Properties

Label 8018.2.a.j.1.18
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.833135 q^{3}\) \(+1.00000 q^{4}\) \(-3.18557 q^{5}\) \(-0.833135 q^{6}\) \(+0.455061 q^{7}\) \(+1.00000 q^{8}\) \(-2.30589 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.833135 q^{3}\) \(+1.00000 q^{4}\) \(-3.18557 q^{5}\) \(-0.833135 q^{6}\) \(+0.455061 q^{7}\) \(+1.00000 q^{8}\) \(-2.30589 q^{9}\) \(-3.18557 q^{10}\) \(-1.37320 q^{11}\) \(-0.833135 q^{12}\) \(+5.32549 q^{13}\) \(+0.455061 q^{14}\) \(+2.65401 q^{15}\) \(+1.00000 q^{16}\) \(-7.33327 q^{17}\) \(-2.30589 q^{18}\) \(-1.00000 q^{19}\) \(-3.18557 q^{20}\) \(-0.379127 q^{21}\) \(-1.37320 q^{22}\) \(-4.82410 q^{23}\) \(-0.833135 q^{24}\) \(+5.14783 q^{25}\) \(+5.32549 q^{26}\) \(+4.42052 q^{27}\) \(+0.455061 q^{28}\) \(+1.65207 q^{29}\) \(+2.65401 q^{30}\) \(+5.97363 q^{31}\) \(+1.00000 q^{32}\) \(+1.14406 q^{33}\) \(-7.33327 q^{34}\) \(-1.44963 q^{35}\) \(-2.30589 q^{36}\) \(-8.53380 q^{37}\) \(-1.00000 q^{38}\) \(-4.43685 q^{39}\) \(-3.18557 q^{40}\) \(-2.32519 q^{41}\) \(-0.379127 q^{42}\) \(-5.06700 q^{43}\) \(-1.37320 q^{44}\) \(+7.34555 q^{45}\) \(-4.82410 q^{46}\) \(+3.59352 q^{47}\) \(-0.833135 q^{48}\) \(-6.79292 q^{49}\) \(+5.14783 q^{50}\) \(+6.10961 q^{51}\) \(+5.32549 q^{52}\) \(+0.902921 q^{53}\) \(+4.42052 q^{54}\) \(+4.37442 q^{55}\) \(+0.455061 q^{56}\) \(+0.833135 q^{57}\) \(+1.65207 q^{58}\) \(-0.573811 q^{59}\) \(+2.65401 q^{60}\) \(-0.904971 q^{61}\) \(+5.97363 q^{62}\) \(-1.04932 q^{63}\) \(+1.00000 q^{64}\) \(-16.9647 q^{65}\) \(+1.14406 q^{66}\) \(+7.39328 q^{67}\) \(-7.33327 q^{68}\) \(+4.01912 q^{69}\) \(-1.44963 q^{70}\) \(+11.9031 q^{71}\) \(-2.30589 q^{72}\) \(+1.44472 q^{73}\) \(-8.53380 q^{74}\) \(-4.28884 q^{75}\) \(-1.00000 q^{76}\) \(-0.624890 q^{77}\) \(-4.43685 q^{78}\) \(-1.09630 q^{79}\) \(-3.18557 q^{80}\) \(+3.23477 q^{81}\) \(-2.32519 q^{82}\) \(-16.3459 q^{83}\) \(-0.379127 q^{84}\) \(+23.3606 q^{85}\) \(-5.06700 q^{86}\) \(-1.37640 q^{87}\) \(-1.37320 q^{88}\) \(-7.72987 q^{89}\) \(+7.34555 q^{90}\) \(+2.42342 q^{91}\) \(-4.82410 q^{92}\) \(-4.97684 q^{93}\) \(+3.59352 q^{94}\) \(+3.18557 q^{95}\) \(-0.833135 q^{96}\) \(+11.9548 q^{97}\) \(-6.79292 q^{98}\) \(+3.16644 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.833135 −0.481011 −0.240505 0.970648i \(-0.577313\pi\)
−0.240505 + 0.970648i \(0.577313\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.18557 −1.42463 −0.712314 0.701861i \(-0.752353\pi\)
−0.712314 + 0.701861i \(0.752353\pi\)
\(6\) −0.833135 −0.340126
\(7\) 0.455061 0.171997 0.0859985 0.996295i \(-0.472592\pi\)
0.0859985 + 0.996295i \(0.472592\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.30589 −0.768629
\(10\) −3.18557 −1.00736
\(11\) −1.37320 −0.414035 −0.207018 0.978337i \(-0.566376\pi\)
−0.207018 + 0.978337i \(0.566376\pi\)
\(12\) −0.833135 −0.240505
\(13\) 5.32549 1.47702 0.738512 0.674240i \(-0.235529\pi\)
0.738512 + 0.674240i \(0.235529\pi\)
\(14\) 0.455061 0.121620
\(15\) 2.65401 0.685261
\(16\) 1.00000 0.250000
\(17\) −7.33327 −1.77858 −0.889290 0.457344i \(-0.848801\pi\)
−0.889290 + 0.457344i \(0.848801\pi\)
\(18\) −2.30589 −0.543503
\(19\) −1.00000 −0.229416
\(20\) −3.18557 −0.712314
\(21\) −0.379127 −0.0827324
\(22\) −1.37320 −0.292767
\(23\) −4.82410 −1.00589 −0.502947 0.864317i \(-0.667751\pi\)
−0.502947 + 0.864317i \(0.667751\pi\)
\(24\) −0.833135 −0.170063
\(25\) 5.14783 1.02957
\(26\) 5.32549 1.04441
\(27\) 4.42052 0.850729
\(28\) 0.455061 0.0859985
\(29\) 1.65207 0.306782 0.153391 0.988166i \(-0.450981\pi\)
0.153391 + 0.988166i \(0.450981\pi\)
\(30\) 2.65401 0.484553
\(31\) 5.97363 1.07290 0.536448 0.843934i \(-0.319766\pi\)
0.536448 + 0.843934i \(0.319766\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.14406 0.199155
\(34\) −7.33327 −1.25765
\(35\) −1.44963 −0.245032
\(36\) −2.30589 −0.384314
\(37\) −8.53380 −1.40295 −0.701474 0.712695i \(-0.747474\pi\)
−0.701474 + 0.712695i \(0.747474\pi\)
\(38\) −1.00000 −0.162221
\(39\) −4.43685 −0.710464
\(40\) −3.18557 −0.503682
\(41\) −2.32519 −0.363134 −0.181567 0.983379i \(-0.558117\pi\)
−0.181567 + 0.983379i \(0.558117\pi\)
\(42\) −0.379127 −0.0585006
\(43\) −5.06700 −0.772710 −0.386355 0.922350i \(-0.626266\pi\)
−0.386355 + 0.922350i \(0.626266\pi\)
\(44\) −1.37320 −0.207018
\(45\) 7.34555 1.09501
\(46\) −4.82410 −0.711275
\(47\) 3.59352 0.524169 0.262085 0.965045i \(-0.415590\pi\)
0.262085 + 0.965045i \(0.415590\pi\)
\(48\) −0.833135 −0.120253
\(49\) −6.79292 −0.970417
\(50\) 5.14783 0.728013
\(51\) 6.10961 0.855516
\(52\) 5.32549 0.738512
\(53\) 0.902921 0.124026 0.0620129 0.998075i \(-0.480248\pi\)
0.0620129 + 0.998075i \(0.480248\pi\)
\(54\) 4.42052 0.601556
\(55\) 4.37442 0.589846
\(56\) 0.455061 0.0608101
\(57\) 0.833135 0.110351
\(58\) 1.65207 0.216928
\(59\) −0.573811 −0.0747038 −0.0373519 0.999302i \(-0.511892\pi\)
−0.0373519 + 0.999302i \(0.511892\pi\)
\(60\) 2.65401 0.342631
\(61\) −0.904971 −0.115870 −0.0579348 0.998320i \(-0.518452\pi\)
−0.0579348 + 0.998320i \(0.518452\pi\)
\(62\) 5.97363 0.758651
\(63\) −1.04932 −0.132202
\(64\) 1.00000 0.125000
\(65\) −16.9647 −2.10421
