Properties

Label 6047.2.a.a.1.14
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 1.14
Character \(\chi\) = 6047.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +O(q^{10})\) \(q-2.50842 q^{2} +0.797647 q^{3} +4.29216 q^{4} -3.82675 q^{5} -2.00083 q^{6} -2.73995 q^{7} -5.74970 q^{8} -2.36376 q^{9} +9.59909 q^{10} -5.60819 q^{11} +3.42363 q^{12} -3.88072 q^{13} +6.87293 q^{14} -3.05239 q^{15} +5.83833 q^{16} +5.63162 q^{17} +5.92930 q^{18} +2.10379 q^{19} -16.4250 q^{20} -2.18551 q^{21} +14.0677 q^{22} +7.90160 q^{23} -4.58623 q^{24} +9.64401 q^{25} +9.73447 q^{26} -4.27839 q^{27} -11.7603 q^{28} +0.651671 q^{29} +7.65668 q^{30} -5.09052 q^{31} -3.14556 q^{32} -4.47335 q^{33} -14.1265 q^{34} +10.4851 q^{35} -10.1456 q^{36} -6.71710 q^{37} -5.27719 q^{38} -3.09545 q^{39} +22.0027 q^{40} -4.35077 q^{41} +5.48217 q^{42} -1.70416 q^{43} -24.0713 q^{44} +9.04552 q^{45} -19.8205 q^{46} +4.66238 q^{47} +4.65692 q^{48} +0.507306 q^{49} -24.1912 q^{50} +4.49204 q^{51} -16.6567 q^{52} +11.1345 q^{53} +10.7320 q^{54} +21.4611 q^{55} +15.7539 q^{56} +1.67808 q^{57} -1.63466 q^{58} +9.47754 q^{59} -13.1014 q^{60} +2.91065 q^{61} +12.7692 q^{62} +6.47658 q^{63} -3.78626 q^{64} +14.8506 q^{65} +11.2210 q^{66} -1.65908 q^{67} +24.1718 q^{68} +6.30268 q^{69} -26.3010 q^{70} +0.503886 q^{71} +13.5909 q^{72} -9.84757 q^{73} +16.8493 q^{74} +7.69252 q^{75} +9.02981 q^{76} +15.3661 q^{77} +7.76467 q^{78} -3.32775 q^{79} -22.3418 q^{80} +3.67864 q^{81} +10.9135 q^{82} +1.28193 q^{83} -9.38056 q^{84} -21.5508 q^{85} +4.27474 q^{86} +0.519804 q^{87} +32.2454 q^{88} +5.89206 q^{89} -22.6899 q^{90} +10.6330 q^{91} +33.9149 q^{92} -4.06044 q^{93} -11.6952 q^{94} -8.05068 q^{95} -2.50905 q^{96} +6.57155 q^{97} -1.27254 q^{98} +13.2564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} + O(q^{10}) \) \( 217q - 20q^{2} - 27q^{3} + 184q^{4} - 19q^{5} - 17q^{6} - 48q^{7} - 57q^{8} + 152q^{9} - 46q^{10} - 32q^{11} - 72q^{12} - 80q^{13} - 22q^{14} - 43q^{15} + 122q^{16} - 61q^{17} - 88q^{18} - 43q^{19} - 41q^{20} - 61q^{21} - 93q^{22} - 60q^{23} - 41q^{24} + 26q^{25} - 9q^{26} - 93q^{27} - 126q^{28} - 47q^{29} - 36q^{30} - 100q^{31} - 114q^{32} - 133q^{33} - 75q^{34} - 37q^{35} + 75q^{36} - 264q^{37} - 35q^{38} - 47q^{39} - 118q^{40} - 72q^{41} - 64q^{42} - 107q^{43} - 59q^{44} - 69q^{45} - 111q^{46} - 54q^{47} - 135q^{48} + 33q^{49} - 42q^{50} - 26q^{51} - 173q^{52} - 103q^{53} - 28q^{54} - 78q^{55} - 44q^{56} - 205q^{57} - 189q^{58} - 38q^{59} - 105q^{60} - 108q^{61} - 14q^{62} - 116q^{63} + 39q^{64} - 146q^{65} + 5q^{66} - 206q^{67} - 62q^{68} - 55q^{69} - 125q^{70} - 78q^{71} - 225q^{72} - 326q^{73} + 3q^{74} - 95q^{75} - 84q^{76} - 79q^{77} - 86q^{78} - 117q^{79} - 39q^{80} + q^{81} - 96q^{82} - 23q^{83} - 57q^{84} - 224q^{85} - 7q^{86} - 45q^{87} - 250q^{88} - 104q^{89} - 36q^{90} - 96q^{91} - 137q^{92} - 155q^{93} - 48q^{94} - 38q^{95} - 33q^{96} - 447q^{97} - 46q^{98} - 94q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50842 −1.77372 −0.886860 0.462039i \(-0.847118\pi\)
−0.886860 + 0.462039i \(0.847118\pi\)
\(3\) 0.797647 0.460522 0.230261 0.973129i \(-0.426042\pi\)
0.230261 + 0.973129i \(0.426042\pi\)
\(4\) 4.29216 2.14608
\(5\) −3.82675 −1.71137 −0.855687 0.517493i \(-0.826865\pi\)
−0.855687 + 0.517493i \(0.826865\pi\)
\(6\) −2.00083 −0.816836
\(7\) −2.73995 −1.03560 −0.517801 0.855501i \(-0.673249\pi\)
−0.517801 + 0.855501i \(0.673249\pi\)
\(8\) −5.74970 −2.03283
\(9\) −2.36376 −0.787920
\(10\) 9.59909 3.03550
\(11\) −5.60819 −1.69093 −0.845466 0.534029i \(-0.820677\pi\)
−0.845466 + 0.534029i \(0.820677\pi\)
\(12\) 3.42363 0.988316
\(13\) −3.88072 −1.07632 −0.538159 0.842843i \(-0.680880\pi\)
−0.538159 + 0.842843i \(0.680880\pi\)
\(14\) 6.87293 1.83687
\(15\) −3.05239 −0.788125
\(16\) 5.83833 1.45958
\(17\) 5.63162 1.36587 0.682935 0.730480i \(-0.260703\pi\)
0.682935 + 0.730480i \(0.260703\pi\)
\(18\) 5.92930 1.39755
\(19\) 2.10379 0.482643 0.241321 0.970445i \(-0.422419\pi\)
0.241321 + 0.970445i \(0.422419\pi\)
\(20\) −16.4250 −3.67275
\(21\) −2.18551 −0.476917
\(22\) 14.0677 2.99924
\(23\) 7.90160 1.64760 0.823799 0.566883i \(-0.191851\pi\)
0.823799 + 0.566883i \(0.191851\pi\)
\(24\) −4.58623 −0.936160
\(25\) 9.64401 1.92880
\(26\) 9.73447 1.90909
\(27\) −4.27839 −0.823376
\(28\) −11.7603 −2.22249
\(29\) 0.651671 0.121012 0.0605062 0.998168i \(-0.480729\pi\)
0.0605062 + 0.998168i \(0.480729\pi\)
\(30\) 7.65668 1.39791
\(31\) −5.09052 −0.914285 −0.457142 0.889393i \(-0.651127\pi\)
−0.457142 + 0.889393i \(0.651127\pi\)
\(32\) −3.14556 −0.556063
\(33\) −4.47335 −0.778711
\(34\) −14.1265 −2.42267
\(35\) 10.4851 1.77230
\(36\) −10.1456 −1.69094
\(37\) −6.71710 −1.10428 −0.552142 0.833750i \(-0.686189\pi\)
−0.552142 + 0.833750i \(0.686189\pi\)
\(38\) −5.27719 −0.856073
\(39\) −3.09545 −0.495668
\(40\) 22.0027 3.47893
\(41\) −4.35077 −0.679475 −0.339738 0.940520i \(-0.610338\pi\)
−0.339738 + 0.940520i \(0.610338\pi\)
\(42\) 5.48217 0.845917
\(43\) −1.70416 −0.259882 −0.129941 0.991522i \(-0.541479\pi\)
−0.129941 + 0.991522i \(0.541479\pi\)
\(44\) −24.0713 −3.62888
\(45\) 9.04552 1.34843
\(46\) −19.8205 −2.92237
