Properties

Label 4026.2.a.bc.1.9
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-3.36977\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+4.36977 q^{5}\) \(+1.00000 q^{6}\) \(+4.52139 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+4.36977 q^{5}\) \(+1.00000 q^{6}\) \(+4.52139 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+4.36977 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(-6.17357 q^{13}\) \(+4.52139 q^{14}\) \(+4.36977 q^{15}\) \(+1.00000 q^{16}\) \(+4.36848 q^{17}\) \(+1.00000 q^{18}\) \(-5.40291 q^{19}\) \(+4.36977 q^{20}\) \(+4.52139 q^{21}\) \(+1.00000 q^{22}\) \(-7.65005 q^{23}\) \(+1.00000 q^{24}\) \(+14.0949 q^{25}\) \(-6.17357 q^{26}\) \(+1.00000 q^{27}\) \(+4.52139 q^{28}\) \(-7.78539 q^{29}\) \(+4.36977 q^{30}\) \(-1.28028 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(+4.36848 q^{34}\) \(+19.7575 q^{35}\) \(+1.00000 q^{36}\) \(-0.611833 q^{37}\) \(-5.40291 q^{38}\) \(-6.17357 q^{39}\) \(+4.36977 q^{40}\) \(+9.12644 q^{41}\) \(+4.52139 q^{42}\) \(-9.01275 q^{43}\) \(+1.00000 q^{44}\) \(+4.36977 q^{45}\) \(-7.65005 q^{46}\) \(-0.764742 q^{47}\) \(+1.00000 q^{48}\) \(+13.4430 q^{49}\) \(+14.0949 q^{50}\) \(+4.36848 q^{51}\) \(-6.17357 q^{52}\) \(-0.479321 q^{53}\) \(+1.00000 q^{54}\) \(+4.36977 q^{55}\) \(+4.52139 q^{56}\) \(-5.40291 q^{57}\) \(-7.78539 q^{58}\) \(+7.96627 q^{59}\) \(+4.36977 q^{60}\) \(-1.00000 q^{61}\) \(-1.28028 q^{62}\) \(+4.52139 q^{63}\) \(+1.00000 q^{64}\) \(-26.9771 q^{65}\) \(+1.00000 q^{66}\) \(-6.16309 q^{67}\) \(+4.36848 q^{68}\) \(-7.65005 q^{69}\) \(+19.7575 q^{70}\) \(+8.06263 q^{71}\) \(+1.00000 q^{72}\) \(-6.83739 q^{73}\) \(-0.611833 q^{74}\) \(+14.0949 q^{75}\) \(-5.40291 q^{76}\) \(+4.52139 q^{77}\) \(-6.17357 q^{78}\) \(+2.99625 q^{79}\) \(+4.36977 q^{80}\) \(+1.00000 q^{81}\) \(+9.12644 q^{82}\) \(-12.1436 q^{83}\) \(+4.52139 q^{84}\) \(+19.0893 q^{85}\) \(-9.01275 q^{86}\) \(-7.78539 q^{87}\) \(+1.00000 q^{88}\) \(+10.2015 q^{89}\) \(+4.36977 q^{90}\) \(-27.9131 q^{91}\) \(-7.65005 q^{92}\) \(-1.28028 q^{93}\) \(-0.764742 q^{94}\) \(-23.6095 q^{95}\) \(+1.00000 q^{96}\) \(-12.3249 q^{97}\) \(+13.4430 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 4.36977 1.95422 0.977111 0.212729i \(-0.0682352\pi\)
0.977111 + 0.212729i \(0.0682352\pi\)
\(6\) 1.00000 0.408248
\(7\) 4.52139 1.70893 0.854463 0.519513i \(-0.173886\pi\)
0.854463 + 0.519513i \(0.173886\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 4.36977 1.38184
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −6.17357 −1.71224 −0.856121 0.516776i \(-0.827132\pi\)
−0.856121 + 0.516776i \(0.827132\pi\)
\(14\) 4.52139 1.20839
\(15\) 4.36977 1.12827
\(16\) 1.00000 0.250000
\(17\) 4.36848 1.05951 0.529756 0.848150i \(-0.322283\pi\)
0.529756 + 0.848150i \(0.322283\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.40291 −1.23951 −0.619756 0.784794i \(-0.712768\pi\)
−0.619756 + 0.784794i \(0.712768\pi\)
\(20\) 4.36977 0.977111
\(21\) 4.52139 0.986649
\(22\) 1.00000 0.213201
\(23\) −7.65005 −1.59515 −0.797573 0.603222i \(-0.793883\pi\)
−0.797573 + 0.603222i \(0.793883\pi\)
\(24\) 1.00000 0.204124
\(25\) 14.0949 2.81899
\(26\) −6.17357 −1.21074
\(27\) 1.00000 0.192450
\(28\) 4.52139 0.854463
\(29\) −7.78539 −1.44571 −0.722856 0.690999i \(-0.757171\pi\)
−0.722856 + 0.690999i \(0.757171\pi\)
\(30\) 4.36977 0.797808
\(31\) −1.28028 −0.229945 −0.114972 0.993369i \(-0.536678\pi\)
−0.114972 + 0.993369i \(0.536678\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 4.36848 0.749189
\(35\) 19.7575 3.33962
\(36\) 1.00000 0.166667
\(37\) −0.611833 −0.100585 −0.0502924 0.998735i \(-0.516015\pi\)
−0.0502924 + 0.998735i \(0.516015\pi\)
\(38\) −5.40291 −0.876468
\(39\) −6.17357 −0.988563
\(40\) 4.36977 0.690922
\(41\) 9.12644 1.42531 0.712655 0.701515i \(-0.247492\pi\)
0.712655 + 0.701515i \(0.247492\pi\)
\(42\) 4.52139 0.697666
\(43\) −9.01275 −1.37443 −0.687215 0.726454i \(-0.741167\pi\)
−0.687215 + 0.726454i \(0.741167\pi\)
\(44\) 1.00000 0.150756
\(45\) 4.36977 0.651407
\(46\) −7.65005 −1.12794
\(47\) −0.764742 −0.111549 −0.0557746 0.998443i \(-0.517763\pi\)
−0.0557746 + 0.998443i \(0.517763\pi\)
\(48\) 1.00000 0.144338
\(49\) 13.4430 1.92043
\(50\) 14.0949 1.99332
\(51\) 4.36848 0.611710
\(52\) −6.17357 −0.856121
\(53\) −0.479321 −0.0658398 −0.0329199 0.999458i \(-0.510481\pi\)
−0.0329199 + 0.999458i \(0.510481\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.36977 0.589220
\(56\) 4.52139 0.604196
\(57\) −5.40291 −0.715633
\(58\) −7.78539 −1.02227
\(59\) 7.96627 1.03712 0.518560 0.855041i \(-0.326468\pi\)
0.518560 + 0.855041i \(0.326468\pi\)
\(60\) 4.36977 0.564135
\(61\) −1.00000 −0.128037
\(62\) −1.28028 −0.162596
\(63\) 4.52139 0.569642
\(64\) 1.00000 0.125000
\(65\) −26.9771 −3.34610
\(66\) 1.00000 0.123091
\(67\) −6.16309 −0.752941 −0.376470 0.926429i \(-0.622862\pi\)
−0.376470 + 0.926429i \(0.622862\pi\)
\(68\) 4.36848 0.529756
\(69\) −7.65005 −0.920958
\(70\) 19.7575 2.36147
\(71\) 8.06263 0.956858 0.478429 0.878126i \(-0.341206\pi\)
