Properties

Label 8002.2.a.e.1.17
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 0
Dimension 77
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(77\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.73843 q^{3} +1.00000 q^{4} +4.07186 q^{5} +1.73843 q^{6} -2.38793 q^{7} -1.00000 q^{8} +0.0221381 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.73843 q^{3} +1.00000 q^{4} +4.07186 q^{5} +1.73843 q^{6} -2.38793 q^{7} -1.00000 q^{8} +0.0221381 q^{9} -4.07186 q^{10} +4.57210 q^{11} -1.73843 q^{12} -3.31788 q^{13} +2.38793 q^{14} -7.07864 q^{15} +1.00000 q^{16} +7.27985 q^{17} -0.0221381 q^{18} +6.96966 q^{19} +4.07186 q^{20} +4.15124 q^{21} -4.57210 q^{22} +7.61639 q^{23} +1.73843 q^{24} +11.5800 q^{25} +3.31788 q^{26} +5.17680 q^{27} -2.38793 q^{28} +2.53097 q^{29} +7.07864 q^{30} +5.36879 q^{31} -1.00000 q^{32} -7.94827 q^{33} -7.27985 q^{34} -9.72330 q^{35} +0.0221381 q^{36} +8.55921 q^{37} -6.96966 q^{38} +5.76790 q^{39} -4.07186 q^{40} +9.12763 q^{41} -4.15124 q^{42} +2.29493 q^{43} +4.57210 q^{44} +0.0901431 q^{45} -7.61639 q^{46} +13.1787 q^{47} -1.73843 q^{48} -1.29780 q^{49} -11.5800 q^{50} -12.6555 q^{51} -3.31788 q^{52} -1.72202 q^{53} -5.17680 q^{54} +18.6169 q^{55} +2.38793 q^{56} -12.1163 q^{57} -2.53097 q^{58} -10.7237 q^{59} -7.07864 q^{60} -7.61107 q^{61} -5.36879 q^{62} -0.0528641 q^{63} +1.00000 q^{64} -13.5099 q^{65} +7.94827 q^{66} -5.01292 q^{67} +7.27985 q^{68} -13.2406 q^{69} +9.72330 q^{70} -14.2437 q^{71} -0.0221381 q^{72} -0.562149 q^{73} -8.55921 q^{74} -20.1311 q^{75} +6.96966 q^{76} -10.9178 q^{77} -5.76790 q^{78} -5.14917 q^{79} +4.07186 q^{80} -9.06592 q^{81} -9.12763 q^{82} +0.591408 q^{83} +4.15124 q^{84} +29.6425 q^{85} -2.29493 q^{86} -4.39992 q^{87} -4.57210 q^{88} -7.78532 q^{89} -0.0901431 q^{90} +7.92286 q^{91} +7.61639 q^{92} -9.33326 q^{93} -13.1787 q^{94} +28.3794 q^{95} +1.73843 q^{96} -14.4588 q^{97} +1.29780 q^{98} +0.101217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.73843 −1.00368 −0.501841 0.864960i \(-0.667344\pi\)
−0.501841 + 0.864960i \(0.667344\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.07186 1.82099 0.910495 0.413520i \(-0.135701\pi\)
0.910495 + 0.413520i \(0.135701\pi\)
\(6\) 1.73843 0.709711
\(7\) −2.38793 −0.902552 −0.451276 0.892385i \(-0.649031\pi\)
−0.451276 + 0.892385i \(0.649031\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0.0221381 0.00737936
\(10\) −4.07186 −1.28763
\(11\) 4.57210 1.37854 0.689270 0.724505i \(-0.257931\pi\)
0.689270 + 0.724505i \(0.257931\pi\)
\(12\) −1.73843 −0.501841
\(13\) −3.31788 −0.920214 −0.460107 0.887863i \(-0.652189\pi\)
−0.460107 + 0.887863i \(0.652189\pi\)
\(14\) 2.38793 0.638200
\(15\) −7.07864 −1.82770
\(16\) 1.00000 0.250000
\(17\) 7.27985 1.76562 0.882811 0.469727i \(-0.155648\pi\)
0.882811 + 0.469727i \(0.155648\pi\)
\(18\) −0.0221381 −0.00521800
\(19\) 6.96966 1.59895 0.799474 0.600700i \(-0.205111\pi\)
0.799474 + 0.600700i \(0.205111\pi\)
\(20\) 4.07186 0.910495
\(21\) 4.15124 0.905876
\(22\) −4.57210 −0.974775
\(23\) 7.61639 1.58813 0.794064 0.607834i \(-0.207962\pi\)
0.794064 + 0.607834i \(0.207962\pi\)
\(24\) 1.73843 0.354855
\(25\) 11.5800 2.31601
\(26\) 3.31788 0.650690
\(27\) 5.17680 0.996276
\(28\) −2.38793 −0.451276
\(29\) 2.53097 0.469990 0.234995 0.971997i \(-0.424493\pi\)
0.234995 + 0.971997i \(0.424493\pi\)
\(30\) 7.07864 1.29238
\(31\) 5.36879 0.964263 0.482131 0.876099i \(-0.339863\pi\)
0.482131 + 0.876099i \(0.339863\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.94827 −1.38362
\(34\) −7.27985 −1.24848
\(35\) −9.72330 −1.64354
\(36\) 0.0221381 0.00368968
\(37\) 8.55921 1.40713 0.703563 0.710633i \(-0.251592\pi\)
0.703563 + 0.710633i \(0.251592\pi\)
\(38\) −6.96966 −1.13063
\(39\) 5.76790 0.923603
\(40\) −4.07186 −0.643817
\(41\) 9.12763 1.42550 0.712748 0.701420i \(-0.247450\pi\)
0.712748 + 0.701420i \(0.247450\pi\)
\(42\) −4.15124 −0.640551
\(43\) 2.29493 0.349973 0.174986 0.984571i \(-0.444012\pi\)
0.174986 + 0.984571i \(0.444012\pi\)
\(44\) 4.57210 0.689270
\(45\) 0.0901431 0.0134377
\(46\) −7.61639 −1.12298
\(47\) 13.1787 1.92231 0.961156 0.276005i \(-0.0890107\pi\)
0.961156 + 0.276005i \(0.0890107\pi\)
\(48\) −1.73843 −0.250921
\(49\) −1.29780 −0.185401
\(50\) −11.5800 −1.63766
\(51\) −12.6555 −1.77213
\(52\) −3.31788 −0.460107
\(53\) −1.72202 −0.236538 −0.118269 0.992982i \(-0.537735\pi\)
−0.118269 + 0.992982i \(0.537735\pi\)
\(54\) −5.17680 −0.704474
\(55\) 18.6169 2.51031
\(56\) 2.38793 0.319100
\(57\) −12.1163 −1.60484
\(58\) −2.53097 −0.332333
\(59\) −10.7237 −1.39610 −0.698052 0.716047i \(-0.745950\pi\)
−0.698052 + 0.716047i \(0.745950\pi\)
\(60\) −7.07864 −0.913848
\(61\) −7.61107 −0.974498 −0.487249 0.873263i \(-0.662000\pi\)
−0.487249 + 0.873263i \(0.662000\pi\)
\(62\) −5.36879 −0.681837
\(63\) −0.0528641 −0.00666025
\(64\) 1.00000 0.125000
\(65\) −13.5099 −1.67570
\(66\) 7.94827 0.978365
\(67\) −5.01292 −0.612426 −0.306213 0.951963i \(-0.599062\pi\)
−0.306213 + 0.951963i \(0.599062\pi\)
\(68\) 7.27985 0.882811
\(69\) −13.2406 −1.59398
\(70\) 9.72330 1.16216
