Properties

Label 4009.2.a.c.1.12
Level 4009
Weight 2
Character 4009.1
Self dual Yes
Analytic conductor 32.012
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 4009 = 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4009.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0120261703\)
Analytic rank: \(1\)
Dimension: \(71\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) = 4009.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.25185 q^{2}\) \(-1.69642 q^{3}\) \(+3.07082 q^{4}\) \(-1.12007 q^{5}\) \(+3.82008 q^{6}\) \(-4.02650 q^{7}\) \(-2.41131 q^{8}\) \(-0.122162 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.25185 q^{2}\) \(-1.69642 q^{3}\) \(+3.07082 q^{4}\) \(-1.12007 q^{5}\) \(+3.82008 q^{6}\) \(-4.02650 q^{7}\) \(-2.41131 q^{8}\) \(-0.122162 q^{9}\) \(+2.52222 q^{10}\) \(-2.48572 q^{11}\) \(-5.20939 q^{12}\) \(+4.38293 q^{13}\) \(+9.06706 q^{14}\) \(+1.90010 q^{15}\) \(-0.711723 q^{16}\) \(-3.94588 q^{17}\) \(+0.275090 q^{18}\) \(+1.00000 q^{19}\) \(-3.43952 q^{20}\) \(+6.83063 q^{21}\) \(+5.59746 q^{22}\) \(-3.68526 q^{23}\) \(+4.09060 q^{24}\) \(-3.74545 q^{25}\) \(-9.86969 q^{26}\) \(+5.29650 q^{27}\) \(-12.3646 q^{28}\) \(+3.83383 q^{29}\) \(-4.27874 q^{30}\) \(-4.15303 q^{31}\) \(+6.42532 q^{32}\) \(+4.21682 q^{33}\) \(+8.88552 q^{34}\) \(+4.50995 q^{35}\) \(-0.375136 q^{36}\) \(+6.52957 q^{37}\) \(-2.25185 q^{38}\) \(-7.43529 q^{39}\) \(+2.70083 q^{40}\) \(-4.13530 q^{41}\) \(-15.3815 q^{42}\) \(-4.23897 q^{43}\) \(-7.63319 q^{44}\) \(+0.136829 q^{45}\) \(+8.29865 q^{46}\) \(+7.04135 q^{47}\) \(+1.20738 q^{48}\) \(+9.21269 q^{49}\) \(+8.43418 q^{50}\) \(+6.69387 q^{51}\) \(+13.4592 q^{52}\) \(+2.97967 q^{53}\) \(-11.9269 q^{54}\) \(+2.78417 q^{55}\) \(+9.70915 q^{56}\) \(-1.69642 q^{57}\) \(-8.63319 q^{58}\) \(-11.9334 q^{59}\) \(+5.83487 q^{60}\) \(+1.19622 q^{61}\) \(+9.35199 q^{62}\) \(+0.491884 q^{63}\) \(-13.0454 q^{64}\) \(-4.90918 q^{65}\) \(-9.49564 q^{66}\) \(+8.71052 q^{67}\) \(-12.1171 q^{68}\) \(+6.25175 q^{69}\) \(-10.1557 q^{70}\) \(+9.49978 q^{71}\) \(+0.294570 q^{72}\) \(+11.9836 q^{73}\) \(-14.7036 q^{74}\) \(+6.35385 q^{75}\) \(+3.07082 q^{76}\) \(+10.0087 q^{77}\) \(+16.7431 q^{78}\) \(+5.78566 q^{79}\) \(+0.797177 q^{80}\) \(-8.61859 q^{81}\) \(+9.31206 q^{82}\) \(-14.2548 q^{83}\) \(+20.9756 q^{84}\) \(+4.41965 q^{85}\) \(+9.54552 q^{86}\) \(-6.50378 q^{87}\) \(+5.99385 q^{88}\) \(+14.2616 q^{89}\) \(-0.308119 q^{90}\) \(-17.6479 q^{91}\) \(-11.3168 q^{92}\) \(+7.04528 q^{93}\) \(-15.8560 q^{94}\) \(-1.12007 q^{95}\) \(-10.9000 q^{96}\) \(+2.21368 q^{97}\) \(-20.7456 q^{98}\) \(+0.303660 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 15q^{2} \) \(\mathstrut -\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut +\mathstrut 63q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 15q^{13} \) \(\mathstrut -\mathstrut 53q^{14} \) \(\mathstrut -\mathstrut 33q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut +\mathstrut 71q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 38q^{21} \) \(\mathstrut -\mathstrut 6q^{22} \) \(\mathstrut -\mathstrut 65q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 51q^{25} \) \(\mathstrut -\mathstrut 4q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 29q^{28} \) \(\mathstrut -\mathstrut 97q^{29} \) \(\mathstrut -\mathstrut 27q^{30} \) \(\mathstrut -\mathstrut 53q^{31} \) \(\mathstrut -\mathstrut 78q^{32} \) \(\mathstrut -\mathstrut 17q^{33} \) \(\mathstrut -\mathstrut 24q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 33q^{37} \) \(\mathstrut -\mathstrut 15q^{38} \) \(\mathstrut -\mathstrut 86q^{39} \) \(\mathstrut +\mathstrut 25q^{40} \) \(\mathstrut -\mathstrut 69q^{41} \) \(\mathstrut +\mathstrut 64q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 94q^{44} \) \(\mathstrut -\mathstrut 34q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 37q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 46q^{51} \) \(\mathstrut -\mathstrut 30q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 17q^{54} \) \(\mathstrut -\mathstrut 30q^{55} \) \(\mathstrut -\mathstrut 116q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 11q^{58} \) \(\mathstrut -\mathstrut 93q^{59} \) \(\mathstrut -\mathstrut 56q^{60} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut -\mathstrut q^{62} \) \(\mathstrut -\mathstrut 84q^{63} \) \(\mathstrut +\mathstrut 93q^{64} \) \(\mathstrut -\mathstrut 78q^{65} \) \(\mathstrut -\mathstrut 53q^{66} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut -\mathstrut 9q^{68} \) \(\mathstrut -\mathstrut 69q^{69} \) \(\mathstrut -\mathstrut 10q^{70} \) \(\mathstrut -\mathstrut 221q^{71} \) \(\mathstrut -\mathstrut 73q^{72} \) \(\mathstrut -\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 58q^{74} \) \(\mathstrut -\mathstrut 70q^{75} \) \(\mathstrut +\mathstrut 69q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 68q^{79} \) \(\mathstrut -\mathstrut 71q^{80} \) \(\mathstrut +\mathstrut 39q^{81} \) \(\mathstrut +\mathstrut 26q^{82} \) \(\mathstrut -\mathstrut 45q^{83} \) \(\mathstrut -\mathstrut 10q^{84} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 80q^{86} \) \(\mathstrut -\mathstrut 7q^{87} \) \(\mathstrut -\mathstrut 46q^{88} \) \(\mathstrut -\mathstrut 143q^{89} \) \(\mathstrut +\mathstrut 41q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 46q^{92} \) \(\mathstrut +\mathstrut 32q^{93} \) \(\mathstrut +\mathstrut 41q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut -\mathstrut 140q^{96} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 97q^{98} \) \(\mathstrut -\mathstrut 142q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25185 −1.59230 −0.796148 0.605102i \(-0.793132\pi\)
