Properties

Label 8024.2.a.y.1.13
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 1.13
Character \(\chi\) = 8024.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.587444 q^{3}\) \(+0.0220313 q^{5}\) \(+3.20930 q^{7}\) \(-2.65491 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.587444 q^{3}\) \(+0.0220313 q^{5}\) \(+3.20930 q^{7}\) \(-2.65491 q^{9}\) \(-2.26714 q^{11}\) \(+0.668836 q^{13}\) \(-0.0129422 q^{15}\) \(-1.00000 q^{17}\) \(+4.04514 q^{19}\) \(-1.88528 q^{21}\) \(-0.862508 q^{23}\) \(-4.99951 q^{25}\) \(+3.32194 q^{27}\) \(+3.45358 q^{29}\) \(-1.93354 q^{31}\) \(+1.33182 q^{33}\) \(+0.0707050 q^{35}\) \(-0.186016 q^{37}\) \(-0.392904 q^{39}\) \(+4.18488 q^{41}\) \(-12.0471 q^{43}\) \(-0.0584912 q^{45}\) \(+1.63497 q^{47}\) \(+3.29958 q^{49}\) \(+0.587444 q^{51}\) \(-2.83353 q^{53}\) \(-0.0499480 q^{55}\) \(-2.37629 q^{57}\) \(-1.00000 q^{59}\) \(-3.86022 q^{61}\) \(-8.52039 q^{63}\) \(+0.0147353 q^{65}\) \(+9.45384 q^{67}\) \(+0.506675 q^{69}\) \(+8.22349 q^{71}\) \(-4.56883 q^{73}\) \(+2.93694 q^{75}\) \(-7.27591 q^{77}\) \(-7.12322 q^{79}\) \(+6.01327 q^{81}\) \(+12.1819 q^{83}\) \(-0.0220313 q^{85}\) \(-2.02878 q^{87}\) \(-10.7820 q^{89}\) \(+2.14649 q^{91}\) \(+1.13585 q^{93}\) \(+0.0891197 q^{95}\) \(-7.29356 q^{97}\) \(+6.01904 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(23q \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 23q^{9} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 23q^{17} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut -\mathstrut 29q^{23} \) \(\mathstrut +\mathstrut 31q^{25} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut -\mathstrut 41q^{31} \) \(\mathstrut +\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 11q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 39q^{47} \) \(\mathstrut +\mathstrut 16q^{49} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 35q^{55} \) \(\mathstrut +\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 23q^{59} \) \(\mathstrut -\mathstrut 37q^{61} \) \(\mathstrut +\mathstrut 33q^{65} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut -\mathstrut 66q^{69} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut -\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 81q^{75} \) \(\mathstrut -\mathstrut 4q^{77} \) \(\mathstrut -\mathstrut 61q^{79} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 18q^{91} \) \(\mathstrut -\mathstrut 62q^{93} \) \(\mathstrut -\mathstrut 33q^{95} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.587444 −0.339161 −0.169581 0.985516i \(-0.554241\pi\)
−0.169581 + 0.985516i \(0.554241\pi\)
\(4\) 0 0
\(5\) 0.0220313 0.00985271 0.00492635 0.999988i \(-0.498432\pi\)
0.00492635 + 0.999988i \(0.498432\pi\)
\(6\) 0 0
\(7\) 3.20930 1.21300 0.606500 0.795084i \(-0.292573\pi\)
0.606500 + 0.795084i \(0.292573\pi\)
\(8\) 0 0
\(9\) −2.65491 −0.884970
\(10\) 0 0
\(11\) −2.26714 −0.683567 −0.341784 0.939779i \(-0.611031\pi\)
−0.341784 + 0.939779i \(0.611031\pi\)
\(12\) 0 0
\(13\) 0.668836 0.185502 0.0927508 0.995689i \(-0.470434\pi\)
0.0927508 + 0.995689i \(0.470434\pi\)
\(14\) 0 0
\(15\) −0.0129422 −0.00334165
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 4.04514 0.928018 0.464009 0.885830i \(-0.346410\pi\)
0.464009 + 0.885830i \(0.346410\pi\)
\(20\) 0 0
\(21\) −1.88528 −0.411402
\(22\) 0 0
\(23\) −0.862508 −0.179845 −0.0899227 0.995949i \(-0.528662\pi\)
−0.0899227 + 0.995949i \(0.528662\pi\)
\(24\) 0 0
\(25\) −4.99951 −0.999903
\(26\) 0 0
\(27\) 3.32194 0.639308
\(28\) 0 0
\(29\) 3.45358 0.641313 0.320657 0.947196i \(-0.396096\pi\)
0.320657 + 0.947196i \(0.396096\pi\)
\(30\) 0 0
\(31\) −1.93354 −0.347275 −0.173637 0.984810i \(-0.555552\pi\)
−0.173637 + 0.984810i \(0.555552\pi\)
\(32\) 0 0
\(33\) 1.33182 0.231839
\(34\) 0 0
\(35\) 0.0707050 0.0119513
\(36\) 0 0
\(37\) −0.186016 −0.0305809 −0.0152905 0.999883i \(-0.504867\pi\)
−0.0152905 + 0.999883i \(0.504867\pi\)
\(38\) 0 0
\(39\) −0.392904 −0.0629149
\(40\) 0 0
\(41\) 4.18488 0.653569 0.326785 0.945099i \(-0.394035\pi\)
0.326785 + 0.945099i \(0.394035\pi\)
\(42\) 0 0
\(43\) −12.0471 −1.83716 −0.918582 0.395229i \(-0.870665\pi\)
−0.918582 + 0.395229i \(0.870665\pi\)
\(44\) 0 0
\(45\) −0.0584912 −0.00871935
\(46\) 0 0
\(47\) 1.63497 0.238485 0.119242 0.992865i \(-0.461953\pi\)
