Properties

Label 6017.2.a.c.1.19
Level 6017
Weight 2
Character 6017.1
Self dual Yes
Analytic conductor 48.046
Analytic rank 1
Dimension 106
CM No

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Newspace parameters

Level: \( N \) = \( 6017 = 11 \cdot 547 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0459868962\)
Analytic rank: \(1\)
Dimension: \(106\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 6017.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.01004 q^{2}\) \(-2.26087 q^{3}\) \(+2.04024 q^{4}\) \(-3.50443 q^{5}\) \(+4.54443 q^{6}\) \(+2.31355 q^{7}\) \(-0.0808885 q^{8}\) \(+2.11154 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.01004 q^{2}\) \(-2.26087 q^{3}\) \(+2.04024 q^{4}\) \(-3.50443 q^{5}\) \(+4.54443 q^{6}\) \(+2.31355 q^{7}\) \(-0.0808885 q^{8}\) \(+2.11154 q^{9}\) \(+7.04404 q^{10}\) \(+1.00000 q^{11}\) \(-4.61272 q^{12}\) \(+0.932710 q^{13}\) \(-4.65032 q^{14}\) \(+7.92307 q^{15}\) \(-3.91790 q^{16}\) \(+2.24975 q^{17}\) \(-4.24426 q^{18}\) \(-1.81538 q^{19}\) \(-7.14989 q^{20}\) \(-5.23064 q^{21}\) \(-2.01004 q^{22}\) \(+7.60522 q^{23}\) \(+0.182878 q^{24}\) \(+7.28105 q^{25}\) \(-1.87478 q^{26}\) \(+2.00870 q^{27}\) \(+4.72020 q^{28}\) \(-0.260714 q^{29}\) \(-15.9257 q^{30}\) \(-8.81982 q^{31}\) \(+8.03689 q^{32}\) \(-2.26087 q^{33}\) \(-4.52207 q^{34}\) \(-8.10768 q^{35}\) \(+4.30805 q^{36}\) \(-0.763248 q^{37}\) \(+3.64897 q^{38}\) \(-2.10874 q^{39}\) \(+0.283468 q^{40}\) \(-9.05116 q^{41}\) \(+10.5138 q^{42}\) \(-5.33038 q^{43}\) \(+2.04024 q^{44}\) \(-7.39974 q^{45}\) \(-15.2868 q^{46}\) \(-7.77051 q^{47}\) \(+8.85786 q^{48}\) \(-1.64749 q^{49}\) \(-14.6352 q^{50}\) \(-5.08639 q^{51}\) \(+1.90295 q^{52}\) \(+6.46060 q^{53}\) \(-4.03756 q^{54}\) \(-3.50443 q^{55}\) \(-0.187140 q^{56}\) \(+4.10433 q^{57}\) \(+0.524043 q^{58}\) \(+14.8158 q^{59}\) \(+16.1650 q^{60}\) \(+9.18233 q^{61}\) \(+17.7282 q^{62}\) \(+4.88514 q^{63}\) \(-8.31863 q^{64}\) \(-3.26862 q^{65}\) \(+4.54443 q^{66}\) \(-4.86067 q^{67}\) \(+4.59003 q^{68}\) \(-17.1944 q^{69}\) \(+16.2967 q^{70}\) \(+1.33641 q^{71}\) \(-0.170799 q^{72}\) \(-3.28867 q^{73}\) \(+1.53416 q^{74}\) \(-16.4615 q^{75}\) \(-3.70381 q^{76}\) \(+2.31355 q^{77}\) \(+4.23863 q^{78}\) \(-11.5544 q^{79}\) \(+13.7300 q^{80}\) \(-10.8760 q^{81}\) \(+18.1932 q^{82}\) \(-3.21228 q^{83}\) \(-10.6718 q^{84}\) \(-7.88409 q^{85}\) \(+10.7143 q^{86}\) \(+0.589440 q^{87}\) \(-0.0808885 q^{88}\) \(-9.75901 q^{89}\) \(+14.8737 q^{90}\) \(+2.15787 q^{91}\) \(+15.5165 q^{92}\) \(+19.9405 q^{93}\) \(+15.6190 q^{94}\) \(+6.36187 q^{95}\) \(-18.1704 q^{96}\) \(+3.45493 q^{97}\) \(+3.31151 q^{98}\) \(+2.11154 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(106q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 15q^{3} \) \(\mathstrut +\mathstrut 93q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 22q^{6} \) \(\mathstrut -\mathstrut 66q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 97q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 106q^{11} \) \(\mathstrut -\mathstrut 26q^{12} \) \(\mathstrut -\mathstrut 72q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut -\mathstrut 46q^{15} \) \(\mathstrut +\mathstrut 75q^{16} \) \(\mathstrut -\mathstrut 65q^{17} \) \(\mathstrut -\mathstrut 37q^{18} \) \(\mathstrut -\mathstrut 63q^{19} \) \(\mathstrut -\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 27q^{21} \) \(\mathstrut -\mathstrut 13q^{22} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut -\mathstrut 56q^{24} \) \(\mathstrut +\mathstrut 74q^{25} \) \(\mathstrut +\mathstrut 2q^{26} \) \(\mathstrut -\mathstrut 54q^{27} \) \(\mathstrut -\mathstrut 115q^{28} \) \(\mathstrut -\mathstrut 45q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut -\mathstrut 89q^{31} \) \(\mathstrut -\mathstrut 96q^{32} \) \(\mathstrut -\mathstrut 15q^{33} \) \(\mathstrut -\mathstrut 26q^{34} \) \(\mathstrut -\mathstrut 52q^{35} \) \(\mathstrut +\mathstrut 91q^{36} \) \(\mathstrut -\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 7q^{38} \) \(\mathstrut -\mathstrut 34q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 32q^{41} \) \(\mathstrut -\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 93q^{44} \) \(\mathstrut -\mathstrut 46q^{45} \) \(\mathstrut -\mathstrut 20q^{46} \) \(\mathstrut -\mathstrut 105q^{47} \) \(\mathstrut -\mathstrut 57q^{48} \) \(\mathstrut +\mathstrut 80q^{49} \) \(\mathstrut -\mathstrut 60q^{50} \) \(\mathstrut -\mathstrut 36q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 61q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 32q^{56} \) \(\mathstrut -\mathstrut 71q^{57} \) \(\mathstrut -\mathstrut 28q^{58} \) \(\mathstrut -\mathstrut 15q^{59} \) \(\mathstrut -\mathstrut 21q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 84q^{62} \) \(\mathstrut -\mathstrut 182q^{63} \) \(\mathstrut +\mathstrut 55q^{64} \) \(\mathstrut -\mathstrut 73q^{65} \) \(\mathstrut -\mathstrut 22q^{66} \) \(\mathstrut -\mathstrut 58q^{67} \) \(\mathstrut -\mathstrut 145q^{68} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 39q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut -\mathstrut 100q^{72} \) \(\mathstrut -\mathstrut 155q^{73} \) \(\mathstrut -\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 132q^{76} \) \(\mathstrut -\mathstrut 66q^{77} \) \(\mathstrut -\mathstrut 45q^{78} \) \(\mathstrut -\mathstrut 50q^{79} \) \(\mathstrut -\mathstrut 28q^{80} \) \(\mathstrut +\mathstrut 114q^{81} \) \(\mathstrut -\mathstrut 57q^{82} \) \(\mathstrut -\mathstrut 96q^{83} \) \(\mathstrut -\mathstrut 27q^{84} \) \(\mathstrut -\mathstrut 74q^{85} \) \(\mathstrut +\mathstrut 54q^{86} \) \(\mathstrut -\mathstrut 182q^{87} \) \(\mathstrut -\mathstrut 39q^{88} \) \(\mathstrut +\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 53q^{90} \) \(\mathstrut +\mathstrut 6q^{91} \) \(\mathstrut -\mathstrut 18q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut -\mathstrut 33q^{94} \) \(\mathstrut -\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 56q^{96} \) \(\mathstrut -\mathstrut 102q^{97} \) \(\mathstrut -\mathstrut 76q^{98} \) \(\mathstrut +\mathstrut 97q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.01004 −1.42131 −0.710655 0.703541i \(-0.751601\pi\)
