Properties

Label 8015.2.a.l.1.54
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 1.54
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.34450 q^{2} +3.18379 q^{3} +3.49666 q^{4} -1.00000 q^{5} +7.46437 q^{6} -1.00000 q^{7} +3.50891 q^{8} +7.13649 q^{9} +O(q^{10})\) \(q+2.34450 q^{2} +3.18379 q^{3} +3.49666 q^{4} -1.00000 q^{5} +7.46437 q^{6} -1.00000 q^{7} +3.50891 q^{8} +7.13649 q^{9} -2.34450 q^{10} +4.62370 q^{11} +11.1326 q^{12} -6.35540 q^{13} -2.34450 q^{14} -3.18379 q^{15} +1.23330 q^{16} +7.67508 q^{17} +16.7315 q^{18} +1.74190 q^{19} -3.49666 q^{20} -3.18379 q^{21} +10.8402 q^{22} -2.85788 q^{23} +11.1716 q^{24} +1.00000 q^{25} -14.9002 q^{26} +13.1697 q^{27} -3.49666 q^{28} -0.436806 q^{29} -7.46437 q^{30} +6.66860 q^{31} -4.12635 q^{32} +14.7209 q^{33} +17.9942 q^{34} +1.00000 q^{35} +24.9539 q^{36} +7.63350 q^{37} +4.08386 q^{38} -20.2342 q^{39} -3.50891 q^{40} -6.26035 q^{41} -7.46437 q^{42} +3.17481 q^{43} +16.1675 q^{44} -7.13649 q^{45} -6.70028 q^{46} +2.91581 q^{47} +3.92655 q^{48} +1.00000 q^{49} +2.34450 q^{50} +24.4358 q^{51} -22.2227 q^{52} -5.81869 q^{53} +30.8763 q^{54} -4.62370 q^{55} -3.50891 q^{56} +5.54582 q^{57} -1.02409 q^{58} -12.2957 q^{59} -11.1326 q^{60} +6.19431 q^{61} +15.6345 q^{62} -7.13649 q^{63} -12.1408 q^{64} +6.35540 q^{65} +34.5130 q^{66} +5.00419 q^{67} +26.8371 q^{68} -9.09887 q^{69} +2.34450 q^{70} -9.58599 q^{71} +25.0413 q^{72} +11.9167 q^{73} +17.8967 q^{74} +3.18379 q^{75} +6.09081 q^{76} -4.62370 q^{77} -47.4391 q^{78} -14.5034 q^{79} -1.23330 q^{80} +20.5200 q^{81} -14.6774 q^{82} -11.8857 q^{83} -11.1326 q^{84} -7.67508 q^{85} +7.44332 q^{86} -1.39070 q^{87} +16.2241 q^{88} -2.15278 q^{89} -16.7315 q^{90} +6.35540 q^{91} -9.99302 q^{92} +21.2314 q^{93} +6.83611 q^{94} -1.74190 q^{95} -13.1374 q^{96} -3.13335 q^{97} +2.34450 q^{98} +32.9970 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34450 1.65781 0.828904 0.559391i \(-0.188965\pi\)
0.828904 + 0.559391i \(0.188965\pi\)
\(3\) 3.18379 1.83816 0.919080 0.394072i \(-0.128934\pi\)
0.919080 + 0.394072i \(0.128934\pi\)
\(4\) 3.49666 1.74833
\(5\) −1.00000 −0.447214
\(6\) 7.46437 3.04732
\(7\) −1.00000 −0.377964
\(8\) 3.50891 1.24059
\(9\) 7.13649 2.37883
\(10\) −2.34450 −0.741394
\(11\) 4.62370 1.39410 0.697049 0.717024i \(-0.254496\pi\)
0.697049 + 0.717024i \(0.254496\pi\)
\(12\) 11.1326 3.21371
\(13\) −6.35540 −1.76267 −0.881336 0.472490i \(-0.843355\pi\)
−0.881336 + 0.472490i \(0.843355\pi\)
\(14\) −2.34450 −0.626593
\(15\) −3.18379 −0.822050
\(16\) 1.23330 0.308324
\(17\) 7.67508 1.86148 0.930741 0.365680i \(-0.119164\pi\)
0.930741 + 0.365680i \(0.119164\pi\)
\(18\) 16.7315 3.94364
\(19\) 1.74190 0.399618 0.199809 0.979835i \(-0.435968\pi\)
0.199809 + 0.979835i \(0.435968\pi\)
\(20\) −3.49666 −0.781876
\(21\) −3.18379 −0.694759
\(22\) 10.8402 2.31115
\(23\) −2.85788 −0.595909 −0.297954 0.954580i \(-0.596304\pi\)
−0.297954 + 0.954580i \(0.596304\pi\)
\(24\) 11.1716 2.28039
\(25\) 1.00000 0.200000
\(26\) −14.9002 −2.92217
\(27\) 13.1697 2.53451
\(28\) −3.49666 −0.660806
\(29\) −0.436806 −0.0811128 −0.0405564 0.999177i \(-0.512913\pi\)
−0.0405564 + 0.999177i \(0.512913\pi\)
\(30\) −7.46437 −1.36280
\(31\) 6.66860 1.19772 0.598858 0.800855i \(-0.295621\pi\)
0.598858 + 0.800855i \(0.295621\pi\)
\(32\) −4.12635 −0.729443
\(33\) 14.7209 2.56257
\(34\) 17.9942 3.08598
\(35\) 1.00000 0.169031
\(36\) 24.9539 4.15898
\(37\) 7.63350 1.25494 0.627470 0.778641i \(-0.284091\pi\)
0.627470 + 0.778641i \(0.284091\pi\)
\(38\) 4.08386 0.662490
\(39\) −20.2342 −3.24007
\(40\) −3.50891 −0.554807
\(41\) −6.26035 −0.977702 −0.488851 0.872367i \(-0.662584\pi\)
−0.488851 + 0.872367i \(0.662584\pi\)
\(42\) −7.46437 −1.15178
\(43\) 3.17481 0.484154 0.242077 0.970257i \(-0.422171\pi\)
0.242077 + 0.970257i \(0.422171\pi\)
\(44\) 16.1675 2.43734
\(45\) −7.13649 −1.06384
\(46\) −6.70028 −0.987902
\(47\) 2.91581 0.425315 0.212658 0.977127i \(-0.431788\pi\)
0.212658 + 0.977127i \(0.431788\pi\)
\(48\) 3.92655 0.566749
\(49\) 1.00000 0.142857
\(50\) 2.34450 0.331562
\(51\) 24.4358 3.42170
\(52\) −22.2227 −3.08173
\(53\) −5.81869 −0.799259 −0.399629 0.916677i \(-0.630861\pi\)
−0.399629 + 0.916677i \(0.630861\pi\)
\(54\) 30.8763 4.20173
\(55\) −4.62370 −0.623460
\(56\) −3.50891 −0.468897
\(57\) 5.54582 0.734562
\(58\) −1.02409 −0.134469
\(59\) −12.2957 −1.60077 −0.800383 0.599489i \(-0.795370\pi\)
−0.800383 + 0.599489i \(0.795370\pi\)
\(60\) −11.1326 −1.43721
\(61\) 6.19431 0.793100 0.396550 0.918013i \(-0.370207\pi\)
0.396550 + 0.918013i \(0.370207\pi\)
\(62\) 15.6345 1.98558
\(63\) −7.13649 −0.899113
\(64\) −12.1408 −1.51760
\(65\) 6.35540 0.788291
\(66\) 34.5130 4.24826
\(67\) 5.00419 0.611359 0.305680 0.952134i \(-0.401116\pi\)
0.305680 + 0.952134i \(0.401116\pi\)
\(68\) 26.8371 3.25448
\(69\) −9.09887 −1.09538
\(70\) 2.34450 0.280221
\(71\) −9.58599 −1.13765 −0.568824 0.822459i \(-0.692601\pi\)
−0.568824 + 0.822459i \(0.692601\pi\)
\(72\) 25.0413 2.95114