0.119242 + 0.992865i \(0.461953\pi\)
\(48\) 0 0
\(49\) 3.29958 0.471368
\(50\) 0 0
\(51\) 0.587444 0.0822586
\(52\) 0 0
\(53\) −2.83353 −0.389215 −0.194608 0.980881i \(-0.562343\pi\)
−0.194608 + 0.980881i \(0.562343\pi\)
\(54\) 0 0
\(55\) −0.0499480 −0.00673499
\(56\) 0 0
\(57\) −2.37629 −0.314748
\(58\) 0 0
\(59\) −1.00000 −0.130189
\(60\) 0 0
\(61\) −3.86022 −0.494250 −0.247125 0.968984i \(-0.579486\pi\)
−0.247125 + 0.968984i \(0.579486\pi\)
\(62\) 0 0
\(63\) −8.52039 −1.07347
\(64\) 0 0
\(65\) 0.0147353 0.00182769
\(66\) 0 0
\(67\) 9.45384 1.15497 0.577485 0.816401i \(-0.304034\pi\)
0.577485 + 0.816401i \(0.304034\pi\)
\(68\) 0 0
\(69\) 0.506675 0.0609965
\(70\) 0 0
\(71\) 8.22349 0.975948 0.487974 0.872858i \(-0.337736\pi\)
0.487974 + 0.872858i \(0.337736\pi\)
\(72\) 0 0
\(73\) −4.56883 −0.534741 −0.267371 0.963594i \(-0.586155\pi\)
−0.267371 + 0.963594i \(0.586155\pi\)
\(74\) 0 0
\(75\) 2.93694 0.339128
\(76\) 0 0
\(77\) −7.27591 −0.829167
\(78\) 0 0
\(79\) −7.12322 −0.801425 −0.400713 0.916204i \(-0.631237\pi\)
−0.400713 + 0.916204i \(0.631237\pi\)
\(80\) 0 0
\(81\) 6.01327 0.668141
\(82\) 0 0
\(83\) 12.1819 1.33714 0.668571 0.743648i \(-0.266906\pi\)
0.668571 + 0.743648i \(0.266906\pi\)
\(84\) 0 0
\(85\) −0.0220313 −0.00238963
\(86\) 0 0
\(87\) −2.02878 −0.217508
\(88\) 0 0
\(89\) −10.7820 −1.14289 −0.571443 0.820642i \(-0.693616\pi\)
−0.571443 + 0.820642i \(0.693616\pi\)
\(90\) 0 0
\(91\) 2.14649 0.225013
\(92\) 0 0
\(93\) 1.13585 0.117782
\(94\) 0 0
\(95\) 0.0891197 0.00914349
\(96\) 0 0
\(97\) −7.29356 −0.740549 −0.370274 0.928922i \(-0.620736\pi\)
−0.370274 + 0.928922i \(0.620736\pi\)
\(98\) 0 0
\(99\) 6.01904 0.604936
\(100\) 0 0
\(101\) −13.3364 −1.32702 −0.663511 0.748167i \(-0.730934\pi\)
−0.663511 + 0.748167i \(0.730934\pi\)
\(102\) 0 0
\(103\) 11.5486 1.13792 0.568959 0.822366i \(-0.307346\pi\)
0.568959 + 0.822366i \(0.307346\pi\)
\(104\) 0 0
\(105\) −0.0415353 −0.00405343
\(106\) 0 0
\(107\) −14.0411 −1.35740 −0.678700 0.734415i \(-0.737457\pi\)
−0.678700 + 0.734415i \(0.737457\pi\)
\(108\) 0 0
\(109\) −2.08212 −0.199431 −0.0997154 0.995016i \(-0.531793\pi\)
−0.0997154 + 0.995016i \(0.531793\pi\)
\(110\) 0 0
\(111\) 0.109274 0.0103719
\(112\) 0 0
\(113\) 5.73495 0.539499 0.269749 0.962931i \(-0.413059\pi\)
0.269749 + 0.962931i \(0.413059\pi\)
\(114\) 0 0
\(115\) −0.0190022 −0.00177196
\(116\) 0 0
\(117\) −1.77570 −0.164163
\(118\) 0 0
\(119\) −3.20930 −0.294196
\(120\) 0 0
\(121\) −5.86010 −0.532736
\(122\) 0 0
\(123\) −2.45839 −0.221665
\(124\) 0 0
\(125\) −0.220303 −0.0197045
\(126\) 0 0
\(127\) 2.87285 0.254924 0.127462 0.991843i \(-0.459317\pi\)
0.127462 + 0.991843i \(0.459317\pi\)
\(128\) 0 0
\(129\) 7.07700 0.623095
\(130\) 0 0
\(131\) −10.7520 −0.939407 −0.469704 0.882824i \(-0.655639\pi\)
−0.469704 + 0.882824i \(0.655639\pi\)
\(132\) 0 0
\(133\) 12.9820 1.12569
\(134\) 0 0
\(135\) 0.0731868 0.00629892
\(136\) 0 0
\(137\) −5.79203 −0.494847 −0.247423 0.968907i \(-0.579584\pi\)
−0.247423 + 0.968907i \(0.579584\pi\)
\(138\) 0 0
\(139\) −14.6874 −1.24577 −0.622885 0.782314i \(-0.714039\pi\)
−0.622885 + 0.782314i \(0.714039\pi\)
\(140\) 0 0
\(141\) −0.960453 −0.0808848
\(142\) 0 0
\(143\) −1.51634 −0.126803
\(144\) 0 0
\(145\) 0.0760869 0.00631867
\(146\) 0 0
\(147\) −1.93832 −0.159870
\(148\) 0 0
\(149\) 8.68522 0.711521 0.355761 0.934577i \(-0.384222\pi\)
0.355761 + 0.934577i \(0.384222\pi\)
\(150\) 0 0
\(151\) 1.26667 0.103080 0.0515399 0.998671i \(-0.483587\pi\)
0.0515399 + 0.998671i \(0.483587\pi\)
\(152\) 0 0
\(153\) 2.65491 0.214637
\(154\) 0 0
\(155\) −0.0425985 −0.00342160
\(156\) 0 0
\(157\) 7.26993 0.580204 0.290102 0.956996i \(-0.406311\pi\)
0.290102 + 0.956996i \(0.406311\pi\)
\(158\) 0 0
\(159\) 1.66454 0.132007
\(160\) 0 0
\(161\) −2.76804 −0.218152
\(162\) 0 0
\(163\) −20.4351 −1.60060 −0.800300 0.599599i \(-0.795327\pi\)
−0.800300 + 0.599599i \(0.795327\pi\)
\(164\) 0 0
\(165\) 0.0293417 0.00228425
\(166\) 0 0
\(167\) −8.28845 −0.641380 −0.320690 0.947184i \(-0.603915\pi\)
−0.320690 + 0.947184i \(0.603915\pi\)
\(168\) 0 0
\(169\) −12.5527 −0.965589
\(170\) 0 0
\(171\) −10.7395 −0.821268
\(172\) 0 0
\(173\) 2.65371 0.201758 0.100879 0.994899i \(-0.467834\pi\)
0.100879 + 0.994899i \(0.467834\pi\)
\(174\) 0 0
\(175\) −16.0449 −1.21288
