Properties

Label 6001.2.a.b.1.5
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.69250 q^{2}\) \(+0.578947 q^{3}\) \(+5.24958 q^{4}\) \(+4.35539 q^{5}\) \(-1.55882 q^{6}\) \(-1.96736 q^{7}\) \(-8.74952 q^{8}\) \(-2.66482 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.69250 q^{2}\) \(+0.578947 q^{3}\) \(+5.24958 q^{4}\) \(+4.35539 q^{5}\) \(-1.55882 q^{6}\) \(-1.96736 q^{7}\) \(-8.74952 q^{8}\) \(-2.66482 q^{9}\) \(-11.7269 q^{10}\) \(+2.40712 q^{11}\) \(+3.03923 q^{12}\) \(+3.82566 q^{13}\) \(+5.29713 q^{14}\) \(+2.52154 q^{15}\) \(+13.0590 q^{16}\) \(+1.00000 q^{17}\) \(+7.17504 q^{18}\) \(-4.69379 q^{19}\) \(+22.8640 q^{20}\) \(-1.13900 q^{21}\) \(-6.48119 q^{22}\) \(-0.242259 q^{23}\) \(-5.06550 q^{24}\) \(+13.9695 q^{25}\) \(-10.3006 q^{26}\) \(-3.27963 q^{27}\) \(-10.3278 q^{28}\) \(+2.26369 q^{29}\) \(-6.78926 q^{30}\) \(-9.72579 q^{31}\) \(-17.6623 q^{32}\) \(+1.39360 q^{33}\) \(-2.69250 q^{34}\) \(-8.56863 q^{35}\) \(-13.9892 q^{36}\) \(-7.73625 q^{37}\) \(+12.6380 q^{38}\) \(+2.21485 q^{39}\) \(-38.1076 q^{40}\) \(-1.87982 q^{41}\) \(+3.06676 q^{42}\) \(-11.1724 q^{43}\) \(+12.6364 q^{44}\) \(-11.6063 q^{45}\) \(+0.652283 q^{46}\) \(-5.16445 q^{47}\) \(+7.56044 q^{48}\) \(-3.12949 q^{49}\) \(-37.6129 q^{50}\) \(+0.578947 q^{51}\) \(+20.0831 q^{52}\) \(-2.26203 q^{53}\) \(+8.83042 q^{54}\) \(+10.4840 q^{55}\) \(+17.2135 q^{56}\) \(-2.71745 q^{57}\) \(-6.09499 q^{58}\) \(-14.1284 q^{59}\) \(+13.2370 q^{60}\) \(+1.16500 q^{61}\) \(+26.1867 q^{62}\) \(+5.24266 q^{63}\) \(+21.4378 q^{64}\) \(+16.6623 q^{65}\) \(-3.75226 q^{66}\) \(-3.92378 q^{67}\) \(+5.24958 q^{68}\) \(-0.140255 q^{69}\) \(+23.0711 q^{70}\) \(-3.51936 q^{71}\) \(+23.3159 q^{72}\) \(+16.2155 q^{73}\) \(+20.8299 q^{74}\) \(+8.08757 q^{75}\) \(-24.6404 q^{76}\) \(-4.73568 q^{77}\) \(-5.96350 q^{78}\) \(-5.97141 q^{79}\) \(+56.8769 q^{80}\) \(+6.09573 q^{81}\) \(+5.06141 q^{82}\) \(-2.20212 q^{83}\) \(-5.97926 q^{84}\) \(+4.35539 q^{85}\) \(+30.0817 q^{86}\) \(+1.31055 q^{87}\) \(-21.0612 q^{88}\) \(-6.72046 q^{89}\) \(+31.2501 q^{90}\) \(-7.52646 q^{91}\) \(-1.27176 q^{92}\) \(-5.63071 q^{93}\) \(+13.9053 q^{94}\) \(-20.4433 q^{95}\) \(-10.2255 q^{96}\) \(-18.8572 q^{97}\) \(+8.42617 q^{98}\) \(-6.41455 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.69250 −1.90389 −0.951944 0.306271i \(-0.900918\pi\)
−0.951944 + 0.306271i \(0.900918\pi\)
\(3\) 0.578947 0.334255 0.167127 0.985935i \(-0.446551\pi\)
0.167127 + 0.985935i \(0.446551\pi\)
\(4\) 5.24958 2.62479
\(5\) 4.35539 1.94779 0.973896 0.226995i \(-0.0728901\pi\)
0.973896 + 0.226995i \(0.0728901\pi\)
\(6\) −1.55882 −0.636384
\(7\) −1.96736 −0.743593 −0.371796 0.928314i \(-0.621258\pi\)
−0.371796 + 0.928314i \(0.621258\pi\)
\(8\) −8.74952 −3.09342
\(9\) −2.66482 −0.888274
\(10\) −11.7269 −3.70838
\(11\) 2.40712 0.725775 0.362887 0.931833i \(-0.381791\pi\)
0.362887 + 0.931833i \(0.381791\pi\)
\(12\) 3.03923 0.877350
\(13\) 3.82566 1.06105 0.530524 0.847670i \(-0.321995\pi\)
0.530524 + 0.847670i \(0.321995\pi\)
\(14\) 5.29713 1.41572
\(15\) 2.52154 0.651059
\(16\) 13.0590 3.26474
\(17\) 1.00000 0.242536
\(18\) 7.17504 1.69117
\(19\) −4.69379 −1.07683 −0.538414 0.842680i \(-0.680976\pi\)
−0.538414 + 0.842680i \(0.680976\pi\)
\(20\) 22.8640 5.11255
\(21\) −1.13900 −0.248550
\(22\) −6.48119 −1.38179
\(23\) −0.242259 −0.0505144 −0.0252572 0.999681i \(-0.508040\pi\)
−0.0252572 + 0.999681i \(0.508040\pi\)
\(24\) −5.06550 −1.03399
\(25\) 13.9695 2.79389
\(26\) −10.3006 −2.02012
\(27\) −3.27963 −0.631165
\(28\) −10.3278 −1.95178
\(29\) 2.26369 0.420356 0.210178 0.977663i \(-0.432596\pi\)
0.210178 + 0.977663i \(0.432596\pi\)
\(30\) −6.78926 −1.23954
\(31\) −9.72579 −1.74680 −0.873402 0.487001i \(-0.838091\pi\)
−0.873402 + 0.487001i \(0.838091\pi\)
\(32\) −17.6623 −3.12228
\(33\) 1.39360 0.242594
\(34\) −2.69250 −0.461761
\(35\) −8.56863 −1.44836
\(36\) −13.9892 −2.33153
\(37\) −7.73625 −1.27183 −0.635916 0.771758i \(-0.719378\pi\)
−0.635916 + 0.771758i \(0.719378\pi\)
\(38\) 12.6380 2.05016
\(39\) 2.21485 0.354660
\(40\) −38.1076 −6.02534
\(41\) −1.87982 −0.293578 −0.146789 0.989168i \(-0.546894\pi\)
−0.146789 + 0.989168i \(0.546894\pi\)
\(42\) 3.06676 0.473211
\(43\) −11.1724 −1.70377 −0.851887 0.523726i \(-0.824542\pi\)
−0.851887 + 0.523726i \(0.824542\pi\)
\(44\) 12.6364 1.90501
\(45\) −11.6063 −1.73017
\(46\) 0.652283 0.0961738
\(47\) −5.16445 −0.753312 −0.376656 0.926353i \(-0.622926\pi\)
−0.376656 + 0.926353i \(0.622926\pi\)
\(48\) 7.56044 1.09125
\(49\) −3.12949 −0.447070
\(50\) −37.6129 −5.31926
\(51\) 0.578947 0.0810687
\(52\) 20.0831 2.78503
\(53\) −2.26203 −0.310714 −0.155357 0.987858i \(-0.549653\pi\)
−0.155357 + 0.987858i \(0.549653\pi\)
\(54\) 8.83042 1.20167
\(55\) 10.4840 1.41366
\(56\) 17.2135 2.30025
\(57\) −2.71745 −0.359935
\(58\) −6.09499 −0.800311
\(59\) −14.1284 −1.83935 −0.919677 0.392675i \(-0.871550\pi\)
−0.919677 + 0.392675i \(0.871550\pi\)
\(60\) 13.2370 1.70889
\(61\) 1.16500 0.149163 0.0745814 0.997215i \(-0.476238\pi\)
0.0745814 + 0.997215i \(0.476238\pi\)
\(62\) 26.1867 3.32572
