Properties

Label 6019.2.a.c.1.3
Level 6019
Weight 2
Character 6019.1
Self dual Yes
Analytic conductor 48.062
Analytic rank 1
Dimension 108
CM No

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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 1.3
Character \(\chi\) = 6019.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.64969 q^{2}\) \(-0.413927 q^{3}\) \(+5.02086 q^{4}\) \(-1.95969 q^{5}\) \(+1.09678 q^{6}\) \(-0.899778 q^{7}\) \(-8.00435 q^{8}\) \(-2.82866 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.64969 q^{2}\) \(-0.413927 q^{3}\) \(+5.02086 q^{4}\) \(-1.95969 q^{5}\) \(+1.09678 q^{6}\) \(-0.899778 q^{7}\) \(-8.00435 q^{8}\) \(-2.82866 q^{9}\) \(+5.19257 q^{10}\) \(+4.83103 q^{11}\) \(-2.07827 q^{12}\) \(-1.00000 q^{13}\) \(+2.38413 q^{14}\) \(+0.811168 q^{15}\) \(+11.1673 q^{16}\) \(+2.65234 q^{17}\) \(+7.49509 q^{18}\) \(-3.64749 q^{19}\) \(-9.83933 q^{20}\) \(+0.372442 q^{21}\) \(-12.8007 q^{22}\) \(+5.87423 q^{23}\) \(+3.31322 q^{24}\) \(-1.15962 q^{25}\) \(+2.64969 q^{26}\) \(+2.41264 q^{27}\) \(-4.51766 q^{28}\) \(-4.43883 q^{29}\) \(-2.14935 q^{30}\) \(+5.22174 q^{31}\) \(-13.5813 q^{32}\) \(-1.99969 q^{33}\) \(-7.02788 q^{34}\) \(+1.76329 q^{35}\) \(-14.2023 q^{36}\) \(+3.29448 q^{37}\) \(+9.66472 q^{38}\) \(+0.413927 q^{39}\) \(+15.6860 q^{40}\) \(-10.9911 q^{41}\) \(-0.986857 q^{42}\) \(-3.92099 q^{43}\) \(+24.2559 q^{44}\) \(+5.54330 q^{45}\) \(-15.5649 q^{46}\) \(-3.93450 q^{47}\) \(-4.62246 q^{48}\) \(-6.19040 q^{49}\) \(+3.07263 q^{50}\) \(-1.09788 q^{51}\) \(-5.02086 q^{52}\) \(+2.69311 q^{53}\) \(-6.39276 q^{54}\) \(-9.46732 q^{55}\) \(+7.20214 q^{56}\) \(+1.50980 q^{57}\) \(+11.7615 q^{58}\) \(-14.7234 q^{59}\) \(+4.07276 q^{60}\) \(+11.8266 q^{61}\) \(-13.8360 q^{62}\) \(+2.54517 q^{63}\) \(+13.6515 q^{64}\) \(+1.95969 q^{65}\) \(+5.29857 q^{66}\) \(+2.89289 q^{67}\) \(+13.3170 q^{68}\) \(-2.43150 q^{69}\) \(-4.67216 q^{70}\) \(+4.80128 q^{71}\) \(+22.6416 q^{72}\) \(+14.0811 q^{73}\) \(-8.72935 q^{74}\) \(+0.479998 q^{75}\) \(-18.3135 q^{76}\) \(-4.34686 q^{77}\) \(-1.09678 q^{78}\) \(+15.3643 q^{79}\) \(-21.8845 q^{80}\) \(+7.48734 q^{81}\) \(+29.1229 q^{82}\) \(-14.6641 q^{83}\) \(+1.86998 q^{84}\) \(-5.19776 q^{85}\) \(+10.3894 q^{86}\) \(+1.83735 q^{87}\) \(-38.6693 q^{88}\) \(+1.94412 q^{89}\) \(-14.6880 q^{90}\) \(+0.899778 q^{91}\) \(+29.4937 q^{92}\) \(-2.16142 q^{93}\) \(+10.4252 q^{94}\) \(+7.14795 q^{95}\) \(+5.62166 q^{96}\) \(+12.1069 q^{97}\) \(+16.4026 q^{98}\) \(-13.6654 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(108q \) \(\mathstrut -\mathstrut 11q^{2} \) \(\mathstrut +\mathstrut q^{3} \) \(\mathstrut +\mathstrut 95q^{4} \) \(\mathstrut -\mathstrut 40q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 79q^{9} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 45q^{11} \) \(\mathstrut -\mathstrut 6q^{12} \) \(\mathstrut -\mathstrut 108q^{13} \) \(\mathstrut -\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 35q^{18} \) \(\mathstrut -\mathstrut 19q^{19} \) \(\mathstrut -\mathstrut 79q^{20} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut -\mathstrut 26q^{23} \) \(\mathstrut -\mathstrut 23q^{24} \) \(\mathstrut +\mathstrut 92q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 21q^{28} \) \(\mathstrut -\mathstrut 94q^{29} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 77q^{32} \) \(\mathstrut -\mathstrut 32q^{33} \) \(\mathstrut -\mathstrut 58q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 17q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 12q^{38} \) \(\mathstrut -\mathstrut q^{39} \) \(\mathstrut -\mathstrut 4q^{40} \) \(\mathstrut -\mathstrut 68q^{41} \) \(\mathstrut -\mathstrut 11q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut -\mathstrut 151q^{44} \) \(\mathstrut -\mathstrut 121q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut -\mathstrut 51q^{47} \) \(\mathstrut -\mathstrut 27q^{48} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 45q^{50} \) \(\mathstrut -\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 95q^{52} \) \(\mathstrut -\mathstrut 81q^{53} \) \(\mathstrut -\mathstrut 29q^{54} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut -\mathstrut 68q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 94q^{59} \) \(\mathstrut -\mathstrut 108q^{60} \) \(\mathstrut -\mathstrut 39q^{61} \) \(\mathstrut -\mathstrut 9q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 31q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 47q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 66q^{70} \) \(\mathstrut -\mathstrut 86q^{71} \) \(\mathstrut -\mathstrut 91q^{72} \) \(\mathstrut -\mathstrut 51q^{73} \) \(\mathstrut -\mathstrut 110q^{74} \) \(\mathstrut -\mathstrut 7q^{75} \) \(\mathstrut -\mathstrut 51q^{76} \) \(\mathstrut -\mathstrut 96q^{77} \) \(\mathstrut +\mathstrut 10q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 136q^{80} \) \(\mathstrut -\mathstrut 24q^{81} \) \(\mathstrut -\mathstrut 33q^{82} \) \(\mathstrut -\mathstrut 77q^{83} \) \(\mathstrut -\mathstrut 113q^{84} \) \(\mathstrut -\mathstrut 95q^{85} \) \(\mathstrut -\mathstrut 137q^{86} \) \(\mathstrut +\mathstrut 23q^{87} \) \(\mathstrut +\mathstrut 19q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 19q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 111q^{92} \) \(\mathstrut -\mathstrut 124q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 73q^{95} \) \(\mathstrut -\mathstrut 77q^{96} \) \(\mathstrut -\mathstrut 41q^{97} \) \(\mathstrut -\mathstrut 80q^{98} \) \(\mathstrut -\mathstrut 154q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64969 −1.87361 −0.936807 0.349846i \(-0.886234\pi\)
