Properties

Label 8002.2.a.e.1.3
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 1.3
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.14624 q^{3} +1.00000 q^{4} +3.08369 q^{5} +3.14624 q^{6} +2.61077 q^{7} -1.00000 q^{8} +6.89883 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.14624 q^{3} +1.00000 q^{4} +3.08369 q^{5} +3.14624 q^{6} +2.61077 q^{7} -1.00000 q^{8} +6.89883 q^{9} -3.08369 q^{10} +3.38926 q^{11} -3.14624 q^{12} +4.00517 q^{13} -2.61077 q^{14} -9.70203 q^{15} +1.00000 q^{16} +0.238806 q^{17} -6.89883 q^{18} +0.0258865 q^{19} +3.08369 q^{20} -8.21409 q^{21} -3.38926 q^{22} +2.40323 q^{23} +3.14624 q^{24} +4.50915 q^{25} -4.00517 q^{26} -12.2666 q^{27} +2.61077 q^{28} -7.95586 q^{29} +9.70203 q^{30} +4.55958 q^{31} -1.00000 q^{32} -10.6634 q^{33} -0.238806 q^{34} +8.05079 q^{35} +6.89883 q^{36} -9.29097 q^{37} -0.0258865 q^{38} -12.6012 q^{39} -3.08369 q^{40} -0.667693 q^{41} +8.21409 q^{42} +11.2716 q^{43} +3.38926 q^{44} +21.2738 q^{45} -2.40323 q^{46} +6.01678 q^{47} -3.14624 q^{48} -0.183905 q^{49} -4.50915 q^{50} -0.751340 q^{51} +4.00517 q^{52} +4.53839 q^{53} +12.2666 q^{54} +10.4514 q^{55} -2.61077 q^{56} -0.0814452 q^{57} +7.95586 q^{58} -5.43268 q^{59} -9.70203 q^{60} +5.12334 q^{61} -4.55958 q^{62} +18.0112 q^{63} +1.00000 q^{64} +12.3507 q^{65} +10.6634 q^{66} -10.0561 q^{67} +0.238806 q^{68} -7.56113 q^{69} -8.05079 q^{70} +9.94308 q^{71} -6.89883 q^{72} -0.921882 q^{73} +9.29097 q^{74} -14.1869 q^{75} +0.0258865 q^{76} +8.84856 q^{77} +12.6012 q^{78} -3.59191 q^{79} +3.08369 q^{80} +17.8973 q^{81} +0.667693 q^{82} -2.35994 q^{83} -8.21409 q^{84} +0.736403 q^{85} -11.2716 q^{86} +25.0311 q^{87} -3.38926 q^{88} +5.42030 q^{89} -21.2738 q^{90} +10.4566 q^{91} +2.40323 q^{92} -14.3455 q^{93} -6.01678 q^{94} +0.0798260 q^{95} +3.14624 q^{96} +6.57243 q^{97} +0.183905 q^{98} +23.3819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} + O(q^{10}) \) \( 77q - 77q^{2} + 10q^{3} + 77q^{4} + 18q^{5} - 10q^{6} + 21q^{7} - 77q^{8} + 71q^{9} - 18q^{10} + 30q^{11} + 10q^{12} - 2q^{13} - 21q^{14} + 21q^{15} + 77q^{16} + 60q^{17} - 71q^{18} - 3q^{19} + 18q^{20} + 10q^{21} - 30q^{22} + 53q^{23} - 10q^{24} + 59q^{25} + 2q^{26} + 43q^{27} + 21q^{28} + 30q^{29} - 21q^{30} + 22q^{31} - 77q^{32} + 31q^{33} - 60q^{34} + 41q^{35} + 71q^{36} - 3q^{37} + 3q^{38} + 44q^{39} - 18q^{40} + 48q^{41} - 10q^{42} + 21q^{43} + 30q^{44} + 33q^{45} - 53q^{46} + 107q^{47} + 10q^{48} + 24q^{49} - 59q^{50} + 18q^{51} - 2q^{52} + 42q^{53} - 43q^{54} + 49q^{55} - 21q^{56} + 32q^{57} - 30q^{58} + 42q^{59} + 21q^{60} - 31q^{61} - 22q^{62} + 109q^{63} + 77q^{64} + 39q^{65} - 31q^{66} - q^{67} + 60q^{68} - 33q^{69} - 41q^{70} + 58q^{71} - 71q^{72} + 35q^{73} + 3q^{74} + 34q^{75} - 3q^{76} + 86q^{77} - 44q^{78} + 25q^{79} + 18q^{80} + 53q^{81} - 48q^{82} + 107q^{83} + 10q^{84} + 21q^{85} - 21q^{86} + 100q^{87} - 30q^{88} + 34q^{89} - 33q^{90} - 51q^{91} + 53q^{92} + 48q^{93} - 107q^{94} + 118q^{95} - 10q^{96} - 13q^{97} - 24q^{98} + 63q^{99} + O(q^{100}) \)

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
\(3\) −3.14624 −1.81648 −0.908241 0.418447i \(-0.862575\pi\)
−0.908241 + 0.418447i \(0.862575\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.08369 1.37907 0.689534 0.724253i \(-0.257815\pi\)
0.689534 + 0.724253i \(0.257815\pi\)
\(6\) 3.14624 1.28445
\(7\) 2.61077 0.986777 0.493388 0.869809i \(-0.335758\pi\)
0.493388 + 0.869809i \(0.335758\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.89883 2.29961
\(10\) −3.08369 −0.975148
\(11\) 3.38926 1.02190 0.510950 0.859611i \(-0.329294\pi\)
0.510950 + 0.859611i \(0.329294\pi\)
\(12\) −3.14624 −0.908241
\(13\) 4.00517 1.11084 0.555418 0.831572i \(-0.312558\pi\)
0.555418 + 0.831572i \(0.312558\pi\)
\(14\) −2.61077 −0.697756
\(15\) −9.70203 −2.50505
\(16\) 1.00000 0.250000
\(17\) 0.238806 0.0579189 0.0289595 0.999581i \(-0.490781\pi\)
0.0289595 + 0.999581i \(0.490781\pi\)
\(18\) −6.89883 −1.62607
\(19\) 0.0258865 0.00593878 0.00296939 0.999996i \(-0.499055\pi\)
0.00296939 + 0.999996i \(0.499055\pi\)
\(20\) 3.08369 0.689534
\(21\) −8.21409 −1.79246
\(22\) −3.38926 −0.722592
\(23\) 2.40323 0.501107 0.250554 0.968103i \(-0.419387\pi\)
0.250554 + 0.968103i \(0.419387\pi\)
\(24\) 3.14624 0.642224
\(25\) 4.50915 0.901829
\(26\) −4.00517 −0.785479
\(27\) −12.2666 −2.36072
\(28\) 2.61077 0.493388
\(29\) −7.95586 −1.47737 −0.738683 0.674053i \(-0.764552\pi\)
−0.738683 + 0.674053i \(0.764552\pi\)
\(30\) 9.70203 1.77134
\(31\) 4.55958 0.818924 0.409462 0.912327i \(-0.365716\pi\)
0.409462 + 0.912327i \(0.365716\pi\)
\(32\) −1.00000 −0.176777
\(33\) −10.6634 −1.85626
\(34\) −0.238806 −0.0409548
\(35\) 8.05079 1.36083
\(36\) 6.89883 1.14980
\(37\) −9.29097 −1.52743 −0.763713 0.645556i \(-0.776626\pi\)
−0.763713 + 0.645556i \(0.776626\pi\)
\(38\) −0.0258865 −0.00419935
\(39\) −12.6012 −2.01781
\(40\) −3.08369 −0.487574
\(41\) −0.667693 −0.104276 −0.0521380 0.998640i \(-0.516604\pi\)
−0.0521380 + 0.998640i \(0.516604\pi\)
\(42\) 8.21409 1.26746
\(43\) 11.2716 1.71891 0.859454 0.511213i \(-0.170804\pi\)
0.859454 + 0.511213i \(0.170804\pi\)
\(44\) 3.38926 0.510950
\(45\) 21.2738 3.17132
\(46\) −2.40323 −0.354336
\(47\) 6.01678 0.877637 0.438818 0.898576i \(-0.355397\pi\)
