Properties

Label 4019.2.a.b.1.1
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.80607 q^{2}\) \(-1.31751 q^{3}\) \(+5.87400 q^{4}\) \(-0.399238 q^{5}\) \(+3.69703 q^{6}\) \(-2.36747 q^{7}\) \(-10.8707 q^{8}\) \(-1.26416 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.80607 q^{2}\) \(-1.31751 q^{3}\) \(+5.87400 q^{4}\) \(-0.399238 q^{5}\) \(+3.69703 q^{6}\) \(-2.36747 q^{7}\) \(-10.8707 q^{8}\) \(-1.26416 q^{9}\) \(+1.12029 q^{10}\) \(+2.46090 q^{11}\) \(-7.73907 q^{12}\) \(-3.67009 q^{13}\) \(+6.64328 q^{14}\) \(+0.526001 q^{15}\) \(+18.7559 q^{16}\) \(+0.403400 q^{17}\) \(+3.54731 q^{18}\) \(-3.40499 q^{19}\) \(-2.34512 q^{20}\) \(+3.11918 q^{21}\) \(-6.90544 q^{22}\) \(-1.68571 q^{23}\) \(+14.3223 q^{24}\) \(-4.84061 q^{25}\) \(+10.2985 q^{26}\) \(+5.61809 q^{27}\) \(-13.9065 q^{28}\) \(+4.26751 q^{29}\) \(-1.47599 q^{30}\) \(+7.68319 q^{31}\) \(-30.8888 q^{32}\) \(-3.24227 q^{33}\) \(-1.13197 q^{34}\) \(+0.945184 q^{35}\) \(-7.42567 q^{36}\) \(-4.32879 q^{37}\) \(+9.55462 q^{38}\) \(+4.83540 q^{39}\) \(+4.33999 q^{40}\) \(-9.31616 q^{41}\) \(-8.75261 q^{42}\) \(+5.43144 q^{43}\) \(+14.4553 q^{44}\) \(+0.504700 q^{45}\) \(+4.73023 q^{46}\) \(-10.1972 q^{47}\) \(-24.7111 q^{48}\) \(-1.39507 q^{49}\) \(+13.5831 q^{50}\) \(-0.531485 q^{51}\) \(-21.5581 q^{52}\) \(-11.7397 q^{53}\) \(-15.7647 q^{54}\) \(-0.982484 q^{55}\) \(+25.7361 q^{56}\) \(+4.48612 q^{57}\) \(-11.9749 q^{58}\) \(-12.9488 q^{59}\) \(+3.08973 q^{60}\) \(-9.90635 q^{61}\) \(-21.5595 q^{62}\) \(+2.99286 q^{63}\) \(+49.1643 q^{64}\) \(+1.46524 q^{65}\) \(+9.09801 q^{66}\) \(+11.3238 q^{67}\) \(+2.36957 q^{68}\) \(+2.22095 q^{69}\) \(-2.65225 q^{70}\) \(-5.90895 q^{71}\) \(+13.7423 q^{72}\) \(+12.9985 q^{73}\) \(+12.1469 q^{74}\) \(+6.37757 q^{75}\) \(-20.0009 q^{76}\) \(-5.82611 q^{77}\) \(-13.5684 q^{78}\) \(+1.30020 q^{79}\) \(-7.48806 q^{80}\) \(-3.60943 q^{81}\) \(+26.1417 q^{82}\) \(+1.89580 q^{83}\) \(+18.3220 q^{84}\) \(-0.161053 q^{85}\) \(-15.2410 q^{86}\) \(-5.62250 q^{87}\) \(-26.7517 q^{88}\) \(+7.84277 q^{89}\) \(-1.41622 q^{90}\) \(+8.68885 q^{91}\) \(-9.90189 q^{92}\) \(-10.1227 q^{93}\) \(+28.6139 q^{94}\) \(+1.35940 q^{95}\) \(+40.6965 q^{96}\) \(-13.3027 q^{97}\) \(+3.91467 q^{98}\) \(-3.11097 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.80607 −1.98419 −0.992094 0.125498i \(-0.959947\pi\)
−0.992094 + 0.125498i \(0.959947\pi\)
\(3\) −1.31751 −0.760667 −0.380333 0.924849i \(-0.624191\pi\)
−0.380333 + 0.924849i \(0.624191\pi\)
\(4\) 5.87400 2.93700
\(5\) −0.399238 −0.178545 −0.0892723 0.996007i \(-0.528454\pi\)
−0.0892723 + 0.996007i \(0.528454\pi\)
\(6\) 3.69703 1.50931
\(7\) −2.36747 −0.894820 −0.447410 0.894329i \(-0.647654\pi\)
−0.447410 + 0.894329i \(0.647654\pi\)
\(8\) −10.8707 −3.84337
\(9\) −1.26416 −0.421386
\(10\) 1.12029 0.354266
\(11\) 2.46090 0.741989 0.370995 0.928635i \(-0.379017\pi\)
0.370995 + 0.928635i \(0.379017\pi\)
\(12\) −7.73907 −2.23408
\(13\) −3.67009 −1.01790 −0.508951 0.860796i \(-0.669966\pi\)
−0.508951 + 0.860796i \(0.669966\pi\)
\(14\) 6.64328 1.77549
\(15\) 0.526001 0.135813
\(16\) 18.7559 4.68897
\(17\) 0.403400 0.0978389 0.0489195 0.998803i \(-0.484422\pi\)
0.0489195 + 0.998803i \(0.484422\pi\)
\(18\) 3.54731 0.836109
\(19\) −3.40499 −0.781158 −0.390579 0.920569i \(-0.627725\pi\)
−0.390579 + 0.920569i \(0.627725\pi\)
\(20\) −2.34512 −0.524385
\(21\) 3.11918 0.680660
\(22\) −6.90544 −1.47225
\(23\) −1.68571 −0.351496 −0.175748 0.984435i \(-0.556234\pi\)
−0.175748 + 0.984435i \(0.556234\pi\)
\(24\) 14.3223 2.92353
\(25\) −4.84061 −0.968122
\(26\) 10.2985 2.01971
\(27\) 5.61809 1.08120
\(28\) −13.9065 −2.62809
\(29\) 4.26751 0.792457 0.396228 0.918152i \(-0.370319\pi\)
0.396228 + 0.918152i \(0.370319\pi\)
\(30\) −1.47599 −0.269478
\(31\) 7.68319 1.37994 0.689971 0.723837i \(-0.257623\pi\)
0.689971 + 0.723837i \(0.257623\pi\)
\(32\) −30.8888 −5.46043
\(33\) −3.24227 −0.564406
\(34\) −1.13197 −0.194131
\(35\) 0.945184 0.159765
\(36\) −7.42567 −1.23761
\(37\) −4.32879 −0.711648 −0.355824 0.934553i \(-0.615800\pi\)
−0.355824 + 0.934553i \(0.615800\pi\)
\(38\) 9.55462 1.54996
\(39\) 4.83540 0.774283
\(40\) 4.33999 0.686213
\(41\) −9.31616 −1.45494 −0.727470 0.686140i \(-0.759304\pi\)
−0.727470 + 0.686140i \(0.759304\pi\)
\(42\) −8.75261 −1.35056
\(43\) 5.43144 0.828287 0.414143 0.910212i \(-0.364081\pi\)
0.414143 + 0.910212i \(0.364081\pi\)
\(44\) 14.4553 2.17922
\(45\) 0.504700 0.0752362
\(46\) 4.73023 0.697434
\(47\) −10.1972 −1.48741 −0.743705 0.668508i \(-0.766933\pi\)
−0.743705 + 0.668508i \(0.766933\pi\)
\(48\) −24.7111 −3.56674
\(49\) −1.39507 −0.199296
\(50\) 13.5831 1.92094
\(51\) −0.531485 −0.0744228
\(52\) −21.5581 −2.98958
\(53\) −11.7397 −1.61257 −0.806286 0.591525i \(-0.798526\pi\)
−0.806286 + 0.591525i \(0.798526\pi\)
\(54\) −15.7647 −2.14531
\(55\) −0.982484 −0.132478
\(56\) 25.7361 3.43913
\(57\) 4.48612 0.594201
\(58\) −11.9749 −1.57238
\(59\) −12.9488 −1.68579 −0.842897 0.538075i \(-0.819152\pi\)
−0.842897 + 0.538075i \(0.819152\pi\)
\(60\) 3.08973 0.398883
\(61\) −9.90635 −1.26838 −0.634189 0.773178i \(-0.718666\pi\)
