Properties

Label 6027.2.a.m.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 2
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: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.00000 q^{3} -3.41421 q^{5} +1.41421 q^{6} +2.82843 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.00000 q^{3} -3.41421 q^{5} +1.41421 q^{6} +2.82843 q^{8} +1.00000 q^{9} +4.82843 q^{10} +2.41421 q^{11} -6.24264 q^{13} +3.41421 q^{15} -4.00000 q^{16} +0.414214 q^{17} -1.41421 q^{18} +5.41421 q^{19} -3.41421 q^{22} -1.41421 q^{23} -2.82843 q^{24} +6.65685 q^{25} +8.82843 q^{26} -1.00000 q^{27} -6.07107 q^{29} -4.82843 q^{30} +3.00000 q^{31} -2.41421 q^{33} -0.585786 q^{34} -9.48528 q^{37} -7.65685 q^{38} +6.24264 q^{39} -9.65685 q^{40} +1.00000 q^{41} -5.00000 q^{43} -3.41421 q^{45} +2.00000 q^{46} -10.4142 q^{47} +4.00000 q^{48} -9.41421 q^{50} -0.414214 q^{51} +6.82843 q^{53} +1.41421 q^{54} -8.24264 q^{55} -5.41421 q^{57} +8.58579 q^{58} +8.48528 q^{59} +4.65685 q^{61} -4.24264 q^{62} +8.00000 q^{64} +21.3137 q^{65} +3.41421 q^{66} +10.4853 q^{67} +1.41421 q^{69} +10.0711 q^{71} +2.82843 q^{72} +10.3137 q^{73} +13.4142 q^{74} -6.65685 q^{75} -8.82843 q^{78} -7.65685 q^{79} +13.6569 q^{80} +1.00000 q^{81} -1.41421 q^{82} -1.07107 q^{83} -1.41421 q^{85} +7.07107 q^{86} +6.07107 q^{87} +6.82843 q^{88} +11.6569 q^{89} +4.82843 q^{90} -3.00000 q^{93} +14.7279 q^{94} -18.4853 q^{95} -7.75736 q^{97} +2.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{3} - 4q^{5} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 4q^{5} + 2q^{9} + 4q^{10} + 2q^{11} - 4q^{13} + 4q^{15} - 8q^{16} - 2q^{17} + 8q^{19} - 4q^{22} + 2q^{25} + 12q^{26} - 2q^{27} + 2q^{29} - 4q^{30} + 6q^{31} - 2q^{33} - 4q^{34} - 2q^{37} - 4q^{38} + 4q^{39} - 8q^{40} + 2q^{41} - 10q^{43} - 4q^{45} + 4q^{46} - 18q^{47} + 8q^{48} - 16q^{50} + 2q^{51} + 8q^{53} - 8q^{55} - 8q^{57} + 20q^{58} - 2q^{61} + 16q^{64} + 20q^{65} + 4q^{66} + 4q^{67} + 6q^{71} - 2q^{73} + 24q^{74} - 2q^{75} - 12q^{78} - 4q^{79} + 16q^{80} + 2q^{81} + 12q^{83} - 2q^{87} + 8q^{88} + 12q^{89} + 4q^{90} - 6q^{93} + 4q^{94} - 20q^{95} - 24q^{97} + 2q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −3.41421 −1.52688 −0.763441 0.645877i \(-0.776492\pi\)
−0.763441 + 0.645877i \(0.776492\pi\)
\(6\) 1.41421 0.577350
\(7\) 0 0
\(8\) 2.82843 1.00000
\(9\) 1.00000 0.333333
\(10\) 4.82843 1.52688
\(11\) 2.41421 0.727913 0.363956 0.931416i \(-0.381426\pi\)
0.363956 + 0.931416i \(0.381426\pi\)
\(12\) 0 0
\(13\) −6.24264 −1.73140 −0.865699 0.500566i \(-0.833125\pi\)
−0.865699 + 0.500566i \(0.833125\pi\)
\(14\) 0 0
\(15\) 3.41421 0.881546
\(16\) −4.00000 −1.00000
\(17\) 0.414214 0.100462 0.0502308 0.998738i \(-0.484004\pi\)
0.0502308 + 0.998738i \(0.484004\pi\)
\(18\) −1.41421 −0.333333
\(19\) 5.41421 1.24211 0.621053 0.783769i \(-0.286705\pi\)
0.621053 + 0.783769i \(0.286705\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.41421 −0.727913
\(23\) −1.41421 −0.294884 −0.147442 0.989071i \(-0.547104\pi\)
−0.147442 + 0.989071i \(0.547104\pi\)
\(24\) −2.82843 −0.577350
\(25\) 6.65685 1.33137
\(26\) 8.82843 1.73140
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.07107 −1.12737 −0.563684 0.825990i \(-0.690617\pi\)
−0.563684 + 0.825990i \(0.690617\pi\)
\(30\) −4.82843 −0.881546
\(31\) 3.00000 0.538816 0.269408 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 0 0
\(33\) −2.41421 −0.420261
\(34\) −0.585786 −0.100462
\(35\) 0 0
\(36\) 0 0
\(37\) −9.48528 −1.55937 −0.779685 0.626172i \(-0.784621\pi\)
−0.779685 + 0.626172i \(0.784621\pi\)
\(38\) −7.65685 −1.24211
\(39\) 6.24264 0.999623
\(40\) −9.65685 −1.52688
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) 0 0
\(45\) −3.41421 −0.508961
\(46\) 2.00000 0.294884
\(47\) −10.4142 −1.51907 −0.759535 0.650467i \(-0.774573\pi\)
−0.759535 + 0.650467i \(0.774573\pi\)
\(48\) 4.00000 0.577350
\(49\) 0 0
\(50\) −9.41421 −1.33137
\(51\) −0.414214 −0.0580015
\(52\) 0 0
\(53\) 6.82843 0.937957 0.468978 0.883210i \(-0.344622\pi\)
0.468978 + 0.883210i \(0.344622\pi\)
\(54\) 1.41421 0.192450
\(55\) −8.24264 −1.11144
\(56\) 0 0
\(57\) −5.41421 −0.717130
\(58\) 8.58579 1.12737
\(59\) 8.48528 1.10469 0.552345 0.833616i \(-0.313733\pi\)
0.552345 + 0.833616i \(0.313733\pi\)
\(60\) 0 0
\(61\) 4.65685 0.596249 0.298125 0.954527i \(-0.403639\pi\)
0.298125 + 0.954527i \(0.403639\pi\)
\(62\) −4.24264 −0.538816
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 21.3137 2.64364
\(66\) 3.41421 0.420261
\(67\) 10.4853 1.28098 0.640490 0.767966i \(-0.278731\pi\)
0.640490 + 0.767966i \(0.278731\pi\)
