Properties

Label 6036.2.a.i.1.4
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 1.4
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-2.74974 q^{5}\) \(+1.46678 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-2.74974 q^{5}\) \(+1.46678 q^{7}\) \(+1.00000 q^{9}\) \(+4.30996 q^{11}\) \(+3.43074 q^{13}\) \(+2.74974 q^{15}\) \(+7.91411 q^{17}\) \(+1.80273 q^{19}\) \(-1.46678 q^{21}\) \(+1.83865 q^{23}\) \(+2.56107 q^{25}\) \(-1.00000 q^{27}\) \(+8.64332 q^{29}\) \(+3.70268 q^{31}\) \(-4.30996 q^{33}\) \(-4.03326 q^{35}\) \(+11.8125 q^{37}\) \(-3.43074 q^{39}\) \(+0.510657 q^{41}\) \(-7.96228 q^{43}\) \(-2.74974 q^{45}\) \(-4.97314 q^{47}\) \(-4.84856 q^{49}\) \(-7.91411 q^{51}\) \(-13.7075 q^{53}\) \(-11.8513 q^{55}\) \(-1.80273 q^{57}\) \(-1.90341 q^{59}\) \(-0.965055 q^{61}\) \(+1.46678 q^{63}\) \(-9.43365 q^{65}\) \(+9.78064 q^{67}\) \(-1.83865 q^{69}\) \(-2.19283 q^{71}\) \(-8.61320 q^{73}\) \(-2.56107 q^{75}\) \(+6.32176 q^{77}\) \(+4.80388 q^{79}\) \(+1.00000 q^{81}\) \(+9.61818 q^{83}\) \(-21.7617 q^{85}\) \(-8.64332 q^{87}\) \(+6.41609 q^{89}\) \(+5.03214 q^{91}\) \(-3.70268 q^{93}\) \(-4.95703 q^{95}\) \(+11.8923 q^{97}\) \(+4.30996 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −2.74974 −1.22972 −0.614861 0.788636i \(-0.710788\pi\)
−0.614861 + 0.788636i \(0.710788\pi\)
\(6\) 0 0
\(7\) 1.46678 0.554390 0.277195 0.960814i \(-0.410595\pi\)
0.277195 + 0.960814i \(0.410595\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 4.30996 1.29950 0.649751 0.760147i \(-0.274873\pi\)
0.649751 + 0.760147i \(0.274873\pi\)
\(12\) 0 0
\(13\) 3.43074 0.951517 0.475758 0.879576i \(-0.342174\pi\)
0.475758 + 0.879576i \(0.342174\pi\)
\(14\) 0 0
\(15\) 2.74974 0.709980
\(16\) 0 0
\(17\) 7.91411 1.91945 0.959727 0.280935i \(-0.0906445\pi\)
0.959727 + 0.280935i \(0.0906445\pi\)
\(18\) 0 0
\(19\) 1.80273 0.413574 0.206787 0.978386i \(-0.433699\pi\)
0.206787 + 0.978386i \(0.433699\pi\)
\(20\) 0 0
\(21\) −1.46678 −0.320077
\(22\) 0 0
\(23\) 1.83865 0.383385 0.191692 0.981455i \(-0.438602\pi\)
0.191692 + 0.981455i \(0.438602\pi\)
\(24\) 0 0
\(25\) 2.56107 0.512214
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 8.64332 1.60502 0.802512 0.596636i \(-0.203496\pi\)
0.802512 + 0.596636i \(0.203496\pi\)
\(30\) 0 0
\(31\) 3.70268 0.665021 0.332510 0.943100i \(-0.392104\pi\)
0.332510 + 0.943100i \(0.392104\pi\)
\(32\) 0 0
\(33\) −4.30996 −0.750268
\(34\) 0 0
\(35\) −4.03326 −0.681746
\(36\) 0 0
\(37\) 11.8125 1.94196 0.970981 0.239156i \(-0.0768706\pi\)
0.970981 + 0.239156i \(0.0768706\pi\)
\(38\) 0 0
\(39\) −3.43074 −0.549358
\(40\) 0 0
\(41\) 0.510657 0.0797513 0.0398756 0.999205i \(-0.487304\pi\)
0.0398756 + 0.999205i \(0.487304\pi\)
\(42\) 0 0
\(43\) −7.96228 −1.21424 −0.607118 0.794612i \(-0.707675\pi\)
−0.607118 + 0.794612i \(0.707675\pi\)
\(44\) 0 0
\(45\) −2.74974 −0.409907
\(46\) 0 0
\(47\) −4.97314 −0.725407 −0.362704 0.931904i \(-0.618146\pi\)
−0.362704 + 0.931904i \(0.618146\pi\)
\(48\) 0 0
\(49\) −4.84856 −0.692651
\(50\) 0 0
\(51\) −7.91411 −1.10820
\(52\) 0 0
\(53\) −13.7075 −1.88287 −0.941435 0.337195i \(-0.890522\pi\)
−0.941435 + 0.337195i \(0.890522\pi\)
\(54\) 0 0
\(55\) −11.8513 −1.59803
\(56\) 0 0
\(57\) −1.80273 −0.238777
\(58\) 0 0
\(59\) −1.90341 −0.247802 −0.123901 0.992295i \(-0.539541\pi\)
−0.123901 + 0.992295i \(0.539541\pi\)
\(60\) 0 0
\(61\) −0.965055 −0.123563 −0.0617813 0.998090i \(-0.519678\pi\)
−0.0617813 + 0.998090i \(0.519678\pi\)
\(62\) 0 0
\(63\) 1.46678 0.184797
\(64\) 0 0
\(65\) −9.43365 −1.17010
\(66\) 0 0
\(67\) 9.78064 1.19490 0.597448 0.801908i \(-0.296182\pi\)
0.597448 + 0.801908i \(0.296182\pi\)
\(68\) 0 0
\(69\) −1.83865 −0.221347
\(70\) 0 0
\(71\) −2.19283 −0.260241 −0.130121 0.991498i \(-0.541536\pi\)
−0.130121 + 0.991498i \(0.541536\pi\)
\(72\) 0 0
\(73\) −8.61320 −1.00810 −0.504049 0.863675i \(-0.668157\pi\)
−0.504049 + 0.863675i \(0.668157\pi\)
\(74\) 0 0
\(75\) −2.56107 −0.295727
\(76\) 0 0
\(77\) 6.32176 0.720432
\(78\) 0 0
\(79\) 4.80388 0.540479 0.270239 0.962793i \(-0.412897\pi\)
