Properties

Label 8001.2.a.u.1.7
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-0.432278\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.432278 q^{2} -1.81314 q^{4} +4.10000 q^{5} +1.00000 q^{7} +1.64833 q^{8} +O(q^{10})\) \(q-0.432278 q^{2} -1.81314 q^{4} +4.10000 q^{5} +1.00000 q^{7} +1.64833 q^{8} -1.77234 q^{10} -2.19453 q^{11} -2.36622 q^{13} -0.432278 q^{14} +2.91373 q^{16} +2.91068 q^{17} +6.73030 q^{19} -7.43385 q^{20} +0.948646 q^{22} -4.56353 q^{23} +11.8100 q^{25} +1.02287 q^{26} -1.81314 q^{28} +4.17078 q^{29} -0.485432 q^{31} -4.55621 q^{32} -1.25822 q^{34} +4.10000 q^{35} +5.48926 q^{37} -2.90936 q^{38} +6.75816 q^{40} -10.6000 q^{41} -6.67190 q^{43} +3.97898 q^{44} +1.97271 q^{46} +10.8486 q^{47} +1.00000 q^{49} -5.10519 q^{50} +4.29028 q^{52} +9.15995 q^{53} -8.99757 q^{55} +1.64833 q^{56} -1.80293 q^{58} +1.66364 q^{59} -14.4307 q^{61} +0.209841 q^{62} -3.85792 q^{64} -9.70151 q^{65} +14.4051 q^{67} -5.27746 q^{68} -1.77234 q^{70} -2.63479 q^{71} -0.610455 q^{73} -2.37288 q^{74} -12.2029 q^{76} -2.19453 q^{77} -7.36638 q^{79} +11.9463 q^{80} +4.58214 q^{82} +11.0482 q^{83} +11.9338 q^{85} +2.88412 q^{86} -3.61732 q^{88} +7.36625 q^{89} -2.36622 q^{91} +8.27431 q^{92} -4.68960 q^{94} +27.5942 q^{95} +10.8692 q^{97} -0.432278 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} + O(q^{10}) \) \( 18q + 6q^{2} + 22q^{4} + 10q^{5} + 18q^{7} + 21q^{8} - 4q^{10} + 9q^{11} - 25q^{13} + 6q^{14} + 34q^{16} + 17q^{17} - 5q^{19} + 21q^{20} + 5q^{22} + 14q^{23} + 28q^{25} + 8q^{26} + 22q^{28} + 17q^{29} + 5q^{31} + 53q^{32} - 19q^{34} + 10q^{35} - 15q^{37} + 22q^{38} - q^{40} + 17q^{41} + q^{43} + 33q^{44} + 10q^{46} + 31q^{47} + 18q^{49} + 35q^{50} - 70q^{52} + 35q^{53} + 4q^{55} + 21q^{56} + 3q^{58} + 46q^{59} - 5q^{61} + 10q^{62} + 63q^{64} + 12q^{65} + 6q^{67} + 56q^{68} - 4q^{70} + 22q^{71} - 16q^{73} - 18q^{74} + 32q^{76} + 9q^{77} + 46q^{79} + 30q^{80} - 12q^{82} + 46q^{83} + 4q^{85} - 18q^{86} + 30q^{88} + 42q^{89} - 25q^{91} + 48q^{92} + 3q^{94} + 2q^{95} - 35q^{97} + 6q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.432278 −0.305667 −0.152833 0.988252i \(-0.548840\pi\)
−0.152833 + 0.988252i \(0.548840\pi\)
\(3\) 0 0
\(4\) −1.81314 −0.906568
\(5\) 4.10000 1.83357 0.916787 0.399376i \(-0.130773\pi\)
0.916787 + 0.399376i \(0.130773\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.64833 0.582774
\(9\) 0 0
\(10\) −1.77234 −0.560462
\(11\) −2.19453 −0.661676 −0.330838 0.943688i \(-0.607331\pi\)
−0.330838 + 0.943688i \(0.607331\pi\)
\(12\) 0 0
\(13\) −2.36622 −0.656272 −0.328136 0.944631i \(-0.606420\pi\)
−0.328136 + 0.944631i \(0.606420\pi\)
\(14\) −0.432278 −0.115531
\(15\) 0 0
\(16\) 2.91373 0.728433
\(17\) 2.91068 0.705944 0.352972 0.935634i \(-0.385171\pi\)
0.352972 + 0.935634i \(0.385171\pi\)
\(18\) 0 0
\(19\) 6.73030 1.54404 0.772018 0.635601i \(-0.219247\pi\)
0.772018 + 0.635601i \(0.219247\pi\)
\(20\) −7.43385 −1.66226
\(21\) 0 0
\(22\) 0.948646 0.202252
\(23\) −4.56353 −0.951563 −0.475781 0.879564i \(-0.657835\pi\)
−0.475781 + 0.879564i \(0.657835\pi\)
\(24\) 0 0
\(25\) 11.8100 2.36200
\(26\) 1.02287 0.200600
\(27\) 0 0
\(28\) −1.81314 −0.342650
\(29\) 4.17078 0.774494 0.387247 0.921976i \(-0.373426\pi\)
0.387247 + 0.921976i \(0.373426\pi\)
\(30\) 0 0
\(31\) −0.485432 −0.0871861 −0.0435931 0.999049i \(-0.513881\pi\)
−0.0435931 + 0.999049i \(0.513881\pi\)
\(32\) −4.55621 −0.805432
\(33\) 0 0
\(34\) −1.25822 −0.215783
\(35\) 4.10000 0.693026
\(36\) 0 0
\(37\) 5.48926 0.902428 0.451214 0.892416i \(-0.350991\pi\)
0.451214 + 0.892416i \(0.350991\pi\)
\(38\) −2.90936 −0.471960
\(39\) 0 0
\(40\) 6.75816 1.06856
\(41\) −10.6000 −1.65544 −0.827721 0.561140i \(-0.810363\pi\)
−0.827721 + 0.561140i \(0.810363\pi\)
\(42\) 0 0
\(43\) −6.67190 −1.01746 −0.508728 0.860927i \(-0.669884\pi\)
−0.508728 + 0.860927i \(0.669884\pi\)
\(44\) 3.97898 0.599854
\(45\) 0 0
\(46\) 1.97271 0.290861
\(47\) 10.8486 1.58243 0.791215 0.611538i \(-0.209449\pi\)
0.791215 + 0.611538i \(0.209449\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −5.10519 −0.721983
\(51\) 0 0
\(52\) 4.29028 0.594955
\(53\) 9.15995 1.25822 0.629108 0.777318i \(-0.283420\pi\)
0.629108 + 0.777318i \(0.283420\pi\)
\(54\) 0 0
\(55\) −8.99757 −1.21323
\(56\) 1.64833 0.220268
\(57\) 0 0
\(58\) −1.80293 −0.236737
\(59\) 1.66364 0.216587 0.108293 0.994119i \(-0.465461\pi\)
0.108293 + 0.994119i \(0.465461\pi\)
\(60\) 0 0
\(61\) −14.4307 −1.84766 −0.923830 0.382803i \(-0.874959\pi\)
