Properties

Label 8015.2.a.l.1.27
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.27
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +O(q^{10})\) \(q-0.521477 q^{2} +2.21540 q^{3} -1.72806 q^{4} -1.00000 q^{5} -1.15528 q^{6} -1.00000 q^{7} +1.94410 q^{8} +1.90801 q^{9} +0.521477 q^{10} +1.94603 q^{11} -3.82835 q^{12} +1.76780 q^{13} +0.521477 q^{14} -2.21540 q^{15} +2.44232 q^{16} +3.17335 q^{17} -0.994983 q^{18} +8.00800 q^{19} +1.72806 q^{20} -2.21540 q^{21} -1.01481 q^{22} +8.06739 q^{23} +4.30696 q^{24} +1.00000 q^{25} -0.921868 q^{26} -2.41920 q^{27} +1.72806 q^{28} -9.38093 q^{29} +1.15528 q^{30} +4.44905 q^{31} -5.16181 q^{32} +4.31124 q^{33} -1.65483 q^{34} +1.00000 q^{35} -3.29716 q^{36} -5.76682 q^{37} -4.17599 q^{38} +3.91639 q^{39} -1.94410 q^{40} -2.45236 q^{41} +1.15528 q^{42} +5.49412 q^{43} -3.36286 q^{44} -1.90801 q^{45} -4.20696 q^{46} -7.29838 q^{47} +5.41073 q^{48} +1.00000 q^{49} -0.521477 q^{50} +7.03024 q^{51} -3.05487 q^{52} -3.09207 q^{53} +1.26156 q^{54} -1.94603 q^{55} -1.94410 q^{56} +17.7409 q^{57} +4.89194 q^{58} -4.07297 q^{59} +3.82835 q^{60} +13.1374 q^{61} -2.32008 q^{62} -1.90801 q^{63} -2.19288 q^{64} -1.76780 q^{65} -2.24821 q^{66} +2.43612 q^{67} -5.48374 q^{68} +17.8725 q^{69} -0.521477 q^{70} -2.59448 q^{71} +3.70936 q^{72} +14.4455 q^{73} +3.00726 q^{74} +2.21540 q^{75} -13.8383 q^{76} -1.94603 q^{77} -2.04231 q^{78} +1.80474 q^{79} -2.44232 q^{80} -11.0835 q^{81} +1.27885 q^{82} -6.57950 q^{83} +3.82835 q^{84} -3.17335 q^{85} -2.86506 q^{86} -20.7825 q^{87} +3.78327 q^{88} -11.5305 q^{89} +0.994983 q^{90} -1.76780 q^{91} -13.9410 q^{92} +9.85644 q^{93} +3.80594 q^{94} -8.00800 q^{95} -11.4355 q^{96} +4.26564 q^{97} -0.521477 q^{98} +3.71304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.521477 −0.368740 −0.184370 0.982857i \(-0.559024\pi\)
−0.184370 + 0.982857i \(0.559024\pi\)
\(3\) 2.21540 1.27906 0.639532 0.768765i \(-0.279128\pi\)
0.639532 + 0.768765i \(0.279128\pi\)
\(4\) −1.72806 −0.864031
\(5\) −1.00000 −0.447214
\(6\) −1.15528 −0.471642
\(7\) −1.00000 −0.377964
\(8\) 1.94410 0.687342
\(9\) 1.90801 0.636003
\(10\) 0.521477 0.164905
\(11\) 1.94603 0.586750 0.293375 0.955997i \(-0.405222\pi\)
0.293375 + 0.955997i \(0.405222\pi\)
\(12\) −3.82835 −1.10515
\(13\) 1.76780 0.490300 0.245150 0.969485i \(-0.421163\pi\)
0.245150 + 0.969485i \(0.421163\pi\)
\(14\) 0.521477 0.139371
\(15\) −2.21540 −0.572015
\(16\) 2.44232 0.610580
\(17\) 3.17335 0.769649 0.384825 0.922990i \(-0.374262\pi\)
0.384825 + 0.922990i \(0.374262\pi\)
\(18\) −0.994983 −0.234520
\(19\) 8.00800 1.83716 0.918580 0.395234i \(-0.129337\pi\)
0.918580 + 0.395234i \(0.129337\pi\)
\(20\) 1.72806 0.386406
\(21\) −2.21540 −0.483441
\(22\) −1.01481 −0.216358
\(23\) 8.06739 1.68217 0.841084 0.540905i \(-0.181918\pi\)
0.841084 + 0.540905i \(0.181918\pi\)
\(24\) 4.30696 0.879155
\(25\) 1.00000 0.200000
\(26\) −0.921868 −0.180793
\(27\) −2.41920 −0.465575
\(28\) 1.72806 0.326573
\(29\) −9.38093 −1.74199 −0.870997 0.491288i \(-0.836526\pi\)
−0.870997 + 0.491288i \(0.836526\pi\)
\(30\) 1.15528 0.210925
\(31\) 4.44905 0.799074 0.399537 0.916717i \(-0.369171\pi\)
0.399537 + 0.916717i \(0.369171\pi\)
\(32\) −5.16181 −0.912488
\(33\) 4.31124 0.750490
\(34\) −1.65483 −0.283800
\(35\) 1.00000 0.169031
\(36\) −3.29716 −0.549527
\(37\) −5.76682 −0.948060 −0.474030 0.880509i \(-0.657201\pi\)
−0.474030 + 0.880509i \(0.657201\pi\)
\(38\) −4.17599 −0.677434
\(39\) 3.91639 0.627125
\(40\) −1.94410 −0.307389
\(41\) −2.45236 −0.382994 −0.191497 0.981493i \(-0.561334\pi\)
−0.191497 + 0.981493i \(0.561334\pi\)
\(42\) 1.15528 0.178264
\(43\) 5.49412 0.837845 0.418923 0.908022i \(-0.362408\pi\)
0.418923 + 0.908022i \(0.362408\pi\)
\(44\) −3.36286 −0.506970
\(45\) −1.90801 −0.284429
\(46\) −4.20696 −0.620282
\(47\) −7.29838 −1.06458 −0.532289 0.846563i \(-0.678668\pi\)
−0.532289 + 0.846563i \(0.678668\pi\)
\(48\) 5.41073 0.780971
\(49\) 1.00000 0.142857
\(50\) −0.521477 −0.0737480
\(51\) 7.03024 0.984431
\(52\) −3.05487 −0.423634
\(53\) −3.09207 −0.424729 −0.212364 0.977191i \(-0.568116\pi\)
−0.212364 + 0.977191i \(0.568116\pi\)
\(54\) 1.26156 0.171676
\(55\) −1.94603 −0.262402
\(56\) −1.94410 −0.259791
\(57\) 17.7409 2.34985
\(58\) 4.89194 0.642343
\(59\) −4.07297 −0.530255 −0.265128 0.964213i \(-0.585414\pi\)
−0.265128 + 0.964213i \(0.585414\pi\)
\(60\) 3.82835 0.494238
\(61\) 13.1374 1.68207 0.841033 0.540983i \(-0.181948\pi\)
0.841033 + 0.540983i \(0.181948\pi\)
\(62\) −2.32008 −0.294650
\(63\) −1.90801 −0.240387
\(64\) −2.19288 −0.274110
\(65\) −1.76780 −0.219269
\(66\) −2.24821 −0.276736
\(67\) 2.43612 0.297620 0.148810 0.988866i \(-0.452456\pi\)
0.148810 + 0.988866i \(0.452456\pi\)
\(68\) −5.48374 −0.665001
\(69\) 17.8725 2.15160
\(70\) −0.521477 −0.0623284
\(71\) −2.59448 −0.307909 −0.153954 0.988078i \(-0.549201\pi\)
−0.153954 + 0.988078i \(0.549201\pi\)
\(72\) 3.70936 0.437152
\(73\) 14.4455 1.69071 0.845357 0.534202i \(-0.179388\pi\)
0.845357 + 0.534202i \(0.179388\pi\)
\(74\) 3.00726 0.349587