\(47\) 4.66238 0.680078 0.340039 0.940411i \(-0.389560\pi\)
0.340039 + 0.940411i \(0.389560\pi\)
\(48\) 4.65692 0.672169
\(49\) 0.507306 0.0724723
\(50\) −24.1912 −3.42115
\(51\) 4.49204 0.629012
\(52\) −16.6567 −2.30987
\(53\) 11.1345 1.52944 0.764721 0.644362i \(-0.222877\pi\)
0.764721 + 0.644362i \(0.222877\pi\)
\(54\) 10.7320 1.46044
\(55\) 21.4611 2.89382
\(56\) 15.7539 2.10520
\(57\) 1.67808 0.222267
\(58\) −1.63466 −0.214642
\(59\) 9.47754 1.23387 0.616935 0.787014i \(-0.288374\pi\)
0.616935 + 0.787014i \(0.288374\pi\)
\(60\) −13.1014 −1.69138
\(61\) 2.91065 0.372670 0.186335 0.982486i \(-0.440339\pi\)
0.186335 + 0.982486i \(0.440339\pi\)
\(62\) 12.7692 1.62169
\(63\) 6.47658 0.815972
\(64\) −3.78626 −0.473283
\(65\) 14.8506 1.84198
\(66\) 11.2210 1.38121
\(67\) −1.65908 −0.202689 −0.101344 0.994851i \(-0.532314\pi\)
−0.101344 + 0.994851i \(0.532314\pi\)
\(68\) 24.1718 2.93127
\(69\) 6.30268 0.758754
\(70\) −26.3010 −3.14357
\(71\) 0.503886 0.0598003 0.0299002 0.999553i \(-0.490481\pi\)
0.0299002 + 0.999553i \(0.490481\pi\)
\(72\) 13.5909 1.60170
\(73\) −9.84757 −1.15257 −0.576286 0.817248i \(-0.695498\pi\)
−0.576286 + 0.817248i \(0.695498\pi\)
\(74\) 16.8493 1.95869
\(75\) 7.69252 0.888255
\(76\) 9.02981 1.03579
\(77\) 15.3661 1.75113
\(78\) 7.76467 0.879176
\(79\) −3.32775 −0.374401 −0.187201 0.982322i \(-0.559941\pi\)
−0.187201 + 0.982322i \(0.559941\pi\)
\(80\) −22.3418 −2.49789
\(81\) 3.67864 0.408738
\(82\) 10.9135 1.20520
\(83\) 1.28193 0.140711 0.0703553 0.997522i \(-0.477587\pi\)
0.0703553 + 0.997522i \(0.477587\pi\)
\(84\) −9.38056 −1.02350
\(85\) −21.5508 −2.33751
\(86\) 4.27474 0.460957
\(87\) 0.519804 0.0557288
\(88\) 32.2454 3.43737
\(89\) 5.89206 0.624557 0.312279 0.949991i \(-0.398908\pi\)
0.312279 + 0.949991i \(0.398908\pi\)
\(90\) −22.6899 −2.39173
\(91\) 10.6330 1.11464
\(92\) 33.9149 3.53588
\(93\) −4.06044 −0.421048
\(94\) −11.6952 −1.20627
\(95\) −8.05068 −0.825983
\(96\) −2.50905 −0.256079
\(97\) 6.57155 0.667240 0.333620 0.942708i \(-0.391730\pi\)
0.333620 + 0.942708i \(0.391730\pi\)
\(98\) −1.27254 −0.128546
\(99\) 13.2564 1.33232
\(100\) 41.3937 4.13937
\(101\) 7.85113 0.781217 0.390608 0.920557i \(-0.372265\pi\)
0.390608 + 0.920557i \(0.372265\pi\)
\(102\) −11.2679 −1.11569
\(103\) −9.47514 −0.933613 −0.466807 0.884359i \(-0.654596\pi\)
−0.466807 + 0.884359i \(0.654596\pi\)
\(104\) 22.3130 2.18797
\(105\) 8.36340 0.816184
\(106\) −27.9300 −2.71280
\(107\) 7.97421 0.770896 0.385448 0.922730i \(-0.374047\pi\)
0.385448 + 0.922730i \(0.374047\pi\)
\(108\) −18.3635 −1.76703
\(109\) 14.8357 1.42100 0.710501 0.703696i \(-0.248468\pi\)
0.710501 + 0.703696i \(0.248468\pi\)
\(110\) −53.8335 −5.13282
\(111\) −5.35787 −0.508547
\(112\) −15.9967 −1.51155
\(113\) −2.59495 −0.244112 −0.122056 0.992523i \(-0.538949\pi\)
−0.122056 + 0.992523i \(0.538949\pi\)
\(114\) −4.20933 −0.394240
\(115\) −30.2374 −2.81966
\(116\) 2.79708 0.259702
\(117\) 9.17310 0.848053
\(118\) −23.7736 −2.18854
\(119\) −15.4303 −1.41450
\(120\) 17.5503 1.60212
\(121\) 20.4518 1.85925
\(122\) −7.30112 −0.661012
\(123\) −3.47037 −0.312913
\(124\) −21.8493 −1.96213
\(125\) −17.7715 −1.58953
\(126\) −16.2460 −1.44730
\(127\) 20.2609 1.79786 0.898932 0.438087i \(-0.144344\pi\)
0.898932 + 0.438087i \(0.144344\pi\)
\(128\) 15.7887 1.39553
\(129\) −1.35932 −0.119681
\(130\) −37.2514 −3.26716
\(131\) 2.83667 0.247841 0.123921 0.992292i \(-0.460453\pi\)
0.123921 + 0.992292i \(0.460453\pi\)
\(132\) −19.2004 −1.67118
\(133\) −5.76428 −0.499826
\(134\) 4.16166 0.359513
\(135\) 16.3723 1.40910
\(136\) −32.3801 −2.77657
\(137\) −0.181981 −0.0155477 −0.00777386 0.999970i \(-0.502475\pi\)
−0.00777386 + 0.999970i \(0.502475\pi\)
\(138\) −15.8098 −1.34582
\(139\) −2.61399 −0.221715 −0.110858 0.993836i \(-0.535360\pi\)
−0.110858 + 0.993836i \(0.535360\pi\)
\(140\) 45.0037 3.80351
\(141\) 3.71893 0.313191
\(142\) −1.26396 −0.106069
\(143\) 21.7638 1.81998
\(144\) −13.8004 −1.15003
\(145\) −2.49378 −0.207097
\(146\) 24.7018 2.04434
\(147\) 0.404651 0.0333751
\(148\) −28.8309 −2.36988
\(149\) 6.06087 0.496526 0.248263 0.968693i \(-0.420140\pi\)
0.248263 + 0.968693i \(0.420140\pi\)
\(150\) −19.2960 −1.57552
\(151\) −7.24202 −0.589348 −0.294674 0.955598i \(-0.595211\pi\)
−0.294674 + 0.955598i \(0.595211\pi\)
\(152\) −12.0962 −0.981129
\(153\) −13.3118 −1.07620
\(154\) −38.5447 −3.10602
\(155\) 19.4802 1.56468
\(156\) −13.2862 −1.06374
\(157\) 6.79982 0.542685 0.271342 0.962483i \(-0.412532\pi\)
0.271342 + 0.962483i \(0.412532\pi\)
\(158\) 8.34739 0.664083
\(159\) 8.88140 0.704341
\(160\) 12.0373 0.951631
\(161\) −21.6500 −1.70626
\(162\) −9.22757 −0.724986
\(163\) 8.07057 0.632136 0.316068 0.948737i \(-0.397637\pi\)
0.316068 + 0.948737i \(0.397637\pi\)
\(164\) −18.6742 −1.45821
\(165\) 17.1184 1.33267
\(166\) −3.21563 −0.249581
\(167\) −17.7922 −1.37680 −0.688401 0.725331i \(-0.741687\pi\)
−0.688401 + 0.725331i \(0.741687\pi\)
\(168\) 12.5660 0.969489
\(169\) 2.06001 0.158462
\(170\) 54.0584 4.14609
\(171\) −4.97286 −0.380284
\(172\) −7.31452 −0.557727
\(173\) 18.9038 1.43723 0.718614 0.695410i \(-0.244777\pi\)
0.718614 + 0.695410i \(0.244777\pi\)
\(174\) −1.30388 −0.0988472
