Properties

Label 6047.2.a.a.1.5
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.70650 q^{2}\) \(+0.217632 q^{3}\) \(+5.32513 q^{4}\) \(+0.669687 q^{5}\) \(-0.589021 q^{6}\) \(-0.581450 q^{7}\) \(-8.99946 q^{8}\) \(-2.95264 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.70650 q^{2}\) \(+0.217632 q^{3}\) \(+5.32513 q^{4}\) \(+0.669687 q^{5}\) \(-0.589021 q^{6}\) \(-0.581450 q^{7}\) \(-8.99946 q^{8}\) \(-2.95264 q^{9}\) \(-1.81251 q^{10}\) \(-2.09470 q^{11}\) \(+1.15892 q^{12}\) \(-1.27506 q^{13}\) \(+1.57369 q^{14}\) \(+0.145745 q^{15}\) \(+13.7068 q^{16}\) \(+6.59154 q^{17}\) \(+7.99130 q^{18}\) \(-4.01430 q^{19}\) \(+3.56617 q^{20}\) \(-0.126542 q^{21}\) \(+5.66931 q^{22}\) \(+2.82786 q^{23}\) \(-1.95857 q^{24}\) \(-4.55152 q^{25}\) \(+3.45093 q^{26}\) \(-1.29548 q^{27}\) \(-3.09630 q^{28}\) \(-3.48393 q^{29}\) \(-0.394459 q^{30}\) \(+8.58007 q^{31}\) \(-19.0984 q^{32}\) \(-0.455875 q^{33}\) \(-17.8400 q^{34}\) \(-0.389389 q^{35}\) \(-15.7232 q^{36}\) \(-3.81952 q^{37}\) \(+10.8647 q^{38}\) \(-0.277493 q^{39}\) \(-6.02682 q^{40}\) \(+2.91956 q^{41}\) \(+0.342486 q^{42}\) \(+5.77672 q^{43}\) \(-11.1546 q^{44}\) \(-1.97734 q^{45}\) \(-7.65359 q^{46}\) \(+1.70843 q^{47}\) \(+2.98303 q^{48}\) \(-6.66192 q^{49}\) \(+12.3187 q^{50}\) \(+1.43453 q^{51}\) \(-6.78984 q^{52}\) \(-1.05962 q^{53}\) \(+3.50623 q^{54}\) \(-1.40280 q^{55}\) \(+5.23273 q^{56}\) \(-0.873640 q^{57}\) \(+9.42924 q^{58}\) \(+6.85318 q^{59}\) \(+0.776113 q^{60}\) \(+14.3547 q^{61}\) \(-23.2219 q^{62}\) \(+1.71681 q^{63}\) \(+24.2763 q^{64}\) \(-0.853887 q^{65}\) \(+1.23382 q^{66}\) \(-8.78790 q^{67}\) \(+35.1008 q^{68}\) \(+0.615432 q^{69}\) \(+1.05388 q^{70}\) \(-3.66465 q^{71}\) \(+26.5721 q^{72}\) \(+10.4476 q^{73}\) \(+10.3375 q^{74}\) \(-0.990557 q^{75}\) \(-21.3767 q^{76}\) \(+1.21797 q^{77}\) \(+0.751034 q^{78}\) \(+0.565292 q^{79}\) \(+9.17924 q^{80}\) \(+8.57597 q^{81}\) \(-7.90179 q^{82}\) \(+6.64938 q^{83}\) \(-0.673853 q^{84}\) \(+4.41426 q^{85}\) \(-15.6347 q^{86}\) \(-0.758214 q^{87}\) \(+18.8512 q^{88}\) \(-3.22389 q^{89}\) \(+5.35167 q^{90}\) \(+0.741380 q^{91}\) \(+15.0587 q^{92}\) \(+1.86730 q^{93}\) \(-4.62386 q^{94}\) \(-2.68832 q^{95}\) \(-4.15642 q^{96}\) \(+0.206961 q^{97}\) \(+18.0305 q^{98}\) \(+6.18490 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(217q \) \(\mathstrut -\mathstrut 20q^{2} \) \(\mathstrut -\mathstrut 27q^{3} \) \(\mathstrut +\mathstrut 184q^{4} \) \(\mathstrut -\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 48q^{7} \) \(\mathstrut -\mathstrut 57q^{8} \) \(\mathstrut +\mathstrut 152q^{9} \) \(\mathstrut -\mathstrut 46q^{10} \) \(\mathstrut -\mathstrut 32q^{11} \) \(\mathstrut -\mathstrut 72q^{12} \) \(\mathstrut -\mathstrut 80q^{13} \) \(\mathstrut -\mathstrut 22q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 61q^{17} \) \(\mathstrut -\mathstrut 88q^{18} \) \(\mathstrut -\mathstrut 43q^{19} \) \(\mathstrut -\mathstrut 41q^{20} \) \(\mathstrut -\mathstrut 61q^{21} \) \(\mathstrut -\mathstrut 93q^{22} \) \(\mathstrut -\mathstrut 60q^{23} \) \(\mathstrut -\mathstrut 41q^{24} \) \(\mathstrut +\mathstrut 26q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut -\mathstrut 93q^{27} \) \(\mathstrut -\mathstrut 126q^{28} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 100q^{31} \) \(\mathstrut -\mathstrut 114q^{32} \) \(\mathstrut -\mathstrut 133q^{33} \) \(\mathstrut -\mathstrut 75q^{34} \) \(\mathstrut -\mathstrut 37q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 264q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 118q^{40} \) \(\mathstrut -\mathstrut 72q^{41} \) \(\mathstrut -\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 107q^{43} \) \(\mathstrut -\mathstrut 59q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 111q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 135q^{48} \) \(\mathstrut +\mathstrut 33q^{49} \) \(\mathstrut -\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 26q^{51} \) \(\mathstrut -\mathstrut 173q^{52} \) \(\mathstrut -\mathstrut 103q^{53} \) \(\mathstrut -\mathstrut 28q^{54} \) \(\mathstrut -\mathstrut 78q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 205q^{57} \) \(\mathstrut -\mathstrut 189q^{58} \) \(\mathstrut -\mathstrut 38q^{59} \) \(\mathstrut -\mathstrut 105q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut -\mathstrut 116q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 146q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut -\mathstrut 206q^{67} \) \(\mathstrut -\mathstrut 62q^{68} \) \(\mathstrut -\mathstrut 55q^{69} \) \(\mathstrut -\mathstrut 125q^{70} \) \(\mathstrut -\mathstrut 78q^{71} \) \(\mathstrut -\mathstrut 225q^{72} \) \(\mathstrut -\mathstrut 326q^{73} \) \(\mathstrut +\mathstrut 3q^{74} \) \(\mathstrut -\mathstrut 95q^{75} \) \(\mathstrut -\mathstrut 84q^{76} \) \(\mathstrut -\mathstrut 79q^{77} \) \(\mathstrut -\mathstrut 86q^{78} \) \(\mathstrut -\mathstrut 117q^{79} \) \(\mathstrut -\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut -\mathstrut 96q^{82} \) \(\mathstrut -\mathstrut 23q^{83} \) \(\mathstrut -\mathstrut 57q^{84} \) \(\mathstrut -\mathstrut 224q^{85} \) \(\mathstrut -\mathstrut 7q^{86} \) \(\mathstrut -\mathstrut 45q^{87} \) \(\mathstrut -\mathstrut 250q^{88} \) \(\mathstrut -\mathstrut 104q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 96q^{91} \) \(\mathstrut -\mathstrut 137q^{92} \) \(\mathstrut -\mathstrut 155q^{93} \) \(\mathstrut -\mathstrut 48q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 33q^{96} \) \(\mathstrut -\mathstrut 447q^{97} \) \(\mathstrut -\mathstrut 46q^{98} \) \(\mathstrut -\mathstrut 94q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.70650 −1.91378 −0.956892 0.290445i \(-0.906197\pi\)
