Properties

Label 6004.2.a.g.1.17
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.551494 q^{3}\) \(-2.33245 q^{5}\) \(+1.71388 q^{7}\) \(-2.69585 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.551494 q^{3}\) \(-2.33245 q^{5}\) \(+1.71388 q^{7}\) \(-2.69585 q^{9}\) \(-3.53671 q^{11}\) \(+4.69844 q^{13}\) \(-1.28633 q^{15}\) \(+5.32909 q^{17}\) \(+1.00000 q^{19}\) \(+0.945194 q^{21}\) \(-3.91953 q^{23}\) \(+0.440343 q^{25}\) \(-3.14123 q^{27}\) \(-0.324961 q^{29}\) \(+3.84244 q^{31}\) \(-1.95047 q^{33}\) \(-3.99755 q^{35}\) \(-2.10127 q^{37}\) \(+2.59116 q^{39}\) \(-11.2921 q^{41}\) \(+4.62033 q^{43}\) \(+6.28796 q^{45}\) \(+2.89204 q^{47}\) \(-4.06262 q^{49}\) \(+2.93896 q^{51}\) \(-0.546107 q^{53}\) \(+8.24922 q^{55}\) \(+0.551494 q^{57}\) \(+0.300059 q^{59}\) \(+9.09363 q^{61}\) \(-4.62037 q^{63}\) \(-10.9589 q^{65}\) \(+2.81788 q^{67}\) \(-2.16160 q^{69}\) \(-2.90768 q^{71}\) \(-4.70923 q^{73}\) \(+0.242846 q^{75}\) \(-6.06150 q^{77}\) \(-1.00000 q^{79}\) \(+6.35520 q^{81}\) \(-7.18505 q^{83}\) \(-12.4299 q^{85}\) \(-0.179214 q^{87}\) \(-0.382983 q^{89}\) \(+8.05256 q^{91}\) \(+2.11908 q^{93}\) \(-2.33245 q^{95}\) \(+9.48403 q^{97}\) \(+9.53446 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.551494 0.318405 0.159203 0.987246i \(-0.449108\pi\)
0.159203 + 0.987246i \(0.449108\pi\)
\(4\) 0 0
\(5\) −2.33245 −1.04311 −0.521553 0.853219i \(-0.674647\pi\)
−0.521553 + 0.853219i \(0.674647\pi\)
\(6\) 0 0
\(7\) 1.71388 0.647786 0.323893 0.946094i \(-0.395008\pi\)
0.323893 + 0.946094i \(0.395008\pi\)
\(8\) 0 0
\(9\) −2.69585 −0.898618
\(10\) 0 0
\(11\) −3.53671 −1.06636 −0.533179 0.846002i \(-0.679003\pi\)
−0.533179 + 0.846002i \(0.679003\pi\)
\(12\) 0 0
\(13\) 4.69844 1.30311 0.651557 0.758600i \(-0.274116\pi\)
0.651557 + 0.758600i \(0.274116\pi\)
\(14\) 0 0
\(15\) −1.28633 −0.332130
\(16\) 0 0
\(17\) 5.32909 1.29250 0.646248 0.763128i \(-0.276337\pi\)
0.646248 + 0.763128i \(0.276337\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 0.945194 0.206258
\(22\) 0 0
\(23\) −3.91953 −0.817278 −0.408639 0.912696i \(-0.633997\pi\)
−0.408639 + 0.912696i \(0.633997\pi\)
\(24\) 0 0
\(25\) 0.440343 0.0880686
\(26\) 0 0
\(27\) −3.14123 −0.604530
\(28\) 0 0
\(29\) −0.324961 −0.0603438 −0.0301719 0.999545i \(-0.509605\pi\)
−0.0301719 + 0.999545i \(0.509605\pi\)
\(30\) 0 0
\(31\) 3.84244 0.690123 0.345062 0.938580i \(-0.387858\pi\)
0.345062 + 0.938580i \(0.387858\pi\)
\(32\) 0 0
\(33\) −1.95047 −0.339534
\(34\) 0 0
\(35\) −3.99755 −0.675709
\(36\) 0 0
\(37\) −2.10127 −0.345447 −0.172724 0.984970i \(-0.555257\pi\)
−0.172724 + 0.984970i \(0.555257\pi\)
\(38\) 0 0
\(39\) 2.59116 0.414918
\(40\) 0 0
\(41\) −11.2921 −1.76353 −0.881764 0.471691i \(-0.843644\pi\)
−0.881764 + 0.471691i \(0.843644\pi\)
\(42\) 0 0
\(43\) 4.62033 0.704593 0.352297 0.935888i \(-0.385401\pi\)
0.352297 + 0.935888i \(0.385401\pi\)
\(44\) 0 0
\(45\) 6.28796 0.937353
\(46\) 0 0
\(47\) 2.89204 0.421848 0.210924 0.977502i \(-0.432353\pi\)
0.210924 + 0.977502i \(0.432353\pi\)
\(48\) 0 0
\(49\) −4.06262 −0.580374
\(50\) 0 0
\(51\) 2.93896 0.411537
\(52\) 0 0
\(53\) −0.546107 −0.0750136 −0.0375068 0.999296i \(-0.511942\pi\)
−0.0375068 + 0.999296i \(0.511942\pi\)
\(54\) 0 0
\(55\) 8.24922 1.11232
\(56\) 0 0
\(57\) 0.551494 0.0730471
\(58\) 0 0
\(59\) 0.300059 0.0390644 0.0195322 0.999809i \(-0.493782\pi\)
0.0195322 + 0.999809i \(0.493782\pi\)
\(60\) 0 0
\(61\) 9.09363 1.16432 0.582160 0.813074i \(-0.302208\pi\)
0.582160 + 0.813074i \(0.302208\pi\)
\(62\) 0 0
\(63\) −4.62037 −0.582112
\(64\) 0 0
\(65\) −10.9589 −1.35928
\(66\) 0 0
\(67\) 2.81788 0.344259 0.172130 0.985074i \(-0.444935\pi\)
0.172130 + 0.985074i \(0.444935\pi\)
\(68\) 0 0
\(69\) −2.16160 −0.260226
\(70\) 0 0
\(71\) −2.90768 −0.345078 −0.172539 0.985003i \(-0.555197\pi\)
−0.172539 + 0.985003i \(0.555197\pi\)
\(72\) 0 0
\(73\) −4.70923 −0.551174 −0.275587 0.961276i \(-0.588872\pi\)
−0.275587 + 0.961276i \(0.588872\pi\)
\(74\) 0 0
\(75\) 0.242846 0.0280415
\(76\) 0 0
\(77\) −6.06150 −0.690772
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 6.35520 0.706133
