Properties

Label 6039.2.a.j.1.3
Level 6039
Weight 2
Character 6039.1
Self dual Yes
Analytic conductor 48.222
Analytic rank 0
Dimension 14
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6039 = 3^{2} \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6039.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2216577807\)
Analytic rank: \(0\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.76637\)
Character \(\chi\) = 6039.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.76637 q^{2}\) \(+1.12006 q^{4}\) \(+2.50284 q^{5}\) \(-4.08919 q^{7}\) \(+1.55430 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.76637 q^{2}\) \(+1.12006 q^{4}\) \(+2.50284 q^{5}\) \(-4.08919 q^{7}\) \(+1.55430 q^{8}\) \(-4.42094 q^{10}\) \(+1.00000 q^{11}\) \(+4.58176 q^{13}\) \(+7.22301 q^{14}\) \(-4.98559 q^{16}\) \(+1.68948 q^{17}\) \(+2.54310 q^{19}\) \(+2.80332 q^{20}\) \(-1.76637 q^{22}\) \(-6.64905 q^{23}\) \(+1.26422 q^{25}\) \(-8.09307 q^{26}\) \(-4.58012 q^{28}\) \(-2.87310 q^{29}\) \(+5.77320 q^{31}\) \(+5.69777 q^{32}\) \(-2.98424 q^{34}\) \(-10.2346 q^{35}\) \(+10.5546 q^{37}\) \(-4.49204 q^{38}\) \(+3.89018 q^{40}\) \(+7.50568 q^{41}\) \(-5.62451 q^{43}\) \(+1.12006 q^{44}\) \(+11.7447 q^{46}\) \(-8.24063 q^{47}\) \(+9.72144 q^{49}\) \(-2.23307 q^{50}\) \(+5.13183 q^{52}\) \(+6.73746 q^{53}\) \(+2.50284 q^{55}\) \(-6.35584 q^{56}\) \(+5.07495 q^{58}\) \(-1.44956 q^{59}\) \(+1.00000 q^{61}\) \(-10.1976 q^{62}\) \(-0.0931904 q^{64}\) \(+11.4674 q^{65}\) \(-2.89684 q^{67}\) \(+1.89231 q^{68}\) \(+18.0780 q^{70}\) \(+3.64666 q^{71}\) \(-1.53009 q^{73}\) \(-18.6433 q^{74}\) \(+2.84841 q^{76}\) \(-4.08919 q^{77}\) \(+6.59373 q^{79}\) \(-12.4781 q^{80}\) \(-13.2578 q^{82}\) \(-4.68950 q^{83}\) \(+4.22850 q^{85}\) \(+9.93495 q^{86}\) \(+1.55430 q^{88}\) \(-8.01389 q^{89}\) \(-18.7357 q^{91}\) \(-7.44732 q^{92}\) \(+14.5560 q^{94}\) \(+6.36497 q^{95}\) \(-8.48718 q^{97}\) \(-17.1716 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(14q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 15q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 17q^{16} \) \(\mathstrut +\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 37q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 9q^{31} \) \(\mathstrut -\mathstrut 4q^{32} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 18q^{35} \) \(\mathstrut +\mathstrut 18q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut +\mathstrut 16q^{40} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 25q^{43} \) \(\mathstrut +\mathstrut 15q^{44} \) \(\mathstrut +\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 13q^{52} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 40q^{56} \) \(\mathstrut +\mathstrut 33q^{58} \) \(\mathstrut -\mathstrut 17q^{59} \) \(\mathstrut +\mathstrut 14q^{61} \) \(\mathstrut +\mathstrut 13q^{62} \) \(\mathstrut -\mathstrut 6q^{64} \) \(\mathstrut +\mathstrut 61q^{65} \) \(\mathstrut +\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 66q^{68} \) \(\mathstrut +\mathstrut 44q^{70} \) \(\mathstrut +\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 20q^{73} \) \(\mathstrut +\mathstrut 12q^{74} \) \(\mathstrut +\mathstrut 49q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 88q^{80} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 32q^{83} \) \(\mathstrut +\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut +\mathstrut 21q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut -\mathstrut 31q^{94} \) \(\mathstrut -\mathstrut 23q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut +\mathstrut 38q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76637 −1.24901 −0.624505 0.781020i \(-0.714699\pi\)
−0.624505 + 0.781020i \(0.714699\pi\)
\(3\) 0 0
\(4\) 1.12006 0.560028
\(5\) 2.50284 1.11930 0.559652 0.828727i \(-0.310935\pi\)
0.559652 + 0.828727i \(0.310935\pi\)
\(6\) 0 0
\(7\) −4.08919 −1.54557 −0.772784 0.634670i \(-0.781136\pi\)
−0.772784 + 0.634670i \(0.781136\pi\)
\(8\) 1.55430 0.549530
\(9\) 0 0
\(10\) −4.42094 −1.39802
\(11\) 1.00000 0.301511
\(12\) 0 0
\(13\) 4.58176 1.27075 0.635376 0.772203i \(-0.280845\pi\)
0.635376 + 0.772203i \(0.280845\pi\)
\(14\) 7.22301 1.93043
\(15\) 0 0
\(16\) −4.98559 −1.24640
\(17\) 1.68948 0.409759 0.204879 0.978787i \(-0.434320\pi\)
0.204879 + 0.978787i \(0.434320\pi\)
\(18\) 0 0
\(19\) 2.54310 0.583426 0.291713 0.956506i \(-0.405775\pi\)
0.291713 + 0.956506i \(0.405775\pi\)
\(20\) 2.80332 0.626842
\(21\) 0 0
\(22\) −1.76637 −0.376591
\(23\) −6.64905 −1.38642 −0.693212 0.720734i \(-0.743805\pi\)
−0.693212 + 0.720734i \(0.743805\pi\)
\(24\) 0 0
\(25\) 1.26422 0.252844
\(26\) −8.09307 −1.58718
