Properties

Label 6023.2.a.b.1.5
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 1.5
Character \(\chi\) = 6023.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.57189 q^{2}\) \(+2.00338 q^{3}\) \(+4.61464 q^{4}\) \(+2.67910 q^{5}\) \(-5.15249 q^{6}\) \(-0.0453210 q^{7}\) \(-6.72459 q^{8}\) \(+1.01355 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.57189 q^{2}\) \(+2.00338 q^{3}\) \(+4.61464 q^{4}\) \(+2.67910 q^{5}\) \(-5.15249 q^{6}\) \(-0.0453210 q^{7}\) \(-6.72459 q^{8}\) \(+1.01355 q^{9}\) \(-6.89035 q^{10}\) \(-1.71421 q^{11}\) \(+9.24490 q^{12}\) \(-0.159583 q^{13}\) \(+0.116561 q^{14}\) \(+5.36726 q^{15}\) \(+8.06564 q^{16}\) \(-4.56077 q^{17}\) \(-2.60674 q^{18}\) \(-1.00000 q^{19}\) \(+12.3631 q^{20}\) \(-0.0907954 q^{21}\) \(+4.40877 q^{22}\) \(-0.753976 q^{23}\) \(-13.4719 q^{24}\) \(+2.17755 q^{25}\) \(+0.410432 q^{26}\) \(-3.97963 q^{27}\) \(-0.209140 q^{28}\) \(+5.11629 q^{29}\) \(-13.8040 q^{30}\) \(-5.02771 q^{31}\) \(-7.29481 q^{32}\) \(-3.43422 q^{33}\) \(+11.7298 q^{34}\) \(-0.121419 q^{35}\) \(+4.67716 q^{36}\) \(-3.38558 q^{37}\) \(+2.57189 q^{38}\) \(-0.319707 q^{39}\) \(-18.0158 q^{40}\) \(-5.43845 q^{41}\) \(+0.233516 q^{42}\) \(+1.37314 q^{43}\) \(-7.91047 q^{44}\) \(+2.71539 q^{45}\) \(+1.93915 q^{46}\) \(-3.67114 q^{47}\) \(+16.1586 q^{48}\) \(-6.99795 q^{49}\) \(-5.60044 q^{50}\) \(-9.13698 q^{51}\) \(-0.736420 q^{52}\) \(+3.57753 q^{53}\) \(+10.2352 q^{54}\) \(-4.59254 q^{55}\) \(+0.304765 q^{56}\) \(-2.00338 q^{57}\) \(-13.1586 q^{58}\) \(+5.99338 q^{59}\) \(+24.7680 q^{60}\) \(+1.57027 q^{61}\) \(+12.9308 q^{62}\) \(-0.0459350 q^{63}\) \(+2.63019 q^{64}\) \(-0.427539 q^{65}\) \(+8.83246 q^{66}\) \(-6.48722 q^{67}\) \(-21.0463 q^{68}\) \(-1.51050 q^{69}\) \(+0.312278 q^{70}\) \(+5.31172 q^{71}\) \(-6.81569 q^{72}\) \(+12.3506 q^{73}\) \(+8.70735 q^{74}\) \(+4.36248 q^{75}\) \(-4.61464 q^{76}\) \(+0.0776898 q^{77}\) \(+0.822252 q^{78}\) \(+3.40787 q^{79}\) \(+21.6086 q^{80}\) \(-11.0134 q^{81}\) \(+13.9871 q^{82}\) \(+4.78052 q^{83}\) \(-0.418988 q^{84}\) \(-12.2187 q^{85}\) \(-3.53157 q^{86}\) \(+10.2499 q^{87}\) \(+11.5274 q^{88}\) \(-9.47975 q^{89}\) \(-6.98370 q^{90}\) \(+0.00723248 q^{91}\) \(-3.47933 q^{92}\) \(-10.0724 q^{93}\) \(+9.44178 q^{94}\) \(-2.67910 q^{95}\) \(-14.6143 q^{96}\) \(-13.4552 q^{97}\) \(+17.9980 q^{98}\) \(-1.73743 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(99q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 80q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 58q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 27q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut -\mathstrut 13q^{14} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 36q^{17} \) \(\mathstrut -\mathstrut 14q^{18} \) \(\mathstrut -\mathstrut 99q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 20q^{21} \) \(\mathstrut -\mathstrut 53q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut -\mathstrut 8q^{25} \) \(\mathstrut -\mathstrut 3q^{26} \) \(\mathstrut -\mathstrut 3q^{27} \) \(\mathstrut -\mathstrut 63q^{28} \) \(\mathstrut -\mathstrut 34q^{29} \) \(\mathstrut -\mathstrut 30q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 43q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut -\mathstrut 25q^{35} \) \(\mathstrut -\mathstrut 16q^{36} \) \(\mathstrut -\mathstrut 80q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 10q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 37q^{42} \) \(\mathstrut -\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 21q^{44} \) \(\mathstrut -\mathstrut 53q^{45} \) \(\mathstrut -\mathstrut 23q^{46} \) \(\mathstrut -\mathstrut 31q^{47} \) \(\mathstrut -\mathstrut 74q^{48} \) \(\mathstrut -\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 29q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut -\mathstrut 71q^{52} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 45q^{55} \) \(\mathstrut -\mathstrut 33q^{56} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 91q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 61q^{61} \) \(\mathstrut -\mathstrut 46q^{62} \) \(\mathstrut -\mathstrut 43q^{63} \) \(\mathstrut -\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 46q^{65} \) \(\mathstrut -\mathstrut 75q^{66} \) \(\mathstrut -\mathstrut 26q^{67} \) \(\mathstrut -\mathstrut 55q^{68} \) \(\mathstrut -\mathstrut 45q^{69} \) \(\mathstrut -\mathstrut 76q^{70} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 77q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 8q^{75} \) \(\mathstrut -\mathstrut 80q^{76} \) \(\mathstrut -\mathstrut 58q^{77} \) \(\mathstrut -\mathstrut 34q^{78} \) \(\mathstrut -\mathstrut 22q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut -\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 109q^{82} \) \(\mathstrut -\mathstrut 7q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 80q^{85} \) \(\mathstrut +\mathstrut 32q^{86} \) \(\mathstrut -\mathstrut 57q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 12q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 107q^{92} \) \(\mathstrut -\mathstrut 121q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 4q^{96} \) \(\mathstrut -\mathstrut 128q^{97} \) \(\mathstrut +\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 34q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57189 −1.81860 −0.909302 0.416137i \(-0.863384\pi\)
−0.909302 + 0.416137i \(0.863384\pi\)
\(3\) 2.00338 1.15665 0.578327 0.815805i \(-0.303706\pi\)