\(82\) 0 0
\(83\) −7.18505 −0.788662 −0.394331 0.918969i \(-0.629024\pi\)
−0.394331 + 0.918969i \(0.629024\pi\)
\(84\) 0 0
\(85\) −12.4299 −1.34821
\(86\) 0 0
\(87\) −0.179214 −0.0192138
\(88\) 0 0
\(89\) −0.382983 −0.0405961 −0.0202981 0.999794i \(-0.506462\pi\)
−0.0202981 + 0.999794i \(0.506462\pi\)
\(90\) 0 0
\(91\) 8.05256 0.844138
\(92\) 0 0
\(93\) 2.11908 0.219739
\(94\) 0 0
\(95\) −2.33245 −0.239305
\(96\) 0 0
\(97\) 9.48403 0.962958 0.481479 0.876458i \(-0.340100\pi\)
0.481479 + 0.876458i \(0.340100\pi\)
\(98\) 0 0
\(99\) 9.53446 0.958249
\(100\) 0 0
\(101\) −10.5762 −1.05237 −0.526184 0.850371i \(-0.676378\pi\)
−0.526184 + 0.850371i \(0.676378\pi\)
\(102\) 0 0
\(103\) 7.86609 0.775069 0.387534 0.921855i \(-0.373327\pi\)
0.387534 + 0.921855i \(0.373327\pi\)
\(104\) 0 0
\(105\) −2.20462 −0.215149
\(106\) 0 0
\(107\) 1.91970 0.185585 0.0927923 0.995685i \(-0.470421\pi\)
0.0927923 + 0.995685i \(0.470421\pi\)
\(108\) 0 0
\(109\) −7.90135 −0.756812 −0.378406 0.925640i \(-0.623528\pi\)
−0.378406 + 0.925640i \(0.623528\pi\)
\(110\) 0 0
\(111\) −1.15884 −0.109992
\(112\) 0 0
\(113\) 10.1650 0.956244 0.478122 0.878294i \(-0.341318\pi\)
0.478122 + 0.878294i \(0.341318\pi\)
\(114\) 0 0
\(115\) 9.14212 0.852507
\(116\) 0 0
\(117\) −12.6663 −1.17100
\(118\) 0 0
\(119\) 9.13342 0.837260
\(120\) 0 0
\(121\) 1.50832 0.137120
\(122\) 0 0
\(123\) −6.22752 −0.561516
\(124\) 0 0
\(125\) 10.6352 0.951240
\(126\) 0 0
\(127\) −2.60435 −0.231099 −0.115549 0.993302i \(-0.536863\pi\)
−0.115549 + 0.993302i \(0.536863\pi\)
\(128\) 0 0
\(129\) 2.54808 0.224346
\(130\) 0 0
\(131\) −19.2620 −1.68293 −0.841466 0.540310i \(-0.818307\pi\)
−0.841466 + 0.540310i \(0.818307\pi\)
\(132\) 0 0
\(133\) 1.71388 0.148612
\(134\) 0 0
\(135\) 7.32677 0.630588
\(136\) 0 0
\(137\) −9.62735 −0.822520 −0.411260 0.911518i \(-0.634911\pi\)
−0.411260 + 0.911518i \(0.634911\pi\)
\(138\) 0 0
\(139\) −9.73621 −0.825815 −0.412907 0.910773i \(-0.635487\pi\)
−0.412907 + 0.910773i \(0.635487\pi\)
\(140\) 0 0
\(141\) 1.59494 0.134318
\(142\) 0 0
\(143\) −16.6170 −1.38959
\(144\) 0 0
\(145\) 0.757958 0.0629449
\(146\) 0 0
\(147\) −2.24051 −0.184794
\(148\) 0 0
\(149\) 7.49126 0.613708 0.306854 0.951757i \(-0.400724\pi\)
0.306854 + 0.951757i \(0.400724\pi\)
\(150\) 0 0
\(151\) −15.9995 −1.30202 −0.651009 0.759070i \(-0.725654\pi\)
−0.651009 + 0.759070i \(0.725654\pi\)
\(152\) 0 0
\(153\) −14.3665 −1.16146
\(154\) 0 0
\(155\) −8.96233 −0.719871
\(156\) 0 0
\(157\) −4.30349 −0.343456 −0.171728 0.985144i \(-0.554935\pi\)
−0.171728 + 0.985144i \(0.554935\pi\)
\(158\) 0 0
\(159\) −0.301175 −0.0238847
\(160\) 0 0
\(161\) −6.71760 −0.529421
\(162\) 0 0
\(163\) −13.6145 −1.06637 −0.533186 0.845998i \(-0.679005\pi\)
−0.533186 + 0.845998i \(0.679005\pi\)
\(164\) 0 0
\(165\) 4.54939 0.354170
\(166\) 0 0
\(167\) −12.1152 −0.937499 −0.468749 0.883331i \(-0.655295\pi\)
−0.468749 + 0.883331i \(0.655295\pi\)
\(168\) 0 0
\(169\) 9.07536 0.698105
\(170\) 0 0
\(171\) −2.69585 −0.206157
\(172\) 0 0
\(173\) −9.49273 −0.721719 −0.360860 0.932620i \(-0.617517\pi\)
−0.360860 + 0.932620i \(0.617517\pi\)
\(174\) 0 0
\(175\) 0.754695 0.0570495
\(176\) 0 0
\(177\) 0.165481 0.0124383
\(178\) 0 0
\(179\) −11.5105 −0.860339 −0.430169 0.902748i \(-0.641546\pi\)
−0.430169 + 0.902748i \(0.641546\pi\)
\(180\) 0 0
\(181\) −14.4754 −1.07595 −0.537974 0.842962i \(-0.680810\pi\)
−0.537974 + 0.842962i \(0.680810\pi\)
\(182\) 0 0
\(183\) 5.01508 0.370725
\(184\) 0 0
\(185\) 4.90112 0.360338
\(186\) 0 0
\(187\) −18.8475 −1.37826
\(188\) 0 0
\(189\) −5.38369 −0.391606
\(190\) 0 0
\(191\) 16.2866 1.17846 0.589230 0.807966i \(-0.299431\pi\)
0.589230 + 0.807966i \(0.299431\pi\)
\(192\) 0 0
\(193\) −18.9798 −1.36620 −0.683098 0.730327i \(-0.739368\pi\)
−0.683098 + 0.730327i \(0.739368\pi\)
\(194\) 0 0
\(195\) −6.04377 −0.432803
\(196\) 0 0
\(197\) −20.9355 −1.49159 −0.745795 0.666176i \(-0.767930\pi\)
−0.745795 + 0.666176i \(0.767930\pi\)
\(198\) 0 0
\(199\) −7.29571 −0.517179 −0.258590 0.965987i \(-0.583258\pi\)
−0.258590 + 0.965987i \(0.583258\pi\)
\(200\) 0 0
