Properties

Label 8043.2.a.t.1.19
Level 8043
Weight 2
Character 8043.1
Self dual Yes
Analytic conductor 64.224
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8043.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2236783457\)
Analytic rank: \(0\)
Dimension: \(52\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 8043.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.869058 q^{2}\) \(-1.00000 q^{3}\) \(-1.24474 q^{4}\) \(-3.05181 q^{5}\) \(+0.869058 q^{6}\) \(+1.00000 q^{7}\) \(+2.81987 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.869058 q^{2}\) \(-1.00000 q^{3}\) \(-1.24474 q^{4}\) \(-3.05181 q^{5}\) \(+0.869058 q^{6}\) \(+1.00000 q^{7}\) \(+2.81987 q^{8}\) \(+1.00000 q^{9}\) \(+2.65220 q^{10}\) \(+0.712082 q^{11}\) \(+1.24474 q^{12}\) \(-4.02159 q^{13}\) \(-0.869058 q^{14}\) \(+3.05181 q^{15}\) \(+0.0388458 q^{16}\) \(+1.21971 q^{17}\) \(-0.869058 q^{18}\) \(-3.38040 q^{19}\) \(+3.79870 q^{20}\) \(-1.00000 q^{21}\) \(-0.618841 q^{22}\) \(+2.85470 q^{23}\) \(-2.81987 q^{24}\) \(+4.31353 q^{25}\) \(+3.49499 q^{26}\) \(-1.00000 q^{27}\) \(-1.24474 q^{28}\) \(-3.20901 q^{29}\) \(-2.65220 q^{30}\) \(-5.18946 q^{31}\) \(-5.67349 q^{32}\) \(-0.712082 q^{33}\) \(-1.06000 q^{34}\) \(-3.05181 q^{35}\) \(-1.24474 q^{36}\) \(+10.3804 q^{37}\) \(+2.93776 q^{38}\) \(+4.02159 q^{39}\) \(-8.60569 q^{40}\) \(-2.02565 q^{41}\) \(+0.869058 q^{42}\) \(+5.92118 q^{43}\) \(-0.886355 q^{44}\) \(-3.05181 q^{45}\) \(-2.48090 q^{46}\) \(-4.02786 q^{47}\) \(-0.0388458 q^{48}\) \(+1.00000 q^{49}\) \(-3.74871 q^{50}\) \(-1.21971 q^{51}\) \(+5.00582 q^{52}\) \(+1.52434 q^{53}\) \(+0.869058 q^{54}\) \(-2.17314 q^{55}\) \(+2.81987 q^{56}\) \(+3.38040 q^{57}\) \(+2.78882 q^{58}\) \(+4.36113 q^{59}\) \(-3.79870 q^{60}\) \(-1.75357 q^{61}\) \(+4.50994 q^{62}\) \(+1.00000 q^{63}\) \(+4.85291 q^{64}\) \(+12.2731 q^{65}\) \(+0.618841 q^{66}\) \(+3.24868 q^{67}\) \(-1.51822 q^{68}\) \(-2.85470 q^{69}\) \(+2.65220 q^{70}\) \(+11.4733 q^{71}\) \(+2.81987 q^{72}\) \(+6.96468 q^{73}\) \(-9.02120 q^{74}\) \(-4.31353 q^{75}\) \(+4.20770 q^{76}\) \(+0.712082 q^{77}\) \(-3.49499 q^{78}\) \(-11.0316 q^{79}\) \(-0.118550 q^{80}\) \(+1.00000 q^{81}\) \(+1.76040 q^{82}\) \(-12.8639 q^{83}\) \(+1.24474 q^{84}\) \(-3.72231 q^{85}\) \(-5.14586 q^{86}\) \(+3.20901 q^{87}\) \(+2.00798 q^{88}\) \(+0.646252 q^{89}\) \(+2.65220 q^{90}\) \(-4.02159 q^{91}\) \(-3.55335 q^{92}\) \(+5.18946 q^{93}\) \(+3.50044 q^{94}\) \(+10.3163 q^{95}\) \(+5.67349 q^{96}\) \(-18.1231 q^{97}\) \(-0.869058 q^{98}\) \(+0.712082 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 52q^{3} \) \(\mathstrut +\mathstrut 61q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut -\mathstrut 3q^{6} \) \(\mathstrut +\mathstrut 52q^{7} \) \(\mathstrut +\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 52q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 61q^{12} \) \(\mathstrut +\mathstrut 44q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 7q^{15} \) \(\mathstrut +\mathstrut 95q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 7q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 52q^{21} \) \(\mathstrut +\mathstrut 19q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 24q^{24} \) \(\mathstrut +\mathstrut 83q^{25} \) \(\mathstrut -\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 61q^{28} \) \(\mathstrut +\mathstrut 31q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut +\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 61q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut -\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 44q^{39} \) \(\mathstrut +\mathstrut 20q^{40} \) \(\mathstrut -\mathstrut 25q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut +\mathstrut 75q^{43} \) \(\mathstrut +\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 7q^{45} \) \(\mathstrut +\mathstrut 36q^{46} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut +\mathstrut 26q^{50} \) \(\mathstrut +\mathstrut 6q^{51} \) \(\mathstrut +\mathstrut 88q^{52} \) \(\mathstrut +\mathstrut 70q^{53} \) \(\mathstrut -\mathstrut 3q^{54} \) \(\mathstrut +\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 7q^{57} \) \(\mathstrut +\mathstrut 48q^{58} \) \(\mathstrut -\mathstrut 27q^{59} \) \(\mathstrut +\mathstrut 21q^{60} \) \(\mathstrut +\mathstrut 59q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 138q^{64} \) \(\mathstrut +\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 19q^{66} \) \(\mathstrut +\mathstrut 65q^{67} \) \(\mathstrut -\mathstrut 8q^{68} \) \(\mathstrut +\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut +\mathstrut 38q^{74} \) \(\mathstrut -\mathstrut 83q^{75} \) \(\mathstrut +\mathstrut 31q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 5q^{80} \) \(\mathstrut +\mathstrut 52q^{81} \) \(\mathstrut +\mathstrut 51q^{82} \) \(\mathstrut -\mathstrut 30q^{83} \) \(\mathstrut -\mathstrut 61q^{84} \) \(\mathstrut +\mathstrut 70q^{85} \) \(\mathstrut +\mathstrut 29q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut +\mathstrut 90q^{88} \) \(\mathstrut -\mathstrut q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut +\mathstrut 44q^{91} \) \(\mathstrut +\mathstrut 34q^{92} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 27q^{94} \) \(\mathstrut +\mathstrut 9q^{95} \) \(\mathstrut -\mathstrut 71q^{96} \) \(\mathstrut +\mathstrut 73q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.869058 −0.614517 −0.307259 0.951626i \(-0.599412\pi\)