−0.923830 + 0.382803i \(0.874959\pi\)
\(62\) 0.209841 0.0266499
\(63\) 0 0
\(64\) −3.85792 −0.482240
\(65\) −9.70151 −1.20332
\(66\) 0 0
\(67\) 14.4051 1.75987 0.879933 0.475097i \(-0.157587\pi\)
0.879933 + 0.475097i \(0.157587\pi\)
\(68\) −5.27746 −0.639986
\(69\) 0 0
\(70\) −1.77234 −0.211835
\(71\) −2.63479 −0.312693 −0.156346 0.987702i \(-0.549972\pi\)
−0.156346 + 0.987702i \(0.549972\pi\)
\(72\) 0 0
\(73\) −0.610455 −0.0714484 −0.0357242 0.999362i \(-0.511374\pi\)
−0.0357242 + 0.999362i \(0.511374\pi\)
\(74\) −2.37288 −0.275842
\(75\) 0 0
\(76\) −12.2029 −1.39977
\(77\) −2.19453 −0.250090
\(78\) 0 0
\(79\) −7.36638 −0.828783 −0.414391 0.910099i \(-0.636006\pi\)
−0.414391 + 0.910099i \(0.636006\pi\)
\(80\) 11.9463 1.33564
\(81\) 0 0
\(82\) 4.58214 0.506013
\(83\) 11.0482 1.21269 0.606346 0.795201i \(-0.292634\pi\)
0.606346 + 0.795201i \(0.292634\pi\)
\(84\) 0 0
\(85\) 11.9338 1.29440
\(86\) 2.88412 0.311002
\(87\) 0 0
\(88\) −3.61732 −0.385607
\(89\) 7.36625 0.780821 0.390411 0.920641i \(-0.372333\pi\)
0.390411 + 0.920641i \(0.372333\pi\)
\(90\) 0 0
\(91\) −2.36622 −0.248047
\(92\) 8.27431 0.862656
\(93\) 0 0
\(94\) −4.68960 −0.483696
\(95\) 27.5942 2.83111
\(96\) 0 0
\(97\) 10.8692 1.10360 0.551799 0.833977i \(-0.313941\pi\)
0.551799 + 0.833977i \(0.313941\pi\)
\(98\) −0.432278 −0.0436666
\(99\) 0 0
\(100\) −21.4131 −2.14131
\(101\) −19.7064 −1.96086 −0.980432 0.196857i \(-0.936927\pi\)
−0.980432 + 0.196857i \(0.936927\pi\)
\(102\) 0 0
\(103\) −0.487774 −0.0480618 −0.0240309 0.999711i \(-0.507650\pi\)
−0.0240309 + 0.999711i \(0.507650\pi\)
\(104\) −3.90032 −0.382458
\(105\) 0 0
\(106\) −3.95964 −0.384594
\(107\) 13.5828 1.31310 0.656550 0.754283i \(-0.272015\pi\)
0.656550 + 0.754283i \(0.272015\pi\)
\(108\) 0 0
\(109\) 17.7637 1.70146 0.850729 0.525604i \(-0.176161\pi\)
0.850729 + 0.525604i \(0.176161\pi\)
\(110\) 3.88945 0.370844
\(111\) 0 0
\(112\) 2.91373 0.275322
\(113\) −12.6518 −1.19019 −0.595093 0.803657i \(-0.702885\pi\)
−0.595093 + 0.803657i \(0.702885\pi\)
\(114\) 0 0
\(115\) −18.7105 −1.74476
\(116\) −7.56219 −0.702132
\(117\) 0 0
\(118\) −0.719152 −0.0662033
\(119\) 2.91068 0.266822
\(120\) 0 0
\(121\) −6.18404 −0.562185
\(122\) 6.23806 0.564768
\(123\) 0 0
\(124\) 0.880154 0.0790402
\(125\) 27.9209 2.49732
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 10.7801 0.952836
\(129\) 0 0
\(130\) 4.19374 0.367816
\(131\) 6.74380 0.589209 0.294604 0.955619i \(-0.404812\pi\)
0.294604 + 0.955619i \(0.404812\pi\)
\(132\) 0 0
\(133\) 6.73030 0.583591
\(134\) −6.22702 −0.537932
\(135\) 0 0
\(136\) 4.79777 0.411406
\(137\) −4.74982 −0.405805 −0.202902 0.979199i \(-0.565037\pi\)
−0.202902 + 0.979199i \(0.565037\pi\)
\(138\) 0 0
\(139\) −2.17516 −0.184495 −0.0922473 0.995736i \(-0.529405\pi\)
−0.0922473 + 0.995736i \(0.529405\pi\)
\(140\) −7.43385 −0.628275
\(141\) 0 0
\(142\) 1.13896 0.0955796
\(143\) 5.19274 0.434239
\(144\) 0 0
\(145\) 17.1002 1.42009
\(146\) 0.263886 0.0218394
\(147\) 0 0
\(148\) −9.95277 −0.818113
\(149\) −4.19763 −0.343883 −0.171941 0.985107i \(-0.555004\pi\)
−0.171941 + 0.985107i \(0.555004\pi\)
\(150\) 0 0
\(151\) 15.4354 1.25612 0.628059 0.778166i \(-0.283850\pi\)
0.628059 + 0.778166i \(0.283850\pi\)
\(152\) 11.0938 0.899824
\(153\) 0 0
\(154\) 0.948646 0.0764441
\(155\) −1.99027 −0.159862
\(156\) 0 0
\(157\) −9.92564 −0.792152 −0.396076 0.918218i \(-0.629628\pi\)
−0.396076 + 0.918218i \(0.629628\pi\)
\(158\) 3.18432 0.253331
\(159\) 0 0
\(160\) −18.6805 −1.47682
\(161\) −4.56353 −0.359657
\(162\) 0 0
\(163\) −11.6931 −0.915875 −0.457938 0.888984i \(-0.651412\pi\)
−0.457938 + 0.888984i \(0.651412\pi\)
\(164\) 19.2192 1.50077
\(165\) 0 0
\(166\) −4.77587 −0.370680
\(167\) 15.2201 1.17776 0.588882 0.808219i \(-0.299568\pi\)
0.588882 + 0.808219i \(0.299568\pi\)
\(168\) 0 0
\(169\) −7.40099 −0.569307
\(170\) −5.15871 −0.395655
\(171\) 0 0
\(172\) 12.0971 0.922393
\(173\) 15.7272 1.19572 0.597858 0.801602i \(-0.296018\pi\)
0.597858 + 0.801602i \(0.296018\pi\)
\(174\) 0 0
\(175\) 11.8100 0.892751
\(176\) −6.39428 −0.481987
\(177\) 0 0
\(178\) −3.18427 −0.238671
\(179\) 3.56031 0.266110 0.133055 0.991109i \(-0.457521\pi\)
0.133055 + 0.991109i \(0.457521\pi\)
\(180\) 0 0
\(181\) −12.1994 −0.906777 −0.453389 0.891313i \(-0.649785\pi\)
−0.453389 + 0.891313i \(0.649785\pi\)
\(182\) 1.02287 0.0758198
\(183\) 0 0
\(184\) −7.52223 −0.554546
\(185\) 22.5059 1.65467
\(186\) 0 0
\(187\) −6.38758 −0.467106
\(188\) −19.6700 −1.43458
