Properties

Label 6027.2.a.bo.1.19
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 1.19
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.26259 q^{2} +1.00000 q^{3} +3.11931 q^{4} +3.51535 q^{5} +2.26259 q^{6} +2.53253 q^{8} +1.00000 q^{9} +7.95379 q^{10} -3.79341 q^{11} +3.11931 q^{12} +1.46159 q^{13} +3.51535 q^{15} -0.508546 q^{16} +6.67693 q^{17} +2.26259 q^{18} -2.27770 q^{19} +10.9654 q^{20} -8.58292 q^{22} +8.49274 q^{23} +2.53253 q^{24} +7.35768 q^{25} +3.30698 q^{26} +1.00000 q^{27} -5.04769 q^{29} +7.95379 q^{30} -1.44795 q^{31} -6.21568 q^{32} -3.79341 q^{33} +15.1071 q^{34} +3.11931 q^{36} -0.996436 q^{37} -5.15350 q^{38} +1.46159 q^{39} +8.90272 q^{40} -1.00000 q^{41} +10.8446 q^{43} -11.8328 q^{44} +3.51535 q^{45} +19.2156 q^{46} -0.748913 q^{47} -0.508546 q^{48} +16.6474 q^{50} +6.67693 q^{51} +4.55916 q^{52} +9.47305 q^{53} +2.26259 q^{54} -13.3352 q^{55} -2.27770 q^{57} -11.4208 q^{58} -9.62699 q^{59} +10.9654 q^{60} -13.5721 q^{61} -3.27611 q^{62} -13.0464 q^{64} +5.13801 q^{65} -8.58292 q^{66} +8.40378 q^{67} +20.8274 q^{68} +8.49274 q^{69} -6.50992 q^{71} +2.53253 q^{72} -2.28092 q^{73} -2.25452 q^{74} +7.35768 q^{75} -7.10484 q^{76} +3.30698 q^{78} -1.03517 q^{79} -1.78772 q^{80} +1.00000 q^{81} -2.26259 q^{82} -1.84818 q^{83} +23.4718 q^{85} +24.5369 q^{86} -5.04769 q^{87} -9.60691 q^{88} -1.76420 q^{89} +7.95379 q^{90} +26.4914 q^{92} -1.44795 q^{93} -1.69448 q^{94} -8.00692 q^{95} -6.21568 q^{96} +17.4604 q^{97} -3.79341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.26259 1.59989 0.799946 0.600072i \(-0.204862\pi\)
0.799946 + 0.600072i \(0.204862\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.11931 1.55965
\(5\) 3.51535 1.57211 0.786056 0.618155i \(-0.212120\pi\)
0.786056 + 0.618155i \(0.212120\pi\)
\(6\) 2.26259 0.923698
\(7\) 0 0
\(8\) 2.53253 0.895383
\(9\) 1.00000 0.333333
\(10\) 7.95379 2.51521
\(11\) −3.79341 −1.14376 −0.571878 0.820339i \(-0.693785\pi\)
−0.571878 + 0.820339i \(0.693785\pi\)
\(12\) 3.11931 0.900466
\(13\) 1.46159 0.405373 0.202687 0.979244i \(-0.435033\pi\)
0.202687 + 0.979244i \(0.435033\pi\)
\(14\) 0 0
\(15\) 3.51535 0.907659
\(16\) −0.508546 −0.127136
\(17\) 6.67693 1.61939 0.809697 0.586848i \(-0.199631\pi\)
0.809697 + 0.586848i \(0.199631\pi\)
\(18\) 2.26259 0.533297
\(19\) −2.27770 −0.522540 −0.261270 0.965266i \(-0.584141\pi\)
−0.261270 + 0.965266i \(0.584141\pi\)
\(20\) 10.9654 2.45195
\(21\) 0 0
\(22\) −8.58292 −1.82988
\(23\) 8.49274 1.77086 0.885429 0.464774i \(-0.153864\pi\)
0.885429 + 0.464774i \(0.153864\pi\)
\(24\) 2.53253 0.516950
\(25\) 7.35768 1.47154
\(26\) 3.30698 0.648553
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.04769 −0.937332 −0.468666 0.883376i \(-0.655265\pi\)
−0.468666 + 0.883376i \(0.655265\pi\)
\(30\) 7.95379 1.45216
\(31\) −1.44795 −0.260059 −0.130029 0.991510i \(-0.541507\pi\)
−0.130029 + 0.991510i \(0.541507\pi\)
\(32\) −6.21568 −1.09879
\(33\) −3.79341 −0.660348
\(34\) 15.1071 2.59085
\(35\) 0 0
\(36\) 3.11931 0.519884
\(37\) −0.996436 −0.163813 −0.0819066 0.996640i \(-0.526101\pi\)
−0.0819066 + 0.996640i \(0.526101\pi\)
\(38\) −5.15350 −0.836008
\(39\) 1.46159 0.234042
\(40\) 8.90272 1.40764
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 10.8446 1.65379 0.826893 0.562359i \(-0.190106\pi\)
0.826893 + 0.562359i \(0.190106\pi\)
\(44\) −11.8328 −1.78386
\(45\) 3.51535 0.524037
\(46\) 19.2156 2.83318
\(47\) −0.748913 −0.109240 −0.0546201 0.998507i \(-0.517395\pi\)
−0.0546201 + 0.998507i \(0.517395\pi\)
\(48\) −0.508546 −0.0734023
\(49\) 0 0
\(50\) 16.6474 2.35430
\(51\) 6.67693 0.934958
\(52\) 4.55916 0.632241
\(53\) 9.47305 1.30122 0.650611 0.759411i \(-0.274513\pi\)
0.650611 + 0.759411i \(0.274513\pi\)
\(54\) 2.26259 0.307899
\(55\) −13.3352 −1.79811
\(56\) 0 0
\(57\) −2.27770 −0.301689
\(58\) −11.4208 −1.49963
\(59\) −9.62699 −1.25333 −0.626664 0.779290i \(-0.715580\pi\)
−0.626664 + 0.779290i \(0.715580\pi\)
\(60\) 10.9654 1.41563
\(61\) −13.5721 −1.73773 −0.868867 0.495046i \(-0.835151\pi\)
−0.868867 + 0.495046i \(0.835151\pi\)
\(62\) −3.27611 −0.416066
\(63\) 0 0
\(64\) −13.0464 −1.63080
\(65\) 5.13801 0.637292
\(66\) −8.58292 −1.05648
\(67\) 8.40378 1.02668 0.513342 0.858184i \(-0.328407\pi\)
0.513342 + 0.858184i \(0.328407\pi\)
\(68\) 20.8274 2.52569
\(69\) 8.49274 1.02241
\(70\) 0 0
\(71\) −6.50992 −0.772585 −0.386293 0.922376i \(-0.626245\pi\)
−0.386293 + 0.922376i \(0.626245\pi\)
\(72\) 2.53253 0.298461
\(73\) −2.28092 −0.266962 −0.133481 0.991051i \(-0.542615\pi\)
−0.133481 + 0.991051i \(0.542615\pi\)
\(74\) −2.25452 −0.262083
\(75\) 7.35768 0.849592
\(76\) −7.10484 −0.814982
\(77\) 0 0
\(78\) 3.30698 0.374442
\(79\) −1.03517 −0.116466 −0.0582331 0.998303i \(-0.518547\pi\)