0.578327 + 0.815805i \(0.303706\pi\)
\(4\) 4.61464 2.30732
\(5\) 2.67910 1.19813 0.599064 0.800701i \(-0.295539\pi\)
0.599064 + 0.800701i \(0.295539\pi\)
\(6\) −5.15249 −2.10350
\(7\) −0.0453210 −0.0171297 −0.00856487 0.999963i \(-0.502726\pi\)
−0.00856487 + 0.999963i \(0.502726\pi\)
\(8\) −6.72459 −2.37750
\(9\) 1.01355 0.337849
\(10\) −6.89035 −2.17892
\(11\) −1.71421 −0.516854 −0.258427 0.966031i \(-0.583204\pi\)
−0.258427 + 0.966031i \(0.583204\pi\)
\(12\) 9.24490 2.66877
\(13\) −0.159583 −0.0442605 −0.0221302 0.999755i \(-0.507045\pi\)
−0.0221302 + 0.999755i \(0.507045\pi\)
\(14\) 0.116561 0.0311522
\(15\) 5.36726 1.38582
\(16\) 8.06564 2.01641
\(17\) −4.56077 −1.10615 −0.553075 0.833131i \(-0.686546\pi\)
−0.553075 + 0.833131i \(0.686546\pi\)
\(18\) −2.60674 −0.614414
\(19\) −1.00000 −0.229416
\(20\) 12.3631 2.76447
\(21\) −0.0907954 −0.0198132
\(22\) 4.40877 0.939953
\(23\) −0.753976 −0.157215 −0.0786074 0.996906i \(-0.525047\pi\)
−0.0786074 + 0.996906i \(0.525047\pi\)
\(24\) −13.4719 −2.74995
\(25\) 2.17755 0.435511
\(26\) 0.410432 0.0804922
\(27\) −3.97963 −0.765880
\(28\) −0.209140 −0.0395238
\(29\) 5.11629 0.950071 0.475035 0.879967i \(-0.342435\pi\)
0.475035 + 0.879967i \(0.342435\pi\)
\(30\) −13.8040 −2.52026
\(31\) −5.02771 −0.903004 −0.451502 0.892270i \(-0.649112\pi\)
−0.451502 + 0.892270i \(0.649112\pi\)
\(32\) −7.29481 −1.28955
\(33\) −3.43422 −0.597822
\(34\) 11.7298 2.01165
\(35\) −0.121419 −0.0205236
\(36\) 4.67716 0.779526
\(37\) −3.38558 −0.556586 −0.278293 0.960496i \(-0.589769\pi\)
−0.278293 + 0.960496i \(0.589769\pi\)
\(38\) 2.57189 0.417216
\(39\) −0.319707 −0.0511940
\(40\) −18.0158 −2.84855
\(41\) −5.43845 −0.849344 −0.424672 0.905347i \(-0.639610\pi\)
−0.424672 + 0.905347i \(0.639610\pi\)
\(42\) 0.233516 0.0360323
\(43\) 1.37314 0.209402 0.104701 0.994504i \(-0.466611\pi\)
0.104701 + 0.994504i \(0.466611\pi\)
\(44\) −7.91047 −1.19255
\(45\) 2.71539 0.404787
\(46\) 1.93915 0.285911
\(47\) −3.67114 −0.535491 −0.267745 0.963490i \(-0.586279\pi\)
−0.267745 + 0.963490i \(0.586279\pi\)
\(48\) 16.1586 2.33229
\(49\) −6.99795 −0.999707
\(50\) −5.60044 −0.792022
\(51\) −9.13698 −1.27943
\(52\) −0.736420 −0.102123
\(53\) 3.57753 0.491411 0.245706 0.969344i \(-0.420980\pi\)
0.245706 + 0.969344i \(0.420980\pi\)
\(54\) 10.2352 1.39283
\(55\) −4.59254 −0.619258
\(56\) 0.304765 0.0407259
\(57\) −2.00338 −0.265355
\(58\) −13.1586 −1.72780
\(59\) 5.99338 0.780271 0.390136 0.920757i \(-0.372428\pi\)
0.390136 + 0.920757i \(0.372428\pi\)
\(60\) 24.7680 3.19753
\(61\) 1.57027 0.201052 0.100526 0.994934i \(-0.467947\pi\)
0.100526 + 0.994934i \(0.467947\pi\)
\(62\) 12.9308 1.64221
\(63\) −0.0459350 −0.00578727
\(64\) 2.63019 0.328774
\(65\) −0.427539 −0.0530297
\(66\) 8.83246 1.08720
\(67\) −6.48722 −0.792540 −0.396270 0.918134i \(-0.629696\pi\)
−0.396270 + 0.918134i \(0.629696\pi\)
\(68\) −21.0463 −2.55224
\(69\) −1.51050 −0.181843
\(70\) 0.312278 0.0373243
\(71\) 5.31172 0.630385 0.315192 0.949028i \(-0.397931\pi\)
0.315192 + 0.949028i \(0.397931\pi\)
\(72\) −6.81569 −0.803236
\(73\) 12.3506 1.44553 0.722765 0.691094i \(-0.242871\pi\)
0.722765 + 0.691094i \(0.242871\pi\)
\(74\) 8.70735 1.01221
\(75\) 4.36248 0.503736
\(76\) −4.61464 −0.529336
\(77\) 0.0776898 0.00885357
\(78\) 0.822252 0.0931017
\(79\) 3.40787 0.383415 0.191707 0.981452i \(-0.438598\pi\)
0.191707 + 0.981452i \(0.438598\pi\)
\(80\) 21.6086 2.41592
\(81\) −11.0134 −1.22371
\(82\) 13.9871 1.54462
\(83\) 4.78052 0.524730 0.262365 0.964969i \(-0.415498\pi\)
0.262365 + 0.964969i \(0.415498\pi\)
\(84\) −0.418988 −0.0457154
\(85\) −12.2187 −1.32531
\(86\) −3.53157 −0.380819
\(87\) 10.2499 1.09890
\(88\) 11.5274 1.22882
\(89\) −9.47975 −1.00485 −0.502426 0.864620i \(-0.667559\pi\)
−0.502426 + 0.864620i \(0.667559\pi\)
\(90\) −6.98370 −0.736147
\(91\) 0.00723248 0.000758170 0
\(92\) −3.47933 −0.362745
\(93\) −10.0724 −1.04446
\(94\) 9.44178 0.973846
\(95\) −2.67910 −0.274869
\(96\) −14.6143 −1.49157
\(97\) −13.4552 −1.36617 −0.683084 0.730340i \(-0.739362\pi\)
−0.683084 + 0.730340i \(0.739362\pi\)
\(98\) 17.9980 1.81807
\(99\) −1.73743 −0.174619
\(100\) 10.0486 1.00486
\(101\) 2.82695 0.281292 0.140646 0.990060i \(-0.455082\pi\)
0.140646 + 0.990060i \(0.455082\pi\)
\(102\) 23.4994 2.32678
\(103\) −13.4379 −1.32407 −0.662036 0.749472i \(-0.730307\pi\)
−0.662036 + 0.749472i \(0.730307\pi\)
\(104\) 1.07313 0.105229
\(105\) −0.243250 −0.0237387
\(106\) −9.20103 −0.893683
\(107\) −11.4303 −1.10501 −0.552504 0.833510i \(-0.686328\pi\)
−0.552504 + 0.833510i \(0.686328\pi\)
\(108\) −18.3646 −1.76713
\(109\) 13.9902 1.34002 0.670010 0.742352i \(-0.266290\pi\)
0.670010 + 0.742352i \(0.266290\pi\)
\(110\) 11.8115 1.12618
\(111\) −6.78261 −0.643777
\(112\) −0.365543 −0.0345406
\(113\) 16.6819 1.56931 0.784653 0.619936i \(-0.212841\pi\)
0.784653 + 0.619936i \(0.212841\pi\)
\(114\) 5.15249 0.482575
\(115\) −2.01997 −0.188363
\(116\) 23.6098 2.19212
\(117\) −0.161745 −0.0149534
\(118\) −15.4143 −1.41900
\(119\) 0.206699 0.0189481
\(120\) −36.0926 −3.29479
\(121\) −8.06148 −0.732862
\(122\) −4.03856 −0.365634
\(123\) −10.8953 −0.982397
\(124\) −23.2011 −2.08352
\(125\) −7.56160 −0.676330
\(126\) 0.118140 0.0105247
\(127\) 1.53700 0.136387 0.0681933 0.997672i \(-0.478277\pi\)
0.0681933 + 0.997672i \(0.478277\pi\)
\(128\) 7.82503 0.691641
\(129\) 2.75092 0.242205
\(130\) 1.09959 0.0964400
\(131\) 17.9998 1.57265 0.786327 0.617811i \(-0.211980\pi\)
0.786327 + 0.617811i \(0.211980\pi\)
\(132\) −15.8477 −1.37937