−0.634189 + 0.773178i \(0.718666\pi\)
\(62\) −21.5595 −2.73806
\(63\) 2.99286 0.377065
\(64\) 49.1643 6.14554
\(65\) 1.46524 0.181741
\(66\) 9.09801 1.11989
\(67\) 11.3238 1.38342 0.691711 0.722174i \(-0.256857\pi\)
0.691711 + 0.722174i \(0.256857\pi\)
\(68\) 2.36957 0.287353
\(69\) 2.22095 0.267371
\(70\) −2.65225 −0.317004
\(71\) −5.90895 −0.701263 −0.350631 0.936514i \(-0.614033\pi\)
−0.350631 + 0.936514i \(0.614033\pi\)
\(72\) 13.7423 1.61954
\(73\) 12.9985 1.52136 0.760678 0.649130i \(-0.224867\pi\)
0.760678 + 0.649130i \(0.224867\pi\)
\(74\) 12.1469 1.41204
\(75\) 6.37757 0.736418
\(76\) −20.0009 −2.29426
\(77\) −5.82611 −0.663947
\(78\) −13.5684 −1.53632
\(79\) 1.30020 0.146284 0.0731421 0.997322i \(-0.476697\pi\)
0.0731421 + 0.997322i \(0.476697\pi\)
\(80\) −7.48806 −0.837190
\(81\) −3.60943 −0.401047
\(82\) 26.1417 2.88687
\(83\) 1.89580 0.208091 0.104045 0.994573i \(-0.466821\pi\)
0.104045 + 0.994573i \(0.466821\pi\)
\(84\) 18.3220 1.99910
\(85\) −0.161053 −0.0174686
\(86\) −15.2410 −1.64348
\(87\) −5.62250 −0.602795
\(88\) −26.7517 −2.85174
\(89\) 7.84277 0.831332 0.415666 0.909517i \(-0.363549\pi\)
0.415666 + 0.909517i \(0.363549\pi\)
\(90\) −1.41622 −0.149283
\(91\) 8.68885 0.910839
\(92\) −9.90189 −1.03234
\(93\) −10.1227 −1.04968
\(94\) 28.6139 2.95130
\(95\) 1.35940 0.139472
\(96\) 40.6965 4.15357
\(97\) −13.3027 −1.35068 −0.675342 0.737505i \(-0.736004\pi\)
−0.675342 + 0.737505i \(0.736004\pi\)
\(98\) 3.91467 0.395441
\(99\) −3.11097 −0.312664
\(100\) −28.4337 −2.84337
\(101\) −2.98936 −0.297452 −0.148726 0.988878i \(-0.547517\pi\)
−0.148726 + 0.988878i \(0.547517\pi\)
\(102\) 1.49138 0.147669
\(103\) −3.38243 −0.333281 −0.166640 0.986018i \(-0.553292\pi\)
−0.166640 + 0.986018i \(0.553292\pi\)
\(104\) 39.8965 3.91217
\(105\) −1.24529 −0.121528
\(106\) 32.9424 3.19965
\(107\) −7.50356 −0.725396 −0.362698 0.931907i \(-0.618144\pi\)
−0.362698 + 0.931907i \(0.618144\pi\)
\(108\) 33.0006 3.17549
\(109\) 9.15852 0.877227 0.438613 0.898676i \(-0.355470\pi\)
0.438613 + 0.898676i \(0.355470\pi\)
\(110\) 2.75691 0.262861
\(111\) 5.70324 0.541327
\(112\) −44.4041 −4.19579
\(113\) −5.10977 −0.480687 −0.240343 0.970688i \(-0.577260\pi\)
−0.240343 + 0.970688i \(0.577260\pi\)
\(114\) −12.5883 −1.17901
\(115\) 0.673001 0.0627577
\(116\) 25.0674 2.32745
\(117\) 4.63958 0.428930
\(118\) 36.3353 3.34493
\(119\) −0.955039 −0.0875483
\(120\) −5.71800 −0.521980
\(121\) −4.94397 −0.449452
\(122\) 27.7979 2.51670
\(123\) 12.2742 1.10672
\(124\) 45.1311 4.05289
\(125\) 3.92874 0.351397
\(126\) −8.39816 −0.748168
\(127\) −7.98790 −0.708812 −0.354406 0.935092i \(-0.615317\pi\)
−0.354406 + 0.935092i \(0.615317\pi\)
\(128\) −76.1806 −6.73348
\(129\) −7.15599 −0.630050
\(130\) −4.11156 −0.360608
\(131\) −5.30698 −0.463673 −0.231837 0.972755i \(-0.574473\pi\)
−0.231837 + 0.972755i \(0.574473\pi\)
\(132\) −19.0451 −1.65766
\(133\) 8.06122 0.698996
\(134\) −31.7753 −2.74497
\(135\) −2.24295 −0.193043
\(136\) −4.38524 −0.376031
\(137\) 3.17044 0.270869 0.135435 0.990786i \(-0.456757\pi\)
0.135435 + 0.990786i \(0.456757\pi\)
\(138\) −6.23214 −0.530515
\(139\) 11.9222 1.01123 0.505616 0.862759i \(-0.331265\pi\)
0.505616 + 0.862759i \(0.331265\pi\)
\(140\) 5.55201 0.469231
\(141\) 13.4349 1.13142
\(142\) 16.5809 1.39144
\(143\) −9.03173 −0.755272
\(144\) −23.7104 −1.97587
\(145\) −1.70375 −0.141489
\(146\) −36.4745 −3.01865
\(147\) 1.83803 0.151598
\(148\) −25.4273 −2.09011
\(149\) 19.0771 1.56285 0.781427 0.623997i \(-0.214492\pi\)
0.781427 + 0.623997i \(0.214492\pi\)
\(150\) −17.8959 −1.46119
\(151\) 9.04612 0.736163 0.368081 0.929794i \(-0.380015\pi\)
0.368081 + 0.929794i \(0.380015\pi\)
\(152\) 37.0146 3.00228
\(153\) −0.509962 −0.0412280
\(154\) 16.3484 1.31740
\(155\) −3.06742 −0.246381
\(156\) 28.4031 2.27407
\(157\) −11.2720 −0.899600 −0.449800 0.893129i \(-0.648505\pi\)
−0.449800 + 0.893129i \(0.648505\pi\)
\(158\) −3.64846 −0.290255
\(159\) 15.4672 1.22663
\(160\) 12.3320 0.974930
\(161\) 3.99088 0.314526
\(162\) 10.1283 0.795753
\(163\) −12.8532 −1.00674 −0.503369 0.864071i \(-0.667906\pi\)
−0.503369 + 0.864071i \(0.667906\pi\)
\(164\) −54.7231 −4.27316
\(165\) 1.29444 0.100772
\(166\) −5.31973 −0.412891
\(167\) 16.3194 1.26283 0.631416 0.775444i \(-0.282474\pi\)
0.631416 + 0.775444i \(0.282474\pi\)
\(168\) −33.9076 −2.61603
\(169\) 0.469596 0.0361227
\(170\) 0.451924 0.0346610
\(171\) 4.30445 0.329169
\(172\) 31.9043 2.43268
\(173\) −21.8224 −1.65913 −0.829564 0.558411i \(-0.811411\pi\)
−0.829564 + 0.558411i \(0.811411\pi\)
\(174\) 15.7771 1.19606
\(175\) 11.4600 0.866295
\(176\) 46.1564 3.47917
\(177\) 17.0603 1.28233
\(178\) −22.0073 −1.64952
\(179\) −22.2411 −1.66238 −0.831190 0.555989i \(-0.812340\pi\)
−0.831190 + 0.555989i \(0.812340\pi\)
\(180\) 2.96461 0.220969
\(181\) 12.6304 0.938811 0.469405 0.882983i \(-0.344468\pi\)
0.469405 + 0.882983i \(0.344468\pi\)
\(182\) −24.3815 −1.80728
\(183\) 13.0517 0.964813
\(184\) 18.3249 1.35093
\(185\) 1.72822 0.127061
\(186\) 28.4050 2.08275
\(187\) 0.992727 0.0725954
\(188\) −59.8982 −4.36853
