Properties

Label 4019.2.a.b.1.6
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 1.6
Character \(\chi\) = 4019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.71067 q^{2}\) \(-2.48956 q^{3}\) \(+5.34775 q^{4}\) \(-1.96358 q^{5}\) \(+6.74838 q^{6}\) \(+3.14635 q^{7}\) \(-9.07467 q^{8}\) \(+3.19790 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.71067 q^{2}\) \(-2.48956 q^{3}\) \(+5.34775 q^{4}\) \(-1.96358 q^{5}\) \(+6.74838 q^{6}\) \(+3.14635 q^{7}\) \(-9.07467 q^{8}\) \(+3.19790 q^{9}\) \(+5.32263 q^{10}\) \(-0.760163 q^{11}\) \(-13.3135 q^{12}\) \(-3.23629 q^{13}\) \(-8.52873 q^{14}\) \(+4.88845 q^{15}\) \(+13.9030 q^{16}\) \(-6.89437 q^{17}\) \(-8.66846 q^{18}\) \(+5.80103 q^{19}\) \(-10.5007 q^{20}\) \(-7.83302 q^{21}\) \(+2.06055 q^{22}\) \(-2.00733 q^{23}\) \(+22.5919 q^{24}\) \(-1.14435 q^{25}\) \(+8.77254 q^{26}\) \(-0.492681 q^{27}\) \(+16.8259 q^{28}\) \(-3.67543 q^{29}\) \(-13.2510 q^{30}\) \(-6.53081 q^{31}\) \(-19.5371 q^{32}\) \(+1.89247 q^{33}\) \(+18.6884 q^{34}\) \(-6.17812 q^{35}\) \(+17.1016 q^{36}\) \(-8.82183 q^{37}\) \(-15.7247 q^{38}\) \(+8.05694 q^{39}\) \(+17.8188 q^{40}\) \(-3.43051 q^{41}\) \(+21.2328 q^{42}\) \(+0.759370 q^{43}\) \(-4.06516 q^{44}\) \(-6.27933 q^{45}\) \(+5.44120 q^{46}\) \(+0.514988 q^{47}\) \(-34.6122 q^{48}\) \(+2.89952 q^{49}\) \(+3.10196 q^{50}\) \(+17.1639 q^{51}\) \(-17.3069 q^{52}\) \(+0.447477 q^{53}\) \(+1.33550 q^{54}\) \(+1.49264 q^{55}\) \(-28.5521 q^{56}\) \(-14.4420 q^{57}\) \(+9.96289 q^{58}\) \(+7.42963 q^{59}\) \(+26.1422 q^{60}\) \(+6.72321 q^{61}\) \(+17.7029 q^{62}\) \(+10.0617 q^{63}\) \(+25.1527 q^{64}\) \(+6.35473 q^{65}\) \(-5.12987 q^{66}\) \(-7.29726 q^{67}\) \(-36.8694 q^{68}\) \(+4.99735 q^{69}\) \(+16.7469 q^{70}\) \(+9.64369 q^{71}\) \(-29.0199 q^{72}\) \(+9.23105 q^{73}\) \(+23.9131 q^{74}\) \(+2.84892 q^{75}\) \(+31.0225 q^{76}\) \(-2.39174 q^{77}\) \(-21.8397 q^{78}\) \(+8.16355 q^{79}\) \(-27.2996 q^{80}\) \(-8.36714 q^{81}\) \(+9.29899 q^{82}\) \(+5.79023 q^{83}\) \(-41.8891 q^{84}\) \(+13.5377 q^{85}\) \(-2.05841 q^{86}\) \(+9.15019 q^{87}\) \(+6.89822 q^{88}\) \(-4.81803 q^{89}\) \(+17.0212 q^{90}\) \(-10.1825 q^{91}\) \(-10.7347 q^{92}\) \(+16.2588 q^{93}\) \(-1.39597 q^{94}\) \(-11.3908 q^{95}\) \(+48.6386 q^{96}\) \(-16.2672 q^{97}\) \(-7.85966 q^{98}\) \(-2.43092 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(186q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 212q^{4} \) \(\mathstrut +\mathstrut 38q^{5} \) \(\mathstrut +\mathstrut 47q^{6} \) \(\mathstrut +\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 216q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut +\mathstrut 25q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 113q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut +\mathstrut 252q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 13q^{18} \) \(\mathstrut +\mathstrut 97q^{19} \) \(\mathstrut +\mathstrut 55q^{20} \) \(\mathstrut +\mathstrut 115q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 27q^{23} \) \(\mathstrut +\mathstrut 122q^{24} \) \(\mathstrut +\mathstrut 244q^{25} \) \(\mathstrut +\mathstrut 39q^{26} \) \(\mathstrut +\mathstrut 34q^{27} \) \(\mathstrut +\mathstrut 66q^{28} \) \(\mathstrut +\mathstrut 91q^{29} \) \(\mathstrut +\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 135q^{31} \) \(\mathstrut +\mathstrut 21q^{32} \) \(\mathstrut +\mathstrut 32q^{33} \) \(\mathstrut +\mathstrut 58q^{34} \) \(\mathstrut +\mathstrut 17q^{35} \) \(\mathstrut +\mathstrut 273q^{36} \) \(\mathstrut +\mathstrut 133q^{37} \) \(\mathstrut -\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 55q^{39} \) \(\mathstrut +\mathstrut 142q^{40} \) \(\mathstrut +\mathstrut 97q^{41} \) \(\mathstrut -\mathstrut 8q^{42} \) \(\mathstrut +\mathstrut 67q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 101q^{46} \) \(\mathstrut +\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut +\mathstrut 312q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut +\mathstrut 141q^{54} \) \(\mathstrut +\mathstrut 88q^{55} \) \(\mathstrut +\mathstrut 28q^{56} \) \(\mathstrut +\mathstrut 65q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut +\mathstrut q^{60} \) \(\mathstrut +\mathstrut 377q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 39q^{63} \) \(\mathstrut +\mathstrut 311q^{64} \) \(\mathstrut +\mathstrut 21q^{65} \) \(\mathstrut +\mathstrut 35q^{66} \) \(\mathstrut +\mathstrut 42q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut +\mathstrut 137q^{69} \) \(\mathstrut +\mathstrut 35q^{70} \) \(\mathstrut +\mathstrut 17q^{71} \) \(\mathstrut -\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 213q^{73} \) \(\mathstrut -\mathstrut 9q^{74} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut +\mathstrut 242q^{76} \) \(\mathstrut +\mathstrut 60q^{77} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 80q^{80} \) \(\mathstrut +\mathstrut 270q^{81} \) \(\mathstrut +\mathstrut 84q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 137q^{84} \) \(\mathstrut +\mathstrut 294q^{85} \) \(\mathstrut -\mathstrut 9q^{86} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 118q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 93q^{94} \) \(\mathstrut +\mathstrut 10q^{95} \) \(\mathstrut +\mathstrut 260q^{96} \) \(\mathstrut +\mathstrut 142q^{97} \) \(\mathstrut -\mathstrut 31q^{98} \) \(\mathstrut +\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.71067 −1.91674 −0.958368 0.285536i \(-0.907828\pi\)
