Properties

Label 8018.2.a.f.1.13
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(34\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.39250 q^{3}\) \(+1.00000 q^{4}\) \(+3.35741 q^{5}\) \(+1.39250 q^{6}\) \(-0.849778 q^{7}\) \(-1.00000 q^{8}\) \(-1.06096 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.39250 q^{3}\) \(+1.00000 q^{4}\) \(+3.35741 q^{5}\) \(+1.39250 q^{6}\) \(-0.849778 q^{7}\) \(-1.00000 q^{8}\) \(-1.06096 q^{9}\) \(-3.35741 q^{10}\) \(-2.14482 q^{11}\) \(-1.39250 q^{12}\) \(-0.777327 q^{13}\) \(+0.849778 q^{14}\) \(-4.67518 q^{15}\) \(+1.00000 q^{16}\) \(+4.54820 q^{17}\) \(+1.06096 q^{18}\) \(-1.00000 q^{19}\) \(+3.35741 q^{20}\) \(+1.18331 q^{21}\) \(+2.14482 q^{22}\) \(-6.97945 q^{23}\) \(+1.39250 q^{24}\) \(+6.27221 q^{25}\) \(+0.777327 q^{26}\) \(+5.65486 q^{27}\) \(-0.849778 q^{28}\) \(-0.251361 q^{29}\) \(+4.67518 q^{30}\) \(-8.19038 q^{31}\) \(-1.00000 q^{32}\) \(+2.98666 q^{33}\) \(-4.54820 q^{34}\) \(-2.85305 q^{35}\) \(-1.06096 q^{36}\) \(+7.04638 q^{37}\) \(+1.00000 q^{38}\) \(+1.08242 q^{39}\) \(-3.35741 q^{40}\) \(+3.52467 q^{41}\) \(-1.18331 q^{42}\) \(+7.32249 q^{43}\) \(-2.14482 q^{44}\) \(-3.56206 q^{45}\) \(+6.97945 q^{46}\) \(-4.32443 q^{47}\) \(-1.39250 q^{48}\) \(-6.27788 q^{49}\) \(-6.27221 q^{50}\) \(-6.33335 q^{51}\) \(-0.777327 q^{52}\) \(+11.9004 q^{53}\) \(-5.65486 q^{54}\) \(-7.20106 q^{55}\) \(+0.849778 q^{56}\) \(+1.39250 q^{57}\) \(+0.251361 q^{58}\) \(-3.78474 q^{59}\) \(-4.67518 q^{60}\) \(+7.33146 q^{61}\) \(+8.19038 q^{62}\) \(+0.901576 q^{63}\) \(+1.00000 q^{64}\) \(-2.60981 q^{65}\) \(-2.98666 q^{66}\) \(-6.16364 q^{67}\) \(+4.54820 q^{68}\) \(+9.71886 q^{69}\) \(+2.85305 q^{70}\) \(+11.0621 q^{71}\) \(+1.06096 q^{72}\) \(+10.9956 q^{73}\) \(-7.04638 q^{74}\) \(-8.73403 q^{75}\) \(-1.00000 q^{76}\) \(+1.82262 q^{77}\) \(-1.08242 q^{78}\) \(-3.21842 q^{79}\) \(+3.35741 q^{80}\) \(-4.69151 q^{81}\) \(-3.52467 q^{82}\) \(-11.3967 q^{83}\) \(+1.18331 q^{84}\) \(+15.2702 q^{85}\) \(-7.32249 q^{86}\) \(+0.350019 q^{87}\) \(+2.14482 q^{88}\) \(+3.27588 q^{89}\) \(+3.56206 q^{90}\) \(+0.660555 q^{91}\) \(-6.97945 q^{92}\) \(+11.4051 q^{93}\) \(+4.32443 q^{94}\) \(-3.35741 q^{95}\) \(+1.39250 q^{96}\) \(-7.35547 q^{97}\) \(+6.27788 q^{98}\) \(+2.27556 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(34q \) \(\mathstrut -\mathstrut 34q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 34q^{4} \) \(\mathstrut +\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 34q^{8} \) \(\mathstrut +\mathstrut 38q^{9} \) \(\mathstrut -\mathstrut 7q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 38q^{18} \) \(\mathstrut -\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 7q^{20} \) \(\mathstrut -\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 31q^{27} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut +\mathstrut 17q^{30} \) \(\mathstrut -\mathstrut 28q^{31} \) \(\mathstrut -\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 36q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 7q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 24q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 22q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 29q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 21q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut -\mathstrut 9q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut -\mathstrut 28q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 24q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 17q^{60} \) \(\mathstrut +\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 28q^{62} \) \(\mathstrut -\mathstrut 27q^{63} \) \(\mathstrut +\mathstrut 34q^{64} \) \(\mathstrut -\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 51q^{67} \) \(\mathstrut +\mathstrut 8q^{68} \) \(\mathstrut -\mathstrut 17q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut -\mathstrut 38q^{72} \) \(\mathstrut -\mathstrut 26q^{73} \) \(\mathstrut +\mathstrut 36q^{74} \) \(\mathstrut -\mathstrut 109q^{75} \) \(\mathstrut -\mathstrut 34q^{76} \) \(\mathstrut -\mathstrut 28q^{77} \) \(\mathstrut +\mathstrut 9q^{78} \) \(\mathstrut -\mathstrut 36q^{79} \) \(\mathstrut +\mathstrut 7q^{80} \) \(\mathstrut +\mathstrut 6q^{81} \) \(\mathstrut -\mathstrut 9q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 32q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 34q^{89} \) \(\mathstrut -\mathstrut 22q^{90} \) \(\mathstrut -\mathstrut 41q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut -\mathstrut 33q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 22q^{98} \) \(\mathstrut -\mathstrut 28q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.39250 −0.803958 −0.401979 0.915649i \(-0.631677\pi\)
−0.401979 + 0.915649i \(0.631677\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.35741 1.50148 0.750740 0.660598i \(-0.229697\pi\)
0.750740 + 0.660598i \(0.229697\pi\)
\(6\) 1.39250 0.568484
\(7\) −0.849778 −0.321186 −0.160593 0.987021i \(-0.551341\pi\)
−0.160593 + 0.987021i \(0.551341\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.06096 −0.353652
\(10\) −3.35741 −1.06171
\(11\) −2.14482 −0.646689 −0.323344 0.946281i \(-0.604807\pi\)
−0.323344 + 0.946281i \(0.604807\pi\)
\(12\) −1.39250 −0.401979
\(13\) −0.777327 −0.215592 −0.107796 0.994173i \(-0.534379\pi\)
−0.107796 + 0.994173i \(0.534379\pi\)
\(14\) 0.849778 0.227113
\(15\) −4.67518 −1.20713