\(73\) 11.9167 1.39474 0.697371 0.716711i \(-0.254353\pi\)
0.697371 + 0.716711i \(0.254353\pi\)
\(74\) 17.8967 2.08045
\(75\) 3.18379 0.367632
\(76\) 6.09081 0.698664
\(77\) −4.62370 −0.526920
\(78\) −47.4391 −5.37142
\(79\) −14.5034 −1.63176 −0.815878 0.578224i \(-0.803746\pi\)
−0.815878 + 0.578224i \(0.803746\pi\)
\(80\) −1.23330 −0.137887
\(81\) 20.5200 2.28000
\(82\) −14.6774 −1.62084
\(83\) −11.8857 −1.30462 −0.652311 0.757952i \(-0.726200\pi\)
−0.652311 + 0.757952i \(0.726200\pi\)
\(84\) −11.1326 −1.21467
\(85\) −7.67508 −0.832480
\(86\) 7.44332 0.802634
\(87\) −1.39070 −0.149098
\(88\) 16.2241 1.72950
\(89\) −2.15278 −0.228194 −0.114097 0.993470i \(-0.536398\pi\)
−0.114097 + 0.993470i \(0.536398\pi\)
\(90\) −16.7315 −1.76365
\(91\) 6.35540 0.666227
\(92\) −9.99302 −1.04184
\(93\) 21.2314 2.20159
\(94\) 6.83611 0.705091
\(95\) −1.74190 −0.178715
\(96\) −13.1374 −1.34083
\(97\) −3.13335 −0.318144 −0.159072 0.987267i \(-0.550850\pi\)
−0.159072 + 0.987267i \(0.550850\pi\)
\(98\) 2.34450 0.236830
\(99\) 32.9970 3.31632
\(100\) 3.49666 0.349666
\(101\) 0.851516 0.0847290 0.0423645 0.999102i \(-0.486511\pi\)
0.0423645 + 0.999102i \(0.486511\pi\)
\(102\) 57.2896 5.67252
\(103\) 13.5334 1.33349 0.666745 0.745286i \(-0.267687\pi\)
0.666745 + 0.745286i \(0.267687\pi\)
\(104\) −22.3005 −2.18674
\(105\) 3.18379 0.310706
\(106\) −13.6419 −1.32502
\(107\) −15.0392 −1.45389 −0.726947 0.686694i \(-0.759061\pi\)
−0.726947 + 0.686694i \(0.759061\pi\)
\(108\) 46.0499 4.43115
\(109\) −3.11964 −0.298808 −0.149404 0.988776i \(-0.547735\pi\)
−0.149404 + 0.988776i \(0.547735\pi\)
\(110\) −10.8402 −1.03358
\(111\) 24.3034 2.30678
\(112\) −1.23330 −0.116536
\(113\) 8.89667 0.836928 0.418464 0.908233i \(-0.362569\pi\)
0.418464 + 0.908233i \(0.362569\pi\)
\(114\) 13.0021 1.21776
\(115\) 2.85788 0.266498
\(116\) −1.52736 −0.141812
\(117\) −45.3553 −4.19310
\(118\) −28.8272 −2.65376
\(119\) −7.67508 −0.703574
\(120\) −11.1716 −1.01982
\(121\) 10.3786 0.943509
\(122\) 14.5225 1.31481
\(123\) −19.9316 −1.79717
\(124\) 23.3178 2.09400
\(125\) −1.00000 −0.0894427
\(126\) −16.7315 −1.49056
\(127\) −9.71689 −0.862234 −0.431117 0.902296i \(-0.641880\pi\)
−0.431117 + 0.902296i \(0.641880\pi\)
\(128\) −20.2114 −1.78645
\(129\) 10.1079 0.889952
\(130\) 14.9002 1.30684
\(131\) 21.9981 1.92199 0.960994 0.276571i \(-0.0891981\pi\)
0.960994 + 0.276571i \(0.0891981\pi\)
\(132\) 51.4738 4.48022
\(133\) −1.74190 −0.151041
\(134\) 11.7323 1.01352
\(135\) −13.1697 −1.13347
\(136\) 26.9311 2.30933
\(137\) 16.4551 1.40586 0.702929 0.711260i \(-0.251875\pi\)
0.702929 + 0.711260i \(0.251875\pi\)
\(138\) −21.3323 −1.81592
\(139\) −8.30480 −0.704404 −0.352202 0.935924i \(-0.614567\pi\)
−0.352202 + 0.935924i \(0.614567\pi\)
\(140\) 3.49666 0.295521
\(141\) 9.28332 0.781797
\(142\) −22.4743 −1.88600
\(143\) −29.3855 −2.45734
\(144\) 8.80141 0.733450
\(145\) 0.436806 0.0362748
\(146\) 27.9386 2.31221
\(147\) 3.18379 0.262594
\(148\) 26.6917 2.19405
\(149\) 2.02340 0.165763 0.0828816 0.996559i \(-0.473588\pi\)
0.0828816 + 0.996559i \(0.473588\pi\)
\(150\) 7.46437 0.609463
\(151\) −1.07016 −0.0870883 −0.0435441 0.999052i \(-0.513865\pi\)
−0.0435441 + 0.999052i \(0.513865\pi\)
\(152\) 6.11214 0.495760
\(153\) 54.7731 4.42815
\(154\) −10.8402 −0.873532
\(155\) −6.66860 −0.535635
\(156\) −70.7522 −5.66471
\(157\) −15.0419 −1.20047 −0.600237 0.799822i \(-0.704927\pi\)
−0.600237 + 0.799822i \(0.704927\pi\)
\(158\) −34.0031 −2.70514
\(159\) −18.5255 −1.46916
\(160\) 4.12635 0.326217
\(161\) 2.85788 0.225232
\(162\) 48.1090 3.77980
\(163\) −17.8488 −1.39803 −0.699014 0.715107i \(-0.746378\pi\)
−0.699014 + 0.715107i \(0.746378\pi\)
\(164\) −21.8903 −1.70935
\(165\) −14.7209 −1.14602
\(166\) −27.8659 −2.16281
\(167\) 13.5074 1.04523 0.522616 0.852568i \(-0.324956\pi\)
0.522616 + 0.852568i \(0.324956\pi\)
\(168\) −11.1716 −0.861908
\(169\) 27.3912 2.10701
\(170\) −17.9942 −1.38009
\(171\) 12.4310 0.950623
\(172\) 11.1012 0.846460
\(173\) 4.93056 0.374864 0.187432 0.982278i \(-0.439984\pi\)
0.187432 + 0.982278i \(0.439984\pi\)
\(174\) −3.26048 −0.247176
\(175\) −1.00000 −0.0755929
\(176\) 5.70239 0.429834
\(177\) −39.1469 −2.94246
\(178\) −5.04719 −0.378303
\(179\) −3.36333 −0.251387 −0.125694 0.992069i \(-0.540116\pi\)
−0.125694 + 0.992069i \(0.540116\pi\)
\(180\) −24.9539 −1.85995
\(181\) 22.5617 1.67700 0.838500 0.544902i \(-0.183433\pi\)
0.838500 + 0.544902i \(0.183433\pi\)
\(182\) 14.9002 1.10448
\(183\) 19.7214 1.45784
\(184\) −10.0280 −0.739276
\(185\) −7.63350 −0.561226
\(186\) 49.7769 3.64982
\(187\) 35.4873 2.59509
\(188\) 10.1956 0.743591
\(189\) −13.1697 −0.957954
\(190\) −4.08386 −0.296275
\(191\) 4.12671 0.298598 0.149299 0.988792i \(-0.452298\pi\)
0.149299 + 0.988792i \(0.452298\pi\)
\(192\) −38.6537 −2.78959
\(193\) −18.8951 −1.36010 −0.680050 0.733165i \(-0.738042\pi\)
−0.680050 + 0.733165i \(0.738042\pi\)
\(194\) −7.34613 −0.527421
\(195\) 20.2342 1.44900
\(196\) 3.49666 0.249761
\(197\) −7.20048 −0.513013 −0.256506 0.966543i \(-0.582571\pi\)
