Properties

Label 8002.2.a.d.1.3
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.22228 q^{3}\) \(+1.00000 q^{4}\) \(-3.24951 q^{5}\) \(-3.22228 q^{6}\) \(+4.15498 q^{7}\) \(+1.00000 q^{8}\) \(+7.38311 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.22228 q^{3}\) \(+1.00000 q^{4}\) \(-3.24951 q^{5}\) \(-3.22228 q^{6}\) \(+4.15498 q^{7}\) \(+1.00000 q^{8}\) \(+7.38311 q^{9}\) \(-3.24951 q^{10}\) \(+4.01228 q^{11}\) \(-3.22228 q^{12}\) \(-1.31798 q^{13}\) \(+4.15498 q^{14}\) \(+10.4708 q^{15}\) \(+1.00000 q^{16}\) \(-5.05365 q^{17}\) \(+7.38311 q^{18}\) \(-3.54118 q^{19}\) \(-3.24951 q^{20}\) \(-13.3885 q^{21}\) \(+4.01228 q^{22}\) \(+0.910439 q^{23}\) \(-3.22228 q^{24}\) \(+5.55929 q^{25}\) \(-1.31798 q^{26}\) \(-14.1236 q^{27}\) \(+4.15498 q^{28}\) \(+1.83498 q^{29}\) \(+10.4708 q^{30}\) \(+4.10189 q^{31}\) \(+1.00000 q^{32}\) \(-12.9287 q^{33}\) \(-5.05365 q^{34}\) \(-13.5016 q^{35}\) \(+7.38311 q^{36}\) \(+0.633925 q^{37}\) \(-3.54118 q^{38}\) \(+4.24691 q^{39}\) \(-3.24951 q^{40}\) \(-1.02441 q^{41}\) \(-13.3885 q^{42}\) \(-6.99386 q^{43}\) \(+4.01228 q^{44}\) \(-23.9915 q^{45}\) \(+0.910439 q^{46}\) \(-9.55466 q^{47}\) \(-3.22228 q^{48}\) \(+10.2638 q^{49}\) \(+5.55929 q^{50}\) \(+16.2843 q^{51}\) \(-1.31798 q^{52}\) \(-8.16514 q^{53}\) \(-14.1236 q^{54}\) \(-13.0379 q^{55}\) \(+4.15498 q^{56}\) \(+11.4107 q^{57}\) \(+1.83498 q^{58}\) \(-10.3152 q^{59}\) \(+10.4708 q^{60}\) \(+8.82410 q^{61}\) \(+4.10189 q^{62}\) \(+30.6767 q^{63}\) \(+1.00000 q^{64}\) \(+4.28279 q^{65}\) \(-12.9287 q^{66}\) \(-8.71303 q^{67}\) \(-5.05365 q^{68}\) \(-2.93369 q^{69}\) \(-13.5016 q^{70}\) \(+11.9175 q^{71}\) \(+7.38311 q^{72}\) \(-0.173148 q^{73}\) \(+0.633925 q^{74}\) \(-17.9136 q^{75}\) \(-3.54118 q^{76}\) \(+16.6709 q^{77}\) \(+4.24691 q^{78}\) \(+0.271615 q^{79}\) \(-3.24951 q^{80}\) \(+23.3610 q^{81}\) \(-1.02441 q^{82}\) \(+0.170942 q^{83}\) \(-13.3885 q^{84}\) \(+16.4219 q^{85}\) \(-6.99386 q^{86}\) \(-5.91282 q^{87}\) \(+4.01228 q^{88}\) \(+16.3950 q^{89}\) \(-23.9915 q^{90}\) \(-5.47619 q^{91}\) \(+0.910439 q^{92}\) \(-13.2175 q^{93}\) \(-9.55466 q^{94}\) \(+11.5071 q^{95}\) \(-3.22228 q^{96}\) \(-3.23701 q^{97}\) \(+10.2638 q^{98}\) \(+29.6231 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −3.22228 −1.86039 −0.930193 0.367071i \(-0.880361\pi\)
−0.930193 + 0.367071i \(0.880361\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.24951 −1.45322 −0.726612 0.687048i \(-0.758906\pi\)
−0.726612 + 0.687048i \(0.758906\pi\)
\(6\) −3.22228 −1.31549
\(7\) 4.15498 1.57043 0.785217 0.619221i \(-0.212551\pi\)
0.785217 + 0.619221i \(0.212551\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.38311 2.46104
\(10\) −3.24951 −1.02758
\(11\) 4.01228 1.20975 0.604873 0.796322i \(-0.293224\pi\)
0.604873 + 0.796322i \(0.293224\pi\)
\(12\) −3.22228 −0.930193
\(13\) −1.31798 −0.365543 −0.182771 0.983155i \(-0.558507\pi\)
−0.182771 + 0.983155i \(0.558507\pi\)
\(14\) 4.15498 1.11046
\(15\) 10.4708 2.70356
\(16\) 1.00000 0.250000
\(17\) −5.05365 −1.22569 −0.612845 0.790203i \(-0.709975\pi\)
−0.612845 + 0.790203i \(0.709975\pi\)
\(18\) 7.38311 1.74022
\(19\) −3.54118 −0.812402 −0.406201 0.913784i \(-0.633147\pi\)
−0.406201 + 0.913784i \(0.633147\pi\)
\(20\) −3.24951 −0.726612
\(21\) −13.3885 −2.92161
\(22\) 4.01228 0.855420
\(23\) 0.910439 0.189840 0.0949198 0.995485i \(-0.469741\pi\)
0.0949198 + 0.995485i \(0.469741\pi\)
\(24\) −3.22228 −0.657746
\(25\) 5.55929 1.11186
\(26\) −1.31798 −0.258478
\(27\) −14.1236 −2.71809
\(28\) 4.15498 0.785217
\(29\) 1.83498 0.340747 0.170373 0.985380i \(-0.445503\pi\)
0.170373 + 0.985380i \(0.445503\pi\)
\(30\) 10.4708 1.91170
\(31\) 4.10189 0.736721 0.368361 0.929683i \(-0.379919\pi\)
0.368361 + 0.929683i \(0.379919\pi\)
\(32\) 1.00000 0.176777
\(33\) −12.9287 −2.25060
\(34\) −5.05365 −0.866694
\(35\) −13.5016 −2.28219
\(36\) 7.38311 1.23052
\(37\) 0.633925 0.104217 0.0521084 0.998641i \(-0.483406\pi\)
0.0521084 + 0.998641i \(0.483406\pi\)
\(38\) −3.54118 −0.574455
\(39\) 4.24691 0.680050
\(40\) −3.24951 −0.513792
\(41\) −1.02441 −0.159986 −0.0799928 0.996795i \(-0.525490\pi\)
−0.0799928 + 0.996795i \(0.525490\pi\)
\(42\) −13.3885 −2.06589
\(43\) −6.99386 −1.06655 −0.533277 0.845941i \(-0.679040\pi\)
−0.533277 + 0.845941i \(0.679040\pi\)
\(44\) 4.01228 0.604873
\(45\) −23.9915 −3.57644
\(46\) 0.910439 0.134237
\(47\) −9.55466 −1.39369 −0.696845 0.717222i \(-0.745413\pi\)
−0.696845 + 0.717222i \(0.745413\pi\)
\(48\) −3.22228 −0.465097
\(49\) 10.2638 1.46626
\(50\) 5.55929 0.786203
\(51\) 16.2843 2.28026
\(52\) −1.31798 −0.182771
\(53\) −8.16514 −1.12157 −0.560784 0.827962i \(-0.689500\pi\)
−0.560784 + 0.827962i \(0.689500\pi\)
\(54\) −14.1236 −1.92198
\(55\) −13.0379 −1.75803
\(56\) 4.15498 0.555232
\(57\) 11.4107 1.51138
\(58\) 1.83498 0.240944
\(59\) −10.3152 −1.34293 −0.671465 0.741036i \(-0.734335\pi\)
−0.671465 + 0.741036i \(0.734335\pi\)
\(60\) 10.4708 1.35178
\(61\) 8.82410 1.12981 0.564905 0.825156i \(-0.308913\pi\)
0.564905 + 0.825156i \(0.308913\pi\)
\(62\) 4.10189 0.520941
\(63\) 30.6767 3.86490
\(64\) 1.00000 0.125000