−0.307259 + 0.951626i \(0.599412\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.24474 −0.622369
\(5\) −3.05181 −1.36481 −0.682405 0.730974i \(-0.739066\pi\)
−0.682405 + 0.730974i \(0.739066\pi\)
\(6\) 0.869058 0.354792
\(7\) 1.00000 0.377964
\(8\) 2.81987 0.996973
\(9\) 1.00000 0.333333
\(10\) 2.65220 0.838699
\(11\) 0.712082 0.214701 0.107350 0.994221i \(-0.465763\pi\)
0.107350 + 0.994221i \(0.465763\pi\)
\(12\) 1.24474 0.359325
\(13\) −4.02159 −1.11539 −0.557694 0.830047i \(-0.688314\pi\)
−0.557694 + 0.830047i \(0.688314\pi\)
\(14\) −0.869058 −0.232266
\(15\) 3.05181 0.787973
\(16\) 0.0388458 0.00971145
\(17\) 1.21971 0.295823 0.147911 0.989001i \(-0.452745\pi\)
0.147911 + 0.989001i \(0.452745\pi\)
\(18\) −0.869058 −0.204839
\(19\) −3.38040 −0.775516 −0.387758 0.921761i \(-0.626750\pi\)
−0.387758 + 0.921761i \(0.626750\pi\)
\(20\) 3.79870 0.849415
\(21\) −1.00000 −0.218218
\(22\) −0.618841 −0.131937
\(23\) 2.85470 0.595245 0.297623 0.954684i \(-0.403806\pi\)
0.297623 + 0.954684i \(0.403806\pi\)
\(24\) −2.81987 −0.575603
\(25\) 4.31353 0.862706
\(26\) 3.49499 0.685425
\(27\) −1.00000 −0.192450
\(28\) −1.24474 −0.235233
\(29\) −3.20901 −0.595898 −0.297949 0.954582i \(-0.596303\pi\)
−0.297949 + 0.954582i \(0.596303\pi\)
\(30\) −2.65220 −0.484223
\(31\) −5.18946 −0.932054 −0.466027 0.884770i \(-0.654315\pi\)
−0.466027 + 0.884770i \(0.654315\pi\)
\(32\) −5.67349 −1.00294
\(33\) −0.712082 −0.123958
\(34\) −1.06000 −0.181788
\(35\) −3.05181 −0.515850
\(36\) −1.24474 −0.207456
\(37\) 10.3804 1.70653 0.853266 0.521476i \(-0.174618\pi\)
0.853266 + 0.521476i \(0.174618\pi\)
\(38\) 2.93776 0.476568
\(39\) 4.02159 0.643969
\(40\) −8.60569 −1.36068
\(41\) −2.02565 −0.316353 −0.158176 0.987411i \(-0.550561\pi\)
−0.158176 + 0.987411i \(0.550561\pi\)
\(42\) 0.869058 0.134099
\(43\) 5.92118 0.902972 0.451486 0.892278i \(-0.350894\pi\)
0.451486 + 0.892278i \(0.350894\pi\)
\(44\) −0.886355 −0.133623
\(45\) −3.05181 −0.454937
\(46\) −2.48090 −0.365789
\(47\) −4.02786 −0.587524 −0.293762 0.955879i \(-0.594907\pi\)
−0.293762 + 0.955879i \(0.594907\pi\)
\(48\) −0.0388458 −0.00560691
\(49\) 1.00000 0.142857
\(50\) −3.74871 −0.530148
\(51\) −1.21971 −0.170793
\(52\) 5.00582 0.694182
\(53\) 1.52434 0.209385 0.104692 0.994505i \(-0.466614\pi\)
0.104692 + 0.994505i \(0.466614\pi\)
\(54\) 0.869058 0.118264
\(55\) −2.17314 −0.293026
\(56\) 2.81987 0.376821
\(57\) 3.38040 0.447744
\(58\) 2.78882 0.366190
\(59\) 4.36113 0.567771 0.283885 0.958858i \(-0.408377\pi\)
0.283885 + 0.958858i \(0.408377\pi\)
\(60\) −3.79870 −0.490410
\(61\) −1.75357 −0.224522 −0.112261 0.993679i \(-0.535809\pi\)
−0.112261 + 0.993679i \(0.535809\pi\)
\(62\) 4.50994 0.572763
\(63\) 1.00000 0.125988
\(64\) 4.85291 0.606613
\(65\) 12.2731 1.52229
\(66\) 0.618841 0.0761741
\(67\) 3.24868 0.396890 0.198445 0.980112i \(-0.436411\pi\)
0.198445 + 0.980112i \(0.436411\pi\)
\(68\) −1.51822 −0.184111
\(69\) −2.85470 −0.343665
\(70\) 2.65220 0.316998
\(71\) 11.4733 1.36162 0.680812 0.732458i \(-0.261627\pi\)
0.680812 + 0.732458i \(0.261627\pi\)
\(72\) 2.81987 0.332324
\(73\) 6.96468 0.815154 0.407577 0.913171i \(-0.366374\pi\)
0.407577 + 0.913171i \(0.366374\pi\)
\(74\) −9.02120 −1.04869
\(75\) −4.31353 −0.498084
\(76\) 4.20770 0.482657
\(77\) 0.712082 0.0811493
\(78\) −3.49499 −0.395730
\(79\) −11.0316 −1.24116 −0.620578 0.784145i \(-0.713102\pi\)
−0.620578 + 0.784145i \(0.713102\pi\)
\(80\) −0.118550 −0.0132543
\(81\) 1.00000 0.111111
\(82\) 1.76040 0.194404
\(83\) −12.8639 −1.41199 −0.705996 0.708216i \(-0.749500\pi\)
−0.705996 + 0.708216i \(0.749500\pi\)
\(84\) 1.24474 0.135812
\(85\) −3.72231 −0.403742
\(86\) −5.14586 −0.554892
\(87\) 3.20901 0.344042
\(88\) 2.00798 0.214051
\(89\) 0.646252 0.0685026 0.0342513 0.999413i \(-0.489095\pi\)
0.0342513 + 0.999413i \(0.489095\pi\)
\(90\) 2.65220 0.279566
\(91\) −4.02159 −0.421577
\(92\) −3.55335 −0.370462
\(93\) 5.18946 0.538122
\(94\) 3.50044 0.361043
\(95\) 10.3163 1.05843
\(96\) 5.67349 0.579048
\(97\) −18.1231 −1.84012 −0.920061 0.391776i \(-0.871861\pi\)
−0.920061 + 0.391776i \(0.871861\pi\)
\(98\) −0.869058 −0.0877882
\(99\) 0.712082 0.0715670
\(100\) −5.36921 −0.536921
\(101\) −1.30201 −0.129555 −0.0647773 0.997900i \(-0.520634\pi\)
−0.0647773 + 0.997900i \(0.520634\pi\)
\(102\) 1.06000 0.104955
\(103\) −12.0119 −1.18357 −0.591783 0.806098i \(-0.701576\pi\)
−0.591783 + 0.806098i \(0.701576\pi\)
\(104\) −11.3403 −1.11201
\(105\) 3.05181 0.297826
\(106\) −1.32474 −0.128670
\(107\) −14.4434 −1.39629 −0.698146 0.715955i \(-0.745991\pi\)
−0.698146 + 0.715955i \(0.745991\pi\)
\(108\) 1.24474 0.119775
\(109\) −1.06043 −0.101571 −0.0507854 0.998710i \(-0.516172\pi\)
−0.0507854 + 0.998710i \(0.516172\pi\)
\(110\) 1.88858 0.180069
\(111\) −10.3804 −0.985267
\(112\) 0.0388458 0.00367058
\(113\) −11.4615 −1.07821 −0.539104 0.842239i \(-0.681237\pi\)
−0.539104 + 0.842239i \(0.681237\pi\)
\(114\) −2.93776 −0.275147
\(115\) −8.71199 −0.812397
\(116\) 3.99437 0.370868
\(117\) −4.02159 −0.371796
\(118\) −3.79008 −0.348905
\(119\) 1.21971 0.111810
\(120\) 8.60569 0.785588
\(121\) −10.4929 −0.953904
\(122\) 1.52396 0.137973
\(123\) 2.02565 0.182646
\(124\) 6.45951 0.580081
\(125\) 2.09497 0.187380
\(126\) −0.869058 −0.0774219
\(127\) −13.0003 −1.15359 −0.576797 0.816888i \(-0.695698\pi\)
−0.576797 + 0.816888i \(0.695698\pi\)
\(128\) 7.12953 0.630167
\(129\) −5.92118 −0.521331
\(130\) −10.6661 −0.935475
\(131\) −21.7017 −1.89609 −0.948045 0.318135i \(-0.896943\pi\)
−0.948045 + 0.318135i \(0.896943\pi\)
