Properties

Label 6036.2.a.g.1.11
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(1.33620\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+0.336200 q^{5}\) \(+0.568501 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+0.336200 q^{5}\) \(+0.568501 q^{7}\) \(+1.00000 q^{9}\) \(+5.54286 q^{11}\) \(-5.92976 q^{13}\) \(+0.336200 q^{15}\) \(+0.0480914 q^{17}\) \(-3.03166 q^{19}\) \(+0.568501 q^{21}\) \(-5.32774 q^{23}\) \(-4.88697 q^{25}\) \(+1.00000 q^{27}\) \(+0.918207 q^{29}\) \(-8.65025 q^{31}\) \(+5.54286 q^{33}\) \(+0.191130 q^{35}\) \(-6.04634 q^{37}\) \(-5.92976 q^{39}\) \(+1.72602 q^{41}\) \(-6.69093 q^{43}\) \(+0.336200 q^{45}\) \(-0.136711 q^{47}\) \(-6.67681 q^{49}\) \(+0.0480914 q^{51}\) \(-1.99811 q^{53}\) \(+1.86351 q^{55}\) \(-3.03166 q^{57}\) \(-11.7881 q^{59}\) \(+6.84008 q^{61}\) \(+0.568501 q^{63}\) \(-1.99358 q^{65}\) \(+7.26008 q^{67}\) \(-5.32774 q^{69}\) \(+12.1144 q^{71}\) \(-5.77178 q^{73}\) \(-4.88697 q^{75}\) \(+3.15112 q^{77}\) \(-15.6180 q^{79}\) \(+1.00000 q^{81}\) \(-5.52142 q^{83}\) \(+0.0161683 q^{85}\) \(+0.918207 q^{87}\) \(-7.27474 q^{89}\) \(-3.37108 q^{91}\) \(-8.65025 q^{93}\) \(-1.01924 q^{95}\) \(+6.99135 q^{97}\) \(+5.54286 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 0.336200 0.150353 0.0751766 0.997170i \(-0.476048\pi\)
0.0751766 + 0.997170i \(0.476048\pi\)
\(6\) 0 0
\(7\) 0.568501 0.214873 0.107437 0.994212i \(-0.465736\pi\)
0.107437 + 0.994212i \(0.465736\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.54286 1.67123 0.835617 0.549312i \(-0.185110\pi\)
0.835617 + 0.549312i \(0.185110\pi\)
\(12\) 0 0
\(13\) −5.92976 −1.64462 −0.822310 0.569040i \(-0.807315\pi\)
−0.822310 + 0.569040i \(0.807315\pi\)
\(14\) 0 0
\(15\) 0.336200 0.0868064
\(16\) 0 0
\(17\) 0.0480914 0.0116639 0.00583194 0.999983i \(-0.498144\pi\)
0.00583194 + 0.999983i \(0.498144\pi\)
\(18\) 0 0
\(19\) −3.03166 −0.695510 −0.347755 0.937585i \(-0.613056\pi\)
−0.347755 + 0.937585i \(0.613056\pi\)
\(20\) 0 0
\(21\) 0.568501 0.124057
\(22\) 0 0
\(23\) −5.32774 −1.11091 −0.555455 0.831546i \(-0.687456\pi\)
−0.555455 + 0.831546i \(0.687456\pi\)
\(24\) 0 0
\(25\) −4.88697 −0.977394
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 0.918207 0.170507 0.0852534 0.996359i \(-0.472830\pi\)
0.0852534 + 0.996359i \(0.472830\pi\)
\(30\) 0 0
\(31\) −8.65025 −1.55363 −0.776815 0.629729i \(-0.783166\pi\)
−0.776815 + 0.629729i \(0.783166\pi\)
\(32\) 0 0
\(33\) 5.54286 0.964888
\(34\) 0 0
\(35\) 0.191130 0.0323069
\(36\) 0 0
\(37\) −6.04634 −0.994012 −0.497006 0.867747i \(-0.665567\pi\)
−0.497006 + 0.867747i \(0.665567\pi\)
\(38\) 0 0
\(39\) −5.92976 −0.949521
\(40\) 0 0
\(41\) 1.72602 0.269559 0.134780 0.990876i \(-0.456967\pi\)
0.134780 + 0.990876i \(0.456967\pi\)
\(42\) 0 0
\(43\) −6.69093 −1.02036 −0.510179 0.860068i \(-0.670421\pi\)
−0.510179 + 0.860068i \(0.670421\pi\)
\(44\) 0 0
\(45\) 0.336200 0.0501177
\(46\) 0 0
\(47\) −0.136711 −0.0199413 −0.00997066 0.999950i \(-0.503174\pi\)
−0.00997066 + 0.999950i \(0.503174\pi\)
\(48\) 0 0
\(49\) −6.67681 −0.953829
\(50\) 0 0
\(51\) 0.0480914 0.00673414
\(52\) 0 0
\(53\) −1.99811 −0.274462 −0.137231 0.990539i \(-0.543820\pi\)
−0.137231 + 0.990539i \(0.543820\pi\)
\(54\) 0 0
\(55\) 1.86351 0.251275
\(56\) 0 0
\(57\) −3.03166 −0.401553
\(58\) 0 0
\(59\) −11.7881 −1.53468 −0.767338 0.641242i \(-0.778419\pi\)
−0.767338 + 0.641242i \(0.778419\pi\)
\(60\) 0 0
\(61\) 6.84008 0.875782 0.437891 0.899028i \(-0.355726\pi\)
0.437891 + 0.899028i \(0.355726\pi\)
\(62\) 0 0
\(63\) 0.568501 0.0716244
\(64\) 0 0
\(65\) −1.99358 −0.247274
\(66\) 0 0
\(67\) 7.26008 0.886960 0.443480 0.896284i \(-0.353744\pi\)
0.443480 + 0.896284i \(0.353744\pi\)
\(68\) 0 0
\(69\) −5.32774 −0.641385
\(70\) 0 0
\(71\) 12.1144 1.43772 0.718858 0.695157i \(-0.244665\pi\)
0.718858 + 0.695157i \(0.244665\pi\)
\(72\) 0 0
\(73\) −5.77178 −0.675536 −0.337768 0.941229i \(-0.609672\pi\)
−0.337768 + 0.941229i \(0.609672\pi\)
\(74\) 0 0
\(75\) −4.88697 −0.564299
\(76\) 0 0
\(77\) 3.15112 0.359104
\(78\) 0 0
\(79\) −15.6180 −1.75717 −0.878583 0.477590i \(-0.841510\pi\)