\(133\) 0.0453210 0.00392983
\(134\) 16.6844 1.44132
\(135\) −10.6618 −0.917622
\(136\) 30.6693 2.62987
\(137\) −8.07232 −0.689665 −0.344832 0.938664i \(-0.612064\pi\)
−0.344832 + 0.938664i \(0.612064\pi\)
\(138\) 3.88485 0.330701
\(139\) −12.3743 −1.04957 −0.524785 0.851235i \(-0.675854\pi\)
−0.524785 + 0.851235i \(0.675854\pi\)
\(140\) −0.560307 −0.0473546
\(141\) −7.35470 −0.619378
\(142\) −13.6612 −1.14642
\(143\) 0.273560 0.0228762
\(144\) 8.17491 0.681242
\(145\) 13.7070 1.13831
\(146\) −31.7645 −2.62885
\(147\) −14.0196 −1.15631
\(148\) −15.6232 −1.28422
\(149\) −1.44024 −0.117989 −0.0589945 0.998258i \(-0.518789\pi\)
−0.0589945 + 0.998258i \(0.518789\pi\)
\(150\) −11.2198 −0.916096
\(151\) −6.66305 −0.542231 −0.271116 0.962547i \(-0.587393\pi\)
−0.271116 + 0.962547i \(0.587393\pi\)
\(152\) 6.72459 0.545436
\(153\) −4.62256 −0.373712
\(154\) −0.199810 −0.0161011
\(155\) −13.4697 −1.08191
\(156\) −1.47533 −0.118121
\(157\) −19.8118 −1.58115 −0.790577 0.612362i \(-0.790220\pi\)
−0.790577 + 0.612362i \(0.790220\pi\)
\(158\) −8.76467 −0.697280
\(159\) 7.16716 0.568393
\(160\) −19.5435 −1.54505
\(161\) 0.0341709 0.00269305
\(162\) 28.3252 2.22544
\(163\) 4.61994 0.361861 0.180931 0.983496i \(-0.442089\pi\)
0.180931 + 0.983496i \(0.442089\pi\)
\(164\) −25.0965 −1.95971
\(165\) −9.20061 −0.716267
\(166\) −12.2950 −0.954276
\(167\) −5.02867 −0.389130 −0.194565 0.980890i \(-0.562330\pi\)
−0.194565 + 0.980890i \(0.562330\pi\)
\(168\) 0.610561 0.0471058
\(169\) −12.9745 −0.998041
\(170\) 31.4253 2.41021
\(171\) −1.01355 −0.0775079
\(172\) 6.33654 0.483157
\(173\) −23.5331 −1.78919 −0.894596 0.446876i \(-0.852536\pi\)
−0.894596 + 0.446876i \(0.852536\pi\)
\(174\) −26.3616 −1.99847
\(175\) −0.0986890 −0.00746019
\(176\) −13.8262 −1.04219
\(177\) 12.0070 0.902504
\(178\) 24.3809 1.82743
\(179\) 1.62641 0.121564 0.0607818 0.998151i \(-0.480641\pi\)
0.0607818 + 0.998151i \(0.480641\pi\)
\(180\) 12.5306 0.933973
\(181\) 4.49585 0.334174 0.167087 0.985942i \(-0.446564\pi\)
0.167087 + 0.985942i \(0.446564\pi\)
\(182\) −0.0186012 −0.00137881
\(183\) 3.14585 0.232548
\(184\) 5.07017 0.373778
\(185\) −9.07029 −0.666861
\(186\) 25.9053 1.89947
\(187\) 7.81813 0.571718
\(188\) −16.9410 −1.23555
\(189\) 0.180361 0.0131193
\(190\) 6.89035 0.499879
\(191\) −22.0003 −1.59189 −0.795945 0.605369i \(-0.793025\pi\)
−0.795945 + 0.605369i \(0.793025\pi\)
\(192\) 5.26929 0.380278
\(193\) −4.43301 −0.319095 −0.159548 0.987190i \(-0.551004\pi\)
−0.159548 + 0.987190i \(0.551004\pi\)
\(194\) 34.6053 2.48452
\(195\) −0.856525 −0.0613370
\(196\) −32.2930 −2.30664
\(197\) −17.3597 −1.23683 −0.618413 0.785854i \(-0.712224\pi\)
−0.618413 + 0.785854i \(0.712224\pi\)
\(198\) 4.46850 0.317562
\(199\) −18.0719 −1.28108 −0.640542 0.767923i \(-0.721290\pi\)
−0.640542 + 0.767923i \(0.721290\pi\)
\(200\) −14.6432 −1.03543
\(201\) −12.9964 −0.916694
\(202\) −7.27063 −0.511560
\(203\) −0.231875 −0.0162745
\(204\) −42.1639 −2.95206
\(205\) −14.5701 −1.01762
\(206\) 34.5608 2.40796
\(207\) −0.764190 −0.0531149
\(208\) −1.28714 −0.0892472
\(209\) 1.71421 0.118574
\(210\) 0.625612 0.0431713
\(211\) 0.698799 0.0481073 0.0240537 0.999711i \(-0.492343\pi\)
0.0240537 + 0.999711i \(0.492343\pi\)
\(212\) 16.5090 1.13384
\(213\) 10.6414 0.729137
\(214\) 29.3975 2.00957
\(215\) 3.67877 0.250890
\(216\) 26.7613 1.82088
\(217\) 0.227861 0.0154682
\(218\) −35.9814 −2.43697
\(219\) 24.7430 1.67198
\(220\) −21.1929 −1.42883
\(221\) 0.727823 0.0489587
\(222\) 17.4442 1.17078
\(223\) −1.83991 −0.123209 −0.0616047 0.998101i \(-0.519622\pi\)
−0.0616047 + 0.998101i \(0.519622\pi\)
\(224\) 0.330608 0.0220897
\(225\) 2.20705 0.147137
\(226\) −42.9042 −2.85395
\(227\) 9.77645 0.648886 0.324443 0.945905i \(-0.394823\pi\)
0.324443 + 0.945905i \(0.394823\pi\)
\(228\) −9.24490 −0.612259
\(229\) −21.7250 −1.43563 −0.717815 0.696234i \(-0.754857\pi\)
−0.717815 + 0.696234i \(0.754857\pi\)
\(230\) 5.19516 0.342559
\(231\) 0.155642 0.0102405
\(232\) −34.4049 −2.25879
\(233\) 1.84279 0.120725 0.0603625 0.998177i \(-0.480774\pi\)
0.0603625 + 0.998177i \(0.480774\pi\)
\(234\) 0.415992 0.0271942
\(235\) −9.83533 −0.641587
\(236\) 27.6573 1.80034
\(237\) 6.82726 0.443478
\(238\) −0.531608 −0.0344590
\(239\) −4.88031 −0.315681 −0.157841 0.987465i \(-0.550453\pi\)
−0.157841 + 0.987465i \(0.550453\pi\)
\(240\) 43.2904 2.79438
\(241\) −7.82021 −0.503744 −0.251872 0.967761i \(-0.581046\pi\)
−0.251872 + 0.967761i \(0.581046\pi\)
\(242\) 20.7333 1.33279
\(243\) −10.1251 −0.649526
\(244\) 7.24621 0.463891
\(245\) −18.7482 −1.19778
\(246\) 28.0216 1.78659
\(247\) 0.159583 0.0101540
\(248\) 33.8093 2.14689
\(249\) 9.57722 0.606931
\(250\) 19.4476 1.22998
\(251\) 6.09664 0.384816 0.192408 0.981315i \(-0.438370\pi\)
0.192408 + 0.981315i \(0.438370\pi\)
\(252\) −0.211974 −0.0133531
\(253\) 1.29247 0.0812571
\(254\) −3.95300 −0.248033
\(255\) −24.4788 −1.53292
\(256\) −25.3855 −1.58660
\(257\) −1.28324 −0.0800465 −0.0400233 0.999199i \(-0.512743\pi\)
−0.0400233 + 0.999199i \(0.512743\pi\)
\(258\) −7.07509 −0.440476
\(259\) 0.153438 0.00953416
\(260\) −1.97294 −0.122357
\(261\) 5.18560 0.320981
\(262\) −46.2937 −2.86003
\(263\) −3.63017 −0.223846 −0.111923 0.993717i \(-0.535701\pi\)
−0.111923 + 0.993717i \(0.535701\pi\)
\(264\) 23.0937 1.42132
\(265\) 9.58454 0.588774
\(266\) −0.116561 −0.00714681
\(267\) −18.9916 −1.16227
\(268\) −29.9362 −1.82864
\(269\) −3.48192 −0.212296 −0.106148 0.994350i \(-0.533852\pi\)
−0.106148 + 0.994350i \(0.533852\pi\)