−0.936807 + 0.349846i \(0.886234\pi\)
\(3\) −0.413927 −0.238981 −0.119490 0.992835i \(-0.538126\pi\)
−0.119490 + 0.992835i \(0.538126\pi\)
\(4\) 5.02086 2.51043
\(5\) −1.95969 −0.876400 −0.438200 0.898878i \(-0.644384\pi\)
−0.438200 + 0.898878i \(0.644384\pi\)
\(6\) 1.09678 0.447758
\(7\) −0.899778 −0.340084 −0.170042 0.985437i \(-0.554390\pi\)
−0.170042 + 0.985437i \(0.554390\pi\)
\(8\) −8.00435 −2.82997
\(9\) −2.82866 −0.942888
\(10\) 5.19257 1.64203
\(11\) 4.83103 1.45661 0.728305 0.685253i \(-0.240308\pi\)
0.728305 + 0.685253i \(0.240308\pi\)
\(12\) −2.07827 −0.599945
\(13\) −1.00000 −0.277350
\(14\) 2.38413 0.637187
\(15\) 0.811168 0.209443
\(16\) 11.1673 2.79183
\(17\) 2.65234 0.643287 0.321644 0.946861i \(-0.395765\pi\)
0.321644 + 0.946861i \(0.395765\pi\)
\(18\) 7.49509 1.76661
\(19\) −3.64749 −0.836792 −0.418396 0.908265i \(-0.637408\pi\)
−0.418396 + 0.908265i \(0.637408\pi\)
\(20\) −9.83933 −2.20014
\(21\) 0.372442 0.0812736
\(22\) −12.8007 −2.72913
\(23\) 5.87423 1.22486 0.612431 0.790524i \(-0.290192\pi\)
0.612431 + 0.790524i \(0.290192\pi\)
\(24\) 3.31322 0.676308
\(25\) −1.15962 −0.231924
\(26\) 2.64969 0.519647
\(27\) 2.41264 0.464313
\(28\) −4.51766 −0.853758
\(29\) −4.43883 −0.824271 −0.412135 0.911123i \(-0.635217\pi\)
−0.412135 + 0.911123i \(0.635217\pi\)
\(30\) −2.14935 −0.392415
\(31\) 5.22174 0.937851 0.468926 0.883238i \(-0.344641\pi\)
0.468926 + 0.883238i \(0.344641\pi\)
\(32\) −13.5813 −2.40085
\(33\) −1.99969 −0.348102
\(34\) −7.02788 −1.20527
\(35\) 1.76329 0.298050
\(36\) −14.2023 −2.36706
\(37\) 3.29448 0.541609 0.270804 0.962634i \(-0.412710\pi\)
0.270804 + 0.962634i \(0.412710\pi\)
\(38\) 9.66472 1.56783
\(39\) 0.413927 0.0662814
\(40\) 15.6860 2.48018
\(41\) −10.9911 −1.71651 −0.858257 0.513219i \(-0.828453\pi\)
−0.858257 + 0.513219i \(0.828453\pi\)
\(42\) −0.986857 −0.152275
\(43\) −3.92099 −0.597945 −0.298973 0.954262i \(-0.596644\pi\)
−0.298973 + 0.954262i \(0.596644\pi\)
\(44\) 24.2559 3.65672
\(45\) 5.54330 0.826347
\(46\) −15.5649 −2.29492
\(47\) −3.93450 −0.573906 −0.286953 0.957945i \(-0.592642\pi\)
−0.286953 + 0.957945i \(0.592642\pi\)
\(48\) −4.62246 −0.667195
\(49\) −6.19040 −0.884343
\(50\) 3.07263 0.434536
\(51\) −1.09788 −0.153733
\(52\) −5.02086 −0.696268
\(53\) 2.69311 0.369927 0.184963 0.982745i \(-0.440783\pi\)
0.184963 + 0.982745i \(0.440783\pi\)
\(54\) −6.39276 −0.869944
\(55\) −9.46732 −1.27657
\(56\) 7.20214 0.962426
\(57\) 1.50980 0.199977
\(58\) 11.7615 1.54437
\(59\) −14.7234 −1.91682 −0.958409 0.285398i \(-0.907874\pi\)
−0.958409 + 0.285398i \(0.907874\pi\)
\(60\) 4.07276 0.525792
\(61\) 11.8266 1.51424 0.757122 0.653274i \(-0.226605\pi\)
0.757122 + 0.653274i \(0.226605\pi\)
\(62\) −13.8360 −1.75717
\(63\) 2.54517 0.320661
\(64\) 13.6515 1.70644
\(65\) 1.95969 0.243070
\(66\) 5.29857 0.652209
\(67\) 2.89289 0.353422 0.176711 0.984263i \(-0.443454\pi\)
0.176711 + 0.984263i \(0.443454\pi\)
\(68\) 13.3170 1.61493
\(69\) −2.43150 −0.292719
\(70\) −4.67216 −0.558430
\(71\) 4.80128 0.569807 0.284904 0.958556i \(-0.408038\pi\)
0.284904 + 0.958556i \(0.408038\pi\)
\(72\) 22.6416 2.66834
\(73\) 14.0811 1.64807 0.824037 0.566536i \(-0.191717\pi\)
0.824037 + 0.566536i \(0.191717\pi\)
\(74\) −8.72935 −1.01477
\(75\) 0.479998 0.0554254
\(76\) −18.3135 −2.10071
\(77\) −4.34686 −0.495370
\(78\) −1.09678 −0.124186
\(79\) 15.3643 1.72862 0.864310 0.502960i \(-0.167756\pi\)
0.864310 + 0.502960i \(0.167756\pi\)
\(80\) −21.8845 −2.44676
\(81\) 7.48734 0.831926
\(82\) 29.1229 3.21609
\(83\) −14.6641 −1.60959 −0.804797 0.593551i \(-0.797726\pi\)
−0.804797 + 0.593551i \(0.797726\pi\)
\(84\) 1.86998 0.204032
\(85\) −5.19776 −0.563777
\(86\) 10.3894 1.12032
\(87\) 1.83735 0.196985
\(88\) −38.6693 −4.12216
\(89\) 1.94412 0.206076 0.103038 0.994677i \(-0.467144\pi\)
0.103038 + 0.994677i \(0.467144\pi\)
\(90\) −14.6880 −1.54826
\(91\) 0.899778 0.0943224
\(92\) 29.4937 3.07493
\(93\) −2.16142 −0.224129
\(94\) 10.4252 1.07528
\(95\) 7.14795 0.733364
\(96\) 5.62166 0.573758
\(97\) 12.1069 1.22927 0.614636 0.788811i \(-0.289303\pi\)
0.614636 + 0.788811i \(0.289303\pi\)
\(98\) 16.4026 1.65692
\(99\) −13.6654 −1.37342
\(100\) −5.82229 −0.582229
\(101\) −1.89217 −0.188278 −0.0941389 0.995559i \(-0.530010\pi\)
−0.0941389 + 0.995559i \(0.530010\pi\)
\(102\) 2.90903 0.288037
\(103\) 3.41117 0.336113 0.168056 0.985777i \(-0.446251\pi\)
0.168056 + 0.985777i \(0.446251\pi\)
\(104\) 8.00435 0.784891
\(105\) −0.729871 −0.0712282
\(106\) −7.13590 −0.693100
\(107\) −5.91694 −0.572013 −0.286006 0.958228i \(-0.592328\pi\)
−0.286006 + 0.958228i \(0.592328\pi\)
\(108\) 12.1135 1.16563
\(109\) −7.22686 −0.692208 −0.346104 0.938196i \(-0.612496\pi\)
−0.346104 + 0.938196i \(0.612496\pi\)
\(110\) 25.0855 2.39181
\(111\) −1.36367 −0.129434
\(112\) −10.0481 −0.949458
\(113\) −12.0550 −1.13404 −0.567018 0.823705i \(-0.691903\pi\)
−0.567018 + 0.823705i \(0.691903\pi\)
\(114\) −4.00049 −0.374680
\(115\) −11.5117 −1.07347
\(116\) −22.2868 −2.06927
\(117\) 2.82866 0.261510
\(118\) 39.0124 3.59138
\(119\) −2.38652 −0.218772
\(120\) −6.49288 −0.592716
\(121\) 12.3389 1.12172
\(122\) −31.3369 −2.83711
\(123\) 4.54950 0.410214
\(124\) 26.2176 2.35441
\(125\) 12.0709 1.07966
\(126\) −6.74391 −0.600796
\(127\) 5.79873 0.514554 0.257277 0.966338i \(-0.417175\pi\)