\(68\) 0 0
\(69\) 1.41421 0.170251
\(70\) 0 0
\(71\) 10.0711 1.19522 0.597608 0.801788i \(-0.296118\pi\)
0.597608 + 0.801788i \(0.296118\pi\)
\(72\) 2.82843 0.333333
\(73\) 10.3137 1.20713 0.603564 0.797314i \(-0.293747\pi\)
0.603564 + 0.797314i \(0.293747\pi\)
\(74\) 13.4142 1.55937
\(75\) −6.65685 −0.768667
\(76\) 0 0
\(77\) 0 0
\(78\) −8.82843 −0.999623
\(79\) −7.65685 −0.861463 −0.430732 0.902480i \(-0.641744\pi\)
−0.430732 + 0.902480i \(0.641744\pi\)
\(80\) 13.6569 1.52688
\(81\) 1.00000 0.111111
\(82\) −1.41421 −0.156174
\(83\) −1.07107 −0.117565 −0.0587825 0.998271i \(-0.518722\pi\)
−0.0587825 + 0.998271i \(0.518722\pi\)
\(84\) 0 0
\(85\) −1.41421 −0.153393
\(86\) 7.07107 0.762493
\(87\) 6.07107 0.650887
\(88\) 6.82843 0.727913
\(89\) 11.6569 1.23562 0.617812 0.786326i \(-0.288019\pi\)
0.617812 + 0.786326i \(0.288019\pi\)
\(90\) 4.82843 0.508961
\(91\) 0 0
\(92\) 0 0
\(93\) −3.00000 −0.311086
\(94\) 14.7279 1.51907
\(95\) −18.4853 −1.89655
\(96\) 0 0
\(97\) −7.75736 −0.787641 −0.393820 0.919187i \(-0.628847\pi\)
−0.393820 + 0.919187i \(0.628847\pi\)
\(98\) 0 0
\(99\) 2.41421 0.242638
\(100\) 0 0
\(101\) 0.414214 0.0412158 0.0206079 0.999788i \(-0.493440\pi\)
0.0206079 + 0.999788i \(0.493440\pi\)
\(102\) 0.585786 0.0580015
\(103\) −6.31371 −0.622108 −0.311054 0.950392i \(-0.600682\pi\)
−0.311054 + 0.950392i \(0.600682\pi\)
\(104\) −17.6569 −1.73140
\(105\) 0 0
\(106\) −9.65685 −0.937957
\(107\) −0.343146 −0.0331732 −0.0165866 0.999862i \(-0.505280\pi\)
−0.0165866 + 0.999862i \(0.505280\pi\)
\(108\) 0 0
\(109\) 7.89949 0.756634 0.378317 0.925676i \(-0.376503\pi\)
0.378317 + 0.925676i \(0.376503\pi\)
\(110\) 11.6569 1.11144
\(111\) 9.48528 0.900303
\(112\) 0 0
\(113\) 6.72792 0.632910 0.316455 0.948608i \(-0.397507\pi\)
0.316455 + 0.948608i \(0.397507\pi\)
\(114\) 7.65685 0.717130
\(115\) 4.82843 0.450253
\(116\) 0 0
\(117\) −6.24264 −0.577132
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) 9.65685 0.881546
\(121\) −5.17157 −0.470143
\(122\) −6.58579 −0.596249
\(123\) −1.00000 −0.0901670
\(124\) 0 0
\(125\) −5.65685 −0.505964
\(126\) 0 0
\(127\) 9.31371 0.826458 0.413229 0.910627i \(-0.364401\pi\)
0.413229 + 0.910627i \(0.364401\pi\)
\(128\) −11.3137 −1.00000
\(129\) 5.00000 0.440225
\(130\) −30.1421 −2.64364
\(131\) 10.5858 0.924884 0.462442 0.886649i \(-0.346973\pi\)
0.462442 + 0.886649i \(0.346973\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −14.8284 −1.28098
\(135\) 3.41421 0.293849
\(136\) 1.17157 0.100462
\(137\) 3.92893 0.335671 0.167836 0.985815i \(-0.446322\pi\)
0.167836 + 0.985815i \(0.446322\pi\)
\(138\) −2.00000 −0.170251
\(139\) −3.65685 −0.310170 −0.155085 0.987901i \(-0.549565\pi\)
−0.155085 + 0.987901i \(0.549565\pi\)
\(140\) 0 0
\(141\) 10.4142 0.877035
\(142\) −14.2426 −1.19522
\(143\) −15.0711 −1.26031
\(144\) −4.00000 −0.333333
\(145\) 20.7279 1.72136
\(146\) −14.5858 −1.20713
\(147\) 0 0
\(148\) 0 0
\(149\) 17.3137 1.41839 0.709197 0.705010i \(-0.249058\pi\)
0.709197 + 0.705010i \(0.249058\pi\)
\(150\) 9.41421 0.768667
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 15.3137 1.24211
\(153\) 0.414214 0.0334872
\(154\) 0 0
\(155\) −10.2426 −0.822709
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 10.8284 0.861463
\(159\) −6.82843 −0.541529
\(160\) 0 0
\(161\) 0 0
\(162\) −1.41421 −0.111111
\(163\) −9.48528 −0.742945 −0.371472 0.928444i \(-0.621147\pi\)
−0.371472 + 0.928444i \(0.621147\pi\)
\(164\) 0 0
\(165\) 8.24264 0.641689
\(166\) 1.51472 0.117565
\(167\) 3.65685 0.282976 0.141488 0.989940i \(-0.454811\pi\)
0.141488 + 0.989940i \(0.454811\pi\)
\(168\) 0 0
\(169\) 25.9706 1.99774
\(170\) 2.00000 0.153393
\(171\) 5.41421 0.414035
\(172\) 0 0
\(173\) 9.07107 0.689661 0.344830 0.938665i \(-0.387936\pi\)
0.344830 + 0.938665i \(0.387936\pi\)
\(174\) −8.58579 −0.650887
\(175\) 0 0
\(176\) −9.65685 −0.727913
\(177\) −8.48528 −0.637793
\(178\) −16.4853 −1.23562
\(179\) −4.89949 −0.366205 −0.183103 0.983094i \(-0.558614\pi\)
−0.183103 + 0.983094i \(0.558614\pi\)
\(180\) 0 0
\(181\) 7.31371 0.543624 0.271812 0.962350i \(-0.412377\pi\)
0.271812 + 0.962350i \(0.412377\pi\)
\(182\) 0 0
\(183\) −4.65685 −0.344245
\(184\) −4.00000 −0.294884
\(185\) 32.3848 2.38098
\(186\) 4.24264 0.311086
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 0 0
\(190\) 26.1421 1.89655
\(191\) 18.8284 1.36238 0.681189 0.732108i \(-0.261463\pi\)
0.681189 + 0.732108i \(0.261463\pi\)
\(192\) −8.00000 −0.577350
\(193\) 0.585786 0.0421658 0.0210829 0.999778i \(-0.493289\pi\)
0.0210829 + 0.999778i \(0.493289\pi\)
