Properties

Label 8015.2.a.l.1.45
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.45
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} +O(q^{10})\) \(q+1.36075 q^{2} -0.257132 q^{3} -0.148369 q^{4} -1.00000 q^{5} -0.349892 q^{6} -1.00000 q^{7} -2.92339 q^{8} -2.93388 q^{9} -1.36075 q^{10} +2.45315 q^{11} +0.0381503 q^{12} -6.54712 q^{13} -1.36075 q^{14} +0.257132 q^{15} -3.68125 q^{16} +2.41213 q^{17} -3.99227 q^{18} -1.82799 q^{19} +0.148369 q^{20} +0.257132 q^{21} +3.33812 q^{22} -3.40426 q^{23} +0.751696 q^{24} +1.00000 q^{25} -8.90897 q^{26} +1.52579 q^{27} +0.148369 q^{28} -6.44943 q^{29} +0.349892 q^{30} -5.10199 q^{31} +0.837522 q^{32} -0.630784 q^{33} +3.28230 q^{34} +1.00000 q^{35} +0.435296 q^{36} -4.22793 q^{37} -2.48743 q^{38} +1.68347 q^{39} +2.92339 q^{40} +2.29311 q^{41} +0.349892 q^{42} +3.23324 q^{43} -0.363970 q^{44} +2.93388 q^{45} -4.63233 q^{46} -5.65402 q^{47} +0.946567 q^{48} +1.00000 q^{49} +1.36075 q^{50} -0.620236 q^{51} +0.971386 q^{52} +2.83506 q^{53} +2.07622 q^{54} -2.45315 q^{55} +2.92339 q^{56} +0.470034 q^{57} -8.77605 q^{58} -2.81329 q^{59} -0.0381503 q^{60} +13.5670 q^{61} -6.94252 q^{62} +2.93388 q^{63} +8.50216 q^{64} +6.54712 q^{65} -0.858337 q^{66} -6.06202 q^{67} -0.357884 q^{68} +0.875344 q^{69} +1.36075 q^{70} +5.47026 q^{71} +8.57687 q^{72} +4.63235 q^{73} -5.75315 q^{74} -0.257132 q^{75} +0.271216 q^{76} -2.45315 q^{77} +2.29078 q^{78} -0.283484 q^{79} +3.68125 q^{80} +8.40932 q^{81} +3.12034 q^{82} +16.5586 q^{83} -0.0381503 q^{84} -2.41213 q^{85} +4.39963 q^{86} +1.65836 q^{87} -7.17150 q^{88} -15.1817 q^{89} +3.99227 q^{90} +6.54712 q^{91} +0.505085 q^{92} +1.31189 q^{93} -7.69369 q^{94} +1.82799 q^{95} -0.215354 q^{96} +18.0448 q^{97} +1.36075 q^{98} -7.19726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36075 0.962193 0.481097 0.876668i \(-0.340239\pi\)
0.481097 + 0.876668i \(0.340239\pi\)
\(3\) −0.257132 −0.148455 −0.0742276 0.997241i \(-0.523649\pi\)
−0.0742276 + 0.997241i \(0.523649\pi\)
\(4\) −0.148369 −0.0741843
\(5\) −1.00000 −0.447214
\(6\) −0.349892 −0.142843
\(7\) −1.00000 −0.377964
\(8\) −2.92339 −1.03357
\(9\) −2.93388 −0.977961
\(10\) −1.36075 −0.430306
\(11\) 2.45315 0.739653 0.369826 0.929101i \(-0.379417\pi\)
0.369826 + 0.929101i \(0.379417\pi\)
\(12\) 0.0381503 0.0110130
\(13\) −6.54712 −1.81584 −0.907922 0.419139i \(-0.862332\pi\)
−0.907922 + 0.419139i \(0.862332\pi\)
\(14\) −1.36075 −0.363675
\(15\) 0.257132 0.0663912
\(16\) −3.68125 −0.920312
\(17\) 2.41213 0.585027 0.292514 0.956261i \(-0.405508\pi\)
0.292514 + 0.956261i \(0.405508\pi\)
\(18\) −3.99227 −0.940987
\(19\) −1.82799 −0.419369 −0.209685 0.977769i \(-0.567244\pi\)
−0.209685 + 0.977769i \(0.567244\pi\)
\(20\) 0.148369 0.0331762
\(21\) 0.257132 0.0561108
\(22\) 3.33812 0.711689
\(23\) −3.40426 −0.709837 −0.354918 0.934897i \(-0.615491\pi\)
−0.354918 + 0.934897i \(0.615491\pi\)
\(24\) 0.751696 0.153439
\(25\) 1.00000 0.200000
\(26\) −8.90897 −1.74719
\(27\) 1.52579 0.293639
\(28\) 0.148369 0.0280390
\(29\) −6.44943 −1.19763 −0.598815 0.800887i \(-0.704362\pi\)
−0.598815 + 0.800887i \(0.704362\pi\)
\(30\) 0.349892 0.0638812
\(31\) −5.10199 −0.916344 −0.458172 0.888863i \(-0.651496\pi\)
−0.458172 + 0.888863i \(0.651496\pi\)
\(32\) 0.837522 0.148054
\(33\) −0.630784 −0.109805
\(34\) 3.28230 0.562909
\(35\) 1.00000 0.169031
\(36\) 0.435296 0.0725493
\(37\) −4.22793 −0.695068 −0.347534 0.937667i \(-0.612981\pi\)
−0.347534 + 0.937667i \(0.612981\pi\)
\(38\) −2.48743 −0.403514
\(39\) 1.68347 0.269572
\(40\) 2.92339 0.462228
\(41\) 2.29311 0.358124 0.179062 0.983838i \(-0.442694\pi\)
0.179062 + 0.983838i \(0.442694\pi\)
\(42\) 0.349892 0.0539894
\(43\) 3.23324 0.493065 0.246533 0.969135i \(-0.420709\pi\)
0.246533 + 0.969135i \(0.420709\pi\)
\(44\) −0.363970 −0.0548706
\(45\) 2.93388 0.437357
\(46\) −4.63233 −0.683000
\(47\) −5.65402 −0.824723 −0.412362 0.911020i \(-0.635296\pi\)
−0.412362 + 0.911020i \(0.635296\pi\)
\(48\) 0.946567 0.136625
\(49\) 1.00000 0.142857
\(50\) 1.36075 0.192439
\(51\) −0.620236 −0.0868504
\(52\) 0.971386 0.134707
\(53\) 2.83506 0.389426 0.194713 0.980860i \(-0.437622\pi\)
0.194713 + 0.980860i \(0.437622\pi\)
\(54\) 2.07622 0.282537
\(55\) −2.45315 −0.330783
\(56\) 2.92339 0.390654
\(57\) 0.470034 0.0622576
\(58\) −8.77605 −1.15235
\(59\) −2.81329 −0.366260 −0.183130 0.983089i \(-0.558623\pi\)
−0.183130 + 0.983089i \(0.558623\pi\)
\(60\) −0.0381503 −0.00492518
\(61\) 13.5670 1.73708 0.868540 0.495619i \(-0.165059\pi\)
0.868540 + 0.495619i \(0.165059\pi\)
\(62\) −6.94252 −0.881700
\(63\) 2.93388 0.369635
\(64\) 8.50216 1.06277
\(65\) 6.54712 0.812070
\(66\) −0.858337 −0.105654
\(67\) −6.06202 −0.740593 −0.370297 0.928914i \(-0.620744\pi\)
−0.370297 + 0.928914i \(0.620744\pi\)
\(68\) −0.357884 −0.0433998
\(69\) 0.875344 0.105379
\(70\) 1.36075 0.162640
\(71\) 5.47026 0.649201 0.324600 0.945851i \(-0.394770\pi\)
0.324600 + 0.945851i \(0.394770\pi\)
\(72\) 8.57687 1.01079
\(73\) 4.63235 0.542176 0.271088 0.962555i \(-0.412617\pi\)
0.271088 + 0.962555i \(0.412617\pi\)
\(74\) −5.75315 −0.668790