\(71\) −14.2437 −1.69042 −0.845211 0.534433i \(-0.820525\pi\)
−0.845211 + 0.534433i \(0.820525\pi\)
\(72\) −0.0221381 −0.00260900
\(73\) −0.562149 −0.0657945 −0.0328973 0.999459i \(-0.510473\pi\)
−0.0328973 + 0.999459i \(0.510473\pi\)
\(74\) −8.55921 −0.994988
\(75\) −20.1311 −2.32454
\(76\) 6.96966 0.799474
\(77\) −10.9178 −1.24420
\(78\) −5.76790 −0.653086
\(79\) −5.14917 −0.579327 −0.289663 0.957129i \(-0.593543\pi\)
−0.289663 + 0.957129i \(0.593543\pi\)
\(80\) 4.07186 0.455248
\(81\) −9.06592 −1.00732
\(82\) −9.12763 −1.00798
\(83\) 0.591408 0.0649155 0.0324578 0.999473i \(-0.489667\pi\)
0.0324578 + 0.999473i \(0.489667\pi\)
\(84\) 4.15124 0.452938
\(85\) 29.6425 3.21518
\(86\) −2.29493 −0.247468
\(87\) −4.39992 −0.471721
\(88\) −4.57210 −0.487387
\(89\) −7.78532 −0.825242 −0.412621 0.910903i \(-0.635387\pi\)
−0.412621 + 0.910903i \(0.635387\pi\)
\(90\) −0.0901431 −0.00950192
\(91\) 7.92286 0.830541
\(92\) 7.61639 0.794064
\(93\) −9.33326 −0.967814
\(94\) −13.1787 −1.35928
\(95\) 28.3794 2.91167
\(96\) 1.73843 0.177428
\(97\) −14.4588 −1.46807 −0.734033 0.679114i \(-0.762364\pi\)
−0.734033 + 0.679114i \(0.762364\pi\)
\(98\) 1.29780 0.131098
\(99\) 0.101217 0.0101727
\(100\) 11.5800 1.15800
\(101\) −5.51473 −0.548736 −0.274368 0.961625i \(-0.588469\pi\)
−0.274368 + 0.961625i \(0.588469\pi\)
\(102\) 12.6555 1.25308
\(103\) 11.7681 1.15954 0.579770 0.814780i \(-0.303142\pi\)
0.579770 + 0.814780i \(0.303142\pi\)
\(104\) 3.31788 0.325345
\(105\) 16.9033 1.64959
\(106\) 1.72202 0.167258
\(107\) 1.15542 0.111699 0.0558493 0.998439i \(-0.482213\pi\)
0.0558493 + 0.998439i \(0.482213\pi\)
\(108\) 5.17680 0.498138
\(109\) −1.06109 −0.101634 −0.0508168 0.998708i \(-0.516182\pi\)
−0.0508168 + 0.998708i \(0.516182\pi\)
\(110\) −18.6169 −1.77506
\(111\) −14.8796 −1.41231
\(112\) −2.38793 −0.225638
\(113\) 14.5492 1.36868 0.684339 0.729164i \(-0.260091\pi\)
0.684339 + 0.729164i \(0.260091\pi\)
\(114\) 12.1163 1.13479
\(115\) 31.0129 2.89197
\(116\) 2.53097 0.234995
\(117\) −0.0734515 −0.00679059
\(118\) 10.7237 0.987195
\(119\) −17.3838 −1.59357
\(120\) 7.07864 0.646188
\(121\) 9.90409 0.900371
\(122\) 7.61107 0.689074
\(123\) −15.8677 −1.43075
\(124\) 5.36879 0.482131
\(125\) 26.7929 2.39643
\(126\) 0.0528641 0.00470951
\(127\) −6.25091 −0.554679 −0.277339 0.960772i \(-0.589453\pi\)
−0.277339 + 0.960772i \(0.589453\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.98957 −0.351262
\(130\) 13.5099 1.18490
\(131\) −2.42136 −0.211556 −0.105778 0.994390i \(-0.533733\pi\)
−0.105778 + 0.994390i \(0.533733\pi\)
\(132\) −7.94827 −0.691808
\(133\) −16.6430 −1.44313
\(134\) 5.01292 0.433051
\(135\) 21.0792 1.81421
\(136\) −7.27985 −0.624242
\(137\) −8.96139 −0.765623 −0.382812 0.923826i \(-0.625044\pi\)
−0.382812 + 0.923826i \(0.625044\pi\)
\(138\) 13.2406 1.12711
\(139\) −0.542216 −0.0459902 −0.0229951 0.999736i \(-0.507320\pi\)
−0.0229951 + 0.999736i \(0.507320\pi\)
\(140\) −9.72330 −0.821769
\(141\) −22.9103 −1.92939
\(142\) 14.2437 1.19531
\(143\) −15.1697 −1.26855
\(144\) 0.0221381 0.00184484
\(145\) 10.3058 0.855847
\(146\) 0.562149 0.0465238
\(147\) 2.25614 0.186083
\(148\) 8.55921 0.703563
\(149\) −22.2401 −1.82198 −0.910988 0.412432i \(-0.864680\pi\)
−0.910988 + 0.412432i \(0.864680\pi\)
\(150\) 20.1311 1.64369
\(151\) 21.9221 1.78399 0.891997 0.452042i \(-0.149304\pi\)
0.891997 + 0.452042i \(0.149304\pi\)
\(152\) −6.96966 −0.565314
\(153\) 0.161162 0.0130292
\(154\) 10.9178 0.879785
\(155\) 21.8609 1.75591
\(156\) 5.76790 0.461802
\(157\) −8.14095 −0.649719 −0.324859 0.945762i \(-0.605317\pi\)
−0.324859 + 0.945762i \(0.605317\pi\)
\(158\) 5.14917 0.409646
\(159\) 2.99362 0.237409
\(160\) −4.07186 −0.321909
\(161\) −18.1874 −1.43337
\(162\) 9.06592 0.712286
\(163\) 1.82196 0.142707 0.0713533 0.997451i \(-0.477268\pi\)
0.0713533 + 0.997451i \(0.477268\pi\)
\(164\) 9.12763 0.712748
\(165\) −32.3642 −2.51955
\(166\) −0.591408 −0.0459022
\(167\) 15.8130 1.22365 0.611824 0.790994i \(-0.290436\pi\)
0.611824 + 0.790994i \(0.290436\pi\)
\(168\) −4.15124 −0.320275
\(169\) −1.99167 −0.153206
\(170\) −29.6425 −2.27348
\(171\) 0.154295 0.0117992
\(172\) 2.29493 0.174986
\(173\) −7.99538 −0.607877 −0.303939 0.952692i \(-0.598302\pi\)
−0.303939 + 0.952692i \(0.598302\pi\)
\(174\) 4.39992 0.333557
\(175\) −27.6523 −2.09031
\(176\) 4.57210 0.344635
\(177\) 18.6424 1.40125
\(178\) 7.78532 0.583534
\(179\) −4.44776 −0.332441 −0.166221 0.986089i \(-0.553156\pi\)
−0.166221 + 0.986089i \(0.553156\pi\)
\(180\) 0.0901431 0.00671887
\(181\) −7.70175 −0.572467 −0.286233 0.958160i \(-0.592403\pi\)
−0.286233 + 0.958160i \(0.592403\pi\)
\(182\) −7.92286 −0.587281
\(183\) 13.2313 0.978087
\(184\) −7.61639 −0.561488
\(185\) 34.8519 2.56236
\(186\) 9.33326 0.684348
\(187\) 33.2842 2.43398
\(188\) 13.1787 0.961156
\(189\) −12.3618 −0.899191
\(190\) −28.3794 −2.05886
\(191\) −3.76241 −0.272238 −0.136119 0.990692i \(-0.543463\pi\)
−0.136119 + 0.990692i \(0.543463\pi\)
\(192\) −1.73843 −0.125460
\(193\) 19.2791 1.38774 0.693871 0.720099i \(-0.255904\pi\)
0.693871 + 0.720099i \(0.255904\pi\)
