Properties

Label 6041.2.a.f.1.15
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.46575 q^{2}\) \(+3.35396 q^{3}\) \(+4.07990 q^{4}\) \(-4.25898 q^{5}\) \(-8.27001 q^{6}\) \(+1.00000 q^{7}\) \(-5.12851 q^{8}\) \(+8.24904 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.46575 q^{2}\) \(+3.35396 q^{3}\) \(+4.07990 q^{4}\) \(-4.25898 q^{5}\) \(-8.27001 q^{6}\) \(+1.00000 q^{7}\) \(-5.12851 q^{8}\) \(+8.24904 q^{9}\) \(+10.5016 q^{10}\) \(-5.52446 q^{11}\) \(+13.6838 q^{12}\) \(+3.47803 q^{13}\) \(-2.46575 q^{14}\) \(-14.2844 q^{15}\) \(+4.48579 q^{16}\) \(-2.75465 q^{17}\) \(-20.3400 q^{18}\) \(-1.06532 q^{19}\) \(-17.3762 q^{20}\) \(+3.35396 q^{21}\) \(+13.6219 q^{22}\) \(+2.80312 q^{23}\) \(-17.2008 q^{24}\) \(+13.1389 q^{25}\) \(-8.57595 q^{26}\) \(+17.6051 q^{27}\) \(+4.07990 q^{28}\) \(-2.56337 q^{29}\) \(+35.2218 q^{30}\) \(+8.67230 q^{31}\) \(-0.803810 q^{32}\) \(-18.5288 q^{33}\) \(+6.79228 q^{34}\) \(-4.25898 q^{35}\) \(+33.6553 q^{36}\) \(-9.07307 q^{37}\) \(+2.62681 q^{38}\) \(+11.6652 q^{39}\) \(+21.8422 q^{40}\) \(+0.671375 q^{41}\) \(-8.27001 q^{42}\) \(-4.24433 q^{43}\) \(-22.5392 q^{44}\) \(-35.1324 q^{45}\) \(-6.91178 q^{46}\) \(-6.80643 q^{47}\) \(+15.0452 q^{48}\) \(+1.00000 q^{49}\) \(-32.3971 q^{50}\) \(-9.23900 q^{51}\) \(+14.1900 q^{52}\) \(+14.2673 q^{53}\) \(-43.4096 q^{54}\) \(+23.5285 q^{55}\) \(-5.12851 q^{56}\) \(-3.57304 q^{57}\) \(+6.32061 q^{58}\) \(-5.20494 q^{59}\) \(-58.2791 q^{60}\) \(-1.41300 q^{61}\) \(-21.3837 q^{62}\) \(+8.24904 q^{63}\) \(-6.98960 q^{64}\) \(-14.8129 q^{65}\) \(+45.6873 q^{66}\) \(-8.04907 q^{67}\) \(-11.2387 q^{68}\) \(+9.40154 q^{69}\) \(+10.5016 q^{70}\) \(+13.8920 q^{71}\) \(-42.3053 q^{72}\) \(+11.5073 q^{73}\) \(+22.3719 q^{74}\) \(+44.0672 q^{75}\) \(-4.34640 q^{76}\) \(-5.52446 q^{77}\) \(-28.7634 q^{78}\) \(-9.91043 q^{79}\) \(-19.1049 q^{80}\) \(+34.2995 q^{81}\) \(-1.65544 q^{82}\) \(+3.31929 q^{83}\) \(+13.6838 q^{84}\) \(+11.7320 q^{85}\) \(+10.4654 q^{86}\) \(-8.59742 q^{87}\) \(+28.3322 q^{88}\) \(+6.18902 q^{89}\) \(+86.6277 q^{90}\) \(+3.47803 q^{91}\) \(+11.4364 q^{92}\) \(+29.0865 q^{93}\) \(+16.7829 q^{94}\) \(+4.53717 q^{95}\) \(-2.69594 q^{96}\) \(-9.83314 q^{97}\) \(-2.46575 q^{98}\) \(-45.5714 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46575 −1.74355 −0.871773 0.489911i \(-0.837029\pi\)
−0.871773 + 0.489911i \(0.837029\pi\)
\(3\) 3.35396 1.93641 0.968204 0.250160i \(-0.0804834\pi\)
0.968204 + 0.250160i \(0.0804834\pi\)
\(4\) 4.07990 2.03995
\(5\) −4.25898 −1.90467 −0.952336 0.305051i \(-0.901326\pi\)
−0.952336 + 0.305051i \(0.901326\pi\)
\(6\) −8.27001 −3.37622
\(7\) 1.00000 0.377964
\(8\) −5.12851 −1.81320
\(9\) 8.24904 2.74968
\(10\) 10.5016 3.32088
\(11\) −5.52446 −1.66569 −0.832843 0.553509i \(-0.813288\pi\)
−0.832843 + 0.553509i \(0.813288\pi\)
\(12\) 13.6838 3.95018
\(13\) 3.47803 0.964633 0.482317 0.875997i \(-0.339795\pi\)
0.482317 + 0.875997i \(0.339795\pi\)
\(14\) −2.46575 −0.658998
\(15\) −14.2844 −3.68822
\(16\) 4.48579 1.12145
\(17\) −2.75465 −0.668102 −0.334051 0.942555i \(-0.608416\pi\)
−0.334051 + 0.942555i \(0.608416\pi\)
\(18\) −20.3400 −4.79419
\(19\) −1.06532 −0.244401 −0.122201 0.992505i \(-0.538995\pi\)
−0.122201 + 0.992505i \(0.538995\pi\)
\(20\) −17.3762 −3.88544
\(21\) 3.35396 0.731894
\(22\) 13.6219 2.90420
\(23\) 2.80312 0.584491 0.292245 0.956343i \(-0.405598\pi\)
0.292245 + 0.956343i \(0.405598\pi\)
\(24\) −17.2008 −3.51110
\(25\) 13.1389 2.62777
\(26\) −8.57595 −1.68188
\(27\) 17.6051 3.38809
\(28\) 4.07990 0.771029
\(29\) −2.56337 −0.476005 −0.238003 0.971265i \(-0.576493\pi\)
−0.238003 + 0.971265i \(0.576493\pi\)
\(30\) 35.2218 6.43059
\(31\) 8.67230 1.55759 0.778795 0.627278i \(-0.215831\pi\)
0.778795 + 0.627278i \(0.215831\pi\)
\(32\) −0.803810 −0.142095
\(33\) −18.5288 −3.22545
\(34\) 6.79228 1.16487
\(35\) −4.25898 −0.719898
\(36\) 33.6553 5.60921
\(37\) −9.07307 −1.49160 −0.745801 0.666168i \(-0.767933\pi\)
−0.745801 + 0.666168i \(0.767933\pi\)
\(38\) 2.62681 0.426125
\(39\) 11.6652 1.86792
\(40\) 21.8422 3.45355
\(41\) 0.671375 0.104851 0.0524256 0.998625i \(-0.483305\pi\)
0.0524256 + 0.998625i \(0.483305\pi\)
\(42\) −8.27001 −1.27609
\(43\) −4.24433 −0.647255 −0.323627 0.946185i \(-0.604902\pi\)
−0.323627 + 0.946185i \(0.604902\pi\)
\(44\) −22.5392 −3.39792
\(45\) −35.1324 −5.23724
\(46\) −6.91178 −1.01909
\(47\) −6.80643 −0.992820 −0.496410 0.868088i \(-0.665349\pi\)
−0.496410 + 0.868088i \(0.665349\pi\)
\(48\) 15.0452 2.17158
\(49\) 1.00000 0.142857
\(50\) −32.3971 −4.58164
\(51\) −9.23900 −1.29372
\(52\) 14.1900 1.96780
\(53\) 14.2673 1.95976 0.979882 0.199577i \(-0.0639568\pi\)
0.979882 + 0.199577i \(0.0639568\pi\)
\(54\) −43.4096 −5.90730
\(55\) 23.5285 3.17259
\(56\) −5.12851 −0.685326
\(57\) −3.57304 −0.473261
\(58\) 6.32061 0.829937
\(59\) −5.20494 −0.677625 −0.338813 0.940854i \(-0.610025\pi\)
−0.338813 + 0.940854i \(0.610025\pi\)
\(60\) −58.2791 −7.52379
\(61\) −1.41300 −0.180917 −0.0904583 0.995900i \(-0.528833\pi\)
−0.0904583 + 0.995900i \(0.528833\pi\)
