Properties

Label 6036.2.a.i.1.10
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 1.10
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(-0.970233 q^{5}\) \(+3.74274 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(-0.970233 q^{5}\) \(+3.74274 q^{7}\) \(+1.00000 q^{9}\) \(-5.32343 q^{11}\) \(-0.298043 q^{13}\) \(+0.970233 q^{15}\) \(-7.82451 q^{17}\) \(-3.73515 q^{19}\) \(-3.74274 q^{21}\) \(+1.49696 q^{23}\) \(-4.05865 q^{25}\) \(-1.00000 q^{27}\) \(+3.78584 q^{29}\) \(-2.76588 q^{31}\) \(+5.32343 q^{33}\) \(-3.63133 q^{35}\) \(+0.959694 q^{37}\) \(+0.298043 q^{39}\) \(+1.24222 q^{41}\) \(+0.457677 q^{43}\) \(-0.970233 q^{45}\) \(+8.90957 q^{47}\) \(+7.00812 q^{49}\) \(+7.82451 q^{51}\) \(+6.31057 q^{53}\) \(+5.16497 q^{55}\) \(+3.73515 q^{57}\) \(-3.00315 q^{59}\) \(-2.73984 q^{61}\) \(+3.74274 q^{63}\) \(+0.289171 q^{65}\) \(+14.8495 q^{67}\) \(-1.49696 q^{69}\) \(-6.26414 q^{71}\) \(+7.46514 q^{73}\) \(+4.05865 q^{75}\) \(-19.9242 q^{77}\) \(+5.85609 q^{79}\) \(+1.00000 q^{81}\) \(+4.58704 q^{83}\) \(+7.59160 q^{85}\) \(-3.78584 q^{87}\) \(+9.45136 q^{89}\) \(-1.11550 q^{91}\) \(+2.76588 q^{93}\) \(+3.62396 q^{95}\) \(+17.7241 q^{97}\) \(-5.32343 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(26q \) \(\mathstrut -\mathstrut 26q^{3} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 5q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 13q^{13} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut q^{19} \) \(\mathstrut -\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 48q^{25} \) \(\mathstrut -\mathstrut 26q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 19q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 21q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 13q^{39} \) \(\mathstrut +\mathstrut 25q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 6q^{45} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 67q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut -\mathstrut 5q^{53} \) \(\mathstrut +\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut q^{57} \) \(\mathstrut -\mathstrut 18q^{59} \) \(\mathstrut +\mathstrut 43q^{61} \) \(\mathstrut +\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 41q^{65} \) \(\mathstrut +\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 22q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 22q^{73} \) \(\mathstrut -\mathstrut 48q^{75} \) \(\mathstrut +\mathstrut 23q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut -\mathstrut 19q^{83} \) \(\mathstrut +\mathstrut 29q^{85} \) \(\mathstrut -\mathstrut 6q^{87} \) \(\mathstrut +\mathstrut 49q^{89} \) \(\mathstrut -\mathstrut 13q^{91} \) \(\mathstrut -\mathstrut 19q^{93} \) \(\mathstrut -\mathstrut 26q^{95} \) \(\mathstrut +\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.970233 −0.433901 −0.216951 0.976183i \(-0.569611\pi\)
−0.216951 + 0.976183i \(0.569611\pi\)
\(6\) 0 0
\(7\) 3.74274 1.41462 0.707312 0.706902i \(-0.249908\pi\)
0.707312 + 0.706902i \(0.249908\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −5.32343 −1.60507 −0.802537 0.596603i \(-0.796517\pi\)
−0.802537 + 0.596603i \(0.796517\pi\)
\(12\) 0 0
\(13\) −0.298043 −0.0826622 −0.0413311 0.999146i \(-0.513160\pi\)
−0.0413311 + 0.999146i \(0.513160\pi\)
\(14\) 0 0
\(15\) 0.970233 0.250513
\(16\) 0 0
\(17\) −7.82451 −1.89772 −0.948861 0.315694i \(-0.897763\pi\)
−0.948861 + 0.315694i \(0.897763\pi\)
\(18\) 0 0
\(19\) −3.73515 −0.856902 −0.428451 0.903565i \(-0.640940\pi\)
−0.428451 + 0.903565i \(0.640940\pi\)
\(20\) 0 0
\(21\) −3.74274 −0.816733
\(22\) 0 0
\(23\) 1.49696 0.312137 0.156068 0.987746i \(-0.450118\pi\)
0.156068 + 0.987746i \(0.450118\pi\)
\(24\) 0 0
\(25\) −4.05865 −0.811730
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 3.78584 0.703013 0.351507 0.936185i \(-0.385669\pi\)
0.351507 + 0.936185i \(0.385669\pi\)
\(30\) 0 0
\(31\) −2.76588 −0.496767 −0.248384 0.968662i \(-0.579899\pi\)
−0.248384 + 0.968662i \(0.579899\pi\)
\(32\) 0 0
\(33\) 5.32343 0.926690
\(34\) 0 0
\(35\) −3.63133 −0.613807
\(36\) 0 0
\(37\) 0.959694 0.157773 0.0788864 0.996884i \(-0.474864\pi\)
0.0788864 + 0.996884i \(0.474864\pi\)
\(38\) 0 0
\(39\) 0.298043 0.0477250
\(40\) 0 0
\(41\) 1.24222 0.194002 0.0970012 0.995284i \(-0.469075\pi\)
