Properties

Label 4003.2.a.b.1.1
Level 4003
Weight 2
Character 4003.1
Self dual Yes
Analytic conductor 31.964
Analytic rank 1
Dimension 152
CM No

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Newspace parameters

Level: \( N \) = \( 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(31.9641159291\)
Analytic rank: \(1\)
Dimension: \(152\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 4003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} +O(q^{10})\) \(q-2.81629 q^{2} +1.48630 q^{3} +5.93147 q^{4} +2.03150 q^{5} -4.18584 q^{6} -2.55919 q^{7} -11.0722 q^{8} -0.790918 q^{9} -5.72129 q^{10} +3.01593 q^{11} +8.81594 q^{12} +2.19057 q^{13} +7.20742 q^{14} +3.01942 q^{15} +19.3194 q^{16} -4.87502 q^{17} +2.22745 q^{18} +3.05249 q^{19} +12.0498 q^{20} -3.80372 q^{21} -8.49373 q^{22} -2.52458 q^{23} -16.4565 q^{24} -0.872998 q^{25} -6.16927 q^{26} -5.63443 q^{27} -15.1798 q^{28} +4.33871 q^{29} -8.50355 q^{30} -7.97929 q^{31} -32.2647 q^{32} +4.48257 q^{33} +13.7294 q^{34} -5.19901 q^{35} -4.69131 q^{36} -4.37466 q^{37} -8.59668 q^{38} +3.25584 q^{39} -22.4931 q^{40} +7.43043 q^{41} +10.7124 q^{42} +3.81685 q^{43} +17.8889 q^{44} -1.60675 q^{45} +7.10995 q^{46} -11.2833 q^{47} +28.7144 q^{48} -0.450529 q^{49} +2.45861 q^{50} -7.24573 q^{51} +12.9933 q^{52} -2.47557 q^{53} +15.8682 q^{54} +6.12687 q^{55} +28.3358 q^{56} +4.53691 q^{57} -12.2191 q^{58} -13.3144 q^{59} +17.9096 q^{60} -9.04921 q^{61} +22.4720 q^{62} +2.02411 q^{63} +52.2278 q^{64} +4.45015 q^{65} -12.6242 q^{66} +3.65186 q^{67} -28.9160 q^{68} -3.75228 q^{69} +14.6419 q^{70} -1.86745 q^{71} +8.75716 q^{72} +13.5051 q^{73} +12.3203 q^{74} -1.29754 q^{75} +18.1057 q^{76} -7.71835 q^{77} -9.16938 q^{78} +13.6991 q^{79} +39.2474 q^{80} -6.00169 q^{81} -20.9262 q^{82} +2.47599 q^{83} -22.5617 q^{84} -9.90361 q^{85} -10.7493 q^{86} +6.44862 q^{87} -33.3929 q^{88} +1.92010 q^{89} +4.52507 q^{90} -5.60609 q^{91} -14.9745 q^{92} -11.8596 q^{93} +31.7770 q^{94} +6.20114 q^{95} -47.9550 q^{96} -16.5638 q^{97} +1.26882 q^{98} -2.38535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} + O(q^{10}) \) \( 152q - 22q^{2} - 18q^{3} + 138q^{4} - 59q^{5} - 17q^{6} - 19q^{7} - 66q^{8} + 106q^{9} - 15q^{10} - 40q^{11} - 53q^{12} - 59q^{13} - 36q^{14} - 40q^{15} + 118q^{16} - 93q^{17} - 59q^{18} - 16q^{19} - 108q^{20} - 62q^{21} - 37q^{22} - 107q^{23} - 31q^{24} + 101q^{25} - 64q^{26} - 63q^{27} - 53q^{28} - 124q^{29} - 68q^{30} - 15q^{31} - 129q^{32} - 49q^{33} - 76q^{35} + 45q^{36} - 98q^{37} - 125q^{38} - 47q^{39} - 7q^{40} - 56q^{41} - 84q^{42} - 62q^{43} - 114q^{44} - 142q^{45} - 3q^{46} - 111q^{47} - 92q^{48} + 117q^{49} - 64q^{50} - 21q^{51} - 85q^{52} - 347q^{53} + 3q^{54} - 16q^{55} - 73q^{56} - 115q^{57} - 29q^{58} - 50q^{59} - 54q^{60} - 62q^{61} - 55q^{62} - 70q^{63} + 64q^{64} - 147q^{65} + 34q^{66} - 86q^{67} - 174q^{68} - 104q^{69} - 7q^{70} - 86q^{71} - 139q^{72} - 27q^{73} - 52q^{74} - 49q^{75} - 11q^{76} - 346q^{77} - 59q^{78} - 17q^{79} - 149q^{80} - 8q^{81} - 31q^{82} - 106q^{83} - 51q^{84} - 69q^{85} - 85q^{86} - 32q^{87} - 113q^{88} - 59q^{89} + 10q^{90} - 9q^{91} - 314q^{92} - 230q^{93} + 7q^{94} - 74q^{95} - 54q^{96} - 60q^{97} - 77q^{98} - 96q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.81629 −1.99142 −0.995708 0.0925529i \(-0.970497\pi\)
−0.995708 + 0.0925529i \(0.970497\pi\)
\(3\) 1.48630 0.858115 0.429057 0.903277i \(-0.358846\pi\)
0.429057 + 0.903277i \(0.358846\pi\)
\(4\) 5.93147 2.96574
\(5\) 2.03150 0.908515 0.454258 0.890870i \(-0.349905\pi\)
0.454258 + 0.890870i \(0.349905\pi\)
\(6\) −4.18584 −1.70886
\(7\) −2.55919 −0.967284 −0.483642 0.875266i \(-0.660686\pi\)
−0.483642 + 0.875266i \(0.660686\pi\)
\(8\) −11.0722 −3.91460
\(9\) −0.790918 −0.263639
\(10\) −5.72129 −1.80923
\(11\) 3.01593 0.909338 0.454669 0.890661i \(-0.349758\pi\)
0.454669 + 0.890661i \(0.349758\pi\)
\(12\) 8.81594 2.54494
\(13\) 2.19057 0.607555 0.303777 0.952743i \(-0.401752\pi\)
0.303777 + 0.952743i \(0.401752\pi\)
\(14\) 7.20742 1.92626
\(15\) 3.01942 0.779610
\(16\) 19.3194 4.82985
\(17\) −4.87502 −1.18237 −0.591183 0.806538i \(-0.701339\pi\)
−0.591183 + 0.806538i \(0.701339\pi\)
\(18\) 2.22745 0.525015
\(19\) 3.05249 0.700289 0.350144 0.936696i \(-0.386132\pi\)
0.350144 + 0.936696i \(0.386132\pi\)
\(20\) 12.0498 2.69442
\(21\) −3.80372 −0.830041
\(22\) −8.49373 −1.81087
\(23\) −2.52458 −0.526412 −0.263206 0.964740i \(-0.584780\pi\)
−0.263206 + 0.964740i \(0.584780\pi\)
\(24\) −16.4565 −3.35917
\(25\) −0.872998 −0.174600
\(26\) −6.16927 −1.20989
\(27\) −5.63443 −1.08435
\(28\) −15.1798 −2.86871
\(29\) 4.33871 0.805678 0.402839 0.915271i \(-0.368023\pi\)
0.402839 + 0.915271i \(0.368023\pi\)
\(30\) −8.50355 −1.55253
\(31\) −7.97929 −1.43312 −0.716562 0.697524i \(-0.754285\pi\)
−0.716562 + 0.697524i \(0.754285\pi\)
\(32\) −32.2647 −5.70365
\(33\) 4.48257 0.780316
\(34\) 13.7294 2.35458
\(35\) −5.19901 −0.878793
\(36\) −4.69131 −0.781885
\(37\) −4.37466 −0.719190 −0.359595 0.933108i \(-0.617085\pi\)
−0.359595 + 0.933108i \(0.617085\pi\)
\(38\) −8.59668 −1.39457
\(39\) 3.25584 0.521352
\(40\) −22.4931 −3.55647
\(41\) 7.43043 1.16044 0.580219 0.814460i \(-0.302967\pi\)