\(62\) −21.3837 −2.71573
\(63\) 8.24904 1.03928
\(64\) −6.98960 −0.873700
\(65\) −14.8129 −1.83731
\(66\) 45.6873 5.62372
\(67\) −8.04907 −0.983350 −0.491675 0.870779i \(-0.663615\pi\)
−0.491675 + 0.870779i \(0.663615\pi\)
\(68\) −11.2387 −1.36289
\(69\) 9.40154 1.13181
\(70\) 10.5016 1.25518
\(71\) 13.8920 1.64867 0.824337 0.566099i \(-0.191548\pi\)
0.824337 + 0.566099i \(0.191548\pi\)
\(72\) −42.3053 −4.98572
\(73\) 11.5073 1.34683 0.673415 0.739265i \(-0.264827\pi\)
0.673415 + 0.739265i \(0.264827\pi\)
\(74\) 22.3719 2.60068
\(75\) 44.0672 5.08845
\(76\) −4.34640 −0.498566
\(77\) −5.52446 −0.629570
\(78\) −28.7634 −3.25681
\(79\) −9.91043 −1.11501 −0.557505 0.830174i \(-0.688241\pi\)
−0.557505 + 0.830174i \(0.688241\pi\)
\(80\) −19.1049 −2.13599
\(81\) 34.2995 3.81106
\(82\) −1.65544 −0.182813
\(83\) 3.31929 0.364340 0.182170 0.983267i \(-0.441688\pi\)
0.182170 + 0.983267i \(0.441688\pi\)
\(84\) 13.6838 1.49303
\(85\) 11.7320 1.27251
\(86\) 10.4654 1.12852
\(87\) −8.59742 −0.921741
\(88\) 28.3322 3.02022
\(89\) 6.18902 0.656035 0.328017 0.944672i \(-0.393620\pi\)
0.328017 + 0.944672i \(0.393620\pi\)
\(90\) 86.6277 9.13136
\(91\) 3.47803 0.364597
\(92\) 11.4364 1.19233
\(93\) 29.0865 3.01613
\(94\) 16.7829 1.73103
\(95\) 4.53717 0.465504
\(96\) −2.69594 −0.275154
\(97\) −9.83314 −0.998405 −0.499202 0.866485i \(-0.666374\pi\)
−0.499202 + 0.866485i \(0.666374\pi\)
\(98\) −2.46575 −0.249078
\(99\) −45.5714 −4.58010
\(100\) 53.6053 5.36053
\(101\) −14.1995 −1.41290 −0.706450 0.707763i \(-0.749705\pi\)
−0.706450 + 0.707763i \(0.749705\pi\)
\(102\) 22.7810 2.25566
\(103\) −9.12069 −0.898688 −0.449344 0.893359i \(-0.648342\pi\)
−0.449344 + 0.893359i \(0.648342\pi\)
\(104\) −17.8371 −1.74907
\(105\) −14.2844 −1.39402
\(106\) −35.1795 −3.41694
\(107\) 10.0417 0.970764 0.485382 0.874302i \(-0.338681\pi\)
0.485382 + 0.874302i \(0.338681\pi\)
\(108\) 71.8269 6.91154
\(109\) 8.51272 0.815371 0.407685 0.913122i \(-0.366336\pi\)
0.407685 + 0.913122i \(0.366336\pi\)
\(110\) −58.0154 −5.53155
\(111\) −30.4307 −2.88835
\(112\) 4.48579 0.423868
\(113\) 3.72077 0.350021 0.175010 0.984567i \(-0.444004\pi\)
0.175010 + 0.984567i \(0.444004\pi\)
\(114\) 8.81021 0.825151
\(115\) −11.9384 −1.11326
\(116\) −10.4583 −0.971027
\(117\) 28.6904 2.65243
\(118\) 12.8341 1.18147
\(119\) −2.75465 −0.252519
\(120\) 73.2578 6.68749
\(121\) 19.5196 1.77451
\(122\) 3.48411 0.315436
\(123\) 2.25176 0.203035
\(124\) 35.3821 3.17741
\(125\) −34.6633 −3.10038
\(126\) −20.3400 −1.81203
\(127\) 4.49397 0.398775 0.199388 0.979921i \(-0.436105\pi\)
0.199388 + 0.979921i \(0.436105\pi\)
\(128\) 18.8422 1.66543
\(129\) −14.2353 −1.25335
\(130\) 36.5248 3.20343
\(131\) −7.76097 −0.678079 −0.339039 0.940772i \(-0.610102\pi\)
−0.339039 + 0.940772i \(0.610102\pi\)
\(132\) −75.5957 −6.57976
\(133\) −1.06532 −0.0923750
\(134\) 19.8470 1.71452
\(135\) −74.9795 −6.45321
\(136\) 14.1273 1.21140
\(137\) 18.3230 1.56544 0.782719 0.622376i \(-0.213832\pi\)
0.782719 + 0.622376i \(0.213832\pi\)
\(138\) −23.1818 −1.97337
\(139\) 10.7308 0.910172 0.455086 0.890448i \(-0.349609\pi\)
0.455086 + 0.890448i \(0.349609\pi\)
\(140\) −17.3762 −1.46856
\(141\) −22.8285 −1.92251
\(142\) −34.2541 −2.87454
\(143\) −19.2143 −1.60678
\(144\) 37.0035 3.08362
\(145\) 10.9173 0.906634
\(146\) −28.3741 −2.34826
\(147\) 3.35396 0.276630
\(148\) −37.0172 −3.04280
\(149\) 7.28748 0.597014 0.298507 0.954408i \(-0.403511\pi\)
0.298507 + 0.954408i \(0.403511\pi\)
\(150\) −108.659 −8.87194
\(151\) 1.93362 0.157356 0.0786779 0.996900i \(-0.474930\pi\)
0.0786779 + 0.996900i \(0.474930\pi\)
\(152\) 5.46350 0.443149
\(153\) −22.7232 −1.83707
\(154\) 13.6219 1.09768
\(155\) −36.9351 −2.96670
\(156\) 47.5928 3.81047
\(157\) −4.91386 −0.392169 −0.196084 0.980587i \(-0.562823\pi\)
−0.196084 + 0.980587i \(0.562823\pi\)
\(158\) 24.4366 1.94407
\(159\) 47.8519 3.79490
\(160\) 3.42341 0.270644
\(161\) 2.80312 0.220917
\(162\) −84.5739 −6.64475
\(163\) 17.6763 1.38452 0.692258 0.721650i \(-0.256616\pi\)
0.692258 + 0.721650i \(0.256616\pi\)
\(164\) 2.73914 0.213891
\(165\) 78.9137 6.14342
\(166\) −8.18453 −0.635243
\(167\) −14.4577 −1.11877 −0.559384 0.828909i \(-0.688962\pi\)
−0.559384 + 0.828909i \(0.688962\pi\)
\(168\) −17.2008 −1.32707
\(169\) −0.903273 −0.0694826
\(170\) −28.9281 −2.21869
\(171\) −8.78786 −0.672025
\(172\) −17.3165 −1.32037
\(173\) 18.6978 1.42157 0.710784 0.703411i \(-0.248340\pi\)
0.710784 + 0.703411i \(0.248340\pi\)
\(174\) 21.1991 1.60710
\(175\) 13.1389 0.993206
\(176\) −24.7816 −1.86798
\(177\) −17.4572 −1.31216
\(178\) −15.2606 −1.14383
\(179\) 5.65129 0.422397 0.211199 0.977443i \(-0.432263\pi\)
0.211199 + 0.977443i \(0.432263\pi\)
\(180\) −143.337 −10.6837
\(181\) 21.2000 1.57578 0.787890 0.615815i \(-0.211173\pi\)
0.787890 + 0.615815i \(0.211173\pi\)
\(182\) −8.57595 −0.635692
\(183\) −4.73915 −0.350328
\(184\) −14.3758 −1.05980
\(185\) 38.6420 2.84101
\(186\) −71.7200 −5.25876
\(187\) 15.2180 1.11285
\(188\) −27.7696 −2.02530
\(189\) 17.6051 1.28058
\(190\) −11.1875 −0.811627
