Properties

Label 6027.2.a.bk.1.8
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(0.181424\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.181424 q^{2} +1.00000 q^{3} -1.96709 q^{4} +3.75467 q^{5} -0.181424 q^{6} +0.719724 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.181424 q^{2} +1.00000 q^{3} -1.96709 q^{4} +3.75467 q^{5} -0.181424 q^{6} +0.719724 q^{8} +1.00000 q^{9} -0.681187 q^{10} +0.260903 q^{11} -1.96709 q^{12} -5.44669 q^{13} +3.75467 q^{15} +3.80360 q^{16} +0.644297 q^{17} -0.181424 q^{18} -4.44030 q^{19} -7.38576 q^{20} -0.0473341 q^{22} -9.20056 q^{23} +0.719724 q^{24} +9.09756 q^{25} +0.988159 q^{26} +1.00000 q^{27} +4.61039 q^{29} -0.681187 q^{30} -1.77314 q^{31} -2.12951 q^{32} +0.260903 q^{33} -0.116891 q^{34} -1.96709 q^{36} -5.73974 q^{37} +0.805577 q^{38} -5.44669 q^{39} +2.70233 q^{40} -1.00000 q^{41} -1.73846 q^{43} -0.513219 q^{44} +3.75467 q^{45} +1.66920 q^{46} -0.476598 q^{47} +3.80360 q^{48} -1.65051 q^{50} +0.644297 q^{51} +10.7141 q^{52} -2.26468 q^{53} -0.181424 q^{54} +0.979606 q^{55} -4.44030 q^{57} -0.836435 q^{58} +10.3925 q^{59} -7.38576 q^{60} -12.3888 q^{61} +0.321690 q^{62} -7.22085 q^{64} -20.4505 q^{65} -0.0473341 q^{66} -7.53205 q^{67} -1.26739 q^{68} -9.20056 q^{69} -6.69685 q^{71} +0.719724 q^{72} -14.7968 q^{73} +1.04133 q^{74} +9.09756 q^{75} +8.73445 q^{76} +0.988159 q^{78} -6.26859 q^{79} +14.2812 q^{80} +1.00000 q^{81} +0.181424 q^{82} +8.81328 q^{83} +2.41912 q^{85} +0.315399 q^{86} +4.61039 q^{87} +0.187778 q^{88} -5.73591 q^{89} -0.681187 q^{90} +18.0983 q^{92} -1.77314 q^{93} +0.0864664 q^{94} -16.6719 q^{95} -2.12951 q^{96} -2.67661 q^{97} +0.260903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.181424 −0.128286 −0.0641431 0.997941i \(-0.520431\pi\)
−0.0641431 + 0.997941i \(0.520431\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.96709 −0.983543
\(5\) 3.75467 1.67914 0.839570 0.543252i \(-0.182807\pi\)
0.839570 + 0.543252i \(0.182807\pi\)
\(6\) −0.181424 −0.0740660
\(7\) 0 0
\(8\) 0.719724 0.254461
\(9\) 1.00000 0.333333
\(10\) −0.681187 −0.215410
\(11\) 0.260903 0.0786653 0.0393327 0.999226i \(-0.487477\pi\)
0.0393327 + 0.999226i \(0.487477\pi\)
\(12\) −1.96709 −0.567849
\(13\) −5.44669 −1.51064 −0.755319 0.655357i \(-0.772518\pi\)
−0.755319 + 0.655357i \(0.772518\pi\)
\(14\) 0 0
\(15\) 3.75467 0.969452
\(16\) 3.80360 0.950899
\(17\) 0.644297 0.156265 0.0781325 0.996943i \(-0.475104\pi\)
0.0781325 + 0.996943i \(0.475104\pi\)
\(18\) −0.181424 −0.0427620
\(19\) −4.44030 −1.01867 −0.509337 0.860567i \(-0.670109\pi\)
−0.509337 + 0.860567i \(0.670109\pi\)
\(20\) −7.38576 −1.65151
\(21\) 0 0
\(22\) −0.0473341 −0.0100917
\(23\) −9.20056 −1.91845 −0.959225 0.282644i \(-0.908788\pi\)
−0.959225 + 0.282644i \(0.908788\pi\)
\(24\) 0.719724 0.146913
\(25\) 9.09756 1.81951
\(26\) 0.988159 0.193794
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.61039 0.856128 0.428064 0.903748i \(-0.359196\pi\)
0.428064 + 0.903748i \(0.359196\pi\)
\(30\) −0.681187 −0.124367
\(31\) −1.77314 −0.318465 −0.159233 0.987241i \(-0.550902\pi\)
−0.159233 + 0.987241i \(0.550902\pi\)
\(32\) −2.12951 −0.376448
\(33\) 0.260903 0.0454174
\(34\) −0.116891 −0.0200466
\(35\) 0 0
\(36\) −1.96709 −0.327848
\(37\) −5.73974 −0.943608 −0.471804 0.881704i \(-0.656397\pi\)
−0.471804 + 0.881704i \(0.656397\pi\)
\(38\) 0.805577 0.130682
\(39\) −5.44669 −0.872168
\(40\) 2.70233 0.427276
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −1.73846 −0.265113 −0.132556 0.991175i \(-0.542319\pi\)
−0.132556 + 0.991175i \(0.542319\pi\)
\(44\) −0.513219 −0.0773707
\(45\) 3.75467 0.559713
\(46\) 1.66920 0.246110
\(47\) −0.476598 −0.0695190 −0.0347595 0.999396i \(-0.511067\pi\)
−0.0347595 + 0.999396i \(0.511067\pi\)
\(48\) 3.80360 0.549002
\(49\) 0 0
\(50\) −1.65051 −0.233418
\(51\) 0.644297 0.0902197
\(52\) 10.7141 1.48578
\(53\) −2.26468 −0.311078 −0.155539 0.987830i \(-0.549711\pi\)
−0.155539 + 0.987830i \(0.549711\pi\)
\(54\) −0.181424 −0.0246887
\(55\) 0.979606 0.132090
\(56\) 0 0
\(57\) −4.44030 −0.588132
\(58\) −0.836435 −0.109829
\(59\) 10.3925 1.35299 0.676495 0.736448i \(-0.263498\pi\)
0.676495 + 0.736448i \(0.263498\pi\)
\(60\) −7.38576 −0.953497
\(61\) −12.3888 −1.58622 −0.793109 0.609079i \(-0.791539\pi\)
−0.793109 + 0.609079i \(0.791539\pi\)
\(62\) 0.321690 0.0408546
\(63\) 0 0
\(64\) −7.22085 −0.902606
\(65\) −20.4505 −2.53657
\(66\) −0.0473341 −0.00582643
\(67\) −7.53205 −0.920187 −0.460093 0.887871i \(-0.652184\pi\)
−0.460093 + 0.887871i \(0.652184\pi\)
\(68\) −1.26739 −0.153693
\(69\) −9.20056 −1.10762
\(70\) 0 0
\(71\) −6.69685 −0.794770 −0.397385 0.917652i \(-0.630082\pi\)
−0.397385 + 0.917652i \(0.630082\pi\)
\(72\) 0.719724 0.0848203
\(73\) −14.7968 −1.73183 −0.865915 0.500191i \(-0.833263\pi\)
−0.865915 + 0.500191i \(0.833263\pi\)