\(270\) 27.4210 1.66879
\(271\) 19.0482 1.15710 0.578548 0.815649i \(-0.303620\pi\)
0.578548 + 0.815649i \(0.303620\pi\)
\(272\) −36.7856 −2.23045
\(273\) 0.0144894 0.000876940 0
\(274\) 20.7612 1.25423
\(275\) −3.73279 −0.225096
\(276\) −6.97043 −0.419571
\(277\) 8.03324 0.482671 0.241335 0.970442i \(-0.422415\pi\)
0.241335 + 0.970442i \(0.422415\pi\)
\(278\) 31.8253 1.90875
\(279\) −5.09583 −0.305079
\(280\) 0.816495 0.0487949
\(281\) 16.6402 0.992671 0.496336 0.868131i \(-0.334679\pi\)
0.496336 + 0.868131i \(0.334679\pi\)
\(282\) 18.9155 1.12640
\(283\) 11.4326 0.679600 0.339800 0.940498i \(-0.389641\pi\)
0.339800 + 0.940498i \(0.389641\pi\)
\(284\) 24.5117 1.45450
\(285\) −5.36726 −0.317929
\(286\) −0.703566 −0.0416028
\(287\) 0.246476 0.0145490
\(288\) −7.39363 −0.435674
\(289\) 3.80065 0.223568
\(290\) −35.2530 −2.07013
\(291\) −26.9559 −1.58018
\(292\) 56.9937 3.33530
\(293\) −6.71705 −0.392414 −0.196207 0.980562i \(-0.562862\pi\)
−0.196207 + 0.980562i \(0.562862\pi\)
\(294\) 36.0569 2.10288
\(295\) 16.0568 0.934865
\(296\) 22.7666 1.32328
\(297\) 6.82192 0.395848
\(298\) 3.70415 0.214575
\(299\) 0.120322 0.00695840
\(300\) 20.1313 1.16228
\(301\) −0.0622320 −0.00358700
\(302\) 17.1367 0.986104
\(303\) 5.66347 0.325358
\(304\) −8.06564 −0.462596
\(305\) 4.20689 0.240886
\(306\) 11.8887 0.679634
\(307\) −21.8895 −1.24930 −0.624651 0.780904i \(-0.714759\pi\)
−0.624651 + 0.780904i \(0.714759\pi\)
\(308\) 0.358511 0.0204280
\(309\) −26.9212 −1.53149
\(310\) 34.6427 1.96757
\(311\) −15.1705 −0.860240 −0.430120 0.902772i \(-0.641529\pi\)
−0.430120 + 0.902772i \(0.641529\pi\)
\(312\) 2.14989 0.121714
\(313\) 13.4554 0.760543 0.380272 0.924875i \(-0.375831\pi\)
0.380272 + 0.924875i \(0.375831\pi\)
\(314\) 50.9539 2.87550
\(315\) −0.123064 −0.00693389
\(316\) 15.7261 0.884661
\(317\) −1.00000 −0.0561656
\(318\) −18.4332 −1.03368
\(319\) −8.77040 −0.491048
\(320\) 7.04654 0.393914
\(321\) −22.8993 −1.27811
\(322\) −0.0878841 −0.00489759
\(323\) 4.56077 0.253768
\(324\) −50.8227 −2.82349
\(325\) −0.347501 −0.0192759
\(326\) −11.8820 −0.658082
\(327\) 28.0278 1.54994
\(328\) 36.5713 2.01931
\(329\) 0.166380 0.00917281
\(330\) 23.6630 1.30261
\(331\) 8.25169 0.453554 0.226777 0.973947i \(-0.427181\pi\)
0.226777 + 0.973947i \(0.427181\pi\)
\(332\) 22.0604 1.21072
\(333\) −3.43144 −0.188042
\(334\) 12.9332 0.707674
\(335\) −17.3799 −0.949564
\(336\) −0.732323 −0.0399515
\(337\) −3.28692 −0.179050 −0.0895250 0.995985i \(-0.528535\pi\)
−0.0895250 + 0.995985i \(0.528535\pi\)
\(338\) 33.3691 1.81504
\(339\) 33.4203 1.81514
\(340\) −56.3852 −3.05791
\(341\) 8.61856 0.466721
\(342\) 2.60674 0.140956
\(343\) 0.634401 0.0342544
\(344\) −9.23379 −0.497853
\(345\) −4.04678 −0.217871
\(346\) 60.5248 3.25383
\(347\) −5.96566 −0.320254 −0.160127 0.987096i \(-0.551190\pi\)
−0.160127 + 0.987096i \(0.551190\pi\)
\(348\) 47.2996 2.53552
\(349\) −8.39802 −0.449536 −0.224768 0.974412i \(-0.572162\pi\)
−0.224768 + 0.974412i \(0.572162\pi\)
\(350\) 0.253818 0.0135671
\(351\) 0.635082 0.0338982
\(352\) 12.5048 0.666510
\(353\) 21.2463 1.13083 0.565414 0.824807i \(-0.308716\pi\)
0.565414 + 0.824807i \(0.308716\pi\)
\(354\) −30.8808 −1.64130
\(355\) 14.2306 0.755282
\(356\) −43.7457 −2.31852
\(357\) 0.414097 0.0219163
\(358\) −4.18296 −0.221076
\(359\) 22.9704 1.21233 0.606165 0.795339i \(-0.292707\pi\)
0.606165 + 0.795339i \(0.292707\pi\)
\(360\) −18.2599 −0.962380
\(361\) 1.00000 0.0526316
\(362\) −11.5629 −0.607730
\(363\) −16.1502 −0.847668
\(364\) 0.0333753 0.00174934
\(365\) 33.0885 1.73193
\(366\) −8.09078 −0.422912
\(367\) −11.3266 −0.591244 −0.295622 0.955305i \(-0.595527\pi\)
−0.295622 + 0.955305i \(0.595527\pi\)
\(368\) −6.08130 −0.317009
\(369\) −5.51213 −0.286950
\(370\) 23.3278 1.21276
\(371\) −0.162137 −0.00841775
\(372\) −46.4807 −2.40991
\(373\) 11.8114 0.611573 0.305786 0.952100i \(-0.401081\pi\)
0.305786 + 0.952100i \(0.401081\pi\)
\(374\) −20.1074 −1.03973
\(375\) −15.1488 −0.782280
\(376\) 24.6869 1.27313
\(377\) −0.816474 −0.0420506
\(378\) −0.463869 −0.0238588
\(379\) 24.5631 1.26172 0.630862 0.775895i \(-0.282702\pi\)
0.630862 + 0.775895i \(0.282702\pi\)
\(380\) −12.3631 −0.634212
\(381\) 3.07920 0.157752
\(382\) 56.5826 2.89502
\(383\) 25.3113 1.29335 0.646675 0.762766i \(-0.276159\pi\)
0.646675 + 0.762766i \(0.276159\pi\)
\(384\) 15.6765 0.799990
\(385\) 0.208138 0.0106077
\(386\) 11.4012 0.580308
\(387\) 1.39174 0.0707462
\(388\) −62.0909 −3.15219
\(389\) 22.3299 1.13217 0.566084 0.824347i \(-0.308458\pi\)
0.566084 + 0.824347i \(0.308458\pi\)
\(390\) 2.20289 0.111548
\(391\) 3.43871 0.173903
\(392\) 47.0583 2.37680
\(393\) 36.0606 1.81902
\(394\) 44.6472 2.24930
\(395\) 9.13000 0.459380
\(396\) −8.01764 −0.402902
\(397\) −29.7196 −1.49158 −0.745791 0.666180i \(-0.767928\pi\)
−0.745791 + 0.666180i \(0.767928\pi\)
\(398\) 46.4791 2.32978
\(399\) 0.0907954 0.00454545
\(400\) 17.5634 0.878169
\(401\) 30.9415 1.54515 0.772573 0.634926i \(-0.218969\pi\)
0.772573 + 0.634926i \(0.218969\pi\)
\(402\) 33.4253 1.66710
\(403\) 0.802339 0.0399674
\(404\) 13.0454 0.649032
\(405\) −29.5059 −1.46616
\(406\) 0.596359 0.0295968
\(407\) 5.80360 0.287674
\(408\) 61.4424 3.04185
\(409\) 20.8914 1.03302 0.516508 0.856283i \(-0.327232\pi\)
0.516508 + 0.856283i \(0.327232\pi\)
\(410\) 37.4729 1.85065
\(411\) −16.1720 −0.797704
\(412\) −62.0109 −3.05506
\(413\) −0.271626 −0.0133658
\(414\) 1.96542 0.0965949
\(415\) 12.8075 0.628694
\(416\) 1.16413 0.0570761
\(417\) −24.7904 −1.21399
