Properties

Label 6027.2.a.bk.1.12
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-1.68292\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.68292 q^{2} +1.00000 q^{3} +0.832222 q^{4} -3.40481 q^{5} +1.68292 q^{6} -1.96528 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.68292 q^{2} +1.00000 q^{3} +0.832222 q^{4} -3.40481 q^{5} +1.68292 q^{6} -1.96528 q^{8} +1.00000 q^{9} -5.73002 q^{10} +1.02548 q^{11} +0.832222 q^{12} +3.49993 q^{13} -3.40481 q^{15} -4.97185 q^{16} +0.830651 q^{17} +1.68292 q^{18} +1.63689 q^{19} -2.83356 q^{20} +1.72580 q^{22} -1.51995 q^{23} -1.96528 q^{24} +6.59272 q^{25} +5.89010 q^{26} +1.00000 q^{27} -1.17009 q^{29} -5.73002 q^{30} -8.40087 q^{31} -4.43667 q^{32} +1.02548 q^{33} +1.39792 q^{34} +0.832222 q^{36} +8.14512 q^{37} +2.75476 q^{38} +3.49993 q^{39} +6.69139 q^{40} -1.00000 q^{41} +8.80082 q^{43} +0.853425 q^{44} -3.40481 q^{45} -2.55795 q^{46} -10.3255 q^{47} -4.97185 q^{48} +11.0950 q^{50} +0.830651 q^{51} +2.91272 q^{52} -0.417313 q^{53} +1.68292 q^{54} -3.49155 q^{55} +1.63689 q^{57} -1.96916 q^{58} -14.7168 q^{59} -2.83356 q^{60} -11.6289 q^{61} -14.1380 q^{62} +2.47713 q^{64} -11.9166 q^{65} +1.72580 q^{66} -2.21248 q^{67} +0.691286 q^{68} -1.51995 q^{69} -1.00451 q^{71} -1.96528 q^{72} -12.7925 q^{73} +13.7076 q^{74} +6.59272 q^{75} +1.36226 q^{76} +5.89010 q^{78} -9.00439 q^{79} +16.9282 q^{80} +1.00000 q^{81} -1.68292 q^{82} -1.44935 q^{83} -2.82821 q^{85} +14.8111 q^{86} -1.17009 q^{87} -2.01535 q^{88} -10.4048 q^{89} -5.73002 q^{90} -1.26493 q^{92} -8.40087 q^{93} -17.3769 q^{94} -5.57331 q^{95} -4.43667 q^{96} -2.85223 q^{97} +1.02548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.68292 1.19000 0.595002 0.803724i \(-0.297151\pi\)
0.595002 + 0.803724i \(0.297151\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.832222 0.416111
\(5\) −3.40481 −1.52268 −0.761338 0.648355i \(-0.775457\pi\)
−0.761338 + 0.648355i \(0.775457\pi\)
\(6\) 1.68292 0.687049
\(7\) 0 0
\(8\) −1.96528 −0.694831
\(9\) 1.00000 0.333333
\(10\) −5.73002 −1.81199
\(11\) 1.02548 0.309193 0.154597 0.987978i \(-0.450592\pi\)
0.154597 + 0.987978i \(0.450592\pi\)
\(12\) 0.832222 0.240242
\(13\) 3.49993 0.970705 0.485353 0.874318i \(-0.338691\pi\)
0.485353 + 0.874318i \(0.338691\pi\)
\(14\) 0 0
\(15\) −3.40481 −0.879118
\(16\) −4.97185 −1.24296
\(17\) 0.830651 0.201462 0.100731 0.994914i \(-0.467882\pi\)
0.100731 + 0.994914i \(0.467882\pi\)
\(18\) 1.68292 0.396668
\(19\) 1.63689 0.375529 0.187765 0.982214i \(-0.439876\pi\)
0.187765 + 0.982214i \(0.439876\pi\)
\(20\) −2.83356 −0.633602
\(21\) 0 0
\(22\) 1.72580 0.367941
\(23\) −1.51995 −0.316931 −0.158465 0.987365i \(-0.550655\pi\)
−0.158465 + 0.987365i \(0.550655\pi\)
\(24\) −1.96528 −0.401161
\(25\) 6.59272 1.31854
\(26\) 5.89010 1.15514
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.17009 −0.217280 −0.108640 0.994081i \(-0.534649\pi\)
−0.108640 + 0.994081i \(0.534649\pi\)
\(30\) −5.73002 −1.04615
\(31\) −8.40087 −1.50884 −0.754421 0.656391i \(-0.772082\pi\)
−0.754421 + 0.656391i \(0.772082\pi\)
\(32\) −4.43667 −0.784301
\(33\) 1.02548 0.178513
\(34\) 1.39792 0.239741
\(35\) 0 0
\(36\) 0.832222 0.138704
\(37\) 8.14512 1.33905 0.669524 0.742790i \(-0.266498\pi\)
0.669524 + 0.742790i \(0.266498\pi\)
\(38\) 2.75476 0.446881
\(39\) 3.49993 0.560437
\(40\) 6.69139 1.05800
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 8.80082 1.34211 0.671056 0.741407i \(-0.265841\pi\)
0.671056 + 0.741407i \(0.265841\pi\)
\(44\) 0.853425 0.128659
\(45\) −3.40481 −0.507559
\(46\) −2.55795 −0.377149
\(47\) −10.3255 −1.50612 −0.753061 0.657951i \(-0.771423\pi\)
−0.753061 + 0.657951i \(0.771423\pi\)
\(48\) −4.97185 −0.717625
\(49\) 0 0
\(50\) 11.0950 1.56907
\(51\) 0.830651 0.116314
\(52\) 2.91272 0.403921
\(53\) −0.417313 −0.0573224 −0.0286612 0.999589i \(-0.509124\pi\)
−0.0286612 + 0.999589i \(0.509124\pi\)
\(54\) 1.68292 0.229016
\(55\) −3.49155 −0.470801
\(56\) 0 0
\(57\) 1.63689 0.216812
\(58\) −1.96916 −0.258564
\(59\) −14.7168 −1.91597 −0.957983 0.286826i \(-0.907400\pi\)
−0.957983 + 0.286826i \(0.907400\pi\)
\(60\) −2.83356 −0.365810
\(61\) −11.6289 −1.48892 −0.744461 0.667665i \(-0.767294\pi\)
−0.744461 + 0.667665i \(0.767294\pi\)
\(62\) −14.1380 −1.79553
\(63\) 0 0
\(64\) 2.47713 0.309641
\(65\) −11.9166 −1.47807
\(66\) 1.72580 0.212431
\(67\) −2.21248 −0.270297 −0.135149 0.990825i \(-0.543151\pi\)
−0.135149 + 0.990825i \(0.543151\pi\)
\(68\) 0.691286 0.0838307
\(69\) −1.51995 −0.182980
\(70\) 0 0
\(71\) −1.00451 −0.119213 −0.0596067 0.998222i \(-0.518985\pi\)
−0.0596067 + 0.998222i \(0.518985\pi\)
\(72\) −1.96528 −0.231610
\(73\) −12.7925 −1.49725 −0.748626 0.662993i \(-0.769286\pi\)
−0.748626 + 0.662993i \(0.769286\pi\)
\(74\) 13.7076 1.59347
\(75\) 6.59272 0.761261