0.0970012 + 0.995284i \(0.469075\pi\)
\(42\) 0 0
\(43\) 0.457677 0.0697951 0.0348975 0.999391i \(-0.488890\pi\)
0.0348975 + 0.999391i \(0.488890\pi\)
\(44\) 0 0
\(45\) −0.970233 −0.144634
\(46\) 0 0
\(47\) 8.90957 1.29959 0.649797 0.760108i \(-0.274854\pi\)
0.649797 + 0.760108i \(0.274854\pi\)
\(48\) 0 0
\(49\) 7.00812 1.00116
\(50\) 0 0
\(51\) 7.82451 1.09565
\(52\) 0 0
\(53\) 6.31057 0.866823 0.433411 0.901196i \(-0.357310\pi\)
0.433411 + 0.901196i \(0.357310\pi\)
\(54\) 0 0
\(55\) 5.16497 0.696444
\(56\) 0 0
\(57\) 3.73515 0.494732
\(58\) 0 0
\(59\) −3.00315 −0.390976 −0.195488 0.980706i \(-0.562629\pi\)
−0.195488 + 0.980706i \(0.562629\pi\)
\(60\) 0 0
\(61\) −2.73984 −0.350801 −0.175400 0.984497i \(-0.556122\pi\)
−0.175400 + 0.984497i \(0.556122\pi\)
\(62\) 0 0
\(63\) 3.74274 0.471541
\(64\) 0 0
\(65\) 0.289171 0.0358672
\(66\) 0 0
\(67\) 14.8495 1.81416 0.907079 0.420961i \(-0.138307\pi\)
0.907079 + 0.420961i \(0.138307\pi\)
\(68\) 0 0
\(69\) −1.49696 −0.180212
\(70\) 0 0
\(71\) −6.26414 −0.743416 −0.371708 0.928350i \(-0.621228\pi\)
−0.371708 + 0.928350i \(0.621228\pi\)
\(72\) 0 0
\(73\) 7.46514 0.873728 0.436864 0.899528i \(-0.356089\pi\)
0.436864 + 0.899528i \(0.356089\pi\)
\(74\) 0 0
\(75\) 4.05865 0.468652
\(76\) 0 0
\(77\) −19.9242 −2.27058
\(78\) 0 0
\(79\) 5.85609 0.658862 0.329431 0.944180i \(-0.393143\pi\)
0.329431 + 0.944180i \(0.393143\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.58704 0.503493 0.251746 0.967793i \(-0.418995\pi\)
0.251746 + 0.967793i \(0.418995\pi\)
\(84\) 0 0
\(85\) 7.59160 0.823424
\(86\) 0 0
\(87\) −3.78584 −0.405885
\(88\) 0 0
\(89\) 9.45136 1.00184 0.500921 0.865493i \(-0.332995\pi\)
0.500921 + 0.865493i \(0.332995\pi\)
\(90\) 0 0
\(91\) −1.11550 −0.116936
\(92\) 0 0
\(93\) 2.76588 0.286809
\(94\) 0 0
\(95\) 3.62396 0.371811
\(96\) 0 0
\(97\) 17.7241 1.79961 0.899803 0.436296i \(-0.143710\pi\)
0.899803 + 0.436296i \(0.143710\pi\)
\(98\) 0 0
\(99\) −5.32343 −0.535025
\(100\) 0 0
\(101\) −7.92972 −0.789036 −0.394518 0.918888i \(-0.629088\pi\)
−0.394518 + 0.918888i \(0.629088\pi\)
\(102\) 0 0
\(103\) 3.52201 0.347034 0.173517 0.984831i \(-0.444487\pi\)
0.173517 + 0.984831i \(0.444487\pi\)
\(104\) 0 0
\(105\) 3.63133 0.354382
\(106\) 0 0
\(107\) −11.3582 −1.09804 −0.549021 0.835808i \(-0.684999\pi\)
−0.549021 + 0.835808i \(0.684999\pi\)
\(108\) 0 0
\(109\) 3.06134 0.293224 0.146612 0.989194i \(-0.453163\pi\)
0.146612 + 0.989194i \(0.453163\pi\)
\(110\) 0 0
\(111\) −0.959694 −0.0910902
\(112\) 0 0
\(113\) −18.9256 −1.78038 −0.890188 0.455594i \(-0.849427\pi\)
−0.890188 + 0.455594i \(0.849427\pi\)
\(114\) 0 0
\(115\) −1.45240 −0.135437
\(116\) 0 0
\(117\) −0.298043 −0.0275541
\(118\) 0 0
\(119\) −29.2851 −2.68456
\(120\) 0 0
\(121\) 17.3389 1.57626
\(122\) 0 0
\(123\) −1.24222 −0.112007
\(124\) 0 0
\(125\) 8.78900 0.786112
\(126\) 0 0
\(127\) 10.0897 0.895312 0.447656 0.894206i \(-0.352259\pi\)
0.447656 + 0.894206i \(0.352259\pi\)
\(128\) 0 0
\(129\) −0.457677 −0.0402962
\(130\) 0 0
\(131\) 2.69545 0.235503 0.117751 0.993043i \(-0.462431\pi\)
0.117751 + 0.993043i \(0.462431\pi\)
\(132\) 0 0
\(133\) −13.9797 −1.21219
\(134\) 0 0
\(135\) 0.970233 0.0835044
\(136\) 0 0
\(137\) 14.4558 1.23504 0.617521 0.786554i \(-0.288137\pi\)
0.617521 + 0.786554i \(0.288137\pi\)
\(138\) 0 0
\(139\) −2.63180 −0.223226 −0.111613 0.993752i \(-0.535602\pi\)
−0.111613 + 0.993752i \(0.535602\pi\)
\(140\) 0 0
\(141\) −8.90957 −0.750321
\(142\) 0 0
\(143\) 1.58661 0.132679
\(144\) 0 0
\(145\) −3.67315 −0.305038
\(146\) 0 0
\(147\) −7.00812 −0.578020
\(148\) 0 0
\(149\) −14.9613 −1.22568 −0.612839 0.790208i \(-0.709973\pi\)
−0.612839 + 0.790208i \(0.709973\pi\)
\(150\) 0 0
\(151\) 20.1181 1.63719 0.818595 0.574372i \(-0.194754\pi\)
0.818595 + 0.574372i \(0.194754\pi\)
\(152\) 0 0
\(153\) −7.82451 −0.632574
\(154\) 0 0
\(155\) 2.68355 0.215548
\(156\) 0 0
\(157\) 6.89091 0.549954 0.274977 0.961451i \(-0.411330\pi\)
0.274977 + 0.961451i \(0.411330\pi\)
\(158\) 0 0
\(159\) −6.31057 −0.500460
\(160\) 0 0
\(161\) 5.60272 0.441556
\(162\) 0 0
\(163\) −11.4193 −0.894427 −0.447214 0.894427i \(-0.647584\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(164\) 0 0
\(165\) −5.16497 −0.402092
\(166\) 0 0
\(167\) 13.4307 1.03930 0.519650 0.854379i \(-0.326062\pi\)
