Properties

Label 6027.2.a.u.1.4
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 4
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: \(0\)
Dimension: \(4\)
Coefficient field: 4.4.8468.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.27841\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.27841 q^{2} +1.00000 q^{3} +3.19117 q^{4} +3.19117 q^{5} +2.27841 q^{6} +2.71397 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.27841 q^{2} +1.00000 q^{3} +3.19117 q^{4} +3.19117 q^{5} +2.27841 q^{6} +2.71397 q^{8} +1.00000 q^{9} +7.27080 q^{10} -2.80122 q^{11} +3.19117 q^{12} +4.10392 q^{13} +3.19117 q^{15} -0.198780 q^{16} +0.365659 q^{17} +2.27841 q^{18} +1.56444 q^{19} +10.1836 q^{20} -6.38234 q^{22} -0.452904 q^{23} +2.71397 q^{24} +5.18356 q^{25} +9.35044 q^{26} +1.00000 q^{27} +8.07202 q^{29} +7.27080 q^{30} +4.36566 q^{31} -5.88085 q^{32} -2.80122 q^{33} +0.833122 q^{34} +3.19117 q^{36} -2.16688 q^{37} +3.56444 q^{38} +4.10392 q^{39} +8.66075 q^{40} +1.00000 q^{41} -7.06229 q^{43} -8.93916 q^{44} +3.19117 q^{45} -1.03190 q^{46} -11.8027 q^{47} -0.198780 q^{48} +11.8103 q^{50} +0.365659 q^{51} +13.0963 q^{52} +5.23280 q^{53} +2.27841 q^{54} -8.93916 q^{55} +1.56444 q^{57} +18.3914 q^{58} +0.833122 q^{59} +10.1836 q^{60} +9.06229 q^{61} +9.94678 q^{62} -13.0015 q^{64} +13.0963 q^{65} -6.38234 q^{66} +0.145556 q^{67} +1.16688 q^{68} -0.452904 q^{69} -2.88780 q^{71} +2.71397 q^{72} +12.7480 q^{73} -4.93705 q^{74} +5.18356 q^{75} +4.99239 q^{76} +9.35044 q^{78} -4.01371 q^{79} -0.634341 q^{80} +1.00000 q^{81} +2.27841 q^{82} -8.93916 q^{83} +1.16688 q^{85} -16.0908 q^{86} +8.07202 q^{87} -7.60244 q^{88} -0.731317 q^{89} +7.27080 q^{90} -1.44529 q^{92} +4.36566 q^{93} -26.8914 q^{94} +4.99239 q^{95} -5.88085 q^{96} -14.7820 q^{97} -2.80122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + O(q^{10}) \) \( 4q + q^{2} + 4q^{3} + 3q^{4} + 3q^{5} + q^{6} + 3q^{8} + 4q^{9} + 5q^{10} - 5q^{11} + 3q^{12} + 5q^{13} + 3q^{15} - 7q^{16} - 5q^{17} + q^{18} + 6q^{19} + 15q^{20} - 6q^{22} + 3q^{23} + 3q^{24} - 5q^{25} - q^{26} + 4q^{27} + 2q^{29} + 5q^{30} + 11q^{31} - 3q^{32} - 5q^{33} + 16q^{34} + 3q^{36} + 4q^{37} + 14q^{38} + 5q^{39} + 7q^{40} + 4q^{41} - 19q^{43} + 3q^{45} - 23q^{46} + 4q^{47} - 7q^{48} + 12q^{50} - 5q^{51} + 25q^{52} + 9q^{53} + q^{54} + 6q^{57} + 25q^{58} + 16q^{59} + 15q^{60} + 27q^{61} + 20q^{62} - 7q^{64} + 25q^{65} - 6q^{66} - 13q^{67} - 8q^{68} + 3q^{69} + q^{71} + 3q^{72} + 25q^{73} - 21q^{74} - 5q^{75} + 4q^{76} - q^{78} - q^{79} - 9q^{80} + 4q^{81} + q^{82} - 8q^{85} + 16q^{86} + 2q^{87} - 18q^{88} + 10q^{89} + 5q^{90} + 15q^{92} + 11q^{93} - 13q^{94} + 4q^{95} - 3q^{96} - 15q^{97} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.27841 1.61108 0.805541 0.592540i \(-0.201875\pi\)
0.805541 + 0.592540i \(0.201875\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.19117 1.59558
\(5\) 3.19117 1.42713 0.713567 0.700587i \(-0.247078\pi\)
0.713567 + 0.700587i \(0.247078\pi\)
\(6\) 2.27841 0.930158
\(7\) 0 0
\(8\) 2.71397 0.959535
\(9\) 1.00000 0.333333
\(10\) 7.27080 2.29923
\(11\) −2.80122 −0.844600 −0.422300 0.906456i \(-0.638777\pi\)
−0.422300 + 0.906456i \(0.638777\pi\)
\(12\) 3.19117 0.921211
\(13\) 4.10392 1.13822 0.569112 0.822260i \(-0.307287\pi\)
0.569112 + 0.822260i \(0.307287\pi\)
\(14\) 0 0
\(15\) 3.19117 0.823956
\(16\) −0.198780 −0.0496951
\(17\) 0.365659 0.0886852 0.0443426 0.999016i \(-0.485881\pi\)
0.0443426 + 0.999016i \(0.485881\pi\)
\(18\) 2.27841 0.537027
\(19\) 1.56444 0.358907 0.179453 0.983766i \(-0.442567\pi\)
0.179453 + 0.983766i \(0.442567\pi\)
\(20\) 10.1836 2.27711
\(21\) 0 0
\(22\) −6.38234 −1.36072
\(23\) −0.452904 −0.0944369 −0.0472185 0.998885i \(-0.515036\pi\)
−0.0472185 + 0.998885i \(0.515036\pi\)
\(24\) 2.71397 0.553988
\(25\) 5.18356 1.03671
\(26\) 9.35044 1.83377
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 8.07202 1.49894 0.749468 0.662040i \(-0.230309\pi\)
0.749468 + 0.662040i \(0.230309\pi\)
\(30\) 7.27080 1.32746
\(31\) 4.36566 0.784095 0.392048 0.919945i \(-0.371767\pi\)
0.392048 + 0.919945i \(0.371767\pi\)
\(32\) −5.88085 −1.03960
\(33\) −2.80122 −0.487630
\(34\) 0.833122 0.142879
\(35\) 0 0
\(36\) 3.19117 0.531861
\(37\) −2.16688 −0.356233 −0.178116 0.984009i \(-0.557000\pi\)
−0.178116 + 0.984009i \(0.557000\pi\)
\(38\) 3.56444 0.578228
\(39\) 4.10392 0.657154
\(40\) 8.66075 1.36938
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −7.06229 −1.07699 −0.538495 0.842629i \(-0.681007\pi\)
−0.538495 + 0.842629i \(0.681007\pi\)
\(44\) −8.93916 −1.34763
\(45\) 3.19117 0.475711
\(46\) −1.03190 −0.152146
\(47\) −11.8027 −1.72160 −0.860799 0.508946i \(-0.830035\pi\)
−0.860799 + 0.508946i \(0.830035\pi\)
\(48\) −0.198780 −0.0286915
\(49\) 0 0
\(50\) 11.8103 1.67023
\(51\) 0.365659 0.0512025
\(52\) 13.0963 1.81613
\(53\) 5.23280 0.718781 0.359390 0.933187i \(-0.382985\pi\)
