Properties

Label 6036.2.a.i.1.14
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 0
Dimension 26
CM No

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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: \(0\)
Dimension: \(26\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.344611 q^{5}\) \(+2.72948 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.344611 q^{5}\) \(+2.72948 q^{7}\) \(+1.00000 q^{9}\) \(-0.712991 q^{11}\) \(+6.42474 q^{13}\) \(-0.344611 q^{15}\) \(-5.96822 q^{17}\) \(+1.12134 q^{19}\) \(-2.72948 q^{21}\) \(+2.47994 q^{23}\) \(-4.88124 q^{25}\) \(-1.00000 q^{27}\) \(+1.35862 q^{29}\) \(+3.54555 q^{31}\) \(+0.712991 q^{33}\) \(+0.940610 q^{35}\) \(+8.77120 q^{37}\) \(-6.42474 q^{39}\) \(+3.02539 q^{41}\) \(+12.8201 q^{43}\) \(+0.344611 q^{45}\) \(-9.01538 q^{47}\) \(+0.450076 q^{49}\) \(+5.96822 q^{51}\) \(-5.26873 q^{53}\) \(-0.245704 q^{55}\) \(-1.12134 q^{57}\) \(+9.02996 q^{59}\) \(+7.78442 q^{61}\) \(+2.72948 q^{63}\) \(+2.21404 q^{65}\) \(-12.5521 q^{67}\) \(-2.47994 q^{69}\) \(+4.01561 q^{71}\) \(+8.39756 q^{73}\) \(+4.88124 q^{75}\) \(-1.94610 q^{77}\) \(-1.26540 q^{79}\) \(+1.00000 q^{81}\) \(-14.6297 q^{83}\) \(-2.05672 q^{85}\) \(-1.35862 q^{87}\) \(+0.273555 q^{89}\) \(+17.5362 q^{91}\) \(-3.54555 q^{93}\) \(+0.386427 q^{95}\) \(-0.105936 q^{97}\) \(-0.712991 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 0.344611 0.154115 0.0770574 0.997027i \(-0.475448\pi\)
0.0770574 + 0.997027i \(0.475448\pi\)
\(6\) 0 0
\(7\) 2.72948 1.03165 0.515824 0.856695i \(-0.327486\pi\)
0.515824 + 0.856695i \(0.327486\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −0.712991 −0.214975 −0.107487 0.994206i \(-0.534281\pi\)
−0.107487 + 0.994206i \(0.534281\pi\)
\(12\) 0 0
\(13\) 6.42474 1.78190 0.890952 0.454098i \(-0.150038\pi\)
0.890952 + 0.454098i \(0.150038\pi\)
\(14\) 0 0
\(15\) −0.344611 −0.0889782
\(16\) 0 0
\(17\) −5.96822 −1.44751 −0.723753 0.690059i \(-0.757585\pi\)
−0.723753 + 0.690059i \(0.757585\pi\)
\(18\) 0 0
\(19\) 1.12134 0.257254 0.128627 0.991693i \(-0.458943\pi\)
0.128627 + 0.991693i \(0.458943\pi\)
\(20\) 0 0
\(21\) −2.72948 −0.595622
\(22\) 0 0
\(23\) 2.47994 0.517103 0.258552 0.965997i \(-0.416755\pi\)
0.258552 + 0.965997i \(0.416755\pi\)
\(24\) 0 0
\(25\) −4.88124 −0.976249
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 1.35862 0.252290 0.126145 0.992012i \(-0.459740\pi\)
0.126145 + 0.992012i \(0.459740\pi\)
\(30\) 0 0
\(31\) 3.54555 0.636800 0.318400 0.947956i \(-0.396854\pi\)
0.318400 + 0.947956i \(0.396854\pi\)
\(32\) 0 0
\(33\) 0.712991 0.124116
\(34\) 0 0
\(35\) 0.940610 0.158992
\(36\) 0 0
\(37\) 8.77120 1.44198 0.720988 0.692947i \(-0.243688\pi\)
0.720988 + 0.692947i \(0.243688\pi\)
\(38\) 0 0
\(39\) −6.42474 −1.02878
\(40\) 0 0
\(41\) 3.02539 0.472486 0.236243 0.971694i \(-0.424084\pi\)
0.236243 + 0.971694i \(0.424084\pi\)
\(42\) 0 0
\(43\) 12.8201 1.95505 0.977527 0.210810i \(-0.0676100\pi\)
0.977527 + 0.210810i \(0.0676100\pi\)
\(44\) 0 0
\(45\) 0.344611 0.0513716
\(46\) 0 0
\(47\) −9.01538 −1.31503 −0.657514 0.753442i \(-0.728392\pi\)
−0.657514 + 0.753442i \(0.728392\pi\)
\(48\) 0 0
\(49\) 0.450076 0.0642965
\(50\) 0 0
\(51\) 5.96822 0.835718
\(52\) 0 0
\(53\) −5.26873 −0.723715 −0.361858 0.932233i \(-0.617857\pi\)
−0.361858 + 0.932233i \(0.617857\pi\)
\(54\) 0 0
\(55\) −0.245704 −0.0331308
\(56\) 0 0
\(57\) −1.12134 −0.148525
\(58\) 0 0
\(59\) 9.02996 1.17560 0.587800 0.809006i \(-0.299994\pi\)
0.587800 + 0.809006i \(0.299994\pi\)
\(60\) 0 0
\(61\) 7.78442 0.996693 0.498347 0.866978i \(-0.333941\pi\)
0.498347 + 0.866978i \(0.333941\pi\)
\(62\) 0 0
\(63\) 2.72948 0.343882
\(64\) 0 0
\(65\) 2.21404 0.274618
\(66\) 0 0
\(67\) −12.5521 −1.53349 −0.766744 0.641953i \(-0.778124\pi\)
−0.766744 + 0.641953i \(0.778124\pi\)
\(68\) 0 0
\(69\) −2.47994 −0.298550
\(70\) 0 0
\(71\) 4.01561 0.476565 0.238282 0.971196i \(-0.423416\pi\)
0.238282 + 0.971196i \(0.423416\pi\)
\(72\) 0 0
\(73\) 8.39756 0.982860 0.491430 0.870917i \(-0.336474\pi\)
0.491430 + 0.870917i \(0.336474\pi\)
\(74\) 0 0
\(75\) 4.88124 0.563637
\(76\) 0 0
