Properties

Label 6019.2.a.c.1.6
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.61467 q^{2}\) \(+0.516414 q^{3}\) \(+4.83649 q^{4}\) \(-3.96792 q^{5}\) \(-1.35025 q^{6}\) \(+3.66433 q^{7}\) \(-7.41648 q^{8}\) \(-2.73332 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.61467 q^{2}\) \(+0.516414 q^{3}\) \(+4.83649 q^{4}\) \(-3.96792 q^{5}\) \(-1.35025 q^{6}\) \(+3.66433 q^{7}\) \(-7.41648 q^{8}\) \(-2.73332 q^{9}\) \(+10.3748 q^{10}\) \(-4.05913 q^{11}\) \(+2.49763 q^{12}\) \(-1.00000 q^{13}\) \(-9.58102 q^{14}\) \(-2.04909 q^{15}\) \(+9.71866 q^{16}\) \(+6.83477 q^{17}\) \(+7.14672 q^{18}\) \(+5.65862 q^{19}\) \(-19.1908 q^{20}\) \(+1.89231 q^{21}\) \(+10.6133 q^{22}\) \(-4.75842 q^{23}\) \(-3.82998 q^{24}\) \(+10.7444 q^{25}\) \(+2.61467 q^{26}\) \(-2.96077 q^{27}\) \(+17.7225 q^{28}\) \(+2.57174 q^{29}\) \(+5.35769 q^{30}\) \(-3.95962 q^{31}\) \(-10.5781 q^{32}\) \(-2.09619 q^{33}\) \(-17.8707 q^{34}\) \(-14.5398 q^{35}\) \(-13.2197 q^{36}\) \(-7.21708 q^{37}\) \(-14.7954 q^{38}\) \(-0.516414 q^{39}\) \(+29.4280 q^{40}\) \(-9.50552 q^{41}\) \(-4.94777 q^{42}\) \(-5.45391 q^{43}\) \(-19.6319 q^{44}\) \(+10.8456 q^{45}\) \(+12.4417 q^{46}\) \(+9.77351 q^{47}\) \(+5.01885 q^{48}\) \(+6.42734 q^{49}\) \(-28.0929 q^{50}\) \(+3.52957 q^{51}\) \(-4.83649 q^{52}\) \(+2.55531 q^{53}\) \(+7.74142 q^{54}\) \(+16.1063 q^{55}\) \(-27.1765 q^{56}\) \(+2.92219 q^{57}\) \(-6.72423 q^{58}\) \(+1.66855 q^{59}\) \(-9.91039 q^{60}\) \(+6.44218 q^{61}\) \(+10.3531 q^{62}\) \(-10.0158 q^{63}\) \(+8.22091 q^{64}\) \(+3.96792 q^{65}\) \(+5.48085 q^{66}\) \(-12.3003 q^{67}\) \(+33.0563 q^{68}\) \(-2.45732 q^{69}\) \(+38.0167 q^{70}\) \(+11.6516 q^{71}\) \(+20.2716 q^{72}\) \(+9.66772 q^{73}\) \(+18.8703 q^{74}\) \(+5.54854 q^{75}\) \(+27.3678 q^{76}\) \(-14.8740 q^{77}\) \(+1.35025 q^{78}\) \(+17.0304 q^{79}\) \(-38.5628 q^{80}\) \(+6.67097 q^{81}\) \(+24.8538 q^{82}\) \(-5.34508 q^{83}\) \(+9.15216 q^{84}\) \(-27.1198 q^{85}\) \(+14.2602 q^{86}\) \(+1.32808 q^{87}\) \(+30.1044 q^{88}\) \(+1.55773 q^{89}\) \(-28.3576 q^{90}\) \(-3.66433 q^{91}\) \(-23.0140 q^{92}\) \(-2.04480 q^{93}\) \(-25.5545 q^{94}\) \(-22.4529 q^{95}\) \(-5.46268 q^{96}\) \(-8.63999 q^{97}\) \(-16.8054 q^{98}\) \(+11.0949 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61467 −1.84885 −0.924425 0.381364i \(-0.875454\pi\)
−0.924425 + 0.381364i \(0.875454\pi\)
\(3\) 0.516414 0.298152 0.149076 0.988826i \(-0.452370\pi\)
0.149076 + 0.988826i \(0.452370\pi\)
\(4\) 4.83649 2.41825
\(5\) −3.96792 −1.77451 −0.887253 0.461283i \(-0.847389\pi\)
−0.887253 + 0.461283i \(0.847389\pi\)
\(6\) −1.35025 −0.551238
\(7\) 3.66433 1.38499 0.692494 0.721424i \(-0.256512\pi\)
0.692494 + 0.721424i \(0.256512\pi\)
\(8\) −7.41648 −2.62212
\(9\) −2.73332 −0.911105
\(10\) 10.3748 3.28079
\(11\) −4.05913 −1.22387 −0.611937 0.790907i \(-0.709609\pi\)
−0.611937 + 0.790907i \(0.709609\pi\)
\(12\) 2.49763 0.721004
\(13\) −1.00000 −0.277350
\(14\) −9.58102 −2.56063
\(15\) −2.04909 −0.529072
\(16\) 9.71866 2.42966
\(17\) 6.83477 1.65768 0.828838 0.559489i \(-0.189002\pi\)
0.828838 + 0.559489i \(0.189002\pi\)
\(18\) 7.14672 1.68450
\(19\) 5.65862 1.29818 0.649088 0.760713i \(-0.275151\pi\)
0.649088 + 0.760713i \(0.275151\pi\)
\(20\) −19.1908 −4.29119
\(21\) 1.89231 0.412937
\(22\) 10.6133 2.26276
\(23\) −4.75842 −0.992199 −0.496099 0.868266i \(-0.665235\pi\)
−0.496099 + 0.868266i \(0.665235\pi\)
\(24\) −3.82998 −0.781791
\(25\) 10.7444 2.14887
\(26\) 2.61467 0.512779
\(27\) −2.96077 −0.569800
\(28\) 17.7225 3.34924
\(29\) 2.57174 0.477559 0.238780 0.971074i \(-0.423253\pi\)
0.238780 + 0.971074i \(0.423253\pi\)
\(30\) 5.35769 0.978175
\(31\) −3.95962 −0.711169 −0.355584 0.934644i \(-0.615718\pi\)
−0.355584 + 0.934644i \(0.615718\pi\)
\(32\) −10.5781 −1.86996
\(33\) −2.09619 −0.364900
\(34\) −17.8707 −3.06479
\(35\) −14.5398 −2.45767
\(36\) −13.2197 −2.20328
\(37\) −7.21708 −1.18648 −0.593240 0.805026i \(-0.702151\pi\)
−0.593240 + 0.805026i \(0.702151\pi\)
\(38\) −14.7954 −2.40013
\(39\) −0.516414 −0.0826925
\(40\) 29.4280 4.65297
\(41\) −9.50552 −1.48451 −0.742256 0.670116i \(-0.766244\pi\)
−0.742256 + 0.670116i \(0.766244\pi\)
\(42\) −4.94777 −0.763458
\(43\) −5.45391 −0.831714 −0.415857 0.909430i \(-0.636518\pi\)
−0.415857 + 0.909430i \(0.636518\pi\)
\(44\) −19.6319 −2.95963
\(45\) 10.8456 1.61676
\(46\) 12.4417 1.83443
\(47\) 9.77351 1.42561 0.712806 0.701361i \(-0.247424\pi\)
0.712806 + 0.701361i \(0.247424\pi\)
\(48\) 5.01885 0.724409
\(49\) 6.42734 0.918192
\(50\) −28.0929 −3.97294
\(51\) 3.52957 0.494239
\(52\) −4.83649 −0.670700
\(53\) 2.55531 0.350999 0.175500 0.984479i \(-0.443846\pi\)
0.175500 + 0.984479i \(0.443846\pi\)
\(54\) 7.74142 1.05347
\(55\) 16.1063 2.17177
\(56\) −27.1765 −3.63161
\(57\) 2.92219 0.387054
\(58\) −6.72423 −0.882935
\(59\) 1.66855 0.217227 0.108614 0.994084i \(-0.465359\pi\)
0.108614 + 0.994084i \(0.465359\pi\)
\(60\) −9.91039 −1.27943
\(61\) 6.44218 0.824837 0.412418 0.910995i \(-0.364684\pi\)
0.412418 + 0.910995i \(0.364684\pi\)
\(62\) 10.3531 1.31484