−0.0582331 + 0.998303i \(0.518547\pi\)
\(80\) −1.78772 −0.199873
\(81\) 1.00000 0.111111
\(82\) −2.26259 −0.249861
\(83\) −1.84818 −0.202865 −0.101432 0.994842i \(-0.532343\pi\)
−0.101432 + 0.994842i \(0.532343\pi\)
\(84\) 0 0
\(85\) 23.4718 2.54587
\(86\) 24.5369 2.64588
\(87\) −5.04769 −0.541169
\(88\) −9.60691 −1.02410
\(89\) −1.76420 −0.187005 −0.0935023 0.995619i \(-0.529806\pi\)
−0.0935023 + 0.995619i \(0.529806\pi\)
\(90\) 7.95379 0.838403
\(91\) 0 0
\(92\) 26.4914 2.76192
\(93\) −1.44795 −0.150145
\(94\) −1.69448 −0.174773
\(95\) −8.00692 −0.821492
\(96\) −6.21568 −0.634385
\(97\) 17.4604 1.77284 0.886419 0.462883i \(-0.153185\pi\)
0.886419 + 0.462883i \(0.153185\pi\)
\(98\) 0 0
\(99\) −3.79341 −0.381252
\(100\) 22.9509 2.29509
\(101\) 19.4496 1.93531 0.967653 0.252287i \(-0.0811826\pi\)
0.967653 + 0.252287i \(0.0811826\pi\)
\(102\) 15.1071 1.49583
\(103\) −4.41489 −0.435012 −0.217506 0.976059i \(-0.569792\pi\)
−0.217506 + 0.976059i \(0.569792\pi\)
\(104\) 3.70152 0.362964
\(105\) 0 0
\(106\) 21.4336 2.08182
\(107\) −15.1587 −1.46544 −0.732721 0.680529i \(-0.761750\pi\)
−0.732721 + 0.680529i \(0.761750\pi\)
\(108\) 3.11931 0.300155
\(109\) −9.37929 −0.898374 −0.449187 0.893438i \(-0.648286\pi\)
−0.449187 + 0.893438i \(0.648286\pi\)
\(110\) −30.1720 −2.87678
\(111\) −0.996436 −0.0945775
\(112\) 0 0
\(113\) 1.40865 0.132515 0.0662574 0.997803i \(-0.478894\pi\)
0.0662574 + 0.997803i \(0.478894\pi\)
\(114\) −5.15350 −0.482669
\(115\) 29.8549 2.78399
\(116\) −15.7453 −1.46191
\(117\) 1.46159 0.135124
\(118\) −21.7819 −2.00519
\(119\) 0 0
\(120\) 8.90272 0.812703
\(121\) 3.38994 0.308177
\(122\) −30.7081 −2.78018
\(123\) −1.00000 −0.0901670
\(124\) −4.51659 −0.405601
\(125\) 8.28808 0.741309
\(126\) 0 0
\(127\) −2.83967 −0.251980 −0.125990 0.992032i \(-0.540211\pi\)
−0.125990 + 0.992032i \(0.540211\pi\)
\(128\) −17.0874 −1.51032
\(129\) 10.8446 0.954814
\(130\) 11.6252 1.01960
\(131\) −14.7028 −1.28459 −0.642295 0.766458i \(-0.722018\pi\)
−0.642295 + 0.766458i \(0.722018\pi\)
\(132\) −11.8328 −1.02991
\(133\) 0 0
\(134\) 19.0143 1.64258
\(135\) 3.51535 0.302553
\(136\) 16.9095 1.44998
\(137\) −9.39271 −0.802474 −0.401237 0.915974i \(-0.631420\pi\)
−0.401237 + 0.915974i \(0.631420\pi\)
\(138\) 19.2156 1.63574
\(139\) −11.1571 −0.946333 −0.473166 0.880973i \(-0.656889\pi\)
−0.473166 + 0.880973i \(0.656889\pi\)
\(140\) 0 0
\(141\) −0.748913 −0.0630699
\(142\) −14.7293 −1.23605
\(143\) −5.54442 −0.463648
\(144\) −0.508546 −0.0423788
\(145\) −17.7444 −1.47359
\(146\) −5.16078 −0.427109
\(147\) 0 0
\(148\) −3.10819 −0.255492
\(149\) 0.818797 0.0670785 0.0335392 0.999437i \(-0.489322\pi\)
0.0335392 + 0.999437i \(0.489322\pi\)
\(150\) 16.6474 1.35926
\(151\) 20.6578 1.68111 0.840554 0.541728i \(-0.182230\pi\)
0.840554 + 0.541728i \(0.182230\pi\)
\(152\) −5.76834 −0.467874
\(153\) 6.67693 0.539798
\(154\) 0 0
\(155\) −5.09004 −0.408842
\(156\) 4.55916 0.365025
\(157\) −3.57661 −0.285445 −0.142722 0.989763i \(-0.545586\pi\)
−0.142722 + 0.989763i \(0.545586\pi\)
\(158\) −2.34217 −0.186333
\(159\) 9.47305 0.751261
\(160\) −21.8503 −1.72742
\(161\) 0 0
\(162\) 2.26259 0.177766
\(163\) 12.6245 0.988830 0.494415 0.869226i \(-0.335382\pi\)
0.494415 + 0.869226i \(0.335382\pi\)
\(164\) −3.11931 −0.243577
\(165\) −13.3352 −1.03814
\(166\) −4.18168 −0.324561
\(167\) 4.48125 0.346770 0.173385 0.984854i \(-0.444530\pi\)
0.173385 + 0.984854i \(0.444530\pi\)
\(168\) 0 0
\(169\) −10.8637 −0.835673
\(170\) 53.1069 4.07311
\(171\) −2.27770 −0.174180
\(172\) 33.8276 2.57933
\(173\) −22.5618 −1.71534 −0.857670 0.514201i \(-0.828089\pi\)
−0.857670 + 0.514201i \(0.828089\pi\)
\(174\) −11.4208 −0.865811
\(175\) 0 0
\(176\) 1.92912 0.145413
\(177\) −9.62699 −0.723609
\(178\) −3.99165 −0.299187
\(179\) 14.9892 1.12035 0.560173 0.828375i \(-0.310735\pi\)
0.560173 + 0.828375i \(0.310735\pi\)
\(180\) 10.9654 0.817316
\(181\) 1.00879 0.0749830 0.0374915 0.999297i \(-0.488063\pi\)
0.0374915 + 0.999297i \(0.488063\pi\)
\(182\) 0 0
\(183\) −13.5721 −1.00328
\(184\) 21.5081 1.58560
\(185\) −3.50282 −0.257533
\(186\) −3.27611 −0.240216
\(187\) −25.3283 −1.85219
\(188\) −2.33609 −0.170377
\(189\) 0 0
\(190\) −18.1164 −1.31430
\(191\) 20.0147 1.44821 0.724106 0.689689i \(-0.242253\pi\)
0.724106 + 0.689689i \(0.242253\pi\)
\(192\) −13.0464 −0.941546
\(193\) 3.47028 0.249796 0.124898 0.992170i \(-0.460140\pi\)
0.124898 + 0.992170i \(0.460140\pi\)
\(194\) 39.5058 2.83635
\(195\) 5.13801 0.367941
\(196\) 0 0
\(197\) 11.6030 0.826681 0.413340 0.910577i \(-0.364362\pi\)
0.413340 + 0.910577i \(0.364362\pi\)
\(198\) −8.58292 −0.609962
\(199\) −7.82824 −0.554929 −0.277464 0.960736i \(-0.589494\pi\)
−0.277464 + 0.960736i \(0.589494\pi\)
\(200\) 18.6335 1.31759
\(201\) 8.40378 0.592757
