Properties

Label 6036.2.a.i.1.6
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 1.6
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -2.57233 q^{5} -0.722776 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -2.57233 q^{5} -0.722776 q^{7} +1.00000 q^{9} -1.16379 q^{11} +2.87974 q^{13} +2.57233 q^{15} +6.88201 q^{17} +0.0742278 q^{19} +0.722776 q^{21} +6.64876 q^{23} +1.61688 q^{25} -1.00000 q^{27} -8.36633 q^{29} -6.34718 q^{31} +1.16379 q^{33} +1.85922 q^{35} -4.23390 q^{37} -2.87974 q^{39} +1.08057 q^{41} +3.62336 q^{43} -2.57233 q^{45} -1.46403 q^{47} -6.47759 q^{49} -6.88201 q^{51} +9.12358 q^{53} +2.99366 q^{55} -0.0742278 q^{57} -4.35277 q^{59} +5.87947 q^{61} -0.722776 q^{63} -7.40763 q^{65} +0.793907 q^{67} -6.64876 q^{69} -11.3782 q^{71} +9.16804 q^{73} -1.61688 q^{75} +0.841163 q^{77} -6.61559 q^{79} +1.00000 q^{81} -9.56912 q^{83} -17.7028 q^{85} +8.36633 q^{87} -9.56938 q^{89} -2.08140 q^{91} +6.34718 q^{93} -0.190938 q^{95} +1.48629 q^{97} -1.16379 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26q - 26q^{3} + 6q^{5} + 5q^{7} + 26q^{9} + O(q^{10}) \) \( 26q - 26q^{3} + 6q^{5} + 5q^{7} + 26q^{9} - 11q^{11} + 13q^{13} - 6q^{15} + 12q^{17} - q^{19} - 5q^{21} - 22q^{23} + 48q^{25} - 26q^{27} + 6q^{29} + 19q^{31} + 11q^{33} - 21q^{35} + 20q^{37} - 13q^{39} + 25q^{41} + 4q^{43} + 6q^{45} + 8q^{47} + 67q^{49} - 12q^{51} - 5q^{53} + 20q^{55} + q^{57} - 18q^{59} + 43q^{61} + 5q^{63} + 41q^{65} + 5q^{67} + 22q^{69} - q^{71} + 22q^{73} - 48q^{75} + 23q^{77} + 16q^{79} + 26q^{81} - 19q^{83} + 29q^{85} - 6q^{87} + 49q^{89} - 13q^{91} - 19q^{93} - 26q^{95} + 25q^{97} - 11q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −2.57233 −1.15038 −0.575191 0.818019i \(-0.695072\pi\)
−0.575191 + 0.818019i \(0.695072\pi\)
\(6\) 0 0
\(7\) −0.722776 −0.273184 −0.136592 0.990627i \(-0.543615\pi\)
−0.136592 + 0.990627i \(0.543615\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.16379 −0.350897 −0.175449 0.984489i \(-0.556138\pi\)
−0.175449 + 0.984489i \(0.556138\pi\)
\(12\) 0 0
\(13\) 2.87974 0.798695 0.399347 0.916800i \(-0.369237\pi\)
0.399347 + 0.916800i \(0.369237\pi\)
\(14\) 0 0
\(15\) 2.57233 0.664173
\(16\) 0 0
\(17\) 6.88201 1.66913 0.834566 0.550908i \(-0.185718\pi\)
0.834566 + 0.550908i \(0.185718\pi\)
\(18\) 0 0
\(19\) 0.0742278 0.0170290 0.00851451 0.999964i \(-0.497290\pi\)
0.00851451 + 0.999964i \(0.497290\pi\)
\(20\) 0 0
\(21\) 0.722776 0.157723
\(22\) 0 0
\(23\) 6.64876 1.38636 0.693181 0.720763i \(-0.256208\pi\)
0.693181 + 0.720763i \(0.256208\pi\)
\(24\) 0 0
\(25\) 1.61688 0.323377
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.36633 −1.55359 −0.776794 0.629755i \(-0.783155\pi\)
−0.776794 + 0.629755i \(0.783155\pi\)
\(30\) 0 0
\(31\) −6.34718 −1.13999 −0.569993 0.821649i \(-0.693054\pi\)
−0.569993 + 0.821649i \(0.693054\pi\)
\(32\) 0 0
\(33\) 1.16379 0.202591
\(34\) 0 0
\(35\) 1.85922 0.314265
\(36\) 0 0
\(37\) −4.23390 −0.696049 −0.348024 0.937486i \(-0.613147\pi\)
−0.348024 + 0.937486i \(0.613147\pi\)
\(38\) 0 0
\(39\) −2.87974 −0.461127
\(40\) 0 0
\(41\) 1.08057 0.168757 0.0843785 0.996434i \(-0.473110\pi\)
0.0843785 + 0.996434i \(0.473110\pi\)
\(42\) 0 0
\(43\) 3.62336 0.552557 0.276278 0.961078i \(-0.410899\pi\)
0.276278 + 0.961078i \(0.410899\pi\)
\(44\) 0 0
\(45\) −2.57233 −0.383460
\(46\) 0 0
\(47\) −1.46403 −0.213550 −0.106775 0.994283i \(-0.534052\pi\)
−0.106775 + 0.994283i \(0.534052\pi\)
\(48\) 0 0
\(49\) −6.47759 −0.925371
\(50\) 0 0
\(51\) −6.88201 −0.963674
\(52\) 0 0
\(53\) 9.12358 1.25322 0.626610 0.779333i \(-0.284442\pi\)
0.626610 + 0.779333i \(0.284442\pi\)
\(54\) 0 0
\(55\) 2.99366 0.403666
\(56\) 0 0
\(57\) −0.0742278 −0.00983171
\(58\) 0 0
\(59\) −4.35277 −0.566682 −0.283341 0.959019i \(-0.591443\pi\)
−0.283341 + 0.959019i \(0.591443\pi\)
\(60\) 0 0
\(61\) 5.87947 0.752789 0.376395 0.926459i \(-0.377164\pi\)
0.376395 + 0.926459i \(0.377164\pi\)
\(62\) 0 0
\(63\) −0.722776 −0.0910613
\(64\) 0 0
\(65\) −7.40763 −0.918804
\(66\) 0 0
\(67\) 0.793907 0.0969912 0.0484956 0.998823i \(-0.484557\pi\)
0.0484956 + 0.998823i \(0.484557\pi\)
\(68\) 0 0
\(69\) −6.64876 −0.800417