\(77\) −1.94610 −0.221778
\(78\) 0 0
\(79\) −1.26540 −0.142369 −0.0711844 0.997463i \(-0.522678\pi\)
−0.0711844 + 0.997463i \(0.522678\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −14.6297 −1.60582 −0.802909 0.596102i \(-0.796715\pi\)
−0.802909 + 0.596102i \(0.796715\pi\)
\(84\) 0 0
\(85\) −2.05672 −0.223082
\(86\) 0 0
\(87\) −1.35862 −0.145659
\(88\) 0 0
\(89\) 0.273555 0.0289967 0.0144984 0.999895i \(-0.495385\pi\)
0.0144984 + 0.999895i \(0.495385\pi\)
\(90\) 0 0
\(91\) 17.5362 1.83830
\(92\) 0 0
\(93\) −3.54555 −0.367657
\(94\) 0 0
\(95\) 0.386427 0.0396466
\(96\) 0 0
\(97\) −0.105936 −0.0107562 −0.00537808 0.999986i \(-0.501712\pi\)
−0.00537808 + 0.999986i \(0.501712\pi\)
\(98\) 0 0
\(99\) −0.712991 −0.0716583
\(100\) 0 0
\(101\) 11.4179 1.13612 0.568062 0.822985i \(-0.307693\pi\)
0.568062 + 0.822985i \(0.307693\pi\)
\(102\) 0 0
\(103\) 6.63462 0.653728 0.326864 0.945071i \(-0.394008\pi\)
0.326864 + 0.945071i \(0.394008\pi\)
\(104\) 0 0
\(105\) −0.940610 −0.0917941
\(106\) 0 0
\(107\) 8.41570 0.813576 0.406788 0.913523i \(-0.366649\pi\)
0.406788 + 0.913523i \(0.366649\pi\)
\(108\) 0 0
\(109\) −3.93390 −0.376799 −0.188400 0.982092i \(-0.560330\pi\)
−0.188400 + 0.982092i \(0.560330\pi\)
\(110\) 0 0
\(111\) −8.77120 −0.832526
\(112\) 0 0
\(113\) 12.1560 1.14354 0.571772 0.820412i \(-0.306256\pi\)
0.571772 + 0.820412i \(0.306256\pi\)
\(114\) 0 0
\(115\) 0.854615 0.0796933
\(116\) 0 0
\(117\) 6.42474 0.593968
\(118\) 0 0
\(119\) −16.2902 −1.49332
\(120\) 0 0
\(121\) −10.4916 −0.953786
\(122\) 0 0
\(123\) −3.02539 −0.272790
\(124\) 0 0
\(125\) −3.40519 −0.304569
\(126\) 0 0
\(127\) −12.2409 −1.08620 −0.543101 0.839667i \(-0.682750\pi\)
−0.543101 + 0.839667i \(0.682750\pi\)
\(128\) 0 0
\(129\) −12.8201 −1.12875
\(130\) 0 0
\(131\) −11.5682 −1.01072 −0.505358 0.862910i \(-0.668640\pi\)
−0.505358 + 0.862910i \(0.668640\pi\)
\(132\) 0 0
\(133\) 3.06069 0.265395
\(134\) 0 0
\(135\) −0.344611 −0.0296594
\(136\) 0 0
\(137\) −20.2770 −1.73238 −0.866191 0.499712i \(-0.833439\pi\)
−0.866191 + 0.499712i \(0.833439\pi\)
\(138\) 0 0
\(139\) 0.686829 0.0582561 0.0291280 0.999576i \(-0.490727\pi\)
0.0291280 + 0.999576i \(0.490727\pi\)
\(140\) 0 0
\(141\) 9.01538 0.759232
\(142\) 0 0
\(143\) −4.58078 −0.383064
\(144\) 0 0
\(145\) 0.468196 0.0388815
\(146\) 0 0
\(147\) −0.450076 −0.0371216
\(148\) 0 0
\(149\) 3.07076 0.251567 0.125783 0.992058i \(-0.459856\pi\)
0.125783 + 0.992058i \(0.459856\pi\)
\(150\) 0 0
\(151\) 11.2823 0.918142 0.459071 0.888400i \(-0.348182\pi\)
0.459071 + 0.888400i \(0.348182\pi\)
\(152\) 0 0
\(153\) −5.96822 −0.482502
\(154\) 0 0
\(155\) 1.22184 0.0981403
\(156\) 0 0
\(157\) −16.8937 −1.34827 −0.674134 0.738609i \(-0.735483\pi\)
−0.674134 + 0.738609i \(0.735483\pi\)
\(158\) 0 0
\(159\) 5.26873 0.417837
\(160\) 0 0
\(161\) 6.76896 0.533468
\(162\) 0 0
\(163\) 13.9112 1.08961 0.544806 0.838562i \(-0.316603\pi\)
0.544806 + 0.838562i \(0.316603\pi\)
\(164\) 0 0
\(165\) 0.245704 0.0191281
\(166\) 0 0
\(167\) −12.3646 −0.956798 −0.478399 0.878143i \(-0.658783\pi\)
−0.478399 + 0.878143i \(0.658783\pi\)
\(168\) 0 0
\(169\) 28.2773 2.17518
\(170\) 0 0
\(171\) 1.12134 0.0857512
\(172\) 0 0
\(173\) 15.5946 1.18563 0.592817 0.805337i \(-0.298016\pi\)
0.592817 + 0.805337i \(0.298016\pi\)
\(174\) 0 0
\(175\) −13.3233 −1.00714
\(176\) 0 0
\(177\) −9.02996 −0.678733
\(178\) 0 0
\(179\) −15.6541 −1.17004 −0.585020 0.811019i \(-0.698913\pi\)
−0.585020 + 0.811019i \(0.698913\pi\)
\(180\) 0 0
\(181\) −6.78808 −0.504554 −0.252277 0.967655i \(-0.581179\pi\)
−0.252277 + 0.967655i \(0.581179\pi\)
\(182\) 0 0
\(183\) −7.78442 −0.575441
\(184\) 0 0
\(185\) 3.02265 0.222230
\(186\) 0 0
\(187\) 4.25529 0.311177
\(188\) 0 0
\(189\) −2.72948 −0.198541
\(190\) 0 0
\(191\) 1.54867 0.112058 0.0560291 0.998429i \(-0.482156\pi\)
0.0560291 + 0.998429i \(0.482156\pi\)
\(192\) 0 0
\(193\) 19.2987 1.38915 0.694574 0.719421i \(-0.255593\pi\)
0.694574 + 0.719421i \(0.255593\pi\)
\(194\) 0 0
\(195\) −2.21404 −0.158551
\(196\) 0 0
\(197\) 19.1837 1.36678 0.683391 0.730052i \(-0.260504\pi\)
0.683391 + 0.730052i \(0.260504\pi\)