−0.878583 + 0.477590i \(0.841510\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −5.52142 −0.606054 −0.303027 0.952982i \(-0.597997\pi\)
−0.303027 + 0.952982i \(0.597997\pi\)
\(84\) 0 0
\(85\) 0.0161683 0.00175370
\(86\) 0 0
\(87\) 0.918207 0.0984422
\(88\) 0 0
\(89\) −7.27474 −0.771121 −0.385561 0.922683i \(-0.625992\pi\)
−0.385561 + 0.922683i \(0.625992\pi\)
\(90\) 0 0
\(91\) −3.37108 −0.353385
\(92\) 0 0
\(93\) −8.65025 −0.896989
\(94\) 0 0
\(95\) −1.01924 −0.104572
\(96\) 0 0
\(97\) 6.99135 0.709864 0.354932 0.934892i \(-0.384504\pi\)
0.354932 + 0.934892i \(0.384504\pi\)
\(98\) 0 0
\(99\) 5.54286 0.557078
\(100\) 0 0
\(101\) −1.90051 −0.189108 −0.0945538 0.995520i \(-0.530142\pi\)
−0.0945538 + 0.995520i \(0.530142\pi\)
\(102\) 0 0
\(103\) 4.87606 0.480452 0.240226 0.970717i \(-0.422778\pi\)
0.240226 + 0.970717i \(0.422778\pi\)
\(104\) 0 0
\(105\) 0.191130 0.0186524
\(106\) 0 0
\(107\) 1.45469 0.140630 0.0703149 0.997525i \(-0.477600\pi\)
0.0703149 + 0.997525i \(0.477600\pi\)
\(108\) 0 0
\(109\) 3.07174 0.294219 0.147110 0.989120i \(-0.453003\pi\)
0.147110 + 0.989120i \(0.453003\pi\)
\(110\) 0 0
\(111\) −6.04634 −0.573893
\(112\) 0 0
\(113\) 16.1872 1.52277 0.761384 0.648301i \(-0.224520\pi\)
0.761384 + 0.648301i \(0.224520\pi\)
\(114\) 0 0
\(115\) −1.79119 −0.167029
\(116\) 0 0
\(117\) −5.92976 −0.548206
\(118\) 0 0
\(119\) 0.0273400 0.00250626
\(120\) 0 0
\(121\) 19.7233 1.79302
\(122\) 0 0
\(123\) 1.72602 0.155630
\(124\) 0 0
\(125\) −3.32400 −0.297307
\(126\) 0 0
\(127\) −0.483648 −0.0429168 −0.0214584 0.999770i \(-0.506831\pi\)
−0.0214584 + 0.999770i \(0.506831\pi\)
\(128\) 0 0
\(129\) −6.69093 −0.589104
\(130\) 0 0
\(131\) 5.65627 0.494190 0.247095 0.968991i \(-0.420524\pi\)
0.247095 + 0.968991i \(0.420524\pi\)
\(132\) 0 0
\(133\) −1.72350 −0.149446
\(134\) 0 0
\(135\) 0.336200 0.0289355
\(136\) 0 0
\(137\) 7.57562 0.647229 0.323615 0.946189i \(-0.395102\pi\)
0.323615 + 0.946189i \(0.395102\pi\)
\(138\) 0 0
\(139\) −9.55882 −0.810769 −0.405384 0.914146i \(-0.632862\pi\)
−0.405384 + 0.914146i \(0.632862\pi\)
\(140\) 0 0
\(141\) −0.136711 −0.0115131
\(142\) 0 0
\(143\) −32.8678 −2.74854
\(144\) 0 0
\(145\) 0.308701 0.0256362
\(146\) 0 0
\(147\) −6.67681 −0.550694
\(148\) 0 0
\(149\) −6.79959 −0.557044 −0.278522 0.960430i \(-0.589845\pi\)
−0.278522 + 0.960430i \(0.589845\pi\)
\(150\) 0 0
\(151\) −5.77057 −0.469603 −0.234801 0.972043i \(-0.575444\pi\)
−0.234801 + 0.972043i \(0.575444\pi\)
\(152\) 0 0
\(153\) 0.0480914 0.00388796
\(154\) 0 0
\(155\) −2.90821 −0.233593
\(156\) 0 0
\(157\) 18.7887 1.49950 0.749750 0.661722i \(-0.230174\pi\)
0.749750 + 0.661722i \(0.230174\pi\)
\(158\) 0 0
\(159\) −1.99811 −0.158461
\(160\) 0 0
\(161\) −3.02883 −0.238705
\(162\) 0 0
\(163\) −6.77830 −0.530918 −0.265459 0.964122i \(-0.585523\pi\)
−0.265459 + 0.964122i \(0.585523\pi\)
\(164\) 0 0
\(165\) 1.86351 0.145074
\(166\) 0 0
\(167\) 12.2654 0.949128 0.474564 0.880221i \(-0.342606\pi\)
0.474564 + 0.880221i \(0.342606\pi\)
\(168\) 0 0
\(169\) 22.1620 1.70477
\(170\) 0 0
\(171\) −3.03166 −0.231837
\(172\) 0 0
\(173\) −19.8113 −1.50623 −0.753113 0.657891i \(-0.771449\pi\)
−0.753113 + 0.657891i \(0.771449\pi\)
\(174\) 0 0
\(175\) −2.77825 −0.210016
\(176\) 0 0
\(177\) −11.7881 −0.886046
\(178\) 0 0
\(179\) 9.16149 0.684762 0.342381 0.939561i \(-0.388767\pi\)
0.342381 + 0.939561i \(0.388767\pi\)
\(180\) 0 0
\(181\) −4.84269 −0.359954 −0.179977 0.983671i \(-0.557602\pi\)
−0.179977 + 0.983671i \(0.557602\pi\)
\(182\) 0 0
\(183\) 6.84008 0.505633
\(184\) 0 0
\(185\) −2.03278 −0.149453
\(186\) 0 0
\(187\) 0.266564 0.0194931
\(188\) 0 0
\(189\) 0.568501 0.0413524
\(190\) 0 0
\(191\) −15.7260 −1.13790 −0.568948 0.822373i \(-0.692650\pi\)
−0.568948 + 0.822373i \(0.692650\pi\)
\(192\) 0 0
\(193\) 6.40289 0.460890 0.230445 0.973085i \(-0.425982\pi\)
0.230445 + 0.973085i \(0.425982\pi\)
\(194\) 0 0
\(195\) −1.99358 −0.142764
\(196\) 0 0
\(197\) 21.5420 1.53481 0.767404 0.641164i \(-0.221548\pi\)
0.767404 + 0.641164i \(0.221548\pi\)
\(198\) 0 0
\(199\) 10.7287 0.760540 0.380270 0.924876i \(-0.375831\pi\)