\(175\) −26.4241 −1.99747
\(176\) −32.7424 −2.46805
\(177\) 7.55973 0.568224
\(178\) −14.7798 −1.10779
\(179\) −1.92075 −0.143564 −0.0717818 0.997420i \(-0.522869\pi\)
−0.0717818 + 0.997420i \(0.522869\pi\)
\(180\) 38.8248 2.89383
\(181\) −8.96377 −0.666272 −0.333136 0.942879i \(-0.608107\pi\)
−0.333136 + 0.942879i \(0.608107\pi\)
\(182\) −26.6719 −1.97706
\(183\) 2.32167 0.171623
\(184\) −45.4318 −3.34928
\(185\) 25.7047 1.88984
\(186\) 10.1853 0.746821
\(187\) −31.5832 −2.30959
\(188\) 20.0117 1.45950
\(189\) 11.7225 0.852690
\(190\) 20.1945 1.46506
\(191\) −14.1041 −1.02054 −0.510270 0.860014i \(-0.670455\pi\)
−0.510270 + 0.860014i \(0.670455\pi\)
\(192\) −3.02010 −0.217957
\(193\) −25.5029 −1.83574 −0.917868 0.396885i \(-0.870091\pi\)
−0.917868 + 0.396885i \(0.870091\pi\)
\(194\) −16.4842 −1.18350
\(195\) 11.8455 0.848273
\(196\) 2.17744 0.155531
\(197\) −15.9911 −1.13932 −0.569660 0.821880i \(-0.692925\pi\)
−0.569660 + 0.821880i \(0.692925\pi\)
\(198\) −33.2526 −2.36316
\(199\) 18.3626 1.30169 0.650843 0.759212i \(-0.274415\pi\)
0.650843 + 0.759212i \(0.274415\pi\)
\(200\) −55.4502 −3.92092
\(201\) −1.32336 −0.0933425
\(202\) −19.6939 −1.38566
\(203\) −1.78554 −0.125321
\(204\) 19.2806 1.34991
\(205\) 16.6493 1.16284
\(206\) 23.7676 1.65597
\(207\) −18.6775 −1.29817
\(208\) −22.6569 −1.57097
\(209\) −11.7985 −0.816117
\(210\) −20.9789 −1.44768
\(211\) −15.3314 −1.05546 −0.527729 0.849413i \(-0.676956\pi\)
−0.527729 + 0.849413i \(0.676956\pi\)
\(212\) 47.7911 3.28231
\(213\) 0.401923 0.0275393
\(214\) −20.0026 −1.36735
\(215\) 6.52138 0.444755
\(216\) 24.5994 1.67378
\(217\) 13.9478 0.946836
\(218\) −37.2141 −2.52046
\(219\) −7.85488 −0.530784
\(220\) 92.1147 6.21037
\(221\) −21.8548 −1.47011
\(222\) 13.4398 0.902019
\(223\) 0.206615 0.0138359 0.00691797 0.999976i \(-0.497798\pi\)
0.00691797 + 0.999976i \(0.497798\pi\)
\(224\) 8.61868 0.575860
\(225\) −22.7961 −1.51974
\(226\) 6.50922 0.432987
\(227\) 24.5613 1.63019 0.815096 0.579326i \(-0.196684\pi\)
0.815096 + 0.579326i \(0.196684\pi\)
\(228\) 7.20260 0.477004
\(229\) 3.46125 0.228726 0.114363 0.993439i \(-0.463517\pi\)
0.114363 + 0.993439i \(0.463517\pi\)
\(230\) 75.8481 5.00128
\(231\) 12.2567 0.806435
\(232\) −3.74691 −0.245997
\(233\) −11.6876 −0.765677 −0.382839 0.923815i \(-0.625053\pi\)
−0.382839 + 0.923815i \(0.625053\pi\)
\(234\) −23.0100 −1.50421
\(235\) −17.8418 −1.16387
\(236\) 40.6791 2.64799
\(237\) −2.65437 −0.172420
\(238\) 38.7058 2.50892
\(239\) 0.445399 0.0288104 0.0144052 0.999896i \(-0.495415\pi\)
0.0144052 + 0.999896i \(0.495415\pi\)
\(240\) −17.8209 −1.15033
\(241\) 17.8012 1.14668 0.573339 0.819318i \(-0.305648\pi\)
0.573339 + 0.819318i \(0.305648\pi\)
\(242\) −51.3016 −3.29779
\(243\) 15.7694 1.01161
\(244\) 12.4930 0.799780
\(245\) −1.94133 −0.124027
\(246\) 8.70515 0.555020
\(247\) −8.16423 −0.519478
\(248\) 29.2690 1.85858
\(249\) 1.02253 0.0648002
\(250\) 44.5783 2.81938
\(251\) −20.6732 −1.30488 −0.652440 0.757840i \(-0.726255\pi\)
−0.652440 + 0.757840i \(0.726255\pi\)
\(252\) 27.7985 1.75114
\(253\) −44.3137 −2.78598
\(254\) −50.8228 −3.18891
\(255\) −17.1899 −1.07648
\(256\) −32.0320 −2.00200
\(257\) −27.3898 −1.70853 −0.854266 0.519837i \(-0.825993\pi\)
−0.854266 + 0.519837i \(0.825993\pi\)
\(258\) 3.40973 0.212281
\(259\) 18.4045 1.14360
\(260\) 63.7410 3.95305
\(261\) −1.54039 −0.0953480
\(262\) −7.11555 −0.439600
\(263\) −7.33219 −0.452122 −0.226061 0.974113i \(-0.572585\pi\)
−0.226061 + 0.974113i \(0.572585\pi\)
\(264\) 25.7204 1.58298
\(265\) −42.6090 −2.61745
\(266\) 14.4592 0.886551
\(267\) 4.69978 0.287622
\(268\) −7.12104 −0.434986
\(269\) −11.7942 −0.719104 −0.359552 0.933125i \(-0.617070\pi\)
−0.359552 + 0.933125i \(0.617070\pi\)
\(270\) −41.0686 −2.49936
\(271\) 32.1286 1.95167 0.975837 0.218499i \(-0.0701160\pi\)
0.975837 + 0.218499i \(0.0701160\pi\)
\(272\) 32.8792 1.99360
\(273\) 8.48135 0.513315
\(274\) 0.456485 0.0275773
\(275\) −54.0855 −3.26148
\(276\) 27.0521 1.62835
\(277\) 13.5855 0.816275 0.408138 0.912920i \(-0.366178\pi\)
0.408138 + 0.912920i \(0.366178\pi\)
\(278\) 6.55697 0.393261
\(279\) 12.0328 0.720383
\(280\) −60.2861 −3.60278
\(281\) 5.27350 0.314590 0.157295 0.987552i \(-0.449723\pi\)
0.157295 + 0.987552i \(0.449723\pi\)
\(282\) −9.32864 −0.555512
\(283\) −23.4347 −1.39305 −0.696525 0.717532i \(-0.745272\pi\)
−0.696525 + 0.717532i \(0.745272\pi\)
\(284\) 2.16276 0.128336
\(285\) −6.42160 −0.380383
\(286\) −54.5928 −3.22814
\(287\) 11.9209 0.703666
\(288\) 7.43536 0.438133
\(289\) 14.7152 0.865598
\(290\) 6.25545 0.367333
\(291\) 5.24178 0.307278
\(292\) −42.2674 −2.47351
\(293\) −29.9421 −1.74924 −0.874618 0.484812i \(-0.838888\pi\)
−0.874618 + 0.484812i \(0.838888\pi\)
\(294\) −1.01503 −0.0591980
\(295\) −36.2682 −2.11161
\(296\) 38.6213 2.24482
\(297\) 23.9940 1.39227
\(298\) −15.2032 −0.880698
\(299\) −30.6639 −1.77334
\(300\) 33.0175 1.90627
\(301\) 4.66930 0.269134
\(302\) 18.1660 1.04534
\(303\) 6.26243 0.359767
\(304\) 12.2826 0.704457
\(305\) −11.1383 −0.637778
\(306\) 33.3916 1.90887
\(307\) 20.4527 1.16730 0.583648 0.812007i \(-0.301625\pi\)
0.583648 + 0.812007i \(0.301625\pi\)
\(308\) 65.9539 3.75807