−0.256506 + 0.966543i \(0.582571\pi\)
\(198\) 77.3613 5.49782
\(199\) 10.9880 0.778920 0.389460 0.921043i \(-0.372662\pi\)
0.389460 + 0.921043i \(0.372662\pi\)
\(200\) 3.50891 0.248117
\(201\) 15.9323 1.12378
\(202\) 1.99637 0.140464
\(203\) 0.436806 0.0306578
\(204\) 85.4437 5.98225
\(205\) 6.26035 0.437242
\(206\) 31.7291 2.21067
\(207\) −20.3952 −1.41756
\(208\) −7.83810 −0.543474
\(209\) 8.05400 0.557107
\(210\) 7.46437 0.515090
\(211\) −10.0405 −0.691215 −0.345607 0.938379i \(-0.612327\pi\)
−0.345607 + 0.938379i \(0.612327\pi\)
\(212\) −20.3460 −1.39737
\(213\) −30.5197 −2.09118
\(214\) −35.2593 −2.41028
\(215\) −3.17481 −0.216520
\(216\) 46.2112 3.14427
\(217\) −6.66860 −0.452694
\(218\) −7.31399 −0.495366
\(219\) 37.9401 2.56376
\(220\) −16.1675 −1.09001
\(221\) −48.7782 −3.28118
\(222\) 56.9793 3.82420
\(223\) −17.4845 −1.17085 −0.585425 0.810726i \(-0.699073\pi\)
−0.585425 + 0.810726i \(0.699073\pi\)
\(224\) 4.12635 0.275704
\(225\) 7.13649 0.475766
\(226\) 20.8582 1.38747
\(227\) 15.8550 1.05233 0.526166 0.850382i \(-0.323629\pi\)
0.526166 + 0.850382i \(0.323629\pi\)
\(228\) 19.3918 1.28426
\(229\) 1.00000 0.0660819
\(230\) 6.70028 0.441803
\(231\) −14.7209 −0.968562
\(232\) −1.53271 −0.100627
\(233\) −26.8236 −1.75727 −0.878636 0.477491i \(-0.841546\pi\)
−0.878636 + 0.477491i \(0.841546\pi\)
\(234\) −106.335 −6.95135
\(235\) −2.91581 −0.190207
\(236\) −42.9939 −2.79866
\(237\) −46.1756 −2.99943
\(238\) −17.9942 −1.16639
\(239\) −8.99690 −0.581961 −0.290980 0.956729i \(-0.593981\pi\)
−0.290980 + 0.956729i \(0.593981\pi\)
\(240\) −3.92655 −0.253458
\(241\) 9.69859 0.624741 0.312370 0.949960i \(-0.398877\pi\)
0.312370 + 0.949960i \(0.398877\pi\)
\(242\) 24.3326 1.56416
\(243\) 25.8222 1.65649
\(244\) 21.6594 1.38660
\(245\) −1.00000 −0.0638877
\(246\) −46.7296 −2.97937
\(247\) −11.0704 −0.704396
\(248\) 23.3995 1.48587
\(249\) −37.8414 −2.39810
\(250\) −2.34450 −0.148279
\(251\) −19.8552 −1.25325 −0.626624 0.779322i \(-0.715564\pi\)
−0.626624 + 0.779322i \(0.715564\pi\)
\(252\) −24.9539 −1.57194
\(253\) −13.2140 −0.830755
\(254\) −22.7812 −1.42942
\(255\) −24.4358 −1.53023
\(256\) −23.1038 −1.44399
\(257\) 2.34686 0.146393 0.0731965 0.997318i \(-0.476680\pi\)
0.0731965 + 0.997318i \(0.476680\pi\)
\(258\) 23.6979 1.47537
\(259\) −7.63350 −0.474323
\(260\) 22.2227 1.37819
\(261\) −3.11726 −0.192954
\(262\) 51.5745 3.18629
\(263\) 14.2690 0.879864 0.439932 0.898031i \(-0.355003\pi\)
0.439932 + 0.898031i \(0.355003\pi\)
\(264\) 51.6541 3.17909
\(265\) 5.81869 0.357439
\(266\) −4.08386 −0.250398
\(267\) −6.85399 −0.419458
\(268\) 17.4979 1.06886
\(269\) −3.29441 −0.200864 −0.100432 0.994944i \(-0.532022\pi\)
−0.100432 + 0.994944i \(0.532022\pi\)
\(270\) −30.8763 −1.87907
\(271\) −19.1249 −1.16175 −0.580877 0.813991i \(-0.697290\pi\)
−0.580877 + 0.813991i \(0.697290\pi\)
\(272\) 9.46565 0.573939
\(273\) 20.2342 1.22463
\(274\) 38.5790 2.33064
\(275\) 4.62370 0.278820
\(276\) −31.8156 −1.91508
\(277\) −31.8034 −1.91088 −0.955441 0.295181i \(-0.904620\pi\)
−0.955441 + 0.295181i \(0.904620\pi\)
\(278\) −19.4706 −1.16777
\(279\) 47.5904 2.84916
\(280\) 3.50891 0.209697
\(281\) 11.2034 0.668341 0.334170 0.942513i \(-0.391544\pi\)
0.334170 + 0.942513i \(0.391544\pi\)
\(282\) 21.7647 1.29607
\(283\) −19.2711 −1.14555 −0.572774 0.819713i \(-0.694133\pi\)
−0.572774 + 0.819713i \(0.694133\pi\)
\(284\) −33.5189 −1.98898
\(285\) −5.54582 −0.328506
\(286\) −68.8941 −4.07379
\(287\) 6.26035 0.369537
\(288\) −29.4477 −1.73522
\(289\) 41.9069 2.46511
\(290\) 1.02409 0.0601366
\(291\) −9.97592 −0.584799
\(292\) 41.6685 2.43847
\(293\) −9.47060 −0.553278 −0.276639 0.960974i \(-0.589221\pi\)
−0.276639 + 0.960974i \(0.589221\pi\)
\(294\) 7.46437 0.435331
\(295\) 12.2957 0.715884
\(296\) 26.7852 1.55686
\(297\) 60.8927 3.53335
\(298\) 4.74385 0.274804
\(299\) 18.1630 1.05039
\(300\) 11.1326 0.642741
\(301\) −3.17481 −0.182993
\(302\) −2.50898 −0.144376
\(303\) 2.71104 0.155745
\(304\) 2.14827 0.123212
\(305\) −6.19431 −0.354685
\(306\) 128.415 7.34102
\(307\) 1.81624 0.103658 0.0518292 0.998656i \(-0.483495\pi\)
0.0518292 + 0.998656i \(0.483495\pi\)
\(308\) −16.1675 −0.921228
\(309\) 43.0876 2.45117
\(310\) −15.6345 −0.887980
\(311\) −25.3930 −1.43991 −0.719953 0.694022i \(-0.755837\pi\)
−0.719953 + 0.694022i \(0.755837\pi\)
\(312\) −71.0000 −4.01958
\(313\) −7.02854 −0.397277 −0.198638 0.980073i \(-0.563652\pi\)
−0.198638 + 0.980073i \(0.563652\pi\)
\(314\) −35.2657 −1.99016
\(315\) 7.13649 0.402096
\(316\) −50.7133 −2.85285
\(317\) −12.9572 −0.727748 −0.363874 0.931448i \(-0.618546\pi\)
−0.363874 + 0.931448i \(0.618546\pi\)
\(318\) −43.4329 −2.43559
\(319\) −2.01966 −0.113079
\(320\) 12.1408 0.678692
\(321\) −47.8816 −2.67249
\(322\) 6.70028 0.373392
\(323\) 13.3692 0.743882
\(324\) 71.7514 3.98619
\(325\) −6.35540 −0.352534
\(326\) −41.8465 −2.31766
\(327\) −9.93228 −0.549256
\(328\) −21.9670 −1.21292
\(329\) −2.91581 −0.160754
\(330\) −34.5130 −1.89988