0.438818 + 0.898576i \(0.355397\pi\)
\(48\) −3.14624 −0.454121
\(49\) −0.183905 −0.0262721
\(50\) −4.50915 −0.637689
\(51\) −0.751340 −0.105209
\(52\) 4.00517 0.555418
\(53\) 4.53839 0.623396 0.311698 0.950181i \(-0.399102\pi\)
0.311698 + 0.950181i \(0.399102\pi\)
\(54\) 12.2666 1.66928
\(55\) 10.4514 1.40927
\(56\) −2.61077 −0.348878
\(57\) −0.0814452 −0.0107877
\(58\) 7.95586 1.04466
\(59\) −5.43268 −0.707275 −0.353637 0.935383i \(-0.615055\pi\)
−0.353637 + 0.935383i \(0.615055\pi\)
\(60\) −9.70203 −1.25253
\(61\) 5.12334 0.655976 0.327988 0.944682i \(-0.393629\pi\)
0.327988 + 0.944682i \(0.393629\pi\)
\(62\) −4.55958 −0.579067
\(63\) 18.0112 2.26920
\(64\) 1.00000 0.125000
\(65\) 12.3507 1.53192
\(66\) 10.6634 1.31258
\(67\) −10.0561 −1.22855 −0.614273 0.789094i \(-0.710551\pi\)
−0.614273 + 0.789094i \(0.710551\pi\)
\(68\) 0.238806 0.0289595
\(69\) −7.56113 −0.910252
\(70\) −8.05079 −0.962254
\(71\) 9.94308 1.18003 0.590013 0.807394i \(-0.299122\pi\)
0.590013 + 0.807394i \(0.299122\pi\)
\(72\) −6.89883 −0.813035
\(73\) −0.921882 −0.107898 −0.0539491 0.998544i \(-0.517181\pi\)
−0.0539491 + 0.998544i \(0.517181\pi\)
\(74\) 9.29097 1.08005
\(75\) −14.1869 −1.63816
\(76\) 0.0258865 0.00296939
\(77\) 8.84856 1.00839
\(78\) 12.6012 1.42681
\(79\) −3.59191 −0.404121 −0.202061 0.979373i \(-0.564764\pi\)
−0.202061 + 0.979373i \(0.564764\pi\)
\(80\) 3.08369 0.344767
\(81\) 17.8973 1.98859
\(82\) 0.667693 0.0737343
\(83\) −2.35994 −0.259037 −0.129519 0.991577i \(-0.541343\pi\)
−0.129519 + 0.991577i \(0.541343\pi\)
\(84\) −8.21409 −0.896231
\(85\) 0.736403 0.0798741
\(86\) −11.2716 −1.21545
\(87\) 25.0311 2.68361
\(88\) −3.38926 −0.361296
\(89\) 5.42030 0.574551 0.287275 0.957848i \(-0.407251\pi\)
0.287275 + 0.957848i \(0.407251\pi\)
\(90\) −21.2738 −2.24246
\(91\) 10.4566 1.09615
\(92\) 2.40323 0.250554
\(93\) −14.3455 −1.48756
\(94\) −6.01678 −0.620583
\(95\) 0.0798260 0.00818998
\(96\) 3.14624 0.321112
\(97\) 6.57243 0.667329 0.333665 0.942692i \(-0.391715\pi\)
0.333665 + 0.942692i \(0.391715\pi\)
\(98\) 0.183905 0.0185772
\(99\) 23.3819 2.34997
\(100\) 4.50915 0.450915
\(101\) 15.5393 1.54622 0.773109 0.634274i \(-0.218701\pi\)
0.773109 + 0.634274i \(0.218701\pi\)
\(102\) 0.751340 0.0743938
\(103\) 16.6555 1.64112 0.820558 0.571563i \(-0.193663\pi\)
0.820558 + 0.571563i \(0.193663\pi\)
\(104\) −4.00517 −0.392740
\(105\) −25.3297 −2.47193
\(106\) −4.53839 −0.440807
\(107\) 13.1120 1.26759 0.633793 0.773503i \(-0.281497\pi\)
0.633793 + 0.773503i \(0.281497\pi\)
\(108\) −12.2666 −1.18036
\(109\) −7.46706 −0.715215 −0.357608 0.933872i \(-0.616407\pi\)
−0.357608 + 0.933872i \(0.616407\pi\)
\(110\) −10.4514 −0.996504
\(111\) 29.2316 2.77454
\(112\) 2.61077 0.246694
\(113\) 0.107346 0.0100983 0.00504913 0.999987i \(-0.498393\pi\)
0.00504913 + 0.999987i \(0.498393\pi\)
\(114\) 0.0814452 0.00762805
\(115\) 7.41080 0.691061
\(116\) −7.95586 −0.738683
\(117\) 27.6310 2.55449
\(118\) 5.43268 0.500119
\(119\) 0.623466 0.0571530
\(120\) 9.70203 0.885670
\(121\) 0.487066 0.0442788
\(122\) −5.12334 −0.463845
\(123\) 2.10072 0.189416
\(124\) 4.55958 0.409462
\(125\) −1.51364 −0.135384
\(126\) −18.0112 −1.60457
\(127\) −2.97087 −0.263622 −0.131811 0.991275i \(-0.542079\pi\)
−0.131811 + 0.991275i \(0.542079\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −35.4633 −3.12237
\(130\) −12.3507 −1.08323
\(131\) 10.6464 0.930178 0.465089 0.885264i \(-0.346022\pi\)
0.465089 + 0.885264i \(0.346022\pi\)
\(132\) −10.6634 −0.928131
\(133\) 0.0675836 0.00586025
\(134\) 10.0561 0.868713
\(135\) −37.8265 −3.25559
\(136\) −0.238806 −0.0204774
\(137\) 18.7855 1.60495 0.802477 0.596683i \(-0.203515\pi\)
0.802477 + 0.596683i \(0.203515\pi\)
\(138\) 7.56113 0.643646
\(139\) −4.48551 −0.380456 −0.190228 0.981740i \(-0.560923\pi\)
−0.190228 + 0.981740i \(0.560923\pi\)
\(140\) 8.05079 0.680416
\(141\) −18.9302 −1.59421
\(142\) −9.94308 −0.834405
\(143\) 13.5746 1.13516
\(144\) 6.89883 0.574902
\(145\) −24.5334 −2.03739
\(146\) 0.921882 0.0762955
\(147\) 0.578609 0.0477229
\(148\) −9.29097 −0.763713
\(149\) −15.2436 −1.24881 −0.624403 0.781103i \(-0.714657\pi\)
−0.624403 + 0.781103i \(0.714657\pi\)
\(150\) 14.1869 1.15835
\(151\) −1.68603 −0.137207 −0.0686037 0.997644i \(-0.521854\pi\)
−0.0686037 + 0.997644i \(0.521854\pi\)
\(152\) −0.0258865 −0.00209967
\(153\) 1.64748 0.133191
\(154\) −8.84856 −0.713037
\(155\) 14.0603 1.12935
\(156\) −12.6012 −1.00891
\(157\) −11.9385 −0.952796 −0.476398 0.879230i \(-0.658058\pi\)
−0.476398 + 0.879230i \(0.658058\pi\)
\(158\) 3.59191 0.285757
\(159\) −14.2789 −1.13239
\(160\) −3.08369 −0.243787
\(161\) 6.27426 0.494481
\(162\) −17.8973 −1.40615
\(163\) 3.33451 0.261179 0.130589 0.991437i \(-0.458313\pi\)
0.130589 + 0.991437i \(0.458313\pi\)
\(164\) −0.667693 −0.0521380
\(165\) −32.8827 −2.55991
\(166\) 2.35994 0.183167
\(167\) −20.8102 −1.61034 −0.805170 0.593044i \(-0.797926\pi\)
−0.805170 + 0.593044i \(0.797926\pi\)
\(168\) 8.21409 0.633731
\(169\) 3.04142 0.233955
\(170\) −0.736403 −0.0564795
\(171\) 0.178587 0.0136569
\(172\) 11.2716 0.859454
\(173\) −14.2446 −1.08300 −0.541499 0.840701i \(-0.682143\pi\)
−0.541499 + 0.840701i \(0.682143\pi\)
\(174\) −25.0311 −1.89760