\(309\) −7.55781 −0.429949
\(310\) −48.8644 −2.77531
\(311\) −4.10842 −0.232967 −0.116484 0.993193i \(-0.537162\pi\)
−0.116484 + 0.993193i \(0.537162\pi\)
\(312\) 17.7979 1.00761
\(313\) 8.95959 0.506426 0.253213 0.967411i \(-0.418513\pi\)
0.253213 + 0.967411i \(0.418513\pi\)
\(314\) −17.0568 −0.962571
\(315\) −24.7842 −1.39643
\(316\) −14.2832 −0.803495
\(317\) 19.4562 1.09277 0.546384 0.837535i \(-0.316004\pi\)
0.546384 + 0.837535i \(0.316004\pi\)
\(318\) −22.2783 −1.24930
\(319\) −3.65470 −0.204624
\(320\) 14.4891 0.809964
\(321\) 6.36060 0.355014
\(322\) 54.3071 3.02642
\(323\) 11.8478 0.659227
\(324\) 15.7893 0.877184
\(325\) −37.4257 −2.07601
\(326\) −20.2444 −1.12123
\(327\) 11.8336 0.654402
\(328\) 25.0156 1.38125
\(329\) −12.7747 −0.704290
\(330\) −42.9401 −2.36378
\(331\) −29.6941 −1.63214 −0.816069 0.577955i \(-0.803851\pi\)
−0.816069 + 0.577955i \(0.803851\pi\)
\(332\) 5.50227 0.301976
\(333\) 15.8776 0.870087
\(334\) 44.6303 2.44206
\(335\) 6.34888 0.346876
\(336\) −12.7597 −0.696099
\(337\) −30.8021 −1.67789 −0.838947 0.544213i \(-0.816829\pi\)
−0.838947 + 0.544213i \(0.816829\pi\)
\(338\) −5.16736 −0.281067
\(339\) −2.06985 −0.112419
\(340\) −92.4995 −5.01649
\(341\) 28.5486 1.54599
\(342\) 12.4740 0.674517
\(343\) 17.7896 0.960550
\(344\) 9.79839 0.528294
\(345\) −24.1188 −1.29851
\(346\) −47.4186 −2.54924
\(347\) 23.9740 1.28699 0.643496 0.765450i \(-0.277483\pi\)
0.643496 + 0.765450i \(0.277483\pi\)
\(348\) 2.23108 0.119598
\(349\) 21.1679 1.13309 0.566546 0.824030i \(-0.308279\pi\)
0.566546 + 0.824030i \(0.308279\pi\)
\(350\) 66.2826 3.54296
\(351\) 16.6032 0.886215
\(352\) 17.6409 0.940264
\(353\) −37.4900 −1.99539 −0.997695 0.0678605i \(-0.978383\pi\)
−0.997695 + 0.0678605i \(0.978383\pi\)
\(354\) −18.9630 −1.00787
\(355\) −1.92825 −0.102341
\(356\) 25.2897 1.34035
\(357\) −12.3080 −0.651406
\(358\) 4.81805 0.254642
\(359\) 1.48284 0.0782615 0.0391308 0.999234i \(-0.487541\pi\)
0.0391308 + 0.999234i \(0.487541\pi\)
\(360\) −52.0090 −2.74111
\(361\) −14.5741 −0.767056
\(362\) 22.4849 1.18178
\(363\) 16.3133 0.856226
\(364\) 45.6384 2.39210
\(365\) 37.6842 1.97248
\(366\) −5.82371 −0.304410
\(367\) −8.13675 −0.424735 −0.212367 0.977190i \(-0.568117\pi\)
−0.212367 + 0.977190i \(0.568117\pi\)
\(368\) 46.1321 2.40480
\(369\) 10.2842 0.535372
\(370\) −64.4780 −3.35205
\(371\) −30.5079 −1.58389
\(372\) −17.4281 −0.903603
\(373\) 14.2159 0.736071 0.368036 0.929812i \(-0.380030\pi\)
0.368036 + 0.929812i \(0.380030\pi\)
\(374\) 79.2239 4.09657
\(375\) −14.1754 −0.732013
\(376\) −26.8073 −1.38248
\(377\) −2.52896 −0.130248
\(378\) −29.4050 −1.51243
\(379\) 18.3273 0.941411 0.470706 0.882290i \(-0.343999\pi\)
0.470706 + 0.882290i \(0.343999\pi\)
\(380\) −34.5548 −1.77263
\(381\) 16.1610 0.827956
\(382\) 35.3791 1.81015
\(383\) 6.48635 0.331437 0.165719 0.986173i \(-0.447006\pi\)
0.165719 + 0.986173i \(0.447006\pi\)
\(384\) 12.5938 0.642673
\(385\) −58.8024 −2.99685
\(386\) 63.9719 3.25608
\(387\) 4.02822 0.204766
\(388\) 28.2062 1.43195
\(389\) 0.363153 0.0184126 0.00920630 0.999958i \(-0.497070\pi\)
0.00920630 + 0.999958i \(0.497070\pi\)
\(390\) −29.7135 −1.50460
\(391\) 44.4988 2.25040
\(392\) −2.91686 −0.147324
\(393\) 2.26266 0.114136
\(394\) 40.1124 2.02084
\(395\) 12.7345 0.640741
\(396\) 56.8987 2.85927
\(397\) −6.43917 −0.323173 −0.161586 0.986859i \(-0.551661\pi\)
−0.161586 + 0.986859i \(0.551661\pi\)
\(398\) −46.0610 −2.30883
\(399\) −4.59786 −0.230181
\(400\) 56.3049 2.81524
\(401\) −12.7008 −0.634246 −0.317123 0.948384i \(-0.602717\pi\)
−0.317123 + 0.948384i \(0.602717\pi\)
\(402\) 3.31954 0.165563
\(403\) 19.7549 0.984062
\(404\) 33.6983 1.67655
\(405\) −14.0772 −0.699503
\(406\) 4.47889 0.222284
\(407\) 37.6708 1.86727
\(408\) −25.8279 −1.27867
\(409\) −34.9491 −1.72812 −0.864062 0.503385i \(-0.832088\pi\)
−0.864062 + 0.503385i \(0.832088\pi\)
\(410\) −41.7634 −2.06255
\(411\) −0.145157 −0.00716006
\(412\) −40.6688 −2.00361
\(413\) −25.9680 −1.27780
\(414\) 46.8509 2.30260
\(415\) −4.90564 −0.240808
\(416\) 12.2071 0.598501
\(417\) −2.08504 −0.102105
\(418\) 29.5955 1.44756
\(419\) −13.0082 −0.635495 −0.317747 0.948175i \(-0.602926\pi\)
−0.317747 + 0.948175i \(0.602926\pi\)
\(420\) 35.8970 1.75160
\(421\) 27.2192 1.32658 0.663290 0.748362i \(-0.269159\pi\)
0.663290 + 0.748362i \(0.269159\pi\)
\(422\) 38.4576 1.87209
\(423\) −11.0207 −0.535847
\(424\) −64.0201 −3.10909
\(425\) 54.3114 2.63449
\(426\) −1.00819 −0.0488470
\(427\) −7.97502 −0.385938
\(428\) 34.2266 1.65440
\(429\) 17.3598 0.838141
\(430\) −16.3584 −0.788870
\(431\) −15.6792 −0.755240 −0.377620 0.925961i \(-0.623258\pi\)
−0.377620 + 0.925961i \(0.623258\pi\)
\(432\) −24.9786 −1.20178
\(433\) −1.19642 −0.0574962 −0.0287481 0.999587i \(-0.509152\pi\)
−0.0287481 + 0.999587i \(0.509152\pi\)
\(434\) −34.9868 −1.67942
\(435\) −1.98916 −0.0953728
\(436\) 63.6772 3.04959
\(437\) 16.6233 0.795201
\(438\) 19.7033 0.941461
\(439\) 12.3969 0.591670 0.295835 0.955239i \(-0.404402\pi\)
0.295835 + 0.955239i \(0.404402\pi\)
\(440\) −123.395 −5.88263
\(441\) −1.19915 −0.0571024
\(442\) 54.8209 2.60756
\(443\) −9.10072 −0.432388 −0.216194 0.976350i \(-0.569364\pi\)