0.380270 + 0.924876i \(0.375831\pi\)
\(200\) 0 0
\(201\) 7.26008 0.512086
\(202\) 0 0
\(203\) 0.522002 0.0366374
\(204\) 0 0
\(205\) 0.580289 0.0405291
\(206\) 0 0
\(207\) −5.32774 −0.370304
\(208\) 0 0
\(209\) −16.8040 −1.16236
\(210\) 0 0
\(211\) 18.5669 1.27820 0.639098 0.769125i \(-0.279308\pi\)
0.639098 + 0.769125i \(0.279308\pi\)
\(212\) 0 0
\(213\) 12.1144 0.830066
\(214\) 0 0
\(215\) −2.24949 −0.153414
\(216\) 0 0
\(217\) −4.91768 −0.333834
\(218\) 0 0
\(219\) −5.77178 −0.390021
\(220\) 0 0
\(221\) −0.285170 −0.0191826
\(222\) 0 0
\(223\) −13.2813 −0.889382 −0.444691 0.895684i \(-0.646686\pi\)
−0.444691 + 0.895684i \(0.646686\pi\)
\(224\) 0 0
\(225\) −4.88697 −0.325798
\(226\) 0 0
\(227\) −6.03830 −0.400776 −0.200388 0.979717i \(-0.564220\pi\)
−0.200388 + 0.979717i \(0.564220\pi\)
\(228\) 0 0
\(229\) −6.52759 −0.431356 −0.215678 0.976465i \(-0.569196\pi\)
−0.215678 + 0.976465i \(0.569196\pi\)
\(230\) 0 0
\(231\) 3.15112 0.207329
\(232\) 0 0
\(233\) 18.2938 1.19847 0.599234 0.800574i \(-0.295472\pi\)
0.599234 + 0.800574i \(0.295472\pi\)
\(234\) 0 0
\(235\) −0.0459622 −0.00299824
\(236\) 0 0
\(237\) −15.6180 −1.01450
\(238\) 0 0
\(239\) 8.30923 0.537480 0.268740 0.963213i \(-0.413393\pi\)
0.268740 + 0.963213i \(0.413393\pi\)
\(240\) 0 0
\(241\) 0.796935 0.0513351 0.0256676 0.999671i \(-0.491829\pi\)
0.0256676 + 0.999671i \(0.491829\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −2.24474 −0.143411
\(246\) 0 0
\(247\) 17.9770 1.14385
\(248\) 0 0
\(249\) −5.52142 −0.349906
\(250\) 0 0
\(251\) −9.06101 −0.571926 −0.285963 0.958241i \(-0.592313\pi\)
−0.285963 + 0.958241i \(0.592313\pi\)
\(252\) 0 0
\(253\) −29.5309 −1.85659
\(254\) 0 0
\(255\) 0.0161683 0.00101250
\(256\) 0 0
\(257\) 8.10088 0.505319 0.252660 0.967555i \(-0.418695\pi\)
0.252660 + 0.967555i \(0.418695\pi\)
\(258\) 0 0
\(259\) −3.43735 −0.213587
\(260\) 0 0
\(261\) 0.918207 0.0568356
\(262\) 0 0
\(263\) −23.8160 −1.46856 −0.734278 0.678848i \(-0.762479\pi\)
−0.734278 + 0.678848i \(0.762479\pi\)
\(264\) 0 0
\(265\) −0.671766 −0.0412662
\(266\) 0 0
\(267\) −7.27474 −0.445207
\(268\) 0 0
\(269\) −30.4623 −1.85732 −0.928661 0.370929i \(-0.879039\pi\)
−0.928661 + 0.370929i \(0.879039\pi\)
\(270\) 0 0
\(271\) 4.18720 0.254354 0.127177 0.991880i \(-0.459408\pi\)
0.127177 + 0.991880i \(0.459408\pi\)
\(272\) 0 0
\(273\) −3.37108 −0.204027
\(274\) 0 0
\(275\) −27.0878 −1.63345
\(276\) 0 0
\(277\) −27.5699 −1.65652 −0.828259 0.560346i \(-0.810668\pi\)
−0.828259 + 0.560346i \(0.810668\pi\)
\(278\) 0 0
\(279\) −8.65025 −0.517877
\(280\) 0 0
\(281\) −16.1734 −0.964823 −0.482411 0.875945i \(-0.660239\pi\)
−0.482411 + 0.875945i \(0.660239\pi\)
\(282\) 0 0
\(283\) 25.6248 1.52323 0.761617 0.648027i \(-0.224406\pi\)
0.761617 + 0.648027i \(0.224406\pi\)
\(284\) 0 0
\(285\) −1.01924 −0.0603747
\(286\) 0 0
\(287\) 0.981246 0.0579211
\(288\) 0 0
\(289\) −16.9977 −0.999864
\(290\) 0 0
\(291\) 6.99135 0.409840
\(292\) 0 0
\(293\) 18.2763 1.06771 0.533857 0.845575i \(-0.320742\pi\)
0.533857 + 0.845575i \(0.320742\pi\)
\(294\) 0 0
\(295\) −3.96315 −0.230744
\(296\) 0 0
\(297\) 5.54286 0.321629
\(298\) 0 0
\(299\) 31.5922 1.82703
\(300\) 0 0
\(301\) −3.80380 −0.219248
\(302\) 0 0
\(303\) −1.90051 −0.109181
\(304\) 0 0
\(305\) 2.29963 0.131677
\(306\) 0 0
\(307\) 6.44082 0.367597 0.183799 0.982964i \(-0.441161\pi\)
0.183799 + 0.982964i \(0.441161\pi\)
\(308\) 0 0
\(309\) 4.87606 0.277389
\(310\) 0 0
\(311\) −19.9197 −1.12954 −0.564771 0.825247i \(-0.691036\pi\)
−0.564771 + 0.825247i \(0.691036\pi\)
\(312\) 0 0
\(313\) 2.71046 0.153204 0.0766021 0.997062i \(-0.475593\pi\)
0.0766021 + 0.997062i \(0.475593\pi\)
\(314\) 0 0
\(315\) 0.191130 0.0107690
\(316\) 0 0
\(317\) −18.1488 −1.01934 −0.509669 0.860371i \(-0.670232\pi\)
−0.509669 + 0.860371i \(0.670232\pi\)
\(318\) 0 0
\(319\) 5.08949 0.284957
\(320\) 0 0
\(321\) 1.45469 0.0811926
\(322\) 0 0
\(323\) −0.145797 −0.00811234
\(324\) 0 0
\(325\) 28.9786 1.60744
\(326\) 0 0
\(327\) 3.07174 0.169867
\(328\) 0 0
\(329\) −0.0777203 −0.00428486
\(330\) 0 0
\(331\) −3.42591 −0.188305 −0.0941527 0.995558i \(-0.530014\pi\)
