Properties

Label 5077.2.a.c.1.5
Level 5077
Weight 2
Character 5077.1
Self dual Yes
Analytic conductor 40.540
Analytic rank 0
Dimension 216
CM No

Related objects

Downloads

Learn more about

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 1.5
Character \(\chi\) = 5077.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} +O(q^{10})\) \(q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} -7.01664 q^{10} -2.00479 q^{11} -8.22206 q^{12} +4.17557 q^{13} -1.81174 q^{14} -4.26249 q^{15} +11.6862 q^{16} +0.911396 q^{17} +1.02590 q^{18} +5.60915 q^{19} +13.4043 q^{20} -1.10060 q^{21} +5.33622 q^{22} +4.77034 q^{23} +13.2771 q^{24} +1.94906 q^{25} -11.1143 q^{26} +5.47411 q^{27} +3.46106 q^{28} +9.83723 q^{29} +11.3457 q^{30} -3.67394 q^{31} -14.6833 q^{32} +3.24167 q^{33} -2.42590 q^{34} +1.79429 q^{35} -1.95984 q^{36} -5.92639 q^{37} -14.9301 q^{38} -6.75175 q^{39} -21.6454 q^{40} +2.80330 q^{41} +2.92951 q^{42} +2.17855 q^{43} -10.1941 q^{44} -1.01602 q^{45} -12.6974 q^{46} +9.07110 q^{47} -18.8961 q^{48} -6.53670 q^{49} -5.18790 q^{50} -1.47369 q^{51} +21.2322 q^{52} +3.95561 q^{53} -14.5707 q^{54} -5.28483 q^{55} -5.58897 q^{56} -9.06980 q^{57} -26.1842 q^{58} +9.57314 q^{59} -21.6742 q^{60} -10.3558 q^{61} +9.77907 q^{62} -0.262343 q^{63} +15.7109 q^{64} +11.0072 q^{65} -8.62849 q^{66} -13.7957 q^{67} +4.63433 q^{68} -7.71348 q^{69} -4.77593 q^{70} -0.634066 q^{71} +3.16478 q^{72} +14.2099 q^{73} +15.7745 q^{74} -3.15157 q^{75} +28.5218 q^{76} -1.36457 q^{77} +17.9714 q^{78} +8.42465 q^{79} +30.8060 q^{80} -7.69517 q^{81} -7.46167 q^{82} +3.21676 q^{83} -5.59641 q^{84} +2.40254 q^{85} -5.79873 q^{86} -15.9065 q^{87} +16.4616 q^{88} +3.50180 q^{89} +2.70439 q^{90} +2.84213 q^{91} +24.2566 q^{92} +5.94062 q^{93} -24.1449 q^{94} +14.7863 q^{95} +23.7424 q^{96} -14.4961 q^{97} +17.3990 q^{98} +0.772696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + O(q^{10}) \) \( 216q + 25q^{2} + 62q^{3} + 223q^{4} + 46q^{5} + 26q^{6} + 30q^{7} + 75q^{8} + 234q^{9} + 24q^{10} + 89q^{11} + 114q^{12} + 34q^{13} + 53q^{14} + 61q^{15} + 229q^{16} + 76q^{17} + 57q^{18} + 54q^{19} + 118q^{20} + 25q^{21} + 26q^{22} + 109q^{23} + 65q^{24} + 232q^{25} + 58q^{26} + 236q^{27} + 57q^{28} + 54q^{29} + 6q^{30} + 77q^{31} + 155q^{32} + 80q^{33} + 28q^{34} + 137q^{35} + 257q^{36} + 42q^{37} + 104q^{38} + 46q^{39} + 47q^{40} + 109q^{41} + 27q^{42} + 68q^{43} + 145q^{44} + 109q^{45} - 7q^{46} + 264q^{47} + 198q^{48} + 222q^{49} + 86q^{50} + 57q^{51} + 68q^{52} + 95q^{53} + 79q^{54} + 50q^{55} + 108q^{56} + 55q^{57} + 38q^{58} + 292q^{59} + 91q^{60} + 16q^{61} + 91q^{62} + 113q^{63} + 231q^{64} + 68q^{65} - 15q^{66} + 152q^{67} + 199q^{68} + 83q^{69} + 24q^{70} + 131q^{71} + 162q^{72} + 71q^{73} + 10q^{74} + 232q^{75} + 60q^{76} + 131q^{77} + 102q^{78} + 10q^{79} + 236q^{80} + 268q^{81} + 54q^{82} + 299q^{83} - 9q^{85} + 35q^{86} + 103q^{87} + 45q^{88} + 134q^{89} + 8q^{90} + 79q^{91} + 206q^{92} + 95q^{93} + 18q^{94} + 119q^{95} + 77q^{96} + 129q^{97} + 150q^{98} + 221q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.66174 −1.88214 −0.941068 0.338217i \(-0.890176\pi\)
−0.941068 + 0.338217i \(0.890176\pi\)
\(3\) −1.61696 −0.933555 −0.466777 0.884375i \(-0.654585\pi\)
−0.466777 + 0.884375i \(0.654585\pi\)
\(4\) 5.08487 2.54244
\(5\) 2.63611 1.17890 0.589452 0.807804i \(-0.299344\pi\)
0.589452 + 0.807804i \(0.299344\pi\)
\(6\) 4.30394 1.75708
\(7\) 0.680658 0.257265 0.128632 0.991692i \(-0.458941\pi\)
0.128632 + 0.991692i \(0.458941\pi\)
\(8\) −8.21113 −2.90307
\(9\) −0.385425 −0.128475
\(10\) −7.01664 −2.21886
\(11\) −2.00479 −0.604466 −0.302233 0.953234i \(-0.597732\pi\)
−0.302233 + 0.953234i \(0.597732\pi\)
\(12\) −8.22206 −2.37350
\(13\) 4.17557 1.15809 0.579047 0.815294i \(-0.303425\pi\)
0.579047 + 0.815294i \(0.303425\pi\)
\(14\) −1.81174 −0.484207
\(15\) −4.26249 −1.10057
\(16\) 11.6862 2.92154
\(17\) 0.911396 0.221046 0.110523 0.993874i \(-0.464747\pi\)
0.110523 + 0.993874i \(0.464747\pi\)
\(18\) 1.02590 0.241808
\(19\) 5.60915 1.28683 0.643414 0.765518i \(-0.277517\pi\)
0.643414 + 0.765518i \(0.277517\pi\)
\(20\) 13.4043 2.99729
\(21\) −1.10060 −0.240171
\(22\) 5.33622 1.13769
\(23\) 4.77034 0.994685 0.497343 0.867554i \(-0.334309\pi\)
0.497343 + 0.867554i \(0.334309\pi\)
\(24\) 13.2771 2.71018
\(25\) 1.94906 0.389813
\(26\) −11.1143 −2.17969
\(27\) 5.47411 1.05349
\(28\) 3.46106 0.654079
\(29\) 9.83723 1.82673 0.913364 0.407144i \(-0.133475\pi\)
0.913364 + 0.407144i \(0.133475\pi\)
\(30\) 11.3457 2.07142
\(31\) −3.67394 −0.659858 −0.329929 0.944006i \(-0.607025\pi\)
−0.329929 + 0.944006i \(0.607025\pi\)
\(32\) −14.6833 −2.59567
\(33\) 3.24167 0.564302
\(34\) −2.42590 −0.416039
\(35\) 1.79429 0.303290
\(36\) −1.95984 −0.326640
\(37\) −5.92639 −0.974293 −0.487146 0.873320i \(-0.661962\pi\)
−0.487146 + 0.873320i \(0.661962\pi\)
\(38\) −14.9301 −2.42199
\(39\) −6.75175 −1.08114
\(40\) −21.6454 −3.42244
\(41\) 2.80330 0.437802 0.218901 0.975747i \(-0.429753\pi\)
0.218901 + 0.975747i \(0.429753\pi\)
\(42\) 2.92951 0.452034
\(43\) 2.17855 0.332226 0.166113 0.986107i \(-0.446878\pi\)
0.166113 + 0.986107i \(0.446878\pi\)
\(44\) −10.1941 −1.53682