\(194\) 10.9706 0.787641
\(195\) −21.3137 −1.52631
\(196\) 0 0
\(197\) 22.2426 1.58472 0.792361 0.610052i \(-0.208852\pi\)
0.792361 + 0.610052i \(0.208852\pi\)
\(198\) −3.41421 −0.242638
\(199\) 16.2426 1.15141 0.575705 0.817657i \(-0.304728\pi\)
0.575705 + 0.817657i \(0.304728\pi\)
\(200\) 18.8284 1.33137
\(201\) −10.4853 −0.739575
\(202\) −0.585786 −0.0412158
\(203\) 0 0
\(204\) 0 0
\(205\) −3.41421 −0.238459
\(206\) 8.92893 0.622108
\(207\) −1.41421 −0.0982946
\(208\) 24.9706 1.73140
\(209\) 13.0711 0.904145
\(210\) 0 0
\(211\) −24.4853 −1.68564 −0.842818 0.538198i \(-0.819105\pi\)
−0.842818 + 0.538198i \(0.819105\pi\)
\(212\) 0 0
\(213\) −10.0711 −0.690058
\(214\) 0.485281 0.0331732
\(215\) 17.0711 1.16424
\(216\) −2.82843 −0.192450
\(217\) 0 0
\(218\) −11.1716 −0.756634
\(219\) −10.3137 −0.696936
\(220\) 0 0
\(221\) −2.58579 −0.173939
\(222\) −13.4142 −0.900303
\(223\) −10.3431 −0.692628 −0.346314 0.938119i \(-0.612567\pi\)
−0.346314 + 0.938119i \(0.612567\pi\)
\(224\) 0 0
\(225\) 6.65685 0.443790
\(226\) −9.51472 −0.632910
\(227\) −1.10051 −0.0730431 −0.0365215 0.999333i \(-0.511628\pi\)
−0.0365215 + 0.999333i \(0.511628\pi\)
\(228\) 0 0
\(229\) 0.242641 0.0160341 0.00801707 0.999968i \(-0.497448\pi\)
0.00801707 + 0.999968i \(0.497448\pi\)
\(230\) −6.82843 −0.450253
\(231\) 0 0
\(232\) −17.1716 −1.12737
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 8.82843 0.577132
\(235\) 35.5563 2.31944
\(236\) 0 0
\(237\) 7.65685 0.497366
\(238\) 0 0
\(239\) 18.1421 1.17352 0.586759 0.809762i \(-0.300404\pi\)
0.586759 + 0.809762i \(0.300404\pi\)
\(240\) −13.6569 −0.881546
\(241\) −9.48528 −0.611001 −0.305500 0.952192i \(-0.598824\pi\)
−0.305500 + 0.952192i \(0.598824\pi\)
\(242\) 7.31371 0.470143
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 1.41421 0.0901670
\(247\) −33.7990 −2.15058
\(248\) 8.48528 0.538816
\(249\) 1.07107 0.0678762
\(250\) 8.00000 0.505964
\(251\) −8.82843 −0.557245 −0.278623 0.960401i \(-0.589878\pi\)
−0.278623 + 0.960401i \(0.589878\pi\)
\(252\) 0 0
\(253\) −3.41421 −0.214650
\(254\) −13.1716 −0.826458
\(255\) 1.41421 0.0885615
\(256\) 0 0
\(257\) 5.10051 0.318161 0.159080 0.987266i \(-0.449147\pi\)
0.159080 + 0.987266i \(0.449147\pi\)
\(258\) −7.07107 −0.440225
\(259\) 0 0
\(260\) 0 0
\(261\) −6.07107 −0.375790
\(262\) −14.9706 −0.924884
\(263\) 2.41421 0.148867 0.0744334 0.997226i \(-0.476285\pi\)
0.0744334 + 0.997226i \(0.476285\pi\)
\(264\) −6.82843 −0.420261
\(265\) −23.3137 −1.43215
\(266\) 0 0
\(267\) −11.6569 −0.713388
\(268\) 0 0
\(269\) 8.48528 0.517357 0.258678 0.965964i \(-0.416713\pi\)
0.258678 + 0.965964i \(0.416713\pi\)
\(270\) −4.82843 −0.293849
\(271\) −18.7990 −1.14196 −0.570979 0.820965i \(-0.693436\pi\)
−0.570979 + 0.820965i \(0.693436\pi\)
\(272\) −1.65685 −0.100462
\(273\) 0 0
\(274\) −5.55635 −0.335671
\(275\) 16.0711 0.969122
\(276\) 0 0
\(277\) −27.2843 −1.63935 −0.819676 0.572827i \(-0.805847\pi\)
−0.819676 + 0.572827i \(0.805847\pi\)
\(278\) 5.17157 0.310170
\(279\) 3.00000 0.179605
\(280\) 0 0
\(281\) 17.3848 1.03709 0.518544 0.855051i \(-0.326474\pi\)
0.518544 + 0.855051i \(0.326474\pi\)
\(282\) −14.7279 −0.877035
\(283\) −16.1716 −0.961300 −0.480650 0.876912i \(-0.659599\pi\)
−0.480650 + 0.876912i \(0.659599\pi\)
\(284\) 0 0
\(285\) 18.4853 1.09497
\(286\) 21.3137 1.26031
\(287\) 0 0
\(288\) 0 0
\(289\) −16.8284 −0.989907
\(290\) −29.3137 −1.72136
\(291\) 7.75736 0.454744
\(292\) 0 0
\(293\) −9.58579 −0.560008 −0.280004 0.959999i \(-0.590336\pi\)
−0.280004 + 0.959999i \(0.590336\pi\)
\(294\) 0 0
\(295\) −28.9706 −1.68673
\(296\) −26.8284 −1.55937
\(297\) −2.41421 −0.140087
\(298\) −24.4853 −1.41839
\(299\) 8.82843 0.510561
\(300\) 0 0
\(301\) 0 0
\(302\) 22.6274 1.30206
\(303\) −0.414214 −0.0237959
\(304\) −21.6569 −1.24211
\(305\) −15.8995 −0.910402
\(306\) −0.585786 −0.0334872
\(307\) 0.313708 0.0179043 0.00895214 0.999960i \(-0.497150\pi\)
0.00895214 + 0.999960i \(0.497150\pi\)
\(308\) 0 0
\(309\) 6.31371 0.359174
\(310\) 14.4853 0.822709
\(311\) −26.8284 −1.52130 −0.760650 0.649162i \(-0.775120\pi\)
−0.760650 + 0.649162i \(0.775120\pi\)
\(312\) 17.6569 0.999623
\(313\) 28.8701 1.63183 0.815916 0.578170i \(-0.196233\pi\)
0.815916 + 0.578170i \(0.196233\pi\)
\(314\) 25.4558 1.43656
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0711 −0.677979 −0.338989 0.940790i \(-0.610085\pi\)
−0.338989 + 0.940790i \(0.610085\pi\)
\(318\) 9.65685 0.541529
\(319\) −14.6569 −0.820626
\(320\) −27.3137 −1.52688
\(321\) 0.343146 0.0191525
\(322\) 0 0
\(323\) 2.24264 0.124784
\(324\) 0 0