−0.958368 + 0.285536i \(0.907828\pi\)
\(3\) −2.48956 −1.43735 −0.718673 0.695348i \(-0.755250\pi\)
−0.718673 + 0.695348i \(0.755250\pi\)
\(4\) 5.34775 2.67388
\(5\) −1.96358 −0.878140 −0.439070 0.898453i \(-0.644692\pi\)
−0.439070 + 0.898453i \(0.644692\pi\)
\(6\) 6.74838 2.75501
\(7\) 3.14635 1.18921 0.594604 0.804018i \(-0.297309\pi\)
0.594604 + 0.804018i \(0.297309\pi\)
\(8\) −9.07467 −3.20838
\(9\) 3.19790 1.06597
\(10\) 5.32263 1.68316
\(11\) −0.760163 −0.229198 −0.114599 0.993412i \(-0.536558\pi\)
−0.114599 + 0.993412i \(0.536558\pi\)
\(12\) −13.3135 −3.84329
\(13\) −3.23629 −0.897587 −0.448793 0.893636i \(-0.648146\pi\)
−0.448793 + 0.893636i \(0.648146\pi\)
\(14\) −8.52873 −2.27940
\(15\) 4.88845 1.26219
\(16\) 13.9030 3.47574
\(17\) −6.89437 −1.67213 −0.836065 0.548630i \(-0.815150\pi\)
−0.836065 + 0.548630i \(0.815150\pi\)
\(18\) −8.66846 −2.04318
\(19\) 5.80103 1.33085 0.665424 0.746465i \(-0.268251\pi\)
0.665424 + 0.746465i \(0.268251\pi\)
\(20\) −10.5007 −2.34804
\(21\) −7.83302 −1.70931
\(22\) 2.06055 0.439311
\(23\) −2.00733 −0.418556 −0.209278 0.977856i \(-0.567111\pi\)
−0.209278 + 0.977856i \(0.567111\pi\)
\(24\) 22.5919 4.61155
\(25\) −1.14435 −0.228870
\(26\) 8.77254 1.72044
\(27\) −0.492681 −0.0948166
\(28\) 16.8259 3.17980
\(29\) −3.67543 −0.682510 −0.341255 0.939971i \(-0.610852\pi\)
−0.341255 + 0.939971i \(0.610852\pi\)
\(30\) −13.2510 −2.41929
\(31\) −6.53081 −1.17297 −0.586484 0.809961i \(-0.699488\pi\)
−0.586484 + 0.809961i \(0.699488\pi\)
\(32\) −19.5371 −3.45370
\(33\) 1.89247 0.329437
\(34\) 18.6884 3.20503
\(35\) −6.17812 −1.04429
\(36\) 17.1016 2.85026
\(37\) −8.82183 −1.45030 −0.725150 0.688591i \(-0.758230\pi\)
−0.725150 + 0.688591i \(0.758230\pi\)
\(38\) −15.7247 −2.55089
\(39\) 8.05694 1.29014
\(40\) 17.8188 2.81741
\(41\) −3.43051 −0.535755 −0.267878 0.963453i \(-0.586322\pi\)
−0.267878 + 0.963453i \(0.586322\pi\)
\(42\) 21.2328 3.27629
\(43\) 0.759370 0.115803 0.0579014 0.998322i \(-0.481559\pi\)
0.0579014 + 0.998322i \(0.481559\pi\)
\(44\) −4.06516 −0.612846
\(45\) −6.27933 −0.936068
\(46\) 5.44120 0.802262
\(47\) 0.514988 0.0751188 0.0375594 0.999294i \(-0.488042\pi\)
0.0375594 + 0.999294i \(0.488042\pi\)
\(48\) −34.6122 −4.99584
\(49\) 2.89952 0.414218
\(50\) 3.10196 0.438683
\(51\) 17.1639 2.40343
\(52\) −17.3069 −2.40004
\(53\) 0.447477 0.0614657 0.0307328 0.999528i \(-0.490216\pi\)
0.0307328 + 0.999528i \(0.490216\pi\)
\(54\) 1.33550 0.181738
\(55\) 1.49264 0.201268
\(56\) −28.5521 −3.81543
\(57\) −14.4420 −1.91289
\(58\) 9.96289 1.30819
\(59\) 7.42963 0.967256 0.483628 0.875274i \(-0.339319\pi\)
0.483628 + 0.875274i \(0.339319\pi\)
\(60\) 26.1422 3.37495
\(61\) 6.72321 0.860819 0.430410 0.902634i \(-0.358369\pi\)
0.430410 + 0.902634i \(0.358369\pi\)
\(62\) 17.7029 2.24827
\(63\) 10.0617 1.26766
\(64\) 25.1527 3.14408
\(65\) 6.35473 0.788207
\(66\) −5.12987 −0.631443
\(67\) −7.29726 −0.891502 −0.445751 0.895157i \(-0.647063\pi\)
−0.445751 + 0.895157i \(0.647063\pi\)
\(68\) −36.8694 −4.47107
\(69\) 4.99735 0.601611
\(70\) 16.7469 2.00163
\(71\) 9.64369 1.14450 0.572248 0.820081i \(-0.306071\pi\)
0.572248 + 0.820081i \(0.306071\pi\)
\(72\) −29.0199 −3.42002
\(73\) 9.23105 1.08041 0.540206 0.841533i \(-0.318346\pi\)
0.540206 + 0.841533i \(0.318346\pi\)
\(74\) 23.9131 2.77984
\(75\) 2.84892 0.328965
\(76\) 31.0225 3.55852
\(77\) −2.39174 −0.272564
\(78\) −21.8397 −2.47286
\(79\) 8.16355 0.918471 0.459236 0.888315i \(-0.348123\pi\)
0.459236 + 0.888315i \(0.348123\pi\)
\(80\) −27.2996 −3.05219
\(81\) −8.36714 −0.929682
\(82\) 9.29899 1.02690
\(83\) 5.79023 0.635560 0.317780 0.948164i \(-0.397063\pi\)
0.317780 + 0.948164i \(0.397063\pi\)
\(84\) −41.8891 −4.57047
\(85\) 13.5377 1.46837
\(86\) −2.05841 −0.221964
\(87\) 9.15019 0.981004
\(88\) 6.89822 0.735353
\(89\) −4.81803 −0.510711 −0.255355 0.966847i \(-0.582192\pi\)
−0.255355 + 0.966847i \(0.582192\pi\)
\(90\) 17.0212 1.79420
\(91\) −10.1825 −1.06742
\(92\) −10.7347 −1.11917
\(93\) 16.2588 1.68596
\(94\) −1.39597 −0.143983
\(95\) −11.3908 −1.16867
\(96\) 48.6386 4.96416
\(97\) −16.2672 −1.65168 −0.825840 0.563904i \(-0.809299\pi\)
−0.825840 + 0.563904i \(0.809299\pi\)
\(98\) −7.85966 −0.793946
\(99\) −2.43092 −0.244317
\(100\) −6.11969 −0.611969
\(101\) −15.7220 −1.56440 −0.782199 0.623028i \(-0.785902\pi\)
−0.782199 + 0.623028i \(0.785902\pi\)
\(102\) −46.5258 −4.60674
\(103\) −3.71893 −0.366437 −0.183219 0.983072i \(-0.558652\pi\)
−0.183219 + 0.983072i \(0.558652\pi\)
\(104\) 29.3683 2.87980
\(105\) 15.3808 1.50101
\(106\) −1.21296 −0.117814
\(107\) −9.49161 −0.917588 −0.458794 0.888543i \(-0.651718\pi\)
−0.458794 + 0.888543i \(0.651718\pi\)
\(108\) −2.63474 −0.253528
\(109\) −8.64832 −0.828359 −0.414180 0.910195i \(-0.635931\pi\)
−0.414180 + 0.910195i \(0.635931\pi\)
\(110\) −4.04606 −0.385777
\(111\) 21.9625 2.08458
\(112\) 43.7436 4.13338
\(113\) 6.24207 0.587205 0.293602 0.955928i \(-0.405146\pi\)
0.293602 + 0.955928i \(0.405146\pi\)
\(114\) 39.1476 3.66651
\(115\) 3.94155 0.367551
\(116\) −19.6553 −1.82495
\(117\) −10.3493 −0.956797
\(118\) −20.1393 −1.85397
\(119\) −21.6921 −1.98851
\(120\) −44.3611 −4.04959
\(121\) −10.4222 −0.947468
\(122\) −18.2244 −1.64996
\(123\) 8.54045 0.770066
\(124\) −34.9252 −3.13637
\(125\) 12.0649 1.07912
\(126\) −27.2740 −2.42976
\(127\) −4.13447 −0.366875 −0.183437 0.983031i \(-0.558722\pi\)
−0.183437 + 0.983031i \(0.558722\pi\)
\(128\) −29.1066 −2.57268
