Properties

Label 4026.2.a.bc.1.8
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 1.8
Root \(-2.63661\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.63661 q^{5}\) \(+1.00000 q^{6}\) \(-1.65542 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.63661 q^{5}\) \(+1.00000 q^{6}\) \(-1.65542 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.63661 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(+6.43612 q^{13}\) \(-1.65542 q^{14}\) \(+3.63661 q^{15}\) \(+1.00000 q^{16}\) \(-1.11715 q^{17}\) \(+1.00000 q^{18}\) \(-5.55489 q^{19}\) \(+3.63661 q^{20}\) \(-1.65542 q^{21}\) \(+1.00000 q^{22}\) \(-3.64436 q^{23}\) \(+1.00000 q^{24}\) \(+8.22493 q^{25}\) \(+6.43612 q^{26}\) \(+1.00000 q^{27}\) \(-1.65542 q^{28}\) \(-1.74243 q^{29}\) \(+3.63661 q^{30}\) \(+1.99225 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(-1.11715 q^{34}\) \(-6.02012 q^{35}\) \(+1.00000 q^{36}\) \(+10.6804 q^{37}\) \(-5.55489 q^{38}\) \(+6.43612 q^{39}\) \(+3.63661 q^{40}\) \(-3.65909 q^{41}\) \(-1.65542 q^{42}\) \(+6.64405 q^{43}\) \(+1.00000 q^{44}\) \(+3.63661 q^{45}\) \(-3.64436 q^{46}\) \(+11.2187 q^{47}\) \(+1.00000 q^{48}\) \(-4.25958 q^{49}\) \(+8.22493 q^{50}\) \(-1.11715 q^{51}\) \(+6.43612 q^{52}\) \(-7.64051 q^{53}\) \(+1.00000 q^{54}\) \(+3.63661 q^{55}\) \(-1.65542 q^{56}\) \(-5.55489 q^{57}\) \(-1.74243 q^{58}\) \(-0.0748538 q^{59}\) \(+3.63661 q^{60}\) \(-1.00000 q^{61}\) \(+1.99225 q^{62}\) \(-1.65542 q^{63}\) \(+1.00000 q^{64}\) \(+23.4056 q^{65}\) \(+1.00000 q^{66}\) \(-13.9718 q^{67}\) \(-1.11715 q^{68}\) \(-3.64436 q^{69}\) \(-6.02012 q^{70}\) \(-5.87217 q^{71}\) \(+1.00000 q^{72}\) \(-7.77814 q^{73}\) \(+10.6804 q^{74}\) \(+8.22493 q^{75}\) \(-5.55489 q^{76}\) \(-1.65542 q^{77}\) \(+6.43612 q^{78}\) \(+1.55257 q^{79}\) \(+3.63661 q^{80}\) \(+1.00000 q^{81}\) \(-3.65909 q^{82}\) \(+15.0909 q^{83}\) \(-1.65542 q^{84}\) \(-4.06265 q^{85}\) \(+6.64405 q^{86}\) \(-1.74243 q^{87}\) \(+1.00000 q^{88}\) \(-3.71513 q^{89}\) \(+3.63661 q^{90}\) \(-10.6545 q^{91}\) \(-3.64436 q^{92}\) \(+1.99225 q^{93}\) \(+11.2187 q^{94}\) \(-20.2010 q^{95}\) \(+1.00000 q^{96}\) \(+11.9593 q^{97}\) \(-4.25958 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 3.63661 1.62634 0.813171 0.582026i \(-0.197740\pi\)
0.813171 + 0.582026i \(0.197740\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.65542 −0.625690 −0.312845 0.949804i \(-0.601282\pi\)
−0.312845 + 0.949804i \(0.601282\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 3.63661 1.15000
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 6.43612 1.78506 0.892529 0.450991i \(-0.148929\pi\)
0.892529 + 0.450991i \(0.148929\pi\)
\(14\) −1.65542 −0.442430
\(15\) 3.63661 0.938968
\(16\) 1.00000 0.250000
\(17\) −1.11715 −0.270950 −0.135475 0.990781i \(-0.543256\pi\)
−0.135475 + 0.990781i \(0.543256\pi\)
\(18\) 1.00000 0.235702
\(19\) −5.55489 −1.27438 −0.637190 0.770707i \(-0.719903\pi\)
−0.637190 + 0.770707i \(0.719903\pi\)
\(20\) 3.63661 0.813171
\(21\) −1.65542 −0.361243
\(22\) 1.00000 0.213201
\(23\) −3.64436 −0.759901 −0.379951 0.925007i \(-0.624059\pi\)
−0.379951 + 0.925007i \(0.624059\pi\)
\(24\) 1.00000 0.204124
\(25\) 8.22493 1.64499
\(26\) 6.43612 1.26223
\(27\) 1.00000 0.192450
\(28\) −1.65542 −0.312845
\(29\) −1.74243 −0.323561 −0.161780 0.986827i \(-0.551724\pi\)
−0.161780 + 0.986827i \(0.551724\pi\)
\(30\) 3.63661 0.663951
\(31\) 1.99225 0.357819 0.178909 0.983866i \(-0.442743\pi\)
0.178909 + 0.983866i \(0.442743\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −1.11715 −0.191590
\(35\) −6.02012 −1.01759
\(36\) 1.00000 0.166667
\(37\) 10.6804 1.75585 0.877924 0.478801i \(-0.158928\pi\)
0.877924 + 0.478801i \(0.158928\pi\)
\(38\) −5.55489 −0.901122
\(39\) 6.43612 1.03060
\(40\) 3.63661 0.574998
\(41\) −3.65909 −0.571454 −0.285727 0.958311i \(-0.592235\pi\)
−0.285727 + 0.958311i \(0.592235\pi\)
\(42\) −1.65542 −0.255437
\(43\) 6.64405 1.01321 0.506604 0.862179i \(-0.330901\pi\)
0.506604 + 0.862179i \(0.330901\pi\)
\(44\) 1.00000 0.150756
\(45\) 3.63661 0.542114
\(46\) −3.64436 −0.537331
\(47\) 11.2187 1.63641 0.818205 0.574926i \(-0.194969\pi\)
0.818205 + 0.574926i \(0.194969\pi\)
\(48\) 1.00000 0.144338
\(49\) −4.25958 −0.608511
\(50\) 8.22493 1.16318
\(51\) −1.11715 −0.156433
\(52\) 6.43612 0.892529
\(53\) −7.64051 −1.04951 −0.524753 0.851255i \(-0.675842\pi\)
−0.524753 + 0.851255i \(0.675842\pi\)
\(54\) 1.00000 0.136083
\(55\) 3.63661 0.490360
\(56\) −1.65542 −0.221215
\(57\) −5.55489 −0.735763
\(58\) −1.74243 −0.228792
\(59\) −0.0748538 −0.00974514 −0.00487257 0.999988i \(-0.501551\pi\)
−0.00487257 + 0.999988i \(0.501551\pi\)
\(60\) 3.63661 0.469484
\(61\) −1.00000 −0.128037
\(62\) 1.99225 0.253016
\(63\) −1.65542 −0.208563
\(64\) 1.00000 0.125000
\(65\) 23.4056 2.90311
\(66\) 1.00000 0.123091
\(67\) −13.9718 −1.70693 −0.853465 0.521150i \(-0.825503\pi\)
−0.853465 + 0.521150i \(0.825503\pi\)
\(68\) −1.11715 −0.135475
\(69\) −3.64436 −0.438729
\(70\) −6.02012 −0.719542
\(71\) −5.87217 −0.696899 −0.348449 0.937328i \(-0.613292\pi\)
−0.348449 + 0.937328i \(0.613292\pi\)