\(16\) 1.00000 0.250000
\(17\) 4.54820 1.10310 0.551550 0.834142i \(-0.314037\pi\)
0.551550 + 0.834142i \(0.314037\pi\)
\(18\) 1.06096 0.250070
\(19\) −1.00000 −0.229416
\(20\) 3.35741 0.750740
\(21\) 1.18331 0.258220
\(22\) 2.14482 0.457278
\(23\) −6.97945 −1.45532 −0.727658 0.685940i \(-0.759391\pi\)
−0.727658 + 0.685940i \(0.759391\pi\)
\(24\) 1.39250 0.284242
\(25\) 6.27221 1.25444
\(26\) 0.777327 0.152446
\(27\) 5.65486 1.08828
\(28\) −0.849778 −0.160593
\(29\) −0.251361 −0.0466766 −0.0233383 0.999728i \(-0.507429\pi\)
−0.0233383 + 0.999728i \(0.507429\pi\)
\(30\) 4.67518 0.853568
\(31\) −8.19038 −1.47104 −0.735518 0.677506i \(-0.763061\pi\)
−0.735518 + 0.677506i \(0.763061\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.98666 0.519911
\(34\) −4.54820 −0.780009
\(35\) −2.85305 −0.482254
\(36\) −1.06096 −0.176826
\(37\) 7.04638 1.15842 0.579209 0.815179i \(-0.303362\pi\)
0.579209 + 0.815179i \(0.303362\pi\)
\(38\) 1.00000 0.162221
\(39\) 1.08242 0.173327
\(40\) −3.35741 −0.530853
\(41\) 3.52467 0.550462 0.275231 0.961378i \(-0.411246\pi\)
0.275231 + 0.961378i \(0.411246\pi\)
\(42\) −1.18331 −0.182589
\(43\) 7.32249 1.11667 0.558335 0.829616i \(-0.311440\pi\)
0.558335 + 0.829616i \(0.311440\pi\)
\(44\) −2.14482 −0.323344
\(45\) −3.56206 −0.531001
\(46\) 6.97945 1.02906
\(47\) −4.32443 −0.630783 −0.315391 0.948962i \(-0.602136\pi\)
−0.315391 + 0.948962i \(0.602136\pi\)
\(48\) −1.39250 −0.200989
\(49\) −6.27788 −0.896840
\(50\) −6.27221 −0.887025
\(51\) −6.33335 −0.886846
\(52\) −0.777327 −0.107796
\(53\) 11.9004 1.63464 0.817321 0.576182i \(-0.195458\pi\)
0.817321 + 0.576182i \(0.195458\pi\)
\(54\) −5.65486 −0.769529
\(55\) −7.20106 −0.970990
\(56\) 0.849778 0.113556
\(57\) 1.39250 0.184441
\(58\) 0.251361 0.0330053
\(59\) −3.78474 −0.492731 −0.246366 0.969177i \(-0.579236\pi\)
−0.246366 + 0.969177i \(0.579236\pi\)
\(60\) −4.67518 −0.603563
\(61\) 7.33146 0.938697 0.469349 0.883013i \(-0.344489\pi\)
0.469349 + 0.883013i \(0.344489\pi\)
\(62\) 8.19038 1.04018
\(63\) 0.901576 0.113588
\(64\) 1.00000 0.125000
\(65\) −2.60981 −0.323707
\(66\) −2.98666 −0.367632
\(67\) −6.16364 −0.753009 −0.376504 0.926415i \(-0.622874\pi\)
−0.376504 + 0.926415i \(0.622874\pi\)
\(68\) 4.54820 0.551550
\(69\) 9.71886 1.17001
\(70\) 2.85305 0.341005
\(71\) 11.0621 1.31283 0.656414 0.754401i \(-0.272072\pi\)
0.656414 + 0.754401i \(0.272072\pi\)
\(72\) 1.06096 0.125035
\(73\) 10.9956 1.28694 0.643470 0.765471i \(-0.277494\pi\)
0.643470 + 0.765471i \(0.277494\pi\)
\(74\) −7.04638 −0.819125
\(75\) −8.73403 −1.00852
\(76\) −1.00000 −0.114708
\(77\) 1.82262 0.207707
\(78\) −1.08242 −0.122560
\(79\) −3.21842 −0.362101 −0.181051 0.983474i \(-0.557950\pi\)
−0.181051 + 0.983474i \(0.557950\pi\)
\(80\) 3.35741 0.375370
\(81\) −4.69151 −0.521279
\(82\) −3.52467 −0.389235
\(83\) −11.3967 −1.25095 −0.625475 0.780244i \(-0.715095\pi\)
−0.625475 + 0.780244i \(0.715095\pi\)
\(84\) 1.18331 0.129110
\(85\) 15.2702 1.65628
\(86\) −7.32249 −0.789605
\(87\) 0.350019 0.0375260
\(88\) 2.14482 0.228639
\(89\) 3.27588 0.347243 0.173622 0.984812i \(-0.444453\pi\)
0.173622 + 0.984812i \(0.444453\pi\)
\(90\) 3.56206 0.375474
\(91\) 0.660555 0.0692450
\(92\) −6.97945 −0.727658
\(93\) 11.4051 1.18265
\(94\) 4.32443 0.446031
\(95\) −3.35741 −0.344463
\(96\) 1.39250 0.142121
\(97\) −7.35547 −0.746835 −0.373417 0.927663i \(-0.621814\pi\)
−0.373417 + 0.927663i \(0.621814\pi\)
\(98\) 6.27788 0.634161
\(99\) 2.27556 0.228703
\(100\) 6.27221 0.627221
\(101\) −0.891342 −0.0886919 −0.0443459 0.999016i \(-0.514120\pi\)
−0.0443459 + 0.999016i \(0.514120\pi\)
\(102\) 6.33335 0.627095
\(103\) 12.5025 1.23191 0.615953 0.787783i \(-0.288771\pi\)
0.615953 + 0.787783i \(0.288771\pi\)
\(104\) 0.777327 0.0762232
\(105\) 3.97287 0.387712
\(106\) −11.9004 −1.15587
\(107\) −4.18210 −0.404299 −0.202149 0.979355i \(-0.564793\pi\)
−0.202149 + 0.979355i \(0.564793\pi\)
\(108\) 5.65486 0.544139
\(109\) −19.1368 −1.83298 −0.916488 0.400061i \(-0.868989\pi\)
−0.916488 + 0.400061i \(0.868989\pi\)
\(110\) 7.20106 0.686594
\(111\) −9.81206 −0.931319
\(112\) −0.849778 −0.0802965
\(113\) −10.2146 −0.960911 −0.480456 0.877019i \(-0.659529\pi\)
−0.480456 + 0.877019i \(0.659529\pi\)
\(114\) −1.39250 −0.130419
\(115\) −23.4329 −2.18513
\(116\) −0.251361 −0.0233383
\(117\) 0.824709 0.0762444
\(118\) 3.78474 0.348414
\(119\) −3.86496 −0.354300
\(120\) 4.67518 0.426784
\(121\) −6.39973 −0.581794
\(122\) −7.33146 −0.663759
\(123\) −4.90810 −0.442548
\(124\) −8.19038 −0.735518
\(125\) 4.27135 0.382041
\(126\) −0.901576 −0.0803188
\(127\) 2.76687 0.245520 0.122760 0.992436i \(-0.460826\pi\)
0.122760 + 0.992436i \(0.460826\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −10.1965 −0.897756
\(130\) 2.60981 0.228895
\(131\) −1.09375 −0.0955616 −0.0477808 0.998858i \(-0.515215\pi\)
−0.0477808 + 0.998858i \(0.515215\pi\)
\(132\) 2.98666 0.259955
\(133\) 0.849778 0.0736851
\(134\) 6.16364 0.532458
\(135\) 18.9857 1.63403
\(136\) −4.54820 −0.390005
\(137\) 6.26379 0.535152 0.267576 0.963537i \(-0.413777\pi\)
0.267576 + 0.963537i \(0.413777\pi\)
\(138\) −9.71886 −0.827325
\(139\) 0.717250 0.0608364 0.0304182 0.999537i \(-0.490316\pi\)
0.0304182 + 0.999537i \(0.490316\pi\)
\(140\) −2.85305 −0.241127
\(141\) 6.02175 0.507123
\(142\) −11.0621 −0.928310
\(143\) 1.66723 0.139421
\(144\) −1.06096 −0.0884129
\(145\) −0.843923 −0.0700840
\(146\) −10.9956 −0.910004
