Properties

Label 6027.2.a.bm.1.8
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 1.8
Root \(0.631061\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.631061 q^{2} +1.00000 q^{3} -1.60176 q^{4} -1.65938 q^{5} -0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.631061 q^{2} +1.00000 q^{3} -1.60176 q^{4} -1.65938 q^{5} -0.631061 q^{6} +2.27293 q^{8} +1.00000 q^{9} +1.04717 q^{10} +2.82239 q^{11} -1.60176 q^{12} -3.15999 q^{13} -1.65938 q^{15} +1.76917 q^{16} +1.11961 q^{17} -0.631061 q^{18} +3.11082 q^{19} +2.65794 q^{20} -1.78110 q^{22} -6.51222 q^{23} +2.27293 q^{24} -2.24644 q^{25} +1.99415 q^{26} +1.00000 q^{27} +9.16578 q^{29} +1.04717 q^{30} -4.35118 q^{31} -5.66231 q^{32} +2.82239 q^{33} -0.706545 q^{34} -1.60176 q^{36} -11.1252 q^{37} -1.96312 q^{38} -3.15999 q^{39} -3.77167 q^{40} +1.00000 q^{41} -0.684567 q^{43} -4.52079 q^{44} -1.65938 q^{45} +4.10961 q^{46} +6.17414 q^{47} +1.76917 q^{48} +1.41764 q^{50} +1.11961 q^{51} +5.06155 q^{52} -13.0735 q^{53} -0.631061 q^{54} -4.68342 q^{55} +3.11082 q^{57} -5.78417 q^{58} +7.71075 q^{59} +2.65794 q^{60} +0.419560 q^{61} +2.74586 q^{62} +0.0349308 q^{64} +5.24364 q^{65} -1.78110 q^{66} +9.95583 q^{67} -1.79336 q^{68} -6.51222 q^{69} +7.39023 q^{71} +2.27293 q^{72} +13.9295 q^{73} +7.02071 q^{74} -2.24644 q^{75} -4.98280 q^{76} +1.99415 q^{78} -0.195831 q^{79} -2.93573 q^{80} +1.00000 q^{81} -0.631061 q^{82} -2.50464 q^{83} -1.85787 q^{85} +0.432003 q^{86} +9.16578 q^{87} +6.41509 q^{88} -12.4999 q^{89} +1.04717 q^{90} +10.4310 q^{92} -4.35118 q^{93} -3.89626 q^{94} -5.16206 q^{95} -5.66231 q^{96} +11.3773 q^{97} +2.82239 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.631061 −0.446227 −0.223114 0.974792i \(-0.571622\pi\)
−0.223114 + 0.974792i \(0.571622\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.60176 −0.800881
\(5\) −1.65938 −0.742100 −0.371050 0.928613i \(-0.621002\pi\)
−0.371050 + 0.928613i \(0.621002\pi\)
\(6\) −0.631061 −0.257629
\(7\) 0 0
\(8\) 2.27293 0.803602
\(9\) 1.00000 0.333333
\(10\) 1.04717 0.331145
\(11\) 2.82239 0.850981 0.425491 0.904963i \(-0.360102\pi\)
0.425491 + 0.904963i \(0.360102\pi\)
\(12\) −1.60176 −0.462389
\(13\) −3.15999 −0.876423 −0.438212 0.898872i \(-0.644388\pi\)
−0.438212 + 0.898872i \(0.644388\pi\)
\(14\) 0 0
\(15\) −1.65938 −0.428451
\(16\) 1.76917 0.442292
\(17\) 1.11961 0.271547 0.135773 0.990740i \(-0.456648\pi\)
0.135773 + 0.990740i \(0.456648\pi\)
\(18\) −0.631061 −0.148742
\(19\) 3.11082 0.713672 0.356836 0.934167i \(-0.383855\pi\)
0.356836 + 0.934167i \(0.383855\pi\)
\(20\) 2.65794 0.594333
\(21\) 0 0
\(22\) −1.78110 −0.379731
\(23\) −6.51222 −1.35789 −0.678946 0.734188i \(-0.737563\pi\)
−0.678946 + 0.734188i \(0.737563\pi\)
\(24\) 2.27293 0.463960
\(25\) −2.24644 −0.449288
\(26\) 1.99415 0.391084
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.16578 1.70204 0.851021 0.525131i \(-0.175984\pi\)
0.851021 + 0.525131i \(0.175984\pi\)
\(30\) 1.04717 0.191187
\(31\) −4.35118 −0.781495 −0.390748 0.920498i \(-0.627783\pi\)
−0.390748 + 0.920498i \(0.627783\pi\)
\(32\) −5.66231 −1.00097
\(33\) 2.82239 0.491314
\(34\) −0.706545 −0.121171
\(35\) 0 0
\(36\) −1.60176 −0.266960
\(37\) −11.1252 −1.82898 −0.914490 0.404609i \(-0.867407\pi\)
−0.914490 + 0.404609i \(0.867407\pi\)
\(38\) −1.96312 −0.318460
\(39\) −3.15999 −0.506003
\(40\) −3.77167 −0.596353
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −0.684567 −0.104395 −0.0521977 0.998637i \(-0.516623\pi\)
−0.0521977 + 0.998637i \(0.516623\pi\)
\(44\) −4.52079 −0.681535
\(45\) −1.65938 −0.247367
\(46\) 4.10961 0.605929
\(47\) 6.17414 0.900591 0.450296 0.892880i \(-0.351319\pi\)
0.450296 + 0.892880i \(0.351319\pi\)
\(48\) 1.76917 0.255357
\(49\) 0 0
\(50\) 1.41764 0.200485
\(51\) 1.11961 0.156777
\(52\) 5.06155 0.701911
\(53\) −13.0735 −1.79579 −0.897894 0.440212i \(-0.854903\pi\)
−0.897894 + 0.440212i \(0.854903\pi\)
\(54\) −0.631061 −0.0858765
\(55\) −4.68342 −0.631513
\(56\) 0 0
\(57\) 3.11082 0.412039
\(58\) −5.78417 −0.759498
\(59\) 7.71075 1.00385 0.501927 0.864910i \(-0.332625\pi\)
0.501927 + 0.864910i \(0.332625\pi\)
\(60\) 2.65794 0.343139
\(61\) 0.419560 0.0537192 0.0268596 0.999639i \(-0.491449\pi\)
0.0268596 + 0.999639i \(0.491449\pi\)
\(62\) 2.74586 0.348725
\(63\) 0 0
\(64\) 0.0349308 0.00436635
\(65\) 5.24364 0.650393
\(66\) −1.78110 −0.219238
\(67\) 9.95583 1.21630 0.608149 0.793823i \(-0.291912\pi\)
0.608149 + 0.793823i \(0.291912\pi\)
\(68\) −1.79336 −0.217476
\(69\) −6.51222 −0.783979
\(70\) 0 0
\(71\) 7.39023 0.877059 0.438529 0.898717i \(-0.355499\pi\)
0.438529 + 0.898717i \(0.355499\pi\)
\(72\) 2.27293 0.267867
\(73\) 13.9295 1.63033 0.815165 0.579228i \(-0.196646\pi\)
0.815165 + 0.579228i \(0.196646\pi\)
\(74\) 7.02071 0.816141
\(75\) −2.24644 −0.259397