\(189\) −13.3007 −0.967481
\(190\) −3.81457 −0.276738
\(191\) −20.9551 −1.51626 −0.758130 0.652104i \(-0.773887\pi\)
−0.758130 + 0.652104i \(0.773887\pi\)
\(192\) −64.7747 −4.67471
\(193\) 4.98417 0.358768 0.179384 0.983779i \(-0.442590\pi\)
0.179384 + 0.983779i \(0.442590\pi\)
\(194\) 37.3282 2.68001
\(195\) −1.93047 −0.138244
\(196\) −8.19467 −0.585333
\(197\) −14.2455 −1.01495 −0.507475 0.861667i \(-0.669421\pi\)
−0.507475 + 0.861667i \(0.669421\pi\)
\(198\) 8.72958 0.620384
\(199\) 5.18056 0.367240 0.183620 0.982997i \(-0.441218\pi\)
0.183620 + 0.982997i \(0.441218\pi\)
\(200\) 52.6208 3.72085
\(201\) −14.9193 −1.05232
\(202\) 8.38833 0.590201
\(203\) −10.1032 −0.709106
\(204\) −3.12194 −0.218580
\(205\) 3.71936 0.259772
\(206\) 9.49132 0.661292
\(207\) 2.13101 0.148116
\(208\) −68.8359 −4.77291
\(209\) −8.37933 −0.579611
\(210\) 3.49437 0.241135
\(211\) −20.9880 −1.44487 −0.722437 0.691437i \(-0.756978\pi\)
−0.722437 + 0.691437i \(0.756978\pi\)
\(212\) −68.9590 −4.73613
\(213\) 7.78512 0.533427
\(214\) 21.0555 1.43932
\(215\) −2.16844 −0.147886
\(216\) −61.0725 −4.15546
\(217\) −18.1897 −1.23480
\(218\) −25.6994 −1.74058
\(219\) −17.1256 −1.15724
\(220\) −5.77111 −0.389088
\(221\) −1.48052 −0.0995903
\(222\) −16.0037 −1.07409
\(223\) 1.97301 0.132122 0.0660612 0.997816i \(-0.478957\pi\)
0.0660612 + 0.997816i \(0.478957\pi\)
\(224\) 73.1285 4.88610
\(225\) 6.11930 0.407953
\(226\) 14.3383 0.953773
\(227\) −23.8469 −1.58278 −0.791388 0.611314i \(-0.790641\pi\)
−0.791388 + 0.611314i \(0.790641\pi\)
\(228\) 26.3515 1.74517
\(229\) 4.30631 0.284569 0.142285 0.989826i \(-0.454555\pi\)
0.142285 + 0.989826i \(0.454555\pi\)
\(230\) −1.88848 −0.124523
\(231\) 7.67598 0.505042
\(232\) −46.3908 −3.04571
\(233\) −2.52111 −0.165163 −0.0825817 0.996584i \(-0.526317\pi\)
−0.0825817 + 0.996584i \(0.526317\pi\)
\(234\) −13.0190 −0.851077
\(235\) 4.07110 0.265569
\(236\) −76.0614 −4.95118
\(237\) −1.71304 −0.111274
\(238\) 2.67990 0.173712
\(239\) 7.26385 0.469860 0.234930 0.972012i \(-0.424514\pi\)
0.234930 + 0.972012i \(0.424514\pi\)
\(240\) 9.86562 0.636823
\(241\) 13.9609 0.899299 0.449649 0.893205i \(-0.351549\pi\)
0.449649 + 0.893205i \(0.351549\pi\)
\(242\) 13.8731 0.891797
\(243\) −12.0988 −0.776138
\(244\) −58.1899 −3.72523
\(245\) 0.556966 0.0355833
\(246\) −34.4421 −2.19595
\(247\) 12.4966 0.795142
\(248\) −83.5216 −5.30363
\(249\) −2.49774 −0.158288
\(250\) −11.0243 −0.697238
\(251\) −17.8133 −1.12437 −0.562183 0.827013i \(-0.690038\pi\)
−0.562183 + 0.827013i \(0.690038\pi\)
\(252\) 17.5801 1.10744
\(253\) −4.14837 −0.260806
\(254\) 22.4146 1.40642
\(255\) 0.212189 0.0132878
\(256\) 115.439 7.21495
\(257\) 12.3465 0.770152 0.385076 0.922885i \(-0.374175\pi\)
0.385076 + 0.922885i \(0.374175\pi\)
\(258\) 20.0802 1.25014
\(259\) 10.2483 0.636798
\(260\) 8.60682 0.533773
\(261\) −5.39481 −0.333930
\(262\) 14.8917 0.920015
\(263\) −1.84256 −0.113617 −0.0568086 0.998385i \(-0.518092\pi\)
−0.0568086 + 0.998385i \(0.518092\pi\)
\(264\) 35.2457 2.16922
\(265\) 4.68693 0.287916
\(266\) −22.6203 −1.38694
\(267\) −10.3329 −0.632366
\(268\) 66.5160 4.06311
\(269\) 22.7172 1.38509 0.692545 0.721375i \(-0.256490\pi\)
0.692545 + 0.721375i \(0.256490\pi\)
\(270\) 6.29387 0.383033
\(271\) 5.56723 0.338185 0.169093 0.985600i \(-0.445916\pi\)
0.169093 + 0.985600i \(0.445916\pi\)
\(272\) 7.56613 0.458764
\(273\) −11.4477 −0.692845
\(274\) −8.89647 −0.537455
\(275\) −11.9123 −0.718336
\(276\) 13.0459 0.785269
\(277\) 15.3698 0.923479 0.461739 0.887016i \(-0.347225\pi\)
0.461739 + 0.887016i \(0.347225\pi\)
\(278\) −33.4546 −2.00647
\(279\) −9.71277 −0.581488
\(280\) −10.2748 −0.614038
\(281\) 19.6602 1.17283 0.586414 0.810012i \(-0.300539\pi\)
0.586414 + 0.810012i \(0.300539\pi\)
\(282\) −37.6992 −2.24496
\(283\) −1.06753 −0.0634583 −0.0317292 0.999497i \(-0.510101\pi\)
−0.0317292 + 0.999497i \(0.510101\pi\)
\(284\) −34.7092 −2.05961
\(285\) −1.79103 −0.106091
\(286\) 25.3436 1.49860
\(287\) 22.0558 1.30191
\(288\) 39.0484 2.30095
\(289\) −16.8373 −0.990428
\(290\) 4.78084 0.280740
\(291\) 17.5265 1.02742
\(292\) 76.3530 4.46822
\(293\) 18.8943 1.10381 0.551907 0.833905i \(-0.313900\pi\)
0.551907 + 0.833905i \(0.313900\pi\)
\(294\) −5.15763 −0.300799
\(295\) 5.16966 0.300989
\(296\) 47.0570 2.73513
\(297\) 13.8255 0.802239
\(298\) −53.5315 −3.10099
\(299\) 6.18673 0.357788
\(300\) 37.4618 2.16286
\(301\) −12.8588 −0.741168
\(302\) −25.3840 −1.46069
\(303\) 3.93852 0.226262
\(304\) −63.8636 −3.66283
\(305\) 3.95499 0.226462
\(306\) 1.43099 0.0818040
\(307\) 24.6949 1.40941 0.704706 0.709499i \(-0.251079\pi\)
0.704706 + 0.709499i \(0.251079\pi\)
\(308\) −34.2226 −1.95001
\(309\) 4.45640 0.253516
\(310\) 8.60738 0.488866
\(311\) 25.1873 1.42824 0.714121 0.700022i \(-0.246827\pi\)
0.714121 + 0.700022i \(0.246827\pi\)
\(312\) −52.5642 −2.97586
\(313\) 20.9808 1.18591 0.592954 0.805236i \(-0.297962\pi\)
0.592954 + 0.805236i \(0.297962\pi\)
\(314\) 31.6299 1.78498
\(315\) −1.19486 −0.0673229
\(316\) 7.63740 0.429637
\(317\) −13.4668 −0.756372 −0.378186 0.925730i \(-0.623452\pi\)