\(70\) 0 0
\(71\) −11.3782 −1.35035 −0.675174 0.737658i \(-0.735932\pi\)
−0.675174 + 0.737658i \(0.735932\pi\)
\(72\) 0 0
\(73\) 9.16804 1.07304 0.536519 0.843888i \(-0.319739\pi\)
0.536519 + 0.843888i \(0.319739\pi\)
\(74\) 0 0
\(75\) −1.61688 −0.186702
\(76\) 0 0
\(77\) 0.841163 0.0958594
\(78\) 0 0
\(79\) −6.61559 −0.744313 −0.372156 0.928170i \(-0.621381\pi\)
−0.372156 + 0.928170i \(0.621381\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −9.56912 −1.05035 −0.525174 0.850995i \(-0.676000\pi\)
−0.525174 + 0.850995i \(0.676000\pi\)
\(84\) 0 0
\(85\) −17.7028 −1.92014
\(86\) 0 0
\(87\) 8.36633 0.896965
\(88\) 0 0
\(89\) −9.56938 −1.01435 −0.507176 0.861842i \(-0.669311\pi\)
−0.507176 + 0.861842i \(0.669311\pi\)
\(90\) 0 0
\(91\) −2.08140 −0.218190
\(92\) 0 0
\(93\) 6.34718 0.658172
\(94\) 0 0
\(95\) −0.190938 −0.0195899
\(96\) 0 0
\(97\) 1.48629 0.150910 0.0754550 0.997149i \(-0.475959\pi\)
0.0754550 + 0.997149i \(0.475959\pi\)
\(98\) 0 0
\(99\) −1.16379 −0.116966
\(100\) 0 0
\(101\) −7.12534 −0.708998 −0.354499 0.935056i \(-0.615349\pi\)
−0.354499 + 0.935056i \(0.615349\pi\)
\(102\) 0 0
\(103\) 15.8664 1.56336 0.781681 0.623678i \(-0.214363\pi\)
0.781681 + 0.623678i \(0.214363\pi\)
\(104\) 0 0
\(105\) −1.85922 −0.181441
\(106\) 0 0
\(107\) −11.7466 −1.13559 −0.567793 0.823171i \(-0.692203\pi\)
−0.567793 + 0.823171i \(0.692203\pi\)
\(108\) 0 0
\(109\) 6.74173 0.645741 0.322870 0.946443i \(-0.395352\pi\)
0.322870 + 0.946443i \(0.395352\pi\)
\(110\) 0 0
\(111\) 4.23390 0.401864
\(112\) 0 0
\(113\) 10.6407 1.00099 0.500494 0.865740i \(-0.333152\pi\)
0.500494 + 0.865740i \(0.333152\pi\)
\(114\) 0 0
\(115\) −17.1028 −1.59485
\(116\) 0 0
\(117\) 2.87974 0.266232
\(118\) 0 0
\(119\) −4.97415 −0.455980
\(120\) 0 0
\(121\) −9.64558 −0.876871
\(122\) 0 0
\(123\) −1.08057 −0.0974319
\(124\) 0 0
\(125\) 8.70249 0.778374
\(126\) 0 0
\(127\) 14.9124 1.32326 0.661631 0.749830i \(-0.269865\pi\)
0.661631 + 0.749830i \(0.269865\pi\)
\(128\) 0 0
\(129\) −3.62336 −0.319019
\(130\) 0 0
\(131\) −14.8252 −1.29528 −0.647640 0.761947i \(-0.724244\pi\)
−0.647640 + 0.761947i \(0.724244\pi\)
\(132\) 0 0
\(133\) −0.0536501 −0.00465205
\(134\) 0 0
\(135\) 2.57233 0.221391
\(136\) 0 0
\(137\) 7.36156 0.628941 0.314470 0.949267i \(-0.398173\pi\)
0.314470 + 0.949267i \(0.398173\pi\)
\(138\) 0 0
\(139\) 10.7613 0.912760 0.456380 0.889785i \(-0.349146\pi\)
0.456380 + 0.889785i \(0.349146\pi\)
\(140\) 0 0
\(141\) 1.46403 0.123293
\(142\) 0 0
\(143\) −3.35142 −0.280260
\(144\) 0 0
\(145\) 21.5210 1.78722
\(146\) 0 0
\(147\) 6.47759 0.534263
\(148\) 0 0
\(149\) 4.55528 0.373183 0.186592 0.982438i \(-0.440256\pi\)
0.186592 + 0.982438i \(0.440256\pi\)
\(150\) 0 0
\(151\) 16.8097 1.36796 0.683978 0.729503i \(-0.260248\pi\)
0.683978 + 0.729503i \(0.260248\pi\)
\(152\) 0 0
\(153\) 6.88201 0.556377
\(154\) 0 0
\(155\) 16.3270 1.31142
\(156\) 0 0
\(157\) 20.8841 1.66673 0.833365 0.552724i \(-0.186412\pi\)
0.833365 + 0.552724i \(0.186412\pi\)
\(158\) 0 0
\(159\) −9.12358 −0.723547
\(160\) 0 0
\(161\) −4.80557 −0.378732
\(162\) 0 0
\(163\) 14.1953 1.11186 0.555931 0.831229i \(-0.312362\pi\)
0.555931 + 0.831229i \(0.312362\pi\)
\(164\) 0 0
\(165\) −2.99366 −0.233056
\(166\) 0 0
\(167\) −8.19459 −0.634116 −0.317058 0.948406i \(-0.602695\pi\)
−0.317058 + 0.948406i \(0.602695\pi\)
\(168\) 0 0
\(169\) −4.70712 −0.362086
\(170\) 0 0
\(171\) 0.0742278 0.00567634
\(172\) 0 0
\(173\) −9.82182 −0.746739 −0.373370 0.927683i \(-0.621798\pi\)
−0.373370 + 0.927683i \(0.621798\pi\)
\(174\) 0 0
\(175\) −1.16865 −0.0883413
\(176\) 0 0
\(177\) 4.35277 0.327174
\(178\) 0 0
\(179\) 2.55904 0.191271 0.0956357 0.995416i \(-0.469512\pi\)
0.0956357 + 0.995416i \(0.469512\pi\)
\(180\) 0 0
\(181\) 24.1502 1.79507 0.897535 0.440944i \(-0.145356\pi\)
0.897535 + 0.440944i \(0.145356\pi\)
\(182\) 0 0
\(183\) −5.87947 −0.434623
\(184\) 0 0
\(185\) 10.8910 0.800721
\(186\) 0 0
\(187\) −8.00924 −0.585694
\(188\) 0 0
\(189\) 0.722776 0.0525742
\(190\) 0 0
\(191\) 25.3924 1.83733 0.918663 0.395042i \(-0.129270\pi\)
0.918663 + 0.395042i \(0.129270\pi\)
\(192\) 0 0
