Properties

Label 6047.2.a.a.1.7
Level 6047
Weight 2
Character 6047.1
Self dual Yes
Analytic conductor 48.286
Analytic rank 1
Dimension 217
CM No

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Newspace parameters

Level: \( N \) = \( 6047 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6047.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2855381023\)
Analytic rank: \(1\)
Dimension: \(217\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} +O(q^{10})\) \(q-2.65722 q^{2} +0.109936 q^{3} +5.06084 q^{4} +0.753739 q^{5} -0.292126 q^{6} +3.98656 q^{7} -8.13334 q^{8} -2.98791 q^{9} -2.00285 q^{10} +0.383918 q^{11} +0.556370 q^{12} +2.64293 q^{13} -10.5932 q^{14} +0.0828634 q^{15} +11.4904 q^{16} +8.14277 q^{17} +7.93956 q^{18} -5.99205 q^{19} +3.81456 q^{20} +0.438268 q^{21} -1.02016 q^{22} -1.73696 q^{23} -0.894150 q^{24} -4.43188 q^{25} -7.02285 q^{26} -0.658289 q^{27} +20.1753 q^{28} +5.51678 q^{29} -0.220187 q^{30} -10.8615 q^{31} -14.2660 q^{32} +0.0422065 q^{33} -21.6372 q^{34} +3.00483 q^{35} -15.1214 q^{36} +2.46709 q^{37} +15.9222 q^{38} +0.290554 q^{39} -6.13042 q^{40} -11.2355 q^{41} -1.16458 q^{42} -9.53031 q^{43} +1.94295 q^{44} -2.25211 q^{45} +4.61548 q^{46} +9.71406 q^{47} +1.26322 q^{48} +8.89264 q^{49} +11.7765 q^{50} +0.895187 q^{51} +13.3754 q^{52} -6.80202 q^{53} +1.74922 q^{54} +0.289374 q^{55} -32.4240 q^{56} -0.658744 q^{57} -14.6593 q^{58} -1.90748 q^{59} +0.419358 q^{60} -11.7282 q^{61} +28.8615 q^{62} -11.9115 q^{63} +14.9270 q^{64} +1.99208 q^{65} -0.112152 q^{66} -6.26307 q^{67} +41.2093 q^{68} -0.190955 q^{69} -7.98450 q^{70} +3.63989 q^{71} +24.3017 q^{72} +4.38284 q^{73} -6.55561 q^{74} -0.487224 q^{75} -30.3248 q^{76} +1.53051 q^{77} -0.772067 q^{78} -13.0161 q^{79} +8.66079 q^{80} +8.89137 q^{81} +29.8553 q^{82} -4.10504 q^{83} +2.21800 q^{84} +6.13753 q^{85} +25.3242 q^{86} +0.606495 q^{87} -3.12254 q^{88} -1.79972 q^{89} +5.98436 q^{90} +10.5362 q^{91} -8.79046 q^{92} -1.19408 q^{93} -25.8124 q^{94} -4.51645 q^{95} -1.56835 q^{96} -11.3226 q^{97} -23.6297 q^{98} -1.14711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.65722 −1.87894 −0.939471 0.342629i \(-0.888683\pi\)
−0.939471 + 0.342629i \(0.888683\pi\)
\(3\) 0.109936 0.0634718 0.0317359 0.999496i \(-0.489896\pi\)
0.0317359 + 0.999496i \(0.489896\pi\)
\(4\) 5.06084 2.53042
\(5\) 0.753739 0.337083 0.168541 0.985695i \(-0.446094\pi\)
0.168541 + 0.985695i \(0.446094\pi\)
\(6\) −0.292126 −0.119260
\(7\) 3.98656 1.50678 0.753389 0.657576i \(-0.228418\pi\)
0.753389 + 0.657576i \(0.228418\pi\)
\(8\) −8.13334 −2.87557
\(9\) −2.98791 −0.995971
\(10\) −2.00285 −0.633358
\(11\) 0.383918 0.115756 0.0578778 0.998324i \(-0.481567\pi\)
0.0578778 + 0.998324i \(0.481567\pi\)
\(12\) 0.556370 0.160610
\(13\) 2.64293 0.733016 0.366508 0.930415i \(-0.380553\pi\)
0.366508 + 0.930415i \(0.380553\pi\)
\(14\) −10.5932 −2.83115
\(15\) 0.0828634 0.0213952
\(16\) 11.4904 2.87261
\(17\) 8.14277 1.97491 0.987456 0.157891i \(-0.0504696\pi\)
0.987456 + 0.157891i \(0.0504696\pi\)
\(18\) 7.93956 1.87137
\(19\) −5.99205 −1.37467 −0.687336 0.726340i \(-0.741220\pi\)
−0.687336 + 0.726340i \(0.741220\pi\)
\(20\) 3.81456 0.852961
\(21\) 0.438268 0.0956378
\(22\) −1.02016 −0.217498
\(23\) −1.73696 −0.362180 −0.181090 0.983467i \(-0.557963\pi\)
−0.181090 + 0.983467i \(0.557963\pi\)
\(24\) −0.894150 −0.182518
\(25\) −4.43188 −0.886375
\(26\) −7.02285 −1.37729
\(27\) −0.658289 −0.126688
\(28\) 20.1753 3.81278
\(29\) 5.51678 1.02444 0.512220 0.858854i \(-0.328823\pi\)
0.512220 + 0.858854i \(0.328823\pi\)
\(30\) −0.220187 −0.0402004
\(31\) −10.8615 −1.95079 −0.975394 0.220471i \(-0.929241\pi\)
−0.975394 + 0.220471i \(0.929241\pi\)
\(32\) −14.2660 −2.52189
\(33\) 0.0422065 0.00734721
\(34\) −21.6372 −3.71075
\(35\) 3.00483 0.507908
\(36\) −15.1214 −2.52023
\(37\) 2.46709 0.405587 0.202793 0.979222i \(-0.434998\pi\)
0.202793 + 0.979222i \(0.434998\pi\)
\(38\) 15.9222 2.58293
\(39\) 0.290554 0.0465258
\(40\) −6.13042 −0.969305
\(41\) −11.2355 −1.75469 −0.877345 0.479859i \(-0.840688\pi\)
−0.877345 + 0.479859i \(0.840688\pi\)
\(42\) −1.16458 −0.179698
\(43\) −9.53031 −1.45336 −0.726679 0.686977i \(-0.758937\pi\)
−0.726679 + 0.686977i \(0.758937\pi\)
\(44\) 1.94295 0.292910
\(45\) −2.25211 −0.335725
\(46\) 4.61548 0.680516
\(47\) 9.71406 1.41694 0.708470 0.705740i \(-0.249386\pi\)
0.708470 + 0.705740i \(0.249386\pi\)
\(48\) 1.26322 0.182330
\(49\) 8.89264 1.27038
\(50\) 11.7765 1.66545
\(51\) 0.895187 0.125351
\(52\) 13.3754 1.85484
\(53\) −6.80202 −0.934329 −0.467164 0.884170i \(-0.654724\pi\)
−0.467164 + 0.884170i \(0.654724\pi\)
\(54\) 1.74922 0.238039
\(55\) 0.289374 0.0390192
\(56\) −32.4240 −4.33285
\(57\) −0.658744 −0.0872528
\(58\) −14.6593 −1.92486
\(59\) −1.90748 −0.248332 −0.124166 0.992261i \(-0.539626\pi\)
−0.124166 + 0.992261i \(0.539626\pi\)
\(60\) 0.419358 0.0541389
\(61\) −11.7282 −1.50164 −0.750819 0.660509i \(-0.770341\pi\)
−0.750819 + 0.660509i \(0.770341\pi\)
\(62\) 28.8615 3.66541
\(63\) −11.9115 −1.50071
\(64\) 14.9270 1.86588
\(65\) 1.99208 0.247087
\(66\) −0.112152 −0.0138050
