Properties

Label 6027.2.a.bo.1.11
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.0650408 q^{2} +1.00000 q^{3} -1.99577 q^{4} -2.65358 q^{5} -0.0650408 q^{6} +0.259888 q^{8} +1.00000 q^{9} +0.172591 q^{10} -5.47071 q^{11} -1.99577 q^{12} -3.40299 q^{13} -2.65358 q^{15} +3.97464 q^{16} -6.28311 q^{17} -0.0650408 q^{18} -4.25848 q^{19} +5.29593 q^{20} +0.355819 q^{22} -1.06746 q^{23} +0.259888 q^{24} +2.04147 q^{25} +0.221333 q^{26} +1.00000 q^{27} -6.10576 q^{29} +0.172591 q^{30} -10.4918 q^{31} -0.778289 q^{32} -5.47071 q^{33} +0.408658 q^{34} -1.99577 q^{36} +3.83754 q^{37} +0.276975 q^{38} -3.40299 q^{39} -0.689632 q^{40} -1.00000 q^{41} -4.68577 q^{43} +10.9183 q^{44} -2.65358 q^{45} +0.0694285 q^{46} +11.1163 q^{47} +3.97464 q^{48} -0.132779 q^{50} -6.28311 q^{51} +6.79158 q^{52} +8.14739 q^{53} -0.0650408 q^{54} +14.5169 q^{55} -4.25848 q^{57} +0.397124 q^{58} +14.0580 q^{59} +5.29593 q^{60} -14.1386 q^{61} +0.682395 q^{62} -7.89865 q^{64} +9.03008 q^{65} +0.355819 q^{66} -6.51962 q^{67} +12.5396 q^{68} -1.06746 q^{69} -10.1718 q^{71} +0.259888 q^{72} -4.82870 q^{73} -0.249597 q^{74} +2.04147 q^{75} +8.49894 q^{76} +0.221333 q^{78} +9.32274 q^{79} -10.5470 q^{80} +1.00000 q^{81} +0.0650408 q^{82} -5.03523 q^{83} +16.6727 q^{85} +0.304766 q^{86} -6.10576 q^{87} -1.42177 q^{88} +8.62706 q^{89} +0.172591 q^{90} +2.13041 q^{92} -10.4918 q^{93} -0.723014 q^{94} +11.3002 q^{95} -0.778289 q^{96} -16.5259 q^{97} -5.47071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0650408 −0.0459908 −0.0229954 0.999736i \(-0.507320\pi\)
−0.0229954 + 0.999736i \(0.507320\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.99577 −0.997885
\(5\) −2.65358 −1.18672 −0.593358 0.804939i \(-0.702198\pi\)
−0.593358 + 0.804939i \(0.702198\pi\)
\(6\) −0.0650408 −0.0265528
\(7\) 0 0
\(8\) 0.259888 0.0918843
\(9\) 1.00000 0.333333
\(10\) 0.172591 0.0545779
\(11\) −5.47071 −1.64948 −0.824740 0.565512i \(-0.808678\pi\)
−0.824740 + 0.565512i \(0.808678\pi\)
\(12\) −1.99577 −0.576129
\(13\) −3.40299 −0.943819 −0.471909 0.881647i \(-0.656435\pi\)
−0.471909 + 0.881647i \(0.656435\pi\)
\(14\) 0 0
\(15\) −2.65358 −0.685150
\(16\) 3.97464 0.993659
\(17\) −6.28311 −1.52388 −0.761939 0.647649i \(-0.775752\pi\)
−0.761939 + 0.647649i \(0.775752\pi\)
\(18\) −0.0650408 −0.0153303
\(19\) −4.25848 −0.976962 −0.488481 0.872574i \(-0.662449\pi\)
−0.488481 + 0.872574i \(0.662449\pi\)
\(20\) 5.29593 1.18421
\(21\) 0 0
\(22\) 0.355819 0.0758608
\(23\) −1.06746 −0.222581 −0.111291 0.993788i \(-0.535498\pi\)
−0.111291 + 0.993788i \(0.535498\pi\)
\(24\) 0.259888 0.0530494
\(25\) 2.04147 0.408293
\(26\) 0.221333 0.0434069
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.10576 −1.13381 −0.566906 0.823783i \(-0.691860\pi\)
−0.566906 + 0.823783i \(0.691860\pi\)
\(30\) 0.172591 0.0315106
\(31\) −10.4918 −1.88438 −0.942192 0.335072i \(-0.891239\pi\)
−0.942192 + 0.335072i \(0.891239\pi\)
\(32\) −0.778289 −0.137583
\(33\) −5.47071 −0.952328
\(34\) 0.408658 0.0700843
\(35\) 0 0
\(36\) −1.99577 −0.332628
\(37\) 3.83754 0.630888 0.315444 0.948944i \(-0.397847\pi\)
0.315444 + 0.948944i \(0.397847\pi\)
\(38\) 0.276975 0.0449312
\(39\) −3.40299 −0.544914
\(40\) −0.689632 −0.109040
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.68577 −0.714573 −0.357286 0.933995i \(-0.616298\pi\)
−0.357286 + 0.933995i \(0.616298\pi\)
\(44\) 10.9183 1.64599
\(45\) −2.65358 −0.395572
\(46\) 0.0694285 0.0102367
\(47\) 11.1163 1.62148 0.810741 0.585405i \(-0.199064\pi\)
0.810741 + 0.585405i \(0.199064\pi\)
\(48\) 3.97464 0.573689
\(49\) 0 0
\(50\) −0.132779 −0.0187777
\(51\) −6.28311 −0.879811
\(52\) 6.79158 0.941822
\(53\) 8.14739 1.11913 0.559565 0.828786i \(-0.310968\pi\)
0.559565 + 0.828786i \(0.310968\pi\)
\(54\) −0.0650408 −0.00885093
\(55\) 14.5169 1.95746
\(56\) 0 0
\(57\) −4.25848 −0.564049
\(58\) 0.397124 0.0521449
\(59\) 14.0580 1.83020 0.915100 0.403228i \(-0.132112\pi\)
0.915100 + 0.403228i \(0.132112\pi\)
\(60\) 5.29593 0.683701
\(61\) −14.1386 −1.81027 −0.905133 0.425128i \(-0.860229\pi\)
−0.905133 + 0.425128i \(0.860229\pi\)
\(62\) 0.682395 0.0866643
\(63\) 0 0
\(64\) −7.89865 −0.987331
\(65\) 9.03008 1.12004
\(66\) 0.355819 0.0437983
\(67\) −6.51962 −0.796498 −0.398249 0.917277i \(-0.630382\pi\)
−0.398249 + 0.917277i \(0.630382\pi\)
\(68\) 12.5396 1.52065
\(69\) −1.06746 −0.128507
\(70\) 0 0
\(71\) −10.1718 −1.20717 −0.603587 0.797297i \(-0.706262\pi\)
−0.603587 + 0.797297i \(0.706262\pi\)
\(72\) 0.259888 0.0306281
\(73\) −4.82870 −0.565157 −0.282578 0.959244i \(-0.591190\pi\)
−0.282578 + 0.959244i \(0.591190\pi\)
\(74\) −0.249597 −0.0290150
\(75\) 2.04147 0.235728
\(76\) 8.49894 0.974896
\(77\) 0 0
\(78\) 0.221333 0.0250610
\(79\) 9.32274 1.04889 0.524445 0.851444i \(-0.324273\pi\)
0.524445 + 0.851444i \(0.324273\pi\)