0.359390 + 0.933187i \(0.382985\pi\)
\(54\) 2.27841 0.310053
\(55\) −8.93916 −1.20536
\(56\) 0 0
\(57\) 1.56444 0.207215
\(58\) 18.3914 2.41491
\(59\) 0.833122 0.108463 0.0542316 0.998528i \(-0.482729\pi\)
0.0542316 + 0.998528i \(0.482729\pi\)
\(60\) 10.1836 1.31469
\(61\) 9.06229 1.16031 0.580154 0.814507i \(-0.302992\pi\)
0.580154 + 0.814507i \(0.302992\pi\)
\(62\) 9.94678 1.26324
\(63\) 0 0
\(64\) −13.0015 −1.62518
\(65\) 13.0963 1.62440
\(66\) −6.38234 −0.785611
\(67\) 0.145556 0.0177825 0.00889127 0.999960i \(-0.497170\pi\)
0.00889127 + 0.999960i \(0.497170\pi\)
\(68\) 1.16688 0.141505
\(69\) −0.452904 −0.0545232
\(70\) 0 0
\(71\) −2.88780 −0.342719 −0.171359 0.985209i \(-0.554816\pi\)
−0.171359 + 0.985209i \(0.554816\pi\)
\(72\) 2.71397 0.319845
\(73\) 12.7480 1.49204 0.746020 0.665924i \(-0.231962\pi\)
0.746020 + 0.665924i \(0.231962\pi\)
\(74\) −4.93705 −0.573920
\(75\) 5.18356 0.598546
\(76\) 4.99239 0.572666
\(77\) 0 0
\(78\) 9.35044 1.05873
\(79\) −4.01371 −0.451578 −0.225789 0.974176i \(-0.572496\pi\)
−0.225789 + 0.974176i \(0.572496\pi\)
\(80\) −0.634341 −0.0709215
\(81\) 1.00000 0.111111
\(82\) 2.27841 0.251609
\(83\) −8.93916 −0.981201 −0.490600 0.871385i \(-0.663223\pi\)
−0.490600 + 0.871385i \(0.663223\pi\)
\(84\) 0 0
\(85\) 1.16688 0.126566
\(86\) −16.0908 −1.73512
\(87\) 8.07202 0.865412
\(88\) −7.60244 −0.810423
\(89\) −0.731317 −0.0775195 −0.0387597 0.999249i \(-0.512341\pi\)
−0.0387597 + 0.999249i \(0.512341\pi\)
\(90\) 7.27080 0.766410
\(91\) 0 0
\(92\) −1.44529 −0.150682
\(93\) 4.36566 0.452698
\(94\) −26.8914 −2.77363
\(95\) 4.99239 0.512208
\(96\) −5.88085 −0.600212
\(97\) −14.7820 −1.50089 −0.750443 0.660935i \(-0.770160\pi\)
−0.750443 + 0.660935i \(0.770160\pi\)
\(98\) 0 0
\(99\) −2.80122 −0.281533
\(100\) 16.5416 1.65416
\(101\) 9.96345 0.991401 0.495700 0.868494i \(-0.334911\pi\)
0.495700 + 0.868494i \(0.334911\pi\)
\(102\) 0.833122 0.0824913
\(103\) −14.8367 −1.46190 −0.730952 0.682429i \(-0.760923\pi\)
−0.730952 + 0.682429i \(0.760923\pi\)
\(104\) 11.1379 1.09217
\(105\) 0 0
\(106\) 11.9225 1.15801
\(107\) −3.02031 −0.291984 −0.145992 0.989286i \(-0.546637\pi\)
−0.145992 + 0.989286i \(0.546637\pi\)
\(108\) 3.19117 0.307070
\(109\) 2.42034 0.231826 0.115913 0.993259i \(-0.463021\pi\)
0.115913 + 0.993259i \(0.463021\pi\)
\(110\) −20.3671 −1.94193
\(111\) −2.16688 −0.205671
\(112\) 0 0
\(113\) 6.39756 0.601832 0.300916 0.953651i \(-0.402708\pi\)
0.300916 + 0.953651i \(0.402708\pi\)
\(114\) 3.56444 0.333840
\(115\) −1.44529 −0.134774
\(116\) 25.7592 2.39168
\(117\) 4.10392 0.379408
\(118\) 1.89820 0.174743
\(119\) 0 0
\(120\) 8.66075 0.790615
\(121\) −3.15317 −0.286652
\(122\) 20.6476 1.86935
\(123\) 1.00000 0.0901670
\(124\) 13.9316 1.25109
\(125\) 0.585761 0.0523921
\(126\) 0 0
\(127\) −4.60541 −0.408664 −0.204332 0.978902i \(-0.565502\pi\)
−0.204332 + 0.978902i \(0.565502\pi\)
\(128\) −17.8610 −1.57870
\(129\) −7.06229 −0.621800
\(130\) 29.8388 2.61704
\(131\) 15.0257 1.31281 0.656403 0.754411i \(-0.272077\pi\)
0.656403 + 0.754411i \(0.272077\pi\)
\(132\) −8.93916 −0.778054
\(133\) 0 0
\(134\) 0.331638 0.0286491
\(135\) 3.19117 0.274652
\(136\) 0.992388 0.0850966
\(137\) 9.51519 0.812938 0.406469 0.913665i \(-0.366760\pi\)
0.406469 + 0.913665i \(0.366760\pi\)
\(138\) −1.03190 −0.0878413
\(139\) −6.64553 −0.563666 −0.281833 0.959463i \(-0.590942\pi\)
−0.281833 + 0.959463i \(0.590942\pi\)
\(140\) 0 0
\(141\) −11.8027 −0.993965
\(142\) −6.57960 −0.552148
\(143\) −11.4960 −0.961343
\(144\) −0.198780 −0.0165650
\(145\) 25.7592 2.13918
\(146\) 29.0452 2.40380
\(147\) 0 0
\(148\) −6.91487 −0.568399
\(149\) −9.53399 −0.781055 −0.390528 0.920591i \(-0.627707\pi\)
−0.390528 + 0.920591i \(0.627707\pi\)
\(150\) 11.8103 0.964306
\(151\) 6.93916 0.564701 0.282351 0.959311i \(-0.408886\pi\)
0.282351 + 0.959311i \(0.408886\pi\)
\(152\) 4.24585 0.344384
\(153\) 0.365659 0.0295617
\(154\) 0 0
\(155\) 13.9316 1.11901
\(156\) 13.0963 1.04854
\(157\) 12.6629 1.01061 0.505304 0.862942i \(-0.331381\pi\)
0.505304 + 0.862942i \(0.331381\pi\)
\(158\) −9.14489 −0.727529
\(159\) 5.23280 0.414988
\(160\) −18.7668 −1.48365
\(161\) 0 0
\(162\) 2.27841 0.179009
\(163\) −12.2245 −0.957499 −0.478749 0.877952i \(-0.658910\pi\)
−0.478749 + 0.877952i \(0.658910\pi\)
\(164\) 3.19117 0.249188
\(165\) −8.93916 −0.695913
\(166\) −20.3671 −1.58079
\(167\) 15.6948 1.21450 0.607249 0.794512i \(-0.292273\pi\)
0.607249 + 0.794512i \(0.292273\pi\)
\(168\) 0 0
\(169\) 3.84219 0.295553
\(170\) 2.65863 0.203908
\(171\) 1.56444 0.119636
\(172\) −22.5370 −1.71843
\(173\) 16.4188 1.24830 0.624150 0.781304i \(-0.285445\pi\)
0.624150 + 0.781304i \(0.285445\pi\)
\(174\) 18.3914 1.39425
\(175\) 0 0
\(176\) 0.556827 0.0419724
\(177\) 0.833122 0.0626213
\(178\) −1.66624 −0.124890
\(179\) −18.7175 −1.39902 −0.699508 0.714625i \(-0.746597\pi\)
−0.699508 + 0.714625i \(0.746597\pi\)