\(65\) 4.28279 0.531215
\(66\) −12.9287 −1.59141
\(67\) −8.71303 −1.06447 −0.532233 0.846598i \(-0.678647\pi\)
−0.532233 + 0.846598i \(0.678647\pi\)
\(68\) −5.05365 −0.612845
\(69\) −2.93369 −0.353175
\(70\) −13.5016 −1.61375
\(71\) 11.9175 1.41435 0.707173 0.707041i \(-0.249970\pi\)
0.707173 + 0.707041i \(0.249970\pi\)
\(72\) 7.38311 0.870108
\(73\) −0.173148 −0.0202655 −0.0101327 0.999949i \(-0.503225\pi\)
−0.0101327 + 0.999949i \(0.503225\pi\)
\(74\) 0.633925 0.0736923
\(75\) −17.9136 −2.06849
\(76\) −3.54118 −0.406201
\(77\) 16.6709 1.89983
\(78\) 4.24691 0.480868
\(79\) 0.271615 0.0305591 0.0152795 0.999883i \(-0.495136\pi\)
0.0152795 + 0.999883i \(0.495136\pi\)
\(80\) −3.24951 −0.363306
\(81\) 23.3610 2.59567
\(82\) −1.02441 −0.113127
\(83\) 0.170942 0.0187633 0.00938166 0.999956i \(-0.497014\pi\)
0.00938166 + 0.999956i \(0.497014\pi\)
\(84\) −13.3885 −1.46081
\(85\) 16.4219 1.78120
\(86\) −6.99386 −0.754167
\(87\) −5.91282 −0.633921
\(88\) 4.01228 0.427710
\(89\) 16.3950 1.73786 0.868932 0.494931i \(-0.164807\pi\)
0.868932 + 0.494931i \(0.164807\pi\)
\(90\) −23.9915 −2.52892
\(91\) −5.47619 −0.574060
\(92\) 0.910439 0.0949198
\(93\) −13.2175 −1.37059
\(94\) −9.55466 −0.985488
\(95\) 11.5071 1.18060
\(96\) −3.22228 −0.328873
\(97\) −3.23701 −0.328669 −0.164334 0.986405i \(-0.552548\pi\)
−0.164334 + 0.986405i \(0.552548\pi\)
\(98\) 10.2638 1.03680
\(99\) 29.6231 2.97723
\(100\) 5.55929 0.555929
\(101\) −12.5159 −1.24538 −0.622691 0.782468i \(-0.713961\pi\)
−0.622691 + 0.782468i \(0.713961\pi\)
\(102\) 16.2843 1.61239
\(103\) 4.18616 0.412475 0.206237 0.978502i \(-0.433878\pi\)
0.206237 + 0.978502i \(0.433878\pi\)
\(104\) −1.31798 −0.129239
\(105\) 43.5061 4.24576
\(106\) −8.16514 −0.793069
\(107\) −2.30019 −0.222368 −0.111184 0.993800i \(-0.535464\pi\)
−0.111184 + 0.993800i \(0.535464\pi\)
\(108\) −14.1236 −1.35905
\(109\) 12.3776 1.18556 0.592780 0.805364i \(-0.298030\pi\)
0.592780 + 0.805364i \(0.298030\pi\)
\(110\) −13.0379 −1.24312
\(111\) −2.04269 −0.193883
\(112\) 4.15498 0.392608
\(113\) −2.00849 −0.188943 −0.0944716 0.995528i \(-0.530116\pi\)
−0.0944716 + 0.995528i \(0.530116\pi\)
\(114\) 11.4107 1.06871
\(115\) −2.95848 −0.275880
\(116\) 1.83498 0.170373
\(117\) −9.73081 −0.899614
\(118\) −10.3152 −0.949595
\(119\) −20.9978 −1.92487
\(120\) 10.4708 0.955852
\(121\) 5.09836 0.463487
\(122\) 8.82410 0.798896
\(123\) 3.30093 0.297635
\(124\) 4.10189 0.368361
\(125\) −1.81743 −0.162556
\(126\) 30.6767 2.73289
\(127\) 8.53198 0.757091 0.378545 0.925583i \(-0.376424\pi\)
0.378545 + 0.925583i \(0.376424\pi\)
\(128\) 1.00000 0.0883883
\(129\) 22.5362 1.98420
\(130\) 4.28279 0.375626
\(131\) −1.51561 −0.132420 −0.0662098 0.997806i \(-0.521091\pi\)
−0.0662098 + 0.997806i \(0.521091\pi\)
\(132\) −12.9287 −1.12530
\(133\) −14.7135 −1.27582
\(134\) −8.71303 −0.752691
\(135\) 45.8948 3.95000
\(136\) −5.05365 −0.433347
\(137\) −2.17483 −0.185808 −0.0929039 0.995675i \(-0.529615\pi\)
−0.0929039 + 0.995675i \(0.529615\pi\)
\(138\) −2.93369 −0.249733
\(139\) 15.1915 1.28853 0.644263 0.764804i \(-0.277164\pi\)
0.644263 + 0.764804i \(0.277164\pi\)
\(140\) −13.5016 −1.14110
\(141\) 30.7878 2.59280
\(142\) 11.9175 1.00009
\(143\) −5.28811 −0.442214
\(144\) 7.38311 0.615259
\(145\) −5.96277 −0.495181
\(146\) −0.173148 −0.0143299
\(147\) −33.0730 −2.72781
\(148\) 0.633925 0.0521084
\(149\) 8.77423 0.718813 0.359407 0.933181i \(-0.382979\pi\)
0.359407 + 0.933181i \(0.382979\pi\)
\(150\) −17.9136 −1.46264
\(151\) −8.85813 −0.720865 −0.360432 0.932785i \(-0.617371\pi\)
−0.360432 + 0.932785i \(0.617371\pi\)
\(152\) −3.54118 −0.287228
\(153\) −37.3117 −3.01647
\(154\) 16.6709 1.34338
\(155\) −13.3291 −1.07062
\(156\) 4.24691 0.340025
\(157\) −3.20786 −0.256015 −0.128008 0.991773i \(-0.540858\pi\)
−0.128008 + 0.991773i \(0.540858\pi\)
\(158\) 0.271615 0.0216085
\(159\) 26.3104 2.08655
\(160\) −3.24951 −0.256896
\(161\) 3.78285 0.298131
\(162\) 23.3610 1.83541
\(163\) 4.69438 0.367692 0.183846 0.982955i \(-0.441145\pi\)
0.183846 + 0.982955i \(0.441145\pi\)
\(164\) −1.02441 −0.0799928
\(165\) 42.0119 3.27062
\(166\) 0.170942 0.0132677
\(167\) −20.6282 −1.59625 −0.798127 0.602489i \(-0.794176\pi\)
−0.798127 + 0.602489i \(0.794176\pi\)
\(168\) −13.3885 −1.03295
\(169\) −11.2629 −0.866379
\(170\) 16.4219 1.25950
\(171\) −26.1449 −1.99935
\(172\) −6.99386 −0.533277
\(173\) −6.66495 −0.506727 −0.253363 0.967371i \(-0.581537\pi\)
−0.253363 + 0.967371i \(0.581537\pi\)
\(174\) −5.91282 −0.448250
\(175\) 23.0987 1.74610
\(176\) 4.01228 0.302437
\(177\) 33.2386 2.49837
\(178\) 16.3950 1.22886
\(179\) 0.610096 0.0456007 0.0228004 0.999740i \(-0.492742\pi\)
0.0228004 + 0.999740i \(0.492742\pi\)
\(180\) −23.9915 −1.78822
\(181\) 4.37792 0.325408 0.162704 0.986675i \(-0.447978\pi\)
0.162704 + 0.986675i \(0.447978\pi\)
\(182\) −5.47619 −0.405922
\(183\) −28.4337 −2.10188
\(184\) 0.910439 0.0671185
\(185\) −2.05995 −0.151450
\(186\) −13.2175 −0.969151
\(187\) −20.2766 −1.48277
\(188\) −9.55466 −0.696845
\(189\) −58.6833 −4.26858
\(190\) 11.5071 0.834812