\(418\) −4.40877 −0.215640
\(419\) −25.6788 −1.25449 −0.627246 0.778821i \(-0.715818\pi\)
−0.627246 + 0.778821i \(0.715818\pi\)
\(420\) −1.12251 −0.0547729
\(421\) 1.29284 0.0630091 0.0315046 0.999504i \(-0.489970\pi\)
0.0315046 + 0.999504i \(0.489970\pi\)
\(422\) −1.79724 −0.0874882
\(423\) −3.72087 −0.180915
\(424\) −24.0574 −1.16833
\(425\) −9.93133 −0.481740
\(426\) −27.3686 −1.32601
\(427\) −0.0711660 −0.00344397
\(428\) −52.7467 −2.54961
\(429\) 0.548045 0.0264599
\(430\) −9.46141 −0.456270
\(431\) −5.97831 −0.287965 −0.143983 0.989580i \(-0.545991\pi\)
−0.143983 + 0.989580i \(0.545991\pi\)
\(432\) −32.0982 −1.54433
\(433\) −10.9615 −0.526777 −0.263388 0.964690i \(-0.584840\pi\)
−0.263388 + 0.964690i \(0.584840\pi\)
\(434\) −0.586035 −0.0281306
\(435\) 27.4604 1.31663
\(436\) 64.5599 3.09186
\(437\) 0.753976 0.0360675
\(438\) −63.6364 −3.04067
\(439\) 25.7960 1.23117 0.615587 0.788069i \(-0.288919\pi\)
0.615587 + 0.788069i \(0.288919\pi\)
\(440\) 30.8829 1.47228
\(441\) −7.09275 −0.337750
\(442\) −1.87189 −0.0890365
\(443\) 14.5444 0.691027 0.345514 0.938414i \(-0.387705\pi\)
0.345514 + 0.938414i \(0.387705\pi\)
\(444\) −31.2993 −1.48540
\(445\) −25.3972 −1.20394
\(446\) 4.73205 0.224069
\(447\) −2.88535 −0.136473
\(448\) −0.119203 −0.00563182
\(449\) 22.2306 1.04913 0.524565 0.851371i \(-0.324228\pi\)
0.524565 + 0.851371i \(0.324228\pi\)
\(450\) −5.67631 −0.267584
\(451\) 9.32266 0.438987
\(452\) 76.9812 3.62089
\(453\) −13.3487 −0.627174
\(454\) −25.1440 −1.18007
\(455\) 0.0193765 0.000908384 0
\(456\) 13.4719 0.630881
\(457\) −40.2190 −1.88136 −0.940682 0.339290i \(-0.889813\pi\)
−0.940682 + 0.339290i \(0.889813\pi\)
\(458\) 55.8744 2.61084
\(459\) 18.1502 0.847178
\(460\) −9.32145 −0.434615
\(461\) 14.7408 0.686548 0.343274 0.939235i \(-0.388464\pi\)
0.343274 + 0.939235i \(0.388464\pi\)
\(462\) −0.400296 −0.0186235
\(463\) 9.70346 0.450958 0.225479 0.974248i \(-0.427605\pi\)
0.225479 + 0.974248i \(0.427605\pi\)
\(464\) 41.2661 1.91573
\(465\) −26.9850 −1.25140
\(466\) −4.73946 −0.219551
\(467\) −20.5076 −0.948980 −0.474490 0.880261i \(-0.657367\pi\)
−0.474490 + 0.880261i \(0.657367\pi\)
\(468\) −0.746397 −0.0345022
\(469\) 0.294007 0.0135760
\(470\) 25.2954 1.16679
\(471\) −39.6907 −1.82885
\(472\) −40.3030 −1.85509
\(473\) −2.35385 −0.108230
\(474\) −17.5590 −0.806512
\(475\) −2.17755 −0.0999131
\(476\) 0.953841 0.0437192
\(477\) 3.62600 0.166023
\(478\) 12.5517 0.574099
\(479\) −17.5402 −0.801432 −0.400716 0.916202i \(-0.631239\pi\)
−0.400716 + 0.916202i \(0.631239\pi\)
\(480\) −39.1531 −1.78709
\(481\) 0.540282 0.0246347
\(482\) 20.1128 0.916111
\(483\) 0.0684575 0.00311492
\(484\) −37.2008 −1.69095
\(485\) −36.0477 −1.63684
\(486\) 26.0407 1.18123
\(487\) −12.8001 −0.580030 −0.290015 0.957022i \(-0.593660\pi\)
−0.290015 + 0.957022i \(0.593660\pi\)
\(488\) −10.5594 −0.478001
\(489\) 9.25551 0.418548
\(490\) 48.2183 2.17828
\(491\) 28.7433 1.29717 0.648584 0.761143i \(-0.275361\pi\)
0.648584 + 0.761143i \(0.275361\pi\)
\(492\) −50.2780 −2.26671
\(493\) −23.3342 −1.05092
\(494\) −0.410432 −0.0184662
\(495\) −4.65475 −0.209216
\(496\) −40.5517 −1.82083
\(497\) −0.240732 −0.0107983
\(498\) −24.6316 −1.10377
\(499\) −11.1429 −0.498823 −0.249412 0.968398i \(-0.580237\pi\)
−0.249412 + 0.968398i \(0.580237\pi\)
\(500\) −34.8941 −1.56051
\(501\) −10.0744 −0.450089
\(502\) −15.6799 −0.699828
\(503\) 6.12978 0.273314 0.136657 0.990618i \(-0.456364\pi\)
0.136657 + 0.990618i \(0.456364\pi\)
\(504\) 0.308894 0.0137592
\(505\) 7.57368 0.337024
\(506\) −3.32411 −0.147775
\(507\) −25.9930 −1.15439
\(508\) 7.09270 0.314688
\(509\) 30.7647 1.36362 0.681810 0.731530i \(-0.261193\pi\)
0.681810 + 0.731530i \(0.261193\pi\)
\(510\) 62.9570 2.78778
\(511\) −0.559742 −0.0247615
\(512\) 49.6389 2.19375
\(513\) 3.97963 0.175705
\(514\) 3.30037 0.145573
\(515\) −36.0013 −1.58641
\(516\) 12.6945 0.558846
\(517\) 6.29311 0.276771
\(518\) −0.394626 −0.0173389
\(519\) −47.1459 −2.06948
\(520\) 2.87502 0.126078
\(521\) −17.1315 −0.750545 −0.375273 0.926915i \(-0.622451\pi\)
−0.375273 + 0.926915i \(0.622451\pi\)
\(522\) −13.3368 −0.583737
\(523\) 4.07052 0.177991 0.0889957 0.996032i \(-0.471634\pi\)
0.0889957 + 0.996032i \(0.471634\pi\)
\(524\) 83.0628 3.62862
\(525\) −0.197712 −0.00862886
\(526\) 9.33641 0.407087
\(527\) 22.9303 0.998858
\(528\) −27.6992 −1.20545
\(529\) −22.4315 −0.975284
\(530\) −24.6504 −1.07075
\(531\) 6.07457 0.263614
\(532\) 0.209140 0.00906738
\(533\) 0.867886 0.0375923
\(534\) 48.8443 2.11370
\(535\) −30.6228 −1.32394
\(536\) 43.6238 1.88426
\(537\) 3.25832 0.140607
\(538\) 8.95512 0.386083
\(539\) 11.9960 0.516703
\(540\) −49.2004 −2.11725
\(541\) −42.7257 −1.83692 −0.918461 0.395511i \(-0.870567\pi\)
−0.918461 + 0.395511i \(0.870567\pi\)
\(542\) −48.9899 −2.10430
\(543\) 9.00691 0.386524
\(544\) 33.2700 1.42644
\(545\) 37.4812 1.60552
\(546\) −0.0372653 −0.00159481
\(547\) 15.3241 0.655213 0.327607 0.944814i \(-0.393758\pi\)
0.327607 + 0.944814i \(0.393758\pi\)
\(548\) −37.2509 −1.59128
\(549\) 1.59154 0.0679252
\(550\) 9.60034 0.409360
\(551\) −5.11629 −0.217961
\(552\) 10.1575 0.432332
\(553\) −0.154448 −0.00656779
\(554\) −20.6606 −0.877787
\(555\) −18.1713 −0.771327
\(556\) −57.1027 −2.42170
\(557\) −23.4583 −0.993960 −0.496980 0.867762i \(-0.665558\pi\)
−0.496980 + 0.867762i \(0.665558\pi\)
\(558\) 13.1059 0.554818
\(559\) −0.219130 −0.00926821
\(560\) −0.979325 −0.0413840
\(561\) 15.6627 0.661280
\(562\) −42.7969 −1.80528
