Properties

Label 6023.2.a.b.1.19
Level 6023
Weight 2
Character 6023.1
Self dual Yes
Analytic conductor 48.094
Analytic rank 1
Dimension 99
CM No

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Newspace parameters

Level: \( N \) = \( 6023 = 19 \cdot 317 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(99\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.90532 q^{2}\) \(+0.192511 q^{3}\) \(+1.63023 q^{4}\) \(+0.483590 q^{5}\) \(-0.366795 q^{6}\) \(+3.15438 q^{7}\) \(+0.704532 q^{8}\) \(-2.96294 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.90532 q^{2}\) \(+0.192511 q^{3}\) \(+1.63023 q^{4}\) \(+0.483590 q^{5}\) \(-0.366795 q^{6}\) \(+3.15438 q^{7}\) \(+0.704532 q^{8}\) \(-2.96294 q^{9}\) \(-0.921392 q^{10}\) \(+0.275963 q^{11}\) \(+0.313837 q^{12}\) \(-1.15979 q^{13}\) \(-6.01010 q^{14}\) \(+0.0930965 q^{15}\) \(-4.60281 q^{16}\) \(-4.88188 q^{17}\) \(+5.64534 q^{18}\) \(-1.00000 q^{19}\) \(+0.788362 q^{20}\) \(+0.607254 q^{21}\) \(-0.525797 q^{22}\) \(+7.55013 q^{23}\) \(+0.135630 q^{24}\) \(-4.76614 q^{25}\) \(+2.20976 q^{26}\) \(-1.14793 q^{27}\) \(+5.14237 q^{28}\) \(-1.37761 q^{29}\) \(-0.177378 q^{30}\) \(+1.85608 q^{31}\) \(+7.36075 q^{32}\) \(+0.0531260 q^{33}\) \(+9.30153 q^{34}\) \(+1.52543 q^{35}\) \(-4.83027 q^{36}\) \(+8.37268 q^{37}\) \(+1.90532 q^{38}\) \(-0.223272 q^{39}\) \(+0.340704 q^{40}\) \(+2.29793 q^{41}\) \(-1.15701 q^{42}\) \(-7.33007 q^{43}\) \(+0.449883 q^{44}\) \(-1.43285 q^{45}\) \(-14.3854 q^{46}\) \(+3.26360 q^{47}\) \(-0.886093 q^{48}\) \(+2.95014 q^{49}\) \(+9.08100 q^{50}\) \(-0.939817 q^{51}\) \(-1.89071 q^{52}\) \(-4.39939 q^{53}\) \(+2.18718 q^{54}\) \(+0.133453 q^{55}\) \(+2.22236 q^{56}\) \(-0.192511 q^{57}\) \(+2.62479 q^{58}\) \(+2.49711 q^{59}\) \(+0.151769 q^{60}\) \(+8.52919 q^{61}\) \(-3.53641 q^{62}\) \(-9.34625 q^{63}\) \(-4.81892 q^{64}\) \(-0.560860 q^{65}\) \(-0.101222 q^{66}\) \(-10.4770 q^{67}\) \(-7.95858 q^{68}\) \(+1.45348 q^{69}\) \(-2.90642 q^{70}\) \(-6.40455 q^{71}\) \(-2.08748 q^{72}\) \(+8.31413 q^{73}\) \(-15.9526 q^{74}\) \(-0.917536 q^{75}\) \(-1.63023 q^{76}\) \(+0.870493 q^{77}\) \(+0.425403 q^{78}\) \(-1.19875 q^{79}\) \(-2.22587 q^{80}\) \(+8.66783 q^{81}\) \(-4.37828 q^{82}\) \(-4.01360 q^{83}\) \(+0.989963 q^{84}\) \(-2.36083 q^{85}\) \(+13.9661 q^{86}\) \(-0.265206 q^{87}\) \(+0.194425 q^{88}\) \(-14.4394 q^{89}\) \(+2.73003 q^{90}\) \(-3.65841 q^{91}\) \(+12.3084 q^{92}\) \(+0.357316 q^{93}\) \(-6.21819 q^{94}\) \(-0.483590 q^{95}\) \(+1.41703 q^{96}\) \(+3.23977 q^{97}\) \(-5.62094 q^{98}\) \(-0.817662 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.90532 −1.34726 −0.673631 0.739068i \(-0.735266\pi\)
−0.673631 + 0.739068i \(0.735266\pi\)
\(3\) 0.192511 0.111146 0.0555732 0.998455i \(-0.482301\pi\)
0.0555732 + 0.998455i \(0.482301\pi\)
\(4\) 1.63023 0.815114
\(5\) 0.483590 0.216268 0.108134 0.994136i \(-0.465512\pi\)
0.108134 + 0.994136i \(0.465512\pi\)
\(6\) −0.366795 −0.149743
\(7\) 3.15438 1.19224 0.596122 0.802894i \(-0.296707\pi\)
0.596122 + 0.802894i \(0.296707\pi\)
\(8\) 0.704532 0.249090
\(9\) −2.96294 −0.987646
\(10\) −0.921392 −0.291370
\(11\) 0.275963 0.0832060 0.0416030 0.999134i \(-0.486754\pi\)
0.0416030 + 0.999134i \(0.486754\pi\)
\(12\) 0.313837 0.0905970
\(13\) −1.15979 −0.321667 −0.160833 0.986982i \(-0.551418\pi\)
−0.160833 + 0.986982i \(0.551418\pi\)
\(14\) −6.01010 −1.60627
\(15\) 0.0930965 0.0240374
\(16\) −4.60281 −1.15070
\(17\) −4.88188 −1.18403 −0.592015 0.805927i \(-0.701667\pi\)
−0.592015 + 0.805927i \(0.701667\pi\)
\(18\) 5.64534 1.33062
\(19\) −1.00000 −0.229416
\(20\) 0.788362 0.176283
\(21\) 0.607254 0.132514
\(22\) −0.525797 −0.112100
\(23\) 7.55013 1.57431 0.787155 0.616755i \(-0.211553\pi\)
0.787155 + 0.616755i \(0.211553\pi\)
\(24\) 0.135630 0.0276854
\(25\) −4.76614 −0.953228
\(26\) 2.20976 0.433369
\(27\) −1.14793 −0.220920
\(28\) 5.14237 0.971816
\(29\) −1.37761 −0.255816 −0.127908 0.991786i \(-0.540826\pi\)
−0.127908 + 0.991786i \(0.540826\pi\)
\(30\) −0.177378 −0.0323847
\(31\) 1.85608 0.333361 0.166681 0.986011i \(-0.446695\pi\)
0.166681 + 0.986011i \(0.446695\pi\)
\(32\) 7.36075 1.30121
\(33\) 0.0531260 0.00924805
\(34\) 9.30153 1.59520
\(35\) 1.52543 0.257844
\(36\) −4.83027 −0.805045
\(37\) 8.37268 1.37646 0.688230 0.725493i \(-0.258388\pi\)
0.688230 + 0.725493i \(0.258388\pi\)
\(38\) 1.90532 0.309083
\(39\) −0.223272 −0.0357521
\(40\) 0.340704 0.0538701
\(41\) 2.29793 0.358876 0.179438 0.983769i \(-0.442572\pi\)
0.179438 + 0.983769i \(0.442572\pi\)
\(42\) −1.15701 −0.178531
\(43\) −7.33007 −1.11782 −0.558912 0.829227i \(-0.688781\pi\)
−0.558912 + 0.829227i \(0.688781\pi\)
\(44\) 0.449883 0.0678224
\(45\) −1.43285 −0.213596
\(46\) −14.3854 −2.12101
\(47\) 3.26360 0.476045 0.238023 0.971260i \(-0.423501\pi\)
0.238023 + 0.971260i \(0.423501\pi\)
\(48\) −0.886093 −0.127897
\(49\) 2.95014 0.421448
\(50\) 9.08100 1.28425
\(51\) −0.939817 −0.131601
\(52\) −1.89071 −0.262195
\(53\) −4.39939 −0.604303 −0.302151 0.953260i \(-0.597705\pi\)
−0.302151 + 0.953260i \(0.597705\pi\)
\(54\) 2.18718 0.297637
\(55\) 0.133453 0.0179948
\(56\) 2.22236 0.296976
\(57\) −0.192511 −0.0254987
\(58\) 2.62479 0.344651
