Properties

Label 6027.2.a.y.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
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: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
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 1.3
Root \(1.19009\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.190092 q^{2} -1.00000 q^{3} -1.96387 q^{4} -2.28332 q^{5} +0.190092 q^{6} +0.753499 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.190092 q^{2} -1.00000 q^{3} -1.96387 q^{4} -2.28332 q^{5} +0.190092 q^{6} +0.753499 q^{8} +1.00000 q^{9} +0.434041 q^{10} +1.72995 q^{11} +1.96387 q^{12} -1.61662 q^{13} +2.28332 q^{15} +3.78450 q^{16} +3.96707 q^{17} -0.190092 q^{18} -1.10774 q^{19} +4.48414 q^{20} -0.328850 q^{22} -2.20725 q^{23} -0.753499 q^{24} +0.213562 q^{25} +0.307306 q^{26} -1.00000 q^{27} +7.83771 q^{29} -0.434041 q^{30} -3.24019 q^{31} -2.22640 q^{32} -1.72995 q^{33} -0.754109 q^{34} -1.96387 q^{36} +1.90046 q^{37} +0.210573 q^{38} +1.61662 q^{39} -1.72048 q^{40} -1.00000 q^{41} +2.91253 q^{43} -3.39739 q^{44} -2.28332 q^{45} +0.419580 q^{46} -5.86193 q^{47} -3.78450 q^{48} -0.0405965 q^{50} -3.96707 q^{51} +3.17482 q^{52} -2.97657 q^{53} +0.190092 q^{54} -3.95004 q^{55} +1.10774 q^{57} -1.48989 q^{58} -5.61410 q^{59} -4.48414 q^{60} -4.86425 q^{61} +0.615934 q^{62} -7.14577 q^{64} +3.69127 q^{65} +0.328850 q^{66} -13.1894 q^{67} -7.79080 q^{68} +2.20725 q^{69} +11.1166 q^{71} +0.753499 q^{72} +0.406178 q^{73} -0.361261 q^{74} -0.213562 q^{75} +2.17546 q^{76} -0.307306 q^{78} -2.23080 q^{79} -8.64123 q^{80} +1.00000 q^{81} +0.190092 q^{82} +1.25842 q^{83} -9.05811 q^{85} -0.553649 q^{86} -7.83771 q^{87} +1.30352 q^{88} -8.84330 q^{89} +0.434041 q^{90} +4.33474 q^{92} +3.24019 q^{93} +1.11431 q^{94} +2.52934 q^{95} +2.22640 q^{96} +18.9259 q^{97} +1.72995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190092 −0.134415 −0.0672077 0.997739i \(-0.521409\pi\)
−0.0672077 + 0.997739i \(0.521409\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.96387 −0.981933
\(5\) −2.28332 −1.02113 −0.510566 0.859838i \(-0.670564\pi\)
−0.510566 + 0.859838i \(0.670564\pi\)
\(6\) 0.190092 0.0776047
\(7\) 0 0
\(8\) 0.753499 0.266402
\(9\) 1.00000 0.333333
\(10\) 0.434041 0.137256
\(11\) 1.72995 0.521600 0.260800 0.965393i \(-0.416014\pi\)
0.260800 + 0.965393i \(0.416014\pi\)
\(12\) 1.96387 0.566919
\(13\) −1.61662 −0.448370 −0.224185 0.974547i \(-0.571972\pi\)
−0.224185 + 0.974547i \(0.571972\pi\)
\(14\) 0 0
\(15\) 2.28332 0.589551
\(16\) 3.78450 0.946124
\(17\) 3.96707 0.962157 0.481079 0.876678i \(-0.340245\pi\)
0.481079 + 0.876678i \(0.340245\pi\)
\(18\) −0.190092 −0.0448051
\(19\) −1.10774 −0.254134 −0.127067 0.991894i \(-0.540556\pi\)
−0.127067 + 0.991894i \(0.540556\pi\)
\(20\) 4.48414 1.00268
\(21\) 0 0
\(22\) −0.328850 −0.0701111
\(23\) −2.20725 −0.460243 −0.230122 0.973162i \(-0.573912\pi\)
−0.230122 + 0.973162i \(0.573912\pi\)
\(24\) −0.753499 −0.153807
\(25\) 0.213562 0.0427124
\(26\) 0.307306 0.0602678
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 7.83771 1.45543 0.727713 0.685882i \(-0.240583\pi\)
0.727713 + 0.685882i \(0.240583\pi\)
\(30\) −0.434041 −0.0792447
\(31\) −3.24019 −0.581955 −0.290977 0.956730i \(-0.593980\pi\)
−0.290977 + 0.956730i \(0.593980\pi\)
\(32\) −2.22640 −0.393576
\(33\) −1.72995 −0.301146
\(34\) −0.754109 −0.129329
\(35\) 0 0
\(36\) −1.96387 −0.327311
\(37\) 1.90046 0.312433 0.156217 0.987723i \(-0.450070\pi\)
0.156217 + 0.987723i \(0.450070\pi\)
\(38\) 0.210573 0.0341595
\(39\) 1.61662 0.258866
\(40\) −1.72048 −0.272032
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 2.91253 0.444157 0.222078 0.975029i \(-0.428716\pi\)
0.222078 + 0.975029i \(0.428716\pi\)
\(44\) −3.39739 −0.512176
\(45\) −2.28332 −0.340378
\(46\) 0.419580 0.0618637
\(47\) −5.86193 −0.855050 −0.427525 0.904003i \(-0.640614\pi\)
−0.427525 + 0.904003i \(0.640614\pi\)
\(48\) −3.78450 −0.546245
\(49\) 0 0
\(50\) −0.0405965 −0.00574121
\(51\) −3.96707 −0.555502
\(52\) 3.17482 0.440269
\(53\) −2.97657 −0.408864 −0.204432 0.978881i \(-0.565535\pi\)
−0.204432 + 0.978881i \(0.565535\pi\)
\(54\) 0.190092 0.0258682
\(55\) −3.95004 −0.532623
\(56\) 0 0
\(57\) 1.10774 0.146724
\(58\) −1.48989 −0.195632
\(59\) −5.61410 −0.730893 −0.365447 0.930832i \(-0.619084\pi\)
−0.365447 + 0.930832i \(0.619084\pi\)
\(60\) −4.48414 −0.578900
\(61\) −4.86425 −0.622803 −0.311401 0.950278i \(-0.600798\pi\)
−0.311401 + 0.950278i \(0.600798\pi\)
\(62\) 0.615934 0.0782237
\(63\) 0 0
\(64\) −7.14577 −0.893221
\(65\) 3.69127 0.457845
\(66\) 0.328850 0.0404786
\(67\) −13.1894 −1.61134 −0.805672 0.592362i \(-0.798195\pi\)
−0.805672 + 0.592362i \(0.798195\pi\)
\(68\) −7.79080 −0.944773
\(69\) 2.20725 0.265722
\(70\) 0 0
\(71\) 11.1166 1.31930 0.659648 0.751575i \(-0.270705\pi\)
0.659648 + 0.751575i \(0.270705\pi\)
\(72\) 0.753499 0.0888007