0.519650 + 0.854379i \(0.326062\pi\)
\(168\) 0 0
\(169\) −12.9112 −0.993167
\(170\) 0 0
\(171\) −3.73515 −0.285634
\(172\) 0 0
\(173\) −6.82988 −0.519266 −0.259633 0.965707i \(-0.583602\pi\)
−0.259633 + 0.965707i \(0.583602\pi\)
\(174\) 0 0
\(175\) −15.1905 −1.14829
\(176\) 0 0
\(177\) 3.00315 0.225730
\(178\) 0 0
\(179\) 2.56472 0.191696 0.0958482 0.995396i \(-0.469444\pi\)
0.0958482 + 0.995396i \(0.469444\pi\)
\(180\) 0 0
\(181\) 21.9217 1.62943 0.814715 0.579862i \(-0.196893\pi\)
0.814715 + 0.579862i \(0.196893\pi\)
\(182\) 0 0
\(183\) 2.73984 0.202535
\(184\) 0 0
\(185\) −0.931127 −0.0684578
\(186\) 0 0
\(187\) 41.6532 3.04598
\(188\) 0 0
\(189\) −3.74274 −0.272244
\(190\) 0 0
\(191\) −5.26149 −0.380708 −0.190354 0.981715i \(-0.560964\pi\)
−0.190354 + 0.981715i \(0.560964\pi\)
\(192\) 0 0
\(193\) 0.751439 0.0540898 0.0270449 0.999634i \(-0.491390\pi\)
0.0270449 + 0.999634i \(0.491390\pi\)
\(194\) 0 0
\(195\) −0.289171 −0.0207080
\(196\) 0 0
\(197\) −17.2322 −1.22775 −0.613873 0.789405i \(-0.710389\pi\)
−0.613873 + 0.789405i \(0.710389\pi\)
\(198\) 0 0
\(199\) −15.0929 −1.06991 −0.534954 0.844881i \(-0.679671\pi\)
−0.534954 + 0.844881i \(0.679671\pi\)
\(200\) 0 0
\(201\) −14.8495 −1.04740
\(202\) 0 0
\(203\) 14.1694 0.994499
\(204\) 0 0
\(205\) −1.20524 −0.0841780
\(206\) 0 0
\(207\) 1.49696 0.104046
\(208\) 0 0
\(209\) 19.8838 1.37539
\(210\) 0 0
\(211\) 5.52859 0.380604 0.190302 0.981726i \(-0.439053\pi\)
0.190302 + 0.981726i \(0.439053\pi\)
\(212\) 0 0
\(213\) 6.26414 0.429212
\(214\) 0 0
\(215\) −0.444053 −0.0302842
\(216\) 0 0
\(217\) −10.3520 −0.702739
\(218\) 0 0
\(219\) −7.46514 −0.504447
\(220\) 0 0
\(221\) 2.33204 0.156870
\(222\) 0 0
\(223\) −12.3135 −0.824575 −0.412288 0.911054i \(-0.635270\pi\)
−0.412288 + 0.911054i \(0.635270\pi\)
\(224\) 0 0
\(225\) −4.05865 −0.270577
\(226\) 0 0
\(227\) 7.64652 0.507518 0.253759 0.967268i \(-0.418333\pi\)
0.253759 + 0.967268i \(0.418333\pi\)
\(228\) 0 0
\(229\) 5.52010 0.364778 0.182389 0.983226i \(-0.441617\pi\)
0.182389 + 0.983226i \(0.441617\pi\)
\(230\) 0 0
\(231\) 19.9242 1.31092
\(232\) 0 0
\(233\) 12.6031 0.825658 0.412829 0.910808i \(-0.364541\pi\)
0.412829 + 0.910808i \(0.364541\pi\)
\(234\) 0 0
\(235\) −8.64436 −0.563896
\(236\) 0 0
\(237\) −5.85609 −0.380394
\(238\) 0 0
\(239\) −13.6786 −0.884795 −0.442398 0.896819i \(-0.645872\pi\)
−0.442398 + 0.896819i \(0.645872\pi\)
\(240\) 0 0
\(241\) 15.4794 0.997118 0.498559 0.866856i \(-0.333863\pi\)
0.498559 + 0.866856i \(0.333863\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −6.79951 −0.434405
\(246\) 0 0
\(247\) 1.11323 0.0708334
\(248\) 0 0
\(249\) −4.58704 −0.290692
\(250\) 0 0
\(251\) 0.134773 0.00850677 0.00425338 0.999991i \(-0.498646\pi\)
0.00425338 + 0.999991i \(0.498646\pi\)
\(252\) 0 0
\(253\) −7.96893 −0.501002
\(254\) 0 0
\(255\) −7.59160 −0.475404
\(256\) 0 0
\(257\) 13.5452 0.844924 0.422462 0.906381i \(-0.361166\pi\)
0.422462 + 0.906381i \(0.361166\pi\)
\(258\) 0 0
\(259\) 3.59189 0.223189
\(260\) 0 0
\(261\) 3.78584 0.234338
\(262\) 0 0
\(263\) −15.5675 −0.959931 −0.479965 0.877287i \(-0.659351\pi\)
−0.479965 + 0.877287i \(0.659351\pi\)
\(264\) 0 0
\(265\) −6.12272 −0.376116
\(266\) 0 0
\(267\) −9.45136 −0.578414
\(268\) 0 0
\(269\) −25.0315 −1.52620 −0.763098 0.646283i \(-0.776323\pi\)
−0.763098 + 0.646283i \(0.776323\pi\)
\(270\) 0 0
\(271\) −1.28841 −0.0782651 −0.0391325 0.999234i \(-0.512459\pi\)
−0.0391325 + 0.999234i \(0.512459\pi\)
\(272\) 0 0
\(273\) 1.11550 0.0675130
\(274\) 0 0
\(275\) 21.6059 1.30289
\(276\) 0 0
\(277\) −2.22897 −0.133926 −0.0669629 0.997755i \(-0.521331\pi\)
−0.0669629 + 0.997755i \(0.521331\pi\)
\(278\) 0 0
\(279\) −2.76588 −0.165589
\(280\) 0 0
\(281\) 21.5713 1.28683 0.643417 0.765516i \(-0.277516\pi\)
0.643417 + 0.765516i \(0.277516\pi\)
\(282\) 0 0
\(283\) 6.93160 0.412041 0.206020 0.978548i \(-0.433949\pi\)
0.206020 + 0.978548i \(0.433949\pi\)
\(284\) 0 0
\(285\) −3.62396 −0.214665
\(286\) 0 0
\(287\) 4.64932 0.274441
\(288\) 0 0
\(289\) 44.2229 2.60135
\(290\) 0 0
\(291\) −17.7241 −1.03900
\(292\) 0 0
\(293\) 19.4521 1.13640 0.568202 0.822889i \(-0.307639\pi\)
0.568202 + 0.822889i \(0.307639\pi\)
\(294\) 0 0
\(295\) 2.91375 0.169645
\(296\) 0 0
\(297\) 5.32343 0.308897
\(298\) 0 0