\(45\) −1.01602 −0.151460
\(46\) −12.6974 −1.87213
\(47\) 9.07110 1.32316 0.661578 0.749876i \(-0.269887\pi\)
0.661578 + 0.749876i \(0.269887\pi\)
\(48\) −18.8961 −2.72742
\(49\) −6.53670 −0.933815
\(50\) −5.18790 −0.733680
\(51\) −1.47369 −0.206359
\(52\) 21.2322 2.94438
\(53\) 3.95561 0.543345 0.271672 0.962390i \(-0.412423\pi\)
0.271672 + 0.962390i \(0.412423\pi\)
\(54\) −14.5707 −1.98282
\(55\) −5.28483 −0.712607
\(56\) −5.58897 −0.746858
\(57\) −9.06980 −1.20132
\(58\) −26.1842 −3.43815
\(59\) 9.57314 1.24632 0.623158 0.782096i \(-0.285849\pi\)
0.623158 + 0.782096i \(0.285849\pi\)
\(60\) −21.6742 −2.79813
\(61\) −10.3558 −1.32592 −0.662960 0.748655i \(-0.730700\pi\)
−0.662960 + 0.748655i \(0.730700\pi\)
\(62\) 9.77907 1.24194
\(63\) −0.262343 −0.0330521
\(64\) 15.7109 1.96386
\(65\) 11.0072 1.36528
\(66\) −8.62849 −1.06209
\(67\) −13.7957 −1.68541 −0.842707 0.538372i \(-0.819039\pi\)
−0.842707 + 0.538372i \(0.819039\pi\)
\(68\) 4.63433 0.561995
\(69\) −7.71348 −0.928593
\(70\) −4.77593 −0.570833
\(71\) −0.634066 −0.0752497 −0.0376249 0.999292i \(-0.511979\pi\)
−0.0376249 + 0.999292i \(0.511979\pi\)
\(72\) 3.16478 0.372973
\(73\) 14.2099 1.66314 0.831571 0.555418i \(-0.187442\pi\)
0.831571 + 0.555418i \(0.187442\pi\)
\(74\) 15.7745 1.83375
\(75\) −3.15157 −0.363911
\(76\) 28.5218 3.27168
\(77\) −1.36457 −0.155508
\(78\) 17.9714 2.03486
\(79\) 8.42465 0.947847 0.473923 0.880566i \(-0.342837\pi\)
0.473923 + 0.880566i \(0.342837\pi\)
\(80\) 30.8060 3.44422
\(81\) −7.69517 −0.855019
\(82\) −7.46167 −0.824004
\(83\) 3.21676 0.353086 0.176543 0.984293i \(-0.443509\pi\)
0.176543 + 0.984293i \(0.443509\pi\)
\(84\) −5.59641 −0.610618
\(85\) 2.40254 0.260592
\(86\) −5.79873 −0.625294
\(87\) −15.9065 −1.70535
\(88\) 16.4616 1.75481
\(89\) 3.50180 0.371190 0.185595 0.982626i \(-0.440579\pi\)
0.185595 + 0.982626i \(0.440579\pi\)
\(90\) 2.70439 0.285068
\(91\) 2.84213 0.297937
\(92\) 24.2566 2.52892
\(93\) 5.94062 0.616014
\(94\) −24.1449 −2.49036
\(95\) 14.7863 1.51705
\(96\) 23.7424 2.42320
\(97\) −14.4961 −1.47185 −0.735926 0.677062i \(-0.763253\pi\)
−0.735926 + 0.677062i \(0.763253\pi\)
\(98\) 17.3990 1.75757
\(99\) 0.772696 0.0776588
\(100\) 9.91074 0.991074
\(101\) 6.38621 0.635452 0.317726 0.948183i \(-0.397081\pi\)
0.317726 + 0.948183i \(0.397081\pi\)
\(102\) 3.92260 0.388395
\(103\) 9.20612 0.907106 0.453553 0.891229i \(-0.350156\pi\)
0.453553 + 0.891229i \(0.350156\pi\)
\(104\) −34.2862 −3.36203
\(105\) −2.90130 −0.283138
\(106\) −10.5288 −1.02265
\(107\) 7.06637 0.683132 0.341566 0.939858i \(-0.389043\pi\)
0.341566 + 0.939858i \(0.389043\pi\)
\(108\) 27.8352 2.67844
\(109\) −1.67781 −0.160705 −0.0803524 0.996767i \(-0.525605\pi\)
−0.0803524 + 0.996767i \(0.525605\pi\)
\(110\) 14.0669 1.34122
\(111\) 9.58276 0.909556
\(112\) 7.95429 0.751610
\(113\) −13.2686 −1.24821 −0.624103 0.781342i \(-0.714535\pi\)
−0.624103 + 0.781342i \(0.714535\pi\)
\(114\) 24.1415 2.26106
\(115\) 12.5751 1.17264
\(116\) 50.0211 4.64434
\(117\) −1.60937 −0.148786
\(118\) −25.4812 −2.34574
\(119\) 0.620349 0.0568673
\(120\) 34.9999 3.19504
\(121\) −6.98083 −0.634621
\(122\) 27.5644 2.49556
\(123\) −4.53284 −0.408713
\(124\) −18.6815 −1.67765
\(125\) −8.04260 −0.719352
\(126\) 0.698289 0.0622086
\(127\) 17.9809 1.59555 0.797775 0.602955i \(-0.206010\pi\)
0.797775 + 0.602955i \(0.206010\pi\)
\(128\) −12.4517 −1.10058
\(129\) −3.52264 −0.310151
\(130\) −29.2985 −2.56964
\(131\) 8.70288 0.760374 0.380187 0.924910i \(-0.375860\pi\)
0.380187 + 0.924910i \(0.375860\pi\)
\(132\) 16.4835 1.43470
\(133\) 3.81792 0.331055
\(134\) 36.7206 3.17218
\(135\) 14.4304 1.24197
\(136\) −7.48359 −0.641713
\(137\) 18.5888 1.58815 0.794074 0.607821i \(-0.207956\pi\)
0.794074 + 0.607821i \(0.207956\pi\)
\(138\) 20.5313 1.74774
\(139\) −15.9442 −1.35237 −0.676186 0.736731i \(-0.736368\pi\)
−0.676186 + 0.736731i \(0.736368\pi\)
\(140\) 9.12372 0.771095
\(141\) −14.6676 −1.23524
\(142\) 1.68772 0.141630
\(143\) −8.37112 −0.700028
\(144\) −4.50415 −0.375346
\(145\) 25.9320 2.15354
\(146\) −37.8231 −3.13026
\(147\) 10.5696 0.871768
\(148\) −30.1349 −2.47708
\(149\) −2.48712 −0.203753 −0.101876 0.994797i \(-0.532485\pi\)
−0.101876 + 0.994797i \(0.532485\pi\)
\(150\) 8.38866 0.684931
\(151\) −15.8071 −1.28636 −0.643181 0.765714i \(-0.722386\pi\)
−0.643181 + 0.765714i \(0.722386\pi\)
\(152\) −46.0575 −3.73576
\(153\) −0.351275 −0.0283989
\(154\) 3.63214 0.292686
\(155\) −9.68489 −0.777909
\(156\) −34.3318 −2.74874
\(157\) 9.85523 0.786533 0.393267 0.919424i \(-0.371345\pi\)
0.393267 + 0.919424i \(0.371345\pi\)
\(158\) −22.4242 −1.78398
\(159\) −6.39608 −0.507242
\(160\) −38.7068 −3.06004
\(161\) 3.24697 0.255897
\(162\) 20.4826 1.60926
\(163\) −1.02022 −0.0799099 −0.0399550 0.999201i \(-0.512721\pi\)
−0.0399550 + 0.999201i \(0.512721\pi\)
\(164\) 14.2544 1.11308
\(165\) 8.54539 0.665257
\(166\) −8.56219 −0.664555
\(167\) −15.7990 −1.22257 −0.611283 0.791412i \(-0.709346\pi\)
−0.611283 + 0.791412i \(0.709346\pi\)
\(168\) 9.03717 0.697233
\(169\) 4.43537 0.341182
\(170\) −6.39493 −0.490469
\(171\) −2.16191 −0.165325
\(172\) 11.0776 0.844662
\(173\) −4.48033 −0.340633 −0.170317 0.985389i \(-0.554479\pi\)