\(198\) 0 0
\(199\) 8.04744 0.570468 0.285234 0.958458i \(-0.407929\pi\)
0.285234 + 0.958458i \(0.407929\pi\)
\(200\) 0 0
\(201\) 12.5521 0.885360
\(202\) 0 0
\(203\) 3.70833 0.260274
\(204\) 0 0
\(205\) 1.04258 0.0728171
\(206\) 0 0
\(207\) 2.47994 0.172368
\(208\) 0 0
\(209\) −0.799507 −0.0553030
\(210\) 0 0
\(211\) −16.3451 −1.12524 −0.562621 0.826715i \(-0.690207\pi\)
−0.562621 + 0.826715i \(0.690207\pi\)
\(212\) 0 0
\(213\) −4.01561 −0.275145
\(214\) 0 0
\(215\) 4.41796 0.301303
\(216\) 0 0
\(217\) 9.67753 0.656953
\(218\) 0 0
\(219\) −8.39756 −0.567455
\(220\) 0 0
\(221\) −38.3443 −2.57932
\(222\) 0 0
\(223\) −10.6754 −0.714879 −0.357439 0.933936i \(-0.616350\pi\)
−0.357439 + 0.933936i \(0.616350\pi\)
\(224\) 0 0
\(225\) −4.88124 −0.325416
\(226\) 0 0
\(227\) 27.7335 1.84073 0.920367 0.391056i \(-0.127890\pi\)
0.920367 + 0.391056i \(0.127890\pi\)
\(228\) 0 0
\(229\) 2.99849 0.198146 0.0990728 0.995080i \(-0.468412\pi\)
0.0990728 + 0.995080i \(0.468412\pi\)
\(230\) 0 0
\(231\) 1.94610 0.128044
\(232\) 0 0
\(233\) 17.0232 1.11523 0.557614 0.830100i \(-0.311717\pi\)
0.557614 + 0.830100i \(0.311717\pi\)
\(234\) 0 0
\(235\) −3.10680 −0.202665
\(236\) 0 0
\(237\) 1.26540 0.0821967
\(238\) 0 0
\(239\) −19.5646 −1.26553 −0.632766 0.774343i \(-0.718080\pi\)
−0.632766 + 0.774343i \(0.718080\pi\)
\(240\) 0 0
\(241\) 18.6987 1.20449 0.602245 0.798311i \(-0.294273\pi\)
0.602245 + 0.798311i \(0.294273\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0.155101 0.00990905
\(246\) 0 0
\(247\) 7.20434 0.458401
\(248\) 0 0
\(249\) 14.6297 0.927119
\(250\) 0 0
\(251\) 0.722458 0.0456011 0.0228006 0.999740i \(-0.492742\pi\)
0.0228006 + 0.999740i \(0.492742\pi\)
\(252\) 0 0
\(253\) −1.76817 −0.111164
\(254\) 0 0
\(255\) 2.05672 0.128797
\(256\) 0 0
\(257\) 9.73334 0.607149 0.303575 0.952808i \(-0.401820\pi\)
0.303575 + 0.952808i \(0.401820\pi\)
\(258\) 0 0
\(259\) 23.9408 1.48761
\(260\) 0 0
\(261\) 1.35862 0.0840965
\(262\) 0 0
\(263\) 15.8101 0.974896 0.487448 0.873152i \(-0.337928\pi\)
0.487448 + 0.873152i \(0.337928\pi\)
\(264\) 0 0
\(265\) −1.81566 −0.111535
\(266\) 0 0
\(267\) −0.273555 −0.0167413
\(268\) 0 0
\(269\) 7.54823 0.460224 0.230112 0.973164i \(-0.426091\pi\)
0.230112 + 0.973164i \(0.426091\pi\)
\(270\) 0 0
\(271\) 2.83611 0.172282 0.0861408 0.996283i \(-0.472547\pi\)
0.0861408 + 0.996283i \(0.472547\pi\)
\(272\) 0 0
\(273\) −17.5362 −1.06134
\(274\) 0 0
\(275\) 3.48028 0.209869
\(276\) 0 0
\(277\) 0.975302 0.0586002 0.0293001 0.999571i \(-0.490672\pi\)
0.0293001 + 0.999571i \(0.490672\pi\)
\(278\) 0 0
\(279\) 3.54555 0.212267
\(280\) 0 0
\(281\) 23.6666 1.41183 0.705915 0.708296i \(-0.250536\pi\)
0.705915 + 0.708296i \(0.250536\pi\)
\(282\) 0 0
\(283\) −4.46571 −0.265459 −0.132729 0.991152i \(-0.542374\pi\)
−0.132729 + 0.991152i \(0.542374\pi\)
\(284\) 0 0
\(285\) −0.386427 −0.0228900
\(286\) 0 0
\(287\) 8.25774 0.487439
\(288\) 0 0
\(289\) 18.6197 1.09528
\(290\) 0 0
\(291\) 0.105936 0.00621007
\(292\) 0 0
\(293\) 20.1854 1.17924 0.589621 0.807680i \(-0.299277\pi\)
0.589621 + 0.807680i \(0.299277\pi\)
\(294\) 0 0
\(295\) 3.11182 0.181177
\(296\) 0 0
\(297\) 0.712991 0.0413719
\(298\) 0 0
\(299\) 15.9330 0.921429
\(300\) 0 0
\(301\) 34.9924 2.01693
\(302\) 0 0
\(303\) −11.4179 −0.655942
\(304\) 0 0
\(305\) 2.68260 0.153605
\(306\) 0 0
\(307\) −4.34238 −0.247833 −0.123916 0.992293i \(-0.539545\pi\)
−0.123916 + 0.992293i \(0.539545\pi\)
\(308\) 0 0
\(309\) −6.63462 −0.377430
\(310\) 0 0
\(311\) 14.9026 0.845047 0.422523 0.906352i \(-0.361144\pi\)
0.422523 + 0.906352i \(0.361144\pi\)
\(312\) 0 0
\(313\) 6.43464 0.363708 0.181854 0.983326i \(-0.441790\pi\)
0.181854 + 0.983326i \(0.441790\pi\)
\(314\) 0 0
\(315\) 0.940610 0.0529974
\(316\) 0 0
\(317\) 21.9271 1.23155 0.615775 0.787922i \(-0.288843\pi\)
0.615775 + 0.787922i \(0.288843\pi\)
\(318\) 0 0
\(319\) −0.968684 −0.0542359
\(320\) 0 0
\(321\) −8.41570 −0.469718
\(322\) 0 0
\(323\) −6.69242 −0.372376
\(324\) 0 0
\(325\) −31.3607 −1.73958
\(326\) 0 0
\(327\) 3.93390 0.217545
\(328\) 0 0
\(329\) −24.6073 −1.35665
\(330\) 0 0
