Properties

Label 6036.2.a.i.1.17
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 1.17
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+1.66086 q^{5}\) \(-2.19144 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+1.66086 q^{5}\) \(-2.19144 q^{7}\) \(+1.00000 q^{9}\) \(-5.33796 q^{11}\) \(+2.06619 q^{13}\) \(-1.66086 q^{15}\) \(+3.14459 q^{17}\) \(-6.10656 q^{19}\) \(+2.19144 q^{21}\) \(+6.59981 q^{23}\) \(-2.24154 q^{25}\) \(-1.00000 q^{27}\) \(+8.96547 q^{29}\) \(-6.89365 q^{31}\) \(+5.33796 q^{33}\) \(-3.63968 q^{35}\) \(-4.91614 q^{37}\) \(-2.06619 q^{39}\) \(+5.27622 q^{41}\) \(+4.91190 q^{43}\) \(+1.66086 q^{45}\) \(+0.585390 q^{47}\) \(-2.19758 q^{49}\) \(-3.14459 q^{51}\) \(-9.07199 q^{53}\) \(-8.86561 q^{55}\) \(+6.10656 q^{57}\) \(-14.2559 q^{59}\) \(+6.61736 q^{61}\) \(-2.19144 q^{63}\) \(+3.43166 q^{65}\) \(-5.16554 q^{67}\) \(-6.59981 q^{69}\) \(+0.933881 q^{71}\) \(+6.11727 q^{73}\) \(+2.24154 q^{75}\) \(+11.6978 q^{77}\) \(+14.6499 q^{79}\) \(+1.00000 q^{81}\) \(+14.4496 q^{83}\) \(+5.22272 q^{85}\) \(-8.96547 q^{87}\) \(-5.02821 q^{89}\) \(-4.52794 q^{91}\) \(+6.89365 q^{93}\) \(-10.1421 q^{95}\) \(+6.45055 q^{97}\) \(-5.33796 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 1.66086 0.742759 0.371380 0.928481i \(-0.378885\pi\)
0.371380 + 0.928481i \(0.378885\pi\)
\(6\) 0 0
\(7\) −2.19144 −0.828287 −0.414144 0.910212i \(-0.635919\pi\)
−0.414144 + 0.910212i \(0.635919\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.33796 −1.60946 −0.804728 0.593643i \(-0.797689\pi\)
−0.804728 + 0.593643i \(0.797689\pi\)
\(12\) 0 0
\(13\) 2.06619 0.573058 0.286529 0.958072i \(-0.407498\pi\)
0.286529 + 0.958072i \(0.407498\pi\)
\(14\) 0 0
\(15\) −1.66086 −0.428832
\(16\) 0 0
\(17\) 3.14459 0.762675 0.381337 0.924436i \(-0.375464\pi\)
0.381337 + 0.924436i \(0.375464\pi\)
\(18\) 0 0
\(19\) −6.10656 −1.40094 −0.700470 0.713681i \(-0.747026\pi\)
−0.700470 + 0.713681i \(0.747026\pi\)
\(20\) 0 0
\(21\) 2.19144 0.478212
\(22\) 0 0
\(23\) 6.59981 1.37616 0.688078 0.725637i \(-0.258455\pi\)
0.688078 + 0.725637i \(0.258455\pi\)
\(24\) 0 0
\(25\) −2.24154 −0.448309
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.96547 1.66485 0.832423 0.554141i \(-0.186953\pi\)
0.832423 + 0.554141i \(0.186953\pi\)
\(30\) 0 0
\(31\) −6.89365 −1.23814 −0.619068 0.785337i \(-0.712490\pi\)
−0.619068 + 0.785337i \(0.712490\pi\)
\(32\) 0 0
\(33\) 5.33796 0.929220
\(34\) 0 0
\(35\) −3.63968 −0.615218
\(36\) 0 0
\(37\) −4.91614 −0.808208 −0.404104 0.914713i \(-0.632417\pi\)
−0.404104 + 0.914713i \(0.632417\pi\)
\(38\) 0 0
\(39\) −2.06619 −0.330855
\(40\) 0 0
\(41\) 5.27622 0.824007 0.412004 0.911182i \(-0.364829\pi\)
0.412004 + 0.911182i \(0.364829\pi\)
\(42\) 0 0
\(43\) 4.91190 0.749058 0.374529 0.927215i \(-0.377804\pi\)
0.374529 + 0.927215i \(0.377804\pi\)
\(44\) 0 0
\(45\) 1.66086 0.247586
\(46\) 0 0
\(47\) 0.585390 0.0853879 0.0426939 0.999088i \(-0.486406\pi\)
0.0426939 + 0.999088i \(0.486406\pi\)
\(48\) 0 0
\(49\) −2.19758 −0.313940
\(50\) 0 0
\(51\) −3.14459 −0.440330
\(52\) 0 0
\(53\) −9.07199 −1.24613 −0.623067 0.782169i \(-0.714114\pi\)
−0.623067 + 0.782169i \(0.714114\pi\)
\(54\) 0 0
\(55\) −8.86561 −1.19544
\(56\) 0 0
\(57\) 6.10656 0.808834
\(58\) 0 0
\(59\) −14.2559 −1.85596 −0.927980 0.372630i \(-0.878456\pi\)
−0.927980 + 0.372630i \(0.878456\pi\)
\(60\) 0 0
\(61\) 6.61736 0.847266 0.423633 0.905834i \(-0.360755\pi\)
0.423633 + 0.905834i \(0.360755\pi\)
\(62\) 0 0
\(63\) −2.19144 −0.276096
\(64\) 0 0
\(65\) 3.43166 0.425644
\(66\) 0 0
\(67\) −5.16554 −0.631072 −0.315536 0.948914i \(-0.602184\pi\)
−0.315536 + 0.948914i \(0.602184\pi\)
\(68\) 0 0
\(69\) −6.59981 −0.794524
\(70\) 0 0
\(71\) 0.933881 0.110831 0.0554156 0.998463i \(-0.482352\pi\)
0.0554156 + 0.998463i \(0.482352\pi\)
\(72\) 0 0
\(73\) 6.11727 0.715973 0.357986 0.933727i \(-0.383463\pi\)
0.357986 + 0.933727i \(0.383463\pi\)
\(74\) 0 0
\(75\) 2.24154 0.258831
\(76\) 0 0
\(77\) 11.6978 1.33309
\(78\) 0 0
\(79\) 14.6499 1.64824 0.824121 0.566414i \(-0.191669\pi\)