−0.956892 + 0.290445i \(0.906197\pi\)
\(3\) 0.217632 0.125650 0.0628250 0.998025i \(-0.479989\pi\)
0.0628250 + 0.998025i \(0.479989\pi\)
\(4\) 5.32513 2.66257
\(5\) 0.669687 0.299493 0.149746 0.988724i \(-0.452154\pi\)
0.149746 + 0.988724i \(0.452154\pi\)
\(6\) −0.589021 −0.240467
\(7\) −0.581450 −0.219767 −0.109884 0.993944i \(-0.535048\pi\)
−0.109884 + 0.993944i \(0.535048\pi\)
\(8\) −8.99946 −3.18179
\(9\) −2.95264 −0.984212
\(10\) −1.81251 −0.573165
\(11\) −2.09470 −0.631577 −0.315789 0.948830i \(-0.602269\pi\)
−0.315789 + 0.948830i \(0.602269\pi\)
\(12\) 1.15892 0.334551
\(13\) −1.27506 −0.353637 −0.176818 0.984244i \(-0.556581\pi\)
−0.176818 + 0.984244i \(0.556581\pi\)
\(14\) 1.57369 0.420587
\(15\) 0.145745 0.0376313
\(16\) 13.7068 3.42669
\(17\) 6.59154 1.59868 0.799341 0.600878i \(-0.205182\pi\)
0.799341 + 0.600878i \(0.205182\pi\)
\(18\) 7.99130 1.88357
\(19\) −4.01430 −0.920943 −0.460472 0.887674i \(-0.652320\pi\)
−0.460472 + 0.887674i \(0.652320\pi\)
\(20\) 3.56617 0.797420
\(21\) −0.126542 −0.0276138
\(22\) 5.66931 1.20870
\(23\) 2.82786 0.589649 0.294824 0.955551i \(-0.404739\pi\)
0.294824 + 0.955551i \(0.404739\pi\)
\(24\) −1.95857 −0.399792
\(25\) −4.55152 −0.910304
\(26\) 3.45093 0.676784
\(27\) −1.29548 −0.249316
\(28\) −3.09630 −0.585145
\(29\) −3.48393 −0.646949 −0.323474 0.946237i \(-0.604851\pi\)
−0.323474 + 0.946237i \(0.604851\pi\)
\(30\) −0.394459 −0.0720181
\(31\) 8.58007 1.54103 0.770513 0.637424i \(-0.220000\pi\)
0.770513 + 0.637424i \(0.220000\pi\)
\(32\) −19.0984 −3.37615
\(33\) −0.455875 −0.0793576
\(34\) −17.8400 −3.05953
\(35\) −0.389389 −0.0658188
\(36\) −15.7232 −2.62053
\(37\) −3.81952 −0.627925 −0.313963 0.949435i \(-0.601657\pi\)
−0.313963 + 0.949435i \(0.601657\pi\)
\(38\) 10.8647 1.76249
\(39\) −0.277493 −0.0444344
\(40\) −6.02682 −0.952924
\(41\) 2.91956 0.455959 0.227980 0.973666i \(-0.426788\pi\)
0.227980 + 0.973666i \(0.426788\pi\)
\(42\) 0.342486 0.0528467
\(43\) 5.77672 0.880942 0.440471 0.897767i \(-0.354811\pi\)
0.440471 + 0.897767i \(0.354811\pi\)
\(44\) −11.1546 −1.68162
\(45\) −1.97734 −0.294765
\(46\) −7.65359 −1.12846
\(47\) 1.70843 0.249200 0.124600 0.992207i \(-0.460235\pi\)
0.124600 + 0.992207i \(0.460235\pi\)
\(48\) 2.98303 0.430563
\(49\) −6.66192 −0.951702
\(50\) 12.3187 1.74212
\(51\) 1.43453 0.200874
\(52\) −6.78984 −0.941581
\(53\) −1.05962 −0.145550 −0.0727752 0.997348i \(-0.523186\pi\)
−0.0727752 + 0.997348i \(0.523186\pi\)
\(54\) 3.50623 0.477137
\(55\) −1.40280 −0.189153
\(56\) 5.23273 0.699254
\(57\) −0.873640 −0.115716
\(58\) 9.42924 1.23812
\(59\) 6.85318 0.892208 0.446104 0.894981i \(-0.352811\pi\)
0.446104 + 0.894981i \(0.352811\pi\)
\(60\) 0.776113 0.100196
\(61\) 14.3547 1.83793 0.918967 0.394335i \(-0.129025\pi\)
0.918967 + 0.394335i \(0.129025\pi\)
\(62\) −23.2219 −2.94919
\(63\) 1.71681 0.216298
\(64\) 24.2763 3.03453
\(65\) −0.853887 −0.105912
\(66\) 1.23382 0.151873
\(67\) −8.78790 −1.07361 −0.536806 0.843706i \(-0.680369\pi\)
−0.536806 + 0.843706i \(0.680369\pi\)
\(68\) 35.1008 4.25660
\(69\) 0.615432 0.0740893
\(70\) 1.05388 0.125963
\(71\) −3.66465 −0.434914 −0.217457 0.976070i \(-0.569776\pi\)
−0.217457 + 0.976070i \(0.569776\pi\)
\(72\) 26.5721 3.13156
\(73\) 10.4476 1.22280 0.611399 0.791323i \(-0.290607\pi\)
0.611399 + 0.791323i \(0.290607\pi\)
\(74\) 10.3375 1.20171
\(75\) −0.990557 −0.114380
\(76\) −21.3767 −2.45207
\(77\) 1.21797 0.138800
\(78\) 0.751034 0.0850378
\(79\) 0.565292 0.0636004 0.0318002 0.999494i \(-0.489876\pi\)
0.0318002 + 0.999494i \(0.489876\pi\)
\(80\) 9.17924 1.02627
\(81\) 8.57597 0.952886
\(82\) −7.90179 −0.872607
\(83\) 6.64938 0.729865 0.364932 0.931034i \(-0.381092\pi\)
0.364932 + 0.931034i \(0.381092\pi\)
\(84\) −0.673853 −0.0735234
\(85\) 4.41426 0.478794
\(86\) −15.6347 −1.68593
\(87\) −0.758214 −0.0812891
\(88\) 18.8512 2.00955
\(89\) −3.22389 −0.341731 −0.170866 0.985294i \(-0.554656\pi\)
−0.170866 + 0.985294i \(0.554656\pi\)
\(90\) 5.35167 0.564116
\(91\) 0.741380 0.0777178
\(92\) 15.0587 1.56998
\(93\) 1.86730 0.193630
\(94\) −4.62386 −0.476915
\(95\) −2.68832 −0.275816
\(96\) −4.15642 −0.424213
\(97\) 0.206961 0.0210137 0.0105068 0.999945i \(-0.496656\pi\)
0.0105068 + 0.999945i \(0.496656\pi\)
\(98\) 18.0305 1.82135
\(99\) 6.18490 0.621606
\(100\) −24.2374 −2.42374
\(101\) 8.44364 0.840173 0.420087 0.907484i \(-0.362000\pi\)
0.420087 + 0.907484i \(0.362000\pi\)
\(102\) −3.88255 −0.384430
\(103\) 7.11224 0.700790 0.350395 0.936602i \(-0.386047\pi\)
0.350395 + 0.936602i \(0.386047\pi\)
\(104\) 11.4748 1.12520
\(105\) −0.0847436 −0.00827013
\(106\) 2.86787 0.278552
\(107\) −17.0600 −1.64925 −0.824625 0.565680i \(-0.808614\pi\)
−0.824625 + 0.565680i \(0.808614\pi\)
\(108\) −6.89863 −0.663821
\(109\) −17.6234 −1.68801 −0.844007 0.536332i \(-0.819809\pi\)
−0.844007 + 0.536332i \(0.819809\pi\)
\(110\) 3.79666 0.361998
\(111\) −0.831250 −0.0788988
\(112\) −7.96979 −0.753075
\(113\) 20.0486 1.88602 0.943009 0.332767i \(-0.107982\pi\)
0.943009 + 0.332767i \(0.107982\pi\)
\(114\) 2.36451 0.221456
\(115\) 1.89378 0.176596
\(116\) −18.5524 −1.72254
\(117\) 3.76477 0.348053
\(118\) −18.5481 −1.70749
\(119\) −3.83265 −0.351338
\(120\) −1.31163 −0.119735
\(121\) −6.61221 −0.601110
\(122\) −38.8510 −3.51741
\(123\) 0.635391 0.0572912
\(124\) 45.6900 4.10308
\(125\) −6.39653 −0.572123
\(126\) −4.64654 −0.413947