\(180\) 10.1836 0.759038
\(181\) −25.1212 −1.86724 −0.933622 0.358259i \(-0.883371\pi\)
−0.933622 + 0.358259i \(0.883371\pi\)
\(182\) 0 0
\(183\) 9.06229 0.669904
\(184\) −1.22917 −0.0906155
\(185\) −6.91487 −0.508392
\(186\) 9.94678 0.729333
\(187\) −1.02429 −0.0749035
\(188\) −37.6643 −2.74695
\(189\) 0 0
\(190\) 11.3747 0.825209
\(191\) −13.5006 −0.976872 −0.488436 0.872600i \(-0.662432\pi\)
−0.488436 + 0.872600i \(0.662432\pi\)
\(192\) −13.0015 −0.938299
\(193\) −18.3139 −1.31826 −0.659131 0.752028i \(-0.729076\pi\)
−0.659131 + 0.752028i \(0.729076\pi\)
\(194\) −33.6795 −2.41805
\(195\) 13.0963 0.937846
\(196\) 0 0
\(197\) 14.6054 1.04059 0.520296 0.853986i \(-0.325822\pi\)
0.520296 + 0.853986i \(0.325822\pi\)
\(198\) −6.38234 −0.453573
\(199\) 19.7917 1.40300 0.701500 0.712670i \(-0.252514\pi\)
0.701500 + 0.712670i \(0.252514\pi\)
\(200\) 14.0680 0.994761
\(201\) 0.145556 0.0102668
\(202\) 22.7009 1.59723
\(203\) 0 0
\(204\) 1.16688 0.0816978
\(205\) 3.19117 0.222881
\(206\) −33.8041 −2.35525
\(207\) −0.452904 −0.0314790
\(208\) −0.815779 −0.0565641
\(209\) −4.38234 −0.303133
\(210\) 0 0
\(211\) −23.5431 −1.62077 −0.810386 0.585897i \(-0.800742\pi\)
−0.810386 + 0.585897i \(0.800742\pi\)
\(212\) 16.6988 1.14687
\(213\) −2.88780 −0.197869
\(214\) −6.88152 −0.470411
\(215\) −22.5370 −1.53701
\(216\) 2.71397 0.184663
\(217\) 0 0
\(218\) 5.51453 0.373491
\(219\) 12.7480 0.861430
\(220\) −28.5264 −1.92325
\(221\) 1.50064 0.100944
\(222\) −4.93705 −0.331353
\(223\) −14.9945 −1.00411 −0.502053 0.864837i \(-0.667422\pi\)
−0.502053 + 0.864837i \(0.667422\pi\)
\(224\) 0 0
\(225\) 5.18356 0.345570
\(226\) 14.5763 0.969600
\(227\) 6.47321 0.429642 0.214821 0.976653i \(-0.431083\pi\)
0.214821 + 0.976653i \(0.431083\pi\)
\(228\) 4.99239 0.330629
\(229\) −24.8914 −1.64487 −0.822434 0.568860i \(-0.807385\pi\)
−0.822434 + 0.568860i \(0.807385\pi\)
\(230\) −3.29297 −0.217132
\(231\) 0 0
\(232\) 21.9073 1.43828
\(233\) 7.89820 0.517428 0.258714 0.965954i \(-0.416701\pi\)
0.258714 + 0.965954i \(0.416701\pi\)
\(234\) 9.35044 0.611257
\(235\) −37.6643 −2.45695
\(236\) 2.65863 0.173062
\(237\) −4.01371 −0.260719
\(238\) 0 0
\(239\) −17.7951 −1.15107 −0.575533 0.817778i \(-0.695206\pi\)
−0.575533 + 0.817778i \(0.695206\pi\)
\(240\) −0.634341 −0.0409466
\(241\) 19.1531 1.23376 0.616880 0.787057i \(-0.288396\pi\)
0.616880 + 0.787057i \(0.288396\pi\)
\(242\) −7.18422 −0.461819
\(243\) 1.00000 0.0641500
\(244\) 28.9193 1.85137
\(245\) 0 0
\(246\) 2.27841 0.145266
\(247\) 6.42034 0.408516
\(248\) 11.8483 0.752367
\(249\) −8.93916 −0.566497
\(250\) 1.33461 0.0844079
\(251\) −2.92394 −0.184558 −0.0922788 0.995733i \(-0.529415\pi\)
−0.0922788 + 0.995733i \(0.529415\pi\)
\(252\) 0 0
\(253\) 1.26868 0.0797614
\(254\) −10.4930 −0.658391
\(255\) 1.16688 0.0730728
\(256\) −14.6918 −0.918238
\(257\) −15.8663 −0.989712 −0.494856 0.868975i \(-0.664779\pi\)
−0.494856 + 0.868975i \(0.664779\pi\)
\(258\) −16.0908 −1.00177
\(259\) 0 0
\(260\) 41.7925 2.59186
\(261\) 8.07202 0.499646
\(262\) 34.2349 2.11504
\(263\) 14.4717 0.892363 0.446182 0.894942i \(-0.352784\pi\)
0.446182 + 0.894942i \(0.352784\pi\)
\(264\) −7.60244 −0.467898
\(265\) 16.6988 1.02580
\(266\) 0 0
\(267\) −0.731317 −0.0447559
\(268\) 0.464495 0.0283735
\(269\) 3.38553 0.206419 0.103210 0.994660i \(-0.467089\pi\)
0.103210 + 0.994660i \(0.467089\pi\)
\(270\) 7.27080 0.442487
\(271\) 1.63646 0.0994079 0.0497039 0.998764i \(-0.484172\pi\)
0.0497039 + 0.998764i \(0.484172\pi\)
\(272\) −0.0726857 −0.00440722
\(273\) 0 0
\(274\) 21.6795 1.30971
\(275\) −14.5203 −0.875606
\(276\) −1.44529 −0.0869964
\(277\) −28.5793 −1.71716 −0.858581 0.512679i \(-0.828653\pi\)
−0.858581 + 0.512679i \(0.828653\pi\)
\(278\) −15.1413 −0.908112
\(279\) 4.36566 0.261365
\(280\) 0 0
\(281\) 17.4814 1.04285 0.521427 0.853296i \(-0.325400\pi\)
0.521427 + 0.853296i \(0.325400\pi\)
\(282\) −26.8914 −1.60136
\(283\) 30.8160 1.83182 0.915912 0.401380i \(-0.131469\pi\)
0.915912 + 0.401380i \(0.131469\pi\)
\(284\) −9.21546 −0.546837
\(285\) 4.99239 0.295724
\(286\) −26.1926 −1.54880
\(287\) 0 0
\(288\) −5.88085 −0.346533
\(289\) −16.8663 −0.992135
\(290\) 58.6901 3.44640
\(291\) −14.7820 −0.866537
\(292\) 40.6810 2.38068
\(293\) −30.7661 −1.79738 −0.898688 0.438588i \(-0.855479\pi\)
−0.898688 + 0.438588i \(0.855479\pi\)
\(294\) 0 0
\(295\) 2.65863 0.154792
\(296\) −5.88085 −0.341818
\(297\) −2.80122 −0.162543
\(298\) −21.7224 −1.25834
\(299\) −1.85868 −0.107490
\(300\) 16.5416 0.955030
\(301\) 0 0
\(302\) 15.8103 0.909780
\(303\) 9.96345 0.572386
\(304\) −0.310980 −0.0178359
\(305\) 28.9193 1.65591
\(306\) 0.833122 0.0476264
\(307\) 30.1966 1.72341 0.861706 0.507409i \(-0.169397\pi\)
0.861706 + 0.507409i \(0.169397\pi\)
\(308\) 0 0
\(309\) −14.8367 −0.844030
\(310\) 31.7418 1.80282
\(311\) −7.18321 −0.407322 −0.203661 0.979041i \(-0.565284\pi\)
−0.203661 + 0.979041i \(0.565284\pi\)