\(63\) 5.24266 0.660514
\(64\) 21.4378 2.67973
\(65\) 16.6623 2.06670
\(66\) −3.75226 −0.461871
\(67\) −3.92378 −0.479365 −0.239683 0.970851i \(-0.577043\pi\)
−0.239683 + 0.970851i \(0.577043\pi\)
\(68\) 5.24958 0.636605
\(69\) −0.140255 −0.0168847
\(70\) 23.0711 2.75752
\(71\) −3.51936 −0.417672 −0.208836 0.977951i \(-0.566967\pi\)
−0.208836 + 0.977951i \(0.566967\pi\)
\(72\) 23.3159 2.74780
\(73\) 16.2155 1.89788 0.948939 0.315458i \(-0.102158\pi\)
0.948939 + 0.315458i \(0.102158\pi\)
\(74\) 20.8299 2.42143
\(75\) 8.08757 0.933873
\(76\) −24.6404 −2.82645
\(77\) −4.73568 −0.539681
\(78\) −5.96350 −0.675234
\(79\) −5.97141 −0.671836 −0.335918 0.941891i \(-0.609047\pi\)
−0.335918 + 0.941891i \(0.609047\pi\)
\(80\) 56.8769 6.35903
\(81\) 6.09573 0.677304
\(82\) 5.06141 0.558940
\(83\) −2.20212 −0.241714 −0.120857 0.992670i \(-0.538564\pi\)
−0.120857 + 0.992670i \(0.538564\pi\)
\(84\) −5.97926 −0.652391
\(85\) 4.35539 0.472409
\(86\) 30.0817 3.24379
\(87\) 1.31055 0.140506
\(88\) −21.0612 −2.24513
\(89\) −6.72046 −0.712367 −0.356184 0.934416i \(-0.615922\pi\)
−0.356184 + 0.934416i \(0.615922\pi\)
\(90\) 31.2501 3.29405
\(91\) −7.52646 −0.788987
\(92\) −1.27176 −0.132590
\(93\) −5.63071 −0.583878
\(94\) 13.9053 1.43422
\(95\) −20.4433 −2.09744
\(96\) −10.2255 −1.04364
\(97\) −18.8572 −1.91466 −0.957329 0.289002i \(-0.906677\pi\)
−0.957329 + 0.289002i \(0.906677\pi\)
\(98\) 8.42617 0.851172
\(99\) −6.41455 −0.644686
\(100\) 73.3339 7.33339
\(101\) 4.88283 0.485859 0.242930 0.970044i \(-0.421892\pi\)
0.242930 + 0.970044i \(0.421892\pi\)
\(102\) −1.55882 −0.154346
\(103\) −4.63590 −0.456789 −0.228395 0.973569i \(-0.573348\pi\)
−0.228395 + 0.973569i \(0.573348\pi\)
\(104\) −33.4727 −3.28227
\(105\) −4.96078 −0.484123
\(106\) 6.09054 0.591566
\(107\) −2.38370 −0.230441 −0.115221 0.993340i \(-0.536758\pi\)
−0.115221 + 0.993340i \(0.536758\pi\)
\(108\) −17.2167 −1.65668
\(109\) 3.92893 0.376323 0.188161 0.982138i \(-0.439747\pi\)
0.188161 + 0.982138i \(0.439747\pi\)
\(110\) −28.2281 −2.69145
\(111\) −4.47888 −0.425116
\(112\) −25.6917 −2.42763
\(113\) −3.90331 −0.367193 −0.183596 0.983002i \(-0.558774\pi\)
−0.183596 + 0.983002i \(0.558774\pi\)
\(114\) 7.31675 0.685277
\(115\) −1.05513 −0.0983916
\(116\) 11.8834 1.10335
\(117\) −10.1947 −0.942501
\(118\) 38.0407 3.50193
\(119\) −1.96736 −0.180348
\(120\) −22.0623 −2.01400
\(121\) −5.20576 −0.473251
\(122\) −3.13676 −0.283989
\(123\) −1.08831 −0.0981299
\(124\) −51.0563 −4.58499
\(125\) 39.0656 3.49413
\(126\) −14.1159 −1.25754
\(127\) 9.82317 0.871665 0.435832 0.900028i \(-0.356454\pi\)
0.435832 + 0.900028i \(0.356454\pi\)
\(128\) −22.3969 −1.97962
\(129\) −6.46822 −0.569495
\(130\) −44.8632 −3.93477
\(131\) −12.1238 −1.05926 −0.529632 0.848228i \(-0.677670\pi\)
−0.529632 + 0.848228i \(0.677670\pi\)
\(132\) 7.31579 0.636758
\(133\) 9.23438 0.800722
\(134\) 10.5648 0.912658
\(135\) −14.2841 −1.22938
\(136\) −8.74952 −0.750265
\(137\) −6.37444 −0.544605 −0.272303 0.962212i \(-0.587785\pi\)
−0.272303 + 0.962212i \(0.587785\pi\)
\(138\) 0.377637 0.0321466
\(139\) 7.25620 0.615463 0.307731 0.951473i \(-0.400430\pi\)
0.307731 + 0.951473i \(0.400430\pi\)
\(140\) −44.9818 −3.80165
\(141\) −2.98994 −0.251798
\(142\) 9.47591 0.795200
\(143\) 9.20883 0.770081
\(144\) −34.7998 −2.89998
\(145\) 9.85925 0.818767
\(146\) −43.6603 −3.61335
\(147\) −1.81181 −0.149435
\(148\) −40.6121 −3.33829
\(149\) −7.53592 −0.617366 −0.308683 0.951165i \(-0.599888\pi\)
−0.308683 + 0.951165i \(0.599888\pi\)
\(150\) −21.7758 −1.77799
\(151\) −7.19691 −0.585676 −0.292838 0.956162i \(-0.594600\pi\)
−0.292838 + 0.956162i \(0.594600\pi\)
\(152\) 41.0684 3.33109
\(153\) −2.66482 −0.215438
\(154\) 12.7508 1.02749
\(155\) −42.3597 −3.40241
\(156\) 11.6271 0.930910
\(157\) 5.65988 0.451708 0.225854 0.974161i \(-0.427483\pi\)
0.225854 + 0.974161i \(0.427483\pi\)
\(158\) 16.0780 1.27910
\(159\) −1.30960 −0.103858
\(160\) −76.9261 −6.08154
\(161\) 0.476610 0.0375621
\(162\) −16.4128 −1.28951
\(163\) 11.7966 0.923982 0.461991 0.886885i \(-0.347135\pi\)
0.461991 + 0.886885i \(0.347135\pi\)
\(164\) −9.86825 −0.770581
\(165\) 6.06966 0.472522
\(166\) 5.92921 0.460196
\(167\) 6.20708 0.480318 0.240159 0.970734i \(-0.422800\pi\)
0.240159 + 0.970734i \(0.422800\pi\)
\(168\) 9.96567 0.768868
\(169\) 1.63569 0.125822
\(170\) −11.7269 −0.899414
\(171\) 12.5081 0.956519
\(172\) −58.6504 −4.47205
\(173\) 25.6014 1.94644 0.973218 0.229885i \(-0.0738349\pi\)
0.973218 + 0.229885i \(0.0738349\pi\)
\(174\) −3.52867 −0.267508
\(175\) −27.4830 −2.07752
\(176\) 31.4345 2.36946
\(177\) −8.17956 −0.614814
\(178\) 18.0949 1.35627
\(179\) −10.0094 −0.748139 −0.374070 0.927401i \(-0.622038\pi\)
−0.374070 + 0.927401i \(0.622038\pi\)
\(180\) −60.9285 −4.54134
\(181\) 2.08321 0.154844 0.0774220 0.996998i \(-0.475331\pi\)
0.0774220 + 0.996998i \(0.475331\pi\)
\(182\) 20.2650 1.50214
\(183\) 0.674472 0.0498584
\(184\) 2.11965 0.156262
\(185\) −33.6944 −2.47726
\(186\) 15.1607 1.11164
\(187\) 2.40712 0.176026
\(188\) −27.1112 −1.97729
\(189\) 6.45221 0.469330
