Properties

Label 8018.2.a.d.1.13
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
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: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.894762 q^{3}\) \(+1.00000 q^{4}\) \(-0.0669598 q^{5}\) \(-0.894762 q^{6}\) \(+1.42997 q^{7}\) \(+1.00000 q^{8}\) \(-2.19940 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.894762 q^{3}\) \(+1.00000 q^{4}\) \(-0.0669598 q^{5}\) \(-0.894762 q^{6}\) \(+1.42997 q^{7}\) \(+1.00000 q^{8}\) \(-2.19940 q^{9}\) \(-0.0669598 q^{10}\) \(-3.23328 q^{11}\) \(-0.894762 q^{12}\) \(+4.17646 q^{13}\) \(+1.42997 q^{14}\) \(+0.0599131 q^{15}\) \(+1.00000 q^{16}\) \(-0.463825 q^{17}\) \(-2.19940 q^{18}\) \(+1.00000 q^{19}\) \(-0.0669598 q^{20}\) \(-1.27948 q^{21}\) \(-3.23328 q^{22}\) \(-2.96000 q^{23}\) \(-0.894762 q^{24}\) \(-4.99552 q^{25}\) \(+4.17646 q^{26}\) \(+4.65223 q^{27}\) \(+1.42997 q^{28}\) \(+5.89722 q^{29}\) \(+0.0599131 q^{30}\) \(-5.02580 q^{31}\) \(+1.00000 q^{32}\) \(+2.89302 q^{33}\) \(-0.463825 q^{34}\) \(-0.0957506 q^{35}\) \(-2.19940 q^{36}\) \(-5.53876 q^{37}\) \(+1.00000 q^{38}\) \(-3.73694 q^{39}\) \(-0.0669598 q^{40}\) \(+3.26660 q^{41}\) \(-1.27948 q^{42}\) \(+0.640662 q^{43}\) \(-3.23328 q^{44}\) \(+0.147271 q^{45}\) \(-2.96000 q^{46}\) \(+0.940223 q^{47}\) \(-0.894762 q^{48}\) \(-4.95518 q^{49}\) \(-4.99552 q^{50}\) \(+0.415013 q^{51}\) \(+4.17646 q^{52}\) \(-11.0185 q^{53}\) \(+4.65223 q^{54}\) \(+0.216500 q^{55}\) \(+1.42997 q^{56}\) \(-0.894762 q^{57}\) \(+5.89722 q^{58}\) \(+3.02758 q^{59}\) \(+0.0599131 q^{60}\) \(+11.8105 q^{61}\) \(-5.02580 q^{62}\) \(-3.14508 q^{63}\) \(+1.00000 q^{64}\) \(-0.279655 q^{65}\) \(+2.89302 q^{66}\) \(-7.46996 q^{67}\) \(-0.463825 q^{68}\) \(+2.64850 q^{69}\) \(-0.0957506 q^{70}\) \(-2.88742 q^{71}\) \(-2.19940 q^{72}\) \(-11.7213 q^{73}\) \(-5.53876 q^{74}\) \(+4.46980 q^{75}\) \(+1.00000 q^{76}\) \(-4.62350 q^{77}\) \(-3.73694 q^{78}\) \(+13.6699 q^{79}\) \(-0.0669598 q^{80}\) \(+2.43557 q^{81}\) \(+3.26660 q^{82}\) \(+1.25135 q^{83}\) \(-1.27948 q^{84}\) \(+0.0310576 q^{85}\) \(+0.640662 q^{86}\) \(-5.27661 q^{87}\) \(-3.23328 q^{88}\) \(-3.46503 q^{89}\) \(+0.147271 q^{90}\) \(+5.97222 q^{91}\) \(-2.96000 q^{92}\) \(+4.49690 q^{93}\) \(+0.940223 q^{94}\) \(-0.0669598 q^{95}\) \(-0.894762 q^{96}\) \(-16.2444 q^{97}\) \(-4.95518 q^{98}\) \(+7.11129 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(30q \) \(\mathstrut +\mathstrut 30q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 15q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 12q^{10} \) \(\mathstrut -\mathstrut 17q^{11} \) \(\mathstrut -\mathstrut 10q^{12} \) \(\mathstrut -\mathstrut 19q^{13} \) \(\mathstrut -\mathstrut 15q^{14} \) \(\mathstrut -\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 30q^{16} \) \(\mathstrut -\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 10q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 14q^{21} \) \(\mathstrut -\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 15q^{23} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 19q^{26} \) \(\mathstrut -\mathstrut 37q^{27} \) \(\mathstrut -\mathstrut 15q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 18q^{34} \) \(\mathstrut -\mathstrut 4q^{35} \) \(\mathstrut +\mathstrut 10q^{36} \) \(\mathstrut -\mathstrut 46q^{37} \) \(\mathstrut +\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 12q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 14q^{42} \) \(\mathstrut -\mathstrut 61q^{43} \) \(\mathstrut -\mathstrut 17q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut -\mathstrut 10q^{48} \) \(\mathstrut -\mathstrut q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 19q^{52} \) \(\mathstrut -\mathstrut 19q^{53} \) \(\mathstrut -\mathstrut 37q^{54} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut -\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut -\mathstrut 11q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut +\mathstrut 30q^{64} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 44q^{67} \) \(\mathstrut -\mathstrut 18q^{68} \) \(\mathstrut -\mathstrut 2q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 10q^{72} \) \(\mathstrut -\mathstrut 58q^{73} \) \(\mathstrut -\mathstrut 46q^{74} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut +\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 42q^{79} \) \(\mathstrut -\mathstrut 12q^{80} \) \(\mathstrut -\mathstrut 38q^{81} \) \(\mathstrut -\mathstrut 28q^{82} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 14q^{84} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 61q^{86} \) \(\mathstrut -\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 39q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 45q^{93} \) \(\mathstrut -\mathstrut 4q^{94} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut -\mathstrut 10q^{96} \) \(\mathstrut -\mathstrut 33q^{97} \) \(\mathstrut -\mathstrut q^{98} \) \(\mathstrut -\mathstrut 38q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.894762 −0.516591 −0.258296 0.966066i \(-0.583161\pi\)
−0.258296 + 0.966066i \(0.583161\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0669598 −0.0299453 −0.0149727 0.999888i \(-0.504766\pi\)
−0.0149727 + 0.999888i \(0.504766\pi\)
\(6\) −0.894762 −0.365285
\(7\) 1.42997 0.540479 0.270239 0.962793i \(-0.412897\pi\)
0.270239 + 0.962793i \(0.412897\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.19940 −0.733134
\(10\) −0.0669598 −0.0211745
\(11\) −3.23328 −0.974872 −0.487436 0.873159i \(-0.662068\pi\)