\(176\) 0 0
\(177\) 0.587444 0.0441550
\(178\) 0 0
\(179\) −7.82162 −0.584615 −0.292308 0.956324i \(-0.594423\pi\)
−0.292308 + 0.956324i \(0.594423\pi\)
\(180\) 0 0
\(181\) 2.54872 0.189445 0.0947226 0.995504i \(-0.469804\pi\)
0.0947226 + 0.995504i \(0.469804\pi\)
\(182\) 0 0
\(183\) 2.26766 0.167630
\(184\) 0 0
\(185\) −0.00409819 −0.000301305 0
\(186\) 0 0
\(187\) 2.26714 0.165789
\(188\) 0 0
\(189\) 10.6611 0.775481
\(190\) 0 0
\(191\) −1.09977 −0.0795766 −0.0397883 0.999208i \(-0.512668\pi\)
−0.0397883 + 0.999208i \(0.512668\pi\)
\(192\) 0 0
\(193\) 5.36752 0.386362 0.193181 0.981163i \(-0.438120\pi\)
0.193181 + 0.981163i \(0.438120\pi\)
\(194\) 0 0
\(195\) −0.00865619 −0.000619882 0
\(196\) 0 0
\(197\) 23.6483 1.68487 0.842436 0.538796i \(-0.181121\pi\)
0.842436 + 0.538796i \(0.181121\pi\)
\(198\) 0 0
\(199\) −5.23442 −0.371058 −0.185529 0.982639i \(-0.559400\pi\)
−0.185529 + 0.982639i \(0.559400\pi\)
\(200\) 0 0
\(201\) −5.55361 −0.391721
\(202\) 0 0
\(203\) 11.0836 0.777913
\(204\) 0 0
\(205\) 0.0921985 0.00643943
\(206\) 0 0
\(207\) 2.28988 0.159158
\(208\) 0 0
\(209\) −9.17088 −0.634363
\(210\) 0 0
\(211\) −10.1578 −0.699295 −0.349648 0.936881i \(-0.613699\pi\)
−0.349648 + 0.936881i \(0.613699\pi\)
\(212\) 0 0
\(213\) −4.83084 −0.331004
\(214\) 0 0
\(215\) −0.265413 −0.0181010
\(216\) 0 0
\(217\) −6.20531 −0.421244
\(218\) 0 0
\(219\) 2.68393 0.181363
\(220\) 0 0
\(221\) −0.668836 −0.0449907
\(222\) 0 0
\(223\) −16.0325 −1.07362 −0.536808 0.843705i \(-0.680370\pi\)
−0.536808 + 0.843705i \(0.680370\pi\)
\(224\) 0 0
\(225\) 13.2733 0.884884
\(226\) 0 0
\(227\) −7.60168 −0.504541 −0.252271 0.967657i \(-0.581177\pi\)
−0.252271 + 0.967657i \(0.581177\pi\)
\(228\) 0 0
\(229\) 6.42985 0.424897 0.212448 0.977172i \(-0.431856\pi\)
0.212448 + 0.977172i \(0.431856\pi\)
\(230\) 0 0
\(231\) 4.27419 0.281221
\(232\) 0 0
\(233\) −18.1111 −1.18650 −0.593249 0.805019i \(-0.702155\pi\)
−0.593249 + 0.805019i \(0.702155\pi\)
\(234\) 0 0
\(235\) 0.0360205 0.00234972
\(236\) 0 0
\(237\) 4.18450 0.271812
\(238\) 0 0
\(239\) 22.1648 1.43372 0.716860 0.697217i \(-0.245579\pi\)
0.716860 + 0.697217i \(0.245579\pi\)
\(240\) 0 0
\(241\) 23.5841 1.51918 0.759592 0.650399i \(-0.225398\pi\)
0.759592 + 0.650399i \(0.225398\pi\)
\(242\) 0 0
\(243\) −13.4983 −0.865916
\(244\) 0 0
\(245\) 0.0726941 0.00464425
\(246\) 0 0
\(247\) 2.70553 0.172149
\(248\) 0 0
\(249\) −7.15622 −0.453507
\(250\) 0 0
\(251\) −5.27505 −0.332958 −0.166479 0.986045i \(-0.553240\pi\)
−0.166479 + 0.986045i \(0.553240\pi\)
\(252\) 0 0
\(253\) 1.95542 0.122936
\(254\) 0 0
\(255\) 0.0129422 0.000810470 0
\(256\) 0 0
\(257\) 10.3956 0.648462 0.324231 0.945978i \(-0.394895\pi\)
0.324231 + 0.945978i \(0.394895\pi\)
\(258\) 0 0
\(259\) −0.596982 −0.0370946
\(260\) 0 0
\(261\) −9.16893 −0.567543
\(262\) 0 0
\(263\) −7.65404 −0.471968 −0.235984 0.971757i \(-0.575831\pi\)
−0.235984 + 0.971757i \(0.575831\pi\)
\(264\) 0 0
\(265\) −0.0624264 −0.00383482
\(266\) 0 0
\(267\) 6.33380 0.387622
\(268\) 0 0
\(269\) 26.2199 1.59866 0.799328 0.600895i \(-0.205189\pi\)
0.799328 + 0.600895i \(0.205189\pi\)
\(270\) 0 0
\(271\) −11.7065 −0.711116 −0.355558 0.934654i \(-0.615709\pi\)
−0.355558 + 0.934654i \(0.615709\pi\)
\(272\) 0 0
\(273\) −1.26094 −0.0763158
\(274\) 0 0
\(275\) 11.3346 0.683501
\(276\) 0 0
\(277\) −23.6846 −1.42307 −0.711536 0.702650i \(-0.752000\pi\)
−0.711536 + 0.702650i \(0.752000\pi\)
\(278\) 0 0
\(279\) 5.13338 0.307328
\(280\) 0 0
\(281\) −2.46117 −0.146821 −0.0734104 0.997302i \(-0.523388\pi\)
−0.0734104 + 0.997302i \(0.523388\pi\)
\(282\) 0 0
\(283\) −28.7555 −1.70934 −0.854668 0.519175i \(-0.826239\pi\)
−0.854668 + 0.519175i \(0.826239\pi\)
\(284\) 0 0
\(285\) −0.0523529 −0.00310112
\(286\) 0 0
\(287\) 13.4305 0.792779
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 4.28456 0.251165
\(292\) 0 0
\(293\) −12.0510 −0.704026 −0.352013 0.935995i \(-0.614503\pi\)
−0.352013 + 0.935995i \(0.614503\pi\)
\(294\) 0 0
\(295\) −0.0220313 −0.00128271
\(296\) 0 0
\(297\) −7.53130 −0.437010
\(298\) 0 0
\(299\) −0.576876 −0.0333616
\(300\) 0 0
\(301\) −38.6627 −2.22848
\(302\) 0 0
\(303\) 7.83439 0.450074
\(304\) 0 0
\(305\) −0.0850457 −0.00486970
\(306\) 0 0
\(307\) −15.0578 −0.859395 −0.429697 0.902973i \(-0.641380\pi\)