\(325\) −41.5563 −2.30513
\(326\) 13.4142 0.742945
\(327\) −7.89949 −0.436843
\(328\) 2.82843 0.156174
\(329\) 0 0
\(330\) −11.6569 −0.641689
\(331\) 16.2426 0.892776 0.446388 0.894839i \(-0.352710\pi\)
0.446388 + 0.894839i \(0.352710\pi\)
\(332\) 0 0
\(333\) −9.48528 −0.519790
\(334\) −5.17157 −0.282976
\(335\) −35.7990 −1.95591
\(336\) 0 0
\(337\) 19.9706 1.08787 0.543933 0.839129i \(-0.316935\pi\)
0.543933 + 0.839129i \(0.316935\pi\)
\(338\) −36.7279 −1.99774
\(339\) −6.72792 −0.365411
\(340\) 0 0
\(341\) 7.24264 0.392211
\(342\) −7.65685 −0.414035
\(343\) 0 0
\(344\) −14.1421 −0.762493
\(345\) −4.82843 −0.259954
\(346\) −12.8284 −0.689661
\(347\) 0.899495 0.0482874 0.0241437 0.999708i \(-0.492314\pi\)
0.0241437 + 0.999708i \(0.492314\pi\)
\(348\) 0 0
\(349\) −9.14214 −0.489367 −0.244684 0.969603i \(-0.578684\pi\)
−0.244684 + 0.969603i \(0.578684\pi\)
\(350\) 0 0
\(351\) 6.24264 0.333208
\(352\) 0 0
\(353\) 34.9706 1.86130 0.930648 0.365917i \(-0.119244\pi\)
0.930648 + 0.365917i \(0.119244\pi\)
\(354\) 12.0000 0.637793
\(355\) −34.3848 −1.82495
\(356\) 0 0
\(357\) 0 0
\(358\) 6.92893 0.366205
\(359\) 16.2426 0.857254 0.428627 0.903482i \(-0.358997\pi\)
0.428627 + 0.903482i \(0.358997\pi\)
\(360\) −9.65685 −0.508961
\(361\) 10.3137 0.542827
\(362\) −10.3431 −0.543624
\(363\) 5.17157 0.271437
\(364\) 0 0
\(365\) −35.2132 −1.84314
\(366\) 6.58579 0.344245
\(367\) 6.65685 0.347485 0.173742 0.984791i \(-0.444414\pi\)
0.173742 + 0.984791i \(0.444414\pi\)
\(368\) 5.65685 0.294884
\(369\) 1.00000 0.0520579
\(370\) −45.7990 −2.38098
\(371\) 0 0
\(372\) 0 0
\(373\) 33.1421 1.71603 0.858017 0.513621i \(-0.171696\pi\)
0.858017 + 0.513621i \(0.171696\pi\)
\(374\) −1.41421 −0.0731272
\(375\) 5.65685 0.292119
\(376\) −29.4558 −1.51907
\(377\) 37.8995 1.95192
\(378\) 0 0
\(379\) 26.9706 1.38538 0.692692 0.721233i \(-0.256424\pi\)
0.692692 + 0.721233i \(0.256424\pi\)
\(380\) 0 0
\(381\) −9.31371 −0.477156
\(382\) −26.6274 −1.36238
\(383\) −17.1005 −0.873795 −0.436897 0.899511i \(-0.643923\pi\)
−0.436897 + 0.899511i \(0.643923\pi\)
\(384\) 11.3137 0.577350
\(385\) 0 0
\(386\) −0.828427 −0.0421658
\(387\) −5.00000 −0.254164
\(388\) 0 0
\(389\) −22.2426 −1.12775 −0.563873 0.825861i \(-0.690689\pi\)
−0.563873 + 0.825861i \(0.690689\pi\)
\(390\) 30.1421 1.52631
\(391\) −0.585786 −0.0296245
\(392\) 0 0
\(393\) −10.5858 −0.533982
\(394\) −31.4558 −1.58472
\(395\) 26.1421 1.31535
\(396\) 0 0
\(397\) −30.5269 −1.53210 −0.766051 0.642780i \(-0.777781\pi\)
−0.766051 + 0.642780i \(0.777781\pi\)
\(398\) −22.9706 −1.15141
\(399\) 0 0
\(400\) −26.6274 −1.33137
\(401\) 10.6274 0.530708 0.265354 0.964151i \(-0.414511\pi\)
0.265354 + 0.964151i \(0.414511\pi\)
\(402\) 14.8284 0.739575
\(403\) −18.7279 −0.932904
\(404\) 0 0
\(405\) −3.41421 −0.169654
\(406\) 0 0
\(407\) −22.8995 −1.13509
\(408\) −1.17157 −0.0580015
\(409\) −16.1716 −0.799633 −0.399816 0.916595i \(-0.630926\pi\)
−0.399816 + 0.916595i \(0.630926\pi\)
\(410\) 4.82843 0.238459
\(411\) −3.92893 −0.193800
\(412\) 0 0
\(413\) 0 0
\(414\) 2.00000 0.0982946
\(415\) 3.65685 0.179508
\(416\) 0 0
\(417\) 3.65685 0.179077
\(418\) −18.4853 −0.904145
\(419\) −15.0711 −0.736270 −0.368135 0.929772i \(-0.620004\pi\)
−0.368135 + 0.929772i \(0.620004\pi\)
\(420\) 0 0
\(421\) −8.97056 −0.437198 −0.218599 0.975815i \(-0.570149\pi\)
−0.218599 + 0.975815i \(0.570149\pi\)
\(422\) 34.6274 1.68564
\(423\) −10.4142 −0.506356
\(424\) 19.3137 0.937957
\(425\) 2.75736 0.133752
\(426\) 14.2426 0.690058
\(427\) 0 0
\(428\) 0 0
\(429\) 15.0711 0.727638
\(430\) −24.1421 −1.16424
\(431\) 24.9289 1.20078 0.600392 0.799706i \(-0.295011\pi\)
0.600392 + 0.799706i \(0.295011\pi\)
\(432\) 4.00000 0.192450
\(433\) −5.48528 −0.263606 −0.131803 0.991276i \(-0.542077\pi\)
−0.131803 + 0.991276i \(0.542077\pi\)
\(434\) 0 0
\(435\) −20.7279 −0.993828
\(436\) 0 0
\(437\) −7.65685 −0.366277
\(438\) 14.5858 0.696936
\(439\) −2.97056 −0.141777 −0.0708886 0.997484i \(-0.522583\pi\)
−0.0708886 + 0.997484i \(0.522583\pi\)
\(440\) −23.3137 −1.11144
\(441\) 0 0
\(442\) 3.65685 0.173939
\(443\) −36.2843 −1.72392 −0.861959 0.506978i \(-0.830762\pi\)
−0.861959 + 0.506978i \(0.830762\pi\)
\(444\) 0 0
\(445\) −39.7990 −1.88665
\(446\) 14.6274 0.692628
\(447\) −17.3137 −0.818910
\(448\) 0 0
\(449\) 3.51472 0.165870 0.0829349 0.996555i \(-0.473571\pi\)
0.0829349 + 0.996555i \(0.473571\pi\)
\(450\) −9.41421 −0.443790
\(451\) 2.41421 0.113681
\(452\) 0 0
\(453\) 16.0000 0.751746
\(454\) 1.55635 0.0730431
\(455\) 0 0
\(456\) −15.3137 −0.717130