\(175\) 11.7723 0.889904
\(176\) 3.38926 0.255475
\(177\) 17.0925 1.28475
\(178\) −5.42030 −0.406269
\(179\) 17.0388 1.27354 0.636770 0.771054i \(-0.280270\pi\)
0.636770 + 0.771054i \(0.280270\pi\)
\(180\) 21.2738 1.58566
\(181\) −6.88283 −0.511597 −0.255798 0.966730i \(-0.582338\pi\)
−0.255798 + 0.966730i \(0.582338\pi\)
\(182\) −10.4566 −0.775092
\(183\) −16.1193 −1.19157
\(184\) −2.40323 −0.177168
\(185\) −28.6505 −2.10643
\(186\) 14.3455 1.05187
\(187\) 0.809374 0.0591873
\(188\) 6.01678 0.438818
\(189\) −32.0253 −2.32950
\(190\) −0.0798260 −0.00579119
\(191\) 13.6450 0.987316 0.493658 0.869656i \(-0.335659\pi\)
0.493658 + 0.869656i \(0.335659\pi\)
\(192\) −3.14624 −0.227060
\(193\) 24.0091 1.72821 0.864106 0.503310i \(-0.167885\pi\)
0.864106 + 0.503310i \(0.167885\pi\)
\(194\) −6.57243 −0.471873
\(195\) −38.8583 −2.78270
\(196\) −0.183905 −0.0131361
\(197\) 2.45319 0.174783 0.0873914 0.996174i \(-0.472147\pi\)
0.0873914 + 0.996174i \(0.472147\pi\)
\(198\) −23.3819 −1.66168
\(199\) 9.03508 0.640480 0.320240 0.947336i \(-0.396236\pi\)
0.320240 + 0.947336i \(0.396236\pi\)
\(200\) −4.50915 −0.318845
\(201\) 31.6388 2.23163
\(202\) −15.5393 −1.09334
\(203\) −20.7709 −1.45783
\(204\) −0.751340 −0.0526043
\(205\) −2.05896 −0.143804
\(206\) −16.6555 −1.16044
\(207\) 16.5794 1.15235
\(208\) 4.00517 0.277709
\(209\) 0.0877361 0.00606883
\(210\) 25.3297 1.74792
\(211\) −5.91599 −0.407274 −0.203637 0.979047i \(-0.565276\pi\)
−0.203637 + 0.979047i \(0.565276\pi\)
\(212\) 4.53839 0.311698
\(213\) −31.2833 −2.14350
\(214\) −13.1120 −0.896319
\(215\) 34.7582 2.37049
\(216\) 12.2666 0.834640
\(217\) 11.9040 0.808095
\(218\) 7.46706 0.505733
\(219\) 2.90046 0.195995
\(220\) 10.4514 0.704635
\(221\) 0.956459 0.0643384
\(222\) −29.2316 −1.96190
\(223\) 0.856135 0.0573311 0.0286655 0.999589i \(-0.490874\pi\)
0.0286655 + 0.999589i \(0.490874\pi\)
\(224\) −2.61077 −0.174439
\(225\) 31.1078 2.07385
\(226\) −0.107346 −0.00714055
\(227\) −13.6768 −0.907761 −0.453881 0.891063i \(-0.649961\pi\)
−0.453881 + 0.891063i \(0.649961\pi\)
\(228\) −0.0814452 −0.00539384
\(229\) −11.4129 −0.754188 −0.377094 0.926175i \(-0.623077\pi\)
−0.377094 + 0.926175i \(0.623077\pi\)
\(230\) −7.41080 −0.488654
\(231\) −27.8397 −1.83172
\(232\) 7.95586 0.522328
\(233\) 6.64772 0.435507 0.217753 0.976004i \(-0.430127\pi\)
0.217753 + 0.976004i \(0.430127\pi\)
\(234\) −27.6310 −1.80630
\(235\) 18.5539 1.21032
\(236\) −5.43268 −0.353637
\(237\) 11.3010 0.734079
\(238\) −0.623466 −0.0404133
\(239\) 10.3920 0.672205 0.336103 0.941825i \(-0.390891\pi\)
0.336103 + 0.941825i \(0.390891\pi\)
\(240\) −9.70203 −0.626263
\(241\) −0.616335 −0.0397016 −0.0198508 0.999803i \(-0.506319\pi\)
−0.0198508 + 0.999803i \(0.506319\pi\)
\(242\) −0.487066 −0.0313098
\(243\) −19.5094 −1.25153
\(244\) 5.12334 0.327988
\(245\) −0.567106 −0.0362311
\(246\) −2.10072 −0.133937
\(247\) 0.103680 0.00659700
\(248\) −4.55958 −0.289533
\(249\) 7.42494 0.470537
\(250\) 1.51364 0.0957312
\(251\) −11.8217 −0.746177 −0.373089 0.927796i \(-0.621701\pi\)
−0.373089 + 0.927796i \(0.621701\pi\)
\(252\) 18.0112 1.13460
\(253\) 8.14515 0.512081
\(254\) 2.97087 0.186409
\(255\) −2.31690 −0.145090
\(256\) 1.00000 0.0625000
\(257\) −24.0463 −1.49997 −0.749985 0.661455i \(-0.769939\pi\)
−0.749985 + 0.661455i \(0.769939\pi\)
\(258\) 35.4633 2.20785
\(259\) −24.2565 −1.50723
\(260\) 12.3507 0.765959
\(261\) −54.8861 −3.39737
\(262\) −10.6464 −0.657735
\(263\) −0.539361 −0.0332584 −0.0166292 0.999862i \(-0.505293\pi\)
−0.0166292 + 0.999862i \(0.505293\pi\)
\(264\) 10.6634 0.656288
\(265\) 13.9950 0.859705
\(266\) −0.0675836 −0.00414382
\(267\) −17.0536 −1.04366
\(268\) −10.0561 −0.614273
\(269\) 9.13670 0.557074 0.278537 0.960425i \(-0.410150\pi\)
0.278537 + 0.960425i \(0.410150\pi\)
\(270\) 37.8265 2.30205
\(271\) −18.0046 −1.09370 −0.546852 0.837229i \(-0.684174\pi\)
−0.546852 + 0.837229i \(0.684174\pi\)
\(272\) 0.238806 0.0144797
\(273\) −32.8989 −1.99113
\(274\) −18.7855 −1.13487
\(275\) 15.2827 0.921579
\(276\) −7.56113 −0.455126
\(277\) 16.5401 0.993799 0.496899 0.867808i \(-0.334472\pi\)
0.496899 + 0.867808i \(0.334472\pi\)
\(278\) 4.48551 0.269023
\(279\) 31.4557 1.88321
\(280\) −8.05079 −0.481127
\(281\) −25.0769 −1.49597 −0.747983 0.663718i \(-0.768977\pi\)
−0.747983 + 0.663718i \(0.768977\pi\)
\(282\) 18.9302 1.12728
\(283\) −6.26724 −0.372549 −0.186274 0.982498i \(-0.559641\pi\)
−0.186274 + 0.982498i \(0.559641\pi\)
\(284\) 9.94308 0.590013
\(285\) −0.251152 −0.0148770
\(286\) −13.5746 −0.802681
\(287\) −1.74319 −0.102897
\(288\) −6.89883 −0.406517
\(289\) −16.9430 −0.996645
\(290\) 24.5334 1.44065
\(291\) −20.6784 −1.21219
\(292\) −0.921882 −0.0539491
\(293\) −3.99615 −0.233458 −0.116729 0.993164i \(-0.537241\pi\)
−0.116729 + 0.993164i \(0.537241\pi\)
\(294\) −0.578609 −0.0337452
\(295\) −16.7527 −0.975380
\(296\) 9.29097 0.540027
\(297\) −41.5748 −2.41242
\(298\) 15.2436 0.883039
\(299\) 9.62534 0.556648
\(300\) −14.1869 −0.819078
\(301\) 29.4276 1.69618
\(302\) 1.68603 0.0970203
\(303\) −48.8903 −2.80868
\(304\) 0.0258865 0.00148469
\(305\) 15.7988 0.904636
\(306\) −1.64748 −0.0941801
\(307\) 30.0684 1.71610 0.858048 0.513569i \(-0.171677\pi\)