0.824121 + 0.566414i \(0.191669\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 14.4496 1.58604 0.793022 0.609193i \(-0.208506\pi\)
0.793022 + 0.609193i \(0.208506\pi\)
\(84\) 0 0
\(85\) 5.22272 0.566484
\(86\) 0 0
\(87\) −8.96547 −0.961199
\(88\) 0 0
\(89\) −5.02821 −0.532989 −0.266494 0.963836i \(-0.585865\pi\)
−0.266494 + 0.963836i \(0.585865\pi\)
\(90\) 0 0
\(91\) −4.52794 −0.474657
\(92\) 0 0
\(93\) 6.89365 0.714839
\(94\) 0 0
\(95\) −10.1421 −1.04056
\(96\) 0 0
\(97\) 6.45055 0.654954 0.327477 0.944859i \(-0.393802\pi\)
0.327477 + 0.944859i \(0.393802\pi\)
\(98\) 0 0
\(99\) −5.33796 −0.536485
\(100\) 0 0
\(101\) 1.19379 0.118787 0.0593933 0.998235i \(-0.481083\pi\)
0.0593933 + 0.998235i \(0.481083\pi\)
\(102\) 0 0
\(103\) −0.0291429 −0.00287153 −0.00143577 0.999999i \(-0.500457\pi\)
−0.00143577 + 0.999999i \(0.500457\pi\)
\(104\) 0 0
\(105\) 3.63968 0.355196
\(106\) 0 0
\(107\) 9.85598 0.952814 0.476407 0.879225i \(-0.341939\pi\)
0.476407 + 0.879225i \(0.341939\pi\)
\(108\) 0 0
\(109\) 2.98381 0.285797 0.142899 0.989737i \(-0.454358\pi\)
0.142899 + 0.989737i \(0.454358\pi\)
\(110\) 0 0
\(111\) 4.91614 0.466619
\(112\) 0 0
\(113\) 17.4015 1.63699 0.818496 0.574512i \(-0.194808\pi\)
0.818496 + 0.574512i \(0.194808\pi\)
\(114\) 0 0
\(115\) 10.9614 1.02215
\(116\) 0 0
\(117\) 2.06619 0.191019
\(118\) 0 0
\(119\) −6.89118 −0.631714
\(120\) 0 0
\(121\) 17.4938 1.59035
\(122\) 0 0
\(123\) −5.27622 −0.475741
\(124\) 0 0
\(125\) −12.0272 −1.07574
\(126\) 0 0
\(127\) 1.66062 0.147357 0.0736783 0.997282i \(-0.476526\pi\)
0.0736783 + 0.997282i \(0.476526\pi\)
\(128\) 0 0
\(129\) −4.91190 −0.432469
\(130\) 0 0
\(131\) 20.1407 1.75970 0.879848 0.475254i \(-0.157644\pi\)
0.879848 + 0.475254i \(0.157644\pi\)
\(132\) 0 0
\(133\) 13.3822 1.16038
\(134\) 0 0
\(135\) −1.66086 −0.142944
\(136\) 0 0
\(137\) −4.06701 −0.347468 −0.173734 0.984793i \(-0.555583\pi\)
−0.173734 + 0.984793i \(0.555583\pi\)
\(138\) 0 0
\(139\) −13.8088 −1.17125 −0.585625 0.810582i \(-0.699151\pi\)
−0.585625 + 0.810582i \(0.699151\pi\)
\(140\) 0 0
\(141\) −0.585390 −0.0492987
\(142\) 0 0
\(143\) −11.0293 −0.922313
\(144\) 0 0
\(145\) 14.8904 1.23658
\(146\) 0 0
\(147\) 2.19758 0.181253
\(148\) 0 0
\(149\) −16.0931 −1.31840 −0.659201 0.751967i \(-0.729105\pi\)
−0.659201 + 0.751967i \(0.729105\pi\)
\(150\) 0 0
\(151\) −4.44235 −0.361514 −0.180757 0.983528i \(-0.557855\pi\)
−0.180757 + 0.983528i \(0.557855\pi\)
\(152\) 0 0
\(153\) 3.14459 0.254225
\(154\) 0 0
\(155\) −11.4494 −0.919638
\(156\) 0 0
\(157\) 13.9994 1.11727 0.558637 0.829412i \(-0.311324\pi\)
0.558637 + 0.829412i \(0.311324\pi\)
\(158\) 0 0
\(159\) 9.07199 0.719456
\(160\) 0 0
\(161\) −14.4631 −1.13985
\(162\) 0 0
\(163\) 19.7013 1.54313 0.771564 0.636152i \(-0.219475\pi\)
0.771564 + 0.636152i \(0.219475\pi\)
\(164\) 0 0
\(165\) 8.86561 0.690187
\(166\) 0 0
\(167\) 3.46294 0.267970 0.133985 0.990983i \(-0.457223\pi\)
0.133985 + 0.990983i \(0.457223\pi\)
\(168\) 0 0
\(169\) −8.73085 −0.671604
\(170\) 0 0
\(171\) −6.10656 −0.466980
\(172\) 0 0
\(173\) 20.4526 1.55498 0.777492 0.628893i \(-0.216492\pi\)
0.777492 + 0.628893i \(0.216492\pi\)
\(174\) 0 0
\(175\) 4.91221 0.371328
\(176\) 0 0
\(177\) 14.2559 1.07154
\(178\) 0 0
\(179\) −2.85284 −0.213231 −0.106616 0.994300i \(-0.534001\pi\)
−0.106616 + 0.994300i \(0.534001\pi\)
\(180\) 0 0
\(181\) −24.3472 −1.80972 −0.904858 0.425714i \(-0.860023\pi\)
−0.904858 + 0.425714i \(0.860023\pi\)
\(182\) 0 0
\(183\) −6.61736 −0.489169
\(184\) 0 0
\(185\) −8.16501 −0.600304
\(186\) 0 0
\(187\) −16.7857 −1.22749
\(188\) 0 0
\(189\) 2.19144 0.159404
\(190\) 0 0
\(191\) −13.5918 −0.983466 −0.491733 0.870746i \(-0.663636\pi\)
−0.491733 + 0.870746i \(0.663636\pi\)
\(192\) 0 0
\(193\) 7.53334 0.542262 0.271131 0.962542i \(-0.412602\pi\)
0.271131 + 0.962542i \(0.412602\pi\)
\(194\) 0 0
\(195\) −3.43166 −0.245746
\(196\) 0 0
\(197\) −14.1311 −1.00680 −0.503400 0.864053i \(-0.667918\pi\)
−0.503400 + 0.864053i \(0.667918\pi\)
\(198\) 0 0
\(199\) 22.7899 1.61553 0.807765 0.589505i \(-0.200677\pi\)
0.807765 + 0.589505i \(0.200677\pi\)
