Properties

Label 4010.2.a.k.1.13
Level 4010
Weight 2
Character 4010.1
Self dual Yes
Analytic conductor 32.020
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4010 = 2 \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4010.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0200112105\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(-1.05167\)
Character \(\chi\) = 4010.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.72412 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.72412 q^{6} -1.94532 q^{7} -1.00000 q^{8} -0.0274146 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.72412 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.72412 q^{6} -1.94532 q^{7} -1.00000 q^{8} -0.0274146 q^{9} +1.00000 q^{10} +1.83810 q^{11} +1.72412 q^{12} -2.05133 q^{13} +1.94532 q^{14} -1.72412 q^{15} +1.00000 q^{16} +1.66033 q^{17} +0.0274146 q^{18} +1.54006 q^{19} -1.00000 q^{20} -3.35396 q^{21} -1.83810 q^{22} +0.544628 q^{23} -1.72412 q^{24} +1.00000 q^{25} +2.05133 q^{26} -5.21962 q^{27} -1.94532 q^{28} +1.03602 q^{29} +1.72412 q^{30} +1.23453 q^{31} -1.00000 q^{32} +3.16911 q^{33} -1.66033 q^{34} +1.94532 q^{35} -0.0274146 q^{36} +8.44302 q^{37} -1.54006 q^{38} -3.53673 q^{39} +1.00000 q^{40} +1.18085 q^{41} +3.35396 q^{42} -10.8505 q^{43} +1.83810 q^{44} +0.0274146 q^{45} -0.544628 q^{46} -9.33896 q^{47} +1.72412 q^{48} -3.21574 q^{49} -1.00000 q^{50} +2.86260 q^{51} -2.05133 q^{52} +3.77155 q^{53} +5.21962 q^{54} -1.83810 q^{55} +1.94532 q^{56} +2.65524 q^{57} -1.03602 q^{58} -3.94882 q^{59} -1.72412 q^{60} +4.41148 q^{61} -1.23453 q^{62} +0.0533300 q^{63} +1.00000 q^{64} +2.05133 q^{65} -3.16911 q^{66} -8.02420 q^{67} +1.66033 q^{68} +0.939003 q^{69} -1.94532 q^{70} -10.8768 q^{71} +0.0274146 q^{72} -2.02924 q^{73} -8.44302 q^{74} +1.72412 q^{75} +1.54006 q^{76} -3.57570 q^{77} +3.53673 q^{78} +16.4487 q^{79} -1.00000 q^{80} -8.91700 q^{81} -1.18085 q^{82} -5.10696 q^{83} -3.35396 q^{84} -1.66033 q^{85} +10.8505 q^{86} +1.78623 q^{87} -1.83810 q^{88} +0.564286 q^{89} -0.0274146 q^{90} +3.99048 q^{91} +0.544628 q^{92} +2.12848 q^{93} +9.33896 q^{94} -1.54006 q^{95} -1.72412 q^{96} -5.43989 q^{97} +3.21574 q^{98} -0.0503908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + O(q^{10}) \) \( 15q - 15q^{2} - 6q^{3} + 15q^{4} - 15q^{5} + 6q^{6} - 5q^{7} - 15q^{8} + 19q^{9} + 15q^{10} - 2q^{11} - 6q^{12} - 13q^{13} + 5q^{14} + 6q^{15} + 15q^{16} + 11q^{17} - 19q^{18} - 15q^{19} - 15q^{20} - 2q^{21} + 2q^{22} - 3q^{23} + 6q^{24} + 15q^{25} + 13q^{26} - 12q^{27} - 5q^{28} + 28q^{29} - 6q^{30} - 12q^{31} - 15q^{32} - 22q^{33} - 11q^{34} + 5q^{35} + 19q^{36} - 23q^{37} + 15q^{38} - 2q^{39} + 15q^{40} + 24q^{41} + 2q^{42} - 24q^{43} - 2q^{44} - 19q^{45} + 3q^{46} - 3q^{47} - 6q^{48} + 20q^{49} - 15q^{50} - 5q^{51} - 13q^{52} + 10q^{53} + 12q^{54} + 2q^{55} + 5q^{56} - 11q^{57} - 28q^{58} + 2q^{59} + 6q^{60} + 15q^{61} + 12q^{62} - 2q^{63} + 15q^{64} + 13q^{65} + 22q^{66} - 48q^{67} + 11q^{68} + 21q^{69} - 5q^{70} + 15q^{71} - 19q^{72} - 47q^{73} + 23q^{74} - 6q^{75} - 15q^{76} + 7q^{77} + 2q^{78} - 34q^{79} - 15q^{80} + 43q^{81} - 24q^{82} - 32q^{83} - 2q^{84} - 11q^{85} + 24q^{86} + 14q^{87} + 2q^{88} + 25q^{89} + 19q^{90} - 32q^{91} - 3q^{92} - 42q^{93} + 3q^{94} + 15q^{95} + 6q^{96} - 34q^{97} - 20q^{98} + 4q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.72412 0.995420 0.497710 0.867343i \(-0.334174\pi\)
0.497710 + 0.867343i \(0.334174\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) −1.72412 −0.703869
\(7\) −1.94532 −0.735261 −0.367630 0.929972i \(-0.619831\pi\)
−0.367630 + 0.929972i \(0.619831\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.0274146 −0.00913819
\(10\) 1.00000 0.316228
\(11\) 1.83810 0.554209 0.277105 0.960840i \(-0.410625\pi\)
0.277105 + 0.960840i \(0.410625\pi\)
\(12\) 1.72412 0.497710
\(13\) −2.05133 −0.568936 −0.284468 0.958686i \(-0.591817\pi\)
−0.284468 + 0.958686i \(0.591817\pi\)
\(14\) 1.94532 0.519908
\(15\) −1.72412 −0.445166
\(16\) 1.00000 0.250000
\(17\) 1.66033 0.402688 0.201344 0.979521i \(-0.435469\pi\)
0.201344 + 0.979521i \(0.435469\pi\)
\(18\) 0.0274146 0.00646167
\(19\) 1.54006 0.353314 0.176657 0.984273i \(-0.443472\pi\)
0.176657 + 0.984273i \(0.443472\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.35396 −0.731893
\(22\) −1.83810 −0.391885
\(23\) 0.544628 0.113563 0.0567814 0.998387i \(-0.481916\pi\)
0.0567814 + 0.998387i \(0.481916\pi\)
\(24\) −1.72412 −0.351934
\(25\) 1.00000 0.200000
\(26\) 2.05133 0.402299
\(27\) −5.21962 −1.00452
\(28\) −1.94532 −0.367630
\(29\) 1.03602 0.192385 0.0961924 0.995363i \(-0.469334\pi\)
0.0961924 + 0.995363i \(0.469334\pi\)
\(30\) 1.72412 0.314780
\(31\) 1.23453 0.221729 0.110864 0.993836i \(-0.464638\pi\)
0.110864 + 0.993836i \(0.464638\pi\)
\(32\) −1.00000 −0.176777
\(33\) 3.16911 0.551671
\(34\) −1.66033 −0.284743
\(35\) 1.94532 0.328819
\(36\) −0.0274146 −0.00456909
\(37\) 8.44302 1.38802 0.694012 0.719964i \(-0.255842\pi\)
0.694012 + 0.719964i \(0.255842\pi\)
\(38\) −1.54006 −0.249830
\(39\) −3.53673 −0.566331
\(40\) 1.00000 0.158114
\(41\) 1.18085 0.184417 0.0922087 0.995740i \(-0.470607\pi\)
0.0922087 + 0.995740i \(0.470607\pi\)
\(42\) 3.35396 0.517527
\(43\) −10.8505 −1.65468 −0.827340 0.561701i \(-0.810147\pi\)