0.858048 + 0.513569i \(0.171677\pi\)
\(308\) 8.84856 0.504193
\(309\) −52.4022 −2.98106
\(310\) −14.0603 −0.798573
\(311\) −32.5024 −1.84304 −0.921521 0.388330i \(-0.873052\pi\)
−0.921521 + 0.388330i \(0.873052\pi\)
\(312\) 12.6012 0.713405
\(313\) −6.14448 −0.347307 −0.173653 0.984807i \(-0.555557\pi\)
−0.173653 + 0.984807i \(0.555557\pi\)
\(314\) 11.9385 0.673729
\(315\) 55.5410 3.12938
\(316\) −3.59191 −0.202061
\(317\) 2.16699 0.121710 0.0608550 0.998147i \(-0.480617\pi\)
0.0608550 + 0.998147i \(0.480617\pi\)
\(318\) 14.2789 0.800719
\(319\) −26.9645 −1.50972
\(320\) 3.08369 0.172384
\(321\) −41.2535 −2.30255
\(322\) −6.27426 −0.349651
\(323\) 0.00618185 0.000343967 0
\(324\) 17.8973 0.994297
\(325\) 18.0599 1.00178
\(326\) −3.33451 −0.184681
\(327\) 23.4932 1.29918
\(328\) 0.667693 0.0368672
\(329\) 15.7084 0.866031
\(330\) 32.8827 1.81013
\(331\) 9.82271 0.539905 0.269952 0.962874i \(-0.412992\pi\)
0.269952 + 0.962874i \(0.412992\pi\)
\(332\) −2.35994 −0.129519
\(333\) −64.0968 −3.51248
\(334\) 20.8102 1.13868
\(335\) −31.0098 −1.69425
\(336\) −8.21409 −0.448116
\(337\) 21.0002 1.14395 0.571976 0.820271i \(-0.306177\pi\)
0.571976 + 0.820271i \(0.306177\pi\)
\(338\) −3.04142 −0.165431
\(339\) −0.337736 −0.0183433
\(340\) 0.736403 0.0399371
\(341\) 15.4536 0.836858
\(342\) −0.178587 −0.00965686
\(343\) −18.7555 −1.01270
\(344\) −11.2716 −0.607726
\(345\) −23.3162 −1.25530
\(346\) 14.2446 0.765796
\(347\) 27.4959 1.47606 0.738029 0.674769i \(-0.235757\pi\)
0.738029 + 0.674769i \(0.235757\pi\)
\(348\) 25.0311 1.34181
\(349\) 9.78992 0.524042 0.262021 0.965062i \(-0.415611\pi\)
0.262021 + 0.965062i \(0.415611\pi\)
\(350\) −11.7723 −0.629257
\(351\) −49.1301 −2.62237
\(352\) −3.38926 −0.180648
\(353\) −23.9154 −1.27289 −0.636445 0.771322i \(-0.719596\pi\)
−0.636445 + 0.771322i \(0.719596\pi\)
\(354\) −17.0925 −0.908457
\(355\) 30.6614 1.62734
\(356\) 5.42030 0.287275
\(357\) −1.96157 −0.103817
\(358\) −17.0388 −0.900528
\(359\) 25.7610 1.35961 0.679806 0.733392i \(-0.262064\pi\)
0.679806 + 0.733392i \(0.262064\pi\)
\(360\) −21.2738 −1.12123
\(361\) −18.9993 −0.999965
\(362\) 6.88283 0.361754
\(363\) −1.53243 −0.0804316
\(364\) 10.4566 0.548073
\(365\) −2.84280 −0.148799
\(366\) 16.1193 0.842567
\(367\) 17.9719 0.938124 0.469062 0.883165i \(-0.344592\pi\)
0.469062 + 0.883165i \(0.344592\pi\)
\(368\) 2.40323 0.125277
\(369\) −4.60630 −0.239794
\(370\) 28.6505 1.48947
\(371\) 11.8487 0.615152
\(372\) −14.3455 −0.743781
\(373\) 33.6059 1.74005 0.870023 0.493011i \(-0.164104\pi\)
0.870023 + 0.493011i \(0.164104\pi\)
\(374\) −0.809374 −0.0418517
\(375\) 4.76228 0.245923
\(376\) −6.01678 −0.310291
\(377\) −31.8646 −1.64111
\(378\) 32.0253 1.64721
\(379\) −0.257592 −0.0132316 −0.00661581 0.999978i \(-0.502106\pi\)
−0.00661581 + 0.999978i \(0.502106\pi\)
\(380\) 0.0798260 0.00409499
\(381\) 9.34708 0.478865
\(382\) −13.6450 −0.698138
\(383\) −0.919190 −0.0469684 −0.0234842 0.999724i \(-0.507476\pi\)
−0.0234842 + 0.999724i \(0.507476\pi\)
\(384\) 3.14624 0.160556
\(385\) 27.2862 1.39063
\(386\) −24.0091 −1.22203
\(387\) 77.7610 3.95282
\(388\) 6.57243 0.333665
\(389\) 28.4290 1.44141 0.720703 0.693244i \(-0.243819\pi\)
0.720703 + 0.693244i \(0.243819\pi\)
\(390\) 38.8583 1.96767
\(391\) 0.573904 0.0290236
\(392\) 0.183905 0.00928860
\(393\) −33.4960 −1.68965
\(394\) −2.45319 −0.123590
\(395\) −11.0763 −0.557311
\(396\) 23.3819 1.17498
\(397\) −33.6514 −1.68892 −0.844459 0.535621i \(-0.820078\pi\)
−0.844459 + 0.535621i \(0.820078\pi\)
\(398\) −9.03508 −0.452888
\(399\) −0.212634 −0.0106450
\(400\) 4.50915 0.225457
\(401\) −8.75579 −0.437243 −0.218622 0.975810i \(-0.570156\pi\)
−0.218622 + 0.975810i \(0.570156\pi\)
\(402\) −31.6388 −1.57800
\(403\) 18.2619 0.909690
\(404\) 15.5393 0.773109
\(405\) 55.1899 2.74241
\(406\) 20.7709 1.03084
\(407\) −31.4895 −1.56088
\(408\) 0.751340 0.0371969
\(409\) −36.8347 −1.82136 −0.910681 0.413111i \(-0.864442\pi\)
−0.910681 + 0.413111i \(0.864442\pi\)
\(410\) 2.05896 0.101685
\(411\) −59.1037 −2.91537
\(412\) 16.6555 0.820558
\(413\) −14.1835 −0.697922
\(414\) −16.5794 −0.814835
\(415\) −7.27733 −0.357230
\(416\) −4.00517 −0.196370
\(417\) 14.1125 0.691092
\(418\) −0.0877361 −0.00429131
\(419\) −0.950481 −0.0464340 −0.0232170 0.999730i \(-0.507391\pi\)
−0.0232170 + 0.999730i \(0.507391\pi\)
\(420\) −25.3297 −1.23596
\(421\) −10.7725 −0.525021 −0.262510 0.964929i \(-0.584550\pi\)
−0.262510 + 0.964929i \(0.584550\pi\)
\(422\) 5.91599 0.287986
\(423\) 41.5087 2.01822
\(424\) −4.53839 −0.220404
\(425\) 1.07681 0.0522330
\(426\) 31.2833 1.51568
\(427\) 13.3758 0.647302
\(428\) 13.1120 0.633793
\(429\) −42.7088 −2.06200
\(430\) −34.7582 −1.67619
\(431\) 27.2947 1.31474 0.657370 0.753568i \(-0.271669\pi\)
0.657370 + 0.753568i \(0.271669\pi\)
\(432\) −12.2666 −0.590179
\(433\) 32.5271 1.56315 0.781576 0.623810i \(-0.214416\pi\)
0.781576 + 0.623810i \(0.214416\pi\)
\(434\) −11.9040 −0.571410
\(435\) 77.1880 3.70088
\(436\) −7.46706 −0.357608
\(437\) 0.0622112 0.00297596
\(438\) −2.90046 −0.138589
\(439\) −10.2456 −0.488997 −0.244498 0.969650i \(-0.578623\pi\)
−0.244498 + 0.969650i \(0.578623\pi\)
\(440\) −10.4514 −0.498252
\(441\) −1.26873 −0.0604156
\(442\) −0.956459 −0.0454941