\(27\) 0 0
\(28\) −4.58012 −0.865561
\(29\) −2.87310 −0.533521 −0.266760 0.963763i \(-0.585953\pi\)
−0.266760 + 0.963763i \(0.585953\pi\)
\(30\) 0 0
\(31\) 5.77320 1.03690 0.518449 0.855109i \(-0.326510\pi\)
0.518449 + 0.855109i \(0.326510\pi\)
\(32\) 5.69777 1.00723
\(33\) 0 0
\(34\) −2.98424 −0.511793
\(35\) −10.2346 −1.72996
\(36\) 0 0
\(37\) 10.5546 1.73516 0.867582 0.497293i \(-0.165673\pi\)
0.867582 + 0.497293i \(0.165673\pi\)
\(38\) −4.49204 −0.728706
\(39\) 0 0
\(40\) 3.89018 0.615091
\(41\) 7.50568 1.17219 0.586095 0.810242i \(-0.300664\pi\)
0.586095 + 0.810242i \(0.300664\pi\)
\(42\) 0 0
\(43\) −5.62451 −0.857729 −0.428865 0.903369i \(-0.641086\pi\)
−0.428865 + 0.903369i \(0.641086\pi\)
\(44\) 1.12006 0.168855
\(45\) 0 0
\(46\) 11.7447 1.73166
\(47\) −8.24063 −1.20202 −0.601010 0.799242i \(-0.705235\pi\)
−0.601010 + 0.799242i \(0.705235\pi\)
\(48\) 0 0
\(49\) 9.72144 1.38878
\(50\) −2.23307 −0.315804
\(51\) 0 0
\(52\) 5.13183 0.711657
\(53\) 6.73746 0.925461 0.462730 0.886499i \(-0.346870\pi\)
0.462730 + 0.886499i \(0.346870\pi\)
\(54\) 0 0
\(55\) 2.50284 0.337483
\(56\) −6.35584 −0.849335
\(57\) 0 0
\(58\) 5.07495 0.666373
\(59\) −1.44956 −0.188717 −0.0943584 0.995538i \(-0.530080\pi\)
−0.0943584 + 0.995538i \(0.530080\pi\)
\(60\) 0 0
\(61\) 1.00000 0.128037
\(62\) −10.1976 −1.29510
\(63\) 0 0
\(64\) −0.0931904 −0.0116488
\(65\) 11.4674 1.42236
\(66\) 0 0
\(67\) −2.89684 −0.353905 −0.176953 0.984219i \(-0.556624\pi\)
−0.176953 + 0.984219i \(0.556624\pi\)
\(68\) 1.89231 0.229477
\(69\) 0 0
\(70\) 18.0780 2.16074
\(71\) 3.64666 0.432779 0.216389 0.976307i \(-0.430572\pi\)
0.216389 + 0.976307i \(0.430572\pi\)
\(72\) 0 0
\(73\) −1.53009 −0.179084 −0.0895419 0.995983i \(-0.528540\pi\)
−0.0895419 + 0.995983i \(0.528540\pi\)
\(74\) −18.6433 −2.16724
\(75\) 0 0
\(76\) 2.84841 0.326735
\(77\) −4.08919 −0.466006
\(78\) 0 0
\(79\) 6.59373 0.741853 0.370926 0.928662i \(-0.379040\pi\)
0.370926 + 0.928662i \(0.379040\pi\)
\(80\) −12.4781 −1.39510
\(81\) 0 0
\(82\) −13.2578 −1.46408
\(83\) −4.68950 −0.514739 −0.257370 0.966313i \(-0.582856\pi\)
−0.257370 + 0.966313i \(0.582856\pi\)
\(84\) 0 0
\(85\) 4.22850 0.458645
\(86\) 9.93495 1.07131
\(87\) 0 0
\(88\) 1.55430 0.165689
\(89\) −8.01389 −0.849471 −0.424735 0.905318i \(-0.639633\pi\)
−0.424735 + 0.905318i \(0.639633\pi\)
\(90\) 0 0
\(91\) −18.7357 −1.96403
\(92\) −7.44732 −0.776436
\(93\) 0 0
\(94\) 14.5560 1.50134
\(95\) 6.36497 0.653032
\(96\) 0 0
\(97\) −8.48718 −0.861743 −0.430871 0.902413i \(-0.641794\pi\)
−0.430871 + 0.902413i \(0.641794\pi\)
\(98\) −17.1716 −1.73460
\(99\) 0 0
\(100\) 1.41600 0.141600
\(101\) 18.2735 1.81828 0.909138 0.416495i \(-0.136742\pi\)
0.909138 + 0.416495i \(0.136742\pi\)
\(102\) 0 0
\(103\) 13.5101 1.33119 0.665594 0.746314i \(-0.268178\pi\)
0.665594 + 0.746314i \(0.268178\pi\)
\(104\) 7.12145 0.698315
\(105\) 0 0
\(106\) −11.9008 −1.15591
\(107\) −6.25580 −0.604771 −0.302385 0.953186i \(-0.597783\pi\)
−0.302385 + 0.953186i \(0.597783\pi\)
\(108\) 0 0
\(109\) 9.80803 0.939439 0.469720 0.882816i \(-0.344355\pi\)
0.469720 + 0.882816i \(0.344355\pi\)
\(110\) −4.42094 −0.421520
\(111\) 0 0
\(112\) 20.3870 1.92639
\(113\) −4.30188 −0.404687 −0.202343 0.979315i \(-0.564856\pi\)
−0.202343 + 0.979315i \(0.564856\pi\)
\(114\) 0 0
\(115\) −16.6415 −1.55183
\(116\) −3.21803 −0.298787
\(117\) 0 0
\(118\) 2.56046 0.235709
\(119\) −6.90859 −0.633310
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −1.76637 −0.159919
\(123\) 0 0
\(124\) 6.46631 0.580692
\(125\) −9.35007 −0.836296
\(126\) 0 0
\(127\) 8.95668 0.794776 0.397388 0.917651i \(-0.369917\pi\)
0.397388 + 0.917651i \(0.369917\pi\)
\(128\) −11.2309 −0.992684
\(129\) 0 0
\(130\) −20.2557 −1.77654
\(131\) −16.6930 −1.45848 −0.729239 0.684259i \(-0.760126\pi\)
−0.729239 + 0.684259i \(0.760126\pi\)
\(132\) 0 0
\(133\) −10.3992 −0.901724
\(134\) 5.11689 0.442032
\(135\) 0 0
\(136\) 2.62596 0.225175
\(137\) −1.84979 −0.158038 −0.0790192 0.996873i \(-0.525179\pi\)
−0.0790192 + 0.996873i \(0.525179\pi\)
\(138\) 0 0
\(139\) −2.09830 −0.177975 −0.0889877 0.996033i \(-0.528363\pi\)
−0.0889877 + 0.996033i \(0.528363\pi\)
\(140\) −11.4633 −0.968827
\(141\) 0 0
\(142\) −6.44134 −0.540545
\(143\) 4.58176 0.383146
\(144\) 0 0
\(145\) −7.19091 −0.597172
\(146\) 2.70271 0.223678
\(147\) 0 0
\(148\) 11.8217 0.971741
\(149\) 10.6609 0.873374 0.436687 0.899614i \(-0.356152\pi\)
0.436687 + 0.899614i \(0.356152\pi\)
\(150\) 0 0
\(151\) −15.9563 −1.29850 −0.649252 0.760573i \(-0.724918\pi\)
−0.649252 + 0.760573i \(0.724918\pi\)
\(152\) 3.95274 0.320610
\(153\) 0 0
\(154\) 7.22301 0.582047
\(155\) 14.4494 1.16060
\(156\) 0 0
