(612\) 0 0
\(613\) 32.9712 1.33169 0.665847 0.746089i \(-0.268071\pi\)
0.665847 + 0.746089i \(0.268071\pi\)
\(614\) 0 0
\(615\) −21.1167 −0.851508
\(616\) 0 0
\(617\) −10.2643 −0.413225 −0.206613 0.978423i \(-0.566244\pi\)
−0.206613 + 0.978423i \(0.566244\pi\)
\(618\) 0 0
\(619\) 2.77427 0.111507 0.0557536 0.998445i \(-0.482244\pi\)
0.0557536 + 0.998445i \(0.482244\pi\)
\(620\) 0 0
\(621\) −29.8785 −1.19898
\(622\) 0 0
\(623\) −1.02442 −0.0410424
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −5.12506 −0.204675
\(628\) 0 0
\(629\) 17.5708 0.700595
\(630\) 0 0
\(631\) −28.6155 −1.13917 −0.569583 0.821934i \(-0.692895\pi\)
−0.569583 + 0.821934i \(0.692895\pi\)
\(632\) 0 0
\(633\) −49.3823 −1.96277
\(634\) 0 0
\(635\) 3.64749 0.144746
\(636\) 0 0
\(637\) 30.7793 1.21952
\(638\) 0 0
\(639\) 53.4443 2.11422
\(640\) 0 0
\(641\) −43.5514 −1.72018 −0.860088 0.510145i \(-0.829592\pi\)
−0.860088 + 0.510145i \(0.829592\pi\)
\(642\) 0 0
\(643\) 47.9037 1.88914 0.944569 0.328314i \(-0.106480\pi\)
0.944569 + 0.328314i \(0.106480\pi\)
\(644\) 0 0
\(645\) −19.4620 −0.766315
\(646\) 0 0
\(647\) 14.2047 0.558443 0.279221 0.960227i \(-0.409924\pi\)
0.279221 + 0.960227i \(0.409924\pi\)
\(648\) 0 0
\(649\) 59.1608 2.32227
\(650\) 0 0
\(651\) −0.677594 −0.0265570
\(652\) 0 0
\(653\) −38.9930 −1.52591 −0.762956 0.646450i \(-0.776253\pi\)
−0.762956 + 0.646450i \(0.776253\pi\)
\(654\) 0 0
\(655\) 7.37463 0.288151
\(656\) 0 0
\(657\) 70.8163 2.76281
\(658\) 0 0
\(659\) −35.1488 −1.36920 −0.684602 0.728917i \(-0.740024\pi\)
−0.684602 + 0.728917i \(0.740024\pi\)
\(660\) 0 0
\(661\) −14.5166 −0.564629 −0.282314 0.959322i \(-0.591102\pi\)
−0.282314 + 0.959322i \(0.591102\pi\)
\(662\) 0 0
\(663\) 38.9573 1.51298
\(664\) 0 0
\(665\) −0.187961 −0.00728881
\(666\) 0 0
\(667\) −7.48496 −0.289819
\(668\) 0 0
\(669\) 5.69967 0.220362
\(670\) 0 0
\(671\) −52.3829 −2.02222
\(672\) 0 0
\(673\) −9.14709 −0.352594 −0.176297 0.984337i \(-0.556412\pi\)
−0.176297 + 0.984337i \(0.556412\pi\)
\(674\) 0 0
\(675\) −6.84288 −0.263383
\(676\) 0 0
\(677\) 35.8250 1.37687 0.688433 0.725300i \(-0.258299\pi\)
0.688433 + 0.725300i \(0.258299\pi\)
\(678\) 0 0
\(679\) 6.59691 0.253166
\(680\) 0 0
\(681\) 60.2313 2.30807
\(682\) 0 0
\(683\) −40.9629 −1.56740 −0.783701 0.621138i \(-0.786671\pi\)
−0.783701 + 0.621138i \(0.786671\pi\)