−0.827340 + 0.561701i \(0.810147\pi\)
\(44\) 1.83810 0.277105
\(45\) 0.0274146 0.00408672
\(46\) −0.544628 −0.0803010
\(47\) −9.33896 −1.36223 −0.681114 0.732178i \(-0.738504\pi\)
−0.681114 + 0.732178i \(0.738504\pi\)
\(48\) 1.72412 0.248855
\(49\) −3.21574 −0.459392
\(50\) −1.00000 −0.141421
\(51\) 2.86260 0.400844
\(52\) −2.05133 −0.284468
\(53\) 3.77155 0.518062 0.259031 0.965869i \(-0.416597\pi\)
0.259031 + 0.965869i \(0.416597\pi\)
\(54\) 5.21962 0.710301
\(55\) −1.83810 −0.247850
\(56\) 1.94532 0.259954
\(57\) 2.65524 0.351696
\(58\) −1.03602 −0.136037
\(59\) −3.94882 −0.514093 −0.257046 0.966399i \(-0.582749\pi\)
−0.257046 + 0.966399i \(0.582749\pi\)
\(60\) −1.72412 −0.222583
\(61\) 4.41148 0.564832 0.282416 0.959292i \(-0.408864\pi\)
0.282416 + 0.959292i \(0.408864\pi\)
\(62\) −1.23453 −0.156786
\(63\) 0.0533300 0.00671895
\(64\) 1.00000 0.125000
\(65\) 2.05133 0.254436
\(66\) −3.16911 −0.390091
\(67\) −8.02420 −0.980312 −0.490156 0.871635i \(-0.663060\pi\)
−0.490156 + 0.871635i \(0.663060\pi\)
\(68\) 1.66033 0.201344
\(69\) 0.939003 0.113043
\(70\) −1.94532 −0.232510
\(71\) −10.8768 −1.29083 −0.645417 0.763830i \(-0.723316\pi\)
−0.645417 + 0.763830i \(0.723316\pi\)
\(72\) 0.0274146 0.00323084
\(73\) −2.02924 −0.237504 −0.118752 0.992924i \(-0.537889\pi\)
−0.118752 + 0.992924i \(0.537889\pi\)
\(74\) −8.44302 −0.981481
\(75\) 1.72412 0.199084
\(76\) 1.54006 0.176657
\(77\) −3.57570 −0.407488
\(78\) 3.53673 0.400456
\(79\) 16.4487 1.85063 0.925313 0.379203i \(-0.123802\pi\)
0.925313 + 0.379203i \(0.123802\pi\)
\(80\) −1.00000 −0.111803
\(81\) −8.91700 −0.990778
\(82\) −1.18085 −0.130403
\(83\) −5.10696 −0.560562 −0.280281 0.959918i \(-0.590428\pi\)
−0.280281 + 0.959918i \(0.590428\pi\)
\(84\) −3.35396 −0.365947
\(85\) −1.66033 −0.180088
\(86\) 10.8505 1.17004
\(87\) 1.78623 0.191504
\(88\) −1.83810 −0.195943
\(89\) 0.564286 0.0598142 0.0299071 0.999553i \(-0.490479\pi\)
0.0299071 + 0.999553i \(0.490479\pi\)
\(90\) −0.0274146 −0.00288975
\(91\) 3.99048 0.418316
\(92\) 0.544628 0.0567814
\(93\) 2.12848 0.220713
\(94\) 9.33896 0.963240
\(95\) −1.54006 −0.158007
\(96\) −1.72412 −0.175967
\(97\) −5.43989 −0.552337 −0.276169 0.961109i \(-0.589065\pi\)
−0.276169 + 0.961109i \(0.589065\pi\)
\(98\) 3.21574 0.324839
\(99\) −0.0503908 −0.00506447
\(100\) 1.00000 0.100000
\(101\) −16.5279 −1.64459 −0.822296 0.569060i \(-0.807307\pi\)
−0.822296 + 0.569060i \(0.807307\pi\)
\(102\) −2.86260 −0.283439
\(103\) 11.1161 1.09530 0.547651 0.836707i \(-0.315522\pi\)
0.547651 + 0.836707i \(0.315522\pi\)
\(104\) 2.05133 0.201149
\(105\) 3.35396 0.327313
\(106\) −3.77155 −0.366325
\(107\) −5.71380 −0.552374 −0.276187 0.961104i \(-0.589071\pi\)
−0.276187 + 0.961104i \(0.589071\pi\)
\(108\) −5.21962 −0.502258
\(109\) −17.0725 −1.63525 −0.817625 0.575751i \(-0.804710\pi\)
−0.817625 + 0.575751i \(0.804710\pi\)
\(110\) 1.83810 0.175256
\(111\) 14.5568 1.38167
\(112\) −1.94532 −0.183815
\(113\) −4.04593 −0.380609 −0.190304 0.981725i \(-0.560948\pi\)
−0.190304 + 0.981725i \(0.560948\pi\)
\(114\) −2.65524 −0.248686
\(115\) −0.544628 −0.0507868
\(116\) 1.03602 0.0961924
\(117\) 0.0562363 0.00519904
\(118\) 3.94882 0.363519
\(119\) −3.22986 −0.296081
\(120\) 1.72412 0.157390
\(121\) −7.62137 −0.692852
\(122\) −4.41148 −0.399396
\(123\) 2.03592 0.183573
\(124\) 1.23453 0.110864
\(125\) −1.00000 −0.0894427
\(126\) −0.0533300 −0.00475101
\(127\) −17.2277 −1.52871 −0.764357 0.644794i \(-0.776943\pi\)
−0.764357 + 0.644794i \(0.776943\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −18.7075 −1.64710
\(130\) −2.05133 −0.179913
\(131\) 11.5742 1.01124 0.505620 0.862757i \(-0.331264\pi\)
0.505620 + 0.862757i \(0.331264\pi\)
\(132\) 3.16911 0.275836
\(133\) −2.99590 −0.259778
\(134\) 8.02420 0.693185
\(135\) 5.21962 0.449234
\(136\) −1.66033 −0.142372
\(137\) −4.60948 −0.393814 −0.196907 0.980422i \(-0.563090\pi\)
−0.196907 + 0.980422i \(0.563090\pi\)
\(138\) −0.939003 −0.0799333
\(139\) −16.5125 −1.40057 −0.700287 0.713862i \(-0.746944\pi\)
−0.700287 + 0.713862i \(0.746944\pi\)
\(140\) 1.94532 0.164409
\(141\) −16.1015 −1.35599
\(142\) 10.8768 0.912758
\(143\) −3.77056 −0.315310
\(144\) −0.0274146 −0.00228455
\(145\) −1.03602 −0.0860371
\(146\) 2.02924 0.167941
\(147\) −5.54432 −0.457288
\(148\) 8.44302 0.694012
\(149\) 6.16182 0.504796 0.252398 0.967623i \(-0.418781\pi\)
0.252398 + 0.967623i \(0.418781\pi\)
\(150\) −1.72412 −0.140774
\(151\) 8.49220 0.691085 0.345543 0.938403i \(-0.387695\pi\)
0.345543 + 0.938403i \(0.387695\pi\)
\(152\) −1.54006 −0.124915
\(153\) −0.0455171 −0.00367984
\(154\) 3.57570 0.288138
\(155\) −1.23453 −0.0991601
\(156\) −3.53673 −0.283165
\(157\) −15.8470 −1.26473 −0.632364 0.774672i \(-0.717915\pi\)
−0.632364 + 0.774672i \(0.717915\pi\)
\(158\) −16.4487 −1.30859
\(159\) 6.50260 0.515690
\(160\) 1.00000 0.0790569
\(161\) −1.05947 −0.0834982
\(162\) 8.91700 0.700586
\(163\) −7.53318 −0.590044 −0.295022 0.955490i \(-0.595327\pi\)
−0.295022 + 0.955490i \(0.595327\pi\)
\(164\) 1.18085 0.0922087
\(165\) −3.16911 −0.246715
\(166\) 5.10696 0.396377
\(167\) −18.5865 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(168\) 3.35396 0.258763
\(169\) −8.79205 −0.676312
\(170\) 1.66033 0.127341
\(171\) −0.0422200 −0.00322865
\(172\) −10.8505 −0.827340