0.580219 + 0.814460i \(0.302967\pi\)
\(42\) 10.7124 1.65296
\(43\) 3.81685 0.582064 0.291032 0.956713i \(-0.406001\pi\)
0.291032 + 0.956713i \(0.406001\pi\)
\(44\) 17.8889 2.69686
\(45\) −1.60675 −0.239520
\(46\) 7.10995 1.04831
\(47\) −11.2833 −1.64584 −0.822918 0.568160i \(-0.807656\pi\)
−0.822918 + 0.568160i \(0.807656\pi\)
\(48\) 28.7144 4.14457
\(49\) −0.450529 −0.0643612
\(50\) 2.45861 0.347700
\(51\) −7.24573 −1.01461
\(52\) 12.9933 1.80185
\(53\) −2.47557 −0.340045 −0.170023 0.985440i \(-0.554384\pi\)
−0.170023 + 0.985440i \(0.554384\pi\)
\(54\) 15.8682 2.15939
\(55\) 6.12687 0.826147
\(56\) 28.3358 3.78653
\(57\) 4.53691 0.600928
\(58\) −12.2191 −1.60444
\(59\) −13.3144 −1.73339 −0.866694 0.498841i \(-0.833759\pi\)
−0.866694 + 0.498841i \(0.833759\pi\)
\(60\) 17.9096 2.31212
\(61\) −9.04921 −1.15863 −0.579316 0.815103i \(-0.696680\pi\)
−0.579316 + 0.815103i \(0.696680\pi\)
\(62\) 22.4720 2.85394
\(63\) 2.02411 0.255014
\(64\) 52.2278 6.52848
\(65\) 4.45015 0.551973
\(66\) −12.6242 −1.55393
\(67\) 3.65186 0.446146 0.223073 0.974802i \(-0.428391\pi\)
0.223073 + 0.974802i \(0.428391\pi\)
\(68\) −28.9160 −3.50658
\(69\) −3.75228 −0.451722
\(70\) 14.6419 1.75004
\(71\) −1.86745 −0.221626 −0.110813 0.993841i \(-0.535345\pi\)
−0.110813 + 0.993841i \(0.535345\pi\)
\(72\) 8.75716 1.03204
\(73\) 13.5051 1.58065 0.790325 0.612687i \(-0.209912\pi\)
0.790325 + 0.612687i \(0.209912\pi\)
\(74\) 12.3203 1.43221
\(75\) −1.29754 −0.149827
\(76\) 18.1057 2.07687
\(77\) −7.71835 −0.879588
\(78\) −9.16938 −1.03823
\(79\) 13.6991 1.54127 0.770633 0.637279i \(-0.219940\pi\)
0.770633 + 0.637279i \(0.219940\pi\)
\(80\) 39.2474 4.38800
\(81\) −6.00169 −0.666855
\(82\) −20.9262 −2.31091
\(83\) 2.47599 0.271775 0.135888 0.990724i \(-0.456611\pi\)
0.135888 + 0.990724i \(0.456611\pi\)
\(84\) −22.5617 −2.46168
\(85\) −9.90361 −1.07420
\(86\) −10.7493 −1.15913
\(87\) 6.44862 0.691364
\(88\) −33.3929 −3.55969
\(89\) 1.92010 0.203530 0.101765 0.994808i \(-0.467551\pi\)
0.101765 + 0.994808i \(0.467551\pi\)
\(90\) 4.52507 0.476985
\(91\) −5.60609 −0.587678
\(92\) −14.9745 −1.56120
\(93\) −11.8596 −1.22978
\(94\) 31.7770 3.27755
\(95\) 6.20114 0.636223
\(96\) −47.9550 −4.89438
\(97\) −16.5638 −1.68180 −0.840899 0.541192i \(-0.817973\pi\)
−0.840899 + 0.541192i \(0.817973\pi\)
\(98\) 1.26882 0.128170
\(99\) −2.38535 −0.239737
\(100\) −5.17816 −0.517816
\(101\) −17.9038 −1.78149 −0.890746 0.454502i \(-0.849817\pi\)
−0.890746 + 0.454502i \(0.849817\pi\)
\(102\) 20.4061 2.02050
\(103\) 13.8252 1.36224 0.681119 0.732173i \(-0.261494\pi\)
0.681119 + 0.732173i \(0.261494\pi\)
\(104\) −24.2543 −2.37833
\(105\) −7.72727 −0.754105
\(106\) 6.97191 0.677172
\(107\) −7.33026 −0.708643 −0.354322 0.935124i \(-0.615288\pi\)
−0.354322 + 0.935124i \(0.615288\pi\)
\(108\) −33.4205 −3.21589
\(109\) 1.38714 0.132864 0.0664318 0.997791i \(-0.478839\pi\)
0.0664318 + 0.997791i \(0.478839\pi\)
\(110\) −17.2550 −1.64520
\(111\) −6.50205 −0.617147
\(112\) −49.4421 −4.67184
\(113\) −14.5427 −1.36806 −0.684030 0.729454i \(-0.739774\pi\)
−0.684030 + 0.729454i \(0.739774\pi\)
\(114\) −12.7772 −1.19670
\(115\) −5.12870 −0.478254
\(116\) 25.7349 2.38943
\(117\) −1.73256 −0.160175
\(118\) 37.4972 3.45189
\(119\) 12.4761 1.14368
\(120\) −33.4315 −3.05186
\(121\) −1.90416 −0.173105
\(122\) 25.4852 2.30732
\(123\) 11.0438 0.995789
\(124\) −47.3289 −4.25026
\(125\) −11.9310 −1.06714
\(126\) −5.70048 −0.507839
\(127\) −16.6270 −1.47541 −0.737706 0.675122i \(-0.764091\pi\)
−0.737706 + 0.675122i \(0.764091\pi\)
\(128\) −82.5592 −7.29727
\(129\) 5.67297 0.499477
\(130\) −12.5329 −1.09921
\(131\) 12.2836 1.07322 0.536612 0.843829i \(-0.319704\pi\)
0.536612 + 0.843829i \(0.319704\pi\)
\(132\) 26.5883 2.31421
\(133\) −7.81191 −0.677378
\(134\) −10.2847 −0.888461
\(135\) −11.4464 −0.985146
\(136\) 53.9769 4.62848
\(137\) 9.56305 0.817027 0.408513 0.912752i \(-0.366047\pi\)
0.408513 + 0.912752i \(0.366047\pi\)
\(138\) 10.5675 0.899566
\(139\) −17.0687 −1.44775 −0.723874 0.689932i \(-0.757640\pi\)
−0.723874 + 0.689932i \(0.757640\pi\)
\(140\) −30.8378 −2.60627
\(141\) −16.7703 −1.41232
\(142\) 5.25929 0.441349
\(143\) 6.60661 0.552472
\(144\) −15.2801 −1.27334
\(145\) 8.81410 0.731971
\(146\) −38.0342 −3.14773
\(147\) −0.669620 −0.0552293
\(148\) −25.9482 −2.13293
\(149\) 9.81087 0.803737 0.401869 0.915697i \(-0.368361\pi\)
0.401869 + 0.915697i \(0.368361\pi\)
\(150\) 3.65423 0.298367
\(151\) 18.9683 1.54362 0.771810 0.635853i \(-0.219352\pi\)
0.771810 + 0.635853i \(0.219352\pi\)
\(152\) −33.7976 −2.74135
\(153\) 3.85574 0.311718
\(154\) 21.7371 1.75163
\(155\) −16.2100 −1.30201
\(156\) 19.3119 1.54619
\(157\) 0.172985 0.0138057 0.00690284 0.999976i \(-0.497803\pi\)
0.00690284 + 0.999976i \(0.497803\pi\)
\(158\) −38.5805 −3.06930
\(159\) −3.67943 −0.291798
\(160\) −65.5458 −5.18185
\(161\) 6.46090 0.509190
\(162\) 16.9025 1.32799
\(163\) 8.36622 0.655293 0.327646 0.944800i \(-0.393745\pi\)
0.327646 + 0.944800i \(0.393745\pi\)
\(164\) 44.0734 3.44155
\(165\) 9.10636 0.708929
\(166\) −6.97310 −0.541217
\(167\) 0.190375 0.0147317 0.00736585 0.999973i \(-0.497655\pi\)
0.00736585 + 0.999973i \(0.497655\pi\)
\(168\) 42.1154 3.24927
\(169\) −8.20140 −0.630877