\(73\) 0.406178 0.0475395 0.0237697 0.999717i \(-0.492433\pi\)
0.0237697 + 0.999717i \(0.492433\pi\)
\(74\) −0.361261 −0.0419958
\(75\) −0.213562 −0.0246600
\(76\) 2.17546 0.249542
\(77\) 0 0
\(78\) −0.307306 −0.0347956
\(79\) −2.23080 −0.250984 −0.125492 0.992095i \(-0.540051\pi\)
−0.125492 + 0.992095i \(0.540051\pi\)
\(80\) −8.64123 −0.966118
\(81\) 1.00000 0.111111
\(82\) 0.190092 0.0209921
\(83\) 1.25842 0.138129 0.0690646 0.997612i \(-0.477999\pi\)
0.0690646 + 0.997612i \(0.477999\pi\)
\(84\) 0 0
\(85\) −9.05811 −0.982490
\(86\) −0.553649 −0.0597015
\(87\) −7.83771 −0.840291
\(88\) 1.30352 0.138955
\(89\) −8.84330 −0.937388 −0.468694 0.883361i \(-0.655275\pi\)
−0.468694 + 0.883361i \(0.655275\pi\)
\(90\) 0.434041 0.0457520
\(91\) 0 0
\(92\) 4.33474 0.451928
\(93\) 3.24019 0.335992
\(94\) 1.11431 0.114932
\(95\) 2.52934 0.259504
\(96\) 2.22640 0.227231
\(97\) 18.9259 1.92163 0.960816 0.277187i \(-0.0894022\pi\)
0.960816 + 0.277187i \(0.0894022\pi\)
\(98\) 0 0
\(99\) 1.72995 0.173867
\(100\) −0.419407 −0.0419407
\(101\) −2.37750 −0.236570 −0.118285 0.992980i \(-0.537740\pi\)
−0.118285 + 0.992980i \(0.537740\pi\)
\(102\) 0.754109 0.0746679
\(103\) −1.27186 −0.125321 −0.0626603 0.998035i \(-0.519958\pi\)
−0.0626603 + 0.998035i \(0.519958\pi\)
\(104\) −1.21812 −0.119447
\(105\) 0 0
\(106\) 0.565823 0.0549576
\(107\) −15.4694 −1.49548 −0.747742 0.663989i \(-0.768862\pi\)
−0.747742 + 0.663989i \(0.768862\pi\)
\(108\) 1.96387 0.188973
\(109\) −5.96439 −0.571285 −0.285643 0.958336i \(-0.592207\pi\)
−0.285643 + 0.958336i \(0.592207\pi\)
\(110\) 0.750871 0.0715927
\(111\) −1.90046 −0.180383
\(112\) 0 0
\(113\) 9.73825 0.916097 0.458049 0.888927i \(-0.348549\pi\)
0.458049 + 0.888927i \(0.348549\pi\)
\(114\) −0.210573 −0.0197220
\(115\) 5.03986 0.469970
\(116\) −15.3922 −1.42913
\(117\) −1.61662 −0.149457
\(118\) 1.06719 0.0982432
\(119\) 0 0
\(120\) 1.72048 0.157058
\(121\) −8.00727 −0.727933
\(122\) 0.924654 0.0837142
\(123\) 1.00000 0.0901670
\(124\) 6.36329 0.571441
\(125\) 10.9290 0.977518
\(126\) 0 0
\(127\) −4.74582 −0.421124 −0.210562 0.977581i \(-0.567529\pi\)
−0.210562 + 0.977581i \(0.567529\pi\)
\(128\) 5.81115 0.513638
\(129\) −2.91253 −0.256434
\(130\) −0.701680 −0.0615414
\(131\) −3.47647 −0.303740 −0.151870 0.988400i \(-0.548530\pi\)
−0.151870 + 0.988400i \(0.548530\pi\)
\(132\) 3.39739 0.295705
\(133\) 0 0
\(134\) 2.50720 0.216589
\(135\) 2.28332 0.196517
\(136\) 2.98919 0.256321
\(137\) −8.28210 −0.707587 −0.353794 0.935324i \(-0.615108\pi\)
−0.353794 + 0.935324i \(0.615108\pi\)
\(138\) −0.419580 −0.0357170
\(139\) 6.78978 0.575902 0.287951 0.957645i \(-0.407026\pi\)
0.287951 + 0.957645i \(0.407026\pi\)
\(140\) 0 0
\(141\) 5.86193 0.493663
\(142\) −2.11317 −0.177334
\(143\) −2.79668 −0.233870
\(144\) 3.78450 0.315375
\(145\) −17.8960 −1.48618
\(146\) −0.0772111 −0.00639004
\(147\) 0 0
\(148\) −3.73224 −0.306788
\(149\) −4.76826 −0.390631 −0.195316 0.980740i \(-0.562573\pi\)
−0.195316 + 0.980740i \(0.562573\pi\)
\(150\) 0.0405965 0.00331469
\(151\) −7.61766 −0.619917 −0.309958 0.950750i \(-0.600315\pi\)
−0.309958 + 0.950750i \(0.600315\pi\)
\(152\) −0.834683 −0.0677017
\(153\) 3.96707 0.320719
\(154\) 0 0
\(155\) 7.39840 0.594253
\(156\) −3.17482 −0.254189
\(157\) 12.4677 0.995031 0.497515 0.867455i \(-0.334246\pi\)
0.497515 + 0.867455i \(0.334246\pi\)
\(158\) 0.424056 0.0337361
\(159\) 2.97657 0.236058
\(160\) 5.08359 0.401893
\(161\) 0 0
\(162\) −0.190092 −0.0149350
\(163\) 22.2666 1.74406 0.872028 0.489457i \(-0.162805\pi\)
0.872028 + 0.489457i \(0.162805\pi\)
\(164\) 1.96387 0.153352
\(165\) 3.95004 0.307510
\(166\) −0.239215 −0.0185667
\(167\) −14.3144 −1.10768 −0.553842 0.832622i \(-0.686839\pi\)
−0.553842 + 0.832622i \(0.686839\pi\)
\(168\) 0 0
\(169\) −10.3865 −0.798965
\(170\) 1.72187 0.132062
\(171\) −1.10774 −0.0847112
\(172\) −5.71982 −0.436132
\(173\) 8.70139 0.661554 0.330777 0.943709i \(-0.392689\pi\)
0.330777 + 0.943709i \(0.392689\pi\)
\(174\) 1.48989 0.112948
\(175\) 0 0
\(176\) 6.54700 0.493498
\(177\) 5.61410 0.421981
\(178\) 1.68104 0.125999
\(179\) −2.03988 −0.152468 −0.0762341 0.997090i \(-0.524290\pi\)
−0.0762341 + 0.997090i \(0.524290\pi\)
\(180\) 4.48414 0.334228
\(181\) 20.5069 1.52427 0.762133 0.647421i \(-0.224152\pi\)
0.762133 + 0.647421i \(0.224152\pi\)
\(182\) 0 0
\(183\) 4.86425 0.359575
\(184\) −1.66316 −0.122610
\(185\) −4.33935 −0.319036
\(186\) −0.615934 −0.0451624
\(187\) 6.86285 0.501861
\(188\) 11.5120 0.839602
\(189\) 0 0
\(190\) −0.480806 −0.0348813
\(191\) 10.2243 0.739803 0.369902 0.929071i \(-0.379391\pi\)
0.369902 + 0.929071i \(0.379391\pi\)
\(192\) 7.14577 0.515702
\(193\) 21.1438 1.52196 0.760982 0.648773i \(-0.224718\pi\)
0.760982 + 0.648773i \(0.224718\pi\)
\(194\) −3.59766 −0.258297
\(195\) −3.69127 −0.264337
\(196\) 0 0