\(75\) 2.21540 0.255813
\(76\) −13.8383 −1.58736
\(77\) −1.94603 −0.221771
\(78\) −2.04231 −0.231246
\(79\) 1.80474 0.203050 0.101525 0.994833i \(-0.467628\pi\)
0.101525 + 0.994833i \(0.467628\pi\)
\(80\) −2.44232 −0.273060
\(81\) −11.0835 −1.23150
\(82\) 1.27885 0.141225
\(83\) −6.57950 −0.722194 −0.361097 0.932528i \(-0.617598\pi\)
−0.361097 + 0.932528i \(0.617598\pi\)
\(84\) 3.82835 0.417708
\(85\) −3.17335 −0.344198
\(86\) −2.86506 −0.308947
\(87\) −20.7825 −2.22812
\(88\) 3.78327 0.403298
\(89\) −11.5305 −1.22223 −0.611115 0.791542i \(-0.709279\pi\)
−0.611115 + 0.791542i \(0.709279\pi\)
\(90\) 0.994983 0.104880
\(91\) −1.76780 −0.185316
\(92\) −13.9410 −1.45344
\(93\) 9.85644 1.02207
\(94\) 3.80594 0.392552
\(95\) −8.00800 −0.821603
\(96\) −11.4355 −1.16713
\(97\) 4.26564 0.433110 0.216555 0.976270i \(-0.430518\pi\)
0.216555 + 0.976270i \(0.430518\pi\)
\(98\) −0.521477 −0.0526771
\(99\) 3.71304 0.373175
\(100\) −1.72806 −0.172806
\(101\) 8.68195 0.863886 0.431943 0.901901i \(-0.357828\pi\)
0.431943 + 0.901901i \(0.357828\pi\)
\(102\) −3.66611 −0.362999
\(103\) −6.86999 −0.676920 −0.338460 0.940981i \(-0.609906\pi\)
−0.338460 + 0.940981i \(0.609906\pi\)
\(104\) 3.43678 0.337004
\(105\) 2.21540 0.216201
\(106\) 1.61244 0.156614
\(107\) 12.2170 1.18106 0.590532 0.807014i \(-0.298918\pi\)
0.590532 + 0.807014i \(0.298918\pi\)
\(108\) 4.18052 0.402271
\(109\) 10.0997 0.967372 0.483686 0.875242i \(-0.339298\pi\)
0.483686 + 0.875242i \(0.339298\pi\)
\(110\) 1.01481 0.0967582
\(111\) −12.7758 −1.21263
\(112\) −2.44232 −0.230778
\(113\) 0.766277 0.0720853 0.0360426 0.999350i \(-0.488525\pi\)
0.0360426 + 0.999350i \(0.488525\pi\)
\(114\) −9.25149 −0.866481
\(115\) −8.06739 −0.752288
\(116\) 16.2108 1.50514
\(117\) 3.37298 0.311833
\(118\) 2.12396 0.195526
\(119\) −3.17335 −0.290900
\(120\) −4.30696 −0.393170
\(121\) −7.21297 −0.655725
\(122\) −6.85083 −0.620245
\(123\) −5.43296 −0.489874
\(124\) −7.68824 −0.690424
\(125\) −1.00000 −0.0894427
\(126\) 0.994983 0.0886401
\(127\) 7.76968 0.689447 0.344724 0.938704i \(-0.387973\pi\)
0.344724 + 0.938704i \(0.387973\pi\)
\(128\) 11.4672 1.01356
\(129\) 12.1717 1.07166
\(130\) 0.921868 0.0808532
\(131\) 4.15239 0.362796 0.181398 0.983410i \(-0.441938\pi\)
0.181398 + 0.983410i \(0.441938\pi\)
\(132\) −7.45009 −0.648447
\(133\) −8.00800 −0.694381
\(134\) −1.27038 −0.109744
\(135\) 2.41920 0.208211
\(136\) 6.16930 0.529013
\(137\) −14.4146 −1.23152 −0.615760 0.787934i \(-0.711151\pi\)
−0.615760 + 0.787934i \(0.711151\pi\)
\(138\) −9.32011 −0.793380
\(139\) −14.0854 −1.19470 −0.597352 0.801979i \(-0.703781\pi\)
−0.597352 + 0.801979i \(0.703781\pi\)
\(140\) −1.72806 −0.146048
\(141\) −16.1688 −1.36166
\(142\) 1.35296 0.113538
\(143\) 3.44019 0.287684
\(144\) 4.65997 0.388331
\(145\) 9.38093 0.779044
\(146\) −7.53297 −0.623433
\(147\) 2.21540 0.182723
\(148\) 9.96542 0.819153
\(149\) 11.5097 0.942914 0.471457 0.881889i \(-0.343728\pi\)
0.471457 + 0.881889i \(0.343728\pi\)
\(150\) −1.15528 −0.0943283
\(151\) −10.4398 −0.849578 −0.424789 0.905292i \(-0.639652\pi\)
−0.424789 + 0.905292i \(0.639652\pi\)
\(152\) 15.5683 1.26276
\(153\) 6.05478 0.489500
\(154\) 1.01481 0.0817756
\(155\) −4.44905 −0.357357
\(156\) −6.76777 −0.541855
\(157\) −24.6599 −1.96807 −0.984036 0.177967i \(-0.943048\pi\)
−0.984036 + 0.177967i \(0.943048\pi\)
\(158\) −0.941133 −0.0748725
\(159\) −6.85018 −0.543255
\(160\) 5.16181 0.408077
\(161\) −8.06739 −0.635800
\(162\) 5.77980 0.454104
\(163\) 16.1527 1.26518 0.632589 0.774487i \(-0.281992\pi\)
0.632589 + 0.774487i \(0.281992\pi\)
\(164\) 4.23783 0.330919
\(165\) −4.31124 −0.335629
\(166\) 3.43106 0.266302
\(167\) 12.4168 0.960842 0.480421 0.877038i \(-0.340484\pi\)
0.480421 + 0.877038i \(0.340484\pi\)
\(168\) −4.30696 −0.332289
\(169\) −9.87488 −0.759606
\(170\) 1.65483 0.126919
\(171\) 15.2793 1.16844
\(172\) −9.49418 −0.723924
\(173\) −14.6928 −1.11707 −0.558536 0.829480i \(-0.688637\pi\)
−0.558536 + 0.829480i \(0.688637\pi\)
\(174\) 10.8376 0.821597
\(175\) −1.00000 −0.0755929
\(176\) 4.75283 0.358258
\(177\) −9.02327 −0.678230
\(178\) 6.01288 0.450685
\(179\) 9.42205 0.704237 0.352119 0.935955i \(-0.385461\pi\)
0.352119 + 0.935955i \(0.385461\pi\)
\(180\) 3.29716 0.245756
\(181\) 20.6969 1.53839 0.769194 0.639016i \(-0.220658\pi\)
0.769194 + 0.639016i \(0.220658\pi\)
\(182\) 0.921868 0.0683334
\(183\) 29.1045 2.15147
\(184\) 15.6838 1.15622
\(185\) 5.76682 0.423985
\(186\) −5.13991 −0.376876
\(187\) 6.17542 0.451592
\(188\) 12.6120 0.919828
\(189\) 2.41920 0.175971
\(190\) 4.17599 0.302958
\(191\) 19.0734 1.38010 0.690052 0.723760i \(-0.257588\pi\)
0.690052 + 0.723760i \(0.257588\pi\)
\(192\) −4.85811 −0.350604
\(193\) 23.5476 1.69499 0.847496 0.530802i \(-0.178109\pi\)
0.847496 + 0.530802i \(0.178109\pi\)
\(194\) −2.22443 −0.159705
\(195\) −3.91639 −0.280459
\(196\) −1.72806 −0.123433
\(197\) 10.3337 0.736243 0.368121 0.929778i \(-0.380001\pi\)
0.368121 + 0.929778i \(0.380001\pi\)
\(198\) −1.93627 −0.137604