\(80\) −10.5470 −1.17919
\(81\) 1.00000 0.111111
\(82\) 0.0650408 0.00718255
\(83\) −5.03523 −0.552688 −0.276344 0.961059i \(-0.589123\pi\)
−0.276344 + 0.961059i \(0.589123\pi\)
\(84\) 0 0
\(85\) 16.6727 1.80841
\(86\) 0.304766 0.0328637
\(87\) −6.10576 −0.654607
\(88\) −1.42177 −0.151561
\(89\) 8.62706 0.914466 0.457233 0.889347i \(-0.348841\pi\)
0.457233 + 0.889347i \(0.348841\pi\)
\(90\) 0.172591 0.0181926
\(91\) 0 0
\(92\) 2.13041 0.222110
\(93\) −10.4918 −1.08795
\(94\) −0.723014 −0.0745732
\(95\) 11.3002 1.15938
\(96\) −0.778289 −0.0794338
\(97\) −16.5259 −1.67795 −0.838977 0.544167i \(-0.816846\pi\)
−0.838977 + 0.544167i \(0.816846\pi\)
\(98\) 0 0
\(99\) −5.47071 −0.549827
\(100\) −4.07430 −0.407430
\(101\) −12.2461 −1.21853 −0.609264 0.792968i \(-0.708535\pi\)
−0.609264 + 0.792968i \(0.708535\pi\)
\(102\) 0.408658 0.0404632
\(103\) −4.18464 −0.412325 −0.206163 0.978518i \(-0.566098\pi\)
−0.206163 + 0.978518i \(0.566098\pi\)
\(104\) −0.884395 −0.0867221
\(105\) 0 0
\(106\) −0.529913 −0.0514697
\(107\) 4.55230 0.440087 0.220044 0.975490i \(-0.429380\pi\)
0.220044 + 0.975490i \(0.429380\pi\)
\(108\) −1.99577 −0.192043
\(109\) −9.25158 −0.886141 −0.443070 0.896487i \(-0.646111\pi\)
−0.443070 + 0.896487i \(0.646111\pi\)
\(110\) −0.944192 −0.0900252
\(111\) 3.83754 0.364243
\(112\) 0 0
\(113\) 6.81242 0.640858 0.320429 0.947272i \(-0.396173\pi\)
0.320429 + 0.947272i \(0.396173\pi\)
\(114\) 0.276975 0.0259411
\(115\) 2.83259 0.264140
\(116\) 12.1857 1.13141
\(117\) −3.40299 −0.314606
\(118\) −0.914345 −0.0841723
\(119\) 0 0
\(120\) −0.689632 −0.0629545
\(121\) 18.9286 1.72078
\(122\) 0.919587 0.0832555
\(123\) −1.00000 −0.0901670
\(124\) 20.9392 1.88040
\(125\) 7.85069 0.702187
\(126\) 0 0
\(127\) −13.5337 −1.20092 −0.600461 0.799654i \(-0.705016\pi\)
−0.600461 + 0.799654i \(0.705016\pi\)
\(128\) 2.07031 0.182992
\(129\) −4.68577 −0.412559
\(130\) −0.587324 −0.0515117
\(131\) 4.69146 0.409895 0.204948 0.978773i \(-0.434298\pi\)
0.204948 + 0.978773i \(0.434298\pi\)
\(132\) 10.9183 0.950313
\(133\) 0 0
\(134\) 0.424041 0.0366316
\(135\) −2.65358 −0.228383
\(136\) −1.63290 −0.140020
\(137\) −12.7773 −1.09164 −0.545818 0.837904i \(-0.683781\pi\)
−0.545818 + 0.837904i \(0.683781\pi\)
\(138\) 0.0694285 0.00591015
\(139\) −12.5370 −1.06338 −0.531688 0.846940i \(-0.678442\pi\)
−0.531688 + 0.846940i \(0.678442\pi\)
\(140\) 0 0
\(141\) 11.1163 0.936163
\(142\) 0.661584 0.0555189
\(143\) 18.6167 1.55681
\(144\) 3.97464 0.331220
\(145\) 16.2021 1.34551
\(146\) 0.314063 0.0259920
\(147\) 0 0
\(148\) −7.65885 −0.629553
\(149\) 2.62732 0.215238 0.107619 0.994192i \(-0.465677\pi\)
0.107619 + 0.994192i \(0.465677\pi\)
\(150\) −0.132779 −0.0108413
\(151\) −5.95876 −0.484917 −0.242458 0.970162i \(-0.577954\pi\)
−0.242458 + 0.970162i \(0.577954\pi\)
\(152\) −1.10673 −0.0897675
\(153\) −6.28311 −0.507959
\(154\) 0 0
\(155\) 27.8408 2.23623
\(156\) 6.79158 0.543761
\(157\) 13.8828 1.10797 0.553983 0.832528i \(-0.313107\pi\)
0.553983 + 0.832528i \(0.313107\pi\)
\(158\) −0.606358 −0.0482393
\(159\) 8.14739 0.646130
\(160\) 2.06525 0.163272
\(161\) 0 0
\(162\) −0.0650408 −0.00511009
\(163\) −0.962223 −0.0753671 −0.0376836 0.999290i \(-0.511998\pi\)
−0.0376836 + 0.999290i \(0.511998\pi\)
\(164\) 1.99577 0.155843
\(165\) 14.5169 1.13014
\(166\) 0.327495 0.0254185
\(167\) −10.9165 −0.844743 −0.422371 0.906423i \(-0.638802\pi\)
−0.422371 + 0.906423i \(0.638802\pi\)
\(168\) 0 0
\(169\) −1.41969 −0.109207
\(170\) −1.08441 −0.0831701
\(171\) −4.25848 −0.325654
\(172\) 9.35171 0.713061
\(173\) −18.1821 −1.38236 −0.691182 0.722681i \(-0.742910\pi\)
−0.691182 + 0.722681i \(0.742910\pi\)
\(174\) 0.397124 0.0301059
\(175\) 0 0
\(176\) −21.7441 −1.63902
\(177\) 14.0580 1.05667
\(178\) −0.561110 −0.0420570
\(179\) 14.3377 1.07165 0.535823 0.844330i \(-0.320001\pi\)
0.535823 + 0.844330i \(0.320001\pi\)
\(180\) 5.29593 0.394735
\(181\) 26.4209 1.96385 0.981925 0.189272i \(-0.0606128\pi\)
0.981925 + 0.189272i \(0.0606128\pi\)
\(182\) 0 0
\(183\) −14.1386 −1.04516
\(184\) −0.277420 −0.0204517
\(185\) −10.1832 −0.748684
\(186\) 0.682395 0.0500357
\(187\) 34.3730 2.51360
\(188\) −22.1856 −1.61805
\(189\) 0 0
\(190\) −0.734974 −0.0533206
\(191\) 4.42857 0.320440 0.160220 0.987081i \(-0.448780\pi\)
0.160220 + 0.987081i \(0.448780\pi\)
\(192\) −7.89865 −0.570036
\(193\) 4.70814 0.338899 0.169450 0.985539i \(-0.445801\pi\)
0.169450 + 0.985539i \(0.445801\pi\)
\(194\) 1.07486 0.0771704
\(195\) 9.03008 0.646658
\(196\) 0 0
\(197\) 25.9342 1.84774 0.923868 0.382712i \(-0.125010\pi\)
0.923868 + 0.382712i \(0.125010\pi\)
\(198\) 0.355819 0.0252869
\(199\) −14.9384 −1.05896 −0.529479 0.848323i \(-0.677612\pi\)
−0.529479 + 0.848323i \(0.677612\pi\)
\(200\) 0.530552 0.0375157
\(201\) −6.51962 −0.459859
\(202\) 0.796493 0.0560410
