Properties

Label 8007.2.a.e.1.9
Level 8007
Weight 2
Character 8007.1
Self dual Yes
Analytic conductor 63.936
Analytic rank 1
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8007.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(46\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) = 8007.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00485 q^{2} +1.00000 q^{3} +2.01944 q^{4} +2.86654 q^{5} -2.00485 q^{6} -1.37721 q^{7} -0.0389655 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.00485 q^{2} +1.00000 q^{3} +2.01944 q^{4} +2.86654 q^{5} -2.00485 q^{6} -1.37721 q^{7} -0.0389655 q^{8} +1.00000 q^{9} -5.74699 q^{10} +4.45661 q^{11} +2.01944 q^{12} -0.546342 q^{13} +2.76110 q^{14} +2.86654 q^{15} -3.96075 q^{16} -1.00000 q^{17} -2.00485 q^{18} -5.48056 q^{19} +5.78879 q^{20} -1.37721 q^{21} -8.93485 q^{22} -5.85867 q^{23} -0.0389655 q^{24} +3.21704 q^{25} +1.09533 q^{26} +1.00000 q^{27} -2.78118 q^{28} +1.43181 q^{29} -5.74699 q^{30} -6.52595 q^{31} +8.01865 q^{32} +4.45661 q^{33} +2.00485 q^{34} -3.94782 q^{35} +2.01944 q^{36} +2.12031 q^{37} +10.9877 q^{38} -0.546342 q^{39} -0.111696 q^{40} +4.65531 q^{41} +2.76110 q^{42} -3.60649 q^{43} +8.99984 q^{44} +2.86654 q^{45} +11.7458 q^{46} -3.40324 q^{47} -3.96075 q^{48} -5.10330 q^{49} -6.44969 q^{50} -1.00000 q^{51} -1.10330 q^{52} -3.06822 q^{53} -2.00485 q^{54} +12.7750 q^{55} +0.0536636 q^{56} -5.48056 q^{57} -2.87056 q^{58} +14.2269 q^{59} +5.78879 q^{60} -4.18725 q^{61} +13.0836 q^{62} -1.37721 q^{63} -8.15472 q^{64} -1.56611 q^{65} -8.93485 q^{66} -10.6886 q^{67} -2.01944 q^{68} -5.85867 q^{69} +7.91479 q^{70} +1.13125 q^{71} -0.0389655 q^{72} -13.2237 q^{73} -4.25091 q^{74} +3.21704 q^{75} -11.0676 q^{76} -6.13768 q^{77} +1.09533 q^{78} -4.80443 q^{79} -11.3536 q^{80} +1.00000 q^{81} -9.33321 q^{82} +2.37540 q^{83} -2.78118 q^{84} -2.86654 q^{85} +7.23048 q^{86} +1.43181 q^{87} -0.173654 q^{88} -11.9624 q^{89} -5.74699 q^{90} +0.752426 q^{91} -11.8312 q^{92} -6.52595 q^{93} +6.82299 q^{94} -15.7102 q^{95} +8.01865 q^{96} -10.3137 q^{97} +10.2314 q^{98} +4.45661 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} + O(q^{10}) \) \( 46q - 5q^{2} + 46q^{3} + 43q^{4} - 19q^{5} - 5q^{6} + q^{7} - 18q^{8} + 46q^{9} - 10q^{10} - 25q^{11} + 43q^{12} - 8q^{13} - 28q^{14} - 19q^{15} + 33q^{16} - 46q^{17} - 5q^{18} - 2q^{19} - 56q^{20} + q^{21} - 19q^{22} - 64q^{23} - 18q^{24} + 11q^{25} - 13q^{26} + 46q^{27} - 38q^{28} - 51q^{29} - 10q^{30} - 19q^{31} - 61q^{32} - 25q^{33} + 5q^{34} - 39q^{35} + 43q^{36} - 46q^{37} - 48q^{38} - 8q^{39} - 10q^{40} - 53q^{41} - 28q^{42} - 33q^{43} - 62q^{44} - 19q^{45} + 2q^{46} - 45q^{47} + 33q^{48} + 21q^{49} - 60q^{50} - 46q^{51} - 63q^{52} - 47q^{53} - 5q^{54} + 5q^{55} - 82q^{56} - 2q^{57} - 21q^{58} - 65q^{59} - 56q^{60} - 37q^{61} - 46q^{62} + q^{63} + 74q^{64} - 85q^{65} - 19q^{66} - 52q^{67} - 43q^{68} - 64q^{69} - 20q^{70} - 48q^{71} - 18q^{72} - 39q^{73} - 16q^{74} + 11q^{75} + 42q^{76} - 78q^{77} - 13q^{78} - 26q^{79} - 78q^{80} + 46q^{81} + 3q^{82} - 47q^{83} - 38q^{84} + 19q^{85} - 6q^{86} - 51q^{87} - 58q^{88} - 58q^{89} - 10q^{90} - 43q^{91} - 68q^{92} - 19q^{93} - 78q^{95} - 61q^{96} - 44q^{97} - 4q^{98} - 25q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00485 −1.41765 −0.708823 0.705387i \(-0.750773\pi\)
−0.708823 + 0.705387i \(0.750773\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.01944 1.00972
\(5\) 2.86654 1.28195 0.640977 0.767560i \(-0.278529\pi\)
0.640977 + 0.767560i \(0.278529\pi\)
\(6\) −2.00485 −0.818478
\(7\) −1.37721 −0.520536 −0.260268 0.965536i \(-0.583811\pi\)
−0.260268 + 0.965536i \(0.583811\pi\)
\(8\) −0.0389655 −0.0137764
\(9\) 1.00000 0.333333
\(10\) −5.74699 −1.81736
\(11\) 4.45661 1.34372 0.671859 0.740679i \(-0.265496\pi\)
0.671859 + 0.740679i \(0.265496\pi\)
\(12\) 2.01944 0.582961
\(13\) −0.546342 −0.151528 −0.0757640 0.997126i \(-0.524140\pi\)
−0.0757640 + 0.997126i \(0.524140\pi\)
\(14\) 2.76110 0.737935
\(15\) 2.86654 0.740137
\(16\) −3.96075 −0.990188
\(17\) −1.00000 −0.242536
\(18\) −2.00485 −0.472548
\(19\) −5.48056 −1.25733 −0.628663 0.777678i \(-0.716398\pi\)
−0.628663 + 0.777678i \(0.716398\pi\)
\(20\) 5.78879 1.29441
\(21\) −1.37721 −0.300531
\(22\) −8.93485 −1.90492
\(23\) −5.85867 −1.22162 −0.610809 0.791778i \(-0.709156\pi\)
−0.610809 + 0.791778i \(0.709156\pi\)
\(24\) −0.0389655 −0.00795381
\(25\) 3.21704 0.643407
\(26\) 1.09533 0.214813
\(27\) 1.00000 0.192450
\(28\) −2.78118 −0.525594
\(29\) 1.43181 0.265880 0.132940 0.991124i \(-0.457558\pi\)
0.132940 + 0.991124i \(0.457558\pi\)
\(30\) −5.74699 −1.04925
\(31\) −6.52595 −1.17209 −0.586047 0.810277i \(-0.699317\pi\)
−0.586047 + 0.810277i \(0.699317\pi\)
\(32\) 8.01865 1.41751
\(33\) 4.45661 0.775796
\(34\) 2.00485 0.343829
\(35\) −3.94782 −0.667303
\(36\) 2.01944 0.336573
\(37\) 2.12031 0.348577 0.174288 0.984695i \(-0.444238\pi\)
0.174288 + 0.984695i \(0.444238\pi\)
\(38\) 10.9877 1.78244
\(39\) −0.546342 −0.0874847
\(40\) −0.111696 −0.0176607
\(41\) 4.65531 0.727037 0.363518 0.931587i \(-0.381575\pi\)
0.363518 + 0.931587i \(0.381575\pi\)
\(42\) 2.76110 0.426047
\(43\) −3.60649 −0.549984 −0.274992 0.961446i \(-0.588675\pi\)
−0.274992 + 0.961446i \(0.588675\pi\)
\(44\) 8.99984 1.35678