\(457\) −4.00000 −0.187112 −0.0935561 0.995614i \(-0.529823\pi\)
−0.0935561 + 0.995614i \(0.529823\pi\)
\(458\) −0.343146 −0.0160341
\(459\) −0.414214 −0.0193338
\(460\) 0 0
\(461\) −28.6274 −1.33331 −0.666656 0.745366i \(-0.732275\pi\)
−0.666656 + 0.745366i \(0.732275\pi\)
\(462\) 0 0
\(463\) −25.5563 −1.18770 −0.593852 0.804574i \(-0.702394\pi\)
−0.593852 + 0.804574i \(0.702394\pi\)
\(464\) 24.2843 1.12737
\(465\) 10.2426 0.474991
\(466\) 25.4558 1.17922
\(467\) 1.31371 0.0607912 0.0303956 0.999538i \(-0.490323\pi\)
0.0303956 + 0.999538i \(0.490323\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −50.2843 −2.31944
\(471\) 18.0000 0.829396
\(472\) 24.0000 1.10469
\(473\) −12.0711 −0.555028
\(474\) −10.8284 −0.497366
\(475\) 36.0416 1.65370
\(476\) 0 0
\(477\) 6.82843 0.312652
\(478\) −25.6569 −1.17352
\(479\) −6.89949 −0.315246 −0.157623 0.987499i \(-0.550383\pi\)
−0.157623 + 0.987499i \(0.550383\pi\)
\(480\) 0 0
\(481\) 59.2132 2.69989
\(482\) 13.4142 0.611001
\(483\) 0 0
\(484\) 0 0
\(485\) 26.4853 1.20263
\(486\) 1.41421 0.0641500
\(487\) 1.97056 0.0892947 0.0446474 0.999003i \(-0.485784\pi\)
0.0446474 + 0.999003i \(0.485784\pi\)
\(488\) 13.1716 0.596249
\(489\) 9.48528 0.428939
\(490\) 0 0
\(491\) −13.0711 −0.589889 −0.294945 0.955514i \(-0.595301\pi\)
−0.294945 + 0.955514i \(0.595301\pi\)
\(492\) 0 0
\(493\) −2.51472 −0.113257
\(494\) 47.7990 2.15058
\(495\) −8.24264 −0.370479
\(496\) −12.0000 −0.538816
\(497\) 0 0
\(498\) −1.51472 −0.0678762
\(499\) −19.5147 −0.873599 −0.436799 0.899559i \(-0.643888\pi\)
−0.436799 + 0.899559i \(0.643888\pi\)
\(500\) 0 0
\(501\) −3.65685 −0.163376
\(502\) 12.4853 0.557245
\(503\) −1.38478 −0.0617441 −0.0308721 0.999523i \(-0.509828\pi\)
−0.0308721 + 0.999523i \(0.509828\pi\)
\(504\) 0 0
\(505\) −1.41421 −0.0629317
\(506\) 4.82843 0.214650
\(507\) −25.9706 −1.15339
\(508\) 0 0
\(509\) −19.8701 −0.880725 −0.440362 0.897820i \(-0.645150\pi\)
−0.440362 + 0.897820i \(0.645150\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) 22.6274 1.00000
\(513\) −5.41421 −0.239043
\(514\) −7.21320 −0.318161
\(515\) 21.5563 0.949886
\(516\) 0 0
\(517\) −25.1421 −1.10575
\(518\) 0 0
\(519\) −9.07107 −0.398176
\(520\) 60.2843 2.64364
\(521\) −31.2426 −1.36876 −0.684382 0.729123i \(-0.739928\pi\)
−0.684382 + 0.729123i \(0.739928\pi\)
\(522\) 8.58579 0.375790
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) −3.41421 −0.148867
\(527\) 1.24264 0.0541303
\(528\) 9.65685 0.420261
\(529\) −21.0000 −0.913043
\(530\) 32.9706 1.43215
\(531\) 8.48528 0.368230
\(532\) 0 0
\(533\) −6.24264 −0.270399
\(534\) 16.4853 0.713388
\(535\) 1.17157 0.0506515
\(536\) 29.6569 1.28098
\(537\) 4.89949 0.211429
\(538\) −12.0000 −0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) −14.9706 −0.643635 −0.321817 0.946802i \(-0.604294\pi\)
−0.321817 + 0.946802i \(0.604294\pi\)
\(542\) 26.5858 1.14196
\(543\) −7.31371 −0.313861
\(544\) 0 0
\(545\) −26.9706 −1.15529
\(546\) 0 0
\(547\) −24.4853 −1.04692 −0.523458 0.852052i \(-0.675358\pi\)
−0.523458 + 0.852052i \(0.675358\pi\)
\(548\) 0 0
\(549\) 4.65685 0.198750
\(550\) −22.7279 −0.969122
\(551\) −32.8701 −1.40031
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) 38.5858 1.63935
\(555\) −32.3848 −1.37466
\(556\) 0 0
\(557\) 14.2721 0.604727 0.302364 0.953193i \(-0.402224\pi\)
0.302364 + 0.953193i \(0.402224\pi\)
\(558\) −4.24264 −0.179605
\(559\) 31.2132 1.32018
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) −24.5858 −1.03709
\(563\) −6.89949 −0.290779 −0.145390 0.989374i \(-0.546444\pi\)
−0.145390 + 0.989374i \(0.546444\pi\)
\(564\) 0 0
\(565\) −22.9706 −0.966379
\(566\) 22.8701 0.961300
\(567\) 0 0
\(568\) 28.4853 1.19522
\(569\) −4.44365 −0.186288 −0.0931438 0.995653i \(-0.529692\pi\)
−0.0931438 + 0.995653i \(0.529692\pi\)
\(570\) −26.1421 −1.09497
\(571\) −2.62742 −0.109954 −0.0549770 0.998488i \(-0.517509\pi\)
−0.0549770 + 0.998488i \(0.517509\pi\)
\(572\) 0 0
\(573\) −18.8284 −0.786569
\(574\) 0 0
\(575\) −9.41421 −0.392600
\(576\) 8.00000 0.333333
\(577\) 36.4853 1.51890 0.759451 0.650564i \(-0.225468\pi\)
0.759451 + 0.650564i \(0.225468\pi\)
\(578\) 23.7990 0.989907
\(579\) −0.585786 −0.0243445
\(580\) 0 0
\(581\) 0 0
\(582\) −10.9706 −0.454744
\(583\) 16.4853 0.682751
\(584\) 29.1716 1.20713
\(585\) 21.3137 0.881213
\(586\) 13.5563 0.560008
\(587\) 29.3848 1.21284 0.606420 0.795145i \(-0.292605\pi\)
0.606420 + 0.795145i \(0.292605\pi\)
\(588\) 0 0
\(589\) 16.2426 0.669266
\(590\) 40.9706 1.68673
\(591\) −22.2426 −0.914940
\(592\) 37.9411 1.55937
\(593\) −1.58579 −0.0651204 −0.0325602 0.999470i \(-0.510366\pi\)