\(132\) 0.886355 0.0771473
\(133\) −3.38040 −0.293117
\(134\) −2.82329 −0.243895
\(135\) 3.05181 0.262658
\(136\) 3.43941 0.294927
\(137\) −12.2984 −1.05073 −0.525363 0.850878i \(-0.676070\pi\)
−0.525363 + 0.850878i \(0.676070\pi\)
\(138\) 2.48090 0.211188
\(139\) 10.5398 0.893973 0.446986 0.894541i \(-0.352497\pi\)
0.446986 + 0.894541i \(0.352497\pi\)
\(140\) 3.79870 0.321049
\(141\) 4.02786 0.339207
\(142\) −9.97093 −0.836742
\(143\) −2.86370 −0.239475
\(144\) 0.0388458 0.00323715
\(145\) 9.79328 0.813288
\(146\) −6.05271 −0.500926
\(147\) −1.00000 −0.0824786
\(148\) −12.9209 −1.06209
\(149\) 18.4051 1.50781 0.753904 0.656984i \(-0.228168\pi\)
0.753904 + 0.656984i \(0.228168\pi\)
\(150\) 3.74871 0.306081
\(151\) 6.75993 0.550115 0.275058 0.961428i \(-0.411303\pi\)
0.275058 + 0.961428i \(0.411303\pi\)
\(152\) −9.53226 −0.773169
\(153\) 1.21971 0.0986075
\(154\) −0.618841 −0.0498676
\(155\) 15.8372 1.27208
\(156\) −5.00582 −0.400786
\(157\) −0.695158 −0.0554796 −0.0277398 0.999615i \(-0.508831\pi\)
−0.0277398 + 0.999615i \(0.508831\pi\)
\(158\) 9.58713 0.762711
\(159\) −1.52434 −0.120888
\(160\) 17.3144 1.36882
\(161\) 2.85470 0.224982
\(162\) −0.869058 −0.0682797
\(163\) 15.8268 1.23965 0.619826 0.784739i \(-0.287203\pi\)
0.619826 + 0.784739i \(0.287203\pi\)
\(164\) 2.52140 0.196888
\(165\) 2.17314 0.169179
\(166\) 11.1794 0.867693
\(167\) −20.4671 −1.58379 −0.791895 0.610657i \(-0.790906\pi\)
−0.791895 + 0.610657i \(0.790906\pi\)
\(168\) −2.81987 −0.217557
\(169\) 3.17317 0.244090
\(170\) 3.23491 0.248106
\(171\) −3.38040 −0.258505
\(172\) −7.37032 −0.561982
\(173\) −15.3906 −1.17013 −0.585064 0.810987i \(-0.698931\pi\)
−0.585064 + 0.810987i \(0.698931\pi\)
\(174\) −2.78882 −0.211420
\(175\) 4.31353 0.326072
\(176\) 0.0276614 0.00208506
\(177\) −4.36113 −0.327803
\(178\) −0.561631 −0.0420960
\(179\) 7.40804 0.553703 0.276852 0.960913i \(-0.410709\pi\)
0.276852 + 0.960913i \(0.410709\pi\)
\(180\) 3.79870 0.283138
\(181\) −3.80490 −0.282816 −0.141408 0.989951i \(-0.545163\pi\)
−0.141408 + 0.989951i \(0.545163\pi\)
\(182\) 3.49499 0.259066
\(183\) 1.75357 0.129628
\(184\) 8.04986 0.593444
\(185\) −31.6791 −2.32909
\(186\) −4.50994 −0.330685
\(187\) 0.868532 0.0635134
\(188\) 5.01363 0.365656
\(189\) −1.00000 −0.0727393
\(190\) −8.96548 −0.650425
\(191\) −11.5600 −0.836451 −0.418226 0.908343i \(-0.637348\pi\)
−0.418226 + 0.908343i \(0.637348\pi\)
\(192\) −4.85291 −0.350228
\(193\) 8.47034 0.609709 0.304854 0.952399i \(-0.401392\pi\)
0.304854 + 0.952399i \(0.401392\pi\)
\(194\) 15.7500 1.13079
\(195\) −12.2731 −0.878896
\(196\) −1.24474 −0.0889098
\(197\) 8.76026 0.624143 0.312071 0.950059i \(-0.398977\pi\)
0.312071 + 0.950059i \(0.398977\pi\)
\(198\) −0.618841 −0.0439791
\(199\) 22.6094 1.60274 0.801371 0.598168i \(-0.204104\pi\)
0.801371 + 0.598168i \(0.204104\pi\)
\(200\) 12.1636 0.860095
\(201\) −3.24868 −0.229144
\(202\) 1.13152 0.0796135
\(203\) −3.20901 −0.225228
\(204\) 1.51822 0.106296
\(205\) 6.18188 0.431761
\(206\) 10.4390 0.727321
\(207\) 2.85470 0.198415
\(208\) −0.156222 −0.0108320
\(209\) −2.40712 −0.166504
\(210\) −2.65220 −0.183019
\(211\) −11.0757 −0.762483 −0.381242 0.924475i \(-0.624503\pi\)
−0.381242 + 0.924475i \(0.624503\pi\)
\(212\) −1.89741 −0.130314
\(213\) −11.4733 −0.786134
\(214\) 12.5521 0.858045
\(215\) −18.0703 −1.23239
\(216\) −2.81987 −0.191868
\(217\) −5.18946 −0.352283
\(218\) 0.921576 0.0624170
\(219\) −6.96468 −0.470629
\(220\) 2.70499 0.182370
\(221\) −4.90516 −0.329957
\(222\) 9.02120 0.605463
\(223\) 12.2137 0.817891 0.408946 0.912559i \(-0.365897\pi\)
0.408946 + 0.912559i \(0.365897\pi\)
\(224\) −5.67349 −0.379076
\(225\) 4.31353 0.287569
\(226\) 9.96072 0.662577
\(227\) 5.02074 0.333238 0.166619 0.986021i \(-0.446715\pi\)
0.166619 + 0.986021i \(0.446715\pi\)
\(228\) −4.20770 −0.278662
\(229\) −17.1485 −1.13320 −0.566601 0.823992i \(-0.691742\pi\)
−0.566601 + 0.823992i \(0.691742\pi\)
\(230\) 7.57123 0.499232
\(231\) −0.712082 −0.0468516
\(232\) −9.04898 −0.594095
\(233\) −26.1749 −1.71477 −0.857386 0.514674i \(-0.827913\pi\)
−0.857386 + 0.514674i \(0.827913\pi\)
\(234\) 3.49499 0.228475
\(235\) 12.2923 0.801858
\(236\) −5.42846 −0.353363
\(237\) 11.0316 0.716581
\(238\) −1.06000 −0.0687094
\(239\) −3.38308 −0.218833 −0.109417 0.993996i \(-0.534898\pi\)
−0.109417 + 0.993996i \(0.534898\pi\)
\(240\) 0.118550 0.00765236
\(241\) 13.9845 0.900819 0.450409 0.892822i \(-0.351278\pi\)
0.450409 + 0.892822i \(0.351278\pi\)
\(242\) 9.11898 0.586190
\(243\) −1.00000 −0.0641500
\(244\) 2.18274 0.139735
\(245\) −3.05181 −0.194973
\(246\) −1.76040 −0.112239
\(247\) 13.5946 0.865001
\(248\) −14.6336 −0.929233
\(249\) 12.8639 0.815214
\(250\) −1.82065 −0.115148
\(251\) 12.9214 0.815589 0.407794 0.913074i \(-0.366298\pi\)
0.407794 + 0.913074i \(0.366298\pi\)
\(252\) −1.24474 −0.0784111
\(253\) 2.03278 0.127800
\(254\) 11.2981 0.708903
\(255\) 3.72231 0.233100
\(256\) −15.9018 −0.993862
\(257\) 4.45689 0.278013 0.139007 0.990291i \(-0.455609\pi\)
0.139007 + 0.990291i \(0.455609\pi\)
\(258\) 5.14586 0.320367
\(259\) 10.3804 0.645008
\(260\) −15.2768 −0.947427
\(261\) −3.20901 −0.198633
\(262\) 18.8601 1.16518
\(263\) −26.0734 −1.60776 −0.803878 0.594795i \(-0.797233\pi\)
−0.803878 + 0.594795i \(0.797233\pi\)
\(264\) −2.00798 −0.123582
\(265\) −4.65200 −0.285770
\(266\) 2.93776 0.180126
\(267\) −0.646252 −0.0395500
\(268\) −4.04375 −0.247012
\(269\) 24.1132 1.47020 0.735102 0.677956i \(-0.237134\pi\)
0.735102 + 0.677956i \(0.237134\pi\)
