Properties

Label 6019.2.a.c.1.1
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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Newspace parameters

Level: \( N \) = \( 6019 = 13 \cdot 463 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.0619569766\)
Analytic rank: \(1\)
Dimension: \(108\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77848 q^{2}\) \(+2.29765 q^{3}\) \(+5.71995 q^{4}\) \(+2.18323 q^{5}\) \(-6.38396 q^{6}\) \(+0.752947 q^{7}\) \(-10.3358 q^{8}\) \(+2.27917 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77848 q^{2}\) \(+2.29765 q^{3}\) \(+5.71995 q^{4}\) \(+2.18323 q^{5}\) \(-6.38396 q^{6}\) \(+0.752947 q^{7}\) \(-10.3358 q^{8}\) \(+2.27917 q^{9}\) \(-6.06605 q^{10}\) \(-5.84116 q^{11}\) \(+13.1424 q^{12}\) \(-1.00000 q^{13}\) \(-2.09205 q^{14}\) \(+5.01628 q^{15}\) \(+17.2779 q^{16}\) \(+1.67477 q^{17}\) \(-6.33264 q^{18}\) \(-0.369876 q^{19}\) \(+12.4880 q^{20}\) \(+1.73000 q^{21}\) \(+16.2295 q^{22}\) \(+1.10881 q^{23}\) \(-23.7480 q^{24}\) \(-0.233522 q^{25}\) \(+2.77848 q^{26}\) \(-1.65620 q^{27}\) \(+4.30682 q^{28}\) \(+3.02051 q^{29}\) \(-13.9376 q^{30}\) \(-7.84456 q^{31}\) \(-27.3348 q^{32}\) \(-13.4209 q^{33}\) \(-4.65332 q^{34}\) \(+1.64385 q^{35}\) \(+13.0368 q^{36}\) \(+0.683881 q^{37}\) \(+1.02769 q^{38}\) \(-2.29765 q^{39}\) \(-22.5654 q^{40}\) \(+2.85496 q^{41}\) \(-4.80678 q^{42}\) \(+2.37080 q^{43}\) \(-33.4112 q^{44}\) \(+4.97595 q^{45}\) \(-3.08081 q^{46}\) \(-11.1830 q^{47}\) \(+39.6986 q^{48}\) \(-6.43307 q^{49}\) \(+0.648836 q^{50}\) \(+3.84803 q^{51}\) \(-5.71995 q^{52}\) \(-10.0200 q^{53}\) \(+4.60172 q^{54}\) \(-12.7526 q^{55}\) \(-7.78232 q^{56}\) \(-0.849843 q^{57}\) \(-8.39242 q^{58}\) \(-7.83855 q^{59}\) \(+28.6929 q^{60}\) \(+7.75538 q^{61}\) \(+21.7960 q^{62}\) \(+1.71610 q^{63}\) \(+41.3933 q^{64}\) \(-2.18323 q^{65}\) \(+37.2897 q^{66}\) \(+3.63717 q^{67}\) \(+9.57962 q^{68}\) \(+2.54766 q^{69}\) \(-4.56741 q^{70}\) \(+8.56799 q^{71}\) \(-23.5571 q^{72}\) \(-0.475662 q^{73}\) \(-1.90015 q^{74}\) \(-0.536551 q^{75}\) \(-2.11567 q^{76}\) \(-4.39808 q^{77}\) \(+6.38396 q^{78}\) \(+0.464395 q^{79}\) \(+37.7217 q^{80}\) \(-10.6429 q^{81}\) \(-7.93244 q^{82}\) \(+3.99696 q^{83}\) \(+9.89554 q^{84}\) \(+3.65641 q^{85}\) \(-6.58723 q^{86}\) \(+6.94006 q^{87}\) \(+60.3731 q^{88}\) \(-3.06289 q^{89}\) \(-13.8256 q^{90}\) \(-0.752947 q^{91}\) \(+6.34235 q^{92}\) \(-18.0240 q^{93}\) \(+31.0717 q^{94}\) \(-0.807522 q^{95}\) \(-62.8057 q^{96}\) \(+4.60043 q^{97}\) \(+17.8742 q^{98}\) \(-13.3130 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77848 −1.96468 −0.982341 0.187099i \(-0.940091\pi\)
−0.982341 + 0.187099i \(0.940091\pi\)
\(3\) 2.29765 1.32655 0.663273 0.748377i \(-0.269167\pi\)
0.663273 + 0.748377i \(0.269167\pi\)
\(4\) 5.71995 2.85998
\(5\) 2.18323 0.976369 0.488184 0.872741i \(-0.337659\pi\)
0.488184 + 0.872741i \(0.337659\pi\)
\(6\) −6.38396 −2.60624
\(7\) 0.752947 0.284587 0.142294 0.989825i \(-0.454552\pi\)
0.142294 + 0.989825i \(0.454552\pi\)
\(8\) −10.3358 −3.65426
\(9\) 2.27917 0.759725
\(10\) −6.06605 −1.91825
\(11\) −5.84116 −1.76118 −0.880588 0.473882i \(-0.842852\pi\)
−0.880588 + 0.473882i \(0.842852\pi\)
\(12\) 13.1424 3.79389
\(13\) −1.00000 −0.277350
\(14\) −2.09205 −0.559123
\(15\) 5.01628 1.29520
\(16\) 17.2779 4.31949
\(17\) 1.67477 0.406192 0.203096 0.979159i \(-0.434900\pi\)
0.203096 + 0.979159i \(0.434900\pi\)
\(18\) −6.33264 −1.49262
\(19\) −0.369876 −0.0848553 −0.0424276 0.999100i \(-0.513509\pi\)
−0.0424276 + 0.999100i \(0.513509\pi\)
\(20\) 12.4880 2.79239
\(21\) 1.73000 0.377518
\(22\) 16.2295 3.46015
\(23\) 1.10881 0.231203 0.115602 0.993296i \(-0.463120\pi\)
0.115602 + 0.993296i \(0.463120\pi\)
\(24\) −23.7480 −4.84755
\(25\) −0.233522 −0.0467044
\(26\) 2.77848 0.544905
\(27\) −1.65620 −0.318736
\(28\) 4.30682 0.813912
\(29\) 3.02051 0.560894 0.280447 0.959869i \(-0.409517\pi\)
0.280447 + 0.959869i \(0.409517\pi\)
\(30\) −13.9376 −2.54465
\(31\) −7.84456 −1.40892 −0.704462 0.709741i \(-0.748812\pi\)
−0.704462 + 0.709741i \(0.748812\pi\)
\(32\) −27.3348 −4.83216
\(33\) −13.4209 −2.33628
\(34\) −4.65332 −0.798038
\(35\) 1.64385 0.277862
\(36\) 13.0368 2.17279
\(37\) 0.683881 0.112429 0.0562146 0.998419i \(-0.482097\pi\)
0.0562146 + 0.998419i \(0.482097\pi\)
\(38\) 1.02769 0.166714
\(39\) −2.29765 −0.367918
\(40\) −22.5654 −3.56791
\(41\) 2.85496 0.445869 0.222935 0.974833i \(-0.428436\pi\)
0.222935 + 0.974833i \(0.428436\pi\)
\(42\) −4.80678 −0.741703
\(43\) 2.37080 0.361544 0.180772 0.983525i \(-0.442140\pi\)
0.180772 + 0.983525i \(0.442140\pi\)
\(44\) −33.4112 −5.03692
\(45\) 4.97595 0.741771
\(46\) −3.08081 −0.454241
\(47\) −11.1830 −1.63120 −0.815602 0.578613i \(-0.803594\pi\)
−0.815602 + 0.578613i \(0.803594\pi\)
\(48\) 39.6986 5.73000
\(49\) −6.43307 −0.919010
\(50\) 0.648836 0.0917593
\(51\) 3.84803 0.538833
\(52\) −5.71995 −0.793215
\(53\) −10.0200 −1.37635 −0.688174 0.725545i \(-0.741588\pi\)
−0.688174 + 0.725545i \(0.741588\pi\)
\(54\) 4.60172 0.626215
\(55\) −12.7526 −1.71956
\(56\) −7.78232 −1.03996
\(57\) −0.849843 −0.112564
\(58\) −8.39242 −1.10198