\(194\) 14.4588 1.03808
\(195\) 23.4861 1.68187
\(196\) −1.29780 −0.0927003
\(197\) −18.9201 −1.34800 −0.674001 0.738730i \(-0.735426\pi\)
−0.674001 + 0.738730i \(0.735426\pi\)
\(198\) −0.101217 −0.00719321
\(199\) 8.76145 0.621083 0.310541 0.950560i \(-0.399490\pi\)
0.310541 + 0.950560i \(0.399490\pi\)
\(200\) −11.5800 −0.818832
\(201\) 8.71462 0.614682
\(202\) 5.51473 0.388015
\(203\) −6.04378 −0.424190
\(204\) −12.6555 −0.886063
\(205\) 37.1664 2.59581
\(206\) −11.7681 −0.819919
\(207\) 0.168612 0.0117194
\(208\) −3.31788 −0.230054
\(209\) 31.8660 2.20421
\(210\) −16.9033 −1.16644
\(211\) −19.7342 −1.35856 −0.679280 0.733879i \(-0.737708\pi\)
−0.679280 + 0.733879i \(0.737708\pi\)
\(212\) −1.72202 −0.118269
\(213\) 24.7618 1.69665
\(214\) −1.15542 −0.0789829
\(215\) 9.34461 0.637297
\(216\) −5.17680 −0.352237
\(217\) −12.8203 −0.870297
\(218\) 1.06109 0.0718659
\(219\) 0.977256 0.0660369
\(220\) 18.6169 1.25515
\(221\) −24.1537 −1.62475
\(222\) 14.8796 0.998652
\(223\) 9.22087 0.617475 0.308738 0.951147i \(-0.400093\pi\)
0.308738 + 0.951147i \(0.400093\pi\)
\(224\) 2.38793 0.159550
\(225\) 0.256360 0.0170906
\(226\) −14.5492 −0.967801
\(227\) −3.74748 −0.248729 −0.124365 0.992237i \(-0.539689\pi\)
−0.124365 + 0.992237i \(0.539689\pi\)
\(228\) −12.1163 −0.802419
\(229\) −2.10228 −0.138923 −0.0694614 0.997585i \(-0.522128\pi\)
−0.0694614 + 0.997585i \(0.522128\pi\)
\(230\) −31.0129 −2.04493
\(231\) 18.9799 1.24879
\(232\) −2.53097 −0.166166
\(233\) 24.8250 1.62634 0.813170 0.582026i \(-0.197740\pi\)
0.813170 + 0.582026i \(0.197740\pi\)
\(234\) 0.0734515 0.00480167
\(235\) 53.6618 3.50051
\(236\) −10.7237 −0.698052
\(237\) 8.95146 0.581460
\(238\) 17.3838 1.12682
\(239\) 3.60732 0.233338 0.116669 0.993171i \(-0.462778\pi\)
0.116669 + 0.993171i \(0.462778\pi\)
\(240\) −7.07864 −0.456924
\(241\) 20.2807 1.30640 0.653198 0.757187i \(-0.273427\pi\)
0.653198 + 0.757187i \(0.273427\pi\)
\(242\) −9.90409 −0.636659
\(243\) 0.230061 0.0147584
\(244\) −7.61107 −0.487249
\(245\) −5.28447 −0.337613
\(246\) 15.8677 1.01169
\(247\) −23.1245 −1.47138
\(248\) −5.36879 −0.340918
\(249\) −1.02812 −0.0651546
\(250\) −26.7929 −1.69453
\(251\) −22.7440 −1.43559 −0.717793 0.696256i \(-0.754848\pi\)
−0.717793 + 0.696256i \(0.754848\pi\)
\(252\) −0.0528641 −0.00333013
\(253\) 34.8229 2.18930
\(254\) 6.25091 0.392217
\(255\) −51.5314 −3.22702
\(256\) 1.00000 0.0625000
\(257\) −17.8225 −1.11174 −0.555869 0.831270i \(-0.687614\pi\)
−0.555869 + 0.831270i \(0.687614\pi\)
\(258\) 3.98957 0.248380
\(259\) −20.4388 −1.27000
\(260\) −13.5099 −0.837851
\(261\) 0.0560309 0.00346822
\(262\) 2.42136 0.149592
\(263\) 26.6279 1.64195 0.820974 0.570965i \(-0.193431\pi\)
0.820974 + 0.570965i \(0.193431\pi\)
\(264\) 7.94827 0.489182
\(265\) −7.01183 −0.430733
\(266\) 16.6430 1.02045
\(267\) 13.5342 0.828281
\(268\) −5.01292 −0.306213
\(269\) −30.1938 −1.84095 −0.920475 0.390801i \(-0.872198\pi\)
−0.920475 + 0.390801i \(0.872198\pi\)
\(270\) −21.0792 −1.28284
\(271\) 20.1446 1.22370 0.611849 0.790974i \(-0.290426\pi\)
0.611849 + 0.790974i \(0.290426\pi\)
\(272\) 7.27985 0.441406
\(273\) −13.7733 −0.833600
\(274\) 8.96139 0.541377
\(275\) 52.9450 3.19271
\(276\) −13.2406 −0.796988
\(277\) −0.493290 −0.0296389 −0.0148195 0.999890i \(-0.504717\pi\)
−0.0148195 + 0.999890i \(0.504717\pi\)
\(278\) 0.542216 0.0325200
\(279\) 0.118855 0.00711564
\(280\) 9.72330 0.581078
\(281\) −27.6877 −1.65171 −0.825856 0.563881i \(-0.809308\pi\)
−0.825856 + 0.563881i \(0.809308\pi\)
\(282\) 22.9103 1.36429
\(283\) 17.4944 1.03994 0.519968 0.854185i \(-0.325944\pi\)
0.519968 + 0.854185i \(0.325944\pi\)
\(284\) −14.2437 −0.845211
\(285\) −49.3357 −2.92239
\(286\) 15.1697 0.897002
\(287\) −21.7961 −1.28658
\(288\) −0.0221381 −0.00130450
\(289\) 35.9962 2.11742
\(290\) −10.3058 −0.605175
\(291\) 25.1356 1.47347
\(292\) −0.562149 −0.0328973
\(293\) −3.38270 −0.197620 −0.0988098 0.995106i \(-0.531504\pi\)
−0.0988098 + 0.995106i \(0.531504\pi\)
\(294\) −2.25614 −0.131581
\(295\) −43.6653 −2.54229
\(296\) −8.55921 −0.497494
\(297\) 23.6689 1.37341
\(298\) 22.2401 1.28833
\(299\) −25.2703 −1.46142
\(300\) −20.1311 −1.16227
\(301\) −5.48011 −0.315869
\(302\) −21.9221 −1.26147
\(303\) 9.58698 0.550757
\(304\) 6.96966 0.399737
\(305\) −30.9912 −1.77455
\(306\) −0.161162 −0.00921301
\(307\) −20.6600 −1.17913 −0.589563 0.807722i \(-0.700700\pi\)
−0.589563 + 0.807722i \(0.700700\pi\)
\(308\) −10.9178 −0.622102
\(309\) −20.4579 −1.16381
\(310\) −21.8609 −1.24162
\(311\) −6.65115 −0.377152 −0.188576 0.982059i \(-0.560387\pi\)
−0.188576 + 0.982059i \(0.560387\pi\)
\(312\) −5.76790 −0.326543
\(313\) −8.33752 −0.471265 −0.235632 0.971842i \(-0.575716\pi\)
−0.235632 + 0.971842i \(0.575716\pi\)
\(314\) 8.14095 0.459420
\(315\) −0.215255 −0.0121283
\(316\) −5.14917 −0.289663
\(317\) −20.7472 −1.16528 −0.582638 0.812732i \(-0.697980\pi\)
−0.582638 + 0.812732i \(0.697980\pi\)
\(318\) −2.99362 −0.167874
\(319\) 11.5719 0.647899
\(320\) 4.07186 0.227624
\(321\) −2.00862 −0.112110
\(322\) 18.1874 1.01354
\(323\) 50.7380 2.82314