\(157\) −12.6000 −1.00559 −0.502795 0.864406i \(-0.667695\pi\)
−0.502795 + 0.864406i \(0.667695\pi\)
\(158\) −11.6470 −0.926582
\(159\) 0 0
\(160\) 14.2606 1.12740
\(161\) 27.1892 2.14281
\(162\) 0 0
\(163\) 19.5726 1.53305 0.766523 0.642217i \(-0.221985\pi\)
0.766523 + 0.642217i \(0.221985\pi\)
\(164\) 8.40679 0.656460
\(165\) 0 0
\(166\) 8.28338 0.642915
\(167\) 1.21481 0.0940045 0.0470023 0.998895i \(-0.485033\pi\)
0.0470023 + 0.998895i \(0.485033\pi\)
\(168\) 0 0
\(169\) 7.99251 0.614809
\(170\) −7.46909 −0.572853
\(171\) 0 0
\(172\) −6.29977 −0.480353
\(173\) 16.2092 1.23236 0.616180 0.787605i \(-0.288679\pi\)
0.616180 + 0.787605i \(0.288679\pi\)
\(174\) 0 0
\(175\) −5.16962 −0.390787
\(176\) −4.98559 −0.375803
\(177\) 0 0
\(178\) 14.1555 1.06100
\(179\) 0.460529 0.0344216 0.0172108 0.999852i \(-0.494521\pi\)
0.0172108 + 0.999852i \(0.494521\pi\)
\(180\) 0 0
\(181\) 21.1108 1.56916 0.784578 0.620030i \(-0.212879\pi\)
0.784578 + 0.620030i \(0.212879\pi\)
\(182\) 33.0941 2.45310
\(183\) 0 0
\(184\) −10.3347 −0.761881
\(185\) 26.4165 1.94218
\(186\) 0 0
\(187\) 1.68948 0.123547
\(188\) −9.22997 −0.673165
\(189\) 0 0
\(190\) −11.2429 −0.815644
\(191\) −20.7120 −1.49867 −0.749333 0.662193i \(-0.769626\pi\)
−0.749333 + 0.662193i \(0.769626\pi\)
\(192\) 0 0
\(193\) 4.36796 0.314413 0.157206 0.987566i \(-0.449751\pi\)
0.157206 + 0.987566i \(0.449751\pi\)
\(194\) 14.9915 1.07633
\(195\) 0 0
\(196\) 10.8886 0.777755
\(197\) 14.9041 1.06187 0.530935 0.847413i \(-0.321841\pi\)
0.530935 + 0.847413i \(0.321841\pi\)
\(198\) 0 0
\(199\) 12.3150 0.872990 0.436495 0.899707i \(-0.356220\pi\)
0.436495 + 0.899707i \(0.356220\pi\)
\(200\) 1.96498 0.138945
\(201\) 0 0
\(202\) −32.2776 −2.27105
\(203\) 11.7486 0.824592
\(204\) 0 0
\(205\) 18.7855 1.31204
\(206\) −23.8638 −1.66267
\(207\) 0 0
\(208\) −22.8428 −1.58386
\(209\) 2.54310 0.175910
\(210\) 0 0
\(211\) −0.624271 −0.0429766 −0.0214883 0.999769i \(-0.506840\pi\)
−0.0214883 + 0.999769i \(0.506840\pi\)
\(212\) 7.54633 0.518284
\(213\) 0 0
\(214\) 11.0500 0.755365
\(215\) −14.0773 −0.960061
\(216\) 0 0
\(217\) −23.6077 −1.60259
\(218\) −17.3246 −1.17337
\(219\) 0 0
\(220\) 2.80332 0.189000
\(221\) 7.74079 0.520702
\(222\) 0 0
\(223\) 1.10168 0.0737740 0.0368870 0.999319i \(-0.488256\pi\)
0.0368870 + 0.999319i \(0.488256\pi\)
\(224\) −23.2993 −1.55675
\(225\) 0 0
\(226\) 7.59871 0.505458
\(227\) −24.3655 −1.61720 −0.808599 0.588360i \(-0.799774\pi\)
−0.808599 + 0.588360i \(0.799774\pi\)
\(228\) 0 0
\(229\) −10.0662 −0.665193 −0.332597 0.943069i \(-0.607925\pi\)
−0.332597 + 0.943069i \(0.607925\pi\)
\(230\) 29.3951 1.93825
\(231\) 0 0
\(232\) −4.46567 −0.293185
\(233\) 2.64216 0.173094 0.0865470 0.996248i \(-0.472417\pi\)
0.0865470 + 0.996248i \(0.472417\pi\)
\(234\) 0 0
\(235\) −20.6250 −1.34543
\(236\) −1.62359 −0.105687
\(237\) 0 0
\(238\) 12.2031 0.791011
\(239\) 24.0202 1.55374 0.776870 0.629662i \(-0.216806\pi\)
0.776870 + 0.629662i \(0.216806\pi\)
\(240\) 0 0
\(241\) 20.2998 1.30763 0.653813 0.756656i \(-0.273168\pi\)
0.653813 + 0.756656i \(0.273168\pi\)
\(242\) −1.76637 −0.113546
\(243\) 0 0
\(244\) 1.12006 0.0717043
\(245\) 24.3312 1.55447
\(246\) 0 0
\(247\) 11.6518 0.741389
\(248\) 8.97331 0.569806
\(249\) 0 0
\(250\) 16.5157 1.04454
\(251\) 7.85638 0.495890 0.247945 0.968774i \(-0.420245\pi\)
0.247945 + 0.968774i \(0.420245\pi\)
\(252\) 0 0
\(253\) −6.64905 −0.418022
\(254\) −15.8208 −0.992684
\(255\) 0 0
\(256\) 20.0243 1.25152
\(257\) −8.43220 −0.525986 −0.262993 0.964798i \(-0.584710\pi\)
−0.262993 + 0.964798i \(0.584710\pi\)
\(258\) 0 0
\(259\) −43.1597 −2.68181
\(260\) 12.8442 0.796561
\(261\) 0 0
\(262\) 29.4861 1.82165
\(263\) 15.8210 0.975563 0.487781 0.872966i \(-0.337806\pi\)
0.487781 + 0.872966i \(0.337806\pi\)
\(264\) 0 0
\(265\) 16.8628 1.03587
\(266\) 18.3688 1.12626
\(267\) 0 0
\(268\) −3.24462 −0.198197
\(269\) −29.6760 −1.80938 −0.904690 0.426070i \(-0.859898\pi\)
−0.904690 + 0.426070i \(0.859898\pi\)
\(270\) 0 0
\(271\) 13.8327 0.840277 0.420139 0.907460i \(-0.361981\pi\)
0.420139 + 0.907460i \(0.361981\pi\)
\(272\) −8.42304 −0.510722
\(273\) 0 0
\(274\) 3.26742 0.197392
\(275\) 1.26422 0.0762352
\(276\) 0 0
\(277\) 10.7545 0.646174 0.323087 0.946369i \(-0.395279\pi\)
0.323087 + 0.946369i \(0.395279\pi\)
\(278\) 3.70637 0.222293
\(279\) 0 0
\(280\) −15.9077 −0.950665
\(281\) −18.7346 −1.11761 −0.558807 0.829298i \(-0.688741\pi\)
−0.558807 + 0.829298i \(0.688741\pi\)
\(282\) 0 0
\(283\) 24.5140 1.45721 0.728603 0.684936i \(-0.240170\pi\)
0.728603 + 0.684936i \(0.240170\pi\)
\(284\) 4.08446 0.242368
\(285\) 0 0
\(286\) −8.09307 −0.478553
\(287\) −30.6921 −1.81170