−0.710655 + 0.703541i \(0.751601\pi\)
\(3\) −2.26087 −1.30531 −0.652657 0.757653i \(-0.726346\pi\)
−0.652657 + 0.757653i \(0.726346\pi\)
\(4\) 2.04024 1.02012
\(5\) −3.50443 −1.56723 −0.783615 0.621247i \(-0.786627\pi\)
−0.783615 + 0.621247i \(0.786627\pi\)
\(6\) 4.54443 1.85526
\(7\) 2.31355 0.874439 0.437220 0.899355i \(-0.355963\pi\)
0.437220 + 0.899355i \(0.355963\pi\)
\(8\) −0.0808885 −0.0285984
\(9\) 2.11154 0.703845
\(10\) 7.04404 2.22752
\(11\) 1.00000 0.301511
\(12\) −4.61272 −1.33158
\(13\) 0.932710 0.258687 0.129344 0.991600i \(-0.458713\pi\)
0.129344 + 0.991600i \(0.458713\pi\)
\(14\) −4.65032 −1.24285
\(15\) 7.92307 2.04573
\(16\) −3.91790 −0.979474
\(17\) 2.24975 0.545644 0.272822 0.962065i \(-0.412043\pi\)
0.272822 + 0.962065i \(0.412043\pi\)
\(18\) −4.24426 −1.00038
\(19\) −1.81538 −0.416476 −0.208238 0.978078i \(-0.566773\pi\)
−0.208238 + 0.978078i \(0.566773\pi\)
\(20\) −7.14989 −1.59876
\(21\) −5.23064 −1.14142
\(22\) −2.01004 −0.428541
\(23\) 7.60522 1.58580 0.792899 0.609353i \(-0.208571\pi\)
0.792899 + 0.609353i \(0.208571\pi\)
\(24\) 0.182878 0.0373299
\(25\) 7.28105 1.45621
\(26\) −1.87478 −0.367674
\(27\) 2.00870 0.386575
\(28\) 4.72020 0.892034
\(29\) −0.260714 −0.0484133 −0.0242066 0.999707i \(-0.507706\pi\)
−0.0242066 + 0.999707i \(0.507706\pi\)
\(30\) −15.9257 −2.90761
\(31\) −8.81982 −1.58409 −0.792043 0.610465i \(-0.790983\pi\)
−0.792043 + 0.610465i \(0.790983\pi\)
\(32\) 8.03689 1.42073
\(33\) −2.26087 −0.393567
\(34\) −4.52207 −0.775529
\(35\) −8.10768 −1.37045
\(36\) 4.30805 0.718008
\(37\) −0.763248 −0.125477 −0.0627386 0.998030i \(-0.519983\pi\)
−0.0627386 + 0.998030i \(0.519983\pi\)
\(38\) 3.64897 0.591941
\(39\) −2.10874 −0.337668
\(40\) 0.283468 0.0448203
\(41\) −9.05116 −1.41355 −0.706777 0.707437i \(-0.749852\pi\)
−0.706777 + 0.707437i \(0.749852\pi\)
\(42\) 10.5138 1.62231
\(43\) −5.33038 −0.812876 −0.406438 0.913678i \(-0.633229\pi\)
−0.406438 + 0.913678i \(0.633229\pi\)
\(44\) 2.04024 0.307578
\(45\) −7.39974 −1.10309
\(46\) −15.2868 −2.25391
\(47\) −7.77051 −1.13344 −0.566722 0.823909i \(-0.691789\pi\)
−0.566722 + 0.823909i \(0.691789\pi\)
\(48\) 8.85786 1.27852
\(49\) −1.64749 −0.235356
\(50\) −14.6352 −2.06973
\(51\) −5.08639 −0.712237
\(52\) 1.90295 0.263892
\(53\) 6.46060 0.887432 0.443716 0.896167i \(-0.353660\pi\)
0.443716 + 0.896167i \(0.353660\pi\)
\(54\) −4.03756 −0.549443
\(55\) −3.50443 −0.472538
\(56\) −0.187140 −0.0250076
\(57\) 4.10433 0.543632
\(58\) 0.524043 0.0688103
\(59\) 14.8158 1.92886 0.964428 0.264344i \(-0.0851555\pi\)
0.964428 + 0.264344i \(0.0851555\pi\)
\(60\) 16.1650 2.08689
\(61\) 9.18233 1.17568 0.587838 0.808978i \(-0.299979\pi\)
0.587838 + 0.808978i \(0.299979\pi\)
\(62\) 17.7282 2.25148
\(63\) 4.88514 0.615470
\(64\) −8.31863 −1.03983
\(65\) −3.26862 −0.405422
\(66\) 4.54443 0.559381
\(67\) −4.86067 −0.593826 −0.296913 0.954905i \(-0.595957\pi\)
−0.296913 + 0.954905i \(0.595957\pi\)
\(68\) 4.59003 0.556623
\(69\) −17.1944 −2.06996
\(70\) 16.2967 1.94783
\(71\) 1.33641 0.158602 0.0793011 0.996851i \(-0.474731\pi\)
0.0793011 + 0.996851i \(0.474731\pi\)
\(72\) −0.170799 −0.0201289
\(73\) −3.28867 −0.384909 −0.192455 0.981306i \(-0.561645\pi\)
−0.192455 + 0.981306i \(0.561645\pi\)
\(74\) 1.53416 0.178342
\(75\) −16.4615 −1.90081
\(76\) −3.70381 −0.424856
\(77\) 2.31355 0.263653
\(78\) 4.23863 0.479931
\(79\) −11.5544 −1.29997 −0.649985 0.759947i \(-0.725225\pi\)
−0.649985 + 0.759947i \(0.725225\pi\)
\(80\) 13.7300 1.53506
\(81\) −10.8760 −1.20845
\(82\) 18.1932 2.00910
\(83\) −3.21228 −0.352593 −0.176297 0.984337i \(-0.556412\pi\)
−0.176297 + 0.984337i \(0.556412\pi\)
\(84\) −10.6718 −1.16438
\(85\) −7.88409 −0.855150
\(86\) 10.7143 1.15535
\(87\) 0.589440 0.0631946
\(88\) −0.0808885 −0.00862274
\(89\) −9.75901 −1.03445 −0.517226 0.855849i \(-0.673035\pi\)
−0.517226 + 0.855849i \(0.673035\pi\)
\(90\) 14.8737 1.56783
\(91\) 2.15787 0.226206
\(92\) 15.5165 1.61771
\(93\) 19.9405 2.06773
\(94\) 15.6190 1.61098
\(95\) 6.36187 0.652714
\(96\) −18.1704 −1.85450
\(97\) 3.45493 0.350795 0.175397 0.984498i \(-0.443879\pi\)
0.175397 + 0.984498i \(0.443879\pi\)
\(98\) 3.31151 0.334513
\(99\) 2.11154 0.212217
\(100\) 14.8551 1.48551
\(101\) −2.21590 −0.220490 −0.110245 0.993904i \(-0.535164\pi\)
−0.110245 + 0.993904i \(0.535164\pi\)
\(102\) 10.2238 1.01231
\(103\) 3.92284 0.386529 0.193265 0.981147i \(-0.438092\pi\)
0.193265 + 0.981147i \(0.438092\pi\)
\(104\) −0.0754455 −0.00739804
\(105\) 18.3304 1.78887
\(106\) −12.9860 −1.26132
\(107\) 1.77673 0.171763 0.0858816 0.996305i \(-0.472629\pi\)
0.0858816 + 0.996305i \(0.472629\pi\)
\(108\) 4.09824 0.394353
\(109\) 9.06939 0.868690 0.434345 0.900747i \(-0.356980\pi\)
0.434345 + 0.900747i \(0.356980\pi\)
\(110\) 7.04404 0.671622
\(111\) 1.72561 0.163787
\(112\) −9.06425 −0.856491
\(113\) −10.4686 −0.984803 −0.492402 0.870368i \(-0.663881\pi\)
−0.492402 + 0.870368i \(0.663881\pi\)
