Properties

Label 4019.2.a.b.1.3
Level 4019
Weight 2
Character 4019.1
Self dual Yes
Analytic conductor 32.092
Analytic rank 0
Dimension 186
CM No

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Newspace parameters

Level: \( N \) = \( 4019 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0918765724\)
Analytic rank: \(0\)
Dimension: \(186\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.78390 q^{2}\) \(+2.40470 q^{3}\) \(+5.75012 q^{4}\) \(-2.23828 q^{5}\) \(-6.69445 q^{6}\) \(-0.0567746 q^{7}\) \(-10.4400 q^{8}\) \(+2.78257 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.78390 q^{2}\) \(+2.40470 q^{3}\) \(+5.75012 q^{4}\) \(-2.23828 q^{5}\) \(-6.69445 q^{6}\) \(-0.0567746 q^{7}\) \(-10.4400 q^{8}\) \(+2.78257 q^{9}\) \(+6.23116 q^{10}\) \(+4.46877 q^{11}\) \(+13.8273 q^{12}\) \(-1.01079 q^{13}\) \(+0.158055 q^{14}\) \(-5.38239 q^{15}\) \(+17.5637 q^{16}\) \(-2.51174 q^{17}\) \(-7.74642 q^{18}\) \(+5.87700 q^{19}\) \(-12.8704 q^{20}\) \(-0.136526 q^{21}\) \(-12.4406 q^{22}\) \(-3.02456 q^{23}\) \(-25.1050 q^{24}\) \(+0.00990820 q^{25}\) \(+2.81394 q^{26}\) \(-0.522847 q^{27}\) \(-0.326461 q^{28}\) \(+3.67472 q^{29}\) \(+14.9841 q^{30}\) \(+1.96933 q^{31}\) \(-28.0156 q^{32}\) \(+10.7460 q^{33}\) \(+6.99244 q^{34}\) \(+0.127078 q^{35}\) \(+16.0001 q^{36}\) \(+8.75339 q^{37}\) \(-16.3610 q^{38}\) \(-2.43064 q^{39}\) \(+23.3676 q^{40}\) \(+1.89435 q^{41}\) \(+0.380075 q^{42}\) \(+5.14850 q^{43}\) \(+25.6960 q^{44}\) \(-6.22818 q^{45}\) \(+8.42007 q^{46}\) \(-3.40230 q^{47}\) \(+42.2353 q^{48}\) \(-6.99678 q^{49}\) \(-0.0275835 q^{50}\) \(-6.03997 q^{51}\) \(-5.81216 q^{52}\) \(+3.90647 q^{53}\) \(+1.45555 q^{54}\) \(-10.0024 q^{55}\) \(+0.592726 q^{56}\) \(+14.1324 q^{57}\) \(-10.2301 q^{58}\) \(+2.25947 q^{59}\) \(-30.9494 q^{60}\) \(+6.85031 q^{61}\) \(-5.48243 q^{62}\) \(-0.157979 q^{63}\) \(+42.8654 q^{64}\) \(+2.26243 q^{65}\) \(-29.9160 q^{66}\) \(-10.1207 q^{67}\) \(-14.4428 q^{68}\) \(-7.27314 q^{69}\) \(-0.353772 q^{70}\) \(+0.569963 q^{71}\) \(-29.0500 q^{72}\) \(-8.05235 q^{73}\) \(-24.3686 q^{74}\) \(+0.0238262 q^{75}\) \(+33.7935 q^{76}\) \(-0.253713 q^{77}\) \(+6.76668 q^{78}\) \(+5.86218 q^{79}\) \(-39.3125 q^{80}\) \(-9.60501 q^{81}\) \(-5.27369 q^{82}\) \(-7.74329 q^{83}\) \(-0.785040 q^{84}\) \(+5.62198 q^{85}\) \(-14.3329 q^{86}\) \(+8.83659 q^{87}\) \(-46.6539 q^{88}\) \(+5.19256 q^{89}\) \(+17.3387 q^{90}\) \(+0.0573871 q^{91}\) \(-17.3916 q^{92}\) \(+4.73565 q^{93}\) \(+9.47167 q^{94}\) \(-13.1544 q^{95}\) \(-67.3691 q^{96}\) \(+14.6535 q^{97}\) \(+19.4784 q^{98}\) \(+12.4347 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78390 −1.96852 −0.984259 0.176733i \(-0.943447\pi\)
−0.984259 + 0.176733i \(0.943447\pi\)
\(3\) 2.40470 1.38835 0.694177 0.719805i \(-0.255769\pi\)
0.694177 + 0.719805i \(0.255769\pi\)
\(4\) 5.75012 2.87506
\(5\) −2.23828 −1.00099 −0.500495 0.865739i \(-0.666849\pi\)
−0.500495 + 0.865739i \(0.666849\pi\)
\(6\) −6.69445 −2.73300
\(7\) −0.0567746 −0.0214588 −0.0107294 0.999942i \(-0.503415\pi\)
−0.0107294 + 0.999942i \(0.503415\pi\)
\(8\) −10.4400 −3.69109
\(9\) 2.78257 0.927524
\(10\) 6.23116 1.97047
\(11\) 4.46877 1.34739 0.673693 0.739012i \(-0.264707\pi\)
0.673693 + 0.739012i \(0.264707\pi\)
\(12\) 13.8273 3.99160
\(13\) −1.01079 −0.280342 −0.140171 0.990127i \(-0.544765\pi\)
−0.140171 + 0.990127i \(0.544765\pi\)
\(14\) 0.158055 0.0422420
\(15\) −5.38239 −1.38973
\(16\) 17.5637 4.39092
\(17\) −2.51174 −0.609186 −0.304593 0.952483i \(-0.598520\pi\)
−0.304593 + 0.952483i \(0.598520\pi\)
\(18\) −7.74642 −1.82585
\(19\) 5.87700 1.34828 0.674139 0.738605i \(-0.264515\pi\)
0.674139 + 0.738605i \(0.264515\pi\)
\(20\) −12.8704 −2.87791
\(21\) −0.136526 −0.0297924
\(22\) −12.4406 −2.65235
\(23\) −3.02456 −0.630663 −0.315332 0.948982i \(-0.602116\pi\)
−0.315332 + 0.948982i \(0.602116\pi\)
\(24\) −25.1050 −5.12454
\(25\) 0.00990820 0.00198164
\(26\) 2.81394 0.551859
\(27\) −0.522847 −0.100622
\(28\) −0.326461 −0.0616953
\(29\) 3.67472 0.682378 0.341189 0.939995i \(-0.389170\pi\)
0.341189 + 0.939995i \(0.389170\pi\)
\(30\) 14.9841 2.73570
\(31\) 1.96933 0.353702 0.176851 0.984238i \(-0.443409\pi\)
0.176851 + 0.984238i \(0.443409\pi\)
\(32\) −28.0156 −4.95251
\(33\) 10.7460 1.87065
\(34\) 6.99244 1.19919
\(35\) 0.127078 0.0214800
\(36\) 16.0001 2.66669
\(37\) 8.75339 1.43905 0.719524 0.694468i \(-0.244360\pi\)
0.719524 + 0.694468i \(0.244360\pi\)
\(38\) −16.3610 −2.65411
\(39\) −2.43064 −0.389214
\(40\) 23.3676 3.69475
\(41\) 1.89435 0.295848 0.147924 0.988999i \(-0.452741\pi\)
0.147924 + 0.988999i \(0.452741\pi\)
\(42\) 0.380075 0.0586468
\(43\) 5.14850 0.785138 0.392569 0.919722i \(-0.371586\pi\)
0.392569 + 0.919722i \(0.371586\pi\)
\(44\) 25.6960 3.87382
\(45\) −6.22818 −0.928443
\(46\) 8.42007 1.24147
\(47\) −3.40230 −0.496276 −0.248138 0.968725i \(-0.579819\pi\)
−0.248138 + 0.968725i \(0.579819\pi\)
\(48\) 42.2353 6.09614
\(49\) −6.99678 −0.999540
\(50\) −0.0275835 −0.00390089
\(51\) −6.03997 −0.845765
\(52\) −5.81216 −0.806002
\(53\) 3.90647 0.536594 0.268297 0.963336i \(-0.413539\pi\)
0.268297 + 0.963336i \(0.413539\pi\)
\(54\) 1.45555 0.198076
\(55\) −10.0024 −1.34872