\(74\) 1.04133 0.121052
\(75\) 9.09756 1.05050
\(76\) 8.73445 1.00191
\(77\) 0 0
\(78\) 0.988159 0.111887
\(79\) −6.26859 −0.705272 −0.352636 0.935761i \(-0.614715\pi\)
−0.352636 + 0.935761i \(0.614715\pi\)
\(80\) 14.2812 1.59669
\(81\) 1.00000 0.111111
\(82\) 0.181424 0.0200349
\(83\) 8.81328 0.967384 0.483692 0.875238i \(-0.339296\pi\)
0.483692 + 0.875238i \(0.339296\pi\)
\(84\) 0 0
\(85\) 2.41912 0.262391
\(86\) 0.315399 0.0340103
\(87\) 4.61039 0.494286
\(88\) 0.187778 0.0200173
\(89\) −5.73591 −0.608005 −0.304002 0.952671i \(-0.598323\pi\)
−0.304002 + 0.952671i \(0.598323\pi\)
\(90\) −0.681187 −0.0718035
\(91\) 0 0
\(92\) 18.0983 1.88688
\(93\) −1.77314 −0.183866
\(94\) 0.0864664 0.00891833
\(95\) −16.6719 −1.71050
\(96\) −2.12951 −0.217342
\(97\) −2.67661 −0.271768 −0.135884 0.990725i \(-0.543387\pi\)
−0.135884 + 0.990725i \(0.543387\pi\)
\(98\) 0 0
\(99\) 0.260903 0.0262218
\(100\) −17.8957 −1.78957
\(101\) 10.8832 1.08292 0.541460 0.840727i \(-0.317872\pi\)
0.541460 + 0.840727i \(0.317872\pi\)
\(102\) −0.116891 −0.0115739
\(103\) −6.46670 −0.637182 −0.318591 0.947892i \(-0.603210\pi\)
−0.318591 + 0.947892i \(0.603210\pi\)
\(104\) −3.92011 −0.384399
\(105\) 0 0
\(106\) 0.410868 0.0399070
\(107\) 13.7274 1.32708 0.663539 0.748141i \(-0.269054\pi\)
0.663539 + 0.748141i \(0.269054\pi\)
\(108\) −1.96709 −0.189283
\(109\) −4.61957 −0.442474 −0.221237 0.975220i \(-0.571009\pi\)
−0.221237 + 0.975220i \(0.571009\pi\)
\(110\) −0.177724 −0.0169453
\(111\) −5.73974 −0.544792
\(112\) 0 0
\(113\) −7.96683 −0.749456 −0.374728 0.927135i \(-0.622264\pi\)
−0.374728 + 0.927135i \(0.622264\pi\)
\(114\) 0.805577 0.0754492
\(115\) −34.5451 −3.22135
\(116\) −9.06903 −0.842038
\(117\) −5.44669 −0.503546
\(118\) −1.88545 −0.173570
\(119\) 0 0
\(120\) 2.70233 0.246688
\(121\) −10.9319 −0.993812
\(122\) 2.24762 0.203490
\(123\) −1.00000 −0.0901670
\(124\) 3.48791 0.313224
\(125\) 15.3850 1.37607
\(126\) 0 0
\(127\) −9.53266 −0.845886 −0.422943 0.906156i \(-0.639003\pi\)
−0.422943 + 0.906156i \(0.639003\pi\)
\(128\) 5.56906 0.492240
\(129\) −1.73846 −0.153063
\(130\) 3.71021 0.325407
\(131\) 7.89826 0.690074 0.345037 0.938589i \(-0.387866\pi\)
0.345037 + 0.938589i \(0.387866\pi\)
\(132\) −0.513219 −0.0446700
\(133\) 0 0
\(134\) 1.36649 0.118047
\(135\) 3.75467 0.323151
\(136\) 0.463716 0.0397634
\(137\) 12.1886 1.04134 0.520671 0.853757i \(-0.325682\pi\)
0.520671 + 0.853757i \(0.325682\pi\)
\(138\) 1.66920 0.142092
\(139\) 23.4534 1.98929 0.994647 0.103335i \(-0.0329515\pi\)
0.994647 + 0.103335i \(0.0329515\pi\)
\(140\) 0 0
\(141\) −0.476598 −0.0401368
\(142\) 1.21497 0.101958
\(143\) −1.42106 −0.118835
\(144\) 3.80360 0.316966
\(145\) 17.3105 1.43756
\(146\) 2.68449 0.222170
\(147\) 0 0
\(148\) 11.2906 0.928078
\(149\) 1.91828 0.157152 0.0785759 0.996908i \(-0.474963\pi\)
0.0785759 + 0.996908i \(0.474963\pi\)
\(150\) −1.65051 −0.134764
\(151\) −0.875982 −0.0712864 −0.0356432 0.999365i \(-0.511348\pi\)
−0.0356432 + 0.999365i \(0.511348\pi\)
\(152\) −3.19579 −0.259213
\(153\) 0.644297 0.0520883
\(154\) 0 0
\(155\) −6.65755 −0.534747
\(156\) 10.7141 0.857814
\(157\) −21.4256 −1.70995 −0.854975 0.518669i \(-0.826428\pi\)
−0.854975 + 0.518669i \(0.826428\pi\)
\(158\) 1.13727 0.0904766
\(159\) −2.26468 −0.179601
\(160\) −7.99562 −0.632109
\(161\) 0 0
\(162\) −0.181424 −0.0142540
\(163\) 20.4306 1.60025 0.800123 0.599836i \(-0.204768\pi\)
0.800123 + 0.599836i \(0.204768\pi\)
\(164\) 1.96709 0.153604
\(165\) 0.979606 0.0762622
\(166\) −1.59894 −0.124102
\(167\) −8.65888 −0.670044 −0.335022 0.942210i \(-0.608744\pi\)
−0.335022 + 0.942210i \(0.608744\pi\)
\(168\) 0 0
\(169\) 16.6664 1.28203
\(170\) −0.438887 −0.0336611
\(171\) −4.44030 −0.339558
\(172\) 3.41970 0.260750
\(173\) −7.01283 −0.533176 −0.266588 0.963811i \(-0.585896\pi\)
−0.266588 + 0.963811i \(0.585896\pi\)
\(174\) −0.836435 −0.0634100
\(175\) 0 0
\(176\) 0.992371 0.0748027
\(177\) 10.3925 0.781149
\(178\) 1.04063 0.0779986
\(179\) 7.18201 0.536808 0.268404 0.963306i \(-0.413504\pi\)
0.268404 + 0.963306i \(0.413504\pi\)
\(180\) −7.38576 −0.550502
\(181\) 7.76715 0.577328 0.288664 0.957431i \(-0.406789\pi\)
0.288664 + 0.957431i \(0.406789\pi\)
\(182\) 0 0
\(183\) −12.3888 −0.915804
\(184\) −6.62187 −0.488171
\(185\) −21.5508 −1.58445
\(186\) 0.321690 0.0235874
\(187\) 0.168099 0.0122926
\(188\) 0.937510 0.0683749
\(189\) 0 0
\(190\) 3.02467 0.219433
\(191\) 4.77261 0.345334 0.172667 0.984980i \(-0.444762\pi\)
0.172667 + 0.984980i \(0.444762\pi\)
\(192\) −7.22085 −0.521120
\(193\) −24.8481 −1.78861 −0.894303 0.447461i \(-0.852328\pi\)
−0.894303 + 0.447461i \(0.852328\pi\)
\(194\) 0.485601 0.0348641
\(195\) −20.4505 −1.46449
\(196\) 0 0
\(197\) 21.9653 1.56497 0.782483 0.622672i \(-0.213953\pi\)
0.782483 + 0.622672i \(0.213953\pi\)
\(198\) −0.0473341 −0.00336389