\(76\) 1.36226 0.156262
\(77\) 0 0
\(78\) 5.89010 0.666923
\(79\) −9.00439 −1.01307 −0.506536 0.862219i \(-0.669074\pi\)
−0.506536 + 0.862219i \(0.669074\pi\)
\(80\) 16.9282 1.89263
\(81\) 1.00000 0.111111
\(82\) −1.68292 −0.185847
\(83\) −1.44935 −0.159087 −0.0795437 0.996831i \(-0.525346\pi\)
−0.0795437 + 0.996831i \(0.525346\pi\)
\(84\) 0 0
\(85\) −2.82821 −0.306762
\(86\) 14.8111 1.59712
\(87\) −1.17009 −0.125446
\(88\) −2.01535 −0.214837
\(89\) −10.4048 −1.10290 −0.551451 0.834207i \(-0.685926\pi\)
−0.551451 + 0.834207i \(0.685926\pi\)
\(90\) −5.73002 −0.603997
\(91\) 0 0
\(92\) −1.26493 −0.131878
\(93\) −8.40087 −0.871130
\(94\) −17.3769 −1.79229
\(95\) −5.57331 −0.571809
\(96\) −4.43667 −0.452816
\(97\) −2.85223 −0.289600 −0.144800 0.989461i \(-0.546254\pi\)
−0.144800 + 0.989461i \(0.546254\pi\)
\(98\) 0 0
\(99\) 1.02548 0.103064
\(100\) 5.48660 0.548660
\(101\) −2.50244 −0.249003 −0.124501 0.992219i \(-0.539733\pi\)
−0.124501 + 0.992219i \(0.539733\pi\)
\(102\) 1.39792 0.138415
\(103\) −1.62814 −0.160426 −0.0802129 0.996778i \(-0.525560\pi\)
−0.0802129 + 0.996778i \(0.525560\pi\)
\(104\) −6.87833 −0.674476
\(105\) 0 0
\(106\) −0.702305 −0.0682139
\(107\) −13.0578 −1.26234 −0.631170 0.775644i \(-0.717425\pi\)
−0.631170 + 0.775644i \(0.717425\pi\)
\(108\) 0.832222 0.0800806
\(109\) −10.1224 −0.969555 −0.484777 0.874638i \(-0.661099\pi\)
−0.484777 + 0.874638i \(0.661099\pi\)
\(110\) −5.87601 −0.560255
\(111\) 8.14512 0.773100
\(112\) 0 0
\(113\) −14.3018 −1.34540 −0.672701 0.739914i \(-0.734866\pi\)
−0.672701 + 0.739914i \(0.734866\pi\)
\(114\) 2.75476 0.258007
\(115\) 5.17512 0.482583
\(116\) −0.973771 −0.0904124
\(117\) 3.49993 0.323568
\(118\) −24.7672 −2.28001
\(119\) 0 0
\(120\) 6.69139 0.610838
\(121\) −9.94840 −0.904400
\(122\) −19.5704 −1.77183
\(123\) −1.00000 −0.0901670
\(124\) −6.99139 −0.627846
\(125\) −5.42289 −0.485038
\(126\) 0 0
\(127\) −2.21842 −0.196853 −0.0984266 0.995144i \(-0.531381\pi\)
−0.0984266 + 0.995144i \(0.531381\pi\)
\(128\) 13.0422 1.15278
\(129\) 8.80082 0.774869
\(130\) −20.0547 −1.75891
\(131\) 8.00260 0.699190 0.349595 0.936901i \(-0.386319\pi\)
0.349595 + 0.936901i \(0.386319\pi\)
\(132\) 0.853425 0.0742811
\(133\) 0 0
\(134\) −3.72343 −0.321655
\(135\) −3.40481 −0.293039
\(136\) −1.63246 −0.139982
\(137\) 5.55967 0.474995 0.237497 0.971388i \(-0.423673\pi\)
0.237497 + 0.971388i \(0.423673\pi\)
\(138\) −2.55795 −0.217747
\(139\) 12.3095 1.04408 0.522040 0.852921i \(-0.325171\pi\)
0.522040 + 0.852921i \(0.325171\pi\)
\(140\) 0 0
\(141\) −10.3255 −0.869560
\(142\) −1.69051 −0.141864
\(143\) 3.58910 0.300135
\(144\) −4.97185 −0.414321
\(145\) 3.98392 0.330846
\(146\) −21.5288 −1.78174
\(147\) 0 0
\(148\) 6.77854 0.557193
\(149\) 17.9547 1.47090 0.735452 0.677577i \(-0.236970\pi\)
0.735452 + 0.677577i \(0.236970\pi\)
\(150\) 11.0950 0.905904
\(151\) 10.8220 0.880684 0.440342 0.897830i \(-0.354857\pi\)
0.440342 + 0.897830i \(0.354857\pi\)
\(152\) −3.21695 −0.260929
\(153\) 0.830651 0.0671541
\(154\) 0 0
\(155\) 28.6034 2.29748
\(156\) 2.91272 0.233204
\(157\) 8.60868 0.687047 0.343524 0.939144i \(-0.388379\pi\)
0.343524 + 0.939144i \(0.388379\pi\)
\(158\) −15.1537 −1.20556
\(159\) −0.417313 −0.0330951
\(160\) 15.1060 1.19424
\(161\) 0 0
\(162\) 1.68292 0.132223
\(163\) 17.3793 1.36125 0.680627 0.732630i \(-0.261708\pi\)
0.680627 + 0.732630i \(0.261708\pi\)
\(164\) −0.832222 −0.0649856
\(165\) −3.49155 −0.271817
\(166\) −2.43915 −0.189315
\(167\) −2.73619 −0.211733 −0.105866 0.994380i \(-0.533762\pi\)
−0.105866 + 0.994380i \(0.533762\pi\)
\(168\) 0 0
\(169\) −0.750505 −0.0577311
\(170\) −4.75965 −0.365048
\(171\) 1.63689 0.125176
\(172\) 7.32423 0.558467
\(173\) −17.2827 −1.31398 −0.656988 0.753901i \(-0.728170\pi\)
−0.656988 + 0.753901i \(0.728170\pi\)
\(174\) −1.96916 −0.149282
\(175\) 0 0
\(176\) −5.09852 −0.384315
\(177\) −14.7168 −1.10618
\(178\) −17.5104 −1.31246
\(179\) 11.7765 0.880214 0.440107 0.897945i \(-0.354940\pi\)
0.440107 + 0.897945i \(0.354940\pi\)
\(180\) −2.83356 −0.211201
\(181\) 1.80377 0.134073 0.0670366 0.997751i \(-0.478646\pi\)
0.0670366 + 0.997751i \(0.478646\pi\)
\(182\) 0 0
\(183\) −11.6289 −0.859630
\(184\) 2.98712 0.220213
\(185\) −27.7326 −2.03894
\(186\) −14.1380 −1.03665
\(187\) 0.851813 0.0622908
\(188\) −8.59307 −0.626714
\(189\) 0 0
\(190\) −9.37943 −0.680456
\(191\) −19.2126 −1.39018 −0.695089 0.718924i \(-0.744635\pi\)
−0.695089 + 0.718924i \(0.744635\pi\)
\(192\) 2.47713 0.178771
\(193\) 15.9487 1.14801 0.574006 0.818851i \(-0.305388\pi\)
0.574006 + 0.818851i \(0.305388\pi\)
\(194\) −4.80008 −0.344625
\(195\) −11.9166 −0.853364
\(196\) 0 0
\(197\) 5.49324 0.391377 0.195689 0.980666i \(-0.437306\pi\)
0.195689 + 0.980666i \(0.437306\pi\)
\(198\) 1.72580 0.122647