\(129\) −1.89050 −0.166449
\(130\) −17.2256 −1.51078
\(131\) 9.10277 0.795313 0.397657 0.917534i \(-0.369824\pi\)
0.397657 + 0.917534i \(0.369824\pi\)
\(132\) 10.1205 0.880873
\(133\) 18.2521 1.58266
\(134\) 19.7805 1.70877
\(135\) 0.967420 0.0832622
\(136\) 62.5641 5.36483
\(137\) −5.28083 −0.451172 −0.225586 0.974223i \(-0.572430\pi\)
−0.225586 + 0.974223i \(0.572430\pi\)
\(138\) −13.5462 −1.15313
\(139\) −14.4174 −1.22287 −0.611434 0.791296i \(-0.709407\pi\)
−0.611434 + 0.791296i \(0.709407\pi\)
\(140\) −33.0390 −2.79231
\(141\) −1.28209 −0.107972
\(142\) −26.1409 −2.19370
\(143\) 2.46011 0.205725
\(144\) 44.4603 3.70502
\(145\) 7.21700 0.599339
\(146\) −25.0224 −2.07087
\(147\) −7.21853 −0.595374
\(148\) −47.1770 −3.87792
\(149\) −22.1086 −1.81120 −0.905602 0.424128i \(-0.860581\pi\)
−0.905602 + 0.424128i \(0.860581\pi\)
\(150\) −7.72250 −0.630539
\(151\) −1.78018 −0.144869 −0.0724346 0.997373i \(-0.523077\pi\)
−0.0724346 + 0.997373i \(0.523077\pi\)
\(152\) −52.6425 −4.26987
\(153\) −22.0475 −1.78244
\(154\) 6.48322 0.522433
\(155\) 12.8238 1.03003
\(156\) 43.0865 3.44968
\(157\) 2.24791 0.179402 0.0897012 0.995969i \(-0.471409\pi\)
0.0897012 + 0.995969i \(0.471409\pi\)
\(158\) −22.1287 −1.76047
\(159\) −1.11402 −0.0883475
\(160\) 38.3626 3.03283
\(161\) −6.31575 −0.497751
\(162\) 22.6806 1.78196
\(163\) 17.8027 1.39442 0.697208 0.716869i \(-0.254426\pi\)
0.697208 + 0.716869i \(0.254426\pi\)
\(164\) −18.3455 −1.43254
\(165\) −3.71602 −0.289292
\(166\) −15.6954 −1.21820
\(167\) 1.98721 0.153775 0.0768874 0.997040i \(-0.475502\pi\)
0.0768874 + 0.997040i \(0.475502\pi\)
\(168\) 71.0821 5.48410
\(169\) −2.52640 −0.194338
\(170\) −36.6962 −2.81447
\(171\) 18.5511 1.41864
\(172\) 4.06093 0.309643
\(173\) −11.9449 −0.908155 −0.454077 0.890962i \(-0.650031\pi\)
−0.454077 + 0.890962i \(0.650031\pi\)
\(174\) −24.8032 −1.88032
\(175\) −3.60052 −0.272174
\(176\) −10.5685 −0.796632
\(177\) −18.4965 −1.39028
\(178\) 13.0601 0.978898
\(179\) 8.79944 0.657701 0.328850 0.944382i \(-0.393339\pi\)
0.328850 + 0.944382i \(0.393339\pi\)
\(180\) −33.5803 −2.50293
\(181\) −14.8249 −1.10193 −0.550964 0.834529i \(-0.685740\pi\)
−0.550964 + 0.834529i \(0.685740\pi\)
\(182\) 27.6015 2.04596
\(183\) −16.7378 −1.23730
\(184\) 18.2158 1.34289
\(185\) 17.3224 1.27357
\(186\) −44.0724 −3.23155
\(187\) 5.24084 0.383249
\(188\) 2.75403 0.200858
\(189\) −1.55015 −0.112757
\(190\) 30.8767 2.24003
\(191\) 24.8645 1.79913 0.899567 0.436784i \(-0.143883\pi\)
0.899567 + 0.436784i \(0.143883\pi\)
\(192\) −62.6190 −4.51914
\(193\) −7.78597 −0.560447 −0.280223 0.959935i \(-0.590409\pi\)
−0.280223 + 0.959935i \(0.590409\pi\)
\(194\) 44.0950 3.16584
\(195\) −15.8205 −1.13293
\(196\) 15.5059 1.10757
\(197\) −9.63954 −0.686789 −0.343394 0.939191i \(-0.611577\pi\)
−0.343394 + 0.939191i \(0.611577\pi\)
\(198\) 6.58944 0.468291
\(199\) 4.71053 0.333920 0.166960 0.985964i \(-0.446605\pi\)
0.166960 + 0.985964i \(0.446605\pi\)
\(200\) 10.3846 0.734301
\(201\) 18.1669 1.28140
\(202\) 42.6172 2.99854
\(203\) −11.5642 −0.811647
\(204\) 91.7885 6.42648
\(205\) 6.73608 0.470468
\(206\) 10.0808 0.702364
\(207\) −6.41922 −0.446167
\(208\) −44.9941 −3.11978
\(209\) −4.40973 −0.305027
\(210\) −41.6923 −2.87704
\(211\) 18.0847 1.24500 0.622500 0.782620i \(-0.286117\pi\)
0.622500 + 0.782620i \(0.286117\pi\)
\(212\) 2.39300 0.164352
\(213\) −24.0085 −1.64504
\(214\) 25.7286 1.75877
\(215\) −1.49109 −0.101691
\(216\) 4.47092 0.304208
\(217\) −20.5482 −1.39490
\(218\) 23.4428 1.58775
\(219\) −22.9812 −1.55293
\(220\) 7.98228 0.538165
\(221\) 22.3122 1.50088
\(222\) −59.5331 −3.99560
\(223\) −25.4753 −1.70595 −0.852975 0.521952i \(-0.825204\pi\)
−0.852975 + 0.521952i \(0.825204\pi\)
\(224\) −61.4704 −4.10717
\(225\) −3.65951 −0.243967
\(226\) −16.9202 −1.12552
\(227\) −0.233345 −0.0154876 −0.00774381 0.999970i \(-0.502465\pi\)
−0.00774381 + 0.999970i \(0.502465\pi\)
\(228\) −77.2323 −5.11483
\(229\) 8.60966 0.568943 0.284471 0.958685i \(-0.408182\pi\)
0.284471 + 0.958685i \(0.408182\pi\)
\(230\) −10.6842 −0.704498
\(231\) 5.95437 0.391769
\(232\) 33.3533 2.18975
\(233\) −12.5073 −0.819379 −0.409690 0.912225i \(-0.634363\pi\)
−0.409690 + 0.912225i \(0.634363\pi\)
\(234\) 28.0537 1.83393
\(235\) −1.01122 −0.0659648
\(236\) 39.7318 2.58632
\(237\) −20.3236 −1.32016
\(238\) 58.8002 3.81145
\(239\) −23.1892 −1.49999 −0.749993 0.661446i \(-0.769943\pi\)
−0.749993 + 0.661446i \(0.769943\pi\)
\(240\) 67.9639 4.38705
\(241\) −26.2160 −1.68872 −0.844360 0.535777i \(-0.820019\pi\)
−0.844360 + 0.535777i \(0.820019\pi\)
\(242\) 28.2511 1.81605
\(243\) 22.3085 1.43109
\(244\) 35.9541 2.30172
\(245\) −5.69345 −0.363741
\(246\) −23.1504 −1.47601
\(247\) −18.7739 −1.19455
\(248\) 59.2650 3.76333
\(249\) −14.4151 −0.913521
\(250\) −32.7041 −2.06839
\(251\) 19.6395 1.23964 0.619818 0.784745i \(-0.287206\pi\)
0.619818 + 0.784745i \(0.287206\pi\)
\(252\) 53.8076 3.38956
\(253\) 1.52589 0.0959321
\(254\) 11.2072 0.703202
\(255\) −33.7028 −2.11055
\(256\) 28.5931 1.78707
\(257\) −3.96992 −0.247637 −0.123818 0.992305i \(-0.539514\pi\)
−0.123818 + 0.992305i \(0.539514\pi\)
\(258\) 5.12452 0.319039
\(259\) −27.7566 −1.72471
\(260\) 33.9835 2.10757
\(261\) −11.7536 −0.727533
\(262\) −24.6747 −1.52441
\(263\) −18.7296 −1.15492 −0.577459 0.816420i \(-0.695956\pi\)
−0.577459 + 0.816420i \(0.695956\pi\)
\(264\) −17.1735 −1.05696
\(265\) −0.878657 −0.0539755
\(266\) −49.4755 −3.03353
\(267\) 11.9948 0.734068