\(191\) 6.80399 0.492319 0.246160 0.969229i \(-0.420831\pi\)
0.246160 + 0.969229i \(0.420831\pi\)
\(192\) −23.4428 −1.69184
\(193\) −10.4885 −0.754976 −0.377488 0.926014i \(-0.623212\pi\)
−0.377488 + 0.926014i \(0.623212\pi\)
\(194\) 24.2460 1.74076
\(195\) −49.6817 −3.55778
\(196\) 4.07990 0.291422
\(197\) 4.95884 0.353303 0.176651 0.984273i \(-0.443473\pi\)
0.176651 + 0.984273i \(0.443473\pi\)
\(198\) 112.368 7.98562
\(199\) 10.3038 0.730416 0.365208 0.930926i \(-0.380998\pi\)
0.365208 + 0.930926i \(0.380998\pi\)
\(200\) −67.3828 −4.76469
\(201\) −26.9962 −1.90417
\(202\) 35.0123 2.46346
\(203\) −2.56337 −0.179913
\(204\) −37.6942 −2.63912
\(205\) −2.85937 −0.199707
\(206\) 22.4893 1.56690
\(207\) 23.1230 1.60716
\(208\) 15.6017 1.08179
\(209\) 5.88531 0.407096
\(210\) 35.2218 2.43053
\(211\) −11.4303 −0.786894 −0.393447 0.919347i \(-0.628717\pi\)
−0.393447 + 0.919347i \(0.628717\pi\)
\(212\) 58.2092 3.99782
\(213\) 46.5931 3.19251
\(214\) −24.7602 −1.69257
\(215\) 18.0765 1.23281
\(216\) −90.2877 −6.14330
\(217\) 8.67230 0.588714
\(218\) −20.9902 −1.42164
\(219\) 38.5951 2.60801
\(220\) 95.9941 6.47192
\(221\) −9.58078 −0.644473
\(222\) 75.0343 5.03597
\(223\) 14.7124 0.985213 0.492607 0.870252i \(-0.336044\pi\)
0.492607 + 0.870252i \(0.336044\pi\)
\(224\) −0.803810 −0.0537068
\(225\) 108.383 7.22554
\(226\) −9.17447 −0.610277
\(227\) 24.3080 1.61338 0.806688 0.590978i \(-0.201258\pi\)
0.806688 + 0.590978i \(0.201258\pi\)
\(228\) −14.5776 −0.965428
\(229\) −0.439300 −0.0290298 −0.0145149 0.999895i \(-0.504620\pi\)
−0.0145149 + 0.999895i \(0.504620\pi\)
\(230\) 29.4371 1.94102
\(231\) −18.5288 −1.21911
\(232\) 13.1462 0.863093
\(233\) −4.65957 −0.305258 −0.152629 0.988284i \(-0.548774\pi\)
−0.152629 + 0.988284i \(0.548774\pi\)
\(234\) −70.7433 −4.62464
\(235\) 28.9884 1.89100
\(236\) −21.2356 −1.38232
\(237\) −33.2392 −2.15912
\(238\) 6.79228 0.440278
\(239\) −5.00249 −0.323584 −0.161792 0.986825i \(-0.551727\pi\)
−0.161792 + 0.986825i \(0.551727\pi\)
\(240\) −64.0770 −4.13615
\(241\) −29.6103 −1.90737 −0.953683 0.300812i \(-0.902742\pi\)
−0.953683 + 0.300812i \(0.902742\pi\)
\(242\) −48.1304 −3.09394
\(243\) 62.2240 3.99167
\(244\) −5.76492 −0.369061
\(245\) −4.25898 −0.272096
\(246\) −5.55227 −0.354000
\(247\) −3.70522 −0.235758
\(248\) −44.4759 −2.82423
\(249\) 11.1328 0.705511
\(250\) 85.4708 5.40565
\(251\) 23.2429 1.46708 0.733538 0.679648i \(-0.237868\pi\)
0.733538 + 0.679648i \(0.237868\pi\)
\(252\) 33.6553 2.12008
\(253\) −15.4857 −0.973578
\(254\) −11.0810 −0.695283
\(255\) 39.3487 2.46411
\(256\) −32.4808 −2.03005
\(257\) 17.3206 1.08043 0.540213 0.841528i \(-0.318344\pi\)
0.540213 + 0.841528i \(0.318344\pi\)
\(258\) 35.1007 2.18527
\(259\) −9.07307 −0.563773
\(260\) −60.4350 −3.74802
\(261\) −21.1453 −1.30886
\(262\) 19.1366 1.18226
\(263\) 9.33768 0.575786 0.287893 0.957663i \(-0.407045\pi\)
0.287893 + 0.957663i \(0.407045\pi\)
\(264\) 95.0251 5.84839
\(265\) −60.7641 −3.73271
\(266\) 2.62681 0.161060
\(267\) 20.7577 1.27035
\(268\) −32.8394 −2.00599
\(269\) 19.2813 1.17560 0.587802 0.809005i \(-0.299993\pi\)
0.587802 + 0.809005i \(0.299993\pi\)
\(270\) 184.880 11.2515
\(271\) −6.32725 −0.384353 −0.192177 0.981360i \(-0.561555\pi\)
−0.192177 + 0.981360i \(0.561555\pi\)
\(272\) −12.3568 −0.749242
\(273\) 11.6652 0.706009
\(274\) −45.1798 −2.72941
\(275\) −72.5851 −4.37705
\(276\) 38.3574 2.30884
\(277\) 29.1799 1.75325 0.876626 0.481172i \(-0.159789\pi\)
0.876626 + 0.481172i \(0.159789\pi\)
\(278\) −26.4593 −1.58693
\(279\) 71.5381 4.28287
\(280\) 21.8422 1.30532
\(281\) −3.27661 −0.195466 −0.0977331 0.995213i \(-0.531159\pi\)
−0.0977331 + 0.995213i \(0.531159\pi\)
\(282\) 56.2893 3.35198
\(283\) 18.9277 1.12513 0.562567 0.826752i \(-0.309814\pi\)
0.562567 + 0.826752i \(0.309814\pi\)
\(284\) 56.6779 3.36321
\(285\) 15.2175 0.901406
\(286\) 47.3775 2.80149
\(287\) 0.671375 0.0396300
\(288\) −6.63065 −0.390715
\(289\) −9.41188 −0.553640
\(290\) −26.9193 −1.58076
\(291\) −32.9800 −1.93332
\(292\) 46.9487 2.74747
\(293\) −23.1755 −1.35392 −0.676962 0.736018i \(-0.736704\pi\)
−0.676962 + 0.736018i \(0.736704\pi\)
\(294\) −8.27001 −0.482317
\(295\) 22.1677 1.29065
\(296\) 46.5313 2.70458
\(297\) −97.2583 −5.64350
\(298\) −17.9691 −1.04092
\(299\) 9.74934 0.563819
\(300\) 179.790 10.3802
\(301\) −4.24433 −0.244639
\(302\) −4.76781 −0.274357
\(303\) −47.6244 −2.73595
\(304\) −4.77881 −0.274083
\(305\) 6.01795 0.344587
\(306\) 56.0297 3.20301
\(307\) 12.5119 0.714091 0.357045 0.934087i \(-0.383784\pi\)
0.357045 + 0.934087i \(0.383784\pi\)
\(308\) −22.5392 −1.28429
\(309\) −30.5904 −1.74023
\(310\) 91.0726 5.17257
\(311\) 24.2907 1.37740 0.688700 0.725047i \(-0.258182\pi\)
0.688700 + 0.725047i \(0.258182\pi\)
\(312\) −59.8250 −3.38692
\(313\) −3.78541 −0.213964 −0.106982 0.994261i \(-0.534119\pi\)
−0.106982 + 0.994261i \(0.534119\pi\)
\(314\) 12.1163 0.683764
\(315\) −35.1324 −1.97949
\(316\) −40.4336 −2.27457
\(317\) 3.68456 0.206946 0.103473 0.994632i \(-0.467005\pi\)