\(56\) 0.592726 0.0792063
\(57\) 14.1324 1.87189
\(58\) −10.2301 −1.34327
\(59\) 2.25947 0.294158 0.147079 0.989125i \(-0.453013\pi\)
0.147079 + 0.989125i \(0.453013\pi\)
\(60\) −30.9494 −3.99555
\(61\) 6.85031 0.877092 0.438546 0.898709i \(-0.355494\pi\)
0.438546 + 0.898709i \(0.355494\pi\)
\(62\) −5.48243 −0.696269
\(63\) −0.157979 −0.0199035
\(64\) 42.8654 5.35818
\(65\) 2.26243 0.280620
\(66\) −29.9160 −3.68240
\(67\) −10.1207 −1.23643 −0.618217 0.786007i \(-0.712145\pi\)
−0.618217 + 0.786007i \(0.712145\pi\)
\(68\) −14.4428 −1.75145
\(69\) −7.27314 −0.875583
\(70\) −0.353772 −0.0422838
\(71\) 0.569963 0.0676422 0.0338211 0.999428i \(-0.489232\pi\)
0.0338211 + 0.999428i \(0.489232\pi\)
\(72\) −29.0500 −3.42358
\(73\) −8.05235 −0.942456 −0.471228 0.882011i \(-0.656189\pi\)
−0.471228 + 0.882011i \(0.656189\pi\)
\(74\) −24.3686 −2.83279
\(75\) 0.0238262 0.00275121
\(76\) 33.7935 3.87638
\(77\) −0.253713 −0.0289132
\(78\) 6.76668 0.766175
\(79\) 5.86218 0.659547 0.329774 0.944060i \(-0.393028\pi\)
0.329774 + 0.944060i \(0.393028\pi\)
\(80\) −39.3125 −4.39527
\(81\) −9.60501 −1.06722
\(82\) −5.27369 −0.582382
\(83\) −7.74329 −0.849937 −0.424968 0.905208i \(-0.639715\pi\)
−0.424968 + 0.905208i \(0.639715\pi\)
\(84\) −0.785040 −0.0856549
\(85\) 5.62198 0.609789
\(86\) −14.3329 −1.54556
\(87\) 8.83659 0.947382
\(88\) −46.6539 −4.97332
\(89\) 5.19256 0.550411 0.275205 0.961385i \(-0.411254\pi\)
0.275205 + 0.961385i \(0.411254\pi\)
\(90\) 17.3387 1.82766
\(91\) 0.0573871 0.00601581
\(92\) −17.3916 −1.81320
\(93\) 4.73565 0.491064
\(94\) 9.47167 0.976928
\(95\) −13.1544 −1.34961
\(96\) −67.3691 −6.87583
\(97\) 14.6535 1.48784 0.743918 0.668270i \(-0.232965\pi\)
0.743918 + 0.668270i \(0.232965\pi\)
\(98\) 19.4784 1.96761
\(99\) 12.4347 1.24973
\(100\) 0.0569733 0.00569733
\(101\) 6.20740 0.617659 0.308830 0.951117i \(-0.400063\pi\)
0.308830 + 0.951117i \(0.400063\pi\)
\(102\) 16.8147 1.66490
\(103\) −1.03737 −0.102215 −0.0511073 0.998693i \(-0.516275\pi\)
−0.0511073 + 0.998693i \(0.516275\pi\)
\(104\) 10.5526 1.03477
\(105\) 0.305583 0.0298219
\(106\) −10.8752 −1.05630
\(107\) −5.23587 −0.506170 −0.253085 0.967444i \(-0.581445\pi\)
−0.253085 + 0.967444i \(0.581445\pi\)
\(108\) −3.00643 −0.289294
\(109\) 8.82149 0.844946 0.422473 0.906376i \(-0.361162\pi\)
0.422473 + 0.906376i \(0.361162\pi\)
\(110\) 27.8457 2.65498
\(111\) 21.0493 1.99791
\(112\) −0.997170 −0.0942237
\(113\) −5.71607 −0.537723 −0.268861 0.963179i \(-0.586647\pi\)
−0.268861 + 0.963179i \(0.586647\pi\)
\(114\) −39.3433 −3.68484
\(115\) 6.76981 0.631288
\(116\) 21.1301 1.96188
\(117\) −2.81259 −0.260024
\(118\) −6.29015 −0.579055
\(119\) 0.142603 0.0130724
\(120\) 56.1921 5.12961
\(121\) 8.96992 0.815448
\(122\) −19.0706 −1.72657
\(123\) 4.55534 0.410742
\(124\) 11.3239 1.01692
\(125\) 11.1692 0.999007
\(126\) 0.439800 0.0391805
\(127\) 17.5406 1.55648 0.778240 0.627967i \(-0.216113\pi\)
0.778240 + 0.627967i \(0.216113\pi\)
\(128\) −63.3020 −5.59516
\(129\) 12.3806 1.09005
\(130\) −6.29839 −0.552406
\(131\) 2.07094 0.180939 0.0904696 0.995899i \(-0.471163\pi\)
0.0904696 + 0.995899i \(0.471163\pi\)
\(132\) 61.7911 5.37822
\(133\) −0.333665 −0.0289324
\(134\) 28.1749 2.43394
\(135\) 1.17028 0.100722
\(136\) 26.2225 2.24856
\(137\) −8.40350 −0.717959 −0.358980 0.933345i \(-0.616875\pi\)
−0.358980 + 0.933345i \(0.616875\pi\)
\(138\) 20.2477 1.72360
\(139\) −17.2908 −1.46659 −0.733294 0.679912i \(-0.762018\pi\)
−0.733294 + 0.679912i \(0.762018\pi\)
\(140\) 0.730712 0.0617564
\(141\) −8.18149 −0.689006
\(142\) −1.58672 −0.133155
\(143\) −4.51699 −0.377729
\(144\) 48.8722 4.07268
\(145\) −8.22506 −0.683054
\(146\) 22.4170 1.85524
\(147\) −16.8251 −1.38771
\(148\) 50.3331 4.13735
\(149\) 7.76103 0.635809 0.317904 0.948123i \(-0.397021\pi\)
0.317904 + 0.948123i \(0.397021\pi\)
\(150\) −0.0663299 −0.00541581
\(151\) 18.0287 1.46715 0.733577 0.679606i \(-0.237849\pi\)
0.733577 + 0.679606i \(0.237849\pi\)
\(152\) −61.3558 −4.97662
\(153\) −6.98909 −0.565035
\(154\) 0.706312 0.0569162
\(155\) −4.40792 −0.354053
\(156\) −13.9765 −1.11902
\(157\) 22.0998 1.76376 0.881878 0.471477i \(-0.156279\pi\)
0.881878 + 0.471477i \(0.156279\pi\)
\(158\) −16.3198 −1.29833
\(159\) 9.39387 0.744983
\(160\) 62.7068 4.95741
\(161\) 0.171718 0.0135333
\(162\) 26.7394 2.10085
\(163\) 10.7572 0.842571 0.421285 0.906928i \(-0.361579\pi\)
0.421285 + 0.906928i \(0.361579\pi\)
\(164\) 10.8928 0.850581
\(165\) −24.0527 −1.87250
\(166\) 21.5566 1.67312
\(167\) 17.4264 1.34850 0.674249 0.738504i \(-0.264468\pi\)
0.674249 + 0.738504i \(0.264468\pi\)
\(168\) 1.42533 0.109966
\(169\) −11.9783 −0.921408
\(170\) −15.6511 −1.20038
\(171\) 16.3532 1.25056
\(172\) 29.6045 2.25732
\(173\) −17.0785 −1.29846 −0.649228 0.760594i \(-0.724908\pi\)
−0.649228 + 0.760594i \(0.724908\pi\)
\(174\) −24.6002 −1.86494
\(175\) −0.000562534 0 −4.25236e−5 0
\(176\) 78.4880 5.91626
\(177\) 5.43334 0.408395
\(178\) −14.4556 −1.08349
\(179\) 18.0292 1.34757 0.673785 0.738928i \(-0.264668\pi\)
0.673785 + 0.738928i \(0.264668\pi\)
\(180\) −35.8128 −2.66933
\(181\) −12.3621 −0.918868 −0.459434 0.888212i \(-0.651948\pi\)