\(203\) 0 0
\(204\) 12.5396 0.877950
\(205\) 2.65358 0.185334
\(206\) 0.272172 0.0189632
\(207\) −1.06746 −0.0741937
\(208\) −13.5256 −0.937834
\(209\) 23.2969 1.61148
\(210\) 0 0
\(211\) 12.7550 0.878091 0.439045 0.898465i \(-0.355317\pi\)
0.439045 + 0.898465i \(0.355317\pi\)
\(212\) −16.2603 −1.11676
\(213\) −10.1718 −0.696962
\(214\) −0.296085 −0.0202400
\(215\) 12.4340 0.847994
\(216\) 0.259888 0.0176831
\(217\) 0 0
\(218\) 0.601730 0.0407543
\(219\) −4.82870 −0.326294
\(220\) −28.9725 −1.95332
\(221\) 21.3813 1.43826
\(222\) −0.249597 −0.0167518
\(223\) 7.54896 0.505515 0.252758 0.967530i \(-0.418662\pi\)
0.252758 + 0.967530i \(0.418662\pi\)
\(224\) 0 0
\(225\) 2.04147 0.136098
\(226\) −0.443085 −0.0294736
\(227\) −7.98410 −0.529923 −0.264962 0.964259i \(-0.585359\pi\)
−0.264962 + 0.964259i \(0.585359\pi\)
\(228\) 8.49894 0.562856
\(229\) −15.2575 −1.00825 −0.504123 0.863632i \(-0.668184\pi\)
−0.504123 + 0.863632i \(0.668184\pi\)
\(230\) −0.184234 −0.0121480
\(231\) 0 0
\(232\) −1.58681 −0.104179
\(233\) −13.1497 −0.861468 −0.430734 0.902479i \(-0.641745\pi\)
−0.430734 + 0.902479i \(0.641745\pi\)
\(234\) 0.221333 0.0144690
\(235\) −29.4980 −1.92424
\(236\) −28.0566 −1.82633
\(237\) 9.32274 0.605577
\(238\) 0 0
\(239\) 24.1988 1.56529 0.782645 0.622469i \(-0.213870\pi\)
0.782645 + 0.622469i \(0.213870\pi\)
\(240\) −10.5470 −0.680806
\(241\) 15.7240 1.01287 0.506436 0.862278i \(-0.330963\pi\)
0.506436 + 0.862278i \(0.330963\pi\)
\(242\) −1.23113 −0.0791401
\(243\) 1.00000 0.0641500
\(244\) 28.2175 1.80644
\(245\) 0 0
\(246\) 0.0650408 0.00414685
\(247\) 14.4915 0.922075
\(248\) −2.72669 −0.173145
\(249\) −5.03523 −0.319095
\(250\) −0.510615 −0.0322941
\(251\) 2.62369 0.165606 0.0828028 0.996566i \(-0.473613\pi\)
0.0828028 + 0.996566i \(0.473613\pi\)
\(252\) 0 0
\(253\) 5.83977 0.367143
\(254\) 0.880243 0.0552313
\(255\) 16.6727 1.04409
\(256\) 15.6626 0.978916
\(257\) −19.5935 −1.22221 −0.611104 0.791550i \(-0.709274\pi\)
−0.611104 + 0.791550i \(0.709274\pi\)
\(258\) 0.304766 0.0189739
\(259\) 0 0
\(260\) −18.0220 −1.11767
\(261\) −6.10576 −0.377937
\(262\) −0.305136 −0.0188514
\(263\) 1.27756 0.0787776 0.0393888 0.999224i \(-0.487459\pi\)
0.0393888 + 0.999224i \(0.487459\pi\)
\(264\) −1.42177 −0.0875039
\(265\) −21.6197 −1.32809
\(266\) 0 0
\(267\) 8.62706 0.527967
\(268\) 13.0117 0.794814
\(269\) −10.3127 −0.628779 −0.314389 0.949294i \(-0.601800\pi\)
−0.314389 + 0.949294i \(0.601800\pi\)
\(270\) 0.172591 0.0105035
\(271\) −6.53411 −0.396919 −0.198459 0.980109i \(-0.563594\pi\)
−0.198459 + 0.980109i \(0.563594\pi\)
\(272\) −24.9731 −1.51421
\(273\) 0 0
\(274\) 0.831044 0.0502052
\(275\) −11.1683 −0.673471
\(276\) 2.13041 0.128235
\(277\) −14.7541 −0.886486 −0.443243 0.896401i \(-0.646172\pi\)
−0.443243 + 0.896401i \(0.646172\pi\)
\(278\) 0.815417 0.0489055
\(279\) −10.4918 −0.628128
\(280\) 0 0
\(281\) −9.67355 −0.577075 −0.288538 0.957469i \(-0.593169\pi\)
−0.288538 + 0.957469i \(0.593169\pi\)
\(282\) −0.723014 −0.0430549
\(283\) −18.0256 −1.07151 −0.535756 0.844373i \(-0.679973\pi\)
−0.535756 + 0.844373i \(0.679973\pi\)
\(284\) 20.3006 1.20462
\(285\) 11.3002 0.669366
\(286\) −1.21085 −0.0715989
\(287\) 0 0
\(288\) −0.778289 −0.0458611
\(289\) 22.4774 1.32220
\(290\) −1.05380 −0.0618811
\(291\) −16.5259 −0.968767
\(292\) 9.63698 0.563962
\(293\) 30.2323 1.76619 0.883094 0.469195i \(-0.155456\pi\)
0.883094 + 0.469195i \(0.155456\pi\)
\(294\) 0 0
\(295\) −37.3040 −2.17193
\(296\) 0.997330 0.0579686
\(297\) −5.47071 −0.317443
\(298\) −0.170883 −0.00989898
\(299\) 3.63256 0.210076
\(300\) −4.07430 −0.235230
\(301\) 0 0
\(302\) 0.387562 0.0223017
\(303\) −12.2461 −0.703517
\(304\) −16.9259 −0.970767
\(305\) 37.5179 2.14827
\(306\) 0.408658 0.0233614
\(307\) −5.59004 −0.319040 −0.159520 0.987195i \(-0.550995\pi\)
−0.159520 + 0.987195i \(0.550995\pi\)
\(308\) 0 0
\(309\) −4.18464 −0.238056
\(310\) −1.81079 −0.102846
\(311\) −2.84702 −0.161440 −0.0807200 0.996737i \(-0.525722\pi\)
−0.0807200 + 0.996737i \(0.525722\pi\)
\(312\) −0.884395 −0.0500690
\(313\) 7.97569 0.450813 0.225406 0.974265i \(-0.427629\pi\)
0.225406 + 0.974265i \(0.427629\pi\)
\(314\) −0.902947 −0.0509562
\(315\) 0 0
\(316\) −18.6060 −1.04667
\(317\) −9.27505 −0.520939 −0.260469 0.965482i \(-0.583877\pi\)
−0.260469 + 0.965482i \(0.583877\pi\)
\(318\) −0.529913 −0.0297160
\(319\) 33.4028 1.87020
\(320\) 20.9597 1.17168
\(321\) 4.55230 0.254085
\(322\) 0 0
\(323\) 26.7565 1.48877
\(324\) −1.99577 −0.110876
\(325\) −6.94708 −0.385355
\(326\) 0.0625837 0.00346619
\(327\) −9.25158 −0.511613
\(328\) −0.259888 −0.0143499
\(329\) 0 0
\(330\) −0.944192 −0.0519761
\(331\) 14.6322 0.804257 0.402129 0.915583i \(-0.368270\pi\)
0.402129 + 0.915583i \(0.368270\pi\)
\(332\) 10.0492 0.551519
\(333\) 3.83754 0.210296