\(200\) 0 0
\(201\) 5.16554 0.364349
\(202\) 0 0
\(203\) −19.6473 −1.37897
\(204\) 0 0
\(205\) 8.76307 0.612039
\(206\) 0 0
\(207\) 6.59981 0.458719
\(208\) 0 0
\(209\) 32.5966 2.25475
\(210\) 0 0
\(211\) −7.65829 −0.527218 −0.263609 0.964630i \(-0.584913\pi\)
−0.263609 + 0.964630i \(0.584913\pi\)
\(212\) 0 0
\(213\) −0.933881 −0.0639884
\(214\) 0 0
\(215\) 8.15798 0.556370
\(216\) 0 0
\(217\) 15.1070 1.02553
\(218\) 0 0
\(219\) −6.11727 −0.413367
\(220\) 0 0
\(221\) 6.49732 0.437057
\(222\) 0 0
\(223\) 8.07674 0.540858 0.270429 0.962740i \(-0.412834\pi\)
0.270429 + 0.962740i \(0.412834\pi\)
\(224\) 0 0
\(225\) −2.24154 −0.149436
\(226\) 0 0
\(227\) −0.147080 −0.00976204 −0.00488102 0.999988i \(-0.501554\pi\)
−0.00488102 + 0.999988i \(0.501554\pi\)
\(228\) 0 0
\(229\) 7.49007 0.494958 0.247479 0.968893i \(-0.420398\pi\)
0.247479 + 0.968893i \(0.420398\pi\)
\(230\) 0 0
\(231\) −11.6978 −0.769661
\(232\) 0 0
\(233\) 4.92844 0.322873 0.161436 0.986883i \(-0.448387\pi\)
0.161436 + 0.986883i \(0.448387\pi\)
\(234\) 0 0
\(235\) 0.972250 0.0634226
\(236\) 0 0
\(237\) −14.6499 −0.951613
\(238\) 0 0
\(239\) 22.3298 1.44440 0.722198 0.691687i \(-0.243132\pi\)
0.722198 + 0.691687i \(0.243132\pi\)
\(240\) 0 0
\(241\) 24.4515 1.57506 0.787531 0.616275i \(-0.211359\pi\)
0.787531 + 0.616275i \(0.211359\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −3.64988 −0.233182
\(246\) 0 0
\(247\) −12.6173 −0.802821
\(248\) 0 0
\(249\) −14.4496 −0.915703
\(250\) 0 0
\(251\) 21.0449 1.32834 0.664171 0.747581i \(-0.268785\pi\)
0.664171 + 0.747581i \(0.268785\pi\)
\(252\) 0 0
\(253\) −35.2295 −2.21486
\(254\) 0 0
\(255\) −5.22272 −0.327060
\(256\) 0 0
\(257\) 2.75251 0.171697 0.0858483 0.996308i \(-0.472640\pi\)
0.0858483 + 0.996308i \(0.472640\pi\)
\(258\) 0 0
\(259\) 10.7734 0.669428
\(260\) 0 0
\(261\) 8.96547 0.554949
\(262\) 0 0
\(263\) −13.6221 −0.839974 −0.419987 0.907530i \(-0.637965\pi\)
−0.419987 + 0.907530i \(0.637965\pi\)
\(264\) 0 0
\(265\) −15.0673 −0.925577
\(266\) 0 0
\(267\) 5.02821 0.307721
\(268\) 0 0
\(269\) 14.7203 0.897512 0.448756 0.893654i \(-0.351867\pi\)
0.448756 + 0.893654i \(0.351867\pi\)
\(270\) 0 0
\(271\) 24.6221 1.49569 0.747843 0.663875i \(-0.231089\pi\)
0.747843 + 0.663875i \(0.231089\pi\)
\(272\) 0 0
\(273\) 4.52794 0.274043
\(274\) 0 0
\(275\) 11.9653 0.721533
\(276\) 0 0
\(277\) −9.30852 −0.559295 −0.279647 0.960103i \(-0.590218\pi\)
−0.279647 + 0.960103i \(0.590218\pi\)
\(278\) 0 0
\(279\) −6.89365 −0.412712
\(280\) 0 0
\(281\) 16.6196 0.991439 0.495720 0.868483i \(-0.334904\pi\)
0.495720 + 0.868483i \(0.334904\pi\)
\(282\) 0 0
\(283\) 20.3083 1.20720 0.603601 0.797287i \(-0.293732\pi\)
0.603601 + 0.797287i \(0.293732\pi\)
\(284\) 0 0
\(285\) 10.1421 0.600769
\(286\) 0 0
\(287\) −11.5625 −0.682515
\(288\) 0 0
\(289\) −7.11156 −0.418327
\(290\) 0 0
\(291\) −6.45055 −0.378138
\(292\) 0 0
\(293\) −24.6240 −1.43855 −0.719274 0.694726i \(-0.755526\pi\)
−0.719274 + 0.694726i \(0.755526\pi\)
\(294\) 0 0
\(295\) −23.6771 −1.37853
\(296\) 0 0
\(297\) 5.33796 0.309740
\(298\) 0 0
\(299\) 13.6365 0.788618
\(300\) 0 0
\(301\) −10.7641 −0.620435
\(302\) 0 0
\(303\) −1.19379 −0.0685815
\(304\) 0 0
\(305\) 10.9905 0.629315
\(306\) 0 0
\(307\) −10.4179 −0.594583 −0.297291 0.954787i \(-0.596083\pi\)
−0.297291 + 0.954787i \(0.596083\pi\)
\(308\) 0 0
\(309\) 0.0291429 0.00165788
\(310\) 0 0
\(311\) −1.91872 −0.108801 −0.0544004 0.998519i \(-0.517325\pi\)
−0.0544004 + 0.998519i \(0.517325\pi\)
\(312\) 0 0
\(313\) 1.82382 0.103089 0.0515443 0.998671i \(-0.483586\pi\)
0.0515443 + 0.998671i \(0.483586\pi\)
\(314\) 0 0
\(315\) −3.63968 −0.205073
\(316\) 0 0
\(317\) 3.41306 0.191696 0.0958482 0.995396i \(-0.469444\pi\)
0.0958482 + 0.995396i \(0.469444\pi\)
\(318\) 0 0
\(319\) −47.8574 −2.67950
\(320\) 0 0
\(321\) −9.85598 −0.550107
\(322\) 0 0
\(323\) −19.2026 −1.06846
\(324\) 0 0
\(325\) −4.63146 −0.256907
\(326\) 0 0
\(327\) −2.98381 −0.165005
\(328\) 0 0
\(329\) −1.28285 −0.0707257
\(330\) 0 0
\(331\) 9.04725 0.497282 0.248641 0.968596i \(-0.420016\pi\)