\(76\) −4.98280 −0.571567
\(77\) 0 0
\(78\) 1.99415 0.225792
\(79\) −0.195831 −0.0220327 −0.0110164 0.999939i \(-0.503507\pi\)
−0.0110164 + 0.999939i \(0.503507\pi\)
\(80\) −2.93573 −0.328224
\(81\) 1.00000 0.111111
\(82\) −0.631061 −0.0696890
\(83\) −2.50464 −0.274919 −0.137460 0.990507i \(-0.543894\pi\)
−0.137460 + 0.990507i \(0.543894\pi\)
\(84\) 0 0
\(85\) −1.85787 −0.201515
\(86\) 0.432003 0.0465841
\(87\) 9.16578 0.982675
\(88\) 6.41509 0.683851
\(89\) −12.4999 −1.32499 −0.662493 0.749068i \(-0.730502\pi\)
−0.662493 + 0.749068i \(0.730502\pi\)
\(90\) 1.04717 0.110382
\(91\) 0 0
\(92\) 10.4310 1.08751
\(93\) −4.35118 −0.451196
\(94\) −3.89626 −0.401868
\(95\) −5.16206 −0.529616
\(96\) −5.66231 −0.577907
\(97\) 11.3773 1.15519 0.577593 0.816325i \(-0.303992\pi\)
0.577593 + 0.816325i \(0.303992\pi\)
\(98\) 0 0
\(99\) 2.82239 0.283660
\(100\) 3.59827 0.359827
\(101\) 14.9268 1.48527 0.742634 0.669697i \(-0.233576\pi\)
0.742634 + 0.669697i \(0.233576\pi\)
\(102\) −0.706545 −0.0699584
\(103\) −9.93429 −0.978854 −0.489427 0.872044i \(-0.662794\pi\)
−0.489427 + 0.872044i \(0.662794\pi\)
\(104\) −7.18244 −0.704296
\(105\) 0 0
\(106\) 8.25019 0.801330
\(107\) −16.6479 −1.60941 −0.804707 0.593673i \(-0.797677\pi\)
−0.804707 + 0.593673i \(0.797677\pi\)
\(108\) −1.60176 −0.154130
\(109\) 17.3263 1.65956 0.829779 0.558092i \(-0.188466\pi\)
0.829779 + 0.558092i \(0.188466\pi\)
\(110\) 2.95553 0.281798
\(111\) −11.1252 −1.05596
\(112\) 0 0
\(113\) −10.5963 −0.996820 −0.498410 0.866941i \(-0.666083\pi\)
−0.498410 + 0.866941i \(0.666083\pi\)
\(114\) −1.96312 −0.183863
\(115\) 10.8063 1.00769
\(116\) −14.6814 −1.36313
\(117\) −3.15999 −0.292141
\(118\) −4.86595 −0.447947
\(119\) 0 0
\(120\) −3.77167 −0.344305
\(121\) −3.03414 −0.275831
\(122\) −0.264768 −0.0239710
\(123\) 1.00000 0.0901670
\(124\) 6.96956 0.625885
\(125\) 12.0246 1.07552
\(126\) 0 0
\(127\) −6.33759 −0.562371 −0.281185 0.959653i \(-0.590728\pi\)
−0.281185 + 0.959653i \(0.590728\pi\)
\(128\) 11.3026 0.999017
\(129\) −0.684567 −0.0602727
\(130\) −3.30905 −0.290223
\(131\) −5.07981 −0.443825 −0.221913 0.975067i \(-0.571230\pi\)
−0.221913 + 0.975067i \(0.571230\pi\)
\(132\) −4.52079 −0.393484
\(133\) 0 0
\(134\) −6.28273 −0.542745
\(135\) −1.65938 −0.142817
\(136\) 2.54481 0.218215
\(137\) −8.11444 −0.693263 −0.346632 0.938001i \(-0.612675\pi\)
−0.346632 + 0.938001i \(0.612675\pi\)
\(138\) 4.10961 0.349833
\(139\) −21.7599 −1.84565 −0.922826 0.385216i \(-0.874127\pi\)
−0.922826 + 0.385216i \(0.874127\pi\)
\(140\) 0 0
\(141\) 6.17414 0.519957
\(142\) −4.66368 −0.391368
\(143\) −8.91871 −0.745820
\(144\) 1.76917 0.147431
\(145\) −15.2096 −1.26309
\(146\) −8.79039 −0.727498
\(147\) 0 0
\(148\) 17.8200 1.46479
\(149\) 14.2646 1.16860 0.584301 0.811537i \(-0.301369\pi\)
0.584301 + 0.811537i \(0.301369\pi\)
\(150\) 1.41764 0.115750
\(151\) 2.29265 0.186573 0.0932867 0.995639i \(-0.470263\pi\)
0.0932867 + 0.995639i \(0.470263\pi\)
\(152\) 7.07069 0.573509
\(153\) 1.11961 0.0905155
\(154\) 0 0
\(155\) 7.22028 0.579947
\(156\) 5.06155 0.405248
\(157\) −24.1517 −1.92751 −0.963756 0.266786i \(-0.914038\pi\)
−0.963756 + 0.266786i \(0.914038\pi\)
\(158\) 0.123581 0.00983161
\(159\) −13.0735 −1.03680
\(160\) 9.39596 0.742816
\(161\) 0 0
\(162\) −0.631061 −0.0495808
\(163\) −0.309243 −0.0242218 −0.0121109 0.999927i \(-0.503855\pi\)
−0.0121109 + 0.999927i \(0.503855\pi\)
\(164\) −1.60176 −0.125077
\(165\) −4.68342 −0.364604
\(166\) 1.58058 0.122677
\(167\) −3.45676 −0.267492 −0.133746 0.991016i \(-0.542701\pi\)
−0.133746 + 0.991016i \(0.542701\pi\)
\(168\) 0 0
\(169\) −3.01447 −0.231882
\(170\) 1.17243 0.0899213
\(171\) 3.11082 0.237891
\(172\) 1.09651 0.0836083
\(173\) −15.7701 −1.19898 −0.599489 0.800383i \(-0.704630\pi\)
−0.599489 + 0.800383i \(0.704630\pi\)
\(174\) −5.78417 −0.438496
\(175\) 0 0
\(176\) 4.99327 0.376382
\(177\) 7.71075 0.579575
\(178\) 7.88820 0.591245
\(179\) 16.6359 1.24343 0.621714 0.783244i \(-0.286437\pi\)
0.621714 + 0.783244i \(0.286437\pi\)
\(180\) 2.65794 0.198111
\(181\) 15.8774 1.18016 0.590078 0.807346i \(-0.299097\pi\)
0.590078 + 0.807346i \(0.299097\pi\)
\(182\) 0 0
\(183\) 0.419560 0.0310148
\(184\) −14.8018 −1.09121
\(185\) 18.4611 1.35728
\(186\) 2.74586 0.201336
\(187\) 3.15999 0.231081
\(188\) −9.88951 −0.721267
\(189\) 0 0
\(190\) 3.25757 0.236329
\(191\) −21.0219 −1.52109 −0.760545 0.649285i \(-0.775068\pi\)
−0.760545 + 0.649285i \(0.775068\pi\)
\(192\) 0.0349308 0.00252091
\(193\) −19.9012 −1.43252 −0.716261 0.697833i \(-0.754148\pi\)
−0.716261 + 0.697833i \(0.754148\pi\)
\(194\) −7.17975 −0.515476
\(195\) 5.24364 0.375505
\(196\) 0 0
\(197\) −20.1886 −1.43838 −0.719189 0.694814i \(-0.755487\pi\)
−0.719189 + 0.694814i \(0.755487\pi\)
\(198\) −1.78110 −0.126577