\(189\) 0 0
\(190\) −11.9284 −0.865374
\(191\) 14.2793 1.03322 0.516608 0.856222i \(-0.327194\pi\)
0.516608 + 0.856222i \(0.327194\pi\)
\(192\) 0 0
\(193\) −14.3589 −1.03358 −0.516789 0.856113i \(-0.672873\pi\)
−0.516789 + 0.856113i \(0.672873\pi\)
\(194\) −4.69851 −0.337333
\(195\) 0 0
\(196\) −1.81314 −0.129510
\(197\) 24.3173 1.73254 0.866269 0.499578i \(-0.166512\pi\)
0.866269 + 0.499578i \(0.166512\pi\)
\(198\) 0 0
\(199\) −7.20059 −0.510437 −0.255218 0.966883i \(-0.582147\pi\)
−0.255218 + 0.966883i \(0.582147\pi\)
\(200\) 19.4668 1.37651
\(201\) 0 0
\(202\) 8.51866 0.599371
\(203\) 4.17078 0.292731
\(204\) 0 0
\(205\) −43.4600 −3.03538
\(206\) 0.210854 0.0146909
\(207\) 0 0
\(208\) −6.89454 −0.478050
\(209\) −14.7698 −1.02165
\(210\) 0 0
\(211\) 18.6526 1.28410 0.642048 0.766665i \(-0.278085\pi\)
0.642048 + 0.766665i \(0.278085\pi\)
\(212\) −16.6082 −1.14066
\(213\) 0 0
\(214\) −5.87155 −0.401371
\(215\) −27.3548 −1.86558
\(216\) 0 0
\(217\) −0.485432 −0.0329533
\(218\) −7.67887 −0.520079
\(219\) 0 0
\(220\) 16.3138 1.09988
\(221\) −6.88732 −0.463291
\(222\) 0 0
\(223\) −13.2348 −0.886265 −0.443132 0.896456i \(-0.646133\pi\)
−0.443132 + 0.896456i \(0.646133\pi\)
\(224\) −4.55621 −0.304425
\(225\) 0 0
\(226\) 5.46911 0.363800
\(227\) 9.57693 0.635643 0.317822 0.948151i \(-0.397049\pi\)
0.317822 + 0.948151i \(0.397049\pi\)
\(228\) 0 0
\(229\) 12.0868 0.798717 0.399358 0.916795i \(-0.369233\pi\)
0.399358 + 0.916795i \(0.369233\pi\)
\(230\) 8.08812 0.533315
\(231\) 0 0
\(232\) 6.87484 0.451355
\(233\) −2.80656 −0.183864 −0.0919321 0.995765i \(-0.529304\pi\)
−0.0919321 + 0.995765i \(0.529304\pi\)
\(234\) 0 0
\(235\) 44.4792 2.90150
\(236\) −3.01640 −0.196351
\(237\) 0 0
\(238\) −1.25822 −0.0815584
\(239\) −9.56442 −0.618671 −0.309335 0.950953i \(-0.600107\pi\)
−0.309335 + 0.950953i \(0.600107\pi\)
\(240\) 0 0
\(241\) 12.4142 0.799668 0.399834 0.916588i \(-0.369068\pi\)
0.399834 + 0.916588i \(0.369068\pi\)
\(242\) 2.67322 0.171841
\(243\) 0 0
\(244\) 26.1648 1.67503
\(245\) 4.10000 0.261939
\(246\) 0 0
\(247\) −15.9254 −1.01331
\(248\) −0.800154 −0.0508098
\(249\) 0 0
\(250\) −12.0696 −0.763348
\(251\) 4.18927 0.264424 0.132212 0.991221i \(-0.457792\pi\)
0.132212 + 0.991221i \(0.457792\pi\)
\(252\) 0 0
\(253\) 10.0148 0.629626
\(254\) −0.432278 −0.0271235
\(255\) 0 0
\(256\) 3.05584 0.190990
\(257\) −6.16033 −0.384271 −0.192135 0.981368i \(-0.561541\pi\)
−0.192135 + 0.981368i \(0.561541\pi\)
\(258\) 0 0
\(259\) 5.48926 0.341086
\(260\) 17.5901 1.09089
\(261\) 0 0
\(262\) −2.91519 −0.180101
\(263\) 17.8032 1.09779 0.548895 0.835891i \(-0.315049\pi\)
0.548895 + 0.835891i \(0.315049\pi\)
\(264\) 0 0
\(265\) 37.5558 2.30703
\(266\) −2.90936 −0.178384
\(267\) 0 0
\(268\) −26.1185 −1.59544
\(269\) −5.14395 −0.313632 −0.156816 0.987628i \(-0.550123\pi\)
−0.156816 + 0.987628i \(0.550123\pi\)
\(270\) 0 0
\(271\) −10.1569 −0.616990 −0.308495 0.951226i \(-0.599825\pi\)
−0.308495 + 0.951226i \(0.599825\pi\)
\(272\) 8.48095 0.514233
\(273\) 0 0
\(274\) 2.05324 0.124041
\(275\) −25.9174 −1.56288
\(276\) 0 0
\(277\) −23.2773 −1.39860 −0.699299 0.714829i \(-0.746505\pi\)
−0.699299 + 0.714829i \(0.746505\pi\)
\(278\) 0.940273 0.0563938
\(279\) 0 0
\(280\) 6.75816 0.403878
\(281\) −2.39036 −0.142597 −0.0712986 0.997455i \(-0.522714\pi\)
−0.0712986 + 0.997455i \(0.522714\pi\)
\(282\) 0 0
\(283\) 11.7401 0.697874 0.348937 0.937146i \(-0.386543\pi\)
0.348937 + 0.937146i \(0.386543\pi\)
\(284\) 4.77724 0.283477
\(285\) 0 0
\(286\) −2.24471 −0.132732
\(287\) −10.6000 −0.625698
\(288\) 0 0
\(289\) −8.52794 −0.501643
\(290\) −7.39203 −0.434075
\(291\) 0 0
\(292\) 1.10684 0.0647728
\(293\) −11.3005 −0.660184 −0.330092 0.943949i \(-0.607080\pi\)
−0.330092 + 0.943949i \(0.607080\pi\)
\(294\) 0 0
\(295\) 6.82090 0.397128
\(296\) 9.04813 0.525912
\(297\) 0 0
\(298\) 1.81454 0.105113
\(299\) 10.7983 0.624484
\(300\) 0 0
\(301\) −6.67190 −0.384562
\(302\) −6.67239 −0.383953
\(303\) 0 0
\(304\) 19.6103 1.12473
\(305\) −59.1658 −3.38782
\(306\) 0 0
\(307\) 30.1721 1.72201 0.861006 0.508595i \(-0.169835\pi\)
0.861006 + 0.508595i \(0.169835\pi\)
\(308\) 3.97898 0.226723
\(309\) 0 0
\(310\) 0.860349 0.0488646
\(311\) −2.51056 −0.142361 −0.0711805 0.997463i \(-0.522677\pi\)
−0.0711805 + 0.997463i \(0.522677\pi\)
\(312\) 0 0
\(313\) −3.42071 −0.193350 −0.0966751 0.995316i \(-0.530821\pi\)
−0.0966751 + 0.995316i \(0.530821\pi\)
\(314\) 4.29063 0.242134
\(315\) 0 0
\(316\) 13.3563 0.751348