\(199\) 3.47751 0.246514 0.123257 0.992375i \(-0.460666\pi\)
0.123257 + 0.992375i \(0.460666\pi\)
\(200\) 6.54773 0.462995
\(201\) −7.53205 −0.531270
\(202\) −1.97447 −0.138923
\(203\) 0 0
\(204\) −1.26739 −0.0887349
\(205\) −3.75467 −0.262238
\(206\) 1.17321 0.0817417
\(207\) −9.20056 −0.639483
\(208\) −20.7170 −1.43646
\(209\) −1.15849 −0.0801343
\(210\) 0 0
\(211\) −8.73884 −0.601606 −0.300803 0.953686i \(-0.597255\pi\)
−0.300803 + 0.953686i \(0.597255\pi\)
\(212\) 4.45482 0.305959
\(213\) −6.69685 −0.458861
\(214\) −2.49048 −0.170246
\(215\) −6.52735 −0.445162
\(216\) 0.719724 0.0489710
\(217\) 0 0
\(218\) 0.838100 0.0567633
\(219\) −14.7968 −0.999873
\(220\) −1.92697 −0.129916
\(221\) −3.50928 −0.236060
\(222\) 1.04133 0.0698893
\(223\) −11.8901 −0.796223 −0.398111 0.917337i \(-0.630334\pi\)
−0.398111 + 0.917337i \(0.630334\pi\)
\(224\) 0 0
\(225\) 9.09756 0.606504
\(226\) 1.44537 0.0961448
\(227\) 17.4021 1.15502 0.577508 0.816385i \(-0.304025\pi\)
0.577508 + 0.816385i \(0.304025\pi\)
\(228\) 8.73445 0.578453
\(229\) 4.00125 0.264410 0.132205 0.991222i \(-0.457794\pi\)
0.132205 + 0.991222i \(0.457794\pi\)
\(230\) 6.26731 0.413254
\(231\) 0 0
\(232\) 3.31821 0.217851
\(233\) −4.04892 −0.265253 −0.132627 0.991166i \(-0.542341\pi\)
−0.132627 + 0.991166i \(0.542341\pi\)
\(234\) 0.988159 0.0645980
\(235\) −1.78947 −0.116732
\(236\) −20.4430 −1.33072
\(237\) −6.26859 −0.407189
\(238\) 0 0
\(239\) −3.86710 −0.250142 −0.125071 0.992148i \(-0.539916\pi\)
−0.125071 + 0.992148i \(0.539916\pi\)
\(240\) 14.2812 0.921851
\(241\) −21.9664 −1.41498 −0.707490 0.706724i \(-0.750172\pi\)
−0.707490 + 0.706724i \(0.750172\pi\)
\(242\) 1.98331 0.127492
\(243\) 1.00000 0.0641500
\(244\) 24.3698 1.56011
\(245\) 0 0
\(246\) 0.181424 0.0115672
\(247\) 24.1849 1.53885
\(248\) −1.27617 −0.0810369
\(249\) 8.81328 0.558519
\(250\) −2.79120 −0.176531
\(251\) 18.8607 1.19048 0.595238 0.803549i \(-0.297058\pi\)
0.595238 + 0.803549i \(0.297058\pi\)
\(252\) 0 0
\(253\) −2.40046 −0.150915
\(254\) 1.72945 0.108515
\(255\) 2.41912 0.151491
\(256\) 13.4313 0.839458
\(257\) −26.3411 −1.64311 −0.821556 0.570127i \(-0.806894\pi\)
−0.821556 + 0.570127i \(0.806894\pi\)
\(258\) 0.315399 0.0196359
\(259\) 0 0
\(260\) 40.2279 2.49483
\(261\) 4.61039 0.285376
\(262\) −1.43293 −0.0885269
\(263\) 29.7738 1.83593 0.917964 0.396663i \(-0.129832\pi\)
0.917964 + 0.396663i \(0.129832\pi\)
\(264\) 0.187778 0.0115570
\(265\) −8.50314 −0.522344
\(266\) 0 0
\(267\) −5.73591 −0.351032
\(268\) 14.8162 0.905043
\(269\) −0.162754 −0.00992327 −0.00496164 0.999988i \(-0.501579\pi\)
−0.00496164 + 0.999988i \(0.501579\pi\)
\(270\) −0.681187 −0.0414557
\(271\) −7.55601 −0.458995 −0.229498 0.973309i \(-0.573708\pi\)
−0.229498 + 0.973309i \(0.573708\pi\)
\(272\) 2.45065 0.148592
\(273\) 0 0
\(274\) −2.21130 −0.133590
\(275\) 2.37358 0.143132
\(276\) 18.0983 1.08939
\(277\) −19.1220 −1.14893 −0.574466 0.818529i \(-0.694790\pi\)
−0.574466 + 0.818529i \(0.694790\pi\)
\(278\) −4.25501 −0.255199
\(279\) −1.77314 −0.106155
\(280\) 0 0
\(281\) 25.1709 1.50157 0.750786 0.660546i \(-0.229675\pi\)
0.750786 + 0.660546i \(0.229675\pi\)
\(282\) 0.0864664 0.00514900
\(283\) 11.8362 0.703587 0.351793 0.936078i \(-0.385572\pi\)
0.351793 + 0.936078i \(0.385572\pi\)
\(284\) 13.1733 0.781690
\(285\) −16.6719 −0.987556
\(286\) 0.257814 0.0152449
\(287\) 0 0
\(288\) −2.12951 −0.125483
\(289\) −16.5849 −0.975581
\(290\) −3.14054 −0.184419
\(291\) −2.67661 −0.156905
\(292\) 29.1065 1.70333
\(293\) −28.0330 −1.63770 −0.818852 0.574005i \(-0.805389\pi\)
−0.818852 + 0.574005i \(0.805389\pi\)
\(294\) 0 0
\(295\) 39.0205 2.27186
\(296\) −4.13103 −0.240111
\(297\) 0.260903 0.0151391
\(298\) −0.348022 −0.0201604
\(299\) 50.1126 2.89808
\(300\) −17.8957 −1.03321
\(301\) 0 0
\(302\) 0.158924 0.00914506
\(303\) 10.8832 0.625224
\(304\) −16.8891 −0.968656
\(305\) −46.5157 −2.66348
\(306\) −0.116891 −0.00668221
\(307\) 9.82237 0.560592 0.280296 0.959914i \(-0.409567\pi\)
0.280296 + 0.959914i \(0.409567\pi\)
\(308\) 0 0
\(309\) −6.46670 −0.367877
\(310\) 1.20784 0.0686007
\(311\) −32.7287 −1.85588 −0.927938 0.372734i \(-0.878420\pi\)
−0.927938 + 0.372734i \(0.878420\pi\)
\(312\) −3.92011 −0.221933
\(313\) −7.01115 −0.396293 −0.198147 0.980172i \(-0.563492\pi\)
−0.198147 + 0.980172i \(0.563492\pi\)
\(314\) 3.88712 0.219363
\(315\) 0 0
\(316\) 12.3309 0.693665
\(317\) −24.3997 −1.37043 −0.685213 0.728343i \(-0.740291\pi\)
−0.685213 + 0.728343i \(0.740291\pi\)
\(318\) 0.410868 0.0230403
\(319\) 1.20287 0.0673476
\(320\) −27.1119 −1.51560
\(321\) 13.7274 0.766189
\(322\) 0 0
\(323\) −2.86087 −0.159183
\(324\) −1.96709 −0.109283
\(325\) −49.5515 −2.74862
\(326\) −3.70660 −0.205289
\(327\) −4.61957 −0.255463
\(328\) −0.719724 −0.0397401
\(329\) 0 0
\(330\) −0.177724 −0.00978339
