Properties

Label 6027.2.a.bm.1.7
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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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: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.04648\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.04648 q^{2} +1.00000 q^{3} -0.904885 q^{4} +1.81328 q^{5} -1.04648 q^{6} +3.03990 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.04648 q^{2} +1.00000 q^{3} -0.904885 q^{4} +1.81328 q^{5} -1.04648 q^{6} +3.03990 q^{8} +1.00000 q^{9} -1.89755 q^{10} -0.445995 q^{11} -0.904885 q^{12} -2.67032 q^{13} +1.81328 q^{15} -1.37141 q^{16} +2.86907 q^{17} -1.04648 q^{18} -4.73993 q^{19} -1.64081 q^{20} +0.466723 q^{22} +3.59833 q^{23} +3.03990 q^{24} -1.71203 q^{25} +2.79443 q^{26} +1.00000 q^{27} -4.22128 q^{29} -1.89755 q^{30} +6.94583 q^{31} -4.64464 q^{32} -0.445995 q^{33} -3.00242 q^{34} -0.904885 q^{36} -9.17863 q^{37} +4.96023 q^{38} -2.67032 q^{39} +5.51217 q^{40} +1.00000 q^{41} -7.79959 q^{43} +0.403574 q^{44} +1.81328 q^{45} -3.76557 q^{46} -11.4891 q^{47} -1.37141 q^{48} +1.79160 q^{50} +2.86907 q^{51} +2.41633 q^{52} +10.4400 q^{53} -1.04648 q^{54} -0.808712 q^{55} -4.73993 q^{57} +4.41747 q^{58} +5.38717 q^{59} -1.64081 q^{60} -7.26684 q^{61} -7.26865 q^{62} +7.60334 q^{64} -4.84203 q^{65} +0.466723 q^{66} -14.2182 q^{67} -2.59618 q^{68} +3.59833 q^{69} +15.4800 q^{71} +3.03990 q^{72} -12.6484 q^{73} +9.60523 q^{74} -1.71203 q^{75} +4.28909 q^{76} +2.79443 q^{78} +5.02198 q^{79} -2.48675 q^{80} +1.00000 q^{81} -1.04648 q^{82} -7.60824 q^{83} +5.20242 q^{85} +8.16210 q^{86} -4.22128 q^{87} -1.35578 q^{88} +2.20300 q^{89} -1.89755 q^{90} -3.25607 q^{92} +6.94583 q^{93} +12.0230 q^{94} -8.59480 q^{95} -4.64464 q^{96} +1.75062 q^{97} -0.445995 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04648 −0.739971 −0.369986 0.929037i \(-0.620637\pi\)
−0.369986 + 0.929037i \(0.620637\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.904885 −0.452442
\(5\) 1.81328 0.810922 0.405461 0.914112i \(-0.367111\pi\)
0.405461 + 0.914112i \(0.367111\pi\)
\(6\) −1.04648 −0.427223
\(7\) 0 0
\(8\) 3.03990 1.07477
\(9\) 1.00000 0.333333
\(10\) −1.89755 −0.600059
\(11\) −0.445995 −0.134472 −0.0672362 0.997737i \(-0.521418\pi\)
−0.0672362 + 0.997737i \(0.521418\pi\)
\(12\) −0.904885 −0.261218
\(13\) −2.67032 −0.740613 −0.370307 0.928910i \(-0.620747\pi\)
−0.370307 + 0.928910i \(0.620747\pi\)
\(14\) 0 0
\(15\) 1.81328 0.468186
\(16\) −1.37141 −0.342854
\(17\) 2.86907 0.695853 0.347926 0.937522i \(-0.386886\pi\)
0.347926 + 0.937522i \(0.386886\pi\)
\(18\) −1.04648 −0.246657
\(19\) −4.73993 −1.08741 −0.543707 0.839275i \(-0.682980\pi\)
−0.543707 + 0.839275i \(0.682980\pi\)
\(20\) −1.64081 −0.366895
\(21\) 0 0
\(22\) 0.466723 0.0995058
\(23\) 3.59833 0.750303 0.375152 0.926963i \(-0.377591\pi\)
0.375152 + 0.926963i \(0.377591\pi\)
\(24\) 3.03990 0.620516
\(25\) −1.71203 −0.342406
\(26\) 2.79443 0.548033
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.22128 −0.783871 −0.391936 0.919993i \(-0.628194\pi\)
−0.391936 + 0.919993i \(0.628194\pi\)
\(30\) −1.89755 −0.346444
\(31\) 6.94583 1.24751 0.623754 0.781621i \(-0.285607\pi\)
0.623754 + 0.781621i \(0.285607\pi\)
\(32\) −4.64464 −0.821064
\(33\) −0.445995 −0.0776377
\(34\) −3.00242 −0.514911
\(35\) 0 0
\(36\) −0.904885 −0.150814
\(37\) −9.17863 −1.50896 −0.754479 0.656324i \(-0.772110\pi\)
−0.754479 + 0.656324i \(0.772110\pi\)
\(38\) 4.96023 0.804656
\(39\) −2.67032 −0.427593
\(40\) 5.51217 0.871551
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −7.79959 −1.18943 −0.594713 0.803938i \(-0.702735\pi\)
−0.594713 + 0.803938i \(0.702735\pi\)
\(44\) 0.403574 0.0608410
\(45\) 1.81328 0.270307
\(46\) −3.76557 −0.555203
\(47\) −11.4891 −1.67585 −0.837926 0.545783i \(-0.816232\pi\)
−0.837926 + 0.545783i \(0.816232\pi\)
\(48\) −1.37141 −0.197947
\(49\) 0 0
\(50\) 1.79160 0.253370
\(51\) 2.86907 0.401751
\(52\) 2.41633 0.335085
\(53\) 10.4400 1.43405 0.717025 0.697048i \(-0.245503\pi\)
0.717025 + 0.697048i \(0.245503\pi\)
\(54\) −1.04648 −0.142408
\(55\) −0.808712 −0.109047
\(56\) 0 0
\(57\) −4.73993 −0.627819
\(58\) 4.41747 0.580042
\(59\) 5.38717 0.701350 0.350675 0.936497i \(-0.385952\pi\)
0.350675 + 0.936497i \(0.385952\pi\)
\(60\) −1.64081 −0.211827
\(61\) −7.26684 −0.930423 −0.465212 0.885199i \(-0.654022\pi\)
−0.465212 + 0.885199i \(0.654022\pi\)
\(62\) −7.26865 −0.923120
\(63\) 0 0
\(64\) 7.60334 0.950417
\(65\) −4.84203 −0.600580
\(66\) 0.466723 0.0574497
\(67\) −14.2182 −1.73702 −0.868512 0.495668i \(-0.834923\pi\)
−0.868512 + 0.495668i \(0.834923\pi\)
\(68\) −2.59618 −0.314833
\(69\) 3.59833 0.433188
\(70\) 0 0
\(71\) 15.4800 1.83713 0.918567 0.395265i \(-0.129347\pi\)
0.918567 + 0.395265i \(0.129347\pi\)
\(72\) 3.03990 0.358255