\(173\) 9.98907 0.759455 0.379727 0.925098i \(-0.376018\pi\)
0.379727 + 0.925098i \(0.376018\pi\)
\(174\) −1.78623 −0.135414
\(175\) −1.94532 −0.147052
\(176\) 1.83810 0.138552
\(177\) −6.80824 −0.511739
\(178\) −0.564286 −0.0422950
\(179\) 17.4916 1.30738 0.653691 0.756761i \(-0.273219\pi\)
0.653691 + 0.756761i \(0.273219\pi\)
\(180\) 0.0274146 0.00204336
\(181\) −9.51269 −0.707073 −0.353536 0.935421i \(-0.615021\pi\)
−0.353536 + 0.935421i \(0.615021\pi\)
\(182\) −3.99048 −0.295794
\(183\) 7.60591 0.562245
\(184\) −0.544628 −0.0401505
\(185\) −8.44302 −0.620743
\(186\) −2.12848 −0.156068
\(187\) 3.05185 0.223174
\(188\) −9.33896 −0.681114
\(189\) 10.1538 0.738582
\(190\) 1.54006 0.111728
\(191\) 15.1580 1.09679 0.548396 0.836218i \(-0.315238\pi\)
0.548396 + 0.836218i \(0.315238\pi\)
\(192\) 1.72412 0.124428
\(193\) 12.2141 0.879189 0.439595 0.898196i \(-0.355122\pi\)
0.439595 + 0.898196i \(0.355122\pi\)
\(194\) 5.43989 0.390561
\(195\) 3.53673 0.253271
\(196\) −3.21574 −0.229696
\(197\) −26.5971 −1.89496 −0.947481 0.319811i \(-0.896381\pi\)
−0.947481 + 0.319811i \(0.896381\pi\)
\(198\) 0.0503908 0.00358112
\(199\) −17.2394 −1.22207 −0.611035 0.791603i \(-0.709247\pi\)
−0.611035 + 0.791603i \(0.709247\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −13.8347 −0.975822
\(202\) 16.5279 1.16290
\(203\) −2.01540 −0.141453
\(204\) 2.86260 0.200422
\(205\) −1.18085 −0.0824740
\(206\) −11.1161 −0.774496
\(207\) −0.0149307 −0.00103776
\(208\) −2.05133 −0.142234
\(209\) 2.83079 0.195810
\(210\) −3.35396 −0.231445
\(211\) −18.4808 −1.27227 −0.636135 0.771578i \(-0.719468\pi\)
−0.636135 + 0.771578i \(0.719468\pi\)
\(212\) 3.77155 0.259031
\(213\) −18.7528 −1.28492
\(214\) 5.71380 0.390588
\(215\) 10.8505 0.739996
\(216\) 5.21962 0.355150
\(217\) −2.40156 −0.163028
\(218\) 17.0725 1.15630
\(219\) −3.49865 −0.236417
\(220\) −1.83810 −0.123925
\(221\) −3.40587 −0.229104
\(222\) −14.5568 −0.976986
\(223\) −18.0052 −1.20572 −0.602859 0.797848i \(-0.705972\pi\)
−0.602859 + 0.797848i \(0.705972\pi\)
\(224\) 1.94532 0.129977
\(225\) −0.0274146 −0.00182764
\(226\) 4.04593 0.269131
\(227\) 17.2948 1.14789 0.573947 0.818892i \(-0.305411\pi\)
0.573947 + 0.818892i \(0.305411\pi\)
\(228\) 2.65524 0.175848
\(229\) 21.6346 1.42966 0.714828 0.699300i \(-0.246505\pi\)
0.714828 + 0.699300i \(0.246505\pi\)
\(230\) 0.544628 0.0359117
\(231\) −6.16492 −0.405622
\(232\) −1.03602 −0.0680183
\(233\) −13.4681 −0.882323 −0.441161 0.897428i \(-0.645433\pi\)
−0.441161 + 0.897428i \(0.645433\pi\)
\(234\) −0.0562363 −0.00367628
\(235\) 9.33896 0.609207
\(236\) −3.94882 −0.257046
\(237\) 28.3596 1.84215
\(238\) 3.22986 0.209361
\(239\) 11.0188 0.712744 0.356372 0.934344i \(-0.384014\pi\)
0.356372 + 0.934344i \(0.384014\pi\)
\(240\) −1.72412 −0.111291
\(241\) −0.143227 −0.00922606 −0.00461303 0.999989i \(-0.501468\pi\)
−0.00461303 + 0.999989i \(0.501468\pi\)
\(242\) 7.62137 0.489920
\(243\) 0.284892 0.0182758
\(244\) 4.41148 0.282416
\(245\) 3.21574 0.205446
\(246\) −2.03592 −0.129806
\(247\) −3.15917 −0.201013
\(248\) −1.23453 −0.0783929
\(249\) −8.80501 −0.557995
\(250\) 1.00000 0.0632456
\(251\) 1.97385 0.124589 0.0622943 0.998058i \(-0.480158\pi\)
0.0622943 + 0.998058i \(0.480158\pi\)
\(252\) 0.0533300 0.00335947
\(253\) 1.00108 0.0629376
\(254\) 17.2277 1.08096
\(255\) −2.86260 −0.179263
\(256\) 1.00000 0.0625000
\(257\) −4.40506 −0.274780 −0.137390 0.990517i \(-0.543871\pi\)
−0.137390 + 0.990517i \(0.543871\pi\)
\(258\) 18.7075 1.16468
\(259\) −16.4243 −1.02056
\(260\) 2.05133 0.127218
\(261\) −0.0284022 −0.00175805
\(262\) −11.5742 −0.715054
\(263\) 30.7542 1.89638 0.948192 0.317699i \(-0.102910\pi\)
0.948192 + 0.317699i \(0.102910\pi\)
\(264\) −3.16911 −0.195045
\(265\) −3.77155 −0.231685
\(266\) 2.99590 0.183691
\(267\) 0.972896 0.0595402
\(268\) −8.02420 −0.490156
\(269\) 25.4603 1.55234 0.776171 0.630522i \(-0.217159\pi\)
0.776171 + 0.630522i \(0.217159\pi\)
\(270\) −5.21962 −0.317656
\(271\) −17.3366 −1.05312 −0.526562 0.850137i \(-0.676519\pi\)
−0.526562 + 0.850137i \(0.676519\pi\)
\(272\) 1.66033 0.100672
\(273\) 6.88007 0.416401
\(274\) 4.60948 0.278469
\(275\) 1.83810 0.110842
\(276\) 0.939003 0.0565213
\(277\) 29.1086 1.74896 0.874482 0.485057i \(-0.161201\pi\)
0.874482 + 0.485057i \(0.161201\pi\)
\(278\) 16.5125 0.990355
\(279\) −0.0338442 −0.00202620
\(280\) −1.94532 −0.116255
\(281\) 21.3534 1.27384 0.636919 0.770931i \(-0.280208\pi\)
0.636919 + 0.770931i \(0.280208\pi\)
\(282\) 16.1015 0.958829
\(283\) 25.7112 1.52837 0.764187 0.644995i \(-0.223140\pi\)
0.764187 + 0.644995i \(0.223140\pi\)
\(284\) −10.8768 −0.645417
\(285\) −2.65524 −0.157283
\(286\) 3.77056 0.222958
\(287\) −2.29712 −0.135595
\(288\) 0.0274146 0.00161542
\(289\) −14.2433 −0.837842
\(290\) 1.03602 0.0608374
\(291\) −9.37902 −0.549808
\(292\) −2.02924 −0.118752
\(293\) 18.1782 1.06198 0.530992 0.847377i \(-0.321819\pi\)
0.530992 + 0.847377i \(0.321819\pi\)
\(294\) 5.54432 0.323352
\(295\) 3.94882 0.229909
\(296\) −8.44302 −0.490740
\(297\) −9.59421 −0.556713
\(298\) −6.16182 −0.356945
\(299\) −1.11721 −0.0646099
\(300\) 1.72412 0.0995420
\(301\) 21.1076 1.21662
\(302\) −8.49220 −0.488671
\(303\) −28.4961 −1.63706
\(304\) 1.54006 0.0883284
\(305\) −4.41148 −0.252601
\(306\) 0.0455171 0.00260204