\(312\) 11.1379 0.630562
\(313\) −26.1415 −1.47761 −0.738803 0.673921i \(-0.764609\pi\)
−0.738803 + 0.673921i \(0.764609\pi\)
\(314\) 28.8513 1.62817
\(315\) 0 0
\(316\) −12.8084 −0.720530
\(317\) −29.7226 −1.66939 −0.834695 0.550713i \(-0.814356\pi\)
−0.834695 + 0.550713i \(0.814356\pi\)
\(318\) 11.9225 0.668580
\(319\) −22.6115 −1.26600
\(320\) −41.4898 −2.31935
\(321\) −3.02031 −0.168577
\(322\) 0 0
\(323\) 0.572051 0.0318297
\(324\) 3.19117 0.177287
\(325\) 21.2729 1.18001
\(326\) −27.8525 −1.54261
\(327\) 2.42034 0.133845
\(328\) 2.71397 0.149854
\(329\) 0 0
\(330\) −20.3671 −1.12117
\(331\) 8.41882 0.462740 0.231370 0.972866i \(-0.425679\pi\)
0.231370 + 0.972866i \(0.425679\pi\)
\(332\) −28.5264 −1.56559
\(333\) −2.16688 −0.118744
\(334\) 35.7592 1.95666
\(335\) 0.464495 0.0253781
\(336\) 0 0
\(337\) 21.6708 1.18049 0.590243 0.807226i \(-0.299032\pi\)
0.590243 + 0.807226i \(0.299032\pi\)
\(338\) 8.75409 0.476160
\(339\) 6.39756 0.347468
\(340\) 3.72371 0.201946
\(341\) −12.2292 −0.662247
\(342\) 3.56444 0.192743
\(343\) 0 0
\(344\) −19.1669 −1.03341
\(345\) −1.44529 −0.0778119
\(346\) 37.4089 2.01111
\(347\) −16.4865 −0.885043 −0.442521 0.896758i \(-0.645916\pi\)
−0.442521 + 0.896758i \(0.645916\pi\)
\(348\) 25.7592 1.38084
\(349\) 3.67699 0.196825 0.0984123 0.995146i \(-0.468624\pi\)
0.0984123 + 0.995146i \(0.468624\pi\)
\(350\) 0 0
\(351\) 4.10392 0.219051
\(352\) 16.4736 0.878044
\(353\) −25.1817 −1.34029 −0.670143 0.742232i \(-0.733767\pi\)
−0.670143 + 0.742232i \(0.733767\pi\)
\(354\) 1.89820 0.100888
\(355\) −9.21546 −0.489106
\(356\) −2.33376 −0.123689
\(357\) 0 0
\(358\) −42.6463 −2.25393
\(359\) −7.27807 −0.384122 −0.192061 0.981383i \(-0.561517\pi\)
−0.192061 + 0.981383i \(0.561517\pi\)
\(360\) 8.66075 0.456462
\(361\) −16.5525 −0.871186
\(362\) −57.2365 −3.00828
\(363\) −3.15317 −0.165498
\(364\) 0 0
\(365\) 40.6810 2.12934
\(366\) 20.6476 1.07927
\(367\) 6.77592 0.353700 0.176850 0.984238i \(-0.443409\pi\)
0.176850 + 0.984238i \(0.443409\pi\)
\(368\) 0.0900283 0.00469305
\(369\) 1.00000 0.0520579
\(370\) −15.7549 −0.819061
\(371\) 0 0
\(372\) 13.9316 0.722317
\(373\) 28.4956 1.47545 0.737723 0.675104i \(-0.235901\pi\)
0.737723 + 0.675104i \(0.235901\pi\)
\(374\) −2.33376 −0.120676
\(375\) 0.585761 0.0302486
\(376\) −32.0322 −1.65193
\(377\) 33.1270 1.70613
\(378\) 0 0
\(379\) 20.8301 1.06997 0.534985 0.844862i \(-0.320317\pi\)
0.534985 + 0.844862i \(0.320317\pi\)
\(380\) 15.9316 0.817271
\(381\) −4.60541 −0.235942
\(382\) −30.7600 −1.57382
\(383\) −1.92567 −0.0983974 −0.0491987 0.998789i \(-0.515667\pi\)
−0.0491987 + 0.998789i \(0.515667\pi\)
\(384\) −17.8610 −0.911465
\(385\) 0 0
\(386\) −41.7266 −2.12383
\(387\) −7.06229 −0.358996
\(388\) −47.1719 −2.39479
\(389\) −22.8513 −1.15860 −0.579302 0.815113i \(-0.696675\pi\)
−0.579302 + 0.815113i \(0.696675\pi\)
\(390\) 29.8388 1.51095
\(391\) −0.165608 −0.00837516
\(392\) 0 0
\(393\) 15.0257 0.757949
\(394\) 33.2772 1.67648
\(395\) −12.8084 −0.644462
\(396\) −8.93916 −0.449210
\(397\) 11.3189 0.568078 0.284039 0.958813i \(-0.408325\pi\)
0.284039 + 0.958813i \(0.408325\pi\)
\(398\) 45.0938 2.26035
\(399\) 0 0
\(400\) −1.03039 −0.0515194
\(401\) −3.89355 −0.194435 −0.0972174 0.995263i \(-0.530994\pi\)
−0.0972174 + 0.995263i \(0.530994\pi\)
\(402\) 0.331638 0.0165406
\(403\) 17.9163 0.892476
\(404\) 31.7951 1.58186
\(405\) 3.19117 0.158570
\(406\) 0 0
\(407\) 6.06990 0.300874
\(408\) 0.992388 0.0491305
\(409\) −1.72225 −0.0851598 −0.0425799 0.999093i \(-0.513558\pi\)
−0.0425799 + 0.999093i \(0.513558\pi\)
\(410\) 7.27080 0.359079
\(411\) 9.51519 0.469350
\(412\) −47.3464 −2.33259
\(413\) 0 0
\(414\) −1.03190 −0.0507152
\(415\) −28.5264 −1.40030
\(416\) −24.1346 −1.18329
\(417\) −6.64553 −0.325433
\(418\) −9.98478 −0.488371
\(419\) 9.49640 0.463929 0.231965 0.972724i \(-0.425485\pi\)
0.231965 + 0.972724i \(0.425485\pi\)
\(420\) 0 0
\(421\) 23.1183 1.12672 0.563358 0.826213i \(-0.309509\pi\)
0.563358 + 0.826213i \(0.309509\pi\)
\(422\) −53.6408 −2.61119
\(423\) −11.8027 −0.573866
\(424\) 14.2017 0.689695
\(425\) 1.89541 0.0919410
\(426\) −6.57960 −0.318783
\(427\) 0 0
\(428\) −9.63832 −0.465886
\(429\) −11.4960 −0.555032
\(430\) −51.3485 −2.47625
\(431\) 21.0105 1.01204 0.506021 0.862521i \(-0.331116\pi\)
0.506021 + 0.862521i \(0.331116\pi\)
\(432\) −0.198780 −0.00956382
\(433\) 18.5550 0.891695 0.445847 0.895109i \(-0.352902\pi\)
0.445847 + 0.895109i \(0.352902\pi\)
\(434\) 0 0
\(435\) 25.7592 1.23506
\(436\) 7.72371 0.369898
\(437\) −0.708540 −0.0338941
\(438\) 29.0452 1.38783
\(439\) −20.7042 −0.988157 −0.494078 0.869417i \(-0.664494\pi\)
−0.494078 + 0.869417i \(0.664494\pi\)
\(440\) −24.2607 −1.15658
\(441\) 0 0
\(442\) 3.41907 0.162628
\(443\) 19.7904 0.940271 0.470136 0.882594i \(-0.344205\pi\)
0.470136 + 0.882594i \(0.344205\pi\)
\(444\) −6.91487 −0.328165
\(445\) −2.33376 −0.110631