\(202\) 44.0064 3.09628
\(203\) 0 0
\(204\) 20.8274 1.45821
\(205\) −3.51535 −0.245523
\(206\) −9.98908 −0.695972
\(207\) 8.49274 0.590286
\(208\) −0.743287 −0.0515377
\(209\) 8.64025 0.597659
\(210\) 0 0
\(211\) −0.767110 −0.0528100 −0.0264050 0.999651i \(-0.508406\pi\)
−0.0264050 + 0.999651i \(0.508406\pi\)
\(212\) 29.5493 2.02946
\(213\) −6.50992 −0.446052
\(214\) −34.2978 −2.34455
\(215\) 38.1226 2.59994
\(216\) 2.53253 0.172317
\(217\) 0 0
\(218\) −21.2215 −1.43730
\(219\) −2.28092 −0.154130
\(220\) −41.5964 −2.80443
\(221\) 9.75896 0.656459
\(222\) −2.25452 −0.151314
\(223\) −5.48934 −0.367594 −0.183797 0.982964i \(-0.558839\pi\)
−0.183797 + 0.982964i \(0.558839\pi\)
\(224\) 0 0
\(225\) 7.35768 0.490512
\(226\) 3.18720 0.212009
\(227\) −24.0590 −1.59685 −0.798426 0.602093i \(-0.794334\pi\)
−0.798426 + 0.602093i \(0.794334\pi\)
\(228\) −7.10484 −0.470530
\(229\) −10.3429 −0.683476 −0.341738 0.939795i \(-0.611015\pi\)
−0.341738 + 0.939795i \(0.611015\pi\)
\(230\) 67.5495 4.45408
\(231\) 0 0
\(232\) −12.7834 −0.839271
\(233\) −17.3807 −1.13865 −0.569325 0.822112i \(-0.692795\pi\)
−0.569325 + 0.822112i \(0.692795\pi\)
\(234\) 3.30698 0.216184
\(235\) −2.63269 −0.171738
\(236\) −30.0295 −1.95476
\(237\) −1.03517 −0.0672418
\(238\) 0 0
\(239\) −7.43783 −0.481113 −0.240557 0.970635i \(-0.577330\pi\)
−0.240557 + 0.970635i \(0.577330\pi\)
\(240\) −1.78772 −0.115397
\(241\) −7.82930 −0.504329 −0.252165 0.967684i \(-0.581142\pi\)
−0.252165 + 0.967684i \(0.581142\pi\)
\(242\) 7.67005 0.493049
\(243\) 1.00000 0.0641500
\(244\) −42.3356 −2.71026
\(245\) 0 0
\(246\) −2.26259 −0.144257
\(247\) −3.32907 −0.211824
\(248\) −3.66696 −0.232852
\(249\) −1.84818 −0.117124
\(250\) 18.7525 1.18601
\(251\) −11.4230 −0.721012 −0.360506 0.932757i \(-0.617396\pi\)
−0.360506 + 0.932757i \(0.617396\pi\)
\(252\) 0 0
\(253\) −32.2164 −2.02543
\(254\) −6.42500 −0.403141
\(255\) 23.4718 1.46986
\(256\) −12.5688 −0.785548
\(257\) −14.8155 −0.924168 −0.462084 0.886836i \(-0.652898\pi\)
−0.462084 + 0.886836i \(0.652898\pi\)
\(258\) 24.5369 1.52760
\(259\) 0 0
\(260\) 16.0270 0.993954
\(261\) −5.04769 −0.312444
\(262\) −33.2664 −2.05520
\(263\) −21.3829 −1.31853 −0.659264 0.751912i \(-0.729132\pi\)
−0.659264 + 0.751912i \(0.729132\pi\)
\(264\) −9.60691 −0.591264
\(265\) 33.3011 2.04567
\(266\) 0 0
\(267\) −1.76420 −0.107967
\(268\) 26.2139 1.60127
\(269\) 29.0758 1.77278 0.886391 0.462937i \(-0.153204\pi\)
0.886391 + 0.462937i \(0.153204\pi\)
\(270\) 7.95379 0.484052
\(271\) −21.8299 −1.32607 −0.663035 0.748588i \(-0.730732\pi\)
−0.663035 + 0.748588i \(0.730732\pi\)
\(272\) −3.39553 −0.205884
\(273\) 0 0
\(274\) −21.2518 −1.28387
\(275\) −27.9107 −1.68308
\(276\) 26.4914 1.59460
\(277\) −26.3880 −1.58550 −0.792751 0.609546i \(-0.791352\pi\)
−0.792751 + 0.609546i \(0.791352\pi\)
\(278\) −25.2439 −1.51403
\(279\) −1.44795 −0.0866863
\(280\) 0 0
\(281\) 10.8668 0.648256 0.324128 0.946013i \(-0.394929\pi\)
0.324128 + 0.946013i \(0.394929\pi\)
\(282\) −1.69448 −0.100905
\(283\) −30.8486 −1.83376 −0.916879 0.399165i \(-0.869300\pi\)
−0.916879 + 0.399165i \(0.869300\pi\)
\(284\) −20.3064 −1.20496
\(285\) −8.00692 −0.474289
\(286\) −12.5447 −0.741786
\(287\) 0 0
\(288\) −6.21568 −0.366263
\(289\) 27.5814 1.62244
\(290\) −40.1482 −2.35759
\(291\) 17.4604 1.02355
\(292\) −7.11489 −0.416367
\(293\) 10.1999 0.595885 0.297942 0.954584i \(-0.403700\pi\)
0.297942 + 0.954584i \(0.403700\pi\)
\(294\) 0 0
\(295\) −33.8422 −1.97037
\(296\) −2.52350 −0.146676
\(297\) −3.79341 −0.220116
\(298\) 1.85260 0.107318
\(299\) 12.4129 0.717858
\(300\) 22.9509 1.32507
\(301\) 0 0
\(302\) 46.7401 2.68959
\(303\) 19.4496 1.11735
\(304\) 1.15832 0.0664340
\(305\) −47.7108 −2.73191
\(306\) 15.1071 0.863618
\(307\) 22.0097 1.25616 0.628081 0.778148i \(-0.283841\pi\)
0.628081 + 0.778148i \(0.283841\pi\)
\(308\) 0 0
\(309\) −4.41489 −0.251154
\(310\) −11.5167 −0.654102
\(311\) −0.628039 −0.0356128 −0.0178064 0.999841i \(-0.505668\pi\)
−0.0178064 + 0.999841i \(0.505668\pi\)
\(312\) 3.70152 0.209557
\(313\) 17.9356 1.01378 0.506891 0.862010i \(-0.330795\pi\)
0.506891 + 0.862010i \(0.330795\pi\)
\(314\) −8.09240 −0.456681
\(315\) 0 0
\(316\) −3.22902 −0.181647
\(317\) 15.2704 0.857668 0.428834 0.903383i \(-0.358924\pi\)
0.428834 + 0.903383i \(0.358924\pi\)
\(318\) 21.4336 1.20194
\(319\) 19.1479 1.07208
\(320\) −45.8628 −2.56381
\(321\) −15.1587 −0.846074
\(322\) 0 0
\(323\) −15.2081 −0.846199
\(324\) 3.11931 0.173295
\(325\) 10.7539 0.596521
\(326\) 28.5641 1.58202
\(327\) −9.37929 −0.518676
\(328\) −2.53253 −0.139835
\(329\) 0 0
\(330\) −30.1720 −1.66091
\(331\) 30.8713 1.69684 0.848421 0.529322i \(-0.177554\pi\)
0.848421 + 0.529322i \(0.177554\pi\)
\(332\) −5.76505 −0.316398