\(307\) −13.6166 −0.777141 −0.388570 0.921419i \(-0.627031\pi\)
−0.388570 + 0.921419i \(0.627031\pi\)
\(308\) −3.57570 −0.203744
\(309\) 19.1655 1.09029
\(310\) 1.23453 0.0701168
\(311\) −0.107193 −0.00607837 −0.00303919 0.999995i \(-0.500967\pi\)
−0.00303919 + 0.999995i \(0.500967\pi\)
\(312\) 3.53673 0.200228
\(313\) −26.1637 −1.47886 −0.739430 0.673233i \(-0.764905\pi\)
−0.739430 + 0.673233i \(0.764905\pi\)
\(314\) 15.8470 0.894297
\(315\) −0.0533300 −0.00300481
\(316\) 16.4487 0.925313
\(317\) −14.5197 −0.815508 −0.407754 0.913092i \(-0.633688\pi\)
−0.407754 + 0.913092i \(0.633688\pi\)
\(318\) −6.50260 −0.364648
\(319\) 1.90432 0.106622
\(320\) −1.00000 −0.0559017
\(321\) −9.85128 −0.549845
\(322\) 1.05947 0.0590422
\(323\) 2.55700 0.142275
\(324\) −8.91700 −0.495389
\(325\) −2.05133 −0.113787
\(326\) 7.53318 0.417224
\(327\) −29.4350 −1.62776
\(328\) −1.18085 −0.0652014
\(329\) 18.1672 1.00159
\(330\) 3.16911 0.174454
\(331\) −13.7827 −0.757567 −0.378783 0.925485i \(-0.623657\pi\)
−0.378783 + 0.925485i \(0.623657\pi\)
\(332\) −5.10696 −0.280281
\(333\) −0.231462 −0.0126840
\(334\) 18.5865 1.01701
\(335\) 8.02420 0.438409
\(336\) −3.35396 −0.182973
\(337\) −0.152670 −0.00831645 −0.00415822 0.999991i \(-0.501324\pi\)
−0.00415822 + 0.999991i \(0.501324\pi\)
\(338\) 8.79205 0.478225
\(339\) −6.97566 −0.378866
\(340\) −1.66033 −0.0900438
\(341\) 2.26920 0.122884
\(342\) 0.0422200 0.00228300
\(343\) 19.8729 1.07303
\(344\) 10.8505 0.585018
\(345\) −0.939003 −0.0505542
\(346\) −9.98907 −0.537016
\(347\) −31.9305 −1.71412 −0.857059 0.515218i \(-0.827711\pi\)
−0.857059 + 0.515218i \(0.827711\pi\)
\(348\) 1.78623 0.0957519
\(349\) −0.490583 −0.0262603 −0.0131302 0.999914i \(-0.504180\pi\)
−0.0131302 + 0.999914i \(0.504180\pi\)
\(350\) 1.94532 0.103982
\(351\) 10.7072 0.571506
\(352\) −1.83810 −0.0979713
\(353\) 22.3431 1.18920 0.594602 0.804020i \(-0.297310\pi\)
0.594602 + 0.804020i \(0.297310\pi\)
\(354\) 6.80824 0.361854
\(355\) 10.8768 0.577279
\(356\) 0.564286 0.0299071
\(357\) −5.56866 −0.294725
\(358\) −17.4916 −0.924459
\(359\) −29.0754 −1.53454 −0.767270 0.641324i \(-0.778385\pi\)
−0.767270 + 0.641324i \(0.778385\pi\)
\(360\) −0.0274146 −0.00144487
\(361\) −16.6282 −0.875169
\(362\) 9.51269 0.499976
\(363\) −13.1401 −0.689679
\(364\) 3.99048 0.209158
\(365\) 2.02924 0.106215
\(366\) −7.60591 −0.397567
\(367\) 9.83490 0.513378 0.256689 0.966494i \(-0.417368\pi\)
0.256689 + 0.966494i \(0.417368\pi\)
\(368\) 0.544628 0.0283907
\(369\) −0.0323724 −0.00168524
\(370\) 8.44302 0.438932
\(371\) −7.33686 −0.380911
\(372\) 2.12848 0.110357
\(373\) 16.0683 0.831985 0.415992 0.909368i \(-0.363434\pi\)
0.415992 + 0.909368i \(0.363434\pi\)
\(374\) −3.05185 −0.157808
\(375\) −1.72412 −0.0890331
\(376\) 9.33896 0.481620
\(377\) −2.12523 −0.109455
\(378\) −10.1538 −0.522256
\(379\) −30.0765 −1.54493 −0.772463 0.635059i \(-0.780976\pi\)
−0.772463 + 0.635059i \(0.780976\pi\)
\(380\) −1.54006 −0.0790033
\(381\) −29.7026 −1.52171
\(382\) −15.1580 −0.775550
\(383\) 19.0125 0.971495 0.485747 0.874099i \(-0.338547\pi\)
0.485747 + 0.874099i \(0.338547\pi\)
\(384\) −1.72412 −0.0879836
\(385\) 3.57570 0.182234
\(386\) −12.2141 −0.621681
\(387\) 0.297461 0.0151208
\(388\) −5.43989 −0.276169
\(389\) −10.8795 −0.551614 −0.275807 0.961213i \(-0.588945\pi\)
−0.275807 + 0.961213i \(0.588945\pi\)
\(390\) −3.53673 −0.179089
\(391\) 0.904259 0.0457304
\(392\) 3.21574 0.162420
\(393\) 19.9552 1.00661
\(394\) 26.5971 1.33994
\(395\) −16.4487 −0.827625
\(396\) −0.0503908 −0.00253224
\(397\) −13.3201 −0.668519 −0.334260 0.942481i \(-0.608486\pi\)
−0.334260 + 0.942481i \(0.608486\pi\)
\(398\) 17.2394 0.864134
\(399\) −5.16529 −0.258588
\(400\) 1.00000 0.0500000
\(401\) −1.00000 −0.0499376
\(402\) 13.8347 0.690011
\(403\) −2.53243 −0.126149
\(404\) −16.5279 −0.822296
\(405\) 8.91700 0.443090
\(406\) 2.01540 0.100022
\(407\) 15.5191 0.769256
\(408\) −2.86260 −0.141720
\(409\) 15.4727 0.765075 0.382538 0.923940i \(-0.375050\pi\)
0.382538 + 0.923940i \(0.375050\pi\)
\(410\) 1.18085 0.0583179
\(411\) −7.94729 −0.392011
\(412\) 11.1161 0.547651
\(413\) 7.68171 0.377992
\(414\) 0.0149307 0.000733806 0
\(415\) 5.10696 0.250691
\(416\) 2.05133 0.100575
\(417\) −28.4695 −1.39416
\(418\) −2.83079 −0.138458
\(419\) 30.2832 1.47943 0.739716 0.672919i \(-0.234960\pi\)
0.739716 + 0.672919i \(0.234960\pi\)
\(420\) 3.35396 0.163656
\(421\) 29.6085 1.44303 0.721516 0.692398i \(-0.243446\pi\)
0.721516 + 0.692398i \(0.243446\pi\)
\(422\) 18.4808 0.899631
\(423\) 0.256024 0.0124483
\(424\) −3.77155 −0.183163
\(425\) 1.66033 0.0805376
\(426\) 18.7528 0.908578
\(427\) −8.58172 −0.415299
\(428\) −5.71380 −0.276187
\(429\) −6.50089 −0.313866
\(430\) −10.8505 −0.523256
\(431\) 18.6154 0.896673 0.448336 0.893865i \(-0.352017\pi\)
0.448336 + 0.893865i \(0.352017\pi\)
\(432\) −5.21962 −0.251129
\(433\) −9.69199 −0.465767 −0.232884 0.972505i \(-0.574816\pi\)
−0.232884 + 0.972505i \(0.574816\pi\)
\(434\) 2.40156 0.115278
\(435\) −1.78623 −0.0856431
\(436\) −17.0725 −0.817625
\(437\) 0.838759 0.0401233
\(438\) 3.49865 0.167172
\(439\) 21.1167 1.00785 0.503923 0.863749i \(-0.331890\pi\)
0.503923 + 0.863749i \(0.331890\pi\)
\(440\) 1.83810 0.0876282
\(441\) 0.0881582 0.00419801
\(442\) 3.40587 0.162001