\(331\) −19.6652 −1.08090 −0.540450 0.841376i \(-0.681746\pi\)
−0.540450 + 0.841376i \(0.681746\pi\)
\(332\) −41.5601 −2.28091
\(333\) 54.4764 2.98529
\(334\) 31.6679 1.73279
\(335\) −5.00419 −0.273408
\(336\) −3.92655 −0.214211
\(337\) 20.7344 1.12947 0.564737 0.825271i \(-0.308978\pi\)
0.564737 + 0.825271i \(0.308978\pi\)
\(338\) 64.2184 3.49302
\(339\) 28.3251 1.53841
\(340\) −26.8371 −1.45545
\(341\) 30.8336 1.66973
\(342\) 29.1445 1.57595
\(343\) −1.00000 −0.0539949
\(344\) 11.1401 0.600634
\(345\) 9.09887 0.489867
\(346\) 11.5597 0.621452
\(347\) 4.30683 0.231203 0.115601 0.993296i \(-0.463121\pi\)
0.115601 + 0.993296i \(0.463121\pi\)
\(348\) −4.86279 −0.260673
\(349\) −3.77394 −0.202014 −0.101007 0.994886i \(-0.532207\pi\)
−0.101007 + 0.994886i \(0.532207\pi\)
\(350\) −2.34450 −0.125319
\(351\) −83.6987 −4.46751
\(352\) −19.0790 −1.01692
\(353\) 0.549800 0.0292629 0.0146315 0.999893i \(-0.495342\pi\)
0.0146315 + 0.999893i \(0.495342\pi\)
\(354\) −91.7798 −4.87804
\(355\) 9.58599 0.508771
\(356\) −7.52754 −0.398959
\(357\) −24.4358 −1.29328
\(358\) −7.88532 −0.416752
\(359\) −27.4370 −1.44807 −0.724033 0.689765i \(-0.757714\pi\)
−0.724033 + 0.689765i \(0.757714\pi\)
\(360\) −25.0413 −1.31979
\(361\) −15.9658 −0.840305
\(362\) 52.8959 2.78014
\(363\) 33.0432 1.73432
\(364\) 22.2227 1.16478
\(365\) −11.9167 −0.623747
\(366\) 46.2366 2.41683
\(367\) 19.8255 1.03488 0.517442 0.855718i \(-0.326884\pi\)
0.517442 + 0.855718i \(0.326884\pi\)
\(368\) −3.52461 −0.183733
\(369\) −44.6769 −2.32579
\(370\) −17.8967 −0.930405
\(371\) 5.81869 0.302091
\(372\) 74.2389 3.84911
\(373\) −5.02476 −0.260172 −0.130086 0.991503i \(-0.541525\pi\)
−0.130086 + 0.991503i \(0.541525\pi\)
\(374\) 83.1998 4.30216
\(375\) −3.18379 −0.164410
\(376\) 10.2313 0.527640
\(377\) 2.77608 0.142975
\(378\) −30.8763 −1.58810
\(379\) 10.1911 0.523484 0.261742 0.965138i \(-0.415703\pi\)
0.261742 + 0.965138i \(0.415703\pi\)
\(380\) −6.09081 −0.312452
\(381\) −30.9365 −1.58492
\(382\) 9.67504 0.495018
\(383\) 14.5669 0.744333 0.372167 0.928166i \(-0.378615\pi\)
0.372167 + 0.928166i \(0.378615\pi\)
\(384\) −64.3486 −3.28378
\(385\) 4.62370 0.235646
\(386\) −44.2995 −2.25479
\(387\) 22.6570 1.15172
\(388\) −10.9563 −0.556220
\(389\) −22.9517 −1.16370 −0.581849 0.813297i \(-0.697671\pi\)
−0.581849 + 0.813297i \(0.697671\pi\)
\(390\) 47.4391 2.40217
\(391\) −21.9344 −1.10927
\(392\) 3.50891 0.177226
\(393\) 70.0374 3.53292
\(394\) −16.8815 −0.850477
\(395\) 14.5034 0.729743
\(396\) 115.379 5.79802
\(397\) 10.5328 0.528626 0.264313 0.964437i \(-0.414855\pi\)
0.264313 + 0.964437i \(0.414855\pi\)
\(398\) 25.7614 1.29130
\(399\) −5.54582 −0.277638
\(400\) 1.23330 0.0616648
\(401\) −18.8976 −0.943699 −0.471850 0.881679i \(-0.656414\pi\)
−0.471850 + 0.881679i \(0.656414\pi\)
\(402\) 37.3531 1.86300
\(403\) −42.3816 −2.11118
\(404\) 2.97746 0.148134
\(405\) −20.5200 −1.01965
\(406\) 1.02409 0.0508247
\(407\) 35.2950 1.74951
\(408\) 85.7430 4.24491
\(409\) −32.4892 −1.60649 −0.803243 0.595651i \(-0.796894\pi\)
−0.803243 + 0.595651i \(0.796894\pi\)
\(410\) 14.6774 0.724863
\(411\) 52.3896 2.58419
\(412\) 47.3218 2.33138
\(413\) 12.2957 0.605033
\(414\) −47.8165 −2.35005
\(415\) 11.8857 0.583444
\(416\) 26.2246 1.28577
\(417\) −26.4407 −1.29481
\(418\) 18.8826 0.923576
\(419\) −34.3633 −1.67876 −0.839378 0.543549i \(-0.817080\pi\)
−0.839378 + 0.543549i \(0.817080\pi\)
\(420\) 11.1326 0.543215
\(421\) 27.3474 1.33283 0.666416 0.745580i \(-0.267828\pi\)
0.666416 + 0.745580i \(0.267828\pi\)
\(422\) −23.5398 −1.14590
\(423\) 20.8087 1.01175
\(424\) −20.4172 −0.991549
\(425\) 7.67508 0.372296
\(426\) −71.5533 −3.46677
\(427\) −6.19431 −0.299764
\(428\) −52.5869 −2.54188
\(429\) −93.5570 −4.51698
\(430\) −7.44332 −0.358949
\(431\) −30.5338 −1.47076 −0.735381 0.677653i \(-0.762997\pi\)
−0.735381 + 0.677653i \(0.762997\pi\)
\(432\) 16.2421 0.781450
\(433\) 24.8658 1.19497 0.597486 0.801879i \(-0.296166\pi\)
0.597486 + 0.801879i \(0.296166\pi\)
\(434\) −15.6345 −0.750480
\(435\) 1.39070 0.0666788
\(436\) −10.9083 −0.522414
\(437\) −4.97812 −0.238136
\(438\) 88.9504 4.25022
\(439\) 3.57471 0.170612 0.0853059 0.996355i \(-0.472813\pi\)
0.0853059 + 0.996355i \(0.472813\pi\)
\(440\) −16.2241 −0.773455
\(441\) 7.13649 0.339833
\(442\) −114.360 −5.43957
\(443\) −16.7373 −0.795212 −0.397606 0.917556i \(-0.630159\pi\)
−0.397606 + 0.917556i \(0.630159\pi\)
\(444\) 84.9808 4.03301
\(445\) 2.15278 0.102052
\(446\) −40.9924 −1.94105
\(447\) 6.44207 0.304699
\(448\) 12.1408 0.573599
\(449\) 38.2407 1.80469 0.902345 0.431014i \(-0.141844\pi\)
0.902345 + 0.431014i \(0.141844\pi\)
\(450\) 16.7315 0.788729
\(451\) −28.9460 −1.36301
\(452\) 31.1086 1.46323
\(453\) −3.40716 −0.160082
\(454\) 37.1719 1.74456
\(455\) −6.35540 −0.297946
\(456\) 19.4598 0.911287
\(457\) 4.23337 0.198029 0.0990144 0.995086i \(-0.468431\pi\)
0.0990144 + 0.995086i \(0.468431\pi\)
\(458\) 2.34450 0.109551
\(459\) 101.078 4.71794
\(460\) 9.99302 0.465927