\(191\) −4.79662 −0.347071 −0.173536 0.984828i \(-0.555519\pi\)
−0.173536 + 0.984828i \(0.555519\pi\)
\(192\) −3.22228 −0.232548
\(193\) −7.60851 −0.547673 −0.273836 0.961776i \(-0.588293\pi\)
−0.273836 + 0.961776i \(0.588293\pi\)
\(194\) −3.23701 −0.232404
\(195\) −13.8004 −0.988265
\(196\) 10.2638 0.733131
\(197\) −21.7451 −1.54927 −0.774636 0.632407i \(-0.782067\pi\)
−0.774636 + 0.632407i \(0.782067\pi\)
\(198\) 29.6231 2.10522
\(199\) 0.904665 0.0641300 0.0320650 0.999486i \(-0.489792\pi\)
0.0320650 + 0.999486i \(0.489792\pi\)
\(200\) 5.55929 0.393102
\(201\) 28.0759 1.98032
\(202\) −12.5159 −0.880618
\(203\) 7.62429 0.535120
\(204\) 16.2843 1.14013
\(205\) 3.32882 0.232495
\(206\) 4.18616 0.291664
\(207\) 6.72187 0.467202
\(208\) −1.31798 −0.0913856
\(209\) −14.2082 −0.982801
\(210\) 43.5061 3.00220
\(211\) −12.4416 −0.856512 −0.428256 0.903657i \(-0.640872\pi\)
−0.428256 + 0.903657i \(0.640872\pi\)
\(212\) −8.16514 −0.560784
\(213\) −38.4015 −2.63123
\(214\) −2.30019 −0.157238
\(215\) 22.7266 1.54994
\(216\) −14.1236 −0.960991
\(217\) 17.0433 1.15697
\(218\) 12.3776 0.838318
\(219\) 0.557933 0.0377016
\(220\) −13.0379 −0.879016
\(221\) 6.66062 0.448042
\(222\) −2.04269 −0.137096
\(223\) −5.36978 −0.359587 −0.179794 0.983704i \(-0.557543\pi\)
−0.179794 + 0.983704i \(0.557543\pi\)
\(224\) 4.15498 0.277616
\(225\) 41.0449 2.73633
\(226\) −2.00849 −0.133603
\(227\) 2.64894 0.175816 0.0879080 0.996129i \(-0.471982\pi\)
0.0879080 + 0.996129i \(0.471982\pi\)
\(228\) 11.4107 0.755691
\(229\) −27.2277 −1.79926 −0.899630 0.436653i \(-0.856164\pi\)
−0.899630 + 0.436653i \(0.856164\pi\)
\(230\) −2.95848 −0.195076
\(231\) −53.7184 −3.53441
\(232\) 1.83498 0.120472
\(233\) 7.53866 0.493874 0.246937 0.969032i \(-0.420576\pi\)
0.246937 + 0.969032i \(0.420576\pi\)
\(234\) −9.73081 −0.636123
\(235\) 31.0479 2.02534
\(236\) −10.3152 −0.671465
\(237\) −0.875220 −0.0568517
\(238\) −20.9978 −1.36109
\(239\) −14.9478 −0.966892 −0.483446 0.875374i \(-0.660615\pi\)
−0.483446 + 0.875374i \(0.660615\pi\)
\(240\) 10.4708 0.675889
\(241\) 23.6181 1.52137 0.760687 0.649119i \(-0.224862\pi\)
0.760687 + 0.649119i \(0.224862\pi\)
\(242\) 5.09836 0.327735
\(243\) −32.9049 −2.11085
\(244\) 8.82410 0.564905
\(245\) −33.3524 −2.13081
\(246\) 3.30093 0.210460
\(247\) 4.66721 0.296968
\(248\) 4.10189 0.260470
\(249\) −0.550823 −0.0349070
\(250\) −1.81743 −0.114945
\(251\) −18.4620 −1.16531 −0.582656 0.812719i \(-0.697987\pi\)
−0.582656 + 0.812719i \(0.697987\pi\)
\(252\) 30.6767 1.93245
\(253\) 3.65293 0.229658
\(254\) 8.53198 0.535344
\(255\) −52.9159 −3.31372
\(256\) 1.00000 0.0625000
\(257\) −6.70260 −0.418096 −0.209048 0.977905i \(-0.567037\pi\)
−0.209048 + 0.977905i \(0.567037\pi\)
\(258\) 22.5362 1.40304
\(259\) 2.63395 0.163665
\(260\) 4.28279 0.265608
\(261\) 13.5478 0.838591
\(262\) −1.51561 −0.0936348
\(263\) −21.4031 −1.31977 −0.659887 0.751365i \(-0.729396\pi\)
−0.659887 + 0.751365i \(0.729396\pi\)
\(264\) −12.9287 −0.795706
\(265\) 26.5327 1.62989
\(266\) −14.7135 −0.902144
\(267\) −52.8293 −3.23310
\(268\) −8.71303 −0.532233
\(269\) 23.4274 1.42839 0.714196 0.699945i \(-0.246792\pi\)
0.714196 + 0.699945i \(0.246792\pi\)
\(270\) 45.8948 2.79307
\(271\) 25.6175 1.55615 0.778075 0.628171i \(-0.216196\pi\)
0.778075 + 0.628171i \(0.216196\pi\)
\(272\) −5.05365 −0.306423
\(273\) 17.6458 1.06797
\(274\) −2.17483 −0.131386
\(275\) 22.3054 1.34507
\(276\) −2.93369 −0.176588
\(277\) −16.8074 −1.00986 −0.504928 0.863161i \(-0.668481\pi\)
−0.504928 + 0.863161i \(0.668481\pi\)
\(278\) 15.1915 0.911125
\(279\) 30.2847 1.81310
\(280\) −13.5016 −0.806876
\(281\) −12.7635 −0.761408 −0.380704 0.924697i \(-0.624318\pi\)
−0.380704 + 0.924697i \(0.624318\pi\)
\(282\) 30.7878 1.83339
\(283\) 26.3964 1.56910 0.784552 0.620063i \(-0.212893\pi\)
0.784552 + 0.620063i \(0.212893\pi\)
\(284\) 11.9175 0.707173
\(285\) −37.0791 −2.19638
\(286\) −5.28811 −0.312692
\(287\) −4.25639 −0.251247
\(288\) 7.38311 0.435054
\(289\) 8.53938 0.502316
\(290\) −5.96277 −0.350146
\(291\) 10.4306 0.611451
\(292\) −0.173148 −0.0101327
\(293\) 30.3087 1.77065 0.885327 0.464968i \(-0.153934\pi\)
0.885327 + 0.464968i \(0.153934\pi\)
\(294\) −33.0730 −1.92886
\(295\) 33.5195 1.95158
\(296\) 0.633925 0.0368462
\(297\) −56.6679 −3.28820
\(298\) 8.77423 0.508278
\(299\) −1.19994 −0.0693945
\(300\) −17.9136 −1.03424
\(301\) −29.0593 −1.67495
\(302\) −8.85813 −0.509728
\(303\) 40.3299 2.31689
\(304\) −3.54118 −0.203101
\(305\) −28.6740 −1.64187
\(306\) −37.3117 −2.13297
\(307\) −17.4097 −0.993625 −0.496812 0.867858i \(-0.665496\pi\)
−0.496812 + 0.867858i \(0.665496\pi\)
\(308\) 16.6709 0.949914
\(309\) −13.4890 −0.767362
\(310\) −13.3291 −0.757043
\(311\) −28.8678 −1.63694 −0.818470 0.574549i \(-0.805177\pi\)
−0.818470 + 0.574549i \(0.805177\pi\)
\(312\) 4.24691 0.240434
\(313\) 10.8881 0.615432 0.307716 0.951478i \(-0.400435\pi\)
0.307716 + 0.951478i \(0.400435\pi\)
\(314\) −3.20786 −0.181030
\(315\) −99.6840 −5.61656
\(316\) 0.271615 0.0152795
\(317\) −34.1716 −1.91927 −0.959635 0.281248i \(-0.909252\pi\)
−0.959635 + 0.281248i \(0.909252\pi\)