\(331\) 8.36105 0.459565 0.229782 0.973242i \(-0.426199\pi\)
0.229782 + 0.973242i \(0.426199\pi\)
\(332\) 0 0
\(333\) 8.77120 0.480659
\(334\) 0 0
\(335\) −4.32561 −0.236333
\(336\) 0 0
\(337\) 32.7567 1.78437 0.892187 0.451666i \(-0.149170\pi\)
0.892187 + 0.451666i \(0.149170\pi\)
\(338\) 0 0
\(339\) −12.1560 −0.660226
\(340\) 0 0
\(341\) −2.52795 −0.136896
\(342\) 0 0
\(343\) −17.8779 −0.965316
\(344\) 0 0
\(345\) −0.854615 −0.0460109
\(346\) 0 0
\(347\) 19.8361 1.06486 0.532430 0.846474i \(-0.321279\pi\)
0.532430 + 0.846474i \(0.321279\pi\)
\(348\) 0 0
\(349\) −1.38519 −0.0741478 −0.0370739 0.999313i \(-0.511804\pi\)
−0.0370739 + 0.999313i \(0.511804\pi\)
\(350\) 0 0
\(351\) −6.42474 −0.342928
\(352\) 0 0
\(353\) −7.44035 −0.396010 −0.198005 0.980201i \(-0.563446\pi\)
−0.198005 + 0.980201i \(0.563446\pi\)
\(354\) 0 0
\(355\) 1.38382 0.0734457
\(356\) 0 0
\(357\) 16.2902 0.862167
\(358\) 0 0
\(359\) −23.1414 −1.22136 −0.610679 0.791878i \(-0.709103\pi\)
−0.610679 + 0.791878i \(0.709103\pi\)
\(360\) 0 0
\(361\) −17.7426 −0.933821
\(362\) 0 0
\(363\) 10.4916 0.550669
\(364\) 0 0
\(365\) 2.89389 0.151473
\(366\) 0 0
\(367\) −19.7366 −1.03024 −0.515121 0.857118i \(-0.672253\pi\)
−0.515121 + 0.857118i \(0.672253\pi\)
\(368\) 0 0
\(369\) 3.02539 0.157495
\(370\) 0 0
\(371\) −14.3809 −0.746619
\(372\) 0 0
\(373\) −15.2414 −0.789172 −0.394586 0.918859i \(-0.629112\pi\)
−0.394586 + 0.918859i \(0.629112\pi\)
\(374\) 0 0
\(375\) 3.40519 0.175843
\(376\) 0 0
\(377\) 8.72879 0.449556
\(378\) 0 0
\(379\) −6.52495 −0.335164 −0.167582 0.985858i \(-0.553596\pi\)
−0.167582 + 0.985858i \(0.553596\pi\)
\(380\) 0 0
\(381\) 12.2409 0.627119
\(382\) 0 0
\(383\) 4.99961 0.255468 0.127734 0.991808i \(-0.459230\pi\)
0.127734 + 0.991808i \(0.459230\pi\)
\(384\) 0 0
\(385\) −0.670646 −0.0341793
\(386\) 0 0
\(387\) 12.8201 0.651685
\(388\) 0 0
\(389\) −20.3083 −1.02967 −0.514836 0.857289i \(-0.672147\pi\)
−0.514836 + 0.857289i \(0.672147\pi\)
\(390\) 0 0
\(391\) −14.8008 −0.748511
\(392\) 0 0
\(393\) 11.5682 0.583538
\(394\) 0 0
\(395\) −0.436072 −0.0219411
\(396\) 0 0
\(397\) −3.23966 −0.162594 −0.0812970 0.996690i \(-0.525906\pi\)
−0.0812970 + 0.996690i \(0.525906\pi\)
\(398\) 0 0
\(399\) −3.06069 −0.153226
\(400\) 0 0
\(401\) 27.9754 1.39702 0.698511 0.715599i \(-0.253846\pi\)
0.698511 + 0.715599i \(0.253846\pi\)
\(402\) 0 0
\(403\) 22.7793 1.13472
\(404\) 0 0
\(405\) 0.344611 0.0171239
\(406\) 0 0
\(407\) −6.25378 −0.309989
\(408\) 0 0
\(409\) 17.6848 0.874459 0.437229 0.899350i \(-0.355960\pi\)
0.437229 + 0.899350i \(0.355960\pi\)
\(410\) 0 0
\(411\) 20.2770 1.00019
\(412\) 0 0
\(413\) 24.6471 1.21281
\(414\) 0 0
\(415\) −5.04155 −0.247480
\(416\) 0 0
\(417\) −0.686829 −0.0336342
\(418\) 0 0
\(419\) −25.4621 −1.24391 −0.621953 0.783054i \(-0.713661\pi\)
−0.621953 + 0.783054i \(0.713661\pi\)
\(420\) 0 0
\(421\) −25.6786 −1.25150 −0.625748 0.780025i \(-0.715206\pi\)
−0.625748 + 0.780025i \(0.715206\pi\)
\(422\) 0 0
\(423\) −9.01538 −0.438343
\(424\) 0 0
\(425\) 29.1324 1.41313
\(426\) 0 0
\(427\) 21.2474 1.02824
\(428\) 0 0
\(429\) 4.58078 0.221162
\(430\) 0 0
\(431\) 18.1431 0.873921 0.436961 0.899481i \(-0.356055\pi\)
0.436961 + 0.899481i \(0.356055\pi\)
\(432\) 0 0
\(433\) 3.31062 0.159098 0.0795491 0.996831i \(-0.474652\pi\)
0.0795491 + 0.996831i \(0.474652\pi\)
\(434\) 0 0
\(435\) −0.468196 −0.0224483
\(436\) 0 0
\(437\) 2.78086 0.133027
\(438\) 0 0
\(439\) 23.2782 1.11101 0.555503 0.831515i \(-0.312526\pi\)
0.555503 + 0.831515i \(0.312526\pi\)
\(440\) 0 0
\(441\) 0.450076 0.0214322
\(442\) 0 0
\(443\) 29.9935 1.42503 0.712517 0.701655i \(-0.247555\pi\)
0.712517 + 0.701655i \(0.247555\pi\)
\(444\) 0 0
\(445\) 0.0942700 0.00446883
\(446\) 0 0
\(447\) −3.07076 −0.145242
\(448\) 0 0
\(449\) 16.9309 0.799019 0.399509 0.916729i \(-0.369180\pi\)
0.399509 + 0.916729i \(0.369180\pi\)
\(450\) 0 0
\(451\) −2.15707 −0.101573
\(452\) 0 0
\(453\) −11.2823 −0.530089
\(454\) 0 0
\(455\) 6.04318 0.283309
\(456\) 0 0
\(457\) −14.0052 −0.655135 −0.327568 0.944828i \(-0.606229\pi\)
−0.327568 + 0.944828i \(0.606229\pi\)
\(458\) 0 0