\(201\) 1.55404 0.109614
\(202\) 0 0
\(203\) −0.556945 −0.0390899
\(204\) 0 0
\(205\) 26.3383 1.83955
\(206\) 0 0
\(207\) 10.5665 0.734421
\(208\) 0 0
\(209\) −3.53671 −0.244639
\(210\) 0 0
\(211\) −13.1473 −0.905095 −0.452548 0.891740i \(-0.649485\pi\)
−0.452548 + 0.891740i \(0.649485\pi\)
\(212\) 0 0
\(213\) −1.60357 −0.109874
\(214\) 0 0
\(215\) −10.7767 −0.734965
\(216\) 0 0
\(217\) 6.58549 0.447052
\(218\) 0 0
\(219\) −2.59711 −0.175497
\(220\) 0 0
\(221\) 25.0384 1.68427
\(222\) 0 0
\(223\) 19.6177 1.31370 0.656848 0.754023i \(-0.271889\pi\)
0.656848 + 0.754023i \(0.271889\pi\)
\(224\) 0 0
\(225\) −1.18710 −0.0791400
\(226\) 0 0
\(227\) −23.9438 −1.58921 −0.794604 0.607128i \(-0.792321\pi\)
−0.794604 + 0.607128i \(0.792321\pi\)
\(228\) 0 0
\(229\) 14.6084 0.965348 0.482674 0.875800i \(-0.339666\pi\)
0.482674 + 0.875800i \(0.339666\pi\)
\(230\) 0 0
\(231\) −3.34288 −0.219945
\(232\) 0 0
\(233\) −18.1942 −1.19194 −0.595972 0.803005i \(-0.703233\pi\)
−0.595972 + 0.803005i \(0.703233\pi\)
\(234\) 0 0
\(235\) −6.74556 −0.440032
\(236\) 0 0
\(237\) −0.551494 −0.0358234
\(238\) 0 0
\(239\) 5.60613 0.362631 0.181315 0.983425i \(-0.441965\pi\)
0.181315 + 0.983425i \(0.441965\pi\)
\(240\) 0 0
\(241\) −28.7704 −1.85327 −0.926634 0.375965i \(-0.877311\pi\)
−0.926634 + 0.375965i \(0.877311\pi\)
\(242\) 0 0
\(243\) 12.9285 0.829366
\(244\) 0 0
\(245\) 9.47587 0.605391
\(246\) 0 0
\(247\) 4.69844 0.298955
\(248\) 0 0
\(249\) −3.96251 −0.251114
\(250\) 0 0
\(251\) 10.7276 0.677123 0.338561 0.940944i \(-0.390060\pi\)
0.338561 + 0.940944i \(0.390060\pi\)
\(252\) 0 0
\(253\) 13.8622 0.871511
\(254\) 0 0
\(255\) −6.85499 −0.429276
\(256\) 0 0
\(257\) −2.13682 −0.133291 −0.0666456 0.997777i \(-0.521230\pi\)
−0.0666456 + 0.997777i \(0.521230\pi\)
\(258\) 0 0
\(259\) −3.60133 −0.223776
\(260\) 0 0
\(261\) 0.876049 0.0542260
\(262\) 0 0
\(263\) −22.6137 −1.39442 −0.697211 0.716866i \(-0.745576\pi\)
−0.697211 + 0.716866i \(0.745576\pi\)
\(264\) 0 0
\(265\) 1.27377 0.0782471
\(266\) 0 0
\(267\) −0.211213 −0.0129260
\(268\) 0 0
\(269\) 12.7666 0.778394 0.389197 0.921154i \(-0.372752\pi\)
0.389197 + 0.921154i \(0.372752\pi\)
\(270\) 0 0
\(271\) 3.49307 0.212189 0.106095 0.994356i \(-0.466165\pi\)
0.106095 + 0.994356i \(0.466165\pi\)
\(272\) 0 0
\(273\) 4.44094 0.268778
\(274\) 0 0
\(275\) −1.55737 −0.0939126
\(276\) 0 0
\(277\) −4.82775 −0.290071 −0.145036 0.989426i \(-0.546330\pi\)
−0.145036 + 0.989426i \(0.546330\pi\)
\(278\) 0 0
\(279\) −10.3587 −0.620157
\(280\) 0 0
\(281\) 15.4094 0.919246 0.459623 0.888114i \(-0.347984\pi\)
0.459623 + 0.888114i \(0.347984\pi\)
\(282\) 0 0
\(283\) 12.4756 0.741596 0.370798 0.928714i \(-0.379084\pi\)
0.370798 + 0.928714i \(0.379084\pi\)
\(284\) 0 0
\(285\) −1.28633 −0.0761959
\(286\) 0 0
\(287\) −19.3533 −1.14239
\(288\) 0 0
\(289\) 11.3992 0.670544
\(290\) 0 0
\(291\) 5.23039 0.306611
\(292\) 0 0
\(293\) −5.82125 −0.340081 −0.170040 0.985437i \(-0.554390\pi\)
−0.170040 + 0.985437i \(0.554390\pi\)
\(294\) 0 0
\(295\) −0.699875 −0.0407483
\(296\) 0 0
\(297\) 11.1096 0.644645
\(298\) 0 0
\(299\) −18.4157 −1.06501
\(300\) 0 0
\(301\) 7.91869 0.456425
\(302\) 0 0
\(303\) −5.83269 −0.335079
\(304\) 0 0
\(305\) −21.2105 −1.21451
\(306\) 0 0
\(307\) −17.3336 −0.989282 −0.494641 0.869097i \(-0.664700\pi\)
−0.494641 + 0.869097i \(0.664700\pi\)
\(308\) 0 0
\(309\) 4.33810 0.246786
\(310\) 0 0
\(311\) −27.0959 −1.53647 −0.768233 0.640170i \(-0.778864\pi\)
−0.768233 + 0.640170i \(0.778864\pi\)
\(312\) 0 0
\(313\) −9.12639 −0.515854 −0.257927 0.966164i \(-0.583039\pi\)
−0.257927 + 0.966164i \(0.583039\pi\)
\(314\) 0 0
\(315\) 10.7768 0.607204
\(316\) 0 0
\(317\) 18.6116 1.04533 0.522667 0.852537i \(-0.324937\pi\)
0.522667 + 0.852537i \(0.324937\pi\)
\(318\) 0 0
\(319\) 1.14929 0.0643481
\(320\) 0 0
\(321\) 1.05870 0.0590911
\(322\) 0 0
\(323\) 5.32909 0.296519
\(324\) 0 0
\(325\) 2.06893 0.114763
\(326\) 0 0
\(327\) −4.35755 −0.240973
\(328\) 0 0
\(329\) 4.95661 0.273267
\(330\) 0 0
\(331\) 25.6394 1.40927 0.704635 0.709570i \(-0.251111\pi\)
0.704635 + 0.709570i \(0.251111\pi\)