\(563\) 27.1072 1.14243 0.571216 0.820799i \(-0.306472\pi\)
0.571216 + 0.820799i \(0.306472\pi\)
\(564\) −33.9393 −1.42910
\(565\) 44.6925 1.88023
\(566\) −29.4036 −1.23592
\(567\) 0.499137 0.0209618
\(568\) −35.7191 −1.49874
\(569\) −33.6232 −1.40956 −0.704779 0.709427i \(-0.748954\pi\)
−0.704779 + 0.709427i \(0.748954\pi\)
\(570\) 13.8040 0.578187
\(571\) −18.3753 −0.768981 −0.384491 0.923129i \(-0.625623\pi\)
−0.384491 + 0.923129i \(0.625623\pi\)
\(572\) 1.26238 0.0527827
\(573\) −44.0751 −1.84127
\(574\) −0.633911 −0.0264589
\(575\) −1.64182 −0.0684688
\(576\) 2.66583 0.111076
\(577\) 35.7124 1.48673 0.743363 0.668888i \(-0.233229\pi\)
0.743363 + 0.668888i \(0.233229\pi\)
\(578\) −9.77488 −0.406581
\(579\) −8.88103 −0.369083
\(580\) 63.2530 2.62644
\(581\) −0.216658 −0.00898849
\(582\) 69.3278 2.87373
\(583\) −6.13264 −0.253988
\(584\) −83.0527 −3.43675
\(585\) −0.433331 −0.0179160
\(586\) 17.2755 0.713646
\(587\) −34.5173 −1.42468 −0.712342 0.701833i \(-0.752365\pi\)
−0.712342 + 0.701833i \(0.752365\pi\)
\(588\) −64.6953 −2.66799
\(589\) 5.02771 0.207163
\(590\) −41.2965 −1.70015
\(591\) −34.7781 −1.43058
\(592\) −27.3069 −1.12230
\(593\) 3.83383 0.157436 0.0787182 0.996897i \(-0.474917\pi\)
0.0787182 + 0.996897i \(0.474917\pi\)
\(594\) −17.5453 −0.719891
\(595\) 0.553766 0.0227022
\(596\) −6.64619 −0.272239
\(597\) −36.2050 −1.48177
\(598\) −0.309455 −0.0126546
\(599\) 31.8560 1.30160 0.650801 0.759248i \(-0.274433\pi\)
0.650801 + 0.759248i \(0.274433\pi\)
\(600\) −29.3359 −1.19763
\(601\) 3.55332 0.144943 0.0724715 0.997370i \(-0.476911\pi\)
0.0724715 + 0.997370i \(0.476911\pi\)
\(602\) 0.160054 0.00652332
\(603\) −6.57510 −0.267759
\(604\) −30.7476 −1.25110
\(605\) −21.5975 −0.878062
\(606\) −14.5659 −0.591698
\(607\) −20.6847 −0.839566 −0.419783 0.907624i \(-0.637894\pi\)
−0.419783 + 0.907624i \(0.637894\pi\)
\(608\) 7.29481 0.295843
\(609\) −0.464535 −0.0188239
\(610\) −10.8197 −0.438076
\(611\) 0.585853 0.0237011
\(612\) −21.3315 −0.862273
\(613\) 6.63922 0.268156 0.134078 0.990971i \(-0.457193\pi\)
0.134078 + 0.990971i \(0.457193\pi\)
\(614\) 56.2976 2.27198
\(615\) −29.1896 −1.17704
\(616\) −0.522432 −0.0210494
\(617\) 22.9040 0.922080 0.461040 0.887379i \(-0.347477\pi\)
0.461040 + 0.887379i \(0.347477\pi\)
\(618\) 69.2385 2.78518
\(619\) −16.9595 −0.681658 −0.340829 0.940125i \(-0.610708\pi\)
−0.340829 + 0.940125i \(0.610708\pi\)
\(620\) −62.1580 −2.49632
\(621\) 3.00054 0.120408
\(622\) 39.0169 1.56444
\(623\) 0.429632 0.0172128
\(624\) −2.57864 −0.103228
\(625\) −31.1460 −1.24584
\(626\) −34.6058 −1.38313
\(627\) 3.43422 0.137150
\(628\) −91.4244 −3.64823
\(629\) 15.4409 0.615667
\(630\) 0.316508 0.0126100
\(631\) 20.6358 0.821498 0.410749 0.911748i \(-0.365267\pi\)
0.410749 + 0.911748i \(0.365267\pi\)
\(632\) −22.9165 −0.911569
\(633\) 1.39996 0.0556435
\(634\) 2.57189 0.102143
\(635\) 4.11777 0.163409
\(636\) 33.0739 1.31147
\(637\) 1.11676 0.0442475
\(638\) 22.5565 0.893022
\(639\) 5.38368 0.212975
\(640\) 20.9640 0.828675
\(641\) 34.1749 1.34983 0.674913 0.737897i \(-0.264181\pi\)
0.674913 + 0.737897i \(0.264181\pi\)
\(642\) 58.8945 2.32438
\(643\) 32.9382 1.29896 0.649478 0.760381i \(-0.274988\pi\)
0.649478 + 0.760381i \(0.274988\pi\)
\(644\) 0.157687 0.00621373
\(645\) 7.36999 0.290193
\(646\) −11.7298 −0.461504
\(647\) −10.6900 −0.420266 −0.210133 0.977673i \(-0.567390\pi\)
−0.210133 + 0.977673i \(0.567390\pi\)
\(648\) 74.0603 2.90936
\(649\) −10.2739 −0.403286
\(650\) 0.893737 0.0350553
\(651\) 0.456493 0.0178914
\(652\) 21.3194 0.834930
\(653\) −3.83445 −0.150054 −0.0750269 0.997182i \(-0.523904\pi\)
−0.0750269 + 0.997182i \(0.523904\pi\)
\(654\) −72.0845 −2.81873
\(655\) 48.2233 1.88424
\(656\) −43.8646 −1.71262
\(657\) 12.5179 0.488371
\(658\) −0.427911 −0.0166817
\(659\) 25.7026 1.00123 0.500615 0.865670i \(-0.333107\pi\)
0.500615 + 0.865670i \(0.333107\pi\)
\(660\) −42.4575 −1.65266
\(661\) −2.03423 −0.0791225 −0.0395612 0.999217i \(-0.512596\pi\)
−0.0395612 + 0.999217i \(0.512596\pi\)
\(662\) −21.2225 −0.824835
\(663\) 1.45811 0.0566283
\(664\) −32.1470 −1.24755
\(665\) 0.121419 0.00470844
\(666\) 8.82531 0.341974
\(667\) −3.85756 −0.149365
\(668\) −23.2055 −0.897849
\(669\) −3.68604 −0.142511
\(670\) 44.6992 1.72688
\(671\) −2.69177 −0.103915
\(672\) 0.662335 0.0255501
\(673\) 1.58169 0.0609696 0.0304848 0.999535i \(-0.490295\pi\)
0.0304848 + 0.999535i \(0.490295\pi\)
\(674\) 8.45361 0.325621
\(675\) −8.66586 −0.333549
\(676\) −59.8728 −2.30280
\(677\) 10.9675 0.421516 0.210758 0.977538i \(-0.432407\pi\)
0.210758 + 0.977538i \(0.432407\pi\)
\(678\) −85.9536 −3.30103
\(679\) 0.609803 0.0234021
\(680\) 82.1660 3.15092
\(681\) 19.5860 0.750536
\(682\) −22.1660 −0.848782
\(683\) 0.621889 0.0237959 0.0118980 0.999929i \(-0.496213\pi\)
0.0118980 + 0.999929i \(0.496213\pi\)
\(684\) −4.67716 −0.178836
\(685\) −21.6265 −0.826307
\(686\) −1.63161 −0.0622953
\(687\) −43.5235 −1.66053
\(688\) 11.0752 0.422240
\(689\) −0.570914 −0.0217501
\(690\) 10.4079 0.396222
\(691\) 2.02479 0.0770267 0.0385134 0.999258i \(-0.487738\pi\)
0.0385134 + 0.999258i \(0.487738\pi\)
\(692\) −108.597 −4.12824
\(693\) 0.0787423 0.00299117
\(694\) 15.3431 0.582414
\(695\) −33.1518 −1.25752
\(696\) −68.9262 −2.61264
\(697\) 24.8035 0.939501
\(698\) 21.5988 0.817527
\(699\) 3.69181 0.139637
\(700\) −0.455414 −0.0172130
\(701\) 27.0295 1.02089 0.510445 0.859910i \(-0.329481\pi\)
0.510445 + 0.859910i \(0.329481\pi\)
\(702\) −1.63336 −0.0616474
\(703\) 3.38558 0.127689
\(704\) −4.50871 −0.169928