\(333\) −0.996436 −0.0546044
\(334\) 10.1392 0.554794
\(335\) 29.5422 1.61406
\(336\) 0 0
\(337\) −13.7318 −0.748017 −0.374008 0.927425i \(-0.622017\pi\)
−0.374008 + 0.927425i \(0.622017\pi\)
\(338\) −24.5802 −1.33699
\(339\) 1.40865 0.0765074
\(340\) 73.2156 3.97067
\(341\) 5.49265 0.297444
\(342\) −5.15350 −0.278669
\(343\) 0 0
\(344\) 27.4642 1.48077
\(345\) 29.8549 1.60734
\(346\) −51.0480 −2.74436
\(347\) −16.9673 −0.910854 −0.455427 0.890273i \(-0.650513\pi\)
−0.455427 + 0.890273i \(0.650513\pi\)
\(348\) −15.7453 −0.844035
\(349\) 5.94969 0.318479 0.159240 0.987240i \(-0.449096\pi\)
0.159240 + 0.987240i \(0.449096\pi\)
\(350\) 0 0
\(351\) 1.46159 0.0780141
\(352\) 23.5786 1.25674
\(353\) −5.44568 −0.289844 −0.144922 0.989443i \(-0.546293\pi\)
−0.144922 + 0.989443i \(0.546293\pi\)
\(354\) −21.7819 −1.15770
\(355\) −22.8846 −1.21459
\(356\) −5.50307 −0.291662
\(357\) 0 0
\(358\) 33.9144 1.79243
\(359\) −23.9295 −1.26295 −0.631476 0.775396i \(-0.717550\pi\)
−0.631476 + 0.775396i \(0.717550\pi\)
\(360\) 8.90272 0.469214
\(361\) −13.8121 −0.726951
\(362\) 2.28248 0.119965
\(363\) 3.38994 0.177926
\(364\) 0 0
\(365\) −8.01823 −0.419694
\(366\) −30.7081 −1.60514
\(367\) −3.62240 −0.189088 −0.0945438 0.995521i \(-0.530139\pi\)
−0.0945438 + 0.995521i \(0.530139\pi\)
\(368\) −4.31895 −0.225141
\(369\) −1.00000 −0.0520579
\(370\) −7.92544 −0.412024
\(371\) 0 0
\(372\) −4.51659 −0.234174
\(373\) 30.5324 1.58091 0.790455 0.612521i \(-0.209844\pi\)
0.790455 + 0.612521i \(0.209844\pi\)
\(374\) −57.3076 −2.96330
\(375\) 8.28808 0.427995
\(376\) −1.89664 −0.0978119
\(377\) −7.37766 −0.379969
\(378\) 0 0
\(379\) −14.5620 −0.748002 −0.374001 0.927428i \(-0.622014\pi\)
−0.374001 + 0.927428i \(0.622014\pi\)
\(380\) −24.9760 −1.28124
\(381\) −2.83967 −0.145481
\(382\) 45.2850 2.31698
\(383\) −4.84686 −0.247663 −0.123831 0.992303i \(-0.539518\pi\)
−0.123831 + 0.992303i \(0.539518\pi\)
\(384\) −17.0874 −0.871985
\(385\) 0 0
\(386\) 7.85181 0.399646
\(387\) 10.8446 0.551262
\(388\) 54.4644 2.76501
\(389\) −0.685686 −0.0347657 −0.0173828 0.999849i \(-0.505533\pi\)
−0.0173828 + 0.999849i \(0.505533\pi\)
\(390\) 11.6252 0.588665
\(391\) 56.7054 2.86772
\(392\) 0 0
\(393\) −14.7028 −0.741658
\(394\) 26.2529 1.32260
\(395\) −3.63900 −0.183098
\(396\) −11.8328 −0.594620
\(397\) 0.404290 0.0202907 0.0101454 0.999949i \(-0.496771\pi\)
0.0101454 + 0.999949i \(0.496771\pi\)
\(398\) −17.7121 −0.887826
\(399\) 0 0
\(400\) −3.74172 −0.187086
\(401\) −28.1364 −1.40506 −0.702532 0.711652i \(-0.747947\pi\)
−0.702532 + 0.711652i \(0.747947\pi\)
\(402\) 19.0143 0.948347
\(403\) −2.11631 −0.105421
\(404\) 60.6692 3.01840
\(405\) 3.51535 0.174679
\(406\) 0 0
\(407\) 3.77989 0.187362
\(408\) 16.9095 0.837145
\(409\) −16.9935 −0.840273 −0.420137 0.907461i \(-0.638018\pi\)
−0.420137 + 0.907461i \(0.638018\pi\)
\(410\) −7.95379 −0.392810
\(411\) −9.39271 −0.463308
\(412\) −13.7714 −0.678468
\(413\) 0 0
\(414\) 19.2156 0.944394
\(415\) −6.49702 −0.318926
\(416\) −9.08480 −0.445419
\(417\) −11.1571 −0.546366
\(418\) 19.5493 0.956189
\(419\) 10.1348 0.495116 0.247558 0.968873i \(-0.420372\pi\)
0.247558 + 0.968873i \(0.420372\pi\)
\(420\) 0 0
\(421\) 7.95651 0.387777 0.193888 0.981024i \(-0.437890\pi\)
0.193888 + 0.981024i \(0.437890\pi\)
\(422\) −1.73565 −0.0844903
\(423\) −0.748913 −0.0364134
\(424\) 23.9907 1.16509
\(425\) 49.1268 2.38300
\(426\) −14.7293 −0.713635
\(427\) 0 0
\(428\) −47.2845 −2.28558
\(429\) −5.54442 −0.267687
\(430\) 86.2557 4.15962
\(431\) −27.1478 −1.30766 −0.653832 0.756640i \(-0.726840\pi\)
−0.653832 + 0.756640i \(0.726840\pi\)
\(432\) −0.508546 −0.0244674
\(433\) 27.6879 1.33060 0.665298 0.746578i \(-0.268304\pi\)
0.665298 + 0.746578i \(0.268304\pi\)
\(434\) 0 0
\(435\) −17.7444 −0.850778
\(436\) −29.2569 −1.40115
\(437\) −19.3439 −0.925345
\(438\) −5.16078 −0.246592
\(439\) −8.75911 −0.418049 −0.209025 0.977910i \(-0.567029\pi\)
−0.209025 + 0.977910i \(0.567029\pi\)
\(440\) −33.7716 −1.61000
\(441\) 0 0
\(442\) 22.0805 1.05026
\(443\) −35.5985 −1.69133 −0.845667 0.533711i \(-0.820797\pi\)
−0.845667 + 0.533711i \(0.820797\pi\)
\(444\) −3.10819 −0.147508
\(445\) −6.20177 −0.293992
\(446\) −12.4201 −0.588110
\(447\) 0.818797 0.0387278
\(448\) 0 0
\(449\) 35.3648 1.66897 0.834484 0.551032i \(-0.185766\pi\)
0.834484 + 0.551032i \(0.185766\pi\)
\(450\) 16.6474 0.784766
\(451\) 3.79341 0.178625
\(452\) 4.39401 0.206677
\(453\) 20.6578 0.970588
\(454\) −54.4356 −2.55479
\(455\) 0 0
\(456\) −5.76834 −0.270127
\(457\) 19.7650 0.924570 0.462285 0.886731i \(-0.347030\pi\)
0.462285 + 0.886731i \(0.347030\pi\)
\(458\) −23.4016 −1.09349
\(459\) 6.67693 0.311653
\(460\) 93.1267 4.34205
\(461\) 10.7489 0.500626 0.250313 0.968165i \(-0.419466\pi\)