\(170\) 27.8914 2.13917
\(171\) −2.41427 −0.184624
\(172\) 22.6395 1.72625
\(173\) −20.6229 −1.56793 −0.783965 0.620805i \(-0.786806\pi\)
−0.783965 + 0.620805i \(0.786806\pi\)
\(174\) −18.1612 −1.37679
\(175\) 2.23417 0.168888
\(176\) 58.2660 4.39197
\(177\) −19.7892 −1.48744
\(178\) −5.40754 −0.405312
\(179\) −1.27139 −0.0950281 −0.0475140 0.998871i \(-0.515130\pi\)
−0.0475140 + 0.998871i \(0.515130\pi\)
\(180\) −9.53040 −0.710354
\(181\) 3.27974 0.243782 0.121891 0.992544i \(-0.461104\pi\)
0.121891 + 0.992544i \(0.461104\pi\)
\(182\) 15.7884 1.17031
\(183\) −13.4498 −0.994240
\(184\) 27.9526 2.06069
\(185\) −8.88714 −0.653395
\(186\) 33.4001 2.44901
\(187\) −14.7027 −1.07517
\(188\) −66.9265 −4.88112
\(189\) 14.4196 1.04887
\(190\) −17.4642 −1.26698
\(191\) 9.90175 0.716466 0.358233 0.933632i \(-0.383379\pi\)
0.358233 + 0.933632i \(0.383379\pi\)
\(192\) 77.6261 5.60218
\(193\) −0.457067 −0.0329004 −0.0164502 0.999865i \(-0.505236\pi\)
−0.0164502 + 0.999865i \(0.505236\pi\)
\(194\) 46.6484 3.34916
\(195\) 6.61425 0.473656
\(196\) −2.67230 −0.190878
\(197\) −3.46518 −0.246884 −0.123442 0.992352i \(-0.539393\pi\)
−0.123442 + 0.992352i \(0.539393\pi\)
\(198\) 6.71784 0.477416
\(199\) 10.1540 0.719795 0.359898 0.932992i \(-0.382812\pi\)
0.359898 + 0.932992i \(0.382812\pi\)
\(200\) 9.66597 0.683487
\(201\) 5.42775 0.382844
\(202\) 50.4221 3.54769
\(203\) −11.1036 −0.779320
\(204\) −42.9778 −3.00905
\(205\) 15.0949 1.05428
\(206\) −38.9357 −2.71278
\(207\) 1.99674 0.138783
\(208\) 42.3205 2.93440
\(209\) 9.20610 0.636799
\(210\) 21.7622 1.50174
\(211\) 13.6537 0.939959 0.469979 0.882677i \(-0.344261\pi\)
0.469979 + 0.882677i \(0.344261\pi\)
\(212\) −14.6838 −1.00848
\(213\) −2.77559 −0.190181
\(214\) 20.6441 1.41120
\(215\) 7.75393 0.528814
\(216\) 62.3853 4.24478
\(217\) 20.4206 1.38624
\(218\) −3.90658 −0.264587
\(219\) 20.0726 1.35638
\(220\) 36.3414 2.45013
\(221\) −10.6791 −0.718352
\(222\) 18.3116 1.22900
\(223\) −3.28824 −0.220197 −0.110098 0.993921i \(-0.535117\pi\)
−0.110098 + 0.993921i \(0.535117\pi\)
\(224\) 82.5716 5.51705
\(225\) 0.690470 0.0460313
\(226\) 40.9563 2.72437
\(227\) −28.2516 −1.87512 −0.937562 0.347819i \(-0.886922\pi\)
−0.937562 + 0.347819i \(0.886922\pi\)
\(228\) 26.9105 1.78219
\(229\) −13.8737 −0.916803 −0.458401 0.888745i \(-0.651578\pi\)
−0.458401 + 0.888745i \(0.651578\pi\)
\(230\) 14.4439 0.952402
\(231\) −11.4718 −0.754787
\(232\) −48.0389 −3.15391
\(233\) 8.45035 0.553601 0.276800 0.960927i \(-0.410726\pi\)
0.276800 + 0.960927i \(0.410726\pi\)
\(234\) 4.87939 0.318976
\(235\) −22.9220 −1.49527
\(236\) −78.9740 −5.14077
\(237\) 20.3609 1.32258
\(238\) −35.1363 −2.27755
\(239\) −13.7979 −0.892509 −0.446254 0.894906i \(-0.647242\pi\)
−0.446254 + 0.894906i \(0.647242\pi\)
\(240\) 58.3334 3.76540
\(241\) 20.4498 1.31729 0.658644 0.752455i \(-0.271130\pi\)
0.658644 + 0.752455i \(0.271130\pi\)
\(242\) 5.36265 0.344724
\(243\) 7.98299 0.512109
\(244\) −53.6751 −3.43620
\(245\) −0.915250 −0.0584732
\(246\) −31.1026 −1.98303
\(247\) 6.68669 0.425464
\(248\) 88.3479 5.61010
\(249\) 3.68006 0.233214
\(250\) 33.6011 2.12512
\(251\) 15.8650 1.00139 0.500696 0.865623i \(-0.333077\pi\)
0.500696 + 0.865623i \(0.333077\pi\)
\(252\) 12.0060 0.756305
\(253\) −7.61397 −0.478686
\(254\) 46.8265 2.93816
\(255\) −14.7197 −0.921784
\(256\) 128.055 8.00341
\(257\) −14.0306 −0.875202 −0.437601 0.899169i \(-0.644172\pi\)
−0.437601 + 0.899169i \(0.644172\pi\)
\(258\) −15.9767 −0.994667
\(259\) 11.1956 0.695661
\(260\) 26.3959 1.63701
\(261\) −3.43156 −0.212409
\(262\) −34.5942 −2.13724
\(263\) −11.3597 −0.700468 −0.350234 0.936662i \(-0.613898\pi\)
−0.350234 + 0.936662i \(0.613898\pi\)
\(264\) −49.6317 −3.05462
\(265\) −5.02912 −0.308937
\(266\) 22.0006 1.34894
\(267\) 2.85384 0.174652
\(268\) 21.6609 1.32315
\(269\) −4.45571 −0.271670 −0.135835 0.990731i \(-0.543372\pi\)
−0.135835 + 0.990731i \(0.543372\pi\)
\(270\) 32.2363 1.96184
\(271\) −18.6220 −1.13120 −0.565602 0.824678i \(-0.691356\pi\)
−0.565602 + 0.824678i \(0.691356\pi\)
\(272\) −94.1825 −5.71065
\(273\) −8.33232 −0.504295
\(274\) −26.9323 −1.62704
\(275\) −2.63290 −0.158770
\(276\) −22.2566 −1.33969
\(277\) −13.2756 −0.797651 −0.398825 0.917027i \(-0.630582\pi\)
−0.398825 + 0.917027i \(0.630582\pi\)
\(278\) 48.0704 2.88307
\(279\) 6.31097 0.377828
\(280\) 57.5642 3.44012
\(281\) −20.5189 −1.22406 −0.612029 0.790836i \(-0.709646\pi\)
−0.612029 + 0.790836i \(0.709646\pi\)
\(282\) 47.2301 2.81251
\(283\) 25.3166 1.50492 0.752459 0.658640i \(-0.228868\pi\)
0.752459 + 0.658640i \(0.228868\pi\)
\(284\) −11.0768 −0.657284
\(285\) 9.21674 0.545952
\(286\) −18.6061 −1.10020
\(287\) −19.0159 −1.12247
\(288\) 25.5187 1.50371
\(289\) 6.76580 0.397988
\(290\) −24.8230 −1.45766
\(291\) −24.6187 −1.44318
\(292\) 80.1050 4.68779
\(293\) 21.0101 1.22743 0.613713 0.789530i \(-0.289675\pi\)
0.613713 + 0.789530i \(0.289675\pi\)
\(294\) 1.88584 0.109985
\(295\) −27.0482 −1.57481
\(296\) 48.4369 2.81534
\(297\) −16.9931 −0.986038
\(298\) −27.6302 −1.60058
\(299\) −5.53028 −0.319824
\(300\) −7.69630 −0.444346
\(301\) −9.76805 −0.563021
\(302\) −53.4202 −3.07399
\(303\) −26.6103 −1.52872
\(304\) 58.9723 3.38229