\(190\) 55.0437 3.99329
\(191\) 5.35449 0.387437 0.193719 0.981057i \(-0.437945\pi\)
0.193719 + 0.981057i \(0.437945\pi\)
\(192\) 12.4113 0.895712
\(193\) −13.8144 −0.994382 −0.497191 0.867641i \(-0.665635\pi\)
−0.497191 + 0.867641i \(0.665635\pi\)
\(194\) 50.7731 3.64529
\(195\) 9.64656 0.690805
\(196\) −16.4285 −1.17347
\(197\) −25.5850 −1.82286 −0.911428 0.411460i \(-0.865019\pi\)
−0.911428 + 0.411460i \(0.865019\pi\)
\(198\) 17.2712 1.22741
\(199\) 22.1085 1.56723 0.783615 0.621247i \(-0.213373\pi\)
0.783615 + 0.621247i \(0.213373\pi\)
\(200\) −122.226 −8.64269
\(201\) −2.27166 −0.160230
\(202\) −13.1470 −0.925022
\(203\) −4.45349 −0.312574
\(204\) 3.03923 0.212789
\(205\) −8.18734 −0.571829
\(206\) 12.4822 0.869676
\(207\) 0.645576 0.0448706
\(208\) 49.9591 3.46404
\(209\) −11.2985 −0.781535
\(210\) 13.3569 0.921716
\(211\) −2.14083 −0.147381 −0.0736905 0.997281i \(-0.523478\pi\)
−0.0736905 + 0.997281i \(0.523478\pi\)
\(212\) −11.8747 −0.815560
\(213\) −2.03752 −0.139609
\(214\) 6.41814 0.438735
\(215\) −48.6602 −3.31860
\(216\) 28.6952 1.95246
\(217\) 19.1341 1.29891
\(218\) −10.5787 −0.716477
\(219\) 9.38790 0.634375
\(220\) 55.0364 3.71056
\(221\) 3.82566 0.257342
\(222\) 12.0594 0.809374
\(223\) −10.7208 −0.717918 −0.358959 0.933353i \(-0.616868\pi\)
−0.358959 + 0.933353i \(0.616868\pi\)
\(224\) 34.7480 2.32170
\(225\) −37.2261 −2.48174
\(226\) 10.5097 0.699094
\(227\) 20.3745 1.35231 0.676153 0.736762i \(-0.263646\pi\)
0.676153 + 0.736762i \(0.263646\pi\)
\(228\) −14.2655 −0.944755
\(229\) 15.4128 1.01851 0.509254 0.860616i \(-0.329921\pi\)
0.509254 + 0.860616i \(0.329921\pi\)
\(230\) 2.84095 0.187327
\(231\) −2.74170 −0.180391
\(232\) −19.8062 −1.30034
\(233\) 29.1057 1.90678 0.953388 0.301749i \(-0.0975703\pi\)
0.953388 + 0.301749i \(0.0975703\pi\)
\(234\) 27.4493 1.79442
\(235\) −22.4932 −1.46729
\(236\) −74.1680 −4.82792
\(237\) −3.45713 −0.224565
\(238\) 5.29713 0.343362
\(239\) −3.61041 −0.233538 −0.116769 0.993159i \(-0.537254\pi\)
−0.116769 + 0.993159i \(0.537254\pi\)
\(240\) 32.9287 2.12554
\(241\) 11.0836 0.713956 0.356978 0.934113i \(-0.383807\pi\)
0.356978 + 0.934113i \(0.383807\pi\)
\(242\) 14.0165 0.901018
\(243\) 13.3680 0.857557
\(244\) 6.11576 0.391521
\(245\) −13.6302 −0.870799
\(246\) 2.93029 0.186828
\(247\) −17.9568 −1.14257
\(248\) 85.0960 5.40360
\(249\) −1.27491 −0.0807940
\(250\) −105.184 −6.65243
\(251\) −12.0481 −0.760468 −0.380234 0.924890i \(-0.624157\pi\)
−0.380234 + 0.924890i \(0.624157\pi\)
\(252\) 27.5218 1.73371
\(253\) −0.583146 −0.0366621
\(254\) −26.4489 −1.65955
\(255\) 2.52154 0.157905
\(256\) 17.4281 1.08926
\(257\) 8.97975 0.560142 0.280071 0.959979i \(-0.409642\pi\)
0.280071 + 0.959979i \(0.409642\pi\)
\(258\) 17.4157 1.08425
\(259\) 15.2200 0.945725
\(260\) 87.4699 5.42466
\(261\) −6.03232 −0.373391
\(262\) 32.6434 2.01672
\(263\) 15.5660 0.959840 0.479920 0.877312i \(-0.340666\pi\)
0.479920 + 0.877312i \(0.340666\pi\)
\(264\) −12.1933 −0.750445
\(265\) −9.85206 −0.605207
\(266\) −24.8636 −1.52449
\(267\) −3.89079 −0.238112
\(268\) −20.5982 −1.25823
\(269\) −23.0578 −1.40586 −0.702930 0.711259i \(-0.748125\pi\)
−0.702930 + 0.711259i \(0.748125\pi\)
\(270\) 38.4600 2.34060
\(271\) −28.2651 −1.71698 −0.858492 0.512827i \(-0.828598\pi\)
−0.858492 + 0.512827i \(0.828598\pi\)
\(272\) 13.0590 0.791815
\(273\) −4.35742 −0.263723
\(274\) 17.1632 1.03687
\(275\) 33.6262 2.02774
\(276\) −0.736279 −0.0443188
\(277\) −15.2700 −0.917488 −0.458744 0.888568i \(-0.651701\pi\)
−0.458744 + 0.888568i \(0.651701\pi\)
\(278\) −19.5373 −1.17177
\(279\) 25.9175 1.55164
\(280\) 74.9714 4.48040
\(281\) 7.84550 0.468023 0.234012 0.972234i \(-0.424815\pi\)
0.234012 + 0.972234i \(0.424815\pi\)
\(282\) 8.05043 0.479396
\(283\) 0.299888 0.0178265 0.00891323 0.999960i \(-0.497163\pi\)
0.00891323 + 0.999960i \(0.497163\pi\)
\(284\) −18.4752 −1.09630
\(285\) −11.8356 −0.701079
\(286\) −24.7948 −1.46615
\(287\) 3.69828 0.218302
\(288\) 47.0667 2.77343
\(289\) 1.00000 0.0588235
\(290\) −26.5461 −1.55884
\(291\) −10.9173 −0.639984
\(292\) 85.1245 4.98154
\(293\) −12.8401 −0.750128 −0.375064 0.926999i \(-0.622379\pi\)
−0.375064 + 0.926999i \(0.622379\pi\)
\(294\) 4.87830 0.284508
\(295\) −61.5346 −3.58268
\(296\) 67.6885 3.93431
\(297\) −7.89447 −0.458083
\(298\) 20.2905 1.17540
\(299\) −0.926799 −0.0535982
\(300\) 42.4564 2.45122
\(301\) 21.9801 1.26691
\(302\) 19.3777 1.11506
\(303\) 2.82690 0.162401
\(304\) −61.2959 −3.51556
\(305\) 5.07403 0.290538
\(306\) 7.17504 0.410170
\(307\) 25.6965 1.46658 0.733289 0.679917i \(-0.237984\pi\)
0.733289 + 0.679917i \(0.237984\pi\)
\(308\) −24.8603 −1.41655
\(309\) −2.68394 −0.152684
\(310\) 114.054 6.47781
\(311\) −5.46339 −0.309801 −0.154900 0.987930i \(-0.549506\pi\)
−0.154900 + 0.987930i \(0.549506\pi\)
\(312\) −19.3789 −1.09711
\(313\) 0.773421 0.0437163 0.0218582 0.999761i \(-0.493042\pi\)
0.0218582 + 0.999761i \(0.493042\pi\)
\(314\) −15.2393 −0.860001
\(315\) 22.8339 1.28654
\(316\) −31.3474 −1.76343
\(317\) −13.8154 −0.775951 −0.387975 0.921670i \(-0.626825\pi\)