0.250313 + 0.968165i \(0.419466\pi\)
\(462\) 0 0
\(463\) 2.89539 0.134560 0.0672801 0.997734i \(-0.478568\pi\)
0.0672801 + 0.997734i \(0.478568\pi\)
\(464\) 2.56698 0.119169
\(465\) −5.09004 −0.236045
\(466\) −39.3255 −1.82172
\(467\) −5.98144 −0.276788 −0.138394 0.990377i \(-0.544194\pi\)
−0.138394 + 0.990377i \(0.544194\pi\)
\(468\) 4.55916 0.210747
\(469\) 0 0
\(470\) −5.95670 −0.274762
\(471\) −3.57661 −0.164802
\(472\) −24.3806 −1.12221
\(473\) −41.1380 −1.89153
\(474\) −2.34217 −0.107580
\(475\) −16.7586 −0.768937
\(476\) 0 0
\(477\) 9.47305 0.433741
\(478\) −16.8287 −0.769729
\(479\) −15.0728 −0.688693 −0.344346 0.938843i \(-0.611899\pi\)
−0.344346 + 0.938843i \(0.611899\pi\)
\(480\) −21.8503 −0.997325
\(481\) −1.45638 −0.0664054
\(482\) −17.7145 −0.806872
\(483\) 0 0
\(484\) 10.5743 0.480649
\(485\) 61.3795 2.78710
\(486\) 2.26259 0.102633
\(487\) −26.7979 −1.21433 −0.607165 0.794576i \(-0.707693\pi\)
−0.607165 + 0.794576i \(0.707693\pi\)
\(488\) −34.3718 −1.55594
\(489\) 12.6245 0.570901
\(490\) 0 0
\(491\) 14.6716 0.662120 0.331060 0.943610i \(-0.392594\pi\)
0.331060 + 0.943610i \(0.392594\pi\)
\(492\) −3.11931 −0.140629
\(493\) −33.7031 −1.51791
\(494\) −7.53232 −0.338895
\(495\) −13.3352 −0.599371
\(496\) 0.736347 0.0330630
\(497\) 0 0
\(498\) −4.18168 −0.187386
\(499\) 33.3116 1.49123 0.745616 0.666376i \(-0.232155\pi\)
0.745616 + 0.666376i \(0.232155\pi\)
\(500\) 25.8531 1.15618
\(501\) 4.48125 0.200208
\(502\) −25.8455 −1.15354
\(503\) −36.2073 −1.61440 −0.807201 0.590277i \(-0.799019\pi\)
−0.807201 + 0.590277i \(0.799019\pi\)
\(504\) 0 0
\(505\) 68.3721 3.04252
\(506\) −72.8925 −3.24047
\(507\) −10.8637 −0.482476
\(508\) −8.85780 −0.393001
\(509\) 17.9330 0.794867 0.397433 0.917631i \(-0.369901\pi\)
0.397433 + 0.917631i \(0.369901\pi\)
\(510\) 53.1069 2.35161
\(511\) 0 0
\(512\) 5.73677 0.253532
\(513\) −2.27770 −0.100563
\(514\) −33.5215 −1.47857
\(515\) −15.5199 −0.683888
\(516\) 33.8276 1.48918
\(517\) 2.84093 0.124944
\(518\) 0 0
\(519\) −22.5618 −0.990352
\(520\) 13.0121 0.570621
\(521\) 34.4137 1.50769 0.753846 0.657051i \(-0.228197\pi\)
0.753846 + 0.657051i \(0.228197\pi\)
\(522\) −11.4208 −0.499876
\(523\) 1.82322 0.0797237 0.0398618 0.999205i \(-0.487308\pi\)
0.0398618 + 0.999205i \(0.487308\pi\)
\(524\) −45.8625 −2.00351
\(525\) 0 0
\(526\) −48.3808 −2.10950
\(527\) −9.66784 −0.421138
\(528\) 1.92912 0.0839543
\(529\) 49.1266 2.13594
\(530\) 75.3466 3.27285
\(531\) −9.62699 −0.417776
\(532\) 0 0
\(533\) −1.46159 −0.0633086
\(534\) −3.99165 −0.172736
\(535\) −53.2880 −2.30384
\(536\) 21.2828 0.919277
\(537\) 14.9892 0.646832
\(538\) 65.7865 2.83626
\(539\) 0 0
\(540\) 10.9654 0.471878
\(541\) 31.9421 1.37330 0.686650 0.726988i \(-0.259080\pi\)
0.686650 + 0.726988i \(0.259080\pi\)
\(542\) −49.3920 −2.12157
\(543\) 1.00879 0.0432915
\(544\) −41.5017 −1.77937
\(545\) −32.9715 −1.41234
\(546\) 0 0
\(547\) −0.486837 −0.0208156 −0.0104078 0.999946i \(-0.503313\pi\)
−0.0104078 + 0.999946i \(0.503313\pi\)
\(548\) −29.2987 −1.25158
\(549\) −13.5721 −0.579244
\(550\) −63.1504 −2.69274
\(551\) 11.4971 0.489794
\(552\) 21.5081 0.915445
\(553\) 0 0
\(554\) −59.7052 −2.53663
\(555\) −3.50282 −0.148687
\(556\) −34.8024 −1.47595
\(557\) 22.0350 0.933653 0.466827 0.884349i \(-0.345397\pi\)
0.466827 + 0.884349i \(0.345397\pi\)
\(558\) −3.27611 −0.138689
\(559\) 15.8504 0.670400
\(560\) 0 0
\(561\) −25.3283 −1.06936
\(562\) 24.5870 1.03714
\(563\) 2.55811 0.107812 0.0539058 0.998546i \(-0.482833\pi\)
0.0539058 + 0.998546i \(0.482833\pi\)
\(564\) −2.33609 −0.0983671
\(565\) 4.95190 0.208328
\(566\) −69.7976 −2.93381
\(567\) 0 0
\(568\) −16.4865 −0.691760
\(569\) 31.6305 1.32602 0.663010 0.748610i \(-0.269279\pi\)
0.663010 + 0.748610i \(0.269279\pi\)
\(570\) −18.1164 −0.758810
\(571\) −34.5220 −1.44470 −0.722349 0.691528i \(-0.756938\pi\)
−0.722349 + 0.691528i \(0.756938\pi\)
\(572\) −17.2947 −0.723129
\(573\) 20.0147 0.836125
\(574\) 0 0
\(575\) 62.4869 2.60588
\(576\) −13.0464 −0.543602
\(577\) 41.9733 1.74737 0.873686 0.486491i \(-0.161723\pi\)
0.873686 + 0.486491i \(0.161723\pi\)
\(578\) 62.4054 2.59572
\(579\) 3.47028 0.144220
\(580\) −55.3501 −2.29829
\(581\) 0 0
\(582\) 39.5058 1.63757
\(583\) −35.9351 −1.48828
\(584\) −5.77649 −0.239033
\(585\) 5.13801 0.212431
\(586\) 23.0782 0.953351
\(587\) 27.5287 1.13623 0.568115 0.822949i \(-0.307673\pi\)
0.568115 + 0.822949i \(0.307673\pi\)
\(588\) 0 0
\(589\) 3.29799 0.135891
\(590\) −76.5710 −3.15238
\(591\) 11.6030 0.477284
\(592\) 0.506734 0.0208266
\(593\) −2.59633 −0.106618 −0.0533092 0.998578i \(-0.516977\pi\)
−0.0533092 + 0.998578i \(0.516977\pi\)
\(594\) −8.58292 −0.352161
\(595\) 0 0
\(596\) 2.55408 0.104619
\(597\) −7.82824 −0.320388
\(598\) 28.0853 1.14850