\(334\) 0.710016 0.0388504
\(335\) 17.3003 0.945217
\(336\) 0 0
\(337\) 14.1264 0.769517 0.384758 0.923017i \(-0.374285\pi\)
0.384758 + 0.923017i \(0.374285\pi\)
\(338\) 0.0923374 0.00502249
\(339\) 6.81242 0.370000
\(340\) −33.2749 −1.80458
\(341\) 57.3976 3.10825
\(342\) 0.276975 0.0149771
\(343\) 0 0
\(344\) −1.21777 −0.0656580
\(345\) 2.83259 0.152502
\(346\) 1.18258 0.0635759
\(347\) 20.2540 1.08729 0.543645 0.839315i \(-0.317044\pi\)
0.543645 + 0.839315i \(0.317044\pi\)
\(348\) 12.1857 0.653222
\(349\) −23.8877 −1.27868 −0.639339 0.768925i \(-0.720792\pi\)
−0.639339 + 0.768925i \(0.720792\pi\)
\(350\) 0 0
\(351\) −3.40299 −0.181638
\(352\) 4.25779 0.226941
\(353\) 19.9546 1.06208 0.531039 0.847347i \(-0.321802\pi\)
0.531039 + 0.847347i \(0.321802\pi\)
\(354\) −0.914345 −0.0485969
\(355\) 26.9917 1.43257
\(356\) −17.2176 −0.912532
\(357\) 0 0
\(358\) −0.932532 −0.0492859
\(359\) −4.70206 −0.248165 −0.124082 0.992272i \(-0.539599\pi\)
−0.124082 + 0.992272i \(0.539599\pi\)
\(360\) −0.689632 −0.0363468
\(361\) −0.865350 −0.0455448
\(362\) −1.71844 −0.0903189
\(363\) 18.9286 0.993495
\(364\) 0 0
\(365\) 12.8133 0.670680
\(366\) 0.919587 0.0480676
\(367\) −12.9579 −0.676398 −0.338199 0.941075i \(-0.609818\pi\)
−0.338199 + 0.941075i \(0.609818\pi\)
\(368\) −4.24277 −0.221170
\(369\) −1.00000 −0.0520579
\(370\) 0.662323 0.0344326
\(371\) 0 0
\(372\) 20.9392 1.08565
\(373\) 24.5509 1.27120 0.635599 0.772019i \(-0.280753\pi\)
0.635599 + 0.772019i \(0.280753\pi\)
\(374\) −2.23565 −0.115603
\(375\) 7.85069 0.405408
\(376\) 2.88900 0.148989
\(377\) 20.7778 1.07011
\(378\) 0 0
\(379\) 33.8102 1.73671 0.868356 0.495941i \(-0.165177\pi\)
0.868356 + 0.495941i \(0.165177\pi\)
\(380\) −22.5526 −1.15692
\(381\) −13.5337 −0.693353
\(382\) −0.288038 −0.0147373
\(383\) −23.0463 −1.17761 −0.588805 0.808275i \(-0.700401\pi\)
−0.588805 + 0.808275i \(0.700401\pi\)
\(384\) 2.07031 0.105650
\(385\) 0 0
\(386\) −0.306221 −0.0155862
\(387\) −4.68577 −0.238191
\(388\) 32.9820 1.67440
\(389\) −4.13177 −0.209489 −0.104745 0.994499i \(-0.533402\pi\)
−0.104745 + 0.994499i \(0.533402\pi\)
\(390\) −0.587324 −0.0297403
\(391\) 6.70697 0.339186
\(392\) 0 0
\(393\) 4.69146 0.236653
\(394\) −1.68678 −0.0849788
\(395\) −24.7386 −1.24473
\(396\) 10.9183 0.548664
\(397\) 25.3153 1.27054 0.635268 0.772292i \(-0.280890\pi\)
0.635268 + 0.772292i \(0.280890\pi\)
\(398\) 0.971607 0.0487023
\(399\) 0 0
\(400\) 8.11409 0.405704
\(401\) 27.0679 1.35171 0.675853 0.737037i \(-0.263776\pi\)
0.675853 + 0.737037i \(0.263776\pi\)
\(402\) 0.424041 0.0211492
\(403\) 35.7035 1.77852
\(404\) 24.4403 1.21595
\(405\) −2.65358 −0.131857
\(406\) 0 0
\(407\) −20.9941 −1.04064
\(408\) −1.63290 −0.0808408
\(409\) −36.0335 −1.78174 −0.890870 0.454258i \(-0.849904\pi\)
−0.890870 + 0.454258i \(0.849904\pi\)
\(410\) −0.172591 −0.00852364
\(411\) −12.7773 −0.630256
\(412\) 8.35159 0.411453
\(413\) 0 0
\(414\) 0.0694285 0.00341223
\(415\) 13.3614 0.655883
\(416\) 2.64851 0.129854
\(417\) −12.5370 −0.613940
\(418\) −1.51525 −0.0741132
\(419\) 28.2596 1.38057 0.690287 0.723536i \(-0.257484\pi\)
0.690287 + 0.723536i \(0.257484\pi\)
\(420\) 0 0
\(421\) 18.5570 0.904415 0.452207 0.891913i \(-0.350637\pi\)
0.452207 + 0.891913i \(0.350637\pi\)
\(422\) −0.829595 −0.0403841
\(423\) 11.1163 0.540494
\(424\) 2.11741 0.102830
\(425\) −12.8268 −0.622189
\(426\) 0.661584 0.0320538
\(427\) 0 0
\(428\) −9.08534 −0.439157
\(429\) 18.6167 0.898824
\(430\) −0.808719 −0.0389999
\(431\) −1.77967 −0.0857239 −0.0428619 0.999081i \(-0.513648\pi\)
−0.0428619 + 0.999081i \(0.513648\pi\)
\(432\) 3.97464 0.191230
\(433\) −28.5720 −1.37308 −0.686541 0.727092i \(-0.740872\pi\)
−0.686541 + 0.727092i \(0.740872\pi\)
\(434\) 0 0
\(435\) 16.2021 0.776832
\(436\) 18.4640 0.884266
\(437\) 4.54576 0.217453
\(438\) 0.314063 0.0150065
\(439\) −6.39885 −0.305400 −0.152700 0.988273i \(-0.548797\pi\)
−0.152700 + 0.988273i \(0.548797\pi\)
\(440\) 3.77278 0.179860
\(441\) 0 0
\(442\) −1.39066 −0.0661468
\(443\) −25.5094 −1.21199 −0.605995 0.795468i \(-0.707225\pi\)
−0.605995 + 0.795468i \(0.707225\pi\)
\(444\) −7.65885 −0.363473
\(445\) −22.8925 −1.08521
\(446\) −0.490990 −0.0232490
\(447\) 2.62732 0.124268
\(448\) 0 0
\(449\) −15.3343 −0.723671 −0.361835 0.932242i \(-0.617850\pi\)
−0.361835 + 0.932242i \(0.617850\pi\)
\(450\) −0.132779 −0.00625924
\(451\) 5.47071 0.257605
\(452\) −13.5960 −0.639503
\(453\) −5.95876 −0.279967
\(454\) 0.519292 0.0243716
\(455\) 0 0
\(456\) −1.10673 −0.0518273
\(457\) −12.4509 −0.582430 −0.291215 0.956658i \(-0.594059\pi\)
−0.291215 + 0.956658i \(0.594059\pi\)
\(458\) 0.992361 0.0463700
\(459\) −6.28311 −0.293270
\(460\) −5.65320 −0.263582
\(461\) −37.9754 −1.76869 −0.884345 0.466833i \(-0.845395\pi\)
−0.884345 + 0.466833i \(0.845395\pi\)