−0.170317 + 0.985389i \(0.554479\pi\)
\(174\) 42.3389 3.20970
\(175\) 1.32665 0.100285
\(176\) −23.4283 −1.76597
\(177\) −15.4794 −1.16350
\(178\) −9.32089 −0.698630
\(179\) 18.4353 1.37792 0.688959 0.724801i \(-0.258068\pi\)
0.688959 + 0.724801i \(0.258068\pi\)
\(180\) −5.16635 −0.385077
\(181\) −23.4153 −1.74045 −0.870223 0.492657i \(-0.836026\pi\)
−0.870223 + 0.492657i \(0.836026\pi\)
\(182\) −7.56503 −0.560757
\(183\) 16.7449 1.23782
\(184\) −39.1699 −2.88765
\(185\) −15.6226 −1.14860
\(186\) −15.8124 −1.15942
\(187\) −1.82715 −0.133615
\(188\) 46.1254 3.36404
\(189\) 3.72600 0.271027
\(190\) −39.3574 −2.85529
\(191\) −8.06028 −0.583221 −0.291611 0.956537i \(-0.594191\pi\)
−0.291611 + 0.956537i \(0.594191\pi\)
\(192\) −25.4039 −1.83337
\(193\) 25.7615 1.85436 0.927178 0.374621i \(-0.122227\pi\)
0.927178 + 0.374621i \(0.122227\pi\)
\(194\) 38.5848 2.77023
\(195\) −17.7983 −1.27456
\(196\) −33.2383 −2.37416
\(197\) −21.0855 −1.50228 −0.751141 0.660142i \(-0.770496\pi\)
−0.751141 + 0.660142i \(0.770496\pi\)
\(198\) −2.05672 −0.146164
\(199\) 19.1203 1.35540 0.677701 0.735337i \(-0.262976\pi\)
0.677701 + 0.735337i \(0.262976\pi\)
\(200\) −16.0040 −1.13165
\(201\) 22.3072 1.57343
\(202\) −16.9984 −1.19601
\(203\) 6.69579 0.469952
\(204\) −7.49355 −0.524653
\(205\) 7.38981 0.516127
\(206\) −24.5043 −1.70730
\(207\) −1.83861 −0.127792
\(208\) 48.7964 3.38342
\(209\) −11.2452 −0.777844
\(210\) 7.72251 0.532904
\(211\) −16.4658 −1.13355 −0.566775 0.823872i \(-0.691809\pi\)
−0.566775 + 0.823872i \(0.691809\pi\)
\(212\) 20.1138 1.38142
\(213\) 1.02526 0.0702498
\(214\) −18.8088 −1.28575
\(215\) 5.74289 0.391662
\(216\) −44.9487 −3.05837
\(217\) −2.50069 −0.169758
\(218\) 4.46589 0.302468
\(219\) −22.9769 −1.55264
\(220\) −26.8727 −1.81176
\(221\) 3.80560 0.255992
\(222\) −25.5068 −1.71191
\(223\) 9.76731 0.654068 0.327034 0.945013i \(-0.393951\pi\)
0.327034 + 0.945013i \(0.393951\pi\)
\(224\) −9.99433 −0.667774
\(225\) −0.751218 −0.0500812
\(226\) 35.3176 2.34929
\(227\) 22.1171 1.46796 0.733980 0.679171i \(-0.237660\pi\)
0.733980 + 0.679171i \(0.237660\pi\)
\(228\) −46.1188 −3.05429
\(229\) 6.38480 0.421919 0.210960 0.977495i \(-0.432341\pi\)
0.210960 + 0.977495i \(0.432341\pi\)
\(230\) −33.4718 −2.20706
\(231\) 2.20647 0.145175
\(232\) −80.7748 −5.30313
\(233\) −23.4136 −1.53388 −0.766940 0.641719i \(-0.778221\pi\)
−0.766940 + 0.641719i \(0.778221\pi\)
\(234\) 4.28373 0.280036
\(235\) 23.9124 1.55987
\(236\) 48.6782 3.16868
\(237\) −13.6224 −0.884867
\(238\) −1.65121 −0.107032
\(239\) −2.80201 −0.181247 −0.0906235 0.995885i \(-0.528886\pi\)
−0.0906235 + 0.995885i \(0.528886\pi\)
\(240\) −49.8123 −3.21537
\(241\) −15.4865 −0.997572 −0.498786 0.866725i \(-0.666221\pi\)
−0.498786 + 0.866725i \(0.666221\pi\)
\(242\) 18.5812 1.19444
\(243\) −3.97952 −0.255286
\(244\) −52.6577 −3.37107
\(245\) −17.2315 −1.10088
\(246\) 12.0653 0.769253
\(247\) 23.4214 1.49027
\(248\) 30.1672 1.91562
\(249\) −5.20139 −0.329625
\(250\) 21.4073 1.35392
\(251\) −9.68107 −0.611064 −0.305532 0.952182i \(-0.598834\pi\)
−0.305532 + 0.952182i \(0.598834\pi\)
\(252\) −1.33398 −0.0840329
\(253\) −9.56352 −0.601253
\(254\) −47.8606 −3.00304
\(255\) −3.88482 −0.243277
\(256\) 1.72134 0.107584
\(257\) −30.7802 −1.92001 −0.960007 0.279975i \(-0.909674\pi\)
−0.960007 + 0.279975i \(0.909674\pi\)
\(258\) 9.37635 0.583746
\(259\) −4.03385 −0.250651
\(260\) 55.9704 3.47114
\(261\) −3.79152 −0.234689
\(262\) −23.1648 −1.43113
\(263\) −0.0904159 −0.00557529 −0.00278764 0.999996i \(-0.500887\pi\)
−0.00278764 + 0.999996i \(0.500887\pi\)
\(264\) −26.6178 −1.63821
\(265\) 10.4274 0.640551
\(266\) −10.1623 −0.623091
\(267\) −5.66229 −0.346526
\(268\) −70.1494 −4.28506
\(269\) 27.7840 1.69402 0.847010 0.531577i \(-0.178400\pi\)
0.847010 + 0.531577i \(0.178400\pi\)
\(270\) −38.4099 −2.33755
\(271\) 2.25199 0.136799 0.0683995 0.997658i \(-0.478211\pi\)
0.0683995 + 0.997658i \(0.478211\pi\)
\(272\) 10.6507 0.645796
\(273\) −4.59563 −0.278140
\(274\) −49.4786 −2.98911
\(275\) −3.90745 −0.235628
\(276\) −39.2220 −2.36089
\(277\) 19.8887 1.19499 0.597497 0.801871i \(-0.296162\pi\)
0.597497 + 0.801871i \(0.296162\pi\)
\(278\) 42.4394 2.54535
\(279\) 1.41603 0.0847754
\(280\) −14.7331 −0.880473
\(281\) −17.0303 −1.01594 −0.507972 0.861374i \(-0.669605\pi\)
−0.507972 + 0.861374i \(0.669605\pi\)
\(282\) 39.0415 2.32489
\(283\) 19.0078 1.12990 0.564949 0.825126i \(-0.308896\pi\)
0.564949 + 0.825126i \(0.308896\pi\)
\(284\) −3.22414 −0.191318
\(285\) −23.9090 −1.41625
\(286\) 22.2818 1.31755
\(287\) 1.90809 0.112631
\(288\) 5.65933 0.333479
\(289\) −16.1694 −0.951139
\(290\) −69.0243 −4.05325
\(291\) 23.4396 1.37405
\(292\) 72.2555 4.22843
\(293\) 13.0262 0.760999 0.380499 0.924781i \(-0.375752\pi\)
0.380499 + 0.924781i \(0.375752\pi\)
\(294\) −28.1336 −1.64079
\(295\) 25.2358 1.46929
\(296\) 48.6624 2.82844
\(297\) −10.9744 −0.636801
\(298\) 6.62007 0.383490
\(299\) 19.9189 1.15194
\(300\) −16.0253 −0.925222
\(301\) 1.48285 0.0854699
\(302\) 42.0744 2.42111
\(303\) −10.3263 −0.593229
\(304\) 65.5496 3.75953
\(305\) −27.2989 −1.56313
\(306\) 0.935004 0.0534506