\(288\) 0 0
\(289\) −14.1457 −0.832098
\(290\) 12.7018 0.745875
\(291\) 0 0
\(292\) −1.71379 −0.100292
\(293\) −22.3094 −1.30333 −0.651665 0.758507i \(-0.725929\pi\)
−0.651665 + 0.758507i \(0.725929\pi\)
\(294\) 0 0
\(295\) −3.62802 −0.211232
\(296\) 16.4051 0.953524
\(297\) 0 0
\(298\) −18.8310 −1.09085
\(299\) −30.4644 −1.76180
\(300\) 0 0
\(301\) 22.9997 1.32568
\(302\) 28.1847 1.62185
\(303\) 0 0
\(304\) −12.6788 −0.727180
\(305\) 2.50284 0.143312
\(306\) 0 0
\(307\) 9.79575 0.559073 0.279536 0.960135i \(-0.409819\pi\)
0.279536 + 0.960135i \(0.409819\pi\)
\(308\) −4.58012 −0.260977
\(309\) 0 0
\(310\) −25.5230 −1.44961
\(311\) −21.0159 −1.19170 −0.595852 0.803094i \(-0.703186\pi\)
−0.595852 + 0.803094i \(0.703186\pi\)
\(312\) 0 0
\(313\) −11.8868 −0.671880 −0.335940 0.941883i \(-0.609054\pi\)
−0.335940 + 0.941883i \(0.609054\pi\)
\(314\) 22.2563 1.25599
\(315\) 0 0
\(316\) 7.38535 0.415458
\(317\) 20.3584 1.14344 0.571720 0.820449i \(-0.306277\pi\)
0.571720 + 0.820449i \(0.306277\pi\)
\(318\) 0 0
\(319\) −2.87310 −0.160863
\(320\) −0.233241 −0.0130386
\(321\) 0 0
\(322\) −48.0262 −2.67639
\(323\) 4.29651 0.239064
\(324\) 0 0
\(325\) 5.79234 0.321301
\(326\) −34.5725 −1.91479
\(327\) 0 0
\(328\) 11.6661 0.644153
\(329\) 33.6975 1.85780
\(330\) 0 0
\(331\) −18.5600 −1.02015 −0.510074 0.860130i \(-0.670382\pi\)
−0.510074 + 0.860130i \(0.670382\pi\)
\(332\) −5.25250 −0.288268
\(333\) 0 0
\(334\) −2.14579 −0.117413
\(335\) −7.25033 −0.396128
\(336\) 0 0
\(337\) 10.9967 0.599029 0.299515 0.954092i \(-0.403175\pi\)
0.299515 + 0.954092i \(0.403175\pi\)
\(338\) −14.1177 −0.767903
\(339\) 0 0
\(340\) 4.73616 0.256854
\(341\) 5.77320 0.312636
\(342\) 0 0
\(343\) −11.1285 −0.600882
\(344\) −8.74220 −0.471348
\(345\) 0 0
\(346\) −28.6314 −1.53923
\(347\) 6.33081 0.339856 0.169928 0.985457i \(-0.445647\pi\)
0.169928 + 0.985457i \(0.445647\pi\)
\(348\) 0 0
\(349\) −14.8101 −0.792766 −0.396383 0.918085i \(-0.629735\pi\)
−0.396383 + 0.918085i \(0.629735\pi\)
\(350\) 9.13146 0.488097
\(351\) 0 0
\(352\) 5.69777 0.303692
\(353\) −18.2039 −0.968897 −0.484448 0.874820i \(-0.660980\pi\)
−0.484448 + 0.874820i \(0.660980\pi\)
\(354\) 0 0
\(355\) 9.12701 0.484411
\(356\) −8.97601 −0.475728
\(357\) 0 0
\(358\) −0.813464 −0.0429929
\(359\) 31.9112 1.68421 0.842105 0.539313i \(-0.181316\pi\)
0.842105 + 0.539313i \(0.181316\pi\)
\(360\) 0 0
\(361\) −12.5327 −0.659614
\(362\) −37.2895 −1.95989
\(363\) 0 0
\(364\) −20.9850 −1.09991
\(365\) −3.82958 −0.200449
\(366\) 0 0
\(367\) 27.3610 1.42823 0.714117 0.700026i \(-0.246828\pi\)
0.714117 + 0.700026i \(0.246828\pi\)
\(368\) 33.1494 1.72803
\(369\) 0 0
\(370\) −46.6612 −2.42580
\(371\) −27.5507 −1.43036
\(372\) 0 0
\(373\) −10.8401 −0.561279 −0.280639 0.959813i \(-0.590546\pi\)
−0.280639 + 0.959813i \(0.590546\pi\)
\(374\) −2.98424 −0.154311
\(375\) 0 0
\(376\) −12.8084 −0.660545
\(377\) −13.1638 −0.677972
\(378\) 0 0
\(379\) 28.1412 1.44552 0.722758 0.691101i \(-0.242874\pi\)
0.722758 + 0.691101i \(0.242874\pi\)
\(380\) 7.12912 0.365716
\(381\) 0 0
\(382\) 36.5850 1.87185
\(383\) −12.3294 −0.630003 −0.315002 0.949091i \(-0.602005\pi\)
−0.315002 + 0.949091i \(0.602005\pi\)
\(384\) 0 0
\(385\) −10.2346 −0.521603
\(386\) −7.71543 −0.392705
\(387\) 0 0
\(388\) −9.50612 −0.482600
\(389\) −2.35013 −0.119156 −0.0595782 0.998224i \(-0.518976\pi\)
−0.0595782 + 0.998224i \(0.518976\pi\)
\(390\) 0 0
\(391\) −11.2334 −0.568099
\(392\) 15.1101 0.763174
\(393\) 0 0
\(394\) −26.3261 −1.32629
\(395\) 16.5031 0.830359
\(396\) 0 0
\(397\) 7.28324 0.365535 0.182768 0.983156i \(-0.441494\pi\)
0.182768 + 0.983156i \(0.441494\pi\)
\(398\) −21.7529 −1.09037
\(399\) 0 0
\(400\) −6.30287 −0.315143
\(401\) 5.92148 0.295704 0.147852 0.989009i \(-0.452764\pi\)
0.147852 + 0.989009i \(0.452764\pi\)
\(402\) 0 0
\(403\) 26.4514 1.31764
\(404\) 20.4673 1.01829
\(405\) 0 0
\(406\) −20.7524 −1.02992
\(407\) 10.5546 0.523172
\(408\) 0 0
\(409\) 37.5868 1.85855 0.929273 0.369395i \(-0.120435\pi\)
0.929273 + 0.369395i \(0.120435\pi\)
\(410\) −33.1822 −1.63875
\(411\) 0 0
\(412\) 15.1321 0.745503
\(413\) 5.92753 0.291675
\(414\) 0 0
\(415\) −11.7371 −0.576150
\(416\) 26.1058 1.27994
\(417\) 0 0
\(418\) −4.49204 −0.219713
\(419\) −2.49710 −0.121991 −0.0609957 0.998138i \(-0.519428\pi\)
−0.0609957 + 0.998138i \(0.519428\pi\)
\(420\) 0 0
\(421\) −4.42273 −0.215551 −0.107775 0.994175i \(-0.534373\pi\)
−0.107775 + 0.994175i \(0.534373\pi\)
\(422\) 1.10269 0.0536783
\(423\) 0 0
\(424\) 10.4721 0.508568
\(425\) 2.13587 0.103605
\(426\) 0 0
\(427\) −4.08919 −0.197890
\(428\) −7.00684 −0.338689
\(429\) 0 0
\(430\) 24.8656 1.19913