\(72\) 1.00000 0.117851
\(73\) −7.77814 −0.910362 −0.455181 0.890399i \(-0.650425\pi\)
−0.455181 + 0.890399i \(0.650425\pi\)
\(74\) 10.6804 1.24157
\(75\) 8.22493 0.949733
\(76\) −5.55489 −0.637190
\(77\) −1.65542 −0.188653
\(78\) 6.43612 0.728747
\(79\) 1.55257 0.174677 0.0873387 0.996179i \(-0.472164\pi\)
0.0873387 + 0.996179i \(0.472164\pi\)
\(80\) 3.63661 0.406585
\(81\) 1.00000 0.111111
\(82\) −3.65909 −0.404079
\(83\) 15.0909 1.65644 0.828222 0.560399i \(-0.189352\pi\)
0.828222 + 0.560399i \(0.189352\pi\)
\(84\) −1.65542 −0.180621
\(85\) −4.06265 −0.440657
\(86\) 6.64405 0.716446
\(87\) −1.74243 −0.186808
\(88\) 1.00000 0.106600
\(89\) −3.71513 −0.393803 −0.196902 0.980423i \(-0.563088\pi\)
−0.196902 + 0.980423i \(0.563088\pi\)
\(90\) 3.63661 0.383332
\(91\) −10.6545 −1.11689
\(92\) −3.64436 −0.379951
\(93\) 1.99225 0.206587
\(94\) 11.2187 1.15712
\(95\) −20.2010 −2.07258
\(96\) 1.00000 0.102062
\(97\) 11.9593 1.21428 0.607141 0.794594i \(-0.292316\pi\)
0.607141 + 0.794594i \(0.292316\pi\)
\(98\) −4.25958 −0.430283
\(99\) 1.00000 0.100504
\(100\) 8.22493 0.822493
\(101\) 1.24249 0.123632 0.0618161 0.998088i \(-0.480311\pi\)
0.0618161 + 0.998088i \(0.480311\pi\)
\(102\) −1.11715 −0.110615
\(103\) −19.1188 −1.88384 −0.941918 0.335844i \(-0.890978\pi\)
−0.941918 + 0.335844i \(0.890978\pi\)
\(104\) 6.43612 0.631113
\(105\) −6.02012 −0.587504
\(106\) −7.64051 −0.742112
\(107\) −6.86786 −0.663941 −0.331971 0.943290i \(-0.607713\pi\)
−0.331971 + 0.943290i \(0.607713\pi\)
\(108\) 1.00000 0.0962250
\(109\) 2.33976 0.224108 0.112054 0.993702i \(-0.464257\pi\)
0.112054 + 0.993702i \(0.464257\pi\)
\(110\) 3.63661 0.346737
\(111\) 10.6804 1.01374
\(112\) −1.65542 −0.156423
\(113\) 13.9624 1.31347 0.656736 0.754120i \(-0.271937\pi\)
0.656736 + 0.754120i \(0.271937\pi\)
\(114\) −5.55489 −0.520263
\(115\) −13.2531 −1.23586
\(116\) −1.74243 −0.161780
\(117\) 6.43612 0.595019
\(118\) −0.0748538 −0.00689085
\(119\) 1.84936 0.169531
\(120\) 3.63661 0.331975
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) −3.65909 −0.329929
\(124\) 1.99225 0.178909
\(125\) 11.7278 1.04897
\(126\) −1.65542 −0.147477
\(127\) −9.26320 −0.821976 −0.410988 0.911641i \(-0.634816\pi\)
−0.410988 + 0.911641i \(0.634816\pi\)
\(128\) 1.00000 0.0883883
\(129\) 6.64405 0.584976
\(130\) 23.4056 2.05281
\(131\) −11.9435 −1.04351 −0.521756 0.853095i \(-0.674723\pi\)
−0.521756 + 0.853095i \(0.674723\pi\)
\(132\) 1.00000 0.0870388
\(133\) 9.19568 0.797367
\(134\) −13.9718 −1.20698
\(135\) 3.63661 0.312989
\(136\) −1.11715 −0.0957952
\(137\) 19.9918 1.70802 0.854008 0.520260i \(-0.174165\pi\)
0.854008 + 0.520260i \(0.174165\pi\)
\(138\) −3.64436 −0.310228
\(139\) −2.90764 −0.246623 −0.123311 0.992368i \(-0.539351\pi\)
−0.123311 + 0.992368i \(0.539351\pi\)
\(140\) −6.02012 −0.508793
\(141\) 11.2187 0.944782
\(142\) −5.87217 −0.492782
\(143\) 6.43612 0.538215
\(144\) 1.00000 0.0833333
\(145\) −6.33653 −0.526220
\(146\) −7.77814 −0.643723
\(147\) −4.25958 −0.351324
\(148\) 10.6804 0.877924
\(149\) −15.0404 −1.23215 −0.616077 0.787686i \(-0.711279\pi\)
−0.616077 + 0.787686i \(0.711279\pi\)
\(150\) 8.22493 0.671562
\(151\) −14.3901 −1.17105 −0.585526 0.810654i \(-0.699112\pi\)
−0.585526 + 0.810654i \(0.699112\pi\)
\(152\) −5.55489 −0.450561
\(153\) −1.11715 −0.0903166
\(154\) −1.65542 −0.133398
\(155\) 7.24504 0.581935
\(156\) 6.43612 0.515302
\(157\) −1.62798 −0.129927 −0.0649635 0.997888i \(-0.520693\pi\)
−0.0649635 + 0.997888i \(0.520693\pi\)
\(158\) 1.55257 0.123516
\(159\) −7.64051 −0.605932
\(160\) 3.63661 0.287499
\(161\) 6.03295 0.475463
\(162\) 1.00000 0.0785674
\(163\) 20.7016 1.62147 0.810737 0.585410i \(-0.199066\pi\)
0.810737 + 0.585410i \(0.199066\pi\)
\(164\) −3.65909 −0.285727
\(165\) 3.63661 0.283110
\(166\) 15.0909 1.17128
\(167\) 1.30094 0.100670 0.0503349 0.998732i \(-0.483971\pi\)
0.0503349 + 0.998732i \(0.483971\pi\)
\(168\) −1.65542 −0.127719
\(169\) 28.4236 2.18643
\(170\) −4.06265 −0.311591
\(171\) −5.55489 −0.424793
\(172\) 6.64405 0.506604
\(173\) −24.3719 −1.85296 −0.926482 0.376340i \(-0.877182\pi\)
−0.926482 + 0.376340i \(0.877182\pi\)
\(174\) −1.74243 −0.132093
\(175\) −13.6157 −1.02925
\(176\) 1.00000 0.0753778
\(177\) −0.0748538 −0.00562636
\(178\) −3.71513 −0.278461
\(179\) 9.74345 0.728260 0.364130 0.931348i \(-0.381366\pi\)
0.364130 + 0.931348i \(0.381366\pi\)
\(180\) 3.63661 0.271057
\(181\) 11.1669 0.830030 0.415015 0.909815i \(-0.363776\pi\)
0.415015 + 0.909815i \(0.363776\pi\)
\(182\) −10.6545 −0.789763
\(183\) −1.00000 −0.0739221
\(184\) −3.64436 −0.268666
\(185\) 38.8404 2.85561
\(186\) 1.99225 0.146079
\(187\) −1.11715 −0.0816944
\(188\) 11.2187 0.818205
\(189\) −1.65542 −0.120414
\(190\) −20.2010 −1.46553
\(191\) −24.2346 −1.75356 −0.876779 0.480894i \(-0.840312\pi\)
−0.876779 + 0.480894i \(0.840312\pi\)
\(192\) 1.00000 0.0721688
\(193\) 3.02708 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(194\) 11.9593 0.858628
\(195\) 23.4056 1.67611
\(196\) −4.25958 −0.304256
\(197\) −13.1681 −0.938191 −0.469096 0.883147i \(-0.655420\pi\)