\(307\) 17.1830 0.980686 0.490343 0.871530i \(-0.336872\pi\)
0.490343 + 0.871530i \(0.336872\pi\)
\(308\) −6.93868 −0.395368
\(309\) −14.8860 −0.846833
\(310\) 25.7787 1.46413
\(311\) −22.9925 −1.30379 −0.651893 0.758311i \(-0.726025\pi\)
−0.651893 + 0.758311i \(0.726025\pi\)
\(312\) 55.4395 3.13864
\(313\) 13.5496 0.765871 0.382936 0.923775i \(-0.374913\pi\)
0.382936 + 0.923775i \(0.374913\pi\)
\(314\) −26.2321 −1.48036
\(315\) −0.691564 −0.0389652
\(316\) 42.8382 2.40984
\(317\) 9.09508 0.510831 0.255415 0.966831i \(-0.417788\pi\)
0.255415 + 0.966831i \(0.417788\pi\)
\(318\) 17.0247 0.954699
\(319\) −19.7215 −1.10419
\(320\) 41.4156 2.31520
\(321\) −11.4261 −0.637741
\(322\) −8.64260 −0.481634
\(323\) 5.11216 0.284448
\(324\) −39.1290 −2.17383
\(325\) 8.13845 0.451440
\(326\) 2.71557 0.150401
\(327\) 2.71295 0.150027
\(328\) −23.0183 −1.27097
\(329\) 6.17432 0.340401
\(330\) −22.7456 −1.25210
\(331\) 4.96006 0.272629 0.136315 0.990666i \(-0.456474\pi\)
0.136315 + 0.990666i \(0.456474\pi\)
\(332\) 16.3568 0.897697
\(333\) 2.28418 0.125172
\(334\) 42.0530 2.30104
\(335\) −36.3670 −1.98694
\(336\) −12.8618 −0.701669
\(337\) −8.84982 −0.482080 −0.241040 0.970515i \(-0.577489\pi\)
−0.241040 + 0.970515i \(0.577489\pi\)
\(338\) −11.8058 −0.642152
\(339\) 21.4549 1.16527
\(340\) 12.2166 0.662538
\(341\) 7.36546 0.398862
\(342\) 5.75445 0.311165
\(343\) −9.21387 −0.497502
\(344\) −17.8884 −0.964475
\(345\) −20.3336 −1.09472
\(346\) 11.9255 0.641118
\(347\) 25.7960 1.38480 0.692402 0.721512i \(-0.256553\pi\)
0.692402 + 0.721512i \(0.256553\pi\)
\(348\) −80.8823 −4.33575
\(349\) −27.0834 −1.44974 −0.724872 0.688884i \(-0.758101\pi\)
−0.724872 + 0.688884i \(0.758101\pi\)
\(350\) −3.53119 −0.188750
\(351\) 22.8575 1.22004
\(352\) 29.4369 1.56899
\(353\) 21.9967 1.17077 0.585384 0.810756i \(-0.300944\pi\)
0.585384 + 0.810756i \(0.300944\pi\)
\(354\) 41.2022 2.18987
\(355\) −1.67146 −0.0887121
\(356\) 17.8062 0.943727
\(357\) −1.00308 −0.0530887
\(358\) −49.0700 −2.59343
\(359\) −15.1633 −0.800286 −0.400143 0.916453i \(-0.631040\pi\)
−0.400143 + 0.916453i \(0.631040\pi\)
\(360\) 8.34270 0.439699
\(361\) 12.4626 0.655927
\(362\) 62.3255 3.27576
\(363\) 11.2878 0.592454
\(364\) 14.4519 0.757485
\(365\) 37.4588 1.96068
\(366\) −44.5706 −2.32974
\(367\) −35.5893 −1.85775 −0.928874 0.370397i \(-0.879222\pi\)
−0.928874 + 0.370397i \(0.879222\pi\)
\(368\) 55.7471 2.90602
\(369\) −1.08046 −0.0562467
\(370\) 41.5833 2.16182
\(371\) 2.69242 0.139783
\(372\) 30.2073 1.56618
\(373\) −8.18005 −0.423547 −0.211774 0.977319i \(-0.567924\pi\)
−0.211774 + 0.977319i \(0.567924\pi\)
\(374\) 4.86341 0.251481
\(375\) 13.0046 0.671554
\(376\) −74.4840 −3.84122
\(377\) 41.0760 2.11552
\(378\) −9.91765 −0.510109
\(379\) 21.6650 1.11286 0.556428 0.830896i \(-0.312172\pi\)
0.556428 + 0.830896i \(0.312172\pi\)
\(380\) 75.1866 3.85699
\(381\) −29.0745 −1.48953
\(382\) 21.4544 1.09770
\(383\) 8.48955 0.433796 0.216898 0.976194i \(-0.430406\pi\)
0.216898 + 0.976194i \(0.430406\pi\)
\(384\) 20.1339 1.02745
\(385\) −3.59716 −0.183328
\(386\) −68.5706 −3.49015
\(387\) −0.839668 −0.0426827
\(388\) −73.7106 −3.74209
\(389\) −22.5242 −1.14202 −0.571010 0.820943i \(-0.693448\pi\)
−0.571010 + 0.820943i \(0.693448\pi\)
\(390\) 47.3746 2.39890
\(391\) 4.34767 0.219871
\(392\) 53.6738 2.71093
\(393\) −14.0722 −0.709851
\(394\) 56.1242 2.82750
\(395\) 22.2083 1.11742
\(396\) 3.92906 0.197443
\(397\) −16.5501 −0.830628 −0.415314 0.909678i \(-0.636328\pi\)
−0.415314 + 0.909678i \(0.636328\pi\)
\(398\) −50.8933 −2.55105
\(399\) −6.17343 −0.309058
\(400\) 22.7771 1.13885
\(401\) 17.8378 0.890779 0.445390 0.895337i \(-0.353065\pi\)
0.445390 + 0.895337i \(0.353065\pi\)
\(402\) −59.3759 −2.96140
\(403\) −15.3408 −0.764178
\(404\) 32.4731 1.61560
\(405\) −20.2853 −1.00798
\(406\) −17.8225 −0.884514
\(407\) 11.8811 0.588927
\(408\) 12.1007 0.599074
\(409\) 16.8763 0.834479 0.417240 0.908797i \(-0.362998\pi\)
0.417240 + 0.908797i \(0.362998\pi\)
\(410\) −19.6698 −0.971421
\(411\) −30.0574 −1.48262
\(412\) 46.8119 2.30626
\(413\) 6.51603 0.320633
\(414\) 4.89391 0.240523
\(415\) 8.47973 0.416254
\(416\) −61.3112 −3.00603
\(417\) 25.7813 1.26251
\(418\) 29.9317 1.46401
\(419\) −31.6886 −1.54809 −0.774044 0.633132i \(-0.781769\pi\)
−0.774044 + 0.633132i \(0.781769\pi\)
\(420\) −14.7527 −0.719860
\(421\) −16.0953 −0.784438 −0.392219 0.919872i \(-0.628292\pi\)
−0.392219 + 0.919872i \(0.628292\pi\)
\(422\) 43.8277 2.13350
\(423\) −3.49623 −0.169993
\(424\) −32.4800 −1.57737
\(425\) 1.77637 0.0861665
\(426\) −2.72898 −0.132220
\(427\) −7.04873 −0.341112
\(428\) 35.9316 1.73682
\(429\) 13.5358 0.653515
\(430\) −15.2861 −0.737161
\(431\) −7.36666 −0.354839 −0.177420 0.984135i \(-0.556775\pi\)
−0.177420 + 0.984135i \(0.556775\pi\)
\(432\) 63.9715 3.07783
\(433\) 32.9697 1.58442 0.792211 0.610247i \(-0.208930\pi\)
0.792211 + 0.610247i \(0.208930\pi\)
\(434\) 6.65620 0.319508
\(435\) −41.9311 −2.01044
\(436\) −8.53143 −0.408581
\(437\) 26.7576 1.27999
\(438\) 61.1586 2.92227
\(439\) 11.2381 0.536363 0.268181 0.963368i \(-0.413577\pi\)
0.268181 + 0.963368i \(0.413577\pi\)
\(440\) 43.3945 2.06875
\(441\) 2.51941 0.119972