\(63\) −10.0158 −1.26187
\(64\) 8.22091 1.02761
\(65\) 3.96792 0.492159
\(66\) 5.48085 0.674646
\(67\) −12.3003 −1.50272 −0.751362 0.659890i \(-0.770603\pi\)
−0.751362 + 0.659890i \(0.770603\pi\)
\(68\) 33.0563 4.00867
\(69\) −2.45732 −0.295826
\(70\) 38.0167 4.54386
\(71\) 11.6516 1.38279 0.691397 0.722475i \(-0.256996\pi\)
0.691397 + 0.722475i \(0.256996\pi\)
\(72\) 20.2716 2.38903
\(73\) 9.66772 1.13152 0.565761 0.824570i \(-0.308583\pi\)
0.565761 + 0.824570i \(0.308583\pi\)
\(74\) 18.8703 2.19362
\(75\) 5.54854 0.640690
\(76\) 27.3678 3.13931
\(77\) −14.8740 −1.69505
\(78\) 1.35025 0.152886
\(79\) 17.0304 1.91606 0.958032 0.286661i \(-0.0925453\pi\)
0.958032 + 0.286661i \(0.0925453\pi\)
\(80\) −38.5628 −4.31145
\(81\) 6.67097 0.741219
\(82\) 24.8538 2.74464
\(83\) −5.34508 −0.586699 −0.293350 0.956005i \(-0.594770\pi\)
−0.293350 + 0.956005i \(0.594770\pi\)
\(84\) 9.15216 0.998583
\(85\) −27.1198 −2.94156
\(86\) 14.2602 1.53771
\(87\) 1.32808 0.142385
\(88\) 30.1044 3.20914
\(89\) 1.55773 0.165119 0.0825597 0.996586i \(-0.473690\pi\)
0.0825597 + 0.996586i \(0.473690\pi\)
\(90\) −28.3576 −2.98915
\(91\) −3.66433 −0.384127
\(92\) −23.0140 −2.39938
\(93\) −2.04480 −0.212036
\(94\) −25.5545 −2.63574
\(95\) −22.4529 −2.30362
\(96\) −5.46268 −0.557533
\(97\) −8.63999 −0.877258 −0.438629 0.898668i \(-0.644536\pi\)
−0.438629 + 0.898668i \(0.644536\pi\)
\(98\) −16.8054 −1.69760
\(99\) 11.0949 1.11508
\(100\) 51.9649 5.19649
\(101\) 2.63471 0.262163 0.131082 0.991372i \(-0.458155\pi\)
0.131082 + 0.991372i \(0.458155\pi\)
\(102\) −9.22867 −0.913774
\(103\) −4.04364 −0.398432 −0.199216 0.979956i \(-0.563839\pi\)
−0.199216 + 0.979956i \(0.563839\pi\)
\(104\) 7.41648 0.727246
\(105\) −7.50854 −0.732759
\(106\) −6.68130 −0.648945
\(107\) 6.85131 0.662342 0.331171 0.943571i \(-0.392556\pi\)
0.331171 + 0.943571i \(0.392556\pi\)
\(108\) −14.3197 −1.37792
\(109\) −8.75770 −0.838835 −0.419418 0.907793i \(-0.637766\pi\)
−0.419418 + 0.907793i \(0.637766\pi\)
\(110\) −42.1126 −4.01528
\(111\) −3.72700 −0.353751
\(112\) 35.6124 3.36506
\(113\) 5.02085 0.472322 0.236161 0.971714i \(-0.424111\pi\)
0.236161 + 0.971714i \(0.424111\pi\)
\(114\) −7.64056 −0.715604
\(115\) 18.8810 1.76066
\(116\) 12.4382 1.15486
\(117\) 2.73332 0.252695
\(118\) −4.36272 −0.401620
\(119\) 25.0449 2.29586
\(120\) 15.1970 1.38729
\(121\) 5.47652 0.497866
\(122\) −16.8442 −1.52500
\(123\) −4.90879 −0.442610
\(124\) −19.1507 −1.71978
\(125\) −22.7931 −2.03868
\(126\) 26.1880 2.33301
\(127\) 11.8635 1.05272 0.526359 0.850262i \(-0.323557\pi\)
0.526359 + 0.850262i \(0.323557\pi\)
\(128\) −0.338753 −0.0299419
\(129\) −2.81648 −0.247977
\(130\) −10.3748 −0.909929
\(131\) −16.0397 −1.40140 −0.700699 0.713457i \(-0.747129\pi\)
−0.700699 + 0.713457i \(0.747129\pi\)
\(132\) −10.1382 −0.882418
\(133\) 20.7351 1.79796
\(134\) 32.1613 2.77831
\(135\) 11.7481 1.01111
\(136\) −50.6900 −4.34663
\(137\) −11.3458 −0.969334 −0.484667 0.874699i \(-0.661059\pi\)
−0.484667 + 0.874699i \(0.661059\pi\)
\(138\) 6.42506 0.546938
\(139\) 6.10627 0.517927 0.258963 0.965887i \(-0.416619\pi\)
0.258963 + 0.965887i \(0.416619\pi\)
\(140\) −70.3214 −5.94325
\(141\) 5.04718 0.425049
\(142\) −30.4651 −2.55658
\(143\) 4.05913 0.339441
\(144\) −26.5642 −2.21368
\(145\) −10.2044 −0.847432
\(146\) −25.2779 −2.09201
\(147\) 3.31917 0.273761
\(148\) −34.9053 −2.86920
\(149\) 3.37099 0.276162 0.138081 0.990421i \(-0.455907\pi\)
0.138081 + 0.990421i \(0.455907\pi\)
\(150\) −14.5076 −1.18454
\(151\) −5.03260 −0.409547 −0.204773 0.978809i \(-0.565646\pi\)
−0.204773 + 0.978809i \(0.565646\pi\)
\(152\) −41.9670 −3.40397
\(153\) −18.6816 −1.51032
\(154\) 38.8906 3.13389
\(155\) 15.7114 1.26197
\(156\) −2.49763 −0.199971
\(157\) −0.156318 −0.0124755 −0.00623775 0.999981i \(-0.501986\pi\)
−0.00623775 + 0.999981i \(0.501986\pi\)
\(158\) −44.5287 −3.54251
\(159\) 1.31960 0.104651
\(160\) 41.9730 3.31826
\(161\) −17.4364 −1.37418
\(162\) −17.4424 −1.37040
\(163\) 16.1465 1.26469 0.632347 0.774685i \(-0.282092\pi\)
0.632347 + 0.774685i \(0.282092\pi\)
\(164\) −45.9733 −3.58991
\(165\) 8.31751 0.647517
\(166\) 13.9756 1.08472
\(167\) 17.1965 1.33071 0.665354 0.746528i \(-0.268281\pi\)
0.665354 + 0.746528i \(0.268281\pi\)
\(168\) −14.0343 −1.08277
\(169\) 1.00000 0.0769231
\(170\) 70.9093 5.43849
\(171\) −15.4668 −1.18277
\(172\) −26.3778 −2.01129
\(173\) 6.29881 0.478890 0.239445 0.970910i \(-0.423035\pi\)
0.239445 + 0.970910i \(0.423035\pi\)
\(174\) −3.47249 −0.263249
\(175\) 39.3709 2.97616
\(176\) −39.4493 −2.97360
\(177\) 0.861665 0.0647667
\(178\) −4.07295 −0.305281
\(179\) −16.7790 −1.25412 −0.627062 0.778969i \(-0.715743\pi\)
−0.627062 + 0.778969i \(0.715743\pi\)
\(180\) 52.4545 3.90973
\(181\) −12.8676 −0.956438 −0.478219 0.878241i \(-0.658717\pi\)
−0.478219 + 0.878241i \(0.658717\pi\)
\(182\) 9.58102 0.710192
\(183\) 3.32683 0.245927
\(184\) 35.2907 2.60167
\(185\) 28.6367 2.10542
\(186\) 5.34648 0.392023
\(187\) −27.7432 −2.02879
\(188\) 47.2695 3.44748
\(189\) −10.8492 −0.789166
\(190\) 58.7069 4.25905