\(114\) −8.24985 −0.772670
\(115\) −26.6520 −2.48531
\(116\) −0.531919 −0.0493874
\(117\) 1.96945 0.182076
\(118\) −29.7803 −2.74150
\(119\) 5.20490 0.477132
\(120\) −0.640885 −0.0585046
\(121\) 1.00000 0.0909091
\(122\) −18.4568 −1.67100
\(123\) 20.4635 1.84513
\(124\) −17.9946 −1.61596
\(125\) −7.99380 −0.714987
\(126\) −9.81931 −0.874774
\(127\) 4.28096 0.379874 0.189937 0.981796i \(-0.439172\pi\)
0.189937 + 0.981796i \(0.439172\pi\)
\(128\) 0.646977 0.0571852
\(129\) 12.0513 1.06106
\(130\) 6.57004 0.576231
\(131\) 22.8795 1.99899 0.999495 0.0317873i \(-0.0101199\pi\)
0.999495 + 0.0317873i \(0.0101199\pi\)
\(132\) −4.61272 −0.401486
\(133\) −4.19996 −0.364183
\(134\) 9.77013 0.844010
\(135\) −7.03936 −0.605852
\(136\) −0.181979 −0.0156045
\(137\) −11.5420 −0.986099 −0.493050 0.870001i \(-0.664118\pi\)
−0.493050 + 0.870001i \(0.664118\pi\)
\(138\) 34.5614 2.94206
\(139\) −16.1738 −1.37184 −0.685922 0.727675i \(-0.740601\pi\)
−0.685922 + 0.727675i \(0.740601\pi\)
\(140\) −16.5416 −1.39802
\(141\) 17.5681 1.47950
\(142\) −2.68622 −0.225423
\(143\) 0.932710 0.0779971
\(144\) −8.27278 −0.689398
\(145\) 0.913653 0.0758748
\(146\) 6.61034 0.547075
\(147\) 3.72476 0.307213
\(148\) −1.55721 −0.128002
\(149\) 17.5665 1.43910 0.719552 0.694438i \(-0.244347\pi\)
0.719552 + 0.694438i \(0.244347\pi\)
\(150\) 33.0882 2.70164
\(151\) 21.1298 1.71952 0.859759 0.510699i \(-0.170614\pi\)
0.859759 + 0.510699i \(0.170614\pi\)
\(152\) 0.146843 0.0119106
\(153\) 4.75042 0.384049
\(154\) −4.65032 −0.374733
\(155\) 30.9085 2.48263
\(156\) −4.30233 −0.344462
\(157\) 20.4171 1.62946 0.814730 0.579841i \(-0.196885\pi\)
0.814730 + 0.579841i \(0.196885\pi\)
\(158\) 23.2247 1.84766
\(159\) −14.6066 −1.15838
\(160\) −28.1647 −2.22662
\(161\) 17.5951 1.38668
\(162\) 21.8612 1.71758
\(163\) −19.6856 −1.54189 −0.770947 0.636900i \(-0.780217\pi\)
−0.770947 + 0.636900i \(0.780217\pi\)
\(164\) −18.4666 −1.44200
\(165\) 7.92307 0.616810
\(166\) 6.45679 0.501144
\(167\) 13.7573 1.06457 0.532284 0.846566i \(-0.321334\pi\)
0.532284 + 0.846566i \(0.321334\pi\)
\(168\) 0.423098 0.0326427
\(169\) −12.1301 −0.933081
\(170\) 15.8473 1.21543
\(171\) −3.83323 −0.293135
\(172\) −10.8753 −0.829232
\(173\) −0.793270 −0.0603112 −0.0301556 0.999545i \(-0.509600\pi\)
−0.0301556 + 0.999545i \(0.509600\pi\)
\(174\) −1.18479 −0.0898190
\(175\) 16.8451 1.27337
\(176\) −3.91790 −0.295323
\(177\) −33.4967 −2.51776
\(178\) 19.6160 1.47028
\(179\) −0.814349 −0.0608673 −0.0304336 0.999537i \(-0.509689\pi\)
−0.0304336 + 0.999537i \(0.509689\pi\)
\(180\) −15.0973 −1.12528
\(181\) −12.8153 −0.952551 −0.476276 0.879296i \(-0.658014\pi\)
−0.476276 + 0.879296i \(0.658014\pi\)
\(182\) −4.33739 −0.321509
\(183\) −20.7601 −1.53463
\(184\) −0.615175 −0.0453513
\(185\) 2.67475 0.196652
\(186\) −40.0811 −2.93889
\(187\) 2.24975 0.164518
\(188\) −15.8537 −1.15625
\(189\) 4.64723 0.338036
\(190\) −12.7876 −0.927708
\(191\) 24.8604 1.79884 0.899418 0.437089i \(-0.143990\pi\)
0.899418 + 0.437089i \(0.143990\pi\)
\(192\) 18.8074 1.35730
\(193\) 8.20499 0.590608 0.295304 0.955403i \(-0.404579\pi\)
0.295304 + 0.955403i \(0.404579\pi\)
\(194\) −6.94453 −0.498588
\(195\) 7.38992 0.529203
\(196\) −3.36128 −0.240091
\(197\) 9.64035 0.686847 0.343423 0.939181i \(-0.388413\pi\)
0.343423 + 0.939181i \(0.388413\pi\)
\(198\) −4.24426 −0.301627
\(199\) 9.92421 0.703509 0.351754 0.936092i \(-0.385585\pi\)
0.351754 + 0.936092i \(0.385585\pi\)
\(200\) −0.588954 −0.0416453
\(201\) 10.9894 0.775129
\(202\) 4.45404 0.313385
\(203\) −0.603174 −0.0423345
\(204\) −10.3775 −0.726568
\(205\) 31.7192 2.21536
\(206\) −7.88505 −0.549378
\(207\) 16.0587 1.11616
\(208\) −3.65426 −0.253377
\(209\) −1.81538 −0.125572
\(210\) −36.8448 −2.54253
\(211\) 4.75228 0.327161 0.163580 0.986530i \(-0.447696\pi\)
0.163580 + 0.986530i \(0.447696\pi\)
\(212\) 13.1812 0.905288
\(213\) −3.02144 −0.207026
\(214\) −3.57130 −0.244129
\(215\) 18.6800 1.27396
\(216\) −0.162481 −0.0110554
\(217\) −20.4051 −1.38519
\(218\) −18.2298 −1.23468
\(219\) 7.43525 0.502428
\(220\) −7.14989 −0.482046
\(221\) 2.09836 0.141151
\(222\) −3.46853 −0.232792
\(223\) 24.7024 1.65420 0.827098 0.562058i \(-0.189990\pi\)
0.827098 + 0.562058i \(0.189990\pi\)
\(224\) 18.5937 1.24235
\(225\) 15.3742 1.02495
\(226\) 21.0423 1.39971
\(227\) 8.42187 0.558979 0.279490 0.960149i \(-0.409835\pi\)
0.279490 + 0.960149i \(0.409835\pi\)
\(228\) 8.37383 0.554571
\(229\) −21.9274 −1.44900 −0.724502 0.689273i \(-0.757930\pi\)
−0.724502 + 0.689273i \(0.757930\pi\)
\(230\) 53.5714 3.53240
\(231\) −5.23064 −0.344151
\(232\) 0.0210887 0.00138454
\(233\) 5.82125 0.381363 0.190681 0.981652i \(-0.438930\pi\)
0.190681 + 0.981652i \(0.438930\pi\)
\(234\) −3.95866 −0.258786
\(235\) 27.2312 1.77637
\(236\) 30.2279 1.96767
\(237\) 26.1230 1.69687
\(238\) −10.4620 −0.678153
\(239\) 3.33427 0.215676 0.107838 0.994168i \(-0.465607\pi\)
0.107838 + 0.994168i \(0.465607\pi\)
\(240\) −31.0418 −2.00374
\(241\) −25.7942 −1.66155 −0.830775 0.556609i \(-0.812102\pi\)
−0.830775 + 0.556609i \(0.812102\pi\)
\(242\) −2.01004 −0.129210
\(243\) 18.5632 1.19083
\(244\) 18.7342 1.19933
\(245\) 5.77352 0.368857
\(246\) −41.1324 −2.62250
\(247\) −1.69322 −0.107737
\(248\) 0.713422 0.0453023
\(249\) 7.26254 0.460245
\(250\) 16.0678 1.01622
\(251\) −17.4887 −1.10388 −0.551939 0.833884i \(-0.686112\pi\)
−0.551939 + 0.833884i \(0.686112\pi\)
\(252\) 9.96688 0.627854
\(253\) 7.60522 0.478136
\(254\) −8.60489 −0.539919
\(255\) 17.8249 1.11624
\(256\) 15.3368 0.958551
\(257\) −15.2016 −0.948249 −0.474124 0.880458i \(-0.657235\pi\)