\(442\) −10.1295 −0.481812
\(443\) −10.2615 −0.487539 −0.243769 0.969833i \(-0.578384\pi\)
−0.243769 + 0.969833i \(0.578384\pi\)
\(444\) 48.7271 2.31249
\(445\) 9.23112 0.437597
\(446\) −25.9981 −1.23104
\(447\) 4.02158 0.190214
\(448\) 10.6937 0.505232
\(449\) 30.7370 1.45057 0.725285 0.688449i \(-0.241708\pi\)
0.725285 + 0.688449i \(0.241708\pi\)
\(450\) 1.99955 0.0942597
\(451\) −5.62002 −0.264637
\(452\) −67.4692 −3.17348
\(453\) 25.5595 1.20089
\(454\) −58.8699 −2.76290
\(455\) 7.49217 0.351238
\(456\) 74.4734 3.48754
\(457\) 15.2764 0.714599 0.357300 0.933990i \(-0.383697\pi\)
0.357300 + 0.933990i \(0.383697\pi\)
\(458\) −16.9947 −0.794109
\(459\) 4.98908 0.232870
\(460\) 63.9430 2.98136
\(461\) −32.3365 −1.50606 −0.753031 0.657985i \(-0.771409\pi\)
−0.753031 + 0.657985i \(0.771409\pi\)
\(462\) −5.87305 −0.273239
\(463\) 32.5799 1.51411 0.757057 0.653349i \(-0.226636\pi\)
0.757057 + 0.653349i \(0.226636\pi\)
\(464\) 114.960 5.33687
\(465\) 15.6601 0.726221
\(466\) 62.3211 2.88697
\(467\) −14.9305 −0.690900 −0.345450 0.938437i \(-0.612274\pi\)
−0.345450 + 0.938437i \(0.612274\pi\)
\(468\) −8.18344 −0.378280
\(469\) −9.39016 −0.433597
\(470\) −63.6486 −2.93589
\(471\) −15.9356 −0.734272
\(472\) −78.6063 −3.61815
\(473\) −4.36752 −0.200819
\(474\) 36.2592 1.66544
\(475\) 10.9326 0.501622
\(476\) 3.15439 0.144581
\(477\) −1.52459 −0.0698063
\(478\) 7.45823 0.341132
\(479\) 34.3785 1.57079 0.785396 0.618993i \(-0.212459\pi\)
0.785396 + 0.618993i \(0.212459\pi\)
\(480\) 62.5876 2.85672
\(481\) −24.7460 −1.12832
\(482\) 41.2210 1.87757
\(483\) −5.25024 −0.238894
\(484\) −35.4966 −1.61348
\(485\) −38.2132 −1.73517
\(486\) 10.5925 0.480484
\(487\) 12.9336 0.586078 0.293039 0.956100i \(-0.405333\pi\)
0.293039 + 0.956100i \(0.405333\pi\)
\(488\) 85.0326 3.84924
\(489\) 1.64966 0.0746003
\(490\) 45.8657 2.07200
\(491\) 6.86706 0.309906 0.154953 0.987922i \(-0.450477\pi\)
0.154953 + 0.987922i \(0.450477\pi\)
\(492\) −23.0489 −1.03913
\(493\) 8.96561 0.403791
\(494\) −62.3417 −2.80489
\(495\) 2.03691 0.0915522
\(496\) −42.9343 −1.92781
\(497\) −0.431582 −0.0193591
\(498\) 13.8448 0.620399
\(499\) −19.7705 −0.885050 −0.442525 0.896756i \(-0.645917\pi\)
−0.442525 + 0.896756i \(0.645917\pi\)
\(500\) −40.8956 −1.82891
\(501\) 25.5465 1.14133
\(502\) 25.7685 1.15010
\(503\) 29.5126 1.31590 0.657951 0.753061i \(-0.271423\pi\)
0.657951 + 0.753061i \(0.271423\pi\)
\(504\) 2.15413 0.0959527
\(505\) 16.8347 0.749136
\(506\) 25.4556 1.13164
\(507\) −7.17184 −0.318512
\(508\) 91.4308 4.05658
\(509\) 14.5122 0.643244 0.321622 0.946868i \(-0.395772\pi\)
0.321622 + 0.946868i \(0.395772\pi\)
\(510\) 10.3404 0.457880
\(511\) 9.67208 0.427868
\(512\) 20.3216 0.898094
\(513\) 30.7051 1.35567
\(514\) 81.9289 3.61373
\(515\) 24.2683 1.06939
\(516\) −17.9122 −0.788539
\(517\) −18.1856 −0.799803
\(518\) 10.7371 0.471759
\(519\) 7.24453 0.318000
\(520\) −90.3820 −3.96351
\(521\) −23.9637 −1.04987 −0.524935 0.851142i \(-0.675910\pi\)
−0.524935 + 0.851142i \(0.675910\pi\)
\(522\) 10.0920 0.441717
\(523\) −6.51305 −0.284796 −0.142398 0.989809i \(-0.545481\pi\)
−0.142398 + 0.989809i \(0.545481\pi\)
\(524\) 44.2530 1.93320
\(525\) −2.14514 −0.0936215
\(526\) 0.240664 0.0104934
\(527\) −3.34841 −0.145859
\(528\) 37.8827 1.64863
\(529\) −0.243822 −0.0106009
\(530\) −27.7551 −1.20560
\(531\) −3.68973 −0.160121
\(532\) 19.4136 0.841687
\(533\) 11.7054 0.507017
\(534\) 15.0715 0.652210
\(535\) 18.6277 0.805346
\(536\) 113.278 4.89288
\(537\) −29.8092 −1.28636
\(538\) −73.9538 −3.18838
\(539\) 13.1047 0.564459
\(540\) 73.3765 3.15762
\(541\) −2.72116 −0.116992 −0.0584959 0.998288i \(-0.518630\pi\)
−0.0584959 + 0.998288i \(0.518630\pi\)
\(542\) −5.99423 −0.257474
\(543\) 37.8617 1.62480
\(544\) −13.3823 −0.573762
\(545\) −4.42288 −0.189455
\(546\) 12.2324 0.523498
\(547\) 23.3099 0.996661 0.498330 0.866987i \(-0.333947\pi\)
0.498330 + 0.866987i \(0.333947\pi\)
\(548\) 94.5217 4.03777
\(549\) 3.99138 0.170348
\(550\) 10.4006 0.443485
\(551\) 55.1785 2.35069
\(552\) 63.3364 2.69578
\(553\) 5.73430 0.243847
\(554\) −52.9385 −2.24914
\(555\) 25.2612 1.07228
\(556\) −81.0744 −3.43832
\(557\) −34.8636 −1.47722 −0.738610 0.674133i \(-0.764517\pi\)
−0.738610 + 0.674133i \(0.764517\pi\)
\(558\) −3.76910 −0.159559
\(559\) 9.09668 0.384749
\(560\) 20.9684 0.886075
\(561\) 2.95444 0.124737
\(562\) 45.3303 1.91214
\(563\) −18.9316 −0.797870 −0.398935 0.916979i \(-0.630620\pi\)
−0.398935 + 0.916979i \(0.630620\pi\)
\(564\) −74.5831 −3.14052
\(565\) −34.9775 −1.47151
\(566\) −50.5940 −2.12662
\(567\) −5.23778 −0.219966
\(568\) 5.20640 0.218456
\(569\) 18.3113 0.767651 0.383826 0.923406i \(-0.374606\pi\)
0.383826 + 0.923406i \(0.374606\pi\)
\(570\) 63.6395 2.66557
\(571\) −5.74605 −0.240465 −0.120232 0.992746i \(-0.538364\pi\)
−0.120232 + 0.992746i \(0.538364\pi\)
\(572\) −42.5661 −1.77978
\(573\) 13.0332 0.544469
\(574\) −5.07885 −0.211987
\(575\) 9.29770 0.387741
\(576\) −6.05537 −0.252307
\(577\) 27.5417 1.14658 0.573288 0.819354i \(-0.305667\pi\)
0.573288 + 0.819354i \(0.305667\pi\)
\(578\) 43.0387 1.79017
\(579\) −41.6555 −1.73114
\(580\) 131.861 5.47523
\(581\) 2.18952 0.0908364