−0.459434 + 0.888212i \(0.651948\pi\)
\(182\) −0.159760 −0.0118422
\(183\) 16.4729 1.21771
\(184\) 31.5763 2.32784
\(185\) −19.5926 −1.44047
\(186\) −13.1836 −0.966668
\(187\) −11.2244 −0.820808
\(188\) −19.5636 −1.42682
\(189\) 0.0296844 0.00215922
\(190\) 36.6206 2.65674
\(191\) −11.1927 −0.809872 −0.404936 0.914345i \(-0.632706\pi\)
−0.404936 + 0.914345i \(0.632706\pi\)
\(192\) 103.078 7.43904
\(193\) 0.729995 0.0525462 0.0262731 0.999655i \(-0.491636\pi\)
0.0262731 + 0.999655i \(0.491636\pi\)
\(194\) −40.7939 −2.92883
\(195\) 5.44046 0.389600
\(196\) −40.2323 −2.87374
\(197\) 10.1791 0.725233 0.362616 0.931938i \(-0.381884\pi\)
0.362616 + 0.931938i \(0.381884\pi\)
\(198\) −34.6170 −2.46012
\(199\) 26.1440 1.85330 0.926649 0.375927i \(-0.122676\pi\)
0.926649 + 0.375927i \(0.122676\pi\)
\(200\) −0.103441 −0.00731441
\(201\) −24.3371 −1.71661
\(202\) −17.2808 −1.21587
\(203\) −0.208631 −0.0146430
\(204\) −34.7306 −2.43163
\(205\) −4.24009 −0.296141
\(206\) 2.88793 0.201211
\(207\) −8.41605 −0.584956
\(208\) −17.7532 −1.23096
\(209\) 26.2630 1.81665
\(210\) −0.850714 −0.0587049
\(211\) −8.53671 −0.587691 −0.293846 0.955853i \(-0.594935\pi\)
−0.293846 + 0.955853i \(0.594935\pi\)
\(212\) 22.4627 1.54274
\(213\) 1.37059 0.0939112
\(214\) 14.5762 0.996405
\(215\) −11.5238 −0.785916
\(216\) 5.45851 0.371405
\(217\) −0.111808 −0.00759002
\(218\) −24.5582 −1.66329
\(219\) −19.3635 −1.30846
\(220\) −57.5149 −3.87765
\(221\) 2.53884 0.170781
\(222\) −58.5991 −3.93291
\(223\) −1.05085 −0.0703702 −0.0351851 0.999381i \(-0.511202\pi\)
−0.0351851 + 0.999381i \(0.511202\pi\)
\(224\) 1.59057 0.106275
\(225\) 0.0275703 0.00183802
\(226\) 15.9130 1.05852
\(227\) 6.64009 0.440718 0.220359 0.975419i \(-0.429277\pi\)
0.220359 + 0.975419i \(0.429277\pi\)
\(228\) 81.2632 5.38178
\(229\) −13.1696 −0.870274 −0.435137 0.900364i \(-0.643300\pi\)
−0.435137 + 0.900364i \(0.643300\pi\)
\(230\) −18.8465 −1.24270
\(231\) −0.610102 −0.0401418
\(232\) −38.3640 −2.51872
\(233\) 19.2115 1.25858 0.629292 0.777169i \(-0.283345\pi\)
0.629292 + 0.777169i \(0.283345\pi\)
\(234\) 7.82999 0.511863
\(235\) 7.61530 0.496767
\(236\) 12.9922 0.845722
\(237\) 14.0968 0.915685
\(238\) −0.396993 −0.0257332
\(239\) 14.2038 0.918768 0.459384 0.888238i \(-0.348070\pi\)
0.459384 + 0.888238i \(0.348070\pi\)
\(240\) −94.5346 −6.10218
\(241\) 14.7231 0.948401 0.474200 0.880417i \(-0.342737\pi\)
0.474200 + 0.880417i \(0.342737\pi\)
\(242\) −24.9714 −1.60522
\(243\) −21.5286 −1.38106
\(244\) 39.3901 2.52169
\(245\) 15.6608 1.00053
\(246\) −12.6816 −0.808552
\(247\) −5.94041 −0.377979
\(248\) −20.5598 −1.30555
\(249\) −18.6203 −1.18001
\(250\) −31.0941 −1.96656
\(251\) 18.4452 1.16425 0.582124 0.813100i \(-0.302222\pi\)
0.582124 + 0.813100i \(0.302222\pi\)
\(252\) −0.908401 −0.0572239
\(253\) −13.5160 −0.849747
\(254\) −48.8315 −3.06396
\(255\) 13.5192 0.846603
\(256\) 90.4960 5.65600
\(257\) 1.10325 0.0688190 0.0344095 0.999408i \(-0.489045\pi\)
0.0344095 + 0.999408i \(0.489045\pi\)
\(258\) −34.4664 −2.14578
\(259\) −0.496970 −0.0308802
\(260\) 13.0093 0.806800
\(261\) 10.2252 0.632923
\(262\) −5.76531 −0.356182
\(263\) 3.75153 0.231329 0.115665 0.993288i \(-0.463100\pi\)
0.115665 + 0.993288i \(0.463100\pi\)
\(264\) −112.189 −6.90473
\(265\) −8.74378 −0.537126
\(266\) 0.928890 0.0569539
\(267\) 12.4866 0.764164
\(268\) −58.1950 −3.55482
\(269\) −17.3095 −1.05538 −0.527690 0.849437i \(-0.676942\pi\)
−0.527690 + 0.849437i \(0.676942\pi\)
\(270\) −3.25794 −0.198272
\(271\) 10.5614 0.641560 0.320780 0.947154i \(-0.396055\pi\)
0.320780 + 0.947154i \(0.396055\pi\)
\(272\) −44.1153 −2.67489
\(273\) 0.137999 0.00835206
\(274\) 23.3945 1.41332
\(275\) 0.0442775 0.00267003
\(276\) −41.8215 −2.51736
\(277\) −27.4220 −1.64763 −0.823815 0.566859i \(-0.808158\pi\)
−0.823815 + 0.566859i \(0.808158\pi\)
\(278\) 48.1360 2.88700
\(279\) 5.47981 0.328068
\(280\) −1.32669 −0.0792848
\(281\) 4.46092 0.266116 0.133058 0.991108i \(-0.457520\pi\)
0.133058 + 0.991108i \(0.457520\pi\)
\(282\) 22.7765 1.35632
\(283\) −8.18035 −0.486272 −0.243136 0.969992i \(-0.578176\pi\)
−0.243136 + 0.969992i \(0.578176\pi\)
\(284\) 3.27736 0.194475
\(285\) −31.6324 −1.87374
\(286\) 12.5749 0.743567
\(287\) −0.107551 −0.00634854
\(288\) −77.9555 −4.59357
\(289\) −10.6912 −0.628893
\(290\) 22.8978 1.34460
\(291\) 35.2372 2.06564
\(292\) −46.3020 −2.70962
\(293\) 20.1651 1.17806 0.589030 0.808111i \(-0.299510\pi\)
0.589030 + 0.808111i \(0.299510\pi\)
\(294\) 46.8396 2.73174
\(295\) −5.05733 −0.294449
\(296\) −91.3852 −5.31166
\(297\) −2.33648 −0.135576
\(298\) −21.6060 −1.25160
\(299\) 3.05719 0.176802
\(300\) 0.137004 0.00790991
\(301\) −0.292304 −0.0168481
\(302\) −50.1902 −2.88812
\(303\) 14.9269 0.857529
\(304\) 103.222 5.92017
\(305\) −15.3329 −0.877961
\(306\) 19.4570 1.11228
\(307\) 19.2709 1.09985 0.549924 0.835215i \(-0.314657\pi\)
0.549924 + 0.835215i \(0.314657\pi\)
\(308\) −1.45888 −0.0831274
\(309\) −2.49455 −0.141910
\(310\) 12.2712 0.696959
\(311\) −14.8811 −0.843829 −0.421914 0.906636i \(-0.638642\pi\)
−0.421914 + 0.906636i \(0.638642\pi\)
\(312\) 25.3759 1.43663
\(313\) 7.69713 0.435068 0.217534 0.976053i \(-0.430199\pi\)
