Properties

Label 8046.2.a.l.1.3
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
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 1.3
Root \(-1.20126\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.20126 q^{5}\) \(-4.29383 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.20126 q^{5}\) \(-4.29383 q^{7}\) \(-1.00000 q^{8}\) \(+1.20126 q^{10}\) \(+1.67350 q^{11}\) \(-2.77189 q^{13}\) \(+4.29383 q^{14}\) \(+1.00000 q^{16}\) \(-5.75270 q^{17}\) \(+5.66708 q^{19}\) \(-1.20126 q^{20}\) \(-1.67350 q^{22}\) \(-3.89843 q^{23}\) \(-3.55698 q^{25}\) \(+2.77189 q^{26}\) \(-4.29383 q^{28}\) \(-3.66521 q^{29}\) \(-10.2309 q^{31}\) \(-1.00000 q^{32}\) \(+5.75270 q^{34}\) \(+5.15800 q^{35}\) \(-7.55661 q^{37}\) \(-5.66708 q^{38}\) \(+1.20126 q^{40}\) \(-1.38760 q^{41}\) \(-7.29901 q^{43}\) \(+1.67350 q^{44}\) \(+3.89843 q^{46}\) \(+5.85394 q^{47}\) \(+11.4370 q^{49}\) \(+3.55698 q^{50}\) \(-2.77189 q^{52}\) \(-0.209993 q^{53}\) \(-2.01031 q^{55}\) \(+4.29383 q^{56}\) \(+3.66521 q^{58}\) \(+1.94740 q^{59}\) \(+1.99514 q^{61}\) \(+10.2309 q^{62}\) \(+1.00000 q^{64}\) \(+3.32976 q^{65}\) \(-2.36095 q^{67}\) \(-5.75270 q^{68}\) \(-5.15800 q^{70}\) \(+9.26740 q^{71}\) \(+7.84474 q^{73}\) \(+7.55661 q^{74}\) \(+5.66708 q^{76}\) \(-7.18575 q^{77}\) \(-10.3332 q^{79}\) \(-1.20126 q^{80}\) \(+1.38760 q^{82}\) \(+3.69755 q^{83}\) \(+6.91048 q^{85}\) \(+7.29901 q^{86}\) \(-1.67350 q^{88}\) \(-12.8667 q^{89}\) \(+11.9020 q^{91}\) \(-3.89843 q^{92}\) \(-5.85394 q^{94}\) \(-6.80763 q^{95}\) \(-5.85506 q^{97}\) \(-11.4370 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.20126 −0.537219 −0.268610 0.963249i \(-0.586564\pi\)
−0.268610 + 0.963249i \(0.586564\pi\)
\(6\) 0 0
\(7\) −4.29383 −1.62292 −0.811458 0.584410i \(-0.801326\pi\)
−0.811458 + 0.584410i \(0.801326\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.20126 0.379871
\(11\) 1.67350 0.504581 0.252290 0.967652i \(-0.418816\pi\)
0.252290 + 0.967652i \(0.418816\pi\)
\(12\) 0 0
\(13\) −2.77189 −0.768785 −0.384392 0.923170i \(-0.625589\pi\)
−0.384392 + 0.923170i \(0.625589\pi\)
\(14\) 4.29383 1.14758
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −5.75270 −1.39524 −0.697618 0.716470i \(-0.745757\pi\)
−0.697618 + 0.716470i \(0.745757\pi\)
\(18\) 0 0
\(19\) 5.66708 1.30012 0.650058 0.759884i \(-0.274744\pi\)
0.650058 + 0.759884i \(0.274744\pi\)
\(20\) −1.20126 −0.268610
\(21\) 0 0
\(22\) −1.67350 −0.356792
\(23\) −3.89843 −0.812878 −0.406439 0.913678i \(-0.633230\pi\)
−0.406439 + 0.913678i \(0.633230\pi\)
\(24\) 0 0
\(25\) −3.55698 −0.711396
\(26\) 2.77189 0.543613
\(27\) 0 0
\(28\) −4.29383 −0.811458
\(29\) −3.66521 −0.680613 −0.340306 0.940315i \(-0.610531\pi\)
−0.340306 + 0.940315i \(0.610531\pi\)
\(30\) 0 0
\(31\) −10.2309 −1.83752 −0.918761 0.394813i \(-0.870809\pi\)
−0.918761 + 0.394813i \(0.870809\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 5.75270 0.986581
\(35\) 5.15800 0.871862
\(36\) 0 0
\(37\) −7.55661 −1.24230 −0.621150 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(38\) −5.66708 −0.919322
\(39\) 0 0
\(40\) 1.20126 0.189936
\(41\) −1.38760 −0.216706 −0.108353 0.994112i \(-0.534558\pi\)
−0.108353 + 0.994112i \(0.534558\pi\)
\(42\) 0 0
\(43\) −7.29901 −1.11309 −0.556544 0.830818i \(-0.687873\pi\)
−0.556544 + 0.830818i \(0.687873\pi\)
\(44\) 1.67350 0.252290
\(45\) 0 0
\(46\) 3.89843 0.574792
\(47\) 5.85394 0.853885 0.426943 0.904279i \(-0.359591\pi\)
0.426943 + 0.904279i \(0.359591\pi\)
\(48\) 0 0
\(49\) 11.4370 1.63386
\(50\) 3.55698 0.503033
\(51\) 0 0
\(52\) −2.77189 −0.384392
\(53\) −0.209993 −0.0288448 −0.0144224 0.999896i \(-0.504591\pi\)
−0.0144224 + 0.999896i \(0.504591\pi\)
\(54\) 0 0
\(55\) −2.01031 −0.271070
\(56\) 4.29383 0.573788
\(57\) 0 0
\(58\) 3.66521 0.481266
\(59\) 1.94740 0.253529 0.126765 0.991933i \(-0.459541\pi\)
0.126765 + 0.991933i \(0.459541\pi\)
\(60\) 0 0
\(61\) 1.99514 0.255452 0.127726 0.991810i \(-0.459232\pi\)
0.127726 + 0.991810i \(0.459232\pi\)
\(62\) 10.2309 1.29932
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.32976 0.413006
\(66\) 0 0
\(67\) −2.36095 −0.288436 −0.144218 0.989546i \(-0.546067\pi\)
−0.144218 + 0.989546i \(0.546067\pi\)
\(68\) −5.75270 −0.697618
\(69\) 0 0
\(70\) −5.15800 −0.616499
\(71\) 9.26740 1.09984 0.549919 0.835218i \(-0.314659\pi\)
0.549919 + 0.835218i \(0.314659\pi\)
\(72\) 0 0
\(73\) 7.84474 0.918158 0.459079 0.888395i \(-0.348180\pi\)