\(332\) 0 0
\(333\) 5.66473 0.310425
\(334\) 0 0
\(335\) −6.57258 −0.359098
\(336\) 0 0
\(337\) 11.0201 0.600301 0.300150 0.953892i \(-0.402963\pi\)
0.300150 + 0.953892i \(0.402963\pi\)
\(338\) 0 0
\(339\) 5.60594 0.304473
\(340\) 0 0
\(341\) −13.5896 −0.735919
\(342\) 0 0
\(343\) −18.9600 −1.02374
\(344\) 0 0
\(345\) 5.04182 0.271443
\(346\) 0 0
\(347\) 4.36718 0.234443 0.117221 0.993106i \(-0.462601\pi\)
0.117221 + 0.993106i \(0.462601\pi\)
\(348\) 0 0
\(349\) 3.57504 0.191367 0.0956837 0.995412i \(-0.469496\pi\)
0.0956837 + 0.995412i \(0.469496\pi\)
\(350\) 0 0
\(351\) −14.7589 −0.787771
\(352\) 0 0
\(353\) −22.2322 −1.18330 −0.591650 0.806195i \(-0.701523\pi\)
−0.591650 + 0.806195i \(0.701523\pi\)
\(354\) 0 0
\(355\) 6.78202 0.359952
\(356\) 0 0
\(357\) 5.03703 0.266588
\(358\) 0 0
\(359\) −4.85641 −0.256312 −0.128156 0.991754i \(-0.540906\pi\)
−0.128156 + 0.991754i \(0.540906\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0.831830 0.0436597
\(364\) 0 0
\(365\) 10.9841 0.574932
\(366\) 0 0
\(367\) −6.91138 −0.360771 −0.180385 0.983596i \(-0.557735\pi\)
−0.180385 + 0.983596i \(0.557735\pi\)
\(368\) 0 0
\(369\) 30.4418 1.58474
\(370\) 0 0
\(371\) −0.935962 −0.0485927
\(372\) 0 0
\(373\) 24.0299 1.24422 0.622111 0.782929i \(-0.286275\pi\)
0.622111 + 0.782929i \(0.286275\pi\)
\(374\) 0 0
\(375\) 5.86524 0.302880
\(376\) 0 0
\(377\) −1.52681 −0.0786348
\(378\) 0 0
\(379\) −25.4010 −1.30476 −0.652381 0.757891i \(-0.726230\pi\)
−0.652381 + 0.757891i \(0.726230\pi\)
\(380\) 0 0
\(381\) −1.43628 −0.0735830
\(382\) 0 0
\(383\) −1.77378 −0.0906361 −0.0453181 0.998973i \(-0.514430\pi\)
−0.0453181 + 0.998973i \(0.514430\pi\)
\(384\) 0 0
\(385\) 14.1382 0.720547
\(386\) 0 0
\(387\) −12.4557 −0.633161
\(388\) 0 0
\(389\) −23.9456 −1.21409 −0.607045 0.794668i \(-0.707645\pi\)
−0.607045 + 0.794668i \(0.707645\pi\)
\(390\) 0 0
\(391\) −20.8875 −1.05633
\(392\) 0 0
\(393\) −10.6229 −0.535854
\(394\) 0 0
\(395\) 2.33245 0.117359
\(396\) 0 0
\(397\) −15.9045 −0.798224 −0.399112 0.916902i \(-0.630681\pi\)
−0.399112 + 0.916902i \(0.630681\pi\)
\(398\) 0 0
\(399\) 0.945194 0.0473189
\(400\) 0 0
\(401\) 33.2798 1.66191 0.830956 0.556338i \(-0.187794\pi\)
0.830956 + 0.556338i \(0.187794\pi\)
\(402\) 0 0
\(403\) 18.0535 0.899309
\(404\) 0 0
\(405\) −14.8232 −0.736571
\(406\) 0 0
\(407\) 7.43160 0.368371
\(408\) 0 0
\(409\) 7.01715 0.346976 0.173488 0.984836i \(-0.444496\pi\)
0.173488 + 0.984836i \(0.444496\pi\)
\(410\) 0 0
\(411\) −5.30942 −0.261895
\(412\) 0 0
\(413\) 0.514266 0.0253054
\(414\) 0 0
\(415\) 16.7588 0.822657
\(416\) 0 0
\(417\) −5.36946 −0.262944
\(418\) 0 0
\(419\) 17.4745 0.853684 0.426842 0.904326i \(-0.359626\pi\)
0.426842 + 0.904326i \(0.359626\pi\)
\(420\) 0 0
\(421\) 12.4501 0.606778 0.303389 0.952867i \(-0.401882\pi\)
0.303389 + 0.952867i \(0.401882\pi\)
\(422\) 0 0
\(423\) −7.79653 −0.379080
\(424\) 0 0
\(425\) 2.34663 0.113828
\(426\) 0 0
\(427\) 15.5854 0.754230
\(428\) 0 0
\(429\) −9.16419 −0.442451
\(430\) 0 0
\(431\) 2.27235 0.109455 0.0547277 0.998501i \(-0.482571\pi\)
0.0547277 + 0.998501i \(0.482571\pi\)
\(432\) 0 0
\(433\) −18.9362 −0.910016 −0.455008 0.890487i \(-0.650364\pi\)
−0.455008 + 0.890487i \(0.650364\pi\)
\(434\) 0 0
\(435\) 0.418009 0.0200420
\(436\) 0 0
\(437\) −3.91953 −0.187496
\(438\) 0 0
\(439\) 20.3208 0.969858 0.484929 0.874553i \(-0.338845\pi\)
0.484929 + 0.874553i \(0.338845\pi\)
\(440\) 0 0
\(441\) 10.9522 0.521535
\(442\) 0 0
\(443\) 10.8608 0.516014 0.258007 0.966143i \(-0.416934\pi\)
0.258007 + 0.966143i \(0.416934\pi\)
\(444\) 0 0
\(445\) 0.893291 0.0423460
\(446\) 0 0
\(447\) 4.13138 0.195408
\(448\) 0 0
\(449\) −0.0385882 −0.00182109 −0.000910544 1.00000i \(-0.500290\pi\)
−0.000910544 1.00000i \(0.500290\pi\)
\(450\) 0 0
\(451\) 39.9369 1.88055
\(452\) 0 0
\(453\) −8.82360 −0.414569
\(454\) 0 0
\(455\) −18.7822 −0.880525
\(456\) 0 0
\(457\) −24.6041 −1.15093 −0.575465 0.817827i \(-0.695179\pi\)
−0.575465 + 0.817827i \(0.695179\pi\)
\(458\) 0 0
\(459\) −16.7399 −0.781352
\(460\) 0 0
\(461\) −3.44396 −0.160401 −0.0802006 0.996779i \(-0.525556\pi\)