−0.0325602 + 0.999470i \(0.510366\pi\)
\(594\) 3.41421 0.140087
\(595\) 0 0
\(596\) 0 0
\(597\) −16.2426 −0.664767
\(598\) −12.4853 −0.510561
\(599\) −35.3553 −1.44458 −0.722290 0.691590i \(-0.756910\pi\)
−0.722290 + 0.691590i \(0.756910\pi\)
\(600\) −18.8284 −0.768667
\(601\) 26.4853 1.08036 0.540179 0.841550i \(-0.318357\pi\)
0.540179 + 0.841550i \(0.318357\pi\)
\(602\) 0 0
\(603\) 10.4853 0.426994
\(604\) 0 0
\(605\) 17.6569 0.717853
\(606\) 0.585786 0.0237959
\(607\) 34.4853 1.39971 0.699857 0.714283i \(-0.253247\pi\)
0.699857 + 0.714283i \(0.253247\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 22.4853 0.910402
\(611\) 65.0122 2.63011
\(612\) 0 0
\(613\) 19.3137 0.780073 0.390037 0.920799i \(-0.372462\pi\)
0.390037 + 0.920799i \(0.372462\pi\)
\(614\) −0.443651 −0.0179043
\(615\) 3.41421 0.137674
\(616\) 0 0
\(617\) −15.2132 −0.612461 −0.306230 0.951957i \(-0.599068\pi\)
−0.306230 + 0.951957i \(0.599068\pi\)
\(618\) −8.92893 −0.359174
\(619\) 10.3137 0.414543 0.207271 0.978283i \(-0.433542\pi\)
0.207271 + 0.978283i \(0.433542\pi\)
\(620\) 0 0
\(621\) 1.41421 0.0567504
\(622\) 37.9411 1.52130
\(623\) 0 0
\(624\) −24.9706 −0.999623
\(625\) −13.9706 −0.558823
\(626\) −40.8284 −1.63183
\(627\) −13.0711 −0.522008
\(628\) 0 0
\(629\) −3.92893 −0.156657
\(630\) 0 0
\(631\) −28.4558 −1.13281 −0.566405 0.824127i \(-0.691666\pi\)
−0.566405 + 0.824127i \(0.691666\pi\)
\(632\) −21.6569 −0.861463
\(633\) 24.4853 0.973203
\(634\) 17.0711 0.677979
\(635\) −31.7990 −1.26190
\(636\) 0 0
\(637\) 0 0
\(638\) 20.7279 0.820626
\(639\) 10.0711 0.398405
\(640\) 38.6274 1.52688
\(641\) −8.55635 −0.337955 −0.168978 0.985620i \(-0.554047\pi\)
−0.168978 + 0.985620i \(0.554047\pi\)
\(642\) −0.485281 −0.0191525
\(643\) −37.4558 −1.47711 −0.738557 0.674191i \(-0.764493\pi\)
−0.738557 + 0.674191i \(0.764493\pi\)
\(644\) 0 0
\(645\) −17.0711 −0.672173
\(646\) −3.17157 −0.124784
\(647\) 23.5563 0.926096 0.463048 0.886333i \(-0.346756\pi\)
0.463048 + 0.886333i \(0.346756\pi\)
\(648\) 2.82843 0.111111
\(649\) 20.4853 0.804118
\(650\) 58.7696 2.30513
\(651\) 0 0
\(652\) 0 0
\(653\) −6.89949 −0.269998 −0.134999 0.990846i \(-0.543103\pi\)
−0.134999 + 0.990846i \(0.543103\pi\)
\(654\) 11.1716 0.436843
\(655\) −36.1421 −1.41219
\(656\) −4.00000 −0.156174
\(657\) 10.3137 0.402376
\(658\) 0 0
\(659\) −34.8284 −1.35672 −0.678361 0.734728i \(-0.737310\pi\)
−0.678361 + 0.734728i \(0.737310\pi\)
\(660\) 0 0
\(661\) −13.4558 −0.523372 −0.261686 0.965153i \(-0.584278\pi\)
−0.261686 + 0.965153i \(0.584278\pi\)
\(662\) −22.9706 −0.892776
\(663\) 2.58579 0.100424
\(664\) −3.02944 −0.117565
\(665\) 0 0
\(666\) 13.4142 0.519790
\(667\) 8.58579 0.332443
\(668\) 0 0
\(669\) 10.3431 0.399889
\(670\) 50.6274 1.95591
\(671\) 11.2426 0.434017
\(672\) 0 0
\(673\) 21.7990 0.840289 0.420145 0.907457i \(-0.361979\pi\)
0.420145 + 0.907457i \(0.361979\pi\)
\(674\) −28.2426 −1.08787
\(675\) −6.65685 −0.256222
\(676\) 0 0
\(677\) −33.5563 −1.28968 −0.644838 0.764320i \(-0.723075\pi\)
−0.644838 + 0.764320i \(0.723075\pi\)
\(678\) 9.51472 0.365411
\(679\) 0 0
\(680\) −4.00000 −0.153393
\(681\) 1.10051 0.0421714
\(682\) −10.2426 −0.392211
\(683\) −6.28427 −0.240461 −0.120230 0.992746i \(-0.538363\pi\)
−0.120230 + 0.992746i \(0.538363\pi\)
\(684\) 0 0
\(685\) −13.4142 −0.512531
\(686\) 0 0
\(687\) −0.242641 −0.00925732
\(688\) 20.0000 0.762493
\(689\) −42.6274 −1.62398
\(690\) 6.82843 0.259954
\(691\) −10.7279 −0.408109 −0.204055 0.978959i \(-0.565412\pi\)
−0.204055 + 0.978959i \(0.565412\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.27208 −0.0482874
\(695\) 12.4853 0.473594
\(696\) 17.1716 0.650887
\(697\) 0.414214 0.0156895
\(698\) 12.9289 0.489367
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −45.7990 −1.72980 −0.864902 0.501941i \(-0.832620\pi\)
−0.864902 + 0.501941i \(0.832620\pi\)
\(702\) −8.82843 −0.333208
\(703\) −51.3553 −1.93690
\(704\) 19.3137 0.727913
\(705\) −35.5563 −1.33913
\(706\) −49.4558 −1.86130
\(707\) 0 0
\(708\) 0 0
\(709\) −30.4853 −1.14490 −0.572449 0.819940i \(-0.694007\pi\)
−0.572449 + 0.819940i \(0.694007\pi\)
\(710\) 48.6274 1.82495
\(711\) −7.65685 −0.287154
\(712\) 32.9706 1.23562
\(713\) −4.24264 −0.158888
\(714\) 0 0
\(715\) 51.4558 1.92434
\(716\) 0 0
\(717\) −18.1421 −0.677530
\(718\) −22.9706 −0.857254
\(719\) −40.5563 −1.51250 −0.756248 0.654285i \(-0.772970\pi\)
−0.756248 + 0.654285i \(0.772970\pi\)
\(720\) 13.6569 0.508961
\(721\) 0 0
\(722\) −14.5858 −0.542827
\(723\) 9.48528 0.352761
\(724\) 0 0
\(725\) −40.4142 −1.50095