\(324\) −9.06592 −0.503662
\(325\) −38.4211 −2.13122
\(326\) −1.82196 −0.100909
\(327\) 1.84462 0.102008
\(328\) −9.12763 −0.503989
\(329\) −31.4698 −1.73499
\(330\) 32.3642 1.78159
\(331\) 14.7031 0.808157 0.404078 0.914724i \(-0.367592\pi\)
0.404078 + 0.914724i \(0.367592\pi\)
\(332\) 0.591408 0.0324578
\(333\) 0.189484 0.0103837
\(334\) −15.8130 −0.865250
\(335\) −20.4119 −1.11522
\(336\) 4.15124 0.226469
\(337\) −20.5633 −1.12015 −0.560077 0.828441i \(-0.689228\pi\)
−0.560077 + 0.828441i \(0.689228\pi\)
\(338\) 1.99167 0.108333
\(339\) −25.2928 −1.37372
\(340\) 29.6425 1.60759
\(341\) 24.5466 1.32927
\(342\) −0.154295 −0.00834331
\(343\) 19.8146 1.06989
\(344\) −2.29493 −0.123734
\(345\) −53.9137 −2.90262
\(346\) 7.99538 0.429834
\(347\) 29.9834 1.60959 0.804797 0.593550i \(-0.202274\pi\)
0.804797 + 0.593550i \(0.202274\pi\)
\(348\) −4.39992 −0.235860
\(349\) −16.4215 −0.879021 −0.439510 0.898237i \(-0.644848\pi\)
−0.439510 + 0.898237i \(0.644848\pi\)
\(350\) 27.6523 1.47808
\(351\) −17.1760 −0.916788
\(352\) −4.57210 −0.243694
\(353\) 3.84501 0.204649 0.102325 0.994751i \(-0.467372\pi\)
0.102325 + 0.994751i \(0.467372\pi\)
\(354\) −18.6424 −0.990831
\(355\) −57.9985 −3.07824
\(356\) −7.78532 −0.412621
\(357\) 30.2204 1.59943
\(358\) 4.44776 0.235071
\(359\) −15.2603 −0.805409 −0.402704 0.915330i \(-0.631930\pi\)
−0.402704 + 0.915330i \(0.631930\pi\)
\(360\) −0.0901431 −0.00475096
\(361\) 29.5761 1.55664
\(362\) 7.70175 0.404795
\(363\) −17.2176 −0.903687
\(364\) 7.92286 0.415270
\(365\) −2.28899 −0.119811
\(366\) −13.2313 −0.691612
\(367\) −11.7180 −0.611674 −0.305837 0.952084i \(-0.598936\pi\)
−0.305837 + 0.952084i \(0.598936\pi\)
\(368\) 7.61639 0.397032
\(369\) 0.202068 0.0105192
\(370\) −34.8519 −1.81186
\(371\) 4.11206 0.213488
\(372\) −9.33326 −0.483907
\(373\) 31.8546 1.64937 0.824684 0.565593i \(-0.191353\pi\)
0.824684 + 0.565593i \(0.191353\pi\)
\(374\) −33.2842 −1.72108
\(375\) −46.5777 −2.40526
\(376\) −13.1787 −0.679640
\(377\) −8.39746 −0.432491
\(378\) 12.3618 0.635824
\(379\) 19.8770 1.02101 0.510506 0.859874i \(-0.329458\pi\)
0.510506 + 0.859874i \(0.329458\pi\)
\(380\) 28.3794 1.45583
\(381\) 10.8668 0.556722
\(382\) 3.76241 0.192501
\(383\) −3.26449 −0.166807 −0.0834037 0.996516i \(-0.526579\pi\)
−0.0834037 + 0.996516i \(0.526579\pi\)
\(384\) 1.73843 0.0887139
\(385\) −44.4559 −2.26568
\(386\) −19.2791 −0.981282
\(387\) 0.0508052 0.00258258
\(388\) −14.4588 −0.734033
\(389\) 1.07557 0.0545334 0.0272667 0.999628i \(-0.491320\pi\)
0.0272667 + 0.999628i \(0.491320\pi\)
\(390\) −23.4861 −1.18926
\(391\) 55.4462 2.80403
\(392\) 1.29780 0.0655490
\(393\) 4.20937 0.212335
\(394\) 18.9201 0.953182
\(395\) −20.9667 −1.05495
\(396\) 0.101217 0.00508637
\(397\) 7.64431 0.383657 0.191828 0.981428i \(-0.438558\pi\)
0.191828 + 0.981428i \(0.438558\pi\)
\(398\) −8.76145 −0.439172
\(399\) 28.9327 1.44845
\(400\) 11.5800 0.579001
\(401\) −11.0183 −0.550229 −0.275114 0.961411i \(-0.588716\pi\)
−0.275114 + 0.961411i \(0.588716\pi\)
\(402\) −8.71462 −0.434646
\(403\) −17.8130 −0.887328
\(404\) −5.51473 −0.274368
\(405\) −36.9152 −1.83433
\(406\) 6.04378 0.299948
\(407\) 39.1335 1.93978
\(408\) 12.6555 0.626541
\(409\) −4.12639 −0.204037 −0.102018 0.994783i \(-0.532530\pi\)
−0.102018 + 0.994783i \(0.532530\pi\)
\(410\) −37.1664 −1.83552
\(411\) 15.5787 0.768443
\(412\) 11.7681 0.579770
\(413\) 25.6074 1.26006
\(414\) −0.168612 −0.00828684
\(415\) 2.40813 0.118211
\(416\) 3.31788 0.162672
\(417\) 0.942605 0.0461596
\(418\) −31.8660 −1.55861
\(419\) 3.62912 0.177294 0.0886472 0.996063i \(-0.471746\pi\)
0.0886472 + 0.996063i \(0.471746\pi\)
\(420\) 16.9033 0.824795
\(421\) 18.3450 0.894080 0.447040 0.894514i \(-0.352478\pi\)
0.447040 + 0.894514i \(0.352478\pi\)
\(422\) 19.7342 0.960647
\(423\) 0.291751 0.0141854
\(424\) 1.72202 0.0836288
\(425\) 84.3009 4.08919
\(426\) −24.7618 −1.19971
\(427\) 18.1747 0.879535
\(428\) 1.15542 0.0558493
\(429\) 26.3714 1.27322
\(430\) −9.34461 −0.450637
\(431\) −28.1164 −1.35432 −0.677159 0.735837i \(-0.736789\pi\)
−0.677159 + 0.735837i \(0.736789\pi\)
\(432\) 5.17680 0.249069
\(433\) −32.9621 −1.58406 −0.792029 0.610484i \(-0.790975\pi\)
−0.792029 + 0.610484i \(0.790975\pi\)
\(434\) 12.8203 0.615393
\(435\) −17.9158 −0.858999
\(436\) −1.06109 −0.0508168
\(437\) 53.0836 2.53933
\(438\) −0.977256 −0.0466951
\(439\) −38.8435 −1.85390 −0.926951 0.375184i \(-0.877580\pi\)
−0.926951 + 0.375184i \(0.877580\pi\)
\(440\) −18.6169 −0.887528
\(441\) −0.0287309 −0.00136814
\(442\) 24.1537 1.14887
\(443\) −3.92747 −0.186600 −0.0932999 0.995638i \(-0.529742\pi\)
−0.0932999 + 0.995638i \(0.529742\pi\)
\(444\) −14.8796 −0.706154
\(445\) −31.7007 −1.50276
\(446\) −9.22087 −0.436621
\(447\) 38.6628 1.82869
\(448\) −2.38793 −0.112819
\(449\) −8.74236 −0.412578 −0.206289 0.978491i \(-0.566139\pi\)
−0.206289 + 0.978491i \(0.566139\pi\)
\(450\) −0.256360 −0.0120849
\(451\) 41.7324 1.96510
\(452\) 14.5492 0.684339
\(453\) −38.1100 −1.79056
\(454\) 3.74748 0.175878
\(455\) 32.2607 1.51241
\(456\) 12.1163 0.567396