\(317\) 3.84950 0.216209 0.108105 0.994140i \(-0.465522\pi\)
0.108105 + 0.994140i \(0.465522\pi\)
\(318\) 0 0
\(319\) −9.15290 −0.512464
\(320\) −15.8175 −0.884223
\(321\) 0 0
\(322\) 1.97271 0.109935
\(323\) 19.5897 1.09000
\(324\) 0 0
\(325\) −27.9450 −1.55011
\(326\) 5.05467 0.279952
\(327\) 0 0
\(328\) −17.4723 −0.964748
\(329\) 10.8486 0.598102
\(330\) 0 0
\(331\) −0.0166221 −0.000913635 0 −0.000456817 1.00000i \(-0.500145\pi\)
−0.000456817 1.00000i \(0.500145\pi\)
\(332\) −20.0318 −1.09939
\(333\) 0 0
\(334\) −6.57930 −0.360003
\(335\) 59.0610 3.22685
\(336\) 0 0
\(337\) 11.7639 0.640819 0.320410 0.947279i \(-0.396179\pi\)
0.320410 + 0.947279i \(0.396179\pi\)
\(338\) 3.19928 0.174018
\(339\) 0 0
\(340\) −21.6376 −1.17346
\(341\) 1.06529 0.0576890
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −10.9975 −0.592947
\(345\) 0 0
\(346\) −6.79852 −0.365491
\(347\) −23.9938 −1.28806 −0.644028 0.765002i \(-0.722738\pi\)
−0.644028 + 0.765002i \(0.722738\pi\)
\(348\) 0 0
\(349\) −15.6506 −0.837755 −0.418877 0.908043i \(-0.637576\pi\)
−0.418877 + 0.908043i \(0.637576\pi\)
\(350\) −5.10519 −0.272884
\(351\) 0 0
\(352\) 9.99874 0.532935
\(353\) −6.48439 −0.345129 −0.172565 0.984998i \(-0.555205\pi\)
−0.172565 + 0.984998i \(0.555205\pi\)
\(354\) 0 0
\(355\) −10.8026 −0.573345
\(356\) −13.3560 −0.707867
\(357\) 0 0
\(358\) −1.53904 −0.0813410
\(359\) −6.97556 −0.368156 −0.184078 0.982912i \(-0.558930\pi\)
−0.184078 + 0.982912i \(0.558930\pi\)
\(360\) 0 0
\(361\) 26.2969 1.38405
\(362\) 5.27355 0.277171
\(363\) 0 0
\(364\) 4.29028 0.224872
\(365\) −2.50286 −0.131006
\(366\) 0 0
\(367\) −25.0425 −1.30721 −0.653603 0.756838i \(-0.726743\pi\)
−0.653603 + 0.756838i \(0.726743\pi\)
\(368\) −13.2969 −0.693150
\(369\) 0 0
\(370\) −9.72882 −0.505777
\(371\) 9.15995 0.475561
\(372\) 0 0
\(373\) 12.1651 0.629883 0.314941 0.949111i \(-0.398015\pi\)
0.314941 + 0.949111i \(0.398015\pi\)
\(374\) 2.76121 0.142779
\(375\) 0 0
\(376\) 17.8821 0.922199
\(377\) −9.86899 −0.508279
\(378\) 0 0
\(379\) −15.1220 −0.776765 −0.388383 0.921498i \(-0.626966\pi\)
−0.388383 + 0.921498i \(0.626966\pi\)
\(380\) −50.0320 −2.56659
\(381\) 0 0
\(382\) −6.17264 −0.315820
\(383\) −25.4746 −1.30169 −0.650845 0.759211i \(-0.725585\pi\)
−0.650845 + 0.759211i \(0.725585\pi\)
\(384\) 0 0
\(385\) −8.99757 −0.458559
\(386\) 6.20704 0.315930
\(387\) 0 0
\(388\) −19.7073 −1.00049
\(389\) 20.9955 1.06452 0.532258 0.846582i \(-0.321344\pi\)
0.532258 + 0.846582i \(0.321344\pi\)
\(390\) 0 0
\(391\) −13.2830 −0.671750
\(392\) 1.64833 0.0832534
\(393\) 0 0
\(394\) −10.5118 −0.529579
\(395\) −30.2022 −1.51964
\(396\) 0 0
\(397\) −10.7159 −0.537813 −0.268907 0.963166i \(-0.586662\pi\)
−0.268907 + 0.963166i \(0.586662\pi\)
\(398\) 3.11266 0.156023
\(399\) 0 0
\(400\) 34.4111 1.72056
\(401\) −20.6307 −1.03025 −0.515123 0.857116i \(-0.672254\pi\)
−0.515123 + 0.857116i \(0.672254\pi\)
\(402\) 0 0
\(403\) 1.14864 0.0572178
\(404\) 35.7305 1.77766
\(405\) 0 0
\(406\) −1.80293 −0.0894782
\(407\) −12.0463 −0.597115
\(408\) 0 0
\(409\) 10.3576 0.512150 0.256075 0.966657i \(-0.417571\pi\)
0.256075 + 0.966657i \(0.417571\pi\)
\(410\) 18.7868 0.927813
\(411\) 0 0
\(412\) 0.884401 0.0435713
\(413\) 1.66364 0.0818621
\(414\) 0 0
\(415\) 45.2974 2.22356
\(416\) 10.7810 0.528582
\(417\) 0 0
\(418\) 6.38467 0.312284
\(419\) 25.7023 1.25564 0.627820 0.778359i \(-0.283947\pi\)
0.627820 + 0.778359i \(0.283947\pi\)
\(420\) 0 0
\(421\) −7.00604 −0.341453 −0.170727 0.985318i \(-0.554612\pi\)
−0.170727 + 0.985318i \(0.554612\pi\)
\(422\) −8.06309 −0.392505
\(423\) 0 0
\(424\) 15.0986 0.733255
\(425\) 34.3751 1.66744
\(426\) 0 0
\(427\) −14.4307 −0.698350
\(428\) −24.6275 −1.19041
\(429\) 0 0
\(430\) 11.8249 0.570246
\(431\) −11.7752 −0.567193 −0.283596 0.958944i \(-0.591528\pi\)
−0.283596 + 0.958944i \(0.591528\pi\)
\(432\) 0 0
\(433\) −21.7699 −1.04619 −0.523097 0.852273i \(-0.675224\pi\)
−0.523097 + 0.852273i \(0.675224\pi\)
\(434\) 0.209841 0.0100727
\(435\) 0 0
\(436\) −32.2081 −1.54249
\(437\) −30.7139 −1.46925
\(438\) 0 0
\(439\) 31.9471 1.52475 0.762377 0.647133i \(-0.224032\pi\)
0.762377 + 0.647133i \(0.224032\pi\)
\(440\) −14.8310 −0.707040
\(441\) 0 0
\(442\) 2.97723 0.141613
\(443\) 36.6620 1.74186 0.870932 0.491403i \(-0.163516\pi\)
0.870932 + 0.491403i \(0.163516\pi\)
\(444\) 0 0
\(445\) 30.2016 1.43169
\(446\) 5.72109 0.270902
\(447\) 0 0
\(448\) −3.85792 −0.182270
\(449\) −11.6838 −0.551394 −0.275697 0.961245i \(-0.588909\pi\)