\(45\) 2.86654 0.427318
\(46\) 11.7458 1.73182
\(47\) −3.40324 −0.496413 −0.248207 0.968707i \(-0.579841\pi\)
−0.248207 + 0.968707i \(0.579841\pi\)
\(48\) −3.96075 −0.571685
\(49\) −5.10330 −0.729043
\(50\) −6.44969 −0.912123
\(51\) −1.00000 −0.140028
\(52\) −1.10330 −0.153000
\(53\) −3.06822 −0.421452 −0.210726 0.977545i \(-0.567583\pi\)
−0.210726 + 0.977545i \(0.567583\pi\)
\(54\) −2.00485 −0.272826
\(55\) 12.7750 1.72259
\(56\) 0.0536636 0.00717110
\(57\) −5.48056 −0.725918
\(58\) −2.87056 −0.376923
\(59\) 14.2269 1.85218 0.926092 0.377299i \(-0.123147\pi\)
0.926092 + 0.377299i \(0.123147\pi\)
\(60\) 5.78879 0.747329
\(61\) −4.18725 −0.536122 −0.268061 0.963402i \(-0.586383\pi\)
−0.268061 + 0.963402i \(0.586383\pi\)
\(62\) 13.0836 1.66161
\(63\) −1.37721 −0.173512
\(64\) −8.15472 −1.01934
\(65\) −1.56611 −0.194252
\(66\) −8.93485 −1.09980
\(67\) −10.6886 −1.30582 −0.652910 0.757435i \(-0.726452\pi\)
−0.652910 + 0.757435i \(0.726452\pi\)
\(68\) −2.01944 −0.244893
\(69\) −5.85867 −0.705301
\(70\) 7.91479 0.945999
\(71\) 1.13125 0.134255 0.0671273 0.997744i \(-0.478617\pi\)
0.0671273 + 0.997744i \(0.478617\pi\)
\(72\) −0.0389655 −0.00459213
\(73\) −13.2237 −1.54772 −0.773860 0.633356i \(-0.781677\pi\)
−0.773860 + 0.633356i \(0.781677\pi\)
\(74\) −4.25091 −0.494158
\(75\) 3.21704 0.371471
\(76\) −11.0676 −1.26954
\(77\) −6.13768 −0.699453
\(78\) 1.09533 0.124022
\(79\) −4.80443 −0.540541 −0.270271 0.962784i \(-0.587113\pi\)
−0.270271 + 0.962784i \(0.587113\pi\)
\(80\) −11.3536 −1.26938
\(81\) 1.00000 0.111111
\(82\) −9.33321 −1.03068
\(83\) 2.37540 0.260734 0.130367 0.991466i \(-0.458384\pi\)
0.130367 + 0.991466i \(0.458384\pi\)
\(84\) −2.78118 −0.303452
\(85\) −2.86654 −0.310920
\(86\) 7.23048 0.779682
\(87\) 1.43181 0.153506
\(88\) −0.173654 −0.0185116
\(89\) −11.9624 −1.26801 −0.634006 0.773328i \(-0.718590\pi\)
−0.634006 + 0.773328i \(0.718590\pi\)
\(90\) −5.74699 −0.605786
\(91\) 0.752426 0.0788757
\(92\) −11.8312 −1.23349
\(93\) −6.52595 −0.676709
\(94\) 6.82299 0.703738
\(95\) −15.7102 −1.61183
\(96\) 8.01865 0.818401
\(97\) −10.3137 −1.04720 −0.523599 0.851965i \(-0.675411\pi\)
−0.523599 + 0.851965i \(0.675411\pi\)
\(98\) 10.2314 1.03352
\(99\) 4.45661 0.447906
\(100\) 6.49660 0.649660
\(101\) −8.96292 −0.891843 −0.445922 0.895072i \(-0.647124\pi\)
−0.445922 + 0.895072i \(0.647124\pi\)
\(102\) 2.00485 0.198510
\(103\) 0.659899 0.0650218 0.0325109 0.999471i \(-0.489650\pi\)
0.0325109 + 0.999471i \(0.489650\pi\)
\(104\) 0.0212885 0.00208751
\(105\) −3.94782 −0.385267
\(106\) 6.15132 0.597469
\(107\) 6.63959 0.641873 0.320937 0.947101i \(-0.396002\pi\)
0.320937 + 0.947101i \(0.396002\pi\)
\(108\) 2.01944 0.194320
\(109\) 3.59660 0.344492 0.172246 0.985054i \(-0.444898\pi\)
0.172246 + 0.985054i \(0.444898\pi\)
\(110\) −25.6121 −2.44202
\(111\) 2.12031 0.201251
\(112\) 5.45478 0.515428
\(113\) −2.47427 −0.232760 −0.116380 0.993205i \(-0.537129\pi\)
−0.116380 + 0.993205i \(0.537129\pi\)
\(114\) 10.9877 1.02909
\(115\) −16.7941 −1.56606
\(116\) 2.89144 0.268463
\(117\) −0.546342 −0.0505093
\(118\) −28.5228 −2.62574
\(119\) 1.37721 0.126248
\(120\) −0.111696 −0.0101964
\(121\) 8.86138 0.805580
\(122\) 8.39482 0.760031
\(123\) 4.65531 0.419755
\(124\) −13.1787 −1.18348
\(125\) −5.11093 −0.457136
\(126\) 2.76110 0.245978
\(127\) −8.77605 −0.778749 −0.389374 0.921080i \(-0.627309\pi\)
−0.389374 + 0.921080i \(0.627309\pi\)
\(128\) 0.311710 0.0275515
\(129\) −3.60649 −0.317534
\(130\) 3.13982 0.275380
\(131\) −8.43184 −0.736693 −0.368346 0.929689i \(-0.620076\pi\)
−0.368346 + 0.929689i \(0.620076\pi\)
\(132\) 8.99984 0.783335
\(133\) 7.54787 0.654483
\(134\) 21.4291 1.85119
\(135\) 2.86654 0.246712
\(136\) 0.0389655 0.00334127
\(137\) 3.68715 0.315015 0.157507 0.987518i \(-0.449654\pi\)
0.157507 + 0.987518i \(0.449654\pi\)
\(138\) 11.7458 0.999867
\(139\) 13.4100 1.13742 0.568709 0.822539i \(-0.307443\pi\)
0.568709 + 0.822539i \(0.307443\pi\)
\(140\) −7.97236 −0.673788
\(141\) −3.40324 −0.286604
\(142\) −2.26799 −0.190325
\(143\) −2.43483 −0.203611
\(144\) −3.96075 −0.330063
\(145\) 4.10432 0.340846
\(146\) 26.5116 2.19412
\(147\) −5.10330 −0.420913
\(148\) 4.28183 0.351964
\(149\) 3.58913 0.294033 0.147016 0.989134i \(-0.453033\pi\)
0.147016 + 0.989134i \(0.453033\pi\)
\(150\) −6.44969 −0.526615
\(151\) −2.87926 −0.234311 −0.117156 0.993114i \(-0.537378\pi\)
−0.117156 + 0.993114i \(0.537378\pi\)
\(152\) 0.213553 0.0173214
\(153\) −1.00000 −0.0808452
\(154\) 12.3051 0.991577
\(155\) −18.7069 −1.50257
\(156\) −1.10330 −0.0883348
\(157\) 1.00000 0.0798087
\(158\) 9.63218 0.766295
\(159\) −3.06822 −0.243325
\(160\) 22.9858 1.81718
\(161\) 8.06861 0.635896
\(162\) −2.00485 −0.157516
\(163\) 3.02948 0.237287 0.118644 0.992937i \(-0.462145\pi\)
0.118644 + 0.992937i \(0.462145\pi\)
\(164\) 9.40109 0.734102
\(165\) 12.7750 0.994536
\(166\) −4.76232 −0.369628
\(167\) −8.82241 −0.682698 −0.341349 0.939937i \(-0.610884\pi\)
−0.341349 + 0.939937i \(0.610884\pi\)
\(168\) 0.0536636 0.00414024
\(169\) −12.7015 −0.977039
\(170\) 5.74699 0.440774
\(171\) −5.48056 −0.419109
\(172\) −7.28307 −0.555329
\(173\) −3.88762 −0.295571 −0.147785 0.989019i \(-0.547214\pi\)
−0.147785 + 0.989019i \(0.547214\pi\)