\(270\) −2.65220 −0.161408
\(271\) 17.6735 1.07359 0.536793 0.843714i \(-0.319636\pi\)
0.536793 + 0.843714i \(0.319636\pi\)
\(272\) 0.0473805 0.00287287
\(273\) 4.02159 0.243398
\(274\) 10.6881 0.645689
\(275\) 3.07159 0.185224
\(276\) 3.55335 0.213886
\(277\) 13.5147 0.812021 0.406010 0.913868i \(-0.366920\pi\)
0.406010 + 0.913868i \(0.366920\pi\)
\(278\) −9.15969 −0.549361
\(279\) −5.18946 −0.310685
\(280\) −8.60569 −0.514288
\(281\) 11.0748 0.660667 0.330333 0.943864i \(-0.392839\pi\)
0.330333 + 0.943864i \(0.392839\pi\)
\(282\) −3.50044 −0.208448
\(283\) 14.9421 0.888217 0.444109 0.895973i \(-0.353520\pi\)
0.444109 + 0.895973i \(0.353520\pi\)
\(284\) −14.2812 −0.847433
\(285\) −10.3163 −0.611086
\(286\) 2.48872 0.147161
\(287\) −2.02565 −0.119570
\(288\) −5.67349 −0.334314
\(289\) −15.5123 −0.912489
\(290\) −8.51093 −0.499779
\(291\) 18.1231 1.06239
\(292\) −8.66919 −0.507326
\(293\) −19.3031 −1.12770 −0.563851 0.825877i \(-0.690681\pi\)
−0.563851 + 0.825877i \(0.690681\pi\)
\(294\) 0.869058 0.0506845
\(295\) −13.3093 −0.774899
\(296\) 29.2714 1.70137
\(297\) −0.712082 −0.0413192
\(298\) −15.9951 −0.926574
\(299\) −11.4804 −0.663929
\(300\) 5.36921 0.309992
\(301\) 5.92118 0.341291
\(302\) −5.87477 −0.338055
\(303\) 1.30201 0.0747983
\(304\) −0.131314 −0.00753138
\(305\) 5.35156 0.306430
\(306\) −1.06000 −0.0605960
\(307\) 25.4155 1.45054 0.725270 0.688465i \(-0.241715\pi\)
0.725270 + 0.688465i \(0.241715\pi\)
\(308\) −0.886355 −0.0505048
\(309\) 12.0119 0.683332
\(310\) −13.7635 −0.781713
\(311\) −24.6491 −1.39772 −0.698861 0.715257i \(-0.746310\pi\)
−0.698861 + 0.715257i \(0.746310\pi\)
\(312\) 11.3403 0.642020
\(313\) −8.72404 −0.493112 −0.246556 0.969129i \(-0.579299\pi\)
−0.246556 + 0.969129i \(0.579299\pi\)
\(314\) 0.604133 0.0340932
\(315\) −3.05181 −0.171950
\(316\) 13.7315 0.772456
\(317\) 11.9952 0.673716 0.336858 0.941555i \(-0.390636\pi\)
0.336858 + 0.941555i \(0.390636\pi\)
\(318\) 1.32474 0.0742879
\(319\) −2.28508 −0.127940
\(320\) −14.8101 −0.827912
\(321\) 14.4434 0.806150
\(322\) −2.48090 −0.138255
\(323\) −4.12310 −0.229415
\(324\) −1.24474 −0.0691521
\(325\) −17.3472 −0.962252
\(326\) −13.7544 −0.761787
\(327\) 1.06043 0.0586419
\(328\) −5.71205 −0.315395
\(329\) −4.02786 −0.222063
\(330\) −1.88858 −0.103963
\(331\) 28.5858 1.57122 0.785610 0.618722i \(-0.212349\pi\)
0.785610 + 0.618722i \(0.212349\pi\)
\(332\) 16.0121 0.878780
\(333\) 10.3804 0.568844
\(334\) 17.7871 0.973267
\(335\) −9.91435 −0.541679
\(336\) −0.0388458 −0.00211921
\(337\) 29.0305 1.58139 0.790697 0.612208i \(-0.209718\pi\)
0.790697 + 0.612208i \(0.209718\pi\)
\(338\) −2.75767 −0.149997
\(339\) 11.4615 0.622503
\(340\) 4.63330 0.251276
\(341\) −3.69532 −0.200113
\(342\) 2.93776 0.158856
\(343\) 1.00000 0.0539949
\(344\) 16.6969 0.900239
\(345\) 8.71199 0.469038
\(346\) 13.3754 0.719064
\(347\) 32.8486 1.76340 0.881701 0.471808i \(-0.156398\pi\)
0.881701 + 0.471808i \(0.156398\pi\)
\(348\) −3.99437 −0.214121
\(349\) 25.5987 1.37027 0.685134 0.728417i \(-0.259744\pi\)
0.685134 + 0.728417i \(0.259744\pi\)
\(350\) −3.74871 −0.200377
\(351\) 4.02159 0.214656
\(352\) −4.03999 −0.215332
\(353\) −25.0781 −1.33477 −0.667385 0.744713i \(-0.732587\pi\)
−0.667385 + 0.744713i \(0.732587\pi\)
\(354\) 3.79008 0.201440
\(355\) −35.0142 −1.85836
\(356\) −0.804414 −0.0426339
\(357\) −1.21971 −0.0645538
\(358\) −6.43802 −0.340260
\(359\) 13.8151 0.729135 0.364568 0.931177i \(-0.381217\pi\)
0.364568 + 0.931177i \(0.381217\pi\)
\(360\) −8.60569 −0.453560
\(361\) −7.57292 −0.398575
\(362\) 3.30668 0.173795
\(363\) 10.4929 0.550736
\(364\) 5.00582 0.262376
\(365\) −21.2549 −1.11253
\(366\) −1.52396 −0.0796585
\(367\) 27.5782 1.43957 0.719784 0.694198i \(-0.244241\pi\)
0.719784 + 0.694198i \(0.244241\pi\)
\(368\) 0.110893 0.00578069
\(369\) −2.02565 −0.105451
\(370\) 27.5310 1.43127
\(371\) 1.52434 0.0791399
\(372\) −6.45951 −0.334910
\(373\) −7.20808 −0.373220 −0.186610 0.982434i \(-0.559750\pi\)
−0.186610 + 0.982434i \(0.559750\pi\)
\(374\) −0.754805 −0.0390301
\(375\) −2.09497 −0.108184
\(376\) −11.3580 −0.585745
\(377\) 12.9053 0.664657
\(378\) 0.869058 0.0446995
\(379\) −21.5284 −1.10584 −0.552920 0.833234i \(-0.686486\pi\)
−0.552920 + 0.833234i \(0.686486\pi\)
\(380\) −12.8411 −0.658735
\(381\) 13.0003 0.666027
\(382\) 10.0463 0.514014
\(383\) −1.00000 −0.0510976
\(384\) −7.12953 −0.363827
\(385\) −2.17314 −0.110753
\(386\) −7.36122 −0.374676
\(387\) 5.92118 0.300991
\(388\) 22.5585 1.14523
\(389\) −12.8543 −0.651737 −0.325869 0.945415i \(-0.605657\pi\)
−0.325869 + 0.945415i \(0.605657\pi\)
\(390\) 10.6661 0.540097
\(391\) 3.48190 0.176087
\(392\) 2.81987 0.142425
\(393\) 21.7017 1.09471
\(394\) −7.61318 −0.383547
\(395\) 33.6664 1.69394
\(396\) −0.886355 −0.0445410
\(397\) −2.78599 −0.139825 −0.0699123 0.997553i \(-0.522272\pi\)
−0.0699123 + 0.997553i \(0.522272\pi\)
\(398\) −19.6489 −0.984912
\(399\) 3.38040 0.169231
\(400\) 0.167563 0.00837813
\(401\) −3.30807 −0.165197 −0.0825986 0.996583i \(-0.526322\pi\)
−0.0825986 + 0.996583i \(0.526322\pi\)
\(402\) 2.82329 0.140813
\(403\) 20.8699 1.03960
\(404\) 1.62066 0.0806307
\(405\) −3.05181 −0.151646
\(406\) 2.78882 0.138407
\(407\) 7.39172 0.366394
\(408\) −3.43941 −0.170276
\(409\) 10.3338 0.510972 0.255486 0.966813i \(-0.417765\pi\)
0.255486 + 0.966813i \(0.417765\pi\)
\(410\) −5.37242 −0.265325
\(411\) 12.2984 0.606637
\(412\) 14.9516 0.736614
\(413\) 4.36113 0.214597
\(414\) −2.48090 −0.121930
\(415\) 39.2580 1.92710
\(416\) 22.8164 1.11867