−0.487436 + 0.873159i \(0.662068\pi\)
\(12\) −0.894762 −0.258296
\(13\) 4.17646 1.15834 0.579171 0.815206i \(-0.303376\pi\)
0.579171 + 0.815206i \(0.303376\pi\)
\(14\) 1.42997 0.382176
\(15\) 0.0599131 0.0154695
\(16\) 1.00000 0.250000
\(17\) −0.463825 −0.112494 −0.0562471 0.998417i \(-0.517913\pi\)
−0.0562471 + 0.998417i \(0.517913\pi\)
\(18\) −2.19940 −0.518404
\(19\) 1.00000 0.229416
\(20\) −0.0669598 −0.0149727
\(21\) −1.27948 −0.279206
\(22\) −3.23328 −0.689338
\(23\) −2.96000 −0.617203 −0.308602 0.951191i \(-0.599861\pi\)
−0.308602 + 0.951191i \(0.599861\pi\)
\(24\) −0.894762 −0.182643
\(25\) −4.99552 −0.999103
\(26\) 4.17646 0.819071
\(27\) 4.65223 0.895321
\(28\) 1.42997 0.270239
\(29\) 5.89722 1.09509 0.547543 0.836778i \(-0.315563\pi\)
0.547543 + 0.836778i \(0.315563\pi\)
\(30\) 0.0599131 0.0109386
\(31\) −5.02580 −0.902660 −0.451330 0.892357i \(-0.649050\pi\)
−0.451330 + 0.892357i \(0.649050\pi\)
\(32\) 1.00000 0.176777
\(33\) 2.89302 0.503610
\(34\) −0.463825 −0.0795454
\(35\) −0.0957506 −0.0161848
\(36\) −2.19940 −0.366567
\(37\) −5.53876 −0.910566 −0.455283 0.890347i \(-0.650462\pi\)
−0.455283 + 0.890347i \(0.650462\pi\)
\(38\) 1.00000 0.162221
\(39\) −3.73694 −0.598389
\(40\) −0.0669598 −0.0105873
\(41\) 3.26660 0.510157 0.255079 0.966920i \(-0.417899\pi\)
0.255079 + 0.966920i \(0.417899\pi\)
\(42\) −1.27948 −0.197429
\(43\) 0.640662 0.0977000 0.0488500 0.998806i \(-0.484444\pi\)
0.0488500 + 0.998806i \(0.484444\pi\)
\(44\) −3.23328 −0.487436
\(45\) 0.147271 0.0219539
\(46\) −2.96000 −0.436428
\(47\) 0.940223 0.137146 0.0685728 0.997646i \(-0.478155\pi\)
0.0685728 + 0.997646i \(0.478155\pi\)
\(48\) −0.894762 −0.129148
\(49\) −4.95518 −0.707883
\(50\) −4.99552 −0.706473
\(51\) 0.415013 0.0581135
\(52\) 4.17646 0.579171
\(53\) −11.0185 −1.51351 −0.756756 0.653698i \(-0.773217\pi\)
−0.756756 + 0.653698i \(0.773217\pi\)
\(54\) 4.65223 0.633088
\(55\) 0.216500 0.0291928
\(56\) 1.42997 0.191088
\(57\) −0.894762 −0.118514
\(58\) 5.89722 0.774343
\(59\) 3.02758 0.394157 0.197079 0.980388i \(-0.436855\pi\)
0.197079 + 0.980388i \(0.436855\pi\)
\(60\) 0.0599131 0.00773474
\(61\) 11.8105 1.51218 0.756092 0.654465i \(-0.227106\pi\)
0.756092 + 0.654465i \(0.227106\pi\)
\(62\) −5.02580 −0.638277
\(63\) −3.14508 −0.396243
\(64\) 1.00000 0.125000
\(65\) −0.279655 −0.0346869
\(66\) 2.89302 0.356106
\(67\) −7.46996 −0.912601 −0.456301 0.889826i \(-0.650826\pi\)
−0.456301 + 0.889826i \(0.650826\pi\)
\(68\) −0.463825 −0.0562471
\(69\) 2.64850 0.318842
\(70\) −0.0957506 −0.0114444
\(71\) −2.88742 −0.342674 −0.171337 0.985212i \(-0.554809\pi\)
−0.171337 + 0.985212i \(0.554809\pi\)
\(72\) −2.19940 −0.259202
\(73\) −11.7213 −1.37188 −0.685938 0.727660i \(-0.740608\pi\)
−0.685938 + 0.727660i \(0.740608\pi\)
\(74\) −5.53876 −0.643867
\(75\) 4.46980 0.516128
\(76\) 1.00000 0.114708
\(77\) −4.62350 −0.526897
\(78\) −3.73694 −0.423125
\(79\) 13.6699 1.53798 0.768990 0.639261i \(-0.220760\pi\)
0.768990 + 0.639261i \(0.220760\pi\)
\(80\) −0.0669598 −0.00748633
\(81\) 2.43557 0.270618
\(82\) 3.26660 0.360736
\(83\) 1.25135 0.137354 0.0686768 0.997639i \(-0.478122\pi\)
0.0686768 + 0.997639i \(0.478122\pi\)
\(84\) −1.27948 −0.139603
\(85\) 0.0310576 0.00336867
\(86\) 0.640662 0.0690844
\(87\) −5.27661 −0.565712
\(88\) −3.23328 −0.344669
\(89\) −3.46503 −0.367292 −0.183646 0.982992i \(-0.558790\pi\)
−0.183646 + 0.982992i \(0.558790\pi\)
\(90\) 0.147271 0.0155238
\(91\) 5.97222 0.626059
\(92\) −2.96000 −0.308602
\(93\) 4.49690 0.466306
\(94\) 0.940223 0.0969766
\(95\) −0.0669598 −0.00686993
\(96\) −0.894762 −0.0913213
\(97\) −16.2444 −1.64937 −0.824684 0.565593i \(-0.808647\pi\)
−0.824684 + 0.565593i \(0.808647\pi\)
\(98\) −4.95518 −0.500549
\(99\) 7.11129 0.714711
\(100\) −4.99552 −0.499552
\(101\) 0.143986 0.0143271 0.00716355 0.999974i \(-0.497720\pi\)
0.00716355 + 0.999974i \(0.497720\pi\)
\(102\) 0.415013 0.0410924
\(103\) −17.1246 −1.68734 −0.843669 0.536864i \(-0.819609\pi\)
−0.843669 + 0.536864i \(0.819609\pi\)
\(104\) 4.17646 0.409536
\(105\) 0.0856740 0.00836092
\(106\) −11.0185 −1.07021
\(107\) 3.36857 0.325652 0.162826 0.986655i \(-0.447939\pi\)
0.162826 + 0.986655i \(0.447939\pi\)
\(108\) 4.65223 0.447661
\(109\) 2.29513 0.219834 0.109917 0.993941i \(-0.464941\pi\)
0.109917 + 0.993941i \(0.464941\pi\)
\(110\) 0.216500 0.0206425
\(111\) 4.95587 0.470390
\(112\) 1.42997 0.135120
\(113\) 4.15323 0.390703 0.195352 0.980733i \(-0.437415\pi\)
0.195352 + 0.980733i \(0.437415\pi\)
\(114\) −0.894762 −0.0838021
\(115\) 0.198201 0.0184823
\(116\) 5.89722 0.547543
\(117\) −9.18571 −0.849219
\(118\) 3.02758 0.278711
\(119\) −0.663257 −0.0608007
\(120\) 0.0599131 0.00546929
\(121\) −0.545879 −0.0496254
\(122\) 11.8105 1.06928
\(123\) −2.92283 −0.263543
\(124\) −5.02580 −0.451330
\(125\) 0.669297 0.0598638
\(126\) −3.14508 −0.280186
\(127\) 5.73201 0.508634 0.254317 0.967121i \(-0.418149\pi\)
0.254317 + 0.967121i \(0.418149\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.573240 −0.0504710
\(130\) −0.279655 −0.0245274
\(131\) −21.0961 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(132\) 2.89302 0.251805
\(133\) 1.42997 0.123994
\(134\) −7.46996 −0.645306
\(135\) −0.311512 −0.0268107
\(136\) −0.463825 −0.0397727
\(137\) 10.7451 0.918019 0.459009 0.888431i \(-0.348204\pi\)
0.459009 + 0.888431i \(0.348204\pi\)
\(138\) 2.64850 0.225455
\(139\) −2.46250 −0.208867 −0.104433 0.994532i \(-0.533303\pi\)
−0.104433 + 0.994532i \(0.533303\pi\)
\(140\) −0.0957506 −0.00809240