0.217534 + 0.976053i \(0.430199\pi\)
\(314\) −61.5237 −3.47199
\(315\) 0.353603 0.0199232
\(316\) 33.7083 1.89624
\(317\) 8.39183 0.471332 0.235666 0.971834i \(-0.424273\pi\)
0.235666 + 0.971834i \(0.424273\pi\)
\(318\) −26.1516 −1.46651
\(319\) 16.4215 0.919427
\(320\) −95.9449 −5.36349
\(321\) −12.5907 −0.702743
\(322\) −0.478046 −0.0266405
\(323\) −14.7615 −0.821352
\(324\) −55.2300 −3.06833
\(325\) −0.0100151 −0.000555538 0
\(326\) −29.9471 −1.65862
\(327\) 21.2130 1.17308
\(328\) −19.7770 −1.09200
\(329\) 0.193164 0.0106495
\(330\) 66.9604 3.68605
\(331\) −31.0620 −1.70732 −0.853662 0.520827i \(-0.825624\pi\)
−0.853662 + 0.520827i \(0.825624\pi\)
\(332\) −44.5249 −2.44362
\(333\) 24.3569 1.33475
\(334\) −48.5135 −2.65454
\(335\) 22.6529 1.23766
\(336\) −2.39789 −0.130816
\(337\) 6.34005 0.345364 0.172682 0.984978i \(-0.444757\pi\)
0.172682 + 0.984978i \(0.444757\pi\)
\(338\) 33.3465 1.81381
\(339\) −13.7454 −0.746549
\(340\) 32.3271 1.75318
\(341\) 8.80049 0.476573
\(342\) −45.5257 −2.46175
\(343\) 0.794661 0.0429077
\(344\) −53.7502 −2.89802
\(345\) 16.2793 0.876451
\(346\) 47.5449 2.55603
\(347\) −24.9725 −1.34060 −0.670298 0.742092i \(-0.733834\pi\)
−0.670298 + 0.742092i \(0.733834\pi\)
\(348\) 50.8115 2.72378
\(349\) −1.90366 −0.101900 −0.0509502 0.998701i \(-0.516225\pi\)
−0.0509502 + 0.998701i \(0.516225\pi\)
\(350\) 0.00156604 8.37084e−5 0
\(351\) 0.528488 0.0282086
\(352\) −125.195 −6.67294
\(353\) 4.32797 0.230354 0.115177 0.993345i \(-0.463256\pi\)
0.115177 + 0.993345i \(0.463256\pi\)
\(354\) −15.1259 −0.803933
\(355\) −1.27574 −0.0677092
\(356\) 29.8579 1.58246
\(357\) 0.342917 0.0181491
\(358\) −50.1917 −2.65271
\(359\) 16.4668 0.869084 0.434542 0.900651i \(-0.356910\pi\)
0.434542 + 0.900651i \(0.356910\pi\)
\(360\) 65.0221 3.42697
\(361\) 15.5392 0.817852
\(362\) 34.4149 1.80881
\(363\) 21.5700 1.13213
\(364\) 0.329983 0.0172958
\(365\) 18.0234 0.943389
\(366\) −45.8590 −2.39709
\(367\) −13.1276 −0.685255 −0.342627 0.939471i \(-0.611317\pi\)
−0.342627 + 0.939471i \(0.611317\pi\)
\(368\) −53.1223 −2.76919
\(369\) 5.27117 0.274406
\(370\) 54.5438 2.83560
\(371\) −0.221788 −0.0115147
\(372\) 27.2306 1.41184
\(373\) 15.6166 0.808594 0.404297 0.914628i \(-0.367516\pi\)
0.404297 + 0.914628i \(0.367516\pi\)
\(374\) 31.2476 1.61578
\(375\) 26.8586 1.38697
\(376\) 35.5199 1.83180
\(377\) −3.71437 −0.191300
\(378\) −0.0826385 −0.00425047
\(379\) 17.2449 0.885811 0.442905 0.896568i \(-0.353948\pi\)
0.442905 + 0.896568i \(0.353948\pi\)
\(380\) −75.6394 −3.88022
\(381\) 42.1799 2.16094
\(382\) 31.1593 1.59425
\(383\) 7.85704 0.401476 0.200738 0.979645i \(-0.435666\pi\)
0.200738 + 0.979645i \(0.435666\pi\)
\(384\) −152.222 −7.76806
\(385\) 0.567881 0.0289419
\(386\) −2.03224 −0.103438
\(387\) 14.3261 0.728235
\(388\) 84.2594 4.27762
\(389\) −35.5138 −1.80062 −0.900310 0.435250i \(-0.856660\pi\)
−0.900310 + 0.435250i \(0.856660\pi\)
\(390\) −15.1457 −0.766934
\(391\) 7.59689 0.384191
\(392\) 73.0462 3.68939
\(393\) 4.97999 0.251207
\(394\) −28.3377 −1.42763
\(395\) −13.1212 −0.660200
\(396\) 71.5010 3.59306
\(397\) 7.95230 0.399115 0.199557 0.979886i \(-0.436050\pi\)
0.199557 + 0.979886i \(0.436050\pi\)
\(398\) −72.7824 −3.64825
\(399\) −0.802363 −0.0401684
\(400\) 0.174024 0.00870121
\(401\) 1.36633 0.0682310 0.0341155 0.999418i \(-0.489139\pi\)
0.0341155 + 0.999418i \(0.489139\pi\)
\(402\) 67.7522 3.37917
\(403\) −1.99058 −0.0991578
\(404\) 35.6933 1.77581
\(405\) 21.4987 1.06828
\(406\) 0.580808 0.0288250
\(407\) 39.1169 1.93895
\(408\) 63.0572 3.12180
\(409\) 15.7814 0.780340 0.390170 0.920743i \(-0.372416\pi\)
0.390170 + 0.920743i \(0.372416\pi\)
\(410\) 11.8040 0.582959
\(411\) −20.2079 −0.996781
\(412\) −5.96498 −0.293874
\(413\) −0.128280 −0.00631227
\(414\) 23.4295 1.15150
\(415\) 17.3317 0.850779
\(416\) 28.3179 1.38840
\(417\) −41.5792 −2.03614
\(418\) −73.1137 −3.57611
\(419\) 17.3206 0.846166 0.423083 0.906091i \(-0.360948\pi\)
0.423083 + 0.906091i \(0.360948\pi\)
\(420\) 1.75714 0.0857397
\(421\) 23.6432 1.15230 0.576150 0.817344i \(-0.304554\pi\)
0.576150 + 0.817344i \(0.304554\pi\)
\(422\) 23.7654 1.15688
\(423\) −9.46714 −0.460308
\(424\) −40.7835 −1.98062
\(425\) −0.0248868 −0.00120719
\(426\) −3.81559 −0.184866
\(427\) −0.388923 −0.0188213
\(428\) −30.1069 −1.45527
\(429\) −10.8620 −0.524422
\(430\) 32.0811 1.54709
\(431\) 26.2928 1.26648 0.633240 0.773955i \(-0.281724\pi\)
0.633240 + 0.773955i \(0.281724\pi\)
\(432\) −9.18310 −0.441822
\(433\) 13.8904 0.667529 0.333765 0.942656i \(-0.391681\pi\)
0.333765 + 0.942656i \(0.391681\pi\)
\(434\) 0.311263 0.0149411
\(435\) −19.7788 −0.948320
\(436\) 50.7247 2.42927
\(437\) −17.7753 −0.850309
\(438\) 53.9060 2.57573
\(439\) −8.88645 −0.424127 −0.212063 0.977256i \(-0.568018\pi\)
−0.212063 + 0.977256i \(0.568018\pi\)
\(440\) 104.425 4.97825
\(441\) −19.4690 −0.927097
\(442\) −7.06788 −0.336185
\(443\) 37.5090 1.78211 0.891054 0.453897i \(-0.149967\pi\)
0.891054 + 0.453897i \(0.149967\pi\)
\(444\) 121.036 5.74410
\(445\) −11.6224 −0.550956
\(446\) 2.92547 0.138525
\(447\) 18.6629 0.882727
\(448\) −2.43367 −0.114980