\(191\) 1.64260 0.118854 0.0594272 0.998233i \(-0.481073\pi\)
0.0594272 + 0.998233i \(0.481073\pi\)
\(192\) 4.24540 0.306385
\(193\) −10.0442 −0.722999 −0.361499 0.932372i \(-0.617735\pi\)
−0.361499 + 0.932372i \(0.617735\pi\)
\(194\) 22.5907 1.62192
\(195\) 2.04909 0.146738
\(196\) 31.0858 2.22041
\(197\) −5.42575 −0.386569 −0.193284 0.981143i \(-0.561914\pi\)
−0.193284 + 0.981143i \(0.561914\pi\)
\(198\) −29.0094 −2.06161
\(199\) 20.1230 1.42648 0.713239 0.700921i \(-0.247227\pi\)
0.713239 + 0.700921i \(0.247227\pi\)
\(200\) −79.6853 −5.63460
\(201\) −6.35206 −0.448040
\(202\) −6.88889 −0.484701
\(203\) 9.42370 0.661414
\(204\) 17.0708 1.19519
\(205\) 37.7171 2.63428
\(206\) 10.5728 0.736640
\(207\) 13.0063 0.903998
\(208\) −9.71866 −0.673868
\(209\) −22.9691 −1.58880
\(210\) 19.6323 1.35476
\(211\) −5.86848 −0.404003 −0.202001 0.979385i \(-0.564745\pi\)
−0.202001 + 0.979385i \(0.564745\pi\)
\(212\) 12.3587 0.848802
\(213\) 6.01707 0.412283
\(214\) −17.9139 −1.22457
\(215\) 21.6407 1.47588
\(216\) 21.9585 1.49408
\(217\) −14.5094 −0.984960
\(218\) 22.8985 1.55088
\(219\) 4.99255 0.337365
\(220\) 77.8978 5.25187
\(221\) −6.83477 −0.459757
\(222\) 9.74487 0.654033
\(223\) −13.8753 −0.929161 −0.464581 0.885531i \(-0.653795\pi\)
−0.464581 + 0.885531i \(0.653795\pi\)
\(224\) −38.7617 −2.58987
\(225\) −29.3677 −1.95785
\(226\) −13.1279 −0.873253
\(227\) −1.13422 −0.0752811 −0.0376405 0.999291i \(-0.511984\pi\)
−0.0376405 + 0.999291i \(0.511984\pi\)
\(228\) 14.1331 0.935990
\(229\) 6.71154 0.443511 0.221756 0.975102i \(-0.428821\pi\)
0.221756 + 0.975102i \(0.428821\pi\)
\(230\) −49.3676 −3.25520
\(231\) −7.68115 −0.505382
\(232\) −19.0732 −1.25222
\(233\) −4.49394 −0.294408 −0.147204 0.989106i \(-0.547027\pi\)
−0.147204 + 0.989106i \(0.547027\pi\)
\(234\) −7.14672 −0.467195
\(235\) −38.7804 −2.52976
\(236\) 8.06995 0.525309
\(237\) 8.79472 0.571278
\(238\) −65.4841 −4.24470
\(239\) −15.9542 −1.03199 −0.515997 0.856590i \(-0.672578\pi\)
−0.515997 + 0.856590i \(0.672578\pi\)
\(240\) −19.9144 −1.28547
\(241\) 24.6518 1.58796 0.793980 0.607944i \(-0.208006\pi\)
0.793980 + 0.607944i \(0.208006\pi\)
\(242\) −14.3193 −0.920479
\(243\) 12.3273 0.790796
\(244\) 31.1575 1.99466
\(245\) −25.5032 −1.62934
\(246\) 12.8348 0.818320
\(247\) −5.65862 −0.360049
\(248\) 29.3664 1.86477
\(249\) −2.76028 −0.174925
\(250\) 59.5964 3.76921
\(251\) 29.1834 1.84204 0.921019 0.389518i \(-0.127358\pi\)
0.921019 + 0.389518i \(0.127358\pi\)
\(252\) −48.4412 −3.05151
\(253\) 19.3150 1.21433
\(254\) −31.0192 −1.94632
\(255\) −14.0051 −0.877030
\(256\) −15.5561 −0.972256
\(257\) −28.7805 −1.79528 −0.897641 0.440728i \(-0.854720\pi\)
−0.897641 + 0.440728i \(0.854720\pi\)
\(258\) 7.36416 0.458472
\(259\) −26.4458 −1.64326
\(260\) 19.1908 1.19016
\(261\) −7.02937 −0.435107
\(262\) 41.9386 2.59098
\(263\) 22.3088 1.37562 0.687810 0.725890i \(-0.258572\pi\)
0.687810 + 0.725890i \(0.258572\pi\)
\(264\) 15.5464 0.956813
\(265\) −10.1393 −0.622850
\(266\) −54.2153 −3.32415
\(267\) 0.804435 0.0492306
\(268\) −59.4904 −3.63395
\(269\) 10.8353 0.660638 0.330319 0.943869i \(-0.392844\pi\)
0.330319 + 0.943869i \(0.392844\pi\)
\(270\) −30.7173 −1.86940
\(271\) −32.4903 −1.97364 −0.986822 0.161812i \(-0.948266\pi\)
−0.986822 + 0.161812i \(0.948266\pi\)
\(272\) 66.4248 4.02760
\(273\) −1.89231 −0.114528
\(274\) 29.6654 1.79215
\(275\) −43.6127 −2.62994
\(276\) −11.8848 −0.715380
\(277\) −30.5687 −1.83670 −0.918349 0.395772i \(-0.870477\pi\)
−0.918349 + 0.395772i \(0.870477\pi\)
\(278\) −15.9659 −0.957569
\(279\) 10.8229 0.647950
\(280\) 107.834 6.44431
\(281\) 18.5659 1.10755 0.553774 0.832667i \(-0.313187\pi\)
0.553774 + 0.832667i \(0.313187\pi\)
\(282\) −13.1967 −0.785852
\(283\) −5.44527 −0.323688 −0.161844 0.986816i \(-0.551744\pi\)
−0.161844 + 0.986816i \(0.551744\pi\)
\(284\) 56.3530 3.34393
\(285\) −11.5950 −0.686829
\(286\) −10.6133 −0.627576
\(287\) −34.8314 −2.05603
\(288\) 28.9133 1.70373
\(289\) 29.7141 1.74789
\(290\) 26.6812 1.56677
\(291\) −4.46181 −0.261556
\(292\) 46.7578 2.73630
\(293\) −2.81750 −0.164600 −0.0823000 0.996608i \(-0.526227\pi\)
−0.0823000 + 0.996608i \(0.526227\pi\)
\(294\) −8.67853 −0.506142
\(295\) −6.62068 −0.385471
\(296\) 53.5253 3.11109
\(297\) 12.0181 0.697363
\(298\) −8.81401 −0.510582
\(299\) 4.75842 0.275186
\(300\) 26.8354 1.54935
\(301\) −19.9850 −1.15191
\(302\) 13.1586 0.757191
\(303\) 1.36060 0.0781645
\(304\) 54.9941 3.15413
\(305\) −25.5620 −1.46368
\(306\) 48.8462 2.79235
\(307\) −16.7456 −0.955721 −0.477860 0.878436i \(-0.658588\pi\)
−0.477860 + 0.878436i \(0.658588\pi\)
\(308\) −71.9380 −4.09905
\(309\) −2.08819 −0.118793
\(310\) −41.0802 −2.33320
\(311\) −29.3352 −1.66344 −0.831722 0.555192i \(-0.812645\pi\)
−0.831722 + 0.555192i \(0.812645\pi\)
\(312\) 3.82998 0.216830
\(313\) 20.3749 1.15166 0.575830 0.817570i \(-0.304679\pi\)
0.575830 + 0.817570i \(0.304679\pi\)
\(314\) 0.408719 0.0230653
\(315\) 39.7418 2.23920
\(316\) 82.3671 4.63351
\(317\) −2.12437 −0.119316 −0.0596582 0.998219i \(-0.519001\pi\)
−0.0596582 + 0.998219i \(0.519001\pi\)