\(446\) −34.1637 −1.61770
\(447\) −9.53399 −0.450942
\(448\) 0 0
\(449\) 2.86648 0.135277 0.0676387 0.997710i \(-0.478453\pi\)
0.0676387 + 0.997710i \(0.478453\pi\)
\(450\) 11.8103 0.556742
\(451\) −2.80122 −0.131904
\(452\) 20.4157 0.960273
\(453\) 6.93916 0.326030
\(454\) 14.7487 0.692189
\(455\) 0 0
\(456\) 4.24585 0.198830
\(457\) −2.53737 −0.118693 −0.0593465 0.998237i \(-0.518902\pi\)
−0.0593465 + 0.998237i \(0.518902\pi\)
\(458\) −56.7128 −2.65002
\(459\) 0.365659 0.0170675
\(460\) −4.61217 −0.215044
\(461\) −39.8223 −1.85471 −0.927354 0.374186i \(-0.877922\pi\)
−0.927354 + 0.374186i \(0.877922\pi\)
\(462\) 0 0
\(463\) 29.8841 1.38883 0.694415 0.719574i \(-0.255663\pi\)
0.694415 + 0.719574i \(0.255663\pi\)
\(464\) −1.60456 −0.0744898
\(465\) 13.9316 0.646060
\(466\) 17.9954 0.833619
\(467\) −4.18931 −0.193858 −0.0969290 0.995291i \(-0.530902\pi\)
−0.0969290 + 0.995291i \(0.530902\pi\)
\(468\) 13.0963 0.605377
\(469\) 0 0
\(470\) −85.8149 −3.95835
\(471\) 12.6629 0.583474
\(472\) 2.26107 0.104074
\(473\) 19.7830 0.909625
\(474\) −9.14489 −0.420039
\(475\) 8.10936 0.372083
\(476\) 0 0
\(477\) 5.23280 0.239594
\(478\) −40.5445 −1.85446
\(479\) −16.2393 −0.741995 −0.370997 0.928634i \(-0.620984\pi\)
−0.370997 + 0.928634i \(0.620984\pi\)
\(480\) −18.7668 −0.856583
\(481\) −8.89270 −0.405472
\(482\) 43.6387 1.98769
\(483\) 0 0
\(484\) −10.0623 −0.457377
\(485\) −47.1719 −2.14197
\(486\) 2.27841 0.103351
\(487\) 38.6296 1.75048 0.875238 0.483692i \(-0.160705\pi\)
0.875238 + 0.483692i \(0.160705\pi\)
\(488\) 24.5948 1.11336
\(489\) −12.2245 −0.552812
\(490\) 0 0
\(491\) −43.1119 −1.94561 −0.972807 0.231618i \(-0.925598\pi\)
−0.972807 + 0.231618i \(0.925598\pi\)
\(492\) 3.19117 0.143869
\(493\) 2.95160 0.132934
\(494\) 14.6282 0.658153
\(495\) −8.93916 −0.401786
\(496\) −0.867807 −0.0389657
\(497\) 0 0
\(498\) −20.3671 −0.912672
\(499\) −23.4401 −1.04933 −0.524663 0.851310i \(-0.675808\pi\)
−0.524663 + 0.851310i \(0.675808\pi\)
\(500\) 1.86926 0.0835959
\(501\) 15.6948 0.701191
\(502\) −6.66195 −0.297337
\(503\) 38.4461 1.71423 0.857113 0.515128i \(-0.172256\pi\)
0.857113 + 0.515128i \(0.172256\pi\)
\(504\) 0 0
\(505\) 31.7951 1.41486
\(506\) 2.89058 0.128502
\(507\) 3.84219 0.170638
\(508\) −14.6966 −0.652058
\(509\) −5.36136 −0.237638 −0.118819 0.992916i \(-0.537911\pi\)
−0.118819 + 0.992916i \(0.537911\pi\)
\(510\) 2.65863 0.117726
\(511\) 0 0
\(512\) 2.24797 0.0993470
\(513\) 1.56444 0.0690717
\(514\) −36.1500 −1.59451
\(515\) −47.3464 −2.08633
\(516\) −22.5370 −0.992134
\(517\) 33.0619 1.45406
\(518\) 0 0
\(519\) 16.4188 0.720706
\(520\) 35.5431 1.55867
\(521\) 17.0851 0.748510 0.374255 0.927326i \(-0.377898\pi\)
0.374255 + 0.927326i \(0.377898\pi\)
\(522\) 18.3914 0.804970
\(523\) 42.0270 1.83771 0.918857 0.394592i \(-0.129114\pi\)
0.918857 + 0.394592i \(0.129114\pi\)
\(524\) 47.9497 2.09469
\(525\) 0 0
\(526\) 32.9725 1.43767
\(527\) 1.59634 0.0695377
\(528\) 0.556827 0.0242328
\(529\) −22.7949 −0.991082
\(530\) 38.0467 1.65264
\(531\) 0.833122 0.0361544
\(532\) 0 0
\(533\) 4.10392 0.177761
\(534\) −1.66624 −0.0721054
\(535\) −9.63832 −0.416701
\(536\) 0.395036 0.0170630
\(537\) −18.7175 −0.807722
\(538\) 7.71363 0.332558
\(539\) 0 0
\(540\) 10.1836 0.438231
\(541\) −15.4916 −0.666035 −0.333017 0.942921i \(-0.608067\pi\)
−0.333017 + 0.942921i \(0.608067\pi\)
\(542\) 3.72853 0.160154
\(543\) −25.1212 −1.07805
\(544\) −2.15038 −0.0921970
\(545\) 7.72371 0.330847
\(546\) 0 0
\(547\) 13.2850 0.568026 0.284013 0.958820i \(-0.408334\pi\)
0.284013 + 0.958820i \(0.408334\pi\)
\(548\) 30.3646 1.29711
\(549\) 9.06229 0.386769
\(550\) −33.0832 −1.41067
\(551\) 12.6282 0.537979
\(552\) −1.22917 −0.0523169
\(553\) 0 0
\(554\) −65.1154 −2.76649
\(555\) −6.91487 −0.293520
\(556\) −21.2070 −0.899377
\(557\) 24.5401 1.03980 0.519900 0.854227i \(-0.325969\pi\)
0.519900 + 0.854227i \(0.325969\pi\)
\(558\) 9.94678 0.421081
\(559\) −28.9831 −1.22585
\(560\) 0 0
\(561\) −1.02429 −0.0432456
\(562\) 39.8299 1.68012
\(563\) −5.33376 −0.224791 −0.112396 0.993664i \(-0.535852\pi\)
−0.112396 + 0.993664i \(0.535852\pi\)
\(564\) −37.6643 −1.58595
\(565\) 20.4157 0.858895
\(566\) 70.2117 2.95122
\(567\) 0 0
\(568\) −7.83742 −0.328851
\(569\) 35.9729 1.50806 0.754031 0.656839i \(-0.228107\pi\)
0.754031 + 0.656839i \(0.228107\pi\)
\(570\) 11.3747 0.476435
\(571\) 0.235268 0.00984565 0.00492282 0.999988i \(-0.498433\pi\)
0.00492282 + 0.999988i \(0.498433\pi\)
\(572\) −36.6856 −1.53390
\(573\) −13.5006 −0.563997
\(574\) 0 0
\(575\) −2.34765 −0.0979039
\(576\) −13.0015 −0.541727
\(577\) −2.22639 −0.0926857 −0.0463428 0.998926i \(-0.514757\pi\)
−0.0463428 + 0.998926i \(0.514757\pi\)
\(578\) −38.4284 −1.59841
\(579\) −18.3139 −0.761099
\(580\) 82.2019 3.41325
\(581\) 0 0
\(582\) −33.6795 −1.39606
\(583\) −14.6582 −0.607082
\(584\) 34.5977 1.43166
\(585\) 13.0963 0.541466
\(586\) −70.0980 −2.89572