\(318\) 26.3104 1.47541
\(319\) 7.36244 0.412217
\(320\) −3.24951 −0.181653
\(321\) 7.41188 0.413691
\(322\) 3.78285 0.210810
\(323\) 17.8959 0.995754
\(324\) 23.3610 1.29783
\(325\) −7.32705 −0.406432
\(326\) 4.69438 0.259998
\(327\) −39.8842 −2.20560
\(328\) −1.02441 −0.0565635
\(329\) −39.6994 −2.18870
\(330\) 42.0119 2.31268
\(331\) −18.2828 −1.00491 −0.502456 0.864603i \(-0.667570\pi\)
−0.502456 + 0.864603i \(0.667570\pi\)
\(332\) 0.170942 0.00938166
\(333\) 4.68034 0.256481
\(334\) −20.6282 −1.12872
\(335\) 28.3131 1.54691
\(336\) −13.3885 −0.730403
\(337\) −25.1174 −1.36823 −0.684115 0.729374i \(-0.739812\pi\)
−0.684115 + 0.729374i \(0.739812\pi\)
\(338\) −11.2629 −0.612622
\(339\) 6.47194 0.351507
\(340\) 16.4219 0.890601
\(341\) 16.4579 0.891246
\(342\) −26.1449 −1.41376
\(343\) 13.5612 0.732233
\(344\) −6.99386 −0.377084
\(345\) 9.53306 0.513242
\(346\) −6.66495 −0.358310
\(347\) 16.8830 0.906325 0.453162 0.891428i \(-0.350296\pi\)
0.453162 + 0.891428i \(0.350296\pi\)
\(348\) −5.91282 −0.316960
\(349\) −8.99134 −0.481295 −0.240648 0.970613i \(-0.577360\pi\)
−0.240648 + 0.970613i \(0.577360\pi\)
\(350\) 23.0987 1.23468
\(351\) 18.6147 0.993579
\(352\) 4.01228 0.213855
\(353\) 30.3918 1.61759 0.808795 0.588091i \(-0.200120\pi\)
0.808795 + 0.588091i \(0.200120\pi\)
\(354\) 33.2386 1.76661
\(355\) −38.7260 −2.05536
\(356\) 16.3950 0.868932
\(357\) 67.6609 3.58099
\(358\) 0.610096 0.0322446
\(359\) −17.5605 −0.926805 −0.463403 0.886148i \(-0.653372\pi\)
−0.463403 + 0.886148i \(0.653372\pi\)
\(360\) −23.9915 −1.26446
\(361\) −6.46004 −0.340002
\(362\) 4.37792 0.230098
\(363\) −16.4284 −0.862265
\(364\) −5.47619 −0.287030
\(365\) 0.562647 0.0294503
\(366\) −28.4337 −1.48626
\(367\) 7.02086 0.366486 0.183243 0.983068i \(-0.441340\pi\)
0.183243 + 0.983068i \(0.441340\pi\)
\(368\) 0.910439 0.0474599
\(369\) −7.56332 −0.393731
\(370\) −2.05995 −0.107091
\(371\) −33.9260 −1.76135
\(372\) −13.2175 −0.685293
\(373\) 11.6776 0.604645 0.302323 0.953206i \(-0.402238\pi\)
0.302323 + 0.953206i \(0.402238\pi\)
\(374\) −20.2766 −1.04848
\(375\) 5.85628 0.302417
\(376\) −9.55466 −0.492744
\(377\) −2.41847 −0.124557
\(378\) −58.6833 −3.01834
\(379\) −3.27561 −0.168257 −0.0841285 0.996455i \(-0.526811\pi\)
−0.0841285 + 0.996455i \(0.526811\pi\)
\(380\) 11.5071 0.590301
\(381\) −27.4925 −1.40848
\(382\) −4.79662 −0.245417
\(383\) −29.6332 −1.51419 −0.757093 0.653307i \(-0.773381\pi\)
−0.757093 + 0.653307i \(0.773381\pi\)
\(384\) −3.22228 −0.164436
\(385\) −54.1723 −2.76087
\(386\) −7.60851 −0.387263
\(387\) −51.6364 −2.62483
\(388\) −3.23701 −0.164334
\(389\) −24.3437 −1.23427 −0.617136 0.786856i \(-0.711707\pi\)
−0.617136 + 0.786856i \(0.711707\pi\)
\(390\) −13.8004 −0.698809
\(391\) −4.60104 −0.232685
\(392\) 10.2638 0.518402
\(393\) 4.88373 0.246352
\(394\) −21.7451 −1.09550
\(395\) −0.882614 −0.0444091
\(396\) 29.6231 1.48862
\(397\) −37.5789 −1.88603 −0.943015 0.332750i \(-0.892023\pi\)
−0.943015 + 0.332750i \(0.892023\pi\)
\(398\) 0.904665 0.0453468
\(399\) 47.4111 2.37353
\(400\) 5.55929 0.277965
\(401\) −9.45682 −0.472251 −0.236126 0.971723i \(-0.575878\pi\)
−0.236126 + 0.971723i \(0.575878\pi\)
\(402\) 28.0759 1.40030
\(403\) −5.40622 −0.269303
\(404\) −12.5159 −0.622691
\(405\) −75.9117 −3.77208
\(406\) 7.62429 0.378387
\(407\) 2.54348 0.126076
\(408\) 16.2843 0.806193
\(409\) −32.7404 −1.61891 −0.809453 0.587184i \(-0.800236\pi\)
−0.809453 + 0.587184i \(0.800236\pi\)
\(410\) 3.32882 0.164399
\(411\) 7.00790 0.345674
\(412\) 4.18616 0.206237
\(413\) −42.8596 −2.10898
\(414\) 6.72187 0.330362
\(415\) −0.555477 −0.0272673
\(416\) −1.31798 −0.0646194
\(417\) −48.9513 −2.39715
\(418\) −14.2082 −0.694945
\(419\) −5.40318 −0.263962 −0.131981 0.991252i \(-0.542134\pi\)
−0.131981 + 0.991252i \(0.542134\pi\)
\(420\) 43.5061 2.12288
\(421\) −20.5428 −1.00119 −0.500597 0.865680i \(-0.666886\pi\)
−0.500597 + 0.865680i \(0.666886\pi\)
\(422\) −12.4416 −0.605645
\(423\) −70.5431 −3.42992
\(424\) −8.16514 −0.396534
\(425\) −28.0947 −1.36279
\(426\) −38.4015 −1.86056
\(427\) 36.6639 1.77429
\(428\) −2.30019 −0.111184
\(429\) 17.0398 0.822689
\(430\) 22.7266 1.09597
\(431\) 21.5927 1.04008 0.520041 0.854141i \(-0.325917\pi\)
0.520041 + 0.854141i \(0.325917\pi\)
\(432\) −14.1236 −0.679523
\(433\) 28.4300 1.36626 0.683130 0.730297i \(-0.260618\pi\)
0.683130 + 0.730297i \(0.260618\pi\)
\(434\) 17.0433 0.818103
\(435\) 19.2137 0.921229
\(436\) 12.3776 0.592780
\(437\) −3.22403 −0.154226
\(438\) 0.557933 0.0266591
\(439\) −8.47822 −0.404644 −0.202322 0.979319i \(-0.564849\pi\)
−0.202322 + 0.979319i \(0.564849\pi\)
\(440\) −13.0379 −0.621558
\(441\) 75.7790 3.60852
\(442\) 6.66062 0.316813
\(443\) 22.8282 1.08460 0.542300 0.840185i \(-0.317554\pi\)
0.542300 + 0.840185i \(0.317554\pi\)
\(444\) −2.04269 −0.0969417
\(445\) −53.2756 −2.52551
\(446\) −5.36978 −0.254266
\(447\) −28.2731 −1.33727
\(448\) 4.15498 0.196304
\(449\) −20.7064 −0.977194 −0.488597 0.872510i \(-0.662491\pi\)
−0.488597 + 0.872510i \(0.662491\pi\)
\(450\) 41.0449 1.93487
\(451\) −4.11021 −0.193542
\(452\) −2.00849 −0.0944716