−0.387975 + 0.921670i \(0.626825\pi\)
\(318\) 3.52610 0.197734
\(319\) 5.44897 0.305084
\(320\) 93.3701 5.21955
\(321\) −1.38004 −0.0770262
\(322\) −1.28328 −0.0715141
\(323\) −4.69379 −0.261169
\(324\) 32.0000 1.77778
\(325\) 53.4424 2.96445
\(326\) −31.7624 −1.75916
\(327\) 2.27464 0.125788
\(328\) 16.4475 0.908160
\(329\) 10.1603 0.560157
\(330\) −16.3426 −0.899629
\(331\) 22.8517 1.25604 0.628021 0.778196i \(-0.283865\pi\)
0.628021 + 0.778196i \(0.283865\pi\)
\(332\) −11.5602 −0.634448
\(333\) 20.6157 1.12974
\(334\) −16.7126 −0.914473
\(335\) −17.0896 −0.933704
\(336\) −14.8741 −0.811449
\(337\) 32.1850 1.75323 0.876615 0.481192i \(-0.159796\pi\)
0.876615 + 0.481192i \(0.159796\pi\)
\(338\) −4.40409 −0.239551
\(339\) −2.25981 −0.122736
\(340\) 22.8640 1.23997
\(341\) −23.4112 −1.26779
\(342\) −33.6781 −1.82110
\(343\) 19.9284 1.07603
\(344\) 97.7530 5.27049
\(345\) −0.610865 −0.0328879
\(346\) −68.9318 −3.70580
\(347\) −14.0641 −0.754999 −0.377499 0.926010i \(-0.623216\pi\)
−0.377499 + 0.926010i \(0.623216\pi\)
\(348\) 6.87986 0.368799
\(349\) 26.3694 1.41152 0.705761 0.708450i \(-0.250605\pi\)
0.705761 + 0.708450i \(0.250605\pi\)
\(350\) 73.9981 3.95536
\(351\) −12.5468 −0.669696
\(352\) −42.5152 −2.26607
\(353\) 1.00000 0.0532246
\(354\) 22.0235 1.17054
\(355\) −15.3282 −0.813537
\(356\) −35.2796 −1.86982
\(357\) −1.13900 −0.0602821
\(358\) 26.9504 1.42437
\(359\) −8.44042 −0.445468 −0.222734 0.974879i \(-0.571498\pi\)
−0.222734 + 0.974879i \(0.571498\pi\)
\(360\) 101.550 5.35215
\(361\) 3.03165 0.159560
\(362\) −5.60906 −0.294806
\(363\) −3.01386 −0.158187
\(364\) −39.5108 −2.07093
\(365\) 70.6248 3.69667
\(366\) −1.81602 −0.0949248
\(367\) 17.2351 0.899663 0.449831 0.893114i \(-0.351484\pi\)
0.449831 + 0.893114i \(0.351484\pi\)
\(368\) −3.16364 −0.164916
\(369\) 5.00937 0.260778
\(370\) 90.7225 4.71644
\(371\) 4.45024 0.231045
\(372\) −29.5589 −1.53256
\(373\) 2.56498 0.132810 0.0664049 0.997793i \(-0.478847\pi\)
0.0664049 + 0.997793i \(0.478847\pi\)
\(374\) −6.48119 −0.335134
\(375\) 22.6169 1.16793
\(376\) 45.1864 2.33031
\(377\) 8.66010 0.446018
\(378\) −17.3726 −0.893551
\(379\) −29.6961 −1.52538 −0.762692 0.646761i \(-0.776123\pi\)
−0.762692 + 0.646761i \(0.776123\pi\)
\(380\) −107.319 −5.50534
\(381\) 5.68709 0.291358
\(382\) −14.4170 −0.737637
\(383\) −15.6091 −0.797585 −0.398793 0.917041i \(-0.630571\pi\)
−0.398793 + 0.917041i \(0.630571\pi\)
\(384\) −12.9666 −0.661699
\(385\) −20.6257 −1.05119
\(386\) 37.1953 1.89319
\(387\) 29.7724 1.51342
\(388\) −98.9924 −5.02558
\(389\) 7.79792 0.395370 0.197685 0.980266i \(-0.436658\pi\)
0.197685 + 0.980266i \(0.436658\pi\)
\(390\) −25.9734 −1.31522
\(391\) −0.242259 −0.0122515
\(392\) 27.3815 1.38298
\(393\) −7.01905 −0.354064
\(394\) 68.8877 3.47051
\(395\) −26.0078 −1.30860
\(396\) −33.6737 −1.69217
\(397\) 21.1464 1.06131 0.530653 0.847589i \(-0.321947\pi\)
0.530653 + 0.847589i \(0.321947\pi\)
\(398\) −59.5273 −2.98383
\(399\) 5.34621 0.267645
\(400\) 182.427 9.12133
\(401\) −12.4153 −0.619991 −0.309996 0.950738i \(-0.600328\pi\)
−0.309996 + 0.950738i \(0.600328\pi\)
\(402\) 6.11645 0.305061
\(403\) −37.2076 −1.85344
\(404\) 25.6328 1.27528
\(405\) 26.5493 1.31925
\(406\) 11.9910 0.595106
\(407\) −18.6221 −0.923064
\(408\) −5.06550 −0.250780
\(409\) −11.1828 −0.552954 −0.276477 0.961021i \(-0.589167\pi\)
−0.276477 + 0.961021i \(0.589167\pi\)
\(410\) 22.0445 1.08870
\(411\) −3.69046 −0.182037
\(412\) −24.3366 −1.19898
\(413\) 27.7956 1.36773
\(414\) −1.73822 −0.0854287
\(415\) −9.59109 −0.470808
\(416\) −67.5698 −3.31288
\(417\) 4.20095 0.205721
\(418\) 30.4213 1.48796
\(419\) −9.81638 −0.479562 −0.239781 0.970827i \(-0.577076\pi\)
−0.239781 + 0.970827i \(0.577076\pi\)
\(420\) −26.0420 −1.27072
\(421\) 24.2613 1.18242 0.591212 0.806516i \(-0.298650\pi\)
0.591212 + 0.806516i \(0.298650\pi\)
\(422\) 5.76420 0.280597
\(423\) 13.7623 0.669147
\(424\) 19.7917 0.961170
\(425\) 13.9695 0.677619
\(426\) 5.48604 0.265800
\(427\) −2.29197 −0.110916
\(428\) −12.5135 −0.604861
\(429\) 5.33142 0.257404
\(430\) 131.018 6.31824
\(431\) 19.0614 0.918158 0.459079 0.888396i \(-0.348180\pi\)
0.459079 + 0.888396i \(0.348180\pi\)
\(432\) −42.8285 −2.06059
\(433\) 1.34682 0.0647240 0.0323620 0.999476i \(-0.489697\pi\)
0.0323620 + 0.999476i \(0.489697\pi\)
\(434\) −51.5188 −2.47298
\(435\) 5.70798 0.273677
\(436\) 20.6252 0.987769
\(437\) 1.13711 0.0543954
\(438\) −25.2770 −1.20778
\(439\) 12.7792 0.609918 0.304959 0.952365i \(-0.401357\pi\)
0.304959 + 0.952365i \(0.401357\pi\)
\(440\) −91.7296 −4.37304
\(441\) 8.33953 0.397121
\(442\) −10.3006 −0.489950
\(443\) 25.5572 1.21426 0.607130 0.794603i \(-0.292321\pi\)
0.607130 + 0.794603i \(0.292321\pi\)
\(444\) −23.5122 −1.11584
\(445\) −29.2703 −1.38754
\(446\) 28.8658 1.36684
\(447\) −4.36289 −0.206358
\(448\) −42.1759 −1.99262
\(449\) −38.7111 −1.82689 −0.913445 0.406962i \(-0.866588\pi\)
−0.913445 + 0.406962i \(0.866588\pi\)
\(450\) 100.232 4.72496
\(451\) −4.52495 −0.213071
\(452\) −20.4908 −0.963805
\(453\) −4.16662 −0.195765