0.270239 + 0.962793i \(0.412897\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 9.61818 1.05573 0.527866 0.849328i \(-0.322992\pi\)
0.527866 + 0.849328i \(0.322992\pi\)
\(84\) 0 0
\(85\) −21.7617 −2.36039
\(86\) 0 0
\(87\) −8.64332 −0.926661
\(88\) 0 0
\(89\) 6.41609 0.680104 0.340052 0.940407i \(-0.389555\pi\)
0.340052 + 0.940407i \(0.389555\pi\)
\(90\) 0 0
\(91\) 5.03214 0.527512
\(92\) 0 0
\(93\) −3.70268 −0.383950
\(94\) 0 0
\(95\) −4.95703 −0.508581
\(96\) 0 0
\(97\) 11.8923 1.20748 0.603741 0.797181i \(-0.293676\pi\)
0.603741 + 0.797181i \(0.293676\pi\)
\(98\) 0 0
\(99\) 4.30996 0.433167
\(100\) 0 0
\(101\) −9.25137 −0.920546 −0.460273 0.887777i \(-0.652248\pi\)
−0.460273 + 0.887777i \(0.652248\pi\)
\(102\) 0 0
\(103\) 7.66988 0.755735 0.377868 0.925860i \(-0.376657\pi\)
0.377868 + 0.925860i \(0.376657\pi\)
\(104\) 0 0
\(105\) 4.03326 0.393606
\(106\) 0 0
\(107\) −14.0197 −1.35533 −0.677667 0.735369i \(-0.737009\pi\)
−0.677667 + 0.735369i \(0.737009\pi\)
\(108\) 0 0
\(109\) 5.36889 0.514246 0.257123 0.966379i \(-0.417225\pi\)
0.257123 + 0.966379i \(0.417225\pi\)
\(110\) 0 0
\(111\) −11.8125 −1.12119
\(112\) 0 0
\(113\) 3.52883 0.331965 0.165982 0.986129i \(-0.446921\pi\)
0.165982 + 0.986129i \(0.446921\pi\)
\(114\) 0 0
\(115\) −5.05581 −0.471457
\(116\) 0 0
\(117\) 3.43074 0.317172
\(118\) 0 0
\(119\) 11.6083 1.06413
\(120\) 0 0
\(121\) 7.57577 0.688706
\(122\) 0 0
\(123\) −0.510657 −0.0460444
\(124\) 0 0
\(125\) 6.70642 0.599840
\(126\) 0 0
\(127\) 15.8045 1.40243 0.701213 0.712952i \(-0.252642\pi\)
0.701213 + 0.712952i \(0.252642\pi\)
\(128\) 0 0
\(129\) 7.96228 0.701040
\(130\) 0 0
\(131\) −6.40460 −0.559572 −0.279786 0.960062i \(-0.590264\pi\)
−0.279786 + 0.960062i \(0.590264\pi\)
\(132\) 0 0
\(133\) 2.64420 0.229282
\(134\) 0 0
\(135\) 2.74974 0.236660
\(136\) 0 0
\(137\) −17.1833 −1.46807 −0.734036 0.679111i \(-0.762366\pi\)
−0.734036 + 0.679111i \(0.762366\pi\)
\(138\) 0 0
\(139\) 11.1249 0.943598 0.471799 0.881706i \(-0.343605\pi\)
0.471799 + 0.881706i \(0.343605\pi\)
\(140\) 0 0
\(141\) 4.97314 0.418814
\(142\) 0 0
\(143\) 14.7864 1.23650
\(144\) 0 0
\(145\) −23.7669 −1.97373
\(146\) 0 0
\(147\) 4.84856 0.399902
\(148\) 0 0
\(149\) −2.91714 −0.238981 −0.119491 0.992835i \(-0.538126\pi\)
−0.119491 + 0.992835i \(0.538126\pi\)
\(150\) 0 0
\(151\) 3.96133 0.322368 0.161184 0.986924i \(-0.448469\pi\)
0.161184 + 0.986924i \(0.448469\pi\)
\(152\) 0 0
\(153\) 7.91411 0.639818
\(154\) 0 0
\(155\) −10.1814 −0.817790
\(156\) 0 0
\(157\) −3.65103 −0.291384 −0.145692 0.989330i \(-0.546541\pi\)
−0.145692 + 0.989330i \(0.546541\pi\)
\(158\) 0 0
\(159\) 13.7075 1.08708
\(160\) 0 0
\(161\) 2.69689 0.212545
\(162\) 0 0
\(163\) −18.8328 −1.47510 −0.737551 0.675292i \(-0.764018\pi\)
−0.737551 + 0.675292i \(0.764018\pi\)
\(164\) 0 0
\(165\) 11.8513 0.922621
\(166\) 0 0
\(167\) −2.46173 −0.190495 −0.0952474 0.995454i \(-0.530364\pi\)
−0.0952474 + 0.995454i \(0.530364\pi\)
\(168\) 0 0
\(169\) −1.23001 −0.0946161
\(170\) 0 0
\(171\) 1.80273 0.137858
\(172\) 0 0
\(173\) −9.43332 −0.717202 −0.358601 0.933491i \(-0.616746\pi\)
−0.358601 + 0.933491i \(0.616746\pi\)
\(174\) 0 0
\(175\) 3.75653 0.283967
\(176\) 0 0
\(177\) 1.90341 0.143069
\(178\) 0 0
\(179\) −3.86292 −0.288728 −0.144364 0.989525i \(-0.546114\pi\)
−0.144364 + 0.989525i \(0.546114\pi\)
\(180\) 0 0
\(181\) −15.5937 −1.15907 −0.579534 0.814948i \(-0.696765\pi\)
−0.579534 + 0.814948i \(0.696765\pi\)
\(182\) 0 0
\(183\) 0.965055 0.0713389
\(184\) 0 0
\(185\) −32.4813 −2.38807
\(186\) 0 0
\(187\) 34.1095 2.49433
\(188\) 0 0
\(189\) −1.46678 −0.106692
\(190\) 0 0
\(191\) −22.0305 −1.59407 −0.797037 0.603931i \(-0.793600\pi\)
−0.797037 + 0.603931i \(0.793600\pi\)
\(192\) 0 0
\(193\) 21.5335 1.55001 0.775006 0.631953i \(-0.217747\pi\)
0.775006 + 0.631953i \(0.217747\pi\)
\(194\) 0 0
\(195\) 9.43365 0.675558
\(196\) 0 0
\(197\) −18.0230 −1.28408 −0.642042 0.766669i \(-0.721913\pi\)
−0.642042 + 0.766669i \(0.721913\pi\)
\(198\) 0 0
\(199\) 20.6122 1.46116 0.730579 0.682828i \(-0.239250\pi\)
0.730579 + 0.682828i \(0.239250\pi\)