\(59\) 2.49711 0.325097 0.162548 0.986701i \(-0.448029\pi\)
0.162548 + 0.986701i \(0.448029\pi\)
\(60\) 0.151769 0.0195932
\(61\) 8.52919 1.09205 0.546026 0.837768i \(-0.316140\pi\)
0.546026 + 0.837768i \(0.316140\pi\)
\(62\) −3.53641 −0.449125
\(63\) −9.34625 −1.17752
\(64\) −4.81892 −0.602366
\(65\) −0.560860 −0.0695662
\(66\) −0.101222 −0.0124595
\(67\) −10.4770 −1.27996 −0.639982 0.768390i \(-0.721058\pi\)
−0.639982 + 0.768390i \(0.721058\pi\)
\(68\) −7.95858 −0.965120
\(69\) 1.45348 0.174979
\(70\) −2.90642 −0.347384
\(71\) −6.40455 −0.760081 −0.380040 0.924970i \(-0.624090\pi\)
−0.380040 + 0.924970i \(0.624090\pi\)
\(72\) −2.08748 −0.246012
\(73\) 8.31413 0.973096 0.486548 0.873654i \(-0.338256\pi\)
0.486548 + 0.873654i \(0.338256\pi\)
\(74\) −15.9526 −1.85445
\(75\) −0.917536 −0.105948
\(76\) −1.63023 −0.187000
\(77\) 0.870493 0.0992019
\(78\) 0.425403 0.0481674
\(79\) −1.19875 −0.134870 −0.0674350 0.997724i \(-0.521482\pi\)
−0.0674350 + 0.997724i \(0.521482\pi\)
\(80\) −2.22587 −0.248860
\(81\) 8.66783 0.963092
\(82\) −4.37828 −0.483500
\(83\) −4.01360 −0.440550 −0.220275 0.975438i \(-0.570695\pi\)
−0.220275 + 0.975438i \(0.570695\pi\)
\(84\) 0.989963 0.108014
\(85\) −2.36083 −0.256068
\(86\) 13.9661 1.50600
\(87\) −0.265206 −0.0284330
\(88\) 0.194425 0.0207257
\(89\) −14.4394 −1.53058 −0.765289 0.643687i \(-0.777404\pi\)
−0.765289 + 0.643687i \(0.777404\pi\)
\(90\) 2.73003 0.287770
\(91\) −3.65841 −0.383505
\(92\) 12.3084 1.28324
\(93\) 0.357316 0.0370519
\(94\) −6.21819 −0.641358
\(95\) −0.483590 −0.0496153
\(96\) 1.41703 0.144625
\(97\) 3.23977 0.328949 0.164475 0.986381i \(-0.447407\pi\)
0.164475 + 0.986381i \(0.447407\pi\)
\(98\) −5.62094 −0.567801
\(99\) −0.817662 −0.0821781
\(100\) −7.76990 −0.776990
\(101\) −10.9631 −1.09087 −0.545437 0.838152i \(-0.683636\pi\)
−0.545437 + 0.838152i \(0.683636\pi\)
\(102\) 1.79065 0.177301
\(103\) 8.05610 0.793791 0.396896 0.917864i \(-0.370087\pi\)
0.396896 + 0.917864i \(0.370087\pi\)
\(104\) −0.817105 −0.0801238
\(105\) 0.293662 0.0286585
\(106\) 8.38223 0.814154
\(107\) −10.7610 −1.04031 −0.520153 0.854073i \(-0.674125\pi\)
−0.520153 + 0.854073i \(0.674125\pi\)
\(108\) −1.87139 −0.180075
\(109\) −14.4526 −1.38431 −0.692154 0.721750i \(-0.743338\pi\)
−0.692154 + 0.721750i \(0.743338\pi\)
\(110\) −0.254270 −0.0242437
\(111\) 1.61184 0.152989
\(112\) −14.5190 −1.37192
\(113\) −14.2216 −1.33786 −0.668928 0.743327i \(-0.733246\pi\)
−0.668928 + 0.743327i \(0.733246\pi\)
\(114\) 0.366795 0.0343535
\(115\) 3.65117 0.340473
\(116\) −2.24582 −0.208519
\(117\) 3.43637 0.317693
\(118\) −4.75779 −0.437990
\(119\) −15.3993 −1.41165
\(120\) 0.0655894 0.00598747
\(121\) −10.9238 −0.993077
\(122\) −16.2508 −1.47128
\(123\) 0.442377 0.0398878
\(124\) 3.02583 0.271728
\(125\) −4.72281 −0.422421
\(126\) 17.8076 1.58642
\(127\) 8.13952 0.722266 0.361133 0.932514i \(-0.382390\pi\)
0.361133 + 0.932514i \(0.382390\pi\)
\(128\) −5.53992 −0.489665
\(129\) −1.41112 −0.124242
\(130\) 1.06862 0.0937238
\(131\) 4.55518 0.397988 0.198994 0.980001i \(-0.436233\pi\)
0.198994 + 0.980001i \(0.436233\pi\)
\(132\) 0.0866075 0.00753822
\(133\) −3.15438 −0.273520
\(134\) 19.9619 1.72445
\(135\) −0.555129 −0.0477779
\(136\) −3.43944 −0.294930
\(137\) 19.9708 1.70622 0.853111 0.521729i \(-0.174713\pi\)
0.853111 + 0.521729i \(0.174713\pi\)
\(138\) −2.76935 −0.235743
\(139\) −6.98302 −0.592292 −0.296146 0.955143i \(-0.595701\pi\)
−0.296146 + 0.955143i \(0.595701\pi\)
\(140\) 2.48680 0.210173
\(141\) 0.628280 0.0529108
\(142\) 12.2027 1.02403
\(143\) −0.320058 −0.0267646
\(144\) 13.6379 1.13649
\(145\) −0.666199 −0.0553248
\(146\) −15.8411 −1.31101
\(147\) 0.567934 0.0468424
\(148\) 13.6494 1.12197
\(149\) 6.68046 0.547285 0.273642 0.961832i \(-0.411772\pi\)
0.273642 + 0.961832i \(0.411772\pi\)
\(150\) 1.74820 0.142740
\(151\) −11.7844 −0.959003 −0.479501 0.877541i \(-0.659182\pi\)
−0.479501 + 0.877541i \(0.659182\pi\)
\(152\) −0.704532 −0.0571451
\(153\) 14.4647 1.16940
\(154\) −1.65856 −0.133651
\(155\) 0.897581 0.0720954
\(156\) −0.363984 −0.0291420
\(157\) 1.62321 0.129547 0.0647733 0.997900i \(-0.479368\pi\)
0.0647733 + 0.997900i \(0.479368\pi\)
\(158\) 2.28400 0.181705
\(159\) −0.846933 −0.0671661
\(160\) 3.55958 0.281410
\(161\) 23.8160 1.87696
\(162\) −16.5150 −1.29754
\(163\) 6.52174 0.510822 0.255411 0.966833i \(-0.417789\pi\)
0.255411 + 0.966833i \(0.417789\pi\)
\(164\) 3.74615 0.292525
\(165\) 0.0256912 0.00200006
\(166\) 7.64717 0.593536
\(167\) 21.7814 1.68549 0.842747 0.538310i \(-0.180937\pi\)
0.842747 + 0.538310i \(0.180937\pi\)
\(168\) 0.427830 0.0330078
\(169\) −11.6549 −0.896531
\(170\) 4.49812 0.344990
\(171\) 2.96294 0.226582
\(172\) −11.9497 −0.911155
\(173\) 1.37783 0.104755 0.0523773 0.998627i \(-0.483320\pi\)
0.0523773 + 0.998627i \(0.483320\pi\)
\(174\) 0.505301 0.0383068
\(175\) −15.0342 −1.13648
\(176\) −1.27021 −0.0957454
\(177\) 0.480723 0.0361333
\(178\) 27.5117 2.06209
\(179\) 14.9624 1.11834 0.559170 0.829053i \(-0.311120\pi\)
0.559170 + 0.829053i \(0.311120\pi\)
\(180\) −2.33587 −0.174105
\(181\) −12.2335 −0.909311 −0.454655 0.890667i \(-0.650238\pi\)
−0.454655 + 0.890667i \(0.650238\pi\)
\(182\) 6.97042 0.516682