\(197\) −15.1685 −1.08071 −0.540355 0.841437i \(-0.681710\pi\)
−0.540355 + 0.841437i \(0.681710\pi\)
\(198\) −0.328850 −0.0233704
\(199\) 7.99926 0.567053 0.283526 0.958964i \(-0.408496\pi\)
0.283526 + 0.958964i \(0.408496\pi\)
\(200\) 0.160919 0.0113787
\(201\) 13.1894 0.930310
\(202\) 0.451944 0.0317987
\(203\) 0 0
\(204\) 7.79080 0.545465
\(205\) 2.28332 0.159474
\(206\) 0.241771 0.0168450
\(207\) −2.20725 −0.153414
\(208\) −6.11809 −0.424213
\(209\) −1.91634 −0.132556
\(210\) 0 0
\(211\) −18.1670 −1.25067 −0.625335 0.780356i \(-0.715038\pi\)
−0.625335 + 0.780356i \(0.715038\pi\)
\(212\) 5.84559 0.401477
\(213\) −11.1166 −0.761696
\(214\) 2.94061 0.201016
\(215\) −6.65025 −0.453543
\(216\) −0.753499 −0.0512691
\(217\) 0 0
\(218\) 1.13378 0.0767895
\(219\) −0.406178 −0.0274469
\(220\) 7.75734 0.523000
\(221\) −6.41325 −0.431402
\(222\) 0.361261 0.0242463
\(223\) 15.1901 1.01720 0.508601 0.861002i \(-0.330163\pi\)
0.508601 + 0.861002i \(0.330163\pi\)
\(224\) 0 0
\(225\) 0.213562 0.0142375
\(226\) −1.85116 −0.123138
\(227\) 11.3294 0.751958 0.375979 0.926628i \(-0.377307\pi\)
0.375979 + 0.926628i \(0.377307\pi\)
\(228\) −2.17546 −0.144073
\(229\) 16.3760 1.08216 0.541079 0.840972i \(-0.318016\pi\)
0.541079 + 0.840972i \(0.318016\pi\)
\(230\) −0.958037 −0.0631711
\(231\) 0 0
\(232\) 5.90570 0.387729
\(233\) −2.40958 −0.157857 −0.0789284 0.996880i \(-0.525150\pi\)
−0.0789284 + 0.996880i \(0.525150\pi\)
\(234\) 0.307306 0.0200893
\(235\) 13.3847 0.873120
\(236\) 11.0253 0.717688
\(237\) 2.23080 0.144906
\(238\) 0 0
\(239\) 8.04273 0.520241 0.260120 0.965576i \(-0.416238\pi\)
0.260120 + 0.965576i \(0.416238\pi\)
\(240\) 8.64123 0.557789
\(241\) 16.4724 1.06108 0.530541 0.847659i \(-0.321989\pi\)
0.530541 + 0.847659i \(0.321989\pi\)
\(242\) 1.52212 0.0978454
\(243\) −1.00000 −0.0641500
\(244\) 9.55272 0.611550
\(245\) 0 0
\(246\) −0.190092 −0.0121198
\(247\) 1.79080 0.113946
\(248\) −2.44148 −0.155034
\(249\) −1.25842 −0.0797489
\(250\) −2.07751 −0.131393
\(251\) 12.7762 0.806430 0.403215 0.915105i \(-0.367893\pi\)
0.403215 + 0.915105i \(0.367893\pi\)
\(252\) 0 0
\(253\) −3.81844 −0.240063
\(254\) 0.902143 0.0566055
\(255\) 9.05811 0.567241
\(256\) 13.1869 0.824181
\(257\) −17.5803 −1.09663 −0.548315 0.836272i \(-0.684731\pi\)
−0.548315 + 0.836272i \(0.684731\pi\)
\(258\) 0.553649 0.0344687
\(259\) 0 0
\(260\) −7.24915 −0.449573
\(261\) 7.83771 0.485142
\(262\) 0.660848 0.0408273
\(263\) 2.61090 0.160995 0.0804976 0.996755i \(-0.474349\pi\)
0.0804976 + 0.996755i \(0.474349\pi\)
\(264\) −1.30352 −0.0802259
\(265\) 6.79648 0.417504
\(266\) 0 0
\(267\) 8.84330 0.541201
\(268\) 25.9022 1.58223
\(269\) 18.5601 1.13163 0.565816 0.824532i \(-0.308561\pi\)
0.565816 + 0.824532i \(0.308561\pi\)
\(270\) −0.434041 −0.0264149
\(271\) −21.3817 −1.29885 −0.649423 0.760427i \(-0.724990\pi\)
−0.649423 + 0.760427i \(0.724990\pi\)
\(272\) 15.0134 0.910320
\(273\) 0 0
\(274\) 1.57436 0.0951105
\(275\) 0.369452 0.0222788
\(276\) −4.33474 −0.260921
\(277\) 14.0879 0.846462 0.423231 0.906022i \(-0.360896\pi\)
0.423231 + 0.906022i \(0.360896\pi\)
\(278\) −1.29068 −0.0774100
\(279\) −3.24019 −0.193985
\(280\) 0 0
\(281\) −22.3895 −1.33565 −0.667823 0.744320i \(-0.732774\pi\)
−0.667823 + 0.744320i \(0.732774\pi\)
\(282\) −1.11431 −0.0663559
\(283\) 10.5639 0.627961 0.313980 0.949429i \(-0.398337\pi\)
0.313980 + 0.949429i \(0.398337\pi\)
\(284\) −21.8315 −1.29546
\(285\) −2.52934 −0.149825
\(286\) 0.531625 0.0314357
\(287\) 0 0
\(288\) −2.22640 −0.131192
\(289\) −1.26232 −0.0742539
\(290\) 3.40189 0.199766
\(291\) −18.9259 −1.10945
\(292\) −0.797678 −0.0466806
\(293\) 8.74247 0.510740 0.255370 0.966843i \(-0.417803\pi\)
0.255370 + 0.966843i \(0.417803\pi\)
\(294\) 0 0
\(295\) 12.8188 0.746339
\(296\) 1.43199 0.0832328
\(297\) −1.72995 −0.100382
\(298\) 0.906408 0.0525068
\(299\) 3.56828 0.206359
\(300\) 0.419407 0.0242145
\(301\) 0 0
\(302\) 1.44806 0.0833263
\(303\) 2.37750 0.136584
\(304\) −4.19225 −0.240442
\(305\) 11.1066 0.635964
\(306\) −0.754109 −0.0431095
\(307\) −7.97557 −0.455190 −0.227595 0.973756i \(-0.573086\pi\)
−0.227595 + 0.973756i \(0.573086\pi\)
\(308\) 0 0
\(309\) 1.27186 0.0723538
\(310\) −1.40638 −0.0798767
\(311\) −14.1483 −0.802276 −0.401138 0.916018i \(-0.631385\pi\)
−0.401138 + 0.916018i \(0.631385\pi\)
\(312\) 1.21812 0.0689625
\(313\) 8.96795 0.506898 0.253449 0.967349i \(-0.418435\pi\)
0.253449 + 0.967349i \(0.418435\pi\)
\(314\) −2.37001 −0.133747
\(315\) 0 0
\(316\) 4.38098 0.246449
\(317\) 8.04996 0.452131 0.226065 0.974112i \(-0.427414\pi\)
0.226065 + 0.974112i \(0.427414\pi\)
\(318\) −0.565823 −0.0317298
\(319\) 13.5589 0.759151
\(320\) 16.3161 0.912098
\(321\) 15.4694 0.863419
\(322\) 0 0
\(323\) −4.39450 −0.244517
\(324\) −1.96387 −0.109104
\(325\) −0.345249 −0.0191510
\(326\) −4.23270 −0.234428
\(327\) 5.96439 0.329832
\(328\) −0.753499 −0.0416050