\(200\) 0 0
\(201\) −9.78064 −0.689873
\(202\) 0 0
\(203\) 12.6778 0.889810
\(204\) 0 0
\(205\) −1.40418 −0.0980718
\(206\) 0 0
\(207\) 1.83865 0.127795
\(208\) 0 0
\(209\) 7.76969 0.537441
\(210\) 0 0
\(211\) 28.0898 1.93378 0.966890 0.255194i \(-0.0821393\pi\)
0.966890 + 0.255194i \(0.0821393\pi\)
\(212\) 0 0
\(213\) 2.19283 0.150250
\(214\) 0 0
\(215\) 21.8942 1.49317
\(216\) 0 0
\(217\) 5.43101 0.368681
\(218\) 0 0
\(219\) 8.61320 0.582026
\(220\) 0 0
\(221\) 27.1513 1.82639
\(222\) 0 0
\(223\) −17.7735 −1.19020 −0.595102 0.803650i \(-0.702888\pi\)
−0.595102 + 0.803650i \(0.702888\pi\)
\(224\) 0 0
\(225\) 2.56107 0.170738
\(226\) 0 0
\(227\) 23.8817 1.58508 0.792541 0.609819i \(-0.208758\pi\)
0.792541 + 0.609819i \(0.208758\pi\)
\(228\) 0 0
\(229\) 5.85550 0.386942 0.193471 0.981106i \(-0.438025\pi\)
0.193471 + 0.981106i \(0.438025\pi\)
\(230\) 0 0
\(231\) −6.32176 −0.415941
\(232\) 0 0
\(233\) 17.3891 1.13920 0.569599 0.821923i \(-0.307098\pi\)
0.569599 + 0.821923i \(0.307098\pi\)
\(234\) 0 0
\(235\) 13.6749 0.892049
\(236\) 0 0
\(237\) −4.80388 −0.312045
\(238\) 0 0
\(239\) −29.4336 −1.90390 −0.951951 0.306250i \(-0.900926\pi\)
−0.951951 + 0.306250i \(0.900926\pi\)
\(240\) 0 0
\(241\) 18.9487 1.22059 0.610296 0.792173i \(-0.291050\pi\)
0.610296 + 0.792173i \(0.291050\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 13.3323 0.851768
\(246\) 0 0
\(247\) 6.18470 0.393523
\(248\) 0 0
\(249\) −9.61818 −0.609527
\(250\) 0 0
\(251\) −29.0508 −1.83367 −0.916834 0.399268i \(-0.869264\pi\)
−0.916834 + 0.399268i \(0.869264\pi\)
\(252\) 0 0
\(253\) 7.92451 0.498210
\(254\) 0 0
\(255\) 21.7617 1.36277
\(256\) 0 0
\(257\) 5.09395 0.317752 0.158876 0.987299i \(-0.449213\pi\)
0.158876 + 0.987299i \(0.449213\pi\)
\(258\) 0 0
\(259\) 17.3263 1.07661
\(260\) 0 0
\(261\) 8.64332 0.535008
\(262\) 0 0
\(263\) −0.308249 −0.0190075 −0.00950374 0.999955i \(-0.503025\pi\)
−0.00950374 + 0.999955i \(0.503025\pi\)
\(264\) 0 0
\(265\) 37.6921 2.31541
\(266\) 0 0
\(267\) −6.41609 −0.392658
\(268\) 0 0
\(269\) 22.9962 1.40210 0.701052 0.713110i \(-0.252714\pi\)
0.701052 + 0.713110i \(0.252714\pi\)
\(270\) 0 0
\(271\) 13.0506 0.792766 0.396383 0.918085i \(-0.370265\pi\)
0.396383 + 0.918085i \(0.370265\pi\)
\(272\) 0 0
\(273\) −5.03214 −0.304559
\(274\) 0 0
\(275\) 11.0381 0.665624
\(276\) 0 0
\(277\) 26.2985 1.58012 0.790062 0.613026i \(-0.210048\pi\)
0.790062 + 0.613026i \(0.210048\pi\)
\(278\) 0 0
\(279\) 3.70268 0.221674
\(280\) 0 0
\(281\) −25.9918 −1.55054 −0.775270 0.631630i \(-0.782386\pi\)
−0.775270 + 0.631630i \(0.782386\pi\)
\(282\) 0 0
\(283\) −27.6377 −1.64289 −0.821447 0.570285i \(-0.806833\pi\)
−0.821447 + 0.570285i \(0.806833\pi\)
\(284\) 0 0
\(285\) 4.95703 0.293629
\(286\) 0 0
\(287\) 0.749022 0.0442133
\(288\) 0 0
\(289\) 45.6331 2.68430
\(290\) 0 0
\(291\) −11.8923 −0.697140
\(292\) 0 0
\(293\) 0.689548 0.0402838 0.0201419 0.999797i \(-0.493588\pi\)
0.0201419 + 0.999797i \(0.493588\pi\)
\(294\) 0 0
\(295\) 5.23387 0.304728
\(296\) 0 0
\(297\) −4.30996 −0.250089
\(298\) 0 0
\(299\) 6.30793 0.364797
\(300\) 0 0
\(301\) −11.6789 −0.673161
\(302\) 0 0
\(303\) 9.25137 0.531478
\(304\) 0 0
\(305\) 2.65365 0.151948
\(306\) 0 0
\(307\) −28.1808 −1.60836 −0.804180 0.594385i \(-0.797395\pi\)
−0.804180 + 0.594385i \(0.797395\pi\)
\(308\) 0 0
\(309\) −7.66988 −0.436324
\(310\) 0 0
\(311\) 11.2398 0.637352 0.318676 0.947864i \(-0.396762\pi\)
0.318676 + 0.947864i \(0.396762\pi\)
\(312\) 0 0
\(313\) 2.55110 0.144196 0.0720982 0.997398i \(-0.477030\pi\)
0.0720982 + 0.997398i \(0.477030\pi\)
\(314\) 0 0
\(315\) −4.03326 −0.227249
\(316\) 0 0
\(317\) 3.47272 0.195047 0.0975237 0.995233i \(-0.468908\pi\)
0.0975237 + 0.995233i \(0.468908\pi\)
\(318\) 0 0
\(319\) 37.2524 2.08573
\(320\) 0 0
\(321\) 14.0197 0.782503
\(322\) 0 0
\(323\) 14.2670 0.793837
\(324\) 0 0
\(325\) 8.78638 0.487381
\(326\) 0 0
\(327\) −5.36889 −0.296900
\(328\) 0 0
\(329\) −7.29450 −0.402159
\(330\) 0 0
\(331\) −27.7879 −1.52736 −0.763680 0.645595i \(-0.776609\pi\)
−0.763680 + 0.645595i \(0.776609\pi\)