\(147\) 8.74192 0.721021
\(148\) 7.04638 0.579209
\(149\) −3.01148 −0.246710 −0.123355 0.992363i \(-0.539365\pi\)
−0.123355 + 0.992363i \(0.539365\pi\)
\(150\) 8.73403 0.713131
\(151\) −24.0081 −1.95375 −0.976874 0.213814i \(-0.931411\pi\)
−0.976874 + 0.213814i \(0.931411\pi\)
\(152\) 1.00000 0.0811107
\(153\) −4.82543 −0.390113
\(154\) −1.82262 −0.146871
\(155\) −27.4985 −2.20873
\(156\) 1.08242 0.0866633
\(157\) 6.15466 0.491196 0.245598 0.969372i \(-0.421016\pi\)
0.245598 + 0.969372i \(0.421016\pi\)
\(158\) 3.21842 0.256044
\(159\) −16.5712 −1.31418
\(160\) −3.35741 −0.265427
\(161\) 5.93099 0.467427
\(162\) 4.69151 0.368600
\(163\) −6.53091 −0.511540 −0.255770 0.966738i \(-0.582329\pi\)
−0.255770 + 0.966738i \(0.582329\pi\)
\(164\) 3.52467 0.275231
\(165\) 10.0274 0.780635
\(166\) 11.3967 0.884556
\(167\) −4.15551 −0.321563 −0.160781 0.986990i \(-0.551401\pi\)
−0.160781 + 0.986990i \(0.551401\pi\)
\(168\) −1.18331 −0.0912945
\(169\) −12.3958 −0.953520
\(170\) −15.2702 −1.17117
\(171\) 1.06096 0.0811333
\(172\) 7.32249 0.558335
\(173\) −25.4570 −1.93546 −0.967730 0.251989i \(-0.918915\pi\)
−0.967730 + 0.251989i \(0.918915\pi\)
\(174\) −0.350019 −0.0265349
\(175\) −5.32999 −0.402909
\(176\) −2.14482 −0.161672
\(177\) 5.27024 0.396135
\(178\) −3.27588 −0.245538
\(179\) −7.90890 −0.591139 −0.295569 0.955321i \(-0.595509\pi\)
−0.295569 + 0.955321i \(0.595509\pi\)
\(180\) −3.56206 −0.265501
\(181\) −14.1270 −1.05005 −0.525027 0.851086i \(-0.675945\pi\)
−0.525027 + 0.851086i \(0.675945\pi\)
\(182\) −0.660555 −0.0489636
\(183\) −10.2090 −0.754673
\(184\) 6.97945 0.514532
\(185\) 23.6576 1.73934
\(186\) −11.4051 −0.836260
\(187\) −9.75508 −0.713362
\(188\) −4.32443 −0.315391
\(189\) −4.80538 −0.349540
\(190\) 3.35741 0.243572
\(191\) 10.5742 0.765120 0.382560 0.923931i \(-0.375043\pi\)
0.382560 + 0.923931i \(0.375043\pi\)
\(192\) −1.39250 −0.100495
\(193\) −9.74050 −0.701137 −0.350568 0.936537i \(-0.614012\pi\)
−0.350568 + 0.936537i \(0.614012\pi\)
\(194\) 7.35547 0.528092
\(195\) 3.63415 0.260247
\(196\) −6.27788 −0.448420
\(197\) 3.06523 0.218389 0.109194 0.994020i \(-0.465173\pi\)
0.109194 + 0.994020i \(0.465173\pi\)
\(198\) −2.27556 −0.161717
\(199\) 26.2375 1.85993 0.929964 0.367649i \(-0.119837\pi\)
0.929964 + 0.367649i \(0.119837\pi\)
\(200\) −6.27221 −0.443513
\(201\) 8.58285 0.605387
\(202\) 0.891342 0.0627146
\(203\) 0.213601 0.0149919
\(204\) −6.33335 −0.443423
\(205\) 11.8338 0.826507
\(206\) −12.5025 −0.871089
\(207\) 7.40489 0.514675
\(208\) −0.777327 −0.0538979
\(209\) 2.14482 0.148361
\(210\) −3.97287 −0.274154
\(211\) −1.00000 −0.0688428
\(212\) 11.9004 0.817321
\(213\) −15.4039 −1.05546
\(214\) 4.18210 0.285883
\(215\) 24.5846 1.67666
\(216\) −5.65486 −0.384765
\(217\) 6.96000 0.472476
\(218\) 19.1368 1.29611
\(219\) −15.3114 −1.03465
\(220\) −7.20106 −0.485495
\(221\) −3.53544 −0.237819
\(222\) 9.81206 0.658542
\(223\) −6.86014 −0.459389 −0.229694 0.973263i \(-0.573773\pi\)
−0.229694 + 0.973263i \(0.573773\pi\)
\(224\) 0.849778 0.0567782
\(225\) −6.65454 −0.443636
\(226\) 10.2146 0.679467
\(227\) −20.4334 −1.35621 −0.678105 0.734965i \(-0.737198\pi\)
−0.678105 + 0.734965i \(0.737198\pi\)
\(228\) 1.39250 0.0922203
\(229\) 17.0542 1.12697 0.563486 0.826126i \(-0.309460\pi\)
0.563486 + 0.826126i \(0.309460\pi\)
\(230\) 23.4329 1.54512
\(231\) −2.53800 −0.166988
\(232\) 0.251361 0.0165027
\(233\) −12.4324 −0.814477 −0.407238 0.913322i \(-0.633508\pi\)
−0.407238 + 0.913322i \(0.633508\pi\)
\(234\) −0.824709 −0.0539129
\(235\) −14.5189 −0.947108
\(236\) −3.78474 −0.246366
\(237\) 4.48164 0.291114
\(238\) 3.86496 0.250528
\(239\) −13.7443 −0.889046 −0.444523 0.895767i \(-0.646627\pi\)
−0.444523 + 0.895767i \(0.646627\pi\)
\(240\) −4.67518 −0.301782
\(241\) 16.4439 1.05924 0.529622 0.848234i \(-0.322334\pi\)
0.529622 + 0.848234i \(0.322334\pi\)
\(242\) 6.39973 0.411390
\(243\) −10.4317 −0.669193
\(244\) 7.33146 0.469349
\(245\) −21.0774 −1.34659
\(246\) 4.90810 0.312929
\(247\) 0.777327 0.0494601
\(248\) 8.19038 0.520089
\(249\) 15.8699 1.00571
\(250\) −4.27135 −0.270144
\(251\) 6.17856 0.389987 0.194994 0.980805i \(-0.437531\pi\)
0.194994 + 0.980805i \(0.437531\pi\)
\(252\) 0.901576 0.0567940
\(253\) 14.9697 0.941137
\(254\) −2.76687 −0.173609
\(255\) −21.2636 −1.33158
\(256\) 1.00000 0.0625000
\(257\) −10.2880 −0.641749 −0.320875 0.947122i \(-0.603977\pi\)
−0.320875 + 0.947122i \(0.603977\pi\)
\(258\) 10.1965 0.634809
\(259\) −5.98786 −0.372067
\(260\) −2.60981 −0.161853
\(261\) 0.266683 0.0165073
\(262\) 1.09375 0.0675722
\(263\) 17.8019 1.09771 0.548857 0.835916i \(-0.315063\pi\)
0.548857 + 0.835916i \(0.315063\pi\)
\(264\) −2.98666 −0.183816
\(265\) 39.9545 2.45438
\(266\) −0.849778 −0.0521032
\(267\) −4.56166 −0.279169
\(268\) −6.16364 −0.376504
\(269\) −28.1483 −1.71623 −0.858115 0.513457i \(-0.828365\pi\)
−0.858115 + 0.513457i \(0.828365\pi\)
\(270\) −18.9857 −1.15543
\(271\) 18.1743 1.10401 0.552005 0.833841i \(-0.313863\pi\)
0.552005 + 0.833841i \(0.313863\pi\)
\(272\) 4.54820 0.275775
\(273\) −0.919821 −0.0556701
\(274\) −6.26379 −0.378409
\(275\) −13.4528 −0.811234
\(276\) 9.71886 0.585007
\(277\) −12.9510 −0.778148 −0.389074 0.921207i \(-0.627205\pi\)
−0.389074 + 0.921207i \(0.627205\pi\)
\(278\) −0.717250 −0.0430178
\(279\) 8.68962 0.520234
\(280\) 2.85305 0.170503
\(281\) 24.5209 1.46279 0.731396 0.681953i \(-0.238869\pi\)
0.731396 + 0.681953i \(0.238869\pi\)
