Properties

Label 5077.2.a.c.1.6
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 1.6
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} +O(q^{10})\) \(q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} -11.4628 q^{10} -3.68509 q^{11} +1.93677 q^{12} -5.03583 q^{13} -2.58850 q^{14} +1.64489 q^{15} +11.6009 q^{16} -1.29329 q^{17} +7.59187 q^{18} -2.92984 q^{19} +21.8691 q^{20} +0.371446 q^{21} +9.80151 q^{22} +1.79674 q^{23} -3.12105 q^{24} +13.5733 q^{25} +13.3942 q^{26} -2.23444 q^{27} +4.93844 q^{28} +1.44401 q^{29} -4.37504 q^{30} +0.755240 q^{31} -14.5012 q^{32} -1.40650 q^{33} +3.43987 q^{34} +4.19419 q^{35} -14.4840 q^{36} +0.566761 q^{37} +7.79272 q^{38} -1.92204 q^{39} -35.2414 q^{40} -3.17553 q^{41} -0.987963 q^{42} +5.25035 q^{43} -18.6997 q^{44} -12.3012 q^{45} -4.77894 q^{46} +2.65339 q^{47} +4.42774 q^{48} -6.05288 q^{49} -36.1020 q^{50} -0.493615 q^{51} -25.5539 q^{52} +5.19541 q^{53} +5.94312 q^{54} -15.8815 q^{55} -7.95813 q^{56} -1.11824 q^{57} -3.84075 q^{58} +9.86596 q^{59} +8.34685 q^{60} +10.2285 q^{61} -2.00877 q^{62} -2.77784 q^{63} +15.3682 q^{64} -21.7028 q^{65} +3.74098 q^{66} +6.37354 q^{67} -6.56270 q^{68} +0.685769 q^{69} -11.1556 q^{70} +5.36311 q^{71} +23.3406 q^{72} -16.7987 q^{73} -1.50746 q^{74} +5.18057 q^{75} -14.8672 q^{76} -3.58634 q^{77} +5.11221 q^{78} +9.71960 q^{79} +49.9960 q^{80} +7.71015 q^{81} +8.44621 q^{82} -1.63442 q^{83} +1.88487 q^{84} -5.57367 q^{85} -13.9648 q^{86} +0.551141 q^{87} +30.1339 q^{88} +9.92552 q^{89} +32.7185 q^{90} -4.90088 q^{91} +9.11742 q^{92} +0.288255 q^{93} -7.05742 q^{94} -12.6267 q^{95} -5.53473 q^{96} +17.5691 q^{97} +16.0993 q^{98} +10.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65978 −1.88075 −0.940373 0.340144i \(-0.889524\pi\)
−0.940373 + 0.340144i \(0.889524\pi\)
\(3\) 0.381674 0.220359 0.110180 0.993912i \(-0.464857\pi\)
0.110180 + 0.993912i \(0.464857\pi\)
\(4\) 5.07442 2.53721
\(5\) 4.30968 1.92735 0.963673 0.267085i \(-0.0860606\pi\)
0.963673 + 0.267085i \(0.0860606\pi\)
\(6\) −1.01517 −0.414440
\(7\) 0.973203 0.367836 0.183918 0.982942i \(-0.441122\pi\)
0.183918 + 0.982942i \(0.441122\pi\)
\(8\) −8.17726 −2.89110
\(9\) −2.85433 −0.951442
\(10\) −11.4628 −3.62485
\(11\) −3.68509 −1.11110 −0.555548 0.831485i \(-0.687491\pi\)
−0.555548 + 0.831485i \(0.687491\pi\)
\(12\) 1.93677 0.559098
\(13\) −5.03583 −1.39669 −0.698344 0.715762i \(-0.746079\pi\)
−0.698344 + 0.715762i \(0.746079\pi\)
\(14\) −2.58850 −0.691806
\(15\) 1.64489 0.424709
\(16\) 11.6009 2.90022
\(17\) −1.29329 −0.313669 −0.156835 0.987625i \(-0.550129\pi\)
−0.156835 + 0.987625i \(0.550129\pi\)
\(18\) 7.59187 1.78942
\(19\) −2.92984 −0.672151 −0.336076 0.941835i \(-0.609100\pi\)
−0.336076 + 0.941835i \(0.609100\pi\)
\(20\) 21.8691 4.89008
\(21\) 0.371446 0.0810561
\(22\) 9.80151 2.08969
\(23\) 1.79674 0.374647 0.187323 0.982298i \(-0.440019\pi\)
0.187323 + 0.982298i \(0.440019\pi\)
\(24\) −3.12105 −0.637081
\(25\) 13.5733 2.71466
\(26\) 13.3942 2.62682
\(27\) −2.23444 −0.430018
\(28\) 4.93844 0.933277
\(29\) 1.44401 0.268146 0.134073 0.990971i \(-0.457194\pi\)
0.134073 + 0.990971i \(0.457194\pi\)
\(30\) −4.37504 −0.798769
\(31\) 0.755240 0.135645 0.0678225 0.997697i \(-0.478395\pi\)
0.0678225 + 0.997697i \(0.478395\pi\)
\(32\) −14.5012 −2.56347
\(33\) −1.40650 −0.244840
\(34\) 3.43987 0.589933
\(35\) 4.19419 0.708947
\(36\) −14.4840 −2.41401
\(37\) 0.566761 0.0931749 0.0465875 0.998914i \(-0.485165\pi\)
0.0465875 + 0.998914i \(0.485165\pi\)
\(38\) 7.79272 1.26415
\(39\) −1.92204 −0.307773
\(40\) −35.2414 −5.57215
\(41\) −3.17553 −0.495935 −0.247967 0.968768i \(-0.579763\pi\)
−0.247967 + 0.968768i \(0.579763\pi\)
\(42\) −0.987963 −0.152446
\(43\) 5.25035 0.800671 0.400336 0.916369i \(-0.368894\pi\)
0.400336 + 0.916369i \(0.368894\pi\)
\(44\) −18.6997 −2.81908
\(45\) −12.3012 −1.83376
\(46\) −4.77894 −0.704616
\(47\) 2.65339 0.387036 0.193518 0.981097i \(-0.438010\pi\)
0.193518 + 0.981097i \(0.438010\pi\)
\(48\) 4.42774 0.639090
\(49\) −6.05288 −0.864697
\(50\) −36.1020 −5.10559
\(51\) −0.493615 −0.0691200
\(52\) −25.5539 −3.54369
\(53\) 5.19541 0.713645 0.356822 0.934172i \(-0.383860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(54\) 5.94312 0.808756
\(55\) −15.8815 −2.14147
\(56\) −7.95813 −1.06345
\(57\) −1.11824 −0.148115
\(58\) −3.84075 −0.504315
\(59\) 9.86596 1.28444 0.642219 0.766521i \(-0.278014\pi\)
0.642219 + 0.766521i \(0.278014\pi\)
\(60\) 8.34685 1.07757
\(61\) 10.2285 1.30962 0.654810 0.755793i \(-0.272748\pi\)
0.654810 + 0.755793i \(0.272748\pi\)
\(62\) −2.00877 −0.255114
\(63\) −2.77784 −0.349975
\(64\) 15.3682 1.92103
\(65\) −21.7028 −2.69190
\(66\) 3.74098 0.460483
\(67\) 6.37354 0.778651 0.389326 0.921100i \(-0.372708\pi\)
0.389326 + 0.921100i \(0.372708\pi\)
\(68\) −6.56270 −0.795844
\(69\) 0.685769 0.0825569
\(70\) −11.1556 −1.33335
\(71\) 5.36311 0.636484 0.318242 0.948009i \(-0.396907\pi\)
0.318242 + 0.948009i \(0.396907\pi\)
\(72\) 23.3406 2.75071
\(73\) −16.7987 −1.96614 −0.983071 0.183225i \(-0.941346\pi\)