0.459079 + 0.888395i \(0.348180\pi\)
\(74\) 7.55661 0.878438
\(75\) 0 0
\(76\) 5.66708 0.650058
\(77\) −7.18575 −0.818892
\(78\) 0 0
\(79\) −10.3332 −1.16258 −0.581289 0.813697i \(-0.697452\pi\)
−0.581289 + 0.813697i \(0.697452\pi\)
\(80\) −1.20126 −0.134305
\(81\) 0 0
\(82\) 1.38760 0.153235
\(83\) 3.69755 0.405859 0.202929 0.979193i \(-0.434954\pi\)
0.202929 + 0.979193i \(0.434954\pi\)
\(84\) 0 0
\(85\) 6.91048 0.749547
\(86\) 7.29901 0.787072
\(87\) 0 0
\(88\) −1.67350 −0.178396
\(89\) −12.8667 −1.36387 −0.681933 0.731414i \(-0.738861\pi\)
−0.681933 + 0.731414i \(0.738861\pi\)
\(90\) 0 0
\(91\) 11.9020 1.24767
\(92\) −3.89843 −0.406439
\(93\) 0 0
\(94\) −5.85394 −0.603788
\(95\) −6.80763 −0.698448
\(96\) 0 0
\(97\) −5.85506 −0.594492 −0.297246 0.954801i \(-0.596068\pi\)
−0.297246 + 0.954801i \(0.596068\pi\)
\(98\) −11.4370 −1.15531
\(99\) 0 0
\(100\) −3.55698 −0.355698
\(101\) 6.32189 0.629052 0.314526 0.949249i \(-0.398154\pi\)
0.314526 + 0.949249i \(0.398154\pi\)
\(102\) 0 0
\(103\) −10.9039 −1.07439 −0.537196 0.843457i \(-0.680517\pi\)
−0.537196 + 0.843457i \(0.680517\pi\)
\(104\) 2.77189 0.271807
\(105\) 0 0
\(106\) 0.209993 0.0203964
\(107\) −12.2897 −1.18809 −0.594043 0.804433i \(-0.702469\pi\)
−0.594043 + 0.804433i \(0.702469\pi\)
\(108\) 0 0
\(109\) 9.50134 0.910064 0.455032 0.890475i \(-0.349628\pi\)
0.455032 + 0.890475i \(0.349628\pi\)
\(110\) 2.01031 0.191676
\(111\) 0 0
\(112\) −4.29383 −0.405729
\(113\) −2.21368 −0.208246 −0.104123 0.994564i \(-0.533204\pi\)
−0.104123 + 0.994564i \(0.533204\pi\)
\(114\) 0 0
\(115\) 4.68302 0.436694
\(116\) −3.66521 −0.340306
\(117\) 0 0
\(118\) −1.94740 −0.179272
\(119\) 24.7012 2.26435
\(120\) 0 0
\(121\) −8.19938 −0.745398
\(122\) −1.99514 −0.180632
\(123\) 0 0
\(124\) −10.2309 −0.918761
\(125\) 10.2791 0.919394
\(126\) 0 0
\(127\) −10.9132 −0.968391 −0.484195 0.874960i \(-0.660888\pi\)
−0.484195 + 0.874960i \(0.660888\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −3.32976 −0.292039
\(131\) 7.79020 0.680633 0.340317 0.940311i \(-0.389466\pi\)
0.340317 + 0.940311i \(0.389466\pi\)
\(132\) 0 0
\(133\) −24.3335 −2.10998
\(134\) 2.36095 0.203955
\(135\) 0 0
\(136\) 5.75270 0.493290
\(137\) −8.27186 −0.706713 −0.353356 0.935489i \(-0.614960\pi\)
−0.353356 + 0.935489i \(0.614960\pi\)
\(138\) 0 0
\(139\) −7.15365 −0.606765 −0.303382 0.952869i \(-0.598116\pi\)
−0.303382 + 0.952869i \(0.598116\pi\)
\(140\) 5.15800 0.435931
\(141\) 0 0
\(142\) −9.26740 −0.777703
\(143\) −4.63878 −0.387914
\(144\) 0 0
\(145\) 4.40287 0.365638
\(146\) −7.84474 −0.649236
\(147\) 0 0
\(148\) −7.55661 −0.621150
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 0.135399 0.0110186 0.00550931 0.999985i \(-0.498246\pi\)
0.00550931 + 0.999985i \(0.498246\pi\)
\(152\) −5.66708 −0.459661
\(153\) 0 0
\(154\) 7.18575 0.579044
\(155\) 12.2899 0.987152
\(156\) 0 0
\(157\) −12.5865 −1.00451 −0.502257 0.864718i \(-0.667497\pi\)
−0.502257 + 0.864718i \(0.667497\pi\)
\(158\) 10.3332 0.822067
\(159\) 0 0
\(160\) 1.20126 0.0949678
\(161\) 16.7392 1.31923
\(162\) 0 0
\(163\) 14.2103 1.11304 0.556518 0.830836i \(-0.312137\pi\)
0.556518 + 0.830836i \(0.312137\pi\)
\(164\) −1.38760 −0.108353
\(165\) 0 0
\(166\) −3.69755 −0.286985
\(167\) −4.15585 −0.321589 −0.160795 0.986988i \(-0.551406\pi\)
−0.160795 + 0.986988i \(0.551406\pi\)
\(168\) 0 0
\(169\) −5.31661 −0.408970
\(170\) −6.91048 −0.530010
\(171\) 0 0
\(172\) −7.29901 −0.556544
\(173\) −8.90193 −0.676801 −0.338401 0.941002i \(-0.609886\pi\)
−0.338401 + 0.941002i \(0.609886\pi\)
\(174\) 0 0
\(175\) 15.2731 1.15454
\(176\) 1.67350 0.126145
\(177\) 0 0
\(178\) 12.8667 0.964399
\(179\) −12.9099 −0.964930 −0.482465 0.875915i \(-0.660258\pi\)
−0.482465 + 0.875915i \(0.660258\pi\)
\(180\) 0 0
\(181\) −10.5212 −0.782035 −0.391018 0.920383i \(-0.627877\pi\)
−0.391018 + 0.920383i \(0.627877\pi\)
\(182\) −11.9020 −0.882239
\(183\) 0 0
\(184\) 3.89843 0.287396
\(185\) 9.07744 0.667387
\(186\) 0 0
\(187\) −9.62718 −0.704009
\(188\) 5.85394 0.426943
\(189\) 0 0
\(190\) 6.80763 0.493877
\(191\) 23.8419 1.72514 0.862568 0.505941i \(-0.168855\pi\)
0.862568 + 0.505941i \(0.168855\pi\)
\(192\) 0 0
\(193\) −17.2482 −1.24155 −0.620775 0.783989i \(-0.713182\pi\)
−0.620775 + 0.783989i \(0.713182\pi\)
\(194\) 5.85506 0.420369
\(195\) 0 0
\(196\) 11.4370 0.816929
\(197\) 21.3458 1.52082 0.760412 0.649441i \(-0.224997\pi\)
0.760412 + 0.649441i \(0.224997\pi\)