0.257277 + 0.966338i \(0.417175\pi\)
\(128\) −9.00976 −0.796358
\(129\) 1.62300 0.142897
\(130\) −5.19257 −0.455419
\(131\) 16.7921 1.46714 0.733568 0.679616i \(-0.237853\pi\)
0.733568 + 0.679616i \(0.237853\pi\)
\(132\) −10.0402 −0.873887
\(133\) 3.28193 0.284580
\(134\) −7.66525 −0.662177
\(135\) −4.72803 −0.406924
\(136\) −21.2303 −1.82048
\(137\) 14.8934 1.27243 0.636214 0.771512i \(-0.280499\pi\)
0.636214 + 0.771512i \(0.280499\pi\)
\(138\) 6.44273 0.548442
\(139\) 21.3712 1.81268 0.906342 0.422545i \(-0.138863\pi\)
0.906342 + 0.422545i \(0.138863\pi\)
\(140\) 8.85321 0.748233
\(141\) 1.62860 0.137153
\(142\) −12.7219 −1.06760
\(143\) −4.83103 −0.403991
\(144\) −31.5886 −2.63239
\(145\) 8.69873 0.722390
\(146\) −37.3107 −3.08785
\(147\) 2.56237 0.211341
\(148\) 16.5411 1.35967
\(149\) −20.2929 −1.66246 −0.831231 0.555927i \(-0.812363\pi\)
−0.831231 + 0.555927i \(0.812363\pi\)
\(150\) −1.27185 −0.103846
\(151\) 1.51776 0.123513 0.0617566 0.998091i \(-0.480330\pi\)
0.0617566 + 0.998091i \(0.480330\pi\)
\(152\) 29.1958 2.36809
\(153\) −7.50258 −0.606548
\(154\) 11.5178 0.928133
\(155\) −10.2330 −0.821933
\(156\) 2.07827 0.166395
\(157\) −14.7567 −1.17771 −0.588855 0.808238i \(-0.700421\pi\)
−0.588855 + 0.808238i \(0.700421\pi\)
\(158\) −40.7107 −3.23877
\(159\) −1.11475 −0.0884054
\(160\) 26.6151 2.10411
\(161\) −5.28551 −0.416556
\(162\) −19.8391 −1.55871
\(163\) −16.6154 −1.30142 −0.650710 0.759327i \(-0.725528\pi\)
−0.650710 + 0.759327i \(0.725528\pi\)
\(164\) −55.1846 −4.30919
\(165\) 3.91878 0.305077
\(166\) 38.8553 3.01576
\(167\) −4.98367 −0.385648 −0.192824 0.981233i \(-0.561765\pi\)
−0.192824 + 0.981233i \(0.561765\pi\)
\(168\) −2.98116 −0.230001
\(169\) 1.00000 0.0769231
\(170\) 13.7725 1.05630
\(171\) 10.3175 0.789001
\(172\) −19.6867 −1.50110
\(173\) 21.2173 1.61312 0.806562 0.591150i \(-0.201326\pi\)
0.806562 + 0.591150i \(0.201326\pi\)
\(174\) −4.86842 −0.369074
\(175\) 1.04340 0.0788736
\(176\) 53.9497 4.06661
\(177\) 6.09440 0.458083
\(178\) −5.15132 −0.386108
\(179\) 4.40911 0.329553 0.164776 0.986331i \(-0.447310\pi\)
0.164776 + 0.986331i \(0.447310\pi\)
\(180\) 27.8322 2.07449
\(181\) 12.0691 0.897089 0.448545 0.893760i \(-0.351942\pi\)
0.448545 + 0.893760i \(0.351942\pi\)
\(182\) −2.38413 −0.176724
\(183\) −4.89536 −0.361875
\(184\) −47.0194 −3.46632
\(185\) −6.45615 −0.474666
\(186\) 5.72709 0.419931
\(187\) 12.8135 0.937019
\(188\) −19.7546 −1.44075
\(189\) −2.17084 −0.157906
\(190\) −18.9399 −1.37404
\(191\) −7.01101 −0.507299 −0.253650 0.967296i \(-0.581631\pi\)
−0.253650 + 0.967296i \(0.581631\pi\)
\(192\) −5.65073 −0.407807
\(193\) −2.96284 −0.213270 −0.106635 0.994298i \(-0.534008\pi\)
−0.106635 + 0.994298i \(0.534008\pi\)
\(194\) −32.0796 −2.30318
\(195\) −0.811168 −0.0580890
\(196\) −31.0811 −2.22008
\(197\) 0.242144 0.0172520 0.00862601 0.999963i \(-0.497254\pi\)
0.00862601 + 0.999963i \(0.497254\pi\)
\(198\) 36.2090 2.57326
\(199\) −21.8303 −1.54751 −0.773754 0.633487i \(-0.781623\pi\)
−0.773754 + 0.633487i \(0.781623\pi\)
\(200\) 9.28200 0.656336
\(201\) −1.19744 −0.0844611
\(202\) 5.01366 0.352760
\(203\) 3.99396 0.280321
\(204\) −5.51228 −0.385937
\(205\) 21.5391 1.50435
\(206\) −9.03856 −0.629746
\(207\) −16.6162 −1.15491
\(208\) −11.1673 −0.774315
\(209\) −17.6211 −1.21888
\(210\) 1.93393 0.133454
\(211\) 11.9531 0.822888 0.411444 0.911435i \(-0.365024\pi\)
0.411444 + 0.911435i \(0.365024\pi\)
\(212\) 13.5217 0.928676
\(213\) −1.98738 −0.136173
\(214\) 15.6781 1.07173
\(215\) 7.68392 0.524039
\(216\) −19.3116 −1.31399
\(217\) −4.69840 −0.318948
\(218\) 19.1490 1.29693
\(219\) −5.82857 −0.393858
\(220\) −47.5341 −3.20475
\(221\) −2.65234 −0.178416
\(222\) 3.61331 0.242510
\(223\) 4.58527 0.307052 0.153526 0.988145i \(-0.450937\pi\)
0.153526 + 0.988145i \(0.450937\pi\)
\(224\) 12.2201 0.816492
\(225\) 3.28017 0.218678
\(226\) 31.9420 2.12475
\(227\) −20.5188 −1.36188 −0.680941 0.732338i \(-0.738429\pi\)
−0.680941 + 0.732338i \(0.738429\pi\)
\(228\) 7.58047 0.502029
\(229\) −28.0049 −1.85061 −0.925307 0.379219i \(-0.876193\pi\)
−0.925307 + 0.379219i \(0.876193\pi\)
\(230\) 30.5024 2.01127
\(231\) 1.79928 0.118384
\(232\) 35.5300 2.33266
\(233\) −2.40928 −0.157837 −0.0789186 0.996881i \(-0.525147\pi\)
−0.0789186 + 0.996881i \(0.525147\pi\)
\(234\) −7.49509 −0.489969
\(235\) 7.71040 0.502971
\(236\) −73.9240 −4.81204
\(237\) −6.35970 −0.413107
\(238\) 6.32354 0.409894
\(239\) −18.7938 −1.21567 −0.607834 0.794064i \(-0.707961\pi\)
−0.607834 + 0.794064i \(0.707961\pi\)
\(240\) 9.05859 0.584729
\(241\) 22.7407 1.46486 0.732428 0.680844i \(-0.238387\pi\)
0.732428 + 0.680844i \(0.238387\pi\)
\(242\) −32.6942 −2.10166
\(243\) −10.3371 −0.663128
\(244\) 59.3798 3.80140
\(245\) 12.1313 0.775038
\(246\) −12.0548 −0.768583
\(247\) 3.64749 0.232084
\(248\) −41.7966 −2.65409
\(249\) 6.06986 0.384662
\(250\) −31.9843 −2.02286
\(251\) −17.9850 −1.13520 −0.567602 0.823303i \(-0.692129\pi\)
−0.567602 + 0.823303i \(0.692129\pi\)
\(252\) 12.7789 0.804998
\(253\) 28.3786 1.78415
\(254\) −15.3648 −0.964076
\(255\) 2.15150 0.134732
\(256\) −3.42997 −0.214373
\(257\) 9.96098 0.621349 0.310674 0.950516i \(-0.399445\pi\)
0.310674 + 0.950516i \(0.399445\pi\)
\(258\) −4.30046 −0.267735
\(259\) −2.96430 −0.184193
\(260\) 9.83933 0.610209
\(261\) 12.5560 0.777195
\(262\) −44.4940 −2.74885
\(263\) 4.29805 0.265029 0.132515 0.991181i \(-0.457695\pi\)
0.132515 + 0.991181i \(0.457695\pi\)
\(264\) 16.0063 0.985117
\(265\) −5.27765 −0.324204