\(331\) 19.1012 1.04990 0.524949 0.851134i \(-0.324084\pi\)
0.524949 + 0.851134i \(0.324084\pi\)
\(332\) −17.3365 −0.951463
\(333\) −5.73974 −0.314536
\(334\) 1.57093 0.0859574
\(335\) −28.2804 −1.54512
\(336\) 0 0
\(337\) −2.03171 −0.110674 −0.0553372 0.998468i \(-0.517623\pi\)
−0.0553372 + 0.998468i \(0.517623\pi\)
\(338\) −3.02368 −0.164467
\(339\) −7.96683 −0.432699
\(340\) −4.75862 −0.258073
\(341\) −0.462618 −0.0250521
\(342\) 0.805577 0.0435606
\(343\) 0 0
\(344\) −1.25121 −0.0674609
\(345\) −34.5451 −1.85984
\(346\) 1.27230 0.0683990
\(347\) 11.7438 0.630438 0.315219 0.949019i \(-0.397922\pi\)
0.315219 + 0.949019i \(0.397922\pi\)
\(348\) −9.06903 −0.486151
\(349\) 27.2116 1.45660 0.728302 0.685257i \(-0.240310\pi\)
0.728302 + 0.685257i \(0.240310\pi\)
\(350\) 0 0
\(351\) −5.44669 −0.290723
\(352\) −0.555597 −0.0296134
\(353\) −0.380286 −0.0202406 −0.0101203 0.999949i \(-0.503221\pi\)
−0.0101203 + 0.999949i \(0.503221\pi\)
\(354\) −1.88545 −0.100211
\(355\) −25.1445 −1.33453
\(356\) 11.2830 0.597999
\(357\) 0 0
\(358\) −1.30299 −0.0688651
\(359\) −9.44080 −0.498267 −0.249133 0.968469i \(-0.580146\pi\)
−0.249133 + 0.968469i \(0.580146\pi\)
\(360\) 2.70233 0.142425
\(361\) 0.716247 0.0376972
\(362\) −1.40915 −0.0740631
\(363\) −10.9319 −0.573777
\(364\) 0 0
\(365\) −55.5570 −2.90799
\(366\) 2.24762 0.117485
\(367\) −15.8328 −0.826466 −0.413233 0.910625i \(-0.635600\pi\)
−0.413233 + 0.910625i \(0.635600\pi\)
\(368\) −34.9952 −1.82425
\(369\) −1.00000 −0.0520579
\(370\) 3.90984 0.203263
\(371\) 0 0
\(372\) 3.48791 0.180840
\(373\) 20.7543 1.07462 0.537309 0.843386i \(-0.319441\pi\)
0.537309 + 0.843386i \(0.319441\pi\)
\(374\) −0.0304972 −0.00157697
\(375\) 15.3850 0.794477
\(376\) −0.343020 −0.0176899
\(377\) −25.1113 −1.29330
\(378\) 0 0
\(379\) 0.409160 0.0210171 0.0105086 0.999945i \(-0.496655\pi\)
0.0105086 + 0.999945i \(0.496655\pi\)
\(380\) 32.7950 1.68235
\(381\) −9.53266 −0.488373
\(382\) −0.865865 −0.0443015
\(383\) 38.9703 1.99129 0.995646 0.0932202i \(-0.0297161\pi\)
0.995646 + 0.0932202i \(0.0297161\pi\)
\(384\) 5.56906 0.284195
\(385\) 0 0
\(386\) 4.50804 0.229453
\(387\) −1.73846 −0.0883709
\(388\) 5.26511 0.267296
\(389\) 22.8774 1.15993 0.579965 0.814642i \(-0.303066\pi\)
0.579965 + 0.814642i \(0.303066\pi\)
\(390\) 3.71021 0.187874
\(391\) −5.92790 −0.299787
\(392\) 0 0
\(393\) 7.89826 0.398414
\(394\) −3.98504 −0.200763
\(395\) −23.5365 −1.18425
\(396\) −0.513219 −0.0257902
\(397\) −24.1253 −1.21081 −0.605406 0.795917i \(-0.706989\pi\)
−0.605406 + 0.795917i \(0.706989\pi\)
\(398\) −0.630904 −0.0316244
\(399\) 0 0
\(400\) 34.6034 1.73017
\(401\) −28.1838 −1.40743 −0.703716 0.710481i \(-0.748477\pi\)
−0.703716 + 0.710481i \(0.748477\pi\)
\(402\) 1.36649 0.0681546
\(403\) 9.65773 0.481086
\(404\) −21.4082 −1.06510
\(405\) 3.75467 0.186571
\(406\) 0 0
\(407\) −1.49752 −0.0742292
\(408\) 0.463716 0.0229574
\(409\) 22.9535 1.13498 0.567489 0.823381i \(-0.307915\pi\)
0.567489 + 0.823381i \(0.307915\pi\)
\(410\) 0.681187 0.0336414
\(411\) 12.1886 0.601219
\(412\) 12.7205 0.626696
\(413\) 0 0
\(414\) 1.66920 0.0820368
\(415\) 33.0910 1.62437
\(416\) 11.5988 0.568677
\(417\) 23.4534 1.14852
\(418\) 0.210178 0.0102801
\(419\) −7.20087 −0.351785 −0.175893 0.984409i \(-0.556281\pi\)
−0.175893 + 0.984409i \(0.556281\pi\)
\(420\) 0 0
\(421\) 19.3097 0.941096 0.470548 0.882374i \(-0.344056\pi\)
0.470548 + 0.882374i \(0.344056\pi\)
\(422\) 1.58543 0.0771778
\(423\) −0.476598 −0.0231730
\(424\) −1.62995 −0.0791572
\(425\) 5.86153 0.284326
\(426\) 1.21497 0.0588655
\(427\) 0 0
\(428\) −27.0030 −1.30524
\(429\) −1.42106 −0.0686093
\(430\) 1.18422 0.0571080
\(431\) −18.8713 −0.909000 −0.454500 0.890747i \(-0.650182\pi\)
−0.454500 + 0.890747i \(0.650182\pi\)
\(432\) 3.80360 0.183001
\(433\) −14.0523 −0.675311 −0.337655 0.941270i \(-0.609634\pi\)
−0.337655 + 0.941270i \(0.609634\pi\)
\(434\) 0 0
\(435\) 17.3105 0.829975
\(436\) 9.08708 0.435192
\(437\) 40.8532 1.95428
\(438\) 2.68449 0.128270
\(439\) −31.8321 −1.51926 −0.759631 0.650355i \(-0.774620\pi\)
−0.759631 + 0.650355i \(0.774620\pi\)
\(440\) 0.705046 0.0336118
\(441\) 0 0
\(442\) 0.636668 0.0302832
\(443\) −27.6185 −1.31220 −0.656098 0.754676i \(-0.727794\pi\)
−0.656098 + 0.754676i \(0.727794\pi\)
\(444\) 11.2906 0.535826
\(445\) −21.5364 −1.02093
\(446\) 2.15716 0.102144
\(447\) 1.91828 0.0907316
\(448\) 0 0
\(449\) 5.46660 0.257985 0.128992 0.991646i \(-0.458826\pi\)
0.128992 + 0.991646i \(0.458826\pi\)
\(450\) −1.65051 −0.0778060
\(451\) −0.260903 −0.0122855
\(452\) 15.6714 0.737122
\(453\) −0.875982 −0.0411572
\(454\) −3.15716 −0.148173
\(455\) 0 0
\(456\) −3.19579 −0.149657
\(457\) −14.8767 −0.695905 −0.347952 0.937512i \(-0.613123\pi\)
−0.347952 + 0.937512i \(0.613123\pi\)
\(458\) −0.725923 −0.0339202
\(459\) 0.644297 0.0300732