\(453\) 28.5434 1.34109
\(454\) 2.64894 0.124321
\(455\) 17.7949 0.834238
\(456\) 11.4107 0.534354
\(457\) 31.9285 1.49355 0.746775 0.665077i \(-0.231601\pi\)
0.746775 + 0.665077i \(0.231601\pi\)
\(458\) −27.2277 −1.27227
\(459\) 71.3758 3.33154
\(460\) −2.95848 −0.137940
\(461\) 23.3573 1.08786 0.543928 0.839132i \(-0.316936\pi\)
0.543928 + 0.839132i \(0.316936\pi\)
\(462\) −53.7184 −2.49921
\(463\) 12.0630 0.560617 0.280308 0.959910i \(-0.409563\pi\)
0.280308 + 0.959910i \(0.409563\pi\)
\(464\) 1.83498 0.0851867
\(465\) 42.9502 1.99177
\(466\) 7.53866 0.349222
\(467\) 7.60503 0.351919 0.175959 0.984397i \(-0.443697\pi\)
0.175959 + 0.984397i \(0.443697\pi\)
\(468\) −9.73081 −0.449807
\(469\) −36.2024 −1.67167
\(470\) 31.0479 1.43213
\(471\) 10.3366 0.476287
\(472\) −10.3152 −0.474798
\(473\) −28.0613 −1.29026
\(474\) −0.875220 −0.0402002
\(475\) −19.6865 −0.903277
\(476\) −20.9978 −0.962433
\(477\) −60.2841 −2.76022
\(478\) −14.9478 −0.683696
\(479\) −24.2770 −1.10925 −0.554623 0.832102i \(-0.687137\pi\)
−0.554623 + 0.832102i \(0.687137\pi\)
\(480\) 10.4708 0.477926
\(481\) −0.835503 −0.0380956
\(482\) 23.6181 1.07577
\(483\) −12.1894 −0.554638
\(484\) 5.09836 0.231744
\(485\) 10.5187 0.477629
\(486\) −32.9049 −1.49259
\(487\) 28.9530 1.31199 0.655994 0.754766i \(-0.272250\pi\)
0.655994 + 0.754766i \(0.272250\pi\)
\(488\) 8.82410 0.399448
\(489\) −15.1266 −0.684050
\(490\) −33.3524 −1.50671
\(491\) 25.3134 1.14238 0.571189 0.820819i \(-0.306483\pi\)
0.571189 + 0.820819i \(0.306483\pi\)
\(492\) 3.30093 0.148818
\(493\) −9.27334 −0.417650
\(494\) 4.66721 0.209988
\(495\) −96.2604 −4.32658
\(496\) 4.10189 0.184180
\(497\) 49.5169 2.22114
\(498\) −0.550823 −0.0246830
\(499\) −27.7596 −1.24269 −0.621345 0.783537i \(-0.713413\pi\)
−0.621345 + 0.783537i \(0.713413\pi\)
\(500\) −1.81743 −0.0812780
\(501\) 66.4698 2.96965
\(502\) −18.4620 −0.824000
\(503\) 8.99347 0.400999 0.200499 0.979694i \(-0.435744\pi\)
0.200499 + 0.979694i \(0.435744\pi\)
\(504\) 30.6767 1.36645
\(505\) 40.6706 1.80982
\(506\) 3.65293 0.162393
\(507\) 36.2923 1.61180
\(508\) 8.53198 0.378545
\(509\) −1.97858 −0.0876990 −0.0438495 0.999038i \(-0.513962\pi\)
−0.0438495 + 0.999038i \(0.513962\pi\)
\(510\) −52.9159 −2.34316
\(511\) −0.719427 −0.0318256
\(512\) 1.00000 0.0441942
\(513\) 50.0143 2.20819
\(514\) −6.70260 −0.295639
\(515\) −13.6030 −0.599418
\(516\) 22.5362 0.992101
\(517\) −38.3359 −1.68601
\(518\) 2.63395 0.115729
\(519\) 21.4764 0.942708
\(520\) 4.28279 0.187813
\(521\) −12.9049 −0.565376 −0.282688 0.959212i \(-0.591226\pi\)
−0.282688 + 0.959212i \(0.591226\pi\)
\(522\) 13.5478 0.592973
\(523\) −17.9372 −0.784339 −0.392169 0.919893i \(-0.628275\pi\)
−0.392169 + 0.919893i \(0.628275\pi\)
\(524\) −1.51561 −0.0662098
\(525\) −74.4307 −3.24842
\(526\) −21.4031 −0.933221
\(527\) −20.7295 −0.902992
\(528\) −12.9287 −0.562649
\(529\) −22.1711 −0.963961
\(530\) 26.5327 1.15251
\(531\) −76.1586 −3.30500
\(532\) −14.7135 −0.637912
\(533\) 1.35015 0.0584816
\(534\) −52.8293 −2.28615
\(535\) 7.47450 0.323151
\(536\) −8.71303 −0.376346
\(537\) −1.96590 −0.0848350
\(538\) 23.4274 1.01003
\(539\) 41.1813 1.77381
\(540\) 45.8948 1.97500
\(541\) −31.4229 −1.35098 −0.675488 0.737371i \(-0.736067\pi\)
−0.675488 + 0.737371i \(0.736067\pi\)
\(542\) 25.6175 1.10036
\(543\) −14.1069 −0.605385
\(544\) −5.05365 −0.216673
\(545\) −40.2211 −1.72288
\(546\) 17.6458 0.755172
\(547\) 30.5503 1.30623 0.653117 0.757257i \(-0.273461\pi\)
0.653117 + 0.757257i \(0.273461\pi\)
\(548\) −2.17483 −0.0929039
\(549\) 65.1493 2.78050
\(550\) 22.3054 0.951107
\(551\) −6.49799 −0.276824
\(552\) −2.93369 −0.124866
\(553\) 1.12855 0.0479910
\(554\) −16.8074 −0.714077
\(555\) 6.63773 0.281756
\(556\) 15.1915 0.644263
\(557\) 5.22241 0.221281 0.110640 0.993861i \(-0.464710\pi\)
0.110640 + 0.993861i \(0.464710\pi\)
\(558\) 30.2847 1.28205
\(559\) 9.21778 0.389871
\(560\) −13.5016 −0.570548
\(561\) 65.3371 2.75853
\(562\) −12.7635 −0.538397
\(563\) −3.35396 −0.141353 −0.0706764 0.997499i \(-0.522516\pi\)
−0.0706764 + 0.997499i \(0.522516\pi\)
\(564\) 30.7878 1.29640
\(565\) 6.52662 0.274577
\(566\) 26.3964 1.10952
\(567\) 97.0644 4.07632
\(568\) 11.9175 0.500047
\(569\) 6.37811 0.267384 0.133692 0.991023i \(-0.457317\pi\)
0.133692 + 0.991023i \(0.457317\pi\)
\(570\) −37.0791 −1.55307
\(571\) 13.6188 0.569929 0.284964 0.958538i \(-0.408018\pi\)
0.284964 + 0.958538i \(0.408018\pi\)
\(572\) −5.28811 −0.221107
\(573\) 15.4561 0.645687
\(574\) −4.25639 −0.177658
\(575\) 5.06140 0.211075
\(576\) 7.38311 0.307630
\(577\) 32.1498 1.33841 0.669207 0.743076i \(-0.266634\pi\)
0.669207 + 0.743076i \(0.266634\pi\)
\(578\) 8.53938 0.355191
\(579\) 24.5168 1.01888
\(580\) −5.96277 −0.247591
\(581\) 0.710260 0.0294665
\(582\) 10.4306 0.432361
\(583\) −32.7608 −1.35681
\(584\) −0.173148 −0.00716493
\(585\) 31.6203 1.30734
\(586\) 30.3087 1.25204
\(587\) −39.9900 −1.65057 −0.825283 0.564719i \(-0.808984\pi\)
−0.825283 + 0.564719i \(0.808984\pi\)
\(588\) −33.0730 −1.36391
\(589\) −14.5255 −0.598514
\(590\) 33.5195 1.37997
\(591\) 70.0688 2.88224