\(266\) −8.69611 −0.533192
\(267\) −0.804724 −0.0492483
\(268\) 14.5248 0.887242
\(269\) −8.98038 −0.547544 −0.273772 0.961795i \(-0.588271\pi\)
−0.273772 + 0.961795i \(0.588271\pi\)
\(270\) 12.5278 0.762418
\(271\) −4.78584 −0.290719 −0.145359 0.989379i \(-0.546434\pi\)
−0.145359 + 0.989379i \(0.546434\pi\)
\(272\) 29.6196 1.79595
\(273\) −0.372442 −0.0225412
\(274\) −39.4629 −2.38404
\(275\) −5.60216 −0.337823
\(276\) −12.2082 −0.734850
\(277\) 18.4811 1.11042 0.555209 0.831711i \(-0.312638\pi\)
0.555209 + 0.831711i \(0.312638\pi\)
\(278\) −56.6272 −3.39627
\(279\) −14.7705 −0.884289
\(280\) −14.1140 −0.843470
\(281\) −11.4528 −0.683214 −0.341607 0.939843i \(-0.610971\pi\)
−0.341607 + 0.939843i \(0.610971\pi\)
\(282\) −4.31528 −0.256971
\(283\) −7.32082 −0.435177 −0.217589 0.976041i \(-0.569819\pi\)
−0.217589 + 0.976041i \(0.569819\pi\)
\(284\) 24.1066 1.43046
\(285\) −2.95873 −0.175260
\(286\) 12.8007 0.756924
\(287\) 9.88951 0.583759
\(288\) 38.4169 2.26374
\(289\) −9.96509 −0.586182
\(290\) −23.0490 −1.35348
\(291\) −5.01138 −0.293773
\(292\) 70.6995 4.13738
\(293\) 12.3922 0.723961 0.361981 0.932186i \(-0.382101\pi\)
0.361981 + 0.932186i \(0.382101\pi\)
\(294\) −6.78950 −0.395972
\(295\) 28.8532 1.67990
\(296\) −26.3702 −1.53273
\(297\) 11.6556 0.676324
\(298\) 53.7700 3.11481
\(299\) −5.87423 −0.339716
\(300\) 2.41000 0.139142
\(301\) 3.52802 0.203352
\(302\) −4.02158 −0.231416
\(303\) 0.783220 0.0449948
\(304\) −40.7327 −2.33618
\(305\) −23.1765 −1.32708
\(306\) 19.8795 1.13644
\(307\) 19.0913 1.08960 0.544799 0.838566i \(-0.316606\pi\)
0.544799 + 0.838566i \(0.316606\pi\)
\(308\) −21.8250 −1.24359
\(309\) −1.41198 −0.0803246
\(310\) 27.1142 1.53998
\(311\) −7.14971 −0.405423 −0.202712 0.979238i \(-0.564975\pi\)
−0.202712 + 0.979238i \(0.564975\pi\)
\(312\) −3.31322 −0.187574
\(313\) 28.6971 1.62206 0.811028 0.585007i \(-0.198908\pi\)
0.811028 + 0.585007i \(0.198908\pi\)
\(314\) 39.1006 2.20658
\(315\) −4.98774 −0.281027
\(316\) 77.1421 4.33958
\(317\) 2.50653 0.140781 0.0703903 0.997520i \(-0.477576\pi\)
0.0703903 + 0.997520i \(0.477576\pi\)
\(318\) 2.95374 0.165638
\(319\) −21.4441 −1.20064
\(320\) −26.7527 −1.49552
\(321\) 2.44918 0.136700
\(322\) 14.0050 0.780466
\(323\) −9.67439 −0.538298
\(324\) 37.5929 2.08849
\(325\) 1.15962 0.0643241
\(326\) 44.0257 2.43836
\(327\) 2.99139 0.165424
\(328\) 87.9763 4.85768
\(329\) 3.54018 0.195176
\(330\) −10.3836 −0.571596
\(331\) −28.4339 −1.56287 −0.781433 0.623989i \(-0.785511\pi\)
−0.781433 + 0.623989i \(0.785511\pi\)
\(332\) −73.6264 −4.04077
\(333\) −9.31897 −0.510677
\(334\) 13.2052 0.722556
\(335\) −5.66916 −0.309739
\(336\) 4.15919 0.226902
\(337\) 8.77352 0.477924 0.238962 0.971029i \(-0.423193\pi\)
0.238962 + 0.971029i \(0.423193\pi\)
\(338\) −2.64969 −0.144124
\(339\) 4.98988 0.271013
\(340\) −26.0973 −1.41532
\(341\) 25.2264 1.36608
\(342\) −27.3383 −1.47828
\(343\) 11.8684 0.640835
\(344\) 31.3850 1.69216
\(345\) 4.76499 0.256539
\(346\) −56.2194 −3.02237
\(347\) 30.3148 1.62738 0.813691 0.581297i \(-0.197455\pi\)
0.813691 + 0.581297i \(0.197455\pi\)
\(348\) 9.22510 0.494517
\(349\) 26.6175 1.42480 0.712402 0.701771i \(-0.247607\pi\)
0.712402 + 0.701771i \(0.247607\pi\)
\(350\) −2.76469 −0.147779
\(351\) −2.41264 −0.128777
\(352\) −65.6116 −3.49711
\(353\) 21.9385 1.16767 0.583835 0.811872i \(-0.301551\pi\)
0.583835 + 0.811872i \(0.301551\pi\)
\(354\) −16.1483 −0.858271
\(355\) −9.40902 −0.499379
\(356\) 9.76116 0.517341
\(357\) 0.987844 0.0522823
\(358\) −11.6828 −0.617455
\(359\) 31.3915 1.65678 0.828391 0.560150i \(-0.189256\pi\)
0.828391 + 0.560150i \(0.189256\pi\)
\(360\) −44.3705 −2.33853
\(361\) −5.69581 −0.299779
\(362\) −31.9794 −1.68080
\(363\) −5.10739 −0.268069
\(364\) 4.51766 0.236790
\(365\) −27.5947 −1.44437
\(366\) 12.9712 0.678015
\(367\) 24.8320 1.29622 0.648111 0.761546i \(-0.275559\pi\)
0.648111 + 0.761546i \(0.275559\pi\)
\(368\) 65.5995 3.41961
\(369\) 31.0900 1.61848
\(370\) 17.1068 0.889341
\(371\) −2.42320 −0.125806
\(372\) −10.8522 −0.562659
\(373\) 37.6810 1.95105 0.975524 0.219893i \(-0.0705708\pi\)
0.975524 + 0.219893i \(0.0705708\pi\)
\(374\) −33.9519 −1.75561
\(375\) −4.99649 −0.258018
\(376\) 31.4931 1.62413
\(377\) 4.43883 0.228612
\(378\) 5.75206 0.295854
\(379\) −31.6292 −1.62469 −0.812343 0.583181i \(-0.801808\pi\)
−0.812343 + 0.583181i \(0.801808\pi\)
\(380\) 35.8889 1.84106
\(381\) −2.40025 −0.122969
\(382\) 18.5770 0.950483
\(383\) −2.72712 −0.139350 −0.0696748 0.997570i \(-0.522196\pi\)
−0.0696748 + 0.997570i \(0.522196\pi\)
\(384\) 3.72938 0.190314
\(385\) 8.51849 0.434142
\(386\) 7.85062 0.399586
\(387\) 11.0912 0.563795
\(388\) 60.7872 3.08600
\(389\) −15.4717 −0.784446 −0.392223 0.919870i \(-0.628294\pi\)
−0.392223 + 0.919870i \(0.628294\pi\)
\(390\) 2.14935 0.108836
\(391\) 15.5805 0.787938
\(392\) 49.5501 2.50266
\(393\) −6.95072 −0.350618
\(394\) −0.641606 −0.0323236
\(395\) −30.1093 −1.51496
\(396\) −68.6119 −3.44788
\(397\) −8.31160 −0.417147 −0.208574 0.978007i \(-0.566882\pi\)
−0.208574 + 0.978007i \(0.566882\pi\)
\(398\) 57.8435 2.89943
\(399\) −1.35848 −0.0680091
\(400\) −12.9499 −0.647493
\(401\) 3.81218 0.190371 0.0951856 0.995460i \(-0.469656\pi\)
0.0951856 + 0.995460i \(0.469656\pi\)
\(402\) 3.17286 0.158248
\(403\) −5.22174 −0.260113
\(404\) −9.50032 −0.472659
\(405\) −14.6728 −0.729100
\(406\) −10.5828 −0.525214
\(407\) 15.9157 0.788914
\(408\) 8.78778 0.435060
\(409\) −22.0866 −1.09211 −0.546056 0.837748i \(-0.683872\pi\)