−0.378186 + 0.925730i \(0.623452\pi\)
\(318\) −43.4020 −2.43386
\(319\) 10.5019 0.587994
\(320\) −19.6283 −1.09725
\(321\) 9.88604 0.551785
\(322\) −11.1987 −0.624078
\(323\) −1.37357 −0.0764276
\(324\) −21.2018 −1.17788
\(325\) 17.7655 0.985452
\(326\) 36.0668 1.99756
\(327\) −12.0665 −0.667277
\(328\) 101.273 5.59188
\(329\) 24.1415 1.33097
\(330\) −3.63227 −0.199950
\(331\) −8.42310 −0.462976 −0.231488 0.972838i \(-0.574359\pi\)
−0.231488 + 0.972838i \(0.574359\pi\)
\(332\) 11.1359 0.611163
\(333\) 5.47228 0.299879
\(334\) −45.7932 −2.50569
\(335\) −4.52089 −0.247003
\(336\) 58.5029 3.19160
\(337\) 1.41767 0.0772253 0.0386127 0.999254i \(-0.487706\pi\)
0.0386127 + 0.999254i \(0.487706\pi\)
\(338\) −1.31772 −0.0716743
\(339\) 6.73219 0.365642
\(340\) −0.946023 −0.0513053
\(341\) 18.9076 1.02390
\(342\) −12.0786 −0.653134
\(343\) 19.8751 1.07315
\(344\) −59.0436 −3.18342
\(345\) −0.886688 −0.0477377
\(346\) 61.2352 3.29202
\(347\) 20.9307 1.12362 0.561809 0.827267i \(-0.310105\pi\)
0.561809 + 0.827267i \(0.310105\pi\)
\(348\) −33.0266 −1.77041
\(349\) 28.3384 1.51692 0.758459 0.651721i \(-0.225953\pi\)
0.758459 + 0.651721i \(0.225953\pi\)
\(350\) −32.1575 −1.71889
\(351\) −20.6189 −1.10056
\(352\) −76.0143 −4.05158
\(353\) −16.6230 −0.884755 −0.442377 0.896829i \(-0.645865\pi\)
−0.442377 + 0.896829i \(0.645865\pi\)
\(354\) −47.8722 −2.54438
\(355\) 2.35907 0.125207
\(356\) 46.0684 2.44162
\(357\) 1.25828 0.0665950
\(358\) 62.4100 3.29847
\(359\) −10.8523 −0.572765 −0.286382 0.958115i \(-0.592453\pi\)
−0.286382 + 0.958115i \(0.592453\pi\)
\(360\) −5.48644 −0.289161
\(361\) −7.40605 −0.389792
\(362\) −35.4417 −1.86278
\(363\) 6.51375 0.341883
\(364\) 51.0383 2.67513
\(365\) −5.18948 −0.271630
\(366\) −36.6240 −1.91437
\(367\) 30.3976 1.58674 0.793372 0.608737i \(-0.208324\pi\)
0.793372 + 0.608737i \(0.208324\pi\)
\(368\) −31.6171 −1.64815
\(369\) 11.7771 0.613092
\(370\) −4.84949 −0.252113
\(371\) 27.7934 1.44296
\(372\) −59.4608 −3.08290
\(373\) 6.35223 0.328906 0.164453 0.986385i \(-0.447414\pi\)
0.164453 + 0.986385i \(0.447414\pi\)
\(374\) −2.78566 −0.144043
\(375\) −5.17617 −0.267296
\(376\) 110.850 5.71667
\(377\) −15.6622 −0.806643
\(378\) 37.3225 1.91966
\(379\) −6.10324 −0.313503 −0.156751 0.987638i \(-0.550102\pi\)
−0.156751 + 0.987638i \(0.550102\pi\)
\(380\) 7.98512 0.409628
\(381\) 10.5242 0.539169
\(382\) 58.8014 3.00854
\(383\) −23.8827 −1.22035 −0.610173 0.792268i \(-0.708900\pi\)
−0.610173 + 0.792268i \(0.708900\pi\)
\(384\) 100.369 5.12193
\(385\) 2.32600 0.118544
\(386\) −13.9859 −0.711863
\(387\) −6.86620 −0.349029
\(388\) −78.1400 −3.96696
\(389\) 0.968740 0.0491171 0.0245585 0.999698i \(-0.492182\pi\)
0.0245585 + 0.999698i \(0.492182\pi\)
\(390\) 5.41703 0.274302
\(391\) −0.680018 −0.0343900
\(392\) 15.1654 0.765970
\(393\) 6.99202 0.352701
\(394\) 39.9738 2.01385
\(395\) −0.519090 −0.0261183
\(396\) −18.2738 −0.918294
\(397\) 15.7193 0.788931 0.394466 0.918911i \(-0.370930\pi\)
0.394466 + 0.918911i \(0.370930\pi\)
\(398\) −14.5370 −0.728673
\(399\) −10.6208 −0.531703
\(400\) −90.7899 −4.53950
\(401\) −4.41247 −0.220348 −0.110174 0.993912i \(-0.535141\pi\)
−0.110174 + 0.993912i \(0.535141\pi\)
\(402\) 41.8644 2.08801
\(403\) −28.1980 −1.40464
\(404\) −17.5595 −0.873617
\(405\) 1.44102 0.0716048
\(406\) 28.3503 1.40700
\(407\) −10.6527 −0.528035
\(408\) 5.77761 0.286035
\(409\) 14.6260 0.723211 0.361606 0.932331i \(-0.382229\pi\)
0.361606 + 0.932331i \(0.382229\pi\)
\(410\) −10.4368 −0.515435
\(411\) −4.17710 −0.206041
\(412\) −19.8684 −0.978846
\(413\) 30.6560 1.50848
\(414\) −5.97976 −0.293889
\(415\) −0.756874 −0.0371535
\(416\) 113.365 5.55818
\(417\) −15.7077 −0.769210
\(418\) 23.5130 1.15006
\(419\) −25.2896 −1.23548 −0.617738 0.786384i \(-0.711951\pi\)
−0.617738 + 0.786384i \(0.711951\pi\)
\(420\) −7.31485 −0.356928
\(421\) −29.4671 −1.43614 −0.718068 0.695972i \(-0.754974\pi\)
−0.718068 + 0.695972i \(0.754974\pi\)
\(422\) 58.8937 2.86690
\(423\) 12.8908 0.626774
\(424\) 127.619 6.19772
\(425\) −1.95270 −0.0947200
\(426\) −21.8455 −1.05842
\(427\) 23.4530 1.13497
\(428\) −44.0759 −2.13049
\(429\) 11.8994 0.574510
\(430\) 6.08477 0.293434
\(431\) −18.0201 −0.867998 −0.433999 0.900913i \(-0.642898\pi\)
−0.433999 + 0.900913i \(0.642898\pi\)
\(432\) 105.372 5.06972
\(433\) 10.1534 0.487942 0.243971 0.969783i \(-0.421550\pi\)
0.243971 + 0.969783i \(0.421550\pi\)
\(434\) 51.0416 2.45007
\(435\) 2.24471 0.107626
\(436\) 53.7971 2.57642
\(437\) 5.73984 0.274574
\(438\) 48.0557 2.29619
\(439\) −21.1296 −1.00846 −0.504231 0.863569i \(-0.668224\pi\)
−0.504231 + 0.863569i \(0.668224\pi\)
\(440\) 10.6803 0.509163
\(441\) 1.76360 0.0839807
\(442\) 4.15443 0.197606
\(443\) 27.6393 1.31318 0.656590 0.754247i \(-0.271998\pi\)
0.656590 + 0.754247i \(0.271998\pi\)
\(444\) 33.5008 1.58988
\(445\) −3.13113 −0.148430
\(446\) −5.53639 −0.262156
\(447\) −25.1343 −1.18881
\(448\) −116.395 −5.49916
\(449\) 15.6488 0.738513 0.369257 0.929327i \(-0.379612\pi\)
0.369257 + 0.929327i \(0.379612\pi\)
\(450\) −17.1712 −0.809456
\(451\) −22.9261 −1.07955