\(684\) 0 0
\(685\) 22.7441 0.869007
\(686\) 0 0
\(687\) 32.8526 1.25340
\(688\) 0 0
\(689\) 38.6532 1.47257
\(690\) 0 0
\(691\) −46.1245 −1.75466 −0.877330 0.479888i \(-0.840677\pi\)
−0.877330 + 0.479888i \(0.840677\pi\)
\(692\) 0 0
\(693\) −10.2970 −0.391150
\(694\) 0 0
\(695\) 14.9027 0.565291
\(696\) 0 0
\(697\) 21.7134 0.822455
\(698\) 0 0
\(699\) 15.5952 0.589865
\(700\) 0 0
\(701\) −8.19095 −0.309368 −0.154684 0.987964i \(-0.549436\pi\)
−0.154684 + 0.987964i \(0.549436\pi\)
\(702\) 0 0
\(703\) −2.46124 −0.0928276
\(704\) 0 0
\(705\) 21.2405 0.799965
\(706\) 0 0
\(707\) 3.83116 0.144085
\(708\) 0 0
\(709\) 7.12455 0.267568 0.133784 0.991010i \(-0.457287\pi\)
0.133784 + 0.991010i \(0.457287\pi\)
\(710\) 0 0
\(711\) −92.1658 −3.45649
\(712\) 0 0
\(713\) 2.26718 0.0849067
\(714\) 0 0
\(715\) 19.2620 0.720359
\(716\) 0 0
\(717\) 7.20686 0.269145
\(718\) 0 0
\(719\) 33.0778 1.23359 0.616797 0.787122i \(-0.288430\pi\)
0.616797 + 0.787122i \(0.288430\pi\)
\(720\) 0 0
\(721\) −0.596697 −0.0222222
\(722\) 0 0
\(723\) 76.3577 2.83977
\(724\) 0 0
\(725\) −1.71423 −0.0636650
\(726\) 0 0
\(727\) −28.5515 −1.05892 −0.529458 0.848336i \(-0.677605\pi\)
−0.529458 + 0.848336i \(0.677605\pi\)
\(728\) 0 0
\(729\) −39.5515 −1.46487
\(730\) 0 0
\(731\) 20.0120 0.740169
\(732\) 0 0
\(733\) 3.73152 0.137827 0.0689134 0.997623i \(-0.478047\pi\)
0.0689134 + 0.997623i \(0.478047\pi\)
\(734\) 0 0
\(735\) 19.6579 0.725091
\(736\) 0 0
\(737\) 16.0753 0.592141
\(738\) 0 0
\(739\) −15.5110 −0.570582 −0.285291 0.958441i \(-0.592090\pi\)
−0.285291 + 0.958441i \(0.592090\pi\)
\(740\) 0 0
\(741\) −5.45697 −0.200467
\(742\) 0 0
\(743\) −43.0936 −1.58095 −0.790475 0.612494i \(-0.790166\pi\)
−0.790475 + 0.612494i \(0.790166\pi\)
\(744\) 0 0
\(745\) 1.10295 0.0404089
\(746\) 0 0
\(747\) −69.4771 −2.54204
\(748\) 0 0
\(749\) 3.74655 0.136896
\(750\) 0 0
\(751\) 28.8861 1.05407 0.527034 0.849844i \(-0.323304\pi\)
0.527034 + 0.849844i \(0.323304\pi\)
\(752\) 0 0
\(753\) 11.9463 0.435347
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) −12.5168 −0.454931 −0.227466 0.973786i \(-0.573044\pi\)
−0.227466 + 0.973786i \(0.573044\pi\)
\(758\) 0 0
\(759\) 53.7154 1.94975
\(760\) 0 0
\(761\) 11.1642 0.404701 0.202351 0.979313i \(-0.435142\pi\)
0.202351 + 0.979313i \(0.435142\pi\)
\(762\) 0 0
\(763\) −3.66309 −0.132613
\(764\) 0 0