\(299\) −0.446157 −0.0258019
\(300\) 0 0
\(301\) 1.71297 0.0987338
\(302\) 0 0
\(303\) 7.92972 0.455550
\(304\) 0 0
\(305\) 2.65828 0.152213
\(306\) 0 0
\(307\) −11.0657 −0.631551 −0.315775 0.948834i \(-0.602265\pi\)
−0.315775 + 0.948834i \(0.602265\pi\)
\(308\) 0 0
\(309\) −3.52201 −0.200360
\(310\) 0 0
\(311\) 3.72332 0.211130 0.105565 0.994412i \(-0.466335\pi\)
0.105565 + 0.994412i \(0.466335\pi\)
\(312\) 0 0
\(313\) 18.1184 1.02411 0.512057 0.858952i \(-0.328884\pi\)
0.512057 + 0.858952i \(0.328884\pi\)
\(314\) 0 0
\(315\) −3.63133 −0.204602
\(316\) 0 0
\(317\) 10.7581 0.604233 0.302116 0.953271i \(-0.402307\pi\)
0.302116 + 0.953271i \(0.402307\pi\)
\(318\) 0 0
\(319\) −20.1537 −1.12839
\(320\) 0 0
\(321\) 11.3582 0.633955
\(322\) 0 0
\(323\) 29.2257 1.62616
\(324\) 0 0
\(325\) 1.20965 0.0670993
\(326\) 0 0
\(327\) −3.06134 −0.169293
\(328\) 0 0
\(329\) 33.3462 1.83844
\(330\) 0 0
\(331\) 19.8675 1.09201 0.546007 0.837781i \(-0.316147\pi\)
0.546007 + 0.837781i \(0.316147\pi\)
\(332\) 0 0
\(333\) 0.959694 0.0525909
\(334\) 0 0
\(335\) −14.4075 −0.787166
\(336\) 0 0
\(337\) 10.7228 0.584107 0.292053 0.956402i \(-0.405661\pi\)
0.292053 + 0.956402i \(0.405661\pi\)
\(338\) 0 0
\(339\) 18.9256 1.02790
\(340\) 0 0
\(341\) 14.7240 0.797348
\(342\) 0 0
\(343\) 0.0303972 0.00164129
\(344\) 0 0
\(345\) 1.45240 0.0781943
\(346\) 0 0
\(347\) −15.1013 −0.810681 −0.405340 0.914166i \(-0.632847\pi\)
−0.405340 + 0.914166i \(0.632847\pi\)
\(348\) 0 0
\(349\) 19.3068 1.03347 0.516734 0.856146i \(-0.327148\pi\)
0.516734 + 0.856146i \(0.327148\pi\)
\(350\) 0 0
\(351\) 0.298043 0.0159083
\(352\) 0 0
\(353\) 30.2247 1.60870 0.804350 0.594156i \(-0.202514\pi\)
0.804350 + 0.594156i \(0.202514\pi\)
\(354\) 0 0
\(355\) 6.07767 0.322569
\(356\) 0 0
\(357\) 29.2851 1.54993
\(358\) 0 0
\(359\) −3.49088 −0.184241 −0.0921207 0.995748i \(-0.529365\pi\)
−0.0921207 + 0.995748i \(0.529365\pi\)
\(360\) 0 0
\(361\) −5.04867 −0.265720
\(362\) 0 0
\(363\) −17.3389 −0.910055
\(364\) 0 0
\(365\) −7.24292 −0.379112
\(366\) 0 0
\(367\) 21.7768 1.13674 0.568370 0.822773i \(-0.307574\pi\)
0.568370 + 0.822773i \(0.307574\pi\)
\(368\) 0 0
\(369\) 1.24222 0.0646675
\(370\) 0 0
\(371\) 23.6188 1.22623
\(372\) 0 0
\(373\) −10.9810 −0.568573 −0.284287 0.958739i \(-0.591757\pi\)
−0.284287 + 0.958739i \(0.591757\pi\)
\(374\) 0 0
\(375\) −8.78900 −0.453862
\(376\) 0 0
\(377\) −1.12834 −0.0581126
\(378\) 0 0
\(379\) −24.6997 −1.26874 −0.634370 0.773030i \(-0.718740\pi\)
−0.634370 + 0.773030i \(0.718740\pi\)
\(380\) 0 0
\(381\) −10.0897 −0.516909
\(382\) 0 0
\(383\) 21.0750 1.07688 0.538442 0.842663i \(-0.319013\pi\)
0.538442 + 0.842663i \(0.319013\pi\)
\(384\) 0 0
\(385\) 19.3311 0.985206
\(386\) 0 0
\(387\) 0.457677 0.0232650
\(388\) 0 0
\(389\) −8.39614 −0.425701 −0.212851 0.977085i \(-0.568275\pi\)
−0.212851 + 0.977085i \(0.568275\pi\)
\(390\) 0 0
\(391\) −11.7129 −0.592349
\(392\) 0 0
\(393\) −2.69545 −0.135967
\(394\) 0 0
\(395\) −5.68177 −0.285881
\(396\) 0 0
\(397\) 9.59364 0.481491 0.240745 0.970588i \(-0.422608\pi\)
0.240745 + 0.970588i \(0.422608\pi\)
\(398\) 0 0
\(399\) 13.9797 0.699860
\(400\) 0 0
\(401\) 8.30491 0.414727 0.207364 0.978264i \(-0.433512\pi\)
0.207364 + 0.978264i \(0.433512\pi\)
\(402\) 0 0
\(403\) 0.824351 0.0410639
\(404\) 0 0
\(405\) −0.970233 −0.0482113
\(406\) 0 0
\(407\) −5.10886 −0.253237
\(408\) 0 0
\(409\) −14.4707 −0.715529 −0.357764 0.933812i \(-0.616461\pi\)
−0.357764 + 0.933812i \(0.616461\pi\)
\(410\) 0 0
\(411\) −14.4558 −0.713052
\(412\) 0 0
\(413\) −11.2400 −0.553084
\(414\) 0 0
\(415\) −4.45050 −0.218466
\(416\) 0 0
\(417\) 2.63180 0.128880
\(418\) 0 0
\(419\) −7.40307 −0.361664 −0.180832 0.983514i \(-0.557879\pi\)
−0.180832 + 0.983514i \(0.557879\pi\)
\(420\) 0 0
\(421\) −9.57152 −0.466487 −0.233244 0.972418i \(-0.574934\pi\)
−0.233244 + 0.972418i \(0.574934\pi\)
\(422\) 0 0
\(423\) 8.90957 0.433198
\(424\) 0 0
\(425\) 31.7569 1.54044
\(426\) 0 0
\(427\) −10.2545 −0.496251
\(428\) 0 0
\(429\) −1.58661 −0.0766022
\(430\) 0 0
\(431\) −15.8802 −0.764922 −0.382461 0.923972i \(-0.624923\pi\)
−0.382461 + 0.923972i \(0.624923\pi\)
\(432\) 0 0
\(433\) −5.04520 −0.242457 −0.121228 0.992625i \(-0.538683\pi\)
−0.121228 + 0.992625i \(0.538683\pi\)
\(434\) 0 0
\(435\) 3.67315 0.176114