−0.546056 + 0.837748i \(0.683872\pi\)
\(410\) −57.0718 −2.81858
\(411\) −6.16478 −0.304086
\(412\) 17.1270 0.843788
\(413\) 13.2478 0.651879
\(414\) 44.0279 2.16385
\(415\) 28.7371 1.41065
\(416\) 13.5813 0.665877
\(417\) −8.84613 −0.433197
\(418\) 46.6906 2.28371
\(419\) 9.13359 0.446205 0.223102 0.974795i \(-0.428382\pi\)
0.223102 + 0.974795i \(0.428382\pi\)
\(420\) −3.66458 −0.178813
\(421\) −21.9095 −1.06780 −0.533901 0.845547i \(-0.679274\pi\)
−0.533901 + 0.845547i \(0.679274\pi\)
\(422\) −31.6721 −1.54178
\(423\) 11.1294 0.541129
\(424\) −21.5566 −1.04688
\(425\) −3.07571 −0.149194
\(426\) 5.26594 0.255136
\(427\) −10.6413 −0.514970
\(428\) −29.7082 −1.43600
\(429\) 1.99969 0.0965462
\(430\) −20.3600 −0.981847
\(431\) −18.9657 −0.913547 −0.456773 0.889583i \(-0.650995\pi\)
−0.456773 + 0.889583i \(0.650995\pi\)
\(432\) 26.9428 1.29628
\(433\) −25.0396 −1.20333 −0.601664 0.798749i \(-0.705496\pi\)
−0.601664 + 0.798749i \(0.705496\pi\)
\(434\) 12.4493 0.597586
\(435\) −3.60064 −0.172637
\(436\) −36.2851 −1.73774
\(437\) −21.4262 −1.02495
\(438\) 15.4439 0.737938
\(439\) −26.7623 −1.27730 −0.638648 0.769499i \(-0.720506\pi\)
−0.638648 + 0.769499i \(0.720506\pi\)
\(440\) 75.7798 3.61266
\(441\) 17.5106 0.833836
\(442\) 7.02788 0.334282
\(443\) −25.9016 −1.23062 −0.615312 0.788283i \(-0.710970\pi\)
−0.615312 + 0.788283i \(0.710970\pi\)
\(444\) −6.84682 −0.324936
\(445\) −3.80987 −0.180605
\(446\) −12.1495 −0.575298
\(447\) 8.39979 0.397297
\(448\) −12.2833 −0.580333
\(449\) 13.1287 0.619582 0.309791 0.950805i \(-0.399741\pi\)
0.309791 + 0.950805i \(0.399741\pi\)
\(450\) −8.69145 −0.409719
\(451\) −53.0982 −2.50029
\(452\) −60.5264 −2.84692
\(453\) −0.628240 −0.0295173
\(454\) 54.3686 2.55164
\(455\) −1.76329 −0.0826641
\(456\) −12.0849 −0.565929
\(457\) −23.8514 −1.11572 −0.557860 0.829935i \(-0.688377\pi\)
−0.557860 + 0.829935i \(0.688377\pi\)
\(458\) 74.2042 3.46734
\(459\) 6.39915 0.298687
\(460\) −57.7985 −2.69487
\(461\) −31.8061 −1.48136 −0.740680 0.671858i \(-0.765496\pi\)
−0.740680 + 0.671858i \(0.765496\pi\)
\(462\) −4.76754 −0.221806
\(463\) −1.00000 −0.0464739
\(464\) −49.5699 −2.30123
\(465\) 4.23571 0.196426
\(466\) 6.38384 0.295726
\(467\) −28.0531 −1.29814 −0.649071 0.760728i \(-0.724842\pi\)
−0.649071 + 0.760728i \(0.724842\pi\)
\(468\) 14.2023 0.656503
\(469\) −2.60295 −0.120193
\(470\) −20.4302 −0.942374
\(471\) 6.10819 0.281450
\(472\) 117.851 5.42453
\(473\) −18.9424 −0.870973
\(474\) 16.8512 0.774003
\(475\) 4.22970 0.194072
\(476\) −11.9824 −0.549211
\(477\) −7.61790 −0.348800
\(478\) 49.7977 2.27769
\(479\) −38.2009 −1.74544 −0.872722 0.488217i \(-0.837647\pi\)
−0.872722 + 0.488217i \(0.837647\pi\)
\(480\) −11.0167 −0.502841
\(481\) −3.29448 −0.150215
\(482\) −60.2558 −2.74458
\(483\) 2.18781 0.0995490
\(484\) 61.9518 2.81599
\(485\) −23.7258 −1.07733
\(486\) 27.3902 1.24245
\(487\) −17.0616 −0.773134 −0.386567 0.922261i \(-0.626339\pi\)
−0.386567 + 0.922261i \(0.626339\pi\)
\(488\) −94.6644 −4.28526
\(489\) 6.87757 0.311014
\(490\) −32.1441 −1.45212
\(491\) −18.6717 −0.842641 −0.421321 0.906912i \(-0.638433\pi\)
−0.421321 + 0.906912i \(0.638433\pi\)
\(492\) 22.8424 1.02981
\(493\) −11.7733 −0.530243
\(494\) −9.66472 −0.434836
\(495\) 26.7799 1.20367
\(496\) 58.3129 2.61832
\(497\) −4.32009 −0.193782
\(498\) −16.0833 −0.720708
\(499\) −42.9725 −1.92371 −0.961857 0.273554i \(-0.911801\pi\)
−0.961857 + 0.273554i \(0.911801\pi\)
\(500\) 60.6065 2.71041
\(501\) 2.06288 0.0921626
\(502\) 47.6548 2.12694
\(503\) −28.0379 −1.25015 −0.625073 0.780566i \(-0.714931\pi\)
−0.625073 + 0.780566i \(0.714931\pi\)
\(504\) −20.3724 −0.907460
\(505\) 3.70806 0.165007
\(506\) −75.1946 −3.34281
\(507\) −0.413927 −0.0183831
\(508\) 29.1146 1.29175
\(509\) 7.33703 0.325208 0.162604 0.986691i \(-0.448011\pi\)
0.162604 + 0.986691i \(0.448011\pi\)
\(510\) −5.70080 −0.252436
\(511\) −12.6699 −0.560484
\(512\) 27.1079 1.19801
\(513\) −8.80009 −0.388533
\(514\) −26.3935 −1.16417
\(515\) −6.68484 −0.294569
\(516\) 8.14887 0.358734
\(517\) −19.0077 −0.835958
\(518\) 7.85448 0.345106
\(519\) −8.78242 −0.385506
\(520\) −15.6860 −0.687878
\(521\) −8.67880 −0.380225 −0.190113 0.981762i \(-0.560885\pi\)
−0.190113 + 0.981762i \(0.560885\pi\)
\(522\) −33.2694 −1.45616
\(523\) 28.4641 1.24465 0.622323 0.782760i \(-0.286189\pi\)
0.622323 + 0.782760i \(0.286189\pi\)
\(524\) 84.3110 3.68314
\(525\) −0.431891 −0.0188493
\(526\) −11.3885 −0.496562
\(527\) 13.8498 0.603308
\(528\) −22.3313 −0.971843
\(529\) 11.5066 0.500288
\(530\) 13.9842 0.607433
\(531\) 41.6474 1.80735
\(532\) 16.4781 0.714417
\(533\) 10.9911 0.476076
\(534\) 2.13227 0.0922724
\(535\) 11.5954 0.501312
\(536\) −23.1557 −1.00017
\(537\) −1.82505 −0.0787568
\(538\) 23.7952 1.02589
\(539\) −29.9060 −1.28814
\(540\) −23.7388 −1.02155
\(541\) 8.04305 0.345798 0.172899 0.984940i \(-0.444687\pi\)
0.172899 + 0.984940i \(0.444687\pi\)
\(542\) 12.6810 0.544695
\(543\) −4.99573 −0.214387
\(544\) −36.0222 −1.54444
\(545\) 14.1624 0.606651
\(546\) 0.986857 0.0422336
\(547\) −5.87315 −0.251118 −0.125559 0.992086i \(-0.540072\pi\)
−0.125559 + 0.992086i \(0.540072\pi\)
\(548\) 74.7777 3.19434
\(549\) −33.4535 −1.42776
\(550\) 14.8440 0.632950
\(551\) 16.1906 0.689743
\(552\) 19.4626 0.828384
\(553\) −13.8245 −0.587876
\(554\) −48.9691 −2.08050
\(555\) 2.67238 0.113436
\(556\) 107.302 4.55062
\(557\) −3.33356 −0.141248 −0.0706238 0.997503i \(-0.522499\pi\)
−0.0706238 + 0.997503i \(0.522499\pi\)