0.478429 + 0.878126i \(0.341206\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.83739 −0.800256 −0.400128 0.916459i \(-0.631034\pi\)
−0.400128 + 0.916459i \(0.631034\pi\)
\(74\) −0.611833 −0.0711242
\(75\) 14.0949 1.62754
\(76\) −5.40291 −0.619756
\(77\) 4.52139 0.515260
\(78\) −6.17357 −0.699019
\(79\) 2.99625 0.337104 0.168552 0.985693i \(-0.446091\pi\)
0.168552 + 0.985693i \(0.446091\pi\)
\(80\) 4.36977 0.488556
\(81\) 1.00000 0.111111
\(82\) 9.12644 1.00785
\(83\) −12.1436 −1.33294 −0.666469 0.745533i \(-0.732195\pi\)
−0.666469 + 0.745533i \(0.732195\pi\)
\(84\) 4.52139 0.493324
\(85\) 19.0893 2.07052
\(86\) −9.01275 −0.971869
\(87\) −7.78539 −0.834682
\(88\) 1.00000 0.106600
\(89\) 10.2015 1.08136 0.540680 0.841228i \(-0.318167\pi\)
0.540680 + 0.841228i \(0.318167\pi\)
\(90\) 4.36977 0.460615
\(91\) −27.9131 −2.92609
\(92\) −7.65005 −0.797573
\(93\) −1.28028 −0.132759
\(94\) −0.764742 −0.0788771
\(95\) −23.6095 −2.42228
\(96\) 1.00000 0.102062
\(97\) −12.3249 −1.25140 −0.625701 0.780063i \(-0.715187\pi\)
−0.625701 + 0.780063i \(0.715187\pi\)
\(98\) 13.4430 1.35795
\(99\) 1.00000 0.100504
\(100\) 14.0949 1.40949
\(101\) −15.7838 −1.57055 −0.785273 0.619150i \(-0.787477\pi\)
−0.785273 + 0.619150i \(0.787477\pi\)
\(102\) 4.36848 0.432544
\(103\) −3.21980 −0.317256 −0.158628 0.987338i \(-0.550707\pi\)
−0.158628 + 0.987338i \(0.550707\pi\)
\(104\) −6.17357 −0.605369
\(105\) 19.7575 1.92813
\(106\) −0.479321 −0.0465557
\(107\) 1.80234 0.174239 0.0871195 0.996198i \(-0.472234\pi\)
0.0871195 + 0.996198i \(0.472234\pi\)
\(108\) 1.00000 0.0962250
\(109\) 4.31978 0.413760 0.206880 0.978366i \(-0.433669\pi\)
0.206880 + 0.978366i \(0.433669\pi\)
\(110\) 4.36977 0.416642
\(111\) −0.611833 −0.0580727
\(112\) 4.52139 0.427231
\(113\) 6.52957 0.614250 0.307125 0.951669i \(-0.400633\pi\)
0.307125 + 0.951669i \(0.400633\pi\)
\(114\) −5.40291 −0.506029
\(115\) −33.4290 −3.11727
\(116\) −7.78539 −0.722856
\(117\) −6.17357 −0.570747
\(118\) 7.96627 0.733354
\(119\) 19.7516 1.81063
\(120\) 4.36977 0.398904
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 9.12644 0.822903
\(124\) −1.28028 −0.114972
\(125\) 39.7428 3.55470
\(126\) 4.52139 0.402798
\(127\) 6.04195 0.536137 0.268068 0.963400i \(-0.413615\pi\)
0.268068 + 0.963400i \(0.413615\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.01275 −0.793528
\(130\) −26.9771 −2.36605
\(131\) −0.440775 −0.0385107 −0.0192553 0.999815i \(-0.506130\pi\)
−0.0192553 + 0.999815i \(0.506130\pi\)
\(132\) 1.00000 0.0870388
\(133\) −24.4287 −2.11823
\(134\) −6.16309 −0.532410
\(135\) 4.36977 0.376090
\(136\) 4.36848 0.374594
\(137\) −23.2581 −1.98707 −0.993535 0.113524i \(-0.963786\pi\)
−0.993535 + 0.113524i \(0.963786\pi\)
\(138\) −7.65005 −0.651216
\(139\) −16.3664 −1.38818 −0.694088 0.719890i \(-0.744192\pi\)
−0.694088 + 0.719890i \(0.744192\pi\)
\(140\) 19.7575 1.66981
\(141\) −0.764742 −0.0644029
\(142\) 8.06263 0.676601
\(143\) −6.17357 −0.516260
\(144\) 1.00000 0.0833333
\(145\) −34.0204 −2.82524
\(146\) −6.83739 −0.565866
\(147\) 13.4430 1.10876
\(148\) −0.611833 −0.0502924
\(149\) 7.80061 0.639051 0.319526 0.947578i \(-0.396476\pi\)
0.319526 + 0.947578i \(0.396476\pi\)
\(150\) 14.0949 1.15085
\(151\) 20.5763 1.67447 0.837236 0.546842i \(-0.184170\pi\)
0.837236 + 0.546842i \(0.184170\pi\)
\(152\) −5.40291 −0.438234
\(153\) 4.36848 0.353171
\(154\) 4.52139 0.364344
\(155\) −5.59453 −0.449363
\(156\) −6.17357 −0.494281
\(157\) 8.51977 0.679952 0.339976 0.940434i \(-0.389581\pi\)
0.339976 + 0.940434i \(0.389581\pi\)
\(158\) 2.99625 0.238369
\(159\) −0.479321 −0.0380126
\(160\) 4.36977 0.345461
\(161\) −34.5889 −2.72599
\(162\) 1.00000 0.0785674
\(163\) −15.6757 −1.22782 −0.613909 0.789377i \(-0.710404\pi\)
−0.613909 + 0.789377i \(0.710404\pi\)
\(164\) 9.12644 0.712655
\(165\) 4.36977 0.340186
\(166\) −12.1436 −0.942529
\(167\) −3.55356 −0.274982 −0.137491 0.990503i \(-0.543904\pi\)
−0.137491 + 0.990503i \(0.543904\pi\)
\(168\) 4.52139 0.348833
\(169\) 25.1130 1.93177
\(170\) 19.0893 1.46408
\(171\) −5.40291 −0.413171
\(172\) −9.01275 −0.687215
\(173\) 10.0811 0.766451 0.383225 0.923655i \(-0.374813\pi\)
0.383225 + 0.923655i \(0.374813\pi\)
\(174\) −7.78539 −0.590209
\(175\) 63.7287 4.81744
\(176\) 1.00000 0.0753778
\(177\) 7.96627 0.598781
\(178\) 10.2015 0.764638
\(179\) 16.8091 1.25637 0.628187 0.778063i \(-0.283797\pi\)
0.628187 + 0.778063i \(0.283797\pi\)
\(180\) 4.36977 0.325704
\(181\) −12.7394 −0.946915 −0.473457 0.880817i \(-0.656994\pi\)
−0.473457 + 0.880817i \(0.656994\pi\)
\(182\) −27.9131 −2.06906
\(183\) −1.00000 −0.0739221
\(184\) −7.65005 −0.563969
\(185\) −2.67357 −0.196565
\(186\) −1.28028 −0.0938746
\(187\) 4.36848 0.319455
\(188\) −0.764742 −0.0557746
\(189\) 4.52139 0.328883
\(190\) −23.6095 −1.71281
\(191\) −11.0407 −0.798877 −0.399439 0.916760i \(-0.630795\pi\)
−0.399439 + 0.916760i \(0.630795\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.31091 0.166343 0.0831715 0.996535i \(-0.473495\pi\)
0.0831715 + 0.996535i \(0.473495\pi\)
\(194\) −12.3249 −0.884875
\(195\) −26.9771 −1.93187