\(459\) 5.96822 0.278573
\(460\) 0 0
\(461\) −12.1453 −0.565663 −0.282832 0.959170i \(-0.591274\pi\)
−0.282832 + 0.959170i \(0.591274\pi\)
\(462\) 0 0
\(463\) −26.4655 −1.22995 −0.614977 0.788545i \(-0.710835\pi\)
−0.614977 + 0.788545i \(0.710835\pi\)
\(464\) 0 0
\(465\) −1.22184 −0.0566613
\(466\) 0 0
\(467\) 13.8836 0.642458 0.321229 0.947002i \(-0.395904\pi\)
0.321229 + 0.947002i \(0.395904\pi\)
\(468\) 0 0
\(469\) −34.2609 −1.58202
\(470\) 0 0
\(471\) 16.8937 0.778423
\(472\) 0 0
\(473\) −9.14065 −0.420287
\(474\) 0 0
\(475\) −5.47355 −0.251144
\(476\) 0 0
\(477\) −5.26873 −0.241238
\(478\) 0 0
\(479\) −18.5052 −0.845525 −0.422762 0.906241i \(-0.638939\pi\)
−0.422762 + 0.906241i \(0.638939\pi\)
\(480\) 0 0
\(481\) 56.3527 2.56946
\(482\) 0 0
\(483\) −6.76896 −0.307998
\(484\) 0 0
\(485\) −0.0365067 −0.00165768
\(486\) 0 0
\(487\) 4.61242 0.209009 0.104504 0.994524i \(-0.466674\pi\)
0.104504 + 0.994524i \(0.466674\pi\)
\(488\) 0 0
\(489\) −13.9112 −0.629088
\(490\) 0 0
\(491\) 5.71153 0.257758 0.128879 0.991660i \(-0.458862\pi\)
0.128879 + 0.991660i \(0.458862\pi\)
\(492\) 0 0
\(493\) −8.10855 −0.365191
\(494\) 0 0
\(495\) −0.245704 −0.0110436
\(496\) 0 0
\(497\) 10.9605 0.491647
\(498\) 0 0
\(499\) −10.1365 −0.453773 −0.226887 0.973921i \(-0.572855\pi\)
−0.226887 + 0.973921i \(0.572855\pi\)
\(500\) 0 0
\(501\) 12.3646 0.552408
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 3.93474 0.175094
\(506\) 0 0
\(507\) −28.2773 −1.25584
\(508\) 0 0
\(509\) −19.1486 −0.848746 −0.424373 0.905487i \(-0.639506\pi\)
−0.424373 + 0.905487i \(0.639506\pi\)
\(510\) 0 0
\(511\) 22.9210 1.01397
\(512\) 0 0
\(513\) −1.12134 −0.0495085
\(514\) 0 0
\(515\) 2.28636 0.100749
\(516\) 0 0
\(517\) 6.42788 0.282698
\(518\) 0 0
\(519\) −15.5946 −0.684526
\(520\) 0 0
\(521\) −34.0158 −1.49026 −0.745129 0.666920i \(-0.767612\pi\)
−0.745129 + 0.666920i \(0.767612\pi\)
\(522\) 0 0
\(523\) 29.0719 1.27123 0.635613 0.772008i \(-0.280747\pi\)
0.635613 + 0.772008i \(0.280747\pi\)
\(524\) 0 0
\(525\) 13.3233 0.581475
\(526\) 0 0
\(527\) −21.1607 −0.921773
\(528\) 0 0
\(529\) −16.8499 −0.732604
\(530\) 0 0
\(531\) 9.02996 0.391867
\(532\) 0 0
\(533\) 19.4373 0.841924
\(534\) 0 0
\(535\) 2.90014 0.125384
\(536\) 0 0
\(537\) 15.6541 0.675522
\(538\) 0 0
\(539\) −0.320900 −0.0138221
\(540\) 0 0
\(541\) −22.1986 −0.954394 −0.477197 0.878796i \(-0.658347\pi\)
−0.477197 + 0.878796i \(0.658347\pi\)
\(542\) 0 0
\(543\) 6.78808 0.291304
\(544\) 0 0
\(545\) −1.35567 −0.0580703
\(546\) 0 0
\(547\) 23.3015 0.996298 0.498149 0.867091i \(-0.334013\pi\)
0.498149 + 0.867091i \(0.334013\pi\)
\(548\) 0 0
\(549\) 7.78442 0.332231
\(550\) 0 0
\(551\) 1.52348 0.0649024
\(552\) 0 0
\(553\) −3.45389 −0.146874
\(554\) 0 0
\(555\) −3.02265 −0.128304
\(556\) 0 0
\(557\) 11.5058 0.487515 0.243757 0.969836i \(-0.421620\pi\)
0.243757 + 0.969836i \(0.421620\pi\)
\(558\) 0 0
\(559\) 82.3662 3.48372
\(560\) 0 0
\(561\) −4.25529 −0.179658
\(562\) 0 0
\(563\) 1.72703 0.0727857 0.0363928 0.999338i \(-0.488413\pi\)
0.0363928 + 0.999338i \(0.488413\pi\)
\(564\) 0 0
\(565\) 4.18911 0.176237
\(566\) 0 0
\(567\) 2.72948 0.114627
\(568\) 0 0
\(569\) 10.1662 0.426189 0.213094 0.977032i \(-0.431646\pi\)
0.213094 + 0.977032i \(0.431646\pi\)
\(570\) 0 0
\(571\) −13.2680 −0.555248 −0.277624 0.960690i \(-0.589547\pi\)
−0.277624 + 0.960690i \(0.589547\pi\)
\(572\) 0 0
\(573\) −1.54867 −0.0646968
\(574\) 0 0
\(575\) −12.1052 −0.504822
\(576\) 0 0
\(577\) 34.0954 1.41941 0.709705 0.704499i \(-0.248828\pi\)
0.709705 + 0.704499i \(0.248828\pi\)
\(578\) 0 0
\(579\) −19.2987 −0.802025
\(580\) 0 0
\(581\) −39.9315 −1.65664
\(582\) 0 0
\(583\) 3.75655 0.155581
\(584\) 0 0
\(585\) 2.21404 0.0915392
\(586\) 0 0
\(587\) −37.0120 −1.52765 −0.763824 0.645424i \(-0.776681\pi\)
−0.763824 + 0.645424i \(0.776681\pi\)
\(588\) 0 0
\(589\) 3.97578 0.163819
\(590\) 0 0
\(591\) −19.1837 −0.789112
\(592\) 0 0
\(593\) 11.8805 0.487874 0.243937 0.969791i \(-0.421561\pi\)
0.243937 + 0.969791i \(0.421561\pi\)
\(594\) 0 0
\(595\) −5.61377 −0.230142
\(596\) 0 0
\(597\) −8.04744 −0.329360