\(199\) −22.6327 −1.60439 −0.802195 0.597062i \(-0.796335\pi\)
−0.802195 + 0.597062i \(0.796335\pi\)
\(200\) −5.10601 −0.361049
\(201\) 9.95583 0.702230
\(202\) −9.41969 −0.662767
\(203\) 0 0
\(204\) −1.79336 −0.125560
\(205\) −1.65938 −0.115896
\(206\) 6.26914 0.436792
\(207\) −6.51222 −0.452631
\(208\) −5.59055 −0.387635
\(209\) 8.77995 0.607322
\(210\) 0 0
\(211\) −4.48974 −0.309086 −0.154543 0.987986i \(-0.549391\pi\)
−0.154543 + 0.987986i \(0.549391\pi\)
\(212\) 20.9407 1.43821
\(213\) 7.39023 0.506370
\(214\) 10.5058 0.718164
\(215\) 1.13596 0.0774718
\(216\) 2.27293 0.154653
\(217\) 0 0
\(218\) −10.9340 −0.740541
\(219\) 13.9295 0.941272
\(220\) 7.50173 0.505767
\(221\) −3.53797 −0.237990
\(222\) 7.02071 0.471199
\(223\) 22.8364 1.52924 0.764620 0.644481i \(-0.222926\pi\)
0.764620 + 0.644481i \(0.222926\pi\)
\(224\) 0 0
\(225\) −2.24644 −0.149763
\(226\) 6.68694 0.444808
\(227\) −14.6770 −0.974148 −0.487074 0.873361i \(-0.661936\pi\)
−0.487074 + 0.873361i \(0.661936\pi\)
\(228\) −4.98280 −0.329994
\(229\) 10.8858 0.719352 0.359676 0.933077i \(-0.382887\pi\)
0.359676 + 0.933077i \(0.382887\pi\)
\(230\) −6.81942 −0.449659
\(231\) 0 0
\(232\) 20.8332 1.36777
\(233\) −10.6391 −0.696994 −0.348497 0.937310i \(-0.613308\pi\)
−0.348497 + 0.937310i \(0.613308\pi\)
\(234\) 1.99415 0.130361
\(235\) −10.2453 −0.668328
\(236\) −12.3508 −0.803968
\(237\) −0.195831 −0.0127206
\(238\) 0 0
\(239\) 3.02612 0.195743 0.0978716 0.995199i \(-0.468797\pi\)
0.0978716 + 0.995199i \(0.468797\pi\)
\(240\) −2.93573 −0.189500
\(241\) 18.4381 1.18770 0.593851 0.804575i \(-0.297607\pi\)
0.593851 + 0.804575i \(0.297607\pi\)
\(242\) 1.91473 0.123083
\(243\) 1.00000 0.0641500
\(244\) −0.672036 −0.0430227
\(245\) 0 0
\(246\) −0.631061 −0.0402350
\(247\) −9.83017 −0.625479
\(248\) −9.88993 −0.628011
\(249\) −2.50464 −0.158725
\(250\) −7.58828 −0.479925
\(251\) 1.85759 0.117250 0.0586252 0.998280i \(-0.481328\pi\)
0.0586252 + 0.998280i \(0.481328\pi\)
\(252\) 0 0
\(253\) −18.3800 −1.15554
\(254\) 3.99941 0.250945
\(255\) −1.85787 −0.116344
\(256\) −7.20248 −0.450155
\(257\) −10.6305 −0.663113 −0.331557 0.943435i \(-0.607574\pi\)
−0.331557 + 0.943435i \(0.607574\pi\)
\(258\) 0.432003 0.0268953
\(259\) 0 0
\(260\) −8.39906 −0.520888
\(261\) 9.16578 0.567348
\(262\) 3.20567 0.198047
\(263\) −29.4520 −1.81609 −0.908043 0.418878i \(-0.862424\pi\)
−0.908043 + 0.418878i \(0.862424\pi\)
\(264\) 6.41509 0.394821
\(265\) 21.6940 1.33265
\(266\) 0 0
\(267\) −12.4999 −0.764981
\(268\) −15.9469 −0.974110
\(269\) −9.23627 −0.563145 −0.281573 0.959540i \(-0.590856\pi\)
−0.281573 + 0.959540i \(0.590856\pi\)
\(270\) 1.04717 0.0637289
\(271\) −7.69672 −0.467542 −0.233771 0.972292i \(-0.575107\pi\)
−0.233771 + 0.972292i \(0.575107\pi\)
\(272\) 1.98079 0.120103
\(273\) 0 0
\(274\) 5.12070 0.309353
\(275\) −6.34032 −0.382336
\(276\) 10.4310 0.627874
\(277\) −19.4269 −1.16725 −0.583624 0.812024i \(-0.698366\pi\)
−0.583624 + 0.812024i \(0.698366\pi\)
\(278\) 13.7318 0.823581
\(279\) −4.35118 −0.260498
\(280\) 0 0
\(281\) 0.197677 0.0117924 0.00589622 0.999983i \(-0.498123\pi\)
0.00589622 + 0.999983i \(0.498123\pi\)
\(282\) −3.89626 −0.232019
\(283\) 31.9961 1.90197 0.950985 0.309238i \(-0.100074\pi\)
0.950985 + 0.309238i \(0.100074\pi\)
\(284\) −11.8374 −0.702420
\(285\) −5.16206 −0.305774
\(286\) 5.62825 0.332805
\(287\) 0 0
\(288\) −5.66231 −0.333655
\(289\) −15.7465 −0.926262
\(290\) 9.59816 0.563623
\(291\) 11.3773 0.666947
\(292\) −22.3118 −1.30570
\(293\) −17.2175 −1.00586 −0.502930 0.864327i \(-0.667745\pi\)
−0.502930 + 0.864327i \(0.667745\pi\)
\(294\) 0 0
\(295\) −12.7951 −0.744960
\(296\) −25.2869 −1.46977
\(297\) 2.82239 0.163771
\(298\) −9.00183 −0.521462
\(299\) 20.5786 1.19009
\(300\) 3.59827 0.207746
\(301\) 0 0
\(302\) −1.44680 −0.0832542
\(303\) 14.9268 0.857520
\(304\) 5.50357 0.315651
\(305\) −0.696212 −0.0398650
\(306\) −0.706545 −0.0403905
\(307\) −24.2479 −1.38390 −0.691950 0.721946i \(-0.743248\pi\)
−0.691950 + 0.721946i \(0.743248\pi\)
\(308\) 0 0
\(309\) −9.93429 −0.565142
\(310\) −4.55644 −0.258788
\(311\) 10.2592 0.581744 0.290872 0.956762i \(-0.406055\pi\)
0.290872 + 0.956762i \(0.406055\pi\)
\(312\) −7.18244 −0.406625
\(313\) −25.6802 −1.45153 −0.725765 0.687943i \(-0.758514\pi\)
−0.725765 + 0.687943i \(0.758514\pi\)
\(314\) 15.2412 0.860109
\(315\) 0 0
\(316\) 0.313675 0.0176456
\(317\) −19.2173 −1.07935 −0.539675 0.841874i \(-0.681453\pi\)
−0.539675 + 0.841874i \(0.681453\pi\)
\(318\) 8.25019 0.462648
\(319\) 25.8694 1.44841
\(320\) −0.0579636 −0.00324026
\(321\) −16.6479 −0.929195
\(322\) 0 0
\(323\) 3.48293 0.193795
\(324\) −1.60176 −0.0889868
\(325\) 7.09873 0.393767
\(326\) 0.195151 0.0108084
\(327\) 17.3263 0.958147
\(328\) 2.27293 0.125502
\(329\) 0 0
\(330\) 2.95553 0.162696