−0.0802006 + 0.996779i \(0.525556\pi\)
\(462\) 0 0
\(463\) −3.63555 −0.168958 −0.0844792 0.996425i \(-0.526923\pi\)
−0.0844792 + 0.996425i \(0.526923\pi\)
\(464\) 0 0
\(465\) −4.94267 −0.229211
\(466\) 0 0
\(467\) 6.99303 0.323599 0.161799 0.986824i \(-0.448270\pi\)
0.161799 + 0.986824i \(0.448270\pi\)
\(468\) 0 0
\(469\) 4.82951 0.223006
\(470\) 0 0
\(471\) −2.37335 −0.109358
\(472\) 0 0
\(473\) −16.3408 −0.751349
\(474\) 0 0
\(475\) 0.440343 0.0202043
\(476\) 0 0
\(477\) 1.47223 0.0674086
\(478\) 0 0
\(479\) −11.4283 −0.522173 −0.261087 0.965315i \(-0.584081\pi\)
−0.261087 + 0.965315i \(0.584081\pi\)
\(480\) 0 0
\(481\) −9.87271 −0.450157
\(482\) 0 0
\(483\) −3.70471 −0.168570
\(484\) 0 0
\(485\) −22.1211 −1.00447
\(486\) 0 0
\(487\) −9.46872 −0.429069 −0.214534 0.976716i \(-0.568823\pi\)
−0.214534 + 0.976716i \(0.568823\pi\)
\(488\) 0 0
\(489\) −7.50833 −0.339538
\(490\) 0 0
\(491\) 27.5301 1.24242 0.621208 0.783646i \(-0.286642\pi\)
0.621208 + 0.783646i \(0.286642\pi\)
\(492\) 0 0
\(493\) −1.73175 −0.0779941
\(494\) 0 0
\(495\) −22.2387 −0.999555
\(496\) 0 0
\(497\) −4.98341 −0.223536
\(498\) 0 0
\(499\) 23.3914 1.04714 0.523571 0.851982i \(-0.324600\pi\)
0.523571 + 0.851982i \(0.324600\pi\)
\(500\) 0 0
\(501\) −6.68143 −0.298504
\(502\) 0 0
\(503\) −15.3259 −0.683349 −0.341675 0.939818i \(-0.610994\pi\)
−0.341675 + 0.939818i \(0.610994\pi\)
\(504\) 0 0
\(505\) 24.6684 1.09773
\(506\) 0 0
\(507\) 5.00500 0.222280
\(508\) 0 0
\(509\) −4.88553 −0.216547 −0.108274 0.994121i \(-0.534532\pi\)
−0.108274 + 0.994121i \(0.534532\pi\)
\(510\) 0 0
\(511\) −8.07105 −0.357042
\(512\) 0 0
\(513\) −3.14123 −0.138689
\(514\) 0 0
\(515\) −18.3473 −0.808478
\(516\) 0 0
\(517\) −10.2283 −0.449841
\(518\) 0 0
\(519\) −5.23518 −0.229799
\(520\) 0 0
\(521\) −26.1291 −1.14474 −0.572368 0.819997i \(-0.693975\pi\)
−0.572368 + 0.819997i \(0.693975\pi\)
\(522\) 0 0
\(523\) 36.3655 1.59015 0.795076 0.606510i \(-0.207431\pi\)
0.795076 + 0.606510i \(0.207431\pi\)
\(524\) 0 0
\(525\) 0.416209 0.0181649
\(526\) 0 0
\(527\) 20.4767 0.891981
\(528\) 0 0
\(529\) −7.63730 −0.332056
\(530\) 0 0
\(531\) −0.808916 −0.0351040
\(532\) 0 0
\(533\) −53.0552 −2.29808
\(534\) 0 0
\(535\) −4.47762 −0.193584
\(536\) 0 0
\(537\) −6.34800 −0.273936
\(538\) 0 0
\(539\) 14.3683 0.618886
\(540\) 0 0
\(541\) −5.96783 −0.256577 −0.128288 0.991737i \(-0.540948\pi\)
−0.128288 + 0.991737i \(0.540948\pi\)
\(542\) 0 0
\(543\) −7.98309 −0.342587
\(544\) 0 0
\(545\) 18.4295 0.789435
\(546\) 0 0
\(547\) 16.1536 0.690677 0.345338 0.938478i \(-0.387764\pi\)
0.345338 + 0.938478i \(0.387764\pi\)
\(548\) 0 0
\(549\) −24.5151 −1.04628
\(550\) 0 0
\(551\) −0.324961 −0.0138438
\(552\) 0 0
\(553\) −1.71388 −0.0728816
\(554\) 0 0
\(555\) 2.70294 0.114733
\(556\) 0 0
\(557\) 3.78564 0.160403 0.0802014 0.996779i \(-0.474444\pi\)
0.0802014 + 0.996779i \(0.474444\pi\)
\(558\) 0 0
\(559\) 21.7083 0.918165
\(560\) 0 0
\(561\) −10.3943 −0.438846
\(562\) 0 0
\(563\) 35.8237 1.50979 0.754894 0.655847i \(-0.227688\pi\)
0.754894 + 0.655847i \(0.227688\pi\)
\(564\) 0 0
\(565\) −23.7094 −0.997463
\(566\) 0 0
\(567\) 10.8920 0.457423
\(568\) 0 0
\(569\) 3.96194 0.166093 0.0830466 0.996546i \(-0.473535\pi\)
0.0830466 + 0.996546i \(0.473535\pi\)
\(570\) 0 0
\(571\) 5.11927 0.214235 0.107117 0.994246i \(-0.465838\pi\)
0.107117 + 0.994246i \(0.465838\pi\)
\(572\) 0 0
\(573\) 8.98198 0.375227
\(574\) 0 0
\(575\) −1.72594 −0.0719765
\(576\) 0 0
\(577\) 6.84993 0.285166 0.142583 0.989783i \(-0.454459\pi\)
0.142583 + 0.989783i \(0.454459\pi\)
\(578\) 0 0
\(579\) −10.4672 −0.435004
\(580\) 0 0
\(581\) −12.3143 −0.510884
\(582\) 0 0
\(583\) 1.93142 0.0799914
\(584\) 0 0
\(585\) 29.5436 1.22148
\(586\) 0 0
\(587\) −41.6010 −1.71706 −0.858529 0.512765i \(-0.828621\pi\)
−0.858529 + 0.512765i \(0.828621\pi\)
\(588\) 0 0
\(589\) 3.84244 0.158325
\(590\) 0 0
\(591\) −11.5458 −0.474930
\(592\) 0 0
\(593\) −27.4100 −1.12560 −0.562798 0.826595i \(-0.690275\pi\)
−0.562798 + 0.826595i \(0.690275\pi\)
\(594\) 0 0
\(595\) −21.3033 −0.873350
\(596\) 0 0
\(597\) −4.02354 −0.164673