\(461\) −3.07057 −0.143011 −0.0715054 0.997440i \(-0.522780\pi\)
−0.0715054 + 0.997440i \(0.522780\pi\)
\(462\) −34.5130 −1.60569
\(463\) 4.29879 0.199781 0.0998907 0.994998i \(-0.468151\pi\)
0.0998907 + 0.994998i \(0.468151\pi\)
\(464\) −0.538711 −0.0250090
\(465\) −21.2314 −0.984582
\(466\) −62.8878 −2.91322
\(467\) −25.9976 −1.20302 −0.601512 0.798863i \(-0.705435\pi\)
−0.601512 + 0.798863i \(0.705435\pi\)
\(468\) −158.592 −7.33091
\(469\) −5.00419 −0.231072
\(470\) −6.83611 −0.315326
\(471\) −47.8902 −2.20666
\(472\) −43.1445 −1.98589
\(473\) 14.6794 0.674958
\(474\) −108.258 −4.97247
\(475\) 1.74190 0.0799236
\(476\) −26.8371 −1.23008
\(477\) −41.5250 −1.90130
\(478\) −21.0932 −0.964780
\(479\) 32.0979 1.46659 0.733296 0.679909i \(-0.237981\pi\)
0.733296 + 0.679909i \(0.237981\pi\)
\(480\) 13.1374 0.599638
\(481\) −48.5140 −2.21205
\(482\) 22.7383 1.03570
\(483\) 9.09887 0.414013
\(484\) 36.2904 1.64956
\(485\) 3.13335 0.142278
\(486\) 60.5400 2.74615
\(487\) −16.7925 −0.760939 −0.380470 0.924793i \(-0.624238\pi\)
−0.380470 + 0.924793i \(0.624238\pi\)
\(488\) 21.7353 0.983909
\(489\) −56.8269 −2.56980
\(490\) −2.34450 −0.105913
\(491\) −2.17755 −0.0982715 −0.0491358 0.998792i \(-0.515647\pi\)
−0.0491358 + 0.998792i \(0.515647\pi\)
\(492\) −69.6940 −3.14205
\(493\) −3.35252 −0.150990
\(494\) −25.9546 −1.16775
\(495\) −32.9970 −1.48310
\(496\) 8.22436 0.369285
\(497\) 9.58599 0.429990
\(498\) −88.7190 −3.97559
\(499\) 1.49228 0.0668038 0.0334019 0.999442i \(-0.489366\pi\)
0.0334019 + 0.999442i \(0.489366\pi\)
\(500\) −3.49666 −0.156375
\(501\) 43.0045 1.92130
\(502\) −46.5504 −2.07765
\(503\) 7.02270 0.313127 0.156563 0.987668i \(-0.449958\pi\)
0.156563 + 0.987668i \(0.449958\pi\)
\(504\) −25.0413 −1.11543
\(505\) −0.851516 −0.0378920
\(506\) −30.9801 −1.37723
\(507\) 87.2075 3.87302
\(508\) −33.9766 −1.50747
\(509\) 35.6581 1.58052 0.790260 0.612772i \(-0.209946\pi\)
0.790260 + 0.612772i \(0.209946\pi\)
\(510\) −57.2896 −2.53683
\(511\) −11.9167 −0.527163
\(512\) −13.7441 −0.607407
\(513\) 22.9402 1.01284
\(514\) 5.50220 0.242692
\(515\) −13.5334 −0.596355
\(516\) 35.3439 1.55593
\(517\) 13.4818 0.592931
\(518\) −17.8967 −0.786336
\(519\) 15.6978 0.689059
\(520\) 22.3005 0.977942
\(521\) −13.5613 −0.594131 −0.297066 0.954857i \(-0.596008\pi\)
−0.297066 + 0.954857i \(0.596008\pi\)
\(522\) −7.30840 −0.319880
\(523\) −16.1682 −0.706988 −0.353494 0.935437i \(-0.615006\pi\)
−0.353494 + 0.935437i \(0.615006\pi\)
\(524\) 76.9200 3.36026
\(525\) −3.18379 −0.138952
\(526\) 33.4536 1.45865
\(527\) 51.1821 2.22953
\(528\) 18.1552 0.790103
\(529\) −14.8325 −0.644893
\(530\) 13.6419 0.592566
\(531\) −87.7482 −3.80795
\(532\) −6.09081 −0.264070
\(533\) 39.7871 1.72337
\(534\) −16.0692 −0.695380
\(535\) 15.0392 0.650201
\(536\) 17.5592 0.758443
\(537\) −10.7081 −0.462090
\(538\) −7.72372 −0.332993
\(539\) 4.62370 0.199157
\(540\) −46.0499 −1.98167
\(541\) 10.6742 0.458921 0.229461 0.973318i \(-0.426304\pi\)
0.229461 + 0.973318i \(0.426304\pi\)
\(542\) −44.8382 −1.92597
\(543\) 71.8317 3.08259
\(544\) −31.6701 −1.35784
\(545\) 3.11964 0.133631
\(546\) 47.4391 2.03020
\(547\) −18.7787 −0.802918 −0.401459 0.915877i \(-0.631497\pi\)
−0.401459 + 0.915877i \(0.631497\pi\)
\(548\) 57.5380 2.45790
\(549\) 44.2056 1.88665
\(550\) 10.8402 0.462229
\(551\) −0.760870 −0.0324142
\(552\) −31.9271 −1.35891
\(553\) 14.5034 0.616746
\(554\) −74.5630 −3.16788
\(555\) −24.3034 −1.03162
\(556\) −29.0390 −1.23153
\(557\) 35.3903 1.49954 0.749769 0.661700i \(-0.230165\pi\)
0.749769 + 0.661700i \(0.230165\pi\)
\(558\) 111.575 4.72336
\(559\) −20.1772 −0.853404
\(560\) 1.23330 0.0521163
\(561\) 112.984 4.77018
\(562\) 26.2664 1.10798
\(563\) 15.4970 0.653119 0.326560 0.945177i \(-0.394111\pi\)
0.326560 + 0.945177i \(0.394111\pi\)
\(564\) 32.4606 1.36684
\(565\) −8.89667 −0.374286
\(566\) −45.1810 −1.89910
\(567\) −20.5200 −0.861759
\(568\) −33.6363 −1.41135
\(569\) −10.5479 −0.442191 −0.221095 0.975252i \(-0.570963\pi\)
−0.221095 + 0.975252i \(0.570963\pi\)
\(570\) −13.0021 −0.544600
\(571\) 15.9870 0.669034 0.334517 0.942390i \(-0.391427\pi\)
0.334517 + 0.942390i \(0.391427\pi\)
\(572\) −102.751 −4.29623
\(573\) 13.1385 0.548871
\(574\) 14.6774 0.612621
\(575\) −2.85788 −0.119182
\(576\) −86.6427 −3.61011
\(577\) 8.13214 0.338546 0.169273 0.985569i \(-0.445858\pi\)
0.169273 + 0.985569i \(0.445858\pi\)
\(578\) 98.2505 4.08668
\(579\) −60.1580 −2.50008
\(580\) 1.52736 0.0634202
\(581\) 11.8857 0.493101
\(582\) −23.3885 −0.969484
\(583\) −26.9039 −1.11424
\(584\) 41.8145 1.73030
\(585\) 45.3553 1.87521
\(586\) −22.2038 −0.917229
\(587\) 44.4834 1.83603 0.918014 0.396548i \(-0.129792\pi\)
0.918014 + 0.396548i \(0.129792\pi\)
\(588\) 11.1326 0.459101
\(589\) 11.6160 0.478629
\(590\) 28.8272 1.18680
\(591\) −22.9248 −0.942999
\(592\) 9.41437 0.386928
\(593\) 31.8482 1.30785 0.653925 0.756559i \(-0.273121\pi\)
0.653925 + 0.756559i \(0.273121\pi\)
\(594\) 142.763 5.85762
\(595\) 7.67508 0.314648
\(596\) 7.07513 0.289809