\(73\) −12.6484 −1.48038 −0.740192 0.672396i \(-0.765265\pi\)
−0.740192 + 0.672396i \(0.765265\pi\)
\(74\) 9.60523 1.11659
\(75\) −1.71203 −0.197688
\(76\) 4.28909 0.491992
\(77\) 0 0
\(78\) 2.79443 0.316407
\(79\) 5.02198 0.565017 0.282508 0.959265i \(-0.408834\pi\)
0.282508 + 0.959265i \(0.408834\pi\)
\(80\) −2.48675 −0.278027
\(81\) 1.00000 0.111111
\(82\) −1.04648 −0.115564
\(83\) −7.60824 −0.835113 −0.417557 0.908651i \(-0.637113\pi\)
−0.417557 + 0.908651i \(0.637113\pi\)
\(84\) 0 0
\(85\) 5.20242 0.564282
\(86\) 8.16210 0.880142
\(87\) −4.22128 −0.452568
\(88\) −1.35578 −0.144526
\(89\) 2.20300 0.233518 0.116759 0.993160i \(-0.462750\pi\)
0.116759 + 0.993160i \(0.462750\pi\)
\(90\) −1.89755 −0.200020
\(91\) 0 0
\(92\) −3.25607 −0.339469
\(93\) 6.94583 0.720249
\(94\) 12.0230 1.24008
\(95\) −8.59480 −0.881808
\(96\) −4.64464 −0.474042
\(97\) 1.75062 0.177748 0.0888742 0.996043i \(-0.471673\pi\)
0.0888742 + 0.996043i \(0.471673\pi\)
\(98\) 0 0
\(99\) −0.445995 −0.0448242
\(100\) 1.54919 0.154919
\(101\) −10.0727 −1.00227 −0.501134 0.865370i \(-0.667084\pi\)
−0.501134 + 0.865370i \(0.667084\pi\)
\(102\) −3.00242 −0.297284
\(103\) −15.6394 −1.54099 −0.770496 0.637445i \(-0.779991\pi\)
−0.770496 + 0.637445i \(0.779991\pi\)
\(104\) −8.11749 −0.795986
\(105\) 0 0
\(106\) −10.9253 −1.06116
\(107\) −11.1705 −1.07990 −0.539948 0.841699i \(-0.681556\pi\)
−0.539948 + 0.841699i \(0.681556\pi\)
\(108\) −0.904885 −0.0870726
\(109\) 14.9447 1.43145 0.715723 0.698384i \(-0.246097\pi\)
0.715723 + 0.698384i \(0.246097\pi\)
\(110\) 0.846299 0.0806914
\(111\) −9.17863 −0.871197
\(112\) 0 0
\(113\) 11.9484 1.12401 0.562007 0.827133i \(-0.310030\pi\)
0.562007 + 0.827133i \(0.310030\pi\)
\(114\) 4.96023 0.464568
\(115\) 6.52477 0.608437
\(116\) 3.81977 0.354657
\(117\) −2.67032 −0.246871
\(118\) −5.63755 −0.518979
\(119\) 0 0
\(120\) 5.51217 0.503190
\(121\) −10.8011 −0.981917
\(122\) 7.60458 0.688487
\(123\) 1.00000 0.0901670
\(124\) −6.28517 −0.564425
\(125\) −12.1708 −1.08859
\(126\) 0 0
\(127\) −4.63833 −0.411586 −0.205793 0.978596i \(-0.565977\pi\)
−0.205793 + 0.978596i \(0.565977\pi\)
\(128\) 1.33256 0.117782
\(129\) −7.79959 −0.686716
\(130\) 5.06707 0.444412
\(131\) 7.50200 0.655453 0.327726 0.944773i \(-0.393718\pi\)
0.327726 + 0.944773i \(0.393718\pi\)
\(132\) 0.403574 0.0351266
\(133\) 0 0
\(134\) 14.8790 1.28535
\(135\) 1.81328 0.156062
\(136\) 8.72169 0.747879
\(137\) −18.9937 −1.62274 −0.811370 0.584533i \(-0.801278\pi\)
−0.811370 + 0.584533i \(0.801278\pi\)
\(138\) −3.76557 −0.320547
\(139\) 12.7746 1.08353 0.541766 0.840530i \(-0.317756\pi\)
0.541766 + 0.840530i \(0.317756\pi\)
\(140\) 0 0
\(141\) −11.4891 −0.967554
\(142\) −16.1994 −1.35943
\(143\) 1.19095 0.0995921
\(144\) −1.37141 −0.114285
\(145\) −7.65434 −0.635658
\(146\) 13.2363 1.09544
\(147\) 0 0
\(148\) 8.30561 0.682717
\(149\) −6.86535 −0.562431 −0.281216 0.959645i \(-0.590738\pi\)
−0.281216 + 0.959645i \(0.590738\pi\)
\(150\) 1.79160 0.146283
\(151\) −6.76282 −0.550351 −0.275175 0.961394i \(-0.588736\pi\)
−0.275175 + 0.961394i \(0.588736\pi\)
\(152\) −14.4089 −1.16872
\(153\) 2.86907 0.231951
\(154\) 0 0
\(155\) 12.5947 1.01163
\(156\) 2.41633 0.193461
\(157\) 3.74193 0.298639 0.149319 0.988789i \(-0.452292\pi\)
0.149319 + 0.988789i \(0.452292\pi\)
\(158\) −5.25539 −0.418096
\(159\) 10.4400 0.827949
\(160\) −8.42202 −0.665819
\(161\) 0 0
\(162\) −1.04648 −0.0822190
\(163\) −18.3200 −1.43494 −0.717468 0.696592i \(-0.754699\pi\)
−0.717468 + 0.696592i \(0.754699\pi\)
\(164\) −0.904885 −0.0706596
\(165\) −0.808712 −0.0629581
\(166\) 7.96186 0.617960
\(167\) 12.9443 1.00166 0.500829 0.865546i \(-0.333029\pi\)
0.500829 + 0.865546i \(0.333029\pi\)
\(168\) 0 0
\(169\) −5.86940 −0.451492
\(170\) −5.44422 −0.417553
\(171\) −4.73993 −0.362472
\(172\) 7.05773 0.538147
\(173\) 14.8684 1.13042 0.565212 0.824946i \(-0.308795\pi\)
0.565212 + 0.824946i \(0.308795\pi\)
\(174\) 4.41747 0.334888
\(175\) 0 0
\(176\) 0.611643 0.0461044
\(177\) 5.38717 0.404925
\(178\) −2.30539 −0.172796
\(179\) −0.390628 −0.0291969 −0.0145984 0.999893i \(-0.504647\pi\)
−0.0145984 + 0.999893i \(0.504647\pi\)
\(180\) −1.64081 −0.122298
\(181\) −1.88861 −0.140380 −0.0701898 0.997534i \(-0.522360\pi\)
−0.0701898 + 0.997534i \(0.522360\pi\)
\(182\) 0 0
\(183\) −7.26684 −0.537180
\(184\) 10.9385 0.806400
\(185\) −16.6434 −1.22365
\(186\) −7.26865 −0.532963
\(187\) −1.27959 −0.0935730
\(188\) 10.3963 0.758227
\(189\) 0 0
\(190\) 8.99427 0.652513
\(191\) −8.98328 −0.650007 −0.325004 0.945713i \(-0.605366\pi\)
−0.325004 + 0.945713i \(0.605366\pi\)
\(192\) 7.60334 0.548724
\(193\) 16.2969 1.17307 0.586537 0.809922i \(-0.300491\pi\)
0.586537 + 0.809922i \(0.300491\pi\)
\(194\) −1.83198 −0.131529
\(195\) −4.84203 −0.346745
\(196\) 0 0