\(449\) −24.6199 −1.16188 −0.580942 0.813945i \(-0.697316\pi\)
−0.580942 + 0.813945i \(0.697316\pi\)
\(450\) −0.0767530 −0.00361817
\(451\) 8.46543 0.398621
\(452\) −32.8681 −1.54599
\(453\) 43.3536 2.03693
\(454\) −18.4854 −0.867562
\(455\) −0.128449 −0.00602176
\(456\) −147.542 −6.90930
\(457\) 5.64598 0.264108 0.132054 0.991243i \(-0.457843\pi\)
0.132054 + 0.991243i \(0.457843\pi\)
\(458\) 36.6630 1.71315
\(459\) 1.31325 0.0612974
\(460\) 38.9272 1.81499
\(461\) 34.3504 1.59986 0.799929 0.600094i \(-0.204870\pi\)
0.799929 + 0.600094i \(0.204870\pi\)
\(462\) 1.69847 0.0790198
\(463\) 10.2102 0.474507 0.237253 0.971448i \(-0.423753\pi\)
0.237253 + 0.971448i \(0.423753\pi\)
\(464\) 64.5416 2.99627
\(465\) −10.5997 −0.491550
\(466\) −53.4829 −2.47755
\(467\) −29.2100 −1.35168 −0.675839 0.737049i \(-0.736219\pi\)
−0.675839 + 0.737049i \(0.736219\pi\)
\(468\) −16.1728 −0.747586
\(469\) 0.574596 0.0265324
\(470\) −21.2003 −0.977895
\(471\) 53.1434 2.44872
\(472\) −23.5888 −1.08576
\(473\) 23.0075 1.05788
\(474\) −39.2441 −1.80254
\(475\) 0.0582305 0.00267180
\(476\) 0.819984 0.0375839
\(477\) 10.8700 0.497704
\(478\) −39.5420 −1.80861
\(479\) 31.7894 1.45250 0.726248 0.687433i \(-0.241263\pi\)
0.726248 + 0.687433i \(0.241263\pi\)
\(480\) 150.791 6.88264
\(481\) −8.84783 −0.403426
\(482\) −40.9878 −1.86694
\(483\) 0.412930 0.0187890
\(484\) 51.5782 2.34446
\(485\) −32.7987 −1.48931
\(486\) 59.9336 2.71864
\(487\) 3.65311 0.165538 0.0827692 0.996569i \(-0.473624\pi\)
0.0827692 + 0.996569i \(0.473624\pi\)
\(488\) −71.5171 −3.23743
\(489\) 25.8679 1.16979
\(490\) −43.5981 −1.96956
\(491\) −38.0504 −1.71719 −0.858595 0.512655i \(-0.828662\pi\)
−0.858595 + 0.512655i \(0.828662\pi\)
\(492\) 26.1938 1.18091
\(493\) −9.22993 −0.415695
\(494\) 16.5375 0.744059
\(495\) −27.8323 −1.25097
\(496\) 34.5887 1.55308
\(497\) −0.0323594 −0.00145152
\(498\) 51.8371 2.32288
\(499\) 8.21311 0.367669 0.183835 0.982957i \(-0.441149\pi\)
0.183835 + 0.982957i \(0.441149\pi\)
\(500\) 64.2245 2.87221
\(501\) 41.9053 1.87219
\(502\) −51.3496 −2.29184
\(503\) 41.8858 1.86760 0.933799 0.357799i \(-0.116473\pi\)
0.933799 + 0.357799i \(0.116473\pi\)
\(504\) 1.64930 0.0734658
\(505\) −13.8939 −0.618271
\(506\) 37.6274 1.67274
\(507\) −28.8042 −1.27924
\(508\) 100.861 4.47498
\(509\) −36.1271 −1.60131 −0.800653 0.599129i \(-0.795514\pi\)
−0.800653 + 0.599129i \(0.795514\pi\)
\(510\) −37.6361 −1.66655
\(511\) 0.457169 0.0202240
\(512\) −125.328 −5.53877
\(513\) −3.07277 −0.135666
\(514\) −3.07135 −0.135471
\(515\) 2.32192 0.102316
\(516\) 71.1899 3.13396
\(517\) −15.2041 −0.668675
\(518\) 1.38352 0.0607882
\(519\) −41.0687 −1.80271
\(520\) −23.6197 −1.03579
\(521\) −13.3411 −0.584482 −0.292241 0.956345i \(-0.594401\pi\)
−0.292241 + 0.956345i \(0.594401\pi\)
\(522\) −28.4659 −1.24592
\(523\) 22.7016 0.992670 0.496335 0.868131i \(-0.334679\pi\)
0.496335 + 0.868131i \(0.334679\pi\)
\(524\) 11.9082 0.520211
\(525\) −0.00135272 −5.90377e−5 0
\(526\) −10.4439 −0.455376
\(527\) −4.94644 −0.215471
\(528\) 188.740 8.21386
\(529\) −13.8521 −0.602264
\(530\) 24.3418 1.05734
\(531\) 6.28714 0.272839
\(532\) −1.91861 −0.0831824
\(533\) −1.91479 −0.0829388
\(534\) −34.7614 −1.50427
\(535\) 11.7193 0.506672
\(536\) 105.659 4.56379
\(537\) 43.3549 1.87090
\(538\) 48.1880 2.07753
\(539\) −31.2670 −1.34677
\(540\) 6.72924 0.289581
\(541\) −37.2425 −1.60118 −0.800591 0.599212i \(-0.795481\pi\)
−0.800591 + 0.599212i \(0.795481\pi\)
\(542\) −29.4020 −1.26292
\(543\) −29.7271 −1.27571
\(544\) 70.3679 3.01700
\(545\) −19.7450 −0.845783
\(546\) −0.384175 −0.0164412
\(547\) −24.5951 −1.05161 −0.525804 0.850605i \(-0.676236\pi\)
−0.525804 + 0.850605i \(0.676236\pi\)
\(548\) −48.3212 −2.06418
\(549\) 19.0615 0.813524
\(550\) −0.123264 −0.00525600
\(551\) 21.5964 0.920035
\(552\) 75.9315 3.23186
\(553\) −0.332823 −0.0141531
\(554\) 76.3403 3.24339
\(555\) −47.1142 −1.99989
\(556\) −99.4243 −4.21653
\(557\) −23.7094 −1.00460 −0.502300 0.864694i \(-0.667513\pi\)
−0.502300 + 0.864694i \(0.667513\pi\)
\(558\) −15.2553 −0.645807
\(559\) −5.20404 −0.220108
\(560\) 2.23195 0.0943170
\(561\) −26.9913 −1.13957
\(562\) −12.4188 −0.523855
\(563\) −26.8891 −1.13324 −0.566620 0.823979i \(-0.691749\pi\)
−0.566620 + 0.823979i \(0.691749\pi\)
\(564\) −47.0446 −1.98094
\(565\) 12.7942 0.538255
\(566\) 22.7733 0.957234
\(567\) 0.545320 0.0229013
\(568\) −5.95041 −0.249673
\(569\) −3.35316 −0.140572 −0.0702859 0.997527i \(-0.522391\pi\)
−0.0702859 + 0.997527i \(0.522391\pi\)
\(570\) 88.0614 3.68849
\(571\) 16.6016 0.694757 0.347378 0.937725i \(-0.387072\pi\)
0.347378 + 0.937725i \(0.387072\pi\)
\(572\) −25.9732 −1.08600
\(573\) −26.9150 −1.12439
\(574\) 0.299412 0.0124972
\(575\) −0.0299679 −0.00124975
\(576\) 119.276 4.96984
\(577\) −41.9998 −1.74847 −0.874237 0.485500i \(-0.838638\pi\)
−0.874237 + 0.485500i \(0.838638\pi\)
\(578\) 29.7632 1.23799
\(579\) 1.75542 0.0729526
\(580\) −47.2951 −1.96382
\(581\) 0.439622 0.0182386
\(582\) −98.0971 −4.06625
\(583\) 17.4571 0.723000
\(584\) 84.0664 3.47869
\(585\) 6.29538 0.260282
\(586\) −56.1378 −2.31903
\(587\) −19.1794 −0.791617 −0.395808 0.918333i \(-0.629536\pi\)