\(75\) −0.257132 −0.0296911
\(76\) 0.271216 0.0311106
\(77\) −2.45315 −0.279562
\(78\) 2.29078 0.259380
\(79\) −0.283484 −0.0318944 −0.0159472 0.999873i \(-0.505076\pi\)
−0.0159472 + 0.999873i \(0.505076\pi\)
\(80\) 3.68125 0.411576
\(81\) 8.40932 0.934369
\(82\) 3.12034 0.344584
\(83\) 16.5586 1.81754 0.908772 0.417293i \(-0.137021\pi\)
0.908772 + 0.417293i \(0.137021\pi\)
\(84\) −0.0381503 −0.00416254
\(85\) −2.41213 −0.261632
\(86\) 4.39963 0.474424
\(87\) 1.65836 0.177794
\(88\) −7.17150 −0.764485
\(89\) −15.1817 −1.60925 −0.804627 0.593781i \(-0.797635\pi\)
−0.804627 + 0.593781i \(0.797635\pi\)
\(90\) 3.99227 0.420822
\(91\) 6.54712 0.686325
\(92\) 0.505085 0.0526587
\(93\) 1.31189 0.136036
\(94\) −7.69369 −0.793543
\(95\) 1.82799 0.187548
\(96\) −0.215354 −0.0219795
\(97\) 18.0448 1.83217 0.916085 0.400984i \(-0.131332\pi\)
0.916085 + 0.400984i \(0.131332\pi\)
\(98\) 1.36075 0.137456
\(99\) −7.19726 −0.723352
\(100\) −0.148369 −0.0148369
\(101\) −13.1455 −1.30803 −0.654014 0.756482i \(-0.726916\pi\)
−0.654014 + 0.756482i \(0.726916\pi\)
\(102\) −0.843984 −0.0835668
\(103\) −15.2547 −1.50309 −0.751545 0.659681i \(-0.770691\pi\)
−0.751545 + 0.659681i \(0.770691\pi\)
\(104\) 19.1397 1.87681
\(105\) −0.257132 −0.0250935
\(106\) 3.85780 0.374703
\(107\) 1.60109 0.154783 0.0773914 0.997001i \(-0.475341\pi\)
0.0773914 + 0.997001i \(0.475341\pi\)
\(108\) −0.226379 −0.0217834
\(109\) −6.34412 −0.607656 −0.303828 0.952727i \(-0.598265\pi\)
−0.303828 + 0.952727i \(0.598265\pi\)
\(110\) −3.33812 −0.318277
\(111\) 1.08714 0.103186
\(112\) 3.68125 0.347845
\(113\) −12.8340 −1.20732 −0.603660 0.797242i \(-0.706292\pi\)
−0.603660 + 0.797242i \(0.706292\pi\)
\(114\) 0.639598 0.0599038
\(115\) 3.40426 0.317449
\(116\) 0.956893 0.0888453
\(117\) 19.2085 1.77582
\(118\) −3.82818 −0.352413
\(119\) −2.41213 −0.221120
\(120\) −0.751696 −0.0686201
\(121\) −4.98205 −0.452914
\(122\) 18.4613 1.67141
\(123\) −0.589632 −0.0531654
\(124\) 0.756975 0.0679783
\(125\) −1.00000 −0.0894427
\(126\) 3.99227 0.355660
\(127\) 5.69003 0.504908 0.252454 0.967609i \(-0.418762\pi\)
0.252454 + 0.967609i \(0.418762\pi\)
\(128\) 9.89423 0.874535
\(129\) −0.831371 −0.0731981
\(130\) 8.90897 0.781368
\(131\) 10.0008 0.873772 0.436886 0.899517i \(-0.356081\pi\)
0.436886 + 0.899517i \(0.356081\pi\)
\(132\) 0.0935884 0.00814583
\(133\) 1.82799 0.158507
\(134\) −8.24887 −0.712594
\(135\) −1.52579 −0.131319
\(136\) −7.05158 −0.604668
\(137\) −1.29589 −0.110715 −0.0553575 0.998467i \(-0.517630\pi\)
−0.0553575 + 0.998467i \(0.517630\pi\)
\(138\) 1.19112 0.101395
\(139\) −15.5953 −1.32278 −0.661389 0.750043i \(-0.730033\pi\)
−0.661389 + 0.750043i \(0.730033\pi\)
\(140\) −0.148369 −0.0125394
\(141\) 1.45383 0.122435
\(142\) 7.44364 0.624656
\(143\) −16.0611 −1.34309
\(144\) 10.8004 0.900030
\(145\) 6.44943 0.535596
\(146\) 6.30346 0.521678
\(147\) −0.257132 −0.0212079
\(148\) 0.627292 0.0515631
\(149\) 4.95261 0.405733 0.202867 0.979206i \(-0.434974\pi\)
0.202867 + 0.979206i \(0.434974\pi\)
\(150\) −0.349892 −0.0285685
\(151\) 9.06032 0.737319 0.368659 0.929565i \(-0.379817\pi\)
0.368659 + 0.929565i \(0.379817\pi\)
\(152\) 5.34392 0.433449
\(153\) −7.07691 −0.572134
\(154\) −3.33812 −0.268993
\(155\) 5.10199 0.409802
\(156\) −0.249775 −0.0199980
\(157\) 13.0286 1.03980 0.519899 0.854228i \(-0.325970\pi\)
0.519899 + 0.854228i \(0.325970\pi\)
\(158\) −0.385750 −0.0306886
\(159\) −0.728986 −0.0578123
\(160\) −0.837522 −0.0662120
\(161\) 3.40426 0.268293
\(162\) 11.4430 0.899043
\(163\) −14.8154 −1.16043 −0.580216 0.814463i \(-0.697032\pi\)
−0.580216 + 0.814463i \(0.697032\pi\)
\(164\) −0.340226 −0.0265672
\(165\) 0.630784 0.0491064
\(166\) 22.5321 1.74883
\(167\) 21.1167 1.63406 0.817030 0.576595i \(-0.195619\pi\)
0.817030 + 0.576595i \(0.195619\pi\)
\(168\) −0.751696 −0.0579946
\(169\) 29.8648 2.29729
\(170\) −3.28230 −0.251741
\(171\) 5.36310 0.410127
\(172\) −0.479712 −0.0365777
\(173\) −1.60426 −0.121969 −0.0609847 0.998139i \(-0.519424\pi\)
−0.0609847 + 0.998139i \(0.519424\pi\)
\(174\) 2.25660 0.171073
\(175\) −1.00000 −0.0755929
\(176\) −9.03066 −0.680712
\(177\) 0.723388 0.0543732
\(178\) −20.6584 −1.54841
\(179\) 21.2800 1.59054 0.795271 0.606254i \(-0.207329\pi\)
0.795271 + 0.606254i \(0.207329\pi\)
\(180\) −0.435296 −0.0324450
\(181\) 17.7462 1.31906 0.659532 0.751677i \(-0.270755\pi\)
0.659532 + 0.751677i \(0.270755\pi\)
\(182\) 8.90897 0.660377
\(183\) −3.48852 −0.257879
\(184\) 9.95196 0.733668
\(185\) 4.22793 0.310844
\(186\) 1.78514 0.130893
\(187\) 5.91732 0.432717
\(188\) 0.838878 0.0611815
\(189\) −1.52579 −0.110985
\(190\) 2.48743 0.180457
\(191\) −0.375150 −0.0271449 −0.0135724 0.999908i \(-0.504320\pi\)
−0.0135724 + 0.999908i \(0.504320\pi\)
\(192\) −2.18618 −0.157774
\(193\) −25.4886 −1.83471 −0.917355 0.398070i \(-0.869680\pi\)
−0.917355 + 0.398070i \(0.869680\pi\)
\(194\) 24.5544 1.76290
\(195\) −1.68347 −0.120556
\(196\) −0.148369 −0.0105978
\(197\) −15.4933 −1.10385 −0.551925 0.833894i \(-0.686106\pi\)
−0.551925 + 0.833894i \(0.686106\pi\)
\(198\) −9.79364 −0.696004