\(417\) −10.5398 −0.516135
\(418\) 2.09193 0.102320
\(419\) 17.3773 0.848937 0.424469 0.905443i \(-0.360461\pi\)
0.424469 + 0.905443i \(0.360461\pi\)
\(420\) −3.79870 −0.185358
\(421\) 3.35597 0.163560 0.0817801 0.996650i \(-0.473939\pi\)
0.0817801 + 0.996650i \(0.473939\pi\)
\(422\) 9.62544 0.468559
\(423\) −4.02786 −0.195841
\(424\) 4.29844 0.208751
\(425\) 5.26125 0.255208
\(426\) 9.97093 0.483093
\(427\) −1.75357 −0.0848613
\(428\) 17.9782 0.869009
\(429\) 2.86370 0.138261
\(430\) 15.7042 0.757322
\(431\) −1.68530 −0.0811778 −0.0405889 0.999176i \(-0.512923\pi\)
−0.0405889 + 0.999176i \(0.512923\pi\)
\(432\) −0.0388458 −0.00186897
\(433\) 29.4616 1.41583 0.707917 0.706296i \(-0.249635\pi\)
0.707917 + 0.706296i \(0.249635\pi\)
\(434\) 4.50994 0.216484
\(435\) −9.79328 −0.469552
\(436\) 1.31996 0.0632145
\(437\) −9.65001 −0.461622
\(438\) 6.05271 0.289210
\(439\) −4.58842 −0.218994 −0.109497 0.993987i \(-0.534924\pi\)
−0.109497 + 0.993987i \(0.534924\pi\)
\(440\) −6.12796 −0.292139
\(441\) 1.00000 0.0476190
\(442\) 4.26287 0.202764
\(443\) −26.7679 −1.27178 −0.635891 0.771779i \(-0.719367\pi\)
−0.635891 + 0.771779i \(0.719367\pi\)
\(444\) 12.9209 0.613199
\(445\) −1.97224 −0.0934930
\(446\) −10.6144 −0.502608
\(447\) −18.4051 −0.870534
\(448\) 4.85291 0.229278
\(449\) 4.15361 0.196021 0.0980104 0.995185i \(-0.468752\pi\)
0.0980104 + 0.995185i \(0.468752\pi\)
\(450\) −3.74871 −0.176716
\(451\) −1.44243 −0.0679212
\(452\) 14.2666 0.671043
\(453\) −6.75993 −0.317609
\(454\) −4.36332 −0.204781
\(455\) 12.2731 0.575372
\(456\) 9.53226 0.446389
\(457\) −37.4012 −1.74955 −0.874777 0.484525i \(-0.838992\pi\)
−0.874777 + 0.484525i \(0.838992\pi\)
\(458\) 14.9030 0.696372
\(459\) −1.21971 −0.0569311
\(460\) 10.8441 0.505610
\(461\) −30.6301 −1.42659 −0.713293 0.700866i \(-0.752797\pi\)
−0.713293 + 0.700866i \(0.752797\pi\)
\(462\) 0.618841 0.0287911
\(463\) 13.2222 0.614488 0.307244 0.951631i \(-0.400593\pi\)
0.307244 + 0.951631i \(0.400593\pi\)
\(464\) −0.124657 −0.00578703
\(465\) −15.8372 −0.734434
\(466\) 22.7475 1.05376
\(467\) 3.84353 0.177857 0.0889286 0.996038i \(-0.471656\pi\)
0.0889286 + 0.996038i \(0.471656\pi\)
\(468\) 5.00582 0.231394
\(469\) 3.24868 0.150010
\(470\) −10.6827 −0.492756
\(471\) 0.695158 0.0320312
\(472\) 12.2978 0.566052
\(473\) 4.21637 0.193869
\(474\) −9.58713 −0.440351
\(475\) −14.5814 −0.669042
\(476\) −1.51822 −0.0695873
\(477\) 1.52434 0.0697949
\(478\) 2.94009 0.134477
\(479\) 14.0308 0.641085 0.320542 0.947234i \(-0.396135\pi\)
0.320542 + 0.947234i \(0.396135\pi\)
\(480\) −17.3144 −0.790291
\(481\) −41.7458 −1.90344
\(482\) −12.1533 −0.553569
\(483\) −2.85470 −0.129893
\(484\) 13.0610 0.593680
\(485\) 55.3082 2.51142
\(486\) 0.869058 0.0394213
\(487\) 21.7892 0.987363 0.493681 0.869643i \(-0.335651\pi\)
0.493681 + 0.869643i \(0.335651\pi\)
\(488\) −4.94484 −0.223842
\(489\) −15.8268 −0.715713
\(490\) 2.65220 0.119814
\(491\) −29.1929 −1.31746 −0.658730 0.752380i \(-0.728906\pi\)
−0.658730 + 0.752380i \(0.728906\pi\)
\(492\) −2.52140 −0.113673
\(493\) −3.91405 −0.176280
\(494\) −11.8145 −0.531558
\(495\) −2.17314 −0.0976753
\(496\) −0.201589 −0.00905159
\(497\) 11.4733 0.514646
\(498\) −11.1794 −0.500963
\(499\) 15.3039 0.685095 0.342547 0.939501i \(-0.388710\pi\)
0.342547 + 0.939501i \(0.388710\pi\)
\(500\) −2.60769 −0.116619
\(501\) 20.4671 0.914402
\(502\) −11.2294 −0.501193
\(503\) −27.8533 −1.24192 −0.620958 0.783844i \(-0.713256\pi\)
−0.620958 + 0.783844i \(0.713256\pi\)
\(504\) 2.81987 0.125607
\(505\) 3.97348 0.176817
\(506\) −1.76660 −0.0785351
\(507\) −3.17317 −0.140925
\(508\) 16.1820 0.717960
\(509\) 31.6478 1.40276 0.701382 0.712786i \(-0.252567\pi\)
0.701382 + 0.712786i \(0.252567\pi\)
\(510\) −3.23491 −0.143244
\(511\) 6.96468 0.308099
\(512\) −0.439471 −0.0194221
\(513\) 3.38040 0.149248
\(514\) −3.87330 −0.170844
\(515\) 36.6579 1.61534
\(516\) 7.37032 0.324460
\(517\) −2.86817 −0.126142
\(518\) −9.02120 −0.396369
\(519\) 15.3906 0.675574
\(520\) 34.6085 1.51768
\(521\) 5.61037 0.245795 0.122897 0.992419i \(-0.460781\pi\)
0.122897 + 0.992419i \(0.460781\pi\)
\(522\) 2.78882 0.122063
\(523\) −2.61486 −0.114340 −0.0571700 0.998364i \(-0.518208\pi\)
−0.0571700 + 0.998364i \(0.518208\pi\)
\(524\) 27.0130 1.18007
\(525\) −4.31353 −0.188258
\(526\) 22.6593 0.987993
\(527\) −6.32962 −0.275723
\(528\) −0.0276614 −0.00120381
\(529\) −14.8507 −0.645683
\(530\) 4.04286 0.175611
\(531\) 4.36113 0.189257
\(532\) 4.20770 0.182427
\(533\) 8.14631 0.352856
\(534\) 0.561631 0.0243042
\(535\) 44.0784 1.90567
\(536\) 9.16085 0.395688
\(537\) −7.40804 −0.319681
\(538\) −20.9557 −0.903466
\(539\) 0.712082 0.0306716
\(540\) −3.79870 −0.163470
\(541\) 26.5094 1.13973 0.569863 0.821740i \(-0.306996\pi\)
0.569863 + 0.821740i \(0.306996\pi\)
\(542\) −15.3593 −0.659737
\(543\) 3.80490 0.163284
\(544\) −6.92000 −0.296693
\(545\) 3.23623 0.138625
\(546\) −3.49499 −0.149572
\(547\) 6.33115 0.270700 0.135350 0.990798i \(-0.456784\pi\)
0.135350 + 0.990798i \(0.456784\pi\)
\(548\) 15.3083 0.653939
\(549\) −1.75357 −0.0748406
\(550\) −2.66939 −0.113823
\(551\) 10.8477 0.462129
\(552\) −8.04986 −0.342625
\(553\) −11.0316 −0.469113
\(554\) −11.7451 −0.499001
\(555\) 31.6791 1.34470
\(556\) −13.1193 −0.556381
\(557\) 29.3754 1.24468 0.622339 0.782748i \(-0.286183\pi\)
0.622339 + 0.782748i \(0.286183\pi\)
\(558\) 4.50994 0.190921
\(559\) −23.8126 −1.00716
\(560\) −0.118550 −0.00500965
\(561\) −0.868532 −0.0366695
\(562\) −9.62464 −0.405991