\(457\) −21.4303 −1.00247 −0.501233 0.865313i \(-0.667120\pi\)
−0.501233 + 0.865313i \(0.667120\pi\)
\(458\) 2.10228 0.0982332
\(459\) 37.6864 1.75905
\(460\) 31.0129 1.44598
\(461\) −2.07110 −0.0964605 −0.0482303 0.998836i \(-0.515358\pi\)
−0.0482303 + 0.998836i \(0.515358\pi\)
\(462\) −18.9799 −0.883025
\(463\) −21.6822 −1.00766 −0.503829 0.863804i \(-0.668076\pi\)
−0.503829 + 0.863804i \(0.668076\pi\)
\(464\) 2.53097 0.117497
\(465\) −38.0037 −1.76238
\(466\) −24.8250 −1.15000
\(467\) −36.1603 −1.67330 −0.836650 0.547738i \(-0.815489\pi\)
−0.836650 + 0.547738i \(0.815489\pi\)
\(468\) −0.0734515 −0.00339530
\(469\) 11.9705 0.552746
\(470\) −53.6618 −2.47524
\(471\) 14.1525 0.652111
\(472\) 10.7237 0.493598
\(473\) 10.4926 0.482451
\(474\) −8.95146 −0.411154
\(475\) 80.7088 3.70317
\(476\) −17.3838 −0.796783
\(477\) −0.0381223 −0.00174550
\(478\) −3.60732 −0.164995
\(479\) 20.7692 0.948967 0.474483 0.880264i \(-0.342635\pi\)
0.474483 + 0.880264i \(0.342635\pi\)
\(480\) 7.07864 0.323094
\(481\) −28.3984 −1.29486
\(482\) −20.2807 −0.923762
\(483\) 31.6175 1.43865
\(484\) 9.90409 0.450186
\(485\) −58.8741 −2.67333
\(486\) −0.230061 −0.0104358
\(487\) −27.1702 −1.23120 −0.615599 0.788059i \(-0.711086\pi\)
−0.615599 + 0.788059i \(0.711086\pi\)
\(488\) 7.61107 0.344537
\(489\) −3.16734 −0.143232
\(490\) 5.28447 0.238728
\(491\) −10.4613 −0.472113 −0.236056 0.971739i \(-0.575855\pi\)
−0.236056 + 0.971739i \(0.575855\pi\)
\(492\) −15.8677 −0.715373
\(493\) 18.4251 0.829825
\(494\) 23.1245 1.04042
\(495\) 0.412143 0.0185245
\(496\) 5.36879 0.241066
\(497\) 34.0130 1.52569
\(498\) 1.02812 0.0460712
\(499\) 19.8841 0.890133 0.445066 0.895498i \(-0.353180\pi\)
0.445066 + 0.895498i \(0.353180\pi\)
\(500\) 26.7929 1.19822
\(501\) −27.4898 −1.22815
\(502\) 22.7440 1.01511
\(503\) 26.5016 1.18165 0.590824 0.806801i \(-0.298803\pi\)
0.590824 + 0.806801i \(0.298803\pi\)
\(504\) 0.0528641 0.00235476
\(505\) −22.4552 −0.999244
\(506\) −34.8229 −1.54807
\(507\) 3.46238 0.153770
\(508\) −6.25091 −0.277339
\(509\) −26.8185 −1.18871 −0.594355 0.804203i \(-0.702593\pi\)
−0.594355 + 0.804203i \(0.702593\pi\)
\(510\) 51.5314 2.28185
\(511\) 1.34237 0.0593830
\(512\) −1.00000 −0.0441942
\(513\) 36.0805 1.59299
\(514\) 17.8225 0.786117
\(515\) 47.9178 2.11151
\(516\) −3.98957 −0.175631
\(517\) 60.2544 2.64998
\(518\) 20.4388 0.898028
\(519\) 13.8994 0.610116
\(520\) 13.5099 0.592450
\(521\) 23.2460 1.01843 0.509213 0.860640i \(-0.329936\pi\)
0.509213 + 0.860640i \(0.329936\pi\)
\(522\) −0.0560309 −0.00245240
\(523\) 18.1821 0.795049 0.397525 0.917591i \(-0.369869\pi\)
0.397525 + 0.917591i \(0.369869\pi\)
\(524\) −2.42136 −0.105778
\(525\) 48.0715 2.09801
\(526\) −26.6279 −1.16103
\(527\) 39.0840 1.70252
\(528\) −7.94827 −0.345904
\(529\) 35.0094 1.52215
\(530\) 7.01183 0.304574
\(531\) −0.237402 −0.0103024
\(532\) −16.6430 −0.721567
\(533\) −30.2844 −1.31176
\(534\) −13.5342 −0.585683
\(535\) 4.70471 0.203402
\(536\) 5.01292 0.216525
\(537\) 7.73212 0.333665
\(538\) 30.1938 1.30175
\(539\) −5.93369 −0.255582
\(540\) 21.0792 0.907105
\(541\) −19.7616 −0.849617 −0.424809 0.905283i \(-0.639659\pi\)
−0.424809 + 0.905283i \(0.639659\pi\)
\(542\) −20.1446 −0.865286
\(543\) 13.3890 0.574575
\(544\) −7.27985 −0.312121
\(545\) −4.32059 −0.185074
\(546\) 13.7733 0.589444
\(547\) −35.6462 −1.52412 −0.762060 0.647506i \(-0.775812\pi\)
−0.762060 + 0.647506i \(0.775812\pi\)
\(548\) −8.96139 −0.382812
\(549\) −0.168495 −0.00719117
\(550\) −52.9450 −2.25758
\(551\) 17.6400 0.751489
\(552\) 13.2406 0.563556
\(553\) 12.2958 0.522872
\(554\) 0.493290 0.0209579
\(555\) −60.5875 −2.57180
\(556\) −0.542216 −0.0229951
\(557\) 1.24815 0.0528859 0.0264430 0.999650i \(-0.491582\pi\)
0.0264430 + 0.999650i \(0.491582\pi\)
\(558\) −0.118855 −0.00503152
\(559\) −7.61429 −0.322050
\(560\) −9.72330 −0.410884
\(561\) −57.8622 −2.44295
\(562\) 27.6877 1.16794
\(563\) 27.9056 1.17608 0.588040 0.808832i \(-0.299900\pi\)
0.588040 + 0.808832i \(0.299900\pi\)
\(564\) −22.9103 −0.964696
\(565\) 59.2424 2.49235
\(566\) −17.4944 −0.735346
\(567\) 21.6488 0.909163
\(568\) 14.2437 0.597654
\(569\) −14.5305 −0.609150 −0.304575 0.952488i \(-0.598514\pi\)
−0.304575 + 0.952488i \(0.598514\pi\)
\(570\) 49.3357 2.06644
\(571\) −1.31868 −0.0551852 −0.0275926 0.999619i \(-0.508784\pi\)
−0.0275926 + 0.999619i \(0.508784\pi\)
\(572\) −15.1697 −0.634276
\(573\) 6.54068 0.273241
\(574\) 21.7961 0.909752
\(575\) 88.1980 3.67811
\(576\) 0.0221381 0.000922420 0
\(577\) 8.24906 0.343413 0.171706 0.985148i \(-0.445072\pi\)
0.171706 + 0.985148i \(0.445072\pi\)
\(578\) −35.9962 −1.49725
\(579\) −33.5154 −1.39285
\(580\) 10.3058 0.427923
\(581\) −1.41224 −0.0585896
\(582\) −25.1356 −1.04190
\(583\) −7.87326 −0.326077
\(584\) 0.562149 0.0232619
\(585\) −0.299084 −0.0123656
\(586\) 3.38270 0.139738
\(587\) 4.26028 0.175841 0.0879203 0.996128i \(-0.471978\pi\)
0.0879203 + 0.996128i \(0.471978\pi\)
\(588\) 2.25614 0.0930417
\(589\) 37.4186 1.54181
\(590\) 43.6653 1.79767
\(591\) 32.8913 1.35297
\(592\) 8.55921 0.351781
\(593\) −2.96489 −0.121753 −0.0608766 0.998145i \(-0.519390\pi\)