\(705\) −19.7040 −0.742094
\(706\) −54.6433 −2.05653
\(707\) −0.128120 −0.00481846
\(708\) 55.4082 2.08237
\(709\) −2.11778 −0.0795348 −0.0397674 0.999209i \(-0.512662\pi\)
−0.0397674 + 0.999209i \(0.512662\pi\)
\(710\) −36.5996 −1.37356
\(711\) 3.45403 0.129536
\(712\) 63.7474 2.38903
\(713\) 3.79077 0.141966
\(714\) −1.06501 −0.0398572
\(715\) 0.732892 0.0274086
\(716\) 7.50530 0.280486
\(717\) −9.77714 −0.365134
\(718\) −59.0774 −2.20475
\(719\) −1.97385 −0.0736123 −0.0368062 0.999322i \(-0.511718\pi\)
−0.0368062 + 0.999322i \(0.511718\pi\)
\(720\) 21.9014 0.816216
\(721\) 0.609018 0.0226810
\(722\) −2.57189 −0.0957160
\(723\) −15.6669 −0.582658
\(724\) 20.7467 0.771046
\(725\) 11.1410 0.413766
\(726\) 41.5367 1.54157
\(727\) −20.3535 −0.754871 −0.377435 0.926036i \(-0.623194\pi\)
−0.377435 + 0.926036i \(0.623194\pi\)
\(728\) −0.0486354 −0.00180255
\(729\) 12.7556 0.472430
\(730\) −85.1001 −3.14969
\(731\) −6.26257 −0.231630
\(732\) 14.5170 0.536562
\(733\) 44.0849 1.62831 0.814156 0.580646i \(-0.197200\pi\)
0.814156 + 0.580646i \(0.197200\pi\)
\(734\) 29.1308 1.07524
\(735\) −37.5598 −1.38541
\(736\) 5.50011 0.202737
\(737\) 11.1205 0.409627
\(738\) 14.1766 0.521848
\(739\) −7.25687 −0.266948 −0.133474 0.991052i \(-0.542613\pi\)
−0.133474 + 0.991052i \(0.542613\pi\)
\(740\) −41.8561 −1.53866
\(741\) 0.319707 0.0117447
\(742\) 0.417000 0.0153085
\(743\) 8.83598 0.324161 0.162080 0.986778i \(-0.448180\pi\)
0.162080 + 0.986778i \(0.448180\pi\)
\(744\) 67.7330 2.48321
\(745\) −3.85854 −0.141366
\(746\) −30.3778 −1.11221
\(747\) 4.84528 0.177280
\(748\) 36.0779 1.31914
\(749\) 0.518032 0.0189285
\(750\) 38.9611 1.42266
\(751\) 8.49376 0.309942 0.154971 0.987919i \(-0.450472\pi\)
0.154971 + 0.987919i \(0.450472\pi\)
\(752\) −29.6101 −1.07977
\(753\) 12.2139 0.445099
\(754\) 2.09989 0.0764733
\(755\) −17.8510 −0.649663
\(756\) 0.832300 0.0302705
\(757\) −31.7010 −1.15219 −0.576096 0.817382i \(-0.695425\pi\)
−0.576096 + 0.817382i \(0.695425\pi\)
\(758\) −63.1738 −2.29458
\(759\) 2.58932 0.0939864
\(760\) 18.0158 0.653502
\(761\) 11.6770 0.423292 0.211646 0.977346i \(-0.432118\pi\)
0.211646 + 0.977346i \(0.432118\pi\)
\(762\) −7.91937 −0.286889
\(763\) −0.634051 −0.0229542
\(764\) −101.524 −3.67300
\(765\) −12.3843 −0.447755
\(766\) −65.0981 −2.35209
\(767\) −0.956443 −0.0345351
\(768\) −50.8570 −1.83514
\(769\) −5.90563 −0.212963 −0.106481 0.994315i \(-0.533958\pi\)
−0.106481 + 0.994315i \(0.533958\pi\)
\(770\) −0.535310 −0.0192912
\(771\) −2.57083 −0.0925862
\(772\) −20.4568 −0.736255
\(773\) −19.8436 −0.713725 −0.356863 0.934157i \(-0.616154\pi\)
−0.356863 + 0.934157i \(0.616154\pi\)
\(774\) −3.57941 −0.128659
\(775\) −10.9481 −0.393268
\(776\) 90.4806 3.24806
\(777\) 0.307395 0.0110277
\(778\) −57.4300 −2.05897
\(779\) 5.43845 0.194853
\(780\) −3.95256 −0.141524
\(781\) −9.10541 −0.325817
\(782\) −8.84401 −0.316261
\(783\) −20.3609 −0.727640
\(784\) −56.4429 −2.01582
\(785\) −53.0778 −1.89443
\(786\) −92.7441 −3.30807
\(787\) −39.3823 −1.40383 −0.701913 0.712263i \(-0.747671\pi\)
−0.701913 + 0.712263i \(0.747671\pi\)
\(788\) −80.1087 −2.85375
\(789\) −7.27262 −0.258912
\(790\) −23.4814 −0.835431
\(791\) −0.756043 −0.0268818
\(792\) 11.6835 0.415156
\(793\) −0.250588 −0.00889865
\(794\) 76.4356 2.71260
\(795\) 19.2015 0.681008
\(796\) −83.3954 −2.95587
\(797\) 18.9185 0.670128 0.335064 0.942195i \(-0.391242\pi\)
0.335064 + 0.942195i \(0.391242\pi\)
\(798\) −0.233516 −0.00826638
\(799\) 16.7432 0.592333
\(800\) −15.8848 −0.561614
\(801\) −9.60818 −0.339488
\(802\) −79.5784 −2.81001
\(803\) −21.1716 −0.747128
\(804\) −59.9737 −2.11511
\(805\) 0.0915472 0.00322662
\(806\) −2.06353 −0.0726848
\(807\) −6.97562 −0.245553
\(808\) −19.0101 −0.668773
\(809\) 0.467747 0.0164451 0.00822255 0.999966i \(-0.497383\pi\)
0.00822255 + 0.999966i \(0.497383\pi\)
\(810\) 75.8860 2.66636
\(811\) −8.85342 −0.310886 −0.155443 0.987845i \(-0.549680\pi\)
−0.155443 + 0.987845i \(0.549680\pi\)
\(812\) −1.07002 −0.0375504
\(813\) 38.1608 1.33836
\(814\) −14.9262 −0.523164
\(815\) 12.3773 0.433556
\(816\) −73.6956 −2.57986
\(817\) −1.37314 −0.0480400
\(818\) −53.7306 −1.87865
\(819\) 0.00733046 0.000256147 0
\(820\) −67.2360 −2.34798
\(821\) −33.8258 −1.18053 −0.590264 0.807210i \(-0.700976\pi\)
−0.590264 + 0.807210i \(0.700976\pi\)
\(822\) 41.5926 1.45071
\(823\) −23.5885 −0.822243 −0.411122 0.911581i \(-0.634863\pi\)
−0.411122 + 0.911581i \(0.634863\pi\)
\(824\) 90.3641 3.14798
\(825\) −7.47821 −0.260358
\(826\) 0.698593 0.0243072
\(827\) −15.0842 −0.524528 −0.262264 0.964996i \(-0.584469\pi\)
−0.262264 + 0.964996i \(0.584469\pi\)
\(828\) −3.52646 −0.122553
\(829\) 35.0074 1.21586 0.607929 0.793991i \(-0.292000\pi\)
0.607929 + 0.793991i \(0.292000\pi\)
\(830\) −32.9395 −1.14335
\(831\) 16.0937 0.558283
\(832\) −0.419735 −0.0145517
\(833\) 31.9160 1.10583
\(834\) 63.7582 2.20777
\(835\) −13.4723 −0.466228
\(836\) 7.91047 0.273589
\(837\) 20.0084 0.691592
\(838\) 66.0432 2.28142
\(839\) 25.9029 0.894266 0.447133 0.894467i \(-0.352445\pi\)
0.447133 + 0.894467i \(0.352445\pi\)
\(840\) 1.63575 0.0564388
\(841\) −2.82361 −0.0973659
\(842\) −3.32505 −0.114589
\(843\) 33.3367 1.14818
\(844\) 3.22471 0.110999
\(845\) −34.7600 −1.19578
\(846\) 9.56970 0.329013
\(847\) 0.365354 0.0125537
\(848\) 28.8551 0.990887
\(849\) 22.9040 0.786063
\(850\) 25.5423 0.876095
\(851\) 2.55264 0.0875035
\(852\) 49.1063 1.68235
\(853\) −0.0269675 −0.000923348 0 −0.000461674 1.00000i \(-0.500147\pi\)