−0.474124 + 0.880458i \(0.657235\pi\)
\(258\) −24.2236 −1.50809
\(259\) −1.76581 −0.109722
\(260\) −6.66877 −0.413580
\(261\) −0.550506 −0.0340755
\(262\) −45.9886 −2.84118
\(263\) −7.62342 −0.470080 −0.235040 0.971986i \(-0.575522\pi\)
−0.235040 + 0.971986i \(0.575522\pi\)
\(264\) 0.182878 0.0112554
\(265\) −22.6407 −1.39081
\(266\) 8.44208 0.517617
\(267\) 22.0639 1.35029
\(268\) −9.91695 −0.605774
\(269\) 17.1807 1.04753 0.523764 0.851864i \(-0.324527\pi\)
0.523764 + 0.851864i \(0.324527\pi\)
\(270\) 14.1494 0.861103
\(271\) −17.1951 −1.04453 −0.522265 0.852783i \(-0.674913\pi\)
−0.522265 + 0.852783i \(0.674913\pi\)
\(272\) −8.81428 −0.534444
\(273\) −4.87866 −0.295270
\(274\) 23.1998 1.40155
\(275\) 7.28105 0.439064
\(276\) −35.0808 −2.11161
\(277\) 7.27007 0.436816 0.218408 0.975858i \(-0.429914\pi\)
0.218408 + 0.975858i \(0.429914\pi\)
\(278\) 32.5099 1.94982
\(279\) −18.6234 −1.11495
\(280\) 0.655818 0.0391926
\(281\) 28.0082 1.67083 0.835415 0.549619i \(-0.185227\pi\)
0.835415 + 0.549619i \(0.185227\pi\)
\(282\) −35.3125 −2.10283
\(283\) −4.00734 −0.238212 −0.119106 0.992882i \(-0.538003\pi\)
−0.119106 + 0.992882i \(0.538003\pi\)
\(284\) 2.72659 0.161794
\(285\) −14.3834 −0.851997
\(286\) −1.87478 −0.110858
\(287\) −20.9403 −1.23607
\(288\) 16.9702 0.999977
\(289\) −11.9386 −0.702273
\(290\) −1.83648 −0.107842
\(291\) −7.81114 −0.457897
\(292\) −6.70968 −0.392654
\(293\) −25.1586 −1.46978 −0.734892 0.678184i \(-0.762767\pi\)
−0.734892 + 0.678184i \(0.762767\pi\)
\(294\) −7.48690 −0.436645
\(295\) −51.9211 −3.02296
\(296\) 0.0617380 0.00358845
\(297\) 2.00870 0.116557
\(298\) −35.3093 −2.04541
\(299\) 7.09346 0.410225
\(300\) −33.5855 −1.93906
\(301\) −12.3321 −0.710811
\(302\) −42.4716 −2.44397
\(303\) 5.00987 0.287809
\(304\) 7.11246 0.407927
\(305\) −32.1789 −1.84256
\(306\) −9.54852 −0.545852
\(307\) −32.2330 −1.83963 −0.919817 0.392347i \(-0.871663\pi\)
−0.919817 + 0.392347i \(0.871663\pi\)
\(308\) 4.72020 0.268958
\(309\) −8.86904 −0.504542
\(310\) −62.1271 −3.52858
\(311\) 1.34046 0.0760105 0.0380053 0.999278i \(-0.487900\pi\)
0.0380053 + 0.999278i \(0.487900\pi\)
\(312\) 0.170572 0.00965677
\(313\) 27.2252 1.53886 0.769430 0.638731i \(-0.220540\pi\)
0.769430 + 0.638731i \(0.220540\pi\)
\(314\) −41.0390 −2.31597
\(315\) −17.1197 −0.964583
\(316\) −23.5738 −1.32613
\(317\) −28.6058 −1.60666 −0.803332 0.595532i \(-0.796941\pi\)
−0.803332 + 0.595532i \(0.796941\pi\)
\(318\) 29.3598 1.64641
\(319\) −0.260714 −0.0145972
\(320\) 29.1521 1.62965
\(321\) −4.01696 −0.224205
\(322\) −35.3667 −1.97091
\(323\) −4.08414 −0.227248
\(324\) −22.1897 −1.23276
\(325\) 6.79111 0.376703
\(326\) 39.5687 2.19151
\(327\) −20.5047 −1.13391
\(328\) 0.732135 0.0404254
\(329\) −17.9775 −0.991129
\(330\) −15.9257 −0.876678
\(331\) 14.1311 0.776717 0.388358 0.921508i \(-0.373042\pi\)
0.388358 + 0.921508i \(0.373042\pi\)
\(332\) −6.55383 −0.359688
\(333\) −1.61163 −0.0883166
\(334\) −27.6526 −1.51308
\(335\) 17.0339 0.930662
\(336\) 20.4931 1.11799
\(337\) 13.2250 0.720413 0.360207 0.932873i \(-0.382706\pi\)
0.360207 + 0.932873i \(0.382706\pi\)
\(338\) 24.3818 1.32620
\(339\) 23.6682 1.28548
\(340\) −16.0855 −0.872356
\(341\) −8.81982 −0.477620
\(342\) 7.70494 0.416635
\(343\) −20.0064 −1.08024
\(344\) 0.431167 0.0232470
\(345\) 60.2567 3.24411
\(346\) 1.59450 0.0857209
\(347\) 23.3255 1.25218 0.626089 0.779752i \(-0.284655\pi\)
0.626089 + 0.779752i \(0.284655\pi\)
\(348\) 1.20260 0.0644661
\(349\) 25.7753 1.37972 0.689860 0.723943i \(-0.257672\pi\)
0.689860 + 0.723943i \(0.257672\pi\)
\(350\) −33.8592 −1.80985
\(351\) 1.87354 0.100002
\(352\) 8.03689 0.428367
\(353\) −12.2977 −0.654542 −0.327271 0.944930i \(-0.606129\pi\)
−0.327271 + 0.944930i \(0.606129\pi\)
\(354\) 67.3295 3.57852
\(355\) −4.68335 −0.248566
\(356\) −19.9107 −1.05527
\(357\) −11.7676 −0.622808
\(358\) 1.63687 0.0865113
\(359\) 21.5225 1.13592 0.567958 0.823058i \(-0.307734\pi\)
0.567958 + 0.823058i \(0.307734\pi\)
\(360\) 0.598554 0.0315466
\(361\) −15.7044 −0.826548
\(362\) 25.7591 1.35387
\(363\) −2.26087 −0.118665
\(364\) 4.40258 0.230758
\(365\) 11.5249 0.603242
\(366\) 41.7285 2.18118
\(367\) −4.55110 −0.237566 −0.118783 0.992920i \(-0.537899\pi\)
−0.118783 + 0.992920i \(0.537899\pi\)
\(368\) −29.7965 −1.55325
\(369\) −19.1119 −0.994923
\(370\) −5.37635 −0.279503
\(371\) 14.9469 0.776005
\(372\) 40.6834 2.10934
\(373\) −3.18621 −0.164976 −0.0824879 0.996592i \(-0.526287\pi\)
−0.0824879 + 0.996592i \(0.526287\pi\)
\(374\) −4.52207 −0.233831
\(375\) 18.0729 0.933283
\(376\) 0.628545 0.0324147
\(377\) −0.243170 −0.0125239
\(378\) −9.34110 −0.480454
\(379\) −33.1587 −1.70325 −0.851624 0.524152i \(-0.824382\pi\)
−0.851624 + 0.524152i \(0.824382\pi\)
\(380\) 12.9798 0.665847
\(381\) −9.67871 −0.495855
\(382\) −49.9703 −2.55670
\(383\) −8.23616 −0.420848 −0.210424 0.977610i \(-0.567484\pi\)
−0.210424 + 0.977610i \(0.567484\pi\)
\(384\) −1.46273 −0.0746447
\(385\) −8.10768 −0.413206
\(386\) −16.4923 −0.839436
\(387\) −11.2553 −0.572139
\(388\) 7.04889 0.357853
\(389\) −5.75199 −0.291638 −0.145819 0.989311i \(-0.546582\pi\)
−0.145819 + 0.989311i \(0.546582\pi\)
\(390\) −14.8540 −0.752162
\(391\) 17.1098 0.865281
\(392\) 0.133263 0.00673080
\(393\) −51.7275 −2.60931
\(394\) −19.3774 −0.976222
\(395\) 40.4916 2.03735
\(396\) 4.30805 0.216487
\(397\) −16.7872 −0.842525 −0.421263 0.906939i \(-0.638413\pi\)
−0.421263 + 0.906939i \(0.638413\pi\)
\(398\) −19.9480 −0.999903
\(399\) 9.49557 0.475373
\(400\) −28.5264 −1.42632
\(401\) 32.7393 1.63492 0.817461 0.575983i \(-0.195381\pi\)