\(268\) −39.0239 −2.38377
\(269\) 25.4097 1.54926 0.774628 0.632417i \(-0.217937\pi\)
0.774628 + 0.632417i \(0.217937\pi\)
\(270\) −2.62236 −0.159592
\(271\) −0.902749 −0.0548381 −0.0274191 0.999624i \(-0.508729\pi\)
−0.0274191 + 0.999624i \(0.508729\pi\)
\(272\) −95.8522 −5.81189
\(273\) 25.3500 1.53425
\(274\) 14.3146 0.864777
\(275\) 0.869891 0.0524564
\(276\) 26.7246 1.60863
\(277\) 29.4004 1.76650 0.883251 0.468901i \(-0.155350\pi\)
0.883251 + 0.468901i \(0.155350\pi\)
\(278\) 39.0809 2.34391
\(279\) −20.8849 −1.25035
\(280\) 56.0643 3.35049
\(281\) 15.6373 0.932842 0.466421 0.884563i \(-0.345543\pi\)
0.466421 + 0.884563i \(0.345543\pi\)
\(282\) 3.47534 0.206953
\(283\) 1.67109 0.0993358 0.0496679 0.998766i \(-0.484184\pi\)
0.0496679 + 0.998766i \(0.484184\pi\)
\(284\) 51.5721 3.06024
\(285\) 28.3581 1.67979
\(286\) −6.66856 −0.394320
\(287\) −10.7936 −0.637125
\(288\) −62.4775 −3.68152
\(289\) 30.5324 1.79602
\(290\) −19.5629 −1.14878
\(291\) 40.4981 2.37404
\(292\) 49.3654 2.88889
\(293\) 11.3596 0.663634 0.331817 0.943344i \(-0.392338\pi\)
0.331817 + 0.943344i \(0.392338\pi\)
\(294\) 19.5671 1.14118
\(295\) −14.5887 −0.849386
\(296\) 80.0552 4.65311
\(297\) 0.374518 0.0217317
\(298\) 59.9291 3.47160
\(299\) 6.49629 0.375690
\(300\) 15.2353 0.879612
\(301\) 2.38925 0.137714
\(302\) 4.82550 0.277676
\(303\) 39.1409 2.24858
\(304\) 80.6515 4.62568
\(305\) −13.2016 −0.755920
\(306\) 59.7636 3.41646
\(307\) 31.5720 1.80191 0.900954 0.433915i \(-0.142868\pi\)
0.900954 + 0.433915i \(0.142868\pi\)
\(308\) −12.7904 −0.728802
\(309\) 9.25850 0.526698
\(310\) −34.7611 −1.97430
\(311\) −2.50240 −0.141898 −0.0709491 0.997480i \(-0.522603\pi\)
−0.0709491 + 0.997480i \(0.522603\pi\)
\(312\) −73.1141 −4.13927
\(313\) −25.0610 −1.41653 −0.708266 0.705945i \(-0.750522\pi\)
−0.708266 + 0.705945i \(0.750522\pi\)
\(314\) −6.09334 −0.343867
\(315\) −19.7570 −1.11318
\(316\) 43.6566 2.45588
\(317\) −2.84292 −0.159675 −0.0798373 0.996808i \(-0.525440\pi\)
−0.0798373 + 0.996808i \(0.525440\pi\)
\(318\) 3.01974 0.169339
\(319\) 2.79392 0.156430
\(320\) −49.3893 −2.76095
\(321\) 23.6299 1.31889
\(322\) 17.1199 0.954057
\(323\) −39.9945 −2.22535
\(324\) −44.7454 −2.48586
\(325\) 3.70345 0.205430
\(326\) −48.2573 −2.67273
\(327\) 21.5305 1.19064
\(328\) 31.1307 1.71891
\(329\) 1.62033 0.0893319
\(330\) 10.0729 0.554496
\(331\) −23.8977 −1.31354 −0.656769 0.754092i \(-0.728077\pi\)
−0.656769 + 0.754092i \(0.728077\pi\)
\(332\) 30.9647 1.69941
\(333\) −28.2113 −1.54597
\(334\) −5.38667 −0.294746
\(335\) 14.3288 0.782864
\(336\) −108.902 −5.94110
\(337\) −21.7396 −1.18423 −0.592116 0.805853i \(-0.701707\pi\)
−0.592116 + 0.805853i \(0.701707\pi\)
\(338\) 6.84824 0.372495
\(339\) −15.5400 −0.844017
\(340\) 72.3961 3.92623
\(341\) 4.96448 0.268842
\(342\) −50.2860 −2.71916
\(343\) −12.9015 −0.696618
\(344\) −6.89103 −0.371540
\(345\) −9.81271 −0.528298
\(346\) 32.3788 1.74069
\(347\) 25.5731 1.37284 0.686418 0.727207i \(-0.259182\pi\)
0.686418 + 0.727207i \(0.259182\pi\)
\(348\) 48.9330 2.62308
\(349\) −9.36695 −0.501401 −0.250701 0.968065i \(-0.580661\pi\)
−0.250701 + 0.968065i \(0.580661\pi\)
\(350\) 9.75984 0.521685
\(351\) 1.59446 0.0851061
\(352\) 14.8513 0.791579
\(353\) −13.2181 −0.703529 −0.351764 0.936089i \(-0.614418\pi\)
−0.351764 + 0.936089i \(0.614418\pi\)
\(354\) 50.1380 2.66480
\(355\) −18.9362 −1.00503
\(356\) −25.7657 −1.36558
\(357\) 54.0038 2.85818
\(358\) −23.8524 −1.26064
\(359\) 17.0003 0.897241 0.448620 0.893722i \(-0.351916\pi\)
0.448620 + 0.893722i \(0.351916\pi\)
\(360\) 56.9829 3.00326
\(361\) 14.6520 0.771158
\(362\) 40.1855 2.11211
\(363\) 25.9466 1.36184
\(364\) −54.4536 −2.85414
\(365\) −18.1259 −0.948754
\(366\) 45.3708 2.37157
\(367\) 6.73353 0.351487 0.175744 0.984436i \(-0.443767\pi\)
0.175744 + 0.984436i \(0.443767\pi\)
\(368\) −27.9078 −1.45479
\(369\) −10.9704 −0.571097
\(370\) −46.9553 −2.44109
\(371\) 1.40792 0.0730955
\(372\) 86.9483 4.50806
\(373\) 25.9401 1.34313 0.671564 0.740947i \(-0.265623\pi\)
0.671564 + 0.740947i \(0.265623\pi\)
\(374\) −14.2062 −0.734586
\(375\) −30.0363 −1.55107
\(376\) −4.67335 −0.241010
\(377\) 11.8948 0.612612
\(378\) 4.20195 0.216125
\(379\) −19.9717 −1.02588 −0.512940 0.858425i \(-0.671444\pi\)
−0.512940 + 0.858425i \(0.671444\pi\)
\(380\) −60.9152 −3.12488
\(381\) 10.2930 0.527326
\(382\) −67.3996 −3.44846
\(383\) −4.81142 −0.245852 −0.122926 0.992416i \(-0.539228\pi\)
−0.122926 + 0.992416i \(0.539228\pi\)
\(384\) 72.4625 3.69784
\(385\) 4.69637 0.239349
\(386\) 21.1052 1.07423
\(387\) 2.42839 0.123442
\(388\) −86.9928 −4.41639
\(389\) 19.0592 0.966342 0.483171 0.875526i \(-0.339485\pi\)
0.483171 + 0.875526i \(0.339485\pi\)
\(390\) 42.8841 2.17152
\(391\) 13.8392 0.699881
\(392\) −26.3122 −1.32897
\(393\) −22.6619 −1.14314
\(394\) 26.1297 1.31639
\(395\) −16.0298 −0.806546
\(396\) −13.0000 −0.653274
\(397\) 19.8208 0.994775 0.497388 0.867528i \(-0.334293\pi\)
0.497388 + 0.867528i \(0.334293\pi\)
\(398\) −12.7687 −0.640037
\(399\) −45.4396 −2.27483
\(400\) −15.9098 −0.795492
\(401\) 10.1980 0.509265 0.254633 0.967038i \(-0.418045\pi\)
0.254633 + 0.967038i \(0.418045\pi\)
\(402\) −49.2447 −2.45610
\(403\) 21.1356 1.05284
\(404\) −84.0774 −4.18301
\(405\) 16.4296 0.816391
\(406\) 31.3467 1.55571
\(407\) 6.70603 0.332405
\(408\) −155.757 −7.71112
\(409\) 38.2717 1.89241 0.946206 0.323566i \(-0.104882\pi\)
0.946206 + 0.323566i \(0.104882\pi\)
\(410\) −18.2593 −0.901763