\(183\) 1.64197 0.121378
\(184\) 5.31931 0.392144
\(185\) 4.04894 0.297684
\(186\) −0.680800 −0.0499187
\(187\) −1.34722 −0.0985184
\(188\) 5.32042 0.388031
\(189\) −3.62102 −0.263391
\(190\) 0.921392 0.0668448
\(191\) −6.10667 −0.441863 −0.220932 0.975289i \(-0.570910\pi\)
−0.220932 + 0.975289i \(0.570910\pi\)
\(192\) −0.927697 −0.0669508
\(193\) −11.2876 −0.812498 −0.406249 0.913762i \(-0.633163\pi\)
−0.406249 + 0.913762i \(0.633163\pi\)
\(194\) −6.17279 −0.443181
\(195\) −0.107972 −0.00773203
\(196\) 4.80939 0.343528
\(197\) 16.2734 1.15943 0.579717 0.814818i \(-0.303163\pi\)
0.579717 + 0.814818i \(0.303163\pi\)
\(198\) 1.55790 0.110715
\(199\) −24.9455 −1.76834 −0.884169 0.467168i \(-0.845274\pi\)
−0.884169 + 0.467168i \(0.845274\pi\)
\(200\) −3.35790 −0.237439
\(201\) −2.01693 −0.142263
\(202\) 20.8882 1.46969
\(203\) −4.34552 −0.304995
\(204\) −1.53212 −0.107270
\(205\) 1.11125 0.0776134
\(206\) −15.3494 −1.06944
\(207\) −22.3706 −1.55486
\(208\) 5.33827 0.370143
\(209\) −0.275963 −0.0190888
\(210\) −0.559519 −0.0386105
\(211\) −7.56706 −0.520938 −0.260469 0.965482i \(-0.583877\pi\)
−0.260469 + 0.965482i \(0.583877\pi\)
\(212\) −7.17201 −0.492576
\(213\) −1.23295 −0.0844803
\(214\) 20.5031 1.40156
\(215\) −3.54475 −0.241750
\(216\) −0.808755 −0.0550288
\(217\) 5.85478 0.397448
\(218\) 27.5368 1.86502
\(219\) 1.60056 0.108156
\(220\) 0.217559 0.0146678
\(221\) 5.66193 0.380863
\(222\) −3.07106 −0.206116
\(223\) −21.3191 −1.42763 −0.713817 0.700332i \(-0.753035\pi\)
−0.713817 + 0.700332i \(0.753035\pi\)
\(224\) 23.2186 1.55136
\(225\) 14.1218 0.941452
\(226\) 27.0966 1.80244
\(227\) 15.6393 1.03801 0.519007 0.854770i \(-0.326302\pi\)
0.519007 + 0.854770i \(0.326302\pi\)
\(228\) −0.313837 −0.0207844
\(229\) −6.15833 −0.406954 −0.203477 0.979080i \(-0.565224\pi\)
−0.203477 + 0.979080i \(0.565224\pi\)
\(230\) −6.95662 −0.458706
\(231\) 0.167580 0.0110259
\(232\) −0.970571 −0.0637211
\(233\) −13.4709 −0.882509 −0.441255 0.897382i \(-0.645466\pi\)
−0.441255 + 0.897382i \(0.645466\pi\)
\(234\) −6.54738 −0.428015
\(235\) 1.57825 0.102953
\(236\) 4.07087 0.264991
\(237\) −0.230773 −0.0149903
\(238\) 29.3406 1.90187
\(239\) 10.7874 0.697780 0.348890 0.937164i \(-0.386559\pi\)
0.348890 + 0.937164i \(0.386559\pi\)
\(240\) −0.428506 −0.0276599
\(241\) −12.0072 −0.773450 −0.386725 0.922195i \(-0.626394\pi\)
−0.386725 + 0.922195i \(0.626394\pi\)
\(242\) 20.8134 1.33793
\(243\) 5.11245 0.327964
\(244\) 13.9045 0.890147
\(245\) 1.42666 0.0911457
\(246\) −0.842868 −0.0537393
\(247\) 1.15979 0.0737954
\(248\) 1.30767 0.0830369
\(249\) −0.772663 −0.0489655
\(250\) 8.99844 0.569111
\(251\) −18.3238 −1.15659 −0.578295 0.815828i \(-0.696282\pi\)
−0.578295 + 0.815828i \(0.696282\pi\)
\(252\) −15.2365 −0.959810
\(253\) 2.08356 0.130992
\(254\) −15.5084 −0.973081
\(255\) −0.454486 −0.0284610
\(256\) 20.1932 1.26207
\(257\) 9.04924 0.564476 0.282238 0.959344i \(-0.408923\pi\)
0.282238 + 0.959344i \(0.408923\pi\)
\(258\) 2.68863 0.167387
\(259\) 26.4106 1.64108
\(260\) −0.914331 −0.0567044
\(261\) 4.08178 0.252656
\(262\) −8.67905 −0.536194
\(263\) −19.1515 −1.18093 −0.590465 0.807063i \(-0.701056\pi\)
−0.590465 + 0.807063i \(0.701056\pi\)
\(264\) 0.0374290 0.00230359
\(265\) −2.12750 −0.130691
\(266\) 6.01010 0.368503
\(267\) −2.77976 −0.170118
\(268\) −17.0798 −1.04332
\(269\) 9.03702 0.550997 0.275498 0.961302i \(-0.411157\pi\)
0.275498 + 0.961302i \(0.411157\pi\)
\(270\) 1.05770 0.0643693
\(271\) −26.0810 −1.58431 −0.792153 0.610323i \(-0.791040\pi\)
−0.792153 + 0.610323i \(0.791040\pi\)
\(272\) 22.4704 1.36247
\(273\) −0.704285 −0.0426252
\(274\) −38.0507 −2.29873
\(275\) −1.31528 −0.0793143
\(276\) 2.36951 0.142628
\(277\) 19.5523 1.17478 0.587392 0.809303i \(-0.300155\pi\)
0.587392 + 0.809303i \(0.300155\pi\)
\(278\) 13.3049 0.797972
\(279\) −5.49945 −0.329243
\(280\) 1.07471 0.0642264
\(281\) 13.9768 0.833785 0.416892 0.908956i \(-0.363119\pi\)
0.416892 + 0.908956i \(0.363119\pi\)
\(282\) −1.19707 −0.0712846
\(283\) −15.5358 −0.923508 −0.461754 0.887008i \(-0.652780\pi\)
−0.461754 + 0.887008i \(0.652780\pi\)
\(284\) −10.4409 −0.619552
\(285\) −0.0930965 −0.00551456
\(286\) 0.609811 0.0360589
\(287\) 7.24855 0.427868
\(288\) −21.8094 −1.28513
\(289\) 6.83277 0.401928
\(290\) 1.26932 0.0745370
\(291\) 0.623693 0.0365615
\(292\) 13.5539 0.793184
\(293\) 26.8607 1.56922 0.784610 0.619990i \(-0.212863\pi\)
0.784610 + 0.619990i \(0.212863\pi\)
\(294\) −1.08209 −0.0631090
\(295\) 1.20758 0.0703080
\(296\) 5.89882 0.342862
\(297\) −0.316787 −0.0183819
\(298\) −12.7284 −0.737336
\(299\) −8.75653 −0.506403
\(300\) −1.49579 −0.0863596
\(301\) −23.1218 −1.33272
\(302\) 22.4530 1.29203
\(303\) −2.11053 −0.121247
\(304\) 4.60281 0.263989
\(305\) 4.12463 0.236176
\(306\) −27.5599 −1.57549
\(307\) −14.6776 −0.837696 −0.418848 0.908056i \(-0.637566\pi\)
−0.418848 + 0.908056i \(0.637566\pi\)
\(308\) 1.41910 0.0808609
\(309\) 1.55089 0.0882271
\(310\) −1.71017 −0.0971314
\(311\) −3.49593 −0.198236 −0.0991181 0.995076i \(-0.531602\pi\)
−0.0991181 + 0.995076i \(0.531602\pi\)
\(312\) −0.157302 −0.00890547
\(313\) −18.3347 −1.03634 −0.518168 0.855279i \(-0.673386\pi\)