−0.796148 + 0.605102i \(0.793132\pi\)
\(3\) −1.69642 −0.979428 −0.489714 0.871883i \(-0.662899\pi\)
−0.489714 + 0.871883i \(0.662899\pi\)
\(4\) 3.07082 1.53541
\(5\) −1.12007 −0.500909 −0.250455 0.968128i \(-0.580580\pi\)
−0.250455 + 0.968128i \(0.580580\pi\)
\(6\) 3.82008 1.55954
\(7\) −4.02650 −1.52187 −0.760937 0.648826i \(-0.775260\pi\)
−0.760937 + 0.648826i \(0.775260\pi\)
\(8\) −2.41131 −0.852528
\(9\) −0.122162 −0.0407206
\(10\) 2.52222 0.797596
\(11\) −2.48572 −0.749473 −0.374736 0.927131i \(-0.622267\pi\)
−0.374736 + 0.927131i \(0.622267\pi\)
\(12\) −5.20939 −1.50382
\(13\) 4.38293 1.21561 0.607803 0.794088i \(-0.292051\pi\)
0.607803 + 0.794088i \(0.292051\pi\)
\(14\) 9.06706 2.42327
\(15\) 1.90010 0.490604
\(16\) −0.711723 −0.177931
\(17\) −3.94588 −0.957016 −0.478508 0.878083i \(-0.658822\pi\)
−0.478508 + 0.878083i \(0.658822\pi\)
\(18\) 0.275090 0.0648393
\(19\) 1.00000 0.229416
\(20\) −3.43952 −0.769100
\(21\) 6.83063 1.49057
\(22\) 5.59746 1.19338
\(23\) −3.68526 −0.768430 −0.384215 0.923244i \(-0.625528\pi\)
−0.384215 + 0.923244i \(0.625528\pi\)
\(24\) 4.09060 0.834990
\(25\) −3.74545 −0.749090
\(26\) −9.86969 −1.93561
\(27\) 5.29650 1.01931
\(28\) −12.3646 −2.33670
\(29\) 3.83383 0.711924 0.355962 0.934500i \(-0.384153\pi\)
0.355962 + 0.934500i \(0.384153\pi\)
\(30\) −4.27874 −0.781188
\(31\) −4.15303 −0.745906 −0.372953 0.927850i \(-0.621655\pi\)
−0.372953 + 0.927850i \(0.621655\pi\)
\(32\) 6.42532 1.13585
\(33\) 4.21682 0.734055
\(34\) 8.88552 1.52385
\(35\) 4.50995 0.762320
\(36\) −0.375136 −0.0625227
\(37\) 6.52957 1.07346 0.536728 0.843756i \(-0.319660\pi\)
0.536728 + 0.843756i \(0.319660\pi\)
\(38\) −2.25185 −0.365298
\(39\) −7.43529 −1.19060
\(40\) 2.70083 0.427039
\(41\) −4.13530 −0.645825 −0.322913 0.946429i \(-0.604662\pi\)
−0.322913 + 0.946429i \(0.604662\pi\)
\(42\) −15.3815 −2.37342
\(43\) −4.23897 −0.646437 −0.323219 0.946324i \(-0.604765\pi\)
−0.323219 + 0.946324i \(0.604765\pi\)
\(44\) −7.63319 −1.15075
\(45\) 0.136829 0.0203973
\(46\) 8.29865 1.22357
\(47\) 7.04135 1.02709 0.513543 0.858064i \(-0.328333\pi\)
0.513543 + 0.858064i \(0.328333\pi\)
\(48\) 1.20738 0.174270
\(49\) 9.21269 1.31610
\(50\) 8.43418 1.19277
\(51\) 6.69387 0.937329
\(52\) 13.4592 1.86645
\(53\) 2.97967 0.409289 0.204644 0.978836i \(-0.434396\pi\)
0.204644 + 0.978836i \(0.434396\pi\)
\(54\) −11.9269 −1.62305
\(55\) 2.78417 0.375418
\(56\) 9.70915 1.29744
\(57\) −1.69642 −0.224696
\(58\) −8.63319 −1.13359
\(59\) −11.9334 −1.55360 −0.776801 0.629746i \(-0.783159\pi\)
−0.776801 + 0.629746i \(0.783159\pi\)
\(60\) 5.83487 0.753278
\(61\) 1.19622 0.153160 0.0765799 0.997063i \(-0.475600\pi\)
0.0765799 + 0.997063i \(0.475600\pi\)
\(62\) 9.35199 1.18770
\(63\) 0.491884 0.0619716
\(64\) −13.0454 −1.63067
\(65\) −4.90918 −0.608909
\(66\) −9.49564 −1.16883
\(67\) 8.71052 1.06416 0.532080 0.846694i \(-0.321411\pi\)
0.532080 + 0.846694i \(0.321411\pi\)
\(68\) −12.1171 −1.46941
\(69\) 6.25175 0.752622
\(70\) −10.1557 −1.21384
\(71\) 9.49978 1.12742 0.563708 0.825974i \(-0.309374\pi\)
0.563708 + 0.825974i \(0.309374\pi\)
\(72\) 0.294570 0.0347154
\(73\) 11.9836 1.40258 0.701288 0.712878i \(-0.252609\pi\)
0.701288 + 0.712878i \(0.252609\pi\)
\(74\) −14.7036 −1.70926
\(75\) 6.35385 0.733680
\(76\) 3.07082 0.352247
\(77\) 10.0087 1.14060
\(78\) 16.7431 1.89579
\(79\) 5.78566 0.650938 0.325469 0.945553i \(-0.394478\pi\)
0.325469 + 0.945553i \(0.394478\pi\)
\(80\) 0.797177 0.0891271
\(81\) −8.61859 −0.957621
\(82\) 9.31206 1.02835
\(83\) −14.2548 −1.56467 −0.782334 0.622859i \(-0.785971\pi\)
−0.782334 + 0.622859i \(0.785971\pi\)
\(84\) 20.9756 2.28863
\(85\) 4.41965 0.479378
\(86\) 9.54552 1.02932
\(87\) −6.50378 −0.697278
\(88\) 5.99385 0.638947
\(89\) 14.2616 1.51173 0.755865 0.654727i \(-0.227217\pi\)
0.755865 + 0.654727i \(0.227217\pi\)
\(90\) −0.308119 −0.0324786
\(91\) −17.6479 −1.85000
\(92\) −11.3168 −1.17985
\(93\) 7.04528 0.730562
\(94\) −15.8560 −1.63542
\(95\) −1.12007 −0.114916
\(96\) −10.9000 −1.11248
\(97\) 2.21368 0.224765 0.112383 0.993665i \(-0.464152\pi\)
0.112383 + 0.993665i \(0.464152\pi\)
\(98\) −20.7456 −2.09562
\(99\) 0.303660 0.0305190
\(100\) −11.5016 −1.15016
\(101\) −4.48942 −0.446714 −0.223357 0.974737i \(-0.571702\pi\)
−0.223357 + 0.974737i \(0.571702\pi\)
\(102\) −15.0736 −1.49251
\(103\) 17.9596 1.76961 0.884805 0.465961i \(-0.154291\pi\)
0.884805 + 0.465961i \(0.154291\pi\)
\(104\) −10.5686 −1.03634
\(105\) −7.65076 −0.746638
\(106\) −6.70975 −0.651709
\(107\) −5.37537 −0.519656 −0.259828 0.965655i \(-0.583666\pi\)
−0.259828 + 0.965655i \(0.583666\pi\)
\(108\) 16.2646 1.56506
\(109\) −1.59754 −0.153017 −0.0765085 0.997069i \(-0.524377\pi\)
−0.0765085 + 0.997069i \(0.524377\pi\)
\(110\) −6.26953 −0.597776
\(111\) −11.0769 −1.05137
\(112\) 2.86575 0.270788
\(113\) −4.95133 −0.465782 −0.232891 0.972503i \(-0.574818\pi\)
−0.232891 + 0.972503i \(0.574818\pi\)
\(114\) 3.82008 0.357783
\(115\) 4.12774 0.384914
\(116\) 11.7730 1.09309
\(117\) −0.535427 −0.0495002
\(118\) 26.8723 2.47380
\(119\) 15.8881 1.45646
\(120\) −4.58174 −0.418254
\(121\) −4.82119 −0.438290
\(122\) −2.69370 −0.243876
\(123\) 7.01520 0.632539
\(124\) −12.7532 −1.14527
\(125\) 9.79549 0.876135
\(126\) −1.10765 −0.0986771
\(127\) 15.9156 1.41228 0.706142 0.708071i \(-0.250434\pi\)