\(597\) 34.9835 1.43178
\(598\) 42.5830 1.74135
\(599\) 25.9005 1.05827 0.529133 0.848539i \(-0.322517\pi\)
0.529133 + 0.848539i \(0.322517\pi\)
\(600\) 11.1716 0.456079
\(601\) −1.11544 −0.0454997 −0.0227499 0.999741i \(-0.507242\pi\)
−0.0227499 + 0.999741i \(0.507242\pi\)
\(602\) −7.44332 −0.303367
\(603\) 35.7123 1.45432
\(604\) −3.74198 −0.152259
\(605\) −10.3786 −0.421950
\(606\) 6.35603 0.258196
\(607\) 14.8404 0.602354 0.301177 0.953568i \(-0.402621\pi\)
0.301177 + 0.953568i \(0.402621\pi\)
\(608\) −7.18767 −0.291499
\(609\) 1.39070 0.0563538
\(610\) −14.5225 −0.588000
\(611\) −18.5312 −0.749691
\(612\) 191.523 7.74185
\(613\) −29.1535 −1.17750 −0.588750 0.808315i \(-0.700380\pi\)
−0.588750 + 0.808315i \(0.700380\pi\)
\(614\) 4.25817 0.171846
\(615\) 19.9316 0.803720
\(616\) −16.2241 −0.653689
\(617\) 7.88980 0.317631 0.158816 0.987308i \(-0.449232\pi\)
0.158816 + 0.987308i \(0.449232\pi\)
\(618\) 101.019 4.06356
\(619\) −17.0250 −0.684293 −0.342146 0.939647i \(-0.611154\pi\)
−0.342146 + 0.939647i \(0.611154\pi\)
\(620\) −23.3178 −0.936466
\(621\) −37.6374 −1.51034
\(622\) −59.5338 −2.38709
\(623\) 2.15278 0.0862494
\(624\) −24.9548 −0.998992
\(625\) 1.00000 0.0400000
\(626\) −16.4784 −0.658609
\(627\) 25.6422 1.02405
\(628\) −52.5964 −2.09882
\(629\) 58.5878 2.33605
\(630\) 16.7315 0.666597
\(631\) 48.1342 1.91619 0.958097 0.286444i \(-0.0924733\pi\)
0.958097 + 0.286444i \(0.0924733\pi\)
\(632\) −50.8909 −2.02433
\(633\) −31.9667 −1.27056
\(634\) −30.3781 −1.20647
\(635\) 9.71689 0.385603
\(636\) −64.7772 −2.56858
\(637\) −6.35540 −0.251810
\(638\) −4.73508 −0.187464
\(639\) −68.4103 −2.70627
\(640\) 20.2114 0.798924
\(641\) 30.8315 1.21777 0.608885 0.793259i \(-0.291617\pi\)
0.608885 + 0.793259i \(0.291617\pi\)
\(642\) −112.258 −4.43047
\(643\) −6.30659 −0.248708 −0.124354 0.992238i \(-0.539686\pi\)
−0.124354 + 0.992238i \(0.539686\pi\)
\(644\) 9.99302 0.393780
\(645\) −10.1079 −0.397998
\(646\) 31.3440 1.23321
\(647\) −12.0561 −0.473974 −0.236987 0.971513i \(-0.576160\pi\)
−0.236987 + 0.971513i \(0.576160\pi\)
\(648\) 72.0027 2.82853
\(649\) −56.8517 −2.23162
\(650\) −14.9002 −0.584434
\(651\) −21.2314 −0.832124
\(652\) −62.4113 −2.44421
\(653\) 14.3360 0.561012 0.280506 0.959852i \(-0.409498\pi\)
0.280506 + 0.959852i \(0.409498\pi\)
\(654\) −23.2862 −0.910562
\(655\) −21.9981 −0.859539
\(656\) −7.72087 −0.301449
\(657\) 85.0432 3.31785
\(658\) −6.83611 −0.266499
\(659\) 37.1853 1.44853 0.724267 0.689520i \(-0.242178\pi\)
0.724267 + 0.689520i \(0.242178\pi\)
\(660\) −51.4738 −2.00362
\(661\) −46.3963 −1.80461 −0.902303 0.431102i \(-0.858125\pi\)
−0.902303 + 0.431102i \(0.858125\pi\)
\(662\) −46.1051 −1.79192
\(663\) −155.299 −6.03133
\(664\) −41.7057 −1.61849
\(665\) 1.74190 0.0675478
\(666\) 127.720 4.94903
\(667\) 1.24834 0.0483358
\(668\) 47.2306 1.82741
\(669\) −55.6670 −2.15221
\(670\) −11.7323 −0.453258
\(671\) 28.6406 1.10566
\(672\) 13.1374 0.506787
\(673\) 17.1050 0.659349 0.329674 0.944095i \(-0.393061\pi\)
0.329674 + 0.944095i \(0.393061\pi\)
\(674\) 48.6116 1.87245
\(675\) 13.1697 0.506902
\(676\) 95.7775 3.68375
\(677\) 40.7373 1.56566 0.782832 0.622233i \(-0.213775\pi\)
0.782832 + 0.622233i \(0.213775\pi\)
\(678\) 66.4080 2.55038
\(679\) 3.13335 0.120247
\(680\) −26.9311 −1.03276
\(681\) 50.4789 1.93435
\(682\) 72.2892 2.76810
\(683\) 17.6571 0.675631 0.337815 0.941212i \(-0.390312\pi\)
0.337815 + 0.941212i \(0.390312\pi\)
\(684\) 43.4670 1.66200
\(685\) −16.4551 −0.628719
\(686\) −2.34450 −0.0895132
\(687\) 3.18379 0.121469
\(688\) 3.91548 0.149276
\(689\) 36.9801 1.40883
\(690\) 21.3323 0.812105
\(691\) 46.4122 1.76560 0.882802 0.469746i \(-0.155654\pi\)
0.882802 + 0.469746i \(0.155654\pi\)
\(692\) 17.2405 0.655385
\(693\) −32.9970 −1.25345
\(694\) 10.0973 0.383290
\(695\) 8.30480 0.315019
\(696\) −4.87982 −0.184969
\(697\) −48.0487 −1.81997
\(698\) −8.84799 −0.334901
\(699\) −85.4006 −3.23015
\(700\) −3.49666 −0.132161
\(701\) −34.4033 −1.29940 −0.649698 0.760192i \(-0.725105\pi\)
−0.649698 + 0.760192i \(0.725105\pi\)
\(702\) −196.231 −7.40627
\(703\) 13.2968 0.501497
\(704\) −56.1354 −2.11568
\(705\) −9.28332 −0.349630
\(706\) 1.28900 0.0485123
\(707\) −0.851516 −0.0320245
\(708\) −136.883 −5.14439
\(709\) 37.8527 1.42159 0.710794 0.703400i \(-0.248336\pi\)
0.710794 + 0.703400i \(0.248336\pi\)
\(710\) 22.4743 0.843445
\(711\) −103.503 −3.88167
\(712\) −7.55391 −0.283095
\(713\) −19.0580 −0.713729
\(714\) −57.2896 −2.14401
\(715\) 29.3855 1.09895
\(716\) −11.7604 −0.439508
\(717\) −28.6442 −1.06974
\(718\) −64.3258 −2.40062
\(719\) 15.0869 0.562646 0.281323 0.959613i \(-0.409227\pi\)
0.281323 + 0.959613i \(0.409227\pi\)
\(720\) −8.80141 −0.328009
\(721\) −13.5334 −0.504012
\(722\) −37.4317 −1.39307
\(723\) 30.8782 1.14837
\(724\) 78.8906 2.93195
\(725\) −0.436806 −0.0162226
\(726\) 77.4697 2.87517
\(727\) −13.6374 −0.505782 −0.252891 0.967495i \(-0.581381\pi\)
−0.252891 + 0.967495i \(0.581381\pi\)
\(728\) 22.3005 0.826512