\(67\) −6.26307 −0.765156 −0.382578 0.923923i \(-0.624964\pi\)
−0.382578 + 0.923923i \(0.624964\pi\)
\(68\) 41.2093 4.99736
\(69\) −0.190955 −0.0229882
\(70\) −7.98450 −0.954330
\(71\) 3.63989 0.431976 0.215988 0.976396i \(-0.430703\pi\)
0.215988 + 0.976396i \(0.430703\pi\)
\(72\) 24.3017 2.86399
\(73\) 4.38284 0.512972 0.256486 0.966548i \(-0.417435\pi\)
0.256486 + 0.966548i \(0.417435\pi\)
\(74\) −6.55561 −0.762074
\(75\) −0.487224 −0.0562598
\(76\) −30.3248 −3.47850
\(77\) 1.53051 0.174418
\(78\) −0.772067 −0.0874193
\(79\) −13.0161 −1.46442 −0.732211 0.681078i \(-0.761511\pi\)
−0.732211 + 0.681078i \(0.761511\pi\)
\(80\) 8.66079 0.968306
\(81\) 8.89137 0.987930
\(82\) 29.8553 3.29696
\(83\) −4.10504 −0.450587 −0.225293 0.974291i \(-0.572334\pi\)
−0.225293 + 0.974291i \(0.572334\pi\)
\(84\) 2.21800 0.242004
\(85\) 6.13753 0.665709
\(86\) 25.3242 2.73078
\(87\) 0.606495 0.0650230
\(88\) −3.12254 −0.332863
\(89\) −1.79972 −0.190770 −0.0953850 0.995440i \(-0.530408\pi\)
−0.0953850 + 0.995440i \(0.530408\pi\)
\(90\) 5.98436 0.630807
\(91\) 10.5362 1.10449
\(92\) −8.79046 −0.916469
\(93\) −1.19408 −0.123820
\(94\) −25.8124 −2.66235
\(95\) −4.51645 −0.463378
\(96\) −1.56835 −0.160069
\(97\) −11.3226 −1.14964 −0.574819 0.818281i \(-0.694928\pi\)
−0.574819 + 0.818281i \(0.694928\pi\)
\(98\) −23.6297 −2.38697
\(99\) −1.14711 −0.115289
\(100\) −22.4290 −2.24290
\(101\) −14.2990 −1.42281 −0.711403 0.702784i \(-0.751940\pi\)
−0.711403 + 0.702784i \(0.751940\pi\)
\(102\) −2.37871 −0.235528
\(103\) 11.1978 1.10335 0.551677 0.834058i \(-0.313988\pi\)
0.551677 + 0.834058i \(0.313988\pi\)
\(104\) −21.4958 −2.10784
\(105\) 0.330340 0.0322378
\(106\) 18.0745 1.75555
\(107\) 14.1082 1.36389 0.681946 0.731403i \(-0.261134\pi\)
0.681946 + 0.731403i \(0.261134\pi\)
\(108\) −3.33150 −0.320574
\(109\) 2.33398 0.223555 0.111777 0.993733i \(-0.464346\pi\)
0.111777 + 0.993733i \(0.464346\pi\)
\(110\) −0.768932 −0.0733147
\(111\) 0.271223 0.0257433
\(112\) 45.8073 4.32838
\(113\) −11.9901 −1.12794 −0.563968 0.825797i \(-0.690726\pi\)
−0.563968 + 0.825797i \(0.690726\pi\)
\(114\) 1.75043 0.163943
\(115\) −1.30921 −0.122085
\(116\) 27.9195 2.59226
\(117\) −7.89684 −0.730063
\(118\) 5.06859 0.466602
\(119\) 32.4616 2.97575
\(120\) −0.673956 −0.0615235
\(121\) −10.8526 −0.986601
\(122\) 31.1644 2.82149
\(123\) −1.23519 −0.111373
\(124\) −54.9684 −4.93631
\(125\) −7.10918 −0.635864
\(126\) 31.6515 2.81974
\(127\) 9.95970 0.883781 0.441890 0.897069i \(-0.354308\pi\)
0.441890 + 0.897069i \(0.354308\pi\)
\(128\) −11.1325 −0.983986
\(129\) −1.04773 −0.0922473
\(130\) −5.29340 −0.464262
\(131\) −16.6878 −1.45802 −0.729012 0.684501i \(-0.760020\pi\)
−0.729012 + 0.684501i \(0.760020\pi\)
\(132\) 0.213600 0.0185915
\(133\) −23.8877 −2.07132
\(134\) 16.6424 1.43768
\(135\) −0.496179 −0.0427043
\(136\) −66.2280 −5.67900
\(137\) −20.9167 −1.78703 −0.893517 0.449030i \(-0.851770\pi\)
−0.893517 + 0.449030i \(0.851770\pi\)
\(138\) 0.507409 0.0431935
\(139\) −1.43452 −0.121674 −0.0608371 0.998148i \(-0.519377\pi\)
−0.0608371 + 0.998148i \(0.519377\pi\)
\(140\) 15.2069 1.28522
\(141\) 1.06793 0.0899358
\(142\) −9.67201 −0.811657
\(143\) 1.01467 0.0848507
\(144\) −34.3324 −2.86104
\(145\) 4.15821 0.345321
\(146\) −11.6462 −0.963845
\(147\) 0.977625 0.0806331
\(148\) 12.4855 1.02631
\(149\) −6.60260 −0.540906 −0.270453 0.962733i \(-0.587174\pi\)
−0.270453 + 0.962733i \(0.587174\pi\)
\(150\) 1.29466 0.105709
\(151\) −19.6075 −1.59564 −0.797819 0.602896i \(-0.794013\pi\)
−0.797819 + 0.602896i \(0.794013\pi\)
\(152\) 48.7354 3.95296
\(153\) −24.3299 −1.96696
\(154\) −4.06691 −0.327721
\(155\) −8.18676 −0.657576
\(156\) 1.47045 0.117730
\(157\) −19.8002 −1.58023 −0.790113 0.612961i \(-0.789978\pi\)
−0.790113 + 0.612961i \(0.789978\pi\)
\(158\) 34.5866 2.75156
\(159\) −0.747789 −0.0593035
\(160\) −10.7528 −0.850086
\(161\) −6.92447 −0.545725
\(162\) −23.6264 −1.85626
\(163\) 17.3114 1.35594 0.677968 0.735092i \(-0.262861\pi\)
0.677968 + 0.735092i \(0.262861\pi\)
\(164\) −56.8611 −4.44011
\(165\) 0.0318127 0.00247662
\(166\) 10.9080 0.846627
\(167\) 2.80771 0.217267 0.108634 0.994082i \(-0.465352\pi\)
0.108634 + 0.994082i \(0.465352\pi\)
\(168\) −3.56458 −0.275013
\(169\) −6.01494 −0.462687
\(170\) −16.3088 −1.25083
\(171\) 17.9037 1.36913
\(172\) −48.2314 −3.67761
\(173\) 7.99607 0.607930 0.303965 0.952683i \(-0.401689\pi\)
0.303965 + 0.952683i \(0.401689\pi\)
\(174\) −1.61159 −0.122174
\(175\) −17.6679 −1.33557
\(176\) 4.41138 0.332520
\(177\) −0.209701 −0.0157621
\(178\) 4.78226 0.358446
\(179\) 15.4206 1.15259 0.576296 0.817241i \(-0.304497\pi\)
0.576296 + 0.817241i \(0.304497\pi\)
\(180\) −11.3976 −0.849524
\(181\) −6.42159 −0.477313 −0.238657 0.971104i \(-0.576707\pi\)
−0.238657 + 0.971104i \(0.576707\pi\)
\(182\) −27.9970 −2.07528
\(183\) −1.28935 −0.0953116
\(184\) 14.1273 1.04148
\(185\) 1.85954 0.136716
\(186\) 3.17293 0.232650
\(187\) 3.12616 0.228607
\(188\) 49.1613 3.58546
\(189\) −2.62431 −0.190890
\(190\) 12.0012 0.870659
\(191\) 8.44303 0.610916 0.305458 0.952206i \(-0.401190\pi\)
