Properties

Label 5077.2.a.c.1.9
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

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Newspace parameters

Level: \( N \) = \( 5077 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 5077.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(40.5400491062\)
Analytic rank: \(0\)
Dimension: \(216\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +O(q^{10})\) \(q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +2.14439 q^{10} +1.79832 q^{11} +15.1985 q^{12} +2.40664 q^{13} +3.70951 q^{14} -2.62799 q^{15} +9.19252 q^{16} +4.37109 q^{17} -18.6358 q^{18} +4.55860 q^{19} -3.92978 q^{20} -4.54607 q^{21} -4.67815 q^{22} -7.24022 q^{23} -22.9504 q^{24} -4.32050 q^{25} -6.26064 q^{26} +13.2744 q^{27} -6.79800 q^{28} +0.631518 q^{29} +6.83645 q^{30} -1.35338 q^{31} -9.51575 q^{32} +5.73316 q^{33} -11.3710 q^{34} +1.17545 q^{35} +34.1518 q^{36} -6.27091 q^{37} -11.8588 q^{38} +7.67253 q^{39} +5.93416 q^{40} +8.27333 q^{41} +11.8262 q^{42} -12.0497 q^{43} +8.57312 q^{44} -5.90524 q^{45} +18.8347 q^{46} +9.30783 q^{47} +29.3064 q^{48} -4.96662 q^{49} +11.2394 q^{50} +13.9353 q^{51} +11.4732 q^{52} +13.0340 q^{53} -34.5320 q^{54} -1.48239 q^{55} +10.2653 q^{56} +14.5331 q^{57} -1.64283 q^{58} +11.9736 q^{59} -12.5284 q^{60} +12.8650 q^{61} +3.52069 q^{62} -10.2153 q^{63} +6.36925 q^{64} -1.98384 q^{65} -14.9143 q^{66} +9.80128 q^{67} +20.8383 q^{68} -23.0823 q^{69} -3.05783 q^{70} -4.27134 q^{71} -51.5709 q^{72} +2.29431 q^{73} +16.3132 q^{74} -13.7740 q^{75} +21.7322 q^{76} -2.56434 q^{77} -19.9594 q^{78} -11.6342 q^{79} -7.57758 q^{80} +20.8283 q^{81} -21.5223 q^{82} +12.8850 q^{83} -21.6725 q^{84} -3.60317 q^{85} +31.3461 q^{86} +2.01332 q^{87} -12.9458 q^{88} -6.50306 q^{89} +15.3619 q^{90} -3.43179 q^{91} -34.5163 q^{92} -4.31467 q^{93} -24.2134 q^{94} -3.75775 q^{95} -30.3368 q^{96} +16.0867 q^{97} +12.9202 q^{98} +12.8827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60140 −1.83947 −0.919735 0.392540i \(-0.871596\pi\)
−0.919735 + 0.392540i \(0.871596\pi\)
\(3\) 3.18807 1.84063 0.920316 0.391177i \(-0.127932\pi\)
0.920316 + 0.391177i \(0.127932\pi\)
\(4\) 4.76730 2.38365
\(5\) −0.824320 −0.368647 −0.184324 0.982866i \(-0.559009\pi\)
−0.184324 + 0.982866i \(0.559009\pi\)
\(6\) −8.29345 −3.38578
\(7\) −1.42597 −0.538964 −0.269482 0.963005i \(-0.586853\pi\)
−0.269482 + 0.963005i \(0.586853\pi\)
\(8\) −7.19885 −2.54518
\(9\) 7.16377 2.38792
\(10\) 2.14439 0.678115
\(11\) 1.79832 0.542214 0.271107 0.962549i \(-0.412610\pi\)
0.271107 + 0.962549i \(0.412610\pi\)
\(12\) 15.1985 4.38742
\(13\) 2.40664 0.667482 0.333741 0.942665i \(-0.391689\pi\)
0.333741 + 0.942665i \(0.391689\pi\)
\(14\) 3.70951 0.991409
\(15\) −2.62799 −0.678543
\(16\) 9.19252 2.29813
\(17\) 4.37109 1.06014 0.530072 0.847953i \(-0.322165\pi\)
0.530072 + 0.847953i \(0.322165\pi\)
\(18\) −18.6358 −4.39251
\(19\) 4.55860 1.04582 0.522908 0.852389i \(-0.324847\pi\)
0.522908 + 0.852389i \(0.324847\pi\)
\(20\) −3.92978 −0.878725
\(21\) −4.54607 −0.992035
\(22\) −4.67815 −0.997385
\(23\) −7.24022 −1.50969 −0.754845 0.655904i \(-0.772288\pi\)
−0.754845 + 0.655904i \(0.772288\pi\)
\(24\) −22.9504 −4.68474
\(25\) −4.32050 −0.864099
\(26\) −6.26064 −1.22781
\(27\) 13.2744 2.55465
\(28\) −6.79800 −1.28470
\(29\) 0.631518 0.117270 0.0586350 0.998279i \(-0.481325\pi\)
0.0586350 + 0.998279i \(0.481325\pi\)
\(30\) 6.83645 1.24816
\(31\) −1.35338 −0.243074 −0.121537 0.992587i \(-0.538782\pi\)
−0.121537 + 0.992587i \(0.538782\pi\)
\(32\) −9.51575 −1.68216
\(33\) 5.73316 0.998015
\(34\) −11.3710 −1.95010
\(35\) 1.17545 0.198688
\(36\) 34.1518 5.69197
\(37\) −6.27091 −1.03093 −0.515466 0.856910i \(-0.672381\pi\)
−0.515466 + 0.856910i \(0.672381\pi\)
\(38\) −11.8588 −1.92375
\(39\) 7.67253 1.22859
\(40\) 5.93416 0.938273
\(41\) 8.27333 1.29208 0.646038 0.763305i \(-0.276425\pi\)
0.646038 + 0.763305i \(0.276425\pi\)
\(42\) 11.8262 1.82482
\(43\) −12.0497 −1.83756 −0.918781 0.394769i \(-0.870825\pi\)
−0.918781 + 0.394769i \(0.870825\pi\)
\(44\) 8.57312 1.29245
\(45\) −5.90524 −0.880301
\(46\) 18.8347 2.77703
\(47\) 9.30783 1.35769 0.678844 0.734283i \(-0.262481\pi\)
0.678844 + 0.734283i \(0.262481\pi\)
\(48\) 29.3064 4.23001
\(49\) −4.96662 −0.709517
\(50\) 11.2394 1.58948
\(51\) 13.9353 1.95133
\(52\) 11.4732 1.59104
\(53\) 13.0340 1.79036 0.895180 0.445705i \(-0.147047\pi\)
0.895180 + 0.445705i \(0.147047\pi\)
\(54\) −34.5320 −4.69921
\(55\) −1.48239 −0.199885
\(56\) 10.2653 1.37176
\(57\) 14.5331 1.92496
\(58\) −1.64283 −0.215715
\(59\) 11.9736 1.55883 0.779415 0.626507i \(-0.215516\pi\)
0.779415 + 0.626507i \(0.215516\pi\)
\(60\) −12.5284 −1.61741
\(61\) 12.8650 1.64719 0.823597 0.567175i \(-0.191964\pi\)
0.823597 + 0.567175i \(0.191964\pi\)
\(62\) 3.52069 0.447128
\(63\) −10.2153 −1.28701
\(64\) 6.36925 0.796157
\(65\) −1.98384 −0.246065
\(66\) −14.9143 −1.83582
\(67\) 9.80128 1.19742 0.598709 0.800967i \(-0.295681\pi\)
0.598709 + 0.800967i \(0.295681\pi\)
\(68\) 20.8383 2.52701