\(198\) 0 0
\(199\) 5.58409 0.395846 0.197923 0.980218i \(-0.436580\pi\)
0.197923 + 0.980218i \(0.436580\pi\)
\(200\) 3.55698 0.251516
\(201\) 0 0
\(202\) −6.32189 −0.444807
\(203\) 15.7378 1.10458
\(204\) 0 0
\(205\) 1.66686 0.116419
\(206\) 10.9039 0.759710
\(207\) 0 0
\(208\) −2.77189 −0.192196
\(209\) 9.48388 0.656014
\(210\) 0 0
\(211\) −8.24942 −0.567914 −0.283957 0.958837i \(-0.591647\pi\)
−0.283957 + 0.958837i \(0.591647\pi\)
\(212\) −0.209993 −0.0144224
\(213\) 0 0
\(214\) 12.2897 0.840104
\(215\) 8.76799 0.597972
\(216\) 0 0
\(217\) 43.9297 2.98215
\(218\) −9.50134 −0.643512
\(219\) 0 0
\(220\) −2.01031 −0.135535
\(221\) 15.9459 1.07264
\(222\) 0 0
\(223\) 10.4684 0.701017 0.350508 0.936560i \(-0.386009\pi\)
0.350508 + 0.936560i \(0.386009\pi\)
\(224\) 4.29383 0.286894
\(225\) 0 0
\(226\) 2.21368 0.147252
\(227\) 25.7810 1.71114 0.855572 0.517684i \(-0.173206\pi\)
0.855572 + 0.517684i \(0.173206\pi\)
\(228\) 0 0
\(229\) −28.9284 −1.91164 −0.955821 0.293950i \(-0.905030\pi\)
−0.955821 + 0.293950i \(0.905030\pi\)
\(230\) −4.68302 −0.308789
\(231\) 0 0
\(232\) 3.66521 0.240633
\(233\) 5.51234 0.361125 0.180563 0.983563i \(-0.442208\pi\)
0.180563 + 0.983563i \(0.442208\pi\)
\(234\) 0 0
\(235\) −7.03210 −0.458724
\(236\) 1.94740 0.126765
\(237\) 0 0
\(238\) −24.7012 −1.60114
\(239\) −20.3231 −1.31459 −0.657295 0.753634i \(-0.728299\pi\)
−0.657295 + 0.753634i \(0.728299\pi\)
\(240\) 0 0
\(241\) −23.3767 −1.50582 −0.752911 0.658122i \(-0.771351\pi\)
−0.752911 + 0.658122i \(0.771351\pi\)
\(242\) 8.19938 0.527076
\(243\) 0 0
\(244\) 1.99514 0.127726
\(245\) −13.7388 −0.877740
\(246\) 0 0
\(247\) −15.7085 −0.999510
\(248\) 10.2309 0.649662
\(249\) 0 0
\(250\) −10.2791 −0.650110
\(251\) 26.5660 1.67683 0.838416 0.545031i \(-0.183482\pi\)
0.838416 + 0.545031i \(0.183482\pi\)
\(252\) 0 0
\(253\) −6.52404 −0.410163
\(254\) 10.9132 0.684756
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 13.1963 0.823165 0.411582 0.911373i \(-0.364976\pi\)
0.411582 + 0.911373i \(0.364976\pi\)
\(258\) 0 0
\(259\) 32.4468 2.01615
\(260\) 3.32976 0.206503
\(261\) 0 0
\(262\) −7.79020 −0.481280
\(263\) −10.4667 −0.645406 −0.322703 0.946500i \(-0.604592\pi\)
−0.322703 + 0.946500i \(0.604592\pi\)
\(264\) 0 0
\(265\) 0.252256 0.0154960
\(266\) 24.3335 1.49198
\(267\) 0 0
\(268\) −2.36095 −0.144218
\(269\) 27.7593 1.69251 0.846257 0.532775i \(-0.178851\pi\)
0.846257 + 0.532775i \(0.178851\pi\)
\(270\) 0 0
\(271\) −26.9635 −1.63792 −0.818958 0.573853i \(-0.805448\pi\)
−0.818958 + 0.573853i \(0.805448\pi\)
\(272\) −5.75270 −0.348809
\(273\) 0 0
\(274\) 8.27186 0.499721
\(275\) −5.95262 −0.358957
\(276\) 0 0
\(277\) 14.7080 0.883717 0.441858 0.897085i \(-0.354319\pi\)
0.441858 + 0.897085i \(0.354319\pi\)
\(278\) 7.15365 0.429048
\(279\) 0 0
\(280\) −5.15800 −0.308250
\(281\) −6.64235 −0.396249 −0.198125 0.980177i \(-0.563485\pi\)
−0.198125 + 0.980177i \(0.563485\pi\)
\(282\) 0 0
\(283\) 12.4512 0.740149 0.370075 0.929002i \(-0.379332\pi\)
0.370075 + 0.929002i \(0.379332\pi\)
\(284\) 9.26740 0.549919
\(285\) 0 0
\(286\) 4.63878 0.274297
\(287\) 5.95811 0.351696
\(288\) 0 0
\(289\) 16.0936 0.946683
\(290\) −4.40287 −0.258545
\(291\) 0 0
\(292\) 7.84474 0.459079
\(293\) −13.0780 −0.764026 −0.382013 0.924157i \(-0.624769\pi\)
−0.382013 + 0.924157i \(0.624769\pi\)
\(294\) 0 0
\(295\) −2.33933 −0.136201
\(296\) 7.55661 0.439219
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) 10.8060 0.624929
\(300\) 0 0
\(301\) 31.3407 1.80645
\(302\) −0.135399 −0.00779135
\(303\) 0 0
\(304\) 5.66708 0.325029
\(305\) −2.39668 −0.137233
\(306\) 0 0
\(307\) 31.0940 1.77463 0.887315 0.461164i \(-0.152568\pi\)
0.887315 + 0.461164i \(0.152568\pi\)
\(308\) −7.18575 −0.409446
\(309\) 0 0
\(310\) −12.2899 −0.698022
\(311\) 20.7301 1.17550 0.587748 0.809044i \(-0.300014\pi\)
0.587748 + 0.809044i \(0.300014\pi\)
\(312\) 0 0
\(313\) −14.9338 −0.844107 −0.422053 0.906571i \(-0.638690\pi\)
−0.422053 + 0.906571i \(0.638690\pi\)
\(314\) 12.5865 0.710299
\(315\) 0 0
\(316\) −10.3332 −0.581289
\(317\) 9.30324 0.522522 0.261261 0.965268i \(-0.415862\pi\)
0.261261 + 0.965268i \(0.415862\pi\)
\(318\) 0 0
\(319\) −6.13375 −0.343424
\(320\) −1.20126 −0.0671524
\(321\) 0 0
\(322\) −16.7392 −0.932839
\(323\) −32.6010 −1.81397
\(324\) 0 0
\(325\) 9.85957 0.546910
\(326\) −14.2103 −0.787035
\(327\) 0 0
\(328\) 1.38760 0.0766173
\(329\) −25.1359 −1.38578
\(330\) 0 0