\(462\) 0 0
\(463\) 7.28313 0.338476 0.169238 0.985575i \(-0.445869\pi\)
0.169238 + 0.985575i \(0.445869\pi\)
\(464\) −24.2682 −1.12662
\(465\) 27.8408 1.29109
\(466\) 0.855269 0.0396196
\(467\) −12.6148 −0.583743 −0.291871 0.956458i \(-0.594278\pi\)
−0.291871 + 0.956458i \(0.594278\pi\)
\(468\) 6.79158 0.313941
\(469\) 0 0
\(470\) 1.91857 0.0884972
\(471\) 13.8828 0.639685
\(472\) 3.65351 0.168166
\(473\) 25.6344 1.17867
\(474\) −0.606358 −0.0278509
\(475\) −8.69354 −0.398887
\(476\) 0 0
\(477\) 8.14739 0.373043
\(478\) −1.57391 −0.0719888
\(479\) −42.8999 −1.96015 −0.980073 0.198638i \(-0.936348\pi\)
−0.980073 + 0.198638i \(0.936348\pi\)
\(480\) 2.06525 0.0942653
\(481\) −13.0591 −0.595443
\(482\) −1.02270 −0.0465827
\(483\) 0 0
\(484\) −37.7772 −1.71714
\(485\) 43.8528 1.99125
\(486\) −0.0650408 −0.00295031
\(487\) −31.2404 −1.41564 −0.707819 0.706394i \(-0.750321\pi\)
−0.707819 + 0.706394i \(0.750321\pi\)
\(488\) −3.67446 −0.166335
\(489\) −0.962223 −0.0435132
\(490\) 0 0
\(491\) 39.3972 1.77797 0.888985 0.457936i \(-0.151411\pi\)
0.888985 + 0.457936i \(0.151411\pi\)
\(492\) 1.99577 0.0899762
\(493\) 38.3632 1.72779
\(494\) −0.942541 −0.0424069
\(495\) 14.5169 0.652488
\(496\) −41.7011 −1.87244
\(497\) 0 0
\(498\) 0.327495 0.0146754
\(499\) 11.5175 0.515594 0.257797 0.966199i \(-0.417003\pi\)
0.257797 + 0.966199i \(0.417003\pi\)
\(500\) −15.6682 −0.700702
\(501\) −10.9165 −0.487712
\(502\) −0.170647 −0.00761633
\(503\) −4.15133 −0.185099 −0.0925494 0.995708i \(-0.529502\pi\)
−0.0925494 + 0.995708i \(0.529502\pi\)
\(504\) 0 0
\(505\) 32.4958 1.44605
\(506\) −0.379823 −0.0168852
\(507\) −1.41969 −0.0630505
\(508\) 27.0102 1.19838
\(509\) 5.60204 0.248306 0.124153 0.992263i \(-0.460379\pi\)
0.124153 + 0.992263i \(0.460379\pi\)
\(510\) −1.08441 −0.0480183
\(511\) 0 0
\(512\) −5.15934 −0.228013
\(513\) −4.25848 −0.188016
\(514\) 1.27437 0.0562103
\(515\) 11.1043 0.489313
\(516\) 9.35171 0.411686
\(517\) −60.8141 −2.67460
\(518\) 0 0
\(519\) −18.1821 −0.798108
\(520\) 2.34681 0.102914
\(521\) −6.60586 −0.289408 −0.144704 0.989475i \(-0.546223\pi\)
−0.144704 + 0.989475i \(0.546223\pi\)
\(522\) 0.397124 0.0173816
\(523\) −14.2512 −0.623163 −0.311581 0.950219i \(-0.600859\pi\)
−0.311581 + 0.950219i \(0.600859\pi\)
\(524\) −9.36308 −0.409028
\(525\) 0 0
\(526\) −0.0830934 −0.00362304
\(527\) 65.9212 2.87157
\(528\) −21.7441 −0.946289
\(529\) −21.8605 −0.950458
\(530\) 1.40616 0.0610798
\(531\) 14.0580 0.610066
\(532\) 0 0
\(533\) 3.40299 0.147400
\(534\) −0.561110 −0.0242816
\(535\) −12.0799 −0.522259
\(536\) −1.69437 −0.0731857
\(537\) 14.3377 0.618715
\(538\) 0.670748 0.0289180
\(539\) 0 0
\(540\) 5.29593 0.227900
\(541\) 40.0215 1.72066 0.860329 0.509738i \(-0.170258\pi\)
0.860329 + 0.509738i \(0.170258\pi\)
\(542\) 0.424983 0.0182546
\(543\) 26.4209 1.13383
\(544\) 4.89007 0.209660
\(545\) 24.5498 1.05160
\(546\) 0 0
\(547\) −12.9488 −0.553651 −0.276826 0.960920i \(-0.589282\pi\)
−0.276826 + 0.960920i \(0.589282\pi\)
\(548\) 25.5005 1.08933
\(549\) −14.1386 −0.603422
\(550\) 0.726392 0.0309735
\(551\) 26.0013 1.10769
\(552\) −0.277420 −0.0118078
\(553\) 0 0
\(554\) 0.959616 0.0407702
\(555\) −10.1832 −0.432253
\(556\) 25.0210 1.06113
\(557\) −11.4145 −0.483648 −0.241824 0.970320i \(-0.577746\pi\)
−0.241824 + 0.970320i \(0.577746\pi\)
\(558\) 0.682395 0.0288881
\(559\) 15.9456 0.674427
\(560\) 0 0
\(561\) 34.3730 1.45123
\(562\) 0.629175 0.0265401
\(563\) −34.8335 −1.46806 −0.734028 0.679119i \(-0.762362\pi\)
−0.734028 + 0.679119i \(0.762362\pi\)
\(564\) −22.1856 −0.934183
\(565\) −18.0773 −0.760516
\(566\) 1.17240 0.0492796
\(567\) 0 0
\(568\) −2.64354 −0.110920
\(569\) −41.6149 −1.74459 −0.872294 0.488982i \(-0.837369\pi\)
−0.872294 + 0.488982i \(0.837369\pi\)
\(570\) −0.734974 −0.0307847
\(571\) −40.2264 −1.68342 −0.841711 0.539929i \(-0.818451\pi\)
−0.841711 + 0.539929i \(0.818451\pi\)
\(572\) −37.1547 −1.55352
\(573\) 4.42857 0.185006
\(574\) 0 0
\(575\) −2.17919 −0.0908784
\(576\) −7.89865 −0.329110
\(577\) 22.0329 0.917242 0.458621 0.888632i \(-0.348343\pi\)
0.458621 + 0.888632i \(0.348343\pi\)
\(578\) −1.46195 −0.0608091
\(579\) 4.70814 0.195664
\(580\) −32.3357 −1.34267
\(581\) 0 0
\(582\) 1.07486 0.0445544
\(583\) −44.5720 −1.84598
\(584\) −1.25492 −0.0519290
\(585\) 9.03008 0.373348
\(586\) −1.96633 −0.0812284
\(587\) −14.1762 −0.585116 −0.292558 0.956248i \(-0.594506\pi\)
−0.292558 + 0.956248i \(0.594506\pi\)
\(588\) 0 0
\(589\) 44.6792 1.84097
\(590\) 2.42628 0.0998885
\(591\) 25.9342 1.06679
\(592\) 15.2528 0.626887
\(593\) −0.457779 −0.0187987 −0.00939936 0.999956i \(-0.502992\pi\)
−0.00939936 + 0.999956i \(0.502992\pi\)
\(594\) 0.355819 0.0145994
\(595\) 0 0
\(596\) −5.24352 −0.214783
\(597\) −14.9384 −0.611389
\(598\) −0.236264 −0.00966156