−0.469096 + 0.883147i \(0.655420\pi\)
\(198\) 1.00000 0.0710669
\(199\) −22.3693 −1.58572 −0.792860 0.609404i \(-0.791409\pi\)
−0.792860 + 0.609404i \(0.791409\pi\)
\(200\) 8.22493 0.581590
\(201\) −13.9718 −0.985497
\(202\) 1.24249 0.0874211
\(203\) 2.88445 0.202449
\(204\) −1.11715 −0.0782165
\(205\) −13.3067 −0.929379
\(206\) −19.1188 −1.33207
\(207\) −3.64436 −0.253300
\(208\) 6.43612 0.446264
\(209\) −5.55489 −0.384240
\(210\) −6.02012 −0.415428
\(211\) −3.82917 −0.263611 −0.131806 0.991276i \(-0.542077\pi\)
−0.131806 + 0.991276i \(0.542077\pi\)
\(212\) −7.64051 −0.524753
\(213\) −5.87217 −0.402355
\(214\) −6.86786 −0.469477
\(215\) 24.1618 1.64782
\(216\) 1.00000 0.0680414
\(217\) −3.29801 −0.223884
\(218\) 2.33976 0.158468
\(219\) −7.77814 −0.525598
\(220\) 3.63661 0.245180
\(221\) −7.19014 −0.483661
\(222\) 10.6804 0.716822
\(223\) 11.0856 0.742346 0.371173 0.928564i \(-0.378956\pi\)
0.371173 + 0.928564i \(0.378956\pi\)
\(224\) −1.65542 −0.110607
\(225\) 8.22493 0.548328
\(226\) 13.9624 0.928765
\(227\) 15.8836 1.05423 0.527116 0.849794i \(-0.323273\pi\)
0.527116 + 0.849794i \(0.323273\pi\)
\(228\) −5.55489 −0.367882
\(229\) 15.1029 0.998028 0.499014 0.866594i \(-0.333696\pi\)
0.499014 + 0.866594i \(0.333696\pi\)
\(230\) −13.2531 −0.873884
\(231\) −1.65542 −0.108919
\(232\) −1.74243 −0.114396
\(233\) 8.29255 0.543263 0.271631 0.962401i \(-0.412437\pi\)
0.271631 + 0.962401i \(0.412437\pi\)
\(234\) 6.43612 0.420742
\(235\) 40.7979 2.66136
\(236\) −0.0748538 −0.00487257
\(237\) 1.55257 0.100850
\(238\) 1.84936 0.119876
\(239\) 19.3939 1.25449 0.627245 0.778822i \(-0.284182\pi\)
0.627245 + 0.778822i \(0.284182\pi\)
\(240\) 3.63661 0.234742
\(241\) −1.41796 −0.0913387 −0.0456694 0.998957i \(-0.514542\pi\)
−0.0456694 + 0.998957i \(0.514542\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) −15.4904 −0.989647
\(246\) −3.65909 −0.233295
\(247\) −35.7519 −2.27484
\(248\) 1.99225 0.126508
\(249\) 15.0909 0.956349
\(250\) 11.7278 0.741731
\(251\) 7.12400 0.449663 0.224831 0.974398i \(-0.427817\pi\)
0.224831 + 0.974398i \(0.427817\pi\)
\(252\) −1.65542 −0.104282
\(253\) −3.64436 −0.229119
\(254\) −9.26320 −0.581225
\(255\) −4.06265 −0.254413
\(256\) 1.00000 0.0625000
\(257\) −11.5558 −0.720829 −0.360415 0.932792i \(-0.617365\pi\)
−0.360415 + 0.932792i \(0.617365\pi\)
\(258\) 6.64405 0.413640
\(259\) −17.6806 −1.09862
\(260\) 23.4056 1.45156
\(261\) −1.74243 −0.107854
\(262\) −11.9435 −0.737875
\(263\) −0.693770 −0.0427797 −0.0213898 0.999771i \(-0.506809\pi\)
−0.0213898 + 0.999771i \(0.506809\pi\)
\(264\) 1.00000 0.0615457
\(265\) −27.7856 −1.70685
\(266\) 9.19568 0.563824
\(267\) −3.71513 −0.227362
\(268\) −13.9718 −0.853465
\(269\) 8.18407 0.498992 0.249496 0.968376i \(-0.419735\pi\)
0.249496 + 0.968376i \(0.419735\pi\)
\(270\) 3.63661 0.221317
\(271\) 4.99753 0.303578 0.151789 0.988413i \(-0.451497\pi\)
0.151789 + 0.988413i \(0.451497\pi\)
\(272\) −1.11715 −0.0677374
\(273\) −10.6545 −0.644839
\(274\) 19.9918 1.20775
\(275\) 8.22493 0.495982
\(276\) −3.64436 −0.219365
\(277\) −2.65986 −0.159815 −0.0799077 0.996802i \(-0.525463\pi\)
−0.0799077 + 0.996802i \(0.525463\pi\)
\(278\) −2.90764 −0.174389
\(279\) 1.99225 0.119273
\(280\) −6.02012 −0.359771
\(281\) −22.2999 −1.33030 −0.665152 0.746708i \(-0.731633\pi\)
−0.665152 + 0.746708i \(0.731633\pi\)
\(282\) 11.2187 0.668062
\(283\) −22.3131 −1.32638 −0.663189 0.748452i \(-0.730797\pi\)
−0.663189 + 0.748452i \(0.730797\pi\)
\(284\) −5.87217 −0.348449
\(285\) −20.2010 −1.19660
\(286\) 6.43612 0.380575
\(287\) 6.05734 0.357553
\(288\) 1.00000 0.0589256
\(289\) −15.7520 −0.926586
\(290\) −6.33653 −0.372094
\(291\) 11.9593 0.701066
\(292\) −7.77814 −0.455181
\(293\) 22.0617 1.28886 0.644429 0.764664i \(-0.277095\pi\)
0.644429 + 0.764664i \(0.277095\pi\)
\(294\) −4.25958 −0.248424
\(295\) −0.272214 −0.0158489
\(296\) 10.6804 0.620786
\(297\) 1.00000 0.0580259
\(298\) −15.0404 −0.871265
\(299\) −23.4555 −1.35647
\(300\) 8.22493 0.474866
\(301\) −10.9987 −0.633954
\(302\) −14.3901 −0.828058
\(303\) 1.24249 0.0713790
\(304\) −5.55489 −0.318595
\(305\) −3.63661 −0.208232
\(306\) −1.11715 −0.0638635
\(307\) −25.4026 −1.44980 −0.724902 0.688852i \(-0.758115\pi\)
−0.724902 + 0.688852i \(0.758115\pi\)
\(308\) −1.65542 −0.0943264
\(309\) −19.1188 −1.08763
\(310\) 7.24504 0.411490
\(311\) −4.07486 −0.231064 −0.115532 0.993304i \(-0.536857\pi\)
−0.115532 + 0.993304i \(0.536857\pi\)
\(312\) 6.43612 0.364373
\(313\) 9.02954 0.510380 0.255190 0.966891i \(-0.417862\pi\)
0.255190 + 0.966891i \(0.417862\pi\)
\(314\) −1.62798 −0.0918723
\(315\) −6.02012 −0.339195
\(316\) 1.55257 0.0873387
\(317\) 16.4782 0.925509 0.462755 0.886486i \(-0.346861\pi\)
0.462755 + 0.886486i \(0.346861\pi\)
\(318\) −7.64051 −0.428459
\(319\) −1.74243 −0.0975573
\(320\) 3.63661 0.203293
\(321\) −6.86786 −0.383327
\(322\) 6.03295 0.336203
\(323\) 6.20567 0.345293
\(324\) 1.00000 0.0555556
\(325\) 52.9366 2.93639
\(326\) 20.7016 1.14656
\(327\) 2.33976 0.129389
\(328\) −3.65909 −0.202039
\(329\) −18.5716 −1.02389
\(330\) 3.63661 0.200189