\(199\) 0.785333 0.0556708 0.0278354 0.999613i \(-0.491139\pi\)
0.0278354 + 0.999613i \(0.491139\pi\)
\(200\) −12.9565 −0.916164
\(201\) −2.21248 −0.156056
\(202\) −4.21142 −0.296314
\(203\) 0 0
\(204\) 0.691286 0.0483997
\(205\) 3.40481 0.237802
\(206\) −2.74004 −0.190907
\(207\) −1.51995 −0.105644
\(208\) −17.4011 −1.20655
\(209\) 1.67860 0.116111
\(210\) 0 0
\(211\) −19.7215 −1.35769 −0.678843 0.734284i \(-0.737518\pi\)
−0.678843 + 0.734284i \(0.737518\pi\)
\(212\) −0.347297 −0.0238525
\(213\) −1.00451 −0.0688278
\(214\) −21.9752 −1.50219
\(215\) −29.9651 −2.04360
\(216\) −1.96528 −0.133720
\(217\) 0 0
\(218\) −17.0353 −1.15377
\(219\) −12.7925 −0.864439
\(220\) −2.90575 −0.195905
\(221\) 2.90722 0.195561
\(222\) 13.7076 0.919993
\(223\) 14.0160 0.938579 0.469290 0.883044i \(-0.344510\pi\)
0.469290 + 0.883044i \(0.344510\pi\)
\(224\) 0 0
\(225\) 6.59272 0.439514
\(226\) −24.0688 −1.60103
\(227\) 13.5192 0.897299 0.448649 0.893708i \(-0.351905\pi\)
0.448649 + 0.893708i \(0.351905\pi\)
\(228\) 1.36226 0.0902178
\(229\) 0.208217 0.0137594 0.00687969 0.999976i \(-0.497810\pi\)
0.00687969 + 0.999976i \(0.497810\pi\)
\(230\) 8.70932 0.574276
\(231\) 0 0
\(232\) 2.29954 0.150972
\(233\) 15.6507 1.02531 0.512655 0.858595i \(-0.328662\pi\)
0.512655 + 0.858595i \(0.328662\pi\)
\(234\) 5.89010 0.385048
\(235\) 35.1562 2.29334
\(236\) −12.2477 −0.797254
\(237\) −9.00439 −0.584898
\(238\) 0 0
\(239\) −14.7846 −0.956334 −0.478167 0.878269i \(-0.658699\pi\)
−0.478167 + 0.878269i \(0.658699\pi\)
\(240\) 16.9282 1.09271
\(241\) 6.77989 0.436731 0.218366 0.975867i \(-0.429927\pi\)
0.218366 + 0.975867i \(0.429927\pi\)
\(242\) −16.7424 −1.07624
\(243\) 1.00000 0.0641500
\(244\) −9.67779 −0.619557
\(245\) 0 0
\(246\) −1.68292 −0.107299
\(247\) 5.72901 0.364528
\(248\) 16.5101 1.04839
\(249\) −1.44935 −0.0918491
\(250\) −9.12630 −0.577198
\(251\) 28.5862 1.80434 0.902171 0.431379i \(-0.141973\pi\)
0.902171 + 0.431379i \(0.141973\pi\)
\(252\) 0 0
\(253\) −1.55867 −0.0979927
\(254\) −3.73343 −0.234256
\(255\) −2.82821 −0.177109
\(256\) 16.9947 1.06217
\(257\) −24.5785 −1.53316 −0.766582 0.642147i \(-0.778044\pi\)
−0.766582 + 0.642147i \(0.778044\pi\)
\(258\) 14.8111 0.922097
\(259\) 0 0
\(260\) −9.91724 −0.615041
\(261\) −1.17009 −0.0724265
\(262\) 13.4677 0.832040
\(263\) 2.67564 0.164987 0.0824936 0.996592i \(-0.473712\pi\)
0.0824936 + 0.996592i \(0.473712\pi\)
\(264\) −2.01535 −0.124036
\(265\) 1.42087 0.0872834
\(266\) 0 0
\(267\) −10.4048 −0.636761
\(268\) −1.84127 −0.112474
\(269\) −20.4028 −1.24398 −0.621990 0.783026i \(-0.713675\pi\)
−0.621990 + 0.783026i \(0.713675\pi\)
\(270\) −5.73002 −0.348718
\(271\) −25.9779 −1.57805 −0.789023 0.614364i \(-0.789413\pi\)
−0.789023 + 0.614364i \(0.789413\pi\)
\(272\) −4.12987 −0.250410
\(273\) 0 0
\(274\) 9.35648 0.565246
\(275\) 6.76068 0.407684
\(276\) −1.26493 −0.0761400
\(277\) −11.8244 −0.710461 −0.355230 0.934779i \(-0.615598\pi\)
−0.355230 + 0.934779i \(0.615598\pi\)
\(278\) 20.7160 1.24246
\(279\) −8.40087 −0.502947
\(280\) 0 0
\(281\) −7.86950 −0.469455 −0.234727 0.972061i \(-0.575420\pi\)
−0.234727 + 0.972061i \(0.575420\pi\)
\(282\) −17.3769 −1.03478
\(283\) 16.7613 0.996353 0.498177 0.867076i \(-0.334003\pi\)
0.498177 + 0.867076i \(0.334003\pi\)
\(284\) −0.835975 −0.0496060
\(285\) −5.57331 −0.330134
\(286\) 6.04016 0.357162
\(287\) 0 0
\(288\) −4.43667 −0.261434
\(289\) −16.3100 −0.959413
\(290\) 6.70462 0.393709
\(291\) −2.85223 −0.167201
\(292\) −10.6462 −0.623023
\(293\) 13.3389 0.779270 0.389635 0.920969i \(-0.372601\pi\)
0.389635 + 0.920969i \(0.372601\pi\)
\(294\) 0 0
\(295\) 50.1079 2.91740
\(296\) −16.0074 −0.930412
\(297\) 1.02548 0.0595042
\(298\) 30.2163 1.75038
\(299\) −5.31970 −0.307646
\(300\) 5.48660 0.316769
\(301\) 0 0
\(302\) 18.2126 1.04802
\(303\) −2.50244 −0.143762
\(304\) −8.13839 −0.466769
\(305\) 39.5940 2.26715
\(306\) 1.39792 0.0799137
\(307\) 0.258573 0.0147575 0.00737877 0.999973i \(-0.497651\pi\)
0.00737877 + 0.999973i \(0.497651\pi\)
\(308\) 0 0
\(309\) −1.62814 −0.0926218
\(310\) 48.1372 2.73401
\(311\) 22.9830 1.30325 0.651624 0.758542i \(-0.274088\pi\)
0.651624 + 0.758542i \(0.274088\pi\)
\(312\) −6.87833 −0.389409
\(313\) 5.78960 0.327247 0.163624 0.986523i \(-0.447682\pi\)
0.163624 + 0.986523i \(0.447682\pi\)
\(314\) 14.4877 0.817590
\(315\) 0 0
\(316\) −7.49365 −0.421551
\(317\) −25.7608 −1.44687 −0.723434 0.690393i \(-0.757438\pi\)
−0.723434 + 0.690393i \(0.757438\pi\)
\(318\) −0.702305 −0.0393833
\(319\) −1.19990 −0.0671813
\(320\) −8.43415 −0.471483
\(321\) −13.0578 −0.728813
\(322\) 0 0
\(323\) 1.35969 0.0756550
\(324\) 0.832222 0.0462346
\(325\) 23.0740 1.27992
\(326\) 29.2480 1.61990
\(327\) −10.1224 −0.559773
\(328\) 1.96528 0.108514
\(329\) 0 0
\(330\) −5.87601 −0.323464