−0.395808 + 0.918333i \(0.629536\pi\)
\(588\) −96.7466 −3.98976
\(589\) 11.5738 0.476889
\(590\) 14.0791 0.579628
\(591\) 24.4777 1.00688
\(592\) 153.742 6.31874
\(593\) 46.0608 1.89149 0.945745 0.324909i \(-0.105334\pi\)
0.945745 + 0.324909i \(0.105334\pi\)
\(594\) 6.50454 0.266885
\(595\) −0.319186 −0.0130853
\(596\) 44.6269 1.82799
\(597\) 62.8684 2.57303
\(598\) −8.51092 −0.348037
\(599\) −3.92338 −0.160305 −0.0801524 0.996783i \(-0.525541\pi\)
−0.0801524 + 0.996783i \(0.525541\pi\)
\(600\) −0.248745 −0.0101550
\(601\) −44.3363 −1.80851 −0.904257 0.426989i \(-0.859574\pi\)
−0.904257 + 0.426989i \(0.859574\pi\)
\(602\) 0.813746 0.0331658
\(603\) −28.1614 −1.14682
\(604\) 103.667 4.21816
\(605\) −20.0772 −0.816255
\(606\) −41.5551 −1.68806
\(607\) 33.5928 1.36349 0.681745 0.731590i \(-0.261221\pi\)
0.681745 + 0.731590i \(0.261221\pi\)
\(608\) −164.648 −6.67735
\(609\) −0.501694 −0.0203297
\(610\) 42.6854 1.72828
\(611\) 3.43900 0.139127
\(612\) −40.1881 −1.62451
\(613\) 38.2029 1.54300 0.771500 0.636229i \(-0.219507\pi\)
0.771500 + 0.636229i \(0.219507\pi\)
\(614\) −53.6483 −2.16507
\(615\) −10.1961 −0.411148
\(616\) 2.64876 0.106721
\(617\) −17.0650 −0.687012 −0.343506 0.939151i \(-0.611615\pi\)
−0.343506 + 0.939151i \(0.611615\pi\)
\(618\) 6.94459 0.279353
\(619\) 38.0997 1.53136 0.765678 0.643224i \(-0.222403\pi\)
0.765678 + 0.643224i \(0.222403\pi\)
\(620\) −25.3461 −1.01792
\(621\) 1.58138 0.0634585
\(622\) 41.4275 1.66109
\(623\) −0.294806 −0.0118111
\(624\) −42.6910 −1.70901
\(625\) −25.0494 −1.00198
\(626\) −21.4281 −0.856438
\(627\) 63.1546 2.52215
\(628\) 127.077 5.07091
\(629\) −21.9862 −0.876648
\(630\) −0.984396 −0.0392193
\(631\) −25.3340 −1.00853 −0.504265 0.863549i \(-0.668237\pi\)
−0.504265 + 0.863549i \(0.668237\pi\)
\(632\) −61.2011 −2.43445
\(633\) −20.5282 −0.815923
\(634\) −23.3621 −0.927826
\(635\) −39.2609 −1.55802
\(636\) 54.0159 2.14187
\(637\) 7.07227 0.280213
\(638\) −45.7159 −1.80991
\(639\) 1.58596 0.0627398
\(640\) 141.688 5.60070
\(641\) −9.05500 −0.357651 −0.178825 0.983881i \(-0.557230\pi\)
−0.178825 + 0.983881i \(0.557230\pi\)
\(642\) 35.0512 1.38336
\(643\) 7.79552 0.307425 0.153713 0.988116i \(-0.450877\pi\)
0.153713 + 0.988116i \(0.450877\pi\)
\(644\) 0.987399 0.0389090
\(645\) −27.7112 −1.09113
\(646\) 41.0946 1.61685
\(647\) 36.4734 1.43392 0.716959 0.697116i \(-0.245534\pi\)
0.716959 + 0.697116i \(0.245534\pi\)
\(648\) 100.276 3.93922
\(649\) 10.0971 0.396344
\(650\) 0.0278811 0.00109359
\(651\) −0.268864 −0.0105376
\(652\) 61.8554 2.42244
\(653\) 47.4205 1.85571 0.927855 0.372942i \(-0.121651\pi\)
0.927855 + 0.372942i \(0.121651\pi\)
\(654\) −59.0550 −2.30923
\(655\) −4.63536 −0.181118
\(656\) 33.2718 1.29904
\(657\) −22.4062 −0.874151
\(658\) −0.537750 −0.0209637
\(659\) 1.74351 0.0679177 0.0339588 0.999423i \(-0.489188\pi\)
0.0339588 + 0.999423i \(0.489188\pi\)
\(660\) −138.306 −5.38355
\(661\) 25.1401 0.977836 0.488918 0.872330i \(-0.337392\pi\)
0.488918 + 0.872330i \(0.337392\pi\)
\(662\) 86.4738 3.36090
\(663\) 6.10514 0.237104
\(664\) 80.8399 3.13720
\(665\) 0.746836 0.0289610
\(666\) −67.8074 −2.62748
\(667\) −11.1144 −0.430351
\(668\) 100.204 3.87701
\(669\) −2.52698 −0.0976986
\(670\) −63.0634 −2.43635
\(671\) 30.6125 1.18178
\(672\) 3.82485 0.147547
\(673\) 46.2881 1.78428 0.892138 0.451763i \(-0.149205\pi\)
0.892138 + 0.451763i \(0.149205\pi\)
\(674\) −17.6501 −0.679856
\(675\) −0.00518047 −0.000199396 0
\(676\) −68.8767 −2.64911
\(677\) −33.3594 −1.28211 −0.641053 0.767497i \(-0.721502\pi\)
−0.641053 + 0.767497i \(0.721502\pi\)
\(678\) 38.2660 1.46960
\(679\) −0.831946 −0.0319272
\(680\) −58.6934 −2.25079
\(681\) 15.9674 0.611873
\(682\) −24.4997 −0.938143
\(683\) 11.8600 0.453812 0.226906 0.973917i \(-0.427139\pi\)
0.226906 + 0.973917i \(0.427139\pi\)
\(684\) 94.0329 3.59544
\(685\) 18.8094 0.718670
\(686\) −2.21226 −0.0844645
\(687\) −31.6690 −1.20825
\(688\) 90.4265 3.44748
\(689\) −3.94861 −0.150430
\(690\) −45.3201 −1.72531
\(691\) −18.6628 −0.709966 −0.354983 0.934873i \(-0.615513\pi\)
−0.354983 + 0.934873i \(0.615513\pi\)
\(692\) −98.2036 −3.73314
\(693\) −0.705974 −0.0268177
\(694\) 69.5211 2.63899
\(695\) 38.7017 1.46804
\(696\) −92.2539 −3.49687
\(697\) −4.75812 −0.180226
\(698\) 5.29959 0.200593
\(699\) 46.1978 1.74736
\(700\) −0.00323464 −0.000122258 0
\(701\) 6.71903 0.253774 0.126887 0.991917i \(-0.459501\pi\)
0.126887 + 0.991917i \(0.459501\pi\)
\(702\) −1.47126 −0.0555291
\(703\) 51.4437 1.94024
\(704\) 191.556 7.21953
\(705\) 18.3125 0.689689
\(706\) −12.0486 −0.453457
\(707\) −0.352423 −0.0132542
\(708\) 31.2424 1.17416
\(709\) −45.6265 −1.71354 −0.856769 0.515701i \(-0.827532\pi\)
−0.856769 + 0.515701i \(0.827532\pi\)
\(710\) 3.55153 0.133287
\(711\) 16.3120 0.611746
\(712\) −54.2103 −2.03162
\(713\) −5.95635 −0.223067
\(714\) −0.954648 −0.0357268
\(715\) 10.1103 0.378103
\(716\) 103.670 3.87434
\(717\) 34.1559 1.27557
\(718\) −45.8420 −1.71081
\(719\) 13.2163 0.492883 0.246442 0.969158i \(-0.420739\pi\)
0.246442 + 0.969158i \(0.420739\pi\)
\(720\) −109.390 −4.07672
\(721\) 0.0588960 0.00219340
\(722\) −43.2596 −1.60996
\(723\) 35.4047 1.31672