\(332\) 0 0
\(333\) 11.8125 0.647321
\(334\) 0 0
\(335\) −26.8942 −1.46939
\(336\) 0 0
\(337\) 18.5986 1.01313 0.506565 0.862202i \(-0.330915\pi\)
0.506565 + 0.862202i \(0.330915\pi\)
\(338\) 0 0
\(339\) −3.52883 −0.191660
\(340\) 0 0
\(341\) 15.9584 0.864196
\(342\) 0 0
\(343\) −17.3792 −0.938390
\(344\) 0 0
\(345\) 5.05581 0.272196
\(346\) 0 0
\(347\) −28.8362 −1.54801 −0.774004 0.633181i \(-0.781749\pi\)
−0.774004 + 0.633181i \(0.781749\pi\)
\(348\) 0 0
\(349\) −29.5016 −1.57918 −0.789592 0.613632i \(-0.789708\pi\)
−0.789592 + 0.613632i \(0.789708\pi\)
\(350\) 0 0
\(351\) −3.43074 −0.183119
\(352\) 0 0
\(353\) 12.0505 0.641383 0.320691 0.947184i \(-0.396085\pi\)
0.320691 + 0.947184i \(0.396085\pi\)
\(354\) 0 0
\(355\) 6.02971 0.320024
\(356\) 0 0
\(357\) −11.6083 −0.614374
\(358\) 0 0
\(359\) 18.6952 0.986694 0.493347 0.869833i \(-0.335773\pi\)
0.493347 + 0.869833i \(0.335773\pi\)
\(360\) 0 0
\(361\) −15.7502 −0.828956
\(362\) 0 0
\(363\) −7.57577 −0.397625
\(364\) 0 0
\(365\) 23.6841 1.23968
\(366\) 0 0
\(367\) 1.79781 0.0938450 0.0469225 0.998899i \(-0.485059\pi\)
0.0469225 + 0.998899i \(0.485059\pi\)
\(368\) 0 0
\(369\) 0.510657 0.0265838
\(370\) 0 0
\(371\) −20.1059 −1.04385
\(372\) 0 0
\(373\) −3.23876 −0.167697 −0.0838484 0.996479i \(-0.526721\pi\)
−0.0838484 + 0.996479i \(0.526721\pi\)
\(374\) 0 0
\(375\) −6.70642 −0.346318
\(376\) 0 0
\(377\) 29.6530 1.52721
\(378\) 0 0
\(379\) 24.2653 1.24643 0.623213 0.782052i \(-0.285827\pi\)
0.623213 + 0.782052i \(0.285827\pi\)
\(380\) 0 0
\(381\) −15.8045 −0.809691
\(382\) 0 0
\(383\) 3.78210 0.193256 0.0966282 0.995321i \(-0.469194\pi\)
0.0966282 + 0.995321i \(0.469194\pi\)
\(384\) 0 0
\(385\) −17.3832 −0.885930
\(386\) 0 0
\(387\) −7.96228 −0.404745
\(388\) 0 0
\(389\) −22.4387 −1.13769 −0.568843 0.822446i \(-0.692609\pi\)
−0.568843 + 0.822446i \(0.692609\pi\)
\(390\) 0 0
\(391\) 14.5513 0.735890
\(392\) 0 0
\(393\) 6.40460 0.323069
\(394\) 0 0
\(395\) −13.2094 −0.664638
\(396\) 0 0
\(397\) −3.46414 −0.173860 −0.0869300 0.996214i \(-0.527706\pi\)
−0.0869300 + 0.996214i \(0.527706\pi\)
\(398\) 0 0
\(399\) −2.64420 −0.132376
\(400\) 0 0
\(401\) 31.5980 1.57793 0.788963 0.614440i \(-0.210618\pi\)
0.788963 + 0.614440i \(0.210618\pi\)
\(402\) 0 0
\(403\) 12.7029 0.632778
\(404\) 0 0
\(405\) −2.74974 −0.136636
\(406\) 0 0
\(407\) 50.9114 2.52358
\(408\) 0 0
\(409\) 19.6908 0.973649 0.486824 0.873500i \(-0.338155\pi\)
0.486824 + 0.873500i \(0.338155\pi\)
\(410\) 0 0
\(411\) 17.1833 0.847592
\(412\) 0 0
\(413\) −2.79188 −0.137379
\(414\) 0 0
\(415\) −26.4475 −1.29826
\(416\) 0 0
\(417\) −11.1249 −0.544787
\(418\) 0 0
\(419\) −31.8208 −1.55455 −0.777274 0.629162i \(-0.783398\pi\)
−0.777274 + 0.629162i \(0.783398\pi\)
\(420\) 0 0
\(421\) 2.42733 0.118301 0.0591503 0.998249i \(-0.481161\pi\)
0.0591503 + 0.998249i \(0.481161\pi\)
\(422\) 0 0
\(423\) −4.97314 −0.241802
\(424\) 0 0
\(425\) 20.2686 0.983172
\(426\) 0 0
\(427\) −1.41552 −0.0685019
\(428\) 0 0
\(429\) −14.7864 −0.713892
\(430\) 0 0
\(431\) −24.4858 −1.17944 −0.589719 0.807608i \(-0.700762\pi\)
−0.589719 + 0.807608i \(0.700762\pi\)
\(432\) 0 0
\(433\) 23.9179 1.14942 0.574711 0.818356i \(-0.305114\pi\)
0.574711 + 0.818356i \(0.305114\pi\)
\(434\) 0 0
\(435\) 23.7669 1.13953
\(436\) 0 0
\(437\) 3.31459 0.158558
\(438\) 0 0
\(439\) −5.17762 −0.247114 −0.123557 0.992337i \(-0.539430\pi\)
−0.123557 + 0.992337i \(0.539430\pi\)
\(440\) 0 0
\(441\) −4.84856 −0.230884
\(442\) 0 0
\(443\) −7.28618 −0.346177 −0.173088 0.984906i \(-0.555375\pi\)
−0.173088 + 0.984906i \(0.555375\pi\)
\(444\) 0 0
\(445\) −17.6426 −0.836339
\(446\) 0 0
\(447\) 2.91714 0.137976
\(448\) 0 0
\(449\) −17.8547 −0.842617 −0.421309 0.906917i \(-0.638429\pi\)
−0.421309 + 0.906917i \(0.638429\pi\)
\(450\) 0 0
\(451\) 2.20091 0.103637
\(452\) 0 0
\(453\) −3.96133 −0.186119
\(454\) 0 0
\(455\) −13.8371 −0.648692
\(456\) 0 0
\(457\) −41.2178 −1.92809 −0.964044 0.265744i \(-0.914382\pi\)
−0.964044 + 0.265744i \(0.914382\pi\)
\(458\) 0 0
\(459\) −7.91411 −0.369399
\(460\) 0 0