\(199\) −4.58436 −0.324976 −0.162488 0.986710i \(-0.551952\pi\)
−0.162488 + 0.986710i \(0.551952\pi\)
\(200\) 1.94410 0.137468
\(201\) 5.39700 0.380675
\(202\) −4.52743 −0.318549
\(203\) 9.38093 0.658412
\(204\) −12.1487 −0.850578
\(205\) 2.45236 0.171280
\(206\) 3.58254 0.249607
\(207\) 15.3927 1.06986
\(208\) 4.31754 0.299368
\(209\) 15.5838 1.07795
\(210\) −1.15528 −0.0797220
\(211\) 9.78267 0.673467 0.336733 0.941600i \(-0.390678\pi\)
0.336733 + 0.941600i \(0.390678\pi\)
\(212\) 5.34329 0.366979
\(213\) −5.74783 −0.393835
\(214\) −6.37089 −0.435505
\(215\) −5.49412 −0.374696
\(216\) −4.70316 −0.320009
\(217\) −4.44905 −0.302021
\(218\) −5.26674 −0.356709
\(219\) 32.0025 2.16253
\(220\) 3.36286 0.226724
\(221\) 5.60985 0.377359
\(222\) 6.66230 0.447144
\(223\) 4.86837 0.326010 0.163005 0.986625i \(-0.447881\pi\)
0.163005 + 0.986625i \(0.447881\pi\)
\(224\) 5.16181 0.344888
\(225\) 1.90801 0.127201
\(226\) −0.399596 −0.0265807
\(227\) 21.3861 1.41944 0.709722 0.704482i \(-0.248820\pi\)
0.709722 + 0.704482i \(0.248820\pi\)
\(228\) −30.6574 −2.03034
\(229\) 1.00000 0.0660819
\(230\) 4.20696 0.277399
\(231\) −4.31124 −0.283659
\(232\) −18.2374 −1.19735
\(233\) 3.40775 0.223249 0.111624 0.993750i \(-0.464395\pi\)
0.111624 + 0.993750i \(0.464395\pi\)
\(234\) −1.75893 −0.114985
\(235\) 7.29838 0.476094
\(236\) 7.03834 0.458157
\(237\) 3.99824 0.259713
\(238\) 1.65483 0.107266
\(239\) 13.2065 0.854255 0.427127 0.904191i \(-0.359526\pi\)
0.427127 + 0.904191i \(0.359526\pi\)
\(240\) −5.41073 −0.349261
\(241\) 20.7817 1.33867 0.669334 0.742962i \(-0.266580\pi\)
0.669334 + 0.742962i \(0.266580\pi\)
\(242\) 3.76140 0.241792
\(243\) −17.2969 −1.10960
\(244\) −22.7022 −1.45336
\(245\) −1.00000 −0.0638877
\(246\) 2.83316 0.180636
\(247\) 14.1566 0.900760
\(248\) 8.64939 0.549237
\(249\) −14.5762 −0.923732
\(250\) 0.521477 0.0329811
\(251\) 22.6681 1.43080 0.715400 0.698715i \(-0.246244\pi\)
0.715400 + 0.698715i \(0.246244\pi\)
\(252\) 3.29716 0.207702
\(253\) 15.6994 0.987011
\(254\) −4.05171 −0.254227
\(255\) −7.03024 −0.440251
\(256\) −1.59410 −0.0996311
\(257\) 6.45052 0.402372 0.201186 0.979553i \(-0.435520\pi\)
0.201186 + 0.979553i \(0.435520\pi\)
\(258\) −6.34725 −0.395163
\(259\) 5.76682 0.358333
\(260\) 3.05487 0.189455
\(261\) −17.8989 −1.10791
\(262\) −2.16537 −0.133777
\(263\) 5.20949 0.321231 0.160616 0.987017i \(-0.448652\pi\)
0.160616 + 0.987017i \(0.448652\pi\)
\(264\) 8.38147 0.515844
\(265\) 3.09207 0.189944
\(266\) 4.17599 0.256046
\(267\) −25.5447 −1.56331
\(268\) −4.20977 −0.257153
\(269\) −22.1049 −1.34776 −0.673881 0.738840i \(-0.735374\pi\)
−0.673881 + 0.738840i \(0.735374\pi\)
\(270\) −1.26156 −0.0767758
\(271\) −2.22456 −0.135132 −0.0675661 0.997715i \(-0.521523\pi\)
−0.0675661 + 0.997715i \(0.521523\pi\)
\(272\) 7.75033 0.469933
\(273\) −3.91639 −0.237031
\(274\) 7.51686 0.454110
\(275\) 1.94603 0.117350
\(276\) −30.8848 −1.85905
\(277\) −26.0570 −1.56562 −0.782808 0.622264i \(-0.786213\pi\)
−0.782808 + 0.622264i \(0.786213\pi\)
\(278\) 7.34519 0.440535
\(279\) 8.48884 0.508213
\(280\) 1.94410 0.116182
\(281\) −28.3543 −1.69148 −0.845739 0.533597i \(-0.820840\pi\)
−0.845739 + 0.533597i \(0.820840\pi\)
\(282\) 8.43168 0.502099
\(283\) 7.94287 0.472154 0.236077 0.971734i \(-0.424138\pi\)
0.236077 + 0.971734i \(0.424138\pi\)
\(284\) 4.48343 0.266043
\(285\) −17.7409 −1.05088
\(286\) −1.79398 −0.106080
\(287\) 2.45236 0.144758
\(288\) −9.84879 −0.580345
\(289\) −6.92987 −0.407640
\(290\) −4.89194 −0.287264
\(291\) 9.45011 0.553975
\(292\) −24.9627 −1.46083
\(293\) 4.74681 0.277311 0.138656 0.990341i \(-0.455722\pi\)
0.138656 + 0.990341i \(0.455722\pi\)
\(294\) −1.15528 −0.0673774
\(295\) 4.07297 0.237137
\(296\) −11.2113 −0.651642
\(297\) −4.70783 −0.273176
\(298\) −6.00206 −0.347690
\(299\) 14.2616 0.824767
\(300\) −3.82835 −0.221030
\(301\) −5.49412 −0.316676
\(302\) 5.44411 0.313273
\(303\) 19.2340 1.10497
\(304\) 19.5581 1.12173
\(305\) −13.1374 −0.752243
\(306\) −3.15743 −0.180498
\(307\) 21.7657 1.24224 0.621118 0.783717i \(-0.286679\pi\)
0.621118 + 0.783717i \(0.286679\pi\)
\(308\) 3.36286 0.191617
\(309\) −15.2198 −0.865823
\(310\) 2.32008 0.131772
\(311\) −3.62981 −0.205828 −0.102914 0.994690i \(-0.532817\pi\)
−0.102914 + 0.994690i \(0.532817\pi\)
\(312\) 7.61385 0.431050
\(313\) −31.8759 −1.80173 −0.900865 0.434099i \(-0.857067\pi\)
−0.900865 + 0.434099i \(0.857067\pi\)
\(314\) 12.8596 0.725707
\(315\) 1.90801 0.107504
\(316\) −3.11871 −0.175441
\(317\) −11.3583 −0.637948 −0.318974 0.947763i \(-0.603338\pi\)
−0.318974 + 0.947763i \(0.603338\pi\)
\(318\) 3.57221 0.200320
\(319\) −18.2556 −1.02211
\(320\) 2.19288 0.122586
\(321\) 27.0656 1.51066
\(322\) 4.20696 0.234445
\(323\) 25.4121 1.41397
\(324\) 19.1530 1.06406
\(325\) 1.76780 0.0980600
\(326\) −8.42327 −0.466522
\(327\) 22.3748 1.23733
\(328\) −4.76762 −0.263248
\(329\) 7.29838 0.402373
\(330\) 2.24821 0.123760
\(331\) −5.58681 −0.307079 −0.153540 0.988143i \(-0.549067\pi\)
−0.153540 + 0.988143i \(0.549067\pi\)
\(332\) 11.3698 0.623998
\(333\) −11.0032 −0.602969