0.103473 + 0.994632i \(0.467005\pi\)
\(318\) −117.991 −6.61659
\(319\) 14.1612 0.792875
\(320\) 29.7685 1.66411
\(321\) 33.6793 1.87980
\(322\) −6.91178 −0.385178
\(323\) 2.93459 0.163285
\(324\) 139.939 7.77437
\(325\) 45.6975 2.53484
\(326\) −43.5853 −2.41397
\(327\) 28.5513 1.57889
\(328\) −3.44315 −0.190116
\(329\) −6.80643 −0.375251
\(330\) −194.581 −10.7113
\(331\) −4.16323 −0.228832 −0.114416 0.993433i \(-0.536500\pi\)
−0.114416 + 0.993433i \(0.536500\pi\)
\(332\) 13.5424 0.743235
\(333\) −74.8441 −4.10143
\(334\) 35.6489 1.95062
\(335\) 34.2808 1.87296
\(336\) 15.0452 0.820781
\(337\) −0.494308 −0.0269266 −0.0134633 0.999909i \(-0.504286\pi\)
−0.0134633 + 0.999909i \(0.504286\pi\)
\(338\) 2.22724 0.121146
\(339\) 12.4793 0.677783
\(340\) 47.8654 2.59587
\(341\) −47.9097 −2.59446
\(342\) 21.6686 1.17171
\(343\) 1.00000 0.0539949
\(344\) 21.7671 1.17360
\(345\) −40.0409 −2.15573
\(346\) −46.1040 −2.47857
\(347\) −5.01899 −0.269434 −0.134717 0.990884i \(-0.543012\pi\)
−0.134717 + 0.990884i \(0.543012\pi\)
\(348\) −35.0766 −1.88031
\(349\) 3.34125 0.178853 0.0894265 0.995993i \(-0.471497\pi\)
0.0894265 + 0.995993i \(0.471497\pi\)
\(350\) −32.3971 −1.73170
\(351\) 61.2310 3.26827
\(352\) 4.44061 0.236685
\(353\) 18.5659 0.988165 0.494082 0.869415i \(-0.335504\pi\)
0.494082 + 0.869415i \(0.335504\pi\)
\(354\) 43.0449 2.28781
\(355\) −59.1656 −3.14018
\(356\) 25.2506 1.33828
\(357\) −9.23900 −0.488979
\(358\) −13.9346 −0.736469
\(359\) 24.2770 1.28129 0.640645 0.767837i \(-0.278667\pi\)
0.640645 + 0.767837i \(0.278667\pi\)
\(360\) 180.177 9.49616
\(361\) −17.8651 −0.940268
\(362\) −52.2737 −2.74745
\(363\) 65.4680 3.43618
\(364\) 14.1900 0.743760
\(365\) −49.0094 −2.56527
\(366\) 11.6856 0.610814
\(367\) −11.8222 −0.617115 −0.308557 0.951206i \(-0.599846\pi\)
−0.308557 + 0.951206i \(0.599846\pi\)
\(368\) 12.5742 0.655476
\(369\) 5.53819 0.288307
\(370\) −95.2813 −4.95344
\(371\) 14.2673 0.740721
\(372\) 118.670 6.15276
\(373\) 12.3030 0.637023 0.318512 0.947919i \(-0.396817\pi\)
0.318512 + 0.947919i \(0.396817\pi\)
\(374\) −37.5236 −1.94030
\(375\) −116.259 −6.00360
\(376\) 34.9068 1.80018
\(377\) −8.91548 −0.459170
\(378\) −43.4096 −2.23275
\(379\) −8.00180 −0.411025 −0.205512 0.978655i \(-0.565886\pi\)
−0.205512 + 0.978655i \(0.565886\pi\)
\(380\) 18.5112 0.949605
\(381\) 15.0726 0.772192
\(382\) −16.7769 −0.858381
\(383\) 35.9327 1.83607 0.918037 0.396494i \(-0.129773\pi\)
0.918037 + 0.396494i \(0.129773\pi\)
\(384\) 63.1959 3.22495
\(385\) 23.5285 1.19912
\(386\) 25.8619 1.31634
\(387\) −35.0117 −1.77974
\(388\) −40.1183 −2.03670
\(389\) −3.68765 −0.186971 −0.0934857 0.995621i \(-0.529801\pi\)
−0.0934857 + 0.995621i \(0.529801\pi\)
\(390\) 122.503 6.20316
\(391\) −7.72162 −0.390499
\(392\) −5.12851 −0.259029
\(393\) −26.0300 −1.31304
\(394\) −12.2272 −0.615999
\(395\) 42.2083 2.12373
\(396\) −185.927 −9.34318
\(397\) 28.3891 1.42481 0.712405 0.701769i \(-0.247606\pi\)
0.712405 + 0.701769i \(0.247606\pi\)
\(398\) −25.4065 −1.27351
\(399\) −3.57304 −0.178876
\(400\) 58.9383 2.94691
\(401\) 11.9271 0.595609 0.297804 0.954627i \(-0.403746\pi\)
0.297804 + 0.954627i \(0.403746\pi\)
\(402\) 66.5659 3.32000
\(403\) 30.1626 1.50250
\(404\) −57.9324 −2.88225
\(405\) −146.081 −7.25881
\(406\) 6.32061 0.313687
\(407\) 50.1238 2.48454
\(408\) 47.3823 2.34577
\(409\) −0.726585 −0.0359273 −0.0179637 0.999839i \(-0.505718\pi\)
−0.0179637 + 0.999839i \(0.505718\pi\)
\(410\) 7.05048 0.348198
\(411\) 61.4545 3.03133
\(412\) −37.2115 −1.83328
\(413\) −5.20494 −0.256118
\(414\) −57.0155 −2.80216
\(415\) −14.1368 −0.693948
\(416\) −2.79568 −0.137069
\(417\) 35.9905 1.76246
\(418\) −14.5117 −0.709790
\(419\) −23.3257 −1.13954 −0.569768 0.821806i \(-0.692967\pi\)
−0.569768 + 0.821806i \(0.692967\pi\)
\(420\) −58.2791 −2.84373
\(421\) −11.4531 −0.558191 −0.279096 0.960263i \(-0.590035\pi\)
−0.279096 + 0.960263i \(0.590035\pi\)
\(422\) 28.1842 1.37199
\(423\) −56.1465 −2.72994
\(424\) −73.1700 −3.55345
\(425\) −36.1931 −1.75562
\(426\) −114.887 −5.56628
\(427\) −1.41300 −0.0683800
\(428\) 40.9690 1.98031
\(429\) −64.4438 −3.11138
\(430\) −44.5721 −2.14946
\(431\) 14.8856 0.717012 0.358506 0.933527i \(-0.383286\pi\)
0.358506 + 0.933527i \(0.383286\pi\)
\(432\) 78.9726 3.79957
\(433\) 0.307255 0.0147657 0.00738286 0.999973i \(-0.497650\pi\)
0.00738286 + 0.999973i \(0.497650\pi\)
\(434\) −21.3837 −1.02645
\(435\) 36.6162 1.75561
\(436\) 34.7311 1.66332
\(437\) −2.98622 −0.142850
\(438\) −95.1656 −4.54719
\(439\) 9.88411 0.471743 0.235871 0.971784i \(-0.424206\pi\)
0.235871 + 0.971784i \(0.424206\pi\)
\(440\) −120.666 −5.75254
\(441\) 8.24904 0.392811
\(442\) 23.6238 1.12367
\(443\) −25.1472 −1.19478 −0.597389 0.801951i \(-0.703795\pi\)
−0.597389 + 0.801951i \(0.703795\pi\)
\(444\) −124.154 −5.89210
\(445\) −26.3589 −1.24953
\(446\) −36.2770 −1.71776
\(447\) 24.4419 1.15606
\(448\) −6.98960 −0.330227
\(449\) −5.23965 −0.247274 −0.123637 0.992327i \(-0.539456\pi\)
−0.123637 + 0.992327i \(0.539456\pi\)
\(450\) −267.245 −12.5981