\(127\) −19.4786 −1.72844 −0.864221 0.503112i \(-0.832188\pi\)
−0.864221 + 0.503112i \(0.832188\pi\)
\(128\) −27.5069 −2.43129
\(129\) 1.25720 0.110690
\(130\) 2.31104 0.202692
\(131\) 2.56356 0.223979 0.111990 0.993709i \(-0.464278\pi\)
0.111990 + 0.993709i \(0.464278\pi\)
\(132\) −2.42759 −0.211295
\(133\) 2.33411 0.202393
\(134\) 23.7844 2.05466
\(135\) −0.867569 −0.0746684
\(136\) −59.3203 −5.08667
\(137\) −2.86288 −0.244592 −0.122296 0.992494i \(-0.539026\pi\)
−0.122296 + 0.992494i \(0.539026\pi\)
\(138\) −1.66567 −0.141791
\(139\) 4.62755 0.392504 0.196252 0.980554i \(-0.437123\pi\)
0.196252 + 0.980554i \(0.437123\pi\)
\(140\) −2.07355 −0.175247
\(141\) 0.371809 0.0313120
\(142\) 9.91837 0.832331
\(143\) 2.67086 0.223349
\(144\) −40.4711 −3.37259
\(145\) −2.33314 −0.193757
\(146\) −28.2764 −2.34017
\(147\) −1.44985 −0.119581
\(148\) −20.3394 −1.67189
\(149\) 2.68939 0.220323 0.110162 0.993914i \(-0.464863\pi\)
0.110162 + 0.993914i \(0.464863\pi\)
\(150\) 2.68094 0.218898
\(151\) −9.85565 −0.802042 −0.401021 0.916069i \(-0.631345\pi\)
−0.401021 + 0.916069i \(0.631345\pi\)
\(152\) 36.1265 2.93025
\(153\) −19.4624 −1.57344
\(154\) −3.29642 −0.265633
\(155\) 5.74596 0.461526
\(156\) −1.47769 −0.118310
\(157\) −1.42261 −0.113537 −0.0567684 0.998387i \(-0.518080\pi\)
−0.0567684 + 0.998387i \(0.518080\pi\)
\(158\) −1.52996 −0.121717
\(159\) −0.230608 −0.0182884
\(160\) −12.7899 −1.01113
\(161\) −1.64426 −0.129586
\(162\) −23.2108 −1.82362
\(163\) −16.4538 −1.28876 −0.644381 0.764704i \(-0.722885\pi\)
−0.644381 + 0.764704i \(0.722885\pi\)
\(164\) 15.5471 1.21402
\(165\) −0.305293 −0.0237671
\(166\) −17.9965 −1.39680
\(167\) −16.6390 −1.28756 −0.643782 0.765209i \(-0.722636\pi\)
−0.643782 + 0.765209i \(0.722636\pi\)
\(168\) 1.13881 0.0878612
\(169\) −11.3742 −0.874941
\(170\) −11.9472 −0.916308
\(171\) 11.8528 0.906404
\(172\) 30.7618 2.34557
\(173\) −14.7900 −1.12446 −0.562232 0.826979i \(-0.690057\pi\)
−0.562232 + 0.826979i \(0.690057\pi\)
\(174\) 2.05211 0.155570
\(175\) 2.64648 0.200055
\(176\) −28.7116 −2.16422
\(177\) 1.49147 0.112106
\(178\) 8.72545 0.654000
\(179\) −11.1337 −0.832169 −0.416085 0.909326i \(-0.636598\pi\)
−0.416085 + 0.909326i \(0.636598\pi\)
\(180\) −10.5296 −0.784830
\(181\) 3.24798 0.241420 0.120710 0.992688i \(-0.461483\pi\)
0.120710 + 0.992688i \(0.461483\pi\)
\(182\) −2.00654 −0.148735
\(183\) 3.12405 0.230936
\(184\) −25.4492 −1.87614
\(185\) −2.55788 −0.188059
\(186\) −5.05384 −0.370565
\(187\) −13.8073 −1.00969
\(188\) 9.09761 0.663512
\(189\) 0.753259 0.0547915
\(190\) 7.27594 0.527852
\(191\) 26.6498 1.92831 0.964155 0.265341i \(-0.0854845\pi\)
0.964155 + 0.265341i \(0.0854845\pi\)
\(192\) 5.28329 0.381289
\(193\) −7.10402 −0.511358 −0.255679 0.966762i \(-0.582299\pi\)
−0.255679 + 0.966762i \(0.582299\pi\)
\(194\) −0.560139 −0.0402156
\(195\) −0.185833 −0.0133078
\(196\) −35.4756 −2.53397
\(197\) 2.45024 0.174572 0.0872862 0.996183i \(-0.472181\pi\)
0.0872862 + 0.996183i \(0.472181\pi\)
\(198\) −16.7394 −1.18962
\(199\) −13.3090 −0.943451 −0.471726 0.881745i \(-0.656369\pi\)
−0.471726 + 0.881745i \(0.656369\pi\)
\(200\) 40.9612 2.89640
\(201\) −1.91253 −0.134899
\(202\) −22.8527 −1.60791
\(203\) 2.02573 0.142178
\(204\) 7.63906 0.534841
\(205\) 1.95519 0.136557
\(206\) −19.2493 −1.34116
\(207\) −8.34963 −0.580339
\(208\) −17.4769 −1.21180
\(209\) 8.40877 0.581647
\(210\) 0.229358 0.0158272
\(211\) 2.88312 0.198482 0.0992412 0.995063i \(-0.468358\pi\)
0.0992412 + 0.995063i \(0.468358\pi\)
\(212\) −5.64263 −0.387537
\(213\) −0.797546 −0.0546469
\(214\) 46.1728 3.15631
\(215\) 3.86859 0.263836
\(216\) 11.6587 0.793272
\(217\) −4.98888 −0.338667
\(218\) 47.6977 3.23049
\(219\) 2.27373 0.153644
\(220\) −7.47007 −0.503632
\(221\) −8.40457 −0.565353
\(222\) 2.24978 0.150995
\(223\) −13.3865 −0.896423 −0.448212 0.893927i \(-0.647939\pi\)
−0.448212 + 0.893927i \(0.647939\pi\)
\(224\) 11.1048 0.741968
\(225\) 13.4390 0.895932
\(226\) −54.2616 −3.60943
\(227\) −2.30914 −0.153263 −0.0766316 0.997059i \(-0.524417\pi\)
−0.0766316 + 0.997059i \(0.524417\pi\)
\(228\) −4.65225 −0.308103
\(229\) 4.97368 0.328670 0.164335 0.986405i \(-0.447452\pi\)
0.164335 + 0.986405i \(0.447452\pi\)
\(230\) −5.12551 −0.337966
\(231\) 0.265068 0.0174402
\(232\) 31.3535 2.05846
\(233\) 10.2712 0.672890 0.336445 0.941703i \(-0.390775\pi\)
0.336445 + 0.941703i \(0.390775\pi\)
\(234\) −10.1894 −0.666099
\(235\) 1.14411 0.0746337
\(236\) 36.4941 2.37556
\(237\) 0.123026 0.00799138
\(238\) 10.3731 0.672385
\(239\) −8.79636 −0.568989 −0.284495 0.958678i \(-0.591826\pi\)
−0.284495 + 0.958678i \(0.591826\pi\)
\(240\) 1.99770 0.128951
\(241\) −24.0906 −1.55181 −0.775905 0.630849i \(-0.782707\pi\)
−0.775905 + 0.630849i \(0.782707\pi\)
\(242\) 17.8959 1.15039
\(243\) 5.75286 0.369046
\(244\) 76.4408 4.89362
\(245\) −4.46140 −0.285028
\(246\) −1.71968 −0.109643
\(247\) 5.11845 0.325679
\(248\) −77.2160 −4.90322
\(249\) 1.44712 0.0917074
\(250\) 17.3122 1.09492
\(251\) 6.78046 0.427979 0.213989 0.976836i \(-0.431354\pi\)
0.213989 + 0.976836i \(0.431354\pi\)
\(252\) 9.14224 0.575907
\(253\) −5.92352 −0.372409
\(254\) 52.7187 3.30786
\(255\) 0.960685 0.0601604
\(256\) 25.8947 1.61842
\(257\) −23.6940 −1.47799 −0.738996 0.673710i \(-0.764700\pi\)
−0.738996 + 0.673710i \(0.764700\pi\)
\(258\) −3.40261 −0.211837
\(259\) 2.22086 0.137997
\(260\) −4.54706 −0.281997
\(261\) 10.2868 0.636735
\(262\) −6.93827 −0.428648
\(263\) 9.76786 0.602312 0.301156 0.953575i \(-0.402627\pi\)
0.301156 + 0.953575i \(0.402627\pi\)
\(264\) 4.10263 0.252499