\(331\) −28.0374 −1.54108 −0.770538 0.637394i \(-0.780012\pi\)
−0.770538 + 0.637394i \(0.780012\pi\)
\(332\) 15.0909 0.828222
\(333\) 10.6804 0.585282
\(334\) 1.30094 0.0711842
\(335\) −50.8101 −2.77605
\(336\) −1.65542 −0.0903106
\(337\) 1.51410 0.0824785 0.0412392 0.999149i \(-0.486869\pi\)
0.0412392 + 0.999149i \(0.486869\pi\)
\(338\) 28.4236 1.54604
\(339\) 13.9624 0.758334
\(340\) −4.06265 −0.220328
\(341\) 1.99225 0.107886
\(342\) −5.55489 −0.300374
\(343\) 18.6393 1.00643
\(344\) 6.64405 0.358223
\(345\) −13.2531 −0.713523
\(346\) −24.3719 −1.31024
\(347\) −35.7721 −1.92034 −0.960172 0.279409i \(-0.909861\pi\)
−0.960172 + 0.279409i \(0.909861\pi\)
\(348\) −1.74243 −0.0934040
\(349\) −20.5072 −1.09773 −0.548863 0.835912i \(-0.684939\pi\)
−0.548863 + 0.835912i \(0.684939\pi\)
\(350\) −13.6157 −0.727791
\(351\) 6.43612 0.343534
\(352\) 1.00000 0.0533002
\(353\) −9.01885 −0.480025 −0.240012 0.970770i \(-0.577152\pi\)
−0.240012 + 0.970770i \(0.577152\pi\)
\(354\) −0.0748538 −0.00397844
\(355\) −21.3548 −1.13339
\(356\) −3.71513 −0.196902
\(357\) 1.84936 0.0978786
\(358\) 9.74345 0.514958
\(359\) −35.2663 −1.86128 −0.930642 0.365930i \(-0.880751\pi\)
−0.930642 + 0.365930i \(0.880751\pi\)
\(360\) 3.63661 0.191666
\(361\) 11.8568 0.624042
\(362\) 11.1669 0.586920
\(363\) 1.00000 0.0524864
\(364\) −10.6545 −0.558447
\(365\) −28.2860 −1.48056
\(366\) −1.00000 −0.0522708
\(367\) 13.8581 0.723387 0.361693 0.932297i \(-0.382199\pi\)
0.361693 + 0.932297i \(0.382199\pi\)
\(368\) −3.64436 −0.189975
\(369\) −3.65909 −0.190485
\(370\) 38.8404 2.01922
\(371\) 12.6483 0.656665
\(372\) 1.99225 0.103293
\(373\) 28.1145 1.45571 0.727856 0.685730i \(-0.240517\pi\)
0.727856 + 0.685730i \(0.240517\pi\)
\(374\) −1.11715 −0.0577667
\(375\) 11.7278 0.605621
\(376\) 11.2187 0.578559
\(377\) −11.2145 −0.577575
\(378\) −1.65542 −0.0851457
\(379\) 31.8925 1.63821 0.819104 0.573645i \(-0.194471\pi\)
0.819104 + 0.573645i \(0.194471\pi\)
\(380\) −20.2010 −1.03629
\(381\) −9.26320 −0.474568
\(382\) −24.2346 −1.23995
\(383\) 13.1481 0.671836 0.335918 0.941891i \(-0.390954\pi\)
0.335918 + 0.941891i \(0.390954\pi\)
\(384\) 1.00000 0.0510310
\(385\) −6.02012 −0.306814
\(386\) 3.02708 0.154074
\(387\) 6.64405 0.337736
\(388\) 11.9593 0.607141
\(389\) −20.7562 −1.05238 −0.526190 0.850367i \(-0.676380\pi\)
−0.526190 + 0.850367i \(0.676380\pi\)
\(390\) 23.4056 1.18519
\(391\) 4.07131 0.205895
\(392\) −4.25958 −0.215141
\(393\) −11.9435 −0.602472
\(394\) −13.1681 −0.663401
\(395\) 5.64608 0.284085
\(396\) 1.00000 0.0502519
\(397\) −7.09454 −0.356065 −0.178032 0.984025i \(-0.556973\pi\)
−0.178032 + 0.984025i \(0.556973\pi\)
\(398\) −22.3693 −1.12127
\(399\) 9.19568 0.460360
\(400\) 8.22493 0.411246
\(401\) −10.1912 −0.508923 −0.254462 0.967083i \(-0.581898\pi\)
−0.254462 + 0.967083i \(0.581898\pi\)
\(402\) −13.9718 −0.696851
\(403\) 12.8224 0.638727
\(404\) 1.24249 0.0618161
\(405\) 3.63661 0.180705
\(406\) 2.88445 0.143153
\(407\) 10.6804 0.529408
\(408\) −1.11715 −0.0553074
\(409\) 31.7800 1.57142 0.785710 0.618595i \(-0.212298\pi\)
0.785710 + 0.618595i \(0.212298\pi\)
\(410\) −13.3067 −0.657170
\(411\) 19.9918 0.986123
\(412\) −19.1188 −0.941918
\(413\) 0.123915 0.00609744
\(414\) −3.64436 −0.179110
\(415\) 54.8798 2.69394
\(416\) 6.43612 0.315557
\(417\) −2.90764 −0.142388
\(418\) −5.55489 −0.271699
\(419\) 0.276412 0.0135036 0.00675180 0.999977i \(-0.497851\pi\)
0.00675180 + 0.999977i \(0.497851\pi\)
\(420\) −6.02012 −0.293752
\(421\) 15.1425 0.738002 0.369001 0.929429i \(-0.379700\pi\)
0.369001 + 0.929429i \(0.379700\pi\)
\(422\) −3.82917 −0.186401
\(423\) 11.2187 0.545470
\(424\) −7.64051 −0.371056
\(425\) −9.18851 −0.445708
\(426\) −5.87217 −0.284508
\(427\) 1.65542 0.0801115
\(428\) −6.86786 −0.331971
\(429\) 6.43612 0.310739
\(430\) 24.1618 1.16519
\(431\) −15.3738 −0.740532 −0.370266 0.928926i \(-0.620733\pi\)
−0.370266 + 0.928926i \(0.620733\pi\)
\(432\) 1.00000 0.0481125
\(433\) 36.5498 1.75647 0.878235 0.478229i \(-0.158721\pi\)
0.878235 + 0.478229i \(0.158721\pi\)
\(434\) −3.29801 −0.158310
\(435\) −6.33653 −0.303813
\(436\) 2.33976 0.112054
\(437\) 20.2440 0.968402
\(438\) −7.77814 −0.371654
\(439\) −26.9431 −1.28592 −0.642962 0.765898i \(-0.722295\pi\)
−0.642962 + 0.765898i \(0.722295\pi\)
\(440\) 3.63661 0.173369
\(441\) −4.25958 −0.202837
\(442\) −7.19014 −0.342000
\(443\) 29.1747 1.38613 0.693065 0.720875i \(-0.256260\pi\)
0.693065 + 0.720875i \(0.256260\pi\)
\(444\) 10.6804 0.506869
\(445\) −13.5105 −0.640458
\(446\) 11.0856 0.524918
\(447\) −15.0404 −0.711385
\(448\) −1.65542 −0.0782113
\(449\) −9.37976 −0.442658 −0.221329 0.975199i \(-0.571040\pi\)
−0.221329 + 0.975199i \(0.571040\pi\)
\(450\) 8.22493 0.387727
\(451\) −3.65909 −0.172300
\(452\) 13.9624 0.656736
\(453\) −14.3901 −0.676107
\(454\) 15.8836 0.745454
\(455\) −38.7462 −1.81645
\(456\) −5.55489 −0.260132
\(457\) −14.1878 −0.663679 −0.331839 0.943336i \(-0.607669\pi\)
−0.331839 + 0.943336i \(0.607669\pi\)
\(458\) 15.1029 0.705713
\(459\) −1.11715 −0.0521443
\(460\) −13.2531 −0.617929