\(331\) −12.0711 −0.663490 −0.331745 0.943369i \(-0.607637\pi\)
−0.331745 + 0.943369i \(0.607637\pi\)
\(332\) −1.20618 −0.0661980
\(333\) 8.14512 0.446350
\(334\) −4.60479 −0.251963
\(335\) 7.53307 0.411576
\(336\) 0 0
\(337\) 24.7963 1.35074 0.675371 0.737478i \(-0.263983\pi\)
0.675371 + 0.737478i \(0.263983\pi\)
\(338\) −1.26304 −0.0687003
\(339\) −14.3018 −0.776768
\(340\) −2.35370 −0.127647
\(341\) −8.61491 −0.466523
\(342\) 2.75476 0.148960
\(343\) 0 0
\(344\) −17.2960 −0.932540
\(345\) 5.17512 0.278619
\(346\) −29.0853 −1.56364
\(347\) −5.85866 −0.314509 −0.157255 0.987558i \(-0.550264\pi\)
−0.157255 + 0.987558i \(0.550264\pi\)
\(348\) −0.973771 −0.0521996
\(349\) −36.1859 −1.93699 −0.968494 0.249038i \(-0.919886\pi\)
−0.968494 + 0.249038i \(0.919886\pi\)
\(350\) 0 0
\(351\) 3.49993 0.186812
\(352\) −4.54971 −0.242500
\(353\) −5.24732 −0.279287 −0.139643 0.990202i \(-0.544596\pi\)
−0.139643 + 0.990202i \(0.544596\pi\)
\(354\) −24.7672 −1.31636
\(355\) 3.42016 0.181523
\(356\) −8.65907 −0.458930
\(357\) 0 0
\(358\) 19.8189 1.04746
\(359\) −4.84702 −0.255816 −0.127908 0.991786i \(-0.540826\pi\)
−0.127908 + 0.991786i \(0.540826\pi\)
\(360\) 6.69139 0.352667
\(361\) −16.3206 −0.858978
\(362\) 3.03560 0.159548
\(363\) −9.94840 −0.522155
\(364\) 0 0
\(365\) 43.5561 2.27983
\(366\) −19.5704 −1.02296
\(367\) 24.3441 1.27075 0.635375 0.772204i \(-0.280846\pi\)
0.635375 + 0.772204i \(0.280846\pi\)
\(368\) 7.55694 0.393933
\(369\) −1.00000 −0.0520579
\(370\) −46.6717 −2.42635
\(371\) 0 0
\(372\) −6.99139 −0.362487
\(373\) −9.41811 −0.487651 −0.243826 0.969819i \(-0.578402\pi\)
−0.243826 + 0.969819i \(0.578402\pi\)
\(374\) 1.43353 0.0741263
\(375\) −5.42289 −0.280037
\(376\) 20.2924 1.04650
\(377\) −4.09522 −0.210914
\(378\) 0 0
\(379\) 17.5719 0.902606 0.451303 0.892371i \(-0.350959\pi\)
0.451303 + 0.892371i \(0.350959\pi\)
\(380\) −4.63823 −0.237936
\(381\) −2.21842 −0.113653
\(382\) −32.3334 −1.65432
\(383\) −36.4451 −1.86226 −0.931130 0.364688i \(-0.881176\pi\)
−0.931130 + 0.364688i \(0.881176\pi\)
\(384\) 13.0422 0.665555
\(385\) 0 0
\(386\) 26.8404 1.36614
\(387\) 8.80082 0.447371
\(388\) −2.37369 −0.120506
\(389\) 5.42387 0.275001 0.137500 0.990502i \(-0.456093\pi\)
0.137500 + 0.990502i \(0.456093\pi\)
\(390\) −20.0547 −1.01551
\(391\) −1.26254 −0.0638496
\(392\) 0 0
\(393\) 8.00260 0.403678
\(394\) 9.24468 0.465740
\(395\) 30.6582 1.54258
\(396\) 0.853425 0.0428862
\(397\) 33.0276 1.65761 0.828803 0.559540i \(-0.189022\pi\)
0.828803 + 0.559540i \(0.189022\pi\)
\(398\) 1.32165 0.0662485
\(399\) 0 0
\(400\) −32.7780 −1.63890
\(401\) −4.18181 −0.208830 −0.104415 0.994534i \(-0.533297\pi\)
−0.104415 + 0.994534i \(0.533297\pi\)
\(402\) −3.72343 −0.185708
\(403\) −29.4025 −1.46464
\(404\) −2.08259 −0.103613
\(405\) −3.40481 −0.169186
\(406\) 0 0
\(407\) 8.35263 0.414025
\(408\) −1.63246 −0.0808188
\(409\) −11.7978 −0.583365 −0.291682 0.956515i \(-0.594215\pi\)
−0.291682 + 0.956515i \(0.594215\pi\)
\(410\) 5.73002 0.282986
\(411\) 5.55967 0.274238
\(412\) −1.35498 −0.0667549
\(413\) 0 0
\(414\) −2.55795 −0.125716
\(415\) 4.93477 0.242238
\(416\) −15.5280 −0.761325
\(417\) 12.3095 0.602800
\(418\) 2.82495 0.138173
\(419\) −28.0765 −1.37163 −0.685813 0.727777i \(-0.740553\pi\)
−0.685813 + 0.727777i \(0.740553\pi\)
\(420\) 0 0
\(421\) 14.7916 0.720899 0.360450 0.932779i \(-0.382623\pi\)
0.360450 + 0.932779i \(0.382623\pi\)
\(422\) −33.1897 −1.61565
\(423\) −10.3255 −0.502041
\(424\) 0.820136 0.0398293
\(425\) 5.47625 0.265637
\(426\) −1.69051 −0.0819054
\(427\) 0 0
\(428\) −10.8670 −0.525274
\(429\) 3.58910 0.173283
\(430\) −50.4289 −2.43190
\(431\) −2.77927 −0.133873 −0.0669364 0.997757i \(-0.521322\pi\)
−0.0669364 + 0.997757i \(0.521322\pi\)
\(432\) −4.97185 −0.239208
\(433\) −27.8722 −1.33945 −0.669727 0.742607i \(-0.733589\pi\)
−0.669727 + 0.742607i \(0.733589\pi\)
\(434\) 0 0
\(435\) 3.98392 0.191014
\(436\) −8.42412 −0.403442
\(437\) −2.48799 −0.119017
\(438\) −21.5288 −1.02869
\(439\) 18.9919 0.906435 0.453218 0.891400i \(-0.350276\pi\)
0.453218 + 0.891400i \(0.350276\pi\)
\(440\) 6.86187 0.327127
\(441\) 0 0
\(442\) 4.89262 0.232718
\(443\) −17.4345 −0.828339 −0.414170 0.910200i \(-0.635928\pi\)
−0.414170 + 0.910200i \(0.635928\pi\)
\(444\) 6.77854 0.321696
\(445\) 35.4262 1.67936
\(446\) 23.5878 1.11691
\(447\) 17.9547 0.849226
\(448\) 0 0
\(449\) 7.12272 0.336142 0.168071 0.985775i \(-0.446246\pi\)
0.168071 + 0.985775i \(0.446246\pi\)
\(450\) 11.0950 0.523024
\(451\) −1.02548 −0.0482878
\(452\) −11.9023 −0.559837
\(453\) 10.8220 0.508463
\(454\) 22.7517 1.06779
\(455\) 0 0
\(456\) −3.21695 −0.150647
\(457\) 38.4769 1.79987 0.899936 0.436021i \(-0.143613\pi\)
0.899936 + 0.436021i \(0.143613\pi\)
\(458\) 0.350413 0.0163737
\(459\) 0.830651 0.0387715
\(460\) 4.30685 0.200808