−0.0608766 + 0.998145i \(0.519390\pi\)
\(594\) −23.6689 −0.971145
\(595\) −70.7842 −2.90187
\(596\) −22.2401 −0.910988
\(597\) −15.2312 −0.623370
\(598\) 25.2703 1.03338
\(599\) 33.0778 1.35152 0.675761 0.737121i \(-0.263815\pi\)
0.675761 + 0.737121i \(0.263815\pi\)
\(600\) 20.1311 0.821847
\(601\) 2.09323 0.0853846 0.0426923 0.999088i \(-0.486406\pi\)
0.0426923 + 0.999088i \(0.486406\pi\)
\(602\) 5.48011 0.223353
\(603\) −0.110977 −0.00451931
\(604\) 21.9221 0.891997
\(605\) 40.3280 1.63957
\(606\) −9.58698 −0.389444
\(607\) −39.5427 −1.60499 −0.802495 0.596659i \(-0.796495\pi\)
−0.802495 + 0.596659i \(0.796495\pi\)
\(608\) −6.96966 −0.282657
\(609\) 10.5067 0.425752
\(610\) 30.9912 1.25480
\(611\) −43.7254 −1.76894
\(612\) 0.161162 0.00651458
\(613\) −6.65960 −0.268979 −0.134489 0.990915i \(-0.542939\pi\)
−0.134489 + 0.990915i \(0.542939\pi\)
\(614\) 20.6600 0.833769
\(615\) −64.6112 −2.60537
\(616\) 10.9178 0.439892
\(617\) 32.9038 1.32466 0.662329 0.749213i \(-0.269568\pi\)
0.662329 + 0.749213i \(0.269568\pi\)
\(618\) 20.4579 0.822939
\(619\) −2.84125 −0.114200 −0.0570998 0.998368i \(-0.518185\pi\)
−0.0570998 + 0.998368i \(0.518185\pi\)
\(620\) 21.8609 0.877956
\(621\) 39.4286 1.58221
\(622\) 6.65115 0.266687
\(623\) 18.5908 0.744823
\(624\) 5.76790 0.230901
\(625\) 51.1969 2.04788
\(626\) 8.33752 0.333234
\(627\) −55.3967 −2.21233
\(628\) −8.14095 −0.324859
\(629\) 62.3097 2.48445
\(630\) 0.215255 0.00857597
\(631\) −34.2621 −1.36395 −0.681977 0.731374i \(-0.738880\pi\)
−0.681977 + 0.731374i \(0.738880\pi\)
\(632\) 5.14917 0.204823
\(633\) 34.3066 1.36356
\(634\) 20.7472 0.823975
\(635\) −25.4528 −1.01006
\(636\) 2.99362 0.118705
\(637\) 4.30596 0.170608
\(638\) −11.5719 −0.458134
\(639\) −0.315329 −0.0124742
\(640\) −4.07186 −0.160954
\(641\) −43.8522 −1.73206 −0.866030 0.499992i \(-0.833336\pi\)
−0.866030 + 0.499992i \(0.833336\pi\)
\(642\) 2.00862 0.0792738
\(643\) −12.8328 −0.506078 −0.253039 0.967456i \(-0.581430\pi\)
−0.253039 + 0.967456i \(0.581430\pi\)
\(644\) −18.1874 −0.716684
\(645\) −16.2449 −0.639644
\(646\) −50.7380 −1.99626
\(647\) −4.37468 −0.171986 −0.0859932 0.996296i \(-0.527406\pi\)
−0.0859932 + 0.996296i \(0.527406\pi\)
\(648\) 9.06592 0.356143
\(649\) −49.0297 −1.92459
\(650\) 38.4211 1.50700
\(651\) 22.2871 0.873502
\(652\) 1.82196 0.0713533
\(653\) 15.5406 0.608151 0.304075 0.952648i \(-0.401653\pi\)
0.304075 + 0.952648i \(0.401653\pi\)
\(654\) −1.84462 −0.0721305
\(655\) −9.85945 −0.385241
\(656\) 9.12763 0.356374
\(657\) −0.0124449 −0.000485522 0
\(658\) 31.4698 1.22682
\(659\) −42.1126 −1.64048 −0.820238 0.572023i \(-0.806159\pi\)
−0.820238 + 0.572023i \(0.806159\pi\)
\(660\) −32.3642 −1.25978
\(661\) 29.4406 1.14511 0.572553 0.819868i \(-0.305953\pi\)
0.572553 + 0.819868i \(0.305953\pi\)
\(662\) −14.7031 −0.571453
\(663\) 41.9895 1.63074
\(664\) −0.591408 −0.0229511
\(665\) −67.7681 −2.62793
\(666\) −0.189484 −0.00734237
\(667\) 19.2769 0.746404
\(668\) 15.8130 0.611824
\(669\) −16.0298 −0.619749
\(670\) 20.4119 0.788581
\(671\) −34.7986 −1.34338
\(672\) −4.15124 −0.160138
\(673\) −32.8780 −1.26735 −0.633677 0.773597i \(-0.718455\pi\)
−0.633677 + 0.773597i \(0.718455\pi\)
\(674\) 20.5633 0.792068
\(675\) 59.9475 2.30738
\(676\) −1.99167 −0.0766028
\(677\) −16.1654 −0.621286 −0.310643 0.950527i \(-0.600544\pi\)
−0.310643 + 0.950527i \(0.600544\pi\)
\(678\) 25.2928 0.971365
\(679\) 34.5265 1.32501
\(680\) −29.6425 −1.13674
\(681\) 6.51474 0.249645
\(682\) −24.5466 −0.939939
\(683\) −17.7512 −0.679231 −0.339615 0.940564i \(-0.610297\pi\)
−0.339615 + 0.940564i \(0.610297\pi\)
\(684\) 0.154295 0.00589961
\(685\) −36.4895 −1.39419
\(686\) −19.8146 −0.756523
\(687\) 3.65467 0.139434
\(688\) 2.29493 0.0874932
\(689\) 5.71346 0.217666
\(690\) 53.9137 2.05246
\(691\) −7.42356 −0.282406 −0.141203 0.989981i \(-0.545097\pi\)
−0.141203 + 0.989981i \(0.545097\pi\)
\(692\) −7.99538 −0.303939
\(693\) −0.241700 −0.00918142
\(694\) −29.9834 −1.13815
\(695\) −2.20783 −0.0837477
\(696\) 4.39992 0.166778
\(697\) 66.4478 2.51689
\(698\) 16.4215 0.621562
\(699\) −43.1565 −1.63233
\(700\) −27.6523 −1.04516
\(701\) 50.8533 1.92070 0.960351 0.278794i \(-0.0899345\pi\)
0.960351 + 0.278794i \(0.0899345\pi\)
\(702\) 17.1760 0.648267
\(703\) 59.6547 2.24992
\(704\) 4.57210 0.172317
\(705\) −93.2873 −3.51340
\(706\) −3.84501 −0.144709
\(707\) 13.1688 0.495263
\(708\) 18.6424 0.700623
\(709\) 19.5614 0.734643 0.367321 0.930094i \(-0.380275\pi\)
0.367321 + 0.930094i \(0.380275\pi\)
\(710\) 57.9985 2.17665
\(711\) −0.113993 −0.00427506
\(712\) 7.78532 0.291767
\(713\) 40.8908 1.53137
\(714\) −30.2204 −1.13097
\(715\) −61.7688 −2.31002
\(716\) −4.44776 −0.166221
\(717\) −6.27107 −0.234197
\(718\) 15.2603 0.569510
\(719\) 5.22916 0.195015 0.0975074 0.995235i \(-0.468913\pi\)
0.0975074 + 0.995235i \(0.468913\pi\)
\(720\) 0.0901431 0.00335944
\(721\) −28.1013 −1.04655
\(722\) −29.5761 −1.10071
\(723\) −35.2566 −1.31121
\(724\) −7.70175 −0.286233
\(725\) 29.3087 1.08850
\(726\) 17.2176 0.639004
\(727\) −29.8793 −1.10816 −0.554080 0.832463i \(-0.686930\pi\)