\(461\) 11.8385 0.551376 0.275688 0.961247i \(-0.411094\pi\)
0.275688 + 0.961247i \(0.411094\pi\)
\(462\) −1.65542 −0.0770172
\(463\) 40.2318 1.86973 0.934865 0.355004i \(-0.115520\pi\)
0.934865 + 0.355004i \(0.115520\pi\)
\(464\) −1.74243 −0.0808902
\(465\) 7.24504 0.335981
\(466\) 8.29255 0.384145
\(467\) −24.7775 −1.14657 −0.573284 0.819357i \(-0.694331\pi\)
−0.573284 + 0.819357i \(0.694331\pi\)
\(468\) 6.43612 0.297510
\(469\) 23.1293 1.06801
\(470\) 40.7979 1.88187
\(471\) −1.62798 −0.0750134
\(472\) −0.0748538 −0.00344543
\(473\) 6.64405 0.305494
\(474\) 1.55257 0.0713118
\(475\) −45.6886 −2.09633
\(476\) 1.84936 0.0847654
\(477\) −7.64051 −0.349835
\(478\) 19.3939 0.887058
\(479\) 18.1197 0.827909 0.413955 0.910297i \(-0.364147\pi\)
0.413955 + 0.910297i \(0.364147\pi\)
\(480\) 3.63661 0.165988
\(481\) 68.7403 3.13429
\(482\) −1.41796 −0.0645862
\(483\) 6.03295 0.274509
\(484\) 1.00000 0.0454545
\(485\) 43.4913 1.97484
\(486\) 1.00000 0.0453609
\(487\) −25.4064 −1.15127 −0.575636 0.817706i \(-0.695246\pi\)
−0.575636 + 0.817706i \(0.695246\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 20.7016 0.936159
\(490\) −15.4904 −0.699786
\(491\) 18.8016 0.848503 0.424251 0.905544i \(-0.360537\pi\)
0.424251 + 0.905544i \(0.360537\pi\)
\(492\) −3.65909 −0.164965
\(493\) 1.94656 0.0876688
\(494\) −35.7519 −1.60855
\(495\) 3.63661 0.163453
\(496\) 1.99225 0.0894547
\(497\) 9.72092 0.436043
\(498\) 15.0909 0.676241
\(499\) 20.5895 0.921711 0.460856 0.887475i \(-0.347543\pi\)
0.460856 + 0.887475i \(0.347543\pi\)
\(500\) 11.7278 0.524483
\(501\) 1.30094 0.0581217
\(502\) 7.12400 0.317959
\(503\) −32.5168 −1.44985 −0.724927 0.688825i \(-0.758127\pi\)
−0.724927 + 0.688825i \(0.758127\pi\)
\(504\) −1.65542 −0.0737383
\(505\) 4.51844 0.201068
\(506\) −3.64436 −0.162011
\(507\) 28.4236 1.26234
\(508\) −9.26320 −0.410988
\(509\) 35.6052 1.57817 0.789086 0.614283i \(-0.210555\pi\)
0.789086 + 0.614283i \(0.210555\pi\)
\(510\) −4.06265 −0.179897
\(511\) 12.8761 0.569605
\(512\) 1.00000 0.0441942
\(513\) −5.55489 −0.245254
\(514\) −11.5558 −0.509703
\(515\) −69.5277 −3.06376
\(516\) 6.64405 0.292488
\(517\) 11.2187 0.493396
\(518\) −17.6806 −0.776839
\(519\) −24.3719 −1.06981
\(520\) 23.4056 1.02641
\(521\) −25.2607 −1.10669 −0.553345 0.832952i \(-0.686649\pi\)
−0.553345 + 0.832952i \(0.686649\pi\)
\(522\) −1.74243 −0.0762640
\(523\) −18.9119 −0.826961 −0.413480 0.910513i \(-0.635687\pi\)
−0.413480 + 0.910513i \(0.635687\pi\)
\(524\) −11.9435 −0.521756
\(525\) −13.6157 −0.594239
\(526\) −0.693770 −0.0302498
\(527\) −2.22565 −0.0969509
\(528\) 1.00000 0.0435194
\(529\) −9.71865 −0.422550
\(530\) −27.7856 −1.20693
\(531\) −0.0748538 −0.00324838
\(532\) 9.19568 0.398683
\(533\) −23.5503 −1.02008
\(534\) −3.71513 −0.160769
\(535\) −24.9757 −1.07979
\(536\) −13.9718 −0.603491
\(537\) 9.74345 0.420461
\(538\) 8.18407 0.352840
\(539\) −4.25958 −0.183473
\(540\) 3.63661 0.156495
\(541\) −8.67386 −0.372918 −0.186459 0.982463i \(-0.559701\pi\)
−0.186459 + 0.982463i \(0.559701\pi\)
\(542\) 4.99753 0.214662
\(543\) 11.1669 0.479218
\(544\) −1.11715 −0.0478976
\(545\) 8.50878 0.364476
\(546\) −10.6545 −0.455970
\(547\) 32.4376 1.38693 0.693466 0.720489i \(-0.256083\pi\)
0.693466 + 0.720489i \(0.256083\pi\)
\(548\) 19.9918 0.854008
\(549\) −1.00000 −0.0426790
\(550\) 8.22493 0.350712
\(551\) 9.67900 0.412339
\(552\) −3.64436 −0.155114
\(553\) −2.57015 −0.109294
\(554\) −2.65986 −0.113007
\(555\) 38.8404 1.64869
\(556\) −2.90764 −0.123311
\(557\) 28.9515 1.22672 0.613358 0.789805i \(-0.289818\pi\)
0.613358 + 0.789805i \(0.289818\pi\)
\(558\) 1.99225 0.0843387
\(559\) 42.7619 1.80863
\(560\) −6.02012 −0.254397
\(561\) −1.11715 −0.0471663
\(562\) −22.2999 −0.940666
\(563\) 23.5430 0.992220 0.496110 0.868260i \(-0.334761\pi\)
0.496110 + 0.868260i \(0.334761\pi\)
\(564\) 11.2187 0.472391
\(565\) 50.7758 2.13615
\(566\) −22.3131 −0.937891
\(567\) −1.65542 −0.0695212
\(568\) −5.87217 −0.246391
\(569\) −21.4678 −0.899978 −0.449989 0.893034i \(-0.648572\pi\)
−0.449989 + 0.893034i \(0.648572\pi\)
\(570\) −20.2010 −0.846125
\(571\) 16.5881 0.694192 0.347096 0.937830i \(-0.387168\pi\)
0.347096 + 0.937830i \(0.387168\pi\)
\(572\) 6.43612 0.269108
\(573\) −24.2346 −1.01242
\(574\) 6.05734 0.252828
\(575\) −29.9746 −1.25003
\(576\) 1.00000 0.0416667
\(577\) −30.5258 −1.27081 −0.635404 0.772180i \(-0.719166\pi\)
−0.635404 + 0.772180i \(0.719166\pi\)
\(578\) −15.7520 −0.655195
\(579\) 3.02708 0.125801
\(580\) −6.33653 −0.263110
\(581\) −24.9819 −1.03642
\(582\) 11.9593 0.495729
\(583\) −7.64051 −0.316438
\(584\) −7.77814 −0.321862
\(585\) 23.4056 0.967704
\(586\) 22.0617 0.911360
\(587\) −22.4814 −0.927907 −0.463953 0.885860i \(-0.653570\pi\)
−0.463953 + 0.885860i \(0.653570\pi\)
\(588\) −4.25958 −0.175662
\(589\) −11.0667 −0.455997
\(590\) −0.272214 −0.0112069
\(591\) −13.1681 −0.541665
\(592\) 10.6804 0.438962
\(593\) −22.6452 −0.929928 −0.464964 0.885329i \(-0.653933\pi\)
−0.464964 + 0.885329i \(0.653933\pi\)
\(594\) 1.00000 0.0410305
\(595\) 6.72541 0.275715