−0.983071 + 0.183225i \(0.941346\pi\)
\(74\) −1.50746 −0.175238
\(75\) 5.18057 0.598201
\(76\) −14.8672 −1.70539
\(77\) −3.58634 −0.408701
\(78\) 5.11221 0.578843
\(79\) 9.71960 1.09354 0.546770 0.837283i \(-0.315857\pi\)
0.546770 + 0.837283i \(0.315857\pi\)
\(80\) 49.9960 5.58972
\(81\) 7.71015 0.856683
\(82\) 8.44621 0.932728
\(83\) −1.63442 −0.179400 −0.0897002 0.995969i \(-0.528591\pi\)
−0.0897002 + 0.995969i \(0.528591\pi\)
\(84\) 1.88487 0.205656
\(85\) −5.57367 −0.604549
\(86\) −13.9648 −1.50586
\(87\) 0.551141 0.0590885
\(88\) 30.1339 3.21229
\(89\) 9.92552 1.05210 0.526051 0.850453i \(-0.323672\pi\)
0.526051 + 0.850453i \(0.323672\pi\)
\(90\) 32.7185 3.44883
\(91\) −4.90088 −0.513752
\(92\) 9.11742 0.950557
\(93\) 0.288255 0.0298907
\(94\) −7.05742 −0.727917
\(95\) −12.6267 −1.29547
\(96\) −5.53473 −0.564886
\(97\) 17.5691 1.78388 0.891938 0.452158i \(-0.149346\pi\)
0.891938 + 0.452158i \(0.149346\pi\)
\(98\) 16.0993 1.62628
\(99\) 10.5184 1.05714
\(100\) 68.8766 6.88766
\(101\) 9.74201 0.969367 0.484683 0.874690i \(-0.338935\pi\)
0.484683 + 0.874690i \(0.338935\pi\)
\(102\) 1.31291 0.129997
\(103\) −10.2660 −1.01154 −0.505772 0.862667i \(-0.668792\pi\)
−0.505772 + 0.862667i \(0.668792\pi\)
\(104\) 41.1793 4.03796
\(105\) 1.60081 0.156223
\(106\) −13.8186 −1.34218
\(107\) −3.44250 −0.332799 −0.166399 0.986058i \(-0.553214\pi\)
−0.166399 + 0.986058i \(0.553214\pi\)
\(108\) −11.3385 −1.09105
\(109\) −3.55270 −0.340287 −0.170143 0.985419i \(-0.554423\pi\)
−0.170143 + 0.985419i \(0.554423\pi\)
\(110\) 42.2413 4.02755
\(111\) 0.216318 0.0205320
\(112\) 11.2900 1.06680
\(113\) 15.7759 1.48407 0.742036 0.670360i \(-0.233860\pi\)
0.742036 + 0.670360i \(0.233860\pi\)
\(114\) 2.97428 0.278566
\(115\) 7.74338 0.722074
\(116\) 7.32751 0.680342
\(117\) 14.3739 1.32887
\(118\) −26.2413 −2.41570
\(119\) −1.25863 −0.115379
\(120\) −13.4507 −1.22787
\(121\) 2.57986 0.234533
\(122\) −27.2054 −2.46307
\(123\) −1.21202 −0.109284
\(124\) 3.83240 0.344160
\(125\) 36.9482 3.30475
\(126\) 7.38843 0.658213
\(127\) 16.2957 1.44601 0.723005 0.690843i \(-0.242760\pi\)
0.723005 + 0.690843i \(0.242760\pi\)
\(128\) −11.8737 −1.04949
\(129\) 2.00392 0.176435
\(130\) 57.7246 5.06278
\(131\) −10.7018 −0.935019 −0.467509 0.883988i \(-0.654849\pi\)
−0.467509 + 0.883988i \(0.654849\pi\)
\(132\) −7.13717 −0.621211
\(133\) −2.85133 −0.247241
\(134\) −16.9522 −1.46445
\(135\) −9.62972 −0.828794
\(136\) 10.5756 0.906849
\(137\) 2.12116 0.181223 0.0906113 0.995886i \(-0.471118\pi\)
0.0906113 + 0.995886i \(0.471118\pi\)
\(138\) −1.82399 −0.155269
\(139\) −16.2412 −1.37756 −0.688780 0.724971i \(-0.741853\pi\)
−0.688780 + 0.724971i \(0.741853\pi\)
\(140\) 21.2831 1.79875
\(141\) 1.01273 0.0852870
\(142\) −14.2647 −1.19707
\(143\) 18.5575 1.55185
\(144\) −33.1126 −2.75939
\(145\) 6.22322 0.516810
\(146\) 44.6809 3.69781
\(147\) −2.31022 −0.190544
\(148\) 2.87598 0.236404
\(149\) 4.90088 0.401496 0.200748 0.979643i \(-0.435663\pi\)
0.200748 + 0.979643i \(0.435663\pi\)
\(150\) −13.7792 −1.12506
\(151\) 13.2338 1.07695 0.538474 0.842642i \(-0.319001\pi\)
0.538474 + 0.842642i \(0.319001\pi\)
\(152\) 23.9581 1.94326
\(153\) 3.69148 0.298438
\(154\) 9.53886 0.768663
\(155\) 3.25484 0.261435
\(156\) −9.75325 −0.780885
\(157\) 13.8167 1.10270 0.551348 0.834276i \(-0.314114\pi\)
0.551348 + 0.834276i \(0.314114\pi\)
\(158\) −25.8520 −2.05667
\(159\) 1.98295 0.157258
\(160\) −62.4955 −4.94070
\(161\) 1.74859 0.137809
\(162\) −20.5073 −1.61120
\(163\) 4.71147 0.369031 0.184515 0.982830i \(-0.440928\pi\)
0.184515 + 0.982830i \(0.440928\pi\)
\(164\) −16.1140 −1.25829
\(165\) −6.06156 −0.471892
\(166\) 4.34718 0.337407
\(167\) −6.84022 −0.529312 −0.264656 0.964343i \(-0.585258\pi\)
−0.264656 + 0.964343i \(0.585258\pi\)
\(168\) −3.03741 −0.234341
\(169\) 12.3596 0.950736
\(170\) 14.8247 1.13700
\(171\) 8.36271 0.639513
\(172\) 26.6425 2.03147
\(173\) −0.751253 −0.0571167 −0.0285584 0.999592i \(-0.509092\pi\)
−0.0285584 + 0.999592i \(0.509092\pi\)
\(174\) −1.46591 −0.111131
\(175\) 13.2096 0.998550
\(176\) −42.7502 −3.22242
\(177\) 3.76558 0.283038
\(178\) −26.3997 −1.97874
\(179\) 2.53323 0.189343 0.0946713 0.995509i \(-0.469820\pi\)
0.0946713 + 0.995509i \(0.469820\pi\)
\(180\) −62.4215 −4.65262
\(181\) −18.8652 −1.40224 −0.701119 0.713044i \(-0.747316\pi\)
−0.701119 + 0.713044i \(0.747316\pi\)
\(182\) 13.0353 0.966237
\(183\) 3.90394 0.288587
\(184\) −14.6924 −1.08314
\(185\) 2.44256 0.179580
\(186\) −0.766694 −0.0562167
\(187\) 4.76589 0.348517
\(188\) 13.4644 0.981991
\(189\) −2.17456 −0.158176
\(190\) 33.5841 2.43645
\(191\) 15.5155 1.12266 0.561331 0.827592i \(-0.310290\pi\)
0.561331 + 0.827592i \(0.310290\pi\)
\(192\) 5.86565 0.423317
\(193\) 12.8400 0.924241 0.462121 0.886817i \(-0.347089\pi\)
0.462121 + 0.886817i \(0.347089\pi\)
\(194\) −46.7300 −3.35502
\(195\) −8.28338 −0.593185
\(196\) −30.7148 −2.19392
\(197\) −6.85528 −0.488419 −0.244209 0.969723i \(-0.578528\pi\)
−0.244209 + 0.969723i \(0.578528\pi\)