\(461\) −6.67458 −0.310866 −0.155433 0.987846i \(-0.549677\pi\)
−0.155433 + 0.987846i \(0.549677\pi\)
\(462\) 0 0
\(463\) −29.7433 −1.38229 −0.691144 0.722717i \(-0.742893\pi\)
−0.691144 + 0.722717i \(0.742893\pi\)
\(464\) 5.81749 0.270070
\(465\) 28.6034 1.32645
\(466\) 26.3388 1.22012
\(467\) −34.5371 −1.59819 −0.799094 0.601206i \(-0.794687\pi\)
−0.799094 + 0.601206i \(0.794687\pi\)
\(468\) 2.91272 0.134640
\(469\) 0 0
\(470\) 59.1651 2.72908
\(471\) 8.60868 0.396667
\(472\) 28.9226 1.33127
\(473\) 9.02504 0.414972
\(474\) −15.1537 −0.696031
\(475\) 10.7916 0.495151
\(476\) 0 0
\(477\) −0.417313 −0.0191075
\(478\) −24.8813 −1.13804
\(479\) −26.2082 −1.19748 −0.598742 0.800942i \(-0.704333\pi\)
−0.598742 + 0.800942i \(0.704333\pi\)
\(480\) 15.1060 0.689492
\(481\) 28.5073 1.29982
\(482\) 11.4100 0.519712
\(483\) 0 0
\(484\) −8.27927 −0.376331
\(485\) 9.71129 0.440967
\(486\) 1.68292 0.0763388
\(487\) −4.32368 −0.195924 −0.0979622 0.995190i \(-0.531232\pi\)
−0.0979622 + 0.995190i \(0.531232\pi\)
\(488\) 22.8539 1.03455
\(489\) 17.3793 0.785920
\(490\) 0 0
\(491\) −1.30432 −0.0588630 −0.0294315 0.999567i \(-0.509370\pi\)
−0.0294315 + 0.999567i \(0.509370\pi\)
\(492\) −0.832222 −0.0375195
\(493\) −0.971933 −0.0437737
\(494\) 9.64147 0.433790
\(495\) −3.49155 −0.156934
\(496\) 41.7679 1.87543
\(497\) 0 0
\(498\) −2.43915 −0.109301
\(499\) 2.10363 0.0941713 0.0470857 0.998891i \(-0.485007\pi\)
0.0470857 + 0.998891i \(0.485007\pi\)
\(500\) −4.51305 −0.201830
\(501\) −2.73619 −0.122244
\(502\) 48.1082 2.14718
\(503\) 33.4139 1.48985 0.744926 0.667147i \(-0.232485\pi\)
0.744926 + 0.667147i \(0.232485\pi\)
\(504\) 0 0
\(505\) 8.52034 0.379150
\(506\) −2.62312 −0.116612
\(507\) −0.750505 −0.0333311
\(508\) −1.84622 −0.0819128
\(509\) −14.0498 −0.622745 −0.311373 0.950288i \(-0.600789\pi\)
−0.311373 + 0.950288i \(0.600789\pi\)
\(510\) −4.75965 −0.210761
\(511\) 0 0
\(512\) 2.51635 0.111208
\(513\) 1.63689 0.0722706
\(514\) −41.3636 −1.82447
\(515\) 5.54352 0.244276
\(516\) 7.32423 0.322431
\(517\) −10.5885 −0.465682
\(518\) 0 0
\(519\) −17.2827 −0.758624
\(520\) 23.4194 1.02701
\(521\) −8.62481 −0.377860 −0.188930 0.981991i \(-0.560502\pi\)
−0.188930 + 0.981991i \(0.560502\pi\)
\(522\) −1.96916 −0.0861879
\(523\) 8.15795 0.356722 0.178361 0.983965i \(-0.442920\pi\)
0.178361 + 0.983965i \(0.442920\pi\)
\(524\) 6.65994 0.290941
\(525\) 0 0
\(526\) 4.50290 0.196336
\(527\) −6.97819 −0.303975
\(528\) −5.09852 −0.221885
\(529\) −20.6898 −0.899555
\(530\) 2.39121 0.103868
\(531\) −14.7168 −0.638655
\(532\) 0 0
\(533\) −3.49993 −0.151599
\(534\) −17.5104 −0.757748
\(535\) 44.4591 1.92214
\(536\) 4.34814 0.187811
\(537\) 11.7765 0.508192
\(538\) −34.3362 −1.48034
\(539\) 0 0
\(540\) −2.83356 −0.121937
\(541\) 7.04980 0.303095 0.151547 0.988450i \(-0.451574\pi\)
0.151547 + 0.988450i \(0.451574\pi\)
\(542\) −43.7188 −1.87788
\(543\) 1.80377 0.0774072
\(544\) −3.68533 −0.158007
\(545\) 34.4650 1.47632
\(546\) 0 0
\(547\) 37.1767 1.58956 0.794781 0.606896i \(-0.207585\pi\)
0.794781 + 0.606896i \(0.207585\pi\)
\(548\) 4.62688 0.197650
\(549\) −11.6289 −0.496308
\(550\) 11.3777 0.485146
\(551\) −1.91531 −0.0815948
\(552\) 2.98712 0.127140
\(553\) 0 0
\(554\) −19.8996 −0.845451
\(555\) −27.7326 −1.17718
\(556\) 10.2443 0.434453
\(557\) −4.16417 −0.176441 −0.0882207 0.996101i \(-0.528118\pi\)
−0.0882207 + 0.996101i \(0.528118\pi\)
\(558\) −14.1380 −0.598509
\(559\) 30.8022 1.30280
\(560\) 0 0
\(561\) 0.851813 0.0359636
\(562\) −13.2437 −0.558653
\(563\) −8.11995 −0.342215 −0.171108 0.985252i \(-0.554735\pi\)
−0.171108 + 0.985252i \(0.554735\pi\)
\(564\) −8.59307 −0.361833
\(565\) 48.6950 2.04861
\(566\) 28.2079 1.18566
\(567\) 0 0
\(568\) 1.97414 0.0828331
\(569\) 1.33633 0.0560217 0.0280109 0.999608i \(-0.491083\pi\)
0.0280109 + 0.999608i \(0.491083\pi\)
\(570\) −9.37943 −0.392861
\(571\) −41.0462 −1.71773 −0.858866 0.512201i \(-0.828830\pi\)
−0.858866 + 0.512201i \(0.828830\pi\)
\(572\) 2.98692 0.124890
\(573\) −19.2126 −0.802620
\(574\) 0 0
\(575\) −10.0206 −0.417887
\(576\) 2.47713 0.103214
\(577\) −19.1094 −0.795534 −0.397767 0.917487i \(-0.630215\pi\)
−0.397767 + 0.917487i \(0.630215\pi\)
\(578\) −27.4485 −1.14171
\(579\) 15.9487 0.662806
\(580\) 3.31550 0.137669
\(581\) 0 0
\(582\) −4.80008 −0.198970
\(583\) −0.427945 −0.0177237
\(584\) 25.1409 1.04034
\(585\) −11.9166 −0.492690
\(586\) 22.4484 0.927334
\(587\) 2.30359 0.0950794 0.0475397 0.998869i \(-0.484862\pi\)
0.0475397 + 0.998869i \(0.484862\pi\)
\(588\) 0 0
\(589\) −13.7513 −0.566614
\(590\) 84.3276 3.47171
\(591\) 5.49324 0.225962
\(592\) −40.4963 −1.66439
\(593\) 15.7840 0.648169 0.324085 0.946028i \(-0.394944\pi\)
0.324085 + 0.946028i \(0.394944\pi\)
\(594\) 1.72580 0.0708103
\(595\) 0 0