\(69\) −23.0823 −2.77878
\(70\) −3.05783 −0.365480
\(71\) −4.27134 −0.506914 −0.253457 0.967347i \(-0.581568\pi\)
−0.253457 + 0.967347i \(0.581568\pi\)
\(72\) −51.5709 −6.07769
\(73\) 2.29431 0.268528 0.134264 0.990946i \(-0.457133\pi\)
0.134264 + 0.990946i \(0.457133\pi\)
\(74\) 16.3132 1.89637
\(75\) −13.7740 −1.59049
\(76\) 21.7322 2.49286
\(77\) −2.56434 −0.292234
\(78\) −19.9594 −2.25995
\(79\) −11.6342 −1.30894 −0.654472 0.756086i \(-0.727109\pi\)
−0.654472 + 0.756086i \(0.727109\pi\)
\(80\) −7.57758 −0.847199
\(81\) 20.8283 2.31425
\(82\) −21.5223 −2.37674
\(83\) 12.8850 1.41431 0.707156 0.707057i \(-0.249978\pi\)
0.707156 + 0.707057i \(0.249978\pi\)
\(84\) −21.6725 −2.36466
\(85\) −3.60317 −0.390819
\(86\) 31.3461 3.38014
\(87\) 2.01332 0.215851
\(88\) −12.9458 −1.38003
\(89\) −6.50306 −0.689323 −0.344661 0.938727i \(-0.612006\pi\)
−0.344661 + 0.938727i \(0.612006\pi\)
\(90\) 15.3619 1.61929
\(91\) −3.43179 −0.359749
\(92\) −34.5163 −3.59857
\(93\) −4.31467 −0.447410
\(94\) −24.2134 −2.49742
\(95\) −3.75775 −0.385537
\(96\) −30.3368 −3.09624
\(97\) 16.0867 1.63336 0.816681 0.577090i \(-0.195812\pi\)
0.816681 + 0.577090i \(0.195812\pi\)
\(98\) 12.9202 1.30514
\(99\) 12.8827 1.29476
\(100\) −20.5971 −2.05971
\(101\) −12.2866 −1.22256 −0.611279 0.791415i \(-0.709345\pi\)
−0.611279 + 0.791415i \(0.709345\pi\)
\(102\) −36.2514 −3.58942
\(103\) 16.9779 1.67288 0.836441 0.548057i \(-0.184632\pi\)
0.836441 + 0.548057i \(0.184632\pi\)
\(104\) −17.3251 −1.69886
\(105\) 3.74742 0.365711
\(106\) −33.9067 −3.29331
\(107\) 1.93951 0.187499 0.0937496 0.995596i \(-0.470115\pi\)
0.0937496 + 0.995596i \(0.470115\pi\)
\(108\) 63.2829 6.08940
\(109\) −4.72629 −0.452697 −0.226348 0.974046i \(-0.572679\pi\)
−0.226348 + 0.974046i \(0.572679\pi\)
\(110\) 3.85629 0.367683
\(111\) −19.9921 −1.89756
\(112\) −13.1082 −1.23861
\(113\) 3.71323 0.349312 0.174656 0.984630i \(-0.444119\pi\)
0.174656 + 0.984630i \(0.444119\pi\)
\(114\) −37.8065 −3.54091
\(115\) 5.96825 0.556543
\(116\) 3.01063 0.279530
\(117\) 17.2406 1.59390
\(118\) −31.1482 −2.86742
\(119\) −6.23302 −0.571380
\(120\) 18.9185 1.72701
\(121\) −7.76605 −0.706005
\(122\) −33.4671 −3.02997
\(123\) 26.3759 2.37824
\(124\) −6.45197 −0.579404
\(125\) 7.68307 0.687195
\(126\) 26.5741 2.36741
\(127\) −12.1852 −1.08126 −0.540632 0.841259i \(-0.681815\pi\)
−0.540632 + 0.841259i \(0.681815\pi\)
\(128\) 2.46251 0.217657
\(129\) −38.4152 −3.38227
\(130\) 5.16077 0.452630
\(131\) −6.74280 −0.589121 −0.294561 0.955633i \(-0.595173\pi\)
−0.294561 + 0.955633i \(0.595173\pi\)
\(132\) 27.3317 2.37892
\(133\) −6.50041 −0.563657
\(134\) −25.4971 −2.20261
\(135\) −10.9423 −0.941766
\(136\) −31.4668 −2.69826
\(137\) 5.09238 0.435071 0.217536 0.976052i \(-0.430198\pi\)
0.217536 + 0.976052i \(0.430198\pi\)
\(138\) 60.0463 5.11148
\(139\) −15.2190 −1.29086 −0.645430 0.763819i \(-0.723322\pi\)
−0.645430 + 0.763819i \(0.723322\pi\)
\(140\) 5.60373 0.473602
\(141\) 29.6740 2.49900
\(142\) 11.1115 0.932453
\(143\) 4.32791 0.361918
\(144\) 65.8531 5.48776
\(145\) −0.520573 −0.0432312
\(146\) −5.96841 −0.493949
\(147\) −15.8339 −1.30596
\(148\) −29.8953 −2.45738
\(149\) 3.49502 0.286323 0.143161 0.989699i \(-0.454273\pi\)
0.143161 + 0.989699i \(0.454273\pi\)
\(150\) 35.8318 2.92565
\(151\) −15.1087 −1.22953 −0.614766 0.788710i \(-0.710750\pi\)
−0.614766 + 0.788710i \(0.710750\pi\)
\(152\) −32.8167 −2.66179
\(153\) 31.3134 2.53154
\(154\) 6.67088 0.537555
\(155\) 1.11562 0.0896087
\(156\) 36.5772 2.92852
\(157\) 14.2490 1.13720 0.568599 0.822615i \(-0.307486\pi\)
0.568599 + 0.822615i \(0.307486\pi\)
\(158\) 30.2651 2.40776
\(159\) 41.5533 3.29539
\(160\) 7.84402 0.620125
\(161\) 10.3243 0.813669
\(162\) −54.1827 −4.25700
\(163\) 15.6366 1.22475 0.612377 0.790566i \(-0.290213\pi\)
0.612377 + 0.790566i \(0.290213\pi\)
\(164\) 39.4414 3.07986
\(165\) −4.72596 −0.367915
\(166\) −33.5191 −2.60158
\(167\) 14.0828 1.08976 0.544880 0.838514i \(-0.316575\pi\)
0.544880 + 0.838514i \(0.316575\pi\)
\(168\) 32.7265 2.52491
\(169\) −7.20808 −0.554467
\(170\) 9.37330 0.718900
\(171\) 32.6568 2.49733
\(172\) −57.4445 −4.38010
\(173\) −20.3110 −1.54422 −0.772110 0.635489i \(-0.780799\pi\)
−0.772110 + 0.635489i \(0.780799\pi\)
\(174\) −5.23746 −0.397051
\(175\) 6.16088 0.465719
\(176\) 16.5311 1.24608
\(177\) 38.1727 2.86923
\(178\) 16.9171 1.26799
\(179\) 0.0792077 0.00592026 0.00296013 0.999996i \(-0.499058\pi\)
0.00296013 + 0.999996i \(0.499058\pi\)
\(180\) −28.1520 −2.09833
\(181\) −24.1900 −1.79803 −0.899013 0.437922i \(-0.855715\pi\)
−0.899013 + 0.437922i \(0.855715\pi\)
\(182\) 8.92747 0.661748
\(183\) 41.0145 3.03188
\(184\) 52.1212 3.84243
\(185\) 5.16924 0.380050
\(186\) 11.2242 0.822998
\(187\) 7.86060 0.574824
\(188\) 44.3732 3.23625
\(189\) −18.9288 −1.37687
\(190\) 9.77542 0.709183
\(191\) 11.6848 0.845483 0.422742 0.906250i \(-0.361068\pi\)
0.422742 + 0.906250i \(0.361068\pi\)
\(192\) 20.3056 1.46543
\(193\) 7.24176 0.521273 0.260637 0.965437i \(-0.416068\pi\)