−0.216194 + 0.976350i \(0.569364\pi\)
\(444\) −22.9968 −1.09138
\(445\) −22.5474 −1.06885
\(446\) −0.518276 −0.0245411
\(447\) 4.83443 0.228661
\(448\) 10.3742 0.490133
\(449\) 28.0838 1.32535 0.662677 0.748905i \(-0.269420\pi\)
0.662677 + 0.748905i \(0.269420\pi\)
\(450\) 57.1822 2.69560
\(451\) 24.3999 1.14895
\(452\) −11.1379 −0.523885
\(453\) −5.77658 −0.271407
\(454\) −61.6101 −2.89150
\(455\) −40.6897 −1.90756
\(456\) −9.64847 −0.451831
\(457\) −22.9255 −1.07241 −0.536205 0.844088i \(-0.680143\pi\)
−0.536205 + 0.844088i \(0.680143\pi\)
\(458\) −8.68225 −0.405695
\(459\) −24.0942 −1.12462
\(460\) −129.784 −6.05121
\(461\) 29.7326 1.38478 0.692392 0.721522i \(-0.256557\pi\)
0.692392 + 0.721522i \(0.256557\pi\)
\(462\) −30.7451 −1.43039
\(463\) 22.2063 1.03201 0.516006 0.856585i \(-0.327418\pi\)
0.516006 + 0.856585i \(0.327418\pi\)
\(464\) 3.80467 0.176627
\(465\) 15.5383 0.720571
\(466\) 29.3173 1.35810
\(467\) −15.3562 −0.710601 −0.355301 0.934752i \(-0.615622\pi\)
−0.355301 + 0.934752i \(0.615622\pi\)
\(468\) 39.3724 1.81999
\(469\) 4.54579 0.209905
\(470\) 44.7546 2.06438
\(471\) 5.42385 0.249918
\(472\) −54.4930 −2.50824
\(473\) 9.55724 0.439442
\(474\) 6.65827 0.305824
\(475\) 20.2890 0.930923
\(476\) −66.2295 −3.03563
\(477\) −26.3193 −1.20508
\(478\) −1.11725 −0.0511016
\(479\) −11.9476 −0.545902 −0.272951 0.962028i \(-0.588000\pi\)
−0.272951 + 0.962028i \(0.588000\pi\)
\(480\) 9.60150 0.438247
\(481\) 26.0672 1.18856
\(482\) −44.6530 −2.03389
\(483\) −17.2690 −0.785767
\(484\) 87.7824 3.99011
\(485\) −25.1477 −1.14190
\(486\) −39.5563 −1.79431
\(487\) −27.2350 −1.23414 −0.617068 0.786910i \(-0.711680\pi\)
−0.617068 + 0.786910i \(0.711680\pi\)
\(488\) −16.7353 −0.757574
\(489\) 6.43746 0.291112
\(490\) 4.86968 0.219990
\(491\) 10.5833 0.477620 0.238810 0.971066i \(-0.423243\pi\)
0.238810 + 0.971066i \(0.423243\pi\)
\(492\) −14.8954 −0.671537
\(493\) 3.66997 0.165287
\(494\) 20.4793 0.921407
\(495\) −50.7290 −2.28010
\(496\) −29.7201 −1.33447
\(497\) −1.38062 −0.0619293
\(498\) −2.56493 −0.114937
\(499\) 16.8036 0.752233 0.376117 0.926572i \(-0.377259\pi\)
0.376117 + 0.926572i \(0.377259\pi\)
\(500\) −76.2781 −3.41126
\(501\) −14.1919 −0.634047
\(502\) 51.8570 2.31449
\(503\) −6.51389 −0.290440 −0.145220 0.989399i \(-0.546389\pi\)
−0.145220 + 0.989399i \(0.546389\pi\)
\(504\) −37.2384 −1.65873
\(505\) −30.0443 −1.33695
\(506\) 111.157 4.94154
\(507\) 1.64316 0.0729752
\(508\) 86.9631 3.85836
\(509\) 26.7959 1.18771 0.593854 0.804573i \(-0.297606\pi\)
0.593854 + 0.804573i \(0.297606\pi\)
\(510\) 43.1195 1.90937
\(511\) 26.9818 1.19361
\(512\) 48.7724 2.15546
\(513\) −9.00083 −0.397396
\(514\) 68.7052 3.03046
\(515\) 36.2590 1.59776
\(516\) −5.83440 −0.256845
\(517\) −26.1475 −1.14997
\(518\) −46.1662 −2.02842
\(519\) 15.0785 0.661874
\(520\) −85.3862 −3.74443
\(521\) 15.0458 0.659169 0.329584 0.944126i \(-0.393091\pi\)
0.329584 + 0.944126i \(0.393091\pi\)
\(522\) 3.86395 0.169121
\(523\) −25.8335 −1.12962 −0.564809 0.825221i \(-0.691050\pi\)
−0.564809 + 0.825221i \(0.691050\pi\)
\(524\) 12.1754 0.531887
\(525\) −21.0771 −0.919879
\(526\) 18.3922 0.801938
\(527\) −28.6679 −1.24879
\(528\) −26.1169 −1.13659
\(529\) 39.4352 1.71458
\(530\) 106.881 4.64262
\(531\) −22.4026 −0.972191
\(532\) −24.7412 −1.07267
\(533\) 16.8841 0.731332
\(534\) −11.7890 −0.510161
\(535\) −30.5153 −1.31929
\(536\) 9.53921 0.412031
\(537\) −1.53208 −0.0661142
\(538\) 29.5847 1.27549
\(539\) −2.84507 −0.122546
\(540\) 70.2726 3.02405
\(541\) 35.1762 1.51234 0.756171 0.654375i \(-0.227068\pi\)
0.756171 + 0.654375i \(0.227068\pi\)
\(542\) −80.5920 −3.46172
\(543\) −7.14992 −0.306833
\(544\) −17.7146 −0.759509
\(545\) −56.7725 −2.43187
\(546\) −21.2748 −0.910477
\(547\) 28.7830 1.23067 0.615335 0.788266i \(-0.289021\pi\)
0.615335 + 0.788266i \(0.289021\pi\)
\(548\) −0.781093 −0.0333667
\(549\) −6.88007 −0.293634
\(550\) 135.669 5.78494
\(551\) 1.37098 0.0584057
\(552\) −36.2385 −1.54241
\(553\) 9.11786 0.387731
\(554\) −34.0782 −1.44784
\(555\) 20.5032 0.870314
\(556\) −11.2197 −0.475819
\(557\) 0.761025 0.0322456 0.0161228 0.999870i \(-0.494868\pi\)
0.0161228 + 0.999870i \(0.494868\pi\)
\(558\) −30.1832 −1.27776
\(559\) 6.61336 0.279715
\(560\) 61.2154 2.58682
\(561\) −25.1922 −1.06362
\(562\) −13.2281 −0.557995
\(563\) −15.7133 −0.662237 −0.331119 0.943589i \(-0.607426\pi\)
−0.331119 + 0.943589i \(0.607426\pi\)
\(564\) 15.9623 0.672132
\(565\) 9.93022 0.417768
\(566\) 58.7841 2.47088
\(567\) −10.0793 −0.423290
\(568\) −2.89720 −0.121564
\(569\) −42.9261 −1.79956 −0.899778 0.436348i \(-0.856272\pi\)
−0.899778 + 0.436348i \(0.856272\pi\)
\(570\) 16.1081 0.674692
\(571\) −2.59736 −0.108696 −0.0543480 0.998522i \(-0.517308\pi\)
−0.0543480 + 0.998522i \(0.517308\pi\)
\(572\) 93.4139 3.90583
\(573\) −11.2501 −0.469981
\(574\) −29.9025 −1.24811
\(575\) 76.2031 3.17789
\(576\) 8.94981 0.372909
\(577\) 28.5632 1.18910 0.594550 0.804059i \(-0.297330\pi\)
0.594550 + 0.804059i \(0.297330\pi\)
\(578\) −36.9118 −1.53533
\(579\) −20.3423 −0.845396
\(580\) −10.7037 −0.444448
\(581\) −3.51243 −0.145720
\(582\) −13.1486 −0.545026
\(583\) −62.4444 −2.58618