\(436\) 0 0
\(437\) −5.59135 −0.267470
\(438\) 0 0
\(439\) 21.0761 1.00591 0.502953 0.864314i \(-0.332247\pi\)
0.502953 + 0.864314i \(0.332247\pi\)
\(440\) 0 0
\(441\) 7.00812 0.333720
\(442\) 0 0
\(443\) −22.4139 −1.06492 −0.532458 0.846457i \(-0.678731\pi\)
−0.532458 + 0.846457i \(0.678731\pi\)
\(444\) 0 0
\(445\) −9.17003 −0.434701
\(446\) 0 0
\(447\) 14.9613 0.707645
\(448\) 0 0
\(449\) 25.1571 1.18724 0.593618 0.804747i \(-0.297699\pi\)
0.593618 + 0.804747i \(0.297699\pi\)
\(450\) 0 0
\(451\) −6.61288 −0.311388
\(452\) 0 0
\(453\) −20.1181 −0.945232
\(454\) 0 0
\(455\) 1.08229 0.0507387
\(456\) 0 0
\(457\) 26.3626 1.23319 0.616596 0.787280i \(-0.288511\pi\)
0.616596 + 0.787280i \(0.288511\pi\)
\(458\) 0 0
\(459\) 7.82451 0.365217
\(460\) 0 0
\(461\) −24.9810 −1.16348 −0.581740 0.813375i \(-0.697628\pi\)
−0.581740 + 0.813375i \(0.697628\pi\)
\(462\) 0 0
\(463\) 27.9821 1.30044 0.650218 0.759748i \(-0.274678\pi\)
0.650218 + 0.759748i \(0.274678\pi\)
\(464\) 0 0
\(465\) −2.68355 −0.124447
\(466\) 0 0
\(467\) 29.2586 1.35393 0.676964 0.736016i \(-0.263295\pi\)
0.676964 + 0.736016i \(0.263295\pi\)
\(468\) 0 0
\(469\) 55.5779 2.56635
\(470\) 0 0
\(471\) −6.89091 −0.317516
\(472\) 0 0
\(473\) −2.43641 −0.112026
\(474\) 0 0
\(475\) 15.1596 0.695572
\(476\) 0 0
\(477\) 6.31057 0.288941
\(478\) 0 0
\(479\) 18.5009 0.845327 0.422663 0.906287i \(-0.361095\pi\)
0.422663 + 0.906287i \(0.361095\pi\)
\(480\) 0 0
\(481\) −0.286030 −0.0130418
\(482\) 0 0
\(483\) −5.60272 −0.254932
\(484\) 0 0
\(485\) −17.1965 −0.780852
\(486\) 0 0
\(487\) −10.5977 −0.480225 −0.240113 0.970745i \(-0.577184\pi\)
−0.240113 + 0.970745i \(0.577184\pi\)
\(488\) 0 0
\(489\) 11.4193 0.516398
\(490\) 0 0
\(491\) −7.28208 −0.328636 −0.164318 0.986407i \(-0.552542\pi\)
−0.164318 + 0.986407i \(0.552542\pi\)
\(492\) 0 0
\(493\) −29.6223 −1.33412
\(494\) 0 0
\(495\) 5.16497 0.232148
\(496\) 0 0
\(497\) −23.4451 −1.05165
\(498\) 0 0
\(499\) −7.94263 −0.355561 −0.177781 0.984070i \(-0.556892\pi\)
−0.177781 + 0.984070i \(0.556892\pi\)
\(500\) 0 0
\(501\) −13.4307 −0.600041
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 7.69367 0.342364
\(506\) 0 0
\(507\) 12.9112 0.573405
\(508\) 0 0
\(509\) 36.8195 1.63199 0.815997 0.578056i \(-0.196189\pi\)
0.815997 + 0.578056i \(0.196189\pi\)
\(510\) 0 0
\(511\) 27.9401 1.23600
\(512\) 0 0
\(513\) 3.73515 0.164911
\(514\) 0 0
\(515\) −3.41717 −0.150579
\(516\) 0 0
\(517\) −47.4294 −2.08594
\(518\) 0 0
\(519\) 6.82988 0.299798
\(520\) 0 0
\(521\) −14.1581 −0.620277 −0.310139 0.950691i \(-0.600375\pi\)
−0.310139 + 0.950691i \(0.600375\pi\)
\(522\) 0 0
\(523\) 0.736288 0.0321956 0.0160978 0.999870i \(-0.494876\pi\)
0.0160978 + 0.999870i \(0.494876\pi\)
\(524\) 0 0
\(525\) 15.1905 0.662967
\(526\) 0 0
\(527\) 21.6417 0.942726
\(528\) 0 0
\(529\) −20.7591 −0.902571
\(530\) 0 0
\(531\) −3.00315 −0.130325
\(532\) 0 0
\(533\) −0.370235 −0.0160367
\(534\) 0 0
\(535\) 11.0201 0.476442
\(536\) 0 0
\(537\) −2.56472 −0.110676
\(538\) 0 0
\(539\) −37.3072 −1.60694
\(540\) 0 0
\(541\) 31.7599 1.36547 0.682733 0.730668i \(-0.260791\pi\)
0.682733 + 0.730668i \(0.260791\pi\)
\(542\) 0 0
\(543\) −21.9217 −0.940752
\(544\) 0 0
\(545\) −2.97022 −0.127230
\(546\) 0 0
\(547\) −4.83682 −0.206808 −0.103404 0.994639i \(-0.532973\pi\)
−0.103404 + 0.994639i \(0.532973\pi\)
\(548\) 0 0
\(549\) −2.73984 −0.116934
\(550\) 0 0
\(551\) −14.1407 −0.602413
\(552\) 0 0
\(553\) 21.9178 0.932041
\(554\) 0 0
\(555\) 0.931127 0.0395242
\(556\) 0 0
\(557\) −3.19223 −0.135259 −0.0676296 0.997710i \(-0.521544\pi\)
−0.0676296 + 0.997710i \(0.521544\pi\)
\(558\) 0 0
\(559\) −0.136407 −0.00576941
\(560\) 0 0
\(561\) −41.6532 −1.75860
\(562\) 0 0
\(563\) 18.9982 0.800679 0.400340 0.916367i \(-0.368892\pi\)
0.400340 + 0.916367i \(0.368892\pi\)
\(564\) 0 0
\(565\) 18.3623 0.772507
\(566\) 0 0
\(567\) 3.74274 0.157180
\(568\) 0 0
\(569\) 15.6807 0.657369 0.328684 0.944440i \(-0.393395\pi\)
0.328684 + 0.944440i \(0.393395\pi\)
\(570\) 0 0
\(571\) −34.1347 −1.42849 −0.714247 0.699894i \(-0.753231\pi\)
−0.714247 + 0.699894i \(0.753231\pi\)
\(572\) 0 0
\(573\) 5.26149 0.219802
\(574\) 0 0
\(575\) −6.07561 −0.253371
\(576\) 0 0
\(577\) 19.8710 0.827240 0.413620 0.910450i \(-0.364264\pi\)