\(582\) −62.3902 −2.58616
\(583\) −7.93015 −0.328433
\(584\) −116.679 −4.82823
\(585\) −4.24247 −0.175405
\(586\) −34.6724 −1.43230
\(587\) −19.0635 −0.786833 −0.393416 0.919360i \(-0.628707\pi\)
−0.393416 + 0.919360i \(0.628707\pi\)
\(588\) 53.7452 2.21641
\(589\) −20.6077 −0.849124
\(590\) −67.1712 −2.76540
\(591\) 34.0945 1.40246
\(592\) −69.2569 −2.84644
\(593\) −38.7243 −1.59021 −0.795107 0.606469i \(-0.792586\pi\)
−0.795107 + 0.606469i \(0.792586\pi\)
\(594\) 29.2111 1.19855
\(595\) 1.63531 0.0670410
\(596\) −12.6467 −0.518028
\(597\) −30.9168 −1.26534
\(598\) −53.0190 −2.16811
\(599\) 17.2168 0.703458 0.351729 0.936102i \(-0.385594\pi\)
0.351729 + 0.936102i \(0.385594\pi\)
\(600\) 25.8779 1.05646
\(601\) 42.6850 1.74116 0.870580 0.492027i \(-0.163744\pi\)
0.870580 + 0.492027i \(0.163744\pi\)
\(602\) −3.94696 −0.160866
\(603\) 5.31722 0.216534
\(604\) −80.3770 −3.27050
\(605\) −18.4022 −0.748157
\(606\) 27.4859 1.11654
\(607\) −1.61173 −0.0654182 −0.0327091 0.999465i \(-0.510413\pi\)
−0.0327091 + 0.999465i \(0.510413\pi\)
\(608\) −82.3611 −3.34018
\(609\) −10.8269 −0.438726
\(610\) 72.6627 2.94202
\(611\) 37.8770 1.53234
\(612\) −1.78619 −0.0722024
\(613\) 38.0835 1.53818 0.769089 0.639142i \(-0.220710\pi\)
0.769089 + 0.639142i \(0.220710\pi\)
\(614\) −45.7367 −1.84578
\(615\) −11.9491 −0.481833
\(616\) 11.2047 0.451450
\(617\) 30.5323 1.22918 0.614591 0.788846i \(-0.289321\pi\)
0.614591 + 0.788846i \(0.289321\pi\)
\(618\) 39.6226 1.59386
\(619\) −39.8407 −1.60133 −0.800666 0.599112i \(-0.795521\pi\)
−0.800666 + 0.599112i \(0.795521\pi\)
\(620\) −49.2464 −1.97778
\(621\) 26.1134 1.04789
\(622\) 61.2001 2.45390
\(623\) 2.38353 0.0954941
\(624\) −78.9021 −3.15861
\(625\) −30.9465 −1.23786
\(626\) −36.0657 −1.44147
\(627\) 18.1830 0.726160
\(628\) 50.1126 1.99971
\(629\) −5.40129 −0.215363
\(630\) 1.84077 0.0733379
\(631\) 36.8049 1.46518 0.732589 0.680671i \(-0.238312\pi\)
0.732589 + 0.680671i \(0.238312\pi\)
\(632\) −69.1759 −2.75167
\(633\) 26.6246 1.05823
\(634\) −24.2088 −0.961453
\(635\) 47.3997 1.88100
\(636\) −32.5233 −1.28963
\(637\) −27.2945 −1.08145
\(638\) 52.4937 2.07824
\(639\) 0.244385 0.00966772
\(640\) −32.8239 −1.29748
\(641\) 21.6913 0.856753 0.428377 0.903600i \(-0.359086\pi\)
0.428377 + 0.903600i \(0.359086\pi\)
\(642\) 30.4132 1.20031
\(643\) 19.9996 0.788706 0.394353 0.918959i \(-0.370969\pi\)
0.394353 + 0.918959i \(0.370969\pi\)
\(644\) 16.5104 0.650603
\(645\) −9.28605 −0.365638
\(646\) −13.6072 −0.535370
\(647\) −10.4150 −0.409457 −0.204729 0.978819i \(-0.565631\pi\)
−0.204729 + 0.978819i \(0.565631\pi\)
\(648\) 63.1861 2.48218
\(649\) −19.1921 −0.753355
\(650\) −21.6624 −0.849671
\(651\) 4.04353 0.158479
\(652\) −5.18770 −0.203166
\(653\) −16.7596 −0.655855 −0.327928 0.944703i \(-0.606350\pi\)
−0.327928 + 0.944703i \(0.606350\pi\)
\(654\) −7.22118 −0.282371
\(655\) 22.9417 0.896407
\(656\) 32.7599 1.27906
\(657\) −5.47686 −0.213673
\(658\) −16.4344 −0.640681
\(659\) −8.46774 −0.329856 −0.164928 0.986306i \(-0.552739\pi\)
−0.164928 + 0.986306i \(0.552739\pi\)
\(660\) 43.4522 1.69137
\(661\) −23.8168 −0.926368 −0.463184 0.886262i \(-0.653293\pi\)
−0.463184 + 0.886262i \(0.653293\pi\)
\(662\) −13.2024 −0.513126
\(663\) −6.15351 −0.238983
\(664\) −26.4133 −1.02503
\(665\) 10.0644 0.390282
\(666\) −6.07990 −0.235591
\(667\) 46.9270 1.81702
\(668\) −80.3361 −3.10830
\(669\) −15.7934 −0.610608
\(670\) 96.7995 3.73969
\(671\) 20.7611 0.801473
\(672\) 16.1605 0.623404
\(673\) −6.38265 −0.246033 −0.123017 0.992405i \(-0.539257\pi\)
−0.123017 + 0.992405i \(0.539257\pi\)
\(674\) 23.5559 0.907341
\(675\) 10.6694 0.410665
\(676\) 22.5533 0.867434
\(677\) −1.83434 −0.0704995 −0.0352498 0.999379i \(-0.511223\pi\)
−0.0352498 + 0.999379i \(0.511223\pi\)
\(678\) −57.1074 −2.19320
\(679\) −9.86686 −0.378655
\(680\) −19.7276 −0.756517
\(681\) −35.7625 −1.37042
\(682\) −19.6049 −0.750712
\(683\) 35.3606 1.35304 0.676519 0.736425i \(-0.263488\pi\)
0.676519 + 0.736425i \(0.263488\pi\)
\(684\) −10.9930 −0.420329
\(685\) 49.0021 1.87227
\(686\) 24.5249 0.936367
\(687\) −10.3240 −0.393885
\(688\) 25.4589 0.970612
\(689\) 16.5169 0.629244
\(690\) 54.1227 2.06042
\(691\) −14.5132 −0.552107 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(692\) −22.7819 −0.866038
\(693\) 0.525941 0.0199789
\(694\) −68.6624 −2.60639
\(695\) −42.0307 −1.59432
\(696\) 130.610 4.95076
\(697\) 2.55492 0.0967745
\(698\) 72.0892 2.72862
\(699\) 37.8590 1.43196
\(700\) 6.74582 0.254968
\(701\) 11.2428 0.424635 0.212317 0.977201i \(-0.431899\pi\)
0.212317 + 0.977201i \(0.431899\pi\)
\(702\) −60.8409 −2.29629
\(703\) −33.2420 −1.25375
\(704\) −31.4970 −1.18709
\(705\) −38.6655 −1.45623
\(706\) −58.5496 −2.20354
\(707\) 4.34682 0.163479
\(708\) −78.7109 −2.95814
\(709\) −17.2272 −0.646979 −0.323490 0.946232i \(-0.604856\pi\)
−0.323490 + 0.946232i \(0.604856\pi\)
\(710\) 4.44901 0.166968
\(711\) −3.24707 −0.121775
\(712\) −28.7538 −1.07759
\(713\) −17.5259 −0.656351
\(714\) 2.66995 0.0999202
\(715\) −22.0672 −0.825266
\(716\) 93.7410 3.50327
\(717\) 4.53075 0.169204
\(718\) 40.3607 1.50625
\(719\) 17.9695 0.670148 0.335074 0.942192i \(-0.391239\pi\)