\(196\) 13.4430 0.960213
\(197\) −19.4329 −1.38453 −0.692267 0.721641i \(-0.743388\pi\)
−0.692267 + 0.721641i \(0.743388\pi\)
\(198\) 1.00000 0.0710669
\(199\) 9.49175 0.672853 0.336426 0.941710i \(-0.390782\pi\)
0.336426 + 0.941710i \(0.390782\pi\)
\(200\) 14.0949 0.996662
\(201\) −6.16309 −0.434711
\(202\) −15.7838 −1.11054
\(203\) −35.2008 −2.47061
\(204\) 4.36848 0.305855
\(205\) 39.8805 2.78537
\(206\) −3.21980 −0.224334
\(207\) −7.65005 −0.531715
\(208\) −6.17357 −0.428060
\(209\) −5.40291 −0.373727
\(210\) 19.7575 1.36339
\(211\) −14.2323 −0.979791 −0.489895 0.871781i \(-0.662965\pi\)
−0.489895 + 0.871781i \(0.662965\pi\)
\(212\) −0.479321 −0.0329199
\(213\) 8.06263 0.552442
\(214\) 1.80234 0.123206
\(215\) −39.3837 −2.68594
\(216\) 1.00000 0.0680414
\(217\) −5.78864 −0.392959
\(218\) 4.31978 0.292573
\(219\) −6.83739 −0.462028
\(220\) 4.36977 0.294610
\(221\) −26.9691 −1.81414
\(222\) −0.611833 −0.0410636
\(223\) −6.11859 −0.409731 −0.204865 0.978790i \(-0.565676\pi\)
−0.204865 + 0.978790i \(0.565676\pi\)
\(224\) 4.52139 0.302098
\(225\) 14.0949 0.939662
\(226\) 6.52957 0.434340
\(227\) 11.2276 0.745201 0.372600 0.927992i \(-0.378466\pi\)
0.372600 + 0.927992i \(0.378466\pi\)
\(228\) −5.40291 −0.357816
\(229\) 19.3616 1.27945 0.639724 0.768605i \(-0.279049\pi\)
0.639724 + 0.768605i \(0.279049\pi\)
\(230\) −33.4290 −2.20424
\(231\) 4.52139 0.297486
\(232\) −7.78539 −0.511136
\(233\) 5.77018 0.378017 0.189009 0.981975i \(-0.439473\pi\)
0.189009 + 0.981975i \(0.439473\pi\)
\(234\) −6.17357 −0.403579
\(235\) −3.34175 −0.217992
\(236\) 7.96627 0.518560
\(237\) 2.99625 0.194627
\(238\) 19.7516 1.28031
\(239\) 21.9886 1.42232 0.711162 0.703028i \(-0.248169\pi\)
0.711162 + 0.703028i \(0.248169\pi\)
\(240\) 4.36977 0.282068
\(241\) 7.82691 0.504176 0.252088 0.967704i \(-0.418883\pi\)
0.252088 + 0.967704i \(0.418883\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 58.7428 3.75294
\(246\) 9.12644 0.581880
\(247\) 33.3553 2.12234
\(248\) −1.28028 −0.0812978
\(249\) −12.1436 −0.769572
\(250\) 39.7428 2.51355
\(251\) −14.2970 −0.902420 −0.451210 0.892418i \(-0.649007\pi\)
−0.451210 + 0.892418i \(0.649007\pi\)
\(252\) 4.52139 0.284821
\(253\) −7.65005 −0.480955
\(254\) 6.04195 0.379106
\(255\) 19.0893 1.19542
\(256\) 1.00000 0.0625000
\(257\) −11.8679 −0.740298 −0.370149 0.928972i \(-0.620693\pi\)
−0.370149 + 0.928972i \(0.620693\pi\)
\(258\) −9.01275 −0.561109
\(259\) −2.76634 −0.171892
\(260\) −26.9771 −1.67305
\(261\) −7.78539 −0.481904
\(262\) −0.440775 −0.0272312
\(263\) −0.830033 −0.0511820 −0.0255910 0.999672i \(-0.508147\pi\)
−0.0255910 + 0.999672i \(0.508147\pi\)
\(264\) 1.00000 0.0615457
\(265\) −2.09452 −0.128666
\(266\) −24.4287 −1.49782
\(267\) 10.2015 0.624324
\(268\) −6.16309 −0.376470
\(269\) 2.06778 0.126075 0.0630375 0.998011i \(-0.479921\pi\)
0.0630375 + 0.998011i \(0.479921\pi\)
\(270\) 4.36977 0.265936
\(271\) 18.7718 1.14031 0.570154 0.821538i \(-0.306883\pi\)
0.570154 + 0.821538i \(0.306883\pi\)
\(272\) 4.36848 0.264878
\(273\) −27.9131 −1.68938
\(274\) −23.2581 −1.40507
\(275\) 14.0949 0.849956
\(276\) −7.65005 −0.460479
\(277\) −23.7427 −1.42656 −0.713280 0.700880i \(-0.752791\pi\)
−0.713280 + 0.700880i \(0.752791\pi\)
\(278\) −16.3664 −0.981589
\(279\) −1.28028 −0.0766483
\(280\) 19.7575 1.18073
\(281\) 15.2565 0.910126 0.455063 0.890459i \(-0.349617\pi\)
0.455063 + 0.890459i \(0.349617\pi\)
\(282\) −0.764742 −0.0455397
\(283\) 10.0897 0.599770 0.299885 0.953975i \(-0.403052\pi\)
0.299885 + 0.953975i \(0.403052\pi\)
\(284\) 8.06263 0.478429
\(285\) −23.6095 −1.39851
\(286\) −6.17357 −0.365051
\(287\) 41.2642 2.43575
\(288\) 1.00000 0.0589256
\(289\) 2.08364 0.122567
\(290\) −34.0204 −1.99775
\(291\) −12.3249 −0.722497
\(292\) −6.83739 −0.400128
\(293\) −22.1467 −1.29382 −0.646911 0.762565i \(-0.723940\pi\)
−0.646911 + 0.762565i \(0.723940\pi\)
\(294\) 13.4430 0.784011
\(295\) 34.8108 2.02676
\(296\) −0.611833 −0.0355621
\(297\) 1.00000 0.0580259
\(298\) 7.80061 0.451877
\(299\) 47.2282 2.73127
\(300\) 14.0949 0.813771
\(301\) −40.7502 −2.34880
\(302\) 20.5763 1.18403
\(303\) −15.7838 −0.906755
\(304\) −5.40291 −0.309878
\(305\) −4.36977 −0.250213
\(306\) 4.36848 0.249730
\(307\) 2.13389 0.121788 0.0608939 0.998144i \(-0.480605\pi\)
0.0608939 + 0.998144i \(0.480605\pi\)
\(308\) 4.52139 0.257630
\(309\) −3.21980 −0.183168
\(310\) −5.59453 −0.317748
\(311\) 13.5648 0.769190 0.384595 0.923085i \(-0.374341\pi\)
0.384595 + 0.923085i \(0.374341\pi\)
\(312\) −6.17357 −0.349510
\(313\) 6.44538 0.364315 0.182157 0.983269i \(-0.441692\pi\)
0.182157 + 0.983269i \(0.441692\pi\)
\(314\) 8.51977 0.480799
\(315\) 19.7575 1.11321
\(316\) 2.99625 0.168552
\(317\) 28.0311 1.57438 0.787191 0.616709i \(-0.211535\pi\)
0.787191 + 0.616709i \(0.211535\pi\)
\(318\) −0.479321 −0.0268790
\(319\) −7.78539 −0.435898
\(320\) 4.36977 0.244278
\(321\) 1.80234 0.100597
\(322\) −34.5889 −1.92756
\(323\) −23.6025 −1.31328
\(324\) 1.00000 0.0555556
\(325\) −87.0161 −4.82678
\(326\) −15.6757 −0.868198