\(596\) 14.9423 0.612059
\(597\) 0.785333 0.0321415
\(598\) −8.95263 −0.366100
\(599\) −22.0285 −0.900061 −0.450030 0.893013i \(-0.648587\pi\)
−0.450030 + 0.893013i \(0.648587\pi\)
\(600\) −12.9565 −0.528948
\(601\) 40.6668 1.65883 0.829416 0.558632i \(-0.188674\pi\)
0.829416 + 0.558632i \(0.188674\pi\)
\(602\) 0 0
\(603\) −2.21248 −0.0900991
\(604\) 9.00633 0.366462
\(605\) 33.8724 1.37711
\(606\) −4.21142 −0.171077
\(607\) −12.5914 −0.511069 −0.255534 0.966800i \(-0.582251\pi\)
−0.255534 + 0.966800i \(0.582251\pi\)
\(608\) −7.26236 −0.294528
\(609\) 0 0
\(610\) 66.6336 2.69792
\(611\) −36.1383 −1.46200
\(612\) 0.691286 0.0279436
\(613\) −26.8645 −1.08505 −0.542523 0.840041i \(-0.682531\pi\)
−0.542523 + 0.840041i \(0.682531\pi\)
\(614\) 0.435158 0.0175615
\(615\) 3.40481 0.137295
\(616\) 0 0
\(617\) 19.1864 0.772416 0.386208 0.922412i \(-0.373785\pi\)
0.386208 + 0.922412i \(0.373785\pi\)
\(618\) −2.74004 −0.110220
\(619\) 30.6480 1.23185 0.615923 0.787806i \(-0.288783\pi\)
0.615923 + 0.787806i \(0.288783\pi\)
\(620\) 23.8043 0.956006
\(621\) −1.51995 −0.0609933
\(622\) 38.6786 1.55087
\(623\) 0 0
\(624\) −17.4011 −0.696602
\(625\) −14.4997 −0.579987
\(626\) 9.74343 0.389426
\(627\) 1.67860 0.0670367
\(628\) 7.16433 0.285888
\(629\) 6.76575 0.269768
\(630\) 0 0
\(631\) −18.1250 −0.721545 −0.360772 0.932654i \(-0.617487\pi\)
−0.360772 + 0.932654i \(0.617487\pi\)
\(632\) 17.6961 0.703914
\(633\) −19.7215 −0.783860
\(634\) −43.3533 −1.72178
\(635\) 7.55330 0.299744
\(636\) −0.347297 −0.0137712
\(637\) 0 0
\(638\) −2.01933 −0.0799461
\(639\) −1.00451 −0.0397378
\(640\) −44.4061 −1.75530
\(641\) 20.3664 0.804424 0.402212 0.915546i \(-0.368241\pi\)
0.402212 + 0.915546i \(0.368241\pi\)
\(642\) −21.9752 −0.867291
\(643\) 47.8847 1.88839 0.944195 0.329387i \(-0.106842\pi\)
0.944195 + 0.329387i \(0.106842\pi\)
\(644\) 0 0
\(645\) −29.9651 −1.17987
\(646\) 2.28824 0.0900298
\(647\) 45.2884 1.78047 0.890236 0.455499i \(-0.150539\pi\)
0.890236 + 0.455499i \(0.150539\pi\)
\(648\) −1.96528 −0.0772034
\(649\) −15.0918 −0.592403
\(650\) 38.8318 1.52311
\(651\) 0 0
\(652\) 14.4635 0.566432
\(653\) 49.0869 1.92092 0.960459 0.278421i \(-0.0898111\pi\)
0.960459 + 0.278421i \(0.0898111\pi\)
\(654\) −17.0353 −0.666132
\(655\) −27.2473 −1.06464
\(656\) 4.97185 0.194118
\(657\) −12.7925 −0.499084
\(658\) 0 0
\(659\) 47.8228 1.86291 0.931456 0.363853i \(-0.118539\pi\)
0.931456 + 0.363853i \(0.118539\pi\)
\(660\) −2.90575 −0.113106
\(661\) −38.8838 −1.51240 −0.756202 0.654339i \(-0.772947\pi\)
−0.756202 + 0.654339i \(0.772947\pi\)
\(662\) −20.3148 −0.789557
\(663\) 2.90722 0.112907
\(664\) 2.84838 0.110539
\(665\) 0 0
\(666\) 13.7076 0.531158
\(667\) 1.77847 0.0688625
\(668\) −2.27712 −0.0881043
\(669\) 14.0160 0.541889
\(670\) 12.6776 0.489777
\(671\) −11.9251 −0.460365
\(672\) 0 0
\(673\) 19.8958 0.766926 0.383463 0.923556i \(-0.374731\pi\)
0.383463 + 0.923556i \(0.374731\pi\)
\(674\) 41.7303 1.60739
\(675\) 6.59272 0.253754
\(676\) −0.624586 −0.0240226
\(677\) −14.7663 −0.567514 −0.283757 0.958896i \(-0.591581\pi\)
−0.283757 + 0.958896i \(0.591581\pi\)
\(678\) −24.0688 −0.924358
\(679\) 0 0
\(680\) 5.55821 0.213148
\(681\) 13.5192 0.518056
\(682\) −14.4982 −0.555165
\(683\) 34.9130 1.33591 0.667954 0.744203i \(-0.267170\pi\)
0.667954 + 0.744203i \(0.267170\pi\)
\(684\) 1.36226 0.0520872
\(685\) −18.9296 −0.723263
\(686\) 0 0
\(687\) 0.208217 0.00794398
\(688\) −43.7563 −1.66819
\(689\) −1.46057 −0.0556431
\(690\) 8.70932 0.331558
\(691\) −26.3787 −1.00349 −0.501746 0.865015i \(-0.667309\pi\)
−0.501746 + 0.865015i \(0.667309\pi\)
\(692\) −14.3830 −0.546760
\(693\) 0 0
\(694\) −9.85966 −0.374268
\(695\) −41.9116 −1.58980
\(696\) 2.29954 0.0871640
\(697\) −0.830651 −0.0314631
\(698\) −60.8980 −2.30502
\(699\) 15.6507 0.591963
\(700\) 0 0
\(701\) −21.5243 −0.812962 −0.406481 0.913659i \(-0.633244\pi\)
−0.406481 + 0.913659i \(0.633244\pi\)
\(702\) 5.89010 0.222308
\(703\) 13.3327 0.502852
\(704\) 2.54024 0.0957389
\(705\) 35.1562 1.32406
\(706\) −8.83083 −0.332353
\(707\) 0 0
\(708\) −12.2477 −0.460295
\(709\) 37.6979 1.41577 0.707887 0.706325i \(-0.249648\pi\)
0.707887 + 0.706325i \(0.249648\pi\)
\(710\) 5.75586 0.216014
\(711\) −9.00439 −0.337691
\(712\) 20.4482 0.766330
\(713\) 12.7689 0.478198
\(714\) 0 0
\(715\) −12.2202 −0.457009
\(716\) 9.80063 0.366267
\(717\) −14.7846 −0.552140
\(718\) −8.15716 −0.304422
\(719\) 41.4883 1.54725 0.773627 0.633642i \(-0.218441\pi\)
0.773627 + 0.633642i \(0.218441\pi\)
\(720\) 16.9282 0.630877
\(721\) 0 0
\(722\) −27.4662 −1.02219
\(723\) 6.77989 0.252147
\(724\) 1.50114 0.0557893
\(725\) −7.71405 −0.286492
\(726\) −16.7424 −0.621367
\(727\) 2.82371 0.104726 0.0523629 0.998628i \(-0.483325\pi\)
0.0523629 + 0.998628i \(0.483325\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 73.3014 2.71301