\(198\) −27.9767 −1.98822
\(199\) −16.5138 −1.17063 −0.585315 0.810806i \(-0.699029\pi\)
−0.585315 + 0.810806i \(0.699029\pi\)
\(200\) −110.993 −7.84835
\(201\) 2.43261 0.171583
\(202\) −25.9116 −1.82313
\(203\) 1.40532 0.0986338
\(204\) −2.50481 −0.175372
\(205\) −13.6855 −0.955838
\(206\) 27.3054 1.90246
\(207\) −5.12849 −0.356455
\(208\) −58.4200 −4.05070
\(209\) 10.7967 0.746824
\(210\) −4.25780 −0.293816
\(211\) 9.70985 0.668454 0.334227 0.942493i \(-0.391525\pi\)
0.334227 + 0.942493i \(0.391525\pi\)
\(212\) 26.3637 1.81066
\(213\) 2.04696 0.140255
\(214\) 9.15628 0.625910
\(215\) 22.6273 1.54317
\(216\) 18.2716 1.24323
\(217\) 0.735001 0.0498951
\(218\) 9.44938 0.639993
\(219\) −6.41163 −0.433258
\(220\) −80.5895 −5.43334
\(221\) 6.51280 0.438098
\(222\) −0.575357 −0.0386154
\(223\) 17.7638 1.18955 0.594777 0.803891i \(-0.297240\pi\)
0.594777 + 0.803891i \(0.297240\pi\)
\(224\) −14.1126 −0.942938
\(225\) −38.7426 −2.58284
\(226\) −41.9604 −2.79117
\(227\) 20.2750 1.34570 0.672849 0.739780i \(-0.265071\pi\)
0.672849 + 0.739780i \(0.265071\pi\)
\(228\) −5.67443 −0.375798
\(229\) 8.18159 0.540655 0.270327 0.962768i \(-0.412868\pi\)
0.270327 + 0.962768i \(0.412868\pi\)
\(230\) −20.5957 −1.35804
\(231\) −1.36881 −0.0900611
\(232\) −11.8081 −0.775237
\(233\) 15.8469 1.03817 0.519084 0.854723i \(-0.326273\pi\)
0.519084 + 0.854723i \(0.326273\pi\)
\(234\) −38.2314 −2.49926
\(235\) 11.4352 0.745953
\(236\) 50.0640 3.25889
\(237\) 3.70971 0.240972
\(238\) 3.34769 0.216998
\(239\) −7.89563 −0.510726 −0.255363 0.966845i \(-0.582195\pi\)
−0.255363 + 0.966845i \(0.582195\pi\)
\(240\) 19.0821 1.23175
\(241\) −10.7055 −0.689600 −0.344800 0.938676i \(-0.612053\pi\)
−0.344800 + 0.938676i \(0.612053\pi\)
\(242\) −6.86186 −0.441097
\(243\) 9.64608 0.618797
\(244\) 51.9035 3.32278
\(245\) −26.0859 −1.66657
\(246\) 3.22370 0.205535
\(247\) 14.7542 0.938785
\(248\) −6.17579 −0.392163
\(249\) −0.623813 −0.0395326
\(250\) −98.2739 −6.21539
\(251\) 24.5457 1.54931 0.774654 0.632385i \(-0.217924\pi\)
0.774654 + 0.632385i \(0.217924\pi\)
\(252\) −14.0959 −0.887958
\(253\) −6.62115 −0.416268
\(254\) −43.3430 −2.71958
\(255\) −2.12732 −0.133218
\(256\) 0.844866 0.0528042
\(257\) −3.85826 −0.240672 −0.120336 0.992733i \(-0.538397\pi\)
−0.120336 + 0.992733i \(0.538397\pi\)
\(258\) −5.32998 −0.331830
\(259\) 0.551573 0.0342731
\(260\) −110.129 −6.82991
\(261\) −4.12168 −0.255125
\(262\) 28.4644 1.75853
\(263\) 4.63435 0.285766 0.142883 0.989740i \(-0.454363\pi\)
0.142883 + 0.989740i \(0.454363\pi\)
\(264\) 11.5013 0.707858
\(265\) 22.3905 1.37544
\(266\) 7.58390 0.464998
\(267\) 3.78831 0.231841
\(268\) 32.3420 1.97560
\(269\) −19.9946 −1.21909 −0.609547 0.792750i \(-0.708649\pi\)
−0.609547 + 0.792750i \(0.708649\pi\)
\(270\) 25.6129 1.55875
\(271\) 20.3466 1.23597 0.617983 0.786191i \(-0.287950\pi\)
0.617983 + 0.786191i \(0.287950\pi\)
\(272\) −15.0033 −0.909709
\(273\) −1.87054 −0.113210
\(274\) −5.64180 −0.340834
\(275\) −50.0188 −3.01625
\(276\) 3.47988 0.209464
\(277\) 0.262854 0.0157934 0.00789669 0.999969i \(-0.497486\pi\)
0.00789669 + 0.999969i \(0.497486\pi\)
\(278\) 43.1979 2.59084
\(279\) −2.15570 −0.129058
\(280\) −34.2970 −2.04964
\(281\) 17.8023 1.06200 0.530999 0.847372i \(-0.321817\pi\)
0.530999 + 0.847372i \(0.321817\pi\)
\(282\) −2.69363 −0.160403
\(283\) −17.2900 −1.02779 −0.513893 0.857854i \(-0.671797\pi\)
−0.513893 + 0.857854i \(0.671797\pi\)
\(284\) 27.2147 1.61489
\(285\) −4.81926 −0.285468
\(286\) −49.3587 −2.91864
\(287\) −3.09044 −0.182423
\(288\) 41.3911 2.43900
\(289\) −15.3274 −0.901612
\(290\) −16.5524 −0.971989
\(291\) 6.70568 0.393094
\(292\) −85.2437 −4.98851
\(293\) 11.3547 0.663346 0.331673 0.943394i \(-0.392387\pi\)
0.331673 + 0.943394i \(0.392387\pi\)
\(294\) 6.14468 0.358365
\(295\) 42.5191 2.47556
\(296\) −4.63455 −0.269378
\(297\) 8.23411 0.477792
\(298\) −13.0353 −0.755112
\(299\) −9.04809 −0.523264
\(300\) 26.2884 1.51776
\(301\) 5.10966 0.294516
\(302\) −35.1989 −2.02547
\(303\) 3.71827 0.213609
\(304\) −33.9887 −1.94938
\(305\) 44.0814 2.52409
\(306\) −9.81850 −0.561286
\(307\) −18.9996 −1.08436 −0.542182 0.840261i \(-0.682402\pi\)
−0.542182 + 0.840261i \(0.682402\pi\)
\(308\) −18.1986 −1.03696
\(309\) −3.91828 −0.222903
\(310\) −8.65714 −0.491693
\(311\) −13.1901 −0.747940 −0.373970 0.927441i \(-0.622004\pi\)
−0.373970 + 0.927441i \(0.622004\pi\)
\(312\) 15.7171 0.889803
\(313\) −8.29781 −0.469020 −0.234510 0.972114i \(-0.575349\pi\)
−0.234510 + 0.972114i \(0.575349\pi\)
\(314\) −36.7494 −2.07389
\(315\) −11.9716 −0.674522
\(316\) 49.3213 2.77454
\(317\) 3.03897 0.170686 0.0853429 0.996352i \(-0.472801\pi\)
0.0853429 + 0.996352i \(0.472801\pi\)
\(318\) −5.27421 −0.295763
\(319\) −5.32131 −0.297936
\(320\) 66.2321 3.70249
\(321\) −1.31391 −0.0733353
\(322\) −4.65087 −0.259183
\(323\) 3.78914 0.210833
\(324\) 39.1245 2.17358
\(325\) −68.3529 −3.79153
\(326\) −12.5315 −0.694053
\(327\) −1.35597 −0.0749853
\(328\) 25.9672 1.43380
\(329\) 2.58228 0.142366