\(596\) −15.0404 −0.616077
\(597\) −22.3693 −0.915515
\(598\) −23.4555 −0.959167
\(599\) −32.8541 −1.34238 −0.671191 0.741284i \(-0.734217\pi\)
−0.671191 + 0.741284i \(0.734217\pi\)
\(600\) 8.22493 0.335781
\(601\) −33.6150 −1.37118 −0.685592 0.727986i \(-0.740457\pi\)
−0.685592 + 0.727986i \(0.740457\pi\)
\(602\) −10.9987 −0.448273
\(603\) −13.9718 −0.568977
\(604\) −14.3901 −0.585526
\(605\) 3.63661 0.147849
\(606\) 1.24249 0.0504726
\(607\) 17.9685 0.729318 0.364659 0.931141i \(-0.381186\pi\)
0.364659 + 0.931141i \(0.381186\pi\)
\(608\) −5.55489 −0.225281
\(609\) 2.88445 0.116884
\(610\) −3.63661 −0.147242
\(611\) 72.2046 2.92109
\(612\) −1.11715 −0.0451583
\(613\) −7.34476 −0.296652 −0.148326 0.988939i \(-0.547389\pi\)
−0.148326 + 0.988939i \(0.547389\pi\)
\(614\) −25.4026 −1.02517
\(615\) −13.3067 −0.536577
\(616\) −1.65542 −0.0666988
\(617\) −46.2309 −1.86119 −0.930593 0.366055i \(-0.880708\pi\)
−0.930593 + 0.366055i \(0.880708\pi\)
\(618\) −19.1188 −0.769072
\(619\) −19.5755 −0.786807 −0.393403 0.919366i \(-0.628702\pi\)
−0.393403 + 0.919366i \(0.628702\pi\)
\(620\) 7.24504 0.290968
\(621\) −3.64436 −0.146243
\(622\) −4.07486 −0.163387
\(623\) 6.15011 0.246399
\(624\) 6.43612 0.257651
\(625\) 1.52478 0.0609911
\(626\) 9.02954 0.360893
\(627\) −5.55489 −0.221841
\(628\) −1.62798 −0.0649635
\(629\) −11.9317 −0.475746
\(630\) −6.02012 −0.239847
\(631\) 33.1579 1.32000 0.659998 0.751267i \(-0.270557\pi\)
0.659998 + 0.751267i \(0.270557\pi\)
\(632\) 1.55257 0.0617578
\(633\) −3.82917 −0.152196
\(634\) 16.4782 0.654434
\(635\) −33.6867 −1.33681
\(636\) −7.64051 −0.302966
\(637\) −27.4151 −1.08623
\(638\) −1.74243 −0.0689834
\(639\) −5.87217 −0.232300
\(640\) 3.63661 0.143750
\(641\) 48.8512 1.92951 0.964754 0.263154i \(-0.0847627\pi\)
0.964754 + 0.263154i \(0.0847627\pi\)
\(642\) −6.86786 −0.271053
\(643\) 5.83417 0.230077 0.115039 0.993361i \(-0.463301\pi\)
0.115039 + 0.993361i \(0.463301\pi\)
\(644\) 6.03295 0.237731
\(645\) 24.1618 0.951370
\(646\) 6.20567 0.244159
\(647\) −15.7920 −0.620846 −0.310423 0.950599i \(-0.600471\pi\)
−0.310423 + 0.950599i \(0.600471\pi\)
\(648\) 1.00000 0.0392837
\(649\) −0.0748538 −0.00293827
\(650\) 52.9366 2.07634
\(651\) −3.29801 −0.129259
\(652\) 20.7016 0.810737
\(653\) −21.1007 −0.825733 −0.412867 0.910791i \(-0.635472\pi\)
−0.412867 + 0.910791i \(0.635472\pi\)
\(654\) 2.33976 0.0914918
\(655\) −43.4340 −1.69711
\(656\) −3.65909 −0.142863
\(657\) −7.77814 −0.303454
\(658\) −18.5716 −0.723997
\(659\) −34.4141 −1.34058 −0.670291 0.742098i \(-0.733831\pi\)
−0.670291 + 0.742098i \(0.733831\pi\)
\(660\) 3.63661 0.141555
\(661\) −2.08847 −0.0812321 −0.0406161 0.999175i \(-0.512932\pi\)
−0.0406161 + 0.999175i \(0.512932\pi\)
\(662\) −28.0374 −1.08971
\(663\) −7.19014 −0.279242
\(664\) 15.0909 0.585642
\(665\) 33.4411 1.29679
\(666\) 10.6804 0.413857
\(667\) 6.35004 0.245874
\(668\) 1.30094 0.0503349
\(669\) 11.0856 0.428594
\(670\) −50.8101 −1.96296
\(671\) −1.00000 −0.0386046
\(672\) −1.65542 −0.0638593
\(673\) 39.0930 1.50693 0.753463 0.657491i \(-0.228382\pi\)
0.753463 + 0.657491i \(0.228382\pi\)
\(674\) 1.51410 0.0583211
\(675\) 8.22493 0.316578
\(676\) 28.4236 1.09321
\(677\) −1.69822 −0.0652679 −0.0326340 0.999467i \(-0.510390\pi\)
−0.0326340 + 0.999467i \(0.510390\pi\)
\(678\) 13.9624 0.536223
\(679\) −19.7977 −0.759765
\(680\) −4.06265 −0.155796
\(681\) 15.8836 0.608661
\(682\) 1.99225 0.0762872
\(683\) 28.3151 1.08345 0.541723 0.840557i \(-0.317772\pi\)
0.541723 + 0.840557i \(0.317772\pi\)
\(684\) −5.55489 −0.212397
\(685\) 72.7024 2.77782
\(686\) 18.6393 0.711654
\(687\) 15.1029 0.576212
\(688\) 6.64405 0.253302
\(689\) −49.1752 −1.87343
\(690\) −13.2531 −0.504537
\(691\) 2.91790 0.111002 0.0555010 0.998459i \(-0.482324\pi\)
0.0555010 + 0.998459i \(0.482324\pi\)
\(692\) −24.3719 −0.926482
\(693\) −1.65542 −0.0628843
\(694\) −35.7721 −1.35789
\(695\) −10.5740 −0.401093
\(696\) −1.74243 −0.0660466
\(697\) 4.08777 0.154835
\(698\) −20.5072 −0.776210
\(699\) 8.29255 0.313653
\(700\) −13.6157 −0.514626
\(701\) 1.03383 0.0390471 0.0195235 0.999809i \(-0.493785\pi\)
0.0195235 + 0.999809i \(0.493785\pi\)
\(702\) 6.43612 0.242916
\(703\) −59.3285 −2.23762
\(704\) 1.00000 0.0376889
\(705\) 40.7979 1.53654
\(706\) −9.01885 −0.339429
\(707\) −2.05684 −0.0773554
\(708\) −0.0748538 −0.00281318
\(709\) −13.8243 −0.519183 −0.259592 0.965718i \(-0.583588\pi\)
−0.259592 + 0.965718i \(0.583588\pi\)
\(710\) −21.3548 −0.801431
\(711\) 1.55257 0.0582258
\(712\) −3.71513 −0.139230
\(713\) −7.26048 −0.271907
\(714\) 1.84936 0.0692106
\(715\) 23.4056 0.875321
\(716\) 9.74345 0.364130
\(717\) 19.3939 0.724280
\(718\) −35.2663 −1.31613
\(719\) −13.7830 −0.514018 −0.257009 0.966409i \(-0.582737\pi\)
−0.257009 + 0.966409i \(0.582737\pi\)
\(720\) 3.63661 0.135528
\(721\) 31.6497 1.17870
\(722\) 11.8568 0.441265
\(723\) −1.41796 −0.0527344
\(724\) 11.1669 0.415015
\(725\) −14.3313 −0.532253
\(726\) 1.00000 0.0371135
\(727\) −11.8953 −0.441171 −0.220585 0.975368i \(-0.570797\pi\)
−0.220585 + 0.975368i \(0.570797\pi\)