\(452\) −30.0148 −1.41178
\(453\) −11.9184 −0.559975
\(454\) 66.9160 3.14052
\(455\) −3.46892 −0.162625
\(456\) −48.7672 −2.28374
\(457\) 28.5797 1.33690 0.668452 0.743756i \(-0.266957\pi\)
0.668452 + 0.743756i \(0.266957\pi\)
\(458\) −12.0838 −0.564639
\(459\) 2.26634 0.105784
\(460\) 3.95321 0.184319
\(461\) 11.8062 0.549869 0.274934 0.961463i \(-0.411344\pi\)
0.274934 + 0.961463i \(0.411344\pi\)
\(462\) −21.5393 −1.00210
\(463\) −21.2583 −0.987956 −0.493978 0.869474i \(-0.664458\pi\)
−0.493978 + 0.869474i \(0.664458\pi\)
\(464\) 80.0409 3.71581
\(465\) 4.04136 0.187414
\(466\) 7.07440 0.327715
\(467\) 25.9948 1.20289 0.601447 0.798912i \(-0.294591\pi\)
0.601447 + 0.798912i \(0.294591\pi\)
\(468\) 27.2529 1.25977
\(469\) −26.8088 −1.23791
\(470\) −11.4238 −0.526939
\(471\) 14.8510 0.684296
\(472\) 140.763 6.47913
\(473\) 13.3662 0.614580
\(474\) 4.80689 0.220788
\(475\) 16.4822 0.756256
\(476\) −5.60990 −0.257129
\(477\) 14.8409 0.679516
\(478\) −20.3828 −0.932290
\(479\) 35.6872 1.63059 0.815294 0.579047i \(-0.196575\pi\)
0.815294 + 0.579047i \(0.196575\pi\)
\(480\) −16.2476 −0.741596
\(481\) 15.8871 0.724388
\(482\) −39.1751 −1.78438
\(483\) −5.25804 −0.239249
\(484\) −29.0409 −1.32004
\(485\) 5.31094 0.241157
\(486\) 33.9500 1.54000
\(487\) 25.0893 1.13690 0.568452 0.822717i \(-0.307543\pi\)
0.568452 + 0.822717i \(0.307543\pi\)
\(488\) 107.689 4.87485
\(489\) 16.9342 0.765792
\(490\) −1.56288 −0.0706039
\(491\) −8.52607 −0.384776 −0.192388 0.981319i \(-0.561623\pi\)
−0.192388 + 0.981319i \(0.561623\pi\)
\(492\) 72.0984 3.25045
\(493\) 1.72151 0.0775331
\(494\) −35.0664 −1.57771
\(495\) 1.24202 0.0558245
\(496\) 144.105 6.47051
\(497\) 13.9893 0.627504
\(498\) 7.00881 0.314072
\(499\) −14.6142 −0.654223 −0.327112 0.944986i \(-0.606075\pi\)
−0.327112 + 0.944986i \(0.606075\pi\)
\(500\) 23.0774 1.03205
\(501\) −21.5010 −0.960594
\(502\) 49.9853 2.23095
\(503\) 22.2387 0.991575 0.495787 0.868444i \(-0.334880\pi\)
0.495787 + 0.868444i \(0.334880\pi\)
\(504\) −32.5345 −1.44920
\(505\) 1.19346 0.0531085
\(506\) 11.6406 0.517488
\(507\) −0.618698 −0.0274774
\(508\) −46.9210 −2.08178
\(509\) 4.78603 0.212137 0.106069 0.994359i \(-0.466174\pi\)
0.106069 + 0.994359i \(0.466174\pi\)
\(510\) −0.595416 −0.0263655
\(511\) −30.7735 −1.36134
\(512\) −171.568 −7.58233
\(513\) −19.1295 −0.844589
\(514\) −34.6450 −1.52813
\(515\) 1.35039 0.0595055
\(516\) −42.0343 −1.85046
\(517\) −25.0942 −1.10364
\(518\) −28.7574 −1.26353
\(519\) 28.7513 1.26204
\(520\) −15.9282 −0.698497
\(521\) 33.4542 1.46566 0.732828 0.680414i \(-0.238200\pi\)
0.732828 + 0.680414i \(0.238200\pi\)
\(522\) 15.1382 0.662580
\(523\) −34.4130 −1.50478 −0.752388 0.658720i \(-0.771098\pi\)
−0.752388 + 0.658720i \(0.771098\pi\)
\(524\) −31.1732 −1.36181
\(525\) −15.0987 −0.658962
\(526\) 5.17035 0.225438
\(527\) 3.09940 0.135012
\(528\) −60.8116 −2.64649
\(529\) −20.1584 −0.876451
\(530\) −13.1518 −0.571279
\(531\) 16.3694 0.710370
\(532\) 47.3516 2.05295
\(533\) 34.1912 1.48098
\(534\) 28.9949 1.25473
\(535\) 2.99570 0.129516
\(536\) −123.098 −5.31701
\(537\) 29.3030 1.26452
\(538\) −63.7458 −2.74828
\(539\) −3.43314 −0.147876
\(540\) −13.1751 −0.566966
\(541\) −39.5432 −1.70010 −0.850048 0.526705i \(-0.823427\pi\)
−0.850048 + 0.526705i \(0.823427\pi\)
\(542\) −15.6220 −0.671023
\(543\) −16.6407 −0.714122
\(544\) −12.4606 −0.534242
\(545\) −3.65643 −0.156624
\(546\) 32.1229 1.37473
\(547\) 16.5009 0.705526 0.352763 0.935713i \(-0.385242\pi\)
0.352763 + 0.935713i \(0.385242\pi\)
\(548\) 18.6232 0.795543
\(549\) 12.5232 0.534477
\(550\) 33.4266 1.42531
\(551\) −14.5308 −0.619034
\(552\) −24.1433 −1.02761
\(553\) −3.07820 −0.130898
\(554\) −43.1285 −1.83236
\(555\) −2.27695 −0.0966510
\(556\) 70.0313 2.96999
\(557\) 38.7550 1.64210 0.821051 0.570855i \(-0.193388\pi\)
0.821051 + 0.570855i \(0.193388\pi\)
\(558\) 27.2547 1.15378
\(559\) −19.9339 −0.843114
\(560\) 17.7278 0.749135
\(561\) −1.30793 −0.0552209
\(562\) −55.1677 −2.32711
\(563\) 17.9462 0.756343 0.378172 0.925736i \(-0.376553\pi\)
0.378172 + 0.925736i \(0.376553\pi\)
\(564\) 78.9167 3.32299
\(565\) 2.04001 0.0858240
\(566\) 2.99557 0.125913
\(567\) 8.54522 0.358865
\(568\) 64.2344 2.69522
\(569\) 11.7737 0.493581 0.246790 0.969069i \(-0.420624\pi\)
0.246790 + 0.969069i \(0.420624\pi\)
\(570\) 5.02574 0.210505
\(571\) −23.8001 −0.996001 −0.498001 0.867177i \(-0.665932\pi\)
−0.498001 + 0.867177i \(0.665932\pi\)
\(572\) −53.0524 −2.21823
\(573\) 27.6086 1.15337
\(574\) −61.8899 −2.58323
\(575\) 8.15989 0.340291
\(576\) −62.1515 −2.58965
\(577\) −27.1677 −1.13101 −0.565504 0.824746i \(-0.691318\pi\)
−0.565504 + 0.824746i \(0.691318\pi\)
\(578\) 47.2465 1.96519
\(579\) −6.56670 −0.272903
\(580\) −10.0078 −0.415553
\(581\) −4.48825 −0.186204
\(582\) −49.1804 −2.03859
\(583\) −28.8902 −1.19651
\(584\) −141.302 −5.84714
\(585\) −1.85230 −0.0765830
\(586\) −53.0185 −2.19018
\(587\) 39.6797 1.63776 0.818879 0.573967i \(-0.194596\pi\)
0.818879 + 0.573967i \(0.194596\pi\)
\(588\) 10.7966 0.445244
\(589\) −26.1612 −1.07795
\(590\) −14.5064 −0.597219