0.248641 + 0.968596i \(0.420016\pi\)
\(332\) 0 0
\(333\) −4.91614 −0.269403
\(334\) 0 0
\(335\) −8.57925 −0.468734
\(336\) 0 0
\(337\) 11.3261 0.616973 0.308486 0.951229i \(-0.400178\pi\)
0.308486 + 0.951229i \(0.400178\pi\)
\(338\) 0 0
\(339\) −17.4015 −0.945118
\(340\) 0 0
\(341\) 36.7981 1.99273
\(342\) 0 0
\(343\) 20.1560 1.08832
\(344\) 0 0
\(345\) −10.9614 −0.590140
\(346\) 0 0
\(347\) 20.7826 1.11567 0.557835 0.829952i \(-0.311632\pi\)
0.557835 + 0.829952i \(0.311632\pi\)
\(348\) 0 0
\(349\) −31.2172 −1.67102 −0.835510 0.549475i \(-0.814828\pi\)
−0.835510 + 0.549475i \(0.814828\pi\)
\(350\) 0 0
\(351\) −2.06619 −0.110285
\(352\) 0 0
\(353\) −0.358336 −0.0190723 −0.00953615 0.999955i \(-0.503035\pi\)
−0.00953615 + 0.999955i \(0.503035\pi\)
\(354\) 0 0
\(355\) 1.55105 0.0823209
\(356\) 0 0
\(357\) 6.89118 0.364720
\(358\) 0 0
\(359\) 4.61015 0.243315 0.121657 0.992572i \(-0.461179\pi\)
0.121657 + 0.992572i \(0.461179\pi\)
\(360\) 0 0
\(361\) 18.2901 0.962635
\(362\) 0 0
\(363\) −17.4938 −0.918189
\(364\) 0 0
\(365\) 10.1599 0.531795
\(366\) 0 0
\(367\) 22.2475 1.16131 0.580654 0.814151i \(-0.302797\pi\)
0.580654 + 0.814151i \(0.302797\pi\)
\(368\) 0 0
\(369\) 5.27622 0.274669
\(370\) 0 0
\(371\) 19.8807 1.03216
\(372\) 0 0
\(373\) 11.6478 0.603101 0.301551 0.953450i \(-0.402496\pi\)
0.301551 + 0.953450i \(0.402496\pi\)
\(374\) 0 0
\(375\) 12.0272 0.621081
\(376\) 0 0
\(377\) 18.5244 0.954054
\(378\) 0 0
\(379\) 29.2261 1.50125 0.750623 0.660731i \(-0.229753\pi\)
0.750623 + 0.660731i \(0.229753\pi\)
\(380\) 0 0
\(381\) −1.66062 −0.0850764
\(382\) 0 0
\(383\) −11.6186 −0.593684 −0.296842 0.954927i \(-0.595934\pi\)
−0.296842 + 0.954927i \(0.595934\pi\)
\(384\) 0 0
\(385\) 19.4285 0.990167
\(386\) 0 0
\(387\) 4.91190 0.249686
\(388\) 0 0
\(389\) −11.4729 −0.581700 −0.290850 0.956769i \(-0.593938\pi\)
−0.290850 + 0.956769i \(0.593938\pi\)
\(390\) 0 0
\(391\) 20.7537 1.04956
\(392\) 0 0
\(393\) −20.1407 −1.01596
\(394\) 0 0
\(395\) 24.3314 1.22425
\(396\) 0 0
\(397\) 32.3119 1.62169 0.810844 0.585263i \(-0.199009\pi\)
0.810844 + 0.585263i \(0.199009\pi\)
\(398\) 0 0
\(399\) −13.3822 −0.669947
\(400\) 0 0
\(401\) 27.0821 1.35241 0.676207 0.736712i \(-0.263622\pi\)
0.676207 + 0.736712i \(0.263622\pi\)
\(402\) 0 0
\(403\) −14.2436 −0.709525
\(404\) 0 0
\(405\) 1.66086 0.0825288
\(406\) 0 0
\(407\) 26.2421 1.30078
\(408\) 0 0
\(409\) −4.54024 −0.224501 −0.112250 0.993680i \(-0.535806\pi\)
−0.112250 + 0.993680i \(0.535806\pi\)
\(410\) 0 0
\(411\) 4.06701 0.200611
\(412\) 0 0
\(413\) 31.2410 1.53727
\(414\) 0 0
\(415\) 23.9987 1.17805
\(416\) 0 0
\(417\) 13.8088 0.676222
\(418\) 0 0
\(419\) 2.64005 0.128975 0.0644874 0.997919i \(-0.479459\pi\)
0.0644874 + 0.997919i \(0.479459\pi\)
\(420\) 0 0
\(421\) 6.17913 0.301153 0.150576 0.988598i \(-0.451887\pi\)
0.150576 + 0.988598i \(0.451887\pi\)
\(422\) 0 0
\(423\) 0.585390 0.0284626
\(424\) 0 0
\(425\) −7.04873 −0.341914
\(426\) 0 0
\(427\) −14.5016 −0.701779
\(428\) 0 0
\(429\) 11.0293 0.532497
\(430\) 0 0
\(431\) −24.9296 −1.20081 −0.600407 0.799694i \(-0.704995\pi\)
−0.600407 + 0.799694i \(0.704995\pi\)
\(432\) 0 0
\(433\) −33.2764 −1.59916 −0.799582 0.600557i \(-0.794945\pi\)
−0.799582 + 0.600557i \(0.794945\pi\)
\(434\) 0 0
\(435\) −14.8904 −0.713940
\(436\) 0 0
\(437\) −40.3021 −1.92791
\(438\) 0 0
\(439\) −9.63803 −0.459998 −0.229999 0.973191i \(-0.573872\pi\)
−0.229999 + 0.973191i \(0.573872\pi\)
\(440\) 0 0
\(441\) −2.19758 −0.104647
\(442\) 0 0
\(443\) 0.0899656 0.00427439 0.00213720 0.999998i \(-0.499320\pi\)
0.00213720 + 0.999998i \(0.499320\pi\)
\(444\) 0 0
\(445\) −8.35115 −0.395882
\(446\) 0 0
\(447\) 16.0931 0.761179
\(448\) 0 0
\(449\) −35.5182 −1.67621 −0.838105 0.545509i \(-0.816336\pi\)
−0.838105 + 0.545509i \(0.816336\pi\)
\(450\) 0 0
\(451\) −28.1643 −1.32620
\(452\) 0 0
\(453\) 4.44235 0.208720
\(454\) 0 0
\(455\) −7.52027 −0.352556
\(456\) 0 0
\(457\) −1.84536 −0.0863224 −0.0431612 0.999068i \(-0.513743\pi\)
−0.0431612 + 0.999068i \(0.513743\pi\)
\(458\) 0 0
\(459\) −3.14459 −0.146777
\(460\) 0 0