\(443\) 29.3010 1.39213 0.696066 0.717978i \(-0.254932\pi\)
0.696066 + 0.717978i \(0.254932\pi\)
\(444\) 29.2316 1.38727
\(445\) 16.7145 0.792345
\(446\) −0.856135 −0.0405392
\(447\) 47.9601 2.26843
\(448\) 2.61077 0.123347
\(449\) 3.99304 0.188443 0.0942215 0.995551i \(-0.469964\pi\)
0.0942215 + 0.995551i \(0.469964\pi\)
\(450\) −31.1078 −1.46644
\(451\) −2.26298 −0.106560
\(452\) 0.107346 0.00504913
\(453\) 5.30467 0.249235
\(454\) 13.6768 0.641884
\(455\) 32.2448 1.51166
\(456\) 0.0814452 0.00381402
\(457\) −31.1775 −1.45842 −0.729211 0.684289i \(-0.760113\pi\)
−0.729211 + 0.684289i \(0.760113\pi\)
\(458\) 11.4129 0.533291
\(459\) −2.92935 −0.136730
\(460\) 7.41080 0.345530
\(461\) −14.3164 −0.666783 −0.333391 0.942788i \(-0.608193\pi\)
−0.333391 + 0.942788i \(0.608193\pi\)
\(462\) 27.8397 1.29522
\(463\) 42.6472 1.98198 0.990992 0.133919i \(-0.0427561\pi\)
0.990992 + 0.133919i \(0.0427561\pi\)
\(464\) −7.95586 −0.369342
\(465\) −44.2372 −2.05145
\(466\) −6.64772 −0.307950
\(467\) −23.4726 −1.08618 −0.543092 0.839673i \(-0.682746\pi\)
−0.543092 + 0.839673i \(0.682746\pi\)
\(468\) 27.6310 1.27724
\(469\) −26.2541 −1.21230
\(470\) −18.5539 −0.855826
\(471\) 37.5614 1.73074
\(472\) 5.43268 0.250059
\(473\) 38.2025 1.75655
\(474\) −11.3010 −0.519072
\(475\) 0.116726 0.00535576
\(476\) 0.623466 0.0285765
\(477\) 31.3096 1.43357
\(478\) −10.3920 −0.475321
\(479\) 9.85431 0.450255 0.225127 0.974329i \(-0.427720\pi\)
0.225127 + 0.974329i \(0.427720\pi\)
\(480\) 9.70203 0.442835
\(481\) −37.2120 −1.69672
\(482\) 0.616335 0.0280733
\(483\) −19.7403 −0.898216
\(484\) 0.487066 0.0221394
\(485\) 20.2673 0.920292
\(486\) 19.5094 0.884964
\(487\) −11.1216 −0.503967 −0.251984 0.967732i \(-0.581083\pi\)
−0.251984 + 0.967732i \(0.581083\pi\)
\(488\) −5.12334 −0.231923
\(489\) −10.4912 −0.474427
\(490\) 0.567106 0.0256192
\(491\) −13.1409 −0.593042 −0.296521 0.955026i \(-0.595826\pi\)
−0.296521 + 0.955026i \(0.595826\pi\)
\(492\) 2.10072 0.0947078
\(493\) −1.89991 −0.0855675
\(494\) −0.103680 −0.00466479
\(495\) 72.1025 3.24077
\(496\) 4.55958 0.204731
\(497\) 25.9591 1.16442
\(498\) −7.42494 −0.332720
\(499\) −35.3049 −1.58046 −0.790232 0.612807i \(-0.790040\pi\)
−0.790232 + 0.612807i \(0.790040\pi\)
\(500\) −1.51364 −0.0676922
\(501\) 65.4738 2.92515
\(502\) 11.8217 0.527627
\(503\) 20.1758 0.899596 0.449798 0.893130i \(-0.351496\pi\)
0.449798 + 0.893130i \(0.351496\pi\)
\(504\) −18.0112 −0.802283
\(505\) 47.9184 2.13234
\(506\) −8.14515 −0.362096
\(507\) −9.56903 −0.424975
\(508\) −2.97087 −0.131811
\(509\) 23.3159 1.03346 0.516730 0.856149i \(-0.327149\pi\)
0.516730 + 0.856149i \(0.327149\pi\)
\(510\) 2.31690 0.102594
\(511\) −2.40682 −0.106471
\(512\) −1.00000 −0.0441942
\(513\) −0.317541 −0.0140198
\(514\) 24.0463 1.06064
\(515\) 51.3604 2.26321
\(516\) −35.4633 −1.56118
\(517\) 20.3924 0.896857
\(518\) 24.2565 1.06577
\(519\) 44.8170 1.96725
\(520\) −12.3507 −0.541615
\(521\) 3.72546 0.163215 0.0816077 0.996665i \(-0.473995\pi\)
0.0816077 + 0.996665i \(0.473995\pi\)
\(522\) 54.8861 2.40230
\(523\) 16.5874 0.725317 0.362659 0.931922i \(-0.381869\pi\)
0.362659 + 0.931922i \(0.381869\pi\)
\(524\) 10.6464 0.465089
\(525\) −37.0385 −1.61649
\(526\) 0.539361 0.0235172
\(527\) 1.08885 0.0474312
\(528\) −10.6634 −0.464066
\(529\) −17.2245 −0.748892
\(530\) −13.9950 −0.607904
\(531\) −37.4791 −1.62646
\(532\) 0.0675836 0.00293012
\(533\) −2.67422 −0.115834
\(534\) 17.0536 0.737980
\(535\) 40.4334 1.74809
\(536\) 10.0561 0.434357
\(537\) −53.6081 −2.31336
\(538\) −9.13670 −0.393911
\(539\) −0.623301 −0.0268475
\(540\) −37.8265 −1.62780
\(541\) −4.65675 −0.200209 −0.100105 0.994977i \(-0.531918\pi\)
−0.100105 + 0.994977i \(0.531918\pi\)
\(542\) 18.0046 0.773365
\(543\) 21.6550 0.929307
\(544\) −0.238806 −0.0102387
\(545\) −23.0261 −0.986330
\(546\) 32.8989 1.40794
\(547\) −16.8673 −0.721195 −0.360598 0.932721i \(-0.617427\pi\)
−0.360598 + 0.932721i \(0.617427\pi\)
\(548\) 18.7855 0.802477
\(549\) 35.3450 1.50849
\(550\) −15.2827 −0.651655
\(551\) −0.205950 −0.00877375
\(552\) 7.56113 0.321823
\(553\) −9.37763 −0.398777
\(554\) −16.5401 −0.702722
\(555\) 90.1413 3.82629
\(556\) −4.48551 −0.190228
\(557\) −0.750506 −0.0317999 −0.0159000 0.999874i \(-0.505061\pi\)
−0.0159000 + 0.999874i \(0.505061\pi\)
\(558\) −31.4557 −1.33163
\(559\) 45.1448 1.90942
\(560\) 8.05079 0.340208
\(561\) −2.54649 −0.107513
\(562\) 25.0769 1.05781
\(563\) 23.2228 0.978726 0.489363 0.872080i \(-0.337229\pi\)
0.489363 + 0.872080i \(0.337229\pi\)
\(564\) −18.9302 −0.797106
\(565\) 0.331022 0.0139262
\(566\) 6.26724 0.263432
\(567\) 46.7258 1.96230
\(568\) −9.94308 −0.417202
\(569\) −33.3465 −1.39796 −0.698978 0.715143i \(-0.746362\pi\)
−0.698978 + 0.715143i \(0.746362\pi\)
\(570\) 0.251152 0.0105196
\(571\) −15.2711 −0.639074 −0.319537 0.947574i \(-0.603527\pi\)
−0.319537 + 0.947574i \(0.603527\pi\)
\(572\) 13.5746 0.567581
\(573\) −42.9304 −1.79344
\(574\) 1.74319 0.0727593
\(575\) 10.8365 0.451913
\(576\) 6.89883 0.287451
\(577\) 22.2326 0.925555 0.462777 0.886475i \(-0.346853\pi\)
0.462777 + 0.886475i \(0.346853\pi\)
\(578\) 16.9430 0.704735
\(579\) −75.5383 −3.13927
\(580\) −24.5334 −1.01869
\(581\) −6.16125 −0.255612