\(199\) −23.6269 −1.67486 −0.837432 0.546542i \(-0.815944\pi\)
−0.837432 + 0.546542i \(0.815944\pi\)
\(200\) −2.92339 −0.206715
\(201\) 1.55874 0.109945
\(202\) −17.8877 −1.25858
\(203\) 6.44943 0.452662
\(204\) 0.0920235 0.00644293
\(205\) −2.29311 −0.160158
\(206\) −20.7578 −1.44626
\(207\) 9.98770 0.694193
\(208\) 24.1016 1.67114
\(209\) −4.48433 −0.310188
\(210\) −0.349892 −0.0241448
\(211\) 10.2622 0.706479 0.353239 0.935533i \(-0.385080\pi\)
0.353239 + 0.935533i \(0.385080\pi\)
\(212\) −0.420634 −0.0288893
\(213\) −1.40658 −0.0963773
\(214\) 2.17867 0.148931
\(215\) −3.23324 −0.220505
\(216\) −4.46048 −0.303497
\(217\) 5.10199 0.346346
\(218\) −8.63274 −0.584683
\(219\) −1.19113 −0.0804889
\(220\) 0.363970 0.0245389
\(221\) −15.7925 −1.06232
\(222\) 1.47932 0.0992853
\(223\) 25.3651 1.69857 0.849285 0.527935i \(-0.177034\pi\)
0.849285 + 0.527935i \(0.177034\pi\)
\(224\) −0.837522 −0.0559593
\(225\) −2.93388 −0.195592
\(226\) −17.4638 −1.16168
\(227\) 18.0852 1.20035 0.600177 0.799867i \(-0.295097\pi\)
0.600177 + 0.799867i \(0.295097\pi\)
\(228\) −0.0697383 −0.00461853
\(229\) 1.00000 0.0660819
\(230\) 4.63233 0.305447
\(231\) 0.630784 0.0415025
\(232\) 18.8542 1.23784
\(233\) 22.2252 1.45602 0.728011 0.685566i \(-0.240445\pi\)
0.728011 + 0.685566i \(0.240445\pi\)
\(234\) 26.1379 1.70869
\(235\) 5.65402 0.368827
\(236\) 0.417404 0.0271707
\(237\) 0.0728928 0.00473489
\(238\) −3.28230 −0.212760
\(239\) 18.8965 1.22231 0.611156 0.791510i \(-0.290705\pi\)
0.611156 + 0.791510i \(0.290705\pi\)
\(240\) −0.946567 −0.0611007
\(241\) 17.0858 1.10059 0.550297 0.834969i \(-0.314514\pi\)
0.550297 + 0.834969i \(0.314514\pi\)
\(242\) −6.77931 −0.435791
\(243\) −6.73968 −0.432351
\(244\) −2.01292 −0.128864
\(245\) −1.00000 −0.0638877
\(246\) −0.802340 −0.0511553
\(247\) 11.9681 0.761509
\(248\) 14.9151 0.947109
\(249\) −4.25775 −0.269824
\(250\) −1.36075 −0.0860612
\(251\) −3.38783 −0.213838 −0.106919 0.994268i \(-0.534099\pi\)
−0.106919 + 0.994268i \(0.534099\pi\)
\(252\) −0.435296 −0.0274211
\(253\) −8.35116 −0.525033
\(254\) 7.74269 0.485819
\(255\) 0.620236 0.0388407
\(256\) −3.54076 −0.221298
\(257\) 5.98187 0.373139 0.186569 0.982442i \(-0.440263\pi\)
0.186569 + 0.982442i \(0.440263\pi\)
\(258\) −1.13129 −0.0704307
\(259\) 4.22793 0.262711
\(260\) −0.971386 −0.0602428
\(261\) 18.9219 1.17124
\(262\) 13.6085 0.840738
\(263\) 14.6794 0.905171 0.452586 0.891721i \(-0.350502\pi\)
0.452586 + 0.891721i \(0.350502\pi\)
\(264\) 1.84402 0.113492
\(265\) −2.83506 −0.174157
\(266\) 2.48743 0.152514
\(267\) 3.90369 0.238902
\(268\) 0.899413 0.0549404
\(269\) −19.5727 −1.19337 −0.596683 0.802477i \(-0.703515\pi\)
−0.596683 + 0.802477i \(0.703515\pi\)
\(270\) −2.07622 −0.126354
\(271\) −30.3199 −1.84180 −0.920900 0.389798i \(-0.872545\pi\)
−0.920900 + 0.389798i \(0.872545\pi\)
\(272\) −8.87965 −0.538408
\(273\) −1.68347 −0.101888
\(274\) −1.76337 −0.106529
\(275\) 2.45315 0.147931
\(276\) −0.129873 −0.00781747
\(277\) −10.3698 −0.623063 −0.311531 0.950236i \(-0.600842\pi\)
−0.311531 + 0.950236i \(0.600842\pi\)
\(278\) −21.2213 −1.27277
\(279\) 14.9686 0.896149
\(280\) −2.92339 −0.174706
\(281\) −5.60689 −0.334479 −0.167240 0.985916i \(-0.553485\pi\)
−0.167240 + 0.985916i \(0.553485\pi\)
\(282\) 1.97829 0.117806
\(283\) 16.9436 1.00719 0.503597 0.863939i \(-0.332010\pi\)
0.503597 + 0.863939i \(0.332010\pi\)
\(284\) −0.811615 −0.0481605
\(285\) −0.470034 −0.0278424
\(286\) −21.8550 −1.29232
\(287\) −2.29311 −0.135358
\(288\) −2.45719 −0.144791
\(289\) −11.1816 −0.657743
\(290\) 8.77605 0.515347
\(291\) −4.63989 −0.271995
\(292\) −0.687296 −0.0402209
\(293\) 20.8585 1.21856 0.609282 0.792953i \(-0.291458\pi\)
0.609282 + 0.792953i \(0.291458\pi\)
\(294\) −0.349892 −0.0204061
\(295\) 2.81329 0.163796
\(296\) 12.3599 0.718403
\(297\) 3.74300 0.217191
\(298\) 6.73924 0.390394
\(299\) 22.2881 1.28895
\(300\) 0.0381503 0.00220261
\(301\) −3.23324 −0.186361
\(302\) 12.3288 0.709443
\(303\) 3.38013 0.194184
\(304\) 6.72928 0.385951
\(305\) −13.5670 −0.776846
\(306\) −9.62987 −0.550503
\(307\) −7.05883 −0.402868 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(308\) 0.363970 0.0207391
\(309\) 3.92247 0.223142
\(310\) 6.94252 0.394308
\(311\) 29.2429 1.65821 0.829107 0.559089i \(-0.188849\pi\)
0.829107 + 0.559089i \(0.188849\pi\)
\(312\) −4.92144 −0.278622
\(313\) −4.35508 −0.246164 −0.123082 0.992397i \(-0.539278\pi\)
−0.123082 + 0.992397i \(0.539278\pi\)
\(314\) 17.7287 1.00049
\(315\) −2.93388 −0.165306
\(316\) 0.0420601 0.00236606
\(317\) 8.45347 0.474794 0.237397 0.971413i \(-0.423706\pi\)
0.237397 + 0.971413i \(0.423706\pi\)
\(318\) −0.991965 −0.0556266
\(319\) −15.8214 −0.885830
\(320\) −8.50216 −0.475285
\(321\) −0.411691 −0.0229783
\(322\) 4.63233 0.258150
\(323\) −4.40934 −0.245343
\(324\) −1.24768 −0.0693155
\(325\) −6.54712 −0.363169
\(326\) −20.1600 −1.11656
\(327\) 1.63128 0.0902098
\(328\) −6.70365 −0.370147
\(329\) 5.65402 0.311716
\(330\) 0.858337 0.0472499
\(331\) 3.24624 0.178429 0.0892146 0.996012i \(-0.471564\pi\)
0.0892146 + 0.996012i \(0.471564\pi\)