\(584\) 56.6206 2.34298
\(585\) −35.1031 −1.45134
\(586\) 75.1073 3.10265
\(587\) 23.9417 0.988178 0.494089 0.869411i \(-0.335502\pi\)
0.494089 + 0.869411i \(0.335502\pi\)
\(588\) 1.73683 0.0716255
\(589\) −10.7094 −0.441273
\(590\) 90.9757 3.74541
\(591\) −12.7553 −0.524682
\(592\) −39.2166 −1.61179
\(593\) 17.1447 0.704048 0.352024 0.935991i \(-0.385494\pi\)
0.352024 + 0.935991i \(0.385494\pi\)
\(594\) −60.1870 −2.46950
\(595\) 59.0481 2.42073
\(596\) 26.0142 1.06558
\(597\) 14.6468 0.599455
\(598\) 76.9179 3.14541
\(599\) −34.0951 −1.39309 −0.696543 0.717515i \(-0.745280\pi\)
−0.696543 + 0.717515i \(0.745280\pi\)
\(600\) −44.2296 −1.80567
\(601\) −42.9126 −1.75044 −0.875221 0.483723i \(-0.839284\pi\)
−0.875221 + 0.483723i \(0.839284\pi\)
\(602\) −11.7126 −0.477368
\(603\) 3.92166 0.159703
\(604\) −31.0839 −1.26479
\(605\) −78.2639 −3.18188
\(606\) −15.7088 −0.638126
\(607\) −38.2094 −1.55087 −0.775435 0.631427i \(-0.782469\pi\)
−0.775435 + 0.631427i \(0.782469\pi\)
\(608\) −6.61761 −0.268380
\(609\) −1.42423 −0.0577129
\(610\) 27.9396 1.13124
\(611\) −18.0934 −0.731981
\(612\) −57.1364 −2.30960
\(613\) −32.0675 −1.29519 −0.647596 0.761984i \(-0.724226\pi\)
−0.647596 + 0.761984i \(0.724226\pi\)
\(614\) −51.3038 −2.07045
\(615\) 13.2803 0.535511
\(616\) −88.3507 −3.55975
\(617\) −20.5144 −0.825878 −0.412939 0.910759i \(-0.635498\pi\)
−0.412939 + 0.910759i \(0.635498\pi\)
\(618\) 18.9582 0.762609
\(619\) −1.64660 −0.0661826 −0.0330913 0.999452i \(-0.510535\pi\)
−0.0330913 + 0.999452i \(0.510535\pi\)
\(620\) 83.6120 3.35794
\(621\) −33.8061 −1.35659
\(622\) 10.3056 0.413218
\(623\) −16.1439 −0.646793
\(624\) −18.0722 −0.723468
\(625\) 19.7869 0.791477
\(626\) −22.4744 −0.898257
\(627\) −9.41100 −0.375839
\(628\) 29.1859 1.16465
\(629\) −37.8282 −1.50831
\(630\) 62.1692 2.47688
\(631\) 7.19763 0.286533 0.143267 0.989684i \(-0.454239\pi\)
0.143267 + 0.989684i \(0.454239\pi\)
\(632\) 19.1336 0.761092
\(633\) −12.2290 −0.486061
\(634\) −48.8042 −1.93826
\(635\) −77.5334 −3.07682
\(636\) 38.1204 1.51157
\(637\) −1.96871 −0.0780033
\(638\) 9.16751 0.362945
\(639\) −1.19107 −0.0471179
\(640\) −60.4192 −2.38828
\(641\) 32.4144 1.28029 0.640146 0.768253i \(-0.278874\pi\)
0.640146 + 0.768253i \(0.278874\pi\)
\(642\) −15.9550 −0.629695
\(643\) −0.706102 −0.0278460 −0.0139230 0.999903i \(-0.504432\pi\)
−0.0139230 + 0.999903i \(0.504432\pi\)
\(644\) −92.9251 −3.66176
\(645\) 5.20176 0.204819
\(646\) −29.7191 −1.16928
\(647\) −2.10828 −0.0828852 −0.0414426 0.999141i \(-0.513195\pi\)
−0.0414426 + 0.999141i \(0.513195\pi\)
\(648\) −21.1511 −0.830893
\(649\) −53.1518 −2.08639
\(650\) 93.8794 3.68225
\(651\) 11.1254 0.436038
\(652\) 34.6402 1.35661
\(653\) −21.0453 −0.823564 −0.411782 0.911282i \(-0.635094\pi\)
−0.411782 + 0.911282i \(0.635094\pi\)
\(654\) −29.6837 −1.16073
\(655\) −10.8552 −0.424149
\(656\) −25.4012 −0.991750
\(657\) 23.2773 0.908134
\(658\) 32.0442 1.24921
\(659\) 2.44396 0.0952031 0.0476015 0.998866i \(-0.484842\pi\)
0.0476015 + 0.998866i \(0.484842\pi\)
\(660\) 73.4750 2.86001
\(661\) 33.5690 1.30568 0.652841 0.757495i \(-0.273577\pi\)
0.652841 + 0.757495i \(0.273577\pi\)
\(662\) 74.4853 2.89495
\(663\) −17.4324 −0.677017
\(664\) −7.37073 −0.286040
\(665\) 22.0584 0.855390
\(666\) −39.8277 −1.54329
\(667\) 5.14925 0.199380
\(668\) −76.3670 −2.95473
\(669\) 0.164805 0.00637175
\(670\) −15.9256 −0.615261
\(671\) −16.3235 −0.630160
\(672\) 6.87466 0.265196
\(673\) −15.8190 −0.609777 −0.304888 0.952388i \(-0.598619\pi\)
−0.304888 + 0.952388i \(0.598619\pi\)
\(674\) 77.2644 2.97611
\(675\) −41.2608 −1.58813
\(676\) 8.84188 0.340072
\(677\) −26.5728 −1.02128 −0.510638 0.859796i \(-0.670591\pi\)
−0.510638 + 0.859796i \(0.670591\pi\)
\(678\) 5.19206 0.199400
\(679\) −18.0057 −0.690996
\(680\) 123.911 4.75176
\(681\) 19.5913 0.750739
\(682\) −71.6119 −2.74216
\(683\) 22.9405 0.877792 0.438896 0.898538i \(-0.355370\pi\)
0.438896 + 0.898538i \(0.355370\pi\)
\(684\) −21.3443 −0.816120
\(685\) 0.696397 0.0266080
\(686\) −44.6238 −1.70375
\(687\) 2.76085 0.105333
\(688\) −9.94943 −0.379318
\(689\) −43.2099 −1.64617
\(690\) 60.5000 2.30320
\(691\) 27.9413 1.06294 0.531468 0.847078i \(-0.321641\pi\)
0.531468 + 0.847078i \(0.321641\pi\)
\(692\) 81.1380 3.08441
\(693\) −36.3219 −1.37975
\(694\) −60.1368 −2.28276
\(695\) 10.0031 0.379438
\(696\) −2.98871 −0.113287
\(697\) −24.5019 −0.928074
\(698\) −53.0979 −2.00979
\(699\) −9.32254 −0.352611
\(700\) −113.416 −4.28674
\(701\) 29.5810 1.11726 0.558629 0.829417i \(-0.311327\pi\)
0.558629 + 0.829417i \(0.311327\pi\)
\(702\) −41.6478 −1.57190
\(703\) −14.1314 −0.532975
\(704\) 21.2341 0.800289
\(705\) −14.2314 −0.535986
\(706\) 94.0405 3.53926
\(707\) −21.5117 −0.809030
\(708\) 32.4476 1.21945
\(709\) −2.12544 −0.0798226 −0.0399113 0.999203i \(-0.512708\pi\)
−0.0399113 + 0.999203i \(0.512708\pi\)
\(710\) 4.83685 0.181524
\(711\) 7.86600 0.294998
\(712\) −33.8776 −1.26962
\(713\) −40.2233 −1.50637
\(714\) 30.8735 1.15541
\(715\) −83.2847 −3.11467
\(716\) −8.24417 −0.308099
\(717\) 0.355271 0.0132678
\(718\) −3.71959 −0.138814
\(719\) −21.0245 −0.784082 −0.392041 0.919948i \(-0.628231\pi\)