\(599\) −7.58409 −0.309878 −0.154939 0.987924i \(-0.549518\pi\)
−0.154939 + 0.987924i \(0.549518\pi\)
\(600\) 18.6335 0.760711
\(601\) −25.1438 −1.02564 −0.512818 0.858497i \(-0.671398\pi\)
−0.512818 + 0.858497i \(0.671398\pi\)
\(602\) 0 0
\(603\) 8.40378 0.342228
\(604\) 64.4380 2.62194
\(605\) 11.9168 0.484488
\(606\) 44.0064 1.78764
\(607\) 36.2667 1.47202 0.736011 0.676970i \(-0.236707\pi\)
0.736011 + 0.676970i \(0.236707\pi\)
\(608\) 14.1575 0.574161
\(609\) 0 0
\(610\) −107.950 −4.37076
\(611\) −1.09461 −0.0442830
\(612\) 20.8274 0.841897
\(613\) 42.1617 1.70290 0.851448 0.524439i \(-0.175725\pi\)
0.851448 + 0.524439i \(0.175725\pi\)
\(614\) 49.7990 2.00972
\(615\) −3.51535 −0.141753
\(616\) 0 0
\(617\) −5.94775 −0.239447 −0.119724 0.992807i \(-0.538201\pi\)
−0.119724 + 0.992807i \(0.538201\pi\)
\(618\) −9.98908 −0.401820
\(619\) −11.3756 −0.457224 −0.228612 0.973518i \(-0.573419\pi\)
−0.228612 + 0.973518i \(0.573419\pi\)
\(620\) −15.8774 −0.637651
\(621\) 8.49274 0.340802
\(622\) −1.42099 −0.0569766
\(623\) 0 0
\(624\) −0.743287 −0.0297553
\(625\) −7.65291 −0.306116
\(626\) 40.5810 1.62194
\(627\) 8.64025 0.345058
\(628\) −11.1565 −0.445195
\(629\) −6.65314 −0.265278
\(630\) 0 0
\(631\) 34.5226 1.37432 0.687161 0.726505i \(-0.258857\pi\)
0.687161 + 0.726505i \(0.258857\pi\)
\(632\) −2.62161 −0.104282
\(633\) −0.767110 −0.0304899
\(634\) 34.5505 1.37218
\(635\) −9.98243 −0.396141
\(636\) 29.5493 1.17171
\(637\) 0 0
\(638\) 43.3239 1.71521
\(639\) −6.50992 −0.257528
\(640\) −60.0680 −2.37440
\(641\) −10.2549 −0.405044 −0.202522 0.979278i \(-0.564914\pi\)
−0.202522 + 0.979278i \(0.564914\pi\)
\(642\) −34.2978 −1.35363
\(643\) −14.0531 −0.554199 −0.277100 0.960841i \(-0.589373\pi\)
−0.277100 + 0.960841i \(0.589373\pi\)
\(644\) 0 0
\(645\) 38.1226 1.50107
\(646\) −34.4096 −1.35383
\(647\) −12.1956 −0.479458 −0.239729 0.970840i \(-0.577059\pi\)
−0.239729 + 0.970840i \(0.577059\pi\)
\(648\) 2.53253 0.0994870
\(649\) 36.5191 1.43350
\(650\) 24.3317 0.954369
\(651\) 0 0
\(652\) 39.3798 1.54223
\(653\) 3.31551 0.129746 0.0648729 0.997894i \(-0.479336\pi\)
0.0648729 + 0.997894i \(0.479336\pi\)
\(654\) −21.2215 −0.829826
\(655\) −51.6855 −2.01952
\(656\) 0.508546 0.0198554
\(657\) −2.28092 −0.0889872
\(658\) 0 0
\(659\) −8.07950 −0.314733 −0.157366 0.987540i \(-0.550300\pi\)
−0.157366 + 0.987540i \(0.550300\pi\)
\(660\) −41.5964 −1.61914
\(661\) 33.3359 1.29661 0.648307 0.761379i \(-0.275477\pi\)
0.648307 + 0.761379i \(0.275477\pi\)
\(662\) 69.8491 2.71476
\(663\) 9.75896 0.379007
\(664\) −4.68058 −0.181642
\(665\) 0 0
\(666\) −2.25452 −0.0873611
\(667\) −42.8687 −1.65988
\(668\) 13.9784 0.540841
\(669\) −5.48934 −0.212230
\(670\) 66.8419 2.58233
\(671\) 51.4846 1.98754
\(672\) 0 0
\(673\) 16.8487 0.649469 0.324735 0.945805i \(-0.394725\pi\)
0.324735 + 0.945805i \(0.394725\pi\)
\(674\) −31.0693 −1.19675
\(675\) 7.35768 0.283197
\(676\) −33.8873 −1.30336
\(677\) 28.5473 1.09716 0.548580 0.836098i \(-0.315169\pi\)
0.548580 + 0.836098i \(0.315169\pi\)
\(678\) 3.18720 0.122404
\(679\) 0 0
\(680\) 59.4428 2.27953
\(681\) −24.0590 −0.921943
\(682\) 12.4276 0.475878
\(683\) 18.4684 0.706674 0.353337 0.935496i \(-0.385047\pi\)
0.353337 + 0.935496i \(0.385047\pi\)
\(684\) −7.10484 −0.271661
\(685\) −33.0187 −1.26158
\(686\) 0 0
\(687\) −10.3429 −0.394605
\(688\) −5.51498 −0.210257
\(689\) 13.8457 0.527481
\(690\) 67.5495 2.57156
\(691\) −33.1686 −1.26179 −0.630896 0.775868i \(-0.717312\pi\)
−0.630896 + 0.775868i \(0.717312\pi\)
\(692\) −70.3770 −2.67533
\(693\) 0 0
\(694\) −38.3901 −1.45727
\(695\) −39.2211 −1.48774
\(696\) −12.7834 −0.484553
\(697\) −6.67693 −0.252907
\(698\) 13.4617 0.509533
\(699\) −17.3807 −0.657400
\(700\) 0 0
\(701\) 44.1339 1.66692 0.833458 0.552583i \(-0.186358\pi\)
0.833458 + 0.552583i \(0.186358\pi\)
\(702\) 3.30698 0.124814
\(703\) 2.26958 0.0855990
\(704\) 49.4905 1.86524
\(705\) −2.63269 −0.0991529
\(706\) −12.3213 −0.463719
\(707\) 0 0
\(708\) −30.0295 −1.12858
\(709\) −22.1547 −0.832039 −0.416019 0.909356i \(-0.636575\pi\)
−0.416019 + 0.909356i \(0.636575\pi\)
\(710\) −51.7785 −1.94321
\(711\) −1.03517 −0.0388221
\(712\) −4.46788 −0.167441
\(713\) −12.2970 −0.460528
\(714\) 0 0
\(715\) −19.4906 −0.728906
\(716\) 46.7559 1.74735
\(717\) −7.43783 −0.277771
\(718\) −54.1426 −2.02059
\(719\) 2.80563 0.104633 0.0523163 0.998631i \(-0.483340\pi\)
0.0523163 + 0.998631i \(0.483340\pi\)
\(720\) −1.78772 −0.0666243
\(721\) 0 0
\(722\) −31.2510 −1.16304
\(723\) −7.82930 −0.291175
\(724\) 3.14674 0.116947
\(725\) −37.1393 −1.37932
\(726\) 7.67005 0.284662
\(727\) −25.3472 −0.940076 −0.470038 0.882646i \(-0.655760\pi\)
−0.470038 + 0.882646i \(0.655760\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −18.1420 −0.671464