\(265\) −0.709615 −0.0435913
\(266\) −6.31727 −0.387337
\(267\) −0.701621 −0.0429385
\(268\) −46.7967 −2.85856
\(269\) 18.4600 1.12553 0.562763 0.826618i \(-0.309738\pi\)
0.562763 + 0.826618i \(0.309738\pi\)
\(270\) 2.34807 0.142899
\(271\) −10.2547 −0.622929 −0.311465 0.950258i \(-0.600820\pi\)
−0.311465 + 0.950258i \(0.600820\pi\)
\(272\) 90.3486 5.47819
\(273\) 0.161348 0.00976524
\(274\) 7.74838 0.468097
\(275\) 9.53409 0.574927
\(276\) 3.27726 0.197268
\(277\) −19.7680 −1.18774 −0.593872 0.804560i \(-0.702401\pi\)
−0.593872 + 0.804560i \(0.702401\pi\)
\(278\) −12.5244 −0.751167
\(279\) −25.3338 −1.51670
\(280\) 3.50429 0.209422
\(281\) 23.0895 1.37741 0.688703 0.725043i \(-0.258180\pi\)
0.688703 + 0.725043i \(0.258180\pi\)
\(282\) −1.00630 −0.0599243
\(283\) −28.4358 −1.69033 −0.845167 0.534502i \(-0.820499\pi\)
−0.845167 + 0.534502i \(0.820499\pi\)
\(284\) −19.5147 −1.15799
\(285\) −0.585065 −0.0346563
\(286\) −7.22869 −0.427441
\(287\) −1.69758 −0.100205
\(288\) 56.3906 3.32285
\(289\) 26.4483 1.55578
\(290\) 6.31464 0.370808
\(291\) 0.0450413 0.00264037
\(292\) 55.6348 3.25578
\(293\) 20.3034 1.18614 0.593069 0.805151i \(-0.297916\pi\)
0.593069 + 0.805151i \(0.297916\pi\)
\(294\) 3.92401 0.228853
\(295\) 4.58948 0.267210
\(296\) 34.3736 1.99793
\(297\) 2.71366 0.157462
\(298\) −7.27882 −0.421651
\(299\) −3.60567 −0.208521
\(300\) −5.27484 −0.304543
\(301\) −3.35887 −0.193602
\(302\) 26.6743 1.53493
\(303\) 1.83761 0.105568
\(304\) −55.0231 −3.15579
\(305\) 9.61316 0.550448
\(306\) 52.6750 3.01123
\(307\) −14.0249 −0.800443 −0.400222 0.916418i \(-0.631067\pi\)
−0.400222 + 0.916418i \(0.631067\pi\)
\(308\) 6.48583 0.369564
\(309\) 1.54785 0.0880542
\(310\) −15.5514 −0.883262
\(311\) −13.2955 −0.753917 −0.376958 0.926230i \(-0.623030\pi\)
−0.376958 + 0.926230i \(0.623030\pi\)
\(312\) 2.49729 0.141381
\(313\) −18.1087 −1.02357 −0.511783 0.859115i \(-0.671015\pi\)
−0.511783 + 0.859115i \(0.671015\pi\)
\(314\) 3.85030 0.217285
\(315\) 1.14972 0.0647796
\(316\) 3.01026 0.169340
\(317\) 7.68093 0.431404 0.215702 0.976459i \(-0.430796\pi\)
0.215702 + 0.976459i \(0.430796\pi\)
\(318\) 0.624140 0.0350000
\(319\) 7.29780 0.408598
\(320\) 16.2575 0.908821
\(321\) −3.71280 −0.207228
\(322\) 4.45018 0.247999
\(323\) −26.4604 −1.47230
\(324\) 45.6682 2.53712
\(325\) 5.80344 0.321917
\(326\) 44.5322 2.46641
\(327\) −3.83541 −0.212099
\(328\) −26.2745 −1.45077
\(329\) −0.993366 −0.0547660
\(330\) 0.826276 0.0454850
\(331\) 25.5687 1.40538 0.702691 0.711495i \(-0.251982\pi\)
0.702691 + 0.711495i \(0.251982\pi\)
\(332\) 35.4088 1.94331
\(333\) 11.2777 0.618012
\(334\) 45.0334 2.46412
\(335\) −5.88514 −0.321539
\(336\) −1.73448 −0.0946238
\(337\) −12.5263 −0.682352 −0.341176 0.939999i \(-0.610825\pi\)
−0.341176 + 0.939999i \(0.610825\pi\)
\(338\) 30.7843 1.67445
\(339\) 4.36323 0.236978
\(340\) 23.5065 1.27482
\(341\) −17.9727 −0.973277
\(342\) −32.0795 −1.73466
\(343\) 7.94372 0.428920
\(344\) −51.9874 −2.80297
\(345\) 0.412147 0.0221892
\(346\) 40.0292 2.15198
\(347\) 25.6782 1.37848 0.689240 0.724533i \(-0.257945\pi\)
0.689240 + 0.724533i \(0.257945\pi\)
\(348\) −4.03759 −0.216438
\(349\) 1.05495 0.0564701 0.0282350 0.999601i \(-0.491011\pi\)
0.0282350 + 0.999601i \(0.491011\pi\)
\(350\) −7.16269 −0.382862
\(351\) 1.65181 0.0881673
\(352\) 40.0055 2.13230
\(353\) −32.7325 −1.74218 −0.871088 0.491127i \(-0.836585\pi\)
−0.871088 + 0.491127i \(0.836585\pi\)
\(354\) −4.03667 −0.214546
\(355\) −2.45417 −0.130254
\(356\) −17.1676 −0.909882
\(357\) −0.834107 −0.0441456
\(358\) 30.1332 1.59259
\(359\) 24.0674 1.27023 0.635114 0.772418i \(-0.280953\pi\)
0.635114 + 0.772418i \(0.280953\pi\)
\(360\) 17.7950 0.937879
\(361\) −2.88540 −0.151863
\(362\) −8.79064 −0.462026
\(363\) −1.43903 −0.0755295
\(364\) 3.94795 0.206929
\(365\) 6.99661 0.366219
\(366\) −8.45523 −0.441962
\(367\) −12.7656 −0.666359 −0.333180 0.942863i \(-0.608122\pi\)
−0.333180 + 0.942863i \(0.608122\pi\)
\(368\) 38.7608 2.02054
\(369\) −8.62041 −0.448760
\(370\) 6.92290 0.359905
\(371\) 0.616117 0.0319872
\(372\) 9.94361 0.515552
\(373\) 11.6300 0.602177 0.301089 0.953596i \(-0.402650\pi\)
0.301089 + 0.953596i \(0.402650\pi\)
\(374\) 37.3695 1.93233
\(375\) −1.39209 −0.0718872
\(376\) −15.3749 −0.792902
\(377\) 4.44220 0.228785
\(378\) −2.03869 −0.104859
\(379\) −7.83457 −0.402435 −0.201217 0.979547i \(-0.564490\pi\)
−0.201217 + 0.979547i \(0.564490\pi\)
\(380\) −14.3157 −0.734379
\(381\) −4.23916 −0.217179
\(382\) −72.1275 −3.69037
\(383\) 9.14411 0.467242 0.233621 0.972328i \(-0.424942\pi\)
0.233621 + 0.972328i \(0.424942\pi\)
\(384\) −5.98637 −0.305491
\(385\) 0.815655 0.0415696
\(386\) 19.2270 0.978629
\(387\) −17.0566 −0.867034
\(388\) 1.10209 0.0559503
\(389\) −34.2182 −1.73493 −0.867465 0.497497i \(-0.834252\pi\)
−0.867465 + 0.497497i \(0.834252\pi\)
\(390\) 0.502957 0.0254682
\(391\) 18.6399 0.942661
\(392\) 59.9537 3.02812
\(393\) 0.557913 0.0281430
\(394\) −6.63157 −0.334094
\(395\) 0.378569 0.0190479
\(396\) 32.9354 1.65507
\(397\) −20.0938 −1.00848 −0.504241 0.863563i \(-0.668228\pi\)
−0.504241 + 0.863563i \(0.668228\pi\)
\(398\) 36.0208 1.80556
\(399\) 0.507978 0.0254307
\(400\) −62.3866 −3.11933
\(401\) −5.89247 −0.294256 −0.147128 0.989117i \(-0.547003\pi\)
−0.147128 + 0.989117i \(0.547003\pi\)
\(402\) 5.17625 0.258168
\(403\) −10.9401 −0.544963
\(404\) 44.9635 2.23702
\(405\) 5.74321 0.285383
\(406\) −5.48263 −0.272098
\(407\) 8.00077 0.396583
\(408\) −12.9100 −0.639140
\(409\) 10.9711 0.542487 0.271243 0.962511i \(-0.412565\pi\)