\(174\) −2.87056 −0.217617
\(175\) −4.43053 −0.334916
\(176\) −17.6515 −1.33053
\(177\) 14.2269 1.06936
\(178\) 23.9828 1.79759
\(179\) −20.5037 −1.53252 −0.766261 0.642530i \(-0.777885\pi\)
−0.766261 + 0.642530i \(0.777885\pi\)
\(180\) 5.78879 0.431471
\(181\) 3.89160 0.289260 0.144630 0.989486i \(-0.453801\pi\)
0.144630 + 0.989486i \(0.453801\pi\)
\(182\) −1.50850 −0.111818
\(183\) −4.18725 −0.309530
\(184\) 0.228286 0.0168295
\(185\) 6.07795 0.446860
\(186\) 13.0836 0.959333
\(187\) −4.45661 −0.325900
\(188\) −6.87262 −0.501237
\(189\) −1.37721 −0.100177
\(190\) 31.4967 2.28501
\(191\) 6.57405 0.475682 0.237841 0.971304i \(-0.423560\pi\)
0.237841 + 0.971304i \(0.423560\pi\)
\(192\) −8.15472 −0.588516
\(193\) −17.4354 −1.25503 −0.627514 0.778605i \(-0.715927\pi\)
−0.627514 + 0.778605i \(0.715927\pi\)
\(194\) 20.6775 1.48456
\(195\) −1.56611 −0.112151
\(196\) −10.3058 −0.736127
\(197\) 0.733484 0.0522586 0.0261293 0.999659i \(-0.491682\pi\)
0.0261293 + 0.999659i \(0.491682\pi\)
\(198\) −8.93485 −0.634972
\(199\) 18.3345 1.29970 0.649849 0.760063i \(-0.274832\pi\)
0.649849 + 0.760063i \(0.274832\pi\)
\(200\) −0.125354 −0.00886383
\(201\) −10.6886 −0.753916
\(202\) 17.9693 1.26432
\(203\) −1.97189 −0.138400
\(204\) −2.01944 −0.141389
\(205\) 13.3446 0.932028
\(206\) −1.32300 −0.0921778
\(207\) −5.85867 −0.407206
\(208\) 2.16392 0.150041
\(209\) −24.4247 −1.68949
\(210\) 7.91479 0.546173
\(211\) 13.7689 0.947887 0.473944 0.880555i \(-0.342830\pi\)
0.473944 + 0.880555i \(0.342830\pi\)
\(212\) −6.19606 −0.425547
\(213\) 1.13125 0.0775120
\(214\) −13.3114 −0.909948
\(215\) −10.3381 −0.705055
\(216\) −0.0389655 −0.00265127
\(217\) 8.98758 0.610117
\(218\) −7.21066 −0.488368
\(219\) −13.2237 −0.893577
\(220\) 25.7984 1.73933
\(221\) 0.546342 0.0367509
\(222\) −4.25091 −0.285302
\(223\) 28.8546 1.93225 0.966123 0.258081i \(-0.0830901\pi\)
0.966123 + 0.258081i \(0.0830901\pi\)
\(224\) −11.0434 −0.737865
\(225\) 3.21704 0.214469
\(226\) 4.96054 0.329971
\(227\) 5.52235 0.366531 0.183266 0.983063i \(-0.441333\pi\)
0.183266 + 0.983063i \(0.441333\pi\)
\(228\) −11.0676 −0.732972
\(229\) −17.8130 −1.17711 −0.588557 0.808456i \(-0.700304\pi\)
−0.588557 + 0.808456i \(0.700304\pi\)
\(230\) 33.6697 2.22012
\(231\) −6.13768 −0.403830
\(232\) −0.0557911 −0.00366286
\(233\) −14.8035 −0.969807 −0.484903 0.874568i \(-0.661145\pi\)
−0.484903 + 0.874568i \(0.661145\pi\)
\(234\) 1.09533 0.0716043
\(235\) −9.75551 −0.636379
\(236\) 28.7303 1.87018
\(237\) −4.80443 −0.312081
\(238\) −2.76110 −0.178975
\(239\) 29.1103 1.88299 0.941495 0.337028i \(-0.109422\pi\)
0.941495 + 0.337028i \(0.109422\pi\)
\(240\) −11.3536 −0.732874
\(241\) −13.6700 −0.880559 −0.440280 0.897861i \(-0.645121\pi\)
−0.440280 + 0.897861i \(0.645121\pi\)
\(242\) −17.7658 −1.14203
\(243\) 1.00000 0.0641500
\(244\) −8.45588 −0.541332
\(245\) −14.6288 −0.934600
\(246\) −9.33321 −0.595064
\(247\) 2.99426 0.190520
\(248\) 0.254287 0.0161472
\(249\) 2.37540 0.150535
\(250\) 10.2467 0.648056
\(251\) 5.63943 0.355958 0.177979 0.984034i \(-0.443044\pi\)
0.177979 + 0.984034i \(0.443044\pi\)
\(252\) −2.78118 −0.175198
\(253\) −26.1098 −1.64151
\(254\) 17.5947 1.10399
\(255\) −2.86654 −0.179510
\(256\) 15.6845 0.980282
\(257\) 2.42232 0.151100 0.0755502 0.997142i \(-0.475929\pi\)
0.0755502 + 0.997142i \(0.475929\pi\)
\(258\) 7.23048 0.450150
\(259\) −2.92011 −0.181447
\(260\) −3.16266 −0.196140
\(261\) 1.43181 0.0886266
\(262\) 16.9046 1.04437
\(263\) −19.6566 −1.21208 −0.606039 0.795435i \(-0.707242\pi\)
−0.606039 + 0.795435i \(0.707242\pi\)
\(264\) −0.173654 −0.0106877
\(265\) −8.79516 −0.540282
\(266\) −15.1324 −0.927825
\(267\) −11.9624 −0.732087
\(268\) −21.5849 −1.31851
\(269\) −21.6628 −1.32081 −0.660403 0.750912i \(-0.729614\pi\)
−0.660403 + 0.750912i \(0.729614\pi\)
\(270\) −5.74699 −0.349750
\(271\) −4.11345 −0.249874 −0.124937 0.992165i \(-0.539873\pi\)
−0.124937 + 0.992165i \(0.539873\pi\)
\(272\) 3.96075 0.240156
\(273\) 0.752426 0.0455389
\(274\) −7.39220 −0.446579
\(275\) 14.3371 0.864558
\(276\) −11.8312 −0.712155
\(277\) −10.6252 −0.638409 −0.319205 0.947686i \(-0.603416\pi\)
−0.319205 + 0.947686i \(0.603416\pi\)
\(278\) −26.8850 −1.61246
\(279\) −6.52595 −0.390698
\(280\) 0.153829 0.00919303
\(281\) 14.6100 0.871558 0.435779 0.900054i \(-0.356473\pi\)
0.435779 + 0.900054i \(0.356473\pi\)
\(282\) 6.82299 0.406303
\(283\) 32.4691 1.93009 0.965043 0.262093i \(-0.0844126\pi\)
0.965043 + 0.262093i \(0.0844126\pi\)
\(284\) 2.28449 0.135559
\(285\) −15.7102 −0.930593
\(286\) 4.88148 0.288648
\(287\) −6.41133 −0.378449
\(288\) 8.01865 0.472504
\(289\) 1.00000 0.0588235
\(290\) −8.22857 −0.483198
\(291\) −10.3137 −0.604600
\(292\) −26.7045 −1.56276
\(293\) 5.62523 0.328629 0.164315 0.986408i \(-0.447459\pi\)
0.164315 + 0.986408i \(0.447459\pi\)
\(294\) 10.2314 0.596705
\(295\) 40.7819 2.37441
\(296\) −0.0826190 −0.00480213
\(297\) 4.45661 0.258599
\(298\) −7.19567 −0.416834
\(299\) 3.20084 0.185109
\(300\) 6.49660 0.375081
\(301\) 4.96688 0.286286
\(302\) 5.77250 0.332170
\(303\) −8.96292 −0.514906
\(304\) 21.7071 1.24499
\(305\) −12.0029 −0.687284
\(306\) 2.00485 0.114610
\(307\) 1.44141 0.0822656 0.0411328 0.999154i \(-0.486903\pi\)
0.0411328 + 0.999154i \(0.486903\pi\)