−0.518168 + 0.855279i \(0.673386\pi\)
\(314\) −3.09274 −0.174533
\(315\) −4.51975 −0.254659
\(316\) −1.95424 −0.109934
\(317\) −1.00000 −0.0561656
\(318\) 1.61367 0.0904903
\(319\) −0.380170 −0.0212854
\(320\) −2.33038 −0.130272
\(321\) −2.07162 −0.115626
\(322\) −45.3770 −2.52876
\(323\) 4.88188 0.271635
\(324\) 14.1305 0.785030
\(325\) 5.52770 0.306622
\(326\) −12.4260 −0.688211
\(327\) −2.78229 −0.153861
\(328\) 1.61896 0.0893923
\(329\) 10.2947 0.567563
\(330\) −0.0489498 −0.00269460
\(331\) 6.95525 0.382295 0.191148 0.981561i \(-0.438779\pi\)
0.191148 + 0.981561i \(0.438779\pi\)
\(332\) −6.54308 −0.359098
\(333\) −24.8077 −1.35946
\(334\) −41.5004 −2.27080
\(335\) −5.06655 −0.276815
\(336\) −2.79508 −0.152484
\(337\) −1.25226 −0.0682151 −0.0341076 0.999418i \(-0.510859\pi\)
−0.0341076 + 0.999418i \(0.510859\pi\)
\(338\) 22.2063 1.20786
\(339\) −2.73782 −0.148698
\(340\) −3.84869 −0.208725
\(341\) 0.512209 0.0277377
\(342\) −5.64534 −0.305265
\(343\) −12.7748 −0.689776
\(344\) −5.16426 −0.278438
\(345\) 0.702891 0.0378424
\(346\) −2.62520 −0.141132
\(347\) 30.5851 1.64190 0.820948 0.571002i \(-0.193445\pi\)
0.820948 + 0.571002i \(0.193445\pi\)
\(348\) −0.432346 −0.0231762
\(349\) 7.79138 0.417063 0.208532 0.978016i \(-0.433132\pi\)
0.208532 + 0.978016i \(0.433132\pi\)
\(350\) 28.6450 1.53114
\(351\) 1.33136 0.0710625
\(352\) 2.03129 0.108268
\(353\) 17.5016 0.931516 0.465758 0.884912i \(-0.345782\pi\)
0.465758 + 0.884912i \(0.345782\pi\)
\(354\) −0.915929 −0.0486811
\(355\) −3.09718 −0.164381
\(356\) −23.5396 −1.24760
\(357\) −2.96454 −0.156900
\(358\) −28.5080 −1.50670
\(359\) −31.8635 −1.68169 −0.840846 0.541275i \(-0.817942\pi\)
−0.840846 + 0.541275i \(0.817942\pi\)
\(360\) −1.00949 −0.0532046
\(361\) 1.00000 0.0526316
\(362\) 23.3087 1.22508
\(363\) −2.10296 −0.110377
\(364\) −5.96404 −0.312601
\(365\) 4.02063 0.210449
\(366\) −3.12846 −0.163527
\(367\) −20.0046 −1.04423 −0.522117 0.852874i \(-0.674858\pi\)
−0.522117 + 0.852874i \(0.674858\pi\)
\(368\) −34.7518 −1.81156
\(369\) −6.80862 −0.354443
\(370\) −7.71452 −0.401059
\(371\) −13.8774 −0.720477
\(372\) 0.582507 0.0302016
\(373\) 5.25846 0.272273 0.136136 0.990690i \(-0.456531\pi\)
0.136136 + 0.990690i \(0.456531\pi\)
\(374\) 2.56688 0.132730
\(375\) −0.909194 −0.0469506
\(376\) 2.29931 0.118578
\(377\) 1.59773 0.0822875
\(378\) 6.89919 0.354856
\(379\) 19.7180 1.01285 0.506423 0.862285i \(-0.330967\pi\)
0.506423 + 0.862285i \(0.330967\pi\)
\(380\) −0.788362 −0.0404421
\(381\) 1.56695 0.0802773
\(382\) 11.6351 0.595305
\(383\) −1.80538 −0.0922507 −0.0461253 0.998936i \(-0.514687\pi\)
−0.0461253 + 0.998936i \(0.514687\pi\)
\(384\) −1.06650 −0.0544245
\(385\) 0.420962 0.0214542
\(386\) 21.5064 1.09465
\(387\) 21.7185 1.10402
\(388\) 5.28157 0.268131
\(389\) 15.7186 0.796965 0.398483 0.917176i \(-0.369537\pi\)
0.398483 + 0.917176i \(0.369537\pi\)
\(390\) 0.205721 0.0104171
\(391\) −36.8588 −1.86403
\(392\) 2.07846 0.104978
\(393\) 0.876923 0.0442349
\(394\) −31.0060 −1.56206
\(395\) −0.579703 −0.0291680
\(396\) −1.33298 −0.0669845
\(397\) −17.4261 −0.874591 −0.437295 0.899318i \(-0.644064\pi\)
−0.437295 + 0.899318i \(0.644064\pi\)
\(398\) 47.5290 2.38241
\(399\) −0.607254 −0.0304007
\(400\) 21.9377 1.09688
\(401\) 8.64815 0.431868 0.215934 0.976408i \(-0.430720\pi\)
0.215934 + 0.976408i \(0.430720\pi\)
\(402\) 3.84289 0.191666
\(403\) −2.15265 −0.107231
\(404\) −17.8724 −0.889186
\(405\) 4.19167 0.208286
\(406\) 8.27958 0.410909
\(407\) 2.31055 0.114530
\(408\) −0.662131 −0.0327804
\(409\) 2.61074 0.129093 0.0645463 0.997915i \(-0.479440\pi\)
0.0645463 + 0.997915i \(0.479440\pi\)
\(410\) −2.11729 −0.104566
\(411\) 3.84461 0.189641
\(412\) 13.1333 0.647031
\(413\) 7.87686 0.387595
\(414\) 42.6230 2.09481
\(415\) −1.94094 −0.0952768
\(416\) −8.53689 −0.418555
\(417\) −1.34431 −0.0658311
\(418\) 0.525797 0.0257176
\(419\) −34.5804 −1.68936 −0.844681 0.535270i \(-0.820210\pi\)
−0.844681 + 0.535270i \(0.820210\pi\)
\(420\) 0.478736 0.0233599
\(421\) 3.83716 0.187012 0.0935060 0.995619i \(-0.470193\pi\)
0.0935060 + 0.995619i \(0.470193\pi\)
\(422\) 14.4176 0.701840
\(423\) −9.66986 −0.470165
\(424\) −3.09951 −0.150526
\(425\) 23.2677 1.12865
\(426\) 2.34916 0.113817
\(427\) 26.9043 1.30199
\(428\) −17.5429 −0.847968
\(429\) −0.0616147 −0.00297479
\(430\) 6.75386 0.325700
\(431\) −16.7423 −0.806449 −0.403225 0.915101i \(-0.632111\pi\)
−0.403225 + 0.915101i \(0.632111\pi\)
\(432\) 5.28372 0.254213
\(433\) −2.86215 −0.137546 −0.0687730 0.997632i \(-0.521908\pi\)
−0.0687730 + 0.997632i \(0.521908\pi\)
\(434\) −11.1552 −0.535467
\(435\) −0.128251 −0.00614916
\(436\) −23.5610 −1.12837
\(437\) −7.55013 −0.361172
\(438\) −3.04958 −0.145715
\(439\) 13.9130 0.664034 0.332017 0.943273i \(-0.392271\pi\)
0.332017 + 0.943273i \(0.392271\pi\)
\(440\) 0.0940218 0.00448232
\(441\) −8.74107 −0.416242
\(442\) −10.7878 −0.513122
\(443\) −24.0423 −1.14228 −0.571141 0.820852i \(-0.693499\pi\)
−0.571141 + 0.820852i \(0.693499\pi\)
\(444\) 2.62766 0.124703
\(445\) −6.98277 −0.331015
\(446\) 40.6196 1.92340
\(447\) 1.28606 0.0608288
\(448\) −15.2007 −0.718167
\(449\) 6.22590 0.293818 0.146909 0.989150i \(-0.453068\pi\)