\(197\) 18.0411 1.28538 0.642688 0.766128i \(-0.277819\pi\)
0.642688 + 0.766128i \(0.277819\pi\)
\(198\) 0.466723 0.0331686
\(199\) 3.32264 0.235535 0.117768 0.993041i \(-0.462426\pi\)
0.117768 + 0.993041i \(0.462426\pi\)
\(200\) −5.20439 −0.368006
\(201\) −14.2182 −1.00287
\(202\) 10.5408 0.741650
\(203\) 0 0
\(204\) −2.59618 −0.181769
\(205\) 1.81328 0.126645
\(206\) 16.3662 1.14029
\(207\) 3.59833 0.250101
\(208\) 3.66211 0.253922
\(209\) 2.11398 0.146227
\(210\) 0 0
\(211\) 18.3821 1.26547 0.632737 0.774367i \(-0.281932\pi\)
0.632737 + 0.774367i \(0.281932\pi\)
\(212\) −9.44703 −0.648825
\(213\) 15.4800 1.06067
\(214\) 11.6897 0.799092
\(215\) −14.1428 −0.964532
\(216\) 3.03990 0.206839
\(217\) 0 0
\(218\) −15.6393 −1.05923
\(219\) −12.6484 −0.854700
\(220\) 0.731791 0.0493373
\(221\) −7.66134 −0.515358
\(222\) 9.60523 0.644661
\(223\) −8.28572 −0.554853 −0.277427 0.960747i \(-0.589482\pi\)
−0.277427 + 0.960747i \(0.589482\pi\)
\(224\) 0 0
\(225\) −1.71203 −0.114135
\(226\) −12.5038 −0.831738
\(227\) −7.06231 −0.468742 −0.234371 0.972147i \(-0.575303\pi\)
−0.234371 + 0.972147i \(0.575303\pi\)
\(228\) 4.28909 0.284052
\(229\) −20.2997 −1.34144 −0.670720 0.741711i \(-0.734015\pi\)
−0.670720 + 0.741711i \(0.734015\pi\)
\(230\) −6.82802 −0.450226
\(231\) 0 0
\(232\) −12.8322 −0.842478
\(233\) 4.13151 0.270664 0.135332 0.990800i \(-0.456790\pi\)
0.135332 + 0.990800i \(0.456790\pi\)
\(234\) 2.79443 0.182678
\(235\) −20.8329 −1.35899
\(236\) −4.87477 −0.317320
\(237\) 5.02198 0.326213
\(238\) 0 0
\(239\) −5.65744 −0.365950 −0.182975 0.983118i \(-0.558573\pi\)
−0.182975 + 0.983118i \(0.558573\pi\)
\(240\) −2.48675 −0.160519
\(241\) 18.0436 1.16229 0.581145 0.813800i \(-0.302605\pi\)
0.581145 + 0.813800i \(0.302605\pi\)
\(242\) 11.3031 0.726591
\(243\) 1.00000 0.0641500
\(244\) 6.57565 0.420963
\(245\) 0 0
\(246\) −1.04648 −0.0667210
\(247\) 12.6571 0.805354
\(248\) 21.1146 1.34078
\(249\) −7.60824 −0.482153
\(250\) 12.7364 0.805523
\(251\) −16.5321 −1.04349 −0.521747 0.853100i \(-0.674720\pi\)
−0.521747 + 0.853100i \(0.674720\pi\)
\(252\) 0 0
\(253\) −1.60484 −0.100895
\(254\) 4.85391 0.304562
\(255\) 5.20242 0.325788
\(256\) −16.6012 −1.03757
\(257\) −27.2214 −1.69802 −0.849012 0.528373i \(-0.822802\pi\)
−0.849012 + 0.528373i \(0.822802\pi\)
\(258\) 8.16210 0.508150
\(259\) 0 0
\(260\) 4.38148 0.271728
\(261\) −4.22128 −0.261290
\(262\) −7.85067 −0.485016
\(263\) 0.195115 0.0120313 0.00601567 0.999982i \(-0.498085\pi\)
0.00601567 + 0.999982i \(0.498085\pi\)
\(264\) −1.35578 −0.0834424
\(265\) 18.9307 1.16290
\(266\) 0 0
\(267\) 2.20300 0.134822
\(268\) 12.8658 0.785904
\(269\) 23.1477 1.41134 0.705670 0.708541i \(-0.250646\pi\)
0.705670 + 0.708541i \(0.250646\pi\)
\(270\) −1.89755 −0.115481
\(271\) 6.82658 0.414685 0.207343 0.978268i \(-0.433519\pi\)
0.207343 + 0.978268i \(0.433519\pi\)
\(272\) −3.93469 −0.238575
\(273\) 0 0
\(274\) 19.8765 1.20078
\(275\) 0.763555 0.0460441
\(276\) −3.25607 −0.195993
\(277\) 27.7102 1.66495 0.832474 0.554065i \(-0.186924\pi\)
0.832474 + 0.554065i \(0.186924\pi\)
\(278\) −13.3684 −0.801782
\(279\) 6.94583 0.415836
\(280\) 0 0
\(281\) −3.97578 −0.237175 −0.118587 0.992944i \(-0.537837\pi\)
−0.118587 + 0.992944i \(0.537837\pi\)
\(282\) 12.0230 0.715962
\(283\) 12.5932 0.748590 0.374295 0.927310i \(-0.377885\pi\)
0.374295 + 0.927310i \(0.377885\pi\)
\(284\) −14.0076 −0.831197
\(285\) −8.59480 −0.509112
\(286\) −1.24630 −0.0736953
\(287\) 0 0
\(288\) −4.64464 −0.273688
\(289\) −8.76842 −0.515789
\(290\) 8.01010 0.470369
\(291\) 1.75062 0.102623
\(292\) 11.4453 0.669788
\(293\) −18.7975 −1.09816 −0.549081 0.835769i \(-0.685022\pi\)
−0.549081 + 0.835769i \(0.685022\pi\)
\(294\) 0 0
\(295\) 9.76843 0.568740
\(296\) −27.9021 −1.62178
\(297\) −0.445995 −0.0258792
\(298\) 7.18443 0.416183
\(299\) −9.60868 −0.555685
\(300\) 1.54919 0.0894424
\(301\) 0 0
\(302\) 7.07714 0.407244
\(303\) −10.0727 −0.578660
\(304\) 6.50041 0.372824
\(305\) −13.1768 −0.754501
\(306\) −3.00242 −0.171637
\(307\) 15.8413 0.904109 0.452055 0.891990i \(-0.350691\pi\)
0.452055 + 0.891990i \(0.350691\pi\)
\(308\) 0 0
\(309\) −15.6394 −0.889692
\(310\) −13.1801 −0.748578
\(311\) −22.9872 −1.30349 −0.651743 0.758439i \(-0.725962\pi\)
−0.651743 + 0.758439i \(0.725962\pi\)
\(312\) −8.11749 −0.459563
\(313\) 13.7375 0.776489 0.388244 0.921556i \(-0.373082\pi\)
0.388244 + 0.921556i \(0.373082\pi\)
\(314\) −3.91585 −0.220984
\(315\) 0 0
\(316\) −4.54431 −0.255638
\(317\) 2.04989 0.115133 0.0575666 0.998342i \(-0.481666\pi\)
0.0575666 + 0.998342i \(0.481666\pi\)
\(318\) −10.9253 −0.612658
\(319\) 1.88267 0.105409
\(320\) 13.7870 0.770714
\(321\) −11.1705 −0.623478
\(322\) 0 0
\(323\) −13.5992 −0.756680
\(324\) −0.904885 −0.0502714
\(325\) 4.57166 0.253590
\(326\) 19.1715 1.06181
\(327\) 14.9447 0.826446