−0.0941527 + 0.995558i \(0.530014\pi\)
\(332\) 0 0
\(333\) −6.04634 −0.331337
\(334\) 0 0
\(335\) 2.44084 0.133357
\(336\) 0 0
\(337\) 11.8658 0.646370 0.323185 0.946336i \(-0.395246\pi\)
0.323185 + 0.946336i \(0.395246\pi\)
\(338\) 0 0
\(339\) 16.1872 0.879171
\(340\) 0 0
\(341\) −47.9471 −2.59648
\(342\) 0 0
\(343\) −7.77528 −0.419826
\(344\) 0 0
\(345\) −1.79119 −0.0964342
\(346\) 0 0
\(347\) 0.195187 0.0104782 0.00523910 0.999986i \(-0.498332\pi\)
0.00523910 + 0.999986i \(0.498332\pi\)
\(348\) 0 0
\(349\) −16.1755 −0.865856 −0.432928 0.901428i \(-0.642520\pi\)
−0.432928 + 0.901428i \(0.642520\pi\)
\(350\) 0 0
\(351\) −5.92976 −0.316507
\(352\) 0 0
\(353\) 4.38986 0.233649 0.116824 0.993153i \(-0.462729\pi\)
0.116824 + 0.993153i \(0.462729\pi\)
\(354\) 0 0
\(355\) 4.07286 0.216165
\(356\) 0 0
\(357\) 0.0273400 0.00144699
\(358\) 0 0
\(359\) 12.9668 0.684361 0.342180 0.939634i \(-0.388835\pi\)
0.342180 + 0.939634i \(0.388835\pi\)
\(360\) 0 0
\(361\) −9.80906 −0.516266
\(362\) 0 0
\(363\) 19.7233 1.03520
\(364\) 0 0
\(365\) −1.94047 −0.101569
\(366\) 0 0
\(367\) 14.1768 0.740024 0.370012 0.929027i \(-0.379354\pi\)
0.370012 + 0.929027i \(0.379354\pi\)
\(368\) 0 0
\(369\) 1.72602 0.0898531
\(370\) 0 0
\(371\) −1.13593 −0.0589746
\(372\) 0 0
\(373\) −3.89627 −0.201741 −0.100871 0.994900i \(-0.532163\pi\)
−0.100871 + 0.994900i \(0.532163\pi\)
\(374\) 0 0
\(375\) −3.32400 −0.171651
\(376\) 0 0
\(377\) −5.44475 −0.280419
\(378\) 0 0
\(379\) −12.0492 −0.618926 −0.309463 0.950911i \(-0.600149\pi\)
−0.309463 + 0.950911i \(0.600149\pi\)
\(380\) 0 0
\(381\) −0.483648 −0.0247781
\(382\) 0 0
\(383\) 2.80286 0.143220 0.0716099 0.997433i \(-0.477186\pi\)
0.0716099 + 0.997433i \(0.477186\pi\)
\(384\) 0 0
\(385\) 1.05941 0.0539924
\(386\) 0 0
\(387\) −6.69093 −0.340119
\(388\) 0 0
\(389\) −25.5777 −1.29684 −0.648420 0.761283i \(-0.724570\pi\)
−0.648420 + 0.761283i \(0.724570\pi\)
\(390\) 0 0
\(391\) −0.256219 −0.0129575
\(392\) 0 0
\(393\) 5.65627 0.285321
\(394\) 0 0
\(395\) −5.25078 −0.264195
\(396\) 0 0
\(397\) 5.22753 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(398\) 0 0
\(399\) −1.72350 −0.0862830
\(400\) 0 0
\(401\) 19.0644 0.952030 0.476015 0.879437i \(-0.342081\pi\)
0.476015 + 0.879437i \(0.342081\pi\)
\(402\) 0 0
\(403\) 51.2939 2.55513
\(404\) 0 0
\(405\) 0.336200 0.0167059
\(406\) 0 0
\(407\) −33.5140 −1.66123
\(408\) 0 0
\(409\) −17.0060 −0.840893 −0.420447 0.907317i \(-0.638127\pi\)
−0.420447 + 0.907317i \(0.638127\pi\)
\(410\) 0 0
\(411\) 7.57562 0.373678
\(412\) 0 0
\(413\) −6.70154 −0.329761
\(414\) 0 0
\(415\) −1.85630 −0.0911222
\(416\) 0 0
\(417\) −9.55882 −0.468098
\(418\) 0 0
\(419\) −17.3133 −0.845812 −0.422906 0.906173i \(-0.638990\pi\)
−0.422906 + 0.906173i \(0.638990\pi\)
\(420\) 0 0
\(421\) 16.1150 0.785395 0.392697 0.919668i \(-0.371542\pi\)
0.392697 + 0.919668i \(0.371542\pi\)
\(422\) 0 0
\(423\) −0.136711 −0.00664711
\(424\) 0 0
\(425\) −0.235021 −0.0114002
\(426\) 0 0
\(427\) 3.88859 0.188182
\(428\) 0 0
\(429\) −32.8678 −1.58687
\(430\) 0 0
\(431\) 1.73736 0.0836859 0.0418429 0.999124i \(-0.486677\pi\)
0.0418429 + 0.999124i \(0.486677\pi\)
\(432\) 0 0
\(433\) 32.3803 1.55610 0.778049 0.628204i \(-0.216210\pi\)
0.778049 + 0.628204i \(0.216210\pi\)
\(434\) 0 0
\(435\) 0.308701 0.0148011
\(436\) 0 0
\(437\) 16.1519 0.772649
\(438\) 0 0
\(439\) −11.0108 −0.525516 −0.262758 0.964862i \(-0.584632\pi\)
−0.262758 + 0.964862i \(0.584632\pi\)
\(440\) 0 0
\(441\) −6.67681 −0.317943
\(442\) 0 0
\(443\) 33.8002 1.60590 0.802948 0.596050i \(-0.203264\pi\)
0.802948 + 0.596050i \(0.203264\pi\)
\(444\) 0 0
\(445\) −2.44577 −0.115940
\(446\) 0 0
\(447\) −6.79959 −0.321609
\(448\) 0 0
\(449\) −21.1168 −0.996564 −0.498282 0.867015i \(-0.666035\pi\)
−0.498282 + 0.867015i \(0.666035\pi\)
\(450\) 0 0
\(451\) 9.56710 0.450497
\(452\) 0 0
\(453\) −5.77057 −0.271125
\(454\) 0 0
\(455\) −1.13336 −0.0531325
\(456\) 0 0
\(457\) −12.9348 −0.605063 −0.302532 0.953139i \(-0.597832\pi\)
−0.302532 + 0.953139i \(0.597832\pi\)
\(458\) 0 0
\(459\) 0.0480914 0.00224471
\(460\) 0 0