\(461\) 8.49076 0.395454 0.197727 0.980257i \(-0.436644\pi\)
0.197727 + 0.980257i \(0.436644\pi\)
\(462\) 0 0
\(463\) 17.7515 0.824980 0.412490 0.910962i \(-0.364659\pi\)
0.412490 + 0.910962i \(0.364659\pi\)
\(464\) 0 0
\(465\) 11.4494 0.530953
\(466\) 0 0
\(467\) 21.8382 1.01055 0.505277 0.862957i \(-0.331390\pi\)
0.505277 + 0.862957i \(0.331390\pi\)
\(468\) 0 0
\(469\) 11.3200 0.522709
\(470\) 0 0
\(471\) −13.9994 −0.645059
\(472\) 0 0
\(473\) −26.2196 −1.20558
\(474\) 0 0
\(475\) 13.6881 0.628054
\(476\) 0 0
\(477\) −9.07199 −0.415378
\(478\) 0 0
\(479\) −10.5567 −0.482346 −0.241173 0.970482i \(-0.577532\pi\)
−0.241173 + 0.970482i \(0.577532\pi\)
\(480\) 0 0
\(481\) −10.1577 −0.463150
\(482\) 0 0
\(483\) 14.4631 0.658094
\(484\) 0 0
\(485\) 10.7135 0.486473
\(486\) 0 0
\(487\) 38.4461 1.74216 0.871079 0.491143i \(-0.163421\pi\)
0.871079 + 0.491143i \(0.163421\pi\)
\(488\) 0 0
\(489\) −19.7013 −0.890925
\(490\) 0 0
\(491\) 23.5555 1.06305 0.531523 0.847044i \(-0.321620\pi\)
0.531523 + 0.847044i \(0.321620\pi\)
\(492\) 0 0
\(493\) 28.1927 1.26974
\(494\) 0 0
\(495\) −8.86561 −0.398480
\(496\) 0 0
\(497\) −2.04655 −0.0918001
\(498\) 0 0
\(499\) −9.38552 −0.420153 −0.210077 0.977685i \(-0.567371\pi\)
−0.210077 + 0.977685i \(0.567371\pi\)
\(500\) 0 0
\(501\) −3.46294 −0.154713
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 1.98272 0.0882299
\(506\) 0 0
\(507\) 8.73085 0.387751
\(508\) 0 0
\(509\) −25.7744 −1.14243 −0.571216 0.820800i \(-0.693528\pi\)
−0.571216 + 0.820800i \(0.693528\pi\)
\(510\) 0 0
\(511\) −13.4056 −0.593031
\(512\) 0 0
\(513\) 6.10656 0.269611
\(514\) 0 0
\(515\) −0.0484022 −0.00213286
\(516\) 0 0
\(517\) −3.12479 −0.137428
\(518\) 0 0
\(519\) −20.4526 −0.897770
\(520\) 0 0
\(521\) 24.0801 1.05497 0.527485 0.849565i \(-0.323135\pi\)
0.527485 + 0.849565i \(0.323135\pi\)
\(522\) 0 0
\(523\) −6.63721 −0.290225 −0.145112 0.989415i \(-0.546354\pi\)
−0.145112 + 0.989415i \(0.546354\pi\)
\(524\) 0 0
\(525\) −4.91221 −0.214387
\(526\) 0 0
\(527\) −21.6777 −0.944295
\(528\) 0 0
\(529\) 20.5575 0.893804
\(530\) 0 0
\(531\) −14.2559 −0.618653
\(532\) 0 0
\(533\) 10.9017 0.472204
\(534\) 0 0
\(535\) 16.3694 0.707711
\(536\) 0 0
\(537\) 2.85284 0.123109
\(538\) 0 0
\(539\) 11.7306 0.505273
\(540\) 0 0
\(541\) 12.9536 0.556920 0.278460 0.960448i \(-0.410176\pi\)
0.278460 + 0.960448i \(0.410176\pi\)
\(542\) 0 0
\(543\) 24.3472 1.04484
\(544\) 0 0
\(545\) 4.95569 0.212279
\(546\) 0 0
\(547\) −2.34331 −0.100193 −0.0500963 0.998744i \(-0.515953\pi\)
−0.0500963 + 0.998744i \(0.515953\pi\)
\(548\) 0 0
\(549\) 6.61736 0.282422
\(550\) 0 0
\(551\) −54.7482 −2.33235
\(552\) 0 0
\(553\) −32.1044 −1.36522
\(554\) 0 0
\(555\) 8.16501 0.346586
\(556\) 0 0
\(557\) −5.61332 −0.237844 −0.118922 0.992904i \(-0.537944\pi\)
−0.118922 + 0.992904i \(0.537944\pi\)
\(558\) 0 0
\(559\) 10.1489 0.429254
\(560\) 0 0
\(561\) 16.7857 0.708693
\(562\) 0 0
\(563\) −12.7429 −0.537051 −0.268526 0.963273i \(-0.586536\pi\)
−0.268526 + 0.963273i \(0.586536\pi\)
\(564\) 0 0
\(565\) 28.9014 1.21589
\(566\) 0 0
\(567\) −2.19144 −0.0920319
\(568\) 0 0
\(569\) 17.8081 0.746556 0.373278 0.927719i \(-0.378234\pi\)
0.373278 + 0.927719i \(0.378234\pi\)
\(570\) 0 0
\(571\) −8.87762 −0.371517 −0.185758 0.982595i \(-0.559474\pi\)
−0.185758 + 0.982595i \(0.559474\pi\)
\(572\) 0 0
\(573\) 13.5918 0.567804
\(574\) 0 0
\(575\) −14.7938 −0.616942
\(576\) 0 0
\(577\) −16.2463 −0.676343 −0.338171 0.941085i \(-0.609808\pi\)
−0.338171 + 0.941085i \(0.609808\pi\)
\(578\) 0 0
\(579\) −7.53334 −0.313075
\(580\) 0 0
\(581\) −31.6654 −1.31370
\(582\) 0 0
\(583\) 48.4259 2.00560
\(584\) 0 0
\(585\) 3.43166 0.141881
\(586\) 0 0
\(587\) 11.3685 0.469230 0.234615 0.972088i \(-0.424617\pi\)
0.234615 + 0.972088i \(0.424617\pi\)
\(588\) 0 0
\(589\) 42.0965 1.73456
\(590\) 0 0
\(591\) 14.1311 0.581277
\(592\) 0 0
\(593\) 9.05429 0.371815 0.185908 0.982567i \(-0.440477\pi\)
0.185908 + 0.982567i \(0.440477\pi\)
\(594\) 0 0
\(595\) −11.4453 −0.469211
\(596\) 0 0
\(597\) −22.7899 −0.932727
\(598\) 0 0