\(582\) 20.6784 0.857149
\(583\) 15.3818 0.637048
\(584\) 0.921882 0.0381478
\(585\) 85.2055 3.52281
\(586\) 3.99615 0.165079
\(587\) −11.4075 −0.470836 −0.235418 0.971894i \(-0.575646\pi\)
−0.235418 + 0.971894i \(0.575646\pi\)
\(588\) 0.578609 0.0238614
\(589\) 0.118032 0.00486341
\(590\) 16.7527 0.689698
\(591\) −7.71833 −0.317490
\(592\) −9.29097 −0.381857
\(593\) 30.6077 1.25691 0.628454 0.777846i \(-0.283688\pi\)
0.628454 + 0.777846i \(0.283688\pi\)
\(594\) 41.5748 1.70584
\(595\) 1.92258 0.0788179
\(596\) −15.2436 −0.624403
\(597\) −28.4265 −1.16342
\(598\) −9.62534 −0.393609
\(599\) −25.6496 −1.04801 −0.524006 0.851714i \(-0.675563\pi\)
−0.524006 + 0.851714i \(0.675563\pi\)
\(600\) 14.1869 0.579176
\(601\) 8.68896 0.354430 0.177215 0.984172i \(-0.443291\pi\)
0.177215 + 0.984172i \(0.443291\pi\)
\(602\) −29.4276 −1.19938
\(603\) −69.3752 −2.82518
\(604\) −1.68603 −0.0686037
\(605\) 1.50196 0.0610634
\(606\) 48.8903 1.98603
\(607\) 5.94745 0.241399 0.120700 0.992689i \(-0.461486\pi\)
0.120700 + 0.992689i \(0.461486\pi\)
\(608\) −0.0258865 −0.00104984
\(609\) 65.3502 2.64812
\(610\) −15.7988 −0.639674
\(611\) 24.0982 0.974910
\(612\) 1.64748 0.0665954
\(613\) −9.24727 −0.373494 −0.186747 0.982408i \(-0.559794\pi\)
−0.186747 + 0.982408i \(0.559794\pi\)
\(614\) −30.0684 −1.21346
\(615\) 6.47797 0.261217
\(616\) −8.84856 −0.356518
\(617\) −9.12218 −0.367245 −0.183622 0.982997i \(-0.558782\pi\)
−0.183622 + 0.982997i \(0.558782\pi\)
\(618\) 52.4022 2.10793
\(619\) 12.1582 0.488680 0.244340 0.969690i \(-0.421429\pi\)
0.244340 + 0.969690i \(0.421429\pi\)
\(620\) 14.0603 0.564676
\(621\) −29.4795 −1.18297
\(622\) 32.5024 1.30323
\(623\) 14.1511 0.566953
\(624\) −12.6012 −0.504453
\(625\) −27.2133 −1.08853
\(626\) 6.14448 0.245583
\(627\) −0.276039 −0.0110239
\(628\) −11.9385 −0.476398
\(629\) −2.21874 −0.0884669
\(630\) −55.5410 −2.21281
\(631\) −38.6267 −1.53771 −0.768853 0.639426i \(-0.779172\pi\)
−0.768853 + 0.639426i \(0.779172\pi\)
\(632\) 3.59191 0.142878
\(633\) 18.6131 0.739805
\(634\) −2.16699 −0.0860620
\(635\) −9.16125 −0.363553
\(636\) −14.2789 −0.566194
\(637\) −0.736571 −0.0291840
\(638\) 26.9645 1.06753
\(639\) 68.5956 2.71360
\(640\) −3.08369 −0.121894
\(641\) 23.7027 0.936198 0.468099 0.883676i \(-0.344939\pi\)
0.468099 + 0.883676i \(0.344939\pi\)
\(642\) 41.2535 1.62815
\(643\) −9.69181 −0.382208 −0.191104 0.981570i \(-0.561207\pi\)
−0.191104 + 0.981570i \(0.561207\pi\)
\(644\) 6.27426 0.247240
\(645\) −109.358 −4.30596
\(646\) −0.00618185 −0.000243222 0
\(647\) 15.5086 0.609706 0.304853 0.952399i \(-0.401393\pi\)
0.304853 + 0.952399i \(0.401393\pi\)
\(648\) −17.8973 −0.703074
\(649\) −18.4128 −0.722764
\(650\) −18.0599 −0.708368
\(651\) −37.4528 −1.46789
\(652\) 3.33451 0.130589
\(653\) −8.73305 −0.341751 −0.170875 0.985293i \(-0.554660\pi\)
−0.170875 + 0.985293i \(0.554660\pi\)
\(654\) −23.4932 −0.918656
\(655\) 32.8301 1.28278
\(656\) −0.667693 −0.0260690
\(657\) −6.35991 −0.248124
\(658\) −15.7084 −0.612377
\(659\) 18.7596 0.730770 0.365385 0.930857i \(-0.380937\pi\)
0.365385 + 0.930857i \(0.380937\pi\)
\(660\) −32.8827 −1.27996
\(661\) 32.6408 1.26958 0.634790 0.772685i \(-0.281087\pi\)
0.634790 + 0.772685i \(0.281087\pi\)
\(662\) −9.82271 −0.381770
\(663\) −3.00925 −0.116870
\(664\) 2.35994 0.0915835
\(665\) 0.208407 0.00808168
\(666\) 64.0968 2.48370
\(667\) −19.1197 −0.740319
\(668\) −20.8102 −0.805170
\(669\) −2.69361 −0.104141
\(670\) 31.0098 1.19801
\(671\) 17.3643 0.670342
\(672\) 8.21409 0.316866
\(673\) 5.60520 0.216064 0.108032 0.994147i \(-0.465545\pi\)
0.108032 + 0.994147i \(0.465545\pi\)
\(674\) −21.0002 −0.808896
\(675\) −55.3121 −2.12896
\(676\) 3.04142 0.116978
\(677\) −4.24856 −0.163285 −0.0816427 0.996662i \(-0.526017\pi\)
−0.0816427 + 0.996662i \(0.526017\pi\)
\(678\) 0.337736 0.0129707
\(679\) 17.1591 0.658505
\(680\) −0.736403 −0.0282398
\(681\) 43.0305 1.64893
\(682\) −15.4536 −0.591748
\(683\) 21.8681 0.836760 0.418380 0.908272i \(-0.362598\pi\)
0.418380 + 0.908272i \(0.362598\pi\)
\(684\) 0.178587 0.00682843
\(685\) 57.9287 2.21334
\(686\) 18.7555 0.716088
\(687\) 35.9078 1.36997
\(688\) 11.2716 0.429727
\(689\) 18.1770 0.692490
\(690\) 23.3162 0.887631
\(691\) −1.27015 −0.0483188 −0.0241594 0.999708i \(-0.507691\pi\)
−0.0241594 + 0.999708i \(0.507691\pi\)
\(692\) −14.2446 −0.541499
\(693\) 61.0447 2.31889
\(694\) −27.4959 −1.04373
\(695\) −13.8319 −0.524675
\(696\) −25.0311 −0.948800
\(697\) −0.159449 −0.00603956
\(698\) −9.78992 −0.370554
\(699\) −20.9153 −0.791090
\(700\) 11.7723 0.444952
\(701\) −25.2956 −0.955401 −0.477700 0.878523i \(-0.658530\pi\)
−0.477700 + 0.878523i \(0.658530\pi\)
\(702\) 49.1301 1.85429
\(703\) −0.240511 −0.00907105
\(704\) 3.38926 0.127737
\(705\) −58.3749 −2.19853
\(706\) 23.9154 0.900069
\(707\) 40.5694 1.52577
\(708\) 17.0925 0.642376
\(709\) 25.8575 0.971100 0.485550 0.874209i \(-0.338619\pi\)
0.485550 + 0.874209i \(0.338619\pi\)
\(710\) −30.6614 −1.15070
\(711\) −24.7800 −0.929321
\(712\) −5.42030 −0.203134
\(713\) 10.9577 0.410369
\(714\) 1.96157 0.0734100
\(715\) 41.8598 1.56547
\(716\) 17.0388 0.636770
\(717\) −32.6958 −1.22105
\(718\) −25.7610 −0.961391
\(719\) −6.73270 −0.251087 −0.125544 0.992088i \(-0.540068\pi\)