\(141\) −0.841276 −0.0708482
\(142\) −2.88742 −0.242307
\(143\) −13.5037 −1.12923
\(144\) −2.19940 −0.183283
\(145\) −0.394876 −0.0327927
\(146\) −11.7213 −0.970063
\(147\) 4.43371 0.365686
\(148\) −5.53876 −0.455283
\(149\) 9.41318 0.771157 0.385579 0.922675i \(-0.374002\pi\)
0.385579 + 0.922675i \(0.374002\pi\)
\(150\) 4.46980 0.364958
\(151\) 10.1727 0.827839 0.413920 0.910313i \(-0.364159\pi\)
0.413920 + 0.910313i \(0.364159\pi\)
\(152\) 1.00000 0.0811107
\(153\) 1.02014 0.0824732
\(154\) −4.62350 −0.372573
\(155\) 0.336526 0.0270304
\(156\) −3.73694 −0.299195
\(157\) −17.5166 −1.39797 −0.698987 0.715135i \(-0.746365\pi\)
−0.698987 + 0.715135i \(0.746365\pi\)
\(158\) 13.6699 1.08752
\(159\) 9.85896 0.781867
\(160\) −0.0669598 −0.00529363
\(161\) −4.23272 −0.333585
\(162\) 2.43557 0.191356
\(163\) 4.95308 0.387955 0.193977 0.981006i \(-0.437861\pi\)
0.193977 + 0.981006i \(0.437861\pi\)
\(164\) 3.26660 0.255079
\(165\) −0.193716 −0.0150808
\(166\) 1.25135 0.0971236
\(167\) −19.9309 −1.54230 −0.771151 0.636652i \(-0.780319\pi\)
−0.771151 + 0.636652i \(0.780319\pi\)
\(168\) −1.27948 −0.0987144
\(169\) 4.44283 0.341756
\(170\) 0.0310576 0.00238201
\(171\) −2.19940 −0.168192
\(172\) 0.640662 0.0488500
\(173\) −12.1777 −0.925851 −0.462926 0.886397i \(-0.653200\pi\)
−0.462926 + 0.886397i \(0.653200\pi\)
\(174\) −5.27661 −0.400019
\(175\) −7.14345 −0.539994
\(176\) −3.23328 −0.243718
\(177\) −2.70896 −0.203618
\(178\) −3.46503 −0.259715
\(179\) −18.0969 −1.35263 −0.676314 0.736614i \(-0.736424\pi\)
−0.676314 + 0.736614i \(0.736424\pi\)
\(180\) 0.147271 0.0109770
\(181\) −8.35520 −0.621037 −0.310518 0.950567i \(-0.600503\pi\)
−0.310518 + 0.950567i \(0.600503\pi\)
\(182\) 5.97222 0.442691
\(183\) −10.5676 −0.781181
\(184\) −2.96000 −0.218214
\(185\) 0.370874 0.0272672
\(186\) 4.49690 0.329728
\(187\) 1.49968 0.109667
\(188\) 0.940223 0.0685728
\(189\) 6.65255 0.483902
\(190\) −0.0669598 −0.00485777
\(191\) 3.42398 0.247750 0.123875 0.992298i \(-0.460468\pi\)
0.123875 + 0.992298i \(0.460468\pi\)
\(192\) −0.894762 −0.0645739
\(193\) −23.2628 −1.67449 −0.837247 0.546824i \(-0.815837\pi\)
−0.837247 + 0.546824i \(0.815837\pi\)
\(194\) −16.2444 −1.16628
\(195\) 0.250225 0.0179190
\(196\) −4.95518 −0.353941
\(197\) 8.23004 0.586366 0.293183 0.956056i \(-0.405285\pi\)
0.293183 + 0.956056i \(0.405285\pi\)
\(198\) 7.11129 0.505377
\(199\) 13.7781 0.976704 0.488352 0.872647i \(-0.337598\pi\)
0.488352 + 0.872647i \(0.337598\pi\)
\(200\) −4.99552 −0.353236
\(201\) 6.68384 0.471442
\(202\) 0.143986 0.0101308
\(203\) 8.43286 0.591871
\(204\) 0.415013 0.0290567
\(205\) −0.218731 −0.0152768
\(206\) −17.1246 −1.19313
\(207\) 6.51023 0.452492
\(208\) 4.17646 0.289585
\(209\) −3.23328 −0.223651
\(210\) 0.0856740 0.00591207
\(211\) −1.00000 −0.0688428
\(212\) −11.0185 −0.756756
\(213\) 2.58355 0.177022
\(214\) 3.36857 0.230271
\(215\) −0.0428986 −0.00292566
\(216\) 4.65223 0.316544
\(217\) −7.18675 −0.487869
\(218\) 2.29513 0.155446
\(219\) 10.4878 0.708699
\(220\) 0.216500 0.0145964
\(221\) −1.93715 −0.130307
\(222\) 4.95587 0.332616
\(223\) 0.0330141 0.00221079 0.00110539 0.999999i \(-0.499648\pi\)
0.00110539 + 0.999999i \(0.499648\pi\)
\(224\) 1.42997 0.0955440
\(225\) 10.9871 0.732476
\(226\) 4.15323 0.276269
\(227\) 9.85789 0.654291 0.327146 0.944974i \(-0.393913\pi\)
0.327146 + 0.944974i \(0.393913\pi\)
\(228\) −0.894762 −0.0592571
\(229\) −26.1817 −1.73013 −0.865066 0.501657i \(-0.832724\pi\)
−0.865066 + 0.501657i \(0.832724\pi\)
\(230\) 0.198201 0.0130690
\(231\) 4.13694 0.272190
\(232\) 5.89722 0.387171
\(233\) −18.5618 −1.21602 −0.608011 0.793929i \(-0.708032\pi\)
−0.608011 + 0.793929i \(0.708032\pi\)
\(234\) −9.18571 −0.600489
\(235\) −0.0629571 −0.00410687
\(236\) 3.02758 0.197079
\(237\) −12.2313 −0.794507
\(238\) −0.663257 −0.0429926
\(239\) 10.0354 0.649137 0.324568 0.945862i \(-0.394781\pi\)
0.324568 + 0.945862i \(0.394781\pi\)
\(240\) 0.0599131 0.00386737
\(241\) 9.53632 0.614289 0.307144 0.951663i \(-0.400627\pi\)
0.307144 + 0.951663i \(0.400627\pi\)
\(242\) −0.545879 −0.0350904
\(243\) −16.1359 −1.03512
\(244\) 11.8105 0.756092
\(245\) 0.331798 0.0211978
\(246\) −2.92283 −0.186353
\(247\) 4.17646 0.265742
\(248\) −5.02580 −0.319139
\(249\) −1.11966 −0.0709556
\(250\) 0.669297 0.0423301
\(251\) 24.8990 1.57161 0.785807 0.618472i \(-0.212248\pi\)
0.785807 + 0.618472i \(0.212248\pi\)
\(252\) −3.14508 −0.198121
\(253\) 9.57053 0.601694
\(254\) 5.73201 0.359658
\(255\) −0.0277892 −0.00174023
\(256\) 1.00000 0.0625000
\(257\) 1.12662 0.0702763 0.0351382 0.999382i \(-0.488813\pi\)
0.0351382 + 0.999382i \(0.488813\pi\)
\(258\) −0.573240 −0.0356884
\(259\) −7.92027 −0.492141
\(260\) −0.279655 −0.0173435
\(261\) −12.9703 −0.802844
\(262\) −21.0961 −1.30332
\(263\) −1.34463 −0.0829133 −0.0414567 0.999140i \(-0.513200\pi\)
−0.0414567 + 0.999140i \(0.513200\pi\)
\(264\) 2.89302 0.178053
\(265\) 0.737798 0.0453226
\(266\) 1.42997 0.0876772
\(267\) 3.10037 0.189740
\(268\) −7.46996 −0.456301
\(269\) −16.7280 −1.01992 −0.509961 0.860197i \(-0.670340\pi\)
−0.509961 + 0.860197i \(0.670340\pi\)
\(270\) −0.311512 −0.0189580
\(271\) −17.8311 −1.08316 −0.541582 0.840648i \(-0.682174\pi\)
−0.541582 + 0.840648i \(0.682174\pi\)
\(272\) −0.463825 −0.0281235
\(273\) −5.34372 −0.323417
\(274\) 10.7451 0.649137
\(275\) 16.1519 0.973997
\(276\) 2.64850 0.159421
\(277\) −2.04524 −0.122887 −0.0614434 0.998111i \(-0.519570\pi\)
−0.0614434 + 0.998111i \(0.519570\pi\)
\(278\) −2.46250 −0.147691