\(308\) −12.3946 −0.706250
\(309\) 0.659899 0.0375403
\(310\) 37.5045 2.13011
\(311\) −8.16060 −0.462745 −0.231373 0.972865i \(-0.574322\pi\)
−0.231373 + 0.972865i \(0.574322\pi\)
\(312\) 0.0212885 0.00120522
\(313\) 8.94216 0.505441 0.252720 0.967539i \(-0.418675\pi\)
0.252720 + 0.967539i \(0.418675\pi\)
\(314\) −2.00485 −0.113140
\(315\) −3.94782 −0.222434
\(316\) −9.70224 −0.545794
\(317\) −24.7048 −1.38756 −0.693781 0.720186i \(-0.744056\pi\)
−0.693781 + 0.720186i \(0.744056\pi\)
\(318\) 6.15132 0.344949
\(319\) 6.38100 0.357267
\(320\) −23.3758 −1.30675
\(321\) 6.63959 0.370586
\(322\) −16.1764 −0.901474
\(323\) 5.48056 0.304946
\(324\) 2.01944 0.112191
\(325\) −1.75760 −0.0974942
\(326\) −6.07367 −0.336389
\(327\) 3.59660 0.198893
\(328\) −0.181397 −0.0100159
\(329\) 4.68697 0.258401
\(330\) −25.6121 −1.40990
\(331\) −24.1392 −1.32681 −0.663404 0.748261i \(-0.730889\pi\)
−0.663404 + 0.748261i \(0.730889\pi\)
\(332\) 4.79696 0.263268
\(333\) 2.12031 0.116192
\(334\) 17.6876 0.967824
\(335\) −30.6393 −1.67400
\(336\) 5.45478 0.297582
\(337\) −11.7248 −0.638693 −0.319347 0.947638i \(-0.603463\pi\)
−0.319347 + 0.947638i \(0.603463\pi\)
\(338\) 25.4647 1.38510
\(339\) −2.47427 −0.134384
\(340\) −5.78879 −0.313941
\(341\) −29.0836 −1.57497
\(342\) 10.9877 0.594147
\(343\) 16.6688 0.900028
\(344\) 0.140529 0.00757680
\(345\) −16.7941 −0.904164
\(346\) 7.79411 0.419014
\(347\) −5.40933 −0.290388 −0.145194 0.989403i \(-0.546381\pi\)
−0.145194 + 0.989403i \(0.546381\pi\)
\(348\) 2.89144 0.154997
\(349\) 24.0487 1.28730 0.643650 0.765320i \(-0.277419\pi\)
0.643650 + 0.765320i \(0.277419\pi\)
\(350\) 8.88256 0.474793
\(351\) −0.546342 −0.0291616
\(352\) 35.7360 1.90474
\(353\) 9.10689 0.484711 0.242356 0.970187i \(-0.422080\pi\)
0.242356 + 0.970187i \(0.422080\pi\)
\(354\) −28.5228 −1.51597
\(355\) 3.24277 0.172108
\(356\) −24.1573 −1.28033
\(357\) 1.37721 0.0728896
\(358\) 41.1070 2.17257
\(359\) −3.07887 −0.162497 −0.0812484 0.996694i \(-0.525891\pi\)
−0.0812484 + 0.996694i \(0.525891\pi\)
\(360\) −0.111696 −0.00588690
\(361\) 11.0365 0.580869
\(362\) −7.80208 −0.410068
\(363\) 8.86138 0.465102
\(364\) 1.51948 0.0796422
\(365\) −37.9063 −1.98411
\(366\) 8.39482 0.438804
\(367\) 26.9074 1.40455 0.702276 0.711904i \(-0.252167\pi\)
0.702276 + 0.711904i \(0.252167\pi\)
\(368\) 23.2047 1.20963
\(369\) 4.65531 0.242346
\(370\) −12.1854 −0.633488
\(371\) 4.22557 0.219381
\(372\) −13.1787 −0.683285
\(373\) 10.9041 0.564593 0.282296 0.959327i \(-0.408904\pi\)
0.282296 + 0.959327i \(0.408904\pi\)
\(374\) 8.93485 0.462010
\(375\) −5.11093 −0.263927
\(376\) 0.132609 0.00683879
\(377\) −0.782255 −0.0402882
\(378\) 2.76110 0.142016
\(379\) −13.3333 −0.684888 −0.342444 0.939538i \(-0.611255\pi\)
−0.342444 + 0.939538i \(0.611255\pi\)
\(380\) −31.7258 −1.62750
\(381\) −8.77605 −0.449611
\(382\) −13.1800 −0.674348
\(383\) −14.6781 −0.750016 −0.375008 0.927022i \(-0.622360\pi\)
−0.375008 + 0.927022i \(0.622360\pi\)
\(384\) 0.311710 0.0159069
\(385\) −17.5939 −0.896667
\(386\) 34.9554 1.77918
\(387\) −3.60649 −0.183328
\(388\) −20.8279 −1.05738
\(389\) −25.0472 −1.26994 −0.634972 0.772535i \(-0.718988\pi\)
−0.634972 + 0.772535i \(0.718988\pi\)
\(390\) 3.13982 0.158991
\(391\) 5.85867 0.296286
\(392\) 0.198853 0.0100436
\(393\) −8.43184 −0.425330
\(394\) −1.47053 −0.0740841
\(395\) −13.7721 −0.692949
\(396\) 8.99984 0.452259
\(397\) −2.41395 −0.121153 −0.0605764 0.998164i \(-0.519294\pi\)
−0.0605764 + 0.998164i \(0.519294\pi\)
\(398\) −36.7580 −1.84251
\(399\) 7.54787 0.377866
\(400\) −12.7419 −0.637094
\(401\) −1.35431 −0.0676313 −0.0338156 0.999428i \(-0.510766\pi\)
−0.0338156 + 0.999428i \(0.510766\pi\)
\(402\) 21.4291 1.06879
\(403\) 3.56540 0.177605
\(404\) −18.1000 −0.900510
\(405\) 2.86654 0.142439
\(406\) 3.95336 0.196202
\(407\) 9.44939 0.468389
\(408\) 0.0389655 0.00192908
\(409\) −25.6765 −1.26962 −0.634811 0.772667i \(-0.718922\pi\)
−0.634811 + 0.772667i \(0.718922\pi\)
\(410\) −26.7540 −1.32129
\(411\) 3.68715 0.181874
\(412\) 1.33262 0.0656537
\(413\) −19.5934 −0.964127
\(414\) 11.7458 0.577274
\(415\) 6.80917 0.334249
\(416\) −4.38093 −0.214793
\(417\) 13.4100 0.656689
\(418\) 48.9680 2.39510
\(419\) −8.36614 −0.408713 −0.204356 0.978897i \(-0.565510\pi\)
−0.204356 + 0.978897i \(0.565510\pi\)
\(420\) −7.97236 −0.389011
\(421\) 31.3435 1.52759 0.763795 0.645459i \(-0.223334\pi\)
0.763795 + 0.645459i \(0.223334\pi\)
\(422\) −27.6045 −1.34377
\(423\) −3.40324 −0.165471
\(424\) 0.119555 0.00580609
\(425\) −3.21704 −0.156049
\(426\) −2.26799 −0.109884
\(427\) 5.76671 0.279071
\(428\) 13.4082 0.648111
\(429\) −2.43483 −0.117555
\(430\) 20.7264 0.999517
\(431\) 28.8096 1.38771 0.693855 0.720114i \(-0.255911\pi\)
0.693855 + 0.720114i \(0.255911\pi\)
\(432\) −3.96075 −0.190562
\(433\) −16.4592 −0.790977 −0.395489 0.918471i \(-0.629425\pi\)
−0.395489 + 0.918471i \(0.629425\pi\)
\(434\) −18.0188 −0.864929
\(435\) 4.10432 0.196787
\(436\) 7.26311 0.347840
\(437\) 32.1088 1.53597
\(438\) 26.5116 1.26677
\(439\) 35.5319 1.69584 0.847922 0.530121i \(-0.177854\pi\)
0.847922 + 0.530121i \(0.177854\pi\)
\(440\) −0.497786 −0.0237310
\(441\) −5.10330 −0.243014
\(442\) −1.09533 −0.0520998