\(454\) −54.8585 −2.57464
\(455\) −32.7807 −1.53678
\(456\) 23.7764 1.11343
\(457\) −37.2898 −1.74434 −0.872172 0.489199i \(-0.837289\pi\)
−0.872172 + 0.489199i \(0.837289\pi\)
\(458\) −41.4991 −1.93913
\(459\) −3.27963 −0.153080
\(460\) −5.53900 −0.258257
\(461\) 16.7272 0.779062 0.389531 0.921013i \(-0.372637\pi\)
0.389531 + 0.921013i \(0.372637\pi\)
\(462\) 7.38205 0.343444
\(463\) 42.4563 1.97311 0.986557 0.163418i \(-0.0522521\pi\)
0.986557 + 0.163418i \(0.0522521\pi\)
\(464\) 29.5614 1.37235
\(465\) −24.5240 −1.13727
\(466\) −78.3671 −3.63029
\(467\) 20.3855 0.943328 0.471664 0.881778i \(-0.343654\pi\)
0.471664 + 0.881778i \(0.343654\pi\)
\(468\) −53.5179 −2.47387
\(469\) 7.71948 0.356453
\(470\) 60.5631 2.79357
\(471\) 3.27677 0.150986
\(472\) 123.616 5.68990
\(473\) −26.8933 −1.23656
\(474\) 9.30833 0.427546
\(475\) −65.5697 −3.00854
\(476\) −10.3278 −0.473375
\(477\) 6.02792 0.275999
\(478\) 9.72106 0.444631
\(479\) −27.5629 −1.25938 −0.629690 0.776847i \(-0.716818\pi\)
−0.629690 + 0.776847i \(0.716818\pi\)
\(480\) −44.5361 −2.03279
\(481\) −29.5963 −1.34947
\(482\) −29.8426 −1.35929
\(483\) 0.275932 0.0125553
\(484\) −27.3281 −1.24219
\(485\) −82.1305 −3.72935
\(486\) −35.9934 −1.63269
\(487\) −4.68052 −0.212095 −0.106047 0.994361i \(-0.533819\pi\)
−0.106047 + 0.994361i \(0.533819\pi\)
\(488\) −10.1932 −0.461423
\(489\) 6.82961 0.308846
\(490\) 36.6993 1.65791
\(491\) 7.63422 0.344527 0.172264 0.985051i \(-0.444892\pi\)
0.172264 + 0.985051i \(0.444892\pi\)
\(492\) −5.71319 −0.257570
\(493\) 2.26369 0.101951
\(494\) 48.3489 2.17532
\(495\) −27.9379 −1.25571
\(496\) −127.009 −5.70285
\(497\) 6.92386 0.310578
\(498\) 3.43270 0.153823
\(499\) −5.15145 −0.230611 −0.115305 0.993330i \(-0.536785\pi\)
−0.115305 + 0.993330i \(0.536785\pi\)
\(500\) 205.078 9.17136
\(501\) 3.59357 0.160549
\(502\) 32.4395 1.44785
\(503\) −16.5271 −0.736908 −0.368454 0.929646i \(-0.620113\pi\)
−0.368454 + 0.929646i \(0.620113\pi\)
\(504\) −45.8708 −2.04325
\(505\) 21.2666 0.946353
\(506\) 1.57012 0.0698005
\(507\) 0.946975 0.0420566
\(508\) 51.5675 2.28794
\(509\) −38.7966 −1.71963 −0.859814 0.510607i \(-0.829421\pi\)
−0.859814 + 0.510607i \(0.829421\pi\)
\(510\) −6.78926 −0.300634
\(511\) −31.9017 −1.41125
\(512\) −2.13152 −0.0942010
\(513\) 15.3939 0.679657
\(514\) −24.1780 −1.06645
\(515\) −20.1912 −0.889730
\(516\) −33.9554 −1.49480
\(517\) −12.4315 −0.546735
\(518\) −40.9799 −1.80056
\(519\) 14.8218 0.650606
\(520\) −145.787 −6.39317
\(521\) −2.29483 −0.100538 −0.0502692 0.998736i \(-0.516008\pi\)
−0.0502692 + 0.998736i \(0.516008\pi\)
\(522\) 16.2421 0.710896
\(523\) 4.67119 0.204257 0.102129 0.994771i \(-0.467435\pi\)
0.102129 + 0.994771i \(0.467435\pi\)
\(524\) −63.6450 −2.78034
\(525\) −15.9112 −0.694421
\(526\) −41.9115 −1.82743
\(527\) −9.72579 −0.423662
\(528\) 18.1989 0.792005
\(529\) −22.9413 −0.997448
\(530\) 26.5267 1.15225
\(531\) 37.6495 1.63385
\(532\) 48.4766 2.10173
\(533\) −7.19154 −0.311500
\(534\) 10.4760 0.453339
\(535\) −10.3820 −0.448852
\(536\) 34.3311 1.48288
\(537\) −5.79492 −0.250069
\(538\) 62.0833 2.67660
\(539\) −7.53307 −0.324472
\(540\) −74.9855 −3.22686
\(541\) −25.7674 −1.10783 −0.553914 0.832574i \(-0.686866\pi\)
−0.553914 + 0.832574i \(0.686866\pi\)
\(542\) 76.1040 3.26895
\(543\) 1.20607 0.0517574
\(544\) −17.6623 −0.757263
\(545\) 17.1120 0.732999
\(546\) 11.7324 0.502099
\(547\) 33.2582 1.42202 0.711008 0.703183i \(-0.248239\pi\)
0.711008 + 0.703183i \(0.248239\pi\)
\(548\) −33.4631 −1.42947
\(549\) −3.10451 −0.132497
\(550\) −90.5387 −3.86058
\(551\) −10.6253 −0.452652
\(552\) 1.22716 0.0522315
\(553\) 11.7479 0.499572
\(554\) 41.1147 1.74680
\(555\) −19.5073 −0.828038
\(556\) 38.0920 1.61546
\(557\) 10.5891 0.448673 0.224337 0.974512i \(-0.427979\pi\)
0.224337 + 0.974512i \(0.427979\pi\)
\(558\) −69.7830 −2.95415
\(559\) −42.7418 −1.80778
\(560\) −111.897 −4.72853
\(561\) 1.39360 0.0588376
\(562\) −21.1240 −0.891064
\(563\) 7.39860 0.311814 0.155907 0.987772i \(-0.450170\pi\)
0.155907 + 0.987772i \(0.450170\pi\)
\(564\) −15.6959 −0.660918
\(565\) −17.0005 −0.715215
\(566\) −0.807449 −0.0339396
\(567\) −11.9925 −0.503638
\(568\) 30.7927 1.29203
\(569\) 5.69078 0.238570 0.119285 0.992860i \(-0.461940\pi\)
0.119285 + 0.992860i \(0.461940\pi\)
\(570\) 31.8674 1.33478
\(571\) 9.54424 0.399414 0.199707 0.979856i \(-0.436001\pi\)
0.199707 + 0.979856i \(0.436001\pi\)
\(572\) 48.3425 2.02130
\(573\) 3.09996 0.129503
\(574\) −9.95763 −0.415623
\(575\) −3.38422 −0.141132
\(576\) −57.1279 −2.38033
\(577\) −35.4649 −1.47642 −0.738211 0.674570i \(-0.764329\pi\)
−0.738211 + 0.674570i \(0.764329\pi\)
\(578\) −2.69250 −0.111993
\(579\) −7.99780 −0.332377
\(580\) 51.7570 2.14909
\(581\) 4.33236 0.179737
\(582\) 29.3949 1.21846
\(583\) −5.44499 −0.225509
\(584\) −141.878 −5.87094
\(585\) −44.4020 −1.83579
\(586\) 34.5721 1.42816
\(587\) 7.32282 0.302245 0.151123 0.988515i \(-0.451711\pi\)
0.151123 + 0.988515i \(0.451711\pi\)
\(588\) −9.51124 −0.392237
\(589\) 45.6508 1.88101
\(590\) 165.682 6.82102
\(591\) −14.8124 −0.609299