\(598\) 0 0
\(599\) 2.09978 0.0857947 0.0428973 0.999079i \(-0.486341\pi\)
0.0428973 + 0.999079i \(0.486341\pi\)
\(600\) 0 0
\(601\) 18.3572 0.748805 0.374403 0.927266i \(-0.377848\pi\)
0.374403 + 0.927266i \(0.377848\pi\)
\(602\) 0 0
\(603\) −12.5521 −0.511163
\(604\) 0 0
\(605\) −3.61554 −0.146992
\(606\) 0 0
\(607\) 1.34608 0.0546357 0.0273178 0.999627i \(-0.491303\pi\)
0.0273178 + 0.999627i \(0.491303\pi\)
\(608\) 0 0
\(609\) −3.70833 −0.150269
\(610\) 0 0
\(611\) −57.9215 −2.34325
\(612\) 0 0
\(613\) −0.540113 −0.0218149 −0.0109075 0.999941i \(-0.503472\pi\)
−0.0109075 + 0.999941i \(0.503472\pi\)
\(614\) 0 0
\(615\) −1.04258 −0.0420409
\(616\) 0 0
\(617\) −30.6285 −1.23306 −0.616529 0.787332i \(-0.711462\pi\)
−0.616529 + 0.787332i \(0.711462\pi\)
\(618\) 0 0
\(619\) 17.4834 0.702718 0.351359 0.936241i \(-0.385720\pi\)
0.351359 + 0.936241i \(0.385720\pi\)
\(620\) 0 0
\(621\) −2.47994 −0.0995166
\(622\) 0 0
\(623\) 0.746663 0.0299144
\(624\) 0 0
\(625\) 23.2328 0.929310
\(626\) 0 0
\(627\) 0.799507 0.0319292
\(628\) 0 0
\(629\) −52.3485 −2.08727
\(630\) 0 0
\(631\) 34.0691 1.35627 0.678134 0.734938i \(-0.262789\pi\)
0.678134 + 0.734938i \(0.262789\pi\)
\(632\) 0 0
\(633\) 16.3451 0.649659
\(634\) 0 0
\(635\) −4.21834 −0.167400
\(636\) 0 0
\(637\) 2.89162 0.114570
\(638\) 0 0
\(639\) 4.01561 0.158855
\(640\) 0 0
\(641\) 46.3734 1.83164 0.915820 0.401589i \(-0.131542\pi\)
0.915820 + 0.401589i \(0.131542\pi\)
\(642\) 0 0
\(643\) −21.2735 −0.838946 −0.419473 0.907768i \(-0.637785\pi\)
−0.419473 + 0.907768i \(0.637785\pi\)
\(644\) 0 0
\(645\) −4.41796 −0.173957
\(646\) 0 0
\(647\) 5.69695 0.223970 0.111985 0.993710i \(-0.464279\pi\)
0.111985 + 0.993710i \(0.464279\pi\)
\(648\) 0 0
\(649\) −6.43828 −0.252724
\(650\) 0 0
\(651\) −9.67753 −0.379292
\(652\) 0 0
\(653\) 5.03281 0.196949 0.0984746 0.995140i \(-0.468604\pi\)
0.0984746 + 0.995140i \(0.468604\pi\)
\(654\) 0 0
\(655\) −3.98652 −0.155766
\(656\) 0 0
\(657\) 8.39756 0.327620
\(658\) 0 0
\(659\) 1.44130 0.0561449 0.0280725 0.999606i \(-0.491063\pi\)
0.0280725 + 0.999606i \(0.491063\pi\)
\(660\) 0 0
\(661\) 43.7236 1.70065 0.850325 0.526259i \(-0.176406\pi\)
0.850325 + 0.526259i \(0.176406\pi\)
\(662\) 0 0
\(663\) 38.3443 1.48917
\(664\) 0 0
\(665\) 1.05475 0.0409013
\(666\) 0 0
\(667\) 3.36930 0.130460
\(668\) 0 0
\(669\) 10.6754 0.412735
\(670\) 0 0
\(671\) −5.55022 −0.214264
\(672\) 0 0
\(673\) 20.6739 0.796922 0.398461 0.917185i \(-0.369544\pi\)
0.398461 + 0.917185i \(0.369544\pi\)
\(674\) 0 0
\(675\) 4.88124 0.187879
\(676\) 0 0
\(677\) −17.8278 −0.685177 −0.342588 0.939486i \(-0.611304\pi\)
−0.342588 + 0.939486i \(0.611304\pi\)
\(678\) 0 0
\(679\) −0.289150 −0.0110966
\(680\) 0 0
\(681\) −27.7335 −1.06275
\(682\) 0 0
\(683\) −31.7317 −1.21418 −0.607090 0.794633i \(-0.707663\pi\)
−0.607090 + 0.794633i \(0.707663\pi\)
\(684\) 0 0
\(685\) −6.98769 −0.266986
\(686\) 0 0
\(687\) −2.99849 −0.114399
\(688\) 0 0
\(689\) −33.8502 −1.28959
\(690\) 0 0
\(691\) 16.2469 0.618060 0.309030 0.951052i \(-0.399996\pi\)
0.309030 + 0.951052i \(0.399996\pi\)
\(692\) 0 0
\(693\) −1.94610 −0.0739261
\(694\) 0 0
\(695\) 0.236689 0.00897812
\(696\) 0 0
\(697\) −18.0562 −0.683927
\(698\) 0 0
\(699\) −17.0232 −0.643877
\(700\) 0 0
\(701\) −17.0334 −0.643343 −0.321671 0.946851i \(-0.604245\pi\)
−0.321671 + 0.946851i \(0.604245\pi\)
\(702\) 0 0
\(703\) 9.83552 0.370954
\(704\) 0 0
\(705\) 3.10680 0.117009
\(706\) 0 0
\(707\) 31.1650 1.17208
\(708\) 0 0
\(709\) 46.3174 1.73949 0.869743 0.493506i \(-0.164285\pi\)
0.869743 + 0.493506i \(0.164285\pi\)
\(710\) 0 0
\(711\) −1.26540 −0.0474563
\(712\) 0 0
\(713\) 8.79276 0.329292
\(714\) 0 0
\(715\) −1.57859 −0.0590359
\(716\) 0 0
\(717\) 19.5646 0.730655
\(718\) 0 0
\(719\) 43.2054 1.61129 0.805645 0.592398i \(-0.201819\pi\)
0.805645 + 0.592398i \(0.201819\pi\)
\(720\) 0 0
\(721\) 18.1091 0.674417
\(722\) 0 0
\(723\) −18.6987 −0.695413
\(724\) 0 0
\(725\) −6.63176 −0.246297
\(726\) 0 0
\(727\) 10.7377 0.398239 0.199119 0.979975i \(-0.436192\pi\)
0.199119 + 0.979975i \(0.436192\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −76.5135 −2.82995