\(327\) 4.31978 0.238885
\(328\) 9.12644 0.503923
\(329\) −3.45770 −0.190629
\(330\) 4.36977 0.240548
\(331\) 11.8382 0.650685 0.325342 0.945596i \(-0.394520\pi\)
0.325342 + 0.945596i \(0.394520\pi\)
\(332\) −12.1436 −0.666469
\(333\) −0.611833 −0.0335283
\(334\) −3.55356 −0.194442
\(335\) −26.9313 −1.47141
\(336\) 4.52139 0.246662
\(337\) 1.26199 0.0687449 0.0343724 0.999409i \(-0.489057\pi\)
0.0343724 + 0.999409i \(0.489057\pi\)
\(338\) 25.1130 1.36597
\(339\) 6.52957 0.354638
\(340\) 19.0893 1.03526
\(341\) −1.28028 −0.0693310
\(342\) −5.40291 −0.292156
\(343\) 29.1313 1.57294
\(344\) −9.01275 −0.485935
\(345\) −33.4290 −1.79976
\(346\) 10.0811 0.541962
\(347\) −8.59566 −0.461439 −0.230720 0.973020i \(-0.574108\pi\)
−0.230720 + 0.973020i \(0.574108\pi\)
\(348\) −7.78539 −0.417341
\(349\) 15.7282 0.841912 0.420956 0.907081i \(-0.361695\pi\)
0.420956 + 0.907081i \(0.361695\pi\)
\(350\) 63.7287 3.40644
\(351\) −6.17357 −0.329521
\(352\) 1.00000 0.0533002
\(353\) 34.0373 1.81163 0.905813 0.423678i \(-0.139261\pi\)
0.905813 + 0.423678i \(0.139261\pi\)
\(354\) 7.96627 0.423402
\(355\) 35.2319 1.86991
\(356\) 10.2015 0.540680
\(357\) 19.7516 1.04537
\(358\) 16.8091 0.888390
\(359\) −27.7906 −1.46673 −0.733366 0.679834i \(-0.762052\pi\)
−0.733366 + 0.679834i \(0.762052\pi\)
\(360\) 4.36977 0.230307
\(361\) 10.1914 0.536391
\(362\) −12.7394 −0.669570
\(363\) 1.00000 0.0524864
\(364\) −27.9131 −1.46305
\(365\) −29.8778 −1.56388
\(366\) −1.00000 −0.0522708
\(367\) 18.3450 0.957601 0.478801 0.877924i \(-0.341072\pi\)
0.478801 + 0.877924i \(0.341072\pi\)
\(368\) −7.65005 −0.398787
\(369\) 9.12644 0.475103
\(370\) −2.67357 −0.138992
\(371\) −2.16720 −0.112515
\(372\) −1.28028 −0.0663794
\(373\) 32.5317 1.68443 0.842214 0.539143i \(-0.181252\pi\)
0.842214 + 0.539143i \(0.181252\pi\)
\(374\) 4.36848 0.225889
\(375\) 39.7428 2.05231
\(376\) −0.764742 −0.0394386
\(377\) 48.0637 2.47541
\(378\) 4.52139 0.232555
\(379\) 15.5430 0.798393 0.399196 0.916865i \(-0.369289\pi\)
0.399196 + 0.916865i \(0.369289\pi\)
\(380\) −23.6095 −1.21114
\(381\) 6.04195 0.309539
\(382\) −11.0407 −0.564892
\(383\) 22.9515 1.17277 0.586383 0.810034i \(-0.300551\pi\)
0.586383 + 0.810034i \(0.300551\pi\)
\(384\) 1.00000 0.0510310
\(385\) 19.7575 1.00693
\(386\) 2.31091 0.117622
\(387\) −9.01275 −0.458144
\(388\) −12.3249 −0.625701
\(389\) 13.3563 0.677189 0.338595 0.940932i \(-0.390048\pi\)
0.338595 + 0.940932i \(0.390048\pi\)
\(390\) −26.9771 −1.36604
\(391\) −33.4191 −1.69008
\(392\) 13.4430 0.678973
\(393\) −0.440775 −0.0222342
\(394\) −19.4329 −0.979014
\(395\) 13.0929 0.658777
\(396\) 1.00000 0.0502519
\(397\) −8.33191 −0.418167 −0.209083 0.977898i \(-0.567048\pi\)
−0.209083 + 0.977898i \(0.567048\pi\)
\(398\) 9.49175 0.475779
\(399\) −24.4287 −1.22296
\(400\) 14.0949 0.704746
\(401\) 21.1298 1.05517 0.527585 0.849502i \(-0.323097\pi\)
0.527585 + 0.849502i \(0.323097\pi\)
\(402\) −6.16309 −0.307387
\(403\) 7.90389 0.393721
\(404\) −15.7838 −0.785273
\(405\) 4.36977 0.217136
\(406\) −35.2008 −1.74699
\(407\) −0.611833 −0.0303275
\(408\) 4.36848 0.216272
\(409\) −21.2533 −1.05091 −0.525454 0.850822i \(-0.676104\pi\)
−0.525454 + 0.850822i \(0.676104\pi\)
\(410\) 39.8805 1.96956
\(411\) −23.2581 −1.14724
\(412\) −3.21980 −0.158628
\(413\) 36.0186 1.77236
\(414\) −7.65005 −0.375980
\(415\) −53.0650 −2.60486
\(416\) −6.17357 −0.302684
\(417\) −16.3664 −0.801464
\(418\) −5.40291 −0.264265
\(419\) 3.08019 0.150477 0.0752385 0.997166i \(-0.476028\pi\)
0.0752385 + 0.997166i \(0.476028\pi\)
\(420\) 19.7575 0.964065
\(421\) −16.1588 −0.787533 −0.393766 0.919211i \(-0.628828\pi\)
−0.393766 + 0.919211i \(0.628828\pi\)
\(422\) −14.2323 −0.692817
\(423\) −0.764742 −0.0371830
\(424\) −0.479321 −0.0232779
\(425\) 61.5734 2.98675
\(426\) 8.06263 0.390636
\(427\) −4.52139 −0.218805
\(428\) 1.80234 0.0871195
\(429\) −6.17357 −0.298063
\(430\) −39.3837 −1.89925
\(431\) −5.91170 −0.284757 −0.142378 0.989812i \(-0.545475\pi\)
−0.142378 + 0.989812i \(0.545475\pi\)
\(432\) 1.00000 0.0481125
\(433\) 5.07766 0.244017 0.122008 0.992529i \(-0.461067\pi\)
0.122008 + 0.992529i \(0.461067\pi\)
\(434\) −5.78864 −0.277864
\(435\) −34.0204 −1.63115
\(436\) 4.31978 0.206880
\(437\) 41.3325 1.97720
\(438\) −6.83739 −0.326703
\(439\) 15.8377 0.755892 0.377946 0.925828i \(-0.376630\pi\)
0.377946 + 0.925828i \(0.376630\pi\)
\(440\) 4.36977 0.208321
\(441\) 13.4430 0.640142
\(442\) −26.9691 −1.28279
\(443\) −14.2435 −0.676730 −0.338365 0.941015i \(-0.609874\pi\)
−0.338365 + 0.941015i \(0.609874\pi\)
\(444\) −0.611833 −0.0290363
\(445\) 44.5784 2.11322
\(446\) −6.11859 −0.289724
\(447\) 7.80061 0.368956
\(448\) 4.52139 0.213616
\(449\) 5.96861 0.281676 0.140838 0.990033i \(-0.455020\pi\)
0.140838 + 0.990033i \(0.455020\pi\)
\(450\) 14.0949 0.664441
\(451\) 9.12644 0.429747
\(452\) 6.52957 0.307125
\(453\) 20.5763 0.966757
\(454\) 11.2276 0.526937
\(455\) −121.974 −5.71824
\(456\) −5.40291 −0.253014
\(457\) 17.9080 0.837699 0.418850 0.908056i \(-0.362433\pi\)
0.418850 + 0.908056i \(0.362433\pi\)