\(563\) 41.2453 1.73828 0.869140 0.494565i \(-0.164673\pi\)
0.869140 + 0.494565i \(0.164673\pi\)
\(564\) −5.01363 −0.211112
\(565\) 34.9783 1.47155
\(566\) −12.9856 −0.545825
\(567\) 1.00000 0.0419961
\(568\) 32.3530 1.35750
\(569\) 20.4837 0.858720 0.429360 0.903133i \(-0.358739\pi\)
0.429360 + 0.903133i \(0.358739\pi\)
\(570\) 8.96548 0.375523
\(571\) −6.02327 −0.252066 −0.126033 0.992026i \(-0.540225\pi\)
−0.126033 + 0.992026i \(0.540225\pi\)
\(572\) 3.56456 0.149042
\(573\) 11.5600 0.482925
\(574\) 1.76040 0.0734779
\(575\) 12.3138 0.513522
\(576\) 4.85291 0.202204
\(577\) 1.08710 0.0452566 0.0226283 0.999744i \(-0.492797\pi\)
0.0226283 + 0.999744i \(0.492797\pi\)
\(578\) 13.4811 0.560740
\(579\) −8.47034 −0.352015
\(580\) −12.1901 −0.506165
\(581\) −12.8639 −0.533683
\(582\) −15.7500 −0.652860
\(583\) 1.08546 0.0449551
\(584\) 19.6395 0.812687
\(585\) 12.2731 0.507431
\(586\) 16.7756 0.692992
\(587\) −19.6433 −0.810765 −0.405382 0.914147i \(-0.632862\pi\)
−0.405382 + 0.914147i \(0.632862\pi\)
\(588\) 1.24474 0.0513321
\(589\) 17.5424 0.722823
\(590\) 11.5666 0.476189
\(591\) −8.76026 −0.360349
\(592\) 0.403236 0.0165729
\(593\) 20.3632 0.836216 0.418108 0.908397i \(-0.362693\pi\)
0.418108 + 0.908397i \(0.362693\pi\)
\(594\) 0.618841 0.0253914
\(595\) −3.72231 −0.152600
\(596\) −22.9096 −0.938413
\(597\) −22.6094 −0.925343
\(598\) 9.97715 0.407996
\(599\) −31.0351 −1.26806 −0.634030 0.773308i \(-0.718601\pi\)
−0.634030 + 0.773308i \(0.718601\pi\)
\(600\) −12.1636 −0.496576
\(601\) −35.8022 −1.46040 −0.730201 0.683232i \(-0.760574\pi\)
−0.730201 + 0.683232i \(0.760574\pi\)
\(602\) −5.14586 −0.209729
\(603\) 3.24868 0.132297
\(604\) −8.41433 −0.342374
\(605\) 32.0224 1.30190
\(606\) −1.13152 −0.0459649
\(607\) −27.9748 −1.13546 −0.567731 0.823214i \(-0.692179\pi\)
−0.567731 + 0.823214i \(0.692179\pi\)
\(608\) 19.1786 0.777797
\(609\) 3.20901 0.130036
\(610\) −4.65082 −0.188306
\(611\) 16.1984 0.655317
\(612\) −1.51822 −0.0613702
\(613\) 11.4650 0.463068 0.231534 0.972827i \(-0.425626\pi\)
0.231534 + 0.972827i \(0.425626\pi\)
\(614\) −22.0876 −0.891381
\(615\) −6.18188 −0.249277
\(616\) 2.00798 0.0809037
\(617\) 34.2539 1.37901 0.689504 0.724281i \(-0.257828\pi\)
0.689504 + 0.724281i \(0.257828\pi\)
\(618\) −10.4390 −0.419919
\(619\) 41.3180 1.66071 0.830355 0.557235i \(-0.188138\pi\)
0.830355 + 0.557235i \(0.188138\pi\)
\(620\) −19.7132 −0.791701
\(621\) −2.85470 −0.114555
\(622\) 21.4215 0.858925
\(623\) 0.646252 0.0258916
\(624\) 0.156222 0.00625387
\(625\) −27.9611 −1.11844
\(626\) 7.58170 0.303026
\(627\) 2.40712 0.0961311
\(628\) 0.865289 0.0345288
\(629\) 12.6611 0.504831
\(630\) 2.65220 0.105666
\(631\) −2.97622 −0.118481 −0.0592407 0.998244i \(-0.518868\pi\)
−0.0592407 + 0.998244i \(0.518868\pi\)
\(632\) −31.1077 −1.23740
\(633\) 11.0757 0.440220
\(634\) −10.4245 −0.414010
\(635\) 39.6745 1.57444
\(636\) 1.89741 0.0752371
\(637\) −4.02159 −0.159341
\(638\) 1.98587 0.0786212
\(639\) 11.4733 0.453875
\(640\) −21.7579 −0.860058
\(641\) 23.5025 0.928293 0.464147 0.885758i \(-0.346361\pi\)
0.464147 + 0.885758i \(0.346361\pi\)
\(642\) −12.5521 −0.495393
\(643\) 36.0438 1.42143 0.710715 0.703480i \(-0.248372\pi\)
0.710715 + 0.703480i \(0.248372\pi\)
\(644\) −3.55335 −0.140022
\(645\) 18.0703 0.711518
\(646\) 3.58321 0.140980
\(647\) 23.0074 0.904514 0.452257 0.891888i \(-0.350619\pi\)
0.452257 + 0.891888i \(0.350619\pi\)
\(648\) 2.81987 0.110775
\(649\) 3.10548 0.121901
\(650\) 15.0758 0.591320
\(651\) 5.18946 0.203391
\(652\) −19.7002 −0.771521
\(653\) −6.42806 −0.251549 −0.125775 0.992059i \(-0.540142\pi\)
−0.125775 + 0.992059i \(0.540142\pi\)
\(654\) −0.921576 −0.0360365
\(655\) 66.2296 2.58780
\(656\) −0.0786878 −0.00307224
\(657\) 6.96468 0.271718
\(658\) 3.50044 0.136462
\(659\) −26.7353 −1.04146 −0.520731 0.853721i \(-0.674340\pi\)
−0.520731 + 0.853721i \(0.674340\pi\)
\(660\) −2.70499 −0.105291
\(661\) 11.7644 0.457580 0.228790 0.973476i \(-0.426523\pi\)
0.228790 + 0.973476i \(0.426523\pi\)
\(662\) −24.8428 −0.965542
\(663\) 4.90516 0.190501
\(664\) −36.2744 −1.40772
\(665\) 10.3163 0.400050
\(666\) −9.02120 −0.349564
\(667\) −9.16075 −0.354706
\(668\) 25.4762 0.985702
\(669\) −12.2137 −0.472210
\(670\) 8.61615 0.332871
\(671\) −1.24869 −0.0482050
\(672\) 5.67349 0.218860
\(673\) 16.8939 0.651212 0.325606 0.945505i \(-0.394432\pi\)
0.325606 + 0.945505i \(0.394432\pi\)
\(674\) −25.2292 −0.971794
\(675\) −4.31353 −0.166028
\(676\) −3.94976 −0.151914
\(677\) −12.5088 −0.480753 −0.240377 0.970680i \(-0.577271\pi\)
−0.240377 + 0.970680i \(0.577271\pi\)
\(678\) −9.96072 −0.382539
\(679\) −18.1231 −0.695500
\(680\) −10.4964 −0.402520
\(681\) −5.02074 −0.192395
\(682\) 3.21145 0.122973
\(683\) 24.1673 0.924737 0.462368 0.886688i \(-0.347000\pi\)
0.462368 + 0.886688i \(0.347000\pi\)
\(684\) 4.20770 0.160886
\(685\) 37.5324 1.43404
\(686\) −0.869058 −0.0331808
\(687\) 17.1485 0.654254
\(688\) 0.230013 0.00876917
\(689\) −6.13028 −0.233545
\(690\) −7.57123 −0.288232
\(691\) −26.1032 −0.993014 −0.496507 0.868033i \(-0.665384\pi\)
−0.496507 + 0.868033i \(0.665384\pi\)
\(692\) 19.1573 0.728251
\(693\) 0.712082 0.0270498
\(694\) −28.5473 −1.08364
\(695\) −32.1654 −1.22010
\(696\) 9.04898 0.343001
\(697\) −2.47070 −0.0935843
\(698\) −22.2468 −0.842053
\(699\) 26.1749 0.990024
\(700\) −5.36921 −0.202937
\(701\) 2.19236 0.0828042 0.0414021 0.999143i \(-0.486818\pi\)
0.0414021 + 0.999143i \(0.486818\pi\)
\(702\) −3.49499 −0.131910
\(703\) −35.0900 −1.32344