0.335074 + 0.942192i \(0.391239\pi\)
\(720\) −11.8734 −0.442496
\(721\) 6.26622 0.233366
\(722\) −33.1722 −1.23454
\(723\) 25.0411 0.931288
\(724\) −119.064 −4.42498
\(725\) 19.1734 0.712082
\(726\) −30.0451 −1.11508
\(727\) −5.77920 −0.214339 −0.107169 0.994241i \(-0.534179\pi\)
−0.107169 + 0.994241i \(0.534179\pi\)
\(728\) −23.3371 −0.864932
\(729\) 29.5203 1.09334
\(730\) −99.7057 −3.69027
\(731\) 1.98552 0.0734371
\(732\) 85.1457 3.14708
\(733\) 1.63100 0.0602423 0.0301211 0.999546i \(-0.490411\pi\)
0.0301211 + 0.999546i \(0.490411\pi\)
\(734\) 94.7296 3.49653
\(735\) 27.8627 1.02773
\(736\) −70.0445 −2.58188
\(737\) 27.6574 1.01878
\(738\) 2.87592 0.105864
\(739\) −15.3862 −0.565989 −0.282994 0.959122i \(-0.591328\pi\)
−0.282994 + 0.959122i \(0.591328\pi\)
\(740\) −79.4389 −2.92023
\(741\) −37.8716 −1.39125
\(742\) −7.16652 −0.263091
\(743\) −7.43856 −0.272894 −0.136447 0.990647i \(-0.543568\pi\)
−0.136447 + 0.990647i \(0.543568\pi\)
\(744\) −48.7793 −1.78833
\(745\) −6.55631 −0.240205
\(746\) 21.7732 0.797173
\(747\) −1.23982 −0.0453627
\(748\) −9.29084 −0.339707
\(749\) 4.80978 0.175746
\(750\) −34.6149 −1.26396
\(751\) 40.8810 1.49177 0.745884 0.666076i \(-0.232027\pi\)
0.745884 + 0.666076i \(0.232027\pi\)
\(752\) 106.007 3.86566
\(753\) 15.6539 0.570461
\(754\) −109.334 −3.98170
\(755\) −41.6692 −1.51650
\(756\) 18.9462 0.689068
\(757\) −38.1164 −1.38537 −0.692683 0.721243i \(-0.743571\pi\)
−0.692683 + 0.721243i \(0.743571\pi\)
\(758\) −57.6666 −2.09455
\(759\) 15.4639 0.561303
\(760\) −121.413 −4.40410
\(761\) 36.3184 1.31654 0.658270 0.752782i \(-0.271288\pi\)
0.658270 + 0.752782i \(0.271288\pi\)
\(762\) 77.3889 2.80351
\(763\) −1.14201 −0.0413436
\(764\) −40.9855 −1.48280
\(765\) −0.925999 −0.0334796
\(766\) −22.5970 −0.816463
\(767\) 39.9733 1.44335
\(768\) −2.78334 −0.100435
\(769\) −42.6925 −1.53953 −0.769765 0.638328i \(-0.779626\pi\)
−0.769765 + 0.638328i \(0.779626\pi\)
\(770\) 9.57472 0.345049
\(771\) 49.7705 1.79244
\(772\) 130.994 4.71458
\(773\) 29.8969 1.07532 0.537659 0.843162i \(-0.319309\pi\)
0.537659 + 0.843162i \(0.319309\pi\)
\(774\) 2.23498 0.0803347
\(775\) −7.16073 −0.257221
\(776\) 119.029 4.27290
\(777\) 6.52259 0.233996
\(778\) 59.9535 2.14944
\(779\) 15.7242 0.563377
\(780\) −90.5022 −3.24050
\(781\) 1.27117 0.0454859
\(782\) −11.5724 −0.413827
\(783\) 53.8501 1.92445
\(784\) −76.3891 −2.72818
\(785\) 25.9795 0.927246
\(786\) 37.4567 1.33604
\(787\) 3.86180 0.137658 0.0688291 0.997628i \(-0.478074\pi\)
0.0688291 + 0.997628i \(0.478074\pi\)
\(788\) −107.217 −3.81945
\(789\) 0.146199 0.00520484
\(790\) −59.1127 −2.10314
\(791\) −9.03139 −0.321119
\(792\) −6.34471 −0.225449
\(793\) −43.2412 −1.53554
\(794\) 44.0522 1.56335
\(795\) −16.8608 −0.597989
\(796\) 97.2243 3.44602
\(797\) 2.06707 0.0732194 0.0366097 0.999330i \(-0.488344\pi\)
0.0366097 + 0.999330i \(0.488344\pi\)
\(798\) 16.4321 0.581690
\(799\) 8.26736 0.292478
\(800\) −28.6187 −1.01183
\(801\) −1.34968 −0.0476887
\(802\) −47.4797 −1.67657
\(803\) −28.4878 −1.00531
\(804\) 113.429 4.00034
\(805\) 8.55937 0.301678
\(806\) 40.8332 1.43829
\(807\) −44.9257 −1.58146
\(808\) −52.4380 −1.84476
\(809\) −33.3770 −1.17347 −0.586737 0.809778i \(-0.699588\pi\)
−0.586737 + 0.809778i \(0.699588\pi\)
\(810\) 53.9942 1.89716
\(811\) −7.62688 −0.267816 −0.133908 0.990994i \(-0.542753\pi\)
−0.133908 + 0.990994i \(0.542753\pi\)
\(812\) 34.0472 1.19482
\(813\) −3.64140 −0.127709
\(814\) −31.6245 −1.10844
\(815\) −2.68941 −0.0942061
\(816\) −17.2219 −0.602886
\(817\) 12.2198 0.427517
\(818\) −44.9204 −1.57060
\(819\) −1.09543 −0.0382775
\(820\) 37.5762 1.31222
\(821\) 10.9776 0.383121 0.191561 0.981481i \(-0.438645\pi\)
0.191561 + 0.981481i \(0.438645\pi\)
\(822\) 80.0051 2.79050
\(823\) 55.1854 1.92364 0.961821 0.273681i \(-0.0882411\pi\)
0.961821 + 0.273681i \(0.0882411\pi\)
\(824\) −75.5927 −2.63340
\(825\) 6.31822 0.219972
\(826\) −17.3440 −0.603475
\(827\) −28.7320 −0.999110 −0.499555 0.866282i \(-0.666503\pi\)
−0.499555 + 0.866282i \(0.666503\pi\)
\(828\) −9.34911 −0.324904
\(829\) −17.9299 −0.622731 −0.311365 0.950290i \(-0.600786\pi\)
−0.311365 + 0.950290i \(0.600786\pi\)
\(830\) −22.5709 −0.783446
\(831\) −32.1593 −1.11559
\(832\) 65.6019 2.27434
\(833\) −5.95752 −0.206416
\(834\) −68.6231 −2.37622
\(835\) −41.6480 −1.44129
\(836\) −57.1802 −1.97762
\(837\) −20.1115 −0.695157
\(838\) 84.3468 2.91371
\(839\) 7.56294 0.261102 0.130551 0.991442i \(-0.458325\pi\)
0.130551 + 0.991442i \(0.458325\pi\)
\(840\) 23.8230 0.821970
\(841\) 67.7711 2.33694
\(842\) 42.8416 1.47642
\(843\) 27.5374 0.948440
\(844\) −83.7264 −2.88198
\(845\) 11.6921 0.402221
\(846\) 9.30607 0.319949
\(847\) −4.75156 −0.163266
\(848\) 46.2260 1.58741
\(849\) −30.7350 −1.05482
\(850\) −4.72823 −0.162177
\(851\) −28.2709 −0.969115
\(852\) 5.21332 0.178606
\(853\) −16.9372 −0.579919 −0.289960 0.957039i \(-0.593642\pi\)
−0.289960 + 0.957039i \(0.593642\pi\)
\(854\) 18.7619 0.642019
\(855\) −5.69903 −0.194903
\(856\) −58.0229 −1.98318
\(857\) −9.79698 −0.334658 −0.167329 0.985901i \(-0.553514\pi\)
−0.167329 + 0.985901i \(0.553514\pi\)
\(858\) −36.0288 −1.23000
\(859\) 11.3842 0.388424 0.194212 0.980960i \(-0.437785\pi\)