0.260637 + 0.965437i \(0.416068\pi\)
\(194\) −41.8481 −3.00452
\(195\) −6.32462 −0.452916
\(196\) −23.6774 −1.69124
\(197\) 3.57292 0.254560 0.127280 0.991867i \(-0.459375\pi\)
0.127280 + 0.991867i \(0.459375\pi\)
\(198\) −33.5132 −2.38168
\(199\) 20.6847 1.46630 0.733149 0.680068i \(-0.238050\pi\)
0.733149 + 0.680068i \(0.238050\pi\)
\(200\) 31.1026 2.19929
\(201\) 31.2471 2.20400
\(202\) 31.9623 2.24886
\(203\) −0.900524 −0.0632044
\(204\) 66.4338 4.65129
\(205\) −6.81987 −0.476320
\(206\) −44.1663 −3.07722
\(207\) −51.8672 −3.60502
\(208\) 22.1231 1.53396
\(209\) 8.19782 0.567055
\(210\) −9.74855 −0.672714
\(211\) 20.9021 1.43896 0.719482 0.694511i \(-0.244379\pi\)
0.719482 + 0.694511i \(0.244379\pi\)
\(212\) 62.1370 4.26759
\(213\) −13.6173 −0.933042
\(214\) −5.04544 −0.344899
\(215\) 9.93280 0.677412
\(216\) −95.5603 −6.50205
\(217\) 1.92988 0.131008
\(218\) 12.2950 0.832722
\(219\) 7.31440 0.494261
\(220\) −7.06699 −0.476457
\(221\) 10.5196 0.707627
\(222\) 52.0074 3.49051
\(223\) −12.4520 −0.833846 −0.416923 0.908942i \(-0.636892\pi\)
−0.416923 + 0.908942i \(0.636892\pi\)
\(224\) 13.5691 0.906626
\(225\) −30.9510 −2.06340
\(226\) −9.65961 −0.642548
\(227\) −20.0231 −1.32898 −0.664492 0.747296i \(-0.731352\pi\)
−0.664492 + 0.747296i \(0.731352\pi\)
\(228\) 69.2837 4.58843
\(229\) −2.59238 −0.171309 −0.0856546 0.996325i \(-0.527298\pi\)
−0.0856546 + 0.996325i \(0.527298\pi\)
\(230\) −15.5258 −1.02374
\(231\) −8.17529 −0.537895
\(232\) −4.54621 −0.298473
\(233\) 9.58978 0.628247 0.314124 0.949382i \(-0.398289\pi\)
0.314124 + 0.949382i \(0.398289\pi\)
\(234\) −44.8498 −2.93192
\(235\) −7.67263 −0.500507
\(236\) 57.0817 3.71570
\(237\) −37.0905 −2.40928
\(238\) 16.2146 1.05104
\(239\) −22.0491 −1.42624 −0.713120 0.701042i \(-0.752719\pi\)
−0.713120 + 0.701042i \(0.752719\pi\)
\(240\) −24.1578 −1.55938
\(241\) −19.6537 −1.26601 −0.633003 0.774149i \(-0.718178\pi\)
−0.633003 + 0.774149i \(0.718178\pi\)
\(242\) 20.2026 1.29867
\(243\) 26.5788 1.70503
\(244\) 61.3313 3.92633
\(245\) 4.09409 0.261562
\(246\) −68.6144 −4.37469
\(247\) 10.9709 0.698063
\(248\) 9.74279 0.618668
\(249\) 41.0782 2.60323
\(250\) −19.9868 −1.26407
\(251\) −0.714104 −0.0450739 −0.0225369 0.999746i \(-0.507174\pi\)
−0.0225369 + 0.999746i \(0.507174\pi\)
\(252\) −48.6993 −3.06777
\(253\) −13.0202 −0.818574
\(254\) 31.6987 1.98895
\(255\) −11.4872 −0.719354
\(256\) −19.1445 −1.19653
\(257\) 8.40799 0.524476 0.262238 0.965003i \(-0.415539\pi\)
0.262238 + 0.965003i \(0.415539\pi\)
\(258\) 99.9335 6.22159
\(259\) 8.94210 0.555635
\(260\) −9.45757 −0.586533
\(261\) 4.52405 0.280032
\(262\) 17.5407 1.08367
\(263\) −13.8084 −0.851463 −0.425732 0.904849i \(-0.639983\pi\)
−0.425732 + 0.904849i \(0.639983\pi\)
\(264\) −41.2722 −2.54013
\(265\) −10.7442 −0.660011
\(266\) 16.9102 1.03683
\(267\) −20.7322 −1.26879
\(268\) 46.7256 2.85422
\(269\) 9.63031 0.587170 0.293585 0.955933i \(-0.405152\pi\)
0.293585 + 0.955933i \(0.405152\pi\)
\(270\) 28.4654 1.73235
\(271\) −25.0498 −1.52167 −0.760834 0.648947i \(-0.775210\pi\)
−0.760834 + 0.648947i \(0.775210\pi\)
\(272\) 40.1813 2.43635
\(273\) −10.9408 −0.662166
\(274\) −13.2473 −0.800300
\(275\) −7.76963 −0.468526
\(276\) −110.040 −6.62364
\(277\) 14.2425 0.855748 0.427874 0.903838i \(-0.359263\pi\)
0.427874 + 0.903838i \(0.359263\pi\)
\(278\) 39.5908 2.37450
\(279\) −9.69531 −0.580443
\(280\) −8.46191 −0.505696
\(281\) 21.9930 1.31199 0.655996 0.754765i \(-0.272249\pi\)
0.655996 + 0.754765i \(0.272249\pi\)
\(282\) −77.1940 −4.59684
\(283\) 20.7316 1.23237 0.616184 0.787602i \(-0.288678\pi\)
0.616184 + 0.787602i \(0.288678\pi\)
\(284\) −20.3627 −1.20831
\(285\) −11.9800 −0.709631
\(286\) −11.2586 −0.665737
\(287\) −11.7975 −0.696383
\(288\) −68.1686 −4.01688
\(289\) 2.10638 0.123905
\(290\) 1.35422 0.0795226
\(291\) 51.2856 3.00642
\(292\) 10.9376 0.640077
\(293\) 3.16247 0.184753 0.0923767 0.995724i \(-0.470554\pi\)
0.0923767 + 0.995724i \(0.470554\pi\)
\(294\) 41.1904 2.40227
\(295\) −9.87008 −0.574659
\(296\) 45.1434 2.62390
\(297\) 23.8716 1.38517
\(298\) −9.09195 −0.526682
\(299\) −17.4246 −1.00769
\(300\) −65.6649 −3.79116
\(301\) 17.1825 0.990380
\(302\) 39.3039 2.26169
\(303\) −39.1704 −2.25028
\(304\) 41.9051 2.40342
\(305\) −10.6049 −0.607234
\(306\) −81.4589 −4.65669
\(307\) 3.20797 0.183088 0.0915442 0.995801i \(-0.470820\pi\)
0.0915442 + 0.995801i \(0.470820\pi\)
\(308\) −12.2250 −0.696583
\(309\) 54.1267 3.07916
\(310\) −2.90217 −0.164832
\(311\) 14.7951 0.838952 0.419476 0.907766i \(-0.362214\pi\)
0.419476 + 0.907766i \(0.362214\pi\)
\(312\) −55.2334 −3.12698
\(313\) 18.2214 1.02993 0.514966 0.857210i \(-0.327804\pi\)
0.514966 + 0.857210i \(0.327804\pi\)
\(314\) −37.0675 −2.09184
\(315\) 8.42067 0.474451
\(316\) −55.4635 −3.12006
\(317\) 2.65399 0.149063 0.0745315 0.997219i \(-0.476254\pi\)
0.0745315 + 0.997219i \(0.476254\pi\)
\(318\) −108.097 −6.06177
\(319\) 1.13567 0.0635854
\(320\) −5.25030 −0.293501
\(321\) 6.18328 0.345117
\(322\) −26.8577 −1.49672
\(323\) 19.9260 1.10871