\(305\) −18.3835 −1.05264
\(306\) −10.8589 −0.620760
\(307\) 9.65309 0.550931 0.275466 0.961311i \(-0.411168\pi\)
0.275466 + 0.961311i \(0.411168\pi\)
\(308\) −45.7812 −2.60863
\(309\) 20.5484 1.16896
\(310\) 45.6519 2.59285
\(311\) −15.8888 −0.900973 −0.450486 0.892783i \(-0.648749\pi\)
−0.450486 + 0.892783i \(0.648749\pi\)
\(312\) −36.0492 −2.04088
\(313\) 16.1994 0.915645 0.457823 0.889044i \(-0.348629\pi\)
0.457823 + 0.889044i \(0.348629\pi\)
\(314\) −0.487175 −0.0274929
\(315\) 4.11199 0.231684
\(316\) 81.2557 4.57099
\(317\) 3.60294 0.202361 0.101181 0.994868i \(-0.467738\pi\)
0.101181 + 0.994868i \(0.467738\pi\)
\(318\) 10.3623 0.581091
\(319\) 13.0853 0.732634
\(320\) 106.101 5.93122
\(321\) −10.8950 −0.608097
\(322\) −18.1957 −1.01401
\(323\) −14.8809 −0.827997
\(324\) −35.5989 −1.97772
\(325\) −1.91236 −0.106079
\(326\) −23.5617 −1.30496
\(327\) 2.06170 0.114012
\(328\) −82.2708 −4.54265
\(329\) 28.8761 1.59199
\(330\) −25.6461 −1.41177
\(331\) −33.9941 −1.86848 −0.934241 0.356642i \(-0.883922\pi\)
−0.934241 + 0.356642i \(0.883922\pi\)
\(332\) 14.6863 0.806013
\(333\) 3.46000 0.189607
\(334\) −0.536152 −0.0293369
\(335\) 7.41876 0.405330
\(336\) −73.4857 −4.00897
\(337\) 6.78669 0.369695 0.184847 0.982767i \(-0.440821\pi\)
0.184847 + 0.982767i \(0.440821\pi\)
\(338\) 23.0975 1.25634
\(339\) −21.6147 −1.17395
\(340\) −58.7430 −3.18579
\(341\) −24.0650 −1.30319
\(342\) 6.79927 0.367662
\(343\) 19.0673 1.02954
\(344\) −42.2607 −2.27855
\(345\) −7.62278 −0.410396
\(346\) 58.0800 3.12240
\(347\) −23.3272 −1.25227 −0.626134 0.779716i \(-0.715364\pi\)
−0.626134 + 0.779716i \(0.715364\pi\)
\(348\) 38.2498 2.05040
\(349\) −4.89243 −0.261886 −0.130943 0.991390i \(-0.541800\pi\)
−0.130943 + 0.991390i \(0.541800\pi\)
\(350\) −6.29207 −0.336325
\(351\) −12.3426 −0.658800
\(352\) −97.3081 −5.18654
\(353\) 8.81005 0.468911 0.234456 0.972127i \(-0.424669\pi\)
0.234456 + 0.972127i \(0.424669\pi\)
\(354\) 55.7320 2.96212
\(355\) −3.79374 −0.201351
\(356\) 11.3890 0.603616
\(357\) 18.5432 0.981412
\(358\) 3.58060 0.189240
\(359\) −20.2522 −1.06887 −0.534435 0.845209i \(-0.679476\pi\)
−0.534435 + 0.845209i \(0.679476\pi\)
\(360\) 17.7902 0.937626
\(361\) −9.68231 −0.509595
\(362\) −9.23670 −0.485470
\(363\) −2.83014 −0.148544
\(364\) −33.2524 −1.74290
\(365\) 27.4356 1.43605
\(366\) 37.8786 1.97994
\(367\) −18.8012 −0.981413 −0.490707 0.871325i \(-0.663261\pi\)
−0.490707 + 0.871325i \(0.663261\pi\)
\(368\) −48.7735 −2.54249
\(369\) −5.87686 −0.305937
\(370\) 25.0287 1.30118
\(371\) 6.33546 0.328921
\(372\) −70.3449 −3.64721
\(373\) 10.4843 0.542857 0.271428 0.962459i \(-0.412504\pi\)
0.271428 + 0.962459i \(0.412504\pi\)
\(374\) 41.4071 2.14111
\(375\) −17.7330 −0.915730
\(376\) 124.930 6.44279
\(377\) 9.50425 0.489494
\(378\) −40.6098 −2.08874
\(379\) −0.572538 −0.0294093 −0.0147047 0.999892i \(-0.504681\pi\)
−0.0147047 + 0.999892i \(0.504681\pi\)
\(380\) 36.7819 1.88687
\(381\) −24.7127 −1.26607
\(382\) −27.8862 −1.42678
\(383\) 7.59912 0.388297 0.194148 0.980972i \(-0.437806\pi\)
0.194148 + 0.980972i \(0.437806\pi\)
\(384\) −122.708 −6.26189
\(385\) −15.6799 −0.799119
\(386\) 1.28723 0.0655183
\(387\) −3.01881 −0.153455
\(388\) −98.2477 −4.98777
\(389\) −16.6276 −0.843051 −0.421525 0.906817i \(-0.638505\pi\)
−0.421525 + 0.906817i \(0.638505\pi\)
\(390\) −18.6276 −0.943246
\(391\) 12.3074 0.622412
\(392\) 4.98832 0.251948
\(393\) 18.2571 0.920950
\(394\) 9.75895 0.491649
\(395\) 27.8297 1.40026
\(396\) −14.1487 −0.710997
\(397\) −24.2546 −1.21730 −0.608651 0.793438i \(-0.708289\pi\)
−0.608651 + 0.793438i \(0.708289\pi\)
\(398\) −28.5965 −1.43341
\(399\) −11.6108 −0.581268
\(400\) −16.8658 −0.843291
\(401\) −9.21474 −0.460162 −0.230081 0.973171i \(-0.573899\pi\)
−0.230081 + 0.973171i \(0.573899\pi\)
\(402\) −15.2861 −0.762402
\(403\) −17.4792 −0.870701
\(404\) −106.196 −5.28343
\(405\) −12.1925 −0.605848
\(406\) 31.2709 1.55195
\(407\) −13.1937 −0.653986
\(408\) 80.2258 3.97177
\(409\) 32.1400 1.58922 0.794610 0.607120i \(-0.207675\pi\)
0.794610 + 0.607120i \(0.207675\pi\)
\(410\) −42.5117 −2.09950
\(411\) 14.2135 0.701102
\(412\) 82.0038 4.04004
\(413\) 34.0741 1.67668
\(414\) −5.62339 −0.276375
\(415\) 5.02998 0.246912
\(416\) −70.6781 −3.46528
\(417\) −25.3692 −1.24233
\(418\) −25.9270 −1.26813
\(419\) −28.2051 −1.37791 −0.688954 0.724805i \(-0.741930\pi\)
−0.688954 + 0.724805i \(0.741930\pi\)
\(420\) −45.8341 −2.23648
\(421\) 22.8254 1.11244 0.556222 0.831034i \(-0.312250\pi\)
0.556222 + 0.831034i \(0.312250\pi\)
\(422\) −38.4527 −1.87185
\(423\) 8.92416 0.433907
\(424\) 27.4099 1.33114
\(425\) 4.25588 0.206441
\(426\) 7.81687 0.378728
\(427\) 23.1587 1.12073
\(428\) −43.4792 −2.10165
\(429\) 9.81939 0.474085
\(430\) −21.8373 −1.05309
\(431\) −17.6511 −0.850221 −0.425111 0.905141i \(-0.639765\pi\)
−0.425111 + 0.905141i \(0.639765\pi\)
\(432\) −108.854 −5.23724
\(433\) 26.9746 1.29632 0.648158 0.761506i \(-0.275540\pi\)
0.648158 + 0.761506i \(0.275540\pi\)
\(434\) −57.5101 −2.76057
\(435\) 13.1004 0.628115
\(436\) 8.22777 0.394039
\(437\) −7.70626 −0.368641
\(438\) −56.5301 −2.70112
\(439\) −35.0299 −1.67188 −0.835942 0.548817i \(-0.815078\pi\)