−0.275697 + 0.961245i \(0.588909\pi\)
\(450\) 0 0
\(451\) 23.2620 1.09537
\(452\) 22.9395 1.07898
\(453\) 0 0
\(454\) −4.13989 −0.194295
\(455\) −9.70151 −0.454814
\(456\) 0 0
\(457\) 3.13913 0.146842 0.0734212 0.997301i \(-0.476608\pi\)
0.0734212 + 0.997301i \(0.476608\pi\)
\(458\) −5.22484 −0.244141
\(459\) 0 0
\(460\) 33.9246 1.58174
\(461\) 37.6820 1.75503 0.877513 0.479553i \(-0.159201\pi\)
0.877513 + 0.479553i \(0.159201\pi\)
\(462\) 0 0
\(463\) 31.3727 1.45801 0.729007 0.684506i \(-0.239982\pi\)
0.729007 + 0.684506i \(0.239982\pi\)
\(464\) 12.1525 0.564168
\(465\) 0 0
\(466\) 1.21321 0.0562011
\(467\) −0.680845 −0.0315057 −0.0157529 0.999876i \(-0.505015\pi\)
−0.0157529 + 0.999876i \(0.505015\pi\)
\(468\) 0 0
\(469\) 14.4051 0.665167
\(470\) −19.2274 −0.886892
\(471\) 0 0
\(472\) 2.74223 0.126221
\(473\) 14.6417 0.673226
\(474\) 0 0
\(475\) 79.4847 3.64701
\(476\) −5.27746 −0.241892
\(477\) 0 0
\(478\) 4.13449 0.189107
\(479\) 37.0258 1.69175 0.845876 0.533379i \(-0.179078\pi\)
0.845876 + 0.533379i \(0.179078\pi\)
\(480\) 0 0
\(481\) −12.9888 −0.592238
\(482\) −5.36638 −0.244432
\(483\) 0 0
\(484\) 11.2125 0.509659
\(485\) 44.5636 2.02353
\(486\) 0 0
\(487\) 10.9255 0.495081 0.247541 0.968877i \(-0.420378\pi\)
0.247541 + 0.968877i \(0.420378\pi\)
\(488\) −23.7866 −1.07677
\(489\) 0 0
\(490\) −1.77234 −0.0800661
\(491\) 25.0361 1.12987 0.564933 0.825137i \(-0.308902\pi\)
0.564933 + 0.825137i \(0.308902\pi\)
\(492\) 0 0
\(493\) 12.1398 0.546749
\(494\) 6.88419 0.309734
\(495\) 0 0
\(496\) −1.41442 −0.0635093
\(497\) −2.63479 −0.118187
\(498\) 0 0
\(499\) −34.5673 −1.54744 −0.773721 0.633526i \(-0.781607\pi\)
−0.773721 + 0.633526i \(0.781607\pi\)
\(500\) −50.6244 −2.26399
\(501\) 0 0
\(502\) −1.81093 −0.0808256
\(503\) 18.9830 0.846410 0.423205 0.906034i \(-0.360905\pi\)
0.423205 + 0.906034i \(0.360905\pi\)
\(504\) 0 0
\(505\) −80.7964 −3.59539
\(506\) −4.32918 −0.192456
\(507\) 0 0
\(508\) −1.81314 −0.0804449
\(509\) 1.07444 0.0476237 0.0238119 0.999716i \(-0.492420\pi\)
0.0238119 + 0.999716i \(0.492420\pi\)
\(510\) 0 0
\(511\) −0.610455 −0.0270049
\(512\) −22.8812 −1.01122
\(513\) 0 0
\(514\) 2.66297 0.117459
\(515\) −1.99987 −0.0881249
\(516\) 0 0
\(517\) −23.8076 −1.04706
\(518\) −2.37288 −0.104259
\(519\) 0 0
\(520\) −15.9913 −0.701266
\(521\) −1.02818 −0.0450456 −0.0225228 0.999746i \(-0.507170\pi\)
−0.0225228 + 0.999746i \(0.507170\pi\)
\(522\) 0 0
\(523\) −19.0103 −0.831264 −0.415632 0.909533i \(-0.636440\pi\)
−0.415632 + 0.909533i \(0.636440\pi\)
\(524\) −12.2274 −0.534158
\(525\) 0 0
\(526\) −7.69591 −0.335558
\(527\) −1.41294 −0.0615485
\(528\) 0 0
\(529\) −2.17416 −0.0945286
\(530\) −16.2345 −0.705182
\(531\) 0 0
\(532\) −12.2029 −0.529065
\(533\) 25.0820 1.08642
\(534\) 0 0
\(535\) 55.6895 2.40767
\(536\) 23.7445 1.02560
\(537\) 0 0
\(538\) 2.22362 0.0958669
\(539\) −2.19453 −0.0945251
\(540\) 0 0
\(541\) −30.4975 −1.31119 −0.655594 0.755113i \(-0.727582\pi\)
−0.655594 + 0.755113i \(0.727582\pi\)
\(542\) 4.39062 0.188593
\(543\) 0 0
\(544\) −13.2617 −0.568590
\(545\) 72.8313 3.11975
\(546\) 0 0
\(547\) 10.5343 0.450415 0.225207 0.974311i \(-0.427694\pi\)
0.225207 + 0.974311i \(0.427694\pi\)
\(548\) 8.61207 0.367889
\(549\) 0 0
\(550\) 11.2035 0.477719
\(551\) 28.0706 1.19585
\(552\) 0 0
\(553\) −7.36638 −0.313251
\(554\) 10.0623 0.427505
\(555\) 0 0
\(556\) 3.94386 0.167257
\(557\) −20.4261 −0.865480 −0.432740 0.901519i \(-0.642453\pi\)
−0.432740 + 0.901519i \(0.642453\pi\)
\(558\) 0 0
\(559\) 15.7872 0.667728
\(560\) 11.9463 0.504823
\(561\) 0 0
\(562\) 1.03330 0.0435872
\(563\) 41.1411 1.73389 0.866945 0.498404i \(-0.166080\pi\)
0.866945 + 0.498404i \(0.166080\pi\)
\(564\) 0 0
\(565\) −51.8725 −2.18229
\(566\) −5.07496 −0.213317
\(567\) 0 0
\(568\) −4.34302 −0.182229
\(569\) 11.3486 0.475759 0.237879 0.971295i \(-0.423548\pi\)
0.237879 + 0.971295i \(0.423548\pi\)
\(570\) 0 0
\(571\) −35.4620 −1.48404 −0.742020 0.670378i \(-0.766132\pi\)
−0.742020 + 0.670378i \(0.766132\pi\)
\(572\) −9.41515 −0.393667
\(573\) 0 0
\(574\) 4.58214 0.191255
\(575\) −53.8953 −2.24759
\(576\) 0 0
\(577\) 40.7787 1.69764 0.848819 0.528683i \(-0.177314\pi\)
0.848819 + 0.528683i \(0.177314\pi\)
\(578\) 3.68644 0.153336
\(579\) 0 0
\(580\) −31.0050 −1.28741
\(581\) 11.0482 0.458355
\(582\) 0 0
\(583\) −20.1018 −0.832530
\(584\) −1.00623 −0.0416383
\(585\) 0 0
\(586\) 4.88497 0.201796
\(587\) 30.2579 1.24888 0.624439 0.781073i \(-0.285327\pi\)
0.624439 + 0.781073i \(0.285327\pi\)