\(765\) 15.9586 0.576984
\(766\) 0 0
\(767\) 62.9921 2.27451
\(768\) 0 0
\(769\) 26.9100 0.970398 0.485199 0.874404i \(-0.338747\pi\)
0.485199 + 0.874404i \(0.338747\pi\)
\(770\) 0 0
\(771\) 27.6928 0.997333
\(772\) 0 0
\(773\) −53.4862 −1.92377 −0.961883 0.273463i \(-0.911831\pi\)
−0.961883 + 0.273463i \(0.911831\pi\)
\(774\) 0 0
\(775\) 0.519238 0.0186516
\(776\) 0 0
\(777\) −7.70970 −0.276584
\(778\) 0 0
\(779\) −3.04152 −0.108974
\(780\) 0 0
\(781\) −42.3632 −1.51587
\(782\) 0 0
\(783\) 11.7303 0.419207
\(784\) 0 0
\(785\) −9.71155 −0.346620
\(786\) 0 0
\(787\) −9.94048 −0.354340 −0.177170 0.984180i \(-0.556694\pi\)
−0.177170 + 0.984180i \(0.556694\pi\)
\(788\) 0 0
\(789\) −3.52089 −0.125347
\(790\) 0 0
\(791\) 2.70506 0.0961809
\(792\) 0 0
\(793\) −55.7753 −1.98064
\(794\) 0 0
\(795\) 24.6867 0.875547
\(796\) 0 0
\(797\) 10.3057 0.365045 0.182523 0.983202i \(-0.441574\pi\)
0.182523 + 0.983202i \(0.441574\pi\)
\(798\) 0 0
\(799\) −21.8408 −0.772671
\(800\) 0 0
\(801\) −12.1833 −0.430476
\(802\) 0 0
\(803\) −56.1333 −1.98090
\(804\) 0 0
\(805\) 1.97001 0.0694336
\(806\) 0 0
\(807\) 84.9437 2.99016
\(808\) 0 0
\(809\) −10.6334 −0.373850 −0.186925 0.982374i \(-0.559852\pi\)
−0.186925 + 0.982374i \(0.559852\pi\)
\(810\) 0 0
\(811\) −2.58363 −0.0907235 −0.0453617 0.998971i \(-0.514444\pi\)
−0.0453617 + 0.998971i \(0.514444\pi\)
\(812\) 0 0
\(813\) −59.7636 −2.09600
\(814\) 0 0
\(815\) −9.78801 −0.342859
\(816\) 0 0
\(817\) −2.80319 −0.0980711
\(818\) 0 0
\(819\) −10.9638 −0.383107
\(820\) 0 0
\(821\) 5.20798 0.181760 0.0908799 0.995862i \(-0.471032\pi\)
0.0908799 + 0.995862i \(0.471032\pi\)
\(822\) 0 0
\(823\) −5.58046 −0.194523 −0.0972614 0.995259i \(-0.531008\pi\)
−0.0972614 + 0.995259i \(0.531008\pi\)
\(824\) 0 0
\(825\) 12.3021 0.428305
\(826\) 0 0
\(827\) 31.7547 1.10422 0.552109 0.833772i \(-0.313823\pi\)
0.552109 + 0.833772i \(0.313823\pi\)
\(828\) 0 0
\(829\) 6.92092 0.240373 0.120187 0.992751i \(-0.461651\pi\)
0.120187 + 0.992751i \(0.461651\pi\)
\(830\) 0 0
\(831\) 67.9931 2.35866
\(832\) 0 0
\(833\) −20.2134 −0.700351
\(834\) 0 0
\(835\) 4.81946 0.166784
\(836\) 0 0
\(837\) −3.55309 −0.122813
\(838\) 0 0
\(839\) −24.7877 −0.855767 −0.427883 0.903834i \(-0.640741\pi\)
−0.427883 + 0.903834i \(0.640741\pi\)
\(840\) 0 0
\(841\) −26.0614 −0.898669
\(842\) 0 0
\(843\) 77.5899 2.67234