\(59\) −7.83855 −1.02049 −0.510246 0.860028i \(-0.670446\pi\)
−0.510246 + 0.860028i \(0.670446\pi\)
\(60\) 28.6929 3.70424
\(61\) 7.75538 0.992974 0.496487 0.868044i \(-0.334623\pi\)
0.496487 + 0.868044i \(0.334623\pi\)
\(62\) 21.7960 2.76809
\(63\) 1.71610 0.216208
\(64\) 41.3933 5.17416
\(65\) −2.18323 −0.270796
\(66\) 37.2897 4.59005
\(67\) 3.63717 0.444351 0.222176 0.975007i \(-0.428684\pi\)
0.222176 + 0.975007i \(0.428684\pi\)
\(68\) 9.57962 1.16170
\(69\) 2.54766 0.306702
\(70\) −4.56741 −0.545910
\(71\) 8.56799 1.01683 0.508417 0.861111i \(-0.330231\pi\)
0.508417 + 0.861111i \(0.330231\pi\)
\(72\) −23.5571 −2.77623
\(73\) −0.475662 −0.0556720 −0.0278360 0.999613i \(-0.508862\pi\)
−0.0278360 + 0.999613i \(0.508862\pi\)
\(74\) −1.90015 −0.220888
\(75\) −0.536551 −0.0619555
\(76\) −2.11567 −0.242684
\(77\) −4.39808 −0.501208
\(78\) 6.38396 0.722841
\(79\) 0.464395 0.0522486 0.0261243 0.999659i \(-0.491683\pi\)
0.0261243 + 0.999659i \(0.491683\pi\)
\(80\) 37.7217 4.21741
\(81\) −10.6429 −1.18254
\(82\) −7.93244 −0.875992
\(83\) 3.99696 0.438723 0.219362 0.975644i \(-0.429603\pi\)
0.219362 + 0.975644i \(0.429603\pi\)
\(84\) 9.89554 1.07969
\(85\) 3.65641 0.396593
\(86\) −6.58723 −0.710319
\(87\) 6.94006 0.744052
\(88\) 60.3731 6.43580
\(89\) −3.06289 −0.324666 −0.162333 0.986736i \(-0.551902\pi\)
−0.162333 + 0.986736i \(0.551902\pi\)
\(90\) −13.8256 −1.45735
\(91\) −0.752947 −0.0789303
\(92\) 6.34235 0.661235
\(93\) −18.0240 −1.86900
\(94\) 31.0717 3.20480
\(95\) −0.807522 −0.0828500
\(96\) −62.8057 −6.41008
\(97\) 4.60043 0.467103 0.233551 0.972344i \(-0.424965\pi\)
0.233551 + 0.972344i \(0.424965\pi\)
\(98\) 17.8742 1.80556
\(99\) −13.3130 −1.33801
\(100\) −1.33573 −0.133573
\(101\) −11.0352 −1.09804 −0.549020 0.835809i \(-0.684999\pi\)
−0.549020 + 0.835809i \(0.684999\pi\)
\(102\) −10.6917 −1.05863
\(103\) −6.49925 −0.640390 −0.320195 0.947352i \(-0.603748\pi\)
−0.320195 + 0.947352i \(0.603748\pi\)
\(104\) 10.3358 1.01351
\(105\) 3.77699 0.368597
\(106\) 27.8403 2.70409
\(107\) −14.1368 −1.36665 −0.683327 0.730113i \(-0.739468\pi\)
−0.683327 + 0.730113i \(0.739468\pi\)
\(108\) −9.47339 −0.911577
\(109\) −12.9703 −1.24233 −0.621163 0.783682i \(-0.713339\pi\)
−0.621163 + 0.783682i \(0.713339\pi\)
\(110\) 35.4328 3.37838
\(111\) 1.57132 0.149143
\(112\) 13.0094 1.22927
\(113\) 8.18100 0.769604 0.384802 0.922999i \(-0.374270\pi\)
0.384802 + 0.922999i \(0.374270\pi\)
\(114\) 2.36127 0.221153
\(115\) 2.42079 0.225740
\(116\) 17.2772 1.60414
\(117\) −2.27917 −0.210710
\(118\) 21.7793 2.00494
\(119\) 1.26101 0.115597
\(120\) −51.8473 −4.73299
\(121\) 23.1192 2.10174
\(122\) −21.5482 −1.95088
\(123\) 6.55968 0.591466
\(124\) −44.8705 −4.02949
\(125\) −11.4260 −1.02197
\(126\) −4.76814 −0.424780
\(127\) 17.9154 1.58973 0.794867 0.606784i \(-0.207541\pi\)
0.794867 + 0.606784i \(0.207541\pi\)
\(128\) −60.3409 −5.33343
\(129\) 5.44726 0.479605
\(130\) 6.06605 0.532028
\(131\) 4.88211 0.426552 0.213276 0.976992i \(-0.431587\pi\)
0.213276 + 0.976992i \(0.431587\pi\)
\(132\) −76.7670 −6.68171
\(133\) −0.278497 −0.0241487
\(134\) −10.1058 −0.873009
\(135\) −3.61586 −0.311204
\(136\) −17.3101 −1.48433
\(137\) −15.1486 −1.29423 −0.647114 0.762393i \(-0.724024\pi\)
−0.647114 + 0.762393i \(0.724024\pi\)
\(138\) −7.07861 −0.602571
\(139\) 7.46948 0.633553 0.316777 0.948500i \(-0.397399\pi\)
0.316777 + 0.948500i \(0.397399\pi\)
\(140\) 9.40276 0.794678
\(141\) −25.6945 −2.16387
\(142\) −23.8060 −1.99775
\(143\) 5.84116 0.488462
\(144\) 39.3795 3.28162
\(145\) 6.59445 0.547639
\(146\) 1.32162 0.109378
\(147\) −14.7809 −1.21911
\(148\) 3.91176 0.321545
\(149\) −13.1913 −1.08068 −0.540338 0.841448i \(-0.681704\pi\)
−0.540338 + 0.841448i \(0.681704\pi\)
\(150\) 1.49080 0.121723
\(151\) 19.7800 1.60967 0.804837 0.593496i \(-0.202253\pi\)
0.804837 + 0.593496i \(0.202253\pi\)
\(152\) 3.82296 0.310083
\(153\) 3.81710 0.308594
\(154\) 12.2200 0.984714
\(155\) −17.1264 −1.37563
\(156\) −13.1424 −1.05224
\(157\) −4.82393 −0.384992 −0.192496 0.981298i \(-0.561658\pi\)
−0.192496 + 0.981298i \(0.561658\pi\)
\(158\) −1.29031 −0.102652
\(159\) −23.0223 −1.82579
\(160\) −59.6781 −4.71797
\(161\) 0.834876 0.0657974
\(162\) 29.5710 2.32332
\(163\) −5.72813 −0.448662 −0.224331 0.974513i \(-0.572020\pi\)
−0.224331 + 0.974513i \(0.572020\pi\)
\(164\) 16.3302 1.27518
\(165\) −29.3009 −2.28107
\(166\) −11.1055 −0.861952
\(167\) −1.03747 −0.0802822 −0.0401411 0.999194i \(-0.512781\pi\)
−0.0401411 + 0.999194i \(0.512781\pi\)
\(168\) −17.8810 −1.37955
\(169\) 1.00000 0.0769231
\(170\) −10.1593 −0.779180
\(171\) −0.843011 −0.0644667
\(172\) 13.5609 1.03401
\(173\) −18.5954 −1.41378 −0.706892 0.707322i \(-0.749903\pi\)
−0.706892 + 0.707322i \(0.749903\pi\)
\(174\) −19.2828 −1.46183
\(175\) −0.175830 −0.0132915
\(176\) −100.923 −7.60738
\(177\) −18.0102 −1.35373
\(178\) 8.51019 0.637866
\(179\) −12.0081 −0.897529 −0.448765 0.893650i \(-0.648136\pi\)
−0.448765 + 0.893650i \(0.648136\pi\)
\(180\) 28.4622 2.12145
\(181\) −17.7919 −1.32246 −0.661229 0.750184i \(-0.729965\pi\)
−0.661229 + 0.750184i \(0.729965\pi\)
\(182\) 2.09205 0.155073