\(431\) 9.88068 0.475936 0.237968 0.971273i \(-0.423519\pi\)
0.237968 + 0.971273i \(0.423519\pi\)
\(432\) 0 0
\(433\) −39.0060 −1.87451 −0.937254 0.348648i \(-0.886641\pi\)
−0.937254 + 0.348648i \(0.886641\pi\)
\(434\) 41.6999 2.00166
\(435\) 0 0
\(436\) 10.9855 0.526112
\(437\) −16.9092 −0.808876
\(438\) 0 0
\(439\) 20.6364 0.984924 0.492462 0.870334i \(-0.336097\pi\)
0.492462 + 0.870334i \(0.336097\pi\)
\(440\) 3.89018 0.185457
\(441\) 0 0
\(442\) −13.6731 −0.650362
\(443\) 32.1706 1.52847 0.764235 0.644938i \(-0.223117\pi\)
0.764235 + 0.644938i \(0.223117\pi\)
\(444\) 0 0
\(445\) −20.0575 −0.950817
\(446\) −1.94597 −0.0921445
\(447\) 0 0
\(448\) 0.381073 0.0180040
\(449\) 5.85730 0.276423 0.138212 0.990403i \(-0.455865\pi\)
0.138212 + 0.990403i \(0.455865\pi\)
\(450\) 0 0
\(451\) 7.50568 0.353429
\(452\) −4.81835 −0.226636
\(453\) 0 0
\(454\) 43.0385 2.01990
\(455\) −46.8924 −2.19835
\(456\) 0 0
\(457\) −1.68219 −0.0786896 −0.0393448 0.999226i \(-0.512527\pi\)
−0.0393448 + 0.999226i \(0.512527\pi\)
\(458\) 17.7806 0.830833
\(459\) 0 0
\(460\) −18.6395 −0.869069
\(461\) 6.22874 0.290101 0.145051 0.989424i \(-0.453665\pi\)
0.145051 + 0.989424i \(0.453665\pi\)
\(462\) 0 0
\(463\) 20.0233 0.930560 0.465280 0.885163i \(-0.345954\pi\)
0.465280 + 0.885163i \(0.345954\pi\)
\(464\) 14.3241 0.664978
\(465\) 0 0
\(466\) −4.66704 −0.216196
\(467\) −11.2040 −0.518457 −0.259229 0.965816i \(-0.583468\pi\)
−0.259229 + 0.965816i \(0.583468\pi\)
\(468\) 0 0
\(469\) 11.8457 0.546985
\(470\) 36.4313 1.68045
\(471\) 0 0
\(472\) −2.25306 −0.103705
\(473\) −5.62451 −0.258615
\(474\) 0 0
\(475\) 3.21503 0.147516
\(476\) −7.73802 −0.354671
\(477\) 0 0
\(478\) −42.4286 −1.94064
\(479\) 36.8757 1.68490 0.842448 0.538778i \(-0.181114\pi\)
0.842448 + 0.538778i \(0.181114\pi\)
\(480\) 0 0
\(481\) 48.3586 2.20496
\(482\) −35.8569 −1.63324
\(483\) 0 0
\(484\) 1.12006 0.0509117
\(485\) −21.2421 −0.964553
\(486\) 0 0
\(487\) −27.2350 −1.23414 −0.617069 0.786909i \(-0.711680\pi\)
−0.617069 + 0.786909i \(0.711680\pi\)
\(488\) 1.55430 0.0703601
\(489\) 0 0
\(490\) −42.9779 −1.94154
\(491\) 9.95507 0.449266 0.224633 0.974443i \(-0.427882\pi\)
0.224633 + 0.974443i \(0.427882\pi\)
\(492\) 0 0
\(493\) −4.85404 −0.218615
\(494\) −20.5815 −0.926003
\(495\) 0 0
\(496\) −28.7828 −1.29239
\(497\) −14.9119 −0.668888
\(498\) 0 0
\(499\) −24.8590 −1.11284 −0.556421 0.830901i \(-0.687826\pi\)
−0.556421 + 0.830901i \(0.687826\pi\)
\(500\) −10.4726 −0.468349
\(501\) 0 0
\(502\) −13.8773 −0.619372
\(503\) 7.90956 0.352670 0.176335 0.984330i \(-0.443576\pi\)
0.176335 + 0.984330i \(0.443576\pi\)
\(504\) 0 0
\(505\) 45.7356 2.03521
\(506\) 11.7447 0.522115
\(507\) 0 0
\(508\) 10.0320 0.445097
\(509\) 26.7176 1.18423 0.592117 0.805852i \(-0.298292\pi\)
0.592117 + 0.805852i \(0.298292\pi\)
\(510\) 0 0
\(511\) 6.25683 0.276786
\(512\) −12.9085 −0.570480
\(513\) 0 0
\(514\) 14.8944 0.656963
\(515\) 33.8136 1.49001
\(516\) 0 0
\(517\) −8.24063 −0.362422
\(518\) 76.2359 3.34961
\(519\) 0 0
\(520\) 17.8239 0.781628
\(521\) 44.3858 1.94458 0.972288 0.233788i \(-0.0751123\pi\)
0.972288 + 0.233788i \(0.0751123\pi\)
\(522\) 0 0
\(523\) −9.29556 −0.406466 −0.203233 0.979130i \(-0.565145\pi\)
−0.203233 + 0.979130i \(0.565145\pi\)
\(524\) −18.6971 −0.816789
\(525\) 0 0
\(526\) −27.9457 −1.21849
\(527\) 9.75370 0.424878
\(528\) 0 0
\(529\) 21.2099 0.922171
\(530\) −29.7859 −1.29382
\(531\) 0 0
\(532\) −11.6477 −0.504991
\(533\) 34.3892 1.48956
\(534\) 0 0
\(535\) −15.6573 −0.676923
\(536\) −4.50257 −0.194481
\(537\) 0 0
\(538\) 52.4188 2.25994
\(539\) 9.72144 0.418732
\(540\) 0 0
\(541\) −12.2230 −0.525508 −0.262754 0.964863i \(-0.584631\pi\)
−0.262754 + 0.964863i \(0.584631\pi\)
\(542\) −24.4337 −1.04952
\(543\) 0 0
\(544\) 9.62627 0.412723
\(545\) 24.5480 1.05152
\(546\) 0 0
\(547\) 41.0194 1.75386 0.876932 0.480615i \(-0.159587\pi\)
0.876932 + 0.480615i \(0.159587\pi\)
\(548\) −2.07187 −0.0885060
\(549\) 0 0
\(550\) −2.23307 −0.0952186
\(551\) −7.30656 −0.311270
\(552\) 0 0
\(553\) −26.9630 −1.14658
\(554\) −18.9964 −0.807079
\(555\) 0 0
\(556\) −2.35021 −0.0996713
\(557\) −37.2860 −1.57986 −0.789930 0.613197i \(-0.789883\pi\)
−0.789930 + 0.613197i \(0.789883\pi\)
\(558\) 0 0
\(559\) −25.7701 −1.08996
\(560\) 51.0254 2.15622
\(561\) 0 0
\(562\) 33.0922 1.39591
\(563\) 21.0358 0.886553 0.443276 0.896385i \(-0.353816\pi\)
0.443276 + 0.896385i \(0.353816\pi\)
\(564\) 0 0
\(565\) −10.7669 −0.452968
\(566\) −43.3007 −1.82007
\(567\) 0 0
\(568\) 5.66802 0.237825
\(569\) 14.9610 0.627198 0.313599 0.949556i \(-0.398465\pi\)
0.313599 + 0.949556i \(0.398465\pi\)
\(570\) 0 0
\(571\) 22.6822 0.949220 0.474610 0.880196i \(-0.342589\pi\)