\(451\) −3.70898 −0.174649
\(452\) 15.1804 0.714025
\(453\) 6.48528 0.304705
\(454\) −59.9372 −2.81299
\(455\) −14.8129 −0.694438
\(456\) 18.3244 0.858117
\(457\) 36.7782 1.72041 0.860206 0.509947i \(-0.170335\pi\)
0.860206 + 0.509947i \(0.170335\pi\)
\(458\) 1.08320 0.0506147
\(459\) −48.4958 −2.26359
\(460\) −48.7076 −2.27100
\(461\) −2.76903 −0.128967 −0.0644833 0.997919i \(-0.520540\pi\)
−0.0644833 + 0.997919i \(0.520540\pi\)
\(462\) 45.6873 2.12557
\(463\) 19.5372 0.907973 0.453986 0.891009i \(-0.350001\pi\)
0.453986 + 0.891009i \(0.350001\pi\)
\(464\) −11.4987 −0.533815
\(465\) −123.879 −5.74474
\(466\) 11.4893 0.532232
\(467\) −22.6795 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(468\) 117.054 5.41083
\(469\) −8.04907 −0.371671
\(470\) −71.4781 −3.29704
\(471\) −16.4809 −0.759399
\(472\) 26.6936 1.22867
\(473\) 23.4476 1.07812
\(474\) 81.9593 3.76452
\(475\) −13.9971 −0.642231
\(476\) −11.2387 −0.515126
\(477\) 117.691 5.38872
\(478\) 12.3349 0.564183
\(479\) 35.9680 1.64342 0.821710 0.569906i \(-0.193020\pi\)
0.821710 + 0.569906i \(0.193020\pi\)
\(480\) 11.4820 0.524077
\(481\) −31.5564 −1.43885
\(482\) 73.0115 3.32558
\(483\) 9.40154 0.427785
\(484\) 79.6381 3.61991
\(485\) 41.8791 1.90163
\(486\) −153.428 −6.95966
\(487\) −20.4848 −0.928255 −0.464128 0.885768i \(-0.653632\pi\)
−0.464128 + 0.885768i \(0.653632\pi\)
\(488\) 7.24660 0.328038
\(489\) 59.2857 2.68099
\(490\) 10.5016 0.474412
\(491\) −3.93132 −0.177418 −0.0887090 0.996058i \(-0.528274\pi\)
−0.0887090 + 0.996058i \(0.528274\pi\)
\(492\) 9.18697 0.414181
\(493\) 7.06119 0.318020
\(494\) 9.13613 0.411054
\(495\) 194.088 8.72359
\(496\) 38.9021 1.74676
\(497\) 13.8920 0.623140
\(498\) −27.4506 −1.23009
\(499\) −28.5187 −1.27667 −0.638336 0.769758i \(-0.720377\pi\)
−0.638336 + 0.769758i \(0.720377\pi\)
\(500\) −141.423 −6.32462
\(501\) −48.4904 −2.16639
\(502\) −57.3110 −2.55791
\(503\) −3.27288 −0.145931 −0.0729653 0.997334i \(-0.523246\pi\)
−0.0729653 + 0.997334i \(0.523246\pi\)
\(504\) −42.3053 −1.88443
\(505\) 60.4752 2.69111
\(506\) 38.1838 1.69748
\(507\) −3.02954 −0.134547
\(508\) 18.3350 0.813482
\(509\) 14.4707 0.641403 0.320702 0.947180i \(-0.396081\pi\)
0.320702 + 0.947180i \(0.396081\pi\)
\(510\) −97.0238 −4.29629
\(511\) 11.5073 0.509054
\(512\) 42.4051 1.87406
\(513\) −18.7550 −0.828054
\(514\) −42.7081 −1.88377
\(515\) 38.8448 1.71171
\(516\) −58.0787 −2.55677
\(517\) 37.6018 1.65373
\(518\) 22.3719 0.982964
\(519\) 62.7116 2.75274
\(520\) 75.9679 3.33141
\(521\) 22.2153 0.973268 0.486634 0.873606i \(-0.338224\pi\)
0.486634 + 0.873606i \(0.338224\pi\)
\(522\) 52.1389 2.28206
\(523\) 16.6772 0.729243 0.364621 0.931156i \(-0.381198\pi\)
0.364621 + 0.931156i \(0.381198\pi\)
\(524\) −31.6640 −1.38325
\(525\) 44.0672 1.92325
\(526\) −23.0244 −1.00391
\(527\) −23.8892 −1.04063
\(528\) −83.1164 −3.61718
\(529\) −15.1425 −0.658371
\(530\) 149.829 6.50815
\(531\) −42.9357 −1.86325
\(532\) −4.34640 −0.188440
\(533\) 2.33506 0.101143
\(534\) −51.1833 −2.21492
\(535\) −42.7672 −1.84899
\(536\) 41.2797 1.78301
\(537\) 18.9542 0.817934
\(538\) −47.5429 −2.04972
\(539\) −5.52446 −0.237955
\(540\) −305.909 −13.1642
\(541\) −3.88661 −0.167099 −0.0835493 0.996504i \(-0.526626\pi\)
−0.0835493 + 0.996504i \(0.526626\pi\)
\(542\) 15.6014 0.670137
\(543\) 71.1038 3.05136
\(544\) 2.21422 0.0949338
\(545\) −36.2555 −1.55301
\(546\) −28.7634 −1.23096
\(547\) 14.1136 0.603453 0.301727 0.953395i \(-0.402437\pi\)
0.301727 + 0.953395i \(0.402437\pi\)
\(548\) 74.7559 3.19341
\(549\) −11.6559 −0.497462
\(550\) 178.976 7.63158
\(551\) 2.73081 0.116336
\(552\) −48.2159 −2.05220
\(553\) −9.91043 −0.421434
\(554\) −71.9503 −3.05688
\(555\) 129.604 5.50136
\(556\) 43.7805 1.85671
\(557\) 20.9743 0.888711 0.444356 0.895851i \(-0.353433\pi\)
0.444356 + 0.895851i \(0.353433\pi\)
\(558\) −176.395 −7.46739
\(559\) −14.7619 −0.624363
\(560\) −19.1049 −0.807329
\(561\) 51.0404 2.15493
\(562\) 8.07929 0.340804
\(563\) −44.1936 −1.86254 −0.931269 0.364333i \(-0.881297\pi\)
−0.931269 + 0.364333i \(0.881297\pi\)
\(564\) −93.1380 −3.92182
\(565\) −15.8467 −0.666675
\(566\) −46.6709 −1.96172
\(567\) 34.2995 1.44044
\(568\) −71.2451 −2.98938
\(569\) −42.5906 −1.78549 −0.892746 0.450560i \(-0.851225\pi\)
−0.892746 + 0.450560i \(0.851225\pi\)
\(570\) −37.5225 −1.57164
\(571\) −24.9025 −1.04214 −0.521069 0.853514i \(-0.674467\pi\)
−0.521069 + 0.853514i \(0.674467\pi\)
\(572\) −78.3923 −3.27775
\(573\) 22.8203 0.953331
\(574\) −1.65544 −0.0690967
\(575\) 36.8298 1.53591
\(576\) −57.6574 −2.40239
\(577\) −23.0131 −0.958049 −0.479024 0.877802i \(-0.659009\pi\)
−0.479024 + 0.877802i \(0.659009\pi\)
\(578\) 23.2073 0.965297
\(579\) −35.1779 −1.46194
\(580\) 44.5416 1.84949
\(581\) 3.31929 0.137707
\(582\) 81.3202 3.37083
\(583\) −78.8191 −3.26435
\(584\) −59.0154 −2.44207
\(585\) −122.192 −5.05201
\(586\) 57.1448 2.36063
\(587\) −33.4029 −1.37869 −0.689343 0.724435i \(-0.742101\pi\)
−0.689343 + 0.724435i \(0.742101\pi\)
\(588\) 13.6838 0.564311
\(589\) −9.23877 −0.380677