\(332\) −2.45678 −0.134833
\(333\) 12.4043 0.679749
\(334\) 28.7345 1.57228
\(335\) 6.06202 0.331203
\(336\) −0.946567 −0.0516395
\(337\) 11.9661 0.651833 0.325916 0.945399i \(-0.394327\pi\)
0.325916 + 0.945399i \(0.394327\pi\)
\(338\) 40.6384 2.21044
\(339\) 3.30003 0.179233
\(340\) 0.357884 0.0194090
\(341\) −12.5159 −0.677777
\(342\) 7.29783 0.394621
\(343\) −1.00000 −0.0539949
\(344\) −9.45202 −0.509619
\(345\) −0.875344 −0.0471269
\(346\) −2.18299 −0.117358
\(347\) 22.7992 1.22393 0.611963 0.790887i \(-0.290380\pi\)
0.611963 + 0.790887i \(0.290380\pi\)
\(348\) −0.246048 −0.0131896
\(349\) 1.06720 0.0571260 0.0285630 0.999592i \(-0.490907\pi\)
0.0285630 + 0.999592i \(0.490907\pi\)
\(350\) −1.36075 −0.0727350
\(351\) −9.98954 −0.533202
\(352\) 2.05457 0.109509
\(353\) −1.72208 −0.0916573 −0.0458286 0.998949i \(-0.514593\pi\)
−0.0458286 + 0.998949i \(0.514593\pi\)
\(354\) 0.984348 0.0523175
\(355\) −5.47026 −0.290331
\(356\) 2.25248 0.119381
\(357\) 0.620236 0.0328264
\(358\) 28.9567 1.53041
\(359\) −6.23114 −0.328867 −0.164433 0.986388i \(-0.552580\pi\)
−0.164433 + 0.986388i \(0.552580\pi\)
\(360\) −8.57687 −0.452041
\(361\) −15.6585 −0.824129
\(362\) 24.1481 1.26919
\(363\) 1.28105 0.0672374
\(364\) −0.971386 −0.0509145
\(365\) −4.63235 −0.242469
\(366\) −4.74699 −0.248129
\(367\) −15.1775 −0.792257 −0.396128 0.918195i \(-0.629646\pi\)
−0.396128 + 0.918195i \(0.629646\pi\)
\(368\) 12.5319 0.653272
\(369\) −6.72772 −0.350231
\(370\) 5.75315 0.299092
\(371\) −2.83506 −0.147189
\(372\) −0.194642 −0.0100917
\(373\) 9.06530 0.469384 0.234692 0.972070i \(-0.424592\pi\)
0.234692 + 0.972070i \(0.424592\pi\)
\(374\) 8.05197 0.416357
\(375\) 0.257132 0.0132782
\(376\) 16.5289 0.852412
\(377\) 42.2252 2.17471
\(378\) −2.07622 −0.106789
\(379\) −10.3267 −0.530448 −0.265224 0.964187i \(-0.585446\pi\)
−0.265224 + 0.964187i \(0.585446\pi\)
\(380\) −0.271216 −0.0139131
\(381\) −1.46309 −0.0749563
\(382\) −0.510484 −0.0261186
\(383\) −1.14557 −0.0585360 −0.0292680 0.999572i \(-0.509318\pi\)
−0.0292680 + 0.999572i \(0.509318\pi\)
\(384\) −2.54412 −0.129829
\(385\) 2.45315 0.125024
\(386\) −34.6835 −1.76535
\(387\) −9.48596 −0.482199
\(388\) −2.67728 −0.135918
\(389\) −12.6708 −0.642435 −0.321218 0.947005i \(-0.604092\pi\)
−0.321218 + 0.947005i \(0.604092\pi\)
\(390\) −2.29078 −0.115998
\(391\) −8.21151 −0.415274
\(392\) −2.92339 −0.147653
\(393\) −2.57152 −0.129716
\(394\) −21.0824 −1.06212
\(395\) 0.283484 0.0142636
\(396\) 1.06785 0.0536613
\(397\) −15.7512 −0.790529 −0.395264 0.918567i \(-0.629347\pi\)
−0.395264 + 0.918567i \(0.629347\pi\)
\(398\) −32.1502 −1.61154
\(399\) −0.470034 −0.0235312
\(400\) −3.68125 −0.184062
\(401\) −30.5113 −1.52366 −0.761832 0.647775i \(-0.775700\pi\)
−0.761832 + 0.647775i \(0.775700\pi\)
\(402\) 2.12105 0.105788
\(403\) 33.4033 1.66394
\(404\) 1.95038 0.0970351
\(405\) −8.40932 −0.417862
\(406\) 8.77605 0.435548
\(407\) −10.3718 −0.514109
\(408\) 1.81319 0.0897662
\(409\) −9.50078 −0.469783 −0.234892 0.972022i \(-0.575474\pi\)
−0.234892 + 0.972022i \(0.575474\pi\)
\(410\) −3.12034 −0.154103
\(411\) 0.333214 0.0164362
\(412\) 2.26332 0.111506
\(413\) 2.81329 0.138433
\(414\) 13.5907 0.667948
\(415\) −16.5586 −0.812830
\(416\) −5.48336 −0.268844
\(417\) 4.01006 0.196373
\(418\) −6.10204 −0.298460
\(419\) −37.1451 −1.81466 −0.907329 0.420421i \(-0.861882\pi\)
−0.907329 + 0.420421i \(0.861882\pi\)
\(420\) 0.0381503 0.00186154
\(421\) −29.8844 −1.45648 −0.728239 0.685324i \(-0.759661\pi\)
−0.728239 + 0.685324i \(0.759661\pi\)
\(422\) 13.9643 0.679769
\(423\) 16.5882 0.806547
\(424\) −8.28799 −0.402500
\(425\) 2.41213 0.117005
\(426\) −1.91400 −0.0927335
\(427\) −13.5670 −0.656554
\(428\) −0.237551 −0.0114825
\(429\) 4.12982 0.199389
\(430\) −4.39963 −0.212169
\(431\) 10.6556 0.513262 0.256631 0.966509i \(-0.417387\pi\)
0.256631 + 0.966509i \(0.417387\pi\)
\(432\) −5.61682 −0.270239
\(433\) −13.5004 −0.648789 −0.324395 0.945922i \(-0.605161\pi\)
−0.324395 + 0.945922i \(0.605161\pi\)
\(434\) 6.94252 0.333251
\(435\) −1.65836 −0.0795121
\(436\) 0.941268 0.0450785
\(437\) 6.22295 0.297684
\(438\) −1.62082 −0.0774459
\(439\) −23.5744 −1.12514 −0.562571 0.826749i \(-0.690188\pi\)
−0.562571 + 0.826749i \(0.690188\pi\)
\(440\) 7.17150 0.341888
\(441\) −2.93388 −0.139709
\(442\) −21.4896 −1.02216
\(443\) −3.22835 −0.153383 −0.0766917 0.997055i \(-0.524436\pi\)
−0.0766917 + 0.997055i \(0.524436\pi\)
\(444\) −0.161297 −0.00765481
\(445\) 15.1817 0.719680
\(446\) 34.5154 1.63435
\(447\) −1.27347 −0.0602333
\(448\) −8.50216 −0.401689
\(449\) 0.148445 0.00700554 0.00350277 0.999994i \(-0.498885\pi\)
0.00350277 + 0.999994i \(0.498885\pi\)
\(450\) −3.99227 −0.188197
\(451\) 5.62535 0.264887
\(452\) 1.90416 0.0895642
\(453\) −2.32970 −0.109459
\(454\) 24.6093 1.15497
\(455\) −6.54712 −0.306934
\(456\) −1.37409 −0.0643477
\(457\) −29.1669 −1.36437 −0.682184 0.731180i \(-0.738970\pi\)
−0.682184 + 0.731180i \(0.738970\pi\)
\(458\) 1.36075 0.0635835
\(459\) 3.68041 0.171787
\(460\) −0.505085 −0.0235497
\(461\) −1.40469 −0.0654230 −0.0327115 0.999465i \(-0.510414\pi\)