\(66\) 1.14406 0.140824
\(67\) 7.39328 0.903232 0.451616 0.892212i \(-0.350848\pi\)
0.451616 + 0.892212i \(0.350848\pi\)
\(68\) −7.33327 −0.889290
\(69\) 4.01912 0.483846
\(70\) −1.44963 −0.173264
\(71\) 11.9031 1.41264 0.706321 0.707892i \(-0.250353\pi\)
0.706321 + 0.707892i \(0.250353\pi\)
\(72\) −2.30589 −0.271751
\(73\) 1.44472 0.169092 0.0845461 0.996420i \(-0.473056\pi\)
0.0845461 + 0.996420i \(0.473056\pi\)
\(74\) −8.53380 −0.992035
\(75\) −4.28884 −0.495232
\(76\) −1.00000 −0.114708
\(77\) −0.624890 −0.0712128
\(78\) −4.43685 −0.502374
\(79\) −1.09630 −0.123344 −0.0616718 0.998096i \(-0.519643\pi\)
−0.0616718 + 0.998096i \(0.519643\pi\)
\(80\) −3.18557 −0.356157
\(81\) 3.23477 0.359419
\(82\) −2.32519 −0.256774
\(83\) −16.3459 −1.79420 −0.897098 0.441831i \(-0.854329\pi\)
−0.897098 + 0.441831i \(0.854329\pi\)
\(84\) −0.379127 −0.0413662
\(85\) 23.3606 2.53382
\(86\) −5.06700 −0.546388
\(87\) −1.37640 −0.147565
\(88\) −1.37320 −0.146384
\(89\) −7.72987 −0.819364 −0.409682 0.912228i \(-0.634360\pi\)
−0.409682 + 0.912228i \(0.634360\pi\)
\(90\) 7.34555 0.774289
\(91\) 2.42342 0.254044
\(92\) −4.82410 −0.502947
\(93\) −4.97684 −0.516074
\(94\) 3.59352 0.370644
\(95\) 3.18557 0.326832
\(96\) −0.833135 −0.0850315
\(97\) 11.9548 1.21382 0.606911 0.794770i \(-0.292408\pi\)
0.606911 + 0.794770i \(0.292408\pi\)
\(98\) −6.79292 −0.686188
\(99\) 3.16644 0.318239
\(100\) 5.14783 0.514783
\(101\) 2.91069 0.289625 0.144812 0.989459i \(-0.453742\pi\)
0.144812 + 0.989459i \(0.453742\pi\)
\(102\) 6.10961 0.604941
\(103\) −4.95450 −0.488181 −0.244091 0.969752i \(-0.578489\pi\)
−0.244091 + 0.969752i \(0.578489\pi\)
\(104\) 5.32549 0.522207
\(105\) 1.20774 0.117863
\(106\) 0.902921 0.0876995
\(107\) 9.71232 0.938926 0.469463 0.882952i \(-0.344448\pi\)
0.469463 + 0.882952i \(0.344448\pi\)
\(108\) 4.42052 0.425365
\(109\) 1.66637 0.159609 0.0798045 0.996811i \(-0.474570\pi\)
0.0798045 + 0.996811i \(0.474570\pi\)
\(110\) 4.37442 0.417084
\(111\) 7.10981 0.674833
\(112\) 0.455061 0.0429993
\(113\) −12.1584 −1.14377 −0.571885 0.820334i \(-0.693788\pi\)
−0.571885 + 0.820334i \(0.693788\pi\)
\(114\) 0.833135 0.0780302
\(115\) 15.3675 1.43303
\(116\) 1.65207 0.153391
\(117\) −12.2800 −1.13528
\(118\) −0.573811 −0.0528236
\(119\) −3.33709 −0.305910
\(120\) 2.65401 0.242276
\(121\) −9.11432 −0.828575
\(122\) −0.904971 −0.0819322
\(123\) 1.93720 0.174671
\(124\) 5.97363 0.536448
\(125\) −0.470923 −0.0421206
\(126\) −1.04932 −0.0934808
\(127\) 15.9802 1.41801 0.709006 0.705203i \(-0.249144\pi\)
0.709006 + 0.705203i \(0.249144\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.22149 0.371682
\(130\) −16.9647 −1.48790
\(131\) 6.63129 0.579378 0.289689 0.957121i \(-0.406448\pi\)
0.289689 + 0.957121i \(0.406448\pi\)
\(132\) 1.14406 0.0995777
\(133\) −0.455061 −0.0394588
\(134\) 7.39328 0.638682
\(135\) −14.0819 −1.21197
\(136\) −7.33327 −0.628823
\(137\) 16.9545 1.44852 0.724261 0.689526i \(-0.242181\pi\)
0.724261 + 0.689526i \(0.242181\pi\)
\(138\) 4.01912 0.342131
\(139\) 4.46835 0.379000 0.189500 0.981881i \(-0.439313\pi\)
0.189500 + 0.981881i \(0.439313\pi\)
\(140\) −1.44963 −0.122516
\(141\) −2.99389 −0.252131
\(142\) 11.9031 0.998889
\(143\) −7.31296 −0.611540
\(144\) −2.30589 −0.192157
\(145\) −5.26279 −0.437051
\(146\) 1.44472 0.119566
\(147\) 5.65942 0.466781
\(148\) −8.53380 −0.701474
\(149\) 3.87568 0.317508 0.158754 0.987318i \(-0.449252\pi\)
0.158754 + 0.987318i \(0.449252\pi\)
\(150\) −4.28884 −0.350182
\(151\) 7.69964 0.626587 0.313294 0.949656i \(-0.398568\pi\)
0.313294 + 0.949656i \(0.398568\pi\)
\(152\) −1.00000 −0.0811107
\(153\) 16.9097 1.36707
\(154\) −0.624890 −0.0503551
\(155\) −19.0294 −1.52848
\(156\) −4.43685 −0.355232
\(157\) 2.51487 0.200709 0.100354 0.994952i \(-0.468002\pi\)
0.100354 + 0.994952i \(0.468002\pi\)
\(158\) −1.09630 −0.0872171
\(159\) −0.752255 −0.0596577
\(160\) −3.18557 −0.251841
\(161\) −2.19526 −0.173011
\(162\) 3.23477 0.254148
\(163\) −17.0284 −1.33377 −0.666885 0.745161i \(-0.732373\pi\)
−0.666885 + 0.745161i \(0.732373\pi\)
\(164\) −2.32519 −0.181567
\(165\) −3.64448 −0.283722
\(166\) −16.3459 −1.26869
\(167\) 3.30469 0.255725 0.127862 0.991792i \(-0.459188\pi\)
0.127862 + 0.991792i \(0.459188\pi\)
\(168\) −0.379127 −0.0292503
\(169\) 15.3608 1.18160
\(170\) 23.3606 1.79168
\(171\) 2.30589 0.176336
\(172\) −5.06700 −0.386355
\(173\) 23.1168 1.75753 0.878767 0.477251i \(-0.158367\pi\)
0.878767 + 0.477251i \(0.158367\pi\)
\(174\) −1.37640 −0.104345
\(175\) 2.34258 0.177082
\(176\) −1.37320 −0.103509
\(177\) 0.478062 0.0359333
\(178\) −7.72987 −0.579378
\(179\) −8.85098 −0.661553 −0.330777 0.943709i \(-0.607311\pi\)
−0.330777 + 0.943709i \(0.607311\pi\)
\(180\) 7.34555 0.547505
\(181\) −20.1368 −1.49675 −0.748377 0.663273i \(-0.769167\pi\)
−0.748377 + 0.663273i \(0.769167\pi\)
\(182\) 2.42342 0.179636
\(183\) 0.753963 0.0557345
\(184\) −4.82410 −0.355637
\(185\) 27.1850 1.99868
\(186\) −4.97684 −0.364919
\(187\) 10.0700 0.736395
\(188\) 3.59352 0.262085
\(189\) 2.01161 0.146323
\(190\) 3.18557 0.231105
\(191\) −0.896810 −0.0648909 −0.0324454 0.999474i \(-0.510330\pi\)