0.817461 + 0.575983i \(0.195381\pi\)
\(402\) −22.0890 −1.10170
\(403\) −8.22633 −0.409783
\(404\) −4.52097 −0.224927
\(405\) 38.1143 1.89391
\(406\) 1.21240 0.0601704
\(407\) −0.763248 −0.0378328
\(408\) 0.411430 0.0203688
\(409\) −32.1549 −1.58996 −0.794978 0.606638i \(-0.792518\pi\)
−0.794978 + 0.606638i \(0.792518\pi\)
\(410\) −63.7567 −3.14872
\(411\) 26.0950 1.28717
\(412\) 8.00355 0.394307
\(413\) 34.2772 1.68667
\(414\) −32.2785 −1.58640
\(415\) 11.2572 0.552595
\(416\) 7.49608 0.367526
\(417\) 36.5669 1.79069
\(418\) 3.64897 0.178477
\(419\) 0.0347615 0.00169821 0.000849106 1.00000i \(-0.499730\pi\)
0.000849106 1.00000i \(0.499730\pi\)
\(420\) 37.3985 1.82486
\(421\) −7.23701 −0.352710 −0.176355 0.984327i \(-0.556431\pi\)
−0.176355 + 0.984327i \(0.556431\pi\)
\(422\) −9.55225 −0.464996
\(423\) −16.4077 −0.797770
\(424\) −0.522588 −0.0253791
\(425\) 16.3805 0.794572
\(426\) 6.07321 0.294248
\(427\) 21.2438 1.02806
\(428\) 3.62496 0.175219
\(429\) −2.10874 −0.101811
\(430\) −37.5474 −1.81070
\(431\) 0.508803 0.0245082 0.0122541 0.999925i \(-0.496099\pi\)
0.0122541 + 0.999925i \(0.496099\pi\)
\(432\) −7.86988 −0.378640
\(433\) −3.32438 −0.159760 −0.0798798 0.996805i \(-0.525454\pi\)
−0.0798798 + 0.996805i \(0.525454\pi\)
\(434\) 41.0149 1.96878
\(435\) −2.06565 −0.0990404
\(436\) 18.5037 0.886169
\(437\) −13.8063 −0.660447
\(438\) −14.9451 −0.714105
\(439\) 20.1137 0.959975 0.479988 0.877275i \(-0.340641\pi\)
0.479988 + 0.877275i \(0.340641\pi\)
\(440\) 0.283468 0.0135138
\(441\) −3.47873 −0.165654
\(442\) −4.21778 −0.200619
\(443\) 18.4878 0.878380 0.439190 0.898394i \(-0.355265\pi\)
0.439190 + 0.898394i \(0.355265\pi\)
\(444\) 3.52065 0.167083
\(445\) 34.1998 1.62123
\(446\) −49.6527 −2.35113
\(447\) −39.7156 −1.87848
\(448\) −19.2456 −0.909268
\(449\) 6.95664 0.328304 0.164152 0.986435i \(-0.447511\pi\)
0.164152 + 0.986435i \(0.447511\pi\)
\(450\) −30.9027 −1.45677
\(451\) −9.05116 −0.426202
\(452\) −21.3585 −1.00462
\(453\) −47.7717 −2.24451
\(454\) −16.9283 −0.794482
\(455\) −7.56211 −0.354517
\(456\) −0.331993 −0.0155470
\(457\) 12.3110 0.575885 0.287943 0.957648i \(-0.407029\pi\)
0.287943 + 0.957648i \(0.407029\pi\)
\(458\) 44.0748 2.05948
\(459\) 4.51907 0.210932
\(460\) −54.3765 −2.53532
\(461\) 4.99936 0.232843 0.116422 0.993200i \(-0.462858\pi\)
0.116422 + 0.993200i \(0.462858\pi\)
\(462\) 10.5138 0.489145
\(463\) −24.0374 −1.11711 −0.558557 0.829466i \(-0.688645\pi\)
−0.558557 + 0.829466i \(0.688645\pi\)
\(464\) 1.02145 0.0474196
\(465\) −69.8801 −3.24061
\(466\) −11.7009 −0.542034
\(467\) 8.20936 0.379884 0.189942 0.981795i \(-0.439170\pi\)
0.189942 + 0.981795i \(0.439170\pi\)
\(468\) 4.01816 0.185739
\(469\) −11.2454 −0.519265
\(470\) −54.7357 −2.52477
\(471\) −46.1604 −2.12696
\(472\) −1.19843 −0.0551622
\(473\) −5.33038 −0.245091
\(474\) −52.5081 −2.41178
\(475\) −13.2179 −0.606477
\(476\) 10.6193 0.486733
\(477\) 13.6418 0.624615
\(478\) −6.70200 −0.306542
\(479\) −18.6176 −0.850660 −0.425330 0.905038i \(-0.639842\pi\)
−0.425330 + 0.905038i \(0.639842\pi\)
\(480\) 63.6768 2.90644
\(481\) −0.711889 −0.0324593
\(482\) 51.8472 2.36158
\(483\) −39.7801 −1.81006
\(484\) 2.04024 0.0927383
\(485\) −12.1076 −0.549776
\(486\) −37.3126 −1.69254
\(487\) −4.37826 −0.198398 −0.0991990 0.995068i \(-0.531628\pi\)
−0.0991990 + 0.995068i \(0.531628\pi\)
\(488\) −0.742745 −0.0336225
\(489\) 44.5065 2.01266
\(490\) −11.6050 −0.524259
\(491\) −1.71768 −0.0775178 −0.0387589 0.999249i \(-0.512340\pi\)
−0.0387589 + 0.999249i \(0.512340\pi\)
\(492\) 41.7505 1.88226
\(493\) −0.586540 −0.0264164
\(494\) 3.40343 0.153128
\(495\) −7.39974 −0.332593
\(496\) 34.5551 1.55157
\(497\) 3.09184 0.138688
\(498\) −14.5980 −0.654151
\(499\) 23.6332 1.05797 0.528983 0.848633i \(-0.322574\pi\)
0.528983 + 0.848633i \(0.322574\pi\)
\(500\) −16.3093 −0.729373
\(501\) −31.1034 −1.38960
\(502\) 35.1530 1.56895
\(503\) −40.5158 −1.80651 −0.903256 0.429102i \(-0.858830\pi\)
−0.903256 + 0.429102i \(0.858830\pi\)
\(504\) −0.395152 −0.0176015
\(505\) 7.76548 0.345559
\(506\) −15.2868 −0.679579
\(507\) 27.4245 1.21796
\(508\) 8.73420 0.387518
\(509\) 16.3939 0.726647 0.363324 0.931663i \(-0.381642\pi\)
0.363324 + 0.931663i \(0.381642\pi\)
\(510\) −35.8287 −1.58652
\(511\) −7.60849 −0.336580
\(512\) −32.1215 −1.41958
\(513\) −3.64655 −0.160999
\(514\) 30.5557 1.34775
\(515\) −13.7473 −0.605780
\(516\) 24.5876 1.08241
\(517\) −7.77051 −0.341747
\(518\) 3.54934 0.155949
\(519\) 1.79348 0.0787251
\(520\) 0.264394 0.0115944
\(521\) 30.5139 1.33684 0.668420 0.743784i \(-0.266971\pi\)
0.668420 + 0.743784i \(0.266971\pi\)
\(522\) 1.10654 0.0484318
\(523\) 19.4440 0.850225 0.425113 0.905140i \(-0.360234\pi\)
0.425113 + 0.905140i \(0.360234\pi\)
\(524\) 46.6797 2.03921
\(525\) −38.0845 −1.66215
\(526\) 15.3233 0.668130
\(527\) −19.8424 −0.864347
\(528\) 8.85786 0.385489
\(529\) 34.8394 1.51476
\(530\) 45.5087 1.97677
\(531\) 31.2842 1.35762
\(532\) −8.56894 −0.371511
\(533\) −8.44210 −0.365668
\(534\) −44.3491 −1.91917
\(535\) −6.22644 −0.269192
\(536\) 0.393173 0.0169825
\(537\) 1.84114 0.0794510
\(538\) −34.5339 −1.48886
\(539\) −1.64749 −0.0709624
\(540\) −14.3620 −0.618042
\(541\) −7.86025 −0.337939 −0.168969 0.985621i \(-0.554044\pi\)
−0.168969 + 0.985621i \(0.554044\pi\)
\(542\) 34.5628 1.48460
\(543\) 28.9737 1.24338
\(544\) 18.0810 0.775215
\(545\) −31.7831 −1.36144
\(546\) 9.80629 0.419670
\(547\) 1.00000 0.0427569
\(548\) −23.5485 −1.00594
\(549\) 19.3888 0.827495
\(550\) −14.6352 −0.624046
\(551\) 0.473293 0.0201630
\(552\) 1.39083 0.0591977