−0.554080 + 0.832463i \(0.686930\pi\)
\(728\) −7.92286 −0.293641
\(729\) 26.7978 0.992512
\(730\) 2.28899 0.0847193
\(731\) 16.7067 0.617920
\(732\) 13.2313 0.489043
\(733\) −49.8669 −1.84188 −0.920938 0.389710i \(-0.872575\pi\)
−0.920938 + 0.389710i \(0.872575\pi\)
\(734\) 11.7180 0.432519
\(735\) 9.18668 0.338856
\(736\) −7.61639 −0.280744
\(737\) −22.9196 −0.844254
\(738\) −0.202068 −0.00743823
\(739\) −27.8292 −1.02371 −0.511857 0.859070i \(-0.671042\pi\)
−0.511857 + 0.859070i \(0.671042\pi\)
\(740\) 34.8519 1.28118
\(741\) 40.2003 1.47679
\(742\) −4.11206 −0.150959
\(743\) 6.47096 0.237396 0.118698 0.992930i \(-0.462128\pi\)
0.118698 + 0.992930i \(0.462128\pi\)
\(744\) 9.33326 0.342174
\(745\) −90.5584 −3.31780
\(746\) −31.8546 −1.16628
\(747\) 0.0130926 0.000479035 0
\(748\) 33.2842 1.21699
\(749\) −2.75906 −0.100814
\(750\) 46.5777 1.70078
\(751\) 33.4418 1.22031 0.610155 0.792282i \(-0.291107\pi\)
0.610155 + 0.792282i \(0.291107\pi\)
\(752\) 13.1787 0.480578
\(753\) 39.5388 1.44087
\(754\) 8.39746 0.305817
\(755\) 89.2636 3.24864
\(756\) −12.3618 −0.449595
\(757\) −27.7711 −1.00936 −0.504680 0.863307i \(-0.668389\pi\)
−0.504680 + 0.863307i \(0.668389\pi\)
\(758\) −19.8770 −0.721965
\(759\) −60.5372 −2.19736
\(760\) −28.3794 −1.02943
\(761\) −41.0460 −1.48792 −0.743958 0.668226i \(-0.767054\pi\)
−0.743958 + 0.668226i \(0.767054\pi\)
\(762\) −10.8668 −0.393662
\(763\) 2.53380 0.0917296
\(764\) −3.76241 −0.136119
\(765\) 0.656228 0.0237260
\(766\) 3.26449 0.117951
\(767\) 35.5799 1.28472
\(768\) −1.73843 −0.0627302
\(769\) −30.1552 −1.08742 −0.543712 0.839272i \(-0.682982\pi\)
−0.543712 + 0.839272i \(0.682982\pi\)
\(770\) 44.4559 1.60208
\(771\) 30.9832 1.11583
\(772\) 19.2791 0.693871
\(773\) 28.6642 1.03098 0.515490 0.856896i \(-0.327610\pi\)
0.515490 + 0.856896i \(0.327610\pi\)
\(774\) −0.0508052 −0.00182616
\(775\) 62.1707 2.23324
\(776\) 14.4588 0.519040
\(777\) 35.5314 1.27468
\(778\) −1.07557 −0.0385609
\(779\) 63.6164 2.27929
\(780\) 23.4861 0.840936
\(781\) −65.1238 −2.33031
\(782\) −55.4462 −1.98275
\(783\) 13.1023 0.468240
\(784\) −1.29780 −0.0463501
\(785\) −33.1488 −1.18313
\(786\) −4.20937 −0.150143
\(787\) 15.8650 0.565527 0.282764 0.959190i \(-0.408749\pi\)
0.282764 + 0.959190i \(0.408749\pi\)
\(788\) −18.9201 −0.674001
\(789\) −46.2908 −1.64800
\(790\) 20.9667 0.745961
\(791\) −34.7425 −1.23530
\(792\) −0.101217 −0.00359661
\(793\) 25.2526 0.896747
\(794\) −7.64431 −0.271286
\(795\) 12.1896 0.432320
\(796\) 8.76145 0.310541
\(797\) −18.2564 −0.646673 −0.323337 0.946284i \(-0.604805\pi\)
−0.323337 + 0.946284i \(0.604805\pi\)
\(798\) −28.9327 −1.02421
\(799\) 95.9390 3.39408
\(800\) −11.5800 −0.409416
\(801\) −0.172352 −0.00608976
\(802\) 11.0183 0.389071
\(803\) −2.57020 −0.0907004
\(804\) 8.71462 0.307341
\(805\) −74.0565 −2.61015
\(806\) 17.8130 0.627436
\(807\) 52.4898 1.84773
\(808\) 5.51473 0.194008
\(809\) 40.5243 1.42476 0.712379 0.701795i \(-0.247618\pi\)
0.712379 + 0.701795i \(0.247618\pi\)
\(810\) 36.9152 1.29707
\(811\) 6.46438 0.226995 0.113498 0.993538i \(-0.463795\pi\)
0.113498 + 0.993538i \(0.463795\pi\)
\(812\) −6.04378 −0.212095
\(813\) −35.0200 −1.22821
\(814\) −39.1335 −1.37163
\(815\) 7.41874 0.259867
\(816\) −12.6555 −0.443031
\(817\) 15.9948 0.559589
\(818\) 4.12639 0.144276
\(819\) 0.175397 0.00612886
\(820\) 37.1664 1.29791
\(821\) −8.72261 −0.304421 −0.152211 0.988348i \(-0.548639\pi\)
−0.152211 + 0.988348i \(0.548639\pi\)
\(822\) −15.5787 −0.543371
\(823\) 3.79429 0.132261 0.0661303 0.997811i \(-0.478935\pi\)
0.0661303 + 0.997811i \(0.478935\pi\)
\(824\) −11.7681 −0.409960
\(825\) −92.0412 −3.20446
\(826\) −25.6074 −0.890995
\(827\) −11.3093 −0.393264 −0.196632 0.980477i \(-0.563000\pi\)
−0.196632 + 0.980477i \(0.563000\pi\)
\(828\) 0.168612 0.00585968
\(829\) −17.1890 −0.596999 −0.298500 0.954410i \(-0.596486\pi\)
−0.298500 + 0.954410i \(0.596486\pi\)
\(830\) −2.40813 −0.0835875
\(831\) 0.857550 0.0297481
\(832\) −3.31788 −0.115027
\(833\) −9.44782 −0.327347
\(834\) −0.942605 −0.0326397
\(835\) 64.3884 2.22825
\(836\) 31.8660 1.10211
\(837\) 27.7932 0.960672
\(838\) −3.62912 −0.125366
\(839\) −6.04137 −0.208571 −0.104286 0.994547i \(-0.533256\pi\)
−0.104286 + 0.994547i \(0.533256\pi\)
\(840\) −16.9033 −0.583218
\(841\) −22.5942 −0.779110
\(842\) −18.3450 −0.632210
\(843\) 48.1332 1.65780
\(844\) −19.7342 −0.679280
\(845\) −8.10981 −0.278986
\(846\) −0.291751 −0.0100306
\(847\) −23.6502 −0.812632
\(848\) −1.72202 −0.0591345
\(849\) −30.4129 −1.04377
\(850\) −84.3009 −2.89150
\(851\) 65.1903 2.23469
\(852\) 24.7618 0.848324
\(853\) 38.1037 1.30465 0.652323 0.757941i \(-0.273795\pi\)
0.652323 + 0.757941i \(0.273795\pi\)
\(854\) −18.1747 −0.621925
\(855\) 0.628267 0.0214863
\(856\) −1.15542 −0.0394914
\(857\) 37.8607 1.29330 0.646648 0.762788i \(-0.276170\pi\)
0.646648 + 0.762788i \(0.276170\pi\)
\(858\) −26.3714 −0.900305
\(859\) −45.0060 −1.53558 −0.767792 0.640699i \(-0.778645\pi\)
−0.767792 + 0.640699i \(0.778645\pi\)
\(860\) 9.34461 0.318649
\(861\) 37.8910 1.29132