−0.429697 + 0.902973i \(0.641380\pi\)
\(308\) 0 0
\(309\) −6.78416 −0.385938
\(310\) 0 0
\(311\) 25.4901 1.44541 0.722705 0.691157i \(-0.242899\pi\)
0.722705 + 0.691157i \(0.242899\pi\)
\(312\) 0 0
\(313\) −8.61581 −0.486994 −0.243497 0.969902i \(-0.578295\pi\)
−0.243497 + 0.969902i \(0.578295\pi\)
\(314\) 0 0
\(315\) −0.187715 −0.0105766
\(316\) 0 0
\(317\) 31.3992 1.76355 0.881777 0.471667i \(-0.156348\pi\)
0.881777 + 0.471667i \(0.156348\pi\)
\(318\) 0 0
\(319\) −7.82973 −0.438381
\(320\) 0 0
\(321\) 8.24834 0.460378
\(322\) 0 0
\(323\) −4.04514 −0.225077
\(324\) 0 0
\(325\) −3.34385 −0.185484
\(326\) 0 0
\(327\) 1.22313 0.0676391
\(328\) 0 0
\(329\) 5.24710 0.289282
\(330\) 0 0
\(331\) −31.9977 −1.75875 −0.879376 0.476128i \(-0.842040\pi\)
−0.879376 + 0.476128i \(0.842040\pi\)
\(332\) 0 0
\(333\) 0.493857 0.0270632
\(334\) 0 0
\(335\) 0.208281 0.0113796
\(336\) 0 0
\(337\) −5.38951 −0.293585 −0.146793 0.989167i \(-0.546895\pi\)
−0.146793 + 0.989167i \(0.546895\pi\)
\(338\) 0 0
\(339\) −3.36896 −0.182977
\(340\) 0 0
\(341\) 4.38361 0.237386
\(342\) 0 0
\(343\) −11.8757 −0.641230
\(344\) 0 0
\(345\) 0.0111627 0.000600981 0
\(346\) 0 0
\(347\) −4.91938 −0.264086 −0.132043 0.991244i \(-0.542154\pi\)
−0.132043 + 0.991244i \(0.542154\pi\)
\(348\) 0 0
\(349\) 24.6544 1.31972 0.659859 0.751389i \(-0.270616\pi\)
0.659859 + 0.751389i \(0.270616\pi\)
\(350\) 0 0
\(351\) 2.22183 0.118593
\(352\) 0 0
\(353\) 25.0436 1.33294 0.666468 0.745534i \(-0.267805\pi\)
0.666468 + 0.745534i \(0.267805\pi\)
\(354\) 0 0
\(355\) 0.181174 0.00961573
\(356\) 0 0
\(357\) 1.88528 0.0997797
\(358\) 0 0
\(359\) −31.0701 −1.63982 −0.819910 0.572493i \(-0.805976\pi\)
−0.819910 + 0.572493i \(0.805976\pi\)
\(360\) 0 0
\(361\) −2.63686 −0.138782
\(362\) 0 0
\(363\) 3.44248 0.180683
\(364\) 0 0
\(365\) −0.100657 −0.00526865
\(366\) 0 0
\(367\) 27.9369 1.45830 0.729148 0.684356i \(-0.239917\pi\)
0.729148 + 0.684356i \(0.239917\pi\)
\(368\) 0 0
\(369\) −11.1105 −0.578389
\(370\) 0 0
\(371\) −9.09363 −0.472118
\(372\) 0 0
\(373\) −6.65809 −0.344743 −0.172371 0.985032i \(-0.555143\pi\)
−0.172371 + 0.985032i \(0.555143\pi\)
\(374\) 0 0
\(375\) 0.129415 0.00668299
\(376\) 0 0
\(377\) 2.30988 0.118965
\(378\) 0 0
\(379\) 2.32357 0.119354 0.0596770 0.998218i \(-0.480993\pi\)
0.0596770 + 0.998218i \(0.480993\pi\)
\(380\) 0 0
\(381\) −1.68764 −0.0864602
\(382\) 0 0
\(383\) 0.571701 0.0292126 0.0146063 0.999893i \(-0.495351\pi\)
0.0146063 + 0.999893i \(0.495351\pi\)
\(384\) 0 0
\(385\) −0.160298 −0.00816954
\(386\) 0 0
\(387\) 31.9839 1.62584
\(388\) 0 0
\(389\) −12.4281 −0.630128 −0.315064 0.949070i \(-0.602026\pi\)
−0.315064 + 0.949070i \(0.602026\pi\)
\(390\) 0 0
\(391\) 0.862508 0.0436189
\(392\) 0 0
\(393\) 6.31620 0.318610
\(394\) 0 0
\(395\) −0.156934 −0.00789621
\(396\) 0 0
\(397\) −13.7171 −0.688444 −0.344222 0.938888i \(-0.611857\pi\)
−0.344222 + 0.938888i \(0.611857\pi\)
\(398\) 0 0
\(399\) −7.62623 −0.381789
\(400\) 0 0
\(401\) −28.5365 −1.42505 −0.712523 0.701649i \(-0.752447\pi\)
−0.712523 + 0.701649i \(0.752447\pi\)
\(402\) 0 0
\(403\) −1.29322 −0.0644200
\(404\) 0 0
\(405\) 0.132480 0.00658300
\(406\) 0 0
\(407\) 0.421725 0.0209041
\(408\) 0 0
\(409\) 27.2128 1.34558 0.672792 0.739832i \(-0.265095\pi\)
0.672792 + 0.739832i \(0.265095\pi\)
\(410\) 0 0
\(411\) 3.40250 0.167833
\(412\) 0 0
\(413\) −3.20930 −0.157919
\(414\) 0 0
\(415\) 0.268384 0.0131745
\(416\) 0 0
\(417\) 8.62803 0.422517
\(418\) 0 0
\(419\) 28.6425 1.39928 0.699638 0.714497i \(-0.253345\pi\)
0.699638 + 0.714497i \(0.253345\pi\)
\(420\) 0 0
\(421\) −16.0563 −0.782536 −0.391268 0.920277i \(-0.627964\pi\)
−0.391268 + 0.920277i \(0.627964\pi\)
\(422\) 0 0
\(423\) −4.34070 −0.211052
\(424\) 0 0
\(425\) 4.99951 0.242512
\(426\) 0 0
\(427\) −12.3886 −0.599525
\(428\) 0 0
\(429\) 0.890766 0.0430066
\(430\) 0 0
\(431\) −23.6386 −1.13863 −0.569316 0.822119i \(-0.692792\pi\)
−0.569316 + 0.822119i \(0.692792\pi\)
\(432\) 0 0
\(433\) 21.5499 1.03562 0.517812 0.855495i \(-0.326747\pi\)
0.517812 + 0.855495i \(0.326747\pi\)
\(434\) 0 0
\(435\) −0.0446968 −0.00214305
\(436\) 0 0
\(437\) −3.48896 −0.166900
\(438\) 0 0
\(439\) −29.4401 −1.40510 −0.702550 0.711634i \(-0.747955\pi\)
−0.702550 + 0.711634i \(0.747955\pi\)
\(440\) 0 0
\(441\) −8.76008 −0.417147
\(442\) 0 0