0.413620 + 0.910450i \(0.364264\pi\)
\(578\) 0 0
\(579\) −0.751439 −0.0312287
\(580\) 0 0
\(581\) 17.1681 0.712253
\(582\) 0 0
\(583\) −33.5938 −1.39131
\(584\) 0 0
\(585\) 0.289171 0.0119557
\(586\) 0 0
\(587\) 20.6230 0.851203 0.425602 0.904911i \(-0.360063\pi\)
0.425602 + 0.904911i \(0.360063\pi\)
\(588\) 0 0
\(589\) 10.3310 0.425681
\(590\) 0 0
\(591\) 17.2322 0.708839
\(592\) 0 0
\(593\) 22.0694 0.906280 0.453140 0.891439i \(-0.350304\pi\)
0.453140 + 0.891439i \(0.350304\pi\)
\(594\) 0 0
\(595\) 28.4134 1.16484
\(596\) 0 0
\(597\) 15.0929 0.617712
\(598\) 0 0
\(599\) 31.1111 1.27116 0.635582 0.772033i \(-0.280760\pi\)
0.635582 + 0.772033i \(0.280760\pi\)
\(600\) 0 0
\(601\) −24.6052 −1.00367 −0.501833 0.864965i \(-0.667341\pi\)
−0.501833 + 0.864965i \(0.667341\pi\)
\(602\) 0 0
\(603\) 14.8495 0.604719
\(604\) 0 0
\(605\) −16.8228 −0.683942
\(606\) 0 0
\(607\) 5.52096 0.224089 0.112044 0.993703i \(-0.464260\pi\)
0.112044 + 0.993703i \(0.464260\pi\)
\(608\) 0 0
\(609\) −14.1694 −0.574174
\(610\) 0 0
\(611\) −2.65543 −0.107427
\(612\) 0 0
\(613\) −29.0268 −1.17238 −0.586190 0.810174i \(-0.699373\pi\)
−0.586190 + 0.810174i \(0.699373\pi\)
\(614\) 0 0
\(615\) 1.20524 0.0486002
\(616\) 0 0
\(617\) 14.5378 0.585270 0.292635 0.956224i \(-0.405468\pi\)
0.292635 + 0.956224i \(0.405468\pi\)
\(618\) 0 0
\(619\) −26.5159 −1.06576 −0.532882 0.846190i \(-0.678891\pi\)
−0.532882 + 0.846190i \(0.678891\pi\)
\(620\) 0 0
\(621\) −1.49696 −0.0600707
\(622\) 0 0
\(623\) 35.3740 1.41723
\(624\) 0 0
\(625\) 11.7659 0.470634
\(626\) 0 0
\(627\) −19.8838 −0.794082
\(628\) 0 0
\(629\) −7.50914 −0.299409
\(630\) 0 0
\(631\) 16.4460 0.654707 0.327353 0.944902i \(-0.393843\pi\)
0.327353 + 0.944902i \(0.393843\pi\)
\(632\) 0 0
\(633\) −5.52859 −0.219742
\(634\) 0 0
\(635\) −9.78932 −0.388477
\(636\) 0 0
\(637\) −2.08872 −0.0827581
\(638\) 0 0
\(639\) −6.26414 −0.247805
\(640\) 0 0
\(641\) −17.0432 −0.673166 −0.336583 0.941654i \(-0.609271\pi\)
−0.336583 + 0.941654i \(0.609271\pi\)
\(642\) 0 0
\(643\) −22.7389 −0.896736 −0.448368 0.893849i \(-0.647995\pi\)
−0.448368 + 0.893849i \(0.647995\pi\)
\(644\) 0 0
\(645\) 0.444053 0.0174846
\(646\) 0 0
\(647\) −36.2181 −1.42388 −0.711940 0.702240i \(-0.752183\pi\)
−0.711940 + 0.702240i \(0.752183\pi\)
\(648\) 0 0
\(649\) 15.9870 0.627546
\(650\) 0 0
\(651\) 10.3520 0.405726
\(652\) 0 0
\(653\) −5.28226 −0.206711 −0.103355 0.994644i \(-0.532958\pi\)
−0.103355 + 0.994644i \(0.532958\pi\)
\(654\) 0 0
\(655\) −2.61522 −0.102185
\(656\) 0 0
\(657\) 7.46514 0.291243
\(658\) 0 0
\(659\) −36.4887 −1.42140 −0.710699 0.703496i \(-0.751621\pi\)
−0.710699 + 0.703496i \(0.751621\pi\)
\(660\) 0 0
\(661\) −1.99609 −0.0776390 −0.0388195 0.999246i \(-0.512360\pi\)
−0.0388195 + 0.999246i \(0.512360\pi\)
\(662\) 0 0
\(663\) −2.33204 −0.0905689
\(664\) 0 0
\(665\) 13.5636 0.525972
\(666\) 0 0
\(667\) 5.66723 0.219436
\(668\) 0 0
\(669\) 12.3135 0.476069
\(670\) 0 0
\(671\) 14.5853 0.563061
\(672\) 0 0
\(673\) 39.8922 1.53773 0.768865 0.639411i \(-0.220822\pi\)
0.768865 + 0.639411i \(0.220822\pi\)
\(674\) 0 0
\(675\) 4.05865 0.156217
\(676\) 0 0
\(677\) 12.0538 0.463267 0.231634 0.972803i \(-0.425593\pi\)
0.231634 + 0.972803i \(0.425593\pi\)
\(678\) 0 0
\(679\) 66.3366 2.54577
\(680\) 0 0
\(681\) −7.64652 −0.293015
\(682\) 0 0
\(683\) 11.7370 0.449103 0.224552 0.974462i \(-0.427908\pi\)
0.224552 + 0.974462i \(0.427908\pi\)
\(684\) 0 0
\(685\) −14.0255 −0.535887
\(686\) 0 0
\(687\) −5.52010 −0.210605
\(688\) 0 0
\(689\) −1.88082 −0.0716535
\(690\) 0 0
\(691\) 4.15214 0.157955 0.0789774 0.996876i \(-0.474834\pi\)
0.0789774 + 0.996876i \(0.474834\pi\)
\(692\) 0 0
\(693\) −19.9242 −0.756858
\(694\) 0 0
\(695\) 2.55346 0.0968581
\(696\) 0 0
\(697\) −9.71978 −0.368163
\(698\) 0 0
\(699\) −12.6031 −0.476694
\(700\) 0 0
\(701\) −32.6446 −1.23297 −0.616485 0.787367i \(-0.711444\pi\)
−0.616485 + 0.787367i \(0.711444\pi\)
\(702\) 0 0
\(703\) −3.58460 −0.135196
\(704\) 0 0
\(705\) 8.64436 0.325565
\(706\) 0 0
\(707\) −29.6789 −1.11619
\(708\) 0 0
\(709\) 22.1300 0.831110 0.415555 0.909568i \(-0.363587\pi\)
0.415555 + 0.909568i \(0.363587\pi\)
\(710\) 0 0
\(711\) 5.85609 0.219621
\(712\) 0 0
\(713\) −4.14040 −0.155059
\(714\) 0 0
\(715\) −1.53938 −0.0575696
\(716\) 0 0
\(717\) 13.6786 0.510837