\(282\) −6.02175 −0.358590
\(283\) 21.1643 1.25809 0.629044 0.777370i \(-0.283447\pi\)
0.629044 + 0.777370i \(0.283447\pi\)
\(284\) 11.0621 0.656414
\(285\) 4.67518 0.276934
\(286\) −1.66723 −0.0985854
\(287\) −2.99519 −0.176801
\(288\) 1.06096 0.0625174
\(289\) 3.68609 0.216829
\(290\) 0.843923 0.0495569
\(291\) 10.2425 0.600424
\(292\) 10.9956 0.643470
\(293\) −25.2265 −1.47375 −0.736873 0.676031i \(-0.763699\pi\)
−0.736873 + 0.676031i \(0.763699\pi\)
\(294\) −8.74192 −0.509839
\(295\) −12.7069 −0.739826
\(296\) −7.04638 −0.409563
\(297\) −12.1287 −0.703778
\(298\) 3.01148 0.174451
\(299\) 5.42532 0.313754
\(300\) −8.73403 −0.504260
\(301\) −6.22249 −0.358659
\(302\) 24.0081 1.38151
\(303\) 1.24119 0.0713045
\(304\) −1.00000 −0.0573539
\(305\) 24.6147 1.40944
\(306\) 4.82543 0.275852
\(307\) −21.7084 −1.23896 −0.619482 0.785011i \(-0.712657\pi\)
−0.619482 + 0.785011i \(0.712657\pi\)
\(308\) 1.82262 0.103854
\(309\) −17.4096 −0.990400
\(310\) 27.4985 1.56181
\(311\) −4.79442 −0.271867 −0.135933 0.990718i \(-0.543403\pi\)
−0.135933 + 0.990718i \(0.543403\pi\)
\(312\) −1.08242 −0.0612802
\(313\) 1.43081 0.0808744 0.0404372 0.999182i \(-0.487125\pi\)
0.0404372 + 0.999182i \(0.487125\pi\)
\(314\) −6.15466 −0.347328
\(315\) 3.02696 0.170550
\(316\) −3.21842 −0.181051
\(317\) −24.2901 −1.36427 −0.682133 0.731228i \(-0.738948\pi\)
−0.682133 + 0.731228i \(0.738948\pi\)
\(318\) 16.5712 0.929268
\(319\) 0.539126 0.0301852
\(320\) 3.35741 0.187685
\(321\) 5.82356 0.325039
\(322\) −5.93099 −0.330521
\(323\) −4.54820 −0.253068
\(324\) −4.69151 −0.260639
\(325\) −4.87556 −0.270448
\(326\) 6.53091 0.361714
\(327\) 26.6480 1.47364
\(328\) −3.52467 −0.194618
\(329\) 3.67480 0.202599
\(330\) −10.0274 −0.551993
\(331\) 26.9152 1.47939 0.739695 0.672942i \(-0.234970\pi\)
0.739695 + 0.672942i \(0.234970\pi\)
\(332\) −11.3967 −0.625475
\(333\) −7.47589 −0.409677
\(334\) 4.15551 0.227379
\(335\) −20.6939 −1.13063
\(336\) 1.18331 0.0645550
\(337\) −33.1035 −1.80326 −0.901632 0.432503i \(-0.857630\pi\)
−0.901632 + 0.432503i \(0.857630\pi\)
\(338\) 12.3958 0.674241
\(339\) 14.2238 0.772532
\(340\) 15.2702 0.828141
\(341\) 17.5669 0.951302
\(342\) −1.06096 −0.0573699
\(343\) 11.2832 0.609238
\(344\) −7.32249 −0.394802
\(345\) 32.6302 1.75675
\(346\) 25.4570 1.36858
\(347\) −3.45265 −0.185348 −0.0926741 0.995696i \(-0.529541\pi\)
−0.0926741 + 0.995696i \(0.529541\pi\)
\(348\) 0.350019 0.0187630
\(349\) −20.8504 −1.11609 −0.558047 0.829809i \(-0.688449\pi\)
−0.558047 + 0.829809i \(0.688449\pi\)
\(350\) 5.32999 0.284900
\(351\) −4.39568 −0.234624
\(352\) 2.14482 0.114320
\(353\) 16.1395 0.859016 0.429508 0.903063i \(-0.358687\pi\)
0.429508 + 0.903063i \(0.358687\pi\)
\(354\) −5.27024 −0.280110
\(355\) 37.1400 1.97119
\(356\) 3.27588 0.173622
\(357\) 5.38194 0.284842
\(358\) 7.90890 0.417998
\(359\) 25.4051 1.34083 0.670416 0.741986i \(-0.266116\pi\)
0.670416 + 0.741986i \(0.266116\pi\)
\(360\) 3.56206 0.187737
\(361\) 1.00000 0.0526316
\(362\) 14.1270 0.742500
\(363\) 8.91160 0.467738
\(364\) 0.660555 0.0346225
\(365\) 36.9168 1.93232
\(366\) 10.2090 0.533634
\(367\) −30.7769 −1.60654 −0.803271 0.595613i \(-0.796909\pi\)
−0.803271 + 0.595613i \(0.796909\pi\)
\(368\) −6.97945 −0.363829
\(369\) −3.73952 −0.194672
\(370\) −23.6576 −1.22990
\(371\) −10.1127 −0.525024
\(372\) 11.4051 0.591325
\(373\) 10.6394 0.550885 0.275442 0.961318i \(-0.411176\pi\)
0.275442 + 0.961318i \(0.411176\pi\)
\(374\) 9.75508 0.504423
\(375\) −5.94783 −0.307145
\(376\) 4.32443 0.223015
\(377\) 0.195390 0.0100631
\(378\) 4.80538 0.247162
\(379\) −0.975664 −0.0501165 −0.0250582 0.999686i \(-0.507977\pi\)
−0.0250582 + 0.999686i \(0.507977\pi\)
\(380\) −3.35741 −0.172232
\(381\) −3.85285 −0.197387
\(382\) −10.5742 −0.541021
\(383\) −9.27974 −0.474173 −0.237086 0.971489i \(-0.576192\pi\)
−0.237086 + 0.971489i \(0.576192\pi\)
\(384\) 1.39250 0.0710605
\(385\) 6.11930 0.311868
\(386\) 9.74050 0.495778
\(387\) −7.76884 −0.394912
\(388\) −7.35547 −0.373417
\(389\) −7.83048 −0.397021 −0.198511 0.980099i \(-0.563610\pi\)
−0.198511 + 0.980099i \(0.563610\pi\)
\(390\) −3.63415 −0.184022
\(391\) −31.7439 −1.60536
\(392\) 6.27788 0.317081
\(393\) 1.52305 0.0768275
\(394\) −3.06523 −0.154424
\(395\) −10.8056 −0.543688
\(396\) 2.27556 0.114351
\(397\) 17.8431 0.895519 0.447759 0.894154i \(-0.352222\pi\)
0.447759 + 0.894154i \(0.352222\pi\)
\(398\) −26.2375 −1.31517
\(399\) −1.18331 −0.0592397
\(400\) 6.27221 0.313611
\(401\) −11.1835 −0.558477 −0.279239 0.960222i \(-0.590082\pi\)
−0.279239 + 0.960222i \(0.590082\pi\)
\(402\) −8.58285 −0.428074
\(403\) 6.36660 0.317143
\(404\) −0.891342 −0.0443459
\(405\) −15.7513 −0.782690
\(406\) −0.213601 −0.0106009
\(407\) −15.1132 −0.749136
\(408\) 6.33335 0.313547
\(409\) 19.1858 0.948674 0.474337 0.880343i \(-0.342688\pi\)
0.474337 + 0.880343i \(0.342688\pi\)
\(410\) −11.8338 −0.584429
\(411\) −8.72230 −0.430240
\(412\) 12.5025 0.615953
\(413\) 3.21619 0.158258
\(414\) −7.40489 −0.363930
\(415\) −38.2634 −1.87828
\(416\) 0.777327 0.0381116
\(417\) −0.998768 −0.0489099
\(418\) −2.14482 −0.104907
\(419\) 12.9192 0.631142 0.315571 0.948902i \(-0.397804\pi\)
0.315571 + 0.948902i \(0.397804\pi\)
\(420\) 3.97287 0.193856
\(421\) −13.5680 −0.661262 −0.330631 0.943760i \(-0.607262\pi\)
−0.330631 + 0.943760i \(0.607262\pi\)
\(422\) 1.00000 0.0486792
\(423\) 4.58803 0.223077
\(424\) −11.9004 −0.577933