\(334\) −6.47508 −0.354301
\(335\) −2.43612 −0.133100
\(336\) −5.41073 −0.295179
\(337\) 34.2765 1.86716 0.933579 0.358371i \(-0.116668\pi\)
0.933579 + 0.358371i \(0.116668\pi\)
\(338\) 5.14952 0.280097
\(339\) 1.69761 0.0922016
\(340\) 5.48374 0.297397
\(341\) 8.65799 0.468856
\(342\) −7.96782 −0.430850
\(343\) −1.00000 −0.0539949
\(344\) 10.6811 0.575887
\(345\) −17.8725 −0.962224
\(346\) 7.66195 0.411909
\(347\) −6.91428 −0.371178 −0.185589 0.982627i \(-0.559419\pi\)
−0.185589 + 0.982627i \(0.559419\pi\)
\(348\) 35.9135 1.92517
\(349\) −34.7541 −1.86035 −0.930173 0.367123i \(-0.880343\pi\)
−0.930173 + 0.367123i \(0.880343\pi\)
\(350\) 0.521477 0.0278741
\(351\) −4.27666 −0.228271
\(352\) −10.0450 −0.535402
\(353\) −3.26561 −0.173811 −0.0869054 0.996217i \(-0.527698\pi\)
−0.0869054 + 0.996217i \(0.527698\pi\)
\(354\) 4.70542 0.250090
\(355\) 2.59448 0.137701
\(356\) 19.9254 1.05604
\(357\) −7.03024 −0.372080
\(358\) −4.91338 −0.259680
\(359\) 24.6523 1.30110 0.650550 0.759463i \(-0.274538\pi\)
0.650550 + 0.759463i \(0.274538\pi\)
\(360\) −3.70936 −0.195500
\(361\) 45.1280 2.37516
\(362\) −10.7929 −0.567265
\(363\) −15.9796 −0.838713
\(364\) 3.05487 0.160119
\(365\) −14.4455 −0.756110
\(366\) −15.1773 −0.793333
\(367\) 10.6833 0.557665 0.278832 0.960340i \(-0.410053\pi\)
0.278832 + 0.960340i \(0.410053\pi\)
\(368\) 19.7032 1.02710
\(369\) −4.67912 −0.243585
\(370\) −3.00726 −0.156340
\(371\) 3.09207 0.160532
\(372\) −17.0325 −0.883096
\(373\) −16.3923 −0.848761 −0.424381 0.905484i \(-0.639508\pi\)
−0.424381 + 0.905484i \(0.639508\pi\)
\(374\) −3.22034 −0.166520
\(375\) −2.21540 −0.114403
\(376\) −14.1888 −0.731730
\(377\) −16.5836 −0.854100
\(378\) −1.26156 −0.0648874
\(379\) 36.8033 1.89046 0.945228 0.326410i \(-0.105839\pi\)
0.945228 + 0.326410i \(0.105839\pi\)
\(380\) 13.8383 0.709891
\(381\) 17.2130 0.881847
\(382\) −9.94634 −0.508899
\(383\) −17.1835 −0.878036 −0.439018 0.898478i \(-0.644674\pi\)
−0.439018 + 0.898478i \(0.644674\pi\)
\(384\) 25.4044 1.29641
\(385\) 1.94603 0.0991788
\(386\) −12.2795 −0.625011
\(387\) 10.4828 0.532872
\(388\) −7.37129 −0.374220
\(389\) 32.5302 1.64935 0.824675 0.565608i \(-0.191358\pi\)
0.824675 + 0.565608i \(0.191358\pi\)
\(390\) 2.04231 0.103416
\(391\) 25.6006 1.29468
\(392\) 1.94410 0.0981918
\(393\) 9.19921 0.464039
\(394\) −5.38876 −0.271482
\(395\) −1.80474 −0.0908066
\(396\) −6.41637 −0.322435
\(397\) −9.64015 −0.483825 −0.241913 0.970298i \(-0.577775\pi\)
−0.241913 + 0.970298i \(0.577775\pi\)
\(398\) 2.39064 0.119832
\(399\) −17.7409 −0.888158
\(400\) 2.44232 0.122116
\(401\) −22.6165 −1.12941 −0.564707 0.825291i \(-0.691011\pi\)
−0.564707 + 0.825291i \(0.691011\pi\)
\(402\) −2.81441 −0.140370
\(403\) 7.86505 0.391786
\(404\) −15.0029 −0.746424
\(405\) 11.0835 0.550745
\(406\) −4.89194 −0.242783
\(407\) −11.2224 −0.556274
\(408\) 13.6675 0.676641
\(409\) 33.3648 1.64979 0.824893 0.565289i \(-0.191236\pi\)
0.824893 + 0.565289i \(0.191236\pi\)
\(410\) −1.27885 −0.0631578
\(411\) −31.9341 −1.57519
\(412\) 11.8718 0.584880
\(413\) 4.07297 0.200418
\(414\) −8.02692 −0.394501
\(415\) 6.57950 0.322975
\(416\) −9.12506 −0.447393
\(417\) −31.2047 −1.52810
\(418\) −8.12659 −0.397484
\(419\) 40.1626 1.96207 0.981036 0.193824i \(-0.0620892\pi\)
0.981036 + 0.193824i \(0.0620892\pi\)
\(420\) −3.82835 −0.186805
\(421\) −6.45628 −0.314660 −0.157330 0.987546i \(-0.550289\pi\)
−0.157330 + 0.987546i \(0.550289\pi\)
\(422\) −5.10144 −0.248334
\(423\) −13.9254 −0.677075
\(424\) −6.01129 −0.291934
\(425\) 3.17335 0.153930
\(426\) 2.99736 0.145223
\(427\) −13.1374 −0.635761
\(428\) −21.1118 −1.02048
\(429\) 7.62142 0.367965
\(430\) 2.86506 0.138165
\(431\) −6.82850 −0.328917 −0.164459 0.986384i \(-0.552588\pi\)
−0.164459 + 0.986384i \(0.552588\pi\)
\(432\) −5.90846 −0.284271
\(433\) −1.09315 −0.0525335 −0.0262667 0.999655i \(-0.508362\pi\)
−0.0262667 + 0.999655i \(0.508362\pi\)
\(434\) 2.32008 0.111367
\(435\) 20.7825 0.996446
\(436\) −17.4528 −0.835839
\(437\) 64.6036 3.09041
\(438\) −16.6886 −0.797411
\(439\) 23.0556 1.10038 0.550192 0.835038i \(-0.314554\pi\)
0.550192 + 0.835038i \(0.314554\pi\)
\(440\) −3.78327 −0.180360
\(441\) 1.90801 0.0908576
\(442\) −2.92541 −0.139147
\(443\) 12.2707 0.582999 0.291500 0.956571i \(-0.405846\pi\)
0.291500 + 0.956571i \(0.405846\pi\)
\(444\) 22.0774 1.04775
\(445\) 11.5305 0.546598
\(446\) −2.53874 −0.120213
\(447\) 25.4987 1.20605
\(448\) 2.19288 0.103604
\(449\) −20.3262 −0.959254 −0.479627 0.877473i \(-0.659228\pi\)
−0.479627 + 0.877473i \(0.659228\pi\)
\(450\) −0.994983 −0.0469040
\(451\) −4.77236 −0.224722
\(452\) −1.32417 −0.0622839
\(453\) −23.1283 −1.08666
\(454\) −11.1523 −0.523406
\(455\) 1.76780 0.0828758
\(456\) 34.4901 1.61515
\(457\) 21.2711 0.995022 0.497511 0.867458i \(-0.334247\pi\)
0.497511 + 0.867458i \(0.334247\pi\)
\(458\) −0.521477 −0.0243670
\(459\) −7.67695 −0.358329
\(460\) 13.9410 0.650000
\(461\) 29.7055 1.38352 0.691762 0.722126i \(-0.256835\pi\)
0.691762 + 0.722126i \(0.256835\pi\)