\(329\) 0 0
\(330\) −0.750871 −0.0413341
\(331\) 17.3497 0.953628 0.476814 0.879004i \(-0.341792\pi\)
0.476814 + 0.879004i \(0.341792\pi\)
\(332\) −2.47136 −0.135634
\(333\) 1.90046 0.104144
\(334\) 2.72106 0.148890
\(335\) 30.1157 1.64540
\(336\) 0 0
\(337\) −29.8239 −1.62461 −0.812307 0.583230i \(-0.801788\pi\)
−0.812307 + 0.583230i \(0.801788\pi\)
\(338\) 1.97440 0.107393
\(339\) −9.73825 −0.528909
\(340\) 17.7889 0.964739
\(341\) −5.60537 −0.303548
\(342\) 0.210573 0.0113865
\(343\) 0 0
\(344\) 2.19459 0.118324
\(345\) −5.03986 −0.271337
\(346\) −1.65406 −0.0889230
\(347\) 18.3160 0.983255 0.491628 0.870805i \(-0.336402\pi\)
0.491628 + 0.870805i \(0.336402\pi\)
\(348\) 15.3922 0.825109
\(349\) 6.08069 0.325492 0.162746 0.986668i \(-0.447965\pi\)
0.162746 + 0.986668i \(0.447965\pi\)
\(350\) 0 0
\(351\) 1.61662 0.0862888
\(352\) −3.85157 −0.205289
\(353\) 6.85088 0.364635 0.182318 0.983240i \(-0.441640\pi\)
0.182318 + 0.983240i \(0.441640\pi\)
\(354\) −1.06719 −0.0567207
\(355\) −25.3827 −1.34718
\(356\) 17.3670 0.920452
\(357\) 0 0
\(358\) 0.387766 0.0204940
\(359\) 0.354000 0.0186834 0.00934171 0.999956i \(-0.497026\pi\)
0.00934171 + 0.999956i \(0.497026\pi\)
\(360\) −1.72048 −0.0906773
\(361\) −17.7729 −0.935416
\(362\) −3.89820 −0.204885
\(363\) 8.00727 0.420272
\(364\) 0 0
\(365\) −0.927435 −0.0485441
\(366\) −0.924654 −0.0483324
\(367\) 20.8456 1.08813 0.544065 0.839043i \(-0.316884\pi\)
0.544065 + 0.839043i \(0.316884\pi\)
\(368\) −8.35333 −0.435447
\(369\) −1.00000 −0.0520579
\(370\) 0.824876 0.0428833
\(371\) 0 0
\(372\) −6.36329 −0.329921
\(373\) 35.6438 1.84557 0.922783 0.385320i \(-0.125909\pi\)
0.922783 + 0.385320i \(0.125909\pi\)
\(374\) −1.30457 −0.0674578
\(375\) −10.9290 −0.564370
\(376\) −4.41696 −0.227787
\(377\) −12.6706 −0.652569
\(378\) 0 0
\(379\) 15.9661 0.820125 0.410063 0.912057i \(-0.365507\pi\)
0.410063 + 0.912057i \(0.365507\pi\)
\(380\) −4.96727 −0.254816
\(381\) 4.74582 0.243136
\(382\) −1.94355 −0.0994408
\(383\) 14.1502 0.723043 0.361521 0.932364i \(-0.382257\pi\)
0.361521 + 0.932364i \(0.382257\pi\)
\(384\) −5.81115 −0.296549
\(385\) 0 0
\(386\) −4.01926 −0.204575
\(387\) 2.91253 0.148052
\(388\) −37.1679 −1.88691
\(389\) 9.66026 0.489795 0.244897 0.969549i \(-0.421246\pi\)
0.244897 + 0.969549i \(0.421246\pi\)
\(390\) 0.701680 0.0355309
\(391\) −8.75632 −0.442826
\(392\) 0 0
\(393\) 3.47647 0.175365
\(394\) 2.88340 0.145264
\(395\) 5.09363 0.256288
\(396\) −3.39739 −0.170725
\(397\) −9.54771 −0.479186 −0.239593 0.970873i \(-0.577014\pi\)
−0.239593 + 0.970873i \(0.577014\pi\)
\(398\) −1.52060 −0.0762206
\(399\) 0 0
\(400\) 0.808225 0.0404113
\(401\) 34.5897 1.72733 0.863663 0.504070i \(-0.168165\pi\)
0.863663 + 0.504070i \(0.168165\pi\)
\(402\) −2.50720 −0.125048
\(403\) 5.23815 0.260931
\(404\) 4.66909 0.232296
\(405\) −2.28332 −0.113459
\(406\) 0 0
\(407\) 3.28770 0.162965
\(408\) −2.98919 −0.147987
\(409\) −27.9927 −1.38415 −0.692074 0.721826i \(-0.743303\pi\)
−0.692074 + 0.721826i \(0.743303\pi\)
\(410\) −0.434041 −0.0214358
\(411\) 8.28210 0.408526
\(412\) 2.49777 0.123056
\(413\) 0 0
\(414\) 0.419580 0.0206212
\(415\) −2.87337 −0.141048
\(416\) 3.59924 0.176467
\(417\) −6.78978 −0.332497
\(418\) 0.364281 0.0178176
\(419\) −20.1883 −0.986263 −0.493131 0.869955i \(-0.664148\pi\)
−0.493131 + 0.869955i \(0.664148\pi\)
\(420\) 0 0
\(421\) 7.88294 0.384191 0.192096 0.981376i \(-0.438472\pi\)
0.192096 + 0.981376i \(0.438472\pi\)
\(422\) 3.45341 0.168109
\(423\) −5.86193 −0.285017
\(424\) −2.24285 −0.108922
\(425\) 0.847217 0.0410961
\(426\) 2.11317 0.102384
\(427\) 0 0
\(428\) 30.3798 1.46847
\(429\) 2.79668 0.135025
\(430\) 1.26416 0.0609631
\(431\) −4.43615 −0.213682 −0.106841 0.994276i \(-0.534074\pi\)
−0.106841 + 0.994276i \(0.534074\pi\)
\(432\) −3.78450 −0.182082
\(433\) 7.00079 0.336436 0.168218 0.985750i \(-0.446199\pi\)
0.168218 + 0.985750i \(0.446199\pi\)
\(434\) 0 0
\(435\) 17.8960 0.858048
\(436\) 11.7133 0.560964
\(437\) 2.44507 0.116963
\(438\) 0.0772111 0.00368929
\(439\) 11.0416 0.526988 0.263494 0.964661i \(-0.415125\pi\)
0.263494 + 0.964661i \(0.415125\pi\)
\(440\) −2.97635 −0.141892
\(441\) 0 0
\(442\) 1.21911 0.0579870
\(443\) −6.88937 −0.327324 −0.163662 0.986516i \(-0.552331\pi\)
−0.163662 + 0.986516i \(0.552331\pi\)
\(444\) 3.73224 0.177124
\(445\) 20.1921 0.957197
\(446\) −2.88751 −0.136728
\(447\) 4.76826 0.225531
\(448\) 0 0
\(449\) 27.0247 1.27538 0.637688 0.770295i \(-0.279891\pi\)
0.637688 + 0.770295i \(0.279891\pi\)
\(450\) −0.0405965 −0.00191374
\(451\) −1.72995 −0.0814603
\(452\) −19.1246 −0.899546
\(453\) 7.61766 0.357909
\(454\) −2.15362 −0.101075
\(455\) 0 0
\(456\) 0.834683 0.0390876
\(457\) 2.39212 0.111899 0.0559494 0.998434i \(-0.482181\pi\)
0.0559494 + 0.998434i \(0.482181\pi\)
\(458\) −3.11295 −0.145459
\(459\) −3.96707 −0.185167