\(193\) 14.8275 1.06731 0.533655 0.845702i \(-0.320818\pi\)
0.533655 + 0.845702i \(0.320818\pi\)
\(194\) 0 0
\(195\) 7.40763 0.530472
\(196\) 0 0
\(197\) 11.6035 0.826716 0.413358 0.910569i \(-0.364356\pi\)
0.413358 + 0.910569i \(0.364356\pi\)
\(198\) 0 0
\(199\) 19.2671 1.36581 0.682904 0.730508i \(-0.260717\pi\)
0.682904 + 0.730508i \(0.260717\pi\)
\(200\) 0 0
\(201\) −0.793907 −0.0559979
\(202\) 0 0
\(203\) 6.04698 0.424415
\(204\) 0 0
\(205\) −2.77959 −0.194135
\(206\) 0 0
\(207\) 6.64876 0.462121
\(208\) 0 0
\(209\) −0.0863859 −0.00597544
\(210\) 0 0
\(211\) −4.79962 −0.330420 −0.165210 0.986258i \(-0.552830\pi\)
−0.165210 + 0.986258i \(0.552830\pi\)
\(212\) 0 0
\(213\) 11.3782 0.779624
\(214\) 0 0
\(215\) −9.32047 −0.635651
\(216\) 0 0
\(217\) 4.58759 0.311426
\(218\) 0 0
\(219\) −9.16804 −0.619519
\(220\) 0 0
\(221\) 19.8184 1.33313
\(222\) 0 0
\(223\) 20.7175 1.38735 0.693674 0.720289i \(-0.255991\pi\)
0.693674 + 0.720289i \(0.255991\pi\)
\(224\) 0 0
\(225\) 1.61688 0.107792
\(226\) 0 0
\(227\) −27.6740 −1.83679 −0.918393 0.395670i \(-0.870512\pi\)
−0.918393 + 0.395670i \(0.870512\pi\)
\(228\) 0 0
\(229\) −21.7378 −1.43648 −0.718238 0.695798i \(-0.755051\pi\)
−0.718238 + 0.695798i \(0.755051\pi\)
\(230\) 0 0
\(231\) −0.841163 −0.0553445
\(232\) 0 0
\(233\) 1.46491 0.0959695 0.0479847 0.998848i \(-0.484720\pi\)
0.0479847 + 0.998848i \(0.484720\pi\)
\(234\) 0 0
\(235\) 3.76596 0.245664
\(236\) 0 0
\(237\) 6.61559 0.429729
\(238\) 0 0
\(239\) −2.03018 −0.131321 −0.0656606 0.997842i \(-0.520915\pi\)
−0.0656606 + 0.997842i \(0.520915\pi\)
\(240\) 0 0
\(241\) −0.739602 −0.0476419 −0.0238210 0.999716i \(-0.507583\pi\)
−0.0238210 + 0.999716i \(0.507583\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 16.6625 1.06453
\(246\) 0 0
\(247\) 0.213756 0.0136010
\(248\) 0 0
\(249\) 9.56912 0.606419
\(250\) 0 0
\(251\) −15.6351 −0.986880 −0.493440 0.869780i \(-0.664261\pi\)
−0.493440 + 0.869780i \(0.664261\pi\)
\(252\) 0 0
\(253\) −7.73779 −0.486471
\(254\) 0 0
\(255\) 17.7028 1.10859
\(256\) 0 0
\(257\) 1.67976 0.104781 0.0523904 0.998627i \(-0.483316\pi\)
0.0523904 + 0.998627i \(0.483316\pi\)
\(258\) 0 0
\(259\) 3.06016 0.190149
\(260\) 0 0
\(261\) −8.36633 −0.517863
\(262\) 0 0
\(263\) −1.85110 −0.114144 −0.0570719 0.998370i \(-0.518176\pi\)
−0.0570719 + 0.998370i \(0.518176\pi\)
\(264\) 0 0
\(265\) −23.4689 −1.44168
\(266\) 0 0
\(267\) 9.56938 0.585637
\(268\) 0 0
\(269\) −7.43192 −0.453132 −0.226566 0.973996i \(-0.572750\pi\)
−0.226566 + 0.973996i \(0.572750\pi\)
\(270\) 0 0
\(271\) 2.02618 0.123082 0.0615408 0.998105i \(-0.480399\pi\)
0.0615408 + 0.998105i \(0.480399\pi\)
\(272\) 0 0
\(273\) 2.08140 0.125972
\(274\) 0 0
\(275\) −1.88172 −0.113472
\(276\) 0 0
\(277\) −5.59687 −0.336283 −0.168142 0.985763i \(-0.553777\pi\)
−0.168142 + 0.985763i \(0.553777\pi\)
\(278\) 0 0
\(279\) −6.34718 −0.379996
\(280\) 0 0
\(281\) 10.9685 0.654328 0.327164 0.944968i \(-0.393907\pi\)
0.327164 + 0.944968i \(0.393907\pi\)
\(282\) 0 0
\(283\) 10.8585 0.645471 0.322736 0.946489i \(-0.395398\pi\)
0.322736 + 0.946489i \(0.395398\pi\)
\(284\) 0 0
\(285\) 0.190938 0.0113102
\(286\) 0 0
\(287\) −0.781012 −0.0461017
\(288\) 0 0
\(289\) 30.3620 1.78600
\(290\) 0 0
\(291\) −1.48629 −0.0871280
\(292\) 0 0
\(293\) −5.01975 −0.293257 −0.146628 0.989192i \(-0.546842\pi\)
−0.146628 + 0.989192i \(0.546842\pi\)
\(294\) 0 0
\(295\) 11.1968 0.651901
\(296\) 0 0
\(297\) 1.16379 0.0675302
\(298\) 0 0
\(299\) 19.1467 1.10728
\(300\) 0 0
\(301\) −2.61888 −0.150949
\(302\) 0 0
\(303\) 7.12534 0.409340
\(304\) 0 0
\(305\) −15.1239 −0.865995
\(306\) 0 0
\(307\) −9.19596 −0.524841 −0.262421 0.964954i \(-0.584521\pi\)
−0.262421 + 0.964954i \(0.584521\pi\)
\(308\) 0 0
\(309\) −15.8664 −0.902607
\(310\) 0 0
\(311\) 11.4505 0.649298 0.324649 0.945835i \(-0.394754\pi\)
0.324649 + 0.945835i \(0.394754\pi\)
\(312\) 0 0
\(313\) 10.0645 0.568879 0.284440 0.958694i \(-0.408193\pi\)
0.284440 + 0.958694i \(0.408193\pi\)
\(314\) 0 0
\(315\) 1.85922 0.104755
\(316\) 0 0
\(317\) 23.0774 1.29616 0.648078 0.761574i \(-0.275573\pi\)
0.648078 + 0.761574i \(0.275573\pi\)
\(318\) 0 0
\(319\) 9.73669 0.545150