−0.392041 + 0.919948i \(0.628231\pi\)
\(720\) 52.8107 1.96814
\(721\) 25.9614 0.966852
\(722\) 36.5578 1.36054
\(723\) 14.1991 0.528070
\(724\) −38.4740 −1.42987
\(725\) 6.28473 0.233409
\(726\) −40.9206 −1.51871
\(727\) −13.9034 −0.515647 −0.257823 0.966192i \(-0.583005\pi\)
−0.257823 + 0.966192i \(0.583005\pi\)
\(728\) −61.1364 −2.26587
\(729\) 1.54250 0.0571296
\(730\) −94.5277 −3.49863
\(731\) −9.59717 −0.354964
\(732\) 9.96497 0.368316
\(733\) −2.53149 −0.0935029 −0.0467514 0.998907i \(-0.514887\pi\)
−0.0467514 + 0.998907i \(0.514887\pi\)
\(734\) 20.4104 0.753361
\(735\) −1.54850 −0.0571172
\(736\) −24.8550 −0.916167
\(737\) 9.30443 0.342733
\(738\) −25.7970 −0.949600
\(739\) 25.3154 0.931243 0.465622 0.884984i \(-0.345831\pi\)
0.465622 + 0.884984i \(0.345831\pi\)
\(740\) 110.329 4.05576
\(741\) −6.51217 −0.239231
\(742\) 76.5267 2.80938
\(743\) 18.2816 0.670685 0.335343 0.942096i \(-0.391148\pi\)
0.335343 + 0.942096i \(0.391148\pi\)
\(744\) 23.3463 0.855917
\(745\) −23.1934 −0.849742
\(746\) −35.6594 −1.30558
\(747\) −3.03018 −0.110869
\(748\) −135.560 −4.95657
\(749\) −21.8489 −0.798341
\(750\) 35.5577 1.29838
\(751\) −40.0447 −1.46125 −0.730626 0.682778i \(-0.760772\pi\)
−0.730626 + 0.682778i \(0.760772\pi\)
\(752\) 27.2205 0.992629
\(753\) −16.4899 −0.600925
\(754\) 6.34368 0.231023
\(755\) 27.7134 1.00859
\(756\) 50.3151 1.82994
\(757\) −12.8028 −0.465325 −0.232663 0.972557i \(-0.574744\pi\)
−0.232663 + 0.972557i \(0.574744\pi\)
\(758\) −45.9726 −1.66980
\(759\) −35.3466 −1.28300
\(760\) 46.2890 1.67908
\(761\) 50.1377 1.81749 0.908745 0.417353i \(-0.137042\pi\)
0.908745 + 0.417353i \(0.137042\pi\)
\(762\) −40.5387 −1.46856
\(763\) −40.6490 −1.47159
\(764\) −60.5373 −2.19016
\(765\) 50.9409 1.84177
\(766\) −16.2705 −0.587876
\(767\) −36.7797 −1.32804
\(768\) −25.5502 −0.921965
\(769\) 31.0656 1.12025 0.560127 0.828406i \(-0.310752\pi\)
0.560127 + 0.828406i \(0.310752\pi\)
\(770\) 147.501 5.31556
\(771\) −21.8474 −0.786816
\(772\) −109.462 −3.93964
\(773\) −18.7560 −0.674605 −0.337303 0.941396i \(-0.609515\pi\)
−0.337303 + 0.941396i \(0.609515\pi\)
\(774\) −10.1045 −0.363197
\(775\) −49.0931 −1.76348
\(776\) −37.7845 −1.35638
\(777\) 14.6803 0.526652
\(778\) −0.910940 −0.0326588
\(779\) −9.15310 −0.327944
\(780\) 50.8428 1.82046
\(781\) −2.82589 −0.101118
\(782\) −111.622 −3.99158
\(783\) −2.78810 −0.0996386
\(784\) 2.96182 0.105779
\(785\) −26.0212 −0.928737
\(786\) −5.67570 −0.202445
\(787\) −42.8730 −1.52826 −0.764129 0.645064i \(-0.776831\pi\)
−0.764129 + 0.645064i \(0.776831\pi\)
\(788\) −68.6365 −2.44507
\(789\) −5.84850 −0.208212
\(790\) −31.9434 −1.13649
\(791\) 7.11002 0.252803
\(792\) −76.2204 −2.70837
\(793\) −11.2954 −0.401112
\(794\) 16.1521 0.573217
\(795\) −33.9869 −1.20539
\(796\) 78.8150 2.79352
\(797\) 51.5677 1.82662 0.913311 0.407263i \(-0.133517\pi\)
0.913311 + 0.407263i \(0.133517\pi\)
\(798\) 11.5333 0.408276
\(799\) 26.2568 0.928897
\(800\) −30.3359 −1.07253
\(801\) −13.9274 −0.492101
\(802\) 31.8588 1.12497
\(803\) 55.2270 1.94892
\(804\) −5.68007 −0.200321
\(805\) 82.8490 2.92004
\(806\) −49.5536 −1.74545
\(807\) −9.40759 −0.331163
\(808\) −45.1416 −1.58808
\(809\) −42.5983 −1.49768 −0.748838 0.662753i \(-0.769388\pi\)
−0.748838 + 0.662753i \(0.769388\pi\)
\(810\) 35.3116 1.24072
\(811\) 5.71588 0.200712 0.100356 0.994952i \(-0.468002\pi\)
0.100356 + 0.994952i \(0.468002\pi\)
\(812\) −7.66385 −0.268948
\(813\) 25.6273 0.898788
\(814\) −94.4940 −3.31201
\(815\) −30.8840 −1.08182
\(816\) 26.2260 0.918094
\(817\) −3.58519 −0.125430
\(818\) 87.6671 3.06521
\(819\) −25.1338 −0.878246
\(820\) 71.4614 2.49554
\(821\) −8.05202 −0.281017 −0.140509 0.990079i \(-0.544874\pi\)
−0.140509 + 0.990079i \(0.544874\pi\)
\(822\) 0.364114 0.0126999
\(823\) 4.53633 0.158126 0.0790632 0.996870i \(-0.474807\pi\)
0.0790632 + 0.996870i \(0.474807\pi\)
\(824\) 54.4792 1.89787
\(825\) −43.1411 −1.50198
\(826\) 65.1385 2.26646
\(827\) −16.9814 −0.590501 −0.295250 0.955420i \(-0.595403\pi\)
−0.295250 + 0.955420i \(0.595403\pi\)
\(828\) −80.1668 −2.78599
\(829\) 49.4435 1.71724 0.858622 0.512609i \(-0.171321\pi\)
0.858622 + 0.512609i \(0.171321\pi\)
\(830\) 12.3054 0.427127
\(831\) 10.8365 0.375912
\(832\) 14.6934 0.509403
\(833\) 2.85696 0.0989877
\(834\) 5.23015 0.181105
\(835\) 68.0863 2.35622
\(836\) −50.6409 −1.75145
\(837\) 21.7792 0.752800
\(838\) 32.6301 1.12719
\(839\) 17.1288 0.591353 0.295677 0.955288i \(-0.404455\pi\)
0.295677 + 0.955288i \(0.404455\pi\)
\(840\) −48.0870 −1.65916
\(841\) −28.5753 −0.985356
\(842\) −68.2770 −2.35298
\(843\) 4.20639 0.144876
\(844\) −65.8049 −2.26510
\(845\) −7.88313 −0.271188
\(846\) 27.6446 0.950442
\(847\) −56.0368 −1.92545
\(848\) 65.0069 2.23235
\(849\) −18.6926 −0.641530
\(850\) −136.236 −4.67285
\(851\) −53.0758 −1.81942
\(852\) 1.72512 0.0591016
\(853\) −24.0109 −0.822117 −0.411059 0.911609i \(-0.634841\pi\)
−0.411059 + 0.911609i \(0.634841\pi\)
\(854\) 20.0047 0.684546
\(855\) 19.0299 0.650808
\(856\) −45.8493 −1.56710
\(857\) 57.4068 1.96098 0.980489 0.196573i \(-0.0629811\pi\)
0.980489 + 0.196573i \(0.0629811\pi\)
\(858\) −43.5457 −1.48663