\(183\) 17.8191 1.31723
\(184\) −11.4605 −0.844877
\(185\) 1.49307 0.109772
\(186\) 50.0794 3.67200
\(187\) −9.78262 −0.715376
\(188\) −63.9661 −4.66521
\(189\) −1.24703 −0.0907082
\(190\) 2.24368 0.162774
\(191\) −24.5105 −1.77352 −0.886759 0.462232i \(-0.847049\pi\)
−0.886759 + 0.462232i \(0.847049\pi\)
\(192\) 95.1072 6.86377
\(193\) 5.65542 0.407086 0.203543 0.979066i \(-0.434754\pi\)
0.203543 + 0.979066i \(0.434754\pi\)
\(194\) −12.7822 −0.917708
\(195\) −5.01628 −0.359223
\(196\) −36.7969 −2.62835
\(197\) 1.04159 0.0742100 0.0371050 0.999311i \(-0.488186\pi\)
0.0371050 + 0.999311i \(0.488186\pi\)
\(198\) 36.9900 2.62876
\(199\) 11.2989 0.800958 0.400479 0.916306i \(-0.368844\pi\)
0.400479 + 0.916306i \(0.368844\pi\)
\(200\) 2.41364 0.170670
\(201\) 8.35693 0.589452
\(202\) 30.6610 2.15730
\(203\) 2.27428 0.159623
\(204\) 22.0106 1.54105
\(205\) 6.23302 0.435333
\(206\) 18.0580 1.25816
\(207\) 2.52717 0.175651
\(208\) −17.2779 −1.19801
\(209\) 2.16050 0.149445
\(210\) −10.4943 −0.724175
\(211\) 17.4147 1.19888 0.599439 0.800421i \(-0.295391\pi\)
0.599439 + 0.800421i \(0.295391\pi\)
\(212\) −57.3137 −3.93632
\(213\) 19.6862 1.34888
\(214\) 39.2787 2.68504
\(215\) 5.17600 0.353000
\(216\) 17.1182 1.16474
\(217\) −5.90653 −0.400962
\(218\) 36.0376 2.44078
\(219\) −1.09290 −0.0738515
\(220\) −72.9441 −4.91789
\(221\) −1.67477 −0.112657
\(222\) −4.36587 −0.293018
\(223\) 25.2593 1.69149 0.845743 0.533590i \(-0.179157\pi\)
0.845743 + 0.533590i \(0.179157\pi\)
\(224\) −20.5816 −1.37517
\(225\) −0.532237 −0.0354825
\(226\) −22.7308 −1.51203
\(227\) −8.14202 −0.540405 −0.270202 0.962804i \(-0.587091\pi\)
−0.270202 + 0.962804i \(0.587091\pi\)
\(228\) −4.86106 −0.321932
\(229\) −7.54801 −0.498786 −0.249393 0.968402i \(-0.580231\pi\)
−0.249393 + 0.968402i \(0.580231\pi\)
\(230\) −6.72611 −0.443506
\(231\) −10.1052 −0.664876
\(232\) −31.2194 −2.04965
\(233\) 23.2242 1.52147 0.760735 0.649062i \(-0.224839\pi\)
0.760735 + 0.649062i \(0.224839\pi\)
\(234\) 6.33264 0.413978
\(235\) −24.4150 −1.59266
\(236\) −44.8361 −2.91858
\(237\) 1.06702 0.0693101
\(238\) −3.50370 −0.227111
\(239\) 19.0857 1.23455 0.617275 0.786747i \(-0.288237\pi\)
0.617275 + 0.786747i \(0.288237\pi\)
\(240\) 86.6710 5.59459
\(241\) −23.8277 −1.53487 −0.767437 0.641124i \(-0.778468\pi\)
−0.767437 + 0.641124i \(0.778468\pi\)
\(242\) −64.2361 −4.12925
\(243\) −19.4850 −1.24996
\(244\) 44.3604 2.83988
\(245\) −14.0449 −0.897293
\(246\) −18.2259 −1.16204
\(247\) 0.369876 0.0235346
\(248\) 81.0799 5.14858
\(249\) 9.18360 0.581987
\(250\) 31.7468 2.00784
\(251\) 7.76343 0.490023 0.245012 0.969520i \(-0.421208\pi\)
0.245012 + 0.969520i \(0.421208\pi\)
\(252\) 9.81599 0.618349
\(253\) −6.47675 −0.407190
\(254\) −49.7776 −3.12332
\(255\) 8.40113 0.526099
\(256\) 84.8694 5.30434
\(257\) −27.8611 −1.73793 −0.868964 0.494875i \(-0.835214\pi\)
−0.868964 + 0.494875i \(0.835214\pi\)
\(258\) −15.1351 −0.942271
\(259\) 0.514926 0.0319959
\(260\) −12.4880 −0.774470
\(261\) 6.88426 0.426125
\(262\) −13.5648 −0.838039
\(263\) −13.3677 −0.824289 −0.412145 0.911118i \(-0.635220\pi\)
−0.412145 + 0.911118i \(0.635220\pi\)
\(264\) 138.716 8.53738
\(265\) −21.8759 −1.34382
\(266\) 0.773797 0.0474445
\(267\) −7.03745 −0.430685
\(268\) 20.8044 1.27083
\(269\) 23.4729 1.43117 0.715583 0.698527i \(-0.246161\pi\)
0.715583 + 0.698527i \(0.246161\pi\)
\(270\) 10.0466 0.611417
\(271\) −5.38154 −0.326906 −0.163453 0.986551i \(-0.552263\pi\)
−0.163453 + 0.986551i \(0.552263\pi\)
\(272\) 28.9366 1.75454
\(273\) −1.73000 −0.104705
\(274\) 42.0900 2.54275
\(275\) 1.36404 0.0822547
\(276\) 14.5725 0.877159
\(277\) −12.8583 −0.772583 −0.386291 0.922377i \(-0.626244\pi\)
−0.386291 + 0.922377i \(0.626244\pi\)
\(278\) −20.7538 −1.24473
\(279\) −17.8791 −1.07039
\(280\) −16.9906 −1.01538
\(281\) −25.7588 −1.53664 −0.768320 0.640065i \(-0.778907\pi\)
−0.768320 + 0.640065i \(0.778907\pi\)
\(282\) 71.3917 4.25131
\(283\) −24.4401 −1.45281 −0.726407 0.687265i \(-0.758811\pi\)
−0.726407 + 0.687265i \(0.758811\pi\)
\(284\) 49.0085 2.90812
\(285\) −1.85540 −0.109904
\(286\) −16.2295 −0.959673
\(287\) 2.14963 0.126889
\(288\) −62.3008 −3.67111
\(289\) −14.1951 −0.835008
\(290\) −18.3226 −1.07594
\(291\) 10.5702 0.619633
\(292\) −2.72076 −0.159221
\(293\) −13.1590 −0.768758 −0.384379 0.923175i \(-0.625584\pi\)
−0.384379 + 0.923175i \(0.625584\pi\)
\(294\) 41.0685 2.39516
\(295\) −17.1133 −0.996377
\(296\) −7.06846 −0.410846
\(297\) 9.67414 0.561350
\(298\) 36.6519 2.12318
\(299\) −1.10881 −0.0641242
\(300\) −3.06904 −0.177191
\(301\) 1.78509 0.102891
\(302\) −54.9583 −3.16250
\(303\) −25.3549 −1.45660
\(304\) −6.39069 −0.366531
\(305\) 16.9317 0.969509
\(306\) −10.6057 −0.606290
\(307\) 27.2775 1.55681 0.778405 0.627762i \(-0.216029\pi\)
0.778405 + 0.627762i \(0.216029\pi\)
\(308\) −25.1568 −1.43344
\(309\) −14.9330 −0.849507
\(310\) 47.5855 2.70267
\(311\) 1.32941 0.0753838 0.0376919 0.999289i \(-0.487999\pi\)
0.0376919 + 0.999289i \(0.487999\pi\)
\(312\) 23.7480 1.34447
\(313\) −3.53001 −0.199528 −0.0997640 0.995011i \(-0.531809\pi\)