0.305458 + 0.952206i \(0.401190\pi\)
\(192\) 1.64102 0.118431
\(193\) −21.2931 −1.53271 −0.766357 0.642415i \(-0.777933\pi\)
−0.766357 + 0.642415i \(0.777933\pi\)
\(194\) 30.0867 2.16010
\(195\) 0.219002 0.0156830
\(196\) 45.0043 3.21459
\(197\) 12.1670 0.866864 0.433432 0.901186i \(-0.357302\pi\)
0.433432 + 0.901186i \(0.357302\pi\)
\(198\) 3.04814 0.216622
\(199\) 2.76874 0.196271 0.0981354 0.995173i \(-0.468712\pi\)
0.0981354 + 0.995173i \(0.468712\pi\)
\(200\) 36.0460 2.54884
\(201\) −0.688539 −0.0485658
\(202\) 37.9957 2.67337
\(203\) 21.9930 1.54360
\(204\) 4.53040 0.317191
\(205\) −8.46864 −0.591476
\(206\) −29.7551 −2.07314
\(207\) 5.18987 0.360721
\(208\) 30.3684 2.10567
\(209\) −2.30046 −0.159126
\(210\) −0.877786 −0.0605730
\(211\) −14.6582 −1.00911 −0.504557 0.863378i \(-0.668344\pi\)
−0.504557 + 0.863378i \(0.668344\pi\)
\(212\) −34.4239 −2.36425
\(213\) 0.400156 0.0274183
\(214\) −37.4887 −2.56267
\(215\) −7.18337 −0.489902
\(216\) 5.35409 0.364300
\(217\) −43.3001 −2.93940
\(218\) −6.20191 −0.420046
\(219\) 0.481833 0.0325593
\(220\) 1.46448 0.0987349
\(221\) 21.5208 1.44764
\(222\) −0.720699 −0.0483702
\(223\) 11.5641 0.774390 0.387195 0.921998i \(-0.373444\pi\)
0.387195 + 0.921998i \(0.373444\pi\)
\(224\) −56.8721 −3.79993
\(225\) 13.2421 0.882804
\(226\) 31.8604 2.11932
\(227\) −11.3874 −0.755807 −0.377904 0.925845i \(-0.623355\pi\)
−0.377904 + 0.925845i \(0.623355\pi\)
\(228\) −3.33380 −0.220786
\(229\) 17.8075 1.17675 0.588376 0.808587i \(-0.299767\pi\)
0.588376 + 0.808587i \(0.299767\pi\)
\(230\) 3.47887 0.229390
\(231\) 0.168259 0.0110706
\(232\) −44.8699 −2.94585
\(233\) 17.3767 1.13838 0.569192 0.822204i \(-0.307256\pi\)
0.569192 + 0.822204i \(0.307256\pi\)
\(234\) 20.9837 1.37175
\(235\) 7.32187 0.477626
\(236\) −9.65343 −0.628385
\(237\) −1.43094 −0.0929495
\(238\) −86.2579 −5.59127
\(239\) −19.5310 −1.26335 −0.631677 0.775232i \(-0.717633\pi\)
−0.631677 + 0.775232i \(0.717633\pi\)
\(240\) 0.952136 0.0614601
\(241\) 19.6798 1.26769 0.633845 0.773460i \(-0.281476\pi\)
0.633845 + 0.773460i \(0.281476\pi\)
\(242\) 28.8378 1.85376
\(243\) 2.95235 0.189394
\(244\) −59.3544 −3.79977
\(245\) 6.70274 0.428222
\(246\) 3.28218 0.209264
\(247\) −15.8366 −1.00766
\(248\) 88.3405 5.60963
\(249\) −0.451293 −0.0285996
\(250\) 18.8907 1.19475
\(251\) 17.6413 1.11351 0.556756 0.830676i \(-0.312046\pi\)
0.556756 + 0.830676i \(0.312046\pi\)
\(252\) −60.2822 −3.79742
\(253\) −0.666848 −0.0419244
\(254\) −26.4652 −1.66057
\(255\) 0.674738 0.0422537
\(256\) −0.272444 −0.0170278
\(257\) 8.66961 0.540796 0.270398 0.962749i \(-0.412845\pi\)
0.270398 + 0.962749i \(0.412845\pi\)
\(258\) 2.78405 0.173327
\(259\) 9.83519 0.611129
\(260\) 10.0816 0.625234
\(261\) −16.4837 −1.02031
\(262\) 44.3434 2.73954
\(263\) 6.35897 0.392111 0.196056 0.980593i \(-0.437187\pi\)
0.196056 + 0.980593i \(0.437187\pi\)
\(264\) −0.343280 −0.0211274
\(265\) −5.12695 −0.314946
\(266\) 63.4749 3.89190
\(267\) −0.197855 −0.0121085
\(268\) −31.6964 −1.93617
\(269\) 6.45664 0.393668 0.196834 0.980437i \(-0.436934\pi\)
0.196834 + 0.980437i \(0.436934\pi\)
\(270\) 1.31846 0.0802388
\(271\) −5.59309 −0.339756 −0.169878 0.985465i \(-0.554337\pi\)
−0.169878 + 0.985465i \(0.554337\pi\)
\(272\) 93.5640 5.67315
\(273\) 1.15831 0.0701041
\(274\) 55.5804 3.35773
\(275\) −1.70148 −0.102603
\(276\) −0.966391 −0.0581699
\(277\) 18.3752 1.10406 0.552031 0.833824i \(-0.313853\pi\)
0.552031 + 0.833824i \(0.313853\pi\)
\(278\) 3.81184 0.228619
\(279\) 32.4533 1.94293
\(280\) −24.4393 −1.46053
\(281\) 10.0851 0.601629 0.300815 0.953683i \(-0.402741\pi\)
0.300815 + 0.953683i \(0.402741\pi\)
\(282\) −2.83772 −0.168984
\(283\) 13.7718 0.818649 0.409324 0.912389i \(-0.365764\pi\)
0.409324 + 0.912389i \(0.365764\pi\)
\(284\) 18.4209 1.09308
\(285\) −0.496522 −0.0294114
\(286\) −2.69620 −0.159429
\(287\) −44.7910 −2.64393
\(288\) 42.6255 2.51173
\(289\) 49.3048 2.90028
\(290\) −11.0493 −0.648838
\(291\) −1.24477 −0.0729696
\(292\) 22.1808 1.29804
\(293\) 3.78930 0.221374 0.110687 0.993855i \(-0.464695\pi\)
0.110687 + 0.993855i \(0.464695\pi\)
\(294\) −2.59777 −0.151505
\(295\) −1.43774 −0.0837084
\(296\) −20.0657 −1.16629
\(297\) −0.252729 −0.0146648
\(298\) 17.5446 1.01633
\(299\) −4.59065 −0.265484
\(300\) −2.46577 −0.142361
\(301\) −37.9931 −2.18989
\(302\) 52.1016 2.99811
\(303\) −1.57198 −0.0903080
\(304\) −68.8513 −3.94889
\(305\) −8.83998 −0.506176
\(306\) 64.6500 3.69580
\(307\) 8.74445 0.499072 0.249536 0.968366i \(-0.419722\pi\)
0.249536 + 0.968366i \(0.419722\pi\)
\(308\) 7.74567 0.441351
\(309\) 1.23105 0.0700318
\(310\) 21.7541 1.23555
\(311\) 3.24763 0.184156 0.0920782 0.995752i \(-0.470649\pi\)
0.0920782 + 0.995752i \(0.470649\pi\)
\(312\) −2.36317 −0.133788
\(313\) 9.96281 0.563131 0.281566 0.959542i \(-0.409146\pi\)
0.281566 + 0.959542i \(0.409146\pi\)
\(314\) 52.6135 2.96915
\(315\) −8.97816 −0.505862
\(316\) −65.8722 −3.70560
\(317\) 17.1522 0.963366 0.481683 0.876345i \(-0.340026\pi\)
0.481683 + 0.876345i \(0.340026\pi\)
\(318\) 1.98704 0.111428
\(319\) 2.11799 0.118585
\(320\) 11.2511 0.628955
\(321\) 1.55100 0.0865686