\(328\) 3.03990 0.167850
\(329\) 0 0
\(330\) 0.846299 0.0465872
\(331\) −29.0301 −1.59564 −0.797819 0.602897i \(-0.794013\pi\)
−0.797819 + 0.602897i \(0.794013\pi\)
\(332\) 6.88458 0.377841
\(333\) −9.17863 −0.502986
\(334\) −13.5459 −0.741198
\(335\) −25.7815 −1.40859
\(336\) 0 0
\(337\) −23.8798 −1.30082 −0.650408 0.759585i \(-0.725402\pi\)
−0.650408 + 0.759585i \(0.725402\pi\)
\(338\) 6.14219 0.334091
\(339\) 11.9484 0.648949
\(340\) −4.70759 −0.255305
\(341\) −3.09780 −0.167755
\(342\) 4.96023 0.268219
\(343\) 0 0
\(344\) −23.7100 −1.27836
\(345\) 6.52477 0.351282
\(346\) −15.5594 −0.836481
\(347\) −6.57264 −0.352838 −0.176419 0.984315i \(-0.556451\pi\)
−0.176419 + 0.984315i \(0.556451\pi\)
\(348\) 3.81977 0.204761
\(349\) 9.91409 0.530689 0.265345 0.964154i \(-0.414514\pi\)
0.265345 + 0.964154i \(0.414514\pi\)
\(350\) 0 0
\(351\) −2.67032 −0.142531
\(352\) 2.07148 0.110411
\(353\) 6.00923 0.319839 0.159920 0.987130i \(-0.448877\pi\)
0.159920 + 0.987130i \(0.448877\pi\)
\(354\) −5.63755 −0.299633
\(355\) 28.0695 1.48977
\(356\) −1.99346 −0.105653
\(357\) 0 0
\(358\) 0.408783 0.0216049
\(359\) 17.1440 0.904826 0.452413 0.891808i \(-0.350563\pi\)
0.452413 + 0.891808i \(0.350563\pi\)
\(360\) 5.51217 0.290517
\(361\) 3.46694 0.182470
\(362\) 1.97639 0.103877
\(363\) −10.8011 −0.566910
\(364\) 0 0
\(365\) −22.9351 −1.20048
\(366\) 7.60458 0.397498
\(367\) 0.197446 0.0103066 0.00515330 0.999987i \(-0.498360\pi\)
0.00515330 + 0.999987i \(0.498360\pi\)
\(368\) −4.93480 −0.257244
\(369\) 1.00000 0.0520579
\(370\) 17.4169 0.905464
\(371\) 0 0
\(372\) −6.28517 −0.325871
\(373\) −35.1529 −1.82015 −0.910074 0.414447i \(-0.863975\pi\)
−0.910074 + 0.414447i \(0.863975\pi\)
\(374\) 1.33906 0.0692414
\(375\) −12.1708 −0.628496
\(376\) −34.9256 −1.80115
\(377\) 11.2722 0.580545
\(378\) 0 0
\(379\) −32.5491 −1.67193 −0.835967 0.548779i \(-0.815093\pi\)
−0.835967 + 0.548779i \(0.815093\pi\)
\(380\) 7.77731 0.398967
\(381\) −4.63833 −0.237629
\(382\) 9.40080 0.480987
\(383\) 16.1072 0.823037 0.411519 0.911401i \(-0.364999\pi\)
0.411519 + 0.911401i \(0.364999\pi\)
\(384\) 1.33256 0.0680017
\(385\) 0 0
\(386\) −17.0543 −0.868041
\(387\) −7.79959 −0.396476
\(388\) −1.58411 −0.0804209
\(389\) −33.7726 −1.71234 −0.856168 0.516697i \(-0.827161\pi\)
−0.856168 + 0.516697i \(0.827161\pi\)
\(390\) 5.06707 0.256581
\(391\) 10.3239 0.522101
\(392\) 0 0
\(393\) 7.50200 0.378426
\(394\) −18.8796 −0.951141
\(395\) 9.10624 0.458184
\(396\) 0.403574 0.0202803
\(397\) −18.8905 −0.948087 −0.474044 0.880501i \(-0.657206\pi\)
−0.474044 + 0.880501i \(0.657206\pi\)
\(398\) −3.47706 −0.174289
\(399\) 0 0
\(400\) 2.34790 0.117395
\(401\) −15.2704 −0.762566 −0.381283 0.924458i \(-0.624518\pi\)
−0.381283 + 0.924458i \(0.624518\pi\)
\(402\) 14.8790 0.742096
\(403\) −18.5476 −0.923920
\(404\) 9.11461 0.453469
\(405\) 1.81328 0.0901024
\(406\) 0 0
\(407\) 4.09362 0.202913
\(408\) 8.72169 0.431788
\(409\) 32.9169 1.62764 0.813818 0.581119i \(-0.197385\pi\)
0.813818 + 0.581119i \(0.197385\pi\)
\(410\) −1.89755 −0.0937135
\(411\) −18.9937 −0.936889
\(412\) 14.1518 0.697210
\(413\) 0 0
\(414\) −3.76557 −0.185068
\(415\) −13.7958 −0.677212
\(416\) 12.4027 0.608091
\(417\) 12.7746 0.625577
\(418\) −2.21224 −0.108204
\(419\) −36.0486 −1.76109 −0.880544 0.473964i \(-0.842823\pi\)
−0.880544 + 0.473964i \(0.842823\pi\)
\(420\) 0 0
\(421\) −2.11308 −0.102985 −0.0514927 0.998673i \(-0.516398\pi\)
−0.0514927 + 0.998673i \(0.516398\pi\)
\(422\) −19.2364 −0.936414
\(423\) −11.4891 −0.558618
\(424\) 31.7366 1.54127
\(425\) −4.91193 −0.238264
\(426\) −16.1994 −0.784865
\(427\) 0 0
\(428\) 10.1080 0.488590
\(429\) 1.19095 0.0574995
\(430\) 14.8001 0.713726
\(431\) 25.2339 1.21547 0.607736 0.794139i \(-0.292078\pi\)
0.607736 + 0.794139i \(0.292078\pi\)
\(432\) −1.37141 −0.0659822
\(433\) 23.1074 1.11047 0.555235 0.831694i \(-0.312628\pi\)
0.555235 + 0.831694i \(0.312628\pi\)
\(434\) 0 0
\(435\) −7.65434 −0.366998
\(436\) −13.5233 −0.647647
\(437\) −17.0558 −0.815891
\(438\) 13.2363 0.632454
\(439\) 21.0733 1.00577 0.502887 0.864352i \(-0.332271\pi\)
0.502887 + 0.864352i \(0.332271\pi\)
\(440\) −2.45840 −0.117200
\(441\) 0 0
\(442\) 8.01742 0.381350
\(443\) 10.7771 0.512035 0.256017 0.966672i \(-0.417590\pi\)
0.256017 + 0.966672i \(0.417590\pi\)
\(444\) 8.30561 0.394167
\(445\) 3.99465 0.189365
\(446\) 8.67082 0.410575
\(447\) −6.86535 −0.324720
\(448\) 0 0
\(449\) −1.96438 −0.0927048 −0.0463524 0.998925i \(-0.514760\pi\)
−0.0463524 + 0.998925i \(0.514760\pi\)
\(450\) 1.79160 0.0844568
\(451\) −0.445995 −0.0210011
\(452\) −10.8119 −0.508551
\(453\) −6.76282 −0.317745
\(454\) 7.39055 0.346856
\(455\) 0 0
\(456\) −14.4089 −0.674758
\(457\) 10.4268 0.487744 0.243872 0.969807i \(-0.421582\pi\)
0.243872 + 0.969807i \(0.421582\pi\)