\(724\) −71.0836 −2.64180
\(725\) 0.0364099 0.00135223
\(726\) −60.0487 −2.22862
\(727\) −40.0931 −1.48697 −0.743486 0.668752i \(-0.766829\pi\)
−0.743486 + 0.668752i \(0.766829\pi\)
\(728\) −0.599121 −0.0222049
\(729\) −22.9548 −0.850177
\(730\) −50.1755 −1.85708
\(731\) −12.9317 −0.478295
\(732\) 94.7213 3.50100
\(733\) −14.6344 −0.540535 −0.270267 0.962785i \(-0.587112\pi\)
−0.270267 + 0.962785i \(0.587112\pi\)
\(734\) 36.5460 1.34894
\(735\) 37.6594 1.38909
\(736\) 84.7348 3.12336
\(737\) −45.2269 −1.66595
\(738\) −14.6744 −0.540174
\(739\) −48.2744 −1.77580 −0.887900 0.460036i \(-0.847837\pi\)
−0.887900 + 0.460036i \(0.847837\pi\)
\(740\) −112.660 −4.14145
\(741\) −14.2849 −0.524769
\(742\) 0.617437 0.0226668
\(743\) −25.2529 −0.926437 −0.463219 0.886244i \(-0.653306\pi\)
−0.463219 + 0.886244i \(0.653306\pi\)
\(744\) −49.4401 −1.81256
\(745\) −17.3714 −0.636438
\(746\) −43.4750 −1.59173
\(747\) −21.5463 −0.788337
\(748\) −64.5416 −2.35987
\(749\) 0.297264 0.0108618
\(750\) −74.7719 −2.73028
\(751\) −15.0796 −0.550261 −0.275131 0.961407i \(-0.588721\pi\)
−0.275131 + 0.961407i \(0.588721\pi\)
\(752\) −59.7568 −2.17911
\(753\) 44.3550 1.61639
\(754\) 10.3404 0.376577
\(755\) −40.3533 −1.46861
\(756\) 0.170689 0.00620790
\(757\) 36.7887 1.33711 0.668553 0.743664i \(-0.266914\pi\)
0.668553 + 0.743664i \(0.266914\pi\)
\(758\) −48.0081 −1.74373
\(759\) −32.5020 −1.17975
\(760\) 137.332 4.98154
\(761\) 30.8702 1.11904 0.559521 0.828816i \(-0.310985\pi\)
0.559521 + 0.828816i \(0.310985\pi\)
\(762\) −117.425 −4.25386
\(763\) −0.500837 −0.0181315
\(764\) −64.3591 −2.32843
\(765\) 15.6436 0.565594
\(766\) −21.8732 −0.790313
\(767\) −2.28385 −0.0824649
\(768\) 217.616 7.85252
\(769\) 29.9751 1.08093 0.540464 0.841367i \(-0.318249\pi\)
0.540464 + 0.841367i \(0.318249\pi\)
\(770\) −1.58093 −0.0569726
\(771\) 2.65299 0.0955451
\(772\) 4.19756 0.151073
\(773\) −3.31481 −0.119225 −0.0596127 0.998222i \(-0.518987\pi\)
−0.0596127 + 0.998222i \(0.518987\pi\)
\(774\) −39.8824 −1.43354
\(775\) 0.0195125 0.000700911 0
\(776\) −152.982 −5.49174
\(777\) −1.19506 −0.0428726
\(778\) 98.8669 3.54455
\(779\) 11.1331 0.398885
\(780\) 31.2833 1.12012
\(781\) 2.54704 0.0911401
\(782\) −21.1490 −0.756287
\(783\) −1.92131 −0.0686622
\(784\) −122.889 −4.38890
\(785\) −49.4656 −1.76550
\(786\) −13.8638 −0.494506
\(787\) 51.0005 1.81797 0.908986 0.416826i \(-0.136858\pi\)
0.908986 + 0.416826i \(0.136858\pi\)
\(788\) 58.5312 2.08509
\(789\) 9.02130 0.321167
\(790\) 36.5282 1.29962
\(791\) 0.324528 0.0115389
\(792\) −129.818 −4.61288
\(793\) −6.92422 −0.245886
\(794\) −22.1384 −0.785664
\(795\) −21.0261 −0.745720
\(796\) 150.331 5.32835
\(797\) −3.27665 −0.116065 −0.0580325 0.998315i \(-0.518483\pi\)
−0.0580325 + 0.998315i \(0.518483\pi\)
\(798\) 2.23370 0.0790721
\(799\) 8.54568 0.302324
\(800\) −0.277584 −0.00981408
\(801\) 14.4487 0.510519
\(802\) −3.80372 −0.134314
\(803\) −35.9841 −1.26985
\(804\) −139.941 −4.93535
\(805\) −0.384353 −0.0135467
\(806\) 5.54158 0.195194
\(807\) −41.6241 −1.46524
\(808\) −64.8052 −2.27984
\(809\) −32.8470 −1.15484 −0.577420 0.816447i \(-0.695941\pi\)
−0.577420 + 0.816447i \(0.695941\pi\)
\(810\) −59.8504 −2.10293
\(811\) −14.6067 −0.512910 −0.256455 0.966556i \(-0.582555\pi\)
−0.256455 + 0.966556i \(0.582555\pi\)
\(812\) −1.19965 −0.0420996
\(813\) 25.3970 0.890712
\(814\) −108.898 −3.81686
\(815\) −24.0777 −0.843405
\(816\) −106.084 −3.71368
\(817\) 30.2577 1.05858
\(818\) −43.9339 −1.53611
\(819\) 0.159684 0.00557981
\(820\) −24.3811 −0.851424
\(821\) −31.2432 −1.09039 −0.545197 0.838308i \(-0.683545\pi\)
−0.545197 + 0.838308i \(0.683545\pi\)
\(822\) 56.2568 1.96218
\(823\) −20.0259 −0.698058 −0.349029 0.937112i \(-0.613488\pi\)
−0.349029 + 0.937112i \(0.613488\pi\)
\(824\) 10.8301 0.377284
\(825\) 0.106474 0.00370695
\(826\) 0.357121 0.0124258
\(827\) −4.55756 −0.158482 −0.0792409 0.996855i \(-0.525250\pi\)
−0.0792409 + 0.996855i \(0.525250\pi\)
\(828\) −48.3933 −1.68178
\(829\) −45.9058 −1.59437 −0.797187 0.603733i \(-0.793679\pi\)
−0.797187 + 0.603733i \(0.793679\pi\)
\(830\) −48.2497 −1.67477
\(831\) −65.9417 −2.28749
\(832\) −43.3279 −1.50213
\(833\) 17.5741 0.608905
\(834\) 115.752 4.00818
\(835\) −39.0053 −1.34983
\(836\) 151.015 5.22298
\(837\) −1.02966 −0.0355902
\(838\) −48.2188 −1.66569
\(839\) 21.0535 0.726848 0.363424 0.931624i \(-0.381608\pi\)
0.363424 + 0.931624i \(0.381608\pi\)
\(840\) −3.19028 −0.110075
\(841\) −15.4964 −0.534360
\(842\) −65.8205 −2.26832
\(843\) 10.7272 0.369463
\(844\) −49.0871 −1.68965
\(845\) 26.8108 0.922321
\(846\) 26.3556 0.906124
\(847\) −0.509264 −0.0174985
\(848\) 68.6119 2.35614
\(849\) −19.6713 −0.675117
\(850\) 0.0692824 0.00237637
\(851\) −26.4751 −0.907555
\(852\) 7.88106 0.270001
\(853\) 2.19428 0.0751307 0.0375653 0.999294i \(-0.488040\pi\)
0.0375653 + 0.999294i \(0.488040\pi\)
\(854\) 1.08273 0.0370501
\(855\) −36.6031 −1.25180
\(856\) 54.6624 1.86832
\(857\) −22.9582 −0.784237 −0.392119 0.919915i \(-0.628258\pi\)
−0.392119 + 0.919915i \(0.628258\pi\)
\(858\) 30.2387 1.03233
\(859\) −28.8325 −0.983752 −0.491876 0.870665i \(-0.663689\pi\)
−0.491876 + 0.870665i \(0.663689\pi\)