\(458\) 19.3616 0.904706
\(459\) 4.36848 0.203903
\(460\) −33.4290 −1.55864
\(461\) −31.1703 −1.45175 −0.725873 0.687829i \(-0.758564\pi\)
−0.725873 + 0.687829i \(0.758564\pi\)
\(462\) 4.52139 0.210354
\(463\) −23.2553 −1.08077 −0.540383 0.841419i \(-0.681721\pi\)
−0.540383 + 0.841419i \(0.681721\pi\)
\(464\) −7.78539 −0.361428
\(465\) −5.59453 −0.259440
\(466\) 5.77018 0.267298
\(467\) −35.0717 −1.62292 −0.811462 0.584405i \(-0.801328\pi\)
−0.811462 + 0.584405i \(0.801328\pi\)
\(468\) −6.17357 −0.285374
\(469\) −27.8657 −1.28672
\(470\) −3.34175 −0.154143
\(471\) 8.51977 0.392570
\(472\) 7.96627 0.366677
\(473\) −9.01275 −0.414407
\(474\) 2.99625 0.137622
\(475\) −76.1536 −3.49417
\(476\) 19.7516 0.905314
\(477\) −0.479321 −0.0219466
\(478\) 21.9886 1.00574
\(479\) −13.2527 −0.605533 −0.302767 0.953065i \(-0.597910\pi\)
−0.302767 + 0.953065i \(0.597910\pi\)
\(480\) 4.36977 0.199452
\(481\) 3.77720 0.172225
\(482\) 7.82691 0.356506
\(483\) −34.5889 −1.57385
\(484\) 1.00000 0.0454545
\(485\) −53.8569 −2.44552
\(486\) 1.00000 0.0453609
\(487\) 25.7716 1.16782 0.583911 0.811818i \(-0.301522\pi\)
0.583911 + 0.811818i \(0.301522\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −15.6757 −0.708881
\(490\) 58.7428 2.65373
\(491\) −25.1818 −1.13644 −0.568220 0.822876i \(-0.692368\pi\)
−0.568220 + 0.822876i \(0.692368\pi\)
\(492\) 9.12644 0.411452
\(493\) −34.0104 −1.53175
\(494\) 33.3553 1.50072
\(495\) 4.36977 0.196407
\(496\) −1.28028 −0.0574862
\(497\) 36.4543 1.63520
\(498\) −12.1436 −0.544170
\(499\) −7.95322 −0.356035 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(500\) 39.7428 1.77735
\(501\) −3.55356 −0.158761
\(502\) −14.2970 −0.638107
\(503\) 4.39401 0.195919 0.0979596 0.995190i \(-0.468768\pi\)
0.0979596 + 0.995190i \(0.468768\pi\)
\(504\) 4.52139 0.201399
\(505\) −68.9716 −3.06920
\(506\) −7.65005 −0.340086
\(507\) 25.1130 1.11531
\(508\) 6.04195 0.268068
\(509\) 18.2141 0.807326 0.403663 0.914908i \(-0.367737\pi\)
0.403663 + 0.914908i \(0.367737\pi\)
\(510\) 19.0893 0.845288
\(511\) −30.9145 −1.36758
\(512\) 1.00000 0.0441942
\(513\) −5.40291 −0.238544
\(514\) −11.8679 −0.523469
\(515\) −14.0698 −0.619990
\(516\) −9.01275 −0.396764
\(517\) −0.764742 −0.0336333
\(518\) −2.76634 −0.121546
\(519\) 10.0811 0.442510
\(520\) −26.9771 −1.18302
\(521\) 31.0861 1.36190 0.680952 0.732328i \(-0.261566\pi\)
0.680952 + 0.732328i \(0.261566\pi\)
\(522\) −7.78539 −0.340757
\(523\) 1.81995 0.0795810 0.0397905 0.999208i \(-0.487331\pi\)
0.0397905 + 0.999208i \(0.487331\pi\)
\(524\) −0.440775 −0.0192553
\(525\) 63.7287 2.78135
\(526\) −0.830033 −0.0361912
\(527\) −5.59288 −0.243629
\(528\) 1.00000 0.0435194
\(529\) 35.5233 1.54449
\(530\) −2.09452 −0.0909803
\(531\) 7.96627 0.345706
\(532\) −24.4287 −1.05912
\(533\) −56.3427 −2.44047
\(534\) 10.2015 0.441464
\(535\) 7.87583 0.340502
\(536\) −6.16309 −0.266205
\(537\) 16.8091 0.725367
\(538\) 2.06778 0.0891485
\(539\) 13.4430 0.579030
\(540\) 4.36977 0.188045
\(541\) 20.5675 0.884266 0.442133 0.896949i \(-0.354222\pi\)
0.442133 + 0.896949i \(0.354222\pi\)
\(542\) 18.7718 0.806320
\(543\) −12.7394 −0.546701
\(544\) 4.36848 0.187297
\(545\) 18.8765 0.808579
\(546\) −27.9131 −1.19457
\(547\) −13.9930 −0.598297 −0.299148 0.954207i \(-0.596703\pi\)
−0.299148 + 0.954207i \(0.596703\pi\)
\(548\) −23.2581 −0.993535
\(549\) −1.00000 −0.0426790
\(550\) 14.0949 0.601010
\(551\) 42.0638 1.79198
\(552\) −7.65005 −0.325608
\(553\) 13.5472 0.576086
\(554\) −23.7427 −1.00873
\(555\) −2.67357 −0.113487
\(556\) −16.3664 −0.694088
\(557\) 40.4315 1.71314 0.856569 0.516033i \(-0.172592\pi\)
0.856569 + 0.516033i \(0.172592\pi\)
\(558\) −1.28028 −0.0541985
\(559\) 55.6408 2.35336
\(560\) 19.7575 0.834905
\(561\) 4.36848 0.184437
\(562\) 15.2565 0.643556
\(563\) −39.7403 −1.67486 −0.837428 0.546548i \(-0.815942\pi\)
−0.837428 + 0.546548i \(0.815942\pi\)
\(564\) −0.764742 −0.0322015
\(565\) 28.5327 1.20038
\(566\) 10.0897 0.424102
\(567\) 4.52139 0.189881
\(568\) 8.06263 0.338300
\(569\) −22.6884 −0.951148 −0.475574 0.879676i \(-0.657760\pi\)
−0.475574 + 0.879676i \(0.657760\pi\)
\(570\) −23.6095 −0.988893
\(571\) 13.6282 0.570323 0.285161 0.958480i \(-0.407953\pi\)
0.285161 + 0.958480i \(0.407953\pi\)
\(572\) −6.17357 −0.258130
\(573\) −11.0407 −0.461232
\(574\) 41.2642 1.72233
\(575\) −107.827 −4.49669
\(576\) 1.00000 0.0416667
\(577\) 6.80917 0.283469 0.141735 0.989905i \(-0.454732\pi\)
0.141735 + 0.989905i \(0.454732\pi\)
\(578\) 2.08364 0.0866682
\(579\) 2.31091 0.0960382
\(580\) −34.0204 −1.41262
\(581\) −54.9062 −2.27789
\(582\) −12.3249 −0.510883
\(583\) −0.479321 −0.0198514
\(584\) −6.83739 −0.282933
\(585\) −26.9771 −1.11537
\(586\) −22.1467 −0.914871
\(587\) −44.8600 −1.85157 −0.925785 0.378052i \(-0.876594\pi\)
−0.925785 + 0.378052i \(0.876594\pi\)
\(588\) 13.4430 0.554379
\(589\) 6.91723 0.285019
\(590\) 34.8108 1.43314
\(591\) −19.4329 −0.799362
\(592\) −0.611833 −0.0251462
\(593\) −33.2409 −1.36504 −0.682519 0.730868i \(-0.739116\pi\)
−0.682519 + 0.730868i \(0.739116\pi\)