−0.835942 + 0.548817i \(0.815078\pi\)
\(440\) −67.8377 −3.23403
\(441\) 0.356331 0.0169682
\(442\) 30.0753 1.43054
\(443\) 26.8827 1.27724 0.638618 0.769524i \(-0.279507\pi\)
0.638618 + 0.769524i \(0.279507\pi\)
\(444\) −38.5667 −1.83030
\(445\) 3.90068 0.184910
\(446\) 9.26063 0.438503
\(447\) 14.5819 0.689699
\(448\) −133.661 −6.31490
\(449\) 23.2977 1.09949 0.549744 0.835333i \(-0.314725\pi\)
0.549744 + 0.835333i \(0.314725\pi\)
\(450\) −1.94456 −0.0916675
\(451\) 22.4097 1.05523
\(452\) −86.2594 −4.05730
\(453\) 28.1926 1.32460
\(454\) 79.5645 3.73415
\(455\) −11.3888 −0.533915
\(456\) −50.2333 −2.35239
\(457\) −0.147124 −0.00688218 −0.00344109 0.999994i \(-0.501095\pi\)
−0.00344109 + 0.999994i \(0.501095\pi\)
\(458\) 39.0725 1.82574
\(459\) 27.4680 1.28209
\(460\) −30.4207 −1.41837
\(461\) 10.0003 0.465762 0.232881 0.972505i \(-0.425185\pi\)
0.232881 + 0.972505i \(0.425185\pi\)
\(462\) 32.3078 1.50309
\(463\) 11.8656 0.551442 0.275721 0.961238i \(-0.411083\pi\)
0.275721 + 0.961238i \(0.411083\pi\)
\(464\) 83.8214 3.89131
\(465\) −24.0928 −1.11728
\(466\) −23.7986 −1.10245
\(467\) 34.2298 1.58396 0.791982 0.610544i \(-0.209049\pi\)
0.791982 + 0.610544i \(0.209049\pi\)
\(468\) −10.2766 −0.475038
\(469\) −9.34581 −0.431550
\(470\) 64.5550 2.97770
\(471\) 0.257107 0.0118469
\(472\) 147.419 6.78551
\(473\) 11.5114 0.529293
\(474\) −57.3422 −2.63381
\(475\) −2.66482 −0.122270
\(476\) 74.0017 3.39186
\(477\) 1.95797 0.0896493
\(478\) 38.8587 1.77736
\(479\) −12.6273 −0.576957 −0.288479 0.957486i \(-0.593149\pi\)
−0.288479 + 0.957486i \(0.593149\pi\)
\(480\) −97.4206 −4.44662
\(481\) −9.58300 −0.436947
\(482\) −57.5925 −2.62327
\(483\) 9.60282 0.436944
\(484\) −11.2945 −0.513384
\(485\) −33.6494 −1.52794
\(486\) −22.4824 −1.01982
\(487\) 21.4702 0.972910 0.486455 0.873706i \(-0.338290\pi\)
0.486455 + 0.873706i \(0.338290\pi\)
\(488\) 100.194 4.53558
\(489\) 12.4347 0.562316
\(490\) 2.57761 0.116444
\(491\) −23.4050 −1.05625 −0.528127 0.849166i \(-0.677105\pi\)
−0.528127 + 0.849166i \(0.677105\pi\)
\(492\) 65.5062 2.95325
\(493\) −21.1513 −0.952606
\(494\) −18.8316 −0.847275
\(495\) −4.84585 −0.217805
\(496\) −154.155 −6.92177
\(497\) 4.77918 0.214375
\(498\) −10.3641 −0.464427
\(499\) 3.02449 0.135395 0.0676975 0.997706i \(-0.478435\pi\)
0.0676975 + 0.997706i \(0.478435\pi\)
\(500\) −70.7684 −3.16486
\(501\) 0.282955 0.0126415
\(502\) −44.6805 −1.99419
\(503\) 8.71329 0.388506 0.194253 0.980951i \(-0.437772\pi\)
0.194253 + 0.980951i \(0.437772\pi\)
\(504\) −22.4113 −0.998278
\(505\) −36.3715 −1.61851
\(506\) 21.4431 0.953264
\(507\) −12.1897 −0.541365
\(508\) −98.6228 −4.37568
\(509\) 13.2435 0.587006 0.293503 0.955958i \(-0.405179\pi\)
0.293503 + 0.955958i \(0.405179\pi\)
\(510\) 41.4549 1.83566
\(511\) −34.5621 −1.52894
\(512\) −195.520 −8.64085
\(513\) −17.1990 −0.759356
\(514\) 39.5141 1.74289
\(515\) 28.0859 1.23761
\(516\) 33.6491 1.48132
\(517\) −34.0296 −1.49662
\(518\) −31.5300 −1.38535
\(519\) −30.6518 −1.34546
\(520\) −49.2727 −2.16075
\(521\) 15.0482 0.659275 0.329637 0.944108i \(-0.393074\pi\)
0.329637 + 0.944108i \(0.393074\pi\)
\(522\) 9.66427 0.422994
\(523\) −33.0303 −1.44431 −0.722157 0.691730i \(-0.756849\pi\)
−0.722157 + 0.691730i \(0.756849\pi\)
\(524\) 72.8599 3.18290
\(525\) 3.32065 0.144925
\(526\) 31.9921 1.39492
\(527\) 38.8992 1.69448
\(528\) 86.6007 3.76881
\(529\) −16.6265 −0.722890
\(530\) 14.1635 0.615221
\(531\) 10.5306 0.456989
\(532\) −46.3361 −2.00893
\(533\) 16.2769 0.705030
\(534\) −8.03722 −0.347805
\(535\) −14.8914 −0.643813
\(536\) −40.4339 −1.74648
\(537\) −1.88966 −0.0815450
\(538\) 12.5486 0.541007
\(539\) −1.35876 −0.0585261
\(540\) −67.8938 −2.92168
\(541\) 25.9573 1.11599 0.557996 0.829844i \(-0.311571\pi\)
0.557996 + 0.829844i \(0.311571\pi\)
\(542\) 52.4448 2.25270
\(543\) 4.87468 0.209192
\(544\) 157.291 6.74380
\(545\) 2.81797 0.120709
\(546\) 23.4662 1.00426
\(547\) 21.0968 0.902036 0.451018 0.892515i \(-0.351061\pi\)
0.451018 + 0.892515i \(0.351061\pi\)
\(548\) 56.7230 2.42308
\(549\) 7.15719 0.305461
\(550\) 7.41501 0.316177
\(551\) 13.2439 0.564208
\(552\) 41.5459 1.76831
\(553\) −35.0586 −1.49084
\(554\) 37.3878 1.58845
\(555\) −13.2089 −0.560688
\(556\) −101.243 −4.29364
\(557\) −4.73538 −0.200645 −0.100322 0.994955i \(-0.531987\pi\)
−0.100322 + 0.994955i \(0.531987\pi\)
\(558\) −17.7735 −0.752412
\(559\) 8.36107 0.353636
\(560\) −100.442 −4.24444
\(561\) −21.8526 −0.922619
\(562\) 57.7872 2.43761
\(563\) −13.6152 −0.573812 −0.286906 0.957959i \(-0.592627\pi\)
−0.286906 + 0.957959i \(0.592627\pi\)
\(564\) −99.4727 −4.18856
\(565\) −29.5435 −1.24290
\(566\) −71.2989 −2.99692
\(567\) 15.3595 0.645038
\(568\) 20.6767 0.867577
\(569\) −28.9909 −1.21536 −0.607681 0.794181i \(-0.707900\pi\)
−0.607681 + 0.794181i \(0.707900\pi\)
\(570\) −25.9570 −1.08722
\(571\) 14.1605 0.592599 0.296299 0.955095i \(-0.404247\pi\)
0.296299 + 0.955095i \(0.404247\pi\)
\(572\) 39.1869 1.63849
\(573\) 14.7170 0.614810
\(574\) 53.5542 2.23531
\(575\) 2.20396 0.0919114
\(576\) −41.3079 −1.72116
\(577\) −34.1981 −1.42369 −0.711843 0.702339i \(-0.752139\pi\)
−0.711843 + 0.702339i \(0.752139\pi\)
\(578\) −19.0544 −0.792560