\(443\) 18.6524 0.886201 0.443100 0.896472i \(-0.353878\pi\)
0.443100 + 0.896472i \(0.353878\pi\)
\(444\) 4.28183 0.203207
\(445\) −34.2907 −1.62553
\(446\) −57.8492 −2.73924
\(447\) 3.58913 0.169760
\(448\) 11.2307 0.530603
\(449\) 17.3506 0.818826 0.409413 0.912349i \(-0.365734\pi\)
0.409413 + 0.912349i \(0.365734\pi\)
\(450\) −6.44969 −0.304041
\(451\) 20.7469 0.976933
\(452\) −4.99663 −0.235022
\(453\) −2.87926 −0.135280
\(454\) −11.0715 −0.519611
\(455\) 2.15686 0.101115
\(456\) 0.213553 0.0100005
\(457\) 30.0523 1.40579 0.702893 0.711295i \(-0.251891\pi\)
0.702893 + 0.711295i \(0.251891\pi\)
\(458\) 35.7124 1.66873
\(459\) −1.00000 −0.0466760
\(460\) −33.9146 −1.58128
\(461\) 14.4897 0.674854 0.337427 0.941352i \(-0.390443\pi\)
0.337427 + 0.941352i \(0.390443\pi\)
\(462\) 12.3051 0.572487
\(463\) −4.00974 −0.186348 −0.0931742 0.995650i \(-0.529701\pi\)
−0.0931742 + 0.995650i \(0.529701\pi\)
\(464\) −5.67103 −0.263271
\(465\) −18.7069 −0.867510
\(466\) 29.6788 1.37484
\(467\) 23.4089 1.08323 0.541617 0.840625i \(-0.317812\pi\)
0.541617 + 0.840625i \(0.317812\pi\)
\(468\) −1.10330 −0.0510001
\(469\) 14.7204 0.679726
\(470\) 19.5584 0.902160
\(471\) 1.00000 0.0460776
\(472\) −0.554358 −0.0255164
\(473\) −16.0727 −0.739024
\(474\) 9.63218 0.442421
\(475\) −17.6312 −0.808973
\(476\) 2.78118 0.127475
\(477\) −3.06822 −0.140484
\(478\) −58.3619 −2.66941
\(479\) −11.7932 −0.538844 −0.269422 0.963022i \(-0.586833\pi\)
−0.269422 + 0.963022i \(0.586833\pi\)
\(480\) 22.9858 1.04915
\(481\) −1.15841 −0.0528191
\(482\) 27.4062 1.24832
\(483\) 8.06861 0.367134
\(484\) 17.8950 0.813408
\(485\) −29.5646 −1.34246
\(486\) −2.00485 −0.0909420
\(487\) −11.9864 −0.543155 −0.271578 0.962417i \(-0.587545\pi\)
−0.271578 + 0.962417i \(0.587545\pi\)
\(488\) 0.163158 0.00738583
\(489\) 3.02948 0.136998
\(490\) 29.3286 1.32493
\(491\) 18.8930 0.852631 0.426315 0.904575i \(-0.359811\pi\)
0.426315 + 0.904575i \(0.359811\pi\)
\(492\) 9.40109 0.423834
\(493\) −1.43181 −0.0644853
\(494\) −6.00305 −0.270090
\(495\) 12.7750 0.574195
\(496\) 25.8476 1.16059
\(497\) −1.55797 −0.0698843
\(498\) −4.76232 −0.213405
\(499\) 16.6378 0.744810 0.372405 0.928070i \(-0.378533\pi\)
0.372405 + 0.928070i \(0.378533\pi\)
\(500\) −10.3212 −0.461578
\(501\) −8.82241 −0.394156
\(502\) −11.3062 −0.504622
\(503\) 37.0162 1.65047 0.825235 0.564790i \(-0.191043\pi\)
0.825235 + 0.564790i \(0.191043\pi\)
\(504\) 0.0536636 0.00239037
\(505\) −25.6925 −1.14330
\(506\) 52.3464 2.32708
\(507\) −12.7015 −0.564094
\(508\) −17.7227 −0.786317
\(509\) 14.9314 0.661823 0.330912 0.943662i \(-0.392644\pi\)
0.330912 + 0.943662i \(0.392644\pi\)
\(510\) 5.74699 0.254481
\(511\) 18.2118 0.805643
\(512\) −32.0686 −1.41724
\(513\) −5.48056 −0.241973
\(514\) −4.85640 −0.214207
\(515\) 1.89163 0.0833550
\(516\) −7.28307 −0.320619
\(517\) −15.1669 −0.667040
\(518\) 5.85438 0.257227
\(519\) −3.88762 −0.170648
\(520\) 0.0610243 0.00267609
\(521\) 40.1220 1.75778 0.878889 0.477027i \(-0.158285\pi\)
0.878889 + 0.477027i \(0.158285\pi\)
\(522\) −2.87056 −0.125641
\(523\) −18.5668 −0.811870 −0.405935 0.913902i \(-0.633054\pi\)
−0.405935 + 0.913902i \(0.633054\pi\)
\(524\) −17.0275 −0.743852
\(525\) −4.43053 −0.193364
\(526\) 39.4086 1.71830
\(527\) 6.52595 0.284275
\(528\) −17.6515 −0.768184
\(529\) 11.3241 0.492350
\(530\) 17.6330 0.765928
\(531\) 14.2269 0.617394
\(532\) 15.2424 0.660843
\(533\) −2.54339 −0.110166
\(534\) 23.9828 1.03784
\(535\) 19.0326 0.822852
\(536\) 0.416487 0.0179895
\(537\) −20.5037 −0.884802
\(538\) 43.4308 1.87243
\(539\) −22.7434 −0.979628
\(540\) 5.78879 0.249110
\(541\) 10.4847 0.450772 0.225386 0.974269i \(-0.427636\pi\)
0.225386 + 0.974269i \(0.427636\pi\)
\(542\) 8.24686 0.354233
\(543\) 3.89160 0.167004
\(544\) −8.01865 −0.343797
\(545\) 10.3098 0.441623
\(546\) −1.50850 −0.0645580
\(547\) 40.1637 1.71727 0.858637 0.512584i \(-0.171312\pi\)
0.858637 + 0.512584i \(0.171312\pi\)
\(548\) 7.44597 0.318076
\(549\) −4.18725 −0.178707
\(550\) −28.7437 −1.22564
\(551\) −7.84709 −0.334297
\(552\) 0.228286 0.00971651
\(553\) 6.61670 0.281371
\(554\) 21.3021 0.905038
\(555\) 6.07795 0.257994
\(556\) 27.0806 1.14847
\(557\) −12.9624 −0.549236 −0.274618 0.961553i \(-0.588551\pi\)
−0.274618 + 0.961553i \(0.588551\pi\)
\(558\) 13.0836 0.553871
\(559\) 1.97037 0.0833380
\(560\) 15.6363 0.660755
\(561\) −4.45661 −0.188158
\(562\) −29.2909 −1.23556
\(563\) 0.331680 0.0139786 0.00698931 0.999976i \(-0.497775\pi\)
0.00698931 + 0.999976i \(0.497775\pi\)
\(564\) −6.87262 −0.289390
\(565\) −7.09258 −0.298387
\(566\) −65.0957 −2.73618
\(567\) −1.37721 −0.0578373
\(568\) −0.0440797 −0.00184955
\(569\) 22.7960 0.955658 0.477829 0.878453i \(-0.341424\pi\)
0.477829 + 0.878453i \(0.341424\pi\)
\(570\) 31.4967 1.31925
\(571\) 8.61150 0.360380 0.180190 0.983632i \(-0.442329\pi\)
0.180190 + 0.983632i \(0.442329\pi\)
\(572\) −4.91699 −0.205590
\(573\) 6.57405 0.274635
\(574\) 12.8538 0.536506
\(575\) −18.8476 −0.785998
\(576\) −8.15472 −0.339780
\(577\) −34.1100 −1.42002 −0.710009 0.704193i \(-0.751309\pi\)
−0.710009 + 0.704193i \(0.751309\pi\)
\(578\) −2.00485 −0.0833909
\(579\) −17.4354 −0.724591
\(580\) 8.28842 0.344158
\(581\) −3.27142 −0.135721
\(582\) 20.6775 0.857109