\(718\) 0 0
\(719\) −36.3052 −1.35395 −0.676977 0.736004i \(-0.736710\pi\)
−0.676977 + 0.736004i \(0.736710\pi\)
\(720\) 0 0
\(721\) 13.1820 0.490923
\(722\) 0 0
\(723\) −15.4794 −0.575686
\(724\) 0 0
\(725\) −15.3654 −0.570657
\(726\) 0 0
\(727\) −25.8308 −0.958011 −0.479006 0.877812i \(-0.659003\pi\)
−0.479006 + 0.877812i \(0.659003\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −3.58110 −0.132452
\(732\) 0 0
\(733\) 17.0373 0.629286 0.314643 0.949210i \(-0.398115\pi\)
0.314643 + 0.949210i \(0.398115\pi\)
\(734\) 0 0
\(735\) 6.79951 0.250804
\(736\) 0 0
\(737\) −79.0503 −2.91186
\(738\) 0 0
\(739\) −25.2451 −0.928657 −0.464328 0.885663i \(-0.653704\pi\)
−0.464328 + 0.885663i \(0.653704\pi\)
\(740\) 0 0
\(741\) −1.11323 −0.0408957
\(742\) 0 0
\(743\) −39.1984 −1.43805 −0.719024 0.694985i \(-0.755411\pi\)
−0.719024 + 0.694985i \(0.755411\pi\)
\(744\) 0 0
\(745\) 14.5160 0.531823
\(746\) 0 0
\(747\) 4.58704 0.167831
\(748\) 0 0
\(749\) −42.5110 −1.55332
\(750\) 0 0
\(751\) 4.18296 0.152638 0.0763192 0.997083i \(-0.475683\pi\)
0.0763192 + 0.997083i \(0.475683\pi\)
\(752\) 0 0
\(753\) −0.134773 −0.00491139
\(754\) 0 0
\(755\) −19.5193 −0.710379
\(756\) 0 0
\(757\) −11.4099 −0.414699 −0.207349 0.978267i \(-0.566484\pi\)
−0.207349 + 0.978267i \(0.566484\pi\)
\(758\) 0 0
\(759\) 7.96893 0.289254
\(760\) 0 0
\(761\) −10.6881 −0.387445 −0.193722 0.981056i \(-0.562056\pi\)
−0.193722 + 0.981056i \(0.562056\pi\)
\(762\) 0 0
\(763\) 11.4578 0.414801
\(764\) 0 0
\(765\) 7.59160 0.274475
\(766\) 0 0
\(767\) 0.895066 0.0323190
\(768\) 0 0
\(769\) −17.7015 −0.638332 −0.319166 0.947699i \(-0.603403\pi\)
−0.319166 + 0.947699i \(0.603403\pi\)
\(770\) 0 0
\(771\) −13.5452 −0.487817
\(772\) 0 0
\(773\) 5.70124 0.205059 0.102530 0.994730i \(-0.467306\pi\)
0.102530 + 0.994730i \(0.467306\pi\)
\(774\) 0 0
\(775\) 11.2257 0.403241
\(776\) 0 0
\(777\) −3.59189 −0.128858
\(778\) 0 0
\(779\) −4.63988 −0.166241
\(780\) 0 0
\(781\) 33.3467 1.19324
\(782\) 0 0
\(783\) −3.78584 −0.135295
\(784\) 0 0
\(785\) −6.68579 −0.238626
\(786\) 0 0
\(787\) −49.5086 −1.76479 −0.882396 0.470507i \(-0.844071\pi\)
−0.882396 + 0.470507i \(0.844071\pi\)
\(788\) 0 0
\(789\) 15.5675 0.554216
\(790\) 0 0
\(791\) −70.8338 −2.51856
\(792\) 0 0
\(793\) 0.816590 0.0289979
\(794\) 0 0
\(795\) 6.12272 0.217150
\(796\) 0 0
\(797\) −16.5838 −0.587429 −0.293714 0.955893i \(-0.594891\pi\)
−0.293714 + 0.955893i \(0.594891\pi\)
\(798\) 0 0
\(799\) −69.7130 −2.46627
\(800\) 0 0
\(801\) 9.45136 0.333947
\(802\) 0 0
\(803\) −39.7401 −1.40240
\(804\) 0 0
\(805\) −5.43594 −0.191592
\(806\) 0 0
\(807\) 25.0315 0.881149
\(808\) 0 0
\(809\) 20.5951 0.724085 0.362042 0.932162i \(-0.382080\pi\)
0.362042 + 0.932162i \(0.382080\pi\)
\(810\) 0 0
\(811\) 36.3640 1.27691 0.638457 0.769657i \(-0.279573\pi\)
0.638457 + 0.769657i \(0.279573\pi\)
\(812\) 0 0
\(813\) 1.28841 0.0451864
\(814\) 0 0
\(815\) 11.0794 0.388093
\(816\) 0 0
\(817\) −1.70949 −0.0598075
\(818\) 0 0
\(819\) −1.11550 −0.0389786
\(820\) 0 0
\(821\) 12.0061 0.419014 0.209507 0.977807i \(-0.432814\pi\)
0.209507 + 0.977807i \(0.432814\pi\)
\(822\) 0 0
\(823\) −41.7419 −1.45503 −0.727516 0.686091i \(-0.759325\pi\)
−0.727516 + 0.686091i \(0.759325\pi\)
\(824\) 0 0
\(825\) −21.6059 −0.752221
\(826\) 0 0
\(827\) 35.1880 1.22361 0.611803 0.791010i \(-0.290445\pi\)
0.611803 + 0.791010i \(0.290445\pi\)
\(828\) 0 0
\(829\) 26.2602 0.912053 0.456026 0.889966i \(-0.349272\pi\)
0.456026 + 0.889966i \(0.349272\pi\)
\(830\) 0 0
\(831\) 2.22897 0.0773222
\(832\) 0 0
\(833\) −54.8351 −1.89992
\(834\) 0 0
\(835\) −13.0309 −0.450954
\(836\) 0 0
\(837\) 2.76588 0.0956029
\(838\) 0 0
\(839\) −11.3329 −0.391256 −0.195628 0.980678i \(-0.562675\pi\)
−0.195628 + 0.980678i \(0.562675\pi\)
\(840\) 0 0
\(841\) −14.6674 −0.505773
\(842\) 0 0
\(843\) −21.5713 −0.742953
\(844\) 0 0
\(845\) 12.5268 0.430937
\(846\) 0 0
\(847\) 64.8950 2.22982
\(848\) 0 0
\(849\) −6.93160 −0.237892
\(850\) 0 0
\(851\) 1.43662 0.0492467
\(852\) 0 0
\(853\) −40.5764 −1.38931 −0.694655 0.719343i \(-0.744443\pi\)
−0.694655 + 0.719343i \(0.744443\pi\)
\(854\) 0 0
\(855\) 3.62396 0.123937
\(856\) 0 0
\(857\) −3.32006 −0.113411 −0.0567055 0.998391i \(-0.518060\pi\)
−0.0567055 + 0.998391i \(0.518060\pi\)
\(858\) 0 0