\(599\) −10.1251 −0.413699 −0.206850 0.978373i \(-0.566321\pi\)
−0.206850 + 0.978373i \(0.566321\pi\)
\(600\) 0 0
\(601\) 20.0267 0.816905 0.408453 0.912780i \(-0.366069\pi\)
0.408453 + 0.912780i \(0.366069\pi\)
\(602\) 0 0
\(603\) −5.16554 −0.210357
\(604\) 0 0
\(605\) 29.0548 1.18125
\(606\) 0 0
\(607\) −8.57996 −0.348250 −0.174125 0.984724i \(-0.555710\pi\)
−0.174125 + 0.984724i \(0.555710\pi\)
\(608\) 0 0
\(609\) 19.6473 0.796149
\(610\) 0 0
\(611\) 1.20953 0.0489322
\(612\) 0 0
\(613\) 42.4875 1.71605 0.858027 0.513605i \(-0.171690\pi\)
0.858027 + 0.513605i \(0.171690\pi\)
\(614\) 0 0
\(615\) −8.76307 −0.353361
\(616\) 0 0
\(617\) −15.4029 −0.620098 −0.310049 0.950721i \(-0.600345\pi\)
−0.310049 + 0.950721i \(0.600345\pi\)
\(618\) 0 0
\(619\) −12.4638 −0.500962 −0.250481 0.968122i \(-0.580589\pi\)
−0.250481 + 0.968122i \(0.580589\pi\)
\(620\) 0 0
\(621\) −6.59981 −0.264841
\(622\) 0 0
\(623\) 11.0190 0.441468
\(624\) 0 0
\(625\) −8.76777 −0.350711
\(626\) 0 0
\(627\) −32.5966 −1.30178
\(628\) 0 0
\(629\) −15.4592 −0.616400
\(630\) 0 0
\(631\) 16.5054 0.657068 0.328534 0.944492i \(-0.393445\pi\)
0.328534 + 0.944492i \(0.393445\pi\)
\(632\) 0 0
\(633\) 7.65829 0.304390
\(634\) 0 0
\(635\) 2.75806 0.109450
\(636\) 0 0
\(637\) −4.54062 −0.179906
\(638\) 0 0
\(639\) 0.933881 0.0369437
\(640\) 0 0
\(641\) −39.5686 −1.56287 −0.781434 0.623988i \(-0.785511\pi\)
−0.781434 + 0.623988i \(0.785511\pi\)
\(642\) 0 0
\(643\) 4.00236 0.157838 0.0789188 0.996881i \(-0.474853\pi\)
0.0789188 + 0.996881i \(0.474853\pi\)
\(644\) 0 0
\(645\) −8.15798 −0.321220
\(646\) 0 0
\(647\) 39.8934 1.56837 0.784185 0.620527i \(-0.213081\pi\)
0.784185 + 0.620527i \(0.213081\pi\)
\(648\) 0 0
\(649\) 76.0975 2.98709
\(650\) 0 0
\(651\) −15.1070 −0.592092
\(652\) 0 0
\(653\) −31.3492 −1.22679 −0.613395 0.789776i \(-0.710197\pi\)
−0.613395 + 0.789776i \(0.710197\pi\)
\(654\) 0 0
\(655\) 33.4508 1.30703
\(656\) 0 0
\(657\) 6.11727 0.238658
\(658\) 0 0
\(659\) −8.50681 −0.331378 −0.165689 0.986178i \(-0.552985\pi\)
−0.165689 + 0.986178i \(0.552985\pi\)
\(660\) 0 0
\(661\) −35.1308 −1.36643 −0.683214 0.730218i \(-0.739419\pi\)
−0.683214 + 0.730218i \(0.739419\pi\)
\(662\) 0 0
\(663\) −6.49732 −0.252335
\(664\) 0 0
\(665\) 22.2259 0.861884
\(666\) 0 0
\(667\) 59.1704 2.29109
\(668\) 0 0
\(669\) −8.07674 −0.312265
\(670\) 0 0
\(671\) −35.3232 −1.36364
\(672\) 0 0
\(673\) 27.9890 1.07889 0.539447 0.842019i \(-0.318633\pi\)
0.539447 + 0.842019i \(0.318633\pi\)
\(674\) 0 0
\(675\) 2.24154 0.0862770
\(676\) 0 0
\(677\) −21.9681 −0.844303 −0.422152 0.906525i \(-0.638725\pi\)
−0.422152 + 0.906525i \(0.638725\pi\)
\(678\) 0 0
\(679\) −14.1360 −0.542490
\(680\) 0 0
\(681\) 0.147080 0.00563612
\(682\) 0 0
\(683\) 42.2488 1.61661 0.808303 0.588767i \(-0.200386\pi\)
0.808303 + 0.588767i \(0.200386\pi\)
\(684\) 0 0
\(685\) −6.75474 −0.258085
\(686\) 0 0
\(687\) −7.49007 −0.285764
\(688\) 0 0
\(689\) −18.7445 −0.714107
\(690\) 0 0
\(691\) −11.7773 −0.448030 −0.224015 0.974586i \(-0.571916\pi\)
−0.224015 + 0.974586i \(0.571916\pi\)
\(692\) 0 0
\(693\) 11.6978 0.444364
\(694\) 0 0
\(695\) −22.9345 −0.869957
\(696\) 0 0
\(697\) 16.5915 0.628450
\(698\) 0 0
\(699\) −4.92844 −0.186411
\(700\) 0 0
\(701\) 35.0699 1.32457 0.662286 0.749251i \(-0.269586\pi\)
0.662286 + 0.749251i \(0.269586\pi\)
\(702\) 0 0
\(703\) 30.0207 1.13225
\(704\) 0 0
\(705\) −0.972250 −0.0366171
\(706\) 0 0
\(707\) −2.61612 −0.0983895
\(708\) 0 0
\(709\) −11.8879 −0.446460 −0.223230 0.974766i \(-0.571660\pi\)
−0.223230 + 0.974766i \(0.571660\pi\)
\(710\) 0 0
\(711\) 14.6499 0.549414
\(712\) 0 0
\(713\) −45.4968 −1.70387
\(714\) 0 0
\(715\) −18.3180 −0.685056
\(716\) 0 0
\(717\) −22.3298 −0.833922
\(718\) 0 0
\(719\) −41.5011 −1.54773 −0.773864 0.633351i \(-0.781679\pi\)
−0.773864 + 0.633351i \(0.781679\pi\)
\(720\) 0 0
\(721\) 0.0638649 0.00237845
\(722\) 0 0
\(723\) −24.4515 −0.909363
\(724\) 0 0
\(725\) −20.0965 −0.746365
\(726\) 0 0
\(727\) −4.63564 −0.171926 −0.0859631 0.996298i \(-0.527397\pi\)
−0.0859631 + 0.996298i \(0.527397\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 15.4459 0.571288