\(460\) −9.89761 −0.461478
\(461\) −15.9987 −0.745136 −0.372568 0.928005i \(-0.621523\pi\)
−0.372568 + 0.928005i \(0.621523\pi\)
\(462\) 0 0
\(463\) 17.3408 0.805893 0.402947 0.915224i \(-0.367986\pi\)
0.402947 + 0.915224i \(0.367986\pi\)
\(464\) 29.6618 1.37701
\(465\) −7.39840 −0.343092
\(466\) 0.458042 0.0212184
\(467\) 31.7666 1.46998 0.734990 0.678078i \(-0.237187\pi\)
0.734990 + 0.678078i \(0.237187\pi\)
\(468\) 3.17482 0.146756
\(469\) 0 0
\(470\) −2.54432 −0.117361
\(471\) −12.4677 −0.574481
\(472\) −4.23022 −0.194711
\(473\) 5.03854 0.231672
\(474\) −0.424056 −0.0194776
\(475\) −0.236572 −0.0108547
\(476\) 0 0
\(477\) −2.97657 −0.136288
\(478\) −1.52886 −0.0699283
\(479\) −12.5261 −0.572331 −0.286166 0.958180i \(-0.592381\pi\)
−0.286166 + 0.958180i \(0.592381\pi\)
\(480\) −5.08359 −0.232033
\(481\) −3.07232 −0.140086
\(482\) −3.13128 −0.142626
\(483\) 0 0
\(484\) 15.7252 0.714781
\(485\) −43.2139 −1.96224
\(486\) 0.190092 0.00862275
\(487\) 18.9271 0.857670 0.428835 0.903383i \(-0.358924\pi\)
0.428835 + 0.903383i \(0.358924\pi\)
\(488\) −3.66520 −0.165916
\(489\) −22.2666 −1.00693
\(490\) 0 0
\(491\) 39.3059 1.77385 0.886926 0.461912i \(-0.152837\pi\)
0.886926 + 0.461912i \(0.152837\pi\)
\(492\) −1.96387 −0.0885379
\(493\) 31.0928 1.40035
\(494\) −0.340417 −0.0153161
\(495\) −3.95004 −0.177541
\(496\) −12.2625 −0.550602
\(497\) 0 0
\(498\) 0.239215 0.0107195
\(499\) −0.0965158 −0.00432064 −0.00216032 0.999998i \(-0.500688\pi\)
−0.00216032 + 0.999998i \(0.500688\pi\)
\(500\) −21.4630 −0.959857
\(501\) 14.3144 0.639521
\(502\) −2.42866 −0.108396
\(503\) −35.7044 −1.59198 −0.795990 0.605310i \(-0.793049\pi\)
−0.795990 + 0.605310i \(0.793049\pi\)
\(504\) 0 0
\(505\) 5.42860 0.241570
\(506\) 0.725854 0.0322681
\(507\) 10.3865 0.461282
\(508\) 9.32016 0.413515
\(509\) −6.76202 −0.299721 −0.149861 0.988707i \(-0.547883\pi\)
−0.149861 + 0.988707i \(0.547883\pi\)
\(510\) −1.72187 −0.0762459
\(511\) 0 0
\(512\) −14.1290 −0.624421
\(513\) 1.10774 0.0489081
\(514\) 3.34188 0.147404
\(515\) 2.90408 0.127969
\(516\) 5.71982 0.251801
\(517\) −10.1409 −0.445994
\(518\) 0 0
\(519\) −8.70139 −0.381949
\(520\) 2.78136 0.121971
\(521\) 10.8582 0.475708 0.237854 0.971301i \(-0.423556\pi\)
0.237854 + 0.971301i \(0.423556\pi\)
\(522\) −1.48989 −0.0652105
\(523\) 8.65423 0.378423 0.189212 0.981936i \(-0.439407\pi\)
0.189212 + 0.981936i \(0.439407\pi\)
\(524\) 6.82731 0.298252
\(525\) 0 0
\(526\) −0.496312 −0.0216402
\(527\) −12.8541 −0.559932
\(528\) −6.54700 −0.284921
\(529\) −18.1281 −0.788176
\(530\) −1.29196 −0.0561190
\(531\) −5.61410 −0.243631
\(532\) 0 0
\(533\) 1.61662 0.0700236
\(534\) −1.68104 −0.0727457
\(535\) 35.3217 1.52709
\(536\) −9.93821 −0.429265
\(537\) 2.03988 0.0880275
\(538\) −3.52813 −0.152109
\(539\) 0 0
\(540\) −4.48414 −0.192967
\(541\) 34.5488 1.48537 0.742684 0.669642i \(-0.233552\pi\)
0.742684 + 0.669642i \(0.233552\pi\)
\(542\) 4.06449 0.174585
\(543\) −20.5069 −0.880035
\(544\) −8.83229 −0.378682
\(545\) 13.6186 0.583358
\(546\) 0 0
\(547\) 6.28734 0.268827 0.134414 0.990925i \(-0.457085\pi\)
0.134414 + 0.990925i \(0.457085\pi\)
\(548\) 16.2649 0.694803
\(549\) −4.86425 −0.207601
\(550\) −0.0702299 −0.00299461
\(551\) −8.68217 −0.369873
\(552\) 1.66316 0.0707888
\(553\) 0 0
\(554\) −2.67800 −0.113777
\(555\) 4.33935 0.184195
\(556\) −13.3342 −0.565497
\(557\) −23.1197 −0.979612 −0.489806 0.871832i \(-0.662932\pi\)
−0.489806 + 0.871832i \(0.662932\pi\)
\(558\) 0.615934 0.0260746
\(559\) −4.70846 −0.199146
\(560\) 0 0
\(561\) −6.86285 −0.289750
\(562\) 4.25606 0.179531
\(563\) −43.4261 −1.83019 −0.915095 0.403238i \(-0.867885\pi\)
−0.915095 + 0.403238i \(0.867885\pi\)
\(564\) −11.5120 −0.484744
\(565\) −22.2356 −0.935457
\(566\) −2.00812 −0.0844076
\(567\) 0 0
\(568\) 8.37633 0.351463
\(569\) 0.0739827 0.00310152 0.00155076 0.999999i \(-0.499506\pi\)
0.00155076 + 0.999999i \(0.499506\pi\)
\(570\) 0.480806 0.0201388
\(571\) −5.95013 −0.249005 −0.124503 0.992219i \(-0.539734\pi\)
−0.124503 + 0.992219i \(0.539734\pi\)
\(572\) 5.49229 0.229644
\(573\) −10.2243 −0.427125
\(574\) 0 0
\(575\) −0.471385 −0.0196581
\(576\) −7.14577 −0.297740
\(577\) 29.6618 1.23484 0.617418 0.786636i \(-0.288179\pi\)
0.617418 + 0.786636i \(0.288179\pi\)
\(578\) 0.239956 0.00998086
\(579\) −21.1438 −0.878706
\(580\) 35.1454 1.45933
\(581\) 0 0
\(582\) 3.59766 0.149128
\(583\) −5.14933 −0.213264
\(584\) 0.306054 0.0126646
\(585\) 3.69127 0.152615
\(586\) −1.66187 −0.0686513
\(587\) 1.71541 0.0708025 0.0354012 0.999373i \(-0.488729\pi\)
0.0354012 + 0.999373i \(0.488729\pi\)
\(588\) 0 0
\(589\) 3.58930 0.147894
\(590\) −2.43675 −0.100319
\(591\) 15.1685 0.623948
\(592\) 7.19227 0.295600
\(593\) −3.69486 −0.151730 −0.0758650 0.997118i \(-0.524172\pi\)
−0.0758650 + 0.997118i \(0.524172\pi\)
\(594\) 0.328850 0.0134929
\(595\) 0 0