\(443\) −13.2897 −0.631413 −0.315707 0.948857i \(-0.602242\pi\)
−0.315707 + 0.948857i \(0.602242\pi\)
\(444\) 14.5568 0.690833
\(445\) −0.564286 −0.0267497
\(446\) 18.0052 0.852571
\(447\) 10.6237 0.502484
\(448\) −1.94532 −0.0919076
\(449\) 26.0789 1.23074 0.615370 0.788239i \(-0.289007\pi\)
0.615370 + 0.788239i \(0.289007\pi\)
\(450\) 0.0274146 0.00129233
\(451\) 2.17052 0.102206
\(452\) −4.04593 −0.190304
\(453\) 14.6416 0.687920
\(454\) −17.2948 −0.811684
\(455\) −3.99048 −0.187077
\(456\) −2.65524 −0.124343
\(457\) −25.0095 −1.16989 −0.584947 0.811072i \(-0.698885\pi\)
−0.584947 + 0.811072i \(0.698885\pi\)
\(458\) −21.6346 −1.01092
\(459\) −8.66627 −0.404507
\(460\) −0.544628 −0.0253934
\(461\) −24.9188 −1.16058 −0.580292 0.814408i \(-0.697062\pi\)
−0.580292 + 0.814408i \(0.697062\pi\)
\(462\) 6.16492 0.286818
\(463\) 36.0122 1.67363 0.836815 0.547486i \(-0.184415\pi\)
0.836815 + 0.547486i \(0.184415\pi\)
\(464\) 1.03602 0.0480962
\(465\) −2.12848 −0.0987060
\(466\) 13.4681 0.623896
\(467\) −35.9059 −1.66153 −0.830763 0.556626i \(-0.812096\pi\)
−0.830763 + 0.556626i \(0.812096\pi\)
\(468\) 0.0562363 0.00259952
\(469\) 15.6096 0.720785
\(470\) −9.33896 −0.430774
\(471\) −27.3221 −1.25894
\(472\) 3.94882 0.181759
\(473\) −19.9443 −0.917040
\(474\) −28.3596 −1.30260
\(475\) 1.54006 0.0706627
\(476\) −3.22986 −0.148040
\(477\) −0.103395 −0.00473415
\(478\) −11.0188 −0.503986
\(479\) 13.6305 0.622791 0.311396 0.950280i \(-0.399204\pi\)
0.311396 + 0.950280i \(0.399204\pi\)
\(480\) 1.72412 0.0786949
\(481\) −17.3194 −0.789697
\(482\) 0.143227 0.00652381
\(483\) −1.82666 −0.0831158
\(484\) −7.62137 −0.346426
\(485\) 5.43989 0.247013
\(486\) −0.284892 −0.0129229
\(487\) −36.5213 −1.65494 −0.827469 0.561512i \(-0.810220\pi\)
−0.827469 + 0.561512i \(0.810220\pi\)
\(488\) −4.41148 −0.199698
\(489\) −12.9881 −0.587342
\(490\) −3.21574 −0.145272
\(491\) 0.632414 0.0285404 0.0142702 0.999898i \(-0.495457\pi\)
0.0142702 + 0.999898i \(0.495457\pi\)
\(492\) 2.03592 0.0917865
\(493\) 1.72014 0.0774711
\(494\) 3.15917 0.142138
\(495\) 0.0503908 0.00226490
\(496\) 1.23453 0.0554322
\(497\) 21.1587 0.949100
\(498\) 8.80501 0.394562
\(499\) 27.1807 1.21677 0.608387 0.793641i \(-0.291817\pi\)
0.608387 + 0.793641i \(0.291817\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −32.0453 −1.43168
\(502\) −1.97385 −0.0880974
\(503\) 21.9270 0.977677 0.488839 0.872374i \(-0.337421\pi\)
0.488839 + 0.872374i \(0.337421\pi\)
\(504\) −0.0533300 −0.00237551
\(505\) 16.5279 0.735484
\(506\) −1.00108 −0.0445036
\(507\) −15.1585 −0.673215
\(508\) −17.2277 −0.764357
\(509\) 10.4997 0.465391 0.232696 0.972550i \(-0.425245\pi\)
0.232696 + 0.972550i \(0.425245\pi\)
\(510\) 2.86260 0.126758
\(511\) 3.94751 0.174628
\(512\) −1.00000 −0.0441942
\(513\) −8.03852 −0.354909
\(514\) 4.40506 0.194299
\(515\) −11.1161 −0.489834
\(516\) −18.7075 −0.823551
\(517\) −17.1660 −0.754959
\(518\) 16.4243 0.721644
\(519\) 17.2223 0.755977
\(520\) −2.05133 −0.0899567
\(521\) 2.03064 0.0889641 0.0444821 0.999010i \(-0.485836\pi\)
0.0444821 + 0.999010i \(0.485836\pi\)
\(522\) 0.0284022 0.00124313
\(523\) −0.611405 −0.0267349 −0.0133674 0.999911i \(-0.504255\pi\)
−0.0133674 + 0.999911i \(0.504255\pi\)
\(524\) 11.5742 0.505620
\(525\) −3.35396 −0.146379
\(526\) −30.7542 −1.34095
\(527\) 2.04973 0.0892875
\(528\) 3.16911 0.137918
\(529\) −22.7034 −0.987104
\(530\) 3.77155 0.163826
\(531\) 0.108255 0.00469788
\(532\) −2.99590 −0.129889
\(533\) −2.42231 −0.104922
\(534\) −0.972896 −0.0421013
\(535\) 5.71380 0.247029
\(536\) 8.02420 0.346593
\(537\) 30.1576 1.30140
\(538\) −25.4603 −1.09767
\(539\) −5.91087 −0.254599
\(540\) 5.21962 0.224617
\(541\) −7.42798 −0.319354 −0.159677 0.987169i \(-0.551045\pi\)
−0.159677 + 0.987169i \(0.551045\pi\)
\(542\) 17.3366 0.744671
\(543\) −16.4010 −0.703835
\(544\) −1.66033 −0.0711859
\(545\) 17.0725 0.731306
\(546\) −6.88007 −0.294440
\(547\) −34.7352 −1.48517 −0.742584 0.669753i \(-0.766400\pi\)
−0.742584 + 0.669753i \(0.766400\pi\)
\(548\) −4.60948 −0.196907
\(549\) −0.120939 −0.00516154
\(550\) −1.83810 −0.0783770
\(551\) 1.59554 0.0679722
\(552\) −0.939003 −0.0399666
\(553\) −31.9980 −1.36069
\(554\) −29.1086 −1.23670
\(555\) −14.5568 −0.617900
\(556\) −16.5125 −0.700287
\(557\) 4.11454 0.174339 0.0871693 0.996194i \(-0.472218\pi\)
0.0871693 + 0.996194i \(0.472218\pi\)
\(558\) 0.0338442 0.00143274
\(559\) 22.2579 0.941407
\(560\) 1.94532 0.0822046
\(561\) 5.26176 0.222151
\(562\) −21.3534 −0.900740
\(563\) 33.1422 1.39678 0.698389 0.715719i \(-0.253901\pi\)
0.698389 + 0.715719i \(0.253901\pi\)
\(564\) −16.1015 −0.677995
\(565\) 4.04593 0.170214
\(566\) −25.7112 −1.08072
\(567\) 17.3464 0.728480
\(568\) 10.8768 0.456379
\(569\) 9.19828 0.385612 0.192806 0.981237i \(-0.438241\pi\)
0.192806 + 0.981237i \(0.438241\pi\)
\(570\) 2.65524 0.111216
\(571\) −10.5379 −0.440998 −0.220499 0.975387i \(-0.570769\pi\)
−0.220499 + 0.975387i \(0.570769\pi\)
\(572\) −3.77056 −0.157655
\(573\) 26.1342 1.09177
\(574\) 2.29712 0.0958801
\(575\) 0.544628 0.0227126
\(576\) −0.0274146 −0.00114227
\(577\) −30.0687 −1.25178 −0.625888 0.779913i \(-0.715263\pi\)
−0.625888 + 0.779913i \(0.715263\pi\)
\(578\) 14.2433 0.592444
\(579\) 21.0585 0.875163
\(580\) −1.03602 −0.0430186