0.706142 + 0.708071i \(0.250434\pi\)
\(128\) 16.5256 1.46067
\(129\) 7.19108 0.633139
\(130\) 11.0547 0.969563
\(131\) −3.44142 −0.300678 −0.150339 0.988634i \(-0.548037\pi\)
−0.150339 + 0.988634i \(0.548037\pi\)
\(132\) 12.9491 1.12707
\(133\) −4.02650 −0.349142
\(134\) −19.6148 −1.69446
\(135\) −5.93243 −0.510582
\(136\) 9.51475 0.815883
\(137\) −11.7639 −1.00505 −0.502527 0.864561i \(-0.667596\pi\)
−0.502527 + 0.864561i \(0.667596\pi\)
\(138\) −14.0780 −1.19840
\(139\) −4.31817 −0.366262 −0.183131 0.983089i \(-0.558623\pi\)
−0.183131 + 0.983089i \(0.558623\pi\)
\(140\) 13.8492 1.17047
\(141\) −11.9451 −1.00596
\(142\) −21.3921 −1.79518
\(143\) −10.8947 −0.911064
\(144\) 0.0869453 0.00724544
\(145\) −4.29414 −0.356609
\(146\) −26.9853 −2.23332
\(147\) −15.6286 −1.28902
\(148\) 20.0511 1.64819
\(149\) 21.3018 1.74511 0.872557 0.488512i \(-0.162460\pi\)
0.872557 + 0.488512i \(0.162460\pi\)
\(150\) −14.3079 −1.16824
\(151\) −9.06852 −0.737986 −0.368993 0.929432i \(-0.620297\pi\)
−0.368993 + 0.929432i \(0.620297\pi\)
\(152\) −2.41131 −0.195583
\(153\) 0.482036 0.0389703
\(154\) −22.5382 −1.81618
\(155\) 4.65167 0.373631
\(156\) −22.8324 −1.82806
\(157\) 10.0060 0.798564 0.399282 0.916828i \(-0.369259\pi\)
0.399282 + 0.916828i \(0.369259\pi\)
\(158\) −13.0284 −1.03649
\(159\) −5.05476 −0.400869
\(160\) −7.19678 −0.568956
\(161\) 14.8387 1.16945
\(162\) 19.4077 1.52482
\(163\) −11.4133 −0.893956 −0.446978 0.894545i \(-0.647500\pi\)
−0.446978 + 0.894545i \(0.647500\pi\)
\(164\) −12.6987 −0.991605
\(165\) −4.72312 −0.367695
\(166\) 32.0997 2.49142
\(167\) −8.18730 −0.633552 −0.316776 0.948500i \(-0.602600\pi\)
−0.316776 + 0.948500i \(0.602600\pi\)
\(168\) −16.4708 −1.27075
\(169\) 6.21010 0.477700
\(170\) −9.95237 −0.763312
\(171\) −0.122162 −0.00934195
\(172\) −13.0171 −0.992545
\(173\) 16.8621 1.28200 0.641002 0.767539i \(-0.278519\pi\)
0.641002 + 0.767539i \(0.278519\pi\)
\(174\) 14.6455 1.11027
\(175\) 15.0811 1.14002
\(176\) 1.76914 0.133354
\(177\) 20.2441 1.52164
\(178\) −32.1150 −2.40712
\(179\) −9.04301 −0.675906 −0.337953 0.941163i \(-0.609735\pi\)
−0.337953 + 0.941163i \(0.609735\pi\)
\(180\) 0.420178 0.0313182
\(181\) 1.49721 0.111287 0.0556433 0.998451i \(-0.482279\pi\)
0.0556433 + 0.998451i \(0.482279\pi\)
\(182\) 39.7403 2.94575
\(183\) −2.02929 −0.150009
\(184\) 8.88632 0.655108
\(185\) −7.31356 −0.537703
\(186\) −15.8649 −1.16327
\(187\) 9.80835 0.717258
\(188\) 21.6227 1.57700
\(189\) −21.3263 −1.55126
\(190\) 2.52222 0.182981
\(191\) 18.2691 1.32191 0.660954 0.750427i \(-0.270152\pi\)
0.660954 + 0.750427i \(0.270152\pi\)
\(192\) 22.1304 1.59713
\(193\) 19.5292 1.40574 0.702870 0.711319i \(-0.251902\pi\)
0.702870 + 0.711319i \(0.251902\pi\)
\(194\) −4.98487 −0.357893
\(195\) 8.32802 0.596382
\(196\) 28.2905 2.02075
\(197\) 6.85772 0.488592 0.244296 0.969701i \(-0.421443\pi\)
0.244296 + 0.969701i \(0.421443\pi\)
\(198\) −0.683796 −0.0485953
\(199\) 3.97573 0.281832 0.140916 0.990022i \(-0.454995\pi\)
0.140916 + 0.990022i \(0.454995\pi\)
\(200\) 9.03145 0.638620
\(201\) −14.7767 −1.04227
\(202\) 10.1095 0.711302
\(203\) −15.4369 −1.08346
\(204\) 20.5556 1.43918
\(205\) 4.63181 0.323500
\(206\) −40.4422 −2.81774
\(207\) 0.450198 0.0312909
\(208\) −3.11943 −0.216294
\(209\) −2.48572 −0.171941
\(210\) 17.2283 1.18887
\(211\) 1.00000 0.0688428
\(212\) 9.15001 0.628425
\(213\) −16.1156 −1.10422
\(214\) 12.1045 0.827447
\(215\) 4.74793 0.323806
\(216\) −12.7715 −0.868991
\(217\) 16.7222 1.13517
\(218\) 3.59743 0.243648
\(219\) −20.3292 −1.37372
\(220\) 8.54968 0.576419
\(221\) −17.2945 −1.16336
\(222\) 24.9435 1.67410
\(223\) 29.1951 1.95505 0.977524 0.210823i \(-0.0676144\pi\)
0.977524 + 0.210823i \(0.0676144\pi\)
\(224\) −25.8715 −1.72861
\(225\) 0.457551 0.0305034
\(226\) 11.1496 0.741663
\(227\) −9.29434 −0.616887 −0.308443 0.951243i \(-0.599808\pi\)
−0.308443 + 0.951243i \(0.599808\pi\)
\(228\) −5.20939 −0.345000
\(229\) −13.4718 −0.890238 −0.445119 0.895471i \(-0.646839\pi\)
−0.445119 + 0.895471i \(0.646839\pi\)
\(230\) −9.29504 −0.612897
\(231\) −16.9790 −1.11714
\(232\) −9.24456 −0.606935
\(233\) 4.47067 0.292883 0.146442 0.989219i \(-0.453218\pi\)
0.146442 + 0.989219i \(0.453218\pi\)
\(234\) 1.20570 0.0788191
\(235\) −7.88678 −0.514477
\(236\) −36.6454 −2.38541
\(237\) −9.81491 −0.637547
\(238\) −35.7775 −2.31911
\(239\) 12.5033 0.808774 0.404387 0.914588i \(-0.367485\pi\)
0.404387 + 0.914588i \(0.367485\pi\)
\(240\) −1.35235 −0.0872936
\(241\) 13.4302 0.865117 0.432559 0.901606i \(-0.357611\pi\)
0.432559 + 0.901606i \(0.357611\pi\)
\(242\) 10.8566 0.697888
\(243\) −1.26874 −0.0813899
\(244\) 3.67336 0.235163
\(245\) −10.3188 −0.659246
\(246\) −15.7972 −1.00719
\(247\) 4.38293 0.278879
\(248\) 10.0143 0.635906
\(249\) 24.1821 1.53248
\(250\) −22.0579 −1.39507
\(251\) 12.3915 0.782145 0.391072 0.920360i \(-0.372104\pi\)
0.391072 + 0.920360i \(0.372104\pi\)
\(252\) 1.51049 0.0951517
\(253\) 9.16053 0.575918
\(254\) −35.8396 −2.24877
\(255\) −7.49758 −0.469516
\(256\) −11.1223 −0.695145
\(257\) 14.7048 0.917258 0.458629 0.888628i \(-0.348341\pi\)
0.458629 + 0.888628i \(0.348341\pi\)
\(258\) −16.1932 −1.00815
\(259\) −26.2913 −1.63366
\(260\) −15.0752 −0.934923
\(261\) −0.468347 −0.0289900
\(262\) 7.74955 0.478769
\(263\) −18.3385 −1.13080 −0.565400 0.824817i \(-0.691278\pi\)
−0.565400 + 0.824817i \(0.691278\pi\)
\(264\) −10.1681 −0.625802
\(265\) −3.33743 −0.205016
\(266\) 9.06706 0.555937
\(267\) −24.1937 −1.48063
\(268\) 26.7484 1.63392