\(461\) −35.9572 −1.67470 −0.837348 0.546671i \(-0.815895\pi\)
−0.837348 + 0.546671i \(0.815895\pi\)
\(462\) 0 0
\(463\) 2.51016 0.116657 0.0583286 0.998297i \(-0.481423\pi\)
0.0583286 + 0.998297i \(0.481423\pi\)
\(464\) 0 0
\(465\) −2.90821 −0.134865
\(466\) 0 0
\(467\) 14.7440 0.682273 0.341136 0.940014i \(-0.389188\pi\)
0.341136 + 0.940014i \(0.389188\pi\)
\(468\) 0 0
\(469\) 4.12736 0.190584
\(470\) 0 0
\(471\) 18.7887 0.865736
\(472\) 0 0
\(473\) −37.0869 −1.70526
\(474\) 0 0
\(475\) 14.8156 0.679787
\(476\) 0 0
\(477\) −1.99811 −0.0914873
\(478\) 0 0
\(479\) −11.2343 −0.513307 −0.256653 0.966503i \(-0.582620\pi\)
−0.256653 + 0.966503i \(0.582620\pi\)
\(480\) 0 0
\(481\) 35.8533 1.63477
\(482\) 0 0
\(483\) −3.02883 −0.137816
\(484\) 0 0
\(485\) 2.35049 0.106730
\(486\) 0 0
\(487\) 19.0292 0.862297 0.431149 0.902281i \(-0.358108\pi\)
0.431149 + 0.902281i \(0.358108\pi\)
\(488\) 0 0
\(489\) −6.77830 −0.306525
\(490\) 0 0
\(491\) −0.513681 −0.0231821 −0.0115911 0.999933i \(-0.503690\pi\)
−0.0115911 + 0.999933i \(0.503690\pi\)
\(492\) 0 0
\(493\) 0.0441579 0.00198877
\(494\) 0 0
\(495\) 1.86351 0.0837585
\(496\) 0 0
\(497\) 6.88706 0.308927
\(498\) 0 0
\(499\) 8.45555 0.378522 0.189261 0.981927i \(-0.439391\pi\)
0.189261 + 0.981927i \(0.439391\pi\)
\(500\) 0 0
\(501\) 12.2654 0.547979
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −0.638951 −0.0284329
\(506\) 0 0
\(507\) 22.1620 0.984251
\(508\) 0 0
\(509\) 23.5281 1.04286 0.521432 0.853293i \(-0.325398\pi\)
0.521432 + 0.853293i \(0.325398\pi\)
\(510\) 0 0
\(511\) −3.28126 −0.145155
\(512\) 0 0
\(513\) −3.03166 −0.133851
\(514\) 0 0
\(515\) 1.63933 0.0722375
\(516\) 0 0
\(517\) −0.757769 −0.0333266
\(518\) 0 0
\(519\) −19.8113 −0.869620
\(520\) 0 0
\(521\) −21.2294 −0.930077 −0.465038 0.885291i \(-0.653959\pi\)
−0.465038 + 0.885291i \(0.653959\pi\)
\(522\) 0 0
\(523\) 9.27776 0.405688 0.202844 0.979211i \(-0.434982\pi\)
0.202844 + 0.979211i \(0.434982\pi\)
\(524\) 0 0
\(525\) −2.77825 −0.121253
\(526\) 0 0
\(527\) −0.416002 −0.0181213
\(528\) 0 0
\(529\) 5.38483 0.234123
\(530\) 0 0
\(531\) −11.7881 −0.511559
\(532\) 0 0
\(533\) −10.2349 −0.443323
\(534\) 0 0
\(535\) 0.489065 0.0211441
\(536\) 0 0
\(537\) 9.16149 0.395347
\(538\) 0 0
\(539\) −37.0086 −1.59407
\(540\) 0 0
\(541\) −37.5396 −1.61396 −0.806978 0.590582i \(-0.798898\pi\)
−0.806978 + 0.590582i \(0.798898\pi\)
\(542\) 0 0
\(543\) −4.84269 −0.207820
\(544\) 0 0
\(545\) 1.03272 0.0442368
\(546\) 0 0
\(547\) 9.44448 0.403817 0.201908 0.979404i \(-0.435286\pi\)
0.201908 + 0.979404i \(0.435286\pi\)
\(548\) 0 0
\(549\) 6.84008 0.291927
\(550\) 0 0
\(551\) −2.78369 −0.118589
\(552\) 0 0
\(553\) −8.87887 −0.377568
\(554\) 0 0
\(555\) −2.03278 −0.0862866
\(556\) 0 0
\(557\) 21.0390 0.891449 0.445725 0.895170i \(-0.352946\pi\)
0.445725 + 0.895170i \(0.352946\pi\)
\(558\) 0 0
\(559\) 39.6756 1.67810
\(560\) 0 0
\(561\) 0.266564 0.0112543
\(562\) 0 0
\(563\) 13.5991 0.573135 0.286567 0.958060i \(-0.407486\pi\)
0.286567 + 0.958060i \(0.407486\pi\)
\(564\) 0 0
\(565\) 5.44215 0.228953
\(566\) 0 0
\(567\) 0.568501 0.0238748
\(568\) 0 0
\(569\) −12.3332 −0.517036 −0.258518 0.966006i \(-0.583234\pi\)
−0.258518 + 0.966006i \(0.583234\pi\)
\(570\) 0 0
\(571\) 34.3361 1.43692 0.718460 0.695568i \(-0.244847\pi\)
0.718460 + 0.695568i \(0.244847\pi\)
\(572\) 0 0
\(573\) −15.7260 −0.656965
\(574\) 0 0
\(575\) 26.0365 1.08580
\(576\) 0 0
\(577\) −41.7402 −1.73767 −0.868834 0.495103i \(-0.835130\pi\)
−0.868834 + 0.495103i \(0.835130\pi\)
\(578\) 0 0
\(579\) 6.40289 0.266095
\(580\) 0 0
\(581\) −3.13893 −0.130225
\(582\) 0 0
\(583\) −11.0753 −0.458690
\(584\) 0 0
\(585\) −1.99358 −0.0824246
\(586\) 0 0
\(587\) −17.9306 −0.740075 −0.370037 0.929017i \(-0.620655\pi\)
−0.370037 + 0.929017i \(0.620655\pi\)
\(588\) 0 0
\(589\) 26.2246 1.08056
\(590\) 0 0
\(591\) 21.5420 0.886121
\(592\) 0 0
\(593\) 30.8101 1.26522 0.632610 0.774471i \(-0.281984\pi\)
0.632610 + 0.774471i \(0.281984\pi\)
\(594\) 0 0
\(595\) 0.00919171 0.000376823 0
\(596\) 0 0
\(597\) 10.7287 0.439098
\(598\) 0 0