\(553\) −26.7316 −1.13675
\(554\) −14.6131 −0.620851
\(555\) −6.04727 −0.256692
\(556\) −32.9985 −1.39945
\(557\) 20.2622 0.858535 0.429268 0.903177i \(-0.358772\pi\)
0.429268 + 0.903177i \(0.358772\pi\)
\(558\) 37.4336 1.58469
\(559\) −4.97170 −0.210281
\(560\) 31.7650 1.34232
\(561\) −5.08639 −0.214747
\(562\) −56.2975 −2.37477
\(563\) 28.9996 1.22219 0.611093 0.791559i \(-0.290730\pi\)
0.611093 + 0.791559i \(0.290730\pi\)
\(564\) 35.8432 1.50927
\(565\) 36.6865 1.54341
\(566\) 8.05490 0.338573
\(567\) −25.1622 −1.05671
\(568\) −0.108100 −0.00453577
\(569\) −19.8095 −0.830458 −0.415229 0.909717i \(-0.636299\pi\)
−0.415229 + 0.909717i \(0.636299\pi\)
\(570\) 28.9111 1.21095
\(571\) −20.9861 −0.878240 −0.439120 0.898428i \(-0.644710\pi\)
−0.439120 + 0.898428i \(0.644710\pi\)
\(572\) 1.90295 0.0795665
\(573\) −56.2062 −2.34805
\(574\) 42.0908 1.75683
\(575\) 55.3740 2.30926
\(576\) −17.5651 −0.731879
\(577\) −37.8828 −1.57708 −0.788541 0.614982i \(-0.789163\pi\)
−0.788541 + 0.614982i \(0.789163\pi\)
\(578\) 23.9971 0.998147
\(579\) −18.5504 −0.770929
\(580\) 1.86407 0.0774015
\(581\) −7.43176 −0.308321
\(582\) 15.7007 0.650814
\(583\) 6.46060 0.267571
\(584\) 0.266015 0.0110078
\(585\) −6.90181 −0.285355
\(586\) 50.5698 2.08902
\(587\) −29.8032 −1.23011 −0.615055 0.788484i \(-0.710866\pi\)
−0.615055 + 0.788484i \(0.710866\pi\)
\(588\) 7.59942 0.313395
\(589\) 16.0113 0.659734
\(590\) 104.363 4.29657
\(591\) −21.7956 −0.896551
\(592\) 2.99033 0.122902
\(593\) −37.2265 −1.52871 −0.764355 0.644796i \(-0.776942\pi\)
−0.764355 + 0.644796i \(0.776942\pi\)
\(594\) −4.03756 −0.165663
\(595\) −18.2402 −0.747776
\(596\) 35.8399 1.46806
\(597\) −22.4374 −0.918300
\(598\) −14.2581 −0.583057
\(599\) 28.4562 1.16269 0.581345 0.813657i \(-0.302527\pi\)
0.581345 + 0.813657i \(0.302527\pi\)
\(600\) 1.33155 0.0543602
\(601\) −10.1810 −0.415291 −0.207646 0.978204i \(-0.566580\pi\)
−0.207646 + 0.978204i \(0.566580\pi\)
\(602\) 24.7880 1.01028
\(603\) −10.2635 −0.417962
\(604\) 43.1099 1.75412
\(605\) −3.50443 −0.142475
\(606\) −10.0700 −0.409066
\(607\) −18.1655 −0.737316 −0.368658 0.929565i \(-0.620183\pi\)
−0.368658 + 0.929565i \(0.620183\pi\)
\(608\) −14.5900 −0.591702
\(609\) 1.36370 0.0552598
\(610\) 64.6807 2.61884
\(611\) −7.24763 −0.293208
\(612\) 9.69201 0.391776
\(613\) 10.9672 0.442961 0.221480 0.975165i \(-0.428911\pi\)
0.221480 + 0.975165i \(0.428911\pi\)
\(614\) 64.7895 2.61469
\(615\) −71.7130 −2.89175
\(616\) −0.187140 −0.00754007
\(617\) −33.4979 −1.34858 −0.674288 0.738469i \(-0.735549\pi\)
−0.674288 + 0.738469i \(0.735549\pi\)
\(618\) 17.8271 0.717111
\(619\) −26.8222 −1.07808 −0.539038 0.842282i \(-0.681212\pi\)
−0.539038 + 0.842282i \(0.681212\pi\)
\(620\) 63.0608 2.53258
\(621\) 15.2766 0.613030
\(622\) −2.69437 −0.108035
\(623\) −22.5779 −0.904566
\(624\) 8.26181 0.330737
\(625\) −8.39153 −0.335661
\(626\) −54.7237 −2.18720
\(627\) 4.10433 0.163911
\(628\) 41.6558 1.66225
\(629\) −1.71712 −0.0684659
\(630\) 34.4111 1.37097
\(631\) −37.7397 −1.50239 −0.751196 0.660079i \(-0.770523\pi\)
−0.751196 + 0.660079i \(0.770523\pi\)
\(632\) 0.934617 0.0371771
\(633\) −10.7443 −0.427047
\(634\) 57.4987 2.28357
\(635\) −15.0024 −0.595350
\(636\) −29.8010 −1.18169
\(637\) −1.53663 −0.0608835
\(638\) 0.524043 0.0207471
\(639\) 2.82187 0.111631
\(640\) −2.26729 −0.0896224
\(641\) −15.7515 −0.622146 −0.311073 0.950386i \(-0.600688\pi\)
−0.311073 + 0.950386i \(0.600688\pi\)
\(642\) 8.07424 0.318665
\(643\) 13.4623 0.530903 0.265451 0.964124i \(-0.414479\pi\)
0.265451 + 0.964124i \(0.414479\pi\)
\(644\) 35.8982 1.41459
\(645\) −42.2330 −1.66292
\(646\) 8.20926 0.322989
\(647\) −39.5673 −1.55555 −0.777776 0.628541i \(-0.783652\pi\)
−0.777776 + 0.628541i \(0.783652\pi\)
\(648\) 0.879745 0.0345597
\(649\) 14.8158 0.581572
\(650\) −13.6504 −0.535411
\(651\) 46.1333 1.80811
\(652\) −40.1633 −1.57292
\(653\) −33.8280 −1.32379 −0.661895 0.749596i \(-0.730248\pi\)
−0.661895 + 0.749596i \(0.730248\pi\)
\(654\) 41.2152 1.61164
\(655\) −80.1796 −3.13288
\(656\) 35.4615 1.38454
\(657\) −6.94414 −0.270917
\(658\) 36.1353 1.40870
\(659\) 29.7582 1.15922 0.579608 0.814896i \(-0.303206\pi\)
0.579608 + 0.814896i \(0.303206\pi\)
\(660\) 16.1650 0.629221
\(661\) 33.7638 1.31326 0.656630 0.754213i \(-0.271981\pi\)
0.656630 + 0.754213i \(0.271981\pi\)
\(662\) −28.4041 −1.10395
\(663\) −4.74412 −0.184246
\(664\) 0.259836 0.0100836
\(665\) 14.7185 0.570759
\(666\) 3.23942 0.125525
\(667\) −1.98278 −0.0767737
\(668\) 28.0681 1.08599
\(669\) −55.8490 −2.15925
\(670\) −34.2388 −1.32276
\(671\) 9.18233 0.354480
\(672\) −42.0380 −1.62165
\(673\) −5.13330 −0.197874 −0.0989372 0.995094i \(-0.531544\pi\)
−0.0989372 + 0.995094i \(0.531544\pi\)
\(674\) −26.5828 −1.02393
\(675\) 14.6255 0.562934
\(676\) −24.7482 −0.951856
\(677\) −22.0451 −0.847260 −0.423630 0.905835i \(-0.639244\pi\)
−0.423630 + 0.905835i \(0.639244\pi\)
\(678\) −47.5738 −1.82706
\(679\) 7.99314 0.306749
\(680\) 0.637732 0.0244559
\(681\) −19.0408 −0.729643
\(682\) 17.7282 0.678846
\(683\) −26.6671 −1.02039 −0.510194 0.860060i \(-0.670426\pi\)
−0.510194 + 0.860060i \(0.670426\pi\)
\(684\) −7.82073 −0.299033
\(685\) 40.4482 1.54544
\(686\) 40.2136 1.53536
\(687\) 49.5750 1.89140
\(688\) 20.8839 0.796191
\(689\) 6.02587 0.229567
\(690\) −121.118 −4.61089
\(691\) −0.838822 −0.0319103 −0.0159551 0.999873i \(-0.505079\pi\)
−0.0159551 + 0.999873i \(0.505079\pi\)
\(692\) −1.61846 −0.0615247
\(693\) 4.88514 0.185571
\(694\) −46.8851 −1.77973
\(695\) 56.6800 2.15000
\(696\) −0.0476789 −0.00180726