−0.0997640 + 0.995011i \(0.531809\pi\)
\(314\) 13.4032 0.756386
\(315\) 3.74663 0.211099
\(316\) 2.65632 0.149430
\(317\) 19.2276 1.07993 0.539963 0.841688i \(-0.318438\pi\)
0.539963 + 0.841688i \(0.318438\pi\)
\(318\) 63.9671 3.58710
\(319\) −17.6433 −0.987833
\(320\) 90.3710 5.05189
\(321\) −32.4813 −1.81293
\(322\) −2.31969 −0.129271
\(323\) −0.619458 −0.0344675
\(324\) −60.8768 −3.38204
\(325\) 0.233522 0.0129535
\(326\) 15.9155 0.881478
\(327\) −29.8011 −1.64800
\(328\) −29.5083 −1.62932
\(329\) −8.42018 −0.464220
\(330\) 81.4120 4.48158
\(331\) −19.2891 −1.06023 −0.530113 0.847927i \(-0.677851\pi\)
−0.530113 + 0.847927i \(0.677851\pi\)
\(332\) 22.8624 1.25474
\(333\) 1.55868 0.0854153
\(334\) 2.88260 0.157729
\(335\) 7.94077 0.433851
\(336\) 29.8909 1.63068
\(337\) 7.98183 0.434798 0.217399 0.976083i \(-0.430243\pi\)
0.217399 + 0.976083i \(0.430243\pi\)
\(338\) −2.77848 −0.151129
\(339\) 18.7970 1.02092
\(340\) 20.9145 1.13425
\(341\) 45.8213 2.48136
\(342\) 2.34229 0.126656
\(343\) −10.1144 −0.546126
\(344\) −24.5042 −1.32118
\(345\) 5.56211 0.299454
\(346\) 51.6670 2.77764
\(347\) 2.46082 0.132104 0.0660520 0.997816i \(-0.478960\pi\)
0.0660520 + 0.997816i \(0.478960\pi\)
\(348\) 39.6968 2.12797
\(349\) −10.7772 −0.576891 −0.288445 0.957496i \(-0.593138\pi\)
−0.288445 + 0.957496i \(0.593138\pi\)
\(350\) 0.488539 0.0261135
\(351\) 1.65620 0.0884015
\(352\) 159.667 8.51028
\(353\) −20.4374 −1.08777 −0.543886 0.839159i \(-0.683048\pi\)
−0.543886 + 0.839159i \(0.683048\pi\)
\(354\) 50.0410 2.65965
\(355\) 18.7059 0.992804
\(356\) −17.5196 −0.928537
\(357\) 2.89736 0.153345
\(358\) 33.3643 1.76336
\(359\) 25.2735 1.33388 0.666941 0.745110i \(-0.267603\pi\)
0.666941 + 0.745110i \(0.267603\pi\)
\(360\) −51.4305 −2.71063
\(361\) −18.8632 −0.992800
\(362\) 49.4343 2.59821
\(363\) 53.1196 2.78806
\(364\) −4.30682 −0.225739
\(365\) −1.03848 −0.0543564
\(366\) −49.5100 −2.58793
\(367\) −5.29893 −0.276602 −0.138301 0.990390i \(-0.544164\pi\)
−0.138301 + 0.990390i \(0.544164\pi\)
\(368\) 19.1580 0.998679
\(369\) 6.50695 0.338738
\(370\) −4.14846 −0.215668
\(371\) −7.54450 −0.391691
\(372\) −103.097 −5.34530
\(373\) 38.0431 1.96980 0.984900 0.173126i \(-0.0553869\pi\)
0.984900 + 0.173126i \(0.0553869\pi\)
\(374\) 27.1808 1.40549
\(375\) −26.2528 −1.35569
\(376\) 115.585 5.96085
\(377\) −3.02051 −0.155564
\(378\) 3.46485 0.178213
\(379\) 11.6631 0.599096 0.299548 0.954081i \(-0.403164\pi\)
0.299548 + 0.954081i \(0.403164\pi\)
\(380\) −4.61899 −0.236949
\(381\) 41.1632 2.10886
\(382\) 68.1019 3.48440
\(383\) 24.9019 1.27243 0.636213 0.771513i \(-0.280500\pi\)
0.636213 + 0.771513i \(0.280500\pi\)
\(384\) −138.642 −7.07504
\(385\) −9.60201 −0.489364
\(386\) −15.7135 −0.799795
\(387\) 5.40347 0.274674
\(388\) 26.3142 1.33590
\(389\) 29.0129 1.47101 0.735506 0.677518i \(-0.236944\pi\)
0.735506 + 0.677518i \(0.236944\pi\)
\(390\) 13.9376 0.705760
\(391\) 1.85701 0.0939129
\(392\) 66.4910 3.35830
\(393\) 11.2174 0.565841
\(394\) −2.89403 −0.145799
\(395\) 1.01388 0.0510139
\(396\) −76.1499 −3.82667
\(397\) −27.4298 −1.37666 −0.688332 0.725396i \(-0.741657\pi\)
−0.688332 + 0.725396i \(0.741657\pi\)
\(398\) −31.3938 −1.57363
\(399\) −0.639886 −0.0320344
\(400\) −4.03478 −0.201739
\(401\) 25.5091 1.27386 0.636931 0.770921i \(-0.280204\pi\)
0.636931 + 0.770921i \(0.280204\pi\)
\(402\) −23.2196 −1.15809
\(403\) 7.84456 0.390765
\(404\) −63.1206 −3.14037
\(405\) −23.2358 −1.15460
\(406\) −6.31904 −0.313609
\(407\) −3.99466 −0.198008
\(408\) −39.7726 −1.96904
\(409\) −19.3315 −0.955883 −0.477941 0.878392i \(-0.658617\pi\)
−0.477941 + 0.878392i \(0.658617\pi\)
\(410\) −17.3183 −0.855291
\(411\) −34.8060 −1.71685
\(412\) −37.1754 −1.83150
\(413\) −5.90201 −0.290419
\(414\) −7.02171 −0.345098
\(415\) 8.72627 0.428356
\(416\) 27.3348 1.34020
\(417\) 17.1622 0.840438
\(418\) −6.00291 −0.293612
\(419\) 4.99707 0.244123 0.122061 0.992523i \(-0.461050\pi\)
0.122061 + 0.992523i \(0.461050\pi\)
\(420\) 21.6042 1.05418
\(421\) −22.9226 −1.11718 −0.558590 0.829444i \(-0.688657\pi\)
−0.558590 + 0.829444i \(0.688657\pi\)
\(422\) −48.3864 −2.35541
\(423\) −25.4879 −1.23927
\(424\) 103.565 5.02954
\(425\) −0.391096 −0.0189710
\(426\) −54.6977 −2.65011
\(427\) 5.83939 0.282588
\(428\) −80.8617 −3.90860
\(429\) 13.4209 0.647968
\(430\) −14.3814 −0.693533
\(431\) −15.3888 −0.741251 −0.370626 0.928782i \(-0.620857\pi\)
−0.370626 + 0.928782i \(0.620857\pi\)
\(432\) −28.6158 −1.37678
\(433\) −3.49976 −0.168188 −0.0840938 0.996458i \(-0.526800\pi\)
−0.0840938 + 0.996458i \(0.526800\pi\)
\(434\) 16.4112 0.787762
\(435\) 15.1517 0.726469
\(436\) −74.1893 −3.55302
\(437\) −0.410122 −0.0196188
\(438\) 3.03661 0.145095
\(439\) 16.7090 0.797479 0.398739 0.917064i \(-0.369448\pi\)
0.398739 + 0.917064i \(0.369448\pi\)
\(440\) 131.808 6.28371
\(441\) −14.6621 −0.698195
\(442\) 4.65332 0.221336
\(443\) −6.74554 −0.320490 −0.160245 0.987077i \(-0.551228\pi\)
−0.160245 + 0.987077i \(0.551228\pi\)
\(444\) 8.98785 0.426544
\(445\) −6.68699 −0.316994
\(446\) −70.1824 −3.32323
\(447\) −30.3090 −1.43357
\(448\) 31.1670 1.47250