\(411\) 13.1469 0.648490
\(412\) −19.8879 −0.979808
\(413\) 23.3762 1.15027
\(414\) 17.4004 0.855184
\(415\) −11.3696 −0.558111
\(416\) 63.2277 3.09999
\(417\) 35.8929 1.75768
\(418\) 11.9533 0.584657
\(419\) 6.96572 0.340298 0.170149 0.985418i \(-0.445575\pi\)
0.170149 + 0.985418i \(0.445575\pi\)
\(420\) 82.2526 4.01352
\(421\) −27.2935 −1.33020 −0.665101 0.746753i \(-0.731612\pi\)
−0.665101 + 0.746753i \(0.731612\pi\)
\(422\) −49.0216 −2.38634
\(423\) 1.64688 0.0800741
\(424\) −4.06071 −0.197205
\(425\) 7.88956 0.382700
\(426\) 65.0793 3.15310
\(427\) 21.1536 1.02369
\(428\) −50.7588 −2.45352
\(429\) −6.12459 −0.295698
\(430\) 4.04185 0.194915
\(431\) −2.24443 −0.108111 −0.0540553 0.998538i \(-0.517215\pi\)
−0.0540553 + 0.998538i \(0.517215\pi\)
\(432\) −6.84973 −0.329558
\(433\) 31.4301 1.51044 0.755218 0.655474i \(-0.227531\pi\)
0.755218 + 0.655474i \(0.227531\pi\)
\(434\) 55.6995 2.67366
\(435\) −17.9671 −0.861459
\(436\) −46.2491 −2.21493
\(437\) −11.6446 −0.557035
\(438\) 62.2946 2.97655
\(439\) −8.44635 −0.403122 −0.201561 0.979476i \(-0.564601\pi\)
−0.201561 + 0.979476i \(0.564601\pi\)
\(440\) −13.5452 −0.645743
\(441\) 9.27238 0.441542
\(442\) −60.4811 −2.87679
\(443\) −5.82437 −0.276724 −0.138362 0.990382i \(-0.544184\pi\)
−0.138362 + 0.990382i \(0.544184\pi\)
\(444\) 117.450 5.57392
\(445\) 9.46060 0.448476
\(446\) 69.0551 3.26985
\(447\) 55.0406 2.60333
\(448\) 79.1391 3.73897
\(449\) −8.16761 −0.385453 −0.192727 0.981252i \(-0.561733\pi\)
−0.192727 + 0.981252i \(0.561733\pi\)
\(450\) 9.91974 0.467621
\(451\) 2.60774 0.122794
\(452\) 33.3811 1.57011
\(453\) 4.43187 0.208227
\(454\) 0.632521 0.0296857
\(455\) 19.9942 0.937343
\(456\) 131.056 6.13728
\(457\) −1.13934 −0.0532962 −0.0266481 0.999645i \(-0.508483\pi\)
−0.0266481 + 0.999645i \(0.508483\pi\)
\(458\) −23.3380 −1.09051
\(459\) 3.39673 0.158546
\(460\) 21.0784 0.982786
\(461\) 40.5258 1.88748 0.943738 0.330693i \(-0.107283\pi\)
0.943738 + 0.330693i \(0.107283\pi\)
\(462\) −16.1404 −0.750918
\(463\) 7.51253 0.349137 0.174568 0.984645i \(-0.444147\pi\)
0.174568 + 0.984645i \(0.444147\pi\)
\(464\) −51.0993 −2.37223
\(465\) −31.9255 −1.48051
\(466\) 33.9032 1.57053
\(467\) 41.5412 1.92230 0.961148 0.276033i \(-0.0890198\pi\)
0.961148 + 0.276033i \(0.0890198\pi\)
\(468\) −55.3457 −2.55836
\(469\) −22.9597 −1.06018
\(470\) 2.74109 0.126437
\(471\) −5.59629 −0.257864
\(472\) −67.4214 −3.10332
\(473\) −0.577245 −0.0265418
\(474\) 55.0907 2.53040
\(475\) −6.63841 −0.304591
\(476\) −116.004 −5.31704
\(477\) 1.43099 0.0655204
\(478\) 62.8584 2.87508
\(479\) 9.40166 0.429573 0.214786 0.976661i \(-0.431094\pi\)
0.214786 + 0.976661i \(0.431094\pi\)
\(480\) −95.5059 −4.35923
\(481\) 28.5500 1.30177
\(482\) 71.0630 3.23683
\(483\) 15.7234 0.715440
\(484\) −55.7351 −2.53341
\(485\) 31.9419 1.45041
\(486\) −60.4711 −2.74303
\(487\) 27.4134 1.24222 0.621110 0.783723i \(-0.286682\pi\)
0.621110 + 0.783723i \(0.286682\pi\)
\(488\) −61.0109 −2.76183
\(489\) −44.3209 −2.00426
\(490\) 15.4331 0.697196
\(491\) −14.0153 −0.632502 −0.316251 0.948676i \(-0.602424\pi\)
−0.316251 + 0.948676i \(0.602424\pi\)
\(492\) 45.6722 2.05906
\(493\) 25.3398 1.14125
\(494\) 50.8898 2.28964
\(495\) 4.77332 0.214545
\(496\) −90.7976 −4.07693
\(497\) 30.3424 1.36104
\(498\) 39.0747 1.75098
\(499\) −21.9365 −0.982013 −0.491006 0.871156i \(-0.663371\pi\)
−0.491006 + 0.871156i \(0.663371\pi\)
\(500\) 64.5203 2.88543
\(501\) −4.94727 −0.221028
\(502\) −53.2364 −2.37606
\(503\) −22.6862 −1.01153 −0.505764 0.862672i \(-0.668789\pi\)
−0.505764 + 0.862672i \(0.668789\pi\)
\(504\) −91.3067 −4.06712
\(505\) 30.8714 1.37376
\(506\) −4.13620 −0.183877
\(507\) 6.28962 0.279332
\(508\) −22.1101 −0.980977
\(509\) 2.58248 0.114467 0.0572333 0.998361i \(-0.481772\pi\)
0.0572333 + 0.998361i \(0.481772\pi\)
\(510\) 91.3573 4.04537
\(511\) 29.0441 1.28484
\(512\) −19.2934 −0.852655
\(513\) −2.85806 −0.126186
\(514\) 10.7612 0.474655
\(515\) 7.30243 0.321783
\(516\) −10.1099 −0.445064
\(517\) −0.391475 −0.0172171
\(518\) 75.2390 3.30581
\(519\) 29.7376 1.30533
\(520\) −57.6670 −2.52887
\(521\) −29.8975 −1.30983 −0.654916 0.755701i \(-0.727296\pi\)
−0.654916 + 0.755701i \(0.727296\pi\)
\(522\) 31.8603 1.39449
\(523\) 3.66846 0.160411 0.0802053 0.996778i \(-0.474442\pi\)
0.0802053 + 0.996778i \(0.474442\pi\)
\(524\) 48.6794 2.12657
\(525\) 8.96371 0.391208
\(526\) 50.7699 2.21367
\(527\) 45.0258 1.96136
\(528\) 26.3109 1.14504
\(529\) −18.9706 −0.824811
\(530\) 2.38175 0.103457
\(531\) 23.7592 1.03106
\(532\) 97.6077 4.23183
\(533\) 11.1021 0.480887
\(534\) −32.5139 −1.40702
\(535\) 18.6375 0.805771
\(536\) 66.2202 2.86028
\(537\) −21.9067 −0.945345
\(538\) −68.8774 −2.96952
\(539\) −2.20411 −0.0949377
\(540\) 5.17352 0.222633
\(541\) 33.8529 1.45545 0.727724 0.685870i \(-0.240578\pi\)
0.727724 + 0.685870i \(0.240578\pi\)
\(542\) 2.44706 0.105110
\(543\) 36.9075 1.58385
\(544\) 134.696 5.77503
\(545\) 16.9817 0.727416
\(546\) −68.7155 −2.94075
\(547\) −20.4548 −0.874583 −0.437292 0.899320i \(-0.644062\pi\)
−0.437292 + 0.899320i \(0.644062\pi\)
\(548\) −28.2406 −1.20638
\(549\) 21.5002 0.917604
\(550\) −2.35799 −0.100545
\(551\) −21.3213 −0.908317
\(552\) −45.3493 −1.93019
\(553\) 25.6854 1.09225
\(554\) −79.6950 −3.38592
\(555\) −43.1251 −1.83056
\(556\) −77.1007 −3.26980
\(557\) 9.30087 0.394091 0.197045 0.980394i \(-0.436865\pi\)
0.197045 + 0.980394i \(0.436865\pi\)
\(558\) 56.6121 2.39658