\(859\) −24.4698 −0.834897 −0.417449 0.908701i \(-0.637076\pi\)
−0.417449 + 0.908701i \(0.637076\pi\)
\(860\) 0 0
\(861\) −4.64932 −0.158448
\(862\) 0 0
\(863\) 48.0824 1.63674 0.818372 0.574689i \(-0.194877\pi\)
0.818372 + 0.574689i \(0.194877\pi\)
\(864\) 0 0
\(865\) 6.62658 0.225310
\(866\) 0 0
\(867\) −44.2229 −1.50189
\(868\) 0 0
\(869\) −31.1745 −1.05752
\(870\) 0 0
\(871\) −4.42579 −0.149962
\(872\) 0 0
\(873\) 17.7241 0.599869
\(874\) 0 0
\(875\) 32.8950 1.11205
\(876\) 0 0
\(877\) 42.1000 1.42162 0.710809 0.703385i \(-0.248329\pi\)
0.710809 + 0.703385i \(0.248329\pi\)
\(878\) 0 0
\(879\) −19.4521 −0.656103
\(880\) 0 0
\(881\) 41.3419 1.39284 0.696422 0.717633i \(-0.254774\pi\)
0.696422 + 0.717633i \(0.254774\pi\)
\(882\) 0 0
\(883\) 8.99926 0.302849 0.151425 0.988469i \(-0.451614\pi\)
0.151425 + 0.988469i \(0.451614\pi\)
\(884\) 0 0
\(885\) −2.91375 −0.0979447
\(886\) 0 0
\(887\) 5.62010 0.188705 0.0943523 0.995539i \(-0.469922\pi\)
0.0943523 + 0.995539i \(0.469922\pi\)
\(888\) 0 0
\(889\) 37.7630 1.26653
\(890\) 0 0
\(891\) −5.32343 −0.178342
\(892\) 0 0
\(893\) −33.2786 −1.11362
\(894\) 0 0
\(895\) −2.48838 −0.0831773
\(896\) 0 0
\(897\) 0.446157 0.0148967
\(898\) 0 0
\(899\) −10.4712 −0.349234
\(900\) 0 0
\(901\) −49.3771 −1.64499
\(902\) 0 0
\(903\) −1.71297 −0.0570040
\(904\) 0 0
\(905\) −21.2692 −0.707012
\(906\) 0 0
\(907\) 31.1705 1.03500 0.517500 0.855683i \(-0.326863\pi\)
0.517500 + 0.855683i \(0.326863\pi\)
\(908\) 0 0
\(909\) −7.92972 −0.263012
\(910\) 0 0
\(911\) −44.5048 −1.47451 −0.737255 0.675614i \(-0.763878\pi\)
−0.737255 + 0.675614i \(0.763878\pi\)
\(912\) 0 0
\(913\) −24.4188 −0.808143
\(914\) 0 0
\(915\) −2.65828 −0.0878802
\(916\) 0 0
\(917\) 10.0884 0.333148
\(918\) 0 0
\(919\) 29.6769 0.978949 0.489475 0.872018i \(-0.337189\pi\)
0.489475 + 0.872018i \(0.337189\pi\)
\(920\) 0 0
\(921\) 11.0657 0.364626
\(922\) 0 0
\(923\) 1.86698 0.0614524
\(924\) 0 0
\(925\) −3.89506 −0.128069
\(926\) 0 0
\(927\) 3.52201 0.115678
\(928\) 0 0
\(929\) 20.6942 0.678954 0.339477 0.940614i \(-0.389750\pi\)
0.339477 + 0.940614i \(0.389750\pi\)
\(930\) 0 0
\(931\) −26.1764 −0.857896
\(932\) 0 0
\(933\) −3.72332 −0.121896
\(934\) 0 0
\(935\) −40.4133 −1.32166
\(936\) 0 0
\(937\) 9.26828 0.302782 0.151391 0.988474i \(-0.451625\pi\)
0.151391 + 0.988474i \(0.451625\pi\)
\(938\) 0 0
\(939\) −18.1184 −0.591272
\(940\) 0 0
\(941\) 37.7530 1.23071 0.615356 0.788249i \(-0.289012\pi\)
0.615356 + 0.788249i \(0.289012\pi\)
\(942\) 0 0
\(943\) 1.85955 0.0605553
\(944\) 0 0
\(945\) 3.63133 0.118127
\(946\) 0 0
\(947\) −38.9781 −1.26662 −0.633310 0.773898i \(-0.718304\pi\)
−0.633310 + 0.773898i \(0.718304\pi\)
\(948\) 0 0
\(949\) −2.22493 −0.0722243
\(950\) 0 0
\(951\) −10.7581 −0.348854
\(952\) 0 0
\(953\) 14.4031 0.466563 0.233282 0.972409i \(-0.425054\pi\)
0.233282 + 0.972409i \(0.425054\pi\)
\(954\) 0 0
\(955\) 5.10488 0.165190
\(956\) 0 0
\(957\) 20.1537 0.651475
\(958\) 0 0
\(959\) 54.1043 1.74712
\(960\) 0 0
\(961\) −23.3499 −0.753222
\(962\) 0 0
\(963\) −11.3582 −0.366014
\(964\) 0 0
\(965\) −0.729071 −0.0234696
\(966\) 0 0
\(967\) −55.7370 −1.79238 −0.896191 0.443669i \(-0.853677\pi\)
−0.896191 + 0.443669i \(0.853677\pi\)
\(968\) 0 0
\(969\) −29.2257 −0.938864
\(970\) 0 0
\(971\) −13.8016 −0.442915 −0.221457 0.975170i \(-0.571081\pi\)
−0.221457 + 0.975170i \(0.571081\pi\)
\(972\) 0 0
\(973\) −9.85013 −0.315781
\(974\) 0 0
\(975\) −1.20965 −0.0387398
\(976\) 0 0
\(977\) 41.1936 1.31790 0.658950 0.752187i \(-0.271001\pi\)
0.658950 + 0.752187i \(0.271001\pi\)
\(978\) 0 0
\(979\) −50.3136 −1.60803
\(980\) 0 0
\(981\) 3.06134 0.0977412
\(982\) 0 0
\(983\) 17.7452 0.565984 0.282992 0.959122i \(-0.408673\pi\)
0.282992 + 0.959122i \(0.408673\pi\)
\(984\) 0 0
\(985\) 16.7193 0.532721
\(986\) 0 0
\(987\) −33.3462 −1.06142
\(988\) 0 0
\(989\) 0.685122 0.0217856
\(990\) 0 0
\(991\) −37.7101 −1.19790 −0.598950 0.800786i \(-0.704415\pi\)
−0.598950 + 0.800786i \(0.704415\pi\)
\(992\) 0 0
\(993\) −19.8675 −0.630474
\(994\) 0 0
\(995\) 14.6436 0.464235
\(996\) 0 0
\(997\) −21.2510 −0.673026 −0.336513 0.941679i \(-0.609248\pi\)
−0.336513 + 0.941679i \(0.609248\pi\)
\(998\) 0 0
\(999\) −0.959694 −0.0303634
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 \(a_p\))