\(697\) −20.3628 −0.771297
\(698\) −51.8092 −1.96101
\(699\) −13.1611 −0.497798
\(700\) 34.3680 1.29899
\(701\) 7.29645 0.275583 0.137792 0.990461i \(-0.456000\pi\)
0.137792 + 0.990461i \(0.456000\pi\)
\(702\) −3.76587 −0.142134
\(703\) 1.38558 0.0522582
\(704\) −8.31863 −0.313520
\(705\) −61.5663 −2.31872
\(706\) 24.7189 0.930307
\(707\) −5.12660 −0.192805
\(708\) −68.3413 −2.56842
\(709\) −1.90352 −0.0714881 −0.0357441 0.999361i \(-0.511380\pi\)
−0.0357441 + 0.999361i \(0.511380\pi\)
\(710\) 9.41370 0.353290
\(711\) −24.3975 −0.914978
\(712\) 0.789392 0.0295837
\(713\) −67.0767 −2.51204
\(714\) 23.6533 0.885203
\(715\) −3.26862 −0.122239
\(716\) −1.66147 −0.0620920
\(717\) −7.53836 −0.281525
\(718\) −43.2610 −1.61449
\(719\) 38.5890 1.43913 0.719564 0.694426i \(-0.244342\pi\)
0.719564 + 0.694426i \(0.244342\pi\)
\(720\) 28.9914 1.08045
\(721\) 9.07569 0.337996
\(722\) 31.5664 1.17478
\(723\) 58.3173 2.16884
\(724\) −26.1462 −0.971718
\(725\) −1.89827 −0.0704999
\(726\) 4.54443 0.168660
\(727\) −13.8078 −0.512104 −0.256052 0.966663i \(-0.582422\pi\)
−0.256052 + 0.966663i \(0.582422\pi\)
\(728\) −0.174547 −0.00646914
\(729\) −9.34087 −0.345958
\(730\) −23.1655 −0.857393
\(731\) −11.9920 −0.443541
\(732\) −42.3556 −1.56551
\(733\) 1.29045 0.0476640 0.0238320 0.999716i \(-0.492413\pi\)
0.0238320 + 0.999716i \(0.492413\pi\)
\(734\) 9.14788 0.337654
\(735\) −13.0532 −0.481474
\(736\) 61.1223 2.25300
\(737\) −4.86067 −0.179045
\(738\) 38.4155 1.41409
\(739\) −23.9818 −0.882184 −0.441092 0.897462i \(-0.645409\pi\)
−0.441092 + 0.897462i \(0.645409\pi\)
\(740\) 5.45714 0.200609
\(741\) 3.82815 0.140631
\(742\) −30.0438 −1.10294
\(743\) −11.1566 −0.409297 −0.204648 0.978836i \(-0.565605\pi\)
−0.204648 + 0.978836i \(0.565605\pi\)
\(744\) −1.61296 −0.0591338
\(745\) −61.5607 −2.25541
\(746\) 6.40440 0.234482
\(747\) −6.78284 −0.248171
\(748\) 4.59003 0.167828
\(749\) 4.11056 0.150197
\(750\) −36.3273 −1.32648
\(751\) −44.7928 −1.63451 −0.817257 0.576274i \(-0.804506\pi\)
−0.817257 + 0.576274i \(0.804506\pi\)
\(752\) 30.4440 1.11018
\(753\) 39.5397 1.44091
\(754\) 0.488780 0.0178003
\(755\) −74.0480 −2.69488
\(756\) 9.48148 0.344838
\(757\) 4.87549 0.177203 0.0886013 0.996067i \(-0.471760\pi\)
0.0886013 + 0.996067i \(0.471760\pi\)
\(758\) 66.6502 2.42084
\(759\) −17.1944 −0.624118
\(760\) −0.514602 −0.0186666
\(761\) 19.3458 0.701283 0.350642 0.936510i \(-0.385964\pi\)
0.350642 + 0.936510i \(0.385964\pi\)
\(762\) 19.4545 0.704764
\(763\) 20.9825 0.759617
\(764\) 50.7213 1.83503
\(765\) −16.6475 −0.601893
\(766\) 16.5550 0.598155
\(767\) 13.8189 0.498970
\(768\) −34.6746 −1.25121
\(769\) 33.5037 1.20817 0.604087 0.796918i \(-0.293538\pi\)
0.604087 + 0.796918i \(0.293538\pi\)
\(770\) 16.2967 0.587293
\(771\) 34.3688 1.23776
\(772\) 16.7402 0.602491
\(773\) −16.0251 −0.576384 −0.288192 0.957573i \(-0.593054\pi\)
−0.288192 + 0.957573i \(0.593054\pi\)
\(774\) 22.6235 0.813187
\(775\) −64.2176 −2.30676
\(776\) −0.279464 −0.0100322
\(777\) 3.99227 0.143222
\(778\) 11.5617 0.414508
\(779\) 16.4313 0.588711
\(780\) 15.0772 0.539852
\(781\) 1.33641 0.0478204
\(782\) −34.3913 −1.22983
\(783\) −0.523696 −0.0187154
\(784\) 6.45469 0.230525
\(785\) −71.5503 −2.55374
\(786\) 103.974 3.70864
\(787\) 36.8159 1.31235 0.656173 0.754610i \(-0.272174\pi\)
0.656173 + 0.754610i \(0.272174\pi\)
\(788\) 19.6687 0.700667
\(789\) 17.2356 0.613603
\(790\) −81.3895 −2.89571
\(791\) −24.2196 −0.861151
\(792\) −0.170799 −0.00606908
\(793\) 8.56445 0.304132
\(794\) 33.7429 1.19749
\(795\) 51.1878 1.81544
\(796\) 20.2478 0.717664
\(797\) −48.2904 −1.71053 −0.855266 0.518189i \(-0.826606\pi\)
−0.855266 + 0.518189i \(0.826606\pi\)
\(798\) −19.0864 −0.675653
\(799\) −17.4817 −0.618457
\(800\) 58.5170 2.06889
\(801\) −20.6065 −0.728095
\(802\) −65.8072 −2.32373
\(803\) −3.28867 −0.116055
\(804\) 22.4209 0.790726
\(805\) −61.6607 −2.17325
\(806\) 16.5352 0.582428
\(807\) −38.8434 −1.36735
\(808\) 0.179241 0.00630567
\(809\) 34.5397 1.21435 0.607175 0.794568i \(-0.292303\pi\)
0.607175 + 0.794568i \(0.292303\pi\)
\(810\) −76.6111 −2.69184
\(811\) −50.5894 −1.77643 −0.888217 0.459424i \(-0.848056\pi\)
−0.888217 + 0.459424i \(0.848056\pi\)
\(812\) −1.23062 −0.0431863
\(813\) 38.8759 1.36344
\(814\) 1.53416 0.0537721
\(815\) 68.9868 2.41650
\(816\) 19.9279 0.697617
\(817\) 9.67666 0.338543
\(818\) 64.6324 2.25982
\(819\) 4.55642 0.159214
\(820\) 64.7148 2.25994
\(821\) −41.1509 −1.43618 −0.718088 0.695952i \(-0.754982\pi\)
−0.718088 + 0.695952i \(0.754982\pi\)
\(822\) −52.4518 −1.82947
\(823\) 22.8544 0.796653 0.398326 0.917244i \(-0.369591\pi\)
0.398326 + 0.917244i \(0.369591\pi\)
\(824\) −0.317313 −0.0110541
\(825\) −16.4615 −0.573117
\(826\) −68.8983 −2.39728
\(827\) 31.1659 1.08374 0.541872 0.840461i \(-0.317716\pi\)
0.541872 + 0.840461i \(0.317716\pi\)
\(828\) 32.7636 1.13861
\(829\) 33.9754 1.18001 0.590006 0.807399i \(-0.299125\pi\)
0.590006 + 0.807399i \(0.299125\pi\)
\(830\) −22.6274 −0.785408
\(831\) −16.4367 −0.570182
\(832\) −7.75887 −0.268990
\(833\) −3.70644 −0.128420
\(834\) −73.5007 −2.54512
\(835\) −48.2114 −1.66842
\(836\) −3.70381 −0.128099
\(837\) −17.7164 −0.612368
\(838\) −0.0698719 −0.00241368
\(839\) −35.8235 −1.23677 −0.618383 0.785877i \(-0.712212\pi\)
−0.618383 + 0.785877i \(0.712212\pi\)
\(840\) −1.48272 −0.0511587
\(841\) −28.9320 −0.997656
\(842\) 14.5467 0.501311
\(843\) −63.3230 −2.18096
\(844\) 9.69580 0.333743
\(845\) 42.5090 1.46235
\(846\) 32.9801 1.13388
\(847\) 2.31355 0.0794945
\(848\) −25.3120 −0.869217
\(849\) 9.06008 0.310941
\(850\) −32.9254 −1.12933