\(318\) −3.45032 −0.193484
\(319\) −10.4390 −0.584472
\(320\) −32.6199 −1.82351
\(321\) 3.53812 0.197478
\(322\) 45.5905 2.54066
\(323\) 38.6754 2.15195
\(324\) 32.2641 1.79245
\(325\) −10.7444 −0.595989
\(326\) −42.2178 −2.33823
\(327\) −4.52260 −0.250100
\(328\) 70.4975 3.89257
\(329\) 35.8134 1.97446
\(330\) −21.7475 −1.19716
\(331\) −6.61479 −0.363581 −0.181791 0.983337i \(-0.558189\pi\)
−0.181791 + 0.983337i \(0.558189\pi\)
\(332\) −25.8514 −1.41878
\(333\) 19.7265 1.08101
\(334\) −44.9632 −2.46028
\(335\) 48.8066 2.66659
\(336\) 18.3908 1.00330
\(337\) −11.7420 −0.639628 −0.319814 0.947480i \(-0.603621\pi\)
−0.319814 + 0.947480i \(0.603621\pi\)
\(338\) −2.61467 −0.142219
\(339\) 2.59284 0.140824
\(340\) −131.165 −7.11340
\(341\) 16.0726 0.870380
\(342\) 40.4405 2.18677
\(343\) −2.09841 −0.113303
\(344\) 40.4488 2.18086
\(345\) 9.75042 0.524945
\(346\) −16.4693 −0.885395
\(347\) −28.2984 −1.51914 −0.759568 0.650428i \(-0.774590\pi\)
−0.759568 + 0.650428i \(0.774590\pi\)
\(348\) 6.42325 0.344322
\(349\) −17.7809 −0.951788 −0.475894 0.879503i \(-0.657875\pi\)
−0.475894 + 0.879503i \(0.657875\pi\)
\(350\) −102.942 −5.50247
\(351\) 2.96077 0.158034
\(352\) 42.9379 2.28860
\(353\) −13.1955 −0.702324 −0.351162 0.936315i \(-0.614213\pi\)
−0.351162 + 0.936315i \(0.614213\pi\)
\(354\) −2.25297 −0.119744
\(355\) −46.2327 −2.45377
\(356\) 7.53396 0.399299
\(357\) 12.9335 0.684516
\(358\) 43.8716 2.31869
\(359\) −27.6771 −1.46074 −0.730372 0.683050i \(-0.760653\pi\)
−0.730372 + 0.683050i \(0.760653\pi\)
\(360\) −80.4359 −4.23935
\(361\) 13.0199 0.685260
\(362\) 33.6444 1.76831
\(363\) 2.82815 0.148440
\(364\) −17.7225 −0.928912
\(365\) −38.3607 −2.00789
\(366\) −8.69857 −0.454681
\(367\) −4.14855 −0.216552 −0.108276 0.994121i \(-0.534533\pi\)
−0.108276 + 0.994121i \(0.534533\pi\)
\(368\) −46.2454 −2.41071
\(369\) 25.9816 1.35255
\(370\) −74.8756 −3.89260
\(371\) 9.36352 0.486130
\(372\) −9.88968 −0.512756
\(373\) 20.9763 1.08611 0.543057 0.839696i \(-0.317267\pi\)
0.543057 + 0.839696i \(0.317267\pi\)
\(374\) 72.5393 3.75092
\(375\) −11.7707 −0.607835
\(376\) −72.4850 −3.73813
\(377\) −2.57174 −0.132451
\(378\) 28.3672 1.45905
\(379\) −0.158477 −0.00814039 −0.00407020 0.999992i \(-0.501296\pi\)
−0.00407020 + 0.999992i \(0.501296\pi\)
\(380\) −108.593 −5.57072
\(381\) 6.12650 0.313870
\(382\) −4.29486 −0.219744
\(383\) −1.59774 −0.0816405 −0.0408203 0.999167i \(-0.512997\pi\)
−0.0408203 + 0.999167i \(0.512997\pi\)
\(384\) −0.174937 −0.00892722
\(385\) 59.0188 3.00788
\(386\) 26.2623 1.33672
\(387\) 14.9073 0.757779
\(388\) −41.7872 −2.12142
\(389\) −21.5650 −1.09339 −0.546694 0.837333i \(-0.684114\pi\)
−0.546694 + 0.837333i \(0.684114\pi\)
\(390\) −5.35769 −0.271297
\(391\) −32.5227 −1.64474
\(392\) −47.6683 −2.40761
\(393\) −8.28315 −0.417830
\(394\) 14.1865 0.714707
\(395\) −67.5750 −3.40007
\(396\) 53.6603 2.69653
\(397\) −12.3672 −0.620691 −0.310345 0.950624i \(-0.600445\pi\)
−0.310345 + 0.950624i \(0.600445\pi\)
\(398\) −52.6149 −2.63734
\(399\) 10.7079 0.536065
\(400\) 104.421 5.22103
\(401\) 27.7093 1.38374 0.691869 0.722023i \(-0.256788\pi\)
0.691869 + 0.722023i \(0.256788\pi\)
\(402\) 16.6085 0.828359
\(403\) 3.95962 0.197243
\(404\) 12.7427 0.633975
\(405\) −26.4698 −1.31530
\(406\) −24.6398 −1.22285
\(407\) 29.2950 1.45210
\(408\) −26.1770 −1.29596
\(409\) −3.32364 −0.164344 −0.0821718 0.996618i \(-0.526186\pi\)
−0.0821718 + 0.996618i \(0.526186\pi\)
\(410\) −98.6177 −4.87038
\(411\) −5.85911 −0.289009
\(412\) −19.5570 −0.963505
\(413\) 6.11414 0.300857
\(414\) −34.0071 −1.67136
\(415\) 21.2088 1.04110
\(416\) 10.5781 0.518634
\(417\) 3.15336 0.154421
\(418\) 60.0564 2.93746
\(419\) 20.8682 1.01948 0.509738 0.860329i \(-0.329742\pi\)
0.509738 + 0.860329i \(0.329742\pi\)
\(420\) −36.3150 −1.77199
\(421\) −17.3042 −0.843355 −0.421677 0.906746i \(-0.638559\pi\)
−0.421677 + 0.906746i \(0.638559\pi\)
\(422\) 15.3441 0.746940
\(423\) −26.7141 −1.29888
\(424\) −18.9514 −0.920363
\(425\) 73.4352 3.56213
\(426\) −15.7326 −0.762248
\(427\) 23.6063 1.14239
\(428\) 33.1363 1.60170
\(429\) 2.09619 0.101205
\(430\) −56.5832 −2.72868
\(431\) 17.8907 0.861765 0.430883 0.902408i \(-0.358202\pi\)
0.430883 + 0.902408i \(0.358202\pi\)
\(432\) −28.7747 −1.38442
\(433\) 5.75906 0.276763 0.138381 0.990379i \(-0.455810\pi\)
0.138381 + 0.990379i \(0.455810\pi\)
\(434\) 37.9372 1.82104
\(435\) −5.26971 −0.252663
\(436\) −42.3565 −2.02851
\(437\) −26.9261 −1.28805
\(438\) −13.0539 −0.623738
\(439\) 4.41924 0.210919 0.105460 0.994424i \(-0.466369\pi\)
0.105460 + 0.994424i \(0.466369\pi\)
\(440\) −119.452 −5.69465
\(441\) −17.5680 −0.836570
\(442\) 17.8707 0.850021
\(443\) 34.4181 1.63525 0.817627 0.575748i \(-0.195289\pi\)
0.817627 + 0.575748i \(0.195289\pi\)
\(444\) −18.0256 −0.855457
\(445\) −6.18095 −0.293005
\(446\) 36.2794 1.71788
\(447\) 1.74083 0.0823383
\(448\) 30.1242 1.42323
\(449\) 8.81167 0.415848 0.207924 0.978145i \(-0.433329\pi\)
0.207924 + 0.978145i \(0.433329\pi\)
\(450\) 76.7868 3.61977
\(451\) 38.5841 1.81686