\(330\) 16.1224 0.887509
\(331\) −27.4222 −1.50726 −0.753630 0.657299i \(-0.771699\pi\)
−0.753630 + 0.657299i \(0.771699\pi\)
\(332\) −8.29370 −0.455176
\(333\) −1.61772 −0.0886505
\(334\) 18.1935 0.995501
\(335\) 27.4679 1.50073
\(336\) 4.30909 0.235080
\(337\) −26.8139 −1.46064 −0.730322 0.683103i \(-0.760630\pi\)
−0.730322 + 0.683103i \(0.760630\pi\)
\(338\) −32.8737 −1.78809
\(339\) 6.02125 0.327029
\(340\) −28.2831 −1.53387
\(341\) −2.78312 −0.150715
\(342\) −22.2430 −1.20276
\(343\) −12.7031 −0.685903
\(344\) −42.9335 −2.31482
\(345\) 2.95544 0.159116
\(346\) 1.99817 0.107422
\(347\) 31.6801 1.70068 0.850339 0.526235i \(-0.176397\pi\)
0.850339 + 0.526235i \(0.176397\pi\)
\(348\) 2.79672 0.149920
\(349\) 10.4359 0.558619 0.279309 0.960201i \(-0.409894\pi\)
0.279309 + 0.960201i \(0.409894\pi\)
\(350\) −35.1345 −1.87802
\(351\) 11.2523 0.600601
\(352\) 53.4382 2.84826
\(353\) 3.53381 0.188086 0.0940429 0.995568i \(-0.470021\pi\)
0.0940429 + 0.995568i \(0.470021\pi\)
\(354\) −10.0156 −0.532323
\(355\) 23.1133 1.22673
\(356\) 50.3662 2.66940
\(357\) −0.480388 −0.0254248
\(358\) −6.73783 −0.356105
\(359\) 31.4728 1.66107 0.830536 0.556965i \(-0.188034\pi\)
0.830536 + 0.556965i \(0.188034\pi\)
\(360\) 100.590 5.30157
\(361\) −10.4160 −0.548213
\(362\) 50.1772 2.63726
\(363\) 0.984666 0.0516816
\(364\) −24.8691 −1.30350
\(365\) −72.3971 −3.78944
\(366\) −10.3836 −0.542759
\(367\) 0.916875 0.0478605 0.0239302 0.999714i \(-0.492382\pi\)
0.0239302 + 0.999714i \(0.492382\pi\)
\(368\) 20.8438 1.08656
\(369\) 9.06400 0.471853
\(370\) −6.49666 −0.337745
\(371\) 5.05619 0.262504
\(372\) 1.46273 0.0758388
\(373\) 31.6486 1.63870 0.819351 0.573292i \(-0.194334\pi\)
0.819351 + 0.573292i \(0.194334\pi\)
\(374\) −12.6762 −0.655471
\(375\) 14.1021 0.728232
\(376\) −21.6974 −1.11896
\(377\) −7.27179 −0.374516
\(378\) 5.78386 0.297489
\(379\) 25.4255 1.30602 0.653011 0.757348i \(-0.273506\pi\)
0.653011 + 0.757348i \(0.273506\pi\)
\(380\) −64.0729 −3.28687
\(381\) 6.21964 0.318642
\(382\) −41.2677 −2.11144
\(383\) −3.72533 −0.190356 −0.0951778 0.995460i \(-0.530342\pi\)
−0.0951778 + 0.995460i \(0.530342\pi\)
\(384\) −4.53187 −0.231266
\(385\) −15.4559 −0.787708
\(386\) −34.1515 −1.73826
\(387\) −14.9862 −0.761792
\(388\) 89.1531 4.52606
\(389\) −30.9040 −1.56690 −0.783448 0.621457i \(-0.786541\pi\)
−0.783448 + 0.621457i \(0.786541\pi\)
\(390\) 22.0320 1.11563
\(391\) −2.32371 −0.117515
\(392\) 49.4960 2.49992
\(393\) −4.08459 −0.206040
\(394\) 18.2335 0.918592
\(395\) 41.8883 2.10763
\(396\) 53.3749 2.68219
\(397\) 0.774018 0.0388468 0.0194234 0.999811i \(-0.493817\pi\)
0.0194234 + 0.999811i \(0.493817\pi\)
\(398\) 43.9229 2.20166
\(399\) −1.08828 −0.0544820
\(400\) 157.462 7.87311
\(401\) −0.316313 −0.0157959 −0.00789796 0.999969i \(-0.502514\pi\)
−0.00789796 + 0.999969i \(0.502514\pi\)
\(402\) −6.47020 −0.322704
\(403\) −3.80326 −0.189454
\(404\) 49.4350 2.45948
\(405\) 33.2282 1.65112
\(406\) −3.73783 −0.185505
\(407\) −2.08856 −0.103526
\(408\) 4.03642 0.199833
\(409\) −14.4091 −0.712483 −0.356241 0.934394i \(-0.615942\pi\)
−0.356241 + 0.934394i \(0.615942\pi\)
\(410\) 36.4004 1.79769
\(411\) 0.809589 0.0399341
\(412\) −52.0942 −2.56650
\(413\) 9.60158 0.472463
\(414\) 13.6406 0.670401
\(415\) −7.04380 −0.345767
\(416\) 73.0256 3.58037
\(417\) −6.19883 −0.303558
\(418\) −28.7168 −1.40459
\(419\) −17.1892 −0.839747 −0.419874 0.907583i \(-0.637926\pi\)
−0.419874 + 0.907583i \(0.637926\pi\)
\(420\) 8.12318 0.396371
\(421\) −39.7919 −1.93934 −0.969670 0.244418i \(-0.921403\pi\)
−0.969670 + 0.244418i \(0.921403\pi\)
\(422\) −25.8260 −1.25719
\(423\) −7.57363 −0.368242
\(424\) −42.4842 −2.06322
\(425\) −17.5542 −0.851506
\(426\) −5.44445 −0.263785
\(427\) 9.95437 0.481726
\(428\) −17.4687 −0.844380
\(429\) 7.08290 0.341965
\(430\) −60.1836 −2.90231
\(431\) 21.9760 1.05855 0.529273 0.848451i \(-0.322465\pi\)
0.529273 + 0.848451i \(0.322465\pi\)
\(432\) −25.9215 −1.24715
\(433\) −20.7102 −0.995268 −0.497634 0.867387i \(-0.665798\pi\)
−0.497634 + 0.867387i \(0.665798\pi\)
\(434\) −1.95494 −0.0938401
\(435\) 2.37524 0.113884
\(436\) −18.0279 −0.863378
\(437\) −5.26417 −0.251819
\(438\) 17.0535 0.814848
\(439\) 20.2231 0.965195 0.482598 0.875842i \(-0.339693\pi\)
0.482598 + 0.875842i \(0.339693\pi\)
\(440\) 129.867 6.19119
\(441\) 17.2769 0.822709
\(442\) −17.3226 −0.823952
\(443\) 26.9756 1.28165 0.640824 0.767688i \(-0.278593\pi\)
0.640824 + 0.767688i \(0.278593\pi\)
\(444\) 1.09769 0.0520939
\(445\) 42.7758 2.02777
\(446\) −47.2479 −2.23725
\(447\) 1.87054 0.0884733
\(448\) 14.9564 0.706624
\(449\) −35.5051 −1.67559 −0.837795 0.545984i \(-0.816156\pi\)
−0.837795 + 0.545984i \(0.816156\pi\)
\(450\) 103.047 4.85767
\(451\) 11.7021 0.551031
\(452\) 80.0535 3.76540
\(453\) 5.05098 0.237316
\(454\) −53.9269 −2.53092
\(455\) −21.1212 −0.990178
\(456\) 9.14416 0.428215
\(457\) −15.6417 −0.731688 −0.365844 0.930676i \(-0.619220\pi\)
−0.365844 + 0.930676i \(0.619220\pi\)
\(458\) −21.7612 −1.01683
\(459\) 2.88978 0.134884