−0.0327115 + 0.999465i \(0.510414\pi\)
\(462\) 0.858337 0.0399334
\(463\) 11.1139 0.516505 0.258253 0.966077i \(-0.416853\pi\)
0.258253 + 0.966077i \(0.416853\pi\)
\(464\) 23.7420 1.10219
\(465\) −1.31189 −0.0608372
\(466\) 30.2429 1.40097
\(467\) 27.1339 1.25561 0.627804 0.778372i \(-0.283954\pi\)
0.627804 + 0.778372i \(0.283954\pi\)
\(468\) −2.84993 −0.131738
\(469\) 6.06202 0.279918
\(470\) 7.69369 0.354883
\(471\) −3.35008 −0.154363
\(472\) 8.22434 0.378556
\(473\) 7.93164 0.364697
\(474\) 0.0991886 0.00455588
\(475\) −1.82799 −0.0838739
\(476\) 0.357884 0.0164036
\(477\) −8.31775 −0.380844
\(478\) 25.7133 1.17610
\(479\) 19.9724 0.912563 0.456282 0.889835i \(-0.349181\pi\)
0.456282 + 0.889835i \(0.349181\pi\)
\(480\) 0.215354 0.00982951
\(481\) 27.6808 1.26213
\(482\) 23.2495 1.05898
\(483\) −0.875344 −0.0398295
\(484\) 0.739180 0.0335991
\(485\) −18.0448 −0.819371
\(486\) −9.17100 −0.416005
\(487\) 1.33355 0.0604289 0.0302145 0.999543i \(-0.490381\pi\)
0.0302145 + 0.999543i \(0.490381\pi\)
\(488\) −39.6616 −1.79540
\(489\) 3.80952 0.172272
\(490\) −1.36075 −0.0614723
\(491\) −28.1494 −1.27036 −0.635182 0.772362i \(-0.719075\pi\)
−0.635182 + 0.772362i \(0.719075\pi\)
\(492\) 0.0874829 0.00394403
\(493\) −15.5569 −0.700646
\(494\) 16.2855 0.732719
\(495\) 7.19726 0.323493
\(496\) 18.7817 0.843323
\(497\) −5.47026 −0.245375
\(498\) −5.79372 −0.259623
\(499\) 37.6786 1.68672 0.843362 0.537346i \(-0.180573\pi\)
0.843362 + 0.537346i \(0.180573\pi\)
\(500\) 0.148369 0.00663524
\(501\) −5.42978 −0.242585
\(502\) −4.60998 −0.205754
\(503\) −2.49071 −0.111055 −0.0555276 0.998457i \(-0.517684\pi\)
−0.0555276 + 0.998457i \(0.517684\pi\)
\(504\) −8.57687 −0.382044
\(505\) 13.1455 0.584968
\(506\) −11.3638 −0.505183
\(507\) −7.67919 −0.341045
\(508\) −0.844221 −0.0374562
\(509\) 22.4737 0.996131 0.498065 0.867139i \(-0.334044\pi\)
0.498065 + 0.867139i \(0.334044\pi\)
\(510\) 0.843984 0.0373722
\(511\) −4.63235 −0.204923
\(512\) −24.6066 −1.08747
\(513\) −2.78913 −0.123143
\(514\) 8.13981 0.359032
\(515\) 15.2547 0.672203
\(516\) 0.123349 0.00543015
\(517\) −13.8702 −0.610009
\(518\) 5.75315 0.252779
\(519\) 0.412506 0.0181070
\(520\) −19.1397 −0.839334
\(521\) 29.9008 1.30998 0.654988 0.755639i \(-0.272674\pi\)
0.654988 + 0.755639i \(0.272674\pi\)
\(522\) 25.7479 1.12695
\(523\) 26.3058 1.15027 0.575137 0.818057i \(-0.304949\pi\)
0.575137 + 0.818057i \(0.304949\pi\)
\(524\) −1.48380 −0.0648202
\(525\) 0.257132 0.0112222
\(526\) 19.9750 0.870950
\(527\) −12.3067 −0.536086
\(528\) 2.32207 0.101055
\(529\) −11.4110 −0.496132
\(530\) −3.85780 −0.167572
\(531\) 8.25388 0.358188
\(532\) −0.271216 −0.0117587
\(533\) −15.0133 −0.650297
\(534\) 5.31194 0.229870
\(535\) −1.60109 −0.0692210
\(536\) 17.7216 0.765457
\(537\) −5.47177 −0.236124
\(538\) −26.6334 −1.14825
\(539\) 2.45315 0.105665
\(540\) 0.226379 0.00974182
\(541\) −6.39561 −0.274969 −0.137484 0.990504i \(-0.543902\pi\)
−0.137484 + 0.990504i \(0.543902\pi\)
\(542\) −41.2577 −1.77217
\(543\) −4.56311 −0.195822
\(544\) 2.02021 0.0866159
\(545\) 6.34412 0.271752
\(546\) −2.29078 −0.0980364
\(547\) −41.1075 −1.75763 −0.878815 0.477163i \(-0.841665\pi\)
−0.878815 + 0.477163i \(0.841665\pi\)
\(548\) 0.192269 0.00821331
\(549\) −39.8041 −1.69880
\(550\) 3.33812 0.142338
\(551\) 11.7895 0.502249
\(552\) −2.55897 −0.108917
\(553\) 0.283484 0.0120550
\(554\) −14.1107 −0.599507
\(555\) −1.08714 −0.0461464
\(556\) 2.31386 0.0981294
\(557\) −5.28448 −0.223911 −0.111955 0.993713i \(-0.535711\pi\)
−0.111955 + 0.993713i \(0.535711\pi\)
\(558\) 20.3685 0.862269
\(559\) −21.1684 −0.895329
\(560\) −3.68125 −0.155561
\(561\) −1.52153 −0.0642391
\(562\) −7.62956 −0.321834
\(563\) −0.231516 −0.00975723 −0.00487861 0.999988i \(-0.501553\pi\)
−0.00487861 + 0.999988i \(0.501553\pi\)
\(564\) −0.215703 −0.00908271
\(565\) 12.8340 0.539930
\(566\) 23.0560 0.969115
\(567\) −8.40932 −0.353158
\(568\) −15.9917 −0.670996
\(569\) 36.9119 1.54743 0.773714 0.633535i \(-0.218397\pi\)
0.773714 + 0.633535i \(0.218397\pi\)
\(570\) −0.639598 −0.0267898
\(571\) −14.4711 −0.605598 −0.302799 0.953055i \(-0.597921\pi\)
−0.302799 + 0.953055i \(0.597921\pi\)
\(572\) 2.38296 0.0996364
\(573\) 0.0964631 0.00402980
\(574\) −3.12034 −0.130241
\(575\) −3.40426 −0.141967
\(576\) −24.9443 −1.03935
\(577\) 29.7407 1.23812 0.619060 0.785344i \(-0.287514\pi\)
0.619060 + 0.785344i \(0.287514\pi\)
\(578\) −15.2154 −0.632876
\(579\) 6.55394 0.272372
\(580\) −0.956893 −0.0397328
\(581\) −16.5586 −0.686967
\(582\) −6.31372 −0.261712
\(583\) 6.95484 0.288040
\(584\) −13.5422 −0.560378
\(585\) −19.2085 −0.794173
\(586\) 28.3831 1.17249
\(587\) 9.11988 0.376418 0.188209 0.982129i \(-0.439732\pi\)
0.188209 + 0.982129i \(0.439732\pi\)
\(588\) 0.0381503 0.00157329
\(589\) 9.32638 0.384287
\(590\) 3.82818 0.157604
\(591\) 3.98381 0.163872
\(592\) 15.5641 0.639680
\(593\) 18.8927 0.775830 0.387915 0.921695i \(-0.373195\pi\)
0.387915 + 0.921695i \(0.373195\pi\)
\(594\) 5.09327 0.208979
\(595\) 2.41213 0.0988877
\(596\) −0.734811 −0.0300990
\(597\) 6.07522 0.248642