0.146909 + 0.989150i \(0.453068\pi\)
\(450\) −26.9065 −1.26838
\(451\) 0.634143 0.0298606
\(452\) −23.1845 −1.09051
\(453\) −2.26863 −0.106590
\(454\) −29.7977 −1.39848
\(455\) −1.76917 −0.0829399
\(456\) −0.135630 −0.00635147
\(457\) 20.7843 0.972250 0.486125 0.873889i \(-0.338410\pi\)
0.486125 + 0.873889i \(0.338410\pi\)
\(458\) 11.7336 0.548274
\(459\) 5.60407 0.261576
\(460\) 5.95223 0.277524
\(461\) −23.0718 −1.07456 −0.537281 0.843403i \(-0.680548\pi\)
−0.537281 + 0.843403i \(0.680548\pi\)
\(462\) −0.319292 −0.0148548
\(463\) −23.8808 −1.10983 −0.554917 0.831906i \(-0.687250\pi\)
−0.554917 + 0.831906i \(0.687250\pi\)
\(464\) 6.34089 0.294368
\(465\) 0.172794 0.00801315
\(466\) 25.6664 1.18897
\(467\) −31.0463 −1.43665 −0.718326 0.695707i \(-0.755091\pi\)
−0.718326 + 0.695707i \(0.755091\pi\)
\(468\) 5.60207 0.258956
\(469\) −33.0483 −1.52603
\(470\) −3.00706 −0.138705
\(471\) 0.312487 0.0143986
\(472\) 1.75930 0.0809782
\(473\) −2.02283 −0.0930097
\(474\) 0.439695 0.0201959
\(475\) 4.76614 0.218686
\(476\) −25.1044 −1.15066
\(477\) 13.0351 0.596838
\(478\) −20.5534 −0.940093
\(479\) −37.9564 −1.73427 −0.867137 0.498070i \(-0.834042\pi\)
−0.867137 + 0.498070i \(0.834042\pi\)
\(480\) 0.685260 0.0312777
\(481\) −9.71051 −0.442761
\(482\) 22.8775 1.04204
\(483\) 4.58485 0.208618
\(484\) −17.8084 −0.809471
\(485\) 1.56672 0.0711412
\(486\) −9.74084 −0.441853
\(487\) −26.8893 −1.21847 −0.609236 0.792989i \(-0.708524\pi\)
−0.609236 + 0.792989i \(0.708524\pi\)
\(488\) 6.00909 0.272019
\(489\) 1.25551 0.0567761
\(490\) −2.71823 −0.122797
\(491\) −31.1045 −1.40373 −0.701863 0.712312i \(-0.747648\pi\)
−0.701863 + 0.712312i \(0.747648\pi\)
\(492\) 0.721176 0.0325131
\(493\) 6.72534 0.302894
\(494\) −2.20976 −0.0994217
\(495\) −0.395413 −0.0177725
\(496\) −8.54318 −0.383600
\(497\) −20.2024 −0.906202
\(498\) 1.47217 0.0659694
\(499\) −6.15626 −0.275592 −0.137796 0.990461i \(-0.544002\pi\)
−0.137796 + 0.990461i \(0.544002\pi\)
\(500\) −7.69925 −0.344321
\(501\) 4.19316 0.187337
\(502\) 34.9127 1.55823
\(503\) −33.9425 −1.51342 −0.756710 0.653750i \(-0.773195\pi\)
−0.756710 + 0.653750i \(0.773195\pi\)
\(504\) −6.58473 −0.293307
\(505\) −5.30166 −0.235921
\(506\) −3.96983 −0.176481
\(507\) −2.24370 −0.0996462
\(508\) 13.2693 0.588729
\(509\) 3.12900 0.138690 0.0693452 0.997593i \(-0.477909\pi\)
0.0693452 + 0.997593i \(0.477909\pi\)
\(510\) 0.865940 0.0383445
\(511\) 26.2260 1.16017
\(512\) −27.3945 −1.21068
\(513\) 1.14793 0.0506825
\(514\) −17.2417 −0.760497
\(515\) 3.89585 0.171672
\(516\) −2.30045 −0.101272
\(517\) 0.900634 0.0396098
\(518\) −50.3206 −2.21096
\(519\) 0.265248 0.0116431
\(520\) −0.395144 −0.0173282
\(521\) 31.8977 1.39746 0.698732 0.715383i \(-0.253748\pi\)
0.698732 + 0.715383i \(0.253748\pi\)
\(522\) −7.77708 −0.340394
\(523\) 7.24919 0.316985 0.158492 0.987360i \(-0.449337\pi\)
0.158492 + 0.987360i \(0.449337\pi\)
\(524\) 7.42598 0.324406
\(525\) −2.89426 −0.126316
\(526\) 36.4896 1.59102
\(527\) −9.06115 −0.394710
\(528\) −0.244529 −0.0106418
\(529\) 34.0044 1.47845
\(530\) 4.05356 0.176076
\(531\) −7.39880 −0.321081
\(532\) −5.14237 −0.222950
\(533\) −2.66510 −0.115438
\(534\) 5.29631 0.229194
\(535\) −5.20392 −0.224985
\(536\) −7.38135 −0.318826
\(537\) 2.88042 0.124299
\(538\) −17.2184 −0.742337
\(539\) 0.814128 0.0350670
\(540\) −0.904987 −0.0389444
\(541\) −23.4682 −1.00898 −0.504489 0.863418i \(-0.668319\pi\)
−0.504489 + 0.863418i \(0.668319\pi\)
\(542\) 49.6925 2.13447
\(543\) −2.35509 −0.101067
\(544\) −35.9343 −1.54067
\(545\) −6.98913 −0.299381
\(546\) 1.34188 0.0574274
\(547\) −4.06876 −0.173968 −0.0869838 0.996210i \(-0.527723\pi\)
−0.0869838 + 0.996210i \(0.527723\pi\)
\(548\) 32.5570 1.39077
\(549\) −25.2715 −1.07856
\(550\) 2.50602 0.106857
\(551\) 1.37761 0.0586882
\(552\) 1.02403 0.0435855
\(553\) −3.78132 −0.160798
\(554\) −37.2533 −1.58274
\(555\) 0.779467 0.0330865
\(556\) −11.3839 −0.482785
\(557\) 13.7567 0.582889 0.291444 0.956588i \(-0.405864\pi\)
0.291444 + 0.956588i \(0.405864\pi\)
\(558\) 10.4782 0.443577
\(559\) 8.50130 0.359567
\(560\) −7.02126 −0.296702
\(561\) −0.259355 −0.0109500
\(562\) −26.6302 −1.12333
\(563\) 21.5907 0.909939 0.454969 0.890507i \(-0.349650\pi\)
0.454969 + 0.890507i \(0.349650\pi\)
\(564\) 1.02424 0.0431283
\(565\) −6.87742 −0.289335
\(566\) 29.6006 1.24421
\(567\) 27.3417 1.14824
\(568\) −4.51221 −0.189328
\(569\) −10.5882 −0.443879 −0.221940 0.975060i \(-0.571239\pi\)
−0.221940 + 0.975060i \(0.571239\pi\)
\(570\) 0.177378 0.00742956
\(571\) −10.6935 −0.447510 −0.223755 0.974645i \(-0.571832\pi\)
−0.223755 + 0.974645i \(0.571832\pi\)
\(572\) −0.521767 −0.0218162
\(573\) −1.17560 −0.0491115
\(574\) −13.8108 −0.576450
\(575\) −35.9850 −1.50068
\(576\) 14.2782 0.594924
\(577\) −31.9517 −1.33016 −0.665082 0.746770i \(-0.731604\pi\)
−0.665082 + 0.746770i \(0.731604\pi\)
\(578\) −13.0186 −0.541502
\(579\) −2.17299 −0.0903063
\(580\) −1.08606 −0.0450960
\(581\) −12.6604 −0.525243
\(582\) −1.18833 −0.0492580
\(583\) −1.21407 −0.0502816
\(584\) 5.85757 0.242388
\(585\) 1.66180 0.0687068
\(586\) −51.1782 −2.11415
\(587\) 5.49886 0.226962 0.113481 0.993540i \(-0.463800\pi\)
0.113481 + 0.993540i \(0.463800\pi\)