\(731\) 72.4087 2.67813
\(732\) −42.3356 −1.56477
\(733\) −10.8205 −0.399664 −0.199832 0.979830i \(-0.564040\pi\)
−0.199832 + 0.979830i \(0.564040\pi\)
\(734\) −8.19600 −0.302520
\(735\) 0 0
\(736\) −52.7882 −1.94580
\(737\) −31.8790 −1.17428
\(738\) −2.26259 −0.0832870
\(739\) 15.7485 0.579318 0.289659 0.957130i \(-0.406458\pi\)
0.289659 + 0.957130i \(0.406458\pi\)
\(740\) −10.9264 −0.401661
\(741\) −3.32907 −0.122297
\(742\) 0 0
\(743\) −30.4834 −1.11833 −0.559164 0.829057i \(-0.688878\pi\)
−0.559164 + 0.829057i \(0.688878\pi\)
\(744\) −3.66696 −0.134437
\(745\) 2.87836 0.105455
\(746\) 69.0823 2.52928
\(747\) −1.84818 −0.0676215
\(748\) −79.0068 −2.88877
\(749\) 0 0
\(750\) 18.7525 0.684745
\(751\) −34.4554 −1.25729 −0.628647 0.777690i \(-0.716391\pi\)
−0.628647 + 0.777690i \(0.716391\pi\)
\(752\) 0.380857 0.0138884
\(753\) −11.4230 −0.416276
\(754\) −16.6926 −0.607909
\(755\) 72.6194 2.64289
\(756\) 0 0
\(757\) −30.0474 −1.09209 −0.546045 0.837756i \(-0.683867\pi\)
−0.546045 + 0.837756i \(0.683867\pi\)
\(758\) −32.9479 −1.19672
\(759\) −32.2164 −1.16938
\(760\) −20.2777 −0.735550
\(761\) −38.0425 −1.37904 −0.689520 0.724266i \(-0.742179\pi\)
−0.689520 + 0.724266i \(0.742179\pi\)
\(762\) −6.42500 −0.232753
\(763\) 0 0
\(764\) 62.4319 2.25871
\(765\) 23.4718 0.848623
\(766\) −10.9664 −0.396234
\(767\) −14.0707 −0.508065
\(768\) −12.5688 −0.453536
\(769\) 44.6290 1.60936 0.804681 0.593708i \(-0.202337\pi\)
0.804681 + 0.593708i \(0.202337\pi\)
\(770\) 0 0
\(771\) −14.8155 −0.533569
\(772\) 10.8249 0.389595
\(773\) 9.92149 0.356851 0.178426 0.983953i \(-0.442900\pi\)
0.178426 + 0.983953i \(0.442900\pi\)
\(774\) 24.5369 0.881960
\(775\) −10.6535 −0.382686
\(776\) 44.2190 1.58737
\(777\) 0 0
\(778\) −1.55142 −0.0556213
\(779\) 2.27770 0.0816071
\(780\) 16.0270 0.573860
\(781\) 24.6948 0.883649
\(782\) 128.301 4.58804
\(783\) −5.04769 −0.180390
\(784\) 0 0
\(785\) −12.5730 −0.448751
\(786\) −33.2664 −1.18657
\(787\) −9.83436 −0.350557 −0.175279 0.984519i \(-0.556083\pi\)
−0.175279 + 0.984519i \(0.556083\pi\)
\(788\) 36.1934 1.28934
\(789\) −21.3829 −0.761253
\(790\) −8.23356 −0.292937
\(791\) 0 0
\(792\) −9.60691 −0.341367
\(793\) −19.8369 −0.704430
\(794\) 0.914742 0.0324630
\(795\) 33.3011 1.18107
\(796\) −24.4187 −0.865496
\(797\) −37.5618 −1.33051 −0.665253 0.746618i \(-0.731677\pi\)
−0.665253 + 0.746618i \(0.731677\pi\)
\(798\) 0 0
\(799\) −5.00044 −0.176903
\(800\) −45.7330 −1.61691
\(801\) −1.76420 −0.0623348
\(802\) −63.6611 −2.24795
\(803\) 8.65246 0.305339
\(804\) 26.2139 0.924495
\(805\) 0 0
\(806\) −4.78834 −0.168662
\(807\) 29.0758 1.02352
\(808\) 49.2566 1.73284
\(809\) 21.9434 0.771489 0.385744 0.922606i \(-0.373945\pi\)
0.385744 + 0.922606i \(0.373945\pi\)
\(810\) 7.95379 0.279468
\(811\) 1.08414 0.0380692 0.0190346 0.999819i \(-0.493941\pi\)
0.0190346 + 0.999819i \(0.493941\pi\)
\(812\) 0 0
\(813\) −21.8299 −0.765607
\(814\) 8.55233 0.299759
\(815\) 44.3796 1.55455
\(816\) −3.39553 −0.118867
\(817\) −24.7008 −0.864170
\(818\) −38.4492 −1.34435
\(819\) 0 0
\(820\) −10.9654 −0.382930
\(821\) 30.1425 1.05198 0.525990 0.850491i \(-0.323695\pi\)
0.525990 + 0.850491i \(0.323695\pi\)
\(822\) −21.2518 −0.741243
\(823\) 8.54130 0.297731 0.148866 0.988857i \(-0.452438\pi\)
0.148866 + 0.988857i \(0.452438\pi\)
\(824\) −11.1808 −0.389503
\(825\) −27.9107 −0.971726
\(826\) 0 0
\(827\) 45.6006 1.58569 0.792843 0.609426i \(-0.208600\pi\)
0.792843 + 0.609426i \(0.208600\pi\)
\(828\) 26.4914 0.920641
\(829\) 34.3490 1.19299 0.596495 0.802617i \(-0.296560\pi\)
0.596495 + 0.802617i \(0.296560\pi\)
\(830\) −14.7001 −0.510247
\(831\) −26.3880 −0.915390
\(832\) −19.0686 −0.661084
\(833\) 0 0
\(834\) −25.2439 −0.874126
\(835\) 15.7532 0.545161
\(836\) 26.9516 0.932140
\(837\) −1.44795 −0.0500484
\(838\) 22.9308 0.792131
\(839\) −40.4048 −1.39493 −0.697464 0.716619i \(-0.745688\pi\)
−0.697464 + 0.716619i \(0.745688\pi\)
\(840\) 0 0
\(841\) −3.52086 −0.121409
\(842\) 18.0023 0.620401
\(843\) 10.8668 0.374271
\(844\) −2.39285 −0.0823653
\(845\) −38.1899 −1.31377
\(846\) −1.69448 −0.0582575
\(847\) 0 0
\(848\) −4.81748 −0.165433
\(849\) −30.8486 −1.05872
\(850\) 111.154 3.81254
\(851\) −8.46247 −0.290090
\(852\) −20.3064 −0.695687
\(853\) 3.69729 0.126593 0.0632965 0.997995i \(-0.479839\pi\)
0.0632965 + 0.997995i \(0.479839\pi\)
\(854\) 0 0
\(855\) −8.00692 −0.273831
\(856\) −38.3897 −1.31213
\(857\) 5.08270 0.173622 0.0868108 0.996225i \(-0.472332\pi\)
0.0868108 + 0.996225i \(0.472332\pi\)
\(858\) −12.5447 −0.428270
\(859\) 47.7419 1.62893 0.814467 0.580210i \(-0.197030\pi\)
0.814467 + 0.580210i \(0.197030\pi\)
\(860\) 118.916 4.05500
\(861\) 0 0
\(862\) −61.4243 −2.09212
\(863\) 16.7136 0.568938 0.284469 0.958685i \(-0.408183\pi\)