\(324\) 99.2946 5.51637
\(325\) −10.3979 −0.576771
\(326\) −40.6771 −2.25290
\(327\) −15.0677 −0.833248
\(328\) −59.5585 −3.28857
\(329\) −13.2727 −0.731745
\(330\) 12.2941 0.676769
\(331\) 21.5491 1.18444 0.592222 0.805775i \(-0.298251\pi\)
0.592222 + 0.805775i \(0.298251\pi\)
\(332\) 61.4266 3.37122
\(333\) −44.9233 −2.46178
\(334\) −36.6350 −2.00458
\(335\) −8.07940 −0.441425
\(336\) −41.7899 −2.27983
\(337\) −22.7359 −1.23850 −0.619252 0.785192i \(-0.712564\pi\)
−0.619252 + 0.785192i \(0.712564\pi\)
\(338\) 18.7511 1.01993
\(339\) 11.8380 0.642954
\(340\) −17.1774 −0.931575
\(341\) −2.43381 −0.131798
\(342\) −84.9534 −4.59376
\(343\) 17.0640 0.921369
\(344\) 86.7440 4.67692
\(345\) 19.0272 1.02439
\(346\) 52.8372 2.84055
\(347\) −28.7558 −1.54369 −0.771847 0.635809i \(-0.780667\pi\)
−0.771847 + 0.635809i \(0.780667\pi\)
\(348\) 9.59810 0.514512
\(349\) −7.60056 −0.406848 −0.203424 0.979091i \(-0.565207\pi\)
−0.203424 + 0.979091i \(0.565207\pi\)
\(350\) −16.0269 −0.856676
\(351\) 31.9467 1.70519
\(352\) −17.1124 −0.912091
\(353\) −31.0886 −1.65468 −0.827341 0.561700i \(-0.810147\pi\)
−0.827341 + 0.561700i \(0.810147\pi\)
\(354\) −99.3025 −5.27787
\(355\) 3.52095 0.186873
\(356\) −31.0020 −1.64310
\(357\) −19.8713 −1.05170
\(358\) −0.206051 −0.0108901
\(359\) 27.5887 1.45607 0.728037 0.685538i \(-0.240433\pi\)
0.728037 + 0.685538i \(0.240433\pi\)
\(360\) 42.5109 2.24052
\(361\) 1.78086 0.0937295
\(362\) 62.9278 3.30741
\(363\) −24.7587 −1.29949
\(364\) −16.3604 −0.857516
\(365\) −1.89124 −0.0989922
\(366\) −106.695 −5.57705
\(367\) 27.6723 1.44448 0.722241 0.691642i \(-0.243112\pi\)
0.722241 + 0.691642i \(0.243112\pi\)
\(368\) −66.5559 −3.46946
\(369\) 59.2682 3.08538
\(370\) −13.4473 −0.699090
\(371\) −18.5861 −0.964941
\(372\) −20.5693 −1.06647
\(373\) −8.14428 −0.421695 −0.210847 0.977519i \(-0.567622\pi\)
−0.210847 + 0.977519i \(0.567622\pi\)
\(374\) −20.4486 −1.05737
\(375\) 24.4941 1.26487
\(376\) −67.0057 −3.45556
\(377\) 1.51984 0.0782756
\(378\) 49.2414 2.53271
\(379\) −1.56581 −0.0804301 −0.0402150 0.999191i \(-0.512804\pi\)
−0.0402150 + 0.999191i \(0.512804\pi\)
\(380\) −17.9143 −0.918984
\(381\) −38.8473 −1.99021
\(382\) −30.3969 −1.55524
\(383\) 24.8717 1.27088 0.635442 0.772149i \(-0.280818\pi\)
0.635442 + 0.772149i \(0.280818\pi\)
\(384\) 7.85064 0.400626
\(385\) 2.11384 0.107731
\(386\) −18.8387 −0.958866
\(387\) −86.3212 −4.38795
\(388\) 76.6903 3.89336
\(389\) −27.2585 −1.38206 −0.691031 0.722825i \(-0.742843\pi\)
−0.691031 + 0.722825i \(0.742843\pi\)
\(390\) 16.4529 0.833125
\(391\) −31.6476 −1.60049
\(392\) 35.7540 1.80585
\(393\) −21.4965 −1.08435
\(394\) −9.29461 −0.468256
\(395\) 9.59027 0.482539
\(396\) 61.4158 3.08626
\(397\) 18.3168 0.919292 0.459646 0.888102i \(-0.347976\pi\)
0.459646 + 0.888102i \(0.347976\pi\)
\(398\) −53.8092 −2.69721
\(399\) −20.7237 −1.03749
\(400\) −39.7163 −1.98581
\(401\) 30.4433 1.52027 0.760133 0.649767i \(-0.225134\pi\)
0.760133 + 0.649767i \(0.225134\pi\)
\(402\) −81.2864 −4.05420
\(403\) −3.25710 −0.162248
\(404\) −58.5737 −2.91415
\(405\) −17.1692 −0.853143
\(406\) 2.34262 0.116262
\(407\) −11.2771 −0.558985
\(408\) −100.318 −4.96649
\(409\) −21.2894 −1.05269 −0.526346 0.850270i \(-0.676438\pi\)
−0.526346 + 0.850270i \(0.676438\pi\)
\(410\) 17.7412 0.876177
\(411\) 16.2348 0.800805
\(412\) 80.9387 3.98756
\(413\) −17.0740 −0.840155
\(414\) 134.928 6.63133
\(415\) −10.6214 −0.521382
\(416\) −22.9010 −1.12281
\(417\) −48.5192 −2.37600
\(418\) −21.3258 −1.04308
\(419\) 33.1648 1.62021 0.810104 0.586286i \(-0.199410\pi\)
0.810104 + 0.586286i \(0.199410\pi\)
\(420\) 17.8651 0.871726
\(421\) −1.26217 −0.0615143 −0.0307571 0.999527i \(-0.509792\pi\)
−0.0307571 + 0.999527i \(0.509792\pi\)
\(422\) −54.3749 −2.64693
\(423\) 66.6792 3.24205
\(424\) −93.8300 −4.55679
\(425\) −18.8853 −0.916070
\(426\) 35.4241 1.71630
\(427\) −18.3451 −0.887780
\(428\) 9.24620 0.446932
\(429\) 13.7977 0.666157
\(430\) −25.8392 −1.24608
\(431\) −1.06547 −0.0513221 −0.0256610 0.999671i \(-0.508169\pi\)
−0.0256610 + 0.999671i \(0.508169\pi\)
\(432\) 122.025 5.87093
\(433\) −0.603457 −0.0290003 −0.0145001 0.999895i \(-0.504616\pi\)
−0.0145001 + 0.999895i \(0.504616\pi\)
\(434\) −5.02038 −0.240986
\(435\) −1.65962 −0.0795728
\(436\) −22.5316 −1.07907
\(437\) −33.0053 −1.57886
\(438\) −19.0277 −0.909179
\(439\) 34.6997 1.65613 0.828064 0.560633i \(-0.189442\pi\)
0.828064 + 0.560633i \(0.189442\pi\)
\(440\) 10.6715 0.508744
\(441\) −35.5797 −1.69427
\(442\) −27.3658 −1.30166
\(443\) 28.8771 1.37199 0.685997 0.727605i \(-0.259366\pi\)
0.685997 + 0.727605i \(0.259366\pi\)
\(444\) −95.3082 −4.52312
\(445\) 5.36060 0.254117
\(446\) 32.3926 1.53383
\(447\) 11.1423 0.527015
\(448\) −9.08234 −0.429100
\(449\) −11.3623 −0.536219 −0.268110 0.963388i \(-0.586399\pi\)
−0.268110 + 0.963388i \(0.586399\pi\)
\(450\) 80.5161 3.79557
\(451\) 14.8781 0.700581
\(452\) 17.7021 0.832636
\(453\) −48.1677 −2.26312
\(454\) 52.0883 2.44462
\(455\) 2.82889 0.132621
\(456\) −104.622 −4.89937