\(592\) 0.633925 0.0260542
\(593\) 16.2840 0.668705 0.334353 0.942448i \(-0.391482\pi\)
0.334353 + 0.942448i \(0.391482\pi\)
\(594\) −56.6679 −2.32511
\(595\) 68.2325 2.79726
\(596\) 8.77423 0.359407
\(597\) −2.91509 −0.119307
\(598\) −1.19994 −0.0490693
\(599\) 17.2849 0.706240 0.353120 0.935578i \(-0.385121\pi\)
0.353120 + 0.935578i \(0.385121\pi\)
\(600\) −17.9136 −0.731321
\(601\) 12.8816 0.525450 0.262725 0.964871i \(-0.415379\pi\)
0.262725 + 0.964871i \(0.415379\pi\)
\(602\) −29.0593 −1.18437
\(603\) −64.3293 −2.61969
\(604\) −8.85813 −0.360432
\(605\) −16.5672 −0.673551
\(606\) 40.3299 1.63829
\(607\) 9.22519 0.374439 0.187219 0.982318i \(-0.440052\pi\)
0.187219 + 0.982318i \(0.440052\pi\)
\(608\) −3.54118 −0.143614
\(609\) −24.5676 −0.995530
\(610\) −28.6740 −1.16097
\(611\) 12.5929 0.509453
\(612\) −37.3117 −1.50823
\(613\) −25.4547 −1.02810 −0.514052 0.857759i \(-0.671856\pi\)
−0.514052 + 0.857759i \(0.671856\pi\)
\(614\) −17.4097 −0.702599
\(615\) −10.7264 −0.432530
\(616\) 16.6709 0.671690
\(617\) −7.92234 −0.318942 −0.159471 0.987203i \(-0.550979\pi\)
−0.159471 + 0.987203i \(0.550979\pi\)
\(618\) −13.4890 −0.542607
\(619\) −21.6602 −0.870597 −0.435298 0.900286i \(-0.643357\pi\)
−0.435298 + 0.900286i \(0.643357\pi\)
\(620\) −13.3291 −0.535310
\(621\) −12.8587 −0.516002
\(622\) −28.8678 −1.15749
\(623\) 68.1208 2.72920
\(624\) 4.24691 0.170013
\(625\) −21.8907 −0.875629
\(626\) 10.8881 0.435176
\(627\) 45.7828 1.82839
\(628\) −3.20786 −0.128008
\(629\) −3.20364 −0.127737
\(630\) −99.6840 −3.97151
\(631\) −28.7491 −1.14448 −0.572242 0.820085i \(-0.693926\pi\)
−0.572242 + 0.820085i \(0.693926\pi\)
\(632\) 0.271615 0.0108043
\(633\) 40.0902 1.59344
\(634\) −34.1716 −1.35713
\(635\) −27.7247 −1.10022
\(636\) 26.3104 1.04328
\(637\) −13.5276 −0.535981
\(638\) 7.36244 0.291482
\(639\) 87.9881 3.48076
\(640\) −3.24951 −0.128448
\(641\) −24.1732 −0.954785 −0.477392 0.878690i \(-0.658418\pi\)
−0.477392 + 0.878690i \(0.658418\pi\)
\(642\) 7.41188 0.292524
\(643\) −27.3609 −1.07901 −0.539505 0.841983i \(-0.681388\pi\)
−0.539505 + 0.841983i \(0.681388\pi\)
\(644\) 3.78285 0.149065
\(645\) −73.2315 −2.88349
\(646\) 17.8959 0.704104
\(647\) −3.86104 −0.151793 −0.0758965 0.997116i \(-0.524182\pi\)
−0.0758965 + 0.997116i \(0.524182\pi\)
\(648\) 23.3610 0.917706
\(649\) −41.3876 −1.62461
\(650\) −7.32705 −0.287391
\(651\) −54.9182 −2.15241
\(652\) 4.69438 0.183846
\(653\) −39.2519 −1.53605 −0.768023 0.640422i \(-0.778759\pi\)
−0.768023 + 0.640422i \(0.778759\pi\)
\(654\) −39.8842 −1.55959
\(655\) 4.92499 0.192435
\(656\) −1.02441 −0.0399964
\(657\) −1.27837 −0.0498741
\(658\) −39.6994 −1.54764
\(659\) 47.5482 1.85221 0.926107 0.377260i \(-0.123134\pi\)
0.926107 + 0.377260i \(0.123134\pi\)
\(660\) 42.0119 1.63531
\(661\) 22.1418 0.861218 0.430609 0.902539i \(-0.358299\pi\)
0.430609 + 0.902539i \(0.358299\pi\)
\(662\) −18.2828 −0.710581
\(663\) −21.4624 −0.833531
\(664\) 0.170942 0.00663383
\(665\) 47.8117 1.85406
\(666\) 4.68034 0.181360
\(667\) 1.67064 0.0646873
\(668\) −20.6282 −0.798127
\(669\) 17.3030 0.668971
\(670\) 28.3131 1.09383
\(671\) 35.4047 1.36678
\(672\) −13.3885 −0.516473
\(673\) −5.53511 −0.213363 −0.106681 0.994293i \(-0.534022\pi\)
−0.106681 + 0.994293i \(0.534022\pi\)
\(674\) −25.1174 −0.967485
\(675\) −78.5174 −3.02214
\(676\) −11.2629 −0.433189
\(677\) 0.342279 0.0131549 0.00657743 0.999978i \(-0.497906\pi\)
0.00657743 + 0.999978i \(0.497906\pi\)
\(678\) 6.47194 0.248553
\(679\) −13.4497 −0.516153
\(680\) 16.4219 0.629750
\(681\) −8.53562 −0.327086
\(682\) 16.4579 0.630206
\(683\) −48.9943 −1.87471 −0.937357 0.348371i \(-0.886735\pi\)
−0.937357 + 0.348371i \(0.886735\pi\)
\(684\) −26.1449 −0.999676
\(685\) 7.06711 0.270020
\(686\) 13.5612 0.517767
\(687\) 87.7355 3.34732
\(688\) −6.99386 −0.266638
\(689\) 10.7615 0.409981
\(690\) 9.53306 0.362917
\(691\) 48.6212 1.84964 0.924819 0.380407i \(-0.124216\pi\)
0.924819 + 0.380407i \(0.124216\pi\)
\(692\) −6.66495 −0.253363
\(693\) 123.083 4.67554
\(694\) 16.8830 0.640868
\(695\) −49.3648 −1.87252
\(696\) −5.91282 −0.224125
\(697\) 5.17700 0.196093
\(698\) −8.99134 −0.340327
\(699\) −24.2917 −0.918797
\(700\) 23.0987 0.873050
\(701\) −0.929734 −0.0351156 −0.0175578 0.999846i \(-0.505589\pi\)
−0.0175578 + 0.999846i \(0.505589\pi\)
\(702\) 18.6147 0.702566
\(703\) −2.24484 −0.0846659
\(704\) 4.01228 0.151218
\(705\) −100.045 −3.76792
\(706\) 30.3918 1.14381
\(707\) −52.0034 −1.95579
\(708\) 33.2386 1.24918
\(709\) −44.4503 −1.66937 −0.834684 0.550729i \(-0.814350\pi\)
−0.834684 + 0.550729i \(0.814350\pi\)
\(710\) −38.7260 −1.45336
\(711\) 2.00536 0.0752070
\(712\) 16.3950 0.614428
\(713\) 3.73452 0.139859
\(714\) 67.6609 2.53214
\(715\) 17.1837 0.642636
\(716\) 0.610096 0.0228004
\(717\) 48.1660 1.79879
\(718\) −17.5605 −0.655350
\(719\) −19.0275 −0.709607 −0.354803 0.934941i \(-0.615452\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(720\) −23.9915 −0.894109
\(721\) 17.3934 0.647764
\(722\) −6.46004 −0.240418
\(723\) −76.1042 −2.83034
\(724\) 4.37792 0.162704
\(725\) 10.2012 0.378862