0.474610 + 0.880196i \(0.342589\pi\)
\(572\) 5.13183 0.214573
\(573\) 0 0
\(574\) 54.2136 2.26283
\(575\) −8.40585 −0.350548
\(576\) 0 0
\(577\) 16.8414 0.701115 0.350558 0.936541i \(-0.385992\pi\)
0.350558 + 0.936541i \(0.385992\pi\)
\(578\) 24.9864 1.03930
\(579\) 0 0
\(580\) −8.05422 −0.334433
\(581\) 19.1762 0.795564
\(582\) 0 0
\(583\) 6.73746 0.279037
\(584\) −2.37823 −0.0984118
\(585\) 0 0
\(586\) 39.4067 1.62787
\(587\) −24.6219 −1.01625 −0.508127 0.861282i \(-0.669662\pi\)
−0.508127 + 0.861282i \(0.669662\pi\)
\(588\) 0 0
\(589\) 14.6818 0.604953
\(590\) 6.40843 0.263831
\(591\) 0 0
\(592\) −52.6208 −2.16270
\(593\) 29.1431 1.19676 0.598381 0.801212i \(-0.295811\pi\)
0.598381 + 0.801212i \(0.295811\pi\)
\(594\) 0 0
\(595\) −17.2911 −0.708867
\(596\) 11.9408 0.489114
\(597\) 0 0
\(598\) 53.8113 2.20051
\(599\) 13.0824 0.534533 0.267266 0.963623i \(-0.413880\pi\)
0.267266 + 0.963623i \(0.413880\pi\)
\(600\) 0 0
\(601\) 23.1391 0.943864 0.471932 0.881635i \(-0.343557\pi\)
0.471932 + 0.881635i \(0.343557\pi\)
\(602\) −40.6259 −1.65579
\(603\) 0 0
\(604\) −17.8719 −0.727199
\(605\) 2.50284 0.101755
\(606\) 0 0
\(607\) 8.61728 0.349765 0.174882 0.984589i \(-0.444046\pi\)
0.174882 + 0.984589i \(0.444046\pi\)
\(608\) 14.4900 0.587646
\(609\) 0 0
\(610\) −4.42094 −0.178999
\(611\) −37.7566 −1.52747
\(612\) 0 0
\(613\) 41.9165 1.69299 0.846496 0.532396i \(-0.178708\pi\)
0.846496 + 0.532396i \(0.178708\pi\)
\(614\) −17.3029 −0.698288
\(615\) 0 0
\(616\) −6.35584 −0.256084
\(617\) −40.7094 −1.63890 −0.819449 0.573152i \(-0.805721\pi\)
−0.819449 + 0.573152i \(0.805721\pi\)
\(618\) 0 0
\(619\) 38.7050 1.55569 0.777843 0.628459i \(-0.216314\pi\)
0.777843 + 0.628459i \(0.216314\pi\)
\(620\) 16.1842 0.649971
\(621\) 0 0
\(622\) 37.1219 1.48845
\(623\) 32.7703 1.31291
\(624\) 0 0
\(625\) −29.7228 −1.18891
\(626\) 20.9964 0.839186
\(627\) 0 0
\(628\) −14.1127 −0.563159
\(629\) 17.8318 0.710999
\(630\) 0 0
\(631\) 2.44555 0.0973560 0.0486780 0.998815i \(-0.484499\pi\)
0.0486780 + 0.998815i \(0.484499\pi\)
\(632\) 10.2487 0.407670
\(633\) 0 0
\(634\) −35.9604 −1.42817
\(635\) 22.4171 0.889597
\(636\) 0 0
\(637\) 44.5413 1.76479
\(638\) 5.07495 0.200919
\(639\) 0 0
\(640\) −28.1093 −1.11112
\(641\) 3.52047 0.139050 0.0695250 0.997580i \(-0.477852\pi\)
0.0695250 + 0.997580i \(0.477852\pi\)
\(642\) 0 0
\(643\) 12.7865 0.504250 0.252125 0.967695i \(-0.418871\pi\)
0.252125 + 0.967695i \(0.418871\pi\)
\(644\) 30.4535 1.20003
\(645\) 0 0
\(646\) −7.58921 −0.298594
\(647\) −7.00044 −0.275216 −0.137608 0.990487i \(-0.543941\pi\)
−0.137608 + 0.990487i \(0.543941\pi\)
\(648\) 0 0
\(649\) −1.44956 −0.0569003
\(650\) −10.2314 −0.401309
\(651\) 0 0
\(652\) 21.9224 0.858549
\(653\) 13.6757 0.535171 0.267586 0.963534i \(-0.413774\pi\)
0.267586 + 0.963534i \(0.413774\pi\)
\(654\) 0 0
\(655\) −41.7800 −1.63248
\(656\) −37.4202 −1.46101
\(657\) 0 0
\(658\) −59.5221 −2.32041
\(659\) 44.0565 1.71620 0.858099 0.513484i \(-0.171645\pi\)
0.858099 + 0.513484i \(0.171645\pi\)
\(660\) 0 0
\(661\) −1.47619 −0.0574170 −0.0287085 0.999588i \(-0.509139\pi\)
−0.0287085 + 0.999588i \(0.509139\pi\)
\(662\) 32.7837 1.27418
\(663\) 0 0
\(664\) −7.28891 −0.282864
\(665\) −26.0275 −1.00930
\(666\) 0 0
\(667\) 19.1034 0.739686
\(668\) 1.36065 0.0526452
\(669\) 0 0
\(670\) 12.8068 0.494768
\(671\) 1.00000 0.0386046
\(672\) 0 0
\(673\) 24.3555 0.938836 0.469418 0.882976i \(-0.344464\pi\)
0.469418 + 0.882976i \(0.344464\pi\)
\(674\) −19.4243 −0.748194
\(675\) 0 0
\(676\) 8.95207 0.344310
\(677\) 23.0375 0.885403 0.442701 0.896669i \(-0.354020\pi\)
0.442701 + 0.896669i \(0.354020\pi\)
\(678\) 0 0
\(679\) 34.7057 1.33188
\(680\) 6.57238 0.252039
\(681\) 0 0
\(682\) −10.1976 −0.390486
\(683\) 48.5599 1.85809 0.929047 0.369962i \(-0.120629\pi\)
0.929047 + 0.369962i \(0.120629\pi\)
\(684\) 0 0
\(685\) −4.62974 −0.176893
\(686\) 19.6570 0.750508
\(687\) 0 0
\(688\) 28.0415 1.06907
\(689\) 30.8694 1.17603
\(690\) 0 0
\(691\) 21.8077 0.829606 0.414803 0.909911i \(-0.363851\pi\)
0.414803 + 0.909911i \(0.363851\pi\)
\(692\) 18.1552 0.690156
\(693\) 0 0
\(694\) −11.1825 −0.424483
\(695\) −5.25171 −0.199209
\(696\) 0 0
\(697\) 12.6807 0.480315
\(698\) 26.1601 0.990173
\(699\) 0 0
\(700\) −5.79027 −0.218852
\(701\) −12.3112 −0.464988 −0.232494 0.972598i \(-0.574689\pi\)
−0.232494 + 0.972598i \(0.574689\pi\)
\(702\) 0 0
\(703\) 26.8413 1.01234
\(704\) −0.0931904 −0.00351224
\(705\) 0 0
\(706\) 32.1548 1.21016
\(707\) −74.7235 −2.81027
\(708\) 0 0
\(709\) 7.64608 0.287155 0.143577 0.989639i \(-0.454139\pi\)
0.143577 + 0.989639i \(0.454139\pi\)
\(710\) −16.1217 −0.605035