\(729\) 20.6523 0.764901
\(730\) −27.9386 −1.03405
\(731\) 24.3669 0.901243
\(732\) 68.9588 2.54879
\(733\) −49.6747 −1.83478 −0.917388 0.397995i \(-0.869706\pi\)
−0.917388 + 0.397995i \(0.869706\pi\)
\(734\) 46.4808 1.71564
\(735\) −3.18379 −0.117436
\(736\) 11.7926 0.434681
\(737\) 23.1379 0.852295
\(738\) −104.745 −3.85571
\(739\) −0.419193 −0.0154203 −0.00771013 0.999970i \(-0.502454\pi\)
−0.00771013 + 0.999970i \(0.502454\pi\)
\(740\) −26.6917 −0.981208
\(741\) −35.2459 −1.29479
\(742\) 13.6419 0.500810
\(743\) −36.8714 −1.35268 −0.676341 0.736589i \(-0.736435\pi\)
−0.676341 + 0.736589i \(0.736435\pi\)
\(744\) 74.4989 2.73126
\(745\) −2.02340 −0.0741316
\(746\) −11.7805 −0.431316
\(747\) −84.8219 −3.10347
\(748\) 124.087 4.53706
\(749\) 15.0392 0.549520
\(750\) −7.46437 −0.272560
\(751\) 41.9205 1.52970 0.764850 0.644208i \(-0.222813\pi\)
0.764850 + 0.644208i \(0.222813\pi\)
\(752\) 3.59606 0.131135
\(753\) −63.2147 −2.30367
\(754\) 6.50850 0.237026
\(755\) 1.07016 0.0389471
\(756\) −46.0499 −1.67482
\(757\) −18.5801 −0.675305 −0.337652 0.941271i \(-0.609633\pi\)
−0.337652 + 0.941271i \(0.609633\pi\)
\(758\) 23.8931 0.867836
\(759\) −42.0704 −1.52706
\(760\) −6.11214 −0.221711
\(761\) 29.5000 1.06937 0.534687 0.845050i \(-0.320429\pi\)
0.534687 + 0.845050i \(0.320429\pi\)
\(762\) −72.5304 −2.62750
\(763\) 3.11964 0.112939
\(764\) 14.4297 0.522047
\(765\) −54.7731 −1.98033
\(766\) 34.1520 1.23396
\(767\) 78.1442 2.82162
\(768\) −73.5576 −2.65428
\(769\) −41.4193 −1.49362 −0.746809 0.665039i \(-0.768415\pi\)
−0.746809 + 0.665039i \(0.768415\pi\)
\(770\) 10.8402 0.390655
\(771\) 7.47190 0.269094
\(772\) −66.0698 −2.37790
\(773\) 11.3633 0.408710 0.204355 0.978897i \(-0.434490\pi\)
0.204355 + 0.978897i \(0.434490\pi\)
\(774\) 53.1192 1.90933
\(775\) 6.66860 0.239543
\(776\) −10.9946 −0.394684
\(777\) −24.3034 −0.871881
\(778\) −53.8102 −1.92919
\(779\) −10.9049 −0.390708
\(780\) 70.7522 2.53333
\(781\) −44.3227 −1.58599
\(782\) −51.4252 −1.83896
\(783\) −5.75260 −0.205581
\(784\) 1.23330 0.0440463
\(785\) 15.0419 0.536869
\(786\) 164.202 5.85690
\(787\) 38.5960 1.37580 0.687900 0.725806i \(-0.258533\pi\)
0.687900 + 0.725806i \(0.258533\pi\)
\(788\) −25.1776 −0.896915
\(789\) 45.4294 1.61733
\(790\) 34.0031 1.20977
\(791\) −8.89667 −0.316329
\(792\) 115.783 4.11418
\(793\) −39.3674 −1.39798
\(794\) 24.6941 0.876360
\(795\) 18.5255 0.657030
\(796\) 38.4213 1.36181
\(797\) −3.21061 −0.113726 −0.0568628 0.998382i \(-0.518110\pi\)
−0.0568628 + 0.998382i \(0.518110\pi\)
\(798\) −13.0021 −0.460271
\(799\) 22.3791 0.791716
\(800\) −4.12635 −0.145889
\(801\) −15.3633 −0.542835
\(802\) −44.3053 −1.56447
\(803\) 55.0991 1.94441
\(804\) 55.7097 1.96473
\(805\) −2.85788 −0.100727
\(806\) −99.3636 −3.49993
\(807\) −10.4887 −0.369219
\(808\) 2.98789 0.105114
\(809\) −39.8833 −1.40222 −0.701111 0.713052i \(-0.747312\pi\)
−0.701111 + 0.713052i \(0.747312\pi\)
\(810\) −48.1090 −1.69038
\(811\) 43.2414 1.51841 0.759206 0.650851i \(-0.225588\pi\)
0.759206 + 0.650851i \(0.225588\pi\)
\(812\) 1.52736 0.0535998
\(813\) −60.8895 −2.13549
\(814\) 82.7490 2.90035
\(815\) 17.8488 0.625218
\(816\) 30.1366 1.05499
\(817\) 5.53018 0.193477
\(818\) −76.1707 −2.66325
\(819\) 45.3553 1.58484
\(820\) 21.8903 0.764442
\(821\) 40.3195 1.40716 0.703579 0.710617i \(-0.251584\pi\)
0.703579 + 0.710617i \(0.251584\pi\)
\(822\) 122.827 4.28409
\(823\) 36.0043 1.25503 0.627516 0.778603i \(-0.284072\pi\)
0.627516 + 0.778603i \(0.284072\pi\)
\(824\) 47.4876 1.65431
\(825\) 14.7209 0.512515
\(826\) 28.8272 1.00303
\(827\) −11.2409 −0.390886 −0.195443 0.980715i \(-0.562614\pi\)
−0.195443 + 0.980715i \(0.562614\pi\)
\(828\) −71.3151 −2.47837
\(829\) −5.03907 −0.175014 −0.0875070 0.996164i \(-0.527890\pi\)
−0.0875070 + 0.996164i \(0.527890\pi\)
\(830\) 27.8659 0.967239
\(831\) −101.255 −3.51251
\(832\) 77.1597 2.67503
\(833\) 7.67508 0.265926
\(834\) −61.9901 −2.14654
\(835\) −13.5074 −0.467442
\(836\) 28.1621 0.974006
\(837\) 87.8234 3.03562
\(838\) −80.5645 −2.78305
\(839\) −1.12900 −0.0389774 −0.0194887 0.999810i \(-0.506204\pi\)
−0.0194887 + 0.999810i \(0.506204\pi\)
\(840\) 11.1716 0.385457
\(841\) −28.8092 −0.993421
\(842\) 64.1159 2.20958
\(843\) 35.6693 1.22852
\(844\) −35.1081 −1.20847
\(845\) −27.3912 −0.942284
\(846\) 48.7858 1.67729
\(847\) −10.3786 −0.356613
\(848\) −7.17617 −0.246431
\(849\) −61.3551 −2.10570
\(850\) 17.9942 0.617196
\(851\) −21.8156 −0.747830
\(852\) −106.717 −3.65606
\(853\) 6.83009 0.233858 0.116929 0.993140i \(-0.462695\pi\)
0.116929 + 0.993140i \(0.462695\pi\)
\(854\) −14.5225 −0.496951
\(855\) −12.4310 −0.425132
\(856\) −52.7711 −1.80368
\(857\) −22.3077 −0.762016 −0.381008 0.924572i \(-0.624423\pi\)
−0.381008 + 0.924572i \(0.624423\pi\)
\(858\) −219.344 −7.48828
\(859\) 31.5613 1.07686 0.538429 0.842671i \(-0.319018\pi\)
0.538429 + 0.842671i \(0.319018\pi\)
\(860\) −11.1012 −0.378548
\(861\) 19.9316 0.679267
\(862\) −71.5864 −2.43824
\(863\) −23.5247 −0.800791 −0.400396 0.916342i \(-0.631127\pi\)