\(732\) 0 0
\(733\) −33.3161 −1.23056 −0.615279 0.788309i \(-0.710957\pi\)
−0.615279 + 0.788309i \(0.710957\pi\)
\(734\) 0 0
\(735\) −0.155101 −0.00572099
\(736\) 0 0
\(737\) 8.94956 0.329661
\(738\) 0 0
\(739\) −1.76650 −0.0649818 −0.0324909 0.999472i \(-0.510344\pi\)
−0.0324909 + 0.999472i \(0.510344\pi\)
\(740\) 0 0
\(741\) −7.20434 −0.264658
\(742\) 0 0
\(743\) −32.5339 −1.19355 −0.596777 0.802407i \(-0.703552\pi\)
−0.596777 + 0.802407i \(0.703552\pi\)
\(744\) 0 0
\(745\) 1.05822 0.0387701
\(746\) 0 0
\(747\) −14.6297 −0.535272
\(748\) 0 0
\(749\) 22.9705 0.839324
\(750\) 0 0
\(751\) 6.28617 0.229386 0.114693 0.993401i \(-0.463412\pi\)
0.114693 + 0.993401i \(0.463412\pi\)
\(752\) 0 0
\(753\) −0.722458 −0.0263278
\(754\) 0 0
\(755\) 3.88801 0.141499
\(756\) 0 0
\(757\) −29.0233 −1.05487 −0.527436 0.849595i \(-0.676846\pi\)
−0.527436 + 0.849595i \(0.676846\pi\)
\(758\) 0 0
\(759\) 1.76817 0.0641807
\(760\) 0 0
\(761\) −26.3405 −0.954842 −0.477421 0.878675i \(-0.658428\pi\)
−0.477421 + 0.878675i \(0.658428\pi\)
\(762\) 0 0
\(763\) −10.7375 −0.388724
\(764\) 0 0
\(765\) −2.05672 −0.0743607
\(766\) 0 0
\(767\) 58.0152 2.09481
\(768\) 0 0
\(769\) −8.44239 −0.304440 −0.152220 0.988347i \(-0.548642\pi\)
−0.152220 + 0.988347i \(0.548642\pi\)
\(770\) 0 0
\(771\) −9.73334 −0.350538
\(772\) 0 0
\(773\) −13.6881 −0.492326 −0.246163 0.969228i \(-0.579170\pi\)
−0.246163 + 0.969228i \(0.579170\pi\)
\(774\) 0 0
\(775\) −17.3067 −0.621675
\(776\) 0 0
\(777\) −23.9408 −0.858873
\(778\) 0 0
\(779\) 3.39250 0.121549
\(780\) 0 0
\(781\) −2.86309 −0.102449
\(782\) 0 0
\(783\) −1.35862 −0.0485532
\(784\) 0 0
\(785\) −5.82177 −0.207788
\(786\) 0 0
\(787\) 18.9696 0.676194 0.338097 0.941111i \(-0.390217\pi\)
0.338097 + 0.941111i \(0.390217\pi\)
\(788\) 0 0
\(789\) −15.8101 −0.562856
\(790\) 0 0
\(791\) 33.1797 1.17974
\(792\) 0 0
\(793\) 50.0129 1.77601
\(794\) 0 0
\(795\) 1.81566 0.0643949
\(796\) 0 0
\(797\) −10.2355 −0.362560 −0.181280 0.983432i \(-0.558024\pi\)
−0.181280 + 0.983432i \(0.558024\pi\)
\(798\) 0 0
\(799\) 53.8058 1.90351
\(800\) 0 0
\(801\) 0.273555 0.00966558
\(802\) 0 0
\(803\) −5.98738 −0.211290
\(804\) 0 0
\(805\) 2.33266 0.0822154
\(806\) 0 0
\(807\) −7.54823 −0.265710
\(808\) 0 0
\(809\) 30.2622 1.06396 0.531981 0.846757i \(-0.321448\pi\)
0.531981 + 0.846757i \(0.321448\pi\)
\(810\) 0 0
\(811\) −4.57459 −0.160636 −0.0803178 0.996769i \(-0.525594\pi\)
−0.0803178 + 0.996769i \(0.525594\pi\)
\(812\) 0 0
\(813\) −2.83611 −0.0994668
\(814\) 0 0
\(815\) 4.79397 0.167925
\(816\) 0 0
\(817\) 14.3758 0.502945
\(818\) 0 0
\(819\) 17.5362 0.612765
\(820\) 0 0
\(821\) 34.9805 1.22083 0.610414 0.792083i \(-0.291003\pi\)
0.610414 + 0.792083i \(0.291003\pi\)
\(822\) 0 0
\(823\) −42.4259 −1.47887 −0.739437 0.673226i \(-0.764908\pi\)
−0.739437 + 0.673226i \(0.764908\pi\)
\(824\) 0 0
\(825\) −3.48028 −0.121168
\(826\) 0 0
\(827\) −34.0267 −1.18323 −0.591613 0.806222i \(-0.701509\pi\)
−0.591613 + 0.806222i \(0.701509\pi\)
\(828\) 0 0
\(829\) −25.9270 −0.900480 −0.450240 0.892908i \(-0.648662\pi\)
−0.450240 + 0.892908i \(0.648662\pi\)
\(830\) 0 0
\(831\) −0.975302 −0.0338329
\(832\) 0 0
\(833\) −2.68615 −0.0930697
\(834\) 0 0
\(835\) −4.26096 −0.147457
\(836\) 0 0
\(837\) −3.54555 −0.122552
\(838\) 0 0
\(839\) −41.7262 −1.44055 −0.720275 0.693689i \(-0.755984\pi\)
−0.720275 + 0.693689i \(0.755984\pi\)
\(840\) 0 0
\(841\) −27.1541 −0.936350
\(842\) 0 0
\(843\) −23.6666 −0.815121
\(844\) 0 0
\(845\) 9.74469 0.335227
\(846\) 0 0
\(847\) −28.6368 −0.983971
\(848\) 0 0
\(849\) 4.46571 0.153263
\(850\) 0 0
\(851\) 21.7521 0.745651
\(852\) 0 0
\(853\) 25.4001 0.869682 0.434841 0.900507i \(-0.356805\pi\)
0.434841 + 0.900507i \(0.356805\pi\)
\(854\) 0 0
\(855\) 0.386427 0.0132155
\(856\) 0 0
\(857\) −11.5988 −0.396207 −0.198103 0.980181i \(-0.563478\pi\)
−0.198103 + 0.980181i \(0.563478\pi\)
\(858\) 0 0
\(859\) 17.4999 0.597088 0.298544 0.954396i \(-0.403499\pi\)
0.298544 + 0.954396i \(0.403499\pi\)
\(860\) 0 0
\(861\) −8.25774 −0.281423
\(862\) 0 0
\(863\) 26.8457 0.913839 0.456920 0.889508i \(-0.348953\pi\)