\(320\) 0 0
\(321\) 11.7466 0.655631
\(322\) 0 0
\(323\) 0.510836 0.0284237
\(324\) 0 0
\(325\) 4.65620 0.258279
\(326\) 0 0
\(327\) −6.74173 −0.372819
\(328\) 0 0
\(329\) 1.05816 0.0583384
\(330\) 0 0
\(331\) −19.4192 −1.06737 −0.533687 0.845682i \(-0.679194\pi\)
−0.533687 + 0.845682i \(0.679194\pi\)
\(332\) 0 0
\(333\) −4.23390 −0.232016
\(334\) 0 0
\(335\) −2.04219 −0.111577
\(336\) 0 0
\(337\) 12.5655 0.684486 0.342243 0.939611i \(-0.388813\pi\)
0.342243 + 0.939611i \(0.388813\pi\)
\(338\) 0 0
\(339\) −10.6407 −0.577921
\(340\) 0 0
\(341\) 7.38681 0.400018
\(342\) 0 0
\(343\) 9.74129 0.525980
\(344\) 0 0
\(345\) 17.1028 0.920785
\(346\) 0 0
\(347\) −13.4344 −0.721194 −0.360597 0.932722i \(-0.617427\pi\)
−0.360597 + 0.932722i \(0.617427\pi\)
\(348\) 0 0
\(349\) 8.55386 0.457878 0.228939 0.973441i \(-0.426474\pi\)
0.228939 + 0.973441i \(0.426474\pi\)
\(350\) 0 0
\(351\) −2.87974 −0.153709
\(352\) 0 0
\(353\) −32.1849 −1.71303 −0.856514 0.516123i \(-0.827375\pi\)
−0.856514 + 0.516123i \(0.827375\pi\)
\(354\) 0 0
\(355\) 29.2686 1.55342
\(356\) 0 0
\(357\) 4.97415 0.263260
\(358\) 0 0
\(359\) −23.1313 −1.22082 −0.610411 0.792085i \(-0.708996\pi\)
−0.610411 + 0.792085i \(0.708996\pi\)
\(360\) 0 0
\(361\) −18.9945 −0.999710
\(362\) 0 0
\(363\) 9.64558 0.506262
\(364\) 0 0
\(365\) −23.5832 −1.23440
\(366\) 0 0
\(367\) −13.3085 −0.694697 −0.347348 0.937736i \(-0.612918\pi\)
−0.347348 + 0.937736i \(0.612918\pi\)
\(368\) 0 0
\(369\) 1.08057 0.0562523
\(370\) 0 0
\(371\) −6.59431 −0.342360
\(372\) 0 0
\(373\) −8.53899 −0.442132 −0.221066 0.975259i \(-0.570954\pi\)
−0.221066 + 0.975259i \(0.570954\pi\)
\(374\) 0 0
\(375\) −8.70249 −0.449395
\(376\) 0 0
\(377\) −24.0928 −1.24084
\(378\) 0 0
\(379\) −1.68583 −0.0865955 −0.0432977 0.999062i \(-0.513786\pi\)
−0.0432977 + 0.999062i \(0.513786\pi\)
\(380\) 0 0
\(381\) −14.9124 −0.763986
\(382\) 0 0
\(383\) 17.9264 0.915998 0.457999 0.888953i \(-0.348566\pi\)
0.457999 + 0.888953i \(0.348566\pi\)
\(384\) 0 0
\(385\) −2.16375 −0.110275
\(386\) 0 0
\(387\) 3.62336 0.184186
\(388\) 0 0
\(389\) 7.27069 0.368639 0.184319 0.982866i \(-0.440992\pi\)
0.184319 + 0.982866i \(0.440992\pi\)
\(390\) 0 0
\(391\) 45.7568 2.31402
\(392\) 0 0
\(393\) 14.8252 0.747830
\(394\) 0 0
\(395\) 17.0175 0.856243
\(396\) 0 0
\(397\) 2.88145 0.144616 0.0723079 0.997382i \(-0.476964\pi\)
0.0723079 + 0.997382i \(0.476964\pi\)
\(398\) 0 0
\(399\) 0.0536501 0.00268586
\(400\) 0 0
\(401\) 18.4803 0.922863 0.461432 0.887176i \(-0.347336\pi\)
0.461432 + 0.887176i \(0.347336\pi\)
\(402\) 0 0
\(403\) −18.2782 −0.910502
\(404\) 0 0
\(405\) −2.57233 −0.127820
\(406\) 0 0
\(407\) 4.92739 0.244242
\(408\) 0 0
\(409\) −0.522001 −0.0258113 −0.0129056 0.999917i \(-0.504108\pi\)
−0.0129056 + 0.999917i \(0.504108\pi\)
\(410\) 0 0
\(411\) −7.36156 −0.363119
\(412\) 0 0
\(413\) 3.14608 0.154808
\(414\) 0 0
\(415\) 24.6149 1.20830
\(416\) 0 0
\(417\) −10.7613 −0.526982
\(418\) 0 0
\(419\) 26.7685 1.30773 0.653864 0.756612i \(-0.273147\pi\)
0.653864 + 0.756612i \(0.273147\pi\)
\(420\) 0 0
\(421\) 5.27029 0.256858 0.128429 0.991719i \(-0.459006\pi\)
0.128429 + 0.991719i \(0.459006\pi\)
\(422\) 0 0
\(423\) −1.46403 −0.0711834
\(424\) 0 0
\(425\) 11.1274 0.539759
\(426\) 0 0
\(427\) −4.24954 −0.205650
\(428\) 0 0
\(429\) 3.35142 0.161808
\(430\) 0 0
\(431\) 25.0709 1.20762 0.603812 0.797127i \(-0.293648\pi\)
0.603812 + 0.797127i \(0.293648\pi\)
\(432\) 0 0
\(433\) 24.0380 1.15519 0.577597 0.816322i \(-0.303990\pi\)
0.577597 + 0.816322i \(0.303990\pi\)
\(434\) 0 0
\(435\) −21.5210 −1.03185
\(436\) 0 0
\(437\) 0.493523 0.0236084
\(438\) 0 0
\(439\) 9.24906 0.441434 0.220717 0.975338i \(-0.429160\pi\)
0.220717 + 0.975338i \(0.429160\pi\)
\(440\) 0 0
\(441\) −6.47759 −0.308457
\(442\) 0 0
\(443\) 10.2431 0.486662 0.243331 0.969943i \(-0.421760\pi\)
0.243331 + 0.969943i \(0.421760\pi\)
\(444\) 0 0
\(445\) 24.6156 1.16689
\(446\) 0 0
\(447\) −4.55528 −0.215457
\(448\) 0 0
\(449\) 38.5705 1.82025 0.910127 0.414330i \(-0.135984\pi\)
0.910127 + 0.414330i \(0.135984\pi\)
\(450\) 0 0
\(451\) −1.25756 −0.0592164
\(452\) 0 0
\(453\) −16.8097 −0.789790