\(594\) 1.00000 0.0410305
\(595\) 86.3101 3.53837
\(596\) 7.80061 0.319526
\(597\) 9.49175 0.388472
\(598\) 47.2282 1.93130
\(599\) −23.0587 −0.942153 −0.471076 0.882092i \(-0.656134\pi\)
−0.471076 + 0.882092i \(0.656134\pi\)
\(600\) 14.0949 0.575423
\(601\) 8.33698 0.340072 0.170036 0.985438i \(-0.445612\pi\)
0.170036 + 0.985438i \(0.445612\pi\)
\(602\) −40.7502 −1.66085
\(603\) −6.16309 −0.250980
\(604\) 20.5763 0.837236
\(605\) 4.36977 0.177657
\(606\) −15.7838 −0.641173
\(607\) 37.4407 1.51967 0.759837 0.650114i \(-0.225279\pi\)
0.759837 + 0.650114i \(0.225279\pi\)
\(608\) −5.40291 −0.219117
\(609\) −35.2008 −1.42641
\(610\) −4.36977 −0.176927
\(611\) 4.72119 0.190999
\(612\) 4.36848 0.176585
\(613\) −13.4997 −0.545247 −0.272623 0.962121i \(-0.587891\pi\)
−0.272623 + 0.962121i \(0.587891\pi\)
\(614\) 2.13389 0.0861169
\(615\) 39.8805 1.60814
\(616\) 4.52139 0.182172
\(617\) 14.8163 0.596482 0.298241 0.954491i \(-0.403600\pi\)
0.298241 + 0.954491i \(0.403600\pi\)
\(618\) −3.21980 −0.129519
\(619\) −13.9425 −0.560395 −0.280197 0.959942i \(-0.590400\pi\)
−0.280197 + 0.959942i \(0.590400\pi\)
\(620\) −5.59453 −0.224682
\(621\) −7.65005 −0.306986
\(622\) 13.5648 0.543899
\(623\) 46.1251 1.84797
\(624\) −6.17357 −0.247141
\(625\) 103.192 4.12769
\(626\) 6.44538 0.257609
\(627\) −5.40291 −0.215771
\(628\) 8.51977 0.339976
\(629\) −2.67278 −0.106571
\(630\) 19.7575 0.787156
\(631\) −22.8178 −0.908361 −0.454180 0.890910i \(-0.650068\pi\)
−0.454180 + 0.890910i \(0.650068\pi\)
\(632\) 2.99625 0.119184
\(633\) −14.2323 −0.565682
\(634\) 28.0311 1.11326
\(635\) 26.4020 1.04773
\(636\) −0.479321 −0.0190063
\(637\) −82.9912 −3.28823
\(638\) −7.78539 −0.308227
\(639\) 8.06263 0.318953
\(640\) 4.36977 0.172730
\(641\) 3.55614 0.140459 0.0702295 0.997531i \(-0.477627\pi\)
0.0702295 + 0.997531i \(0.477627\pi\)
\(642\) 1.80234 0.0711328
\(643\) −33.1329 −1.30664 −0.653318 0.757084i \(-0.726623\pi\)
−0.653318 + 0.757084i \(0.726623\pi\)
\(644\) −34.5889 −1.36299
\(645\) −39.3837 −1.55073
\(646\) −23.6025 −0.928629
\(647\) −47.9054 −1.88335 −0.941677 0.336517i \(-0.890751\pi\)
−0.941677 + 0.336517i \(0.890751\pi\)
\(648\) 1.00000 0.0392837
\(649\) 7.96627 0.312703
\(650\) −87.0161 −3.41305
\(651\) −5.78864 −0.226875
\(652\) −15.6757 −0.613909
\(653\) 24.6014 0.962728 0.481364 0.876521i \(-0.340142\pi\)
0.481364 + 0.876521i \(0.340142\pi\)
\(654\) 4.31978 0.168917
\(655\) −1.92609 −0.0752584
\(656\) 9.12644 0.356328
\(657\) −6.83739 −0.266752
\(658\) −3.45770 −0.134795
\(659\) −4.11041 −0.160119 −0.0800594 0.996790i \(-0.525511\pi\)
−0.0800594 + 0.996790i \(0.525511\pi\)
\(660\) 4.36977 0.170093
\(661\) 34.2325 1.33149 0.665744 0.746180i \(-0.268114\pi\)
0.665744 + 0.746180i \(0.268114\pi\)
\(662\) 11.8382 0.460104
\(663\) −26.9691 −1.04739
\(664\) −12.1436 −0.471265
\(665\) −106.748 −4.13950
\(666\) −0.611833 −0.0237081
\(667\) 59.5587 2.30612
\(668\) −3.55356 −0.137491
\(669\) −6.11859 −0.236558
\(670\) −26.9313 −1.04045
\(671\) −1.00000 −0.0386046
\(672\) 4.52139 0.174416
\(673\) 21.9016 0.844246 0.422123 0.906539i \(-0.361285\pi\)
0.422123 + 0.906539i \(0.361285\pi\)
\(674\) 1.26199 0.0486100
\(675\) 14.0949 0.542514
\(676\) 25.1130 0.965885
\(677\) 43.4742 1.67085 0.835425 0.549605i \(-0.185222\pi\)
0.835425 + 0.549605i \(0.185222\pi\)
\(678\) 6.52957 0.250767
\(679\) −55.7256 −2.13855
\(680\) 19.0893 0.732041
\(681\) 11.2276 0.430242
\(682\) −1.28028 −0.0490244
\(683\) −8.33634 −0.318981 −0.159491 0.987199i \(-0.550985\pi\)
−0.159491 + 0.987199i \(0.550985\pi\)
\(684\) −5.40291 −0.206585
\(685\) −101.632 −3.88318
\(686\) 29.1313 1.11224
\(687\) 19.3616 0.738690
\(688\) −9.01275 −0.343608
\(689\) 2.95912 0.112734
\(690\) −33.4290 −1.27262
\(691\) 9.30293 0.353900 0.176950 0.984220i \(-0.443377\pi\)
0.176950 + 0.984220i \(0.443377\pi\)
\(692\) 10.0811 0.383225
\(693\) 4.52139 0.171753
\(694\) −8.59566 −0.326287
\(695\) −71.5173 −2.71280
\(696\) −7.78539 −0.295105
\(697\) 39.8687 1.51013
\(698\) 15.7282 0.595322
\(699\) 5.77018 0.218248
\(700\) 63.7287 2.40872
\(701\) −14.6044 −0.551601 −0.275800 0.961215i \(-0.588943\pi\)
−0.275800 + 0.961215i \(0.588943\pi\)
\(702\) −6.17357 −0.233006
\(703\) 3.30568 0.124676
\(704\) 1.00000 0.0376889
\(705\) −3.34175 −0.125858
\(706\) 34.0373 1.28101
\(707\) −71.3647 −2.68395
\(708\) 7.96627 0.299391
\(709\) 25.6703 0.964067 0.482034 0.876153i \(-0.339898\pi\)
0.482034 + 0.876153i \(0.339898\pi\)
\(710\) 35.2319 1.32223
\(711\) 2.99625 0.112368
\(712\) 10.2015 0.382319
\(713\) 9.79420 0.366796
\(714\) 19.7516 0.739186
\(715\) −26.9771 −1.00889
\(716\) 16.8091 0.628187
\(717\) 21.9886 0.821180
\(718\) −27.7906 −1.03714
\(719\) −32.1358 −1.19846 −0.599231 0.800576i \(-0.704527\pi\)
−0.599231 + 0.800576i \(0.704527\pi\)
\(720\) 4.36977 0.162852
\(721\) −14.5580 −0.542168
\(722\) 10.1914 0.379286
\(723\) 7.82691 0.291086
\(724\) −12.7394 −0.473457
\(725\) −109.735 −4.07544
\(726\) 1.00000 0.0371135
\(727\) 30.2279 1.12109 0.560545 0.828124i \(-0.310592\pi\)
0.560545 + 0.828124i \(0.310592\pi\)