\(581\) 9.93465 0.412159
\(582\) 9.37902 0.388773
\(583\) 6.93251 0.287115
\(584\) 2.02924 0.0839705
\(585\) −0.0562363 −0.00232508
\(586\) −18.1782 −0.750937
\(587\) −20.0376 −0.827042 −0.413521 0.910495i \(-0.635701\pi\)
−0.413521 + 0.910495i \(0.635701\pi\)
\(588\) −5.54432 −0.228644
\(589\) 1.90125 0.0783398
\(590\) −3.94882 −0.162570
\(591\) −45.8565 −1.88628
\(592\) 8.44302 0.347006
\(593\) −33.8460 −1.38989 −0.694945 0.719063i \(-0.744571\pi\)
−0.694945 + 0.719063i \(0.744571\pi\)
\(594\) 9.59421 0.393655
\(595\) 3.22986 0.132411
\(596\) 6.16182 0.252398
\(597\) −29.7228 −1.21647
\(598\) 1.11721 0.0456861
\(599\) −25.9143 −1.05883 −0.529416 0.848363i \(-0.677589\pi\)
−0.529416 + 0.848363i \(0.677589\pi\)
\(600\) −1.72412 −0.0703869
\(601\) 2.59188 0.105725 0.0528624 0.998602i \(-0.483166\pi\)
0.0528624 + 0.998602i \(0.483166\pi\)
\(602\) −21.1076 −0.860281
\(603\) 0.219980 0.00895827
\(604\) 8.49220 0.345543
\(605\) 7.62137 0.309853
\(606\) 28.4961 1.15758
\(607\) −19.9746 −0.810744 −0.405372 0.914152i \(-0.632858\pi\)
−0.405372 + 0.914152i \(0.632858\pi\)
\(608\) −1.54006 −0.0624576
\(609\) −3.47478 −0.140805
\(610\) 4.41148 0.178616
\(611\) 19.1573 0.775020
\(612\) −0.0455171 −0.00183992
\(613\) −1.89876 −0.0766903 −0.0383451 0.999265i \(-0.512209\pi\)
−0.0383451 + 0.999265i \(0.512209\pi\)
\(614\) 13.6166 0.549521
\(615\) −2.03592 −0.0820963
\(616\) 3.57570 0.144069
\(617\) 18.2366 0.734178 0.367089 0.930186i \(-0.380355\pi\)
0.367089 + 0.930186i \(0.380355\pi\)
\(618\) −19.1655 −0.770949
\(619\) −9.23342 −0.371122 −0.185561 0.982633i \(-0.559410\pi\)
−0.185561 + 0.982633i \(0.559410\pi\)
\(620\) −1.23453 −0.0495801
\(621\) −2.84275 −0.114076
\(622\) 0.107193 0.00429806
\(623\) −1.09771 −0.0439790
\(624\) −3.53673 −0.141583
\(625\) 1.00000 0.0400000
\(626\) 26.1637 1.04571
\(627\) 4.88062 0.194913
\(628\) −15.8470 −0.632364
\(629\) 14.0182 0.558940
\(630\) 0.0533300 0.00212472
\(631\) 22.8126 0.908154 0.454077 0.890963i \(-0.349969\pi\)
0.454077 + 0.890963i \(0.349969\pi\)
\(632\) −16.4487 −0.654295
\(633\) −31.8631 −1.26644
\(634\) 14.5197 0.576651
\(635\) 17.2277 0.683661
\(636\) 6.50260 0.257845
\(637\) 6.59655 0.261365
\(638\) −1.90432 −0.0753928
\(639\) 0.298182 0.0117959
\(640\) 1.00000 0.0395285
\(641\) 34.8840 1.37784 0.688918 0.724839i \(-0.258086\pi\)
0.688918 + 0.724839i \(0.258086\pi\)
\(642\) 9.85128 0.388799
\(643\) −48.9655 −1.93101 −0.965505 0.260385i \(-0.916151\pi\)
−0.965505 + 0.260385i \(0.916151\pi\)
\(644\) −1.05947 −0.0417491
\(645\) 18.7075 0.736607
\(646\) −2.55700 −0.100604
\(647\) 5.10060 0.200525 0.100263 0.994961i \(-0.468032\pi\)
0.100263 + 0.994961i \(0.468032\pi\)
\(648\) 8.91700 0.350293
\(649\) −7.25835 −0.284915
\(650\) 2.05133 0.0804597
\(651\) −4.14057 −0.162282
\(652\) −7.53318 −0.295022
\(653\) 3.64131 0.142495 0.0712477 0.997459i \(-0.477302\pi\)
0.0712477 + 0.997459i \(0.477302\pi\)
\(654\) 29.4350 1.15100
\(655\) −11.5742 −0.452240
\(656\) 1.18085 0.0461044
\(657\) 0.0556307 0.00217036
\(658\) −18.1672 −0.708233
\(659\) −8.27962 −0.322528 −0.161264 0.986911i \(-0.551557\pi\)
−0.161264 + 0.986911i \(0.551557\pi\)
\(660\) −3.16911 −0.123357
\(661\) −16.2956 −0.633826 −0.316913 0.948455i \(-0.602646\pi\)
−0.316913 + 0.948455i \(0.602646\pi\)
\(662\) 13.7827 0.535680
\(663\) −5.87213 −0.228055
\(664\) 5.10696 0.198188
\(665\) 2.99590 0.116176
\(666\) 0.231462 0.00896896
\(667\) 0.564248 0.0218478
\(668\) −18.5865 −0.719132
\(669\) −31.0431 −1.20020
\(670\) −8.02420 −0.310002
\(671\) 8.10876 0.313035
\(672\) 3.35396 0.129382
\(673\) −24.2733 −0.935668 −0.467834 0.883816i \(-0.654965\pi\)
−0.467834 + 0.883816i \(0.654965\pi\)
\(674\) 0.152670 0.00588062
\(675\) −5.21962 −0.200903
\(676\) −8.79205 −0.338156
\(677\) 44.0596 1.69335 0.846674 0.532112i \(-0.178601\pi\)
0.846674 + 0.532112i \(0.178601\pi\)
\(678\) 6.97566 0.267899
\(679\) 10.5823 0.406112
\(680\) 1.66033 0.0636706
\(681\) 29.8183 1.14264
\(682\) −2.26920 −0.0868922
\(683\) −52.0297 −1.99086 −0.995431 0.0954884i \(-0.969559\pi\)
−0.995431 + 0.0954884i \(0.969559\pi\)
\(684\) −0.0422200 −0.00161432
\(685\) 4.60948 0.176119
\(686\) −19.8729 −0.758749
\(687\) 37.3006 1.42311
\(688\) −10.8505 −0.413670
\(689\) −7.73669 −0.294744
\(690\) 0.939003 0.0357472
\(691\) 46.5556 1.77106 0.885529 0.464585i \(-0.153796\pi\)
0.885529 + 0.464585i \(0.153796\pi\)
\(692\) 9.98907 0.379727
\(693\) 0.0980261 0.00372371
\(694\) 31.9305 1.21206
\(695\) 16.5125 0.626355
\(696\) −1.78623 −0.0677068
\(697\) 1.96059 0.0742627
\(698\) 0.490583 0.0185689
\(699\) −23.2206 −0.878282
\(700\) −1.94532 −0.0735261
\(701\) 1.35967 0.0513541 0.0256771 0.999670i \(-0.491826\pi\)
0.0256771 + 0.999670i \(0.491826\pi\)
\(702\) −10.7072 −0.404116
\(703\) 13.0027 0.490408
\(704\) 1.83810 0.0692762
\(705\) 16.1015 0.606417
\(706\) −22.3431 −0.840894
\(707\) 32.1521 1.20920
\(708\) −6.80824 −0.255869
\(709\) −22.9948 −0.863587 −0.431794 0.901972i \(-0.642119\pi\)
−0.431794 + 0.901972i \(0.642119\pi\)
\(710\) −10.8768 −0.408198
\(711\) −0.450935 −0.0169114
\(712\) −0.564286 −0.0211475
\(713\) 0.672361 0.0251801
\(714\) 5.56866 0.208402
\(715\) 3.77056 0.141011
\(716\) 17.4916 0.653691
\(717\) 18.9977 0.709480
\(718\) 29.0754 1.08508
\(719\) −6.99189 −0.260753 −0.130377 0.991465i \(-0.541619\pi\)