\(590\) −54.6599 −2.25031
\(591\) 16.6317 0.684138
\(592\) −40.6999 −1.67276
\(593\) −15.5985 −0.640552 −0.320276 0.947324i \(-0.603776\pi\)
−0.320276 + 0.947324i \(0.603776\pi\)
\(594\) 239.814 9.83970
\(595\) 11.7320 0.480965
\(596\) 29.7322 1.21788
\(597\) 34.5585 1.41438
\(598\) −24.0394 −0.983044
\(599\) 26.8451 1.09686 0.548431 0.836196i \(-0.315225\pi\)
0.548431 + 0.836196i \(0.315225\pi\)
\(600\) −225.999 −9.22638
\(601\) −20.2854 −0.827460 −0.413730 0.910400i \(-0.635774\pi\)
−0.413730 + 0.910400i \(0.635774\pi\)
\(602\) 10.4654 0.426540
\(603\) −66.3971 −2.70390
\(604\) 7.88898 0.320998
\(605\) −83.1336 −3.37986
\(606\) 117.430 4.77026
\(607\) −18.8010 −0.763110 −0.381555 0.924346i \(-0.624611\pi\)
−0.381555 + 0.924346i \(0.624611\pi\)
\(608\) 0.856314 0.0347281
\(609\) −8.59742 −0.348385
\(610\) −14.8387 −0.600803
\(611\) −23.6730 −0.957707
\(612\) −92.7086 −3.74752
\(613\) −9.82830 −0.396961 −0.198481 0.980105i \(-0.563601\pi\)
−0.198481 + 0.980105i \(0.563601\pi\)
\(614\) −30.8511 −1.24505
\(615\) −9.59020 −0.386714
\(616\) 28.3322 1.14154
\(617\) −17.3220 −0.697357 −0.348678 0.937242i \(-0.613369\pi\)
−0.348678 + 0.937242i \(0.613369\pi\)
\(618\) 75.4282 3.03417
\(619\) 44.4608 1.78703 0.893515 0.449034i \(-0.148232\pi\)
0.893515 + 0.449034i \(0.148232\pi\)
\(620\) −150.692 −6.05192
\(621\) 49.3491 1.98031
\(622\) −59.8947 −2.40156
\(623\) 6.18902 0.247958
\(624\) 52.3276 2.09478
\(625\) 81.9356 3.27743
\(626\) 9.33385 0.373056
\(627\) 19.7391 0.788304
\(628\) −20.0481 −0.800005
\(629\) 24.9932 0.996542
\(630\) 86.6277 3.45133
\(631\) 21.6266 0.860943 0.430472 0.902604i \(-0.358347\pi\)
0.430472 + 0.902604i \(0.358347\pi\)
\(632\) 50.8257 2.02174
\(633\) −38.3367 −1.52375
\(634\) −9.08520 −0.360819
\(635\) −19.1397 −0.759536
\(636\) 195.231 7.74142
\(637\) 3.47803 0.137805
\(638\) −34.9179 −1.38241
\(639\) 114.595 4.53333
\(640\) −80.2484 −3.17210
\(641\) −41.1132 −1.62388 −0.811938 0.583744i \(-0.801587\pi\)
−0.811938 + 0.583744i \(0.801587\pi\)
\(642\) −83.0446 −3.27751
\(643\) −11.5323 −0.454789 −0.227395 0.973803i \(-0.573021\pi\)
−0.227395 + 0.973803i \(0.573021\pi\)
\(644\) 11.4364 0.450659
\(645\) 60.6279 2.38722
\(646\) −7.23595 −0.284695
\(647\) 36.0696 1.41804 0.709022 0.705187i \(-0.249137\pi\)
0.709022 + 0.705187i \(0.249137\pi\)
\(648\) −175.905 −6.91021
\(649\) 28.7545 1.12871
\(650\) −112.678 −4.41961
\(651\) 29.0865 1.13999
\(652\) 72.1177 2.82435
\(653\) −37.5525 −1.46954 −0.734772 0.678314i \(-0.762711\pi\)
−0.734772 + 0.678314i \(0.762711\pi\)
\(654\) −70.4003 −2.75287
\(655\) 33.0538 1.29152
\(656\) 3.01165 0.117585
\(657\) 94.9243 3.70335
\(658\) 16.7829 0.654267
\(659\) −26.6759 −1.03915 −0.519573 0.854426i \(-0.673909\pi\)
−0.519573 + 0.854426i \(0.673909\pi\)
\(660\) 321.960 12.5323
\(661\) −5.96588 −0.232046 −0.116023 0.993247i \(-0.537015\pi\)
−0.116023 + 0.993247i \(0.537015\pi\)
\(662\) 10.2655 0.398979
\(663\) −32.1335 −1.24796
\(664\) −17.0230 −0.660621
\(665\) 4.53717 0.175944
\(666\) 184.546 7.15103
\(667\) −7.18542 −0.278221
\(668\) −58.9859 −2.28223
\(669\) 49.3447 1.90778
\(670\) −84.5277 −3.26559
\(671\) 7.80608 0.301350
\(672\) −2.69594 −0.103998
\(673\) 23.1123 0.890913 0.445457 0.895304i \(-0.353041\pi\)
0.445457 + 0.895304i \(0.353041\pi\)
\(674\) 1.21884 0.0469478
\(675\) 231.311 8.90315
\(676\) −3.68527 −0.141741
\(677\) −16.5330 −0.635413 −0.317707 0.948189i \(-0.602913\pi\)
−0.317707 + 0.948189i \(0.602913\pi\)
\(678\) −30.7708 −1.18175
\(679\) −9.83314 −0.377361
\(680\) −60.1677 −2.30733
\(681\) 81.5279 3.12415
\(682\) 118.133 4.52355
\(683\) −9.96495 −0.381298 −0.190649 0.981658i \(-0.561059\pi\)
−0.190649 + 0.981658i \(0.561059\pi\)
\(684\) −35.8536 −1.37090
\(685\) −78.0371 −2.98164
\(686\) −2.46575 −0.0941426
\(687\) −1.47339 −0.0562135
\(688\) −19.0392 −0.725863
\(689\) 49.6222 1.89045
\(690\) 98.7308 3.75862
\(691\) 23.3924 0.889890 0.444945 0.895558i \(-0.353223\pi\)
0.444945 + 0.895558i \(0.353223\pi\)
\(692\) 76.2852 2.89993
\(693\) −45.5714 −1.73112
\(694\) 12.3756 0.469770
\(695\) −45.7021 −1.73358
\(696\) 44.0920 1.67130
\(697\) −1.84940 −0.0700512
\(698\) −8.23867 −0.311838
\(699\) −15.6280 −0.591105
\(700\) 53.6053 2.02609
\(701\) −14.6348 −0.552749 −0.276374 0.961050i \(-0.589133\pi\)
−0.276374 + 0.961050i \(0.589133\pi\)
\(702\) −150.980 −5.69837
\(703\) 9.66572 0.364549
\(704\) 38.6137 1.45531
\(705\) 97.2260 3.66174
\(706\) −45.7789 −1.72291
\(707\) −14.1995 −0.534026
\(708\) −71.2235 −2.67674
\(709\) −0.119246 −0.00447839 −0.00223919 0.999997i \(-0.500713\pi\)
−0.00223919 + 0.999997i \(0.500713\pi\)
\(710\) 145.887 5.47505
\(711\) −81.7515 −3.06592
\(712\) −31.7404 −1.18952
\(713\) 24.3095 0.910397
\(714\) 22.7810 0.852558
\(715\) 81.8330 3.06038
\(716\) 23.0567 0.861669
\(717\) −16.7781 −0.626591
\(718\) −59.8609 −2.23399
\(719\) 17.4170 0.649544 0.324772 0.945792i \(-0.394712\pi\)
0.324772 + 0.945792i \(0.394712\pi\)
\(720\) −157.597 −5.87329
\(721\) −9.12069 −0.339672
\(722\) 44.0508 1.63940
\(723\) −99.3117 −3.69344