\(728\) −10.6545 −0.394881
\(729\) 1.00000 0.0370370
\(730\) −28.2860 −1.04691
\(731\) −7.42243 −0.274528
\(732\) −1.00000 −0.0369611
\(733\) 33.4328 1.23487 0.617434 0.786623i \(-0.288172\pi\)
0.617434 + 0.786623i \(0.288172\pi\)
\(734\) 13.8581 0.511512
\(735\) −15.4904 −0.571373
\(736\) −3.64436 −0.134333
\(737\) −13.9718 −0.514659
\(738\) −3.65909 −0.134693
\(739\) 5.75440 0.211679 0.105839 0.994383i \(-0.466247\pi\)
0.105839 + 0.994383i \(0.466247\pi\)
\(740\) 38.8404 1.42780
\(741\) −35.7519 −1.31338
\(742\) 12.6483 0.464333
\(743\) −27.3948 −1.00502 −0.502508 0.864572i \(-0.667589\pi\)
−0.502508 + 0.864572i \(0.667589\pi\)
\(744\) 1.99225 0.0730395
\(745\) −54.6959 −2.00390
\(746\) 28.1145 1.02934
\(747\) 15.0909 0.552148
\(748\) −1.11715 −0.0408472
\(749\) 11.3692 0.415422
\(750\) 11.7278 0.428239
\(751\) −14.6508 −0.534616 −0.267308 0.963611i \(-0.586134\pi\)
−0.267308 + 0.963611i \(0.586134\pi\)
\(752\) 11.2187 0.409103
\(753\) 7.12400 0.259613
\(754\) −11.2145 −0.408407
\(755\) −52.3312 −1.90453
\(756\) −1.65542 −0.0602071
\(757\) −51.4326 −1.86935 −0.934674 0.355505i \(-0.884309\pi\)
−0.934674 + 0.355505i \(0.884309\pi\)
\(758\) 31.8925 1.15839
\(759\) −3.64436 −0.132282
\(760\) −20.2010 −0.732766
\(761\) −11.4916 −0.416570 −0.208285 0.978068i \(-0.566788\pi\)
−0.208285 + 0.978068i \(0.566788\pi\)
\(762\) −9.26320 −0.335570
\(763\) −3.87328 −0.140222
\(764\) −24.2346 −0.876779
\(765\) −4.06265 −0.146886
\(766\) 13.1481 0.475060
\(767\) −0.481768 −0.0173956
\(768\) 1.00000 0.0360844
\(769\) −3.07212 −0.110783 −0.0553917 0.998465i \(-0.517641\pi\)
−0.0553917 + 0.998465i \(0.517641\pi\)
\(770\) −6.02012 −0.216950
\(771\) −11.5558 −0.416171
\(772\) 3.02708 0.108947
\(773\) 10.5075 0.377929 0.188964 0.981984i \(-0.439487\pi\)
0.188964 + 0.981984i \(0.439487\pi\)
\(774\) 6.64405 0.238815
\(775\) 16.3861 0.588607
\(776\) 11.9593 0.429314
\(777\) −17.6806 −0.634287
\(778\) −20.7562 −0.744146
\(779\) 20.3258 0.728249
\(780\) 23.4056 0.838056
\(781\) −5.87217 −0.210123
\(782\) 4.07131 0.145590
\(783\) −1.74243 −0.0622693
\(784\) −4.25958 −0.152128
\(785\) −5.92033 −0.211306
\(786\) −11.9435 −0.426012
\(787\) 8.30457 0.296026 0.148013 0.988985i \(-0.452712\pi\)
0.148013 + 0.988985i \(0.452712\pi\)
\(788\) −13.1681 −0.469096
\(789\) −0.693770 −0.0246989
\(790\) 5.64608 0.200878
\(791\) −23.1137 −0.821827
\(792\) 1.00000 0.0355335
\(793\) −6.43612 −0.228553
\(794\) −7.09454 −0.251776
\(795\) −27.7856 −0.985452
\(796\) −22.3693 −0.792860
\(797\) −8.69854 −0.308118 −0.154059 0.988062i \(-0.549235\pi\)
−0.154059 + 0.988062i \(0.549235\pi\)
\(798\) 9.19568 0.325524
\(799\) −12.5330 −0.443385
\(800\) 8.22493 0.290795
\(801\) −3.71513 −0.131268
\(802\) −10.1912 −0.359863
\(803\) −7.77814 −0.274484
\(804\) −13.9718 −0.492748
\(805\) 21.9395 0.773265
\(806\) 12.8224 0.451648
\(807\) 8.18407 0.288093
\(808\) 1.24249 0.0437106
\(809\) −14.4754 −0.508930 −0.254465 0.967082i \(-0.581899\pi\)
−0.254465 + 0.967082i \(0.581899\pi\)
\(810\) 3.63661 0.127777
\(811\) −26.1680 −0.918884 −0.459442 0.888208i \(-0.651951\pi\)
−0.459442 + 0.888208i \(0.651951\pi\)
\(812\) 2.88445 0.101224
\(813\) 4.99753 0.175271
\(814\) 10.6804 0.374348
\(815\) 75.2836 2.63707
\(816\) −1.11715 −0.0391082
\(817\) −36.9069 −1.29121
\(818\) 31.7800 1.11116
\(819\) −10.6545 −0.372298
\(820\) −13.3067 −0.464689
\(821\) 41.7457 1.45694 0.728468 0.685080i \(-0.240233\pi\)
0.728468 + 0.685080i \(0.240233\pi\)
\(822\) 19.9918 0.697294
\(823\) 37.6219 1.31142 0.655709 0.755014i \(-0.272370\pi\)
0.655709 + 0.755014i \(0.272370\pi\)
\(824\) −19.1188 −0.666036
\(825\) 8.22493 0.286355
\(826\) 0.123915 0.00431154
\(827\) 2.92736 0.101794 0.0508972 0.998704i \(-0.483792\pi\)
0.0508972 + 0.998704i \(0.483792\pi\)
\(828\) −3.64436 −0.126650
\(829\) 5.38309 0.186963 0.0934813 0.995621i \(-0.470200\pi\)
0.0934813 + 0.995621i \(0.470200\pi\)
\(830\) 54.8798 1.90491
\(831\) −2.65986 −0.0922695
\(832\) 6.43612 0.223132
\(833\) 4.75861 0.164876
\(834\) −2.90764 −0.100683
\(835\) 4.73101 0.163723
\(836\) −5.55489 −0.192120
\(837\) 1.99225 0.0688623
\(838\) 0.276412 0.00954849
\(839\) −34.3874 −1.18719 −0.593593 0.804765i \(-0.702291\pi\)
−0.593593 + 0.804765i \(0.702291\pi\)
\(840\) −6.02012 −0.207714
\(841\) −25.9639 −0.895308
\(842\) 15.1425 0.521846
\(843\) −22.2999 −0.768051
\(844\) −3.82917 −0.131806
\(845\) 103.365 3.55588
\(846\) 11.2187 0.385706
\(847\) −1.65542 −0.0568810
\(848\) −7.64051 −0.262376
\(849\) −22.3131 −0.765784
\(850\) −9.18851 −0.315163
\(851\) −38.9232 −1.33427
\(852\) −5.87217 −0.201177
\(853\) −44.0088 −1.50683 −0.753416 0.657544i \(-0.771595\pi\)
−0.753416 + 0.657544i \(0.771595\pi\)
\(854\) 1.65542 0.0566474
\(855\) −20.2010 −0.690858
\(856\) −6.86786 −0.234739
\(857\) 7.83848 0.267757 0.133879 0.990998i \(-0.457257\pi\)
0.133879 + 0.990998i \(0.457257\pi\)
\(858\) 6.43612 0.219725
\(859\) 27.0073 0.921477 0.460739 0.887536i \(-0.347585\pi\)
0.460739 + 0.887536i \(0.347585\pi\)
\(860\) 24.1618 0.823911
\(861\) 6.05734 0.206433
\(862\) −15.3738 −0.523635