\(588\) 0 0
\(589\) −3.26710 −0.134619
\(590\) −2.94852 −0.121389
\(591\) 0 0
\(592\) 15.9942 0.657359
\(593\) 44.4426 1.82504 0.912519 0.409034i \(-0.134134\pi\)
0.912519 + 0.409034i \(0.134134\pi\)
\(594\) 0 0
\(595\) 11.9338 0.489237
\(596\) 7.61087 0.311753
\(597\) 0 0
\(598\) −4.66788 −0.190884
\(599\) −20.4984 −0.837540 −0.418770 0.908092i \(-0.637539\pi\)
−0.418770 + 0.908092i \(0.637539\pi\)
\(600\) 0 0
\(601\) −15.2297 −0.621234 −0.310617 0.950535i \(-0.600536\pi\)
−0.310617 + 0.950535i \(0.600536\pi\)
\(602\) 2.88412 0.117548
\(603\) 0 0
\(604\) −27.9865 −1.13876
\(605\) −25.3545 −1.03081
\(606\) 0 0
\(607\) 33.8705 1.37476 0.687380 0.726298i \(-0.258761\pi\)
0.687380 + 0.726298i \(0.258761\pi\)
\(608\) −30.6646 −1.24362
\(609\) 0 0
\(610\) 25.5760 1.03554
\(611\) −25.6702 −1.03850
\(612\) 0 0
\(613\) 9.78220 0.395099 0.197550 0.980293i \(-0.436702\pi\)
0.197550 + 0.980293i \(0.436702\pi\)
\(614\) −13.0427 −0.526361
\(615\) 0 0
\(616\) −3.61732 −0.145746
\(617\) −27.4862 −1.10655 −0.553276 0.832998i \(-0.686622\pi\)
−0.553276 + 0.832998i \(0.686622\pi\)
\(618\) 0 0
\(619\) 46.0270 1.84998 0.924990 0.379992i \(-0.124073\pi\)
0.924990 + 0.379992i \(0.124073\pi\)
\(620\) 3.60863 0.144926
\(621\) 0 0
\(622\) 1.08526 0.0435150
\(623\) 7.36625 0.295123
\(624\) 0 0
\(625\) 55.4258 2.21703
\(626\) 1.47870 0.0591007
\(627\) 0 0
\(628\) 17.9965 0.718140
\(629\) 15.9775 0.637064
\(630\) 0 0
\(631\) 6.88781 0.274199 0.137100 0.990557i \(-0.456222\pi\)
0.137100 + 0.990557i \(0.456222\pi\)
\(632\) −12.1423 −0.482993
\(633\) 0 0
\(634\) −1.66405 −0.0660880
\(635\) 4.10000 0.162703
\(636\) 0 0
\(637\) −2.36622 −0.0937531
\(638\) 3.95659 0.156643
\(639\) 0 0
\(640\) 44.1984 1.74710
\(641\) 18.6043 0.734827 0.367414 0.930058i \(-0.380243\pi\)
0.367414 + 0.930058i \(0.380243\pi\)
\(642\) 0 0
\(643\) −32.1894 −1.26942 −0.634712 0.772749i \(-0.718881\pi\)
−0.634712 + 0.772749i \(0.718881\pi\)
\(644\) 8.27431 0.326053
\(645\) 0 0
\(646\) −8.46821 −0.333177
\(647\) −0.965623 −0.0379626 −0.0189813 0.999820i \(-0.506042\pi\)
−0.0189813 + 0.999820i \(0.506042\pi\)
\(648\) 0 0
\(649\) −3.65090 −0.143310
\(650\) 12.0800 0.473817
\(651\) 0 0
\(652\) 21.2012 0.830303
\(653\) 38.7135 1.51498 0.757489 0.652848i \(-0.226426\pi\)
0.757489 + 0.652848i \(0.226426\pi\)
\(654\) 0 0
\(655\) 27.6496 1.08036
\(656\) −30.8856 −1.20588
\(657\) 0 0
\(658\) −4.68960 −0.182820
\(659\) 19.8754 0.774235 0.387117 0.922030i \(-0.373471\pi\)
0.387117 + 0.922030i \(0.373471\pi\)
\(660\) 0 0
\(661\) 40.6662 1.58173 0.790865 0.611990i \(-0.209631\pi\)
0.790865 + 0.611990i \(0.209631\pi\)
\(662\) 0.00718538 0.000279268 0
\(663\) 0 0
\(664\) 18.2111 0.706726
\(665\) 27.5942 1.07006
\(666\) 0 0
\(667\) −19.0335 −0.736980
\(668\) −27.5961 −1.06772
\(669\) 0 0
\(670\) −25.5308 −0.986339
\(671\) 31.6686 1.22255
\(672\) 0 0
\(673\) −22.5654 −0.869832 −0.434916 0.900471i \(-0.643222\pi\)
−0.434916 + 0.900471i \(0.643222\pi\)
\(674\) −5.08526 −0.195877
\(675\) 0 0
\(676\) 13.4190 0.516116
\(677\) 28.7074 1.10332 0.551658 0.834070i \(-0.313995\pi\)
0.551658 + 0.834070i \(0.313995\pi\)
\(678\) 0 0
\(679\) 10.8692 0.417121
\(680\) 19.6709 0.754343
\(681\) 0 0
\(682\) −0.460503 −0.0176336
\(683\) −11.0647 −0.423379 −0.211690 0.977337i \(-0.567897\pi\)
−0.211690 + 0.977337i \(0.567897\pi\)
\(684\) 0 0
\(685\) −19.4743 −0.744073
\(686\) −0.432278 −0.0165044
\(687\) 0 0
\(688\) −19.4402 −0.741149
\(689\) −21.6745 −0.825731
\(690\) 0 0
\(691\) 23.8585 0.907619 0.453809 0.891099i \(-0.350065\pi\)
0.453809 + 0.891099i \(0.350065\pi\)
\(692\) −28.5156 −1.08400
\(693\) 0 0
\(694\) 10.3720 0.393716
\(695\) −8.91815 −0.338285
\(696\) 0 0
\(697\) −30.8532 −1.16865
\(698\) 6.76538 0.256074
\(699\) 0 0
\(700\) −21.4131 −0.809339
\(701\) 38.1381 1.44046 0.720229 0.693737i \(-0.244037\pi\)
0.720229 + 0.693737i \(0.244037\pi\)
\(702\) 0 0
\(703\) 36.9443 1.39338
\(704\) 8.46632 0.319086
\(705\) 0 0
\(706\) 2.80306 0.105495
\(707\) −19.7064 −0.741137
\(708\) 0 0
\(709\) 3.87952 0.145698 0.0728492 0.997343i \(-0.476791\pi\)
0.0728492 + 0.997343i \(0.476791\pi\)
\(710\) 4.66974 0.175252
\(711\) 0 0
\(712\) 12.1420 0.455042
\(713\) 2.21529 0.0829631
\(714\) 0 0
\(715\) 21.2902 0.796210
\(716\) −6.45533 −0.241247
\(717\) 0 0
\(718\) 3.01538 0.112533
\(719\) 3.10342 0.115738 0.0578691 0.998324i \(-0.481569\pi\)
0.0578691 + 0.998324i \(0.481569\pi\)
\(720\) 0 0
\(721\) −0.487774 −0.0181657
\(722\) −11.3676 −0.423057