\(726\) −16.4284 −0.609714
\(727\) 31.3357 1.16218 0.581088 0.813841i \(-0.302627\pi\)
0.581088 + 0.813841i \(0.302627\pi\)
\(728\) −5.47619 −0.202961
\(729\) 35.9458 1.33133
\(730\) 0.562647 0.0208245
\(731\) 35.3445 1.30726
\(732\) −28.4337 −1.05094
\(733\) 20.6537 0.762863 0.381431 0.924397i \(-0.375431\pi\)
0.381431 + 0.924397i \(0.375431\pi\)
\(734\) 7.02086 0.259145
\(735\) 107.471 3.96412
\(736\) 0.910439 0.0335592
\(737\) −34.9591 −1.28773
\(738\) −7.56332 −0.278410
\(739\) 35.6158 1.31015 0.655073 0.755565i \(-0.272638\pi\)
0.655073 + 0.755565i \(0.272638\pi\)
\(740\) −2.05995 −0.0757251
\(741\) −15.0391 −0.552475
\(742\) −33.9260 −1.24546
\(743\) −38.1440 −1.39937 −0.699685 0.714452i \(-0.746676\pi\)
−0.699685 + 0.714452i \(0.746676\pi\)
\(744\) −13.2175 −0.484575
\(745\) −28.5119 −1.04460
\(746\) 11.6776 0.427549
\(747\) 1.26208 0.0461772
\(748\) −20.2766 −0.741387
\(749\) −9.55726 −0.349215
\(750\) 5.85628 0.213841
\(751\) 17.3697 0.633829 0.316915 0.948454i \(-0.397353\pi\)
0.316915 + 0.948454i \(0.397353\pi\)
\(752\) −9.55466 −0.348422
\(753\) 59.4899 2.16793
\(754\) −2.41847 −0.0880754
\(755\) 28.7846 1.04758
\(756\) −58.6833 −2.13429
\(757\) −29.3394 −1.06636 −0.533179 0.846003i \(-0.679003\pi\)
−0.533179 + 0.846003i \(0.679003\pi\)
\(758\) −3.27561 −0.118976
\(759\) −11.7708 −0.427252
\(760\) 11.5071 0.417406
\(761\) 51.0998 1.85237 0.926183 0.377076i \(-0.123070\pi\)
0.926183 + 0.377076i \(0.123070\pi\)
\(762\) −27.4925 −0.995947
\(763\) 51.4287 1.86184
\(764\) −4.79662 −0.173536
\(765\) 121.244 4.38360
\(766\) −29.6332 −1.07069
\(767\) 13.5953 0.490898
\(768\) −3.22228 −0.116274
\(769\) 7.38549 0.266327 0.133164 0.991094i \(-0.457486\pi\)
0.133164 + 0.991094i \(0.457486\pi\)
\(770\) −54.1723 −1.95223
\(771\) 21.5977 0.777821
\(772\) −7.60851 −0.273836
\(773\) −45.1563 −1.62416 −0.812080 0.583546i \(-0.801665\pi\)
−0.812080 + 0.583546i \(0.801665\pi\)
\(774\) −51.6364 −1.85603
\(775\) 22.8036 0.819130
\(776\) −3.23701 −0.116202
\(777\) −8.48732 −0.304481
\(778\) −24.3437 −0.872762
\(779\) 3.62761 0.129973
\(780\) −13.8004 −0.494133
\(781\) 47.8163 1.71100
\(782\) −4.60104 −0.164533
\(783\) −25.9165 −0.926181
\(784\) 10.2638 0.366565
\(785\) 10.4240 0.372047
\(786\) 4.88373 0.174197
\(787\) 0.674944 0.0240591 0.0120296 0.999928i \(-0.496171\pi\)
0.0120296 + 0.999928i \(0.496171\pi\)
\(788\) −21.7451 −0.774636
\(789\) 68.9670 2.45529
\(790\) −0.882614 −0.0314020
\(791\) −8.34525 −0.296723
\(792\) 29.6231 1.05261
\(793\) −11.6300 −0.412994
\(794\) −37.5789 −1.33362
\(795\) −85.4958 −3.03222
\(796\) 0.904665 0.0320650
\(797\) −18.3650 −0.650520 −0.325260 0.945625i \(-0.605452\pi\)
−0.325260 + 0.945625i \(0.605452\pi\)
\(798\) 47.4111 1.67834
\(799\) 48.2859 1.70823
\(800\) 5.55929 0.196551
\(801\) 121.046 4.27695
\(802\) −9.45682 −0.333932
\(803\) −0.694719 −0.0245161
\(804\) 28.0759 0.990159
\(805\) −12.2924 −0.433251
\(806\) −5.40622 −0.190426
\(807\) −75.4897 −2.65736
\(808\) −12.5159 −0.440309
\(809\) −18.1098 −0.636706 −0.318353 0.947972i \(-0.603130\pi\)
−0.318353 + 0.947972i \(0.603130\pi\)
\(810\) −75.9117 −2.66726
\(811\) 50.7246 1.78118 0.890590 0.454807i \(-0.150292\pi\)
0.890590 + 0.454807i \(0.150292\pi\)
\(812\) 7.62429 0.267560
\(813\) −82.5467 −2.89504
\(814\) 2.54348 0.0891491
\(815\) −15.2544 −0.534339
\(816\) 16.2843 0.570064
\(817\) 24.7665 0.866471
\(818\) −32.7404 −1.14474
\(819\) −40.4313 −1.41278
\(820\) 3.32882 0.116247
\(821\) 49.2698 1.71953 0.859764 0.510691i \(-0.170610\pi\)
0.859764 + 0.510691i \(0.170610\pi\)
\(822\) 7.00790 0.244429
\(823\) 0.986461 0.0343859 0.0171929 0.999852i \(-0.494527\pi\)
0.0171929 + 0.999852i \(0.494527\pi\)
\(824\) 4.18616 0.145832
\(825\) −71.8744 −2.50235
\(826\) −42.8596 −1.49128
\(827\) 3.26917 0.113680 0.0568400 0.998383i \(-0.481898\pi\)
0.0568400 + 0.998383i \(0.481898\pi\)
\(828\) 6.72187 0.233601
\(829\) 12.2143 0.424220 0.212110 0.977246i \(-0.431966\pi\)
0.212110 + 0.977246i \(0.431966\pi\)
\(830\) −0.555477 −0.0192809
\(831\) 54.1581 1.87872
\(832\) −1.31798 −0.0456928
\(833\) −51.8698 −1.79718
\(834\) −48.9513 −1.69504
\(835\) 67.0313 2.31971
\(836\) −14.2082 −0.491401
\(837\) −57.9336 −2.00248
\(838\) −5.40318 −0.186650
\(839\) 19.9491 0.688720 0.344360 0.938838i \(-0.388096\pi\)
0.344360 + 0.938838i \(0.388096\pi\)
\(840\) 43.5061 1.50110
\(841\) −25.6329 −0.883892
\(842\) −20.5428 −0.707951
\(843\) 41.1277 1.41651
\(844\) −12.4416 −0.428256
\(845\) 36.5989 1.25904
\(846\) −70.5431 −2.42532
\(847\) 21.1836 0.727876
\(848\) −8.16514 −0.280392
\(849\) −85.0567 −2.91914
\(850\) −28.0947 −0.963641
\(851\) 0.577151 0.0197845
\(852\) −38.4015 −1.31561
\(853\) 26.2853 0.899993 0.449997 0.893030i \(-0.351425\pi\)
0.449997 + 0.893030i \(0.351425\pi\)
\(854\) 36.6639 1.25461
\(855\) 84.9581 2.90551
\(856\) −2.30019 −0.0786190
\(857\) 28.3725 0.969185 0.484592 0.874740i \(-0.338968\pi\)
0.484592 + 0.874740i \(0.338968\pi\)
\(858\) 17.0398 0.581729
\(859\) 47.5443 1.62219 0.811095 0.584915i \(-0.198872\pi\)
0.811095 + 0.584915i \(0.198872\pi\)
\(860\) 22.7266 0.774971