\(279\) 11.0537 0.661771
\(280\) −0.0957506 −0.00572219
\(281\) −9.57838 −0.571398 −0.285699 0.958319i \(-0.592226\pi\)
−0.285699 + 0.958319i \(0.592226\pi\)
\(282\) −0.841276 −0.0500972
\(283\) 13.8347 0.822386 0.411193 0.911548i \(-0.365112\pi\)
0.411193 + 0.911548i \(0.365112\pi\)
\(284\) −2.88742 −0.171337
\(285\) 0.0599131 0.00354894
\(286\) −13.5037 −0.798490
\(287\) 4.67115 0.275729
\(288\) −2.19940 −0.129601
\(289\) −16.7849 −0.987345
\(290\) −0.394876 −0.0231879
\(291\) 14.5349 0.852049
\(292\) −11.7213 −0.685938
\(293\) 28.0241 1.63718 0.818592 0.574376i \(-0.194755\pi\)
0.818592 + 0.574376i \(0.194755\pi\)
\(294\) 4.43371 0.258579
\(295\) −0.202726 −0.0118032
\(296\) −5.53876 −0.321934
\(297\) −15.0420 −0.872823
\(298\) 9.41318 0.545291
\(299\) −12.3623 −0.714932
\(300\) 4.46980 0.258064
\(301\) 0.916129 0.0528048
\(302\) 10.1727 0.585371
\(303\) −0.128833 −0.00740126
\(304\) 1.00000 0.0573539
\(305\) −0.790831 −0.0452828
\(306\) 1.02014 0.0583174
\(307\) −0.669660 −0.0382195 −0.0191098 0.999817i \(-0.506083\pi\)
−0.0191098 + 0.999817i \(0.506083\pi\)
\(308\) −4.62350 −0.263449
\(309\) 15.3224 0.871664
\(310\) 0.336526 0.0191134
\(311\) −26.6499 −1.51118 −0.755589 0.655046i \(-0.772649\pi\)
−0.755589 + 0.655046i \(0.772649\pi\)
\(312\) −3.73694 −0.211563
\(313\) 13.8057 0.780347 0.390173 0.920741i \(-0.372415\pi\)
0.390173 + 0.920741i \(0.372415\pi\)
\(314\) −17.5166 −0.988517
\(315\) 0.210594 0.0118656
\(316\) 13.6699 0.768990
\(317\) −7.28445 −0.409135 −0.204568 0.978852i \(-0.565579\pi\)
−0.204568 + 0.978852i \(0.565579\pi\)
\(318\) 9.85896 0.552863
\(319\) −19.0674 −1.06757
\(320\) −0.0669598 −0.00374316
\(321\) −3.01407 −0.168229
\(322\) −4.23272 −0.235880
\(323\) −0.463825 −0.0258079
\(324\) 2.43557 0.135309
\(325\) −20.8636 −1.15730
\(326\) 4.95308 0.274325
\(327\) −2.05360 −0.113564
\(328\) 3.26660 0.180368
\(329\) 1.34449 0.0741243
\(330\) −0.193716 −0.0106637
\(331\) 20.6018 1.13238 0.566188 0.824276i \(-0.308417\pi\)
0.566188 + 0.824276i \(0.308417\pi\)
\(332\) 1.25135 0.0686768
\(333\) 12.1819 0.667566
\(334\) −19.9309 −1.09057
\(335\) 0.500187 0.0273281
\(336\) −1.27948 −0.0698016
\(337\) −2.81924 −0.153574 −0.0767869 0.997048i \(-0.524466\pi\)
−0.0767869 + 0.997048i \(0.524466\pi\)
\(338\) 4.44283 0.241658
\(339\) −3.71615 −0.201834
\(340\) 0.0310576 0.00168434
\(341\) 16.2498 0.879978
\(342\) −2.19940 −0.118930
\(343\) −17.0956 −0.923074
\(344\) 0.640662 0.0345422
\(345\) −0.177343 −0.00954781
\(346\) −12.1777 −0.654676
\(347\) 27.5593 1.47946 0.739730 0.672904i \(-0.234953\pi\)
0.739730 + 0.672904i \(0.234953\pi\)
\(348\) −5.27661 −0.282856
\(349\) 15.7773 0.844537 0.422269 0.906471i \(-0.361234\pi\)
0.422269 + 0.906471i \(0.361234\pi\)
\(350\) −7.14345 −0.381833
\(351\) 19.4298 1.03709
\(352\) −3.23328 −0.172335
\(353\) −21.9369 −1.16758 −0.583790 0.811904i \(-0.698431\pi\)
−0.583790 + 0.811904i \(0.698431\pi\)
\(354\) −2.70896 −0.143980
\(355\) 0.193341 0.0102615
\(356\) −3.46503 −0.183646
\(357\) 0.593457 0.0314091
\(358\) −18.0969 −0.956452
\(359\) −22.8882 −1.20799 −0.603996 0.796987i \(-0.706426\pi\)
−0.603996 + 0.796987i \(0.706426\pi\)
\(360\) 0.147271 0.00776188
\(361\) 1.00000 0.0526316
\(362\) −8.35520 −0.439139
\(363\) 0.488432 0.0256360
\(364\) 5.97222 0.313030
\(365\) 0.784856 0.0410812
\(366\) −10.5676 −0.552378
\(367\) −27.0452 −1.41175 −0.705874 0.708337i \(-0.749446\pi\)
−0.705874 + 0.708337i \(0.749446\pi\)
\(368\) −2.96000 −0.154301
\(369\) −7.18456 −0.374013
\(370\) 0.370874 0.0192808
\(371\) −15.7562 −0.818020
\(372\) 4.49690 0.233153
\(373\) 14.7445 0.763443 0.381722 0.924277i \(-0.375331\pi\)
0.381722 + 0.924277i \(0.375331\pi\)
\(374\) 1.49968 0.0775465
\(375\) −0.598862 −0.0309251
\(376\) 0.940223 0.0484883
\(377\) 24.6295 1.26848
\(378\) 6.65255 0.342170
\(379\) −17.3322 −0.890298 −0.445149 0.895457i \(-0.646849\pi\)
−0.445149 + 0.895457i \(0.646849\pi\)
\(380\) −0.0669598 −0.00343496
\(381\) −5.12878 −0.262756
\(382\) 3.42398 0.175186
\(383\) −31.3055 −1.59964 −0.799818 0.600243i \(-0.795071\pi\)
−0.799818 + 0.600243i \(0.795071\pi\)
\(384\) −0.894762 −0.0456606
\(385\) 0.309589 0.0157781
\(386\) −23.2628 −1.18405
\(387\) −1.40907 −0.0716272
\(388\) −16.2444 −0.824684
\(389\) −19.1839 −0.972663 −0.486332 0.873774i \(-0.661665\pi\)
−0.486332 + 0.873774i \(0.661665\pi\)
\(390\) 0.250225 0.0126706
\(391\) 1.37292 0.0694317
\(392\) −4.95518 −0.250274
\(393\) 18.8760 0.952169
\(394\) 8.23004 0.414624
\(395\) −0.915331 −0.0460553
\(396\) 7.11129 0.357356
\(397\) 24.9671 1.25306 0.626531 0.779396i \(-0.284474\pi\)
0.626531 + 0.779396i \(0.284474\pi\)
\(398\) 13.7781 0.690634
\(399\) −1.27948 −0.0640543
\(400\) −4.99552 −0.249776
\(401\) 16.2670 0.812336 0.406168 0.913798i \(-0.366865\pi\)
0.406168 + 0.913798i \(0.366865\pi\)
\(402\) 6.68384 0.333360
\(403\) −20.9901 −1.04559
\(404\) 0.143986 0.00716355
\(405\) −0.163085 −0.00810376
\(406\) 8.43286 0.418516
\(407\) 17.9084 0.887685
\(408\) 0.415013 0.0205462
\(409\) −16.4952 −0.815635 −0.407817 0.913064i \(-0.633710\pi\)
−0.407817 + 0.913064i \(0.633710\pi\)
\(410\) −0.218731 −0.0108023
\(411\) −9.61434 −0.474240
\(412\) −17.1246 −0.843669
\(413\) 4.32936 0.213034
\(414\) 6.51023 0.319960
\(415\) −0.0837901 −0.00411310
\(416\) 4.17646 0.204768
\(417\) 2.20335 0.107899
\(418\) −3.23328 −0.158145
\(419\) −18.5736 −0.907380 −0.453690 0.891159i \(-0.649893\pi\)
−0.453690 + 0.891159i \(0.649893\pi\)
\(420\) 0.0856740 0.00418046
\(421\) −27.7847 −1.35414 −0.677072 0.735917i \(-0.736751\pi\)