\(599\) 29.1427 1.19074 0.595370 0.803452i \(-0.297005\pi\)
0.595370 + 0.803452i \(0.297005\pi\)
\(600\) 0 0
\(601\) 25.7001 1.04833 0.524165 0.851617i \(-0.324377\pi\)
0.524165 + 0.851617i \(0.324377\pi\)
\(602\) 0 0
\(603\) 7.26008 0.295653
\(604\) 0 0
\(605\) 6.63096 0.269587
\(606\) 0 0
\(607\) −23.2341 −0.943044 −0.471522 0.881854i \(-0.656295\pi\)
−0.471522 + 0.881854i \(0.656295\pi\)
\(608\) 0 0
\(609\) 0.522002 0.0211526
\(610\) 0 0
\(611\) 0.810662 0.0327959
\(612\) 0 0
\(613\) −32.6732 −1.31966 −0.659828 0.751416i \(-0.729371\pi\)
−0.659828 + 0.751416i \(0.729371\pi\)
\(614\) 0 0
\(615\) 0.580289 0.0233995
\(616\) 0 0
\(617\) 6.49927 0.261651 0.130825 0.991405i \(-0.458237\pi\)
0.130825 + 0.991405i \(0.458237\pi\)
\(618\) 0 0
\(619\) 19.3608 0.778177 0.389088 0.921200i \(-0.372790\pi\)
0.389088 + 0.921200i \(0.372790\pi\)
\(620\) 0 0
\(621\) −5.32774 −0.213795
\(622\) 0 0
\(623\) −4.13570 −0.165693
\(624\) 0 0
\(625\) 23.3173 0.932693
\(626\) 0 0
\(627\) −16.8040 −0.671089
\(628\) 0 0
\(629\) −0.290777 −0.0115940
\(630\) 0 0
\(631\) −38.1142 −1.51730 −0.758651 0.651497i \(-0.774141\pi\)
−0.758651 + 0.651497i \(0.774141\pi\)
\(632\) 0 0
\(633\) 18.5669 0.737967
\(634\) 0 0
\(635\) −0.162603 −0.00645268
\(636\) 0 0
\(637\) 39.5919 1.56869
\(638\) 0 0
\(639\) 12.1144 0.479239
\(640\) 0 0
\(641\) −11.7450 −0.463898 −0.231949 0.972728i \(-0.574510\pi\)
−0.231949 + 0.972728i \(0.574510\pi\)
\(642\) 0 0
\(643\) −10.4611 −0.412545 −0.206273 0.978495i \(-0.566133\pi\)
−0.206273 + 0.978495i \(0.566133\pi\)
\(644\) 0 0
\(645\) −2.24949 −0.0885736
\(646\) 0 0
\(647\) −35.0039 −1.37615 −0.688073 0.725641i \(-0.741543\pi\)
−0.688073 + 0.725641i \(0.741543\pi\)
\(648\) 0 0
\(649\) −65.3396 −2.56480
\(650\) 0 0
\(651\) −4.91768 −0.192739
\(652\) 0 0
\(653\) 38.5534 1.50871 0.754356 0.656466i \(-0.227949\pi\)
0.754356 + 0.656466i \(0.227949\pi\)
\(654\) 0 0
\(655\) 1.90164 0.0743031
\(656\) 0 0
\(657\) −5.77178 −0.225179
\(658\) 0 0
\(659\) −24.5841 −0.957660 −0.478830 0.877908i \(-0.658939\pi\)
−0.478830 + 0.877908i \(0.658939\pi\)
\(660\) 0 0
\(661\) −41.6360 −1.61945 −0.809726 0.586809i \(-0.800384\pi\)
−0.809726 + 0.586809i \(0.800384\pi\)
\(662\) 0 0
\(663\) −0.285170 −0.0110751
\(664\) 0 0
\(665\) −0.579441 −0.0224698
\(666\) 0 0
\(667\) −4.89197 −0.189418
\(668\) 0 0
\(669\) −13.2813 −0.513485
\(670\) 0 0
\(671\) 37.9136 1.46364
\(672\) 0 0
\(673\) −27.7634 −1.07020 −0.535101 0.844788i \(-0.679726\pi\)
−0.535101 + 0.844788i \(0.679726\pi\)
\(674\) 0 0
\(675\) −4.88697 −0.188100
\(676\) 0 0
\(677\) 25.0836 0.964041 0.482021 0.876160i \(-0.339903\pi\)
0.482021 + 0.876160i \(0.339903\pi\)
\(678\) 0 0
\(679\) 3.97459 0.152531
\(680\) 0 0
\(681\) −6.03830 −0.231388
\(682\) 0 0
\(683\) 0.102814 0.00393405 0.00196703 0.999998i \(-0.499374\pi\)
0.00196703 + 0.999998i \(0.499374\pi\)
\(684\) 0 0
\(685\) 2.54692 0.0973130
\(686\) 0 0
\(687\) −6.52759 −0.249043
\(688\) 0 0
\(689\) 11.8483 0.451386
\(690\) 0 0
\(691\) 9.49770 0.361310 0.180655 0.983547i \(-0.442178\pi\)
0.180655 + 0.983547i \(0.442178\pi\)
\(692\) 0 0
\(693\) 3.15112 0.119701
\(694\) 0 0
\(695\) −3.21368 −0.121902
\(696\) 0 0
\(697\) 0.0830068 0.00314411
\(698\) 0 0
\(699\) 18.2938 0.691936
\(700\) 0 0
\(701\) −14.4454 −0.545594 −0.272797 0.962072i \(-0.587949\pi\)
−0.272797 + 0.962072i \(0.587949\pi\)
\(702\) 0 0
\(703\) 18.3304 0.691345
\(704\) 0 0
\(705\) −0.0459622 −0.00173104
\(706\) 0 0
\(707\) −1.08044 −0.0406342
\(708\) 0 0
\(709\) 22.7137 0.853032 0.426516 0.904480i \(-0.359741\pi\)
0.426516 + 0.904480i \(0.359741\pi\)
\(710\) 0 0
\(711\) −15.6180 −0.585722
\(712\) 0 0
\(713\) 46.0863 1.72594
\(714\) 0 0
\(715\) −11.0502 −0.413252
\(716\) 0 0
\(717\) 8.30923 0.310314
\(718\) 0 0
\(719\) 18.8282 0.702172 0.351086 0.936343i \(-0.385812\pi\)
0.351086 + 0.936343i \(0.385812\pi\)
\(720\) 0 0
\(721\) 2.77205 0.103236
\(722\) 0 0
\(723\) 0.796935 0.0296383
\(724\) 0 0
\(725\) −4.48725 −0.166652
\(726\) 0 0
\(727\) −11.6081 −0.430520 −0.215260 0.976557i \(-0.569060\pi\)
−0.215260 + 0.976557i \(0.569060\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.321776 −0.0119013