\(452\) 24.2833 1.14219
\(453\) −2.59890 −0.122107
\(454\) 2.96562 0.139183
\(455\) 14.5398 0.681635
\(456\) −21.6724 −1.01490
\(457\) 22.7634 1.06483 0.532413 0.846485i \(-0.321285\pi\)
0.532413 + 0.846485i \(0.321285\pi\)
\(458\) −17.5485 −0.819985
\(459\) −20.2362 −0.944543
\(460\) 91.3178 4.25771
\(461\) −29.0577 −1.35335 −0.676675 0.736282i \(-0.736580\pi\)
−0.676675 + 0.736282i \(0.736580\pi\)
\(462\) 20.0837 0.934376
\(463\) −1.00000 −0.0464739
\(464\) 24.9938 1.16031
\(465\) 8.11361 0.376260
\(466\) 11.7502 0.544316
\(467\) −30.8878 −1.42932 −0.714658 0.699474i \(-0.753418\pi\)
−0.714658 + 0.699474i \(0.753418\pi\)
\(468\) 13.2197 0.611079
\(469\) −45.0725 −2.08125
\(470\) 101.398 4.67714
\(471\) −0.0807246 −0.00371960
\(472\) −12.3748 −0.569596
\(473\) 22.1381 1.01791
\(474\) −22.9953 −1.05621
\(475\) 60.7982 2.78961
\(476\) 121.129 5.55196
\(477\) −6.98448 −0.319797
\(478\) 41.7150 1.90800
\(479\) −28.7693 −1.31450 −0.657251 0.753672i \(-0.728281\pi\)
−0.657251 + 0.753672i \(0.728281\pi\)
\(480\) 21.6755 0.989345
\(481\) 7.21708 0.329070
\(482\) −64.4562 −2.93590
\(483\) −9.00442 −0.409715
\(484\) 26.4871 1.20396
\(485\) 34.2827 1.55670
\(486\) −32.2318 −1.46206
\(487\) 8.93341 0.404811 0.202406 0.979302i \(-0.435124\pi\)
0.202406 + 0.979302i \(0.435124\pi\)
\(488\) −47.7783 −2.16282
\(489\) 8.33830 0.377071
\(490\) 66.6823 3.01240
\(491\) −26.5992 −1.20041 −0.600203 0.799847i \(-0.704914\pi\)
−0.600203 + 0.799847i \(0.704914\pi\)
\(492\) −23.7413 −1.07034
\(493\) 17.5772 0.791638
\(494\) 14.7954 0.665677
\(495\) −44.0235 −1.97871
\(496\) −38.4822 −1.72790
\(497\) 42.6954 1.91515
\(498\) 7.21721 0.323411
\(499\) −11.8209 −0.529178 −0.264589 0.964361i \(-0.585236\pi\)
−0.264589 + 0.964361i \(0.585236\pi\)
\(500\) −110.239 −4.93002
\(501\) 8.88054 0.396753
\(502\) −76.3048 −3.40565
\(503\) −36.4015 −1.62306 −0.811531 0.584309i \(-0.801366\pi\)
−0.811531 + 0.584309i \(0.801366\pi\)
\(504\) 74.2819 3.30878
\(505\) −10.4543 −0.465210
\(506\) −50.5024 −2.24511
\(507\) 0.516414 0.0229348
\(508\) 57.3778 2.54573
\(509\) 12.5810 0.557642 0.278821 0.960343i \(-0.410056\pi\)
0.278821 + 0.960343i \(0.410056\pi\)
\(510\) 36.6186 1.62150
\(511\) 35.4258 1.56714
\(512\) 41.3515 1.82750
\(513\) −16.7538 −0.739700
\(514\) 75.2516 3.31920
\(515\) 16.0448 0.707019
\(516\) −13.6219 −0.599669
\(517\) −39.6719 −1.74477
\(518\) 69.1469 3.03814
\(519\) 3.25280 0.142782
\(520\) −29.4280 −1.29050
\(521\) 22.4443 0.983303 0.491651 0.870792i \(-0.336393\pi\)
0.491651 + 0.870792i \(0.336393\pi\)
\(522\) 18.3795 0.804447
\(523\) −17.0484 −0.745476 −0.372738 0.927937i \(-0.621581\pi\)
−0.372738 + 0.927937i \(0.621581\pi\)
\(524\) −77.5761 −3.38893
\(525\) 20.3317 0.887348
\(526\) −58.3302 −2.54332
\(527\) −27.0631 −1.17889
\(528\) −20.3722 −0.886585
\(529\) −0.357457 −0.0155416
\(530\) 26.5108 1.15156
\(531\) −4.56069 −0.197917
\(532\) 100.285 4.34790
\(533\) 9.50552 0.411730
\(534\) −2.10333 −0.0910201
\(535\) −27.1854 −1.17533
\(536\) 91.2251 3.94032
\(537\) −8.66494 −0.373920
\(538\) −28.3306 −1.22142
\(539\) −26.0894 −1.12375
\(540\) 56.8194 2.44512
\(541\) −27.9361 −1.20107 −0.600534 0.799599i \(-0.705045\pi\)
−0.600534 + 0.799599i \(0.705045\pi\)
\(542\) 84.9513 3.64897
\(543\) −6.64499 −0.285164
\(544\) −72.2989 −3.09979
\(545\) 34.7498 1.48852
\(546\) 4.94777 0.211745
\(547\) 26.0637 1.11440 0.557201 0.830378i \(-0.311875\pi\)
0.557201 + 0.830378i \(0.311875\pi\)
\(548\) −54.8737 −2.34409
\(549\) −17.6085 −0.751513
\(550\) 114.033 4.86237
\(551\) 14.5525 0.619956
\(552\) 18.2246 0.775692
\(553\) 62.4049 2.65373
\(554\) 79.9271 3.39578
\(555\) 14.7884 0.627734
\(556\) 29.5329 1.25247
\(557\) 40.3163 1.70826 0.854128 0.520063i \(-0.174092\pi\)
0.854128 + 0.520063i \(0.174092\pi\)
\(558\) −28.2983 −1.19796
\(559\) 5.45391 0.230676
\(560\) −141.307 −5.97131
\(561\) −14.3270 −0.604886
\(562\) −48.5437 −2.04769
\(563\) −14.1869 −0.597906 −0.298953 0.954268i \(-0.596637\pi\)
−0.298953 + 0.954268i \(0.596637\pi\)
\(564\) 24.4106 1.02787
\(565\) −19.9223 −0.838138
\(566\) 14.2376 0.598450
\(567\) 24.4446 1.02658
\(568\) −86.4140 −3.62585
\(569\) 3.21884 0.134941 0.0674704 0.997721i \(-0.478507\pi\)
0.0674704 + 0.997721i \(0.478507\pi\)
\(570\) 30.3171 1.26984
\(571\) −19.3074 −0.807991 −0.403996 0.914761i \(-0.632379\pi\)
−0.403996 + 0.914761i \(0.632379\pi\)
\(572\) 19.6319 0.820852
\(573\) 0.848263 0.0354367
\(574\) 91.0725 3.80129
\(575\) −51.1261 −2.13211
\(576\) −22.4703 −0.936265
\(577\) −33.3699 −1.38921 −0.694603 0.719393i \(-0.744420\pi\)
−0.694603 + 0.719393i \(0.744420\pi\)
\(578\) −77.6926 −3.23159
\(579\) −5.18698 −0.215563
\(580\) −49.3536 −2.04930
\(581\) −19.5862 −0.812571
\(582\) 11.6662 0.483578
\(583\) −10.3723 −0.429579
\(584\) −71.7005 −2.96699
\(585\) −10.8456 −0.448409
\(586\) 7.36682 0.304321
\(587\) −15.6739 −0.646932 −0.323466 0.946240i \(-0.604848\pi\)
−0.323466 + 0.946240i \(0.604848\pi\)
\(588\) 16.0531 0.662020
\(589\) −22.4060 −0.923222
\(590\) 17.3109 0.712678
\(591\) −2.80193 −0.115256
\(592\) −70.1403 −2.88275