\(462\) 2.24821 0.104596
\(463\) −7.63301 −0.354736 −0.177368 0.984145i \(-0.556758\pi\)
−0.177368 + 0.984145i \(0.556758\pi\)
\(464\) −22.9112 −1.06363
\(465\) −9.85644 −0.457082
\(466\) −1.77706 −0.0823208
\(467\) −10.7663 −0.498205 −0.249103 0.968477i \(-0.580136\pi\)
−0.249103 + 0.968477i \(0.580136\pi\)
\(468\) −5.82873 −0.269433
\(469\) −2.43612 −0.112490
\(470\) −3.80594 −0.175555
\(471\) −54.6316 −2.51729
\(472\) −7.91825 −0.364467
\(473\) 10.6917 0.491606
\(474\) −2.08499 −0.0957667
\(475\) 8.00800 0.367432
\(476\) 5.48374 0.251347
\(477\) −5.89970 −0.270129
\(478\) −6.88686 −0.314998
\(479\) −18.1989 −0.831528 −0.415764 0.909472i \(-0.636486\pi\)
−0.415764 + 0.909472i \(0.636486\pi\)
\(480\) 11.4355 0.521956
\(481\) −10.1946 −0.464834
\(482\) −10.8372 −0.493620
\(483\) −17.8725 −0.813228
\(484\) 12.4645 0.566566
\(485\) −4.26564 −0.193693
\(486\) 9.01993 0.409152
\(487\) 12.6195 0.571843 0.285922 0.958253i \(-0.407700\pi\)
0.285922 + 0.958253i \(0.407700\pi\)
\(488\) 25.5403 1.15616
\(489\) 35.7848 1.61824
\(490\) 0.521477 0.0235579
\(491\) 14.2955 0.645146 0.322573 0.946545i \(-0.395452\pi\)
0.322573 + 0.946545i \(0.395452\pi\)
\(492\) 9.38849 0.423266
\(493\) −29.7689 −1.34073
\(494\) −7.38232 −0.332146
\(495\) −3.71304 −0.166889
\(496\) 10.8660 0.487899
\(497\) 2.59448 0.116379
\(498\) 7.60118 0.340617
\(499\) 0.229430 0.0102707 0.00513534 0.999987i \(-0.498365\pi\)
0.00513534 + 0.999987i \(0.498365\pi\)
\(500\) 1.72806 0.0772813
\(501\) 27.5083 1.22898
\(502\) −11.8209 −0.527593
\(503\) 22.2710 0.993014 0.496507 0.868033i \(-0.334616\pi\)
0.496507 + 0.868033i \(0.334616\pi\)
\(504\) −3.70936 −0.165228
\(505\) −8.68195 −0.386342
\(506\) −8.18686 −0.363950
\(507\) −21.8768 −0.971584
\(508\) −13.4265 −0.595704
\(509\) 35.8978 1.59114 0.795570 0.605862i \(-0.207171\pi\)
0.795570 + 0.605862i \(0.207171\pi\)
\(510\) 3.66611 0.162338
\(511\) −14.4455 −0.639030
\(512\) −22.1030 −0.976825
\(513\) −19.3729 −0.855336
\(514\) −3.36380 −0.148371
\(515\) 6.86999 0.302728
\(516\) −21.0334 −0.925945
\(517\) −14.2029 −0.624641
\(518\) −3.00726 −0.132132
\(519\) −32.5505 −1.42881
\(520\) −3.43678 −0.150713
\(521\) −29.5646 −1.29525 −0.647625 0.761960i \(-0.724237\pi\)
−0.647625 + 0.761960i \(0.724237\pi\)
\(522\) 9.33386 0.408532
\(523\) 19.2331 0.841004 0.420502 0.907292i \(-0.361854\pi\)
0.420502 + 0.907292i \(0.361854\pi\)
\(524\) −7.17558 −0.313467
\(525\) −2.21540 −0.0966881
\(526\) −2.71663 −0.118451
\(527\) 14.1184 0.615007
\(528\) 10.5294 0.458235
\(529\) 42.0828 1.82969
\(530\) −1.61244 −0.0700401
\(531\) −7.77126 −0.337244
\(532\) 13.8383 0.599967
\(533\) −4.33528 −0.187782
\(534\) 13.3210 0.576454
\(535\) −12.2170 −0.528188
\(536\) 4.73606 0.204567
\(537\) 20.8736 0.900764
\(538\) 11.5272 0.496973
\(539\) 1.94603 0.0838214
\(540\) −4.18052 −0.179901
\(541\) −28.0213 −1.20473 −0.602365 0.798221i \(-0.705775\pi\)
−0.602365 + 0.798221i \(0.705775\pi\)
\(542\) 1.16005 0.0498286
\(543\) 45.8519 1.96770
\(544\) −16.3802 −0.702296
\(545\) −10.0997 −0.432622
\(546\) 2.04231 0.0874028
\(547\) −4.05384 −0.173330 −0.0866648 0.996238i \(-0.527621\pi\)
−0.0866648 + 0.996238i \(0.527621\pi\)
\(548\) 24.9093 1.06407
\(549\) 25.0662 1.06980
\(550\) −1.01481 −0.0432716
\(551\) −75.1224 −3.20032
\(552\) 34.7459 1.47889
\(553\) −1.80474 −0.0767456
\(554\) 13.5881 0.577305
\(555\) 12.7758 0.542304
\(556\) 24.3404 1.03226
\(557\) −5.90559 −0.250228 −0.125114 0.992142i \(-0.539930\pi\)
−0.125114 + 0.992142i \(0.539930\pi\)
\(558\) −4.42673 −0.187399
\(559\) 9.71252 0.410796
\(560\) 2.44232 0.103207
\(561\) 13.6811 0.577614
\(562\) 14.7861 0.623715
\(563\) −0.508143 −0.0214157 −0.0107078 0.999943i \(-0.503408\pi\)
−0.0107078 + 0.999943i \(0.503408\pi\)
\(564\) 27.9408 1.17652
\(565\) −0.766277 −0.0322375
\(566\) −4.14202 −0.174102
\(567\) 11.0835 0.465464
\(568\) −5.04393 −0.211639
\(569\) −42.1989 −1.76907 −0.884535 0.466474i \(-0.845524\pi\)
−0.884535 + 0.466474i \(0.845524\pi\)
\(570\) 9.25149 0.387502
\(571\) 24.4134 1.02167 0.510834 0.859680i \(-0.329337\pi\)
0.510834 + 0.859680i \(0.329337\pi\)
\(572\) −5.94487 −0.248567
\(573\) 42.2553 1.76524
\(574\) −1.27885 −0.0533781
\(575\) 8.06739 0.336433
\(576\) −4.18404 −0.174335
\(577\) 17.7582 0.739285 0.369643 0.929174i \(-0.379480\pi\)
0.369643 + 0.929174i \(0.379480\pi\)
\(578\) 3.61377 0.150313
\(579\) 52.1674 2.16800
\(580\) −16.2108 −0.673118
\(581\) 6.57950 0.272964
\(582\) −4.92801 −0.204273
\(583\) −6.01726 −0.249209
\(584\) 28.0834 1.16210
\(585\) −3.37298 −0.139456
\(586\) −2.47535 −0.102256
\(587\) −10.6472 −0.439455 −0.219728 0.975561i \(-0.570517\pi\)
−0.219728 + 0.975561i \(0.570517\pi\)
\(588\) −3.82835 −0.157879
\(589\) 35.6280 1.46803
\(590\) −2.12396 −0.0874420
\(591\) 22.8932 0.941701
\(592\) −14.0844 −0.578867
\(593\) −39.3692 −1.61670 −0.808349 0.588703i \(-0.799639\pi\)
−0.808349 + 0.588703i \(0.799639\pi\)
\(594\) 2.45502 0.100731
\(595\) 3.17335 0.130095
\(596\) −19.8895 −0.814707
\(597\) −10.1562 −0.415666
\(598\) −7.43707 −0.304124