\(592\) −101.027 −4.15220
\(593\) −7.71402 −0.316777 −0.158388 0.987377i \(-0.550630\pi\)
−0.158388 + 0.987377i \(0.550630\pi\)
\(594\) 21.2559 0.872140
\(595\) −8.56863 −0.351280
\(596\) −39.5604 −1.62046
\(597\) 12.7996 0.523855
\(598\) 2.49541 0.102045
\(599\) −11.0517 −0.451561 −0.225780 0.974178i \(-0.572493\pi\)
−0.225780 + 0.974178i \(0.572493\pi\)
\(600\) −70.7624 −2.88886
\(601\) 34.5067 1.40756 0.703780 0.710418i \(-0.251494\pi\)
0.703780 + 0.710418i \(0.251494\pi\)
\(602\) −59.1816 −2.41206
\(603\) 10.4562 0.425808
\(604\) −37.7807 −1.53728
\(605\) −22.6732 −0.921795
\(606\) −7.61143 −0.309193
\(607\) 18.2206 0.739553 0.369777 0.929121i \(-0.379434\pi\)
0.369777 + 0.929121i \(0.379434\pi\)
\(608\) 82.9029 3.36216
\(609\) −2.57833 −0.104479
\(610\) −13.6618 −0.553152
\(611\) −19.7574 −0.799300
\(612\) −13.9892 −0.565480
\(613\) −10.8366 −0.437685 −0.218842 0.975760i \(-0.570228\pi\)
−0.218842 + 0.975760i \(0.570228\pi\)
\(614\) −69.1880 −2.79220
\(615\) −4.74003 −0.191137
\(616\) 41.4349 1.66946
\(617\) −30.8475 −1.24188 −0.620938 0.783860i \(-0.713248\pi\)
−0.620938 + 0.783860i \(0.713248\pi\)
\(618\) 7.22652 0.290693
\(619\) 42.8934 1.72403 0.862016 0.506881i \(-0.169201\pi\)
0.862016 + 0.506881i \(0.169201\pi\)
\(620\) −222.370 −8.93061
\(621\) 0.794518 0.0318829
\(622\) 14.7102 0.589826
\(623\) 13.2216 0.529711
\(624\) 28.9237 1.15787
\(625\) 100.299 4.01194
\(626\) −2.08244 −0.0832310
\(627\) −6.54124 −0.261232
\(628\) 29.7120 1.18564
\(629\) −7.73625 −0.308465
\(630\) −61.4803 −2.44943
\(631\) −10.1179 −0.402786 −0.201393 0.979511i \(-0.564547\pi\)
−0.201393 + 0.979511i \(0.564547\pi\)
\(632\) 52.2469 2.07827
\(633\) −1.23943 −0.0492629
\(634\) 37.1981 1.47732
\(635\) 42.7838 1.69782
\(636\) −6.87484 −0.272605
\(637\) −11.9724 −0.474363
\(638\) −14.6714 −0.580846
\(639\) 9.37847 0.371007
\(640\) −97.5473 −3.85590
\(641\) −42.4430 −1.67640 −0.838199 0.545364i \(-0.816391\pi\)
−0.838199 + 0.545364i \(0.816391\pi\)
\(642\) 3.71576 0.146649
\(643\) 6.04114 0.238239 0.119120 0.992880i \(-0.461993\pi\)
0.119120 + 0.992880i \(0.461993\pi\)
\(644\) 2.50200 0.0985928
\(645\) −28.1716 −1.10926
\(646\) 12.6380 0.497237
\(647\) −10.8239 −0.425531 −0.212765 0.977103i \(-0.568247\pi\)
−0.212765 + 0.977103i \(0.568247\pi\)
\(648\) −53.3347 −2.09519
\(649\) −34.0087 −1.33496
\(650\) −143.894 −5.64399
\(651\) 11.0776 0.434167
\(652\) 61.9273 2.42526
\(653\) 37.5755 1.47044 0.735221 0.677827i \(-0.237078\pi\)
0.735221 + 0.677827i \(0.237078\pi\)
\(654\) −6.12448 −0.239486
\(655\) −52.8040 −2.06322
\(656\) −24.5484 −0.958455
\(657\) −43.2114 −1.68584
\(658\) −27.3567 −1.06648
\(659\) −43.1288 −1.68006 −0.840030 0.542540i \(-0.817463\pi\)
−0.840030 + 0.542540i \(0.817463\pi\)
\(660\) 31.8632 1.24027
\(661\) 45.3021 1.76205 0.881024 0.473072i \(-0.156855\pi\)
0.881024 + 0.473072i \(0.156855\pi\)
\(662\) −61.5283 −2.39136
\(663\) 2.21485 0.0860178
\(664\) 19.2675 0.747722
\(665\) 40.2194 1.55964
\(666\) −55.5080 −2.15089
\(667\) −0.548398 −0.0212341
\(668\) 32.5846 1.26074
\(669\) −6.20677 −0.239968
\(670\) 46.0138 1.77767
\(671\) 2.80429 0.108259
\(672\) 20.1173 0.776040
\(673\) −6.43977 −0.248235 −0.124117 0.992268i \(-0.539610\pi\)
−0.124117 + 0.992268i \(0.539610\pi\)
\(674\) −86.6583 −3.33795
\(675\) −45.8147 −1.76341
\(676\) 8.58667 0.330256
\(677\) −41.9931 −1.61393 −0.806963 0.590602i \(-0.798890\pi\)
−0.806963 + 0.590602i \(0.798890\pi\)
\(678\) 6.08455 0.233676
\(679\) 37.0989 1.42372
\(680\) −38.1076 −1.46136
\(681\) 11.7958 0.452015
\(682\) 63.0347 2.41372
\(683\) 21.9314 0.839182 0.419591 0.907713i \(-0.362174\pi\)
0.419591 + 0.907713i \(0.362174\pi\)
\(684\) 65.6623 2.51066
\(685\) −27.7632 −1.06078
\(686\) −53.6572 −2.04864
\(687\) 8.92321 0.340442
\(688\) −145.900 −5.56237
\(689\) −8.65378 −0.329683
\(690\) 1.64476 0.0626148
\(691\) 36.8635 1.40235 0.701177 0.712988i \(-0.252658\pi\)
0.701177 + 0.712988i \(0.252658\pi\)
\(692\) 134.396 5.10899
\(693\) 12.6197 0.479384
\(694\) 37.8676 1.43743
\(695\) 31.6036 1.19879
\(696\) −11.4667 −0.434645
\(697\) −1.87982 −0.0712031
\(698\) −70.9997 −2.68738
\(699\) 16.8506 0.637349
\(700\) −144.274 −5.45305
\(701\) −31.2126 −1.17888 −0.589441 0.807811i \(-0.700652\pi\)
−0.589441 + 0.807811i \(0.700652\pi\)
\(702\) 33.7822 1.27503
\(703\) 36.3123 1.36955
\(704\) 51.6034 1.94488
\(705\) −13.0224 −0.490451
\(706\) −2.69250 −0.101334
\(707\) −9.60628 −0.361281
\(708\) −42.9393 −1.61376
\(709\) 38.9362 1.46228 0.731139 0.682228i \(-0.238989\pi\)
0.731139 + 0.682228i \(0.238989\pi\)
\(710\) 41.2713 1.54888
\(711\) 15.9127 0.596774
\(712\) 58.8008 2.20365
\(713\) 2.35616 0.0882387
\(714\) 3.06676 0.114770
\(715\) 40.1081 1.49996
\(716\) −52.5453 −1.96371
\(717\) −2.09024 −0.0780614
\(718\) 22.7259 0.848122
\(719\) −16.8161 −0.627135 −0.313567 0.949566i \(-0.601524\pi\)
−0.313567 + 0.949566i \(0.601524\pi\)
\(720\) −151.567 −5.64856
\(721\) 9.12050 0.339665
\(722\) −8.16272 −0.303785
\(723\) 6.41680 0.238643
\(724\) 10.9360 0.406433
\(725\) 31.6225 1.17443
\(726\) 8.11483 0.301170