\(322\) 18.3999 1.02539
\(323\) −48.7919 −2.71486
\(324\) 44.9978 2.49988
\(325\) −11.7131 −0.649727
\(326\) −46.0003 −2.54772
\(327\) 0.256589 0.0141894
\(328\) 91.3822 5.04574
\(329\) 38.7257 2.13501
\(330\) −0.0845335 −0.00465342
\(331\) −31.9960 −1.75866 −0.879328 0.476216i \(-0.842008\pi\)
−0.879328 + 0.476216i \(0.842008\pi\)
\(332\) −20.7750 −1.14017
\(333\) −7.37145 −0.403953
\(334\) −7.46072 −0.408232
\(335\) −4.72072 −0.257921
\(336\) 5.03589 0.274730
\(337\) −23.8337 −1.29830 −0.649151 0.760660i \(-0.724876\pi\)
−0.649151 + 0.760660i \(0.724876\pi\)
\(338\) 15.9830 0.869363
\(339\) −1.31815 −0.0715921
\(340\) 31.0611 1.68452
\(341\) −4.16993 −0.225814
\(342\) −47.5743 −2.57252
\(343\) 7.54513 0.407399
\(344\) 77.5133 4.17924
\(345\) −0.143930 −0.00774893
\(346\) −21.2474 −1.14226
\(347\) 13.6207 0.731198 0.365599 0.930772i \(-0.380864\pi\)
0.365599 + 0.930772i \(0.380864\pi\)
\(348\) 3.06937 0.164536
\(349\) 0.298770 0.0159928 0.00799638 0.999968i \(-0.497455\pi\)
0.00799638 + 0.999968i \(0.497455\pi\)
\(350\) 46.9477 2.50946
\(351\) −1.73981 −0.0928642
\(352\) −5.47696 −0.291923
\(353\) −4.86633 −0.259009 −0.129504 0.991579i \(-0.541339\pi\)
−0.129504 + 0.991579i \(0.541339\pi\)
\(354\) 0.557222 0.0296160
\(355\) 2.74353 0.145611
\(356\) −9.10810 −0.482728
\(357\) 3.56871 0.188876
\(358\) −40.9761 −2.16565
\(359\) −1.85735 −0.0980273 −0.0490136 0.998798i \(-0.515608\pi\)
−0.0490136 + 0.998798i \(0.515608\pi\)
\(360\) 18.3172 0.965400
\(361\) 16.9047 0.889721
\(362\) 17.0636 0.896844
\(363\) −1.19310 −0.0626213
\(364\) 53.3219 2.79483
\(365\) 3.30352 0.172914
\(366\) 3.42610 0.179085
\(367\) 19.9137 1.03949 0.519745 0.854322i \(-0.326027\pi\)
0.519745 + 0.854322i \(0.326027\pi\)
\(368\) −19.9584 −1.04040
\(369\) 33.5707 1.74762
\(370\) −4.94122 −0.256882
\(371\) −27.1166 −1.40783
\(372\) −6.04303 −0.313317
\(373\) −19.0628 −0.987036 −0.493518 0.869736i \(-0.664289\pi\)
−0.493518 + 0.869736i \(0.664289\pi\)
\(374\) −8.30690 −0.429539
\(375\) −0.781557 −0.0403594
\(376\) −79.0078 −4.07451
\(377\) 14.5804 0.750931
\(378\) 6.97338 0.358672
\(379\) 7.18360 0.368997 0.184498 0.982833i \(-0.440934\pi\)
0.184498 + 0.982833i \(0.440934\pi\)
\(380\) −22.8570 −1.17254
\(381\) 1.09493 0.0560951
\(382\) −22.4350 −1.14788
\(383\) −20.1213 −1.02815 −0.514075 0.857745i \(-0.671865\pi\)
−0.514075 + 0.857745i \(0.671865\pi\)
\(384\) −1.22387 −0.0624553
\(385\) 1.15361 0.0587932
\(386\) 56.5807 2.87988
\(387\) 28.4757 1.44750
\(388\) −57.3020 −2.90907
\(389\) −5.47602 −0.277645 −0.138823 0.990317i \(-0.544332\pi\)
−0.138823 + 0.990317i \(0.544332\pi\)
\(390\) −0.581937 −0.0294675
\(391\) −14.1436 −0.715275
\(392\) −72.3269 −3.65306
\(393\) −1.83460 −0.0925434
\(394\) −32.3305 −1.62879
\(395\) −9.81072 −0.493631
\(396\) −5.80536 −0.291730
\(397\) −21.0567 −1.05680 −0.528402 0.848994i \(-0.677209\pi\)
−0.528402 + 0.848994i \(0.677209\pi\)
\(398\) −7.35716 −0.368781
\(399\) −2.62612 −0.131471
\(400\) −50.9242 −2.54621
\(401\) 2.83248 0.141447 0.0707237 0.997496i \(-0.477469\pi\)
0.0707237 + 0.997496i \(0.477469\pi\)
\(402\) 1.82960 0.0912523
\(403\) −28.7062 −1.42996
\(404\) −72.3651 −3.60030
\(405\) 6.70178 0.333014
\(406\) −58.4402 −2.90034
\(407\) 0.947159 0.0469489
\(408\) −7.28086 −0.360456
\(409\) 0.484995 0.0239815 0.0119907 0.999928i \(-0.496183\pi\)
0.0119907 + 0.999928i \(0.496183\pi\)
\(410\) 22.5031 1.11135
\(411\) −2.29950 −0.113426
\(412\) 56.6704 2.79195
\(413\) −7.60426 −0.374181
\(414\) −13.7907 −0.677774
\(415\) −3.09413 −0.151885
\(416\) −37.7039 −1.84859
\(417\) −0.157706 −0.00772288
\(418\) 6.11283 0.298988
\(419\) 37.0157 1.80833 0.904167 0.427179i \(-0.140492\pi\)
0.904167 + 0.427179i \(0.140492\pi\)
\(420\) 1.67180 0.0815753
\(421\) 17.7645 0.865789 0.432895 0.901445i \(-0.357492\pi\)
0.432895 + 0.901445i \(0.357492\pi\)
\(422\) 38.9502 1.89607
\(423\) −29.0248 −1.41123
\(424\) 55.3231 2.68673
\(425\) −36.0878 −1.75051
\(426\) −1.06331 −0.0515173
\(427\) −46.7550 −2.26263
\(428\) 71.3994 3.45122
\(429\) 0.111549 0.00538562
\(430\) 19.0878 0.920497
\(431\) −29.4236 −1.41729 −0.708644 0.705567i \(-0.750693\pi\)
−0.708644 + 0.705567i \(0.750693\pi\)
\(432\) −7.56403 −0.363925
\(433\) 18.5214 0.890081 0.445040 0.895510i \(-0.353189\pi\)
0.445040 + 0.895510i \(0.353189\pi\)
\(434\) 115.058 5.52296
\(435\) 0.457139 0.0219181
\(436\) 11.8119 0.565687
\(437\) 10.4079 0.497879
\(438\) −1.28034 −0.0611770
\(439\) 17.5923 0.839635 0.419817 0.907609i \(-0.362094\pi\)
0.419817 + 0.907609i \(0.362094\pi\)
\(440\) −2.35358 −0.112202
\(441\) −26.5705 −1.26526
\(442\) −57.1855 −2.72004
\(443\) 7.12922 0.338719 0.169360 0.985554i \(-0.445830\pi\)
0.169360 + 0.985554i \(0.445830\pi\)
\(444\) 1.37261 0.0651414
\(445\) −1.35652 −0.0643052
\(446\) −30.7284 −1.45503
\(447\) −0.725866 −0.0343323
\(448\) 59.5075 2.81146
\(449\) −1.20234 −0.0567419 −0.0283709 0.999597i \(-0.509032\pi\)
−0.0283709 + 0.999597i \(0.509032\pi\)
\(450\) −35.1871 −1.65874
\(451\) −4.31351 −0.203115
\(452\) −60.6801 −2.85415
\(453\) −2.15558 −0.101278
\(454\) 30.2588 1.42012