\(558\) 39.1374 1.65682
\(559\) 3.92099 0.165840
\(560\) 19.6912 0.832105
\(561\) −5.30387 −0.223930
\(562\) 30.3463 1.28008
\(563\) 25.1499 1.05994 0.529971 0.848016i \(-0.322203\pi\)
0.529971 + 0.848016i \(0.322203\pi\)
\(564\) 8.17696 0.344312
\(565\) 23.6240 0.993869
\(566\) 19.3979 0.815355
\(567\) −6.73694 −0.282925
\(568\) −38.4311 −1.61253
\(569\) −26.7075 −1.11964 −0.559819 0.828615i \(-0.689129\pi\)
−0.559819 + 0.828615i \(0.689129\pi\)
\(570\) 7.83972 0.328370
\(571\) −38.5799 −1.61452 −0.807259 0.590198i \(-0.799050\pi\)
−0.807259 + 0.590198i \(0.799050\pi\)
\(572\) −24.2559 −1.01419
\(573\) 2.90205 0.121235
\(574\) −26.2042 −1.09374
\(575\) −6.81187 −0.284075
\(576\) −38.6156 −1.60898
\(577\) 35.1345 1.46267 0.731334 0.682019i \(-0.238898\pi\)
0.731334 + 0.682019i \(0.238898\pi\)
\(578\) 26.4044 1.09828
\(579\) 1.22640 0.0509675
\(580\) 43.6751 1.81351
\(581\) 13.1944 0.547397
\(582\) 13.2786 0.550417
\(583\) 13.0105 0.538839
\(584\) −112.710 −4.66399
\(585\) −5.54330 −0.229187
\(586\) −32.8356 −1.35642
\(587\) 6.89899 0.284752 0.142376 0.989813i \(-0.454526\pi\)
0.142376 + 0.989813i \(0.454526\pi\)
\(588\) 12.8653 0.530557
\(589\) −19.0462 −0.784786
\(590\) −76.4521 −3.14748
\(591\) −0.100230 −0.00412290
\(592\) 36.7905 1.51208
\(593\) −20.5518 −0.843963 −0.421981 0.906605i \(-0.638665\pi\)
−0.421981 + 0.906605i \(0.638665\pi\)
\(594\) −30.8836 −1.26717
\(595\) 4.67683 0.191731
\(596\) −101.888 −4.17350
\(597\) 9.03614 0.369825
\(598\) 15.5649 0.636496
\(599\) 27.9786 1.14318 0.571588 0.820541i \(-0.306328\pi\)
0.571588 + 0.820541i \(0.306328\pi\)
\(600\) −3.84207 −0.156852
\(601\) −26.9961 −1.10120 −0.550598 0.834771i \(-0.685600\pi\)
−0.550598 + 0.834771i \(0.685600\pi\)
\(602\) −9.34816 −0.381003
\(603\) −8.18300 −0.333238
\(604\) 7.62044 0.310071
\(605\) −24.1803 −0.983071
\(606\) −2.07529 −0.0843029
\(607\) 13.0038 0.527810 0.263905 0.964549i \(-0.414989\pi\)
0.263905 + 0.964549i \(0.414989\pi\)
\(608\) 49.5376 2.00901
\(609\) −1.65321 −0.0669914
\(610\) 61.4106 2.48644
\(611\) 3.93450 0.159173
\(612\) −37.6694 −1.52270
\(613\) −19.9874 −0.807282 −0.403641 0.914917i \(-0.632256\pi\)
−0.403641 + 0.914917i \(0.632256\pi\)
\(614\) −50.5861 −2.04149
\(615\) −8.91560 −0.359512
\(616\) 34.7938 1.40188
\(617\) −46.3160 −1.86461 −0.932306 0.361670i \(-0.882207\pi\)
−0.932306 + 0.361670i \(0.882207\pi\)
\(618\) 3.74130 0.150497
\(619\) 20.0857 0.807311 0.403655 0.914911i \(-0.367739\pi\)
0.403655 + 0.914911i \(0.367739\pi\)
\(620\) −51.3784 −2.06341
\(621\) 14.1724 0.568720
\(622\) 18.9445 0.759607
\(623\) −1.74928 −0.0700833
\(624\) 4.62246 0.185047
\(625\) −17.8572 −0.714288
\(626\) −76.0385 −3.03911
\(627\) 7.29387 0.291289
\(628\) −74.0912 −2.95656
\(629\) 8.73808 0.348410
\(630\) 13.2160 0.526537
\(631\) −34.0299 −1.35471 −0.677355 0.735656i \(-0.736874\pi\)
−0.677355 + 0.735656i \(0.736874\pi\)
\(632\) −122.981 −4.89193
\(633\) −4.94773 −0.196655
\(634\) −6.64152 −0.263769
\(635\) −11.3637 −0.450955
\(636\) −5.59701 −0.221936
\(637\) 6.19040 0.245273
\(638\) 56.8204 2.24954
\(639\) −13.5812 −0.537264
\(640\) 17.6563 0.697927
\(641\) −14.0803 −0.556139 −0.278069 0.960561i \(-0.589694\pi\)
−0.278069 + 0.960561i \(0.589694\pi\)
\(642\) −6.48958 −0.256123
\(643\) −23.3635 −0.921367 −0.460683 0.887565i \(-0.652396\pi\)
−0.460683 + 0.887565i \(0.652396\pi\)
\(644\) −26.5378 −1.04574
\(645\) −3.18058 −0.125235
\(646\) 25.6341 1.00856
\(647\) 43.0423 1.69217 0.846083 0.533051i \(-0.178955\pi\)
0.846083 + 0.533051i \(0.178955\pi\)
\(648\) −59.9313 −2.35432
\(649\) −71.1290 −2.79206
\(650\) −3.07263 −0.120519
\(651\) 1.94480 0.0762226
\(652\) −83.4237 −3.26712
\(653\) 11.9834 0.468949 0.234474 0.972122i \(-0.424663\pi\)
0.234474 + 0.972122i \(0.424663\pi\)
\(654\) −7.92627 −0.309942
\(655\) −32.9074 −1.28580
\(656\) −122.741 −4.79222
\(657\) −39.8308 −1.55395
\(658\) −9.38038 −0.365685
\(659\) −18.3732 −0.715720 −0.357860 0.933775i \(-0.616493\pi\)
−0.357860 + 0.933775i \(0.616493\pi\)
\(660\) 19.6757 0.765874
\(661\) 44.6304 1.73592 0.867961 0.496632i \(-0.165430\pi\)
0.867961 + 0.496632i \(0.165430\pi\)
\(662\) 75.3410 2.92821
\(663\) 1.09788 0.0426380
\(664\) 117.377 4.55509
\(665\) −6.43157 −0.249405
\(666\) 24.6924 0.956811
\(667\) −26.0747 −1.00962
\(668\) −25.0223 −0.968144
\(669\) −1.89797 −0.0733797
\(670\) 15.0215 0.580332
\(671\) 57.1348 2.20566
\(672\) −5.05824 −0.195126
\(673\) −28.8970 −1.11390 −0.556950 0.830546i \(-0.688028\pi\)
−0.556950 + 0.830546i \(0.688028\pi\)
\(674\) −23.2471 −0.895445
\(675\) −2.79775 −0.107685
\(676\) 5.02086 0.193110
\(677\) −49.1585 −1.88931 −0.944657 0.328061i \(-0.893605\pi\)
−0.944657 + 0.328061i \(0.893605\pi\)
\(678\) −13.2216 −0.507774
\(679\) −10.8935 −0.418056
\(680\) 41.6047 1.59547
\(681\) 8.49330 0.325464
\(682\) −66.8421 −2.55952
\(683\) 40.8138 1.56170 0.780848 0.624720i \(-0.214787\pi\)
0.780848 + 0.624720i \(0.214787\pi\)
\(684\) 51.8029 1.98073
\(685\) −29.1864 −1.11516
\(686\) −31.4477 −1.20068
\(687\) 11.5920 0.442261
\(688\) −43.7870 −1.66936
\(689\) −2.69311 −0.102599
\(690\) −12.6258 −0.480654
\(691\) 7.27353 0.276698 0.138349 0.990384i \(-0.455820\pi\)
0.138349 + 0.990384i \(0.455820\pi\)
\(692\) 106.529 4.04963
\(693\) 12.2958 0.467079
\(694\) −80.3248 −3.04909
\(695\) −41.8810 −1.58864
\(696\) −14.7068 −0.557460
\(697\) −29.1520 −1.10421
\(698\) −70.5283 −2.66953
\(699\) 0.997266 0.0377201
\(700\) 5.23877 0.198007
\(701\) 48.1641 1.81913 0.909567 0.415557i \(-0.136413\pi\)