\(723\) 0 0
\(724\) 22.1192 0.822055
\(725\) 49.2568 1.82935
\(726\) 0 0
\(727\) −47.6900 −1.76872 −0.884362 0.466802i \(-0.845406\pi\)
−0.884362 + 0.466802i \(0.845406\pi\)
\(728\) −3.90032 −0.144556
\(729\) 0 0
\(730\) 1.08193 0.0400441
\(731\) −19.4198 −0.718267
\(732\) 0 0
\(733\) −37.5015 −1.38515 −0.692574 0.721346i \(-0.743524\pi\)
−0.692574 + 0.721346i \(0.743524\pi\)
\(734\) 10.8253 0.399569
\(735\) 0 0
\(736\) 20.7924 0.766419
\(737\) −31.6125 −1.16446
\(738\) 0 0
\(739\) 4.09825 0.150757 0.0753783 0.997155i \(-0.475984\pi\)
0.0753783 + 0.997155i \(0.475984\pi\)
\(740\) −40.8063 −1.50007
\(741\) 0 0
\(742\) −3.95964 −0.145363
\(743\) 33.2979 1.22158 0.610791 0.791792i \(-0.290852\pi\)
0.610791 + 0.791792i \(0.290852\pi\)
\(744\) 0 0
\(745\) −17.2103 −0.630535
\(746\) −5.25868 −0.192534
\(747\) 0 0
\(748\) 11.5815 0.423463
\(749\) 13.5828 0.496305
\(750\) 0 0
\(751\) 24.6824 0.900674 0.450337 0.892859i \(-0.351304\pi\)
0.450337 + 0.892859i \(0.351304\pi\)
\(752\) 31.6099 1.15269
\(753\) 0 0
\(754\) 4.26614 0.155364
\(755\) 63.2852 2.30319
\(756\) 0 0
\(757\) 26.2286 0.953295 0.476647 0.879095i \(-0.341852\pi\)
0.476647 + 0.879095i \(0.341852\pi\)
\(758\) 6.53690 0.237431
\(759\) 0 0
\(760\) 45.4845 1.64989
\(761\) 25.9623 0.941131 0.470566 0.882365i \(-0.344050\pi\)
0.470566 + 0.882365i \(0.344050\pi\)
\(762\) 0 0
\(763\) 17.7637 0.643091
\(764\) −25.8904 −0.936681
\(765\) 0 0
\(766\) 11.0121 0.397883
\(767\) −3.93653 −0.142140
\(768\) 0 0
\(769\) 32.1020 1.15763 0.578814 0.815459i \(-0.303516\pi\)
0.578814 + 0.815459i \(0.303516\pi\)
\(770\) 3.88945 0.140166
\(771\) 0 0
\(772\) 26.0347 0.937008
\(773\) 35.2474 1.26776 0.633880 0.773431i \(-0.281461\pi\)
0.633880 + 0.773431i \(0.281461\pi\)
\(774\) 0 0
\(775\) −5.73294 −0.205933
\(776\) 17.9160 0.643148
\(777\) 0 0
\(778\) −9.07591 −0.325387
\(779\) −71.3411 −2.55606
\(780\) 0 0
\(781\) 5.78213 0.206901
\(782\) 5.74194 0.205331
\(783\) 0 0
\(784\) 2.91373 0.104062
\(785\) −40.6951 −1.45247
\(786\) 0 0
\(787\) 9.54430 0.340218 0.170109 0.985425i \(-0.445588\pi\)
0.170109 + 0.985425i \(0.445588\pi\)
\(788\) −44.0906 −1.57066
\(789\) 0 0
\(790\) 13.0557 0.464502
\(791\) −12.6518 −0.449848
\(792\) 0 0
\(793\) 34.1462 1.21257
\(794\) 4.63223 0.164392
\(795\) 0 0
\(796\) 13.0557 0.462745
\(797\) −29.9392 −1.06050 −0.530251 0.847841i \(-0.677902\pi\)
−0.530251 + 0.847841i \(0.677902\pi\)
\(798\) 0 0
\(799\) 31.5768 1.11711
\(800\) −53.8088 −1.90243
\(801\) 0 0
\(802\) 8.91817 0.314912
\(803\) 1.33966 0.0472756
\(804\) 0 0
\(805\) −18.7105 −0.659458
\(806\) −0.496531 −0.0174896
\(807\) 0 0
\(808\) −32.4828 −1.14274
\(809\) 52.3491 1.84049 0.920247 0.391337i \(-0.127987\pi\)
0.920247 + 0.391337i \(0.127987\pi\)
\(810\) 0 0
\(811\) −37.5843 −1.31976 −0.659882 0.751369i \(-0.729394\pi\)
−0.659882 + 0.751369i \(0.729394\pi\)
\(812\) −7.56219 −0.265381
\(813\) 0 0
\(814\) 5.20736 0.182518
\(815\) −47.9417 −1.67933
\(816\) 0 0
\(817\) −44.9039 −1.57099
\(818\) −4.47736 −0.156547
\(819\) 0 0
\(820\) 78.7988 2.75178
\(821\) −22.0108 −0.768181 −0.384090 0.923296i \(-0.625485\pi\)
−0.384090 + 0.923296i \(0.625485\pi\)
\(822\) 0 0
\(823\) −36.1421 −1.25983 −0.629917 0.776662i \(-0.716911\pi\)
−0.629917 + 0.776662i \(0.716911\pi\)
\(824\) −0.804014 −0.0280092
\(825\) 0 0
\(826\) −0.719152 −0.0250225
\(827\) 6.82706 0.237400 0.118700 0.992930i \(-0.462127\pi\)
0.118700 + 0.992930i \(0.462127\pi\)
\(828\) 0 0
\(829\) −9.01103 −0.312966 −0.156483 0.987681i \(-0.550016\pi\)
−0.156483 + 0.987681i \(0.550016\pi\)
\(830\) −19.5811 −0.679669
\(831\) 0 0
\(832\) 9.12870 0.316481
\(833\) 2.91068 0.100849
\(834\) 0 0
\(835\) 62.4023 2.15952
\(836\) 26.7797 0.926196
\(837\) 0 0
\(838\) −11.1105 −0.383807
\(839\) −20.9726 −0.724056 −0.362028 0.932167i \(-0.617915\pi\)
−0.362028 + 0.932167i \(0.617915\pi\)
\(840\) 0 0
\(841\) −11.6046 −0.400159
\(842\) 3.02855 0.104371
\(843\) 0 0
\(844\) −33.8196 −1.16412
\(845\) −30.3441 −1.04387
\(846\) 0 0
\(847\) −6.18404 −0.212486
\(848\) 26.6896 0.916526
\(849\) 0 0
\(850\) −14.8596 −0.509680
\(851\) −25.0504 −0.858717
\(852\) 0 0
\(853\) 32.0956 1.09893 0.549466 0.835516i \(-0.314831\pi\)
0.549466 + 0.835516i \(0.314831\pi\)
\(854\) 6.23806 0.213462
\(855\) 0 0
\(856\) 22.3890 0.765240
\(857\) −35.7115 −1.21988 −0.609941 0.792447i \(-0.708807\pi\)
−0.609941 + 0.792447i \(0.708807\pi\)
\(858\) 0 0
\(859\) 20.0861 0.685330 0.342665 0.939458i \(-0.388670\pi\)
0.342665 + 0.939458i \(0.388670\pi\)