\(599\) 24.1593 0.987124 0.493562 0.869711i \(-0.335695\pi\)
0.493562 + 0.869711i \(0.335695\pi\)
\(600\) 4.30696 0.175831
\(601\) 22.0904 0.901085 0.450542 0.892755i \(-0.351231\pi\)
0.450542 + 0.892755i \(0.351231\pi\)
\(602\) 2.86506 0.116771
\(603\) 4.64815 0.189287
\(604\) 18.0406 0.734061
\(605\) 7.21297 0.293249
\(606\) −10.0301 −0.407445
\(607\) −17.0574 −0.692337 −0.346169 0.938172i \(-0.612518\pi\)
−0.346169 + 0.938172i \(0.612518\pi\)
\(608\) −41.3358 −1.67639
\(609\) 20.7825 0.842151
\(610\) 6.85083 0.277382
\(611\) −12.9021 −0.521963
\(612\) −10.4630 −0.422943
\(613\) −39.5793 −1.59859 −0.799296 0.600937i \(-0.794794\pi\)
−0.799296 + 0.600937i \(0.794794\pi\)
\(614\) −11.3503 −0.458062
\(615\) 5.43296 0.219078
\(616\) −3.78327 −0.152432
\(617\) −46.6979 −1.87999 −0.939994 0.341191i \(-0.889170\pi\)
−0.939994 + 0.341191i \(0.889170\pi\)
\(618\) 7.93677 0.319264
\(619\) −7.43674 −0.298908 −0.149454 0.988769i \(-0.547752\pi\)
−0.149454 + 0.988769i \(0.547752\pi\)
\(620\) 7.68824 0.308767
\(621\) −19.5166 −0.783175
\(622\) 1.89286 0.0758968
\(623\) 11.5305 0.461959
\(624\) 9.56510 0.382910
\(625\) 1.00000 0.0400000
\(626\) 16.6225 0.664370
\(627\) 34.5244 1.37877
\(628\) 42.6138 1.70048
\(629\) −18.3001 −0.729674
\(630\) −0.994983 −0.0396411
\(631\) 30.6502 1.22016 0.610082 0.792338i \(-0.291136\pi\)
0.610082 + 0.792338i \(0.291136\pi\)
\(632\) 3.50860 0.139565
\(633\) 21.6726 0.861407
\(634\) 5.92311 0.235237
\(635\) −7.76968 −0.308330
\(636\) 11.8375 0.469389
\(637\) 1.76780 0.0700429
\(638\) 9.51985 0.376894
\(639\) −4.95030 −0.195831
\(640\) −11.4672 −0.453279
\(641\) −24.8632 −0.982039 −0.491020 0.871149i \(-0.663376\pi\)
−0.491020 + 0.871149i \(0.663376\pi\)
\(642\) −14.1141 −0.557039
\(643\) 27.4053 1.08076 0.540380 0.841421i \(-0.318281\pi\)
0.540380 + 0.841421i \(0.318281\pi\)
\(644\) 13.9410 0.549350
\(645\) −12.1717 −0.479260
\(646\) −13.2518 −0.521387
\(647\) −38.7464 −1.52328 −0.761639 0.648001i \(-0.775605\pi\)
−0.761639 + 0.648001i \(0.775605\pi\)
\(648\) −21.5475 −0.846464
\(649\) −7.92611 −0.311127
\(650\) −0.921868 −0.0361586
\(651\) −9.85644 −0.386305
\(652\) −27.9129 −1.09315
\(653\) 0.501317 0.0196180 0.00980902 0.999952i \(-0.496878\pi\)
0.00980902 + 0.999952i \(0.496878\pi\)
\(654\) −11.6680 −0.456253
\(655\) −4.15239 −0.162247
\(656\) −5.98945 −0.233849
\(657\) 27.5621 1.07530
\(658\) −3.80594 −0.148371
\(659\) −8.28075 −0.322572 −0.161286 0.986908i \(-0.551564\pi\)
−0.161286 + 0.986908i \(0.551564\pi\)
\(660\) 7.45009 0.289994
\(661\) −40.6226 −1.58003 −0.790017 0.613085i \(-0.789928\pi\)
−0.790017 + 0.613085i \(0.789928\pi\)
\(662\) 2.91339 0.113232
\(663\) 12.4281 0.482666
\(664\) −12.7912 −0.496395
\(665\) 8.00800 0.310537
\(666\) 5.73789 0.222339
\(667\) −75.6796 −2.93033
\(668\) −21.4570 −0.830198
\(669\) 10.7854 0.416987
\(670\) 1.27038 0.0490792
\(671\) 25.5657 0.986952
\(672\) 11.4355 0.441134
\(673\) −0.619618 −0.0238845 −0.0119423 0.999929i \(-0.503801\pi\)
−0.0119423 + 0.999929i \(0.503801\pi\)
\(674\) −17.8744 −0.688496
\(675\) −2.41920 −0.0931150
\(676\) 17.0644 0.656323
\(677\) 3.34551 0.128578 0.0642892 0.997931i \(-0.479522\pi\)
0.0642892 + 0.997931i \(0.479522\pi\)
\(678\) −0.885265 −0.0339984
\(679\) −4.26564 −0.163700
\(680\) −6.16930 −0.236582
\(681\) 47.3788 1.81556
\(682\) −4.51494 −0.172886
\(683\) −27.2802 −1.04385 −0.521923 0.852993i \(-0.674785\pi\)
−0.521923 + 0.852993i \(0.674785\pi\)
\(684\) −26.4036 −1.00957
\(685\) 14.4146 0.550752
\(686\) 0.521477 0.0199101
\(687\) 2.21540 0.0845229
\(688\) 13.4184 0.511572
\(689\) −5.46617 −0.208245
\(690\) 9.32011 0.354810
\(691\) −44.1591 −1.67989 −0.839946 0.542670i \(-0.817413\pi\)
−0.839946 + 0.542670i \(0.817413\pi\)
\(692\) 25.3901 0.965185
\(693\) −3.71304 −0.141047
\(694\) 3.60564 0.136868
\(695\) 14.0854 0.534288
\(696\) −40.4033 −1.53148
\(697\) −7.78218 −0.294771
\(698\) 18.1235 0.685983
\(699\) 7.54953 0.285550
\(700\) 1.72806 0.0653146
\(701\) −16.0814 −0.607388 −0.303694 0.952770i \(-0.598220\pi\)
−0.303694 + 0.952770i \(0.598220\pi\)
\(702\) 2.23018 0.0841727
\(703\) −46.1807 −1.74174
\(704\) −4.26741 −0.160834
\(705\) 16.1688 0.608954
\(706\) 1.70294 0.0640910
\(707\) −8.68195 −0.326518
\(708\) 15.5928 0.586012
\(709\) 49.1375 1.84540 0.922699 0.385522i \(-0.125979\pi\)
0.922699 + 0.385522i \(0.125979\pi\)
\(710\) −1.35296 −0.0507758
\(711\) 3.44347 0.129140
\(712\) −22.4164 −0.840090
\(713\) 35.8923 1.34418
\(714\) 3.66611 0.137201
\(715\) −3.44019 −0.128656
\(716\) −16.2819 −0.608483
\(717\) 29.2576 1.09265
\(718\) −12.8556 −0.479768
\(719\) −41.6531 −1.55340 −0.776699 0.629872i \(-0.783107\pi\)
−0.776699 + 0.629872i \(0.783107\pi\)
\(720\) −4.65997 −0.173667
\(721\) 6.86999 0.255852
\(722\) −23.5332 −0.875816
\(723\) 46.0399 1.71224
\(724\) −35.7655 −1.32921
\(725\) −9.38093 −0.348399
\(726\) 8.33301 0.309267
\(727\) −32.1494 −1.19235 −0.596177 0.802853i \(-0.703314\pi\)
−0.596177 + 0.802853i \(0.703314\pi\)
\(728\) −3.43678 −0.127376
\(729\) −5.06899 −0.187740
\(730\) 7.53297 0.278808