0.271243 + 0.962511i \(0.412565\pi\)
\(410\) −5.29172 −0.261340
\(411\) −0.623054 −0.0307330
\(412\) 37.8736 1.86590
\(413\) −3.98478 −0.196078
\(414\) 22.5983 1.11064
\(415\) 4.45300 0.218589
\(416\) 24.3515 1.19393
\(417\) 1.00710 0.0493180
\(418\) −22.7583 −1.11315
\(419\) 12.3642 0.604032 0.302016 0.953303i \(-0.402340\pi\)
0.302016 + 0.953303i \(0.402340\pi\)
\(420\) −0.451271 −0.0220198
\(421\) −7.35237 −0.358333 −0.179166 0.983819i \(-0.557340\pi\)
−0.179166 + 0.983819i \(0.557340\pi\)
\(422\) −7.80317 −0.379852
\(423\) −5.04437 −0.245266
\(424\) 9.53603 0.463111
\(425\) −30.0015 −1.45529
\(426\) 2.15856 0.104582
\(427\) −8.34655 −0.403918
\(428\) −90.8466 −4.39124
\(429\) 0.581265 0.0280638
\(430\) −10.4703 −0.504925
\(431\) −24.9459 −1.20160 −0.600800 0.799400i \(-0.705151\pi\)
−0.600800 + 0.799400i \(0.705151\pi\)
\(432\) −17.7569 −0.854329
\(433\) −19.8044 −0.951737 −0.475869 0.879516i \(-0.657866\pi\)
−0.475869 + 0.879516i \(0.657866\pi\)
\(434\) 13.5024 0.648136
\(435\) −0.507766 −0.0243455
\(436\) −93.8468 −4.49445
\(437\) −11.3519 −0.543033
\(438\) −6.15385 −0.294042
\(439\) 19.8668 0.948190 0.474095 0.880474i \(-0.342775\pi\)
0.474095 + 0.880474i \(0.342775\pi\)
\(440\) 12.6244 0.601845
\(441\) 19.6702 0.936677
\(442\) 22.7470 1.08196
\(443\) 27.1666 1.29072 0.645362 0.763877i \(-0.276706\pi\)
0.645362 + 0.763877i \(0.276706\pi\)
\(444\) −4.42652 −0.210073
\(445\) −2.15899 −0.102346
\(446\) 36.2304 1.71556
\(447\) 0.585297 0.0276836
\(448\) −14.1154 −0.666891
\(449\) −20.0601 −0.946692 −0.473346 0.880876i \(-0.656954\pi\)
−0.473346 + 0.880876i \(0.656954\pi\)
\(450\) −36.3726 −1.71462
\(451\) −6.11562 −0.287973
\(452\) 106.762 5.02165
\(453\) −2.14491 −0.100776
\(454\) 6.24969 0.293312
\(455\) 0.496493 0.0232759
\(456\) 7.86229 0.368186
\(457\) 6.96499 0.325809 0.162904 0.986642i \(-0.447914\pi\)
0.162904 + 0.986642i \(0.447914\pi\)
\(458\) −13.4612 −0.629003
\(459\) −8.53923 −0.398577
\(460\) 10.0846 0.470198
\(461\) −7.50412 −0.349502 −0.174751 0.984613i \(-0.555912\pi\)
−0.174751 + 0.984613i \(0.555912\pi\)
\(462\) −0.717407 −0.0333768
\(463\) −25.0705 −1.16513 −0.582563 0.812786i \(-0.697950\pi\)
−0.582563 + 0.812786i \(0.697950\pi\)
\(464\) −47.7534 −2.21689
\(465\) 1.25050 0.0579908
\(466\) −27.7990 −1.28777
\(467\) −3.75329 −0.173682 −0.0868409 0.996222i \(-0.527677\pi\)
−0.0868409 + 0.996222i \(0.527677\pi\)
\(468\) 20.0479 0.926715
\(469\) 5.10972 0.235945
\(470\) −3.09654 −0.142833
\(471\) −0.309606 −0.0142659
\(472\) −61.6749 −2.83882
\(473\) −12.1005 −0.556383
\(474\) −0.332969 −0.0152938
\(475\) 18.2712 0.838338
\(476\) −20.4093 −0.935461
\(477\) 3.12868 0.143252
\(478\) 23.8073 1.08892
\(479\) −35.1882 −1.60779 −0.803896 0.594770i \(-0.797243\pi\)
−0.803896 + 0.594770i \(0.797243\pi\)
\(480\) −2.78350 −0.127049
\(481\) 4.87010 0.222057
\(482\) 65.2011 2.96983
\(483\) −0.357843 −0.0162824
\(484\) −35.2109 −1.60050
\(485\) 0.138599 0.00629345
\(486\) −15.5701 −0.706274
\(487\) −12.7518 −0.577840 −0.288920 0.957353i \(-0.593296\pi\)
−0.288920 + 0.957353i \(0.593296\pi\)
\(488\) −129.185 −5.84792
\(489\) −3.58088 −0.161933
\(490\) 12.0748 0.545482
\(491\) 34.9317 1.57645 0.788223 0.615389i \(-0.211001\pi\)
0.788223 + 0.615389i \(0.211001\pi\)
\(492\) 3.38354 0.152542
\(493\) −22.9644 −1.03427
\(494\) −13.8531 −0.623280
\(495\) 4.14194 0.186167
\(496\) 117.605 5.28062
\(497\) 2.13081 0.0955799
\(498\) −3.91662 −0.175508
\(499\) 40.0358 1.79225 0.896124 0.443803i \(-0.146371\pi\)
0.896124 + 0.443803i \(0.146371\pi\)
\(500\) −34.0623 −1.52331
\(501\) −3.62118 −0.161782
\(502\) −18.3513 −0.819059
\(503\) −29.0439 −1.29500 −0.647501 0.762065i \(-0.724186\pi\)
−0.647501 + 0.762065i \(0.724186\pi\)
\(504\) −15.4504 −0.688214
\(505\) 5.65459 0.251626
\(506\) 16.0320 0.712709
\(507\) −2.47540 −0.109936
\(508\) −103.726 −4.60209
\(509\) 6.88363 0.305112 0.152556 0.988295i \(-0.451250\pi\)
0.152556 + 0.988295i \(0.451250\pi\)
\(510\) −2.60009 −0.115134
\(511\) −6.07475 −0.268731
\(512\) −15.0703 −0.666019
\(513\) 5.20046 0.229606
\(514\) 64.1278 2.82856
\(515\) 4.76297 0.209882
\(516\) 6.69476 0.294720
\(517\) −3.57865 −0.157389
\(518\) −6.01075 −0.264097
\(519\) −3.21878 −0.141289
\(520\) 7.68453 0.336989
\(521\) −29.3595 −1.28626 −0.643132 0.765756i \(-0.722365\pi\)
−0.643132 + 0.765756i \(0.722365\pi\)
\(522\) −27.8411 −1.21857
\(523\) 10.9996 0.480980 0.240490 0.970652i \(-0.422692\pi\)
0.240490 + 0.970652i \(0.422692\pi\)
\(524\) 13.6513 0.596359
\(525\) 0.575959 0.0251369
\(526\) −26.4367 −1.15269
\(527\) 56.5558 2.46361
\(528\) −6.24857 −0.271934
\(529\) −15.0032 −0.652314
\(530\) 1.92057 0.0834243
\(531\) −20.2349 −0.878122
\(532\) 12.4295 0.538886
\(533\) −3.72260 −0.161244
\(534\) 1.89894 0.0821750
\(535\) −11.4248 −0.493939
\(536\) 79.0863 3.41601
\(537\) −2.42304 −0.104562
\(538\) −49.9619 −2.15401
\(539\) 13.9547 0.601073
\(540\) −4.61992 −0.198810
\(541\) 4.40577 0.189419 0.0947094 0.995505i \(-0.469808\pi\)
0.0947094 + 0.995505i \(0.469808\pi\)
\(542\) 27.7543 1.19215
\(543\) 0.706864 0.0303344
\(544\) −125.888 −5.39739
\(545\) −11.8021 −0.505548
\(546\) −0.436688 −0.0186885
\(547\) 20.6198 0.881640 0.440820 0.897595i \(-0.354688\pi\)
0.440820 + 0.897595i \(0.354688\pi\)
\(548\) −15.2452 −0.651243
\(549\) −42.3843 −1.80892
\(550\) −25.8040 −1.10029
\(551\) 13.9855 0.595803
\(552\) −5.53856 −0.235737
\(553\) −0.328689 −0.0139773
\(554\) 53.5020 2.27308
\(555\) −0.556677 −0.0236296
\(556\) 24.6423 1.04507
\(557\) 8.10920 0.343598 0.171799 0.985132i \(-0.445042\pi\)