\(461\) 30.9818 1.44297 0.721484 0.692431i \(-0.243460\pi\)
0.721484 + 0.692431i \(0.243460\pi\)
\(462\) 0 0
\(463\) 28.4680 1.32302 0.661510 0.749937i \(-0.269916\pi\)
0.661510 + 0.749937i \(0.269916\pi\)
\(464\) 0 0
\(465\) 10.1814 0.472151
\(466\) 0 0
\(467\) −6.18707 −0.286303 −0.143152 0.989701i \(-0.545724\pi\)
−0.143152 + 0.989701i \(0.545724\pi\)
\(468\) 0 0
\(469\) 14.3460 0.662439
\(470\) 0 0
\(471\) 3.65103 0.168231
\(472\) 0 0
\(473\) −34.3171 −1.57790
\(474\) 0 0
\(475\) 4.61692 0.211839
\(476\) 0 0
\(477\) −13.7075 −0.627623
\(478\) 0 0
\(479\) 30.4611 1.39180 0.695902 0.718137i \(-0.255005\pi\)
0.695902 + 0.718137i \(0.255005\pi\)
\(480\) 0 0
\(481\) 40.5256 1.84781
\(482\) 0 0
\(483\) −2.69689 −0.122713
\(484\) 0 0
\(485\) −32.7008 −1.48487
\(486\) 0 0
\(487\) 19.1358 0.867127 0.433564 0.901123i \(-0.357256\pi\)
0.433564 + 0.901123i \(0.357256\pi\)
\(488\) 0 0
\(489\) 18.8328 0.851650
\(490\) 0 0
\(491\) −18.4030 −0.830516 −0.415258 0.909704i \(-0.636309\pi\)
−0.415258 + 0.909704i \(0.636309\pi\)
\(492\) 0 0
\(493\) 68.4042 3.08077
\(494\) 0 0
\(495\) −11.8513 −0.532675
\(496\) 0 0
\(497\) −3.21640 −0.144275
\(498\) 0 0
\(499\) 1.98963 0.0890681 0.0445340 0.999008i \(-0.485820\pi\)
0.0445340 + 0.999008i \(0.485820\pi\)
\(500\) 0 0
\(501\) 2.46173 0.109982
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 25.4389 1.13202
\(506\) 0 0
\(507\) 1.23001 0.0546266
\(508\) 0 0
\(509\) 22.3251 0.989544 0.494772 0.869023i \(-0.335251\pi\)
0.494772 + 0.869023i \(0.335251\pi\)
\(510\) 0 0
\(511\) −12.6337 −0.558880
\(512\) 0 0
\(513\) −1.80273 −0.0795924
\(514\) 0 0
\(515\) −21.0902 −0.929344
\(516\) 0 0
\(517\) −21.4341 −0.942669
\(518\) 0 0
\(519\) 9.43332 0.414077
\(520\) 0 0
\(521\) 26.1222 1.14444 0.572218 0.820102i \(-0.306083\pi\)
0.572218 + 0.820102i \(0.306083\pi\)
\(522\) 0 0
\(523\) −31.9411 −1.39669 −0.698343 0.715763i \(-0.746079\pi\)
−0.698343 + 0.715763i \(0.746079\pi\)
\(524\) 0 0
\(525\) −3.75653 −0.163948
\(526\) 0 0
\(527\) 29.3034 1.27648
\(528\) 0 0
\(529\) −19.6194 −0.853016
\(530\) 0 0
\(531\) −1.90341 −0.0826008
\(532\) 0 0
\(533\) 1.75193 0.0758847
\(534\) 0 0
\(535\) 38.5505 1.66668
\(536\) 0 0
\(537\) 3.86292 0.166697
\(538\) 0 0
\(539\) −20.8971 −0.900102
\(540\) 0 0
\(541\) −36.5743 −1.57245 −0.786225 0.617940i \(-0.787967\pi\)
−0.786225 + 0.617940i \(0.787967\pi\)
\(542\) 0 0
\(543\) 15.5937 0.669188
\(544\) 0 0
\(545\) −14.7630 −0.632379
\(546\) 0 0
\(547\) −23.0369 −0.984988 −0.492494 0.870316i \(-0.663915\pi\)
−0.492494 + 0.870316i \(0.663915\pi\)
\(548\) 0 0
\(549\) −0.965055 −0.0411875
\(550\) 0 0
\(551\) 15.5816 0.663796
\(552\) 0 0
\(553\) 7.04623 0.299636
\(554\) 0 0
\(555\) 32.4813 1.37875
\(556\) 0 0
\(557\) −13.3429 −0.565356 −0.282678 0.959215i \(-0.591223\pi\)
−0.282678 + 0.959215i \(0.591223\pi\)
\(558\) 0 0
\(559\) −27.3165 −1.15537
\(560\) 0 0
\(561\) −34.1095 −1.44010
\(562\) 0 0
\(563\) −16.2420 −0.684519 −0.342260 0.939605i \(-0.611192\pi\)
−0.342260 + 0.939605i \(0.611192\pi\)
\(564\) 0 0
\(565\) −9.70338 −0.408224
\(566\) 0 0
\(567\) 1.46678 0.0615989
\(568\) 0 0
\(569\) −44.4645 −1.86405 −0.932024 0.362397i \(-0.881958\pi\)
−0.932024 + 0.362397i \(0.881958\pi\)
\(570\) 0 0
\(571\) −13.2134 −0.552963 −0.276481 0.961019i \(-0.589168\pi\)
−0.276481 + 0.961019i \(0.589168\pi\)
\(572\) 0 0
\(573\) 22.0305 0.920339
\(574\) 0 0
\(575\) 4.70891 0.196375
\(576\) 0 0
\(577\) −12.4856 −0.519781 −0.259891 0.965638i \(-0.583687\pi\)
−0.259891 + 0.965638i \(0.583687\pi\)
\(578\) 0 0
\(579\) −21.5335 −0.894900
\(580\) 0 0
\(581\) 14.1077 0.585288
\(582\) 0 0
\(583\) −59.0788 −2.44679
\(584\) 0 0
\(585\) −9.43365 −0.390033
\(586\) 0 0
\(587\) 31.3818 1.29527 0.647633 0.761952i \(-0.275759\pi\)
0.647633 + 0.761952i \(0.275759\pi\)
\(588\) 0 0
\(589\) 6.67492 0.275035
\(590\) 0 0
\(591\) 18.0230 0.741366
\(592\) 0 0
\(593\) 41.2451 1.69373 0.846867 0.531804i \(-0.178486\pi\)
0.846867 + 0.531804i \(0.178486\pi\)
\(594\) 0 0
\(595\) −31.9197 −1.30858
\(596\) 0 0
\(597\) −20.6122 −0.843600
\(598\) 0 0