\(596\) 9.36422 0.383573
\(597\) −7.99926 −0.327388
\(598\) −0.678302 −0.0277378
\(599\) −23.5445 −0.962002 −0.481001 0.876720i \(-0.659727\pi\)
−0.481001 + 0.876720i \(0.659727\pi\)
\(600\) −0.160919 −0.00656949
\(601\) 9.90791 0.404152 0.202076 0.979370i \(-0.435231\pi\)
0.202076 + 0.979370i \(0.435231\pi\)
\(602\) 0 0
\(603\) −13.1894 −0.537115
\(604\) 14.9601 0.608716
\(605\) 18.2832 0.743317
\(606\) −0.451944 −0.0183590
\(607\) 27.9949 1.13628 0.568139 0.822933i \(-0.307664\pi\)
0.568139 + 0.822933i \(0.307664\pi\)
\(608\) 2.46628 0.100021
\(609\) 0 0
\(610\) −2.11128 −0.0854833
\(611\) 9.47651 0.383379
\(612\) −7.79080 −0.314924
\(613\) −12.2122 −0.493245 −0.246622 0.969112i \(-0.579321\pi\)
−0.246622 + 0.969112i \(0.579321\pi\)
\(614\) 1.51609 0.0611845
\(615\) −2.28332 −0.0920725
\(616\) 0 0
\(617\) 3.44647 0.138750 0.0693748 0.997591i \(-0.477900\pi\)
0.0693748 + 0.997591i \(0.477900\pi\)
\(618\) −0.241771 −0.00972546
\(619\) 19.3249 0.776734 0.388367 0.921505i \(-0.373039\pi\)
0.388367 + 0.921505i \(0.373039\pi\)
\(620\) −14.5294 −0.583517
\(621\) 2.20725 0.0885739
\(622\) 2.68948 0.107838
\(623\) 0 0
\(624\) 6.11809 0.244920
\(625\) −26.0222 −1.04089
\(626\) −1.70473 −0.0681349
\(627\) 1.91634 0.0765314
\(628\) −24.4849 −0.977053
\(629\) 7.53925 0.300610
\(630\) 0 0
\(631\) 11.9587 0.476068 0.238034 0.971257i \(-0.423497\pi\)
0.238034 + 0.971257i \(0.423497\pi\)
\(632\) −1.68090 −0.0668627
\(633\) 18.1670 0.722075
\(634\) −1.53023 −0.0607733
\(635\) 10.8362 0.430023
\(636\) −5.84559 −0.231793
\(637\) 0 0
\(638\) −2.57743 −0.102041
\(639\) 11.1166 0.439765
\(640\) −13.2687 −0.524493
\(641\) −46.6531 −1.84269 −0.921343 0.388751i \(-0.872907\pi\)
−0.921343 + 0.388751i \(0.872907\pi\)
\(642\) −2.94061 −0.116057
\(643\) 7.35668 0.290119 0.145059 0.989423i \(-0.453663\pi\)
0.145059 + 0.989423i \(0.453663\pi\)
\(644\) 0 0
\(645\) 6.65025 0.261853
\(646\) 0.835359 0.0328668
\(647\) −2.57068 −0.101064 −0.0505320 0.998722i \(-0.516092\pi\)
−0.0505320 + 0.998722i \(0.516092\pi\)
\(648\) 0.753499 0.0296002
\(649\) −9.71212 −0.381234
\(650\) 0.0656290 0.00257418
\(651\) 0 0
\(652\) −43.7286 −1.71254
\(653\) −31.3911 −1.22843 −0.614215 0.789139i \(-0.710527\pi\)
−0.614215 + 0.789139i \(0.710527\pi\)
\(654\) −1.13378 −0.0443344
\(655\) 7.93789 0.310159
\(656\) −3.78450 −0.147760
\(657\) 0.406178 0.0158465
\(658\) 0 0
\(659\) 2.55964 0.0997094 0.0498547 0.998756i \(-0.484124\pi\)
0.0498547 + 0.998756i \(0.484124\pi\)
\(660\) −7.75734 −0.301954
\(661\) 19.6281 0.763445 0.381723 0.924277i \(-0.375331\pi\)
0.381723 + 0.924277i \(0.375331\pi\)
\(662\) −3.29805 −0.128182
\(663\) 6.41325 0.249070
\(664\) 0.948216 0.0367979
\(665\) 0 0
\(666\) −0.361261 −0.0139986
\(667\) −17.2998 −0.669850
\(668\) 28.1116 1.08767
\(669\) −15.1901 −0.587282
\(670\) −5.72475 −0.221166
\(671\) −8.41491 −0.324854
\(672\) 0 0
\(673\) 17.9831 0.693198 0.346599 0.938013i \(-0.387337\pi\)
0.346599 + 0.938013i \(0.387337\pi\)
\(674\) 5.66929 0.218373
\(675\) −0.213562 −0.00822001
\(676\) 20.3978 0.784529
\(677\) 49.9993 1.92163 0.960815 0.277189i \(-0.0894029\pi\)
0.960815 + 0.277189i \(0.0894029\pi\)
\(678\) 1.85116 0.0710935
\(679\) 0 0
\(680\) −6.82528 −0.261737
\(681\) −11.3294 −0.434143
\(682\) 1.06554 0.0408015
\(683\) −0.152907 −0.00585081 −0.00292541 0.999996i \(-0.500931\pi\)
−0.00292541 + 0.999996i \(0.500931\pi\)
\(684\) 2.17546 0.0831807
\(685\) 18.9107 0.722541
\(686\) 0 0
\(687\) −16.3760 −0.624784
\(688\) 11.0225 0.420227
\(689\) 4.81199 0.183322
\(690\) 0.958037 0.0364719
\(691\) 5.74600 0.218588 0.109294 0.994009i \(-0.465141\pi\)
0.109294 + 0.994009i \(0.465141\pi\)
\(692\) −17.0884 −0.649602
\(693\) 0 0
\(694\) −3.48173 −0.132165
\(695\) −15.5033 −0.588072
\(696\) −5.90570 −0.223855
\(697\) −3.96707 −0.150264
\(698\) −1.15589 −0.0437511
\(699\) 2.40958 0.0911387
\(700\) 0 0
\(701\) −34.6654 −1.30929 −0.654647 0.755934i \(-0.727183\pi\)
−0.654647 + 0.755934i \(0.727183\pi\)
\(702\) −0.307306 −0.0115985
\(703\) −2.10522 −0.0793998
\(704\) −12.3618 −0.465904
\(705\) −13.3847 −0.504096
\(706\) −1.30230 −0.0490126
\(707\) 0 0
\(708\) −11.0253 −0.414357
\(709\) −12.1602 −0.456684 −0.228342 0.973581i \(-0.573331\pi\)
−0.228342 + 0.973581i \(0.573331\pi\)
\(710\) 4.82506 0.181081
\(711\) −2.23080 −0.0836614
\(712\) −6.66341 −0.249722
\(713\) 7.15190 0.267841
\(714\) 0 0
\(715\) 6.38571 0.238812
\(716\) 4.00606 0.149713
\(717\) −8.04273 −0.300361
\(718\) −0.0672926 −0.00251134
\(719\) −15.6701 −0.584396 −0.292198 0.956358i \(-0.594387\pi\)
−0.292198 + 0.956358i \(0.594387\pi\)
\(720\) −8.64123 −0.322039
\(721\) 0 0
\(722\) 3.37849 0.125734
\(723\) −16.4724 −0.612616
\(724\) −40.2728 −1.49673
\(725\) 1.67384 0.0621648
\(726\) −1.52212 −0.0564910
\(727\) −5.01300 −0.185922 −0.0929609 0.995670i \(-0.529633\pi\)