0.171799 + 0.985132i \(0.445042\pi\)
\(558\) 68.5659 2.90263
\(559\) −7.36564 −0.311533
\(560\) −5.33726 −0.225541
\(561\) −3.00492 −0.126868
\(562\) −62.4918 −2.63606
\(563\) 8.05965 0.339674 0.169837 0.985472i \(-0.445676\pi\)
0.169837 + 0.985472i \(0.445676\pi\)
\(564\) 1.97993 0.0833702
\(565\) 13.4263 0.564849
\(566\) 76.9615 3.23493
\(567\) −4.98650 −0.209413
\(568\) 32.9799 1.38381
\(569\) −34.8232 −1.45986 −0.729932 0.683520i \(-0.760448\pi\)
−0.729932 + 0.683520i \(0.760448\pi\)
\(570\) 1.58348 0.0663246
\(571\) 28.2490 1.18218 0.591092 0.806604i \(-0.298697\pi\)
0.591092 + 0.806604i \(0.298697\pi\)
\(572\) 14.2227 0.594681
\(573\) 5.79984 0.242292
\(574\) 4.59449 0.191770
\(575\) −12.8710 −0.536760
\(576\) −71.6790 −2.98662
\(577\) 0.561769 0.0233868 0.0116934 0.999932i \(-0.496278\pi\)
0.0116934 + 0.999932i \(0.496278\pi\)
\(578\) −71.5824 −2.97743
\(579\) −1.54606 −0.0642521
\(580\) −12.4243 −0.515890
\(581\) −3.86628 −0.160400
\(582\) −0.121904 −0.00505309
\(583\) 2.21960 0.0919263
\(584\) −94.0226 −3.89068
\(585\) 2.52122 0.104240
\(586\) −54.9512 −2.27001
\(587\) −29.4181 −1.21421 −0.607107 0.794620i \(-0.707670\pi\)
−0.607107 + 0.794620i \(0.707670\pi\)
\(588\) −7.72062 −0.318393
\(589\) −34.4430 −1.41920
\(590\) −12.4214 −0.511382
\(591\) 0.533251 0.0219350
\(592\) −52.3533 −2.15171
\(593\) 0.165736 0.00680597 0.00340299 0.999994i \(-0.498917\pi\)
0.00340299 + 0.999994i \(0.498917\pi\)
\(594\) −7.34451 −0.301349
\(595\) −2.56667 −0.105223
\(596\) 14.3213 0.586625
\(597\) −2.89647 −0.118545
\(598\) 9.75875 0.399065
\(599\) 42.1503 1.72221 0.861107 0.508424i \(-0.169772\pi\)
0.861107 + 0.508424i \(0.169772\pi\)
\(600\) 8.91448 0.363932
\(601\) 12.3258 0.502779 0.251389 0.967886i \(-0.419113\pi\)
0.251389 + 0.967886i \(0.419113\pi\)
\(602\) 9.09079 0.370513
\(603\) 25.9475 1.05666
\(604\) −52.4827 −2.13549
\(605\) −4.42811 −0.180028
\(606\) −4.97348 −0.202034
\(607\) −40.2811 −1.63496 −0.817479 0.575958i \(-0.804629\pi\)
−0.817479 + 0.575958i \(0.804629\pi\)
\(608\) 76.6667 3.10925
\(609\) 0.440863 0.0178647
\(610\) −26.0180 −1.05344
\(611\) −2.17834 −0.0881263
\(612\) −103.640 −4.18939
\(613\) 19.4808 0.786820 0.393410 0.919363i \(-0.371295\pi\)
0.393410 + 0.919363i \(0.371295\pi\)
\(614\) 37.9584 1.53188
\(615\) 0.425513 0.0171583
\(616\) −10.9610 −0.441633
\(617\) −12.8179 −0.516030 −0.258015 0.966141i \(-0.583068\pi\)
−0.258015 + 0.966141i \(0.583068\pi\)
\(618\) −4.18926 −0.168517
\(619\) −1.16374 −0.0467747 −0.0233873 0.999726i \(-0.507445\pi\)
−0.0233873 + 0.999726i \(0.507445\pi\)
\(620\) 30.5980 1.22884
\(621\) −3.66344 −0.147009
\(622\) 35.9842 1.44283
\(623\) 1.87453 0.0751014
\(624\) −3.80353 −0.152263
\(625\) 18.4739 0.738957
\(626\) 49.0113 1.95888
\(627\) 1.83002 0.0730839
\(628\) −7.57560 −0.302299
\(629\) −25.1765 −1.00385
\(630\) −3.11173 −0.123974
\(631\) −25.7653 −1.02570 −0.512849 0.858479i \(-0.671410\pi\)
−0.512849 + 0.858479i \(0.671410\pi\)
\(632\) −5.08733 −0.202363
\(633\) 0.627460 0.0249393
\(634\) −20.7884 −0.825614
\(635\) −13.0445 −0.517656
\(636\) −1.22802 −0.0486940
\(637\) 8.49431 0.336557
\(638\) −19.7515 −0.781968
\(639\) 10.8204 0.428048
\(640\) −18.4210 −0.728153
\(641\) −34.9864 −1.38188 −0.690939 0.722913i \(-0.742803\pi\)
−0.690939 + 0.722913i \(0.742803\pi\)
\(642\) 10.0487 0.396590
\(643\) 10.9435 0.431571 0.215786 0.976441i \(-0.430769\pi\)
0.215786 + 0.976441i \(0.430769\pi\)
\(644\) −8.75588 −0.345030
\(645\) 0.841930 0.0331510
\(646\) 71.6150 2.81766
\(647\) 18.9226 0.743922 0.371961 0.928248i \(-0.378685\pi\)
0.371961 + 0.928248i \(0.378685\pi\)
\(648\) −77.1791 −3.03188
\(649\) −14.3554 −0.563498
\(650\) −15.7070 −0.616079
\(651\) −1.08574 −0.0425535
\(652\) −87.6187 −3.43141
\(653\) −33.4362 −1.30846 −0.654229 0.756296i \(-0.727007\pi\)
−0.654229 + 0.756296i \(0.727007\pi\)
\(654\) 10.3805 0.405911
\(655\) 1.71678 0.0670802
\(656\) 40.0178 1.56243
\(657\) −30.8479 −1.20349
\(658\) 2.68854 0.104810
\(659\) 12.0418 0.469081 0.234541 0.972106i \(-0.424641\pi\)
0.234541 + 0.972106i \(0.424641\pi\)
\(660\) −1.62573 −0.0632813
\(661\) −16.9216 −0.658175 −0.329087 0.944299i \(-0.606741\pi\)
−0.329087 + 0.944299i \(0.606741\pi\)
\(662\) −69.2016 −2.68960
\(663\) −1.82910 −0.0710365
\(664\) −59.8409 −2.32228
\(665\) 1.56312 0.0606154
\(666\) −30.5230 −1.18274
\(667\) −9.85204 −0.381473
\(668\) −88.6049 −3.42823
\(669\) −2.91332 −0.112636
\(670\) 15.9281 0.615357
\(671\) −30.0689 −1.16080
\(672\) 2.41675 0.0932282
\(673\) −22.1813 −0.855028 −0.427514 0.904009i \(-0.640610\pi\)
−0.427514 + 0.904009i \(0.640610\pi\)
\(674\) 33.9024 1.30587
\(675\) 5.89642 0.226953
\(676\) −60.5693 −2.32959
\(677\) 1.24493 0.0478465 0.0239233 0.999714i \(-0.492384\pi\)
0.0239233 + 0.999714i \(0.492384\pi\)
\(678\) −11.8091 −0.453525
\(679\) −0.120337 −0.00461812
\(680\) −39.7260 −1.52342
\(681\) −0.502543 −0.0192575
\(682\) 48.6431 1.86264
\(683\) 10.6798 0.408649 0.204325 0.978903i \(-0.434500\pi\)
0.204325 + 0.978903i \(0.434500\pi\)
\(684\) 63.1175 2.41336
\(685\) −1.91723 −0.0732537
\(686\) −21.4997 −0.820861
\(687\) 1.08243 0.0412973
\(688\) 79.1802 3.01872
\(689\) 1.35108 0.0514719
\(690\) −1.11547 −0.0424654
\(691\) −35.8452 −1.36362 −0.681808 0.731532i \(-0.738806\pi\)
−0.681808 + 0.731532i \(0.738806\pi\)
\(692\) −78.7588 −2.99396
\(693\) −3.59621 −0.136609
\(694\) −69.4981 −2.63811
\(695\) 3.09901 0.117552
\(696\) 6.82352 0.258645
\(697\) 19.2444 0.728934
\(698\) −2.85522 −0.108071
\(699\) 2.23535 0.0845486
\(700\) 14.0929 0.532660
\(701\) 18.8727 0.712812 0.356406 0.934331i \(-0.384002\pi\)