\(587\) 4.42906 0.182807 0.0914034 0.995814i \(-0.470865\pi\)
0.0914034 + 0.995814i \(0.470865\pi\)
\(588\) 0 0
\(589\) 6.82981 0.281417
\(590\) 6.05746 0.249382
\(591\) 14.6054 0.600786
\(592\) 0.430733 0.0177030
\(593\) −5.51308 −0.226395 −0.113197 0.993573i \(-0.536109\pi\)
−0.113197 + 0.993573i \(0.536109\pi\)
\(594\) −6.38234 −0.261870
\(595\) 0 0
\(596\) −30.4246 −1.24624
\(597\) 19.7917 0.810022
\(598\) −4.23485 −0.173176
\(599\) −22.8187 −0.932346 −0.466173 0.884693i \(-0.654368\pi\)
−0.466173 + 0.884693i \(0.654368\pi\)
\(600\) 14.0680 0.574325
\(601\) −5.71233 −0.233011 −0.116505 0.993190i \(-0.537169\pi\)
−0.116505 + 0.993190i \(0.537169\pi\)
\(602\) 0 0
\(603\) 0.145556 0.00592751
\(604\) 22.1440 0.901028
\(605\) −10.0623 −0.409090
\(606\) 22.7009 0.922160
\(607\) −31.4136 −1.27504 −0.637520 0.770434i \(-0.720040\pi\)
−0.637520 + 0.770434i \(0.720040\pi\)
\(608\) −9.20024 −0.373119
\(609\) 0 0
\(610\) 65.8901 2.66781
\(611\) −48.4373 −1.95956
\(612\) 1.16688 0.0471683
\(613\) −32.3543 −1.30678 −0.653389 0.757022i \(-0.726654\pi\)
−0.653389 + 0.757022i \(0.726654\pi\)
\(614\) 68.8004 2.77656
\(615\) 3.19117 0.128680
\(616\) 0 0
\(617\) 23.8668 0.960842 0.480421 0.877038i \(-0.340484\pi\)
0.480421 + 0.877038i \(0.340484\pi\)
\(618\) −33.8041 −1.35980
\(619\) 25.7006 1.03299 0.516496 0.856289i \(-0.327236\pi\)
0.516496 + 0.856289i \(0.327236\pi\)
\(620\) 44.4579 1.78547
\(621\) −0.452904 −0.0181744
\(622\) −16.3663 −0.656230
\(623\) 0 0
\(624\) −0.815779 −0.0326573
\(625\) −24.0485 −0.961941
\(626\) −59.5612 −2.38054
\(627\) −4.38234 −0.175014
\(628\) 40.4094 1.61251
\(629\) −0.792338 −0.0315926
\(630\) 0 0
\(631\) −3.74765 −0.149192 −0.0745958 0.997214i \(-0.523767\pi\)
−0.0745958 + 0.997214i \(0.523767\pi\)
\(632\) −10.8931 −0.433305
\(633\) −23.5431 −0.935753
\(634\) −67.7205 −2.68952
\(635\) −14.6966 −0.583218
\(636\) 16.6988 0.662149
\(637\) 0 0
\(638\) −51.5184 −2.03963
\(639\) −2.88780 −0.114240
\(640\) −56.9974 −2.25302
\(641\) 42.2215 1.66765 0.833824 0.552030i \(-0.186146\pi\)
0.833824 + 0.552030i \(0.186146\pi\)
\(642\) −6.88152 −0.271592
\(643\) 0.685358 0.0270279 0.0135139 0.999909i \(-0.495698\pi\)
0.0135139 + 0.999909i \(0.495698\pi\)
\(644\) 0 0
\(645\) −22.5370 −0.887392
\(646\) 1.30337 0.0512803
\(647\) 26.8433 1.05532 0.527659 0.849456i \(-0.323070\pi\)
0.527659 + 0.849456i \(0.323070\pi\)
\(648\) 2.71397 0.106615
\(649\) −2.33376 −0.0916080
\(650\) 48.4685 1.90109
\(651\) 0 0
\(652\) −39.0105 −1.52777
\(653\) 20.9486 0.819781 0.409891 0.912135i \(-0.365567\pi\)
0.409891 + 0.912135i \(0.365567\pi\)
\(654\) 5.51453 0.215635
\(655\) 47.9497 1.87355
\(656\) −0.198780 −0.00776107
\(657\) 12.7480 0.497347
\(658\) 0 0
\(659\) −40.9586 −1.59552 −0.797761 0.602974i \(-0.793982\pi\)
−0.797761 + 0.602974i \(0.793982\pi\)
\(660\) −28.5264 −1.11039
\(661\) −24.5184 −0.953656 −0.476828 0.878997i \(-0.658214\pi\)
−0.476828 + 0.878997i \(0.658214\pi\)
\(662\) 19.1816 0.745513
\(663\) 1.50064 0.0582798
\(664\) −24.2607 −0.941496
\(665\) 0 0
\(666\) −4.93705 −0.191307
\(667\) −3.65585 −0.141555
\(668\) 50.0847 1.93783
\(669\) −14.9945 −0.579721
\(670\) 1.05831 0.0408861
\(671\) −25.3855 −0.979995
\(672\) 0 0
\(673\) −18.3565 −0.707592 −0.353796 0.935323i \(-0.615109\pi\)
−0.353796 + 0.935323i \(0.615109\pi\)
\(674\) 49.3751 1.90186
\(675\) 5.18356 0.199515
\(676\) 12.2611 0.471580
\(677\) 37.4309 1.43858 0.719292 0.694707i \(-0.244466\pi\)
0.719292 + 0.694707i \(0.244466\pi\)
\(678\) 14.5763 0.559799
\(679\) 0 0
\(680\) 3.16688 0.121444
\(681\) 6.47321 0.248054
\(682\) −27.8631 −1.06693
\(683\) 35.2411 1.34846 0.674232 0.738519i \(-0.264475\pi\)
0.674232 + 0.738519i \(0.264475\pi\)
\(684\) 4.99239 0.190889
\(685\) 30.3646 1.16017
\(686\) 0 0
\(687\) −24.8914 −0.949665
\(688\) 1.40384 0.0535211
\(689\) 21.4750 0.818133
\(690\) −3.29297 −0.125361
\(691\) −19.9907 −0.760483 −0.380241 0.924887i \(-0.624159\pi\)
−0.380241 + 0.924887i \(0.624159\pi\)
\(692\) 52.3952 1.99177
\(693\) 0 0
\(694\) −37.5631 −1.42588
\(695\) −21.2070 −0.804427
\(696\) 21.9073 0.830393
\(697\) 0.365659 0.0138503
\(698\) 8.37769 0.317100
\(699\) 7.89820 0.298737
\(700\) 0 0
\(701\) 27.6705 1.04510 0.522550 0.852609i \(-0.324981\pi\)
0.522550 + 0.852609i \(0.324981\pi\)
\(702\) 9.35044 0.352909
\(703\) −3.38995 −0.127854
\(704\) 36.4199 1.37263
\(705\) −37.6643 −1.41852
\(706\) −57.3743 −2.15931
\(707\) 0 0
\(708\) 2.65863 0.0999175
\(709\) 2.59151 0.0973263 0.0486631 0.998815i \(-0.484504\pi\)
0.0486631 + 0.998815i \(0.484504\pi\)
\(710\) −20.9966 −0.787989
\(711\) −4.01371 −0.150526
\(712\) −1.98478 −0.0743826
\(713\) −1.97722 −0.0740476
\(714\) 0 0
\(715\) −36.6856 −1.37197
\(716\) −59.7309 −2.23225
\(717\) −17.7951 −0.664569
\(718\) −16.5824 −0.618851
\(719\) 46.5093 1.73450 0.867252 0.497869i \(-0.165884\pi\)
0.867252 + 0.497869i \(0.165884\pi\)
\(720\) −0.634341 −0.0236405