\(449\) 7.19925 0.339753 0.169877 0.985465i \(-0.445663\pi\)
0.169877 + 0.985465i \(0.445663\pi\)
\(450\) 1.47881 0.0697118
\(451\) −16.6763 −0.785255
\(452\) 46.7949 2.20105
\(453\) 45.4474 2.13531
\(454\) 22.6224 1.06172
\(455\) −1.64385 −0.0770650
\(456\) 8.78382 0.411340
\(457\) 18.8183 0.880281 0.440140 0.897929i \(-0.354929\pi\)
0.440140 + 0.897929i \(0.354929\pi\)
\(458\) 20.9720 0.979957
\(459\) −2.77376 −0.129468
\(460\) 13.8468 0.645610
\(461\) −29.2948 −1.36440 −0.682198 0.731168i \(-0.738976\pi\)
−0.682198 + 0.731168i \(0.738976\pi\)
\(462\) 28.0772 1.30627
\(463\) −1.00000 −0.0464739
\(464\) 52.1882 2.42277
\(465\) −39.3505 −1.82484
\(466\) −64.5281 −2.98921
\(467\) 28.2975 1.30945 0.654726 0.755867i \(-0.272784\pi\)
0.654726 + 0.755867i \(0.272784\pi\)
\(468\) −13.0368 −0.602625
\(469\) 2.73860 0.126457
\(470\) 67.8365 3.12906
\(471\) −11.0837 −0.510709
\(472\) 81.0178 3.72915
\(473\) −13.8482 −0.636743
\(474\) −2.96468 −0.136172
\(475\) 0.0863740 0.00396311
\(476\) 7.21294 0.330605
\(477\) −22.8373 −1.04565
\(478\) −53.0292 −2.42550
\(479\) 13.4334 0.613788 0.306894 0.951744i \(-0.400710\pi\)
0.306894 + 0.951744i \(0.400710\pi\)
\(480\) −137.119 −6.25860
\(481\) −0.683881 −0.0311823
\(482\) 66.2047 3.01554
\(483\) 1.91825 0.0872833
\(484\) 132.240 6.01093
\(485\) 10.0438 0.456064
\(486\) 54.1386 2.45578
\(487\) 20.5958 0.933284 0.466642 0.884446i \(-0.345464\pi\)
0.466642 + 0.884446i \(0.345464\pi\)
\(488\) −80.1581 −3.62859
\(489\) −13.1612 −0.595171
\(490\) 39.0233 1.76289
\(491\) 25.4077 1.14664 0.573318 0.819333i \(-0.305656\pi\)
0.573318 + 0.819333i \(0.305656\pi\)
\(492\) 37.5211 1.69158
\(493\) 5.05866 0.227831
\(494\) −1.02769 −0.0462380
\(495\) −29.0653 −1.30639
\(496\) −135.538 −6.08583
\(497\) 6.45124 0.289378
\(498\) −25.5164 −1.14342
\(499\) 16.8433 0.754011 0.377006 0.926211i \(-0.376954\pi\)
0.377006 + 0.926211i \(0.376954\pi\)
\(500\) −65.3560 −2.92281
\(501\) −2.38375 −0.106498
\(502\) −21.5705 −0.962740
\(503\) 11.6568 0.519753 0.259877 0.965642i \(-0.416318\pi\)
0.259877 + 0.965642i \(0.416318\pi\)
\(504\) −17.7373 −0.790080
\(505\) −24.0922 −1.07209
\(506\) 17.9955 0.799998
\(507\) 2.29765 0.102042
\(508\) 102.475 4.54660
\(509\) 3.11707 0.138162 0.0690809 0.997611i \(-0.477993\pi\)
0.0690809 + 0.997611i \(0.477993\pi\)
\(510\) −23.3424 −1.03362
\(511\) −0.358148 −0.0158435
\(512\) −115.126 −5.08790
\(513\) 0.612588 0.0270464
\(514\) 77.4116 3.41448
\(515\) −14.1893 −0.625257
\(516\) 31.1581 1.37166
\(517\) 65.3215 2.87284
\(518\) −1.43071 −0.0628618
\(519\) −42.7257 −1.87545
\(520\) 22.5654 0.989559
\(521\) −31.3387 −1.37297 −0.686487 0.727142i \(-0.740848\pi\)
−0.686487 + 0.727142i \(0.740848\pi\)
\(522\) −19.1278 −0.837201
\(523\) −12.0780 −0.528135 −0.264068 0.964504i \(-0.585064\pi\)
−0.264068 + 0.964504i \(0.585064\pi\)
\(524\) 27.9254 1.21993
\(525\) −0.403994 −0.0176317
\(526\) 37.1420 1.61947
\(527\) −13.1379 −0.572294
\(528\) −231.886 −10.0915
\(529\) −21.7705 −0.946545
\(530\) 60.7816 2.64019
\(531\) −17.8654 −0.775294
\(532\) −1.59299 −0.0690647
\(533\) −2.85496 −0.123662
\(534\) 19.5534 0.846159
\(535\) −30.8638 −1.33436
\(536\) −37.5931 −1.62378
\(537\) −27.5904 −1.19061
\(538\) −65.2189 −2.81179
\(539\) 37.5766 1.61854
\(540\) −20.6826 −0.890036
\(541\) 18.2619 0.785140 0.392570 0.919722i \(-0.371586\pi\)
0.392570 + 0.919722i \(0.371586\pi\)
\(542\) 14.9525 0.642265
\(543\) −40.8794 −1.75430
\(544\) −45.7796 −1.96278
\(545\) −28.3170 −1.21297
\(546\) 4.80678 0.205711
\(547\) −17.9515 −0.767550 −0.383775 0.923427i \(-0.625376\pi\)
−0.383775 + 0.923427i \(0.625376\pi\)
\(548\) −86.6490 −3.70146
\(549\) 17.6759 0.754387
\(550\) −3.78996 −0.161604
\(551\) −1.11721 −0.0475948
\(552\) −26.3321 −1.12077
\(553\) 0.349665 0.0148693
\(554\) 35.7266 1.51788
\(555\) 3.43054 0.145618
\(556\) 42.7251 1.81195
\(557\) −11.5189 −0.488072 −0.244036 0.969766i \(-0.578471\pi\)
−0.244036 + 0.969766i \(0.578471\pi\)
\(558\) 49.6768 2.10299
\(559\) −2.37080 −0.100274
\(560\) 28.4024 1.20022
\(561\) −22.4770 −0.948979
\(562\) 71.5703 3.01901
\(563\) 21.1227 0.890216 0.445108 0.895477i \(-0.353165\pi\)
0.445108 + 0.895477i \(0.353165\pi\)
\(564\) −146.971 −6.18861
\(565\) 17.8610 0.751417
\(566\) 67.9064 2.85432
\(567\) −8.01353 −0.336536
\(568\) −88.5571 −3.71577
\(569\) −11.8745 −0.497807 −0.248903 0.968528i \(-0.580070\pi\)
−0.248903 + 0.968528i \(0.580070\pi\)
\(570\) 5.15519 0.215927
\(571\) −31.4473 −1.31603 −0.658015 0.753005i \(-0.728604\pi\)
−0.658015 + 0.753005i \(0.728604\pi\)
\(572\) 33.4112 1.39699
\(573\) −56.3164 −2.35265
\(574\) −5.97271 −0.249296
\(575\) −0.258932 −0.0107982
\(576\) 94.3426 3.93094
\(577\) 18.3040 0.762007 0.381003 0.924574i \(-0.375579\pi\)
0.381003 + 0.924574i \(0.375579\pi\)
\(578\) 39.4409 1.64053
\(579\) 12.9942 0.540018
\(580\) 37.7199 1.56624
\(581\) 3.00950 0.124855
\(582\) −29.3690 −1.21738
\(583\) 58.5282 2.42399
\(584\) 4.91635 0.203440
\(585\) −4.97595 −0.205730
\(586\) 36.5621 1.51036
\(587\) −3.80743 −0.157149 −0.0785747 0.996908i \(-0.525037\pi\)
−0.0785747 + 0.996908i \(0.525037\pi\)
\(588\) −84.5461 −3.48662