\(598\) 30.3284 1.24022
\(599\) −21.2020 −0.866291 −0.433146 0.901324i \(-0.642596\pi\)
−0.433146 + 0.901324i \(0.642596\pi\)
\(600\) 0.751696 0.0306879
\(601\) 27.7285 1.13107 0.565535 0.824724i \(-0.308670\pi\)
0.565535 + 0.824724i \(0.308670\pi\)
\(602\) −4.39963 −0.179315
\(603\) 17.7853 0.724272
\(604\) −1.34427 −0.0546974
\(605\) 4.98205 0.202549
\(606\) 4.59951 0.186842
\(607\) −42.6469 −1.73098 −0.865492 0.500922i \(-0.832994\pi\)
−0.865492 + 0.500922i \(0.832994\pi\)
\(608\) −1.53098 −0.0620895
\(609\) −1.65836 −0.0672000
\(610\) −18.4613 −0.747476
\(611\) 37.0175 1.49757
\(612\) 1.04999 0.0424433
\(613\) −26.4348 −1.06769 −0.533845 0.845582i \(-0.679254\pi\)
−0.533845 + 0.845582i \(0.679254\pi\)
\(614\) −9.60527 −0.387637
\(615\) 0.589632 0.0237763
\(616\) 7.17150 0.288948
\(617\) 12.3532 0.497323 0.248661 0.968591i \(-0.420009\pi\)
0.248661 + 0.968591i \(0.420009\pi\)
\(618\) 5.33749 0.214705
\(619\) 24.8927 1.00052 0.500260 0.865875i \(-0.333238\pi\)
0.500260 + 0.865875i \(0.333238\pi\)
\(620\) −0.756975 −0.0304008
\(621\) −5.19419 −0.208436
\(622\) 39.7922 1.59552
\(623\) 15.1817 0.608241
\(624\) −6.19729 −0.248090
\(625\) 1.00000 0.0400000
\(626\) −5.92616 −0.236857
\(627\) 1.15307 0.0460490
\(628\) −1.93304 −0.0771366
\(629\) −10.1983 −0.406634
\(630\) −3.99227 −0.159056
\(631\) −18.4029 −0.732609 −0.366305 0.930495i \(-0.619377\pi\)
−0.366305 + 0.930495i \(0.619377\pi\)
\(632\) 0.828732 0.0329652
\(633\) −2.63874 −0.104881
\(634\) 11.5030 0.456844
\(635\) −5.69003 −0.225802
\(636\) 0.108159 0.00428877
\(637\) −6.54712 −0.259406
\(638\) −21.5290 −0.852340
\(639\) −16.0491 −0.634893
\(640\) −9.89423 −0.391104
\(641\) 1.32388 0.0522902 0.0261451 0.999658i \(-0.491677\pi\)
0.0261451 + 0.999658i \(0.491677\pi\)
\(642\) −0.560207 −0.0221096
\(643\) 27.0779 1.06785 0.533924 0.845533i \(-0.320717\pi\)
0.533924 + 0.845533i \(0.320717\pi\)
\(644\) −0.505085 −0.0199031
\(645\) 0.831371 0.0327352
\(646\) −6.00000 −0.236067
\(647\) 39.3873 1.54848 0.774238 0.632895i \(-0.218133\pi\)
0.774238 + 0.632895i \(0.218133\pi\)
\(648\) −24.5837 −0.965738
\(649\) −6.90144 −0.270905
\(650\) −8.90897 −0.349439
\(651\) −1.31189 −0.0514168
\(652\) 2.19814 0.0860858
\(653\) −22.4220 −0.877441 −0.438721 0.898624i \(-0.644568\pi\)
−0.438721 + 0.898624i \(0.644568\pi\)
\(654\) 2.21975 0.0867992
\(655\) −10.0008 −0.390763
\(656\) −8.44151 −0.329586
\(657\) −13.5908 −0.530227
\(658\) 7.69369 0.299931
\(659\) 36.2517 1.41216 0.706082 0.708130i \(-0.250461\pi\)
0.706082 + 0.708130i \(0.250461\pi\)
\(660\) −0.0935884 −0.00364293
\(661\) −5.98017 −0.232602 −0.116301 0.993214i \(-0.537104\pi\)
−0.116301 + 0.993214i \(0.537104\pi\)
\(662\) 4.41731 0.171683
\(663\) 4.06076 0.157707
\(664\) −48.4072 −1.87856
\(665\) −1.82799 −0.0708864
\(666\) 16.8791 0.654050
\(667\) 21.9555 0.850122
\(668\) −3.13306 −0.121222
\(669\) −6.52217 −0.252162
\(670\) 8.24887 0.318682
\(671\) 33.2820 1.28484
\(672\) 0.215354 0.00830745
\(673\) 15.4410 0.595207 0.297604 0.954690i \(-0.403813\pi\)
0.297604 + 0.954690i \(0.403813\pi\)
\(674\) 16.2828 0.627189
\(675\) 1.52579 0.0587277
\(676\) −4.43099 −0.170423
\(677\) −17.4510 −0.670698 −0.335349 0.942094i \(-0.608854\pi\)
−0.335349 + 0.942094i \(0.608854\pi\)
\(678\) 4.49051 0.172457
\(679\) −18.0448 −0.692495
\(680\) 7.05158 0.270416
\(681\) −4.65027 −0.178199
\(682\) −17.0310 −0.652152
\(683\) −22.4917 −0.860619 −0.430310 0.902681i \(-0.641596\pi\)
−0.430310 + 0.902681i \(0.641596\pi\)
\(684\) −0.795716 −0.0304250
\(685\) 1.29589 0.0495132
\(686\) −1.36075 −0.0519535
\(687\) −0.257132 −0.00981020
\(688\) −11.9024 −0.453774
\(689\) −18.5615 −0.707137
\(690\) −1.19112 −0.0453452
\(691\) −27.9142 −1.06191 −0.530953 0.847401i \(-0.678166\pi\)
−0.530953 + 0.847401i \(0.678166\pi\)
\(692\) 0.238021 0.00904821
\(693\) 7.19726 0.273401
\(694\) 31.0239 1.17765
\(695\) 15.5953 0.591565
\(696\) −4.84801 −0.183764
\(697\) 5.53128 0.209512
\(698\) 1.45219 0.0549663
\(699\) −5.71481 −0.216154
\(700\) 0.148369 0.00560780
\(701\) −30.2996 −1.14440 −0.572199 0.820114i \(-0.693910\pi\)
−0.572199 + 0.820114i \(0.693910\pi\)
\(702\) −13.5932 −0.513043
\(703\) 7.72861 0.291490
\(704\) 20.8571 0.786080
\(705\) −1.45383 −0.0547544
\(706\) −2.34332 −0.0881920
\(707\) 13.1455 0.494388
\(708\) −0.107328 −0.00403363
\(709\) 40.9315 1.53721 0.768607 0.639721i \(-0.220950\pi\)
0.768607 + 0.639721i \(0.220950\pi\)
\(710\) −7.44364 −0.279355
\(711\) 0.831708 0.0311915
\(712\) 44.3819 1.66328
\(713\) 17.3685 0.650455
\(714\) 0.843984 0.0315853
\(715\) 16.0611 0.600650
\(716\) −3.15728 −0.117993
\(717\) −4.85889 −0.181459
\(718\) −8.47900 −0.316434
\(719\) 47.0285 1.75387 0.876934 0.480610i \(-0.159585\pi\)
0.876934 + 0.480610i \(0.159585\pi\)
\(720\) −10.8004 −0.402506
\(721\) 15.2547 0.568115
\(722\) −21.3072 −0.792972
\(723\) −4.39331 −0.163389
\(724\) −2.63298 −0.0978537
\(725\) −6.44943 −0.239526
\(726\) 1.74318 0.0646954
\(727\) −45.5396 −1.68897 −0.844485 0.535579i \(-0.820094\pi\)
−0.844485 + 0.535579i \(0.820094\pi\)
\(728\) −19.1397 −0.709366
\(729\) −23.4950 −0.870184