−0.400396 + 0.916342i \(0.631127\pi\)
\(864\) −54.3428 −1.84878
\(865\) −4.93056 −0.167644
\(866\) 58.2976 1.98103
\(867\) 133.423 4.53127
\(868\) −23.3178 −0.791458
\(869\) −67.0592 −2.27483
\(870\) 3.26048 0.110541
\(871\) −31.8037 −1.07763
\(872\) −10.9465 −0.370696
\(873\) −22.3611 −0.756810
\(874\) −11.6712 −0.394784
\(875\) 1.00000 0.0338062
\(876\) 132.664 4.48229
\(877\) 25.5082 0.861352 0.430676 0.902507i \(-0.358275\pi\)
0.430676 + 0.902507i \(0.358275\pi\)
\(878\) 8.38090 0.282842
\(879\) −30.1524 −1.01701
\(880\) −5.70239 −0.192228
\(881\) −38.0860 −1.28315 −0.641575 0.767060i \(-0.721719\pi\)
−0.641575 + 0.767060i \(0.721719\pi\)
\(882\) 16.7315 0.563378
\(883\) −43.8969 −1.47725 −0.738624 0.674118i \(-0.764524\pi\)
−0.738624 + 0.674118i \(0.764524\pi\)
\(884\) −170.561 −5.73658
\(885\) 39.1469 1.31591
\(886\) −39.2405 −1.31831
\(887\) −45.5786 −1.53038 −0.765191 0.643804i \(-0.777355\pi\)
−0.765191 + 0.643804i \(0.777355\pi\)
\(888\) 85.2784 2.86176
\(889\) 9.71689 0.325894
\(890\) 5.04719 0.169182
\(891\) 94.8783 3.17854
\(892\) −61.1374 −2.04703
\(893\) 5.07904 0.169964
\(894\) 15.1034 0.505133
\(895\) 3.36333 0.112424
\(896\) 20.2114 0.675214
\(897\) 57.8270 1.93079
\(898\) 89.6552 2.99183
\(899\) −2.91288 −0.0971501
\(900\) 24.9539 0.831795
\(901\) −44.6589 −1.48780
\(902\) −67.8637 −2.25961
\(903\) −10.1079 −0.336370
\(904\) 31.2176 1.03828
\(905\) −22.5617 −0.749977
\(906\) −7.98806 −0.265385
\(907\) 9.33152 0.309848 0.154924 0.987926i \(-0.450487\pi\)
0.154924 + 0.987926i \(0.450487\pi\)
\(908\) 55.4394 1.83982
\(909\) 6.07683 0.201556
\(910\) −14.9002 −0.493937
\(911\) −10.3920 −0.344303 −0.172151 0.985071i \(-0.555072\pi\)
−0.172151 + 0.985071i \(0.555072\pi\)
\(912\) 6.83964 0.226483
\(913\) −54.9558 −1.81877
\(914\) 9.92512 0.328294
\(915\) −19.7214 −0.651968
\(916\) 3.49666 0.115533
\(917\) −21.9981 −0.726443
\(918\) 236.978 7.82144
\(919\) −16.5206 −0.544966 −0.272483 0.962161i \(-0.587845\pi\)
−0.272483 + 0.962161i \(0.587845\pi\)
\(920\) 10.0280 0.330614
\(921\) 5.78253 0.190541
\(922\) −7.19894 −0.237084
\(923\) 60.9228 2.00530
\(924\) −51.4738 −1.69336
\(925\) 7.63350 0.250988
\(926\) 10.0785 0.331199
\(927\) 96.5813 3.17215
\(928\) 1.80242 0.0591672
\(929\) −21.9429 −0.719923 −0.359961 0.932967i \(-0.617210\pi\)
−0.359961 + 0.932967i \(0.617210\pi\)
\(930\) −49.7769 −1.63225
\(931\) 1.74190 0.0570883
\(932\) −93.7930 −3.07229
\(933\) −80.8460 −2.64678
\(934\) −60.9512 −1.99438
\(935\) −35.4873 −1.16056
\(936\) −159.147 −5.20189
\(937\) −17.9933 −0.587816 −0.293908 0.955834i \(-0.594956\pi\)
−0.293908 + 0.955834i \(0.594956\pi\)
\(938\) −11.7323 −0.383073
\(939\) −22.3774 −0.730258
\(940\) −10.1956 −0.332544
\(941\) 2.69099 0.0877237 0.0438618 0.999038i \(-0.486034\pi\)
0.0438618 + 0.999038i \(0.486034\pi\)
\(942\) −112.278 −3.65823
\(943\) 17.8913 0.582621
\(944\) −15.1643 −0.493555
\(945\) 13.1697 0.428410
\(946\) 34.4157 1.11895
\(947\) −26.6755 −0.866839 −0.433419 0.901192i \(-0.642693\pi\)
−0.433419 + 0.901192i \(0.642693\pi\)
\(948\) −161.460 −5.24398
\(949\) −75.7353 −2.45847
\(950\) 4.08386 0.132498
\(951\) −41.2529 −1.33772
\(952\) −26.9311 −0.872843
\(953\) 10.0982 0.327113 0.163557 0.986534i \(-0.447703\pi\)
0.163557 + 0.986534i \(0.447703\pi\)
\(954\) −97.3552 −3.15199
\(955\) −4.12671 −0.133537
\(956\) −31.4591 −1.01746
\(957\) −6.43016 −0.207858
\(958\) 75.2535 2.43133
\(959\) −16.4551 −0.531364
\(960\) 38.6537 1.24754
\(961\) 13.4702 0.434524
\(962\) −113.741 −3.66715
\(963\) −107.327 −3.45856
\(964\) 33.9126 1.09225
\(965\) 18.8951 0.608256
\(966\) 21.3323 0.686354
\(967\) 13.3090 0.427990 0.213995 0.976835i \(-0.431352\pi\)
0.213995 + 0.976835i \(0.431352\pi\)
\(968\) 36.4175 1.17050
\(969\) 42.5646 1.36737
\(970\) 7.34613 0.235870
\(971\) −26.7962 −0.859931 −0.429965 0.902845i \(-0.641474\pi\)
−0.429965 + 0.902845i \(0.641474\pi\)
\(972\) 90.2914 2.89610
\(973\) 8.30480 0.266240
\(974\) −39.3698 −1.26149
\(975\) −20.2342 −0.648014
\(976\) 7.63942 0.244532
\(977\) 15.2817 0.488904 0.244452 0.969661i \(-0.421392\pi\)
0.244452 + 0.969661i \(0.421392\pi\)
\(978\) −133.230 −4.26024
\(979\) −9.95382 −0.318125
\(980\) −3.49666 −0.111697
\(981\) −22.2633 −0.710813
\(982\) −5.10526 −0.162915
\(983\) 2.31086 0.0737051 0.0368526 0.999321i \(-0.488267\pi\)
0.0368526 + 0.999321i \(0.488267\pi\)
\(984\) −69.9381 −2.22955
\(985\) 7.20048 0.229426
\(986\) −7.85997 −0.250312
\(987\) −9.28332 −0.295491
\(988\) −38.7096 −1.23151
\(989\) −9.07321 −0.288511
\(990\) −77.3613 −2.45870
\(991\) −27.1805 −0.863418 −0.431709 0.902013i \(-0.642089\pi\)
−0.431709 + 0.902013i \(0.642089\pi\)
\(992\) −27.5170 −0.873666
\(993\) −62.6099 −1.98687
\(994\) 22.4743 0.712842
\(995\) −10.9880 −0.348344
\(996\) −132.318 −4.19267
\(997\) 19.0305 0.602701 0.301351 0.953513i \(-0.402563\pi\)
0.301351 + 0.953513i \(0.402563\pi\)
\(998\) 3.49865 0.110748
\(999\) 100.531 3.18065
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 \(a_p\))