−0.125544 + 0.992088i \(0.540068\pi\)
\(720\) 21.2738 0.792829
\(721\) 43.4836 1.61941
\(722\) 18.9993 0.707082
\(723\) 1.93914 0.0721173
\(724\) −6.88283 −0.255798
\(725\) −35.8741 −1.33233
\(726\) 1.53243 0.0568737
\(727\) 39.7352 1.47370 0.736849 0.676057i \(-0.236313\pi\)
0.736849 + 0.676057i \(0.236313\pi\)
\(728\) −10.4566 −0.387546
\(729\) 7.68920 0.284785
\(730\) 2.84280 0.105217
\(731\) 2.69173 0.0995572
\(732\) −16.1193 −0.595785
\(733\) −36.7125 −1.35601 −0.678003 0.735059i \(-0.737154\pi\)
−0.678003 + 0.735059i \(0.737154\pi\)
\(734\) −17.9719 −0.663353
\(735\) 1.78425 0.0658131
\(736\) −2.40323 −0.0885841
\(737\) −34.0826 −1.25545
\(738\) 4.60630 0.169560
\(739\) −27.6405 −1.01677 −0.508386 0.861130i \(-0.669758\pi\)
−0.508386 + 0.861130i \(0.669758\pi\)
\(740\) −28.6505 −1.05321
\(741\) −0.326202 −0.0119833
\(742\) −11.8487 −0.434978
\(743\) 40.6209 1.49024 0.745118 0.666933i \(-0.232393\pi\)
0.745118 + 0.666933i \(0.232393\pi\)
\(744\) 14.3455 0.525933
\(745\) −47.0066 −1.72219
\(746\) −33.6059 −1.23040
\(747\) −16.2808 −0.595684
\(748\) 0.809374 0.0295937
\(749\) 34.2324 1.25082
\(750\) −4.76228 −0.173894
\(751\) −38.3572 −1.39968 −0.699838 0.714302i \(-0.746744\pi\)
−0.699838 + 0.714302i \(0.746744\pi\)
\(752\) 6.01678 0.219409
\(753\) 37.1938 1.35542
\(754\) 31.8646 1.16044
\(755\) −5.19921 −0.189218
\(756\) −32.0253 −1.16475
\(757\) 30.2585 1.09976 0.549882 0.835243i \(-0.314673\pi\)
0.549882 + 0.835243i \(0.314673\pi\)
\(758\) 0.257592 0.00935616
\(759\) −25.6266 −0.930187
\(760\) −0.0798260 −0.00289559
\(761\) 26.0598 0.944666 0.472333 0.881420i \(-0.343412\pi\)
0.472333 + 0.881420i \(0.343412\pi\)
\(762\) −9.34708 −0.338609
\(763\) −19.4948 −0.705757
\(764\) 13.6450 0.493658
\(765\) 5.08032 0.183679
\(766\) 0.919190 0.0332117
\(767\) −21.7588 −0.785666
\(768\) −3.14624 −0.113530
\(769\) −27.1532 −0.979169 −0.489585 0.871956i \(-0.662852\pi\)
−0.489585 + 0.871956i \(0.662852\pi\)
\(770\) −27.2862 −0.983327
\(771\) 75.6556 2.72467
\(772\) 24.0091 0.864106
\(773\) 12.5518 0.451456 0.225728 0.974190i \(-0.427524\pi\)
0.225728 + 0.974190i \(0.427524\pi\)
\(774\) −77.7610 −2.79506
\(775\) 20.5598 0.738530
\(776\) −6.57243 −0.235936
\(777\) 76.3169 2.73785
\(778\) −28.4290 −1.01923
\(779\) −0.0172842 −0.000619272 0
\(780\) −38.8583 −1.39135
\(781\) 33.6997 1.20587
\(782\) −0.573904 −0.0205228
\(783\) 97.5918 3.48765
\(784\) −0.183905 −0.00656803
\(785\) −36.8147 −1.31397
\(786\) 33.4960 1.19476
\(787\) 27.8035 0.991086 0.495543 0.868583i \(-0.334969\pi\)
0.495543 + 0.868583i \(0.334969\pi\)
\(788\) 2.45319 0.0873914
\(789\) 1.69696 0.0604133
\(790\) 11.0763 0.394078
\(791\) 0.280255 0.00996472
\(792\) −23.3819 −0.830840
\(793\) 20.5199 0.728682
\(794\) 33.6514 1.19424
\(795\) −44.0316 −1.56164
\(796\) 9.03508 0.320240
\(797\) −31.9823 −1.13287 −0.566435 0.824106i \(-0.691678\pi\)
−0.566435 + 0.824106i \(0.691678\pi\)
\(798\) 0.212634 0.00752718
\(799\) 1.43684 0.0508318
\(800\) −4.50915 −0.159422
\(801\) 37.3937 1.32124
\(802\) 8.75579 0.309178
\(803\) −3.12450 −0.110261
\(804\) 31.6388 1.11582
\(805\) 19.3479 0.681923
\(806\) −18.2619 −0.643248
\(807\) −28.7463 −1.01192
\(808\) −15.5393 −0.546670
\(809\) 7.98539 0.280751 0.140376 0.990098i \(-0.455169\pi\)
0.140376 + 0.990098i \(0.455169\pi\)
\(810\) −55.1899 −1.93917
\(811\) 48.9140 1.71760 0.858801 0.512309i \(-0.171210\pi\)
0.858801 + 0.512309i \(0.171210\pi\)
\(812\) −20.7709 −0.728915
\(813\) 56.6469 1.98669
\(814\) 31.4895 1.10371
\(815\) 10.2826 0.360183
\(816\) −0.751340 −0.0263022
\(817\) 0.291783 0.0102082
\(818\) 36.8347 1.28790
\(819\) 72.1381 2.52071
\(820\) −2.05896 −0.0719019
\(821\) −8.37063 −0.292137 −0.146068 0.989274i \(-0.546662\pi\)
−0.146068 + 0.989274i \(0.546662\pi\)
\(822\) 59.1037 2.06148
\(823\) 22.8868 0.797785 0.398892 0.916998i \(-0.369395\pi\)
0.398892 + 0.916998i \(0.369395\pi\)
\(824\) −16.6555 −0.580222
\(825\) −48.0829 −1.67403
\(826\) 14.1835 0.493505
\(827\) −28.4787 −0.990301 −0.495151 0.868807i \(-0.664887\pi\)
−0.495151 + 0.868807i \(0.664887\pi\)
\(828\) 16.5794 0.576175
\(829\) −40.6456 −1.41168 −0.705841 0.708371i \(-0.749431\pi\)
−0.705841 + 0.708371i \(0.749431\pi\)
\(830\) 7.27733 0.252600
\(831\) −52.0392 −1.80522
\(832\) 4.00517 0.138854
\(833\) −0.0439176 −0.00152165
\(834\) −14.1125 −0.488676
\(835\) −64.1721 −2.22077
\(836\) 0.0877361 0.00303442
\(837\) −55.9307 −1.93325
\(838\) 0.950481 0.0328338
\(839\) 1.27190 0.0439108 0.0219554 0.999759i \(-0.493011\pi\)
0.0219554 + 0.999759i \(0.493011\pi\)
\(840\) 25.3297 0.873958
\(841\) 34.2958 1.18261
\(842\) 10.7725 0.371246
\(843\) 78.8981 2.71740
\(844\) −5.91599 −0.203637
\(845\) 9.37879 0.322640
\(846\) −41.5087 −1.42710
\(847\) 1.27162 0.0436932
\(848\) 4.53839 0.155849
\(849\) 19.7182 0.676728
\(850\) −1.07681 −0.0369343
\(851\) −22.3283 −0.765404
\(852\) −31.2833 −1.07175
\(853\) 45.6111 1.56169 0.780847 0.624723i \(-0.214788\pi\)
0.780847 + 0.624723i \(0.214788\pi\)
\(854\) −13.3758 −0.457712
\(855\) 0.550706 0.0188337
\(856\) −13.1120 −0.448159
\(857\) 14.4680 0.494218 0.247109 0.968988i \(-0.420519\pi\)
0.247109 + 0.968988i \(0.420519\pi\)
\(858\) 42.7088 1.45806
\(859\) −43.8964 −1.49773 −0.748863 0.662725i \(-0.769400\pi\)