\(728\) −27.9131 −1.03453
\(729\) 1.00000 0.0370370
\(730\) −29.8778 −1.10583
\(731\) −39.3720 −1.45623
\(732\) −1.00000 −0.0369611
\(733\) 30.7308 1.13507 0.567533 0.823350i \(-0.307898\pi\)
0.567533 + 0.823350i \(0.307898\pi\)
\(734\) 18.3450 0.677126
\(735\) 58.7428 2.16676
\(736\) −7.65005 −0.281985
\(737\) −6.16309 −0.227020
\(738\) 9.12644 0.335949
\(739\) 13.4294 0.494009 0.247005 0.969014i \(-0.420554\pi\)
0.247005 + 0.969014i \(0.420554\pi\)
\(740\) −2.67357 −0.0982825
\(741\) 33.3553 1.22534
\(742\) −2.16720 −0.0795603
\(743\) 0.0383888 0.00140835 0.000704174 1.00000i \(-0.499776\pi\)
0.000704174 1.00000i \(0.499776\pi\)
\(744\) −1.28028 −0.0469373
\(745\) 34.0869 1.24885
\(746\) 32.5317 1.19107
\(747\) −12.1436 −0.444313
\(748\) 4.36848 0.159728
\(749\) 8.14909 0.297761
\(750\) 39.7428 1.45120
\(751\) −2.62026 −0.0956147 −0.0478073 0.998857i \(-0.515223\pi\)
−0.0478073 + 0.998857i \(0.515223\pi\)
\(752\) −0.764742 −0.0278873
\(753\) −14.2970 −0.521012
\(754\) 48.0637 1.75038
\(755\) 89.9136 3.27229
\(756\) 4.52139 0.164441
\(757\) 5.00749 0.182000 0.0910002 0.995851i \(-0.470994\pi\)
0.0910002 + 0.995851i \(0.470994\pi\)
\(758\) 15.5430 0.564549
\(759\) −7.65005 −0.277679
\(760\) −23.6095 −0.856406
\(761\) −45.7775 −1.65943 −0.829716 0.558186i \(-0.811497\pi\)
−0.829716 + 0.558186i \(0.811497\pi\)
\(762\) 6.04195 0.218877
\(763\) 19.5314 0.707085
\(764\) −11.0407 −0.399439
\(765\) 19.0893 0.690175
\(766\) 22.9515 0.829270
\(767\) −49.1803 −1.77580
\(768\) 1.00000 0.0360844
\(769\) −2.43051 −0.0876465 −0.0438232 0.999039i \(-0.513954\pi\)
−0.0438232 + 0.999039i \(0.513954\pi\)
\(770\) 19.7575 0.712009
\(771\) −11.8679 −0.427411
\(772\) 2.31091 0.0831715
\(773\) −29.1472 −1.04835 −0.524176 0.851610i \(-0.675627\pi\)
−0.524176 + 0.851610i \(0.675627\pi\)
\(774\) −9.01275 −0.323956
\(775\) −18.0454 −0.648211
\(776\) −12.3249 −0.442437
\(777\) −2.76634 −0.0992418
\(778\) 13.3563 0.478845
\(779\) −49.3093 −1.76669
\(780\) −26.9771 −0.965936
\(781\) 8.06263 0.288504
\(782\) −33.4191 −1.19507
\(783\) −7.78539 −0.278227
\(784\) 13.4430 0.480107
\(785\) 37.2295 1.32878
\(786\) −0.440775 −0.0157219
\(787\) −9.04595 −0.322453 −0.161227 0.986917i \(-0.551545\pi\)
−0.161227 + 0.986917i \(0.551545\pi\)
\(788\) −19.4329 −0.692267
\(789\) −0.830033 −0.0295500
\(790\) 13.0929 0.465825
\(791\) 29.5227 1.04971
\(792\) 1.00000 0.0355335
\(793\) 6.17357 0.219230
\(794\) −8.33191 −0.295688
\(795\) −2.09452 −0.0742851
\(796\) 9.49175 0.336426
\(797\) 9.03872 0.320168 0.160084 0.987103i \(-0.448824\pi\)
0.160084 + 0.987103i \(0.448824\pi\)
\(798\) −24.4287 −0.864765
\(799\) −3.34076 −0.118188
\(800\) 14.0949 0.498331
\(801\) 10.2015 0.360454
\(802\) 21.1298 0.746118
\(803\) −6.83739 −0.241286
\(804\) −6.16309 −0.217355
\(805\) −151.146 −5.32718
\(806\) 7.90389 0.278403
\(807\) 2.06778 0.0727895
\(808\) −15.7838 −0.555272
\(809\) 6.99022 0.245763 0.122882 0.992421i \(-0.460786\pi\)
0.122882 + 0.992421i \(0.460786\pi\)
\(810\) 4.36977 0.153538
\(811\) 13.4533 0.472409 0.236205 0.971703i \(-0.424096\pi\)
0.236205 + 0.971703i \(0.424096\pi\)
\(812\) −35.2008 −1.23531
\(813\) 18.7718 0.658357
\(814\) −0.611833 −0.0214447
\(815\) −68.4994 −2.39943
\(816\) 4.36848 0.152927
\(817\) 48.6950 1.70362
\(818\) −21.2533 −0.743104
\(819\) −27.9131 −0.975364
\(820\) 39.8805 1.39269
\(821\) −33.5662 −1.17147 −0.585734 0.810503i \(-0.699194\pi\)
−0.585734 + 0.810503i \(0.699194\pi\)
\(822\) −23.2581 −0.811218
\(823\) −0.780631 −0.0272111 −0.0136055 0.999907i \(-0.504331\pi\)
−0.0136055 + 0.999907i \(0.504331\pi\)
\(824\) −3.21980 −0.112167
\(825\) 14.0949 0.490722
\(826\) 36.0186 1.25325
\(827\) −26.9147 −0.935916 −0.467958 0.883751i \(-0.655010\pi\)
−0.467958 + 0.883751i \(0.655010\pi\)
\(828\) −7.65005 −0.265858
\(829\) −32.4821 −1.12815 −0.564074 0.825724i \(-0.690767\pi\)
−0.564074 + 0.825724i \(0.690767\pi\)
\(830\) −53.0650 −1.84191
\(831\) −23.7427 −0.823624
\(832\) −6.17357 −0.214030
\(833\) 58.7254 2.03472
\(834\) −16.3664 −0.566720
\(835\) −15.5282 −0.537377
\(836\) −5.40291 −0.186864
\(837\) −1.28028 −0.0442529
\(838\) 3.08019 0.106403
\(839\) −2.68221 −0.0926002 −0.0463001 0.998928i \(-0.514743\pi\)
−0.0463001 + 0.998928i \(0.514743\pi\)
\(840\) 19.7575 0.681697
\(841\) 31.6123 1.09008
\(842\) −16.1588 −0.556870
\(843\) 15.2565 0.525462
\(844\) −14.2323 −0.489895
\(845\) 109.738 3.77511
\(846\) −0.764742 −0.0262924
\(847\) 4.52139 0.155357
\(848\) −0.479321 −0.0164599
\(849\) 10.0897 0.346278
\(850\) 61.5734 2.11195
\(851\) 4.68056 0.160447
\(852\) 8.06263 0.276221
\(853\) −17.0441 −0.583577 −0.291789 0.956483i \(-0.594250\pi\)
−0.291789 + 0.956483i \(0.594250\pi\)
\(854\) −4.52139 −0.154719
\(855\) −23.6095 −0.807428
\(856\) 1.80234 0.0616028
\(857\) −38.8172 −1.32597 −0.662985 0.748633i \(-0.730711\pi\)
−0.662985 + 0.748633i \(0.730711\pi\)
\(858\) −6.17357 −0.210762
\(859\) 17.5011 0.597130 0.298565 0.954389i \(-0.403492\pi\)
0.298565 + 0.954389i \(0.403492\pi\)
\(860\) −39.3837 −1.34297
\(861\) 41.2642 1.40628
\(862\) −5.91170 −0.201353