−0.130377 + 0.991465i \(0.541619\pi\)
\(720\) 0.0274146 0.00102168
\(721\) −21.6244 −0.805333
\(722\) 16.6282 0.618838
\(723\) −0.246940 −0.00918381
\(724\) −9.51269 −0.353536
\(725\) 1.03602 0.0384770
\(726\) 13.1401 0.487677
\(727\) −45.5778 −1.69039 −0.845194 0.534459i \(-0.820515\pi\)
−0.845194 + 0.534459i \(0.820515\pi\)
\(728\) −3.99048 −0.147897
\(729\) 27.2422 1.00897
\(730\) −2.02924 −0.0751055
\(731\) −18.0153 −0.666320
\(732\) 7.60591 0.281123
\(733\) −14.8586 −0.548814 −0.274407 0.961614i \(-0.588482\pi\)
−0.274407 + 0.961614i \(0.588482\pi\)
\(734\) −9.83490 −0.363013
\(735\) 5.54432 0.204505
\(736\) −0.544628 −0.0200752
\(737\) −14.7493 −0.543298
\(738\) 0.0323724 0.00119165
\(739\) 8.85326 0.325672 0.162836 0.986653i \(-0.447936\pi\)
0.162836 + 0.986653i \(0.447936\pi\)
\(740\) −8.44302 −0.310371
\(741\) −5.44678 −0.200092
\(742\) 7.33686 0.269345
\(743\) −33.0448 −1.21229 −0.606147 0.795352i \(-0.707286\pi\)
−0.606147 + 0.795352i \(0.707286\pi\)
\(744\) −2.12848 −0.0780339
\(745\) −6.16182 −0.225752
\(746\) −16.0683 −0.588302
\(747\) 0.140005 0.00512252
\(748\) 3.05185 0.111587
\(749\) 11.1152 0.406139
\(750\) 1.72412 0.0629559
\(751\) −1.70576 −0.0622442 −0.0311221 0.999516i \(-0.509908\pi\)
−0.0311221 + 0.999516i \(0.509908\pi\)
\(752\) −9.33896 −0.340557
\(753\) 3.40316 0.124018
\(754\) 2.12523 0.0773962
\(755\) −8.49220 −0.309063
\(756\) 10.1538 0.369291
\(757\) 19.1434 0.695780 0.347890 0.937535i \(-0.386898\pi\)
0.347890 + 0.937535i \(0.386898\pi\)
\(758\) 30.0765 1.09243
\(759\) 1.72599 0.0626493
\(760\) 1.54006 0.0558638
\(761\) −18.6183 −0.674913 −0.337456 0.941341i \(-0.609567\pi\)
−0.337456 + 0.941341i \(0.609567\pi\)
\(762\) 29.7026 1.07601
\(763\) 33.2114 1.20233
\(764\) 15.1580 0.548396
\(765\) 0.0455171 0.00164567
\(766\) −19.0125 −0.686951
\(767\) 8.10033 0.292486
\(768\) 1.72412 0.0622138
\(769\) −25.8580 −0.932462 −0.466231 0.884663i \(-0.654388\pi\)
−0.466231 + 0.884663i \(0.654388\pi\)
\(770\) −3.57570 −0.128859
\(771\) −7.59484 −0.273522
\(772\) 12.2141 0.439595
\(773\) 10.8182 0.389102 0.194551 0.980892i \(-0.437675\pi\)
0.194551 + 0.980892i \(0.437675\pi\)
\(774\) −0.297461 −0.0106920
\(775\) 1.23453 0.0443457
\(776\) 5.43989 0.195281
\(777\) −28.3175 −1.01589
\(778\) 10.8795 0.390050
\(779\) 1.81857 0.0651572
\(780\) 3.53673 0.126635
\(781\) −19.9926 −0.715393
\(782\) −0.904259 −0.0323363
\(783\) −5.40765 −0.193254
\(784\) −3.21574 −0.114848
\(785\) 15.8470 0.565603
\(786\) −19.9552 −0.711779
\(787\) −1.39603 −0.0497633 −0.0248816 0.999690i \(-0.507921\pi\)
−0.0248816 + 0.999690i \(0.507921\pi\)
\(788\) −26.5971 −0.947481
\(789\) 53.0238 1.88770
\(790\) 16.4487 0.585220
\(791\) 7.87061 0.279847
\(792\) 0.0503908 0.00179056
\(793\) −9.04939 −0.321353
\(794\) 13.3201 0.472714
\(795\) −6.50260 −0.230624
\(796\) −17.2394 −0.611035
\(797\) 46.8998 1.66128 0.830638 0.556813i \(-0.187976\pi\)
0.830638 + 0.556813i \(0.187976\pi\)
\(798\) 5.16529 0.182849
\(799\) −15.5057 −0.548553
\(800\) −1.00000 −0.0353553
\(801\) −0.0154696 −0.000546593 0
\(802\) 1.00000 0.0353112
\(803\) −3.72995 −0.131627
\(804\) −13.8347 −0.487911
\(805\) 1.05947 0.0373415
\(806\) 2.53243 0.0892011
\(807\) 43.8966 1.54523
\(808\) 16.5279 0.581451
\(809\) 47.2936 1.66275 0.831377 0.555709i \(-0.187553\pi\)
0.831377 + 0.555709i \(0.187553\pi\)
\(810\) −8.91700 −0.313312
\(811\) 28.4006 0.997281 0.498640 0.866809i \(-0.333833\pi\)
0.498640 + 0.866809i \(0.333833\pi\)
\(812\) −2.01540 −0.0707265
\(813\) −29.8904 −1.04830
\(814\) −15.5191 −0.543946
\(815\) 7.53318 0.263876
\(816\) 2.86260 0.100211
\(817\) −16.7104 −0.584621
\(818\) −15.4727 −0.540990
\(819\) −0.109397 −0.00382265
\(820\) −1.18085 −0.0412370
\(821\) 16.0937 0.561675 0.280837 0.959755i \(-0.409388\pi\)
0.280837 + 0.959755i \(0.409388\pi\)
\(822\) 7.94729 0.277193
\(823\) −3.54993 −0.123743 −0.0618714 0.998084i \(-0.519707\pi\)
−0.0618714 + 0.998084i \(0.519707\pi\)
\(824\) −11.1161 −0.387248
\(825\) 3.16911 0.110334
\(826\) −7.68171 −0.267281
\(827\) 44.2461 1.53859 0.769294 0.638895i \(-0.220608\pi\)
0.769294 + 0.638895i \(0.220608\pi\)
\(828\) −0.0149307 −0.000518879 0
\(829\) 27.9947 0.972295 0.486147 0.873877i \(-0.338402\pi\)
0.486147 + 0.873877i \(0.338402\pi\)
\(830\) −5.10696 −0.177265
\(831\) 50.1866 1.74096
\(832\) −2.05133 −0.0711170
\(833\) −5.33918 −0.184992
\(834\) 28.4695 0.985819
\(835\) 18.5865 0.643211
\(836\) 2.83079 0.0979049
\(837\) −6.44380 −0.222730
\(838\) −30.2832 −1.04612
\(839\) −24.2642 −0.837694 −0.418847 0.908057i \(-0.637566\pi\)
−0.418847 + 0.908057i \(0.637566\pi\)
\(840\) −3.35396 −0.115723
\(841\) −27.9267 −0.962988
\(842\) −29.6085 −1.02038
\(843\) 36.8158 1.26800
\(844\) −18.4808 −0.636135
\(845\) 8.79205 0.302456
\(846\) −0.256024 −0.00880227
\(847\) 14.8260 0.509427
\(848\) 3.77155 0.129516
\(849\) 44.3292 1.52137
\(850\) −1.66033 −0.0569487
\(851\) 4.59830 0.157628
\(852\) −18.7528 −0.642461
\(853\) 5.66471 0.193956 0.0969780 0.995287i \(-0.469082\pi\)
0.0969780 + 0.995287i \(0.469082\pi\)
\(854\) 8.58172 0.293660
\(855\) 0.0422200 0.00144389
\(856\) 5.71380 0.195294
\(857\) 0.292142 0.00997939 0.00498970 0.999988i \(-0.498412\pi\)
0.00498970 + 0.999988i \(0.498412\pi\)
\(858\) 6.50089 0.221937