\(559\) −2.45755 −0.103943
\(560\) −85.8941 −3.62969
\(561\) −13.0474 −0.550861
\(562\) −42.3876 −1.78801
\(563\) −41.2380 −1.73797 −0.868987 0.494834i \(-0.835229\pi\)
−0.868987 + 0.494834i \(0.835229\pi\)
\(564\) −6.85632 −0.288703
\(565\) −12.2568 −0.515648
\(566\) −4.52977 −0.190400
\(567\) −26.3260 −1.10559
\(568\) −87.5133 −3.67198
\(569\) 4.76017 0.199557 0.0997784 0.995010i \(-0.468187\pi\)
0.0997784 + 0.995010i \(0.468187\pi\)
\(570\) −76.8695 −3.21971
\(571\) 7.05451 0.295222 0.147611 0.989045i \(-0.452842\pi\)
0.147611 + 0.989045i \(0.452842\pi\)
\(572\) 13.1561 0.550083
\(573\) −61.9016 −2.58598
\(574\) 29.2579 1.22120
\(575\) 2.29708 0.0957948
\(576\) 80.4357 3.35149
\(577\) 16.8988 0.703507 0.351754 0.936093i \(-0.385586\pi\)
0.351754 + 0.936093i \(0.385586\pi\)
\(578\) −82.7633 −3.44250
\(579\) 19.3836 0.805556
\(580\) 38.5947 1.60256
\(581\) 18.2181 0.755814
\(582\) −109.777 −4.55040
\(583\) −0.340155 −0.0140878
\(584\) −83.7687 −3.46637
\(585\) 20.3218 0.840202
\(586\) −30.7921 −1.27201
\(587\) 19.2572 0.794829 0.397415 0.917639i \(-0.369908\pi\)
0.397415 + 0.917639i \(0.369908\pi\)
\(588\) −38.6029 −1.59196
\(589\) −37.8855 −1.56104
\(590\) 39.5452 1.62805
\(591\) 23.9982 0.987154
\(592\) −122.650 −5.04087
\(593\) −6.81249 −0.279756 −0.139878 0.990169i \(-0.544671\pi\)
−0.139878 + 0.990169i \(0.544671\pi\)
\(594\) −1.01520 −0.0416540
\(595\) 42.5942 1.74619
\(596\) −118.231 −4.84294
\(597\) −11.7271 −0.479960
\(598\) −17.6093 −0.720099
\(599\) −10.6354 −0.434551 −0.217276 0.976110i \(-0.569717\pi\)
−0.217276 + 0.976110i \(0.569717\pi\)
\(600\) −25.8530 −1.05545
\(601\) 8.95573 0.365312 0.182656 0.983177i \(-0.441531\pi\)
0.182656 + 0.983177i \(0.441531\pi\)
\(602\) −6.47646 −0.263961
\(603\) −23.3359 −0.950311
\(604\) −9.51998 −0.387363
\(605\) 20.4647 0.832010
\(606\) −106.098 −4.30994
\(607\) 32.7248 1.32826 0.664129 0.747618i \(-0.268803\pi\)
0.664129 + 0.747618i \(0.268803\pi\)
\(608\) −113.335 −4.59635
\(609\) 28.7897 1.16662
\(610\) 35.7852 1.44890
\(611\) −1.66665 −0.0674256
\(612\) −117.905 −4.76601
\(613\) 4.47171 0.180611 0.0903053 0.995914i \(-0.471216\pi\)
0.0903053 + 0.995914i \(0.471216\pi\)
\(614\) −85.5813 −3.45378
\(615\) −16.7699 −0.676226
\(616\) 21.7042 0.874489
\(617\) −43.3472 −1.74509 −0.872546 0.488533i \(-0.837532\pi\)
−0.872546 + 0.488533i \(0.837532\pi\)
\(618\) −25.0968 −1.00954
\(619\) 20.4229 0.820865 0.410433 0.911891i \(-0.365378\pi\)
0.410433 + 0.911891i \(0.365378\pi\)
\(620\) 68.5784 2.75418
\(621\) 0.988972 0.0396861
\(622\) 6.78320 0.271982
\(623\) −15.1592 −0.607342
\(624\) 112.015 4.48420
\(625\) −17.9687 −0.718749
\(626\) 67.9323 2.71512
\(627\) 10.9783 0.438430
\(628\) 12.0212 0.479700
\(629\) 60.8210 2.42509
\(630\) 53.5548 2.13367
\(631\) 41.5432 1.65381 0.826905 0.562342i \(-0.190100\pi\)
0.826905 + 0.562342i \(0.190100\pi\)
\(632\) −74.0815 −2.94680
\(633\) −45.0228 −1.78950
\(634\) 7.70624 0.306054
\(635\) 8.11836 0.322167
\(636\) −5.95750 −0.236230
\(637\) −9.38371 −0.371796
\(638\) −7.57342 −0.299834
\(639\) 30.8396 1.21999
\(640\) 57.1531 2.25917
\(641\) −14.9749 −0.591472 −0.295736 0.955270i \(-0.595565\pi\)
−0.295736 + 0.955270i \(0.595565\pi\)
\(642\) −64.0530 −2.52797
\(643\) −30.8154 −1.21524 −0.607620 0.794228i \(-0.707876\pi\)
−0.607620 + 0.794228i \(0.707876\pi\)
\(644\) −33.7751 −1.33092
\(645\) 3.71214 0.146166
\(646\) 108.412 4.26541
\(647\) 16.6102 0.653016 0.326508 0.945195i \(-0.394128\pi\)
0.326508 + 0.945195i \(0.394128\pi\)
\(648\) 75.9290 2.98277
\(649\) −5.64773 −0.221693
\(650\) −10.0388 −0.393756
\(651\) 51.1560 2.00496
\(652\) 95.2044 3.72849
\(653\) 37.4975 1.46739 0.733695 0.679479i \(-0.237794\pi\)
0.733695 + 0.679479i \(0.237794\pi\)
\(654\) −58.3622 −2.28214
\(655\) −17.8740 −0.698396
\(656\) −47.6942 −1.86215
\(657\) 29.5200 1.15168
\(658\) −4.39220 −0.171226
\(659\) −35.3137 −1.37563 −0.687814 0.725887i \(-0.741429\pi\)
−0.687814 + 0.725887i \(0.741429\pi\)
\(660\) −19.8723 −0.773530
\(661\) −36.2937 −1.41166 −0.705830 0.708381i \(-0.749426\pi\)
−0.705830 + 0.708381i \(0.749426\pi\)
\(662\) 64.7789 2.51770
\(663\) −55.5476 −2.15729
\(664\) −52.5444 −2.03912
\(665\) −35.8395 −1.38979
\(666\) 76.4717 2.96322
\(667\) 7.37778 0.285669
\(668\) 10.6271 0.411175
\(669\) 63.4221 2.45204
\(670\) −38.8406 −1.50054
\(671\) −5.11074 −0.197298
\(672\) 153.034 5.90342
\(673\) 40.6468 1.56682 0.783409 0.621507i \(-0.213479\pi\)
0.783409 + 0.621507i \(0.213479\pi\)
\(674\) 58.9290 2.26986
\(675\) 0.563799 0.0217006
\(676\) −13.5106 −0.519637
\(677\) 17.3927 0.668455 0.334227 0.942492i \(-0.391525\pi\)
0.334227 + 0.942492i \(0.391525\pi\)
\(678\) 42.1239 1.61776
\(679\) −51.1822 −1.96419
\(680\) −122.850 −4.71107
\(681\) 0.580925 0.0222611
\(682\) −13.4571 −0.515299
\(683\) −33.4432 −1.27967 −0.639834 0.768513i \(-0.720997\pi\)
−0.639834 + 0.768513i \(0.720997\pi\)
\(684\) 99.2068 3.79327
\(685\) 10.3693 0.396192
\(686\) 34.9719 1.33523
\(687\) −21.4343 −0.817768
\(688\) 10.5575 0.402501
\(689\) −1.44817 −0.0551708
\(690\) 26.5990 1.01261
\(691\) −1.05092 −0.0399787 −0.0199894 0.999800i \(-0.506363\pi\)
−0.0199894 + 0.999800i \(0.506363\pi\)
\(692\) −63.8784 −2.42829
\(693\) −7.64854 −0.290544
\(694\) −69.3203 −2.63136
\(695\) 28.3097 1.07385
\(696\) −83.0350 −3.14743
\(697\) 23.6512 0.895853
\(698\) 25.3907 0.961054
\(699\) 31.1376 1.17773
\(700\) −19.2547 −0.727759
\(701\) −35.0393 −1.32342 −0.661709 0.749761i \(-0.730168\pi\)