\(727\) 21.2833 0.789353 0.394677 0.918820i \(-0.370857\pi\)
0.394677 + 0.918820i \(0.370857\pi\)
\(728\) 65.8529 2.44067
\(729\) −10.5478 −0.390661
\(730\) −190.158 −7.03805
\(731\) −11.1724 −0.413226
\(732\) 3.54070 0.130868
\(733\) −47.9327 −1.77043 −0.885217 0.465178i \(-0.845990\pi\)
−0.885217 + 0.465178i \(0.845990\pi\)
\(734\) −46.4055 −1.71286
\(735\) −7.89114 −0.291069
\(736\) 4.27883 0.157720
\(737\) −9.44500 −0.347911
\(738\) −13.4878 −0.496491
\(739\) 24.2502 0.892059 0.446030 0.895018i \(-0.352838\pi\)
0.446030 + 0.895018i \(0.352838\pi\)
\(740\) −176.882 −6.50230
\(741\) −10.3961 −0.381909
\(742\) −11.9823 −0.439884
\(743\) −40.0967 −1.47100 −0.735502 0.677522i \(-0.763054\pi\)
−0.735502 + 0.677522i \(0.763054\pi\)
\(744\) 49.2660 1.80618
\(745\) −32.8219 −1.20250
\(746\) −6.90623 −0.252855
\(747\) 5.86825 0.214708
\(748\) 12.6364 0.462032
\(749\) 4.68961 0.171355
\(750\) −60.8960 −2.22361
\(751\) 33.2447 1.21312 0.606558 0.795040i \(-0.292550\pi\)
0.606558 + 0.795040i \(0.292550\pi\)
\(752\) −67.4423 −2.45937
\(753\) −6.97520 −0.254190
\(754\) −23.3174 −0.849169
\(755\) −31.3454 −1.14077
\(756\) 33.8714 1.23189
\(757\) −16.9208 −0.614998 −0.307499 0.951548i \(-0.599492\pi\)
−0.307499 + 0.951548i \(0.599492\pi\)
\(758\) 79.9568 2.90416
\(759\) −0.337610 −0.0122545
\(760\) 178.869 6.48826
\(761\) 38.1274 1.38212 0.691058 0.722799i \(-0.257145\pi\)
0.691058 + 0.722799i \(0.257145\pi\)
\(762\) −15.3125 −0.554714
\(763\) −7.72962 −0.279831
\(764\) 28.1088 1.01694
\(765\) −11.6063 −0.419628
\(766\) 42.0275 1.51851
\(767\) −54.0503 −1.95164
\(768\) 10.0900 0.364090
\(769\) −4.79264 −0.172827 −0.0864135 0.996259i \(-0.527541\pi\)
−0.0864135 + 0.996259i \(0.527541\pi\)
\(770\) 55.5349 2.00134
\(771\) 5.19880 0.187230
\(772\) −72.5198 −2.61004
\(773\) 42.2915 1.52112 0.760560 0.649268i \(-0.224925\pi\)
0.760560 + 0.649268i \(0.224925\pi\)
\(774\) −80.1624 −2.88138
\(775\) −135.864 −4.88038
\(776\) 164.991 5.92284
\(777\) 8.81157 0.316113
\(778\) −20.9959 −0.752741
\(779\) 8.82346 0.316133
\(780\) 50.6404 1.81322
\(781\) −8.47154 −0.303135
\(782\) 0.652283 0.0233256
\(783\) −7.42406 −0.265314
\(784\) −40.8679 −1.45957
\(785\) 24.6510 0.879833
\(786\) 18.8988 0.674098
\(787\) 17.1003 0.609560 0.304780 0.952423i \(-0.401417\pi\)
0.304780 + 0.952423i \(0.401417\pi\)
\(788\) −134.311 −4.78462
\(789\) 9.01188 0.320831
\(790\) 70.0262 2.49142
\(791\) 7.67923 0.273042
\(792\) 56.1242 1.99429
\(793\) 4.45689 0.158269
\(794\) −56.9367 −2.02061
\(795\) −5.70381 −0.202293
\(796\) 116.060 4.11365
\(797\) 1.45387 0.0514988 0.0257494 0.999668i \(-0.491803\pi\)
0.0257494 + 0.999668i \(0.491803\pi\)
\(798\) −14.3947 −0.509567
\(799\) −5.16445 −0.182705
\(800\) −246.732 −8.72330
\(801\) 17.9088 0.632777
\(802\) 33.4283 1.18039
\(803\) 39.0326 1.37743
\(804\) −11.9252 −0.420571
\(805\) 2.07583 0.0731632
\(806\) 100.182 3.52875
\(807\) −13.3492 −0.469916
\(808\) −42.7224 −1.50297
\(809\) 40.9266 1.43890 0.719452 0.694542i \(-0.244393\pi\)
0.719452 + 0.694542i \(0.244393\pi\)
\(810\) −71.4842 −2.51170
\(811\) −20.0773 −0.705011 −0.352505 0.935810i \(-0.614670\pi\)
−0.352505 + 0.935810i \(0.614670\pi\)
\(812\) −23.3790 −0.820441
\(813\) −16.3640 −0.573911
\(814\) 50.1401 1.75741
\(815\) 51.3789 1.79972
\(816\) 7.56044 0.264668
\(817\) 52.4408 1.83467
\(818\) 30.1097 1.05276
\(819\) 20.0567 0.700836
\(820\) −42.9801 −1.50093
\(821\) −29.2215 −1.01984 −0.509919 0.860223i \(-0.670324\pi\)
−0.509919 + 0.860223i \(0.670324\pi\)
\(822\) 9.93658 0.346578
\(823\) −14.7251 −0.513285 −0.256643 0.966506i \(-0.582616\pi\)
−0.256643 + 0.966506i \(0.582616\pi\)
\(824\) 40.5619 1.41304
\(825\) 19.4678 0.677781
\(826\) −74.8397 −2.60401
\(827\) 35.6780 1.24065 0.620323 0.784346i \(-0.287001\pi\)
0.620323 + 0.784346i \(0.287001\pi\)
\(828\) 3.38900 0.117776
\(829\) 11.0932 0.385284 0.192642 0.981269i \(-0.438294\pi\)
0.192642 + 0.981269i \(0.438294\pi\)
\(830\) 25.8241 0.896366
\(831\) −8.84054 −0.306675
\(832\) 82.0138 2.84332
\(833\) −3.12949 −0.108430
\(834\) −11.3111 −0.391671
\(835\) 27.0343 0.935560
\(836\) −59.3125 −2.05137
\(837\) 31.8970 1.10252
\(838\) 26.4307 0.913032
\(839\) 2.39186 0.0825763 0.0412882 0.999147i \(-0.486854\pi\)
0.0412882 + 0.999147i \(0.486854\pi\)
\(840\) 43.4044 1.49760
\(841\) −23.8757 −0.823301
\(842\) −65.3237 −2.25120
\(843\) 4.54213 0.156439
\(844\) −11.2385 −0.386844
\(845\) 7.12406 0.245075
\(846\) −37.0551 −1.27398
\(847\) 10.2416 0.351906
\(848\) −29.5398 −1.01440
\(849\) 0.173619 0.00595859
\(850\) −37.6129 −1.29011
\(851\) 1.87417 0.0642459
\(852\) −10.6962 −0.366444
\(853\) 35.1312 1.20287 0.601435 0.798922i \(-0.294596\pi\)
0.601435 + 0.798922i \(0.294596\pi\)
\(854\) 6.17115 0.211172
\(855\) 54.4777 1.86310
\(856\) 20.8563 0.712852
\(857\) 17.2762 0.590142 0.295071 0.955475i \(-0.404657\pi\)
0.295071 + 0.955475i \(0.404657\pi\)
\(858\) −14.3549 −0.490068
\(859\) −53.0012 −1.80838 −0.904188 0.427134i \(-0.859523\pi\)
−0.904188 + 0.427134i \(0.859523\pi\)
\(860\) −255.446 −8.71062
\(861\) 2.14110 0.0729687