\(457\) 1.63769 0.0766081 0.0383041 0.999266i \(-0.487804\pi\)
0.0383041 + 0.999266i \(0.487804\pi\)
\(458\) 6.74382 0.315118
\(459\) 58.0234 2.70830
\(460\) 28.4524 1.32660
\(461\) −2.42125 −0.112769 −0.0563844 0.998409i \(-0.517957\pi\)
−0.0563844 + 0.998409i \(0.517957\pi\)
\(462\) 21.2672 0.989441
\(463\) 19.9211 0.925812 0.462906 0.886407i \(-0.346807\pi\)
0.462906 + 0.886407i \(0.346807\pi\)
\(464\) 5.80525 0.269502
\(465\) 3.55667 0.164937
\(466\) −24.9469 −1.15564
\(467\) −15.1931 −0.703054 −0.351527 0.936178i \(-0.614337\pi\)
−0.351527 + 0.936178i \(0.614337\pi\)
\(468\) 82.1912 3.79929
\(469\) −13.9763 −0.645365
\(470\) 19.9596 0.920668
\(471\) 45.4269 2.09316
\(472\) −86.1962 −3.96750
\(473\) −21.6692 −0.996350
\(474\) 96.4872 4.43180
\(475\) −19.6954 −0.903688
\(476\) −29.7146 −1.36197
\(477\) 93.3727 4.27524
\(478\) 57.3587 2.62353
\(479\) 11.0230 0.503656 0.251828 0.967772i \(-0.418968\pi\)
0.251828 + 0.967772i \(0.418968\pi\)
\(480\) 25.0073 1.14142
\(481\) −15.0918 −0.688128
\(482\) 51.1272 2.32878
\(483\) 32.9146 1.49766
\(484\) −37.0231 −1.68287
\(485\) −13.2606 −0.602134
\(486\) −69.1422 −3.13635
\(487\) 22.0897 1.00098 0.500491 0.865742i \(-0.333153\pi\)
0.500491 + 0.865742i \(0.333153\pi\)
\(488\) −92.6133 −4.19241
\(489\) 49.8506 2.25432
\(490\) −10.6504 −0.481134
\(491\) 11.7629 0.530853 0.265426 0.964131i \(-0.414487\pi\)
0.265426 + 0.964131i \(0.414487\pi\)
\(492\) 125.742 5.66888
\(493\) 2.76042 0.124323
\(494\) −28.5398 −1.28407
\(495\) −10.6195 −0.477311
\(496\) −12.4410 −0.558617
\(497\) 6.09078 0.273209
\(498\) −106.861 −4.78856
\(499\) −6.27557 −0.280933 −0.140467 0.990085i \(-0.544860\pi\)
−0.140467 + 0.990085i \(0.544860\pi\)
\(500\) 36.6275 1.63803
\(501\) 44.8969 2.00584
\(502\) 1.85767 0.0829120
\(503\) 5.91347 0.263669 0.131834 0.991272i \(-0.457913\pi\)
0.131834 + 0.991272i \(0.457913\pi\)
\(504\) 73.5384 3.27566
\(505\) 10.1281 0.450693
\(506\) 33.8708 1.50574
\(507\) −22.9798 −1.02057
\(508\) −58.0906 −2.57736
\(509\) −20.6735 −0.916337 −0.458169 0.888865i \(-0.651494\pi\)
−0.458169 + 0.888865i \(0.651494\pi\)
\(510\) 29.8827 1.32323
\(511\) −3.27160 −0.144727
\(512\) 44.8775 1.98332
\(513\) 60.5126 2.67170
\(514\) −21.8726 −0.964757
\(515\) −13.9952 −0.616703
\(516\) −183.137 −8.06215
\(517\) 16.7385 0.736156
\(518\) −23.2620 −1.02207
\(519\) −64.7530 −2.84234
\(520\) 14.2814 0.626281
\(521\) −19.8494 −0.869618 −0.434809 0.900523i \(-0.643184\pi\)
−0.434809 + 0.900523i \(0.643184\pi\)
\(522\) −11.7689 −0.515110
\(523\) 42.9355 1.87744 0.938720 0.344681i \(-0.112013\pi\)
0.938720 + 0.344681i \(0.112013\pi\)
\(524\) −32.1449 −1.40426
\(525\) 19.6413 0.857217
\(526\) 35.9212 1.56624
\(527\) −5.91574 −0.257694
\(528\) 52.7022 2.29357
\(529\) 29.4207 1.27916
\(530\) 27.9500 1.21407
\(531\) 85.7762 3.72237
\(532\) −30.9894 −1.34356
\(533\) 19.9109 0.862438
\(534\) 53.9328 2.33390
\(535\) −1.59877 −0.0691210
\(536\) −70.5580 −3.04764
\(537\) 0.252519 0.0108970
\(538\) −25.0523 −1.08008
\(539\) −8.93157 −0.384710
\(540\) −52.1653 −2.24484
\(541\) −3.01733 −0.129725 −0.0648626 0.997894i \(-0.520661\pi\)
−0.0648626 + 0.997894i \(0.520661\pi\)
\(542\) 65.1646 2.79906
\(543\) −77.1192 −3.30950
\(544\) −41.5942 −1.78333
\(545\) 3.89598 0.166885
\(546\) 28.4614 1.21803
\(547\) −4.87379 −0.208388 −0.104194 0.994557i \(-0.533226\pi\)
−0.104194 + 0.994557i \(0.533226\pi\)
\(548\) 24.2769 1.03706
\(549\) 92.1619 3.93337
\(550\) 20.2119 0.861840
\(551\) 2.87884 0.122643
\(552\) 166.166 7.07250
\(553\) 16.5899 0.705475
\(554\) −37.0504 −1.57412
\(555\) 16.4799 0.699531
\(556\) −72.5536 −3.07696
\(557\) −21.0920 −0.893698 −0.446849 0.894609i \(-0.647454\pi\)
−0.446849 + 0.894609i \(0.647454\pi\)
\(558\) 25.2214 1.06771
\(559\) −28.9993 −1.22654
\(560\) 10.8054 0.456610
\(561\) 25.0601 1.05804
\(562\) −57.2126 −2.41337
\(563\) 15.0170 0.632892 0.316446 0.948611i \(-0.397510\pi\)
0.316446 + 0.948611i \(0.397510\pi\)
\(564\) 141.465 5.95674
\(565\) −3.06089 −0.128773
\(566\) −53.9314 −2.26690
\(567\) −29.7004 −1.24730
\(568\) 30.7487 1.29019
\(569\) 4.00846 0.168043 0.0840217 0.996464i \(-0.473223\pi\)
0.0840217 + 0.996464i \(0.473223\pi\)
\(570\) 31.1647 1.30534
\(571\) −31.6235 −1.32340 −0.661702 0.749767i \(-0.730166\pi\)
−0.661702 + 0.749767i \(0.730166\pi\)
\(572\) 20.6324 0.862685
\(573\) 37.2520 1.55622
\(574\) 30.6900 1.28098
\(575\) 31.2813 1.30452
\(576\) 45.6279 1.90116
\(577\) −6.73542 −0.280399 −0.140200 0.990123i \(-0.544774\pi\)
−0.140200 + 0.990123i \(0.544774\pi\)
\(578\) −5.47956 −0.227919
\(579\) 23.0872 0.959472
\(580\) −2.48173 −0.103048
\(581\) −18.3736 −0.762264
\(582\) −133.415 −5.53021
\(583\) 23.4393 0.970758
\(584\) −16.5164 −0.683452
\(585\) −14.2118 −0.587585
\(586\) −8.22685 −0.339848
\(587\) 33.9177 1.39993 0.699967 0.714175i \(-0.253198\pi\)
0.699967 + 0.714175i \(0.253198\pi\)
\(588\) −75.4850 −3.11295
\(589\) −6.16953 −0.254211
\(590\) 25.6761 1.05707
\(591\) 11.3907 0.468551
\(592\) −57.6455 −2.36921