\(588\) 0.925863 0.0381819
\(589\) −1.85608 −0.0764784
\(590\) −2.30082 −0.0947233
\(591\) 3.13282 0.128867
\(592\) −38.5379 −1.58390
\(593\) 13.5925 0.558178 0.279089 0.960265i \(-0.409968\pi\)
0.279089 + 0.960265i \(0.409968\pi\)
\(594\) 0.603580 0.0247652
\(595\) −7.44696 −0.305296
\(596\) 10.8907 0.446100
\(597\) −4.80228 −0.196544
\(598\) 16.6840 0.682257
\(599\) 34.4227 1.40647 0.703236 0.710957i \(-0.251738\pi\)
0.703236 + 0.710957i \(0.251738\pi\)
\(600\) −0.646433 −0.0263905
\(601\) −5.73276 −0.233844 −0.116922 0.993141i \(-0.537303\pi\)
−0.116922 + 0.993141i \(0.537303\pi\)
\(602\) 44.0544 1.79552
\(603\) 31.0426 1.26415
\(604\) −19.2113 −0.781697
\(605\) −5.28266 −0.214771
\(606\) 4.02122 0.163351
\(607\) 43.9158 1.78249 0.891244 0.453524i \(-0.149833\pi\)
0.891244 + 0.453524i \(0.149833\pi\)
\(608\) −7.36075 −0.298518
\(609\) −0.836561 −0.0338992
\(610\) −7.85873 −0.318191
\(611\) −3.78508 −0.153128
\(612\) 23.5808 0.953197
\(613\) 7.03264 0.284046 0.142023 0.989863i \(-0.454639\pi\)
0.142023 + 0.989863i \(0.454639\pi\)
\(614\) 27.9655 1.12860
\(615\) 0.213929 0.00862645
\(616\) 0.613290 0.0247102
\(617\) −38.7033 −1.55814 −0.779068 0.626940i \(-0.784307\pi\)
−0.779068 + 0.626940i \(0.784307\pi\)
\(618\) −2.95494 −0.118865
\(619\) −45.5247 −1.82979 −0.914896 0.403690i \(-0.867728\pi\)
−0.914896 + 0.403690i \(0.867728\pi\)
\(620\) 1.46326 0.0587660
\(621\) −8.66704 −0.347796
\(622\) 6.66086 0.267076
\(623\) −45.5475 −1.82482
\(624\) 1.02768 0.0411400
\(625\) 21.5468 0.861872
\(626\) 34.9333 1.39622
\(627\) −0.0531260 −0.00212165
\(628\) 2.64621 0.105595
\(629\) −40.8744 −1.62977
\(630\) 8.61155 0.343092
\(631\) 43.2374 1.72125 0.860627 0.509236i \(-0.170072\pi\)
0.860627 + 0.509236i \(0.170072\pi\)
\(632\) −0.844558 −0.0335947
\(633\) −1.45674 −0.0579004
\(634\) 1.90532 0.0756698
\(635\) 3.93619 0.156203
\(636\) −1.38069 −0.0547481
\(637\) −3.42152 −0.135566
\(638\) 0.724344 0.0286770
\(639\) 18.9763 0.750691
\(640\) −2.67905 −0.105899
\(641\) 22.6887 0.896148 0.448074 0.893996i \(-0.352110\pi\)
0.448074 + 0.893996i \(0.352110\pi\)
\(642\) 3.94708 0.155779
\(643\) 32.4261 1.27876 0.639379 0.768891i \(-0.279191\pi\)
0.639379 + 0.768891i \(0.279191\pi\)
\(644\) 38.8255 1.52994
\(645\) −0.682404 −0.0268696
\(646\) −9.30153 −0.365964
\(647\) 19.2569 0.757066 0.378533 0.925588i \(-0.376429\pi\)
0.378533 + 0.925588i \(0.376429\pi\)
\(648\) 6.10676 0.239896
\(649\) 0.689111 0.0270500
\(650\) −10.5320 −0.413100
\(651\) 1.12711 0.0441750
\(652\) 10.6319 0.416378
\(653\) −10.3758 −0.406036 −0.203018 0.979175i \(-0.565075\pi\)
−0.203018 + 0.979175i \(0.565075\pi\)
\(654\) 5.30114 0.207291
\(655\) 2.20284 0.0860720
\(656\) −10.5769 −0.412960
\(657\) −24.6343 −0.961075
\(658\) −19.6146 −0.764656
\(659\) 11.6409 0.453466 0.226733 0.973957i \(-0.427195\pi\)
0.226733 + 0.973957i \(0.427195\pi\)
\(660\) 0.0418825 0.00163027
\(661\) −41.2231 −1.60339 −0.801696 0.597733i \(-0.796068\pi\)
−0.801696 + 0.597733i \(0.796068\pi\)
\(662\) −13.2520 −0.515052
\(663\) 1.08999 0.0423316
\(664\) −2.82771 −0.109736
\(665\) −1.52543 −0.0591536
\(666\) 47.2666 1.83154
\(667\) −10.4011 −0.402734
\(668\) 35.5086 1.37387
\(669\) −4.10417 −0.158676
\(670\) 9.65338 0.372942
\(671\) 2.35374 0.0908652
\(672\) 4.46985 0.172428
\(673\) 34.2744 1.32118 0.660591 0.750746i \(-0.270306\pi\)
0.660591 + 0.750746i \(0.270306\pi\)
\(674\) 2.38596 0.0919036
\(675\) 5.47121 0.210587
\(676\) −19.0001 −0.730775
\(677\) 20.4310 0.785228 0.392614 0.919703i \(-0.371571\pi\)
0.392614 + 0.919703i \(0.371571\pi\)
\(678\) 5.21641 0.200335
\(679\) 10.2195 0.392188
\(680\) −1.66328 −0.0637838
\(681\) 3.01074 0.115372
\(682\) −0.975920 −0.0373699
\(683\) −22.2896 −0.852888 −0.426444 0.904514i \(-0.640234\pi\)
−0.426444 + 0.904514i \(0.640234\pi\)
\(684\) 4.83027 0.184690
\(685\) 9.65769 0.369001
\(686\) 24.3401 0.929308
\(687\) −1.18555 −0.0452315
\(688\) 33.7389 1.28628
\(689\) 5.10235 0.194384
\(690\) −1.33923 −0.0509836
\(691\) −7.67977 −0.292152 −0.146076 0.989273i \(-0.546664\pi\)
−0.146076 + 0.989273i \(0.546664\pi\)
\(692\) 2.24618 0.0853869
\(693\) −2.57922 −0.0979764
\(694\) −58.2744 −2.21206
\(695\) −3.37692 −0.128094
\(696\) −0.186846 −0.00708238
\(697\) −11.2182 −0.424920
\(698\) −14.8450 −0.561893
\(699\) −2.59330 −0.0980878
\(700\) −24.5092 −0.926362
\(701\) 21.3710 0.807173 0.403587 0.914941i \(-0.367763\pi\)
0.403587 + 0.914941i \(0.367763\pi\)
\(702\) −2.53665 −0.0957398
\(703\) −8.37268 −0.315782
\(704\) −1.32985 −0.0501204
\(705\) 0.303830 0.0114429
\(706\) −33.3461 −1.25500
\(707\) −34.5820 −1.30059
\(708\) 0.783688 0.0294528
\(709\) −7.56456 −0.284093 −0.142046 0.989860i \(-0.545368\pi\)
−0.142046 + 0.989860i \(0.545368\pi\)
\(710\) 5.90110 0.221464
\(711\) 3.55182 0.133204
\(712\) −10.1730 −0.381251
\(713\) 14.0136 0.524814
\(714\) 5.64839 0.211386
\(715\) −0.154777 −0.00578832
\(716\) 24.3921 0.911574
\(717\) 2.07670 0.0775558
\(718\) 60.7100 2.26568
\(719\) 34.6906 1.29374 0.646870 0.762600i \(-0.276077\pi\)
0.646870 + 0.762600i \(0.276077\pi\)
\(720\) 6.59513 0.245786
\(721\) 25.4120 0.946394
\(722\) −1.90532 −0.0709085
\(723\) −2.31152 −0.0859662
\(724\) −19.9434 −0.741192