\(732\) 0 0
\(733\) 20.5798 0.760131 0.380066 0.924959i \(-0.375901\pi\)
0.380066 + 0.924959i \(0.375901\pi\)
\(734\) 0 0
\(735\) −2.24474 −0.0827985
\(736\) 0 0
\(737\) 40.2416 1.48232
\(738\) 0 0
\(739\) −15.0843 −0.554885 −0.277443 0.960742i \(-0.589487\pi\)
−0.277443 + 0.960742i \(0.589487\pi\)
\(740\) 0 0
\(741\) 17.9770 0.660401
\(742\) 0 0
\(743\) 30.1216 1.10506 0.552528 0.833495i \(-0.313663\pi\)
0.552528 + 0.833495i \(0.313663\pi\)
\(744\) 0 0
\(745\) −2.28602 −0.0837533
\(746\) 0 0
\(747\) −5.52142 −0.202018
\(748\) 0 0
\(749\) 0.826991 0.0302176
\(750\) 0 0
\(751\) 7.93111 0.289410 0.144705 0.989475i \(-0.453777\pi\)
0.144705 + 0.989475i \(0.453777\pi\)
\(752\) 0 0
\(753\) −9.06101 −0.330202
\(754\) 0 0
\(755\) −1.94007 −0.0706062
\(756\) 0 0
\(757\) 18.2385 0.662890 0.331445 0.943475i \(-0.392464\pi\)
0.331445 + 0.943475i \(0.392464\pi\)
\(758\) 0 0
\(759\) −29.5309 −1.07190
\(760\) 0 0
\(761\) 3.01903 0.109440 0.0547199 0.998502i \(-0.482573\pi\)
0.0547199 + 0.998502i \(0.482573\pi\)
\(762\) 0 0
\(763\) 1.74629 0.0632198
\(764\) 0 0
\(765\) 0.0161683 0.000584567 0
\(766\) 0 0
\(767\) 69.9005 2.52396
\(768\) 0 0
\(769\) −47.4452 −1.71092 −0.855460 0.517870i \(-0.826725\pi\)
−0.855460 + 0.517870i \(0.826725\pi\)
\(770\) 0 0
\(771\) 8.10088 0.291746
\(772\) 0 0
\(773\) 26.0581 0.937247 0.468623 0.883398i \(-0.344750\pi\)
0.468623 + 0.883398i \(0.344750\pi\)
\(774\) 0 0
\(775\) 42.2735 1.51851
\(776\) 0 0
\(777\) −3.43735 −0.123314
\(778\) 0 0
\(779\) −5.23271 −0.187481
\(780\) 0 0
\(781\) 67.1485 2.40276
\(782\) 0 0
\(783\) 0.918207 0.0328141
\(784\) 0 0
\(785\) 6.31675 0.225454
\(786\) 0 0
\(787\) 13.0940 0.466750 0.233375 0.972387i \(-0.425023\pi\)
0.233375 + 0.972387i \(0.425023\pi\)
\(788\) 0 0
\(789\) −23.8160 −0.847872
\(790\) 0 0
\(791\) 9.20247 0.327202
\(792\) 0 0
\(793\) −40.5600 −1.44033
\(794\) 0 0
\(795\) −0.671766 −0.0238251
\(796\) 0 0
\(797\) −51.0395 −1.80791 −0.903957 0.427624i \(-0.859351\pi\)
−0.903957 + 0.427624i \(0.859351\pi\)
\(798\) 0 0
\(799\) −0.00657462 −0.000232593 0
\(800\) 0 0
\(801\) −7.27474 −0.257040
\(802\) 0 0
\(803\) −31.9921 −1.12898
\(804\) 0 0
\(805\) −1.01829 −0.0358901
\(806\) 0 0
\(807\) −30.4623 −1.07233
\(808\) 0 0
\(809\) 2.43758 0.0857007 0.0428504 0.999082i \(-0.486356\pi\)
0.0428504 + 0.999082i \(0.486356\pi\)
\(810\) 0 0
\(811\) −18.8617 −0.662323 −0.331161 0.943574i \(-0.607440\pi\)
−0.331161 + 0.943574i \(0.607440\pi\)
\(812\) 0 0
\(813\) 4.18720 0.146851
\(814\) 0 0
\(815\) −2.27886 −0.0798251
\(816\) 0 0
\(817\) 20.2846 0.709669
\(818\) 0 0
\(819\) −3.37108 −0.117795
\(820\) 0 0
\(821\) −28.5856 −0.997644 −0.498822 0.866704i \(-0.666234\pi\)
−0.498822 + 0.866704i \(0.666234\pi\)
\(822\) 0 0
\(823\) −2.65296 −0.0924762 −0.0462381 0.998930i \(-0.514723\pi\)
−0.0462381 + 0.998930i \(0.514723\pi\)
\(824\) 0 0
\(825\) −27.0878 −0.943075
\(826\) 0 0
\(827\) 24.9577 0.867864 0.433932 0.900946i \(-0.357126\pi\)
0.433932 + 0.900946i \(0.357126\pi\)
\(828\) 0 0
\(829\) −36.7438 −1.27617 −0.638083 0.769967i \(-0.720272\pi\)
−0.638083 + 0.769967i \(0.720272\pi\)
\(830\) 0 0
\(831\) −27.5699 −0.956391
\(832\) 0 0
\(833\) −0.321097 −0.0111253
\(834\) 0 0
\(835\) 4.12364 0.142704
\(836\) 0 0
\(837\) −8.65025 −0.298996
\(838\) 0 0
\(839\) 25.2911 0.873146 0.436573 0.899669i \(-0.356192\pi\)
0.436573 + 0.899669i \(0.356192\pi\)
\(840\) 0 0
\(841\) −28.1569 −0.970927
\(842\) 0 0
\(843\) −16.1734 −0.557041
\(844\) 0 0
\(845\) 7.45088 0.256318
\(846\) 0 0
\(847\) 11.2127 0.385273
\(848\) 0 0
\(849\) 25.6248 0.879440
\(850\) 0 0
\(851\) 32.2133 1.10426
\(852\) 0 0
\(853\) 16.6684 0.570714 0.285357 0.958421i \(-0.407888\pi\)
0.285357 + 0.958421i \(0.407888\pi\)
\(854\) 0 0
\(855\) −1.01924 −0.0348574
\(856\) 0 0
\(857\) 4.14969 0.141751 0.0708754 0.997485i \(-0.477421\pi\)
0.0708754 + 0.997485i \(0.477421\pi\)
\(858\) 0 0
\(859\) 39.5949 1.35096 0.675480 0.737379i \(-0.263937\pi\)
0.675480 + 0.737379i \(0.263937\pi\)
\(860\) 0 0
\(861\) 0.981246 0.0334408
\(862\) 0 0
\(863\) −13.5820 −0.462335 −0.231168 0.972914i \(-0.574255\pi\)