\(730\) −6.30346 −0.233302
\(731\) 7.79900 0.288457
\(732\) 0.517586 0.0191305
\(733\) −43.7539 −1.61609 −0.808044 0.589123i \(-0.799473\pi\)
−0.808044 + 0.589123i \(0.799473\pi\)
\(734\) −20.6527 −0.762304
\(735\) 0.257132 0.00948446
\(736\) −2.85114 −0.105094
\(737\) −14.8710 −0.547782
\(738\) −9.15472 −0.336990
\(739\) −22.6412 −0.832872 −0.416436 0.909165i \(-0.636721\pi\)
−0.416436 + 0.909165i \(0.636721\pi\)
\(740\) −0.627292 −0.0230597
\(741\) −3.07737 −0.113050
\(742\) −3.85780 −0.141624
\(743\) 3.15496 0.115744 0.0578721 0.998324i \(-0.481568\pi\)
0.0578721 + 0.998324i \(0.481568\pi\)
\(744\) −3.83515 −0.140603
\(745\) −4.95261 −0.181449
\(746\) 12.3356 0.451638
\(747\) −48.5810 −1.77749
\(748\) −0.877944 −0.0321008
\(749\) −1.60109 −0.0585024
\(750\) 0.349892 0.0127762
\(751\) 3.29089 0.120086 0.0600432 0.998196i \(-0.480876\pi\)
0.0600432 + 0.998196i \(0.480876\pi\)
\(752\) 20.8139 0.759003
\(753\) 0.871120 0.0317454
\(754\) 57.4578 2.09249
\(755\) −9.06032 −0.329739
\(756\) 0.226379 0.00823334
\(757\) 30.0841 1.09343 0.546713 0.837320i \(-0.315879\pi\)
0.546713 + 0.837320i \(0.315879\pi\)
\(758\) −14.0520 −0.510393
\(759\) 2.14735 0.0779439
\(760\) −5.34392 −0.193844
\(761\) −44.6296 −1.61782 −0.808911 0.587931i \(-0.799943\pi\)
−0.808911 + 0.587931i \(0.799943\pi\)
\(762\) −1.99089 −0.0721224
\(763\) 6.34412 0.229673
\(764\) 0.0556604 0.00201372
\(765\) 7.07691 0.255866
\(766\) −1.55883 −0.0563229
\(767\) 18.4190 0.665071
\(768\) 0.910444 0.0328528
\(769\) 11.3535 0.409418 0.204709 0.978823i \(-0.434375\pi\)
0.204709 + 0.978823i \(0.434375\pi\)
\(770\) 3.33812 0.120297
\(771\) −1.53813 −0.0553944
\(772\) 3.78171 0.136107
\(773\) 24.6584 0.886903 0.443451 0.896298i \(-0.353754\pi\)
0.443451 + 0.896298i \(0.353754\pi\)
\(774\) −12.9080 −0.463968
\(775\) −5.10199 −0.183269
\(776\) −52.7519 −1.89368
\(777\) −1.08714 −0.0390008
\(778\) −17.2418 −0.618147
\(779\) −4.19178 −0.150186
\(780\) 0.249775 0.00894336
\(781\) 13.4194 0.480183
\(782\) −11.1738 −0.399574
\(783\) −9.84049 −0.351671
\(784\) −3.68125 −0.131473
\(785\) −13.0286 −0.465011
\(786\) −3.49919 −0.124812
\(787\) 32.2771 1.15055 0.575277 0.817959i \(-0.304894\pi\)
0.575277 + 0.817959i \(0.304894\pi\)
\(788\) 2.29871 0.0818883
\(789\) −3.77455 −0.134377
\(790\) 0.385750 0.0137244
\(791\) 12.8340 0.456324
\(792\) 21.0404 0.747637
\(793\) −88.8249 −3.15427
\(794\) −21.4334 −0.760641
\(795\) 0.728986 0.0258545
\(796\) 3.50548 0.124248
\(797\) −34.2727 −1.21400 −0.607000 0.794701i \(-0.707627\pi\)
−0.607000 + 0.794701i \(0.707627\pi\)
\(798\) −0.639598 −0.0226415
\(799\) −13.6382 −0.482486
\(800\) 0.837522 0.0296109
\(801\) 44.5412 1.57379
\(802\) −41.5182 −1.46606
\(803\) 11.3639 0.401022
\(804\) −0.231268 −0.00815619
\(805\) −3.40426 −0.119984
\(806\) 45.4535 1.60103
\(807\) 5.03276 0.177161
\(808\) 38.4294 1.35194
\(809\) 21.5274 0.756863 0.378432 0.925629i \(-0.376464\pi\)
0.378432 + 0.925629i \(0.376464\pi\)
\(810\) −11.4430 −0.402064
\(811\) −41.4583 −1.45580 −0.727900 0.685684i \(-0.759503\pi\)
−0.727900 + 0.685684i \(0.759503\pi\)
\(812\) −0.956893 −0.0335804
\(813\) 7.79621 0.273425
\(814\) −14.1133 −0.494672
\(815\) 14.8154 0.518961
\(816\) 2.28324 0.0799295
\(817\) −5.91033 −0.206776
\(818\) −12.9282 −0.452022
\(819\) −19.2085 −0.671199
\(820\) 0.340226 0.0118812
\(821\) −20.0560 −0.699958 −0.349979 0.936758i \(-0.613811\pi\)
−0.349979 + 0.936758i \(0.613811\pi\)
\(822\) 0.453419 0.0158148
\(823\) 11.9200 0.415505 0.207753 0.978181i \(-0.433385\pi\)
0.207753 + 0.978181i \(0.433385\pi\)
\(824\) 44.5954 1.55355
\(825\) −0.630784 −0.0219611
\(826\) 3.82818 0.133199
\(827\) −9.97425 −0.346839 −0.173419 0.984848i \(-0.555482\pi\)
−0.173419 + 0.984848i \(0.555482\pi\)
\(828\) −1.48186 −0.0514982
\(829\) −2.21474 −0.0769211 −0.0384605 0.999260i \(-0.512245\pi\)
−0.0384605 + 0.999260i \(0.512245\pi\)
\(830\) −22.5321 −0.782100
\(831\) 2.66642 0.0924970
\(832\) −55.6646 −1.92982
\(833\) 2.41213 0.0835753
\(834\) 5.45667 0.188949
\(835\) −21.1167 −0.730774
\(836\) 0.665334 0.0230110
\(837\) −7.78457 −0.269074
\(838\) −50.5451 −1.74605
\(839\) −2.20808 −0.0762312 −0.0381156 0.999273i \(-0.512136\pi\)
−0.0381156 + 0.999273i \(0.512136\pi\)
\(840\) 0.751696 0.0259360
\(841\) 12.5952 0.434318
\(842\) −40.6651 −1.40141
\(843\) 1.44171 0.0496552
\(844\) −1.52259 −0.0524096
\(845\) −29.8648 −1.02738
\(846\) 22.5724 0.776054
\(847\) 4.98205 0.171185
\(848\) −10.4366 −0.358394
\(849\) −4.35675 −0.149523
\(850\) 3.28230 0.112582
\(851\) 14.3930 0.493385
\(852\) 0.208692 0.00714968
\(853\) 25.8071 0.883618 0.441809 0.897109i \(-0.354337\pi\)
0.441809 + 0.897109i \(0.354337\pi\)
\(854\) −18.4613 −0.631732
\(855\) −5.36310 −0.183414
\(856\) −4.68059 −0.159979
\(857\) 52.6781 1.79945 0.899724 0.436459i \(-0.143768\pi\)
0.899724 + 0.436459i \(0.143768\pi\)
\(858\) 5.61963 0.191851
\(859\) 21.4872 0.733133 0.366566 0.930392i \(-0.380533\pi\)
0.366566 + 0.930392i \(0.380533\pi\)
\(860\) 0.479712 0.0163580
\(861\) 0.589632 0.0200946
\(862\) 14.4996 0.493857
\(863\) −5.13712 −0.174870 −0.0874348 0.996170i \(-0.527867\pi\)