\(460\) 39.2931 1.83205
\(461\) 38.4059 1.78874 0.894369 0.447329i \(-0.147625\pi\)
0.894369 + 0.447329i \(0.147625\pi\)
\(462\) 3.64073 0.169382
\(463\) −18.6123 −0.864985 −0.432492 0.901638i \(-0.642366\pi\)
−0.432492 + 0.901638i \(0.642366\pi\)
\(464\) 16.7518 0.777682
\(465\) 1.24229 0.0576096
\(466\) −42.1494 −1.95253
\(467\) 31.3497 1.45069 0.725346 0.688384i \(-0.241680\pi\)
0.725346 + 0.688384i \(0.241680\pi\)
\(468\) 72.9391 3.37161
\(469\) 6.20274 0.286416
\(470\) −30.4152 −1.40295
\(471\) 5.27348 0.242989
\(472\) −80.6766 −3.71344
\(473\) −19.3480 −0.889622
\(474\) −9.86701 −0.453207
\(475\) −39.7676 −1.82466
\(476\) −6.38684 −0.292740
\(477\) −14.8294 −0.678991
\(478\) 21.0006 0.960546
\(479\) −14.7356 −0.673288 −0.336644 0.941632i \(-0.609292\pi\)
−0.336644 + 0.941632i \(0.609292\pi\)
\(480\) −23.8529 −1.08873
\(481\) −2.85411 −0.130136
\(482\) 28.4742 1.29696
\(483\) 0.667392 0.0303674
\(484\) 13.0913 0.595059
\(485\) 75.7173 3.43815
\(486\) −25.6564 −1.16380
\(487\) 42.2872 1.91622 0.958108 0.286408i \(-0.0924613\pi\)
0.958108 + 0.286408i \(0.0924613\pi\)
\(488\) −83.6409 −3.78624
\(489\) 1.79824 0.0813194
\(490\) 69.3828 3.13439
\(491\) 2.59784 0.117239 0.0586194 0.998280i \(-0.481330\pi\)
0.0586194 + 0.998280i \(0.481330\pi\)
\(492\) −6.15028 −0.277276
\(493\) −1.86753 −0.0841092
\(494\) −39.2428 −1.76562
\(495\) 45.3311 2.03748
\(496\) 8.76143 0.393400
\(497\) 5.21940 0.234122
\(498\) 1.65920 0.0743507
\(499\) −36.6971 −1.64279 −0.821394 0.570361i \(-0.806804\pi\)
−0.821394 + 0.570361i \(0.806804\pi\)
\(500\) 187.490 8.38483
\(501\) −2.61073 −0.116639
\(502\) −65.2860 −2.91386
\(503\) −21.8764 −0.975420 −0.487710 0.873006i \(-0.662168\pi\)
−0.487710 + 0.873006i \(0.662168\pi\)
\(504\) 22.7151 1.01181
\(505\) 41.9849 1.86830
\(506\) 17.6108 0.782895
\(507\) 4.71732 0.209504
\(508\) 82.6912 3.66883
\(509\) 41.0281 1.81854 0.909268 0.416210i \(-0.136642\pi\)
0.909268 + 0.416210i \(0.136642\pi\)
\(510\) 5.65820 0.250549
\(511\) −16.3486 −0.723218
\(512\) 21.5002 0.950183
\(513\) 6.54655 0.289037
\(514\) 10.2621 0.452643
\(515\) −44.2433 −1.94959
\(516\) 10.1687 0.447653
\(517\) −9.77796 −0.430034
\(518\) −1.46706 −0.0644590
\(519\) −0.286734 −0.0125862
\(520\) 177.469 7.78255
\(521\) −31.8562 −1.39565 −0.697823 0.716270i \(-0.745848\pi\)
−0.697823 + 0.716270i \(0.745848\pi\)
\(522\) 10.9627 0.479826
\(523\) 40.8190 1.78489 0.892446 0.451155i \(-0.148988\pi\)
0.892446 + 0.451155i \(0.148988\pi\)
\(524\) −54.3053 −2.37234
\(525\) 5.04175 0.220040
\(526\) −12.3263 −0.537454
\(527\) −0.976745 −0.0425477
\(528\) −16.3166 −0.710090
\(529\) −19.7717 −0.859640
\(530\) −59.5538 −2.58685
\(531\) −28.1607 −1.22207
\(532\) −14.4688 −0.627303
\(533\) 15.9914 0.692666
\(534\) −10.0761 −0.436034
\(535\) −14.8360 −0.641418
\(536\) −52.1181 −2.25116
\(537\) 0.966868 0.0417234
\(538\) 53.1813 2.29281
\(539\) 22.3054 0.960761
\(540\) −48.8652 −2.10282
\(541\) −18.3008 −0.786813 −0.393406 0.919365i \(-0.628703\pi\)
−0.393406 + 0.919365i \(0.628703\pi\)
\(542\) −54.1174 −2.32454
\(543\) −7.20034 −0.308996
\(544\) 18.7543 0.804083
\(545\) −15.3110 −0.655850
\(546\) 4.97521 0.212919
\(547\) −29.1204 −1.24510 −0.622549 0.782581i \(-0.713903\pi\)
−0.622549 + 0.782581i \(0.713903\pi\)
\(548\) 10.7636 0.459799
\(549\) −29.1954 −1.24603
\(550\) 133.039 5.67280
\(551\) −4.23072 −0.180235
\(552\) −5.60772 −0.238680
\(553\) 9.45914 0.402243
\(554\) −0.699134 −0.0297033
\(555\) 0.932259 0.0395722
\(556\) −82.4145 −3.49516
\(557\) −14.9732 −0.634434 −0.317217 0.948353i \(-0.602748\pi\)
−0.317217 + 0.948353i \(0.602748\pi\)
\(558\) 5.73368 0.242726
\(559\) −26.4399 −1.11829
\(560\) 48.6562 2.05610
\(561\) 1.81902 0.0767989
\(562\) −47.3502 −1.99735
\(563\) 7.38518 0.311248 0.155624 0.987816i \(-0.450261\pi\)
0.155624 + 0.987816i \(0.450261\pi\)
\(564\) 5.13900 0.216391
\(565\) 67.9891 2.86032
\(566\) 45.9876 1.93300
\(567\) 7.50354 0.315119
\(568\) −43.8556 −1.84014
\(569\) −11.3481 −0.475738 −0.237869 0.971297i \(-0.576449\pi\)
−0.237869 + 0.971297i \(0.576449\pi\)
\(570\) 12.8182 0.536894
\(571\) −11.5038 −0.481421 −0.240710 0.970597i \(-0.577380\pi\)
−0.240710 + 0.970597i \(0.577380\pi\)
\(572\) 94.1683 3.93737
\(573\) 5.92185 0.247389
\(574\) 8.21987 0.343091
\(575\) 24.3877 1.01704
\(576\) −43.8659 −1.82775
\(577\) −0.987143 −0.0410953 −0.0205476 0.999789i \(-0.506541\pi\)
−0.0205476 + 0.999789i \(0.506541\pi\)
\(578\) 40.7675 1.69570
\(579\) 4.90068 0.203665
\(580\) 31.5792 1.31126
\(581\) −1.59062 −0.0659899
\(582\) −17.8356 −0.739310
\(583\) −19.1455 −0.792927
\(584\) 137.368 5.68431
\(585\) 61.9468 2.56119
\(586\) −30.2009 −1.24759
\(587\) 11.4599 0.473003 0.236501 0.971631i \(-0.423999\pi\)
0.236501 + 0.971631i \(0.423999\pi\)
\(588\) −11.7230 −0.483450
\(589\) −2.21273 −0.0911740
\(590\) −113.091 −4.65590
\(591\) −2.61648 −0.107628
\(592\) 6.57492 0.270228
\(593\) 22.8000 0.936284 0.468142 0.883653i \(-0.344924\pi\)
0.468142 + 0.883653i \(0.344924\pi\)
\(594\) −21.9009 −0.898605