\(598\) 0 0
\(599\) 19.4747 0.795715 0.397858 0.917447i \(-0.369754\pi\)
0.397858 + 0.917447i \(0.369754\pi\)
\(600\) 0 0
\(601\) 18.9379 0.772494 0.386247 0.922395i \(-0.373771\pi\)
0.386247 + 0.922395i \(0.373771\pi\)
\(602\) 0 0
\(603\) −7.59660 −0.309357
\(604\) 0 0
\(605\) −3.51809 −0.143031
\(606\) 0 0
\(607\) −6.93694 −0.281562 −0.140781 0.990041i \(-0.544961\pi\)
−0.140781 + 0.990041i \(0.544961\pi\)
\(608\) 0 0
\(609\) −0.307152 −0.0124464
\(610\) 0 0
\(611\) 13.5881 0.549715
\(612\) 0 0
\(613\) −3.55651 −0.143646 −0.0718230 0.997417i \(-0.522882\pi\)
−0.0718230 + 0.997417i \(0.522882\pi\)
\(614\) 0 0
\(615\) 14.5254 0.585721
\(616\) 0 0
\(617\) 23.5205 0.946898 0.473449 0.880821i \(-0.343009\pi\)
0.473449 + 0.880821i \(0.343009\pi\)
\(618\) 0 0
\(619\) −34.7111 −1.39516 −0.697579 0.716508i \(-0.745739\pi\)
−0.697579 + 0.716508i \(0.745739\pi\)
\(620\) 0 0
\(621\) 12.3121 0.494069
\(622\) 0 0
\(623\) −0.656387 −0.0262976
\(624\) 0 0
\(625\) −27.0078 −1.08031
\(626\) 0 0
\(627\) −1.95047 −0.0778944
\(628\) 0 0
\(629\) −11.1979 −0.446489
\(630\) 0 0
\(631\) 3.05530 0.121629 0.0608147 0.998149i \(-0.480630\pi\)
0.0608147 + 0.998149i \(0.480630\pi\)
\(632\) 0 0
\(633\) −7.25064 −0.288187
\(634\) 0 0
\(635\) 6.07453 0.241060
\(636\) 0 0
\(637\) −19.0880 −0.756293
\(638\) 0 0
\(639\) 7.83867 0.310093
\(640\) 0 0
\(641\) −23.8983 −0.943926 −0.471963 0.881618i \(-0.656454\pi\)
−0.471963 + 0.881618i \(0.656454\pi\)
\(642\) 0 0
\(643\) 22.4725 0.886230 0.443115 0.896465i \(-0.353873\pi\)
0.443115 + 0.896465i \(0.353873\pi\)
\(644\) 0 0
\(645\) −5.94329 −0.234017
\(646\) 0 0
\(647\) −17.4452 −0.685841 −0.342921 0.939364i \(-0.611416\pi\)
−0.342921 + 0.939364i \(0.611416\pi\)
\(648\) 0 0
\(649\) −1.06122 −0.0416566
\(650\) 0 0
\(651\) 3.63185 0.142344
\(652\) 0 0
\(653\) −34.4384 −1.34768 −0.673838 0.738879i \(-0.735356\pi\)
−0.673838 + 0.738879i \(0.735356\pi\)
\(654\) 0 0
\(655\) 44.9278 1.75548
\(656\) 0 0
\(657\) 12.6954 0.495295
\(658\) 0 0
\(659\) 23.8064 0.927366 0.463683 0.886001i \(-0.346528\pi\)
0.463683 + 0.886001i \(0.346528\pi\)
\(660\) 0 0
\(661\) 13.2148 0.513996 0.256998 0.966412i \(-0.417267\pi\)
0.256998 + 0.966412i \(0.417267\pi\)
\(662\) 0 0
\(663\) 13.8085 0.536279
\(664\) 0 0
\(665\) −3.99755 −0.155018
\(666\) 0 0
\(667\) 1.27370 0.0493177
\(668\) 0 0
\(669\) 10.8190 0.418287
\(670\) 0 0
\(671\) −32.1615 −1.24158
\(672\) 0 0
\(673\) −5.09177 −0.196273 −0.0981367 0.995173i \(-0.531288\pi\)
−0.0981367 + 0.995173i \(0.531288\pi\)
\(674\) 0 0
\(675\) −1.38322 −0.0532401
\(676\) 0 0
\(677\) 34.8295 1.33861 0.669304 0.742989i \(-0.266592\pi\)
0.669304 + 0.742989i \(0.266592\pi\)
\(678\) 0 0
\(679\) 16.2545 0.623790
\(680\) 0 0
\(681\) −13.2049 −0.506012
\(682\) 0 0
\(683\) −2.06932 −0.0791805 −0.0395903 0.999216i \(-0.512605\pi\)
−0.0395903 + 0.999216i \(0.512605\pi\)
\(684\) 0 0
\(685\) 22.4554 0.857975
\(686\) 0 0
\(687\) 8.05642 0.307372
\(688\) 0 0
\(689\) −2.56585 −0.0977512
\(690\) 0 0
\(691\) 21.3673 0.812849 0.406425 0.913684i \(-0.366775\pi\)
0.406425 + 0.913684i \(0.366775\pi\)
\(692\) 0 0
\(693\) 16.3409 0.620740
\(694\) 0 0
\(695\) 22.7093 0.861412
\(696\) 0 0
\(697\) −60.1766 −2.27935
\(698\) 0 0
\(699\) −10.0340 −0.379521
\(700\) 0 0
\(701\) 40.5989 1.53340 0.766699 0.642007i \(-0.221898\pi\)
0.766699 + 0.642007i \(0.221898\pi\)
\(702\) 0 0
\(703\) −2.10127 −0.0792510
\(704\) 0 0
\(705\) −3.72013 −0.140108
\(706\) 0 0
\(707\) −18.1263 −0.681709
\(708\) 0 0
\(709\) 40.2735 1.51250 0.756251 0.654282i \(-0.227029\pi\)
0.756251 + 0.654282i \(0.227029\pi\)
\(710\) 0 0
\(711\) 2.69585 0.101102
\(712\) 0 0
\(713\) −15.0606 −0.564023
\(714\) 0 0
\(715\) 38.7585 1.44948
\(716\) 0 0
\(717\) 3.09175 0.115463
\(718\) 0 0
\(719\) −6.23722 −0.232609 −0.116304 0.993214i \(-0.537105\pi\)
−0.116304 + 0.993214i \(0.537105\pi\)
\(720\) 0 0
\(721\) 13.4815 0.502078
\(722\) 0 0
\(723\) −15.8667 −0.590090
\(724\) 0 0
\(725\) −0.143094 −0.00531439
\(726\) 0 0
\(727\) −1.57859 −0.0585468 −0.0292734 0.999571i \(-0.509319\pi\)
−0.0292734 + 0.999571i \(0.509319\pi\)