\(731\) 7.31040 0.270385
\(732\) −9.67779 −0.357701
\(733\) 3.92493 0.144971 0.0724853 0.997369i \(-0.476907\pi\)
0.0724853 + 0.997369i \(0.476907\pi\)
\(734\) 40.9691 1.51220
\(735\) 0 0
\(736\) 6.74350 0.248569
\(737\) −2.26885 −0.0835741
\(738\) −1.68292 −0.0619492
\(739\) 13.1283 0.482933 0.241467 0.970409i \(-0.422372\pi\)
0.241467 + 0.970409i \(0.422372\pi\)
\(740\) −23.0796 −0.848425
\(741\) 5.72901 0.210460
\(742\) 0 0
\(743\) −20.9382 −0.768148 −0.384074 0.923302i \(-0.625479\pi\)
−0.384074 + 0.923302i \(0.625479\pi\)
\(744\) 16.5101 0.605288
\(745\) −61.1322 −2.23971
\(746\) −15.8499 −0.580307
\(747\) −1.44935 −0.0530291
\(748\) 0.708898 0.0259199
\(749\) 0 0
\(750\) −9.12630 −0.333245
\(751\) −42.0676 −1.53507 −0.767535 0.641008i \(-0.778517\pi\)
−0.767535 + 0.641008i \(0.778517\pi\)
\(752\) 51.3366 1.87205
\(753\) 28.5862 1.04174
\(754\) −6.89192 −0.250989
\(755\) −36.8469 −1.34100
\(756\) 0 0
\(757\) 32.4088 1.17792 0.588959 0.808163i \(-0.299538\pi\)
0.588959 + 0.808163i \(0.299538\pi\)
\(758\) 29.5720 1.07410
\(759\) −1.55867 −0.0565761
\(760\) 10.9531 0.397311
\(761\) 44.6418 1.61826 0.809132 0.587627i \(-0.199938\pi\)
0.809132 + 0.587627i \(0.199938\pi\)
\(762\) −3.73343 −0.135248
\(763\) 0 0
\(764\) −15.9892 −0.578468
\(765\) −2.82821 −0.102254
\(766\) −61.3343 −2.21610
\(767\) −51.5078 −1.85984
\(768\) 16.9947 0.613242
\(769\) −50.2119 −1.81069 −0.905344 0.424678i \(-0.860387\pi\)
−0.905344 + 0.424678i \(0.860387\pi\)
\(770\) 0 0
\(771\) −24.5785 −0.885172
\(772\) 13.2729 0.477701
\(773\) 9.92150 0.356852 0.178426 0.983953i \(-0.442900\pi\)
0.178426 + 0.983953i \(0.442900\pi\)
\(774\) 14.8111 0.532373
\(775\) −55.3846 −1.98947
\(776\) 5.60542 0.201223
\(777\) 0 0
\(778\) 9.12794 0.327252
\(779\) −1.63689 −0.0586478
\(780\) −9.91724 −0.355094
\(781\) −1.03010 −0.0368599
\(782\) −2.12476 −0.0759813
\(783\) −1.17009 −0.0418155
\(784\) 0 0
\(785\) −29.3109 −1.04615
\(786\) 13.4677 0.480378
\(787\) 4.64621 0.165619 0.0828097 0.996565i \(-0.473611\pi\)
0.0828097 + 0.996565i \(0.473611\pi\)
\(788\) 4.57159 0.162856
\(789\) 2.67564 0.0952555
\(790\) 51.5953 1.83568
\(791\) 0 0
\(792\) −2.01535 −0.0716123
\(793\) −40.7002 −1.44531
\(794\) 55.5828 1.97256
\(795\) 1.42087 0.0503931
\(796\) 0.653571 0.0231652
\(797\) −22.7270 −0.805030 −0.402515 0.915413i \(-0.631864\pi\)
−0.402515 + 0.915413i \(0.631864\pi\)
\(798\) 0 0
\(799\) −8.57684 −0.303427
\(800\) −29.2497 −1.03413
\(801\) −10.4048 −0.367634
\(802\) −7.03766 −0.248508
\(803\) −13.1184 −0.462940
\(804\) −1.84127 −0.0649367
\(805\) 0 0
\(806\) −49.4820 −1.74293
\(807\) −20.4028 −0.718212
\(808\) 4.91800 0.173015
\(809\) −3.74399 −0.131632 −0.0658159 0.997832i \(-0.520965\pi\)
−0.0658159 + 0.997832i \(0.520965\pi\)
\(810\) −5.73002 −0.201332
\(811\) 28.8811 1.01415 0.507077 0.861901i \(-0.330726\pi\)
0.507077 + 0.861901i \(0.330726\pi\)
\(812\) 0 0
\(813\) −25.9779 −0.911085
\(814\) 14.0568 0.492691
\(815\) −59.1732 −2.07275
\(816\) −4.12987 −0.144574
\(817\) 14.4060 0.504002
\(818\) −19.8548 −0.694207
\(819\) 0 0
\(820\) 2.83356 0.0989521
\(821\) −22.9214 −0.799961 −0.399981 0.916524i \(-0.630983\pi\)
−0.399981 + 0.916524i \(0.630983\pi\)
\(822\) 9.35648 0.326345
\(823\) 48.0792 1.67594 0.837968 0.545720i \(-0.183744\pi\)
0.837968 + 0.545720i \(0.183744\pi\)
\(824\) 3.19975 0.111469
\(825\) 6.76068 0.235377
\(826\) 0 0
\(827\) 24.9287 0.866856 0.433428 0.901188i \(-0.357304\pi\)
0.433428 + 0.901188i \(0.357304\pi\)
\(828\) −1.26493 −0.0439594
\(829\) −39.6168 −1.37595 −0.687974 0.725736i \(-0.741500\pi\)
−0.687974 + 0.725736i \(0.741500\pi\)
\(830\) 8.30483 0.288265
\(831\) −11.8244 −0.410185
\(832\) 8.66978 0.300570
\(833\) 0 0
\(834\) 20.7160 0.717335
\(835\) 9.31620 0.322401
\(836\) 1.39696 0.0483150
\(837\) −8.40087 −0.290377
\(838\) −47.2505 −1.63224
\(839\) 0.996793 0.0344131 0.0172066 0.999852i \(-0.494523\pi\)
0.0172066 + 0.999852i \(0.494523\pi\)
\(840\) 0 0
\(841\) −27.6309 −0.952790
\(842\) 24.8931 0.857873
\(843\) −7.86950 −0.271040
\(844\) −16.4127 −0.564948
\(845\) 2.55532 0.0879058
\(846\) −17.3769 −0.597431
\(847\) 0 0
\(848\) 2.07482 0.0712496
\(849\) 16.7613 0.575245
\(850\) 9.21609 0.316109
\(851\) −12.3801 −0.424386
\(852\) −0.835975 −0.0286400
\(853\) −14.9102 −0.510517 −0.255258 0.966873i \(-0.582160\pi\)
−0.255258 + 0.966873i \(0.582160\pi\)
\(854\) 0 0
\(855\) −5.57331 −0.190603
\(856\) 25.6621 0.877113
\(857\) 42.8328 1.46314 0.731571 0.681765i \(-0.238787\pi\)
0.731571 + 0.681765i \(0.238787\pi\)
\(858\) 6.04016 0.206208
\(859\) −3.21511 −0.109698 −0.0548490 0.998495i \(-0.517468\pi\)
−0.0548490 + 0.998495i \(0.517468\pi\)
\(860\) −24.9376 −0.850365
\(861\) 0 0
\(862\) −4.67730 −0.159309