\(593\) −18.7228 −0.768853 −0.384427 0.923156i \(-0.625601\pi\)
−0.384427 + 0.923156i \(0.625601\pi\)
\(594\) −31.4234 −1.28932
\(595\) −99.3760 −4.07402
\(596\) 16.3037 0.667828
\(597\) 10.3918 0.425307
\(598\) −12.4417 −0.508778
\(599\) 21.6083 0.882891 0.441446 0.897288i \(-0.354466\pi\)
0.441446 + 0.897288i \(0.354466\pi\)
\(600\) −41.1506 −1.67997
\(601\) −23.6929 −0.966453 −0.483226 0.875495i \(-0.660535\pi\)
−0.483226 + 0.875495i \(0.660535\pi\)
\(602\) 52.2540 2.12972
\(603\) 33.6207 1.36914
\(604\) −24.3401 −0.990385
\(605\) −21.7304 −0.883465
\(606\) −3.55752 −0.144514
\(607\) −5.78819 −0.234935 −0.117468 0.993077i \(-0.537478\pi\)
−0.117468 + 0.993077i \(0.537478\pi\)
\(608\) −59.8574 −2.42754
\(609\) 4.86653 0.197202
\(610\) 66.8362 2.70612
\(611\) −9.77351 −0.395394
\(612\) −90.3534 −3.65232
\(613\) −0.444274 −0.0179441 −0.00897204 0.999960i \(-0.502856\pi\)
−0.00897204 + 0.999960i \(0.502856\pi\)
\(614\) 43.7841 1.76698
\(615\) 19.4776 0.785414
\(616\) 110.313 4.44463
\(617\) 34.8303 1.40221 0.701107 0.713056i \(-0.252690\pi\)
0.701107 + 0.713056i \(0.252690\pi\)
\(618\) 5.45993 0.219631
\(619\) −0.879306 −0.0353423 −0.0176711 0.999844i \(-0.505625\pi\)
−0.0176711 + 0.999844i \(0.505625\pi\)
\(620\) 75.9882 3.05176
\(621\) 14.0886 0.565355
\(622\) 76.7017 3.07546
\(623\) 5.70805 0.228688
\(624\) −5.01885 −0.200915
\(625\) 36.7193 1.46877
\(626\) −53.2737 −2.12924
\(627\) −11.8615 −0.473705
\(628\) −0.756028 −0.0301688
\(629\) −49.3271 −1.96680
\(630\) −103.912 −4.13994
\(631\) −29.6761 −1.18139 −0.590693 0.806897i \(-0.701145\pi\)
−0.590693 + 0.806897i \(0.701145\pi\)
\(632\) −126.305 −5.02415
\(633\) −3.03056 −0.120454
\(634\) 5.55452 0.220598
\(635\) −47.0735 −1.86805
\(636\) 6.38223 0.253072
\(637\) −6.42734 −0.254661
\(638\) 27.2945 1.08060
\(639\) −31.8476 −1.25987
\(640\) 1.34414 0.0531320
\(641\) −7.53264 −0.297521 −0.148761 0.988873i \(-0.547528\pi\)
−0.148761 + 0.988873i \(0.547528\pi\)
\(642\) −9.25100 −0.365108
\(643\) 10.4189 0.410883 0.205441 0.978669i \(-0.434137\pi\)
0.205441 + 0.978669i \(0.434137\pi\)
\(644\) −84.3311 −3.32311
\(645\) 11.1755 0.440037
\(646\) −101.123 −3.97864
\(647\) −3.41329 −0.134190 −0.0670952 0.997747i \(-0.521373\pi\)
−0.0670952 + 0.997747i \(0.521373\pi\)
\(648\) −49.4751 −1.94357
\(649\) −6.77287 −0.265859
\(650\) 28.0929 1.10189
\(651\) −7.49285 −0.293668
\(652\) 78.0925 3.05834
\(653\) 14.4692 0.566223 0.283112 0.959087i \(-0.408633\pi\)
0.283112 + 0.959087i \(0.408633\pi\)
\(654\) 11.8251 0.462398
\(655\) 63.6443 2.48679
\(656\) −92.3809 −3.60687
\(657\) −26.4249 −1.03094
\(658\) −93.6401 −3.65047
\(659\) −40.9706 −1.59599 −0.797995 0.602664i \(-0.794106\pi\)
−0.797995 + 0.602664i \(0.794106\pi\)
\(660\) 40.2276 1.56586
\(661\) −37.2666 −1.44950 −0.724751 0.689010i \(-0.758045\pi\)
−0.724751 + 0.689010i \(0.758045\pi\)
\(662\) 17.2955 0.672207
\(663\) −3.52957 −0.137077
\(664\) 39.6417 1.53840
\(665\) −82.2750 −3.19049
\(666\) −51.5784 −1.99862
\(667\) −12.2374 −0.473834
\(668\) 83.1709 3.21798
\(669\) −7.16542 −0.277031
\(670\) −127.613 −4.93013
\(671\) −26.1496 −1.00950
\(672\) −20.0171 −0.772176
\(673\) −23.2471 −0.896108 −0.448054 0.894007i \(-0.647883\pi\)
−0.448054 + 0.894007i \(0.647883\pi\)
\(674\) 30.7015 1.18258
\(675\) −31.8115 −1.22443
\(676\) 4.83649 0.186019
\(677\) −22.3348 −0.858395 −0.429198 0.903211i \(-0.641204\pi\)
−0.429198 + 0.903211i \(0.641204\pi\)
\(678\) −6.77942 −0.260362
\(679\) −31.6598 −1.21499
\(680\) 201.133 7.71312
\(681\) −0.585729 −0.0224452
\(682\) −42.0245 −1.60920
\(683\) −20.3051 −0.776952 −0.388476 0.921459i \(-0.626998\pi\)
−0.388476 + 0.921459i \(0.626998\pi\)
\(684\) −74.8050 −2.86024
\(685\) 45.0190 1.72009
\(686\) 5.48663 0.209481
\(687\) 3.46594 0.132234
\(688\) −53.0047 −2.02079
\(689\) −2.55531 −0.0973497
\(690\) −25.4941 −0.970544
\(691\) 13.9532 0.530806 0.265403 0.964138i \(-0.414495\pi\)
0.265403 + 0.964138i \(0.414495\pi\)
\(692\) 30.4641 1.15807
\(693\) 40.6554 1.54437
\(694\) 73.9909 2.80866
\(695\) −24.2292 −0.919064
\(696\) −9.84968 −0.373351
\(697\) −64.9681 −2.46084
\(698\) 46.4911 1.75971
\(699\) −2.32073 −0.0877782
\(700\) 190.417 7.19708
\(701\) −43.1435 −1.62951 −0.814753 0.579808i \(-0.803128\pi\)
−0.814753 + 0.579808i \(0.803128\pi\)
\(702\) −7.74142 −0.292181
\(703\) −40.8387 −1.54026
\(704\) −33.3697 −1.25767
\(705\) −20.0268 −0.754252
\(706\) 34.5018 1.29849
\(707\) 9.65445 0.363093
\(708\) 4.16744 0.156622
\(709\) −19.8621 −0.745936 −0.372968 0.927844i \(-0.621660\pi\)
−0.372968 + 0.927844i \(0.621660\pi\)
\(710\) 120.883 4.53666
\(711\) −46.5493 −1.74574
\(712\) −11.5529 −0.432963
\(713\) 18.8415 0.705621
\(714\) −33.8169 −1.26557
\(715\) −16.1063 −0.602341
\(716\) −81.1517 −3.03278
\(717\) −8.23900 −0.307691
\(718\) 72.3666 2.70070
\(719\) −47.3389 −1.76544 −0.882722 0.469896i \(-0.844291\pi\)
−0.882722 + 0.469896i \(0.844291\pi\)
\(720\) 105.404 3.92819
\(721\) −14.8172 −0.551823
\(722\) −34.0428 −1.26694
\(723\) 12.7305 0.473453
\(724\) −62.2338 −2.31290
\(725\) 27.6316 1.02621