\(583\) −13.6738 −0.566313
\(584\) 0.515270 0.0213220
\(585\) −1.56611 −0.0647506
\(586\) −11.2778 −0.465880
\(587\) −45.3401 −1.87139 −0.935693 0.352814i \(-0.885225\pi\)
−0.935693 + 0.352814i \(0.885225\pi\)
\(588\) −10.3058 −0.425003
\(589\) 35.7658 1.47371
\(590\) −81.7617 −3.36608
\(591\) 0.733484 0.0301715
\(592\) −8.39802 −0.345156
\(593\) −25.1697 −1.03360 −0.516799 0.856107i \(-0.672876\pi\)
−0.516799 + 0.856107i \(0.672876\pi\)
\(594\) −8.93485 −0.366601
\(595\) 3.94782 0.161845
\(596\) 7.24801 0.296890
\(597\) 18.3345 0.750381
\(598\) −6.41721 −0.262419
\(599\) 15.3010 0.625181 0.312590 0.949888i \(-0.398803\pi\)
0.312590 + 0.949888i \(0.398803\pi\)
\(600\) −0.125354 −0.00511754
\(601\) −5.36129 −0.218692 −0.109346 0.994004i \(-0.534876\pi\)
−0.109346 + 0.994004i \(0.534876\pi\)
\(602\) −9.95787 −0.405852
\(603\) −10.6886 −0.435274
\(604\) −5.81449 −0.236588
\(605\) 25.4015 1.03272
\(606\) 17.9693 0.729954
\(607\) −43.3910 −1.76119 −0.880593 0.473874i \(-0.842855\pi\)
−0.880593 + 0.473874i \(0.842855\pi\)
\(608\) −43.9467 −1.78227
\(609\) −1.97189 −0.0799052
\(610\) 24.0641 0.974325
\(611\) 1.85933 0.0752205
\(612\) −2.01944 −0.0816308
\(613\) −0.0395570 −0.00159769 −0.000798847 1.00000i \(-0.500254\pi\)
−0.000798847 1.00000i \(0.500254\pi\)
\(614\) −2.88981 −0.116623
\(615\) 13.3446 0.538107
\(616\) 0.239158 0.00963594
\(617\) 21.8066 0.877902 0.438951 0.898511i \(-0.355350\pi\)
0.438951 + 0.898511i \(0.355350\pi\)
\(618\) −1.32300 −0.0532189
\(619\) −21.0830 −0.847396 −0.423698 0.905804i \(-0.639268\pi\)
−0.423698 + 0.905804i \(0.639268\pi\)
\(620\) −37.7773 −1.51717
\(621\) −5.85867 −0.235100
\(622\) 16.3608 0.656008
\(623\) 16.4747 0.660045
\(624\) 2.16392 0.0866263
\(625\) −30.7359 −1.22943
\(626\) −17.9277 −0.716536
\(627\) −24.4247 −0.975429
\(628\) 2.01944 0.0805843
\(629\) −2.12031 −0.0845423
\(630\) 7.91479 0.315333
\(631\) −8.49757 −0.338283 −0.169141 0.985592i \(-0.554099\pi\)
−0.169141 + 0.985592i \(0.554099\pi\)
\(632\) 0.187207 0.00744671
\(633\) 13.7689 0.547263
\(634\) 49.5295 1.96707
\(635\) −25.1569 −0.998321
\(636\) −6.19606 −0.245690
\(637\) 2.78815 0.110470
\(638\) −12.7930 −0.506478
\(639\) 1.13125 0.0447515
\(640\) 0.893527 0.0353198
\(641\) −25.7301 −1.01628 −0.508138 0.861276i \(-0.669666\pi\)
−0.508138 + 0.861276i \(0.669666\pi\)
\(642\) −13.3114 −0.525359
\(643\) 19.3315 0.762362 0.381181 0.924500i \(-0.375518\pi\)
0.381181 + 0.924500i \(0.375518\pi\)
\(644\) 16.2940 0.642075
\(645\) −10.3381 −0.407064
\(646\) −10.9877 −0.432306
\(647\) −5.53680 −0.217674 −0.108837 0.994060i \(-0.534713\pi\)
−0.108837 + 0.994060i \(0.534713\pi\)
\(648\) −0.0389655 −0.00153071
\(649\) 63.4037 2.48881
\(650\) 3.52373 0.138212
\(651\) 8.98758 0.352251
\(652\) 6.11785 0.239593
\(653\) 16.0385 0.627633 0.313817 0.949484i \(-0.398392\pi\)
0.313817 + 0.949484i \(0.398392\pi\)
\(654\) −7.21066 −0.281959
\(655\) −24.1702 −0.944407
\(656\) −18.4385 −0.719903
\(657\) −13.2237 −0.515907
\(658\) −9.39668 −0.366321
\(659\) 8.96517 0.349234 0.174617 0.984636i \(-0.444131\pi\)
0.174617 + 0.984636i \(0.444131\pi\)
\(660\) 25.7984 1.00420
\(661\) −40.7448 −1.58479 −0.792395 0.610008i \(-0.791166\pi\)
−0.792395 + 0.610008i \(0.791166\pi\)
\(662\) 48.3955 1.88094
\(663\) 0.546342 0.0212182
\(664\) −0.0925586 −0.00359197
\(665\) 21.6362 0.839017
\(666\) −4.25091 −0.164719
\(667\) −8.38848 −0.324803
\(668\) −17.8163 −0.689333
\(669\) 28.8546 1.11558
\(670\) 61.4273 2.37314
\(671\) −18.6609 −0.720397
\(672\) −11.0434 −0.426007
\(673\) −49.4249 −1.90519 −0.952596 0.304239i \(-0.901598\pi\)
−0.952596 + 0.304239i \(0.901598\pi\)
\(674\) 23.5066 0.905440
\(675\) 3.21704 0.123824
\(676\) −25.6499 −0.986534
\(677\) −0.821016 −0.0315542 −0.0157771 0.999876i \(-0.505022\pi\)
−0.0157771 + 0.999876i \(0.505022\pi\)
\(678\) 4.96054 0.190509
\(679\) 14.2041 0.545104
\(680\) 0.111696 0.00428335
\(681\) 5.52235 0.211617
\(682\) 58.3083 2.23274
\(683\) −12.9695 −0.496264 −0.248132 0.968726i \(-0.579817\pi\)
−0.248132 + 0.968726i \(0.579817\pi\)
\(684\) −11.0676 −0.423182
\(685\) 10.5694 0.403834
\(686\) −33.4184 −1.27592
\(687\) −17.8130 −0.679607
\(688\) 14.2844 0.544588
\(689\) 1.67629 0.0638617
\(690\) 33.6697 1.28178
\(691\) 14.8609 0.565335 0.282667 0.959218i \(-0.408781\pi\)
0.282667 + 0.959218i \(0.408781\pi\)
\(692\) −7.85080 −0.298443
\(693\) −6.13768 −0.233151
\(694\) 10.8449 0.411667
\(695\) 38.4402 1.45812
\(696\) −0.0557911 −0.00211476
\(697\) −4.65531 −0.176332
\(698\) −48.2142 −1.82493
\(699\) −14.8035 −0.559918
\(700\) −8.94716 −0.338171
\(701\) 43.2251 1.63259 0.816296 0.577634i \(-0.196024\pi\)
0.816296 + 0.577634i \(0.196024\pi\)
\(702\) 1.09533 0.0413407
\(703\) −11.6205 −0.438275
\(704\) −36.3424 −1.36971
\(705\) −9.75551 −0.367414
\(706\) −18.2580 −0.687148
\(707\) 12.3438 0.464236
\(708\) 28.7303 1.07975
\(709\) −43.8415 −1.64650 −0.823250 0.567678i \(-0.807842\pi\)
−0.823250 + 0.567678i \(0.807842\pi\)
\(710\) −6.50128 −0.243989
\(711\) −4.80443 −0.180180
\(712\) 0.466121 0.0174686
\(713\) 38.2334 1.43185
\(714\) −2.76110 −0.103332
\(715\) −6.97954 −0.261020
\(716\) −41.4060 −1.54741
\(717\) 29.1103 1.08714
\(718\) 6.17269 0.230363
\(719\) −34.1706 −1.27435 −0.637174 0.770720i \(-0.719897\pi\)