\(863\) −16.1955 −0.551302 −0.275651 0.961258i \(-0.588893\pi\)
−0.275651 + 0.961258i \(0.588893\pi\)
\(864\) −4.43667 −0.150939
\(865\) 58.8441 2.00076
\(866\) −46.9068 −1.59396
\(867\) −16.3100 −0.553917
\(868\) 0 0
\(869\) −9.23379 −0.313235
\(870\) 6.70462 0.227308
\(871\) −7.74352 −0.262379
\(872\) 19.8934 0.673676
\(873\) −2.85223 −0.0965333
\(874\) −4.18709 −0.141630
\(875\) 0 0
\(876\) −10.6462 −0.359702
\(877\) 8.10740 0.273767 0.136884 0.990587i \(-0.456291\pi\)
0.136884 + 0.990587i \(0.456291\pi\)
\(878\) 31.9619 1.07866
\(879\) 13.3389 0.449912
\(880\) 17.3595 0.585188
\(881\) 42.9107 1.44570 0.722849 0.691006i \(-0.242832\pi\)
0.722849 + 0.691006i \(0.242832\pi\)
\(882\) 0 0
\(883\) 23.6450 0.795718 0.397859 0.917446i \(-0.369753\pi\)
0.397859 + 0.917446i \(0.369753\pi\)
\(884\) 2.41945 0.0813749
\(885\) 50.1079 1.68436
\(886\) −29.3409 −0.985728
\(887\) −49.4383 −1.65998 −0.829989 0.557780i \(-0.811653\pi\)
−0.829989 + 0.557780i \(0.811653\pi\)
\(888\) −16.0074 −0.537174
\(889\) 0 0
\(890\) 59.6195 1.99845
\(891\) 1.02548 0.0343548
\(892\) 11.6644 0.390553
\(893\) −16.9017 −0.565592
\(894\) 30.2163 1.01058
\(895\) −40.0966 −1.34028
\(896\) 0 0
\(897\) −5.31970 −0.177620
\(898\) 11.9870 0.400010
\(899\) 9.82975 0.327840
\(900\) 5.48660 0.182887
\(901\) −0.346641 −0.0115483
\(902\) −1.72580 −0.0574628
\(903\) 0 0
\(904\) 28.1071 0.934827
\(905\) −6.14149 −0.204150
\(906\) 18.2126 0.605073
\(907\) 4.12340 0.136915 0.0684576 0.997654i \(-0.478192\pi\)
0.0684576 + 0.997654i \(0.478192\pi\)
\(908\) 11.2509 0.373376
\(909\) −2.50244 −0.0830009
\(910\) 0 0
\(911\) −14.6414 −0.485090 −0.242545 0.970140i \(-0.577982\pi\)
−0.242545 + 0.970140i \(0.577982\pi\)
\(912\) −8.13839 −0.269489
\(913\) −1.48628 −0.0491887
\(914\) 64.7536 2.14186
\(915\) 39.5940 1.30894
\(916\) 0.173283 0.00572543
\(917\) 0 0
\(918\) 1.39792 0.0461382
\(919\) 60.1835 1.98527 0.992635 0.121147i \(-0.0386573\pi\)
0.992635 + 0.121147i \(0.0386573\pi\)
\(920\) −10.1706 −0.335313
\(921\) 0.258573 0.00852027
\(922\) −11.2328 −0.369932
\(923\) −3.51571 −0.115721
\(924\) 0 0
\(925\) 53.6984 1.76559
\(926\) −50.0556 −1.64493
\(927\) −1.62814 −0.0534752
\(928\) 5.19129 0.170412
\(929\) 58.3675 1.91497 0.957487 0.288476i \(-0.0931487\pi\)
0.957487 + 0.288476i \(0.0931487\pi\)
\(930\) 48.1372 1.57848
\(931\) 0 0
\(932\) 13.0248 0.426643
\(933\) 22.9830 0.752430
\(934\) −58.1232 −1.90185
\(935\) −2.90026 −0.0948487
\(936\) −6.87833 −0.224825
\(937\) 15.7839 0.515637 0.257818 0.966193i \(-0.416996\pi\)
0.257818 + 0.966193i \(0.416996\pi\)
\(938\) 0 0
\(939\) 5.78960 0.188936
\(940\) 29.2577 0.954282
\(941\) 35.9945 1.17339 0.586694 0.809809i \(-0.300429\pi\)
0.586694 + 0.809809i \(0.300429\pi\)
\(942\) 14.4877 0.472036
\(943\) 1.51995 0.0494962
\(944\) 73.1698 2.38147
\(945\) 0 0
\(946\) 15.1884 0.493818
\(947\) −20.8209 −0.676590 −0.338295 0.941040i \(-0.609850\pi\)
−0.338295 + 0.941040i \(0.609850\pi\)
\(948\) −7.49365 −0.243382
\(949\) −44.7729 −1.45339
\(950\) 18.1614 0.589232
\(951\) −25.7608 −0.835350
\(952\) 0 0
\(953\) 16.0984 0.521479 0.260739 0.965409i \(-0.416034\pi\)
0.260739 + 0.965409i \(0.416034\pi\)
\(954\) −0.702305 −0.0227380
\(955\) 65.4154 2.11679
\(956\) −12.3040 −0.397941
\(957\) −1.19990 −0.0387872
\(958\) −44.1064 −1.42501
\(959\) 0 0
\(960\) −8.43415 −0.272211
\(961\) 39.5747 1.27660
\(962\) 47.9756 1.54679
\(963\) −13.0578 −0.420780
\(964\) 5.64237 0.181729
\(965\) −54.3023 −1.74805
\(966\) 0 0
\(967\) −0.604604 −0.0194428 −0.00972138 0.999953i \(-0.503094\pi\)
−0.00972138 + 0.999953i \(0.503094\pi\)
\(968\) 19.5514 0.628405
\(969\) 1.35969 0.0436794
\(970\) 16.3433 0.524753
\(971\) 35.7504 1.14728 0.573642 0.819106i \(-0.305530\pi\)
0.573642 + 0.819106i \(0.305530\pi\)
\(972\) 0.832222 0.0266935
\(973\) 0 0
\(974\) −7.27640 −0.233151
\(975\) 23.0740 0.738960
\(976\) 57.8170 1.85068
\(977\) 31.1492 0.996550 0.498275 0.867019i \(-0.333967\pi\)
0.498275 + 0.867019i \(0.333967\pi\)
\(978\) 29.2480 0.935248
\(979\) −10.6698 −0.341010
\(980\) 0 0
\(981\) −10.1224 −0.323185
\(982\) −2.19506 −0.0700473
\(983\) −21.6780 −0.691421 −0.345710 0.938341i \(-0.612362\pi\)
−0.345710 + 0.938341i \(0.612362\pi\)
\(984\) 1.96528 0.0626508
\(985\) −18.7034 −0.595941
\(986\) −1.63569 −0.0520909
\(987\) 0 0
\(988\) 4.76781 0.151684
\(989\) −13.3768 −0.425356
\(990\) −5.87601 −0.186752
\(991\) −20.6913 −0.657281 −0.328641 0.944455i \(-0.606590\pi\)
−0.328641 + 0.944455i \(0.606590\pi\)
\(992\) 37.2719 1.18339
\(993\) −12.0711 −0.383066
\(994\) 0 0
\(995\) −2.67391 −0.0847686
\(996\) −1.20618 −0.0382194
\(997\) 52.1527 1.65169 0.825847 0.563894i \(-0.190697\pi\)
0.825847 + 0.563894i \(0.190697\pi\)
\(998\) 3.54024 0.112064
\(999\) 8.14512 0.257700
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 \(a_p\))