\(331\) 0.536324 0.0294790 0.0147395 0.999891i \(-0.495308\pi\)
0.0147395 + 0.999891i \(0.495308\pi\)
\(332\) 4.01183 0.220178
\(333\) −11.1252 −0.609660
\(334\) 2.18143 0.119362
\(335\) −16.5205 −0.902614
\(336\) 0 0
\(337\) 11.5251 0.627810 0.313905 0.949454i \(-0.398363\pi\)
0.313905 + 0.949454i \(0.398363\pi\)
\(338\) 1.90231 0.103472
\(339\) −10.5963 −0.575514
\(340\) 2.97587 0.161389
\(341\) −12.2807 −0.665038
\(342\) −1.96312 −0.106153
\(343\) 0 0
\(344\) −1.55597 −0.0838924
\(345\) 10.8063 0.581791
\(346\) 9.95189 0.535017
\(347\) −21.9533 −1.17852 −0.589258 0.807945i \(-0.700580\pi\)
−0.589258 + 0.807945i \(0.700580\pi\)
\(348\) −14.6814 −0.787006
\(349\) 5.35886 0.286853 0.143427 0.989661i \(-0.454188\pi\)
0.143427 + 0.989661i \(0.454188\pi\)
\(350\) 0 0
\(351\) −3.15999 −0.168668
\(352\) −15.9812 −0.851803
\(353\) 9.44187 0.502540 0.251270 0.967917i \(-0.419152\pi\)
0.251270 + 0.967917i \(0.419152\pi\)
\(354\) −4.86595 −0.258622
\(355\) −12.2632 −0.650865
\(356\) 20.0219 1.06116
\(357\) 0 0
\(358\) −10.4983 −0.554852
\(359\) −4.43594 −0.234120 −0.117060 0.993125i \(-0.537347\pi\)
−0.117060 + 0.993125i \(0.537347\pi\)
\(360\) −3.77167 −0.198784
\(361\) −9.32277 −0.490672
\(362\) −10.0196 −0.526618
\(363\) −3.03414 −0.159251
\(364\) 0 0
\(365\) −23.1145 −1.20987
\(366\) −0.264768 −0.0138397
\(367\) −7.96777 −0.415914 −0.207957 0.978138i \(-0.566681\pi\)
−0.207957 + 0.978138i \(0.566681\pi\)
\(368\) −11.5212 −0.600584
\(369\) 1.00000 0.0520579
\(370\) −11.6501 −0.605658
\(371\) 0 0
\(372\) 6.96956 0.361355
\(373\) −16.7465 −0.867103 −0.433552 0.901129i \(-0.642740\pi\)
−0.433552 + 0.901129i \(0.642740\pi\)
\(374\) −1.99414 −0.103115
\(375\) 12.0246 0.620950
\(376\) 14.0334 0.723717
\(377\) −28.9638 −1.49171
\(378\) 0 0
\(379\) −7.02596 −0.360899 −0.180450 0.983584i \(-0.557755\pi\)
−0.180450 + 0.983584i \(0.557755\pi\)
\(380\) 8.26839 0.424159
\(381\) −6.33759 −0.324685
\(382\) 13.2661 0.678752
\(383\) −23.3436 −1.19280 −0.596401 0.802687i \(-0.703403\pi\)
−0.596401 + 0.802687i \(0.703403\pi\)
\(384\) 11.3026 0.576783
\(385\) 0 0
\(386\) 12.5589 0.639230
\(387\) −0.684567 −0.0347985
\(388\) −18.2237 −0.925167
\(389\) 1.37396 0.0696626 0.0348313 0.999393i \(-0.488911\pi\)
0.0348313 + 0.999393i \(0.488911\pi\)
\(390\) −3.30905 −0.167560
\(391\) −7.29118 −0.368731
\(392\) 0 0
\(393\) −5.07981 −0.256243
\(394\) 12.7402 0.641844
\(395\) 0.324960 0.0163505
\(396\) −4.52079 −0.227178
\(397\) 27.4009 1.37521 0.687605 0.726085i \(-0.258662\pi\)
0.687605 + 0.726085i \(0.258662\pi\)
\(398\) 14.2826 0.715923
\(399\) 0 0
\(400\) −3.97433 −0.198716
\(401\) −2.84574 −0.142109 −0.0710547 0.997472i \(-0.522636\pi\)
−0.0710547 + 0.997472i \(0.522636\pi\)
\(402\) −6.28273 −0.313354
\(403\) 13.7497 0.684921
\(404\) −23.9091 −1.18952
\(405\) −1.65938 −0.0824555
\(406\) 0 0
\(407\) −31.3997 −1.55643
\(408\) 2.54481 0.125987
\(409\) 28.4383 1.40619 0.703093 0.711098i \(-0.251802\pi\)
0.703093 + 0.711098i \(0.251802\pi\)
\(410\) 1.04717 0.0517162
\(411\) −8.11444 −0.400256
\(412\) 15.9124 0.783946
\(413\) 0 0
\(414\) 4.10961 0.201976
\(415\) 4.15615 0.204018
\(416\) 17.8928 0.877269
\(417\) −21.7599 −1.06559
\(418\) −5.54068 −0.271004
\(419\) 10.4579 0.510904 0.255452 0.966822i \(-0.417776\pi\)
0.255452 + 0.966822i \(0.417776\pi\)
\(420\) 0 0
\(421\) −18.4016 −0.896839 −0.448419 0.893823i \(-0.648013\pi\)
−0.448419 + 0.893823i \(0.648013\pi\)
\(422\) 2.83330 0.137923
\(423\) 6.17414 0.300197
\(424\) −29.7152 −1.44310
\(425\) −2.51515 −0.122003
\(426\) −4.66368 −0.225956
\(427\) 0 0
\(428\) 26.6660 1.28895
\(429\) −8.91871 −0.430599
\(430\) −0.716860 −0.0345700
\(431\) −7.16006 −0.344888 −0.172444 0.985019i \(-0.555166\pi\)
−0.172444 + 0.985019i \(0.555166\pi\)
\(432\) 1.76917 0.0851191
\(433\) 32.8811 1.58016 0.790082 0.613001i \(-0.210038\pi\)
0.790082 + 0.613001i \(0.210038\pi\)
\(434\) 0 0
\(435\) −15.2096 −0.729243
\(436\) −27.7526 −1.32911
\(437\) −20.2584 −0.969090
\(438\) −8.79039 −0.420021
\(439\) 3.76719 0.179798 0.0898991 0.995951i \(-0.471346\pi\)
0.0898991 + 0.995951i \(0.471346\pi\)
\(440\) −10.6451 −0.507485
\(441\) 0 0
\(442\) 2.23267 0.106198
\(443\) 30.3572 1.44232 0.721158 0.692770i \(-0.243610\pi\)
0.721158 + 0.692770i \(0.243610\pi\)
\(444\) 17.8200 0.845700
\(445\) 20.7421 0.983272
\(446\) −14.4112 −0.682389
\(447\) 14.2646 0.674692
\(448\) 0 0
\(449\) 22.5523 1.06431 0.532154 0.846648i \(-0.321383\pi\)
0.532154 + 0.846648i \(0.321383\pi\)
\(450\) 1.41764 0.0668282
\(451\) 2.82239 0.132901
\(452\) 16.9728 0.798334
\(453\) 2.29265 0.107718
\(454\) 9.26209 0.434691
\(455\) 0 0
\(456\) 7.07069 0.331115
\(457\) −14.6973 −0.687509 −0.343755 0.939060i \(-0.611699\pi\)
−0.343755 + 0.939060i \(0.611699\pi\)
\(458\) −6.86959 −0.320995
\(459\) 1.11961 0.0522591