−0.661709 + 0.749761i \(0.730168\pi\)
\(702\) −4.32207 −0.163126
\(703\) −51.1757 −1.93013
\(704\) −19.1201 −0.720617
\(705\) 2.51749 0.0948143
\(706\) 35.8300 1.34848
\(707\) −49.4670 −1.86040
\(708\) −98.9147 −3.71744
\(709\) 15.5934 0.585624 0.292812 0.956170i \(-0.405409\pi\)
0.292812 + 0.956170i \(0.405409\pi\)
\(710\) 51.3298 1.92637
\(711\) 26.1062 0.979059
\(712\) 43.7221 1.63855
\(713\) 13.1095 0.490953
\(714\) −146.387 −5.47838
\(715\) −4.83063 −0.180655
\(716\) 47.0572 1.75861
\(717\) 57.7309 2.15600
\(718\) −46.0822 −1.71977
\(719\) 44.5927 1.66303 0.831513 0.555505i \(-0.187475\pi\)
0.831513 + 0.555505i \(0.187475\pi\)
\(720\) −87.3013 −3.25353
\(721\) −11.7011 −0.435770
\(722\) −39.7168 −1.47811
\(723\) 65.2662 2.42728
\(724\) −79.2800 −2.94642
\(725\) 4.20597 0.156206
\(726\) −70.3326 −2.61029
\(727\) −43.3424 −1.60748 −0.803741 0.594980i \(-0.797160\pi\)
−0.803741 + 0.594980i \(0.797160\pi\)
\(728\) 92.4030 3.42468
\(729\) −30.4369 −1.12729
\(730\) 49.1335 1.81851
\(731\) −5.23538 −0.193638
\(732\) −89.5098 −3.30838
\(733\) 32.9733 1.21790 0.608949 0.793209i \(-0.291591\pi\)
0.608949 + 0.793209i \(0.291591\pi\)
\(734\) −18.2524 −0.673708
\(735\) 14.1742 0.522822
\(736\) 39.2172 1.44557
\(737\) 5.54710 0.204330
\(738\) 29.7372 1.09464
\(739\) 33.4101 1.22901 0.614505 0.788913i \(-0.289356\pi\)
0.614505 + 0.788913i \(0.289356\pi\)
\(740\) 92.6358 3.40536
\(741\) 46.7386 1.71699
\(742\) −3.81641 −0.140105
\(743\) −14.4451 −0.529940 −0.264970 0.964257i \(-0.585362\pi\)
−0.264970 + 0.964257i \(0.585362\pi\)
\(744\) −147.544 −5.40921
\(745\) 43.4120 1.59049
\(746\) −70.3152 −2.57442
\(747\) 18.5166 0.677486
\(748\) 28.0267 1.02476
\(749\) −29.8639 −1.09120
\(750\) 81.4187 2.97299
\(751\) 13.2742 0.484383 0.242191 0.970229i \(-0.422134\pi\)
0.242191 + 0.970229i \(0.422134\pi\)
\(752\) 7.15986 0.261093
\(753\) −48.8938 −1.78179
\(754\) −32.2428 −1.17421
\(755\) 3.49554 0.127216
\(756\) −8.28981 −0.301497
\(757\) −8.48669 −0.308454 −0.154227 0.988035i \(-0.549289\pi\)
−0.154227 + 0.988035i \(0.549289\pi\)
\(758\) 54.1369 1.96634
\(759\) −3.79880 −0.137888
\(760\) 103.368 3.74954
\(761\) −5.90542 −0.214071 −0.107036 0.994255i \(-0.534136\pi\)
−0.107036 + 0.994255i \(0.534136\pi\)
\(762\) −27.9010 −1.01074
\(763\) −27.2107 −0.985092
\(764\) 132.969 4.81066
\(765\) 43.2921 1.56523
\(766\) 13.0422 0.471234
\(767\) −24.0445 −0.868196
\(768\) −71.1841 −2.56864
\(769\) 17.0472 0.614736 0.307368 0.951591i \(-0.400552\pi\)
0.307368 + 0.951591i \(0.400552\pi\)
\(770\) −12.7303 −0.458770
\(771\) 9.88335 0.355940
\(772\) −41.6375 −1.49857
\(773\) −39.5804 −1.42361 −0.711804 0.702378i \(-0.752122\pi\)
−0.711804 + 0.702378i \(0.752122\pi\)
\(774\) −6.58257 −0.236606
\(775\) 7.47353 0.268457
\(776\) 147.619 5.29922
\(777\) 69.1016 2.47901
\(778\) −51.6634 −1.85222
\(779\) −19.9005 −0.713009
\(780\) −84.6039 −3.02931
\(781\) −7.33078 −0.262316
\(782\) −37.5137 −1.34149
\(783\) 1.81081 0.0647132
\(784\) 40.3119 1.43971
\(785\) −4.41395 −0.157541
\(786\) 61.4290 2.19110
\(787\) −8.89384 −0.317031 −0.158516 0.987356i \(-0.550671\pi\)
−0.158516 + 0.987356i \(0.550671\pi\)
\(788\) −51.5499 −1.83639
\(789\) 46.6285 1.66002
\(790\) 43.4515 1.54594
\(791\) 19.6397 0.698309
\(792\) 22.0598 0.783862
\(793\) −21.7583 −0.772660
\(794\) −53.7276 −1.90672
\(795\) 2.18747 0.0775815
\(796\) 25.1907 0.892862
\(797\) 42.4359 1.50316 0.751579 0.659644i \(-0.229293\pi\)
0.751579 + 0.659644i \(0.229293\pi\)
\(798\) 123.172 4.36024
\(799\) −3.55052 −0.125608
\(800\) 22.3572 0.790446
\(801\) −15.4076 −0.544400
\(802\) −27.6435 −0.976127
\(803\) −7.01710 −0.247628
\(804\) 97.1523 3.42630
\(805\) 12.4015 0.437095
\(806\) −57.2918 −2.01802
\(807\) −63.2589 −2.22682
\(808\) 142.672 5.01918
\(809\) 16.8759 0.593325 0.296663 0.954982i \(-0.404126\pi\)
0.296663 + 0.954982i \(0.404126\pi\)
\(810\) −44.5352 −1.56481
\(811\) 17.6841 0.620974 0.310487 0.950578i \(-0.399508\pi\)
0.310487 + 0.950578i \(0.399508\pi\)
\(812\) −61.8424 −2.17024
\(813\) 2.24745 0.0788214
\(814\) −18.1779 −0.637134
\(815\) −34.9570 −1.22449
\(816\) 238.630 8.35370
\(817\) 4.40513 0.154116
\(818\) −103.742 −3.62725
\(819\) −32.5627 −1.13783
\(820\) 36.0229 1.25797
\(821\) 46.9484 1.63851 0.819255 0.573429i \(-0.194387\pi\)
0.819255 + 0.573429i \(0.194387\pi\)
\(822\) −35.6370 −1.24298
\(823\) 37.9695 1.32354 0.661768 0.749709i \(-0.269807\pi\)
0.661768 + 0.749709i \(0.269807\pi\)
\(824\) 33.7481 1.17567
\(825\) −2.16564 −0.0753981
\(826\) −63.3653 −2.20476
\(827\) −3.82507 −0.133011 −0.0665053 0.997786i \(-0.521185\pi\)
−0.0665053 + 0.997786i \(0.521185\pi\)
\(828\) −34.3284 −1.19300
\(829\) 29.6152 1.02858 0.514290 0.857616i \(-0.328056\pi\)
0.514290 + 0.857616i \(0.328056\pi\)
\(830\) 30.8192 1.06975
\(831\) −73.1941 −2.53908
\(832\) −81.4014 −2.82209
\(833\) −19.9904 −0.692626
\(834\) −97.2941 −3.36902
\(835\) −3.90204 −0.135036
\(836\) −23.5821 −0.815606
\(837\) 3.21761 0.111217
\(838\) −18.8818 −0.652261
\(839\) 0.643477 0.0222153 0.0111076 0.999938i \(-0.496464\pi\)
0.0111076 + 0.999938i \(0.496464\pi\)
\(840\) −139.575 −4.81581
\(841\) −15.4912 −0.534180
\(842\) 73.9837 2.54965
\(843\) −38.9299 −1.34082
\(844\) 96.7123 3.32898
\(845\) 4.96079 0.170656
\(846\) −4.46416 −0.153481
\(847\) −32.7917 −1.12674
\(848\) 6.22125 0.213639
\(849\) −4.16027 −0.142780
\(850\) −21.3860 −0.733535
\(851\) 17.7083 0.607032
\(852\) −128.392 −4.39863
\(853\) 42.4084 1.45204 0.726018 0.687676i \(-0.241369\pi\)