\(331\) 13.1701 0.723893 0.361946 0.932199i \(-0.382112\pi\)
0.361946 + 0.932199i \(0.382112\pi\)
\(332\) 3.69755 0.202929
\(333\) 0 0
\(334\) 4.15585 0.227398
\(335\) 2.83611 0.154953
\(336\) 0 0
\(337\) 16.9942 0.925731 0.462866 0.886428i \(-0.346821\pi\)
0.462866 + 0.886428i \(0.346821\pi\)
\(338\) 5.31661 0.289185
\(339\) 0 0
\(340\) 6.91048 0.374774
\(341\) −17.1214 −0.927178
\(342\) 0 0
\(343\) −19.0518 −1.02870
\(344\) 7.29901 0.393536
\(345\) 0 0
\(346\) 8.90193 0.478571
\(347\) 13.8168 0.741724 0.370862 0.928688i \(-0.379062\pi\)
0.370862 + 0.928688i \(0.379062\pi\)
\(348\) 0 0
\(349\) 2.92340 0.156486 0.0782431 0.996934i \(-0.475069\pi\)
0.0782431 + 0.996934i \(0.475069\pi\)
\(350\) −15.2731 −0.816380
\(351\) 0 0
\(352\) −1.67350 −0.0891981
\(353\) −20.3368 −1.08242 −0.541208 0.840889i \(-0.682033\pi\)
−0.541208 + 0.840889i \(0.682033\pi\)
\(354\) 0 0
\(355\) −11.1325 −0.590854
\(356\) −12.8667 −0.681933
\(357\) 0 0
\(358\) 12.9099 0.682308
\(359\) 28.1691 1.48671 0.743354 0.668898i \(-0.233234\pi\)
0.743354 + 0.668898i \(0.233234\pi\)
\(360\) 0 0
\(361\) 13.1158 0.690304
\(362\) 10.5212 0.552982
\(363\) 0 0
\(364\) 11.9020 0.623837
\(365\) −9.42356 −0.493252
\(366\) 0 0
\(367\) −6.03754 −0.315157 −0.157578 0.987506i \(-0.550369\pi\)
−0.157578 + 0.987506i \(0.550369\pi\)
\(368\) −3.89843 −0.203220
\(369\) 0 0
\(370\) −9.07744 −0.471914
\(371\) 0.901676 0.0468127
\(372\) 0 0
\(373\) 8.31784 0.430681 0.215341 0.976539i \(-0.430914\pi\)
0.215341 + 0.976539i \(0.430914\pi\)
\(374\) 9.62718 0.497810
\(375\) 0 0
\(376\) −5.85394 −0.301894
\(377\) 10.1596 0.523245
\(378\) 0 0
\(379\) 15.4853 0.795425 0.397713 0.917510i \(-0.369804\pi\)
0.397713 + 0.917510i \(0.369804\pi\)
\(380\) −6.80763 −0.349224
\(381\) 0 0
\(382\) −23.8419 −1.21986
\(383\) −15.0484 −0.768938 −0.384469 0.923138i \(-0.625615\pi\)
−0.384469 + 0.923138i \(0.625615\pi\)
\(384\) 0 0
\(385\) 8.63194 0.439925
\(386\) 17.2482 0.877908
\(387\) 0 0
\(388\) −5.85506 −0.297246
\(389\) −2.47122 −0.125296 −0.0626478 0.998036i \(-0.519954\pi\)
−0.0626478 + 0.998036i \(0.519954\pi\)
\(390\) 0 0
\(391\) 22.4265 1.13416
\(392\) −11.4370 −0.577656
\(393\) 0 0
\(394\) −21.3458 −1.07539
\(395\) 12.4129 0.624559
\(396\) 0 0
\(397\) 13.1443 0.659695 0.329847 0.944034i \(-0.393003\pi\)
0.329847 + 0.944034i \(0.393003\pi\)
\(398\) −5.58409 −0.279905
\(399\) 0 0
\(400\) −3.55698 −0.177849
\(401\) 36.1388 1.80469 0.902344 0.431018i \(-0.141845\pi\)
0.902344 + 0.431018i \(0.141845\pi\)
\(402\) 0 0
\(403\) 28.3589 1.41266
\(404\) 6.32189 0.314526
\(405\) 0 0
\(406\) −15.7378 −0.781054
\(407\) −12.6460 −0.626840
\(408\) 0 0
\(409\) 35.8167 1.77102 0.885512 0.464617i \(-0.153808\pi\)
0.885512 + 0.464617i \(0.153808\pi\)
\(410\) −1.66686 −0.0823205
\(411\) 0 0
\(412\) −10.9039 −0.537196
\(413\) −8.36179 −0.411457
\(414\) 0 0
\(415\) −4.44171 −0.218035
\(416\) 2.77189 0.135903
\(417\) 0 0
\(418\) −9.48388 −0.463872
\(419\) −8.65211 −0.422683 −0.211342 0.977412i \(-0.567783\pi\)
−0.211342 + 0.977412i \(0.567783\pi\)
\(420\) 0 0
\(421\) 17.5972 0.857633 0.428817 0.903392i \(-0.358931\pi\)
0.428817 + 0.903392i \(0.358931\pi\)
\(422\) 8.24942 0.401576
\(423\) 0 0
\(424\) 0.209993 0.0101982
\(425\) 20.4622 0.992565
\(426\) 0 0
\(427\) −8.56680 −0.414577
\(428\) −12.2897 −0.594043
\(429\) 0 0
\(430\) −8.76799 −0.422830
\(431\) −31.9670 −1.53980 −0.769898 0.638167i \(-0.779693\pi\)
−0.769898 + 0.638167i \(0.779693\pi\)
\(432\) 0 0
\(433\) 4.92015 0.236448 0.118224 0.992987i \(-0.462280\pi\)
0.118224 + 0.992987i \(0.462280\pi\)
\(434\) −43.9297 −2.10870
\(435\) 0 0
\(436\) 9.50134 0.455032
\(437\) −22.0927 −1.05684
\(438\) 0 0
\(439\) −4.67906 −0.223319 −0.111660 0.993747i \(-0.535617\pi\)
−0.111660 + 0.993747i \(0.535617\pi\)
\(440\) 2.01031 0.0958379
\(441\) 0 0
\(442\) −15.9459 −0.758468
\(443\) −27.0433 −1.28487 −0.642433 0.766342i \(-0.722075\pi\)
−0.642433 + 0.766342i \(0.722075\pi\)
\(444\) 0 0
\(445\) 15.4562 0.732695
\(446\) −10.4684 −0.495694
\(447\) 0 0
\(448\) −4.29383 −0.202865
\(449\) 8.57230 0.404552 0.202276 0.979329i \(-0.435166\pi\)
0.202276 + 0.979329i \(0.435166\pi\)
\(450\) 0 0
\(451\) −2.32215 −0.109346
\(452\) −2.21368 −0.104123
\(453\) 0 0
\(454\) −25.7810 −1.20996
\(455\) −14.2974 −0.670274
\(456\) 0 0
\(457\) 28.7727 1.34593 0.672966 0.739673i \(-0.265020\pi\)
0.672966 + 0.739673i \(0.265020\pi\)
\(458\) 28.9284 1.35173
\(459\) 0 0