−0.748863 + 0.662725i \(0.769400\pi\)
\(860\) 34.7582 1.18525
\(861\) 5.48449 0.186911
\(862\) −27.2947 −0.929662
\(863\) −23.0416 −0.784346 −0.392173 0.919891i \(-0.628277\pi\)
−0.392173 + 0.919891i \(0.628277\pi\)
\(864\) 12.2666 0.417320
\(865\) −43.9260 −1.49353
\(866\) −32.5271 −1.10532
\(867\) 53.3067 1.81039
\(868\) 11.9040 0.404048
\(869\) −12.1739 −0.412971
\(870\) −77.1880 −2.61692
\(871\) −40.2763 −1.36471
\(872\) 7.46706 0.252867
\(873\) 45.3421 1.53460
\(874\) −0.0622112 −0.00210432
\(875\) −3.95177 −0.133594
\(876\) 2.90046 0.0979976
\(877\) −51.1981 −1.72884 −0.864419 0.502772i \(-0.832314\pi\)
−0.864419 + 0.502772i \(0.832314\pi\)
\(878\) 10.2456 0.345773
\(879\) 12.5728 0.424072
\(880\) 10.4514 0.352317
\(881\) 5.69895 0.192002 0.0960012 0.995381i \(-0.469395\pi\)
0.0960012 + 0.995381i \(0.469395\pi\)
\(882\) 1.26873 0.0427203
\(883\) −58.8062 −1.97899 −0.989493 0.144582i \(-0.953816\pi\)
−0.989493 + 0.144582i \(0.953816\pi\)
\(884\) 0.956459 0.0321692
\(885\) 52.7080 1.77176
\(886\) −29.3010 −0.984386
\(887\) 24.2030 0.812656 0.406328 0.913727i \(-0.366809\pi\)
0.406328 + 0.913727i \(0.366809\pi\)
\(888\) −29.2316 −0.980949
\(889\) −7.75625 −0.260136
\(890\) −16.7145 −0.560272
\(891\) 60.6587 2.03214
\(892\) 0.856135 0.0286655
\(893\) 0.155753 0.00521209
\(894\) −47.9601 −1.60402
\(895\) 52.5424 1.75630
\(896\) −2.61077 −0.0872195
\(897\) −30.2836 −1.01114
\(898\) −3.99304 −0.133249
\(899\) −36.2754 −1.20985
\(900\) 31.1078 1.03693
\(901\) 1.08379 0.0361064
\(902\) 2.26298 0.0753491
\(903\) −92.5862 −3.08108
\(904\) −0.107346 −0.00357027
\(905\) −21.2245 −0.705527
\(906\) −5.30467 −0.176236
\(907\) −28.4278 −0.943931 −0.471965 0.881617i \(-0.656455\pi\)
−0.471965 + 0.881617i \(0.656455\pi\)
\(908\) −13.6768 −0.453881
\(909\) 107.203 3.55570
\(910\) −32.2448 −1.06891
\(911\) −19.3928 −0.642511 −0.321256 0.946993i \(-0.604105\pi\)
−0.321256 + 0.946993i \(0.604105\pi\)
\(912\) −0.0814452 −0.00269692
\(913\) −7.99845 −0.264710
\(914\) 31.1775 1.03126
\(915\) −49.7068 −1.64326
\(916\) −11.4129 −0.377094
\(917\) 27.7952 0.917878
\(918\) 2.92935 0.0966828
\(919\) −23.4795 −0.774517 −0.387259 0.921971i \(-0.626578\pi\)
−0.387259 + 0.921971i \(0.626578\pi\)
\(920\) −7.41080 −0.244327
\(921\) −94.6026 −3.11726
\(922\) 14.3164 0.471487
\(923\) 39.8238 1.31082
\(924\) −27.8397 −0.915858
\(925\) −41.8943 −1.37748
\(926\) −42.6472 −1.40147
\(927\) 114.903 3.77393
\(928\) 7.95586 0.261164
\(929\) 59.2756 1.94477 0.972384 0.233387i \(-0.0749808\pi\)
0.972384 + 0.233387i \(0.0749808\pi\)
\(930\) 44.2372 1.45059
\(931\) −0.00476066 −0.000156024 0
\(932\) 6.64772 0.217753
\(933\) 102.260 3.34785
\(934\) 23.4726 0.768048
\(935\) 2.49586 0.0816233
\(936\) −27.6310 −0.903148
\(937\) 8.10621 0.264818 0.132409 0.991195i \(-0.457729\pi\)
0.132409 + 0.991195i \(0.457729\pi\)
\(938\) 26.2541 0.857226
\(939\) 19.3320 0.630877
\(940\) 18.5539 0.605161
\(941\) 31.3013 1.02039 0.510196 0.860058i \(-0.329573\pi\)
0.510196 + 0.860058i \(0.329573\pi\)
\(942\) −37.5614 −1.22382
\(943\) −1.60462 −0.0522535
\(944\) −5.43268 −0.176819
\(945\) −98.7562 −3.21254
\(946\) −38.2025 −1.24207
\(947\) −6.28155 −0.204123 −0.102061 0.994778i \(-0.532544\pi\)
−0.102061 + 0.994778i \(0.532544\pi\)
\(948\) 11.3010 0.367040
\(949\) −3.69230 −0.119857
\(950\) −0.116726 −0.00378710
\(951\) −6.81786 −0.221084
\(952\) −0.623466 −0.0202066
\(953\) 26.2252 0.849517 0.424758 0.905307i \(-0.360359\pi\)
0.424758 + 0.905307i \(0.360359\pi\)
\(954\) −31.3096 −1.01368
\(955\) 42.0769 1.36158
\(956\) 10.3920 0.336103
\(957\) 84.8367 2.74238
\(958\) −9.85431 −0.318378
\(959\) 49.0445 1.58373
\(960\) −9.70203 −0.313132
\(961\) −10.2103 −0.329363
\(962\) 37.2120 1.19976
\(963\) 90.4575 2.91495
\(964\) −0.616335 −0.0198508
\(965\) 74.0366 2.38332
\(966\) 19.7403 0.635134
\(967\) 16.1174 0.518300 0.259150 0.965837i \(-0.416558\pi\)
0.259150 + 0.965837i \(0.416558\pi\)
\(968\) −0.487066 −0.0156549
\(969\) −0.0194496 −0.000624811 0
\(970\) −20.2673 −0.650745
\(971\) −37.4079 −1.20048 −0.600238 0.799822i \(-0.704927\pi\)
−0.600238 + 0.799822i \(0.704927\pi\)
\(972\) −19.5094 −0.625764
\(973\) −11.7106 −0.375425
\(974\) 11.1216 0.356359
\(975\) −56.8208 −1.81972
\(976\) 5.12334 0.163994
\(977\) −16.3221 −0.522189 −0.261094 0.965313i \(-0.584083\pi\)
−0.261094 + 0.965313i \(0.584083\pi\)
\(978\) 10.4912 0.335470
\(979\) 18.3708 0.587133
\(980\) −0.567106 −0.0181155
\(981\) −51.5140 −1.64472
\(982\) 13.1409 0.419344
\(983\) 32.1458 1.02529 0.512646 0.858600i \(-0.328666\pi\)
0.512646 + 0.858600i \(0.328666\pi\)
\(984\) −2.10072 −0.0669686
\(985\) 7.56489 0.241037
\(986\) 1.89991 0.0605053
\(987\) −49.4224 −1.57313
\(988\) 0.103680 0.00329850
\(989\) 27.0883 0.861357
\(990\) −72.1025 −2.29157
\(991\) 18.1019 0.575025 0.287512 0.957777i \(-0.407172\pi\)
0.287512 + 0.957777i \(0.407172\pi\)
\(992\) −4.55958 −0.144767
\(993\) −30.9046 −0.980728
\(994\) −25.9591 −0.823371
\(995\) 27.8614 0.883266
\(996\) 7.42494 0.235268
\(997\) −44.8502 −1.42042 −0.710210 0.703990i \(-0.751400\pi\)
−0.710210 + 0.703990i \(0.751400\pi\)
\(998\) 35.3049 1.11756
\(999\) 113.969 3.60582
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 \(a_p\))