\(599\) −27.7858 −1.13530 −0.567648 0.823271i \(-0.692147\pi\)
−0.567648 + 0.823271i \(0.692147\pi\)
\(600\) 0.530552 0.0216597
\(601\) −30.0070 −1.22401 −0.612007 0.790853i \(-0.709637\pi\)
−0.612007 + 0.790853i \(0.709637\pi\)
\(602\) 0 0
\(603\) −6.51962 −0.265499
\(604\) 11.8923 0.483891
\(605\) −50.2285 −2.04208
\(606\) 0.796493 0.0323553
\(607\) −24.6437 −1.00026 −0.500129 0.865951i \(-0.666714\pi\)
−0.500129 + 0.865951i \(0.666714\pi\)
\(608\) 3.31433 0.134414
\(609\) 0 0
\(610\) −2.44020 −0.0988006
\(611\) −37.8287 −1.53038
\(612\) 12.5396 0.506885
\(613\) 31.1894 1.25973 0.629865 0.776705i \(-0.283110\pi\)
0.629865 + 0.776705i \(0.283110\pi\)
\(614\) 0.363580 0.0146729
\(615\) 2.65358 0.107003
\(616\) 0 0
\(617\) −35.2034 −1.41724 −0.708619 0.705592i \(-0.750681\pi\)
−0.708619 + 0.705592i \(0.750681\pi\)
\(618\) 0.272172 0.0109484
\(619\) −32.5283 −1.30742 −0.653711 0.756744i \(-0.726789\pi\)
−0.653711 + 0.756744i \(0.726789\pi\)
\(620\) −55.5639 −2.23150
\(621\) −1.06746 −0.0428358
\(622\) 0.185173 0.00742475
\(623\) 0 0
\(624\) −13.5256 −0.541459
\(625\) −31.0397 −1.24159
\(626\) −0.518745 −0.0207332
\(627\) 23.2969 0.930388
\(628\) −27.7068 −1.10562
\(629\) −24.1117 −0.961395
\(630\) 0 0
\(631\) 1.97175 0.0784943 0.0392471 0.999230i \(-0.487504\pi\)
0.0392471 + 0.999230i \(0.487504\pi\)
\(632\) 2.42287 0.0963765
\(633\) 12.7550 0.506966
\(634\) 0.603257 0.0239584
\(635\) 35.9127 1.42515
\(636\) −16.2603 −0.644764
\(637\) 0 0
\(638\) −2.17255 −0.0860119
\(639\) −10.1718 −0.402391
\(640\) −5.49373 −0.217159
\(641\) 5.94124 0.234665 0.117333 0.993093i \(-0.462566\pi\)
0.117333 + 0.993093i \(0.462566\pi\)
\(642\) −0.296085 −0.0116855
\(643\) −0.918004 −0.0362025 −0.0181013 0.999836i \(-0.505762\pi\)
−0.0181013 + 0.999836i \(0.505762\pi\)
\(644\) 0 0
\(645\) 12.4340 0.489590
\(646\) −1.74026 −0.0684697
\(647\) 41.6269 1.63652 0.818260 0.574848i \(-0.194939\pi\)
0.818260 + 0.574848i \(0.194939\pi\)
\(648\) 0.259888 0.0102094
\(649\) −76.9073 −3.01888
\(650\) 0.451844 0.0177228
\(651\) 0 0
\(652\) 1.92038 0.0752077
\(653\) −16.7700 −0.656260 −0.328130 0.944633i \(-0.606418\pi\)
−0.328130 + 0.944633i \(0.606418\pi\)
\(654\) 0.601730 0.0235295
\(655\) −12.4492 −0.486429
\(656\) −3.97464 −0.155183
\(657\) −4.82870 −0.188386
\(658\) 0 0
\(659\) 30.2319 1.17767 0.588833 0.808255i \(-0.299588\pi\)
0.588833 + 0.808255i \(0.299588\pi\)
\(660\) −28.9725 −1.12775
\(661\) 1.62355 0.0631488 0.0315744 0.999501i \(-0.489948\pi\)
0.0315744 + 0.999501i \(0.489948\pi\)
\(662\) −0.951688 −0.0369884
\(663\) 21.3813 0.830382
\(664\) −1.30859 −0.0507833
\(665\) 0 0
\(666\) −0.249597 −0.00967167
\(667\) 6.51767 0.252365
\(668\) 21.7868 0.842956
\(669\) 7.54896 0.291859
\(670\) −1.12523 −0.0434712
\(671\) 77.3483 2.98600
\(672\) 0 0
\(673\) −28.1360 −1.08456 −0.542282 0.840196i \(-0.682440\pi\)
−0.542282 + 0.840196i \(0.682440\pi\)
\(674\) −0.918795 −0.0353907
\(675\) 2.04147 0.0785761
\(676\) 2.83337 0.108976
\(677\) −17.6912 −0.679929 −0.339964 0.940438i \(-0.610415\pi\)
−0.339964 + 0.940438i \(0.610415\pi\)
\(678\) −0.443085 −0.0170166
\(679\) 0 0
\(680\) 4.33303 0.166164
\(681\) −7.98410 −0.305951
\(682\) −3.73318 −0.142951
\(683\) 3.62028 0.138526 0.0692630 0.997598i \(-0.477935\pi\)
0.0692630 + 0.997598i \(0.477935\pi\)
\(684\) 8.49894 0.324965
\(685\) 33.9055 1.29546
\(686\) 0 0
\(687\) −15.2575 −0.582111
\(688\) −18.6242 −0.710042
\(689\) −27.7255 −1.05626
\(690\) −0.184234 −0.00701366
\(691\) −10.5745 −0.402273 −0.201136 0.979563i \(-0.564463\pi\)
−0.201136 + 0.979563i \(0.564463\pi\)
\(692\) 36.2874 1.37944
\(693\) 0 0
\(694\) −1.31733 −0.0500053
\(695\) 33.2679 1.26192
\(696\) −1.58681 −0.0601480
\(697\) 6.28311 0.237990
\(698\) 1.55367 0.0588073
\(699\) −13.1497 −0.497369
\(700\) 0 0
\(701\) −38.8486 −1.46729 −0.733645 0.679533i \(-0.762182\pi\)
−0.733645 + 0.679533i \(0.762182\pi\)
\(702\) 0.221333 0.00835367
\(703\) −16.3421 −0.616353
\(704\) 43.2112 1.62858
\(705\) −29.4980 −1.11096
\(706\) −1.29786 −0.0488458
\(707\) 0 0
\(708\) −28.0566 −1.05443
\(709\) 29.2915 1.10006 0.550032 0.835144i \(-0.314616\pi\)
0.550032 + 0.835144i \(0.314616\pi\)
\(710\) −1.75556 −0.0658851
\(711\) 9.32274 0.349630
\(712\) 2.24207 0.0840250
\(713\) 11.1996 0.419428
\(714\) 0 0
\(715\) −49.4009 −1.84749
\(716\) −28.6147 −1.06938
\(717\) 24.1988 0.903720
\(718\) 0.305825 0.0114133
\(719\) −8.04364 −0.299977 −0.149989 0.988688i \(-0.547924\pi\)
−0.149989 + 0.988688i \(0.547924\pi\)
\(720\) −10.5470 −0.393063
\(721\) 0 0
\(722\) 0.0562831 0.00209464
\(723\) 15.7240 0.584782
\(724\) −52.7300 −1.95970
\(725\) −12.4647 −0.462928
\(726\) −1.23113 −0.0456916
\(727\) 45.4403 1.68529 0.842643 0.538472i \(-0.180998\pi\)
0.842643 + 0.538472i \(0.180998\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.833389 −0.0308451