\(454\) 0 0
\(455\) 5.35406 0.251002
\(456\) 0 0
\(457\) 32.7459 1.53179 0.765893 0.642968i \(-0.222297\pi\)
0.765893 + 0.642968i \(0.222297\pi\)
\(458\) 0 0
\(459\) −6.88201 −0.321225
\(460\) 0 0
\(461\) −36.7574 −1.71196 −0.855982 0.517005i \(-0.827047\pi\)
−0.855982 + 0.517005i \(0.827047\pi\)
\(462\) 0 0
\(463\) 4.80280 0.223205 0.111602 0.993753i \(-0.464402\pi\)
0.111602 + 0.993753i \(0.464402\pi\)
\(464\) 0 0
\(465\) −16.3270 −0.757148
\(466\) 0 0
\(467\) 17.4603 0.807968 0.403984 0.914766i \(-0.367625\pi\)
0.403984 + 0.914766i \(0.367625\pi\)
\(468\) 0 0
\(469\) −0.573817 −0.0264964
\(470\) 0 0
\(471\) −20.8841 −0.962287
\(472\) 0 0
\(473\) −4.21684 −0.193891
\(474\) 0 0
\(475\) 0.120018 0.00550679
\(476\) 0 0
\(477\) 9.12358 0.417740
\(478\) 0 0
\(479\) 13.0184 0.594825 0.297412 0.954749i \(-0.403876\pi\)
0.297412 + 0.954749i \(0.403876\pi\)
\(480\) 0 0
\(481\) −12.1925 −0.555931
\(482\) 0 0
\(483\) 4.80557 0.218661
\(484\) 0 0
\(485\) −3.82323 −0.173604
\(486\) 0 0
\(487\) −2.20441 −0.0998913 −0.0499456 0.998752i \(-0.515905\pi\)
−0.0499456 + 0.998752i \(0.515905\pi\)
\(488\) 0 0
\(489\) −14.1953 −0.641934
\(490\) 0 0
\(491\) 12.6437 0.570601 0.285300 0.958438i \(-0.407907\pi\)
0.285300 + 0.958438i \(0.407907\pi\)
\(492\) 0 0
\(493\) −57.5771 −2.59314
\(494\) 0 0
\(495\) 2.99366 0.134555
\(496\) 0 0
\(497\) 8.22392 0.368893
\(498\) 0 0
\(499\) −28.7988 −1.28921 −0.644605 0.764516i \(-0.722978\pi\)
−0.644605 + 0.764516i \(0.722978\pi\)
\(500\) 0 0
\(501\) 8.19459 0.366107
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 18.3287 0.815618
\(506\) 0 0
\(507\) 4.70712 0.209051
\(508\) 0 0
\(509\) 12.4826 0.553282 0.276641 0.960973i \(-0.410779\pi\)
0.276641 + 0.960973i \(0.410779\pi\)
\(510\) 0 0
\(511\) −6.62644 −0.293137
\(512\) 0 0
\(513\) −0.0742278 −0.00327724
\(514\) 0 0
\(515\) −40.8136 −1.79846
\(516\) 0 0
\(517\) 1.70383 0.0749342
\(518\) 0 0
\(519\) 9.82182 0.431130
\(520\) 0 0
\(521\) 26.7837 1.17342 0.586708 0.809798i \(-0.300424\pi\)
0.586708 + 0.809798i \(0.300424\pi\)
\(522\) 0 0
\(523\) 11.9616 0.523042 0.261521 0.965198i \(-0.415776\pi\)
0.261521 + 0.965198i \(0.415776\pi\)
\(524\) 0 0
\(525\) 1.16865 0.0510039
\(526\) 0 0
\(527\) −43.6813 −1.90279
\(528\) 0 0
\(529\) 21.2060 0.922002
\(530\) 0 0
\(531\) −4.35277 −0.188894
\(532\) 0 0
\(533\) 3.11176 0.134785
\(534\) 0 0
\(535\) 30.2161 1.30636
\(536\) 0 0
\(537\) −2.55904 −0.110431
\(538\) 0 0
\(539\) 7.53859 0.324710
\(540\) 0 0
\(541\) 14.1088 0.606587 0.303293 0.952897i \(-0.401914\pi\)
0.303293 + 0.952897i \(0.401914\pi\)
\(542\) 0 0
\(543\) −24.1502 −1.03638
\(544\) 0 0
\(545\) −17.3420 −0.742848
\(546\) 0 0
\(547\) −3.99094 −0.170640 −0.0853201 0.996354i \(-0.527191\pi\)
−0.0853201 + 0.996354i \(0.527191\pi\)
\(548\) 0 0
\(549\) 5.87947 0.250930
\(550\) 0 0
\(551\) −0.621014 −0.0264561
\(552\) 0 0
\(553\) 4.78159 0.203334
\(554\) 0 0
\(555\) −10.8910 −0.462297
\(556\) 0 0
\(557\) 42.4985 1.80072 0.900360 0.435146i \(-0.143303\pi\)
0.900360 + 0.435146i \(0.143303\pi\)
\(558\) 0 0
\(559\) 10.4343 0.441324
\(560\) 0 0
\(561\) 8.00924 0.338151
\(562\) 0 0
\(563\) −29.9247 −1.26118 −0.630588 0.776118i \(-0.717186\pi\)
−0.630588 + 0.776118i \(0.717186\pi\)
\(564\) 0 0
\(565\) −27.3713 −1.15152
\(566\) 0 0
\(567\) −0.722776 −0.0303538
\(568\) 0 0
\(569\) 38.6732 1.62126 0.810632 0.585556i \(-0.199124\pi\)
0.810632 + 0.585556i \(0.199124\pi\)
\(570\) 0 0
\(571\) −6.92014 −0.289599 −0.144799 0.989461i \(-0.546254\pi\)
−0.144799 + 0.989461i \(0.546254\pi\)
\(572\) 0 0
\(573\) −25.3924 −1.06078
\(574\) 0 0
\(575\) 10.7503 0.448318
\(576\) 0 0
\(577\) 21.4161 0.891566 0.445783 0.895141i \(-0.352925\pi\)
0.445783 + 0.895141i \(0.352925\pi\)
\(578\) 0 0
\(579\) −14.8275 −0.616212
\(580\) 0 0
\(581\) 6.91633 0.286938
\(582\) 0 0
\(583\) −10.6180 −0.439752
\(584\) 0 0
\(585\) −7.40763 −0.306268
\(586\) 0 0
\(587\) −1.34161 −0.0553743 −0.0276872 0.999617i \(-0.508814\pi\)
−0.0276872 + 0.999617i \(0.508814\pi\)
\(588\) 0 0
\(589\) −0.471137 −0.0194129
\(590\) 0 0
\(591\) −11.6035 −0.477305
\(592\) 0 0
\(593\) 18.7837 0.771353 0.385676 0.922634i \(-0.373968\pi\)