\(425\) 28.5273 1.38378
\(426\) 15.4039 0.746322
\(427\) −6.23011 −0.301496
\(428\) −4.18210 −0.202149
\(429\) −2.32161 −0.112088
\(430\) −24.5846 −1.18558
\(431\) −21.1833 −1.02036 −0.510182 0.860067i \(-0.670422\pi\)
−0.510182 + 0.860067i \(0.670422\pi\)
\(432\) 5.65486 0.272070
\(433\) 22.9647 1.10361 0.551807 0.833972i \(-0.313939\pi\)
0.551807 + 0.833972i \(0.313939\pi\)
\(434\) −6.96000 −0.334091
\(435\) 1.17516 0.0563446
\(436\) −19.1368 −0.916488
\(437\) 6.97945 0.333873
\(438\) 15.3114 0.731605
\(439\) −1.64684 −0.0785994 −0.0392997 0.999227i \(-0.512513\pi\)
−0.0392997 + 0.999227i \(0.512513\pi\)
\(440\) 7.20106 0.343297
\(441\) 6.66055 0.317169
\(442\) 3.53544 0.168164
\(443\) 28.5103 1.35457 0.677283 0.735723i \(-0.263157\pi\)
0.677283 + 0.735723i \(0.263157\pi\)
\(444\) −9.81206 −0.465660
\(445\) 10.9985 0.521379
\(446\) 6.86014 0.324837
\(447\) 4.19348 0.198345
\(448\) −0.849778 −0.0401482
\(449\) 16.8172 0.793651 0.396825 0.917894i \(-0.370112\pi\)
0.396825 + 0.917894i \(0.370112\pi\)
\(450\) 6.65454 0.313698
\(451\) −7.55981 −0.355977
\(452\) −10.2146 −0.480456
\(453\) 33.4311 1.57073
\(454\) 20.4334 0.958985
\(455\) 2.21776 0.103970
\(456\) −1.39250 −0.0652096
\(457\) −8.86638 −0.414752 −0.207376 0.978261i \(-0.566492\pi\)
−0.207376 + 0.978261i \(0.566492\pi\)
\(458\) −17.0542 −0.796889
\(459\) 25.7194 1.20048
\(460\) −23.4329 −1.09256
\(461\) 21.1207 0.983689 0.491844 0.870683i \(-0.336323\pi\)
0.491844 + 0.870683i \(0.336323\pi\)
\(462\) 2.53800 0.118078
\(463\) 13.7115 0.637227 0.318614 0.947885i \(-0.396783\pi\)
0.318614 + 0.947885i \(0.396783\pi\)
\(464\) −0.251361 −0.0116692
\(465\) 38.2915 1.77573
\(466\) 12.4324 0.575922
\(467\) −20.4409 −0.945890 −0.472945 0.881092i \(-0.656809\pi\)
−0.472945 + 0.881092i \(0.656809\pi\)
\(468\) 0.824709 0.0381222
\(469\) 5.23773 0.241856
\(470\) 14.5189 0.669706
\(471\) −8.57034 −0.394900
\(472\) 3.78474 0.174207
\(473\) −15.7055 −0.722138
\(474\) −4.48164 −0.205849
\(475\) −6.27221 −0.287789
\(476\) −3.86496 −0.177150
\(477\) −12.6258 −0.578094
\(478\) 13.7443 0.628650
\(479\) 28.7313 1.31277 0.656383 0.754428i \(-0.272086\pi\)
0.656383 + 0.754428i \(0.272086\pi\)
\(480\) 4.67518 0.213392
\(481\) −5.47734 −0.249745
\(482\) −16.4439 −0.748999
\(483\) −8.25887 −0.375792
\(484\) −6.39973 −0.290897
\(485\) −24.6953 −1.12136
\(486\) 10.4317 0.473191
\(487\) −28.7492 −1.30275 −0.651375 0.758756i \(-0.725807\pi\)
−0.651375 + 0.758756i \(0.725807\pi\)
\(488\) −7.33146 −0.331880
\(489\) 9.09426 0.411257
\(490\) 21.0774 0.952181
\(491\) 1.12776 0.0508951 0.0254475 0.999676i \(-0.491899\pi\)
0.0254475 + 0.999676i \(0.491899\pi\)
\(492\) −4.90810 −0.221274
\(493\) −1.14324 −0.0514890
\(494\) −0.777327 −0.0349736
\(495\) 7.64000 0.343392
\(496\) −8.19038 −0.367759
\(497\) −9.40032 −0.421662
\(498\) −15.8699 −0.711145
\(499\) −16.3458 −0.731739 −0.365870 0.930666i \(-0.619228\pi\)
−0.365870 + 0.930666i \(0.619228\pi\)
\(500\) 4.27135 0.191020
\(501\) 5.78653 0.258523
\(502\) −6.17856 −0.275763
\(503\) −25.6277 −1.14268 −0.571341 0.820713i \(-0.693577\pi\)
−0.571341 + 0.820713i \(0.693577\pi\)
\(504\) −0.901576 −0.0401594
\(505\) −2.99260 −0.133169
\(506\) −14.9697 −0.665484
\(507\) 17.2610 0.766590
\(508\) 2.76687 0.122760
\(509\) 8.43307 0.373789 0.186895 0.982380i \(-0.440158\pi\)
0.186895 + 0.982380i \(0.440158\pi\)
\(510\) 21.2636 0.941570
\(511\) −9.34384 −0.413347
\(512\) −1.00000 −0.0441942
\(513\) −5.65486 −0.249668
\(514\) 10.2880 0.453785
\(515\) 41.9760 1.84968
\(516\) −10.1965 −0.448878
\(517\) 9.27514 0.407920
\(518\) 5.98786 0.263091
\(519\) 35.4488 1.55603
\(520\) 2.60981 0.114448
\(521\) 4.96436 0.217492 0.108746 0.994070i \(-0.465316\pi\)
0.108746 + 0.994070i \(0.465316\pi\)
\(522\) −0.266683 −0.0116724
\(523\) −45.0053 −1.96795 −0.983973 0.178318i \(-0.942935\pi\)
−0.983973 + 0.178318i \(0.942935\pi\)
\(524\) −1.09375 −0.0477808
\(525\) 7.42199 0.323922
\(526\) −17.8019 −0.776201
\(527\) −37.2514 −1.62270
\(528\) 2.98666 0.129978
\(529\) 25.7128 1.11795
\(530\) −39.9545 −1.73551
\(531\) 4.01544 0.174255
\(532\) 0.849778 0.0368425
\(533\) −2.73983 −0.118675
\(534\) 4.56166 0.197402
\(535\) −14.0410 −0.607047
\(536\) 6.16364 0.266229
\(537\) 11.0131 0.475251
\(538\) 28.1483 1.21356
\(539\) 13.4649 0.579976
\(540\) 18.9857 0.817015
\(541\) −10.6429 −0.457573 −0.228787 0.973477i \(-0.573476\pi\)
−0.228787 + 0.973477i \(0.573476\pi\)
\(542\) −18.1743 −0.780654
\(543\) 19.6718 0.844199
\(544\) −4.54820 −0.195002
\(545\) −64.2503 −2.75218
\(546\) 0.919821 0.0393647
\(547\) 11.2212 0.479784 0.239892 0.970800i \(-0.422888\pi\)
0.239892 + 0.970800i \(0.422888\pi\)
\(548\) 6.26379 0.267576
\(549\) −7.77835 −0.331972
\(550\) 13.4528 0.573629
\(551\) 0.251361 0.0107083
\(552\) −9.71886 −0.413662
\(553\) 2.73495 0.116302
\(554\) 12.9510 0.550233
\(555\) −32.9431 −1.39836
\(556\) 0.717250 0.0304182
\(557\) −1.66300 −0.0704634 −0.0352317 0.999379i \(-0.511217\pi\)
−0.0352317 + 0.999379i \(0.511217\pi\)
\(558\) −8.68962 −0.367861
\(559\) −5.69197 −0.240745
\(560\) −2.85305 −0.120564
\(561\) 13.5839 0.573513
\(562\) −24.5209 −1.03435
\(563\) 29.5273 1.24443 0.622214 0.782847i \(-0.286233\pi\)
0.622214 + 0.782847i \(0.286233\pi\)
\(564\) 6.02175 0.253561
\(565\) −34.2947 −1.44279
\(566\) −21.1643 −0.889602
\(567\) 3.98674 0.167427
\(568\) −11.0621 −0.464155
\(569\) 6.53252 0.273858 0.136929 0.990581i \(-0.456277\pi\)