\(859\) 19.6835 0.671592 0.335796 0.941935i \(-0.390995\pi\)
0.335796 + 0.941935i \(0.390995\pi\)
\(860\) 10.8505 0.369998
\(861\) −3.96051 −0.134974
\(862\) −18.6154 −0.634043
\(863\) −37.5654 −1.27874 −0.639371 0.768898i \(-0.720805\pi\)
−0.639371 + 0.768898i \(0.720805\pi\)
\(864\) 5.21962 0.177575
\(865\) −9.98907 −0.339638
\(866\) 9.69199 0.329347
\(867\) −24.5572 −0.834005
\(868\) −2.40156 −0.0815142
\(869\) 30.2345 1.02563
\(870\) 1.78623 0.0605588
\(871\) 16.4603 0.557735
\(872\) 17.0725 0.578148
\(873\) 0.149132 0.00504736
\(874\) −0.838759 −0.0283714
\(875\) 1.94532 0.0657637
\(876\) −3.49865 −0.118208
\(877\) 33.1322 1.11879 0.559397 0.828900i \(-0.311033\pi\)
0.559397 + 0.828900i \(0.311033\pi\)
\(878\) −21.1167 −0.712655
\(879\) 31.3415 1.05712
\(880\) −1.83810 −0.0619625
\(881\) 53.1407 1.79036 0.895178 0.445709i \(-0.147048\pi\)
0.895178 + 0.445709i \(0.147048\pi\)
\(882\) −0.0881582 −0.00296844
\(883\) 7.90991 0.266190 0.133095 0.991103i \(-0.457509\pi\)
0.133095 + 0.991103i \(0.457509\pi\)
\(884\) −3.40587 −0.114552
\(885\) 6.80824 0.228856
\(886\) 13.2897 0.446477
\(887\) 29.8751 1.00311 0.501554 0.865126i \(-0.332762\pi\)
0.501554 + 0.865126i \(0.332762\pi\)
\(888\) −14.5568 −0.488493
\(889\) 33.5134 1.12400
\(890\) 0.564286 0.0189149
\(891\) −16.3904 −0.549099
\(892\) −18.0052 −0.602859
\(893\) −14.3825 −0.481294
\(894\) −10.6237 −0.355310
\(895\) −17.4916 −0.584679
\(896\) 1.94532 0.0649885
\(897\) −1.92620 −0.0643141
\(898\) −26.0789 −0.870264
\(899\) 1.27901 0.0426573
\(900\) −0.0274146 −0.000913819 0
\(901\) 6.26200 0.208618
\(902\) −2.17052 −0.0722705
\(903\) 36.3920 1.21105
\(904\) 4.04593 0.134566
\(905\) 9.51269 0.316213
\(906\) −14.6416 −0.486433
\(907\) 51.8225 1.72074 0.860369 0.509672i \(-0.170233\pi\)
0.860369 + 0.509672i \(0.170233\pi\)
\(908\) 17.2948 0.573947
\(909\) 0.453106 0.0150286
\(910\) 3.99048 0.132283
\(911\) 35.7953 1.18595 0.592976 0.805220i \(-0.297953\pi\)
0.592976 + 0.805220i \(0.297953\pi\)
\(912\) 2.65524 0.0879239
\(913\) −9.38713 −0.310669
\(914\) 25.0095 0.827240
\(915\) −7.60591 −0.251444
\(916\) 21.6346 0.714828
\(917\) −22.5154 −0.743524
\(918\) 8.66627 0.286030
\(919\) −6.60188 −0.217776 −0.108888 0.994054i \(-0.534729\pi\)
−0.108888 + 0.994054i \(0.534729\pi\)
\(920\) 0.544628 0.0179558
\(921\) −23.4766 −0.773582
\(922\) 24.9188 0.820657
\(923\) 22.3118 0.734402
\(924\) −6.16492 −0.202811
\(925\) 8.44302 0.277605
\(926\) −36.0122 −1.18344
\(927\) −0.304743 −0.0100091
\(928\) −1.03602 −0.0340092
\(929\) 46.8771 1.53799 0.768994 0.639256i \(-0.220758\pi\)
0.768994 + 0.639256i \(0.220758\pi\)
\(930\) 2.12848 0.0697957
\(931\) −4.95243 −0.162309
\(932\) −13.4681 −0.441161
\(933\) −0.184814 −0.00605053
\(934\) 35.9059 1.17488
\(935\) −3.05185 −0.0998062
\(936\) −0.0562363 −0.00183814
\(937\) 40.8058 1.33307 0.666533 0.745475i \(-0.267777\pi\)
0.666533 + 0.745475i \(0.267777\pi\)
\(938\) −15.6096 −0.509672
\(939\) −45.1093 −1.47209
\(940\) 9.33896 0.304603
\(941\) 10.7011 0.348846 0.174423 0.984671i \(-0.444194\pi\)
0.174423 + 0.984671i \(0.444194\pi\)
\(942\) 27.3221 0.890202
\(943\) 0.643123 0.0209430
\(944\) −3.94882 −0.128523
\(945\) −10.1538 −0.330304
\(946\) 19.9443 0.648445
\(947\) −42.3714 −1.37688 −0.688442 0.725291i \(-0.741705\pi\)
−0.688442 + 0.725291i \(0.741705\pi\)
\(948\) 28.3596 0.921076
\(949\) 4.16264 0.135125
\(950\) −1.54006 −0.0499661
\(951\) −25.0337 −0.811773
\(952\) 3.22986 0.104680
\(953\) −15.3842 −0.498343 −0.249172 0.968459i \(-0.580158\pi\)
−0.249172 + 0.968459i \(0.580158\pi\)
\(954\) 0.103395 0.00334755
\(955\) −15.1580 −0.490501
\(956\) 11.0188 0.356372
\(957\) 3.28328 0.106133
\(958\) −13.6305 −0.440380
\(959\) 8.96689 0.289556
\(960\) −1.72412 −0.0556457
\(961\) −29.4759 −0.950836
\(962\) 17.3194 0.558400
\(963\) 0.156641 0.00504770
\(964\) −0.143227 −0.00461303
\(965\) −12.2141 −0.393185
\(966\) 1.82666 0.0587718
\(967\) 44.4010 1.42784 0.713919 0.700228i \(-0.246918\pi\)
0.713919 + 0.700228i \(0.246918\pi\)
\(968\) 7.62137 0.244960
\(969\) 4.40857 0.141624
\(970\) −5.43989 −0.174664
\(971\) −36.1636 −1.16055 −0.580273 0.814422i \(-0.697054\pi\)
−0.580273 + 0.814422i \(0.697054\pi\)
\(972\) 0.284892 0.00913790
\(973\) 32.1221 1.02979
\(974\) 36.5213 1.17022
\(975\) −3.53673 −0.113266
\(976\) 4.41148 0.141208
\(977\) 6.33344 0.202625 0.101312 0.994855i \(-0.467696\pi\)
0.101312 + 0.994855i \(0.467696\pi\)
\(978\) 12.9881 0.415314
\(979\) 1.03722 0.0331496
\(980\) 3.21574 0.102723
\(981\) 0.468036 0.0149432
\(982\) −0.632414 −0.0201811
\(983\) 44.3715 1.41523 0.707615 0.706598i \(-0.249771\pi\)
0.707615 + 0.706598i \(0.249771\pi\)
\(984\) −2.03592 −0.0649028
\(985\) 26.5971 0.847453
\(986\) −1.72014 −0.0547803
\(987\) 31.3225 0.997005
\(988\) −3.15917 −0.100506
\(989\) −5.90947 −0.187910
\(990\) −0.0503908 −0.00160153
\(991\) 45.9359 1.45920 0.729602 0.683872i \(-0.239705\pi\)
0.729602 + 0.683872i \(0.239705\pi\)
\(992\) −1.23453 −0.0391965
\(993\) −23.7630 −0.754097
\(994\) −21.1587 −0.671115
\(995\) 17.2394 0.546527
\(996\) −8.80501 −0.278997
\(997\) −44.2650 −1.40189 −0.700943 0.713217i \(-0.747237\pi\)
−0.700943 + 0.713217i \(0.747237\pi\)
\(998\) −27.1807 −0.860389
\(999\) −44.0694 −1.39429
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 \(a_p\))