\(593\) 18.6364 0.765304 0.382652 0.923893i \(-0.375011\pi\)
0.382652 + 0.923893i \(0.375011\pi\)
\(594\) −62.0995 −2.54797
\(595\) 5.13800 0.210638
\(596\) 16.6618 0.682493
\(597\) 65.9442 2.69891
\(598\) 45.3284 1.85362
\(599\) 5.11087 0.208824 0.104412 0.994534i \(-0.466704\pi\)
0.104412 + 0.994534i \(0.466704\pi\)
\(600\) 99.1572 4.04808
\(601\) 37.8996 1.54596 0.772978 0.634433i \(-0.218766\pi\)
0.772978 + 0.634433i \(0.218766\pi\)
\(602\) −44.6985 −1.82177
\(603\) 70.2141 2.85934
\(604\) −72.0279 −2.93077
\(605\) 6.40171 0.260267
\(606\) 101.898 4.13932
\(607\) −23.1216 −0.938478 −0.469239 0.883071i \(-0.655472\pi\)
−0.469239 + 0.883071i \(0.655472\pi\)
\(608\) −43.3785 −1.75923
\(609\) −2.87093 −0.116336
\(610\) 27.5876 1.11699
\(611\) 22.4006 0.906232
\(612\) 149.280 6.03431
\(613\) −8.32519 −0.336251 −0.168126 0.985766i \(-0.553771\pi\)
−0.168126 + 0.985766i \(0.553771\pi\)
\(614\) −8.34522 −0.336786
\(615\) −21.7422 −0.876730
\(616\) 18.4603 0.743787
\(617\) 40.7735 1.64148 0.820739 0.571303i \(-0.193562\pi\)
0.820739 + 0.571303i \(0.193562\pi\)
\(618\) −140.805 −5.66402
\(619\) 1.31896 0.0530135 0.0265067 0.999649i \(-0.491562\pi\)
0.0265067 + 0.999649i \(0.491562\pi\)
\(620\) 5.31849 0.213596
\(621\) −96.1093 −3.85673
\(622\) −38.4880 −1.54323
\(623\) 9.27314 0.371521
\(624\) 70.5299 2.82346
\(625\) 15.2692 0.610767
\(626\) −47.4011 −1.89453
\(627\) 26.1352 1.04374
\(628\) 67.9294 2.71068
\(629\) −27.4107 −1.09294
\(630\) −21.9056 −0.872738
\(631\) 21.0886 0.839525 0.419763 0.907634i \(-0.362113\pi\)
0.419763 + 0.907634i \(0.362113\pi\)
\(632\) 83.7526 3.33150
\(633\) 66.6374 2.64860
\(634\) −6.90410 −0.274197
\(635\) 10.0445 0.398605
\(636\) 198.097 7.85506
\(637\) −11.9529 −0.473590
\(638\) −2.95434 −0.116963
\(639\) −30.5989 −1.21047
\(640\) −2.02990 −0.0802387
\(641\) −50.4418 −1.99233 −0.996166 0.0874886i \(-0.972116\pi\)
−0.996166 + 0.0874886i \(0.972116\pi\)
\(642\) −16.0852 −0.634832
\(643\) −28.0031 −1.10433 −0.552167 0.833733i \(-0.686199\pi\)
−0.552167 + 0.833733i \(0.686199\pi\)
\(644\) 49.2190 1.93950
\(645\) 31.6664 1.24686
\(646\) −51.8357 −2.03945
\(647\) −14.8178 −0.582549 −0.291274 0.956640i \(-0.594079\pi\)
−0.291274 + 0.956640i \(0.594079\pi\)
\(648\) −149.940 −5.89019
\(649\) 21.5324 0.845219
\(650\) 27.0491 1.06095
\(651\) 6.15257 0.241138
\(652\) 74.5444 2.91938
\(653\) −20.3400 −0.795966 −0.397983 0.917393i \(-0.630290\pi\)
−0.397983 + 0.917393i \(0.630290\pi\)
\(654\) 39.1972 1.53273
\(655\) 5.55823 0.217178
\(656\) 76.0528 2.96936
\(657\) 16.4359 0.641225
\(658\) 34.5275 1.34602
\(659\) 10.7671 0.419426 0.209713 0.977763i \(-0.432747\pi\)
0.209713 + 0.977763i \(0.432747\pi\)
\(660\) −22.5300 −0.876981
\(661\) −38.0378 −1.47950 −0.739750 0.672882i \(-0.765056\pi\)
−0.739750 + 0.672882i \(0.765056\pi\)
\(662\) −56.0578 −2.17875
\(663\) 33.5373 1.30248
\(664\) −92.7572 −3.59968
\(665\) 5.35842 0.207791
\(666\) 116.864 4.52838
\(667\) −4.57233 −0.177041
\(668\) 67.1369 2.59760
\(669\) −39.6977 −1.53480
\(670\) 21.0178 0.811987
\(671\) 23.1354 0.893131
\(672\) 43.2593 1.66876
\(673\) 3.67183 0.141538 0.0707692 0.997493i \(-0.477455\pi\)
0.0707692 + 0.997493i \(0.477455\pi\)
\(674\) 59.1453 2.27819
\(675\) −57.3519 −2.20747
\(676\) −34.3630 −1.32166
\(677\) −27.3889 −1.05264 −0.526320 0.850287i \(-0.676429\pi\)
−0.526320 + 0.850287i \(0.676429\pi\)
\(678\) −30.7955 −1.18269
\(679\) −22.9392 −0.880324
\(680\) 25.9387 0.994704
\(681\) −63.8351 −2.44617
\(682\) 6.33132 0.242439
\(683\) −30.3469 −1.16119 −0.580596 0.814191i \(-0.697181\pi\)
−0.580596 + 0.814191i \(0.697181\pi\)
\(684\) 155.685 5.95275
\(685\) −4.19775 −0.160388
\(686\) −44.3903 −1.69483
\(687\) −8.26467 −0.315317
\(688\) −110.767 −4.22296
\(689\) 31.3682 1.19503
\(690\) −49.4974 −1.88433
\(691\) 2.50557 0.0953164 0.0476582 0.998864i \(-0.484824\pi\)
0.0476582 + 0.998864i \(0.484824\pi\)
\(692\) −96.8288 −3.68088
\(693\) −18.3703 −0.697832
\(694\) 74.8055 2.83958
\(695\) 12.5453 0.475872
\(696\) −14.4936 −0.549379
\(697\) 36.1634 1.36979
\(698\) 19.7721 0.748385
\(699\) 30.5729 1.15637
\(700\) 29.3707 1.11011
\(701\) 24.3239 0.918700 0.459350 0.888255i \(-0.348082\pi\)
0.459350 + 0.888255i \(0.348082\pi\)
\(702\) −83.1061 −3.13664
\(703\) −28.5866 −1.07816
\(704\) 11.4539 0.431687
\(705\) −24.4609 −0.921250
\(706\) 80.8741 3.04374
\(707\) 17.5202 0.658916
\(708\) 181.980 6.83924
\(709\) 25.5022 0.957756 0.478878 0.877881i \(-0.341044\pi\)
0.478878 + 0.877881i \(0.341044\pi\)
\(710\) −9.15940 −0.343746
\(711\) −83.3444 −3.12566
\(712\) 46.8146 1.75445
\(713\) 9.79877 0.366967
\(714\) 51.6932 1.93457
\(715\) −3.56758 −0.133420
\(716\) 0.377606 0.0141118
\(717\) −70.2941 −2.62518
\(718\) −71.7692 −2.67840
\(719\) 5.85169 0.218231 0.109116 0.994029i \(-0.465198\pi\)
0.109116 + 0.994029i \(0.465198\pi\)
\(720\) −54.2840 −2.02305
\(721\) −24.2099 −0.901624
\(722\) −4.63273 −0.172413
\(723\) −62.6573 −2.33025
\(724\) −115.321 −4.28586
\(725\) −2.72847 −0.101333
\(726\) 64.4073 2.39038
\(727\) −30.9860 −1.14921 −0.574603 0.818432i \(-0.694844\pi\)