\(726\) −7.31371 −0.271437
\(727\) 32.7279 1.21381 0.606906 0.794774i \(-0.292411\pi\)
0.606906 + 0.794774i \(0.292411\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 49.7990 1.84314
\(731\) −2.07107 −0.0766012
\(732\) 0 0
\(733\) 31.1421 1.15026 0.575131 0.818062i \(-0.304951\pi\)
0.575131 + 0.818062i \(0.304951\pi\)
\(734\) −9.41421 −0.347485
\(735\) 0 0
\(736\) 0 0
\(737\) 25.3137 0.932442
\(738\) −1.41421 −0.0520579
\(739\) 22.6569 0.833446 0.416723 0.909034i \(-0.363179\pi\)
0.416723 + 0.909034i \(0.363179\pi\)
\(740\) 0 0
\(741\) 33.7990 1.24164
\(742\) 0 0
\(743\) 16.6274 0.610001 0.305000 0.952352i \(-0.401343\pi\)
0.305000 + 0.952352i \(0.401343\pi\)
\(744\) −8.48528 −0.311086
\(745\) −59.1127 −2.16572
\(746\) −46.8701 −1.71603
\(747\) −1.07107 −0.0391883
\(748\) 0 0
\(749\) 0 0
\(750\) −8.00000 −0.292119
\(751\) 34.9706 1.27609 0.638047 0.769997i \(-0.279743\pi\)
0.638047 + 0.769997i \(0.279743\pi\)
\(752\) 41.6569 1.51907
\(753\) 8.82843 0.321726
\(754\) −53.5980 −1.95192
\(755\) 54.6274 1.98810
\(756\) 0 0
\(757\) 8.24264 0.299584 0.149792 0.988718i \(-0.452140\pi\)
0.149792 + 0.988718i \(0.452140\pi\)
\(758\) −38.1421 −1.38538
\(759\) 3.41421 0.123928
\(760\) −52.2843 −1.89655
\(761\) −14.8284 −0.537530 −0.268765 0.963206i \(-0.586616\pi\)
−0.268765 + 0.963206i \(0.586616\pi\)
\(762\) 13.1716 0.477156
\(763\) 0 0
\(764\) 0 0
\(765\) −1.41421 −0.0511310
\(766\) 24.1838 0.873795
\(767\) −52.9706 −1.91266
\(768\) 0 0
\(769\) 33.4853 1.20751 0.603755 0.797170i \(-0.293670\pi\)
0.603755 + 0.797170i \(0.293670\pi\)
\(770\) 0 0
\(771\) −5.10051 −0.183690
\(772\) 0 0
\(773\) −50.4142 −1.81327 −0.906637 0.421912i \(-0.861359\pi\)
−0.906637 + 0.421912i \(0.861359\pi\)
\(774\) 7.07107 0.254164
\(775\) 19.9706 0.717364
\(776\) −21.9411 −0.787641
\(777\) 0 0
\(778\) 31.4558 1.12775
\(779\) 5.41421 0.193984
\(780\) 0 0
\(781\) 24.3137 0.870013
\(782\) 0.828427 0.0296245
\(783\) 6.07107 0.216962
\(784\) 0 0
\(785\) 61.4558 2.19345
\(786\) 14.9706 0.533982
\(787\) 13.9706 0.497997 0.248998 0.968504i \(-0.419899\pi\)
0.248998 + 0.968504i \(0.419899\pi\)
\(788\) 0 0
\(789\) −2.41421 −0.0859483
\(790\) −36.9706 −1.31535
\(791\) 0 0
\(792\) 6.82843 0.242638
\(793\) −29.0711 −1.03234
\(794\) 43.1716 1.53210
\(795\) 23.3137 0.826852
\(796\) 0 0
\(797\) 44.1421 1.56359 0.781797 0.623533i \(-0.214303\pi\)
0.781797 + 0.623533i \(0.214303\pi\)
\(798\) 0 0
\(799\) −4.31371 −0.152608
\(800\) 0 0
\(801\) 11.6569 0.411875
\(802\) −15.0294 −0.530708
\(803\) 24.8995 0.878684
\(804\) 0 0
\(805\) 0 0
\(806\) 26.4853 0.932904
\(807\) −8.48528 −0.298696
\(808\) 1.17157 0.0412158
\(809\) 25.1127 0.882915 0.441458 0.897282i \(-0.354462\pi\)
0.441458 + 0.897282i \(0.354462\pi\)
\(810\) 4.82843 0.169654
\(811\) 17.9706 0.631032 0.315516 0.948920i \(-0.397822\pi\)
0.315516 + 0.948920i \(0.397822\pi\)
\(812\) 0 0
\(813\) 18.7990 0.659309
\(814\) 32.3848 1.13509
\(815\) 32.3848 1.13439
\(816\) 1.65685 0.0580015
\(817\) −27.0711 −0.947097
\(818\) 22.8701 0.799633
\(819\) 0 0
\(820\) 0 0
\(821\) −38.8701 −1.35657 −0.678287 0.734797i \(-0.737277\pi\)
−0.678287 + 0.734797i \(0.737277\pi\)
\(822\) 5.55635 0.193800
\(823\) 32.4264 1.13031 0.565157 0.824984i \(-0.308816\pi\)
0.565157 + 0.824984i \(0.308816\pi\)
\(824\) −17.8579 −0.622108
\(825\) −16.0711 −0.559523
\(826\) 0 0
\(827\) 7.92893 0.275716 0.137858 0.990452i \(-0.455978\pi\)
0.137858 + 0.990452i \(0.455978\pi\)
\(828\) 0 0
\(829\) 24.9411 0.866241 0.433121 0.901336i \(-0.357412\pi\)
0.433121 + 0.901336i \(0.357412\pi\)
\(830\) −5.17157 −0.179508
\(831\) 27.2843 0.946481
\(832\) −49.9411 −1.73140
\(833\) 0 0
\(834\) −5.17157 −0.179077
\(835\) −12.4853 −0.432071
\(836\) 0 0
\(837\) −3.00000 −0.103695
\(838\) 21.3137 0.736270
\(839\) 22.8284 0.788125 0.394062 0.919084i \(-0.371069\pi\)
0.394062 + 0.919084i \(0.371069\pi\)
\(840\) 0 0
\(841\) 7.85786 0.270961
\(842\) 12.6863 0.437198
\(843\) −17.3848 −0.598764
\(844\) 0 0
\(845\) −88.6690 −3.05031
\(846\) 14.7279 0.506356
\(847\) 0 0
\(848\) −27.3137 −0.937957
\(849\) 16.1716 0.555007
\(850\) −3.89949 −0.133752
\(851\) 13.4142 0.459833
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) −18.4853 −0.632183
\(856\) −0.970563 −0.0331732
\(857\) −51.7990 −1.76942 −0.884710 0.466142i \(-0.845644\pi\)
−0.884710 + 0.466142i \(0.845644\pi\)
\(858\) −21.3137 −0.727638
\(859\) −16.6569 −0.568325 −0.284162 0.958776i \(-0.591715\pi\)
−0.284162 + 0.958776i \(0.591715\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −35.2548 −1.20078