\(726\) −7.39469 −0.274443
\(727\) −22.3110 −0.827468 −0.413734 0.910398i \(-0.635776\pi\)
−0.413734 + 0.910398i \(0.635776\pi\)
\(728\) 27.1765 1.00723
\(729\) −13.6469 −0.505441
\(730\) 100.301 3.71229
\(731\) −37.2763 −1.37871
\(732\) 16.0902 0.594711
\(733\) −15.5210 −0.573282 −0.286641 0.958038i \(-0.592539\pi\)
−0.286641 + 0.958038i \(0.592539\pi\)
\(734\) 10.8471 0.400373
\(735\) −13.1702 −0.485790
\(736\) 50.3350 1.85537
\(737\) 49.9286 1.83914
\(738\) −67.9332 −2.50066
\(739\) 51.9562 1.91124 0.955619 0.294604i \(-0.0951879\pi\)
0.955619 + 0.294604i \(0.0951879\pi\)
\(740\) 138.501 5.09141
\(741\) −2.92219 −0.107349
\(742\) −24.4825 −0.898781
\(743\) −42.2515 −1.55006 −0.775029 0.631925i \(-0.782265\pi\)
−0.775029 + 0.631925i \(0.782265\pi\)
\(744\) 15.1653 0.555985
\(745\) −13.3758 −0.490051
\(746\) −54.8462 −2.00806
\(747\) 14.6098 0.534545
\(748\) −134.180 −4.90610
\(749\) 25.1055 0.917335
\(750\) 30.7764 1.12380
\(751\) −45.8553 −1.67328 −0.836642 0.547750i \(-0.815485\pi\)
−0.836642 + 0.547750i \(0.815485\pi\)
\(752\) 94.9853 3.46376
\(753\) 15.0707 0.549207
\(754\) 6.72423 0.244882
\(755\) 19.9689 0.726743
\(756\) −52.4722 −1.90840
\(757\) 22.9495 0.834115 0.417057 0.908880i \(-0.363061\pi\)
0.417057 + 0.908880i \(0.363061\pi\)
\(758\) 0.414364 0.0150504
\(759\) 9.97456 0.362053
\(760\) 166.522 6.04037
\(761\) −16.2527 −0.589162 −0.294581 0.955627i \(-0.595180\pi\)
−0.294581 + 0.955627i \(0.595180\pi\)
\(762\) −16.0188 −0.580298
\(763\) −32.0911 −1.16178
\(764\) 7.94443 0.287419
\(765\) 74.1270 2.68007
\(766\) 4.17755 0.150941
\(767\) −1.66855 −0.0602480
\(768\) −8.03339 −0.289880
\(769\) −27.4349 −0.989327 −0.494663 0.869085i \(-0.664709\pi\)
−0.494663 + 0.869085i \(0.664709\pi\)
\(770\) −154.315 −5.56111
\(771\) −14.8627 −0.535267
\(772\) −48.5788 −1.74839
\(773\) −1.99609 −0.0717944 −0.0358972 0.999355i \(-0.511429\pi\)
−0.0358972 + 0.999355i \(0.511429\pi\)
\(774\) −38.9776 −1.40102
\(775\) −42.5435 −1.52821
\(776\) 64.0783 2.30028
\(777\) −13.6570 −0.489941
\(778\) 56.3852 2.02151
\(779\) −53.7881 −1.92716
\(780\) 9.91039 0.354849
\(781\) −47.2954 −1.69236
\(782\) 85.0361 3.04088
\(783\) −7.61431 −0.272113
\(784\) 62.4651 2.23090
\(785\) 0.620255 0.0221378
\(786\) 21.6577 0.772504
\(787\) −17.9730 −0.640669 −0.320334 0.947305i \(-0.603795\pi\)
−0.320334 + 0.947305i \(0.603795\pi\)
\(788\) −26.2416 −0.934818
\(789\) 11.5206 0.410144
\(790\) 176.686 6.28621
\(791\) 18.3981 0.654161
\(792\) −82.2850 −2.92387
\(793\) −6.44218 −0.228768
\(794\) 32.3361 1.14756
\(795\) −5.23606 −0.185704
\(796\) 97.3245 3.44957
\(797\) 52.9183 1.87446 0.937231 0.348709i \(-0.113380\pi\)
0.937231 + 0.348709i \(0.113380\pi\)
\(798\) −27.9976 −0.991103
\(799\) 66.7997 2.36320
\(800\) −113.655 −4.01830
\(801\) −4.25778 −0.150441
\(802\) −72.4507 −2.55832
\(803\) −39.2425 −1.38484
\(804\) −30.7217 −1.08347
\(805\) 69.1863 2.43850
\(806\) −10.3531 −0.364672
\(807\) 5.59549 0.196971
\(808\) −19.5403 −0.687424
\(809\) −15.8035 −0.555622 −0.277811 0.960636i \(-0.589609\pi\)
−0.277811 + 0.960636i \(0.589609\pi\)
\(810\) 69.2098 2.43179
\(811\) 38.7452 1.36053 0.680263 0.732968i \(-0.261865\pi\)
0.680263 + 0.732968i \(0.261865\pi\)
\(812\) 45.5776 1.59946
\(813\) −16.7784 −0.588446
\(814\) −76.5968 −2.68472
\(815\) −64.0681 −2.24421
\(816\) 34.3027 1.20084
\(817\) −30.8616 −1.07971
\(818\) 8.69022 0.303847
\(819\) 10.0158 0.349980
\(820\) 182.418 6.37032
\(821\) −46.5438 −1.62439 −0.812194 0.583387i \(-0.801727\pi\)
−0.812194 + 0.583387i \(0.801727\pi\)
\(822\) 15.3196 0.534334
\(823\) −33.7574 −1.17671 −0.588355 0.808603i \(-0.700224\pi\)
−0.588355 + 0.808603i \(0.700224\pi\)
\(824\) 29.9896 1.04474
\(825\) −22.5222 −0.784123
\(826\) −15.9864 −0.556240
\(827\) −19.1147 −0.664682 −0.332341 0.943159i \(-0.607838\pi\)
−0.332341 + 0.943159i \(0.607838\pi\)
\(828\) 62.9047 2.18609
\(829\) 42.3630 1.47133 0.735664 0.677347i \(-0.236870\pi\)
0.735664 + 0.677347i \(0.236870\pi\)
\(830\) −55.4541 −1.92484
\(831\) −15.7861 −0.547615
\(832\) −8.22091 −0.285009
\(833\) 43.9294 1.52206
\(834\) −8.24500 −0.285501
\(835\) −68.2344 −2.36135
\(836\) −111.090 −3.84211
\(837\) 11.7235 0.405224
\(838\) −54.5633 −1.88486
\(839\) −12.1013 −0.417782 −0.208891 0.977939i \(-0.566985\pi\)
−0.208891 + 0.977939i \(0.566985\pi\)
\(840\) 55.6870 1.92138
\(841\) −22.3862 −0.771937
\(842\) 45.2447 1.55924
\(843\) 9.58770 0.330218
\(844\) −28.3828 −0.976977
\(845\) −3.96792 −0.136500
\(846\) 69.8485 2.40144
\(847\) 20.0678 0.689538
\(848\) 24.8342 0.852810
\(849\) −2.81202 −0.0965082
\(850\) −192.009 −6.58584
\(851\) 34.3419 1.17722
\(852\) 29.1015 0.997000
\(853\) 20.1866 0.691175 0.345587 0.938387i \(-0.387680\pi\)
0.345587 + 0.938387i \(0.387680\pi\)
\(854\) −61.7226 −2.11210
\(855\) 61.3709 2.09884
\(856\) −50.8126 −1.73674
\(857\) 50.6130 1.72891 0.864454 0.502712i \(-0.167664\pi\)
0.864454 + 0.502712i \(0.167664\pi\)
\(858\) −5.48085 −0.187113
\(859\) −9.30923 −0.317627 −0.158813 0.987309i \(-0.550767\pi\)
−0.158813 + 0.987309i \(0.550767\pi\)
\(860\) 104.665 3.56904