\(443\) −26.4316 −1.25580 −0.627902 0.778292i \(-0.716086\pi\)
−0.627902 + 0.778292i \(0.716086\pi\)
\(444\) 0 0
\(445\) −0.237541 −0.0112605
\(446\) 0 0
\(447\) −5.10208 −0.241320
\(448\) 0 0
\(449\) −20.3621 −0.960945 −0.480472 0.877010i \(-0.659535\pi\)
−0.480472 + 0.877010i \(0.659535\pi\)
\(450\) 0 0
\(451\) −9.48770 −0.446758
\(452\) 0 0
\(453\) −0.744095 −0.0349606
\(454\) 0 0
\(455\) 0.0472900 0.00221699
\(456\) 0 0
\(457\) −15.6623 −0.732652 −0.366326 0.930487i \(-0.619384\pi\)
−0.366326 + 0.930487i \(0.619384\pi\)
\(458\) 0 0
\(459\) −3.32194 −0.155055
\(460\) 0 0
\(461\) −6.66076 −0.310222 −0.155111 0.987897i \(-0.549574\pi\)
−0.155111 + 0.987897i \(0.549574\pi\)
\(462\) 0 0
\(463\) −11.7428 −0.545733 −0.272867 0.962052i \(-0.587972\pi\)
−0.272867 + 0.962052i \(0.587972\pi\)
\(464\) 0 0
\(465\) 0.0250243 0.00116047
\(466\) 0 0
\(467\) 35.7711 1.65529 0.827645 0.561251i \(-0.189680\pi\)
0.827645 + 0.561251i \(0.189680\pi\)
\(468\) 0 0
\(469\) 30.3402 1.40098
\(470\) 0 0
\(471\) −4.27068 −0.196783
\(472\) 0 0
\(473\) 27.3124 1.25583
\(474\) 0 0
\(475\) −20.2237 −0.927928
\(476\) 0 0
\(477\) 7.52276 0.344444
\(478\) 0 0
\(479\) 37.2951 1.70405 0.852027 0.523497i \(-0.175373\pi\)
0.852027 + 0.523497i \(0.175373\pi\)
\(480\) 0 0
\(481\) −0.124414 −0.00567281
\(482\) 0 0
\(483\) 1.62607 0.0739888
\(484\) 0 0
\(485\) −0.160687 −0.00729641
\(486\) 0 0
\(487\) −28.9086 −1.30997 −0.654986 0.755641i \(-0.727325\pi\)
−0.654986 + 0.755641i \(0.727325\pi\)
\(488\) 0 0
\(489\) 12.0045 0.542861
\(490\) 0 0
\(491\) −1.83672 −0.0828898 −0.0414449 0.999141i \(-0.513196\pi\)
−0.0414449 + 0.999141i \(0.513196\pi\)
\(492\) 0 0
\(493\) −3.45358 −0.155541
\(494\) 0 0
\(495\) 0.132607 0.00596026
\(496\) 0 0
\(497\) 26.3916 1.18382
\(498\) 0 0
\(499\) −22.7204 −1.01711 −0.508553 0.861031i \(-0.669819\pi\)
−0.508553 + 0.861031i \(0.669819\pi\)
\(500\) 0 0
\(501\) 4.86900 0.217531
\(502\) 0 0
\(503\) −13.1563 −0.586610 −0.293305 0.956019i \(-0.594755\pi\)
−0.293305 + 0.956019i \(0.594755\pi\)
\(504\) 0 0
\(505\) −0.293819 −0.0130748
\(506\) 0 0
\(507\) 7.37399 0.327490
\(508\) 0 0
\(509\) 33.8884 1.50208 0.751039 0.660258i \(-0.229553\pi\)
0.751039 + 0.660258i \(0.229553\pi\)
\(510\) 0 0
\(511\) −14.6627 −0.648641
\(512\) 0 0
\(513\) 13.4377 0.593290
\(514\) 0 0
\(515\) 0.254431 0.0112116
\(516\) 0 0
\(517\) −3.70670 −0.163020
\(518\) 0 0
\(519\) −1.55891 −0.0684285
\(520\) 0 0
\(521\) −20.9915 −0.919656 −0.459828 0.888008i \(-0.652089\pi\)
−0.459828 + 0.888008i \(0.652089\pi\)
\(522\) 0 0
\(523\) −13.0870 −0.572253 −0.286127 0.958192i \(-0.592368\pi\)
−0.286127 + 0.958192i \(0.592368\pi\)
\(524\) 0 0
\(525\) 9.42550 0.411362
\(526\) 0 0
\(527\) 1.93354 0.0842265
\(528\) 0 0
\(529\) −22.2561 −0.967656
\(530\) 0 0
\(531\) 2.65491 0.115213
\(532\) 0 0
\(533\) 2.79900 0.121238
\(534\) 0 0
\(535\) −0.309343 −0.0133741
\(536\) 0 0
\(537\) 4.59477 0.198279
\(538\) 0 0
\(539\) −7.48059 −0.322212
\(540\) 0 0
\(541\) −41.6834 −1.79211 −0.896055 0.443943i \(-0.853579\pi\)
−0.896055 + 0.443943i \(0.853579\pi\)
\(542\) 0 0
\(543\) −1.49723 −0.0642524
\(544\) 0 0
\(545\) −0.0458718 −0.00196493
\(546\) 0 0
\(547\) −22.0958 −0.944748 −0.472374 0.881398i \(-0.656603\pi\)
−0.472374 + 0.881398i \(0.656603\pi\)
\(548\) 0 0
\(549\) 10.2485 0.437397
\(550\) 0 0
\(551\) 13.9702 0.595150
\(552\) 0 0
\(553\) −22.8605 −0.972129
\(554\) 0 0
\(555\) 0.00240746 0.000102191 0
\(556\) 0 0
\(557\) −39.8742 −1.68952 −0.844761 0.535143i \(-0.820258\pi\)
−0.844761 + 0.535143i \(0.820258\pi\)
\(558\) 0 0
\(559\) −8.05753 −0.340797
\(560\) 0 0
\(561\) −1.33182 −0.0562293
\(562\) 0 0
\(563\) −36.1017 −1.52151 −0.760753 0.649041i \(-0.775170\pi\)
−0.760753 + 0.649041i \(0.775170\pi\)
\(564\) 0 0
\(565\) 0.126349 0.00531553
\(566\) 0 0
\(567\) 19.2984 0.810455
\(568\) 0 0
\(569\) 17.1387 0.718491 0.359245 0.933243i \(-0.383034\pi\)
0.359245 + 0.933243i \(0.383034\pi\)
\(570\) 0 0
\(571\) −6.15355 −0.257518 −0.128759 0.991676i \(-0.541099\pi\)
−0.128759 + 0.991676i \(0.541099\pi\)
\(572\) 0 0
\(573\) 0.646054 0.0269893
\(574\) 0 0
\(575\) 4.31212 0.179828
\(576\) 0 0
\(577\) 14.1061 0.587247 0.293623 0.955921i \(-0.405139\pi\)
0.293623 + 0.955921i \(0.405139\pi\)
\(578\) 0 0
\(579\) −3.15312 −0.131039
\(580\) 0 0