−0.677072 + 0.735917i \(0.736751\pi\)
\(422\) −1.00000 −0.0486792
\(423\) −2.06793 −0.100546
\(424\) −11.0185 −0.535107
\(425\) 2.31705 0.112393
\(426\) 2.58355 0.125174
\(427\) 16.8887 0.817303
\(428\) 3.36857 0.162826
\(429\) 12.0826 0.583353
\(430\) −0.0428986 −0.00206875
\(431\) −34.7106 −1.67195 −0.835977 0.548765i \(-0.815098\pi\)
−0.835977 + 0.548765i \(0.815098\pi\)
\(432\) 4.65223 0.223830
\(433\) −23.7888 −1.14322 −0.571609 0.820526i \(-0.693681\pi\)
−0.571609 + 0.820526i \(0.693681\pi\)
\(434\) −7.18675 −0.344975
\(435\) 0.353320 0.0169404
\(436\) 2.29513 0.109917
\(437\) −2.96000 −0.141596
\(438\) 10.4878 0.501126
\(439\) 36.8791 1.76014 0.880072 0.474840i \(-0.157494\pi\)
0.880072 + 0.474840i \(0.157494\pi\)
\(440\) 0.216500 0.0103212
\(441\) 10.8984 0.518973
\(442\) −1.93715 −0.0921408
\(443\) 18.7710 0.891837 0.445918 0.895074i \(-0.352877\pi\)
0.445918 + 0.895074i \(0.352877\pi\)
\(444\) 4.95587 0.235195
\(445\) 0.232017 0.0109987
\(446\) 0.0330141 0.00156326
\(447\) −8.42255 −0.398373
\(448\) 1.42997 0.0675598
\(449\) 7.66794 0.361873 0.180936 0.983495i \(-0.442087\pi\)
0.180936 + 0.983495i \(0.442087\pi\)
\(450\) 10.9871 0.517939
\(451\) −10.5618 −0.497338
\(452\) 4.15323 0.195352
\(453\) −9.10211 −0.427654
\(454\) 9.85789 0.462654
\(455\) −0.399899 −0.0187475
\(456\) −0.894762 −0.0419011
\(457\) −13.5028 −0.631636 −0.315818 0.948820i \(-0.602279\pi\)
−0.315818 + 0.948820i \(0.602279\pi\)
\(458\) −26.1817 −1.22339
\(459\) −2.15782 −0.100718
\(460\) 0.198201 0.00924117
\(461\) 11.3288 0.527634 0.263817 0.964573i \(-0.415018\pi\)
0.263817 + 0.964573i \(0.415018\pi\)
\(462\) 4.13694 0.192468
\(463\) −2.50054 −0.116210 −0.0581049 0.998310i \(-0.518506\pi\)
−0.0581049 + 0.998310i \(0.518506\pi\)
\(464\) 5.89722 0.273772
\(465\) −0.301111 −0.0139637
\(466\) −18.5618 −0.859857
\(467\) −9.47731 −0.438557 −0.219279 0.975662i \(-0.570370\pi\)
−0.219279 + 0.975662i \(0.570370\pi\)
\(468\) −9.18571 −0.424610
\(469\) −10.6818 −0.493241
\(470\) −0.0629571 −0.00290399
\(471\) 15.6732 0.722181
\(472\) 3.02758 0.139356
\(473\) −2.07144 −0.0952450
\(474\) −12.2313 −0.561801
\(475\) −4.99552 −0.229210
\(476\) −0.663257 −0.0304003
\(477\) 24.2342 1.10961
\(478\) 10.0354 0.459009
\(479\) 25.1951 1.15119 0.575597 0.817734i \(-0.304770\pi\)
0.575597 + 0.817734i \(0.304770\pi\)
\(480\) 0.0599131 0.00273464
\(481\) −23.1324 −1.05475
\(482\) 9.53632 0.434368
\(483\) 3.78728 0.172327
\(484\) −0.545879 −0.0248127
\(485\) 1.08772 0.0493909
\(486\) −16.1359 −0.731941
\(487\) −10.4758 −0.474706 −0.237353 0.971423i \(-0.576280\pi\)
−0.237353 + 0.971423i \(0.576280\pi\)
\(488\) 11.8105 0.534638
\(489\) −4.43182 −0.200414
\(490\) 0.331798 0.0149891
\(491\) 39.2210 1.77002 0.885010 0.465572i \(-0.154151\pi\)
0.885010 + 0.465572i \(0.154151\pi\)
\(492\) −2.92283 −0.131771
\(493\) −2.73528 −0.123191
\(494\) 4.17646 0.187908
\(495\) −0.476170 −0.0214022
\(496\) −5.02580 −0.225665
\(497\) −4.12893 −0.185208
\(498\) −1.11966 −0.0501732
\(499\) −7.95532 −0.356129 −0.178065 0.984019i \(-0.556984\pi\)
−0.178065 + 0.984019i \(0.556984\pi\)
\(500\) 0.669297 0.0299319
\(501\) 17.8335 0.796740
\(502\) 24.8990 1.11130
\(503\) 34.2518 1.52721 0.763605 0.645683i \(-0.223427\pi\)
0.763605 + 0.645683i \(0.223427\pi\)
\(504\) −3.14508 −0.140093
\(505\) −0.00964125 −0.000429030 0
\(506\) 9.57053 0.425462
\(507\) −3.97528 −0.176548
\(508\) 5.73201 0.254317
\(509\) 5.15090 0.228310 0.114155 0.993463i \(-0.463584\pi\)
0.114155 + 0.993463i \(0.463584\pi\)
\(510\) −0.0277892 −0.00123053
\(511\) −16.7611 −0.741469
\(512\) 1.00000 0.0441942
\(513\) 4.65223 0.205401
\(514\) 1.12662 0.0496929
\(515\) 1.14666 0.0505279
\(516\) −0.573240 −0.0252355
\(517\) −3.04001 −0.133699
\(518\) −7.92027 −0.347996
\(519\) 10.8961 0.478287
\(520\) −0.279655 −0.0122637
\(521\) −16.5531 −0.725202 −0.362601 0.931944i \(-0.618111\pi\)
−0.362601 + 0.931944i \(0.618111\pi\)
\(522\) −12.9703 −0.567697
\(523\) −32.7917 −1.43388 −0.716939 0.697135i \(-0.754458\pi\)
−0.716939 + 0.697135i \(0.754458\pi\)
\(524\) −21.0961 −0.921589
\(525\) 6.39169 0.278956
\(526\) −1.34463 −0.0586286
\(527\) 2.33109 0.101544
\(528\) 2.89302 0.125903
\(529\) −14.2384 −0.619060
\(530\) 0.737798 0.0320479
\(531\) −6.65886 −0.288970
\(532\) 1.42997 0.0619971
\(533\) 13.6428 0.590937
\(534\) 3.10037 0.134166
\(535\) −0.225558 −0.00975174
\(536\) −7.46996 −0.322653
\(537\) 16.1924 0.698755
\(538\) −16.7280 −0.721194
\(539\) 16.0215 0.690095
\(540\) −0.311512 −0.0134053
\(541\) −30.1889 −1.29792 −0.648961 0.760822i \(-0.724796\pi\)
−0.648961 + 0.760822i \(0.724796\pi\)
\(542\) −17.8311 −0.765912
\(543\) 7.47591 0.320822
\(544\) −0.463825 −0.0198863
\(545\) −0.153682 −0.00658300
\(546\) −5.34372 −0.228690
\(547\) 10.2456 0.438068 0.219034 0.975717i \(-0.429709\pi\)
0.219034 + 0.975717i \(0.429709\pi\)
\(548\) 10.7451 0.459009
\(549\) −25.9761 −1.10863
\(550\) 16.1519 0.688720
\(551\) 5.89722 0.251230
\(552\) 2.64850 0.112728
\(553\) 19.5475 0.831245
\(554\) −2.04524 −0.0868940
\(555\) −0.331844 −0.0140860
\(556\) −2.46250 −0.104433
\(557\) 34.9497 1.48087 0.740433 0.672130i \(-0.234620\pi\)
0.740433 + 0.672130i \(0.234620\pi\)
\(558\) 11.0537 0.467943
\(559\) 2.67570 0.113170
\(560\) −0.0957506 −0.00404620
\(561\) −1.34186 −0.0566532
\(562\) −9.57838 −0.404039
\(563\) 34.9170 1.47157 0.735787 0.677213i \(-0.236812\pi\)
0.735787 + 0.677213i \(0.236812\pi\)
\(564\) −0.841276 −0.0354241
\(565\) −0.278099 −0.0116997
\(566\) 13.8347 0.581515