\(599\) 37.1847 1.51933 0.759664 0.650316i \(-0.225364\pi\)
0.759664 + 0.650316i \(0.225364\pi\)
\(600\) 0 0
\(601\) 3.40436 0.138867 0.0694335 0.997587i \(-0.477881\pi\)
0.0694335 + 0.997587i \(0.477881\pi\)
\(602\) 0 0
\(603\) 9.78064 0.398298
\(604\) 0 0
\(605\) −20.8314 −0.846917
\(606\) 0 0
\(607\) 15.9840 0.648769 0.324384 0.945925i \(-0.394843\pi\)
0.324384 + 0.945925i \(0.394843\pi\)
\(608\) 0 0
\(609\) −12.6778 −0.513732
\(610\) 0 0
\(611\) −17.0616 −0.690237
\(612\) 0 0
\(613\) 14.8589 0.600145 0.300072 0.953916i \(-0.402989\pi\)
0.300072 + 0.953916i \(0.402989\pi\)
\(614\) 0 0
\(615\) 1.40418 0.0566218
\(616\) 0 0
\(617\) 23.5784 0.949231 0.474616 0.880193i \(-0.342587\pi\)
0.474616 + 0.880193i \(0.342587\pi\)
\(618\) 0 0
\(619\) −5.89002 −0.236740 −0.118370 0.992970i \(-0.537767\pi\)
−0.118370 + 0.992970i \(0.537767\pi\)
\(620\) 0 0
\(621\) −1.83865 −0.0737825
\(622\) 0 0
\(623\) 9.41099 0.377043
\(624\) 0 0
\(625\) −31.2463 −1.24985
\(626\) 0 0
\(627\) −7.76969 −0.310291
\(628\) 0 0
\(629\) 93.4854 3.72751
\(630\) 0 0
\(631\) 26.9322 1.07215 0.536076 0.844169i \(-0.319906\pi\)
0.536076 + 0.844169i \(0.319906\pi\)
\(632\) 0 0
\(633\) −28.0898 −1.11647
\(634\) 0 0
\(635\) −43.4584 −1.72459
\(636\) 0 0
\(637\) −16.6342 −0.659069
\(638\) 0 0
\(639\) −2.19283 −0.0867470
\(640\) 0 0
\(641\) 41.2328 1.62860 0.814299 0.580445i \(-0.197122\pi\)
0.814299 + 0.580445i \(0.197122\pi\)
\(642\) 0 0
\(643\) 16.7823 0.661828 0.330914 0.943661i \(-0.392643\pi\)
0.330914 + 0.943661i \(0.392643\pi\)
\(644\) 0 0
\(645\) −21.8942 −0.862083
\(646\) 0 0
\(647\) −38.2542 −1.50393 −0.751964 0.659204i \(-0.770893\pi\)
−0.751964 + 0.659204i \(0.770893\pi\)
\(648\) 0 0
\(649\) −8.20360 −0.322020
\(650\) 0 0
\(651\) −5.43101 −0.212858
\(652\) 0 0
\(653\) 43.2135 1.69108 0.845538 0.533916i \(-0.179280\pi\)
0.845538 + 0.533916i \(0.179280\pi\)
\(654\) 0 0
\(655\) 17.6110 0.688118
\(656\) 0 0
\(657\) −8.61320 −0.336033
\(658\) 0 0
\(659\) −5.52402 −0.215185 −0.107593 0.994195i \(-0.534314\pi\)
−0.107593 + 0.994195i \(0.534314\pi\)
\(660\) 0 0
\(661\) 37.8576 1.47249 0.736245 0.676716i \(-0.236597\pi\)
0.736245 + 0.676716i \(0.236597\pi\)
\(662\) 0 0
\(663\) −27.1513 −1.05447
\(664\) 0 0
\(665\) −7.27088 −0.281952
\(666\) 0 0
\(667\) 15.8920 0.615342
\(668\) 0 0
\(669\) 17.7735 0.687165
\(670\) 0 0
\(671\) −4.15935 −0.160570
\(672\) 0 0
\(673\) −42.3798 −1.63362 −0.816810 0.576907i \(-0.804259\pi\)
−0.816810 + 0.576907i \(0.804259\pi\)
\(674\) 0 0
\(675\) −2.56107 −0.0985757
\(676\) 0 0
\(677\) 31.6977 1.21824 0.609122 0.793077i \(-0.291522\pi\)
0.609122 + 0.793077i \(0.291522\pi\)
\(678\) 0 0
\(679\) 17.4434 0.669416
\(680\) 0 0
\(681\) −23.8817 −0.915147
\(682\) 0 0
\(683\) −41.2166 −1.57711 −0.788554 0.614966i \(-0.789170\pi\)
−0.788554 + 0.614966i \(0.789170\pi\)
\(684\) 0 0
\(685\) 47.2497 1.80532
\(686\) 0 0
\(687\) −5.85550 −0.223401
\(688\) 0 0
\(689\) −47.0269 −1.79158
\(690\) 0 0
\(691\) 24.7586 0.941861 0.470931 0.882170i \(-0.343918\pi\)
0.470931 + 0.882170i \(0.343918\pi\)
\(692\) 0 0
\(693\) 6.32176 0.240144
\(694\) 0 0
\(695\) −30.5905 −1.16036
\(696\) 0 0
\(697\) 4.04140 0.153079
\(698\) 0 0
\(699\) −17.3891 −0.657717
\(700\) 0 0
\(701\) 47.4789 1.79325 0.896627 0.442787i \(-0.146010\pi\)
0.896627 + 0.442787i \(0.146010\pi\)
\(702\) 0 0
\(703\) 21.2947 0.803146
\(704\) 0 0
\(705\) −13.6749 −0.515025
\(706\) 0 0
\(707\) −13.5697 −0.510342
\(708\) 0 0
\(709\) −29.4616 −1.10645 −0.553226 0.833031i \(-0.686603\pi\)
−0.553226 + 0.833031i \(0.686603\pi\)
\(710\) 0 0
\(711\) 4.80388 0.180160
\(712\) 0 0
\(713\) 6.80793 0.254959
\(714\) 0 0
\(715\) −40.6587 −1.52055
\(716\) 0 0
\(717\) 29.4336 1.09922
\(718\) 0 0
\(719\) −38.3768 −1.43121 −0.715607 0.698503i \(-0.753850\pi\)
−0.715607 + 0.698503i \(0.753850\pi\)
\(720\) 0 0
\(721\) 11.2500 0.418972
\(722\) 0 0
\(723\) −18.9487 −0.704710
\(724\) 0 0
\(725\) 22.1362 0.822116
\(726\) 0 0
\(727\) −30.6862 −1.13809 −0.569045 0.822306i \(-0.692687\pi\)
−0.569045 + 0.822306i \(0.692687\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −63.0144 −2.33067