\(460\) 4.68302 0.218347
\(461\) 8.63284 0.402071 0.201036 0.979584i \(-0.435569\pi\)
0.201036 + 0.979584i \(0.435569\pi\)
\(462\) 0 0
\(463\) −28.1712 −1.30923 −0.654614 0.755963i \(-0.727169\pi\)
−0.654614 + 0.755963i \(0.727169\pi\)
\(464\) −3.66521 −0.170153
\(465\) 0 0
\(466\) −5.51234 −0.255354
\(467\) 20.1411 0.932021 0.466011 0.884779i \(-0.345691\pi\)
0.466011 + 0.884779i \(0.345691\pi\)
\(468\) 0 0
\(469\) 10.1375 0.468107
\(470\) 7.03210 0.324367
\(471\) 0 0
\(472\) −1.94740 −0.0896362
\(473\) −12.2149 −0.561643
\(474\) 0 0
\(475\) −20.1577 −0.924898
\(476\) 24.7012 1.13218
\(477\) 0 0
\(478\) 20.3231 0.929555
\(479\) −28.4710 −1.30087 −0.650437 0.759560i \(-0.725414\pi\)
−0.650437 + 0.759560i \(0.725414\pi\)
\(480\) 0 0
\(481\) 20.9461 0.955061
\(482\) 23.3767 1.06478
\(483\) 0 0
\(484\) −8.19938 −0.372699
\(485\) 7.03344 0.319372
\(486\) 0 0
\(487\) 22.6813 1.02779 0.513894 0.857854i \(-0.328203\pi\)
0.513894 + 0.857854i \(0.328203\pi\)
\(488\) −1.99514 −0.0903158
\(489\) 0 0
\(490\) 13.7388 0.620656
\(491\) 19.6822 0.888246 0.444123 0.895966i \(-0.353515\pi\)
0.444123 + 0.895966i \(0.353515\pi\)
\(492\) 0 0
\(493\) 21.0849 0.949615
\(494\) 15.7085 0.706761
\(495\) 0 0
\(496\) −10.2309 −0.459381
\(497\) −39.7927 −1.78494
\(498\) 0 0
\(499\) 6.11985 0.273962 0.136981 0.990574i \(-0.456260\pi\)
0.136981 + 0.990574i \(0.456260\pi\)
\(500\) 10.2791 0.459697
\(501\) 0 0
\(502\) −26.5660 −1.18570
\(503\) −24.8603 −1.10847 −0.554233 0.832361i \(-0.686988\pi\)
−0.554233 + 0.832361i \(0.686988\pi\)
\(504\) 0 0
\(505\) −7.59423 −0.337939
\(506\) 6.52404 0.290029
\(507\) 0 0
\(508\) −10.9132 −0.484195
\(509\) 4.82156 0.213712 0.106856 0.994275i \(-0.465922\pi\)
0.106856 + 0.994275i \(0.465922\pi\)
\(510\) 0 0
\(511\) −33.6840 −1.49009
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −13.1963 −0.582065
\(515\) 13.0984 0.577184
\(516\) 0 0
\(517\) 9.79660 0.430854
\(518\) −32.4468 −1.42563
\(519\) 0 0
\(520\) −3.32976 −0.146020
\(521\) 24.1264 1.05700 0.528499 0.848934i \(-0.322755\pi\)
0.528499 + 0.848934i \(0.322755\pi\)
\(522\) 0 0
\(523\) 40.2704 1.76090 0.880451 0.474138i \(-0.157240\pi\)
0.880451 + 0.474138i \(0.157240\pi\)
\(524\) 7.79020 0.340317
\(525\) 0 0
\(526\) 10.4667 0.456371
\(527\) 58.8553 2.56378
\(528\) 0 0
\(529\) −7.80226 −0.339229
\(530\) −0.252256 −0.0109573
\(531\) 0 0
\(532\) −24.3335 −1.05499
\(533\) 3.84627 0.166601
\(534\) 0 0
\(535\) 14.7631 0.638263
\(536\) 2.36095 0.101977
\(537\) 0 0
\(538\) −27.7593 −1.19679
\(539\) 19.1399 0.824413
\(540\) 0 0
\(541\) 6.74172 0.289849 0.144925 0.989443i \(-0.453706\pi\)
0.144925 + 0.989443i \(0.453706\pi\)
\(542\) 26.9635 1.15818
\(543\) 0 0
\(544\) 5.75270 0.246645
\(545\) −11.4136 −0.488904
\(546\) 0 0
\(547\) −13.0462 −0.557816 −0.278908 0.960318i \(-0.589972\pi\)
−0.278908 + 0.960318i \(0.589972\pi\)
\(548\) −8.27186 −0.353356
\(549\) 0 0
\(550\) 5.95262 0.253821
\(551\) −20.7710 −0.884876
\(552\) 0 0
\(553\) 44.3692 1.88677
\(554\) −14.7080 −0.624882
\(555\) 0 0
\(556\) −7.15365 −0.303382
\(557\) 1.84618 0.0782254 0.0391127 0.999235i \(-0.487547\pi\)
0.0391127 + 0.999235i \(0.487547\pi\)
\(558\) 0 0
\(559\) 20.2321 0.855725
\(560\) 5.15800 0.217965
\(561\) 0 0
\(562\) 6.64235 0.280191
\(563\) 40.7048 1.71550 0.857750 0.514066i \(-0.171861\pi\)
0.857750 + 0.514066i \(0.171861\pi\)
\(564\) 0 0
\(565\) 2.65921 0.111874
\(566\) −12.4512 −0.523365
\(567\) 0 0
\(568\) −9.26740 −0.388851
\(569\) −20.4802 −0.858574 −0.429287 0.903168i \(-0.641235\pi\)
−0.429287 + 0.903168i \(0.641235\pi\)
\(570\) 0 0
\(571\) 1.93208 0.0808550 0.0404275 0.999182i \(-0.487128\pi\)
0.0404275 + 0.999182i \(0.487128\pi\)
\(572\) −4.63878 −0.193957
\(573\) 0 0
\(574\) −5.95811 −0.248687
\(575\) 13.8666 0.578278
\(576\) 0 0
\(577\) 4.02426 0.167532 0.0837660 0.996485i \(-0.473305\pi\)
0.0837660 + 0.996485i \(0.473305\pi\)
\(578\) −16.0936 −0.669406
\(579\) 0 0
\(580\) 4.40287 0.182819
\(581\) −15.8767 −0.658675
\(582\) 0 0
\(583\) −0.351425 −0.0145545
\(584\) −7.84474 −0.324618
\(585\) 0 0
\(586\) 13.0780 0.540248
\(587\) −5.88313 −0.242823 −0.121411 0.992602i \(-0.538742\pi\)
−0.121411 + 0.992602i \(0.538742\pi\)
\(588\) 0 0
\(589\) −57.9793 −2.38899
\(590\) 2.33933 0.0963085
\(591\) 0 0
\(592\) −7.55661 −0.310575
\(593\) −25.7743 −1.05842 −0.529211 0.848490i \(-0.677512\pi\)
−0.529211 + 0.848490i \(0.677512\pi\)
\(594\) 0 0
\(595\) −29.6725 −1.21645