−0.637174 + 0.770720i \(0.719897\pi\)
\(720\) −11.3536 −0.423125
\(721\) −0.908818 −0.0338461
\(722\) −22.1266 −0.823466
\(723\) −13.6700 −0.508391
\(724\) 7.85883 0.292071
\(725\) 4.60617 0.171069
\(726\) −17.7658 −0.659349
\(727\) −20.5519 −0.762228 −0.381114 0.924528i \(-0.624459\pi\)
−0.381114 + 0.924528i \(0.624459\pi\)
\(728\) −0.0293187 −0.00108662
\(729\) 1.00000 0.0370370
\(730\) 75.9966 2.81276
\(731\) 3.60649 0.133391
\(732\) −8.45588 −0.312538
\(733\) 49.0781 1.81274 0.906371 0.422482i \(-0.138841\pi\)
0.906371 + 0.422482i \(0.138841\pi\)
\(734\) −53.9453 −1.99116
\(735\) −14.6288 −0.539591
\(736\) −46.9787 −1.73166
\(737\) −47.6349 −1.75466
\(738\) −9.33321 −0.343560
\(739\) −21.7901 −0.801563 −0.400782 0.916174i \(-0.631261\pi\)
−0.400782 + 0.916174i \(0.631261\pi\)
\(740\) 12.2740 0.451202
\(741\) 2.99426 0.109997
\(742\) −8.47165 −0.311004
\(743\) −14.1776 −0.520124 −0.260062 0.965592i \(-0.583743\pi\)
−0.260062 + 0.965592i \(0.583743\pi\)
\(744\) 0.254287 0.00932261
\(745\) 10.2884 0.376937
\(746\) −21.8611 −0.800392
\(747\) 2.37540 0.0869113
\(748\) −8.99984 −0.329067
\(749\) −9.14409 −0.334118
\(750\) 10.2467 0.374155
\(751\) 12.7769 0.466235 0.233118 0.972449i \(-0.425107\pi\)
0.233118 + 0.972449i \(0.425107\pi\)
\(752\) 13.4794 0.491542
\(753\) 5.63943 0.205512
\(754\) 1.56831 0.0571144
\(755\) −8.25352 −0.300376
\(756\) −2.78118 −0.101151
\(757\) 19.2523 0.699739 0.349869 0.936799i \(-0.386226\pi\)
0.349869 + 0.936799i \(0.386226\pi\)
\(758\) 26.7314 0.970928
\(759\) −26.1098 −0.947727
\(760\) 0.612157 0.0222053
\(761\) −40.4457 −1.46616 −0.733078 0.680144i \(-0.761917\pi\)
−0.733078 + 0.680144i \(0.761917\pi\)
\(762\) 17.5947 0.637389
\(763\) −4.95327 −0.179320
\(764\) 13.2759 0.480304
\(765\) −2.86654 −0.103640
\(766\) 29.4274 1.06326
\(767\) −7.77274 −0.280657
\(768\) 15.6845 0.565966
\(769\) −31.1093 −1.12183 −0.560916 0.827873i \(-0.689551\pi\)
−0.560916 + 0.827873i \(0.689551\pi\)
\(770\) 35.2731 1.27116
\(771\) 2.42232 0.0872378
\(772\) −35.2097 −1.26722
\(773\) −49.4489 −1.77855 −0.889277 0.457370i \(-0.848792\pi\)
−0.889277 + 0.457370i \(0.848792\pi\)
\(774\) 7.23048 0.259894
\(775\) −20.9942 −0.754134
\(776\) 0.401879 0.0144266
\(777\) −2.92011 −0.104758
\(778\) 50.2160 1.80033
\(779\) −25.5137 −0.914123
\(780\) −3.16266 −0.113241
\(781\) 5.04154 0.180400
\(782\) −11.7458 −0.420028
\(783\) 1.43181 0.0511686
\(784\) 20.2129 0.721889
\(785\) 2.86654 0.102311
\(786\) 16.9046 0.602967
\(787\) −34.2957 −1.22251 −0.611255 0.791434i \(-0.709335\pi\)
−0.611255 + 0.791434i \(0.709335\pi\)
\(788\) 1.48122 0.0527664
\(789\) −19.6566 −0.699793
\(790\) 27.6110 0.982356
\(791\) 3.40758 0.121160
\(792\) −0.173654 −0.00617053
\(793\) 2.28767 0.0812375
\(794\) 4.83962 0.171752
\(795\) −8.79516 −0.311932
\(796\) 37.0253 1.31233
\(797\) 35.4137 1.25442 0.627208 0.778851i \(-0.284197\pi\)
0.627208 + 0.778851i \(0.284197\pi\)
\(798\) −15.1324 −0.535680
\(799\) 3.40324 0.120398
\(800\) 25.7963 0.912037
\(801\) −11.9624 −0.422671
\(802\) 2.71520 0.0958771
\(803\) −58.9330 −2.07970
\(804\) −21.5849 −0.761242
\(805\) 23.1290 0.815189
\(806\) −7.14810 −0.251781
\(807\) −21.6628 −0.762567
\(808\) 0.349245 0.0122864
\(809\) 5.09425 0.179104 0.0895522 0.995982i \(-0.471456\pi\)
0.0895522 + 0.995982i \(0.471456\pi\)
\(810\) −5.74699 −0.201929
\(811\) −22.7353 −0.798346 −0.399173 0.916876i \(-0.630703\pi\)
−0.399173 + 0.916876i \(0.630703\pi\)
\(812\) −3.98211 −0.139745
\(813\) −4.11345 −0.144265
\(814\) −18.9446 −0.664010
\(815\) 8.68413 0.304192
\(816\) 3.96075 0.138654
\(817\) 19.7656 0.691509
\(818\) 51.4777 1.79987
\(819\) 0.752426 0.0262919
\(820\) 26.9486 0.941086
\(821\) 44.3681 1.54846 0.774229 0.632906i \(-0.218138\pi\)
0.774229 + 0.632906i \(0.218138\pi\)
\(822\) −7.39220 −0.257833
\(823\) −10.2472 −0.357196 −0.178598 0.983922i \(-0.557156\pi\)
−0.178598 + 0.983922i \(0.557156\pi\)
\(824\) −0.0257133 −0.000895766 0
\(825\) 14.3371 0.499153
\(826\) 39.2818 1.36679
\(827\) −32.0567 −1.11472 −0.557360 0.830271i \(-0.688186\pi\)
−0.557360 + 0.830271i \(0.688186\pi\)
\(828\) −11.8312 −0.411163
\(829\) 32.8499 1.14092 0.570462 0.821324i \(-0.306764\pi\)
0.570462 + 0.821324i \(0.306764\pi\)
\(830\) −13.6514 −0.473846
\(831\) −10.6252 −0.368586
\(832\) 4.45526 0.154459
\(833\) 5.10330 0.176819
\(834\) −26.8850 −0.930952
\(835\) −25.2898 −0.875188
\(836\) −49.3241 −1.70591
\(837\) −6.52595 −0.225570
\(838\) 16.7729 0.579410
\(839\) −16.0044 −0.552534 −0.276267 0.961081i \(-0.589097\pi\)
−0.276267 + 0.961081i \(0.589097\pi\)
\(840\) 0.153829 0.00530760
\(841\) −26.9499 −0.929308
\(842\) −62.8391 −2.16558
\(843\) 14.6100 0.503195
\(844\) 27.8053 0.957099
\(845\) −36.4094 −1.25252
\(846\) 6.82299 0.234579
\(847\) −12.2040 −0.419333
\(848\) 12.1524 0.417316
\(849\) 32.4691 1.11434
\(850\) 6.44969 0.221222
\(851\) −12.4222 −0.425828
\(852\) 2.28449 0.0782652
\(853\) 21.4611 0.734813 0.367406 0.930061i \(-0.380246\pi\)
0.367406 + 0.930061i \(0.380246\pi\)
\(854\) −11.5614 −0.395623
\(855\) −15.7102 −0.537278
\(856\) −0.258715 −0.00884270
\(857\) −11.7124 −0.400088 −0.200044 0.979787i \(-0.564109\pi\)
−0.200044 + 0.979787i \(0.564109\pi\)
\(858\) 4.88148 0.166651
\(859\) −53.7503 −1.83394 −0.916968 0.398960i \(-0.869371\pi\)