\(269\) −22.3961 −1.36551 −0.682756 0.730646i \(-0.739219\pi\)
−0.682756 + 0.730646i \(0.739219\pi\)
\(270\) 13.3589 0.812998
\(271\) 4.00112 0.243051 0.121525 0.992588i \(-0.461221\pi\)
0.121525 + 0.992588i \(0.461221\pi\)
\(272\) 2.80837 0.170283
\(273\) 29.9382 1.81194
\(274\) 26.4904 1.60034
\(275\) 9.31014 0.561423
\(276\) 19.1980 1.15558
\(277\) 22.0830 1.32684 0.663420 0.748248i \(-0.269104\pi\)
0.663420 + 0.748248i \(0.269104\pi\)
\(278\) 9.72385 0.583198
\(279\) 0.507342 0.0303738
\(280\) −10.8749 −0.649899
\(281\) −21.6769 −1.29314 −0.646569 0.762855i \(-0.723797\pi\)
−0.646569 + 0.762855i \(0.723797\pi\)
\(282\) 26.8985 1.60178
\(283\) 4.33848 0.257896 0.128948 0.991651i \(-0.458840\pi\)
0.128948 + 0.991651i \(0.458840\pi\)
\(284\) 29.1721 1.73104
\(285\) 1.90010 0.112552
\(286\) 24.5333 1.45068
\(287\) 16.6508 0.982864
\(288\) −0.784928 −0.0462523
\(289\) −1.43003 −0.0841196
\(290\) 9.66975 0.567827
\(291\) −3.75533 −0.220142
\(292\) 36.7995 2.15353
\(293\) −10.6239 −0.620654 −0.310327 0.950630i \(-0.600439\pi\)
−0.310327 + 0.950630i \(0.600439\pi\)
\(294\) 35.1932 2.05251
\(295\) 13.3663 0.778214
\(296\) −15.7448 −0.915151
\(297\) −13.1656 −0.763946
\(298\) −47.9685 −2.77874
\(299\) −16.1523 −0.934109
\(300\) 19.5115 1.12650
\(301\) 17.0682 0.983796
\(302\) 20.4209 1.17509
\(303\) 7.61595 0.437525
\(304\) −0.711723 −0.0408201
\(305\) −1.33984 −0.0767192
\(306\) −1.08547 −0.0620522
\(307\) −15.4552 −0.882074 −0.441037 0.897489i \(-0.645389\pi\)
−0.441037 + 0.897489i \(0.645389\pi\)
\(308\) 30.7350 1.75129
\(309\) −30.4670 −1.73321
\(310\) −10.4749 −0.594932
\(311\) −34.1974 −1.93916 −0.969578 0.244784i \(-0.921283\pi\)
−0.969578 + 0.244784i \(0.921283\pi\)
\(312\) 17.9288 1.01502
\(313\) −6.22729 −0.351987 −0.175994 0.984391i \(-0.556314\pi\)
−0.175994 + 0.984391i \(0.556314\pi\)
\(314\) −22.5319 −1.27155
\(315\) −0.550943 −0.0310421
\(316\) 17.7667 0.999455
\(317\) 23.8962 1.34215 0.671073 0.741392i \(-0.265834\pi\)
0.671073 + 0.741392i \(0.265834\pi\)
\(318\) 11.3826 0.638302
\(319\) −9.52982 −0.533567
\(320\) 14.6117 0.816819
\(321\) 9.11887 0.508966
\(322\) −33.4145 −1.86212
\(323\) −3.94588 −0.219555
\(324\) −26.4661 −1.47034
\(325\) −16.4161 −0.910599
\(326\) 25.7009 1.42344
\(327\) 2.71010 0.149869
\(328\) 9.97150 0.550584
\(329\) −28.3520 −1.56309
\(330\) 10.6358 0.585479
\(331\) −30.0572 −1.65209 −0.826046 0.563603i \(-0.809415\pi\)
−0.826046 + 0.563603i \(0.809415\pi\)
\(332\) −43.7739 −2.40240
\(333\) −0.797664 −0.0437117
\(334\) 18.4365 1.00880
\(335\) −9.75636 −0.533047
\(336\) −4.86151 −0.265217
\(337\) −25.9760 −1.41500 −0.707501 0.706712i \(-0.750178\pi\)
−0.707501 + 0.706712i \(0.750178\pi\)
\(338\) −13.9842 −0.760640
\(339\) 8.39953 0.456200
\(340\) 13.5719 0.736041
\(341\) 10.3233 0.559037
\(342\) 0.275090 0.0148751
\(343\) −8.90939 −0.481062
\(344\) 10.2215 0.551106
\(345\) −7.00238 −0.376995
\(346\) −37.9709 −2.04133
\(347\) −2.34371 −0.125817 −0.0629084 0.998019i \(-0.520038\pi\)
−0.0629084 + 0.998019i \(0.520038\pi\)
\(348\) −19.9719 −1.07061
\(349\) −0.786662 −0.0421090 −0.0210545 0.999778i \(-0.506702\pi\)
−0.0210545 + 0.999778i \(0.506702\pi\)
\(350\) −33.9602 −1.81525
\(351\) 23.2142 1.23908
\(352\) −15.9715 −0.851286
\(353\) −26.6744 −1.41974 −0.709868 0.704335i \(-0.751245\pi\)
−0.709868 + 0.704335i \(0.751245\pi\)
\(354\) −45.5867 −2.42290
\(355\) −10.6404 −0.564733
\(356\) 43.7949 2.32112
\(357\) −26.9528 −1.42650
\(358\) 20.3635 1.07624
\(359\) −23.9133 −1.26209 −0.631047 0.775745i \(-0.717374\pi\)
−0.631047 + 0.775745i \(0.717374\pi\)
\(360\) −0.329938 −0.0173893
\(361\) 1.00000 0.0526316
\(362\) −3.37148 −0.177201
\(363\) 8.17877 0.429274
\(364\) −54.1934 −2.84050
\(365\) −13.4224 −0.702563
\(366\) 4.56964 0.238859
\(367\) −2.07338 −0.108230 −0.0541149 0.998535i \(-0.517234\pi\)
−0.0541149 + 0.998535i \(0.517234\pi\)
\(368\) 2.62288 0.136727
\(369\) 0.505176 0.0262984
\(370\) 16.4690 0.856183
\(371\) −11.9976 −0.622886
\(372\) 21.6348 1.12171
\(373\) −10.0392 −0.519809 −0.259905 0.965634i \(-0.583691\pi\)
−0.259905 + 0.965634i \(0.583691\pi\)
\(374\) −22.0869 −1.14209
\(375\) −16.6173 −0.858111
\(376\) −16.9789 −0.875619
\(377\) 16.8034 0.865419
\(378\) 48.0236 2.47007
\(379\) −18.4413 −0.947267 −0.473633 0.880722i \(-0.657058\pi\)
−0.473633 + 0.880722i \(0.657058\pi\)
\(380\) −3.43952 −0.176444
\(381\) −26.9996 −1.38323
\(382\) −41.1393 −2.10487
\(383\) −22.7069 −1.16027 −0.580133 0.814522i \(-0.697000\pi\)
−0.580133 + 0.814522i \(0.697000\pi\)
\(384\) −28.0343 −1.43062
\(385\) −11.2105 −0.571338
\(386\) −43.9767 −2.23835
\(387\) 0.517841 0.0263233
\(388\) 6.79781 0.345107
\(389\) −31.1974 −1.58177 −0.790885 0.611965i \(-0.790379\pi\)
−0.790885 + 0.611965i \(0.790379\pi\)
\(390\) −18.7534 −0.949617
\(391\) 14.5416 0.735400
\(392\) −22.2147 −1.12201
\(393\) 5.83809 0.294493
\(394\) −15.4425 −0.777984
\(395\) −6.48033 −0.326061
\(396\) 0.932484 0.0468591
\(397\) 9.21080 0.462277 0.231138 0.972921i \(-0.425755\pi\)
0.231138 + 0.972921i \(0.425755\pi\)
\(398\) −8.95274 −0.448760
\(399\) 6.83063 0.341959
\(400\) 2.66572 0.133286
\(401\) 25.0044 1.24866 0.624331 0.781160i \(-0.285372\pi\)
0.624331 + 0.781160i \(0.285372\pi\)
\(402\) 33.2749 1.65960
\(403\) −18.2025 −0.906729
\(404\) −13.7862 −0.685889
\(405\) 9.65340 0.479681
\(406\) 34.7615 1.72519
\(407\) −16.2307 −0.804526
\(408\) −16.1410 −0.799099
\(409\) −22.2158 −1.09850 −0.549250 0.835658i \(-0.685087\pi\)
−0.549250 + 0.835658i \(0.685087\pi\)