\(591\) 18.7686 0.772038
\(592\) −81.1903 −3.33690
\(593\) −19.3762 −0.795687 −0.397843 0.917453i \(-0.630241\pi\)
−0.397843 + 0.917453i \(0.630241\pi\)
\(594\) −38.7954 −1.59179
\(595\) 0.381288 0.0156313
\(596\) 112.059 4.59010
\(597\) −6.82545 −0.279347
\(598\) −17.3604 −0.709919
\(599\) 4.16481 0.170170 0.0850848 0.996374i \(-0.472884\pi\)
0.0850848 + 0.996374i \(0.472884\pi\)
\(600\) −69.3286 −2.83033
\(601\) −5.17857 −0.211238 −0.105619 0.994407i \(-0.533682\pi\)
−0.105619 + 0.994407i \(0.533682\pi\)
\(602\) 36.0826 1.47062
\(603\) −14.3151 −0.582955
\(604\) 53.1369 2.16211
\(605\) 1.97382 0.0802472
\(606\) −11.0517 −0.448946
\(607\) −2.00292 −0.0812961 −0.0406481 0.999174i \(-0.512942\pi\)
−0.0406481 + 0.999174i \(0.512942\pi\)
\(608\) 105.176 4.26546
\(609\) 13.3111 0.539394
\(610\) −11.0980 −0.449343
\(611\) 37.4246 1.51404
\(612\) −2.99552 −0.121087
\(613\) 31.0873 1.25560 0.627802 0.778373i \(-0.283955\pi\)
0.627802 + 0.778373i \(0.283955\pi\)
\(614\) −69.2955 −2.79654
\(615\) −4.90031 −0.197600
\(616\) 63.3339 2.55180
\(617\) 9.41782 0.379147 0.189574 0.981867i \(-0.439289\pi\)
0.189574 + 0.981867i \(0.439289\pi\)
\(618\) −12.5049 −0.503023
\(619\) 36.0298 1.44816 0.724081 0.689715i \(-0.242264\pi\)
0.724081 + 0.689715i \(0.242264\pi\)
\(620\) −18.0180 −0.723621
\(621\) −9.47049 −0.380038
\(622\) −70.6773 −2.83390
\(623\) −18.5675 −0.743892
\(624\) 90.6922 3.63059
\(625\) 22.6345 0.905382
\(626\) −58.8736 −2.35306
\(627\) 11.0399 0.440891
\(628\) −66.2115 −2.64213
\(629\) −1.74623 −0.0696269
\(630\) 3.35286 0.133581
\(631\) −41.5836 −1.65542 −0.827709 0.561157i \(-0.810356\pi\)
−0.827709 + 0.561157i \(0.810356\pi\)
\(632\) −14.1341 −0.562225
\(633\) 27.6520 1.09907
\(634\) 37.7888 1.50078
\(635\) 3.18907 0.126554
\(636\) 90.8545 3.60261
\(637\) 5.12005 0.202864
\(638\) −29.4690 −1.16669
\(639\) 7.46985 0.295503
\(640\) 30.4142 1.20223
\(641\) −21.4278 −0.846346 −0.423173 0.906049i \(-0.639084\pi\)
−0.423173 + 0.906049i \(0.639084\pi\)
\(642\) −27.7409 −1.09484
\(643\) 7.60432 0.299885 0.149942 0.988695i \(-0.452091\pi\)
0.149942 + 0.988695i \(0.452091\pi\)
\(644\) 23.4425 0.923762
\(645\) 2.85694 0.112492
\(646\) 3.85434 0.151647
\(647\) −49.7215 −1.95475 −0.977377 0.211504i \(-0.932164\pi\)
−0.977377 + 0.211504i \(0.932164\pi\)
\(648\) 39.2370 1.54137
\(649\) −31.8658 −1.25084
\(650\) −49.8511 −1.95532
\(651\) 23.9652 0.939271
\(652\) −75.4996 −2.95679
\(653\) −29.0775 −1.13789 −0.568946 0.822375i \(-0.692649\pi\)
−0.568946 + 0.822375i \(0.692649\pi\)
\(654\) 33.8593 1.32400
\(655\) 2.11875 0.0827863
\(656\) −174.733 −6.82217
\(657\) −16.4321 −0.641078
\(658\) −67.7427 −2.64089
\(659\) −28.2122 −1.09899 −0.549497 0.835496i \(-0.685180\pi\)
−0.549497 + 0.835496i \(0.685180\pi\)
\(660\) 7.60352 0.295966
\(661\) 41.4779 1.61330 0.806652 0.591026i \(-0.201277\pi\)
0.806652 + 0.591026i \(0.201277\pi\)
\(662\) 23.6358 0.918630
\(663\) 1.95060 0.0757550
\(664\) −20.6086 −0.799770
\(665\) −3.21834 −0.124802
\(666\) −15.3556 −0.595016
\(667\) −7.19380 −0.278545
\(668\) 95.8601 3.70894
\(669\) −2.59947 −0.100501
\(670\) 12.6859 0.490099
\(671\) −24.3785 −0.941123
\(672\) −96.3478 −3.71670
\(673\) 1.75176 0.0675254 0.0337627 0.999430i \(-0.489251\pi\)
0.0337627 + 0.999430i \(0.489251\pi\)
\(674\) −3.97807 −0.153230
\(675\) −27.1950 −1.04673
\(676\) 2.75840 0.106092
\(677\) −20.9541 −0.805332 −0.402666 0.915347i \(-0.631916\pi\)
−0.402666 + 0.915347i \(0.631916\pi\)
\(678\) −18.8910 −0.725503
\(679\) 31.4938 1.20862
\(680\) 1.75075 0.0671384
\(681\) 31.4186 1.20396
\(682\) −53.0558 −2.03161
\(683\) 39.7883 1.52246 0.761228 0.648484i \(-0.224597\pi\)
0.761228 + 0.648484i \(0.224597\pi\)
\(684\) 25.2843 0.966770
\(685\) −1.26576 −0.0483622
\(686\) −55.7708 −2.12934
\(687\) −5.67362 −0.216462
\(688\) 101.871 3.88381
\(689\) 43.0858 1.64144
\(690\) 2.48810 0.0947205
\(691\) 28.6274 1.08904 0.544519 0.838749i \(-0.316712\pi\)
0.544519 + 0.838749i \(0.316712\pi\)
\(692\) −128.185 −4.87286
\(693\) 7.36513 0.279778
\(694\) −58.7329 −2.22947
\(695\) −4.75981 −0.180550
\(696\) 61.1205 2.31677
\(697\) −3.75814 −0.142350
\(698\) −79.5193 −3.00985
\(699\) 3.32160 0.125634
\(700\) 67.3161 2.54431
\(701\) 49.1549 1.85656 0.928278 0.371887i \(-0.121289\pi\)
0.928278 + 0.371887i \(0.121289\pi\)
\(702\) 57.8580 2.18371
\(703\) 14.7395 0.555910
\(704\) 120.988 4.55992
\(705\) −5.36372 −0.202010
\(706\) 46.6453 1.75552
\(707\) 7.07722 0.266166
\(708\) 100.212 3.76620
\(709\) 21.7657 0.817428 0.408714 0.912663i \(-0.365977\pi\)
0.408714 + 0.912663i \(0.365977\pi\)
\(710\) −6.61972 −0.248434
\(711\) −1.64366 −0.0616422
\(712\) −85.2564 −3.19512
\(713\) −12.9517 −0.485044
\(714\) −3.53080 −0.132137
\(715\) 3.60581 0.134850
\(716\) −130.644 −4.88241
\(717\) −9.57022 −0.357407
\(718\) 30.4524 1.13647
\(719\) −15.7889 −0.588825 −0.294412 0.955678i \(-0.595124\pi\)
−0.294412 + 0.955678i \(0.595124\pi\)
\(720\) 9.46610 0.352781
\(721\) 8.00781 0.298227
\(722\) 20.7819 0.773421
\(723\) −18.3936 −0.684067
\(724\) 74.1910 2.75729
\(725\) −20.6573 −0.767195
\(726\) −18.2780 −0.678361