\(732\) 0 0
\(733\) 19.8661 0.733772 0.366886 0.930266i \(-0.380424\pi\)
0.366886 + 0.930266i \(0.380424\pi\)
\(734\) 0 0
\(735\) −13.3323 −0.491768
\(736\) 0 0
\(737\) 42.1542 1.55277
\(738\) 0 0
\(739\) 35.5555 1.30793 0.653966 0.756524i \(-0.273104\pi\)
0.653966 + 0.756524i \(0.273104\pi\)
\(740\) 0 0
\(741\) −6.18470 −0.227200
\(742\) 0 0
\(743\) −4.47104 −0.164027 −0.0820133 0.996631i \(-0.526135\pi\)
−0.0820133 + 0.996631i \(0.526135\pi\)
\(744\) 0 0
\(745\) 8.02137 0.293880
\(746\) 0 0
\(747\) 9.61818 0.351911
\(748\) 0 0
\(749\) −20.5638 −0.751384
\(750\) 0 0
\(751\) 29.0420 1.05976 0.529878 0.848074i \(-0.322238\pi\)
0.529878 + 0.848074i \(0.322238\pi\)
\(752\) 0 0
\(753\) 29.0508 1.05867
\(754\) 0 0
\(755\) −10.8926 −0.396423
\(756\) 0 0
\(757\) 23.0360 0.837259 0.418629 0.908157i \(-0.362511\pi\)
0.418629 + 0.908157i \(0.362511\pi\)
\(758\) 0 0
\(759\) −7.92451 −0.287641
\(760\) 0 0
\(761\) −6.51065 −0.236011 −0.118005 0.993013i \(-0.537650\pi\)
−0.118005 + 0.993013i \(0.537650\pi\)
\(762\) 0 0
\(763\) 7.87497 0.285093
\(764\) 0 0
\(765\) −21.7617 −0.786798
\(766\) 0 0
\(767\) −6.53009 −0.235788
\(768\) 0 0
\(769\) −35.7317 −1.28852 −0.644259 0.764807i \(-0.722834\pi\)
−0.644259 + 0.764807i \(0.722834\pi\)
\(770\) 0 0
\(771\) −5.09395 −0.183454
\(772\) 0 0
\(773\) −10.0259 −0.360606 −0.180303 0.983611i \(-0.557708\pi\)
−0.180303 + 0.983611i \(0.557708\pi\)
\(774\) 0 0
\(775\) 9.48283 0.340633
\(776\) 0 0
\(777\) −17.3263 −0.621578
\(778\) 0 0
\(779\) 0.920576 0.0329831
\(780\) 0 0
\(781\) −9.45102 −0.338184
\(782\) 0 0
\(783\) −8.64332 −0.308887
\(784\) 0 0
\(785\) 10.0394 0.358321
\(786\) 0 0
\(787\) −22.3144 −0.795423 −0.397712 0.917511i \(-0.630196\pi\)
−0.397712 + 0.917511i \(0.630196\pi\)
\(788\) 0 0
\(789\) 0.308249 0.0109740
\(790\) 0 0
\(791\) 5.17602 0.184038
\(792\) 0 0
\(793\) −3.31085 −0.117572
\(794\) 0 0
\(795\) −37.6921 −1.33680
\(796\) 0 0
\(797\) −7.31156 −0.258989 −0.129494 0.991580i \(-0.541335\pi\)
−0.129494 + 0.991580i \(0.541335\pi\)
\(798\) 0 0
\(799\) −39.3580 −1.39239
\(800\) 0 0
\(801\) 6.41609 0.226701
\(802\) 0 0
\(803\) −37.1225 −1.31003
\(804\) 0 0
\(805\) −7.41576 −0.261371
\(806\) 0 0
\(807\) −22.9962 −0.809505
\(808\) 0 0
\(809\) −11.1191 −0.390925 −0.195463 0.980711i \(-0.562621\pi\)
−0.195463 + 0.980711i \(0.562621\pi\)
\(810\) 0 0
\(811\) −22.4291 −0.787594 −0.393797 0.919197i \(-0.628839\pi\)
−0.393797 + 0.919197i \(0.628839\pi\)
\(812\) 0 0
\(813\) −13.0506 −0.457704
\(814\) 0 0
\(815\) 51.7854 1.81396
\(816\) 0 0
\(817\) −14.3538 −0.502177
\(818\) 0 0
\(819\) 5.03214 0.175837
\(820\) 0 0
\(821\) 6.28870 0.219477 0.109739 0.993960i \(-0.464999\pi\)
0.109739 + 0.993960i \(0.464999\pi\)
\(822\) 0 0
\(823\) 28.1969 0.982883 0.491441 0.870911i \(-0.336470\pi\)
0.491441 + 0.870911i \(0.336470\pi\)
\(824\) 0 0
\(825\) −11.0381 −0.384298
\(826\) 0 0
\(827\) −18.4390 −0.641187 −0.320594 0.947217i \(-0.603882\pi\)
−0.320594 + 0.947217i \(0.603882\pi\)
\(828\) 0 0
\(829\) −6.48726 −0.225312 −0.112656 0.993634i \(-0.535936\pi\)
−0.112656 + 0.993634i \(0.535936\pi\)
\(830\) 0 0
\(831\) −26.2985 −0.912286
\(832\) 0 0
\(833\) −38.3720 −1.32951
\(834\) 0 0
\(835\) 6.76913 0.234255
\(836\) 0 0
\(837\) −3.70268 −0.127983
\(838\) 0 0
\(839\) 27.8022 0.959838 0.479919 0.877313i \(-0.340666\pi\)
0.479919 + 0.877313i \(0.340666\pi\)
\(840\) 0 0
\(841\) 45.7069 1.57610
\(842\) 0 0
\(843\) 25.9918 0.895205
\(844\) 0 0
\(845\) 3.38221 0.116351
\(846\) 0 0
\(847\) 11.1120 0.381812
\(848\) 0 0
\(849\) 27.6377 0.948525
\(850\) 0 0
\(851\) 21.7190 0.744519
\(852\) 0 0
\(853\) −43.0165 −1.47286 −0.736428 0.676516i \(-0.763489\pi\)
−0.736428 + 0.676516i \(0.763489\pi\)
\(854\) 0 0
\(855\) −4.95703 −0.169527
\(856\) 0 0
\(857\) 5.19274 0.177381 0.0886904 0.996059i \(-0.471732\pi\)
0.0886904 + 0.996059i \(0.471732\pi\)
\(858\) 0 0
\(859\) 9.82796 0.335326 0.167663 0.985844i \(-0.446378\pi\)
0.167663 + 0.985844i \(0.446378\pi\)
\(860\) 0 0
\(861\) −0.749022 −0.0255266
\(862\) 0 0
\(863\) −38.4544 −1.30900 −0.654502 0.756060i \(-0.727122\pi\)