\(851\) −5.80467 −0.198981
\(852\) −6.16448 −0.211191
\(853\) 33.4260 1.14448 0.572242 0.820085i \(-0.306074\pi\)
0.572242 + 0.820085i \(0.306074\pi\)
\(854\) −42.7007 −1.46119
\(855\) 13.4333 0.459410
\(856\) −0.143717 −0.00491215
\(857\) 30.5860 1.04480 0.522400 0.852701i \(-0.325037\pi\)
0.522400 + 0.852701i \(0.325037\pi\)
\(858\) 4.23863 0.144705
\(859\) 49.5233 1.68971 0.844856 0.534994i \(-0.179686\pi\)
0.844856 + 0.534994i \(0.179686\pi\)
\(860\) 38.1117 1.29960
\(861\) 47.3433 1.61346
\(862\) −1.02271 −0.0348337
\(863\) 18.0332 0.613856 0.306928 0.951733i \(-0.400699\pi\)
0.306928 + 0.951733i \(0.400699\pi\)
\(864\) 16.1437 0.549220
\(865\) 2.77996 0.0945215
\(866\) 6.68212 0.227068
\(867\) 26.9917 0.916687
\(868\) −41.6313 −1.41306
\(869\) −11.5544 −0.391956
\(870\) 4.15203 0.140767
\(871\) −4.53360 −0.153615
\(872\) −0.733609 −0.0248431
\(873\) 7.29520 0.246905
\(874\) 27.7512 0.938699
\(875\) −18.4940 −0.625213
\(876\) 15.1697 0.512537
\(877\) 43.1678 1.45767 0.728836 0.684689i \(-0.240062\pi\)
0.728836 + 0.684689i \(0.240062\pi\)
\(878\) −40.4293 −1.36442
\(879\) 56.8804 1.91853
\(880\) 13.7300 0.462838
\(881\) −4.14944 −0.139798 −0.0698991 0.997554i \(-0.522268\pi\)
−0.0698991 + 0.997554i \(0.522268\pi\)
\(882\) 6.99238 0.235446
\(883\) −36.2827 −1.22101 −0.610505 0.792013i \(-0.709033\pi\)
−0.610505 + 0.792013i \(0.709033\pi\)
\(884\) 4.28116 0.143991
\(885\) 117.387 3.94592
\(886\) −37.1611 −1.24845
\(887\) −31.6444 −1.06252 −0.531258 0.847210i \(-0.678280\pi\)
−0.531258 + 0.847210i \(0.678280\pi\)
\(888\) −0.139582 −0.00468405
\(889\) 9.90422 0.332177
\(890\) −68.7428 −2.30426
\(891\) −10.8760 −0.364360
\(892\) 50.3989 1.68748
\(893\) 14.1064 0.472053
\(894\) 79.8298 2.66991
\(895\) 2.85383 0.0953931
\(896\) 1.49681 0.0500050
\(897\) −16.0374 −0.535473
\(898\) −13.9831 −0.466622
\(899\) 2.29945 0.0766908
\(900\) 31.3671 1.04557
\(901\) 14.5347 0.484222
\(902\) 18.1932 0.605766
\(903\) 27.8813 0.927831
\(904\) 0.846789 0.0281638
\(905\) 44.9102 1.49287
\(906\) 96.0229 3.19015
\(907\) 27.4863 0.912667 0.456333 0.889809i \(-0.349162\pi\)
0.456333 + 0.889809i \(0.349162\pi\)
\(908\) 17.1827 0.570226
\(909\) −4.67895 −0.155191
\(910\) 15.2001 0.503879
\(911\) 16.3125 0.540456 0.270228 0.962796i \(-0.412901\pi\)
0.270228 + 0.962796i \(0.412901\pi\)
\(912\) −16.0803 −0.532473
\(913\) −3.21228 −0.106311
\(914\) −24.7456 −0.818512
\(915\) 72.7523 2.40512
\(916\) −44.7372 −1.47816
\(917\) 52.9328 1.74800
\(918\) −9.08349 −0.299800
\(919\) 19.2632 0.635434 0.317717 0.948186i \(-0.397084\pi\)
0.317717 + 0.948186i \(0.397084\pi\)
\(920\) 2.15584 0.0710759
\(921\) 72.8746 2.40130
\(922\) −10.0489 −0.330942
\(923\) 1.24648 0.0410284
\(924\) −10.6718 −0.351075
\(925\) −5.55725 −0.182721
\(926\) 48.3161 1.58777
\(927\) 8.28323 0.272057
\(928\) −2.09533 −0.0687824
\(929\) 41.7821 1.37083 0.685413 0.728155i \(-0.259622\pi\)
0.685413 + 0.728155i \(0.259622\pi\)
\(930\) 140.461 4.60591
\(931\) 2.99082 0.0980200
\(932\) 11.8768 0.389036
\(933\) −3.03061 −0.0992177
\(934\) −16.5011 −0.539933
\(935\) −7.88409 −0.257837
\(936\) −0.159306 −0.00520708
\(937\) −13.3650 −0.436615 −0.218307 0.975880i \(-0.570054\pi\)
−0.218307 + 0.975880i \(0.570054\pi\)
\(938\) 22.6037 0.738036
\(939\) −61.5527 −2.00870
\(940\) 55.5583 1.81211
\(941\) −46.6373 −1.52033 −0.760166 0.649728i \(-0.774883\pi\)
−0.760166 + 0.649728i \(0.774883\pi\)
\(942\) 92.7839 3.02306
\(943\) −68.8361 −2.24161
\(944\) −58.0469 −1.88927
\(945\) −16.2859 −0.529781
\(946\) 10.7143 0.348351
\(947\) −17.9205 −0.582337 −0.291168 0.956672i \(-0.594044\pi\)
−0.291168 + 0.956672i \(0.594044\pi\)
\(948\) 53.2972 1.73101
\(949\) −3.06737 −0.0995711
\(950\) 26.5684 0.861991
\(951\) 64.6741 2.09720
\(952\) −0.421017 −0.0136452
\(953\) 5.00763 0.162213 0.0811066 0.996705i \(-0.474155\pi\)
0.0811066 + 0.996705i \(0.474155\pi\)
\(954\) −27.4205 −0.887771
\(955\) −87.1217 −2.81919
\(956\) 6.80272 0.220016
\(957\) 0.589440 0.0190539
\(958\) 37.4220 1.20905
\(959\) −26.7030 −0.862284
\(960\) −65.9091 −2.12721
\(961\) 46.7892 1.50933
\(962\) 1.43092 0.0461348
\(963\) 3.75163 0.120895
\(964\) −52.6264 −1.69498
\(965\) −28.7538 −0.925618
\(966\) 79.9595 2.57265
\(967\) 42.0730 1.35298 0.676489 0.736453i \(-0.263501\pi\)
0.676489 + 0.736453i \(0.263501\pi\)
\(968\) −0.0808885 −0.00259986
\(969\) 9.23371 0.296630
\(970\) 24.3366 0.781402
\(971\) 23.2678 0.746699 0.373350 0.927691i \(-0.378209\pi\)
0.373350 + 0.927691i \(0.378209\pi\)
\(972\) 37.8734 1.21479
\(973\) −37.4189 −1.19959
\(974\) 8.80046 0.281985
\(975\) −15.3538 −0.491716
\(976\) −35.9754 −1.15154
\(977\) 11.3184 0.362106 0.181053 0.983473i \(-0.442049\pi\)
0.181053 + 0.983473i \(0.442049\pi\)
\(978\) −89.4597 −2.86061
\(979\) −9.75901 −0.311899
\(980\) 11.7794 0.376278
\(981\) 19.1503 0.611423
\(982\) 3.45260 0.110177
\(983\) 8.38506 0.267442 0.133721 0.991019i \(-0.457307\pi\)
0.133721 + 0.991019i \(0.457307\pi\)
\(984\) −1.65526 −0.0527678
\(985\) −33.7840 −1.07645
\(986\) 1.17897 0.0375459
\(987\) 40.6447 1.29373
\(988\) −3.45458 −0.109905
\(989\) −40.5387 −1.28906
\(990\) 14.8737 0.472718
\(991\) 8.82781 0.280425 0.140212 0.990121i \(-0.455221\pi\)
0.140212 + 0.990121i \(0.455221\pi\)
\(992\) −70.8839 −2.25057
\(993\) −31.9486 −1.01386
\(994\) −6.21471 −0.197119
\(995\) −34.7787 −1.10256
\(996\) 14.8174 0.469506
\(997\) −6.93005 −0.219477 −0.109738 0.993961i \(-0.535001\pi\)
−0.109738 + 0.993961i \(0.535001\pi\)
\(998\) −47.5035 −1.50370
\(999\) −1.53314 −0.0485063
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 \(a_p\))