\(844\) 0 0
\(845\) 7.50945 0.258333
\(846\) 0 0
\(847\) 3.19907 0.109921
\(848\) 0 0
\(849\) −73.0433 −2.50684
\(850\) 0 0
\(851\) 25.7961 0.884280
\(852\) 0 0
\(853\) −0.0282306 −0.000966597 0 −0.000483298 1.00000i \(-0.500154\pi\)
−0.000483298 1.00000i \(0.500154\pi\)
\(854\) 0 0
\(855\) −2.23541 −0.0764494
\(856\) 0 0
\(857\) −29.5176 −1.00830 −0.504151 0.863615i \(-0.668195\pi\)
−0.504151 + 0.863615i \(0.668195\pi\)
\(858\) 0 0
\(859\) 3.60108 0.122867 0.0614336 0.998111i \(-0.480433\pi\)
0.0614336 + 0.998111i \(0.480433\pi\)
\(860\) 0 0
\(861\) −9.52739 −0.324693
\(862\) 0 0
\(863\) 44.2763 1.50718 0.753592 0.657342i \(-0.228319\pi\)
0.753592 + 0.657342i \(0.228319\pi\)
\(864\) 0 0
\(865\) 19.0278 0.646966
\(866\) 0 0
\(867\) 23.5864 0.801035
\(868\) 0 0
\(869\) 73.0562 2.47826
\(870\) 0 0
\(871\) 17.1163 0.579965
\(872\) 0 0
\(873\) 78.4566 2.65536
\(874\) 0 0
\(875\) 0.451178 0.0152526
\(876\) 0 0
\(877\) 24.5938 0.830474 0.415237 0.909713i \(-0.363699\pi\)
0.415237 + 0.909713i \(0.363699\pi\)
\(878\) 0 0
\(879\) −8.93052 −0.301219
\(880\) 0 0
\(881\) 18.4874 0.622857 0.311428 0.950270i \(-0.399193\pi\)
0.311428 + 0.950270i \(0.399193\pi\)
\(882\) 0 0
\(883\) 3.37235 0.113489 0.0567443 0.998389i \(-0.481928\pi\)
0.0567443 + 0.998389i \(0.481928\pi\)
\(884\) 0 0
\(885\) 40.2313 1.35236
\(886\) 0 0
\(887\) −3.21471 −0.107939 −0.0539696 0.998543i \(-0.517187\pi\)
−0.0539696 + 0.998543i \(0.517187\pi\)
\(888\) 0 0
\(889\) 1.64567 0.0551939
\(890\) 0 0
\(891\) −15.7145 −0.526457
\(892\) 0 0
\(893\) 3.05936 0.102378
\(894\) 0 0
\(895\) −13.0012 −0.434582
\(896\) 0 0
\(897\) 57.1941 1.90966
\(898\) 0 0
\(899\) −0.890096 −0.0296864
\(900\) 0 0
\(901\) −25.3843 −0.845674
\(902\) 0 0
\(903\) −8.78082 −0.292208
\(904\) 0 0
\(905\) −20.5584 −0.683383
\(906\) 0 0
\(907\) −8.28771 −0.275189 −0.137594 0.990489i \(-0.543937\pi\)
−0.137594 + 0.990489i \(0.543937\pi\)
\(908\) 0 0
\(909\) 45.5637 1.51125
\(910\) 0 0
\(911\) −38.1356 −1.26349 −0.631744 0.775177i \(-0.717661\pi\)
−0.631744 + 0.775177i \(0.717661\pi\)
\(912\) 0 0
\(913\) 55.0718 1.82261
\(914\) 0 0
\(915\) −35.6221 −1.17763
\(916\) 0 0
\(917\) 3.32727 0.109876
\(918\) 0 0
\(919\) 29.4109 0.970177 0.485088 0.874465i \(-0.338787\pi\)
0.485088 + 0.874465i \(0.338787\pi\)
\(920\) 0 0
\(921\) 59.4320 1.95835
\(922\) 0 0
\(923\) −45.1067 −1.48470