−0.654502 + 0.756060i \(0.727122\pi\)
\(864\) 0 0
\(865\) 25.9392 0.881959
\(866\) 0 0
\(867\) −45.6331 −1.54978
\(868\) 0 0
\(869\) 20.7045 0.702353
\(870\) 0 0
\(871\) 33.5549 1.13696
\(872\) 0 0
\(873\) 11.8923 0.402494
\(874\) 0 0
\(875\) 9.83683 0.332546
\(876\) 0 0
\(877\) −11.9864 −0.404752 −0.202376 0.979308i \(-0.564866\pi\)
−0.202376 + 0.979308i \(0.564866\pi\)
\(878\) 0 0
\(879\) −0.689548 −0.0232579
\(880\) 0 0
\(881\) −43.4989 −1.46551 −0.732757 0.680490i \(-0.761767\pi\)
−0.732757 + 0.680490i \(0.761767\pi\)
\(882\) 0 0
\(883\) −37.7763 −1.27127 −0.635637 0.771988i \(-0.719262\pi\)
−0.635637 + 0.771988i \(0.719262\pi\)
\(884\) 0 0
\(885\) −5.23387 −0.175935
\(886\) 0 0
\(887\) −5.59671 −0.187919 −0.0939596 0.995576i \(-0.529952\pi\)
−0.0939596 + 0.995576i \(0.529952\pi\)
\(888\) 0 0
\(889\) 23.1818 0.777492
\(890\) 0 0
\(891\) 4.30996 0.144389
\(892\) 0 0
\(893\) −8.96523 −0.300010
\(894\) 0 0
\(895\) 10.6220 0.355055
\(896\) 0 0
\(897\) −6.30793 −0.210616
\(898\) 0 0
\(899\) 32.0034 1.06737
\(900\) 0 0
\(901\) −108.483 −3.61408
\(902\) 0 0
\(903\) 11.6789 0.388650
\(904\) 0 0
\(905\) 42.8785 1.42533
\(906\) 0 0
\(907\) 5.32909 0.176950 0.0884748 0.996078i \(-0.471801\pi\)
0.0884748 + 0.996078i \(0.471801\pi\)
\(908\) 0 0
\(909\) −9.25137 −0.306849
\(910\) 0 0
\(911\) −30.1263 −0.998129 −0.499064 0.866565i \(-0.666323\pi\)
−0.499064 + 0.866565i \(0.666323\pi\)
\(912\) 0 0
\(913\) 41.4540 1.37193
\(914\) 0 0
\(915\) −2.65365 −0.0877270
\(916\) 0 0
\(917\) −9.39413 −0.310221
\(918\) 0 0
\(919\) −16.1951 −0.534226 −0.267113 0.963665i \(-0.586070\pi\)
−0.267113 + 0.963665i \(0.586070\pi\)
\(920\) 0 0
\(921\) 28.1808 0.928588
\(922\) 0 0
\(923\) −7.52304 −0.247624
\(924\) 0 0
\(925\) 30.2527 0.994701
\(926\) 0 0
\(927\) 7.66988 0.251912
\(928\) 0 0
\(929\) −21.0043 −0.689130 −0.344565 0.938762i \(-0.611974\pi\)
−0.344565 + 0.938762i \(0.611974\pi\)
\(930\) 0 0
\(931\) −8.74063 −0.286463
\(932\) 0 0
\(933\) −11.2398 −0.367976
\(934\) 0 0
\(935\) −93.7923 −3.06734
\(936\) 0 0
\(937\) −18.1860 −0.594111 −0.297056 0.954860i \(-0.596005\pi\)
−0.297056 + 0.954860i \(0.596005\pi\)
\(938\) 0 0
\(939\) −2.55110 −0.0832519
\(940\) 0 0
\(941\) 28.7973 0.938764 0.469382 0.882995i \(-0.344477\pi\)
0.469382 + 0.882995i \(0.344477\pi\)
\(942\) 0 0
\(943\) 0.938920 0.0305754
\(944\) 0 0
\(945\) 4.03326 0.131202
\(946\) 0 0
\(947\) −16.7495 −0.544287 −0.272143 0.962257i \(-0.587732\pi\)
−0.272143 + 0.962257i \(0.587732\pi\)
\(948\) 0 0
\(949\) −29.5497 −0.959222
\(950\) 0 0
\(951\) −3.47272 −0.112611
\(952\) 0 0
\(953\) 29.7130 0.962500 0.481250 0.876583i \(-0.340183\pi\)
0.481250 + 0.876583i \(0.340183\pi\)
\(954\) 0 0
\(955\) 60.5783 1.96027
\(956\) 0 0
\(957\) −37.2524 −1.20420
\(958\) 0 0
\(959\) −25.2042 −0.813885
\(960\) 0 0
\(961\) −17.2902 −0.557747
\(962\) 0 0
\(963\) −14.0197 −0.451778
\(964\) 0 0
\(965\) −59.2114 −1.90608
\(966\) 0 0
\(967\) 13.7163 0.441087 0.220544 0.975377i \(-0.429217\pi\)
0.220544 + 0.975377i \(0.429217\pi\)
\(968\) 0 0
\(969\) −14.2670 −0.458322
\(970\) 0 0
\(971\) 32.1725 1.03246 0.516232 0.856449i \(-0.327334\pi\)
0.516232 + 0.856449i \(0.327334\pi\)
\(972\) 0 0
\(973\) 16.3177 0.523122
\(974\) 0 0
\(975\) −8.78638 −0.281389
\(976\) 0 0
\(977\) −14.8657 −0.475596 −0.237798 0.971315i \(-0.576426\pi\)
−0.237798 + 0.971315i \(0.576426\pi\)
\(978\) 0 0
\(979\) 27.6531 0.883797
\(980\) 0 0
\(981\) 5.36889 0.171415
\(982\) 0 0
\(983\) 32.4742 1.03577 0.517883 0.855452i \(-0.326720\pi\)
0.517883 + 0.855452i \(0.326720\pi\)
\(984\) 0 0
\(985\) 49.5585 1.57907
\(986\) 0 0
\(987\) 7.29450 0.232187
\(988\) 0 0
\(989\) −14.6398 −0.465520
\(990\) 0 0
\(991\) −31.9577 −1.01517 −0.507585 0.861602i \(-0.669462\pi\)
−0.507585 + 0.861602i \(0.669462\pi\)
\(992\) 0 0
\(993\) 27.7879 0.881821
\(994\) 0 0
\(995\) −56.6781 −1.79682
\(996\) 0 0
\(997\) 40.1961 1.27302 0.636511 0.771267i \(-0.280377\pi\)
0.636511 + 0.771267i \(0.280377\pi\)
\(998\) 0 0
\(999\) −11.8125 −0.373731
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 \(a_p\))