\(581\) 39.0955 1.62195
\(582\) 0 0
\(583\) 6.42399 0.266055
\(584\) 0 0
\(585\) −0.0391210 −0.00161745
\(586\) 0 0
\(587\) −39.2647 −1.62063 −0.810314 0.585996i \(-0.800704\pi\)
−0.810314 + 0.585996i \(0.800704\pi\)
\(588\) 0 0
\(589\) −7.82145 −0.322277
\(590\) 0 0
\(591\) −13.8921 −0.571443
\(592\) 0 0
\(593\) −44.5835 −1.83082 −0.915412 0.402517i \(-0.868135\pi\)
−0.915412 + 0.402517i \(0.868135\pi\)
\(594\) 0 0
\(595\) −0.0707050 −0.00289862
\(596\) 0 0
\(597\) 3.07493 0.125848
\(598\) 0 0
\(599\) 27.7887 1.13542 0.567708 0.823230i \(-0.307830\pi\)
0.567708 + 0.823230i \(0.307830\pi\)
\(600\) 0 0
\(601\) 46.1392 1.88206 0.941029 0.338325i \(-0.109860\pi\)
0.941029 + 0.338325i \(0.109860\pi\)
\(602\) 0 0
\(603\) −25.0991 −1.02211
\(604\) 0 0
\(605\) −0.129106 −0.00524889
\(606\) 0 0
\(607\) −18.6754 −0.758010 −0.379005 0.925395i \(-0.623734\pi\)
−0.379005 + 0.925395i \(0.623734\pi\)
\(608\) 0 0
\(609\) −6.51097 −0.263838
\(610\) 0 0
\(611\) 1.09353 0.0442393
\(612\) 0 0
\(613\) 1.96387 0.0793199 0.0396599 0.999213i \(-0.487373\pi\)
0.0396599 + 0.999213i \(0.487373\pi\)
\(614\) 0 0
\(615\) −0.0541615 −0.00218400
\(616\) 0 0
\(617\) 18.9598 0.763291 0.381646 0.924309i \(-0.375358\pi\)
0.381646 + 0.924309i \(0.375358\pi\)
\(618\) 0 0
\(619\) −40.0582 −1.61007 −0.805037 0.593225i \(-0.797855\pi\)
−0.805037 + 0.593225i \(0.797855\pi\)
\(620\) 0 0
\(621\) −2.86520 −0.114977
\(622\) 0 0
\(623\) −34.6025 −1.38632
\(624\) 0 0
\(625\) 24.9927 0.999709
\(626\) 0 0
\(627\) 5.38738 0.215151
\(628\) 0 0
\(629\) 0.186016 0.00741696
\(630\) 0 0
\(631\) 36.0631 1.43565 0.717824 0.696225i \(-0.245138\pi\)
0.717824 + 0.696225i \(0.245138\pi\)
\(632\) 0 0
\(633\) 5.96717 0.237174
\(634\) 0 0
\(635\) 0.0632926 0.00251169
\(636\) 0 0
\(637\) 2.20687 0.0874396
\(638\) 0 0
\(639\) −21.8326 −0.863685
\(640\) 0 0
\(641\) −3.46753 −0.136959 −0.0684795 0.997653i \(-0.521815\pi\)
−0.0684795 + 0.997653i \(0.521815\pi\)
\(642\) 0 0
\(643\) −21.2150 −0.836640 −0.418320 0.908300i \(-0.637381\pi\)
−0.418320 + 0.908300i \(0.637381\pi\)
\(644\) 0 0
\(645\) 0.155916 0.00613917
\(646\) 0 0
\(647\) 4.77756 0.187825 0.0939127 0.995580i \(-0.470063\pi\)
0.0939127 + 0.995580i \(0.470063\pi\)
\(648\) 0 0
\(649\) 2.26714 0.0889929
\(650\) 0 0
\(651\) 3.64527 0.142870
\(652\) 0 0
\(653\) −14.5540 −0.569541 −0.284770 0.958596i \(-0.591917\pi\)
−0.284770 + 0.958596i \(0.591917\pi\)
\(654\) 0 0
\(655\) −0.236881 −0.00925570
\(656\) 0 0
\(657\) 12.1298 0.473230
\(658\) 0 0
\(659\) −8.16041 −0.317885 −0.158942 0.987288i \(-0.550808\pi\)
−0.158942 + 0.987288i \(0.550808\pi\)
\(660\) 0 0
\(661\) 46.3821 1.80405 0.902027 0.431680i \(-0.142079\pi\)
0.902027 + 0.431680i \(0.142079\pi\)
\(662\) 0 0
\(663\) 0.392904 0.0152591
\(664\) 0 0
\(665\) 0.286012 0.0110911
\(666\) 0 0
\(667\) −2.97874 −0.115337
\(668\) 0 0
\(669\) 9.41820 0.364129
\(670\) 0 0
\(671\) 8.75164 0.337853
\(672\) 0 0
\(673\) 21.6579 0.834849 0.417424 0.908712i \(-0.362933\pi\)
0.417424 + 0.908712i \(0.362933\pi\)
\(674\) 0 0
\(675\) −16.6081 −0.639246
\(676\) 0 0
\(677\) −14.8507 −0.570757 −0.285379 0.958415i \(-0.592119\pi\)
−0.285379 + 0.958415i \(0.592119\pi\)
\(678\) 0 0
\(679\) −23.4072 −0.898285
\(680\) 0 0
\(681\) 4.46556 0.171121
\(682\) 0 0
\(683\) −26.9919 −1.03281 −0.516407 0.856343i \(-0.672731\pi\)
−0.516407 + 0.856343i \(0.672731\pi\)
\(684\) 0 0
\(685\) −0.127606 −0.00487558
\(686\) 0 0
\(687\) −3.77718 −0.144108
\(688\) 0 0
\(689\) −1.89516 −0.0722000
\(690\) 0 0
\(691\) −12.4106 −0.472121 −0.236060 0.971738i \(-0.575856\pi\)
−0.236060 + 0.971738i \(0.575856\pi\)
\(692\) 0 0
\(693\) 19.3169 0.733788
\(694\) 0 0
\(695\) −0.323583 −0.0122742
\(696\) 0 0
\(697\) −4.18488 −0.158514
\(698\) 0 0
\(699\) 10.6393 0.402414
\(700\) 0 0
\(701\) −47.8478 −1.80719 −0.903594 0.428390i \(-0.859081\pi\)
−0.903594 + 0.428390i \(0.859081\pi\)
\(702\) 0 0
\(703\) −0.752462 −0.0283797
\(704\) 0 0
\(705\) −0.0211601 −0.000796934 0
\(706\) 0 0
\(707\) −42.8005 −1.60968
\(708\) 0 0
\(709\) −21.9427 −0.824077 −0.412038 0.911166i \(-0.635183\pi\)
−0.412038 + 0.911166i \(0.635183\pi\)
\(710\) 0 0
\(711\) 18.9115 0.709237
\(712\) 0 0
\(713\) 1.66770 0.0624557
\(714\) 0 0
\(715\) −0.0334070 −0.00124935
\(716\) 0 0
\(717\) −13.0206 −0.486262
\(718\) 0 0