\(924\) 0 0
\(925\) 5.90793 0.194251
\(926\) 0 0
\(927\) −7.09649 −0.233079
\(928\) 0 0
\(929\) 26.1640 0.858412 0.429206 0.903207i \(-0.358793\pi\)
0.429206 + 0.903207i \(0.358793\pi\)
\(930\) 0 0
\(931\) 2.83140 0.0927953
\(932\) 0 0
\(933\) −45.8524 −1.50114
\(934\) 0 0
\(935\) −12.6498 −0.413691
\(936\) 0 0
\(937\) −20.8460 −0.681010 −0.340505 0.940243i \(-0.610598\pi\)
−0.340505 + 0.940243i \(0.610598\pi\)
\(938\) 0 0
\(939\) −80.5580 −2.62891
\(940\) 0 0
\(941\) 23.2085 0.756575 0.378288 0.925688i \(-0.376513\pi\)
0.378288 + 0.925688i \(0.376513\pi\)
\(942\) 0 0
\(943\) 31.8780 1.03809
\(944\) 0 0
\(945\) −3.08736 −0.100432
\(946\) 0 0
\(947\) 2.78439 0.0904805 0.0452402 0.998976i \(-0.485595\pi\)
0.0452402 + 0.998976i \(0.485595\pi\)
\(948\) 0 0
\(949\) −59.7686 −1.94017
\(950\) 0 0
\(951\) −8.73196 −0.283153
\(952\) 0 0
\(953\) −46.9890 −1.52212 −0.761061 0.648680i \(-0.775321\pi\)
−0.761061 + 0.648680i \(0.775321\pi\)
\(954\) 0 0
\(955\) −18.9544 −0.613351
\(956\) 0 0
\(957\) −21.0887 −0.681700
\(958\) 0 0
\(959\) 10.2616 0.331365
\(960\) 0 0
\(961\) −30.7304 −0.991303
\(962\) 0 0
\(963\) 44.5575 1.43585
\(964\) 0 0
\(965\) −27.7140 −0.892145
\(966\) 0 0
\(967\) 45.3169 1.45729 0.728647 0.684890i \(-0.240150\pi\)
0.728647 + 0.684890i \(0.240150\pi\)
\(968\) 0 0
\(969\) 3.58370 0.115125
\(970\) 0 0
\(971\) 60.7065 1.94816 0.974082 0.226194i \(-0.0726284\pi\)
0.974082 + 0.226194i \(0.0726284\pi\)
\(972\) 0 0
\(973\) 6.72376 0.215554
\(974\) 0 0
\(975\) 13.0988 0.419497
\(976\) 0 0
\(977\) −41.0911 −1.31462 −0.657311 0.753619i \(-0.728306\pi\)
−0.657311 + 0.753619i \(0.728306\pi\)
\(978\) 0 0
\(979\) 9.65725 0.308647
\(980\) 0 0
\(981\) −43.5649 −1.39092
\(982\) 0 0
\(983\) 19.7730 0.630661 0.315330 0.948982i \(-0.397885\pi\)
0.315330 + 0.948982i \(0.397885\pi\)
\(984\) 0 0
\(985\) 7.09673 0.226120
\(986\) 0 0
\(987\) 9.58326 0.305039
\(988\) 0 0
\(989\) 29.3800 0.934231
\(990\) 0 0
\(991\) 7.08562 0.225082 0.112541 0.993647i \(-0.464101\pi\)
0.112541 + 0.993647i \(0.464101\pi\)
\(992\) 0 0
\(993\) −73.1060 −2.31995
\(994\) 0 0
\(995\) −22.7907 −0.722513
\(996\) 0 0
\(997\) −3.07362 −0.0973424 −0.0486712 0.998815i \(-0.515499\pi\)
−0.0486712 + 0.998815i \(0.515499\pi\)
\(998\) 0 0
\(999\) −40.4273 −1.27906
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 \(a_p\))