\(732\) 0 0
\(733\) −33.9082 −1.25243 −0.626214 0.779651i \(-0.715396\pi\)
−0.626214 + 0.779651i \(0.715396\pi\)
\(734\) 0 0
\(735\) 3.64988 0.134628
\(736\) 0 0
\(737\) 27.5735 1.01568
\(738\) 0 0
\(739\) 44.4784 1.63617 0.818083 0.575100i \(-0.195037\pi\)
0.818083 + 0.575100i \(0.195037\pi\)
\(740\) 0 0
\(741\) 12.6173 0.463509
\(742\) 0 0
\(743\) 52.3349 1.91998 0.959991 0.280029i \(-0.0903442\pi\)
0.959991 + 0.280029i \(0.0903442\pi\)
\(744\) 0 0
\(745\) −26.7285 −0.979255
\(746\) 0 0
\(747\) 14.4496 0.528681
\(748\) 0 0
\(749\) −21.5988 −0.789204
\(750\) 0 0
\(751\) −12.4116 −0.452907 −0.226453 0.974022i \(-0.572713\pi\)
−0.226453 + 0.974022i \(0.572713\pi\)
\(752\) 0 0
\(753\) −21.0449 −0.766919
\(754\) 0 0
\(755\) −7.37813 −0.268518
\(756\) 0 0
\(757\) 34.2759 1.24578 0.622889 0.782310i \(-0.285959\pi\)
0.622889 + 0.782310i \(0.285959\pi\)
\(758\) 0 0
\(759\) 35.2295 1.27875
\(760\) 0 0
\(761\) 54.8836 1.98953 0.994764 0.102195i \(-0.0325867\pi\)
0.994764 + 0.102195i \(0.0325867\pi\)
\(762\) 0 0
\(763\) −6.53885 −0.236722
\(764\) 0 0
\(765\) 5.22272 0.188828
\(766\) 0 0
\(767\) −29.4554 −1.06357
\(768\) 0 0
\(769\) 41.9900 1.51420 0.757100 0.653299i \(-0.226616\pi\)
0.757100 + 0.653299i \(0.226616\pi\)
\(770\) 0 0
\(771\) −2.75251 −0.0991291
\(772\) 0 0
\(773\) 4.70881 0.169364 0.0846821 0.996408i \(-0.473013\pi\)
0.0846821 + 0.996408i \(0.473013\pi\)
\(774\) 0 0
\(775\) 15.4524 0.555067
\(776\) 0 0
\(777\) −10.7734 −0.386494
\(778\) 0 0
\(779\) −32.2196 −1.15439
\(780\) 0 0
\(781\) −4.98502 −0.178378
\(782\) 0 0
\(783\) −8.96547 −0.320400
\(784\) 0 0
\(785\) 23.2511 0.829866
\(786\) 0 0
\(787\) −10.0114 −0.356869 −0.178434 0.983952i \(-0.557103\pi\)
−0.178434 + 0.983952i \(0.557103\pi\)
\(788\) 0 0
\(789\) 13.6221 0.484959
\(790\) 0 0
\(791\) −38.1343 −1.35590
\(792\) 0 0
\(793\) 13.6727 0.485533
\(794\) 0 0
\(795\) 15.0673 0.534382
\(796\) 0 0
\(797\) −18.9405 −0.670906 −0.335453 0.942057i \(-0.608889\pi\)
−0.335453 + 0.942057i \(0.608889\pi\)
\(798\) 0 0
\(799\) 1.84081 0.0651232
\(800\) 0 0
\(801\) −5.02821 −0.177663
\(802\) 0 0
\(803\) −32.6538 −1.15233
\(804\) 0 0
\(805\) −24.0212 −0.846636
\(806\) 0 0
\(807\) −14.7203 −0.518179
\(808\) 0 0
\(809\) 38.9960 1.37103 0.685513 0.728060i \(-0.259578\pi\)
0.685513 + 0.728060i \(0.259578\pi\)
\(810\) 0 0
\(811\) 14.6649 0.514954 0.257477 0.966284i \(-0.417109\pi\)
0.257477 + 0.966284i \(0.417109\pi\)
\(812\) 0 0
\(813\) −24.6221 −0.863535
\(814\) 0 0
\(815\) 32.7212 1.14617
\(816\) 0 0
\(817\) −29.9948 −1.04939
\(818\) 0 0
\(819\) −4.52794 −0.158219
\(820\) 0 0
\(821\) 34.7644 1.21329 0.606644 0.794974i \(-0.292515\pi\)
0.606644 + 0.794974i \(0.292515\pi\)
\(822\) 0 0
\(823\) 5.09906 0.177742 0.0888710 0.996043i \(-0.471674\pi\)
0.0888710 + 0.996043i \(0.471674\pi\)
\(824\) 0 0
\(825\) −11.9653 −0.416577
\(826\) 0 0
\(827\) −51.4953 −1.79067 −0.895333 0.445397i \(-0.853063\pi\)
−0.895333 + 0.445397i \(0.853063\pi\)
\(828\) 0 0
\(829\) −25.1193 −0.872431 −0.436216 0.899842i \(-0.643681\pi\)
−0.436216 + 0.899842i \(0.643681\pi\)
\(830\) 0 0
\(831\) 9.30852 0.322909
\(832\) 0 0
\(833\) −6.91049 −0.239434
\(834\) 0 0
\(835\) 5.75146 0.199037
\(836\) 0 0
\(837\) 6.89365 0.238280
\(838\) 0 0
\(839\) −16.6231 −0.573894 −0.286947 0.957947i \(-0.592640\pi\)
−0.286947 + 0.957947i \(0.592640\pi\)
\(840\) 0 0
\(841\) 51.3797 1.77171
\(842\) 0 0
\(843\) −16.6196 −0.572408
\(844\) 0 0
\(845\) −14.5007 −0.498840
\(846\) 0 0
\(847\) −38.3368 −1.31727
\(848\) 0 0
\(849\) −20.3083 −0.696978
\(850\) 0 0
\(851\) −32.4456 −1.11222
\(852\) 0 0
\(853\) 29.6366 1.01474 0.507369 0.861729i \(-0.330618\pi\)
0.507369 + 0.861729i \(0.330618\pi\)
\(854\) 0 0
\(855\) −10.1421 −0.346854
\(856\) 0 0
\(857\) −48.9547 −1.67226 −0.836131 0.548530i \(-0.815188\pi\)
−0.836131 + 0.548530i \(0.815188\pi\)
\(858\) 0 0
\(859\) 45.1888 1.54182 0.770911 0.636943i \(-0.219801\pi\)
0.770911 + 0.636943i \(0.219801\pi\)
\(860\) 0 0
\(861\) 11.5625 0.394050
\(862\) 0 0
\(863\) −40.0059 −1.36182 −0.680908 0.732369i \(-0.738415\pi\)