0.136929 + 0.990581i \(0.456277\pi\)
\(570\) −4.67518 −0.195822
\(571\) −13.8230 −0.578474 −0.289237 0.957258i \(-0.593402\pi\)
−0.289237 + 0.957258i \(0.593402\pi\)
\(572\) 1.66723 0.0697104
\(573\) −14.7245 −0.615124
\(574\) 2.99519 0.125017
\(575\) −43.7766 −1.82561
\(576\) −1.06096 −0.0442065
\(577\) −33.2987 −1.38624 −0.693122 0.720820i \(-0.743765\pi\)
−0.693122 + 0.720820i \(0.743765\pi\)
\(578\) −3.68609 −0.153321
\(579\) 13.5636 0.563684
\(580\) −0.843923 −0.0350420
\(581\) 9.68467 0.401788
\(582\) −10.2425 −0.424564
\(583\) −25.5242 −1.05711
\(584\) −10.9956 −0.455002
\(585\) 2.76889 0.114479
\(586\) 25.2265 1.04210
\(587\) −35.3780 −1.46020 −0.730102 0.683338i \(-0.760528\pi\)
−0.730102 + 0.683338i \(0.760528\pi\)
\(588\) 8.74192 0.360511
\(589\) 8.19038 0.337479
\(590\) 12.7069 0.523136
\(591\) −4.26832 −0.175575
\(592\) 7.04638 0.289604
\(593\) −37.2644 −1.53027 −0.765133 0.643872i \(-0.777327\pi\)
−0.765133 + 0.643872i \(0.777327\pi\)
\(594\) 12.1287 0.497646
\(595\) −12.9763 −0.531975
\(596\) −3.01148 −0.123355
\(597\) −36.5356 −1.49530
\(598\) −5.42532 −0.221858
\(599\) −42.1481 −1.72212 −0.861061 0.508501i \(-0.830200\pi\)
−0.861061 + 0.508501i \(0.830200\pi\)
\(600\) 8.73403 0.356565
\(601\) −37.2608 −1.51990 −0.759950 0.649981i \(-0.774777\pi\)
−0.759950 + 0.649981i \(0.774777\pi\)
\(602\) 6.22249 0.253610
\(603\) 6.53935 0.266303
\(604\) −24.0081 −0.976874
\(605\) −21.4865 −0.873552
\(606\) −1.24119 −0.0504199
\(607\) −12.0230 −0.488000 −0.244000 0.969775i \(-0.578460\pi\)
−0.244000 + 0.969775i \(0.578460\pi\)
\(608\) 1.00000 0.0405554
\(609\) −0.297439 −0.0120528
\(610\) −24.6147 −0.996621
\(611\) 3.36150 0.135992
\(612\) −4.82543 −0.195057
\(613\) 13.2090 0.533507 0.266753 0.963765i \(-0.414049\pi\)
0.266753 + 0.963765i \(0.414049\pi\)
\(614\) 21.7084 0.876080
\(615\) −16.4785 −0.664477
\(616\) −1.82262 −0.0734356
\(617\) 1.53422 0.0617654 0.0308827 0.999523i \(-0.490168\pi\)
0.0308827 + 0.999523i \(0.490168\pi\)
\(618\) 17.4096 0.700319
\(619\) −25.9259 −1.04205 −0.521024 0.853542i \(-0.674450\pi\)
−0.521024 + 0.853542i \(0.674450\pi\)
\(620\) −27.4985 −1.10437
\(621\) −39.4679 −1.58379
\(622\) 4.79442 0.192239
\(623\) −2.78377 −0.111530
\(624\) 1.08242 0.0433317
\(625\) −17.0204 −0.680816
\(626\) −1.43081 −0.0571869
\(627\) −2.98666 −0.119276
\(628\) 6.15466 0.245598
\(629\) 32.0483 1.27785
\(630\) −3.02696 −0.120597
\(631\) −13.2570 −0.527752 −0.263876 0.964557i \(-0.585001\pi\)
−0.263876 + 0.964557i \(0.585001\pi\)
\(632\) 3.21842 0.128022
\(633\) 1.39250 0.0553467
\(634\) 24.2901 0.964682
\(635\) 9.28951 0.368643
\(636\) −16.5712 −0.657092
\(637\) 4.87996 0.193351
\(638\) −0.539126 −0.0213442
\(639\) −11.7364 −0.464284
\(640\) −3.35741 −0.132713
\(641\) −0.315487 −0.0124610 −0.00623049 0.999981i \(-0.501983\pi\)
−0.00623049 + 0.999981i \(0.501983\pi\)
\(642\) −5.82356 −0.229838
\(643\) 12.6930 0.500564 0.250282 0.968173i \(-0.419477\pi\)
0.250282 + 0.968173i \(0.419477\pi\)
\(644\) 5.93099 0.233714
\(645\) −34.2340 −1.34796
\(646\) 4.54820 0.178946
\(647\) 0.454440 0.0178659 0.00893294 0.999960i \(-0.497157\pi\)
0.00893294 + 0.999960i \(0.497157\pi\)
\(648\) 4.69151 0.184300
\(649\) 8.11760 0.318644
\(650\) 4.87556 0.191235
\(651\) −9.69177 −0.379851
\(652\) −6.53091 −0.255770
\(653\) −22.1696 −0.867562 −0.433781 0.901018i \(-0.642821\pi\)
−0.433781 + 0.901018i \(0.642821\pi\)
\(654\) −26.6480 −1.04202
\(655\) −3.67218 −0.143484
\(656\) 3.52467 0.137615
\(657\) −11.6659 −0.455129
\(658\) −3.67480 −0.143259
\(659\) −13.8961 −0.541315 −0.270658 0.962676i \(-0.587241\pi\)
−0.270658 + 0.962676i \(0.587241\pi\)
\(660\) 10.0274 0.390318
\(661\) −39.2335 −1.52601 −0.763003 0.646394i \(-0.776276\pi\)
−0.763003 + 0.646394i \(0.776276\pi\)
\(662\) −26.9152 −1.04609
\(663\) 4.92308 0.191197
\(664\) 11.3967 0.442278
\(665\) 2.85305 0.110637
\(666\) 7.47589 0.289685
\(667\) 1.75436 0.0679293
\(668\) −4.15551 −0.160781
\(669\) 9.55271 0.369329
\(670\) 20.6939 0.799475
\(671\) −15.7247 −0.607045
\(672\) −1.18331 −0.0456473
\(673\) 2.02221 0.0779503 0.0389752 0.999240i \(-0.487591\pi\)
0.0389752 + 0.999240i \(0.487591\pi\)
\(674\) 33.1035 1.27510
\(675\) 35.4685 1.36518
\(676\) −12.3958 −0.476760
\(677\) −3.13448 −0.120468 −0.0602340 0.998184i \(-0.519185\pi\)
−0.0602340 + 0.998184i \(0.519185\pi\)
\(678\) −14.2238 −0.546263
\(679\) 6.25052 0.239873
\(680\) −15.2702 −0.585584
\(681\) 28.4534 1.09033
\(682\) −17.5669 −0.672672
\(683\) −14.7763 −0.565398 −0.282699 0.959209i \(-0.591230\pi\)
−0.282699 + 0.959209i \(0.591230\pi\)
\(684\) 1.06096 0.0405666
\(685\) 21.0301 0.803520
\(686\) −11.2832 −0.430796
\(687\) −23.7479 −0.906038
\(688\) 7.32249 0.279167
\(689\) −9.25049 −0.352415
\(690\) −32.6302 −1.24221
\(691\) 33.7133 1.28251 0.641257 0.767326i \(-0.278413\pi\)
0.641257 + 0.767326i \(0.278413\pi\)
\(692\) −25.4570 −0.967730
\(693\) −1.93372 −0.0734560
\(694\) 3.45265 0.131061
\(695\) 2.40811 0.0913446
\(696\) −0.350019 −0.0132675
\(697\) 16.0309 0.607214
\(698\) 20.8504 0.789198
\(699\) 17.3121 0.654805
\(700\) −5.32999 −0.201455
\(701\) −13.7241 −0.518353 −0.259176 0.965830i \(-0.583451\pi\)
−0.259176 + 0.965830i \(0.583451\pi\)
\(702\) 4.39568 0.165904
\(703\) −7.04638 −0.265759
\(704\) −2.14482 −0.0808361
\(705\) 20.2175 0.761435
\(706\) −16.1395 −0.607416
\(707\) 0.757443 0.0284866
\(708\) 5.27024 0.198068
\(709\) −1.64024 −0.0616004 −0.0308002 0.999526i \(-0.509806\pi\)