\(567\) 3.48279 0.146263
\(568\) −2.88742 −0.121153
\(569\) 33.2616 1.39440 0.697199 0.716878i \(-0.254429\pi\)
0.697199 + 0.716878i \(0.254429\pi\)
\(570\) 0.0599131 0.00250948
\(571\) −32.2694 −1.35043 −0.675217 0.737619i \(-0.735950\pi\)
−0.675217 + 0.737619i \(0.735950\pi\)
\(572\) −13.5037 −0.564617
\(573\) −3.06365 −0.127986
\(574\) 4.67115 0.194970
\(575\) 14.7867 0.616650
\(576\) −2.19940 −0.0916417
\(577\) −24.6167 −1.02481 −0.512403 0.858745i \(-0.671245\pi\)
−0.512403 + 0.858745i \(0.671245\pi\)
\(578\) −16.7849 −0.698158
\(579\) 20.8147 0.865029
\(580\) −0.394876 −0.0163963
\(581\) 1.78940 0.0742367
\(582\) 14.5349 0.602490
\(583\) 35.6260 1.47548
\(584\) −11.7213 −0.485031
\(585\) 0.615073 0.0254301
\(586\) 28.0241 1.15766
\(587\) 32.2113 1.32950 0.664752 0.747064i \(-0.268537\pi\)
0.664752 + 0.747064i \(0.268537\pi\)
\(588\) 4.43371 0.182843
\(589\) −5.02580 −0.207085
\(590\) −0.202726 −0.00834610
\(591\) −7.36393 −0.302912
\(592\) −5.53876 −0.227641
\(593\) 32.0403 1.31574 0.657869 0.753132i \(-0.271458\pi\)
0.657869 + 0.753132i \(0.271458\pi\)
\(594\) −15.0420 −0.617179
\(595\) 0.0444115 0.00182070
\(596\) 9.41318 0.385579
\(597\) −12.3281 −0.504557
\(598\) −12.3623 −0.505533
\(599\) 19.9390 0.814687 0.407343 0.913275i \(-0.366455\pi\)
0.407343 + 0.913275i \(0.366455\pi\)
\(600\) 4.46980 0.182479
\(601\) −8.82658 −0.360044 −0.180022 0.983663i \(-0.557617\pi\)
−0.180022 + 0.983663i \(0.557617\pi\)
\(602\) 0.916129 0.0373386
\(603\) 16.4294 0.669059
\(604\) 10.1727 0.413920
\(605\) 0.0365519 0.00148605
\(606\) −0.128833 −0.00523348
\(607\) −6.03639 −0.245009 −0.122505 0.992468i \(-0.539093\pi\)
−0.122505 + 0.992468i \(0.539093\pi\)
\(608\) 1.00000 0.0405554
\(609\) −7.54540 −0.305755
\(610\) −0.790831 −0.0320198
\(611\) 3.92680 0.158862
\(612\) 1.02014 0.0412366
\(613\) 15.5906 0.629699 0.314850 0.949142i \(-0.398046\pi\)
0.314850 + 0.949142i \(0.398046\pi\)
\(614\) −0.669660 −0.0270253
\(615\) 0.195712 0.00789187
\(616\) −4.62350 −0.186286
\(617\) −9.28165 −0.373665 −0.186833 0.982392i \(-0.559822\pi\)
−0.186833 + 0.982392i \(0.559822\pi\)
\(618\) 15.3224 0.616359
\(619\) 5.34460 0.214817 0.107409 0.994215i \(-0.465745\pi\)
0.107409 + 0.994215i \(0.465745\pi\)
\(620\) 0.336526 0.0135152
\(621\) −13.7706 −0.552595
\(622\) −26.6499 −1.06856
\(623\) −4.95489 −0.198514
\(624\) −3.73694 −0.149597
\(625\) 24.9328 0.997311
\(626\) 13.8057 0.551788
\(627\) 2.89302 0.115536
\(628\) −17.5166 −0.698987
\(629\) 2.56902 0.102433
\(630\) 0.210594 0.00839026
\(631\) −21.5798 −0.859079 −0.429540 0.903048i \(-0.641324\pi\)
−0.429540 + 0.903048i \(0.641324\pi\)
\(632\) 13.6699 0.543758
\(633\) 0.894762 0.0355636
\(634\) −7.28445 −0.289302
\(635\) −0.383814 −0.0152312
\(636\) 9.85896 0.390933
\(637\) −20.6951 −0.819971
\(638\) −19.0674 −0.754885
\(639\) 6.35060 0.251226
\(640\) −0.0669598 −0.00264682
\(641\) 24.7578 0.977874 0.488937 0.872319i \(-0.337385\pi\)
0.488937 + 0.872319i \(0.337385\pi\)
\(642\) −3.01407 −0.118956
\(643\) 1.69702 0.0669241 0.0334621 0.999440i \(-0.489347\pi\)
0.0334621 + 0.999440i \(0.489347\pi\)
\(644\) −4.23272 −0.166793
\(645\) 0.0383840 0.00151137
\(646\) −0.463825 −0.0182490
\(647\) 15.4827 0.608686 0.304343 0.952562i \(-0.401563\pi\)
0.304343 + 0.952562i \(0.401563\pi\)
\(648\) 2.43557 0.0956781
\(649\) −9.78903 −0.384253
\(650\) −20.8636 −0.818337
\(651\) 6.43043 0.252029
\(652\) 4.95308 0.193977
\(653\) 3.27690 0.128235 0.0641175 0.997942i \(-0.479577\pi\)
0.0641175 + 0.997942i \(0.479577\pi\)
\(654\) −2.05360 −0.0803021
\(655\) 1.41259 0.0551945
\(656\) 3.26660 0.127539
\(657\) 25.7799 1.00577
\(658\) 1.34449 0.0524138
\(659\) −10.5496 −0.410954 −0.205477 0.978662i \(-0.565875\pi\)
−0.205477 + 0.978662i \(0.565875\pi\)
\(660\) −0.193716 −0.00754038
\(661\) −26.4876 −1.03025 −0.515125 0.857115i \(-0.672255\pi\)
−0.515125 + 0.857115i \(0.672255\pi\)
\(662\) 20.6018 0.800711
\(663\) 1.73329 0.0673153
\(664\) 1.25135 0.0485618
\(665\) −0.0957506 −0.00371305
\(666\) 12.1819 0.472041
\(667\) −17.4558 −0.675890
\(668\) −19.9309 −0.771151
\(669\) −0.0295398 −0.00114207
\(670\) 0.500187 0.0193239
\(671\) −38.1868 −1.47419
\(672\) −1.27948 −0.0493572
\(673\) −4.62534 −0.178294 −0.0891468 0.996018i \(-0.528414\pi\)
−0.0891468 + 0.996018i \(0.528414\pi\)
\(674\) −2.81924 −0.108593
\(675\) −23.2403 −0.894519
\(676\) 4.44283 0.170878
\(677\) 26.1516 1.00509 0.502543 0.864552i \(-0.332398\pi\)
0.502543 + 0.864552i \(0.332398\pi\)
\(678\) −3.71615 −0.142718
\(679\) −23.2290 −0.891448
\(680\) 0.0310576 0.00119101
\(681\) −8.82047 −0.338001
\(682\) 16.2498 0.622238
\(683\) −30.8227 −1.17940 −0.589699 0.807623i \(-0.700754\pi\)
−0.589699 + 0.807623i \(0.700754\pi\)
\(684\) −2.19940 −0.0840962
\(685\) −0.719492 −0.0274904
\(686\) −17.0956 −0.652712
\(687\) 23.4264 0.893771
\(688\) 0.640662 0.0244250
\(689\) −46.0185 −1.75316
\(690\) −0.177343 −0.00675132
\(691\) 11.0033 0.418586 0.209293 0.977853i \(-0.432884\pi\)
0.209293 + 0.977853i \(0.432884\pi\)
\(692\) −12.1777 −0.462926
\(693\) 10.1689 0.386286
\(694\) 27.5593 1.04614
\(695\) 0.164888 0.00625458
\(696\) −5.27661 −0.200009
\(697\) −1.51513 −0.0573897
\(698\) 15.7773 0.597178
\(699\) 16.6084 0.628186
\(700\) −7.14345 −0.269997
\(701\) −32.5727 −1.23025 −0.615126 0.788429i \(-0.710895\pi\)
−0.615126 + 0.788429i \(0.710895\pi\)
\(702\) 19.4298 0.733332
\(703\) −5.53876 −0.208898
\(704\) −3.23328 −0.121859
\(705\) 0.0563316 0.00212157
\(706\) −21.9369 −0.825604
\(707\) 0.205895 0.00774350
\(708\) −2.70896 −0.101809