\(862\) 28.1164 0.957647
\(863\) −37.8986 −1.29008 −0.645042 0.764148i \(-0.723160\pi\)
−0.645042 + 0.764148i \(0.723160\pi\)
\(864\) −5.17680 −0.176118
\(865\) −32.5561 −1.10694
\(866\) 32.9621 1.12010
\(867\) −62.5769 −2.12522
\(868\) −12.8203 −0.435148
\(869\) −23.5425 −0.798625
\(870\) 17.9158 0.607404
\(871\) 16.6323 0.563563
\(872\) 1.06109 0.0359329
\(873\) −0.320089 −0.0108334
\(874\) −53.0836 −1.79558
\(875\) −63.9796 −2.16291
\(876\) 0.977256 0.0330184
\(877\) 27.7815 0.938114 0.469057 0.883168i \(-0.344594\pi\)
0.469057 + 0.883168i \(0.344594\pi\)
\(878\) 38.8435 1.31091
\(879\) 5.88059 0.198347
\(880\) 18.6169 0.627577
\(881\) 12.6032 0.424613 0.212307 0.977203i \(-0.431902\pi\)
0.212307 + 0.977203i \(0.431902\pi\)
\(882\) 0.0287309 0.000967419 0
\(883\) 51.2580 1.72497 0.862485 0.506083i \(-0.168907\pi\)
0.862485 + 0.506083i \(0.168907\pi\)
\(884\) −24.1537 −0.812376
\(885\) 75.9091 2.55166
\(886\) 3.92747 0.131946
\(887\) 35.0683 1.17748 0.588739 0.808323i \(-0.299625\pi\)
0.588739 + 0.808323i \(0.299625\pi\)
\(888\) 14.8796 0.499326
\(889\) 14.9267 0.500626
\(890\) 31.7007 1.06261
\(891\) −41.4503 −1.38864
\(892\) 9.22087 0.308738
\(893\) 91.8511 3.07368
\(894\) −38.6628 −1.29308
\(895\) −18.1106 −0.605372
\(896\) 2.38793 0.0797750
\(897\) 43.9306 1.46680
\(898\) 8.74236 0.291736
\(899\) 13.5882 0.453193
\(900\) 0.256360 0.00854532
\(901\) −12.5361 −0.417637
\(902\) −41.7324 −1.38954
\(903\) 9.52679 0.317032
\(904\) −14.5492 −0.483900
\(905\) −31.3604 −1.04246
\(906\) 38.1100 1.26612
\(907\) 7.80443 0.259142 0.129571 0.991570i \(-0.458640\pi\)
0.129571 + 0.991570i \(0.458640\pi\)
\(908\) −3.74748 −0.124365
\(909\) −0.122086 −0.00404932
\(910\) −32.2607 −1.06943
\(911\) 18.8363 0.624074 0.312037 0.950070i \(-0.398989\pi\)
0.312037 + 0.950070i \(0.398989\pi\)
\(912\) −12.1163 −0.401209
\(913\) 2.70398 0.0894886
\(914\) 21.4303 0.708850
\(915\) 53.8760 1.78109
\(916\) −2.10228 −0.0694614
\(917\) 5.78204 0.190940
\(918\) −37.6864 −1.24384
\(919\) 48.3188 1.59389 0.796945 0.604052i \(-0.206448\pi\)
0.796945 + 0.604052i \(0.206448\pi\)
\(920\) −31.0129 −1.02246
\(921\) 35.9159 1.18347
\(922\) 2.07110 0.0682079
\(923\) 47.2590 1.55555
\(924\) 18.9799 0.624393
\(925\) 99.1159 3.25891
\(926\) 21.6822 0.712521
\(927\) 0.260522 0.00855667
\(928\) −2.53097 −0.0830832
\(929\) −34.3210 −1.12604 −0.563018 0.826445i \(-0.690360\pi\)
−0.563018 + 0.826445i \(0.690360\pi\)
\(930\) 38.0037 1.24619
\(931\) −9.04524 −0.296446
\(932\) 24.8250 0.813170
\(933\) 11.5626 0.378541
\(934\) 36.1603 1.18320
\(935\) 135.529 4.43226
\(936\) 0.0734515 0.00240084
\(937\) 12.1778 0.397830 0.198915 0.980017i \(-0.436258\pi\)
0.198915 + 0.980017i \(0.436258\pi\)
\(938\) −11.9705 −0.390851
\(939\) 14.4942 0.473000
\(940\) 53.6618 1.75026
\(941\) 42.8898 1.39817 0.699083 0.715040i \(-0.253592\pi\)
0.699083 + 0.715040i \(0.253592\pi\)
\(942\) −14.1525 −0.461112
\(943\) 69.5196 2.26387
\(944\) −10.7237 −0.349026
\(945\) −50.3356 −1.63742
\(946\) −10.4926 −0.341145
\(947\) −11.8894 −0.386354 −0.193177 0.981164i \(-0.561879\pi\)
−0.193177 + 0.981164i \(0.561879\pi\)
\(948\) 8.95146 0.290730
\(949\) 1.86514 0.0605451
\(950\) −80.7088 −2.61854
\(951\) 36.0675 1.16957
\(952\) 17.3838 0.563411
\(953\) −20.3147 −0.658059 −0.329029 0.944320i \(-0.606722\pi\)
−0.329029 + 0.944320i \(0.606722\pi\)
\(954\) 0.0381223 0.00123425
\(955\) −15.3200 −0.495743
\(956\) 3.60732 0.116669
\(957\) −20.1169 −0.650286
\(958\) −20.7692 −0.671021
\(959\) 21.3992 0.691015
\(960\) −7.07864 −0.228462
\(961\) −2.17613 −0.0701976
\(962\) 28.3984 0.915602
\(963\) 0.0255788 0.000824265 0
\(964\) 20.2807 0.653198
\(965\) 78.5019 2.52707
\(966\) −31.6175 −1.01728
\(967\) −9.76555 −0.314039 −0.157019 0.987596i \(-0.550189\pi\)
−0.157019 + 0.987596i \(0.550189\pi\)
\(968\) −9.90409 −0.318329
\(969\) −88.2045 −2.83354
\(970\) 58.8741 1.89033
\(971\) −27.3994 −0.879290 −0.439645 0.898172i \(-0.644896\pi\)
−0.439645 + 0.898172i \(0.644896\pi\)
\(972\) 0.230061 0.00737921
\(973\) 1.29477 0.0415085
\(974\) 27.1702 0.870589
\(975\) 66.7925 2.13907
\(976\) −7.61107 −0.243624
\(977\) −41.6786 −1.33342 −0.666709 0.745318i \(-0.732297\pi\)
−0.666709 + 0.745318i \(0.732297\pi\)
\(978\) 3.16734 0.101280
\(979\) −35.5952 −1.13763
\(980\) −5.28447 −0.168806
\(981\) −0.0234904 −0.000749992 0
\(982\) 10.4613 0.333834
\(983\) −34.6888 −1.10640 −0.553200 0.833048i \(-0.686594\pi\)
−0.553200 + 0.833048i \(0.686594\pi\)
\(984\) 15.8677 0.505845
\(985\) −77.0400 −2.45470
\(986\) −18.4251 −0.586775
\(987\) 54.7080 1.74138
\(988\) −23.1245 −0.735688
\(989\) 17.4791 0.555801
\(990\) −0.412143 −0.0130988
\(991\) 18.8669 0.599326 0.299663 0.954045i \(-0.403126\pi\)
0.299663 + 0.954045i \(0.403126\pi\)
\(992\) −5.36879 −0.170459
\(993\) −25.5603 −0.811133
\(994\) −34.0130 −1.07883
\(995\) 35.6754 1.13099
\(996\) −1.02812 −0.0325773
\(997\) 12.5787 0.398371 0.199186 0.979962i \(-0.436170\pi\)
0.199186 + 0.979962i \(0.436170\pi\)
\(998\) −19.8841 −0.629419
\(999\) 44.3093 1.40189
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 \(a_p\))