0.385676 + 0.922634i \(0.373968\pi\)
\(594\) 0 0
\(595\) 12.7952 0.524551
\(596\) 0 0
\(597\) −19.2671 −0.788550
\(598\) 0 0
\(599\) −24.7971 −1.01318 −0.506591 0.862186i \(-0.669095\pi\)
−0.506591 + 0.862186i \(0.669095\pi\)
\(600\) 0 0
\(601\) 2.99006 0.121967 0.0609836 0.998139i \(-0.480576\pi\)
0.0609836 + 0.998139i \(0.480576\pi\)
\(602\) 0 0
\(603\) 0.793907 0.0323304
\(604\) 0 0
\(605\) 24.8116 1.00874
\(606\) 0 0
\(607\) 19.9071 0.808005 0.404002 0.914758i \(-0.367619\pi\)
0.404002 + 0.914758i \(0.367619\pi\)
\(608\) 0 0
\(609\) −6.04698 −0.245036
\(610\) 0 0
\(611\) −4.21601 −0.170561
\(612\) 0 0
\(613\) 19.0313 0.768667 0.384333 0.923194i \(-0.374431\pi\)
0.384333 + 0.923194i \(0.374431\pi\)
\(614\) 0 0
\(615\) 2.77959 0.112084
\(616\) 0 0
\(617\) −28.2349 −1.13670 −0.568348 0.822788i \(-0.692417\pi\)
−0.568348 + 0.822788i \(0.692417\pi\)
\(618\) 0 0
\(619\) −28.0463 −1.12727 −0.563637 0.826022i \(-0.690598\pi\)
−0.563637 + 0.826022i \(0.690598\pi\)
\(620\) 0 0
\(621\) −6.64876 −0.266806
\(622\) 0 0
\(623\) 6.91652 0.277105
\(624\) 0 0
\(625\) −30.4701 −1.21880
\(626\) 0 0
\(627\) 0.0863859 0.00344992
\(628\) 0 0
\(629\) −29.1377 −1.16180
\(630\) 0 0
\(631\) −48.7128 −1.93923 −0.969613 0.244645i \(-0.921329\pi\)
−0.969613 + 0.244645i \(0.921329\pi\)
\(632\) 0 0
\(633\) 4.79962 0.190768
\(634\) 0 0
\(635\) −38.3596 −1.52226
\(636\) 0 0
\(637\) −18.6538 −0.739089
\(638\) 0 0
\(639\) −11.3782 −0.450116
\(640\) 0 0
\(641\) −13.3127 −0.525822 −0.262911 0.964820i \(-0.584682\pi\)
−0.262911 + 0.964820i \(0.584682\pi\)
\(642\) 0 0
\(643\) 3.14076 0.123859 0.0619297 0.998081i \(-0.480275\pi\)
0.0619297 + 0.998081i \(0.480275\pi\)
\(644\) 0 0
\(645\) 9.32047 0.366993
\(646\) 0 0
\(647\) 10.4882 0.412333 0.206166 0.978517i \(-0.433901\pi\)
0.206166 + 0.978517i \(0.433901\pi\)
\(648\) 0 0
\(649\) 5.06573 0.198847
\(650\) 0 0
\(651\) −4.58759 −0.179802
\(652\) 0 0
\(653\) −25.9881 −1.01699 −0.508497 0.861064i \(-0.669799\pi\)
−0.508497 + 0.861064i \(0.669799\pi\)
\(654\) 0 0
\(655\) 38.1352 1.49007
\(656\) 0 0
\(657\) 9.16804 0.357679
\(658\) 0 0
\(659\) 36.8964 1.43728 0.718641 0.695382i \(-0.244765\pi\)
0.718641 + 0.695382i \(0.244765\pi\)
\(660\) 0 0
\(661\) 1.26856 0.0493414 0.0246707 0.999696i \(-0.492146\pi\)
0.0246707 + 0.999696i \(0.492146\pi\)
\(662\) 0 0
\(663\) −19.8184 −0.769681
\(664\) 0 0
\(665\) 0.138006 0.00535163
\(666\) 0 0
\(667\) −55.6257 −2.15384
\(668\) 0 0
\(669\) −20.7175 −0.800986
\(670\) 0 0
\(671\) −6.84250 −0.264152
\(672\) 0 0
\(673\) 11.3186 0.436299 0.218150 0.975915i \(-0.429998\pi\)
0.218150 + 0.975915i \(0.429998\pi\)
\(674\) 0 0
\(675\) −1.61688 −0.0622339
\(676\) 0 0
\(677\) 44.2752 1.70163 0.850816 0.525463i \(-0.176108\pi\)
0.850816 + 0.525463i \(0.176108\pi\)
\(678\) 0 0
\(679\) −1.07426 −0.0412262
\(680\) 0 0
\(681\) 27.6740 1.06047
\(682\) 0 0
\(683\) 3.88334 0.148592 0.0742960 0.997236i \(-0.476329\pi\)
0.0742960 + 0.997236i \(0.476329\pi\)
\(684\) 0 0
\(685\) −18.9364 −0.723522
\(686\) 0 0
\(687\) 21.7378 0.829350
\(688\) 0 0
\(689\) 26.2735 1.00094
\(690\) 0 0
\(691\) 36.4599 1.38700 0.693499 0.720458i \(-0.256068\pi\)
0.693499 + 0.720458i \(0.256068\pi\)
\(692\) 0 0
\(693\) 0.841163 0.0319531
\(694\) 0 0
\(695\) −27.6816 −1.05002
\(696\) 0 0
\(697\) 7.43650 0.281678
\(698\) 0 0
\(699\) −1.46491 −0.0554080
\(700\) 0 0
\(701\) −3.20540 −0.121066 −0.0605331 0.998166i \(-0.519280\pi\)
−0.0605331 + 0.998166i \(0.519280\pi\)
\(702\) 0 0
\(703\) −0.314273 −0.0118530
\(704\) 0 0
\(705\) −3.76596 −0.141834
\(706\) 0 0
\(707\) 5.15003 0.193687
\(708\) 0 0
\(709\) 2.29626 0.0862377 0.0431189 0.999070i \(-0.486271\pi\)
0.0431189 + 0.999070i \(0.486271\pi\)
\(710\) 0 0
\(711\) −6.61559 −0.248104
\(712\) 0 0
\(713\) −42.2009 −1.58044
\(714\) 0 0
\(715\) 8.62096 0.322406
\(716\) 0 0
\(717\) 2.03018 0.0758183
\(718\) 0 0
\(719\) −2.65049 −0.0988466 −0.0494233 0.998778i \(-0.515738\pi\)
−0.0494233 + 0.998778i \(0.515738\pi\)
\(720\) 0 0
\(721\) −11.4679 −0.427085
\(722\) 0 0
\(723\) 0.739602 0.0275061
\(724\) 0 0
\(725\) −13.5274 −0.502395
\(726\) 0 0
\(727\) 33.4593 1.24094 0.620468 0.784232i \(-0.286943\pi\)