0.456920 + 0.889508i \(0.348953\pi\)
\(864\) 0 0
\(865\) 5.37406 0.182724
\(866\) 0 0
\(867\) −18.6197 −0.632358
\(868\) 0 0
\(869\) 0.902220 0.0306057
\(870\) 0 0
\(871\) −80.6443 −2.73253
\(872\) 0 0
\(873\) −0.105936 −0.00358538
\(874\) 0 0
\(875\) −9.29440 −0.314208
\(876\) 0 0
\(877\) 50.1483 1.69339 0.846693 0.532081i \(-0.178590\pi\)
0.846693 + 0.532081i \(0.178590\pi\)
\(878\) 0 0
\(879\) −20.1854 −0.680836
\(880\) 0 0
\(881\) −0.651404 −0.0219464 −0.0109732 0.999940i \(-0.503493\pi\)
−0.0109732 + 0.999940i \(0.503493\pi\)
\(882\) 0 0
\(883\) −55.1415 −1.85566 −0.927829 0.373006i \(-0.878327\pi\)
−0.927829 + 0.373006i \(0.878327\pi\)
\(884\) 0 0
\(885\) −3.11182 −0.104603
\(886\) 0 0
\(887\) 7.78991 0.261560 0.130780 0.991411i \(-0.458252\pi\)
0.130780 + 0.991411i \(0.458252\pi\)
\(888\) 0 0
\(889\) −33.4113 −1.12058
\(890\) 0 0
\(891\) −0.712991 −0.0238861
\(892\) 0 0
\(893\) −10.1093 −0.338296
\(894\) 0 0
\(895\) −5.39456 −0.180320
\(896\) 0 0
\(897\) −15.9330 −0.531987
\(898\) 0 0
\(899\) 4.81706 0.160658
\(900\) 0 0
\(901\) 31.4449 1.04758
\(902\) 0 0
\(903\) −34.9924 −1.16447
\(904\) 0 0
\(905\) −2.33925 −0.0777592
\(906\) 0 0
\(907\) −32.3796 −1.07515 −0.537574 0.843216i \(-0.680659\pi\)
−0.537574 + 0.843216i \(0.680659\pi\)
\(908\) 0 0
\(909\) 11.4179 0.378708
\(910\) 0 0
\(911\) −8.11484 −0.268857 −0.134428 0.990923i \(-0.542920\pi\)
−0.134428 + 0.990923i \(0.542920\pi\)
\(912\) 0 0
\(913\) 10.4308 0.345210
\(914\) 0 0
\(915\) −2.68260 −0.0886840
\(916\) 0 0
\(917\) −31.5752 −1.04270
\(918\) 0 0
\(919\) −45.5173 −1.50148 −0.750738 0.660600i \(-0.770302\pi\)
−0.750738 + 0.660600i \(0.770302\pi\)
\(920\) 0 0
\(921\) 4.34238 0.143086
\(922\) 0 0
\(923\) 25.7993 0.849193
\(924\) 0 0
\(925\) −42.8144 −1.40773
\(926\) 0 0
\(927\) 6.63462 0.217909
\(928\) 0 0
\(929\) 53.3233 1.74948 0.874741 0.484591i \(-0.161031\pi\)
0.874741 + 0.484591i \(0.161031\pi\)
\(930\) 0 0
\(931\) 0.504689 0.0165405
\(932\) 0 0
\(933\) −14.9026 −0.487888
\(934\) 0 0
\(935\) 1.46642 0.0479570
\(936\) 0 0
\(937\) 22.8542 0.746613 0.373306 0.927708i \(-0.378224\pi\)
0.373306 + 0.927708i \(0.378224\pi\)
\(938\) 0 0
\(939\) −6.43464 −0.209987
\(940\) 0 0
\(941\) −32.8691 −1.07150 −0.535751 0.844376i \(-0.679972\pi\)
−0.535751 + 0.844376i \(0.679972\pi\)
\(942\) 0 0
\(943\) 7.50278 0.244324
\(944\) 0 0
\(945\) −0.940610 −0.0305980
\(946\) 0 0
\(947\) −46.0958 −1.49791 −0.748956 0.662619i \(-0.769445\pi\)
−0.748956 + 0.662619i \(0.769445\pi\)
\(948\) 0 0
\(949\) 53.9522 1.75136
\(950\) 0 0
\(951\) −21.9271 −0.711036
\(952\) 0 0
\(953\) 32.9711 1.06804 0.534020 0.845472i \(-0.320681\pi\)
0.534020 + 0.845472i \(0.320681\pi\)
\(954\) 0 0
\(955\) 0.533690 0.0172698
\(956\) 0 0
\(957\) 0.968684 0.0313131
\(958\) 0 0
\(959\) −55.3458 −1.78721
\(960\) 0 0
\(961\) −18.4291 −0.594486
\(962\) 0 0
\(963\) 8.41570 0.271192
\(964\) 0 0
\(965\) 6.65054 0.214088
\(966\) 0 0
\(967\) −28.8857 −0.928902 −0.464451 0.885599i \(-0.653748\pi\)
−0.464451 + 0.885599i \(0.653748\pi\)
\(968\) 0 0
\(969\) 6.69242 0.214992
\(970\) 0 0
\(971\) −40.4882 −1.29933 −0.649664 0.760222i \(-0.725090\pi\)
−0.649664 + 0.760222i \(0.725090\pi\)
\(972\) 0 0
\(973\) 1.87469 0.0600998
\(974\) 0 0
\(975\) 31.3607 1.00435
\(976\) 0 0
\(977\) −30.0252 −0.960592 −0.480296 0.877106i \(-0.659471\pi\)
−0.480296 + 0.877106i \(0.659471\pi\)
\(978\) 0 0
\(979\) −0.195042 −0.00623357
\(980\) 0 0
\(981\) −3.93390 −0.125600
\(982\) 0 0
\(983\) −54.5180 −1.73886 −0.869428 0.494060i \(-0.835512\pi\)
−0.869428 + 0.494060i \(0.835512\pi\)
\(984\) 0 0
\(985\) 6.61092 0.210641
\(986\) 0 0
\(987\) 24.6073 0.783260
\(988\) 0 0
\(989\) 31.7932 1.01097
\(990\) 0 0
\(991\) −3.08348 −0.0979500 −0.0489750 0.998800i \(-0.515595\pi\)
−0.0489750 + 0.998800i \(0.515595\pi\)
\(992\) 0 0
\(993\) −8.36105 −0.265330
\(994\) 0 0
\(995\) 2.77324 0.0879176
\(996\) 0 0
\(997\) 40.8492 1.29371 0.646853 0.762615i \(-0.276085\pi\)
0.646853 + 0.762615i \(0.276085\pi\)
\(998\) 0 0
\(999\) −8.77120 −0.277509
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 \(a_p\))