−0.0308002 + 0.999526i \(0.509806\pi\)
\(710\) −37.1400 −1.39384
\(711\) 3.41460 0.128058
\(712\) −3.27588 −0.122769
\(713\) 57.1644 2.14082
\(714\) −5.38194 −0.201414
\(715\) 5.59758 0.209337
\(716\) −7.90890 −0.295569
\(717\) 19.1389 0.714756
\(718\) −25.4051 −0.948111
\(719\) 0.225491 0.00840938 0.00420469 0.999991i \(-0.498662\pi\)
0.00420469 + 0.999991i \(0.498662\pi\)
\(720\) −3.56206 −0.132750
\(721\) −10.6243 −0.395671
\(722\) −1.00000 −0.0372161
\(723\) −22.8980 −0.851588
\(724\) −14.1270 −0.525027
\(725\) −1.57659 −0.0585531
\(726\) −8.91160 −0.330740
\(727\) −23.2646 −0.862836 −0.431418 0.902152i \(-0.641987\pi\)
−0.431418 + 0.902152i \(0.641987\pi\)
\(728\) −0.660555 −0.0244818
\(729\) 28.6006 1.05928
\(730\) −36.9168 −1.36635
\(731\) 33.3041 1.23180
\(732\) −10.2090 −0.377337
\(733\) 26.2032 0.967838 0.483919 0.875113i \(-0.339213\pi\)
0.483919 + 0.875113i \(0.339213\pi\)
\(734\) 30.7769 1.13600
\(735\) 29.3502 1.08260
\(736\) 6.97945 0.257266
\(737\) 13.2199 0.486962
\(738\) 3.73952 0.137654
\(739\) 32.2217 1.18529 0.592646 0.805463i \(-0.298083\pi\)
0.592646 + 0.805463i \(0.298083\pi\)
\(740\) 23.6576 0.869671
\(741\) −1.08242 −0.0397639
\(742\) 10.1127 0.371248
\(743\) 41.5597 1.52468 0.762340 0.647177i \(-0.224051\pi\)
0.762340 + 0.647177i \(0.224051\pi\)
\(744\) −11.4051 −0.418130
\(745\) −10.1108 −0.370431
\(746\) −10.6394 −0.389534
\(747\) 12.0914 0.442401
\(748\) −9.75508 −0.356681
\(749\) 3.55386 0.129855
\(750\) 5.94783 0.217184
\(751\) −36.8167 −1.34346 −0.671730 0.740796i \(-0.734448\pi\)
−0.671730 + 0.740796i \(0.734448\pi\)
\(752\) −4.32443 −0.157696
\(753\) −8.60362 −0.313533
\(754\) −0.195390 −0.00711568
\(755\) −80.6050 −2.93352
\(756\) −4.80538 −0.174770
\(757\) 33.6429 1.22277 0.611385 0.791333i \(-0.290613\pi\)
0.611385 + 0.791333i \(0.290613\pi\)
\(758\) 0.975664 0.0354377
\(759\) −20.8452 −0.756635
\(760\) 3.35741 0.121786
\(761\) 13.0996 0.474862 0.237431 0.971404i \(-0.423695\pi\)
0.237431 + 0.971404i \(0.423695\pi\)
\(762\) 3.85285 0.139574
\(763\) 16.2621 0.588726
\(764\) 10.5742 0.382560
\(765\) −16.2010 −0.585747
\(766\) 9.27974 0.335291
\(767\) 2.94198 0.106229
\(768\) −1.39250 −0.0502474
\(769\) −2.82864 −0.102003 −0.0510016 0.998699i \(-0.516241\pi\)
−0.0510016 + 0.998699i \(0.516241\pi\)
\(770\) −6.11930 −0.220524
\(771\) 14.3260 0.515939
\(772\) −9.74050 −0.350568
\(773\) −15.2922 −0.550023 −0.275011 0.961441i \(-0.588682\pi\)
−0.275011 + 0.961441i \(0.588682\pi\)
\(774\) 7.76884 0.279245
\(775\) −51.3718 −1.84533
\(776\) 7.35547 0.264046
\(777\) 8.33807 0.299127
\(778\) 7.83048 0.280736
\(779\) −3.52467 −0.126285
\(780\) 3.63415 0.130123
\(781\) −23.7262 −0.848991
\(782\) 31.7439 1.13516
\(783\) −1.42141 −0.0507972
\(784\) −6.27788 −0.224210
\(785\) 20.6637 0.737520
\(786\) −1.52305 −0.0543252
\(787\) −25.4071 −0.905667 −0.452833 0.891595i \(-0.649587\pi\)
−0.452833 + 0.891595i \(0.649587\pi\)
\(788\) 3.06523 0.109194
\(789\) −24.7891 −0.882516
\(790\) 10.8056 0.384445
\(791\) 8.68017 0.308631
\(792\) −2.27556 −0.0808586
\(793\) −5.69894 −0.202375
\(794\) −17.8431 −0.633227
\(795\) −55.6364 −1.97322
\(796\) 26.2375 0.929964
\(797\) 34.3776 1.21772 0.608859 0.793278i \(-0.291627\pi\)
0.608859 + 0.793278i \(0.291627\pi\)
\(798\) 1.18331 0.0418888
\(799\) −19.6684 −0.695816
\(800\) −6.27221 −0.221756
\(801\) −3.47557 −0.122803
\(802\) 11.1835 0.394903
\(803\) −23.5837 −0.832250
\(804\) 8.58285 0.302694
\(805\) 19.9128 0.701833
\(806\) −6.36660 −0.224254
\(807\) 39.1964 1.37978
\(808\) 0.891342 0.0313573
\(809\) −38.7471 −1.36228 −0.681138 0.732155i \(-0.738515\pi\)
−0.681138 + 0.732155i \(0.738515\pi\)
\(810\) 15.7513 0.553445
\(811\) 10.8228 0.380038 0.190019 0.981780i \(-0.439145\pi\)
0.190019 + 0.981780i \(0.439145\pi\)
\(812\) 0.213601 0.00749593
\(813\) −25.3077 −0.887578
\(814\) 15.1132 0.529719
\(815\) −21.9269 −0.768068
\(816\) −6.33335 −0.221711
\(817\) −7.32249 −0.256182
\(818\) −19.1858 −0.670814
\(819\) −0.700820 −0.0244886
\(820\) 11.8338 0.413254
\(821\) −9.93060 −0.346580 −0.173290 0.984871i \(-0.555440\pi\)
−0.173290 + 0.984871i \(0.555440\pi\)
\(822\) 8.72230 0.304225
\(823\) 49.1566 1.71349 0.856746 0.515739i \(-0.172483\pi\)
0.856746 + 0.515739i \(0.172483\pi\)
\(824\) −12.5025 −0.435544
\(825\) 18.7330 0.652198
\(826\) −3.21619 −0.111906
\(827\) −8.07138 −0.280669 −0.140335 0.990104i \(-0.544818\pi\)
−0.140335 + 0.990104i \(0.544818\pi\)
\(828\) 7.40489 0.257338
\(829\) −35.5026 −1.23306 −0.616529 0.787332i \(-0.711462\pi\)
−0.616529 + 0.787332i \(0.711462\pi\)
\(830\) 38.2634 1.32814
\(831\) 18.0342 0.625598
\(832\) −0.777327 −0.0269490
\(833\) −28.5530 −0.989304
\(834\) 0.998768 0.0345845
\(835\) −13.9518 −0.482820
\(836\) 2.14482 0.0741803
\(837\) −46.3155 −1.60090
\(838\) −12.9192 −0.446285
\(839\) −34.3719 −1.18665 −0.593325 0.804963i \(-0.702185\pi\)
−0.593325 + 0.804963i \(0.702185\pi\)
\(840\) −3.97287 −0.137077
\(841\) −28.9368 −0.997821
\(842\) 13.5680 0.467583
\(843\) −34.1452 −1.17602
\(844\) −1.00000 −0.0344214
\(845\) −41.6177 −1.43169
\(846\) −4.58803 −0.157740
\(847\) 5.43835 0.186864
\(848\) 11.9004 0.408661
\(849\) −29.4712 −1.01145
\(850\) −28.5273 −0.978477
\(851\) −49.1799 −1.68587
\(852\) −15.4039 −0.527729
\(853\) −39.8769 −1.36536 −0.682680 0.730717i \(-0.739186\pi\)
−0.682680 + 0.730717i \(0.739186\pi\)
\(854\) 6.23011 0.213190
\(855\) 3.56206 0.121820