\(589\) 2.90151 0.119555
\(590\) 47.5491 1.95756
\(591\) 2.39320 0.0984429
\(592\) 11.8161 0.485637
\(593\) 1.16574 0.0478711 0.0239355 0.999714i \(-0.492380\pi\)
0.0239355 + 0.999714i \(0.492380\pi\)
\(594\) −26.8794 −1.10288
\(595\) 2.75308 0.112865
\(596\) −75.4538 −3.09071
\(597\) 25.9609 1.06251
\(598\) 3.08081 0.125984
\(599\) 23.4851 0.959575 0.479787 0.877385i \(-0.340714\pi\)
0.479787 + 0.877385i \(0.340714\pi\)
\(600\) 5.54569 0.226402
\(601\) −11.7693 −0.480080 −0.240040 0.970763i \(-0.577161\pi\)
−0.240040 + 0.970763i \(0.577161\pi\)
\(602\) −4.95983 −0.202148
\(603\) 8.28975 0.337585
\(604\) 113.141 4.60363
\(605\) 50.4744 2.05207
\(606\) 70.4480 2.86176
\(607\) −41.7676 −1.69529 −0.847647 0.530561i \(-0.821981\pi\)
−0.847647 + 0.530561i \(0.821981\pi\)
\(608\) 10.1105 0.410034
\(609\) 5.22549 0.211748
\(610\) −47.0445 −1.90478
\(611\) 11.1830 0.452415
\(612\) 21.8336 0.882572
\(613\) −9.81613 −0.396470 −0.198235 0.980155i \(-0.563521\pi\)
−0.198235 + 0.980155i \(0.563521\pi\)
\(614\) −75.7901 −3.05864
\(615\) 14.3213 0.577489
\(616\) 45.4578 1.83155
\(617\) −35.2518 −1.41918 −0.709592 0.704612i \(-0.751121\pi\)
−0.709592 + 0.704612i \(0.751121\pi\)
\(618\) 41.4910 1.66901
\(619\) −16.5190 −0.663953 −0.331976 0.943288i \(-0.607715\pi\)
−0.331976 + 0.943288i \(0.607715\pi\)
\(620\) −97.9625 −3.93427
\(621\) −1.83641 −0.0736928
\(622\) −3.69373 −0.148105
\(623\) −2.30620 −0.0923958
\(624\) −39.6986 −1.58922
\(625\) −23.7779 −0.951114
\(626\) 9.80806 0.392009
\(627\) 4.96407 0.198246
\(628\) −27.5927 −1.10107
\(629\) 1.14534 0.0456679
\(630\) −10.4099 −0.414742
\(631\) 49.4754 1.96958 0.984792 0.173737i \(-0.0555843\pi\)
0.984792 + 0.173737i \(0.0555843\pi\)
\(632\) −4.79990 −0.190930
\(633\) 40.0128 1.59037
\(634\) −53.4234 −2.12171
\(635\) 39.1134 1.55217
\(636\) −131.687 −5.22172
\(637\) 6.43307 0.254888
\(638\) 49.0215 1.94078
\(639\) 19.5279 0.772513
\(640\) −131.738 −5.20740
\(641\) −6.82915 −0.269735 −0.134868 0.990864i \(-0.543061\pi\)
−0.134868 + 0.990864i \(0.543061\pi\)
\(642\) 90.2486 3.56183
\(643\) −13.1536 −0.518727 −0.259363 0.965780i \(-0.583513\pi\)
−0.259363 + 0.965780i \(0.583513\pi\)
\(644\) 4.77545 0.188179
\(645\) 11.8926 0.468271
\(646\) 1.72115 0.0677178
\(647\) 12.8153 0.503820 0.251910 0.967751i \(-0.418941\pi\)
0.251910 + 0.967751i \(0.418941\pi\)
\(648\) 110.003 4.32132
\(649\) 45.7862 1.79727
\(650\) −0.648836 −0.0254494
\(651\) −13.5711 −0.531894
\(652\) −32.7646 −1.28316
\(653\) −5.82415 −0.227917 −0.113958 0.993486i \(-0.536353\pi\)
−0.113958 + 0.993486i \(0.536353\pi\)
\(654\) 82.8017 3.23780
\(655\) 10.6588 0.416472
\(656\) 49.3278 1.92593
\(657\) −1.08412 −0.0422954
\(658\) 23.3953 0.912044
\(659\) −28.4595 −1.10863 −0.554313 0.832308i \(-0.687019\pi\)
−0.554313 + 0.832308i \(0.687019\pi\)
\(660\) −167.600 −6.52381
\(661\) 26.3632 1.02541 0.512705 0.858565i \(-0.328643\pi\)
0.512705 + 0.858565i \(0.328643\pi\)
\(662\) 53.5944 2.08301
\(663\) −3.84803 −0.149445
\(664\) −41.3118 −1.60321
\(665\) −0.608021 −0.0235780
\(666\) −4.33077 −0.167814
\(667\) 3.34917 0.129681
\(668\) −5.93431 −0.229605
\(669\) 58.0369 2.24384
\(670\) −22.0633 −0.852378
\(671\) −45.3004 −1.74880
\(672\) −47.2893 −1.82423
\(673\) 32.4688 1.25158 0.625791 0.779991i \(-0.284776\pi\)
0.625791 + 0.779991i \(0.284776\pi\)
\(674\) −22.1774 −0.854240
\(675\) 0.386759 0.0148864
\(676\) 5.71995 0.219998
\(677\) 2.01286 0.0773605 0.0386802 0.999252i \(-0.487685\pi\)
0.0386802 + 0.999252i \(0.487685\pi\)
\(678\) −52.2272 −2.00577
\(679\) 3.46388 0.132931
\(680\) −37.7920 −1.44926
\(681\) −18.7075 −0.716872
\(682\) −127.314 −4.87509
\(683\) −0.612667 −0.0234430 −0.0117215 0.999931i \(-0.503731\pi\)
−0.0117215 + 0.999931i \(0.503731\pi\)
\(684\) −4.82198 −0.184373
\(685\) −33.0727 −1.26364
\(686\) 28.1026 1.07296
\(687\) −17.3426 −0.661663
\(688\) 40.9626 1.56168
\(689\) 10.0200 0.381730
\(690\) −15.4542 −0.588332
\(691\) 20.9842 0.798277 0.399138 0.916891i \(-0.369309\pi\)
0.399138 + 0.916891i \(0.369309\pi\)
\(692\) −106.365 −4.04339
\(693\) −10.0240 −0.380780
\(694\) −6.83735 −0.259542
\(695\) 16.3076 0.618582
\(696\) −71.7311 −2.71896
\(697\) 4.78141 0.181109
\(698\) 29.9443 1.13341
\(699\) 53.3611 2.01830
\(700\) −1.00574 −0.0380133
\(701\) −30.7394 −1.16101 −0.580505 0.814257i \(-0.697145\pi\)
−0.580505 + 0.814257i \(0.697145\pi\)
\(702\) −4.60172 −0.173681
\(703\) −0.252951 −0.00954022
\(704\) −241.785 −9.11262
\(705\) −56.0969 −2.11273
\(706\) 56.7849 2.13713
\(707\) −8.30888 −0.312488
\(708\) −103.018 −3.87164
\(709\) −41.2906 −1.55070 −0.775350 0.631531i \(-0.782427\pi\)
−0.775350 + 0.631531i \(0.782427\pi\)
\(710\) −51.9739 −1.95054
\(711\) 1.05844 0.0396945
\(712\) 31.6575 1.18642
\(713\) −8.69814 −0.325748
\(714\) −8.05027 −0.301274
\(715\) 12.7526 0.476919
\(716\) −68.6859 −2.56691
\(717\) 43.8521 1.63769
\(718\) −70.2218 −2.62066
\(719\) −17.3516 −0.647105 −0.323553 0.946210i \(-0.604877\pi\)
−0.323553 + 0.946210i \(0.604877\pi\)
\(720\) 85.9743 3.20407
\(721\) −4.89359 −0.182247
\(722\) 52.4110 1.95054
\(723\) −54.7475 −2.03608
\(724\) −101.769 −3.78220