−0.0324454 + 0.999474i \(0.510330\pi\)
\(192\) −0.833135 −0.0601263
\(193\) 15.7414 1.13309 0.566544 0.824031i \(-0.308280\pi\)
0.566544 + 0.824031i \(0.308280\pi\)
\(194\) 11.9548 0.858302
\(195\) 14.1339 1.01215
\(196\) −6.79292 −0.485209
\(197\) 18.1808 1.29533 0.647664 0.761926i \(-0.275746\pi\)
0.647664 + 0.761926i \(0.275746\pi\)
\(198\) 3.16644 0.225029
\(199\) 21.6872 1.53736 0.768681 0.639633i \(-0.220914\pi\)
0.768681 + 0.639633i \(0.220914\pi\)
\(200\) 5.14783 0.364007
\(201\) −6.15960 −0.434464
\(202\) 2.91069 0.204796
\(203\) 0.751794 0.0527656
\(204\) 6.10961 0.427758
\(205\) 7.40704 0.517330
\(206\) −4.95450 −0.345196
\(207\) 11.1238 0.773159
\(208\) 5.32549 0.369256
\(209\) 1.37320 0.0949862
\(210\) 1.20774 0.0833417
\(211\) −1.00000 −0.0688428
\(212\) 0.902921 0.0620129
\(213\) −9.91692 −0.679496
\(214\) 9.71232 0.663921
\(215\) 16.1413 1.10082
\(216\) 4.42052 0.300778
\(217\) 2.71837 0.184535
\(218\) 1.66637 0.112861
\(219\) −1.20365 −0.0813351
\(220\) 4.37442 0.294923
\(221\) −39.0533 −2.62701
\(222\) 7.10981 0.477179
\(223\) 22.8355 1.52918 0.764588 0.644520i \(-0.222943\pi\)
0.764588 + 0.644520i \(0.222943\pi\)
\(224\) 0.455061 0.0304051
\(225\) −11.8703 −0.791354
\(226\) −12.1584 −0.808767
\(227\) 14.3922 0.955247 0.477623 0.878565i \(-0.341498\pi\)
0.477623 + 0.878565i \(0.341498\pi\)
\(228\) 0.833135 0.0551757
\(229\) −3.06103 −0.202279 −0.101139 0.994872i \(-0.532249\pi\)
−0.101139 + 0.994872i \(0.532249\pi\)
\(230\) 15.3675 1.01330
\(231\) 0.520618 0.0342541
\(232\) 1.65207 0.108464
\(233\) 8.74764 0.573077 0.286539 0.958069i \(-0.407495\pi\)
0.286539 + 0.958069i \(0.407495\pi\)
\(234\) −12.2800 −0.802767
\(235\) −11.4474 −0.746746
\(236\) −0.573811 −0.0373519
\(237\) 0.913367 0.0593296
\(238\) −3.33709 −0.216311
\(239\) 16.8769 1.09168 0.545838 0.837891i \(-0.316211\pi\)
0.545838 + 0.837891i \(0.316211\pi\)
\(240\) 2.65401 0.171315
\(241\) 8.38468 0.540105 0.270052 0.962846i \(-0.412959\pi\)
0.270052 + 0.962846i \(0.412959\pi\)
\(242\) −9.11432 −0.585891
\(243\) −15.9566 −1.02361
\(244\) −0.904971 −0.0579348
\(245\) 21.6393 1.38248
\(246\) 1.93720 0.123511
\(247\) −5.32549 −0.338853
\(248\) 5.97363 0.379326
\(249\) 13.6183 0.863027
\(250\) −0.470923 −0.0297838
\(251\) −19.9311 −1.25804 −0.629020 0.777389i \(-0.716544\pi\)
−0.629020 + 0.777389i \(0.716544\pi\)
\(252\) −1.04932 −0.0661009
\(253\) 6.62445 0.416476
\(254\) 15.9802 1.00269
\(255\) −19.4625 −1.21879
\(256\) 1.00000 0.0625000
\(257\) −10.1018 −0.630133 −0.315066 0.949070i \(-0.602027\pi\)
−0.315066 + 0.949070i \(0.602027\pi\)
\(258\) 4.22149 0.262819
\(259\) −3.88340 −0.241303
\(260\) −16.9647 −1.05211
\(261\) −3.80949 −0.235802
\(262\) 6.63129 0.409682
\(263\) −9.27824 −0.572121 −0.286060 0.958212i \(-0.592346\pi\)
−0.286060 + 0.958212i \(0.592346\pi\)
\(264\) 1.14406 0.0704120
\(265\) −2.87631 −0.176691
\(266\) −0.455061 −0.0279016
\(267\) 6.44002 0.394123
\(268\) 7.39328 0.451616
\(269\) −18.6878 −1.13941 −0.569707 0.821848i \(-0.692943\pi\)
−0.569707 + 0.821848i \(0.692943\pi\)
\(270\) −14.0819 −0.856994
\(271\) 22.5817 1.37174 0.685869 0.727725i \(-0.259422\pi\)
0.685869 + 0.727725i \(0.259422\pi\)
\(272\) −7.33327 −0.444645
\(273\) −2.01904 −0.122198
\(274\) 16.9545 1.02426
\(275\) −7.06900 −0.426277
\(276\) 4.01912 0.241923
\(277\) −5.78007 −0.347291 −0.173645 0.984808i \(-0.555555\pi\)
−0.173645 + 0.984808i \(0.555555\pi\)
\(278\) 4.46835 0.267994
\(279\) −13.7745 −0.824658
\(280\) −1.44963 −0.0866318
\(281\) −27.1568 −1.62004 −0.810020 0.586402i \(-0.800544\pi\)
−0.810020 + 0.586402i \(0.800544\pi\)
\(282\) −2.99389 −0.178283
\(283\) 18.8095 1.11811 0.559054 0.829132i \(-0.311165\pi\)
0.559054 + 0.829132i \(0.311165\pi\)
\(284\) 11.9031 0.706321
\(285\) −2.65401 −0.157210
\(286\) −7.31296 −0.432424
\(287\) −1.05810 −0.0624579
\(288\) −2.30589 −0.135876
\(289\) 36.7769 2.16335
\(290\) −5.26279 −0.309041
\(291\) −9.95993 −0.583862
\(292\) 1.44472 0.0845461
\(293\) 33.1965 1.93936 0.969680 0.244377i \(-0.0785835\pi\)
0.969680 + 0.244377i \(0.0785835\pi\)
\(294\) 5.65942 0.330064
\(295\) 1.82791 0.106425
\(296\) −8.53380 −0.496017
\(297\) −6.07025 −0.352232
\(298\) 3.87568 0.224512
\(299\) −25.6907 −1.48573
\(300\) −4.28884 −0.247616
\(301\) −2.30579 −0.132904
\(302\) 7.69964 0.443064
\(303\) −2.42500 −0.139313
\(304\) −1.00000 −0.0573539
\(305\) 2.88284 0.165071
\(306\) 16.9097 0.966663
\(307\) −2.16914 −0.123799 −0.0618996 0.998082i \(-0.519716\pi\)
−0.0618996 + 0.998082i \(0.519716\pi\)
\(308\) −0.624890 −0.0356064
\(309\) 4.12776 0.234820
\(310\) −19.0294 −1.08080
\(311\) 30.4081 1.72429 0.862143 0.506666i \(-0.169122\pi\)
0.862143 + 0.506666i \(0.169122\pi\)
\(312\) −4.43685 −0.251187
\(313\) −33.7663 −1.90859 −0.954293 0.298873i \(-0.903389\pi\)
−0.954293 + 0.298873i \(0.903389\pi\)
\(314\) 2.51487 0.141922
\(315\) 3.34268 0.188339
\(316\) −1.09630 −0.0616718
\(317\) −28.5722 −1.60477 −0.802386 0.596805i \(-0.796437\pi\)
−0.802386 + 0.596805i \(0.796437\pi\)
\(318\) −0.752255 −0.0421844
\(319\) −2.26863 −0.127019
\(320\) −3.18557 −0.178079
\(321\) −8.09167 −0.451633