\(460\) −17.3091 −0.807041
\(461\) −19.3426 −0.900874 −0.450437 0.892808i \(-0.648732\pi\)
−0.450437 + 0.892808i \(0.648732\pi\)
\(462\) 0 0
\(463\) 3.19576 0.148520 0.0742598 0.997239i \(-0.476341\pi\)
0.0742598 + 0.997239i \(0.476341\pi\)
\(464\) 16.2158 0.752799
\(465\) 7.22028 0.334833
\(466\) 6.71395 0.311018
\(467\) −17.7807 −0.822791 −0.411396 0.911457i \(-0.634958\pi\)
−0.411396 + 0.911457i \(0.634958\pi\)
\(468\) 5.06155 0.233970
\(469\) 0 0
\(470\) 6.46539 0.298226
\(471\) −24.1517 −1.11285
\(472\) 17.5260 0.806700
\(473\) −1.93211 −0.0888386
\(474\) 0.123581 0.00567628
\(475\) −6.98829 −0.320645
\(476\) 0 0
\(477\) −13.0735 −0.598596
\(478\) −1.90966 −0.0873460
\(479\) −34.2608 −1.56542 −0.782709 0.622388i \(-0.786163\pi\)
−0.782709 + 0.622388i \(0.786163\pi\)
\(480\) 9.39596 0.428865
\(481\) 35.1557 1.60296
\(482\) −11.6356 −0.529985
\(483\) 0 0
\(484\) 4.85997 0.220908
\(485\) −18.8793 −0.857263
\(486\) −0.631061 −0.0286255
\(487\) 29.6230 1.34234 0.671172 0.741301i \(-0.265791\pi\)
0.671172 + 0.741301i \(0.265791\pi\)
\(488\) 0.953632 0.0431689
\(489\) −0.309243 −0.0139845
\(490\) 0 0
\(491\) −15.7558 −0.711049 −0.355525 0.934667i \(-0.615698\pi\)
−0.355525 + 0.934667i \(0.615698\pi\)
\(492\) −1.60176 −0.0722130
\(493\) 10.2621 0.462184
\(494\) 6.20344 0.279106
\(495\) −4.68342 −0.210504
\(496\) −7.69796 −0.345649
\(497\) 0 0
\(498\) 1.58058 0.0708274
\(499\) 3.95585 0.177088 0.0885441 0.996072i \(-0.471779\pi\)
0.0885441 + 0.996072i \(0.471779\pi\)
\(500\) −19.2606 −0.861361
\(501\) −3.45676 −0.154437
\(502\) −1.17226 −0.0523203
\(503\) −33.0299 −1.47273 −0.736366 0.676583i \(-0.763460\pi\)
−0.736366 + 0.676583i \(0.763460\pi\)
\(504\) 0 0
\(505\) −24.7692 −1.10222
\(506\) 11.5989 0.515634
\(507\) −3.01447 −0.133877
\(508\) 10.1513 0.450392
\(509\) 25.8609 1.14626 0.573131 0.819463i \(-0.305728\pi\)
0.573131 + 0.819463i \(0.305728\pi\)
\(510\) 1.17243 0.0519161
\(511\) 0 0
\(512\) −18.0600 −0.798145
\(513\) 3.11082 0.137346
\(514\) 6.70850 0.295899
\(515\) 16.4848 0.726407
\(516\) 1.09651 0.0482713
\(517\) 17.4258 0.766386
\(518\) 0 0
\(519\) −15.7701 −0.692230
\(520\) 11.9184 0.522658
\(521\) 1.48131 0.0648972 0.0324486 0.999473i \(-0.489669\pi\)
0.0324486 + 0.999473i \(0.489669\pi\)
\(522\) −5.78417 −0.253166
\(523\) 30.6601 1.34067 0.670336 0.742057i \(-0.266150\pi\)
0.670336 + 0.742057i \(0.266150\pi\)
\(524\) 8.13665 0.355451
\(525\) 0 0
\(526\) 18.5860 0.810387
\(527\) −4.87165 −0.212212
\(528\) 4.99327 0.217304
\(529\) 19.4090 0.843871
\(530\) −13.6902 −0.594666
\(531\) 7.71075 0.334618
\(532\) 0 0
\(533\) −3.15999 −0.136874
\(534\) 7.88820 0.341356
\(535\) 27.6253 1.19434
\(536\) 22.6289 0.977420
\(537\) 16.6359 0.717894
\(538\) 5.82865 0.251291
\(539\) 0 0
\(540\) 2.65794 0.114380
\(541\) −6.28709 −0.270303 −0.135151 0.990825i \(-0.543152\pi\)
−0.135151 + 0.990825i \(0.543152\pi\)
\(542\) 4.85710 0.208630
\(543\) 15.8774 0.681363
\(544\) −6.33961 −0.271809
\(545\) −28.7510 −1.23156
\(546\) 0 0
\(547\) 13.2731 0.567515 0.283758 0.958896i \(-0.408419\pi\)
0.283758 + 0.958896i \(0.408419\pi\)
\(548\) 12.9974 0.555221
\(549\) 0.419560 0.0179064
\(550\) 4.00113 0.170609
\(551\) 28.5131 1.21470
\(552\) −14.8018 −0.630008
\(553\) 0 0
\(554\) 12.2595 0.520858
\(555\) 18.4611 0.783629
\(556\) 34.8542 1.47815
\(557\) −31.4107 −1.33091 −0.665457 0.746436i \(-0.731763\pi\)
−0.665457 + 0.746436i \(0.731763\pi\)
\(558\) 2.74586 0.116242
\(559\) 2.16322 0.0914946
\(560\) 0 0
\(561\) 3.15999 0.133415
\(562\) −0.124746 −0.00526211
\(563\) 0.492351 0.0207501 0.0103751 0.999946i \(-0.496697\pi\)
0.0103751 + 0.999946i \(0.496697\pi\)
\(564\) −9.88951 −0.416423
\(565\) 17.5834 0.739740
\(566\) −20.1915 −0.848711
\(567\) 0 0
\(568\) 16.7975 0.704807
\(569\) 8.70460 0.364916 0.182458 0.983214i \(-0.441595\pi\)
0.182458 + 0.983214i \(0.441595\pi\)
\(570\) 3.25757 0.136445
\(571\) −36.8663 −1.54281 −0.771403 0.636347i \(-0.780445\pi\)
−0.771403 + 0.636347i \(0.780445\pi\)
\(572\) 14.2856 0.597313
\(573\) −21.0219 −0.878202
\(574\) 0 0
\(575\) 14.6293 0.610085
\(576\) 0.0349308 0.00145545
\(577\) 0.227862 0.00948604 0.00474302 0.999989i \(-0.498490\pi\)
0.00474302 + 0.999989i \(0.498490\pi\)
\(578\) 9.93698 0.413324
\(579\) −19.9012 −0.827067
\(580\) 24.3621 1.01158
\(581\) 0 0
\(582\) −7.17975 −0.297610
\(583\) −36.8985 −1.52818
\(584\) 31.6609 1.31014
\(585\) 5.24364 0.216798
\(586\) 10.8653 0.448842
\(587\) −4.58547 −0.189262 −0.0946312 0.995512i \(-0.530167\pi\)
−0.0946312 + 0.995512i \(0.530167\pi\)
\(588\) 0 0
\(589\) −13.5358 −0.557731
\(590\) 8.07449 0.332421
\(591\) −20.1886 −0.830448
\(592\) −19.6824 −0.808942
\(593\) −9.17184 −0.376642 −0.188321 0.982108i \(-0.560305\pi\)
−0.188321 + 0.982108i \(0.560305\pi\)
\(594\) −1.78110 −0.0730793
\(595\) 0 0