−0.0929609 + 0.995670i \(0.529633\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0.176298 0.00652508
\(731\) 11.5542 0.427349
\(732\) −9.55272 −0.353079
\(733\) −8.01404 −0.296005 −0.148003 0.988987i \(-0.547284\pi\)
−0.148003 + 0.988987i \(0.547284\pi\)
\(734\) −3.96258 −0.146261
\(735\) 0 0
\(736\) 4.91422 0.181141
\(737\) −22.8171 −0.840477
\(738\) 0.190092 0.00699738
\(739\) 0.161151 0.00592802 0.00296401 0.999996i \(-0.499057\pi\)
0.00296401 + 0.999996i \(0.499057\pi\)
\(740\) 8.52191 0.313272
\(741\) −1.79080 −0.0657867
\(742\) 0 0
\(743\) −10.1913 −0.373884 −0.186942 0.982371i \(-0.559858\pi\)
−0.186942 + 0.982371i \(0.559858\pi\)
\(744\) 2.44148 0.0895089
\(745\) 10.8875 0.398886
\(746\) −6.77560 −0.248072
\(747\) 1.25842 0.0460431
\(748\) −13.4777 −0.492794
\(749\) 0 0
\(750\) 2.07751 0.0758600
\(751\) −5.99474 −0.218751 −0.109376 0.994000i \(-0.534885\pi\)
−0.109376 + 0.994000i \(0.534885\pi\)
\(752\) −22.1844 −0.808983
\(753\) −12.7762 −0.465592
\(754\) 2.40858 0.0877153
\(755\) 17.3936 0.633017
\(756\) 0 0
\(757\) −45.7296 −1.66207 −0.831035 0.556220i \(-0.812251\pi\)
−0.831035 + 0.556220i \(0.812251\pi\)
\(758\) −3.03503 −0.110237
\(759\) 3.81844 0.138600
\(760\) 1.90585 0.0691325
\(761\) −5.82408 −0.211123 −0.105561 0.994413i \(-0.533664\pi\)
−0.105561 + 0.994413i \(0.533664\pi\)
\(762\) −0.902143 −0.0326812
\(763\) 0 0
\(764\) −20.0791 −0.726437
\(765\) −9.05811 −0.327497
\(766\) −2.68984 −0.0971880
\(767\) 9.07586 0.327710
\(768\) −13.1869 −0.475841
\(769\) −18.0668 −0.651506 −0.325753 0.945455i \(-0.605618\pi\)
−0.325753 + 0.945455i \(0.605618\pi\)
\(770\) 0 0
\(771\) 17.5803 0.633140
\(772\) −41.5235 −1.49447
\(773\) −6.14546 −0.221037 −0.110518 0.993874i \(-0.535251\pi\)
−0.110518 + 0.993874i \(0.535251\pi\)
\(774\) −0.553649 −0.0199005
\(775\) −0.691982 −0.0248567
\(776\) 14.2606 0.511927
\(777\) 0 0
\(778\) −1.83634 −0.0658359
\(779\) 1.10774 0.0396890
\(780\) 7.24915 0.259561
\(781\) 19.2312 0.688145
\(782\) 1.66451 0.0595226
\(783\) −7.83771 −0.280097
\(784\) 0 0
\(785\) −28.4678 −1.01606
\(786\) −0.660848 −0.0235717
\(787\) −42.5487 −1.51670 −0.758349 0.651849i \(-0.773993\pi\)
−0.758349 + 0.651849i \(0.773993\pi\)
\(788\) 29.7888 1.06118
\(789\) −2.61090 −0.0929506
\(790\) −0.968257 −0.0344491
\(791\) 0 0
\(792\) 1.30352 0.0463185
\(793\) 7.86364 0.279246
\(794\) 1.81494 0.0644099
\(795\) −6.79648 −0.241046
\(796\) −15.7095 −0.556808
\(797\) −40.4705 −1.43354 −0.716770 0.697310i \(-0.754380\pi\)
−0.716770 + 0.697310i \(0.754380\pi\)
\(798\) 0 0
\(799\) −23.2547 −0.822692
\(800\) −0.475475 −0.0168106
\(801\) −8.84330 −0.312463
\(802\) −6.57522 −0.232179
\(803\) 0.702668 0.0247966
\(804\) −25.9022 −0.913501
\(805\) 0 0
\(806\) −0.995731 −0.0350731
\(807\) −18.5601 −0.653348
\(808\) −1.79144 −0.0630228
\(809\) 52.1135 1.83221 0.916107 0.400934i \(-0.131314\pi\)
0.916107 + 0.400934i \(0.131314\pi\)
\(810\) 0.434041 0.0152507
\(811\) −15.9764 −0.561006 −0.280503 0.959853i \(-0.590501\pi\)
−0.280503 + 0.959853i \(0.590501\pi\)
\(812\) 0 0
\(813\) 21.3817 0.749889
\(814\) −0.624965 −0.0219050
\(815\) −50.8418 −1.78091
\(816\) −15.0134 −0.525573
\(817\) −3.22634 −0.112875
\(818\) 5.32118 0.186051
\(819\) 0 0
\(820\) −4.48414 −0.156593
\(821\) 23.4163 0.817235 0.408617 0.912706i \(-0.366011\pi\)
0.408617 + 0.912706i \(0.366011\pi\)
\(822\) −1.57436 −0.0549121
\(823\) 50.2024 1.74994 0.874972 0.484173i \(-0.160880\pi\)
0.874972 + 0.484173i \(0.160880\pi\)
\(824\) −0.958348 −0.0333856
\(825\) −0.369452 −0.0128627
\(826\) 0 0
\(827\) −4.03629 −0.140355 −0.0701777 0.997535i \(-0.522357\pi\)
−0.0701777 + 0.997535i \(0.522357\pi\)
\(828\) 4.33474 0.150643
\(829\) 49.7726 1.72867 0.864337 0.502913i \(-0.167738\pi\)
0.864337 + 0.502913i \(0.167738\pi\)
\(830\) 0.546205 0.0189590
\(831\) −14.0879 −0.488705
\(832\) 11.5520 0.400493
\(833\) 0 0
\(834\) 1.29068 0.0446927
\(835\) 32.6845 1.13109
\(836\) 3.76344 0.130161
\(837\) 3.24019 0.111997
\(838\) 3.83763 0.132569
\(839\) 7.36072 0.254120 0.127060 0.991895i \(-0.459446\pi\)
0.127060 + 0.991895i \(0.459446\pi\)
\(840\) 0 0
\(841\) 32.4297 1.11827
\(842\) −1.49848 −0.0516412
\(843\) 22.3895 0.771135
\(844\) 35.6776 1.22807
\(845\) 23.7158 0.815849
\(846\) 1.11431 0.0383106
\(847\) 0 0
\(848\) −11.2648 −0.386836
\(849\) −10.5639 −0.362553
\(850\) −0.161049 −0.00552394
\(851\) −4.19478 −0.143795
\(852\) 21.8315 0.747934
\(853\) −12.6755 −0.434001 −0.217001 0.976171i \(-0.569627\pi\)
−0.217001 + 0.976171i \(0.569627\pi\)
\(854\) 0 0
\(855\) 2.52934 0.0865014
\(856\) −11.6562 −0.398400
\(857\) −14.3118 −0.488883 −0.244442 0.969664i \(-0.578605\pi\)
−0.244442 + 0.969664i \(0.578605\pi\)
\(858\) −0.531625 −0.0181494
\(859\) −12.6064 −0.430126 −0.215063 0.976600i \(-0.568996\pi\)
−0.215063 + 0.976600i \(0.568996\pi\)
\(860\) 13.0602 0.445349
\(861\) 0 0
\(862\) 0.843276 0.0287221