−0.916968 + 0.398960i \(0.869371\pi\)
\(860\) −20.8772 −0.711906
\(861\) −6.41133 −0.218497
\(862\) −57.7591 −1.96728
\(863\) 44.7672 1.52389 0.761947 0.647640i \(-0.224244\pi\)
0.761947 + 0.647640i \(0.224244\pi\)
\(864\) 8.01865 0.272800
\(865\) −11.1440 −0.378908
\(866\) 32.9982 1.12132
\(867\) 1.00000 0.0339618
\(868\) 18.1498 0.616046
\(869\) −21.4115 −0.726335
\(870\) −8.22857 −0.278975
\(871\) 5.83963 0.197868
\(872\) −0.140144 −0.00474586
\(873\) −10.3137 −0.349066
\(874\) −64.3734 −2.17746
\(875\) 7.03881 0.237955
\(876\) −26.7045 −0.902260
\(877\) 14.5576 0.491575 0.245787 0.969324i \(-0.420954\pi\)
0.245787 + 0.969324i \(0.420954\pi\)
\(878\) −71.2362 −2.40410
\(879\) 5.62523 0.189734
\(880\) −50.5988 −1.70568
\(881\) −24.0683 −0.810882 −0.405441 0.914121i \(-0.632882\pi\)
−0.405441 + 0.914121i \(0.632882\pi\)
\(882\) 10.2314 0.344508
\(883\) 11.2915 0.379990 0.189995 0.981785i \(-0.439153\pi\)
0.189995 + 0.981785i \(0.439153\pi\)
\(884\) 1.10330 0.0371081
\(885\) 40.7819 1.37087
\(886\) −37.3953 −1.25632
\(887\) −36.3464 −1.22039 −0.610196 0.792251i \(-0.708909\pi\)
−0.610196 + 0.792251i \(0.708909\pi\)
\(888\) −0.0826190 −0.00277251
\(889\) 12.0864 0.405366
\(890\) 68.7477 2.30443
\(891\) 4.45661 0.149302
\(892\) 58.2700 1.95102
\(893\) 18.6516 0.624153
\(894\) −7.19567 −0.240659
\(895\) −58.7748 −1.96462
\(896\) −0.429289 −0.0143415
\(897\) 3.20084 0.106873
\(898\) −34.7854 −1.16080
\(899\) −9.34389 −0.311636
\(900\) 6.49660 0.216553
\(901\) 3.06822 0.102217
\(902\) −41.5945 −1.38494
\(903\) 4.96688 0.165287
\(904\) 0.0964112 0.00320659
\(905\) 11.1554 0.370818
\(906\) 5.77250 0.191779
\(907\) −26.7496 −0.888205 −0.444102 0.895976i \(-0.646477\pi\)
−0.444102 + 0.895976i \(0.646477\pi\)
\(908\) 11.1520 0.370093
\(909\) −8.96292 −0.297281
\(910\) −4.32418 −0.143345
\(911\) 52.2270 1.73036 0.865178 0.501465i \(-0.167205\pi\)
0.865178 + 0.501465i \(0.167205\pi\)
\(912\) 21.7071 0.718795
\(913\) 10.5862 0.350353
\(914\) −60.2504 −1.99291
\(915\) −12.0029 −0.396804
\(916\) −35.9721 −1.18855
\(917\) 11.6124 0.383475
\(918\) 2.00485 0.0661700
\(919\) −23.3069 −0.768824 −0.384412 0.923162i \(-0.625596\pi\)
−0.384412 + 0.923162i \(0.625596\pi\)
\(920\) 0.654391 0.0215746
\(921\) 1.44141 0.0474960
\(922\) −29.0498 −0.956704
\(923\) −0.618049 −0.0203433
\(924\) −12.3946 −0.407754
\(925\) 6.82111 0.224277
\(926\) 8.03894 0.264176
\(927\) 0.659899 0.0216739
\(928\) 11.4812 0.376887
\(929\) 59.7918 1.96170 0.980852 0.194753i \(-0.0623905\pi\)
0.980852 + 0.194753i \(0.0623905\pi\)
\(930\) 37.5045 1.22982
\(931\) 27.9689 0.916645
\(932\) −29.8946 −0.979231
\(933\) −8.16060 −0.267166
\(934\) −46.9314 −1.53564
\(935\) −12.7750 −0.417788
\(936\) 0.0212885 0.000695836 0
\(937\) 3.43822 0.112322 0.0561609 0.998422i \(-0.482114\pi\)
0.0561609 + 0.998422i \(0.482114\pi\)
\(938\) −29.5123 −0.963610
\(939\) 8.94216 0.291816
\(940\) −19.7006 −0.642564
\(941\) 44.7685 1.45941 0.729705 0.683762i \(-0.239657\pi\)
0.729705 + 0.683762i \(0.239657\pi\)
\(942\) −2.00485 −0.0653216
\(943\) −27.2739 −0.888161
\(944\) −56.3492 −1.83401
\(945\) −3.94782 −0.128422
\(946\) 32.2234 1.04767
\(947\) −34.4910 −1.12081 −0.560403 0.828220i \(-0.689354\pi\)
−0.560403 + 0.828220i \(0.689354\pi\)
\(948\) −9.70224 −0.315114
\(949\) 7.22467 0.234523
\(950\) 35.3479 1.14684
\(951\) −24.7048 −0.801109
\(952\) −0.0536636 −0.00173925
\(953\) 18.2568 0.591395 0.295698 0.955282i \(-0.404448\pi\)
0.295698 + 0.955282i \(0.404448\pi\)
\(954\) 6.15132 0.199156
\(955\) 18.8448 0.609802
\(956\) 58.7864 1.90129
\(957\) 6.38100 0.206268
\(958\) 23.6436 0.763889
\(959\) −5.07797 −0.163976
\(960\) −23.3758 −0.754451
\(961\) 11.5880 0.373806
\(962\) 2.32245 0.0748788
\(963\) 6.63959 0.213958
\(964\) −27.6056 −0.889116
\(965\) −49.9792 −1.60889
\(966\) −16.1764 −0.520466
\(967\) −29.0458 −0.934049 −0.467024 0.884244i \(-0.654674\pi\)
−0.467024 + 0.884244i \(0.654674\pi\)
\(968\) −0.345288 −0.0110980
\(969\) 5.48056 0.176061
\(970\) 59.2727 1.90313
\(971\) −14.0115 −0.449651 −0.224825 0.974399i \(-0.572181\pi\)
−0.224825 + 0.974399i \(0.572181\pi\)
\(972\) 2.01944 0.0647734
\(973\) −18.4683 −0.592067
\(974\) 24.0309 0.770001
\(975\) −1.75760 −0.0562883
\(976\) 16.5846 0.530862
\(977\) −59.4231 −1.90111 −0.950556 0.310552i \(-0.899486\pi\)
−0.950556 + 0.310552i \(0.899486\pi\)
\(978\) −6.07367 −0.194215
\(979\) −53.3117 −1.70385
\(980\) −29.5419 −0.943682
\(981\) 3.59660 0.114831
\(982\) −37.8778 −1.20873
\(983\) −22.4552 −0.716210 −0.358105 0.933681i \(-0.616577\pi\)
−0.358105 + 0.933681i \(0.616577\pi\)
\(984\) −0.181397 −0.00578271
\(985\) 2.10256 0.0669931
\(986\) 2.87056 0.0914173
\(987\) 4.68697 0.149188
\(988\) 6.04671 0.192371
\(989\) 21.1292 0.671871
\(990\) −25.6121 −0.814005
\(991\) 27.4415 0.871710 0.435855 0.900017i \(-0.356446\pi\)
0.435855 + 0.900017i \(0.356446\pi\)
\(992\) −52.3293 −1.66146
\(993\) −24.1392 −0.766033
\(994\) 3.12349 0.0990712
\(995\) 52.5565 1.66615
\(996\) 4.79696 0.151998
\(997\) −56.5822 −1.79198 −0.895988 0.444079i \(-0.853531\pi\)
−0.895988 + 0.444079i \(0.853531\pi\)
\(998\) −33.3563 −1.05588
\(999\) 2.12031 0.0670836
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 \(a_p\))