\(596\) −22.8485 −0.935911
\(597\) −22.6327 −0.926295
\(598\) −12.9863 −0.531050
\(599\) −36.1676 −1.47777 −0.738884 0.673832i \(-0.764647\pi\)
−0.738884 + 0.673832i \(0.764647\pi\)
\(600\) −5.10601 −0.208452
\(601\) 1.30057 0.0530515 0.0265258 0.999648i \(-0.491556\pi\)
0.0265258 + 0.999648i \(0.491556\pi\)
\(602\) 0 0
\(603\) 9.95583 0.405433
\(604\) −3.67229 −0.149423
\(605\) 5.03480 0.204694
\(606\) −9.41969 −0.382649
\(607\) 19.2109 0.779745 0.389872 0.920869i \(-0.372519\pi\)
0.389872 + 0.920869i \(0.372519\pi\)
\(608\) −17.6145 −0.714361
\(609\) 0 0
\(610\) 0.439352 0.0177889
\(611\) −19.5102 −0.789299
\(612\) −1.79336 −0.0724922
\(613\) 8.59390 0.347104 0.173552 0.984825i \(-0.444475\pi\)
0.173552 + 0.984825i \(0.444475\pi\)
\(614\) 15.3019 0.617534
\(615\) −1.65938 −0.0669129
\(616\) 0 0
\(617\) 1.93896 0.0780595 0.0390298 0.999238i \(-0.487573\pi\)
0.0390298 + 0.999238i \(0.487573\pi\)
\(618\) 6.26914 0.252182
\(619\) 4.54259 0.182582 0.0912910 0.995824i \(-0.470901\pi\)
0.0912910 + 0.995824i \(0.470901\pi\)
\(620\) −11.5652 −0.464469
\(621\) −6.51222 −0.261326
\(622\) −6.47416 −0.259590
\(623\) 0 0
\(624\) −5.59055 −0.223801
\(625\) −8.72129 −0.348852
\(626\) 16.2058 0.647712
\(627\) 8.77995 0.350637
\(628\) 38.6852 1.54371
\(629\) −12.4560 −0.496653
\(630\) 0 0
\(631\) −42.7975 −1.70374 −0.851870 0.523754i \(-0.824531\pi\)
−0.851870 + 0.523754i \(0.824531\pi\)
\(632\) −0.445111 −0.0177056
\(633\) −4.48974 −0.178451
\(634\) 12.1273 0.481635
\(635\) 10.5165 0.417335
\(636\) 20.9407 0.830352
\(637\) 0 0
\(638\) −16.3251 −0.646319
\(639\) 7.39023 0.292353
\(640\) −18.7553 −0.741370
\(641\) 30.8886 1.22003 0.610013 0.792391i \(-0.291164\pi\)
0.610013 + 0.792391i \(0.291164\pi\)
\(642\) 10.5058 0.414632
\(643\) 16.5004 0.650712 0.325356 0.945592i \(-0.394516\pi\)
0.325356 + 0.945592i \(0.394516\pi\)
\(644\) 0 0
\(645\) 1.13596 0.0447284
\(646\) −2.19794 −0.0864767
\(647\) −22.9982 −0.904152 −0.452076 0.891979i \(-0.649316\pi\)
−0.452076 + 0.891979i \(0.649316\pi\)
\(648\) 2.27293 0.0892892
\(649\) 21.7627 0.854261
\(650\) −4.47973 −0.175709
\(651\) 0 0
\(652\) 0.495334 0.0193988
\(653\) 26.0313 1.01868 0.509342 0.860564i \(-0.329889\pi\)
0.509342 + 0.860564i \(0.329889\pi\)
\(654\) −10.9340 −0.427551
\(655\) 8.42936 0.329362
\(656\) 1.76917 0.0690744
\(657\) 13.9295 0.543443
\(658\) 0 0
\(659\) 13.0247 0.507369 0.253684 0.967287i \(-0.418358\pi\)
0.253684 + 0.967287i \(0.418358\pi\)
\(660\) 7.50173 0.292005
\(661\) −26.1475 −1.01702 −0.508510 0.861056i \(-0.669803\pi\)
−0.508510 + 0.861056i \(0.669803\pi\)
\(662\) −0.338453 −0.0131544
\(663\) −3.53797 −0.137403
\(664\) −5.69286 −0.220926
\(665\) 0 0
\(666\) 7.02071 0.272047
\(667\) −59.6896 −2.31119
\(668\) 5.53691 0.214229
\(669\) 22.8364 0.882908
\(670\) 10.4255 0.402771
\(671\) 1.18416 0.0457140
\(672\) 0 0
\(673\) 10.6856 0.411901 0.205951 0.978562i \(-0.433971\pi\)
0.205951 + 0.978562i \(0.433971\pi\)
\(674\) −7.27302 −0.280146
\(675\) −2.24644 −0.0864656
\(676\) 4.82846 0.185710
\(677\) −16.2993 −0.626431 −0.313216 0.949682i \(-0.601406\pi\)
−0.313216 + 0.949682i \(0.601406\pi\)
\(678\) 6.68694 0.256810
\(679\) 0 0
\(680\) −4.22282 −0.161938
\(681\) −14.6770 −0.562424
\(682\) 7.74987 0.296758
\(683\) 6.89890 0.263979 0.131990 0.991251i \(-0.457863\pi\)
0.131990 + 0.991251i \(0.457863\pi\)
\(684\) −4.98280 −0.190522
\(685\) 13.4650 0.514470
\(686\) 0 0
\(687\) 10.8858 0.415318
\(688\) −1.21111 −0.0461732
\(689\) 41.3122 1.57387
\(690\) −6.81942 −0.259611
\(691\) 10.9192 0.415385 0.207692 0.978194i \(-0.433405\pi\)
0.207692 + 0.978194i \(0.433405\pi\)
\(692\) 25.2599 0.960239
\(693\) 0 0
\(694\) 13.8539 0.525886
\(695\) 36.1081 1.36966
\(696\) 20.8332 0.789680
\(697\) 1.11961 0.0424084
\(698\) −3.38177 −0.128002
\(699\) −10.6391 −0.402409
\(700\) 0 0
\(701\) −34.1965 −1.29158 −0.645791 0.763514i \(-0.723472\pi\)
−0.645791 + 0.763514i \(0.723472\pi\)
\(702\) 1.99415 0.0752642
\(703\) −34.6087 −1.30529
\(704\) 0.0985881 0.00371568
\(705\) −10.2453 −0.385860
\(706\) −5.95840 −0.224247
\(707\) 0 0
\(708\) −12.3508 −0.464171
\(709\) 16.4538 0.617934 0.308967 0.951073i \(-0.400017\pi\)
0.308967 + 0.951073i \(0.400017\pi\)
\(710\) 7.73885 0.290434
\(711\) −0.195831 −0.00734425
\(712\) −28.4114 −1.06476
\(713\) 28.3359 1.06119
\(714\) 0 0
\(715\) 14.7996 0.553473
\(716\) −26.6468 −0.995838
\(717\) 3.02612 0.113012
\(718\) 2.79935 0.104471
\(719\) 17.6106 0.656764 0.328382 0.944545i \(-0.393497\pi\)
0.328382 + 0.944545i \(0.393497\pi\)
\(720\) −2.93573 −0.109408
\(721\) 0 0
\(722\) 5.88323 0.218951
\(723\) 18.4381 0.685720
\(724\) −25.4318 −0.945164
\(725\) −20.5904 −0.764708
\(726\) 1.91473 0.0710622
\(727\) 34.6841 1.28636 0.643181 0.765714i \(-0.277614\pi\)