\(455\) 7.94154 0.372305
\(456\) 5.35779 0.250902
\(457\) −12.9134 −0.604064 −0.302032 0.953298i \(-0.597665\pi\)
−0.302032 + 0.953298i \(0.597665\pi\)
\(458\) −47.3185 −2.21105
\(459\) −5.36030 −0.250197
\(460\) −6.62571 −0.308926
\(461\) 30.6969 1.42970 0.714849 0.699279i \(-0.246495\pi\)
0.714849 + 0.699279i \(0.246495\pi\)
\(462\) −0.447101 −0.0208010
\(463\) 34.0402 1.58198 0.790992 0.611827i \(-0.209565\pi\)
0.790992 + 0.611827i \(0.209565\pi\)
\(464\) 63.3902 2.94282
\(465\) −0.900022 −0.0417375
\(466\) −46.1738 −2.13896
\(467\) −25.6968 −1.18911 −0.594554 0.804056i \(-0.702671\pi\)
−0.594554 + 0.804056i \(0.702671\pi\)
\(468\) −39.9647 −1.84737
\(469\) −24.9681 −1.15292
\(470\) −19.4558 −0.897431
\(471\) −2.17676 −0.100300
\(472\) 15.5142 0.714097
\(473\) −3.65886 −0.168234
\(474\) 3.80233 0.174647
\(475\) 26.5560 1.21847
\(476\) 164.283 7.52991
\(477\) 20.3238 0.930565
\(478\) 51.8982 2.37377
\(479\) 18.3110 0.836650 0.418325 0.908297i \(-0.362617\pi\)
0.418325 + 0.908297i \(0.362617\pi\)
\(480\) −1.18213 −0.0539565
\(481\) 6.52033 0.297302
\(482\) −52.2937 −2.38191
\(483\) −0.761251 −0.0346381
\(484\) −54.9233 −2.49651
\(485\) −8.53431 −0.387523
\(486\) −7.84506 −0.355859
\(487\) 1.48411 0.0672513 0.0336257 0.999434i \(-0.489295\pi\)
0.0336257 + 0.999434i \(0.489295\pi\)
\(488\) 95.3892 4.31806
\(489\) 1.90315 0.0860636
\(490\) −17.8107 −0.804604
\(491\) 7.06142 0.318677 0.159339 0.987224i \(-0.449064\pi\)
0.159339 + 0.987224i \(0.449064\pi\)
\(492\) −6.25110 −0.281821
\(493\) 44.9219 2.02318
\(494\) 42.0813 1.89333
\(495\) −0.864624 −0.0388620
\(496\) −124.804 −5.60385
\(497\) 14.5106 0.650891
\(498\) 1.19919 0.0537369
\(499\) 39.4725 1.76703 0.883516 0.468401i \(-0.155170\pi\)
0.883516 + 0.468401i \(0.155170\pi\)
\(500\) −35.9784 −1.60900
\(501\) 0.308670 0.0137903
\(502\) −46.8770 −2.09222
\(503\) −3.32698 −0.148343 −0.0741714 0.997246i \(-0.523631\pi\)
−0.0741714 + 0.997246i \(0.523631\pi\)
\(504\) 96.8803 4.31539
\(505\) −10.7777 −0.479603
\(506\) 1.77197 0.0787735
\(507\) −0.661260 −0.0293676
\(508\) 50.4045 2.23634
\(509\) −42.1004 −1.86607 −0.933033 0.359791i \(-0.882848\pi\)
−0.933033 + 0.359791i \(0.882848\pi\)
\(510\) −1.79293 −0.0793922
\(511\) 17.4724 0.772935
\(512\) 22.9890 1.01598
\(513\) 3.94450 0.174154
\(514\) −23.0371 −1.01612
\(515\) 8.44024 0.371921
\(516\) −5.30238 −0.233424
\(517\) 3.72940 0.164019
\(518\) −26.1343 −1.14828
\(519\) 0.879059 0.0385864
\(520\) −16.2023 −0.710516
\(521\) −22.4586 −0.983929 −0.491965 0.870615i \(-0.663721\pi\)
−0.491965 + 0.870615i \(0.663721\pi\)
\(522\) 43.8008 1.91711
\(523\) 26.6651 1.16599 0.582993 0.812477i \(-0.301882\pi\)
0.582993 + 0.812477i \(0.301882\pi\)
\(524\) −84.4546 −3.68941
\(525\) −1.94235 −0.0847710
\(526\) −16.8972 −0.736754
\(527\) −88.4429 −3.85263
\(528\) 0.484971 0.0211057
\(529\) −19.9830 −0.868825
\(530\) 13.6235 0.591765
\(531\) 5.69937 0.247332
\(532\) −120.892 −5.24132
\(533\) −29.6946 −1.28622
\(534\) 0.525744 0.0227512
\(535\) 10.6339 0.459744
\(536\) 50.9397 2.20026
\(537\) 1.69529 0.0731571
\(538\) −17.1567 −0.739679
\(539\) 3.41404 0.147053
\(540\) −2.51108 −0.108060
\(541\) 31.6347 1.36008 0.680040 0.733175i \(-0.261962\pi\)
0.680040 + 0.733175i \(0.261962\pi\)
\(542\) 14.8621 0.638382
\(543\) −0.705967 −0.0302959
\(544\) −116.165 −4.98052
\(545\) 1.75921 0.0753564
\(546\) −3.07789 −0.131721
\(547\) 10.7409 0.459248 0.229624 0.973279i \(-0.426250\pi\)
0.229624 + 0.973279i \(0.426250\pi\)
\(548\) −105.856 −4.52195
\(549\) 35.0427 1.49559
\(550\) 4.52120 0.192785
\(551\) −33.0568 −1.40827
\(552\) 1.55310 0.0661043
\(553\) −51.8893 −2.20656
\(554\) −48.8271 −2.07447
\(555\) 0.204431 0.00867762
\(556\) −7.25987 −0.307887
\(557\) −17.0507 −0.722461 −0.361230 0.932477i \(-0.617643\pi\)
−0.361230 + 0.932477i \(0.617643\pi\)
\(558\) −86.2357 −3.65065
\(559\) −25.1879 −1.06534
\(560\) 34.5268 1.45902
\(561\) 0.343678 0.0145101
\(562\) −26.7985 −1.13043
\(563\) −36.3197 −1.53069 −0.765345 0.643620i \(-0.777432\pi\)
−0.765345 + 0.643620i \(0.777432\pi\)
\(564\) 5.40461 0.227575
\(565\) −9.03742 −0.380207
\(566\) −36.5948 −1.53819
\(567\) 35.4460 1.48859
\(568\) −29.6045 −1.24218
\(569\) −2.42060 −0.101477 −0.0507384 0.998712i \(-0.516157\pi\)
−0.0507384 + 0.998712i \(0.516157\pi\)
\(570\) 1.31937 0.0552623
\(571\) 33.6527 1.40832 0.704161 0.710040i \(-0.251323\pi\)
0.704161 + 0.710040i \(0.251323\pi\)
\(572\) 5.13507 0.214708
\(573\) 0.928195 0.0387759
\(574\) 119.020 4.96779
\(575\) 7.69797 0.321028
\(576\) −44.6007 −1.85836
\(577\) −0.640483 −0.0266637 −0.0133318 0.999911i \(-0.504244\pi\)
−0.0133318 + 0.999911i \(0.504244\pi\)
\(578\) −131.014 −5.44946
\(579\) −2.34089 −0.0972841
\(580\) 21.0441 0.873807
\(581\) −16.3650 −0.678934
\(582\) 3.30763 0.137106
\(583\) −2.61142 −0.108154
\(584\) −35.6471 −1.47509
\(585\) −5.95216 −0.246091
\(586\) −10.0690 −0.415948
\(587\) −5.56835 −0.229831 −0.114915 0.993375i \(-0.536660\pi\)
−0.114915 + 0.993375i \(0.536660\pi\)
\(588\) 4.94760 0.204036
\(589\) 65.0828 2.68169
\(590\) 3.82040 0.157283
\(591\) 1.33760 0.0550214
\(592\) 28.3479 1.16509