\(719\) 18.7010 0.697431 0.348716 0.937229i \(-0.386618\pi\)
0.348716 + 0.937229i \(0.386618\pi\)
\(720\) 0 0
\(721\) 37.0629 1.38029
\(722\) 0 0
\(723\) −13.8543 −0.515248
\(724\) 0 0
\(725\) −17.2662 −0.641251
\(726\) 0 0
\(727\) 13.6358 0.505724 0.252862 0.967502i \(-0.418628\pi\)
0.252862 + 0.967502i \(0.418628\pi\)
\(728\) 0 0
\(729\) −10.1103 −0.374456
\(730\) 0 0
\(731\) 12.0471 0.445578
\(732\) 0 0
\(733\) −4.42271 −0.163357 −0.0816783 0.996659i \(-0.526028\pi\)
−0.0816783 + 0.996659i \(0.526028\pi\)
\(734\) 0 0
\(735\) −0.0427037 −0.00157515
\(736\) 0 0
\(737\) −21.4331 −0.789500
\(738\) 0 0
\(739\) −15.6163 −0.574454 −0.287227 0.957863i \(-0.592733\pi\)
−0.287227 + 0.957863i \(0.592733\pi\)
\(740\) 0 0
\(741\) −1.58935 −0.0583862
\(742\) 0 0
\(743\) −26.4436 −0.970121 −0.485061 0.874481i \(-0.661202\pi\)
−0.485061 + 0.874481i \(0.661202\pi\)
\(744\) 0 0
\(745\) 0.191347 0.00701041
\(746\) 0 0
\(747\) −32.3420 −1.18333
\(748\) 0 0
\(749\) −45.0619 −1.64653
\(750\) 0 0
\(751\) 6.77317 0.247156 0.123578 0.992335i \(-0.460563\pi\)
0.123578 + 0.992335i \(0.460563\pi\)
\(752\) 0 0
\(753\) 3.09880 0.112926
\(754\) 0 0
\(755\) 0.0279063 0.00101561
\(756\) 0 0
\(757\) −35.3066 −1.28324 −0.641620 0.767023i \(-0.721737\pi\)
−0.641620 + 0.767023i \(0.721737\pi\)
\(758\) 0 0
\(759\) −1.14870 −0.0416952
\(760\) 0 0
\(761\) −3.08997 −0.112011 −0.0560057 0.998430i \(-0.517837\pi\)
−0.0560057 + 0.998430i \(0.517837\pi\)
\(762\) 0 0
\(763\) −6.68213 −0.241909
\(764\) 0 0
\(765\) 0.0584912 0.00211475
\(766\) 0 0
\(767\) −0.668836 −0.0241503
\(768\) 0 0
\(769\) −16.9659 −0.611805 −0.305903 0.952063i \(-0.598958\pi\)
−0.305903 + 0.952063i \(0.598958\pi\)
\(770\) 0 0
\(771\) −6.10685 −0.219933
\(772\) 0 0
\(773\) −32.0456 −1.15260 −0.576299 0.817239i \(-0.695504\pi\)
−0.576299 + 0.817239i \(0.695504\pi\)
\(774\) 0 0
\(775\) 9.66678 0.347241
\(776\) 0 0
\(777\) 0.350694 0.0125811
\(778\) 0 0
\(779\) 16.9284 0.606524
\(780\) 0 0
\(781\) −18.6438 −0.667126
\(782\) 0 0
\(783\) 11.4726 0.409997
\(784\) 0 0
\(785\) 0.160166 0.00571658
\(786\) 0 0
\(787\) −5.19384 −0.185140 −0.0925701 0.995706i \(-0.529508\pi\)
−0.0925701 + 0.995706i \(0.529508\pi\)
\(788\) 0 0
\(789\) 4.49632 0.160073
\(790\) 0 0
\(791\) 18.4052 0.654412
\(792\) 0 0
\(793\) −2.58185 −0.0916842
\(794\) 0 0
\(795\) 0.0366720 0.00130062
\(796\) 0 0
\(797\) 44.2619 1.56784 0.783919 0.620863i \(-0.213218\pi\)
0.783919 + 0.620863i \(0.213218\pi\)
\(798\) 0 0
\(799\) −1.63497 −0.0578411
\(800\) 0 0
\(801\) 28.6251 1.01142
\(802\) 0 0
\(803\) 10.3582 0.365532
\(804\) 0 0
\(805\) −0.0609837 −0.00214939
\(806\) 0 0
\(807\) −15.4027 −0.542202
\(808\) 0 0
\(809\) 45.1742 1.58824 0.794120 0.607761i \(-0.207932\pi\)
0.794120 + 0.607761i \(0.207932\pi\)
\(810\) 0 0
\(811\) 39.4189 1.38419 0.692093 0.721808i \(-0.256689\pi\)
0.692093 + 0.721808i \(0.256689\pi\)
\(812\) 0 0
\(813\) 6.87689 0.241183
\(814\) 0 0
\(815\) −0.450212 −0.0157702
\(816\) 0 0
\(817\) −48.7322 −1.70492
\(818\) 0 0
\(819\) −5.69874 −0.199130
\(820\) 0 0
\(821\) −7.04745 −0.245958 −0.122979 0.992409i \(-0.539245\pi\)
−0.122979 + 0.992409i \(0.539245\pi\)
\(822\) 0 0
\(823\) 6.13057 0.213698 0.106849 0.994275i \(-0.465924\pi\)
0.106849 + 0.994275i \(0.465924\pi\)
\(824\) 0 0
\(825\) −6.65843 −0.231817
\(826\) 0 0
\(827\) −32.0038 −1.11288 −0.556440 0.830888i \(-0.687833\pi\)
−0.556440 + 0.830888i \(0.687833\pi\)
\(828\) 0 0
\(829\) 42.9441 1.49151 0.745755 0.666220i \(-0.232089\pi\)
0.745755 + 0.666220i \(0.232089\pi\)
\(830\) 0 0
\(831\) 13.9134 0.482650
\(832\) 0 0
\(833\) −3.29958 −0.114324
\(834\) 0 0
\(835\) −0.182606 −0.00631933
\(836\) 0 0
\(837\) −6.42312 −0.222016
\(838\) 0 0
\(839\) −19.3461 −0.667902 −0.333951 0.942590i \(-0.608382\pi\)
−0.333951 + 0.942590i \(0.608382\pi\)
\(840\) 0 0
\(841\) −17.0728 −0.588717
\(842\) 0 0
\(843\) 1.44580 0.0497959
\(844\) 0 0
\(845\) −0.276552 −0.00951367
\(846\) 0 0
\(847\) −18.8068 −0.646209
\(848\) 0 0
\(849\) 16.8922 0.579740
\(850\) 0 0
\(851\) 0.160441 0.00549984
\(852\) 0 0
\(853\) −15.6761 −0.536738 −0.268369 0.963316i \(-0.586485\pi\)
−0.268369 + 0.963316i \(0.586485\pi\)
\(854\) 0 0
\(855\) −0.236605 −0.00809171
\(856\) 0 0
\(857\) 30.5849 1.04476 0.522381 0.852712i \(-0.325044\pi\)
0.522381 + 0.852712i \(0.325044\pi\)
\(858\) 0 0