\(856\) 4.18210 0.142941
\(857\) 1.92791 0.0658560 0.0329280 0.999458i \(-0.489517\pi\)
0.0329280 + 0.999458i \(0.489517\pi\)
\(858\) 2.32161 0.0792585
\(859\) 29.0474 0.991085 0.495542 0.868584i \(-0.334969\pi\)
0.495542 + 0.868584i \(0.334969\pi\)
\(860\) 24.5846 0.838329
\(861\) 4.17079 0.142140
\(862\) 21.1833 0.721506
\(863\) 34.2769 1.16680 0.583399 0.812186i \(-0.301722\pi\)
0.583399 + 0.812186i \(0.301722\pi\)
\(864\) −5.65486 −0.192382
\(865\) −85.4696 −2.90605
\(866\) −22.9647 −0.780373
\(867\) −5.13287 −0.174321
\(868\) 6.96000 0.236238
\(869\) 6.90295 0.234167
\(870\) −1.17516 −0.0398416
\(871\) 4.79117 0.162342
\(872\) 19.1368 0.648055
\(873\) 7.80383 0.264119
\(874\) −6.97945 −0.236084
\(875\) −3.62970 −0.122706
\(876\) −15.3114 −0.517323
\(877\) 15.4852 0.522897 0.261449 0.965217i \(-0.415800\pi\)
0.261449 + 0.965217i \(0.415800\pi\)
\(878\) 1.64684 0.0555782
\(879\) 35.1278 1.18483
\(880\) −7.20106 −0.242748
\(881\) −48.3720 −1.62969 −0.814847 0.579675i \(-0.803179\pi\)
−0.814847 + 0.579675i \(0.803179\pi\)
\(882\) −6.66055 −0.224272
\(883\) −7.41026 −0.249375 −0.124688 0.992196i \(-0.539793\pi\)
−0.124688 + 0.992196i \(0.539793\pi\)
\(884\) −3.53544 −0.118910
\(885\) 17.6944 0.594789
\(886\) −28.5103 −0.957822
\(887\) −0.367165 −0.0123282 −0.00616409 0.999981i \(-0.501962\pi\)
−0.00616409 + 0.999981i \(0.501962\pi\)
\(888\) 9.81206 0.329271
\(889\) −2.35122 −0.0788575
\(890\) −10.9985 −0.368670
\(891\) 10.0625 0.337105
\(892\) −6.86014 −0.229694
\(893\) 4.32443 0.144711
\(894\) −4.19348 −0.140251
\(895\) −26.5534 −0.887583
\(896\) 0.849778 0.0283891
\(897\) −7.55473 −0.252245
\(898\) −16.8172 −0.561196
\(899\) 2.05874 0.0686629
\(900\) −6.65454 −0.221818
\(901\) 54.1253 1.80317
\(902\) 7.55981 0.251714
\(903\) 8.66480 0.288346
\(904\) 10.2146 0.339733
\(905\) −47.4303 −1.57664
\(906\) −33.4311 −1.11068
\(907\) −49.7330 −1.65136 −0.825679 0.564141i \(-0.809208\pi\)
−0.825679 + 0.564141i \(0.809208\pi\)
\(908\) −20.4334 −0.678105
\(909\) 0.945674 0.0313660
\(910\) −2.21776 −0.0735179
\(911\) 51.6919 1.71263 0.856315 0.516455i \(-0.172749\pi\)
0.856315 + 0.516455i \(0.172749\pi\)
\(912\) 1.39250 0.0461101
\(913\) 24.4439 0.808976
\(914\) 8.86638 0.293274
\(915\) −34.2759 −1.13313
\(916\) 17.0542 0.563486
\(917\) 0.929446 0.0306930
\(918\) −25.7194 −0.848868
\(919\) −34.8366 −1.14915 −0.574576 0.818451i \(-0.694833\pi\)
−0.574576 + 0.818451i \(0.694833\pi\)
\(920\) 23.4329 0.772560
\(921\) 30.2289 0.996075
\(922\) −21.1207 −0.695573
\(923\) −8.59886 −0.283035
\(924\) −2.53800 −0.0834940
\(925\) 44.1964 1.45317
\(926\) −13.7115 −0.450588
\(927\) −13.2646 −0.435666
\(928\) 0.251361 0.00825134
\(929\) 32.4167 1.06356 0.531778 0.846884i \(-0.321524\pi\)
0.531778 + 0.846884i \(0.321524\pi\)
\(930\) −38.2915 −1.25563
\(931\) 6.27788 0.205749
\(932\) −12.4324 −0.407238
\(933\) 6.67621 0.218569
\(934\) 20.4409 0.668845
\(935\) −32.7518 −1.07110
\(936\) −0.824709 −0.0269565
\(937\) −33.6149 −1.09815 −0.549075 0.835773i \(-0.685020\pi\)
−0.549075 + 0.835773i \(0.685020\pi\)
\(938\) −5.23773 −0.171018
\(939\) −1.99240 −0.0650196
\(940\) −14.5189 −0.473554
\(941\) 47.3598 1.54388 0.771942 0.635693i \(-0.219285\pi\)
0.771942 + 0.635693i \(0.219285\pi\)
\(942\) 8.57034 0.279237
\(943\) −24.6003 −0.801096
\(944\) −3.78474 −0.123183
\(945\) −16.1336 −0.524827
\(946\) 15.7055 0.510629
\(947\) −16.9913 −0.552144 −0.276072 0.961137i \(-0.589033\pi\)
−0.276072 + 0.961137i \(0.589033\pi\)
\(948\) 4.48164 0.145557
\(949\) −8.54719 −0.277454
\(950\) 6.27221 0.203498
\(951\) 33.8238 1.09681
\(952\) 3.86496 0.125264
\(953\) 49.9263 1.61727 0.808637 0.588309i \(-0.200206\pi\)
0.808637 + 0.588309i \(0.200206\pi\)
\(954\) 12.6258 0.408774
\(955\) 35.5018 1.14881
\(956\) −13.7443 −0.444523
\(957\) −0.750730 −0.0242677
\(958\) −28.7313 −0.928266
\(959\) −5.32283 −0.171883
\(960\) −4.67518 −0.150891
\(961\) 36.0823 1.16394
\(962\) 5.47734 0.176597
\(963\) 4.43702 0.142981
\(964\) 16.4439 0.529622
\(965\) −32.7029 −1.05274
\(966\) 8.25887 0.265725
\(967\) −5.14364 −0.165408 −0.0827042 0.996574i \(-0.526356\pi\)
−0.0827042 + 0.996574i \(0.526356\pi\)
\(968\) 6.39973 0.205695
\(969\) 6.33335 0.203456
\(970\) 24.6953 0.792920
\(971\) 2.93073 0.0940517 0.0470259 0.998894i \(-0.485026\pi\)
0.0470259 + 0.998894i \(0.485026\pi\)
\(972\) −10.4317 −0.334596
\(973\) −0.609504 −0.0195398
\(974\) 28.7492 0.921183
\(975\) 6.78920 0.217428
\(976\) 7.33146 0.234674
\(977\) 11.6691 0.373328 0.186664 0.982424i \(-0.440232\pi\)
0.186664 + 0.982424i \(0.440232\pi\)
\(978\) −9.09426 −0.290802
\(979\) −7.02620 −0.224558
\(980\) −21.0774 −0.673293
\(981\) 20.3033 0.648235
\(982\) −1.12776 −0.0359882
\(983\) −4.45089 −0.141961 −0.0709806 0.997478i \(-0.522613\pi\)
−0.0709806 + 0.997478i \(0.522613\pi\)
\(984\) 4.90810 0.156464
\(985\) 10.2912 0.327906
\(986\) 1.14324 0.0364082
\(987\) −5.11715 −0.162881
\(988\) 0.777327 0.0247301
\(989\) −51.1070 −1.62511
\(990\) −7.64000 −0.242815
\(991\) 47.0891 1.49583 0.747917 0.663793i \(-0.231054\pi\)
0.747917 + 0.663793i \(0.231054\pi\)
\(992\) 8.19038 0.260045
\(993\) −37.4792 −1.18937
\(994\) 9.40032 0.298160
\(995\) 88.0902 2.79265
\(996\) 15.8699 0.502856
\(997\) −44.9972 −1.42507 −0.712537 0.701634i \(-0.752454\pi\)
−0.712537 + 0.701634i \(0.752454\pi\)
\(998\) 16.3458 0.517418
\(999\) 39.8463 1.26068
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 \(a_p\))