\(711\) 0 0
\(712\) −12.4560 −0.466809
\(713\) −38.3863 −1.43758
\(714\) 0 0
\(715\) 11.4674 0.428857
\(716\) 0.515819 0.0192771
\(717\) 0 0
\(718\) −56.3670 −2.10360
\(719\) 19.7235 0.735564 0.367782 0.929912i \(-0.380117\pi\)
0.367782 + 0.929912i \(0.380117\pi\)
\(720\) 0 0
\(721\) −55.2452 −2.05744
\(722\) 22.1373 0.823865
\(723\) 0 0
\(724\) 23.6453 0.878772
\(725\) −3.63222 −0.134897
\(726\) 0 0
\(727\) −12.7551 −0.473061 −0.236531 0.971624i \(-0.576010\pi\)
−0.236531 + 0.971624i \(0.576010\pi\)
\(728\) −29.1209 −1.07929
\(729\) 0 0
\(730\) 6.76445 0.250363
\(731\) −9.50249 −0.351462
\(732\) 0 0
\(733\) 40.2693 1.48738 0.743690 0.668524i \(-0.233074\pi\)
0.743690 + 0.668524i \(0.233074\pi\)
\(734\) −48.3297 −1.78388
\(735\) 0 0
\(736\) −37.8848 −1.39645
\(737\) −2.89684 −0.106706
\(738\) 0 0
\(739\) 13.7457 0.505644 0.252822 0.967513i \(-0.418641\pi\)
0.252822 + 0.967513i \(0.418641\pi\)
\(740\) 29.5880 1.08767
\(741\) 0 0
\(742\) 48.6647 1.78654
\(743\) −44.8666 −1.64599 −0.822997 0.568045i \(-0.807700\pi\)
−0.822997 + 0.568045i \(0.807700\pi\)
\(744\) 0 0
\(745\) 26.6825 0.977571
\(746\) 19.1476 0.701043
\(747\) 0 0
\(748\) 1.89231 0.0691898
\(749\) 25.5811 0.934713
\(750\) 0 0
\(751\) −23.6834 −0.864219 −0.432109 0.901821i \(-0.642231\pi\)
−0.432109 + 0.901821i \(0.642231\pi\)
\(752\) 41.0844 1.49819
\(753\) 0 0
\(754\) 23.2522 0.846794
\(755\) −39.9361 −1.45342
\(756\) 0 0
\(757\) 23.5395 0.855557 0.427778 0.903884i \(-0.359296\pi\)
0.427778 + 0.903884i \(0.359296\pi\)
\(758\) −49.7077 −1.80546
\(759\) 0 0
\(760\) 9.89309 0.358860
\(761\) −14.0136 −0.507992 −0.253996 0.967205i \(-0.581745\pi\)
−0.253996 + 0.967205i \(0.581745\pi\)
\(762\) 0 0
\(763\) −40.1069 −1.45197
\(764\) −23.1986 −0.839296
\(765\) 0 0
\(766\) 21.7783 0.786881
\(767\) −6.64154 −0.239812
\(768\) 0 0
\(769\) 44.6655 1.61068 0.805339 0.592814i \(-0.201983\pi\)
0.805339 + 0.592814i \(0.201983\pi\)
\(770\) 18.0780 0.651488
\(771\) 0 0
\(772\) 4.89237 0.176080
\(773\) −36.4789 −1.31205 −0.656027 0.754737i \(-0.727764\pi\)
−0.656027 + 0.754737i \(0.727764\pi\)
\(774\) 0 0
\(775\) 7.29858 0.262173
\(776\) −13.1917 −0.473553
\(777\) 0 0
\(778\) 4.15120 0.148828
\(779\) 19.0877 0.683886
\(780\) 0 0
\(781\) 3.64666 0.130488
\(782\) 19.8424 0.709562
\(783\) 0 0
\(784\) −48.4671 −1.73097
\(785\) −31.5358 −1.12556
\(786\) 0 0
\(787\) 41.9161 1.49415 0.747075 0.664740i \(-0.231458\pi\)
0.747075 + 0.664740i \(0.231458\pi\)
\(788\) 16.6934 0.594677
\(789\) 0 0
\(790\) −29.1505 −1.03713
\(791\) 17.5912 0.625471
\(792\) 0 0
\(793\) 4.58176 0.162703
\(794\) −12.8649 −0.456558
\(795\) 0 0
\(796\) 13.7935 0.488899
\(797\) −7.04587 −0.249577 −0.124789 0.992183i \(-0.539825\pi\)
−0.124789 + 0.992183i \(0.539825\pi\)
\(798\) 0 0
\(799\) −13.9224 −0.492538
\(800\) 7.20323 0.254673
\(801\) 0 0
\(802\) −10.4595 −0.369338
\(803\) −1.53009 −0.0539958
\(804\) 0 0
\(805\) 68.0503 2.39846
\(806\) −46.7229 −1.64575
\(807\) 0 0
\(808\) 28.4025 0.999197
\(809\) 37.9979 1.33594 0.667968 0.744190i \(-0.267164\pi\)
0.667968 + 0.744190i \(0.267164\pi\)
\(810\) 0 0
\(811\) −54.3212 −1.90748 −0.953738 0.300641i \(-0.902800\pi\)
−0.953738 + 0.300641i \(0.902800\pi\)
\(812\) 13.1591 0.461795
\(813\) 0 0
\(814\) −18.6433 −0.653447
\(815\) 48.9872 1.71595
\(816\) 0 0
\(817\) −14.3037 −0.500422
\(818\) −66.3920 −2.32134
\(819\) 0 0
\(820\) 21.0409 0.734779
\(821\) −0.336067 −0.0117288 −0.00586440 0.999983i \(-0.501867\pi\)
−0.00586440 + 0.999983i \(0.501867\pi\)
\(822\) 0 0
\(823\) −26.5549 −0.925646 −0.462823 0.886451i \(-0.653163\pi\)
−0.462823 + 0.886451i \(0.653163\pi\)
\(824\) 20.9988 0.731527
\(825\) 0 0
\(826\) −10.4702 −0.364305
\(827\) −28.7699 −1.00043 −0.500214 0.865902i \(-0.666745\pi\)
−0.500214 + 0.865902i \(0.666745\pi\)
\(828\) 0 0
\(829\) 36.5733 1.27024 0.635122 0.772412i \(-0.280950\pi\)
0.635122 + 0.772412i \(0.280950\pi\)
\(830\) 20.7320 0.719618
\(831\) 0 0
\(832\) −0.426976 −0.0148027
\(833\) 16.4242 0.569064
\(834\) 0 0
\(835\) 3.04047 0.105220
\(836\) 2.84841 0.0985143
\(837\) 0 0
\(838\) 4.41080 0.152369
\(839\) 36.5200 1.26081 0.630405 0.776267i \(-0.282889\pi\)
0.630405 + 0.776267i \(0.282889\pi\)
\(840\) 0 0
\(841\) −20.7453 −0.715356
\(842\) 7.81217 0.269225
\(843\) 0 0
\(844\) −0.699219 −0.0240681
\(845\) 20.0040 0.688159
\(846\) 0 0
\(847\) −4.08919 −0.140506
\(848\) −33.5902 −1.15349
\(849\) 0 0
\(850\) −3.77273 −0.129404
\(851\) −70.1781 −2.40567
\(852\) 0 0
\(853\) −30.1362 −1.03184 −0.515922 0.856635i \(-0.672551\pi\)
−0.515922 + 0.856635i \(0.672551\pi\)
\(854\) 7.22301 0.247166
\(855\) 0 0
\(856\) −9.72341 −0.332339