\(721\) 0 0
\(722\) −37.7135 −1.40355
\(723\) 19.1531 0.712312
\(724\) −80.1660 −2.97935
\(725\) 41.8418 1.55396
\(726\) −7.18422 −0.266631
\(727\) −48.2686 −1.79018 −0.895092 0.445881i \(-0.852890\pi\)
−0.895092 + 0.445881i \(0.852890\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 92.6882 3.43054
\(731\) −2.58239 −0.0955131
\(732\) 28.9193 1.06889
\(733\) −18.7387 −0.692131 −0.346066 0.938210i \(-0.612483\pi\)
−0.346066 + 0.938210i \(0.612483\pi\)
\(734\) 15.4383 0.569840
\(735\) 0 0
\(736\) 2.66346 0.0981764
\(737\) −0.407735 −0.0150191
\(738\) 2.27841 0.0838696
\(739\) 1.91819 0.0705617 0.0352809 0.999377i \(-0.488767\pi\)
0.0352809 + 0.999377i \(0.488767\pi\)
\(740\) −22.0665 −0.811182
\(741\) 6.42034 0.235857
\(742\) 0 0
\(743\) −12.7346 −0.467188 −0.233594 0.972334i \(-0.575049\pi\)
−0.233594 + 0.972334i \(0.575049\pi\)
\(744\) 11.8483 0.434379
\(745\) −30.4246 −1.11467
\(746\) 64.9247 2.37706
\(747\) −8.93916 −0.327067
\(748\) −3.26868 −0.119515
\(749\) 0 0
\(750\) 1.33461 0.0487329
\(751\) −33.0529 −1.20612 −0.603060 0.797696i \(-0.706052\pi\)
−0.603060 + 0.797696i \(0.706052\pi\)
\(752\) 2.34614 0.0855549
\(753\) −2.92394 −0.106554
\(754\) 75.4769 2.74871
\(755\) 22.1440 0.805904
\(756\) 0 0
\(757\) 31.8255 1.15672 0.578359 0.815782i \(-0.303693\pi\)
0.578359 + 0.815782i \(0.303693\pi\)
\(758\) 47.4596 1.72381
\(759\) 1.26868 0.0460503
\(760\) 13.5492 0.491482
\(761\) 11.3657 0.412005 0.206002 0.978551i \(-0.433955\pi\)
0.206002 + 0.978551i \(0.433955\pi\)
\(762\) −10.4930 −0.380122
\(763\) 0 0
\(764\) −43.0828 −1.55868
\(765\) 1.16688 0.0421886
\(766\) −4.38748 −0.158526
\(767\) 3.41907 0.123455
\(768\) −14.6918 −0.530145
\(769\) 21.5566 0.777351 0.388676 0.921375i \(-0.372933\pi\)
0.388676 + 0.921375i \(0.372933\pi\)
\(770\) 0 0
\(771\) −15.8663 −0.571411
\(772\) −58.4427 −2.10340
\(773\) −21.2790 −0.765353 −0.382677 0.923882i \(-0.624998\pi\)
−0.382677 + 0.923882i \(0.624998\pi\)
\(774\) −16.0908 −0.578373
\(775\) 22.6296 0.812881
\(776\) −40.1180 −1.44015
\(777\) 0 0
\(778\) −52.0646 −1.86661
\(779\) 1.56444 0.0560518
\(780\) 41.7925 1.49641
\(781\) 8.08936 0.289460
\(782\) −0.377324 −0.0134931
\(783\) 8.07202 0.288471
\(784\) 0 0
\(785\) 40.4094 1.44227
\(786\) 34.2349 1.22112
\(787\) 3.79573 0.135303 0.0676515 0.997709i \(-0.478449\pi\)
0.0676515 + 0.997709i \(0.478449\pi\)
\(788\) 46.6083 1.66035
\(789\) 14.4717 0.515206
\(790\) −29.1829 −1.03828
\(791\) 0 0
\(792\) −7.60244 −0.270141
\(793\) 37.1909 1.32069
\(794\) 25.7891 0.915221
\(795\) 16.6988 0.592244
\(796\) 63.1588 2.23860
\(797\) −25.8936 −0.917197 −0.458598 0.888644i \(-0.651648\pi\)
−0.458598 + 0.888644i \(0.651648\pi\)
\(798\) 0 0
\(799\) −4.31575 −0.152680
\(800\) −30.4837 −1.07776
\(801\) −0.731317 −0.0258398
\(802\) −8.87112 −0.313250
\(803\) −35.7099 −1.26018
\(804\) 0.464495 0.0163815
\(805\) 0 0
\(806\) 40.8208 1.43785
\(807\) 3.38553 0.119176
\(808\) 27.0406 0.951284
\(809\) 13.1402 0.461987 0.230993 0.972955i \(-0.425802\pi\)
0.230993 + 0.972955i \(0.425802\pi\)
\(810\) 7.27080 0.255470
\(811\) 4.66221 0.163712 0.0818561 0.996644i \(-0.473915\pi\)
0.0818561 + 0.996644i \(0.473915\pi\)
\(812\) 0 0
\(813\) 1.63646 0.0573932
\(814\) 13.8297 0.484732
\(815\) −39.0105 −1.36648
\(816\) −0.0726857 −0.00254451
\(817\) −11.0485 −0.386539
\(818\) −3.92400 −0.137199
\(819\) 0 0
\(820\) 10.1836 0.355625
\(821\) 34.3697 1.19951 0.599756 0.800183i \(-0.295264\pi\)
0.599756 + 0.800183i \(0.295264\pi\)
\(822\) 21.6795 0.756161
\(823\) 8.02673 0.279794 0.139897 0.990166i \(-0.455323\pi\)
0.139897 + 0.990166i \(0.455323\pi\)
\(824\) −40.2664 −1.40275
\(825\) −14.5203 −0.505531
\(826\) 0 0
\(827\) −42.5305 −1.47893 −0.739464 0.673196i \(-0.764921\pi\)
−0.739464 + 0.673196i \(0.764921\pi\)
\(828\) −1.44529 −0.0502274
\(829\) −43.9410 −1.52613 −0.763066 0.646320i \(-0.776307\pi\)
−0.763066 + 0.646320i \(0.776307\pi\)
\(830\) −64.9949 −2.25601
\(831\) −28.5793 −0.991403
\(832\) −53.3570 −1.84982
\(833\) 0 0
\(834\) −15.1413 −0.524299
\(835\) 50.0847 1.73325
\(836\) −13.9848 −0.483674
\(837\) 4.36566 0.150899
\(838\) 21.6367 0.747428
\(839\) 16.2516 0.561068 0.280534 0.959844i \(-0.409489\pi\)
0.280534 + 0.959844i \(0.409489\pi\)
\(840\) 0 0
\(841\) 36.1575 1.24681
\(842\) 52.6730 1.81523
\(843\) 17.4814 0.602093
\(844\) −75.1299 −2.58608
\(845\) 12.2611 0.421794
\(846\) −26.8914 −0.924545
\(847\) 0 0
\(848\) −1.04018 −0.0357198
\(849\) 30.8160 1.05760
\(850\) 4.31853 0.148124
\(851\) 0.981387 0.0336415
\(852\) −9.21546 −0.315716
\(853\) −29.6899 −1.01656 −0.508282 0.861191i \(-0.669719\pi\)
−0.508282 + 0.861191i \(0.669719\pi\)
\(854\) 0 0
\(855\) 4.99239 0.170736
\(856\) −8.19705 −0.280169
\(857\) −24.4882 −0.836500 −0.418250 0.908332i \(-0.637356\pi\)
−0.418250 + 0.908332i \(0.637356\pi\)
\(858\) −26.1926 −0.894201
\(859\) 13.8849 0.473748 0.236874 0.971540i \(-0.423877\pi\)