\(725\) −0.705355 −0.0261962
\(726\) −147.592 −5.47765
\(727\) 3.67125 0.136159 0.0680796 0.997680i \(-0.478313\pi\)
0.0680796 + 0.997680i \(0.478313\pi\)
\(728\) 7.78232 0.288432
\(729\) −12.8409 −0.475589
\(730\) 2.88539 0.106793
\(731\) 3.97056 0.146856
\(732\) 101.924 3.76724
\(733\) 26.5535 0.980775 0.490387 0.871505i \(-0.336855\pi\)
0.490387 + 0.871505i \(0.336855\pi\)
\(734\) 14.7230 0.543435
\(735\) −32.2701 −1.19030
\(736\) −30.3091 −1.11721
\(737\) −21.2453 −0.782581
\(738\) −18.0794 −0.665513
\(739\) 17.8837 0.657861 0.328930 0.944354i \(-0.393312\pi\)
0.328930 + 0.944354i \(0.393312\pi\)
\(740\) 8.54027 0.313947
\(741\) 0.849843 0.0312198
\(742\) 20.9622 0.769548
\(743\) 17.5483 0.643784 0.321892 0.946776i \(-0.395681\pi\)
0.321892 + 0.946776i \(0.395681\pi\)
\(744\) 186.293 6.82983
\(745\) −28.7997 −1.05514
\(746\) −105.702 −3.87003
\(747\) 9.10977 0.333309
\(748\) −55.9561 −2.04596
\(749\) −10.6442 −0.388932
\(750\) 72.9429 2.66350
\(751\) 28.6922 1.04699 0.523497 0.852028i \(-0.324627\pi\)
0.523497 + 0.852028i \(0.324627\pi\)
\(752\) −193.219 −7.04596
\(753\) 17.8376 0.650038
\(754\) 8.39242 0.305634
\(755\) 43.1842 1.57163
\(756\) −7.13296 −0.259423
\(757\) 37.4151 1.35988 0.679938 0.733269i \(-0.262007\pi\)
0.679938 + 0.733269i \(0.262007\pi\)
\(758\) −32.4058 −1.17703
\(759\) −14.8813 −0.540156
\(760\) 8.34640 0.302756
\(761\) −1.84781 −0.0669829 −0.0334915 0.999439i \(-0.510663\pi\)
−0.0334915 + 0.999439i \(0.510663\pi\)
\(762\) −114.371 −4.14323
\(763\) −9.76591 −0.353550
\(764\) −140.199 −5.07222
\(765\) 8.33359 0.301302
\(766\) −69.1894 −2.49991
\(767\) 7.83855 0.283034
\(768\) 195.000 7.03645
\(769\) 2.01045 0.0724988 0.0362494 0.999343i \(-0.488459\pi\)
0.0362494 + 0.999343i \(0.488459\pi\)
\(770\) 26.6790 0.961444
\(771\) −64.0150 −2.30544
\(772\) 32.3487 1.16426
\(773\) −7.34161 −0.264059 −0.132030 0.991246i \(-0.542149\pi\)
−0.132030 + 0.991246i \(0.542149\pi\)
\(774\) −15.0134 −0.539647
\(775\) 1.83188 0.0658029
\(776\) −47.5492 −1.70692
\(777\) 1.18312 0.0424441
\(778\) −80.6118 −2.89007
\(779\) −1.05598 −0.0378344
\(780\) −28.6929 −1.02737
\(781\) −50.0470 −1.79082
\(782\) −5.15966 −0.184509
\(783\) −5.00257 −0.178777
\(784\) −111.150 −3.96965
\(785\) −10.5317 −0.375894
\(786\) −31.1672 −1.11170
\(787\) 44.3513 1.58095 0.790477 0.612491i \(-0.209833\pi\)
0.790477 + 0.612491i \(0.209833\pi\)
\(788\) 5.95782 0.212239
\(789\) −30.7143 −1.09346
\(790\) −2.81705 −0.100226
\(791\) 6.15986 0.219019
\(792\) 137.601 4.88944
\(793\) −7.75538 −0.275402
\(794\) 76.2132 2.70471
\(795\) −50.2630 −1.78264
\(796\) 64.6291 2.29072
\(797\) 42.5152 1.50596 0.752982 0.658041i \(-0.228615\pi\)
0.752982 + 0.658041i \(0.228615\pi\)
\(798\) 1.77791 0.0629374
\(799\) −18.7289 −0.662582
\(800\) 6.38328 0.225683
\(801\) −6.98087 −0.246657
\(802\) −70.8764 −2.50273
\(803\) 2.77842 0.0980482
\(804\) 47.8012 1.68582
\(805\) 1.82272 0.0642426
\(806\) −21.7960 −0.767730
\(807\) 53.9323 1.89851
\(808\) 114.057 4.01252
\(809\) −3.11472 −0.109508 −0.0547539 0.998500i \(-0.517437\pi\)
−0.0547539 + 0.998500i \(0.517437\pi\)
\(810\) 64.5603 2.26842
\(811\) −15.3377 −0.538580 −0.269290 0.963059i \(-0.586789\pi\)
−0.269290 + 0.963059i \(0.586789\pi\)
\(812\) 13.0088 0.456519
\(813\) −12.3649 −0.433655
\(814\) 11.0991 0.389022
\(815\) −12.5058 −0.438059
\(816\) 66.4861 2.32748
\(817\) −0.876902 −0.0306789
\(818\) 53.7123 1.87801
\(819\) −1.71610 −0.0599653
\(820\) 35.6526 1.24504
\(821\) −27.0450 −0.943875 −0.471938 0.881632i \(-0.656445\pi\)
−0.471938 + 0.881632i \(0.656445\pi\)
\(822\) 96.7078 3.37307
\(823\) −7.79780 −0.271814 −0.135907 0.990722i \(-0.543395\pi\)
−0.135907 + 0.990722i \(0.543395\pi\)
\(824\) 67.1751 2.34015
\(825\) 3.13408 0.109115
\(826\) 16.3986 0.570581
\(827\) −9.93355 −0.345424 −0.172712 0.984972i \(-0.555253\pi\)
−0.172712 + 0.984972i \(0.555253\pi\)
\(828\) 14.4553 0.502357
\(829\) 55.9754 1.94410 0.972052 0.234764i \(-0.0754317\pi\)
0.972052 + 0.234764i \(0.0754317\pi\)
\(830\) −24.2458 −0.841583
\(831\) −29.5439 −1.02487
\(832\) −41.3933 −1.43506
\(833\) −10.7739 −0.373295
\(834\) −47.6849 −1.65119
\(835\) −2.26504 −0.0783850
\(836\) 12.3580 0.427409
\(837\) 12.9922 0.449075
\(838\) −13.8843 −0.479624
\(839\) 36.8493 1.27218 0.636090 0.771615i \(-0.280551\pi\)
0.636090 + 0.771615i \(0.280551\pi\)
\(840\) −39.0383 −1.34695
\(841\) −19.8765 −0.685398
\(842\) 63.6900 2.19490
\(843\) −59.1846 −2.03842
\(844\) 99.6112 3.42876
\(845\) 2.18323 0.0751053
\(846\) 70.8178 2.43476
\(847\) 17.4075 0.598129
\(848\) −173.124 −5.94512
\(849\) −56.1547 −1.92723
\(850\) 1.08665 0.0372719
\(851\) 0.758295 0.0259940
\(852\) 112.604 3.85775
\(853\) −20.5407 −0.703300 −0.351650 0.936132i \(-0.614379\pi\)
−0.351650 + 0.936132i \(0.614379\pi\)
\(854\) −16.2246 −0.555195
\(855\) −1.84048 −0.0629432
\(856\) 146.115 4.99411
\(857\) 21.4551 0.732892 0.366446 0.930439i \(-0.380574\pi\)
0.366446 + 0.930439i \(0.380574\pi\)
\(858\) −37.2897 −1.27305
\(859\) −38.8471 −1.32545 −0.662723 0.748864i \(-0.730599\pi\)
−0.662723 + 0.748864i \(0.730599\pi\)
\(860\) 29.6065 1.00957
\(861\) 4.93909 0.168324