−0.574603 + 0.818432i \(0.694844\pi\)
\(728\) 24.7049 0.915626
\(729\) 22.2502 0.824082
\(730\) 4.91988 0.182093
\(731\) −52.6702 −1.94808
\(732\) 195.528 7.22693
\(733\) 37.1073 1.37059 0.685295 0.728266i \(-0.259673\pi\)
0.685295 + 0.728266i \(0.259673\pi\)
\(734\) −71.9867 −2.65708
\(735\) 13.0522 0.481438
\(736\) 68.8961 2.53954
\(737\) 17.6258 0.649256
\(738\) −154.180 −5.67546
\(739\) 34.8479 1.28190 0.640950 0.767583i \(-0.278541\pi\)
0.640950 + 0.767583i \(0.278541\pi\)
\(740\) 24.6433 0.905905
\(741\) 34.9760 1.28488
\(742\) 48.3499 1.77498
\(743\) −37.7360 −1.38440 −0.692200 0.721706i \(-0.743358\pi\)
−0.692200 + 0.721706i \(0.743358\pi\)
\(744\) 31.0607 1.13874
\(745\) −2.88101 −0.105552
\(746\) 21.1865 0.775695
\(747\) 92.3051 3.37727
\(748\) 37.4738 1.37018
\(749\) −2.76567 −0.101055
\(750\) −63.7191 −2.32669
\(751\) −32.7059 −1.19346 −0.596728 0.802443i \(-0.703533\pi\)
−0.596728 + 0.802443i \(0.703533\pi\)
\(752\) 85.5625 3.12014
\(753\) −2.27661 −0.0829643
\(754\) −3.95371 −0.143986
\(755\) 12.4544 0.453263
\(756\) −90.2392 −3.28197
\(757\) 3.73832 0.135871 0.0679357 0.997690i \(-0.478359\pi\)
0.0679357 + 0.997690i \(0.478359\pi\)
\(758\) 4.07329 0.147949
\(759\) −41.5093 −1.50669
\(760\) 27.0515 0.981260
\(761\) −24.9894 −0.905867 −0.452933 0.891544i \(-0.649622\pi\)
−0.452933 + 0.891544i \(0.649622\pi\)
\(762\) 101.058 3.66093
\(763\) 6.73953 0.243987
\(764\) 55.7050 2.01533
\(765\) −25.8123 −0.933246
\(766\) −64.7013 −2.33775
\(767\) 28.8162 1.04049
\(768\) −61.0339 −2.20237
\(769\) −17.1057 −0.616847 −0.308424 0.951249i \(-0.599801\pi\)
−0.308424 + 0.951249i \(0.599801\pi\)
\(770\) −5.49894 −0.198168
\(771\) 26.8052 0.965367
\(772\) 34.5236 1.24253
\(773\) −46.5027 −1.67259 −0.836293 0.548282i \(-0.815282\pi\)
−0.836293 + 0.548282i \(0.815282\pi\)
\(774\) 224.556 8.07151
\(775\) 5.84728 0.210040
\(776\) −115.806 −4.15720
\(777\) 28.5080 1.02272
\(778\) 70.9104 2.54226
\(779\) 37.7148 1.35127
\(780\) −30.1514 −1.07959
\(781\) −7.68122 −0.274856
\(782\) 82.3282 2.94405
\(783\) 8.38301 0.299584
\(784\) −45.6558 −1.63056
\(785\) −11.7458 −0.419225
\(786\) 55.9210 1.99464
\(787\) −31.1264 −1.10954 −0.554769 0.832005i \(-0.687193\pi\)
−0.554769 + 0.832005i \(0.687193\pi\)
\(788\) 17.0332 0.606782
\(789\) −44.0221 −1.56723
\(790\) −24.9481 −0.887615
\(791\) −5.29494 −0.188267
\(792\) −92.7410 −3.29541
\(793\) 30.9615 1.09947
\(794\) −47.6493 −1.69101
\(795\) −34.2532 −1.21484
\(796\) 98.6100 3.49514
\(797\) 26.8002 0.949312 0.474656 0.880171i \(-0.342573\pi\)
0.474656 + 0.880171i \(0.342573\pi\)
\(798\) 53.9108 1.90842
\(799\) 40.6853 1.43934
\(800\) 41.1128 1.45356
\(801\) −46.5864 −1.64605
\(802\) −79.1953 −2.79648
\(803\) 4.12589 0.145600
\(804\) 148.964 5.25357
\(805\) −8.51053 −0.299957
\(806\) 8.47304 0.298450
\(807\) 30.7021 1.08076
\(808\) 88.4492 3.11163
\(809\) 15.1798 0.533694 0.266847 0.963739i \(-0.414018\pi\)
0.266847 + 0.963739i \(0.414018\pi\)
\(810\) 44.6639 1.56933
\(811\) −37.7197 −1.32452 −0.662259 0.749275i \(-0.730402\pi\)
−0.662259 + 0.749275i \(0.730402\pi\)
\(812\) −4.29306 −0.150657
\(813\) −79.8604 −2.80083
\(814\) 29.3363 1.02824
\(815\) −12.8896 −0.451502
\(816\) 128.101 4.48442
\(817\) −54.9298 −1.92175
\(818\) 55.3823 1.93640
\(819\) −24.5845 −0.859053
\(820\) −32.5123 −1.13538
\(821\) 20.2932 0.708238 0.354119 0.935200i \(-0.384781\pi\)
0.354119 + 0.935200i \(0.384781\pi\)
\(822\) −42.2334 −1.47306
\(823\) −24.6537 −0.859373 −0.429686 0.902978i \(-0.641376\pi\)
−0.429686 + 0.902978i \(0.641376\pi\)
\(824\) −122.221 −4.25778
\(825\) −24.7701 −0.862384
\(826\) 44.4162 1.54544
\(827\) 15.6082 0.542749 0.271375 0.962474i \(-0.412522\pi\)
0.271375 + 0.962474i \(0.412522\pi\)
\(828\) −247.266 −8.59310
\(829\) −10.0770 −0.349987 −0.174994 0.984570i \(-0.555991\pi\)
−0.174994 + 0.984570i \(0.555991\pi\)
\(830\) 27.6304 0.959067
\(831\) 45.4060 1.57512
\(832\) 15.3285 0.531420
\(833\) −21.7095 −0.752190
\(834\) 126.218 4.37058
\(835\) −11.6087 −0.401737
\(836\) 39.0814 1.35166
\(837\) −17.9653 −0.620971
\(838\) −86.2751 −2.98032
\(839\) 37.5963 1.29797 0.648983 0.760803i \(-0.275194\pi\)
0.648983 + 0.760803i \(0.275194\pi\)
\(840\) −26.9771 −0.930799
\(841\) −28.6012 −0.986248
\(842\) 3.28341 0.113154
\(843\) 70.1151 2.41489
\(844\) 99.6467 3.42998
\(845\) 5.94176 0.204403
\(846\) −173.459 −5.96366
\(847\) 11.0741 0.380511
\(848\) 119.816 4.11448
\(849\) 66.0939 2.26834
\(850\) 49.1282 1.68508
\(851\) 45.4027 1.55639
\(852\) −64.9177 −2.22404
\(853\) −42.3545 −1.45019 −0.725095 0.688649i \(-0.758204\pi\)
−0.725095 + 0.688649i \(0.758204\pi\)
\(854\) 47.7229 1.63304
\(855\) −26.9196 −0.920632
\(856\) −13.9622 −0.477219
\(857\) 31.8298 1.08729 0.543643 0.839317i \(-0.317045\pi\)
0.543643 + 0.839317i \(0.317045\pi\)
\(858\) −35.8933 −1.22538
\(859\) −27.2677 −0.930361 −0.465181 0.885216i \(-0.654011\pi\)
−0.465181 + 0.885216i \(0.654011\pi\)
\(860\) 47.3526 1.61471
\(861\) −37.6112 −1.28178
\(862\) 2.77173 0.0944054