\(857\) 31.6160 1.07998 0.539991 0.841671i \(-0.318428\pi\)
0.539991 + 0.841671i \(0.318428\pi\)
\(858\) 0 0
\(859\) 44.5621 1.52044 0.760219 0.649667i \(-0.225092\pi\)
0.760219 + 0.649667i \(0.225092\pi\)
\(860\) −15.7673 −0.537661
\(861\) 0 0
\(862\) −17.4529 −0.594449
\(863\) −15.9335 −0.542382 −0.271191 0.962526i \(-0.587417\pi\)
−0.271191 + 0.962526i \(0.587417\pi\)
\(864\) 0 0
\(865\) 40.5690 1.37939
\(866\) 68.8989 2.34128
\(867\) 0 0
\(868\) −26.4419 −0.897498
\(869\) 6.59373 0.223677
\(870\) 0 0
\(871\) −13.2726 −0.449726
\(872\) 15.2447 0.516250
\(873\) 0 0
\(874\) 29.8678 1.01029
\(875\) 38.2342 1.29255
\(876\) 0 0
\(877\) −19.4169 −0.655662 −0.327831 0.944736i \(-0.606318\pi\)
−0.327831 + 0.944736i \(0.606318\pi\)
\(878\) −36.4516 −1.23018
\(879\) 0 0
\(880\) −12.4781 −0.420638
\(881\) 37.0820 1.24932 0.624661 0.780896i \(-0.285237\pi\)
0.624661 + 0.780896i \(0.285237\pi\)
\(882\) 0 0
\(883\) 9.54777 0.321308 0.160654 0.987011i \(-0.448640\pi\)
0.160654 + 0.987011i \(0.448640\pi\)
\(884\) 8.67012 0.291608
\(885\) 0 0
\(886\) −56.8251 −1.90908
\(887\) −34.6540 −1.16357 −0.581783 0.813344i \(-0.697645\pi\)
−0.581783 + 0.813344i \(0.697645\pi\)
\(888\) 0 0
\(889\) −36.6255 −1.22838
\(890\) 35.4289 1.18758
\(891\) 0 0
\(892\) 1.23394 0.0413155
\(893\) −20.9567 −0.701289
\(894\) 0 0
\(895\) 1.15263 0.0385282
\(896\) 45.9254 1.53426
\(897\) 0 0
\(898\) −10.3462 −0.345256
\(899\) −16.5870 −0.553206
\(900\) 0 0
\(901\) 11.3828 0.379216
\(902\) −13.2578 −0.441436
\(903\) 0 0
\(904\) −6.68643 −0.222387
\(905\) 52.8371 1.75636
\(906\) 0 0
\(907\) 39.5498 1.31323 0.656614 0.754227i \(-0.271988\pi\)
0.656614 + 0.754227i \(0.271988\pi\)
\(908\) −27.2908 −0.905677
\(909\) 0 0
\(910\) 82.8293 2.74576
\(911\) −57.7089 −1.91198 −0.955991 0.293395i \(-0.905215\pi\)
−0.955991 + 0.293395i \(0.905215\pi\)
\(912\) 0 0
\(913\) −4.68950 −0.155200
\(914\) 2.97137 0.0982842
\(915\) 0 0
\(916\) −11.2747 −0.372527
\(917\) 68.2610 2.25418
\(918\) 0 0
\(919\) −36.0033 −1.18764 −0.593820 0.804598i \(-0.702381\pi\)
−0.593820 + 0.804598i \(0.702381\pi\)
\(920\) −25.8660 −0.852777
\(921\) 0 0
\(922\) −11.0022 −0.362340
\(923\) 16.7081 0.549954
\(924\) 0 0
\(925\) 13.3433 0.438725
\(926\) −35.3685 −1.16228
\(927\) 0 0
\(928\) −16.3702 −0.537380
\(929\) 5.93686 0.194782 0.0973910 0.995246i \(-0.468950\pi\)
0.0973910 + 0.995246i \(0.468950\pi\)
\(930\) 0 0
\(931\) 24.7226 0.810249
\(932\) 2.95937 0.0969375
\(933\) 0 0
\(934\) 19.7903 0.647559
\(935\) 4.22850 0.138287
\(936\) 0 0
\(937\) 31.8437 1.04029 0.520145 0.854078i \(-0.325878\pi\)
0.520145 + 0.854078i \(0.325878\pi\)
\(938\) −20.9239 −0.683190
\(939\) 0 0
\(940\) −23.1012 −0.753477
\(941\) −39.0802 −1.27398 −0.636989 0.770873i \(-0.719820\pi\)
−0.636989 + 0.770873i \(0.719820\pi\)
\(942\) 0 0
\(943\) −49.9057 −1.62515
\(944\) 7.22691 0.235216
\(945\) 0 0
\(946\) 9.93495 0.323013
\(947\) −24.9953 −0.812237 −0.406119 0.913820i \(-0.633118\pi\)
−0.406119 + 0.913820i \(0.633118\pi\)
\(948\) 0 0
\(949\) −7.01051 −0.227571
\(950\) −5.67892 −0.184249
\(951\) 0 0
\(952\) −10.7381 −0.348023
\(953\) −20.1451 −0.652564 −0.326282 0.945273i \(-0.605796\pi\)
−0.326282 + 0.945273i \(0.605796\pi\)
\(954\) 0 0
\(955\) −51.8388 −1.67747
\(956\) 26.9040 0.870138
\(957\) 0 0
\(958\) −65.1361 −2.10445
\(959\) 7.56415 0.244259
\(960\) 0 0
\(961\) 2.32984 0.0751562
\(962\) −85.4191 −2.75402
\(963\) 0 0
\(964\) 22.7369 0.732307
\(965\) 10.9323 0.351924
\(966\) 0 0
\(967\) −19.5208 −0.627746 −0.313873 0.949465i \(-0.601627\pi\)
−0.313873 + 0.949465i \(0.601627\pi\)
\(968\) 1.55430 0.0499572
\(969\) 0 0
\(970\) 37.5213 1.20474
\(971\) 23.1778 0.743811 0.371905 0.928271i \(-0.378705\pi\)
0.371905 + 0.928271i \(0.378705\pi\)
\(972\) 0 0
\(973\) 8.58034 0.275073
\(974\) 48.1071 1.54145
\(975\) 0 0
\(976\) −4.98559 −0.159585
\(977\) −25.0807 −0.802401 −0.401201 0.915990i \(-0.631407\pi\)
−0.401201 + 0.915990i \(0.631407\pi\)
\(978\) 0 0
\(979\) −8.01389 −0.256125
\(980\) 27.2524 0.870545
\(981\) 0 0
\(982\) −17.5843 −0.561138
\(983\) −23.1549 −0.738527 −0.369263 0.929325i \(-0.620390\pi\)
−0.369263 + 0.929325i \(0.620390\pi\)
\(984\) 0 0
\(985\) 37.3025 1.18856
\(986\) 8.57402 0.273052
\(987\) 0 0
\(988\) 13.0507 0.415199
\(989\) 37.3977 1.18918
\(990\) 0 0
\(991\) −20.3916 −0.647762 −0.323881 0.946098i \(-0.604988\pi\)
−0.323881 + 0.946098i \(0.604988\pi\)
\(992\) 32.8944 1.04440
\(993\) 0 0
\(994\) 26.3398 0.835449
\(995\) 30.8226 0.977142
\(996\) 0 0
\(997\) −37.9430 −1.20167 −0.600834 0.799374i \(-0.705165\pi\)
−0.600834 + 0.799374i \(0.705165\pi\)
\(998\) 43.9101 1.38995
\(999\) 0 0
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 \(a_p\))