\(579\) −0.679337 −0.0282323
\(580\) 52.2806 2.17083
\(581\) −6.33654 −0.262884
\(582\) 69.3334 2.87396
\(583\) −7.46614 −0.309216
\(584\) −149.530 −6.18761
\(585\) −3.51970 −0.145522
\(586\) −59.1706 −2.44431
\(587\) 36.8976 1.52293 0.761463 0.648208i \(-0.224481\pi\)
0.761463 + 0.648208i \(0.224481\pi\)
\(588\) −3.97183 −0.163796
\(589\) −24.3567 −1.00360
\(590\) 76.1756 3.13610
\(591\) −5.15029 −0.211855
\(592\) −84.5159 −3.47358
\(593\) 8.08364 0.331955 0.165978 0.986130i \(-0.446922\pi\)
0.165978 + 0.986130i \(0.446922\pi\)
\(594\) 47.8574 1.96361
\(595\) 25.3453 1.03905
\(596\) 58.1929 2.38367
\(597\) 15.0918 0.617667
\(598\) 15.5748 0.636903
\(599\) −13.5911 −0.555316 −0.277658 0.960680i \(-0.589558\pi\)
−0.277658 + 0.960680i \(0.589558\pi\)
\(600\) 14.3665 0.586510
\(601\) −1.41714 −0.0578062 −0.0289031 0.999582i \(-0.509201\pi\)
−0.0289031 + 0.999582i \(0.509201\pi\)
\(602\) 27.5096 1.12121
\(603\) −2.88832 −0.117622
\(604\) 112.510 4.57797
\(605\) −3.86830 −0.157269
\(606\) 74.9423 3.04432
\(607\) −2.38137 −0.0966567 −0.0483284 0.998832i \(-0.515389\pi\)
−0.0483284 + 0.998832i \(0.515389\pi\)
\(608\) −98.4876 −3.99420
\(609\) −16.5033 −0.668746
\(610\) 51.7732 2.09624
\(611\) −24.7168 −0.999936
\(612\) 22.8702 0.924473
\(613\) 16.7338 0.675871 0.337936 0.941169i \(-0.390271\pi\)
0.337936 + 0.941169i \(0.390271\pi\)
\(614\) −27.1859 −1.09713
\(615\) 22.4356 0.904690
\(616\) 85.4588 3.44323
\(617\) 18.4652 0.743381 0.371690 0.928357i \(-0.378778\pi\)
0.371690 + 0.928357i \(0.378778\pi\)
\(618\) −57.8701 −2.32788
\(619\) 32.7168 1.31500 0.657500 0.753455i \(-0.271614\pi\)
0.657500 + 0.753455i \(0.271614\pi\)
\(620\) −96.1489 −3.86143
\(621\) 14.2246 0.570814
\(622\) 44.7475 1.79421
\(623\) −4.91390 −0.196871
\(624\) 62.9009 2.51805
\(625\) −19.8729 −0.794915
\(626\) −45.6222 −1.82343
\(627\) 13.6830 0.546447
\(628\) 1.02605 0.0409440
\(629\) 21.3266 0.850345
\(630\) −11.5805 −0.461380
\(631\) −9.98542 −0.397513 −0.198757 0.980049i \(-0.563690\pi\)
−0.198757 + 0.980049i \(0.563690\pi\)
\(632\) −151.678 −6.03344
\(633\) 20.2935 0.806592
\(634\) −10.1469 −0.402986
\(635\) −33.7779 −1.34043
\(636\) −21.8244 −0.865396
\(637\) −0.986915 −0.0391030
\(638\) −36.8518 −1.45898
\(639\) 1.47700 0.0584293
\(640\) −167.719 −6.62968
\(641\) −43.1288 −1.70349 −0.851743 0.523959i \(-0.824454\pi\)
−0.851743 + 0.523959i \(0.824454\pi\)
\(642\) 30.6833 1.21097
\(643\) 14.5594 0.574165 0.287082 0.957906i \(-0.407315\pi\)
0.287082 + 0.957906i \(0.407315\pi\)
\(644\) 38.3226 1.51012
\(645\) 11.5247 0.453783
\(646\) 41.9090 1.64889
\(647\) 6.24930 0.245685 0.122843 0.992426i \(-0.460799\pi\)
0.122843 + 0.992426i \(0.460799\pi\)
\(648\) 66.4517 2.61047
\(649\) −40.1553 −1.57623
\(650\) 5.38576 0.211247
\(651\) 30.3510 1.18955
\(652\) 49.6240 1.94343
\(653\) −15.2811 −0.597997 −0.298999 0.954254i \(-0.596653\pi\)
−0.298999 + 0.954254i \(0.596653\pi\)
\(654\) −5.80634 −0.227046
\(655\) 24.9542 0.975041
\(656\) 143.552 5.60475
\(657\) −10.6814 −0.416722
\(658\) −81.3234 −3.17032
\(659\) 17.6474 0.687446 0.343723 0.939071i \(-0.388312\pi\)
0.343723 + 0.939071i \(0.388312\pi\)
\(660\) 54.0141 2.10250
\(661\) 23.7077 0.922124 0.461062 0.887368i \(-0.347469\pi\)
0.461062 + 0.887368i \(0.347469\pi\)
\(662\) 95.7370 3.72092
\(663\) −15.8723 −0.616428
\(664\) −27.4145 −1.06389
\(665\) −15.8699 −0.615409
\(666\) −9.74435 −0.377586
\(667\) −10.9534 −0.424119
\(668\) 1.12921 0.0436903
\(669\) −4.88730 −0.188954
\(670\) −20.8934 −0.807181
\(671\) −27.2918 −1.05359
\(672\) 122.726 4.73426
\(673\) −34.9503 −1.34724 −0.673618 0.739080i \(-0.735260\pi\)
−0.673618 + 0.739080i \(0.735260\pi\)
\(674\) −19.1133 −0.736216
\(675\) 4.91885 0.189327
\(676\) −48.6464 −1.87102
\(677\) −8.41778 −0.323522 −0.161761 0.986830i \(-0.551717\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(678\) 60.8733 2.33783
\(679\) 42.3900 1.62678
\(680\) 109.654 4.20505
\(681\) −41.9903 −1.60907
\(682\) 67.7739 2.59520
\(683\) −3.03009 −0.115943 −0.0579716 0.998318i \(-0.518463\pi\)
−0.0579716 + 0.998318i \(0.518463\pi\)
\(684\) −14.3202 −0.547545
\(685\) 19.4274 0.742281
\(686\) −53.6991 −2.05024
\(687\) −20.6205 −0.786722
\(688\) 73.7393 2.81128
\(689\) −5.42290 −0.206596
\(690\) 21.4679 0.817270
\(691\) 8.46062 0.321857 0.160929 0.986966i \(-0.448551\pi\)
0.160929 + 0.986966i \(0.448551\pi\)
\(692\) −122.324 −4.65007
\(693\) 6.10458 0.231894
\(694\) 65.6960 2.49378
\(695\) −34.6751 −1.31530
\(696\) −71.4001 −2.70641
\(697\) −36.2235 −1.37206
\(698\) 13.7785 0.521523
\(699\) 12.5597 0.475053
\(700\) 13.2519 0.500876
\(701\) −7.40067 −0.279520 −0.139760 0.990185i \(-0.544633\pi\)
−0.139760 + 0.990185i \(0.544633\pi\)
\(702\) 34.7604 1.31195
\(703\) −13.3536 −0.503641
\(704\) 157.516 5.93659
\(705\) −34.0690 −1.28311
\(706\) −24.8116 −0.933797
\(707\) 45.8192 1.72321
\(708\) −117.379 −4.41137
\(709\) 9.96829 0.374367 0.187184 0.982325i \(-0.440064\pi\)
0.187184 + 0.982325i \(0.440064\pi\)
\(710\) 10.6843 0.400973
\(711\) −10.8348 −0.406338
\(712\) −21.2596 −0.796737
\(713\) 20.1444 0.754414
\(714\) −52.2230 −1.95440
\(715\) 13.4213 0.501930
\(716\) −7.54121 −0.281828
\(717\) −20.5077 −0.765875
\(718\) 57.0360 2.12857