\(862\) 42.7574 1.45632
\(863\) 0.562745 0.0191560 0.00957802 0.999954i \(-0.496951\pi\)
0.00957802 + 0.999954i \(0.496951\pi\)
\(864\) 45.2719 1.54018
\(865\) −40.5980 −1.38037
\(866\) 9.72401 0.330435
\(867\) −32.6154 −1.10768
\(868\) −33.7851 −1.14674
\(869\) −2.71261 −0.0920189
\(870\) −42.0987 −1.42728
\(871\) −3.63717 −0.123241
\(872\) 134.058 4.53978
\(873\) 10.4852 0.354870
\(874\) 1.13952 0.0385447
\(875\) −8.60314 −0.290839
\(876\) −6.25135 −0.211214
\(877\) −0.774064 −0.0261383 −0.0130691 0.999915i \(-0.504160\pi\)
−0.0130691 + 0.999915i \(0.504160\pi\)
\(878\) −46.4257 −1.56679
\(879\) −30.2347 −1.01979
\(880\) −220.338 −7.42760
\(881\) 30.8052 1.03785 0.518927 0.854819i \(-0.326332\pi\)
0.518927 + 0.854819i \(0.326332\pi\)
\(882\) 40.7383 1.37173
\(883\) 46.5200 1.56552 0.782761 0.622322i \(-0.213811\pi\)
0.782761 + 0.622322i \(0.213811\pi\)
\(884\) −9.57962 −0.322198
\(885\) −39.3204 −1.32174
\(886\) 18.7423 0.629661
\(887\) 18.3353 0.615640 0.307820 0.951445i \(-0.400401\pi\)
0.307820 + 0.951445i \(0.400401\pi\)
\(888\) −16.2408 −0.545006
\(889\) 13.4893 0.452418
\(890\) 18.5797 0.622792
\(891\) 62.1668 2.08267
\(892\) 144.482 4.83761
\(893\) 4.13631 0.138416
\(894\) 84.2130 2.81650
\(895\) −26.2165 −0.876320
\(896\) −45.4335 −1.51783
\(897\) −2.54766 −0.0850637
\(898\) −20.0030 −0.667507
\(899\) −23.6945 −0.790257
\(900\) −3.04437 −0.101479
\(901\) −16.7812 −0.559062
\(902\) 46.3347 1.54278
\(903\) 4.10150 0.136489
\(904\) −84.5573 −2.81233
\(905\) −38.8437 −1.29121
\(906\) −126.275 −4.19520
\(907\) −2.37725 −0.0789354 −0.0394677 0.999221i \(-0.512566\pi\)
−0.0394677 + 0.999221i \(0.512566\pi\)
\(908\) −46.5720 −1.54555
\(909\) −25.1510 −0.834208
\(910\) 4.56741 0.151408
\(911\) −27.5129 −0.911542 −0.455771 0.890097i \(-0.650636\pi\)
−0.455771 + 0.890097i \(0.650636\pi\)
\(912\) −14.6835 −0.486221
\(913\) −23.3469 −0.772669
\(914\) −52.2862 −1.72947
\(915\) 38.9031 1.28610
\(916\) −43.1742 −1.42652
\(917\) 3.67597 0.121391
\(918\) 7.70684 0.254364
\(919\) −59.6427 −1.96743 −0.983715 0.179733i \(-0.942477\pi\)
−0.983715 + 0.179733i \(0.942477\pi\)
\(920\) −25.0208 −0.824911
\(921\) 62.6741 2.06518
\(922\) 81.3950 2.68060
\(923\) −8.56799 −0.282019
\(924\) −57.8015 −1.90153
\(925\) −0.159701 −0.00525094
\(926\) 2.77848 0.0913065
\(927\) −14.8129 −0.486520
\(928\) −82.5650 −2.71033
\(929\) −14.4760 −0.474943 −0.237472 0.971394i \(-0.576319\pi\)
−0.237472 + 0.971394i \(0.576319\pi\)
\(930\) 109.335 3.58522
\(931\) 2.37944 0.0779829
\(932\) 132.842 4.35137
\(933\) 3.05451 0.100000
\(934\) −78.6240 −2.57266
\(935\) −21.3577 −0.698471
\(936\) 23.5571 0.769989
\(937\) −11.3662 −0.371317 −0.185659 0.982614i \(-0.559442\pi\)
−0.185659 + 0.982614i \(0.559442\pi\)
\(938\) −7.60914 −0.248447
\(939\) −8.11071 −0.264683
\(940\) −139.652 −4.55496
\(941\) −16.0302 −0.522568 −0.261284 0.965262i \(-0.584146\pi\)
−0.261284 + 0.965262i \(0.584146\pi\)
\(942\) 30.7958 1.00338
\(943\) 3.16561 0.103086
\(944\) −135.434 −4.40800
\(945\) −2.72255 −0.0885646
\(946\) 38.4771 1.25100
\(947\) −36.0414 −1.17119 −0.585594 0.810604i \(-0.699139\pi\)
−0.585594 + 0.810604i \(0.699139\pi\)
\(948\) 6.10328 0.198225
\(949\) 0.475662 0.0154406
\(950\) −0.239989 −0.00778626
\(951\) 44.1781 1.43257
\(952\) −13.0336 −0.422422
\(953\) −24.7339 −0.801211 −0.400606 0.916251i \(-0.631200\pi\)
−0.400606 + 0.916251i \(0.631200\pi\)
\(954\) 63.4529 2.05436
\(955\) −53.5120 −1.73161
\(956\) 109.169 3.53078
\(957\) −40.5380 −1.31041
\(958\) −37.3245 −1.20590
\(959\) −11.4061 −0.368321
\(960\) 207.640 6.70157
\(961\) 30.5371 0.985068
\(962\) 1.90015 0.0612633
\(963\) −32.2202 −1.03828
\(964\) −136.293 −4.38970
\(965\) 12.3471 0.397466
\(966\) −5.32982 −0.171484
\(967\) 32.6388 1.04959 0.524797 0.851227i \(-0.324141\pi\)
0.524797 + 0.851227i \(0.324141\pi\)
\(968\) −238.955 −7.68031
\(969\) −1.42329 −0.0457228
\(970\) −27.9064 −0.896022
\(971\) −5.66265 −0.181723 −0.0908616 0.995864i \(-0.528962\pi\)
−0.0908616 + 0.995864i \(0.528962\pi\)
\(972\) −111.453 −3.57486
\(973\) 5.62412 0.180301
\(974\) −57.2250 −1.83361
\(975\) 0.536551 0.0171834
\(976\) 133.997 4.28914
\(977\) 2.31925 0.0741993 0.0370996 0.999312i \(-0.488188\pi\)
0.0370996 + 0.999312i \(0.488188\pi\)
\(978\) 36.5682 1.16932
\(979\) 17.8909 0.571794
\(980\) −80.3359 −2.56624
\(981\) −29.5615 −0.943826
\(982\) −70.5949 −2.25277
\(983\) 34.6904 1.10645 0.553226 0.833031i \(-0.313397\pi\)
0.553226 + 0.833031i \(0.313397\pi\)
\(984\) −67.7996 −2.16137
\(985\) 2.27402 0.0724563
\(986\) −14.0554 −0.447615
\(987\) −19.3466 −0.615809
\(988\) 2.11567 0.0673084
\(989\) 2.62877 0.0835901
\(990\) 80.7575 2.56664
\(991\) −13.3713 −0.424753 −0.212376 0.977188i \(-0.568120\pi\)
−0.212376 + 0.977188i \(0.568120\pi\)
\(992\) 214.429 6.80814
\(993\) −44.3196 −1.40644
\(994\) −17.9246 −0.568535
\(995\) 24.6680 0.782030
\(996\) 52.5297 1.66447
\(997\) 37.2498 1.17971 0.589857 0.807508i \(-0.299184\pi\)
0.589857 + 0.807508i \(0.299184\pi\)
\(998\) −46.7989 −1.48139
\(999\) −1.13264 −0.0358353
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 \(a_p\))