\(863\) −9.87885 −0.336280 −0.168140 0.985763i \(-0.553776\pi\)
−0.168140 + 0.985763i \(0.553776\pi\)
\(864\) −126.316 −4.29734
\(865\) 16.7428 0.569272
\(866\) 1.56983 0.0533451
\(867\) 6.71529 0.228063
\(868\) 9.20029 0.312278
\(869\) −20.9219 −0.709727
\(870\) 4.31735 0.146372
\(871\) 23.5882 0.799255
\(872\) 34.0239 1.15219
\(873\) 115.242 3.90034
\(874\) 85.8600 2.90426
\(875\) −10.9558 −0.370374
\(876\) 34.8699 1.17815
\(877\) 9.42358 0.318212 0.159106 0.987262i \(-0.449139\pi\)
0.159106 + 0.987262i \(0.449139\pi\)
\(878\) −90.2680 −3.04640
\(879\) 10.0822 0.340063
\(880\) −13.6269 −0.459363
\(881\) 13.1083 0.441628 0.220814 0.975316i \(-0.429129\pi\)
0.220814 + 0.975316i \(0.429129\pi\)
\(882\) 92.5572 3.11656
\(883\) 36.1622 1.21696 0.608478 0.793571i \(-0.291780\pi\)
0.608478 + 0.793571i \(0.291780\pi\)
\(884\) 50.1502 1.68673
\(885\) −31.4665 −1.05773
\(886\) −75.1210 −2.52374
\(887\) −45.8068 −1.53804 −0.769021 0.639224i \(-0.779256\pi\)
−0.769021 + 0.639224i \(0.779256\pi\)
\(888\) 143.920 4.82964
\(889\) 17.3757 0.582763
\(890\) −13.9451 −0.467440
\(891\) 37.4559 1.25482
\(892\) −59.3623 −1.98760
\(893\) 42.4307 1.41989
\(894\) −28.9857 −0.969428
\(895\) −0.0652925 −0.00218249
\(896\) −3.51145 −0.117309
\(897\) −55.5508 −1.85479
\(898\) 29.5579 0.986359
\(899\) −0.854685 −0.0285053
\(900\) −147.553 −4.91843
\(901\) 56.9728 1.89804
\(902\) −38.7039 −1.28870
\(903\) 54.7788 1.82292
\(904\) −26.7310 −0.889060
\(905\) 19.9403 0.662837
\(906\) 125.304 4.16293
\(907\) −39.2536 −1.30340 −0.651698 0.758479i \(-0.725943\pi\)
−0.651698 + 0.758479i \(0.725943\pi\)
\(908\) −95.4563 −3.16783
\(909\) −88.0181 −2.91938
\(910\) −7.35909 −0.243951
\(911\) −22.2348 −0.736670 −0.368335 0.929693i \(-0.620072\pi\)
−0.368335 + 0.929693i \(0.620072\pi\)
\(912\) 133.596 4.42381
\(913\) 23.1713 0.766859
\(914\) −4.26030 −0.140918
\(915\) −33.8091 −1.11769
\(916\) −12.3586 −0.408341
\(917\) 9.61500 0.317515
\(918\) −150.942 −4.98184
\(919\) −44.3861 −1.46416 −0.732080 0.681218i \(-0.761450\pi\)
−0.732080 + 0.681218i \(0.761450\pi\)
\(920\) −42.9646 −1.41650
\(921\) 10.2272 0.336998
\(922\) 6.29864 0.207435
\(923\) −10.2796 −0.338356
\(924\) −38.9740 −1.28215
\(925\) 27.0934 0.890827
\(926\) −51.8228 −1.70300
\(927\) 121.626 3.99471
\(928\) −6.00937 −0.197267
\(929\) 36.2956 1.19082 0.595411 0.803422i \(-0.296989\pi\)
0.595411 + 0.803422i \(0.296989\pi\)
\(930\) −9.25233 −0.303396
\(931\) −22.6409 −0.742024
\(932\) 45.7173 1.49752
\(933\) 47.1677 1.54420
\(934\) 39.5234 1.29325
\(935\) −6.47965 −0.211907
\(936\) −124.113 −4.05675
\(937\) −39.7978 −1.30014 −0.650069 0.759875i \(-0.725260\pi\)
−0.650069 + 0.759875i \(0.725260\pi\)
\(938\) 36.3580 1.18713
\(939\) 58.0909 1.89573
\(940\) −36.5777 −1.19303
\(941\) −19.7247 −0.643006 −0.321503 0.946909i \(-0.604188\pi\)
−0.321503 + 0.946909i \(0.604188\pi\)
\(942\) −118.174 −3.85031
\(943\) −59.9007 −1.95063
\(944\) 110.068 3.58240
\(945\) 15.6034 0.507578
\(946\) 56.3703 1.83276
\(947\) −39.6986 −1.29003 −0.645016 0.764169i \(-0.723149\pi\)
−0.645016 + 0.764169i \(0.723149\pi\)
\(948\) −176.821 −5.74289
\(949\) 5.52157 0.179238
\(950\) 51.2357 1.66231
\(951\) 8.46111 0.274370
\(952\) 44.8706 1.45426
\(953\) −52.7575 −1.70898 −0.854491 0.519467i \(-0.826131\pi\)
−0.854491 + 0.519467i \(0.826131\pi\)
\(954\) −242.900 −7.86418
\(955\) −9.63202 −0.311685
\(956\) −105.115 −3.39966
\(957\) 3.62060 0.117037
\(958\) −28.6754 −0.926460
\(959\) −7.26156 −0.234488
\(960\) −16.7383 −0.540227
\(961\) −29.1684 −0.940915
\(962\) 39.2599 1.26579
\(963\) 13.8942 0.447734
\(964\) −93.6951 −3.01772
\(965\) −5.96953 −0.192166
\(966\) −85.6240 −2.75491
\(967\) −9.53586 −0.306653 −0.153326 0.988176i \(-0.548999\pi\)
−0.153326 + 0.988176i \(0.548999\pi\)
\(968\) 55.9067 1.79691
\(969\) 63.5255 2.04073
\(970\) 34.4962 1.10761
\(971\) −38.3400 −1.23039 −0.615194 0.788375i \(-0.710922\pi\)
−0.615194 + 0.788375i \(0.710922\pi\)
\(972\) 126.709 4.06420
\(973\) 21.7018 0.695728
\(974\) −57.4643 −1.84127
\(975\) −33.1492 −1.06162
\(976\) 118.262 3.78547
\(977\) 12.5427 0.401277 0.200639 0.979665i \(-0.435698\pi\)
0.200639 + 0.979665i \(0.435698\pi\)
\(978\) −129.681 −4.14676
\(979\) −11.6946 −0.373760
\(980\) 19.5177 0.623471
\(981\) −33.8581 −1.08100
\(982\) −30.6001 −0.976487
\(983\) 9.55640 0.304802 0.152401 0.988319i \(-0.451300\pi\)
0.152401 + 0.988319i \(0.451300\pi\)
\(984\) −189.876 −6.05304
\(985\) −2.94523 −0.0938429
\(986\) −7.18096 −0.228688
\(987\) −42.3141 −1.34687
\(988\) 52.3016 1.66394
\(989\) 87.2424 2.77415
\(990\) 27.6256 0.877999
\(991\) 0.216805 0.00688705 0.00344353 0.999994i \(-0.498904\pi\)
0.00344353 + 0.999994i \(0.498904\pi\)
\(992\) 12.8784 0.408891
\(993\) 68.6999 2.18012
\(994\) −15.8446 −0.502559
\(995\) −17.0508 −0.540547
\(996\) 195.832 6.20518
\(997\) −17.5624 −0.556208 −0.278104 0.960551i \(-0.589706\pi\)
−0.278104 + 0.960551i \(0.589706\pi\)
\(998\) 16.3253 0.516768
\(999\) −83.2424 −2.63367
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 \(a_p\))