\(731\) 29.4412 1.08892
\(732\) 28.2175 1.04295
\(733\) −36.2630 −1.33940 −0.669702 0.742630i \(-0.733578\pi\)
−0.669702 + 0.742630i \(0.733578\pi\)
\(734\) 0.842794 0.0311081
\(735\) 0 0
\(736\) 0.830794 0.0306235
\(737\) 35.6669 1.31381
\(738\) 0.0650408 0.00239418
\(739\) −34.1511 −1.25627 −0.628134 0.778105i \(-0.716181\pi\)
−0.628134 + 0.778105i \(0.716181\pi\)
\(740\) 20.3233 0.747101
\(741\) 14.4915 0.532360
\(742\) 0 0
\(743\) 19.8077 0.726673 0.363337 0.931658i \(-0.381637\pi\)
0.363337 + 0.931658i \(0.381637\pi\)
\(744\) −2.72669 −0.0999655
\(745\) −6.97179 −0.255427
\(746\) −1.59681 −0.0584634
\(747\) −5.03523 −0.184229
\(748\) −68.6006 −2.50829
\(749\) 0 0
\(750\) −0.510615 −0.0186450
\(751\) 22.2356 0.811387 0.405694 0.914009i \(-0.367030\pi\)
0.405694 + 0.914009i \(0.367030\pi\)
\(752\) 44.1833 1.61120
\(753\) 2.62369 0.0956124
\(754\) −1.35141 −0.0492153
\(755\) 15.8120 0.575458
\(756\) 0 0
\(757\) −38.0167 −1.38174 −0.690870 0.722979i \(-0.742772\pi\)
−0.690870 + 0.722979i \(0.742772\pi\)
\(758\) −2.19904 −0.0798727
\(759\) 5.83977 0.211970
\(760\) 2.93679 0.106528
\(761\) −18.8243 −0.682382 −0.341191 0.939994i \(-0.610830\pi\)
−0.341191 + 0.939994i \(0.610830\pi\)
\(762\) 0.880243 0.0318878
\(763\) 0 0
\(764\) −8.83841 −0.319762
\(765\) 16.6727 0.602803
\(766\) 1.49895 0.0541591
\(767\) −47.8393 −1.72738
\(768\) 15.6626 0.565177
\(769\) −2.09557 −0.0755682 −0.0377841 0.999286i \(-0.512030\pi\)
−0.0377841 + 0.999286i \(0.512030\pi\)
\(770\) 0 0
\(771\) −19.5935 −0.705642
\(772\) −9.39637 −0.338183
\(773\) 6.12334 0.220241 0.110121 0.993918i \(-0.464876\pi\)
0.110121 + 0.993918i \(0.464876\pi\)
\(774\) 0.304766 0.0109546
\(775\) −21.4187 −0.769382
\(776\) −4.29489 −0.154178
\(777\) 0 0
\(778\) 0.268734 0.00963456
\(779\) 4.25848 0.152576
\(780\) −18.0220 −0.645290
\(781\) 55.6471 1.99121
\(782\) −0.436227 −0.0155994
\(783\) −6.10576 −0.218202
\(784\) 0 0
\(785\) −36.8390 −1.31484
\(786\) −0.305136 −0.0108839
\(787\) 25.8179 0.920310 0.460155 0.887839i \(-0.347794\pi\)
0.460155 + 0.887839i \(0.347794\pi\)
\(788\) −51.7587 −1.84383
\(789\) 1.27756 0.0454823
\(790\) 1.60902 0.0572463
\(791\) 0 0
\(792\) −1.42177 −0.0505204
\(793\) 48.1136 1.70856
\(794\) −1.64652 −0.0584329
\(795\) −21.6197 −0.766773
\(796\) 29.8137 1.05672
\(797\) 17.1847 0.608714 0.304357 0.952558i \(-0.401558\pi\)
0.304357 + 0.952558i \(0.401558\pi\)
\(798\) 0 0
\(799\) −69.8450 −2.47094
\(800\) −1.58885 −0.0561744
\(801\) 8.62706 0.304822
\(802\) −1.76052 −0.0621660
\(803\) 26.4164 0.932215
\(804\) 13.0117 0.458886
\(805\) 0 0
\(806\) −2.32218 −0.0817954
\(807\) −10.3127 −0.363026
\(808\) −3.18260 −0.111964
\(809\) −4.69562 −0.165089 −0.0825446 0.996587i \(-0.526305\pi\)
−0.0825446 + 0.996587i \(0.526305\pi\)
\(810\) 0.172591 0.00606422
\(811\) 18.8630 0.662371 0.331185 0.943566i \(-0.392551\pi\)
0.331185 + 0.943566i \(0.392551\pi\)
\(812\) 0 0
\(813\) −6.53411 −0.229161
\(814\) 1.36547 0.0478597
\(815\) 2.55333 0.0894393
\(816\) −24.9731 −0.874232
\(817\) 19.9542 0.698110
\(818\) 2.34364 0.0819436
\(819\) 0 0
\(820\) −5.29593 −0.184942
\(821\) 37.6024 1.31233 0.656167 0.754616i \(-0.272177\pi\)
0.656167 + 0.754616i \(0.272177\pi\)
\(822\) 0.831044 0.0289860
\(823\) −45.6703 −1.59197 −0.795983 0.605320i \(-0.793045\pi\)
−0.795983 + 0.605320i \(0.793045\pi\)
\(824\) −1.08754 −0.0378862
\(825\) −11.1683 −0.388829
\(826\) 0 0
\(827\) −23.4857 −0.816678 −0.408339 0.912830i \(-0.633892\pi\)
−0.408339 + 0.912830i \(0.633892\pi\)
\(828\) 2.13041 0.0740368
\(829\) −27.5826 −0.957982 −0.478991 0.877820i \(-0.658997\pi\)
−0.478991 + 0.877820i \(0.658997\pi\)
\(830\) −0.869033 −0.0301646
\(831\) −14.7541 −0.511813
\(832\) 26.8790 0.931862
\(833\) 0 0
\(834\) 0.815417 0.0282356
\(835\) 28.9677 1.00247
\(836\) −46.4952 −1.60807
\(837\) −10.4918 −0.362650
\(838\) −1.83803 −0.0634937
\(839\) 11.7966 0.407263 0.203631 0.979048i \(-0.434726\pi\)
0.203631 + 0.979048i \(0.434726\pi\)
\(840\) 0 0
\(841\) 8.28036 0.285530
\(842\) −1.20696 −0.0415947
\(843\) −9.67355 −0.333175
\(844\) −25.4561 −0.876233
\(845\) 3.76724 0.129597
\(846\) −0.723014 −0.0248577
\(847\) 0 0
\(848\) 32.3829 1.11203
\(849\) −18.0256 −0.618637
\(850\) 0.834262 0.0286149
\(851\) −4.09643 −0.140424
\(852\) 20.3006 0.695488
\(853\) −6.50215 −0.222629 −0.111315 0.993785i \(-0.535506\pi\)
−0.111315 + 0.993785i \(0.535506\pi\)
\(854\) 0 0
\(855\) 11.3002 0.386459
\(856\) 1.18309 0.0404371
\(857\) 50.2945 1.71803 0.859014 0.511952i \(-0.171078\pi\)
0.859014 + 0.511952i \(0.171078\pi\)
\(858\) −1.21085 −0.0413376
\(859\) 0.973780 0.0332249 0.0166125 0.999862i \(-0.494712\pi\)
0.0166125 + 0.999862i \(0.494712\pi\)
\(860\) −24.8155 −0.846201
\(861\) 0 0
\(862\) 0.115751 0.00394251
\(863\) −40.4421 −1.37667 −0.688333 0.725395i \(-0.741657\pi\)