\(728\) 0 0
\(729\) −11.9356 −0.442058
\(730\) 0 0
\(731\) 24.6222 0.910684
\(732\) 0 0
\(733\) −40.6866 −1.50279 −0.751397 0.659850i \(-0.770620\pi\)
−0.751397 + 0.659850i \(0.770620\pi\)
\(734\) 0 0
\(735\) 5.22588 0.192760
\(736\) 0 0
\(737\) −9.96603 −0.367103
\(738\) 0 0
\(739\) 11.5017 0.423097 0.211549 0.977367i \(-0.432149\pi\)
0.211549 + 0.977367i \(0.432149\pi\)
\(740\) 0 0
\(741\) 2.59116 0.0951887
\(742\) 0 0
\(743\) 33.8782 1.24287 0.621436 0.783465i \(-0.286550\pi\)
0.621436 + 0.783465i \(0.286550\pi\)
\(744\) 0 0
\(745\) −17.4730 −0.640162
\(746\) 0 0
\(747\) 19.3699 0.708706
\(748\) 0 0
\(749\) 3.29014 0.120219
\(750\) 0 0
\(751\) −13.8925 −0.506946 −0.253473 0.967342i \(-0.581573\pi\)
−0.253473 + 0.967342i \(0.581573\pi\)
\(752\) 0 0
\(753\) 5.91623 0.215599
\(754\) 0 0
\(755\) 37.3180 1.35814
\(756\) 0 0
\(757\) 9.65414 0.350886 0.175443 0.984490i \(-0.443864\pi\)
0.175443 + 0.984490i \(0.443864\pi\)
\(758\) 0 0
\(759\) 7.64494 0.277494
\(760\) 0 0
\(761\) 39.5418 1.43339 0.716695 0.697387i \(-0.245654\pi\)
0.716695 + 0.697387i \(0.245654\pi\)
\(762\) 0 0
\(763\) −13.5420 −0.490252
\(764\) 0 0
\(765\) 33.5091 1.21152
\(766\) 0 0
\(767\) 1.40981 0.0509053
\(768\) 0 0
\(769\) 12.1385 0.437725 0.218863 0.975756i \(-0.429765\pi\)
0.218863 + 0.975756i \(0.429765\pi\)
\(770\) 0 0
\(771\) −1.17844 −0.0424406
\(772\) 0 0
\(773\) −24.9702 −0.898116 −0.449058 0.893503i \(-0.648240\pi\)
−0.449058 + 0.893503i \(0.648240\pi\)
\(774\) 0 0
\(775\) 1.69199 0.0607782
\(776\) 0 0
\(777\) −1.98611 −0.0712513
\(778\) 0 0
\(779\) −11.2921 −0.404581
\(780\) 0 0
\(781\) 10.2836 0.367976
\(782\) 0 0
\(783\) 1.02078 0.0364796
\(784\) 0 0
\(785\) 10.0377 0.358261
\(786\) 0 0
\(787\) 13.8195 0.492611 0.246306 0.969192i \(-0.420783\pi\)
0.246306 + 0.969192i \(0.420783\pi\)
\(788\) 0 0
\(789\) −12.4713 −0.443991
\(790\) 0 0
\(791\) 17.4216 0.619441
\(792\) 0 0
\(793\) 42.7259 1.51724
\(794\) 0 0
\(795\) 0.702476 0.0249143
\(796\) 0 0
\(797\) −43.3248 −1.53464 −0.767322 0.641262i \(-0.778411\pi\)
−0.767322 + 0.641262i \(0.778411\pi\)
\(798\) 0 0
\(799\) 15.4120 0.545236
\(800\) 0 0
\(801\) 1.03247 0.0364804
\(802\) 0 0
\(803\) 16.6552 0.587749
\(804\) 0 0
\(805\) 15.6685 0.552242
\(806\) 0 0
\(807\) 7.04071 0.247845
\(808\) 0 0
\(809\) −34.8498 −1.22525 −0.612626 0.790373i \(-0.709887\pi\)
−0.612626 + 0.790373i \(0.709887\pi\)
\(810\) 0 0
\(811\) 6.98390 0.245238 0.122619 0.992454i \(-0.460871\pi\)
0.122619 + 0.992454i \(0.460871\pi\)
\(812\) 0 0
\(813\) 1.92641 0.0675621
\(814\) 0 0
\(815\) 31.7553 1.11234
\(816\) 0 0
\(817\) 4.62033 0.161645
\(818\) 0 0
\(819\) −21.7085 −0.758558
\(820\) 0 0
\(821\) 4.67463 0.163146 0.0815729 0.996667i \(-0.474006\pi\)
0.0815729 + 0.996667i \(0.474006\pi\)
\(822\) 0 0
\(823\) −32.1574 −1.12094 −0.560468 0.828176i \(-0.689379\pi\)
−0.560468 + 0.828176i \(0.689379\pi\)
\(824\) 0 0
\(825\) −0.858877 −0.0299023
\(826\) 0 0
\(827\) 11.0811 0.385326 0.192663 0.981265i \(-0.438288\pi\)
0.192663 + 0.981265i \(0.438288\pi\)
\(828\) 0 0
\(829\) 33.8575 1.17592 0.587960 0.808890i \(-0.299931\pi\)
0.587960 + 0.808890i \(0.299931\pi\)
\(830\) 0 0
\(831\) −2.66247 −0.0923602
\(832\) 0 0
\(833\) −21.6501 −0.750130
\(834\) 0 0
\(835\) 28.2580 0.977910
\(836\) 0 0
\(837\) −12.0700 −0.417200
\(838\) 0 0
\(839\) 22.4869 0.776335 0.388167 0.921589i \(-0.373108\pi\)
0.388167 + 0.921589i \(0.373108\pi\)
\(840\) 0 0
\(841\) −28.8944 −0.996359
\(842\) 0 0
\(843\) 8.49817 0.292693
\(844\) 0 0
\(845\) −21.1679 −0.728197
\(846\) 0 0
\(847\) 2.58508 0.0888244
\(848\) 0 0
\(849\) 6.88020 0.236128
\(850\) 0 0
\(851\) 8.23600 0.282326
\(852\) 0 0
\(853\) −15.3748 −0.526424 −0.263212 0.964738i \(-0.584782\pi\)
−0.263212 + 0.964738i \(0.584782\pi\)
\(854\) 0 0
\(855\) 6.28796 0.215044
\(856\) 0 0
\(857\) −20.0666 −0.685461 −0.342731 0.939434i \(-0.611352\pi\)
−0.342731 + 0.939434i \(0.611352\pi\)
\(858\) 0 0
\(859\) 55.6464 1.89863 0.949316 0.314324i \(-0.101778\pi\)
0.949316 + 0.314324i \(0.101778\pi\)
\(860\) 0 0
\(861\) −10.6732 −0.363742
\(862\) 0 0
\(863\) 7.38734 0.251468 0.125734 0.992064i \(-0.459871\pi\)