\(863\) 24.5863 0.836928 0.418464 0.908233i \(-0.362569\pi\)
0.418464 + 0.908233i \(0.362569\pi\)
\(864\) 1.00000 0.0340207
\(865\) 44.0521 1.49781
\(866\) 5.07766 0.172546
\(867\) 2.08364 0.0707642
\(868\) −5.78864 −0.196479
\(869\) 2.99625 0.101641
\(870\) −34.0204 −1.15340
\(871\) 38.0483 1.28922
\(872\) 4.31978 0.146286
\(873\) −12.3249 −0.417134
\(874\) 41.3325 1.39809
\(875\) 179.693 6.07472
\(876\) −6.83739 −0.231014
\(877\) −46.5387 −1.57150 −0.785749 0.618545i \(-0.787722\pi\)
−0.785749 + 0.618545i \(0.787722\pi\)
\(878\) 15.8377 0.534497
\(879\) −22.1467 −0.746989
\(880\) 4.36977 0.147305
\(881\) −4.66697 −0.157234 −0.0786171 0.996905i \(-0.525050\pi\)
−0.0786171 + 0.996905i \(0.525050\pi\)
\(882\) 13.4430 0.452649
\(883\) 30.6222 1.03052 0.515259 0.857034i \(-0.327696\pi\)
0.515259 + 0.857034i \(0.327696\pi\)
\(884\) −26.9691 −0.907071
\(885\) 34.8108 1.17015
\(886\) −14.2435 −0.478520
\(887\) −30.6653 −1.02964 −0.514820 0.857298i \(-0.672141\pi\)
−0.514820 + 0.857298i \(0.672141\pi\)
\(888\) −0.611833 −0.0205318
\(889\) 27.3180 0.916218
\(890\) 44.5784 1.49427
\(891\) 1.00000 0.0335013
\(892\) −6.11859 −0.204865
\(893\) 4.13183 0.138267
\(894\) 7.80061 0.260892
\(895\) 73.4521 2.45523
\(896\) 4.52139 0.151049
\(897\) 47.2282 1.57690
\(898\) 5.96861 0.199175
\(899\) 9.96747 0.332434
\(900\) 14.0949 0.469831
\(901\) −2.09390 −0.0697581
\(902\) 9.12644 0.303877
\(903\) −40.7502 −1.35608
\(904\) 6.52957 0.217170
\(905\) −55.6684 −1.85048
\(906\) 20.5763 0.683600
\(907\) 11.2629 0.373978 0.186989 0.982362i \(-0.440127\pi\)
0.186989 + 0.982362i \(0.440127\pi\)
\(908\) 11.2276 0.372600
\(909\) −15.7838 −0.523515
\(910\) −121.974 −4.04340
\(911\) −32.0029 −1.06030 −0.530152 0.847903i \(-0.677865\pi\)
−0.530152 + 0.847903i \(0.677865\pi\)
\(912\) −5.40291 −0.178908
\(913\) −12.1436 −0.401896
\(914\) 17.9080 0.592343
\(915\) −4.36977 −0.144460
\(916\) 19.3616 0.639724
\(917\) −1.99292 −0.0658119
\(918\) 4.36848 0.144181
\(919\) −18.3317 −0.604708 −0.302354 0.953196i \(-0.597773\pi\)
−0.302354 + 0.953196i \(0.597773\pi\)
\(920\) −33.4290 −1.10212
\(921\) 2.13389 0.0703142
\(922\) −31.1703 −1.02654
\(923\) −49.7752 −1.63837
\(924\) 4.52139 0.148743
\(925\) −8.62375 −0.283547
\(926\) −23.2553 −0.764217
\(927\) −3.21980 −0.105752
\(928\) −7.78539 −0.255568
\(929\) 55.9316 1.83506 0.917528 0.397672i \(-0.130182\pi\)
0.917528 + 0.397672i \(0.130182\pi\)
\(930\) −5.59453 −0.183452
\(931\) −72.6312 −2.38039
\(932\) 5.77018 0.189009
\(933\) 13.5648 0.444092
\(934\) −35.0717 −1.14758
\(935\) 19.0893 0.624286
\(936\) −6.17357 −0.201790
\(937\) −36.6902 −1.19862 −0.599309 0.800518i \(-0.704558\pi\)
−0.599309 + 0.800518i \(0.704558\pi\)
\(938\) −27.8657 −0.909848
\(939\) 6.44538 0.210337
\(940\) −3.34175 −0.108996
\(941\) 52.2649 1.70379 0.851893 0.523716i \(-0.175455\pi\)
0.851893 + 0.523716i \(0.175455\pi\)
\(942\) 8.51977 0.277589
\(943\) −69.8177 −2.27358
\(944\) 7.96627 0.259280
\(945\) 19.7575 0.642710
\(946\) −9.01275 −0.293030
\(947\) −28.7089 −0.932915 −0.466457 0.884544i \(-0.654470\pi\)
−0.466457 + 0.884544i \(0.654470\pi\)
\(948\) 2.99625 0.0973136
\(949\) 42.2111 1.37023
\(950\) −76.1536 −2.47075
\(951\) 28.0311 0.908970
\(952\) 19.7516 0.640154
\(953\) −54.9641 −1.78046 −0.890230 0.455511i \(-0.849457\pi\)
−0.890230 + 0.455511i \(0.849457\pi\)
\(954\) −0.479321 −0.0155186
\(955\) −48.2454 −1.56118
\(956\) 21.9886 0.711162
\(957\) −7.78539 −0.251666
\(958\) −13.2527 −0.428177
\(959\) −105.159 −3.39576
\(960\) 4.36977 0.141034
\(961\) −29.3609 −0.947125
\(962\) 3.77720 0.121782
\(963\) 1.80234 0.0580797
\(964\) 7.82691 0.252088
\(965\) 10.0982 0.325071
\(966\) −34.5889 −1.11288
\(967\) −11.7674 −0.378415 −0.189208 0.981937i \(-0.560592\pi\)
−0.189208 + 0.981937i \(0.560592\pi\)
\(968\) 1.00000 0.0321412
\(969\) −23.6025 −0.758222
\(970\) −53.8569 −1.72924
\(971\) 26.4661 0.849338 0.424669 0.905349i \(-0.360391\pi\)
0.424669 + 0.905349i \(0.360391\pi\)
\(972\) 1.00000 0.0320750
\(973\) −73.9987 −2.37229
\(974\) 25.7716 0.825774
\(975\) −87.0161 −2.78674
\(976\) −1.00000 −0.0320092
\(977\) 27.5807 0.882386 0.441193 0.897412i \(-0.354555\pi\)
0.441193 + 0.897412i \(0.354555\pi\)
\(978\) −15.6757 −0.501255
\(979\) 10.2015 0.326043
\(980\) 58.7428 1.87647
\(981\) 4.31978 0.137920
\(982\) −25.1818 −0.803585
\(983\) 7.46974 0.238248 0.119124 0.992879i \(-0.461991\pi\)
0.119124 + 0.992879i \(0.461991\pi\)
\(984\) 9.12644 0.290940
\(985\) −84.9173 −2.70569
\(986\) −34.0104 −1.08311
\(987\) −3.45770 −0.110060
\(988\) 33.3553 1.06117
\(989\) 68.9480 2.19242
\(990\) 4.36977 0.138881
\(991\) 6.76266 0.214823 0.107412 0.994215i \(-0.465744\pi\)
0.107412 + 0.994215i \(0.465744\pi\)
\(992\) −1.28028 −0.0406489
\(993\) 11.8382 0.375673
\(994\) 36.4543 1.15626
\(995\) 41.4768 1.31490
\(996\) −12.1436 −0.384786
\(997\) 50.8630 1.61085 0.805423 0.592700i \(-0.201938\pi\)
0.805423 + 0.592700i \(0.201938\pi\)
\(998\) −7.95322 −0.251755
\(999\) −0.611833 −0.0193576
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 \(a_p\))