0.909567 + 0.415557i \(0.136413\pi\)
\(702\) 6.39276 0.241279
\(703\) −12.0166 −0.453214
\(704\) 65.9509 2.48562
\(705\) −3.19154 −0.120200
\(706\) −58.1303 −2.18776
\(707\) 1.70253 0.0640303
\(708\) 30.5991 1.14999
\(709\) −36.6537 −1.37656 −0.688280 0.725445i \(-0.741634\pi\)
−0.688280 + 0.725445i \(0.741634\pi\)
\(710\) 24.9310 0.935643
\(711\) −43.4605 −1.62990
\(712\) −15.5614 −0.583189
\(713\) 30.6737 1.14874
\(714\) −2.61748 −0.0979568
\(715\) 9.46732 0.354058
\(716\) 22.1376 0.827319
\(717\) 7.77925 0.290521
\(718\) −83.1779 −3.10417
\(719\) −50.4954 −1.88316 −0.941580 0.336790i \(-0.890659\pi\)
−0.941580 + 0.336790i \(0.890659\pi\)
\(720\) 61.9039 2.30702
\(721\) −3.06930 −0.114307
\(722\) 15.0921 0.561671
\(723\) −9.41299 −0.350073
\(724\) 60.5973 2.25208
\(725\) 5.14736 0.191168
\(726\) 13.5330 0.502257
\(727\) −2.96134 −0.109830 −0.0549150 0.998491i \(-0.517489\pi\)
−0.0549150 + 0.998491i \(0.517489\pi\)
\(728\) −7.20214 −0.266929
\(729\) −18.1832 −0.673451
\(730\) 73.1174 2.70619
\(731\) −10.3998 −0.384650
\(732\) −24.5789 −0.908463
\(733\) −23.6914 −0.875063 −0.437531 0.899203i \(-0.644147\pi\)
−0.437531 + 0.899203i \(0.644147\pi\)
\(734\) −65.7972 −2.42862
\(735\) −5.02146 −0.185219
\(736\) −79.7796 −2.94071
\(737\) 13.9756 0.514799
\(738\) −82.3789 −3.03241
\(739\) −6.25918 −0.230248 −0.115124 0.993351i \(-0.536727\pi\)
−0.115124 + 0.993351i \(0.536727\pi\)
\(740\) −32.4155 −1.19162
\(741\) −1.50980 −0.0554637
\(742\) 6.42073 0.235712
\(743\) 6.71458 0.246334 0.123167 0.992386i \(-0.460695\pi\)
0.123167 + 0.992386i \(0.460695\pi\)
\(744\) 17.3007 0.634276
\(745\) 39.7678 1.45698
\(746\) −99.8430 −3.65551
\(747\) 41.4798 1.51767
\(748\) 64.3350 2.35232
\(749\) 5.32394 0.194532
\(750\) 13.2391 0.483425
\(751\) −24.6319 −0.898829 −0.449415 0.893323i \(-0.648367\pi\)
−0.449415 + 0.893323i \(0.648367\pi\)
\(752\) −43.9379 −1.60225
\(753\) 7.44449 0.271292
\(754\) −11.7615 −0.428330
\(755\) −2.97433 −0.108247
\(756\) −10.8995 −0.396411
\(757\) −1.56738 −0.0569674 −0.0284837 0.999594i \(-0.509068\pi\)
−0.0284837 + 0.999594i \(0.509068\pi\)
\(758\) 83.8077 3.04403
\(759\) −11.7467 −0.426377
\(760\) −57.2147 −2.07539
\(761\) 10.6864 0.387383 0.193692 0.981062i \(-0.437954\pi\)
0.193692 + 0.981062i \(0.437954\pi\)
\(762\) 6.35993 0.230396
\(763\) 6.50257 0.235409
\(764\) −35.2013 −1.27354
\(765\) 14.7027 0.531578
\(766\) 7.22604 0.261087
\(767\) 14.7234 0.531630
\(768\) 1.41976 0.0512310
\(769\) 42.5838 1.53561 0.767805 0.640684i \(-0.221349\pi\)
0.767805 + 0.640684i \(0.221349\pi\)
\(770\) −22.5714 −0.813415
\(771\) −4.12312 −0.148491
\(772\) −14.8760 −0.535400
\(773\) −23.3805 −0.840938 −0.420469 0.907307i \(-0.638134\pi\)
−0.420469 + 0.907307i \(0.638134\pi\)
\(774\) −29.3881 −1.05634
\(775\) −6.05522 −0.217510
\(776\) −96.9081 −3.47880
\(777\) 1.22700 0.0440185
\(778\) 40.9952 1.46975
\(779\) 40.0898 1.43637
\(780\) −4.07276 −0.145828
\(781\) 23.1951 0.829987
\(782\) −41.2834 −1.47629
\(783\) −10.7093 −0.382720
\(784\) −69.1302 −2.46894
\(785\) 28.9185 1.03214
\(786\) 18.4173 0.656922
\(787\) −13.6241 −0.485647 −0.242824 0.970070i \(-0.578074\pi\)
−0.242824 + 0.970070i \(0.578074\pi\)
\(788\) 1.21577 0.0433100
\(789\) −1.77908 −0.0633369
\(790\) 79.7802 2.83845
\(791\) 10.8468 0.385668
\(792\) 109.382 3.88673
\(793\) −11.8266 −0.419976
\(794\) 22.0232 0.781573
\(795\) 2.18456 0.0774785
\(796\) −109.607 −3.88491
\(797\) −22.5701 −0.799473 −0.399736 0.916630i \(-0.630898\pi\)
−0.399736 + 0.916630i \(0.630898\pi\)
\(798\) 3.59955 0.127423
\(799\) −10.4356 −0.369187
\(800\) 15.7491 0.556815
\(801\) −5.49926 −0.194307
\(802\) −10.1011 −0.356682
\(803\) 68.0265 2.40060
\(804\) −6.01220 −0.212034
\(805\) 10.3579 0.365070
\(806\) 13.8360 0.487352
\(807\) 3.71722 0.130852
\(808\) 15.1456 0.532820
\(809\) −1.17991 −0.0414833 −0.0207416 0.999785i \(-0.506603\pi\)
−0.0207416 + 0.999785i \(0.506603\pi\)
\(810\) 38.8785 1.36605
\(811\) −6.85550 −0.240729 −0.120365 0.992730i \(-0.538406\pi\)
−0.120365 + 0.992730i \(0.538406\pi\)
\(812\) 20.0531 0.703727
\(813\) 1.98099 0.0694763
\(814\) −42.1718 −1.47812
\(815\) 32.5610 1.14056
\(816\) −12.2603 −0.429198
\(817\) 14.3018 0.500356
\(818\) 58.5227 2.04620
\(819\) −2.54517 −0.0889354
\(820\) 108.145 3.77657
\(821\) −40.1981 −1.40292 −0.701462 0.712707i \(-0.747469\pi\)
−0.701462 + 0.712707i \(0.747469\pi\)
\(822\) 16.3348 0.569740
\(823\) 14.0483 0.489694 0.244847 0.969562i \(-0.421262\pi\)
0.244847 + 0.969562i \(0.421262\pi\)
\(824\) −27.3042 −0.951188
\(825\) 2.31888 0.0807332
\(826\) −35.1025 −1.22137
\(827\) −17.4584 −0.607089 −0.303544 0.952817i \(-0.598170\pi\)
−0.303544 + 0.952817i \(0.598170\pi\)
\(828\) −83.4278 −2.89932
\(829\) 7.07316 0.245661 0.122831 0.992428i \(-0.460803\pi\)
0.122831 + 0.992428i \(0.460803\pi\)
\(830\) −76.1443 −2.64301
\(831\) −7.64981 −0.265369
\(832\) −13.6515 −0.473281
\(833\) −16.4191 −0.568886
\(834\) 23.4395 0.811644
\(835\) 9.76645 0.337982
\(836\) −88.4733 −3.05991
\(837\) 12.5982 0.435457
\(838\) −24.2012 −0.836016
\(839\) 25.1413 0.867975 0.433987 0.900919i \(-0.357106\pi\)
0.433987 + 0.900919i \(0.357106\pi\)
\(840\) 5.84215 0.201573
\(841\) −9.29676 −0.320578
\(842\) 58.0533 2.00065
\(843\) 4.74061 0.163275
\(844\) 60.0151 2.06580
\(845\) −1.95969 −0.0674154
\(846\) −29.4894 −1.01387
\(847\) −11.1022 −0.381478
\(848\) 30.0748 1.03277
\(849\) 3.03028 0.103999
\(850\) 8.14967 0.279531
\(851\) 19.3525 0.663396
\(852\) −9.97836 −0.341853