\(862\) −51.3230 −1.74807
\(863\) 26.2830 0.894683 0.447341 0.894363i \(-0.352371\pi\)
0.447341 + 0.894363i \(0.352371\pi\)
\(864\) 57.9256 1.97067
\(865\) 111.504 3.79125
\(866\) −3.62631 −0.123227
\(867\) 0.578947 0.0196621
\(868\) 100.446 3.40937
\(869\) −14.3739 −0.487601
\(870\) −15.3688 −0.521050
\(871\) −15.0110 −0.508630
\(872\) −34.3762 −1.16413
\(873\) 50.2510 1.70074
\(874\) −3.06168 −0.103563
\(875\) −76.8561 −2.59821
\(876\) 49.2826 1.66510
\(877\) −37.4231 −1.26369 −0.631844 0.775096i \(-0.717702\pi\)
−0.631844 + 0.775096i \(0.717702\pi\)
\(878\) −34.4081 −1.16122
\(879\) −7.43375 −0.250734
\(880\) 136.910 4.61522
\(881\) −36.7620 −1.23854 −0.619271 0.785177i \(-0.712572\pi\)
−0.619271 + 0.785177i \(0.712572\pi\)
\(882\) −22.4542 −0.756073
\(883\) −45.0552 −1.51623 −0.758115 0.652121i \(-0.773879\pi\)
−0.758115 + 0.652121i \(0.773879\pi\)
\(884\) 20.0831 0.675469
\(885\) −35.6252 −1.19753
\(886\) −68.8129 −2.31182
\(887\) 12.6703 0.425427 0.212713 0.977115i \(-0.431770\pi\)
0.212713 + 0.977115i \(0.431770\pi\)
\(888\) 39.1880 1.31506
\(889\) −19.3257 −0.648164
\(890\) 78.8103 2.64173
\(891\) 14.6732 0.491570
\(892\) −56.2797 −1.88438
\(893\) 24.2408 0.811188
\(894\) 11.7471 0.392882
\(895\) −43.5950 −1.45722
\(896\) 44.0628 1.47203
\(897\) −0.536567 −0.0179155
\(898\) 104.230 3.47819
\(899\) −22.0162 −0.734280
\(900\) −195.422 −6.51405
\(901\) −2.26203 −0.0753593
\(902\) 12.1834 0.405664
\(903\) 12.7253 0.423472
\(904\) 34.1521 1.13588
\(905\) 9.07321 0.301604
\(906\) 11.2187 0.372715
\(907\) 4.73160 0.157110 0.0785551 0.996910i \(-0.474969\pi\)
0.0785551 + 0.996910i \(0.474969\pi\)
\(908\) 106.958 3.54952
\(909\) −13.0119 −0.431576
\(910\) 88.2622 2.92586
\(911\) −2.49328 −0.0826059 −0.0413030 0.999147i \(-0.513151\pi\)
−0.0413030 + 0.999147i \(0.513151\pi\)
\(912\) −35.4871 −1.17509
\(913\) −5.30076 −0.175430
\(914\) 100.403 3.32104
\(915\) 2.93759 0.0971138
\(916\) 80.9109 2.67337
\(917\) 23.8519 0.787660
\(918\) 8.83042 0.291447
\(919\) 45.3839 1.49708 0.748538 0.663091i \(-0.230756\pi\)
0.748538 + 0.663091i \(0.230756\pi\)
\(920\) 9.23189 0.304367
\(921\) 14.8769 0.490211
\(922\) −45.0380 −1.48325
\(923\) −13.4639 −0.443170
\(924\) −14.3928 −0.473488
\(925\) −108.071 −3.55336
\(926\) −114.314 −3.75659
\(927\) 12.3539 0.405754
\(928\) −39.9818 −1.31247
\(929\) −4.34099 −0.142423 −0.0712116 0.997461i \(-0.522687\pi\)
−0.0712116 + 0.997461i \(0.522687\pi\)
\(930\) 66.0309 2.16524
\(931\) 14.6892 0.481418
\(932\) 152.793 5.00489
\(933\) −3.16301 −0.103552
\(934\) −54.8880 −1.79599
\(935\) 10.4840 0.342862
\(936\) 89.1987 2.91555
\(937\) −12.9542 −0.423195 −0.211597 0.977357i \(-0.567867\pi\)
−0.211597 + 0.977357i \(0.567867\pi\)
\(938\) −20.7847 −0.678646
\(939\) 0.447769 0.0146124
\(940\) −118.080 −3.85134
\(941\) −2.38003 −0.0775869 −0.0387934 0.999247i \(-0.512351\pi\)
−0.0387934 + 0.999247i \(0.512351\pi\)
\(942\) −8.82272 −0.287460
\(943\) 0.455402 0.0148299
\(944\) −184.501 −6.00501
\(945\) 28.1019 0.914156
\(946\) 72.4103 2.35426
\(947\) 17.4532 0.567152 0.283576 0.958950i \(-0.408479\pi\)
0.283576 + 0.958950i \(0.408479\pi\)
\(948\) −18.1485 −0.589435
\(949\) 62.0349 2.01374
\(950\) 176.547 5.72793
\(951\) −7.99839 −0.259365
\(952\) 17.2135 0.557891
\(953\) −39.5626 −1.28156 −0.640779 0.767725i \(-0.721389\pi\)
−0.640779 + 0.767725i \(0.721389\pi\)
\(954\) −16.2302 −0.525472
\(955\) 23.3209 0.754647
\(956\) −18.9532 −0.612989
\(957\) 3.15466 0.101976
\(958\) 74.2132 2.39772
\(959\) 12.5408 0.404964
\(960\) 54.0563 1.74466
\(961\) 63.5910 2.05132
\(962\) 79.6882 2.56925
\(963\) 6.35215 0.204695
\(964\) 58.1841 1.87398
\(965\) −60.1671 −1.93685
\(966\) −0.742948 −0.0239040
\(967\) −24.8917 −0.800464 −0.400232 0.916414i \(-0.631070\pi\)
−0.400232 + 0.916414i \(0.631070\pi\)
\(968\) 45.5479 1.46397
\(969\) −2.71745 −0.0872972
\(970\) 221.137 7.10027
\(971\) −6.32141 −0.202864 −0.101432 0.994842i \(-0.532342\pi\)
−0.101432 + 0.994842i \(0.532342\pi\)
\(972\) 70.1764 2.25091
\(973\) −14.2756 −0.457653
\(974\) 12.6023 0.403804
\(975\) 30.9403 0.990883
\(976\) 15.2137 0.486977
\(977\) −43.1950 −1.38193 −0.690965 0.722889i \(-0.742814\pi\)
−0.690965 + 0.722889i \(0.742814\pi\)
\(978\) −18.3888 −0.588008
\(979\) −16.1770 −0.517018
\(980\) −71.5527 −2.28567
\(981\) −10.4699 −0.334278
\(982\) −20.5552 −0.655942
\(983\) −38.4324 −1.22580 −0.612902 0.790159i \(-0.709998\pi\)
−0.612902 + 0.790159i \(0.709998\pi\)
\(984\) 9.52221 0.303557
\(985\) −111.433 −3.55054
\(986\) −6.09499 −0.194104
\(987\) 5.88229 0.187235
\(988\) −94.2659 −2.99900
\(989\) 2.70661 0.0860651
\(990\) 75.2229 2.39074
\(991\) −9.71022 −0.308455 −0.154228 0.988035i \(-0.549289\pi\)
−0.154228 + 0.988035i \(0.549289\pi\)
\(992\) 171.779 5.45400
\(993\) 13.2299 0.419838
\(994\) −18.6425 −0.591305
\(995\) 96.2913 3.05264
\(996\) −6.69274 −0.212067
\(997\) −10.4351 −0.330483 −0.165241 0.986253i \(-0.552840\pi\)
−0.165241 + 0.986253i \(0.552840\pi\)
\(998\) 13.8703 0.439057
\(999\) 25.3720 0.802736
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 \(a_p\))