\(322\) −2.19526 −0.122337
\(323\) 7.33327 0.408034
\(324\) 3.23477 0.179710
\(325\) 27.4147 1.52069
\(326\) −17.0284 −0.943118
\(327\) −1.38831 −0.0767736
\(328\) −2.32519 −0.128387
\(329\) 1.63527 0.0901555
\(330\) −3.64448 −0.200622
\(331\) −4.88317 −0.268403 −0.134202 0.990954i \(-0.542847\pi\)
−0.134202 + 0.990954i \(0.542847\pi\)
\(332\) −16.3459 −0.897098
\(333\) 19.6780 1.07835
\(334\) 3.30469 0.180825
\(335\) −23.5518 −1.28677
\(336\) −0.379127 −0.0206831
\(337\) 36.3051 1.97766 0.988832 0.149033i \(-0.0476162\pi\)
0.988832 + 0.149033i \(0.0476162\pi\)
\(338\) 15.3608 0.835519
\(339\) 10.1296 0.550165
\(340\) 23.3606 1.26691
\(341\) −8.20298 −0.444216
\(342\) 2.30589 0.124688
\(343\) −6.27662 −0.338906
\(344\) −5.06700 −0.273194
\(345\) −12.8032 −0.689300
\(346\) 23.1168 1.24276
\(347\) −9.37740 −0.503405 −0.251703 0.967805i \(-0.580991\pi\)
−0.251703 + 0.967805i \(0.580991\pi\)
\(348\) −1.37640 −0.0737827
\(349\) 19.9950 1.07031 0.535153 0.844755i \(-0.320254\pi\)
0.535153 + 0.844755i \(0.320254\pi\)
\(350\) 2.34258 0.125216
\(351\) 23.5414 1.25655
\(352\) −1.37320 −0.0731918
\(353\) −19.6389 −1.04527 −0.522637 0.852555i \(-0.675052\pi\)
−0.522637 + 0.852555i \(0.675052\pi\)
\(354\) 0.478062 0.0254087
\(355\) −37.9182 −2.01249
\(356\) −7.72987 −0.409682
\(357\) 2.78024 0.147146
\(358\) −8.85098 −0.467789
\(359\) −12.3866 −0.653740 −0.326870 0.945069i \(-0.605994\pi\)
−0.326870 + 0.945069i \(0.605994\pi\)
\(360\) 7.34555 0.387145
\(361\) 1.00000 0.0526316
\(362\) −20.1368 −1.05837
\(363\) 7.59346 0.398553
\(364\) 2.42342 0.127022
\(365\) −4.60227 −0.240894
\(366\) 0.753963 0.0394103
\(367\) 14.2061 0.741551 0.370776 0.928723i \(-0.379092\pi\)
0.370776 + 0.928723i \(0.379092\pi\)
\(368\) −4.82410 −0.251474
\(369\) 5.36162 0.279115
\(370\) 27.1850 1.41328
\(371\) 0.410884 0.0213321
\(372\) −4.97684 −0.258037
\(373\) 30.1257 1.55985 0.779925 0.625872i \(-0.215257\pi\)
0.779925 + 0.625872i \(0.215257\pi\)
\(374\) 10.0700 0.520710
\(375\) 0.392342 0.0202605
\(376\) 3.59352 0.185322
\(377\) 8.79809 0.453125
\(378\) 2.01161 0.103466
\(379\) 0.617767 0.0317326 0.0158663 0.999874i \(-0.494949\pi\)
0.0158663 + 0.999874i \(0.494949\pi\)
\(380\) 3.18557 0.163416
\(381\) −13.3136 −0.682079
\(382\) −0.896810 −0.0458848
\(383\) 12.4877 0.638093 0.319046 0.947739i \(-0.396637\pi\)
0.319046 + 0.947739i \(0.396637\pi\)
\(384\) −0.833135 −0.0425157
\(385\) 1.99063 0.101452
\(386\) 15.7414 0.801215
\(387\) 11.6839 0.593927
\(388\) 11.9548 0.606911
\(389\) 22.5256 1.14209 0.571047 0.820918i \(-0.306538\pi\)
0.571047 + 0.820918i \(0.306538\pi\)
\(390\) 14.1339 0.715697
\(391\) 35.3764 1.78906
\(392\) −6.79292 −0.343094
\(393\) −5.52476 −0.278687
\(394\) 18.1808 0.915935
\(395\) 3.49234 0.175719
\(396\) 3.16644 0.159120
\(397\) 2.21743 0.111290 0.0556449 0.998451i \(-0.482279\pi\)
0.0556449 + 0.998451i \(0.482279\pi\)
\(398\) 21.6872 1.08708
\(399\) 0.379127 0.0189801
\(400\) 5.14783 0.257392
\(401\) −21.1119 −1.05428 −0.527138 0.849780i \(-0.676735\pi\)
−0.527138 + 0.849780i \(0.676735\pi\)
\(402\) −6.15960 −0.307213
\(403\) 31.8125 1.58469
\(404\) 2.91069 0.144812
\(405\) −10.3046 −0.512039
\(406\) 0.751794 0.0373109
\(407\) 11.7186 0.580870
\(408\) 6.10961 0.302471
\(409\) −27.5064 −1.36010 −0.680052 0.733164i \(-0.738043\pi\)
−0.680052 + 0.733164i \(0.738043\pi\)
\(410\) 7.40704 0.365808
\(411\) −14.1254 −0.696755
\(412\) −4.95450 −0.244091
\(413\) −0.261119 −0.0128488
\(414\) 11.1238 0.546706
\(415\) 52.0710 2.55606
\(416\) 5.32549 0.261104
\(417\) −3.72274 −0.182303
\(418\) 1.37320 0.0671654
\(419\) −8.97773 −0.438591 −0.219296 0.975658i \(-0.570376\pi\)
−0.219296 + 0.975658i \(0.570376\pi\)
\(420\) 1.20774 0.0589314
\(421\) 29.8005 1.45239 0.726194 0.687489i \(-0.241287\pi\)
0.726194 + 0.687489i \(0.241287\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −8.28625 −0.402892
\(424\) 0.902921 0.0438497
\(425\) −37.7504 −1.83117
\(426\) −9.91692 −0.480476
\(427\) −0.411817 −0.0199292
\(428\) 9.71232 0.469463
\(429\) 6.09268 0.294157
\(430\) 16.1413 0.778400
\(431\) 27.8167 1.33988 0.669941 0.742414i \(-0.266319\pi\)
0.669941 + 0.742414i \(0.266319\pi\)
\(432\) 4.42052 0.212682
\(433\) 1.22663 0.0589483 0.0294741 0.999566i \(-0.490617\pi\)
0.0294741 + 0.999566i \(0.490617\pi\)
\(434\) 2.71837 0.130486
\(435\) 4.38461 0.210226
\(436\) 1.66637 0.0798045
\(437\) 4.82410 0.230768
\(438\) −1.20365 −0.0575126
\(439\) 35.1401 1.67714 0.838572 0.544790i \(-0.183391\pi\)
0.838572 + 0.544790i \(0.183391\pi\)
\(440\) 4.37442 0.208542
\(441\) 15.6637 0.745890
\(442\) −39.0533 −1.85757
\(443\) −0.756700 −0.0359519 −0.0179759 0.999838i \(-0.505722\pi\)
−0.0179759 + 0.999838i \(0.505722\pi\)
\(444\) 7.10981 0.337417
\(445\) 24.6240 1.16729
\(446\) 22.8355 1.08129
\(447\) −3.22896 −0.152725
\(448\) 0.455061 0.0214996
\(449\) 13.1481 0.620497 0.310249 0.950655i \(-0.399588\pi\)
0.310249 + 0.950655i \(0.399588\pi\)
\(450\) −11.8703 −0.559572
\(451\) 3.19295 0.150350
\(452\) −12.1584 −0.571885
\(453\) −6.41483 −0.301395
\(454\) 14.3922 0.675461
\(455\) −7.71998 −0.361918
\(456\) 0.833135 0.0390151