\(860\) 49.5980 1.69128
\(861\) 0 0
\(862\) 5.09017 0.173372
\(863\) −10.7248 −0.365077 −0.182538 0.983199i \(-0.558431\pi\)
−0.182538 + 0.983199i \(0.558431\pi\)
\(864\) 0 0
\(865\) 64.4815 2.19244
\(866\) 9.41064 0.319787
\(867\) 0 0
\(868\) 0.880154 0.0298744
\(869\) 16.1657 0.548385
\(870\) 0 0
\(871\) −34.0857 −1.15495
\(872\) 29.2806 0.991566
\(873\) 0 0
\(874\) 13.2770 0.449100
\(875\) 27.9209 0.943899
\(876\) 0 0
\(877\) −23.0168 −0.777223 −0.388612 0.921402i \(-0.627045\pi\)
−0.388612 + 0.921402i \(0.627045\pi\)
\(878\) −13.8100 −0.466066
\(879\) 0 0
\(880\) −26.2165 −0.883759
\(881\) 5.44399 0.183413 0.0917063 0.995786i \(-0.470768\pi\)
0.0917063 + 0.995786i \(0.470768\pi\)
\(882\) 0 0
\(883\) −24.2700 −0.816750 −0.408375 0.912814i \(-0.633904\pi\)
−0.408375 + 0.912814i \(0.633904\pi\)
\(884\) 12.4876 0.420005
\(885\) 0 0
\(886\) −15.8482 −0.532430
\(887\) 44.8788 1.50688 0.753441 0.657516i \(-0.228393\pi\)
0.753441 + 0.657516i \(0.228393\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −13.0555 −0.437621
\(891\) 0 0
\(892\) 23.9964 0.803459
\(893\) 73.0142 2.44333
\(894\) 0 0
\(895\) 14.5973 0.487933
\(896\) 10.7801 0.360138
\(897\) 0 0
\(898\) 5.05066 0.168543
\(899\) −2.02463 −0.0675252
\(900\) 0 0
\(901\) 26.6617 0.888229
\(902\) −10.0557 −0.334817
\(903\) 0 0
\(904\) −20.8545 −0.693609
\(905\) −50.0177 −1.66264
\(906\) 0 0
\(907\) 56.6797 1.88202 0.941009 0.338382i \(-0.109880\pi\)
0.941009 + 0.338382i \(0.109880\pi\)
\(908\) −17.3643 −0.576254
\(909\) 0 0
\(910\) 4.19374 0.139021
\(911\) 1.65229 0.0547428 0.0273714 0.999625i \(-0.491286\pi\)
0.0273714 + 0.999625i \(0.491286\pi\)
\(912\) 0 0
\(913\) −24.2455 −0.802409
\(914\) −1.35698 −0.0448848
\(915\) 0 0
\(916\) −21.9150 −0.724091
\(917\) 6.74380 0.222700
\(918\) 0 0
\(919\) −30.1884 −0.995823 −0.497912 0.867228i \(-0.665900\pi\)
−0.497912 + 0.867228i \(0.665900\pi\)
\(920\) −30.8411 −1.01680
\(921\) 0 0
\(922\) −16.2891 −0.536453
\(923\) 6.23451 0.205211
\(924\) 0 0
\(925\) 64.8280 2.13153
\(926\) −13.5617 −0.445666
\(927\) 0 0
\(928\) −19.0029 −0.623802
\(929\) −48.4510 −1.58963 −0.794813 0.606854i \(-0.792431\pi\)
−0.794813 + 0.606854i \(0.792431\pi\)
\(930\) 0 0
\(931\) 6.73030 0.220577
\(932\) 5.08868 0.166685
\(933\) 0 0
\(934\) 0.294314 0.00963025
\(935\) −26.1890 −0.856473
\(936\) 0 0
\(937\) −46.7524 −1.52734 −0.763668 0.645609i \(-0.776604\pi\)
−0.763668 + 0.645609i \(0.776604\pi\)
\(938\) −6.22702 −0.203319
\(939\) 0 0
\(940\) −80.6468 −2.63041
\(941\) 55.8314 1.82005 0.910026 0.414550i \(-0.136061\pi\)
0.910026 + 0.414550i \(0.136061\pi\)
\(942\) 0 0
\(943\) 48.3735 1.57526
\(944\) 4.84739 0.157769
\(945\) 0 0
\(946\) −6.32928 −0.205783
\(947\) −42.8711 −1.39312 −0.696561 0.717497i \(-0.745288\pi\)
−0.696561 + 0.717497i \(0.745288\pi\)
\(948\) 0 0
\(949\) 1.44447 0.0468896
\(950\) −34.3595 −1.11477
\(951\) 0 0
\(952\) 4.79777 0.155497
\(953\) 15.0549 0.487677 0.243838 0.969816i \(-0.421593\pi\)
0.243838 + 0.969816i \(0.421593\pi\)
\(954\) 0 0
\(955\) 58.5453 1.89448
\(956\) 17.3416 0.560867
\(957\) 0 0
\(958\) −16.0054 −0.517112
\(959\) −4.74982 −0.153380
\(960\) 0 0
\(961\) −30.7644 −0.992399
\(962\) 5.61477 0.181027
\(963\) 0 0
\(964\) −22.5086 −0.724953
\(965\) −58.8715 −1.89514
\(966\) 0 0
\(967\) −23.6827 −0.761585 −0.380793 0.924660i \(-0.624349\pi\)
−0.380793 + 0.924660i \(0.624349\pi\)
\(968\) −10.1934 −0.327627
\(969\) 0 0
\(970\) −19.2639 −0.618525
\(971\) −25.6083 −0.821810 −0.410905 0.911678i \(-0.634787\pi\)
−0.410905 + 0.911678i \(0.634787\pi\)
\(972\) 0 0
\(973\) −2.17516 −0.0697324
\(974\) −4.72285 −0.151330
\(975\) 0 0
\(976\) −42.0472 −1.34590
\(977\) −10.4357 −0.333869 −0.166935 0.985968i \(-0.553387\pi\)
−0.166935 + 0.985968i \(0.553387\pi\)
\(978\) 0 0
\(979\) −16.1655 −0.516650
\(980\) −7.43385 −0.237466
\(981\) 0 0
\(982\) −10.8226 −0.345362
\(983\) 31.3815 1.00092 0.500458 0.865761i \(-0.333165\pi\)
0.500458 + 0.865761i \(0.333165\pi\)
\(984\) 0 0
\(985\) 99.7010 3.17674
\(986\) −5.24777 −0.167123
\(987\) 0 0
\(988\) 28.8749 0.918632
\(989\) 30.4475 0.968173
\(990\) 0 0
\(991\) −17.0297 −0.540967 −0.270483 0.962725i \(-0.587184\pi\)
−0.270483 + 0.962725i \(0.587184\pi\)
\(992\) 2.21173 0.0702225
\(993\) 0 0
\(994\) 1.13896 0.0361257
\(995\) −29.5224 −0.935924
\(996\) 0 0
\(997\) 1.32135 0.0418476 0.0209238 0.999781i \(-0.493339\pi\)
0.0209238 + 0.999781i \(0.493339\pi\)
\(998\) 14.9427 0.473001
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))