\(593\) −19.6020 −0.804957 −0.402479 0.915429i \(-0.631851\pi\)
−0.402479 + 0.915429i \(0.631851\pi\)
\(594\) 0.671558 0.0275543
\(595\) 24.4676 1.00307
\(596\) −33.4147 −1.36872
\(597\) 0.304385 0.0124577
\(598\) 12.1984 0.498829
\(599\) 18.3350 0.749147 0.374574 0.927197i \(-0.377789\pi\)
0.374574 + 0.927197i \(0.377789\pi\)
\(600\) 3.96276 0.161779
\(601\) 15.5256 0.633302 0.316651 0.948542i \(-0.397442\pi\)
0.316651 + 0.948542i \(0.397442\pi\)
\(602\) 100.956 4.11467
\(603\) 18.7135 0.762073
\(604\) −99.2306 −4.03764
\(605\) −8.18004 −0.332566
\(606\) 4.17711 0.169684
\(607\) −10.6175 −0.430953 −0.215476 0.976509i \(-0.569130\pi\)
−0.215476 + 0.976509i \(0.569130\pi\)
\(608\) 85.4825 3.46677
\(609\) 2.41783 0.0979752
\(610\) 23.4898 0.951074
\(611\) 25.6735 1.03864
\(612\) −123.130 −4.97723
\(613\) 28.0835 1.13428 0.567141 0.823621i \(-0.308050\pi\)
0.567141 + 0.823621i \(0.308050\pi\)
\(614\) −23.2360 −0.937727
\(615\) −0.931011 −0.0375420
\(616\) −12.4482 −0.501551
\(617\) 39.4781 1.58933 0.794665 0.607049i \(-0.207647\pi\)
0.794665 + 0.607049i \(0.207647\pi\)
\(618\) −3.27117 −0.131586
\(619\) −7.02842 −0.282496 −0.141248 0.989974i \(-0.545112\pi\)
−0.141248 + 0.989974i \(0.545112\pi\)
\(620\) −41.4319 −1.66394
\(621\) 1.14342 0.0458838
\(622\) −8.62969 −0.346019
\(623\) −7.17469 −0.287448
\(624\) 3.33859 0.133651
\(625\) 16.8009 0.672037
\(626\) −26.4734 −1.05809
\(627\) −0.252904 −0.0101000
\(628\) −100.206 −3.99864
\(629\) 20.0889 0.800999
\(630\) 23.8570 0.950485
\(631\) −31.8567 −1.26820 −0.634098 0.773252i \(-0.718629\pi\)
−0.634098 + 0.773252i \(0.718629\pi\)
\(632\) 105.864 4.21105
\(633\) −1.61147 −0.0640503
\(634\) −45.5774 −1.81011
\(635\) 7.50702 0.297907
\(636\) −3.78444 −0.150063
\(637\) 23.5026 0.931207
\(638\) −5.62797 −0.222814
\(639\) −10.8757 −0.430235
\(640\) −8.39103 −0.331684
\(641\) −38.0304 −1.50211 −0.751055 0.660240i \(-0.770455\pi\)
−0.751055 + 0.660240i \(0.770455\pi\)
\(642\) −4.12137 −0.162657
\(643\) −30.0898 −1.18662 −0.593312 0.804973i \(-0.702180\pi\)
−0.593312 + 0.804973i \(0.702180\pi\)
\(644\) −35.0437 −1.38091
\(645\) −0.789713 −0.0310949
\(646\) 129.651 5.10106
\(647\) −23.8488 −0.937593 −0.468796 0.883306i \(-0.655312\pi\)
−0.468796 + 0.883306i \(0.655312\pi\)
\(648\) −72.3166 −2.84086
\(649\) −0.732314 −0.0287458
\(650\) 31.1244 1.22080
\(651\) −4.76025 −0.186569
\(652\) 87.6104 3.43109
\(653\) 26.3396 1.03075 0.515374 0.856965i \(-0.327653\pi\)
0.515374 + 0.856965i \(0.327653\pi\)
\(654\) −0.681815 −0.0266611
\(655\) −12.5783 −0.491474
\(656\) −129.101 −5.04054
\(657\) −13.0955 −0.510906
\(658\) −102.903 −4.01157
\(659\) −25.9335 −1.01023 −0.505113 0.863053i \(-0.668549\pi\)
−0.505113 + 0.863053i \(0.668549\pi\)
\(660\) 0.160999 0.00626688
\(661\) −8.14032 −0.316622 −0.158311 0.987389i \(-0.550605\pi\)
−0.158311 + 0.987389i \(0.550605\pi\)
\(662\) 85.0204 3.30441
\(663\) 2.36591 0.0918845
\(664\) 33.3877 1.29569
\(665\) −18.0051 −0.698207
\(666\) 19.5876 0.759004
\(667\) −9.58240 −0.371032
\(668\) 14.2094 0.549778
\(669\) 1.27132 0.0491519
\(670\) 12.5440 0.484618
\(671\) −4.50265 −0.173823
\(672\) −6.25232 −0.241188
\(673\) −45.6503 −1.75969 −0.879845 0.475261i \(-0.842354\pi\)
−0.879845 + 0.475261i \(0.842354\pi\)
\(674\) 63.3314 2.43943
\(675\) 2.91746 0.112293
\(676\) −30.4406 −1.17079
\(677\) −25.6800 −0.986964 −0.493482 0.869756i \(-0.664276\pi\)
−0.493482 + 0.869756i \(0.664276\pi\)
\(678\) 3.50262 0.134517
\(679\) −45.1383 −1.73225
\(680\) −49.9186 −1.91429
\(681\) −1.25189 −0.0479724
\(682\) 11.0804 0.424292
\(683\) 4.08897 0.156460 0.0782300 0.996935i \(-0.475073\pi\)
0.0782300 + 0.996935i \(0.475073\pi\)
\(684\) 90.6080 3.46448
\(685\) −15.7657 −0.602378
\(686\) −20.0491 −0.765478
\(687\) 1.95769 0.0746906
\(688\) −109.507 −4.17493
\(689\) −17.9772 −0.684878
\(690\) 0.382454 0.0145598
\(691\) 12.6631 0.481728 0.240864 0.970559i \(-0.422569\pi\)
0.240864 + 0.970559i \(0.422569\pi\)
\(692\) 40.4668 1.53832
\(693\) −4.57303 −0.173715
\(694\) −36.1933 −1.37388
\(695\) −1.08125 −0.0410143
\(696\) −4.93283 −0.186978
\(697\) −91.4882 −3.46536
\(698\) −0.793898 −0.0300495
\(699\) 1.91033 0.0722553
\(700\) −89.4146 −3.37955
\(701\) −39.6328 −1.49691 −0.748455 0.663185i \(-0.769204\pi\)
−0.748455 + 0.663185i \(0.769204\pi\)
\(702\) 4.62307 0.174486
\(703\) −14.7829 −0.557548
\(704\) 5.73075 0.215986
\(705\) 0.804939 0.0303158
\(706\) 12.9309 0.486662
\(707\) −57.0039 −2.14385
\(708\) −1.06126 −0.0398847
\(709\) −35.5949 −1.33679 −0.668397 0.743804i \(-0.733019\pi\)
−0.668397 + 0.743804i \(0.733019\pi\)
\(710\) −7.29018 −0.273595
\(711\) 38.8909 1.45852
\(712\) 14.6377 0.548573
\(713\) 18.8660 0.706537
\(714\) −9.48287 −0.354888
\(715\) 0.764794 0.0286017
\(716\) 78.0414 2.91654
\(717\) −2.14716 −0.0801873
\(718\) 4.93540 0.184188
\(719\) −17.3147 −0.645731 −0.322866 0.946445i \(-0.604646\pi\)
−0.322866 + 0.946445i \(0.604646\pi\)
\(720\) −25.8777 −0.964405
\(721\) 44.6408 1.66251
\(722\) −44.9196 −1.67173
\(723\) 2.16353 0.0804625
\(724\) −32.4987 −1.20780
\(725\) −24.4497 −0.908039
\(726\) 3.17032 0.117662