\(861\) −17.9874 −0.613010
\(862\) −46.7783 −1.59327
\(863\) 40.5687 1.38097 0.690487 0.723345i \(-0.257396\pi\)
0.690487 + 0.723345i \(0.257396\pi\)
\(864\) 31.3193 1.06550
\(865\) −24.9932 −0.849793
\(866\) −15.0580 −0.511693
\(867\) 15.3448 0.521137
\(868\) −70.1744 −2.38187
\(869\) −69.1284 −2.34502
\(870\) 13.7785 0.467137
\(871\) 12.3003 0.416781
\(872\) 64.9513 2.19953
\(873\) 23.6158 0.799274
\(874\) 70.4027 2.38141
\(875\) −83.5215 −2.82354
\(876\) 24.1464 0.815832
\(877\) 35.6136 1.20259 0.601293 0.799028i \(-0.294652\pi\)
0.601293 + 0.799028i \(0.294652\pi\)
\(878\) −11.5549 −0.389958
\(879\) −1.45500 −0.0490758
\(880\) 156.531 5.27667
\(881\) −29.6146 −0.997741 −0.498871 0.866676i \(-0.666252\pi\)
−0.498871 + 0.866676i \(0.666252\pi\)
\(882\) 45.9344 1.54669
\(883\) 45.8761 1.54385 0.771927 0.635712i \(-0.219293\pi\)
0.771927 + 0.635712i \(0.219293\pi\)
\(884\) −33.0563 −1.11180
\(885\) −3.41901 −0.114929
\(886\) −89.9920 −3.02334
\(887\) −10.4274 −0.350117 −0.175059 0.984558i \(-0.556011\pi\)
−0.175059 + 0.984558i \(0.556011\pi\)
\(888\) 27.6412 0.927579
\(889\) 43.4719 1.45800
\(890\) 16.1611 0.541723
\(891\) −27.0783 −0.907157
\(892\) −67.1079 −2.24694
\(893\) 55.3045 1.85070
\(894\) −4.55168 −0.152231
\(895\) 66.5778 2.22545
\(896\) −1.24131 −0.0414691
\(897\) 2.45732 0.0820474
\(898\) −23.0396 −0.768841
\(899\) −10.1831 −0.339625
\(900\) −142.037 −4.73455
\(901\) 17.4650 0.581843
\(902\) −100.885 −3.35909
\(903\) −10.3205 −0.343445
\(904\) −37.2371 −1.23849
\(905\) 51.0574 1.69720
\(906\) 6.79527 0.225758
\(907\) 21.2084 0.704213 0.352107 0.935960i \(-0.385465\pi\)
0.352107 + 0.935960i \(0.385465\pi\)
\(908\) −5.48566 −0.182048
\(909\) −7.20149 −0.238858
\(910\) −38.0167 −1.26024
\(911\) 6.90102 0.228641 0.114320 0.993444i \(-0.463531\pi\)
0.114320 + 0.993444i \(0.463531\pi\)
\(912\) 28.3998 0.940410
\(913\) 21.6964 0.718045
\(914\) −59.5187 −1.96870
\(915\) −13.2006 −0.436398
\(916\) 32.4603 1.07252
\(917\) −58.7750 −1.94092
\(918\) 52.9109 1.74632
\(919\) 28.6539 0.945204 0.472602 0.881276i \(-0.343315\pi\)
0.472602 + 0.881276i \(0.343315\pi\)
\(920\) −140.031 −4.61667
\(921\) −8.64766 −0.284950
\(922\) 75.9761 2.50214
\(923\) −11.6516 −0.383518
\(924\) −37.1498 −1.22214
\(925\) −77.5428 −2.54959
\(926\) 2.61467 0.0859233
\(927\) 11.0525 0.363013
\(928\) −27.2041 −0.893017
\(929\) −29.6861 −0.973969 −0.486984 0.873411i \(-0.661903\pi\)
−0.486984 + 0.873411i \(0.661903\pi\)
\(930\) −21.2144 −0.695648
\(931\) 36.3699 1.19197
\(932\) −21.7349 −0.711950
\(933\) −15.1491 −0.495959
\(934\) 80.7613 2.64259
\(935\) 110.083 3.60009
\(936\) −20.2716 −0.662598
\(937\) −18.2151 −0.595062 −0.297531 0.954712i \(-0.596163\pi\)
−0.297531 + 0.954712i \(0.596163\pi\)
\(938\) 117.850 3.84793
\(939\) 10.5219 0.343369
\(940\) −187.561 −6.11757
\(941\) 27.0873 0.883020 0.441510 0.897256i \(-0.354443\pi\)
0.441510 + 0.897256i \(0.354443\pi\)
\(942\) 0.211068 0.00687697
\(943\) 45.2312 1.47293
\(944\) 16.2161 0.527789
\(945\) 43.0489 1.40038
\(946\) −57.8839 −1.88197
\(947\) 34.7395 1.12888 0.564441 0.825474i \(-0.309092\pi\)
0.564441 + 0.825474i \(0.309092\pi\)
\(948\) 42.5356 1.38149
\(949\) −9.66772 −0.313828
\(950\) −158.967 −5.15757
\(951\) −1.09705 −0.0355744
\(952\) −185.745 −6.02003
\(953\) 48.4186 1.56843 0.784215 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(954\) 18.2621 0.591257
\(955\) −6.51770 −0.210908
\(956\) −77.1625 −2.49561
\(957\) −5.39085 −0.174261
\(958\) 75.2221 2.43032
\(959\) −41.5747 −1.34252
\(960\) −16.8454 −0.543682
\(961\) −15.3214 −0.494239
\(962\) −18.8703 −0.608402
\(963\) −18.7268 −0.603463
\(964\) 119.228 3.84007
\(965\) 39.8546 1.28297
\(966\) 23.5436 0.757502
\(967\) 26.8726 0.864166 0.432083 0.901834i \(-0.357779\pi\)
0.432083 + 0.901834i \(0.357779\pi\)
\(968\) −40.6165 −1.30546
\(969\) 19.9725 0.641609
\(970\) −89.6380 −2.87810
\(971\) 50.6696 1.62607 0.813033 0.582217i \(-0.197815\pi\)
0.813033 + 0.582217i \(0.197815\pi\)
\(972\) 59.6208 1.91234
\(973\) 22.3754 0.717322
\(974\) −23.3579 −0.748435
\(975\) −5.54854 −0.177695
\(976\) 62.6093 2.00408
\(977\) −51.9373 −1.66162 −0.830811 0.556555i \(-0.812123\pi\)
−0.830811 + 0.556555i \(0.812123\pi\)
\(978\) −21.8019 −0.697147
\(979\) −6.32304 −0.202085
\(980\) −123.346 −3.94014
\(981\) 23.9376 0.764267
\(982\) 69.5482 2.21937
\(983\) −46.3978 −1.47986 −0.739929 0.672685i \(-0.765141\pi\)
−0.739929 + 0.672685i \(0.765141\pi\)
\(984\) 36.4059 1.16058
\(985\) 21.5289 0.685968
\(986\) −45.9586 −1.46362
\(987\) 18.4945 0.588688
\(988\) −27.3678 −0.870687
\(989\) 25.9520 0.825226
\(990\) 115.107 3.65834
\(991\) −37.9464 −1.20541 −0.602703 0.797965i \(-0.705910\pi\)
−0.602703 + 0.797965i \(0.705910\pi\)
\(992\) 41.8853 1.32986
\(993\) −3.41597 −0.108403
\(994\) −111.634 −3.54083
\(995\) −79.8462 −2.53129
\(996\) −13.3501 −0.423013
\(997\) −45.8252 −1.45130 −0.725649 0.688065i \(-0.758461\pi\)
−0.725649 + 0.688065i \(0.758461\pi\)
\(998\) 30.9078 0.978370
\(999\) 21.3681 0.676056
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 \(a_p\))