\(410\) −10.4301 −0.515107
\(411\) 19.9564 0.984378
\(412\) 55.1506 2.71707
\(413\) 48.0500 2.36439
\(414\) −1.01378 −0.0498244
\(415\) 15.9663 0.783757
\(416\) 28.1617 1.38074
\(417\) 7.32542 0.358727
\(418\) 5.59746 0.273781
\(419\) −27.8399 −1.36007 −0.680033 0.733182i \(-0.738035\pi\)
−0.680033 + 0.733182i \(0.738035\pi\)
\(420\) −23.4941 −1.14639
\(421\) −6.78808 −0.330831 −0.165415 0.986224i \(-0.552896\pi\)
−0.165415 + 0.986224i \(0.552896\pi\)
\(422\) −2.25185 −0.109618
\(423\) −0.860183 −0.0418235
\(424\) −7.18491 −0.348930
\(425\) 14.7791 0.716892
\(426\) 36.2899 1.75825
\(427\) −4.81657 −0.233090
\(428\) −16.5068 −0.797884
\(429\) 18.4821 0.892322
\(430\) −10.6916 −0.515596
\(431\) −5.23567 −0.252193 −0.126097 0.992018i \(-0.540245\pi\)
−0.126097 + 0.992018i \(0.540245\pi\)
\(432\) −3.76964 −0.181367
\(433\) 18.7965 0.903303 0.451651 0.892195i \(-0.350835\pi\)
0.451651 + 0.892195i \(0.350835\pi\)
\(434\) −37.6558 −1.80753
\(435\) 7.28466 0.349273
\(436\) −4.90576 −0.234943
\(437\) −3.68526 −0.176290
\(438\) 45.7783 2.18737
\(439\) −18.1490 −0.866206 −0.433103 0.901345i \(-0.642581\pi\)
−0.433103 + 0.901345i \(0.642581\pi\)
\(440\) −6.71351 −0.320054
\(441\) −1.12544 −0.0535923
\(442\) 38.9446 1.85241
\(443\) −38.4985 −1.82912 −0.914560 0.404451i \(-0.867463\pi\)
−0.914560 + 0.404451i \(0.867463\pi\)
\(444\) −34.0151 −1.61429
\(445\) −15.9740 −0.757240
\(446\) −65.7429 −3.11302
\(447\) −36.1368 −1.70921
\(448\) 52.5272 2.48168
\(449\) −7.60038 −0.358684 −0.179342 0.983787i \(-0.557397\pi\)
−0.179342 + 0.983787i \(0.557397\pi\)
\(450\) −1.03033 −0.0485704
\(451\) 10.2792 0.484029
\(452\) −15.2046 −0.715165
\(453\) 15.3840 0.722804
\(454\) 20.9294 0.982267
\(455\) 19.7668 0.926682
\(456\) 4.09060 0.191560
\(457\) −3.86933 −0.181000 −0.0904999 0.995896i \(-0.528846\pi\)
−0.0904999 + 0.995896i \(0.528846\pi\)
\(458\) 30.3363 1.41752
\(459\) −20.8993 −0.975497
\(460\) 12.6755 0.590999
\(461\) −37.6000 −1.75121 −0.875604 0.483030i \(-0.839536\pi\)
−0.875604 + 0.483030i \(0.839536\pi\)
\(462\) 38.2342 1.77882
\(463\) 34.8066 1.61760 0.808800 0.588083i \(-0.200117\pi\)
0.808800 + 0.588083i \(0.200117\pi\)
\(464\) −2.72862 −0.126673
\(465\) −7.89118 −0.365945
\(466\) −10.0673 −0.466357
\(467\) 20.4310 0.945436 0.472718 0.881214i \(-0.343273\pi\)
0.472718 + 0.881214i \(0.343273\pi\)
\(468\) −1.64420 −0.0760031
\(469\) −35.0729 −1.61952
\(470\) 17.7598 0.819199
\(471\) −16.9743 −0.782136
\(472\) 28.7753 1.32449
\(473\) 10.5369 0.484487
\(474\) 22.1017 1.01516
\(475\) −3.74545 −0.171853
\(476\) 48.7894 2.23626
\(477\) −0.364001 −0.0166665
\(478\) −28.1556 −1.28781
\(479\) −19.2739 −0.880646 −0.440323 0.897840i \(-0.645136\pi\)
−0.440323 + 0.897840i \(0.645136\pi\)
\(480\) 12.2088 0.557251
\(481\) 28.6187 1.30490
\(482\) −30.2428 −1.37752
\(483\) −25.1727 −1.14540
\(484\) −14.8050 −0.672954
\(485\) −2.47947 −0.112587
\(486\) 2.85701 0.129597
\(487\) 8.21480 0.372248 0.186124 0.982526i \(-0.440407\pi\)
0.186124 + 0.982526i \(0.440407\pi\)
\(488\) −2.88445 −0.130573
\(489\) 19.3617 0.875566
\(490\) 23.2364 1.04971
\(491\) 38.6937 1.74622 0.873112 0.487520i \(-0.162098\pi\)
0.873112 + 0.487520i \(0.162098\pi\)
\(492\) 21.5424 0.971206
\(493\) −15.1278 −0.681323
\(494\) −9.86969 −0.444059
\(495\) −0.340120 −0.0152872
\(496\) 2.95581 0.132720
\(497\) −38.2509 −1.71579
\(498\) −54.4545 −2.44016
\(499\) −30.7776 −1.37779 −0.688897 0.724859i \(-0.741905\pi\)
−0.688897 + 0.724859i \(0.741905\pi\)
\(500\) 30.0801 1.34522
\(501\) 13.8891 0.620519
\(502\) −27.9038 −1.24541
\(503\) −7.64072 −0.340683 −0.170341 0.985385i \(-0.554487\pi\)
−0.170341 + 0.985385i \(0.554487\pi\)
\(504\) −1.18609 −0.0528325
\(505\) 5.02846 0.223763
\(506\) −20.6281 −0.917031
\(507\) −10.5349 −0.467873
\(508\) 48.8740 2.16843
\(509\) 32.5693 1.44361 0.721805 0.692097i \(-0.243313\pi\)
0.721805 + 0.692097i \(0.243313\pi\)
\(510\) 16.8834 0.747609
\(511\) −48.2520 −2.13454
\(512\) −8.00541 −0.353793
\(513\) 5.29650 0.233846
\(514\) −33.1129 −1.46055
\(515\) −20.1159 −0.886414
\(516\) 22.0825 0.972127
\(517\) −17.5028 −0.769773
\(518\) 59.2040 2.60128
\(519\) −28.6052 −1.25563
\(520\) 11.8376 0.519112
\(521\) 1.36055 0.0596066 0.0298033 0.999556i \(-0.490512\pi\)
0.0298033 + 0.999556i \(0.490512\pi\)
\(522\) 1.05465 0.0461606
\(523\) −14.7344 −0.644290 −0.322145 0.946690i \(-0.604404\pi\)
−0.322145 + 0.946690i \(0.604404\pi\)
\(524\) −10.5680 −0.461664
\(525\) −25.5838 −1.11657
\(526\) 41.2955 1.80057
\(527\) 16.3874 0.713845
\(528\) −3.00121 −0.130611
\(529\) −9.41885 −0.409515
\(530\) 7.51537 0.326447
\(531\) 1.45781 0.0632636
\(532\) −12.3646 −0.536075
\(533\) −18.1247 −0.785070
\(534\) 54.4805 2.35760
\(535\) 6.02077 0.260301
\(536\) −21.0038 −0.907226
\(537\) 15.3407 0.662001
\(538\) 50.4325 2.17430
\(539\) −22.9002 −0.986380
\(540\) −18.2174 −0.783952
\(541\) −16.8589 −0.724820 −0.362410 0.932019i \(-0.618046\pi\)
−0.362410 + 0.932019i \(0.618046\pi\)
\(542\) −9.00990 −0.387008
\(543\) −2.53989 −0.108997
\(544\) −25.3535 −1.08702
\(545\) 1.78936 0.0766476
\(546\) −67.4162 −2.88515
\(547\) 45.3508 1.93906 0.969529 0.244976i \(-0.0787800\pi\)
0.969529 + 0.244976i \(0.0787800\pi\)
\(548\) −36.1246 −1.54317
\(549\) −0.146132 −0.00623676
\(550\) −20.9650 −0.893951
\(551\) 3.83383 0.163326
\(552\) −15.0749 −0.641631
\(553\) −23.2960 −0.990645
\(554\) −49.7276 −2.11272
\(555\) 12.4069 0.526642
\(556\) −13.2603 −0.562362
\(557\) 4.93287 0.209013 0.104506 0.994524i \(-0.466674\pi\)
0.104506 + 0.994524i \(0.466674\pi\)