\(724\) 86.4938 3.21452
\(725\) −33.6797 −1.25083
\(726\) −161.427 −5.99113
\(727\) 28.4709 1.05593 0.527963 0.849267i \(-0.322956\pi\)
0.527963 + 0.849267i \(0.322956\pi\)
\(728\) −17.8371 −0.661088
\(729\) 105.798 3.91845
\(730\) 120.845 4.47266
\(731\) 11.6917 0.432432
\(732\) −19.3353 −0.714653
\(733\) −20.7455 −0.766251 −0.383126 0.923696i \(-0.625152\pi\)
−0.383126 + 0.923696i \(0.625152\pi\)
\(734\) 29.1506 1.07597
\(735\) −14.2844 −0.526889
\(736\) −2.25317 −0.0830531
\(737\) 44.4667 1.63795
\(738\) −13.6558 −0.502676
\(739\) 36.3132 1.33580 0.667902 0.744250i \(-0.267193\pi\)
0.667902 + 0.744250i \(0.267193\pi\)
\(740\) 157.655 5.79553
\(741\) −12.4272 −0.456523
\(742\) −35.1795 −1.29148
\(743\) 24.5894 0.902099 0.451050 0.892499i \(-0.351050\pi\)
0.451050 + 0.892499i \(0.351050\pi\)
\(744\) −149.170 −5.46885
\(745\) −31.0372 −1.13712
\(746\) −30.3360 −1.11068
\(747\) 27.3810 1.00182
\(748\) 62.0878 2.27015
\(749\) 10.0417 0.366914
\(750\) 286.666 10.4675
\(751\) 0.985237 0.0359518 0.0179759 0.999838i \(-0.494278\pi\)
0.0179759 + 0.999838i \(0.494278\pi\)
\(752\) −30.5322 −1.11340
\(753\) 77.9556 2.84086
\(754\) 21.9833 0.800584
\(755\) −8.23524 −0.299711
\(756\) 71.8269 2.61232
\(757\) 24.8344 0.902621 0.451311 0.892367i \(-0.350957\pi\)
0.451311 + 0.892367i \(0.350957\pi\)
\(758\) 19.7304 0.716640
\(759\) −51.9384 −1.88525
\(760\) −23.2689 −0.844053
\(761\) −19.5849 −0.709950 −0.354975 0.934876i \(-0.615511\pi\)
−0.354975 + 0.934876i \(0.615511\pi\)
\(762\) −37.1652 −1.34635
\(763\) 8.51272 0.308181
\(764\) 27.7596 1.00431
\(765\) 96.7777 3.49901
\(766\) −88.6009 −3.20128
\(767\) −18.1030 −0.653660
\(768\) −108.939 −3.93101
\(769\) 29.0499 1.04757 0.523784 0.851851i \(-0.324520\pi\)
0.523784 + 0.851851i \(0.324520\pi\)
\(770\) −58.0154 −2.09073
\(771\) 58.0924 2.09215
\(772\) −42.7919 −1.54011
\(773\) 0.972114 0.0349645 0.0174823 0.999847i \(-0.494435\pi\)
0.0174823 + 0.999847i \(0.494435\pi\)
\(774\) 86.3298 3.10306
\(775\) 113.944 4.09300
\(776\) 50.4294 1.81031
\(777\) −30.4307 −1.09169
\(778\) 9.09281 0.325993
\(779\) −0.715229 −0.0256257
\(780\) −202.697 −7.25770
\(781\) −76.7456 −2.74617
\(782\) 19.0396 0.680853
\(783\) −45.1282 −1.61275
\(784\) 4.48579 0.160207
\(785\) 20.9280 0.746952
\(786\) 64.1833 2.28934
\(787\) 18.6902 0.666233 0.333117 0.942886i \(-0.391900\pi\)
0.333117 + 0.942886i \(0.391900\pi\)
\(788\) 20.2316 0.720720
\(789\) 31.3182 1.11496
\(790\) −104.075 −3.70282
\(791\) 3.72077 0.132295
\(792\) 233.714 8.30465
\(793\) −4.91448 −0.174518
\(794\) −70.0004 −2.48422
\(795\) −203.800 −7.22805
\(796\) 42.0385 1.49001
\(797\) 19.9350 0.706135 0.353068 0.935598i \(-0.385139\pi\)
0.353068 + 0.935598i \(0.385139\pi\)
\(798\) 8.81021 0.311878
\(799\) 18.7494 0.663305
\(800\) −10.5612 −0.373393
\(801\) 51.0535 1.80389
\(802\) −29.4091 −1.03847
\(803\) −63.5717 −2.24340
\(804\) −110.142 −3.88441
\(805\) −11.9384 −0.420774
\(806\) −74.3732 −2.61968
\(807\) 64.6688 2.27645
\(808\) 72.8221 2.56187
\(809\) 4.65922 0.163809 0.0819047 0.996640i \(-0.473900\pi\)
0.0819047 + 0.996640i \(0.473900\pi\)
\(810\) 360.198 12.6561
\(811\) −15.1755 −0.532882 −0.266441 0.963851i \(-0.585848\pi\)
−0.266441 + 0.963851i \(0.585848\pi\)
\(812\) −10.4583 −0.367014
\(813\) −21.2213 −0.744265
\(814\) −123.592 −4.33191
\(815\) −75.2831 −2.63705
\(816\) −41.4442 −1.45084
\(817\) 4.52157 0.158190
\(818\) 1.79157 0.0626409
\(819\) 28.6904 1.00253
\(820\) −11.6659 −0.407392
\(821\) −0.224077 −0.00782035 −0.00391017 0.999992i \(-0.501245\pi\)
−0.00391017 + 0.999992i \(0.501245\pi\)
\(822\) −151.531 −5.28525
\(823\) 26.3007 0.916786 0.458393 0.888750i \(-0.348425\pi\)
0.458393 + 0.888750i \(0.348425\pi\)
\(824\) 46.7755 1.62950
\(825\) −243.448 −8.47576
\(826\) 12.8341 0.446554
\(827\) −32.6954 −1.13693 −0.568465 0.822708i \(-0.692462\pi\)
−0.568465 + 0.822708i \(0.692462\pi\)
\(828\) 94.3397 3.27853
\(829\) 28.0653 0.974747 0.487373 0.873194i \(-0.337955\pi\)
0.487373 + 0.873194i \(0.337955\pi\)
\(830\) 34.8577 1.20993
\(831\) 97.8683 3.39501
\(832\) −24.3101 −0.842800
\(833\) −2.75465 −0.0954431
\(834\) −88.7435 −3.07294
\(835\) 61.5749 2.13089
\(836\) 24.0115 0.830455
\(837\) 152.676 5.27726
\(838\) 57.5153 1.98683
\(839\) 25.5160 0.880910 0.440455 0.897775i \(-0.354817\pi\)
0.440455 + 0.897775i \(0.354817\pi\)
\(840\) 73.2578 2.52763
\(841\) −22.4292 −0.773419
\(842\) 28.2405 0.973232
\(843\) −10.9896 −0.378503
\(844\) −46.6345 −1.60522
\(845\) 3.84702 0.132341
\(846\) 138.443 4.75977
\(847\) 19.5196 0.670702
\(848\) 64.0002 2.19777
\(849\) 63.4827 2.17872
\(850\) 89.2429 3.06100
\(851\) −25.4329 −0.871828
\(852\) 190.095 6.51256
\(853\) 2.18717 0.0748874 0.0374437 0.999299i \(-0.488079\pi\)
0.0374437 + 0.999299i \(0.488079\pi\)
\(854\) 3.48411 0.119224
\(855\) 37.4273 1.27999
\(856\) −51.4987 −1.76019
\(857\) 12.8845 0.440127 0.220063 0.975486i \(-0.429374\pi\)
0.220063 + 0.975486i \(0.429374\pi\)
\(858\) 158.902 5.42483
\(859\) −20.9235 −0.713901 −0.356951 0.934123i \(-0.616184\pi\)
−0.356951 + 0.934123i \(0.616184\pi\)