\(595\) −5.42431 −0.222375
\(596\) 24.8691 1.01868
\(597\) −6.30287 −0.257959
\(598\) 24.0659 0.984128
\(599\) 16.2486 0.663898 0.331949 0.943297i \(-0.392294\pi\)
0.331949 + 0.943297i \(0.392294\pi\)
\(600\) −42.3629 −1.72946
\(601\) 9.55812 0.389884 0.194942 0.980815i \(-0.437548\pi\)
0.194942 + 0.980815i \(0.437548\pi\)
\(602\) −13.5905 −0.553909
\(603\) −18.1921 −0.740842
\(604\) 67.1536 2.73244
\(605\) 11.1184 0.452026
\(606\) −9.88977 −0.401744
\(607\) 15.2516 0.619042 0.309521 0.950893i \(-0.399831\pi\)
0.309521 + 0.950893i \(0.399831\pi\)
\(608\) 42.4862 1.72304
\(609\) 0.536372 0.0217349
\(610\) −117.247 −4.74718
\(611\) −13.3620 −0.540569
\(612\) 18.7321 0.757200
\(613\) −21.9613 −0.887009 −0.443505 0.896272i \(-0.646265\pi\)
−0.443505 + 0.896272i \(0.646265\pi\)
\(614\) 50.5347 2.03941
\(615\) −5.22340 −0.210628
\(616\) 29.3264 1.18159
\(617\) 20.8786 0.840541 0.420270 0.907399i \(-0.361935\pi\)
0.420270 + 0.907399i \(0.361935\pi\)
\(618\) 10.4217 0.419224
\(619\) 10.3499 0.415998 0.207999 0.978129i \(-0.433305\pi\)
0.207999 + 0.978129i \(0.433305\pi\)
\(620\) 16.5164 0.663315
\(621\) −4.01472 −0.161105
\(622\) 35.0826 1.40669
\(623\) 9.65954 0.387001
\(624\) −22.2974 −0.892609
\(625\) 91.3681 3.65472
\(626\) 22.0703 0.882108
\(627\) 4.12082 0.164570
\(628\) 70.1118 2.79777
\(629\) −0.732987 −0.0292261
\(630\) 31.8417 1.26860
\(631\) −42.4745 −1.69088 −0.845441 0.534069i \(-0.820662\pi\)
−0.845441 + 0.534069i \(0.820662\pi\)
\(632\) −79.4797 −3.16153
\(633\) 3.70599 0.147300
\(634\) −8.08299 −0.321017
\(635\) 70.2292 2.78696
\(636\) 10.0623 0.398997
\(637\) 30.4813 1.20771
\(638\) 14.1535 0.560342
\(639\) −15.3081 −0.605578
\(640\) −51.1717 −2.02274
\(641\) −30.8240 −1.21748 −0.608738 0.793371i \(-0.708324\pi\)
−0.608738 + 0.793371i \(0.708324\pi\)
\(642\) 3.49471 0.137925
\(643\) −24.8861 −0.981413 −0.490707 0.871325i \(-0.663261\pi\)
−0.490707 + 0.871325i \(0.663261\pi\)
\(644\) 8.87310 0.349649
\(645\) 8.63625 0.340052
\(646\) −10.0783 −0.396524
\(647\) −9.85005 −0.387245 −0.193623 0.981076i \(-0.562024\pi\)
−0.193623 + 0.981076i \(0.562024\pi\)
\(648\) −63.0479 −2.47676
\(649\) −36.3569 −1.42713
\(650\) 181.803 7.13092
\(651\) 0.280531 0.0109949
\(652\) 23.9080 0.936308
\(653\) −29.1305 −1.13996 −0.569982 0.821657i \(-0.693050\pi\)
−0.569982 + 0.821657i \(0.693050\pi\)
\(654\) 3.60658 0.141028
\(655\) −46.1212 −1.80210
\(656\) −36.8389 −1.43832
\(657\) 47.9490 1.87067
\(658\) −6.86830 −0.267754
\(659\) −14.4102 −0.561343 −0.280671 0.959804i \(-0.590557\pi\)
−0.280671 + 0.959804i \(0.590557\pi\)
\(660\) −30.7589 −1.19729
\(661\) −1.99796 −0.0777117 −0.0388559 0.999245i \(-0.512371\pi\)
−0.0388559 + 0.999245i \(0.512371\pi\)
\(662\) 72.9369 2.83477
\(663\) 2.48576 0.0965390
\(664\) 13.3650 0.518664
\(665\) −12.2883 −0.476520
\(666\) 4.30278 0.166729
\(667\) 2.59452 0.100460
\(668\) −34.7101 −1.34297
\(669\) 6.77999 0.262129
\(670\) −73.0584 −2.82249
\(671\) −37.6928 −1.45511
\(672\) −5.38641 −0.207785
\(673\) 8.23879 0.317582 0.158791 0.987312i \(-0.449240\pi\)
0.158791 + 0.987312i \(0.449240\pi\)
\(674\) 71.3189 2.74710
\(675\) −30.3288 −1.16735
\(676\) 62.7176 2.41222
\(677\) 45.0078 1.72979 0.864894 0.501954i \(-0.167385\pi\)
0.864894 + 0.501954i \(0.167385\pi\)
\(678\) −16.0152 −0.615059
\(679\) 17.0983 0.656174
\(680\) 45.5774 1.74781
\(681\) 7.73842 0.296537
\(682\) 7.40249 0.283456
\(683\) 10.5565 0.403934 0.201967 0.979392i \(-0.435267\pi\)
0.201967 + 0.979392i \(0.435267\pi\)
\(684\) 42.4359 1.62258
\(685\) 9.14149 0.349279
\(686\) 33.7874 1.29001
\(687\) 3.12270 0.119138
\(688\) 60.9086 2.32212
\(689\) −26.1632 −0.996738
\(690\) −7.86082 −0.299256
\(691\) 21.6051 0.821895 0.410948 0.911659i \(-0.365198\pi\)
0.410948 + 0.911659i \(0.365198\pi\)
\(692\) −3.81217 −0.144917
\(693\) 10.2366 0.388855
\(694\) −84.2621 −3.19855
\(695\) −69.9943 −2.65503
\(696\) −4.50682 −0.170831
\(697\) 4.10689 0.155560
\(698\) −27.7571 −1.05062
\(699\) 6.04836 0.228770
\(700\) 67.0309 2.53353
\(701\) −18.7447 −0.707979 −0.353990 0.935249i \(-0.615175\pi\)
−0.353990 + 0.935249i \(0.615175\pi\)
\(702\) −29.9285 −1.12958
\(703\) −1.66052 −0.0626276
\(704\) −56.6333 −2.13445
\(705\) 4.36453 0.164378
\(706\) −9.39915 −0.353742
\(707\) 9.48095 0.356568
\(708\) 19.1081 0.718127
\(709\) −26.6013 −0.999032 −0.499516 0.866305i \(-0.666489\pi\)
−0.499516 + 0.866305i \(0.666489\pi\)
\(710\) −61.4762 −2.30716
\(711\) −27.7429 −1.04044
\(712\) −81.1636 −3.04173
\(713\) 1.35697 0.0508190
\(714\) 1.27772 0.0478176
\(715\) 79.9767 2.99096
\(716\) 12.8547 0.480402
\(717\) −3.01355 −0.112543
\(718\) −83.7107 −3.12406
\(719\) −32.0325 −1.19461 −0.597306 0.802013i \(-0.703762\pi\)
−0.597306 + 0.802013i \(0.703762\pi\)
\(720\) −142.705 −5.31829
\(721\) −9.99094 −0.372082
\(722\) 27.7044 1.03105
\(723\) −4.08600 −0.151960
\(724\) −95.7298 −3.55777
\(725\) 19.6000 0.727926
\(726\) −2.61899 −0.0971999
\(727\) −30.2168 −1.12068 −0.560339 0.828263i \(-0.689329\pi\)
−0.560339 + 0.828263i \(0.689329\pi\)
\(728\) 40.0758 1.48531