\(727\) 33.3354 1.23634 0.618170 0.786044i \(-0.287874\pi\)
0.618170 + 0.786044i \(0.287874\pi\)
\(728\) −85.6944 −3.17605
\(729\) −26.3495 −0.975909
\(730\) −8.77819 −0.324895
\(731\) −77.6032 −2.87026
\(732\) −6.52520 −0.241178
\(733\) −46.6450 −1.72287 −0.861436 0.507866i \(-0.830435\pi\)
−0.861436 + 0.507866i \(0.830435\pi\)
\(734\) −52.9153 −1.95314
\(735\) 0.736874 0.0271800
\(736\) 24.7794 0.913380
\(737\) −2.40450 −0.0885711
\(738\) −89.2049 −3.28368
\(739\) 1.85287 0.0681589 0.0340795 0.999419i \(-0.489150\pi\)
0.0340795 + 0.999419i \(0.489150\pi\)
\(740\) 9.41085 0.345950
\(741\) −1.74101 −0.0639577
\(742\) 72.0550 2.64522
\(743\) −4.21611 −0.154674 −0.0773370 0.997005i \(-0.524642\pi\)
−0.0773370 + 0.997005i \(0.524642\pi\)
\(744\) 9.71183 0.356053
\(745\) −4.97664 −0.182330
\(746\) 50.6542 1.85458
\(747\) 12.2655 0.448772
\(748\) 15.8210 0.578472
\(749\) 56.2432 2.05508
\(750\) 2.07677 0.0758330
\(751\) −14.8585 −0.542195 −0.271097 0.962552i \(-0.587387\pi\)
−0.271097 + 0.962552i \(0.587387\pi\)
\(752\) 111.619 4.07032
\(753\) 1.93943 0.0706766
\(754\) −38.7435 −1.41096
\(755\) −14.7790 −0.537862
\(756\) −13.2812 −0.483033
\(757\) −24.4764 −0.889610 −0.444805 0.895627i \(-0.646727\pi\)
−0.444805 + 0.895627i \(0.646727\pi\)
\(758\) −19.0884 −0.693323
\(759\) −0.0733108 −0.00266102
\(760\) 36.7338 1.33248
\(761\) 38.1800 1.38402 0.692012 0.721886i \(-0.256725\pi\)
0.692012 + 0.721886i \(0.256725\pi\)
\(762\) −2.90948 −0.105399
\(763\) 9.30454 0.336847
\(764\) 42.7288 1.54587
\(765\) −18.3384 −0.663027
\(766\) 53.4668 1.93183
\(767\) −5.04132 −0.182031
\(768\) −0.0299515 −0.00108078
\(769\) −47.9659 −1.72969 −0.864847 0.502035i \(-0.832585\pi\)
−0.864847 + 0.502035i \(0.832585\pi\)
\(770\) −3.06539 −0.110469
\(771\) 0.953106 0.0343253
\(772\) −107.761 −3.87841
\(773\) 22.4050 0.805852 0.402926 0.915233i \(-0.367993\pi\)
0.402926 + 0.915233i \(0.367993\pi\)
\(774\) −75.6665 −2.71977
\(775\) 48.1369 1.72913
\(776\) 92.0908 3.30587
\(777\) 1.08124 0.0387894
\(778\) 14.5510 0.521679
\(779\) 67.3237 2.41212
\(780\) 1.10833 0.0396847
\(781\) 1.39742 0.0500036
\(782\) 37.5828 1.34396
\(783\) −3.63164 −0.129784
\(784\) 102.180 3.64930
\(785\) −14.9242 −0.532666
\(786\) 4.87495 0.173884
\(787\) 9.22688 0.328903 0.164451 0.986385i \(-0.447415\pi\)
0.164451 + 0.986385i \(0.447415\pi\)
\(788\) 61.5754 2.19353
\(789\) 0.699082 0.0248880
\(790\) 26.0693 0.927504
\(791\) −47.7993 −1.69955
\(792\) 9.32987 0.331522
\(793\) −30.9967 −1.10072
\(794\) 55.9523 1.98567
\(795\) −0.563638 −0.0199902
\(796\) 14.0122 0.496648
\(797\) 25.7836 0.913303 0.456652 0.889646i \(-0.349049\pi\)
0.456652 + 0.889646i \(0.349049\pi\)
\(798\) 6.97820 0.247025
\(799\) 79.0994 2.79834
\(800\) 63.2251 2.23534
\(801\) 5.37741 0.190001
\(802\) −7.52654 −0.265772
\(803\) 1.68265 0.0593794
\(804\) −3.48459 −0.122892
\(805\) −5.21925 −0.183954
\(806\) 76.2789 2.68681
\(807\) 0.709819 0.0249868
\(808\) 116.299 4.09138
\(809\) 19.3004 0.678564 0.339282 0.940685i \(-0.389816\pi\)
0.339282 + 0.940685i \(0.389816\pi\)
\(810\) −17.8081 −0.625714
\(811\) 7.77316 0.272953 0.136476 0.990643i \(-0.456422\pi\)
0.136476 + 0.990643i \(0.456422\pi\)
\(812\) 111.303 3.90597
\(813\) −0.614884 −0.0215649
\(814\) −2.51681 −0.0882143
\(815\) 13.0483 0.457062
\(816\) 10.2861 0.360085
\(817\) 57.1061 1.99789
\(818\) −1.28874 −0.0450598
\(819\) −31.4812 −1.10004
\(820\) −42.8585 −1.49668
\(821\) 4.82228 0.168299 0.0841494 0.996453i \(-0.473183\pi\)
0.0841494 + 0.996453i \(0.473183\pi\)
\(822\) 6.11030 0.213121
\(823\) −31.0432 −1.08210 −0.541048 0.840991i \(-0.681972\pi\)
−0.541048 + 0.840991i \(0.681972\pi\)
\(824\) −91.0757 −3.17277
\(825\) −0.187054 −0.00651239
\(826\) 20.2062 0.703065
\(827\) 38.3255 1.33271 0.666354 0.745636i \(-0.267854\pi\)
0.666354 + 0.745636i \(0.267854\pi\)
\(828\) 26.2651 0.912776
\(829\) −13.5111 −0.469261 −0.234631 0.972085i \(-0.575388\pi\)
−0.234631 + 0.972085i \(0.575388\pi\)
\(830\) 8.22180 0.285383
\(831\) 2.02011 0.0700767
\(832\) 39.4511 1.36772
\(833\) 72.4108 2.50889
\(834\) 0.419059 0.0145108
\(835\) 2.11628 0.0732370
\(836\) −11.6422 −0.402655
\(837\) 7.15003 0.247141
\(838\) −98.3590 −3.39775
\(839\) −19.9246 −0.687872 −0.343936 0.938993i \(-0.611760\pi\)
−0.343936 + 0.938993i \(0.611760\pi\)
\(840\) −2.68676 −0.0927022
\(841\) 1.43486 0.0494778
\(842\) −47.2043 −1.62677
\(843\) 1.10872 0.0381865
\(844\) −74.1830 −2.55348
\(845\) −4.53369 −0.155964
\(846\) 77.1253 2.65162
\(847\) −43.2645 −1.48659
\(848\) −78.1581 −2.68396
\(849\) 1.51402 0.0519611
\(850\) 95.8933 3.28911
\(851\) −4.28522 −0.146896
\(852\) 2.02513 0.0693798
\(853\) 47.2304 1.61714 0.808569 0.588401i \(-0.200242\pi\)
0.808569 + 0.588401i \(0.200242\pi\)
\(854\) 124.239 4.25135
\(855\) 13.4948 0.461511
\(856\) −114.747 −3.92197
\(857\) −11.4042 −0.389561 −0.194780 0.980847i \(-0.562399\pi\)
−0.194780 + 0.980847i \(0.562399\pi\)
\(858\) −0.296410 −0.0101193
\(859\) 0.357189 0.0121871 0.00609356 0.999981i \(-0.498060\pi\)
0.00609356 + 0.999981i \(0.498060\pi\)
\(860\) −36.3539 −1.23966
\(861\) −4.92416 −0.167815