0.643181 + 0.765714i \(0.277614\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 14.5866 0.539876
\(731\) −0.766451 −0.0283482
\(732\) −0.672036 −0.0248392
\(733\) 14.9917 0.553731 0.276865 0.960909i \(-0.410704\pi\)
0.276865 + 0.960909i \(0.410704\pi\)
\(734\) 5.02814 0.185592
\(735\) 0 0
\(736\) 36.8742 1.35920
\(737\) 28.0992 1.03505
\(738\) −0.631061 −0.0232297
\(739\) 11.5757 0.425820 0.212910 0.977072i \(-0.431706\pi\)
0.212910 + 0.977072i \(0.431706\pi\)
\(740\) −29.5702 −1.08702
\(741\) −9.83017 −0.361120
\(742\) 0 0
\(743\) 25.7503 0.944687 0.472343 0.881415i \(-0.343408\pi\)
0.472343 + 0.881415i \(0.343408\pi\)
\(744\) −9.88993 −0.362583
\(745\) −23.6705 −0.867218
\(746\) 10.5681 0.386925
\(747\) −2.50464 −0.0916398
\(748\) −5.06154 −0.185068
\(749\) 0 0
\(750\) −7.58828 −0.277085
\(751\) −14.3476 −0.523550 −0.261775 0.965129i \(-0.584308\pi\)
−0.261775 + 0.965129i \(0.584308\pi\)
\(752\) 10.9231 0.398324
\(753\) 1.85759 0.0676945
\(754\) 18.2779 0.665642
\(755\) −3.80439 −0.138456
\(756\) 0 0
\(757\) 52.9415 1.92419 0.962095 0.272714i \(-0.0879213\pi\)
0.962095 + 0.272714i \(0.0879213\pi\)
\(758\) 4.43381 0.161043
\(759\) −18.3800 −0.667152
\(760\) −11.7330 −0.425601
\(761\) 23.8612 0.864969 0.432485 0.901641i \(-0.357637\pi\)
0.432485 + 0.901641i \(0.357637\pi\)
\(762\) 3.99941 0.144883
\(763\) 0 0
\(764\) 33.6721 1.21821
\(765\) −1.85787 −0.0671715
\(766\) 14.7312 0.532261
\(767\) −24.3659 −0.879801
\(768\) −7.20248 −0.259897
\(769\) 40.3431 1.45481 0.727405 0.686208i \(-0.240726\pi\)
0.727405 + 0.686208i \(0.240726\pi\)
\(770\) 0 0
\(771\) −10.6305 −0.382849
\(772\) 31.8770 1.14728
\(773\) −23.3193 −0.838736 −0.419368 0.907816i \(-0.637748\pi\)
−0.419368 + 0.907816i \(0.637748\pi\)
\(774\) 0.432003 0.0155280
\(775\) 9.77467 0.351117
\(776\) 25.8597 0.928311
\(777\) 0 0
\(778\) −0.867053 −0.0310854
\(779\) 3.11082 0.111457
\(780\) −8.39906 −0.300735
\(781\) 20.8581 0.746361
\(782\) 4.60118 0.164538
\(783\) 9.16578 0.327558
\(784\) 0 0
\(785\) 40.0769 1.43041
\(786\) 3.20567 0.114342
\(787\) −38.4755 −1.37150 −0.685752 0.727835i \(-0.740527\pi\)
−0.685752 + 0.727835i \(0.740527\pi\)
\(788\) 32.3373 1.15197
\(789\) −29.4520 −1.04852
\(790\) −0.205069 −0.00729604
\(791\) 0 0
\(792\) 6.41509 0.227950
\(793\) −1.32581 −0.0470808
\(794\) −17.2916 −0.613657
\(795\) 21.6940 0.769408
\(796\) 36.2522 1.28493
\(797\) 8.86744 0.314101 0.157050 0.987591i \(-0.449802\pi\)
0.157050 + 0.987591i \(0.449802\pi\)
\(798\) 0 0
\(799\) 6.91266 0.244552
\(800\) 12.7201 0.449722
\(801\) −12.4999 −0.441662
\(802\) 1.79583 0.0634131
\(803\) 39.3146 1.38738
\(804\) −15.9469 −0.562403
\(805\) 0 0
\(806\) −8.67689 −0.305630
\(807\) −9.23627 −0.325132
\(808\) 33.9275 1.19357
\(809\) −8.17161 −0.287299 −0.143649 0.989629i \(-0.545884\pi\)
−0.143649 + 0.989629i \(0.545884\pi\)
\(810\) 1.04717 0.0367939
\(811\) 5.53278 0.194282 0.0971411 0.995271i \(-0.469030\pi\)
0.0971411 + 0.995271i \(0.469030\pi\)
\(812\) 0 0
\(813\) −7.69672 −0.269936
\(814\) 19.8151 0.694520
\(815\) 0.513153 0.0179750
\(816\) 1.98079 0.0693414
\(817\) −2.12957 −0.0745041
\(818\) −17.9463 −0.627478
\(819\) 0 0
\(820\) 2.65794 0.0928193
\(821\) 6.89627 0.240681 0.120341 0.992733i \(-0.461601\pi\)
0.120341 + 0.992733i \(0.461601\pi\)
\(822\) 5.12070 0.178605
\(823\) −37.9259 −1.32201 −0.661006 0.750380i \(-0.729870\pi\)
−0.661006 + 0.750380i \(0.729870\pi\)
\(824\) −22.5800 −0.786610
\(825\) −6.34032 −0.220742
\(826\) 0 0
\(827\) 22.6357 0.787121 0.393561 0.919299i \(-0.371243\pi\)
0.393561 + 0.919299i \(0.371243\pi\)
\(828\) 10.4310 0.362503
\(829\) 34.6081 1.20199 0.600995 0.799253i \(-0.294771\pi\)
0.600995 + 0.799253i \(0.294771\pi\)
\(830\) −2.62279 −0.0910382
\(831\) −19.4269 −0.673910
\(832\) −0.110381 −0.00382677
\(833\) 0 0
\(834\) 13.7318 0.475495
\(835\) 5.73610 0.198506
\(836\) −14.0634 −0.486392
\(837\) −4.35118 −0.150399
\(838\) −6.59960 −0.227979
\(839\) −53.3934 −1.84334 −0.921672 0.387969i \(-0.873177\pi\)
−0.921672 + 0.387969i \(0.873177\pi\)
\(840\) 0 0
\(841\) 55.0116 1.89695
\(842\) 11.6125 0.400194
\(843\) 0.197677 0.00680837
\(844\) 7.19149 0.247541
\(845\) 5.00216 0.172080
\(846\) −3.89626 −0.133956
\(847\) 0 0
\(848\) −23.1293 −0.794262
\(849\) 31.9961 1.09810
\(850\) 1.58721 0.0544409
\(851\) 72.4501 2.48356
\(852\) −11.8374 −0.405542
\(853\) 9.56536 0.327512 0.163756 0.986501i \(-0.447639\pi\)
0.163756 + 0.986501i \(0.447639\pi\)
\(854\) 0 0
\(855\) −5.16206 −0.176539
\(856\) −37.8395 −1.29333
\(857\) 2.78473 0.0951246 0.0475623 0.998868i \(-0.484855\pi\)
0.0475623 + 0.998868i \(0.484855\pi\)
\(858\) 5.62825 0.192145
\(859\) −11.2578 −0.384110 −0.192055 0.981384i \(-0.561515\pi\)
−0.192055 + 0.981384i \(0.561515\pi\)
\(860\) −1.81954 −0.0620457
\(861\) 0 0
\(862\) 4.51843 0.153899