\(860\) −66.2632 −2.25956
\(861\) −0.258628 −0.00881401
\(862\) −73.1967 −2.49309
\(863\) 20.3072 0.691265 0.345633 0.938370i \(-0.387664\pi\)
0.345633 + 0.938370i \(0.387664\pi\)
\(864\) 14.6479 0.498330
\(865\) 38.2265 1.29974
\(866\) −38.6695 −1.31404
\(867\) −25.7090 −0.873125
\(868\) −0.642910 −0.0218218
\(869\) 26.1968 0.888664
\(870\) 55.0623 1.86679
\(871\) 10.2298 0.346625
\(872\) −92.0962 −3.11877
\(873\) 40.7744 1.38000
\(874\) 49.4848 1.67385
\(875\) −0.634129 −0.0214375
\(876\) −111.342 −3.76191
\(877\) −4.45487 −0.150430 −0.0752152 0.997167i \(-0.523964\pi\)
−0.0752152 + 0.997167i \(0.523964\pi\)
\(878\) 24.7390 0.834901
\(879\) 48.4910 1.63556
\(880\) −175.678 −5.92212
\(881\) 39.7804 1.34024 0.670118 0.742255i \(-0.266244\pi\)
0.670118 + 0.742255i \(0.266244\pi\)
\(882\) 54.1999 1.82501
\(883\) −10.3635 −0.348758 −0.174379 0.984679i \(-0.555792\pi\)
−0.174379 + 0.984679i \(0.555792\pi\)
\(884\) 14.5986 0.491005
\(885\) −12.1614 −0.408799
\(886\) −104.422 −3.50811
\(887\) 20.4859 0.687849 0.343924 0.938997i \(-0.388244\pi\)
0.343924 + 0.938997i \(0.388244\pi\)
\(888\) −219.754 −7.37446
\(889\) −0.995863 −0.0334002
\(890\) 32.3557 1.08457
\(891\) −42.9226 −1.43796
\(892\) −6.04252 −0.202319
\(893\) −19.9953 −0.669118
\(894\) −51.9559 −1.73766
\(895\) −40.3545 −1.34890
\(896\) 3.59395 0.120065
\(897\) 7.35161 0.245463
\(898\) 68.5394 2.28719
\(899\) 7.23674 0.241359
\(900\) 0.158532 0.00528442
\(901\) −9.81202 −0.326886
\(902\) −23.5669 −0.784693
\(903\) −0.702902 −0.0233911
\(904\) 59.6757 1.98478
\(905\) 27.6699 0.919778
\(906\) −120.692 −4.00973
\(907\) 39.2596 1.30359 0.651796 0.758394i \(-0.274016\pi\)
0.651796 + 0.758394i \(0.274016\pi\)
\(908\) 38.1814 1.26709
\(909\) 17.2725 0.572894
\(910\) 0.357589 0.0118539
\(911\) 25.0309 0.829310 0.414655 0.909979i \(-0.363902\pi\)
0.414655 + 0.909979i \(0.363902\pi\)
\(912\) 248.217 8.21929
\(913\) −34.6030 −1.14519
\(914\) −15.7179 −0.519901
\(915\) −36.8710 −1.21892
\(916\) −75.7270 −2.50209
\(917\) −0.117577 −0.00388273
\(918\) −3.65597 −0.120665
\(919\) −29.4287 −0.970763 −0.485381 0.874303i \(-0.661319\pi\)
−0.485381 + 0.874303i \(0.661319\pi\)
\(920\) −70.6767 −2.33014
\(921\) 46.3407 1.52698
\(922\) −95.6283 −3.14935
\(923\) −0.576112 −0.0189630
\(924\) −3.50816 −0.115410
\(925\) 0.0867303 0.00285167
\(926\) −28.4241 −0.934075
\(927\) −2.88655 −0.0948066
\(928\) −102.950 −3.37948
\(929\) 27.2482 0.893984 0.446992 0.894538i \(-0.352495\pi\)
0.446992 + 0.894538i \(0.352495\pi\)
\(930\) 29.5086 0.967625
\(931\) −41.1201 −1.34766
\(932\) 110.468 3.61851
\(933\) −35.7845 −1.17153
\(934\) 81.3179 2.66080
\(935\) 25.1233 0.821621
\(936\) 29.3634 0.959774
\(937\) −26.6447 −0.870445 −0.435222 0.900323i \(-0.643330\pi\)
−0.435222 + 0.900323i \(0.643330\pi\)
\(938\) −1.59962 −0.0522294
\(939\) 18.5093 0.604027
\(940\) 43.7889 1.42824
\(941\) 41.2145 1.34355 0.671777 0.740753i \(-0.265531\pi\)
0.671777 + 0.740753i \(0.265531\pi\)
\(942\) −147.946 −4.82034
\(943\) −5.72957 −0.186581
\(944\) 39.6846 1.29162
\(945\) −0.0664421 −0.00216136
\(946\) −64.0506 −2.08246
\(947\) 22.1283 0.719072 0.359536 0.933131i \(-0.382935\pi\)
0.359536 + 0.933131i \(0.382935\pi\)
\(948\) 81.0582 2.63265
\(949\) 8.13923 0.264210
\(950\) −0.162108 −0.00525948
\(951\) 20.1798 0.654376
\(952\) −1.48877 −0.0482514
\(953\) 44.0188 1.42591 0.712954 0.701211i \(-0.247357\pi\)
0.712954 + 0.701211i \(0.247357\pi\)
\(954\) −30.2611 −0.979740
\(955\) 25.0523 0.810674
\(956\) 81.6736 2.64151
\(957\) 39.4887 1.27649
\(958\) −88.4987 −2.85926
\(959\) 0.477105 0.0154065
\(960\) −230.719 −7.44641
\(961\) −27.1217 −0.874895
\(962\) 24.6315 0.794152
\(963\) −14.5692 −0.469485
\(964\) 84.6599 2.72671
\(965\) −1.63393 −0.0525982
\(966\) −1.14956 −0.0369864
\(967\) −57.7420 −1.85686 −0.928429 0.371510i \(-0.878840\pi\)
−0.928429 + 0.371510i \(0.878840\pi\)
\(968\) −93.6459 −3.00989
\(969\) −35.4969 −1.14033
\(970\) 91.3083 2.93173
\(971\) 6.71945 0.215638 0.107819 0.994171i \(-0.465613\pi\)
0.107819 + 0.994171i \(0.465613\pi\)
\(972\) −123.792 −3.97063
\(973\) 0.981679 0.0314712
\(974\) −10.1699 −0.325865
\(975\) −0.0240833 −0.000771282 0
\(976\) 120.317 3.85124
\(977\) −58.3875 −1.86798 −0.933991 0.357297i \(-0.883698\pi\)
−0.933991 + 0.357297i \(0.883698\pi\)
\(978\) −72.0137 −2.30274
\(979\) 23.2044 0.741615
\(980\) 90.0513 2.87658
\(981\) 24.5464 0.783708
\(982\) 105.929 3.38032
\(983\) −25.2729 −0.806081 −0.403041 0.915182i \(-0.632047\pi\)
−0.403041 + 0.915182i \(0.632047\pi\)
\(984\) −47.5577 −1.51608
\(985\) −22.7838 −0.725951
\(986\) 25.6953 0.818304
\(987\) 0.464501 0.0147852
\(988\) −34.1581 −1.08671
\(989\) −15.5719 −0.495158
\(990\) 77.4826 2.46256
\(991\) −21.3350 −0.677727 −0.338864 0.940835i \(-0.610043\pi\)
−0.338864 + 0.940835i \(0.610043\pi\)
\(992\) −55.1720 −1.75171
\(993\) −74.6948 −2.37037
\(994\) 0.0900855 0.00285734
\(995\) −58.5176 −1.85513
\(996\) −107.069 −3.39261
\(997\) −23.5253 −0.745054 −0.372527 0.928021i \(-0.621509\pi\)
−0.372527 + 0.928021i \(0.621509\pi\)
\(998\) −22.8645 −0.723763
\(999\) −4.57668 −0.144800
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 \(a_p\))