0.726018 + 0.687676i \(0.241369\pi\)
\(854\) −57.3405 −1.96215
\(855\) −36.4266 −1.24576
\(856\) 86.1332 2.94397
\(857\) −4.59827 −0.157074 −0.0785370 0.996911i \(-0.525025\pi\)
−0.0785370 + 0.996911i \(0.525025\pi\)
\(858\) 16.6018 0.566775
\(859\) 2.47609 0.0844831 0.0422415 0.999107i \(-0.486550\pi\)
0.0422415 + 0.999107i \(0.486550\pi\)
\(860\) −7.97396 −0.271910
\(861\) 26.8712 0.915769
\(862\) 6.08392 0.207219
\(863\) 28.8473 0.981972 0.490986 0.871167i \(-0.336637\pi\)
0.490986 + 0.871167i \(0.336637\pi\)
\(864\) 9.62554 0.327468
\(865\) 23.4548 0.797487
\(866\) −85.1969 −2.89511
\(867\) −76.0121 −2.58151
\(868\) −109.887 −3.72980
\(869\) −6.20563 −0.210511
\(870\) 48.7031 1.65119
\(871\) 23.6161 0.800200
\(872\) 78.4807 2.65769
\(873\) −52.0208 −1.76064
\(874\) 31.5646 1.06769
\(875\) 37.9605 1.28330
\(876\) −122.898 −4.15234
\(877\) −28.1144 −0.949355 −0.474678 0.880160i \(-0.657435\pi\)
−0.474678 + 0.880160i \(0.657435\pi\)
\(878\) 22.8953 0.772679
\(879\) −28.2803 −0.953872
\(880\) 20.7521 0.699554
\(881\) −25.4031 −0.855853 −0.427927 0.903814i \(-0.640756\pi\)
−0.427927 + 0.903814i \(0.640756\pi\)
\(882\) −25.1344 −0.846319
\(883\) 18.6923 0.629046 0.314523 0.949250i \(-0.398155\pi\)
0.314523 + 0.949250i \(0.398155\pi\)
\(884\) 119.320 4.01317
\(885\) 36.3194 1.22086
\(886\) 15.7880 0.530407
\(887\) 1.33166 0.0447129 0.0223565 0.999750i \(-0.492883\pi\)
0.0223565 + 0.999750i \(0.492883\pi\)
\(888\) −199.302 −6.68814
\(889\) −13.0085 −0.436290
\(890\) −25.6446 −0.859609
\(891\) 6.36039 0.213081
\(892\) −136.235 −4.56150
\(893\) 2.98747 0.0999717
\(894\) −149.197 −4.98990
\(895\) −17.2784 −0.577554
\(896\) −91.5794 −3.05945
\(897\) −16.1729 −0.539998
\(898\) 22.1397 0.738812
\(899\) 24.0035 0.800563
\(900\) −19.5702 −0.652339
\(901\) −3.08507 −0.102779
\(902\) −7.06874 −0.235363
\(903\) −5.94816 −0.197943
\(904\) −56.6447 −1.88398
\(905\) 29.1099 0.967647
\(906\) −12.0134 −0.399117
\(907\) −2.78524 −0.0924825 −0.0462412 0.998930i \(-0.514724\pi\)
−0.0462412 + 0.998930i \(0.514724\pi\)
\(908\) −1.24787 −0.0414120
\(909\) −50.2774 −1.66760
\(910\) −54.1978 −1.79664
\(911\) −6.16899 −0.204388 −0.102194 0.994765i \(-0.532586\pi\)
−0.102194 + 0.994765i \(0.532586\pi\)
\(912\) −200.787 −6.64871
\(913\) −4.40152 −0.145669
\(914\) 3.08839 0.102155
\(915\) 32.8661 1.08652
\(916\) 46.0424 1.52128
\(917\) 28.6405 0.945793
\(918\) −9.20742 −0.303890
\(919\) −16.8411 −0.555536 −0.277768 0.960648i \(-0.589595\pi\)
−0.277768 + 0.960648i \(0.589595\pi\)
\(920\) −35.7682 −1.17924
\(921\) −78.6003 −2.58997
\(922\) −109.852 −3.61779
\(923\) −31.2098 −1.02728
\(924\) 31.8425 1.04754
\(925\) 10.0953 0.331930
\(926\) −20.3640 −0.669203
\(927\) −11.8928 −0.390610
\(928\) 71.8070 2.35718
\(929\) −15.4258 −0.506104 −0.253052 0.967453i \(-0.581434\pi\)
−0.253052 + 0.967453i \(0.581434\pi\)
\(930\) 86.5398 2.83775
\(931\) 16.8202 0.551261
\(932\) −66.8858 −2.19092
\(933\) 6.22988 0.203957
\(934\) −112.605 −3.68453
\(935\) −10.2908 −0.336546
\(936\) 93.9168 3.06977
\(937\) 12.0587 0.393939 0.196969 0.980410i \(-0.436890\pi\)
0.196969 + 0.980410i \(0.436890\pi\)
\(938\) 62.2363 2.03209
\(939\) 62.3909 2.03605
\(940\) −5.40776 −0.176382
\(941\) 53.9637 1.75917 0.879583 0.475745i \(-0.157821\pi\)
0.879583 + 0.475745i \(0.157821\pi\)
\(942\) 15.1697 0.494256
\(943\) 6.88614 0.224244
\(944\) 103.294 3.36193
\(945\) 3.04384 0.0990162
\(946\) 1.56472 0.0508735
\(947\) 23.6666 0.769060 0.384530 0.923112i \(-0.374364\pi\)
0.384530 + 0.923112i \(0.374364\pi\)
\(948\) −108.686 −3.52995
\(949\) −29.8744 −0.969764
\(950\) 17.9946 0.583820
\(951\) 7.07763 0.229508
\(952\) 196.849 6.37990
\(953\) 0.431503 0.0139777 0.00698887 0.999976i \(-0.497775\pi\)
0.00698887 + 0.999976i \(0.497775\pi\)
\(954\) −3.87894 −0.125585
\(955\) −48.8235 −1.57989
\(956\) −124.010 −4.01078
\(957\) −6.95564 −0.224844
\(958\) −25.4848 −0.823378
\(959\) −16.6153 −0.536537
\(960\) 122.958 3.96844
\(961\) 11.6515 0.375855
\(962\) −77.3899 −2.49515
\(963\) −30.3532 −0.978118
\(964\) −140.197 −4.51543
\(965\) 15.2884 0.492151
\(966\) −42.6211 −1.37131
\(967\) −17.6874 −0.568787 −0.284394 0.958708i \(-0.591792\pi\)
−0.284394 + 0.958708i \(0.591792\pi\)
\(968\) 94.5776 3.03984
\(969\) 99.5686 3.19860
\(970\) −86.5841 −2.78005
\(971\) −59.2061 −1.90001 −0.950007 0.312227i \(-0.898925\pi\)
−0.950007 + 0.312227i \(0.898925\pi\)
\(972\) 119.300 3.82656
\(973\) −45.3622 −1.45424
\(974\) −74.3088 −2.38101
\(975\) −9.21995 −0.295275
\(976\) 93.4726 2.99198
\(977\) 10.2612 0.328284 0.164142 0.986437i \(-0.447514\pi\)
0.164142 + 0.986437i \(0.447514\pi\)
\(978\) 120.139 3.84163
\(979\) 3.66249 0.117054
\(980\) −30.4472 −0.972599
\(981\) −27.6565 −0.883003
\(982\) 37.9909 1.21234
\(983\) 42.1307 1.34376 0.671881 0.740659i \(-0.265487\pi\)
0.671881 + 0.740659i \(0.265487\pi\)
\(984\) −77.5017 −2.47066
\(985\) 18.9280 0.603097
\(986\) −68.6878 −2.18747
\(987\) −4.03392 −0.128401
\(988\) −100.398 −3.19408
\(989\) −1.52430 −0.0484700
\(990\) −12.9389 −0.411225
\(991\) 26.1634 0.831109 0.415555 0.909568i \(-0.363588\pi\)
0.415555 + 0.909568i \(0.363588\pi\)
\(992\) 127.593 4.05108
\(993\) 59.4948 1.88801
\(994\) −82.2485 −2.60876
\(995\) −9.24950 −0.293229
\(996\) −77.0885 −2.44264
\(997\) −7.02785 −0.222574 −0.111287 0.993788i \(-0.535497\pi\)
−0.111287 + 0.993788i \(0.535497\pi\)
\(998\) 59.4627 1.88226
\(999\) 4.34635 0.137512
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 \(a_p\))