0.620468 + 0.784232i \(0.286943\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 24.9360 0.922290
\(732\) 0 0
\(733\) 31.6822 1.17021 0.585104 0.810958i \(-0.301054\pi\)
0.585104 + 0.810958i \(0.301054\pi\)
\(734\) 0 0
\(735\) −16.6625 −0.614606
\(736\) 0 0
\(737\) −0.923945 −0.0340339
\(738\) 0 0
\(739\) −23.9975 −0.882763 −0.441381 0.897320i \(-0.645511\pi\)
−0.441381 + 0.897320i \(0.645511\pi\)
\(740\) 0 0
\(741\) −0.213756 −0.00785254
\(742\) 0 0
\(743\) −35.2534 −1.29332 −0.646662 0.762777i \(-0.723835\pi\)
−0.646662 + 0.762777i \(0.723835\pi\)
\(744\) 0 0
\(745\) −11.7177 −0.429303
\(746\) 0 0
\(747\) −9.56912 −0.350116
\(748\) 0 0
\(749\) 8.49017 0.310224
\(750\) 0 0
\(751\) −34.7924 −1.26959 −0.634796 0.772680i \(-0.718916\pi\)
−0.634796 + 0.772680i \(0.718916\pi\)
\(752\) 0 0
\(753\) 15.6351 0.569775
\(754\) 0 0
\(755\) −43.2402 −1.57367
\(756\) 0 0
\(757\) −20.4069 −0.741701 −0.370850 0.928693i \(-0.620934\pi\)
−0.370850 + 0.928693i \(0.620934\pi\)
\(758\) 0 0
\(759\) 7.73779 0.280864
\(760\) 0 0
\(761\) 37.2926 1.35186 0.675929 0.736967i \(-0.263743\pi\)
0.675929 + 0.736967i \(0.263743\pi\)
\(762\) 0 0
\(763\) −4.87276 −0.176406
\(764\) 0 0
\(765\) −17.7028 −0.640046
\(766\) 0 0
\(767\) −12.5348 −0.452606
\(768\) 0 0
\(769\) 22.5785 0.814203 0.407101 0.913383i \(-0.366540\pi\)
0.407101 + 0.913383i \(0.366540\pi\)
\(770\) 0 0
\(771\) −1.67976 −0.0604952
\(772\) 0 0
\(773\) 41.5941 1.49604 0.748019 0.663678i \(-0.231005\pi\)
0.748019 + 0.663678i \(0.231005\pi\)
\(774\) 0 0
\(775\) −10.2627 −0.368645
\(776\) 0 0
\(777\) −3.06016 −0.109783
\(778\) 0 0
\(779\) 0.0802084 0.00287377
\(780\) 0 0
\(781\) 13.2419 0.473834
\(782\) 0 0
\(783\) 8.36633 0.298988
\(784\) 0 0
\(785\) −53.7207 −1.91737
\(786\) 0 0
\(787\) 41.1243 1.46592 0.732961 0.680271i \(-0.238138\pi\)
0.732961 + 0.680271i \(0.238138\pi\)
\(788\) 0 0
\(789\) 1.85110 0.0659009
\(790\) 0 0
\(791\) −7.69081 −0.273454
\(792\) 0 0
\(793\) 16.9313 0.601249
\(794\) 0 0
\(795\) 23.4689 0.832355
\(796\) 0 0
\(797\) 39.3180 1.39271 0.696357 0.717695i \(-0.254803\pi\)
0.696357 + 0.717695i \(0.254803\pi\)
\(798\) 0 0
\(799\) −10.0754 −0.356444
\(800\) 0 0
\(801\) −9.56938 −0.338117
\(802\) 0 0
\(803\) −10.6697 −0.376526
\(804\) 0 0
\(805\) 12.3615 0.435686
\(806\) 0 0
\(807\) 7.43192 0.261616
\(808\) 0 0
\(809\) −15.1504 −0.532661 −0.266330 0.963882i \(-0.585811\pi\)
−0.266330 + 0.963882i \(0.585811\pi\)
\(810\) 0 0
\(811\) −36.1738 −1.27023 −0.635117 0.772416i \(-0.719048\pi\)
−0.635117 + 0.772416i \(0.719048\pi\)
\(812\) 0 0
\(813\) −2.02618 −0.0710612
\(814\) 0 0
\(815\) −36.5150 −1.27906
\(816\) 0 0
\(817\) 0.268954 0.00940950
\(818\) 0 0
\(819\) −2.08140 −0.0727302
\(820\) 0 0
\(821\) 13.0699 0.456144 0.228072 0.973644i \(-0.426758\pi\)
0.228072 + 0.973644i \(0.426758\pi\)
\(822\) 0 0
\(823\) 5.77380 0.201262 0.100631 0.994924i \(-0.467914\pi\)
0.100631 + 0.994924i \(0.467914\pi\)
\(824\) 0 0
\(825\) 1.88172 0.0655131
\(826\) 0 0
\(827\) 16.0476 0.558031 0.279016 0.960287i \(-0.409992\pi\)
0.279016 + 0.960287i \(0.409992\pi\)
\(828\) 0 0
\(829\) 24.9625 0.866983 0.433492 0.901158i \(-0.357281\pi\)
0.433492 + 0.901158i \(0.357281\pi\)
\(830\) 0 0
\(831\) 5.59687 0.194153
\(832\) 0 0
\(833\) −44.5789 −1.54457
\(834\) 0 0
\(835\) 21.0792 0.729475
\(836\) 0 0
\(837\) 6.34718 0.219391
\(838\) 0 0
\(839\) 15.9000 0.548929 0.274464 0.961597i \(-0.411499\pi\)
0.274464 + 0.961597i \(0.411499\pi\)
\(840\) 0 0
\(841\) 40.9955 1.41364
\(842\) 0 0
\(843\) −10.9685 −0.377776
\(844\) 0 0
\(845\) 12.1083 0.416537
\(846\) 0 0
\(847\) 6.97160 0.239547
\(848\) 0 0
\(849\) −10.8585 −0.372663
\(850\) 0 0
\(851\) −28.1502 −0.964976
\(852\) 0 0
\(853\) −43.4168 −1.48656 −0.743282 0.668978i \(-0.766732\pi\)
−0.743282 + 0.668978i \(0.766732\pi\)
\(854\) 0 0
\(855\) −0.190938 −0.00652995
\(856\) 0 0
\(857\) −15.8811 −0.542487 −0.271243 0.962511i \(-0.587435\pi\)
−0.271243 + 0.962511i \(0.587435\pi\)
\(858\) 0 0
\(859\) 28.8203 0.983335 0.491668 0.870783i \(-0.336388\pi\)
0.491668 + 0.870783i \(0.336388\pi\)
\(860\) 0 0
\(861\) 0.781012 0.0266168
\(862\) 0 0