\(725\) 6.56589 0.243851
\(726\) 4.00681 0.148707
\(727\) −11.1343 −0.412949 −0.206475 0.978452i \(-0.566199\pi\)
−0.206475 + 0.978452i \(0.566199\pi\)
\(728\) −2.57746 −0.0955272
\(729\) −25.0193 −0.926640
\(730\) −7.66057 −0.283531
\(731\) 35.7845 1.32354
\(732\) 2.67678 0.0989366
\(733\) −42.0339 −1.55256 −0.776279 0.630390i \(-0.782895\pi\)
−0.776279 + 0.630390i \(0.782895\pi\)
\(734\) 38.1152 1.40686
\(735\) 0.274647 0.0101305
\(736\) 55.5746 2.04851
\(737\) −2.89125 −0.106501
\(738\) 12.9726 0.477527
\(739\) 13.7933 0.507394 0.253697 0.967284i \(-0.418353\pi\)
0.253697 + 0.967284i \(0.418353\pi\)
\(740\) 6.60070 0.242647
\(741\) 0.223272 0.00820209
\(742\) 26.4408 0.970671
\(743\) −46.6466 −1.71130 −0.855648 0.517558i \(-0.826841\pi\)
−0.855648 + 0.517558i \(0.826841\pi\)
\(744\) 0.251740 0.00922925
\(745\) 3.23060 0.118360
\(746\) −10.0190 −0.366823
\(747\) 11.8921 0.435107
\(748\) −2.19627 −0.0803038
\(749\) −33.9444 −1.24030
\(750\) 1.73230 0.0632547
\(751\) 32.0437 1.16929 0.584646 0.811289i \(-0.301233\pi\)
0.584646 + 0.811289i \(0.301233\pi\)
\(752\) −15.0218 −0.547787
\(753\) −3.52754 −0.128551
\(754\) −3.04419 −0.110863
\(755\) −5.69883 −0.207402
\(756\) −5.90309 −0.214693
\(757\) −15.9303 −0.578996 −0.289498 0.957179i \(-0.593488\pi\)
−0.289498 + 0.957179i \(0.593488\pi\)
\(758\) −37.5690 −1.36457
\(759\) 0.401108 0.0145593
\(760\) −0.340704 −0.0123586
\(761\) −32.0099 −1.16036 −0.580178 0.814489i \(-0.697017\pi\)
−0.580178 + 0.814489i \(0.697017\pi\)
\(762\) −2.98553 −0.108154
\(763\) −45.5890 −1.65043
\(764\) −9.95527 −0.360169
\(765\) 6.99499 0.252905
\(766\) 3.43982 0.124286
\(767\) −2.89612 −0.104573
\(768\) 3.88741 0.140275
\(769\) −47.5896 −1.71613 −0.858063 0.513545i \(-0.828332\pi\)
−0.858063 + 0.513545i \(0.828332\pi\)
\(770\) −0.802065 −0.0289044
\(771\) 1.74208 0.0627395
\(772\) −18.4013 −0.662279
\(773\) 24.1627 0.869073 0.434537 0.900654i \(-0.356912\pi\)
0.434537 + 0.900654i \(0.356912\pi\)
\(774\) −41.3807 −1.48740
\(775\) −8.84633 −0.317770
\(776\) 2.28252 0.0819378
\(777\) 5.08435 0.182400
\(778\) −29.9489 −1.07372
\(779\) −2.29793 −0.0823318
\(780\) −0.176019 −0.00630249
\(781\) −1.76742 −0.0632433
\(782\) 70.2277 2.51134
\(783\) 1.58141 0.0565148
\(784\) −13.5789 −0.484961
\(785\) 0.784970 0.0280168
\(786\) −1.67082 −0.0595960
\(787\) −36.4965 −1.30096 −0.650479 0.759524i \(-0.725432\pi\)
−0.650479 + 0.759524i \(0.725432\pi\)
\(788\) 26.5294 0.945072
\(789\) −3.68687 −0.131256
\(790\) 1.10452 0.0392970
\(791\) −44.8604 −1.59505
\(792\) −0.576069 −0.0204697
\(793\) −9.89203 −0.351276
\(794\) 33.2022 1.17830
\(795\) −0.409568 −0.0145259
\(796\) −40.6668 −1.44140
\(797\) −56.1672 −1.98954 −0.994771 0.102126i \(-0.967435\pi\)
−0.994771 + 0.102126i \(0.967435\pi\)
\(798\) 1.15701 0.0409578
\(799\) −15.9325 −0.563652
\(800\) −35.0824 −1.24035
\(801\) 42.7832 1.51167
\(802\) −16.4775 −0.581840
\(803\) 2.29439 0.0809674
\(804\) −3.28806 −0.115961
\(805\) 11.5172 0.405927
\(806\) 4.10148 0.144469
\(807\) 1.73973 0.0612413
\(808\) −7.72388 −0.271725
\(809\) 33.5262 1.17872 0.589359 0.807872i \(-0.299381\pi\)
0.589359 + 0.807872i \(0.299381\pi\)
\(810\) −7.98646 −0.280616
\(811\) −2.38310 −0.0836819 −0.0418409 0.999124i \(-0.513322\pi\)
−0.0418409 + 0.999124i \(0.513322\pi\)
\(812\) −7.08418 −0.248606
\(813\) −5.02088 −0.176090
\(814\) −4.40233 −0.154302
\(815\) 3.15385 0.110474
\(816\) 4.32580 0.151433
\(817\) 7.33007 0.256447
\(818\) −4.97428 −0.173922
\(819\) 10.8396 0.378768
\(820\) 1.81160 0.0632638
\(821\) −28.5564 −0.996625 −0.498312 0.866998i \(-0.666047\pi\)
−0.498312 + 0.866998i \(0.666047\pi\)
\(822\) −7.32519 −0.255495
\(823\) 29.2610 1.01998 0.509988 0.860182i \(-0.329650\pi\)
0.509988 + 0.860182i \(0.329650\pi\)
\(824\) 5.67578 0.197725
\(825\) −0.253206 −0.00881550
\(826\) −15.0079 −0.522192
\(827\) 40.6414 1.41324 0.706620 0.707593i \(-0.250219\pi\)
0.706620 + 0.707593i \(0.250219\pi\)
\(828\) −36.4691 −1.26739
\(829\) −46.1735 −1.60367 −0.801836 0.597545i \(-0.796143\pi\)
−0.801836 + 0.597545i \(0.796143\pi\)
\(830\) 3.69810 0.128363
\(831\) 3.76404 0.130573
\(832\) 5.58892 0.193761
\(833\) −14.4022 −0.499007
\(834\) 2.56133 0.0886918
\(835\) 10.5333 0.364518
\(836\) −0.449883 −0.0155595
\(837\) −2.13065 −0.0736461
\(838\) 65.8866 2.27601
\(839\) −39.8820 −1.37688 −0.688439 0.725294i \(-0.741704\pi\)
−0.688439 + 0.725294i \(0.741704\pi\)
\(840\) 0.206894 0.00713853
\(841\) −27.1022 −0.934558
\(842\) −7.31101 −0.251954
\(843\) 2.69069 0.0926722
\(844\) −12.3360 −0.424624
\(845\) −5.63619 −0.193891
\(846\) 18.4241 0.633435
\(847\) −34.4580 −1.18399
\(848\) 20.2496 0.695373
\(849\) −2.99082 −0.102645
\(850\) −44.3324 −1.52059
\(851\) 63.2148 2.16698
\(852\) −2.00999 −0.0688611
\(853\) −12.0596 −0.412911 −0.206456 0.978456i \(-0.566193\pi\)
−0.206456 + 0.978456i \(0.566193\pi\)
\(854\) −51.2613 −1.75412
\(855\) 1.43285 0.0490024
\(856\) −7.58148 −0.259129
\(857\) −14.5354 −0.496520 −0.248260 0.968693i \(-0.579859\pi\)
−0.248260 + 0.968693i \(0.579859\pi\)
\(858\) 0.117396 0.00400782
\(859\) 33.3997 1.13958 0.569792 0.821789i \(-0.307024\pi\)
0.569792 + 0.821789i \(0.307024\pi\)
\(860\) −5.77875 −0.197054