\(863\) −2.85848 −0.0973037 −0.0486518 0.998816i \(-0.515492\pi\)
−0.0486518 + 0.998816i \(0.515492\pi\)
\(864\) 2.22640 0.0757437
\(865\) −19.8681 −0.675535
\(866\) −1.33079 −0.0452222
\(867\) 1.26232 0.0428705
\(868\) 0 0
\(869\) −3.85917 −0.130913
\(870\) −3.40189 −0.115335
\(871\) 21.3223 0.722478
\(872\) −4.49416 −0.152192
\(873\) 18.9259 0.640544
\(874\) −0.464787 −0.0157217
\(875\) 0 0
\(876\) 0.797678 0.0269510
\(877\) −18.9915 −0.641297 −0.320648 0.947198i \(-0.603901\pi\)
−0.320648 + 0.947198i \(0.603901\pi\)
\(878\) −2.09893 −0.0708353
\(879\) −8.74247 −0.294876
\(880\) −14.9489 −0.503928
\(881\) 4.63709 0.156228 0.0781138 0.996944i \(-0.475110\pi\)
0.0781138 + 0.996944i \(0.475110\pi\)
\(882\) 0 0
\(883\) 44.5951 1.50074 0.750372 0.661016i \(-0.229874\pi\)
0.750372 + 0.661016i \(0.229874\pi\)
\(884\) 12.5948 0.423608
\(885\) −12.8188 −0.430899
\(886\) 1.30961 0.0439973
\(887\) 56.2119 1.88741 0.943706 0.330785i \(-0.107313\pi\)
0.943706 + 0.330785i \(0.107313\pi\)
\(888\) −1.43199 −0.0480545
\(889\) 0 0
\(890\) −3.83836 −0.128662
\(891\) 1.72995 0.0579556
\(892\) −29.8312 −0.998824
\(893\) 6.49351 0.217297
\(894\) −0.906408 −0.0303148
\(895\) 4.65771 0.155690
\(896\) 0 0
\(897\) −3.56828 −0.119142
\(898\) −5.13718 −0.171430
\(899\) −25.3957 −0.846992
\(900\) −0.419407 −0.0139802
\(901\) −11.8083 −0.393391
\(902\) 0.328850 0.0109495
\(903\) 0 0
\(904\) 7.33776 0.244050
\(905\) −46.8239 −1.55648
\(906\) −1.44806 −0.0481085
\(907\) −21.4550 −0.712403 −0.356201 0.934409i \(-0.615928\pi\)
−0.356201 + 0.934409i \(0.615928\pi\)
\(908\) −22.2494 −0.738372
\(909\) −2.37750 −0.0788567
\(910\) 0 0
\(911\) 21.3499 0.707354 0.353677 0.935368i \(-0.384931\pi\)
0.353677 + 0.935368i \(0.384931\pi\)
\(912\) 4.19225 0.138819
\(913\) 2.17700 0.0720482
\(914\) −0.454723 −0.0150409
\(915\) −11.1066 −0.367174
\(916\) −32.1603 −1.06261
\(917\) 0 0
\(918\) 0.754109 0.0248893
\(919\) −12.4136 −0.409487 −0.204744 0.978816i \(-0.565636\pi\)
−0.204744 + 0.978816i \(0.565636\pi\)
\(920\) 3.79753 0.125201
\(921\) 7.97557 0.262804
\(922\) 3.04123 0.100158
\(923\) −17.9713 −0.591532
\(924\) 0 0
\(925\) 0.405866 0.0133448
\(926\) −3.29634 −0.108324
\(927\) −1.27186 −0.0417735
\(928\) −17.4499 −0.572820
\(929\) −12.7962 −0.419829 −0.209914 0.977720i \(-0.567319\pi\)
−0.209914 + 0.977720i \(0.567319\pi\)
\(930\) 1.40638 0.0461169
\(931\) 0 0
\(932\) 4.73209 0.155005
\(933\) 14.1483 0.463194
\(934\) −6.03857 −0.197588
\(935\) −15.6701 −0.512467
\(936\) −1.21812 −0.0398155
\(937\) 40.7436 1.33104 0.665518 0.746382i \(-0.268211\pi\)
0.665518 + 0.746382i \(0.268211\pi\)
\(938\) 0 0
\(939\) −8.96795 −0.292658
\(940\) −26.2857 −0.857345
\(941\) 37.3259 1.21679 0.608395 0.793634i \(-0.291814\pi\)
0.608395 + 0.793634i \(0.291814\pi\)
\(942\) 2.37001 0.0772191
\(943\) 2.20725 0.0718779
\(944\) −21.2465 −0.691516
\(945\) 0 0
\(946\) −0.957786 −0.0311403
\(947\) −3.95826 −0.128626 −0.0643131 0.997930i \(-0.520486\pi\)
−0.0643131 + 0.997930i \(0.520486\pi\)
\(948\) −4.38098 −0.142288
\(949\) −0.656635 −0.0213153
\(950\) 0.0449704 0.00145903
\(951\) −8.04996 −0.261038
\(952\) 0 0
\(953\) −12.5625 −0.406940 −0.203470 0.979081i \(-0.565222\pi\)
−0.203470 + 0.979081i \(0.565222\pi\)
\(954\) 0.565823 0.0183192
\(955\) −23.3453 −0.755437
\(956\) −15.7948 −0.510841
\(957\) −13.5589 −0.438296
\(958\) 2.38111 0.0769301
\(959\) 0 0
\(960\) −16.3161 −0.526600
\(961\) −20.5012 −0.661328
\(962\) 0.584023 0.0188296
\(963\) −15.4694 −0.498495
\(964\) −32.3496 −1.04191
\(965\) −48.2781 −1.55413
\(966\) 0 0
\(967\) 35.4422 1.13974 0.569871 0.821734i \(-0.306993\pi\)
0.569871 + 0.821734i \(0.306993\pi\)
\(968\) −6.03346 −0.193923
\(969\) 4.39450 0.141172
\(970\) 8.21461 0.263755
\(971\) −28.0134 −0.898994 −0.449497 0.893282i \(-0.648397\pi\)
−0.449497 + 0.893282i \(0.648397\pi\)
\(972\) 1.96387 0.0629910
\(973\) 0 0
\(974\) −3.59790 −0.115284
\(975\) 0.345249 0.0110568
\(976\) −18.4087 −0.589249
\(977\) 6.84262 0.218915 0.109457 0.993991i \(-0.465089\pi\)
0.109457 + 0.993991i \(0.465089\pi\)
\(978\) 4.23270 0.135347
\(979\) −15.2985 −0.488942
\(980\) 0 0
\(981\) −5.96439 −0.190428
\(982\) −7.47174 −0.238433
\(983\) 35.9377 1.14623 0.573117 0.819474i \(-0.305734\pi\)
0.573117 + 0.819474i \(0.305734\pi\)
\(984\) 0.753499 0.0240207
\(985\) 34.6345 1.10355
\(986\) −5.91049 −0.188228
\(987\) 0 0
\(988\) −3.51689 −0.111887
\(989\) −6.42868 −0.204420
\(990\) 0.750871 0.0238642
\(991\) 49.4628 1.57124 0.785619 0.618710i \(-0.212345\pi\)
0.785619 + 0.618710i \(0.212345\pi\)
\(992\) 7.21395 0.229043
\(993\) −17.3497 −0.550577
\(994\) 0 0
\(995\) −18.2649 −0.579036
\(996\) 2.47136 0.0783081
\(997\) 47.1017 1.49173 0.745864 0.666099i \(-0.232037\pi\)
0.745864 + 0.666099i \(0.232037\pi\)
\(998\) 0.0183469 0.000580760 0
\(999\) −1.90046 −0.0601278
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 \(a_p\))