\(460\) 67.9531 3.16833
\(461\) 26.0239 1.21205 0.606026 0.795445i \(-0.292763\pi\)
0.606026 + 0.795445i \(0.292763\pi\)
\(462\) 0 0
\(463\) 3.72466 0.173099 0.0865497 0.996248i \(-0.472416\pi\)
0.0865497 + 0.996248i \(0.472416\pi\)
\(464\) 17.5361 0.814091
\(465\) −6.65755 −0.308737
\(466\) 0.734571 0.0340283
\(467\) −6.65419 −0.307919 −0.153960 0.988077i \(-0.549203\pi\)
−0.153960 + 0.988077i \(0.549203\pi\)
\(468\) 10.7141 0.495259
\(469\) 0 0
\(470\) 0.324653 0.0149751
\(471\) −21.4256 −0.987240
\(472\) 7.47974 0.344283
\(473\) −0.453570 −0.0208552
\(474\) 1.13727 0.0522367
\(475\) −40.3959 −1.85349
\(476\) 0 0
\(477\) −2.26468 −0.103693
\(478\) 0.701585 0.0320897
\(479\) 13.1733 0.601903 0.300951 0.953639i \(-0.402696\pi\)
0.300951 + 0.953639i \(0.402696\pi\)
\(480\) −7.99562 −0.364948
\(481\) 31.2626 1.42545
\(482\) 3.98523 0.181522
\(483\) 0 0
\(484\) 21.5040 0.977456
\(485\) −10.0498 −0.456337
\(486\) −0.181424 −0.00822956
\(487\) −34.9155 −1.58217 −0.791085 0.611706i \(-0.790484\pi\)
−0.791085 + 0.611706i \(0.790484\pi\)
\(488\) −8.91650 −0.403631
\(489\) 20.4306 0.923902
\(490\) 0 0
\(491\) 21.7111 0.979810 0.489905 0.871776i \(-0.337032\pi\)
0.489905 + 0.871776i \(0.337032\pi\)
\(492\) 1.96709 0.0886831
\(493\) 2.97046 0.133783
\(494\) −4.38772 −0.197413
\(495\) 0.979606 0.0440300
\(496\) −6.74430 −0.302828
\(497\) 0 0
\(498\) −1.59894 −0.0716503
\(499\) 7.15448 0.320278 0.160139 0.987094i \(-0.448806\pi\)
0.160139 + 0.987094i \(0.448806\pi\)
\(500\) −30.2636 −1.35343
\(501\) −8.65888 −0.386850
\(502\) −3.42178 −0.152722
\(503\) −40.5245 −1.80690 −0.903448 0.428698i \(-0.858973\pi\)
−0.903448 + 0.428698i \(0.858973\pi\)
\(504\) 0 0
\(505\) 40.8628 1.81837
\(506\) 0.435500 0.0193604
\(507\) 16.6664 0.740180
\(508\) 18.7515 0.831965
\(509\) −40.0598 −1.77562 −0.887811 0.460209i \(-0.847774\pi\)
−0.887811 + 0.460209i \(0.847774\pi\)
\(510\) −0.438887 −0.0194342
\(511\) 0 0
\(512\) −13.5749 −0.599931
\(513\) −4.44030 −0.196044
\(514\) 4.77891 0.210789
\(515\) −24.2803 −1.06992
\(516\) 3.41970 0.150544
\(517\) −0.124346 −0.00546874
\(518\) 0 0
\(519\) −7.01283 −0.307829
\(520\) −14.7187 −0.645459
\(521\) 26.8711 1.17724 0.588621 0.808409i \(-0.299671\pi\)
0.588621 + 0.808409i \(0.299671\pi\)
\(522\) −0.836435 −0.0366098
\(523\) −32.0580 −1.40180 −0.700899 0.713261i \(-0.747218\pi\)
−0.700899 + 0.713261i \(0.747218\pi\)
\(524\) −15.5366 −0.678717
\(525\) 0 0
\(526\) −5.40167 −0.235524
\(527\) −1.14243 −0.0497649
\(528\) 0.992371 0.0431874
\(529\) 61.6503 2.68045
\(530\) 1.54267 0.0670094
\(531\) 10.3925 0.450996
\(532\) 0 0
\(533\) 5.44669 0.235922
\(534\) 1.04063 0.0450325
\(535\) 51.5419 2.22835
\(536\) −5.42100 −0.234152
\(537\) 7.18201 0.309926
\(538\) 0.0295274 0.00127302
\(539\) 0 0
\(540\) −7.38576 −0.317832
\(541\) −25.8202 −1.11010 −0.555048 0.831818i \(-0.687300\pi\)
−0.555048 + 0.831818i \(0.687300\pi\)
\(542\) 1.37084 0.0588827
\(543\) 7.76715 0.333320
\(544\) −1.37204 −0.0588257
\(545\) −17.3450 −0.742976
\(546\) 0 0
\(547\) 3.89760 0.166649 0.0833247 0.996522i \(-0.473446\pi\)
0.0833247 + 0.996522i \(0.473446\pi\)
\(548\) −23.9760 −1.02420
\(549\) −12.3888 −0.528740
\(550\) −0.430625 −0.0183619
\(551\) −20.4715 −0.872115
\(552\) −6.62187 −0.281845
\(553\) 0 0
\(554\) 3.46920 0.147392
\(555\) −21.5508 −0.914782
\(556\) −46.1349 −1.95655
\(557\) 8.54683 0.362141 0.181070 0.983470i \(-0.442044\pi\)
0.181070 + 0.983470i \(0.442044\pi\)
\(558\) 0.321690 0.0136182
\(559\) 9.46885 0.400490
\(560\) 0 0
\(561\) 0.168099 0.00709716
\(562\) −4.56661 −0.192631
\(563\) 16.7189 0.704619 0.352309 0.935884i \(-0.385396\pi\)
0.352309 + 0.935884i \(0.385396\pi\)
\(564\) 0.937510 0.0394763
\(565\) −29.9128 −1.25844
\(566\) −2.14736 −0.0902604
\(567\) 0 0
\(568\) −4.81989 −0.202238
\(569\) −6.95737 −0.291668 −0.145834 0.989309i \(-0.546587\pi\)
−0.145834 + 0.989309i \(0.546587\pi\)
\(570\) 3.02467 0.126690
\(571\) 2.95282 0.123572 0.0617858 0.998089i \(-0.480320\pi\)
0.0617858 + 0.998089i \(0.480320\pi\)
\(572\) 2.79534 0.116879
\(573\) 4.77261 0.199379
\(574\) 0 0
\(575\) −83.7026 −3.49064
\(576\) −7.22085 −0.300869
\(577\) 30.0904 1.25268 0.626341 0.779550i \(-0.284552\pi\)
0.626341 + 0.779550i \(0.284552\pi\)
\(578\) 3.00890 0.125154
\(579\) −24.8481 −1.03265
\(580\) −34.0512 −1.41390
\(581\) 0 0
\(582\) 0.485601 0.0201288
\(583\) −0.590863 −0.0244710
\(584\) −10.6496 −0.440683
\(585\) −20.4505 −0.845525
\(586\) 5.08585 0.210095
\(587\) 1.23855 0.0511203 0.0255602 0.999673i \(-0.491863\pi\)
0.0255602 + 0.999673i \(0.491863\pi\)
\(588\) 0 0
\(589\) 7.87326 0.324412
\(590\) −7.07925 −0.291448
\(591\) 21.9653 0.903533
\(592\) −21.8317 −0.897276
\(593\) −37.3341 −1.53313 −0.766564 0.642167i \(-0.778035\pi\)
−0.766564 + 0.642167i \(0.778035\pi\)
\(594\) −0.0473341 −0.00194214
\(595\) 0 0