\(861\) 1.39543 0.0475560
\(862\) 31.8994 1.08650
\(863\) −38.8927 −1.32392 −0.661962 0.749537i \(-0.730276\pi\)
−0.661962 + 0.749537i \(0.730276\pi\)
\(864\) −8.44965 −0.287463
\(865\) 0.666305 0.0226550
\(866\) 5.45330 0.185311
\(867\) 1.31539 0.0446728
\(868\) 9.54463 0.323966
\(869\) −0.330811 −0.0112220
\(870\) 0.244358 0.00828452
\(871\) 12.1510 0.411721
\(872\) −10.1823 −0.344817
\(873\) −9.59925 −0.324886
\(874\) 14.3854 0.486593
\(875\) −14.8975 −0.503629
\(876\) 2.60929 0.0881596
\(877\) −51.0238 −1.72295 −0.861475 0.507799i \(-0.830459\pi\)
−0.861475 + 0.507799i \(0.830459\pi\)
\(878\) −26.5087 −0.894627
\(879\) 5.17099 0.174413
\(880\) −0.614259 −0.0207067
\(881\) 7.84432 0.264282 0.132141 0.991231i \(-0.457815\pi\)
0.132141 + 0.991231i \(0.457815\pi\)
\(882\) 16.6545 0.560786
\(883\) 31.0420 1.04465 0.522323 0.852748i \(-0.325066\pi\)
0.522323 + 0.852748i \(0.325066\pi\)
\(884\) 9.23025 0.310447
\(885\) 0.232473 0.00781448
\(886\) 45.8081 1.53895
\(887\) 7.90835 0.265536 0.132768 0.991147i \(-0.457613\pi\)
0.132768 + 0.991147i \(0.457613\pi\)
\(888\) 1.13559 0.0381079
\(889\) 25.6752 0.861118
\(890\) 13.3044 0.445964
\(891\) 2.39200 0.0801350
\(892\) −34.7550 −1.16368
\(893\) −3.26360 −0.109212
\(894\) −2.45036 −0.0819523
\(895\) 7.23565 0.241861
\(896\) −17.4750 −0.583800
\(897\) −1.68573 −0.0562849
\(898\) −11.8623 −0.395850
\(899\) −2.55695 −0.0852792
\(900\) 23.0217 0.767391
\(901\) 21.4773 0.715513
\(902\) −1.20824 −0.0402301
\(903\) −4.45121 −0.148127
\(904\) −10.0196 −0.333246
\(905\) −5.91601 −0.196655
\(906\) 4.32247 0.143604
\(907\) −16.6993 −0.554492 −0.277246 0.960799i \(-0.589422\pi\)
−0.277246 + 0.960799i \(0.589422\pi\)
\(908\) 25.4956 0.846101
\(909\) 32.4831 1.07740
\(910\) 3.37083 0.111742
\(911\) −6.94656 −0.230150 −0.115075 0.993357i \(-0.536711\pi\)
−0.115075 + 0.993357i \(0.536711\pi\)
\(912\) 0.886093 0.0293415
\(913\) −1.10761 −0.0366564
\(914\) −39.6007 −1.30988
\(915\) 0.794038 0.0262501
\(916\) −10.0395 −0.331714
\(917\) 14.3688 0.474499
\(918\) −10.6775 −0.352411
\(919\) −19.6077 −0.646798 −0.323399 0.946263i \(-0.604826\pi\)
−0.323399 + 0.946263i \(0.604826\pi\)
\(920\) 2.57236 0.0848083
\(921\) −2.82561 −0.0931069
\(922\) 43.9591 1.44772
\(923\) 7.42791 0.244492
\(924\) 0.273193 0.00898740
\(925\) −39.9054 −1.31208
\(926\) 45.5004 1.49524
\(927\) −23.8697 −0.783985
\(928\) −10.1403 −0.332870
\(929\) −13.9927 −0.459085 −0.229542 0.973299i \(-0.573723\pi\)
−0.229542 + 0.973299i \(0.573723\pi\)
\(930\) −0.329228 −0.0107958
\(931\) −2.95014 −0.0966868
\(932\) −21.9607 −0.719346
\(933\) −0.673007 −0.0220332
\(934\) 59.1530 1.93555
\(935\) −0.651502 −0.0213064
\(936\) 2.42103 0.0791340
\(937\) −41.9479 −1.37038 −0.685190 0.728365i \(-0.740281\pi\)
−0.685190 + 0.728365i \(0.740281\pi\)
\(938\) 62.9675 2.05596
\(939\) −3.52963 −0.115185
\(940\) 2.57290 0.0839188
\(941\) 22.0640 0.719265 0.359633 0.933094i \(-0.382902\pi\)
0.359633 + 0.933094i \(0.382902\pi\)
\(942\) −0.595386 −0.0193987
\(943\) 17.3497 0.564982
\(944\) −11.4937 −0.374090
\(945\) −1.75109 −0.0569629
\(946\) 3.85413 0.125308
\(947\) −12.5010 −0.406227 −0.203113 0.979155i \(-0.565106\pi\)
−0.203113 + 0.979155i \(0.565106\pi\)
\(948\) −0.376213 −0.0122188
\(949\) −9.64261 −0.313012
\(950\) −9.08100 −0.294627
\(951\) −0.192511 −0.00624261
\(952\) −10.8493 −0.351628
\(953\) −34.5045 −1.11771 −0.558856 0.829265i \(-0.688759\pi\)
−0.558856 + 0.829265i \(0.688759\pi\)
\(954\) −24.8360 −0.804097
\(955\) −2.95312 −0.0955608
\(956\) 17.5860 0.568771
\(957\) −0.0731870 −0.00236580
\(958\) 72.3190 2.33652
\(959\) 62.9956 2.03423
\(960\) −0.448625 −0.0144793
\(961\) −27.5550 −0.888870
\(962\) 18.5016 0.596515
\(963\) 31.8842 1.02745
\(964\) −19.5744 −0.630450
\(965\) −5.45856 −0.175717
\(966\) −8.73559 −0.281063
\(967\) −1.17818 −0.0378878 −0.0189439 0.999821i \(-0.506030\pi\)
−0.0189439 + 0.999821i \(0.506030\pi\)
\(968\) −7.69620 −0.247365
\(969\) 0.939817 0.0301913
\(970\) −2.98510 −0.0958458
\(971\) 37.2248 1.19460 0.597301 0.802017i \(-0.296240\pi\)
0.597301 + 0.802017i \(0.296240\pi\)
\(972\) 8.33447 0.267328
\(973\) −22.0271 −0.706157
\(974\) 51.2327 1.64160
\(975\) 1.06414 0.0340799
\(976\) −39.2583 −1.25663
\(977\) −12.6335 −0.404182 −0.202091 0.979367i \(-0.564774\pi\)
−0.202091 + 0.979367i \(0.564774\pi\)
\(978\) −2.39214 −0.0764922
\(979\) −3.98475 −0.127353
\(980\) 2.32577 0.0742942
\(981\) 42.8222 1.36721
\(982\) 59.2639 1.89119
\(983\) 22.7119 0.724398 0.362199 0.932101i \(-0.382026\pi\)
0.362199 + 0.932101i \(0.382026\pi\)
\(984\) 0.311669 0.00993564
\(985\) 7.86967 0.250749
\(986\) −12.8139 −0.408077
\(987\) 1.98184 0.0630826
\(988\) 1.89071 0.0601516
\(989\) −55.3429 −1.75980
\(990\) 0.753387 0.0239442
\(991\) −3.85710 −0.122525 −0.0612623 0.998122i \(-0.519513\pi\)
−0.0612623 + 0.998122i \(0.519513\pi\)
\(992\) 13.6621 0.433773
\(993\) 1.33896 0.0424907
\(994\) 38.4920 1.22089
\(995\) −12.0634 −0.382435
\(996\) −1.25962 −0.0399125
\(997\) −24.1860 −0.765977 −0.382989 0.923753i \(-0.625105\pi\)
−0.382989 + 0.923753i \(0.625105\pi\)
\(998\) 11.7296 0.371294
\(999\) −9.61128 −0.304087
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 \(a_p\))