\(719\) −38.8099 −1.44736 −0.723682 0.690133i \(-0.757552\pi\)
−0.723682 + 0.690133i \(0.757552\pi\)
\(720\) −31.0415 −1.15685
\(721\) −35.3814 −1.31767
\(722\) 27.2682 1.01482
\(723\) 30.3945 1.13038
\(724\) 19.4537 0.722992
\(725\) −3.78769 −0.140671
\(726\) 7.97050 0.295813
\(727\) −21.7244 −0.805713 −0.402857 0.915263i \(-0.631983\pi\)
−0.402857 + 0.915263i \(0.631983\pi\)
\(728\) 62.0715 2.30052
\(729\) 29.8702 1.10630
\(730\) −77.2666 −2.85976
\(731\) −18.6072 −0.688212
\(732\) −79.7773 −2.94865
\(733\) 29.5562 1.09168 0.545842 0.837888i \(-0.316210\pi\)
0.545842 + 0.837888i \(0.316210\pi\)
\(734\) 52.9495 1.95440
\(735\) −1.36033 −0.0501767
\(736\) 81.4550 3.00247
\(737\) 11.0138 0.405697
\(738\) 16.5509 0.609248
\(739\) −2.28027 −0.0838809 −0.0419405 0.999120i \(-0.513354\pi\)
−0.0419405 + 0.999120i \(0.513354\pi\)
\(740\) −52.7138 −1.93780
\(741\) 9.93841 0.365097
\(742\) −17.8425 −0.655018
\(743\) 44.6865 1.63939 0.819694 0.572801i \(-0.194143\pi\)
0.819694 + 0.572801i \(0.194143\pi\)
\(744\) 131.311 4.81411
\(745\) 19.9308 0.730208
\(746\) −29.5268 −1.08105
\(747\) −1.95830 −0.0716506
\(748\) −87.2088 −3.18867
\(749\) 18.7596 0.685459
\(750\) 49.9413 1.82360
\(751\) 35.6545 1.30105 0.650526 0.759484i \(-0.274549\pi\)
0.650526 + 0.759484i \(0.274549\pi\)
\(752\) −217.987 −7.94915
\(753\) 23.5802 0.859309
\(754\) −26.7667 −0.974785
\(755\) 38.5342 1.40240
\(756\) 85.5295 3.11068
\(757\) −3.73627 −0.135797 −0.0678986 0.997692i \(-0.521629\pi\)
−0.0678986 + 0.997692i \(0.521629\pi\)
\(758\) 1.61243 0.0585662
\(759\) −11.3166 −0.410768
\(760\) −68.6599 −2.49056
\(761\) −43.5350 −1.57814 −0.789072 0.614301i \(-0.789438\pi\)
−0.789072 + 0.614301i \(0.789438\pi\)
\(762\) 69.5982 2.52128
\(763\) −3.54995 −0.128517
\(764\) 58.7320 2.12485
\(765\) 7.83294 0.283201
\(766\) −21.4013 −0.773260
\(767\) −29.1661 −1.05313
\(768\) 190.327 6.86785
\(769\) −12.2394 −0.441363 −0.220682 0.975346i \(-0.570828\pi\)
−0.220682 + 0.975346i \(0.570828\pi\)
\(770\) 44.1590 1.59138
\(771\) −20.8536 −0.751024
\(772\) −2.71108 −0.0975738
\(773\) −10.7652 −0.387199 −0.193600 0.981081i \(-0.562016\pi\)
−0.193600 + 0.981081i \(0.562016\pi\)
\(774\) 8.50184 0.305593
\(775\) 6.96591 0.250223
\(776\) 183.397 6.58356
\(777\) 16.6400 0.596957
\(778\) 46.8280 1.67886
\(779\) 22.6813 0.812642
\(780\) 39.2322 1.40474
\(781\) −5.63211 −0.201533
\(782\) −34.6612 −1.23948
\(783\) −24.4462 −0.873635
\(784\) −8.70395 −0.310855
\(785\) 0.351419 0.0125427
\(786\) −51.4173 −1.83399
\(787\) 2.45808 0.0876212 0.0438106 0.999040i \(-0.486050\pi\)
0.0438106 + 0.999040i \(0.486050\pi\)
\(788\) −20.5536 −0.732193
\(789\) −16.8839 −0.601082
\(790\) −78.3764 −2.78851
\(791\) 37.2175 1.32330
\(792\) 26.4110 0.938474
\(793\) −19.8229 −0.703933
\(794\) 68.3078 2.42415
\(795\) −7.47477 −0.265103
\(796\) 60.2279 2.13472
\(797\) −20.9977 −0.743777 −0.371888 0.928277i \(-0.621290\pi\)
−0.371888 + 0.928277i \(0.621290\pi\)
\(798\) 32.6994 1.15755
\(799\) 55.0062 1.94598
\(800\) 28.1670 0.995855
\(801\) −1.51864 −0.0536585
\(802\) 25.9514 0.916374
\(803\) 40.7304 1.43735
\(804\) 32.1946 1.13541
\(805\) 13.1253 0.462607
\(806\) 49.2264 1.73393
\(807\) −6.62252 −0.233124
\(808\) 198.233 6.97382
\(809\) −28.8485 −1.01426 −0.507129 0.861870i \(-0.669293\pi\)
−0.507129 + 0.861870i \(0.669293\pi\)
\(810\) 34.3375 1.20650
\(811\) 24.4558 0.858759 0.429380 0.903124i \(-0.358732\pi\)
0.429380 + 0.903124i \(0.358732\pi\)
\(812\) −65.8607 −2.31126
\(813\) −27.6778 −0.970703
\(814\) 37.1572 1.30236
\(815\) 16.9960 0.595344
\(816\) −139.983 −4.90039
\(817\) 11.6509 0.407613
\(818\) −90.5155 −3.16480
\(819\) 4.43396 0.154935
\(820\) 89.5352 3.12670
\(821\) −26.2930 −0.917633 −0.458816 0.888531i \(-0.651726\pi\)
−0.458816 + 0.888531i \(0.651726\pi\)
\(822\) −40.0294 −1.39619
\(823\) −32.8048 −1.14350 −0.571752 0.820427i \(-0.693736\pi\)
−0.571752 + 0.820427i \(0.693736\pi\)
\(824\) −153.075 −5.33261
\(825\) −3.91328 −0.136243
\(826\) −95.9625 −3.33896
\(827\) −39.4766 −1.37273 −0.686367 0.727255i \(-0.740796\pi\)
−0.686367 + 0.727255i \(0.740796\pi\)
\(828\) 11.8436 0.411594
\(829\) −23.7462 −0.824740 −0.412370 0.911017i \(-0.635299\pi\)
−0.412370 + 0.911017i \(0.635299\pi\)
\(830\) −14.1659 −0.491704
\(831\) −19.7314 −0.684476
\(832\) 114.409 3.96641
\(833\) 2.19634 0.0760985
\(834\) 71.4469 2.47400
\(835\) 0.386748 0.0133840
\(836\) 54.6057 1.88858
\(837\) 44.9588 1.55400
\(838\) 79.4336 2.74399
\(839\) 30.7385 1.06121 0.530606 0.847619i \(-0.321964\pi\)
0.530606 + 0.847619i \(0.321964\pi\)
\(840\) 85.5576 2.95202
\(841\) −10.1756 −0.350882
\(842\) −64.2830 −2.21534
\(843\) −30.4973 −1.05038
\(844\) 80.9865 2.78767
\(845\) −16.6612 −0.573162
\(846\) −25.1330 −0.864090
\(847\) 4.87311 0.167442
\(848\) −47.8265 −1.64237
\(849\) 37.6281 1.29139
\(850\) −11.9858 −0.411109
\(851\) 11.0442 0.378590
\(852\) −16.4634 −0.564025
\(853\) −18.1625 −0.621871 −0.310935 0.950431i \(-0.600642\pi\)
−0.310935 + 0.950431i \(0.600642\pi\)
\(854\) −65.2215 −2.23183
\(855\) −4.90459 −0.167733
\(856\) 81.1618 2.77405
\(857\) 54.5035 1.86180 0.930902 0.365268i \(-0.119023\pi\)
0.930902 + 0.365268i \(0.119023\pi\)
\(858\) −27.6542 −0.944099