\(457\) 30.8512 1.44316 0.721580 0.692331i \(-0.243416\pi\)
0.721580 + 0.692331i \(0.243416\pi\)
\(458\) −3.06103 −0.143033
\(459\) −32.4169 −1.51309
\(460\) 15.3675 0.716513
\(461\) 11.9807 0.557997 0.278998 0.960292i \(-0.409998\pi\)
0.278998 + 0.960292i \(0.409998\pi\)
\(462\) 0.520618 0.0242213
\(463\) 24.1856 1.12400 0.562000 0.827137i \(-0.310032\pi\)
0.562000 + 0.827137i \(0.310032\pi\)
\(464\) 1.65207 0.0766955
\(465\) 15.8540 0.735214
\(466\) 8.74764 0.405227
\(467\) −10.4573 −0.483904 −0.241952 0.970288i \(-0.577788\pi\)
−0.241952 + 0.970288i \(0.577788\pi\)
\(468\) −12.2800 −0.567642
\(469\) 3.36439 0.155353
\(470\) −11.4474 −0.528029
\(471\) −2.09523 −0.0965430
\(472\) −0.573811 −0.0264118
\(473\) 6.95800 0.319929
\(474\) 0.913367 0.0419523
\(475\) −5.14783 −0.236199
\(476\) −3.33709 −0.152955
\(477\) −2.08203 −0.0953298
\(478\) 16.8769 0.771931
\(479\) 0.600314 0.0274290 0.0137145 0.999906i \(-0.495634\pi\)
0.0137145 + 0.999906i \(0.495634\pi\)
\(480\) 2.65401 0.121138
\(481\) −45.4467 −2.07219
\(482\) 8.38468 0.381912
\(483\) 1.82895 0.0832200
\(484\) −9.11432 −0.414287
\(485\) −38.0827 −1.72925
\(486\) −15.9566 −0.723804
\(487\) −10.6381 −0.482060 −0.241030 0.970518i \(-0.577485\pi\)
−0.241030 + 0.970518i \(0.577485\pi\)
\(488\) −0.904971 −0.0409661
\(489\) 14.1870 0.641557
\(490\) 21.6393 0.977564
\(491\) 26.5876 1.19988 0.599940 0.800045i \(-0.295191\pi\)
0.599940 + 0.800045i \(0.295191\pi\)
\(492\) 1.93720 0.0873355
\(493\) −12.1151 −0.545637
\(494\) −5.32549 −0.239605
\(495\) −10.0869 −0.453373
\(496\) 5.97363 0.268224
\(497\) 5.41666 0.242970
\(498\) 13.6183 0.610253
\(499\) 29.1220 1.30368 0.651840 0.758356i \(-0.273997\pi\)
0.651840 + 0.758356i \(0.273997\pi\)
\(500\) −0.470923 −0.0210603
\(501\) −2.75325 −0.123006
\(502\) −19.9311 −0.889569
\(503\) −39.3717 −1.75550 −0.877748 0.479123i \(-0.840955\pi\)
−0.877748 + 0.479123i \(0.840955\pi\)
\(504\) −1.04932 −0.0467404
\(505\) −9.27220 −0.412608
\(506\) 6.62445 0.294493
\(507\) −12.7976 −0.568363
\(508\) 15.9802 0.709006
\(509\) −7.79577 −0.345542 −0.172771 0.984962i \(-0.555272\pi\)
−0.172771 + 0.984962i \(0.555272\pi\)
\(510\) −19.4625 −0.861816
\(511\) 0.657438 0.0290834
\(512\) 1.00000 0.0441942
\(513\) −4.42052 −0.195171
\(514\) −10.1018 −0.445571
\(515\) 15.7829 0.695477
\(516\) 4.22149 0.185841
\(517\) −4.93462 −0.217024
\(518\) −3.88340 −0.170627
\(519\) −19.2594 −0.845393
\(520\) −16.9647 −0.743951
\(521\) −7.38055 −0.323348 −0.161674 0.986844i \(-0.551689\pi\)
−0.161674 + 0.986844i \(0.551689\pi\)
\(522\) −3.80949 −0.166737
\(523\) 21.5036 0.940285 0.470142 0.882591i \(-0.344203\pi\)
0.470142 + 0.882591i \(0.344203\pi\)
\(524\) 6.63129 0.289689
\(525\) −1.95168 −0.0851784
\(526\) −9.27824 −0.404550
\(527\) −43.8062 −1.90823
\(528\) 1.14406 0.0497888
\(529\) 0.271927 0.0118229
\(530\) −2.87631 −0.124939
\(531\) 1.32314 0.0574195
\(532\) −0.455061 −0.0197294
\(533\) −12.3828 −0.536357
\(534\) 6.44002 0.278687
\(535\) −30.9392 −1.33762
\(536\) 7.39328 0.319341
\(537\) 7.37406 0.318214
\(538\) −18.6878 −0.805688
\(539\) 9.32803 0.401787
\(540\) −14.0819 −0.605986
\(541\) 21.0641 0.905615 0.452808 0.891608i \(-0.350422\pi\)
0.452808 + 0.891608i \(0.350422\pi\)
\(542\) 22.5817 0.969966
\(543\) 16.7766 0.719955
\(544\) −7.33327 −0.314412
\(545\) −5.30832 −0.227383
\(546\) −2.01904 −0.0864069
\(547\) 3.74167 0.159982 0.0799911 0.996796i \(-0.474511\pi\)
0.0799911 + 0.996796i \(0.474511\pi\)
\(548\) 16.9545 0.724261
\(549\) 2.08676 0.0890607
\(550\) −7.06900 −0.301423
\(551\) −1.65207 −0.0703807
\(552\) 4.01912 0.171065
\(553\) −0.498884 −0.0212147
\(554\) −5.78007 −0.245572
\(555\) −22.6488 −0.961386
\(556\) 4.46835 0.189500
\(557\) −28.4889 −1.20712 −0.603558 0.797319i \(-0.706251\pi\)
−0.603558 + 0.797319i \(0.706251\pi\)
\(558\) −13.7745 −0.583121
\(559\) −26.9842 −1.14131
\(560\) −1.44963 −0.0612580
\(561\) −8.38971 −0.354214
\(562\) −27.1568 −1.14554
\(563\) −23.7436 −1.00067 −0.500337 0.865830i \(-0.666791\pi\)
−0.500337 + 0.865830i \(0.666791\pi\)
\(564\) −2.99389 −0.126065
\(565\) 38.7315 1.62945
\(566\) 18.8095 0.790621
\(567\) 1.47202 0.0618190
\(568\) 11.9031 0.499444
\(569\) −13.2276 −0.554530 −0.277265 0.960793i \(-0.589428\pi\)
−0.277265 + 0.960793i \(0.589428\pi\)
\(570\) −2.65401 −0.111164
\(571\) −2.60624 −0.109068 −0.0545338 0.998512i \(-0.517367\pi\)
−0.0545338 + 0.998512i \(0.517367\pi\)
\(572\) −7.31296 −0.305770
\(573\) 0.747163 0.0312132
\(574\) −1.05810 −0.0441644
\(575\) −24.8336 −1.03563
\(576\) −2.30589 −0.0960786
\(577\) −23.7294 −0.987869 −0.493935 0.869499i \(-0.664442\pi\)
−0.493935 + 0.869499i \(0.664442\pi\)
\(578\) 36.7769 1.52972
\(579\) −13.1147 −0.545028
\(580\) −5.26279 −0.218525
\(581\) −7.43839 −0.308596
\(582\) −9.95993 −0.412852
\(583\) −1.23989 −0.0513510
\(584\) 1.44472 0.0597831
\(585\) 39.1187 1.61736
\(586\) 33.1965 1.37133
\(587\) 15.7660 0.650731 0.325365 0.945588i \(-0.394513\pi\)
0.325365 + 0.945588i \(0.394513\pi\)
\(588\) 5.65942 0.233390
\(589\) −5.97363 −0.246139
\(590\) 1.82791 0.0752539
\(591\) −15.1470 −0.623066
\(592\) −8.53380 −0.350737