\(731\) 17.4347 0.644847
\(732\) −50.2945 −1.85894
\(733\) 5.04428 0.186315 0.0931575 0.995651i \(-0.470304\pi\)
0.0931575 + 0.995651i \(0.470304\pi\)
\(734\) −5.57111 −0.205633
\(735\) −2.21540 −0.0817164
\(736\) −41.6423 −1.53496
\(737\) 4.74077 0.174628
\(738\) 2.44005 0.0898197
\(739\) 2.82188 0.103805 0.0519023 0.998652i \(-0.483472\pi\)
0.0519023 + 0.998652i \(0.483472\pi\)
\(740\) −9.96542 −0.366336
\(741\) 31.3625 1.15213
\(742\) −1.61244 −0.0591947
\(743\) 28.1231 1.03174 0.515869 0.856668i \(-0.327469\pi\)
0.515869 + 0.856668i \(0.327469\pi\)
\(744\) 19.1619 0.702509
\(745\) −11.5097 −0.421684
\(746\) 8.54821 0.312972
\(747\) −12.5538 −0.459318
\(748\) −10.6715 −0.390189
\(749\) −12.2170 −0.446400
\(750\) 1.15528 0.0421849
\(751\) −20.6063 −0.751934 −0.375967 0.926633i \(-0.622689\pi\)
−0.375967 + 0.926633i \(0.622689\pi\)
\(752\) −17.8250 −0.650010
\(753\) 50.2191 1.83008
\(754\) 8.64798 0.314941
\(755\) 10.4398 0.379943
\(756\) −4.18052 −0.152044
\(757\) −21.1983 −0.770466 −0.385233 0.922819i \(-0.625879\pi\)
−0.385233 + 0.922819i \(0.625879\pi\)
\(758\) −19.1920 −0.697087
\(759\) 34.7804 1.26245
\(760\) −15.5683 −0.564723
\(761\) 40.4281 1.46552 0.732759 0.680489i \(-0.238232\pi\)
0.732759 + 0.680489i \(0.238232\pi\)
\(762\) −8.97616 −0.325172
\(763\) −10.0997 −0.365632
\(764\) −32.9600 −1.19245
\(765\) −6.05478 −0.218911
\(766\) 8.96080 0.323767
\(767\) −7.20020 −0.259984
\(768\) −3.53157 −0.127434
\(769\) 24.4831 0.882885 0.441442 0.897290i \(-0.354467\pi\)
0.441442 + 0.897290i \(0.354467\pi\)
\(770\) −1.01481 −0.0365712
\(771\) 14.2905 0.514660
\(772\) −40.6917 −1.46453
\(773\) −34.9088 −1.25558 −0.627792 0.778381i \(-0.716041\pi\)
−0.627792 + 0.778381i \(0.716041\pi\)
\(774\) −5.46656 −0.196491
\(775\) 4.44905 0.159815
\(776\) 8.29282 0.297695
\(777\) 12.7758 0.458330
\(778\) −16.9638 −0.608181
\(779\) −19.6385 −0.703621
\(780\) 6.76777 0.242325
\(781\) −5.04894 −0.180665
\(782\) −13.3501 −0.477400
\(783\) 22.6943 0.811029
\(784\) 2.44232 0.0872258
\(785\) 24.6599 0.880149
\(786\) −4.79718 −0.171110
\(787\) −3.32851 −0.118648 −0.0593242 0.998239i \(-0.518895\pi\)
−0.0593242 + 0.998239i \(0.518895\pi\)
\(788\) −17.8572 −0.636137
\(789\) 11.5411 0.410875
\(790\) 0.941133 0.0334840
\(791\) −0.766277 −0.0272457
\(792\) 7.21852 0.256499
\(793\) 23.2243 0.824718
\(794\) 5.02712 0.178406
\(795\) 6.85018 0.242951
\(796\) 7.92205 0.280790
\(797\) 23.6805 0.838807 0.419403 0.907800i \(-0.362239\pi\)
0.419403 + 0.907800i \(0.362239\pi\)
\(798\) 9.25149 0.327499
\(799\) −23.1603 −0.819352
\(800\) −5.16181 −0.182498
\(801\) −22.0003 −0.777342
\(802\) 11.7940 0.416460
\(803\) 28.1113 0.992026
\(804\) −9.32634 −0.328915
\(805\) 8.06739 0.284338
\(806\) −4.10144 −0.144467
\(807\) −48.9713 −1.72387
\(808\) 16.8786 0.593786
\(809\) −24.5365 −0.862658 −0.431329 0.902195i \(-0.641955\pi\)
−0.431329 + 0.902195i \(0.641955\pi\)
\(810\) −5.77980 −0.203082
\(811\) −14.8574 −0.521715 −0.260858 0.965377i \(-0.584005\pi\)
−0.260858 + 0.965377i \(0.584005\pi\)
\(812\) −16.2108 −0.568888
\(813\) −4.92829 −0.172843
\(814\) 5.85222 0.205120
\(815\) −16.1527 −0.565805
\(816\) 17.1701 0.601074
\(817\) 43.9969 1.53926
\(818\) −17.3990 −0.608341
\(819\) −3.37298 −0.117862
\(820\) −4.23783 −0.147991
\(821\) 5.58022 0.194751 0.0973755 0.995248i \(-0.468955\pi\)
0.0973755 + 0.995248i \(0.468955\pi\)
\(822\) 16.6529 0.580836
\(823\) −28.1659 −0.981802 −0.490901 0.871215i \(-0.663332\pi\)
−0.490901 + 0.871215i \(0.663332\pi\)
\(824\) −13.3559 −0.465276
\(825\) 4.31124 0.150098
\(826\) −2.12396 −0.0739020
\(827\) 40.2445 1.39944 0.699719 0.714418i \(-0.253308\pi\)
0.699719 + 0.714418i \(0.253308\pi\)
\(828\) −26.5995 −0.924396
\(829\) 12.7795 0.443849 0.221925 0.975064i \(-0.428766\pi\)
0.221925 + 0.975064i \(0.428766\pi\)
\(830\) −3.43106 −0.119094
\(831\) −57.7268 −2.00252
\(832\) −3.87658 −0.134396
\(833\) 3.17335 0.109950
\(834\) 16.2725 0.563472
\(835\) −12.4168 −0.429702
\(836\) −26.9298 −0.931385
\(837\) −10.7631 −0.372028
\(838\) −20.9439 −0.723494
\(839\) 31.7421 1.09586 0.547929 0.836525i \(-0.315416\pi\)
0.547929 + 0.836525i \(0.315416\pi\)
\(840\) 4.30696 0.148604
\(841\) 59.0018 2.03454
\(842\) 3.36680 0.116028
\(843\) −62.8163 −2.16351
\(844\) −16.9051 −0.581896
\(845\) 9.87488 0.339706
\(846\) 7.26176 0.249665
\(847\) 7.21297 0.247841
\(848\) −7.55183 −0.259331
\(849\) 17.5966 0.603915
\(850\) −1.65483 −0.0567601
\(851\) −46.5232 −1.59479
\(852\) 9.93260 0.340285
\(853\) −50.8267 −1.74027 −0.870137 0.492809i \(-0.835970\pi\)
−0.870137 + 0.492809i \(0.835970\pi\)
\(854\) 6.85083 0.234431
\(855\) −15.2793 −0.522542
\(856\) 23.7511 0.811795
\(857\) 49.9930 1.70773 0.853864 0.520496i \(-0.174253\pi\)
0.853864 + 0.520496i \(0.174253\pi\)
\(858\) −3.97439 −0.135684
\(859\) 9.67641 0.330155 0.165077 0.986281i \(-0.447213\pi\)
0.165077 + 0.986281i \(0.447213\pi\)
\(860\) 9.49418 0.323749
\(861\) 5.43296 0.185155
\(862\) 3.56090 0.121285
\(863\) 38.3629 1.30589 0.652944 0.757406i \(-0.273534\pi\)