\(458\) 21.2431 0.992627
\(459\) 2.86907 0.133917
\(460\) −5.90416 −0.275283
\(461\) −28.1751 −1.31224 −0.656122 0.754655i \(-0.727804\pi\)
−0.656122 + 0.754655i \(0.727804\pi\)
\(462\) 0 0
\(463\) −5.96875 −0.277392 −0.138696 0.990335i \(-0.544291\pi\)
−0.138696 + 0.990335i \(0.544291\pi\)
\(464\) 5.78912 0.268753
\(465\) 12.5947 0.584065
\(466\) −4.32353 −0.200284
\(467\) −0.120608 −0.00558107 −0.00279053 0.999996i \(-0.500888\pi\)
−0.00279053 + 0.999996i \(0.500888\pi\)
\(468\) 2.41633 0.111695
\(469\) 0 0
\(470\) 21.8011 1.00561
\(471\) 3.74193 0.172419
\(472\) 16.3764 0.753787
\(473\) 3.47858 0.159945
\(474\) −5.25539 −0.241388
\(475\) 8.11489 0.372337
\(476\) 0 0
\(477\) 10.4400 0.478016
\(478\) 5.92039 0.270792
\(479\) −40.6769 −1.85858 −0.929288 0.369356i \(-0.879578\pi\)
−0.929288 + 0.369356i \(0.879578\pi\)
\(480\) −8.42202 −0.384411
\(481\) 24.5099 1.11755
\(482\) −18.8822 −0.860061
\(483\) 0 0
\(484\) 9.77374 0.444261
\(485\) 3.17436 0.144140
\(486\) −1.04648 −0.0474692
\(487\) −28.6842 −1.29981 −0.649903 0.760017i \(-0.725190\pi\)
−0.649903 + 0.760017i \(0.725190\pi\)
\(488\) −22.0904 −0.999987
\(489\) −18.3200 −0.828460
\(490\) 0 0
\(491\) 2.32175 0.104779 0.0523896 0.998627i \(-0.483316\pi\)
0.0523896 + 0.998627i \(0.483316\pi\)
\(492\) −0.904885 −0.0407954
\(493\) −12.1112 −0.545459
\(494\) −13.2454 −0.595939
\(495\) −0.808712 −0.0363489
\(496\) −9.52560 −0.427712
\(497\) 0 0
\(498\) 7.96186 0.356779
\(499\) 11.9822 0.536397 0.268198 0.963364i \(-0.413572\pi\)
0.268198 + 0.963364i \(0.413572\pi\)
\(500\) 11.0131 0.492523
\(501\) 12.9443 0.578307
\(502\) 17.3004 0.772156
\(503\) 8.06028 0.359390 0.179695 0.983722i \(-0.442489\pi\)
0.179695 + 0.983722i \(0.442489\pi\)
\(504\) 0 0
\(505\) −18.2645 −0.812762
\(506\) 1.67942 0.0746595
\(507\) −5.86940 −0.260669
\(508\) 4.19716 0.186219
\(509\) 10.8090 0.479101 0.239550 0.970884i \(-0.423000\pi\)
0.239550 + 0.970884i \(0.423000\pi\)
\(510\) −5.44422 −0.241074
\(511\) 0 0
\(512\) 14.7076 0.649992
\(513\) −4.73993 −0.209273
\(514\) 28.4866 1.25649
\(515\) −28.3585 −1.24962
\(516\) 7.05773 0.310699
\(517\) 5.12406 0.225356
\(518\) 0 0
\(519\) 14.8684 0.652650
\(520\) −14.7193 −0.645482
\(521\) −14.9072 −0.653095 −0.326547 0.945181i \(-0.605885\pi\)
−0.326547 + 0.945181i \(0.605885\pi\)
\(522\) 4.41747 0.193347
\(523\) −24.1148 −1.05447 −0.527233 0.849721i \(-0.676770\pi\)
−0.527233 + 0.849721i \(0.676770\pi\)
\(524\) −6.78844 −0.296554
\(525\) 0 0
\(526\) −0.204184 −0.00890284
\(527\) 19.9281 0.868081
\(528\) 0.611643 0.0266184
\(529\) −10.0520 −0.437045
\(530\) −19.8105 −0.860514
\(531\) 5.38717 0.233783
\(532\) 0 0
\(533\) −2.67032 −0.115664
\(534\) −2.30539 −0.0997641
\(535\) −20.2553 −0.875711
\(536\) −43.2217 −1.86689
\(537\) −0.390628 −0.0168568
\(538\) −24.2235 −1.04435
\(539\) 0 0
\(540\) −1.64081 −0.0706091
\(541\) −21.2142 −0.912072 −0.456036 0.889961i \(-0.650731\pi\)
−0.456036 + 0.889961i \(0.650731\pi\)
\(542\) −7.14386 −0.306855
\(543\) −1.88861 −0.0810482
\(544\) −13.3258 −0.571339
\(545\) 27.0989 1.16079
\(546\) 0 0
\(547\) −5.39628 −0.230728 −0.115364 0.993323i \(-0.536803\pi\)
−0.115364 + 0.993323i \(0.536803\pi\)
\(548\) 17.1871 0.734196
\(549\) −7.26684 −0.310141
\(550\) −0.799044 −0.0340713
\(551\) 20.0086 0.852393
\(552\) 10.9385 0.465575
\(553\) 0 0
\(554\) −28.9981 −1.23201
\(555\) −16.6434 −0.706473
\(556\) −11.5596 −0.490236
\(557\) −42.9811 −1.82117 −0.910584 0.413324i \(-0.864368\pi\)
−0.910584 + 0.413324i \(0.864368\pi\)
\(558\) −7.26865 −0.307707
\(559\) 20.8274 0.880905
\(560\) 0 0
\(561\) −1.27959 −0.0540244
\(562\) 4.16056 0.175503
\(563\) 43.8925 1.84985 0.924924 0.380153i \(-0.124129\pi\)
0.924924 + 0.380153i \(0.124129\pi\)
\(564\) 10.3963 0.437762
\(565\) 21.6658 0.911487
\(566\) −13.1785 −0.553935
\(567\) 0 0
\(568\) 47.0575 1.97449
\(569\) −10.8598 −0.455267 −0.227634 0.973747i \(-0.573099\pi\)
−0.227634 + 0.973747i \(0.573099\pi\)
\(570\) 8.99427 0.376728
\(571\) 14.8272 0.620498 0.310249 0.950655i \(-0.399588\pi\)
0.310249 + 0.950655i \(0.399588\pi\)
\(572\) −1.07767 −0.0450597
\(573\) −8.98328 −0.375282
\(574\) 0 0
\(575\) −6.16044 −0.256908
\(576\) 7.60334 0.316806
\(577\) −17.5161 −0.729204 −0.364602 0.931164i \(-0.618795\pi\)
−0.364602 + 0.931164i \(0.618795\pi\)
\(578\) 9.17595 0.381669
\(579\) 16.2969 0.677275
\(580\) 6.92630 0.287599
\(581\) 0 0
\(582\) −1.83198 −0.0759381
\(583\) −4.65620 −0.192840
\(584\) −38.4498 −1.59107
\(585\) −4.84203 −0.200193
\(586\) 19.6712 0.812608
\(587\) 17.4318 0.719488 0.359744 0.933051i \(-0.382864\pi\)
0.359744 + 0.933051i \(0.382864\pi\)
\(588\) 0 0
\(589\) −32.9227 −1.35656
\(590\) −10.2224 −0.420851
\(591\) 18.0411 0.742112
\(592\) 12.5877 0.517352
\(593\) −33.0499 −1.35720 −0.678598 0.734510i \(-0.737412\pi\)
−0.678598 + 0.734510i \(0.737412\pi\)