−0.000461674 1.00000i \(0.500147\pi\)
\(854\) 0.183032 0.00626321
\(855\) −2.71539 −0.0928644
\(856\) 76.8640 2.62716
\(857\) −17.7820 −0.607422 −0.303711 0.952764i \(-0.598226\pi\)
−0.303711 + 0.952764i \(0.598226\pi\)
\(858\) −1.40951 −0.0481200
\(859\) 7.60240 0.259391 0.129695 0.991554i \(-0.458600\pi\)
0.129695 + 0.991554i \(0.458600\pi\)
\(860\) 16.9762 0.578884
\(861\) 0.493786 0.0168282
\(862\) 15.3756 0.523694
\(863\) 48.1787 1.64002 0.820012 0.572347i \(-0.193967\pi\)
0.820012 + 0.572347i \(0.193967\pi\)
\(864\) 29.0306 0.987641
\(865\) −63.0475 −2.14368
\(866\) 28.1919 0.957998
\(867\) 7.61417 0.258591
\(868\) 1.05150 0.0356901
\(869\) −5.84180 −0.198170
\(870\) −70.6253 −2.39442
\(871\) 1.03525 0.0350782
\(872\) −94.0785 −3.18590
\(873\) −13.6375 −0.461558
\(874\) −1.93915 −0.0655926
\(875\) 0.342699 0.0115854
\(876\) 114.180 3.85779
\(877\) 17.0383 0.575343 0.287671 0.957729i \(-0.407119\pi\)
0.287671 + 0.957729i \(0.407119\pi\)
\(878\) −66.3445 −2.23902
\(879\) −13.4568 −0.453887
\(880\) −37.0417 −1.24868
\(881\) −4.15433 −0.139963 −0.0699815 0.997548i \(-0.522294\pi\)
−0.0699815 + 0.997548i \(0.522294\pi\)
\(882\) 18.2418 0.614234
\(883\) 3.83532 0.129069 0.0645343 0.997915i \(-0.479444\pi\)
0.0645343 + 0.997915i \(0.479444\pi\)
\(884\) 3.35864 0.112963
\(885\) 32.1680 1.08132
\(886\) −37.4068 −1.25670
\(887\) 30.6609 1.02949 0.514746 0.857343i \(-0.327886\pi\)
0.514746 + 0.857343i \(0.327886\pi\)
\(888\) 45.6103 1.53058
\(889\) −0.0696583 −0.00233626
\(890\) 65.3188 2.18949
\(891\) 18.8792 0.632478
\(892\) −8.49051 −0.284283
\(893\) 3.67114 0.122850
\(894\) 7.42083 0.248190
\(895\) 4.35731 0.145649
\(896\) −0.354638 −0.0118476
\(897\) 0.241051 0.00804846
\(898\) −57.1749 −1.90795
\(899\) −25.7232 −0.857918
\(900\) 10.1848 0.339492
\(901\) −16.3163 −0.543575
\(902\) −23.9769 −0.798343
\(903\) −0.124675 −0.00414891
\(904\) −112.179 −3.73102
\(905\) 12.0448 0.400383
\(906\) 34.3313 1.14058
\(907\) 6.81760 0.226375 0.113187 0.993574i \(-0.463894\pi\)
0.113187 + 0.993574i \(0.463894\pi\)
\(908\) 45.1148 1.49719
\(909\) 2.86525 0.0950344
\(910\) −0.0498343 −0.00165199
\(911\) −11.1877 −0.370665 −0.185332 0.982676i \(-0.559336\pi\)
−0.185332 + 0.982676i \(0.559336\pi\)
\(912\) −16.1586 −0.535064
\(913\) −8.19482 −0.271209
\(914\) 103.439 3.42146
\(915\) 8.42802 0.278622
\(916\) −100.253 −3.31246
\(917\) −0.815771 −0.0269391
\(918\) −46.6803 −1.54068
\(919\) −37.4569 −1.23559 −0.617794 0.786340i \(-0.711973\pi\)
−0.617794 + 0.786340i \(0.711973\pi\)
\(920\) 13.5835 0.447834
\(921\) −43.8531 −1.44501
\(922\) −37.9118 −1.24856
\(923\) −0.847662 −0.0279011
\(924\) 0.718234 0.0236282
\(925\) −7.37228 −0.242399
\(926\) −24.9563 −0.820114
\(927\) −13.6199 −0.447337
\(928\) −37.3223 −1.22517
\(929\) 17.4845 0.573649 0.286824 0.957983i \(-0.407400\pi\)
0.286824 + 0.957983i \(0.407400\pi\)
\(930\) 69.4027 2.27580
\(931\) 6.99795 0.229348
\(932\) 8.50381 0.278551
\(933\) −30.3923 −0.995001
\(934\) 52.7434 1.72582
\(935\) 20.9455 0.684992
\(936\) 1.08767 0.0355516
\(937\) 51.8037 1.69235 0.846176 0.532904i \(-0.178899\pi\)
0.846176 + 0.532904i \(0.178899\pi\)
\(938\) −0.756156 −0.0246894
\(939\) 26.9563 0.879685
\(940\) −45.3866 −1.48035
\(941\) −16.7658 −0.546549 −0.273275 0.961936i \(-0.588107\pi\)
−0.273275 + 0.961936i \(0.588107\pi\)
\(942\) 102.080 3.32595
\(943\) 4.10046 0.133529
\(944\) 48.3404 1.57335
\(945\) 0.483204 0.0157186
\(946\) 6.05386 0.196828
\(947\) −7.57306 −0.246091 −0.123046 0.992401i \(-0.539266\pi\)
−0.123046 + 0.992401i \(0.539266\pi\)
\(948\) 31.5054 1.02325
\(949\) −1.97095 −0.0639798
\(950\) 5.60044 0.181702
\(951\) −2.00338 −0.0649642
\(952\) −1.38996 −0.0450490
\(953\) −42.8439 −1.38785 −0.693925 0.720048i \(-0.744120\pi\)
−0.693925 + 0.720048i \(0.744120\pi\)
\(954\) −9.32568 −0.301930
\(955\) −58.9410 −1.90729
\(956\) −22.5209 −0.728378
\(957\) −17.5705 −0.567973
\(958\) 45.1115 1.45749
\(959\) 0.365846 0.0118138
\(960\) 14.1169 0.455622
\(961\) −5.72209 −0.184584
\(962\) −1.38955 −0.0448008
\(963\) −11.5851 −0.373326
\(964\) −36.0875 −1.16230
\(965\) −11.8765 −0.382317
\(966\) −0.176066 −0.00566482
\(967\) 4.42419 0.142272 0.0711362 0.997467i \(-0.477338\pi\)
0.0711362 + 0.997467i \(0.477338\pi\)
\(968\) 54.2101 1.74238
\(969\) 9.13698 0.293522
\(970\) 92.7110 2.97677
\(971\) −3.11268 −0.0998907 −0.0499454 0.998752i \(-0.515905\pi\)
−0.0499454 + 0.998752i \(0.515905\pi\)
\(972\) −46.7238 −1.49867
\(973\) 0.560814 0.0179789
\(974\) 32.9206 1.05484
\(975\) −0.696179 −0.0222956
\(976\) 12.6652 0.405403
\(977\) −56.1802 −1.79736 −0.898682 0.438600i \(-0.855474\pi\)
−0.898682 + 0.438600i \(0.855474\pi\)
\(978\) −23.8042 −0.761174
\(979\) 16.2503 0.519362
\(980\) −86.5161 −2.76366
\(981\) 14.1798 0.452725
\(982\) −73.9248 −2.35904
\(983\) 47.9941 1.53077 0.765386 0.643571i \(-0.222548\pi\)
0.765386 + 0.643571i \(0.222548\pi\)
\(984\) 73.2664 2.33565
\(985\) −46.5082 −1.48187
\(986\) 60.0132 1.91121
\(987\) 0.333323 0.0106098
\(988\) 0.736420 0.0234286
\(989\) −1.03531 −0.0329210
\(990\) 11.9715 0.380480
\(991\) −21.1237 −0.671016 −0.335508 0.942037i \(-0.608908\pi\)
−0.335508 + 0.942037i \(0.608908\pi\)
\(992\) 36.6762 1.16447
\(993\) 16.5313 0.524605
\(994\) 0.619138 0.0196379
\(995\) −48.4164 −1.53490
\(996\) 44.1954 1.40039
\(997\) 7.11560 0.225353 0.112677 0.993632i \(-0.464058\pi\)
0.112677 + 0.993632i \(0.464058\pi\)
\(998\) 28.6583 0.907162
\(999\) 13.4733 0.426278
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 \(a_p\))