\(596\) −3.77342 −0.154565
\(597\) 3.47751 0.142325
\(598\) −9.09162 −0.371784
\(599\) −0.376353 −0.0153774 −0.00768868 0.999970i \(-0.502447\pi\)
−0.00768868 + 0.999970i \(0.502447\pi\)
\(600\) 6.54773 0.267310
\(601\) −22.4269 −0.914810 −0.457405 0.889258i \(-0.651221\pi\)
−0.457405 + 0.889258i \(0.651221\pi\)
\(602\) 0 0
\(603\) −7.53205 −0.306729
\(604\) 1.72313 0.0701132
\(605\) −41.0458 −1.66875
\(606\) −1.97447 −0.0802075
\(607\) −11.8223 −0.479853 −0.239927 0.970791i \(-0.577123\pi\)
−0.239927 + 0.970791i \(0.577123\pi\)
\(608\) 9.45567 0.383478
\(609\) 0 0
\(610\) 8.43907 0.341688
\(611\) 2.59588 0.105018
\(612\) −1.26739 −0.0512311
\(613\) 6.63056 0.267806 0.133903 0.990994i \(-0.457249\pi\)
0.133903 + 0.990994i \(0.457249\pi\)
\(614\) −1.78201 −0.0719162
\(615\) −3.75467 −0.151403
\(616\) 0 0
\(617\) −25.0331 −1.00780 −0.503898 0.863763i \(-0.668101\pi\)
−0.503898 + 0.863763i \(0.668101\pi\)
\(618\) 1.17321 0.0471936
\(619\) 28.6287 1.15069 0.575343 0.817912i \(-0.304869\pi\)
0.575343 + 0.817912i \(0.304869\pi\)
\(620\) 13.0960 0.525947
\(621\) −9.20056 −0.369206
\(622\) 5.93778 0.238083
\(623\) 0 0
\(624\) −20.7170 −0.829343
\(625\) 12.2777 0.491109
\(626\) 1.27199 0.0508389
\(627\) −1.15849 −0.0462656
\(628\) 42.1460 1.68181
\(629\) −3.69810 −0.147453
\(630\) 0 0
\(631\) 19.0807 0.759591 0.379796 0.925070i \(-0.375994\pi\)
0.379796 + 0.925070i \(0.375994\pi\)
\(632\) −4.51166 −0.179464
\(633\) −8.73884 −0.347338
\(634\) 4.42670 0.175807
\(635\) −35.7920 −1.42036
\(636\) 4.45482 0.176645
\(637\) 0 0
\(638\) −0.218229 −0.00863976
\(639\) −6.69685 −0.264923
\(640\) 20.9100 0.826540
\(641\) 9.07184 0.358316 0.179158 0.983820i \(-0.442663\pi\)
0.179158 + 0.983820i \(0.442663\pi\)
\(642\) −2.49048 −0.0982914
\(643\) 3.54904 0.139960 0.0699802 0.997548i \(-0.477706\pi\)
0.0699802 + 0.997548i \(0.477706\pi\)
\(644\) 0 0
\(645\) −6.52735 −0.257014
\(646\) 0.519031 0.0204210
\(647\) −12.4651 −0.490053 −0.245027 0.969516i \(-0.578797\pi\)
−0.245027 + 0.969516i \(0.578797\pi\)
\(648\) 0.719724 0.0282734
\(649\) 2.71144 0.106433
\(650\) 8.98984 0.352610
\(651\) 0 0
\(652\) −40.1887 −1.57391
\(653\) −3.89910 −0.152584 −0.0762918 0.997086i \(-0.524308\pi\)
−0.0762918 + 0.997086i \(0.524308\pi\)
\(654\) 0.838100 0.0327723
\(655\) 29.6554 1.15873
\(656\) −3.80360 −0.148505
\(657\) −14.7968 −0.577277
\(658\) 0 0
\(659\) 25.7940 1.00479 0.502396 0.864638i \(-0.332452\pi\)
0.502396 + 0.864638i \(0.332452\pi\)
\(660\) −1.92697 −0.0750072
\(661\) −22.7358 −0.884321 −0.442160 0.896936i \(-0.645788\pi\)
−0.442160 + 0.896936i \(0.645788\pi\)
\(662\) −3.46542 −0.134687
\(663\) −3.50928 −0.136289
\(664\) 6.34314 0.246161
\(665\) 0 0
\(666\) 1.04133 0.0403506
\(667\) −42.4182 −1.64244
\(668\) 17.0328 0.659017
\(669\) −11.8901 −0.459700
\(670\) 5.13074 0.198218
\(671\) −3.23227 −0.124780
\(672\) 0 0
\(673\) −2.37936 −0.0917177 −0.0458589 0.998948i \(-0.514602\pi\)
−0.0458589 + 0.998948i \(0.514602\pi\)
\(674\) 0.368602 0.0141980
\(675\) 9.09756 0.350165
\(676\) −32.7842 −1.26093
\(677\) 23.5460 0.904945 0.452473 0.891778i \(-0.350542\pi\)
0.452473 + 0.891778i \(0.350542\pi\)
\(678\) 1.44537 0.0555092
\(679\) 0 0
\(680\) 1.74110 0.0667682
\(681\) 17.4021 0.666849
\(682\) 0.0839299 0.00321384
\(683\) 26.6161 1.01844 0.509218 0.860638i \(-0.329935\pi\)
0.509218 + 0.860638i \(0.329935\pi\)
\(684\) 8.73445 0.333970
\(685\) 45.7642 1.74856
\(686\) 0 0
\(687\) 4.00125 0.152657
\(688\) −6.61240 −0.252095
\(689\) 12.3350 0.469927
\(690\) 6.26731 0.238592
\(691\) −34.0673 −1.29598 −0.647990 0.761649i \(-0.724390\pi\)
−0.647990 + 0.761649i \(0.724390\pi\)
\(692\) 13.7948 0.524401
\(693\) 0 0
\(694\) −2.13060 −0.0808764
\(695\) 88.0599 3.34030
\(696\) 3.31821 0.125776
\(697\) −0.644297 −0.0244045
\(698\) −4.93684 −0.186862
\(699\) −4.04892 −0.153144
\(700\) 0 0
\(701\) 19.6554 0.742374 0.371187 0.928558i \(-0.378951\pi\)
0.371187 + 0.928558i \(0.378951\pi\)
\(702\) 0.988159 0.0372957
\(703\) 25.4862 0.961229
\(704\) −1.88394 −0.0710038
\(705\) −1.78947 −0.0673954
\(706\) 0.0689929 0.00259658
\(707\) 0 0
\(708\) −20.4430 −0.768293
\(709\) 1.60380 0.0602318 0.0301159 0.999546i \(-0.490412\pi\)
0.0301159 + 0.999546i \(0.490412\pi\)
\(710\) 4.56181 0.171202
\(711\) −6.26859 −0.235091
\(712\) −4.12827 −0.154713
\(713\) 16.3139 0.610959
\(714\) 0 0
\(715\) −5.33561 −0.199540
\(716\) −14.1276 −0.527974
\(717\) −3.86710 −0.144420
\(718\) 1.71279 0.0639207
\(719\) 50.9143 1.89878 0.949392 0.314093i \(-0.101700\pi\)
0.949392 + 0.314093i \(0.101700\pi\)
\(720\) 14.2812 0.532231
\(721\) 0 0
\(722\) −0.129944 −0.00483603
\(723\) −21.9664 −0.816939
\(724\) −15.2786 −0.567826
\(725\) 41.9433 1.55773
\(726\) 1.98331 0.0736077
\(727\) −13.8327 −0.513026 −0.256513 0.966541i \(-0.582574\pi\)