−0.0874348 + 0.996170i \(0.527867\pi\)
\(864\) 1.27788 0.0434745
\(865\) 1.60426 0.0545464
\(866\) −18.3707 −0.624261
\(867\) 2.87516 0.0976454
\(868\) −0.756975 −0.0256934
\(869\) −0.695429 −0.0235908
\(870\) −2.25660 −0.0765060
\(871\) 39.6888 1.34480
\(872\) 18.5463 0.628057
\(873\) −52.9413 −1.79179
\(874\) 8.46785 0.286429
\(875\) 1.00000 0.0338062
\(876\) 0.176726 0.00597101
\(877\) 16.7997 0.567284 0.283642 0.958930i \(-0.408457\pi\)
0.283642 + 0.958930i \(0.408457\pi\)
\(878\) −32.0787 −1.08260
\(879\) −5.36338 −0.180902
\(880\) 9.03066 0.304423
\(881\) −21.0577 −0.709453 −0.354727 0.934970i \(-0.615426\pi\)
−0.354727 + 0.934970i \(0.615426\pi\)
\(882\) −3.99227 −0.134427
\(883\) 40.5920 1.36603 0.683014 0.730405i \(-0.260669\pi\)
0.683014 + 0.730405i \(0.260669\pi\)
\(884\) 2.34311 0.0788073
\(885\) −0.723388 −0.0243164
\(886\) −4.39296 −0.147584
\(887\) −35.0020 −1.17525 −0.587627 0.809132i \(-0.699938\pi\)
−0.587627 + 0.809132i \(0.699938\pi\)
\(888\) −3.17812 −0.106651
\(889\) −5.69003 −0.190837
\(890\) 20.6584 0.692471
\(891\) 20.6293 0.691108
\(892\) −3.76338 −0.126007
\(893\) 10.3355 0.345864
\(894\) −1.73288 −0.0579560
\(895\) −21.2800 −0.711312
\(896\) −9.89423 −0.330543
\(897\) −5.73098 −0.191352
\(898\) 0.201996 0.00674068
\(899\) 32.9050 1.09744
\(900\) 0.435296 0.0145099
\(901\) 6.83854 0.227825
\(902\) 7.65467 0.254873
\(903\) 0.831371 0.0276663
\(904\) 37.5187 1.24785
\(905\) −17.7462 −0.589903
\(906\) −3.17013 −0.105321
\(907\) −16.8302 −0.558838 −0.279419 0.960169i \(-0.590142\pi\)
−0.279419 + 0.960169i \(0.590142\pi\)
\(908\) −2.68327 −0.0890474
\(909\) 38.5674 1.27920
\(910\) −8.90897 −0.295329
\(911\) −15.2405 −0.504939 −0.252469 0.967605i \(-0.581243\pi\)
−0.252469 + 0.967605i \(0.581243\pi\)
\(912\) −1.73031 −0.0572964
\(913\) 40.6208 1.34435
\(914\) −39.6887 −1.31279
\(915\) 3.48852 0.115327
\(916\) −0.148369 −0.00490223
\(917\) −10.0008 −0.330255
\(918\) 5.00810 0.165292
\(919\) 4.84045 0.159672 0.0798358 0.996808i \(-0.474560\pi\)
0.0798358 + 0.996808i \(0.474560\pi\)
\(920\) −9.95196 −0.328106
\(921\) 1.81505 0.0598079
\(922\) −1.91143 −0.0629495
\(923\) −35.8145 −1.17885
\(924\) −0.0935884 −0.00307883
\(925\) −4.22793 −0.139014
\(926\) 15.1232 0.496978
\(927\) 44.7555 1.46996
\(928\) −5.40155 −0.177314
\(929\) −29.0077 −0.951712 −0.475856 0.879523i \(-0.657862\pi\)
−0.475856 + 0.879523i \(0.657862\pi\)
\(930\) −1.78514 −0.0585372
\(931\) −1.82799 −0.0599099
\(932\) −3.29752 −0.108014
\(933\) −7.51930 −0.246171
\(934\) 36.9224 1.20814
\(935\) −5.91732 −0.193517
\(936\) −56.1538 −1.83544
\(937\) 30.7586 1.00484 0.502420 0.864624i \(-0.332443\pi\)
0.502420 + 0.864624i \(0.332443\pi\)
\(938\) 8.24887 0.269335
\(939\) 1.11983 0.0365443
\(940\) −0.838878 −0.0273612
\(941\) 31.7351 1.03453 0.517267 0.855824i \(-0.326949\pi\)
0.517267 + 0.855824i \(0.326949\pi\)
\(942\) −4.55860 −0.148527
\(943\) −7.80634 −0.254209
\(944\) 10.3564 0.337073
\(945\) 1.52579 0.0496340
\(946\) 10.7929 0.350909
\(947\) −44.6632 −1.45136 −0.725679 0.688033i \(-0.758474\pi\)
−0.725679 + 0.688033i \(0.758474\pi\)
\(948\) −0.0108150 −0.000351255 0
\(949\) −30.3286 −0.984507
\(950\) −2.48743 −0.0807029
\(951\) −2.17366 −0.0704857
\(952\) 7.05158 0.228543
\(953\) −44.8784 −1.45375 −0.726877 0.686768i \(-0.759029\pi\)
−0.726877 + 0.686768i \(0.759029\pi\)
\(954\) −11.3183 −0.366445
\(955\) 0.375150 0.0121396
\(956\) −2.80364 −0.0906763
\(957\) 4.06820 0.131506
\(958\) 27.1774 0.878062
\(959\) 1.29589 0.0418463
\(960\) 2.18618 0.0705585
\(961\) −4.96970 −0.160313
\(962\) 37.6665 1.21442
\(963\) −4.69740 −0.151372
\(964\) −2.53500 −0.0816468
\(965\) 25.4886 0.820507
\(966\) −1.19112 −0.0383237
\(967\) 35.3280 1.13607 0.568036 0.823004i \(-0.307703\pi\)
0.568036 + 0.823004i \(0.307703\pi\)
\(968\) 14.5645 0.468119
\(969\) 1.13378 0.0364224
\(970\) −24.5544 −0.788394
\(971\) 22.2768 0.714897 0.357448 0.933933i \(-0.383647\pi\)
0.357448 + 0.933933i \(0.383647\pi\)
\(972\) 0.999956 0.0320736
\(973\) 15.5953 0.499963
\(974\) 1.81462 0.0581443
\(975\) 1.68347 0.0539143
\(976\) −49.9436 −1.59866
\(977\) −44.8479 −1.43481 −0.717405 0.696656i \(-0.754670\pi\)
−0.717405 + 0.696656i \(0.754670\pi\)
\(978\) 5.18379 0.165759
\(979\) −37.2429 −1.19029
\(980\) 0.148369 0.00473946
\(981\) 18.6129 0.594264
\(982\) −38.3042 −1.22234
\(983\) −9.23765 −0.294635 −0.147318 0.989089i \(-0.547064\pi\)
−0.147318 + 0.989089i \(0.547064\pi\)
\(984\) 1.72372 0.0549503
\(985\) 15.4933 0.493656
\(986\) −21.1690 −0.674157
\(987\) −1.45383 −0.0462759
\(988\) −1.77568 −0.0564920
\(989\) −11.0068 −0.349996
\(990\) 9.79364 0.311262
\(991\) 40.7308 1.29386 0.646928 0.762551i \(-0.276053\pi\)
0.646928 + 0.762551i \(0.276053\pi\)
\(992\) −4.27303 −0.135669
\(993\) −0.834711 −0.0264888
\(994\) −7.44364 −0.236098
\(995\) 23.6269 0.749022
\(996\) 0.631716 0.0200167
\(997\) −15.6236 −0.494805 −0.247402 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(998\) 51.2710 1.62295
\(999\) −6.45094 −0.204099
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 \(a_p\))