\(729\) −19.4488 −0.720326
\(730\) 192.560 7.12697
\(731\) −6.79024 −0.251146
\(732\) 19.8102 0.732206
\(733\) −10.4059 −0.384352 −0.192176 0.981360i \(-0.561554\pi\)
−0.192176 + 0.981360i \(0.561554\pi\)
\(734\) −2.43868 −0.0900134
\(735\) −9.95631 −0.367244
\(736\) −26.0549 −0.960397
\(737\) −23.4870 −0.865156
\(738\) −24.1082 −0.887436
\(739\) −1.81729 −0.0668500 −0.0334250 0.999441i \(-0.510641\pi\)
−0.0334250 + 0.999441i \(0.510641\pi\)
\(740\) 12.3945 0.455633
\(741\) 5.63128 0.206870
\(742\) −13.4483 −0.493704
\(743\) 22.2227 0.815271 0.407635 0.913145i \(-0.366353\pi\)
0.407635 + 0.913145i \(0.366353\pi\)
\(744\) −2.35714 −0.0864168
\(745\) 21.1212 0.773821
\(746\) −84.1782 −3.08198
\(747\) 4.66515 0.170689
\(748\) 24.1841 0.884259
\(749\) −3.35025 −0.122415
\(750\) −37.5086 −1.36962
\(751\) −0.417084 −0.0152196 −0.00760980 0.999971i \(-0.502422\pi\)
−0.00760980 + 0.999971i \(0.502422\pi\)
\(752\) 30.7816 1.12249
\(753\) 9.36843 0.341405
\(754\) 19.3413 0.704370
\(755\) 57.0332 2.07565
\(756\) −11.0346 −0.401326
\(757\) 31.1517 1.13223 0.566114 0.824327i \(-0.308446\pi\)
0.566114 + 0.824327i \(0.308446\pi\)
\(758\) −67.6263 −2.45630
\(759\) −2.52712 −0.0917286
\(760\) 103.251 3.74533
\(761\) −23.8080 −0.863040 −0.431520 0.902103i \(-0.642023\pi\)
−0.431520 + 0.902103i \(0.642023\pi\)
\(762\) −16.5429 −0.599285
\(763\) −3.45749 −0.125170
\(764\) 78.7320 2.84843
\(765\) 15.9091 0.575193
\(766\) 9.90856 0.358011
\(767\) −49.6833 −1.79396
\(768\) 0.322463 0.0116359
\(769\) 23.5490 0.849198 0.424599 0.905382i \(-0.360415\pi\)
0.424599 + 0.905382i \(0.360415\pi\)
\(770\) 41.1094 1.48148
\(771\) −1.47260 −0.0530343
\(772\) 65.1553 2.34499
\(773\) −33.0463 −1.18859 −0.594296 0.804246i \(-0.702569\pi\)
−0.594296 + 0.804246i \(0.702569\pi\)
\(774\) 39.8600 1.43274
\(775\) 10.2511 0.368230
\(776\) −143.667 −5.15736
\(777\) 0.210521 0.00755240
\(778\) 82.1978 2.94693
\(779\) 9.30380 0.333343
\(780\) −42.0333 −1.50503
\(781\) −19.7635 −0.707195
\(782\) 6.18056 0.221016
\(783\) −3.22656 −0.115308
\(784\) −70.2186 −2.50781
\(785\) 59.5456 2.12527
\(786\) 10.8641 0.387509
\(787\) −1.54959 −0.0552368 −0.0276184 0.999619i \(-0.508792\pi\)
−0.0276184 + 0.999619i \(0.508792\pi\)
\(788\) −34.7866 −1.23922
\(789\) 1.76881 0.0629713
\(790\) −111.414 −3.96392
\(791\) 15.3532 0.545895
\(792\) −86.0120 −3.05630
\(793\) −51.5088 −1.82913
\(794\) −2.05871 −0.0730610
\(795\) 8.54588 0.303091
\(796\) −83.7977 −2.97013
\(797\) 21.5306 0.762653 0.381326 0.924440i \(-0.375467\pi\)
0.381326 + 0.924440i \(0.375467\pi\)
\(798\) 2.89457 0.102467
\(799\) −3.43160 −0.121401
\(800\) −196.829 −6.95896
\(801\) −28.3307 −1.00101
\(802\) 0.841322 0.0297081
\(803\) 61.9048 2.18457
\(804\) 12.3441 0.435342
\(805\) 7.53588 0.265605
\(806\) 10.1158 0.356314
\(807\) −7.63142 −0.268639
\(808\) −79.6630 −2.80253
\(809\) 6.72929 0.236589 0.118295 0.992979i \(-0.462257\pi\)
0.118295 + 0.992979i \(0.462257\pi\)
\(810\) −88.3797 −3.10535
\(811\) −41.7926 −1.46754 −0.733768 0.679400i \(-0.762240\pi\)
−0.733768 + 0.679400i \(0.762240\pi\)
\(812\) 7.13115 0.250254
\(813\) 7.76575 0.272357
\(814\) 5.55511 0.194707
\(815\) 20.3049 0.711250
\(816\) −5.72637 −0.200463
\(817\) −15.3827 −0.538172
\(818\) 38.3249 1.34000
\(819\) 13.9887 0.488805
\(820\) −69.4460 −2.42516
\(821\) −39.0111 −1.36150 −0.680749 0.732517i \(-0.738345\pi\)
−0.680749 + 0.732517i \(0.738345\pi\)
\(822\) −2.15333 −0.0751059
\(823\) 41.1351 1.43388 0.716940 0.697135i \(-0.245542\pi\)
0.716940 + 0.697135i \(0.245542\pi\)
\(824\) 83.9481 2.92447
\(825\) −19.0909 −0.664658
\(826\) −25.5381 −0.888583
\(827\) −29.1296 −1.01294 −0.506468 0.862259i \(-0.669049\pi\)
−0.506468 + 0.862259i \(0.669049\pi\)
\(828\) −26.0241 −0.904399
\(829\) 39.1164 1.35857 0.679285 0.733874i \(-0.262290\pi\)
0.679285 + 0.733874i \(0.262290\pi\)
\(830\) 18.7349 0.650299
\(831\) 0.100325 0.00348022
\(832\) −77.3918 −2.68308
\(833\) 7.82814 0.271229
\(834\) 16.4875 0.570916
\(835\) −29.4791 −1.02017
\(836\) 54.7870 1.89485
\(837\) −1.68754 −0.0583299
\(838\) 45.7194 1.57935
\(839\) 45.1837 1.55991 0.779957 0.625833i \(-0.215241\pi\)
0.779957 + 0.625833i \(0.215241\pi\)
\(840\) −13.0903 −0.451657
\(841\) −26.9148 −0.928098
\(842\) 105.838 3.64741
\(843\) 6.79468 0.234021
\(844\) 49.2718 1.69601
\(845\) 53.2658 1.83240
\(846\) 20.1442 0.692571
\(847\) 2.51073 0.0862697
\(848\) 60.2713 2.06972
\(849\) −6.59915 −0.226482
\(850\) 46.6904 1.60147
\(851\) 1.01832 0.0349077
\(852\) 10.3871 0.355857
\(853\) −4.79182 −0.164069 −0.0820344 0.996630i \(-0.526142\pi\)
−0.0820344 + 0.996630i \(0.526142\pi\)
\(854\) −26.4764 −0.906004
\(855\) 36.0406 1.23256
\(856\) 28.1502 0.962154
\(857\) −34.8743 −1.19128 −0.595642 0.803250i \(-0.703102\pi\)
−0.595642 + 0.803250i \(0.703102\pi\)
\(858\) −18.8389 −0.643150
\(859\) 13.0873 0.446532 0.223266 0.974758i \(-0.428328\pi\)
0.223266 + 0.974758i \(0.428328\pi\)
\(860\) 114.820 3.91534
\(861\) −1.17954 −0.0401985
\(862\) −58.4513 −1.99086