\(558\) −1.14246 −0.0483640
\(559\) −18.5791 −0.785814
\(560\) −3.20983 −0.135640
\(561\) −16.6391 −0.702503
\(562\) 48.8132 2.05906
\(563\) 29.9198 1.26097 0.630484 0.776202i \(-0.282856\pi\)
0.630484 + 0.776202i \(0.282856\pi\)
\(564\) −36.6811 −1.54455
\(565\) 5.54582 0.233314
\(566\) −9.76960 −0.410647
\(567\) 34.7027 1.45738
\(568\) −22.9069 −0.961154
\(569\) −1.35117 −0.0566440 −0.0283220 0.999599i \(-0.509016\pi\)
−0.0283220 + 0.999599i \(0.509016\pi\)
\(570\) −4.27874 −0.179217
\(571\) 15.7296 0.658265 0.329132 0.944284i \(-0.393244\pi\)
0.329132 + 0.944284i \(0.393244\pi\)
\(572\) −33.4558 −1.39886
\(573\) −30.9921 −1.29471
\(574\) −37.4950 −1.56501
\(575\) 13.8030 0.575623
\(576\) 1.59365 0.0664020
\(577\) 4.21519 0.175481 0.0877404 0.996143i \(-0.472035\pi\)
0.0877404 + 0.996143i \(0.472035\pi\)
\(578\) 3.22022 0.133943
\(579\) −33.1296 −1.37682
\(580\) −13.1865 −0.547540
\(581\) 57.3970 2.38123
\(582\) 8.45644 0.350531
\(583\) −7.40662 −0.306751
\(584\) −28.8962 −1.19573
\(585\) 0.599714 0.0247951
\(586\) 23.9234 0.988266
\(587\) −42.4642 −1.75269 −0.876343 0.481687i \(-0.840024\pi\)
−0.876343 + 0.481687i \(0.840024\pi\)
\(588\) −47.9925 −1.97918
\(589\) −4.15303 −0.171123
\(590\) −30.0988 −1.23915
\(591\) −11.6336 −0.478541
\(592\) −4.64724 −0.191001
\(593\) −8.01253 −0.329035 −0.164518 0.986374i \(-0.552607\pi\)
−0.164518 + 0.986374i \(0.552607\pi\)
\(594\) 29.6469 1.21643
\(595\) −17.7957 −0.729553
\(596\) 65.4140 2.67946
\(597\) −6.74451 −0.276034
\(598\) 36.3724 1.48738
\(599\) 13.1507 0.537323 0.268661 0.963235i \(-0.413419\pi\)
0.268661 + 0.963235i \(0.413419\pi\)
\(600\) −15.3211 −0.625483
\(601\) 21.4682 0.875705 0.437852 0.899047i \(-0.355739\pi\)
0.437852 + 0.899047i \(0.355739\pi\)
\(602\) −38.4350 −1.56649
\(603\) −1.06409 −0.0433332
\(604\) −27.8478 −1.13311
\(605\) 5.40006 0.219544
\(606\) −17.1499 −0.696669
\(607\) −0.756094 −0.0306889 −0.0153445 0.999882i \(-0.504884\pi\)
−0.0153445 + 0.999882i \(0.504884\pi\)
\(608\) 6.42532 0.260581
\(609\) 26.1874 1.06117
\(610\) 3.01712 0.122160
\(611\) 30.8617 1.24853
\(612\) 1.48024 0.0598353
\(613\) 16.2818 0.657614 0.328807 0.944397i \(-0.393353\pi\)
0.328807 + 0.944397i \(0.393353\pi\)
\(614\) 34.8027 1.40452
\(615\) −7.85749 −0.316845
\(616\) −24.1342 −0.972396
\(617\) −12.8861 −0.518776 −0.259388 0.965773i \(-0.583521\pi\)
−0.259388 + 0.965773i \(0.583521\pi\)
\(618\) 68.6070 2.75978
\(619\) 45.7103 1.83725 0.918627 0.395126i \(-0.129299\pi\)
0.918627 + 0.395126i \(0.129299\pi\)
\(620\) 14.2844 0.573676
\(621\) −19.5190 −0.783269
\(622\) 77.0073 3.08771
\(623\) −57.4245 −2.30066
\(624\) 5.29186 0.211844
\(625\) 7.75565 0.310226
\(626\) 14.0229 0.560468
\(627\) 4.21682 0.168404
\(628\) 30.7265 1.22612
\(629\) −25.7649 −1.02731
\(630\) 1.24064 0.0494283
\(631\) 24.8898 0.990847 0.495423 0.868652i \(-0.335013\pi\)
0.495423 + 0.868652i \(0.335013\pi\)
\(632\) −13.9510 −0.554943
\(633\) −1.69642 −0.0674266
\(634\) −53.8106 −2.13709
\(635\) −17.8266 −0.707426
\(636\) −15.5222 −0.615497
\(637\) 40.3786 1.59986
\(638\) 21.4597 0.849598
\(639\) −1.16051 −0.0459091
\(640\) −18.5098 −0.731662
\(641\) −23.4241 −0.925197 −0.462598 0.886568i \(-0.653083\pi\)
−0.462598 + 0.886568i \(0.653083\pi\)
\(642\) −20.5343 −0.810425
\(643\) −22.3000 −0.879427 −0.439714 0.898138i \(-0.644920\pi\)
−0.439714 + 0.898138i \(0.644920\pi\)
\(644\) 45.5669 1.79559
\(645\) −8.05449 −0.317145
\(646\) 8.88552 0.349596
\(647\) −47.3142 −1.86011 −0.930056 0.367418i \(-0.880242\pi\)
−0.930056 + 0.367418i \(0.880242\pi\)
\(648\) 20.7821 0.816399
\(649\) 29.6632 1.16438
\(650\) 36.9665 1.44994
\(651\) −28.3678 −1.11182
\(652\) −35.0481 −1.37259
\(653\) −18.8337 −0.737019 −0.368510 0.929624i \(-0.620132\pi\)
−0.368510 + 0.929624i \(0.620132\pi\)
\(654\) −6.10274 −0.238636
\(655\) 3.85462 0.150613
\(656\) 2.94319 0.114912
\(657\) −1.46394 −0.0571137
\(658\) 63.8443 2.48891
\(659\) 6.66147 0.259494 0.129747 0.991547i \(-0.458583\pi\)
0.129747 + 0.991547i \(0.458583\pi\)
\(660\) −14.5038 −0.564561
\(661\) 6.19938 0.241128 0.120564 0.992706i \(-0.461530\pi\)
0.120564 + 0.992706i \(0.461530\pi\)
\(662\) 67.6842 2.63062
\(663\) 29.3388 1.13942
\(664\) 34.3728 1.33392
\(665\) 4.50995 0.174888
\(666\) 1.79622 0.0696020
\(667\) −14.1287 −0.547064
\(668\) −25.1417 −0.972761
\(669\) −49.5271 −1.91483
\(670\) 21.9698 0.848769
\(671\) −2.97346 −0.114789
\(672\) 43.8890 1.69305
\(673\) 22.8410 0.880458 0.440229 0.897886i \(-0.354897\pi\)
0.440229 + 0.897886i \(0.354897\pi\)
\(674\) 58.4940 2.25310
\(675\) −19.8378 −0.763556
\(676\) 19.0701 0.733464
\(677\) 48.8853 1.87881 0.939407 0.342804i \(-0.111377\pi\)
0.939407 + 0.342804i \(0.111377\pi\)
\(678\) −18.9145 −0.726405
\(679\) −8.91339 −0.342064
\(680\) −10.6572 −0.408683
\(681\) 15.7671 0.604196
\(682\) −23.2464 −0.890152
\(683\) 13.3277 0.509968 0.254984 0.966945i \(-0.417930\pi\)
0.254984 + 0.966945i \(0.417930\pi\)
\(684\) −0.375136 −0.0143437
\(685\) 13.1763 0.503441
\(686\) 20.0626 0.765993
\(687\) 22.8537 0.871925
\(688\) 3.01697 0.115021
\(689\) 13.0597 0.497534
\(690\) 15.7683 0.600288
\(691\) −3.26772 −0.124310 −0.0621550 0.998067i \(-0.519797\pi\)
−0.0621550 + 0.998067i \(0.519797\pi\)
\(692\) 51.7805 1.96840
\(693\) −1.22269 −0.0464460
\(694\) 5.27767 0.200338
\(695\) 4.83664 0.183464
\(696\) 15.6826 0.594449
\(697\) 16.3174 0.618065
\(698\) 1.77144 0.0670501
\(699\) −7.58412 −0.286858
\(700\) 46.3111 1.75040
\(701\) 44.7460 1.69003 0.845017 0.534739i \(-0.179590\pi\)