\(863\) −5.08316 −0.173033 −0.0865163 0.996250i \(-0.527573\pi\)
−0.0865163 + 0.996250i \(0.527573\pi\)
\(864\) −5.66231 −0.192636
\(865\) 26.1687 0.889761
\(866\) −20.7500 −0.705112
\(867\) −15.7465 −0.534778
\(868\) 0 0
\(869\) −0.552711 −0.0187495
\(870\) 9.59816 0.325408
\(871\) −31.4603 −1.06599
\(872\) 39.3815 1.33363
\(873\) 11.3773 0.385062
\(874\) 12.7843 0.432434
\(875\) 0 0
\(876\) −22.3118 −0.753847
\(877\) −24.7658 −0.836282 −0.418141 0.908382i \(-0.637318\pi\)
−0.418141 + 0.908382i \(0.637318\pi\)
\(878\) −2.37733 −0.0802308
\(879\) −17.2175 −0.580733
\(880\) −8.28576 −0.279313
\(881\) −13.0909 −0.441044 −0.220522 0.975382i \(-0.570776\pi\)
−0.220522 + 0.975382i \(0.570776\pi\)
\(882\) 0 0
\(883\) −44.5002 −1.49755 −0.748775 0.662824i \(-0.769358\pi\)
−0.748775 + 0.662824i \(0.769358\pi\)
\(884\) 5.66699 0.190601
\(885\) −12.7951 −0.430103
\(886\) −19.1573 −0.643601
\(887\) 22.0697 0.741028 0.370514 0.928827i \(-0.379181\pi\)
0.370514 + 0.928827i \(0.379181\pi\)
\(888\) −25.2869 −0.848573
\(889\) 0 0
\(890\) −13.0896 −0.438763
\(891\) 2.82239 0.0945535
\(892\) −36.5785 −1.22474
\(893\) 19.2067 0.642727
\(894\) −9.00183 −0.301066
\(895\) −27.6054 −0.922747
\(896\) 0 0
\(897\) 20.5786 0.687098
\(898\) −14.2319 −0.474923
\(899\) −39.8820 −1.33014
\(900\) 3.59827 0.119942
\(901\) −14.6373 −0.487640
\(902\) −1.78110 −0.0593040
\(903\) 0 0
\(904\) −24.0848 −0.801047
\(905\) −26.3467 −0.875793
\(906\) −1.44680 −0.0480668
\(907\) −9.62739 −0.319672 −0.159836 0.987144i \(-0.551097\pi\)
−0.159836 + 0.987144i \(0.551097\pi\)
\(908\) 23.5091 0.780176
\(909\) 14.9268 0.495089
\(910\) 0 0
\(911\) −55.0618 −1.82428 −0.912140 0.409880i \(-0.865571\pi\)
−0.912140 + 0.409880i \(0.865571\pi\)
\(912\) 5.50357 0.182241
\(913\) −7.06905 −0.233951
\(914\) 9.27487 0.306785
\(915\) −0.696212 −0.0230161
\(916\) −17.4364 −0.576116
\(917\) 0 0
\(918\) −0.706545 −0.0233195
\(919\) −18.9673 −0.625673 −0.312837 0.949807i \(-0.601279\pi\)
−0.312837 + 0.949807i \(0.601279\pi\)
\(920\) 24.5619 0.809783
\(921\) −24.2479 −0.798995
\(922\) 12.2064 0.401995
\(923\) −23.3530 −0.768675
\(924\) 0 0
\(925\) 24.9922 0.821739
\(926\) −2.01672 −0.0662735
\(927\) −9.93429 −0.326285
\(928\) −51.8995 −1.70369
\(929\) 25.2606 0.828773 0.414386 0.910101i \(-0.363996\pi\)
0.414386 + 0.910101i \(0.363996\pi\)
\(930\) −4.55644 −0.149411
\(931\) 0 0
\(932\) 17.0414 0.558209
\(933\) 10.2592 0.335870
\(934\) 11.2207 0.367152
\(935\) −5.24363 −0.171485
\(936\) −7.18244 −0.234765
\(937\) 13.5468 0.442554 0.221277 0.975211i \(-0.428978\pi\)
0.221277 + 0.975211i \(0.428978\pi\)
\(938\) 0 0
\(939\) −25.6802 −0.838041
\(940\) 16.4105 0.535252
\(941\) −33.7758 −1.10106 −0.550529 0.834816i \(-0.685574\pi\)
−0.550529 + 0.834816i \(0.685574\pi\)
\(942\) 15.2412 0.496584
\(943\) −6.51222 −0.212067
\(944\) 13.6416 0.443996
\(945\) 0 0
\(946\) 1.21928 0.0396422
\(947\) 23.8236 0.774162 0.387081 0.922046i \(-0.373483\pi\)
0.387081 + 0.922046i \(0.373483\pi\)
\(948\) 0.313675 0.0101877
\(949\) −44.0172 −1.42886
\(950\) 4.41003 0.143080
\(951\) −19.2173 −0.623163
\(952\) 0 0
\(953\) −18.8482 −0.610553 −0.305277 0.952264i \(-0.598749\pi\)
−0.305277 + 0.952264i \(0.598749\pi\)
\(954\) 8.25019 0.267110
\(955\) 34.8834 1.12880
\(956\) −4.84712 −0.156767
\(957\) 25.8694 0.836238
\(958\) 21.6207 0.698532
\(959\) 0 0
\(960\) −0.0579636 −0.00187077
\(961\) −12.0672 −0.389265
\(962\) −22.1854 −0.715285
\(963\) −16.6479 −0.536471
\(964\) −29.5334 −0.951208
\(965\) 33.0238 1.06307
\(966\) 0 0
\(967\) −45.4505 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(968\) −6.89639 −0.221658
\(969\) 3.48293 0.111888
\(970\) 11.9140 0.382534
\(971\) −57.0677 −1.83139 −0.915695 0.401874i \(-0.868359\pi\)
−0.915695 + 0.401874i \(0.868359\pi\)
\(972\) −1.60176 −0.0513765
\(973\) 0 0
\(974\) −18.6939 −0.598991
\(975\) 7.09873 0.227341
\(976\) 0.742272 0.0237596
\(977\) −15.5246 −0.496675 −0.248337 0.968674i \(-0.579884\pi\)
−0.248337 + 0.968674i \(0.579884\pi\)
\(978\) 0.195151 0.00624025
\(979\) −35.2795 −1.12754
\(980\) 0 0
\(981\) 17.3263 0.553186
\(982\) 9.94287 0.317290
\(983\) −10.3050 −0.328678 −0.164339 0.986404i \(-0.552549\pi\)
−0.164339 + 0.986404i \(0.552549\pi\)
\(984\) 2.27293 0.0724584
\(985\) 33.5007 1.06742
\(986\) −6.47604 −0.206239
\(987\) 0 0
\(988\) 15.7456 0.500934
\(989\) 4.45805 0.141758
\(990\) 2.95553 0.0939328
\(991\) 44.2241 1.40483 0.702413 0.711770i \(-0.252106\pi\)
0.702413 + 0.711770i \(0.252106\pi\)
\(992\) 24.6378 0.782249
\(993\) 0.536324 0.0170197
\(994\) 0 0
\(995\) 37.5564 1.19062
\(996\) 4.01183 0.127120
\(997\) −33.4105 −1.05812 −0.529061 0.848584i \(-0.677456\pi\)
−0.529061 + 0.848584i \(0.677456\pi\)
\(998\) −2.49638 −0.0790216
\(999\) −11.1252 −0.351987
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 \(a_p\))