0.356406 + 0.934331i \(0.384002\pi\)
\(702\) −4.47063 −0.168733
\(703\) 15.3327 0.578284
\(704\) −50.8516 −1.91654
\(705\) 0.248996 0.00937772
\(706\) 88.5905 3.33415
\(707\) −4.90955 −0.184643
\(708\) 7.94228 0.298489
\(709\) 13.9195 0.522759 0.261379 0.965236i \(-0.415823\pi\)
0.261379 + 0.965236i \(0.415823\pi\)
\(710\) 6.64220 0.249277
\(711\) −1.66910 −0.0625963
\(712\) 29.0133 1.08732
\(713\) 24.2632 0.908664
\(714\) 2.25751 0.0844851
\(715\) 1.78864 0.0668914
\(716\) −59.2882 −2.21571
\(717\) −1.91437 −0.0714935
\(718\) −65.1383 −2.43094
\(719\) −11.4871 −0.428398 −0.214199 0.976790i \(-0.568714\pi\)
−0.214199 + 0.976790i \(0.568714\pi\)
\(720\) −27.1029 −1.01007
\(721\) −4.13541 −0.154011
\(722\) 7.80933 0.290633
\(723\) −5.24288 −0.194985
\(724\) 17.2959 0.642797
\(725\) 15.8572 0.588920
\(726\) 3.89473 0.144547
\(727\) −10.4576 −0.387850 −0.193925 0.981016i \(-0.562122\pi\)
−0.193925 + 0.981016i \(0.562122\pi\)
\(728\) −6.67203 −0.247282
\(729\) −24.4759 −0.906515
\(730\) −18.9363 −0.700864
\(731\) 38.0775 1.40835
\(732\) 16.6360 0.614883
\(733\) −53.5300 −1.97717 −0.988587 0.150650i \(-0.951863\pi\)
−0.988587 + 0.150650i \(0.951863\pi\)
\(734\) 34.5501 1.27527
\(735\) −0.970943 −0.0358138
\(736\) −54.0075 −1.99074
\(737\) 18.4080 0.678069
\(738\) 23.3311 0.858830
\(739\) 12.2269 0.449772 0.224886 0.974385i \(-0.427799\pi\)
0.224886 + 0.974385i \(0.427799\pi\)
\(740\) −13.6211 −0.500720
\(741\) 1.11394 0.0409216
\(742\) −1.66752 −0.0612166
\(743\) −41.6763 −1.52895 −0.764477 0.644651i \(-0.777003\pi\)
−0.764477 + 0.644651i \(0.777003\pi\)
\(744\) −16.8047 −0.616089
\(745\) 1.80105 0.0659852
\(746\) −31.4765 −1.15244
\(747\) −19.6332 −0.718341
\(748\) −73.5258 −2.68837
\(749\) 9.91952 0.362451
\(750\) 3.76769 0.137576
\(751\) 31.4829 1.14883 0.574413 0.818566i \(-0.305230\pi\)
0.574413 + 0.818566i \(0.305230\pi\)
\(752\) 23.4170 0.853931
\(753\) 1.47565 0.0537755
\(754\) −12.0228 −0.437845
\(755\) −6.60020 −0.240206
\(756\) 4.01120 0.145886
\(757\) 17.0289 0.618926 0.309463 0.950911i \(-0.399851\pi\)
0.309463 + 0.950911i \(0.399851\pi\)
\(758\) 21.2042 0.770173
\(759\) −1.28915 −0.0467931
\(760\) 24.1935 0.877589
\(761\) −2.47239 −0.0896240 −0.0448120 0.998995i \(-0.514269\pi\)
−0.0448120 + 0.998995i \(0.514269\pi\)
\(762\) 11.4733 0.415633
\(763\) 10.2471 0.370970
\(764\) 141.913 5.13425
\(765\) −13.0337 −0.471235
\(766\) −24.7485 −0.894201
\(767\) −8.73818 −0.315517
\(768\) 5.63552 0.203354
\(769\) 47.8927 1.72705 0.863527 0.504302i \(-0.168250\pi\)
0.863527 + 0.504302i \(0.168250\pi\)
\(770\) −2.20757 −0.0795553
\(771\) −5.15658 −0.185710
\(772\) −37.8298 −1.36153
\(773\) 29.8695 1.07433 0.537165 0.843477i \(-0.319495\pi\)
0.537165 + 0.843477i \(0.319495\pi\)
\(774\) 46.1635 1.65931
\(775\) −39.0524 −1.40280
\(776\) −1.86254 −0.0668611
\(777\) 0.483330 0.0173394
\(778\) 92.6114 3.32028
\(779\) −11.7200 −0.419913
\(780\) −0.989587 −0.0354329
\(781\) 7.67636 0.274682
\(782\) −50.4489 −1.80405
\(783\) 4.51337 0.161295
\(784\) −91.3133 −3.26119
\(785\) −0.952705 −0.0340035
\(786\) −1.50999 −0.0538595
\(787\) 10.9057 0.388747 0.194374 0.980928i \(-0.437733\pi\)
0.194374 + 0.980928i \(0.437733\pi\)
\(788\) 13.0478 0.464810
\(789\) 2.12580 0.0756805
\(790\) −1.02460 −0.0364535
\(791\) −11.6573 −0.414485
\(792\) −55.6608 −1.97782
\(793\) −18.3031 −0.649961
\(794\) 54.3840 1.93001
\(795\) −0.154435 −0.00547724
\(796\) −70.8723 −2.51200
\(797\) −38.2782 −1.35588 −0.677942 0.735115i \(-0.737128\pi\)
−0.677942 + 0.735115i \(0.737128\pi\)
\(798\) −1.37484 −0.0486689
\(799\) 11.2612 0.398392
\(800\) 86.9268 3.07332
\(801\) 9.51897 0.336336
\(802\) 15.9480 0.563142
\(803\) −21.8846 −0.772291
\(804\) −10.1845 −0.359178
\(805\) −1.10114 −0.0388100
\(806\) 29.6093 1.04294
\(807\) 4.01749 0.141422
\(808\) −75.9882 −2.67326
\(809\) 51.0897 1.79622 0.898109 0.439774i \(-0.144941\pi\)
0.898109 + 0.439774i \(0.144941\pi\)
\(810\) −15.5440 −0.546160
\(811\) 24.5774 0.863031 0.431515 0.902106i \(-0.357979\pi\)
0.431515 + 0.902106i \(0.357979\pi\)
\(812\) 10.7873 0.378559
\(813\) −2.23175 −0.0782710
\(814\) −21.6541 −0.758974
\(815\) −11.0189 −0.385975
\(816\) 19.6628 0.688334
\(817\) −23.1895 −0.811298
\(818\) −29.6933 −1.03820
\(819\) −2.18903 −0.0764908
\(820\) 10.4117 0.363591
\(821\) 42.5518 1.48507 0.742535 0.669807i \(-0.233623\pi\)
0.742535 + 0.669807i \(0.233623\pi\)
\(822\) 1.68630 0.0588163
\(823\) 20.3925 0.710838 0.355419 0.934707i \(-0.384338\pi\)
0.355419 + 0.934707i \(0.384338\pi\)
\(824\) −64.0063 −2.22977
\(825\) 2.07492 0.0722396
\(826\) 10.7848 0.375251
\(827\) 7.93401 0.275893 0.137946 0.990440i \(-0.455950\pi\)
0.137946 + 0.990440i \(0.455950\pi\)
\(828\) −44.4629 −1.54519
\(829\) −14.9884 −0.520567 −0.260284 0.965532i \(-0.583816\pi\)
−0.260284 + 0.965532i \(0.583816\pi\)
\(830\) −12.0520 −0.418333
\(831\) −4.30215 −0.149240
\(832\) −30.9536 −1.07312
\(833\) −43.9123 −1.52147
\(834\) −2.72572 −0.0943840
\(835\) −11.1429 −0.385617
\(836\) 44.7778 1.54867
\(837\) −11.1153 −0.384203
\(838\) −33.4637 −1.15599
\(839\) −4.05940 −0.140146 −0.0700731 0.997542i \(-0.522323\pi\)
−0.0700731 + 0.997542i \(0.522323\pi\)
\(840\) 0.762647 0.0263138
\(841\) −16.8623 −0.581457
\(842\) 19.8992 0.685771
\(843\) 5.02502 0.173071
\(844\) 15.3530 0.528472
\(845\) −7.61717 −0.262039
\(846\) 13.6526 0.469385
\(847\) 3.84467 0.132104
\(848\) −14.5240 −0.498756
\(849\) −6.18855 −0.212390
\(850\) 81.1990 2.78510
\(851\) −10.8011 −0.370255
\(852\) −4.24704 −0.145501