\(859\) 13.8291 0.471841 0.235921 0.971772i \(-0.424189\pi\)
0.235921 + 0.971772i \(0.424189\pi\)
\(860\) 45.9922 1.56832
\(861\) −28.2633 −0.963211
\(862\) 49.7104 1.69314
\(863\) −32.9793 −1.12263 −0.561315 0.827602i \(-0.689704\pi\)
−0.561315 + 0.827602i \(0.689704\pi\)
\(864\) 181.793 6.18474
\(865\) −41.8955 −1.42449
\(866\) −75.9681 −2.58150
\(867\) 10.0560 0.341520
\(868\) 121.124 4.11121
\(869\) 41.3155 1.40153
\(870\) −36.8944 −1.25084
\(871\) 7.99965 0.271058
\(872\) −15.3586 −0.520108
\(873\) 13.1006 0.443388
\(874\) 21.7031 0.734117
\(875\) 30.5338 1.03223
\(876\) 119.060 4.02266
\(877\) −36.8505 −1.24435 −0.622176 0.782877i \(-0.713751\pi\)
−0.622176 + 0.782877i \(0.713751\pi\)
\(878\) 98.6542 3.32942
\(879\) 31.2273 1.05327
\(880\) 118.368 3.99017
\(881\) −19.4408 −0.654976 −0.327488 0.944855i \(-0.606202\pi\)
−0.327488 + 0.944855i \(0.606202\pi\)
\(882\) −1.00353 −0.0337906
\(883\) −44.2554 −1.48931 −0.744656 0.667448i \(-0.767386\pi\)
−0.744656 + 0.667448i \(0.767386\pi\)
\(884\) −63.3426 −2.13044
\(885\) −40.2017 −1.35137
\(886\) −75.7094 −2.54351
\(887\) 37.0797 1.24501 0.622507 0.782614i \(-0.286114\pi\)
0.622507 + 0.782614i \(0.286114\pi\)
\(888\) 71.9917 2.41588
\(889\) 42.5518 1.42714
\(890\) −10.9854 −0.368233
\(891\) −18.1007 −0.606396
\(892\) −19.5041 −0.653046
\(893\) −34.4421 −1.15256
\(894\) −41.0667 −1.37348
\(895\) −2.58283 −0.0863345
\(896\) 211.285 7.05853
\(897\) −8.21964 −0.274446
\(898\) −65.6131 −2.18954
\(899\) −34.6198 −1.15464
\(900\) 4.09550 0.136517
\(901\) 12.0684 0.402058
\(902\) −63.1121 −2.10140
\(903\) −14.5182 −0.483137
\(904\) 161.019 5.35540
\(905\) 6.66281 0.221479
\(906\) −79.3984 −2.63784
\(907\) −19.0950 −0.634039 −0.317020 0.948419i \(-0.602682\pi\)
−0.317020 + 0.948419i \(0.602682\pi\)
\(908\) −167.573 −5.56112
\(909\) 14.1604 0.469671
\(910\) 32.0741 1.06325
\(911\) 16.4271 0.544256 0.272128 0.962261i \(-0.412273\pi\)
0.272128 + 0.962261i \(0.412273\pi\)
\(912\) 87.6504 2.90239
\(913\) 7.46742 0.247135
\(914\) 0.414344 0.0137053
\(915\) −27.3234 −0.903282
\(916\) −82.2917 −2.71900
\(917\) −31.4362 −1.03811
\(918\) −77.3577 −2.55318
\(919\) 47.1222 1.55442 0.777209 0.629242i \(-0.216635\pi\)
0.777209 + 0.629242i \(0.216635\pi\)
\(920\) 56.7857 1.87217
\(921\) 14.3474 0.472762
\(922\) −28.1638 −0.927526
\(923\) −4.09079 −0.134650
\(924\) −68.0445 −2.23850
\(925\) 3.81907 0.125570
\(926\) −33.4170 −1.09815
\(927\) −10.9346 −0.359140
\(928\) −139.987 −4.59531
\(929\) 52.3918 1.71892 0.859460 0.511203i \(-0.170800\pi\)
0.859460 + 0.511203i \(0.170800\pi\)
\(930\) 67.8523 2.22496
\(931\) −1.37523 −0.0450715
\(932\) 50.1230 1.64183
\(933\) −23.6155 −0.773138
\(934\) −96.4008 −3.15433
\(935\) −29.8686 −0.976808
\(936\) 19.1832 0.627022
\(937\) −15.8871 −0.519008 −0.259504 0.965742i \(-0.583559\pi\)
−0.259504 + 0.965742i \(0.583559\pi\)
\(938\) 26.3205 0.859395
\(939\) 24.0772 0.785729
\(940\) −135.961 −4.43457
\(941\) −52.4610 −1.71018 −0.855090 0.518480i \(-0.826498\pi\)
−0.855090 + 0.518480i \(0.826498\pi\)
\(942\) −0.724087 −0.0235920
\(943\) −18.7587 −0.610869
\(944\) −257.226 −8.37201
\(945\) 29.2935 0.952917
\(946\) −32.4193 −1.05404
\(947\) −34.4633 −1.11991 −0.559954 0.828524i \(-0.689181\pi\)
−0.559954 + 0.828524i \(0.689181\pi\)
\(948\) 120.770 3.92243
\(949\) 29.5838 0.960332
\(950\) 7.50489 0.243491
\(951\) 5.35505 0.173649
\(952\) −138.137 −4.47706
\(953\) −57.4001 −1.85937 −0.929685 0.368354i \(-0.879921\pi\)
−0.929685 + 0.368354i \(0.879921\pi\)
\(954\) −5.51421 −0.178529
\(955\) 20.1154 0.650920
\(956\) −81.8416 −2.64695
\(957\) 19.4486 0.628684
\(958\) 35.5622 1.14896
\(959\) −24.4737 −0.790297
\(960\) 157.698 5.08967
\(961\) 32.6691 1.05384
\(962\) 26.9885 0.870144
\(963\) 5.79764 0.186826
\(964\) 121.298 3.90673
\(965\) −0.928532 −0.0298905
\(966\) −27.0443 −0.870136
\(967\) 8.50962 0.273651 0.136825 0.990595i \(-0.456310\pi\)
0.136825 + 0.990595i \(0.456310\pi\)
\(968\) 21.0831 0.677637
\(969\) −22.1175 −0.710517
\(970\) 94.7663 3.04276
\(971\) 10.2124 0.327733 0.163866 0.986483i \(-0.447603\pi\)
0.163866 + 0.986483i \(0.447603\pi\)
\(972\) 47.3509 1.51878
\(973\) 43.6821 1.40038
\(974\) −60.4664 −1.93747
\(975\) −2.84234 −0.0910278
\(976\) −174.825 −5.59603
\(977\) −3.01790 −0.0965513 −0.0482756 0.998834i \(-0.515373\pi\)
−0.0482756 + 0.998834i \(0.515373\pi\)
\(978\) −35.0197 −1.11981
\(979\) 5.79088 0.185077
\(980\) −5.42878 −0.173416
\(981\) −1.09711 −0.0350281
\(982\) 65.9152 2.10344
\(983\) 4.84215 0.154441 0.0772203 0.997014i \(-0.475396\pi\)
0.0772203 + 0.997014i \(0.475396\pi\)
\(984\) −122.279 −3.89811
\(985\) −7.03953 −0.224298
\(986\) 59.5681 1.89704
\(987\) 42.9185 1.36611
\(988\) 39.6619 1.26181
\(989\) −9.63595 −0.306405
\(990\) 13.6473 0.433740
\(991\) 3.86210 0.122683 0.0613417 0.998117i \(-0.480462\pi\)
0.0613417 + 0.998117i \(0.480462\pi\)
\(992\) 257.450 8.17403
\(993\) −50.5253 −1.60337
\(994\) −13.4595 −0.426910
\(995\) 20.6278 0.653945
\(996\) 21.8282 0.691652
\(997\) −29.0506 −0.920040 −0.460020 0.887909i \(-0.652158\pi\)
−0.460020 + 0.887909i \(0.652158\pi\)
\(998\) −8.51784 −0.269628
\(999\) 24.6487 0.779852
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 \(a_p\))