−0.680908 + 0.732369i \(0.738415\pi\)
\(864\) 0 0
\(865\) 33.9689 1.15498
\(866\) 0 0
\(867\) 7.11156 0.241521
\(868\) 0 0
\(869\) −78.2006 −2.65277
\(870\) 0 0
\(871\) −10.6730 −0.361641
\(872\) 0 0
\(873\) 6.45055 0.218318
\(874\) 0 0
\(875\) 26.3569 0.891026
\(876\) 0 0
\(877\) −17.2538 −0.582618 −0.291309 0.956629i \(-0.594091\pi\)
−0.291309 + 0.956629i \(0.594091\pi\)
\(878\) 0 0
\(879\) 24.6240 0.830547
\(880\) 0 0
\(881\) −42.0815 −1.41776 −0.708881 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(882\) 0 0
\(883\) −31.7054 −1.06697 −0.533487 0.845809i \(-0.679118\pi\)
−0.533487 + 0.845809i \(0.679118\pi\)
\(884\) 0 0
\(885\) 23.6771 0.795896
\(886\) 0 0
\(887\) −24.0799 −0.808524 −0.404262 0.914643i \(-0.632472\pi\)
−0.404262 + 0.914643i \(0.632472\pi\)
\(888\) 0 0
\(889\) −3.63916 −0.122054
\(890\) 0 0
\(891\) −5.33796 −0.178828
\(892\) 0 0
\(893\) −3.57472 −0.119623
\(894\) 0 0
\(895\) −4.73816 −0.158379
\(896\) 0 0
\(897\) −13.6365 −0.455309
\(898\) 0 0
\(899\) −61.8049 −2.06131
\(900\) 0 0
\(901\) −28.5277 −0.950395
\(902\) 0 0
\(903\) 10.7641 0.358208
\(904\) 0 0
\(905\) −40.4374 −1.34418
\(906\) 0 0
\(907\) −14.3179 −0.475417 −0.237708 0.971337i \(-0.576396\pi\)
−0.237708 + 0.971337i \(0.576396\pi\)
\(908\) 0 0
\(909\) 1.19379 0.0395956
\(910\) 0 0
\(911\) 14.9490 0.495283 0.247641 0.968852i \(-0.420345\pi\)
0.247641 + 0.968852i \(0.420345\pi\)
\(912\) 0 0
\(913\) −77.1312 −2.55267
\(914\) 0 0
\(915\) −10.9905 −0.363335
\(916\) 0 0
\(917\) −44.1371 −1.45753
\(918\) 0 0
\(919\) 17.8620 0.589213 0.294606 0.955619i \(-0.404811\pi\)
0.294606 + 0.955619i \(0.404811\pi\)
\(920\) 0 0
\(921\) 10.4179 0.343283
\(922\) 0 0
\(923\) 1.92958 0.0635128
\(924\) 0 0
\(925\) 11.0197 0.362326
\(926\) 0 0
\(927\) −0.0291429 −0.000957177 0
\(928\) 0 0
\(929\) −25.6229 −0.840660 −0.420330 0.907371i \(-0.638086\pi\)
−0.420330 + 0.907371i \(0.638086\pi\)
\(930\) 0 0
\(931\) 13.4197 0.439812
\(932\) 0 0
\(933\) 1.91872 0.0628162
\(934\) 0 0
\(935\) −27.8787 −0.911731
\(936\) 0 0
\(937\) −32.0701 −1.04769 −0.523843 0.851815i \(-0.675502\pi\)
−0.523843 + 0.851815i \(0.675502\pi\)
\(938\) 0 0
\(939\) −1.82382 −0.0595182
\(940\) 0 0
\(941\) 49.7470 1.62171 0.810853 0.585250i \(-0.199004\pi\)
0.810853 + 0.585250i \(0.199004\pi\)
\(942\) 0 0
\(943\) 34.8221 1.13396
\(944\) 0 0
\(945\) 3.63968 0.118399
\(946\) 0 0
\(947\) −1.22332 −0.0397525 −0.0198762 0.999802i \(-0.506327\pi\)
−0.0198762 + 0.999802i \(0.506327\pi\)
\(948\) 0 0
\(949\) 12.6395 0.410294
\(950\) 0 0
\(951\) −3.41306 −0.110676
\(952\) 0 0
\(953\) −39.0873 −1.26616 −0.633082 0.774085i \(-0.718210\pi\)
−0.633082 + 0.774085i \(0.718210\pi\)
\(954\) 0 0
\(955\) −22.5740 −0.730478
\(956\) 0 0
\(957\) 47.8574 1.54701
\(958\) 0 0
\(959\) 8.91262 0.287804
\(960\) 0 0
\(961\) 16.5225 0.532982
\(962\) 0 0
\(963\) 9.85598 0.317605
\(964\) 0 0
\(965\) 12.5118 0.402770
\(966\) 0 0
\(967\) −13.7425 −0.441931 −0.220965 0.975282i \(-0.570921\pi\)
−0.220965 + 0.975282i \(0.570921\pi\)
\(968\) 0 0
\(969\) 19.2026 0.616877
\(970\) 0 0
\(971\) −35.1756 −1.12884 −0.564419 0.825488i \(-0.690900\pi\)
−0.564419 + 0.825488i \(0.690900\pi\)
\(972\) 0 0
\(973\) 30.2613 0.970132
\(974\) 0 0
\(975\) 4.63146 0.148325
\(976\) 0 0
\(977\) −10.3306 −0.330504 −0.165252 0.986251i \(-0.552844\pi\)
−0.165252 + 0.986251i \(0.552844\pi\)
\(978\) 0 0
\(979\) 26.8404 0.857822
\(980\) 0 0
\(981\) 2.98381 0.0952657
\(982\) 0 0
\(983\) 6.60170 0.210561 0.105281 0.994443i \(-0.466426\pi\)
0.105281 + 0.994443i \(0.466426\pi\)
\(984\) 0 0
\(985\) −23.4698 −0.747810
\(986\) 0 0
\(987\) 1.28285 0.0408335
\(988\) 0 0
\(989\) 32.4176 1.03082
\(990\) 0 0
\(991\) −0.878981 −0.0279217 −0.0139609 0.999903i \(-0.504444\pi\)
−0.0139609 + 0.999903i \(0.504444\pi\)
\(992\) 0 0
\(993\) −9.04725 −0.287106
\(994\) 0 0
\(995\) 37.8508 1.19995
\(996\) 0 0
\(997\) 16.8322 0.533081 0.266541 0.963824i \(-0.414119\pi\)
0.266541 + 0.963824i \(0.414119\pi\)
\(998\) 0 0
\(999\) 4.91614 0.155540
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 \(a_p\))