\(861\) 13.7153 0.467416
\(862\) 21.5927 0.735449
\(863\) 19.8348 0.675185 0.337592 0.941292i \(-0.390387\pi\)
0.337592 + 0.941292i \(0.390387\pi\)
\(864\) −14.1236 −0.480495
\(865\) 21.6578 0.736387
\(866\) 28.4300 0.966091
\(867\) −27.5163 −0.934502
\(868\) 17.0433 0.578486
\(869\) 1.08979 0.0369687
\(870\) 19.2137 0.651407
\(871\) 11.4836 0.389108
\(872\) 12.3776 0.419159
\(873\) −23.8992 −0.808866
\(874\) −3.22403 −0.109054
\(875\) −7.55139 −0.255284
\(876\) 0.557933 0.0188508
\(877\) −45.7623 −1.54528 −0.772641 0.634843i \(-0.781065\pi\)
−0.772641 + 0.634843i \(0.781065\pi\)
\(878\) −8.47822 −0.286126
\(879\) −97.6633 −3.29410
\(880\) −13.0379 −0.439508
\(881\) −46.7616 −1.57544 −0.787720 0.616034i \(-0.788738\pi\)
−0.787720 + 0.616034i \(0.788738\pi\)
\(882\) 75.7790 2.55161
\(883\) 43.2751 1.45632 0.728162 0.685405i \(-0.240375\pi\)
0.728162 + 0.685405i \(0.240375\pi\)
\(884\) 6.66062 0.224021
\(885\) −108.009 −3.63069
\(886\) 22.8282 0.766928
\(887\) −33.7021 −1.13161 −0.565803 0.824540i \(-0.691434\pi\)
−0.565803 + 0.824540i \(0.691434\pi\)
\(888\) −2.04269 −0.0685481
\(889\) 35.4502 1.18896
\(890\) −53.2756 −1.78580
\(891\) 93.7307 3.14010
\(892\) −5.36978 −0.179794
\(893\) 33.8348 1.13224
\(894\) −28.2731 −0.945593
\(895\) −1.98251 −0.0662681
\(896\) 4.15498 0.138808
\(897\) 3.86656 0.129101
\(898\) −20.7064 −0.690980
\(899\) 7.52688 0.251035
\(900\) 41.0449 1.36816
\(901\) 41.2638 1.37470
\(902\) −4.11021 −0.136855
\(903\) 93.6374 3.11606
\(904\) −2.00849 −0.0668015
\(905\) −14.2261 −0.472891
\(906\) 28.5434 0.948292
\(907\) −6.72653 −0.223351 −0.111675 0.993745i \(-0.535622\pi\)
−0.111675 + 0.993745i \(0.535622\pi\)
\(908\) 2.64894 0.0879080
\(909\) −92.4065 −3.06493
\(910\) 17.7949 0.589895
\(911\) −49.5477 −1.64159 −0.820794 0.571225i \(-0.806468\pi\)
−0.820794 + 0.571225i \(0.806468\pi\)
\(912\) 11.4107 0.377846
\(913\) 0.685866 0.0226989
\(914\) 31.9285 1.05610
\(915\) 92.3956 3.05451
\(916\) −27.2277 −0.899630
\(917\) −6.29733 −0.207956
\(918\) 71.3758 2.35575
\(919\) −15.4865 −0.510852 −0.255426 0.966829i \(-0.582216\pi\)
−0.255426 + 0.966829i \(0.582216\pi\)
\(920\) −2.95848 −0.0975381
\(921\) 56.0990 1.84853
\(922\) 23.3573 0.769231
\(923\) −15.7070 −0.517004
\(924\) −53.7184 −1.76721
\(925\) 3.52418 0.115874
\(926\) 12.0630 0.396416
\(927\) 30.9069 1.01512
\(928\) 1.83498 0.0602361
\(929\) −20.8896 −0.685367 −0.342683 0.939451i \(-0.611336\pi\)
−0.342683 + 0.939451i \(0.611336\pi\)
\(930\) 42.9502 1.40839
\(931\) −36.3461 −1.19119
\(932\) 7.53866 0.246937
\(933\) 93.0201 3.04534
\(934\) 7.60503 0.248844
\(935\) 65.8891 2.15480
\(936\) −9.73081 −0.318061
\(937\) −57.7379 −1.88622 −0.943108 0.332487i \(-0.892112\pi\)
−0.943108 + 0.332487i \(0.892112\pi\)
\(938\) −36.2024 −1.18205
\(939\) −35.0846 −1.14494
\(940\) 31.0479 1.01267
\(941\) −36.7870 −1.19922 −0.599611 0.800292i \(-0.704678\pi\)
−0.599611 + 0.800292i \(0.704678\pi\)
\(942\) 10.3366 0.336786
\(943\) −0.932661 −0.0303716
\(944\) −10.3152 −0.335733
\(945\) 190.692 6.20321
\(946\) −28.0613 −0.912352
\(947\) 16.8676 0.548123 0.274062 0.961712i \(-0.411633\pi\)
0.274062 + 0.961712i \(0.411633\pi\)
\(948\) −0.875220 −0.0284258
\(949\) 0.228206 0.00740789
\(950\) −19.6865 −0.638713
\(951\) 110.111 3.57058
\(952\) −20.9978 −0.680543
\(953\) 53.7987 1.74271 0.871355 0.490653i \(-0.163242\pi\)
0.871355 + 0.490653i \(0.163242\pi\)
\(954\) −60.2841 −1.95177
\(955\) 15.5867 0.504372
\(956\) −14.9478 −0.483446
\(957\) −23.7239 −0.766884
\(958\) −24.2770 −0.784355
\(959\) −9.03635 −0.291799
\(960\) 10.4708 0.337945
\(961\) −14.1745 −0.457242
\(962\) −0.835503 −0.0269377
\(963\) −16.9826 −0.547256
\(964\) 23.6181 0.760687
\(965\) 24.7239 0.795891
\(966\) −12.1894 −0.392188
\(967\) −16.8046 −0.540399 −0.270200 0.962804i \(-0.587090\pi\)
−0.270200 + 0.962804i \(0.587090\pi\)
\(968\) 5.09836 0.163867
\(969\) −57.6656 −1.85249
\(970\) 10.5187 0.337735
\(971\) −45.3507 −1.45537 −0.727687 0.685909i \(-0.759405\pi\)
−0.727687 + 0.685909i \(0.759405\pi\)
\(972\) −32.9049 −1.05542
\(973\) 63.1203 2.02354
\(974\) 28.9530 0.927715
\(975\) 23.6098 0.756120
\(976\) 8.82410 0.282452
\(977\) 29.1634 0.933021 0.466510 0.884516i \(-0.345511\pi\)
0.466510 + 0.884516i \(0.345511\pi\)
\(978\) −15.1266 −0.483696
\(979\) 65.7812 2.10238
\(980\) −33.3524 −1.06540
\(981\) 91.3853 2.91771
\(982\) 25.3134 0.807783
\(983\) 14.1756 0.452131 0.226066 0.974112i \(-0.427414\pi\)
0.226066 + 0.974112i \(0.427414\pi\)
\(984\) 3.30093 0.105230
\(985\) 70.6608 2.25144
\(986\) −9.27334 −0.295323
\(987\) 127.923 4.07182
\(988\) 4.66721 0.148484
\(989\) −6.36748 −0.202474
\(990\) −96.2604 −3.05936
\(991\) −45.5764 −1.44778 −0.723891 0.689914i \(-0.757648\pi\)
−0.723891 + 0.689914i \(0.757648\pi\)
\(992\) 4.10189 0.130235
\(993\) 58.9123 1.86953
\(994\) 49.5169 1.57058
\(995\) −2.93971 −0.0931952
\(996\) −0.550823 −0.0174535
\(997\) 15.9140 0.504002 0.252001 0.967727i \(-0.418911\pi\)
0.252001 + 0.967727i \(0.418911\pi\)
\(998\) −27.7596 −0.878714
\(999\) −8.95333 −0.283271
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 \(a_p\))