\(593\) −11.9745 −0.491734 −0.245867 0.969304i \(-0.579073\pi\)
−0.245867 + 0.969304i \(0.579073\pi\)
\(594\) −6.07025 −0.249066
\(595\) 10.6305 0.435809
\(596\) 3.87568 0.158754
\(597\) −18.0683 −0.739487
\(598\) −25.6907 −1.05057
\(599\) −44.9879 −1.83816 −0.919079 0.394074i \(-0.871065\pi\)
−0.919079 + 0.394074i \(0.871065\pi\)
\(600\) −4.28884 −0.175091
\(601\) −28.1297 −1.14743 −0.573717 0.819054i \(-0.694499\pi\)
−0.573717 + 0.819054i \(0.694499\pi\)
\(602\) −2.30579 −0.0939772
\(603\) −17.0481 −0.694250
\(604\) 7.69964 0.313294
\(605\) 29.0343 1.18041
\(606\) −2.42500 −0.0985088
\(607\) −38.4071 −1.55890 −0.779448 0.626466i \(-0.784501\pi\)
−0.779448 + 0.626466i \(0.784501\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −0.626346 −0.0253808
\(610\) 2.88284 0.116723
\(611\) 19.1373 0.774211
\(612\) 16.9097 0.683534
\(613\) −33.3788 −1.34816 −0.674078 0.738660i \(-0.735459\pi\)
−0.674078 + 0.738660i \(0.735459\pi\)
\(614\) −2.16914 −0.0875393
\(615\) −6.17107 −0.248841
\(616\) −0.624890 −0.0251775
\(617\) 47.2890 1.90378 0.951892 0.306434i \(-0.0991358\pi\)
0.951892 + 0.306434i \(0.0991358\pi\)
\(618\) 4.12776 0.166043
\(619\) 21.1255 0.849104 0.424552 0.905404i \(-0.360432\pi\)
0.424552 + 0.905404i \(0.360432\pi\)
\(620\) −19.0294 −0.764238
\(621\) −21.3250 −0.855743
\(622\) 30.4081 1.21925
\(623\) −3.51756 −0.140928
\(624\) −4.43685 −0.177616
\(625\) −24.2390 −0.969560
\(626\) −33.7663 −1.34957
\(627\) −1.14406 −0.0456894
\(628\) 2.51487 0.100354
\(629\) 62.5807 2.49526
\(630\) 3.34268 0.133175
\(631\) 20.5307 0.817313 0.408656 0.912688i \(-0.365997\pi\)
0.408656 + 0.912688i \(0.365997\pi\)
\(632\) −1.09630 −0.0436085
\(633\) 0.833135 0.0331141
\(634\) −28.5722 −1.13475
\(635\) −50.9059 −2.02014
\(636\) −0.752255 −0.0298289
\(637\) −36.1756 −1.43333
\(638\) −2.26863 −0.0898157
\(639\) −27.4473 −1.08580
\(640\) −3.18557 −0.125921
\(641\) −30.8519 −1.21858 −0.609288 0.792949i \(-0.708545\pi\)
−0.609288 + 0.792949i \(0.708545\pi\)
\(642\) −8.09167 −0.319353
\(643\) −34.4269 −1.35766 −0.678832 0.734293i \(-0.737514\pi\)
−0.678832 + 0.734293i \(0.737514\pi\)
\(644\) −2.19526 −0.0865054
\(645\) −13.4478 −0.529508
\(646\) 7.33327 0.288524
\(647\) −38.7395 −1.52301 −0.761504 0.648160i \(-0.775539\pi\)
−0.761504 + 0.648160i \(0.775539\pi\)
\(648\) 3.23477 0.127074
\(649\) 0.787957 0.0309300
\(650\) 27.4147 1.07529
\(651\) −2.26477 −0.0887632
\(652\) −17.0284 −0.666885
\(653\) 11.4101 0.446513 0.223257 0.974760i \(-0.428331\pi\)
0.223257 + 0.974760i \(0.428331\pi\)
\(654\) −1.38831 −0.0542871
\(655\) −21.1244 −0.825399
\(656\) −2.32519 −0.0907834
\(657\) −3.33137 −0.129969
\(658\) 1.63527 0.0637496
\(659\) 17.7793 0.692582 0.346291 0.938127i \(-0.387441\pi\)
0.346291 + 0.938127i \(0.387441\pi\)
\(660\) −3.64448 −0.141861
\(661\) 2.10288 0.0817927 0.0408963 0.999163i \(-0.486979\pi\)
0.0408963 + 0.999163i \(0.486979\pi\)
\(662\) −4.88317 −0.189790
\(663\) 32.5366 1.26362
\(664\) −16.3459 −0.634344
\(665\) 1.44963 0.0562142
\(666\) 19.6780 0.762506
\(667\) −7.96976 −0.308590
\(668\) 3.30469 0.127862
\(669\) −19.0250 −0.735549
\(670\) −23.5518 −0.909884
\(671\) 1.24271 0.0479741
\(672\) −0.379127 −0.0146252
\(673\) −11.5112 −0.443725 −0.221862 0.975078i \(-0.571214\pi\)
−0.221862 + 0.975078i \(0.571214\pi\)
\(674\) 36.3051 1.39842
\(675\) 22.7561 0.875882
\(676\) 15.3608 0.590801
\(677\) −7.77062 −0.298649 −0.149325 0.988788i \(-0.547710\pi\)
−0.149325 + 0.988788i \(0.547710\pi\)
\(678\) 10.1296 0.389026
\(679\) 5.44015 0.208774
\(680\) 23.3606 0.895839
\(681\) −11.9907 −0.459484
\(682\) −8.20298 −0.314108
\(683\) −5.31652 −0.203431 −0.101716 0.994814i \(-0.532433\pi\)
−0.101716 + 0.994814i \(0.532433\pi\)
\(684\) 2.30589 0.0881678
\(685\) −54.0097 −2.06361
\(686\) −6.27662 −0.239643
\(687\) 2.55025 0.0972982
\(688\) −5.06700 −0.193177
\(689\) 4.80850 0.183189
\(690\) −12.8032 −0.487409
\(691\) 12.6891 0.482717 0.241359 0.970436i \(-0.422407\pi\)
0.241359 + 0.970436i \(0.422407\pi\)
\(692\) 23.1168 0.878767
\(693\) 1.44093 0.0547362
\(694\) −9.37740 −0.355961
\(695\) −14.2342 −0.539935
\(696\) −1.37640 −0.0521723
\(697\) 17.0512 0.645862
\(698\) 19.9950 0.756820
\(699\) −7.28797 −0.275656
\(700\) 2.34258 0.0885411
\(701\) −39.1862 −1.48004 −0.740021 0.672583i \(-0.765185\pi\)
−0.740021 + 0.672583i \(0.765185\pi\)
\(702\) 23.5414 0.888514
\(703\) 8.53380 0.321858
\(704\) −1.37320 −0.0517544
\(705\) 9.53723 0.359193
\(706\) −19.6389 −0.739120
\(707\) 1.32454 0.0498146
\(708\) 0.478062 0.0179667
\(709\) 8.99691 0.337886 0.168943 0.985626i \(-0.445965\pi\)
0.168943 + 0.985626i \(0.445965\pi\)
\(710\) −37.9182 −1.42305
\(711\) 2.52795 0.0948054
\(712\) −7.72987 −0.289689
\(713\) −28.8174 −1.07922
\(714\) 2.78024 0.104048
\(715\) 23.2959 0.871218
\(716\) −8.85098 −0.330777
\(717\) −14.0607 −0.525108
\(718\) −12.3866 −0.462264
\(719\) 8.60958 0.321083 0.160541 0.987029i \(-0.448676\pi\)
0.160541 + 0.987029i \(0.448676\pi\)
\(720\) 7.34555 0.273753
\(721\) −2.25460 −0.0839657
\(722\) 1.00000 0.0372161
\(723\) −6.98557 −0.259796
\(724\) −20.1368 −0.748377
\(725\) 8.50459 0.315853