0.845017 + 0.534739i \(0.179590\pi\)
\(702\) −52.2748 −1.97298
\(703\) 6.52957 0.246268
\(704\) 32.4272 1.22215
\(705\) 13.3793 0.503893
\(706\) 60.0667 2.26064
\(707\) 18.0767 0.679843
\(708\) 62.1660 2.33634
\(709\) 5.55058 0.208456 0.104228 0.994553i \(-0.466763\pi\)
0.104228 + 0.994553i \(0.466763\pi\)
\(710\) 23.9605 0.899223
\(711\) −0.706787 −0.0265066
\(712\) −34.3893 −1.28879
\(713\) 15.3050 0.573177
\(714\) 60.6937 2.27140
\(715\) 12.2028 0.456360
\(716\) −27.7694 −1.03779
\(717\) −21.2109 −0.792136
\(718\) 53.8490 2.00963
\(719\) −12.7436 −0.475255 −0.237628 0.971356i \(-0.576370\pi\)
−0.237628 + 0.971356i \(0.576370\pi\)
\(720\) −0.0973845 −0.00362931
\(721\) −72.3142 −2.69312
\(722\) −2.25185 −0.0838051
\(723\) −22.7833 −0.847320
\(724\) 4.59765 0.170870
\(725\) −14.3594 −0.533295
\(726\) −18.4173 −0.683531
\(727\) −2.71026 −0.100518 −0.0502589 0.998736i \(-0.516005\pi\)
−0.0502589 + 0.998736i \(0.516005\pi\)
\(728\) 42.5545 1.57718
\(729\) 28.0081 1.03734
\(730\) 30.2253 1.11869
\(731\) 16.7265 0.618651
\(732\) −6.23156 −0.230325
\(733\) 20.5859 0.760357 0.380179 0.924913i \(-0.375863\pi\)
0.380179 + 0.924913i \(0.375863\pi\)
\(734\) 4.66894 0.172334
\(735\) 17.5051 0.645684
\(736\) −23.6790 −0.872818
\(737\) −21.6519 −0.797559
\(738\) −1.13758 −0.0418748
\(739\) 15.1848 0.558584 0.279292 0.960206i \(-0.409900\pi\)
0.279292 + 0.960206i \(0.409900\pi\)
\(740\) −22.4586 −0.825594
\(741\) −7.43529 −0.273142
\(742\) 27.0168 0.991819
\(743\) −12.0796 −0.443159 −0.221580 0.975142i \(-0.571121\pi\)
−0.221580 + 0.975142i \(0.571121\pi\)
\(744\) −16.9884 −0.622824
\(745\) −23.8595 −0.874144
\(746\) 22.6067 0.827690
\(747\) 1.74139 0.0637142
\(748\) 30.1196 1.10128
\(749\) 21.6439 0.790851
\(750\) 37.4195 1.36637
\(751\) −12.9709 −0.473314 −0.236657 0.971593i \(-0.576052\pi\)
−0.236657 + 0.971593i \(0.576052\pi\)
\(752\) −5.01148 −0.182750
\(753\) −21.0212 −0.766054
\(754\) −37.8387 −1.37800
\(755\) 10.1574 0.369664
\(756\) −65.4892 −2.38182
\(757\) 37.8880 1.37706 0.688532 0.725206i \(-0.258256\pi\)
0.688532 + 0.725206i \(0.258256\pi\)
\(758\) 41.5270 1.50833
\(759\) −15.5401 −0.564070
\(760\) 2.70083 0.0979695
\(761\) 30.8382 1.11788 0.558942 0.829206i \(-0.311207\pi\)
0.558942 + 0.829206i \(0.311207\pi\)
\(762\) 60.7989 2.20251
\(763\) 6.43251 0.232872
\(764\) 56.1011 2.02967
\(765\) −0.539912 −0.0195206
\(766\) 51.1324 1.84749
\(767\) −52.3035 −1.88857
\(768\) 18.8681 0.680844
\(769\) 8.31375 0.299801 0.149901 0.988701i \(-0.452105\pi\)
0.149901 + 0.988701i \(0.452105\pi\)
\(770\) 25.2443 0.909740
\(771\) −24.9454 −0.898388
\(772\) 59.9704 2.15838
\(773\) −43.7621 −1.57401 −0.787007 0.616944i \(-0.788371\pi\)
−0.787007 + 0.616944i \(0.788371\pi\)
\(774\) −1.16610 −0.0419145
\(775\) 15.5550 0.558751
\(776\) −5.33788 −0.191619
\(777\) 44.6011 1.60006
\(778\) 70.2517 2.51865
\(779\) −4.13530 −0.148162
\(780\) 25.5738 0.915690
\(781\) −23.6138 −0.844968
\(782\) −32.7455 −1.17098
\(783\) 20.3058 0.725672
\(784\) −6.55688 −0.234174
\(785\) −11.2074 −0.400008
\(786\) −13.1465 −0.468920
\(787\) −13.4709 −0.480185 −0.240092 0.970750i \(-0.577178\pi\)
−0.240092 + 0.970750i \(0.577178\pi\)
\(788\) 21.0588 0.750189
\(789\) 31.1098 1.10754
\(790\) 14.5927 0.519185
\(791\) 19.9365 0.708861
\(792\) −0.732220 −0.0260183
\(793\) 5.24294 0.186182
\(794\) −20.7413 −0.736081
\(795\) 5.66167 0.200799
\(796\) 12.2087 0.432727
\(797\) −18.9963 −0.672884 −0.336442 0.941704i \(-0.609224\pi\)
−0.336442 + 0.941704i \(0.609224\pi\)
\(798\) −15.3815 −0.544500
\(799\) −27.7843 −0.982938
\(800\) −24.0657 −0.850851
\(801\) −1.74223 −0.0615586
\(802\) −56.3062 −1.98824
\(803\) −29.7879 −1.05119
\(804\) −45.3765 −1.60031
\(805\) −16.6203 −0.585790
\(806\) 40.9891 1.44378
\(807\) 37.9931 1.33742
\(808\) 10.8254 0.380837
\(809\) 53.5150 1.88149 0.940744 0.339118i \(-0.110128\pi\)
0.940744 + 0.339118i \(0.110128\pi\)
\(810\) −21.7380 −0.763795
\(811\) 27.9357 0.980955 0.490477 0.871454i \(-0.336822\pi\)
0.490477 + 0.871454i \(0.336822\pi\)
\(812\) −47.4039 −1.66355
\(813\) −6.78757 −0.238051
\(814\) 36.5490 1.28104
\(815\) 12.7836 0.447791
\(816\) −4.76418 −0.166779
\(817\) −4.23897 −0.148303
\(818\) 50.0266 1.74914
\(819\) 2.15590 0.0753331
\(820\) 14.2234 0.496704
\(821\) −21.3327 −0.744515 −0.372258 0.928129i \(-0.621416\pi\)
−0.372258 + 0.928129i \(0.621416\pi\)
\(822\) −44.9388 −1.56742
\(823\) −20.0414 −0.698599 −0.349300 0.937011i \(-0.613580\pi\)
−0.349300 + 0.937011i \(0.613580\pi\)
\(824\) −43.3062 −1.50864
\(825\) −15.7939 −0.549873
\(826\) −108.201 −3.76480
\(827\) 3.61644 0.125756 0.0628780 0.998021i \(-0.479972\pi\)
0.0628780 + 0.998021i \(0.479972\pi\)
\(828\) 1.38248 0.0480443
\(829\) 27.5824 0.957978 0.478989 0.877821i \(-0.341003\pi\)
0.478989 + 0.877821i \(0.341003\pi\)
\(830\) −35.9538 −1.24797
\(831\) −37.4620 −1.29954
\(832\) −57.1771 −1.98226
\(833\) −36.3522 −1.25953
\(834\) −16.4957 −0.571200
\(835\) 9.17032 0.317352
\(836\) −7.63319 −0.263999
\(837\) −21.9965 −0.760310
\(838\) 62.6911 2.16563
\(839\) −23.0648 −0.796285 −0.398142 0.917324i \(-0.630345\pi\)
−0.398142 + 0.917324i \(0.630345\pi\)
\(840\) 18.4484 0.636530
\(841\) −14.3018 −0.493165
\(842\) 15.2857 0.526781
\(843\) 36.7732 1.26654
\(844\) 3.07082 0.105702
\(845\) −6.95573 −0.239284
\(846\) 1.93700 0.0665955
\(847\) 19.4125 0.667022
\(848\) −2.12070 −0.0728250
\(849\) −7.35988 −0.252591
\(850\) −33.2803 −1.14150
\(851\) −24.0632 −0.824875
\(852\) −49.4881 −1.69543