−0.256513 + 0.966541i \(0.582574\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 10.0794 0.373054
\(731\) −1.12009 −0.0414279
\(732\) 24.3698 0.900732
\(733\) 15.8688 0.586128 0.293064 0.956093i \(-0.405325\pi\)
0.293064 + 0.956093i \(0.405325\pi\)
\(734\) 2.87245 0.106024
\(735\) 0 0
\(736\) 19.5927 0.722197
\(737\) −1.96514 −0.0723868
\(738\) 0.181424 0.00667831
\(739\) −9.23223 −0.339613 −0.169806 0.985477i \(-0.554314\pi\)
−0.169806 + 0.985477i \(0.554314\pi\)
\(740\) 42.3923 1.55837
\(741\) 24.1849 0.888455
\(742\) 0 0
\(743\) −47.1930 −1.73134 −0.865671 0.500613i \(-0.833108\pi\)
−0.865671 + 0.500613i \(0.833108\pi\)
\(744\) −1.27617 −0.0467867
\(745\) 7.20252 0.263880
\(746\) −3.76533 −0.137858
\(747\) 8.81328 0.322461
\(748\) −0.330666 −0.0120903
\(749\) 0 0
\(750\) −2.79120 −0.101920
\(751\) −53.5127 −1.95271 −0.976354 0.216178i \(-0.930641\pi\)
−0.976354 + 0.216178i \(0.930641\pi\)
\(752\) −1.81279 −0.0661056
\(753\) 18.8607 0.687322
\(754\) 4.55580 0.165912
\(755\) −3.28902 −0.119700
\(756\) 0 0
\(757\) 29.7682 1.08194 0.540972 0.841040i \(-0.318056\pi\)
0.540972 + 0.841040i \(0.318056\pi\)
\(758\) −0.0742315 −0.00269621
\(759\) −2.40046 −0.0871311
\(760\) −11.9991 −0.435255
\(761\) 5.31595 0.192703 0.0963515 0.995347i \(-0.469283\pi\)
0.0963515 + 0.995347i \(0.469283\pi\)
\(762\) 1.72945 0.0626515
\(763\) 0 0
\(764\) −9.38813 −0.339650
\(765\) 2.41912 0.0874636
\(766\) −7.07015 −0.255455
\(767\) −56.6047 −2.04388
\(768\) 13.4313 0.484661
\(769\) 22.3645 0.806484 0.403242 0.915093i \(-0.367883\pi\)
0.403242 + 0.915093i \(0.367883\pi\)
\(770\) 0 0
\(771\) −26.3411 −0.948651
\(772\) 48.8784 1.75917
\(773\) −48.1980 −1.73356 −0.866780 0.498690i \(-0.833815\pi\)
−0.866780 + 0.498690i \(0.833815\pi\)
\(774\) 0.315399 0.0113368
\(775\) −16.1312 −0.579451
\(776\) −1.92642 −0.0691544
\(777\) 0 0
\(778\) −4.15051 −0.148803
\(779\) 4.44030 0.159090
\(780\) 40.2279 1.44039
\(781\) −1.74723 −0.0625208
\(782\) 1.07546 0.0384585
\(783\) 4.61039 0.164762
\(784\) 0 0
\(785\) −80.4461 −2.87125
\(786\) −1.43293 −0.0511111
\(787\) 7.84045 0.279482 0.139741 0.990188i \(-0.455373\pi\)
0.139741 + 0.990188i \(0.455373\pi\)
\(788\) −43.2077 −1.53921
\(789\) 29.7738 1.05997
\(790\) 4.27009 0.151923
\(791\) 0 0
\(792\) 0.187778 0.00667242
\(793\) 67.4777 2.39620
\(794\) 4.37690 0.155330
\(795\) −8.50314 −0.301575
\(796\) −6.84057 −0.242457
\(797\) 5.10550 0.180846 0.0904230 0.995903i \(-0.471178\pi\)
0.0904230 + 0.995903i \(0.471178\pi\)
\(798\) 0 0
\(799\) −0.307071 −0.0108634
\(800\) −19.3734 −0.684952
\(801\) −5.73591 −0.202668
\(802\) 5.11322 0.180554
\(803\) −3.86052 −0.136235
\(804\) 14.8162 0.522527
\(805\) 0 0
\(806\) −1.75214 −0.0617166
\(807\) −0.162754 −0.00572920
\(808\) 7.83291 0.275561
\(809\) −2.94662 −0.103598 −0.0517989 0.998658i \(-0.516495\pi\)
−0.0517989 + 0.998658i \(0.516495\pi\)
\(810\) −0.681187 −0.0239345
\(811\) −54.8372 −1.92559 −0.962797 0.270227i \(-0.912901\pi\)
−0.962797 + 0.270227i \(0.912901\pi\)
\(812\) 0 0
\(813\) −7.55601 −0.265001
\(814\) 0.271686 0.00952258
\(815\) 76.7101 2.68704
\(816\) 2.45065 0.0857898
\(817\) 7.71929 0.270064
\(818\) −4.16432 −0.145602
\(819\) 0 0
\(820\) 7.38576 0.257922
\(821\) 14.2257 0.496479 0.248240 0.968699i \(-0.420148\pi\)
0.248240 + 0.968699i \(0.420148\pi\)
\(822\) −2.21130 −0.0771281
\(823\) 20.2318 0.705235 0.352617 0.935768i \(-0.385292\pi\)
0.352617 + 0.935768i \(0.385292\pi\)
\(824\) −4.65424 −0.162138
\(825\) 2.37358 0.0826375
\(826\) 0 0
\(827\) 36.5932 1.27247 0.636235 0.771496i \(-0.280491\pi\)
0.636235 + 0.771496i \(0.280491\pi\)
\(828\) 18.0983 0.628959
\(829\) −26.4761 −0.919551 −0.459776 0.888035i \(-0.652070\pi\)
−0.459776 + 0.888035i \(0.652070\pi\)
\(830\) −6.00350 −0.208384
\(831\) −19.1220 −0.663336
\(832\) 39.3297 1.36351
\(833\) 0 0
\(834\) −4.25501 −0.147339
\(835\) −32.5113 −1.12510
\(836\) 2.27885 0.0788155
\(837\) −1.77314 −0.0612886
\(838\) 1.30641 0.0451292
\(839\) −18.2255 −0.629214 −0.314607 0.949222i \(-0.601873\pi\)
−0.314607 + 0.949222i \(0.601873\pi\)
\(840\) 0 0
\(841\) −7.74431 −0.267045
\(842\) −3.50324 −0.120730
\(843\) 25.1709 0.866933
\(844\) 17.1900 0.591706
\(845\) 62.5768 2.15271
\(846\) 0.0864664 0.00297278
\(847\) 0 0
\(848\) −8.61394 −0.295804
\(849\) 11.8362 0.406216
\(850\) −1.06342 −0.0364751
\(851\) 52.8088 1.81026
\(852\) 13.1733 0.451309
\(853\) 11.2283 0.384450 0.192225 0.981351i \(-0.438430\pi\)
0.192225 + 0.981351i \(0.438430\pi\)
\(854\) 0 0
\(855\) −16.6719 −0.570166
\(856\) 9.87995 0.337690
\(857\) 27.6762 0.945399 0.472700 0.881224i \(-0.343280\pi\)
0.472700 + 0.881224i \(0.343280\pi\)
\(858\) 0.257814 0.00880163
\(859\) −2.69466 −0.0919407 −0.0459704 0.998943i \(-0.514638\pi\)
−0.0459704 + 0.998943i \(0.514638\pi\)
\(860\) 12.8399 0.437835
\(861\) 0 0
\(862\) 3.42371 0.116612