\(726\) 7.59346 0.281820
\(727\) 12.0735 0.447783 0.223891 0.974614i \(-0.428124\pi\)
0.223891 + 0.974614i \(0.428124\pi\)
\(728\) 2.42342 0.0898181
\(729\) 3.58965 0.132950
\(730\) −4.60227 −0.170337
\(731\) 37.1577 1.37433
\(732\) 0.753963 0.0278673
\(733\) 7.15842 0.264402 0.132201 0.991223i \(-0.457796\pi\)
0.132201 + 0.991223i \(0.457796\pi\)
\(734\) 14.2061 0.524356
\(735\) −18.0284 −0.664989
\(736\) −4.82410 −0.177819
\(737\) −10.1524 −0.373970
\(738\) 5.36162 0.197364
\(739\) 34.5839 1.27219 0.636095 0.771611i \(-0.280549\pi\)
0.636095 + 0.771611i \(0.280549\pi\)
\(740\) 27.1850 0.999340
\(741\) 4.43685 0.162992
\(742\) 0.410884 0.0150840
\(743\) 20.8265 0.764049 0.382024 0.924152i \(-0.375227\pi\)
0.382024 + 0.924152i \(0.375227\pi\)
\(744\) −4.97684 −0.182460
\(745\) −12.3462 −0.452331
\(746\) 30.1257 1.10298
\(747\) 37.6918 1.37907
\(748\) 10.0700 0.368197
\(749\) 4.41970 0.161492
\(750\) 0.392342 0.0143263
\(751\) −19.9945 −0.729608 −0.364804 0.931084i \(-0.618864\pi\)
−0.364804 + 0.931084i \(0.618864\pi\)
\(752\) 3.59352 0.131042
\(753\) 16.6053 0.605131
\(754\) 8.79809 0.320408
\(755\) −24.5277 −0.892654
\(756\) 2.01161 0.0731614
\(757\) 11.5252 0.418889 0.209445 0.977821i \(-0.432834\pi\)
0.209445 + 0.977821i \(0.432834\pi\)
\(758\) 0.617767 0.0224383
\(759\) −5.51906 −0.200329
\(760\) 3.18557 0.115553
\(761\) −21.0011 −0.761289 −0.380644 0.924722i \(-0.624298\pi\)
−0.380644 + 0.924722i \(0.624298\pi\)
\(762\) −13.3136 −0.482302
\(763\) 0.758299 0.0274523
\(764\) −0.896810 −0.0324454
\(765\) −53.8669 −1.94756
\(766\) 12.4877 0.451200
\(767\) −3.05582 −0.110339
\(768\) −0.833135 −0.0300632
\(769\) 0.0863922 0.00311538 0.00155769 0.999999i \(-0.499504\pi\)
0.00155769 + 0.999999i \(0.499504\pi\)
\(770\) 1.99063 0.0717373
\(771\) 8.41616 0.303100
\(772\) 15.7414 0.566544
\(773\) 24.6308 0.885910 0.442955 0.896544i \(-0.353930\pi\)
0.442955 + 0.896544i \(0.353930\pi\)
\(774\) 11.6839 0.419970
\(775\) 30.7512 1.10462
\(776\) 11.9548 0.429151
\(777\) 3.23540 0.116069
\(778\) 22.5256 0.807582
\(779\) 2.32519 0.0833085
\(780\) 14.1339 0.506074
\(781\) −16.3454 −0.584884
\(782\) 35.3764 1.26506
\(783\) 7.30302 0.260989
\(784\) −6.79292 −0.242604
\(785\) −8.01129 −0.285935
\(786\) −5.52476 −0.197062
\(787\) 20.9715 0.747553 0.373777 0.927519i \(-0.378063\pi\)
0.373777 + 0.927519i \(0.378063\pi\)
\(788\) 18.1808 0.647664
\(789\) 7.73002 0.275196
\(790\) 3.49234 0.124252
\(791\) −5.53284 −0.196725
\(792\) 3.16644 0.112515
\(793\) −4.81941 −0.171142
\(794\) 2.21743 0.0786938
\(795\) 2.39636 0.0849901
\(796\) 21.6872 0.768681
\(797\) 24.2083 0.857503 0.428751 0.903423i \(-0.358954\pi\)
0.428751 + 0.903423i \(0.358954\pi\)
\(798\) 0.379127 0.0134210
\(799\) −26.3523 −0.932277
\(800\) 5.14783 0.182003
\(801\) 17.8242 0.629787
\(802\) −21.1119 −0.745486
\(803\) −1.98390 −0.0700101
\(804\) −6.15960 −0.217232
\(805\) 6.99315 0.246476
\(806\) 31.8125 1.12055
\(807\) 15.5695 0.548071
\(808\) 2.91069 0.102398
\(809\) 9.72882 0.342047 0.171023 0.985267i \(-0.445293\pi\)
0.171023 + 0.985267i \(0.445293\pi\)
\(810\) −10.3046 −0.362066
\(811\) −48.0361 −1.68677 −0.843387 0.537306i \(-0.819442\pi\)
−0.843387 + 0.537306i \(0.819442\pi\)
\(812\) 0.751794 0.0263828
\(813\) −18.8136 −0.659821
\(814\) 11.7186 0.410737
\(815\) 54.2452 1.90013
\(816\) 6.10961 0.213879
\(817\) 5.06700 0.177272
\(818\) −27.5064 −0.961738
\(819\) −5.58814 −0.195265
\(820\) 7.40704 0.258665
\(821\) 28.2737 0.986759 0.493379 0.869814i \(-0.335761\pi\)
0.493379 + 0.869814i \(0.335761\pi\)
\(822\) −14.1254 −0.492680
\(823\) 8.82928 0.307770 0.153885 0.988089i \(-0.450822\pi\)
0.153885 + 0.988089i \(0.450822\pi\)
\(824\) −4.95450 −0.172598
\(825\) 5.88943 0.205044
\(826\) −0.261119 −0.00908549
\(827\) −21.3964 −0.744024 −0.372012 0.928228i \(-0.621332\pi\)
−0.372012 + 0.928228i \(0.621332\pi\)
\(828\) 11.1238 0.386580
\(829\) 39.6866 1.37837 0.689186 0.724585i \(-0.257968\pi\)
0.689186 + 0.724585i \(0.257968\pi\)
\(830\) 52.0710 1.80741
\(831\) 4.81557 0.167050
\(832\) 5.32549 0.184628
\(833\) 49.8143 1.72596
\(834\) −3.72274 −0.128908
\(835\) −10.5273 −0.364312
\(836\) 1.37320 0.0474931
\(837\) 26.4065 0.912743
\(838\) −8.97773 −0.310131
\(839\) −25.0347 −0.864295 −0.432148 0.901803i \(-0.642244\pi\)
−0.432148 + 0.901803i \(0.642244\pi\)
\(840\) 1.20774 0.0416708
\(841\) −26.2707 −0.905885
\(842\) 29.8005 1.02699
\(843\) 22.6253 0.779257
\(844\) −1.00000 −0.0344214
\(845\) −48.9329 −1.68334
\(846\) −8.28625 −0.284887
\(847\) −4.14758 −0.142512
\(848\) 0.902921 0.0310064
\(849\) −15.6708 −0.537821
\(850\) −37.7504 −1.29483
\(851\) 41.1679 1.41122
\(852\) −9.91692 −0.339748
\(853\) −26.5940 −0.910562 −0.455281 0.890348i \(-0.650461\pi\)
−0.455281 + 0.890348i \(0.650461\pi\)
\(854\) −0.411817 −0.0140921
\(855\) −7.34555 −0.251213
\(856\) 9.71232 0.331960
\(857\) 11.6047 0.396410 0.198205 0.980161i \(-0.436489\pi\)
0.198205 + 0.980161i \(0.436489\pi\)
\(858\) 6.09268 0.208001
\(859\) 18.1323 0.618666 0.309333 0.950954i \(-0.399894\pi\)
0.309333 + 0.950954i \(0.399894\pi\)
\(860\) 16.1413 0.550412
\(861\) 0.881543 0.0300429