\(594\) 0.466723 0.0191499
\(595\) 0 0
\(596\) 6.21235 0.254468
\(597\) 3.32264 0.135986
\(598\) 10.0553 0.411191
\(599\) 47.6320 1.94619 0.973095 0.230405i \(-0.0740052\pi\)
0.973095 + 0.230405i \(0.0740052\pi\)
\(600\) −5.20439 −0.212468
\(601\) −14.1223 −0.576060 −0.288030 0.957621i \(-0.593000\pi\)
−0.288030 + 0.957621i \(0.593000\pi\)
\(602\) 0 0
\(603\) −14.2182 −0.579008
\(604\) 6.11957 0.249002
\(605\) −19.5854 −0.796258
\(606\) 10.5408 0.428192
\(607\) 25.8046 1.04738 0.523688 0.851910i \(-0.324556\pi\)
0.523688 + 0.851910i \(0.324556\pi\)
\(608\) 22.0153 0.892837
\(609\) 0 0
\(610\) 13.7892 0.558309
\(611\) 30.6795 1.24116
\(612\) −2.59618 −0.104944
\(613\) −7.36270 −0.297377 −0.148688 0.988884i \(-0.547505\pi\)
−0.148688 + 0.988884i \(0.547505\pi\)
\(614\) −16.5775 −0.669015
\(615\) 1.81328 0.0731184
\(616\) 0 0
\(617\) −42.7294 −1.72022 −0.860110 0.510109i \(-0.829605\pi\)
−0.860110 + 0.510109i \(0.829605\pi\)
\(618\) 16.3662 0.658347
\(619\) −9.25040 −0.371805 −0.185902 0.982568i \(-0.559521\pi\)
−0.185902 + 0.982568i \(0.559521\pi\)
\(620\) −11.3968 −0.457705
\(621\) 3.59833 0.144396
\(622\) 24.0556 0.964543
\(623\) 0 0
\(624\) 3.66211 0.146602
\(625\) −13.5088 −0.540353
\(626\) −14.3760 −0.574580
\(627\) 2.11398 0.0844244
\(628\) −3.38602 −0.135117
\(629\) −26.3342 −1.05001
\(630\) 0 0
\(631\) −2.08724 −0.0830918 −0.0415459 0.999137i \(-0.513228\pi\)
−0.0415459 + 0.999137i \(0.513228\pi\)
\(632\) 15.2663 0.607261
\(633\) 18.3821 0.730621
\(634\) −2.14516 −0.0851953
\(635\) −8.41058 −0.333764
\(636\) −9.44703 −0.374599
\(637\) 0 0
\(638\) −1.97017 −0.0779997
\(639\) 15.4800 0.612378
\(640\) 2.41629 0.0955123
\(641\) 8.30068 0.327857 0.163929 0.986472i \(-0.447583\pi\)
0.163929 + 0.986472i \(0.447583\pi\)
\(642\) 11.6897 0.461356
\(643\) −39.5985 −1.56161 −0.780807 0.624772i \(-0.785192\pi\)
−0.780807 + 0.624772i \(0.785192\pi\)
\(644\) 0 0
\(645\) −14.1428 −0.556873
\(646\) 14.2313 0.559922
\(647\) 7.17653 0.282139 0.141069 0.990000i \(-0.454946\pi\)
0.141069 + 0.990000i \(0.454946\pi\)
\(648\) 3.03990 0.119418
\(649\) −2.40265 −0.0943123
\(650\) −4.78414 −0.187649
\(651\) 0 0
\(652\) 16.5775 0.649226
\(653\) −25.7808 −1.00888 −0.504440 0.863447i \(-0.668301\pi\)
−0.504440 + 0.863447i \(0.668301\pi\)
\(654\) −15.6393 −0.611546
\(655\) 13.6032 0.531521
\(656\) −1.37141 −0.0535447
\(657\) −12.6484 −0.493461
\(658\) 0 0
\(659\) 2.94995 0.114914 0.0574569 0.998348i \(-0.481701\pi\)
0.0574569 + 0.998348i \(0.481701\pi\)
\(660\) 0.731791 0.0284849
\(661\) 17.7965 0.692204 0.346102 0.938197i \(-0.387505\pi\)
0.346102 + 0.938197i \(0.387505\pi\)
\(662\) 30.3793 1.18073
\(663\) −7.66134 −0.297542
\(664\) −23.1283 −0.897551
\(665\) 0 0
\(666\) 9.60523 0.372195
\(667\) −15.1895 −0.588141
\(668\) −11.7131 −0.453193
\(669\) −8.28572 −0.320345
\(670\) 26.9797 1.04232
\(671\) 3.24097 0.125116
\(672\) 0 0
\(673\) 35.0368 1.35057 0.675285 0.737557i \(-0.264021\pi\)
0.675285 + 0.737557i \(0.264021\pi\)
\(674\) 24.9897 0.962567
\(675\) −1.71203 −0.0658960
\(676\) 5.31113 0.204274
\(677\) 32.5996 1.25291 0.626453 0.779459i \(-0.284506\pi\)
0.626453 + 0.779459i \(0.284506\pi\)
\(678\) −12.5038 −0.480204
\(679\) 0 0
\(680\) 15.8148 0.606471
\(681\) −7.06231 −0.270628
\(682\) 3.24178 0.124134
\(683\) −36.4205 −1.39359 −0.696796 0.717269i \(-0.745392\pi\)
−0.696796 + 0.717269i \(0.745392\pi\)
\(684\) 4.28909 0.163997
\(685\) −34.4408 −1.31592
\(686\) 0 0
\(687\) −20.2997 −0.774480
\(688\) 10.6965 0.407799
\(689\) −27.8782 −1.06208
\(690\) −6.82802 −0.259938
\(691\) 25.8214 0.982293 0.491147 0.871077i \(-0.336578\pi\)
0.491147 + 0.871077i \(0.336578\pi\)
\(692\) −13.4542 −0.511451
\(693\) 0 0
\(694\) 6.87812 0.261090
\(695\) 23.1640 0.878659
\(696\) −12.8322 −0.486405
\(697\) 2.86907 0.108674
\(698\) −10.3749 −0.392695
\(699\) 4.13151 0.156268
\(700\) 0 0
\(701\) −7.64248 −0.288653 −0.144326 0.989530i \(-0.546101\pi\)
−0.144326 + 0.989530i \(0.546101\pi\)
\(702\) 2.79443 0.105469
\(703\) 43.5061 1.64086
\(704\) −3.39105 −0.127805
\(705\) −20.8329 −0.784611
\(706\) −6.28853 −0.236672
\(707\) 0 0
\(708\) −4.87477 −0.183205
\(709\) −16.9791 −0.637664 −0.318832 0.947811i \(-0.603290\pi\)
−0.318832 + 0.947811i \(0.603290\pi\)
\(710\) −29.3741 −1.10239
\(711\) 5.02198 0.188339
\(712\) 6.69690 0.250977
\(713\) 24.9934 0.936009
\(714\) 0 0
\(715\) 2.15952 0.0807614
\(716\) 0.353473 0.0132099
\(717\) −5.65744 −0.211281
\(718\) −17.9408 −0.669545
\(719\) −1.92341 −0.0717310 −0.0358655 0.999357i \(-0.511419\pi\)
−0.0358655 + 0.999357i \(0.511419\pi\)
\(720\) −2.48675 −0.0926758
\(721\) 0 0
\(722\) −3.62807 −0.135023
\(723\) 18.0436 0.671049
\(724\) 1.70898 0.0635137
\(725\) 7.22694 0.268402
\(726\) 11.3031 0.419497
\(727\) −5.46716 −0.202766 −0.101383 0.994847i \(-0.532327\pi\)