\(863\) 7.27400 0.247610 0.123805 0.992307i \(-0.460490\pi\)
0.123805 + 0.992307i \(0.460490\pi\)
\(864\) 1.00000 0.0340207
\(865\) −88.6312 −3.01355
\(866\) 36.5498 1.24201
\(867\) −15.7520 −0.534965
\(868\) −3.29801 −0.111942
\(869\) 1.55257 0.0526672
\(870\) −6.33653 −0.214829
\(871\) −89.9243 −3.04697
\(872\) 2.33976 0.0792342
\(873\) 11.9593 0.404761
\(874\) 20.2440 0.684764
\(875\) −19.4144 −0.656328
\(876\) −7.77814 −0.262799
\(877\) −0.103572 −0.00349739 −0.00174869 0.999998i \(-0.500557\pi\)
−0.00174869 + 0.999998i \(0.500557\pi\)
\(878\) −26.9431 −0.909285
\(879\) 22.0617 0.744122
\(880\) 3.63661 0.122590
\(881\) −38.9913 −1.31365 −0.656825 0.754043i \(-0.728101\pi\)
−0.656825 + 0.754043i \(0.728101\pi\)
\(882\) −4.25958 −0.143428
\(883\) 32.2663 1.08585 0.542924 0.839782i \(-0.317317\pi\)
0.542924 + 0.839782i \(0.317317\pi\)
\(884\) −7.19014 −0.241830
\(885\) −0.272214 −0.00915038
\(886\) 29.1747 0.980142
\(887\) 14.1216 0.474156 0.237078 0.971491i \(-0.423810\pi\)
0.237078 + 0.971491i \(0.423810\pi\)
\(888\) 10.6804 0.358411
\(889\) 15.3345 0.514303
\(890\) −13.5105 −0.452872
\(891\) 1.00000 0.0335013
\(892\) 11.0856 0.371173
\(893\) −62.3185 −2.08541
\(894\) −15.0404 −0.503025
\(895\) 35.4331 1.18440
\(896\) −1.65542 −0.0553037
\(897\) −23.4555 −0.783157
\(898\) −9.37976 −0.313007
\(899\) −3.47135 −0.115776
\(900\) 8.22493 0.274164
\(901\) 8.53564 0.284363
\(902\) −3.65909 −0.121834
\(903\) −10.9987 −0.366014
\(904\) 13.9624 0.464383
\(905\) 40.6097 1.34991
\(906\) −14.3901 −0.478080
\(907\) 8.71656 0.289429 0.144714 0.989473i \(-0.453774\pi\)
0.144714 + 0.989473i \(0.453774\pi\)
\(908\) 15.8836 0.527116
\(909\) 1.24249 0.0412107
\(910\) −38.7462 −1.28442
\(911\) −8.18041 −0.271029 −0.135515 0.990775i \(-0.543269\pi\)
−0.135515 + 0.990775i \(0.543269\pi\)
\(912\) −5.55489 −0.183941
\(913\) 15.0909 0.499437
\(914\) −14.1878 −0.469292
\(915\) −3.63661 −0.120223
\(916\) 15.1029 0.499014
\(917\) 19.7716 0.652916
\(918\) −1.11715 −0.0368716
\(919\) 42.4776 1.40121 0.700603 0.713552i \(-0.252915\pi\)
0.700603 + 0.713552i \(0.252915\pi\)
\(920\) −13.2531 −0.436942
\(921\) −25.4026 −0.837044
\(922\) 11.8385 0.389882
\(923\) −37.7940 −1.24400
\(924\) −1.65542 −0.0544594
\(925\) 87.8455 2.88834
\(926\) 40.2318 1.32210
\(927\) −19.1188 −0.627945
\(928\) −1.74243 −0.0571980
\(929\) −24.5913 −0.806814 −0.403407 0.915021i \(-0.632174\pi\)
−0.403407 + 0.915021i \(0.632174\pi\)
\(930\) 7.24504 0.237574
\(931\) 23.6615 0.775474
\(932\) 8.29255 0.271631
\(933\) −4.07486 −0.133405
\(934\) −24.7775 −0.810746
\(935\) −4.06265 −0.132863
\(936\) 6.43612 0.210371
\(937\) 9.18901 0.300192 0.150096 0.988671i \(-0.452042\pi\)
0.150096 + 0.988671i \(0.452042\pi\)
\(938\) 23.1293 0.755197
\(939\) 9.02954 0.294668
\(940\) 40.7979 1.33068
\(941\) −24.9237 −0.812491 −0.406245 0.913764i \(-0.633162\pi\)
−0.406245 + 0.913764i \(0.633162\pi\)
\(942\) −1.62798 −0.0530425
\(943\) 13.3350 0.434249
\(944\) −0.0748538 −0.00243628
\(945\) −6.02012 −0.195835
\(946\) 6.64405 0.216017
\(947\) −5.98653 −0.194536 −0.0972681 0.995258i \(-0.531010\pi\)
−0.0972681 + 0.995258i \(0.531010\pi\)
\(948\) 1.55257 0.0504250
\(949\) −50.0610 −1.62505
\(950\) −45.6886 −1.48233
\(951\) 16.4782 0.534343
\(952\) 1.84936 0.0599382
\(953\) −36.4885 −1.18198 −0.590990 0.806679i \(-0.701263\pi\)
−0.590990 + 0.806679i \(0.701263\pi\)
\(954\) −7.64051 −0.247371
\(955\) −88.1319 −2.85188
\(956\) 19.3939 0.627245
\(957\) −1.74243 −0.0563247
\(958\) 18.1197 0.585420
\(959\) −33.0949 −1.06869
\(960\) 3.63661 0.117371
\(961\) −27.0309 −0.871966
\(962\) 68.7403 2.21628
\(963\) −6.86786 −0.221314
\(964\) −1.41796 −0.0456694
\(965\) 11.0083 0.354370
\(966\) 6.03295 0.194107
\(967\) −2.75773 −0.0886826 −0.0443413 0.999016i \(-0.514119\pi\)
−0.0443413 + 0.999016i \(0.514119\pi\)
\(968\) 1.00000 0.0321412
\(969\) 6.20567 0.199355
\(970\) 43.4913 1.39642
\(971\) −24.8710 −0.798148 −0.399074 0.916919i \(-0.630668\pi\)
−0.399074 + 0.916919i \(0.630668\pi\)
\(972\) 1.00000 0.0320750
\(973\) 4.81337 0.154310
\(974\) −25.4064 −0.814072
\(975\) 52.9366 1.69533
\(976\) −1.00000 −0.0320092
\(977\) −31.3795 −1.00392 −0.501959 0.864891i \(-0.667387\pi\)
−0.501959 + 0.864891i \(0.667387\pi\)
\(978\) 20.7016 0.661964
\(979\) −3.71513 −0.118736
\(980\) −15.4904 −0.494824
\(981\) 2.33976 0.0747027
\(982\) 18.8016 0.599982
\(983\) 19.4750 0.621155 0.310578 0.950548i \(-0.399478\pi\)
0.310578 + 0.950548i \(0.399478\pi\)
\(984\) −3.65909 −0.116648
\(985\) −47.8874 −1.52582
\(986\) 1.94656 0.0619912
\(987\) −18.5716 −0.591141
\(988\) −35.7519 −1.13742
\(989\) −24.2133 −0.769938
\(990\) 3.63661 0.115579
\(991\) −17.2807 −0.548939 −0.274469 0.961596i \(-0.588502\pi\)
−0.274469 + 0.961596i \(0.588502\pi\)
\(992\) 1.99225 0.0632540
\(993\) −28.0374 −0.889741
\(994\) 9.72092 0.308329
\(995\) −81.3485 −2.57892
\(996\) 15.0909 0.478174
\(997\) 19.2224 0.608781 0.304390 0.952547i \(-0.401547\pi\)
0.304390 + 0.952547i \(0.401547\pi\)
\(998\) 20.5895 0.651748
\(999\) 10.6804 0.337913
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 \(a_p\))