\(862\) 27.8167 0.947440
\(863\) −28.6228 −0.974332 −0.487166 0.873309i \(-0.661969\pi\)
−0.487166 + 0.873309i \(0.661969\pi\)
\(864\) 4.42052 0.150389
\(865\) −73.6400 −2.50383
\(866\) 1.22663 0.0416827
\(867\) −30.6401 −1.04059
\(868\) 2.71837 0.0922674
\(869\) 1.50544 0.0510686
\(870\) 4.38461 0.148652
\(871\) 39.3728 1.33410
\(872\) 1.66637 0.0564303
\(873\) −27.5663 −0.932979
\(874\) 4.82410 0.163178
\(875\) −0.214299 −0.00724462
\(876\) −1.20365 −0.0406676
\(877\) 27.2418 0.919891 0.459945 0.887947i \(-0.347869\pi\)
0.459945 + 0.887947i \(0.347869\pi\)
\(878\) 35.1401 1.18592
\(879\) −27.6572 −0.932853
\(880\) 4.37442 0.147462
\(881\) 6.22330 0.209668 0.104834 0.994490i \(-0.466569\pi\)
0.104834 + 0.994490i \(0.466569\pi\)
\(882\) 15.6637 0.527424
\(883\) −29.6032 −0.996227 −0.498114 0.867112i \(-0.665974\pi\)
−0.498114 + 0.867112i \(0.665974\pi\)
\(884\) −39.0533 −1.31350
\(885\) −1.52290 −0.0511916
\(886\) −0.756700 −0.0254218
\(887\) −42.9830 −1.44323 −0.721614 0.692296i \(-0.756599\pi\)
−0.721614 + 0.692296i \(0.756599\pi\)
\(888\) 7.10981 0.238590
\(889\) 7.27196 0.243894
\(890\) 24.6240 0.825398
\(891\) −4.44199 −0.148812
\(892\) 22.8355 0.764588
\(893\) −3.59352 −0.120253
\(894\) −3.22896 −0.107993
\(895\) 28.1954 0.942467
\(896\) 0.455061 0.0152025
\(897\) 21.4038 0.714652
\(898\) 13.1481 0.438758
\(899\) 9.86887 0.329145
\(900\) −11.8703 −0.395677
\(901\) −6.62137 −0.220590
\(902\) 3.19295 0.106314
\(903\) 1.92104 0.0639281
\(904\) −12.1584 −0.404384
\(905\) 64.1470 2.13232
\(906\) −6.41483 −0.213119
\(907\) 17.1721 0.570189 0.285095 0.958499i \(-0.407975\pi\)
0.285095 + 0.958499i \(0.407975\pi\)
\(908\) 14.3922 0.477623
\(909\) −6.71173 −0.222614
\(910\) −7.71998 −0.255915
\(911\) −32.8096 −1.08703 −0.543515 0.839399i \(-0.682907\pi\)
−0.543515 + 0.839399i \(0.682907\pi\)
\(912\) 0.833135 0.0275878
\(913\) 22.4462 0.742860
\(914\) 30.8512 1.02047
\(915\) −2.40180 −0.0794010
\(916\) −3.06103 −0.101139
\(917\) 3.01764 0.0996513
\(918\) −32.4169 −1.06992
\(919\) 41.4579 1.36757 0.683785 0.729683i \(-0.260333\pi\)
0.683785 + 0.729683i \(0.260333\pi\)
\(920\) 15.3675 0.506651
\(921\) 1.80718 0.0595487
\(922\) 11.9807 0.394563
\(923\) 63.3900 2.08651
\(924\) 0.520618 0.0171271
\(925\) −43.9306 −1.44443
\(926\) 24.1856 0.794788
\(927\) 11.4245 0.375230
\(928\) 1.65207 0.0542319
\(929\) −36.4127 −1.19466 −0.597331 0.801995i \(-0.703772\pi\)
−0.597331 + 0.801995i \(0.703772\pi\)
\(930\) 15.8540 0.519874
\(931\) 6.79292 0.222629
\(932\) 8.74764 0.286539
\(933\) −25.3340 −0.829399
\(934\) −10.4573 −0.342172
\(935\) −32.0788 −1.04909
\(936\) −12.2800 −0.401383
\(937\) −40.8069 −1.33310 −0.666552 0.745458i \(-0.732231\pi\)
−0.666552 + 0.745458i \(0.732231\pi\)
\(938\) 3.36439 0.109851
\(939\) 28.1319 0.918050
\(940\) −11.4474 −0.373373
\(941\) −2.98675 −0.0973654 −0.0486827 0.998814i \(-0.515502\pi\)
−0.0486827 + 0.998814i \(0.515502\pi\)
\(942\) −2.09523 −0.0682662
\(943\) 11.2169 0.365274
\(944\) −0.573811 −0.0186759
\(945\) −6.40811 −0.208456
\(946\) 6.95800 0.226224
\(947\) 2.22578 0.0723280 0.0361640 0.999346i \(-0.488486\pi\)
0.0361640 + 0.999346i \(0.488486\pi\)
\(948\) 0.913367 0.0296648
\(949\) 7.69386 0.249753
\(950\) −5.14783 −0.167018
\(951\) 23.8045 0.771913
\(952\) −3.33709 −0.108156
\(953\) −17.9022 −0.579910 −0.289955 0.957040i \(-0.593640\pi\)
−0.289955 + 0.957040i \(0.593640\pi\)
\(954\) −2.08203 −0.0674083
\(955\) 2.85685 0.0924454
\(956\) 16.8769 0.545838
\(957\) 1.89007 0.0610973
\(958\) 0.600314 0.0193953
\(959\) 7.71535 0.249142
\(960\) 2.65401 0.0856577
\(961\) 4.68422 0.151104
\(962\) −45.4467 −1.46526
\(963\) −22.3955 −0.721685
\(964\) 8.38468 0.270052
\(965\) −50.1452 −1.61423
\(966\) 1.82895 0.0588454
\(967\) −52.3832 −1.68453 −0.842265 0.539064i \(-0.818778\pi\)
−0.842265 + 0.539064i \(0.818778\pi\)
\(968\) −9.11432 −0.292945
\(969\) −6.10961 −0.196269
\(970\) −38.0827 −1.22276
\(971\) −31.0804 −0.997418 −0.498709 0.866770i \(-0.666192\pi\)
−0.498709 + 0.866770i \(0.666192\pi\)
\(972\) −15.9566 −0.511807
\(973\) 2.03337 0.0651869
\(974\) −10.6381 −0.340868
\(975\) −22.8401 −0.731470
\(976\) −0.904971 −0.0289674
\(977\) −23.4741 −0.751003 −0.375501 0.926822i \(-0.622529\pi\)
−0.375501 + 0.926822i \(0.622529\pi\)
\(978\) 14.1870 0.453650
\(979\) 10.6146 0.339246
\(980\) 21.6393 0.691242
\(981\) −3.84245 −0.122680
\(982\) 26.5876 0.848444
\(983\) 18.3699 0.585910 0.292955 0.956126i \(-0.405361\pi\)
0.292955 + 0.956126i \(0.405361\pi\)
\(984\) 1.93720 0.0617555
\(985\) −57.9161 −1.84536
\(986\) −12.1151 −0.385823
\(987\) −1.36240 −0.0433658
\(988\) −5.32549 −0.169426
\(989\) 24.4437 0.777264
\(990\) −10.0869 −0.320583
\(991\) −21.6237 −0.686900 −0.343450 0.939171i \(-0.611596\pi\)
−0.343450 + 0.939171i \(0.611596\pi\)
\(992\) 5.97363 0.189663
\(993\) 4.06833 0.129105
\(994\) 5.41666 0.171806
\(995\) −69.0858 −2.19017
\(996\) 13.6183 0.431514
\(997\) 55.0599 1.74376 0.871882 0.489716i \(-0.162899\pi\)
0.871882 + 0.489716i \(0.162899\pi\)
\(998\) 29.1220 0.921841
\(999\) −37.7238 −1.19353
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 \(a_p\))