\(859\) 17.6436 0.601992 0.300996 0.953625i \(-0.402681\pi\)
0.300996 + 0.953625i \(0.402681\pi\)
\(860\) 27.9908 0.954479
\(861\) 9.50864 0.324053
\(862\) 39.3300 1.33958
\(863\) 36.3579 1.23764 0.618819 0.785534i \(-0.287612\pi\)
0.618819 + 0.785534i \(0.287612\pi\)
\(864\) 13.4579 0.457848
\(865\) −72.3400 −2.45963
\(866\) 3.00112 0.101982
\(867\) 11.7375 0.398627
\(868\) 59.8660 2.03199
\(869\) 18.6627 0.633087
\(870\) 4.98964 0.169165
\(871\) 6.43843 0.218158
\(872\) −85.3008 −2.88865
\(873\) −15.5336 −0.525732
\(874\) −41.6982 −1.41046
\(875\) 48.6929 1.64612
\(876\) −33.7144 −1.13910
\(877\) 9.19392 0.310456 0.155228 0.987879i \(-0.450389\pi\)
0.155228 + 0.987879i \(0.450389\pi\)
\(878\) −31.0965 −1.04946
\(879\) −23.8832 −0.805561
\(880\) 125.297 4.22377
\(881\) 27.3249 0.920600 0.460300 0.887763i \(-0.347742\pi\)
0.460300 + 0.887763i \(0.347742\pi\)
\(882\) 3.00797 0.101284
\(883\) 34.0764 1.14676 0.573380 0.819289i \(-0.305632\pi\)
0.573380 + 0.819289i \(0.305632\pi\)
\(884\) −93.8042 −3.15498
\(885\) −28.9292 −0.972444
\(886\) 22.8284 0.766936
\(887\) −6.80463 −0.228477 −0.114239 0.993453i \(-0.536443\pi\)
−0.114239 + 0.993453i \(0.536443\pi\)
\(888\) 30.8061 1.03379
\(889\) −55.5138 −1.86187
\(890\) 56.5584 1.89584
\(891\) −20.6305 −0.691148
\(892\) 0.886823 0.0296930
\(893\) 9.80867 0.328235
\(894\) −12.1268 −0.405580
\(895\) 7.35023 0.245691
\(896\) −43.2601 −1.44522
\(897\) −24.4590 −0.816661
\(898\) −70.4458 −2.35081
\(899\) −3.31735 −0.110640
\(900\) −97.8447 −3.26149
\(901\) 62.7053 2.08902
\(902\) −61.2052 −2.03791
\(903\) 3.72445 0.123942
\(904\) 14.9202 0.496238
\(905\) 34.3021 1.14024
\(906\) 14.4901 0.481400
\(907\) −45.5504 −1.51248 −0.756238 0.654297i \(-0.772965\pi\)
−0.756238 + 0.654297i \(0.772965\pi\)
\(908\) 105.421 3.49852
\(909\) −18.5582 −0.615536
\(910\) 102.067 3.38348
\(911\) 35.2174 1.16681 0.583403 0.812183i \(-0.301721\pi\)
0.583403 + 0.812183i \(0.301721\pi\)
\(912\) 9.79719 0.324417
\(913\) −7.18933 −0.237932
\(914\) 57.5067 1.90215
\(915\) −8.88444 −0.293711
\(916\) 14.8562 0.490863
\(917\) −7.77232 −0.256665
\(918\) 60.4384 1.99477
\(919\) −56.1119 −1.85096 −0.925481 0.378794i \(-0.876339\pi\)
−0.925481 + 0.378794i \(0.876339\pi\)
\(920\) 173.856 5.73187
\(921\) 16.3140 0.537565
\(922\) −74.5817 −2.45622
\(923\) −1.95544 −0.0643642
\(924\) 52.6079 1.73067
\(925\) −64.7798 −2.12995
\(926\) −55.7026 −1.83050
\(927\) 22.3970 0.735613
\(928\) −2.04987 −0.0672904
\(929\) −1.26998 −0.0416667 −0.0208334 0.999783i \(-0.506632\pi\)
−0.0208334 + 0.999783i \(0.506632\pi\)
\(930\) −38.9765 −1.27809
\(931\) 1.06727 0.0349782
\(932\) −50.1649 −1.64321
\(933\) −3.27707 −0.107286
\(934\) 38.5198 1.26041
\(935\) 120.861 3.95258
\(936\) −52.7425 −1.72394
\(937\) 26.7226 0.872988 0.436494 0.899707i \(-0.356220\pi\)
0.436494 + 0.899707i \(0.356220\pi\)
\(938\) −11.4027 −0.372313
\(939\) 7.14658 0.233220
\(940\) −76.5797 −2.49775
\(941\) 28.1404 0.917351 0.458675 0.888604i \(-0.348324\pi\)
0.458675 + 0.888604i \(0.348324\pi\)
\(942\) −13.6053 −0.443284
\(943\) −34.3780 −1.11950
\(944\) 55.3330 1.80093
\(945\) −44.8592 −1.45927
\(946\) −23.9735 −0.779447
\(947\) 16.9564 0.551008 0.275504 0.961300i \(-0.411155\pi\)
0.275504 + 0.961300i \(0.411155\pi\)
\(948\) −11.3930 −0.370027
\(949\) 38.2157 1.24053
\(950\) −50.8933 −1.65120
\(951\) 15.5192 0.503243
\(952\) 88.7198 2.87543
\(953\) 52.9495 1.71520 0.857601 0.514316i \(-0.171954\pi\)
0.857601 + 0.514316i \(0.171954\pi\)
\(954\) 66.0198 2.13747
\(955\) 53.9730 1.74653
\(956\) 1.91172 0.0618295
\(957\) −2.91516 −0.0942336
\(958\) 29.9697 0.968276
\(959\) 0.498619 0.0161013
\(960\) 11.5572 0.373006
\(961\) −5.08657 −0.164083
\(962\) −65.3874 −2.10818
\(963\) −18.8491 −0.607404
\(964\) 76.4058 2.46087
\(965\) 97.5931 3.14163
\(966\) 43.3179 1.39373
\(967\) −24.0207 −0.772453 −0.386226 0.922404i \(-0.626222\pi\)
−0.386226 + 0.922404i \(0.626222\pi\)
\(968\) −117.592 −3.77954
\(969\) 9.45032 0.303588
\(970\) 63.0809 2.02541
\(971\) 52.9204 1.69830 0.849148 0.528154i \(-0.177116\pi\)
0.849148 + 0.528154i \(0.177116\pi\)
\(972\) 67.6849 2.17099
\(973\) 7.16218 0.229609
\(974\) 68.3168 2.18901
\(975\) −29.8525 −0.956046
\(976\) 16.9933 0.543943
\(977\) 6.71563 0.214852 0.107426 0.994213i \(-0.465739\pi\)
0.107426 + 0.994213i \(0.465739\pi\)
\(978\) −16.1478 −0.516351
\(979\) −33.0438 −1.05608
\(980\) −8.33252 −0.266172
\(981\) −35.0680 −1.11964
\(982\) −26.5475 −0.847163
\(983\) −48.6912 −1.55301 −0.776503 0.630113i \(-0.783009\pi\)
−0.776503 + 0.630113i \(0.783009\pi\)
\(984\) 19.9536 0.636098
\(985\) 61.1940 1.94980
\(986\) −9.20581 −0.293173
\(987\) −10.1897 −0.324341
\(988\) −35.0422 −1.11484
\(989\) −13.4656 −0.428180
\(990\) 127.249 4.04425
\(991\) 5.87714 0.186693 0.0933467 0.995634i \(-0.470244\pi\)
0.0933467 + 0.995634i \(0.470244\pi\)
\(992\) 16.0126 0.508400
\(993\) −23.6854 −0.751634
\(994\) 3.46318 0.109845
\(995\) −70.2689 −2.22767
\(996\) 4.38886 0.139067
\(997\) 5.41215 0.171404 0.0857022 0.996321i \(-0.472687\pi\)
0.0857022 + 0.996321i \(0.472687\pi\)
\(998\) −42.1505 −1.33425
\(999\) 28.7383 0.909241
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 \(a_p\))