0.284469 + 0.958685i \(0.408183\pi\)
\(864\) −6.21568 −0.211462
\(865\) −79.3125 −2.69671
\(866\) 62.6464 2.12881
\(867\) 27.5814 0.936714
\(868\) 0 0
\(869\) 3.92684 0.133209
\(870\) −40.1482 −1.36115
\(871\) 12.2829 0.416190
\(872\) −23.7533 −0.804389
\(873\) 17.4604 0.590946
\(874\) −43.7673 −1.48045
\(875\) 0 0
\(876\) −7.11489 −0.240390
\(877\) −8.44843 −0.285283 −0.142642 0.989774i \(-0.545560\pi\)
−0.142642 + 0.989774i \(0.545560\pi\)
\(878\) −19.8183 −0.668834
\(879\) 10.1999 0.344034
\(880\) 6.78154 0.228606
\(881\) 25.5874 0.862062 0.431031 0.902337i \(-0.358150\pi\)
0.431031 + 0.902337i \(0.358150\pi\)
\(882\) 0 0
\(883\) 54.4322 1.83179 0.915895 0.401418i \(-0.131483\pi\)
0.915895 + 0.401418i \(0.131483\pi\)
\(884\) 30.4412 1.02385
\(885\) −33.8422 −1.13759
\(886\) −80.5446 −2.70595
\(887\) −54.1148 −1.81700 −0.908498 0.417889i \(-0.862770\pi\)
−0.908498 + 0.417889i \(0.862770\pi\)
\(888\) −2.52350 −0.0846832
\(889\) 0 0
\(890\) −14.0321 −0.470355
\(891\) −3.79341 −0.127084
\(892\) −17.1229 −0.573318
\(893\) 1.70580 0.0570824
\(894\) 1.85260 0.0619602
\(895\) 52.6923 1.76131
\(896\) 0 0
\(897\) 12.4129 0.414456
\(898\) 80.0160 2.67017
\(899\) 7.30878 0.243761
\(900\) 22.9509 0.765029
\(901\) 63.2509 2.10719
\(902\) 8.58292 0.285780
\(903\) 0 0
\(904\) 3.56745 0.118651
\(905\) 3.54626 0.117882
\(906\) 46.7401 1.55284
\(907\) −5.56564 −0.184804 −0.0924021 0.995722i \(-0.529455\pi\)
−0.0924021 + 0.995722i \(0.529455\pi\)
\(908\) −75.0474 −2.49053
\(909\) 19.4496 0.645102
\(910\) 0 0
\(911\) 8.67651 0.287466 0.143733 0.989617i \(-0.454089\pi\)
0.143733 + 0.989617i \(0.454089\pi\)
\(912\) 1.15832 0.0383557
\(913\) 7.01092 0.232028
\(914\) 44.7202 1.47921
\(915\) −47.7108 −1.57727
\(916\) −32.2626 −1.06598
\(917\) 0 0
\(918\) 15.1071 0.498610
\(919\) 31.0314 1.02363 0.511816 0.859095i \(-0.328973\pi\)
0.511816 + 0.859095i \(0.328973\pi\)
\(920\) 75.6084 2.49274
\(921\) 22.0097 0.725246
\(922\) 24.3203 0.800947
\(923\) −9.51486 −0.313185
\(924\) 0 0
\(925\) −7.33146 −0.241057
\(926\) 6.55107 0.215282
\(927\) −4.41489 −0.145004
\(928\) 31.3748 1.02993
\(929\) 0.0908696 0.00298133 0.00149067 0.999999i \(-0.499526\pi\)
0.00149067 + 0.999999i \(0.499526\pi\)
\(930\) −11.5167 −0.377646
\(931\) 0 0
\(932\) −54.2158 −1.77590
\(933\) −0.628039 −0.0205611
\(934\) −13.5335 −0.442831
\(935\) −89.0379 −2.91185
\(936\) 3.70152 0.120988
\(937\) −39.5068 −1.29063 −0.645316 0.763916i \(-0.723274\pi\)
−0.645316 + 0.763916i \(0.723274\pi\)
\(938\) 0 0
\(939\) 17.9356 0.585308
\(940\) −8.21217 −0.267851
\(941\) 1.91194 0.0623275 0.0311638 0.999514i \(-0.490079\pi\)
0.0311638 + 0.999514i \(0.490079\pi\)
\(942\) −8.09240 −0.263665
\(943\) −8.49274 −0.276562
\(944\) 4.89577 0.159344
\(945\) 0 0
\(946\) −93.0784 −3.02624
\(947\) 10.0939 0.328007 0.164004 0.986460i \(-0.447559\pi\)
0.164004 + 0.986460i \(0.447559\pi\)
\(948\) −3.22902 −0.104874
\(949\) −3.33378 −0.108219
\(950\) −37.9178 −1.23022
\(951\) 15.2704 0.495175
\(952\) 0 0
\(953\) 54.1757 1.75492 0.877461 0.479647i \(-0.159235\pi\)
0.877461 + 0.479647i \(0.159235\pi\)
\(954\) 21.4336 0.693938
\(955\) 70.3586 2.27675
\(956\) −23.2009 −0.750370
\(957\) 19.1479 0.618965
\(958\) −34.1035 −1.10183
\(959\) 0 0
\(960\) −45.8628 −1.48022
\(961\) −28.9035 −0.932369
\(962\) −3.29520 −0.106241
\(963\) −15.1587 −0.488481
\(964\) −24.4220 −0.786579
\(965\) 12.1992 0.392707
\(966\) 0 0
\(967\) −1.86574 −0.0599983 −0.0299991 0.999550i \(-0.509550\pi\)
−0.0299991 + 0.999550i \(0.509550\pi\)
\(968\) 8.58512 0.275936
\(969\) −15.2081 −0.488553
\(970\) 138.877 4.45906
\(971\) −35.0800 −1.12577 −0.562886 0.826535i \(-0.690309\pi\)
−0.562886 + 0.826535i \(0.690309\pi\)
\(972\) 3.11931 0.100052
\(973\) 0 0
\(974\) −60.6327 −1.94280
\(975\) 10.7539 0.344402
\(976\) 6.90205 0.220929
\(977\) −3.77558 −0.120792 −0.0603958 0.998175i \(-0.519236\pi\)
−0.0603958 + 0.998175i \(0.519236\pi\)
\(978\) 28.5641 0.913380
\(979\) 6.69232 0.213887
\(980\) 0 0
\(981\) −9.37929 −0.299458
\(982\) 33.1958 1.05932
\(983\) −30.5146 −0.973265 −0.486632 0.873607i \(-0.661775\pi\)
−0.486632 + 0.873607i \(0.661775\pi\)
\(984\) −2.53253 −0.0807340
\(985\) 40.7887 1.29964
\(986\) −76.2561 −2.42849
\(987\) 0 0
\(988\) −10.3844 −0.330372
\(989\) 92.1004 2.92862
\(990\) −30.1720 −0.958928
\(991\) −3.83662 −0.121874 −0.0609371 0.998142i \(-0.519409\pi\)
−0.0609371 + 0.998142i \(0.519409\pi\)
\(992\) 8.99998 0.285750
\(993\) 30.8713 0.979672
\(994\) 0 0
\(995\) −27.5190 −0.872411
\(996\) −5.76505 −0.182673
\(997\) 0.932058 0.0295186 0.0147593 0.999891i \(-0.495302\pi\)
0.0147593 + 0.999891i \(0.495302\pi\)
\(998\) 75.3705 2.38581
\(999\) −0.996436 −0.0315258
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 \(a_p\))