−0.101383 + 0.994847i \(0.532327\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 24.0010 0.888318
\(731\) −22.3776 −0.827666
\(732\) 6.57565 0.243043
\(733\) 19.6346 0.725219 0.362609 0.931941i \(-0.381886\pi\)
0.362609 + 0.931941i \(0.381886\pi\)
\(734\) −0.206623 −0.00762659
\(735\) 0 0
\(736\) −16.7129 −0.616047
\(737\) 6.34122 0.233582
\(738\) −1.04648 −0.0385214
\(739\) 33.1279 1.21863 0.609315 0.792929i \(-0.291445\pi\)
0.609315 + 0.792929i \(0.291445\pi\)
\(740\) 15.0604 0.553630
\(741\) 12.6571 0.464971
\(742\) 0 0
\(743\) −14.1798 −0.520206 −0.260103 0.965581i \(-0.583756\pi\)
−0.260103 + 0.965581i \(0.583756\pi\)
\(744\) 21.1146 0.774099
\(745\) −12.4488 −0.456088
\(746\) 36.7867 1.34686
\(747\) −7.60824 −0.278371
\(748\) 1.15788 0.0423364
\(749\) 0 0
\(750\) 12.7364 0.465069
\(751\) −3.84986 −0.140483 −0.0702416 0.997530i \(-0.522377\pi\)
−0.0702416 + 0.997530i \(0.522377\pi\)
\(752\) 15.7563 0.574572
\(753\) −16.5321 −0.602462
\(754\) −11.7961 −0.429587
\(755\) −12.2629 −0.446291
\(756\) 0 0
\(757\) −45.9774 −1.67108 −0.835539 0.549432i \(-0.814844\pi\)
−0.835539 + 0.549432i \(0.814844\pi\)
\(758\) 34.0619 1.23718
\(759\) −1.60484 −0.0582518
\(760\) −26.1273 −0.947737
\(761\) 44.3346 1.60713 0.803564 0.595218i \(-0.202934\pi\)
0.803564 + 0.595218i \(0.202934\pi\)
\(762\) 4.85391 0.175839
\(763\) 0 0
\(764\) 8.12883 0.294091
\(765\) 5.20242 0.188094
\(766\) −16.8558 −0.609024
\(767\) −14.3855 −0.519429
\(768\) −16.6012 −0.599043
\(769\) −4.11151 −0.148265 −0.0741324 0.997248i \(-0.523619\pi\)
−0.0741324 + 0.997248i \(0.523619\pi\)
\(770\) 0 0
\(771\) −27.2214 −0.980355
\(772\) −14.7468 −0.530749
\(773\) −19.1489 −0.688737 −0.344369 0.938835i \(-0.611907\pi\)
−0.344369 + 0.938835i \(0.611907\pi\)
\(774\) 8.16210 0.293381
\(775\) −11.8914 −0.427153
\(776\) 5.32170 0.191038
\(777\) 0 0
\(778\) 35.3422 1.26708
\(779\) −4.73993 −0.169826
\(780\) 4.38148 0.156882
\(781\) −6.90398 −0.247044
\(782\) −10.8037 −0.386339
\(783\) −4.22128 −0.150856
\(784\) 0 0
\(785\) 6.78516 0.242173
\(786\) −7.85067 −0.280024
\(787\) −42.9937 −1.53256 −0.766280 0.642506i \(-0.777895\pi\)
−0.766280 + 0.642506i \(0.777895\pi\)
\(788\) −16.3251 −0.581558
\(789\) 0.195115 0.00694629
\(790\) −9.52947 −0.339043
\(791\) 0 0
\(792\) −1.35578 −0.0481755
\(793\) 19.4048 0.689084
\(794\) 19.7685 0.701557
\(795\) 18.9307 0.671402
\(796\) −3.00660 −0.106566
\(797\) 14.2882 0.506116 0.253058 0.967451i \(-0.418564\pi\)
0.253058 + 0.967451i \(0.418564\pi\)
\(798\) 0 0
\(799\) −32.9630 −1.16615
\(800\) 7.95175 0.281137
\(801\) 2.20300 0.0778392
\(802\) 15.9801 0.564277
\(803\) 5.64112 0.199071
\(804\) 12.8658 0.453742
\(805\) 0 0
\(806\) 19.4096 0.683675
\(807\) 23.1477 0.814837
\(808\) −30.6199 −1.07720
\(809\) −22.9124 −0.805555 −0.402778 0.915298i \(-0.631955\pi\)
−0.402778 + 0.915298i \(0.631955\pi\)
\(810\) −1.89755 −0.0666732
\(811\) 33.4405 1.17425 0.587127 0.809495i \(-0.300259\pi\)
0.587127 + 0.809495i \(0.300259\pi\)
\(812\) 0 0
\(813\) 6.82658 0.239419
\(814\) −4.28388 −0.150150
\(815\) −33.2193 −1.16362
\(816\) −3.93469 −0.137742
\(817\) 36.9695 1.29340
\(818\) −34.4468 −1.20440
\(819\) 0 0
\(820\) −1.64081 −0.0572994
\(821\) −19.3510 −0.675355 −0.337677 0.941262i \(-0.609641\pi\)
−0.337677 + 0.941262i \(0.609641\pi\)
\(822\) 19.8765 0.693271
\(823\) 14.9217 0.520139 0.260070 0.965590i \(-0.416255\pi\)
0.260070 + 0.965590i \(0.416255\pi\)
\(824\) −47.5420 −1.65621
\(825\) 0.763555 0.0265836
\(826\) 0 0
\(827\) −10.1637 −0.353425 −0.176713 0.984262i \(-0.556546\pi\)
−0.176713 + 0.984262i \(0.556546\pi\)
\(828\) −3.25607 −0.113156
\(829\) 7.08509 0.246075 0.123038 0.992402i \(-0.460736\pi\)
0.123038 + 0.992402i \(0.460736\pi\)
\(830\) 14.4370 0.501117
\(831\) 27.7102 0.961258
\(832\) −20.3033 −0.703892
\(833\) 0 0
\(834\) −13.3684 −0.462909
\(835\) 23.4715 0.812266
\(836\) −1.91291 −0.0661594
\(837\) 6.94583 0.240083
\(838\) 37.7240 1.30315
\(839\) 23.0788 0.796770 0.398385 0.917218i \(-0.369571\pi\)
0.398385 + 0.917218i \(0.369571\pi\)
\(840\) 0 0
\(841\) −11.1808 −0.385546
\(842\) 2.21129 0.0762062
\(843\) −3.97578 −0.136933
\(844\) −16.6337 −0.572554
\(845\) −10.6428 −0.366125
\(846\) 12.0230 0.413361
\(847\) 0 0
\(848\) −14.3176 −0.491669
\(849\) 12.5932 0.432199
\(850\) 5.14023 0.176308
\(851\) −33.0277 −1.13218
\(852\) −14.0076 −0.479892
\(853\) 55.1310 1.88765 0.943825 0.330446i \(-0.107199\pi\)
0.943825 + 0.330446i \(0.107199\pi\)
\(854\) 0 0
\(855\) −8.59480 −0.293936
\(856\) −33.9572 −1.16063
\(857\) 21.0816 0.720135 0.360068 0.932926i \(-0.382754\pi\)
0.360068 + 0.932926i \(0.382754\pi\)
\(858\) −1.24630 −0.0425480
\(859\) 35.7227 1.21884 0.609421 0.792847i \(-0.291402\pi\)
0.609421 + 0.792847i \(0.291402\pi\)
\(860\) 12.7976 0.436395
\(861\) 0 0
\(862\) −26.4067 −0.899415