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) −10.8060 −0.441891
\(599\) −24.9795 −1.02064 −0.510318 0.859986i \(-0.670472\pi\)
−0.510318 + 0.859986i \(0.670472\pi\)
\(600\) 0 0
\(601\) 10.1677 0.414748 0.207374 0.978262i \(-0.433508\pi\)
0.207374 + 0.978262i \(0.433508\pi\)
\(602\) −31.3407 −1.27735
\(603\) 0 0
\(604\) 0.135399 0.00550931
\(605\) 9.84958 0.400442
\(606\) 0 0
\(607\) −49.0887 −1.99245 −0.996224 0.0868242i \(-0.972328\pi\)
−0.996224 + 0.0868242i \(0.972328\pi\)
\(608\) −5.66708 −0.229830
\(609\) 0 0
\(610\) 2.39668 0.0970387
\(611\) −16.2265 −0.656454
\(612\) 0 0
\(613\) −14.4594 −0.584009 −0.292004 0.956417i \(-0.594322\pi\)
−0.292004 + 0.956417i \(0.594322\pi\)
\(614\) −31.0940 −1.25485
\(615\) 0 0
\(616\) 7.18575 0.289522
\(617\) −22.0472 −0.887586 −0.443793 0.896129i \(-0.646367\pi\)
−0.443793 + 0.896129i \(0.646367\pi\)
\(618\) 0 0
\(619\) −11.4459 −0.460051 −0.230025 0.973185i \(-0.573881\pi\)
−0.230025 + 0.973185i \(0.573881\pi\)
\(620\) 12.2899 0.493576
\(621\) 0 0
\(622\) −20.7301 −0.831202
\(623\) 55.2474 2.21344
\(624\) 0 0
\(625\) 5.43699 0.217479
\(626\) 14.9338 0.596873
\(627\) 0 0
\(628\) −12.5865 −0.502257
\(629\) 43.4709 1.73330
\(630\) 0 0
\(631\) −40.5672 −1.61496 −0.807478 0.589897i \(-0.799168\pi\)
−0.807478 + 0.589897i \(0.799168\pi\)
\(632\) 10.3332 0.411034
\(633\) 0 0
\(634\) −9.30324 −0.369479
\(635\) 13.1096 0.520238
\(636\) 0 0
\(637\) −31.7022 −1.25609
\(638\) 6.13375 0.242838
\(639\) 0 0
\(640\) 1.20126 0.0474839
\(641\) 40.3310 1.59298 0.796489 0.604653i \(-0.206688\pi\)
0.796489 + 0.604653i \(0.206688\pi\)
\(642\) 0 0
\(643\) −20.4803 −0.807662 −0.403831 0.914834i \(-0.632322\pi\)
−0.403831 + 0.914834i \(0.632322\pi\)
\(644\) 16.7392 0.659617
\(645\) 0 0
\(646\) 32.6010 1.28267
\(647\) −33.0332 −1.29867 −0.649334 0.760504i \(-0.724952\pi\)
−0.649334 + 0.760504i \(0.724952\pi\)
\(648\) 0 0
\(649\) 3.25898 0.127926
\(650\) −9.85957 −0.386724
\(651\) 0 0
\(652\) 14.2103 0.556518
\(653\) −16.9821 −0.664561 −0.332281 0.943181i \(-0.607818\pi\)
−0.332281 + 0.943181i \(0.607818\pi\)
\(654\) 0 0
\(655\) −9.35805 −0.365649
\(656\) −1.38760 −0.0541766
\(657\) 0 0
\(658\) 25.1359 0.979898
\(659\) −1.32800 −0.0517314 −0.0258657 0.999665i \(-0.508234\pi\)
−0.0258657 + 0.999665i \(0.508234\pi\)
\(660\) 0 0
\(661\) 27.7686 1.08007 0.540037 0.841641i \(-0.318410\pi\)
0.540037 + 0.841641i \(0.318410\pi\)
\(662\) −13.1701 −0.511869
\(663\) 0 0
\(664\) −3.69755 −0.143493
\(665\) 29.2308 1.13352
\(666\) 0 0
\(667\) 14.2886 0.553255
\(668\) −4.15585 −0.160795
\(669\) 0 0
\(670\) −2.83611 −0.109568
\(671\) 3.33888 0.128896
\(672\) 0 0
\(673\) 30.5773 1.17867 0.589334 0.807889i \(-0.299390\pi\)
0.589334 + 0.807889i \(0.299390\pi\)
\(674\) −16.9942 −0.654591
\(675\) 0 0
\(676\) −5.31661 −0.204485
\(677\) −9.42825 −0.362357 −0.181178 0.983450i \(-0.557991\pi\)
−0.181178 + 0.983450i \(0.557991\pi\)
\(678\) 0 0
\(679\) 25.1407 0.964810
\(680\) −6.91048 −0.265005
\(681\) 0 0
\(682\) 17.1214 0.655614
\(683\) 25.8146 0.987767 0.493884 0.869528i \(-0.335577\pi\)
0.493884 + 0.869528i \(0.335577\pi\)
\(684\) 0 0
\(685\) 9.93664 0.379660
\(686\) 19.0518 0.727400
\(687\) 0 0
\(688\) −7.29901 −0.278272
\(689\) 0.582079 0.0221754
\(690\) 0 0
\(691\) −19.6482 −0.747454 −0.373727 0.927539i \(-0.621920\pi\)
−0.373727 + 0.927539i \(0.621920\pi\)
\(692\) −8.90193 −0.338401
\(693\) 0 0
\(694\) −13.8168 −0.524478
\(695\) 8.59338 0.325966
\(696\) 0 0
\(697\) 7.98244 0.302356
\(698\) −2.92340 −0.110652
\(699\) 0 0
\(700\) 15.2731 0.577268
\(701\) −2.17682 −0.0822172 −0.0411086 0.999155i \(-0.513089\pi\)
−0.0411086 + 0.999155i \(0.513089\pi\)
\(702\) 0 0
\(703\) −42.8239 −1.61513
\(704\) 1.67350 0.0630726
\(705\) 0 0
\(706\) 20.3368 0.765384
\(707\) −27.1452 −1.02090
\(708\) 0 0
\(709\) −0.337527 −0.0126761 −0.00633805 0.999980i \(-0.502017\pi\)
−0.00633805 + 0.999980i \(0.502017\pi\)
\(710\) 11.1325 0.417797
\(711\) 0 0
\(712\) 12.8667 0.482200
\(713\) 39.8844 1.49368
\(714\) 0 0
\(715\) 5.57237 0.208395
\(716\) −12.9099 −0.482465
\(717\) 0 0
\(718\) −28.1691 −1.05126
\(719\) −30.1660 −1.12500 −0.562501 0.826797i \(-0.690161\pi\)
−0.562501 + 0.826797i \(0.690161\pi\)
\(720\) 0 0
\(721\) 46.8195 1.74365
\(722\) −13.1158 −0.488119
\(723\) 0 0
\(724\) −10.5212 −0.391018
\(725\) 13.0371 0.484185
\(726\) 0 0
\(727\) 1.99176 0.0738705 0.0369352 0.999318i \(-0.488240\pi\)
0.0369352 + 0.999318i \(0.488240\pi\)