0.194212 + 0.980960i \(0.437785\pi\)
\(860\) 29.2019 0.995775
\(861\) −3.08532 −0.105147
\(862\) 19.6081 0.667856
\(863\) 10.6202 0.361514 0.180757 0.983528i \(-0.442145\pi\)
0.180757 + 0.983528i \(0.442145\pi\)
\(864\) −80.3782 −2.73452
\(865\) −11.8106 −0.401573
\(866\) −87.7568 −2.98210
\(867\) 26.1453 0.887940
\(868\) −12.7157 −0.431599
\(869\) −16.8896 −0.572941
\(870\) 111.610 3.78393
\(871\) −57.6049 −1.95187
\(872\) 13.7767 0.466538
\(873\) 5.58715 0.189096
\(874\) −71.2218 −2.40911
\(875\) −5.47426 −0.185064
\(876\) −116.835 −3.94748
\(877\) −30.6423 −1.03472 −0.517359 0.855769i \(-0.673085\pi\)
−0.517359 + 0.855769i \(0.673085\pi\)
\(878\) −29.9128 −1.00951
\(879\) −21.0629 −0.710434
\(880\) −61.7595 −2.08191
\(881\) −24.0134 −0.809034 −0.404517 0.914531i \(-0.632560\pi\)
−0.404517 + 0.914531i \(0.632560\pi\)
\(882\) −6.70603 −0.225804
\(883\) 5.01111 0.168637 0.0843187 0.996439i \(-0.473129\pi\)
0.0843187 + 0.996439i \(0.473129\pi\)
\(884\) 19.3510 0.650843
\(885\) −40.8054 −1.37166
\(886\) 27.3135 0.917614
\(887\) 23.7496 0.797433 0.398717 0.917074i \(-0.369456\pi\)
0.398717 + 0.917074i \(0.369456\pi\)
\(888\) −78.6854 −2.64051
\(889\) 12.2389 0.410479
\(890\) −24.5709 −0.823617
\(891\) 15.4272 0.516830
\(892\) 49.6655 1.66292
\(893\) 50.8812 1.70267
\(894\) −10.7044 −0.358009
\(895\) 48.5974 1.62443
\(896\) −8.47532 −0.283141
\(897\) −32.2081 −1.07540
\(898\) −81.8141 −2.73017
\(899\) −36.1414 −1.20538
\(900\) −3.81985 −0.127328
\(901\) 3.60513 0.120104
\(902\) 14.9591 0.498082
\(903\) −2.39771 −0.0797908
\(904\) 108.950 3.62364
\(905\) −61.7253 −2.05182
\(906\) −68.0328 −2.26024
\(907\) 22.1124 0.734230 0.367115 0.930176i \(-0.380346\pi\)
0.367115 + 0.930176i \(0.380346\pi\)
\(908\) 112.462 3.73220
\(909\) −2.46141 −0.0816397
\(910\) −19.9422 −0.661078
\(911\) 20.6068 0.682732 0.341366 0.939930i \(-0.389110\pi\)
0.341366 + 0.939930i \(0.389110\pi\)
\(912\) −105.991 −3.50972
\(913\) −6.44892 −0.213428
\(914\) −40.6618 −1.34497
\(915\) 44.1414 1.45927
\(916\) 32.4659 1.07270
\(917\) 5.92368 0.195617
\(918\) −13.2797 −0.438294
\(919\) 7.45967 0.246072 0.123036 0.992402i \(-0.460737\pi\)
0.123036 + 0.992402i \(0.460737\pi\)
\(920\) −103.256 −3.40425
\(921\) −27.7843 −0.915524
\(922\) 86.0715 2.83461
\(923\) −2.64758 −0.0871463
\(924\) 11.2196 0.369098
\(925\) −11.5509 −0.379792
\(926\) −86.7192 −2.84977
\(927\) −3.54827 −0.116541
\(928\) −144.443 −4.74158
\(929\) 35.5088 1.16501 0.582503 0.812828i \(-0.302073\pi\)
0.582503 + 0.812828i \(0.302073\pi\)
\(930\) −41.6832 −1.36685
\(931\) −36.6654 −1.20166
\(932\) −119.055 −3.89979
\(933\) 37.1781 1.21716
\(934\) 39.7411 1.30037
\(935\) −4.81657 −0.157519
\(936\) 13.2148 0.431938
\(937\) −11.8146 −0.385965 −0.192983 0.981202i \(-0.561816\pi\)
−0.192983 + 0.981202i \(0.561816\pi\)
\(938\) 24.9942 0.816089
\(939\) −21.9093 −0.714983
\(940\) 121.591 3.96588
\(941\) 17.3855 0.566753 0.283376 0.959009i \(-0.408545\pi\)
0.283376 + 0.959009i \(0.408545\pi\)
\(942\) 42.4164 1.38200
\(943\) 13.3727 0.435476
\(944\) 111.873 3.64117
\(945\) 9.82213 0.319514
\(946\) 11.6252 0.377969
\(947\) −21.5703 −0.700939 −0.350470 0.936574i \(-0.613978\pi\)
−0.350470 + 0.936574i \(0.613978\pi\)
\(948\) −69.2679 −2.24972
\(949\) 59.3344 1.92608
\(950\) −29.0997 −0.944120
\(951\) −14.7064 −0.476888
\(952\) −5.09377 −0.165090
\(953\) 1.39750 0.0452693 0.0226347 0.999744i \(-0.492795\pi\)
0.0226347 + 0.999744i \(0.492795\pi\)
\(954\) 4.05807 0.131385
\(955\) −21.2478 −0.687561
\(956\) −14.2479 −0.460809
\(957\) 31.8890 1.03083
\(958\) −91.5066 −2.95645
\(959\) 12.6526 0.408574
\(960\) −66.9675 −2.16137
\(961\) −17.5022 −0.564587
\(962\) 65.8676 2.12366
\(963\) −2.72356 −0.0877654
\(964\) −78.7467 −2.53626
\(965\) 67.9102 2.18611
\(966\) 13.9748 0.449631
\(967\) 16.1482 0.519291 0.259645 0.965704i \(-0.416394\pi\)
0.259645 + 0.965704i \(0.416394\pi\)
\(968\) 57.3206 1.84235
\(969\) −8.26618 −0.265548
\(970\) 101.714 3.26583
\(971\) 45.7792 1.46913 0.734563 0.678541i \(-0.237387\pi\)
0.734563 + 0.678541i \(0.237387\pi\)
\(972\) −20.2354 −0.649049
\(973\) −10.8526 −0.347917
\(974\) −34.4260 −1.10308
\(975\) −13.1596 −0.421444
\(976\) −121.019 −3.87373
\(977\) 23.2206 0.742893 0.371447 0.928454i \(-0.378862\pi\)
0.371447 + 0.928454i \(0.378862\pi\)
\(978\) −4.39098 −0.140408
\(979\) −7.02036 −0.224372
\(980\) −87.6198 −2.79891
\(981\) 0.646669 0.0206466
\(982\) −18.2783 −0.583285
\(983\) 12.6677 0.404037 0.202019 0.979382i \(-0.435250\pi\)
0.202019 + 0.979382i \(0.435250\pi\)
\(984\) 37.2198 1.18652
\(985\) −55.5837 −1.77104
\(986\) −23.8641 −0.759989
\(987\) −9.98365 −0.317783
\(988\) 119.095 3.78891
\(989\) 10.3924 0.330460
\(990\) −5.42173 −0.172314
\(991\) 23.0838 0.733281 0.366641 0.930363i \(-0.380508\pi\)
0.366641 + 0.930363i \(0.380508\pi\)
\(992\) 53.9456 1.71277
\(993\) −8.02024 −0.254515
\(994\) 1.14876 0.0364364
\(995\) 50.4032 1.59789
\(996\) −26.4484 −0.838050
\(997\) 4.47299 0.141661 0.0708305 0.997488i \(-0.477435\pi\)
0.0708305 + 0.997488i \(0.477435\pi\)
\(998\) 52.6241 1.66579
\(999\) −32.4417 −1.02641
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 \(a_p\))