\(863\) 25.0711 0.853429 0.426715 0.904386i \(-0.359671\pi\)
0.426715 + 0.904386i \(0.359671\pi\)
\(864\) 0 0
\(865\) −30.9706 −1.05303
\(866\) 7.75736 0.263606
\(867\) 16.8284 0.571523
\(868\) 0 0
\(869\) −18.4853 −0.627070
\(870\) 29.3137 0.993828
\(871\) −65.4558 −2.21789
\(872\) 22.3431 0.756634
\(873\) −7.75736 −0.262547
\(874\) 10.8284 0.366277
\(875\) 0 0
\(876\) 0 0
\(877\) −27.1421 −0.916525 −0.458262 0.888817i \(-0.651528\pi\)
−0.458262 + 0.888817i \(0.651528\pi\)
\(878\) 4.20101 0.141777
\(879\) 9.58579 0.323321
\(880\) 32.9706 1.11144
\(881\) 42.6274 1.43615 0.718077 0.695964i \(-0.245023\pi\)
0.718077 + 0.695964i \(0.245023\pi\)
\(882\) 0 0
\(883\) −9.41421 −0.316814 −0.158407 0.987374i \(-0.550636\pi\)
−0.158407 + 0.987374i \(0.550636\pi\)
\(884\) 0 0
\(885\) 28.9706 0.973835
\(886\) 51.3137 1.72392
\(887\) −36.0122 −1.20917 −0.604586 0.796540i \(-0.706661\pi\)
−0.604586 + 0.796540i \(0.706661\pi\)
\(888\) 26.8284 0.900303
\(889\) 0 0
\(890\) 56.2843 1.88665
\(891\) 2.41421 0.0808792
\(892\) 0 0
\(893\) −56.3848 −1.88684
\(894\) 24.4853 0.818910
\(895\) 16.7279 0.559153
\(896\) 0 0
\(897\) −8.82843 −0.294773
\(898\) −4.97056 −0.165870
\(899\) −18.2132 −0.607444
\(900\) 0 0
\(901\) 2.82843 0.0942286
\(902\) −3.41421 −0.113681
\(903\) 0 0
\(904\) 19.0294 0.632910
\(905\) −24.9706 −0.830050
\(906\) −22.6274 −0.751746
\(907\) 15.6569 0.519877 0.259939 0.965625i \(-0.416298\pi\)
0.259939 + 0.965625i \(0.416298\pi\)
\(908\) 0 0
\(909\) 0.414214 0.0137386
\(910\) 0 0
\(911\) 34.1005 1.12980 0.564900 0.825159i \(-0.308915\pi\)
0.564900 + 0.825159i \(0.308915\pi\)
\(912\) 21.6569 0.717130
\(913\) −2.58579 −0.0855770
\(914\) 5.65685 0.187112
\(915\) 15.8995 0.525621
\(916\) 0 0
\(917\) 0 0
\(918\) 0.585786 0.0193338
\(919\) −15.4142 −0.508468 −0.254234 0.967143i \(-0.581823\pi\)
−0.254234 + 0.967143i \(0.581823\pi\)
\(920\) 13.6569 0.450253
\(921\) −0.313708 −0.0103370
\(922\) 40.4853 1.33331
\(923\) −62.8701 −2.06939
\(924\) 0 0
\(925\) −63.1421 −2.07610
\(926\) 36.1421 1.18770
\(927\) −6.31371 −0.207369
\(928\) 0 0
\(929\) 7.87006 0.258208 0.129104 0.991631i \(-0.458790\pi\)
0.129104 + 0.991631i \(0.458790\pi\)
\(930\) −14.4853 −0.474991
\(931\) 0 0
\(932\) 0 0
\(933\) 26.8284 0.878323
\(934\) −1.85786 −0.0607912
\(935\) −3.41421 −0.111657
\(936\) −17.6569 −0.577132
\(937\) −52.9706 −1.73047 −0.865236 0.501364i \(-0.832832\pi\)
−0.865236 + 0.501364i \(0.832832\pi\)
\(938\) 0 0
\(939\) −28.8701 −0.942139
\(940\) 0 0
\(941\) 52.6274 1.71560 0.857802 0.513980i \(-0.171829\pi\)
0.857802 + 0.513980i \(0.171829\pi\)
\(942\) −25.4558 −0.829396
\(943\) −1.41421 −0.0460531
\(944\) −33.9411 −1.10469
\(945\) 0 0
\(946\) 17.0711 0.555028
\(947\) 21.5980 0.701840 0.350920 0.936405i \(-0.385869\pi\)
0.350920 + 0.936405i \(0.385869\pi\)
\(948\) 0 0
\(949\) −64.3848 −2.09002
\(950\) −50.9706 −1.65370
\(951\) 12.0711 0.391431
\(952\) 0 0
\(953\) −41.6985 −1.35075 −0.675373 0.737476i \(-0.736017\pi\)
−0.675373 + 0.737476i \(0.736017\pi\)
\(954\) −9.65685 −0.312652
\(955\) −64.2843 −2.08019
\(956\) 0 0
\(957\) 14.6569 0.473789
\(958\) 9.75736 0.315246
\(959\) 0 0
\(960\) 27.3137 0.881546
\(961\) −22.0000 −0.709677
\(962\) −83.7401 −2.69989
\(963\) −0.343146 −0.0110577
\(964\) 0 0
\(965\) −2.00000 −0.0643823
\(966\) 0 0
\(967\) −1.02944 −0.0331045 −0.0165522 0.999863i \(-0.505269\pi\)
−0.0165522 + 0.999863i \(0.505269\pi\)
\(968\) −14.6274 −0.470143
\(969\) −2.24264 −0.0720440
\(970\) −37.4558 −1.20263
\(971\) −40.5563 −1.30152 −0.650758 0.759286i \(-0.725549\pi\)
−0.650758 + 0.759286i \(0.725549\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −2.78680 −0.0892947
\(975\) 41.5563 1.33087
\(976\) −18.6274 −0.596249
\(977\) 7.58579 0.242691 0.121345 0.992610i \(-0.461279\pi\)
0.121345 + 0.992610i \(0.461279\pi\)
\(978\) −13.4142 −0.428939
\(979\) 28.1421 0.899427
\(980\) 0 0
\(981\) 7.89949 0.252211
\(982\) 18.4853 0.589889
\(983\) 22.9289 0.731319 0.365660 0.930749i \(-0.380843\pi\)
0.365660 + 0.930749i \(0.380843\pi\)
\(984\) −2.82843 −0.0901670
\(985\) −75.9411 −2.41969
\(986\) 3.55635 0.113257
\(987\) 0 0
\(988\) 0 0
\(989\) 7.07107 0.224847
\(990\) 11.6569 0.370479
\(991\) −28.4853 −0.904865 −0.452432 0.891799i \(-0.649444\pi\)
−0.452432 + 0.891799i \(0.649444\pi\)
\(992\) 0 0
\(993\) −16.2426 −0.515445
\(994\) 0 0
\(995\) −55.4558 −1.75807
\(996\) 0 0
\(997\) −15.4142 −0.488173 −0.244087 0.969753i \(-0.578488\pi\)
−0.244087 + 0.969753i \(0.578488\pi\)
\(998\) 27.5980 0.873599
\(999\) 9.48528 0.300101
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 \(a_p\))