\(728\) −11.9020 −0.441119
\(729\) 0 0
\(730\) 9.42356 0.348782
\(731\) 41.9890 1.55302
\(732\) 0 0
\(733\) 18.5615 0.685586 0.342793 0.939411i \(-0.388627\pi\)
0.342793 + 0.939411i \(0.388627\pi\)
\(734\) 6.03754 0.222850
\(735\) 0 0
\(736\) 3.89843 0.143698
\(737\) −3.95106 −0.145539
\(738\) 0 0
\(739\) −5.18207 −0.190625 −0.0953127 0.995447i \(-0.530385\pi\)
−0.0953127 + 0.995447i \(0.530385\pi\)
\(740\) 9.07744 0.333693
\(741\) 0 0
\(742\) −0.901676 −0.0331016
\(743\) −33.6377 −1.23405 −0.617024 0.786944i \(-0.711662\pi\)
−0.617024 + 0.786944i \(0.711662\pi\)
\(744\) 0 0
\(745\) −1.20126 −0.0440107
\(746\) −8.31784 −0.304538
\(747\) 0 0
\(748\) −9.62718 −0.352005
\(749\) 52.7698 1.92817
\(750\) 0 0
\(751\) 18.4176 0.672068 0.336034 0.941850i \(-0.390914\pi\)
0.336034 + 0.941850i \(0.390914\pi\)
\(752\) 5.85394 0.213471
\(753\) 0 0
\(754\) −10.1596 −0.369990
\(755\) −0.162649 −0.00591942
\(756\) 0 0
\(757\) −1.84141 −0.0669272 −0.0334636 0.999440i \(-0.510654\pi\)
−0.0334636 + 0.999440i \(0.510654\pi\)
\(758\) −15.4853 −0.562450
\(759\) 0 0
\(760\) 6.80763 0.246939
\(761\) 14.1293 0.512187 0.256093 0.966652i \(-0.417565\pi\)
0.256093 + 0.966652i \(0.417565\pi\)
\(762\) 0 0
\(763\) −40.7972 −1.47696
\(764\) 23.8419 0.862568
\(765\) 0 0
\(766\) 15.0484 0.543721
\(767\) −5.39797 −0.194910
\(768\) 0 0
\(769\) 37.9796 1.36958 0.684790 0.728741i \(-0.259894\pi\)
0.684790 + 0.728741i \(0.259894\pi\)
\(770\) −8.63194 −0.311074
\(771\) 0 0
\(772\) −17.2482 −0.620775
\(773\) −42.8857 −1.54249 −0.771245 0.636538i \(-0.780366\pi\)
−0.771245 + 0.636538i \(0.780366\pi\)
\(774\) 0 0
\(775\) 36.3911 1.30721
\(776\) 5.85506 0.210185
\(777\) 0 0
\(778\) 2.47122 0.0885974
\(779\) −7.86363 −0.281744
\(780\) 0 0
\(781\) 15.5090 0.554957
\(782\) −22.4265 −0.801970
\(783\) 0 0
\(784\) 11.4370 0.408464
\(785\) 15.1197 0.539645
\(786\) 0 0
\(787\) −25.8911 −0.922917 −0.461458 0.887162i \(-0.652674\pi\)
−0.461458 + 0.887162i \(0.652674\pi\)
\(788\) 21.3458 0.760412
\(789\) 0 0
\(790\) −12.4129 −0.441630
\(791\) 9.50519 0.337966
\(792\) 0 0
\(793\) −5.53032 −0.196387
\(794\) −13.1443 −0.466474
\(795\) 0 0
\(796\) 5.58409 0.197923
\(797\) −20.9646 −0.742604 −0.371302 0.928512i \(-0.621089\pi\)
−0.371302 + 0.928512i \(0.621089\pi\)
\(798\) 0 0
\(799\) −33.6760 −1.19137
\(800\) 3.55698 0.125758
\(801\) 0 0
\(802\) −36.1388 −1.27611
\(803\) 13.1282 0.463285
\(804\) 0 0
\(805\) −20.1081 −0.708717
\(806\) −28.3589 −0.998901
\(807\) 0 0
\(808\) −6.32189 −0.222403
\(809\) 10.8597 0.381805 0.190903 0.981609i \(-0.438859\pi\)
0.190903 + 0.981609i \(0.438859\pi\)
\(810\) 0 0
\(811\) 46.9551 1.64882 0.824408 0.565995i \(-0.191508\pi\)
0.824408 + 0.565995i \(0.191508\pi\)
\(812\) 15.7378 0.552289
\(813\) 0 0
\(814\) 12.6460 0.443243
\(815\) −17.0702 −0.597944
\(816\) 0 0
\(817\) −41.3640 −1.44714
\(818\) −35.8167 −1.25230
\(819\) 0 0
\(820\) 1.66686 0.0582094
\(821\) 11.5063 0.401573 0.200786 0.979635i \(-0.435650\pi\)
0.200786 + 0.979635i \(0.435650\pi\)
\(822\) 0 0
\(823\) −31.4829 −1.09742 −0.548712 0.836012i \(-0.684881\pi\)
−0.548712 + 0.836012i \(0.684881\pi\)
\(824\) 10.9039 0.379855
\(825\) 0 0
\(826\) 8.36179 0.290944
\(827\) 16.5022 0.573837 0.286918 0.957955i \(-0.407369\pi\)
0.286918 + 0.957955i \(0.407369\pi\)
\(828\) 0 0
\(829\) 29.7832 1.03441 0.517207 0.855860i \(-0.326972\pi\)
0.517207 + 0.855860i \(0.326972\pi\)
\(830\) 4.44171 0.154174
\(831\) 0 0
\(832\) −2.77189 −0.0960981
\(833\) −65.7937 −2.27962
\(834\) 0 0
\(835\) 4.99225 0.172764
\(836\) 9.48388 0.328007
\(837\) 0 0
\(838\) 8.65211 0.298882
\(839\) 20.9568 0.723507 0.361754 0.932274i \(-0.382178\pi\)
0.361754 + 0.932274i \(0.382178\pi\)
\(840\) 0 0
\(841\) −15.5662 −0.536766
\(842\) −17.5972 −0.606438
\(843\) 0 0
\(844\) −8.24942 −0.283957
\(845\) 6.38662 0.219706
\(846\) 0 0
\(847\) 35.2068 1.20972
\(848\) −0.209993 −0.00721120
\(849\) 0 0
\(850\) −20.4622 −0.701849
\(851\) 29.4589 1.00984
\(852\) 0 0
\(853\) −5.64517 −0.193287 −0.0966435 0.995319i \(-0.530811\pi\)
−0.0966435 + 0.995319i \(0.530811\pi\)
\(854\) 8.56680 0.293150
\(855\) 0 0
\(856\) 12.2897 0.420052
\(857\) −11.8928 −0.406251 −0.203126 0.979153i \(-0.565110\pi\)
−0.203126 + 0.979153i \(0.565110\pi\)
\(858\) 0 0
\(859\) −6.44572 −0.219925 −0.109963 0.993936i \(-0.535073\pi\)
−0.109963 + 0.993936i \(0.535073\pi\)
\(860\) 8.76799 0.298986
\(861\) 0 0
\(862\) 31.9670 1.08880