0.652944 + 0.757406i \(0.273534\pi\)
\(864\) 12.4874 0.424831
\(865\) 14.6928 0.499570
\(866\) 0.570053 0.0193712
\(867\) −15.3525 −0.521397
\(868\) 7.68824 0.260956
\(869\) 3.51209 0.119139
\(870\) −10.8376 −0.367429
\(871\) 4.30659 0.145923
\(872\) 19.6347 0.664916
\(873\) 8.13888 0.275459
\(874\) −33.6893 −1.13956
\(875\) 1.00000 0.0338062
\(876\) −55.3023 −1.86849
\(877\) −32.2934 −1.09047 −0.545236 0.838283i \(-0.683560\pi\)
−0.545236 + 0.838283i \(0.683560\pi\)
\(878\) −12.0230 −0.405755
\(879\) 10.5161 0.354699
\(880\) −4.75283 −0.160218
\(881\) −4.98135 −0.167826 −0.0839130 0.996473i \(-0.526742\pi\)
−0.0839130 + 0.996473i \(0.526742\pi\)
\(882\) −0.994983 −0.0335028
\(883\) −8.17252 −0.275027 −0.137514 0.990500i \(-0.543911\pi\)
−0.137514 + 0.990500i \(0.543911\pi\)
\(884\) −9.69417 −0.326050
\(885\) 9.02327 0.303314
\(886\) −6.39890 −0.214975
\(887\) −15.3734 −0.516187 −0.258094 0.966120i \(-0.583094\pi\)
−0.258094 + 0.966120i \(0.583094\pi\)
\(888\) −24.8375 −0.833491
\(889\) −7.76968 −0.260587
\(890\) −6.01288 −0.201552
\(891\) −21.5689 −0.722584
\(892\) −8.41284 −0.281683
\(893\) −58.4454 −1.95580
\(894\) −13.2970 −0.444717
\(895\) −9.42205 −0.314944
\(896\) −11.4672 −0.383091
\(897\) 31.5951 1.05493
\(898\) 10.5997 0.353715
\(899\) −41.7362 −1.39198
\(900\) −3.29716 −0.109905
\(901\) −9.81221 −0.326892
\(902\) 2.48868 0.0828638
\(903\) −12.1717 −0.405048
\(904\) 1.48972 0.0495473
\(905\) −20.6969 −0.687988
\(906\) 12.0609 0.400696
\(907\) 45.3723 1.50656 0.753281 0.657698i \(-0.228470\pi\)
0.753281 + 0.657698i \(0.228470\pi\)
\(908\) −36.9565 −1.22644
\(909\) 16.5652 0.549434
\(910\) −0.921868 −0.0305596
\(911\) −11.3484 −0.375988 −0.187994 0.982170i \(-0.560199\pi\)
−0.187994 + 0.982170i \(0.560199\pi\)
\(912\) 43.3291 1.43477
\(913\) −12.8039 −0.423747
\(914\) −11.0924 −0.366904
\(915\) −29.1045 −0.962167
\(916\) −1.72806 −0.0570968
\(917\) −4.15239 −0.137124
\(918\) 4.00335 0.132130
\(919\) 1.39304 0.0459520 0.0229760 0.999736i \(-0.492686\pi\)
0.0229760 + 0.999736i \(0.492686\pi\)
\(920\) −15.6838 −0.517080
\(921\) 48.2199 1.58890
\(922\) −15.4907 −0.510160
\(923\) −4.58654 −0.150968
\(924\) 7.45009 0.245090
\(925\) −5.76682 −0.189612
\(926\) 3.98044 0.130805
\(927\) −13.1080 −0.430523
\(928\) 48.4226 1.58955
\(929\) −11.5469 −0.378842 −0.189421 0.981896i \(-0.560661\pi\)
−0.189421 + 0.981896i \(0.560661\pi\)
\(930\) 5.13991 0.168544
\(931\) 8.00800 0.262452
\(932\) −5.88880 −0.192894
\(933\) −8.04149 −0.263267
\(934\) 5.61438 0.183708
\(935\) −6.17542 −0.201958
\(936\) 6.55741 0.214336
\(937\) 19.9882 0.652986 0.326493 0.945200i \(-0.394133\pi\)
0.326493 + 0.945200i \(0.394133\pi\)
\(938\) 1.27038 0.0414795
\(939\) −70.6179 −2.30453
\(940\) −12.6120 −0.411360
\(941\) −13.2560 −0.432134 −0.216067 0.976379i \(-0.569323\pi\)
−0.216067 + 0.976379i \(0.569323\pi\)
\(942\) 28.4891 0.928225
\(943\) −19.7841 −0.644260
\(944\) −9.94750 −0.323764
\(945\) −2.41920 −0.0786965
\(946\) −5.57548 −0.181275
\(947\) 59.6926 1.93975 0.969875 0.243603i \(-0.0783294\pi\)
0.969875 + 0.243603i \(0.0783294\pi\)
\(948\) −6.90920 −0.224400
\(949\) 25.5367 0.828957
\(950\) −4.17599 −0.135487
\(951\) −25.1633 −0.815976
\(952\) −6.16930 −0.199948
\(953\) 42.0824 1.36318 0.681592 0.731733i \(-0.261288\pi\)
0.681592 + 0.731733i \(0.261288\pi\)
\(954\) 3.07656 0.0996073
\(955\) −19.0734 −0.617201
\(956\) −22.8216 −0.738103
\(957\) −40.4434 −1.30735
\(958\) 9.49030 0.306618
\(959\) 14.4146 0.465471
\(960\) 4.85811 0.156795
\(961\) −11.2059 −0.361482
\(962\) 5.31625 0.171403
\(963\) 23.3102 0.751160
\(964\) −35.9121 −1.15665
\(965\) −23.5476 −0.758023
\(966\) 9.32011 0.299870
\(967\) −1.19110 −0.0383031 −0.0191516 0.999817i \(-0.506097\pi\)
−0.0191516 + 0.999817i \(0.506097\pi\)
\(968\) −14.0227 −0.450707
\(969\) 56.2981 1.80856
\(970\) 2.22443 0.0714222
\(971\) −6.86428 −0.220285 −0.110143 0.993916i \(-0.535131\pi\)
−0.110143 + 0.993916i \(0.535131\pi\)
\(972\) 29.8901 0.958725
\(973\) 14.0854 0.451556
\(974\) −6.58077 −0.210861
\(975\) 3.91639 0.125425
\(976\) 32.0857 1.02704
\(977\) 12.0593 0.385812 0.192906 0.981217i \(-0.438209\pi\)
0.192906 + 0.981217i \(0.438209\pi\)
\(978\) −18.6609 −0.596711
\(979\) −22.4387 −0.717143
\(980\) 1.72806 0.0552009
\(981\) 19.2703 0.615252
\(982\) −7.45476 −0.237891
\(983\) 8.91972 0.284495 0.142247 0.989831i \(-0.454567\pi\)
0.142247 + 0.989831i \(0.454567\pi\)
\(984\) −10.5622 −0.336711
\(985\) −10.3337 −0.329258
\(986\) 15.5238 0.494379
\(987\) 16.1688 0.514660
\(988\) −24.4634 −0.778285
\(989\) 44.3232 1.40940
\(990\) 1.93627 0.0615386
\(991\) −13.1220 −0.416833 −0.208417 0.978040i \(-0.566831\pi\)
−0.208417 + 0.978040i \(0.566831\pi\)
\(992\) −22.9652 −0.729145
\(993\) −12.3770 −0.392774
\(994\) −1.35296 −0.0429134
\(995\) 4.58436 0.145334
\(996\) 25.1887 0.798133
\(997\) −41.2787 −1.30731 −0.653655 0.756793i \(-0.726765\pi\)
−0.653655 + 0.756793i \(0.726765\pi\)
\(998\) −0.119642 −0.00378721
\(999\) 13.9511 0.441393
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 \(a_p\))