0.236874 + 0.971540i \(0.423877\pi\)
\(860\) −71.9192 −2.45243
\(861\) 0 0
\(862\) 47.8707 1.63048
\(863\) 8.72548 0.297019 0.148509 0.988911i \(-0.452552\pi\)
0.148509 + 0.988911i \(0.452552\pi\)
\(864\) −5.88085 −0.200071
\(865\) 52.3952 1.78149
\(866\) 42.2759 1.43659
\(867\) −16.8663 −0.572809
\(868\) 0 0
\(869\) 11.2433 0.381402
\(870\) 58.6901 1.98978
\(871\) 0.597352 0.0202405
\(872\) 6.56874 0.222445
\(873\) −14.7820 −0.500295
\(874\) −1.61435 −0.0546061
\(875\) 0 0
\(876\) 40.6810 1.37448
\(877\) 13.8071 0.466233 0.233116 0.972449i \(-0.425108\pi\)
0.233116 + 0.972449i \(0.425108\pi\)
\(878\) −47.1727 −1.59200
\(879\) −30.7661 −1.03772
\(880\) 1.77693 0.0599003
\(881\) −4.03317 −0.135881 −0.0679405 0.997689i \(-0.521643\pi\)
−0.0679405 + 0.997689i \(0.521643\pi\)
\(882\) 0 0
\(883\) −12.1604 −0.409229 −0.204615 0.978843i \(-0.565594\pi\)
−0.204615 + 0.978843i \(0.565594\pi\)
\(884\) 4.78878 0.161064
\(885\) 2.65863 0.0893689
\(886\) 45.0908 1.51485
\(887\) −41.2121 −1.38377 −0.691883 0.722009i \(-0.743219\pi\)
−0.691883 + 0.722009i \(0.743219\pi\)
\(888\) −5.88085 −0.197349
\(889\) 0 0
\(890\) −5.31726 −0.178235
\(891\) −2.80122 −0.0938444
\(892\) −47.8500 −1.60214
\(893\) −18.4646 −0.617893
\(894\) −21.7224 −0.726505
\(895\) −59.7309 −1.99658
\(896\) 0 0
\(897\) −1.85868 −0.0620596
\(898\) 6.53102 0.217943
\(899\) 35.2397 1.17531
\(900\) 16.5416 0.551387
\(901\) 1.91342 0.0637452
\(902\) −6.38234 −0.212509
\(903\) 0 0
\(904\) 17.3628 0.577479
\(905\) −80.1660 −2.66481
\(906\) 15.8103 0.525262
\(907\) 27.4728 0.912220 0.456110 0.889923i \(-0.349242\pi\)
0.456110 + 0.889923i \(0.349242\pi\)
\(908\) 20.6571 0.685531
\(909\) 9.96345 0.330467
\(910\) 0 0
\(911\) 49.4883 1.63962 0.819811 0.572635i \(-0.194079\pi\)
0.819811 + 0.572635i \(0.194079\pi\)
\(912\) −0.310980 −0.0102976
\(913\) 25.0406 0.828722
\(914\) −5.78117 −0.191224
\(915\) 28.9193 0.956042
\(916\) −79.4326 −2.62453
\(917\) 0 0
\(918\) 0.833122 0.0274971
\(919\) 28.1560 0.928781 0.464391 0.885630i \(-0.346273\pi\)
0.464391 + 0.885630i \(0.346273\pi\)
\(920\) −3.92249 −0.129321
\(921\) 30.1966 0.995012
\(922\) −90.7316 −2.98809
\(923\) −11.8513 −0.390091
\(924\) 0 0
\(925\) −11.2321 −0.369310
\(926\) 68.0883 2.23752
\(927\) −14.8367 −0.487301
\(928\) −47.4704 −1.55829
\(929\) 8.89204 0.291738 0.145869 0.989304i \(-0.453402\pi\)
0.145869 + 0.989304i \(0.453402\pi\)
\(930\) 31.7418 1.04086
\(931\) 0 0
\(932\) 25.2045 0.825600
\(933\) −7.18321 −0.235168
\(934\) −9.54498 −0.312321
\(935\) −3.26868 −0.106897
\(936\) 11.1379 0.364055
\(937\) 34.2560 1.11910 0.559548 0.828798i \(-0.310975\pi\)
0.559548 + 0.828798i \(0.310975\pi\)
\(938\) 0 0
\(939\) −26.1415 −0.853096
\(940\) −120.193 −3.92027
\(941\) 8.67367 0.282754 0.141377 0.989956i \(-0.454847\pi\)
0.141377 + 0.989956i \(0.454847\pi\)
\(942\) 28.8513 0.940025
\(943\) −0.452904 −0.0147486
\(944\) −0.165608 −0.00539009
\(945\) 0 0
\(946\) 45.0739 1.46548
\(947\) 52.3599 1.70147 0.850735 0.525595i \(-0.176157\pi\)
0.850735 + 0.525595i \(0.176157\pi\)
\(948\) −12.8084 −0.415998
\(949\) 52.3168 1.69828
\(950\) 18.4765 0.599456
\(951\) −29.7226 −0.963823
\(952\) 0 0
\(953\) −31.6281 −1.02454 −0.512268 0.858826i \(-0.671194\pi\)
−0.512268 + 0.858826i \(0.671194\pi\)
\(954\) 11.9225 0.386005
\(955\) −43.0828 −1.39413
\(956\) −56.7870 −1.83662
\(957\) −22.6115 −0.730926
\(958\) −36.9999 −1.19541
\(959\) 0 0
\(960\) −41.4898 −1.33908
\(961\) −11.9410 −0.385194
\(962\) −20.2613 −0.653249
\(963\) −3.02031 −0.0973282
\(964\) 61.1208 1.96857
\(965\) −58.4427 −1.88134
\(966\) 0 0
\(967\) −47.9468 −1.54187 −0.770933 0.636916i \(-0.780210\pi\)
−0.770933 + 0.636916i \(0.780210\pi\)
\(968\) −8.55762 −0.275052
\(969\) 0.572051 0.0183769
\(970\) −107.477 −3.45088
\(971\) 22.6526 0.726958 0.363479 0.931602i \(-0.381589\pi\)
0.363479 + 0.931602i \(0.381589\pi\)
\(972\) 3.19117 0.102357
\(973\) 0 0
\(974\) 88.0143 2.82016
\(975\) 21.2729 0.681279
\(976\) −1.80140 −0.0576616
\(977\) −47.6870 −1.52564 −0.762822 0.646609i \(-0.776187\pi\)
−0.762822 + 0.646609i \(0.776187\pi\)
\(978\) −27.8525 −0.890626
\(979\) 2.04858 0.0654729
\(980\) 0 0
\(981\) 2.42034 0.0772754
\(982\) −98.2268 −3.13454
\(983\) 18.4217 0.587560 0.293780 0.955873i \(-0.405087\pi\)
0.293780 + 0.955873i \(0.405087\pi\)
\(984\) 2.71397 0.0865184
\(985\) 46.6083 1.48506
\(986\) 6.72498 0.214167
\(987\) 0 0
\(988\) 20.4884 0.651822
\(989\) 3.19854 0.101708
\(990\) −20.3671 −0.647309
\(991\) −32.0800 −1.01906 −0.509528 0.860454i \(-0.670180\pi\)
−0.509528 + 0.860454i \(0.670180\pi\)
\(992\) −25.6738 −0.815144
\(993\) 8.41882 0.267163
\(994\) 0 0
\(995\) 63.1588 2.00227
\(996\) −28.5264 −0.903893
\(997\) −1.39045 −0.0440360 −0.0220180 0.999758i \(-0.507009\pi\)
−0.0220180 + 0.999758i \(0.507009\pi\)
\(998\) −53.4063 −1.69055
\(999\) −2.16688 −0.0685570
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 \(a_p\))