\(704\) 3.45567 0.130240
\(705\) −12.2923 −0.462953
\(706\) 21.7943 0.820239
\(707\) −1.30201 −0.0489670
\(708\) 5.42846 0.204014
\(709\) −1.02856 −0.0386284 −0.0193142 0.999813i \(-0.506148\pi\)
−0.0193142 + 0.999813i \(0.506148\pi\)
\(710\) 30.4294 1.14199
\(711\) −11.0316 −0.413718
\(712\) 1.82235 0.0682953
\(713\) −14.8143 −0.554801
\(714\) 1.06000 0.0396694
\(715\) 8.73946 0.326837
\(716\) −9.22107 −0.344608
\(717\) 3.38308 0.126343
\(718\) −12.0062 −0.448066
\(719\) 13.3528 0.497975 0.248987 0.968507i \(-0.419902\pi\)
0.248987 + 0.968507i \(0.419902\pi\)
\(720\) −0.118550 −0.00441809
\(721\) −12.0119 −0.447346
\(722\) 6.58131 0.244931
\(723\) −13.9845 −0.520088
\(724\) 4.73611 0.176016
\(725\) −13.8422 −0.514085
\(726\) −9.11898 −0.338437
\(727\) −1.80430 −0.0669177 −0.0334588 0.999440i \(-0.510652\pi\)
−0.0334588 + 0.999440i \(0.510652\pi\)
\(728\) −11.3403 −0.420301
\(729\) 1.00000 0.0370370
\(730\) 18.4717 0.683669
\(731\) 7.22212 0.267120
\(732\) −2.18274 −0.0806762
\(733\) 42.9866 1.58775 0.793873 0.608083i \(-0.208061\pi\)
0.793873 + 0.608083i \(0.208061\pi\)
\(734\) −23.9670 −0.884639
\(735\) 3.05181 0.112568
\(736\) −16.1961 −0.596996
\(737\) 2.31333 0.0852125
\(738\) 1.76040 0.0648014
\(739\) 0.550689 0.0202574 0.0101287 0.999949i \(-0.496776\pi\)
0.0101287 + 0.999949i \(0.496776\pi\)
\(740\) 39.4321 1.44955
\(741\) −13.5946 −0.499409
\(742\) −1.32474 −0.0486328
\(743\) −45.6409 −1.67440 −0.837200 0.546896i \(-0.815809\pi\)
−0.837200 + 0.546896i \(0.815809\pi\)
\(744\) 14.6336 0.536493
\(745\) −56.1690 −2.05787
\(746\) 6.26425 0.229350
\(747\) −12.8639 −0.470664
\(748\) −1.08109 −0.0395287
\(749\) −14.4434 −0.527749
\(750\) 1.82065 0.0664808
\(751\) −7.06296 −0.257731 −0.128865 0.991662i \(-0.541134\pi\)
−0.128865 + 0.991662i \(0.541134\pi\)
\(752\) −0.156465 −0.00570570
\(753\) −12.9214 −0.470880
\(754\) −11.2155 −0.408443
\(755\) −20.6300 −0.750803
\(756\) 1.24474 0.0452707
\(757\) 42.9605 1.56143 0.780713 0.624889i \(-0.214856\pi\)
0.780713 + 0.624889i \(0.214856\pi\)
\(758\) 18.7094 0.679558
\(759\) −2.03278 −0.0737852
\(760\) 29.0906 1.05523
\(761\) −23.6023 −0.855583 −0.427791 0.903877i \(-0.640708\pi\)
−0.427791 + 0.903877i \(0.640708\pi\)
\(762\) −11.2981 −0.409285
\(763\) −1.06043 −0.0383901
\(764\) 14.3891 0.520581
\(765\) −3.72231 −0.134581
\(766\) 0.869058 0.0314004
\(767\) −17.5387 −0.633284
\(768\) 15.9018 0.573806
\(769\) −52.8325 −1.90519 −0.952594 0.304245i \(-0.901596\pi\)
−0.952594 + 0.304245i \(0.901596\pi\)
\(770\) 1.88858 0.0680598
\(771\) −4.45689 −0.160511
\(772\) −10.5434 −0.379463
\(773\) −53.0699 −1.90879 −0.954395 0.298546i \(-0.903499\pi\)
−0.954395 + 0.298546i \(0.903499\pi\)
\(774\) −5.14586 −0.184964
\(775\) −22.3849 −0.804089
\(776\) −51.1047 −1.83455
\(777\) −10.3804 −0.372396
\(778\) 11.1711 0.400504
\(779\) 6.84748 0.245337
\(780\) 15.2768 0.546997
\(781\) 8.16990 0.292342
\(782\) −3.02597 −0.108209
\(783\) 3.20901 0.114681
\(784\) 0.0388458 0.00138735
\(785\) 2.12149 0.0757191
\(786\) −18.8601 −0.672717
\(787\) −39.0547 −1.39215 −0.696075 0.717969i \(-0.745072\pi\)
−0.696075 + 0.717969i \(0.745072\pi\)
\(788\) −10.9042 −0.388447
\(789\) 26.0734 0.928238
\(790\) −29.2581 −1.04096
\(791\) −11.4615 −0.407524
\(792\) 2.00798 0.0713503
\(793\) 7.05214 0.250429
\(794\) 2.42118 0.0859246
\(795\) 4.65200 0.164989
\(796\) −28.1428 −0.997496
\(797\) 36.2988 1.28577 0.642884 0.765963i \(-0.277738\pi\)
0.642884 + 0.765963i \(0.277738\pi\)
\(798\) −2.93776 −0.103996
\(799\) −4.91281 −0.173803
\(800\) −24.4728 −0.865244
\(801\) 0.646252 0.0228342
\(802\) 2.87491 0.101517
\(803\) 4.95942 0.175014
\(804\) 4.04375 0.142612
\(805\) −8.71199 −0.307057
\(806\) −18.1371 −0.638853
\(807\) −24.1132 −0.848823
\(808\) −3.67149 −0.129162
\(809\) 6.16707 0.216823 0.108411 0.994106i \(-0.465424\pi\)
0.108411 + 0.994106i \(0.465424\pi\)
\(810\) 2.65220 0.0931888
\(811\) 25.4290 0.892933 0.446467 0.894800i \(-0.352682\pi\)
0.446467 + 0.894800i \(0.352682\pi\)
\(812\) 3.99437 0.140175
\(813\) −17.6735 −0.619835
\(814\) −6.42384 −0.225155
\(815\) −48.3004 −1.69189
\(816\) −0.0473805 −0.00165865
\(817\) −20.0159 −0.700269
\(818\) −8.98065 −0.314001
\(819\) −4.02159 −0.140526
\(820\) −7.69482 −0.268715
\(821\) −13.6947 −0.477947 −0.238974 0.971026i \(-0.576811\pi\)
−0.238974 + 0.971026i \(0.576811\pi\)
\(822\) −10.6881 −0.372789
\(823\) 25.2952 0.881735 0.440867 0.897572i \(-0.354671\pi\)
0.440867 + 0.897572i \(0.354671\pi\)
\(824\) −33.8719 −1.17998
\(825\) −3.07159 −0.106939
\(826\) −3.79008 −0.131874
\(827\) −35.3224 −1.22828 −0.614140 0.789197i \(-0.710497\pi\)
−0.614140 + 0.789197i \(0.710497\pi\)
\(828\) −3.55335 −0.123487
\(829\) −34.1660 −1.18663 −0.593317 0.804969i \(-0.702182\pi\)
−0.593317 + 0.804969i \(0.702182\pi\)
\(830\) −34.1175 −1.18424
\(831\) −13.5147 −0.468820
\(832\) −19.5164 −0.676609
\(833\) 1.21971 0.0422604
\(834\) 9.15969 0.317174
\(835\) 62.4616 2.16157
\(836\) 2.99623 0.103627
\(837\) 5.18946 0.179374
\(838\) −15.1019 −0.521686
\(839\) 42.2105 1.45727 0.728635 0.684902i \(-0.240155\pi\)
0.728635 + 0.684902i \(0.240155\pi\)
\(840\) 8.60569 0.296925
\(841\) −18.7023 −0.644905
\(842\) −2.91654 −0.100511
\(843\) −11.0748 −0.381436
\(844\) 13.7863 0.474546
\(845\) −9.68389 −0.333136
\(846\) 3.50044 0.120348
\(847\) −10.4929 −0.360542
\(848\) 0.0592143 0.00203343
\(849\) −14.9421 −0.512812
\(850\) −4.57233 −0.156830
\(851\) 29.6330 1.01581
\(852\) 14.2812 0.489265
\(853\) 39.8269 1.36365 0.681823 0.731517i \(-0.261187\pi\)