\(863\) −33.6253 −1.14462 −0.572309 0.820038i \(-0.693952\pi\)
−0.572309 + 0.820038i \(0.693952\pi\)
\(864\) 0 0
\(865\) 25.2650 0.859035
\(866\) 0 0
\(867\) −30.3620 −1.03115
\(868\) 0 0
\(869\) 7.69919 0.261177
\(870\) 0 0
\(871\) 2.28624 0.0774664
\(872\) 0 0
\(873\) 1.48629 0.0503034
\(874\) 0 0
\(875\) −6.28995 −0.212639
\(876\) 0 0
\(877\) 2.13685 0.0721561 0.0360781 0.999349i \(-0.488514\pi\)
0.0360781 + 0.999349i \(0.488514\pi\)
\(878\) 0 0
\(879\) 5.01975 0.169312
\(880\) 0 0
\(881\) −49.2878 −1.66055 −0.830274 0.557355i \(-0.811816\pi\)
−0.830274 + 0.557355i \(0.811816\pi\)
\(882\) 0 0
\(883\) 27.8136 0.936004 0.468002 0.883727i \(-0.344974\pi\)
0.468002 + 0.883727i \(0.344974\pi\)
\(884\) 0 0
\(885\) −11.1968 −0.376375
\(886\) 0 0
\(887\) 0.295664 0.00992743 0.00496371 0.999988i \(-0.498420\pi\)
0.00496371 + 0.999988i \(0.498420\pi\)
\(888\) 0 0
\(889\) −10.7783 −0.361494
\(890\) 0 0
\(891\) −1.16379 −0.0389886
\(892\) 0 0
\(893\) −0.108671 −0.00363655
\(894\) 0 0
\(895\) −6.58269 −0.220035
\(896\) 0 0
\(897\) −19.1467 −0.639289
\(898\) 0 0
\(899\) 53.1026 1.77107
\(900\) 0 0
\(901\) 62.7886 2.09179
\(902\) 0 0
\(903\) 2.61888 0.0871507
\(904\) 0 0
\(905\) −62.1223 −2.06501
\(906\) 0 0
\(907\) −43.2844 −1.43723 −0.718617 0.695406i \(-0.755225\pi\)
−0.718617 + 0.695406i \(0.755225\pi\)
\(908\) 0 0
\(909\) −7.12534 −0.236333
\(910\) 0 0
\(911\) −35.0762 −1.16213 −0.581063 0.813858i \(-0.697363\pi\)
−0.581063 + 0.813858i \(0.697363\pi\)
\(912\) 0 0
\(913\) 11.1365 0.368564
\(914\) 0 0
\(915\) 15.1239 0.499982
\(916\) 0 0
\(917\) 10.7153 0.353849
\(918\) 0 0
\(919\) −5.22975 −0.172513 −0.0862567 0.996273i \(-0.527491\pi\)
−0.0862567 + 0.996273i \(0.527491\pi\)
\(920\) 0 0
\(921\) 9.19596 0.303017
\(922\) 0 0
\(923\) −32.7663 −1.07852
\(924\) 0 0
\(925\) −6.84573 −0.225086
\(926\) 0 0
\(927\) 15.8664 0.521121
\(928\) 0 0
\(929\) −41.3894 −1.35794 −0.678971 0.734165i \(-0.737574\pi\)
−0.678971 + 0.734165i \(0.737574\pi\)
\(930\) 0 0
\(931\) −0.480817 −0.0157582
\(932\) 0 0
\(933\) −11.4505 −0.374872
\(934\) 0 0
\(935\) 20.6024 0.673771
\(936\) 0 0
\(937\) 30.4145 0.993599 0.496799 0.867865i \(-0.334509\pi\)
0.496799 + 0.867865i \(0.334509\pi\)
\(938\) 0 0
\(939\) −10.0645 −0.328442
\(940\) 0 0
\(941\) 35.0814 1.14362 0.571810 0.820386i \(-0.306241\pi\)
0.571810 + 0.820386i \(0.306241\pi\)
\(942\) 0 0
\(943\) 7.18446 0.233958
\(944\) 0 0
\(945\) −1.85922 −0.0604804
\(946\) 0 0
\(947\) −54.0852 −1.75753 −0.878766 0.477253i \(-0.841633\pi\)
−0.878766 + 0.477253i \(0.841633\pi\)
\(948\) 0 0
\(949\) 26.4015 0.857030
\(950\) 0 0
\(951\) −23.0774 −0.748336
\(952\) 0 0
\(953\) −21.7409 −0.704256 −0.352128 0.935952i \(-0.614542\pi\)
−0.352128 + 0.935952i \(0.614542\pi\)
\(954\) 0 0
\(955\) −65.3175 −2.11363
\(956\) 0 0
\(957\) −9.73669 −0.314742
\(958\) 0 0
\(959\) −5.32076 −0.171816
\(960\) 0 0
\(961\) 9.28667 0.299570
\(962\) 0 0
\(963\) −11.7466 −0.378529
\(964\) 0 0
\(965\) −38.1413 −1.22781
\(966\) 0 0
\(967\) −46.2475 −1.48722 −0.743610 0.668614i \(-0.766888\pi\)
−0.743610 + 0.668614i \(0.766888\pi\)
\(968\) 0 0
\(969\) −0.510836 −0.0164104
\(970\) 0 0
\(971\) 35.3342 1.13393 0.566965 0.823742i \(-0.308118\pi\)
0.566965 + 0.823742i \(0.308118\pi\)
\(972\) 0 0
\(973\) −7.77800 −0.249351
\(974\) 0 0
\(975\) −4.65620 −0.149118
\(976\) 0 0
\(977\) 18.9307 0.605645 0.302823 0.953047i \(-0.402071\pi\)
0.302823 + 0.953047i \(0.402071\pi\)
\(978\) 0 0
\(979\) 11.1368 0.355934
\(980\) 0 0
\(981\) 6.74173 0.215247
\(982\) 0 0
\(983\) −23.2239 −0.740727 −0.370363 0.928887i \(-0.620767\pi\)
−0.370363 + 0.928887i \(0.620767\pi\)
\(984\) 0 0
\(985\) −29.8481 −0.951039
\(986\) 0 0
\(987\) −1.05816 −0.0336817
\(988\) 0 0
\(989\) 24.0908 0.766044
\(990\) 0 0
\(991\) −47.8566 −1.52022 −0.760108 0.649797i \(-0.774854\pi\)
−0.760108 + 0.649797i \(0.774854\pi\)
\(992\) 0 0
\(993\) 19.4192 0.616248
\(994\) 0 0
\(995\) −49.5613 −1.57120
\(996\) 0 0
\(997\) −15.4541 −0.489437 −0.244719 0.969594i \(-0.578696\pi\)
−0.244719 + 0.969594i \(0.578696\pi\)
\(998\) 0 0
\(999\) 4.23390 0.133955
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 \(a_p\))