\(860\) 73.7504 2.51487
\(861\) 2.25176 0.0767399
\(862\) −36.7040 −1.25014
\(863\) −1.00000 −0.0340404
\(864\) −14.1511 −0.481431
\(865\) −79.6335 −2.70762
\(866\) −0.757612 −0.0257447
\(867\) −31.5671 −1.07207
\(868\) 35.3821 1.20095
\(869\) 54.7497 1.85726
\(870\) −90.2863 −3.06099
\(871\) −27.9949 −0.948572
\(872\) −43.6576 −1.47843
\(873\) −81.1140 −2.74529
\(874\) 7.36326 0.249066
\(875\) −34.6633 −1.17183
\(876\) 157.464 5.32022
\(877\) 23.1363 0.781257 0.390628 0.920548i \(-0.372258\pi\)
0.390628 + 0.920548i \(0.372258\pi\)
\(878\) −24.3717 −0.822505
\(879\) −77.7295 −2.62175
\(880\) 105.544 3.55789
\(881\) 36.5103 1.23006 0.615031 0.788503i \(-0.289143\pi\)
0.615031 + 0.788503i \(0.289143\pi\)
\(882\) −20.3400 −0.684884
\(883\) 0.957088 0.0322086 0.0161043 0.999870i \(-0.494874\pi\)
0.0161043 + 0.999870i \(0.494874\pi\)
\(884\) −39.0887 −1.31469
\(885\) 74.3496 2.49923
\(886\) 62.0066 2.08315
\(887\) −26.1511 −0.878069 −0.439035 0.898470i \(-0.644679\pi\)
−0.439035 + 0.898470i \(0.644679\pi\)
\(888\) 156.064 5.23717
\(889\) 4.49397 0.150723
\(890\) 64.9943 2.17861
\(891\) −189.486 −6.34802
\(892\) 60.0250 2.00979
\(893\) 7.25103 0.242646
\(894\) −60.2675 −2.01565
\(895\) −24.0687 −0.804528
\(896\) 18.8422 0.629473
\(897\) 32.6989 1.09178
\(898\) 12.9196 0.431134
\(899\) −22.2303 −0.741421
\(900\) 442.192 14.7397
\(901\) −39.3015 −1.30932
\(902\) 9.14540 0.304509
\(903\) −14.2353 −0.473722
\(904\) −19.0820 −0.634658
\(905\) −90.2901 −3.00135
\(906\) −15.9911 −0.531267
\(907\) 15.0160 0.498598 0.249299 0.968427i \(-0.419800\pi\)
0.249299 + 0.968427i \(0.419800\pi\)
\(908\) 99.1741 3.29121
\(909\) −117.132 −3.88502
\(910\) 36.5248 1.21078
\(911\) −6.70471 −0.222137 −0.111068 0.993813i \(-0.535427\pi\)
−0.111068 + 0.993813i \(0.535427\pi\)
\(912\) −16.0279 −0.530737
\(913\) −18.3373 −0.606876
\(914\) −90.6857 −2.99962
\(915\) 20.1839 0.667261
\(916\) −1.79230 −0.0592193
\(917\) −7.76097 −0.256290
\(918\) 119.578 3.94667
\(919\) 47.5253 1.56771 0.783857 0.620941i \(-0.213249\pi\)
0.783857 + 0.620941i \(0.213249\pi\)
\(920\) 61.2263 2.01857
\(921\) 41.9643 1.38277
\(922\) 6.82772 0.224859
\(923\) 48.3168 1.59037
\(924\) −75.5957 −2.48691
\(925\) −119.210 −3.91960
\(926\) −48.1739 −1.58309
\(927\) −75.2369 −2.47110
\(928\) 2.06046 0.0676378
\(929\) −4.43857 −0.145625 −0.0728123 0.997346i \(-0.523197\pi\)
−0.0728123 + 0.997346i \(0.523197\pi\)
\(930\) 305.454 10.0162
\(931\) −1.06532 −0.0349145
\(932\) −19.0106 −0.622712
\(933\) 81.4700 2.66721
\(934\) 55.9219 1.82982
\(935\) −64.8129 −2.11961
\(936\) −147.139 −4.80939
\(937\) −47.3622 −1.54725 −0.773627 0.633641i \(-0.781560\pi\)
−0.773627 + 0.633641i \(0.781560\pi\)
\(938\) 19.8470 0.648026
\(939\) −12.6961 −0.414322
\(940\) 118.270 3.85754
\(941\) −43.7928 −1.42760 −0.713802 0.700348i \(-0.753028\pi\)
−0.713802 + 0.700348i \(0.753028\pi\)
\(942\) 40.6377 1.32405
\(943\) 1.88194 0.0612845
\(944\) −23.3483 −0.759922
\(945\) −74.9795 −2.43908
\(946\) −57.8159 −1.87976
\(947\) 1.73424 0.0563552 0.0281776 0.999603i \(-0.491030\pi\)
0.0281776 + 0.999603i \(0.491030\pi\)
\(948\) −135.613 −4.40449
\(949\) 40.0229 1.29920
\(950\) 34.5133 1.11976
\(951\) 12.3579 0.400732
\(952\) 14.1273 0.457867
\(953\) 61.2258 1.98330 0.991650 0.128960i \(-0.0411640\pi\)
0.991650 + 0.128960i \(0.0411640\pi\)
\(954\) −290.197 −9.39548
\(955\) −28.9780 −0.937707
\(956\) −20.4097 −0.660095
\(957\) 47.4961 1.53533
\(958\) −88.6879 −2.86538
\(959\) 18.3230 0.591680
\(960\) 99.8424 3.22240
\(961\) 44.2087 1.42609
\(962\) 77.8101 2.50870
\(963\) 82.8340 2.66929
\(964\) −120.807 −3.89093
\(965\) 44.6701 1.43798
\(966\) −23.1818 −0.745863
\(967\) −45.6037 −1.46652 −0.733258 0.679951i \(-0.762001\pi\)
−0.733258 + 0.679951i \(0.762001\pi\)
\(968\) −100.107 −3.21755
\(969\) 9.84249 0.316186
\(970\) −103.263 −3.31558
\(971\) 2.35110 0.0754504 0.0377252 0.999288i \(-0.487989\pi\)
0.0377252 + 0.999288i \(0.487989\pi\)
\(972\) 253.868 8.14281
\(973\) 10.7308 0.344013
\(974\) 50.5103 1.61845
\(975\) 153.267 4.90848
\(976\) −6.33844 −0.202889
\(977\) 5.15851 0.165035 0.0825177 0.996590i \(-0.473704\pi\)
0.0825177 + 0.996590i \(0.473704\pi\)
\(978\) −146.183 −4.67443
\(979\) −34.1910 −1.09275
\(980\) −17.3762 −0.555062
\(981\) 70.2218 2.24201
\(982\) 9.69363 0.309336
\(983\) 3.41607 0.108956 0.0544779 0.998515i \(-0.482651\pi\)
0.0544779 + 0.998515i \(0.482651\pi\)
\(984\) −11.5482 −0.368143
\(985\) −21.1196 −0.672926
\(986\) −17.4111 −0.554482
\(987\) −22.8285 −0.726639
\(988\) −15.1169 −0.480934
\(989\) −11.8974 −0.378314
\(990\) −478.571 −15.2100
\(991\) 16.2529 0.516290 0.258145 0.966106i \(-0.416889\pi\)
0.258145 + 0.966106i \(0.416889\pi\)
\(992\) −6.97087 −0.221325
\(993\) −13.9633 −0.443112
\(994\) −34.2541 −1.08647
\(995\) −43.8836 −1.39120
\(996\) 45.4206 1.43921
\(997\) −20.2569 −0.641543 −0.320772 0.947157i \(-0.603942\pi\)
−0.320772 + 0.947157i \(0.603942\pi\)
\(998\) 70.3199 2.22594
\(999\) −159.732 −5.05369
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 \(a_p\))