\(727\) −0.553168 −0.0205159 −0.0102579 0.999947i \(-0.503265\pi\)
−0.0102579 + 0.999947i \(0.503265\pi\)
\(728\) −94.4539 −3.50069
\(729\) 26.7686 0.991429
\(730\) 14.5620 0.538964
\(731\) 2.19104 0.0810387
\(732\) 76.6660 2.83366
\(733\) 19.8051 0.731519 0.365759 0.930709i \(-0.380809\pi\)
0.365759 + 0.930709i \(0.380809\pi\)
\(734\) −85.2978 −3.14840
\(735\) −0.733810 −0.0270670
\(736\) 52.0698 1.91932
\(737\) 27.8667 1.02648
\(738\) −33.0473 −1.21649
\(739\) 50.9179 1.87304 0.936522 0.350608i \(-0.114025\pi\)
0.936522 + 0.350608i \(0.114025\pi\)
\(740\) 10.1515 0.373178
\(741\) −16.4645 −0.604838
\(742\) −77.9902 −2.86311
\(743\) 27.2844 1.00097 0.500484 0.865746i \(-0.333155\pi\)
0.500484 + 0.865746i \(0.333155\pi\)
\(744\) 110.041 4.03429
\(745\) −7.61628 −0.279039
\(746\) −17.8248 −0.652611
\(747\) −2.39659 −0.0876866
\(748\) 5.83128 0.213213
\(749\) 17.7645 0.649099
\(750\) 14.5247 0.530366
\(751\) −8.03394 −0.293163 −0.146581 0.989199i \(-0.546827\pi\)
−0.146581 + 0.989199i \(0.546827\pi\)
\(752\) −191.257 −6.97443
\(753\) 23.4693 0.855267
\(754\) 43.9491 1.60053
\(755\) −3.61155 −0.131438
\(756\) −78.1281 −2.84149
\(757\) −30.9725 −1.12571 −0.562857 0.826554i \(-0.690298\pi\)
−0.562857 + 0.826554i \(0.690298\pi\)
\(758\) 17.1261 0.622048
\(759\) 5.46554 0.198386
\(760\) −14.7776 −0.536041
\(761\) −0.0524583 −0.00190161 −0.000950805 1.00000i \(-0.500303\pi\)
−0.000950805 1.00000i \(0.500303\pi\)
\(762\) −29.5315 −1.06981
\(763\) −21.6825 −0.784960
\(764\) −123.090 −4.45325
\(765\) 0.203596 0.00736103
\(766\) 67.0163 2.42140
\(767\) 47.5234 1.71597
\(768\) −152.093 −5.48817
\(769\) 11.9028 0.429228 0.214614 0.976699i \(-0.431151\pi\)
0.214614 + 0.976699i \(0.431151\pi\)
\(770\) −6.52692 −0.235214
\(771\) −16.2666 −0.585829
\(772\) 29.2770 1.05370
\(773\) 43.8129 1.57584 0.787920 0.615777i \(-0.211158\pi\)
0.787920 + 0.615777i \(0.211158\pi\)
\(774\) 19.2670 0.692538
\(775\) −37.1913 −1.33595
\(776\) 144.610 5.19118
\(777\) −13.5023 −0.484391
\(778\) −2.71835 −0.0974575
\(779\) 31.7214 1.13654
\(780\) −11.3396 −0.406023
\(781\) −14.5413 −0.520329
\(782\) 1.90817 0.0682362
\(783\) 23.9752 0.856805
\(784\) −26.1659 −0.934495
\(785\) 4.50019 0.160619
\(786\) −19.6201 −0.699824
\(787\) 0.0755029 0.00269139 0.00134569 0.999999i \(-0.499572\pi\)
0.00134569 + 0.999999i \(0.499572\pi\)
\(788\) −83.6781 −2.98091
\(789\) 2.42760 0.0864248
\(790\) 1.45660 0.0518235
\(791\) 12.0972 0.430128
\(792\) 33.8184 1.20168
\(793\) 36.3572 1.29108
\(794\) −44.1095 −1.56539
\(795\) −6.17510 −0.219008
\(796\) 30.4306 1.07858
\(797\) 33.1161 1.17303 0.586515 0.809938i \(-0.300499\pi\)
0.586515 + 0.809938i \(0.300499\pi\)
\(798\) 29.8025 1.05500
\(799\) −4.11354 −0.145527
\(800\) 149.521 5.28636
\(801\) −9.91450 −0.350312
\(802\) 12.3817 0.437212
\(803\) 31.9879 1.12883
\(804\) −87.6357 −3.09067
\(805\) −1.59331 −0.0561568
\(806\) 79.1255 2.78708
\(807\) −29.9301 −1.05359
\(808\) 32.4964 1.14322
\(809\) −26.5369 −0.932989 −0.466494 0.884524i \(-0.654483\pi\)
−0.466494 + 0.884524i \(0.654483\pi\)
\(810\) −4.04359 −0.142077
\(811\) −31.2586 −1.09764 −0.548819 0.835941i \(-0.684922\pi\)
−0.548819 + 0.835941i \(0.684922\pi\)
\(812\) −59.3463 −2.08265
\(813\) −7.33490 −0.257246
\(814\) 29.8922 1.04772
\(815\) 5.13147 0.179748
\(816\) −9.96847 −0.348966
\(817\) −18.4940 −0.647023
\(818\) −41.0416 −1.43499
\(819\) −10.9841 −0.383815
\(820\) 21.8475 0.762949
\(821\) 31.5580 1.10138 0.550691 0.834709i \(-0.314364\pi\)
0.550691 + 0.834709i \(0.314364\pi\)
\(822\) 11.7212 0.408824
\(823\) −20.4068 −0.711336 −0.355668 0.934612i \(-0.615747\pi\)
−0.355668 + 0.934612i \(0.615747\pi\)
\(824\) 36.7694 1.28092
\(825\) 15.6946 0.546414
\(826\) −86.0227 −2.99311
\(827\) 26.3798 0.917315 0.458657 0.888613i \(-0.348331\pi\)
0.458657 + 0.888613i \(0.348331\pi\)
\(828\) 12.5176 0.435015
\(829\) −10.2061 −0.354471 −0.177236 0.984168i \(-0.556715\pi\)
−0.177236 + 0.984168i \(0.556715\pi\)
\(830\) 2.12384 0.0737195
\(831\) −20.2499 −0.702460
\(832\) −180.438 −6.25555
\(833\) −0.562773 −0.0194989
\(834\) 44.0769 1.52626
\(835\) −6.51531 −0.225472
\(836\) −49.2202 −1.70232
\(837\) 43.1648 1.49199
\(838\) 70.9641 2.45142
\(839\) −28.6044 −0.987532 −0.493766 0.869595i \(-0.664380\pi\)
−0.493766 + 0.869595i \(0.664380\pi\)
\(840\) 13.5372 0.467078
\(841\) −10.7884 −0.372012
\(842\) 82.6865 2.84957
\(843\) −25.9025 −0.892131
\(844\) −123.284 −4.24360
\(845\) −0.187480 −0.00644952
\(846\) −36.1726 −1.24364
\(847\) 11.7047 0.402179
\(848\) −220.189 −7.56131
\(849\) 1.40649 0.0482706
\(850\) 5.47941 0.187942
\(851\) 7.29710 0.250141
\(852\) 45.7298 1.56668
\(853\) −17.5726 −0.601674 −0.300837 0.953676i \(-0.597266\pi\)
−0.300837 + 0.953676i \(0.597266\pi\)
\(854\) −65.8107 −2.25199
\(855\) −1.71850 −0.0587714
\(856\) 81.5689 2.78797
\(857\) 5.70620 0.194920 0.0974600 0.995239i \(-0.468928\pi\)
0.0974600 + 0.995239i \(0.468928\pi\)
\(858\) −33.3906 −1.13994
\(859\) −12.3043 −0.419818 −0.209909 0.977721i \(-0.567317\pi\)
−0.209909 + 0.977721i \(0.567317\pi\)
\(860\) −12.7374 −0.434342