\(853\) 4.74166 0.162351 0.0811756 0.996700i \(-0.474133\pi\)
0.0811756 + 0.996700i \(0.474133\pi\)
\(854\) 22.5899 0.773011
\(855\) 7.93764 0.271462
\(856\) 153.531 5.24757
\(857\) −3.80527 −0.129986 −0.0649928 0.997886i \(-0.520702\pi\)
−0.0649928 + 0.997886i \(0.520702\pi\)
\(858\) −1.57319 −0.0537080
\(859\) 39.2209 1.33820 0.669100 0.743172i \(-0.266680\pi\)
0.669100 + 0.743172i \(0.266680\pi\)
\(860\) 20.6008 0.702480
\(861\) −0.369448 −0.0125907
\(862\) 67.5159 2.29960
\(863\) −48.2283 −1.64171 −0.820855 0.571137i \(-0.806503\pi\)
−0.820855 + 0.571137i \(0.806503\pi\)
\(864\) 24.7417 0.841729
\(865\) −9.90468 −0.336769
\(866\) 53.6005 1.82142
\(867\) 5.75601 0.195484
\(868\) −26.5664 −0.901724
\(869\) −1.18412 −0.0401685
\(870\) 1.37427 0.0465920
\(871\) 11.2051 0.379669
\(872\) 158.601 5.37091
\(873\) −0.611080 −0.0206819
\(874\) 30.7238 1.03925
\(875\) 3.71926 0.125734
\(876\) 12.1079 0.409088
\(877\) 13.6163 0.459788 0.229894 0.973216i \(-0.426162\pi\)
0.229894 + 0.973216i \(0.426162\pi\)
\(878\) −53.7694 −1.81463
\(879\) 4.41868 0.149038
\(880\) −19.2278 −0.648168
\(881\) −31.0796 −1.04710 −0.523550 0.851995i \(-0.675393\pi\)
−0.523550 + 0.851995i \(0.675393\pi\)
\(882\) −53.2374 −1.79260
\(883\) −52.3510 −1.76175 −0.880876 0.473347i \(-0.843046\pi\)
−0.880876 + 0.473347i \(0.843046\pi\)
\(884\) −44.7554 −1.50529
\(885\) 0.998819 0.0335749
\(886\) −73.5264 −2.47017
\(887\) −11.9010 −0.399598 −0.199799 0.979837i \(-0.564029\pi\)
−0.199799 + 0.979837i \(0.564029\pi\)
\(888\) 7.48080 0.251039
\(889\) 11.3258 0.379855
\(890\) 5.84331 0.195868
\(891\) −17.9641 −0.601821
\(892\) −71.2846 −2.38679
\(893\) −6.85815 −0.229499
\(894\) −1.58410 −0.0529804
\(895\) −7.45607 −0.249229
\(896\) 15.9939 0.534317
\(897\) −0.784710 −0.0262007
\(898\) 54.2925 1.81176
\(899\) −29.8923 −0.996965
\(900\) 71.5643 2.38548
\(901\) −6.98454 −0.232689
\(902\) 16.5519 0.551118
\(903\) −0.730999 −0.0243261
\(904\) −180.427 −6.00091
\(905\) 2.17513 0.0723037
\(906\) 5.80518 0.192864
\(907\) 32.0885 1.06548 0.532740 0.846279i \(-0.321162\pi\)
0.532740 + 0.846279i \(0.321162\pi\)
\(908\) −12.2965 −0.408073
\(909\) −24.9310 −0.826909
\(910\) −1.34376 −0.0445451
\(911\) −17.1093 −0.566856 −0.283428 0.958994i \(-0.591472\pi\)
−0.283428 + 0.958994i \(0.591472\pi\)
\(912\) −11.9748 −0.396525
\(913\) −13.9285 −0.460966
\(914\) −18.8507 −0.623527
\(915\) 2.09213 0.0691638
\(916\) 26.4855 0.875105
\(917\) −1.49058 −0.0492233
\(918\) 23.1114 0.762790
\(919\) −1.37417 −0.0453297 −0.0226649 0.999743i \(-0.507215\pi\)
−0.0226649 + 0.999743i \(0.507215\pi\)
\(920\) −17.0430 −0.561890
\(921\) −3.05227 −0.100576
\(922\) 20.3099 0.668871
\(923\) 4.67263 0.153802
\(924\) 1.41152 0.0464357
\(925\) 17.3846 0.571603
\(926\) 67.8533 2.22980
\(927\) −20.9999 −0.689726
\(928\) 66.5374 2.18420
\(929\) −25.6836 −0.842653 −0.421326 0.906909i \(-0.638435\pi\)
−0.421326 + 0.906909i \(0.638435\pi\)
\(930\) −3.38449 −0.110982
\(931\) 26.7429 0.876464
\(932\) 54.6956 1.79161
\(933\) −2.89352 −0.0947296
\(934\) 10.1583 0.332389
\(935\) −9.24658 −0.302395
\(936\) −33.8809 −1.10743
\(937\) 28.4092 0.928087 0.464044 0.885812i \(-0.346398\pi\)
0.464044 + 0.885812i \(0.346398\pi\)
\(938\) −13.8294 −0.451547
\(939\) −3.94104 −0.128611
\(940\) 6.09255 0.198717
\(941\) −33.0781 −1.07832 −0.539158 0.842204i \(-0.681258\pi\)
−0.539158 + 0.842204i \(0.681258\pi\)
\(942\) 0.837948 0.0273018
\(943\) 8.25610 0.268856
\(944\) 93.9349 3.05732
\(945\) 0.504448 0.0164097
\(946\) 32.7500 1.06480
\(947\) −54.6326 −1.77532 −0.887661 0.460497i \(-0.847671\pi\)
−0.887661 + 0.460497i \(0.847671\pi\)
\(948\) 0.655128 0.0212776
\(949\) −13.3212 −0.432426
\(950\) −49.4509 −1.60440
\(951\) 1.67162 0.0542059
\(952\) 34.4918 1.11788
\(953\) −14.7686 −0.478401 −0.239200 0.970970i \(-0.576885\pi\)
−0.239200 + 0.970970i \(0.576885\pi\)
\(954\) −8.46776 −0.274154
\(955\) 17.8470 0.577515
\(956\) −46.8418 −1.51497
\(957\) 1.58823 0.0513403
\(958\) 95.2369 3.07696
\(959\) 1.66462 0.0537534
\(960\) 3.53815 0.114193
\(961\) 42.6176 1.37476
\(962\) −13.1809 −0.424970
\(963\) 50.3719 1.62321
\(964\) −128.286 −4.13180
\(965\) −4.75747 −0.153148
\(966\) 0.968501 0.0311610
\(967\) −30.4841 −0.980304 −0.490152 0.871637i \(-0.663059\pi\)
−0.490152 + 0.871637i \(0.663059\pi\)
\(968\) 59.5064 1.91261
\(969\) −5.75863 −0.184994
\(970\) −0.375118 −0.0120443
\(971\) −1.42932 −0.0458691 −0.0229346 0.999737i \(-0.507301\pi\)
−0.0229346 + 0.999737i \(0.507301\pi\)
\(972\) 30.6347 0.982610
\(973\) −2.69069 −0.0862595
\(974\) 34.5128 1.10586
\(975\) 1.26301 0.0404488
\(976\) 196.757 6.29803
\(977\) −59.6397 −1.90804 −0.954022 0.299738i \(-0.903101\pi\)
−0.954022 + 0.299738i \(0.903101\pi\)
\(978\) 9.69164 0.309904
\(979\) 6.75309 0.215830
\(980\) −23.7575 −0.758906
\(981\) 52.0354 1.66136
\(982\) −94.5426 −3.01698
\(983\) −4.22266 −0.134682 −0.0673410 0.997730i \(-0.521452\pi\)
−0.0673410 + 0.997730i \(0.521452\pi\)
\(984\) −5.71817 −0.182289
\(985\) 1.64089 0.0522832
\(986\) 62.1532 1.97936
\(987\) −0.216188 −0.00688135
\(988\) 27.2564 0.867143
\(989\) 16.3357 0.519446
\(990\) −11.2102 −0.356282
\(991\) −34.7754 −1.10468 −0.552338 0.833620i \(-0.686264\pi\)
−0.552338 + 0.833620i \(0.686264\pi\)
\(992\) −163.866 −5.20274
\(993\) 5.56457 0.176586
\(994\) −5.76703 −0.182919
\(995\) −8.91287 −0.282557
\(996\) 7.70610 0.244177
\(997\) −43.5659 −1.37975 −0.689873 0.723930i \(-0.742334\pi\)
−0.689873 + 0.723930i \(0.742334\pi\)
\(998\) −108.357 −3.42997
\(999\) 4.94813 0.156552
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 \(a_p\))