\(709\) −10.8216 −0.406415 −0.203208 0.979136i \(-0.565137\pi\)
−0.203208 + 0.979136i \(0.565137\pi\)
\(710\) 0.193341 0.00725596
\(711\) −30.0655 −1.12754
\(712\) −3.46503 −0.129857
\(713\) 14.8764 0.557125
\(714\) 0.593457 0.0222096
\(715\) 0.904203 0.0338153
\(716\) −18.0969 −0.676314
\(717\) −8.97931 −0.335338
\(718\) −22.8882 −0.854180
\(719\) 12.0564 0.449626 0.224813 0.974402i \(-0.427823\pi\)
0.224813 + 0.974402i \(0.427823\pi\)
\(720\) 0.147271 0.00548848
\(721\) −24.4877 −0.911970
\(722\) 1.00000 0.0372161
\(723\) −8.53274 −0.317336
\(724\) −8.35520 −0.310518
\(725\) −29.4597 −1.09410
\(726\) 0.488432 0.0181274
\(727\) 6.97553 0.258708 0.129354 0.991598i \(-0.458710\pi\)
0.129354 + 0.991598i \(0.458710\pi\)
\(728\) 5.97222 0.221345
\(729\) 7.13112 0.264116
\(730\) 0.784856 0.0290488
\(731\) −0.297155 −0.0109907
\(732\) −10.5676 −0.390591
\(733\) −23.8008 −0.879102 −0.439551 0.898218i \(-0.644862\pi\)
−0.439551 + 0.898218i \(0.644862\pi\)
\(734\) −27.0452 −0.998256
\(735\) −0.296880 −0.0109506
\(736\) −2.96000 −0.109107
\(737\) 24.1525 0.889669
\(738\) −7.18456 −0.264467
\(739\) 14.6454 0.538741 0.269371 0.963037i \(-0.413184\pi\)
0.269371 + 0.963037i \(0.413184\pi\)
\(740\) 0.370874 0.0136336
\(741\) −3.73694 −0.137280
\(742\) −15.7562 −0.578428
\(743\) −12.5843 −0.461672 −0.230836 0.972993i \(-0.574146\pi\)
−0.230836 + 0.972993i \(0.574146\pi\)
\(744\) 4.49690 0.164864
\(745\) −0.630304 −0.0230925
\(746\) 14.7445 0.539836
\(747\) −2.75222 −0.100699
\(748\) 1.49968 0.0548337
\(749\) 4.81696 0.176008
\(750\) −0.598862 −0.0218673
\(751\) −8.54675 −0.311875 −0.155938 0.987767i \(-0.549840\pi\)
−0.155938 + 0.987767i \(0.549840\pi\)
\(752\) 0.940223 0.0342864
\(753\) −22.2787 −0.811882
\(754\) 24.6295 0.896954
\(755\) −0.681159 −0.0247899
\(756\) 6.65255 0.241951
\(757\) 1.53898 0.0559351 0.0279675 0.999609i \(-0.491096\pi\)
0.0279675 + 0.999609i \(0.491096\pi\)
\(758\) −17.3322 −0.629535
\(759\) −8.56334 −0.310830
\(760\) −0.0669598 −0.00242889
\(761\) 5.68064 0.205923 0.102961 0.994685i \(-0.467168\pi\)
0.102961 + 0.994685i \(0.467168\pi\)
\(762\) −5.12878 −0.185796
\(763\) 3.28198 0.118816
\(764\) 3.42398 0.123875
\(765\) −0.0683082 −0.00246969
\(766\) −31.3055 −1.13111
\(767\) 12.6446 0.456569
\(768\) −0.894762 −0.0322869
\(769\) −25.4526 −0.917843 −0.458922 0.888477i \(-0.651764\pi\)
−0.458922 + 0.888477i \(0.651764\pi\)
\(770\) 0.309589 0.0111568
\(771\) −1.00805 −0.0363041
\(772\) −23.2628 −0.837247
\(773\) −1.87884 −0.0675772 −0.0337886 0.999429i \(-0.510757\pi\)
−0.0337886 + 0.999429i \(0.510757\pi\)
\(774\) −1.40907 −0.0506481
\(775\) 25.1065 0.901851
\(776\) −16.2444 −0.583140
\(777\) 7.08675 0.254236
\(778\) −19.1839 −0.687777
\(779\) 3.26660 0.117038
\(780\) 0.250225 0.00895948
\(781\) 9.33585 0.334063
\(782\) 1.37292 0.0490957
\(783\) 27.4352 0.980454
\(784\) −4.95518 −0.176971
\(785\) 1.17290 0.0418628
\(786\) 18.8760 0.673285
\(787\) −22.6411 −0.807068 −0.403534 0.914965i \(-0.632218\pi\)
−0.403534 + 0.914965i \(0.632218\pi\)
\(788\) 8.23004 0.293183
\(789\) 1.20312 0.0428323
\(790\) −0.915331 −0.0325660
\(791\) 5.93900 0.211167
\(792\) 7.11129 0.252689
\(793\) 49.3263 1.75163
\(794\) 24.9671 0.886049
\(795\) −0.660154 −0.0234132
\(796\) 13.7781 0.488352
\(797\) −49.2885 −1.74589 −0.872945 0.487819i \(-0.837793\pi\)
−0.872945 + 0.487819i \(0.837793\pi\)
\(798\) −1.27948 −0.0452933
\(799\) −0.436099 −0.0154281
\(800\) −4.99552 −0.176618
\(801\) 7.62098 0.269274
\(802\) 16.2670 0.574408
\(803\) 37.8983 1.33740
\(804\) 6.68384 0.235721
\(805\) 0.283422 0.00998931
\(806\) −20.9901 −0.739343
\(807\) 14.9676 0.526883
\(808\) 0.143986 0.00506540
\(809\) 46.0017 1.61733 0.808667 0.588267i \(-0.200189\pi\)
0.808667 + 0.588267i \(0.200189\pi\)
\(810\) −0.163085 −0.00573022
\(811\) −10.0420 −0.352624 −0.176312 0.984334i \(-0.556417\pi\)
−0.176312 + 0.984334i \(0.556417\pi\)
\(812\) 8.43286 0.295935
\(813\) 15.9546 0.559552
\(814\) 17.9084 0.627688
\(815\) −0.331657 −0.0116174
\(816\) 0.415013 0.0145284
\(817\) 0.640662 0.0224139
\(818\) −16.4952 −0.576741
\(819\) −13.1353 −0.458985
\(820\) −0.218731 −0.00763841
\(821\) −18.0128 −0.628650 −0.314325 0.949315i \(-0.601778\pi\)
−0.314325 + 0.949315i \(0.601778\pi\)
\(822\) −9.61434 −0.335339
\(823\) 9.25191 0.322501 0.161251 0.986913i \(-0.448447\pi\)
0.161251 + 0.986913i \(0.448447\pi\)
\(824\) −17.1246 −0.596564
\(825\) −14.4521 −0.503158
\(826\) 4.32936 0.150638
\(827\) 29.7423 1.03424 0.517121 0.855913i \(-0.327004\pi\)
0.517121 + 0.855913i \(0.327004\pi\)
\(828\) 6.51023 0.226246
\(829\) −7.63241 −0.265085 −0.132542 0.991177i \(-0.542314\pi\)
−0.132542 + 0.991177i \(0.542314\pi\)
\(830\) −0.0837901 −0.00290840
\(831\) 1.83001 0.0634822
\(832\) 4.17646 0.144793
\(833\) 2.29834 0.0796327
\(834\) 2.20335 0.0762959
\(835\) 1.33457 0.0461847
\(836\) −3.23328 −0.111825
\(837\) −23.3812 −0.808171
\(838\) −18.5736 −0.641615
\(839\) 21.6760 0.748337 0.374169 0.927361i \(-0.377928\pi\)
0.374169 + 0.927361i \(0.377928\pi\)
\(840\) 0.0856740 0.00295603
\(841\) 5.77719 0.199213
\(842\) −27.7847 −0.957524
\(843\) 8.57037 0.295179
\(844\) −1.00000 −0.0344214
\(845\) −0.297491 −0.0102340
\(846\) −2.06793 −0.0710968
\(847\) −0.780591 −0.0268214
\(848\) −11.0185 −0.378378
\(849\) −12.3787 −0.424837
\(850\) 2.31705 0.0794740
\(851\) 16.3947 0.562004
\(852\) 2.58355 0.0885111
\(853\) 44.7515 1.53226 0.766132 0.642683i \(-0.222179\pi\)
0.766132 + 0.642683i \(0.222179\pi\)
\(854\) 16.8887 0.577921
\(855\) 0.147271 0.00503657