\(853\) −37.9284 −1.29864 −0.649322 0.760514i \(-0.724947\pi\)
−0.649322 + 0.760514i \(0.724947\pi\)
\(854\) 10.8462 0.371148
\(855\) 0.136829 0.00467947
\(856\) 12.9617 0.443022
\(857\) −17.8439 −0.609537 −0.304769 0.952426i \(-0.598579\pi\)
−0.304769 + 0.952426i \(0.598579\pi\)
\(858\) −41.6188 −1.42084
\(859\) 18.5329 0.632334 0.316167 0.948704i \(-0.397604\pi\)
0.316167 + 0.948704i \(0.397604\pi\)
\(860\) 14.5800 0.497175
\(861\) −28.2467 −0.962645
\(862\) 11.7899 0.401566
\(863\) 38.7756 1.31994 0.659968 0.751294i \(-0.270570\pi\)
0.659968 + 0.751294i \(0.270570\pi\)
\(864\) 34.0317 1.15778
\(865\) −18.8867 −0.642167
\(866\) −42.3269 −1.43833
\(867\) 2.42594 0.0823891
\(868\) 51.3507 1.74296
\(869\) −14.3815 −0.487860
\(870\) −16.4039 −0.556146
\(871\) 38.1776 1.29360
\(872\) 3.85218 0.130451
\(873\) −0.270427 −0.00915258
\(874\) 8.29865 0.280706
\(875\) −39.4415 −1.33337
\(876\) −62.4273 −2.10922
\(877\) 1.77452 0.0599211 0.0299606 0.999551i \(-0.490462\pi\)
0.0299606 + 0.999551i \(0.490462\pi\)
\(878\) 40.8688 1.37926
\(879\) 18.0226 0.607886
\(880\) −1.98156 −0.0667983
\(881\) −2.26884 −0.0764392 −0.0382196 0.999269i \(-0.512169\pi\)
−0.0382196 + 0.999269i \(0.512169\pi\)
\(882\) 2.53432 0.0853349
\(883\) −44.5844 −1.50039 −0.750193 0.661219i \(-0.770039\pi\)
−0.750193 + 0.661219i \(0.770039\pi\)
\(884\) −53.1083 −1.78623
\(885\) −22.6748 −0.762204
\(886\) 86.6928 2.91250
\(887\) 8.29649 0.278569 0.139284 0.990252i \(-0.455520\pi\)
0.139284 + 0.990252i \(0.455520\pi\)
\(888\) 26.7099 0.896324
\(889\) −64.0842 −2.14932
\(890\) 35.9710 1.20575
\(891\) 21.4234 0.717711
\(892\) 89.6528 3.00180
\(893\) 7.04135 0.235630
\(894\) 81.3746 2.72158
\(895\) 10.1288 0.338568
\(896\) −66.5402 −2.22295
\(897\) 27.4010 0.914893
\(898\) 17.1149 0.571131
\(899\) −15.9220 −0.531028
\(900\) 1.40505 0.0468352
\(901\) −11.7574 −0.391696
\(902\) −23.1472 −0.770717
\(903\) −28.9549 −0.963557
\(904\) 11.9392 0.397092
\(905\) −1.67697 −0.0557444
\(906\) −34.6425 −1.15092
\(907\) −5.64883 −0.187566 −0.0937832 0.995593i \(-0.529896\pi\)
−0.0937832 + 0.995593i \(0.529896\pi\)
\(908\) −28.5412 −0.947173
\(909\) 0.548436 0.0181905
\(910\) −44.5118 −1.47555
\(911\) −25.9750 −0.860589 −0.430294 0.902689i \(-0.641590\pi\)
−0.430294 + 0.902689i \(0.641590\pi\)
\(912\) 1.20738 0.0399803
\(913\) 35.4335 1.17268
\(914\) 8.71315 0.288205
\(915\) 2.27294 0.0751409
\(916\) −41.3693 −1.36688
\(917\) 13.8569 0.457594
\(918\) 47.0621 1.55328
\(919\) 7.83511 0.258456 0.129228 0.991615i \(-0.458750\pi\)
0.129228 + 0.991615i \(0.458750\pi\)
\(920\) −9.95327 −0.328150
\(921\) 26.2185 0.863928
\(922\) 84.6695 2.78844
\(923\) 41.6369 1.37050
\(924\) −52.1395 −1.71526
\(925\) −24.4562 −0.804115
\(926\) −78.3792 −2.57570
\(927\) −2.19397 −0.0720596
\(928\) 24.6335 0.808636
\(929\) 19.8932 0.652675 0.326338 0.945253i \(-0.394185\pi\)
0.326338 + 0.945253i \(0.394185\pi\)
\(930\) 17.7697 0.582693
\(931\) 9.21269 0.301934
\(932\) 13.7286 0.449695
\(933\) 58.0131 1.89926
\(934\) −46.0076 −1.50541
\(935\) −10.9860 −0.359281
\(936\) 1.29108 0.0422003
\(937\) 7.08249 0.231375 0.115687 0.993286i \(-0.463093\pi\)
0.115687 + 0.993286i \(0.463093\pi\)
\(938\) 78.9788 2.57875
\(939\) 10.5641 0.344746
\(940\) −24.2188 −0.789931
\(941\) −22.4772 −0.732736 −0.366368 0.930470i \(-0.619399\pi\)
−0.366368 + 0.930470i \(0.619399\pi\)
\(942\) 38.2236 1.24539
\(943\) 15.2397 0.496272
\(944\) 8.49330 0.276433
\(945\) 23.8869 0.777041
\(946\) −23.7275 −0.771448
\(947\) −43.3377 −1.40829 −0.704143 0.710058i \(-0.748669\pi\)
−0.704143 + 0.710058i \(0.748669\pi\)
\(948\) −30.1398 −0.978895
\(949\) 52.5234 1.70498
\(950\) 8.43418 0.273641
\(951\) −40.5380 −1.31453
\(952\) −38.3111 −1.24167
\(953\) 19.1723 0.621052 0.310526 0.950565i \(-0.399495\pi\)
0.310526 + 0.950565i \(0.399495\pi\)
\(954\) 0.819676 0.0265380
\(955\) −20.4626 −0.662155
\(956\) 38.3955 1.24180
\(957\) 16.1666 0.522591
\(958\) 43.4018 1.40225
\(959\) 47.3672 1.52957
\(960\) −24.7876 −0.800016
\(961\) −13.7523 −0.443624
\(962\) −64.4449 −2.07779
\(963\) 0.656664 0.0211607
\(964\) 41.2418 1.32831
\(965\) −21.8740 −0.704148
\(966\) 56.6850 1.82381
\(967\) 37.2765 1.19873 0.599366 0.800475i \(-0.295419\pi\)
0.599366 + 0.800475i \(0.295419\pi\)
\(968\) 11.6254 0.373655
\(969\) 6.69387 0.215038
\(970\) 5.58339 0.179272
\(971\) 48.7357 1.56400 0.782002 0.623276i \(-0.214199\pi\)
0.782002 + 0.623276i \(0.214199\pi\)
\(972\) −3.89607 −0.124967
\(973\) 17.3871 0.557405
\(974\) −18.4985 −0.592729
\(975\) 27.8485 0.891866
\(976\) −0.851375 −0.0272518
\(977\) −0.607532 −0.0194367 −0.00971833 0.999953i \(-0.503093\pi\)
−0.00971833 + 0.999953i \(0.503093\pi\)
\(978\) −43.5996 −1.39416
\(979\) −35.4504 −1.13300
\(980\) −31.6872 −1.01221
\(981\) 0.195159 0.00623094
\(982\) −87.1324 −2.78051
\(983\) −18.7593 −0.598330 −0.299165 0.954201i \(-0.596708\pi\)
−0.299165 + 0.954201i \(0.596708\pi\)
\(984\) −16.9158 −0.539257
\(985\) −7.68111 −0.244740
\(986\) 34.0655 1.08487
\(987\) 48.0968 1.53094
\(988\) 13.4592 0.428194
\(989\) 15.6217 0.496742
\(990\) 0.765897 0.0243418
\(991\) −28.4052 −0.902321 −0.451161 0.892443i \(-0.648990\pi\)
−0.451161 + 0.892443i \(0.648990\pi\)
\(992\) −26.6845 −0.847235
\(993\) 50.9896 1.61811
\(994\) 86.1351 2.73204
\(995\) −4.45309 −0.141172
\(996\) 74.2589 2.35298
\(997\) −34.1448 −1.08138 −0.540689 0.841223i \(-0.681836\pi\)
−0.540689 + 0.841223i \(0.681836\pi\)
\(998\) 69.3064 2.19386
\(999\) 34.5839 1.09418
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 \(a_p\))