\(863\) −41.9838 −1.42914 −0.714572 0.699562i \(-0.753378\pi\)
−0.714572 + 0.699562i \(0.753378\pi\)
\(864\) −4.64464 −0.158014
\(865\) 26.9605 0.916685
\(866\) −24.1814 −0.821716
\(867\) −8.76842 −0.297791
\(868\) 0 0
\(869\) −2.23978 −0.0759792
\(870\) 8.01010 0.271568
\(871\) 37.9670 1.28646
\(872\) 45.4304 1.53847
\(873\) 1.75062 0.0592495
\(874\) 17.8485 0.603736
\(875\) 0 0
\(876\) 11.4453 0.386703
\(877\) −54.7628 −1.84921 −0.924604 0.380931i \(-0.875604\pi\)
−0.924604 + 0.380931i \(0.875604\pi\)
\(878\) −22.0527 −0.744244
\(879\) −18.7975 −0.634024
\(880\) 1.10908 0.0373870
\(881\) −25.1750 −0.848166 −0.424083 0.905623i \(-0.639404\pi\)
−0.424083 + 0.905623i \(0.639404\pi\)
\(882\) 0 0
\(883\) 55.2757 1.86018 0.930088 0.367336i \(-0.119730\pi\)
0.930088 + 0.367336i \(0.119730\pi\)
\(884\) 6.93263 0.233170
\(885\) 9.76843 0.328362
\(886\) −11.2780 −0.378891
\(887\) 10.4173 0.349780 0.174890 0.984588i \(-0.444043\pi\)
0.174890 + 0.984588i \(0.444043\pi\)
\(888\) −27.9021 −0.936333
\(889\) 0 0
\(890\) −4.18031 −0.140124
\(891\) −0.445995 −0.0149414
\(892\) 7.49762 0.251039
\(893\) 54.4574 1.82235
\(894\) 7.18443 0.240283
\(895\) −0.708316 −0.0236764
\(896\) 0 0
\(897\) −9.60868 −0.320825
\(898\) 2.05568 0.0685989
\(899\) −29.3202 −0.977885
\(900\) 1.54919 0.0516396
\(901\) 29.9532 0.997887
\(902\) 0.466723 0.0155402
\(903\) 0 0
\(904\) 36.3220 1.20805
\(905\) −3.42458 −0.113837
\(906\) 7.07714 0.235122
\(907\) 10.0366 0.333258 0.166629 0.986020i \(-0.446712\pi\)
0.166629 + 0.986020i \(0.446712\pi\)
\(908\) 6.39058 0.212079
\(909\) −10.0727 −0.334089
\(910\) 0 0
\(911\) 17.5250 0.580628 0.290314 0.956931i \(-0.406240\pi\)
0.290314 + 0.956931i \(0.406240\pi\)
\(912\) 6.50041 0.215250
\(913\) 3.39324 0.112300
\(914\) −10.9114 −0.360917
\(915\) −13.1768 −0.435611
\(916\) 18.3689 0.606924
\(917\) 0 0
\(918\) −3.00242 −0.0990947
\(919\) −41.1561 −1.35761 −0.678807 0.734317i \(-0.737503\pi\)
−0.678807 + 0.734317i \(0.737503\pi\)
\(920\) 19.8346 0.653928
\(921\) 15.8413 0.521988
\(922\) 29.4846 0.971023
\(923\) −41.3365 −1.36061
\(924\) 0 0
\(925\) 15.7141 0.516676
\(926\) 6.24617 0.205262
\(927\) −15.6394 −0.513664
\(928\) 19.6063 0.643608
\(929\) −19.3546 −0.635002 −0.317501 0.948258i \(-0.602844\pi\)
−0.317501 + 0.948258i \(0.602844\pi\)
\(930\) −13.1801 −0.432192
\(931\) 0 0
\(932\) −3.73854 −0.122460
\(933\) −22.9872 −0.752569
\(934\) 0.126213 0.00412983
\(935\) −2.32025 −0.0758804
\(936\) −8.11749 −0.265329
\(937\) 16.6445 0.543753 0.271876 0.962332i \(-0.412356\pi\)
0.271876 + 0.962332i \(0.412356\pi\)
\(938\) 0 0
\(939\) 13.7375 0.448306
\(940\) 18.8513 0.614863
\(941\) −11.3034 −0.368480 −0.184240 0.982881i \(-0.558982\pi\)
−0.184240 + 0.982881i \(0.558982\pi\)
\(942\) −3.91585 −0.127585
\(943\) 3.59833 0.117178
\(944\) −7.38804 −0.240460
\(945\) 0 0
\(946\) −3.64025 −0.118355
\(947\) 4.08943 0.132889 0.0664443 0.997790i \(-0.478835\pi\)
0.0664443 + 0.997790i \(0.478835\pi\)
\(948\) −4.54431 −0.147592
\(949\) 33.7753 1.09639
\(950\) −8.49205 −0.275519
\(951\) 2.04989 0.0664722
\(952\) 0 0
\(953\) −14.0371 −0.454707 −0.227353 0.973812i \(-0.573007\pi\)
−0.227353 + 0.973812i \(0.573007\pi\)
\(954\) −10.9253 −0.353718
\(955\) −16.2892 −0.527105
\(956\) 5.11934 0.165571
\(957\) 1.88267 0.0608580
\(958\) 42.5675 1.37529
\(959\) 0 0
\(960\) 13.7870 0.444972
\(961\) 17.2445 0.556274
\(962\) −25.6490 −0.826958
\(963\) −11.1705 −0.359965
\(964\) −16.3274 −0.525869
\(965\) 29.5507 0.951272
\(966\) 0 0
\(967\) 43.1943 1.38904 0.694518 0.719475i \(-0.255618\pi\)
0.694518 + 0.719475i \(0.255618\pi\)
\(968\) −32.8342 −1.05533
\(969\) −13.5992 −0.436869
\(970\) −3.32189 −0.106660
\(971\) 34.2336 1.09861 0.549304 0.835623i \(-0.314893\pi\)
0.549304 + 0.835623i \(0.314893\pi\)
\(972\) −0.904885 −0.0290242
\(973\) 0 0
\(974\) 30.0174 0.961819
\(975\) 4.57166 0.146410
\(976\) 9.96585 0.318999
\(977\) −25.7841 −0.824908 −0.412454 0.910978i \(-0.635328\pi\)
−0.412454 + 0.910978i \(0.635328\pi\)
\(978\) 19.1715 0.613037
\(979\) −0.982527 −0.0314017
\(980\) 0 0
\(981\) 14.9447 0.477149
\(982\) −2.42966 −0.0775336
\(983\) 15.7033 0.500858 0.250429 0.968135i \(-0.419428\pi\)
0.250429 + 0.968135i \(0.419428\pi\)
\(984\) 3.03990 0.0969084
\(985\) 32.7135 1.04234
\(986\) 12.6740 0.403624
\(987\) 0 0
\(988\) −11.4532 −0.364376
\(989\) −28.0655 −0.892431
\(990\) 0.846299 0.0268971
\(991\) 47.9872 1.52436 0.762182 0.647363i \(-0.224128\pi\)
0.762182 + 0.647363i \(0.224128\pi\)
\(992\) −32.2609 −1.02428
\(993\) −29.0301 −0.921242
\(994\) 0 0
\(995\) 6.02486 0.191001
\(996\) 6.88458 0.218146
\(997\) −32.6743 −1.03481 −0.517403 0.855742i \(-0.673101\pi\)
−0.517403 + 0.855742i \(0.673101\pi\)
\(998\) −12.5391 −0.396918
\(999\) −9.17863 −0.290399
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 \(a_p\))