\(853\) −17.2532 −0.590738 −0.295369 0.955383i \(-0.595443\pi\)
−0.295369 + 0.955383i \(0.595443\pi\)
\(854\) 28.1962 0.964856
\(855\) −20.2191 −0.691480
\(856\) 47.3613 1.61878
\(857\) 11.1396 0.380521 0.190260 0.981734i \(-0.439067\pi\)
0.190260 + 0.981734i \(0.439067\pi\)
\(858\) −5.29857 −0.180890
\(859\) 21.3998 0.730151 0.365076 0.930978i \(-0.381043\pi\)
0.365076 + 0.930978i \(0.381043\pi\)
\(860\) 38.5799 1.31556
\(861\) −4.09354 −0.139507
\(862\) 50.2533 1.71163
\(863\) 7.13563 0.242900 0.121450 0.992598i \(-0.461246\pi\)
0.121450 + 0.992598i \(0.461246\pi\)
\(864\) −32.7668 −1.11475
\(865\) −41.5794 −1.41374
\(866\) 66.3473 2.25457
\(867\) 4.12482 0.140086
\(868\) −23.5900 −0.800698
\(869\) 74.2255 2.51793
\(870\) 9.54058 0.323456
\(871\) −2.89289 −0.0980217
\(872\) 57.8463 1.95892
\(873\) −34.2464 −1.15907
\(874\) 56.7729 1.92037
\(875\) −10.8612 −0.367174
\(876\) −29.2644 −0.988754
\(877\) 1.03423 0.0349233 0.0174617 0.999848i \(-0.494441\pi\)
0.0174617 + 0.999848i \(0.494441\pi\)
\(878\) 70.9119 2.39316
\(879\) −5.12948 −0.173013
\(880\) −105.725 −3.56398
\(881\) −32.5509 −1.09667 −0.548334 0.836260i \(-0.684738\pi\)
−0.548334 + 0.836260i \(0.684738\pi\)
\(882\) −46.3976 −1.56229
\(883\) −17.5679 −0.591208 −0.295604 0.955311i \(-0.595521\pi\)
−0.295604 + 0.955311i \(0.595521\pi\)
\(884\) −13.3170 −0.447901
\(885\) −11.9431 −0.401464
\(886\) 68.6314 2.30572
\(887\) 3.01691 0.101298 0.0506490 0.998717i \(-0.483871\pi\)
0.0506490 + 0.998717i \(0.483871\pi\)
\(888\) 10.9153 0.366294
\(889\) −5.21757 −0.174992
\(890\) 10.0950 0.338385
\(891\) 36.1716 1.21179
\(892\) 23.0220 0.770834
\(893\) 14.3511 0.480240
\(894\) −22.2569 −0.744381
\(895\) −8.64049 −0.288820
\(896\) 8.10678 0.270829
\(897\) 2.43150 0.0811856
\(898\) −34.7870 −1.16086
\(899\) −23.1784 −0.773043
\(900\) 16.4693 0.548977
\(901\) 7.14304 0.237969
\(902\) 140.694 4.68459
\(903\) −1.46034 −0.0485972
\(904\) 96.4922 3.20928
\(905\) −23.6517 −0.786209
\(906\) 1.66464 0.0553040
\(907\) −27.7579 −0.921687 −0.460843 0.887481i \(-0.652453\pi\)
−0.460843 + 0.887481i \(0.652453\pi\)
\(908\) −103.022 −3.41891
\(909\) 5.35231 0.177525
\(910\) 4.67216 0.154881
\(911\) 8.57527 0.284111 0.142056 0.989859i \(-0.454629\pi\)
0.142056 + 0.989859i \(0.454629\pi\)
\(912\) 16.8604 0.558303
\(913\) −70.8427 −2.34455
\(914\) 63.1987 2.09043
\(915\) 9.59338 0.317147
\(916\) −140.609 −4.64584
\(917\) −15.1092 −0.498950
\(918\) −16.9558 −0.559624
\(919\) 20.0421 0.661129 0.330564 0.943783i \(-0.392761\pi\)
0.330564 + 0.943783i \(0.392761\pi\)
\(920\) 92.1435 3.03788
\(921\) −7.90241 −0.260393
\(922\) 84.2764 2.77550
\(923\) −4.80128 −0.158036
\(924\) 9.03394 0.297195
\(925\) −3.82034 −0.125612
\(926\) 2.64969 0.0870742
\(927\) −9.64907 −0.316917
\(928\) 60.2850 1.97895
\(929\) 2.18252 0.0716062 0.0358031 0.999359i \(-0.488601\pi\)
0.0358031 + 0.999359i \(0.488601\pi\)
\(930\) −11.2233 −0.368027
\(931\) 22.5794 0.740011
\(932\) −12.0967 −0.396239
\(933\) 2.95946 0.0968884
\(934\) 74.3320 2.43222
\(935\) −25.1106 −0.821203
\(936\) −22.6416 −0.740065
\(937\) −58.2317 −1.90235 −0.951173 0.308659i \(-0.900120\pi\)
−0.951173 + 0.308659i \(0.900120\pi\)
\(938\) 6.89702 0.225196
\(939\) −11.8785 −0.387641
\(940\) 38.7129 1.26267
\(941\) −23.4047 −0.762971 −0.381485 0.924375i \(-0.624587\pi\)
−0.381485 + 0.924375i \(0.624587\pi\)
\(942\) −16.1848 −0.527329
\(943\) −64.5641 −2.10249
\(944\) −164.421 −5.35144
\(945\) 4.25418 0.138388
\(946\) 50.1916 1.63187
\(947\) −47.9018 −1.55660 −0.778300 0.627892i \(-0.783918\pi\)
−0.778300 + 0.627892i \(0.783918\pi\)
\(948\) −31.9312 −1.03708
\(949\) −14.0811 −0.457093
\(950\) −11.2074 −0.363616
\(951\) −1.03752 −0.0336439
\(952\) 19.1025 0.619117
\(953\) −48.9451 −1.58549 −0.792744 0.609555i \(-0.791348\pi\)
−0.792744 + 0.609555i \(0.791348\pi\)
\(954\) 20.1851 0.653516
\(955\) 13.7394 0.444597
\(956\) −94.3609 −3.05185
\(957\) 8.87631 0.286930
\(958\) 101.221 3.27029
\(959\) −13.4007 −0.432733
\(960\) 11.0737 0.357401
\(961\) −3.73347 −0.120435
\(962\) 8.72935 0.281446
\(963\) 16.7370 0.539344
\(964\) 114.178 3.67742
\(965\) 5.80625 0.186910
\(966\) −5.79703 −0.186516
\(967\) 4.96610 0.159699 0.0798494 0.996807i \(-0.474556\pi\)
0.0798494 + 0.996807i \(0.474556\pi\)
\(968\) −98.7647 −3.17442
\(969\) 4.00449 0.128643
\(970\) 62.8661 2.01851
\(971\) 40.4627 1.29851 0.649254 0.760571i \(-0.275081\pi\)
0.649254 + 0.760571i \(0.275081\pi\)
\(972\) −51.9013 −1.66474
\(973\) −19.2294 −0.616465
\(974\) 45.2079 1.44856
\(975\) −0.479998 −0.0153722
\(976\) 132.072 4.22752
\(977\) 9.12482 0.291929 0.145964 0.989290i \(-0.453371\pi\)
0.145964 + 0.989290i \(0.453371\pi\)
\(978\) −18.2234 −0.582721
\(979\) 9.39211 0.300173
\(980\) 60.9094 1.94568
\(981\) 20.4424 0.652675
\(982\) 49.4742 1.57879
\(983\) 26.3868 0.841609 0.420804 0.907151i \(-0.361748\pi\)
0.420804 + 0.907151i \(0.361748\pi\)
\(984\) −36.4158 −1.16089
\(985\) −0.474526 −0.0151197
\(986\) 31.1956 0.993470
\(987\) −1.46538 −0.0466434
\(988\) 18.3135 0.582632
\(989\) −23.0328 −0.732400
\(990\) −70.9584 −2.25521
\(991\) −44.7317 −1.42095 −0.710475 0.703723i \(-0.751520\pi\)
−0.710475 + 0.703723i \(0.751520\pi\)
\(992\) −70.9178 −2.25164
\(993\) 11.7695 0.373495
\(994\) 11.4469 0.363073
\(995\) 42.7806 1.35623
\(996\) 30.4760 0.965668
\(997\) 14.5865 0.461960 0.230980 0.972958i \(-0.425807\pi\)
0.230980 + 0.972958i \(0.425807\pi\)
\(998\) 113.864 3.60430
\(999\) 7.94840 0.251476
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 \(a_p\))