\(856\) 3.36857 0.115135
\(857\) −10.1111 −0.345390 −0.172695 0.984975i \(-0.555247\pi\)
−0.172695 + 0.984975i \(0.555247\pi\)
\(858\) 12.0826 0.412493
\(859\) 49.2301 1.67971 0.839854 0.542812i \(-0.182640\pi\)
0.839854 + 0.542812i \(0.182640\pi\)
\(860\) −0.0428986 −0.00146283
\(861\) −4.17956 −0.142439
\(862\) −34.7106 −1.18225
\(863\) −14.1606 −0.482033 −0.241016 0.970521i \(-0.577481\pi\)
−0.241016 + 0.970521i \(0.577481\pi\)
\(864\) 4.65223 0.158272
\(865\) 0.815414 0.0277249
\(866\) −23.7888 −0.808377
\(867\) 15.0185 0.510054
\(868\) −7.18675 −0.243934
\(869\) −44.1985 −1.49933
\(870\) 0.353320 0.0119787
\(871\) −31.1980 −1.05710
\(872\) 2.29513 0.0777231
\(873\) 35.7279 1.20921
\(874\) −2.96000 −0.100124
\(875\) 0.957076 0.0323551
\(876\) 10.4878 0.354349
\(877\) 8.88043 0.299871 0.149935 0.988696i \(-0.452093\pi\)
0.149935 + 0.988696i \(0.452093\pi\)
\(878\) 36.8791 1.24461
\(879\) −25.0749 −0.845755
\(880\) 0.216500 0.00729821
\(881\) 20.7540 0.699219 0.349609 0.936896i \(-0.386314\pi\)
0.349609 + 0.936896i \(0.386314\pi\)
\(882\) 10.8984 0.366969
\(883\) −45.9956 −1.54788 −0.773938 0.633262i \(-0.781716\pi\)
−0.773938 + 0.633262i \(0.781716\pi\)
\(884\) −1.93715 −0.0651534
\(885\) 0.181392 0.00609741
\(886\) 18.7710 0.630624
\(887\) −22.3918 −0.751844 −0.375922 0.926651i \(-0.622674\pi\)
−0.375922 + 0.926651i \(0.622674\pi\)
\(888\) 4.95587 0.166308
\(889\) 8.19661 0.274906
\(890\) 0.232017 0.00777724
\(891\) −7.87488 −0.263818
\(892\) 0.0330141 0.00110539
\(893\) 0.940223 0.0314634
\(894\) −8.42255 −0.281692
\(895\) 1.21177 0.0405048
\(896\) 1.42997 0.0477720
\(897\) 11.0613 0.369328
\(898\) 7.66794 0.255883
\(899\) −29.6382 −0.988491
\(900\) 10.9871 0.366238
\(901\) 5.11067 0.170261
\(902\) −10.5618 −0.351671
\(903\) −0.819717 −0.0272785
\(904\) 4.15323 0.138134
\(905\) 0.559462 0.0185971
\(906\) −9.10211 −0.302397
\(907\) −11.2584 −0.373830 −0.186915 0.982376i \(-0.559849\pi\)
−0.186915 + 0.982376i \(0.559849\pi\)
\(908\) 9.85789 0.327146
\(909\) −0.316682 −0.0105037
\(910\) −0.399899 −0.0132565
\(911\) 15.0265 0.497849 0.248925 0.968523i \(-0.419923\pi\)
0.248925 + 0.968523i \(0.419923\pi\)
\(912\) −0.894762 −0.0296285
\(913\) −4.04597 −0.133902
\(914\) −13.5028 −0.446634
\(915\) 0.707605 0.0233927
\(916\) −26.1817 −0.865066
\(917\) −30.1669 −0.996198
\(918\) −2.15782 −0.0712187
\(919\) −31.0414 −1.02396 −0.511981 0.858997i \(-0.671088\pi\)
−0.511981 + 0.858997i \(0.671088\pi\)
\(920\) 0.198201 0.00653449
\(921\) 0.599186 0.0197439
\(922\) 11.3288 0.373094
\(923\) −12.0592 −0.396933
\(924\) 4.13694 0.136095
\(925\) 27.6689 0.909749
\(926\) −2.50054 −0.0821727
\(927\) 37.6639 1.23704
\(928\) 5.89722 0.193586
\(929\) −31.9212 −1.04730 −0.523650 0.851934i \(-0.675430\pi\)
−0.523650 + 0.851934i \(0.675430\pi\)
\(930\) −0.301111 −0.00987382
\(931\) −4.95518 −0.162399
\(932\) −18.5618 −0.608011
\(933\) 23.8453 0.780661
\(934\) −9.47731 −0.310107
\(935\) −0.100418 −0.00328402
\(936\) −9.18571 −0.300244
\(937\) 35.5515 1.16142 0.580709 0.814111i \(-0.302775\pi\)
0.580709 + 0.814111i \(0.302775\pi\)
\(938\) −10.6818 −0.348774
\(939\) −12.3529 −0.403120
\(940\) −0.0629571 −0.00205343
\(941\) −51.0565 −1.66439 −0.832196 0.554481i \(-0.812917\pi\)
−0.832196 + 0.554481i \(0.812917\pi\)
\(942\) 15.6732 0.510659
\(943\) −9.66914 −0.314871
\(944\) 3.02758 0.0985394
\(945\) −0.445453 −0.0144906
\(946\) −2.07144 −0.0673484
\(947\) −22.4032 −0.728006 −0.364003 0.931398i \(-0.618590\pi\)
−0.364003 + 0.931398i \(0.618590\pi\)
\(948\) −12.2313 −0.397253
\(949\) −48.9536 −1.58910
\(950\) −4.99552 −0.162076
\(951\) 6.51785 0.211356
\(952\) −0.663257 −0.0214963
\(953\) −16.4898 −0.534157 −0.267079 0.963675i \(-0.586058\pi\)
−0.267079 + 0.963675i \(0.586058\pi\)
\(954\) 24.2342 0.784610
\(955\) −0.229269 −0.00741897
\(956\) 10.0354 0.324568
\(957\) 17.0608 0.551496
\(958\) 25.1951 0.814017
\(959\) 15.3652 0.496169
\(960\) 0.0599131 0.00193369
\(961\) −5.74133 −0.185204
\(962\) −23.1324 −0.745819
\(963\) −7.40883 −0.238746
\(964\) 9.53632 0.307144
\(965\) 1.55767 0.0501433
\(966\) 3.78728 0.121854
\(967\) 44.2347 1.42249 0.711246 0.702943i \(-0.248131\pi\)
0.711246 + 0.702943i \(0.248131\pi\)
\(968\) −0.545879 −0.0175452
\(969\) 0.415013 0.0133321
\(970\) 1.08772 0.0349246
\(971\) −8.90513 −0.285779 −0.142890 0.989739i \(-0.545639\pi\)
−0.142890 + 0.989739i \(0.545639\pi\)
\(972\) −16.1359 −0.517560
\(973\) −3.52131 −0.112888
\(974\) −10.4758 −0.335668
\(975\) 18.6679 0.597853
\(976\) 11.8105 0.378046
\(977\) 5.69080 0.182065 0.0910325 0.995848i \(-0.470983\pi\)
0.0910325 + 0.995848i \(0.470983\pi\)
\(978\) −4.43182 −0.141714
\(979\) 11.2034 0.358063
\(980\) 0.331798 0.0105989
\(981\) −5.04792 −0.161168
\(982\) 39.2210 1.25159
\(983\) 1.30631 0.0416648 0.0208324 0.999783i \(-0.493368\pi\)
0.0208324 + 0.999783i \(0.493368\pi\)
\(984\) −2.92283 −0.0931764
\(985\) −0.551082 −0.0175589
\(986\) −2.73528 −0.0871090
\(987\) −1.20300 −0.0382919
\(988\) 4.17646 0.132871
\(989\) −1.89636 −0.0603008
\(990\) −0.476170 −0.0151337
\(991\) 47.8763 1.52084 0.760421 0.649430i \(-0.224993\pi\)
0.760421 + 0.649430i \(0.224993\pi\)
\(992\) −5.02580 −0.159569
\(993\) −18.4337 −0.584976
\(994\) −4.12893 −0.130962
\(995\) −0.922579 −0.0292477
\(996\) −1.11966 −0.0354778
\(997\) −16.9545 −0.536953 −0.268477 0.963286i \(-0.586520\pi\)
−0.268477 + 0.963286i \(0.586520\pi\)
\(998\) −7.95532 −0.251821
\(999\) −25.7675 −0.815249
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 \(a_p\))