\(863\) −18.8692 −0.642314 −0.321157 0.947026i \(-0.604072\pi\)
−0.321157 + 0.947026i \(0.604072\pi\)
\(864\) −2.12951 −0.0724475
\(865\) −26.3309 −0.895277
\(866\) 2.54943 0.0866330
\(867\) −16.5849 −0.563252
\(868\) 0 0
\(869\) −1.63550 −0.0554804
\(870\) −3.14054 −0.106474
\(871\) 41.0247 1.39007
\(872\) −3.32482 −0.112592
\(873\) −2.67661 −0.0905894
\(874\) −7.41176 −0.250706
\(875\) 0 0
\(876\) 29.1065 0.983417
\(877\) 48.9667 1.65349 0.826743 0.562580i \(-0.190191\pi\)
0.826743 + 0.562580i \(0.190191\pi\)
\(878\) 5.77510 0.194900
\(879\) −28.0330 −0.945528
\(880\) 3.72603 0.125604
\(881\) 52.3303 1.76305 0.881526 0.472136i \(-0.156517\pi\)
0.881526 + 0.472136i \(0.156517\pi\)
\(882\) 0 0
\(883\) −13.0442 −0.438971 −0.219486 0.975616i \(-0.570438\pi\)
−0.219486 + 0.975616i \(0.570438\pi\)
\(884\) 6.90306 0.232175
\(885\) 39.0205 1.31166
\(886\) 5.01066 0.168336
\(887\) 21.7131 0.729053 0.364527 0.931193i \(-0.381231\pi\)
0.364527 + 0.931193i \(0.381231\pi\)
\(888\) −4.13103 −0.138628
\(889\) 0 0
\(890\) 3.90723 0.130971
\(891\) 0.260903 0.00874059
\(892\) 23.3889 0.783119
\(893\) 2.11624 0.0708172
\(894\) −0.348022 −0.0116396
\(895\) 26.9661 0.901376
\(896\) 0 0
\(897\) 50.1126 1.67321
\(898\) −0.991772 −0.0330959
\(899\) −8.17486 −0.272647
\(900\) −17.8957 −0.596522
\(901\) −1.45913 −0.0486106
\(902\) 0.0473341 0.00157605
\(903\) 0 0
\(904\) −5.73392 −0.190707
\(905\) 29.1631 0.969414
\(906\) 0.158924 0.00527990
\(907\) 39.7891 1.32117 0.660587 0.750749i \(-0.270307\pi\)
0.660587 + 0.750749i \(0.270307\pi\)
\(908\) −34.2314 −1.13601
\(909\) 10.8832 0.360973
\(910\) 0 0
\(911\) 29.8173 0.987890 0.493945 0.869493i \(-0.335554\pi\)
0.493945 + 0.869493i \(0.335554\pi\)
\(912\) −16.8891 −0.559254
\(913\) 2.29941 0.0760995
\(914\) 2.69900 0.0892749
\(915\) −46.5157 −1.53776
\(916\) −7.87081 −0.260059
\(917\) 0 0
\(918\) −0.116891 −0.00385798
\(919\) 43.1595 1.42370 0.711850 0.702331i \(-0.247857\pi\)
0.711850 + 0.702331i \(0.247857\pi\)
\(920\) −24.8629 −0.819707
\(921\) 9.82237 0.323658
\(922\) −4.72135 −0.155489
\(923\) 36.4757 1.20061
\(924\) 0 0
\(925\) −52.2176 −1.71690
\(926\) −0.675742 −0.0222063
\(927\) −6.46670 −0.212394
\(928\) −9.81788 −0.322288
\(929\) −5.59313 −0.183505 −0.0917524 0.995782i \(-0.529247\pi\)
−0.0917524 + 0.995782i \(0.529247\pi\)
\(930\) 1.20784 0.0396066
\(931\) 0 0
\(932\) 7.96457 0.260888
\(933\) −32.7287 −1.07149
\(934\) 1.20723 0.0395018
\(935\) 0.631157 0.0206411
\(936\) −3.92011 −0.128133
\(937\) 29.0922 0.950400 0.475200 0.879878i \(-0.342376\pi\)
0.475200 + 0.879878i \(0.342376\pi\)
\(938\) 0 0
\(939\) −7.01115 −0.228800
\(940\) 3.52004 0.114811
\(941\) −38.9512 −1.26977 −0.634887 0.772605i \(-0.718953\pi\)
−0.634887 + 0.772605i \(0.718953\pi\)
\(942\) 3.88712 0.126649
\(943\) 9.20056 0.299611
\(944\) 39.5289 1.28656
\(945\) 0 0
\(946\) 0.0822885 0.00267543
\(947\) 29.6641 0.963954 0.481977 0.876184i \(-0.339919\pi\)
0.481977 + 0.876184i \(0.339919\pi\)
\(948\) 12.3309 0.400488
\(949\) 80.5933 2.61617
\(950\) 7.32878 0.237777
\(951\) −24.3997 −0.791216
\(952\) 0 0
\(953\) 22.2806 0.721738 0.360869 0.932616i \(-0.382480\pi\)
0.360869 + 0.932616i \(0.382480\pi\)
\(954\) 0.410868 0.0133023
\(955\) 17.9196 0.579864
\(956\) 7.60692 0.246025
\(957\) 1.20287 0.0388831
\(958\) −2.38995 −0.0772158
\(959\) 0 0
\(960\) −27.1119 −0.875033
\(961\) −27.8560 −0.898580
\(962\) −5.67178 −0.182866
\(963\) 13.7274 0.442360
\(964\) 43.2098 1.39169
\(965\) −93.2965 −3.00332
\(966\) 0 0
\(967\) 44.0980 1.41810 0.709048 0.705160i \(-0.249125\pi\)
0.709048 + 0.705160i \(0.249125\pi\)
\(968\) −7.86798 −0.252886
\(969\) −2.86087 −0.0919044
\(970\) 1.82327 0.0585417
\(971\) −3.31986 −0.106539 −0.0532697 0.998580i \(-0.516964\pi\)
−0.0532697 + 0.998580i \(0.516964\pi\)
\(972\) −1.96709 −0.0630943
\(973\) 0 0
\(974\) 6.33450 0.202971
\(975\) −49.5515 −1.58692
\(976\) −47.1219 −1.50833
\(977\) −7.33853 −0.234780 −0.117390 0.993086i \(-0.537453\pi\)
−0.117390 + 0.993086i \(0.537453\pi\)
\(978\) −3.70660 −0.118524
\(979\) −1.49652 −0.0478289
\(980\) 0 0
\(981\) −4.61957 −0.147491
\(982\) −3.93892 −0.125696
\(983\) −38.0704 −1.21426 −0.607128 0.794604i \(-0.707679\pi\)
−0.607128 + 0.794604i \(0.707679\pi\)
\(984\) −0.719724 −0.0229440
\(985\) 82.4726 2.62780
\(986\) −0.538913 −0.0171625
\(987\) 0 0
\(988\) −47.5738 −1.51352
\(989\) 15.9948 0.508606
\(990\) −0.177724 −0.00564844
\(991\) 38.8149 1.23300 0.616498 0.787357i \(-0.288551\pi\)
0.616498 + 0.787357i \(0.288551\pi\)
\(992\) 3.77592 0.119886
\(993\) 19.1012 0.606159
\(994\) 0 0
\(995\) 13.0569 0.413932
\(996\) −17.3365 −0.549327
\(997\) −18.9298 −0.599514 −0.299757 0.954016i \(-0.596906\pi\)
−0.299757 + 0.954016i \(0.596906\pi\)
\(998\) −1.29799 −0.0410873
\(999\) −5.73974 −0.181597
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 \(a_p\))