\(862\) 78.1852 2.66300
\(863\) 21.2027 0.721750 0.360875 0.932614i \(-0.382478\pi\)
0.360875 + 0.932614i \(0.382478\pi\)
\(864\) 9.39114 0.319493
\(865\) 6.02695 0.204923
\(866\) −49.2155 −1.67241
\(867\) 5.42039 0.184086
\(868\) −219.135 −7.43792
\(869\) −4.99710 −0.169515
\(870\) −1.21472 −0.0411829
\(871\) −16.5528 −0.560872
\(872\) −18.9831 −0.642847
\(873\) 33.8310 1.14501
\(874\) −27.6562 −0.935485
\(875\) −28.3411 −0.958106
\(876\) 2.43848 0.0823886
\(877\) −57.1829 −1.93093 −0.965464 0.260537i \(-0.916100\pi\)
−0.965464 + 0.260537i \(0.916100\pi\)
\(878\) −46.7467 −1.57762
\(879\) 0.416582 0.0140510
\(880\) 3.32503 0.112087
\(881\) 33.6427 1.13345 0.566726 0.823906i \(-0.308210\pi\)
0.566726 + 0.823906i \(0.308210\pi\)
\(882\) 70.6037 2.37735
\(883\) −19.8361 −0.667538 −0.333769 0.942655i \(-0.608321\pi\)
−0.333769 + 0.942655i \(0.608321\pi\)
\(884\) 108.913 3.66315
\(885\) −0.158060 −0.00531312
\(886\) −18.9439 −0.636434
\(887\) 18.1013 0.607782 0.303891 0.952707i \(-0.401714\pi\)
0.303891 + 0.952707i \(0.401714\pi\)
\(888\) −2.20595 −0.0740267
\(889\) 39.7049 1.33166
\(890\) 3.60458 0.120826
\(891\) 3.41356 0.114358
\(892\) 58.5241 1.95953
\(893\) −58.2071 −1.94783
\(894\) 1.92879 0.0645084
\(895\) 11.6231 0.388519
\(896\) −44.3805 −1.48265
\(897\) −0.504679 −0.0168507
\(898\) 3.19488 0.106615
\(899\) −59.9206 −1.99846
\(900\) 67.0160 2.23387
\(901\) −55.3873 −1.84522
\(902\) 11.4620 0.381642
\(903\) −4.17683 −0.138996
\(904\) 97.5197 3.24346
\(905\) −4.84021 −0.160894
\(906\) 5.72786 0.190295
\(907\) −19.0079 −0.631148 −0.315574 0.948901i \(-0.602197\pi\)
−0.315574 + 0.948901i \(0.602197\pi\)
\(908\) −57.6298 −1.91251
\(909\) 42.7243 1.41707
\(910\) −21.1024 −0.699539
\(911\) 0.969427 0.0321185 0.0160593 0.999871i \(-0.494888\pi\)
0.0160593 + 0.999871i \(0.494888\pi\)
\(912\) −7.56926 −0.250643
\(913\) −1.57600 −0.0521580
\(914\) 34.3138 1.13500
\(915\) −0.971835 −0.0321279
\(916\) 90.1210 2.97768
\(917\) −66.5271 −2.19692
\(918\) 14.2435 0.470106
\(919\) 21.5416 0.710593 0.355296 0.934754i \(-0.384380\pi\)
0.355296 + 0.934754i \(0.384380\pi\)
\(920\) 10.6483 0.351063
\(921\) 0.961332 0.0316770
\(922\) −81.5686 −2.68632
\(923\) 9.61997 0.316645
\(924\) 0.851531 0.0280133
\(925\) −10.9338 −0.359502
\(926\) −90.4525 −2.97245
\(927\) −33.4581 −1.09891
\(928\) −78.7023 −2.58353
\(929\) 37.2927 1.22353 0.611767 0.791038i \(-0.290459\pi\)
0.611767 + 0.791038i \(0.290459\pi\)
\(930\) 2.39156 0.0784224
\(931\) −53.2852 −1.74635
\(932\) 87.9407 2.88059
\(933\) 0.357033 0.0116887
\(934\) 68.2822 2.23426
\(935\) 2.35631 0.0770595
\(936\) 64.2277 2.09935
\(937\) −39.3489 −1.28547 −0.642737 0.766087i \(-0.722201\pi\)
−0.642737 + 0.766087i \(0.722201\pi\)
\(938\) 66.3458 2.16627
\(939\) 1.09528 0.0357430
\(940\) 37.0548 1.20859
\(941\) −3.93865 −0.128396 −0.0641982 0.997937i \(-0.520449\pi\)
−0.0641982 + 0.997937i \(0.520449\pi\)
\(942\) 5.78414 0.188457
\(943\) 19.5156 0.635514
\(944\) −21.9177 −0.713361
\(945\) −1.97804 −0.0643458
\(946\) 9.72240 0.316103
\(947\) −31.7228 −1.03085 −0.515427 0.856934i \(-0.672367\pi\)
−0.515427 + 0.856934i \(0.672367\pi\)
\(948\) −7.24175 −0.235201
\(949\) 11.5835 0.376017
\(950\) −70.5654 −2.28944
\(951\) 1.88566 0.0611466
\(952\) −264.022 −8.55699
\(953\) −13.8767 −0.449510 −0.224755 0.974415i \(-0.572158\pi\)
−0.224755 + 0.974415i \(0.572158\pi\)
\(954\) −54.0050 −1.74848
\(955\) 6.36384 0.205929
\(956\) −98.8431 −3.19682
\(957\) 0.232844 0.00752678
\(958\) −48.6564 −1.57202
\(959\) −83.3856 −2.69266
\(960\) 1.23690 0.0399209
\(961\) 86.9727 2.80557
\(962\) −17.3260 −0.558612
\(963\) −42.1541 −1.35840
\(964\) 99.5965 3.20779
\(965\) −16.0495 −0.516651
\(966\) 2.02282 0.0650830
\(967\) 23.6917 0.761873 0.380937 0.924601i \(-0.375602\pi\)
0.380937 + 0.924601i \(0.375602\pi\)
\(968\) 88.2680 2.83704
\(969\) −5.36401 −0.172317
\(970\) 22.6776 0.728133
\(971\) −3.61344 −0.115961 −0.0579804 0.998318i \(-0.518466\pi\)
−0.0579804 + 0.998318i \(0.518466\pi\)
\(972\) 14.9414 0.479245
\(973\) −5.71879 −0.183336
\(974\) −3.94361 −0.126361
\(975\) −1.28770 −0.0412394
\(976\) −134.762 −4.31362
\(977\) 11.5946 0.370944 0.185472 0.982650i \(-0.440619\pi\)
0.185472 + 0.982650i \(0.440619\pi\)
\(978\) −5.05711 −0.161708
\(979\) −0.690945 −0.0220827
\(980\) 33.9215 1.08358
\(981\) −6.97373 −0.222654
\(982\) −18.7638 −0.598776
\(983\) −54.5626 −1.74028 −0.870138 0.492807i \(-0.835971\pi\)
−0.870138 + 0.492807i \(0.835971\pi\)
\(984\) 10.0462 0.320262
\(985\) 9.17076 0.292205
\(986\) −119.368 −3.80144
\(987\) 4.25736 0.135513
\(988\) −80.1463 −2.54979
\(989\) 16.5537 0.526378
\(990\) 2.29750 0.0730194
\(991\) −12.1881 −0.387166 −0.193583 0.981084i \(-0.562011\pi\)
−0.193583 + 0.981084i \(0.562011\pi\)
\(992\) 154.950 4.91968
\(993\) −3.51752 −0.111625
\(994\) −38.5580 −1.22299
\(995\) 2.08691 0.0661595
\(996\) −2.28392 −0.0723689
\(997\) 23.6592 0.749293 0.374647 0.927168i \(-0.377764\pi\)
0.374647 + 0.927168i \(0.377764\pi\)
\(998\) −104.887 −3.32015
\(999\) −1.62406 −0.0513829
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 \(a_p\))