\(859\) −35.2599 −1.20305 −0.601526 0.798853i \(-0.705440\pi\)
−0.601526 + 0.798853i \(0.705440\pi\)
\(860\) 0 0
\(861\) −7.88969 −0.268880
\(862\) 0 0
\(863\) 39.9765 1.36082 0.680408 0.732833i \(-0.261802\pi\)
0.680408 + 0.732833i \(0.261802\pi\)
\(864\) 0 0
\(865\) 0.0584648 0.00198786
\(866\) 0 0
\(867\) −0.587444 −0.0199507
\(868\) 0 0
\(869\) 16.1493 0.547828
\(870\) 0 0
\(871\) 6.32307 0.214249
\(872\) 0 0
\(873\) 19.3637 0.655363
\(874\) 0 0
\(875\) −0.707016 −0.0239015
\(876\) 0 0
\(877\) −25.1404 −0.848933 −0.424466 0.905444i \(-0.639538\pi\)
−0.424466 + 0.905444i \(0.639538\pi\)
\(878\) 0 0
\(879\) 7.07928 0.238778
\(880\) 0 0
\(881\) −0.314416 −0.0105930 −0.00529648 0.999986i \(-0.501686\pi\)
−0.00529648 + 0.999986i \(0.501686\pi\)
\(882\) 0 0
\(883\) −10.9791 −0.369476 −0.184738 0.982788i \(-0.559144\pi\)
−0.184738 + 0.982788i \(0.559144\pi\)
\(884\) 0 0
\(885\) 0.0129422 0.000435046 0
\(886\) 0 0
\(887\) 1.95616 0.0656814 0.0328407 0.999461i \(-0.489545\pi\)
0.0328407 + 0.999461i \(0.489545\pi\)
\(888\) 0 0
\(889\) 9.21981 0.309223
\(890\) 0 0
\(891\) −13.6329 −0.456719
\(892\) 0 0
\(893\) 6.61368 0.221318
\(894\) 0 0
\(895\) −0.172321 −0.00576004
\(896\) 0 0
\(897\) 0.338883 0.0113150
\(898\) 0 0
\(899\) −6.67764 −0.222712
\(900\) 0 0
\(901\) 2.83353 0.0943985
\(902\) 0 0
\(903\) 22.7122 0.755814
\(904\) 0 0
\(905\) 0.0561518 0.00186655
\(906\) 0 0
\(907\) 12.4367 0.412953 0.206477 0.978452i \(-0.433800\pi\)
0.206477 + 0.978452i \(0.433800\pi\)
\(908\) 0 0
\(909\) 35.4069 1.17437
\(910\) 0 0
\(911\) 37.7372 1.25029 0.625145 0.780509i \(-0.285040\pi\)
0.625145 + 0.780509i \(0.285040\pi\)
\(912\) 0 0
\(913\) −27.6181 −0.914027
\(914\) 0 0
\(915\) 0.0499596 0.00165161
\(916\) 0 0
\(917\) −34.5064 −1.13950
\(918\) 0 0
\(919\) −14.8519 −0.489919 −0.244959 0.969533i \(-0.578775\pi\)
−0.244959 + 0.969533i \(0.578775\pi\)
\(920\) 0 0
\(921\) 8.84562 0.291473
\(922\) 0 0
\(923\) 5.50016 0.181040
\(924\) 0 0
\(925\) 0.929992 0.0305780
\(926\) 0 0
\(927\) −30.6605 −1.00702
\(928\) 0 0
\(929\) 35.6437 1.16943 0.584716 0.811238i \(-0.301206\pi\)
0.584716 + 0.811238i \(0.301206\pi\)
\(930\) 0 0
\(931\) 13.3472 0.437438
\(932\) 0 0
\(933\) −14.9740 −0.490227
\(934\) 0 0
\(935\) 0.0499480 0.00163347
\(936\) 0 0
\(937\) −34.5065 −1.12728 −0.563639 0.826021i \(-0.690599\pi\)
−0.563639 + 0.826021i \(0.690599\pi\)
\(938\) 0 0
\(939\) 5.06131 0.165169
\(940\) 0 0
\(941\) 1.45761 0.0475166 0.0237583 0.999718i \(-0.492437\pi\)
0.0237583 + 0.999718i \(0.492437\pi\)
\(942\) 0 0
\(943\) −3.60950 −0.117541
\(944\) 0 0
\(945\) 0.234878 0.00764059
\(946\) 0 0
\(947\) 29.1014 0.945668 0.472834 0.881151i \(-0.343231\pi\)
0.472834 + 0.881151i \(0.343231\pi\)
\(948\) 0 0
\(949\) −3.05580 −0.0991954
\(950\) 0 0
\(951\) −18.4453 −0.598129
\(952\) 0 0
\(953\) 16.2520 0.526455 0.263227 0.964734i \(-0.415213\pi\)
0.263227 + 0.964734i \(0.415213\pi\)
\(954\) 0 0
\(955\) −0.0242294 −0.000784045 0
\(956\) 0 0
\(957\) 4.59953 0.148682
\(958\) 0 0
\(959\) −18.5883 −0.600249
\(960\) 0 0
\(961\) −27.2614 −0.879400
\(962\) 0 0
\(963\) 37.2778 1.20126
\(964\) 0 0
\(965\) 0.118253 0.00380671
\(966\) 0 0
\(967\) 27.3371 0.879100 0.439550 0.898218i \(-0.355138\pi\)
0.439550 + 0.898218i \(0.355138\pi\)
\(968\) 0 0
\(969\) 2.37629 0.0763375
\(970\) 0 0
\(971\) 12.8321 0.411802 0.205901 0.978573i \(-0.433987\pi\)
0.205901 + 0.978573i \(0.433987\pi\)
\(972\) 0 0
\(973\) −47.1362 −1.51112
\(974\) 0 0
\(975\) 1.96433 0.0629088
\(976\) 0 0
\(977\) 18.5025 0.591946 0.295973 0.955196i \(-0.404356\pi\)
0.295973 + 0.955196i \(0.404356\pi\)
\(978\) 0 0
\(979\) 24.4442 0.781239
\(980\) 0 0
\(981\) 5.52783 0.176490
\(982\) 0 0
\(983\) 46.8957 1.49574 0.747870 0.663845i \(-0.231076\pi\)
0.747870 + 0.663845i \(0.231076\pi\)
\(984\) 0 0
\(985\) 0.521004 0.0166006
\(986\) 0 0
\(987\) −3.08238 −0.0981132
\(988\) 0 0
\(989\) 10.3907 0.330406
\(990\) 0 0
\(991\) 50.5570 1.60600 0.802998 0.595982i \(-0.203237\pi\)
0.802998 + 0.595982i \(0.203237\pi\)
\(992\) 0 0
\(993\) 18.7969 0.596500
\(994\) 0 0
\(995\) −0.115321 −0.00365593
\(996\) 0 0
\(997\) 27.9125 0.883998 0.441999 0.897016i \(-0.354270\pi\)
0.441999 + 0.897016i \(0.354270\pi\)
\(998\) 0 0
\(999\) −0.617936 −0.0195506
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 \(a_p\))