0.125734 + 0.992064i \(0.459871\pi\)
\(864\) 0 0
\(865\) 22.1414 0.752829
\(866\) 0 0
\(867\) 6.28661 0.213504
\(868\) 0 0
\(869\) 3.53671 0.119975
\(870\) 0 0
\(871\) 13.2397 0.448609
\(872\) 0 0
\(873\) −25.5676 −0.865331
\(874\) 0 0
\(875\) 18.2274 0.616200
\(876\) 0 0
\(877\) −33.6251 −1.13544 −0.567719 0.823222i \(-0.692174\pi\)
−0.567719 + 0.823222i \(0.692174\pi\)
\(878\) 0 0
\(879\) −3.21038 −0.108283
\(880\) 0 0
\(881\) −15.1146 −0.509223 −0.254611 0.967043i \(-0.581948\pi\)
−0.254611 + 0.967043i \(0.581948\pi\)
\(882\) 0 0
\(883\) 51.8924 1.74632 0.873159 0.487436i \(-0.162068\pi\)
0.873159 + 0.487436i \(0.162068\pi\)
\(884\) 0 0
\(885\) −0.385977 −0.0129745
\(886\) 0 0
\(887\) 35.6676 1.19760 0.598801 0.800898i \(-0.295644\pi\)
0.598801 + 0.800898i \(0.295644\pi\)
\(888\) 0 0
\(889\) −4.46354 −0.149702
\(890\) 0 0
\(891\) −22.4765 −0.752991
\(892\) 0 0
\(893\) 2.89204 0.0967785
\(894\) 0 0
\(895\) 26.8478 0.897424
\(896\) 0 0
\(897\) −10.1561 −0.339103
\(898\) 0 0
\(899\) −1.24865 −0.0416447
\(900\) 0 0
\(901\) −2.91026 −0.0969547
\(902\) 0 0
\(903\) 4.36711 0.145328
\(904\) 0 0
\(905\) 33.7632 1.12233
\(906\) 0 0
\(907\) −11.7811 −0.391185 −0.195592 0.980685i \(-0.562663\pi\)
−0.195592 + 0.980685i \(0.562663\pi\)
\(908\) 0 0
\(909\) 28.5118 0.945677
\(910\) 0 0
\(911\) −10.4484 −0.346172 −0.173086 0.984907i \(-0.555374\pi\)
−0.173086 + 0.984907i \(0.555374\pi\)
\(912\) 0 0
\(913\) 25.4114 0.840996
\(914\) 0 0
\(915\) −11.6974 −0.386706
\(916\) 0 0
\(917\) −33.0128 −1.09018
\(918\) 0 0
\(919\) −13.2675 −0.437654 −0.218827 0.975764i \(-0.570223\pi\)
−0.218827 + 0.975764i \(0.570223\pi\)
\(920\) 0 0
\(921\) −9.55938 −0.314992
\(922\) 0 0
\(923\) −13.6615 −0.449675
\(924\) 0 0
\(925\) −0.925281 −0.0304230
\(926\) 0 0
\(927\) −21.2058 −0.696491
\(928\) 0 0
\(929\) −21.4918 −0.705122 −0.352561 0.935789i \(-0.614689\pi\)
−0.352561 + 0.935789i \(0.614689\pi\)
\(930\) 0 0
\(931\) −4.06262 −0.133147
\(932\) 0 0
\(933\) −14.9432 −0.489219
\(934\) 0 0
\(935\) 43.9608 1.43767
\(936\) 0 0
\(937\) −49.4503 −1.61547 −0.807736 0.589544i \(-0.799307\pi\)
−0.807736 + 0.589544i \(0.799307\pi\)
\(938\) 0 0
\(939\) −5.03315 −0.164251
\(940\) 0 0
\(941\) −12.0226 −0.391926 −0.195963 0.980611i \(-0.562783\pi\)
−0.195963 + 0.980611i \(0.562783\pi\)
\(942\) 0 0
\(943\) 44.2597 1.44129
\(944\) 0 0
\(945\) 12.5572 0.408486
\(946\) 0 0
\(947\) −7.52851 −0.244644 −0.122322 0.992490i \(-0.539034\pi\)
−0.122322 + 0.992490i \(0.539034\pi\)
\(948\) 0 0
\(949\) −22.1260 −0.718242
\(950\) 0 0
\(951\) 10.2642 0.332839
\(952\) 0 0
\(953\) 45.3137 1.46786 0.733928 0.679227i \(-0.237685\pi\)
0.733928 + 0.679227i \(0.237685\pi\)
\(954\) 0 0
\(955\) −37.9878 −1.22926
\(956\) 0 0
\(957\) 0.633829 0.0204888
\(958\) 0 0
\(959\) −16.5001 −0.532817
\(960\) 0 0
\(961\) −16.2356 −0.523730
\(962\) 0 0
\(963\) −5.17524 −0.166770
\(964\) 0 0
\(965\) 44.2695 1.42509
\(966\) 0 0
\(967\) −10.5612 −0.339626 −0.169813 0.985476i \(-0.554316\pi\)
−0.169813 + 0.985476i \(0.554316\pi\)
\(968\) 0 0
\(969\) 2.93896 0.0944131
\(970\) 0 0
\(971\) −17.9450 −0.575882 −0.287941 0.957648i \(-0.592971\pi\)
−0.287941 + 0.957648i \(0.592971\pi\)
\(972\) 0 0
\(973\) −16.6867 −0.534951
\(974\) 0 0
\(975\) 1.14100 0.0365412
\(976\) 0 0
\(977\) 56.0463 1.79308 0.896541 0.442961i \(-0.146072\pi\)
0.896541 + 0.442961i \(0.146072\pi\)
\(978\) 0 0
\(979\) 1.35450 0.0432900
\(980\) 0 0
\(981\) 21.3009 0.680085
\(982\) 0 0
\(983\) −31.9561 −1.01924 −0.509621 0.860399i \(-0.670215\pi\)
−0.509621 + 0.860399i \(0.670215\pi\)
\(984\) 0 0
\(985\) 48.8310 1.55588
\(986\) 0 0
\(987\) 2.73354 0.0870096
\(988\) 0 0
\(989\) −18.1095 −0.575849
\(990\) 0 0
\(991\) 9.39318 0.298384 0.149192 0.988808i \(-0.452333\pi\)
0.149192 + 0.988808i \(0.452333\pi\)
\(992\) 0 0
\(993\) 14.1400 0.448719
\(994\) 0 0
\(995\) 17.0169 0.539472
\(996\) 0 0
\(997\) −36.1148 −1.14377 −0.571884 0.820335i \(-0.693787\pi\)
−0.571884 + 0.820335i \(0.693787\pi\)
\(998\) 0 0
\(999\) 6.60058 0.208833
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 \(a_p\))