−0.231168 + 0.972914i \(0.574255\pi\)
\(864\) 0 0
\(865\) −6.66056 −0.226466
\(866\) 0 0
\(867\) −16.9977 −0.577272
\(868\) 0 0
\(869\) −86.5685 −2.93664
\(870\) 0 0
\(871\) −43.0505 −1.45871
\(872\) 0 0
\(873\) 6.99135 0.236621
\(874\) 0 0
\(875\) −1.88970 −0.0638834
\(876\) 0 0
\(877\) 49.0070 1.65485 0.827424 0.561578i \(-0.189805\pi\)
0.827424 + 0.561578i \(0.189805\pi\)
\(878\) 0 0
\(879\) 18.2763 0.616445
\(880\) 0 0
\(881\) −3.55703 −0.119839 −0.0599197 0.998203i \(-0.519084\pi\)
−0.0599197 + 0.998203i \(0.519084\pi\)
\(882\) 0 0
\(883\) 36.9287 1.24275 0.621375 0.783513i \(-0.286574\pi\)
0.621375 + 0.783513i \(0.286574\pi\)
\(884\) 0 0
\(885\) −3.96315 −0.133220
\(886\) 0 0
\(887\) −13.5282 −0.454232 −0.227116 0.973868i \(-0.572930\pi\)
−0.227116 + 0.973868i \(0.572930\pi\)
\(888\) 0 0
\(889\) −0.274955 −0.00922168
\(890\) 0 0
\(891\) 5.54286 0.185693
\(892\) 0 0
\(893\) 0.414460 0.0138694
\(894\) 0 0
\(895\) 3.08009 0.102956
\(896\) 0 0
\(897\) 31.5922 1.05483
\(898\) 0 0
\(899\) −7.94272 −0.264905
\(900\) 0 0
\(901\) −0.0960921 −0.00320129
\(902\) 0 0
\(903\) −3.80380 −0.126583
\(904\) 0 0
\(905\) −1.62811 −0.0541202
\(906\) 0 0
\(907\) −21.0281 −0.698227 −0.349113 0.937080i \(-0.613517\pi\)
−0.349113 + 0.937080i \(0.613517\pi\)
\(908\) 0 0
\(909\) −1.90051 −0.0630359
\(910\) 0 0
\(911\) 26.3558 0.873207 0.436603 0.899654i \(-0.356181\pi\)
0.436603 + 0.899654i \(0.356181\pi\)
\(912\) 0 0
\(913\) −30.6044 −1.01286
\(914\) 0 0
\(915\) 2.29963 0.0760235
\(916\) 0 0
\(917\) 3.21560 0.106188
\(918\) 0 0
\(919\) −39.9002 −1.31619 −0.658093 0.752937i \(-0.728637\pi\)
−0.658093 + 0.752937i \(0.728637\pi\)
\(920\) 0 0
\(921\) 6.44082 0.212232
\(922\) 0 0
\(923\) −71.8355 −2.36450
\(924\) 0 0
\(925\) 29.5483 0.971541
\(926\) 0 0
\(927\) 4.87606 0.160151
\(928\) 0 0
\(929\) −31.7964 −1.04320 −0.521602 0.853189i \(-0.674666\pi\)
−0.521602 + 0.853189i \(0.674666\pi\)
\(930\) 0 0
\(931\) 20.2418 0.663398
\(932\) 0 0
\(933\) −19.9197 −0.652142
\(934\) 0 0
\(935\) 0.0896187 0.00293085
\(936\) 0 0
\(937\) 16.9699 0.554381 0.277191 0.960815i \(-0.410597\pi\)
0.277191 + 0.960815i \(0.410597\pi\)
\(938\) 0 0
\(939\) 2.71046 0.0884525
\(940\) 0 0
\(941\) 18.9142 0.616584 0.308292 0.951292i \(-0.400243\pi\)
0.308292 + 0.951292i \(0.400243\pi\)
\(942\) 0 0
\(943\) −9.19580 −0.299456
\(944\) 0 0
\(945\) 0.191130 0.00621746
\(946\) 0 0
\(947\) −14.6973 −0.477600 −0.238800 0.971069i \(-0.576754\pi\)
−0.238800 + 0.971069i \(0.576754\pi\)
\(948\) 0 0
\(949\) 34.2253 1.11100
\(950\) 0 0
\(951\) −18.1488 −0.588515
\(952\) 0 0
\(953\) −18.2332 −0.590630 −0.295315 0.955400i \(-0.595425\pi\)
−0.295315 + 0.955400i \(0.595425\pi\)
\(954\) 0 0
\(955\) −5.28710 −0.171086
\(956\) 0 0
\(957\) 5.08949 0.164520
\(958\) 0 0
\(959\) 4.30675 0.139072
\(960\) 0 0
\(961\) 43.8268 1.41377
\(962\) 0 0
\(963\) 1.45469 0.0468766
\(964\) 0 0
\(965\) 2.15265 0.0692963
\(966\) 0 0
\(967\) 24.0153 0.772280 0.386140 0.922440i \(-0.373808\pi\)
0.386140 + 0.922440i \(0.373808\pi\)
\(968\) 0 0
\(969\) −0.145797 −0.00468366
\(970\) 0 0
\(971\) −56.5272 −1.81404 −0.907021 0.421085i \(-0.861650\pi\)
−0.907021 + 0.421085i \(0.861650\pi\)
\(972\) 0 0
\(973\) −5.43420 −0.174213
\(974\) 0 0
\(975\) 28.9786 0.928057
\(976\) 0 0
\(977\) −30.6477 −0.980506 −0.490253 0.871580i \(-0.663096\pi\)
−0.490253 + 0.871580i \(0.663096\pi\)
\(978\) 0 0
\(979\) −40.3229 −1.28872
\(980\) 0 0
\(981\) 3.07174 0.0980730
\(982\) 0 0
\(983\) −29.3932 −0.937498 −0.468749 0.883331i \(-0.655295\pi\)
−0.468749 + 0.883331i \(0.655295\pi\)
\(984\) 0 0
\(985\) 7.24243 0.230763
\(986\) 0 0
\(987\) −0.0777203 −0.00247386
\(988\) 0 0
\(989\) 35.6476 1.13353
\(990\) 0 0
\(991\) 19.5125 0.619836 0.309918 0.950763i \(-0.399698\pi\)
0.309918 + 0.950763i \(0.399698\pi\)
\(992\) 0 0
\(993\) −3.42591 −0.108718
\(994\) 0 0
\(995\) 3.60700 0.114350
\(996\) 0 0
\(997\) −51.0617 −1.61714 −0.808570 0.588401i \(-0.799758\pi\)
−0.808570 + 0.588401i \(0.799758\pi\)
\(998\) 0 0
\(999\) −6.04634 −0.191298
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 \(a_p\))