\(863\) 41.1000 1.39906 0.699531 0.714603i \(-0.253392\pi\)
0.699531 + 0.714603i \(0.253392\pi\)
\(864\) 32.4021 1.10234
\(865\) −3.23766 −0.110084
\(866\) 55.0845 1.87185
\(867\) −5.85006 −0.198679
\(868\) 3.72970 0.126594
\(869\) −35.8176 −1.21503
\(870\) −6.31761 −0.214187
\(871\) −32.0960 −1.08753
\(872\) 29.0513 0.983802
\(873\) −50.1480 −1.69725
\(874\) 14.0015 0.473608
\(875\) 35.9581 1.21560
\(876\) −32.5353 −1.09927
\(877\) 20.0958 0.678586 0.339293 0.940681i \(-0.389812\pi\)
0.339293 + 0.940681i \(0.389812\pi\)
\(878\) −53.7889 −1.81529
\(879\) 4.33377 0.146175
\(880\) −184.240 −6.21071
\(881\) 39.1032 1.31742 0.658710 0.752397i \(-0.271102\pi\)
0.658710 + 0.752397i \(0.271102\pi\)
\(882\) −45.9527 −1.54731
\(883\) 29.4412 0.990776 0.495388 0.868672i \(-0.335026\pi\)
0.495388 + 0.868672i \(0.335026\pi\)
\(884\) 33.0486 1.11155
\(885\) 16.2284 0.545512
\(886\) −71.7490 −2.41046
\(887\) 9.60624 0.322546 0.161273 0.986910i \(-0.448440\pi\)
0.161273 + 0.986910i \(0.448440\pi\)
\(888\) −1.76889 −0.0593600
\(889\) 15.8590 0.531895
\(890\) −113.774 −3.81371
\(891\) −28.4126 −0.951857
\(892\) 90.1411 3.01815
\(893\) −7.77399 −0.260147
\(894\) −4.97521 −0.166396
\(895\) 10.9174 0.364929
\(896\) −11.5555 −0.386042
\(897\) −3.45342 −0.115306
\(898\) 94.4357 3.15136
\(899\) 1.09057 0.0363727
\(900\) −196.596 −6.55321
\(901\) −6.71918 −0.223848
\(902\) −31.1250 −1.03635
\(903\) 1.95022 0.0648993
\(904\) −129.004 −4.29060
\(905\) −81.3029 −2.70260
\(906\) −13.4345 −0.446331
\(907\) 45.6832 1.51689 0.758443 0.651740i \(-0.225960\pi\)
0.758443 + 0.651740i \(0.225960\pi\)
\(908\) 102.884 3.41431
\(909\) −27.8069 −0.922296
\(910\) 56.1777 1.86227
\(911\) 34.0288 1.12742 0.563712 0.825971i \(-0.309373\pi\)
0.563712 + 0.825971i \(0.309373\pi\)
\(912\) −12.9726 −0.429565
\(913\) 6.02296 0.199331
\(914\) 41.6034 1.37612
\(915\) 16.8247 0.556207
\(916\) 41.5168 1.37175
\(917\) −10.4150 −0.343934
\(918\) −7.68618 −0.253682
\(919\) −19.8316 −0.654185 −0.327092 0.944992i \(-0.606069\pi\)
−0.327092 + 0.944992i \(0.606069\pi\)
\(920\) −63.3196 −2.08759
\(921\) −7.25165 −0.238950
\(922\) −102.151 −3.36416
\(923\) −27.0077 −0.888970
\(924\) −6.94591 −0.228504
\(925\) 7.69282 0.252938
\(926\) 49.5045 1.62682
\(927\) 29.3026 0.962425
\(928\) −20.9399 −0.687386
\(929\) 10.1442 0.332821 0.166410 0.986057i \(-0.446782\pi\)
0.166410 + 0.986057i \(0.446782\pi\)
\(930\) −3.30420 −0.108349
\(931\) 17.7340 0.581207
\(932\) 80.4140 2.63405
\(933\) −5.03430 −0.164816
\(934\) −83.3833 −2.72839
\(935\) 20.5395 0.671712
\(936\) −117.539 −3.84189
\(937\) −34.8160 −1.13739 −0.568695 0.822549i \(-0.692551\pi\)
−0.568695 + 0.822549i \(0.692551\pi\)
\(938\) −16.4979 −0.538676
\(939\) −3.16706 −0.103353
\(940\) 58.0271 1.89264
\(941\) 45.2417 1.47484 0.737418 0.675436i \(-0.236045\pi\)
0.737418 + 0.675436i \(0.236045\pi\)
\(942\) −14.0263 −0.457001
\(943\) −5.70561 −0.185800
\(944\) 114.454 3.72515
\(945\) −9.37167 −0.304860
\(946\) 51.4614 1.67315
\(947\) 2.74647 0.0892484 0.0446242 0.999004i \(-0.485791\pi\)
0.0446242 + 0.999004i \(0.485791\pi\)
\(948\) 18.8246 0.611396
\(949\) 84.5955 2.74609
\(950\) 105.773 3.43173
\(951\) 1.15990 0.0376122
\(952\) 10.2922 0.333572
\(953\) 0.142756 0.00462430 0.00231215 0.999997i \(-0.499264\pi\)
0.00231215 + 0.999997i \(0.499264\pi\)
\(954\) 39.4429 1.27701
\(955\) 66.8667 2.16376
\(956\) −40.0657 −1.29582
\(957\) −2.03100 −0.0656530
\(958\) 39.1935 1.26628
\(959\) 2.06431 0.0666602
\(960\) 25.2790 0.815878
\(961\) −30.4296 −0.981600
\(962\) 7.59130 0.244753
\(963\) 9.82601 0.316639
\(964\) −54.3240 −1.74966
\(965\) 55.3361 1.78133
\(966\) −1.77512 −0.0571134
\(967\) 6.53144 0.210037 0.105018 0.994470i \(-0.466510\pi\)
0.105018 + 0.994470i \(0.466510\pi\)
\(968\) −21.0962 −0.678058
\(969\) 1.44621 0.0464591
\(970\) −201.391 −6.46628
\(971\) −18.7874 −0.602917 −0.301459 0.953479i \(-0.597474\pi\)
−0.301459 + 0.953479i \(0.597474\pi\)
\(972\) 48.9482 1.57002
\(973\) −15.8060 −0.506716
\(974\) −112.475 −3.60392
\(975\) −26.0885 −0.835500
\(976\) 118.659 3.79818
\(977\) −39.2935 −1.25711 −0.628555 0.777765i \(-0.716353\pi\)
−0.628555 + 0.777765i \(0.716353\pi\)
\(978\) −4.78293 −0.152941
\(979\) −36.5764 −1.16899
\(980\) −132.371 −4.22843
\(981\) 10.1406 0.323763
\(982\) −6.90968 −0.220497
\(983\) −21.2400 −0.677451 −0.338725 0.940885i \(-0.609996\pi\)
−0.338725 + 0.940885i \(0.609996\pi\)
\(984\) 9.91098 0.315951
\(985\) −29.5440 −0.941352
\(986\) 4.96721 0.158188
\(987\) 0.985589 0.0313716
\(988\) 74.8688 2.38189
\(989\) 9.43353 0.299969
\(990\) −120.571 −3.83198
\(991\) −32.2931 −1.02582 −0.512912 0.858441i \(-0.671433\pi\)
−0.512912 + 0.858441i \(0.671433\pi\)
\(992\) −10.9519 −0.347723
\(993\) −10.4663 −0.332139
\(994\) −13.8824 −0.440324
\(995\) −71.1690 −2.25621
\(996\) −3.16549 −0.100302
\(997\) −2.03159 −0.0643412 −0.0321706 0.999482i \(-0.510242\pi\)
−0.0321706 + 0.999482i \(0.510242\pi\)
\(998\) 97.6062 3.08967
\(999\) −1.26639 −0.0400669
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 \(a_p\))