−0.688333 + 0.725395i \(0.741657\pi\)
\(864\) −0.778289 −0.0264779
\(865\) 48.2477 1.64047
\(866\) 1.85834 0.0631491
\(867\) 22.4774 0.763373
\(868\) 0 0
\(869\) −51.0019 −1.73012
\(870\) −1.05380 −0.0357271
\(871\) 22.1862 0.751750
\(872\) −2.40437 −0.0814224
\(873\) −16.5259 −0.559318
\(874\) −0.295660 −0.0100008
\(875\) 0 0
\(876\) 9.63698 0.325603
\(877\) −35.9374 −1.21352 −0.606760 0.794885i \(-0.707531\pi\)
−0.606760 + 0.794885i \(0.707531\pi\)
\(878\) 0.416186 0.0140456
\(879\) 30.2323 1.01971
\(880\) 57.6995 1.94505
\(881\) 4.34713 0.146459 0.0732293 0.997315i \(-0.476669\pi\)
0.0732293 + 0.997315i \(0.476669\pi\)
\(882\) 0 0
\(883\) 24.4854 0.824000 0.412000 0.911184i \(-0.364830\pi\)
0.412000 + 0.911184i \(0.364830\pi\)
\(884\) −42.6722 −1.43522
\(885\) −37.3040 −1.25396
\(886\) 1.65915 0.0557404
\(887\) −5.39213 −0.181050 −0.0905250 0.995894i \(-0.528854\pi\)
−0.0905250 + 0.995894i \(0.528854\pi\)
\(888\) 0.997330 0.0334682
\(889\) 0 0
\(890\) 1.48895 0.0499097
\(891\) −5.47071 −0.183276
\(892\) −15.0660 −0.504446
\(893\) −47.3386 −1.58413
\(894\) −0.170883 −0.00571518
\(895\) −38.0461 −1.27174
\(896\) 0 0
\(897\) 3.63256 0.121288
\(898\) 0.997355 0.0332822
\(899\) 64.0605 2.13654
\(900\) −4.07430 −0.135810
\(901\) −51.1909 −1.70542
\(902\) −0.355819 −0.0118475
\(903\) 0 0
\(904\) 1.77046 0.0588848
\(905\) −70.1098 −2.33053
\(906\) 0.387562 0.0128759
\(907\) 25.2422 0.838154 0.419077 0.907951i \(-0.362354\pi\)
0.419077 + 0.907951i \(0.362354\pi\)
\(908\) 15.9344 0.528802
\(909\) −12.2461 −0.406176
\(910\) 0 0
\(911\) −7.07772 −0.234495 −0.117248 0.993103i \(-0.537407\pi\)
−0.117248 + 0.993103i \(0.537407\pi\)
\(912\) −16.9259 −0.560473
\(913\) 27.5462 0.911648
\(914\) 0.809818 0.0267864
\(915\) 37.5179 1.24030
\(916\) 30.4505 1.00611
\(917\) 0 0
\(918\) 0.408658 0.0134877
\(919\) −9.66161 −0.318707 −0.159353 0.987222i \(-0.550941\pi\)
−0.159353 + 0.987222i \(0.550941\pi\)
\(920\) 0.736156 0.0242703
\(921\) −5.59004 −0.184198
\(922\) 2.46995 0.0813435
\(923\) 34.6146 1.13935
\(924\) 0 0
\(925\) 7.83421 0.257587
\(926\) −0.473700 −0.0155668
\(927\) −4.18464 −0.137442
\(928\) 4.75205 0.155994
\(929\) −11.2288 −0.368404 −0.184202 0.982888i \(-0.558970\pi\)
−0.184202 + 0.982888i \(0.558970\pi\)
\(930\) −1.81079 −0.0593781
\(931\) 0 0
\(932\) 26.2438 0.859646
\(933\) −2.84702 −0.0932074
\(934\) 0.820475 0.0268468
\(935\) −91.2114 −2.98293
\(936\) −0.884395 −0.0289074
\(937\) 34.3993 1.12378 0.561888 0.827214i \(-0.310075\pi\)
0.561888 + 0.827214i \(0.310075\pi\)
\(938\) 0 0
\(939\) 7.97569 0.260277
\(940\) 58.8712 1.92017
\(941\) 28.0008 0.912801 0.456401 0.889774i \(-0.349138\pi\)
0.456401 + 0.889774i \(0.349138\pi\)
\(942\) −0.902947 −0.0294196
\(943\) 1.06746 0.0347613
\(944\) 55.8755 1.81859
\(945\) 0 0
\(946\) −1.66728 −0.0542081
\(947\) −1.50126 −0.0487845 −0.0243922 0.999702i \(-0.507765\pi\)
−0.0243922 + 0.999702i \(0.507765\pi\)
\(948\) −18.6060 −0.604296
\(949\) 16.4320 0.533406
\(950\) 0.565435 0.0183451
\(951\) −9.27505 −0.300764
\(952\) 0 0
\(953\) 26.3166 0.852479 0.426240 0.904610i \(-0.359838\pi\)
0.426240 + 0.904610i \(0.359838\pi\)
\(954\) −0.529913 −0.0171566
\(955\) −11.7516 −0.380271
\(956\) −48.2952 −1.56198
\(957\) 33.4028 1.07976
\(958\) 2.79024 0.0901486
\(959\) 0 0
\(960\) 20.9597 0.676471
\(961\) 79.0781 2.55091
\(962\) 0.849374 0.0273849
\(963\) 4.55230 0.146696
\(964\) −31.3815 −1.01073
\(965\) −12.4934 −0.402177
\(966\) 0 0
\(967\) −20.1209 −0.647045 −0.323523 0.946220i \(-0.604867\pi\)
−0.323523 + 0.946220i \(0.604867\pi\)
\(968\) 4.91932 0.158113
\(969\) 26.7565 0.859542
\(970\) −2.85222 −0.0915793
\(971\) −24.1292 −0.774341 −0.387171 0.922008i \(-0.626548\pi\)
−0.387171 + 0.922008i \(0.626548\pi\)
\(972\) −1.99577 −0.0640143
\(973\) 0 0
\(974\) 2.03190 0.0651063
\(975\) −6.94708 −0.222485
\(976\) −56.1959 −1.79879
\(977\) 29.1755 0.933408 0.466704 0.884414i \(-0.345441\pi\)
0.466704 + 0.884414i \(0.345441\pi\)
\(978\) 0.0625837 0.00200121
\(979\) −47.1961 −1.50839
\(980\) 0 0
\(981\) −9.25158 −0.295380
\(982\) −2.56242 −0.0817702
\(983\) −7.77819 −0.248086 −0.124043 0.992277i \(-0.539586\pi\)
−0.124043 + 0.992277i \(0.539586\pi\)
\(984\) −0.259888 −0.00828492
\(985\) −68.8184 −2.19274
\(986\) −2.49517 −0.0794624
\(987\) 0 0
\(988\) −28.9218 −0.920125
\(989\) 5.00187 0.159050
\(990\) −0.944192 −0.0300084
\(991\) −24.9735 −0.793310 −0.396655 0.917968i \(-0.629829\pi\)
−0.396655 + 0.917968i \(0.629829\pi\)
\(992\) 8.16566 0.259260
\(993\) 14.6322 0.464338
\(994\) 0 0
\(995\) 39.6403 1.25668
\(996\) 10.0492 0.318420
\(997\) −38.1977 −1.20973 −0.604866 0.796327i \(-0.706773\pi\)
−0.604866 + 0.796327i \(0.706773\pi\)
\(998\) −0.749106 −0.0237125
\(999\) 3.83754 0.121414
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 \(a_p\))