0.681823 + 0.731517i \(0.261187\pi\)
\(854\) 1.52396 0.0521487
\(855\) 10.3163 0.352811
\(856\) −40.7283 −1.39207
\(857\) −28.8073 −0.984037 −0.492019 0.870585i \(-0.663741\pi\)
−0.492019 + 0.870585i \(0.663741\pi\)
\(858\) −2.48872 −0.0849636
\(859\) 7.89364 0.269328 0.134664 0.990891i \(-0.457005\pi\)
0.134664 + 0.990891i \(0.457005\pi\)
\(860\) 22.4928 0.766998
\(861\) 2.02565 0.0690338
\(862\) 1.46462 0.0498852
\(863\) 22.9224 0.780287 0.390143 0.920754i \(-0.372425\pi\)
0.390143 + 0.920754i \(0.372425\pi\)
\(864\) 5.67349 0.193016
\(865\) 46.9693 1.59700
\(866\) −25.6038 −0.870054
\(867\) 15.5123 0.526826
\(868\) 6.45951 0.219250
\(869\) −7.85543 −0.266477
\(870\) 8.51093 0.288548
\(871\) −13.0649 −0.442686
\(872\) −2.99027 −0.101263
\(873\) −18.1231 −0.613374
\(874\) 8.38642 0.283675
\(875\) 2.09497 0.0708230
\(876\) 8.66919 0.292905
\(877\) −20.0714 −0.677764 −0.338882 0.940829i \(-0.610049\pi\)
−0.338882 + 0.940829i \(0.610049\pi\)
\(878\) 3.98761 0.134575
\(879\) 19.3031 0.651079
\(880\) −0.0844173 −0.00284571
\(881\) −23.1525 −0.780026 −0.390013 0.920809i \(-0.627530\pi\)
−0.390013 + 0.920809i \(0.627530\pi\)
\(882\) −0.869058 −0.0292627
\(883\) −37.3045 −1.25540 −0.627699 0.778456i \(-0.716003\pi\)
−0.627699 + 0.778456i \(0.716003\pi\)
\(884\) 6.10564 0.205355
\(885\) 13.3093 0.447388
\(886\) 23.2629 0.781532
\(887\) 20.3074 0.681855 0.340927 0.940090i \(-0.389259\pi\)
0.340927 + 0.940090i \(0.389259\pi\)
\(888\) −29.2714 −0.982285
\(889\) −13.0003 −0.436017
\(890\) 1.71399 0.0574531
\(891\) 0.712082 0.0238557
\(892\) −15.2029 −0.509030
\(893\) 13.6158 0.455634
\(894\) 15.9951 0.534958
\(895\) −22.6079 −0.755700
\(896\) 7.12953 0.238181
\(897\) 11.4804 0.383320
\(898\) −3.60973 −0.120458
\(899\) 16.6530 0.555409
\(900\) −5.36921 −0.178974
\(901\) 1.85925 0.0619407
\(902\) 1.25355 0.0417387
\(903\) −5.92118 −0.197045
\(904\) −32.3199 −1.07494
\(905\) 11.6118 0.385990
\(906\) 5.87477 0.195176
\(907\) 57.0805 1.89533 0.947664 0.319269i \(-0.103437\pi\)
0.947664 + 0.319269i \(0.103437\pi\)
\(908\) −6.24950 −0.207397
\(909\) −1.30201 −0.0431848
\(910\) −10.6661 −0.353576
\(911\) 33.3581 1.10520 0.552602 0.833445i \(-0.313635\pi\)
0.552602 + 0.833445i \(0.313635\pi\)
\(912\) 0.131314 0.00434825
\(913\) −9.16012 −0.303156
\(914\) 32.5038 1.07513
\(915\) −5.35156 −0.176917
\(916\) 21.3453 0.705269
\(917\) −21.7017 −0.716655
\(918\) 1.06000 0.0349851
\(919\) 43.1144 1.42221 0.711107 0.703084i \(-0.248194\pi\)
0.711107 + 0.703084i \(0.248194\pi\)
\(920\) −24.5666 −0.809938
\(921\) −25.4155 −0.837469
\(922\) 26.6193 0.876661
\(923\) −46.1407 −1.51874
\(924\) 0.886355 0.0291589
\(925\) 44.7763 1.47224
\(926\) −11.4909 −0.377614
\(927\) −12.0119 −0.394522
\(928\) 18.2063 0.597651
\(929\) 31.2176 1.02422 0.512108 0.858921i \(-0.328865\pi\)
0.512108 + 0.858921i \(0.328865\pi\)
\(930\) 13.7635 0.451322
\(931\) −3.38040 −0.110788
\(932\) 32.5808 1.06722
\(933\) 24.6491 0.806976
\(934\) −3.34025 −0.109296
\(935\) −2.65059 −0.0866837
\(936\) −11.3403 −0.370671
\(937\) 59.2654 1.93612 0.968058 0.250727i \(-0.0806695\pi\)
0.968058 + 0.250727i \(0.0806695\pi\)
\(938\) −2.82329 −0.0921838
\(939\) 8.72404 0.284698
\(940\) −15.3006 −0.499051
\(941\) −4.70864 −0.153497 −0.0767486 0.997050i \(-0.524454\pi\)
−0.0767486 + 0.997050i \(0.524454\pi\)
\(942\) −0.604133 −0.0196837
\(943\) −5.78260 −0.188307
\(944\) 0.169411 0.00551387
\(945\) 3.05181 0.0992753
\(946\) −3.66427 −0.119136
\(947\) −25.5318 −0.829672 −0.414836 0.909896i \(-0.636161\pi\)
−0.414836 + 0.909896i \(0.636161\pi\)
\(948\) −13.7315 −0.445978
\(949\) −28.0091 −0.909213
\(950\) 12.6721 0.411138
\(951\) −11.9952 −0.388970
\(952\) 3.43941 0.111472
\(953\) −23.9119 −0.774581 −0.387290 0.921958i \(-0.626589\pi\)
−0.387290 + 0.921958i \(0.626589\pi\)
\(954\) −1.32474 −0.0428901
\(955\) 35.2789 1.14160
\(956\) 4.21104 0.136195
\(957\) 2.28508 0.0738661
\(958\) −12.1936 −0.393958
\(959\) −12.2984 −0.397137
\(960\) 14.8101 0.477995
\(961\) −4.06953 −0.131275
\(962\) 36.2795 1.16970
\(963\) −14.4434 −0.465431
\(964\) −17.4070 −0.560641
\(965\) −25.8499 −0.832136
\(966\) 2.48090 0.0798216
\(967\) 8.91273 0.286614 0.143307 0.989678i \(-0.454226\pi\)
0.143307 + 0.989678i \(0.454226\pi\)
\(968\) −29.5887 −0.951016
\(969\) 4.12310 0.132453
\(970\) −48.0661 −1.54331
\(971\) −17.1131 −0.549185 −0.274593 0.961561i \(-0.588543\pi\)
−0.274593 + 0.961561i \(0.588543\pi\)
\(972\) 1.24474 0.0399250
\(973\) 10.5398 0.337890
\(974\) −18.9361 −0.606751
\(975\) 17.3472 0.555556
\(976\) −0.0681189 −0.00218043
\(977\) 11.8882 0.380336 0.190168 0.981752i \(-0.439097\pi\)
0.190168 + 0.981752i \(0.439097\pi\)
\(978\) 13.7544 0.439818
\(979\) 0.460185 0.0147076
\(980\) 3.79870 0.121345
\(981\) −1.06043 −0.0338569
\(982\) 25.3704 0.809601
\(983\) 43.8613 1.39896 0.699480 0.714653i \(-0.253415\pi\)
0.699480 + 0.714653i \(0.253415\pi\)
\(984\) 5.71205 0.182093
\(985\) −26.7346 −0.851836
\(986\) 3.40154 0.108327
\(987\) 4.02786 0.128208
\(988\) −16.9217 −0.538349
\(989\) 16.9032 0.537490
\(990\) 1.88858 0.0600231
\(991\) 13.6109 0.432365 0.216183 0.976353i \(-0.430639\pi\)
0.216183 + 0.976353i \(0.430639\pi\)
\(992\) 29.4423 0.934795
\(993\) −28.5858 −0.907144
\(994\) −9.97093 −0.316259
\(995\) −68.9997 −2.18744
\(996\) −16.0121 −0.507364
\(997\) 4.27269 0.135317 0.0676587 0.997709i \(-0.478447\pi\)
0.0676587 + 0.997709i \(0.478447\pi\)
\(998\) −13.2999 −0.421002
\(999\) −10.3804 −0.328422
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 \(a_p\))