\(863\) 8.84939 0.301237 0.150618 0.988592i \(-0.451874\pi\)
0.150618 + 0.988592i \(0.451874\pi\)
\(864\) 0 0
\(865\) 10.6935 0.363591
\(866\) −4.92015 −0.167194
\(867\) 0 0
\(868\) 43.9297 1.49107
\(869\) −17.2927 −0.586615
\(870\) 0 0
\(871\) 6.54429 0.221745
\(872\) −9.50134 −0.321756
\(873\) 0 0
\(874\) 22.0927 0.747297
\(875\) −44.1369 −1.49210
\(876\) 0 0
\(877\) 42.5241 1.43594 0.717968 0.696076i \(-0.245072\pi\)
0.717968 + 0.696076i \(0.245072\pi\)
\(878\) 4.67906 0.157911
\(879\) 0 0
\(880\) −2.01031 −0.0677676
\(881\) −24.3006 −0.818708 −0.409354 0.912376i \(-0.634246\pi\)
−0.409354 + 0.912376i \(0.634246\pi\)
\(882\) 0 0
\(883\) −29.0897 −0.978947 −0.489473 0.872018i \(-0.662811\pi\)
−0.489473 + 0.872018i \(0.662811\pi\)
\(884\) 15.9459 0.536318
\(885\) 0 0
\(886\) 27.0433 0.908538
\(887\) −35.5771 −1.19456 −0.597282 0.802032i \(-0.703753\pi\)
−0.597282 + 0.802032i \(0.703753\pi\)
\(888\) 0 0
\(889\) 46.8595 1.57162
\(890\) −15.4562 −0.518094
\(891\) 0 0
\(892\) 10.4684 0.350508
\(893\) 33.1748 1.11015
\(894\) 0 0
\(895\) 15.5081 0.518379
\(896\) 4.29383 0.143447
\(897\) 0 0
\(898\) −8.57230 −0.286061
\(899\) 37.4984 1.25064
\(900\) 0 0
\(901\) 1.20803 0.0402453
\(902\) 2.32215 0.0773192
\(903\) 0 0
\(904\) 2.21368 0.0736260
\(905\) 12.6387 0.420124
\(906\) 0 0
\(907\) 20.9998 0.697286 0.348643 0.937256i \(-0.386643\pi\)
0.348643 + 0.937256i \(0.386643\pi\)
\(908\) 25.7810 0.855572
\(909\) 0 0
\(910\) 14.2974 0.473955
\(911\) −29.5524 −0.979116 −0.489558 0.871971i \(-0.662842\pi\)
−0.489558 + 0.871971i \(0.662842\pi\)
\(912\) 0 0
\(913\) 6.18787 0.204788
\(914\) −28.7727 −0.951718
\(915\) 0 0
\(916\) −28.9284 −0.955821
\(917\) −33.4498 −1.10461
\(918\) 0 0
\(919\) −33.4974 −1.10498 −0.552488 0.833521i \(-0.686322\pi\)
−0.552488 + 0.833521i \(0.686322\pi\)
\(920\) −4.68302 −0.154395
\(921\) 0 0
\(922\) −8.63284 −0.284307
\(923\) −25.6882 −0.845539
\(924\) 0 0
\(925\) 26.8787 0.883766
\(926\) 28.1712 0.925764
\(927\) 0 0
\(928\) 3.66521 0.120316
\(929\) −29.0055 −0.951639 −0.475819 0.879543i \(-0.657848\pi\)
−0.475819 + 0.879543i \(0.657848\pi\)
\(930\) 0 0
\(931\) 64.8144 2.12421
\(932\) 5.51234 0.180563
\(933\) 0 0
\(934\) −20.1411 −0.659038
\(935\) 11.5647 0.378207
\(936\) 0 0
\(937\) −5.51100 −0.180037 −0.0900183 0.995940i \(-0.528693\pi\)
−0.0900183 + 0.995940i \(0.528693\pi\)
\(938\) −10.1375 −0.331002
\(939\) 0 0
\(940\) −7.03210 −0.229362
\(941\) −33.4090 −1.08910 −0.544552 0.838727i \(-0.683300\pi\)
−0.544552 + 0.838727i \(0.683300\pi\)
\(942\) 0 0
\(943\) 5.40945 0.176156
\(944\) 1.94740 0.0633823
\(945\) 0 0
\(946\) 12.2149 0.397141
\(947\) −38.5650 −1.25319 −0.626597 0.779344i \(-0.715553\pi\)
−0.626597 + 0.779344i \(0.715553\pi\)
\(948\) 0 0
\(949\) −21.7448 −0.705866
\(950\) 20.1577 0.654001
\(951\) 0 0
\(952\) −24.7012 −0.800569
\(953\) 34.8019 1.12734 0.563672 0.825999i \(-0.309388\pi\)
0.563672 + 0.825999i \(0.309388\pi\)
\(954\) 0 0
\(955\) −28.6402 −0.926776
\(956\) −20.3231 −0.657295
\(957\) 0 0
\(958\) 28.4710 0.919857
\(959\) 35.5180 1.14694
\(960\) 0 0
\(961\) 73.6712 2.37649
\(962\) −20.9461 −0.675330
\(963\) 0 0
\(964\) −23.3767 −0.752911
\(965\) 20.7195 0.666984
\(966\) 0 0
\(967\) −17.0912 −0.549616 −0.274808 0.961499i \(-0.588614\pi\)
−0.274808 + 0.961499i \(0.588614\pi\)
\(968\) 8.19938 0.263538
\(969\) 0 0
\(970\) −7.03344 −0.225830
\(971\) 7.44521 0.238928 0.119464 0.992839i \(-0.461882\pi\)
0.119464 + 0.992839i \(0.461882\pi\)
\(972\) 0 0
\(973\) 30.7166 0.984729
\(974\) −22.6813 −0.726756
\(975\) 0 0
\(976\) 1.99514 0.0638629
\(977\) −17.4152 −0.557161 −0.278581 0.960413i \(-0.589864\pi\)
−0.278581 + 0.960413i \(0.589864\pi\)
\(978\) 0 0
\(979\) −21.5325 −0.688181
\(980\) −13.7388 −0.438870
\(981\) 0 0
\(982\) −19.6822 −0.628085
\(983\) 56.5864 1.80483 0.902413 0.430872i \(-0.141794\pi\)
0.902413 + 0.430872i \(0.141794\pi\)
\(984\) 0 0
\(985\) −25.6418 −0.817016
\(986\) −21.0849 −0.671479
\(987\) 0 0
\(988\) −15.7085 −0.499755
\(989\) 28.4546 0.904805
\(990\) 0 0
\(991\) −42.9138 −1.36320 −0.681601 0.731724i \(-0.738716\pi\)
−0.681601 + 0.731724i \(0.738716\pi\)
\(992\) 10.2309 0.324831
\(993\) 0 0
\(994\) 39.7927 1.26215
\(995\) −6.70794 −0.212656
\(996\) 0 0
\(997\) 47.3180 1.49858 0.749288 0.662244i \(-0.230396\pi\)
0.749288 + 0.662244i \(0.230396\pi\)
\(998\) −6.11985 −0.193721
\(999\) 0 0
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 \(a_p\))