\(861\) −29.0587 −0.990319
\(862\) 50.5656 1.72227
\(863\) 50.5428 1.72050 0.860248 0.509876i \(-0.170309\pi\)
0.860248 + 0.509876i \(0.170309\pi\)
\(864\) −173.536 −5.90382
\(865\) 8.71234 0.296228
\(866\) −28.4911 −0.968168
\(867\) 22.1833 0.753385
\(868\) −106.847 −3.62661
\(869\) 3.19967 0.108541
\(870\) −6.29881 −0.213550
\(871\) −41.5594 −1.40819
\(872\) −99.5595 −3.37151
\(873\) 16.8167 0.569160
\(874\) −16.1064 −0.544806
\(875\) −9.30119 −0.314438
\(876\) −100.596 −3.39883
\(877\) −8.79695 −0.297052 −0.148526 0.988909i \(-0.547453\pi\)
−0.148526 + 0.988909i \(0.547453\pi\)
\(878\) 59.2912 2.00098
\(879\) −24.8934 −0.839635
\(880\) −18.4274 −0.621186
\(881\) 35.7142 1.20324 0.601622 0.798781i \(-0.294521\pi\)
0.601622 + 0.798781i \(0.294521\pi\)
\(882\) −4.94876 −0.166634
\(883\) −7.70825 −0.259403 −0.129702 0.991553i \(-0.541402\pi\)
−0.129702 + 0.991553i \(0.541402\pi\)
\(884\) −8.69656 −0.292497
\(885\) −6.81110 −0.228953
\(886\) −77.5576 −2.60560
\(887\) 14.8810 0.499654 0.249827 0.968290i \(-0.419626\pi\)
0.249827 + 0.968290i \(0.419626\pi\)
\(888\) −61.9982 −2.08052
\(889\) 18.9111 0.634259
\(890\) 8.78615 0.294512
\(891\) −8.88243 −0.297573
\(892\) 11.5895 0.388044
\(893\) 34.7213 1.16190
\(894\) 70.5284 2.35882
\(895\) 8.87949 0.296809
\(896\) 180.356 6.02526
\(897\) −8.15110 −0.272157
\(898\) −43.9116 −1.46535
\(899\) 32.7881 1.09354
\(900\) 35.9448 1.19816
\(901\) −4.73580 −0.157772
\(902\) 64.3322 2.14203
\(903\) 16.9416 0.563782
\(904\) 55.5468 1.84746
\(905\) −5.04254 −0.167620
\(906\) 33.4438 1.11109
\(907\) 17.2269 0.572009 0.286004 0.958228i \(-0.407673\pi\)
0.286004 + 0.958228i \(0.407673\pi\)
\(908\) −140.077 −4.64861
\(909\) 3.77902 0.125342
\(910\) 9.73401 0.322679
\(911\) −17.4688 −0.578767 −0.289383 0.957213i \(-0.593450\pi\)
−0.289383 + 0.957213i \(0.593450\pi\)
\(912\) 84.1411 2.78619
\(913\) 4.66537 0.154401
\(914\) −80.1966 −2.65267
\(915\) −5.21075 −0.172262
\(916\) 25.2953 0.835780
\(917\) 12.5641 0.414904
\(918\) −6.35949 −0.209894
\(919\) 54.3755 1.79368 0.896842 0.442352i \(-0.145856\pi\)
0.896842 + 0.442352i \(0.145856\pi\)
\(920\) −7.31599 −0.241201
\(921\) −32.5359 −1.07209
\(922\) −33.1289 −1.09104
\(923\) 21.6864 0.713816
\(924\) 45.0887 1.48331
\(925\) 20.9540 0.688962
\(926\) 59.6521 1.96029
\(927\) 4.27593 0.140440
\(928\) −131.818 −4.32715
\(929\) −23.6979 −0.777504 −0.388752 0.921342i \(-0.627094\pi\)
−0.388752 + 0.921342i \(0.627094\pi\)
\(930\) −11.3403 −0.371864
\(931\) 4.75021 0.155682
\(932\) −14.8090 −0.485085
\(933\) −33.1846 −1.08642
\(934\) −72.9430 −2.38677
\(935\) −0.396334 −0.0129615
\(936\) −50.4355 −1.64854
\(937\) −14.7042 −0.480367 −0.240183 0.970728i \(-0.577208\pi\)
−0.240183 + 0.970728i \(0.577208\pi\)
\(938\) 75.2272 2.45626
\(939\) −27.6425 −0.902080
\(940\) 23.9136 0.779977
\(941\) −43.7463 −1.42609 −0.713045 0.701119i \(-0.752684\pi\)
−0.713045 + 0.701119i \(0.752684\pi\)
\(942\) −41.6728 −1.35777
\(943\) 15.7044 0.511405
\(944\) −242.867 −7.90464
\(945\) 5.31013 0.172738
\(946\) −37.5065 −1.21944
\(947\) −39.4897 −1.28324 −0.641622 0.767021i \(-0.721738\pi\)
−0.641622 + 0.767021i \(0.721738\pi\)
\(948\) −10.0624 −0.326811
\(949\) −47.7056 −1.54859
\(950\) −46.2502 −1.50055
\(951\) 17.7427 0.575347
\(952\) 10.3819 0.336481
\(953\) −9.82067 −0.318123 −0.159061 0.987269i \(-0.550847\pi\)
−0.159061 + 0.987269i \(0.550847\pi\)
\(954\) −41.6444 −1.34829
\(955\) 8.36608 0.270720
\(956\) 42.6679 1.37998
\(957\) −13.8364 −0.447268
\(958\) −100.140 −3.23539
\(959\) −7.50594 −0.242379
\(960\) 25.8605 0.834644
\(961\) 28.0314 0.904238
\(962\) −44.5801 −1.43732
\(963\) 9.48569 0.305672
\(964\) 82.0062 2.64124
\(965\) −1.98987 −0.0640561
\(966\) 14.7544 0.474715
\(967\) 49.6628 1.59705 0.798524 0.601963i \(-0.205614\pi\)
0.798524 + 0.601963i \(0.205614\pi\)
\(968\) 53.7445 1.72741
\(969\) 1.80970 0.0581360
\(970\) −14.9028 −0.478501
\(971\) 11.7140 0.375919 0.187960 0.982177i \(-0.439813\pi\)
0.187960 + 0.982177i \(0.439813\pi\)
\(972\) −71.0683 −2.27952
\(973\) −28.2256 −0.904871
\(974\) −70.4021 −2.25583
\(975\) −23.4063 −0.749601
\(976\) −185.802 −5.94739
\(977\) 6.49146 0.207680 0.103840 0.994594i \(-0.466887\pi\)
0.103840 + 0.994594i \(0.466887\pi\)
\(978\) −47.5185 −1.51948
\(979\) 19.3003 0.616839
\(980\) 3.27162 0.104508
\(981\) −11.5778 −0.369651
\(982\) 23.9247 0.763468
\(983\) 9.42429 0.300588 0.150294 0.988641i \(-0.451978\pi\)
0.150294 + 0.988641i \(0.451978\pi\)
\(984\) −133.429 −4.25355
\(985\) 5.68734 0.181214
\(986\) −4.83068 −0.153840
\(987\) −31.8068 −1.01242
\(988\) 73.4052 2.33533
\(989\) −9.15586 −0.291139
\(990\) −3.48518 −0.110766
\(991\) −14.7314 −0.467959 −0.233980 0.972241i \(-0.575175\pi\)
−0.233980 + 0.972241i \(0.575175\pi\)
\(992\) −237.325 −7.53507
\(993\) 11.0975 0.352170
\(994\) −39.2548 −1.24509
\(995\) −2.06827 −0.0655687
\(996\) −14.6717 −0.464891
\(997\) 16.7151 0.529371 0.264686 0.964335i \(-0.414732\pi\)
0.264686 + 0.964335i \(0.414732\pi\)
\(998\) 41.0085 1.29810
\(999\) −24.3195 −0.769435
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 \(a_p\))